LMFDB - Embedded newform 520.2.j.a.469.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(469,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))

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

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

chi := DirichletCharacter("520.469");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.j (of order $2$, degree $1$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.13
Character	$\chi$	$=$	520.469
Dual form			520.2.j.a.469.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.641501 - 1.26035i) q^{2} -1.27105 q^{3} +(-1.17695 + 1.61703i) q^{4} +(2.22857 - 0.182959i) q^{5} +(0.815378 + 1.60196i) q^{6} -0.963418i q^{7} +(2.79303 + 0.446045i) q^{8} -1.38444 q^{9} +O(q^{10})$	\(q+(-0.641501 - 1.26035i) q^{2} -1.27105 q^{3} +(-1.17695 + 1.61703i) q^{4} +(2.22857 - 0.182959i) q^{5} +(0.815378 + 1.60196i) q^{6} -0.963418i q^{7} +(2.79303 + 0.446045i) q^{8} -1.38444 q^{9} +(-1.66022 - 2.69141i) q^{10} +4.73190i q^{11} +(1.49596 - 2.05532i) q^{12} +1.00000 q^{13} +(-1.21424 + 0.618034i) q^{14} +(-2.83262 + 0.232550i) q^{15} +(-1.22956 - 3.80633i) q^{16} -1.12260i q^{17} +(0.888118 + 1.74487i) q^{18} +7.50738i q^{19} +(-2.32707 + 3.81900i) q^{20} +1.22455i q^{21} +(5.96384 - 3.03552i) q^{22} +3.18932i q^{23} +(-3.55008 - 0.566944i) q^{24} +(4.93305 - 0.815475i) q^{25} +(-0.641501 - 1.26035i) q^{26} +5.57283 q^{27} +(1.55788 + 1.13390i) q^{28} -2.37938i q^{29} +(2.11022 + 3.42090i) q^{30} +6.64800 q^{31} +(-4.00854 + 3.99144i) q^{32} -6.01447i q^{33} +(-1.41487 + 0.720148i) q^{34} +(-0.176266 - 2.14705i) q^{35} +(1.62942 - 2.23868i) q^{36} +2.66720 q^{37} +(9.46190 - 4.81599i) q^{38} -1.27105 q^{39} +(6.30608 + 0.483031i) q^{40} +4.61531 q^{41} +(1.54336 - 0.785551i) q^{42} -3.36258 q^{43} +(-7.65161 - 5.56922i) q^{44} +(-3.08532 + 0.253296i) q^{45} +(4.01965 - 2.04595i) q^{46} +0.590988i q^{47} +(1.56283 + 4.83803i) q^{48} +6.07182 q^{49} +(-4.19234 - 5.69423i) q^{50} +1.42688i q^{51} +(-1.17695 + 1.61703i) q^{52} +6.13606 q^{53} +(-3.57498 - 7.02370i) q^{54} +(0.865745 + 10.5454i) q^{55} +(0.429728 - 2.69086i) q^{56} -9.54223i q^{57} +(-2.99884 + 1.52637i) q^{58} -3.58273i q^{59} +(2.95782 - 4.85413i) q^{60} +8.35791i q^{61} +(-4.26470 - 8.37879i) q^{62} +1.33379i q^{63} +(7.60209 + 2.49164i) q^{64} +(2.22857 - 0.182959i) q^{65} +(-7.58032 + 3.85829i) q^{66} -8.67147 q^{67} +(1.81527 + 1.32125i) q^{68} -4.05378i q^{69} +(-2.59295 + 1.59949i) q^{70} +11.9889 q^{71} +(-3.86678 - 0.617521i) q^{72} -3.80031i q^{73} +(-1.71101 - 3.36159i) q^{74} +(-6.27014 + 1.03651i) q^{75} +(-12.1396 - 8.83583i) q^{76} +4.55880 q^{77} +(0.815378 + 1.60196i) q^{78} -14.4169 q^{79} +(-3.43657 - 8.25772i) q^{80} -2.93002 q^{81} +(-2.96073 - 5.81689i) q^{82} -2.23718 q^{83} +(-1.98013 - 1.44124i) q^{84} +(-0.205390 - 2.50179i) q^{85} +(2.15710 + 4.23802i) q^{86} +3.02430i q^{87} +(-2.11064 + 13.2164i) q^{88} -11.0073 q^{89} +(2.29847 + 3.72608i) q^{90} -0.963418i q^{91} +(-5.15722 - 3.75368i) q^{92} -8.44992 q^{93} +(0.744850 - 0.379119i) q^{94} +(1.37354 + 16.7307i) q^{95} +(5.09504 - 5.07331i) q^{96} +17.3960i q^{97} +(-3.89508 - 7.65261i) q^{98} -6.55102i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{3} + 2 q^{4} - 2 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q - 8 * q^3 + 2 * q^4 - 2 * q^6 + 36 * q^9	$ 36 q - 8 q^{3} + 2 q^{4} - 2 q^{6} + 36 q^{9} - 13 q^{10} + 10 q^{12} + 36 q^{13} - 6 q^{14} + 6 q^{16} - 15 q^{20} - 20 q^{22} - 16 q^{24} - 32 q^{27} + 37 q^{30} - 20 q^{31} - 10 q^{32} + 22 q^{34} - 12 q^{36} - 10 q^{38} - 8 q^{39} + 23 q^{40} + 26 q^{42} + 32 q^{43} + 26 q^{44} - 12 q^{45} - 6 q^{46} - 20 q^{48} - 36 q^{49} - 37 q^{50} + 2 q^{52} - 22 q^{54} - 8 q^{55} - 2 q^{56} + 10 q^{58} - 57 q^{60} - 18 q^{62} - 10 q^{64} - 28 q^{66} + 44 q^{67} + 26 q^{68} + 81 q^{70} + 28 q^{71} - 60 q^{72} + 10 q^{74} - 36 q^{76} - 2 q^{78} - 8 q^{79} + 65 q^{80} + 28 q^{81} + 34 q^{82} - 68 q^{83} - 18 q^{84} - 12 q^{86} - 2 q^{88} - 8 q^{89} - 88 q^{90} + 34 q^{92} - 16 q^{93} - 10 q^{94} + 12 q^{95} + 2 q^{96} + 38 q^{98}+O(q^{100}) $ 36 * q - 8 * q^3 + 2 * q^4 - 2 * q^6 + 36 * q^9 - 13 * q^10 + 10 * q^12 + 36 * q^13 - 6 * q^14 + 6 * q^16 - 15 * q^20 - 20 * q^22 - 16 * q^24 - 32 * q^27 + 37 * q^30 - 20 * q^31 - 10 * q^32 + 22 * q^34 - 12 * q^36 - 10 * q^38 - 8 * q^39 + 23 * q^40 + 26 * q^42 + 32 * q^43 + 26 * q^44 - 12 * q^45 - 6 * q^46 - 20 * q^48 - 36 * q^49 - 37 * q^50 + 2 * q^52 - 22 * q^54 - 8 * q^55 - 2 * q^56 + 10 * q^58 - 57 * q^60 - 18 * q^62 - 10 * q^64 - 28 * q^66 + 44 * q^67 + 26 * q^68 + 81 * q^70 + 28 * q^71 - 60 * q^72 + 10 * q^74 - 36 * q^76 - 2 * q^78 - 8 * q^79 + 65 * q^80 + 28 * q^81 + 34 * q^82 - 68 * q^83 - 18 * q^84 - 12 * q^86 - 2 * q^88 - 8 * q^89 - 88 * q^90 + 34 * q^92 - 16 * q^93 - 10 * q^94 + 12 * q^95 + 2 * q^96 + 38 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$	−0.641501	−	1.26035i	−0.453610	−	0.891200i
$2$	−0.641501	−	1.26035i	−0.453610	−	0.891200i
$3$	−1.27105			−0.733840			−0.366920	−	0.930253i	$-0.619588\pi$
$3$	−1.27105			−0.733840			−0.366920	+	0.930253i	$0.619588\pi$
$4$	−1.17695	+	1.61703i	−0.588477	+	0.808514i
$5$	2.22857	−	0.182959i	0.996647	−	0.0818219i
$5$	2.22857	−	0.182959i	0.996647	−	0.0818219i
$6$	0.815378	+	1.60196i	0.332877	+	0.653998i
$7$		−	0.963418i		−	0.364138i	−0.983286	−	0.182069i	$-0.941721\pi$
$7$		−	0.963418i		−	0.364138i	0.983286	−	0.182069i	$-0.0582794\pi$
$8$	2.79303	+	0.446045i	0.987487	+	0.157701i
$9$	−1.38444			−0.461479
$10$	−1.66022	−	2.69141i	−0.525008	−	0.851097i
$11$			4.73190i			1.42672i	0.700797	+	0.713360i	$0.252828\pi$
$11$			4.73190i			1.42672i	−0.700797	+	0.713360i	$0.747172\pi$
$12$	1.49596	−	2.05532i	0.431847	−	0.593320i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−1.21424	+	0.618034i	−0.324520	+	0.165177i
$15$	−2.83262	+	0.232550i	−0.731379	+	0.0600441i
$16$	−1.22956	−	3.80633i	−0.307391	−	0.951583i
$17$		−	1.12260i		−	0.272270i	−0.990690	−	0.136135i	$-0.956532\pi$
$17$		−	1.12260i		−	0.272270i	0.990690	−	0.136135i	$-0.0434681\pi$
$18$	0.888118	+	1.74487i	0.209331	+	0.411271i
$19$			7.50738i			1.72231i	0.508342	+	0.861155i	$0.330258\pi$
$19$			7.50738i			1.72231i	−0.508342	+	0.861155i	$0.669742\pi$
$20$	−2.32707	+	3.81900i	−0.520349	+	0.853954i
$21$			1.22455i			0.267219i
$22$	5.96384	−	3.03552i	1.27149	−	0.647174i
$23$			3.18932i			0.665019i	0.943100	+	0.332509i	$0.107895\pi$
$23$			3.18932i			0.665019i	−0.943100	+	0.332509i	$0.892105\pi$
$24$	−3.55008	−	0.566944i	−0.724657	−	0.115727i
$25$	4.93305	−	0.815475i	0.986610	−	0.163095i
$26$	−0.641501	−	1.26035i	−0.125809	−	0.247175i
$27$	5.57283			1.07249
$28$	1.55788	+	1.13390i	0.294411	+	0.214287i
$29$		−	2.37938i		−	0.441839i	−0.975292	−	0.220920i	$-0.929094\pi$
$29$		−	2.37938i		−	0.441839i	0.975292	−	0.220920i	$-0.0709058\pi$
$30$	2.11022	+	3.42090i	0.385272	+	0.624569i
$31$	6.64800			1.19402			0.597008	−	0.802235i	$-0.296356\pi$
$31$	6.64800			1.19402			0.597008	+	0.802235i	$0.296356\pi$
$32$	−4.00854	+	3.99144i	−0.708616	+	0.705594i
$33$		−	6.01447i		−	1.04698i
$34$	−1.41487	+	0.720148i	−0.242647	+	0.123504i
$35$	−0.176266	−	2.14705i	−0.0297945	−	0.362917i
$36$	1.62942	−	2.23868i	0.271570	−	0.373113i
$37$	2.66720			0.438484			0.219242	−	0.975670i	$-0.429642\pi$
$37$	2.66720			0.438484			0.219242	+	0.975670i	$0.429642\pi$
$38$	9.46190	−	4.81599i	1.53492	−	0.781257i
$39$	−1.27105			−0.203531
$40$	6.30608	+	0.483031i	0.997079	+	0.0763738i
$41$	4.61531			0.720790			0.360395	−	0.932800i	$-0.382642\pi$
$41$	4.61531			0.720790			0.360395	+	0.932800i	$0.382642\pi$
$42$	1.54336	−	0.785551i	0.238146	−	0.121213i
$43$	−3.36258			−0.512789			−0.256394	−	0.966572i	$-0.582535\pi$
$43$	−3.36258			−0.512789			−0.256394	+	0.966572i	$0.582535\pi$
$44$	−7.65161	−	5.56922i	−1.15352	−	0.839592i
$45$	−3.08532	+	0.253296i	−0.459932	+	0.0377591i
$46$	4.01965	−	2.04595i	0.592665	−	0.301659i
$47$			0.590988i			0.0862044i	0.999071	+	0.0431022i	$0.0137241\pi$
$47$			0.590988i			0.0862044i	−0.999071	+	0.0431022i	$0.986276\pi$
$48$	1.56283	+	4.83803i	0.225576	+	0.698310i
$49$	6.07182			0.867404
$50$	−4.19234	−	5.69423i	−0.592886	−	0.805286i
$51$			1.42688i			0.199803i
$52$	−1.17695	+	1.61703i	−0.163214	+	0.224242i
$53$	6.13606			0.842853			0.421426	−	0.906863i	$-0.361530\pi$
$53$	6.13606			0.842853			0.421426	+	0.906863i	$0.361530\pi$
$54$	−3.57498	−	7.02370i	−0.486493	−	0.955805i
$55$	0.865745	+	10.5454i	0.116737	+	1.42194i
$56$	0.429728	−	2.69086i	0.0574248	−	0.359581i
$57$		−	9.54223i		−	1.26390i
$58$	−2.99884	+	1.52637i	−0.393767	+	0.200423i
$59$		−	3.58273i		−	0.466432i	−0.972425	−	0.233216i	$-0.925075\pi$
$59$		−	3.58273i		−	0.466432i	0.972425	−	0.233216i	$-0.0749250\pi$
$60$	2.95782	−	4.85413i	0.381853	−	0.626665i
$61$			8.35791i			1.07012i	0.844814	+	0.535060i	$0.179711\pi$
$61$			8.35791i			1.07012i	−0.844814	+	0.535060i	$0.820289\pi$
$62$	−4.26470	−	8.37879i	−0.541617	−	1.06411i
$63$			1.33379i			0.168042i
$64$	7.60209	+	2.49164i	0.950261	+	0.311455i
$65$	2.22857	−	0.182959i	0.276420	−	0.0226933i
$66$	−7.58032	+	3.85829i	−0.933073	+	0.474922i
$67$	−8.67147			−1.05939			−0.529694	−	0.848189i	$-0.677693\pi$
$67$	−8.67147			−1.05939			−0.529694	+	0.848189i	$0.677693\pi$
$68$	1.81527	+	1.32125i	0.220134	+	0.160225i
$69$		−	4.05378i		−	0.488017i
$70$	−2.59295	+	1.59949i	−0.309917	+	0.191175i
$71$	11.9889			1.42282			0.711410	−	0.702777i	$-0.248057\pi$
$71$	11.9889			1.42282			0.711410	+	0.702777i	$0.248057\pi$
$72$	−3.86678	−	0.617521i	−0.455705	−	0.0727756i
$73$		−	3.80031i		−	0.444792i	−0.974956	−	0.222396i	$-0.928612\pi$
$73$		−	3.80031i		−	0.444792i	0.974956	−	0.222396i	$-0.0713878\pi$
$74$	−1.71101	−	3.36159i	−0.198901	−	0.390777i
$75$	−6.27014	+	1.03651i	−0.724014	+	0.119686i
$76$	−12.1396	−	8.83583i	−1.39251	−	1.01354i
$77$	4.55880			0.519523
$78$	0.815378	+	1.60196i	0.0923234	+	0.181386i
$79$	−14.4169			−1.62203			−0.811013	−	0.585029i	$-0.801083\pi$
$79$	−14.4169			−1.62203			−0.811013	+	0.585029i	$0.801083\pi$
$80$	−3.43657	−	8.25772i	−0.384220	−	0.923241i
$81$	−2.93002			−0.325558
$82$	−2.96073	−	5.81689i	−0.326957	−	0.642369i
$83$	−2.23718			−0.245563			−0.122781	−	0.992434i	$-0.539181\pi$
$83$	−2.23718			−0.245563			−0.122781	+	0.992434i	$0.539181\pi$
$84$	−1.98013	−	1.44124i	−0.216050	−	0.157252i
$85$	−0.205390	−	2.50179i	−0.0222777	−	0.271357i
$86$	2.15710	+	4.23802i	0.232606	+	0.456997i
$87$			3.02430i			0.324239i
$88$	−2.11064	+	13.2164i	−0.224995	+	1.40887i
$89$	−11.0073			−1.16677			−0.583385	−	0.812196i	$-0.698272\pi$
$89$	−11.0073			−1.16677			−0.583385	+	0.812196i	$0.698272\pi$
$90$	2.29847	+	3.72608i	0.242281	+	0.392764i
$91$		−	0.963418i		−	0.100994i
$92$	−5.15722	−	3.75368i	−0.537677	−	0.391348i
$93$	−8.44992			−0.876216
$94$	0.744850	−	0.379119i	0.0768254	−	0.0391032i
$95$	1.37354	+	16.7307i	0.140923	+	1.71654i
$96$	5.09504	−	5.07331i	0.520011	−	0.517793i
$97$			17.3960i			1.76630i	0.469094	+	0.883148i	$0.344581\pi$
$97$			17.3960i			1.76630i	−0.469094	+	0.883148i	$0.655419\pi$
$98$	−3.89508	−	7.65261i	−0.393463	−	0.773030i
$99$		−	6.55102i		−	0.658402i
$100$	−4.48732	+	8.93666i	−0.448732	+	0.893666i
$101$			13.1400i			1.30748i	0.756719	+	0.653740i	$0.226801\pi$
$101$			13.1400i			1.30748i	−0.756719	+	0.653740i	$0.773199\pi$
$102$	1.79836	−	0.915343i	0.178064	−	0.0906324i
$103$		−	2.32131i		−	0.228725i	−0.993439	−	0.114363i	$-0.963517\pi$
$103$		−	2.32131i		−	0.228725i	0.993439	−	0.114363i	$-0.0364826\pi$
$104$	2.79303	+	0.446045i	0.273880	+	0.0437383i
$105$	0.224043	+	2.72900i	0.0218644	+	0.266323i
$106$	−3.93629	−	7.73357i	−0.382326	−	0.751151i
$107$	4.50178			0.435203			0.217602	−	0.976038i	$-0.430177\pi$
$107$	4.50178			0.435203			0.217602	+	0.976038i	$0.430177\pi$
$108$	−6.55896	+	9.01142i	−0.631136	+	0.867125i
$109$			16.6479i			1.59458i	0.603598	+	0.797289i	$0.293733\pi$
$109$			16.6479i			1.59458i	−0.603598	+	0.797289i	$0.706267\pi$
$110$	12.7355	−	7.85600i	1.21428	−	0.749040i
$111$	−3.39013			−0.321777
$112$	−3.66709	+	1.18458i	−0.346508	+	0.111933i
$113$		−	13.2297i		−	1.24454i	−0.782801	−	0.622272i	$-0.786210\pi$
$113$		−	13.2297i		−	1.24454i	0.782801	−	0.622272i	$-0.213790\pi$
$114$	−12.0265	+	6.12135i	−1.12639	+	0.573317i
$115$	0.583515	+	7.10762i	0.0544131	+	0.662789i
$116$	3.84752	+	2.80042i	0.357233	+	0.260012i
$117$	−1.38444			−0.127991
$118$	−4.51549	+	2.29833i	−0.415685	+	0.211578i
$119$	−1.08153			−0.0991439
$120$	−8.01533	−	0.613955i	−0.731696	−	0.0560462i
$121$	−11.3908			−1.03553
$122$	10.5339	−	5.36161i	0.953692	−	0.485417i
$123$	−5.86628			−0.528944
$124$	−7.82438	+	10.7500i	−0.702650	+	0.965379i
$125$	10.8445	−	2.71989i	0.969957	−	0.243275i
$126$	1.68104	−	0.855630i	0.149759	−	0.0762255i
$127$		−	1.31384i		−	0.116584i	−0.998300	−	0.0582920i	$-0.981435\pi$
$127$		−	1.31384i		−	0.116584i	0.998300	−	0.0582920i	$-0.0185655\pi$
$128$	−1.73642	−	11.1797i	−0.153479	−	0.988152i
$129$	4.27400			0.376305
$130$	−1.66022	−	2.69141i	−0.145611	−	0.236052i
$131$		−	19.9816i		−	1.74580i	−0.487898	−	0.872901i	$-0.662236\pi$
$131$		−	19.9816i		−	1.74580i	0.487898	−	0.872901i	$-0.337764\pi$
$132$	9.72556	+	7.07874i	0.846502	+	0.616126i
$133$	7.23274			0.627158
$134$	5.56276	+	10.9291i	0.480549	+	0.944128i
$135$	12.4194	−	1.01960i	1.06890	−	0.0877533i
$136$	0.500729	−	3.13546i	0.0429372	−	0.268863i
$137$		−	11.1754i		−	0.954782i	−0.878691	−	0.477391i	$-0.841582\pi$
$137$		−	11.1754i		−	0.954782i	0.878691	−	0.477391i	$-0.158418\pi$
$138$	−5.10917	+	2.60050i	−0.434921	+	0.221369i
$139$			10.3470i			0.877624i	0.898579	+	0.438812i	$0.144601\pi$
$139$			10.3470i			0.877624i	−0.898579	+	0.438812i	$0.855399\pi$
$140$	3.67929	+	2.24194i	0.310957	+	0.189479i
$141$		−	0.751173i		−	0.0632602i
$142$	−7.69089	−	15.1102i	−0.645405	−	1.26802i
$143$			4.73190i			0.395701i
$144$	1.70225	+	5.26963i	0.141854	+	0.439136i
$145$	−0.435329	−	5.30261i	−0.0361521	−	0.440358i
$146$	−4.78971	+	2.43790i	−0.396399	+	0.201762i
$147$	−7.71758			−0.636535
$148$	−3.13916	+	4.31293i	−0.258038	+	0.354521i
$149$		−	3.98809i		−	0.326717i	−0.986567	−	0.163358i	$-0.947767\pi$
$149$		−	3.98809i		−	0.326717i	0.986567	−	0.163358i	$-0.0522327\pi$
$150$	5.32866	+	7.23764i	0.435084	+	0.590951i
$151$	11.8032			0.960528			0.480264	−	0.877124i	$-0.340541\pi$
$151$	11.8032			0.960528			0.480264	+	0.877124i	$0.340541\pi$
$152$	−3.34863	+	20.9684i	−0.271609	+	1.70076i
$153$			1.55417i			0.125647i
$154$	−2.92447	−	5.74567i	−0.235661	−	0.462999i
$155$	14.8155	−	1.21631i	1.19001	−	0.0976966i
$156$	1.49596	−	2.05532i	0.119773	−	0.164557i
$157$	−19.4791			−1.55460			−0.777299	−	0.629132i	$-0.783411\pi$
$157$	−19.4791			−1.55460			−0.777299	+	0.629132i	$0.783411\pi$
$158$	9.24844	+	18.1703i	0.735766	+	1.44555i
$159$	−7.79923			−0.618519
$160$	−8.20304	+	9.62861i	−0.648507	+	0.761209i
$161$	3.07265			0.242159
$162$	1.87961	+	3.69284i	0.147676	+	0.290137i
$163$	−21.5449			−1.68752			−0.843762	−	0.536717i	$-0.819664\pi$
$163$	−21.5449			−1.68752			−0.843762	+	0.536717i	$0.819664\pi$
$164$	−5.43200	+	7.46309i	−0.424168	+	0.582769i
$165$	−1.10040	−	13.4037i	−0.0856662	−	1.04347i
$166$	1.43515	+	2.81963i	0.111390	+	0.218846i
$167$			7.61285i			0.589100i	0.955636	+	0.294550i	$0.0951698\pi$
$167$			7.61285i			0.589100i	−0.955636	+	0.294550i	$0.904830\pi$
$168$	−0.546205	+	3.42021i	−0.0421406	+	0.263875i
$169$	1.00000			0.0769231
$170$	−3.02137	+	1.86376i	−0.231728	+	0.142944i
$171$		−	10.3935i		−	0.794810i
$172$	3.95760	−	5.43739i	0.301764	−	0.414597i
$173$	−9.86460			−0.749992			−0.374996	−	0.927027i	$-0.622356\pi$
$173$	−9.86460			−0.749992			−0.374996	+	0.927027i	$0.622356\pi$
$174$	3.81167	−	1.94009i	0.288962	−	0.147078i
$175$	−0.785644	−	4.75259i	−0.0593891	−	0.359262i
$176$	18.0112	−	5.81816i	1.35764	−	0.438561i
$177$			4.55383i			0.342286i
$178$	7.06118	+	13.8730i	0.529258	+	1.03983i
$179$		−	5.63756i		−	0.421371i	−0.977554	−	0.210685i	$-0.932430\pi$
$179$		−	5.63756i		−	0.421371i	0.977554	−	0.210685i	$-0.0675696\pi$
$180$	3.22169	−	5.28716i	0.240130	−	0.394082i
$181$		−	4.49672i		−	0.334239i	−0.985937	−	0.167119i	$-0.946553\pi$
$181$		−	4.49672i		−	0.334239i	0.985937	−	0.167119i	$-0.0534466\pi$
$182$	−1.21424	+	0.618034i	−0.0900056	+	0.0458117i
$183$		−	10.6233i		−	0.785297i
$184$	−1.42258	+	8.90788i	−0.104874	+	0.656697i
$185$	5.94403	−	0.487988i	0.437014	−	0.0358776i
$186$	5.42063	+	10.6498i	0.397460	+	0.780884i
$187$	5.31202			0.388454
$188$	−0.955644	−	0.695565i	−0.0696975	−	0.0507293i
$189$		−	5.36897i		−	0.390535i
$190$	20.2054	−	12.4639i	1.46585	−	0.904227i
$191$	−21.1512			−1.53045			−0.765225	−	0.643763i	$-0.777372\pi$
$191$	−21.1512			−1.53045			−0.765225	+	0.643763i	$0.777372\pi$
$192$	−9.66262	−	3.16699i	−0.697339	−	0.228558i
$193$		−	20.9477i		−	1.50785i	−0.656962	−	0.753924i	$-0.728159\pi$
$193$		−	20.9477i		−	1.50785i	0.656962	−	0.753924i	$-0.271841\pi$
$194$	21.9250	−	11.1596i	1.57412	−	0.801209i
$195$	−2.83262	+	0.232550i	−0.202848	+	0.0166533i
$196$	−7.14625	+	9.81831i	−0.510447	+	0.701308i
$197$	6.70780			0.477911			0.238956	−	0.971031i	$-0.423195\pi$
$197$	6.70780			0.477911			0.238956	+	0.971031i	$0.423195\pi$
$198$	−8.25656	+	4.20248i	−0.586768	+	0.298658i
$199$	3.92456			0.278204			0.139102	−	0.990278i	$-0.455578\pi$
$199$	3.92456			0.278204			0.139102	+	0.990278i	$0.455578\pi$
$200$	14.1419	−	0.0772889i	0.999985	−	0.00546515i
$201$	11.0219			0.777421
$202$	16.5610	−	8.42933i	1.16523	−	0.593086i
$203$	−2.29234			−0.160890
$204$	−2.30730	−	1.67937i	−0.161543	−	0.117579i
$205$	10.2855	−	0.844414i	0.718373	−	0.0589764i
$206$	−2.92566	+	1.48912i	−0.203840	+	0.103752i
$207$		−	4.41541i		−	0.306892i
$208$	−1.22956	−	3.80633i	−0.0852549	−	0.263922i
$209$	−35.5241			−2.45726
$210$	3.29576	−	2.03303i	0.227429	−	0.140292i
$211$			1.53640i			0.105770i	0.998601	+	0.0528851i	$0.0168417\pi$
$211$			1.53640i			0.105770i	−0.998601	+	0.0528851i	$0.983158\pi$
$212$	−7.22186	+	9.92219i	−0.495999	+	0.681458i
$213$	−15.2385			−1.04412
$214$	−2.88789	−	5.67381i	−0.197412	−	0.387853i
$215$	−7.49375	+	0.615215i	−0.511069	+	0.0419573i
$216$	15.5651	+	2.48573i	1.05907	+	0.169133i
$217$		−	6.40481i		−	0.434787i
$218$	20.9821	−	10.6796i	1.42109	−	0.723316i
$219$			4.83037i			0.326406i
$220$	−18.0711	−	11.0115i	−1.21835	−	0.742393i
$221$		−	1.12260i		−	0.0755142i
$222$	2.17477	+	4.27275i	0.145961	+	0.286768i
$223$		−	8.62343i		−	0.577467i	−0.957409	−	0.288734i	$-0.906766\pi$
$223$		−	8.62343i		−	0.577467i	0.957409	−	0.288734i	$-0.0932342\pi$
$224$	3.84543	+	3.86190i	0.256934	+	0.258034i
$225$	−6.82950	+	1.12897i	−0.455300	+	0.0752650i
$226$	−16.6740	+	8.48686i	−1.10914	+	0.564537i
$227$	19.9395			1.32343			0.661714	−	0.749756i	$-0.269829\pi$
$227$	19.9395			1.32343			0.661714	+	0.749756i	$0.269829\pi$
$228$	15.4301	+	11.2308i	1.02188	+	0.743775i
$229$		−	15.7314i		−	1.03956i	−0.854300	−	0.519781i	$-0.826014\pi$
$229$		−	15.7314i		−	1.03956i	0.854300	−	0.519781i	$-0.173986\pi$
$230$	8.58375	−	5.29498i	0.565996	−	0.349141i
$231$	−5.79445			−0.381247
$232$	1.06131	−	6.64568i	0.0696783	−	0.436311i
$233$		−	11.8979i		−	0.779460i	−0.920929	−	0.389730i	$-0.872568\pi$
$233$		−	11.8979i		−	0.779460i	0.920929	−	0.389730i	$-0.127432\pi$
$234$	0.888118	+	1.74487i	0.0580581	+	0.114066i
$235$	0.108127	+	1.31706i	0.00705341	+	0.0859154i
$236$	5.79338	+	4.21671i	0.377117	+	0.274484i
$237$	18.3245			1.19031
$238$	0.693804	+	1.36311i	0.0449726	+	0.0883571i
$239$	0.343686			0.0222312			0.0111156	−	0.999938i	$-0.496462\pi$
$239$	0.343686			0.0222312			0.0111156	+	0.999938i	$0.496462\pi$
$240$	4.36805	+	10.4960i	0.281956	+	0.677511i
$241$	0.0922556			0.00594270			0.00297135	−	0.999996i	$-0.499054\pi$
$241$	0.0922556			0.00594270			0.00297135	+	0.999996i	$0.499054\pi$
$242$	7.30724	+	14.3564i	0.469727	+	0.922866i
$243$	−12.9943			−0.833584
$244$	−13.5150	−	9.83686i	−0.865208	−	0.629741i
$245$	13.5315	−	1.11090i	0.864495	−	0.0709726i
$246$	3.76322	+	7.39355i	0.239934	+	0.471396i
$247$			7.50738i			0.477683i
$248$	18.5681	+	2.96531i	1.17908	+	0.188297i
$249$	2.84357			0.180204
$250$	−10.3847	−	11.9230i	−0.656788	−	0.754075i
$251$		−	23.8855i		−	1.50764i	−0.657082	−	0.753819i	$-0.728209\pi$
$251$		−	23.8855i		−	1.50764i	0.657082	−	0.753819i	$-0.271791\pi$
$252$	−2.15678	−	1.56981i	−0.135864	−	0.0988889i
$253$	−15.0915			−0.948796
$254$	−1.65589	+	0.842827i	−0.103900	+	0.0528837i
$255$	0.261060	+	3.17990i	0.0163482	+	0.199133i
$256$	−12.9763	+	9.36025i	−0.811022	+	0.585016i
$257$			18.5605i			1.15777i	0.815408	+	0.578886i	$0.196512\pi$
$257$			18.5605i			1.15777i	−0.815408	+	0.578886i	$0.803488\pi$
$258$	−2.74177	−	5.38673i	−0.170695	−	0.335363i
$259$		−	2.56963i		−	0.159669i
$260$	−2.32707	+	3.81900i	−0.144319	+	0.236844i
$261$			3.29410i			0.203900i
$262$	−25.1838	+	12.8182i	−1.55586	+	0.791913i
$263$			12.1823i			0.751190i	0.926784	+	0.375595i	$0.122562\pi$
$263$			12.1823i			0.751190i	−0.926784	+	0.375595i	$0.877438\pi$
$264$	2.68272	−	16.7986i	0.165110	−	1.03388i
$265$	13.6746	−	1.12265i	0.840027	−	0.0689638i
$266$	−4.63981	−	9.11577i	−0.284485	−	0.558924i
$267$	13.9908			0.856222
$268$	10.2059	−	14.0220i	0.623425	−	0.856531i
$269$		−	19.3587i		−	1.18032i	−0.807287	−	0.590159i	$-0.799065\pi$
$269$		−	19.3587i		−	1.18032i	0.807287	−	0.590159i	$-0.200935\pi$
$270$	−9.25214	−	14.9987i	−0.563067	−	0.912794i
$271$	−12.1633			−0.738866			−0.369433	−	0.929257i	$-0.620448\pi$
$271$	−12.1633			−0.738866			−0.369433	+	0.929257i	$0.620448\pi$
$272$	−4.27299	+	1.38031i	−0.259088	+	0.0836934i
$273$			1.22455i			0.0741132i
$274$	−14.0849	+	7.16906i	−0.850902	+	0.433098i
$275$	3.85875	+	23.3427i	0.232691	+	1.40762i
$276$	6.55507	+	4.77110i	0.394569	+	0.287187i
$277$	18.3966			1.10535			0.552674	−	0.833398i	$-0.313608\pi$
$277$	18.3966			1.10535			0.552674	+	0.833398i	$0.313608\pi$
$278$	13.0409	−	6.63763i	0.782139	−	0.398099i
$279$	−9.20374			−0.551014
$280$	0.465361	−	6.07540i	0.0278106	−	0.363074i
$281$	−2.14953			−0.128230			−0.0641151	−	0.997943i	$-0.520422\pi$
$281$	−2.14953			−0.128230			−0.0641151	+	0.997943i	$0.520422\pi$
$282$	−0.946740	+	0.481878i	−0.0563775	+	0.0286954i
$283$	23.2788			1.38378			0.691891	−	0.722002i	$-0.256778\pi$
$283$	23.2788			1.38378			0.691891	+	0.722002i	$0.256778\pi$
$284$	−14.1104	+	19.3864i	−0.837296	+	1.15037i
$285$	−1.74584	−	21.2655i	−0.103415	−	1.25966i
$286$	5.96384	−	3.03552i	0.352649	−	0.179494i
$287$		−	4.44647i		−	0.262467i
$288$	5.54957	−	5.52591i	0.327012	−	0.325617i
$289$	15.7398			0.925869
$290$	−6.40387	+	3.95030i	−0.376048	+	0.231969i
$291$		−	22.1112i		−	1.29618i
$292$	6.14520	+	4.47278i	0.359621	+	0.261750i
$293$	30.7811			1.79825			0.899126	−	0.437689i	$-0.144203\pi$
$293$	30.7811			1.79825			0.899126	+	0.437689i	$0.144203\pi$
$294$	4.95083	+	9.72683i	0.288739	+	0.567280i
$295$	−0.655494	−	7.98437i	−0.0381644	−	0.464868i
$296$	7.44957	+	1.18969i	0.432997	+	0.0691492i
$297$			26.3701i			1.53015i
$298$	−5.02638	+	2.55836i	−0.291170	+	0.148202i
$299$			3.18932i			0.184443i
$300$	5.70360	−	11.3589i	0.329298	−	0.655808i
$301$			3.23957i			0.186726i
$302$	−7.57174	−	14.8761i	−0.435705	−	0.856023i
$303$		−	16.7016i		−	0.959481i
$304$	28.5756	−	9.23079i	1.63892	−	0.529422i
$305$	1.52916	+	18.6262i	0.0875593	+	1.06653i
$306$	1.95879	−	0.997001i	0.111977	−	0.0569947i
$307$	−3.36481			−0.192040			−0.0960198	−	0.995379i	$-0.530611\pi$
$307$	−3.36481			−0.192040			−0.0960198	+	0.995379i	$0.530611\pi$
$308$	−5.36549	+	7.37170i	−0.305727	+	0.420042i
$309$			2.95050i			0.167848i
$310$	−11.0372	−	17.8925i	−0.626868	−	1.01622i
$311$	18.8152			1.06691			0.533455	−	0.845828i	$-0.320893\pi$
$311$	18.8152			1.06691			0.533455	+	0.845828i	$0.320893\pi$
$312$	−3.55008	−	0.566944i	−0.200984	−	0.0320969i
$313$			33.7541i			1.90790i	0.299970	+	0.953949i	$0.403023\pi$
$313$			33.7541i			1.90790i	−0.299970	+	0.953949i	$0.596977\pi$
$314$	12.4958	+	24.5504i	0.705181	+	1.38546i
$315$	0.244030	+	2.97245i	0.0137495	+	0.167479i
$316$	16.9680	−	23.3125i	0.954524	−	1.31143i
$317$	−10.4193			−0.585208			−0.292604	−	0.956234i	$-0.594522\pi$
$317$	−10.4193			−0.585208			−0.292604	+	0.956234i	$0.594522\pi$
$318$	5.00321	+	9.82974i	0.280566	+	0.551224i
$319$	11.2590			0.630381
$320$	17.3977	+	4.16192i	0.972559	+	0.232658i
$321$	−5.72197			−0.319369
$322$	−1.97111	−	3.87261i	−0.109845	−	0.215812i
$323$	8.42777			0.468934
$324$	3.44849	−	4.73792i	0.191583	−	0.263218i
$325$	4.93305	−	0.815475i	0.273636	−	0.0452344i
$326$	13.8211	+	27.1540i	0.765478	+	1.50392i
$327$		−	21.1603i		−	1.17016i
$328$	12.8907	+	2.05863i	0.711771	+	0.113669i
$329$	0.569368			0.0313903
$330$	−16.1874	+	9.98535i	−0.891085	+	0.549675i
$331$			2.74421i			0.150835i	0.997152	+	0.0754176i	$0.0240290\pi$
$331$			2.74421i			0.150835i	−0.997152	+	0.0754176i	$0.975971\pi$
$332$	2.63306	−	3.61759i	0.144508	−	0.198541i
$333$	−3.69257			−0.202351
$334$	9.59484	−	4.88365i	0.525007	−	0.267222i
$335$	−19.3250	+	1.58653i	−1.05584	+	0.0866812i
$336$	4.66105	−	1.50566i	0.254281	−	0.0821406i
$337$			32.3366i			1.76149i	0.473595	+	0.880743i	$0.342956\pi$
$337$			32.3366i			1.76149i	−0.473595	+	0.880743i	$0.657044\pi$
$338$	−0.641501	−	1.26035i	−0.0348931	−	0.0685539i
$339$			16.8156i			0.913296i
$340$	4.28720	+	2.61237i	0.232506	+	0.141676i
$341$			31.4576i			1.70353i
$342$	−13.0994	+	6.66744i	−0.708335	+	0.360534i
$343$		−	12.5936i		−	0.679993i
$344$	−9.39180	−	1.49986i	−0.506372	−	0.0808671i
$345$	−0.741676	−	9.03412i	−0.0399305	−	0.486381i
$346$	6.32815	+	12.4328i	0.340203	+	0.668393i
$347$	−17.6544			−0.947741			−0.473870	−	0.880595i	$-0.657143\pi$
$347$	−17.6544			−0.947741			−0.473870	+	0.880595i	$0.657143\pi$
$348$	−4.89038	−	3.55946i	−0.262152	−	0.190807i
$349$			1.80063i			0.0963856i	0.998838	+	0.0481928i	$0.0153462\pi$
$349$			1.80063i			0.0963856i	−0.998838	+	0.0481928i	$0.984654\pi$
$350$	−5.48593	+	4.03898i	−0.293235	+	0.215892i
$351$	5.57283			0.297456
$352$	−18.8871	−	18.9680i	−1.00669	−	1.01100i
$353$		−	35.6704i		−	1.89854i	−0.314460	−	0.949271i	$-0.601824\pi$
$353$		−	35.6704i		−	1.89854i	0.314460	−	0.949271i	$-0.398176\pi$
$354$	5.73940	−	2.92128i	0.305046	−	0.155264i
$355$	26.7181	−	2.19348i	1.41805	−	0.116418i
$356$	12.9551	−	17.7991i	0.686616	−	0.943350i
$357$	1.37468			0.0727558
$358$	−7.10529	+	3.61650i	−0.375526	+	0.191138i
$359$	10.6776			0.563542			0.281771	−	0.959482i	$-0.409078\pi$
$359$	10.6776			0.563542			0.281771	+	0.959482i	$0.409078\pi$
$360$	−8.73038	−	0.668726i	−0.460131	−	0.0352449i
$361$	−37.3607			−1.96635
$362$	−5.66744	+	2.88465i	−0.297874	+	0.151614i
$363$	14.4783			0.759914
$364$	1.55788	+	1.13390i	0.0816549	+	0.0594324i
$365$	−0.695301	−	8.46925i	−0.0363937	−	0.443301i
$366$	−13.3891	+	6.81486i	−0.699857	+	0.356218i
$367$			19.6806i			1.02732i	0.857993	+	0.513661i	$0.171711\pi$
$367$			19.6806i			1.02732i	−0.857993	+	0.513661i	$0.828289\pi$
$368$	12.1396	−	3.92147i	0.632821	−	0.204421i
$369$	−6.38961			−0.332630
$370$	−4.42814	−	7.17850i	−0.230208	−	0.373193i
$371$		−	5.91159i		−	0.306915i
$372$	9.94516	−	13.6638i	0.515633	−	0.708433i
$373$	−23.2030			−1.20140			−0.600702	−	0.799473i	$-0.705112\pi$
$373$	−23.2030			−1.20140			−0.600702	+	0.799473i	$0.705112\pi$
$374$	−3.40767	−	6.69500i	−0.176206	−	0.346190i
$375$	−13.7838	+	3.45711i	−0.711793	+	0.178525i
$376$	−0.263607	+	1.65065i	−0.0135945	+	0.0851257i
$377$		−	2.37938i		−	0.122544i
$378$	−6.76677	+	3.44420i	−0.348045	+	0.177150i
$379$			3.85088i			0.197806i	0.995097	+	0.0989031i	$0.0315334\pi$
$379$			3.85088i			0.197806i	−0.995097	+	0.0989031i	$0.968467\pi$
$380$	−28.6706	−	17.4702i	−1.47077	−	0.896203i
$381$			1.66995i			0.0855540i
$382$	13.5685	+	26.6579i	0.694227	+	1.36394i
$383$		−	25.8548i		−	1.32112i	−0.750774	−	0.660559i	$-0.770319\pi$
$383$		−	25.8548i		−	1.32112i	0.750774	−	0.660559i	$-0.229681\pi$
$384$	2.20707	+	14.2099i	0.112629	+	0.725145i
$385$	10.1596	−	0.834074i	0.517781	−	0.0425084i
$386$	−26.4014	+	13.4380i	−1.34379	+	0.683974i
$387$	4.65528			0.236641
$388$	−28.1298	−	20.4743i	−1.42808	−	1.03942i
$389$			14.2152i			0.720740i	0.932809	+	0.360370i	$0.117350\pi$
$389$			14.2152i			0.720740i	−0.932809	+	0.360370i	$0.882650\pi$
$390$	2.11022	+	3.42090i	0.106855	+	0.173224i
$391$	3.58033			0.181065
$392$	16.9588	+	2.70831i	0.856550	+	0.136790i
$393$			25.3976i			1.28114i
$394$	−4.30306	−	8.45416i	−0.216785	−	0.425915i
$395$	−32.1290	+	2.63770i	−1.61659	+	0.132717i
$396$	10.5932	+	7.71024i	0.532327	+	0.387454i
$397$	−25.5902			−1.28433			−0.642167	−	0.766564i	$-0.721965\pi$
$397$	−25.5902			−1.28433			−0.642167	+	0.766564i	$0.721965\pi$
$398$	−2.51761	−	4.94631i	−0.126196	−	0.247936i
$399$	−9.19316			−0.460234
$400$	−9.16947	−	17.7742i	−0.458473	−	0.888708i
$401$	−0.317403			−0.0158503			−0.00792517	−	0.999969i	$-0.502523\pi$
$401$	−0.317403			−0.0158503			−0.00792517	+	0.999969i	$0.502523\pi$
$402$	−7.07053	−	13.8914i	−0.352646	−	0.692838i
$403$	6.64800			0.331160
$404$	−21.2478	−	15.4652i	−1.05712	−	0.769421i
$405$	−6.52975	+	0.536074i	−0.324466	+	0.0266377i
$406$	1.47054	+	2.88914i	0.0729815	+	0.143386i
$407$			12.6209i			0.625594i
$408$	−0.636451	+	3.98532i	−0.0315090	+	0.197303i
$409$	23.1768			1.14602			0.573009	−	0.819549i	$-0.305776\pi$
$409$	23.1768			1.14602			0.573009	+	0.819549i	$0.305776\pi$
$410$	−7.66244	−	12.4217i	−0.378421	−	0.613462i
$411$			14.2045i			0.700657i
$412$	3.75362	+	2.73207i	0.184928	+	0.134600i
$413$	−3.45167			−0.169846
$414$	−5.56496	+	2.83249i	−0.273503	+	0.139209i
$415$	−4.98572	+	0.409313i	−0.244739	+	0.0200924i
$416$	−4.00854	+	3.99144i	−0.196535	+	0.195697i
$417$		−	13.1516i		−	0.644035i
$418$	22.7888	+	44.7728i	1.11463	+	2.18991i
$419$			0.917916i			0.0448431i	0.999749	+	0.0224216i	$0.00713760\pi$
$419$			0.917916i			0.0448431i	−0.999749	+	0.0224216i	$0.992862\pi$
$420$	−4.67656	−	2.84962i	−0.228193	−	0.139047i
$421$			24.9384i			1.21542i	0.794157	+	0.607712i	$0.207913\pi$
$421$			24.9384i			1.21542i	−0.794157	+	0.607712i	$0.792087\pi$
$422$	1.93640	−	0.985602i	0.0942624	−	0.0479783i
$423$		−	0.818186i		−	0.0397815i
$424$	17.1382	+	2.73696i	0.832306	+	0.132918i
$425$	−0.915452	−	5.53784i	−0.0444059	−	0.268625i
$426$	9.77548	+	19.2058i	0.473624	+	0.930522i
$427$	8.05216			0.389671
$428$	−5.29838	+	7.27950i	−0.256107	+	0.351868i
$429$		−	6.01447i		−	0.290381i
$430$	5.58263	+	9.05007i	0.269218	+	0.436433i
$431$	15.0772			0.726243			0.363121	−	0.931742i	$-0.381711\pi$
$431$	15.0772			0.726243			0.363121	+	0.931742i	$0.381711\pi$
$432$	−6.85214	−	21.2120i	−0.329674	−	1.02057i
$433$		−	12.2805i		−	0.590162i	−0.955472	−	0.295081i	$-0.904653\pi$
$433$		−	12.2805i		−	0.590162i	0.955472	−	0.295081i	$-0.0953466\pi$
$434$	−8.07228	+	4.10869i	−0.387482	+	0.197223i
$435$	0.553324	+	6.73987i	0.0265299	+	0.323152i
$436$	−26.9201	−	19.5938i	−1.28924	−	0.938372i
$437$	−23.9434			−1.14537
$438$	6.08795	−	3.09869i	0.290893	−	0.148061i
$439$	37.3369			1.78199			0.890997	−	0.454009i	$-0.150007\pi$
$439$	37.3369			1.78199			0.890997	+	0.454009i	$0.150007\pi$
$440$	−2.28565	+	29.8397i	−0.108964	+	1.42255i
$441$	−8.40606			−0.400289
$442$	−1.41487	+	0.720148i	−0.0672983	+	0.0342540i
$443$	5.86521			0.278664			0.139332	−	0.990246i	$-0.455504\pi$
$443$	5.86521			0.278664			0.139332	+	0.990246i	$0.455504\pi$
$444$	3.99003	−	5.48194i	0.189358	−	0.260161i
$445$	−24.5305	+	2.01388i	−1.16286	+	0.0954673i
$446$	−10.8685	+	5.53194i	−0.514639	+	0.261945i
$447$			5.06905i			0.239758i
$448$	2.40049	−	7.32399i	0.113412	−	0.346026i
$449$	31.6085			1.49170			0.745849	−	0.666115i	$-0.232044\pi$
$449$	31.6085			1.49170			0.745849	+	0.666115i	$0.232044\pi$
$450$	5.80403	+	7.88331i	0.273605	+	0.371623i
$451$			21.8392i			1.02837i
$452$	21.3928	+	15.5707i	1.00623	+	0.732385i
$453$	−15.0024			−0.704873
$454$	−12.7912	−	25.1306i	−0.600320	−	1.17944i
$455$	−0.176266	−	2.14705i	−0.00826350	−	0.100655i
$456$	4.25626	−	26.6518i	0.199318	−	1.24808i
$457$			8.88262i			0.415512i	0.978181	+	0.207756i	$0.0666159\pi$
$457$			8.88262i			0.415512i	−0.978181	+	0.207756i	$0.933384\pi$
$458$	−19.8271	+	10.0917i	−0.926458	+	0.471555i
$459$		−	6.25605i		−	0.292008i
$460$	−12.1800	−	7.42177i	−0.567895	−	0.346042i
$461$		−	28.3614i		−	1.32092i	−0.750861	−	0.660460i	$-0.770361\pi$
$461$		−	28.3614i		−	1.32092i	0.750861	−	0.660460i	$-0.229639\pi$
$462$	3.71714	+	7.30302i	0.172937	+	0.339767i
$463$		−	6.68477i		−	0.310667i	−0.987862	−	0.155334i	$-0.950355\pi$
$463$		−	6.68477i		−	0.310667i	0.987862	−	0.155334i	$-0.0496453\pi$
$464$	−9.05670	+	2.92559i	−0.420447	+	0.135817i
$465$	−18.8312	+	1.54599i	−0.873278	+	0.0716937i
$466$	−14.9955	+	7.63254i	−0.694655	+	0.353571i
$467$	−18.7618			−0.868192			−0.434096	−	0.900867i	$-0.642932\pi$
$467$	−18.7618			−0.868192			−0.434096	+	0.900867i	$0.642932\pi$
$468$	1.62942	−	2.23868i	0.0753199	−	0.103483i
$469$			8.35425i			0.385764i
$470$	1.59059	−	0.981171i	0.0733683	−	0.0452580i
$471$	24.7588			1.14083
$472$	1.59806	−	10.0067i	0.0735567	−	0.460596i
$473$		−	15.9114i		−	0.731606i
$474$	−11.7552	−	23.0953i	−0.539935	−	1.06080i
$475$	6.12208	+	37.0343i	0.280900	+	1.69925i
$476$	1.27291	−	1.74887i	0.0583439	−	0.0801593i
$477$	−8.49499			−0.388959
$478$	−0.220475	−	0.433164i	−0.0100843	−	0.0198125i
$479$	−31.3918			−1.43433			−0.717163	−	0.696905i	$-0.754560\pi$
$479$	−31.3918			−1.43433			−0.717163	+	0.696905i	$0.754560\pi$
$480$	10.4265	−	12.2384i	0.475900	−	0.558605i
$481$	2.66720			0.121614
$482$	−0.0591820	−	0.116274i	−0.00269567	−	0.00529614i
$483$	−3.90548			−0.177706
$484$	13.4065	−	18.4193i	0.609386	−	0.837242i
$485$	3.18276	+	38.7682i	0.144522	+	1.76037i
$486$	8.33585	+	16.3773i	0.378122	+	0.742891i
$487$		−	33.5645i		−	1.52095i	−0.649365	−	0.760477i	$-0.724965\pi$
$487$		−	33.5645i		−	1.52095i	0.649365	−	0.760477i	$-0.275035\pi$
$488$	−3.72800	+	23.3439i	−0.168759	+	1.05673i
$489$	27.3846			1.23837
$490$	−10.0806	−	16.3417i	−0.455394	−	0.738245i
$491$		−	41.0419i		−	1.85220i	−0.377282	−	0.926098i	$-0.623141\pi$
$491$		−	41.0419i		−	1.85220i	0.377282	−	0.926098i	$-0.376859\pi$
$492$	6.90433	−	9.48594i	0.311271	−	0.427659i
$493$	−2.67109			−0.120300
$494$	9.46190	−	4.81599i	0.425711	−	0.216682i
$495$	−1.19857	−	14.5994i	−0.0538717	−	0.656194i
$496$	−8.17413	−	25.3045i	−0.367029	−	1.13621i
$497$		−	11.5503i		−	0.518103i
$498$	−1.82415	−	3.58388i	−0.0817421	−	0.160598i
$499$		−	17.4556i		−	0.781422i	−0.920513	−	0.390711i	$-0.872229\pi$
$499$		−	17.4556i		−	0.781422i	0.920513	−	0.390711i	$-0.127771\pi$
$500$	−8.36527	+	20.7370i	−0.374106	+	0.927386i
$501$		−	9.67630i		−	0.432305i
$502$	−30.1040	+	15.3226i	−1.34361	+	0.683880i
$503$		−	29.7769i		−	1.32768i	−0.747873	−	0.663842i	$-0.768925\pi$
$503$		−	29.7769i		−	1.32768i	0.747873	−	0.663842i	$-0.231075\pi$
$504$	−0.594931	+	3.72533i	−0.0265004	+	0.165939i
$505$	2.40409	+	29.2834i	0.106980	+	1.30310i
$506$	9.68123	+	19.0206i	0.430383	+	0.845568i
$507$	−1.27105			−0.0564492
$508$	2.12451	+	1.54632i	0.0942599	+	0.0686070i
$509$		−	34.0390i		−	1.50875i	−0.656443	−	0.754376i	$-0.727940\pi$
$509$		−	34.0390i		−	1.50875i	0.656443	−	0.754376i	$-0.272060\pi$
$510$	3.84030	−	2.36893i	0.170052	−	0.104898i
$511$	−3.66128			−0.161966
$512$	20.1215	+	10.3501i	0.889254	+	0.457414i
$513$			41.8373i			1.84716i
$514$	23.3927	−	11.9066i	1.03181	−	0.525177i
$515$	−0.424705	−	5.17320i	−0.0187148	−	0.227959i
$516$	−5.03030	+	6.91118i	−0.221446	+	0.304248i
$517$	−2.79649			−0.122990
$518$	−3.23862	+	1.64842i	−0.142297	+	0.0724273i
$519$	12.5384			0.550374
$520$	6.30608	+	0.483031i	0.276540	+	0.0211823i
$521$	−28.6820			−1.25658			−0.628290	−	0.777979i	$-0.716245\pi$
$521$	−28.6820			−1.25658			−0.628290	+	0.777979i	$0.716245\pi$
$522$	4.15171	−	2.11317i	0.181715	−	0.0924909i
$523$	−21.6223			−0.945479			−0.472740	−	0.881202i	$-0.656735\pi$
$523$	−21.6223			−0.945479			−0.472740	+	0.881202i	$0.656735\pi$
$524$	32.3108	+	23.5174i	1.41151	+	1.02736i
$525$	0.998591	+	6.04077i	0.0435821	+	0.263641i
$526$	15.3539	−	7.81493i	0.669461	−	0.340747i
$527$		−	7.46304i		−	0.325095i
$528$	−22.8931	+	7.39516i	−0.996293	+	0.321833i
$529$	12.8282			0.557750
$530$	−10.1872	−	16.5146i	−0.442505	−	0.717349i
$531$			4.96007i			0.215249i
$532$	−8.51260	+	11.6956i	−0.369068	+	0.507067i
$533$	4.61531			0.199911
$534$	−8.97510	−	17.6332i	−0.388390	−	0.763065i
$535$	10.0325	−	0.823642i	0.433744	−	0.0356092i
$536$	−24.2197	−	3.86786i	−1.04613	−	0.167066i
$537$			7.16561i			0.309219i
$538$	−24.3987	+	12.4186i	−1.05190	+	0.535404i
$539$			28.7312i			1.23754i
$540$	−12.9684	+	21.2826i	−0.558070	+	0.915858i
$541$			26.6575i			1.14610i	0.819522	+	0.573048i	$0.194239\pi$
$541$			26.6575i			1.14610i	−0.819522	+	0.573048i	$0.805761\pi$
$542$	7.80275	+	15.3300i	0.335157	+	0.658478i
$543$			5.71555i			0.245278i
$544$	4.48079	+	4.49998i	0.192112	+	0.192935i
$545$	3.04589	+	37.1010i	0.130471	+	1.58923i
$546$	1.54336	−	0.785551i	0.0660497	−	0.0336185i
$547$	3.11507			0.133191			0.0665953	−	0.997780i	$-0.478786\pi$
$547$	3.11507			0.133191			0.0665953	+	0.997780i	$0.478786\pi$
$548$	18.0710	+	13.1530i	0.771955	+	0.561867i
$549$		−	11.5710i		−	0.493838i
$550$	26.9445	−	19.8377i	1.14892	−	0.845883i
$551$	17.8629			0.760984
$552$	1.80817	−	11.3223i	0.0769606	−	0.481911i
$553$			13.8895i			0.590641i
$554$	−11.8015	−	23.1862i	−0.501396	−	0.985086i
$555$	−7.55515	+	0.620256i	−0.320698	+	0.0263284i
$556$	−16.7314	−	12.1780i	−0.709571	−	0.516461i
$557$	38.3488			1.62489			0.812445	−	0.583038i	$-0.198136\pi$
$557$	38.3488			1.62489			0.812445	+	0.583038i	$0.198136\pi$
$558$	5.90421	+	11.5999i	0.249945	+	0.491064i
$559$	−3.36258			−0.142222
$560$	−7.95564	+	3.31086i	−0.336187	+	0.139909i
$561$	−6.75183			−0.285063
$562$	1.37892	+	2.70915i	0.0581664	+	0.114279i
$563$	−19.7237			−0.831255			−0.415627	−	0.909535i	$-0.636438\pi$
$563$	−19.7237			−0.831255			−0.415627	+	0.909535i	$0.636438\pi$
$564$	1.21467	+	0.884096i	0.0511468	+	0.0372272i
$565$	−2.42049	−	29.4833i	−0.101831	−	1.24037i
$566$	−14.9334	−	29.3394i	−0.627697	−	1.23323i
$567$			2.82283i			0.118548i
$568$	33.4854	+	5.34758i	1.40502	+	0.224380i
$569$	0.934074			0.0391584			0.0195792	−	0.999808i	$-0.493767\pi$
$569$	0.934074			0.0391584			0.0195792	+	0.999808i	$0.493767\pi$
$570$	−25.6820	+	15.8422i	−1.07570	+	0.663558i
$571$		−	13.7625i		−	0.575944i	−0.957639	−	0.287972i	$-0.907019\pi$
$571$		−	13.7625i		−	0.575944i	0.957639	−	0.287972i	$-0.0929810\pi$
$572$	−7.65161	−	5.56922i	−0.319930	−	0.232861i
$573$	26.8842			1.12310
$574$	−5.60410	+	2.85242i	−0.233911	+	0.119058i
$575$	2.60081	+	15.7331i	0.108461	+	0.656115i
$576$	−10.5246	−	3.44952i	−0.438526	−	0.143730i
$577$		−	11.4272i		−	0.475721i	−0.971299	−	0.237860i	$-0.923554\pi$
$577$		−	11.4272i		−	0.475721i	0.971299	−	0.237860i	$-0.0764460\pi$
$578$	−10.0971	−	19.8376i	−0.419983	−	0.825135i
$579$			26.6255i			1.10652i
$580$	9.08683	+	5.53698i	0.377310	+	0.229911i
$581$			2.15534i			0.0894187i
$582$	−27.8677	+	14.1843i	−1.15516	+	0.587959i
$583$			29.0352i			1.20252i
$584$	1.69511	−	10.6144i	0.0701440	−	0.439226i
$585$	−3.08532	+	0.253296i	−0.127562	+	0.0104725i
$586$	−19.7461	−	38.7949i	−0.815705	−	1.60260i
$587$	−32.7114			−1.35014			−0.675072	−	0.737751i	$-0.735888\pi$
$587$	−32.7114			−1.35014			−0.675072	+	0.737751i	$0.735888\pi$
$588$	9.08323	−	12.4795i	0.374586	−	0.514648i
$589$			49.9090i			2.05647i
$590$	−9.64259	+	5.94813i	−0.396979	+	0.244881i
$591$	−8.52593			−0.350710
$592$	−3.27948	−	10.1522i	−0.134786	−	0.417254i
$593$		−	9.64147i		−	0.395928i	−0.980209	−	0.197964i	$-0.936567\pi$
$593$		−	9.64147i		−	0.395928i	0.980209	−	0.197964i	$-0.0634329\pi$
$594$	33.2354	−	16.9164i	1.36367	−	0.694089i
$595$	−2.41027	+	0.197876i	−0.0988115	+	0.00811214i
$596$	6.44885	+	4.69379i	0.264155	+	0.192265i
$597$	−4.98830			−0.204157
$598$	4.01965	−	2.04595i	0.164376	−	0.0836652i
$599$	11.3822			0.465064			0.232532	−	0.972589i	$-0.425299\pi$
$599$	11.3822			0.465064			0.232532	+	0.972589i	$0.425299\pi$
$600$	−17.9751	+	0.0982379i	−0.733829	+	0.00401054i
$601$	−23.1485			−0.944247			−0.472123	−	0.881533i	$-0.656512\pi$
$601$	−23.1485			−0.944247			−0.472123	+	0.881533i	$0.656512\pi$
$602$	4.08299	−	2.07819i	0.166410	−	0.0847006i
$603$	12.0051			0.488886
$604$	−13.8918	+	19.0861i	−0.565248	+	0.776600i
$605$	−25.3853	+	2.08406i	−1.03206	+	0.0847291i
$606$	−21.0498	+	10.7141i	−0.855090	+	0.435230i
$607$		−	43.7844i		−	1.77715i	−0.458729	−	0.888576i	$-0.651695\pi$
$607$		−	43.7844i		−	1.77715i	0.458729	−	0.888576i	$-0.348305\pi$
$608$	−29.9653	−	30.0936i	−1.21525	−	1.22046i
$609$	2.91367			0.118068
$610$	22.4945	−	13.8760i	0.910776	−	0.561822i
$611$			0.590988i			0.0239088i
$612$	−2.51314	−	1.82918i	−0.101587	−	0.0739404i
$613$	−25.4976			−1.02984			−0.514920	−	0.857238i	$-0.672178\pi$
$613$	−25.4976			−1.02984			−0.514920	+	0.857238i	$0.672178\pi$
$614$	2.15853	+	4.24083i	0.0871110	+	0.171146i
$615$	−13.0734	+	1.07329i	−0.527171	+	0.0432792i
$616$	12.7329	+	2.03343i	0.513022	+	0.0819291i
$617$		−	33.7352i		−	1.35813i	−0.734079	−	0.679064i	$-0.762386\pi$
$617$		−	33.7352i		−	1.35813i	0.734079	−	0.679064i	$-0.237614\pi$
$618$	3.71865	−	1.89275i	0.149586	−	0.0761374i
$619$		−	26.0296i		−	1.04622i	−0.852266	−	0.523108i	$-0.824772\pi$
$619$		−	26.0296i		−	1.04622i	0.852266	−	0.523108i	$-0.175228\pi$
$620$	−15.4704	+	25.3887i	−0.621305	+	1.01963i
$621$			17.7735i			0.713227i
$622$	−12.0699	−	23.7137i	−0.483961	−	0.950831i
$623$			10.6046i			0.424865i
$624$	1.56283	+	4.83803i	0.0625634	+	0.193676i
$625$	23.6700	−	8.04556i	0.946800	−	0.321823i
$626$	42.5420	−	21.6533i	1.70032	−	0.865441i
$627$	45.1529			1.80323
$628$	22.9259	−	31.4982i	0.914844	−	1.25691i
$629$		−	2.99419i		−	0.119386i
$630$	3.58978	−	2.21439i	0.143020	−	0.0882235i
$631$	12.5465			0.499470			0.249735	−	0.968314i	$-0.419656\pi$
$631$	12.5465			0.499470			0.249735	+	0.968314i	$0.419656\pi$
$632$	−40.2668	−	6.43057i	−1.60173	−	0.255794i
$633$		−	1.95284i		−	0.0776183i
$634$	6.68401	+	13.1320i	0.265456	+	0.521537i
$635$	−0.240378	−	2.92798i	−0.00953913	−	0.116193i
$636$	9.17932	−	12.6116i	0.363984	−	0.500081i
$637$	6.07182			0.240574
$638$	−7.22264	−	14.1902i	−0.285947	−	0.561796i
$639$	−16.5979			−0.656602
$640$	−5.91515	−	24.5970i	−0.233817	−	0.972281i
$641$	25.8297			1.02021			0.510105	−	0.860112i	$-0.329606\pi$
$641$	25.8297			1.02021			0.510105	+	0.860112i	$0.329606\pi$
$642$	3.67065	+	7.21168i	0.144869	+	0.284622i
$643$	25.8861			1.02085			0.510423	−	0.859923i	$-0.329489\pi$
$643$	25.8861			1.02085			0.510423	+	0.859923i	$0.329489\pi$
$644$	−3.61636	+	4.96856i	−0.142505	+	0.195789i
$645$	9.52491	−	0.781968i	0.375043	−	0.0307900i
$646$	−5.40642	−	10.6219i	−0.212713	−	0.417914i
$647$		−	4.27091i		−	0.167907i	−0.996470	−	0.0839534i	$-0.973245\pi$
$647$		−	4.27091i		−	0.167907i	0.996470	−	0.0839534i	$-0.0267547\pi$
$648$	−8.18364	−	1.30692i	−0.321484	−	0.0513406i
$649$	16.9531			0.665468
$650$	−4.19234	−	5.69423i	−0.164437	−	0.223346i
$651$			8.14081i			0.319064i
$652$	25.3573	−	34.8387i	0.993069	−	1.36439i
$653$	14.7307			0.576455			0.288228	−	0.957562i	$-0.406934\pi$
$653$	14.7307			0.576455			0.288228	+	0.957562i	$0.406934\pi$
$654$	−26.6693	+	13.5743i	−1.04285	+	0.530798i
$655$	−3.65582	−	44.5304i	−0.142845	−	1.73995i
$656$	−5.67481	−	17.5674i	−0.221564	−	0.685892i
$657$			5.26129i			0.205262i
$658$	−0.365250	−	0.717602i	−0.0142389	−	0.0279750i
$659$			13.7240i			0.534611i	0.963612	+	0.267306i	$0.0861333\pi$
$659$			13.7240i			0.534611i	−0.963612	+	0.267306i	$0.913867\pi$
$660$	22.9692	+	13.9961i	0.894076	+	0.544797i
$661$		−	12.6514i		−	0.492082i	−0.969259	−	0.246041i	$-0.920870\pi$
$661$		−	12.6514i		−	0.492082i	0.969259	−	0.246041i	$-0.0791298\pi$
$662$	3.45865	−	1.76041i	0.134424	−	0.0684203i
$663$			1.42688i			0.0554153i
$664$	−6.24853	−	0.997884i	−0.242490	−	0.0387254i
$665$	16.1187	−	1.32330i	0.625056	−	0.0513153i
$666$	2.36878	+	4.65392i	0.0917885	+	0.180336i
$667$	7.58859			0.293831
$668$	−12.3102	−	8.95997i	−0.476296	−	0.346672i
$669$			10.9608i			0.423769i
$670$	14.3966	+	23.3384i	0.556188	+	0.901643i
$671$	−39.5488			−1.52676
$672$	−4.88773	−	4.90866i	−0.188548	−	0.189356i
$673$			26.9110i			1.03734i	0.854973	+	0.518672i	$0.173574\pi$
$673$			26.9110i			1.03734i	−0.854973	+	0.518672i	$0.826426\pi$
$674$	40.7553	−	20.7439i	1.56984	−	0.799027i
$675$	27.4911	−	4.54451i	1.05813	−	0.174918i
$676$	−1.17695	+	1.61703i	−0.0452674	+	0.0621934i
$677$	−15.4566			−0.594046			−0.297023	−	0.954870i	$-0.595994\pi$
$677$	−15.4566			−0.594046			−0.297023	+	0.954870i	$0.595994\pi$
$678$	21.1935	−	10.7872i	0.813930	−	0.414280i
$679$	16.7596			0.643176
$680$	0.542250	−	7.07920i	0.0207943	−	0.271475i
$681$	−25.3440			−0.971184
$682$	39.6476	−	20.1801i	1.51818	−	0.772736i
$683$	−17.3098			−0.662341			−0.331171	−	0.943571i	$-0.607444\pi$
$683$	−17.3098			−0.662341			−0.331171	+	0.943571i	$0.607444\pi$
$684$	16.8066	+	12.2327i	0.642616	+	0.467727i
$685$	−2.04465	−	24.9053i	−0.0781221	−	0.951581i
$686$	−15.8724	+	8.07883i	−0.606010	+	0.308451i
$687$			19.9954i			0.762871i
$688$	4.13450	+	12.7991i	0.157626	+	0.487961i
$689$	6.13606			0.233765
$690$	−10.9104	+	6.73017i	−0.415350	+	0.256213i
$691$		−	24.5168i		−	0.932665i	−0.884610	−	0.466332i	$-0.845575\pi$
$691$		−	24.5168i		−	0.932665i	0.884610	−	0.466332i	$-0.154425\pi$
$692$	11.6102	−	15.9513i	0.441352	−	0.606379i
$693$	−6.31137			−0.239749
$694$	11.3253	+	22.2507i	0.429904	+	0.844627i
$695$	1.89309	+	23.0591i	0.0718088	+	0.874681i
$696$	−1.34897	+	8.44698i	−0.0511327	+	0.320182i
$697$		−	5.18114i		−	0.196250i
$698$	2.26942	−	1.15511i	0.0858989	−	0.0437215i
$699$			15.1229i			0.571999i
$700$	8.60975	+	4.32317i	0.325418	+	0.163400i
$701$			35.0071i			1.32220i	0.750299	+	0.661099i	$0.229910\pi$
$701$			35.0071i			1.32220i	−0.750299	+	0.661099i	$0.770090\pi$
$702$	−3.57498	−	7.02370i	−0.134929	−	0.265093i
$703$			20.0236i			0.755206i
$704$	−11.7902	+	35.9723i	−0.444359	+	1.35576i
$705$	−0.137434	−	1.67404i	−0.00517607	−	0.0630481i
$706$	−44.9570	+	22.8826i	−1.69198	+	0.861197i
$707$	12.6593			0.476103
$708$	−7.36367	−	5.35964i	−0.276744	−	0.201428i
$709$		−	11.8882i		−	0.446470i	−0.974765	−	0.223235i	$-0.928338\pi$
$709$		−	11.8882i		−	0.446470i	0.974765	−	0.223235i	$-0.0716617\pi$
$710$	−19.9042	−	32.2670i	−0.746992	−	1.21096i
$711$	19.9593			0.748531
$712$	−30.7437	−	4.90974i	−1.15217	−	0.184000i
$713$			21.2026i			0.794043i
$714$	−0.881858	−	1.73257i	−0.0330027	−	0.0648400i
$715$	0.865745	+	10.5454i	0.0323770	+	0.394374i
$716$	9.11609	+	6.63514i	0.340684	+	0.247967i
$717$	−0.436841			−0.0163141
$718$	−6.84969	−	13.4575i	−0.255628	−	0.502229i
$719$	21.6536			0.807542			0.403771	−	0.914860i	$-0.367699\pi$
$719$	21.6536			0.807542			0.403771	+	0.914860i	$0.367699\pi$
$720$	4.75772	+	11.4323i	0.177310	+	0.426057i
$721$	−2.23639			−0.0832876
$722$	23.9669	+	47.0875i	0.891956	+	1.75241i
$723$	−0.117261			−0.00436099
$724$	7.27133	+	5.29243i	0.270237	+	0.196692i
$725$	−1.94032	−	11.7376i	−0.0720618	−	0.435923i
$726$	−9.28785	−	18.2477i	−0.344704	−	0.677236i
$727$			36.0914i			1.33856i	0.743012	+	0.669278i	$0.233397\pi$
$727$			36.0914i			1.33856i	−0.743012	+	0.669278i	$0.766603\pi$
$728$	0.429728	−	2.69086i	0.0159268	−	0.0997300i
$729$	25.3064			0.937275
$730$	−10.2282	+	6.30935i	−0.378561	+	0.233520i
$731$			3.77483i			0.139617i
$732$	17.1782	+	12.5031i	0.634924	+	0.462129i
$733$	2.67983			0.0989819			0.0494909	−	0.998775i	$-0.484240\pi$
$733$	2.67983			0.0989819			0.0494909	+	0.998775i	$0.484240\pi$
$734$	24.8045	−	12.6252i	0.915549	−	0.466003i
$735$	−17.1992	+	1.41200i	−0.634401	+	0.0520825i
$736$	−12.7300	−	12.7845i	−0.469233	−	0.471243i
$737$		−	41.0325i		−	1.51145i
$738$	4.09894	+	8.05313i	0.150884	+	0.296440i
$739$			5.84157i			0.214886i	0.994211	+	0.107443i	$0.0342662\pi$
$739$			5.84157i			0.214886i	−0.994211	+	0.107443i	$0.965734\pi$
$740$	−6.20676	+	10.1860i	−0.228165	+	0.374445i
$741$		−	9.54223i		−	0.350543i
$742$	−7.45066	+	3.79229i	−0.273522	+	0.139219i
$743$			8.01962i			0.294211i	0.989121	+	0.147106i	$0.0469957\pi$
$743$			8.01962i			0.294211i	−0.989121	+	0.147106i	$0.953004\pi$
$744$	−23.6009	−	3.76904i	−0.865252	−	0.138180i
$745$	−0.729658	−	8.88774i	−0.0267326	−	0.325621i
$746$	14.8847	+	29.2438i	0.544968	+	1.07069i
$747$	3.09724			0.113322
$748$	−6.25200	+	8.58969i	−0.228596	+	0.314070i
$749$		−	4.33710i		−	0.158474i
$750$	13.1995	+	15.1547i	0.481977	+	0.553370i
$751$	21.6765			0.790986			0.395493	−	0.918469i	$-0.370574\pi$
$751$	21.6765			0.790986			0.395493	+	0.918469i	$0.370574\pi$
$752$	2.24950	−	0.726656i	0.0820307	−	0.0264984i
$753$			30.3596i			1.10637i
$754$	−2.99884	+	1.52637i	−0.109211	+	0.0555872i
$755$	26.3042	−	2.15950i	0.957307	−	0.0785922i
$756$	8.68177	+	6.31902i	0.315753	+	0.229821i
$757$	43.2229			1.57096			0.785482	−	0.618885i	$-0.212415\pi$
$757$	43.2229			1.57096			0.785482	+	0.618885i	$0.212415\pi$
$758$	4.85344	−	2.47034i	0.176285	−	0.0897268i
$759$	19.1820			0.696264
$760$	−3.62629	+	47.3421i	−0.131539	+	1.71728i
$761$	18.2972			0.663272			0.331636	−	0.943407i	$-0.392399\pi$
$761$	18.2972			0.663272			0.331636	+	0.943407i	$0.392399\pi$
$762$	2.10472	−	1.07127i	0.0762458	−	0.0388081i
$763$	16.0389			0.580647
$764$	24.8940	−	34.2021i	0.900634	−	1.23739i
$765$	0.284350	+	3.46357i	0.0102807	+	0.125226i
$766$	−32.5860	+	16.5859i	−1.17738	+	0.599272i
$767$		−	3.58273i		−	0.129365i
$768$	16.4936	−	11.8973i	0.595160	−	0.429308i
$769$	−41.6354			−1.50141			−0.750705	−	0.660638i	$-0.770286\pi$
$769$	−41.6354			−1.50141			−0.750705	+	0.660638i	$0.770286\pi$
$770$	−7.56862	−	12.2696i	−0.272754	−	0.442165i
$771$		−	23.5913i		−	0.849619i
$772$	33.8730	+	24.6544i	1.21912	+	0.887333i
$773$	3.26785			0.117536			0.0587682	−	0.998272i	$-0.481283\pi$
$773$	3.26785			0.117536			0.0587682	+	0.998272i	$0.481283\pi$
$774$	−2.98637	−	5.86728i	−0.107343	−	0.210895i
$775$	32.7949	−	5.42128i	1.17803	−	0.194738i
$776$	−7.75940	+	48.5877i	−0.278546	+	1.74420i
$777$			3.26612i			0.117171i
$778$	17.9161	−	9.11907i	0.642324	−	0.326935i
$779$			34.6489i			1.24142i
$780$	2.95782	−	4.85413i	0.105907	−	0.173806i
$781$			56.7302i			2.02997i
$782$	−2.29678	−	4.51246i	−0.0821328	−	0.161365i
$783$		−	13.2599i		−	0.473869i
$784$	−7.46569	−	23.1114i	−0.266632	−	0.825407i
$785$	−43.4104	+	3.56387i	−1.54939	+	0.127200i
$786$	32.0098	−	16.2926i	1.14175	−	0.581137i
$787$	−11.5404			−0.411370			−0.205685	−	0.978618i	$-0.565942\pi$
$787$	−11.5404			−0.411370			−0.205685	+	0.978618i	$0.565942\pi$
$788$	−7.89477	+	10.8467i	−0.281239	+	0.386398i
$789$		−	15.4842i		−	0.551253i
$790$	23.9352	+	38.8017i	0.851577	+	1.38050i
$791$	−12.7457			−0.453186
$792$	2.92205	−	18.2972i	0.103830	−	0.650163i
$793$			8.35791i			0.296798i
$794$	16.4161	+	32.2525i	0.582587	+	1.14460i
$795$	−17.3811	+	1.42694i	−0.616445	+	0.0506084i
$796$	−4.61902	+	6.34612i	−0.163717	+	0.224932i
$797$	−29.1607			−1.03293			−0.516463	−	0.856309i	$-0.672752\pi$
$797$	−29.1607			−1.03293			−0.516463	+	0.856309i	$0.672752\pi$
$798$	5.89742	+	11.5866i	0.208767	+	0.410161i
$799$	0.663442			0.0234709
$800$	−16.5194	+	22.9589i	−0.584049	+	0.811718i
$801$	15.2389			0.538440
$802$	0.203614	+	0.400038i	0.00718987	+	0.0141258i
$803$	17.9827			0.634594
$804$	−12.9722	+	17.8226i	−0.457494	+	0.628556i
$805$	6.84761	−	0.562170i	0.241347	−	0.0198139i
$806$	−4.26470	−	8.37879i	−0.150218	−	0.295130i
$807$			24.6058i			0.866165i
$808$	−5.86103	+	36.7005i	−0.206190	+	1.29112i
$809$	−41.4777			−1.45828			−0.729140	−	0.684365i	$-0.760080\pi$
$809$	−41.4777			−1.45828			−0.729140	+	0.684365i	$0.760080\pi$
$810$	4.86448	+	7.88587i	0.170920	+	0.277081i
$811$		−	41.7294i		−	1.46532i	−0.680596	−	0.732659i	$-0.738279\pi$
$811$		−	41.7294i		−	1.46532i	0.680596	−	0.732659i	$-0.261721\pi$
$812$	2.69797	−	3.70677i	0.0946803	−	0.130082i
$813$	15.4601			0.542209
$814$	15.9067	−	8.09631i	0.557530	−	0.283776i
$815$	−48.0143	+	3.94183i	−1.68187	+	0.138076i
$816$	5.43117	−	1.75443i	0.190129	−	0.0614175i
$817$		−	25.2442i		−	0.883181i
$818$	−14.8679	−	29.2108i	−0.519845	−	1.02133i
$819$			1.33379i			0.0466065i
$820$	−10.7402	+	17.6258i	−0.375063	+	0.615521i
$821$			18.7913i			0.655819i	0.944709	+	0.327910i	$0.106344\pi$
$821$			18.7913i			0.655819i	−0.944709	+	0.327910i	$0.893656\pi$
$822$	17.9026	−	9.11221i	0.624426	−	0.317825i
$823$		−	39.9110i		−	1.39121i	−0.718424	−	0.695605i	$-0.755136\pi$
$823$		−	39.9110i		−	1.39121i	0.718424	−	0.695605i	$-0.244864\pi$
$824$	1.03541	−	6.48350i	0.0360702	−	0.225863i
$825$	−4.90465	−	29.6697i	−0.170758	−	1.03297i
$826$	2.21425	+	4.35031i	0.0770436	+	0.151367i
$827$	−17.6143			−0.612510			−0.306255	−	0.951950i	$-0.599076\pi$
$827$	−17.6143			−0.612510			−0.306255	+	0.951950i	$0.599076\pi$
$828$	7.13985	+	5.19673i	0.248127	+	0.180599i
$829$			21.6578i			0.752208i	0.926578	+	0.376104i	$0.122736\pi$
$829$			21.6578i			0.752208i	−0.926578	+	0.376104i	$0.877264\pi$
$830$	3.71422	+	6.02117i	0.128922	+	0.208998i
$831$	−23.3830			−0.811148
$832$	7.60209	+	2.49164i	0.263555	+	0.0863820i
$833$		−	6.81622i		−	0.236168i
$834$	−16.5756	+	8.43675i	−0.573965	+	0.292141i
$835$	1.39284	+	16.9658i	0.0482013	+	0.587125i
$836$	41.8102	−	57.4435i	1.44604	−	1.98673i
$837$	37.0482			1.28057
$838$	1.15689	−	0.588844i	0.0399642	−	0.0203413i
$839$	−20.8724			−0.720594			−0.360297	−	0.932838i	$-0.617325\pi$
$839$	−20.8724			−0.720594			−0.360297	+	0.932838i	$0.617325\pi$
$840$	−0.591495	+	7.72212i	−0.0204085	+	0.266438i
$841$	23.3386			0.804778
$842$	31.4311	−	15.9980i	1.08319	−	0.551328i
$843$	2.73215			0.0941004
$844$	−2.48440	−	1.80827i	−0.0855166	−	0.0622432i
$845$	2.22857	−	0.182959i	0.0766652	−	0.00629399i
$846$	−1.03120	+	0.524867i	−0.0354533	+	0.0180453i
$847$			10.9742i			0.377076i
$848$	−7.54467	−	23.3559i	−0.259085	−	0.802045i
$849$	−29.5885			−1.01547
$850$	−6.39234	+	4.70632i	−0.219255	+	0.161425i
$851$			8.50654i			0.291600i
$852$	17.9349	−	24.6410i	0.614441	−	0.844187i
$853$	20.8593			0.714208			0.357104	−	0.934065i	$-0.383764\pi$
$853$	20.8593			0.714208			0.357104	+	0.934065i	$0.383764\pi$
$854$	−5.16547	−	10.1485i	−0.176759	−	0.347275i
$855$	−1.90159	−	23.1626i	−0.0650329	−	0.792145i
$856$	12.5736	+	2.00799i	0.429758	+	0.0686318i
$857$		−	6.91410i		−	0.236181i	−0.993003	−	0.118091i	$-0.962323\pi$
$857$		−	6.91410i		−	0.236181i	0.993003	−	0.118091i	$-0.0376773\pi$
$858$	−7.58032	+	3.85829i	−0.258788	+	0.131720i
$859$		−	21.6653i		−	0.739210i	−0.929189	−	0.369605i	$-0.879493\pi$
$859$		−	21.6653i		−	0.739210i	0.929189	−	0.369605i	$-0.120507\pi$
$860$	7.82497	−	12.8417i	0.266829	−	0.437898i
$861$			5.65168i			0.192609i
$862$	−9.67203	−	19.0025i	−0.329431	−	0.647228i
$863$			50.6358i			1.72366i	0.507195	+	0.861831i	$0.330682\pi$
$863$			50.6358i			1.72366i	−0.507195	+	0.861831i	$0.669318\pi$
$864$	−22.3389	+	22.2436i	−0.759985	+	0.756744i
$865$	−21.9840	+	1.80482i	−0.747477	+	0.0613657i
$866$	−15.4777	+	7.87793i	−0.525952	+	0.267703i
$867$	−20.0060			−0.679439
$868$	10.3568	+	7.53816i	0.351531	+	0.255862i
$869$		−	68.2192i		−	2.31418i
$870$	8.13962	−	5.02101i	0.275959	−	0.170228i
$871$	−8.67147			−0.293822
$872$	−7.42570	+	46.4981i	−0.251466	+	1.57463i
$873$		−	24.0837i		−	0.815109i
$874$	15.3597	+	30.1770i	0.519550	+	1.02075i
$875$	−2.62039	−	10.4477i	−0.0885855	−	0.353198i
$876$	−7.81085	−	5.68512i	−0.263904	−	0.192082i
$877$	43.7550			1.47750			0.738750	−	0.673979i	$-0.235416\pi$
$877$	43.7550			1.47750			0.738750	+	0.673979i	$0.235416\pi$
$878$	−23.9517	−	47.0575i	−0.808330	−	1.58811i
$879$	−39.1243			−1.31963
$880$	39.0747	−	16.2615i	1.31721	−	0.548175i
$881$	−2.99078			−0.100762			−0.0503809	−	0.998730i	$-0.516044\pi$
$881$	−2.99078			−0.100762			−0.0503809	+	0.998730i	$0.516044\pi$
$882$	5.39250	+	10.5946i	0.181575	+	0.356738i
$883$	−24.9742			−0.840450			−0.420225	−	0.907420i	$-0.638049\pi$
$883$	−24.9742			−0.840450			−0.420225	+	0.907420i	$0.638049\pi$
$884$	1.81527	+	1.32125i	0.0610543	+	0.0444383i
$885$	0.833165	+	10.1485i	0.0280065	+	0.341139i
$886$	−3.76254	−	7.39220i	−0.126405	−	0.248346i
$887$			11.6642i			0.391646i	0.980639	+	0.195823i	$0.0627378\pi$
$887$			11.6642i			0.391646i	−0.980639	+	0.195823i	$0.937262\pi$
$888$	−9.46876	−	1.51215i	−0.317751	−	0.0507445i
$889$	−1.26577			−0.0424527
$890$	18.2745	+	29.6251i	0.612564	+	0.993034i
$891$		−	13.8645i		−	0.464480i
$892$	13.9443	+	10.1494i	0.466891	+	0.339826i
$893$	−4.43677			−0.148471
$894$	6.38877	−	3.25180i	0.213672	−	0.108757i
$895$	−1.03144	−	12.5637i	−0.0344774	−	0.419958i
$896$	−10.7707	+	1.67290i	−0.359824	+	0.0558875i
$897$		−	4.05378i		−	0.135352i
$898$	−20.2769	−	39.8377i	−0.676649	−	1.32940i
$899$		−	15.8181i		−	0.527563i
$900$	6.21242	−	12.3723i	0.207081	−	0.412408i
$901$		−	6.88834i		−	0.229484i
$902$	27.5249	−	14.0098i	0.916480	−	0.466477i
$903$		−	4.11765i		−	0.137027i
$904$	5.90103	−	36.9510i	0.196265	−	1.22897i
$905$	−0.822718	−	10.0213i	−0.0273481	−	0.333118i
$906$	9.62404	+	18.9082i	0.319737	+	0.628184i
$907$	7.91159			0.262700			0.131350	−	0.991336i	$-0.458069\pi$
$907$	7.91159			0.262700			0.131350	+	0.991336i	$0.458069\pi$
$908$	−23.4678	+	32.2427i	−0.778806	+	1.07001i
$909$		−	18.1915i		−	0.603375i
$910$	−2.59295	+	1.59949i	−0.0859554	+	0.0530225i
$911$	8.60784			0.285190			0.142595	−	0.989781i	$-0.454455\pi$
$911$	8.60784			0.285190			0.142595	+	0.989781i	$0.454455\pi$
$912$	−36.3209	+	11.7328i	−1.20271	+	0.388511i
$913$		−	10.5861i		−	0.350349i
$914$	11.1952	−	5.69821i	0.370304	−	0.188480i
$915$	−1.94363	−	23.6748i	−0.0642545	−	0.782664i
$916$	25.4382	+	18.5151i	0.840500	+	0.611758i
$917$	−19.2507			−0.635713
$918$	−7.88480	+	4.01326i	−0.260237	+	0.132457i
$919$	31.1803			1.02854			0.514272	−	0.857627i	$-0.328062\pi$
$919$	31.1803			1.02854			0.514272	+	0.857627i	$0.328062\pi$
$920$	−1.54054	+	20.1121i	−0.0507900	+	0.663077i
$921$	4.27683			0.140926
$922$	−35.7452	+	18.1938i	−1.17721	+	0.599182i
$923$	11.9889			0.394619
$924$	6.81979	−	9.36979i	0.224355	−	0.308243i
$925$	13.1574	−	2.17503i	0.432613	−	0.0715146i
$926$	−8.42513	+	4.28828i	−0.276867	+	0.140922i
$927$			3.21371i			0.105552i
$928$	9.49715	+	9.53782i	0.311759	+	0.313094i
$929$	11.4465			0.375546			0.187773	−	0.982212i	$-0.439873\pi$
$929$	11.4465			0.375546			0.187773	+	0.982212i	$0.439873\pi$
$930$	14.0288	+	22.7422i	0.460021	+	0.745745i
$931$			45.5835i			1.49394i
$932$	19.2393	+	14.0033i	0.630205	+	0.458694i
$933$	−23.9150			−0.782941
$934$	12.0357	+	23.6464i	0.393820	+	0.773733i
$935$	11.8382	−	0.971884i	0.387151	−	0.0317840i
$936$	−3.86678	−	0.617521i	−0.126390	−	0.0201843i
$937$			5.01140i			0.163715i	0.996644	+	0.0818577i	$0.0260853\pi$
$937$			5.01140i			0.163715i	−0.996644	+	0.0818577i	$0.973915\pi$
$938$	10.5293	−	5.35926i	0.343793	−	0.174986i
$939$		−	42.9031i		−	1.40009i
$940$	−2.25698	−	1.37527i	−0.0736146	−	0.0448564i
$941$			18.8286i			0.613795i	0.951743	+	0.306897i	$0.0992908\pi$
$941$			18.8286i			0.613795i	−0.951743	+	0.306897i	$0.900709\pi$
$942$	−15.8828	−	31.2047i	−0.517489	−	1.01670i
$943$			14.7197i			0.479339i
$944$	−13.6371	+	4.40520i	−0.443849	+	0.143377i
$945$	−0.982302	−	11.9651i	−0.0319543	−	0.389225i
$946$	−20.0539	+	10.2072i	−0.652008	+	0.331864i
$947$	3.60609			0.117182			0.0585911	−	0.998282i	$-0.481339\pi$
$947$	3.60609			0.117182			0.0585911	+	0.998282i	$0.481339\pi$
$948$	−21.5671	+	29.6313i	−0.700467	+	0.962380i
$949$		−	3.80031i		−	0.123363i
$950$	42.7487	−	31.4735i	1.38695	−	1.02113i
$951$	13.2435			0.429449
$952$	−3.02076	−	0.482412i	−0.0979033	−	0.0156351i
$953$			5.58945i			0.181060i	0.995894	+	0.0905301i	$0.0288561\pi$
$953$			5.58945i			0.181060i	−0.995894	+	0.0905301i	$0.971144\pi$
$954$	5.44955	+	10.7066i	0.176436	+	0.346641i
$955$	−47.1370	+	3.86981i	−1.52532	+	0.125224i
$956$	−0.404502	+	0.555750i	−0.0130825	+	0.0179742i
$957$	−14.3107			−0.462599
$958$	20.1379	+	39.5646i	0.650625	+	1.27827i
$959$	−10.7666			−0.347672
$960$	−22.1133	−	5.28999i	−0.713702	−	0.170734i
$961$	13.1959			0.425674
$962$	−1.71101	−	3.36159i	−0.0551651	−	0.108382i
$963$	−6.23243			−0.200837
$964$	−0.108580	+	0.149180i	−0.00349714	+	0.00480476i
$965$	−3.83257	−	46.6834i	−0.123375	−	1.50279i
$966$	2.50537	+	4.92227i	0.0806090	+	0.158371i
$967$		−	28.1760i		−	0.906080i	−0.891490	−	0.453040i	$-0.850340\pi$
$967$		−	28.1760i		−	0.906080i	0.891490	−	0.453040i	$-0.149660\pi$
$968$	−31.8150	−	5.08083i	−1.02257	−	0.163304i
$969$	−10.7121			−0.344122
$970$	46.8197	−	28.8812i	1.50329	−	0.927321i
$971$			28.3687i			0.910394i	0.890391	+	0.455197i	$0.150431\pi$
$971$			28.3687i			0.910394i	−0.890391	+	0.455197i	$0.849569\pi$
$972$	15.2937	−	21.0121i	0.490545	−	0.673965i
$973$	9.96852			0.319576
$974$	−42.3030	+	21.5317i	−1.35547	+	0.689919i
$975$	−6.27014	+	1.03651i	−0.200805	+	0.0331948i
$976$	31.8130	−	10.2766i	1.01831	−	0.328945i
$977$		−	51.7051i		−	1.65419i	−0.562061	−	0.827096i	$-0.689991\pi$
$977$		−	51.7051i		−	1.65419i	0.562061	−	0.827096i	$-0.310009\pi$
$978$	−17.5672	−	34.5141i	−0.561738	−	1.10364i
$979$		−	52.0853i		−	1.66465i
$980$	−14.1296	+	23.1883i	−0.451353	+	0.740722i
$981$		−	23.0480i		−	0.735865i
$982$	−51.7271	+	26.3284i	−1.65068	+	0.840174i
$983$			44.6065i			1.42273i	0.702824	+	0.711363i	$0.251922\pi$
$983$			44.6065i			1.42273i	−0.702824	+	0.711363i	$0.748078\pi$
$984$	−16.3847	−	2.61662i	−0.522326	−	0.0834149i
$985$	14.9488	−	1.22725i	0.476309	−	0.0391036i
$986$	1.71350	+	3.36650i	0.0545691	+	0.107211i
$987$	−0.723694			−0.0230354
$988$	−12.1396	−	8.83583i	−0.386213	−	0.281105i
$989$		−	10.7243i		−	0.341014i
$990$	−17.6314	+	10.8761i	−0.560364	+	0.345667i
$991$	−40.6673			−1.29184			−0.645919	−	0.763406i	$-0.723526\pi$
$991$	−40.6673			−1.29184			−0.645919	+	0.763406i	$0.723526\pi$
$992$	−26.6488	+	26.5351i	−0.846099	+	0.842491i
$993$		−	3.48802i		−	0.110689i
$994$	−14.5574	+	7.40954i	−0.461733	+	0.235016i
$995$	8.74615	−	0.718034i	0.277272	−	0.0227632i
$996$	−3.34674	+	4.59813i	−0.106046	+	0.145697i
$997$	−9.68003			−0.306570			−0.153285	−	0.988182i	$-0.548985\pi$
$997$	−9.68003			−0.306570			−0.153285	+	0.988182i	$0.548985\pi$
$998$	−22.0002	+	11.1978i	−0.696403	+	0.354460i
$999$	14.8638			0.470271

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.j.a.469.13	✓	36
4.3	odd	2		2080.2.j.b.209.24		36
5.4	even	2		520.2.j.b.469.24	yes	36
8.3	odd	2		2080.2.j.a.209.14		36
8.5	even	2		520.2.j.b.469.23	yes	36
20.19	odd	2		2080.2.j.a.209.13		36
40.19	odd	2		2080.2.j.b.209.23		36
40.29	even	2	inner	520.2.j.a.469.14	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.j.a.469.13	✓	36	1.1	even	1	trivial
520.2.j.a.469.14	yes	36	40.29	even	2	inner
520.2.j.b.469.23	yes	36	8.5	even	2
520.2.j.b.469.24	yes	36	5.4	even	2
2080.2.j.a.209.13		36	20.19	odd	2
2080.2.j.a.209.14		36	8.3	odd	2
2080.2.j.b.209.23		36	40.19	odd	2
2080.2.j.b.209.24		36	4.3	odd	2

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.641501 - 1.26035i) q^{2} -1.27105 q^{3} +(-1.17695 + 1.61703i) q^{4} +(2.22857 - 0.182959i) q^{5} +(0.815378 + 1.60196i) q^{6} -0.963418i q^{7} +(2.79303 + 0.446045i) q^{8} -1.38444 q^{9} +O(q^{10})\)	\(q+(-0.641501 - 1.26035i) q^{2} -1.27105 q^{3} +(-1.17695 + 1.61703i) q^{4} +(2.22857 - 0.182959i) q^{5} +(0.815378 + 1.60196i) q^{6} -0.963418i q^{7} +(2.79303 + 0.446045i) q^{8} -1.38444 q^{9} +(-1.66022 - 2.69141i) q^{10} +4.73190i q^{11} +(1.49596 - 2.05532i) q^{12} +1.00000 q^{13} +(-1.21424 + 0.618034i) q^{14} +(-2.83262 + 0.232550i) q^{15} +(-1.22956 - 3.80633i) q^{16} -1.12260i q^{17} +(0.888118 + 1.74487i) q^{18} +7.50738i q^{19} +(-2.32707 + 3.81900i) q^{20} +1.22455i q^{21} +(5.96384 - 3.03552i) q^{22} +3.18932i q^{23} +(-3.55008 - 0.566944i) q^{24} +(4.93305 - 0.815475i) q^{25} +(-0.641501 - 1.26035i) q^{26} +5.57283 q^{27} +(1.55788 + 1.13390i) q^{28} -2.37938i q^{29} +(2.11022 + 3.42090i) q^{30} +6.64800 q^{31} +(-4.00854 + 3.99144i) q^{32} -6.01447i q^{33} +(-1.41487 + 0.720148i) q^{34} +(-0.176266 - 2.14705i) q^{35} +(1.62942 - 2.23868i) q^{36} +2.66720 q^{37} +(9.46190 - 4.81599i) q^{38} -1.27105 q^{39} +(6.30608 + 0.483031i) q^{40} +4.61531 q^{41} +(1.54336 - 0.785551i) q^{42} -3.36258 q^{43} +(-7.65161 - 5.56922i) q^{44} +(-3.08532 + 0.253296i) q^{45} +(4.01965 - 2.04595i) q^{46} +0.590988i q^{47} +(1.56283 + 4.83803i) q^{48} +6.07182 q^{49} +(-4.19234 - 5.69423i) q^{50} +1.42688i q^{51} +(-1.17695 + 1.61703i) q^{52} +6.13606 q^{53} +(-3.57498 - 7.02370i) q^{54} +(0.865745 + 10.5454i) q^{55} +(0.429728 - 2.69086i) q^{56} -9.54223i q^{57} +(-2.99884 + 1.52637i) q^{58} -3.58273i q^{59} +(2.95782 - 4.85413i) q^{60} +8.35791i q^{61} +(-4.26470 - 8.37879i) q^{62} +1.33379i q^{63} +(7.60209 + 2.49164i) q^{64} +(2.22857 - 0.182959i) q^{65} +(-7.58032 + 3.85829i) q^{66} -8.67147 q^{67} +(1.81527 + 1.32125i) q^{68} -4.05378i q^{69} +(-2.59295 + 1.59949i) q^{70} +11.9889 q^{71} +(-3.86678 - 0.617521i) q^{72} -3.80031i q^{73} +(-1.71101 - 3.36159i) q^{74} +(-6.27014 + 1.03651i) q^{75} +(-12.1396 - 8.83583i) q^{76} +4.55880 q^{77} +(0.815378 + 1.60196i) q^{78} -14.4169 q^{79} +(-3.43657 - 8.25772i) q^{80} -2.93002 q^{81} +(-2.96073 - 5.81689i) q^{82} -2.23718 q^{83} +(-1.98013 - 1.44124i) q^{84} +(-0.205390 - 2.50179i) q^{85} +(2.15710 + 4.23802i) q^{86} +3.02430i q^{87} +(-2.11064 + 13.2164i) q^{88} -11.0073 q^{89} +(2.29847 + 3.72608i) q^{90} -0.963418i q^{91} +(-5.15722 - 3.75368i) q^{92} -8.44992 q^{93} +(0.744850 - 0.379119i) q^{94} +(1.37354 + 16.7307i) q^{95} +(5.09504 - 5.07331i) q^{96} +17.3960i q^{97} +(-3.89508 - 7.65261i) q^{98} -6.55102i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{3} + 2 q^{4} - 2 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q - 8 * q^3 + 2 * q^4 - 2 * q^6 + 36 * q^9	\( 36 q - 8 q^{3} + 2 q^{4} - 2 q^{6} + 36 q^{9} - 13 q^{10} + 10 q^{12} + 36 q^{13} - 6 q^{14} + 6 q^{16} - 15 q^{20} - 20 q^{22} - 16 q^{24} - 32 q^{27} + 37 q^{30} - 20 q^{31} - 10 q^{32} + 22 q^{34} - 12 q^{36} - 10 q^{38} - 8 q^{39} + 23 q^{40} + 26 q^{42} + 32 q^{43} + 26 q^{44} - 12 q^{45} - 6 q^{46} - 20 q^{48} - 36 q^{49} - 37 q^{50} + 2 q^{52} - 22 q^{54} - 8 q^{55} - 2 q^{56} + 10 q^{58} - 57 q^{60} - 18 q^{62} - 10 q^{64} - 28 q^{66} + 44 q^{67} + 26 q^{68} + 81 q^{70} + 28 q^{71} - 60 q^{72} + 10 q^{74} - 36 q^{76} - 2 q^{78} - 8 q^{79} + 65 q^{80} + 28 q^{81} + 34 q^{82} - 68 q^{83} - 18 q^{84} - 12 q^{86} - 2 q^{88} - 8 q^{89} - 88 q^{90} + 34 q^{92} - 16 q^{93} - 10 q^{94} + 12 q^{95} + 2 q^{96} + 38 q^{98}+O(q^{100}) \) 36 * q - 8 * q^3 + 2 * q^4 - 2 * q^6 + 36 * q^9 - 13 * q^10 + 10 * q^12 + 36 * q^13 - 6 * q^14 + 6 * q^16 - 15 * q^20 - 20 * q^22 - 16 * q^24 - 32 * q^27 + 37 * q^30 - 20 * q^31 - 10 * q^32 + 22 * q^34 - 12 * q^36 - 10 * q^38 - 8 * q^39 + 23 * q^40 + 26 * q^42 + 32 * q^43 + 26 * q^44 - 12 * q^45 - 6 * q^46 - 20 * q^48 - 36 * q^49 - 37 * q^50 + 2 * q^52 - 22 * q^54 - 8 * q^55 - 2 * q^56 + 10 * q^58 - 57 * q^60 - 18 * q^62 - 10 * q^64 - 28 * q^66 + 44 * q^67 + 26 * q^68 + 81 * q^70 + 28 * q^71 - 60 * q^72 + 10 * q^74 - 36 * q^76 - 2 * q^78 - 8 * q^79 + 65 * q^80 + 28 * q^81 + 34 * q^82 - 68 * q^83 - 18 * q^84 - 12 * q^86 - 2 * q^88 - 8 * q^89 - 88 * q^90 + 34 * q^92 - 16 * q^93 - 10 * q^94 + 12 * q^95 + 2 * q^96 + 38 * q^98

Introduction

L-functions

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