LMFDB - Embedded newform 29.8.d.a.25.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(7,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([6]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.d (of order $7$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05916573904$
Analytic rank:	$0$
Dimension:	$102$
Relative dimension:	$17$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			25.10
Character	$\chi$	$=$	29.25
Dual form			29.8.d.a.7.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.240160 + 1.05221i) q^{2} +(53.2557 - 25.6466i) q^{3} +(114.275 + 55.0317i) q^{4} +(117.842 - 516.297i) q^{5} +(14.1957 + 62.1954i) q^{6} +(-631.923 + 304.318i) q^{7} +(-171.482 + 215.031i) q^{8} +(814.854 - 1021.79i) q^{9} +O(q^{10})$	\(q+(-0.240160 + 1.05221i) q^{2} +(53.2557 - 25.6466i) q^{3} +(114.275 + 55.0317i) q^{4} +(117.842 - 516.297i) q^{5} +(14.1957 + 62.1954i) q^{6} +(-631.923 + 304.318i) q^{7} +(-171.482 + 215.031i) q^{8} +(814.854 - 1021.79i) q^{9} +(514.951 + 247.988i) q^{10} +(356.396 + 446.907i) q^{11} +7497.15 q^{12} +(-5190.67 - 6508.89i) q^{13} +(-168.444 - 738.000i) q^{14} +(-6965.54 - 30518.0i) q^{15} +(9937.22 + 12460.9i) q^{16} +19442.3 q^{17} +(879.445 + 1102.79i) q^{18} +(21869.5 + 10531.8i) q^{19} +(41879.0 - 52514.6i) q^{20} +(-25848.8 + 32413.4i) q^{21} +(-555.831 + 267.674i) q^{22} +(10914.2 + 47818.1i) q^{23} +(-3617.56 + 15849.6i) q^{24} +(-182288. - 87785.4i) q^{25} +(8095.29 - 3898.49i) q^{26} +(-11575.7 + 50716.5i) q^{27} -88959.9 q^{28} +(118743. - 56124.9i) q^{29} +33784.2 q^{30} +(-60381.9 + 264550. i) q^{31} +(-47216.1 + 22738.1i) q^{32} +(30441.8 + 14660.0i) q^{33} +(-4669.26 + 20457.4i) q^{34} +(82651.9 + 362122. i) q^{35} +(149348. - 71922.3i) q^{36} +(133007. - 166786. i) q^{37} +(-16333.8 + 20481.9i) q^{38} +(-443364. - 213513. i) q^{39} +(90812.4 + 113875. i) q^{40} -367982. q^{41} +(-27897.8 - 34982.7i) q^{42} +(-83229.9 - 364654. i) q^{43} +(16133.0 + 70683.1i) q^{44} +(-431526. - 541116. i) q^{45} -52935.7 q^{46} +(576234. + 722574. i) q^{47} +(848794. + 408757. i) q^{48} +(-206753. + 259260. i) q^{49} +(136147. - 170723. i) q^{50} +(1.03541e6 - 498629. i) q^{51} +(-234966. - 1.02945e6i) q^{52} +(-7627.25 + 33417.2i) q^{53} +(-50584.3 - 24360.1i) q^{54} +(272735. - 131342. i) q^{55} +(42925.4 - 188068. i) q^{56} +1.43478e6 q^{57} +(30537.8 + 138421. i) q^{58} -2.88674e6 q^{59} +(883476. - 3.87076e6i) q^{60} +(2.22490e6 - 1.07145e6i) q^{61} +(-263861. - 127069. i) q^{62} +(-203974. + 893670. i) q^{63} +(441373. + 1.93378e6i) q^{64} +(-3.97220e6 + 1.91291e6i) q^{65} +(-22736.2 + 28510.3i) q^{66} +(-1.15478e6 + 1.44805e6i) q^{67} +(2.22176e6 + 1.06994e6i) q^{68} +(1.80762e6 + 2.26668e6i) q^{69} -400877. q^{70} +(124417. + 156014. i) q^{71} +(79985.2 + 350438. i) q^{72} +(-249260. - 1.09208e6i) q^{73} +(143550. + 180006. i) q^{74} -1.19593e7 q^{75} +(1.91954e6 + 2.40703e6i) q^{76} +(-361217. - 173953. i) q^{77} +(331138. - 415234. i) q^{78} +(-1.82696e6 + 2.29093e6i) q^{79} +(7.60454e6 - 3.66215e6i) q^{80} +(1.32025e6 + 5.78440e6i) q^{81} +(88374.4 - 387193. i) q^{82} +(-2.44887e6 - 1.17932e6i) q^{83} +(-4.73763e6 + 2.28152e6i) q^{84} +(2.29111e6 - 1.00380e7i) q^{85} +403680. q^{86} +(4.88433e6 - 6.03433e6i) q^{87} -157214. q^{88} +(-187131. + 819874. i) q^{89} +(673002. - 324101. i) q^{90} +(5.26088e6 + 2.53350e6i) q^{91} +(-1.38430e6 + 6.06502e6i) q^{92} +(3.56914e6 + 1.56374e7i) q^{93} +(-898686. + 432785. i) q^{94} +(8.01466e6 - 1.00501e7i) q^{95} +(-1.93138e6 + 2.42187e6i) q^{96} +(-1.24147e7 - 5.97859e6i) q^{97} +(-223142. - 279811. i) q^{98} +747057. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q + q^{2} - 5 q^{3} - 1275 q^{4} + 133 q^{5} - 2675 q^{6} + 657 q^{7} - 6562 q^{8} - 15054 q^{9}+O(q^{10}) $ 102 * q + q^2 - 5 * q^3 - 1275 * q^4 + 133 * q^5 - 2675 * q^6 + 657 * q^7 - 6562 * q^8 - 15054 * q^9	\( 102 q + q^{2} - 5 q^{3} - 1275 q^{4} + 133 q^{5} - 2675 q^{6} + 657 q^{7} - 6562 q^{8} - 15054 q^{9} + 5611 q^{10} + 2893 q^{11} - 7400 q^{12} + 5655 q^{13} - 5103 q^{14} + 55181 q^{15} - 37531 q^{16} + 66488 q^{17} + 111588 q^{18} + 25497 q^{19} - 69535 q^{20} + 221033 q^{21} - 184180 q^{22} - 357991 q^{23} - 279611 q^{24} - 401432 q^{25} - 304829 q^{26} + 777205 q^{27} - 317084 q^{28} + 345978 q^{29} + 1233614 q^{30} - 191155 q^{31} - 1142836 q^{32} - 446051 q^{33} + 854365 q^{34} - 421273 q^{35} - 915292 q^{36} + 1109067 q^{37} + 3198170 q^{38} + 1816963 q^{39} - 1864493 q^{40} - 68548 q^{41} + 4917730 q^{42} + 1733909 q^{43} - 5516860 q^{44} - 6926991 q^{45} + 7670856 q^{46} + 3560867 q^{47} - 3047946 q^{48} - 6860794 q^{49} - 6723464 q^{50} - 2911378 q^{51} - 9704310 q^{52} - 8343921 q^{53} + 11251300 q^{54} + 6948055 q^{55} - 963169 q^{56} - 679450 q^{57} + 19338341 q^{58} + 10876120 q^{59} + 2379472 q^{60} - 2230165 q^{61} - 11842431 q^{62} - 10985505 q^{63} - 14037070 q^{64} - 11815483 q^{65} - 387401 q^{66} + 3903123 q^{67} + 5327748 q^{68} + 9379769 q^{69} + 51913122 q^{70} + 9175293 q^{71} + 42974969 q^{72} - 22305785 q^{73} - 31357308 q^{74} + 5262752 q^{75} + 27826047 q^{76} - 9623065 q^{77} - 13423495 q^{78} - 43328225 q^{79} - 69999516 q^{80} - 14867886 q^{81} + 39940476 q^{82} + 11503001 q^{83} - 58649317 q^{84} - 493576 q^{85} + 17849216 q^{86} + 28282227 q^{87} + 80429114 q^{88} + 14809627 q^{89} + 43848318 q^{90} - 41942203 q^{91} - 94433178 q^{92} + 3218315 q^{93} + 52700970 q^{94} - 22341683 q^{95} - 153425906 q^{96} - 74993043 q^{97} - 24094580 q^{98} + 258723776 q^{99}+O(q^{100}) \) 102 * q + q^2 - 5 * q^3 - 1275 * q^4 + 133 * q^5 - 2675 * q^6 + 657 * q^7 - 6562 * q^8 - 15054 * q^9 + 5611 * q^10 + 2893 * q^11 - 7400 * q^12 + 5655 * q^13 - 5103 * q^14 + 55181 * q^15 - 37531 * q^16 + 66488 * q^17 + 111588 * q^18 + 25497 * q^19 - 69535 * q^20 + 221033 * q^21 - 184180 * q^22 - 357991 * q^23 - 279611 * q^24 - 401432 * q^25 - 304829 * q^26 + 777205 * q^27 - 317084 * q^28 + 345978 * q^29 + 1233614 * q^30 - 191155 * q^31 - 1142836 * q^32 - 446051 * q^33 + 854365 * q^34 - 421273 * q^35 - 915292 * q^36 + 1109067 * q^37 + 3198170 * q^38 + 1816963 * q^39 - 1864493 * q^40 - 68548 * q^41 + 4917730 * q^42 + 1733909 * q^43 - 5516860 * q^44 - 6926991 * q^45 + 7670856 * q^46 + 3560867 * q^47 - 3047946 * q^48 - 6860794 * q^49 - 6723464 * q^50 - 2911378 * q^51 - 9704310 * q^52 - 8343921 * q^53 + 11251300 * q^54 + 6948055 * q^55 - 963169 * q^56 - 679450 * q^57 + 19338341 * q^58 + 10876120 * q^59 + 2379472 * q^60 - 2230165 * q^61 - 11842431 * q^62 - 10985505 * q^63 - 14037070 * q^64 - 11815483 * q^65 - 387401 * q^66 + 3903123 * q^67 + 5327748 * q^68 + 9379769 * q^69 + 51913122 * q^70 + 9175293 * q^71 + 42974969 * q^72 - 22305785 * q^73 - 31357308 * q^74 + 5262752 * q^75 + 27826047 * q^76 - 9623065 * q^77 - 13423495 * q^78 - 43328225 * q^79 - 69999516 * q^80 - 14867886 * q^81 + 39940476 * q^82 + 11503001 * q^83 - 58649317 * q^84 - 493576 * q^85 + 17849216 * q^86 + 28282227 * q^87 + 80429114 * q^88 + 14809627 * q^89 + 43848318 * q^90 - 41942203 * q^91 - 94433178 * q^92 + 3218315 * q^93 + 52700970 * q^94 - 22341683 * q^95 - 153425906 * q^96 - 74993043 * q^97 - 24094580 * q^98 + 258723776 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{7}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.240160	+	1.05221i	−0.0212273	+	0.0930029i	−0.984432	−	0.175766i	$-0.943760\pi$
$2$	−0.240160	+	1.05221i	−0.0212273	+	0.0930029i	0.963205	+	0.268769i	$0.0866169\pi$
$3$	53.2557	−	25.6466i	1.13879	−	0.548410i	0.233139	−	0.972443i	$-0.425100\pi$
$3$	53.2557	−	25.6466i	1.13879	−	0.548410i	0.905647	+	0.424033i	$0.139386\pi$
$4$	114.275	+	55.0317i	0.892770	+	0.429935i
$5$	117.842	−	516.297i	0.421603	−	1.84716i	−0.101421	−	0.994844i	$-0.532339\pi$
$5$	117.842	−	516.297i	0.421603	−	1.84716i	0.523024	−	0.852318i	$-0.324804\pi$
$6$	14.1957	+	62.1954i	0.0268304	+	0.117552i
$7$	−631.923	+	304.318i	−0.696340	+	0.335340i	−0.748347	−	0.663307i	$-0.769152\pi$
$7$	−631.923	+	304.318i	−0.696340	+	0.335340i	0.0520075	+	0.998647i	$0.483438\pi$
$8$	−171.482	+	215.031i	−0.118414	+	0.148486i
$9$	814.854	−	1021.79i	0.372590	−	0.467213i
$10$	514.951	+	247.988i	0.162842	+	0.0784205i
$11$	356.396	+	446.907i	0.0807344	+	0.101238i	0.820558	−	0.571563i	$-0.193663\pi$
$11$	356.396	+	446.907i	0.0807344	+	0.101238i	−0.739824	+	0.672801i	$0.765091\pi$
$12$	7497.15			1.25245
$13$	−5190.67	−	6508.89i	−0.655272	−	0.821685i	0.337548	−	0.941308i	$-0.390403\pi$
$13$	−5190.67	−	6508.89i	−0.655272	−	0.821685i	−0.992819	+	0.119624i	$0.961831\pi$
$14$	−168.444	−	738.000i	−0.0164061	−	0.0718800i
$15$	−6965.54	−	30518.0i	−0.532888	−	2.33473i
$16$	9937.22	+	12460.9i	0.606520	+	0.760552i
$17$	19442.3			0.959791			0.479895	−	0.877326i	$-0.340675\pi$
$17$	19442.3			0.959791			0.479895	+	0.877326i	$0.340675\pi$
$18$	879.445	+	1102.79i	0.0355431	+	0.0445696i
$19$	21869.5	+	10531.8i	0.731476	+	0.352261i	0.762265	−	0.647265i	$-0.224087\pi$
$19$	21869.5	+	10531.8i	0.731476	+	0.352261i	−0.0307882	+	0.999526i	$0.509802\pi$
$20$	41879.0	−	52514.6i	1.17055	−	1.46783i
$21$	−25848.8	+	32413.4i	−0.609078	+	0.763760i
$22$	−555.831	+	267.674i	−0.0111292	+	0.00535953i
$23$	10914.2	+	47818.1i	0.187044	+	0.819493i	0.978164	+	0.207832i	$0.0666409\pi$
$23$	10914.2	+	47818.1i	0.187044	+	0.819493i	−0.791121	+	0.611660i	$0.790502\pi$
$24$	−3617.56	+	15849.6i	−0.0534167	+	0.234034i
$25$	−182288.	−	87785.4i	−2.33329	−	1.12365i
$26$	8095.29	−	3898.49i	0.0903287	−	0.0435000i
$27$	−11575.7	+	50716.5i	−0.113181	+	0.495880i
$28$	−88959.9			−0.765846
$29$	118743.	−	56124.9i	0.904096	−	0.427329i
$29$	118743.	−	56124.9i	0.904096	−	0.427329i
$30$	33784.2			0.228449
$31$	−60381.9	+	264550.i	−0.364033	+	1.59493i	0.378815	+	0.925472i	$0.376332\pi$
$31$	−60381.9	+	264550.i	−0.364033	+	1.59493i	−0.742848	+	0.669460i	$0.766526\pi$
$32$	−47216.1	+	22738.1i	−0.254721	+	0.122667i
$33$	30441.8	+	14660.0i	0.147459	+	0.0710125i
$34$	−4669.26	+	20457.4i	−0.0203738	+	0.0892634i
$35$	82651.9	+	362122.i	0.325848	+	1.42763i
$36$	149348.	−	71922.3i	0.533508	−	0.256924i
$37$	133007.	−	166786.i	0.431687	−	0.541318i	−0.517644	−	0.855596i	$-0.673191\pi$
$37$	133007.	−	166786.i	0.431687	−	0.541318i	0.949331	+	0.314278i	$0.101762\pi$
$38$	−16333.8	+	20481.9i	−0.0482885	+	0.0605519i
$39$	−443364.	−	213513.i	−1.19683	−	0.576365i
$40$	90812.4	+	113875.i	0.224355	+	0.281332i
$41$	−367982.			−0.833840			−0.416920	−	0.908943i	$-0.636891\pi$
$41$	−367982.			−0.833840			−0.416920	+	0.908943i	$0.636891\pi$
$42$	−27897.8	−	34982.7i	−0.0581028	−	0.0728586i
$43$	−83229.9	−	364654.i	−0.159639	−	0.699426i	−0.989867	−	0.142001i	$-0.954647\pi$
$43$	−83229.9	−	364654.i	−0.159639	−	0.699426i	0.830227	−	0.557425i	$-0.188211\pi$
$44$	16133.0	+	70683.1i	0.0285516	+	0.125093i
$45$	−431526.	−	541116.i	−0.705932	−	0.885211i
$46$	−52935.7			−0.0801856
$47$	576234.	+	722574.i	0.809573	+	1.01517i	0.999443	+	0.0333637i	$0.0106220\pi$
$47$	576234.	+	722574.i	0.809573	+	1.01517i	−0.189870	+	0.981809i	$0.560807\pi$
$48$	848794.	+	408757.i	1.10779	+	0.533484i
$49$	−206753.	+	259260.i	−0.251053	+	0.314811i
$50$	136147.	−	170723.i	0.154032	−	0.193151i
$51$	1.03541e6	−	498629.i	1.09300	−	0.526359i
$52$	−234966.	−	1.02945e6i	−0.231736	−	1.01530i
$53$	−7627.25	+	33417.2i	−0.00703724	+	0.0308322i	−0.978325	−	0.207077i	$-0.933605\pi$
$53$	−7627.25	+	33417.2i	−0.00703724	+	0.0308322i	0.971287	+	0.237909i	$0.0764621\pi$
$54$	−50584.3	−	24360.1i	−0.0437157	−	0.0210524i
$55$	272735.	−	131342.i	0.221040	−	0.106447i
$56$	42925.4	−	188068.i	0.0326630	−	0.143106i
$57$	1.43478e6			1.02618
$58$	30537.8	+	138421.i	0.0205514	+	0.0931546i
$59$	−2.88674e6			−1.82990			−0.914948	−	0.403572i	$-0.867769\pi$
$59$	−2.88674e6			−1.82990			−0.914948	+	0.403572i	$0.867769\pi$
$60$	883476.	−	3.87076e6i	0.528038	−	2.31349i
$61$	2.22490e6	−	1.07145e6i	1.25503	−	0.604392i	0.316177	−	0.948700i	$-0.397601\pi$
$61$	2.22490e6	−	1.07145e6i	1.25503	−	0.604392i	0.938857	+	0.344308i	$0.111886\pi$
$62$	−263861.	−	127069.i	−0.140606	−	0.0677122i
$63$	−203974.	+	893670.i	−0.102774	+	0.450283i
$64$	441373.	+	1.93378e6i	0.210463	+	0.922099i
$65$	−3.97220e6	+	1.91291e6i	−1.79405	+	0.863968i
$66$	−22736.2	+	28510.3i	−0.00973453	+	0.0122067i
$67$	−1.15478e6	+	1.44805e6i	−0.469069	+	0.588194i	−0.958943	−	0.283600i	$-0.908471\pi$
$67$	−1.15478e6	+	1.44805e6i	−0.469069	+	0.588194i	0.489874	+	0.871793i	$0.337043\pi$
$68$	2.22176e6	+	1.06994e6i	0.856873	+	0.412648i
$69$	1.80762e6	+	2.26668e6i	0.662421	+	0.830650i
$70$	−400877.			−0.139691
$71$	124417.	+	156014.i	0.0412548	+	0.0517319i	0.802031	−	0.597283i	$-0.203753\pi$
$71$	124417.	+	156014.i	0.0412548	+	0.0517319i	−0.760776	+	0.649014i	$0.775181\pi$
$72$	79985.2	+	350438.i	0.0252549	+	0.110649i
$73$	−249260.	−	1.09208e6i	−0.0749934	−	0.328567i	0.923490	−	0.383623i	$-0.125324\pi$
$73$	−249260.	−	1.09208e6i	−0.0749934	−	0.328567i	−0.998483	+	0.0550552i	$0.982467\pi$
$74$	143550.	+	180006.i	0.0411806	+	0.0516389i
$75$	−1.19593e7			−3.27334
$76$	1.91954e6	+	2.40703e6i	0.501591	+	0.628975i
$77$	−361217.	−	173953.i	−0.0901676	−	0.0434224i
$78$	331138.	−	415234.i	0.0790092	−	0.0990744i
$79$	−1.82696e6	+	2.29093e6i	−0.416901	+	0.522778i	−0.945293	−	0.326223i	$-0.894224\pi$
$79$	−1.82696e6	+	2.29093e6i	−0.416901	+	0.522778i	0.528392	+	0.849001i	$0.322795\pi$
$80$	7.60454e6	−	3.66215e6i	1.66057	−	0.799690i
$81$	1.32025e6	+	5.78440e6i	0.276032	+	1.20938i
$82$	88374.4	−	387193.i	0.0177002	−	0.0775496i
$83$	−2.44887e6	−	1.17932e6i	−0.470103	−	0.226390i	0.183806	−	0.982962i	$-0.441158\pi$
$83$	−2.44887e6	−	1.17932e6i	−0.470103	−	0.226390i	−0.653910	+	0.756573i	$0.726872\pi$
$84$	−4.73763e6	+	2.28152e6i	−0.872134	+	0.419998i
$85$	2.29111e6	−	1.00380e7i	0.404650	−	1.77289i
$86$	403680.			0.0684373
$87$	4.88433e6	−	6.03433e6i	0.795220	−	0.982452i
$88$	−157214.			−0.0245925
$89$	−187131.	+	819874.i	−0.0281372	+	0.123277i	−0.987046	−	0.160437i	$-0.948710\pi$
$89$	−187131.	+	819874.i	−0.0281372	+	0.123277i	0.958909	+	0.283714i	$0.0915667\pi$
$90$	673002.	−	324101.i	0.0973123	−	0.0468631i
$91$	5.26088e6	+	2.53350e6i	0.731835	+	0.352433i
$92$	−1.38430e6	+	6.06502e6i	−0.185342	+	0.812035i
$93$	3.56914e6	+	1.56374e7i	0.460122	+	2.01593i
$94$	−898686.	+	432785.i	−0.111599	+	0.0537433i
$95$	8.01466e6	−	1.00501e7i	0.959075	−	1.20264i
$96$	−1.93138e6	+	2.42187e6i	−0.222801	+	0.279384i
$97$	−1.24147e7	−	5.97859e6i	−1.38113	−	0.665117i	−0.411889	−	0.911234i	$-0.635131\pi$
$97$	−1.24147e7	−	5.97859e6i	−1.38113	−	0.665117i	−0.969240	+	0.246117i	$0.920845\pi$
$98$	−223142.	−	279811.i	−0.0239491	−	0.0300313i
$99$	747057.			0.0773803
$100$	−1.59999e7	−	2.00633e7i	−1.59999	−	2.00633i
$101$	1.42949e6	+	6.26302e6i	0.138057	+	0.604866i	0.995861	+	0.0908893i	$0.0289710\pi$
$101$	1.42949e6	+	6.26302e6i	0.138057	+	0.604866i	−0.857804	+	0.513976i	$0.828172\pi$
$102$	275997.	+	1.20922e6i	0.0257516	+	0.112825i
$103$	−6.80430e6	−	8.53232e6i	−0.613554	−	0.769373i	0.373867	−	0.927482i	$-0.378031\pi$
$103$	−6.80430e6	−	8.53232e6i	−0.613554	−	0.769373i	−0.987422	+	0.158110i	$0.949460\pi$
$104$	2.28972e6			0.199602
$105$	1.36889e7	+	1.71653e7i	1.15400	+	1.44707i
$106$	−33330.0	−	16050.9i	−0.00271810	−	0.00130897i
$107$	6.89511e6	−	8.64619e6i	0.544124	−	0.682310i	−0.431411	−	0.902156i	$-0.641984\pi$
$107$	6.89511e6	−	8.64619e6i	0.544124	−	0.682310i	0.975535	+	0.219846i	$0.0705554\pi$
$108$	−4.11383e6	+	5.15858e6i	−0.314241	+	0.394046i
$109$	2.21898e7	−	1.06861e7i	1.64120	−	0.790360i	0.641469	−	0.767149i	$-0.278325\pi$
$109$	2.21898e7	−	1.06861e7i	1.64120	−	0.790360i	0.999731	−	0.0232107i	$-0.00738885\pi$
$110$	72699.4	+	318517.i	0.00520783	+	0.0228170i
$111$	2.80591e6	−	1.22935e7i	0.194734	−	0.853187i
$112$	−1.00716e7	−	4.85024e6i	−0.677387	−	0.326212i
$113$	1.03509e7	−	4.98472e6i	0.674842	−	0.324987i	−0.0648860	−	0.997893i	$-0.520668\pi$
$113$	1.03509e7	−	4.98472e6i	0.674842	−	0.324987i	0.739728	+	0.672906i	$0.234954\pi$
$114$	−344576.	+	1.50969e6i	−0.0217830	+	0.0954376i
$115$	2.59745e7			1.59259
$116$	1.66579e7	+	120975.i	0.990874	+	0.00719602i
$117$	−1.08804e7			−0.628049
$118$	693279.	−	3.03746e6i	0.0388438	−	0.170186i
$119$	−1.22860e7	+	5.91665e6i	−0.668341	+	0.321856i
$120$	7.75680e6	+	3.73548e6i	0.409777	+	0.197338i
$121$	4.26360e6	−	1.86800e7i	0.218790	−	0.958581i
$122$	593062.	+	2.59837e6i	0.0295693	+	0.129551i
$123$	−1.95971e7	+	9.43749e6i	−0.949566	+	0.457287i
$124$	−2.14588e7	+	2.69084e7i	−1.01072	+	1.26740i
$125$	−4.10088e7	+	5.14234e7i	−1.87798	+	2.35492i
$126$	−891340.	−	429247.i	−0.0396960	−	0.0191166i
$127$	−9.22628e6	−	1.15694e7i	−0.399681	−	0.501184i	0.540743	−	0.841188i	$-0.318143\pi$
$127$	−9.22628e6	−	1.15694e7i	−0.399681	−	0.501184i	−0.940424	+	0.340004i	$0.889572\pi$
$128$	−8.84870e6			−0.372945
$129$	−1.37846e7	−	1.72854e7i	−0.565367	−	0.708948i
$130$	−1.05882e6	−	4.63898e6i	−0.0422687	−	0.185191i
$131$	1.72786e6	+	7.57025e6i	0.0671521	+	0.294212i	0.997342	−	0.0728670i	$-0.0232149\pi$
$131$	1.72786e6	+	7.57025e6i	0.0671521	+	0.294212i	−0.930190	+	0.367079i	$0.880358\pi$
$132$	2.67196e6	+	3.35053e6i	0.101116	+	0.126796i
$133$	−1.70248e7			−0.627483
$134$	−1.24631e6	−	1.56283e6i	−0.0447467	−	0.0561105i
$135$	2.48207e7	+	1.19530e7i	0.868253	+	0.418128i
$136$	−3.33400e6	+	4.18070e6i	−0.113653	+	0.142516i
$137$	5.78375e6	−	7.25259e6i	0.192171	−	0.240975i	−0.676406	−	0.736529i	$-0.736464\pi$
$137$	5.78375e6	−	7.25259e6i	0.192171	−	0.240975i	0.868577	+	0.495554i	$0.165035\pi$
$138$	−2.81913e6	+	1.35762e6i	−0.0913143	+	0.0439746i
$139$	139055.	+	609240.i	0.00439173	+	0.0192414i	0.977076	−	0.212889i	$-0.0682874\pi$
$139$	139055.	+	609240.i	0.00439173	+	0.0192414i	−0.972685	+	0.232131i	$0.925430\pi$
$140$	−1.04832e7	+	4.59298e7i	−0.322882	+	1.41464i
$141$	4.92193e7	+	2.37028e7i	1.47866	+	0.712086i
$142$	−194039.	+	93444.1i	−0.00568695	+	0.00273869i
$143$	1.05893e6	−	4.63949e6i	0.0302825	−	0.132676i
$144$	2.08298e7			0.581322
$145$	−1.49843e7	−	6.79205e7i	−0.408177	−	1.85017i
$146$	1.20896e6			0.0321496
$147$	−4.36165e6	+	1.91096e7i	−0.113250	+	0.496182i
$148$	2.43778e7	−	1.17397e7i	0.618129	−	0.297675i
$149$	−5.94413e7	−	2.86254e7i	−1.47210	−	0.708924i	−0.485824	−	0.874056i	$-0.661481\pi$
$149$	−5.94413e7	−	2.86254e7i	−1.47210	−	0.708924i	−0.986271	+	0.165132i	$0.947195\pi$
$150$	2.87214e6	−	1.25837e7i	0.0694842	−	0.304430i
$151$	1.08589e6	+	4.75758e6i	0.0256664	+	0.112452i	0.986138	−	0.165925i	$-0.0530608\pi$
$151$	1.08589e6	+	4.75758e6i	0.0256664	+	0.112452i	−0.960472	+	0.278377i	$0.910204\pi$
$152$	−6.01487e6	+	2.89661e6i	−0.138923	+	0.0669017i
$153$	1.58426e7	−	1.98660e7i	0.357608	−	0.448426i
$154$	269784.	−	338299.i	0.00595243	−	0.00746411i
$155$	1.29471e8	+	6.23500e7i	2.79262	+	1.34486i
$156$	−3.89152e7	−	4.87982e7i	−0.820698	−	1.02912i
$157$	−2.39044e7			−0.492980			−0.246490	−	0.969145i	$-0.579277\pi$
$157$	−2.39044e7			−0.492980			−0.246490	+	0.969145i	$0.579277\pi$
$158$	−1.97177e6	−	2.47253e6i	−0.0397701	−	0.0498702i
$159$	450842.	+	1.97527e6i	0.00889477	+	0.0389705i
$160$	6.17560e6	+	2.70571e7i	0.119195	+	0.522229i
$161$	−2.14488e7	−	2.68960e7i	−0.405054	−	0.507922i
$162$	−6.40347e6			−0.118335
$163$	−2.45893e6	−	3.08339e6i	−0.0444722	−	0.0557664i	0.759098	−	0.650976i	$-0.225640\pi$
$163$	−2.45893e6	−	3.08339e6i	−0.0444722	−	0.0557664i	−0.803570	+	0.595210i	$0.797069\pi$
$164$	−4.20510e7	−	2.02507e7i	−0.744428	−	0.358497i
$165$	1.11562e7	−	1.39895e7i	0.193341	−	0.242442i
$166$	1.82901e6	−	2.29350e6i	0.0310339	−	0.0389153i
$167$	−3.91243e7	+	1.88413e7i	−0.650038	+	0.313042i	−0.729687	−	0.683781i	$-0.760334\pi$
$167$	−3.91243e7	+	1.88413e7i	−0.650038	+	0.313042i	0.0796490	+	0.996823i	$0.474620\pi$
$168$	−2.53729e6	−	1.11166e7i	−0.0412846	−	0.180880i
$169$	−1.45977e6	+	6.39567e6i	−0.0232638	+	0.101925i
$170$	1.00118e7	+	4.82145e6i	0.156294	+	0.0752673i
$171$	2.85817e7	−	1.37642e7i	0.437121	−	0.210506i
$172$	1.05565e7	−	4.62510e7i	0.158187	−	0.693061i
$173$	1.02648e8			1.50726			0.753632	−	0.657296i	$-0.228300\pi$
$173$	1.02648e8			1.50726			0.753632	+	0.657296i	$0.228300\pi$
$174$	5.17635e6	+	6.58853e6i	0.0744906	+	0.0948126i
$175$	1.41907e8			2.00157
$176$	−2.02726e6	+	8.88202e6i	−0.0280295	+	0.122805i
$177$	−1.53736e8	+	7.40352e7i	−2.08386	+	1.00353i
$178$	−817737.	−	393801.i	−0.0108678	−	0.00523368i
$179$	2.50845e6	−	1.09902e7i	0.0326904	−	0.143226i	−0.955949	−	0.293533i	$-0.905169\pi$
$179$	2.50845e6	−	1.09902e7i	0.0326904	−	0.143226i	0.988639	+	0.150307i	$0.0480262\pi$
$180$	−1.95339e7	−	8.55835e7i	−0.249652	−	1.09380i
$181$	−5.13309e7	+	2.47197e7i	−0.643434	+	0.309862i	−0.726997	−	0.686641i	$-0.759084\pi$
$181$	−5.13309e7	+	2.47197e7i	−0.643434	+	0.309862i	0.0835625	+	0.996503i	$0.473370\pi$
$182$	−3.92922e6	+	4.92709e6i	−0.0483122	+	0.0605816i
$183$	9.10094e7	−	1.14122e8i	1.09776	−	1.37655i
$184$	−1.21540e7	−	5.85304e6i	−0.143832	−	0.0692659i
$185$	−7.04372e7	−	8.83255e7i	−0.817902	−	1.02562i
$186$	−1.73110e7			−0.197254
$187$	6.92916e6	+	8.68890e6i	0.0774881	+	0.0971670i
$188$	2.60843e7	+	1.14283e8i	0.286304	+	1.25438i
$189$	−8.11900e6	−	3.55717e7i	−0.0874755	−	0.383255i
$190$	8.64996e6	+	1.08467e7i	0.0914906	+	0.114726i
$191$	1.78901e8			1.85779			0.928894	−	0.370346i	$-0.120761\pi$
$191$	1.78901e8			1.85779			0.928894	+	0.370346i	$0.120761\pi$
$192$	7.31006e7	+	9.16653e7i	0.745361	+	0.934653i
$193$	−1.07926e8	−	5.19743e7i	−1.08062	−	0.520401i	−0.193107	−	0.981178i	$-0.561856\pi$
$193$	−1.07926e8	−	5.19743e7i	−1.08062	−	0.520401i	−0.887516	+	0.460777i	$0.847571\pi$
$194$	9.27223e6	−	1.16270e7i	0.0911755	−	0.114330i
$195$	−1.62483e8	+	2.03747e8i	−1.56923	+	1.96775i
$196$	−3.78942e7	+	1.82489e7i	−0.359481	+	0.173117i
$197$	−1.76762e7	−	7.74444e7i	−0.164724	−	0.721703i	−0.988050	−	0.154134i	$-0.950741\pi$
$197$	−1.76762e7	−	7.74444e7i	−0.164724	−	0.721703i	0.823326	−	0.567569i	$-0.192116\pi$
$198$	−179413.	+	786059.i	−0.00164258	+	0.00719660i
$199$	−6.85452e7	−	3.30096e7i	−0.616582	−	0.296930i	0.0994014	−	0.995047i	$-0.468307\pi$
$199$	−6.85452e7	−	3.30096e7i	−0.616582	−	0.296930i	−0.715984	+	0.698117i	$0.754022\pi$
$200$	5.01357e7	−	2.41441e7i	0.443141	−	0.213405i
$201$	−2.43611e7	+	1.06733e8i	−0.211597	+	0.927069i
$202$	−6.93331e6			−0.0591848
$203$	−5.79566e7	+	7.16023e7i	−0.486258	+	0.600746i
$204$	1.45762e8			1.20209
$205$	−4.33635e7	+	1.89988e8i	−0.351549	+	1.54024i
$206$	1.06119e7	−	5.11042e6i	0.0845780	−	0.0407306i
$207$	5.77537e7	+	2.78127e7i	0.452568	+	0.217945i
$208$	2.95257e7	−	1.29361e8i	0.227499	−	0.996736i
$209$	3.08747e6	+	1.35271e7i	0.0233933	+	0.102493i
$210$	−2.13490e7	+	1.02811e7i	−0.159078	+	0.0766079i
$211$	−1.02419e8	+	1.28429e8i	−0.750570	+	0.941185i	−0.999627	−	0.0273034i	$-0.991308\pi$
$211$	−1.02419e8	+	1.28429e8i	−0.750570	+	0.941185i	0.249057	+	0.968489i	$0.419879\pi$
$212$	−2.71060e6	+	3.39899e6i	−0.0195385	+	0.0245005i
$213$	1.06271e7	+	5.11776e6i	0.0753507	+	0.0362870i
$214$	7.44167e6	+	9.33155e6i	0.0519065	+	0.0650887i
$215$	−1.98078e8			−1.35926
$216$	−8.92062e6	−	1.11861e7i	−0.0602291	−	0.0755250i
$217$	−4.23508e7	−	1.85551e8i	−0.281353	−	1.23269i
$218$	5.91486e6	+	2.59147e7i	0.0386675	+	0.169414i
$219$	−4.12827e7	−	5.17669e7i	−0.265591	−	0.333041i
$220$	3.83946e7			0.243104
$221$	−1.00919e8	−	1.26548e8i	−0.628924	−	0.788646i
$222$	1.22614e7	+	5.90479e6i	0.0752152	+	0.0362217i
$223$	8.15713e7	−	1.02287e8i	0.492572	−	0.617666i	−0.471963	−	0.881618i	$-0.656455\pi$
$223$	8.15713e7	−	1.02287e8i	0.492572	−	0.617666i	0.964536	+	0.263952i	$0.0850260\pi$
$224$	2.29174e7	−	2.87375e7i	0.136237	−	0.170836i
$225$	−2.38237e8	+	1.14729e8i	−1.39434	+	0.671481i
$226$	2.75910e6	+	1.20884e7i	0.0158996	+	0.0696609i
$227$	−3.30321e7	+	1.44723e8i	−0.187433	+	0.821196i	0.790531	+	0.612422i	$0.209805\pi$
$227$	−3.30321e7	+	1.44723e8i	−0.187433	+	0.821196i	−0.977964	+	0.208774i	$0.933053\pi$
$228$	1.63959e8	+	7.89583e7i	0.916141	+	0.441190i
$229$	3.39217e7	−	1.63358e7i	0.186661	−	0.0898912i	−0.338219	−	0.941067i	$-0.609824\pi$
$229$	3.39217e7	−	1.63358e7i	0.186661	−	0.0898912i	0.524880	+	0.851176i	$0.324110\pi$
$230$	−6.23803e6	+	2.73306e7i	−0.0338065	+	0.148116i
$231$	−2.36982e7			−0.126495
$232$	−8.29362e6	+	3.51578e7i	−0.0436050	+	0.184848i
$233$	1.29890e8			0.672711			0.336356	−	0.941735i	$-0.390806\pi$
$233$	1.29890e8			0.672711			0.336356	+	0.941735i	$0.390806\pi$
$234$	2.61303e6	−	1.14484e7i	0.0133318	−	0.0584104i
$235$	4.40967e8	−	2.12359e8i	2.21651	−	1.06741i
$236$	−3.29881e8	−	1.58863e8i	−1.63368	−	0.786737i
$237$	−3.85413e7	+	1.68860e8i	−0.188065	+	0.823965i
$238$	−3.27493e6	−	1.43484e7i	−0.0157465	−	0.0689898i
$239$	3.06561e8	−	1.47632e8i	1.45253	−	0.699501i	0.469496	−	0.882934i	$-0.344436\pi$
$239$	3.06561e8	−	1.47632e8i	1.45253	−	0.699501i	0.983032	+	0.183434i	$0.0587212\pi$
$240$	3.11064e8	−	3.90061e8i	1.45248	−	1.82135i
$241$	−1.59914e8	+	2.00525e8i	−0.735912	+	0.922804i	−0.999120	−	0.0419348i	$-0.986648\pi$
$241$	−1.59914e8	+	2.00525e8i	−0.735912	+	0.922804i	0.263209	+	0.964739i	$0.415219\pi$
$242$	1.86313e7	+	8.97238e6i	0.0845065	+	0.0406962i
$243$	1.47727e8	+	1.85244e8i	0.660448	+	0.828176i
$244$	3.13213e8			1.38031
$245$	1.09491e8	+	1.37298e8i	0.475662	+	0.596461i
$246$	−5.22376e6	−	2.28868e7i	−0.0223723	−	0.0980193i
$247$	−4.49669e7	−	1.97013e8i	−0.189869	−	0.831869i
$248$	−4.65322e7	−	5.83495e7i	−0.193719	−	0.242916i
$249$	−1.60662e8			−0.659501
$250$	−4.42595e7	−	5.54996e7i	−0.179150	−	0.224647i
$251$	1.95847e7	+	9.43148e6i	0.0781733	+	0.0376463i	0.472562	−	0.881297i	$-0.343329\pi$
$251$	1.95847e7	+	9.43148e6i	0.0781733	+	0.0376463i	−0.394389	+	0.918944i	$0.629044\pi$
$252$	−7.24893e7	+	9.08987e7i	−0.285346	+	0.357813i
$253$	−1.74805e7	+	2.19198e7i	−0.0678627	+	0.0850971i
$254$	1.43892e7	−	6.92946e6i	0.0550957	−	0.0265327i
$255$	−1.35426e8	−	5.93341e8i	−0.511461	−	2.24086i
$256$	−5.43707e7	+	2.38213e8i	−0.202546	+	0.887414i
$257$	1.27467e8	+	6.13850e7i	0.468417	+	0.225578i	0.653176	−	0.757206i	$-0.273436\pi$
$257$	1.27467e8	+	6.13850e7i	0.468417	+	0.225578i	−0.184759	+	0.982784i	$0.559150\pi$
$258$	2.14983e7	−	1.03530e7i	0.0779355	−	0.0375317i
$259$	−3.32944e7	+	1.45872e8i	−0.119075	+	0.521703i
$260$	−5.59192e8			−1.97312
$261$	3.94099e7	−	1.67064e8i	0.137203	−	0.581624i
$262$	−8.38044e6			−0.0287881
$263$	1.23476e8	−	5.40983e8i	0.418540	−	1.83374i	−0.122135	−	0.992513i	$-0.538974\pi$
$263$	1.23476e8	−	5.40983e8i	0.418540	−	1.83374i	0.540676	−	0.841231i	$-0.318169\pi$
$264$	−8.37256e6	+	4.03201e6i	−0.0280056	+	0.0134868i
$265$	1.63544e7	+	7.87586e6i	0.0539851	+	0.0259978i
$266$	4.08868e6	−	1.79137e7i	0.0133198	−	0.0583578i
$267$	1.10612e7	+	4.84623e7i	0.0355642	+	0.155817i
$268$	−2.11650e8	+	1.01925e8i	−0.671656	+	0.323452i
$269$	−3.50383e8	+	4.39367e8i	−1.09751	+	1.37624i	−0.177609	+	0.984101i	$0.556836\pi$
$269$	−3.50383e8	+	4.39367e8i	−1.09751	+	1.37624i	−0.919906	+	0.392139i	$0.871735\pi$
$270$	−1.85380e7	+	2.32459e7i	−0.0573178	+	0.0718743i
$271$	−2.94053e8	−	1.41608e8i	−0.897497	−	0.432212i	−0.0725128	−	0.997367i	$-0.523102\pi$
$271$	−2.94053e8	−	1.41608e8i	−0.897497	−	0.432212i	−0.824984	+	0.565156i	$0.808816\pi$
$272$	1.93203e8	+	2.42268e8i	0.582132	+	0.729971i
$273$	3.45148e8			1.02668
$274$	6.24221e6	+	7.82749e6i	0.0183321	+	0.0229877i
$275$	−2.57349e7	−	1.12752e8i	−0.0746206	−	0.326934i
$276$	8.18252e7	+	3.58500e8i	0.234264	+	1.02638i
$277$	4.05425e8	+	5.08387e8i	1.14612	+	1.43719i	0.881087	+	0.472955i	$0.156813\pi$
$277$	4.05425e8	+	5.08387e8i	1.14612	+	1.43719i	0.265036	+	0.964238i	$0.414616\pi$
$278$	−674443.			−0.00188273
$279$	2.21113e8	+	2.77268e8i	0.609538	+	0.764336i
$280$	−9.20408e7	−	4.43245e7i	−0.250569	−	0.120668i
$281$	−1.12925e8	+	1.41603e8i	−0.303611	+	0.380716i	−0.910109	−	0.414369i	$-0.864002\pi$
$281$	−1.12925e8	+	1.41603e8i	−0.303611	+	0.380716i	0.606498	+	0.795085i	$0.292574\pi$
$282$	−3.67608e7	+	4.60965e7i	−0.0976141	+	0.122404i
$283$	2.48615e8	−	1.19727e8i	0.652042	−	0.314007i	−0.0784601	−	0.996917i	$-0.525000\pi$
$283$	2.48615e8	−	1.19727e8i	0.652042	−	0.314007i	0.730502	+	0.682910i	$0.239286\pi$
$284$	5.63197e6	+	2.46753e7i	0.0145897	+	0.0639216i
$285$	1.69076e8	−	7.40772e8i	0.432640	−	1.89552i
$286$	4.62739e6	+	2.22843e6i	0.0116965	+	0.00563273i
$287$	2.32536e8	−	1.11984e8i	0.580636	−	0.279620i
$288$	−1.52406e7	+	6.67734e7i	−0.0375948	+	0.164714i
$289$	−3.23352e7			−0.0788013
$290$	7.50651e7	+	545145.i	0.180736	+	0.00131256i
$291$	−8.14483e8			−1.93757
$292$	3.16150e7	−	1.38514e8i	0.0743109	−	0.325577i
$293$	1.72812e8	−	8.32216e7i	0.401362	−	0.193286i	−0.222303	−	0.974978i	$-0.571357\pi$
$293$	1.72812e8	−	8.32216e7i	0.401362	−	0.193286i	0.623665	+	0.781692i	$0.285643\pi$
$294$	−1.90598e7	−	9.17872e6i	−0.0437424	−	0.0210652i
$295$	−3.40178e8	+	1.49042e9i	−0.771489	+	3.38011i
$296$	1.30558e7	+	5.72014e7i	0.0292606	+	0.128199i
$297$	−2.67911e7	+	1.29019e7i	−0.0593394	+	0.0285763i
$298$	4.43953e7	−	5.56699e7i	0.0971806	−	0.121861i
$299$	2.54591e8	−	3.19247e8i	0.550800	−	0.690681i
$300$	−1.36664e9	−	6.58140e8i	−2.92234	−	1.40732i
$301$	1.63566e8	+	2.05105e8i	0.345708	+	0.433505i
$302$	−5.26675e6			−0.0110032
$303$	2.36754e8	+	2.96880e8i	0.488932	+	0.613101i
$304$	8.60864e7	+	3.77169e8i	0.175743	+	0.769979i
$305$	−2.91004e8	−	1.27497e9i	−0.587285	−	2.57306i
$306$	1.70984e7	+	2.14408e7i	0.0341139	+	0.0427775i
$307$	2.56703e8			0.506346			0.253173	−	0.967421i	$-0.418526\pi$
$307$	2.56703e8			0.506346			0.253173	+	0.967421i	$0.418526\pi$
$308$	−3.17050e7	−	3.97568e7i	−0.0618301	−	0.0775325i
$309$	−5.81193e8	−	2.79888e8i	−1.12064	−	0.539671i
$310$	−9.66989e7	+	1.21257e8i	−0.184355	+	0.231174i
$311$	−4.31857e8	+	5.41532e8i	−0.814102	+	1.02085i	0.185170	+	0.982706i	$0.440716\pi$
$311$	−4.31857e8	+	5.41532e8i	−0.814102	+	1.02085i	−0.999272	+	0.0381450i	$0.987855\pi$
$312$	1.21941e8	−	5.87235e7i	0.227304	−	0.109464i
$313$	9.84287e7	+	4.31244e8i	0.181433	+	0.794910i	0.980949	+	0.194265i	$0.0622323\pi$
$313$	9.84287e7	+	4.31244e8i	0.181433	+	0.794910i	−0.799516	+	0.600645i	$0.794911\pi$
$314$	5.74087e6	−	2.51524e7i	0.0104646	−	0.0458485i
$315$	4.37363e8	+	2.10623e8i	0.788415	+	0.379681i
$316$	−3.34848e8	+	1.61254e8i	−0.596957	+	0.287480i
$317$	7.11121e7	−	3.11562e8i	0.125382	−	0.549335i	−0.872746	−	0.488175i	$-0.837663\pi$
$317$	7.11121e7	−	3.11562e8i	0.125382	−	0.549335i	0.998128	−	0.0611603i	$-0.0194801\pi$
$318$	−2.18667e6			−0.00381318
$319$	6.74021e7	+	3.30643e7i	0.116253	+	0.0570284i
$320$	1.05042e9			1.79200
$321$	1.45459e8	−	6.37296e8i	0.245455	−	1.07541i
$322$	3.34513e7	−	1.61093e7i	0.0558365	−	0.0268894i
$323$	4.25193e8	+	2.04762e8i	0.702065	+	0.338096i
$324$	−1.67454e8	+	7.33666e8i	−0.273520	+	1.19837i
$325$	3.74812e8	+	1.64216e9i	0.605650	+	2.65353i
$326$	3.83491e6	−	1.84679e6i	0.00613046	−	0.00295227i
$327$	9.07675e8	−	1.13819e9i	1.43553	−	1.80010i
$328$	6.31022e7	−	7.91276e7i	0.0987383	−	0.123814i
$329$	−5.84028e8	−	2.81253e8i	−0.904166	−	0.435423i
$330$	1.20405e7	+	1.50984e7i	0.0184437	+	0.0231276i
$331$	−7.81711e8			−1.18481			−0.592405	−	0.805641i	$-0.701821\pi$
$331$	−7.81711e8			−1.18481			−0.592405	+	0.805641i	$0.701821\pi$
$332$	−2.14944e8	−	2.69532e8i	−0.322361	−	0.404228i
$333$	−6.20393e7	−	2.71812e8i	−0.0920687	−	0.403379i
$334$	−1.04289e7	−	4.56918e7i	−0.0153152	−	0.0671005i
$335$	6.11541e8	+	7.66848e8i	0.888728	+	1.11443i
$336$	−6.60765e8			−0.950297
$337$	−6.70085e8	−	8.40259e8i	−0.953729	−	1.19594i	−0.980544	−	0.196298i	$-0.937108\pi$
$337$	−6.70085e8	−	8.40259e8i	−0.953729	−	1.19594i	0.0268153	−	0.999640i	$-0.491463\pi$
$338$	−6.37900e6	−	3.07196e6i	−0.00898554	−	0.00432721i
$339$	4.23402e8	−	5.30929e8i	0.590275	−	0.740181i
$340$	8.14225e8	−	1.02101e9i	1.12349	−	1.40881i
$341$	−1.39749e8	+	6.72996e7i	−0.190857	+	0.0919120i
$342$	7.61866e6	+	3.33795e7i	0.0102988	+	0.0451220i
$343$	1.80287e8	−	7.89887e8i	0.241232	−	1.05690i
$344$	9.26844e7	+	4.46345e7i	0.122759	+	0.0591175i
$345$	1.38329e9	−	6.66158e8i	1.81362	−	0.873395i
$346$	−2.46519e7	+	1.08007e8i	−0.0319952	+	0.140180i
$347$	−8.90570e8			−1.14423			−0.572117	−	0.820172i	$-0.693878\pi$
$347$	−8.90570e8			−1.14423			−0.572117	+	0.820172i	$0.693878\pi$
$348$	8.90234e8	−	4.20777e8i	1.13234	−	0.535211i
$349$	−2.23364e7			−0.0281270			−0.0140635	−	0.999901i	$-0.504477\pi$
$349$	−2.23364e7			−0.0281270			−0.0140635	+	0.999901i	$0.504477\pi$
$350$	−3.40803e7	+	1.49315e8i	−0.0424879	+	0.186152i
$351$	3.90194e8	−	1.87908e8i	0.481621	−	0.231937i
$352$	−2.69894e7	−	1.29974e7i	−0.0329833	−	0.0158839i
$353$	−4.39881e7	+	1.92725e8i	−0.0532260	+	0.233199i	−0.994543	−	0.104325i	$-0.966732\pi$
$353$	−4.39881e7	+	1.92725e8i	−0.0532260	+	0.233199i	0.941317	+	0.337523i	$0.109589\pi$
$354$	−4.09793e7	−	1.79542e8i	−0.0490968	−	0.215107i
$355$	9.52109e7	−	4.58512e7i	0.112950	−	0.0543940i
$356$	−6.65034e7	+	8.33926e7i	−0.0781212	+	0.0979609i
$357$	−5.02561e8	+	6.30191e8i	−0.584588	+	0.733050i
$358$	1.09616e7	+	5.27882e6i	0.0126265	+	0.00608060i
$359$	−2.47247e7	−	3.10038e7i	−0.0282034	−	0.0353659i	0.767530	−	0.641013i	$-0.221486\pi$
$359$	−2.47247e7	−	3.10038e7i	−0.0282034	−	0.0353659i	−0.795733	+	0.605647i	$0.792914\pi$
$360$	1.90356e8			0.215034
$361$	−1.89965e8	−	2.38209e8i	−0.212519	−	0.266491i
$362$	−1.36826e7	−	5.99475e7i	−0.0151597	−	0.0664188i
$363$	−2.52019e8	−	1.10417e9i	−0.276541	−	1.21161i
$364$	4.61761e8	+	5.79030e8i	0.501837	+	0.629284i
$365$	−5.93211e8			−0.638535
$366$	9.82234e7	+	1.23168e8i	0.104720	+	0.131315i
$367$	5.18513e7	+	2.49703e7i	0.0547555	+	0.0263689i	0.461061	−	0.887368i	$-0.347469\pi$
$367$	5.18513e7	+	2.49703e7i	0.0547555	+	0.0263689i	−0.406306	+	0.913737i	$0.633183\pi$
$368$	−4.87399e8	+	6.11179e8i	−0.509821	+	0.639295i
$369$	−2.99851e8	+	3.76002e8i	−0.310680	+	0.389581i
$370$	1.09853e8	−	5.29024e7i	0.112747	−	0.0542962i
$371$	−5.34961e6	−	2.34382e7i	−0.00543893	−	0.0238295i
$372$	−4.52692e8	+	1.98337e9i	−0.455935	+	1.99758i
$373$	9.31011e8	+	4.48351e8i	0.928910	+	0.447340i	0.836244	−	0.548358i	$-0.184747\pi$
$373$	9.31011e8	+	4.48351e8i	0.928910	+	0.447340i	0.0926663	+	0.995697i	$0.470461\pi$
$374$	−1.08066e7	+	5.20420e6i	−0.0106817	+	0.00514403i
$375$	−8.65118e8	+	3.79033e9i	−0.847161	+	3.71165i
$376$	−2.54190e8			−0.246604
$377$	−9.81666e8	−	4.81559e8i	−0.943559	−	0.462865i
$378$	3.93786e7			0.0375007
$379$	3.50524e8	−	1.53575e9i	0.330735	−	1.44905i	−0.486975	−	0.873416i	$-0.661900\pi$
$379$	3.50524e8	−	1.53575e9i	0.330735	−	1.44905i	0.817710	−	0.575630i	$-0.195243\pi$
$380$	1.46894e9	−	7.07406e8i	1.37329	−	0.661342i
$381$	−7.88068e8	−	3.79514e8i	−0.730006	−	0.351552i
$382$	−4.29648e7	+	1.88241e8i	−0.0394358	+	0.172780i
$383$	−7.76494e7	−	3.40204e8i	−0.0706224	−	0.309417i	0.927263	−	0.374410i	$-0.122155\pi$
$383$	−7.76494e7	−	3.40204e8i	−0.0706224	−	0.309417i	−0.997886	+	0.0649930i	$0.979298\pi$
$384$	−4.71244e8	+	2.26939e8i	−0.424704	+	0.204527i
$385$	−1.32378e8	+	1.65996e8i	−0.118223	+	0.148247i
$386$	8.06071e7	−	1.01078e8i	0.0713375	−	0.0894544i
$387$	−4.40422e8	−	2.12096e8i	−0.386260	−	0.186013i
$388$	−1.08967e9	−	1.36640e9i	−0.947073	−	1.18759i
$389$	−8.85903e8			−0.763067			−0.381533	−	0.924355i	$-0.624604\pi$
$389$	−8.85903e8			−0.763067			−0.381533	+	0.924355i	$0.624604\pi$
$390$	−1.75362e8	−	2.19897e8i	−0.149696	−	0.187713i
$391$	2.12197e8	+	9.29695e8i	0.179523	+	0.786542i
$392$	−2.02947e7	−	8.89168e7i	−0.0170169	−	0.0745560i
$393$	2.86170e8	+	3.58846e8i	0.237821	+	0.298218i
$394$	8.57327e7			0.0706171
$395$	9.67510e8	+	1.21322e9i	0.789888	+	0.990488i
$396$	8.53696e7	+	4.11118e7i	0.0690828	+	0.0332685i
$397$	−3.76118e8	+	4.71637e8i	−0.301688	+	0.378305i	−0.909449	−	0.415815i	$-0.863496\pi$
$397$	−3.76118e8	+	4.71637e8i	−0.301688	+	0.378305i	0.607761	+	0.794120i	$0.292068\pi$
$398$	5.11948e7	−	6.41962e7i	0.0407038	−	0.0510409i
$399$	−9.06670e8	+	4.36629e8i	−0.714569	+	0.344118i
$400$	−7.17555e8	−	3.14381e9i	−0.560590	−	2.45610i
$401$	−3.37892e8	+	1.48040e9i	−0.261681	+	1.14650i	0.657746	+	0.753240i	$0.271510\pi$
$401$	−3.37892e8	+	1.48040e9i	−0.261681	+	1.14650i	−0.919427	+	0.393260i	$0.871347\pi$
$402$	−1.06455e8	−	5.12658e7i	−0.0817285	−	0.0393583i
$403$	2.03535e9	−	9.80173e8i	1.54907	−	0.745994i
$404$	−1.81310e8	+	7.94371e8i	−0.136800	+	0.599361i
$405$	3.14205e9			2.35029
$406$	−6.14216e7	−	7.81783e7i	−0.0455492	−	0.0579756i
$407$	1.21941e8			0.0896538
$408$	−7.03338e7	+	3.08152e8i	−0.0512688	+	0.224623i
$409$	−1.58883e9	+	7.65139e8i	−1.14827	+	0.552979i	−0.908514	−	0.417854i	$-0.862782\pi$
$409$	−1.58883e9	+	7.65139e8i	−1.14827	+	0.552979i	−0.239758	+	0.970833i	$0.577068\pi$
$410$	−1.89493e8	−	9.12549e7i	−0.135784	−	0.0653902i
$411$	1.22013e8	−	5.34576e8i	0.0866885	−	0.379807i
$412$	−3.08010e8	−	1.34948e9i	−0.216982	−	0.950661i
$413$	1.82420e9	−	8.78489e8i	1.27423	−	0.613637i
$414$	−4.31349e7	+	5.40894e7i	−0.0298763	+	0.0374637i
$415$	−8.97457e8	+	1.12538e9i	−0.616375	+	0.772910i
$416$	3.93083e8	+	1.89299e8i	0.267706	+	0.128920i
$417$	2.30304e7	+	2.88793e7i	0.0155534	+	0.0195034i
$418$	−1.49748e7			−0.0100287
$419$	6.82534e8	+	8.55871e8i	0.453289	+	0.568407i	0.954991	−	0.296634i	$-0.0958641\pi$
$419$	6.82534e8	+	8.55871e8i	0.453289	+	0.568407i	−0.501702	+	0.865040i	$0.667293\pi$
$420$	6.19654e8	+	2.71488e9i	0.408110	+	1.78804i
$421$	−1.16912e8	−	5.12227e8i	−0.0763613	−	0.334561i	0.922289	−	0.386501i	$-0.126317\pi$
$421$	−1.16912e8	−	5.12227e8i	−0.0763613	−	0.334561i	−0.998650	+	0.0519406i	$0.983459\pi$
$422$	−1.10537e8	−	1.38609e8i	−0.0716004	−	0.0897841i
$423$	1.20787e9			0.775940
$424$	−5.87780e6	−	7.37053e6i	−0.00374485	−	0.00469589i
$425$	−3.54410e9	−	1.70675e9i	−2.23947	−	1.07847i
$426$	−7.93715e6	+	9.95287e6i	−0.00497429	+	0.00623756i
$427$	−1.07990e9	+	1.35415e9i	−0.671253	+	0.841725i
$428$	1.26375e9	−	6.08590e8i	0.779127	−	0.375208i
$429$	−6.25929e7	−	2.74237e8i	−0.0382758	−	0.167697i
$430$	4.75703e7	−	2.08419e8i	0.0288534	−	0.126415i
$431$	3.70335e8	+	1.78344e8i	0.222805	+	0.107297i	0.541957	−	0.840407i	$-0.317684\pi$
$431$	3.70335e8	+	1.78344e8i	0.222805	+	0.107297i	−0.319152	+	0.947704i	$0.603398\pi$
$432$	−7.47003e8	+	3.59738e8i	−0.445789	+	0.214681i
$433$	−3.24925e8	+	1.42359e9i	−0.192343	+	0.842708i	0.783002	+	0.622020i	$0.213688\pi$
$433$	−3.24925e8	+	1.42359e9i	−0.192343	+	0.842708i	−0.975344	+	0.220689i	$0.929170\pi$
$434$	2.05409e8			0.120616
$435$	−2.53993e9	−	3.23286e9i	−1.47948	−	1.88310i
$436$	3.12381e9			1.80502
$437$	−2.64923e8	+	1.16070e9i	−0.151857	+	0.665328i
$438$	6.43839e7	−	3.10057e7i	0.0366116	−	0.0176312i
$439$	−1.50778e9	−	7.26110e8i	−0.850576	−	0.409616i	−0.0427846	−	0.999084i	$-0.513623\pi$
$439$	−1.50778e9	−	7.26110e8i	−0.850576	−	0.409616i	−0.807791	+	0.589469i	$0.799337\pi$
$440$	−1.85264e7	+	8.11693e7i	−0.0103683	+	0.0454263i
$441$	9.64371e7	+	4.22518e8i	0.0535438	+	0.234591i
$442$	1.57391e8	−	7.57956e7i	0.0866967	−	0.0417509i
$443$	8.44888e8	−	1.05946e9i	0.461728	−	0.578989i	−0.495396	−	0.868667i	$-0.664977\pi$
$443$	8.44888e8	−	1.05946e9i	0.461728	−	0.578989i	0.957124	+	0.289679i	$0.0935484\pi$
$444$	9.97175e8	−	1.25042e9i	0.540668	−	0.677977i
$445$	4.01247e8	+	1.93230e8i	0.215850	+	0.103948i
$446$	8.80372e7	+	1.10395e8i	0.0469888	+	0.0589221i
$447$	−3.89973e9			−2.06518
$448$	−8.67399e8	−	1.08768e9i	−0.455770	−	0.571518i
$449$	−4.04201e8	−	1.77092e9i	−0.210734	−	0.923287i	−0.964069	−	0.265651i	$-0.914413\pi$
$449$	−4.04201e8	−	1.77092e9i	−0.210734	−	0.923287i	0.753335	−	0.657637i	$-0.228444\pi$
$450$	−6.35037e7	−	2.78228e8i	−0.0328515	−	0.143932i
$451$	−1.31147e8	−	1.64454e8i	−0.0673196	−	0.0844161i
$452$	1.45716e9			0.742202
$453$	1.79846e8	+	2.25519e8i	0.0908984	+	0.113983i
$454$	−1.44346e8	−	6.95132e7i	−0.0723949	−	0.0348636i
$455$	1.92799e9	−	2.41762e9i	0.959545	−	1.20323i
$456$	−2.46038e8	+	3.08522e8i	−0.121514	+	0.152374i
$457$	−7.04732e8	+	3.39381e8i	−0.345396	+	0.166334i	−0.598536	−	0.801096i	$-0.704251\pi$
$457$	−7.04732e8	+	3.39381e8i	−0.345396	+	0.166334i	0.253140	+	0.967430i	$0.418537\pi$
$458$	9.04207e6	+	3.96159e7i	0.00439783	+	0.0192682i
$459$	−2.25059e8	+	9.86047e8i	−0.108630	+	0.475941i
$460$	2.96823e9	+	1.42942e9i	1.42182	+	0.684712i
$461$	2.03201e9	−	9.78566e8i	0.965991	−	0.465197i	0.116727	−	0.993164i	$-0.462760\pi$
$461$	2.03201e9	−	9.78566e8i	0.965991	−	0.465197i	0.849265	+	0.527967i	$0.177046\pi$
$462$	5.69134e6	−	2.49354e7i	0.00268515	−	0.0117644i
$463$	3.76518e8			0.176300			0.0881499	−	0.996107i	$-0.471905\pi$
$463$	3.76518e8			0.176300			0.0881499	+	0.996107i	$0.471905\pi$
$464$	1.87934e9	+	9.21915e8i	0.873358	+	0.428428i
$465$	8.49415e9			3.91773
$466$	−3.11942e7	+	1.36671e8i	−0.0142798	+	0.0625641i
$467$	5.27829e8	−	2.54189e8i	0.239819	−	0.115491i	−0.310114	−	0.950699i	$-0.600367\pi$
$467$	5.27829e8	−	2.54189e8i	0.239819	−	0.115491i	0.549934	+	0.835208i	$0.314653\pi$
$468$	−1.24335e9	−	5.98766e8i	−0.560703	−	0.270020i
$469$	2.89064e8	−	1.26647e9i	0.129387	−	0.566880i
$470$	1.17543e8	+	5.14989e8i	0.0522221	+	0.228800i
$471$	−1.27305e9	+	6.13067e8i	−0.561398	+	0.270355i
$472$	4.95024e8	−	6.20740e8i	0.216685	−	0.271715i
$473$	1.33303e8	−	1.67157e8i	0.0579199	−	0.0726292i
$474$	−1.68420e8	−	8.11069e7i	−0.0726390	−	0.0349811i
$475$	−3.06201e9	−	3.83964e9i	−1.31093	−	1.64385i
$476$	−1.72959e9			−0.735052
$477$	2.79304e7	+	3.50236e7i	0.0117832	+	0.0147756i
$478$	8.17161e7	+	3.58021e8i	0.0342223	+	0.149938i
$479$	3.56041e8	+	1.55992e9i	0.148022	+	0.648525i	0.993434	+	0.114410i	$0.0364979\pi$
$479$	3.56041e8	+	1.55992e9i	0.148022	+	0.648525i	−0.845412	+	0.534115i	$0.820645\pi$
$480$	1.02281e9	+	1.28256e9i	0.422133	+	0.529339i
$481$	−1.77599e9			−0.727665
$482$	−1.72590e8	−	2.16420e8i	−0.0702020	−	0.0880306i
$483$	−1.83207e9	−	8.82276e8i	−0.739820	−	0.356279i
$484$	1.51522e9	−	1.90002e9i	0.607457	−	0.761727i
$485$	−4.54970e9	+	5.70514e9i	−1.81087	+	2.27075i
$486$	−2.30394e8	+	1.10952e8i	−0.0910423	+	0.0438437i
$487$	5.27158e8	+	2.30963e9i	0.206818	+	0.906131i	0.966668	+	0.256032i	$0.0824153\pi$
$487$	5.27158e8	+	2.30963e9i	0.206818	+	0.906131i	−0.759850	+	0.650099i	$0.774728\pi$
$488$	−1.51133e8	+	6.62157e8i	−0.0588694	+	0.257924i
$489$	−2.10031e8	−	1.01145e8i	−0.0812272	−	0.0391170i
$490$	−1.70761e8	+	8.22342e7i	−0.0655696	+	0.0315767i
$491$	1.11268e8	−	4.87498e8i	0.0424215	−	0.185861i	−0.949278	−	0.314438i	$-0.898184\pi$
$491$	1.11268e8	−	4.87498e8i	0.0424215	−	0.185861i	0.991699	+	0.128577i	$0.0410411\pi$
$492$	−2.75882e9			−1.04435
$493$	2.30864e9	−	1.09120e9i	0.867743	−	0.410147i
$494$	2.18098e8			0.0813967
$495$	8.80343e7	−	3.85704e8i	0.0326237	−	0.142934i
$496$	−3.89656e9	+	1.87648e9i	−1.43382	+	0.690492i
$497$	−1.26100e8	−	6.07264e7i	−0.0460751	−	0.0221886i
$498$	3.85845e7	−	1.69050e8i	0.0139994	−	0.0613356i
$499$	−2.89980e6	−	1.27048e7i	−0.00104476	−	0.00457739i	0.974403	−	0.224809i	$-0.0721758\pi$
$499$	−2.89980e6	−	1.27048e7i	−0.00104476	−	0.00457739i	−0.975448	+	0.220232i	$0.929319\pi$
$500$	−7.51618e9	+	3.61960e9i	−2.68907	+	1.29499i
$501$	−1.60038e9	+	2.00681e9i	−0.568579	+	0.712975i
$502$	−1.46273e7	+	1.83421e7i	−0.00516062	+	0.00647122i
$503$	2.51333e9	+	1.21036e9i	0.880566	+	0.424058i	0.818831	−	0.574034i	$-0.194622\pi$
$503$	2.51333e9	+	1.21036e9i	0.880566	+	0.424058i	0.0617347	+	0.998093i	$0.480337\pi$
$504$	−1.57189e8	−	1.97109e8i	−0.0546910	−	0.0685803i
$505$	3.40203e9			1.17549
$506$	−1.88661e7	−	2.36573e7i	−0.00647374	−	0.00811781i
$507$	8.62862e7	+	3.78044e8i	0.0294045	+	0.128829i
$508$	−4.17646e8	−	1.82982e9i	−0.141346	−	0.619279i
$509$	7.99271e7	+	1.00225e8i	0.0268647	+	0.0336873i	0.795082	−	0.606501i	$-0.207428\pi$
$509$	7.99271e7	+	1.00225e8i	0.0268647	+	0.0336873i	−0.768218	+	0.640189i	$0.778856\pi$
$510$	6.56842e8			0.219263
$511$	4.89853e8	+	6.14257e8i	0.162403	+	0.203646i
$512$	−1.25806e9	−	6.05850e8i	−0.414244	−	0.199490i
$513$	−7.87290e8	+	9.87230e8i	−0.257468	+	0.322855i
$514$	−9.52023e7	+	1.19380e8i	−0.0309226	+	0.0387758i
$515$	−5.20704e9	+	2.50758e9i	−1.67983	+	0.808964i
$516$	−6.23988e8	−	2.73387e9i	−0.199941	−	0.875999i
$517$	−1.17556e8	+	5.15045e8i	−0.0374134	+	0.163919i
$518$	−1.45492e8	−	7.00652e7i	−0.0459923	−	0.0221487i
$519$	5.46660e9	−	2.63258e9i	1.71645	−	0.826600i
$520$	2.69824e8	−	1.18218e9i	0.0841528	−	0.368698i
$521$	5.04201e9			1.56197			0.780984	−	0.624551i	$-0.214718\pi$
$521$	5.04201e9			1.56197			0.780984	+	0.624551i	$0.214718\pi$
$522$	1.66322e8	+	8.15896e7i	0.0511802	+	0.0251066i
$523$	−1.87864e9			−0.574233			−0.287116	−	0.957896i	$-0.592697\pi$
$523$	−1.87864e9			−0.574233			−0.287116	+	0.957896i	$0.592697\pi$
$524$	−2.19154e8	+	9.60175e8i	−0.0665410	+	0.291535i
$525$	7.55735e9	−	3.63943e9i	2.27936	−	1.09768i
$526$	5.39573e8	+	2.59845e8i	0.161659	+	0.0778509i
$527$	−1.17396e9	+	5.14347e9i	−0.349395	+	1.53080i
$528$	1.19830e8	+	5.25011e8i	0.0354281	+	0.155221i
$529$	9.00189e8	−	4.33508e8i	0.264386	−	0.127322i
$530$	−1.22147e7	+	1.53167e7i	−0.00356383	+	0.00446890i
$531$	−2.35227e9	+	2.94966e9i	−0.681800	+	0.854950i
$532$	−1.94550e9	−	9.36906e8i	−0.560198	−	0.269777i
$533$	1.91007e9	+	2.39515e9i	0.546392	+	0.685154i
$534$	−5.36489e7			−0.0152464
$535$	−3.65148e9	−	4.57881e9i	−1.03093	−	1.29275i
$536$	−1.13352e8	−	4.96626e8i	−0.0317945	−	0.139301i
$537$	−1.48273e8	−	6.49627e8i	−0.0413192	−	0.181031i
$538$	−3.78157e8	−	4.74194e8i	−0.104697	−	0.131286i
$539$	−1.89551e8			−0.0521394
$540$	2.17858e9	+	2.73185e9i	0.595382	+	0.746585i
$541$	−3.06349e7	−	1.47530e7i	−0.00831814	−	0.00400580i	0.429720	−	0.902962i	$-0.358612\pi$
$541$	−3.06349e7	−	1.47530e7i	−0.00831814	−	0.00400580i	−0.438038	+	0.898956i	$0.644327\pi$
$542$	2.19621e8	−	2.75396e8i	0.0592484	−	0.0742952i
$543$	−2.09969e9	+	2.63293e9i	−0.562802	+	0.705732i
$544$	−9.17991e8	+	4.42081e8i	−0.244479	+	0.117735i
$545$	−2.90230e9	−	1.27158e10i	−0.767989	−	3.36478i
$546$	−8.28905e7	+	3.63167e8i	−0.0217937	+	0.0954844i
$547$	6.50067e9	+	3.13056e9i	1.69825	+	0.817835i	0.994183	+	0.107704i	$0.0343500\pi$
$547$	6.50067e9	+	3.13056e9i	1.69825	+	0.817835i	0.704070	+	0.710131i	$0.251364\pi$
$548$	1.06006e9	−	5.10497e8i	0.275168	−	0.132514i
$549$	7.18160e8	−	3.14646e9i	0.185233	−	0.811558i
$550$	1.24819e8			0.0319898
$551$	3.18794e9	+	2.31517e7i	0.811856	+	0.00589594i
$552$	−7.97380e8			−0.201780
$553$	4.57324e8	−	2.00367e9i	0.114997	−	0.503834i
$554$	−6.32295e8	+	3.04497e8i	−0.157992	+	0.0760851i
$555$	−6.01644e9	−	2.89736e9i	−1.49387	−	0.719412i
$556$	−1.76371e7	+	7.72731e7i	−0.00435176	+	0.0190663i
$557$	1.08788e9	+	4.76633e9i	0.266741	+	1.16867i	0.913779	+	0.406211i	$0.133150\pi$
$557$	1.08788e9	+	4.76633e9i	0.266741	+	1.16867i	−0.647039	+	0.762457i	$0.723993\pi$
$558$	−3.44846e8	+	1.66069e8i	−0.0840243	+	0.0404640i
$559$	−1.94147e9	+	2.43453e9i	−0.470100	+	0.589487i
$560$	−3.69103e9	+	4.62840e9i	−0.888155	+	1.11371i
$561$	5.91859e8	+	2.85024e8i	0.141530	+	0.0681572i
$562$	−1.21876e8	−	1.52828e8i	−0.0289628	−	0.0363182i
$563$	3.56017e9			0.840797			0.420398	−	0.907340i	$-0.361890\pi$
$563$	3.56017e9			0.840797			0.420398	+	0.907340i	$0.361890\pi$
$564$	4.32011e9	+	5.41725e9i	1.01395	+	1.27146i
$565$	−1.35383e9	−	5.93153e9i	−0.315788	−	1.38356i
$566$	6.62702e7	+	2.90349e8i	0.0153625	+	0.0673073i
$567$	−2.59460e9	−	3.25352e9i	−0.597764	−	0.749572i
$568$	−5.48830e7			−0.0125666
$569$	1.99100e9	+	2.49664e9i	0.453085	+	0.568150i	0.954939	−	0.296802i	$-0.0959201\pi$
$569$	1.99100e9	+	2.49664e9i	0.453085	+	0.568150i	−0.501855	+	0.864952i	$0.667349\pi$
$570$	7.38841e8	+	3.55807e8i	0.167105	+	0.0804735i
$571$	−2.90586e9	+	3.64383e9i	−0.653203	+	0.819090i	−0.992584	−	0.121559i	$-0.961211\pi$
$571$	−2.90586e9	+	3.64383e9i	−0.653203	+	0.819090i	0.339382	+	0.940649i	$0.389782\pi$
$572$	3.76328e8	−	4.71900e8i	0.0840776	−	0.105430i
$573$	9.52751e9	−	4.58821e9i	2.11562	−	1.01883i
$574$	6.19842e7	+	2.71570e8i	0.0136801	+	0.0599364i
$575$	2.20821e9	−	9.67478e9i	0.484398	−	2.12228i
$576$	2.33558e9	+	1.12476e9i	0.509233	+	0.245234i
$577$	1.85238e9	−	8.92061e8i	0.401435	−	0.193321i	−0.222262	−	0.974987i	$-0.571344\pi$
$577$	1.85238e9	−	8.92061e8i	0.401435	−	0.193321i	0.623697	+	0.781666i	$0.285630\pi$
$578$	7.76561e6	−	3.40234e7i	0.00167274	−	0.00732875i
$579$	−7.08063e9			−1.51599
$580$	2.02546e9	−	8.58619e9i	0.431047	−	1.82727i
$581$	1.90639e9			0.403269
$582$	1.95606e8	−	8.57006e8i	0.0411293	−	0.180199i
$583$	−1.76527e7	+	8.50108e6i	−0.00368952	+	0.00177678i
$584$	2.77575e8	+	1.33673e8i	0.0576681	+	0.0277715i
$585$	−1.28216e9	+	5.61751e9i	−0.264787	+	1.16011i
$586$	4.60641e7	+	2.01820e8i	0.00945630	+	0.0414307i
$587$	6.09182e9	−	2.93366e9i	1.24312	−	0.598656i	0.307462	−	0.951560i	$-0.400520\pi$
$587$	6.09182e9	−	2.93366e9i	1.24312	−	0.598656i	0.935659	+	0.352905i	$0.114806\pi$
$588$	−1.55006e9	+	1.94371e9i	−0.314433	+	0.394286i
$589$	−4.10670e9	+	5.14964e9i	−0.828113	+	1.03842i
$590$	−1.48653e9	−	7.15877e8i	−0.297984	−	0.143501i
$591$	−2.92755e9	−	3.67103e9i	−0.583375	−	0.731529i
$592$	3.40002e9			0.673527
$593$	1.92400e9	+	2.41262e9i	0.378891	+	0.475114i	0.934313	−	0.356455i	$-0.116015\pi$
$593$	1.92400e9	+	2.41262e9i	0.378891	+	0.475114i	−0.555422	+	0.831569i	$0.687443\pi$
$594$	−7.14135e6	−	3.12883e7i	−0.00139807	−	0.00612533i
$595$	1.60694e9	+	7.04048e9i	0.312746	+	1.37023i
$596$	−5.21732e9	−	6.54231e9i	−1.00945	−	1.26581i
$597$	−4.49701e9			−0.864995
$598$	2.74772e8	+	3.44553e8i	0.0525434	+	0.0658873i
$599$	1.33451e9	+	6.42666e8i	0.253704	+	0.122178i	0.556414	−	0.830905i	$-0.312177\pi$
$599$	1.33451e9	+	6.42666e8i	0.253704	+	0.122178i	−0.302710	+	0.953083i	$0.597891\pi$
$600$	2.05080e9	−	2.57162e9i	0.387609	−	0.486046i
$601$	−1.82609e9	+	2.28984e9i	−0.343132	+	0.430274i	−0.923215	−	0.384283i	$-0.874449\pi$
$601$	−1.82609e9	+	2.28984e9i	−0.343132	+	0.430274i	0.580083	+	0.814557i	$0.303020\pi$
$602$	−2.55095e8	+	1.22847e8i	−0.0476556	+	0.0229497i
$603$	5.38629e8	+	2.35989e9i	0.100041	+	0.438310i
$604$	−1.37729e8	+	6.03429e8i	−0.0254329	+	0.111429i
$605$	−9.14202e9	−	4.40257e9i	−1.67841	−	0.808281i
$606$	−3.69238e8	+	1.77816e8i	−0.0673989	+	0.0324576i
$607$	1.18419e9	−	5.18829e9i	0.214913	−	0.941595i	−0.746261	−	0.665653i	$-0.768153\pi$
$607$	1.18419e9	−	5.18829e9i	0.214913	−	0.941595i	0.961174	−	0.275942i	$-0.0889897\pi$
$608$	−1.27206e9			−0.229534
$609$	−1.25016e9	+	5.29962e9i	−0.224288	+	0.950789i
$610$	1.41142e9			0.251769
$611$	1.71212e9	−	7.50128e9i	0.303662	−	1.33043i
$612$	2.90367e9	−	1.39833e9i	0.512056	−	0.246593i
$613$	−2.39666e9	−	1.15417e9i	−0.420237	−	0.202376i	0.211801	−	0.977313i	$-0.432067\pi$
$613$	−2.39666e9	−	1.15417e9i	−0.420237	−	0.202376i	−0.632038	+	0.774937i	$0.717781\pi$
$614$	−6.16498e7	+	2.70105e8i	−0.0107484	+	0.0470917i
$615$	2.56319e9	+	1.12301e10i	0.444343	+	1.94679i
$616$	9.93474e7	−	4.78432e7i	0.0171247	−	0.00824684i
$617$	4.69536e9	−	5.88779e9i	0.804768	−	1.00915i	−0.194831	−	0.980837i	$-0.562416\pi$
$617$	4.69536e9	−	5.88779e9i	0.804768	−	1.00915i	0.999599	−	0.0283105i	$-0.00901273\pi$
$618$	4.34079e8	−	5.44318e8i	0.0739791	−	0.0927669i
$619$	−9.64226e9	−	4.64347e9i	−1.63404	−	0.786910i	−0.999906	−	0.0136831i	$-0.995644\pi$
$619$	−9.64226e9	−	4.64347e9i	−1.63404	−	0.786910i	−0.634129	−	0.773227i	$-0.718641\pi$
$620$	1.13640e10	+	1.42500e10i	1.91497	+	2.40129i
$621$	−2.55151e9			−0.427540
$622$	−4.66089e8	−	5.84458e8i	−0.0776610	−	0.0973838i
$623$	−1.31250e8	−	5.75045e8i	−0.0217466	−	0.0952782i
$624$	−1.74525e9	−	7.64643e9i	−0.287548	−	1.25983i
$625$	1.18620e10	+	1.48744e10i	1.94347	+	2.43703i
$626$	−4.77397e8			−0.0777803
$627$	5.11349e8	+	6.41212e8i	0.0828479	+	0.103888i
$628$	−2.73166e9	−	1.31550e9i	−0.440117	−	0.211949i
$629$	2.58597e9	−	3.24270e9i	0.414329	−	0.519552i
$630$	−3.26656e8	+	4.09614e8i	−0.0520474	+	0.0652653i
$631$	−3.79271e9	+	1.82647e9i	−0.600961	+	0.289408i	−0.709523	−	0.704682i	$-0.751090\pi$
$631$	−3.79271e9	+	1.82647e9i	−0.600961	+	0.289408i	0.108562	+	0.994090i	$0.465375\pi$
$632$	−1.79332e8	−	7.85705e8i	−0.0282584	−	0.123808i
$633$	−2.16062e9	+	9.46629e9i	−0.338583	+	1.48343i
$634$	3.10750e8	+	1.49649e8i	0.0484283	+	0.0233218i
$635$	−7.06048e9	+	3.40015e9i	−1.09427	+	0.526975i
$636$	−5.71826e7	+	2.50534e8i	−0.00881382	+	0.0386159i
$637$	2.76068e9			0.423183
$638$	−5.09777e7	+	6.29803e7i	−0.00777156	+	0.00960135i
$639$	2.60795e8			0.0395409
$640$	−1.04274e9	+	4.56856e9i	−0.157235	+	0.688890i
$641$	8.63997e8	−	4.16079e8i	0.129571	−	0.0623983i	−0.367975	−	0.929836i	$-0.619949\pi$
$641$	8.63997e8	−	4.16079e8i	0.129571	−	0.0623983i	0.497546	+	0.867437i	$0.334234\pi$
$642$	6.35634e8	+	3.06105e8i	0.0948057	+	0.0456560i
$643$	−1.44138e9	+	6.31510e9i	−0.213816	+	0.936790i	0.748130	+	0.663552i	$0.230952\pi$
$643$	−1.44138e9	+	6.31510e9i	−0.213816	+	0.936790i	−0.961946	+	0.273238i	$0.911905\pi$
$644$	−9.70924e8	−	4.25390e9i	−0.143247	−	0.627605i
$645$	−1.05488e10	+	5.08003e9i	−1.54790	+	0.745430i
$646$	−3.17566e8	+	3.98216e8i	−0.0463469	+	0.0581172i
$647$	4.38042e9	−	5.49288e9i	0.635845	−	0.797324i	−0.354632	−	0.935006i	$-0.615394\pi$
$647$	4.38042e9	−	5.49288e9i	0.635845	−	0.797324i	0.990476	+	0.137682i	$0.0439652\pi$
$648$	−1.47023e9	−	7.08024e8i	−0.212262	−	0.102220i
$649$	−1.02882e9	−	1.29011e9i	−0.147736	−	0.185254i
$650$	−1.81791e9			−0.259642
$651$	−7.01417e9	−	8.79549e9i	−0.996421	−	1.24947i
$652$	−1.11308e8	−	4.87672e8i	−0.0157275	−	0.0689067i
$653$	−7.80876e8	−	3.42124e9i	−0.109745	−	0.480826i	−0.999693	−	0.0247637i	$-0.992117\pi$
$653$	−7.80876e8	−	3.42124e9i	−0.109745	−	0.480826i	0.889948	−	0.456062i	$-0.150740\pi$
$654$	9.79624e8	+	1.22841e9i	0.136942	+	0.171720i
$655$	4.11212e9			0.571769
$656$	−3.65672e9	−	4.58538e9i	−0.505741	−	0.634179i
$657$	−1.31899e9	−	6.35193e8i	−0.181453	−	0.0873830i
$658$	4.36197e8	−	5.46973e8i	0.0596886	−	0.0748472i
$659$	−4.73911e9	+	5.94266e9i	−0.645057	+	0.808876i	−0.991625	−	0.129149i	$-0.958776\pi$
$659$	−4.73911e9	+	5.94266e9i	−0.645057	+	0.808876i	0.346568	+	0.938025i	$0.387347\pi$
$660$	2.04474e9	−	9.84693e8i	0.276843	−	0.133321i
$661$	2.72466e9	+	1.19375e10i	0.366951	+	1.60772i	0.735106	+	0.677952i	$0.237132\pi$
$661$	2.72466e9	+	1.19375e10i	0.366951	+	1.60772i	−0.368155	+	0.929764i	$0.620010\pi$
$662$	1.87735e8	−	8.22523e8i	0.0251503	−	0.110191i
$663$	−8.62002e9	−	4.15118e9i	−1.14871	−	0.553190i
$664$	6.73527e8	−	3.24353e8i	0.0892826	−	0.0429962i
$665$	−2.00623e9	+	8.78987e9i	−0.264549	+	1.15906i
$666$	3.00902e8			0.0394698
$667$	3.97977e9	+	5.06550e9i	0.519299	+	0.660971i
$668$	−5.50778e9			−0.714922
$669$	1.72082e9	−	7.53940e9i	0.222200	−	0.973522i
$670$	−9.53751e8	+	4.59302e8i	−0.122511	+	0.0589980i
$671$	1.27178e9	+	6.12459e8i	0.162512	+	0.0782615i
$672$	4.83462e8	−	2.11819e9i	0.0614569	−	0.269260i
$673$	−1.63739e9	−	7.17389e9i	−0.207062	−	0.907198i	−0.966510	−	0.256630i	$-0.917388\pi$
$673$	−1.63739e9	−	7.17389e9i	−0.207062	−	0.907198i	0.759448	−	0.650568i	$-0.225469\pi$
$674$	1.04505e9	−	5.03272e8i	0.131471	−	0.0633130i
$675$	6.56229e9	−	8.22885e9i	0.821281	−	1.02985i
$676$	−5.18779e8	+	6.50529e8i	−0.0645906	+	0.0809941i
$677$	−4.81529e9	−	2.31892e9i	−0.596434	−	0.287227i	0.111210	−	0.993797i	$-0.464527\pi$
$677$	−4.81529e9	−	2.31892e9i	−0.596434	−	0.287227i	−0.707643	+	0.706570i	$0.750242\pi$
$678$	4.56964e8	+	5.73015e8i	0.0563090	+	0.0706093i
$679$	9.66452e9			1.18478
$680$	1.76560e9	+	2.21400e9i	0.215334	+	0.270020i
$681$	1.95251e9	+	8.55449e9i	0.236907	+	1.03796i
$682$	−3.72511e7	−	1.63208e8i	−0.00449670	−	0.0197013i
$683$	9.98090e7	+	1.25157e8i	0.0119866	+	0.0150308i	0.787789	−	0.615946i	$-0.211226\pi$
$683$	9.98090e7	+	1.25157e8i	0.0119866	+	0.0150308i	−0.775802	+	0.630976i	$0.782654\pi$
$684$	4.02363e9			0.480753
$685$	−3.06293e9	−	3.84079e9i	−0.364099	−	0.456566i
$686$	7.87828e8	+	3.79398e8i	0.0931745	+	0.0448705i
$687$	1.38757e9	−	1.73995e9i	0.163270	−	0.204734i
$688$	3.71684e9	−	4.66077e9i	0.435125	−	0.545630i
$689$	2.57099e8	−	1.23812e8i	0.0299456	−	0.0144210i
$690$	3.68726e8	+	1.61549e9i	0.0427299	+	0.187212i
$691$	−1.09582e8	+	4.80111e8i	−0.0126348	+	0.0553565i	−0.980852	−	0.194753i	$-0.937609\pi$
$691$	−1.09582e8	+	4.80111e8i	−0.0126348	+	0.0553565i	0.968218	+	0.250109i	$0.0804666\pi$
$692$	1.17301e10	+	5.64890e9i	1.34564	+	0.648026i
$693$	−4.72083e8	+	2.27343e8i	−0.0538830	+	0.0259487i
$694$	2.13879e8	−	9.37064e8i	0.0242890	−	0.106417i
$695$	3.30936e8			0.0373936
$696$	4.59996e8	+	2.08506e9i	0.0517157	+	0.234415i
$697$	−7.15442e9			−0.800312
$698$	5.36430e6	−	2.35025e7i	0.000597061	−	0.00261590i
$699$	6.91737e9	−	3.33123e9i	0.766074	−	0.368922i
$700$	1.62163e10	+	7.80938e9i	1.78694	+	0.860544i
$701$	1.60570e9	−	7.03503e9i	0.176056	−	0.771353i	−0.807370	−	0.590045i	$-0.799110\pi$
$701$	1.60570e9	−	7.03503e9i	0.176056	−	0.771353i	0.983426	−	0.181308i	$-0.0580330\pi$
$702$	1.04009e8	+	4.55693e8i	0.0113473	+	0.0497156i
$703$	4.66534e9	−	2.24671e9i	0.506454	−	0.243895i
$704$	−7.06916e8	+	8.86445e8i	−0.0763596	+	0.0957519i
$705$	1.80378e10	−	2.26186e10i	1.93875	−	2.43111i
$706$	−1.92222e8	−	9.25693e7i	−0.0205583	−	0.00990035i
$707$	−2.80928e9	−	3.52273e9i	−0.298970	−	0.374896i
$708$	−2.16424e10			−2.29186
$709$	3.46479e9	+	4.34471e9i	0.365103	+	0.457825i	0.930121	−	0.367254i	$-0.119702\pi$
$709$	3.46479e9	+	4.34471e9i	0.365103	+	0.457825i	−0.565018	+	0.825079i	$0.691131\pi$
$710$	2.53791e7	+	1.11193e8i	0.00266117	+	0.0116593i
$711$	8.52157e8	+	3.73354e9i	0.0889152	+	0.389563i
$712$	−1.44209e8	−	1.80832e8i	−0.0149731	−	0.0187757i
$713$	−1.33093e10			−1.37513
$714$	−5.42397e8	−	6.80145e8i	−0.0557666	−	0.0699291i
$715$	−2.27057e9	−	1.09345e9i	−0.232308	−	0.111873i
$716$	8.91464e8	−	1.11786e9i	0.0907628	−	0.113813i
$717$	1.25399e10	−	1.57245e10i	1.27051	−	1.59316i
$718$	3.85604e7	−	1.85697e7i	0.00388781	−	0.00187227i
$719$	−1.03885e9	−	4.55150e9i	−0.104232	−	0.456671i	−0.999928	−	0.0120038i	$-0.996179\pi$
$719$	−1.03885e9	−	4.55150e9i	−0.104232	−	0.456671i	0.895696	−	0.444668i	$-0.146678\pi$
$720$	2.45462e9	−	1.07544e10i	0.245087	−	1.07380i
$721$	6.89633e9	+	3.32110e9i	0.685243	+	0.329996i
$722$	2.96267e8	−	1.42675e8i	0.0292956	−	0.0141080i
$723$	−3.37352e9	+	1.47804e10i	−0.331971	+	1.45446i
$724$	−7.22618e9			−0.707659
$725$	−2.65724e10	−	1.92976e8i	−2.58969	−	0.0188071i
$726$	1.22234e9			0.118553
$727$	−2.31130e9	+	1.01265e10i	−0.223093	+	0.977433i	0.732042	+	0.681260i	$0.238568\pi$
$727$	−2.31130e9	+	1.01265e10i	−0.223093	+	0.977433i	−0.955134	+	0.296173i	$0.904290\pi$
$728$	−1.44693e9	+	6.96803e8i	−0.138991	+	0.0669345i
$729$	9.27403e8	+	4.46614e8i	0.0886589	+	0.0426959i
$730$	1.42465e8	−	6.24182e8i	0.0135544	−	0.0593856i
$731$	−1.61818e9	−	7.08972e9i	−0.153220	−	0.671302i
$732$	1.66804e10	−	8.03285e9i	1.57187	−	0.756974i
$733$	9.66736e8	−	1.21225e9i	0.0906659	−	0.113691i	−0.734429	−	0.678685i	$-0.762550\pi$
$733$	9.66736e8	−	1.21225e9i	0.0906659	−	0.113691i	0.825095	+	0.564994i	$0.191121\pi$
$734$	−3.87265e7	+	4.85615e7i	−0.00361470	+	0.00453268i
$735$	9.35226e9	+	4.50381e9i	0.868783	+	0.418384i
$736$	−1.60262e9	−	2.00962e9i	−0.148169	−	0.185798i
$737$	−1.05870e9			−0.0974173
$738$	−3.23620e8	−	4.05806e8i	−0.0296372	−	0.0371639i
$739$	1.62597e9	+	7.12383e9i	0.148203	+	0.649318i	0.993384	+	0.114839i	$0.0366352\pi$
$739$	1.62597e9	+	7.12383e9i	0.148203	+	0.649318i	−0.845181	+	0.534480i	$0.820508\pi$
$740$	−3.18848e9	−	1.39696e10i	−0.289250	−	1.26728i
$741$	−7.44746e9	−	9.33882e9i	−0.672426	−	0.843195i
$742$	2.59466e7			0.00233167
$743$	1.06172e9	+	1.33136e9i	0.0949619	+	0.119078i	0.827042	−	0.562140i	$-0.190022\pi$
$743$	1.06172e9	+	1.33136e9i	0.0949619	+	0.119078i	−0.732080	+	0.681218i	$0.761450\pi$
$744$	−3.97457e9	−	1.91405e9i	−0.353822	−	0.170392i
$745$	−2.17839e10	+	2.73161e10i	−1.93014	+	2.42031i
$746$	−6.95350e8	+	8.71941e8i	−0.0613222	+	0.0768955i
$747$	−3.20049e9	+	1.54128e9i	−0.280928	+	0.135288i
$748$	3.13662e8	+	1.37424e9i	0.0274035	+	0.120063i
$749$	−1.72599e9	+	7.56204e9i	−0.150090	+	0.657586i
$750$	−3.78045e9	−	1.82057e9i	−0.327212	−	0.157577i
$751$	1.40794e10	−	6.78030e9i	1.21296	−	0.584130i	0.285616	−	0.958344i	$-0.407802\pi$
$751$	1.40794e10	−	6.78030e9i	1.21296	−	0.584130i	0.927342	+	0.374214i	$0.122088\pi$
$752$	−3.27775e9	+	1.43608e10i	−0.281069	+	1.23145i
$753$	1.28488e9			0.109668
$754$	7.42456e8	−	9.17265e8i	0.0630770	−	0.0779283i
$755$	2.58429e9			0.218538
$756$	1.02977e9	−	4.51174e9i	0.0866794	−	0.379767i
$757$	−1.41886e10	+	6.83289e9i	−1.18879	+	0.572491i	−0.920460	−	0.390836i	$-0.872186\pi$
$757$	−1.41886e10	+	6.83289e9i	−1.18879	+	0.572491i	−0.268330	+	0.963327i	$0.586472\pi$
$758$	1.53174e9	+	7.37648e8i	0.127745	+	0.0615187i
$759$	−3.68766e8	+	1.61567e9i	−0.0306129	+	0.134124i
$760$	7.86710e8	+	3.44680e9i	0.0650081	+	0.284819i
$761$	7.60068e9	−	3.66029e9i	0.625181	−	0.301071i	−0.0943419	−	0.995540i	$-0.530075\pi$
$761$	7.60068e9	−	3.66029e9i	0.625181	−	0.301071i	0.719523	+	0.694468i	$0.244360\pi$
$762$	5.88589e8	−	7.38068e8i	0.0481914	−	0.0604302i
$763$	−1.07703e10	+	1.35055e10i	−0.877793	+	1.10072i
$764$	2.04438e10	+	9.84523e9i	1.65858	+	0.798729i
$765$	−8.38986e9	−	1.05206e10i	−0.677548	−	0.849618i
$766$	3.76614e8			0.0302758
$767$	1.49841e10	+	1.87895e10i	1.19908	+	1.50360i
$768$	3.21382e9	+	1.40807e10i	0.256010	+	1.12165i
$769$	9.84017e8	+	4.31126e9i	0.0780298	+	0.341871i	0.998841	−	0.0481386i	$-0.0153289\pi$
$769$	9.84017e8	+	4.31126e9i	0.0780298	+	0.341871i	−0.920811	+	0.390009i	$0.872472\pi$
$770$	−1.42871e8	−	1.79155e8i	−0.0112779	−	0.0141420i
$771$	8.36268e9			0.657136
$772$	−9.47293e9	−	1.18787e10i	−0.741009	−	0.929196i
$773$	1.86063e10	+	8.96033e9i	1.44888	+	0.697744i	0.982400	−	0.186788i	$-0.0598078\pi$
$773$	1.86063e10	+	8.96033e9i	1.44888	+	0.697744i	0.466480	+	0.884532i	$0.345522\pi$
$774$	3.28940e8	−	4.12478e8i	0.0254990	−	0.0319748i
$775$	3.42305e10	−	4.29237e10i	2.64154	−	3.31239i
$776$	3.41447e9	−	1.64432e9i	0.262306	−	0.126320i
$777$	1.96801e9	+	8.62242e9i	0.150506	+	0.659410i
$778$	2.12758e8	−	9.32154e8i	0.0161979	−	0.0709674i
$779$	−8.04756e9	−	3.87550e9i	−0.609935	−	0.293729i
$780$	−2.97802e10	+	1.43414e10i	−2.24696	+	1.08208i
$781$	−2.53819e7	+	1.11205e8i	−0.00190654	+	0.00835309i
$782$	−1.02919e9			−0.0769615
$783$	1.47193e9	+	6.67191e9i	0.109577	+	0.496689i
$784$	−5.28516e9			−0.391699
$785$	−2.81693e9	+	1.23418e10i	−0.207841	+	0.910613i
$786$	−4.46307e8	+	2.14930e8i	−0.0327834	+	0.0157877i
$787$	−1.42829e10	−	6.87828e9i	−1.04449	−	0.503000i	−0.168688	−	0.985669i	$-0.553953\pi$
$787$	−1.42829e10	−	6.87828e9i	−1.04449	−	0.503000i	−0.875803	+	0.482669i	$0.839667\pi$
$788$	2.24196e9	−	9.82268e9i	0.163225	−	0.715135i
$789$	−7.29859e9	−	3.19772e10i	−0.529017	−	2.31777i
$790$	−1.50892e9	+	7.26655e8i	−0.108885	+	0.0524365i
$791$	−5.02401e9	+	6.29992e9i	−0.360939	+	0.452603i
$792$	−1.28107e8	+	1.60641e8i	−0.00916291	+	0.0114899i
$793$	−1.85227e10	−	8.92005e9i	−1.31901	−	0.635201i
$794$	−4.05932e8	−	5.09023e8i	−0.0287794	−	0.0360882i
$795$	1.07295e9			0.0757349
$796$	−6.01639e9	−	7.54432e9i	−0.422805	−	0.530181i
$797$	−2.69129e9	−	1.17913e10i	−0.188302	−	0.825007i	−0.977511	−	0.210882i	$-0.932366\pi$
$797$	−2.69129e9	−	1.17913e10i	−0.188302	−	0.825007i	0.789209	−	0.614125i	$-0.210491\pi$
$798$	−2.41679e8	−	1.05887e9i	−0.0168356	−	0.0737617i
$799$	1.12033e10	+	1.40485e10i	0.777021	+	0.974354i
$800$	1.06030e10			0.732174
$801$	6.85258e8	+	8.59287e8i	0.0471130	+	0.0590778i
$802$	−1.47654e9	−	7.11065e8i	−0.101073	−	0.0486742i
$803$	3.99222e8	−	5.00609e8i	0.0272089	−	0.0341188i
$804$	−8.65754e9	+	1.08562e10i	−0.587487	+	0.736686i
$805$	−1.64139e10	+	7.90452e9i	−1.10899	+	0.534060i
$806$	5.42537e8	+	2.37701e9i	0.0364970	+	0.159904i
$807$	−7.39165e9	+	3.23849e10i	−0.495090	+	2.16913i
$808$	−1.59188e9	−	7.66608e8i	−0.106162	−	0.0511250i
$809$	−5.76336e9	+	2.77549e9i	−0.382698	+	0.184298i	−0.615334	−	0.788266i	$-0.710979\pi$
$809$	−5.76336e9	+	2.77549e9i	−0.382698	+	0.184298i	0.232636	+	0.972564i	$0.425265\pi$
$810$	−7.54594e8	+	3.30609e9i	−0.0498903	+	0.218584i
$811$	1.29033e10			0.849433			0.424717	−	0.905326i	$-0.360374\pi$
$811$	1.29033e10			0.849433			0.424717	+	0.905326i	$0.360374\pi$
$812$	−1.05634e10	+	4.99287e9i	−0.692398	+	0.327268i
$813$	−1.92918e10			−1.25909
$814$	−2.92853e7	+	1.28307e8i	−0.00190311	+	0.00833807i
$815$	−1.88171e9	+	9.06185e8i	−0.121759	+	0.0586361i
$816$	1.65025e10	+	7.94719e9i	1.06325	+	0.512033i
$817$	2.02026e9	−	8.85135e9i	0.129608	−	0.567848i
$818$	−4.23513e8	−	1.85553e9i	−0.0270539	−	0.118531i
$819$	6.87556e9	−	3.31110e9i	0.437335	−	0.210610i
$820$	−1.54107e10	+	1.93244e10i	−0.976055	+	1.22393i
$821$	1.59317e10	−	1.99777e10i	1.00476	−	1.25992i	0.0393351	−	0.999226i	$-0.487476\pi$
$821$	1.59317e10	−	1.99777e10i	1.00476	−	1.25992i	0.965421	−	0.260698i	$-0.0839525\pi$
$822$	5.33182e8	+	2.56767e8i	0.0334830	+	0.0161246i
$823$	−7.98060e9	−	1.00073e10i	−0.499041	−	0.625777i	0.466972	−	0.884272i	$-0.345345\pi$
$823$	−7.98060e9	−	1.00073e10i	−0.499041	−	0.625777i	−0.966013	+	0.258495i	$0.916773\pi$
$824$	3.00153e9			0.186895
$825$	−4.26224e9	−	5.34469e9i	−0.264271	−	0.331385i
$826$	4.86254e8	+	2.13042e9i	0.0300215	+	0.131533i
$827$	−4.94495e9	−	2.16653e10i	−0.304014	−	1.33197i	−0.864010	−	0.503475i	$-0.832055\pi$
$827$	−4.94495e9	−	2.16653e10i	−0.304014	−	1.33197i	0.559996	−	0.828495i	$-0.310803\pi$
$828$	5.06920e9	+	6.35657e9i	0.310337	+	0.389150i
$829$	2.03298e10			1.23935			0.619674	−	0.784860i	$-0.287265\pi$
$829$	2.03298e10			1.23935			0.619674	+	0.784860i	$0.287265\pi$
$830$	−9.68596e8	−	1.21458e9i	−0.0587989	−	0.0737315i
$831$	3.46296e10	+	1.66767e10i	2.09336	+	1.00811i
$832$	1.02958e10	−	1.29105e10i	0.619764	−	0.777160i
$833$	−4.01976e9	+	5.04062e9i	−0.240959	+	0.302153i
$834$	−3.59180e7	+	1.72972e7i	−0.00214403	+	0.00103251i
$835$	5.11723e9	+	2.24201e10i	0.304181	+	1.33270i
$836$	−3.91600e8	+	1.71571e9i	−0.0231804	+	0.101560i
$837$	−1.27181e10	−	6.12472e9i	−0.749693	−	0.361033i
$838$	−1.06447e9	+	5.12622e8i	−0.0624856	+	0.0300915i
$839$	2.82760e9	−	1.23885e10i	0.165291	−	0.724189i	−0.822546	−	0.568699i	$-0.807447\pi$
$839$	2.82760e9	−	1.23885e10i	0.165291	−	0.724189i	0.987837	−	0.155491i	$-0.0496958\pi$
$840$	−6.03847e9			−0.351520
$841$	1.09499e10	−	1.33289e10i	0.634779	−	0.772694i
$842$	5.67047e8			0.0327361
$843$	−2.38225e9	+	1.04373e10i	−0.136959	+	0.600057i
$844$	−1.87716e10	+	9.03990e9i	−1.07474	+	0.517565i
$845$	3.13005e9	+	1.50735e9i	0.178465	+	0.0859441i
$846$	−2.90081e8	+	1.27093e9i	−0.0164711	+	0.0721647i
$847$	2.99041e9	+	1.31018e10i	0.169098	+	0.740867i
$848$	−4.92201e8	+	2.37031e8i	−0.0277177	+	0.0133481i
$849$	1.01696e10	−	1.27523e10i	0.570332	−	0.715173i
$850$	2.64701e9	−	3.31924e9i	0.147839	−	0.185384i
$851$	9.42704e9	+	4.53982e9i	0.524351	+	0.252514i
$852$	9.32772e8	+	1.16966e9i	0.0516698	+	0.0647919i
$853$	1.92435e10			1.06160			0.530801	−	0.847497i	$-0.321891\pi$
$853$	1.92435e10			1.06160			0.530801	+	0.847497i	$0.321891\pi$
$854$	−1.16550e9	−	1.46149e9i	−0.0640340	−	0.0802961i
$855$	−3.73832e9	−	1.63787e10i	−0.204548	−	0.896183i
$856$	6.76817e8	+	2.96533e9i	0.0368819	+	0.161590i
$857$	7.79832e9	+	9.77878e9i	0.423222	+	0.530704i	0.947035	−	0.321130i	$-0.104062\pi$
$857$	7.79832e9	+	9.77878e9i	0.423222	+	0.530704i	−0.523813	+	0.851833i	$0.675491\pi$
$858$	3.03587e8			0.0164088
$859$	−1.22043e10	−	1.53037e10i	−0.656955	−	0.823795i	0.336053	−	0.941843i	$-0.390908\pi$
$859$	−1.22043e10	−	1.53037e10i	−0.656955	−	0.823795i	−0.993008	+	0.118048i	$0.962336\pi$
$860$	−2.26353e10	−	1.09006e10i	−1.21350	−	0.584392i
$861$	9.51190e9	−	1.19275e10i	0.507874	−	0.636854i
$862$	−2.76594e8	+	3.46838e8i	−0.0147085	+	0.0184439i
$863$	1.43467e9	−	6.90900e8i	0.0759825	−	0.0365912i	−0.395507	−	0.918463i	$-0.629431\pi$
$863$	1.43467e9	−	6.90900e8i	0.0759825	−	0.0365912i	0.471489	+	0.881872i	$0.343717\pi$
$864$	−6.06637e8	−	2.65785e9i	−0.0319986	−	0.140195i
$865$	1.20962e10	−	5.29970e10i	0.635467	−	2.78416i
$866$	−1.41988e9	−	6.83778e8i	−0.0742914	−	0.0357769i
$867$	−1.72204e9	+	8.29289e8i	−0.0897378	+	0.0432154i
$868$	5.37157e9	−	2.35344e10i	0.278793	−	1.22147i
$869$	−1.67495e9			−0.0865831
$870$	4.01163e9	−	1.89613e9i	0.206540	−	0.0976229i
$871$	1.54192e10			0.790677
$872$	−1.50731e9	+	6.60397e9i	−0.0769832	+	0.337285i
$873$	−1.62250e10	+	7.81356e9i	−0.825345	+	0.397465i
$874$	−1.15768e9	−	5.57507e8i	−0.0586539	−	0.0282462i
$875$	1.02653e10	−	4.49754e10i	0.518018	−	2.26959i
$876$	−1.86874e9	−	8.18749e9i	−0.0939258	−	0.411516i
$877$	−1.00406e10	+	4.83529e9i	−0.502644	+	0.242061i	−0.667983	−	0.744176i	$-0.732842\pi$
$877$	−1.00406e10	+	4.83529e9i	−0.502644	+	0.242061i	0.165339	+	0.986237i	$0.447128\pi$
$878$	1.12613e9	−	1.41212e9i	0.0561509	−	0.0704110i
$879$	7.06885e9	−	8.86406e9i	0.351065	−	0.440222i
$880$	4.34687e9	+	2.09334e9i	0.215024	+	0.103550i
$881$	1.94644e10	+	2.44076e10i	0.959015	+	1.20257i	0.979226	+	0.202772i	$0.0649949\pi$
$881$	1.94644e10	+	2.44076e10i	0.959015	+	1.20257i	−0.0202107	+	0.999796i	$0.506434\pi$
$882$	−4.67737e8			−0.0229542
$883$	−1.81395e10	−	2.27462e10i	−0.886672	−	1.11185i	−0.993070	−	0.117528i	$-0.962503\pi$
$883$	−1.81395e10	−	2.27462e10i	−0.886672	−	1.11185i	0.106397	−	0.994324i	$-0.466068\pi$
$884$	−4.56828e9	−	2.00149e10i	−0.222418	−	0.974476i
$885$	2.01077e10	+	8.80978e10i	0.975129	+	4.27232i
$886$	9.11860e8	+	1.14344e9i	0.0440464	+	0.0552324i
$887$	−1.90617e10			−0.917125			−0.458563	−	0.888662i	$-0.651636\pi$
$887$	−1.90617e10			−0.917125			−0.458563	+	0.888662i	$0.651636\pi$
$888$	2.16232e9	+	2.71146e9i	0.103627	+	0.129945i
$889$	9.35108e9	+	4.50324e9i	0.446381	+	0.214966i
$890$	−2.99682e8	+	3.75789e8i	−0.0142494	+	0.0178681i
$891$	−2.11456e9	+	2.65157e9i	−0.100149	+	0.125583i
$892$	1.49506e10	−	7.19981e9i	0.705310	−	0.339660i
$893$	4.99193e9	+	2.18711e10i	0.234579	+	1.02776i
$894$	9.36558e8	−	4.10333e9i	0.0438383	−	0.192068i
$895$	−5.37863e9	−	2.59021e9i	−0.250779	−	0.120769i
$896$	5.59170e9	−	2.69282e9i	0.259696	−	0.125063i
$897$	5.37083e9	−	2.35311e10i	0.248466	−	1.08860i
$898$	1.96045e9			0.0903417
$899$	7.67795e9	+	3.48024e10i	0.352441	+	1.59753i
$900$	−3.35381e10			−1.53352
$901$	−1.48291e8	+	6.49707e8i	−0.00675428	+	0.0295924i
$902$	2.04536e8	−	9.84991e7i	0.00927996	−	0.00446899i
$903$	1.39711e10	+	6.72811e9i	0.631426	+	0.304079i
$904$	−7.03115e8	+	3.08055e9i	−0.0316546	+	0.138688i
$905$	6.71379e9	+	2.94150e10i	0.301091	+	1.31917i
$906$	−2.80485e8	+	1.35074e8i	−0.0125303	+	0.00603427i
$907$	3.39768e9	−	4.26055e9i	0.151202	−	0.189601i	−0.700462	−	0.713690i	$-0.747023\pi$
$907$	3.39768e9	−	4.26055e9i	0.151202	−	0.189601i	0.851664	+	0.524089i	$0.175594\pi$
$908$	−1.17391e10	+	1.47203e10i	−0.520395	+	0.652555i
$909$	7.56434e9	+	3.64280e9i	0.334039	+	0.160865i
$910$	2.08082e9	+	2.60926e9i	0.0915354	+	0.114782i
$911$	−2.94830e10			−1.29198			−0.645992	−	0.763344i	$-0.723556\pi$
$911$	−2.94830e10			−1.29198			−0.645992	+	0.763344i	$0.723556\pi$
$912$	1.42577e10	+	1.78786e10i	0.622398	+	0.780462i
$913$	−3.45725e8	−	1.51472e9i	−0.0150343	−	0.0658696i
$914$	−1.87851e8	−	8.23031e8i	−0.00813772	−	0.0356537i
$915$	−4.81963e10	−	6.04362e10i	−2.07989	−	2.60810i
$916$	4.77538e9			0.205293
$917$	−3.39564e9	−	4.25800e9i	−0.145422	−	0.182353i
$918$	−9.83476e8	−	4.73617e8i	−0.0419580	−	0.0202059i
$919$	−1.59285e10	+	1.99737e10i	−0.676972	+	0.848896i	−0.995071	−	0.0991612i	$-0.968384\pi$
$919$	−1.59285e10	+	1.99737e10i	−0.676972	+	0.848896i	0.318099	+	0.948057i	$0.396955\pi$
$920$	−4.45415e9	+	5.58533e9i	−0.188585	+	0.236478i
$921$	1.36709e10	−	6.58357e9i	0.576620	−	0.277685i
$922$	5.41647e8	+	2.37311e9i	0.0227593	+	0.0997149i
$923$	3.69670e8	−	1.61963e9i	0.0154742	−	0.0677969i
$924$	−2.70810e9	−	1.30415e9i	−0.112931	−	0.0543846i
$925$	−3.88870e10	+	1.87270e10i	−1.61550	+	0.777986i
$926$	−9.04243e7	+	3.96175e8i	−0.00374237	+	0.0163964i
$927$	−1.42628e10			−0.588064
$928$	−4.33041e9	+	5.34999e9i	−0.177873	+	0.219753i
$929$	−1.73308e10			−0.709192			−0.354596	−	0.935020i	$-0.615382\pi$
$929$	−1.73308e10			−0.709192			−0.354596	+	0.935020i	$0.615382\pi$
$930$	−2.03995e9	+	8.93761e9i	−0.0831629	+	0.364360i
$931$	−7.25205e9	+	3.49240e9i	−0.294535	+	0.141841i
$932$	1.48431e10	+	7.14805e9i	0.600576	+	0.289222i
$933$	−9.11042e9	+	3.99154e10i	−0.367242	+	1.60899i
$934$	1.40697e8	+	6.16432e8i	0.00565028	+	0.0247555i
$935$	5.30260e9	−	2.55360e9i	0.212152	−	0.102167i
$936$	1.86579e9	−	2.33962e9i	0.0743697	−	0.0932567i
$937$	−1.48920e10	+	1.86740e10i	−0.591378	+	0.741565i	−0.984007	−	0.178132i	$-0.942994\pi$
$937$	−1.48920e10	+	1.86740e10i	−0.591378	+	0.741565i	0.392628	+	0.919697i	$0.371566\pi$
$938$	1.26317e9	+	6.08311e8i	0.0499750	+	0.0240667i
$939$	1.63018e10	+	2.04419e10i	0.642550	+	0.805733i
$940$	6.20778e10			2.43775
$941$	−8.65315e8	−	1.08507e9i	−0.0338540	−	0.0424516i	0.764616	−	0.644486i	$-0.222929\pi$
$941$	−8.65315e8	−	1.08507e9i	−0.0338540	−	0.0424516i	−0.798470	+	0.602034i	$0.794357\pi$
$942$	−3.39339e8	−	1.48674e9i	−0.0132268	−	0.0579506i
$943$	−4.01622e9	−	1.75962e10i	−0.155965	−	0.683326i
$944$	−2.86862e10	−	3.59714e10i	−1.10987	−	1.39173i
$945$	−1.93223e10			−0.744814
$946$	1.43870e8	+	1.80407e8i	0.00552525	+	0.00692844i
$947$	−2.15125e10	−	1.03599e10i	−0.823126	−	0.396396i	−0.0255931	−	0.999672i	$-0.508147\pi$
$947$	−2.15125e10	−	1.03599e10i	−0.823126	−	0.396396i	−0.797532	+	0.603276i	$0.793862\pi$
$948$	−1.36970e10	+	1.71755e10i	−0.522150	+	0.654755i
$949$	−5.81440e9	+	7.29103e9i	−0.220838	+	0.276922i
$950$	4.77547e9	−	2.29974e9i	0.180710	−	0.0870255i
$951$	−4.20339e9	−	1.84163e10i	−0.158478	−	0.694336i
$952$	8.34568e8	−	3.65648e9i	0.0313496	−	0.137352i
$953$	−4.67133e9	−	2.24959e9i	−0.174830	−	0.0841935i	0.344422	−	0.938815i	$-0.388075\pi$
$953$	−4.67133e9	−	2.24959e9i	−0.174830	−	0.0841935i	−0.519252	+	0.854621i	$0.673789\pi$
$954$	−4.35598e7	+	2.09773e7i	−0.00162430	+	0.000782222i
$955$	2.10820e10	−	9.23662e10i	0.783248	−	3.43163i
$956$	4.31566e10			1.59751
$957$	4.43754e9	+	3.22267e7i	0.163663	+	0.00118857i
$958$	−1.72686e9			−0.0634568
$959$	−1.44779e9	+	6.34318e9i	−0.0530079	+	0.232243i
$960$	5.59408e10	−	2.69397e10i	2.04070	−	0.982750i
$961$	−4.15529e10	−	2.00108e10i	−1.51032	−	0.727332i
$962$	4.26520e8	−	1.86871e9i	0.0154464	−	0.0676750i
$963$	−3.21612e9	−	1.40908e10i	−0.116049	−	0.508443i
$964$	−2.93093e10	+	1.41146e10i	−1.05375	+	0.507457i
$965$	−3.95523e10	+	4.95970e10i	−1.41686	+	1.77668i
$966$	1.36833e9	−	1.71583e9i	0.0488393	−	0.0612426i
$967$	4.59749e10	+	2.21403e10i	1.63504	+	0.787393i	0.999887	+	0.0150043i	$0.00477621\pi$
$967$	4.59749e10	+	2.21403e10i	1.63504	+	0.787393i	0.635150	+	0.772388i	$0.280938\pi$
$968$	3.28566e9	+	4.12009e9i	0.116428	+	0.145997i
$969$	2.78954e10			0.984917
$970$	−4.91034e9	−	6.15737e9i	−0.172747	−	0.216618i
$971$	7.16024e9	+	3.13711e10i	0.250992	+	1.09967i	0.930584	+	0.366078i	$0.119300\pi$
$971$	7.16024e9	+	3.13711e10i	0.250992	+	1.09967i	−0.679592	+	0.733591i	$0.737843\pi$
$972$	6.68717e9	+	2.92984e10i	0.233566	+	1.02332i
$973$	−2.73275e8	−	3.42676e8i	−0.00951054	−	0.0119258i
$974$	−2.55681e9			−0.0886630
$975$	6.20767e10	+	7.78417e10i	2.14493	+	2.68965i
$976$	3.54605e10	+	1.70769e10i	1.22087	+	0.587942i
$977$	2.23214e10	−	2.79902e10i	0.765758	−	0.960230i	−0.234171	−	0.972196i	$-0.575237\pi$
$977$	2.23214e10	−	2.79902e10i	0.765758	−	0.960230i	0.999928	+	0.0119656i	$0.00380887\pi$
$978$	1.56867e8	−	1.96705e8i	0.00536223	−	0.00672402i
$979$	−4.33100e8	+	2.08570e8i	−0.0147519	+	0.00710415i
$980$	4.95634e9	+	2.17151e10i	0.168217	+	0.737006i
$981$	7.16251e9	−	3.13810e10i	0.242228	−	1.06127i
$982$	4.86227e8	+	2.34155e8i	0.0163851	+	0.00789065i
$983$	−3.92417e9	+	1.88978e9i	−0.131768	+	0.0634563i	−0.498606	−	0.866829i	$-0.666155\pi$
$983$	−3.92417e9	+	1.88978e9i	−0.131768	+	0.0634563i	0.366838	+	0.930285i	$0.380440\pi$
$984$	1.33120e9	−	5.83236e9i	0.0445410	−	0.195147i
$985$	−4.20673e10			−1.40255
$986$	5.93726e8	+	2.69123e9i	0.0197250	+	0.0894090i
$987$	−3.83160e10			−1.26844
$988$	5.70338e9	−	2.49882e10i	0.188141	−	0.824299i
$989$	1.65287e10	−	7.95980e9i	0.543315	−	0.261646i
$990$	3.84698e8	+	1.85261e8i	0.0126008	+	0.00606821i
$991$	2.89069e9	−	1.26650e10i	0.0943506	−	0.413377i	−0.905591	−	0.424151i	$-0.860573\pi$
$991$	2.89069e9	−	1.26650e10i	0.0943506	−	0.413377i	0.999942	+	0.0107744i	$0.00342966\pi$
$992$	−3.16437e9	−	1.38640e10i	−0.102919	−	0.450918i
$993$	−4.16306e10	+	2.00483e10i	−1.34924	+	0.649762i
$994$	9.41808e7	−	1.18099e8i	0.00304166	−	0.00381412i
$995$	−2.51202e10	+	3.14998e10i	−0.808431	+	1.01374i
$996$	−1.83596e10	−	8.84151e9i	−0.588783	−	0.283543i
$997$	−1.98601e10	−	2.49038e10i	−0.634670	−	0.795851i	0.355655	−	0.934617i	$-0.384258\pi$
$997$	−1.98601e10	−	2.49038e10i	−0.634670	−	0.795851i	−0.990325	+	0.138766i	$0.955686\pi$
$998$	1.40646e7			0.000447888
$999$	6.91914e9	+	8.67633e9i	0.219570	+	0.275332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.d.a.25.10	yes	102
29.7	even	7	inner	29.8.d.a.7.10	✓	102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.d.a.7.10	✓	102	29.7	even	7	inner
29.8.d.a.25.10	yes	102	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.d (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.240160 + 1.05221i) q^{2} +(53.2557 - 25.6466i) q^{3} +(114.275 + 55.0317i) q^{4} +(117.842 - 516.297i) q^{5} +(14.1957 + 62.1954i) q^{6} +(-631.923 + 304.318i) q^{7} +(-171.482 + 215.031i) q^{8} +(814.854 - 1021.79i) q^{9} +O(q^{10})\)	\(q+(-0.240160 + 1.05221i) q^{2} +(53.2557 - 25.6466i) q^{3} +(114.275 + 55.0317i) q^{4} +(117.842 - 516.297i) q^{5} +(14.1957 + 62.1954i) q^{6} +(-631.923 + 304.318i) q^{7} +(-171.482 + 215.031i) q^{8} +(814.854 - 1021.79i) q^{9} +(514.951 + 247.988i) q^{10} +(356.396 + 446.907i) q^{11} +7497.15 q^{12} +(-5190.67 - 6508.89i) q^{13} +(-168.444 - 738.000i) q^{14} +(-6965.54 - 30518.0i) q^{15} +(9937.22 + 12460.9i) q^{16} +19442.3 q^{17} +(879.445 + 1102.79i) q^{18} +(21869.5 + 10531.8i) q^{19} +(41879.0 - 52514.6i) q^{20} +(-25848.8 + 32413.4i) q^{21} +(-555.831 + 267.674i) q^{22} +(10914.2 + 47818.1i) q^{23} +(-3617.56 + 15849.6i) q^{24} +(-182288. - 87785.4i) q^{25} +(8095.29 - 3898.49i) q^{26} +(-11575.7 + 50716.5i) q^{27} -88959.9 q^{28} +(118743. - 56124.9i) q^{29} +33784.2 q^{30} +(-60381.9 + 264550. i) q^{31} +(-47216.1 + 22738.1i) q^{32} +(30441.8 + 14660.0i) q^{33} +(-4669.26 + 20457.4i) q^{34} +(82651.9 + 362122. i) q^{35} +(149348. - 71922.3i) q^{36} +(133007. - 166786. i) q^{37} +(-16333.8 + 20481.9i) q^{38} +(-443364. - 213513. i) q^{39} +(90812.4 + 113875. i) q^{40} -367982. q^{41} +(-27897.8 - 34982.7i) q^{42} +(-83229.9 - 364654. i) q^{43} +(16133.0 + 70683.1i) q^{44} +(-431526. - 541116. i) q^{45} -52935.7 q^{46} +(576234. + 722574. i) q^{47} +(848794. + 408757. i) q^{48} +(-206753. + 259260. i) q^{49} +(136147. - 170723. i) q^{50} +(1.03541e6 - 498629. i) q^{51} +(-234966. - 1.02945e6i) q^{52} +(-7627.25 + 33417.2i) q^{53} +(-50584.3 - 24360.1i) q^{54} +(272735. - 131342. i) q^{55} +(42925.4 - 188068. i) q^{56} +1.43478e6 q^{57} +(30537.8 + 138421. i) q^{58} -2.88674e6 q^{59} +(883476. - 3.87076e6i) q^{60} +(2.22490e6 - 1.07145e6i) q^{61} +(-263861. - 127069. i) q^{62} +(-203974. + 893670. i) q^{63} +(441373. + 1.93378e6i) q^{64} +(-3.97220e6 + 1.91291e6i) q^{65} +(-22736.2 + 28510.3i) q^{66} +(-1.15478e6 + 1.44805e6i) q^{67} +(2.22176e6 + 1.06994e6i) q^{68} +(1.80762e6 + 2.26668e6i) q^{69} -400877. q^{70} +(124417. + 156014. i) q^{71} +(79985.2 + 350438. i) q^{72} +(-249260. - 1.09208e6i) q^{73} +(143550. + 180006. i) q^{74} -1.19593e7 q^{75} +(1.91954e6 + 2.40703e6i) q^{76} +(-361217. - 173953. i) q^{77} +(331138. - 415234. i) q^{78} +(-1.82696e6 + 2.29093e6i) q^{79} +(7.60454e6 - 3.66215e6i) q^{80} +(1.32025e6 + 5.78440e6i) q^{81} +(88374.4 - 387193. i) q^{82} +(-2.44887e6 - 1.17932e6i) q^{83} +(-4.73763e6 + 2.28152e6i) q^{84} +(2.29111e6 - 1.00380e7i) q^{85} +403680. q^{86} +(4.88433e6 - 6.03433e6i) q^{87} -157214. q^{88} +(-187131. + 819874. i) q^{89} +(673002. - 324101. i) q^{90} +(5.26088e6 + 2.53350e6i) q^{91} +(-1.38430e6 + 6.06502e6i) q^{92} +(3.56914e6 + 1.56374e7i) q^{93} +(-898686. + 432785. i) q^{94} +(8.01466e6 - 1.00501e7i) q^{95} +(-1.93138e6 + 2.42187e6i) q^{96} +(-1.24147e7 - 5.97859e6i) q^{97} +(-223142. - 279811. i) q^{98} +747057. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q + q^{2} - 5 q^{3} - 1275 q^{4} + 133 q^{5} - 2675 q^{6} + 657 q^{7} - 6562 q^{8} - 15054 q^{9}+O(q^{10}) \) 102 * q + q^2 - 5 * q^3 - 1275 * q^4 + 133 * q^5 - 2675 * q^6 + 657 * q^7 - 6562 * q^8 - 15054 * q^9	\( 102 q + q^{2} - 5 q^{3} - 1275 q^{4} + 133 q^{5} - 2675 q^{6} + 657 q^{7} - 6562 q^{8} - 15054 q^{9} + 5611 q^{10} + 2893 q^{11} - 7400 q^{12} + 5655 q^{13} - 5103 q^{14} + 55181 q^{15} - 37531 q^{16} + 66488 q^{17} + 111588 q^{18} + 25497 q^{19} - 69535 q^{20} + 221033 q^{21} - 184180 q^{22} - 357991 q^{23} - 279611 q^{24} - 401432 q^{25} - 304829 q^{26} + 777205 q^{27} - 317084 q^{28} + 345978 q^{29} + 1233614 q^{30} - 191155 q^{31} - 1142836 q^{32} - 446051 q^{33} + 854365 q^{34} - 421273 q^{35} - 915292 q^{36} + 1109067 q^{37} + 3198170 q^{38} + 1816963 q^{39} - 1864493 q^{40} - 68548 q^{41} + 4917730 q^{42} + 1733909 q^{43} - 5516860 q^{44} - 6926991 q^{45} + 7670856 q^{46} + 3560867 q^{47} - 3047946 q^{48} - 6860794 q^{49} - 6723464 q^{50} - 2911378 q^{51} - 9704310 q^{52} - 8343921 q^{53} + 11251300 q^{54} + 6948055 q^{55} - 963169 q^{56} - 679450 q^{57} + 19338341 q^{58} + 10876120 q^{59} + 2379472 q^{60} - 2230165 q^{61} - 11842431 q^{62} - 10985505 q^{63} - 14037070 q^{64} - 11815483 q^{65} - 387401 q^{66} + 3903123 q^{67} + 5327748 q^{68} + 9379769 q^{69} + 51913122 q^{70} + 9175293 q^{71} + 42974969 q^{72} - 22305785 q^{73} - 31357308 q^{74} + 5262752 q^{75} + 27826047 q^{76} - 9623065 q^{77} - 13423495 q^{78} - 43328225 q^{79} - 69999516 q^{80} - 14867886 q^{81} + 39940476 q^{82} + 11503001 q^{83} - 58649317 q^{84} - 493576 q^{85} + 17849216 q^{86} + 28282227 q^{87} + 80429114 q^{88} + 14809627 q^{89} + 43848318 q^{90} - 41942203 q^{91} - 94433178 q^{92} + 3218315 q^{93} + 52700970 q^{94} - 22341683 q^{95} - 153425906 q^{96} - 74993043 q^{97} - 24094580 q^{98} + 258723776 q^{99}+O(q^{100}) \) 102 * q + q^2 - 5 * q^3 - 1275 * q^4 + 133 * q^5 - 2675 * q^6 + 657 * q^7 - 6562 * q^8 - 15054 * q^9 + 5611 * q^10 + 2893 * q^11 - 7400 * q^12 + 5655 * q^13 - 5103 * q^14 + 55181 * q^15 - 37531 * q^16 + 66488 * q^17 + 111588 * q^18 + 25497 * q^19 - 69535 * q^20 + 221033 * q^21 - 184180 * q^22 - 357991 * q^23 - 279611 * q^24 - 401432 * q^25 - 304829 * q^26 + 777205 * q^27 - 317084 * q^28 + 345978 * q^29 + 1233614 * q^30 - 191155 * q^31 - 1142836 * q^32 - 446051 * q^33 + 854365 * q^34 - 421273 * q^35 - 915292 * q^36 + 1109067 * q^37 + 3198170 * q^38 + 1816963 * q^39 - 1864493 * q^40 - 68548 * q^41 + 4917730 * q^42 + 1733909 * q^43 - 5516860 * q^44 - 6926991 * q^45 + 7670856 * q^46 + 3560867 * q^47 - 3047946 * q^48 - 6860794 * q^49 - 6723464 * q^50 - 2911378 * q^51 - 9704310 * q^52 - 8343921 * q^53 + 11251300 * q^54 + 6948055 * q^55 - 963169 * q^56 - 679450 * q^57 + 19338341 * q^58 + 10876120 * q^59 + 2379472 * q^60 - 2230165 * q^61 - 11842431 * q^62 - 10985505 * q^63 - 14037070 * q^64 - 11815483 * q^65 - 387401 * q^66 + 3903123 * q^67 + 5327748 * q^68 + 9379769 * q^69 + 51913122 * q^70 + 9175293 * q^71 + 42974969 * q^72 - 22305785 * q^73 - 31357308 * q^74 + 5262752 * q^75 + 27826047 * q^76 - 9623065 * q^77 - 13423495 * q^78 - 43328225 * q^79 - 69999516 * q^80 - 14867886 * q^81 + 39940476 * q^82 + 11503001 * q^83 - 58649317 * q^84 - 493576 * q^85 + 17849216 * q^86 + 28282227 * q^87 + 80429114 * q^88 + 14809627 * q^89 + 43848318 * q^90 - 41942203 * q^91 - 94433178 * q^92 + 3218315 * q^93 + 52700970 * q^94 - 22341683 * q^95 - 153425906 * q^96 - 74993043 * q^97 - 24094580 * q^98 + 258723776 * q^99

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