LMFDB - Embedded newform 29.7.c.a.12.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,7,Mod(12,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("29.12");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	29.c (of order $4$, degree $2$, 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:	$6.67156842498$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			12.12
Character	$\chi$	$=$	29.12
Dual form			29.7.c.a.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.44805 + 7.44805i) q^{2} +(-22.6252 - 22.6252i) q^{3} +46.9470i q^{4} -114.512i q^{5} -337.027i q^{6} +512.680 q^{7} +(127.012 - 127.012i) q^{8} +294.796i q^{9} +O(q^{10})$	\(q+(7.44805 + 7.44805i) q^{2} +(-22.6252 - 22.6252i) q^{3} +46.9470i q^{4} -114.512i q^{5} -337.027i q^{6} +512.680 q^{7} +(127.012 - 127.012i) q^{8} +294.796i q^{9} +(852.893 - 852.893i) q^{10} +(-1533.66 - 1533.66i) q^{11} +(1062.18 - 1062.18i) q^{12} +1811.23i q^{13} +(3818.47 + 3818.47i) q^{14} +(-2590.86 + 2590.86i) q^{15} +4896.59 q^{16} +(-4218.14 - 4218.14i) q^{17} +(-2195.65 + 2195.65i) q^{18} +(4253.31 + 4253.31i) q^{19} +5376.00 q^{20} +(-11599.5 - 11599.5i) q^{21} -22845.5i q^{22} +2393.24 q^{23} -5747.33 q^{24} +2511.94 q^{25} +(-13490.1 + 13490.1i) q^{26} +(-9823.94 + 9823.94i) q^{27} +24068.8i q^{28} +(16009.4 + 18399.0i) q^{29} -38593.7 q^{30} +(3730.85 + 3730.85i) q^{31} +(28341.3 + 28341.3i) q^{32} +69398.5i q^{33} -62833.9i q^{34} -58708.2i q^{35} -13839.8 q^{36} +(-45114.2 + 45114.2i) q^{37} +63357.7i q^{38} +(40979.4 - 40979.4i) q^{39} +(-14544.4 - 14544.4i) q^{40} +(60382.8 - 60382.8i) q^{41} -172787. i q^{42} +(33778.6 + 33778.6i) q^{43} +(72000.5 - 72000.5i) q^{44} +33757.7 q^{45} +(17825.0 + 17825.0i) q^{46} +(-25538.5 + 25538.5i) q^{47} +(-110786. - 110786. i) q^{48} +145192. q^{49} +(18709.1 + 18709.1i) q^{50} +190872. i q^{51} -85031.7 q^{52} +221001. q^{53} -146338. q^{54} +(-175623. + 175623. i) q^{55} +(65116.5 - 65116.5i) q^{56} -192464. i q^{57} +(-17798.3 + 256275. i) q^{58} +87675.9 q^{59} +(-121633. - 121633. i) q^{60} +(-220659. - 220659. i) q^{61} +55575.1i q^{62} +151136. i q^{63} +108793. i q^{64} +207408. q^{65} +(-516884. + 516884. i) q^{66} +204898. i q^{67} +(198029. - 198029. i) q^{68} +(-54147.4 - 54147.4i) q^{69} +(437262. - 437262. i) q^{70} +441433. i q^{71} +(37442.6 + 37442.6i) q^{72} +(6026.50 - 6026.50i) q^{73} -672026. q^{74} +(-56833.1 - 56833.1i) q^{75} +(-199680. + 199680. i) q^{76} +(-786276. - 786276. i) q^{77} +610433. q^{78} +(36750.7 + 36750.7i) q^{79} -560719. i q^{80} +659443. q^{81} +899469. q^{82} -552442. q^{83} +(544560. - 544560. i) q^{84} +(-483029. + 483029. i) q^{85} +503170. i q^{86} +(54066.3 - 778495. i) q^{87} -389586. q^{88} +(545435. + 545435. i) q^{89} +(251429. + 251429. i) q^{90} +928582. i q^{91} +112355. i q^{92} -168822. i q^{93} -380425. q^{94} +(487056. - 487056. i) q^{95} -1.28245e6i q^{96} +(1.08035e6 - 1.08035e6i) q^{97} +(1.08140e6 + 1.08140e6i) q^{98} +(452116. - 452116. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) $ 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	7.44805	+	7.44805i	0.931007	+	0.931007i	0.997769	−	0.0667624i	$-0.0212670\pi$
$2$	7.44805	+	7.44805i	0.931007	+	0.931007i	−0.0667624	+	0.997769i	$0.521267\pi$
$3$	−22.6252	−	22.6252i	−0.837969	−	0.837969i	0.150622	−	0.988591i	$-0.451872\pi$
$3$	−22.6252	−	22.6252i	−0.837969	−	0.837969i	−0.988591	+	0.150622i	$0.951872\pi$
$4$			46.9470i			0.733546i
$5$		−	114.512i		−	0.916098i	−0.888927	−	0.458049i	$-0.848548\pi$
$5$		−	114.512i		−	0.916098i	0.888927	−	0.458049i	$-0.151452\pi$
$6$		−	337.027i		−	1.56031i
$7$	512.680			1.49469			0.747347	−	0.664433i	$-0.231327\pi$
$7$	512.680			1.49469			0.747347	+	0.664433i	$0.231327\pi$
$8$	127.012	−	127.012i	0.248070	−	0.248070i
$9$			294.796i			0.404384i
$10$	852.893	−	852.893i	0.852893	−	0.852893i
$11$	−1533.66	−	1533.66i	−1.15226	−	1.15226i	−0.986099	−	0.166161i	$-0.946863\pi$
$11$	−1533.66	−	1533.66i	−1.15226	−	1.15226i	−0.166161	−	0.986099i	$-0.553137\pi$
$12$	1062.18	−	1062.18i	0.614689	−	0.614689i
$13$			1811.23i			0.824410i	0.911091	+	0.412205i	$0.135241\pi$
$13$			1811.23i			0.824410i	−0.911091	+	0.412205i	$0.864759\pi$
$14$	3818.47	+	3818.47i	1.39157	+	1.39157i
$15$	−2590.86	+	2590.86i	−0.767662	+	0.767662i
$16$	4896.59			1.19546
$17$	−4218.14	−	4218.14i	−0.858568	−	0.858568i	0.132602	−	0.991169i	$-0.457667\pi$
$17$	−4218.14	−	4218.14i	−0.858568	−	0.858568i	−0.991169	+	0.132602i	$0.957667\pi$
$18$	−2195.65	+	2195.65i	−0.376484	+	0.376484i
$19$	4253.31	+	4253.31i	0.620106	+	0.620106i	0.945558	−	0.325452i	$-0.105517\pi$
$19$	4253.31	+	4253.31i	0.620106	+	0.620106i	−0.325452	+	0.945558i	$0.605517\pi$
$20$	5376.00			0.672000
$21$	−11599.5	−	11599.5i	−1.25251	−	1.25251i
$22$		−	22845.5i		−	2.14552i
$23$	2393.24			0.196699			0.0983495	−	0.995152i	$-0.468644\pi$
$23$	2393.24			0.196699			0.0983495	+	0.995152i	$0.468644\pi$
$24$	−5747.33			−0.415750
$25$	2511.94			0.160764
$26$	−13490.1	+	13490.1i	−0.767531	+	0.767531i
$27$	−9823.94	+	9823.94i	−0.499108	+	0.499108i
$28$			24068.8i			1.09643i
$29$	16009.4	+	18399.0i	0.656417	+	0.754398i
$29$	16009.4	+	18399.0i	0.656417	+	0.754398i
$30$	−38593.7			−1.42940
$31$	3730.85	+	3730.85i	0.125234	+	0.125234i	0.766946	−	0.641712i	$-0.221775\pi$
$31$	3730.85	+	3730.85i	0.125234	+	0.125234i	−0.641712	+	0.766946i	$0.721775\pi$
$32$	28341.3	+	28341.3i	0.864907	+	0.864907i
$33$			69398.5i			1.93112i
$34$		−	62833.9i		−	1.59866i
$35$		−	58708.2i		−	1.36929i
$36$	−13839.8			−0.296634
$37$	−45114.2	+	45114.2i	−0.890652	+	0.890652i	−0.994584	−	0.103932i	$-0.966858\pi$
$37$	−45114.2	+	45114.2i	−0.890652	+	0.890652i	0.103932	+	0.994584i	$0.466858\pi$
$38$			63357.7i			1.15465i
$39$	40979.4	−	40979.4i	0.690830	−	0.690830i
$40$	−14544.4	−	14544.4i	−0.227257	−	0.227257i
$41$	60382.8	−	60382.8i	0.876117	−	0.876117i	−0.117014	−	0.993130i	$-0.537332\pi$
$41$	60382.8	−	60382.8i	0.876117	−	0.876117i	0.993130	+	0.117014i	$0.0373322\pi$
$42$		−	172787.i		−	2.33219i
$43$	33778.6	+	33778.6i	0.424851	+	0.424851i	0.886870	−	0.462019i	$-0.152875\pi$
$43$	33778.6	+	33778.6i	0.424851	+	0.424851i	−0.462019	+	0.886870i	$0.652875\pi$
$44$	72000.5	−	72000.5i	0.845236	−	0.845236i
$45$	33757.7			0.370455
$46$	17825.0	+	17825.0i	0.183128	+	0.183128i
$47$	−25538.5	+	25538.5i	−0.245981	+	0.245981i	−0.819319	−	0.573338i	$-0.805648\pi$
$47$	−25538.5	+	25538.5i	−0.245981	+	0.245981i	0.573338	+	0.819319i	$0.305648\pi$
$48$	−110786.	−	110786.i	−1.00176	−	1.00176i
$49$	145192.			1.23411
$50$	18709.1	+	18709.1i	0.149673	+	0.149673i
$51$			190872.i			1.43891i
$52$	−85031.7			−0.604743
$53$	221001.			1.48445			0.742226	−	0.670149i	$-0.233770\pi$
$53$	221001.			1.48445			0.742226	+	0.670149i	$0.233770\pi$
$54$	−146338.			−0.929345
$55$	−175623.	+	175623.i	−1.05558	+	1.05558i
$56$	65116.5	−	65116.5i	0.370789	−	0.370789i
$57$		−	192464.i		−	1.03926i
$58$	−17798.3	+	256275.i	−0.0912208	+	1.31348i
$59$	87675.9			0.426898			0.213449	−	0.976954i	$-0.431530\pi$
$59$	87675.9			0.426898			0.213449	+	0.976954i	$0.431530\pi$
$60$	−121633.	−	121633.i	−0.563115	−	0.563115i
$61$	−220659.	−	220659.i	−0.972149	−	0.972149i	0.0274737	−	0.999623i	$-0.491254\pi$
$61$	−220659.	−	220659.i	−0.972149	−	0.972149i	−0.999623	+	0.0274737i	$0.991254\pi$
$62$			55575.1i			0.233187i
$63$			151136.i			0.604430i
$64$			108793.i			0.415012i
$65$	207408.			0.755241
$66$	−516884.	+	516884.i	−1.79788	+	1.79788i
$67$			204898.i			0.681261i	0.940197	+	0.340630i	$0.110640\pi$
$67$			204898.i			0.681261i	−0.940197	+	0.340630i	$0.889360\pi$
$68$	198029.	−	198029.i	0.629799	−	0.629799i
$69$	−54147.4	−	54147.4i	−0.164828	−	0.164828i
$70$	437262.	−	437262.i	1.27482	−	1.27482i
$71$			441433.i			1.23336i	0.787214	+	0.616680i	$0.211523\pi$
$71$			441433.i			1.23336i	−0.787214	+	0.616680i	$0.788477\pi$
$72$	37442.6	+	37442.6i	0.100316	+	0.100316i
$73$	6026.50	−	6026.50i	0.0154916	−	0.0154916i	−0.699319	−	0.714810i	$-0.746513\pi$
$73$	6026.50	−	6026.50i	0.0154916	−	0.0154916i	0.714810	+	0.699319i	$0.246513\pi$
$74$	−672026.			−1.65841
$75$	−56833.1	−	56833.1i	−0.134715	−	0.134715i
$76$	−199680.	+	199680.i	−0.454877	+	0.454877i
$77$	−786276.	−	786276.i	−1.72228	−	1.72228i
$78$	610433.			1.28633
$79$	36750.7	+	36750.7i	0.0745392	+	0.0745392i	0.743394	−	0.668854i	$-0.233215\pi$
$79$	36750.7	+	36750.7i	0.0745392	+	0.0745392i	−0.668854	+	0.743394i	$0.733215\pi$
$80$		−	560719.i		−	1.09516i
$81$	659443.			1.24086
$82$	899469.			1.63134
$83$	−552442.			−0.966168			−0.483084	−	0.875574i	$-0.660483\pi$
$83$	−552442.			−0.966168			−0.483084	+	0.875574i	$0.660483\pi$
$84$	544560.	−	544560.i	0.918772	−	0.918772i
$85$	−483029.	+	483029.i	−0.786532	+	0.786532i
$86$			503170.i			0.791078i
$87$	54066.3	−	778495.i	0.0821049	−	1.18222i
$88$	−389586.			−0.571683
$89$	545435.	+	545435.i	0.773700	+	0.773700i	0.978751	−	0.205051i	$-0.0657361\pi$
$89$	545435.	+	545435.i	0.773700	+	0.773700i	−0.205051	+	0.978751i	$0.565736\pi$
$90$	251429.	+	251429.i	0.344896	+	0.344896i
$91$			928582.i			1.23224i
$92$			112355.i			0.144288i
$93$		−	168822.i		−	0.209885i
$94$	−380425.			−0.458021
$95$	487056.	−	487056.i	0.568078	−	0.568078i
$96$		−	1.28245e6i		−	1.44953i
$97$	1.08035e6	−	1.08035e6i	1.18372	−	1.18372i	0.204941	−	0.978774i	$-0.434300\pi$
$97$	1.08035e6	−	1.08035e6i	1.18372	−	1.18372i	0.978774	−	0.204941i	$-0.0657004\pi$
$98$	1.08140e6	+	1.08140e6i	1.14897	+	1.14897i
$99$	452116.	−	452116.i	0.465955	−	0.465955i
$100$			117928.i			0.117928i
$101$	−966705.	−	966705.i	−0.938274	−	0.938274i	0.0599287	−	0.998203i	$-0.480913\pi$
$101$	−966705.	−	966705.i	−0.938274	−	0.938274i	−0.998203	+	0.0599287i	$0.980913\pi$
$102$	−1.42163e6	+	1.42163e6i	−1.33963	+	1.33963i
$103$	−729106.			−0.667235			−0.333618	−	0.942708i	$-0.608269\pi$
$103$	−729106.			−0.667235			−0.333618	+	0.942708i	$0.608269\pi$
$104$	230048.	+	230048.i	0.204512	+	0.204512i
$105$	−1.32828e6	+	1.32828e6i	−1.14742	+	1.14742i
$106$	1.64603e6	+	1.64603e6i	1.38204	+	1.38204i
$107$	−1.02779e6			−0.838979			−0.419490	−	0.907760i	$-0.637791\pi$
$107$	−1.02779e6			−0.838979			−0.419490	+	0.907760i	$0.637791\pi$
$108$	−461204.	−	461204.i	−0.366119	−	0.366119i
$109$		−	1.41921e6i		−	1.09589i	−0.836513	−	0.547947i	$-0.815409\pi$
$109$		−	1.41921e6i		−	1.09589i	0.836513	−	0.547947i	$-0.184591\pi$
$110$	−2.61609e6			−1.96551
$111$	2.04143e6			1.49268
$112$	2.51038e6			1.78684
$113$	−181750.	+	181750.i	−0.125962	+	0.125962i	−0.767277	−	0.641315i	$-0.778389\pi$
$113$	−181750.	+	181750.i	−0.125962	+	0.125962i	0.641315	+	0.767277i	$0.278389\pi$
$114$	1.43348e6	−	1.43348e6i	0.967557	−	0.967557i
$115$		−	274055.i		−	0.180196i
$116$	−863778.	+	751591.i	−0.553386	+	0.481512i
$117$	−533943.			−0.333378
$118$	653015.	+	653015.i	0.397445	+	0.397445i
$119$	−2.16256e6	−	2.16256e6i	−1.28330	−	1.28330i
$120$			658140.i			0.380868i
$121$			2.93265e6i			1.65540i
$122$		−	3.28696e6i		−	1.81015i
$123$	−2.73234e6			−1.46832
$124$	−175152.	+	175152.i	−0.0918650	+	0.0918650i
$125$		−	2.07690e6i		−	1.06337i
$126$	−1.12567e6	+	1.12567e6i	−0.562728	+	0.562728i
$127$	1.09932e6	+	1.09932e6i	0.536679	+	0.536679i	0.922552	−	0.385873i	$-0.126100\pi$
$127$	1.09932e6	+	1.09932e6i	0.536679	+	0.536679i	−0.385873	+	0.922552i	$0.626100\pi$
$128$	1.00355e6	−	1.00355e6i	0.478528	−	0.478528i
$129$		−	1.52849e6i		−	0.712024i
$130$	1.54479e6	+	1.54479e6i	0.703134	+	0.703134i
$131$	−2.39907e6	+	2.39907e6i	−1.06716	+	1.06716i	−0.0695834	+	0.997576i	$0.522167\pi$
$131$	−2.39907e6	+	2.39907e6i	−1.06716	+	1.06716i	−0.997576	+	0.0695834i	$0.977833\pi$
$132$	−3.25805e6			−1.41656
$133$	2.18059e6	+	2.18059e6i	0.926870	+	0.926870i
$134$	−1.52609e6	+	1.52609e6i	−0.634258	+	0.634258i
$135$	1.12496e6	+	1.12496e6i	0.457232	+	0.457232i
$136$	−1.07151e6			−0.425970
$137$	2.72464e6	+	2.72464e6i	1.05962	+	1.05962i	0.998107	+	0.0615085i	$0.0195911\pi$
$137$	2.72464e6	+	2.72464e6i	1.05962	+	1.05962i	0.0615085	+	0.998107i	$0.480409\pi$
$138$		−	806585.i		−	0.306911i
$139$	1.32261e6			0.492480			0.246240	−	0.969209i	$-0.420805\pi$
$139$	1.32261e6			0.492480			0.246240	+	0.969209i	$0.420805\pi$
$140$	2.75617e6			1.00444
$141$	1.15563e6			0.412250
$142$	−3.28782e6	+	3.28782e6i	−1.14827	+	1.14827i
$143$	2.77781e6	−	2.77781e6i	0.949935	−	0.949935i
$144$			1.44349e6i			0.483423i
$145$	2.10691e6	−	1.83327e6i	0.691103	−	0.601343i
$146$	89771.4			0.0288456
$147$	−3.28500e6	−	3.28500e6i	−1.03415	−	1.03415i
$148$	−2.11798e6	−	2.11798e6i	−0.653335	−	0.653335i
$149$		−	1.92714e6i		−	0.582578i	−0.956635	−	0.291289i	$-0.905916\pi$
$149$		−	1.92714e6i		−	0.582578i	0.956635	−	0.291289i	$-0.0940841\pi$
$150$		−	846591.i		−	0.250842i
$151$			6.41171e6i			1.86227i	0.364673	+	0.931136i	$0.381181\pi$
$151$			6.41171e6i			1.86227i	−0.364673	+	0.931136i	$0.618819\pi$
$152$	1.08044e6			0.307660
$153$	1.24349e6	−	1.24349e6i	0.347191	−	0.347191i
$154$		−	1.17124e7i		−	3.20690i
$155$	427228.	−	427228.i	0.114727	−	0.114727i
$156$	1.92386e6	+	1.92386e6i	0.506756	+	0.506756i
$157$	1.82951e6	−	1.82951e6i	0.472754	−	0.472754i	−0.430050	−	0.902805i	$-0.641504\pi$
$157$	1.82951e6	−	1.82951e6i	0.472754	−	0.472754i	0.902805	+	0.430050i	$0.141504\pi$
$158$			547443.i			0.138793i
$159$	−5.00018e6	−	5.00018e6i	−1.24393	−	1.24393i
$160$	3.24542e6	−	3.24542e6i	0.792340	−	0.792340i
$161$	1.22697e6			0.294005
$162$	4.91156e6	+	4.91156e6i	1.15525	+	1.15525i
$163$	−981981.	+	981981.i	−0.226746	+	0.226746i	−0.811332	−	0.584586i	$-0.801257\pi$
$163$	−981981.	+	981981.i	−0.226746	+	0.226746i	0.584586	+	0.811332i	$0.301257\pi$
$164$	2.83479e6	+	2.83479e6i	0.642672	+	0.642672i
$165$	7.94698e6			1.76909
$166$	−4.11462e6	−	4.11462e6i	−0.899509	−	0.899509i
$167$		−	3.52073e6i		−	0.755933i	−0.925819	−	0.377967i	$-0.876623\pi$
$167$		−	3.52073e6i		−	0.755933i	0.925819	−	0.377967i	$-0.123377\pi$
$168$	−2.94654e6			−0.621420
$169$	1.54626e6			0.320348
$170$	−7.19525e6			−1.46453
$171$	−1.25386e6	+	1.25386e6i	−0.250761	+	0.250761i
$172$	−1.58580e6	+	1.58580e6i	−0.311648	+	0.311648i
$173$			9.30057e6i			1.79627i	0.439722	+	0.898134i	$0.355077\pi$
$173$			9.30057e6i			1.79627i	−0.439722	+	0.898134i	$0.644923\pi$
$174$	6.20096e6	−	5.39558e6i	1.17709	−	1.02421i
$175$	1.28782e6			0.240293
$176$	−7.50969e6	−	7.50969e6i	−1.37748	−	1.37748i
$177$	−1.98368e6	−	1.98368e6i	−0.357727	−	0.357727i
$178$			8.12485e6i			1.44064i
$179$			2.59919e6i			0.453189i	0.973989	+	0.226595i	$0.0727593\pi$
$179$			2.59919e6i			0.453189i	−0.973989	+	0.226595i	$0.927241\pi$
$180$			1.58482e6i			0.271746i
$181$	−1.02968e7			−1.73647			−0.868235	−	0.496154i	$-0.834745\pi$
$181$	−1.02968e7			−1.73647			−0.868235	+	0.496154i	$0.834745\pi$
$182$	−6.91612e6	+	6.91612e6i	−1.14723	+	1.14723i
$183$			9.98490e6i			1.62926i
$184$	303970.	−	303970.i	0.0487952	−	0.0487952i
$185$	5.16613e6	+	5.16613e6i	0.815925	+	0.815925i
$186$	1.25740e6	−	1.25740e6i	0.195404	−	0.195404i
$187$			1.29384e7i			1.97859i
$188$	−1.19896e6	−	1.19896e6i	−0.180439	−	0.180439i
$189$	−5.03654e6	+	5.03654e6i	−0.746014	+	0.746014i
$190$	7.25524e6			1.05777
$191$	−4.44965e6	−	4.44965e6i	−0.638596	−	0.638596i	0.311613	−	0.950209i	$-0.399131\pi$
$191$	−4.44965e6	−	4.44965e6i	−0.638596	−	0.638596i	−0.950209	+	0.311613i	$0.899131\pi$
$192$	2.46146e6	−	2.46146e6i	0.347767	−	0.347767i
$193$	−5.80471e6	−	5.80471e6i	−0.807437	−	0.807437i	0.176808	−	0.984245i	$-0.443423\pi$
$193$	−5.80471e6	−	5.80471e6i	−0.807437	−	0.807437i	−0.984245	+	0.176808i	$0.943423\pi$
$194$	1.60929e7			2.20409
$195$	−4.69264e6	−	4.69264e6i	−0.632868	−	0.632868i
$196$			6.81633e6i			0.905279i
$197$	1.20340e6			0.157403			0.0787014	−	0.996898i	$-0.474923\pi$
$197$	1.20340e6			0.157403			0.0787014	+	0.996898i	$0.474923\pi$
$198$	6.73476e6			0.867614
$199$	−9.45910e6			−1.20030			−0.600151	−	0.799887i	$-0.704893\pi$
$199$	−9.45910e6			−1.20030			−0.600151	+	0.799887i	$0.704893\pi$
$200$	319046.	−	319046.i	0.0398808	−	0.0398808i
$201$	4.63585e6	−	4.63585e6i	0.570875	−	0.570875i
$202$		−	1.44001e7i		−	1.74708i
$203$	8.20768e6	+	9.43281e6i	0.981143	+	1.12759i
$204$	−8.96087e6			−1.05550
$205$	−6.91457e6	−	6.91457e6i	−0.802609	−	0.802609i
$206$	−5.43042e6	−	5.43042e6i	−0.621200	−	0.621200i
$207$			705516.i			0.0795419i
$208$			8.86885e6i			0.985546i
$209$		−	1.30462e7i		−	1.42905i
$210$	−1.97862e7			−2.13651
$211$	9.68137e6	−	9.68137e6i	1.03060	−	1.03060i	0.0310818	−	0.999517i	$-0.490105\pi$
$211$	9.68137e6	−	9.68137e6i	1.03060	−	1.03060i	0.999517	−	0.0310818i	$-0.00989523\pi$
$212$			1.03753e7i			1.08891i
$213$	9.98750e6	−	9.98750e6i	1.03352	−	1.03352i
$214$	−7.65500e6	−	7.65500e6i	−0.781095	−	0.781095i
$215$	3.86807e6	−	3.86807e6i	0.389205	−	0.389205i
$216$			2.49552e6i			0.247628i
$217$	1.91273e6	+	1.91273e6i	0.187187	+	0.187187i
$218$	1.05704e7	−	1.05704e7i	1.02028	−	1.02028i
$219$	−272701.			−0.0259630
$220$	−8.24495e6	−	8.24495e6i	−0.774319	−	0.774319i
$221$	7.64002e6	−	7.64002e6i	0.707812	−	0.707812i
$222$	1.52047e7	+	1.52047e7i	1.38969	+	1.38969i
$223$	2.02626e6			0.182717			0.0913586	−	0.995818i	$-0.470879\pi$
$223$	2.02626e6			0.182717			0.0913586	+	0.995818i	$0.470879\pi$
$224$	1.45300e7	+	1.45300e7i	1.29277	+	1.29277i
$225$			740509.i			0.0650104i
$226$	−2.70737e6			−0.234543
$227$	−5.53402e6			−0.473111			−0.236555	−	0.971618i	$-0.576019\pi$
$227$	−5.53402e6			−0.473111			−0.236555	+	0.971618i	$0.576019\pi$
$228$	9.03558e6			0.762345
$229$	−1.21087e7	+	1.21087e7i	−1.00830	+	1.00830i	−0.00833733	+	0.999965i	$0.502654\pi$
$229$	−1.21087e7	+	1.21087e7i	−1.00830	+	1.00830i	−0.999965	+	0.00833733i	$0.997346\pi$
$230$	2.04118e6	−	2.04118e6i	0.167763	−	0.167763i
$231$			3.55792e7i			2.88643i
$232$	4.37027e6	+	303515.i	0.349981	+	0.0243061i
$233$	2.23734e7			1.76874			0.884372	−	0.466782i	$-0.154587\pi$
$233$	2.23734e7			1.76874			0.884372	+	0.466782i	$0.154587\pi$
$234$	−3.97683e6	−	3.97683e6i	−0.310377	−	0.310377i
$235$	2.92447e6	+	2.92447e6i	0.225343	+	0.225343i
$236$			4.11612e6i			0.313150i
$237$		−	1.66298e6i		−	0.124923i
$238$		−	3.22137e7i		−	2.38952i
$239$	−5.90615e6			−0.432624			−0.216312	−	0.976324i	$-0.569403\pi$
$239$	−5.90615e6			−0.432624			−0.216312	+	0.976324i	$0.569403\pi$
$240$	−1.26864e7	+	1.26864e7i	−0.917706	+	0.917706i
$241$		−	1.05936e7i		−	0.756820i	−0.925638	−	0.378410i	$-0.876471\pi$
$241$		−	1.05936e7i		−	0.756820i	0.925638	−	0.378410i	$-0.123529\pi$
$242$	−2.18425e7	+	2.18425e7i	−1.54119	+	1.54119i
$243$	−7.75834e6	−	7.75834e6i	−0.540692	−	0.540692i
$244$	1.03593e7	−	1.03593e7i	0.713116	−	0.713116i
$245$		−	1.66263e7i		−	1.13057i
$246$	−2.03506e7	−	2.03506e7i	−1.36701	−	1.36701i
$247$	−7.70372e6	+	7.70372e6i	−0.511222	+	0.511222i
$248$	947725.			0.0621337
$249$	1.24991e7	+	1.24991e7i	0.809619	+	0.809619i
$250$	1.54689e7	−	1.54689e7i	0.990008	−	0.990008i
$251$	−2.80352e6	−	2.80352e6i	−0.177289	−	0.177289i	0.612884	−	0.790173i	$-0.290009\pi$
$251$	−2.80352e6	−	2.80352e6i	−0.177289	−	0.177289i	−0.790173	+	0.612884i	$0.790009\pi$
$252$	−7.09537e6			−0.443378
$253$	−3.67041e6	−	3.67041e6i	−0.226648	−	0.226648i
$254$			1.63756e7i			0.999303i
$255$	2.18572e7			1.31818
$256$	2.19117e7			1.30604
$257$	1.59801e7			0.941410			0.470705	−	0.882291i	$-0.344000\pi$
$257$	1.59801e7			0.941410			0.470705	+	0.882291i	$0.344000\pi$
$258$	1.13843e7	−	1.13843e7i	0.662899	−	0.662899i
$259$	−2.31292e7	+	2.31292e7i	−1.33125	+	1.33125i
$260$			9.73717e6i			0.554004i
$261$	−5.42395e6	+	4.71949e6i	−0.305066	+	0.265444i
$262$	−3.57368e7			−1.98706
$263$	−6.75821e6	−	6.75821e6i	−0.371505	−	0.371505i	0.496520	−	0.868025i	$-0.334611\pi$
$263$	−6.75821e6	−	6.75821e6i	−0.371505	−	0.371505i	−0.868025	+	0.496520i	$0.834611\pi$
$264$	8.81444e6	+	8.81444e6i	0.479052	+	0.479052i
$265$		−	2.53073e7i		−	1.35990i
$266$			3.24823e7i			1.72584i
$267$		−	2.46811e7i		−	1.29667i
$268$	−9.61934e6			−0.499736
$269$	−8.07984e6	+	8.07984e6i	−0.415093	+	0.415093i	−0.883509	−	0.468415i	$-0.844825\pi$
$269$	−8.07984e6	+	8.07984e6i	−0.415093	+	0.415093i	0.468415	+	0.883509i	$0.344825\pi$
$270$			1.67575e7i			0.851372i
$271$	−1.00739e7	+	1.00739e7i	−0.506160	+	0.506160i	−0.913346	−	0.407185i	$-0.866510\pi$
$271$	−1.00739e7	+	1.00739e7i	−0.506160	+	0.506160i	0.407185	+	0.913346i	$0.366510\pi$
$272$	−2.06545e7	−	2.06545e7i	−1.02638	−	1.02638i
$273$	2.10093e7	−	2.10093e7i	1.03258	−	1.03258i
$274$			4.05866e7i			1.97302i
$275$	−3.85246e6	−	3.85246e6i	−0.185242	−	0.185242i
$276$	2.54205e6	−	2.54205e6i	0.120909	−	0.120909i
$277$	5.34123e6			0.251306			0.125653	−	0.992074i	$-0.459897\pi$
$277$	5.34123e6			0.251306			0.125653	+	0.992074i	$0.459897\pi$
$278$	9.85090e6	+	9.85090e6i	0.458502	+	0.458502i
$279$	−1.09984e6	+	1.09984e6i	−0.0506426	+	0.0506426i
$280$	−7.45664e6	−	7.45664e6i	−0.339679	−	0.339679i
$281$	−2.34232e7			−1.05567			−0.527834	−	0.849347i	$-0.676996\pi$
$281$	−2.34232e7			−1.05567			−0.527834	+	0.849347i	$0.676996\pi$
$282$	8.60717e6	+	8.60717e6i	0.383807	+	0.383807i
$283$			4.78362e6i			0.211056i	0.994416	+	0.105528i	$0.0336532\pi$
$283$			4.78362e6i			0.211056i	−0.994416	+	0.105528i	$0.966347\pi$
$284$	−2.07239e7			−0.904727
$285$	−2.20394e7			−0.952064
$286$	4.13785e7			1.76879
$287$	3.09571e7	−	3.09571e7i	1.30953	−	1.30953i
$288$	−8.35489e6	+	8.35489e6i	−0.349754	+	0.349754i
$289$			1.14479e7i			0.474277i
$290$	2.93467e7	+	2.03812e6i	1.20327	+	0.0835672i
$291$	−4.88860e7			−1.98383
$292$	282926.	+	282926.i	0.0113638	+	0.0113638i
$293$	−3.08476e7	−	3.08476e7i	−1.22636	−	1.22636i	−0.965330	−	0.261032i	$-0.915937\pi$
$293$	−3.08476e7	−	3.08476e7i	−1.22636	−	1.22636i	−0.261032	−	0.965330i	$-0.584063\pi$
$294$		−	4.89336e7i		−	1.92560i
$295$		−	1.00400e7i		−	0.391081i
$296$			1.14601e7i			0.441889i
$297$	3.01331e7			1.15020
$298$	1.43534e7	−	1.43534e7i	0.542384	−	0.542384i
$299$			4.33470e6i			0.162161i
$300$	2.66814e6	−	2.66814e6i	0.0988200	−	0.0988200i
$301$	1.73176e7	+	1.73176e7i	0.635023	+	0.635023i
$302$	−4.77547e7	+	4.77547e7i	−1.73379	+	1.73379i
$303$			4.37437e7i			1.57249i
$304$	2.08267e7	+	2.08267e7i	0.741310	+	0.741310i
$305$	−2.52682e7	+	2.52682e7i	−0.890584	+	0.890584i
$306$	1.85232e7			0.646474
$307$	6.55233e6	+	6.55233e6i	0.226454	+	0.226454i	0.811210	−	0.584755i	$-0.198810\pi$
$307$	6.55233e6	+	6.55233e6i	0.226454	+	0.226454i	−0.584755	+	0.811210i	$0.698810\pi$
$308$	3.69133e7	−	3.69133e7i	1.26337	−	1.26337i
$309$	1.64961e7	+	1.64961e7i	0.559122	+	0.559122i
$310$	6.36403e6			0.213623
$311$	−2.11988e7	−	2.11988e7i	−0.704743	−	0.704743i	0.260682	−	0.965425i	$-0.416053\pi$
$311$	−2.11988e7	−	2.11988e7i	−0.704743	−	0.704743i	−0.965425	+	0.260682i	$0.916053\pi$
$312$		−	1.04097e7i		−	0.342749i
$313$	−1.79310e7			−0.584751			−0.292376	−	0.956304i	$-0.594446\pi$
$313$	−1.79310e7			−0.584751			−0.292376	+	0.956304i	$0.594446\pi$
$314$	2.72526e7			0.880275
$315$	1.73069e7			0.553717
$316$	−1.72534e6	+	1.72534e6i	−0.0546780	+	0.0546780i
$317$	−7.96881e6	+	7.96881e6i	−0.250159	+	0.250159i	−0.821036	−	0.570877i	$-0.806603\pi$
$317$	−7.96881e6	+	7.96881e6i	−0.250159	+	0.250159i	0.570877	+	0.821036i	$0.306603\pi$
$318$		−	7.44832e7i		−	2.31620i
$319$	3.66491e6	−	5.27707e7i	0.112899	−	1.62563i
$320$	1.24581e7			0.380192
$321$	2.32538e7	+	2.32538e7i	0.703038	+	0.703038i
$322$	9.13850e6	+	9.13850e6i	0.273721	+	0.273721i
$323$		−	3.58821e7i		−	1.06481i
$324$			3.09588e7i			0.910226i
$325$			4.54970e6i			0.132536i
$326$	−1.46277e7			−0.422204
$327$	−3.21100e7	+	3.21100e7i	−0.918325	+	0.918325i
$328$		−	1.53387e7i		−	0.434677i
$329$	−1.30931e7	+	1.30931e7i	−0.367667	+	0.367667i
$330$	5.91895e7	+	5.91895e7i	1.64704	+	1.64704i
$331$	−5.45819e6	+	5.45819e6i	−0.150510	+	0.150510i	−0.778346	−	0.627836i	$-0.783941\pi$
$331$	−5.45819e6	+	5.45819e6i	−0.150510	+	0.150510i	0.627836	+	0.778346i	$0.283941\pi$
$332$		−	2.59355e7i		−	0.708729i
$333$	−1.32995e7	−	1.32995e7i	−0.360165	−	0.360165i
$334$	2.62226e7	−	2.62226e7i	0.703779	−	0.703779i
$335$	2.34633e7			0.624102
$336$	−5.67979e7	−	5.67979e7i	−1.49732	−	1.49732i
$337$	1.48421e7	−	1.48421e7i	0.387799	−	0.387799i	−0.486103	−	0.873902i	$-0.661582\pi$
$337$	1.48421e7	−	1.48421e7i	0.387799	−	0.387799i	0.873902	+	0.486103i	$0.161582\pi$
$338$	1.15166e7	+	1.15166e7i	0.298246	+	0.298246i
$339$	8.22425e6			0.211104
$340$	−2.26767e7	−	2.26767e7i	−0.576958	−	0.576958i
$341$		−	1.14437e7i		−	0.288604i
$342$	−1.86776e7			−0.466920
$343$	1.41208e7			0.349927
$344$	8.58058e6			0.210786
$345$	−6.20054e6	+	6.20054e6i	−0.150998	+	0.150998i
$346$	−6.92711e7	+	6.92711e7i	−1.67234	+	1.67234i
$347$		−	2.98853e7i		−	0.715269i	−0.933862	−	0.357635i	$-0.883583\pi$
$347$		−	2.98853e7i		−	0.715269i	0.933862	−	0.357635i	$-0.116417\pi$
$348$	3.65480e7	+	2.53825e6i	0.867212	+	0.0602277i
$349$	−1.23850e7			−0.291354			−0.145677	−	0.989332i	$-0.546536\pi$
$349$	−1.23850e7			−0.291354			−0.145677	+	0.989332i	$0.546536\pi$
$350$	9.59177e6	+	9.59177e6i	0.223715	+	0.223715i
$351$	−1.77934e7	−	1.77934e7i	−0.411470	−	0.411470i
$352$		−	8.69316e7i		−	1.99320i
$353$			2.41030e7i			0.547957i	0.961736	+	0.273978i	$0.0883397\pi$
$353$			2.41030e7i			0.547957i	−0.961736	+	0.273978i	$0.911660\pi$
$354$		−	2.95491e7i		−	0.666093i
$355$	5.05495e7			1.12988
$356$	−2.56065e7	+	2.56065e7i	−0.567545	+	0.567545i
$357$			9.78565e7i			2.15073i
$358$	−1.93589e7	+	1.93589e7i	−0.421922	+	0.421922i
$359$	6.93565e6	+	6.93565e6i	0.149901	+	0.149901i	0.778074	−	0.628173i	$-0.216197\pi$
$359$	6.93565e6	+	6.93565e6i	0.149901	+	0.149901i	−0.628173	+	0.778074i	$0.716197\pi$
$360$	4.28763e6	−	4.28763e6i	0.0918989	−	0.0918989i
$361$		−	1.08646e7i		−	0.230937i
$362$	−7.66912e7	−	7.66912e7i	−1.61666	−	1.61666i
$363$	6.63517e7	−	6.63517e7i	1.38718	−	1.38718i
$364$	−4.35941e7			−0.903906
$365$	−690108.	−	690108.i	−0.0141918	−	0.0141918i
$366$	−7.43681e7	+	7.43681e7i	−1.51685	+	1.51685i
$367$	3.39502e7	+	3.39502e7i	0.686823	+	0.686823i	0.961528	−	0.274706i	$-0.0885804\pi$
$367$	3.39502e7	+	3.39502e7i	0.686823	+	0.686823i	−0.274706	+	0.961528i	$0.588580\pi$
$368$	1.17187e7			0.235145
$369$	1.78006e7	+	1.78006e7i	0.354287	+	0.354287i
$370$			7.69552e7i			1.51926i
$371$	1.13303e8			2.21880
$372$	7.92568e6			0.153960
$373$	3.87217e7			0.746153			0.373077	−	0.927800i	$-0.378303\pi$
$373$	3.87217e7			0.746153			0.373077	+	0.927800i	$0.378303\pi$
$374$	−9.63657e7	+	9.63657e7i	−1.84208	+	1.84208i
$375$	−4.69902e7	+	4.69902e7i	−0.891074	+	0.891074i
$376$			6.48740e6i			0.122041i
$377$	−3.33248e7	+	2.89966e7i	−0.621934	+	0.541157i
$378$	−7.50248e7			−1.38909
$379$	2.88962e7	+	2.88962e7i	0.530790	+	0.530790i	0.920807	−	0.390018i	$-0.127531\pi$
$379$	2.88962e7	+	2.88962e7i	0.530790	+	0.530790i	−0.390018	+	0.920807i	$0.627531\pi$
$380$	2.28658e7	+	2.28658e7i	0.416712	+	0.416712i
$381$		−	4.97448e7i		−	0.899441i
$382$		−	6.62825e7i		−	1.18907i
$383$			4.00773e7i			0.713349i	0.934229	+	0.356674i	$0.116089\pi$
$383$			4.00773e7i			0.713349i	−0.934229	+	0.356674i	$0.883911\pi$
$384$	−4.54108e7			−0.801983
$385$	−9.00382e7	+	9.00382e7i	−1.57777	+	1.57777i
$386$		−	8.64676e7i		−	1.50346i
$387$	−9.95780e6	+	9.95780e6i	−0.171803	+	0.171803i
$388$	5.07189e7	+	5.07189e7i	0.868310	+	0.868310i
$389$	−3.17800e7	+	3.17800e7i	−0.539890	+	0.539890i	−0.923497	−	0.383607i	$-0.874682\pi$
$389$	−3.17800e7	+	3.17800e7i	−0.539890	+	0.539890i	0.383607	+	0.923497i	$0.374682\pi$
$390$		−	6.99020e7i		−	1.17841i
$391$	−1.00950e7	−	1.00950e7i	−0.168879	−	0.168879i
$392$	1.84411e7	−	1.84411e7i	0.306147	−	0.306147i
$393$	1.08559e8			1.78849
$394$	8.96300e6	+	8.96300e6i	0.146543	+	0.146543i
$395$	4.20841e6	−	4.20841e6i	0.0682852	−	0.0682852i
$396$	2.12255e7	+	2.12255e7i	0.341800	+	0.341800i
$397$	−3.99057e7			−0.637769			−0.318884	−	0.947794i	$-0.603308\pi$
$397$	−3.99057e7			−0.637769			−0.318884	+	0.947794i	$0.603308\pi$
$398$	−7.04519e7	−	7.04519e7i	−1.11749	−	1.11749i
$399$		−	9.86723e7i		−	1.55338i
$400$	1.22999e7			0.192187
$401$	−3.74505e7			−0.580797			−0.290398	−	0.956906i	$-0.593788\pi$
$401$	−3.74505e7			−0.580797			−0.290398	+	0.956906i	$0.593788\pi$
$402$	6.90561e7			1.06298
$403$	−6.75742e6	+	6.75742e6i	−0.103244	+	0.103244i
$404$	4.53838e7	−	4.53838e7i	0.688267	−	0.688267i
$405$		−	7.55143e7i		−	1.13675i
$406$	−9.12483e6	+	1.31387e8i	−0.136347	+	1.96325i
$407$	1.38380e8			2.05253
$408$	2.42431e7	+	2.42431e7i	0.356950	+	0.356950i
$409$	7.12972e6	+	7.12972e6i	0.104208	+	0.104208i	0.757289	−	0.653080i	$-0.226524\pi$
$409$	7.12972e6	+	7.12972e6i	0.104208	+	0.104208i	−0.653080	+	0.757289i	$0.726524\pi$
$410$		−	1.03000e8i		−	1.49447i
$411$		−	1.23291e8i		−	1.77585i
$412$		−	3.42293e7i		−	0.489448i
$413$	4.49497e7			0.638083
$414$	−5.25472e6	+	5.25472e6i	−0.0740540	+	0.0740540i
$415$			6.32614e7i			0.885105i
$416$	−5.13326e7	+	5.13326e7i	−0.713038	+	0.713038i
$417$	−2.99243e7	−	2.99243e7i	−0.412683	−	0.412683i
$418$	9.71690e7	−	9.71690e7i	1.33045	−	1.33045i
$419$			6.38370e6i			0.0867821i	0.999058	+	0.0433911i	$0.0138161\pi$
$419$			6.38370e6i			0.0867821i	−0.999058	+	0.0433911i	$0.986184\pi$
$420$	−6.23588e7	−	6.23588e7i	−0.841686	−	0.841686i
$421$	−1.03858e8	+	1.03858e8i	−1.39185	+	1.39185i	−0.570670	+	0.821180i	$0.693316\pi$
$421$	−1.03858e8	+	1.03858e8i	−1.39185	+	1.39185i	−0.821180	+	0.570670i	$0.806684\pi$
$422$	1.44215e8			1.91899
$423$	−7.52865e6	−	7.52865e6i	−0.0994709	−	0.0994709i
$424$	2.80697e7	−	2.80697e7i	0.368248	−	0.368248i
$425$	−1.05957e7	−	1.05957e7i	−0.138027	−	0.138027i
$426$	1.48775e8			1.92442
$427$	−1.13128e8	−	1.13128e8i	−1.45307	−	1.45307i
$428$		−	4.82514e7i		−	0.615430i
$429$	−1.25697e8			−1.59203
$430$	5.76191e7			0.724705
$431$	6.93853e7			0.866633			0.433317	−	0.901242i	$-0.357343\pi$
$431$	6.93853e7			0.866633			0.433317	+	0.901242i	$0.357343\pi$
$432$	−4.81038e7	+	4.81038e7i	−0.596662	+	0.596662i
$433$	7.05074e7	−	7.05074e7i	0.868503	−	0.868503i	−0.123804	−	0.992307i	$-0.539509\pi$
$433$	7.05074e7	−	7.05074e7i	0.868503	−	0.868503i	0.992307	+	0.123804i	$0.0395094\pi$
$434$			2.84923e7i			0.348544i
$435$	−8.91472e7	−	6.19126e6i	−1.08303	−	0.0752162i
$436$	6.66278e7			0.803889
$437$	1.01792e7	+	1.01792e7i	0.121974	+	0.121974i
$438$	−2.03109e6	−	2.03109e6i	−0.0241717	−	0.0241717i
$439$			5.83217e7i			0.689345i	0.938723	+	0.344673i	$0.112010\pi$
$439$			5.83217e7i			0.689345i	−0.938723	+	0.344673i	$0.887990\pi$
$440$			4.46123e7i			0.523717i
$441$			4.28020e7i			0.499055i
$442$	1.13807e8			1.31796
$443$	−1.01835e8	+	1.01835e8i	−1.17135	+	1.17135i	−0.189461	+	0.981888i	$0.560674\pi$
$443$	−1.01835e8	+	1.01835e8i	−1.17135	+	1.17135i	−0.981888	+	0.189461i	$0.939326\pi$
$444$			9.58391e7i			1.09495i
$445$	6.24589e7	−	6.24589e7i	0.708785	−	0.708785i
$446$	1.50917e7	+	1.50917e7i	0.170111	+	0.170111i
$447$	−4.36018e7	+	4.36018e7i	−0.488182	+	0.488182i
$448$			5.57760e7i			0.620317i
$449$	−5.79379e7	−	5.79379e7i	−0.640064	−	0.640064i	0.310507	−	0.950571i	$-0.399501\pi$
$449$	−5.79379e7	−	5.79379e7i	−0.640064	−	0.640064i	−0.950571	+	0.310507i	$0.899501\pi$
$450$	−5.51535e6	+	5.51535e6i	−0.0605251	+	0.0605251i
$451$	−1.85213e8			−2.01903
$452$	−8.53261e6	−	8.53261e6i	−0.0923988	−	0.0923988i
$453$	1.45066e8	−	1.45066e8i	1.56053	−	1.56053i
$454$	−4.12177e7	−	4.12177e7i	−0.440469	−	0.440469i
$455$	1.06334e8			1.12885
$456$	−2.44452e7	−	2.44452e7i	−0.257809	−	0.257809i
$457$			5.13128e7i			0.537622i	0.963193	+	0.268811i	$0.0866307\pi$
$457$			5.13128e7i			0.537622i	−0.963193	+	0.268811i	$0.913369\pi$
$458$	−1.80372e8			−1.87747
$459$	8.28776e7			0.857036
$460$	1.28660e7			0.132182
$461$	−3.14393e7	+	3.14393e7i	−0.320900	+	0.320900i	−0.849112	−	0.528212i	$-0.822862\pi$
$461$	−3.14393e7	+	3.14393e7i	−0.320900	+	0.320900i	0.528212	+	0.849112i	$0.322862\pi$
$462$	−2.64996e8	+	2.64996e8i	−2.68728	+	2.68728i
$463$			5.98536e7i			0.603042i	0.953460	+	0.301521i	$0.0974943\pi$
$463$			5.98536e7i			0.603042i	−0.953460	+	0.301521i	$0.902506\pi$
$464$	7.83912e7	+	9.00924e7i	0.784718	+	0.901850i
$465$	−1.93322e7			−0.192275
$466$	1.66639e8	+	1.66639e8i	1.64671	+	1.64671i
$467$	5.96816e7	+	5.96816e7i	0.585990	+	0.585990i	0.936543	−	0.350553i	$-0.114006\pi$
$467$	5.96816e7	+	5.96816e7i	0.585990	+	0.585990i	−0.350553	+	0.936543i	$0.614006\pi$
$468$		−	2.50670e7i		−	0.244548i
$469$			1.05047e8i			1.01828i
$470$			4.35633e7i			0.419592i
$471$	−8.27859e7			−0.792307
$472$	1.11359e7	−	1.11359e7i	0.105901	−	0.105901i
$473$		−	1.03610e8i		−	0.979077i
$474$	1.23860e7	−	1.23860e7i	0.116304	−	0.116304i
$475$	1.06841e7	+	1.06841e7i	0.0996909	+	0.0996909i
$476$	1.01526e8	−	1.01526e8i	0.941357	−	0.941357i
$477$			6.51501e7i			0.600288i
$478$	−4.39893e7	−	4.39893e7i	−0.402776	−	0.402776i
$479$	1.04664e8	−	1.04664e8i	0.952337	−	0.952337i	−0.0465776	−	0.998915i	$-0.514831\pi$
$479$	1.04664e8	−	1.04664e8i	0.952337	−	0.952337i	0.998915	+	0.0465776i	$0.0148315\pi$
$480$	−1.46856e8			−1.32791
$481$	−8.17122e7	−	8.17122e7i	−0.734263	−	0.734263i
$482$	7.89017e7	−	7.89017e7i	0.704604	−	0.704604i
$483$	−2.77603e7	−	2.77603e7i	−0.246367	−	0.246367i
$484$	−1.37679e8			−1.21432
$485$	−1.23713e8	−	1.23713e8i	−1.08440	−	1.08440i
$486$		−	1.15569e8i		−	1.00678i
$487$	2.12850e6			0.0184284			0.00921419	−	0.999958i	$-0.497067\pi$
$487$	2.12850e6			0.0184284			0.00921419	+	0.999958i	$0.497067\pi$
$488$	−5.60527e7			−0.482322
$489$	4.44349e7			0.380013
$490$	1.23833e8	−	1.23833e8i	1.05257	−	1.05257i
$491$	9.58885e7	−	9.58885e7i	0.810069	−	0.810069i	−0.174575	−	0.984644i	$-0.555855\pi$
$491$	9.58885e7	−	9.58885e7i	0.810069	−	0.810069i	0.984644	+	0.174575i	$0.0558551\pi$
$492$		−	1.28275e8i		−	1.07708i
$493$	1.00799e7	−	1.45139e8i	0.0841232	−	1.21128i
$494$	−1.14755e8			−0.951902
$495$	−5.17728e7	−	5.17728e7i	−0.426860	−	0.426860i
$496$	1.82684e7	+	1.82684e7i	0.149712	+	0.149712i
$497$			2.26314e8i			1.84350i
$498$			1.86188e8i			1.50752i
$499$		−	1.94422e8i		−	1.56475i	−0.622809	−	0.782374i	$-0.714009\pi$
$499$		−	1.94422e8i		−	1.56475i	0.622809	−	0.782374i	$-0.285991\pi$
$500$	9.75042e7			0.780034
$501$	−7.96571e7	+	7.96571e7i	−0.633448	+	0.633448i
$502$		−	4.17615e7i		−	0.330114i
$503$	−1.46457e8	+	1.46457e8i	−1.15082	+	1.15082i	−0.164428	+	0.986389i	$0.552578\pi$
$503$	−1.46457e8	+	1.46457e8i	−1.15082	+	1.15082i	−0.986389	+	0.164428i	$0.947422\pi$
$504$	1.91961e7	+	1.91961e7i	0.149941	+	0.149941i
$505$	−1.10700e8	+	1.10700e8i	−0.859551	+	0.859551i
$506$		−	5.46747e7i		−	0.422022i
$507$	−3.49843e7	−	3.49843e7i	−0.268441	−	0.268441i
$508$	−5.16099e7	+	5.16099e7i	−0.393679	+	0.393679i
$509$	1.26445e8			0.958842			0.479421	−	0.877585i	$-0.340847\pi$
$509$	1.26445e8			0.958842			0.479421	+	0.877585i	$0.340847\pi$
$510$	1.62794e8	+	1.62794e8i	1.22723	+	1.22723i
$511$	3.08967e6	−	3.08967e6i	0.0231552	−	0.0231552i
$512$	9.89724e7	+	9.89724e7i	0.737402	+	0.737402i
$513$	−8.35685e7			−0.619000
$514$	1.19020e8	+	1.19020e8i	0.876459	+	0.876459i
$515$			8.34916e7i			0.611253i
$516$	7.17581e7			0.522302
$517$	7.83347e7			0.566869
$518$	−3.44535e8			−2.47881
$519$	2.10427e8	−	2.10427e8i	1.50522	−	1.50522i
$520$	2.63433e7	−	2.63433e7i	0.187353	−	0.187353i
$521$			9.54093e7i			0.674649i	0.941388	+	0.337324i	$0.109522\pi$
$521$			9.54093e7i			0.674649i	−0.941388	+	0.337324i	$0.890478\pi$
$522$	−7.55489e7	−	5.24686e6i	−0.531149	−	0.0368882i
$523$	2.67560e8			1.87032			0.935159	−	0.354227i	$-0.115256\pi$
$523$	2.67560e8			1.87032			0.935159	+	0.354227i	$0.115256\pi$
$524$	−1.12629e8	−	1.12629e8i	−0.782811	−	0.782811i
$525$	−2.91372e7	−	2.91372e7i	−0.201358	−	0.201358i
$526$		−	1.00671e8i		−	0.691747i
$527$		−	3.14745e7i		−	0.215044i
$528$			3.39816e8i			2.30856i
$529$	−1.42308e8			−0.961310
$530$	1.88490e8	−	1.88490e8i	1.26608	−	1.26608i
$531$			2.58465e7i			0.172631i
$532$	−1.02372e8	+	1.02372e8i	−0.679902	+	0.679902i
$533$	1.09367e8	+	1.09367e8i	0.722280	+	0.722280i
$534$	1.83826e8	−	1.83826e8i	1.20721	−	1.20721i
$535$			1.17694e8i			0.768587i
$536$	2.60245e7	+	2.60245e7i	0.169001	+	0.169001i
$537$	5.88072e7	−	5.88072e7i	0.379759	−	0.379759i
$538$	−1.20358e8			−0.772909
$539$	−2.22675e8	−	2.22675e8i	−1.42202	−	1.42202i
$540$	−5.28135e7	+	5.28135e7i	−0.335401	+	0.335401i
$541$	4.28059e7	+	4.28059e7i	0.270341	+	0.270341i	0.829237	−	0.558897i	$-0.188775\pi$
$541$	4.28059e7	+	4.28059e7i	0.270341	+	0.270341i	−0.558897	+	0.829237i	$0.688775\pi$
$542$	−1.50061e8			−0.942477
$543$	2.32967e8	+	2.32967e8i	1.45511	+	1.45511i
$544$		−	2.39095e8i		−	1.48516i
$545$	−1.62518e8			−1.00395
$546$	3.12957e8			1.92268
$547$	1.14392e8			0.698932			0.349466	−	0.936949i	$-0.386363\pi$
$547$	1.14392e8			0.698932			0.349466	+	0.936949i	$0.386363\pi$
$548$	−1.27914e8	+	1.27914e8i	−0.777277	+	0.777277i
$549$	6.50494e7	−	6.50494e7i	0.393121	−	0.393121i
$550$		−	5.73866e7i		−	0.344923i
$551$	−1.01639e7	+	1.46349e8i	−0.0607585	+	0.874855i
$552$	−1.37547e7			−0.0817777
$553$	1.88414e7	+	1.88414e7i	0.111413	+	0.111413i
$554$	3.97818e7	+	3.97818e7i	0.233967	+	0.233967i
$555$		−	2.33769e8i		−	1.36744i
$556$			6.20927e7i			0.361257i
$557$		−	2.07074e8i		−	1.19828i	−0.800644	−	0.599141i	$-0.795509\pi$
$557$		−	2.07074e8i		−	1.19828i	0.800644	−	0.599141i	$-0.204491\pi$
$558$	−1.63833e7			−0.0942972
$559$	−6.11808e7	+	6.11808e7i	−0.350252	+	0.350252i
$560$		−	2.87470e8i		−	1.63692i
$561$	2.92733e8	−	2.92733e8i	1.65799	−	1.65799i
$562$	−1.74457e8	−	1.74457e8i	−0.982834	−	0.982834i
$563$	−1.50184e8	+	1.50184e8i	−0.841588	+	0.841588i	−0.989065	−	0.147477i	$-0.952885\pi$
$563$	−1.50184e8	+	1.50184e8i	−0.841588	+	0.841588i	0.147477	+	0.989065i	$0.452885\pi$
$564$			5.42531e7i			0.302404i
$565$	2.08126e7	+	2.08126e7i	0.115393	+	0.115393i
$566$	−3.56286e7	+	3.56286e7i	−0.196494	+	0.196494i
$567$	3.38083e8			1.85470
$568$	5.60673e7	+	5.60673e7i	0.305960	+	0.305960i
$569$	−2.12739e8	+	2.12739e8i	−1.15481	+	1.15481i	−0.169231	+	0.985576i	$0.554129\pi$
$569$	−2.12739e8	+	2.12739e8i	−1.15481	+	1.15481i	−0.985576	+	0.169231i	$0.945871\pi$
$570$	−1.64151e8	−	1.64151e8i	−0.886377	−	0.886377i
$571$	−2.11772e7			−0.113752			−0.0568762	−	0.998381i	$-0.518114\pi$
$571$	−2.11772e7			−0.113752			−0.0568762	+	0.998381i	$0.518114\pi$
$572$	1.30410e8	+	1.30410e8i	0.696821	+	0.696821i
$573$			2.01348e8i			1.07025i
$574$	4.61140e8			2.43836
$575$	6.01167e6			0.0316222
$576$	−3.20717e7			−0.167824
$577$	1.11689e8	−	1.11689e8i	0.581413	−	0.581413i	−0.353878	−	0.935291i	$-0.615137\pi$
$577$	1.11689e8	−	1.11689e8i	0.581413	−	0.581413i	0.935291	+	0.353878i	$0.115137\pi$
$578$	−8.52645e7	+	8.52645e7i	−0.441555	+	0.441555i
$579$			2.62665e8i			1.35321i
$580$	8.60664e7	+	9.89131e7i	0.441113	+	0.506956i
$581$	−2.83226e8			−1.44413
$582$	−3.64105e8	−	3.64105e8i	−1.84696	−	1.84696i
$583$	−3.38940e8	−	3.38940e8i	−1.71047	−	1.71047i
$584$		−	1.53087e6i		−	0.00768601i
$585$			6.11430e7i			0.305407i
$586$		−	4.59509e8i		−	2.28350i
$587$	−4.12531e7			−0.203959			−0.101979	−	0.994787i	$-0.532518\pi$
$587$	−4.12531e7			−0.203959			−0.101979	+	0.994787i	$0.532518\pi$
$588$	1.54221e8	−	1.54221e8i	0.758595	−	0.758595i
$589$			3.17369e7i			0.155317i
$590$	7.47782e7	−	7.47782e7i	0.364099	−	0.364099i
$591$	−2.72272e7	−	2.72272e7i	−0.131899	−	0.131899i
$592$	−2.20906e8	+	2.20906e8i	−1.06474	+	1.06474i
$593$		−	1.13009e8i		−	0.541935i	−0.962588	−	0.270968i	$-0.912656\pi$
$593$		−	1.13009e8i		−	0.541935i	0.962588	−	0.270968i	$-0.0873436\pi$
$594$	2.24433e8	+	2.24433e8i	1.07085	+	1.07085i
$595$	−2.47640e8	+	2.47640e8i	−1.17563	+	1.17563i
$596$	9.04733e7			0.427348
$597$	2.14014e8	+	2.14014e8i	1.00582	+	1.00582i
$598$	−3.22851e7	+	3.22851e7i	−0.150973	+	0.150973i
$599$	4.07936e7	+	4.07936e7i	0.189807	+	0.189807i	0.795613	−	0.605806i	$-0.207149\pi$
$599$	4.07936e7	+	4.07936e7i	0.189807	+	0.189807i	−0.605806	+	0.795613i	$0.707149\pi$
$600$	−1.44370e7			−0.0668378
$601$	3.51060e6	+	3.51060e6i	0.0161718	+	0.0161718i	0.715146	−	0.698975i	$-0.246360\pi$
$601$	3.51060e6	+	3.51060e6i	0.0161718	+	0.0161718i	−0.698975	+	0.715146i	$0.746360\pi$
$602$			2.57965e8i			1.18242i
$603$	−6.04031e7			−0.275491
$604$	−3.01010e8			−1.36606
$605$	3.35824e8			1.51651
$606$	−3.25805e8	+	3.25805e8i	−1.46400	+	1.46400i
$607$	1.11926e8	−	1.11926e8i	0.500453	−	0.500453i	−0.411125	−	0.911579i	$-0.634864\pi$
$607$	1.11926e8	−	1.11926e8i	0.500453	−	0.500453i	0.911579	+	0.411125i	$0.134864\pi$
$608$			2.41088e8i			1.07267i
$609$	2.77187e7	−	3.99119e8i	0.122722	−	1.76706i
$610$	−3.76398e8			−1.65828
$611$	−4.62561e7	−	4.62561e7i	−0.202790	−	0.202790i
$612$	5.83781e7	+	5.83781e7i	0.254680	+	0.254680i
$613$			2.17837e8i			0.945693i	0.881145	+	0.472846i	$0.156773\pi$
$613$			2.17837e8i			0.945693i	−0.881145	+	0.472846i	$0.843227\pi$
$614$			9.76042e7i			0.421661i
$615$			3.12887e8i			1.34512i
$616$	−1.99733e8			−0.854491
$617$	1.34913e8	−	1.34913e8i	0.574379	−	0.574379i	−0.358970	−	0.933349i	$-0.616872\pi$
$617$	1.34913e8	−	1.34913e8i	0.574379	−	0.574379i	0.933349	+	0.358970i	$0.116872\pi$
$618$			2.45728e8i			1.04109i
$619$	−6.76593e7	+	6.76593e7i	−0.285270	+	0.285270i	−0.835206	−	0.549937i	$-0.814652\pi$
$619$	−6.76593e7	+	6.76593e7i	−0.285270	+	0.285270i	0.549937	+	0.835206i	$0.314652\pi$
$620$	2.00571e7	+	2.00571e7i	0.0841573	+	0.0841573i
$621$	−2.35110e7	+	2.35110e7i	−0.0981740	+	0.0981740i
$622$		−	3.15780e8i		−	1.31224i
$623$	2.79634e8	+	2.79634e8i	1.15645	+	1.15645i
$624$	2.00659e8	−	2.00659e8i	0.825857	−	0.825857i
$625$	−1.98582e8			−0.813391
$626$	−1.33551e8	−	1.33551e8i	−0.544407	−	0.544407i
$627$	−2.95173e8	+	2.95173e8i	−1.19750	+	1.19750i
$628$	8.58899e7	+	8.58899e7i	0.346787	+	0.346787i
$629$	3.80596e8			1.52937
$630$	1.28903e8	+	1.28903e8i	0.515515	+	0.515515i
$631$		−	3.09818e8i		−	1.23316i	−0.787294	−	0.616578i	$-0.788518\pi$
$631$		−	3.09818e8i		−	1.23316i	0.787294	−	0.616578i	$-0.211482\pi$
$632$	9.33557e6			0.0369819
$633$	−4.38085e8			−1.72722
$634$	−1.18704e8			−0.465799
$635$	1.25886e8	−	1.25886e8i	0.491651	−	0.491651i
$636$	2.34743e8	−	2.34743e8i	0.912477	−	0.912477i
$637$			2.62976e8i			1.01742i
$638$	4.20335e8	−	3.65742e8i	1.61858	−	1.40836i
$639$	−1.30133e8			−0.498751
$640$	−1.14918e8	−	1.14918e8i	−0.438379	−	0.438379i
$641$	1.97356e7	+	1.97356e7i	0.0749335	+	0.0749335i	0.743580	−	0.668647i	$-0.233126\pi$
$641$	1.97356e7	+	1.97356e7i	0.0749335	+	0.0749335i	−0.668647	+	0.743580i	$0.733126\pi$
$642$			3.46391e8i			1.30907i
$643$		−	2.18974e8i		−	0.823684i	−0.911255	−	0.411842i	$-0.864886\pi$
$643$		−	2.18974e8i		−	0.823684i	0.911255	−	0.411842i	$-0.135114\pi$
$644$			5.76023e7i			0.215666i
$645$	−1.75031e8			−0.652284
$646$	2.67252e8	−	2.67252e8i	0.991342	−	0.991342i
$647$		−	4.53547e7i		−	0.167459i	−0.996489	−	0.0837296i	$-0.973317\pi$
$647$		−	4.53547e7i		−	0.167459i	0.996489	−	0.0837296i	$-0.0266832\pi$
$648$	8.37571e7	−	8.37571e7i	0.307820	−	0.307820i
$649$	−1.34465e8	−	1.34465e8i	−0.491898	−	0.491898i
$650$	−3.38864e7	+	3.38864e7i	−0.123392	+	0.123392i
$651$		−	8.65518e7i		−	0.313713i
$652$	−4.61010e7	−	4.61010e7i	−0.166329	−	0.166329i
$653$	−1.42202e8	+	1.42202e8i	−0.510699	+	0.510699i	−0.914741	−	0.404042i	$-0.867605\pi$
$653$	−1.42202e8	+	1.42202e8i	−0.510699	+	0.510699i	0.404042	+	0.914741i	$0.367605\pi$
$654$	−4.78313e8			−1.70993
$655$	2.74723e8	+	2.74723e8i	0.977623	+	0.977623i
$656$	2.95670e8	−	2.95670e8i	1.04736	−	1.04736i
$657$	1.77659e6	+	1.77659e6i	0.00626455	+	0.00626455i
$658$	−1.95036e8			−0.684601
$659$	−1.80256e8	−	1.80256e8i	−0.629844	−	0.629844i	0.318185	−	0.948029i	$-0.396927\pi$
$659$	−1.80256e8	−	1.80256e8i	−0.629844	−	0.629844i	−0.948029	+	0.318185i	$0.896927\pi$
$660$			3.73086e8i			1.29771i
$661$	3.29752e8			1.14178			0.570891	−	0.821026i	$-0.306598\pi$
$661$	3.29752e8			1.14178			0.570891	+	0.821026i	$0.306598\pi$
$662$	−8.13057e7			−0.280251
$663$	−3.45714e8			−1.18625
$664$	−7.01668e7	+	7.01668e7i	−0.239677	+	0.239677i
$665$	2.49704e8	−	2.49704e8i	0.849103	−	0.849103i
$666$		−	1.98110e8i		−	0.670633i
$667$	3.83142e7	+	4.40332e7i	0.129117	+	0.148389i
$668$	1.65288e8			0.554512
$669$	−4.58444e7	−	4.58444e7i	−0.153111	−	0.153111i
$670$	1.74756e8	+	1.74756e8i	0.581043	+	0.581043i
$671$			6.76832e8i			2.24034i
$672$		−	6.57488e8i		−	2.16661i
$673$			3.15353e8i			1.03455i	0.855819	+	0.517275i	$0.173054\pi$
$673$			3.15353e8i			1.03455i	−0.855819	+	0.517275i	$0.826946\pi$
$674$	2.21090e8			0.722086
$675$	−2.46772e7	+	2.46772e7i	−0.0802387	+	0.0802387i
$676$			7.25921e7i			0.234990i
$677$	2.79238e8	−	2.79238e8i	0.899929	−	0.899929i	−0.0955008	−	0.995429i	$-0.530445\pi$
$677$	2.79238e8	−	2.79238e8i	0.899929	−	0.899929i	0.995429	+	0.0955008i	$0.0304453\pi$
$678$	6.12546e7	+	6.12546e7i	0.196539	+	0.196539i
$679$	5.53872e8	−	5.53872e8i	1.76929	−	1.76929i
$680$			1.22701e8i			0.390230i
$681$	1.25208e8	+	1.25208e8i	0.396452	+	0.396452i
$682$	8.52332e7	−	8.52332e7i	0.268692	−	0.268692i
$683$	−3.28363e7			−0.103060			−0.0515302	−	0.998671i	$-0.516410\pi$
$683$	−3.28363e7			−0.103060			−0.0515302	+	0.998671i	$0.516410\pi$
$684$	−5.88648e7	−	5.88648e7i	−0.183945	−	0.183945i
$685$	3.12005e8	−	3.12005e8i	0.970711	−	0.970711i
$686$	1.05173e8	+	1.05173e8i	0.325784	+	0.325784i
$687$	5.47922e8			1.68985
$688$	1.65400e8	+	1.65400e8i	0.507891	+	0.507891i
$689$			4.00283e8i			1.22380i
$690$	−9.23639e7			−0.281161
$691$	−1.05150e8			−0.318696			−0.159348	−	0.987222i	$-0.550939\pi$
$691$	−1.05150e8			−0.318696			−0.159348	+	0.987222i	$0.550939\pi$
$692$	−4.36633e8			−1.31765
$693$	2.31791e8	−	2.31791e8i	0.696461	−	0.696461i
$694$	2.22587e8	−	2.22587e8i	0.665920	−	0.665920i
$695$		−	1.51456e8i		−	0.451160i
$696$	−9.20111e7	−	1.05745e8i	−0.272906	−	0.313641i
$697$	−5.09407e8			−1.50441
$698$	−9.22443e7	−	9.22443e7i	−0.271252	−	0.271252i
$699$	−5.06203e8	−	5.06203e8i	−1.48215	−	1.48215i
$700$			6.04594e7i			0.176266i
$701$		−	3.73558e7i		−	0.108444i	−0.998529	−	0.0542218i	$-0.982732\pi$
$701$		−	3.73558e7i		−	0.108444i	0.998529	−	0.0542218i	$-0.0172678\pi$
$702$		−	2.65053e8i		−	0.766162i
$703$	−3.83769e8			−1.10460
$704$	1.66851e8	−	1.66851e8i	0.478202	−	0.478202i
$705$		−	1.32333e8i		−	0.377661i
$706$	−1.79520e8	+	1.79520e8i	−0.510151	+	0.510151i
$707$	−4.95610e8	−	4.95610e8i	−1.40243	−	1.40243i
$708$	9.31278e7	−	9.31278e7i	0.262410	−	0.262410i
$709$			5.22937e8i			1.46727i	0.679543	+	0.733636i	$0.262178\pi$
$709$			5.22937e8i			1.46727i	−0.679543	+	0.733636i	$0.737822\pi$
$710$	3.76495e8	+	3.76495e8i	1.05192	+	1.05192i
$711$	−1.08340e7	+	1.08340e7i	−0.0301424	+	0.0301424i
$712$	1.38553e8			0.383864
$713$	8.92880e6	+	8.92880e6i	0.0246334	+	0.0246334i
$714$	−7.28840e8	+	7.28840e8i	−2.00234	+	2.00234i
$715$	−3.18093e8	−	3.18093e8i	−0.870233	−	0.870233i
$716$	−1.22024e8			−0.332435
$717$	1.33628e8	+	1.33628e8i	0.362526	+	0.362526i
$718$			1.03314e8i			0.279117i
$719$	−2.52954e7			−0.0680541			−0.0340271	−	0.999421i	$-0.510833\pi$
$719$	−2.52954e7			−0.0680541			−0.0340271	+	0.999421i	$0.510833\pi$
$720$	1.65298e8			0.442863
$721$	−3.73798e8			−0.997313
$722$	8.09202e7	−	8.09202e7i	0.215003	−	0.215003i
$723$	−2.39682e8	+	2.39682e8i	−0.634191	+	0.634191i
$724$		−	4.83404e8i		−	1.27378i
$725$	4.02146e7	+	4.62172e7i	0.105528	+	0.121280i
$726$	9.88381e8			2.58294
$727$	3.89707e8	+	3.89707e8i	1.01423	+	1.01423i	0.999897	+	0.0143299i	$0.00456152\pi$
$727$	3.89707e8	+	3.89707e8i	1.01423	+	1.01423i	0.0143299	+	0.999897i	$0.495438\pi$
$728$	1.17941e8	+	1.17941e8i	0.305682	+	0.305682i
$729$		−	1.29666e8i		−	0.334691i
$730$		−	1.02799e7i		−	0.0264254i
$731$		−	2.84966e8i		−	0.729527i
$732$	−4.68761e8			−1.19514
$733$	−3.71700e7	+	3.71700e7i	−0.0943802	+	0.0943802i	−0.752720	−	0.658340i	$-0.771259\pi$
$733$	−3.71700e7	+	3.71700e7i	−0.0943802	+	0.0943802i	0.658340	+	0.752720i	$0.271259\pi$
$734$			5.05726e8i			1.27887i
$735$	−3.76172e8	+	3.76172e8i	−0.947381	+	0.947381i
$736$	6.78274e7	+	6.78274e7i	0.170126	+	0.170126i
$737$	3.14243e8	−	3.14243e8i	0.784989	−	0.784989i
$738$			2.65160e8i			0.659687i
$739$	4.74859e8	+	4.74859e8i	1.17661	+	1.17661i	0.980603	+	0.196004i	$0.0627965\pi$
$739$	4.74859e8	+	4.74859e8i	1.17661	+	1.17661i	0.196004	+	0.980603i	$0.437203\pi$
$740$	−2.42534e8	+	2.42534e8i	−0.598519	+	0.598519i
$741$	3.48596e8			0.856776
$742$	8.43885e8	+	8.43885e8i	2.06572	+	2.06572i
$743$	−1.90856e8	+	1.90856e8i	−0.465307	+	0.465307i	−0.900390	−	0.435083i	$-0.856719\pi$
$743$	−1.90856e8	+	1.90856e8i	−0.465307	+	0.465307i	0.435083	+	0.900390i	$0.356719\pi$
$744$	−2.14424e7	−	2.14424e7i	−0.0520661	−	0.0520661i
$745$	−2.20681e8			−0.533699
$746$	2.88401e8	+	2.88401e8i	0.694674	+	0.694674i
$747$		−	1.62858e8i		−	0.390703i
$748$	−6.07417e8			−1.45138
$749$	−5.26925e8			−1.25402
$750$	−6.99972e8			−1.65919
$751$	−4.00259e8	+	4.00259e8i	−0.944977	+	0.944977i	−0.998563	−	0.0535864i	$-0.982935\pi$
$751$	−4.00259e8	+	4.00259e8i	−0.944977	+	0.944977i	0.0535864	+	0.998563i	$0.482935\pi$
$752$	−1.25052e8	+	1.25052e8i	−0.294060	+	0.294060i
$753$			1.26860e8i			0.297125i
$754$	−4.64173e8	−	3.22368e7i	−1.08284	−	0.0752034i
$755$	7.34219e8			1.70602
$756$	−2.36450e8	−	2.36450e8i	−0.547236	−	0.547236i
$757$	1.28864e7	+	1.28864e7i	0.0297060	+	0.0297060i	0.721804	−	0.692098i	$-0.243313\pi$
$757$	1.28864e7	+	1.28864e7i	0.0297060	+	0.0297060i	−0.692098	+	0.721804i	$0.743313\pi$
$758$			4.30440e8i			0.988337i
$759$			1.66087e8i			0.379848i
$760$		−	1.23724e8i		−	0.281847i
$761$	3.51811e8			0.798279			0.399140	−	0.916890i	$-0.369309\pi$
$761$	3.51811e8			0.798279			0.399140	+	0.916890i	$0.369309\pi$
$762$	3.70502e8	−	3.70502e8i	0.837385	−	0.837385i
$763$		−	7.27604e8i		−	1.63803i
$764$	2.08898e8	−	2.08898e8i	0.468440	−	0.468440i
$765$	−1.42395e8	−	1.42395e8i	−0.318061	−	0.318061i
$766$	−2.98498e8	+	2.98498e8i	−0.664133	+	0.664133i
$767$			1.58801e8i			0.351939i
$768$	−4.95755e8	−	4.95755e8i	−1.09442	−	1.09442i
$769$	−6.85218e7	+	6.85218e7i	−0.150678	+	0.150678i	−0.778421	−	0.627743i	$-0.783979\pi$
$769$	−6.85218e7	+	6.85218e7i	−0.150678	+	0.150678i	0.627743	+	0.778421i	$0.283979\pi$
$770$	−1.34122e9			−2.93784
$771$	−3.61551e8	−	3.61551e8i	−0.788872	−	0.788872i
$772$	2.72514e8	−	2.72514e8i	0.592292	−	0.592292i
$773$	−4.31731e8	−	4.31731e8i	−0.934705	−	0.934705i	0.0632903	−	0.997995i	$-0.479841\pi$
$773$	−4.31731e8	−	4.31731e8i	−0.934705	−	0.934705i	−0.997995	+	0.0632903i	$0.979841\pi$
$774$	−1.48332e8			−0.319899
$775$	9.37167e6	+	9.37167e6i	0.0201332	+	0.0201332i
$776$		−	2.74434e8i		−	0.587289i
$777$	1.04660e9			2.23110
$778$	−4.73399e8			−1.00528
$779$	5.13654e8			1.08657
$780$	2.20305e8	−	2.20305e8i	0.464238	−	0.464238i
$781$	6.77007e8	−	6.77007e8i	1.42115	−	1.42115i
$782$		−	1.50376e8i		−	0.314456i
$783$	−3.38026e8	−	2.34758e7i	−0.704149	−	0.0489030i
$784$	7.10946e8			1.47533
$785$	−2.09501e8	−	2.09501e8i	−0.433090	−	0.433090i
$786$	8.08551e8	+	8.08551e8i	1.66510	+	1.66510i
$787$			9.42596e7i			0.193375i	0.995315	+	0.0966877i	$0.0308248\pi$
$787$			9.42596e7i			0.193375i	−0.995315	+	0.0966877i	$0.969175\pi$
$788$			5.64961e7i			0.115462i
$789$			3.05811e8i			0.622619i
$790$	6.26889e7			0.127148
$791$	−9.31796e7	+	9.31796e7i	−0.188275	+	0.188275i
$792$		−	1.14848e8i		−	0.231179i
$793$	3.99665e8	−	3.99665e8i	0.801450	−	0.801450i
$794$	−2.97220e8	−	2.97220e8i	−0.593767	−	0.593767i
$795$	−5.72582e8	+	5.72582e8i	−1.13956	+	1.13956i
$796$		−	4.44076e8i		−	0.880477i
$797$	−5.61565e8	−	5.61565e8i	−1.10924	−	1.10924i	−0.993250	−	0.115989i	$-0.962996\pi$
$797$	−5.61565e8	−	5.61565e8i	−1.10924	−	1.10924i	−0.115989	−	0.993250i	$-0.537004\pi$
$798$	7.34916e8	−	7.34916e8i	1.44620	−	1.44620i
$799$	2.15450e8			0.422383
$800$	7.11916e7	+	7.11916e7i	0.139046	+	0.139046i
$801$	−1.60792e8	+	1.60792e8i	−0.312872	+	0.312872i
$802$	−2.78933e8	−	2.78933e8i	−0.540725	−	0.540725i
$803$	−1.84852e7			−0.0357007
$804$	2.17639e8	+	2.17639e8i	0.418763	+	0.418763i
$805$		−	1.40503e8i		−	0.269337i
$806$	−1.00659e8			−0.192242
$807$	3.65615e8			0.695671
$808$	−2.45566e8			−0.465516
$809$	1.64542e8	−	1.64542e8i	0.310765	−	0.310765i	−0.534441	−	0.845206i	$-0.679478\pi$
$809$	1.64542e8	−	1.64542e8i	0.310765	−	0.310765i	0.845206	+	0.534441i	$0.179478\pi$
$810$	5.62434e8	−	5.62434e8i	1.05832	−	1.05832i
$811$			5.89405e8i			1.10497i	0.833522	+	0.552486i	$0.186321\pi$
$811$			5.89405e8i			1.10497i	−0.833522	+	0.552486i	$0.813679\pi$
$812$	−4.42842e8	+	3.85326e8i	−0.827143	+	0.719714i
$813$	4.55845e8			0.848293
$814$	1.03066e9	+	1.03066e9i	1.91091	+	1.91091i
$815$	1.12449e8	+	1.12449e8i	0.207722	+	0.207722i
$816$			9.34623e8i			1.72015i
$817$			2.87342e8i			0.526906i
$818$			1.06205e8i			0.194037i
$819$	−2.73742e8			−0.498299
$820$	3.24618e8	−	3.24618e8i	0.588751	−	0.588751i
$821$		−	7.01336e8i		−	1.26735i	−0.773599	−	0.633675i	$-0.781546\pi$
$821$		−	7.01336e8i		−	1.26735i	0.773599	−	0.633675i	$-0.218454\pi$
$822$	9.18278e8	−	9.18278e8i	1.65333	−	1.65333i
$823$	−1.31731e8	−	1.31731e8i	−0.236314	−	0.236314i	0.579008	−	0.815322i	$-0.303440\pi$
$823$	−1.31731e8	−	1.31731e8i	−0.236314	−	0.236314i	−0.815322	+	0.579008i	$0.803440\pi$
$824$	−9.26052e7	+	9.26052e7i	−0.165521	+	0.165521i
$825$			1.74325e8i			0.310454i
$826$	3.34788e8	+	3.34788e8i	0.594059	+	0.594059i
$827$	−3.76428e8	+	3.76428e8i	−0.665527	+	0.665527i	−0.956677	−	0.291150i	$-0.905962\pi$
$827$	−3.76428e8	+	3.76428e8i	−0.665527	+	0.665527i	0.291150	+	0.956677i	$0.405962\pi$
$828$	−3.31218e7			−0.0583476
$829$	−3.92792e8	−	3.92792e8i	−0.689443	−	0.689443i	0.272666	−	0.962109i	$-0.412095\pi$
$829$	−3.92792e8	−	3.92792e8i	−0.689443	−	0.689443i	−0.962109	+	0.272666i	$0.912095\pi$
$830$	−4.71174e8	+	4.71174e8i	−0.824038	+	0.824038i
$831$	−1.20846e8	−	1.20846e8i	−0.210586	−	0.210586i
$832$	−1.97049e8			−0.342140
$833$	−6.12441e8	−	6.12441e8i	−1.05957	−	1.05957i
$834$		−	4.45756e8i		−	0.768421i
$835$	−4.03167e8			−0.692509
$836$	6.12481e8			1.04827
$837$	−7.33033e7			−0.125011
$838$	−4.75461e7	+	4.75461e7i	−0.0807947	+	0.0807947i
$839$	−4.70437e8	+	4.70437e8i	−0.796555	+	0.796555i	−0.982551	−	0.185995i	$-0.940449\pi$
$839$	−4.70437e8	+	4.70437e8i	−0.796555	+	0.796555i	0.185995	+	0.982551i	$0.440449\pi$
$840$			3.37415e8i			0.569281i
$841$	−8.22241e7	+	5.89113e8i	−0.138233	+	0.990400i
$842$	−1.54707e9			−2.59164
$843$	5.29954e8	+	5.29954e8i	0.884617	+	0.884617i
$844$	4.54511e8	+	4.54511e8i	0.755992	+	0.755992i
$845$		−	1.77065e8i		−	0.293470i
$846$		−	1.12148e8i		−	0.185216i
$847$			1.50351e9i			2.47432i
$848$	1.08215e9			1.77460
$849$	1.08230e8	−	1.08230e8i	0.176858	−	0.176858i
$850$		−	1.57835e8i		−	0.257008i
$851$	−1.07969e8	+	1.07969e8i	−0.175190	+	0.175190i
$852$	4.68883e8	+	4.68883e8i	0.758133	+	0.758133i
$853$	1.54279e8	−	1.54279e8i	0.248576	−	0.248576i	−0.571810	−	0.820386i	$-0.693759\pi$
$853$	1.54279e8	−	1.54279e8i	0.248576	−	0.248576i	0.820386	+	0.571810i	$0.193759\pi$
$854$		−	1.68516e9i		−	2.70563i
$855$	1.43582e8	+	1.43582e8i	0.229722	+	0.229722i
$856$	−1.30541e8	+	1.30541e8i	−0.208126	+	0.208126i
$857$	8.26660e8			1.31336			0.656681	−	0.754169i	$-0.271960\pi$
$857$	8.26660e8			1.31336			0.656681	+	0.754169i	$0.271960\pi$
$858$	−9.36195e8	−	9.36195e8i	−1.48219	−	1.48219i
$859$	4.97255e8	−	4.97255e8i	0.784513	−	0.784513i	−0.196076	−	0.980589i	$-0.562820\pi$
$859$	4.97255e8	−	4.97255e8i	0.784513	−	0.784513i	0.980589	+	0.196076i	$0.0628199\pi$
$860$	1.81594e8	+	1.81594e8i	0.285500	+	0.285500i
$861$	−1.40082e9			−2.19469
$862$	5.16785e8	+	5.16785e8i	0.806841	+	0.806841i
$863$		−	5.96593e8i		−	0.928208i	−0.885781	−	0.464104i	$-0.846376\pi$
$863$		−	5.96593e8i		−	0.928208i	0.885781	−	0.464104i	$-0.153624\pi$
$864$	−5.56846e8			−0.863364
$865$	1.06503e9			1.64556
$866$	1.05029e9			1.61716
$867$	2.59010e8	−	2.59010e8i	0.397429	−	0.397429i
$868$	−8.97970e7	+	8.97970e7i	−0.137310	+	0.137310i
$869$		−	1.12726e8i		−	0.171777i
$870$	−6.17860e8	−	7.10086e8i	−0.938280	−	1.07833i
$871$	−3.71117e8			−0.561638
$872$	−1.80257e8	−	1.80257e8i	−0.271859	−	0.271859i
$873$	3.18481e8	+	3.18481e8i	0.478675	+	0.478675i
$874$			1.51630e8i			0.227118i
$875$		−	1.06479e9i		−	1.58942i
$876$		−	1.28025e7i		−	0.0190450i
$877$	1.94104e7			0.0287763			0.0143882	−	0.999896i	$-0.495420\pi$
$877$	1.94104e7			0.0287763			0.0143882	+	0.999896i	$0.495420\pi$
$878$	−4.34383e8	+	4.34383e8i	−0.641785	+	0.641785i
$879$			1.39586e9i			2.05531i
$880$	−8.59952e8	+	8.59952e8i	−1.26190	+	1.26190i
$881$	−9.51131e7	−	9.51131e7i	−0.139095	−	0.139095i	0.634131	−	0.773226i	$-0.281358\pi$
$881$	−9.51131e7	−	9.51131e7i	−0.139095	−	0.139095i	−0.773226	+	0.634131i	$0.781358\pi$
$882$	−3.18792e8	+	3.18792e8i	−0.464624	+	0.464624i
$883$		−	1.37280e8i		−	0.199400i	−0.995018	−	0.0996999i	$-0.968212\pi$
$883$		−	1.37280e8i		−	0.199400i	0.995018	−	0.0996999i	$-0.0317883\pi$
$884$	3.58676e8	+	3.58676e8i	0.519213	+	0.519213i
$885$	−2.27156e8	+	2.27156e8i	−0.327713	+	0.327713i
$886$	−1.51695e9			−2.18107
$887$	2.51357e7	+	2.51357e7i	0.0360181	+	0.0360181i	0.724886	−	0.688868i	$-0.241892\pi$
$887$	2.51357e7	+	2.51357e7i	0.0360181	+	0.0360181i	−0.688868	+	0.724886i	$0.741892\pi$
$888$	2.59286e8	−	2.59286e8i	0.370289	−	0.370289i
$889$	5.63602e8	+	5.63602e8i	0.802171	+	0.802171i
$890$	9.30395e8			1.31977
$891$	−1.01136e9	−	1.01136e9i	−1.42979	−	1.42979i
$892$			9.51265e7i			0.134032i
$893$	−2.17246e8			−0.305069
$894$	−6.49497e8			−0.909002
$895$	2.97640e8			0.415166
$896$	5.14498e8	−	5.14498e8i	0.715253	−	0.715253i
$897$	9.80733e7	−	9.80733e7i	0.135886	−	0.135886i
$898$		−	8.63048e8i		−	1.19181i
$899$	−8.91544e6	+	1.28372e8i	−0.0122705	+	0.176682i
$900$	−3.47647e7			−0.0476882
$901$	−9.32213e8	−	9.32213e8i	−1.27450	−	1.27450i
$902$	−1.37948e9	−	1.37948e9i	−1.87973	−	1.87973i
$903$		−	7.83629e8i		−	1.06426i
$904$			4.61688e7i			0.0624948i
$905$			1.17911e9i			1.59078i
$906$	2.16092e9			2.90572
$907$	8.31682e8	−	8.31682e8i	1.11464	−	1.11464i	0.122128	−	0.992514i	$-0.461028\pi$
$907$	8.31682e8	−	8.31682e8i	1.11464	−	1.11464i	0.992514	−	0.122128i	$-0.0389719\pi$
$908$		−	2.59805e8i		−	0.347049i
$909$	2.84980e8	−	2.84980e8i	0.379423	−	0.379423i
$910$	7.91981e8	+	7.91981e8i	1.05097	+	1.05097i
$911$	−6.20355e8	+	6.20355e8i	−0.820513	+	0.820513i	−0.986181	−	0.165669i	$-0.947022\pi$
$911$	−6.20355e8	+	6.20355e8i	−0.820513	+	0.820513i	0.165669	+	0.986181i	$0.447022\pi$
$912$		−	9.42415e8i		−	1.24239i
$913$	8.47257e8	+	8.47257e8i	1.11328	+	1.11328i
$914$	−3.82181e8	+	3.82181e8i	−0.500530	+	0.500530i
$915$	1.14339e9			1.49256
$916$	−5.68466e8	−	5.68466e8i	−0.739637	−	0.739637i
$917$	−1.22996e9	+	1.22996e9i	−1.59508	+	1.59508i
$918$	6.17277e8	+	6.17277e8i	0.797906	+	0.797906i
$919$	−7.27880e8			−0.937807			−0.468904	−	0.883249i	$-0.655351\pi$
$919$	−7.27880e8			−0.937807			−0.468904	+	0.883249i	$0.655351\pi$
$920$	−3.48083e7	−	3.48083e7i	−0.0447012	−	0.0447012i
$921$		−	2.96495e8i		−	0.379523i
$922$	−4.68322e8			−0.597520
$923$	−7.99537e8			−1.01679
$924$	−1.67034e9			−2.11733
$925$	−1.13324e8	+	1.13324e8i	−0.143185	+	0.143185i
$926$	−4.45793e8	+	4.45793e8i	−0.561436	+	0.561436i
$927$		−	2.14937e8i		−	0.269819i
$928$	−6.77259e7	+	9.75177e8i	−0.0847444	+	1.22022i
$929$	2.18756e8			0.272843			0.136421	−	0.990651i	$-0.456440\pi$
$929$	2.18756e8			0.272843			0.136421	+	0.990651i	$0.456440\pi$
$930$	−1.43987e8	−	1.43987e8i	−0.179009	−	0.179009i
$931$	6.17547e8	+	6.17547e8i	0.765281	+	0.765281i
$932$			1.05037e9i			1.29746i
$933$			9.59253e8i			1.18110i
$934$			8.89024e8i			1.09112i
$935$	1.48160e9			1.81258
$936$	−6.78171e7	+	6.78171e7i	−0.0827012	+	0.0827012i
$937$		−	9.54406e8i		−	1.16015i	−0.814563	−	0.580075i	$-0.803023\pi$
$937$		−	9.54406e8i		−	1.16015i	0.814563	−	0.580075i	$-0.196977\pi$
$938$	−7.82397e8	+	7.82397e8i	−0.948023	+	0.948023i
$939$	4.05692e8	+	4.05692e8i	0.490004	+	0.490004i
$940$	−1.37295e8	+	1.37295e8i	−0.165300	+	0.165300i
$941$			7.95968e7i			0.0955272i	0.998859	+	0.0477636i	$0.0152094\pi$
$941$			7.95968e7i			0.0955272i	−0.998859	+	0.0477636i	$0.984791\pi$
$942$	−6.16594e8	−	6.16594e8i	−0.737643	−	0.737643i
$943$	1.44510e8	−	1.44510e8i	0.172331	−	0.172331i
$944$	4.29313e8			0.510338
$945$	5.76746e8	+	5.76746e8i	0.683422	+	0.683422i
$946$	7.71690e8	−	7.71690e8i	0.911527	−	0.911527i
$947$	−7.97649e8	−	7.97649e8i	−0.939208	−	0.939208i	0.0590470	−	0.998255i	$-0.481194\pi$
$947$	−7.97649e8	−	7.97649e8i	−0.939208	−	0.939208i	−0.998255	+	0.0590470i	$0.981194\pi$
$948$	7.80720e7			0.0916369
$949$	1.09154e7	+	1.09154e7i	0.0127714	+	0.0127714i
$950$			1.59151e8i			0.185626i
$951$	3.60591e8			0.419250
$952$	−5.49342e8			−0.636695
$953$	−6.72653e8			−0.777164			−0.388582	−	0.921414i	$-0.627035\pi$
$953$	−6.72653e8			−0.777164			−0.388582	+	0.921414i	$0.627035\pi$
$954$	−4.85241e8	+	4.85241e8i	−0.558872	+	0.558872i
$955$	−5.09540e8	+	5.09540e8i	−0.585017	+	0.585017i
$956$		−	2.77276e8i		−	0.317350i
$957$	−1.27686e9	+	1.11103e9i	−1.45683	+	1.26762i
$958$	1.55909e9			1.77326
$959$	1.39687e9	+	1.39687e9i	1.58380	+	1.58380i
$960$	−2.81867e8	−	2.81867e8i	−0.318589	−	0.318589i
$961$		−	8.59665e8i		−	0.968633i
$962$		−	1.21719e9i		−	1.36721i
$963$		−	3.02987e8i		−	0.339269i
$964$	4.97337e8			0.555162
$965$	−6.64711e8	+	6.64711e8i	−0.739692	+	0.739692i
$966$		−	4.13520e8i		−	0.458739i
$967$	8.05364e8	−	8.05364e8i	0.890662	−	0.890662i	−0.103923	−	0.994585i	$-0.533140\pi$
$967$	8.05364e8	−	8.05364e8i	0.890662	−	0.890662i	0.994585	+	0.103923i	$0.0331396\pi$
$968$	3.72481e8	+	3.72481e8i	0.410656	+	0.410656i
$969$	−8.11839e8	+	8.11839e8i	−0.892275	+	0.892275i
$970$		−	1.84284e9i		−	2.01917i
$971$	6.60712e8	+	6.60712e8i	0.721696	+	0.721696i	0.968951	−	0.247255i	$-0.0795284\pi$
$971$	6.60712e8	+	6.60712e8i	0.721696	+	0.721696i	−0.247255	+	0.968951i	$0.579528\pi$
$972$	3.64230e8	−	3.64230e8i	0.396623	−	0.396623i
$973$	6.78078e8			0.736107
$974$	1.58532e7	+	1.58532e7i	0.0171569	+	0.0171569i
$975$	1.02938e8	−	1.02938e8i	0.111061	−	0.111061i
$976$	−1.08048e9	−	1.08048e9i	−1.16216	−	1.16216i
$977$	3.05192e8			0.327258			0.163629	−	0.986522i	$-0.447680\pi$
$977$	3.05192e8			0.327258			0.163629	+	0.986522i	$0.447680\pi$
$978$	3.30954e8	+	3.30954e8i	0.353794	+	0.353794i
$979$		−	1.67302e9i		−	1.78301i
$980$	7.80553e8			0.829324
$981$	4.18378e8			0.443162
$982$	1.42837e9			1.50836
$983$	3.82172e8	−	3.82172e8i	0.402345	−	0.402345i	−0.476714	−	0.879059i	$-0.658172\pi$
$983$	3.82172e8	−	3.82172e8i	0.402345	−	0.402345i	0.879059	+	0.476714i	$0.158172\pi$
$984$	−3.47040e8	+	3.47040e8i	−0.364246	+	0.364246i
$985$		−	1.37804e8i		−	0.144196i
$986$	1.15608e9	−	1.00593e9i	1.20603	−	1.04939i
$987$	5.92467e8			0.616187
$988$	−3.61666e8	−	3.61666e8i	−0.375005	−	0.375005i
$989$	8.08403e7	+	8.08403e7i	0.0835678	+	0.0835678i
$990$		−	7.71213e8i		−	0.794820i
$991$		−	8.99097e8i		−	0.923816i	−0.886928	−	0.461908i	$-0.847165\pi$
$991$		−	8.99097e8i		−	0.923816i	0.886928	−	0.461908i	$-0.152835\pi$
$992$			2.11474e8i			0.216632i
$993$	2.46985e8			0.252245
$994$	−1.68560e9	+	1.68560e9i	−1.71631	+	1.71631i
$995$			1.08318e9i			1.09959i
$996$	−5.86794e8	+	5.86794e8i	−0.593893	+	0.593893i
$997$	6.98275e8	+	6.98275e8i	0.704597	+	0.704597i	0.965394	−	0.260797i	$-0.0839852\pi$
$997$	6.98275e8	+	6.98275e8i	0.704597	+	0.704597i	−0.260797	+	0.965394i	$0.583985\pi$
$998$	1.44807e9	−	1.44807e9i	1.45679	−	1.45679i
$999$		−	8.86399e8i		−	0.889063i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.7.c.a.12.12	✓	28
29.17	odd	4	inner	29.7.c.a.17.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.7.c.a.12.12	✓	28	1.1	even	1	trivial
29.7.c.a.17.12	yes	28	29.17	odd	4	inner

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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	29.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(7.44805 + 7.44805i) q^{2} +(-22.6252 - 22.6252i) q^{3} +46.9470i q^{4} -114.512i q^{5} -337.027i q^{6} +512.680 q^{7} +(127.012 - 127.012i) q^{8} +294.796i q^{9} +O(q^{10})\)	\(q+(7.44805 + 7.44805i) q^{2} +(-22.6252 - 22.6252i) q^{3} +46.9470i q^{4} -114.512i q^{5} -337.027i q^{6} +512.680 q^{7} +(127.012 - 127.012i) q^{8} +294.796i q^{9} +(852.893 - 852.893i) q^{10} +(-1533.66 - 1533.66i) q^{11} +(1062.18 - 1062.18i) q^{12} +1811.23i q^{13} +(3818.47 + 3818.47i) q^{14} +(-2590.86 + 2590.86i) q^{15} +4896.59 q^{16} +(-4218.14 - 4218.14i) q^{17} +(-2195.65 + 2195.65i) q^{18} +(4253.31 + 4253.31i) q^{19} +5376.00 q^{20} +(-11599.5 - 11599.5i) q^{21} -22845.5i q^{22} +2393.24 q^{23} -5747.33 q^{24} +2511.94 q^{25} +(-13490.1 + 13490.1i) q^{26} +(-9823.94 + 9823.94i) q^{27} +24068.8i q^{28} +(16009.4 + 18399.0i) q^{29} -38593.7 q^{30} +(3730.85 + 3730.85i) q^{31} +(28341.3 + 28341.3i) q^{32} +69398.5i q^{33} -62833.9i q^{34} -58708.2i q^{35} -13839.8 q^{36} +(-45114.2 + 45114.2i) q^{37} +63357.7i q^{38} +(40979.4 - 40979.4i) q^{39} +(-14544.4 - 14544.4i) q^{40} +(60382.8 - 60382.8i) q^{41} -172787. i q^{42} +(33778.6 + 33778.6i) q^{43} +(72000.5 - 72000.5i) q^{44} +33757.7 q^{45} +(17825.0 + 17825.0i) q^{46} +(-25538.5 + 25538.5i) q^{47} +(-110786. - 110786. i) q^{48} +145192. q^{49} +(18709.1 + 18709.1i) q^{50} +190872. i q^{51} -85031.7 q^{52} +221001. q^{53} -146338. q^{54} +(-175623. + 175623. i) q^{55} +(65116.5 - 65116.5i) q^{56} -192464. i q^{57} +(-17798.3 + 256275. i) q^{58} +87675.9 q^{59} +(-121633. - 121633. i) q^{60} +(-220659. - 220659. i) q^{61} +55575.1i q^{62} +151136. i q^{63} +108793. i q^{64} +207408. q^{65} +(-516884. + 516884. i) q^{66} +204898. i q^{67} +(198029. - 198029. i) q^{68} +(-54147.4 - 54147.4i) q^{69} +(437262. - 437262. i) q^{70} +441433. i q^{71} +(37442.6 + 37442.6i) q^{72} +(6026.50 - 6026.50i) q^{73} -672026. q^{74} +(-56833.1 - 56833.1i) q^{75} +(-199680. + 199680. i) q^{76} +(-786276. - 786276. i) q^{77} +610433. q^{78} +(36750.7 + 36750.7i) q^{79} -560719. i q^{80} +659443. q^{81} +899469. q^{82} -552442. q^{83} +(544560. - 544560. i) q^{84} +(-483029. + 483029. i) q^{85} +503170. i q^{86} +(54066.3 - 778495. i) q^{87} -389586. q^{88} +(545435. + 545435. i) q^{89} +(251429. + 251429. i) q^{90} +928582. i q^{91} +112355. i q^{92} -168822. i q^{93} -380425. q^{94} +(487056. - 487056. i) q^{95} -1.28245e6i q^{96} +(1.08035e6 - 1.08035e6i) q^{97} +(1.08140e6 + 1.08140e6i) q^{98} +(452116. - 452116. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8}+O(q^{10}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8	\( 28 q - 2 q^{3} - 4 q^{7} + 354 q^{8} - 3714 q^{10} + 1934 q^{11} - 2706 q^{12} + 2648 q^{14} + 16280 q^{15} - 36632 q^{16} - 5236 q^{17} + 5258 q^{18} + 6718 q^{19} + 24828 q^{20} + 7380 q^{21} - 21524 q^{23} + 90648 q^{24} - 73196 q^{25} - 5394 q^{26} + 5824 q^{27} - 12510 q^{29} - 1780 q^{30} + 1150 q^{31} + 104646 q^{32} - 32904 q^{36} - 256832 q^{37} + 127752 q^{39} - 256374 q^{40} + 265716 q^{41} + 80590 q^{43} + 188482 q^{44} - 78008 q^{45} + 405572 q^{46} - 445250 q^{47} - 1016886 q^{48} + 532764 q^{49} - 80230 q^{50} + 619608 q^{52} + 143428 q^{53} + 373816 q^{54} - 533304 q^{55} - 619392 q^{56} + 326848 q^{58} - 957340 q^{59} + 1790622 q^{60} - 115640 q^{61} - 643584 q^{65} - 1821654 q^{66} + 1457028 q^{68} - 1049340 q^{69} + 3024084 q^{70} + 1480560 q^{72} - 627512 q^{73} - 3652060 q^{74} + 586518 q^{75} - 1343752 q^{76} - 115820 q^{77} + 1820304 q^{78} + 235966 q^{79} + 2710496 q^{81} + 796544 q^{82} + 3881892 q^{83} + 219332 q^{84} - 3064608 q^{85} + 900526 q^{87} - 9844332 q^{88} + 3821436 q^{89} - 4192912 q^{90} - 648556 q^{94} - 620200 q^{95} - 620288 q^{97} + 4735296 q^{98} + 4021770 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 - 4 * q^7 + 354 * q^8 - 3714 * q^10 + 1934 * q^11 - 2706 * q^12 + 2648 * q^14 + 16280 * q^15 - 36632 * q^16 - 5236 * q^17 + 5258 * q^18 + 6718 * q^19 + 24828 * q^20 + 7380 * q^21 - 21524 * q^23 + 90648 * q^24 - 73196 * q^25 - 5394 * q^26 + 5824 * q^27 - 12510 * q^29 - 1780 * q^30 + 1150 * q^31 + 104646 * q^32 - 32904 * q^36 - 256832 * q^37 + 127752 * q^39 - 256374 * q^40 + 265716 * q^41 + 80590 * q^43 + 188482 * q^44 - 78008 * q^45 + 405572 * q^46 - 445250 * q^47 - 1016886 * q^48 + 532764 * q^49 - 80230 * q^50 + 619608 * q^52 + 143428 * q^53 + 373816 * q^54 - 533304 * q^55 - 619392 * q^56 + 326848 * q^58 - 957340 * q^59 + 1790622 * q^60 - 115640 * q^61 - 643584 * q^65 - 1821654 * q^66 + 1457028 * q^68 - 1049340 * q^69 + 3024084 * q^70 + 1480560 * q^72 - 627512 * q^73 - 3652060 * q^74 + 586518 * q^75 - 1343752 * q^76 - 115820 * q^77 + 1820304 * q^78 + 235966 * q^79 + 2710496 * q^81 + 796544 * q^82 + 3881892 * q^83 + 219332 * q^84 - 3064608 * q^85 + 900526 * q^87 - 9844332 * q^88 + 3821436 * q^89 - 4192912 * q^90 - 648556 * q^94 - 620200 * q^95 - 620288 * q^97 + 4735296 * q^98 + 4021770 * q^99

Introduction

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