LMFDB - Embedded newform 187.2.g.f.86.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.4
Character	$\chi$	$=$	187.86
Dual form			187.2.g.f.137.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.343162 + 1.05614i) q^{2} +(-2.58082 + 1.87507i) q^{3} +(0.620355 + 0.450715i) q^{4} +(0.625693 + 1.92569i) q^{5} +(-1.09471 - 3.36916i) q^{6} +(2.66865 + 1.93889i) q^{7} +(-2.48572 + 1.80598i) q^{8} +(2.21766 - 6.82526i) q^{9} +O(q^{10})$	\(q+(-0.343162 + 1.05614i) q^{2} +(-2.58082 + 1.87507i) q^{3} +(0.620355 + 0.450715i) q^{4} +(0.625693 + 1.92569i) q^{5} +(-1.09471 - 3.36916i) q^{6} +(2.66865 + 1.93889i) q^{7} +(-2.48572 + 1.80598i) q^{8} +(2.21766 - 6.82526i) q^{9} -2.24851 q^{10} +(-3.19829 - 0.878039i) q^{11} -2.44615 q^{12} +(0.947284 - 2.91544i) q^{13} +(-2.96352 + 2.15313i) q^{14} +(-5.22560 - 3.79662i) q^{15} +(-0.580462 - 1.78648i) q^{16} +(0.309017 + 0.951057i) q^{17} +(6.44744 + 4.68434i) q^{18} +(-0.142964 + 0.103869i) q^{19} +(-0.479783 + 1.47662i) q^{20} -10.5229 q^{21} +(2.02487 - 3.07654i) q^{22} +7.73263 q^{23} +(3.02884 - 9.32181i) q^{24} +(0.728309 - 0.529148i) q^{25} +(2.75405 + 2.00093i) q^{26} +(4.11713 + 12.6712i) q^{27} +(0.781627 + 2.40560i) q^{28} +(-4.10416 - 2.98185i) q^{29} +(5.80300 - 4.21613i) q^{30} +(-2.23860 + 6.88969i) q^{31} -4.05907 q^{32} +(9.90058 - 3.73096i) q^{33} -1.11049 q^{34} +(-2.06393 + 6.35213i) q^{35} +(4.45198 - 3.23456i) q^{36} +(3.97603 + 2.88876i) q^{37} +(-0.0606411 - 0.186634i) q^{38} +(3.02190 + 9.30044i) q^{39} +(-5.03305 - 3.65673i) q^{40} +(1.21025 - 0.879300i) q^{41} +(3.61104 - 11.1136i) q^{42} +3.10597 q^{43} +(-1.58833 - 1.98621i) q^{44} +14.5309 q^{45} +(-2.65354 + 8.16676i) q^{46} +(-6.38953 + 4.64226i) q^{47} +(4.84784 + 3.52216i) q^{48} +(1.19929 + 3.69104i) q^{49} +(0.308928 + 0.950782i) q^{50} +(-2.58082 - 1.87507i) q^{51} +(1.90168 - 1.38165i) q^{52} +(0.0437654 - 0.134696i) q^{53} -14.7955 q^{54} +(-0.310320 - 6.70828i) q^{55} -10.1351 q^{56} +(0.174201 - 0.536134i) q^{57} +(4.55765 - 3.31133i) q^{58} +(0.643032 + 0.467190i) q^{59} +(-1.53054 - 4.71051i) q^{60} +(-0.307782 - 0.947257i) q^{61} +(-6.50830 - 4.72856i) q^{62} +(19.1516 - 13.9144i) q^{63} +(2.55384 - 7.85991i) q^{64} +6.20693 q^{65} +(0.542933 + 11.7368i) q^{66} -10.5393 q^{67} +(-0.236955 + 0.729271i) q^{68} +(-19.9565 + 14.4992i) q^{69} +(-6.00050 - 4.35962i) q^{70} +(1.00568 + 3.09517i) q^{71} +(6.81381 + 20.9707i) q^{72} +(5.28280 + 3.83818i) q^{73} +(-4.41536 + 3.20795i) q^{74} +(-0.887442 + 2.73126i) q^{75} -0.135504 q^{76} +(-6.83270 - 8.54430i) q^{77} -10.8596 q^{78} +(5.23836 - 16.1220i) q^{79} +(3.07700 - 2.23557i) q^{80} +(-16.9673 - 12.3275i) q^{81} +(0.513354 + 1.57994i) q^{82} +(3.42234 + 10.5329i) q^{83} +(-6.52791 - 4.74280i) q^{84} +(-1.63809 + 1.19014i) q^{85} +(-1.06585 + 3.28035i) q^{86} +16.1833 q^{87} +(9.53577 - 3.59349i) q^{88} +16.9672 q^{89} +(-4.98645 + 15.3467i) q^{90} +(8.18068 - 5.94361i) q^{91} +(4.79698 + 3.48521i) q^{92} +(-7.14126 - 21.9785i) q^{93} +(-2.71025 - 8.34130i) q^{94} +(-0.289471 - 0.210313i) q^{95} +(10.4757 - 7.61105i) q^{96} +(-2.09799 + 6.45696i) q^{97} -4.30982 q^{98} +(-13.0856 + 19.8820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.343162	+	1.05614i	−0.242652	+	0.746806i	0.753362	+	0.657606i	$0.228431\pi$
$2$	−0.343162	+	1.05614i	−0.242652	+	0.746806i	−0.996014	+	0.0891998i	$0.971569\pi$
$3$	−2.58082	+	1.87507i	−1.49003	+	1.08257i	−0.515888	+	0.856656i	$0.672538\pi$
$3$	−2.58082	+	1.87507i	−1.49003	+	1.08257i	−0.974146	+	0.225918i	$0.927462\pi$
$4$	0.620355	+	0.450715i	0.310178	+	0.225357i
$5$	0.625693	+	1.92569i	0.279819	+	0.861193i	0.987904	+	0.155066i	$0.0495591\pi$
$5$	0.625693	+	1.92569i	0.279819	+	0.861193i	−0.708085	+	0.706127i	$0.750441\pi$
$6$	−1.09471	−	3.36916i	−0.446913	−	1.37546i
$7$	2.66865	+	1.93889i	1.00866	+	0.732831i	0.963927	−	0.266168i	$-0.0857577\pi$
$7$	2.66865	+	1.93889i	1.00866	+	0.732831i	0.0447287	+	0.998999i	$0.485758\pi$
$8$	−2.48572	+	1.80598i	−0.878835	+	0.638511i
$9$	2.21766	−	6.82526i	0.739221	−	2.27509i
$10$	−2.24851			−0.711043
$11$	−3.19829	−	0.878039i	−0.964320	−	0.264739i
$11$	−3.19829	−	0.878039i	−0.964320	−	0.264739i
$12$	−2.44615			−0.706141
$13$	0.947284	−	2.91544i	0.262729	−	0.808597i	−0.729479	−	0.684004i	$-0.760237\pi$
$13$	0.947284	−	2.91544i	0.262729	−	0.808597i	0.992208	−	0.124594i	$-0.0397628\pi$
$14$	−2.96352	+	2.15313i	−0.792035	+	0.575447i
$15$	−5.22560	−	3.79662i	−1.34924	−	0.980283i
$16$	−0.580462	−	1.78648i	−0.145115	−	0.446619i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	6.44744	+	4.68434i	1.51968	+	1.10411i
$19$	−0.142964	+	0.103869i	−0.0327981	+	0.0238292i	−0.604064	−	0.796936i	$-0.706453\pi$
$19$	−0.142964	+	0.103869i	−0.0327981	+	0.0238292i	0.571265	+	0.820765i	$0.306453\pi$
$20$	−0.479783	+	1.47662i	−0.107283	+	0.330182i
$21$	−10.5229			−2.29627
$22$	2.02487	−	3.07654i	0.431703	−	0.655921i
$23$	7.73263			1.61236			0.806182	−	0.591668i	$-0.201530\pi$
$23$	7.73263			1.61236			0.806182	+	0.591668i	$0.201530\pi$
$24$	3.02884	−	9.32181i	0.618259	−	1.90281i
$25$	0.728309	−	0.529148i	0.145662	−	0.105830i
$26$	2.75405	+	2.00093i	0.540114	+	0.392416i
$27$	4.11713	+	12.6712i	0.792342	+	2.43858i
$28$	0.781627	+	2.40560i	0.147714	+	0.454616i
$29$	−4.10416	−	2.98185i	−0.762124	−	0.553715i	0.137437	−	0.990510i	$-0.456113\pi$
$29$	−4.10416	−	2.98185i	−0.762124	−	0.553715i	−0.899561	+	0.436795i	$0.856113\pi$
$30$	5.80300	−	4.21613i	1.05948	−	0.769756i
$31$	−2.23860	+	6.88969i	−0.402064	+	1.23742i	0.521259	+	0.853399i	$0.325463\pi$
$31$	−2.23860	+	6.88969i	−0.402064	+	1.23742i	−0.923322	+	0.384026i	$0.874537\pi$
$32$	−4.05907			−0.717549
$33$	9.90058	−	3.73096i	1.72347	−	0.649478i
$34$	−1.11049			−0.190448
$35$	−2.06393	+	6.35213i	−0.348868	+	1.07371i
$36$	4.45198	−	3.23456i	0.741997	−	0.539093i
$37$	3.97603	+	2.88876i	0.653656	+	0.474909i	0.864515	−	0.502608i	$-0.167626\pi$
$37$	3.97603	+	2.88876i	0.653656	+	0.474909i	−0.210859	+	0.977517i	$0.567626\pi$
$38$	−0.0606411	−	0.186634i	−0.00983728	−	0.0302760i
$39$	3.02190	+	9.30044i	0.483890	+	1.48926i
$40$	−5.03305	−	3.65673i	−0.795795	−	0.578179i
$41$	1.21025	−	0.879300i	0.189010	−	0.137324i	−0.489256	−	0.872140i	$-0.662732\pi$
$41$	1.21025	−	0.879300i	0.189010	−	0.137324i	0.678266	+	0.734816i	$0.262732\pi$
$42$	3.61104	−	11.1136i	0.557196	−	1.71487i
$43$	3.10597			0.473656			0.236828	−	0.971552i	$-0.423892\pi$
$43$	3.10597			0.473656			0.236828	+	0.971552i	$0.423892\pi$
$44$	−1.58833	−	1.98621i	−0.239450	−	0.299433i
$45$	14.5309			2.16614
$46$	−2.65354	+	8.16676i	−0.391243	+	1.20412i
$47$	−6.38953	+	4.64226i	−0.932008	+	0.677144i	−0.946484	−	0.322752i	$-0.895392\pi$
$47$	−6.38953	+	4.64226i	−0.932008	+	0.677144i	0.0144755	+	0.999895i	$0.495392\pi$
$48$	4.84784	+	3.52216i	0.699725	+	0.508380i
$49$	1.19929	+	3.69104i	0.171327	+	0.527291i
$50$	0.308928	+	0.950782i	0.0436890	+	0.134461i
$51$	−2.58082	−	1.87507i	−0.361386	−	0.262563i
$52$	1.90168	−	1.38165i	0.263716	−	0.191601i
$53$	0.0437654	−	0.134696i	0.00601164	−	0.0185019i	−0.948006	−	0.318253i	$-0.896904\pi$
$53$	0.0437654	−	0.134696i	0.00601164	−	0.0185019i	0.954017	+	0.299751i	$0.0969037\pi$
$54$	−14.7955			−2.01341
$55$	−0.310320	−	6.70828i	−0.0418436	−	0.904545i
$56$	−10.1351			−1.35436
$57$	0.174201	−	0.536134i	0.0230734	−	0.0710127i
$58$	4.55765	−	3.31133i	0.598449	−	0.434798i
$59$	0.643032	+	0.467190i	0.0837157	+	0.0608230i	0.628856	−	0.777522i	$-0.283524\pi$
$59$	0.643032	+	0.467190i	0.0837157	+	0.0608230i	−0.545140	+	0.838345i	$0.683524\pi$
$60$	−1.53054	−	4.71051i	−0.197591	−	0.608124i
$61$	−0.307782	−	0.947257i	−0.0394075	−	0.121284i	0.929417	−	0.369030i	$-0.120310\pi$
$61$	−0.307782	−	0.947257i	−0.0394075	−	0.121284i	−0.968825	+	0.247746i	$0.920310\pi$
$62$	−6.50830	−	4.72856i	−0.826555	−	0.600527i
$63$	19.1516	−	13.9144i	2.41287	−	1.75306i
$64$	2.55384	−	7.85991i	0.319230	−	0.982489i
$65$	6.20693			0.769875
$66$	0.542933	+	11.7368i	0.0668305	+	1.44469i
$67$	−10.5393			−1.28758			−0.643789	−	0.765203i	$-0.722639\pi$
$67$	−10.5393			−1.28758			−0.643789	+	0.765203i	$0.722639\pi$
$68$	−0.236955	+	0.729271i	−0.0287350	+	0.0884372i
$69$	−19.9565	+	14.4992i	−2.40248	+	1.74550i
$70$	−6.00050	−	4.35962i	−0.717197	−	0.521074i
$71$	1.00568	+	3.09517i	0.119352	+	0.367329i	0.992830	−	0.119535i	$-0.0381405\pi$
$71$	1.00568	+	3.09517i	0.119352	+	0.367329i	−0.873477	+	0.486865i	$0.838141\pi$
$72$	6.81381	+	20.9707i	0.803015	+	2.47143i
$73$	5.28280	+	3.83818i	0.618306	+	0.449225i	0.852329	−	0.523006i	$-0.175189\pi$
$73$	5.28280	+	3.83818i	0.618306	+	0.449225i	−0.234024	+	0.972231i	$0.575189\pi$
$74$	−4.41536	+	3.20795i	−0.513276	+	0.372917i
$75$	−0.887442	+	2.73126i	−0.102473	+	0.315379i
$76$	−0.135504			−0.0155433
$77$	−6.83270	−	8.54430i	−0.778658	−	0.973714i
$78$	−10.8596			−1.22961
$79$	5.23836	−	16.1220i	0.589362	−	1.81387i	0.00836098	−	0.999965i	$-0.497339\pi$
$79$	5.23836	−	16.1220i	0.589362	−	1.81387i	0.581001	−	0.813903i	$-0.302661\pi$
$80$	3.07700	−	2.23557i	0.344019	−	0.249945i
$81$	−16.9673	−	12.3275i	−1.88525	−	1.36972i
$82$	0.513354	+	1.57994i	0.0566905	+	0.174475i
$83$	3.42234	+	10.5329i	0.375651	+	1.15613i	0.943039	+	0.332683i	$0.107954\pi$
$83$	3.42234	+	10.5329i	0.375651	+	1.15613i	−0.567388	+	0.823451i	$0.692046\pi$
$84$	−6.52791	−	4.74280i	−0.712253	−	0.517482i
$85$	−1.63809	+	1.19014i	−0.177675	+	0.129089i
$86$	−1.06585	+	3.28035i	−0.114934	+	0.353729i
$87$	16.1833			1.73503
$88$	9.53577	−	3.59349i	1.01652	−	0.383067i
$89$	16.9672			1.79852			0.899258	−	0.437419i	$-0.144107\pi$
$89$	16.9672			1.79852			0.899258	+	0.437419i	$0.144107\pi$
$90$	−4.98645	+	15.3467i	−0.525618	+	1.61768i
$91$	8.18068	−	5.94361i	0.857568	−	0.623060i
$92$	4.79698	+	3.48521i	0.500119	+	0.363358i
$93$	−7.14126	−	21.9785i	−0.740514	−	2.27907i
$94$	−2.71025	−	8.34130i	−0.279541	−	0.860340i
$95$	−0.289471	−	0.210313i	−0.0296991	−	0.0215776i
$96$	10.4757	−	7.61105i	1.06917	−	0.776799i
$97$	−2.09799	+	6.45696i	−0.213019	+	0.655605i	0.786269	+	0.617884i	$0.212010\pi$
$97$	−2.09799	+	6.45696i	−0.213019	+	0.655605i	−0.999288	+	0.0377208i	$0.987990\pi$
$98$	−4.30982			−0.435357
$99$	−13.0856	+	19.8820i	−1.31515	+	1.99821i
$100$	0.690305			0.0690305
$101$	4.32381	−	13.3073i	0.430235	−	1.32413i	−0.467657	−	0.883910i	$-0.654902\pi$
$101$	4.32381	−	13.3073i	0.430235	−	1.32413i	0.897892	−	0.440217i	$-0.145098\pi$
$102$	2.86598	−	2.08226i	0.283775	−	0.206174i
$103$	−2.11637	−	1.53764i	−0.208532	−	0.151508i	0.478617	−	0.878024i	$-0.341138\pi$
$103$	−2.11637	−	1.53764i	−0.208532	−	0.151508i	−0.687149	+	0.726516i	$0.741138\pi$
$104$	2.91055	+	8.95774i	0.285403	+	0.878379i
$105$	−6.58408	−	20.2637i	−0.642540	−	1.97754i
$106$	0.127240	+	0.0924451i	0.0123586	+	0.00897906i
$107$	−3.03642	+	2.20608i	−0.293541	+	0.213270i	−0.724802	−	0.688957i	$-0.758069\pi$
$107$	−3.03642	+	2.20608i	−0.293541	+	0.213270i	0.431261	+	0.902227i	$0.358069\pi$
$108$	−3.15702	+	9.71632i	−0.303785	+	0.934953i
$109$	−11.9606			−1.14562			−0.572811	−	0.819687i	$-0.694147\pi$
$109$	−11.9606			−1.14562			−0.572811	+	0.819687i	$0.694147\pi$
$110$	7.19140	+	1.97428i	0.685673	+	0.188241i
$111$	−15.6780			−1.48809
$112$	1.91473	−	5.89293i	0.180925	−	0.556830i
$113$	−12.5072	+	9.08700i	−1.17658	+	0.854833i	−0.991781	−	0.127944i	$-0.959162\pi$
$113$	−12.5072	+	9.08700i	−1.17658	+	0.854833i	−0.184795	+	0.982777i	$0.559162\pi$
$114$	0.506456	+	0.367962i	0.0474339	+	0.0344628i
$115$	4.83825	+	14.8906i	0.451169	+	1.38856i
$116$	−1.20208	−	3.69961i	−0.111610	−	0.343500i
$117$	−17.7979	−	12.9309i	−1.64541	−	1.19546i
$118$	−0.714084	+	0.518812i	−0.0657368	+	0.0477606i
$119$	−1.01933	+	3.13719i	−0.0934422	+	0.287585i
$120$	19.8460			1.81168
$121$	9.45809	+	5.61644i	0.859827	+	0.510586i
$122$	1.10606			0.100138
$123$	−1.47469	+	4.53862i	−0.132968	+	0.409234i
$124$	−4.49401	+	3.26509i	−0.403574	+	0.293214i
$125$	9.66510	+	7.02211i	0.864473	+	0.628077i
$126$	8.12355	+	25.0017i	0.723704	+	2.22733i
$127$	−2.26951	−	6.98482i	−0.201386	−	0.619803i	−0.999842	−	0.0177502i	$-0.994350\pi$
$127$	−2.26951	−	6.98482i	−0.201386	−	0.619803i	0.798456	−	0.602053i	$-0.205650\pi$
$128$	0.857101	+	0.622721i	0.0757578	+	0.0550412i
$129$	−8.01593	+	5.82392i	−0.705764	+	0.512767i
$130$	−2.12998	+	6.55541i	−0.186812	+	0.574947i
$131$	5.94900			0.519767			0.259883	−	0.965640i	$-0.416316\pi$
$131$	5.94900			0.519767			0.259883	+	0.965640i	$0.416316\pi$
$132$	7.82348	+	2.14781i	0.680946	+	0.186943i
$133$	−0.582911			−0.0505448
$134$	3.61668	−	11.1310i	0.312434	−	0.961572i
$135$	−21.8248	+	15.8566i	−1.87838	+	1.36472i
$136$	−2.48572	−	1.80598i	−0.213149	−	0.154862i
$137$	−3.50933	−	10.8006i	−0.299822	−	0.922757i	−0.981559	−	0.191160i	$-0.938775\pi$
$137$	−3.50933	−	10.8006i	−0.299822	−	0.922757i	0.681737	−	0.731597i	$-0.261225\pi$
$138$	−8.46497	−	26.0525i	−0.720586	−	2.21773i
$139$	3.79221	+	2.75520i	0.321651	+	0.233693i	0.736880	−	0.676024i	$-0.236298\pi$
$139$	3.79221	+	2.75520i	0.321651	+	0.233693i	−0.415229	+	0.909717i	$0.636298\pi$
$140$	−4.14337	+	3.01034i	−0.350179	+	0.254420i
$141$	7.78561	−	23.9616i	0.655667	−	2.01793i
$142$	−3.61405			−0.303285
$143$	−5.58956	+	8.49266i	−0.467422	+	0.710192i
$144$	−13.4804			−1.12337
$145$	3.17416	−	9.76905i	0.263599	−	0.811275i
$146$	−5.86653	+	4.26228i	−0.485517	+	0.352749i
$147$	−10.0161	−	7.27713i	−0.826115	−	0.600208i
$148$	1.16455	+	3.58411i	0.0957253	+	0.294612i
$149$	−1.50213	−	4.62308i	−0.123059	−	0.378737i	0.870483	−	0.492198i	$-0.163806\pi$
$149$	−1.50213	−	4.62308i	−0.123059	−	0.378737i	−0.993542	+	0.113461i	$0.963806\pi$
$150$	−2.58007	−	1.87453i	−0.210662	−	0.153055i
$151$	12.9589	−	9.41523i	1.05458	−	0.766200i	0.0815055	−	0.996673i	$-0.474027\pi$
$151$	12.9589	−	9.41523i	1.05458	−	0.766200i	0.973079	+	0.230473i	$0.0740272\pi$
$152$	0.167782	−	0.516379i	0.0136089	−	0.0418839i
$153$	7.17651			0.580186
$154$	11.3687	−	4.28423i	0.916118	−	0.345233i
$155$	−14.6681			−1.17817
$156$	−2.31719	+	7.13159i	−0.185524	+	0.570984i
$157$	7.51637	−	5.46096i	0.599872	−	0.435832i	−0.245962	−	0.969280i	$-0.579104\pi$
$157$	7.51637	−	5.46096i	0.599872	−	0.435832i	0.845833	+	0.533447i	$0.179104\pi$
$158$	15.2296	+	11.0649i	1.21160	+	0.880278i
$159$	0.139614	+	0.429689i	0.0110721	+	0.0340766i
$160$	−2.53973	−	7.81649i	−0.200784	−	0.617948i
$161$	20.6357	+	14.9927i	1.62632	+	1.18159i
$162$	18.8421	−	13.6896i	1.48037	−	1.07555i
$163$	1.30659	−	4.02127i	0.102340	−	0.314970i	−0.886757	−	0.462236i	$-0.847047\pi$
$163$	1.30659	−	4.02127i	0.102340	−	0.314970i	0.989097	+	0.147266i	$0.0470473\pi$
$164$	1.14710			0.0895735
$165$	13.3794	+	16.7310i	1.04158	+	1.30250i
$166$	−12.2987			−0.954560
$167$	2.69316	−	8.28868i	0.208403	−	0.641397i	−0.791154	−	0.611617i	$-0.790519\pi$
$167$	2.69316	−	8.28868i	0.208403	−	0.641397i	0.999556	−	0.0297801i	$-0.00948070\pi$
$168$	26.1569	−	19.0041i	2.01805	−	1.46620i
$169$	2.91478	+	2.11771i	0.224214	+	0.162901i
$170$	−0.694829	−	2.13846i	−0.0532910	−	0.164013i
$171$	0.391889	+	1.20611i	0.0299685	+	0.0922336i
$172$	1.92680	+	1.39991i	0.146917	+	0.106742i
$173$	14.7975	−	10.7510i	1.12503	−	0.817384i	0.140068	−	0.990142i	$-0.455268\pi$
$173$	14.7975	−	10.7510i	1.12503	−	0.817384i	0.984964	+	0.172758i	$0.0552679\pi$
$174$	−5.55348	+	17.0918i	−0.421008	+	1.29573i
$175$	2.96956			0.224478
$176$	0.287887	+	6.22334i	0.0217003	+	0.469102i
$177$	−2.53556			−0.190585
$178$	−5.82248	+	17.9198i	−0.436413	+	1.34314i
$179$	13.8817	−	10.0856i	1.03757	−	0.753835i	0.0677565	−	0.997702i	$-0.478416\pi$
$179$	13.8817	−	10.0856i	1.03757	−	0.753835i	0.969809	+	0.243867i	$0.0784159\pi$
$180$	9.01432	+	6.54928i	0.671888	+	0.488155i
$181$	3.75406	+	11.5538i	0.279037	+	0.858787i	0.988123	+	0.153665i	$0.0491078\pi$
$181$	3.75406	+	11.5538i	0.279037	+	0.858787i	−0.709086	+	0.705122i	$0.750892\pi$
$182$	3.47001	+	10.6796i	0.257214	+	0.791624i
$183$	2.57050	+	1.86758i	0.190017	+	0.138056i
$184$	−19.2211	+	13.9650i	−1.41700	+	1.02951i
$185$	−3.07506	+	9.46407i	−0.226083	+	0.695812i
$186$	25.6631			1.88171
$187$	−0.153261	−	3.31308i	−0.0112075	−	0.242277i
$188$	−6.05611			−0.441687
$189$	−13.5809	+	41.7978i	−0.987866	+	3.04034i
$190$	0.321456	−	0.233551i	0.0233209	−	0.0169436i
$191$	−2.42215	−	1.75979i	−0.175260	−	0.127334i	0.496697	−	0.867924i	$-0.334546\pi$
$191$	−2.42215	−	1.75979i	−0.175260	−	0.127334i	−0.671957	+	0.740590i	$0.734546\pi$
$192$	8.14691	+	25.0736i	0.587953	+	1.80953i
$193$	−1.53865	−	4.73549i	−0.110755	−	0.340868i	0.880283	−	0.474449i	$-0.157353\pi$
$193$	−1.53865	−	4.73549i	−0.110755	−	0.340868i	−0.991038	+	0.133580i	$0.957353\pi$
$194$	−6.09952	−	4.43156i	−0.437920	−	0.318167i
$195$	−16.0189	+	11.6384i	−1.14714	+	0.833446i
$196$	−0.919618	+	2.83029i	−0.0656870	+	0.202164i
$197$	−10.6916			−0.761747			−0.380873	−	0.924627i	$-0.624377\pi$
$197$	−10.6916			−0.761747			−0.380873	+	0.924627i	$0.624377\pi$
$198$	−16.5077	−	20.6430i	−1.17315	−	1.46703i
$199$	2.15729			0.152927			0.0764633	−	0.997072i	$-0.475637\pi$
$199$	2.15729			0.152927			0.0764633	+	0.997072i	$0.475637\pi$
$200$	−0.854742	+	2.63062i	−0.0604394	+	0.186013i
$201$	27.2000	−	19.7619i	1.91854	−	1.39390i
$202$	12.5707	+	9.13312i	0.884469	+	0.642604i
$203$	−5.17110	−	15.9150i	−0.362940	−	1.11702i
$204$	−0.755900	−	2.32642i	−0.0529236	−	0.162882i
$205$	2.45050	+	1.78040i	0.171151	+	0.124348i
$206$	2.35022	−	1.70754i	0.163748	−	0.118970i
$207$	17.1484	−	52.7772i	1.19189	−	3.66827i
$208$	−5.75823			−0.399261
$209$	0.548440	−	0.206676i	0.0379364	−	0.0142961i
$210$	23.6608			1.63275
$211$	−0.325540	+	1.00191i	−0.0224111	+	0.0689742i	−0.961637	−	0.274327i	$-0.911545\pi$
$211$	−0.325540	+	1.00191i	−0.0224111	+	0.0689742i	0.939225	+	0.343301i	$0.111545\pi$
$212$	0.0878596	−	0.0638337i	0.00603422	−	0.00438412i
$213$	−8.39915	−	6.10234i	−0.575500	−	0.418125i
$214$	−1.28796	−	3.96393i	−0.0880431	−	0.270969i
$215$	1.94338	+	5.98112i	0.132538	+	0.407909i
$216$	−33.1180	−	24.0617i	−2.25340	−	1.63719i
$217$	−19.3324	+	14.0458i	−1.31237	+	0.953490i
$218$	4.10444	−	12.6322i	0.277987	−	0.855558i
$219$	−20.8308			−1.40762
$220$	2.83101	−	4.30139i	0.190867	−	0.289999i
$221$	3.06547			0.206206
$222$	5.38010	−	16.5583i	0.361089	−	1.11132i
$223$	−7.33872	+	5.33189i	−0.491437	+	0.357050i	−0.805737	−	0.592274i	$-0.798230\pi$
$223$	−7.33872	+	5.33189i	−0.491437	+	0.357050i	0.314300	+	0.949324i	$0.398230\pi$
$224$	−10.8322	−	7.87008i	−0.723759	−	0.525842i
$225$	−1.99643	−	6.14437i	−0.133095	−	0.409625i
$226$	−5.30519	−	16.3277i	−0.352896	−	1.08610i
$227$	−4.97824	−	3.61690i	−0.330417	−	0.240062i	0.410190	−	0.912000i	$-0.365462\pi$
$227$	−4.97824	−	3.61690i	−0.330417	−	0.240062i	−0.740608	+	0.671938i	$0.765462\pi$
$228$	0.349710	−	0.254079i	0.0231601	−	0.0168268i
$229$	−4.20338	+	12.9367i	−0.277767	+	0.854879i	0.710707	+	0.703488i	$0.248375\pi$
$229$	−4.20338	+	12.9367i	−0.277767	+	0.854879i	−0.988474	+	0.151391i	$0.951625\pi$
$230$	−17.3869			−1.14646
$231$	33.6551	+	9.23948i	2.21434	+	0.607913i
$232$	15.5870			1.02333
$233$	4.57791	−	14.0893i	0.299909	−	0.923024i	−0.681620	−	0.731707i	$-0.738724\pi$
$233$	4.57791	−	14.0893i	0.299909	−	0.923024i	0.981528	−	0.191317i	$-0.0612759\pi$
$234$	19.7645	−	14.3597i	1.29204	−	0.938724i
$235$	−12.9374	−	9.39959i	−0.843945	−	0.613162i
$236$	0.188339	+	0.579648i	0.0122598	+	0.0377319i
$237$	16.7107	+	51.4302i	1.08548	+	3.34075i
$238$	−2.96352	−	2.15313i	−0.192097	−	0.139566i
$239$	−0.915005	+	0.664790i	−0.0591868	+	0.0430017i	−0.616985	−	0.786975i	$-0.711646\pi$
$239$	−0.915005	+	0.664790i	−0.0591868	+	0.0430017i	0.557798	+	0.829976i	$0.311646\pi$
$240$	−3.74932	+	11.5392i	−0.242017	+	0.744853i
$241$	−10.9760			−0.707028			−0.353514	−	0.935429i	$-0.615013\pi$
$241$	−10.9760			−0.707028			−0.353514	+	0.935429i	$0.615013\pi$
$242$	−9.17743	+	8.06175i	−0.589947	+	0.518229i
$243$	26.9344			1.72784
$244$	0.236008	−	0.726358i	0.0151089	−	0.0465003i
$245$	−6.35739	+	4.61892i	−0.406159	+	0.295092i
$246$	−4.28738	−	3.11496i	−0.273353	−	0.198603i
$247$	0.167397	+	0.515195i	0.0106512	+	0.0327811i
$248$	−6.87813	−	21.1687i	−0.436761	−	1.34421i
$249$	−28.5824	−	20.7663i	−1.81133	−	1.31601i
$250$	−10.7330	+	7.79802i	−0.678818	+	0.493190i
$251$	1.73593	−	5.34265i	0.109571	−	0.337225i	−0.881205	−	0.472734i	$-0.843267\pi$
$251$	1.73593	−	5.34265i	0.109571	−	0.337225i	0.990776	+	0.135509i	$0.0432671\pi$
$252$	18.1522			1.14348
$253$	−24.7312	−	6.78955i	−1.55483	−	0.426855i
$254$	8.15578			0.511739
$255$	1.99600	−	6.14306i	0.124994	−	0.384693i
$256$	12.4203	−	9.02386i	0.776267	−	0.563991i
$257$	18.1710	+	13.2020i	1.13348	+	0.823519i	0.986197	−	0.165576i	$-0.0529484\pi$
$257$	18.1710	+	13.2020i	1.13348	+	0.823519i	0.147279	+	0.989095i	$0.452948\pi$
$258$	−3.40013	−	10.4645i	−0.211683	−	0.651493i
$259$	5.00967	+	15.4182i	0.311286	+	0.958038i
$260$	3.85050	+	2.79755i	0.238798	+	0.173497i
$261$	−29.4535	+	21.3992i	−1.82313	+	1.32458i
$262$	−2.04147	+	6.28300i	−0.126122	+	0.388165i
$263$	10.3098			0.635730			0.317865	−	0.948136i	$-0.397034\pi$
$263$	10.3098			0.635730			0.317865	+	0.948136i	$0.397034\pi$
$264$	−17.8720	+	27.1544i	−1.09995	+	1.67124i
$265$	0.286766			0.0176159
$266$	0.200033	−	0.615637i	0.0122648	−	0.0377471i
$267$	−43.7891	+	31.8147i	−2.67985	+	1.94703i
$268$	−6.53810	−	4.75021i	−0.399378	−	0.290165i
$269$	−3.57698	−	11.0088i	−0.218092	−	0.671219i	−0.998920	−	0.0464719i	$-0.985202\pi$
$269$	−3.57698	−	11.0088i	−0.218092	−	0.671219i	0.780827	−	0.624747i	$-0.214798\pi$
$270$	−9.25743	−	28.4914i	−0.563389	−	1.73393i
$271$	−25.1012	−	18.2371i	−1.52479	−	1.10782i	−0.959049	−	0.283240i	$-0.908591\pi$
$271$	−25.1012	−	18.2371i	−1.52479	−	1.10782i	−0.565740	−	0.824584i	$-0.691409\pi$
$272$	1.51967	−	1.10410i	0.0921434	−	0.0669461i
$273$	−9.96813	+	30.6787i	−0.603298	+	1.85676i
$274$	12.6112			0.761873
$275$	−2.79395	+	1.05288i	−0.168482	+	0.0634912i
$276$	−18.9151			−1.13856
$277$	−6.05181	+	18.6255i	−0.363618	+	1.11910i	0.587224	+	0.809424i	$0.300221\pi$
$277$	−6.05181	+	18.6255i	−0.363618	+	1.11910i	−0.950842	+	0.309676i	$0.899779\pi$
$278$	−4.21123	+	3.05964i	−0.252573	+	0.183505i
$279$	42.0595	+	30.5580i	2.51804	+	1.82946i
$280$	−6.34147	−	19.5171i	−0.378976	−	1.16637i
$281$	−7.31149	−	22.5025i	−0.436167	−	1.34238i	−0.891886	−	0.452260i	$-0.850618\pi$
$281$	−7.31149	−	22.5025i	−0.436167	−	1.34238i	0.455719	−	0.890124i	$-0.349382\pi$
$282$	22.6352	+	16.4454i	1.34791	+	0.979312i
$283$	−3.25106	+	2.36203i	−0.193255	+	0.140408i	−0.680205	−	0.733022i	$-0.738109\pi$
$283$	−3.25106	+	2.36203i	−0.193255	+	0.140408i	0.486950	+	0.873430i	$0.338109\pi$
$284$	−0.771158	+	2.37338i	−0.0457598	+	0.140834i
$285$	1.14142			0.0676120
$286$	−7.05135	−	8.81773i	−0.416955	−	0.521403i
$287$	4.93461			0.291281
$288$	−9.00164	+	27.7042i	−0.530427	+	1.63249i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	9.22827	+	6.70473i	0.541902	+	0.393715i
$291$	−6.69273	−	20.5981i	−0.392335	−	1.20748i
$292$	1.54729	+	4.76207i	0.0905484	+	0.278679i
$293$	12.2333	+	8.88801i	0.714677	+	0.519243i	0.884679	−	0.466201i	$-0.154377\pi$
$293$	12.2333	+	8.88801i	0.714677	+	0.519243i	−0.170002	+	0.985444i	$0.554377\pi$
$294$	11.1228	−	8.08122i	0.648697	−	0.471306i
$295$	−0.497321	+	1.53060i	−0.0289551	+	0.0891148i
$296$	−15.1003			−0.877690
$297$	−2.04194	−	44.1412i	−0.118485	−	2.56134i
$298$	5.39810			0.312704
$299$	7.32499	−	22.5440i	0.423615	−	1.30375i
$300$	−1.78155	+	1.29437i	−0.102858	+	0.0747306i
$301$	8.28875	+	6.02213i	0.477756	+	0.347110i
$302$	5.49681	+	16.9175i	0.316306	+	0.973490i
$303$	13.7932	+	42.4512i	0.792400	+	2.43876i
$304$	0.268545	+	0.195109i	0.0154021	+	0.0111903i
$305$	1.63154	−	1.18538i	0.0934218	−	0.0678749i
$306$	−2.46270	+	7.57942i	−0.140783	+	0.433287i
$307$	−5.05467			−0.288485			−0.144243	−	0.989542i	$-0.546075\pi$
$307$	−5.05467			−0.288485			−0.144243	+	0.989542i	$0.546075\pi$
$308$	−0.387657	−	8.38010i	−0.0220888	−	0.477500i
$309$	8.34515			0.474739
$310$	5.03352	−	15.4916i	0.285884	−	0.879862i
$311$	−17.0957	+	12.4208i	−0.969410	+	0.704317i	−0.955317	−	0.295583i	$-0.904486\pi$
$311$	−17.0957	+	12.4208i	−0.969410	+	0.704317i	−0.0140927	+	0.999901i	$0.504486\pi$
$312$	−24.3080	−	17.6608i	−1.37617	−	0.999846i
$313$	−2.52095	−	7.75868i	−0.142492	−	0.438546i	0.854188	−	0.519965i	$-0.174055\pi$
$313$	−2.52095	−	7.75868i	−0.142492	−	0.438546i	−0.996680	+	0.0814185i	$0.974055\pi$
$314$	3.18823	+	9.81236i	0.179922	+	0.553743i
$315$	38.7779	+	28.1738i	2.18489	+	1.58741i
$316$	10.5161	−	7.64037i	0.591575	−	0.429805i
$317$	−1.54101	+	4.74273i	−0.0865515	+	0.266378i	−0.984960	−	0.172783i	$-0.944724\pi$
$317$	−1.54101	+	4.74273i	−0.0865515	+	0.266378i	0.898408	+	0.439161i	$0.144724\pi$
$318$	−0.501723			−0.0281353
$319$	10.5081	+	13.1404i	0.588341	+	0.735722i
$320$	16.7336			0.935439
$321$	3.69986	−	11.3870i	0.206506	−	0.635560i
$322$	−22.9158	+	16.6493i	−1.27705	+	0.927830i
$323$	−0.142964	−	0.103869i	−0.00795471	−	0.00577943i
$324$	−4.96958	−	15.2948i	−0.276088	−	0.849711i
$325$	−0.852782	−	2.62459i	−0.0473038	−	0.145586i
$326$	3.79867	+	2.75989i	0.210389	+	0.152856i
$327$	30.8682	−	22.4271i	1.70702	−	1.24022i
$328$	−1.42035	+	4.37139i	−0.0784257	+	0.241369i
$329$	−26.0522			−1.43631
$330$	−22.2616	+	8.38913i	−1.22546	+	0.461806i
$331$	9.67518			0.531796			0.265898	−	0.964001i	$-0.414332\pi$
$331$	9.67518			0.531796			0.265898	+	0.964001i	$0.414332\pi$
$332$	−2.62426	+	8.07663i	−0.144025	+	0.443263i
$333$	28.5340	−	20.7312i	1.56365	−	1.13606i
$334$	7.82984	+	5.68872i	0.428430	+	0.311273i
$335$	−6.59436	−	20.2954i	−0.360288	−	1.10885i
$336$	6.10811	+	18.7988i	0.333225	+	1.02556i
$337$	20.5828	+	14.9543i	1.12122	+	0.814610i	0.984393	−	0.175985i	$-0.0563111\pi$
$337$	20.5828	+	14.9543i	1.12122	+	0.814610i	0.136822	+	0.990596i	$0.456311\pi$
$338$	−3.23685	+	2.35171i	−0.176061	+	0.127916i
$339$	15.2399	−	46.9037i	0.827720	−	2.54746i
$340$	−1.55261			−0.0842020
$341$	13.2091	−	20.0696i	0.715312	−	1.08683i
$342$	−1.40831			−0.0761525
$343$	3.17932	−	9.78493i	0.171667	−	0.528337i
$344$	−7.72057	+	5.60932i	−0.416265	+	0.302434i
$345$	−40.4076	−	29.3578i	−2.17547	−	1.58057i
$346$	6.27667	+	19.3176i	0.337436	+	1.03852i
$347$	−5.93466	−	18.2650i	−0.318589	−	0.980517i	−0.974252	−	0.225463i	$-0.927610\pi$
$347$	−5.93466	−	18.2650i	−0.318589	−	0.980517i	0.655662	−	0.755054i	$-0.272390\pi$
$348$	10.0394	+	7.29403i	0.538167	+	0.391001i
$349$	−18.0049	+	13.0813i	−0.963780	+	0.700227i	−0.954026	−	0.299725i	$-0.903105\pi$
$349$	−18.0049	+	13.0813i	−0.963780	+	0.700227i	−0.00975444	+	0.999952i	$0.503105\pi$
$350$	−1.01904	+	3.13628i	−0.0544700	+	0.167641i
$351$	40.8423			2.18000
$352$	12.9821	+	3.56402i	0.691947	+	0.189963i
$353$	5.24806			0.279326			0.139663	−	0.990199i	$-0.455398\pi$
$353$	5.24806			0.279326			0.139663	+	0.990199i	$0.455398\pi$
$354$	0.870109	−	2.67792i	0.0462457	−	0.142330i
$355$	−5.33108	+	3.87325i	−0.282944	+	0.205571i
$356$	10.5257	+	7.64735i	0.557859	+	0.405309i
$357$	−3.25174	−	10.0078i	−0.172100	−	0.529670i
$358$	5.88821	+	18.1220i	0.311202	+	0.957780i
$359$	−5.20163	−	3.77921i	−0.274532	−	0.199459i	0.441997	−	0.897016i	$-0.354270\pi$
$359$	−5.20163	−	3.77921i	−0.274532	−	0.199459i	−0.716529	+	0.697558i	$0.754270\pi$
$360$	−36.1197	+	26.2425i	−1.90368	+	1.38310i
$361$	−5.86167	+	18.0404i	−0.308509	+	0.949493i
$362$	−13.4907			−0.709057
$363$	−34.9408	+	3.23961i	−1.83392	+	0.170035i
$364$	7.75380			0.406410
$365$	−4.08572	+	12.5746i	−0.213856	+	0.658182i
$366$	−2.85453	+	2.07394i	−0.149209	+	0.108406i
$367$	−22.6073	−	16.4252i	−1.18009	−	0.857388i	−0.187911	−	0.982186i	$-0.560172\pi$
$367$	−22.6073	−	16.4252i	−1.18009	−	0.857388i	−0.992182	+	0.124798i	$0.960172\pi$
$368$	−4.48849	−	13.8142i	−0.233979	−	0.720113i
$369$	−3.31752	−	10.2103i	−0.172703	−	0.531526i
$370$	−8.94017	−	6.49541i	−0.464777	−	0.337680i
$371$	0.377955	−	0.274601i	0.0196225	−	0.0142565i
$372$	5.47593	−	16.8532i	0.283914	−	0.873797i
$373$	15.3502			0.794805			0.397403	−	0.917644i	$-0.369912\pi$
$373$	15.3502			0.794805			0.397403	+	0.917644i	$0.369912\pi$
$374$	3.55168	+	0.975058i	0.183653	+	0.0504190i
$375$	−38.1108			−1.96803
$376$	7.49873	−	23.0787i	0.386718	−	1.19019i
$377$	−12.5812	+	9.14078i	−0.647965	+	0.470774i
$378$	−39.4840	−	28.6868i	−2.03084	−	1.47549i
$379$	−6.61834	−	20.3692i	−0.339962	−	1.04629i	−0.964226	−	0.265081i	$-0.914601\pi$
$379$	−6.61834	−	20.3692i	−0.339962	−	1.04629i	0.624265	−	0.781213i	$-0.285399\pi$
$380$	−0.0847837	−	0.260937i	−0.00434931	−	0.0133858i
$381$	18.9542	+	13.7711i	0.971055	+	0.705513i
$382$	2.68978	−	1.95424i	0.137621	−	0.0999876i
$383$	−4.00658	+	12.3310i	−0.204727	+	0.630084i	0.794998	+	0.606612i	$0.207472\pi$
$383$	−4.00658	+	12.3310i	−0.204727	+	0.630084i	−0.999725	+	0.0234718i	$0.992528\pi$
$384$	−3.37967			−0.172468
$385$	12.1785	−	18.5037i	0.620673	−	0.943038i
$386$	5.52936			0.281437
$387$	6.88799	−	21.1991i	0.350136	−	1.07761i
$388$	−4.21174	+	3.06001i	−0.213819	+	0.155349i
$389$	23.6566	+	17.1875i	1.19944	+	0.871442i	0.994229	−	0.107276i	$-0.0342128\pi$
$389$	23.6566	+	17.1875i	1.19944	+	0.871442i	0.205208	+	0.978718i	$0.434213\pi$
$390$	−6.79478	−	20.9122i	−0.344067	−	1.05893i
$391$	2.38951	+	7.35416i	0.120843	+	0.371916i
$392$	−9.64704	−	7.00899i	−0.487249	−	0.354007i
$393$	−15.3533	+	11.1548i	−0.774471	+	0.562686i
$394$	3.66896	−	11.2919i	0.184839	−	0.568877i
$395$	34.3235			1.72701
$396$	−17.0788	+	6.43603i	−0.858242	+	0.323422i
$397$	7.43782			0.373293			0.186647	−	0.982427i	$-0.440238\pi$
$397$	7.43782			0.373293			0.186647	+	0.982427i	$0.440238\pi$
$398$	−0.740301	+	2.27841i	−0.0371079	+	0.114206i
$399$	1.50439	−	1.09300i	0.0753135	−	0.0547184i
$400$	−1.36807	−	0.993958i	−0.0684033	−	0.0496979i
$401$	1.99254	+	6.13241i	0.0995028	+	0.306238i	0.988401	−	0.151867i	$-0.0485284\pi$
$401$	1.99254	+	6.13241i	0.0995028	+	0.306238i	−0.888898	+	0.458105i	$0.848528\pi$
$402$	11.5374	+	35.5086i	0.575435	+	1.77101i
$403$	17.9659	+	13.0530i	0.894944	+	0.650215i
$404$	8.68010	−	6.30646i	0.431851	−	0.313758i
$405$	13.1225	−	40.3869i	0.652062	−	2.00684i
$406$	18.5831			0.922262
$407$	−10.1801	−	12.7302i	−0.504607	−	0.631012i
$408$	9.80153			0.485248
$409$	−7.16623	+	22.0554i	−0.354347	+	1.09057i	0.602040	+	0.798466i	$0.294355\pi$
$409$	−7.16623	+	22.0554i	−0.354347	+	1.09057i	−0.956387	+	0.292103i	$0.905645\pi$
$410$	−2.72127	+	1.97712i	−0.134394	+	0.0976430i
$411$	29.3088	+	21.2941i	1.44570	+	1.05036i
$412$	−0.619869	−	1.90776i	−0.0305388	−	0.0939886i
$413$	0.810199	+	2.49354i	0.0398673	+	0.122699i
$414$	49.8556	+	36.2222i	2.45027	+	1.78023i
$415$	−18.1417	+	13.1807i	−0.890541	+	0.647016i
$416$	−3.84509	+	11.8340i	−0.188521	+	0.580208i
$417$	−14.9532			−0.732261
$418$	0.0300757	+	0.650155i	0.00147105	+	0.0318001i
$419$	−3.91701			−0.191359			−0.0956793	−	0.995412i	$-0.530502\pi$
$419$	−3.91701			−0.191359			−0.0956793	+	0.995412i	$0.530502\pi$
$420$	5.04868	−	15.5382i	0.246350	−	0.758189i
$421$	12.3750	−	8.99093i	0.603119	−	0.438191i	−0.243866	−	0.969809i	$-0.578416\pi$
$421$	12.3750	−	8.99093i	0.603119	−	0.438191i	0.846984	+	0.531618i	$0.178416\pi$
$422$	−0.946446	−	0.687633i	−0.0460723	−	0.0334735i
$423$	17.5149	+	53.9052i	0.851601	+	2.62096i
$424$	0.134470	+	0.413856i	0.00653044	+	0.0200986i
$425$	0.728309	+	0.529148i	0.0353282	+	0.0256674i
$426$	9.32721	−	6.77661i	0.451905	−	0.328328i
$427$	1.01526	−	3.12465i	0.0491319	−	0.151213i
$428$	−2.87797			−0.139112
$429$	−1.49874	−	32.3988i	−0.0723601	−	1.56423i
$430$	−6.98382			−0.336790
$431$	5.20166	−	16.0091i	0.250555	−	0.771129i	−0.744118	−	0.668048i	$-0.767130\pi$
$431$	5.20166	−	16.0091i	0.250555	−	0.771129i	0.994673	−	0.103081i	$-0.0328700\pi$
$432$	20.2470	−	14.7103i	0.974135	−	0.707751i
$433$	11.1253	+	8.08299i	0.534647	+	0.388444i	0.822093	−	0.569353i	$-0.192806\pi$
$433$	11.1253	+	8.08299i	0.534647	+	0.388444i	−0.287446	+	0.957797i	$0.592806\pi$
$434$	−8.20023	−	25.2377i	−0.393624	−	1.21145i
$435$	10.1258	+	31.1639i	0.485493	+	1.49419i
$436$	−7.41985	−	5.39084i	−0.355346	−	0.258174i
$437$	−1.10548	+	0.803181i	−0.0528825	+	0.0384214i
$438$	7.14834	−	22.0003i	0.341561	−	1.05122i
$439$	−28.8368			−1.37630			−0.688152	−	0.725566i	$-0.741578\pi$
$439$	−28.8368			−1.37630			−0.688152	+	0.725566i	$0.741578\pi$
$440$	12.8864	+	16.1145i	0.614335	+	0.768228i
$441$	27.8519			1.32628
$442$	−1.05195	+	3.23758i	−0.0500363	+	0.153996i
$443$	18.0398	−	13.1067i	0.857096	−	0.622717i	−0.0699972	−	0.997547i	$-0.522299\pi$
$443$	18.0398	−	13.1067i	0.857096	−	0.622717i	0.927093	+	0.374830i	$0.122299\pi$
$444$	−9.72595	−	7.06632i	−0.461573	−	0.335353i
$445$	10.6162	+	32.6734i	0.503258	+	1.54887i
$446$	−3.11287	−	9.58044i	−0.147399	−	0.453647i
$447$	12.5453	+	9.11471i	0.593373	+	0.431111i
$448$	22.0548	−	16.0238i	1.04199	−	0.757051i
$449$	9.90415	−	30.4819i	0.467406	−	1.43853i	−0.388525	−	0.921438i	$-0.627015\pi$
$449$	9.90415	−	30.4819i	0.467406	−	1.43853i	0.855931	−	0.517090i	$-0.172985\pi$
$450$	7.17443			0.338206
$451$	−4.64280	+	1.74961i	−0.218621	+	0.0823857i
$452$	−11.8545			−0.557590
$453$	−15.7904	+	48.5979i	−0.741899	+	2.28333i
$454$	5.52831	−	4.01655i	0.259456	−	0.188506i
$455$	16.5641	+	12.0345i	0.776539	+	0.564188i
$456$	0.535235	+	1.64728i	0.0250647	+	0.0771411i
$457$	−0.138925	−	0.427568i	−0.00649864	−	0.0200008i	0.947755	−	0.319000i	$-0.103347\pi$
$457$	−0.138925	−	0.427568i	−0.00649864	−	0.0200008i	−0.954253	+	0.299000i	$0.903347\pi$
$458$	−12.2205	−	8.87874i	−0.571028	−	0.414876i
$459$	−10.7788	+	7.83125i	−0.503111	+	0.365531i
$460$	−3.70998	+	11.4181i	−0.172979	+	0.532374i
$461$	15.0818			0.702431			0.351216	−	0.936295i	$-0.385768\pi$
$461$	15.0818			0.702431			0.351216	+	0.936295i	$0.385768\pi$
$462$	−21.3074	+	32.3740i	−0.991308	+	1.50617i
$463$	15.9764			0.742488			0.371244	−	0.928535i	$-0.378931\pi$
$463$	15.9764			0.742488			0.371244	+	0.928535i	$0.378931\pi$
$464$	−2.94469	+	9.06284i	−0.136704	+	0.420732i
$465$	37.8555	−	27.5037i	1.75551	−	1.27545i
$466$	13.3094	+	9.66985i	0.616546	+	0.447947i
$467$	−10.1782	−	31.3253i	−0.470991	−	1.44956i	−0.851288	−	0.524698i	$-0.824178\pi$
$467$	−10.1782	−	31.3253i	−0.470991	−	1.44956i	0.380297	−	0.924864i	$-0.375822\pi$
$468$	−5.21286	−	16.0435i	−0.240964	−	0.741612i
$469$	−28.1257	−	20.4345i	−1.29872	−	0.943577i
$470$	14.3669	−	10.4382i	0.662698	−	0.481478i
$471$	−9.15867	+	28.1875i	−0.422009	+	1.29881i
$472$	−2.44214			−0.112408
$473$	−9.93379	−	2.72716i	−0.456756	−	0.125395i
$474$	−60.0522			−2.75829
$475$	−0.0491596	+	0.151298i	−0.00225560	+	0.00694201i
$476$	−2.04633	+	1.48674i	−0.0937932	+	0.0681447i
$477$	−0.822279	−	0.597421i	−0.0376496	−	0.0273540i
$478$	−0.388119	−	1.19451i	−0.0177521	−	0.0546355i
$479$	−3.43232	−	10.5636i	−0.156827	−	0.482662i	0.841515	−	0.540234i	$-0.181664\pi$
$479$	−3.43232	−	10.5636i	−0.156827	−	0.482662i	−0.998341	+	0.0575716i	$0.981664\pi$
$480$	21.2111	+	15.4107i	0.968149	+	0.703401i
$481$	12.1884	−	8.85541i	0.555744	−	0.403772i
$482$	3.76655	−	11.5923i	0.171562	−	0.528013i
$483$	−81.3693			−3.70243
$484$	3.33597	+	7.74709i	0.151635	+	0.352141i
$485$	−13.7468			−0.624209
$486$	−9.24284	+	28.4465i	−0.419264	+	1.29036i
$487$	−23.7620	+	17.2641i	−1.07676	+	0.782311i	−0.977115	−	0.212712i	$-0.931770\pi$
$487$	−23.7620	+	17.2641i	−1.07676	+	0.782311i	−0.0996438	+	0.995023i	$0.531770\pi$
$488$	2.47579	+	1.79877i	0.112074	+	0.0814263i
$489$	4.16811	+	12.8281i	0.188488	+	0.580107i
$490$	−2.69662	−	8.29935i	−0.121821	−	0.374927i
$491$	33.0844	+	24.0372i	1.49308	+	1.08478i	0.973039	+	0.230642i	$0.0740825\pi$
$491$	33.0844	+	24.0372i	1.49308	+	1.08478i	0.520039	+	0.854143i	$0.325917\pi$
$492$	−2.96045	+	2.15090i	−0.133468	+	0.0969699i
$493$	1.56765	−	4.82473i	0.0706034	−	0.217295i
$494$	−0.601564			−0.0270657
$495$	−46.4740	−	12.7587i	−2.08885	−	0.573461i
$496$	13.6077			0.611003
$497$	−3.31738	+	10.2098i	−0.148805	+	0.457974i
$498$	31.7406	−	23.0609i	1.42233	−	1.03338i
$499$	32.9971	+	23.9738i	1.47715	+	1.07321i	0.978461	+	0.206433i	$0.0661857\pi$
$499$	32.9971	+	23.9738i	1.47715	+	1.07321i	0.498691	+	0.866780i	$0.333814\pi$
$500$	2.83083	+	8.71241i	0.126599	+	0.389631i
$501$	8.59134	+	26.4414i	0.383833	+	1.18132i
$502$	5.04689	+	3.66678i	0.225254	+	0.163657i
$503$	7.65543	−	5.56200i	0.341339	−	0.247997i	−0.403888	−	0.914809i	$-0.632341\pi$
$503$	7.65543	−	5.56200i	0.341339	−	0.247997i	0.745226	+	0.666811i	$0.232341\pi$
$504$	−22.4763	+	69.1748i	−1.00117	+	3.08129i
$505$	28.3311			1.26072
$506$	15.6575	−	23.7897i	0.696062	−	1.05758i
$507$	−11.4934			−0.510439
$508$	1.74026	−	5.35597i	0.0772116	−	0.237633i
$509$	9.03536	−	6.56457i	0.400485	−	0.290970i	−0.369253	−	0.929329i	$-0.620387\pi$
$509$	9.03536	−	6.56457i	0.400485	−	0.290970i	0.769739	+	0.638359i	$0.220387\pi$
$510$	5.80300	+	4.21613i	0.256961	+	0.186693i
$511$	6.65615	+	20.4855i	0.294451	+	0.906227i
$512$	5.92309	+	18.2294i	0.261766	+	0.805633i
$513$	−1.90475	−	1.38388i	−0.0840968	−	0.0610999i
$514$	−20.1788	+	14.6608i	−0.890049	+	0.646658i
$515$	1.63680	−	5.03756i	0.0721261	−	0.221981i
$516$	−7.59765			−0.334468
$517$	24.5116	−	9.23704i	1.07802	−	0.406245i
$518$	−18.0029			−0.791003
$519$	−18.0307	+	55.4927i	−0.791459	+	2.43586i
$520$	−15.4287	+	11.2096i	−0.676593	+	0.491573i
$521$	−29.8797	−	21.7089i	−1.30906	−	0.951084i	−1.00000		4.03238e-5i	$-0.999987\pi$
$521$	−29.8797	−	21.7089i	−1.30906	−	0.951084i	−0.309055	−	0.951044i	$-0.600013\pi$
$522$	−12.4933	−	38.4506i	−0.546819	−	1.68294i
$523$	−8.02946	−	24.7121i	−0.351104	−	1.08059i	−0.958234	−	0.285984i	$-0.907680\pi$
$523$	−8.02946	−	24.7121i	−0.351104	−	1.08059i	0.607131	−	0.794602i	$-0.292320\pi$
$524$	3.69050	+	2.68130i	0.161220	+	0.117133i
$525$	−7.66389	+	5.56814i	−0.334480	+	0.243014i
$526$	−3.53793	+	10.8886i	−0.154261	+	0.474767i
$527$	−7.24425			−0.315564
$528$	−12.4122	−	15.5215i	−0.540171	−	0.675485i
$529$	36.7935			1.59972
$530$	−0.0984071	+	0.302866i	−0.00427453	+	0.0131557i
$531$	4.61473	−	3.35279i	0.200262	−	0.145499i
$532$	−0.361612	−	0.262726i	−0.0156779	−	0.0113906i
$533$	−1.41709	−	4.36137i	−0.0613811	−	0.188912i
$534$	−18.5741	−	57.1651i	−0.803779	−	2.47378i
$535$	−6.14809	−	4.46685i	−0.265805	−	0.193119i
$536$	26.1977	−	19.0337i	1.13157	−	0.822133i
$537$	−16.9148	+	52.0583i	−0.729926	+	2.24648i
$538$	12.8544			0.554191
$539$	−0.594803	−	12.8580i	−0.0256200	−	0.553834i
$540$	−20.6859			−0.890180
$541$	−7.96308	+	24.5079i	−0.342360	+	1.05367i	0.620622	+	0.784110i	$0.286880\pi$
$541$	−7.96308	+	24.5079i	−0.342360	+	1.05367i	−0.962982	+	0.269565i	$0.913120\pi$
$542$	27.8747	−	20.2522i	1.19732	−	0.869906i
$543$	−31.3527	−	22.7791i	−1.34548	−	0.977545i
$544$	−1.25432	−	3.86040i	−0.0537786	−	0.165513i
$545$	−7.48370	−	23.0325i	−0.320566	−	0.986602i
$546$	−28.9805	−	21.0555i	−1.24025	−	0.901094i
$547$	−27.9716	+	20.3225i	−1.19598	+	0.868929i	−0.993883	−	0.110437i	$-0.964775\pi$
$547$	−27.9716	+	20.3225i	−1.19598	+	0.868929i	−0.202095	+	0.979366i	$0.564775\pi$
$548$	2.69096	−	8.28191i	0.114952	−	0.353786i
$549$	−7.14783			−0.305062
$550$	−0.153216	−	3.31213i	−0.00653317	−	0.141230i
$551$	0.896468			0.0381908
$552$	23.4209	−	72.0821i	0.996859	−	3.06802i
$553$	45.2381	−	32.8674i	1.92372	−	1.39767i
$554$	−17.5945	−	12.7831i	−0.747518	−	0.543104i
$555$	−9.80964	−	30.1910i	−0.416396	−	1.28154i
$556$	1.11071	+	3.41841i	0.0471045	+	0.144973i
$557$	−9.33187	−	6.78000i	−0.395404	−	0.287278i	0.372262	−	0.928128i	$-0.378582\pi$
$557$	−9.33187	−	6.78000i	−0.395404	−	0.287278i	−0.767666	+	0.640850i	$0.778582\pi$
$558$	−46.7068	+	33.9345i	−1.97726	+	1.43656i
$559$	2.94223	−	9.05527i	0.124443	−	0.382997i
$560$	12.5460			0.530164
$561$	6.60781	+	8.26308i	0.278982	+	0.348867i
$562$	26.2748			1.10834
$563$	−9.70098	+	29.8565i	−0.408848	+	1.25830i	0.508792	+	0.860889i	$0.330092\pi$
$563$	−9.70098	+	29.8565i	−0.408848	+	1.25830i	−0.917640	+	0.397414i	$0.869908\pi$
$564$	15.6297	−	11.3556i	0.658129	−	0.478159i
$565$	−25.3244	−	18.3992i	−1.06540	−	0.774061i
$566$	−1.37900	−	4.24414i	−0.0579639	−	0.178395i
$567$	−21.3782	−	65.7954i	−0.897800	−	2.76315i
$568$	−8.08966	−	5.87748i	−0.339435	−	0.246614i
$569$	9.25775	−	6.72615i	0.388105	−	0.281975i	−0.376573	−	0.926387i	$-0.622898\pi$
$569$	9.25775	−	6.72615i	0.388105	−	0.281975i	0.764679	+	0.644412i	$0.222898\pi$
$570$	−0.391693	+	1.20551i	−0.0164062	+	0.0504931i
$571$	−42.4725			−1.77742			−0.888709	−	0.458472i	$-0.848397\pi$
$571$	−42.4725			−1.77742			−0.888709	+	0.458472i	$0.848397\pi$
$572$	−7.29528	+	2.74917i	−0.305031	+	0.114949i
$573$	9.55085			0.398993
$574$	−1.69337	+	5.21165i	−0.0706798	+	0.217530i
$575$	5.63174	−	4.09170i	0.234860	−	0.170636i
$576$	−47.9824	−	34.8613i	−1.99927	−	1.45255i
$577$	−7.42862	−	22.8629i	−0.309257	−	0.951796i	−0.978054	−	0.208351i	$-0.933190\pi$
$577$	−7.42862	−	22.8629i	−0.309257	−	0.951796i	0.668797	−	0.743445i	$-0.266810\pi$
$578$	−0.343162	−	1.05614i	−0.0142736	−	0.0439298i
$579$	12.8504	+	9.33634i	0.534043	+	0.388005i
$580$	6.37216	−	4.62964i	0.264589	−	0.192235i
$581$	−11.2891	+	34.7441i	−0.468349	+	1.44143i
$582$	24.0512			0.996956
$583$	−0.258243	+	0.392369i	−0.0106953	+	0.0162503i
$584$	−20.0633			−0.830223
$585$	13.7649	−	42.3639i	0.569108	−	1.75153i
$586$	−13.5850	+	9.87009i	−0.561192	+	0.407730i
$587$	−12.2626	−	8.90927i	−0.506130	−	0.367725i	0.305224	−	0.952281i	$-0.401269\pi$
$587$	−12.2626	−	8.90927i	−0.506130	−	0.367725i	−0.811353	+	0.584556i	$0.801269\pi$
$588$	−2.93364	−	9.02881i	−0.120981	−	0.372342i
$589$	−0.395588	−	1.21750i	−0.0162999	−	0.0501660i
$590$	−1.44587	−	1.05048i	−0.0595254	−	0.0432478i
$591$	27.5931	−	20.0476i	1.13503	−	0.824647i
$592$	2.85276	−	8.77990i	0.117248	−	0.360852i
$593$	−16.6805			−0.684988			−0.342494	−	0.939520i	$-0.611272\pi$
$593$	−16.6805			−0.684988			−0.342494	+	0.939520i	$0.611272\pi$
$594$	47.3202	+	12.9910i	1.94157	+	0.533027i
$595$	−6.67903			−0.273814
$596$	1.15183	−	3.54498i	0.0471810	−	0.145208i
$597$	−5.56758	+	4.04508i	−0.227866	+	0.165554i
$598$	21.2960	+	15.4725i	0.870860	+	0.632717i
$599$	−3.01661	−	9.28418i	−0.123255	−	0.379341i	0.870324	−	0.492480i	$-0.163910\pi$
$599$	−3.01661	−	9.28418i	−0.123255	−	0.379341i	−0.993579	+	0.113139i	$0.963910\pi$
$600$	−2.72668	−	8.39186i	−0.111316	−	0.342596i
$601$	−10.5524	−	7.66674i	−0.430440	−	0.312733i	0.351385	−	0.936231i	$-0.385711\pi$
$601$	−10.5524	−	7.66674i	−0.430440	−	0.312733i	−0.781825	+	0.623498i	$0.785711\pi$
$602$	−9.20461	+	6.68754i	−0.375152	+	0.272564i
$603$	−23.3726	+	71.9334i	−0.951805	+	2.92935i
$604$	12.2827			0.499777
$605$	−4.89764	+	21.7275i	−0.199117	+	0.883348i
$606$	−49.5678			−2.01356
$607$	−4.97768	+	15.3197i	−0.202038	+	0.621809i	0.797784	+	0.602943i	$0.206005\pi$
$607$	−4.97768	+	15.3197i	−0.202038	+	0.621809i	−0.999822	+	0.0188657i	$0.993995\pi$
$608$	0.580299	−	0.421612i	0.0235342	−	0.0170986i
$609$	43.1875	+	31.3775i	1.75005	+	1.27148i
$610$	0.692053	+	2.12992i	0.0280204	+	0.0862380i
$611$	7.48154	+	23.0258i	0.302671	+	0.931525i
$612$	4.45198	+	3.23456i	0.179961	+	0.130749i
$613$	−9.01313	+	6.54842i	−0.364037	+	0.264488i	−0.754734	−	0.656031i	$-0.772234\pi$
$613$	−9.01313	+	6.54842i	−0.364037	+	0.264488i	0.390697	+	0.920519i	$0.372234\pi$
$614$	1.73457	−	5.33846i	0.0700016	−	0.215443i
$615$	−9.66267			−0.389636
$616$	32.4150	+	8.89903i	1.30604	+	0.358552i
$617$	−35.2876			−1.42063			−0.710313	−	0.703886i	$-0.751447\pi$
$617$	−35.2876			−1.42063			−0.710313	+	0.703886i	$0.751447\pi$
$618$	−2.86374	+	8.81367i	−0.115196	+	0.354538i
$619$	32.1781	−	23.3788i	1.29335	−	0.939673i	0.293481	−	0.955965i	$-0.405186\pi$
$619$	32.1781	−	23.3788i	1.29335	−	0.939673i	0.999867	+	0.0162921i	$0.00518615\pi$
$620$	−9.09941	−	6.61111i	−0.365441	−	0.265508i
$621$	31.8362	+	97.9819i	1.27754	+	3.93188i
$622$	−7.25152	−	22.3179i	−0.290759	−	0.894865i
$623$	45.2794	+	32.8974i	1.81408	+	1.31801i
$624$	14.8609	−	10.7971i	0.594913	−	0.432230i
$625$	−6.08404	+	18.7248i	−0.243362	+	0.748990i
$626$	9.05937			0.362085
$627$	−1.02789	+	1.56176i	−0.0410500	+	0.0623706i
$628$	7.12416			0.284285
$629$	−1.51871	+	4.67411i	−0.0605549	+	0.186369i
$630$	−43.0626	+	31.2868i	−1.71566	+	1.24650i
$631$	−33.3044	−	24.1971i	−1.32583	−	0.963270i	−0.999840	−	0.0178963i	$-0.994303\pi$
$631$	−33.3044	−	24.1971i	−1.32583	−	0.963270i	−0.325988	−	0.945374i	$-0.605697\pi$
$632$	16.0950	+	49.5352i	0.640223	+	1.97040i
$633$	−1.03849	−	3.19615i	−0.0412764	−	0.127036i
$634$	−4.48019	−	3.25505i	−0.177931	−	0.129274i
$635$	12.0306	−	8.74072i	0.477418	−	0.346865i
$636$	−0.107057	+	0.329486i	−0.00424507	+	0.0130650i
$637$	11.8971			0.471379
$638$	−17.4841	+	6.58878i	−0.692204	+	0.260852i
$639$	23.3556			0.923934
$640$	−0.662882	+	2.04014i	−0.0262027	+	0.0806436i
$641$	−28.2789	+	20.5458i	−1.11695	+	0.811511i	−0.983744	−	0.179577i	$-0.942527\pi$
$641$	−28.2789	+	20.5458i	−1.11695	+	0.811511i	−0.133205	+	0.991088i	$0.542527\pi$
$642$	10.7567	+	7.81516i	0.424531	+	0.308440i
$643$	−10.2571	−	31.5680i	−0.404499	−	1.24492i	−0.921313	−	0.388823i	$-0.872882\pi$
$643$	−10.2571	−	31.5680i	−0.404499	−	1.24492i	0.516813	−	0.856098i	$-0.327118\pi$
$644$	6.04403	+	18.6016i	0.238168	+	0.733006i
$645$	−16.2306	−	11.7922i	−0.639078	−	0.464317i
$646$	0.158760	−	0.115346i	0.00624634	−	0.00453823i
$647$	−7.64043	+	23.5148i	−0.300376	+	0.924463i	0.680986	+	0.732296i	$0.261551\pi$
$647$	−7.64043	+	23.5148i	−0.300376	+	0.924463i	−0.981362	+	0.192167i	$0.938449\pi$
$648$	64.4391			2.53141
$649$	−1.64639	−	2.05882i	−0.0646265	−	0.0808156i
$650$	3.06459			0.120203
$651$	23.5564	−	72.4992i	0.923249	−	2.84147i
$652$	2.62300	−	1.90572i	0.102724	−	0.0746337i
$653$	−2.80650	−	2.03904i	−0.109827	−	0.0797939i	0.531516	−	0.847048i	$-0.321622\pi$
$653$	−2.80650	−	2.03904i	−0.109827	−	0.0797939i	−0.641343	+	0.767254i	$0.721622\pi$
$654$	13.0934	+	40.2974i	0.511993	+	1.57575i
$655$	3.72225	+	11.4559i	0.145440	+	0.447620i
$656$	−2.27335	−	1.65169i	−0.0887596	−	0.0644876i
$657$	37.9121	−	27.5447i	1.47909	−	1.07462i
$658$	8.94013	−	27.5149i	0.348523	−	1.07264i
$659$	14.7321			0.573883			0.286942	−	0.957948i	$-0.407361\pi$
$659$	14.7321			0.573883			0.286942	+	0.957948i	$0.407361\pi$
$660$	0.759088	+	16.4094i	0.0295475	+	0.638736i
$661$	1.58052			0.0614750			0.0307375	−	0.999527i	$-0.490214\pi$
$661$	1.58052			0.0614750			0.0307375	+	0.999527i	$0.490214\pi$
$662$	−3.32015	+	10.2184i	−0.129041	+	0.397148i
$663$	−7.91142	+	5.74799i	−0.307254	+	0.223233i
$664$	−27.5292	−	20.0011i	−1.06834	−	0.776194i
$665$	−0.364723	−	1.12250i	−0.0141434	−	0.0435288i
$666$	12.1033	+	37.2502i	0.468994	+	1.44341i
$667$	−31.7359	−	23.0575i	−1.22882	−	0.892790i
$668$	5.40654	−	3.92808i	0.209185	−	0.151982i
$669$	8.94220	−	27.5213i	0.345725	−	1.06403i
$670$	23.6977			0.915524
$671$	0.152648	+	3.29984i	0.00589292	+	0.127389i
$672$	42.7130			1.64769
$673$	0.879369	−	2.70642i	0.0338972	−	0.104325i	−0.932676	−	0.360714i	$-0.882533\pi$
$673$	0.879369	−	2.70642i	0.0338972	−	0.104325i	0.966574	+	0.256389i	$0.0825330\pi$
$674$	−22.8571	+	16.6066i	−0.880421	+	0.639663i
$675$	9.70350	+	7.05000i	0.373488	+	0.271355i
$676$	0.853716	+	2.62747i	0.0328352	+	0.101056i
$677$	−13.7403	−	42.2883i	−0.528082	−	1.62527i	−0.758139	−	0.652092i	$-0.773891\pi$
$677$	−13.7403	−	42.2883i	−0.528082	−	1.62527i	0.230057	−	0.973177i	$-0.426109\pi$
$678$	44.3073	+	32.1911i	1.70161	+	1.23629i
$679$	−18.1181	+	13.1636i	−0.695310	+	0.505172i
$680$	1.92245	−	5.91671i	0.0737228	−	0.226895i
$681$	19.6299			0.752218
$682$	16.6636	+	20.8378i	0.638081	+	0.797921i
$683$	−1.77722			−0.0680035			−0.0340017	−	0.999422i	$-0.510825\pi$
$683$	−1.77722			−0.0680035			−0.0340017	+	0.999422i	$0.510825\pi$
$684$	−0.300501	+	0.924848i	−0.0114900	+	0.0353624i
$685$	18.6028	−	13.5157i	0.710776	−	0.516409i
$686$	9.24327	+	6.71563i	0.352910	+	0.256404i
$687$	−13.4090	−	41.2688i	−0.511587	−	1.57450i
$688$	−1.80290	−	5.54874i	−0.0687348	−	0.211544i
$689$	−0.351240	−	0.255191i	−0.0133812	−	0.00972199i
$690$	44.8724	−	32.6017i	1.70826	−	1.24113i
$691$	8.36181	−	25.7350i	0.318098	−	0.979006i	−0.656362	−	0.754446i	$-0.727906\pi$
$691$	8.36181	−	25.7350i	0.318098	−	0.979006i	0.974460	−	0.224560i	$-0.0720945\pi$
$692$	14.0253			0.533163
$693$	−73.4697	+	27.6866i	−2.79088	+	1.05173i
$694$	21.3270			0.809563
$695$	−2.93289	+	9.02652i	−0.111251	+	0.342395i
$696$	−40.2271	+	29.2267i	−1.52480	+	1.10783i
$697$	1.21025	+	0.879300i	0.0458416	+	0.0333059i
$698$	−7.63716	−	23.5048i	−0.289071	−	0.889668i
$699$	14.6038	+	44.9459i	0.552367	+	1.70001i
$700$	1.84218	+	1.33842i	0.0696280	+	0.0505877i
$701$	6.00399	−	4.36216i	0.226768	−	0.164756i	−0.468600	−	0.883410i	$-0.655241\pi$
$701$	6.00399	−	4.36216i	0.226768	−	0.164756i	0.695368	+	0.718654i	$0.255241\pi$
$702$	−14.0155	+	43.1353i	−0.528981	+	1.62804i
$703$	−0.868481			−0.0327554
$704$	−15.0692	+	22.8959i	−0.567943	+	0.862921i
$705$	51.0140			1.92130
$706$	−1.80093	+	5.54271i	−0.0677791	+	0.208603i
$707$	37.3401	−	27.1292i	1.40432	−	1.02030i
$708$	−1.57295	−	1.14282i	−0.0591151	−	0.0429496i
$709$	5.12529	+	15.7740i	0.192484	+	0.592405i	0.999997	+	0.00255500i	$0.000813282\pi$
$709$	5.12529	+	15.7740i	0.192484	+	0.592405i	−0.807513	+	0.589850i	$0.799187\pi$
$710$	−2.26129	−	6.95953i	−0.0848647	−	0.261187i
$711$	−98.4201	−	71.5064i	−3.69104	−	2.68170i
$712$	−42.1756	+	30.6424i	−1.58060	+	1.14837i
$713$	−17.3102	+	53.2754i	−0.648273	+	1.99518i
$714$	11.6856			0.437322
$715$	−19.8516	−	5.44993i	−0.742406	−	0.203816i
$716$	13.1573			0.491712
$717$	1.11493	−	3.43140i	0.0416378	−	0.128148i
$718$	5.77638	−	4.19679i	0.215573	−	0.156623i
$719$	16.4679	+	11.9647i	0.614150	+	0.446206i	0.850873	−	0.525371i	$-0.176073\pi$
$719$	16.4679	+	11.9647i	0.614150	+	0.446206i	−0.236723	+	0.971577i	$0.576073\pi$
$720$	−8.43462	−	25.9591i	−0.314340	−	0.967439i
$721$	−2.66656	−	8.20682i	−0.0993078	−	0.305638i
$722$	−17.0417	−	12.3815i	−0.634227	−	0.460793i
$723$	28.3271	−	20.5809i	1.05350	−	0.765410i
$724$	−2.87862	+	8.85947i	−0.106983	+	0.329260i
$725$	−4.56694			−0.169612
$726$	8.56887	−	38.0142i	0.318021	−	1.41084i
$727$	−11.5195			−0.427233			−0.213616	−	0.976918i	$-0.568524\pi$
$727$	−11.5195			−0.427233			−0.213616	+	0.976918i	$0.568524\pi$
$728$	−9.60083	+	29.5483i	−0.355830	+	1.09513i
$729$	−18.6107	+	13.5215i	−0.689287	+	0.500796i
$730$	−11.8785	−	8.63021i	−0.439642	−	0.319418i
$731$	0.959797	+	2.95395i	0.0354994	+	0.109256i
$732$	0.752880	+	2.31713i	0.0278273	+	0.0856435i
$733$	−2.08469	−	1.51461i	−0.0769997	−	0.0559435i	0.548619	−	0.836072i	$-0.315154\pi$
$733$	−2.08469	−	1.51461i	−0.0769997	−	0.0559435i	−0.625619	+	0.780129i	$0.715154\pi$
$734$	25.1053	−	18.2401i	0.926655	−	0.673254i
$735$	7.74646	−	23.8411i	0.285732	−	0.879394i
$736$	−31.3873			−1.15695
$737$	33.7077	+	9.25390i	1.24164	+	0.340872i
$738$	11.9220			0.438854
$739$	10.2638	−	31.5886i	0.377559	−	1.16201i	−0.564177	−	0.825654i	$-0.690806\pi$
$739$	10.2638	−	31.5886i	0.377559	−	1.16201i	0.941736	−	0.336353i	$-0.109194\pi$
$740$	−6.17322	+	4.48511i	−0.226932	+	0.164876i
$741$	−1.39805	−	1.01574i	−0.0513586	−	0.0373142i
$742$	0.160318	+	0.493407i	0.00588545	+	0.0181135i
$743$	−1.73542	−	5.34108i	−0.0636665	−	0.195945i	0.914164	−	0.405346i	$-0.132849\pi$
$743$	−1.73542	−	5.34108i	−0.0636665	−	0.195945i	−0.977830	+	0.209400i	$0.932849\pi$
$744$	57.4440	+	41.7355i	2.10600	+	1.53010i
$745$	7.96272	−	5.78526i	0.291732	−	0.211955i
$746$	−5.26761	+	16.2120i	−0.192861	+	0.593565i
$747$	79.4793			2.90800
$748$	1.39818	−	2.12436i	0.0511225	−	0.0776745i
$749$	−12.3805			−0.452373
$750$	13.0782	−	40.2505i	0.477547	−	1.46974i
$751$	2.94954	−	2.14296i	0.107630	−	0.0781979i	−0.532668	−	0.846324i	$-0.678811\pi$
$751$	2.94954	−	2.14296i	0.107630	−	0.0781979i	0.640298	+	0.768126i	$0.278811\pi$
$752$	12.0022	+	8.72009i	0.437674	+	0.317989i
$753$	5.53773	+	17.0434i	0.201806	+	0.621095i
$754$	−5.33658	−	16.4243i	−0.194347	−	0.598138i
$755$	26.2391	+	19.0638i	0.954939	+	0.693804i
$756$	−27.2638	+	19.8083i	−0.991577	+	0.720422i
$757$	2.37597	−	7.31248i	0.0863560	−	0.265777i	−0.898549	−	0.438874i	$-0.855378\pi$
$757$	2.37597	−	7.31248i	0.0863560	−	0.265777i	0.984905	+	0.173097i	$0.0553775\pi$
$758$	23.7839			0.863871
$759$	76.5575	−	28.8502i	2.77886	−	1.04719i
$760$	1.09936			0.0398781
$761$	−1.51715	+	4.66931i	−0.0549967	+	0.169263i	−0.974782	−	0.223160i	$-0.928363\pi$
$761$	−1.51715	+	4.66931i	−0.0549967	+	0.169263i	0.919785	+	0.392422i	$0.128363\pi$
$762$	−21.0486	+	15.2927i	−0.762509	+	0.553996i
$763$	−31.9188	−	23.1904i	−1.15554	−	0.839547i
$764$	−0.709428	−	2.18339i	−0.0256662	−	0.0789924i
$765$	4.49029	+	13.8197i	0.162347	+	0.499652i
$766$	−11.6484	−	8.46305i	−0.420873	−	0.305782i
$767$	1.97120	−	1.43216i	0.0711759	−	0.0517123i
$768$	−15.1341	+	46.5778i	−0.546103	+	1.68073i
$769$	−48.9241			−1.76425			−0.882123	−	0.471019i	$-0.843886\pi$
$769$	−48.9241			−1.76425			−0.882123	+	0.471019i	$0.843886\pi$
$770$	15.3634	+	19.2120i	0.553659	+	0.692352i
$771$	−71.6507			−2.58044
$772$	1.17984	−	3.63118i	0.0424635	−	0.130689i
$773$	5.90899	−	4.29314i	0.212532	−	0.154413i	−0.476427	−	0.879214i	$-0.658068\pi$
$773$	5.90899	−	4.29314i	0.212532	−	0.154413i	0.688958	+	0.724801i	$0.258068\pi$
$774$	20.0255	+	14.5494i	0.719803	+	0.522968i
$775$	2.01527	+	6.20237i	0.0723907	+	0.222796i
$776$	−6.44612	−	19.8391i	−0.231402	−	0.712183i
$777$	−41.8392	−	30.3980i	−1.50097	−	1.09052i
$778$	−26.2705	+	19.0867i	−0.941844	+	0.684290i
$779$	−0.0816900	+	0.251416i	−0.00292685	+	0.00900791i
$780$	−15.1831			−0.543641
$781$	−0.498780	−	10.7823i	−0.0178477	−	0.385820i
$782$	−8.58704			−0.307072
$783$	20.8863	−	64.2814i	0.746416	−	2.29723i
$784$	5.89781	−	4.28501i	0.210636	−	0.153036i
$785$	15.2190	+	11.0573i	0.543191	+	0.394651i
$786$	−6.51242	−	20.0432i	−0.232290	−	0.714916i
$787$	4.57534	+	14.0814i	0.163093	+	0.501949i	0.998891	−	0.0470886i	$-0.0149943\pi$
$787$	4.57534	+	14.0814i	0.163093	+	0.501949i	−0.835798	+	0.549038i	$0.814994\pi$
$788$	−6.63261	−	4.81887i	−0.236277	−	0.171665i
$789$	−26.6077	+	19.3316i	−0.947260	+	0.688225i
$790$	−11.7785	+	36.2506i	−0.419061	+	1.28974i
$791$	−50.9960			−1.81321
$792$	−3.37939	−	73.0533i	−0.120081	−	2.59584i
$793$	−3.05323			−0.108423
$794$	−2.55237	+	7.85540i	−0.0905804	+	0.278778i
$795$	−0.740090	+	0.537707i	−0.0262483	+	0.0190705i
$796$	1.33829	+	0.972324i	0.0474344	+	0.0344631i
$797$	10.6115	+	32.6590i	0.375880	+	1.15684i	0.942883	+	0.333125i	$0.108103\pi$
$797$	10.6115	+	32.6590i	0.375880	+	1.15684i	−0.567002	+	0.823716i	$0.691897\pi$
$798$	0.638117	+	1.96392i	0.0225891	+	0.0695221i
$799$	−6.38953	−	4.64226i	−0.226045	−	0.164231i
$800$	−2.95626	+	2.14785i	−0.104519	+	0.0759378i
$801$	37.6274	−	115.805i	1.32950	−	4.09178i
$802$	−7.16047			−0.252845
$803$	−13.5259	−	16.9141i	−0.477317	−	0.596886i
$804$	25.7806			0.909212
$805$	−15.9596	+	49.1187i	−0.562503	+	1.73121i
$806$	−19.9510	+	14.4953i	−0.702745	+	0.510574i
$807$	29.8738	+	21.7046i	1.05161	+	0.764038i
$808$	13.2850	+	40.8870i	0.467364	+	1.43840i
$809$	15.1589	+	46.6544i	0.532960	+	1.64028i	0.748016	+	0.663681i	$0.231007\pi$
$809$	15.1589	+	46.6544i	0.532960	+	1.64028i	−0.215056	+	0.976602i	$0.568993\pi$
$810$	38.1512	+	27.7185i	1.34050	+	0.973928i
$811$	−2.38463	+	1.73253i	−0.0837357	+	0.0608375i	−0.628865	−	0.777514i	$-0.716480\pi$
$811$	−2.38463	+	1.73253i	−0.0837357	+	0.0608375i	0.545130	+	0.838352i	$0.316480\pi$
$812$	3.96521	−	12.2037i	0.139152	−	0.428265i
$813$	98.9774			3.47129
$814$	16.9383	−	6.38309i	0.593687	−	0.223727i
$815$	8.56123			0.299887
$816$	−1.85171	+	5.69897i	−0.0648228	+	0.199504i
$817$	−0.444041	+	0.322614i	−0.0155350	+	0.0112868i
$818$	−20.8345	−	15.1371i	−0.728460	−	0.529257i
$819$	−22.4247	−	69.0162i	−0.783584	−	2.41162i
$820$	0.717733	+	2.20896i	0.0250643	+	0.0771401i
$821$	−11.6745	−	8.48205i	−0.407444	−	0.296026i	0.365122	−	0.930960i	$-0.381027\pi$
$821$	−11.6745	−	8.48205i	−0.407444	−	0.296026i	−0.772566	+	0.634934i	$0.781027\pi$
$822$	−32.5473	+	23.6470i	−1.13522	+	0.824783i
$823$	8.23068	−	25.3314i	0.286904	−	0.882999i	−0.698918	−	0.715202i	$-0.746335\pi$
$823$	8.23068	−	25.3314i	0.286904	−	0.882999i	0.985822	−	0.167797i	$-0.0536652\pi$
$824$	8.03765			0.280005
$825$	5.23645	−	7.95616i	0.182310	−	0.276998i
$826$	−2.91156			−0.101306
$827$	−4.50540	+	13.8662i	−0.156668	+	0.482175i	−0.998326	−	0.0578360i	$-0.981580\pi$
$827$	−4.50540	+	13.8662i	−0.156668	+	0.482175i	0.841658	+	0.540011i	$0.181580\pi$
$828$	34.4255	−	25.0116i	1.19637	−	0.869213i
$829$	−37.7916	−	27.4572i	−1.31256	−	0.953629i	−0.999993	−	0.00373200i	$-0.998812\pi$
$829$	−37.7916	−	27.4572i	−1.31256	−	0.953629i	−0.312564	−	0.949897i	$-0.601188\pi$
$830$	−7.69519	−	23.6833i	−0.267104	−	0.822061i
$831$	−19.3056	−	59.4167i	−0.669705	−	2.06114i
$832$	−20.4959	−	14.8911i	−0.710567	−	0.516257i
$833$	−3.13978	+	2.28119i	−0.108787	+	0.0790384i
$834$	5.13137	−	15.7927i	0.177685	−	0.546857i
$835$	17.6465			0.610682
$836$	0.433380	+	0.118977i	0.0149887	+	0.00411492i
$837$	−96.5174			−3.33613
$838$	1.34417	−	4.13693i	0.0464335	−	0.142908i
$839$	−23.0943	+	16.7790i	−0.797303	+	0.579275i	−0.910122	−	0.414341i	$-0.864012\pi$
$839$	−23.0943	+	16.7790i	−0.797303	+	0.579275i	0.112819	+	0.993616i	$0.464012\pi$
$840$	52.9621	+	38.4792i	1.82736	+	1.32766i
$841$	−1.00877	−	3.10467i	−0.0347852	−	0.107058i
$842$	5.24910	+	16.1551i	0.180896	+	0.556741i
$843$	61.0633	+	44.3651i	2.10313	+	1.52802i
$844$	−0.653525	+	0.474814i	−0.0224953	+	0.0163438i
$845$	−2.25429	+	6.93799i	−0.0775499	+	0.238674i
$846$	−62.9420			−2.16399
$847$	14.3507	+	33.3265i	0.493096	+	1.14511i
$848$	−0.266035			−0.00913570
$849$	3.96140	−	12.1919i	0.135955	−	0.418426i
$850$	−0.808783	+	0.587616i	−0.0277410	+	0.0201550i
$851$	30.7452	+	22.3377i	1.05393	+	0.765726i
$852$	−2.46004	−	7.57123i	−0.0842797	−	0.259386i
$853$	−10.5994	−	32.6215i	−0.362916	−	1.11694i	−0.951276	−	0.308341i	$-0.900226\pi$
$853$	−10.5994	−	32.6215i	−0.362916	−	1.11694i	0.588360	−	0.808599i	$-0.299774\pi$
$854$	2.95168	+	2.14452i	0.101004	+	0.0733840i
$855$	−2.07739	+	1.50931i	−0.0710452	+	0.0516174i
$856$	3.56353	−	10.9674i	0.121799	−	0.374859i
$857$	8.59759			0.293688			0.146844	−	0.989160i	$-0.453088\pi$
$857$	8.59759			0.293688			0.146844	+	0.989160i	$0.453088\pi$
$858$	34.7321	+	9.53515i	1.18573	+	0.325525i
$859$	11.6675			0.398089			0.199044	−	0.979990i	$-0.436216\pi$
$859$	11.6675			0.398089			0.199044	+	0.979990i	$0.436216\pi$
$860$	−1.49019	+	4.58633i	−0.0508151	+	0.156393i
$861$	−12.7353	+	9.25275i	−0.434018	+	0.315333i
$862$	15.1228	+	10.9874i	0.515086	+	0.374232i
$863$	1.48152	+	4.55963i	0.0504314	+	0.155212i	0.973101	−	0.230381i	$-0.0739971\pi$
$863$	1.48152	+	4.55963i	0.0504314	+	0.155212i	−0.922669	+	0.385592i	$0.873997\pi$
$864$	−16.7117	−	51.4334i	−0.568544	−	1.74980i
$865$	29.9618	+	21.7685i	1.01873	+	0.740151i
$866$	−12.3546	+	8.97612i	−0.419825	+	0.305021i
$867$	0.985784	−	3.03393i	0.0334790	−	0.103038i
$868$	−18.3236			−0.621943
$869$	−30.9095	+	46.9634i	−1.04853	+	1.59312i
$870$	−36.3883			−1.23368
$871$	−9.98369	+	30.7266i	−0.338285	+	1.04113i
$872$	29.7308	−	21.6007i	1.00681	−	0.731492i
$873$	39.4178	+	28.6387i	1.33409	+	0.969273i
$874$	−0.468915	−	1.44317i	−0.0158613	−	0.0488160i
$875$	12.1777	+	37.4791i	0.411682	+	1.26703i
$876$	−12.9225	−	9.38875i	−0.436611	−	0.317216i
$877$	−33.3692	+	24.2441i	−1.12680	+	0.818666i	−0.985226	−	0.171262i	$-0.945216\pi$
$877$	−33.3692	+	24.2441i	−1.12680	+	0.818666i	−0.141572	+	0.989928i	$0.545216\pi$
$878$	9.89568	−	30.4558i	0.333963	−	1.02783i
$879$	−48.2376			−1.62701
$880$	−11.8041	+	4.44828i	−0.397915	+	0.149951i
$881$	−15.9789			−0.538343			−0.269172	−	0.963092i	$-0.586750\pi$
$881$	−15.9789			−0.538343			−0.269172	+	0.963092i	$0.586750\pi$
$882$	−9.55772	+	29.4156i	−0.321825	+	0.990476i
$883$	11.7311	−	8.52317i	0.394784	−	0.286827i	−0.372629	−	0.927980i	$-0.621544\pi$
$883$	11.7311	−	8.52317i	0.394784	−	0.286827i	0.767413	+	0.641153i	$0.221544\pi$
$884$	1.90168	+	1.38165i	0.0639605	+	0.0464700i
$885$	−1.58649	−	4.88270i	−0.0533291	−	0.164130i
$886$	7.65196	+	23.5503i	0.257073	+	0.791188i
$887$	−30.0254	−	21.8147i	−1.00815	−	0.732466i	−0.0443323	−	0.999017i	$-0.514116\pi$
$887$	−30.0254	−	21.8147i	−1.00815	−	0.732466i	−0.963821	+	0.266551i	$0.914116\pi$
$888$	38.9712	−	28.3142i	1.30779	−	0.950164i
$889$	7.48627	−	23.0404i	0.251082	−	0.772750i
$890$	−38.1509			−1.27882
$891$	43.4423	+	54.3247i	1.45537	+	1.81995i
$892$	−6.95578			−0.232897
$893$	0.431282	−	1.32735i	0.0144323	−	0.0444181i
$894$	−13.9315	+	10.1218i	−0.465940	+	0.338525i
$895$	28.1074	+	20.4212i	0.939528	+	0.682607i
$896$	1.07992	+	3.32365i	0.0360775	+	0.111035i
$897$	23.3672	+	71.9168i	0.780208	+	2.40123i
$898$	28.7945	+	20.9204i	0.960884	+	0.698123i
$899$	29.7316	−	21.6012i	0.991603	−	0.720442i
$900$	1.53086	−	4.71151i	0.0510288	−	0.157050i
$901$	0.141628			0.00471831
$902$	−0.254604	−	5.50386i	−0.00847739	−	0.183258i
$903$	−32.6837			−1.08764
$904$	14.6784	−	45.1755i	0.488196	−	1.50251i
$905$	−19.9001	+	14.4583i	−0.661502	+	0.480609i
$906$	−45.9077	−	33.3539i	−1.52518	−	1.10811i
$907$	12.2660	+	37.7510i	0.407287	+	1.25350i	0.918970	+	0.394327i	$0.129022\pi$
$907$	12.2660	+	37.7510i	0.407287	+	1.25350i	−0.511683	+	0.859174i	$0.670978\pi$
$908$	−1.45809	−	4.48753i	−0.0483883	−	0.148924i
$909$	−81.2372	−	59.0222i	−2.69447	−	1.95764i
$910$	−18.3944	+	13.3643i	−0.609768	+	0.443022i
$911$	6.82402	−	21.0022i	0.226090	−	0.695833i	−0.772089	−	0.635514i	$-0.780788\pi$
$911$	6.82402	−	21.0022i	0.226090	−	0.695833i	0.998179	−	0.0603188i	$-0.0192117\pi$
$912$	−1.05891			−0.0350640
$913$	−1.69735	−	36.6921i	−0.0561741	−	1.21433i
$914$	0.499246			0.0165136
$915$	−1.98803	+	6.11852i	−0.0657221	+	0.202272i
$916$	−8.43833	+	6.13080i	−0.278810	+	0.202567i
$917$	15.8758	+	11.5345i	0.524266	+	0.380901i
$918$	−4.57205	−	14.0713i	−0.150900	−	0.464423i
$919$	4.17485	+	12.8489i	0.137716	+	0.423845i	0.996003	−	0.0893251i	$-0.0284710\pi$
$919$	4.17485	+	12.8489i	0.137716	+	0.423845i	−0.858287	+	0.513170i	$0.828471\pi$
$920$	−38.9187	−	28.2761i	−1.28311	−	0.932235i
$921$	13.0452	−	9.47788i	0.429853	−	0.312307i
$922$	−5.17551	+	15.9286i	−0.170446	+	0.524580i
$923$	9.97644			0.328379
$924$	16.7138	+	20.9006i	0.549842	+	0.687580i
$925$	4.42436			0.145472
$926$	−5.48250	+	16.8734i	−0.180166	+	0.554494i
$927$	−15.1882	+	11.0348i	−0.498845	+	0.362432i
$928$	16.6591	+	12.1035i	0.546861	+	0.397318i
$929$	−8.62226	−	26.5366i	−0.282887	−	0.870637i	−0.987024	−	0.160573i	$-0.948666\pi$
$929$	−8.62226	−	26.5366i	−0.282887	−	0.870637i	0.704137	−	0.710064i	$-0.251334\pi$
$930$	16.0572	+	49.4191i	0.526537	+	1.62052i
$931$	−0.554840	−	0.403115i	−0.0181841	−	0.0132116i
$932$	9.19020	−	6.67707i	0.301035	−	0.218715i
$933$	20.8311	−	64.1114i	0.681979	−	2.09891i
$934$	36.5768			1.19683
$935$	6.28406	−	2.36811i	0.205511	−	0.0774453i
$936$	67.5935			2.20936
$937$	−5.23550	+	16.1132i	−0.171036	+	0.526396i	−0.999430	−	0.0337502i	$-0.989255\pi$
$937$	−5.23550	+	16.1132i	−0.171036	+	0.526396i	0.828394	+	0.560146i	$0.189255\pi$
$938$	31.2334	−	22.6924i	1.01981	−	0.740933i
$939$	21.0542	+	15.2968i	0.687077	+	0.499191i
$940$	−3.78927	−	11.6622i	−0.123592	−	0.380378i
$941$	9.09151	+	27.9808i	0.296375	+	0.912147i	0.982756	+	0.184906i	$0.0591980\pi$
$941$	9.09151	+	27.9808i	0.296375	+	0.912147i	−0.686382	+	0.727242i	$0.740802\pi$
$942$	−26.6271	−	19.3457i	−0.867558	−	0.630318i
$943$	9.35843	−	6.79930i	0.304752	−	0.221416i
$944$	0.461369	−	1.41995i	0.0150163	−	0.0462154i
$945$	−88.9868			−2.89474
$946$	6.28917	−	9.55564i	0.204479	−	0.310681i
$947$	−24.3043			−0.789782			−0.394891	−	0.918728i	$-0.629218\pi$
$947$	−24.3043			−0.789782			−0.394891	+	0.918728i	$0.629218\pi$
$948$	−12.8138	+	39.4368i	−0.416173	+	1.28085i
$949$	16.1943	−	11.7658i	0.525689	−	0.381936i
$950$	−0.142922	−	0.103839i	−0.00463701	−	0.00336899i
$951$	−4.91591	−	15.1296i	−0.159409	−	0.490611i
$952$	−3.13192	−	9.63907i	−0.101506	−	0.312404i
$953$	−31.3601	−	22.7845i	−1.01585	−	0.738061i	−0.0504247	−	0.998728i	$-0.516058\pi$
$953$	−31.3601	−	22.7845i	−1.01585	−	0.738061i	−0.965429	+	0.260667i	$0.916058\pi$
$954$	0.913137	−	0.663433i	0.0295639	−	0.0214794i
$955$	1.87329	−	5.76539i	0.0606182	−	0.186563i
$956$	−0.867259			−0.0280492
$957$	−51.7587	−	14.2095i	−1.67312	−	0.459329i
$958$	12.3345			0.398510
$959$	11.5760	−	35.6272i	0.373808	−	1.15046i
$960$	−43.1865	+	31.3768i	−1.39384	+	1.01268i
$961$	−17.3770	−	12.6251i	−0.560548	−	0.407262i
$962$	5.16998	+	15.9116i	0.166687	+	0.513009i
$963$	8.32337	+	25.6167i	0.268217	+	0.825486i
$964$	−6.80904	−	4.94706i	−0.219304	−	0.159334i
$965$	8.15635	−	5.92593i	0.262562	−	0.190763i
$966$	27.9228	−	85.9376i	0.898402	−	2.76500i
$967$	−33.9350			−1.09128			−0.545638	−	0.838021i	$-0.683713\pi$
$967$	−33.9350			−1.09128			−0.545638	+	0.838021i	$0.683713\pi$
$968$	−33.6534	+	3.12024i	−1.08166	+	0.100288i
$969$	0.563725			0.0181095
$970$	4.71737	−	14.5186i	0.151466	−	0.466163i
$971$	−15.7303	+	11.4287i	−0.504810	+	0.366766i	−0.810851	−	0.585252i	$-0.800995\pi$
$971$	−15.7303	+	11.4287i	−0.504810	+	0.366766i	0.306041	+	0.952018i	$0.400995\pi$
$972$	16.7089	+	12.1397i	0.535937	+	0.389381i
$973$	4.77806	+	14.7053i	0.153177	+	0.471432i
$974$	−10.0792	−	31.0204i	−0.322957	−	0.993959i
$975$	7.12218	+	5.17456i	0.228092	+	0.165719i
$976$	−1.51360	+	1.09969i	−0.0484490	+	0.0352003i
$977$	6.36395	−	19.5862i	0.203601	−	0.626619i	−0.796167	−	0.605077i	$-0.793142\pi$
$977$	6.36395	−	19.5862i	0.203601	−	0.626619i	0.999768	−	0.0215421i	$-0.00685761\pi$
$978$	−14.9787			−0.478965
$979$	−54.2659	−	14.8978i	−1.73434	−	0.476137i
$980$	−6.02566			−0.192482
$981$	−26.5247	+	81.6345i	−0.846868	+	2.60639i
$982$	−36.7400	+	26.6932i	−1.17242	+	0.851814i
$983$	−28.8055	−	20.9284i	−0.918754	−	0.667514i	0.0244596	−	0.999701i	$-0.492214\pi$
$983$	−28.8055	−	20.9284i	−0.918754	−	0.667514i	−0.943214	+	0.332187i	$0.892214\pi$
$984$	−4.53101	−	13.9450i	−0.144443	−	0.444550i
$985$	−6.68968	−	20.5887i	−0.213151	−	0.656011i
$986$	4.55765	+	3.31133i	0.145145	+	0.105454i
$987$	67.2360	−	48.8498i	2.14015	−	1.55491i
$988$	−0.128360	+	0.395052i	−0.00408369	+	0.0125683i
$989$	24.0173			0.763706
$990$	29.4231	−	44.7049i	0.935127	−	1.42081i
$991$	27.9402			0.887548			0.443774	−	0.896139i	$-0.353639\pi$
$991$	27.9402			0.887548			0.443774	+	0.896139i	$0.353639\pi$
$992$	9.08661	−	27.9657i	0.288500	−	0.887913i
$993$	−24.9699	+	18.1417i	−0.792394	+	0.575708i
$994$	−9.64465	−	7.00725i	−0.305910	−	0.222256i
$995$	1.34980	+	4.15427i	0.0427917	+	0.131699i
$996$	−8.37154	−	25.7650i	−0.265263	−	0.816394i
$997$	44.2508	+	32.1501i	1.40144	+	1.01820i	0.994499	+	0.104747i	$0.0334032\pi$
$997$	44.2508	+	32.1501i	1.40144	+	1.01820i	0.406937	+	0.913456i	$0.366597\pi$
$998$	−36.6431	+	26.6227i	−1.15992	+	0.842728i
$999$	−20.2343	+	62.2746i	−0.640183	+	1.97028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.f.86.4	✓	36
11.4	even	5		2057.2.a.bd.1.8		18
11.5	even	5	inner	187.2.g.f.137.4	yes	36
11.7	odd	10		2057.2.a.be.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.f.86.4	✓	36	1.1	even	1	trivial
187.2.g.f.137.4	yes	36	11.5	even	5	inner
2057.2.a.bd.1.8		18	11.4	even	5
2057.2.a.be.1.11		18	11.7	odd	10

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.343162 + 1.05614i) q^{2} +(-2.58082 + 1.87507i) q^{3} +(0.620355 + 0.450715i) q^{4} +(0.625693 + 1.92569i) q^{5} +(-1.09471 - 3.36916i) q^{6} +(2.66865 + 1.93889i) q^{7} +(-2.48572 + 1.80598i) q^{8} +(2.21766 - 6.82526i) q^{9} +O(q^{10})\)	\(q+(-0.343162 + 1.05614i) q^{2} +(-2.58082 + 1.87507i) q^{3} +(0.620355 + 0.450715i) q^{4} +(0.625693 + 1.92569i) q^{5} +(-1.09471 - 3.36916i) q^{6} +(2.66865 + 1.93889i) q^{7} +(-2.48572 + 1.80598i) q^{8} +(2.21766 - 6.82526i) q^{9} -2.24851 q^{10} +(-3.19829 - 0.878039i) q^{11} -2.44615 q^{12} +(0.947284 - 2.91544i) q^{13} +(-2.96352 + 2.15313i) q^{14} +(-5.22560 - 3.79662i) q^{15} +(-0.580462 - 1.78648i) q^{16} +(0.309017 + 0.951057i) q^{17} +(6.44744 + 4.68434i) q^{18} +(-0.142964 + 0.103869i) q^{19} +(-0.479783 + 1.47662i) q^{20} -10.5229 q^{21} +(2.02487 - 3.07654i) q^{22} +7.73263 q^{23} +(3.02884 - 9.32181i) q^{24} +(0.728309 - 0.529148i) q^{25} +(2.75405 + 2.00093i) q^{26} +(4.11713 + 12.6712i) q^{27} +(0.781627 + 2.40560i) q^{28} +(-4.10416 - 2.98185i) q^{29} +(5.80300 - 4.21613i) q^{30} +(-2.23860 + 6.88969i) q^{31} -4.05907 q^{32} +(9.90058 - 3.73096i) q^{33} -1.11049 q^{34} +(-2.06393 + 6.35213i) q^{35} +(4.45198 - 3.23456i) q^{36} +(3.97603 + 2.88876i) q^{37} +(-0.0606411 - 0.186634i) q^{38} +(3.02190 + 9.30044i) q^{39} +(-5.03305 - 3.65673i) q^{40} +(1.21025 - 0.879300i) q^{41} +(3.61104 - 11.1136i) q^{42} +3.10597 q^{43} +(-1.58833 - 1.98621i) q^{44} +14.5309 q^{45} +(-2.65354 + 8.16676i) q^{46} +(-6.38953 + 4.64226i) q^{47} +(4.84784 + 3.52216i) q^{48} +(1.19929 + 3.69104i) q^{49} +(0.308928 + 0.950782i) q^{50} +(-2.58082 - 1.87507i) q^{51} +(1.90168 - 1.38165i) q^{52} +(0.0437654 - 0.134696i) q^{53} -14.7955 q^{54} +(-0.310320 - 6.70828i) q^{55} -10.1351 q^{56} +(0.174201 - 0.536134i) q^{57} +(4.55765 - 3.31133i) q^{58} +(0.643032 + 0.467190i) q^{59} +(-1.53054 - 4.71051i) q^{60} +(-0.307782 - 0.947257i) q^{61} +(-6.50830 - 4.72856i) q^{62} +(19.1516 - 13.9144i) q^{63} +(2.55384 - 7.85991i) q^{64} +6.20693 q^{65} +(0.542933 + 11.7368i) q^{66} -10.5393 q^{67} +(-0.236955 + 0.729271i) q^{68} +(-19.9565 + 14.4992i) q^{69} +(-6.00050 - 4.35962i) q^{70} +(1.00568 + 3.09517i) q^{71} +(6.81381 + 20.9707i) q^{72} +(5.28280 + 3.83818i) q^{73} +(-4.41536 + 3.20795i) q^{74} +(-0.887442 + 2.73126i) q^{75} -0.135504 q^{76} +(-6.83270 - 8.54430i) q^{77} -10.8596 q^{78} +(5.23836 - 16.1220i) q^{79} +(3.07700 - 2.23557i) q^{80} +(-16.9673 - 12.3275i) q^{81} +(0.513354 + 1.57994i) q^{82} +(3.42234 + 10.5329i) q^{83} +(-6.52791 - 4.74280i) q^{84} +(-1.63809 + 1.19014i) q^{85} +(-1.06585 + 3.28035i) q^{86} +16.1833 q^{87} +(9.53577 - 3.59349i) q^{88} +16.9672 q^{89} +(-4.98645 + 15.3467i) q^{90} +(8.18068 - 5.94361i) q^{91} +(4.79698 + 3.48521i) q^{92} +(-7.14126 - 21.9785i) q^{93} +(-2.71025 - 8.34130i) q^{94} +(-0.289471 - 0.210313i) q^{95} +(10.4757 - 7.61105i) q^{96} +(-2.09799 + 6.45696i) q^{97} -4.30982 q^{98} +(-13.0856 + 19.8820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9	\( 36 q - 4 q^{2} - q^{3} - 14 q^{4} + q^{5} - 5 q^{6} + q^{7} + 17 q^{8} - 22 q^{9} - 10 q^{10} + 3 q^{11} + 28 q^{12} - 13 q^{13} + 14 q^{14} - 24 q^{15} + 16 q^{16} - 9 q^{17} + 2 q^{18} + 10 q^{19} + 19 q^{20} - 50 q^{21} - 25 q^{22} + 38 q^{23} - 17 q^{24} - 28 q^{25} + 20 q^{26} - 16 q^{27} + 31 q^{28} - 45 q^{29} + 68 q^{30} - 13 q^{31} - 40 q^{32} - 29 q^{33} - 4 q^{34} + 13 q^{35} - 25 q^{36} + q^{37} + 65 q^{38} - 34 q^{39} - 54 q^{40} + 37 q^{41} + 28 q^{42} - 8 q^{43} - 2 q^{44} + 42 q^{45} + 22 q^{46} - 35 q^{47} + 48 q^{48} - 2 q^{49} - 49 q^{50} - q^{51} + 56 q^{52} + 58 q^{53} - 58 q^{54} - 19 q^{55} - 28 q^{56} + 9 q^{57} - 52 q^{58} + 16 q^{59} + 97 q^{60} - 14 q^{61} - 64 q^{62} + 34 q^{63} - 33 q^{64} - 42 q^{65} - 28 q^{66} + 54 q^{67} - 14 q^{68} + 19 q^{69} + 4 q^{70} + 25 q^{71} - 72 q^{72} + 8 q^{73} + 84 q^{74} + 30 q^{75} - 140 q^{76} - 31 q^{77} - 48 q^{78} + 19 q^{79} - 19 q^{80} + 56 q^{81} + 48 q^{82} + 42 q^{83} - 91 q^{84} - 9 q^{85} + 30 q^{86} - 32 q^{87} + 126 q^{88} + 12 q^{89} + 160 q^{90} - 59 q^{91} + 69 q^{92} - 40 q^{93} - 77 q^{94} - 11 q^{95} + 192 q^{96} - 49 q^{97} - 212 q^{98} + 38 q^{99}+O(q^{100}) \) 36 * q - 4 * q^2 - q^3 - 14 * q^4 + q^5 - 5 * q^6 + q^7 + 17 * q^8 - 22 * q^9 - 10 * q^10 + 3 * q^11 + 28 * q^12 - 13 * q^13 + 14 * q^14 - 24 * q^15 + 16 * q^16 - 9 * q^17 + 2 * q^18 + 10 * q^19 + 19 * q^20 - 50 * q^21 - 25 * q^22 + 38 * q^23 - 17 * q^24 - 28 * q^25 + 20 * q^26 - 16 * q^27 + 31 * q^28 - 45 * q^29 + 68 * q^30 - 13 * q^31 - 40 * q^32 - 29 * q^33 - 4 * q^34 + 13 * q^35 - 25 * q^36 + q^37 + 65 * q^38 - 34 * q^39 - 54 * q^40 + 37 * q^41 + 28 * q^42 - 8 * q^43 - 2 * q^44 + 42 * q^45 + 22 * q^46 - 35 * q^47 + 48 * q^48 - 2 * q^49 - 49 * q^50 - q^51 + 56 * q^52 + 58 * q^53 - 58 * q^54 - 19 * q^55 - 28 * q^56 + 9 * q^57 - 52 * q^58 + 16 * q^59 + 97 * q^60 - 14 * q^61 - 64 * q^62 + 34 * q^63 - 33 * q^64 - 42 * q^65 - 28 * q^66 + 54 * q^67 - 14 * q^68 + 19 * q^69 + 4 * q^70 + 25 * q^71 - 72 * q^72 + 8 * q^73 + 84 * q^74 + 30 * q^75 - 140 * q^76 - 31 * q^77 - 48 * q^78 + 19 * q^79 - 19 * q^80 + 56 * q^81 + 48 * q^82 + 42 * q^83 - 91 * q^84 - 9 * q^85 + 30 * q^86 - 32 * q^87 + 126 * q^88 + 12 * q^89 + 160 * q^90 - 59 * q^91 + 69 * q^92 - 40 * q^93 - 77 * q^94 - 11 * q^95 + 192 * q^96 - 49 * q^97 - 212 * q^98 + 38 * q^99

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