LMFDB - Embedded newform 690.2.m.h.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	690.121
Dual form			690.2.m.h.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0949893 + 0.660665i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0949893 + 0.660665i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(-1.84014 - 4.02935i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.175471 + 1.22043i) q^{13} +(-0.561502 - 0.360856i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(2.59966 - 3.00017i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(2.30936 + 2.66514i) q^{19} +(0.959493 + 0.281733i) q^{20} +(0.277272 - 0.607142i) q^{21} +4.42965 q^{22} +(3.69737 + 3.05441i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-1.18304 - 0.347370i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.561502 - 0.360856i) q^{28} +(4.42088 - 5.10197i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-8.87841 + 2.60694i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.630404 + 4.38456i) q^{33} +(1.64911 + 3.61105i) q^{34} +(-0.277272 - 0.607142i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(4.36371 + 2.80438i) q^{37} +(-3.38364 + 0.993525i) q^{38} +(0.175471 - 1.22043i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(8.69865 - 5.59028i) q^{41} +(0.437093 + 0.504432i) q^{42} +(11.0609 + 3.24778i) q^{43} +(-1.84014 + 4.02935i) q^{44} -1.00000 q^{45} +(-4.31433 + 2.09440i) q^{46} +10.9066 q^{47} +(0.415415 - 0.909632i) q^{48} +(6.28900 + 1.84662i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-3.33960 + 2.14623i) q^{51} +(0.807430 - 0.931824i) q^{52} +(-0.349321 + 2.42958i) q^{53} +(0.959493 - 0.281733i) q^{54} +(3.72646 + 2.39485i) q^{55} +(0.0949893 + 0.660665i) q^{56} +(-1.46495 - 3.20780i) q^{57} +(2.80442 + 6.14081i) q^{58} +(-0.637485 - 4.43381i) q^{59} +(-0.841254 - 0.540641i) q^{60} +(-1.47456 + 0.432969i) q^{61} +(1.31687 - 9.15905i) q^{62} +(-0.437093 + 0.504432i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.807430 - 0.931824i) q^{65} +(-4.25021 - 1.24798i) q^{66} +(-0.471056 + 1.03147i) q^{67} -3.96979 q^{68} +(-2.68708 - 3.97236i) q^{69} +0.667459 q^{70} +(-5.53287 + 12.1153i) q^{71} +(0.959493 + 0.281733i) q^{72} +(5.26217 + 6.07286i) q^{73} +(-4.36371 + 2.80438i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.501871 - 3.49059i) q^{76} +(2.83684 - 0.832972i) q^{77} +(1.03725 + 0.666599i) q^{78} +(-1.20547 - 8.38421i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.47155 + 10.2349i) q^{82} +(-13.6578 - 8.77733i) q^{83} +(-0.640422 + 0.188045i) q^{84} +(-0.564960 + 3.92938i) q^{85} +(-7.54917 + 8.71221i) q^{86} +(-5.67920 + 3.64980i) q^{87} +(-2.90080 - 3.34770i) q^{88} +(3.47640 + 1.02076i) q^{89} +(0.415415 - 0.909632i) q^{90} -0.822963 q^{91} +(-0.112895 - 4.79450i) q^{92} +9.25323 q^{93} +(-4.53076 + 9.92098i) q^{94} +(-3.38364 - 0.993525i) q^{95} +(0.654861 + 0.755750i) q^{96} +(9.72437 - 6.24947i) q^{97} +(-4.29228 + 4.95356i) q^{98} +(0.630404 - 4.38456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$2$	−0.415415	+	0.909632i	−0.293743	+	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$5$	−0.841254	+	0.540641i	−0.376220	+	0.241782i
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−0.0949893	+	0.660665i	−0.0359026	+	0.249708i	−0.999867	−	0.0163242i	$-0.994804\pi$
$7$	−0.0949893	+	0.660665i	−0.0359026	+	0.249708i	0.963964	+	0.266032i	$0.0857127\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	−1.84014	−	4.02935i	−0.554824	−	1.21489i	−0.954493	−	0.298235i	$-0.903602\pi$
$11$	−1.84014	−	4.02935i	−0.554824	−	1.21489i	0.399669	−	0.916659i	$-0.369125\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	0.175471	+	1.22043i	0.0486670	+	0.338486i	0.999579	+	0.0290240i	$0.00923993\pi$
$13$	0.175471	+	1.22043i	0.0486670	+	0.338486i	−0.950912	+	0.309462i	$0.899851\pi$
$14$	−0.561502	−	0.360856i	−0.150068	−	0.0964427i
$15$	0.959493	−	0.281733i	0.247740	−	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	2.59966	−	3.00017i	0.630510	−	0.727647i	−0.347157	−	0.937807i	$-0.612853\pi$
$17$	2.59966	−	3.00017i	0.630510	−	0.727647i	0.977667	+	0.210160i	$0.0673985\pi$
$18$	−0.841254	+	0.540641i	−0.198285	+	0.127430i
$19$	2.30936	+	2.66514i	0.529802	+	0.611425i	0.956058	−	0.293178i	$-0.0947129\pi$
$19$	2.30936	+	2.66514i	0.529802	+	0.611425i	−0.426255	+	0.904603i	$0.640167\pi$
$20$	0.959493	+	0.281733i	0.214549	+	0.0629973i
$21$	0.277272	−	0.607142i	0.0605058	−	0.132489i
$22$	4.42965			0.944404
$23$	3.69737	+	3.05441i	0.770956	+	0.636889i
$23$	3.69737	+	3.05441i	0.770956	+	0.636889i
$24$	−1.00000			−0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−1.18304	−	0.347370i	−0.232012	−	0.0681249i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	0.561502	−	0.360856i	0.106114	−	0.0681953i
$29$	4.42088	−	5.10197i	0.820937	−	0.947412i	−0.178394	−	0.983959i	$-0.557090\pi$
$29$	4.42088	−	5.10197i	0.820937	−	0.947412i	0.999332	+	0.0365467i	$0.0116358\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	−8.87841	+	2.60694i	−1.59461	+	0.468220i	−0.954040	−	0.299680i	$-0.903120\pi$
$31$	−8.87841	+	2.60694i	−1.59461	+	0.468220i	−0.640570	+	0.767900i	$0.721302\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$	0.630404	+	4.38456i	0.109739	+	0.763254i
$34$	1.64911	+	3.61105i	0.282820	+	0.619289i
$35$	−0.277272	−	0.607142i	−0.0468676	−	0.102626i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	4.36371	+	2.80438i	0.717389	+	0.461038i	0.847728	−	0.530432i	$-0.177970\pi$
$37$	4.36371	+	2.80438i	0.717389	+	0.461038i	−0.130339	+	0.991469i	$0.541607\pi$
$38$	−3.38364	+	0.993525i	−0.548898	+	0.161171i
$39$	0.175471	−	1.22043i	0.0280979	−	0.195425i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	8.69865	−	5.59028i	1.35850	−	0.873055i	0.360290	−	0.932841i	$-0.382678\pi$
$41$	8.69865	−	5.59028i	1.35850	−	0.873055i	0.998211	+	0.0597850i	$0.0190415\pi$
$42$	0.437093	+	0.504432i	0.0674449	+	0.0778355i
$43$	11.0609	+	3.24778i	1.68678	+	0.495283i	0.977728	−	0.209876i	$-0.0673061\pi$
$43$	11.0609	+	3.24778i	1.68678	+	0.495283i	0.709049	+	0.705159i	$0.249124\pi$
$44$	−1.84014	+	4.02935i	−0.277412	+	0.607447i
$45$	−1.00000			−0.149071
$46$	−4.31433	+	2.09440i	−0.636114	+	0.308803i
$47$	10.9066			1.59089			0.795445	−	0.606026i	$-0.207237\pi$
$47$	10.9066			1.59089			0.795445	+	0.606026i	$0.207237\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	6.28900	+	1.84662i	0.898428	+	0.263802i
$50$	0.654861	+	0.755750i	0.0926113	+	0.106879i
$51$	−3.33960	+	2.14623i	−0.467637	+	0.300532i
$52$	0.807430	−	0.931824i	0.111970	−	0.129221i
$53$	−0.349321	+	2.42958i	−0.0479829	+	0.333728i	0.951664	+	0.307142i	$0.0993727\pi$
$53$	−0.349321	+	2.42958i	−0.0479829	+	0.333728i	−0.999647	+	0.0265861i	$0.991536\pi$
$54$	0.959493	−	0.281733i	0.130570	−	0.0383389i
$55$	3.72646	+	2.39485i	0.502475	+	0.322921i
$56$	0.0949893	+	0.660665i	0.0126935	+	0.0882851i
$57$	−1.46495	−	3.20780i	−0.194038	−	0.424884i
$58$	2.80442	+	6.14081i	0.368238	+	0.806328i
$59$	−0.637485	−	4.43381i	−0.0829935	−	0.577232i	−0.988306	−	0.152486i	$-0.951272\pi$
$59$	−0.637485	−	4.43381i	−0.0829935	−	0.577232i	0.905312	−	0.424747i	$-0.139637\pi$
$60$	−0.841254	−	0.540641i	−0.108605	−	0.0697964i
$61$	−1.47456	+	0.432969i	−0.188798	+	0.0554360i	−0.374765	−	0.927120i	$-0.622276\pi$
$61$	−1.47456	+	0.432969i	−0.188798	+	0.0554360i	0.185967	+	0.982556i	$0.440458\pi$
$62$	1.31687	−	9.15905i	0.167243	−	1.16320i
$63$	−0.437093	+	0.504432i	−0.0550685	+	0.0635524i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−0.807430	−	0.931824i	−0.100149	−	0.115578i
$66$	−4.25021	−	1.24798i	−0.523165	−	0.153615i
$67$	−0.471056	+	1.03147i	−0.0575486	+	0.126014i	−0.936222	−	0.351410i	$-0.885702\pi$
$67$	−0.471056	+	1.03147i	−0.0575486	+	0.126014i	0.878673	+	0.477424i	$0.158429\pi$
$68$	−3.96979			−0.481407
$69$	−2.68708	−	3.97236i	−0.323486	−	0.478216i
$70$	0.667459			0.0797766
$71$	−5.53287	+	12.1153i	−0.656631	+	1.43782i	0.228998	+	0.973427i	$0.426455\pi$
$71$	−5.53287	+	12.1153i	−0.656631	+	1.43782i	−0.885629	+	0.464394i	$0.846272\pi$
$72$	0.959493	+	0.281733i	0.113077	+	0.0332025i
$73$	5.26217	+	6.07286i	0.615890	+	0.710775i	0.974921	−	0.222551i	$-0.0714383\pi$
$73$	5.26217	+	6.07286i	0.615890	+	0.710775i	−0.359031	+	0.933326i	$0.616893\pi$
$74$	−4.36371	+	2.80438i	−0.507270	+	0.326003i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.501871	−	3.49059i	0.0575685	−	0.400398i
$77$	2.83684	−	0.832972i	0.323288	−	0.0949260i
$78$	1.03725	+	0.666599i	0.117445	+	0.0754775i
$79$	−1.20547	−	8.38421i	−0.135626	−	0.943297i	−0.938039	−	0.346529i	$-0.887360\pi$
$79$	−1.20547	−	8.38421i	−0.135626	−	0.943297i	0.802414	−	0.596768i	$-0.203549\pi$
$80$	−0.415415	−	0.909632i	−0.0464448	−	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	1.47155	+	10.2349i	0.162506	+	1.13025i
$83$	−13.6578	−	8.77733i	−1.49914	−	0.963437i	−0.995006	−	0.0998102i	$-0.968176\pi$
$83$	−13.6578	−	8.77733i	−1.49914	−	0.963437i	−0.504131	−	0.863627i	$-0.668187\pi$
$84$	−0.640422	+	0.188045i	−0.0698758	+	0.0205174i
$85$	−0.564960	+	3.92938i	−0.0612785	+	0.426201i
$86$	−7.54917	+	8.71221i	−0.814048	+	0.939461i
$87$	−5.67920	+	3.64980i	−0.608874	+	0.391300i
$88$	−2.90080	−	3.34770i	−0.309226	−	0.356866i
$89$	3.47640	+	1.02076i	0.368498	+	0.108201i	0.460738	−	0.887536i	$-0.347585\pi$
$89$	3.47640	+	1.02076i	0.368498	+	0.108201i	−0.0922405	+	0.995737i	$0.529403\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	−0.822963			−0.0862700
$92$	−0.112895	−	4.79450i	−0.0117701	−	0.499861i
$93$	9.25323			0.959515
$94$	−4.53076	+	9.92098i	−0.467312	+	1.02327i
$95$	−3.38364	−	0.993525i	−0.347154	−	0.101934i
$96$	0.654861	+	0.755750i	0.0668364	+	0.0771334i
$97$	9.72437	−	6.24947i	0.987360	−	0.634538i	0.0559210	−	0.998435i	$-0.482191\pi$
$97$	9.72437	−	6.24947i	0.987360	−	0.634538i	0.931439	+	0.363897i	$0.118554\pi$
$98$	−4.29228	+	4.95356i	−0.433586	+	0.500385i
$99$	0.630404	−	4.38456i	0.0633580	−	0.440665i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	−7.25034	−	4.65951i	−0.721435	−	0.463638i	0.127701	−	0.991813i	$-0.459240\pi$
$101$	−7.25034	−	4.65951i	−0.721435	−	0.463638i	−0.849136	+	0.528174i	$0.822877\pi$
$102$	−0.564960	−	3.92938i	−0.0559393	−	0.389067i
$103$	−6.57722	−	14.4021i	−0.648072	−	1.41908i	−0.893231	−	0.449598i	$-0.851567\pi$
$103$	−6.57722	−	14.4021i	−0.648072	−	1.41908i	0.245159	−	0.969483i	$-0.421160\pi$
$104$	0.512198	+	1.12156i	0.0502252	+	0.109978i
$105$	0.0949893	+	0.660665i	0.00927001	+	0.0644743i
$106$	−2.06491	−	1.32704i	−0.200562	−	0.128893i
$107$	2.19334	−	0.644024i	0.212039	−	0.0622601i	−0.173988	−	0.984748i	$-0.555665\pi$
$107$	2.19334	−	0.644024i	0.212039	−	0.0622601i	0.386027	+	0.922488i	$0.373847\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	−3.54487	+	4.09100i	−0.339537	+	0.391846i	−0.899680	−	0.436549i	$-0.856201\pi$
$109$	−3.54487	+	4.09100i	−0.339537	+	0.391846i	0.560144	+	0.828396i	$0.310746\pi$
$110$	−3.72646	+	2.39485i	−0.355304	+	0.228340i
$111$	−3.39686	−	3.92018i	−0.322416	−	0.372087i
$112$	−0.640422	−	0.188045i	−0.0605142	−	0.0177686i
$113$	−2.84235	+	6.22388i	−0.267386	+	0.585493i	−0.994930	−	0.100567i	$-0.967934\pi$
$113$	−2.84235	+	6.22388i	−0.267386	+	0.585493i	0.727544	+	0.686061i	$0.240662\pi$
$114$	3.52648			0.330285
$115$	−4.76177	−	0.570583i	−0.444037	−	0.0532072i
$116$	−6.75088			−0.626803
$117$	−0.512198	+	1.12156i	−0.0473527	+	0.103688i
$118$	4.29795	+	1.26199i	0.395659	+	0.116176i
$119$	1.73516	+	2.00249i	0.159062	+	0.183568i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	−5.64605	+	6.51589i	−0.513278	+	0.592354i
$122$	0.218711	−	1.52117i	0.0198011	−	0.137720i
$123$	−9.92126	+	2.91314i	−0.894570	+	0.262669i
$124$	7.78431	+	5.00267i	0.699052	+	0.449253i
$125$	0.142315	+	0.989821i	0.0127290	+	0.0885323i
$126$	−0.277272	−	0.607142i	−0.0247014	−	0.0540885i
$127$	3.00330	+	6.57630i	0.266499	+	0.583552i	0.994816	−	0.101688i	$-0.0324244\pi$
$127$	3.00330	+	6.57630i	0.266499	+	0.583552i	−0.728317	+	0.685240i	$0.759697\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$	−9.69789	−	6.23245i	−0.853851	−	0.548737i
$130$	1.18304	−	0.347370i	0.103759	−	0.0304664i
$131$	2.97420	−	20.6860i	0.259857	−	1.80735i	−0.273953	−	0.961743i	$-0.588331\pi$
$131$	2.97420	−	20.6860i	0.259857	−	1.80735i	0.533811	−	0.845604i	$-0.320759\pi$
$132$	2.90080	−	3.34770i	0.252482	−	0.291380i
$133$	−1.98013	+	1.27255i	−0.171699	+	0.110344i
$134$	−0.742573	−	0.856975i	−0.0641485	−	0.0740314i
$135$	0.959493	+	0.281733i	0.0825800	+	0.0242477i
$136$	1.64911	−	3.61105i	0.141410	−	0.309645i
$137$	10.9362			0.934342			0.467171	−	0.884167i	$-0.345273\pi$
$137$	10.9362			0.934342			0.467171	+	0.884167i	$0.345273\pi$
$138$	4.72963	−	0.794074i	0.402613	−	0.0675961i
$139$	5.74430			0.487225			0.243613	−	0.969873i	$-0.421667\pi$
$139$	5.74430			0.487225			0.243613	+	0.969873i	$0.421667\pi$
$140$	−0.277272	+	0.607142i	−0.0234338	+	0.0513129i
$141$	−10.4648	−	3.07274i	−0.881295	−	0.258771i
$142$	−8.72202	−	10.0657i	−0.731936	−	0.844699i
$143$	4.59464	−	2.95280i	0.384223	−	0.246925i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	−0.960750	+	6.68216i	−0.0797859	+	0.554923i
$146$	−7.71005	+	2.26388i	−0.638089	+	0.187360i
$147$	−5.51400	−	3.54363i	−0.454787	−	0.292274i
$148$	−0.738208	−	5.13435i	−0.0606803	−	0.422041i
$149$	−7.14425	−	15.6437i	−0.585280	−	1.28158i	−0.938253	−	0.345950i	$-0.887557\pi$
$149$	−7.14425	−	15.6437i	−0.585280	−	1.28158i	0.352973	−	0.935633i	$-0.385171\pi$
$150$	−0.415415	−	0.909632i	−0.0339185	−	0.0742711i
$151$	−0.471269	−	3.27775i	−0.0383513	−	0.266739i	0.961619	−	0.274387i	$-0.0884748\pi$
$151$	−0.471269	−	3.27775i	−0.0383513	−	0.266739i	−0.999971	+	0.00764747i	$0.997566\pi$
$152$	2.96667	+	1.90656i	0.240628	+	0.154643i
$153$	3.80898	−	1.11842i	0.307938	−	0.0904188i
$154$	−0.420769	+	2.92651i	−0.0339065	+	0.235825i
$155$	6.05958	−	6.99313i	0.486717	−	0.561701i
$156$	−1.03725	+	0.666599i	−0.0830463	+	0.0533706i
$157$	5.28699	+	6.10151i	0.421948	+	0.486954i	0.926429	−	0.376469i	$-0.122862\pi$
$157$	5.28699	+	6.10151i	0.421948	+	0.486954i	−0.504482	+	0.863422i	$0.668316\pi$
$158$	8.12732	+	2.38640i	0.646574	+	0.189851i
$159$	1.01966	−	2.23275i	0.0808645	−	0.177069i
$160$	1.00000			0.0790569
$161$	−2.36915	+	2.15259i	−0.186716	+	0.169648i
$162$	−1.00000			−0.0785674
$163$	3.71278	−	8.12986i	0.290807	−	0.636780i	−0.706687	−	0.707526i	$-0.749811\pi$
$163$	3.71278	−	8.12986i	0.290807	−	0.636780i	0.997494	+	0.0707469i	$0.0225383\pi$
$164$	−9.92126	−	2.91314i	−0.774720	−	0.227478i
$165$	−2.90080	−	3.34770i	−0.225827	−	0.260618i
$166$	13.6578	−	8.77733i	1.06005	−	0.681253i
$167$	−9.50215	+	10.9661i	−0.735298	+	0.848579i	−0.993058	−	0.117630i	$-0.962470\pi$
$167$	−9.50215	+	10.9661i	−0.735298	+	0.848579i	0.257759	+	0.966209i	$0.417016\pi$
$168$	0.0949893	−	0.660665i	0.00732858	−	0.0509714i
$169$	11.0148	−	3.23422i	0.847289	−	0.248786i
$170$	−3.33960	−	2.14623i	−0.256135	−	0.164608i
$171$	0.501871	+	3.49059i	0.0383790	+	0.266932i
$172$	−4.78886	−	10.4861i	−0.365147	−	0.799561i
$173$	−0.782982	−	1.71449i	−0.0595290	−	0.130350i	0.877530	−	0.479523i	$-0.159190\pi$
$173$	−0.782982	−	1.71449i	−0.0595290	−	0.130350i	−0.937059	+	0.349172i	$0.886463\pi$
$174$	−0.960750	−	6.68216i	−0.0728343	−	0.506573i
$175$	0.561502	+	0.360856i	0.0424456	+	0.0272781i
$176$	4.25021	−	1.24798i	0.320372	−	0.0940697i
$177$	−0.637485	+	4.43381i	−0.0479163	+	0.333265i
$178$	−2.37267	+	2.73820i	−0.177839	+	0.205237i
$179$	−11.9836	+	7.70140i	−0.895697	+	0.575629i	−0.905511	−	0.424323i	$-0.860512\pi$
$179$	−11.9836	+	7.70140i	−0.895697	+	0.575629i	0.00981441	+	0.999952i	$0.496876\pi$
$180$	0.654861	+	0.755750i	0.0488104	+	0.0563302i
$181$	−16.8712	−	4.95382i	−1.25402	−	0.368214i	−0.413756	−	0.910388i	$-0.635783\pi$
$181$	−16.8712	−	4.95382i	−1.25402	−	0.368214i	−0.840267	+	0.542173i	$0.817602\pi$
$182$	0.341871	−	0.748594i	0.0253412	−	0.0554894i
$183$	1.53681			0.113604
$184$	4.40813	+	1.88902i	0.324972	+	0.139260i
$185$	−5.18715			−0.381367
$186$	−3.84393	+	8.41703i	−0.281851	+	0.617167i
$187$	−16.8724	−	4.95420i	−1.23384	−	0.362287i
$188$	−7.14230	−	8.24265i	−0.520905	−	0.601157i
$189$	0.561502	−	0.360856i	0.0408433	−	0.0262484i
$190$	2.30936	−	2.66514i	0.167538	−	0.193349i
$191$	−0.800458	+	5.56731i	−0.0579191	+	0.402836i	0.940152	+	0.340755i	$0.110683\pi$
$191$	−0.800458	+	5.56731i	−0.0579191	+	0.402836i	−0.998071	+	0.0620810i	$0.980226\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	10.5668	+	6.79089i	0.760617	+	0.488819i	0.862550	−	0.505972i	$-0.168866\pi$
$193$	10.5668	+	6.79089i	0.760617	+	0.488819i	−0.101932	+	0.994791i	$0.532503\pi$
$194$	1.64507	+	11.4417i	0.118109	+	0.821468i
$195$	0.512198	+	1.12156i	0.0366793	+	0.0803164i
$196$	−2.72284	−	5.96218i	−0.194488	−	0.425870i
$197$	0.465605	+	3.23835i	0.0331730	+	0.230723i	0.999662	−	0.0259834i	$-0.00827170\pi$
$197$	0.465605	+	3.23835i	0.0331730	+	0.230723i	−0.966489	+	0.256707i	$0.917363\pi$
$198$	3.72646	+	2.39485i	0.264828	+	0.170194i
$199$	−12.4420	+	3.65330i	−0.881991	+	0.258976i	−0.691207	−	0.722656i	$-0.742921\pi$
$199$	−12.4420	+	3.65330i	−0.881991	+	0.258976i	−0.190783	+	0.981632i	$0.561103\pi$
$200$	0.142315	−	0.989821i	0.0100632	−	0.0699909i
$201$	0.742573	−	0.856975i	0.0523771	−	0.0604463i
$202$	7.25034	−	4.65951i	0.510132	−	0.327842i
$203$	2.95076	+	3.40536i	0.207103	+	0.239009i
$204$	3.80898	+	1.11842i	0.266682	+	0.0783050i
$205$	−4.29543	+	9.40569i	−0.300006	+	0.656922i
$206$	15.8329			1.10313
$207$	1.45909	+	4.56849i	0.101414	+	0.317532i
$208$	−1.23298			−0.0854917
$209$	6.48923	−	14.2094i	0.448869	−	0.982887i
$210$	−0.640422	−	0.188045i	−0.0441933	−	0.0129763i
$211$	−14.9662	−	17.2719i	−1.03031	−	1.18905i	−0.981740	−	0.190227i	$-0.939078\pi$
$211$	−14.9662	−	17.2719i	−1.03031	−	1.18905i	−0.0485744	−	0.998820i	$-0.515468\pi$
$212$	2.06491	−	1.32704i	0.141819	−	0.0911413i
$213$	8.72202	−	10.0657i	0.597623	−	0.689694i
$214$	−0.325323	+	2.26267i	−0.0222386	+	0.154673i
$215$	−11.0609	+	3.24778i	−0.754350	+	0.221497i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−0.878958	−	6.11329i	−0.0596676	−	0.414997i
$218$	−2.24871	−	4.92399i	−0.152302	−	0.333495i
$219$	−3.33809	−	7.30939i	−0.225567	−	0.493923i
$220$	−0.630404	−	4.38456i	−0.0425019	−	0.295607i
$221$	4.11766	+	2.64626i	0.276983	+	0.178006i
$222$	4.97703	−	1.46139i	0.334036	−	0.0980819i
$223$	−1.75818	+	12.2284i	−0.117736	+	0.818875i	0.842302	+	0.539006i	$0.181200\pi$
$223$	−1.75818	+	12.2284i	−0.117736	+	0.818875i	−0.960038	+	0.279869i	$0.909709\pi$
$224$	0.437093	−	0.504432i	0.0292045	−	0.0337038i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	−4.48069	−	5.17099i	−0.298051	−	0.343969i
$227$	1.07514	+	0.315688i	0.0713592	+	0.0209530i	0.317217	−	0.948353i	$-0.397252\pi$
$227$	1.07514	+	0.315688i	0.0713592	+	0.0209530i	−0.245858	+	0.969306i	$0.579070\pi$
$228$	−1.46495	+	3.20780i	−0.0970190	+	0.212442i
$229$	29.7937			1.96883			0.984413	−	0.175875i	$-0.0562753\pi$
$229$	29.7937			1.96883			0.984413	+	0.175875i	$0.0562753\pi$
$230$	2.49713	−	4.09443i	0.164656	−	0.269979i
$231$	−2.95661			−0.194530
$232$	2.80442	−	6.14081i	0.184119	−	0.403164i
$233$	−4.60237	−	1.35138i	−0.301511	−	0.0885316i	0.127478	−	0.991841i	$-0.459312\pi$
$233$	−4.60237	−	1.35138i	−0.301511	−	0.0885316i	−0.428989	+	0.903310i	$0.641130\pi$
$234$	−0.807430	−	0.931824i	−0.0527833	−	0.0609152i
$235$	−9.17521	+	5.89655i	−0.598524	+	0.384648i
$236$	−2.93338	+	3.38531i	−0.190947	+	0.220365i
$237$	−1.20547	+	8.38421i	−0.0783035	+	0.544613i
$238$	−2.54234	+	0.746498i	−0.164795	+	0.0483883i
$239$	24.5497	+	15.7771i	1.58799	+	1.02054i	0.972650	+	0.232274i	$0.0746165\pi$
$239$	24.5497	+	15.7771i	1.58799	+	1.02054i	0.615337	+	0.788264i	$0.289020\pi$
$240$	0.142315	+	0.989821i	0.00918638	+	0.0638927i
$241$	4.05196	+	8.87256i	0.261010	+	0.571532i	0.994084	−	0.108617i	$-0.0346423\pi$
$241$	4.05196	+	8.87256i	0.261010	+	0.571532i	−0.733074	+	0.680149i	$0.761915\pi$
$242$	−3.58161	−	7.84263i	−0.230235	−	0.504143i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	1.29285	+	0.830861i	0.0827660	+	0.0531905i
$245$	−6.28900	+	1.84662i	−0.401789	+	0.117976i
$246$	1.47155	−	10.2349i	0.0938226	−	0.652551i
$247$	−2.84739	+	3.28606i	−0.181175	+	0.209087i
$248$	−7.78431	+	5.00267i	−0.494304	+	0.317670i
$249$	10.6317	+	12.2696i	0.673756	+	0.777556i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	−4.81239	+	10.5377i	−0.303756	+	0.665132i	−0.998536	−	0.0540899i	$-0.982774\pi$
$251$	−4.81239	+	10.5377i	−0.303756	+	0.665132i	0.694780	+	0.719222i	$0.255502\pi$
$252$	0.667459			0.0420460
$253$	5.50360	−	20.5186i	0.346008	−	1.28999i
$254$	−7.22963			−0.453627
$255$	1.64911	−	3.61105i	0.103271	−	0.226132i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	10.5516	+	12.1772i	0.658190	+	0.759592i	0.982480	−	0.186366i	$-0.0596709\pi$
$257$	10.5516	+	12.1772i	0.658190	+	0.759592i	−0.324290	+	0.945958i	$0.605125\pi$
$258$	9.69789	−	6.23245i	0.603764	−	0.388016i
$259$	−2.26726	+	2.61656i	−0.140881	+	0.162585i
$260$	−0.175471	+	1.22043i	−0.0108823	+	0.0756878i
$261$	6.47742	−	1.90194i	0.400942	−	0.117727i
$262$	17.5811	+	11.2987i	1.08617	+	0.698037i
$263$	−3.77561	−	26.2600i	−0.232814	−	1.61926i	−0.685834	−	0.727758i	$-0.740562\pi$
$263$	−3.77561	−	26.2600i	−0.232814	−	1.61926i	0.453020	−	0.891500i	$-0.350347\pi$
$264$	1.84014	+	4.02935i	0.113253	+	0.247989i
$265$	−1.01966	−	2.23275i	−0.0626374	−	0.137157i
$266$	−0.334978	−	2.32982i	−0.0205388	−	0.142851i
$267$	−3.04800	−	1.95883i	−0.186535	−	0.119878i
$268$	1.08801	−	0.319468i	0.0664606	−	0.0195146i
$269$	2.23860	−	15.5698i	0.136490	−	0.949308i	−0.800346	−	0.599539i	$-0.795351\pi$
$269$	2.23860	−	15.5698i	0.136490	−	0.949308i	0.936836	−	0.349770i	$-0.113740\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	−20.9212	+	13.4453i	−1.27087	+	0.816742i	−0.989734	−	0.142925i	$-0.954349\pi$
$271$	−20.9212	+	13.4453i	−1.27087	+	0.816742i	−0.281141	+	0.959666i	$0.590713\pi$
$272$	2.59966	+	3.00017i	0.157627	+	0.181912i
$273$	0.789627	+	0.231855i	0.0477904	+	0.0140325i
$274$	−4.54306	+	9.94791i	−0.274456	+	0.600975i
$275$	−4.42965			−0.267118
$276$	−1.24245	+	4.63210i	−0.0747865	+	0.278820i
$277$	10.3857			0.624018			0.312009	−	0.950079i	$-0.398998\pi$
$277$	10.3857			0.624018			0.312009	+	0.950079i	$0.398998\pi$
$278$	−2.38627	+	5.22520i	−0.143119	+	0.313387i
$279$	−8.87841	−	2.60694i	−0.531536	−	0.156073i
$280$	−0.437093	−	0.504432i	−0.0261213	−	0.0301456i
$281$	6.12788	−	3.93815i	0.365559	−	0.234930i	−0.344946	−	0.938622i	$-0.612103\pi$
$281$	6.12788	−	3.93815i	0.365559	−	0.234930i	0.710505	+	0.703692i	$0.248467\pi$
$282$	7.14230	−	8.24265i	0.425318	−	0.490843i
$283$	−0.461321	+	3.20856i	−0.0274227	+	0.190729i	−0.998928	−	0.0462883i	$-0.985261\pi$
$283$	−0.461321	+	3.20856i	−0.0274227	+	0.190729i	0.971505	+	0.237017i	$0.0761698\pi$
$284$	12.7794	−	3.75237i	0.758317	−	0.222662i
$285$	2.96667	+	1.90656i	0.175730	+	0.112935i
$286$	0.777276	+	5.40607i	0.0459613	+	0.319668i
$287$	2.86703	+	6.27791i	0.169235	+	0.370573i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	0.176582	+	1.22816i	0.0103872	+	0.0722445i
$290$	−5.67920	−	3.64980i	−0.333494	−	0.214324i
$291$	−11.0911	+	3.25665i	−0.650174	+	0.190908i
$292$	1.14358	−	7.95376i	0.0669228	−	0.465459i
$293$	−13.7528	+	15.8716i	−0.803449	+	0.927230i	−0.998565	−	0.0535504i	$-0.982946\pi$
$293$	−13.7528	+	15.8716i	−0.803449	+	0.927230i	0.195116	+	0.980780i	$0.437492\pi$
$294$	5.51400	−	3.54363i	0.321583	−	0.206669i
$295$	2.93338	+	3.38531i	0.170788	+	0.197100i
$296$	4.97703	+	1.46139i	0.289284	+	0.0849414i
$297$	−1.84014	+	4.02935i	−0.106776	+	0.233806i
$298$	17.1979			0.996245
$299$	−3.07891	+	5.04834i	−0.178058	+	0.291953i
$300$	1.00000			0.0577350
$301$	−3.19637	+	6.99907i	−0.184236	+	0.403420i
$302$	3.17731	+	0.932944i	0.182834	+	0.0536849i
$303$	5.64391	+	6.51342i	0.324234	+	0.374186i
$304$	−2.96667	+	1.90656i	−0.170150	+	0.109349i
$305$	1.00640	−	1.16144i	0.0576260	−	0.0665040i
$306$	−0.564960	+	3.92938i	−0.0322966	+	0.224628i
$307$	−8.60451	+	2.52651i	−0.491085	+	0.144196i	−0.517894	−	0.855445i	$-0.673284\pi$
$307$	−8.60451	+	2.52651i	−0.491085	+	0.144196i	0.0268084	+	0.999641i	$0.491466\pi$
$308$	−2.48726	−	1.59846i	−0.141725	−	0.0910808i
$309$	2.25325	+	15.6717i	0.128183	+	0.891533i
$310$	3.84393	+	8.41703i	0.218321	+	0.478055i
$311$	9.99301	+	21.8816i	0.566652	+	1.24079i	0.948561	+	0.316594i	$0.102539\pi$
$311$	9.99301	+	21.8816i	0.566652	+	1.24079i	−0.381910	+	0.924200i	$0.624733\pi$
$312$	−0.175471	−	1.22043i	−0.00993410	−	0.0690932i
$313$	−14.5555	−	9.35427i	−0.822727	−	0.528735i	0.0602321	−	0.998184i	$-0.480816\pi$
$313$	−14.5555	−	9.35427i	−0.822727	−	0.528735i	−0.882959	+	0.469450i	$0.844452\pi$
$314$	−7.74643	+	2.27456i	−0.437156	+	0.128361i
$315$	0.0949893	−	0.660665i	0.00535204	−	0.0372243i
$316$	−5.54695	+	6.40152i	−0.312040	+	0.360114i
$317$	0.916188	−	0.588798i	0.0514582	−	0.0330702i	−0.514659	−	0.857395i	$-0.672081\pi$
$317$	0.916188	−	0.588798i	0.0514582	−	0.0330702i	0.566117	+	0.824325i	$0.308445\pi$
$318$	1.60740	+	1.85503i	0.0901383	+	0.104025i
$319$	−28.6927	−	8.42493i	−1.60648	−	0.471705i
$320$	−0.415415	+	0.909632i	−0.0232224	+	0.0508500i
$321$	−2.28594			−0.127589
$322$	−0.973882	−	3.04928i	−0.0542723	−	0.169930i
$323$	13.9994			0.778947
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	1.18304	+	0.347370i	0.0656230	+	0.0192686i
$326$	5.85283	+	6.75453i	0.324158	+	0.374099i
$327$	4.55384	−	2.92658i	0.251828	−	0.161840i
$328$	6.77133	−	7.81453i	0.373884	−	0.431485i
$329$	−1.03601	+	7.20560i	−0.0571170	+	0.397258i
$330$	4.25021	−	1.24798i	0.233967	−	0.0686988i
$331$	12.7362	+	8.18508i	0.700047	+	0.449893i	0.841645	−	0.540031i	$-0.181588\pi$
$331$	12.7362	+	8.18508i	0.700047	+	0.449893i	−0.141598	+	0.989924i	$0.545224\pi$
$332$	2.31049	+	16.0698i	0.126805	+	0.881945i
$333$	2.15482	+	4.71839i	0.118083	+	0.258566i
$334$	−6.02775	−	13.1989i	−0.329824	−	0.722213i
$335$	−0.161377	−	1.12240i	−0.00881694	−	0.0613232i
$336$	0.561502	+	0.360856i	0.0306325	+	0.0196863i
$337$	−5.56098	+	1.63285i	−0.302926	+	0.0889471i	−0.429663	−	0.902989i	$-0.641368\pi$
$337$	−5.56098	+	1.63285i	−0.302926	+	0.0889471i	0.126737	+	0.991936i	$0.459550\pi$
$338$	−1.63374	+	11.3629i	−0.0888638	+	0.618061i
$339$	4.48069	−	5.17099i	0.243357	−	0.280849i
$340$	3.33960	−	2.14623i	0.181115	−	0.116396i
$341$	26.8418	+	30.9771i	1.45356	+	1.67750i
$342$	−3.38364	−	0.993525i	−0.182966	−	0.0537237i
$343$	−3.75829	+	8.22951i	−0.202929	+	0.444352i
$344$	11.5279			0.621543
$345$	4.40813	+	1.88902i	0.237326	+	0.101701i
$346$	1.88482			0.101328
$347$	−6.66499	+	14.5943i	−0.357795	+	0.783463i	0.642063	+	0.766652i	$0.278079\pi$
$347$	−6.66499	+	14.5943i	−0.357795	+	0.783463i	−0.999859	+	0.0168109i	$0.994649\pi$
$348$	6.47742	+	1.90194i	0.347226	+	0.101955i
$349$	2.58830	+	2.98706i	0.138549	+	0.159894i	0.820783	−	0.571240i	$-0.193537\pi$
$349$	2.58830	+	2.98706i	0.138549	+	0.159894i	−0.682235	+	0.731133i	$0.738992\pi$
$350$	−0.561502	+	0.360856i	−0.0300136	+	0.0192885i
$351$	0.807430	−	0.931824i	0.0430974	−	0.0497371i
$352$	−0.630404	+	4.38456i	−0.0336007	+	0.233698i
$353$	−35.3656	+	10.3843i	−1.88232	+	0.552699i	−0.886351	+	0.463014i	$0.846768\pi$
$353$	−35.3656	+	10.3843i	−1.88232	+	0.552699i	−0.995970	+	0.0896856i	$0.971414\pi$
$354$	−3.76831	−	2.42175i	−0.200283	−	0.128714i
$355$	−1.89548	−	13.1833i	−0.100601	−	0.699698i
$356$	−1.50512	−	3.29575i	−0.0797710	−	0.174674i
$357$	−1.10071	−	2.41022i	−0.0582559	−	0.127563i
$358$	−2.02727	−	14.0999i	−0.107144	−	0.745205i
$359$	22.3589	+	14.3692i	1.18006	+	0.758375i	0.975396	−	0.220458i	$-0.0707552\pi$
$359$	22.3589	+	14.3692i	1.18006	+	0.758375i	0.204659	+	0.978833i	$0.434392\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	0.934142	−	6.49710i	0.0491654	−	0.341953i
$362$	11.5147	−	13.2887i	0.605198	−	0.698436i
$363$	7.25309	−	4.66128i	0.380688	−	0.244654i
$364$	0.538926	+	0.621954i	0.0282474	+	0.0325992i
$365$	−7.71005	−	2.26388i	−0.403563	−	0.118497i
$366$	−0.638413	+	1.39793i	−0.0333704	+	0.0730710i
$367$	−0.0196338			−0.00102488			−0.000512438	−	1.00000i	$-0.500163\pi$
$367$	−0.0196338			−0.00102488			−0.000512438		1.00000i	$0.500163\pi$
$368$	−3.54951	+	3.22505i	−0.185031	+	0.168117i
$369$	10.3401			0.538284
$370$	2.15482	−	4.71839i	0.112024	−	0.245298i
$371$	−1.57196	−	0.461568i	−0.0816119	−	0.0239634i
$372$	−6.05958	−	6.99313i	−0.314174	−	0.362577i
$373$	8.76521	−	5.63306i	0.453846	−	0.291669i	−0.293678	−	0.955905i	$-0.594879\pi$
$373$	8.76521	−	5.63306i	0.453846	−	0.291669i	0.747523	+	0.664236i	$0.231243\pi$
$374$	11.5156	−	13.2897i	0.595456	−	0.687192i
$375$	0.142315	−	0.989821i	0.00734911	−	0.0511142i
$376$	10.4648	−	3.07274i	0.539681	−	0.158465i
$377$	7.00233	+	4.50013i	0.360639	+	0.231768i
$378$	0.0949893	+	0.660665i	0.00488572	+	0.0339809i
$379$	−3.67415	−	8.04527i	−0.188729	−	0.413258i	0.791488	−	0.611184i	$-0.209307\pi$
$379$	−3.67415	−	8.04527i	−0.188729	−	0.413258i	−0.980217	+	0.197926i	$0.936579\pi$
$380$	1.46495	+	3.20780i	0.0751506	+	0.164557i
$381$	−1.02888	−	7.15604i	−0.0527113	−	0.366615i
$382$	−4.73168	−	3.04087i	−0.242094	−	0.155584i
$383$	22.9451	−	6.73728i	1.17244	−	0.344259i	0.363184	−	0.931717i	$-0.381689\pi$
$383$	22.9451	−	6.73728i	1.17244	−	0.344259i	0.809255	+	0.587458i	$0.199871\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−1.93617	+	2.23445i	−0.0986761	+	0.113878i
$386$	−10.5668	+	6.79089i	−0.537838	+	0.345647i
$387$	7.54917	+	8.71221i	0.383746	+	0.442866i
$388$	−11.0911	−	3.25665i	−0.563067	−	0.165332i
$389$	5.26049	−	11.5189i	0.266717	−	0.584029i	−0.728127	−	0.685442i	$-0.759609\pi$
$389$	5.26049	−	11.5189i	0.266717	−	0.584029i	0.994844	+	0.101413i	$0.0323363\pi$
$390$	−1.23298			−0.0624343
$391$	18.7756	−	3.15231i	0.949525	−	0.159419i
$392$	6.55450			0.331052
$393$	−8.68165	+	19.0102i	−0.437932	+	0.958936i
$394$	−3.13913	−	0.921732i	−0.158147	−	0.0464362i
$395$	5.54695	+	6.40152i	0.279097	+	0.322096i
$396$	−3.72646	+	2.39485i	−0.187261	+	0.120346i
$397$	−19.3681	+	22.3520i	−0.972059	+	1.12182i	0.0204683	+	0.999791i	$0.493484\pi$
$397$	−19.3681	+	22.3520i	−0.972059	+	1.12182i	−0.992527	+	0.122025i	$0.961061\pi$
$398$	1.84544	−	12.8353i	0.0925033	−	0.643375i
$399$	2.25844	−	0.663137i	0.113063	−	0.0331984i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−0.498563	−	3.46759i	−0.0248971	−	0.173163i	0.973579	−	0.228351i	$-0.0733333\pi$
$401$	−0.498563	−	3.46759i	−0.0248971	−	0.173163i	−0.998476	+	0.0551879i	$0.982424\pi$
$402$	0.471056	+	1.03147i	0.0234941	+	0.0514450i
$403$	−4.73949	−	10.3780i	−0.236091	−	0.516967i
$404$	1.22654	+	8.53077i	0.0610226	+	0.424421i
$405$	−0.841254	−	0.540641i	−0.0418022	−	0.0268647i
$406$	−4.32341	+	1.26947i	−0.214567	+	0.0630026i
$407$	3.27000	−	22.7433i	0.162088	−	1.12735i
$408$	−2.59966	+	3.00017i	−0.128702	+	0.148530i
$409$	11.4592	−	7.36440i	0.566623	−	0.364146i	−0.225748	−	0.974186i	$-0.572483\pi$
$409$	11.4592	−	7.36440i	0.566623	−	0.364146i	0.792371	+	0.610039i	$0.208846\pi$
$410$	−6.77133	−	7.81453i	−0.334412	−	0.385932i
$411$	−10.4932	−	3.08108i	−0.517591	−	0.151979i
$412$	−6.57722	+	14.4021i	−0.324036	+	0.709540i
$413$	2.98982			0.147119
$414$	−4.76177	−	0.570583i	−0.234028	−	0.0280426i
$415$	16.2351			0.796947
$416$	0.512198	−	1.12156i	0.0251126	−	0.0549889i
$417$	−5.51162	−	1.61836i	−0.269905	−	0.0792513i
$418$	10.2296	+	11.8056i	0.500347	+	0.577432i
$419$	16.6356	−	10.6911i	0.812703	−	0.522293i	−0.0670353	−	0.997751i	$-0.521354\pi$
$419$	16.6356	−	10.6911i	0.812703	−	0.522293i	0.879738	+	0.475458i	$0.157718\pi$
$420$	0.437093	−	0.504432i	0.0213279	−	0.0246138i
$421$	−0.162747	+	1.13193i	−0.00793180	+	0.0551669i	−0.993403	−	0.114676i	$-0.963417\pi$
$421$	−0.162747	+	1.13193i	−0.00793180	+	0.0551669i	0.985471	+	0.169843i	$0.0543261\pi$
$422$	21.9282	−	6.43871i	1.06745	−	0.313432i
$423$	9.17521	+	5.89655i	0.446114	+	0.286700i
$424$	0.349321	+	2.42958i	0.0169645	+	0.117991i
$425$	−1.64911	−	3.61105i	−0.0799936	−	0.175161i
$426$	5.53287	+	12.1153i	0.268068	+	0.586988i
$427$	−0.145980	−	1.01532i	−0.00706449	−	0.0491346i
$428$	−1.92306	−	1.23587i	−0.0929544	−	0.0597382i
$429$	−5.24043	+	1.53873i	−0.253010	+	0.0742905i
$430$	1.64059	−	11.4106i	0.0791163	−	0.550266i
$431$	18.0430	−	20.8227i	0.869099	−	1.00299i	−0.130834	−	0.991404i	$-0.541765\pi$
$431$	18.0430	−	20.8227i	0.869099	−	1.00299i	0.999933	−	0.0115893i	$-0.00368906\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	−7.74073	−	8.93328i	−0.371996	−	0.429306i	0.538627	−	0.842544i	$-0.318943\pi$
$433$	−7.74073	−	8.93328i	−0.371996	−	0.429306i	−0.910623	+	0.413238i	$0.864398\pi$
$434$	5.92597	+	1.74002i	0.284456	+	0.0835238i
$435$	2.80442	−	6.14081i	0.134461	−	0.294429i
$436$	5.41316			0.259244
$437$	0.398121	+	16.9077i	0.0190447	+	0.808807i
$438$	8.03555			0.383953
$439$	0.462196	−	1.01207i	0.0220594	−	0.0483034i	−0.898282	−	0.439420i	$-0.855184\pi$
$439$	0.462196	−	1.01207i	0.0220594	−	0.0483034i	0.920341	+	0.391117i	$0.127911\pi$
$440$	4.25021	+	1.24798i	0.202621	+	0.0594949i
$441$	4.29228	+	4.95356i	0.204394	+	0.235884i
$442$	−4.11766	+	2.64626i	−0.195857	+	0.125870i
$443$	−17.9572	+	20.7237i	−0.853171	+	0.984612i	−0.999990	−	0.00455147i	$-0.998551\pi$
$443$	−17.9572	+	20.7237i	−0.853171	+	0.984612i	0.146819	+	0.989163i	$0.453097\pi$
$444$	−0.738208	+	5.13435i	−0.0350338	+	0.243665i
$445$	−3.47640	+	1.02076i	−0.164797	+	0.0483888i
$446$	−10.3930	−	6.67916i	−0.492122	−	0.316267i
$447$	2.44751	+	17.0228i	0.115763	+	0.805151i
$448$	0.277272	+	0.607142i	0.0130999	+	0.0286848i
$449$	5.76590	+	12.6256i	0.272110	+	0.595837i	0.995517	−	0.0945846i	$-0.0301523\pi$
$449$	5.76590	+	12.6256i	0.272110	+	0.595837i	−0.723407	+	0.690422i	$0.757425\pi$
$450$	0.142315	+	0.989821i	0.00670879	+	0.0466606i
$451$	−38.5319	−	24.7630i	−1.81440	−	1.16604i
$452$	6.56504	−	1.92767i	0.308793	−	0.0906699i
$453$	−0.471269	+	3.27775i	−0.0221421	+	0.154002i
$454$	−0.733787	+	0.846836i	−0.0344384	+	0.0397440i
$455$	0.692321	−	0.444927i	0.0324565	−	0.0208585i
$456$	−2.30936	−	2.66514i	−0.108145	−	0.124807i
$457$	30.3902	+	8.92337i	1.42159	+	0.417417i	0.900042	−	0.435803i	$-0.143535\pi$
$457$	30.3902	+	8.92337i	1.42159	+	0.417417i	0.521551	+	0.853220i	$0.325354\pi$
$458$	−12.3768	+	27.1013i	−0.578328	+	1.26636i
$459$	−3.96979			−0.185294
$460$	2.68708	+	3.97236i	0.125286	+	0.185212i
$461$	15.8841			0.739795			0.369898	−	0.929072i	$-0.379393\pi$
$461$	15.8841			0.739795			0.369898	+	0.929072i	$0.379393\pi$
$462$	1.22822	−	2.68942i	0.0571419	−	0.125123i
$463$	4.43306	+	1.30166i	0.206022	+	0.0604934i	0.383115	−	0.923701i	$-0.374851\pi$
$463$	4.43306	+	1.30166i	0.206022	+	0.0604934i	−0.177093	+	0.984194i	$0.556669\pi$
$464$	4.42088	+	5.10197i	0.205234	+	0.236853i
$465$	−7.78431	+	5.00267i	−0.360989	+	0.231993i
$466$	3.14115	−	3.62508i	0.145511	−	0.167928i
$467$	−3.51387	+	24.4395i	−0.162602	+	1.13092i	0.731102	+	0.682268i	$0.239006\pi$
$467$	−3.51387	+	24.4395i	−0.162602	+	1.13092i	−0.893704	+	0.448657i	$0.851903\pi$
$468$	1.18304	−	0.347370i	0.0546858	−	0.0160572i
$469$	−0.636710	−	0.409189i	−0.0294005	−	0.0188946i
$470$	−1.55217	−	10.7956i	−0.0715962	−	0.497963i
$471$	−3.35384	−	7.34388i	−0.154537	−	0.338388i
$472$	−1.86081	−	4.07461i	−0.0856507	−	0.187549i
$473$	−7.26724	−	50.5448i	−0.334148	−	2.32405i
$474$	−7.12578	−	4.57946i	−0.327298	−	0.210342i
$475$	3.38364	−	0.993525i	0.155252	−	0.0455861i
$476$	0.377087	−	2.62270i	0.0172838	−	0.120211i
$477$	−1.60740	+	1.85503i	−0.0735976	+	0.0849362i
$478$	−24.5497	+	15.7771i	−1.12288	+	0.721629i
$479$	−24.1453	−	27.8651i	−1.10323	−	1.27319i	−0.958926	−	0.283657i	$-0.908452\pi$
$479$	−24.1453	−	27.8651i	−1.10323	−	1.27319i	−0.144300	−	0.989534i	$-0.546093\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	−2.65685	+	5.81768i	−0.121142	+	0.265263i
$482$	−9.75401			−0.444283
$483$	2.87964	−	1.39793i	0.131028	−	0.0636079i
$484$	8.62176			0.391898
$485$	−4.80194	+	10.5148i	−0.218045	+	0.477452i
$486$	0.959493	+	0.281733i	0.0435235	+	0.0127796i
$487$	−19.2670	−	22.2353i	−0.873071	−	1.00758i	−0.999878	−	0.0156505i	$-0.995018\pi$
$487$	−19.2670	−	22.2353i	−0.873071	−	1.00758i	0.126806	−	0.991928i	$-0.459527\pi$
$488$	−1.29285	+	0.830861i	−0.0585244	+	0.0376113i
$489$	−5.85283	+	6.75453i	−0.264674	+	0.305450i
$490$	0.932802	−	6.48778i	0.0421397	−	0.293088i
$491$	31.1905	−	9.15836i	1.40761	−	0.413311i	0.512319	−	0.858795i	$-0.328787\pi$
$491$	31.1905	−	9.15836i	1.40761	−	0.413311i	0.895290	+	0.445484i	$0.146968\pi$
$492$	8.69865	+	5.59028i	0.392165	+	0.252029i
$493$	−3.81397	−	26.5268i	−0.171773	−	1.19471i
$494$	−1.80626	−	3.95515i	−0.0812674	−	0.177951i
$495$	1.84014	+	4.02935i	0.0827082	+	0.181106i
$496$	−1.31687	−	9.15905i	−0.0591293	−	0.411253i
$497$	−7.47859	−	4.80620i	−0.335460	−	0.215587i
$498$	−15.5774	+	4.57394i	−0.698041	+	0.204963i
$499$	−2.27573	+	15.8280i	−0.101876	+	0.708560i	0.873309	+	0.487167i	$0.161970\pi$
$499$	−2.27573	+	15.8280i	−0.101876	+	0.708560i	−0.975185	+	0.221394i	$0.928939\pi$
$500$	0.654861	−	0.755750i	0.0292863	−	0.0337981i
$501$	12.2067	−	7.84480i	0.545357	−	0.350480i
$502$	−7.58626	−	8.75501i	−0.338591	−	0.390755i
$503$	−17.5983	−	5.16732i	−0.784669	−	0.230399i	−0.135231	−	0.990814i	$-0.543178\pi$
$503$	−17.5983	−	5.16732i	−0.784669	−	0.230399i	−0.649438	+	0.760415i	$0.724996\pi$
$504$	−0.277272	+	0.607142i	−0.0123507	+	0.0270443i
$505$	8.61849			0.383518
$506$	16.3781	+	13.5300i	0.728093	+	0.601480i
$507$	−11.4798			−0.509834
$508$	3.00330	−	6.57630i	0.133250	−	0.291776i
$509$	−30.0304	−	8.81772i	−1.33107	−	0.390839i	−0.462597	−	0.886568i	$-0.653082\pi$
$509$	−30.0304	−	8.81772i	−1.33107	−	0.390839i	−0.868477	+	0.495730i	$0.834901\pi$
$510$	2.59966	+	3.00017i	0.115115	+	0.132850i
$511$	−4.51198	+	2.89967i	−0.199598	+	0.128274i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	0.501871	−	3.49059i	0.0221581	−	0.154113i
$514$	−15.4600	+	4.53948i	−0.681913	+	0.200228i
$515$	13.3195	+	8.55990i	0.586926	+	0.377194i
$516$	1.64059	+	11.4106i	0.0722230	+	0.502322i
$517$	−20.0697	−	43.9464i	−0.882663	−	1.93276i
$518$	−1.43825	−	3.14933i	−0.0631932	−	0.138374i
$519$	0.268238	+	1.86563i	0.0117743	+	0.0818923i
$520$	−1.03725	−	0.666599i	−0.0454863	−	0.0292323i
$521$	25.0426	−	7.35318i	1.09714	−	0.322149i	0.317423	−	0.948284i	$-0.397183\pi$
$521$	25.0426	−	7.35318i	1.09714	−	0.322149i	0.779714	+	0.626136i	$0.215364\pi$
$522$	−0.960750	+	6.68216i	−0.0420509	+	0.292470i
$523$	19.6201	−	22.6428i	0.857928	−	0.990102i	−0.142072	−	0.989856i	$-0.545376\pi$
$523$	19.6201	−	22.6428i	0.857928	−	0.990102i	1.00000		0.000245422i	$-7.81203e-5\pi$
$524$	−17.5811	+	11.2987i	−0.768036	+	0.493587i
$525$	−0.437093	−	0.504432i	−0.0190763	−	0.0220152i
$526$	25.4553	+	7.47436i	1.10991	+	0.325898i
$527$	−15.2596	+	33.4138i	−0.664718	+	1.45553i
$528$	−4.42965			−0.192776
$529$	4.34114	+	22.5866i	0.188745	+	0.982026i
$530$	2.45456			0.106619
$531$	1.86081	−	4.07461i	0.0807523	−	0.176823i
$532$	2.25844	+	0.663137i	0.0979157	+	0.0287506i
$533$	8.34891	+	9.63515i	0.361631	+	0.417345i
$534$	3.04800	−	1.95883i	0.131900	−	0.0847669i
$535$	−1.49697	+	1.72760i	−0.0647198	+	0.0746906i
$536$	−0.161377	+	1.12240i	−0.00697040	+	0.0484802i
$537$	13.6679	−	4.01326i	0.589814	−	0.173185i
$538$	13.2328	+	8.50424i	0.570509	+	0.366644i
$539$	−4.13198	−	28.7386i	−0.177977	−	1.23786i
$540$	−0.415415	−	0.909632i	−0.0178766	−	0.0391443i
$541$	11.2100	+	24.5465i	0.481956	+	1.05534i	0.981921	+	0.189290i	$0.0606187\pi$
$541$	11.2100	+	24.5465i	0.481956	+	1.05534i	−0.499966	+	0.866045i	$0.666654\pi$
$542$	−3.53925	−	24.6160i	−0.152024	−	1.05735i
$543$	14.7921	+	9.50631i	0.634790	+	0.407955i
$544$	−3.80898	+	1.11842i	−0.163309	+	0.0479518i
$545$	0.770374	−	5.35807i	0.0329992	−	0.229514i
$546$	−0.538926	+	0.621954i	−0.0230639	+	0.0266172i
$547$	−0.102451	+	0.0658412i	−0.00438048	+	0.00281516i	−0.542829	−	0.839843i	$-0.682647\pi$
$547$	−0.102451	+	0.0658412i	−0.00438048	+	0.00281516i	0.538449	+	0.842658i	$0.319011\pi$
$548$	−7.16168	−	8.26502i	−0.305932	−	0.353064i
$549$	−1.47456	−	0.432969i	−0.0629326	−	0.0184787i
$550$	1.84014	−	4.02935i	0.0784639	−	0.171812i
$551$	23.8069			1.01421
$552$	−3.69737	−	3.05441i	−0.157371	−	0.130004i
$553$	5.65366			0.240418
$554$	−4.31438	+	9.44719i	−0.183301	+	0.401372i
$555$	4.97703	+	1.46139i	0.211263	+	0.0620325i
$556$	−3.76172	−	4.34125i	−0.159532	−	0.184110i
$557$	2.67238	−	1.71743i	0.113232	−	0.0727699i	−0.482799	−	0.875731i	$-0.660380\pi$
$557$	2.67238	−	1.71743i	0.113232	−	0.0727699i	0.596031	+	0.802961i	$0.296743\pi$
$558$	6.05958	−	6.99313i	0.256522	−	0.296043i
$559$	−2.02282	+	14.0690i	−0.0855560	+	0.595055i
$560$	0.640422	−	0.188045i	0.0270628	−	0.00794635i
$561$	14.7932	+	9.50704i	0.624571	+	0.401387i
$562$	1.03665	+	7.21008i	0.0437286	+	0.304139i
$563$	−8.01454	−	17.5494i	−0.337773	−	0.739619i	0.662180	−	0.749345i	$-0.269631\pi$
$563$	−8.01454	−	17.5494i	−0.337773	−	0.739619i	−0.999953	+	0.00972598i	$0.996904\pi$
$564$	4.53076	+	9.92098i	0.190779	+	0.417749i
$565$	−0.973746	−	6.77255i	−0.0409658	−	0.284923i
$566$	−2.72697	−	1.75252i	−0.114623	−	0.0736637i
$567$	−0.640422	+	0.188045i	−0.0268952	+	0.00789714i
$568$	−1.89548	+	13.1833i	−0.0795324	+	0.553160i
$569$	−14.5216	+	16.7588i	−0.608775	+	0.702564i	−0.973535	−	0.228538i	$-0.926606\pi$
$569$	−14.5216	+	16.7588i	−0.608775	+	0.702564i	0.364760	+	0.931102i	$0.381151\pi$
$570$	−2.96667	+	1.90656i	−0.124260	+	0.0798570i
$571$	1.03286	+	1.19199i	0.0432240	+	0.0498832i	0.776950	−	0.629562i	$-0.216766\pi$
$571$	1.03286	+	1.19199i	0.0432240	+	0.0498832i	−0.733726	+	0.679446i	$0.762220\pi$
$572$	−5.24043	−	1.53873i	−0.219113	−	0.0643374i
$573$	2.33653	−	5.11628i	0.0976098	−	0.213736i
$574$	−6.90160			−0.288067
$575$	4.31433	−	2.09440i	0.179920	−	0.0873426i
$576$	1.00000			0.0416667
$577$	−1.96388	+	4.30031i	−0.0817576	+	0.179024i	−0.946096	−	0.323887i	$-0.895010\pi$
$577$	−1.96388	+	4.30031i	−0.0817576	+	0.179024i	0.864338	+	0.502911i	$0.167738\pi$
$578$	−1.19053	−	0.349570i	−0.0495193	−	0.0145402i
$579$	−8.22559	−	9.49284i	−0.341844	−	0.394509i
$580$	5.67920	−	3.64980i	0.235816	−	0.151550i
$581$	7.09622	−	8.18948i	0.294401	−	0.339757i
$582$	1.64507	−	11.4417i	0.0681904	−	0.474275i
$583$	10.4324	−	3.06323i	0.432067	−	0.126866i
$584$	6.75993	+	4.34435i	0.279728	+	0.179770i
$585$	−0.175471	−	1.22043i	−0.00725484	−	0.0504585i
$586$	−8.72420	−	19.1033i	−0.360393	−	0.789151i
$587$	−14.3205	−	31.3575i	−0.591071	−	1.29426i	−0.934793	−	0.355193i	$-0.884415\pi$
$587$	−14.3205	−	31.3575i	−0.591071	−	1.29426i	0.343722	−	0.939071i	$-0.388312\pi$
$588$	0.932802	+	6.48778i	0.0384681	+	0.267552i
$589$	−27.4513	−	17.6418i	−1.13111	−	0.726920i
$590$	−4.29795	+	1.26199i	−0.176944	+	0.0519554i
$591$	0.465605	−	3.23835i	0.0191524	−	0.133208i
$592$	−3.39686	+	3.92018i	−0.139610	+	0.161119i
$593$	−33.7932	+	21.7176i	−1.38772	+	0.891834i	−0.999557	−	0.0297568i	$-0.990527\pi$
$593$	−33.7932	+	21.7176i	−1.38772	+	0.891834i	−0.388163	+	0.921591i	$0.626890\pi$
$594$	−2.90080	−	3.34770i	−0.119021	−	0.137358i
$595$	−2.54234	−	0.746498i	−0.104226	−	0.0306034i
$596$	−7.14425	+	15.6437i	−0.292640	+	0.640792i
$597$	12.9673			0.530715
$598$	−3.31311	−	4.89783i	−0.135483	−	0.200287i
$599$	−1.38028			−0.0563967			−0.0281983	−	0.999602i	$-0.508977\pi$
$599$	−1.38028			−0.0563967			−0.0281983	+	0.999602i	$0.508977\pi$
$600$	−0.415415	+	0.909632i	−0.0169592	+	0.0371356i
$601$	−40.0790	−	11.7683i	−1.63486	−	0.480037i	−0.669901	−	0.742450i	$-0.733664\pi$
$601$	−40.0790	−	11.7683i	−1.63486	−	0.480037i	−0.964956	+	0.262413i	$0.915482\pi$
$602$	−5.03876	−	5.81504i	−0.205365	−	0.237003i
$603$	−0.953931	+	0.613054i	−0.0388471	+	0.0249655i
$604$	−2.16854	+	2.50263i	−0.0882366	+	0.101830i
$605$	1.22700	−	8.53401i	0.0498848	−	0.346957i
$606$	−8.26938	+	2.42811i	−0.335921	+	0.0986352i
$607$	−0.987365	−	0.634541i	−0.0400759	−	0.0257552i	0.520449	−	0.853892i	$-0.325764\pi$
$607$	−0.987365	−	0.634541i	−0.0400759	−	0.0257552i	−0.560525	+	0.828137i	$0.689401\pi$
$608$	−0.501871	−	3.49059i	−0.0203536	−	0.141562i
$609$	−1.87183	−	4.09874i	−0.0758505	−	0.166089i
$610$	0.638413	+	1.39793i	0.0258486	+	0.0566005i
$611$	1.91379	+	13.3107i	0.0774238	+	0.538494i
$612$	−3.33960	−	2.14623i	−0.134995	−	0.0867562i
$613$	1.90718	−	0.559999i	0.0770304	−	0.0226182i	−0.242990	−	0.970029i	$-0.578128\pi$
$613$	1.90718	−	0.559999i	0.0770304	−	0.0226182i	0.320021	+	0.947411i	$0.396310\pi$
$614$	1.27625	−	8.87649i	0.0515051	−	0.358226i
$615$	6.77133	−	7.81453i	0.273046	−	0.315112i
$616$	2.48726	−	1.59846i	0.100214	−	0.0644039i
$617$	−2.00629	−	2.31539i	−0.0807704	−	0.0932140i	0.713926	−	0.700221i	$-0.246915\pi$
$617$	−2.00629	−	2.31539i	−0.0807704	−	0.0932140i	−0.794696	+	0.607007i	$0.792370\pi$
$618$	−15.1915	−	4.46064i	−0.611093	−	0.179433i
$619$	11.5366	−	25.2617i	0.463696	−	1.01535i	−0.522934	−	0.852373i	$-0.675162\pi$
$619$	11.5366	−	25.2617i	0.463696	−	1.01535i	0.986630	−	0.162979i	$-0.0521103\pi$
$620$	−9.25323			−0.371619
$621$	−0.112895	−	4.79450i	−0.00453030	−	0.192397i
$622$	−24.0555			−0.964537
$623$	−1.00460	+	2.19977i	−0.0402486	+	0.0881321i
$624$	1.18304	+	0.347370i	0.0473593	+	0.0139059i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	14.5555	−	9.35427i	0.581756	−	0.373872i
$627$	−10.2296	+	11.8056i	−0.408532	+	0.471471i
$628$	1.14897	−	7.99128i	0.0458490	−	0.318887i
$629$	19.7578	−	5.80140i	0.787793	−	0.231317i
$630$	0.561502	+	0.360856i	0.0223708	+	0.0143768i
$631$	5.26506	+	36.6193i	0.209599	+	1.45779i	0.774469	+	0.632611i	$0.218017\pi$
$631$	5.26506	+	36.6193i	0.209599	+	1.45779i	−0.564871	+	0.825179i	$0.691074\pi$
$632$	−3.51874	−	7.70497i	−0.139968	−	0.306487i
$633$	9.49389	+	20.7887i	0.377348	+	0.826278i
$634$	0.154992	+	1.07799i	0.00615550	+	0.0428124i
$635$	−6.08195	−	3.90863i	−0.241355	−	0.155109i
$636$	−2.35514	+	0.691530i	−0.0933872	+	0.0274210i
$637$	−1.15013	+	7.99930i	−0.0455697	+	0.316944i
$638$	19.5829	−	22.5999i	0.775296	−	0.894740i
$639$	−11.2046	+	7.20074i	−0.443246	+	0.284857i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	−22.4552	−	6.59345i	−0.886928	−	0.260426i	−0.193628	−	0.981075i	$-0.562026\pi$
$641$	−22.4552	−	6.59345i	−0.886928	−	0.260426i	−0.693300	+	0.720649i	$0.743844\pi$
$642$	0.949614	−	2.07936i	0.0374783	−	0.0820660i
$643$	−1.59213			−0.0627874			−0.0313937	−	0.999507i	$-0.509995\pi$
$643$	−1.59213			−0.0627874			−0.0313937	+	0.999507i	$0.509995\pi$
$644$	3.17828	+	0.380841i	0.125242	+	0.0150072i
$645$	11.5279			0.453911
$646$	−5.81556	+	12.7343i	−0.228810	+	0.501024i
$647$	14.5636	+	4.27626i	0.572554	+	0.168117i	0.555177	−	0.831732i	$-0.312650\pi$
$647$	14.5636	+	4.27626i	0.572554	+	0.168117i	0.0173768	+	0.999849i	$0.494469\pi$
$648$	0.654861	+	0.755750i	0.0257254	+	0.0296886i
$649$	−16.6923	+	10.7275i	−0.655230	+	0.421090i
$650$	−0.807430	+	0.931824i	−0.0316700	+	0.0365491i
$651$	−0.878958	+	6.11329i	−0.0344491	+	0.239599i
$652$	−8.57549	+	2.51799i	−0.335842	+	0.0986122i
$653$	−9.35233	−	6.01038i	−0.365985	−	0.235204i	0.344703	−	0.938712i	$-0.387980\pi$
$653$	−9.35233	−	6.01038i	−0.365985	−	0.235204i	−0.710688	+	0.703508i	$0.751616\pi$
$654$	0.770374	+	5.35807i	0.0301240	+	0.209517i
$655$	8.68165	+	19.0102i	0.339220	+	0.742789i
$656$	4.29543	+	9.40569i	0.167709	+	0.367231i
$657$	1.14358	+	7.95376i	0.0446152	+	0.310306i
$658$	−6.12407	−	3.93570i	−0.238741	−	0.153430i
$659$	−1.06972	+	0.314097i	−0.0416702	+	0.0122355i	−0.302501	−	0.953149i	$-0.597822\pi$
$659$	−1.06972	+	0.314097i	−0.0416702	+	0.0122355i	0.260831	+	0.965384i	$0.416003\pi$
$660$	−0.630404	+	4.38456i	−0.0245385	+	0.170669i
$661$	3.88963	−	4.48887i	0.151289	−	0.174597i	−0.675046	−	0.737776i	$-0.735876\pi$
$661$	3.88963	−	4.48887i	0.151289	−	0.174597i	0.826335	+	0.563179i	$0.190422\pi$
$662$	−12.7362	+	8.18508i	−0.495008	+	0.318122i
$663$	−3.20532	−	3.69914i	−0.124484	−	0.143663i
$664$	−15.5774	−	4.57394i	−0.604521	−	0.177503i
$665$	0.977797	−	2.14108i	0.0379173	−	0.0830274i
$666$	−5.18715			−0.200998
$667$	31.9292	−	5.36070i	1.23630	−	0.207567i
$668$	14.5102			0.561416
$669$	5.13210	−	11.2377i	0.198418	−	0.434476i
$670$	1.08801	+	0.319468i	0.0420334	+	0.0123421i
$671$	4.45798	+	5.14478i	0.172098	+	0.198612i
$672$	−0.561502	+	0.360856i	−0.0216604	+	0.0139203i
$673$	−8.16216	+	9.41964i	−0.314628	+	0.363100i	−0.890933	−	0.454134i	$-0.849949\pi$
$673$	−8.16216	+	9.41964i	−0.314628	+	0.363100i	0.576305	+	0.817235i	$0.304494\pi$
$674$	0.824822	−	5.73676i	0.0317709	−	0.220972i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	−9.65739	−	6.20643i	−0.371438	−	0.238709i
$677$	−3.95811	−	27.5292i	−0.152122	−	1.05803i	−0.912654	−	0.408733i	$-0.865971\pi$
$677$	−3.95811	−	27.5292i	−0.152122	−	1.05803i	0.760531	−	0.649301i	$-0.224939\pi$
$678$	2.84235	+	6.22388i	0.109160	+	0.239027i
$679$	3.20510	+	7.01818i	0.123000	+	0.269333i
$680$	0.564960	+	3.92938i	0.0216652	+	0.150685i
$681$	−0.942645	−	0.605801i	−0.0361222	−	0.0232144i
$682$	−39.3282	+	11.5478i	−1.50596	+	0.442188i
$683$	0.832553	−	5.79054i	0.0318568	−	0.221569i	−0.967674	−	0.252205i	$-0.918844\pi$
$683$	0.832553	−	5.79054i	0.0318568	−	0.221569i	0.999531	+	0.0306363i	$0.00975336\pi$
$684$	2.30936	−	2.66514i	0.0883004	−	0.101904i
$685$	−9.20011	+	5.91255i	−0.351518	+	0.225907i
$686$	−5.92457	−	6.83732i	−0.226201	−	0.261050i
$687$	−28.5869	−	8.39386i	−1.09066	−	0.320246i
$688$	−4.78886	+	10.4861i	−0.182574	+	0.399781i
$689$	−3.02643			−0.115298
$690$	−3.54951	+	3.22505i	−0.135128	+	0.122776i
$691$	−28.7419			−1.09339			−0.546697	−	0.837331i	$-0.684115\pi$
$691$	−28.7419			−1.09339			−0.546697	+	0.837331i	$0.684115\pi$
$692$	−0.782982	+	1.71449i	−0.0297645	+	0.0651752i
$693$	2.83684	+	0.832972i	0.107763	+	0.0316420i
$694$	−10.5067	−	12.1254i	−0.398829	−	0.460273i
$695$	−4.83241	+	3.10560i	−0.183304	+	0.117802i
$696$	−4.42088	+	5.10197i	−0.167573	+	0.193390i
$697$	5.84174	−	40.6302i	0.221272	−	1.53898i
$698$	−3.79234	+	1.11353i	−0.143542	+	0.0421478i
$699$	4.03521	+	2.59327i	0.152626	+	0.0980866i
$700$	−0.0949893	−	0.660665i	−0.00359026	−	0.0249708i
$701$	−3.56000	−	7.79532i	−0.134460	−	0.294425i	0.830411	−	0.557151i	$-0.188106\pi$
$701$	−3.56000	−	7.79532i	−0.134460	−	0.294425i	−0.964870	+	0.262726i	$0.915378\pi$
$702$	0.512198	+	1.12156i	0.0193317	+	0.0423305i
$703$	2.60328	+	18.1062i	0.0981845	+	0.682888i
$704$	−3.72646	−	2.39485i	−0.140446	−	0.0902592i
$705$	10.4648	−	3.07274i	0.394127	−	0.115726i
$706$	5.24553	−	36.4835i	0.197418	−	1.37307i
$707$	3.76708	−	4.34744i	0.141676	−	0.163502i
$708$	3.76831	−	2.42175i	0.141622	−	0.0910148i
$709$	−16.4090	−	18.9370i	−0.616255	−	0.711196i	0.358737	−	0.933439i	$-0.383208\pi$
$709$	−16.4090	−	18.9370i	−0.616255	−	0.711196i	−0.974991	+	0.222243i	$0.928662\pi$
$710$	12.7794	+	3.75237i	0.479602	+	0.140824i
$711$	3.51874	−	7.70497i	0.131963	−	0.288959i
$712$	3.62316			0.135784
$713$	−40.7895	−	17.4795i	−1.52758	−	0.654612i
$714$	2.64967			0.0991614
$715$	−2.26886	+	4.96810i	−0.0848504	+	0.185796i
$716$	13.6679	+	4.01326i	0.510794	+	0.149983i
$717$	−19.1103	−	22.0545i	−0.713688	−	0.823640i
$718$	−22.3589	+	14.3692i	−0.834425	+	0.536252i
$719$	−30.1829	+	34.8329i	−1.12563	+	1.29905i	−0.176455	+	0.984309i	$0.556463\pi$
$719$	−30.1829	+	34.8329i	−1.12563	+	1.29905i	−0.949178	+	0.314741i	$0.898082\pi$
$720$	0.142315	−	0.989821i	0.00530376	−	0.0368885i
$721$	10.1397	−	2.97729i	0.377623	−	0.110880i
$722$	5.52192	+	3.54872i	0.205504	+	0.132070i
$723$	−1.38814	−	9.65472i	−0.0516255	−	0.359063i
$724$	7.30441	+	15.9944i	0.271466	+	0.594428i
$725$	−2.80442	−	6.14081i	−0.104153	−	0.228064i
$726$	1.22700	+	8.53401i	0.0455384	+	0.316727i
$727$	7.30553	+	4.69498i	0.270947	+	0.174127i	0.669058	−	0.743210i	$-0.266698\pi$
$727$	7.30553	+	4.69498i	0.270947	+	0.174127i	−0.398111	+	0.917337i	$0.630334\pi$
$728$	−0.789627	+	0.231855i	−0.0292655	+	0.00859314i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	5.26217	−	6.07286i	0.194762	−	0.224767i
$731$	38.4986	−	24.7415i	1.42392	−	0.915098i
$732$	−1.00640	−	1.16144i	−0.0371975	−	0.0429281i
$733$	−1.50551	−	0.442057i	−0.0556072	−	0.0163277i	0.253811	−	0.967254i	$-0.418316\pi$
$733$	−1.50551	−	0.442057i	−0.0556072	−	0.0163277i	−0.309418	+	0.950926i	$0.600134\pi$
$734$	0.00815617	−	0.0178595i	0.000301050	−	0.000659207i
$735$	6.55450			0.241766
$736$	−1.45909	−	4.56849i	−0.0537827	−	0.168397i
$737$	5.02295			0.185023
$738$	−4.29543	+	9.40569i	−0.158117	+	0.346228i
$739$	−20.1142	−	5.90606i	−0.739912	−	0.217258i	−0.110008	−	0.993931i	$-0.535088\pi$
$739$	−20.1142	−	5.90606i	−0.739912	−	0.217258i	−0.629904	+	0.776673i	$0.716906\pi$
$740$	3.39686	+	3.92018i	0.124871	+	0.144109i
$741$	3.65784	−	2.35075i	0.134374	−	0.0863570i
$742$	1.07287	−	1.23816i	0.0393863	−	0.0454543i
$743$	−6.16939	+	42.9090i	−0.226333	+	1.57418i	0.487030	+	0.873385i	$0.338080\pi$
$743$	−6.16939	+	42.9090i	−0.226333	+	1.57418i	−0.713363	+	0.700795i	$0.752829\pi$
$744$	8.87841	−	2.60694i	0.325498	−	0.0955749i
$745$	14.4678	+	9.29786i	0.530058	+	0.340647i
$746$	1.48281	+	10.3132i	0.0542896	+	0.377592i
$747$	−6.74428	−	14.7679i	−0.246760	−	0.540330i
$748$	7.30497	+	15.9957i	0.267096	+	0.584859i
$749$	0.217140	+	1.51024i	0.00793412	+	0.0551830i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	−4.03108	+	1.18363i	−0.147096	+	0.0431913i	−0.354452	−	0.935074i	$-0.615332\pi$
$751$	−4.03108	+	1.18363i	−0.147096	+	0.0431913i	0.207356	+	0.978266i	$0.433514\pi$
$752$	−1.55217	+	10.7956i	−0.0566018	+	0.393674i
$753$	7.58626	−	8.75501i	0.276459	−	0.319050i
$754$	−7.00233	+	4.50013i	−0.255010	+	0.163885i
$755$	2.16854	+	2.50263i	0.0789212	+	0.0910800i
$756$	−0.640422	−	0.188045i	−0.0232919	−	0.00683913i
$757$	−1.65813	+	3.63081i	−0.0602659	+	0.131964i	−0.937369	−	0.348339i	$-0.886746\pi$
$757$	−1.65813	+	3.63081i	−0.0602659	+	0.131964i	0.877103	+	0.480303i	$0.159473\pi$
$758$	8.84454			0.321248
$759$	−11.0614	+	18.1369i	−0.401504	+	0.658326i
$760$	−3.52648			−0.127919
$761$	1.12519	−	2.46382i	0.0407880	−	0.0893133i	−0.888141	−	0.459571i	$-0.848003\pi$
$761$	1.12519	−	2.46382i	0.0407880	−	0.0893133i	0.928929	+	0.370257i	$0.120731\pi$
$762$	6.93678	+	2.03682i	0.251293	+	0.0737863i
$763$	−2.36605	−	2.73057i	−0.0856569	−	0.0988534i
$764$	4.73168	−	3.04087i	0.171186	−	0.110015i
$765$	−2.59966	+	3.00017i	−0.0939908	+	0.108471i
$766$	−3.40328	+	23.6704i	−0.122966	+	0.855245i
$767$	5.29929	−	1.55601i	0.191346	−	0.0561843i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	−5.27623	−	36.6970i	−0.190266	−	1.32333i	−0.831304	−	0.555818i	$-0.812405\pi$
$769$	−5.27623	−	36.6970i	−0.190266	−	1.32333i	0.641038	−	0.767509i	$-0.278504\pi$
$770$	−1.22822	−	2.68942i	−0.0442619	−	0.0969201i
$771$	−6.69347	−	14.6566i	−0.241059	−	0.527846i
$772$	−1.78759	−	12.4330i	−0.0643368	−	0.447472i
$773$	−7.89991	−	5.07696i	−0.284140	−	0.182606i	0.390805	−	0.920473i	$-0.372197\pi$
$773$	−7.89991	−	5.07696i	−0.284140	−	0.182606i	−0.674945	+	0.737868i	$0.735833\pi$
$774$	−11.0609	+	3.24778i	−0.397577	+	0.116739i
$775$	−1.31687	+	9.15905i	−0.0473034	+	0.329003i
$776$	7.56978	−	8.73600i	0.271739	−	0.313604i
$777$	2.91259	−	1.87181i	0.104489	−	0.0671508i
$778$	8.29264	+	9.57021i	0.297305	+	0.343109i
$779$	34.9872	+	10.2732i	1.25354	+	0.368074i
$780$	0.512198	−	1.12156i	0.0183396	−	0.0401582i
$781$	58.9980			2.11111
$782$	−4.93225	+	18.3884i	−0.176377	+	0.657569i
$783$	−6.75088			−0.241257
$784$	−2.72284	+	5.96218i	−0.0972442	+	0.212935i
$785$	−7.74643	−	2.27456i	−0.276482	−	0.0811824i
$786$	−13.6858	−	15.7942i	−0.488155	−	0.563361i
$787$	−34.6173	+	22.2472i	−1.23397	+	0.793026i	−0.984505	−	0.175357i	$-0.943892\pi$
$787$	−34.6173	+	22.2472i	−1.23397	+	0.793026i	−0.249468	+	0.968383i	$0.580256\pi$
$788$	2.14248	−	2.47255i	0.0763226	−	0.0880810i
$789$	−3.77561	+	26.2600i	−0.134415	+	0.934879i
$790$	−8.12732	+	2.38640i	−0.289157	+	0.0849041i
$791$	−3.84191	−	2.46904i	−0.136603	−	0.0877891i
$792$	−0.630404	−	4.38456i	−0.0224004	−	0.155799i
$793$	−0.787151	−	1.72362i	−0.0279525	−	0.0612075i
$794$	−12.2863	−	26.9032i	−0.436024	−	0.954760i
$795$	0.349321	+	2.42958i	0.0123891	+	0.0861683i
$796$	10.9088	+	7.01064i	0.386651	+	0.248485i
$797$	−46.5645	+	13.6726i	−1.64940	+	0.484307i	−0.968696	−	0.248252i	$-0.920144\pi$
$797$	−46.5645	+	13.6726i	−1.64940	+	0.484307i	−0.680704	+	0.732559i	$0.738326\pi$
$798$	−0.334978	+	2.32982i	−0.0118581	+	0.0824749i
$799$	28.3534	−	32.7216i	1.00307	−	1.15761i
$800$	−0.841254	+	0.540641i	−0.0297428	+	0.0191145i
$801$	2.37267	+	2.73820i	0.0838341	+	0.0967497i
$802$	3.36134	+	0.986978i	0.118693	+	0.0348514i
$803$	14.7865	−	32.3780i	0.521806	−	1.14260i
$804$	−1.13394			−0.0399910
$805$	0.829282	−	3.09173i	0.0292283	−	0.108969i
$806$	11.4090			0.401866
$807$	−6.53444	+	14.3084i	−0.230023	+	0.503681i
$808$	−8.26938	−	2.42811i	−0.290916	−	0.0854206i
$809$	8.75390	+	10.1025i	0.307771	+	0.355186i	0.888472	−	0.458930i	$-0.151767\pi$
$809$	8.75390	+	10.1025i	0.307771	+	0.355186i	−0.580702	+	0.814116i	$0.697222\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	12.9953	−	14.9973i	0.456325	−	0.526628i	−0.480232	−	0.877141i	$-0.659448\pi$
$811$	12.9953	−	14.9973i	0.456325	−	0.526628i	0.936558	+	0.350514i	$0.113993\pi$
$812$	0.641261	−	4.46007i	0.0225039	−	0.156518i
$813$	23.8617	−	7.00644i	0.836868	−	0.245727i
$814$	19.3297	+	12.4224i	0.677505	+	0.435406i
$815$	1.27194	+	8.84655i	0.0445542	+	0.309881i
$816$	−1.64911	−	3.61105i	−0.0577304	−	0.126412i
$817$	16.8878	+	36.9792i	0.590831	+	1.29374i
$818$	1.93856	+	13.4830i	0.0677801	+	0.471421i
$819$	−0.692321	−	0.444927i	−0.0241916	−	0.0155470i
$820$	9.92126	−	2.91314i	0.346465	−	0.101731i
$821$	5.13316	−	35.7019i	0.179149	−	1.24601i	−0.679590	−	0.733592i	$-0.737842\pi$
$821$	5.13316	−	35.7019i	0.179149	−	1.24601i	0.858739	−	0.512413i	$-0.171248\pi$
$822$	7.16168	−	8.26502i	0.249792	−	0.288276i
$823$	27.6347	−	17.7598i	0.963286	−	0.619066i	0.0383806	−	0.999263i	$-0.487780\pi$
$823$	27.6347	−	17.7598i	0.963286	−	0.619066i	0.924906	+	0.380197i	$0.124144\pi$
$824$	−10.3683	−	11.9657i	−0.361198	−	0.416845i
$825$	4.25021	+	1.24798i	0.147973	+	0.0434489i
$826$	−1.24201	+	2.71963i	−0.0432152	+	0.0946281i
$827$	−34.5871			−1.20271			−0.601355	−	0.798982i	$-0.705372\pi$
$827$	−34.5871			−1.20271			−0.601355	+	0.798982i	$0.705372\pi$
$828$	2.49713	−	4.09443i	0.0867813	−	0.142291i
$829$	43.0246			1.49431			0.747153	−	0.664652i	$-0.231420\pi$
$829$	43.0246			1.49431			0.747153	+	0.664652i	$0.231420\pi$
$830$	−6.74428	+	14.7679i	−0.234098	+	0.512602i
$831$	−9.96503	−	2.92600i	−0.345683	−	0.101502i
$832$	0.807430	+	0.931824i	0.0279926	+	0.0323052i
$833$	21.8894	−	14.0675i	0.758422	−	0.487408i
$834$	3.76172	−	4.34125i	0.130258	−	0.150325i
$835$	2.06501	−	14.3625i	0.0714628	−	0.497034i
$836$	−14.9883	+	4.40096i	−0.518382	+	0.152211i
$837$	7.78431	+	5.00267i	0.269065	+	0.172918i
$838$	2.81425	+	19.5735i	0.0972166	+	0.676156i
$839$	5.98278	+	13.1005i	0.206548	+	0.452278i	0.984348	−	0.176234i	$-0.0563915\pi$
$839$	5.98278	+	13.1005i	0.206548	+	0.452278i	−0.777800	+	0.628512i	$0.783664\pi$
$840$	0.277272	+	0.607142i	0.00956681	+	0.0209484i
$841$	−2.35877	−	16.4056i	−0.0813370	−	0.565711i
$842$	−0.962032	−	0.618261i	−0.0331538	−	0.0213067i
$843$	−6.98916	+	2.05220i	−0.240720	+	0.0706816i
$844$	−3.25246	+	22.6214i	−0.111954	+	0.778660i
$845$	−7.51765	+	8.67583i	−0.258615	+	0.298457i
$846$	−9.17521	+	5.89655i	−0.315450	+	0.202727i
$847$	−3.76851	−	4.34909i	−0.129487	−	0.149437i
$848$	−2.35514	−	0.691530i	−0.0808757	−	0.0237472i
$849$	1.34659	−	2.94862i	0.0462148	−	0.101196i
$850$	3.96979			0.136163
$851$	7.56851	+	23.6974i	0.259445	+	0.812336i
$852$	−13.3189			−0.456298
$853$	−21.0641	+	46.1239i	−0.721220	+	1.57925i	0.0909658	+	0.995854i	$0.471005\pi$
$853$	−21.0641	+	46.1239i	−0.721220	+	1.57925i	−0.812186	+	0.583398i	$0.801723\pi$
$854$	0.984206	+	0.288989i	0.0336788	+	0.00988900i
$855$	−2.30936	−	2.66514i	−0.0789783	−	0.0911458i
$856$	1.92306	−	1.23587i	0.0657287	−	0.0422413i
$857$	−27.8652	+	32.1581i	−0.951856	+	1.09850i	0.0431888	+	0.999067i	$0.486248\pi$
$857$	−27.8652	+	32.1581i	−0.951856	+	1.09850i	−0.995044	+	0.0994329i	$0.968297\pi$
$858$	0.777276	−	5.40607i	0.0265357	−	0.184560i
$859$	−8.22571	+	2.41529i	−0.280657	+	0.0824085i	−0.419032	−	0.907972i	$-0.637630\pi$
$859$	−8.22571	+	2.41529i	−0.280657	+	0.0824085i	0.138374	+	0.990380i	$0.455812\pi$
$860$	9.69789	+	6.23245i	0.330695	+	0.212525i
$861$	−0.982199	−	6.83135i	−0.0334733	−	0.232812i
$862$	11.4457	+	25.0625i	0.389841	+	0.853633i
$863$	11.6331	+	25.4730i	0.395997	+	0.867112i	0.997661	+	0.0683627i	$0.0217775\pi$
$863$	11.6331	+	25.4730i	0.395997	+	0.867112i	−0.601664	+	0.798750i	$0.705495\pi$
$864$	0.142315	+	0.989821i	0.00484165	+	0.0336744i
$865$	1.58561	+	1.01901i	0.0539124	+	0.0346474i
$866$	11.3416	−	3.33020i	0.385404	−	0.113165i
$867$	0.176582	−	1.22816i	0.00599705	−	0.0417104i
$868$	−4.04452	+	4.66762i	−0.137280	+	0.158429i
$869$	−31.5647	+	20.2854i	−1.07076	+	0.688134i
$870$	4.42088	+	5.10197i	0.149882	+	0.172973i
$871$	−1.34149	−	0.393897i	−0.0454547	−	0.0133467i
$872$	−2.24871	+	4.92399i	−0.0761509	+	0.166747i
$873$	11.5594			0.391226
$874$	−15.5452	−	6.66158i	−0.525824	−	0.225331i
$875$	−0.667459			−0.0225642
$876$	−3.33809	+	7.30939i	−0.112784	+	0.246962i
$877$	−11.6766	−	3.42854i	−0.394289	−	0.115774i	0.0785770	−	0.996908i	$-0.474962\pi$
$877$	−11.6766	−	3.42854i	−0.394289	−	0.115774i	−0.472866	+	0.881134i	$0.656781\pi$
$878$	0.728606	+	0.840857i	0.0245893	+	0.0283775i
$879$	17.6673	−	11.3541i	0.595903	−	0.382964i
$880$	−2.90080	+	3.34770i	−0.0977860	+	0.112851i
$881$	−0.240192	+	1.67057i	−0.00809227	+	0.0562830i	−0.993467	−	0.114116i	$-0.963596\pi$
$881$	−0.240192	+	1.67057i	−0.00809227	+	0.0562830i	0.985375	+	0.170399i	$0.0545056\pi$
$882$	−6.28900	+	1.84662i	−0.211761	+	0.0621788i
$883$	34.0498	+	21.8825i	1.14587	+	0.736405i	0.968812	−	0.247796i	$-0.0797064\pi$
$883$	34.0498	+	21.8825i	1.14587	+	0.736405i	0.177056	+	0.984201i	$0.443343\pi$
$884$	−0.696584	−	4.84485i	−0.0234286	−	0.162950i
$885$	−1.86081	−	4.07461i	−0.0625505	−	0.136966i
$886$	−11.3912	−	24.9434i	−0.382696	−	0.837988i
$887$	6.07888	+	42.2795i	0.204109	+	1.41961i	0.791927	+	0.610615i	$0.209078\pi$
$887$	6.07888	+	42.2795i	0.204109	+	1.41961i	−0.587819	+	0.808993i	$0.700013\pi$
$888$	−4.36371	−	2.80438i	−0.146436	−	0.0941089i
$889$	−4.63001	+	1.35949i	−0.155286	+	0.0455960i
$890$	0.515630	−	3.58629i	0.0172840	−	0.120213i
$891$	2.90080	−	3.34770i	0.0971805	−	0.112152i
$892$	10.3930	−	6.67916i	0.347983	−	0.223635i
$893$	25.1872	+	29.0676i	0.842857	+	0.972709i
$894$	−16.5012	−	4.84520i	−0.551884	−	0.162048i
$895$	5.91756	−	12.9577i	0.197802	−	0.433127i
$896$	−0.667459			−0.0222982
$897$	4.37648	−	3.97642i	0.146126	−	0.132769i
$898$	−13.8799			−0.463177
$899$	−25.9499	+	56.8224i	−0.865478	+	1.89513i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	6.38102	+	7.36409i	0.212583	+	0.245334i
$902$	38.5319	−	24.7630i	1.28297	−	0.824517i
$903$	5.03876	−	5.81504i	0.167679	−	0.193512i
$904$	−0.973746	+	6.77255i	−0.0323863	+	0.225252i
$905$	16.8712	−	4.95382i	0.560816	−	0.164670i
$906$	−2.78577	−	1.79031i	−0.0925510	−	0.0594789i
$907$	−7.98381	−	55.5286i	−0.265098	−	1.84380i	−0.492894	−	0.870089i	$-0.664061\pi$
$907$	−7.98381	−	55.5286i	−0.265098	−	1.84380i	0.227796	−	0.973709i	$-0.426848\pi$
$908$	−0.465483	−	1.01926i	−0.0154476	−	0.0338255i
$909$	−3.58025	−	7.83965i	−0.118749	−	0.260025i
$910$	0.117120	+	0.814586i	0.00388249	+	0.0270033i
$911$	−13.9278	−	8.95084i	−0.461448	−	0.296555i	0.289186	−	0.957273i	$-0.406615\pi$
$911$	−13.9278	−	8.95084i	−0.461448	−	0.296555i	−0.750634	+	0.660718i	$0.770252\pi$
$912$	3.38364	−	0.993525i	0.112043	−	0.0328989i
$913$	−10.2346	+	71.1835i	−0.338717	+	2.35583i
$914$	−20.7415	+	23.9370i	−0.686069	+	0.791765i
$915$	−1.29285	+	0.830861i	−0.0427402	+	0.0274674i
$916$	−19.5107	−	22.5166i	−0.644653	−	0.743969i
$917$	13.3840	+	3.92990i	0.441979	+	0.129777i
$918$	1.64911	−	3.61105i	0.0544287	−	0.119182i
$919$	−10.2818			−0.339164			−0.169582	−	0.985516i	$-0.554242\pi$
$919$	−10.2818			−0.339164			−0.169582	+	0.985516i	$0.554242\pi$
$920$	−4.72963	+	0.794074i	−0.155931	+	0.0261799i
$921$	8.96777			0.295498
$922$	−6.59849	+	14.4487i	−0.217310	+	0.475842i
$923$	−15.7567	−	4.62659i	−0.518639	−	0.152286i
$924$	1.93617	+	2.23445i	0.0636952	+	0.0735081i
$925$	4.36371	−	2.80438i	0.143478	−	0.0922075i
$926$	−3.02559	+	3.49172i	−0.0994272	+	0.114745i
$927$	2.25325	−	15.6717i	0.0740066	−	0.514727i
$928$	−6.47742	+	1.90194i	−0.212632	+	0.0624343i
$929$	−16.9123	−	10.8689i	−0.554876	−	0.356597i	0.232956	−	0.972487i	$-0.425160\pi$
$929$	−16.9123	−	10.8689i	−0.554876	−	0.356597i	−0.787832	+	0.615890i	$0.788796\pi$
$930$	−1.31687	−	9.15905i	−0.0431819	−	0.300337i
$931$	9.60204	+	21.0255i	0.314694	+	0.689084i
$932$	1.99261	+	4.36320i	0.0652700	+	0.142921i
$933$	−3.42345	−	23.8106i	−0.112079	−	0.779525i
$934$	−20.7712	−	13.3489i	−0.679655	−	0.436788i
$935$	16.8724	−	4.95420i	0.551788	−	0.162020i
$936$	−0.175471	+	1.22043i	−0.00573546	+	0.0398910i
$937$	17.7836	−	20.5234i	0.580965	−	0.670469i	−0.386847	−	0.922144i	$-0.626436\pi$
$937$	17.7836	−	20.5234i	0.580965	−	0.670469i	0.967812	+	0.251675i	$0.0809814\pi$
$938$	0.636710	−	0.409189i	0.0207893	−	0.0133605i
$939$	11.3305	+	13.0761i	0.369758	+	0.426723i
$940$	10.4648	+	3.07274i	0.341324	+	0.100222i
$941$	−2.78867	+	6.10633i	−0.0909080	+	0.199061i	−0.949624	−	0.313390i	$-0.898535\pi$
$941$	−2.78867	+	6.10633i	−0.0909080	+	0.199061i	0.858716	+	0.512451i	$0.171262\pi$
$942$	8.07346			0.263047
$943$	49.2372	+	5.89989i	1.60338	+	0.192127i
$944$	4.47940			0.145792
$945$	−0.277272	+	0.607142i	−0.00901967	+	0.0197503i
$946$	48.9960	+	14.3865i	1.59300	+	0.467747i
$947$	9.52980	+	10.9980i	0.309677	+	0.357386i	0.889159	−	0.457599i	$-0.151290\pi$
$947$	9.52980	+	10.9980i	0.309677	+	0.357386i	−0.579482	+	0.814985i	$0.696745\pi$
$948$	7.12578	−	4.57946i	0.231434	−	0.148734i
$949$	−6.48814	+	7.48772i	−0.210614	+	0.243062i
$950$	−0.501871	+	3.49059i	−0.0162828	+	0.113250i
$951$	−1.04496	+	0.306828i	−0.0338851	+	0.00994957i
$952$	2.22904	+	1.43252i	0.0722437	+	0.0464282i
$953$	−2.99221	−	20.8112i	−0.0969270	−	0.674142i	−0.979124	−	0.203262i	$-0.934846\pi$
$953$	−2.99221	−	20.8112i	−0.0969270	−	0.674142i	0.882197	−	0.470880i	$-0.156064\pi$
$954$	−1.01966	−	2.23275i	−0.0330128	−	0.0722879i
$955$	−2.33653	−	5.11628i	−0.0756082	−	0.165559i
$956$	−4.15307	−	28.8852i	−0.134320	−	0.934216i
$957$	25.1568	+	16.1673i	0.813205	+	0.522615i
$958$	35.3773	−	10.3877i	1.14299	−	0.335612i
$959$	−1.03882	+	7.22516i	−0.0335453	+	0.233313i
$960$	0.654861	−	0.755750i	0.0211355	−	0.0243917i
$961$	45.9512	−	29.5310i	1.48230	−	0.952614i
$962$	−4.18826	−	4.83351i	−0.135035	−	0.155838i
$963$	2.19334	+	0.644024i	0.0706795	+	0.0207534i
$964$	4.05196	−	8.87256i	0.130505	−	0.285766i
$965$	−12.5608			−0.404347
$966$	0.0753525	+	3.20013i	0.00242443	+	0.102963i
$967$	14.4396			0.464347			0.232173	−	0.972674i	$-0.425416\pi$
$967$	14.4396			0.464347			0.232173	+	0.972674i	$0.425416\pi$
$968$	−3.58161	+	7.84263i	−0.115117	+	0.252072i
$969$	−13.4323	−	3.94408i	−0.431508	−	0.126702i
$970$	−7.56978	−	8.73600i	−0.243051	−	0.280496i
$971$	5.71929	−	3.67557i	0.183541	−	0.117955i	−0.445644	−	0.895210i	$-0.647025\pi$
$971$	5.71929	−	3.67557i	0.183541	−	0.117955i	0.629185	+	0.777256i	$0.283389\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−0.545647	+	3.79506i	−0.0174926	+	0.121664i
$974$	28.2298	−	8.28900i	0.904540	−	0.265597i
$975$	−1.03725	−	0.666599i	−0.0332185	−	0.0213483i
$976$	−0.218711	−	1.52117i	−0.00700076	−	0.0486913i
$977$	−19.7088	−	43.1562i	−0.630540	−	1.38069i	−0.907599	−	0.419837i	$-0.862087\pi$
$977$	−19.7088	−	43.1562i	−0.630540	−	1.38069i	0.277059	−	0.960853i	$-0.410640\pi$
$978$	−3.71278	−	8.12986i	−0.118722	−	0.259964i
$979$	−2.28406	−	15.8860i	−0.0729988	−	0.507718i
$980$	5.51400	+	3.54363i	0.176138	+	0.113197i
$981$	−5.19389	+	1.52506i	−0.165828	+	0.0486916i
$982$	−4.62627	+	32.1764i	−0.147630	+	1.02679i
$983$	10.2837	−	11.8680i	0.327999	−	0.378531i	−0.567667	−	0.823258i	$-0.692154\pi$
$983$	10.2837	−	11.8680i	0.327999	−	0.378531i	0.895666	+	0.444727i	$0.146699\pi$
$984$	−8.69865	+	5.59028i	−0.277303	+	0.178212i
$985$	−2.14248	−	2.47255i	−0.0682650	−	0.0787820i
$986$	25.7140	+	7.55030i	0.818900	+	0.240451i
$987$	3.02410	−	6.62185i	0.0962580	−	0.210776i
$988$	4.34808			0.138331
$989$	30.9764	+	45.7929i	0.984991	+	1.45613i
$990$	−4.42965			−0.140783
$991$	21.0346	−	46.0592i	0.668185	−	1.46312i	−0.206510	−	0.978445i	$-0.566210\pi$
$991$	21.0346	−	46.0592i	0.668185	−	1.46312i	0.874694	−	0.484675i	$-0.161062\pi$
$992$	8.87841	+	2.60694i	0.281890	+	0.0827703i
$993$	−9.91433	−	11.4417i	−0.314622	−	0.363093i
$994$	7.47859	−	4.80620i	0.237206	−	0.152443i
$995$	8.49176	−	9.80001i	0.269207	−	0.310681i
$996$	2.31049	−	16.0698i	0.0732106	−	0.509191i
$997$	27.2573	−	8.00347i	0.863248	−	0.253473i	0.180007	−	0.983665i	$-0.442388\pi$
$997$	27.2573	−	8.00347i	0.863248	−	0.253473i	0.683241	+	0.730193i	$0.260570\pi$
$998$	−13.4523	−	8.64528i	−0.425826	−	0.273662i
$999$	−0.738208	−	5.13435i	−0.0233559	−	0.162444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.h.121.2	✓	30
23.4	even	11	inner	690.2.m.h.211.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.h.121.2	✓	30	1.1	even	1	trivial
690.2.m.h.211.2	yes	30	23.4	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0949893 + 0.660665i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.841254 + 0.540641i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.0949893 + 0.660665i) q^{7} +(0.959493 - 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(-1.84014 - 4.02935i) q^{11} +(0.415415 + 0.909632i) q^{12} +(0.175471 + 1.22043i) q^{13} +(-0.561502 - 0.360856i) q^{14} +(0.959493 - 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(2.59966 - 3.00017i) q^{17} +(-0.841254 + 0.540641i) q^{18} +(2.30936 + 2.66514i) q^{19} +(0.959493 + 0.281733i) q^{20} +(0.277272 - 0.607142i) q^{21} +4.42965 q^{22} +(3.69737 + 3.05441i) q^{23} -1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-1.18304 - 0.347370i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.561502 - 0.360856i) q^{28} +(4.42088 - 5.10197i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-8.87841 + 2.60694i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(0.630404 + 4.38456i) q^{33} +(1.64911 + 3.61105i) q^{34} +(-0.277272 - 0.607142i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(4.36371 + 2.80438i) q^{37} +(-3.38364 + 0.993525i) q^{38} +(0.175471 - 1.22043i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(8.69865 - 5.59028i) q^{41} +(0.437093 + 0.504432i) q^{42} +(11.0609 + 3.24778i) q^{43} +(-1.84014 + 4.02935i) q^{44} -1.00000 q^{45} +(-4.31433 + 2.09440i) q^{46} +10.9066 q^{47} +(0.415415 - 0.909632i) q^{48} +(6.28900 + 1.84662i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-3.33960 + 2.14623i) q^{51} +(0.807430 - 0.931824i) q^{52} +(-0.349321 + 2.42958i) q^{53} +(0.959493 - 0.281733i) q^{54} +(3.72646 + 2.39485i) q^{55} +(0.0949893 + 0.660665i) q^{56} +(-1.46495 - 3.20780i) q^{57} +(2.80442 + 6.14081i) q^{58} +(-0.637485 - 4.43381i) q^{59} +(-0.841254 - 0.540641i) q^{60} +(-1.47456 + 0.432969i) q^{61} +(1.31687 - 9.15905i) q^{62} +(-0.437093 + 0.504432i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-0.807430 - 0.931824i) q^{65} +(-4.25021 - 1.24798i) q^{66} +(-0.471056 + 1.03147i) q^{67} -3.96979 q^{68} +(-2.68708 - 3.97236i) q^{69} +0.667459 q^{70} +(-5.53287 + 12.1153i) q^{71} +(0.959493 + 0.281733i) q^{72} +(5.26217 + 6.07286i) q^{73} +(-4.36371 + 2.80438i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.501871 - 3.49059i) q^{76} +(2.83684 - 0.832972i) q^{77} +(1.03725 + 0.666599i) q^{78} +(-1.20547 - 8.38421i) q^{79} +(-0.415415 - 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(1.47155 + 10.2349i) q^{82} +(-13.6578 - 8.77733i) q^{83} +(-0.640422 + 0.188045i) q^{84} +(-0.564960 + 3.92938i) q^{85} +(-7.54917 + 8.71221i) q^{86} +(-5.67920 + 3.64980i) q^{87} +(-2.90080 - 3.34770i) q^{88} +(3.47640 + 1.02076i) q^{89} +(0.415415 - 0.909632i) q^{90} -0.822963 q^{91} +(-0.112895 - 4.79450i) q^{92} +9.25323 q^{93} +(-4.53076 + 9.92098i) q^{94} +(-3.38364 - 0.993525i) q^{95} +(0.654861 + 0.755750i) q^{96} +(9.72437 - 6.24947i) q^{97} +(-4.29228 + 4.95356i) q^{98} +(0.630404 - 4.38456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} - 3 q^{3} - 3 q^{4} + 3 q^{5} + 3 q^{6} + 8 q^{7} + 3 q^{8} - 3 q^{9} - 3 q^{10} - 18 q^{11} - 3 q^{12} + 13 q^{13} - 8 q^{14} + 3 q^{15} - 3 q^{16} - 6 q^{17} + 3 q^{18} + 4 q^{19} + 3 q^{20} - 3 q^{21} - 4 q^{22} - 23 q^{23} - 30 q^{24} - 3 q^{25} + 9 q^{26} - 3 q^{27} + 8 q^{28} + 18 q^{29} - 3 q^{30} - 8 q^{31} + 3 q^{32} + 4 q^{33} - 5 q^{34} + 3 q^{35} - 3 q^{36} - 32 q^{37} - 15 q^{38} + 13 q^{39} - 3 q^{40} + 35 q^{41} + 3 q^{42} + 48 q^{43} - 18 q^{44} - 30 q^{45} + q^{46} + 8 q^{47} - 3 q^{48} - 11 q^{49} + 3 q^{50} + 27 q^{51} + 2 q^{52} + 26 q^{53} + 3 q^{54} - 4 q^{55} - 8 q^{56} - 29 q^{57} - 7 q^{58} + 55 q^{59} + 3 q^{60} + 21 q^{61} + 8 q^{62} - 3 q^{63} - 3 q^{64} - 2 q^{65} + 7 q^{66} + 4 q^{67} - 28 q^{68} - 45 q^{69} - 14 q^{70} - 41 q^{71} + 3 q^{72} - 39 q^{73} + 32 q^{74} - 3 q^{75} + 4 q^{76} - 33 q^{77} - 2 q^{78} + 18 q^{79} + 3 q^{80} - 3 q^{81} + 31 q^{82} - 85 q^{83} - 3 q^{84} - 5 q^{85} + 40 q^{86} + 18 q^{87} - 15 q^{88} + 43 q^{89} - 3 q^{90} + 38 q^{91} + 10 q^{92} + 36 q^{93} - 19 q^{94} - 15 q^{95} + 3 q^{96} + 43 q^{97} + 4 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 - 3 * q^3 - 3 * q^4 + 3 * q^5 + 3 * q^6 + 8 * q^7 + 3 * q^8 - 3 * q^9 - 3 * q^10 - 18 * q^11 - 3 * q^12 + 13 * q^13 - 8 * q^14 + 3 * q^15 - 3 * q^16 - 6 * q^17 + 3 * q^18 + 4 * q^19 + 3 * q^20 - 3 * q^21 - 4 * q^22 - 23 * q^23 - 30 * q^24 - 3 * q^25 + 9 * q^26 - 3 * q^27 + 8 * q^28 + 18 * q^29 - 3 * q^30 - 8 * q^31 + 3 * q^32 + 4 * q^33 - 5 * q^34 + 3 * q^35 - 3 * q^36 - 32 * q^37 - 15 * q^38 + 13 * q^39 - 3 * q^40 + 35 * q^41 + 3 * q^42 + 48 * q^43 - 18 * q^44 - 30 * q^45 + q^46 + 8 * q^47 - 3 * q^48 - 11 * q^49 + 3 * q^50 + 27 * q^51 + 2 * q^52 + 26 * q^53 + 3 * q^54 - 4 * q^55 - 8 * q^56 - 29 * q^57 - 7 * q^58 + 55 * q^59 + 3 * q^60 + 21 * q^61 + 8 * q^62 - 3 * q^63 - 3 * q^64 - 2 * q^65 + 7 * q^66 + 4 * q^67 - 28 * q^68 - 45 * q^69 - 14 * q^70 - 41 * q^71 + 3 * q^72 - 39 * q^73 + 32 * q^74 - 3 * q^75 + 4 * q^76 - 33 * q^77 - 2 * q^78 + 18 * q^79 + 3 * q^80 - 3 * q^81 + 31 * q^82 - 85 * q^83 - 3 * q^84 - 5 * q^85 + 40 * q^86 + 18 * q^87 - 15 * q^88 + 43 * q^89 - 3 * q^90 + 38 * q^91 + 10 * q^92 + 36 * q^93 - 19 * q^94 - 15 * q^95 + 3 * q^96 + 43 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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