LMFDB - Embedded newform 966.2.q.i.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			211.1
Character	$\chi$	$=$	966.211
Dual form			966.2.q.i.673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-2.63117 - 1.69095i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-2.63117 - 1.69095i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.445115 - 3.09584i) q^{10} +(-0.711219 + 1.55735i) q^{11} +(0.415415 - 0.909632i) q^{12} +(0.176194 - 1.22546i) q^{13} +(0.841254 - 0.540641i) q^{14} +(3.00099 + 0.881169i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(3.07207 + 3.54536i) q^{17} +(0.841254 + 0.540641i) q^{18} +(2.37674 - 2.74290i) q^{19} +(3.00099 - 0.881169i) q^{20} +(0.415415 + 0.909632i) q^{21} -1.71207 q^{22} +(0.438117 + 4.77578i) q^{23} +1.00000 q^{24} +(1.98667 + 4.35021i) q^{25} +(1.18791 - 0.348802i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(4.79984 + 5.53931i) q^{29} +(0.445115 + 3.09584i) q^{30} +(0.842693 + 0.247437i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.243653 - 1.69464i) q^{33} +(-1.94879 + 4.26725i) q^{34} +(-1.29929 + 2.84504i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-7.08599 + 4.55389i) q^{37} +(3.48237 + 1.02252i) q^{38} +(0.176194 + 1.22546i) q^{39} +(2.04819 + 2.36374i) q^{40} +(2.26503 + 1.45564i) q^{41} +(-0.654861 + 0.755750i) q^{42} +(7.88742 - 2.31596i) q^{43} +(-0.711219 - 1.55735i) q^{44} -3.12768 q^{45} +(-4.16220 + 2.38245i) q^{46} +9.80517 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(-3.13179 + 3.61428i) q^{50} +(-3.94647 - 2.53624i) q^{51} +(0.810757 + 0.935664i) q^{52} +(0.125234 + 0.871019i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(4.50475 - 2.89503i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(-1.50770 + 3.30140i) q^{57} +(-3.04481 + 6.66720i) q^{58} +(-0.492239 + 3.42360i) q^{59} +(-2.63117 + 1.69095i) q^{60} +(-5.04182 - 1.48041i) q^{61} +(0.124991 + 0.869329i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.53579 + 2.92646i) q^{65} +(1.64272 - 0.482346i) q^{66} +(2.75750 + 6.03807i) q^{67} -4.69118 q^{68} +(-1.76586 - 4.45889i) q^{69} -3.12768 q^{70} +(2.50031 + 5.47492i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(6.11012 - 7.05146i) q^{73} +(-7.08599 - 4.55389i) q^{74} +(-3.13179 - 3.61428i) q^{75} +(0.516515 + 3.59244i) q^{76} +(1.64272 + 0.482346i) q^{77} +(-1.04152 + 0.669346i) q^{78} +(-0.350248 + 2.43603i) q^{79} +(-1.29929 + 2.84504i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.383174 + 2.66504i) q^{82} +(4.53060 - 2.91164i) q^{83} +(-0.959493 - 0.281733i) q^{84} +(-2.08812 - 14.5232i) q^{85} +(5.38322 + 6.21257i) q^{86} +(-6.16602 - 3.96266i) q^{87} +(1.12117 - 1.29390i) q^{88} +(-6.92304 + 2.03279i) q^{89} +(-1.29929 - 2.84504i) q^{90} -1.23806 q^{91} +(-3.89620 - 2.79636i) q^{92} -0.878269 q^{93} +(4.07321 + 8.91910i) q^{94} +(-10.8917 + 3.19810i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(8.37689 + 5.38350i) q^{97} +(-0.654861 - 0.755750i) q^{98} +(0.243653 + 1.69464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{11}\right)$

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
$5$	−2.63117	−	1.69095i	−1.17670	−	0.756216i	−0.201920	−	0.979402i	$-0.564718\pi$
$5$	−2.63117	−	1.69095i	−1.17670	−	0.756216i	−0.974776	+	0.223186i	$0.928354\pi$
$6$	−0.654861	−	0.755750i	−0.267346	−	0.308533i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$7$	−0.142315	−	0.989821i	−0.0537900	−	0.374117i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$	0.445115	−	3.09584i	0.140758	−	0.978992i
$11$	−0.711219	+	1.55735i	−0.214441	+	0.469560i	−0.986031	−	0.166560i	$-0.946734\pi$
$11$	−0.711219	+	1.55735i	−0.214441	+	0.469560i	0.771591	+	0.636119i	$0.219461\pi$
$12$	0.415415	−	0.909632i	0.119920	−	0.262588i
$13$	0.176194	−	1.22546i	0.0488675	−	0.339881i	−0.950690	−	0.310142i	$-0.899623\pi$
$13$	0.176194	−	1.22546i	0.0488675	−	0.339881i	0.999558	−	0.0297389i	$-0.00946758\pi$
$14$	0.841254	−	0.540641i	0.224834	−	0.144492i
$15$	3.00099	+	0.881169i	0.774852	+	0.227517i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	3.07207	+	3.54536i	0.745086	+	0.859875i	0.994082	−	0.108629i	$-0.0346461\pi$
$17$	3.07207	+	3.54536i	0.745086	+	0.859875i	−0.248996	+	0.968504i	$0.580101\pi$
$18$	0.841254	+	0.540641i	0.198285	+	0.127430i
$19$	2.37674	−	2.74290i	0.545262	−	0.629266i	−0.414511	−	0.910044i	$-0.636047\pi$
$19$	2.37674	−	2.74290i	0.545262	−	0.629266i	0.959772	+	0.280779i	$0.0905927\pi$
$20$	3.00099	−	0.881169i	0.671041	−	0.197035i
$21$	0.415415	+	0.909632i	0.0906510	+	0.198498i
$22$	−1.71207			−0.365014
$23$	0.438117	+	4.77578i	0.0913536	+	0.995819i
$23$	0.438117	+	4.77578i	0.0913536	+	0.995819i
$24$	1.00000			0.204124
$25$	1.98667	+	4.35021i	0.397335	+	0.870042i
$26$	1.18791	−	0.348802i	0.232968	−	0.0684057i
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$	0.841254	+	0.540641i	0.158982	+	0.102172i
$29$	4.79984	+	5.53931i	0.891308	+	1.02862i	0.999405	+	0.0344844i	$0.0109789\pi$
$29$	4.79984	+	5.53931i	0.891308	+	1.02862i	−0.108097	+	0.994140i	$0.534476\pi$
$30$	0.445115	+	3.09584i	0.0812666	+	0.565221i
$31$	0.842693	+	0.247437i	0.151352	+	0.0444410i	0.356531	−	0.934284i	$-0.383959\pi$
$31$	0.842693	+	0.247437i	0.151352	+	0.0444410i	−0.205179	+	0.978724i	$0.565778\pi$
$32$	0.841254	−	0.540641i	0.148714	−	0.0955727i
$33$	0.243653	−	1.69464i	0.0424145	−	0.294999i
$34$	−1.94879	+	4.26725i	−0.334214	+	0.731827i
$35$	−1.29929	+	2.84504i	−0.219619	+	0.480899i
$36$	−0.142315	+	0.989821i	−0.0237191	+	0.164970i
$37$	−7.08599	+	4.55389i	−1.16493	+	0.748655i	−0.972556	−	0.232667i	$-0.925255\pi$
$37$	−7.08599	+	4.55389i	−1.16493	+	0.748655i	−0.192373	+	0.981322i	$0.561618\pi$
$38$	3.48237	+	1.02252i	0.564915	+	0.165874i
$39$	0.176194	+	1.22546i	0.0282137	+	0.196230i
$40$	2.04819	+	2.36374i	0.323848	+	0.373741i
$41$	2.26503	+	1.45564i	0.353738	+	0.227333i	0.705426	−	0.708784i	$-0.250756\pi$
$41$	2.26503	+	1.45564i	0.353738	+	0.227333i	−0.351688	+	0.936117i	$0.614392\pi$
$42$	−0.654861	+	0.755750i	−0.101047	+	0.116615i
$43$	7.88742	−	2.31596i	1.20282	−	0.353180i	0.381890	−	0.924208i	$-0.375273\pi$
$43$	7.88742	−	2.31596i	1.20282	−	0.353180i	0.820931	+	0.571028i	$0.193455\pi$
$44$	−0.711219	−	1.55735i	−0.107220	−	0.234780i
$45$	−3.12768			−0.466247
$46$	−4.16220	+	2.38245i	−0.613683	+	0.351274i
$47$	9.80517			1.43023			0.715116	−	0.699006i	$-0.246374\pi$
$47$	9.80517			1.43023			0.715116	+	0.699006i	$0.246374\pi$
$48$	0.415415	+	0.909632i	0.0599600	+	0.131294i
$49$	−0.959493	+	0.281733i	−0.137070	+	0.0402475i
$50$	−3.13179	+	3.61428i	−0.442903	+	0.511137i
$51$	−3.94647	−	2.53624i	−0.552616	−	0.355145i
$52$	0.810757	+	0.935664i	0.112432	+	0.129753i
$53$	0.125234	+	0.871019i	0.0172022	+	0.119644i	0.996613	−	0.0822328i	$-0.0262051\pi$
$53$	0.125234	+	0.871019i	0.0172022	+	0.119644i	−0.979411	+	0.201877i	$0.935296\pi$
$54$	−0.959493	−	0.281733i	−0.130570	−	0.0383389i
$55$	4.50475	−	2.89503i	0.607420	−	0.390365i
$56$	−0.142315	+	0.989821i	−0.0190176	+	0.132270i
$57$	−1.50770	+	3.30140i	−0.199700	+	0.437282i
$58$	−3.04481	+	6.66720i	−0.399803	+	0.875447i
$59$	−0.492239	+	3.42360i	−0.0640840	+	0.445714i	0.932365	+	0.361518i	$0.117741\pi$
$59$	−0.492239	+	3.42360i	−0.0640840	+	0.445714i	−0.996449	+	0.0841963i	$0.973168\pi$
$60$	−2.63117	+	1.69095i	−0.339683	+	0.218301i
$61$	−5.04182	−	1.48041i	−0.645539	−	0.189547i	−0.0574563	−	0.998348i	$-0.518299\pi$
$61$	−5.04182	−	1.48041i	−0.645539	−	0.189547i	−0.588083	+	0.808801i	$0.700117\pi$
$62$	0.124991	+	0.869329i	0.0158738	+	0.110405i
$63$	−0.654861	−	0.755750i	−0.0825047	−	0.0952155i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−2.53579	+	2.92646i	−0.314526	+	0.362982i
$66$	1.64272	−	0.482346i	0.202205	−	0.0593726i
$67$	2.75750	+	6.03807i	0.336882	+	0.737668i	0.999941	−	0.0108993i	$-0.00346941\pi$
$67$	2.75750	+	6.03807i	0.336882	+	0.737668i	−0.663059	+	0.748567i	$0.730742\pi$
$68$	−4.69118			−0.568889
$69$	−1.76586	−	4.45889i	−0.212585	−	0.536788i
$70$	−3.12768			−0.373829
$71$	2.50031	+	5.47492i	0.296732	+	0.649753i	0.998005	−	0.0631403i	$-0.0201116\pi$
$71$	2.50031	+	5.47492i	0.296732	+	0.649753i	−0.701272	+	0.712893i	$0.747384\pi$
$72$	−0.959493	+	0.281733i	−0.113077	+	0.0332025i
$73$	6.11012	−	7.05146i	0.715136	−	0.825311i	−0.275577	−	0.961279i	$-0.588869\pi$
$73$	6.11012	−	7.05146i	0.715136	−	0.825311i	0.990713	+	0.135968i	$0.0434145\pi$
$74$	−7.08599	−	4.55389i	−0.823729	−	0.529379i
$75$	−3.13179	−	3.61428i	−0.361628	−	0.417341i
$76$	0.516515	+	3.59244i	0.0592483	+	0.412081i
$77$	1.64272	+	0.482346i	0.187205	+	0.0549684i
$78$	−1.04152	+	0.669346i	−0.117929	+	0.0757885i
$79$	−0.350248	+	2.43603i	−0.0394059	+	0.274074i	−0.999992	−	0.00390717i	$-0.998756\pi$
$79$	−0.350248	+	2.43603i	−0.0394059	+	0.274074i	0.960586	+	0.277982i	$0.0896654\pi$
$80$	−1.29929	+	2.84504i	−0.145265	+	0.318085i
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$	−0.383174	+	2.66504i	−0.0423145	+	0.294304i
$83$	4.53060	−	2.91164i	0.497298	−	0.319594i	−0.267836	−	0.963464i	$-0.586309\pi$
$83$	4.53060	−	2.91164i	0.497298	−	0.319594i	0.765135	+	0.643870i	$0.222672\pi$
$84$	−0.959493	−	0.281733i	−0.104689	−	0.0307395i
$85$	−2.08812	−	14.5232i	−0.226488	−	1.57526i
$86$	5.38322	+	6.21257i	0.580488	+	0.669919i
$87$	−6.16602	−	3.96266i	−0.661067	−	0.424842i
$88$	1.12117	−	1.29390i	0.119517	−	0.137930i
$89$	−6.92304	+	2.03279i	−0.733841	+	0.215475i	−0.627239	−	0.778827i	$-0.715815\pi$
$89$	−6.92304	+	2.03279i	−0.733841	+	0.215475i	−0.106602	+	0.994302i	$0.533997\pi$
$90$	−1.29929	−	2.84504i	−0.136957	−	0.299893i
$91$	−1.23806			−0.129784
$92$	−3.89620	−	2.79636i	−0.406207	−	0.291541i
$93$	−0.878269			−0.0910722
$94$	4.07321	+	8.91910i	0.420120	+	0.919935i
$95$	−10.8917	+	3.19810i	−1.11747	+	0.328118i
$96$	−0.654861	+	0.755750i	−0.0668364	+	0.0771334i
$97$	8.37689	+	5.38350i	0.850544	+	0.546611i	0.891744	−	0.452540i	$-0.149482\pi$
$97$	8.37689	+	5.38350i	0.850544	+	0.546611i	−0.0412005	+	0.999151i	$0.513118\pi$
$98$	−0.654861	−	0.755750i	−0.0661509	−	0.0763422i
$99$	0.243653	+	1.69464i	0.0244880	+	0.170318i
$100$	−4.58866	−	1.34735i	−0.458866	−	0.134735i
$101$	5.10953	−	3.28369i	0.508417	−	0.326740i	−0.261158	−	0.965296i	$-0.584104\pi$
$101$	5.10953	−	3.28369i	0.508417	−	0.326740i	0.769575	+	0.638556i	$0.220468\pi$
$102$	0.667624	−	4.64343i	0.0661047	−	0.459768i
$103$	1.15510	−	2.52932i	0.113816	−	0.249221i	−0.844149	−	0.536109i	$-0.819893\pi$
$103$	1.15510	−	2.52932i	0.113816	−	0.249221i	0.957964	+	0.286888i	$0.0926207\pi$
$104$	−0.514309	+	1.12618i	−0.0504321	+	0.110431i
$105$	0.445115	−	3.09584i	0.0434388	−	0.302124i
$106$	−0.740283	+	0.475751i	−0.0719027	+	0.0462090i
$107$	−8.45793	−	2.48347i	−0.817659	−	0.240086i	−0.153951	−	0.988078i	$-0.549200\pi$
$107$	−8.45793	−	2.48347i	−0.817659	−	0.240086i	−0.663708	+	0.747992i	$0.731018\pi$
$108$	−0.142315	−	0.989821i	−0.0136943	−	0.0952456i
$109$	−4.99778	−	5.76775i	−0.478701	−	0.552450i	0.464110	−	0.885777i	$-0.346374\pi$
$109$	−4.99778	−	5.76775i	−0.478701	−	0.552450i	−0.942811	+	0.333327i	$0.891829\pi$
$110$	4.50475	+	2.89503i	0.429511	+	0.276030i
$111$	5.51598	−	6.36578i	0.523553	−	0.604213i
$112$	−0.959493	+	0.281733i	−0.0906636	+	0.0266212i
$113$	3.92161	+	8.58713i	0.368914	+	0.807809i	0.999498	+	0.0316881i	$0.0100883\pi$
$113$	3.92161	+	8.58713i	0.368914	+	0.807809i	−0.630584	+	0.776121i	$0.717184\pi$
$114$	−3.62938			−0.339923
$115$	6.92285	−	13.3067i	0.645559	−	1.24086i
$116$	−7.32956			−0.680533
$117$	−0.514309	−	1.12618i	−0.0475479	−	0.104115i
$118$	−3.31870	+	0.974457i	−0.305511	+	0.0897060i
$119$	3.07207	−	3.54536i	0.281616	−	0.325002i
$120$	−2.63117	−	1.69095i	−0.240192	−	0.154362i
$121$	5.28395	+	6.09801i	0.480359	+	0.554364i
$122$	−0.747818	−	5.20119i	−0.0677043	−	0.470894i
$123$	−2.58338	−	0.758548i	−0.232935	−	0.0683960i
$124$	−0.738847	+	0.474828i	−0.0663504	+	0.0426408i
$125$	−0.0968650	+	0.673711i	−0.00866387	+	0.0602585i
$126$	0.415415	−	0.909632i	0.0370081	−	0.0810365i
$127$	6.63855	−	14.5364i	0.589076	−	1.28990i	−0.346923	−	0.937894i	$-0.612773\pi$
$127$	6.63855	−	14.5364i	0.589076	−	1.28990i	0.935999	−	0.352003i	$-0.114499\pi$
$128$	−0.142315	+	0.989821i	−0.0125790	+	0.0874887i
$129$	−6.91545	+	4.44429i	−0.608871	+	0.391298i
$130$	−3.71540	−	1.09094i	−0.325862	−	0.0956818i
$131$	−2.78526	−	19.3719i	−0.243349	−	1.69253i	−0.635078	−	0.772448i	$-0.719032\pi$
$131$	−2.78526	−	19.3719i	−0.243349	−	1.69253i	0.391729	−	0.920081i	$-0.371877\pi$
$132$	1.12117	+	1.29390i	0.0975850	+	0.112619i
$133$	−3.05323	−	1.96219i	−0.264749	−	0.170144i
$134$	−4.34692	+	5.01661i	−0.375517	+	0.433369i
$135$	3.00099	−	0.881169i	0.258284	−	0.0758390i
$136$	−1.94879	−	4.26725i	−0.167107	−	0.365913i
$137$	6.75470			0.577093			0.288546	−	0.957466i	$-0.406828\pi$
$137$	6.75470			0.577093			0.288546	+	0.957466i	$0.406828\pi$
$138$	3.32239	−	3.45858i	0.282820	−	0.294414i
$139$	6.00639			0.509455			0.254728	−	0.967013i	$-0.418014\pi$
$139$	6.00639			0.509455			0.254728	+	0.967013i	$0.418014\pi$
$140$	−1.29929	−	2.84504i	−0.109810	−	0.240450i
$141$	−9.40799	+	2.76244i	−0.792296	+	0.232639i
$142$	−3.94149	+	4.54873i	−0.330763	+	0.381721i
$143$	1.78316	+	1.14597i	0.149115	+	0.0958305i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	−3.26250	−	22.6912i	−0.270936	−	1.88440i
$146$	8.95247	+	2.62868i	0.740912	+	0.217551i
$147$	0.841254	−	0.540641i	0.0693854	−	0.0445913i
$148$	1.19874	−	8.33739i	0.0985355	−	0.685330i
$149$	−8.92425	+	19.5414i	−0.731103	+	1.60089i	0.0665550	+	0.997783i	$0.478799\pi$
$149$	−8.92425	+	19.5414i	−0.731103	+	1.60089i	−0.797658	+	0.603110i	$0.793928\pi$
$150$	1.98667	−	4.35021i	0.162211	−	0.355193i
$151$	−1.19390	+	8.30373i	−0.0971579	+	0.675748i	0.881791	+	0.471641i	$0.156338\pi$
$151$	−1.19390	+	8.30373i	−0.0971579	+	0.675748i	−0.978949	+	0.204107i	$0.934571\pi$
$152$	−3.05323	+	1.96219i	−0.247650	+	0.159155i
$153$	4.50115	+	1.32166i	0.363897	+	0.106850i
$154$	0.243653	+	1.69464i	0.0196341	+	0.136558i
$155$	−1.79887	−	2.07600i	−0.144488	−	0.166748i
$156$	−1.04152	−	0.669346i	−0.0833886	−	0.0535906i
$157$	1.43435	−	1.65532i	0.114473	−	0.132109i	−0.695621	−	0.718409i	$-0.744871\pi$
$157$	1.43435	−	1.65532i	0.114473	−	0.132109i	0.810094	+	0.586300i	$0.199416\pi$
$158$	−2.36139	+	0.693365i	−0.187862	+	0.0551612i
$159$	−0.365555	−	0.800455i	−0.0289904	−	0.0634802i
$160$	−3.12768			−0.247265
$161$	4.66482	−	1.11332i	0.367639	−	0.0877420i
$162$	1.00000			0.0785674
$163$	1.36511	+	2.98917i	0.106924	+	0.234130i	0.955530	−	0.294895i	$-0.0952848\pi$
$163$	1.36511	+	2.98917i	0.106924	+	0.234130i	−0.848606	+	0.529026i	$0.822558\pi$
$164$	−2.58338	+	0.758548i	−0.201728	+	0.0592327i
$165$	−3.50665	+	4.04689i	−0.272992	+	0.315050i
$166$	4.53060	+	2.91164i	0.351643	+	0.225987i
$167$	1.92216	+	2.21829i	0.148741	+	0.171656i	0.825231	−	0.564796i	$-0.191045\pi$
$167$	1.92216	+	2.21829i	0.148741	+	0.171656i	−0.676490	+	0.736452i	$0.736500\pi$
$168$	−0.142315	−	0.989821i	−0.0109798	−	0.0763664i
$169$	11.0027	+	3.23069i	0.846362	+	0.248514i
$170$	12.3433	−	7.93256i	0.946688	−	0.608399i
$171$	0.516515	−	3.59244i	0.0394989	−	0.274721i
$172$	−3.41488	+	7.47755i	−0.260382	+	0.570158i
$173$	−10.0101	+	21.9191i	−0.761054	+	1.66648i	−0.0156376	+	0.999878i	$0.504978\pi$
$173$	−10.0101	+	21.9191i	−0.761054	+	1.66648i	−0.745417	+	0.666599i	$0.767749\pi$
$174$	1.04311	−	7.25496i	0.0790776	−	0.549997i
$175$	4.02320	−	2.58555i	0.304125	−	0.195449i
$176$	1.64272	+	0.482346i	0.123825	+	0.0363582i
$177$	−0.492239	−	3.42360i	−0.0369989	−	0.257333i
$178$	−4.72502	−	5.45297i	−0.354155	−	0.408717i
$179$	4.72173	+	3.03447i	0.352919	+	0.226807i	0.705073	−	0.709135i	$-0.250914\pi$
$179$	4.72173	+	3.03447i	0.352919	+	0.226807i	−0.352154	+	0.935942i	$0.614551\pi$
$180$	2.04819	−	2.36374i	0.152663	−	0.176183i
$181$	10.5760	−	3.10541i	0.786111	−	0.230823i	0.136047	−	0.990702i	$-0.456560\pi$
$181$	10.5760	−	3.10541i	0.786111	−	0.230823i	0.650064	+	0.759879i	$0.274742\pi$
$182$	−0.514309	−	1.12618i	−0.0381231	−	0.0834780i
$183$	5.25467			0.388437
$184$	0.925122	−	4.70576i	0.0682009	−	0.346913i
$185$	26.3449			1.93691
$186$	−0.364846	−	0.798901i	−0.0267518	−	0.0585783i
$187$	−7.70628	+	2.26277i	−0.563539	+	0.165470i
$188$	−6.42102	+	7.41025i	−0.468301	+	0.540448i
$189$	0.841254	+	0.540641i	0.0611922	+	0.0393258i
$190$	−7.43368	−	8.57893i	−0.539296	−	0.622381i
$191$	−3.39673	−	23.6248i	−0.245779	−	1.70943i	−0.622098	−	0.782939i	$-0.713719\pi$
$191$	−3.39673	−	23.6248i	−0.245779	−	1.70943i	0.376319	−	0.926490i	$-0.377190\pi$
$192$	−0.959493	−	0.281733i	−0.0692454	−	0.0203323i
$193$	8.14751	−	5.23609i	0.586471	−	0.376902i	−0.213498	−	0.976943i	$-0.568486\pi$
$193$	8.14751	−	5.23609i	0.586471	−	0.376902i	0.799969	+	0.600042i	$0.204849\pi$
$194$	−1.41712	+	9.85627i	−0.101743	+	0.707639i
$195$	1.60859	−	3.52233i	0.115194	−	0.252239i
$196$	0.415415	−	0.909632i	0.0296725	−	0.0649737i
$197$	−1.35146	+	9.39962i	−0.0962876	+	0.669695i	0.883319	+	0.468772i	$0.155303\pi$
$197$	−1.35146	+	9.39962i	−0.0962876	+	0.669695i	−0.979607	+	0.200923i	$0.935606\pi$
$198$	−1.44028	+	0.925614i	−0.102357	+	0.0657805i
$199$	−14.5910	−	4.28432i	−1.03433	−	0.303707i	−0.279861	−	0.960041i	$-0.590288\pi$
$199$	−14.5910	−	4.28432i	−1.03433	−	0.303707i	−0.754471	+	0.656334i	$0.772106\pi$
$200$	−0.680604	−	4.73370i	−0.0481260	−	0.334723i
$201$	−4.34692	−	5.01661i	−0.306608	−	0.353845i
$202$	5.10953	+	3.28369i	0.359505	+	0.231040i
$203$	4.79984	−	5.53931i	0.336883	−	0.388784i
$204$	4.50115	−	1.32166i	0.315144	−	0.0925346i
$205$	−3.49825	−	7.66010i	−0.244328	−	0.535004i
$206$	2.78060			0.193733
$207$	2.95055	+	3.78078i	0.205077	+	0.262782i
$208$	−1.23806			−0.0858440
$209$	2.58129	+	5.65223i	0.178551	+	0.390973i
$210$	3.00099	−	0.881169i	0.207088	−	0.0608065i
$211$	9.10218	−	10.5045i	0.626620	−	0.723158i	−0.350330	−	0.936626i	$-0.613931\pi$
$211$	9.10218	−	10.5045i	0.626620	−	0.723158i	0.976950	+	0.213468i	$0.0684761\pi$
$212$	−0.740283	−	0.475751i	−0.0508429	−	0.0326747i
$213$	−3.94149	−	4.54873i	−0.270067	−	0.311674i
$214$	−1.25451	−	8.72527i	−0.0857562	−	0.596447i
$215$	−24.6693	−	7.24357i	−1.68243	−	0.494007i
$216$	0.841254	−	0.540641i	0.0572401	−	0.0367859i
$217$	0.124991	−	0.869329i	0.00848492	−	0.0590139i
$218$	3.17038	−	6.94215i	0.214725	−	0.470182i
$219$	−3.87600	+	8.48725i	−0.261916	+	0.573515i
$220$	−0.762068	+	5.30030i	−0.0513786	+	0.357346i
$221$	4.88597	−	3.14002i	0.328666	−	0.211221i
$222$	8.08193	+	2.37307i	0.542424	+	0.159270i
$223$	2.10831	+	14.6636i	0.141183	+	0.981947i	0.930063	+	0.367400i	$0.119752\pi$
$223$	2.10831	+	14.6636i	0.141183	+	0.981947i	−0.788880	+	0.614547i	$0.789339\pi$
$224$	−0.654861	−	0.755750i	−0.0437547	−	0.0504956i
$225$	4.02320	+	2.58555i	0.268213	+	0.172370i
$226$	−6.18203	+	7.13445i	−0.411223	+	0.474576i
$227$	20.2676	−	5.95109i	1.34520	−	0.394988i	0.471681	−	0.881769i	$-0.343647\pi$
$227$	20.2676	−	5.95109i	1.34520	−	0.394988i	0.873524	+	0.486781i	$0.161829\pi$
$228$	−1.50770	−	3.30140i	−0.0998499	−	0.218641i
$229$	−15.8195			−1.04538			−0.522692	−	0.852522i	$-0.675072\pi$
$229$	−15.8195			−1.04538			−0.522692	+	0.852522i	$0.675072\pi$
$230$	14.9801	+	0.769431i	0.987757	+	0.0507348i
$231$	−1.71207			−0.112646
$232$	−3.04481	−	6.66720i	−0.199902	−	0.437723i
$233$	4.12278	−	1.21056i	0.270092	−	0.0793062i	−0.143882	−	0.989595i	$-0.545959\pi$
$233$	4.12278	−	1.21056i	0.270092	−	0.0793062i	0.413974	+	0.910289i	$0.364140\pi$
$234$	0.810757	−	0.935664i	0.0530009	−	0.0611662i
$235$	−25.7991	−	16.5801i	−1.68295	−	1.08156i
$236$	−2.26503	−	2.61399i	−0.147441	−	0.170156i
$237$	−0.350248	−	2.43603i	−0.0227510	−	0.158237i
$238$	4.50115	+	1.32166i	0.291766	+	0.0856704i
$239$	−14.6409	+	9.40915i	−0.947042	+	0.608627i	−0.920383	−	0.391017i	$-0.872123\pi$
$239$	−14.6409	+	9.40915i	−0.947042	+	0.608627i	−0.0266591	+	0.999645i	$0.508487\pi$
$240$	0.445115	−	3.09584i	0.0287321	−	0.199836i
$241$	−8.18206	+	17.9162i	−0.527053	+	1.15409i	0.439646	+	0.898171i	$0.355104\pi$
$241$	−8.18206	+	17.9162i	−0.527053	+	1.15409i	−0.966699	+	0.255914i	$0.917624\pi$
$242$	−3.35191	+	7.33966i	−0.215469	+	0.471811i
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$	4.42051	−	2.84089i	0.282994	−	0.181869i
$245$	3.00099	+	0.881169i	0.191726	+	0.0562958i
$246$	−0.383174	−	2.66504i	−0.0244303	−	0.169916i
$247$	−2.94255	−	3.39588i	−0.187230	−	0.216075i
$248$	−0.738847	−	0.474828i	−0.0469168	−	0.0301516i
$249$	−3.52678	+	4.07012i	−0.223500	+	0.257933i
$250$	−0.653068	+	0.191758i	−0.0413037	+	0.0121278i
$251$	−4.43508	−	9.71148i	−0.279940	−	0.612983i	0.716472	−	0.697616i	$-0.245756\pi$
$251$	−4.43508	−	9.71148i	−0.279940	−	0.612983i	−0.996412	+	0.0846325i	$0.973028\pi$
$252$	1.00000			0.0629941
$253$	−7.74917	−	2.71432i	−0.487186	−	0.170648i
$254$	15.9805			1.00271
$255$	6.09518	+	13.3466i	0.381695	+	0.835795i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−17.9344	+	20.6974i	−1.11871	+	1.29107i	−0.166363	+	0.986065i	$0.553202\pi$
$257$	−17.9344	+	20.6974i	−1.11871	+	1.29107i	−0.952352	+	0.305001i	$0.901343\pi$
$258$	−6.91545	−	4.44429i	−0.430537	−	0.276689i
$259$	5.51598	+	6.36578i	0.342746	+	0.395550i
$260$	−0.551080	−	3.83284i	−0.0341765	−	0.237703i
$261$	7.03266	+	2.06498i	0.435311	+	0.127819i
$262$	16.4642	−	10.5809i	1.01716	−	0.653692i
$263$	0.760374	−	5.28852i	0.0468867	−	0.326104i	−0.952856	−	0.303423i	$-0.901871\pi$
$263$	0.760374	−	5.28852i	0.0468867	−	0.326104i	0.999743	−	0.0226814i	$-0.00722033\pi$
$264$	−0.711219	+	1.55735i	−0.0437725	+	0.0958484i
$265$	1.14334	−	2.50357i	0.0702348	−	0.153793i
$266$	0.516515	−	3.59244i	0.0316696	−	0.220267i
$267$	6.06991	−	3.90089i	0.371472	−	0.238731i
$268$	−6.36905	−	1.87012i	−0.389051	−	0.114236i
$269$	−3.58108	−	24.9070i	−0.218343	−	1.51861i	−0.744156	−	0.668006i	$-0.767148\pi$
$269$	−3.58108	−	24.9070i	−0.218343	−	1.51861i	0.525813	−	0.850600i	$-0.323761\pi$
$270$	2.04819	+	2.36374i	0.124649	+	0.143853i
$271$	12.6404	+	8.12347i	0.767847	+	0.493466i	0.864980	−	0.501806i	$-0.167331\pi$
$271$	12.6404	+	8.12347i	0.767847	+	0.493466i	−0.0971328	+	0.995271i	$0.530967\pi$
$272$	3.07207	−	3.54536i	0.186272	−	0.214969i
$273$	1.18791	−	0.348802i	0.0718956	−	0.0211105i
$274$	2.80600	+	6.14429i	0.169517	+	0.371190i
$275$	−8.18777			−0.493741
$276$	4.52620	+	1.58540i	0.272445	+	0.0954302i
$277$	−18.8405			−1.13201			−0.566007	−	0.824400i	$-0.691513\pi$
$277$	−18.8405			−1.13201			−0.566007	+	0.824400i	$0.691513\pi$
$278$	2.49515	+	5.46361i	0.149649	+	0.327685i
$279$	0.842693	−	0.247437i	0.0504507	−	0.0148137i
$280$	2.04819	−	2.36374i	0.122403	−	0.141261i
$281$	14.2099	+	9.13213i	0.847690	+	0.544777i	0.890853	−	0.454291i	$-0.150107\pi$
$281$	14.2099	+	9.13213i	0.847690	+	0.544777i	−0.0431637	+	0.999068i	$0.513744\pi$
$282$	−6.42102	−	7.41025i	−0.382366	−	0.441274i
$283$	−2.00185	−	13.9232i	−0.118997	−	0.827646i	−0.958663	−	0.284542i	$-0.908158\pi$
$283$	−2.00185	−	13.9232i	−0.118997	−	0.827646i	0.839666	−	0.543103i	$-0.182751\pi$
$284$	−5.77502	−	1.69570i	−0.342684	−	0.100621i
$285$	9.54953	−	6.13711i	0.565665	−	0.363531i
$286$	−0.301657	+	2.09807i	−0.0178373	+	0.124061i
$287$	1.11848	−	2.44913i	0.0660218	−	0.144568i
$288$	0.415415	−	0.909632i	0.0244786	−	0.0536006i
$289$	−0.712593	+	4.95619i	−0.0419173	+	0.291541i
$290$	19.2853	−	12.3939i	1.13247	−	0.727797i
$291$	−9.55427	−	2.80539i	−0.560081	−	0.164455i
$292$	1.32786	+	9.23545i	0.0777069	+	0.540464i
$293$	−11.1263	−	12.8405i	−0.650007	−	0.750148i	0.331104	−	0.943594i	$-0.392579\pi$
$293$	−11.1263	−	12.8405i	−0.650007	−	0.750148i	−0.981111	+	0.193446i	$0.938034\pi$
$294$	0.841254	+	0.540641i	0.0490629	+	0.0315308i
$295$	7.08430	−	8.17572i	0.412464	−	0.476009i
$296$	8.08193	−	2.37307i	0.469753	−	0.137932i
$297$	−0.711219	−	1.55735i	−0.0412691	−	0.0903668i
$298$	−21.4827			−1.24446
$299$	5.92971	+	0.304571i	0.342924	+	0.0176138i
$300$	4.78238			0.276111
$301$	−3.41488	−	7.47755i	−0.196830	−	0.430999i
$302$	−8.04930	+	2.36349i	−0.463185	+	0.136003i
$303$	−3.97743	+	4.59020i	−0.228497	+	0.263700i
$304$	−3.05323	−	1.96219i	−0.175115	−	0.112539i
$305$	10.7626	+	12.4207i	0.616264	+	0.711207i
$306$	0.667624	+	4.64343i	0.0381655	+	0.265447i
$307$	−13.2090	−	3.87853i	−0.753880	−	0.221359i	−0.117858	−	0.993030i	$-0.537603\pi$
$307$	−13.2090	−	3.87853i	−0.753880	−	0.221359i	−0.636022	+	0.771671i	$0.719421\pi$
$308$	−1.44028	+	0.925614i	−0.0820678	+	0.0527418i
$309$	−0.395720	+	2.75230i	−0.0225117	+	0.156573i
$310$	1.14112	−	2.49871i	0.0648114	−	0.141917i
$311$	−5.18943	+	11.3633i	−0.294266	+	0.644352i	−0.997799	−	0.0663103i	$-0.978877\pi$
$311$	−5.18943	+	11.3633i	−0.294266	+	0.644352i	0.703533	+	0.710662i	$0.251605\pi$
$312$	0.176194	−	1.22546i	0.00997504	−	0.0693779i
$313$	−24.8071	+	15.9425i	−1.40218	+	0.901125i	−0.999896	−	0.0143914i	$-0.995419\pi$
$313$	−24.8071	+	15.9425i	−1.40218	+	0.901125i	−0.402281	+	0.915516i	$0.631783\pi$
$314$	2.10158	+	0.617081i	0.118599	+	0.0348239i
$315$	0.445115	+	3.09584i	0.0250794	+	0.174431i
$316$	−1.61166	−	1.85996i	−0.0906631	−	0.104631i
$317$	26.5731	+	17.0775i	1.49249	+	0.959168i	0.995830	+	0.0912251i	$0.0290783\pi$
$317$	26.5731	+	17.0775i	1.49249	+	0.959168i	0.496664	+	0.867943i	$0.334558\pi$
$318$	0.576262	−	0.665042i	0.0323152	−	0.0372937i
$319$	−12.0404	+	3.53538i	−0.674133	+	0.197943i
$320$	−1.29929	−	2.84504i	−0.0726323	−	0.159042i
$321$	8.81500			0.492005
$322$	2.95055	+	3.78078i	0.164428	+	0.210694i
$323$	17.0261			0.947357
$324$	0.415415	+	0.909632i	0.0230786	+	0.0505351i
$325$	5.68104	−	1.66810i	0.315127	−	0.0925298i
$326$	−2.15196	+	2.48349i	−0.119186	+	0.137548i
$327$	6.42030	+	4.12608i	0.355043	+	0.228173i
$328$	−1.76317	−	2.03481i	−0.0973550	−	0.112354i
$329$	−1.39542	−	9.70537i	−0.0769321	−	0.535074i
$330$	−5.13790	−	1.50862i	−0.282832	−	0.0830469i
$331$	10.7194	−	6.88891i	0.589189	−	0.378649i	−0.211813	−	0.977310i	$-0.567937\pi$
$331$	10.7194	−	6.88891i	0.589189	−	0.378649i	0.801002	+	0.598661i	$0.204300\pi$
$332$	−0.766442	+	5.33072i	−0.0420640	+	0.292561i
$333$	−3.49909	+	7.66195i	−0.191749	+	0.419872i
$334$	−1.21933	+	2.66997i	−0.0667189	+	0.146094i
$335$	2.95464	−	20.5500i	0.161429	−	1.12277i
$336$	0.841254	−	0.540641i	0.0458941	−	0.0294944i
$337$	7.18112	+	2.10857i	0.391180	+	0.114861i	0.471407	−	0.881916i	$-0.343746\pi$
$337$	7.18112	+	2.10857i	0.391180	+	0.114861i	−0.0802268	+	0.996777i	$0.525564\pi$
$338$	1.63195	+	11.3505i	0.0887666	+	0.617385i
$339$	−6.18203	−	7.13445i	−0.335762	−	0.387490i
$340$	12.3433	+	7.93256i	0.669409	+	0.430203i
$341$	−0.984686	+	1.13639i	−0.0533237	+	0.0615389i
$342$	3.48237	−	1.02252i	0.188305	−	0.0552913i
$343$	0.415415	+	0.909632i	0.0224303	+	0.0491155i
$344$	−8.22041			−0.443215
$345$	−2.89349	+	14.7181i	−0.155780	+	0.792396i
$346$	−24.0966			−1.29544
$347$	−10.0660	−	22.0414i	−0.540370	−	1.18325i	−0.961136	−	0.276076i	$-0.910966\pi$
$347$	−10.0660	−	22.0414i	−0.540370	−	1.18325i	0.420766	−	0.907169i	$-0.361761\pi$
$348$	7.03266	−	2.06498i	0.376990	−	0.110694i
$349$	−6.03267	+	6.96207i	−0.322921	+	0.372671i	−0.893879	−	0.448308i	$-0.852027\pi$
$349$	−6.03267	+	6.96207i	−0.322921	+	0.372671i	0.570958	+	0.820980i	$0.306572\pi$
$350$	4.02320	+	2.58555i	0.215049	+	0.138204i
$351$	0.810757	+	0.935664i	0.0432750	+	0.0499420i
$352$	0.243653	+	1.69464i	0.0129867	+	0.0903248i
$353$	−0.746938	−	0.219321i	−0.0397555	−	0.0116733i	0.261794	−	0.965124i	$-0.415686\pi$
$353$	−0.746938	−	0.219321i	−0.0397555	−	0.0116733i	−0.301550	+	0.953450i	$0.597504\pi$
$354$	2.90973	−	1.86997i	0.154650	−	0.0993877i
$355$	2.67907	−	18.6334i	0.142190	−	0.988956i
$356$	2.99735	−	6.56328i	0.158859	−	0.347853i
$357$	−1.94879	+	4.26725i	−0.103141	+	0.225847i
$358$	−0.798775	+	5.55561i	−0.0422166	+	0.293623i
$359$	−3.89057	+	2.50032i	−0.205336	+	0.131962i	−0.639268	−	0.768984i	$-0.720762\pi$
$359$	−3.89057	+	2.50032i	−0.205336	+	0.131962i	0.433931	+	0.900946i	$0.357126\pi$
$360$	3.00099	+	0.881169i	0.158166	+	0.0464417i
$361$	0.829351	+	5.76826i	0.0436500	+	0.303593i
$362$	7.21822	+	8.33027i	0.379381	+	0.437830i
$363$	−6.78792	−	4.36233i	−0.356274	−	0.228963i
$364$	0.810757	−	0.935664i	0.0424952	−	0.0490421i
$365$	−28.0005	+	8.22168i	−1.46561	+	0.430342i
$366$	2.18287	+	4.77982i	0.114100	+	0.249845i
$367$	34.7478			1.81382			0.906909	−	0.421326i	$-0.138435\pi$
$367$	34.7478			1.81382			0.906909	+	0.421326i	$0.138435\pi$
$368$	4.66482	−	1.11332i	0.243170	−	0.0580359i
$369$	2.69244			0.140163
$370$	10.9440	+	23.9641i	0.568954	+	1.24584i
$371$	0.844331	−	0.247918i	0.0438355	−	0.0128713i
$372$	0.575144	−	0.663751i	0.0298198	−	0.0344139i
$373$	−31.7664	−	20.4151i	−1.64480	−	1.05705i	−0.936213	−	0.351432i	$-0.885695\pi$
$373$	−31.7664	−	20.4151i	−1.64480	−	1.05705i	−0.708591	−	0.705619i	$-0.750669\pi$
$374$	−5.25959	−	6.06989i	−0.271967	−	0.313867i
$375$	−0.0968650	−	0.673711i	−0.00500209	−	0.0347903i
$376$	−9.40799	−	2.76244i	−0.485180	−	0.142462i
$377$	7.63391	−	4.90601i	0.393166	−	0.252673i
$378$	−0.142315	+	0.989821i	−0.00731989	+	0.0509109i
$379$	−6.62375	+	14.5040i	−0.340239	+	0.745020i	−0.999979	−	0.00647386i	$-0.997939\pi$
$379$	−6.62375	+	14.5040i	−0.340239	+	0.745020i	0.659740	+	0.751494i	$0.270667\pi$
$380$	4.71560	−	10.3257i	0.241905	−	0.529699i
$381$	−2.27427	+	15.8179i	−0.116514	+	0.810374i
$382$	20.0788	−	12.9039i	1.02732	−	0.660219i
$383$	6.25964	+	1.83800i	0.319853	+	0.0939172i	0.437718	−	0.899112i	$-0.355787\pi$
$383$	6.25964	+	1.83800i	0.319853	+	0.0939172i	−0.117865	+	0.993030i	$0.537605\pi$
$384$	−0.142315	−	0.989821i	−0.00726247	−	0.0505116i
$385$	−3.50665	−	4.04689i	−0.178715	−	0.206249i
$386$	8.14751	+	5.23609i	0.414697	+	0.266510i
$387$	5.38322	−	6.21257i	0.273645	−	0.315803i
$388$	−9.55427	+	2.80539i	−0.485045	+	0.142422i
$389$	2.85666	+	6.25521i	0.144838	+	0.317152i	0.968122	−	0.250478i	$-0.0805878\pi$
$389$	2.85666	+	6.25521i	0.144838	+	0.317152i	−0.823284	+	0.567630i	$0.807861\pi$
$390$	3.87226			0.196079
$391$	−15.5859	+	16.2248i	−0.788213	+	0.820523i
$392$	1.00000			0.0505076
$393$	8.13012	+	17.8025i	0.410110	+	0.898016i
$394$	−9.11161	+	2.67541i	−0.459036	+	0.134785i
$395$	5.04076	−	5.81735i	0.253628	−	0.292703i
$396$	−1.44028	−	0.925614i	−0.0723770	−	0.0465139i
$397$	8.99663	+	10.3827i	0.451528	+	0.521091i	0.935182	−	0.354168i	$-0.115236\pi$
$397$	8.99663	+	10.3827i	0.451528	+	0.521091i	−0.483654	+	0.875260i	$0.660691\pi$
$398$	−2.16419	−	15.0522i	−0.108481	−	0.754501i
$399$	3.48237	+	1.02252i	0.174336	+	0.0511898i
$400$	4.02320	−	2.58555i	0.201160	−	0.129278i
$401$	−2.53059	+	17.6006i	−0.126372	+	0.878933i	0.823728	+	0.566986i	$0.191890\pi$
$401$	−2.53059	+	17.6006i	−0.126372	+	0.878933i	−0.950099	+	0.311948i	$0.899019\pi$
$402$	2.75750	−	6.03807i	0.137531	−	0.301152i
$403$	0.451701	−	0.989088i	0.0225009	−	0.0492700i
$404$	−0.864378	+	6.01188i	−0.0430044	+	0.299102i
$405$	−2.63117	+	1.69095i	−0.130744	+	0.0840241i
$406$	7.03266	+	2.06498i	0.349025	+	0.102483i
$407$	−2.05232	−	14.2742i	−0.101730	−	0.707546i
$408$	3.07207	+	3.54536i	0.152090	+	0.175521i
$409$	12.9482	+	8.32132i	0.640249	+	0.411463i	0.820091	−	0.572233i	$-0.193923\pi$
$409$	12.9482	+	8.32132i	0.640249	+	0.411463i	−0.179843	+	0.983695i	$0.557559\pi$
$410$	5.51464	−	6.36424i	0.272349	−	0.314307i
$411$	−6.48108	+	1.90302i	−0.319688	+	0.0938689i
$412$	1.15510	+	2.52932i	0.0569078	+	0.124611i
$413$	3.45880			0.170196
$414$	−2.21341	+	4.25450i	−0.108783	+	0.209097i
$415$	−16.8442			−0.826851
$416$	−0.514309	−	1.12618i	−0.0252161	−	0.0552155i
$417$	−5.76309	+	1.69220i	−0.282220	+	0.0828672i
$418$	−4.06914	+	4.69604i	−0.199028	+	0.229691i
$419$	−10.4590	−	6.72160i	−0.510956	−	0.328372i	0.259629	−	0.965708i	$-0.416400\pi$
$419$	−10.4590	−	6.72160i	−0.510956	−	0.328372i	−0.770585	+	0.637337i	$0.780036\pi$
$420$	2.04819	+	2.36374i	0.0999417	+	0.115339i
$421$	−0.0813859	−	0.566051i	−0.00396651	−	0.0275877i	0.987742	−	0.156095i	$-0.0498906\pi$
$421$	−0.0813859	−	0.566051i	−0.00396651	−	0.0275877i	−0.991709	+	0.128507i	$0.958981\pi$
$422$	13.3364	+	3.91592i	0.649205	+	0.190624i
$423$	8.24863	−	5.30108i	0.401062	−	0.257747i
$424$	0.125234	−	0.871019i	0.00608189	−	0.0423004i
$425$	−9.31984	+	20.4076i	−0.452079	+	0.989914i
$426$	2.50031	−	5.47492i	0.121140	−	0.265261i
$427$	−0.747818	+	5.20119i	−0.0361895	+	0.251703i
$428$	7.41565	−	4.76575i	0.358449	−	0.230361i
$429$	−2.03378	−	0.597173i	−0.0981920	−	0.0288318i
$430$	−3.65903	−	25.4491i	−0.176454	−	1.22727i
$431$	−17.7714	−	20.5093i	−0.856019	−	0.987898i	0.143980	−	0.989581i	$-0.454010\pi$
$431$	−17.7714	−	20.5093i	−0.856019	−	0.987898i	−0.999999	+	0.00168225i	$0.999465\pi$
$432$	0.841254	+	0.540641i	0.0404748	+	0.0260116i
$433$	2.50389	−	2.88964i	0.120329	−	0.138867i	−0.692389	−	0.721525i	$-0.743442\pi$
$433$	2.50389	−	2.88964i	0.120329	−	0.138867i	0.812718	+	0.582657i	$0.197987\pi$
$434$	0.842693	−	0.247437i	0.0404505	−	0.0118774i
$435$	9.52319	+	20.8529i	0.456602	+	0.999819i
$436$	7.63183			0.365498
$437$	14.1408	+	10.1491i	0.676446	+	0.485496i
$438$	−9.33042			−0.445825
$439$	1.49061	+	3.26398i	0.0711430	+	0.155781i	0.941863	−	0.335998i	$-0.109074\pi$
$439$	1.49061	+	3.26398i	0.0711430	+	0.155781i	−0.870720	+	0.491780i	$0.836346\pi$
$440$	−5.13790	+	1.50862i	−0.244940	+	0.0719208i
$441$	−0.654861	+	0.755750i	−0.0311838	+	0.0359881i
$442$	4.88597	+	3.14002i	0.232402	+	0.149356i
$443$	10.1171	+	11.6757i	0.480676	+	0.554729i	0.943350	−	0.331799i	$-0.107656\pi$
$443$	10.1171	+	11.6757i	0.480676	+	0.554729i	−0.462674	+	0.886528i	$0.653110\pi$
$444$	1.19874	+	8.33739i	0.0568895	+	0.395675i
$445$	21.6531	+	6.35791i	1.02645	+	0.301394i
$446$	−12.4627	+	8.00926i	−0.590124	+	0.379250i
$447$	3.05731	−	21.2641i	0.144606	−	1.00576i
$448$	0.415415	−	0.909632i	0.0196265	−	0.0429761i
$449$	−11.8881	+	26.0313i	−0.561034	+	1.22849i	0.390402	+	0.920644i	$0.372336\pi$
$449$	−11.8881	+	26.0313i	−0.561034	+	1.22849i	−0.951436	+	0.307848i	$0.900391\pi$
$450$	−0.680604	+	4.73370i	−0.0320840	+	0.223149i
$451$	−3.87788	+	2.49216i	−0.182602	+	0.117351i
$452$	−9.05783	−	2.65962i	−0.426044	−	0.125098i
$453$	−1.19390	−	8.30373i	−0.0560941	−	0.390143i
$454$	13.8327	+	15.9638i	0.649203	+	0.749220i
$455$	3.25755	+	2.09350i	0.152716	+	0.0981448i
$456$	2.37674	−	2.74290i	0.111301	−	0.128448i
$457$	30.3408	−	8.90886i	1.41928	−	0.416739i	0.520022	−	0.854153i	$-0.325924\pi$
$457$	30.3408	−	8.90886i	1.41928	−	0.416739i	0.899260	+	0.437414i	$0.144105\pi$
$458$	−6.57167	−	14.3900i	−0.307074	−	0.672398i
$459$	−4.69118			−0.218965
$460$	5.52305	+	13.9460i	0.257514	+	0.650235i
$461$	−10.7729			−0.501744			−0.250872	−	0.968020i	$-0.580717\pi$
$461$	−10.7729			−0.501744			−0.250872	+	0.968020i	$0.580717\pi$
$462$	−0.711219	−	1.55735i	−0.0330889	−	0.0724546i
$463$	8.75011	−	2.56926i	0.406652	−	0.119404i	−0.0720081	−	0.997404i	$-0.522941\pi$
$463$	8.75011	−	2.56926i	0.406652	−	0.119404i	0.478660	+	0.878000i	$0.341123\pi$
$464$	4.79984	−	5.53931i	0.222827	−	0.257156i
$465$	2.31088	+	1.48511i	0.107164	+	0.0688703i
$466$	2.81382	+	3.24733i	0.130348	+	0.150429i
$467$	−2.43669	−	16.9475i	−0.112757	−	0.784239i	−0.965218	−	0.261448i	$-0.915800\pi$
$467$	−2.43669	−	16.9475i	−0.112757	−	0.784239i	0.852461	−	0.522791i	$-0.175109\pi$
$468$	1.18791	+	0.348802i	0.0549112	+	0.0161234i
$469$	5.58418	−	3.58874i	0.257854	−	0.165712i
$470$	4.36443	−	30.3553i	0.201316	−	1.40018i
$471$	−0.909887	+	1.99237i	−0.0419254	+	0.0918037i
$472$	1.43684	−	3.14624i	0.0661358	−	0.144817i
$473$	−2.00293	+	13.9307i	−0.0920946	+	0.640532i
$474$	2.07039	−	1.33056i	0.0950961	−	0.0611146i
$475$	16.6540	+	4.89006i	0.764139	+	0.224371i
$476$	0.667624	+	4.64343i	0.0306005	+	0.212831i
$477$	0.576262	+	0.665042i	0.0263852	+	0.0304502i
$478$	−14.6409	−	9.40915i	−0.669660	−	0.430364i
$479$	−27.0453	+	31.2120i	−1.23573	+	1.42611i	−0.367449	+	0.930044i	$0.619769\pi$
$479$	−27.0453	+	31.2120i	−1.23573	+	1.42611i	−0.868284	+	0.496068i	$0.834777\pi$
$480$	3.00099	−	0.881169i	0.136976	−	0.0402197i
$481$	4.33209	+	9.48596i	0.197526	+	0.432522i
$482$	−19.6961			−0.897134
$483$	−4.16220	+	2.38245i	−0.189387	+	0.108405i
$484$	−8.06882			−0.366765
$485$	−12.9378	−	28.3298i	−0.587475	−	1.28639i
$486$	−0.959493	+	0.281733i	−0.0435235	+	0.0127796i
$487$	−20.9680	+	24.1984i	−0.950152	+	1.09653i	0.0450788	+	0.998983i	$0.485646\pi$
$487$	−20.9680	+	24.1984i	−0.950152	+	1.09653i	−0.995231	+	0.0975502i	$0.968899\pi$
$488$	4.42051	+	2.84089i	0.200107	+	0.128601i
$489$	−2.15196	−	2.48349i	−0.0973150	−	0.112308i
$490$	0.445115	+	3.09584i	0.0201083	+	0.139856i
$491$	0.143367	+	0.0420964i	0.00647006	+	0.00189978i	0.284966	−	0.958538i	$-0.408018\pi$
$491$	0.143367	+	0.0420964i	0.00647006	+	0.00189978i	−0.278496	+	0.960437i	$0.589836\pi$
$492$	2.26503	−	1.45564i	0.102115	−	0.0656255i
$493$	−4.89339	+	34.0343i	−0.220387	+	1.53283i
$494$	1.86662	−	4.08734i	0.0839834	−	0.183898i
$495$	2.22447	−	4.87090i	0.0999823	−	0.218931i
$496$	0.124991	−	0.869329i	0.00561225	−	0.0390340i
$497$	5.06336	−	3.25402i	0.227123	−	0.145963i
$498$	−5.16739	−	1.51728i	−0.231556	−	0.0679910i
$499$	3.59889	+	25.0308i	0.161109	+	1.12053i	0.896549	+	0.442945i	$0.146066\pi$
$499$	3.59889	+	25.0308i	0.161109	+	1.12053i	−0.735440	+	0.677590i	$0.763025\pi$
$500$	−0.445724	−	0.514392i	−0.0199334	−	0.0230043i
$501$	−2.46926	−	1.58690i	−0.110318	−	0.0708974i
$502$	6.99147	−	8.06859i	0.312045	−	0.360119i
$503$	−34.0835	+	10.0078i	−1.51971	+	0.446226i	−0.931882	−	0.362762i	$-0.881834\pi$
$503$	−34.0835	+	10.0078i	−1.51971	+	0.446226i	−0.587825	+	0.808988i	$0.700016\pi$
$504$	0.415415	+	0.909632i	0.0185041	+	0.0405182i
$505$	−18.9966			−0.845338
$506$	−0.750086	−	8.17646i	−0.0333454	−	0.363488i
$507$	−11.4672			−0.509277
$508$	6.63855	+	14.5364i	0.294538	+	0.644948i
$509$	−21.6890	+	6.36848i	−0.961350	+	0.282278i	−0.724505	−	0.689270i	$-0.757931\pi$
$509$	−21.6890	+	6.36848i	−0.961350	+	0.282278i	−0.236845	+	0.971547i	$0.576113\pi$
$510$	−9.60845	+	11.0887i	−0.425469	+	0.491018i
$511$	−7.84925	−	5.04440i	−0.347230	−	0.223151i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	0.516515	+	3.59244i	0.0228047	+	0.158610i
$514$	−26.2772	−	7.71568i	−1.15904	−	0.340324i
$515$	−7.31623	+	4.70186i	−0.322392	+	0.207189i
$516$	1.16989	−	8.13674i	0.0515014	−	0.358200i
$517$	−6.97362	+	15.2701i	−0.306700	+	0.671579i
$518$	−3.49909	+	7.66195i	−0.153741	+	0.336647i
$519$	3.42931	−	23.8514i	0.150530	−	1.04696i
$520$	3.25755	−	2.09350i	0.142853	−	0.0918061i
$521$	−3.53875	−	1.03907i	−0.155035	−	0.0455225i	0.203294	−	0.979118i	$-0.434835\pi$
$521$	−3.53875	−	1.03907i	−0.155035	−	0.0455225i	−0.358329	+	0.933595i	$0.616653\pi$
$522$	1.04311	+	7.25496i	0.0456555	+	0.317541i
$523$	−9.30132	−	10.7343i	−0.406718	−	0.469378i	0.515027	−	0.857174i	$-0.327782\pi$
$523$	−9.30132	−	10.7343i	−0.406718	−	0.469378i	−0.921745	+	0.387796i	$0.873236\pi$
$524$	16.4642	+	10.5809i	0.719244	+	0.462230i
$525$	−3.13179	+	3.61428i	−0.136683	+	0.157740i
$526$	5.12648	−	1.50527i	0.223525	−	0.0656329i
$527$	1.71156	+	3.74779i	0.0745566	+	0.163256i
$528$	−1.71207			−0.0745082
$529$	−22.6161	+	4.18470i	−0.983309	+	0.181943i
$530$	2.75228			0.119552
$531$	1.43684	+	3.14624i	0.0623535	+	0.136535i
$532$	3.48237	−	1.02252i	0.150980	−	0.0443317i
$533$	2.18292	−	2.51922i	0.0945526	−	0.109120i
$534$	6.06991	+	3.90089i	0.262670	+	0.168808i
$535$	18.0548	+	20.8364i	0.780579	+	0.900836i
$536$	−0.944676	−	6.57036i	−0.0408038	−	0.283796i
$537$	−5.38538	−	1.58129i	−0.232396	−	0.0682377i
$538$	21.1686	−	13.6042i	0.912641	−	0.586519i
$539$	0.243653	−	1.69464i	0.0104949	−	0.0729934i
$540$	−1.29929	+	2.84504i	−0.0559123	+	0.122431i
$541$	11.6424	−	25.4932i	0.500545	−	1.09604i	−0.475747	−	0.879582i	$-0.657822\pi$
$541$	11.6424	−	25.4932i	0.500545	−	1.09604i	0.976292	−	0.216458i	$-0.0694503\pi$
$542$	−2.13837	+	14.8727i	−0.0918509	+	0.638837i
$543$	−9.27275	+	5.95923i	−0.397932	+	0.255735i
$544$	4.50115	+	1.32166i	0.192985	+	0.0566656i
$545$	3.39704	+	23.6270i	0.145513	+	1.01207i
$546$	0.810757	+	0.935664i	0.0346972	+	0.0400427i
$547$	32.2710	+	20.7393i	1.37981	+	0.886750i	0.999277	−	0.0380169i	$-0.0121041\pi$
$547$	32.2710	+	20.7393i	1.37981	+	0.886750i	0.380533	+	0.924767i	$0.375740\pi$
$548$	−4.42339	+	5.10486i	−0.188958	+	0.218069i
$549$	−5.04182	+	1.48041i	−0.215180	+	0.0631825i
$550$	−3.40132	−	7.44786i	−0.145033	−	0.317578i
$551$	26.6018			1.13327
$552$	0.438117	+	4.77578i	0.0186475	+	0.203271i
$553$	2.46108			0.104656
$554$	−7.82662	−	17.1379i	−0.332521	−	0.728120i
$555$	−25.2777	+	7.42220i	−1.07298	+	0.315055i
$556$	−3.93335	+	4.53933i	−0.166811	+	0.192510i
$557$	−10.6181	−	6.82385i	−0.449904	−	0.289136i	0.296002	−	0.955187i	$-0.404347\pi$
$557$	−10.6181	−	6.82385i	−0.449904	−	0.289136i	−0.745906	+	0.666052i	$0.767983\pi$
$558$	0.575144	+	0.663751i	0.0243478	+	0.0280988i
$559$	−1.44839	−	10.0738i	−0.0612604	−	0.426075i
$560$	3.00099	+	0.881169i	0.126815	+	0.0372362i
$561$	6.75663	−	4.34222i	0.285265	−	0.183329i
$562$	−2.40388	+	16.7194i	−0.101402	+	0.705264i
$563$	15.2117	−	33.3090i	0.641096	−	1.40381i	−0.258039	−	0.966135i	$-0.583076\pi$
$563$	15.2117	−	33.3090i	0.641096	−	1.40381i	0.899135	−	0.437671i	$-0.144197\pi$
$564$	4.07321	−	8.91910i	0.171513	−	0.375562i
$565$	4.20199	−	29.2255i	0.176779	−	1.22952i
$566$	11.8333	−	7.60483i	0.497393	−	0.319655i
$567$	−0.959493	−	0.281733i	−0.0402949	−	0.0118317i
$568$	−0.856568	−	5.95756i	−0.0359408	−	0.249974i
$569$	−22.6913	−	26.1872i	−0.951271	−	1.09782i	−0.995109	−	0.0987862i	$-0.968504\pi$
$569$	−22.6913	−	26.1872i	−0.951271	−	1.09782i	0.0438380	−	0.999039i	$-0.486041\pi$
$570$	9.54953	+	6.13711i	0.399986	+	0.257055i
$571$	−20.5707	+	23.7399i	−0.860857	+	0.993482i	0.139137	+	0.990273i	$0.455567\pi$
$571$	−20.5707	+	23.7399i	−0.860857	+	0.993482i	−0.999995	+	0.00320929i	$0.998978\pi$
$572$	−2.03378	+	0.597173i	−0.0850368	+	0.0249691i
$573$	9.91501	+	21.7108i	0.414206	+	0.906984i
$574$	2.69244			0.112380
$575$	−19.9052	+	11.3938i	−0.830106	+	0.475155i
$576$	1.00000			0.0416667
$577$	7.65681	+	16.7661i	0.318757	+	0.697981i	0.999400	−	0.0346344i	$-0.0110267\pi$
$577$	7.65681	+	16.7661i	0.318757	+	0.697981i	−0.680643	+	0.732615i	$0.738299\pi$
$578$	−4.80434	+	1.41068i	−0.199834	+	0.0586766i
$579$	−6.34230	+	7.31941i	−0.263577	+	0.304184i
$580$	19.2853	+	12.3939i	0.800780	+	0.514630i
$581$	−3.52678	−	4.07012i	−0.146315	−	0.168857i
$582$	−1.41712	−	9.85627i	−0.0587414	−	0.408555i
$583$	−1.44555	−	0.424453i	−0.0598687	−	0.0175790i
$584$	−7.84925	+	5.04440i	−0.324804	+	0.208739i
$585$	−0.551080	+	3.83284i	−0.0227843	+	0.158469i
$586$	7.05806	−	15.4550i	0.291566	−	0.638440i
$587$	1.83604	−	4.02036i	0.0757813	−	0.165938i	−0.867950	−	0.496652i	$-0.834562\pi$
$587$	1.83604	−	4.02036i	0.0757813	−	0.165938i	0.943731	+	0.330714i	$0.107290\pi$
$588$	−0.142315	+	0.989821i	−0.00586897	+	0.0408195i
$589$	2.68156	−	1.72333i	0.110492	−	0.0710087i
$590$	10.3798	+	3.04779i	0.427330	+	0.125475i
$591$	−1.35146	−	9.39962i	−0.0555917	−	0.386649i
$592$	5.51598	+	6.36578i	0.226705	+	0.261632i
$593$	25.0586	+	16.1042i	1.02903	+	0.661320i	0.942251	−	0.334907i	$-0.108705\pi$
$593$	25.0586	+	16.1042i	1.02903	+	0.661320i	0.0867833	+	0.996227i	$0.472341\pi$
$594$	1.12117	−	1.29390i	0.0460020	−	0.0530892i
$595$	−14.0782	+	4.13372i	−0.577149	+	0.169466i
$596$	−8.92425	−	19.5414i	−0.365552	−	0.800446i
$597$	15.2070			0.622382
$598$	2.18624	+	5.52038i	0.0894022	+	0.225745i
$599$	5.40019			0.220646			0.110323	−	0.993896i	$-0.464812\pi$
$599$	5.40019			0.220646			0.110323	+	0.993896i	$0.464812\pi$
$600$	1.98667	+	4.35021i	0.0811056	+	0.177596i
$601$	−5.50015	+	1.61499i	−0.224356	+	0.0658768i	−0.391978	−	0.919974i	$-0.628209\pi$
$601$	−5.50015	+	1.61499i	−0.224356	+	0.0658768i	0.167623	+	0.985851i	$0.446391\pi$
$602$	5.38322	−	6.21257i	0.219404	−	0.253205i
$603$	5.58418	+	3.58874i	0.227405	+	0.146145i
$604$	−5.49370	−	6.34007i	−0.223536	−	0.257974i
$605$	−3.59155	−	24.9798i	−0.146017	−	1.01557i
$606$	−5.82768	−	1.71116i	−0.236733	−	0.0695112i
$607$	34.4908	−	22.1659i	1.39994	−	0.899687i	0.400081	−	0.916480i	$-0.368982\pi$
$607$	34.4908	−	22.1659i	1.39994	−	0.899687i	0.999859	+	0.0167929i	$0.00534559\pi$
$608$	0.516515	−	3.59244i	0.0209475	−	0.145693i
$609$	−3.04481	+	6.66720i	−0.123382	+	0.270169i
$610$	−6.82732	+	14.9497i	−0.276430	+	0.605298i
$611$	1.72762	−	12.0158i	0.0698919	−	0.486109i
$612$	−3.94647	+	2.53624i	−0.159527	+	0.102522i
$613$	20.2494	+	5.94575i	0.817864	+	0.240146i	0.663796	−	0.747914i	$-0.268944\pi$
$613$	20.2494	+	5.94575i	0.817864	+	0.240146i	0.154068	+	0.988060i	$0.450763\pi$
$614$	−1.95920	−	13.6266i	−0.0790671	−	0.549924i
$615$	5.51464	+	6.36424i	0.222372	+	0.256631i
$616$	−1.44028	−	0.925614i	−0.0580307	−	0.0372941i
$617$	20.7834	−	23.9854i	0.836710	−	0.965614i	−0.163070	−	0.986615i	$-0.552140\pi$
$617$	20.7834	−	23.9854i	0.836710	−	0.965614i	0.999779	+	0.0210001i	$0.00668503\pi$
$618$	−2.66796	+	0.783385i	−0.107321	+	0.0315124i
$619$	6.28782	+	13.7684i	0.252729	+	0.553399i	0.992891	−	0.119030i	$-0.0379784\pi$
$619$	6.28782	+	13.7684i	0.252729	+	0.553399i	−0.740162	+	0.672429i	$0.765251\pi$
$620$	2.74694			0.110320
$621$	−3.89620	−	2.79636i	−0.156349	−	0.112214i
$622$	−12.4922			−0.500890
$623$	2.99735	+	6.56328i	0.120086	+	0.262952i
$624$	1.18791	−	0.348802i	0.0475545	−	0.0139633i
$625$	17.0531	−	19.6803i	0.682122	−	0.787211i
$626$	−24.8071	−	15.9425i	−0.991489	−	0.637191i
$627$	−4.06914	−	4.69604i	−0.162506	−	0.187542i
$628$	0.311713	+	2.16801i	0.0124387	+	0.0865131i
$629$	−37.9138	−	11.1325i	−1.51172	−	0.443882i
$630$	−2.63117	+	1.69095i	−0.104828	+	0.0673691i
$631$	6.87972	−	47.8495i	0.273877	−	1.90486i	−0.132553	−	0.991176i	$-0.542318\pi$
$631$	6.87972	−	47.8495i	0.273877	−	1.90486i	0.406430	−	0.913682i	$-0.366773\pi$
$632$	1.02237	−	2.23867i	0.0406676	−	0.0890497i
$633$	−5.77402	+	12.6433i	−0.229497	+	0.502528i
$634$	−4.49537	+	31.2660i	−0.178534	+	1.24173i
$635$	−42.0475	+	27.0223i	−1.66860	+	1.07235i
$636$	0.844331	+	0.247918i	0.0334799	+	0.00983059i
$637$	0.176194	+	1.22546i	0.00698108	+	0.0485544i
$638$	−8.21766	−	9.48369i	−0.325340	−	0.375463i
$639$	5.06336	+	3.25402i	0.200303	+	0.128727i
$640$	2.04819	−	2.36374i	0.0809620	−	0.0934351i
$641$	17.5598	−	5.15602i	0.693571	−	0.203651i	0.0840976	−	0.996458i	$-0.473199\pi$
$641$	17.5598	−	5.15602i	0.693571	−	0.203651i	0.609473	+	0.792807i	$0.291381\pi$
$642$	3.66188	+	8.01840i	0.144523	+	0.316461i
$643$	39.2707			1.54868			0.774342	−	0.632767i	$-0.218081\pi$
$643$	39.2707			1.54868			0.774342	+	0.632767i	$0.218081\pi$
$644$	−2.21341	+	4.25450i	−0.0872207	+	0.167651i
$645$	25.7108			1.01236
$646$	7.07289	+	15.4875i	0.278279	+	0.609347i
$647$	20.0636	−	5.89119i	0.788780	−	0.231607i	0.137558	−	0.990494i	$-0.456075\pi$
$647$	20.0636	−	5.89119i	0.788780	−	0.231607i	0.651222	+	0.758887i	$0.274257\pi$
$648$	−0.654861	+	0.755750i	−0.0257254	+	0.0296886i
$649$	−4.98166	−	3.20152i	−0.195547	−	0.125670i
$650$	3.87735	+	4.47470i	0.152082	+	0.175512i
$651$	0.124991	+	0.869329i	0.00489877	+	0.0340717i
$652$	−3.15302	−	0.925811i	−0.123482	−	0.0362576i
$653$	42.0777	−	27.0417i	1.64663	−	1.05822i	0.712262	−	0.701914i	$-0.247671\pi$
$653$	42.0777	−	27.0417i	1.64663	−	1.05822i	0.934368	−	0.356311i	$-0.115965\pi$
$654$	−1.08612	+	7.55415i	−0.0424707	+	0.295390i
$655$	−25.4284	+	55.6805i	−0.993571	+	2.17562i
$656$	1.11848	−	2.44913i	0.0436693	−	0.0956225i
$657$	1.32786	−	9.23545i	0.0518046	−	0.360309i
$658$	8.24863	−	5.30108i	0.321565	−	0.206657i
$659$	−13.1972	−	3.87506i	−0.514092	−	0.150951i	0.0143887	−	0.999896i	$-0.495420\pi$
$659$	−13.1972	−	3.87506i	−0.514092	−	0.150951i	−0.528480	+	0.848946i	$0.677238\pi$
$660$	−0.762068	−	5.30030i	−0.0296635	−	0.206314i
$661$	10.6132	+	12.2483i	0.412805	+	0.476402i	0.923632	−	0.383281i	$-0.125206\pi$
$661$	10.6132	+	12.2483i	0.412805	+	0.476402i	−0.510827	+	0.859684i	$0.670661\pi$
$662$	10.7194	+	6.88891i	0.416620	+	0.267745i
$663$	−3.80341	+	4.38937i	−0.147712	+	0.170469i
$664$	−5.16739	+	1.51728i	−0.200534	+	0.0588820i
$665$	4.71560	+	10.3257i	0.182863	+	0.400415i
$666$	−8.42313			−0.326390
$667$	−24.3516	+	25.3498i	−0.942899	+	0.981550i
$668$	−2.93522			−0.113567
$669$	−6.15412	−	13.4756i	−0.237932	−	0.520998i
$670$	19.9203	−	5.84914i	0.769590	−	0.225972i
$671$	5.89137	−	6.79900i	0.227434	−	0.262472i
$672$	0.841254	+	0.540641i	0.0324521	+	0.0208557i
$673$	−1.54533	−	1.78340i	−0.0595680	−	0.0687452i	0.725184	−	0.688556i	$-0.241755\pi$
$673$	−1.54533	−	1.78340i	−0.0595680	−	0.0687452i	−0.784752	+	0.619810i	$0.787209\pi$
$674$	1.06512	+	7.40810i	0.0410271	+	0.285349i
$675$	−4.58866	−	1.34735i	−0.176618	−	0.0518596i
$676$	−9.64683	+	6.19964i	−0.371032	+	0.238448i
$677$	−5.56533	+	38.7077i	−0.213893	+	1.48766i	0.546096	+	0.837723i	$0.316113\pi$
$677$	−5.56533	+	38.7077i	−0.213893	+	1.48766i	−0.759989	+	0.649936i	$0.774796\pi$
$678$	3.92161	−	8.58713i	0.150609	−	0.329787i
$679$	4.13655	−	9.05777i	0.158746	−	0.347605i
$680$	−2.08812	+	14.5232i	−0.0800756	+	0.556938i
$681$	−17.7700	+	11.4201i	−0.680946	+	0.437618i
$682$	−1.44275	−	0.423629i	−0.0552457	−	0.0162216i
$683$	6.61903	+	46.0364i	0.253270	+	1.76153i	0.578296	+	0.815827i	$0.303718\pi$
$683$	6.61903	+	46.0364i	0.253270	+	1.76153i	−0.325026	+	0.945705i	$0.605373\pi$
$684$	2.37674	+	2.74290i	0.0908770	+	0.104878i
$685$	−17.7728	−	11.4219i	−0.679062	−	0.436407i
$686$	−0.654861	+	0.755750i	−0.0250027	+	0.0288547i
$687$	15.1787	−	4.45688i	0.579105	−	0.170041i
$688$	−3.41488	−	7.47755i	−0.130191	−	0.285079i
$689$	1.08946			0.0415053
$690$	−14.5901	+	3.48211i	−0.555434	+	0.132562i
$691$	4.26920			0.162408			0.0812041	−	0.996697i	$-0.474123\pi$
$691$	4.26920			0.162408			0.0812041	+	0.996697i	$0.474123\pi$
$692$	−10.0101	−	21.9191i	−0.380527	−	0.833238i
$693$	1.64272	−	0.482346i	0.0624017	−	0.0183228i
$694$	15.8680	−	18.3127i	0.602342	−	0.695140i
$695$	−15.8038	−	10.1565i	−0.599474	−	0.385259i
$696$	4.79984	+	5.53931i	0.181938	+	0.209967i
$697$	1.79754	+	12.5022i	0.0680867	+	0.473553i
$698$	−8.83898	−	2.59536i	−0.334560	−	0.0982358i
$699$	−3.61472	+	2.32304i	−0.136721	+	0.0878655i
$700$	−0.680604	+	4.73370i	−0.0257244	+	0.178917i
$701$	−1.61546	+	3.53735i	−0.0610149	+	0.133604i	−0.937683	−	0.347491i	$-0.887034\pi$
$701$	−1.61546	+	3.53735i	−0.0610149	+	0.133604i	0.876668	+	0.481095i	$0.159761\pi$
$702$	−0.514309	+	1.12618i	−0.0194113	+	0.0425049i
$703$	−4.35067	+	30.2596i	−0.164089	+	1.14126i
$704$	−1.44028	+	0.925614i	−0.0542827	+	0.0348854i
$705$	29.4252	+	8.64001i	1.10822	+	0.325402i
$706$	−0.110788	−	0.770548i	−0.00416957	−	0.0290000i
$707$	−3.97743	−	4.59020i	−0.149587	−	0.172632i
$708$	2.90973	+	1.86997i	0.109354	+	0.0702777i
$709$	7.05620	−	8.14329i	0.265001	−	0.305828i	−0.607618	−	0.794230i	$-0.707875\pi$
$709$	7.05620	−	8.14329i	0.265001	−	0.305828i	0.872619	+	0.488402i	$0.162420\pi$
$710$	18.0624	−	5.30361i	0.677871	−	0.199041i
$711$	1.02237	+	2.23867i	0.0383418	+	0.0839568i
$712$	7.21531			0.270405
$713$	−0.812506	+	4.13292i	−0.0304286	+	0.154779i
$714$	−4.69118			−0.175563
$715$	−2.75402	−	6.03047i	−0.102995	−	0.225527i
$716$	−5.38538	+	1.58129i	−0.201261	+	0.0590956i
$717$	11.3970	−	13.1528i	0.425629	−	0.491202i
$718$	−3.89057	−	2.50032i	−0.145195	−	0.0933110i
$719$	−19.1312	−	22.0786i	−0.713472	−	0.823391i	0.277034	−	0.960860i	$-0.410649\pi$
$719$	−19.1312	−	22.0786i	−0.713472	−	0.823391i	−0.990506	+	0.137469i	$0.956103\pi$
$720$	0.445115	+	3.09584i	0.0165885	+	0.115375i
$721$	−2.66796	−	0.783385i	−0.0993602	−	0.0291748i
$722$	−4.90247	+	3.15063i	−0.182451	+	0.117254i
$723$	2.80305	−	19.4956i	0.104247	−	0.725051i
$724$	−4.57893	+	10.0264i	−0.170174	+	0.372630i
$725$	−14.5614	+	31.8851i	−0.540799	+	1.18418i
$726$	1.14831	−	7.98669i	0.0426179	−	0.296414i
$727$	32.6467	−	20.9808i	1.21080	−	0.778134i	0.230008	−	0.973189i	$-0.426125\pi$
$727$	32.6467	−	20.9808i	1.21080	−	0.778134i	0.980792	+	0.195055i	$0.0624885\pi$
$728$	1.18791	+	0.348802i	0.0440269	+	0.0129275i
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$	−19.1105	−	22.0547i	−0.707312	−	0.816281i
$731$	32.4416	+	20.8490i	1.19990	+	0.771126i
$732$	−3.44108	+	3.97122i	−0.127186	+	0.146780i
$733$	20.1900	−	5.92832i	0.745735	−	0.218967i	0.113278	−	0.993563i	$-0.463865\pi$
$733$	20.1900	−	5.92832i	0.745735	−	0.218967i	0.632456	+	0.774596i	$0.282047\pi$
$734$	14.4347	+	31.6077i	0.532796	+	1.16666i
$735$	−3.12768			−0.115366
$736$	2.95055	+	3.78078i	0.108759	+	0.139361i
$737$	−11.3646			−0.418620
$738$	1.11848	+	2.44913i	0.0411718	+	0.0901537i
$739$	0.194050	−	0.0569782i	0.00713824	−	0.00209598i	−0.278161	−	0.960534i	$-0.589725\pi$
$739$	0.194050	−	0.0569782i	0.00713824	−	0.00209598i	0.285300	+	0.958438i	$0.407907\pi$
$740$	−17.2522	+	19.9101i	−0.634204	+	0.731910i
$741$	3.78009	+	2.42931i	0.138865	+	0.0892431i
$742$	0.576262	+	0.665042i	0.0211552	+	0.0244144i
$743$	4.47407	+	31.1178i	0.164138	+	1.14160i	0.890730	+	0.454533i	$0.150194\pi$
$743$	4.47407	+	31.1178i	0.164138	+	1.14160i	−0.726592	+	0.687069i	$0.758897\pi$
$744$	0.842693	+	0.247437i	0.0308946	+	0.00907148i
$745$	56.5248	−	36.3263i	2.07091	−	1.33089i
$746$	5.37393	−	37.3765i	0.196754	−	1.36845i
$747$	2.23723	−	4.89886i	0.0818561	−	0.179240i
$748$	3.33646	−	7.30582i	0.121993	−	0.267127i
$749$	−1.25451	+	8.72527i	−0.0458386	+	0.318815i
$750$	0.572590	−	0.367981i	0.0209080	−	0.0134368i
$751$	10.4886	+	3.07973i	0.382734	+	0.112381i	0.467439	−	0.884025i	$-0.345177\pi$
$751$	10.4886	+	3.07973i	0.382734	+	0.112381i	−0.0847051	+	0.996406i	$0.526995\pi$
$752$	−1.39542	−	9.70537i	−0.0508858	−	0.353918i
$753$	6.99147	+	8.06859i	0.254783	+	0.294036i
$754$	7.63391	+	4.90601i	0.278010	+	0.178666i
$755$	17.1826	−	19.8297i	0.625337	−	0.721677i
$756$	−0.959493	+	0.281733i	−0.0348964	+	0.0102465i
$757$	8.59932	+	18.8299i	0.312548	+	0.684384i	0.999088	−	0.0427082i	$-0.0135986\pi$
$757$	8.59932	+	18.8299i	0.312548	+	0.684384i	−0.686540	+	0.727092i	$0.740871\pi$
$758$	−15.9449			−0.579145
$759$	8.19998	+	0.421181i	0.297641	+	0.0152879i
$760$	11.3516			0.411764
$761$	−15.4464	−	33.8230i	−0.559933	−	1.22608i	−0.951986	−	0.306140i	$-0.900962\pi$
$761$	−15.4464	−	33.8230i	−0.559933	−	1.22608i	0.392053	−	0.919942i	$-0.371765\pi$
$762$	−15.3332	+	4.50223i	−0.555463	+	0.163099i
$763$	−4.99778	+	5.76775i	−0.180932	+	0.208807i
$764$	20.0788	+	12.9039i	0.726426	+	0.466845i
$765$	−9.60845	−	11.0887i	−0.347394	−	0.400914i
$766$	0.928448	+	6.45750i	0.0335462	+	0.233319i
$767$	4.10875	+	1.20644i	0.148358	+	0.0435619i
$768$	0.841254	−	0.540641i	0.0303561	−	0.0195087i
$769$	1.87601	−	13.0479i	0.0676507	−	0.470521i	−0.927631	−	0.373497i	$-0.878159\pi$
$769$	1.87601	−	13.0479i	0.0676507	−	0.470521i	0.995282	−	0.0970238i	$-0.0309323\pi$
$770$	2.22447	−	4.87090i	0.0801642	−	0.175535i
$771$	11.3768	−	24.9117i	0.409725	−	0.897172i
$772$	−1.37831	+	9.58639i	−0.0496066	+	0.345022i
$773$	−14.8833	+	9.56493i	−0.535316	+	0.344026i	−0.780204	−	0.625525i	$-0.784885\pi$
$773$	−14.8833	+	9.56493i	−0.535316	+	0.344026i	0.244889	+	0.969551i	$0.421249\pi$
$774$	7.88742	+	2.31596i	0.283508	+	0.0832453i
$775$	0.597753	+	4.15746i	0.0214719	+	0.149341i
$776$	−6.52086	−	7.52547i	−0.234085	−	0.270149i
$777$	−7.08599	−	4.55389i	−0.254208	−	0.163370i
$778$	−4.50324	+	5.19702i	−0.161449	+	0.186322i
$779$	9.37607	−	2.75306i	0.335933	−	0.0986387i
$780$	1.60859	+	3.52233i	0.0575969	+	0.126120i
$781$	−10.3046			−0.368729
$782$	−21.2332	−	7.43742i	−0.759298	−	0.265962i
$783$	−7.32956			−0.261937
$784$	0.415415	+	0.909632i	0.0148363	+	0.0324869i
$785$	−6.57308	+	1.93003i	−0.234603	+	0.0688858i
$786$	−12.8163	+	14.7908i	−0.457143	+	0.527572i
$787$	−11.2487	−	7.22910i	−0.400973	−	0.257690i	0.324577	−	0.945859i	$-0.394778\pi$
$787$	−11.2487	−	7.22910i	−0.400973	−	0.257690i	−0.725550	+	0.688170i	$0.758414\pi$
$788$	−6.21874	−	7.17680i	−0.221533	−	0.255663i
$789$	0.760374	+	5.28852i	0.0270700	+	0.188276i
$790$	7.38566	+	2.16862i	0.262770	+	0.0771562i
$791$	7.94162	−	5.10377i	0.282372	−	0.181469i
$792$	0.243653	−	1.69464i	0.00865783	−	0.0602165i
$793$	−2.70253	+	5.91771i	−0.0959695	+	0.210144i
$794$	−5.70707	+	12.4967i	−0.202536	+	0.443493i
$795$	−0.391691	+	2.72427i	−0.0138918	+	0.0966199i
$796$	12.7930	−	8.22154i	0.453435	−	0.291405i
$797$	8.45216	+	2.48178i	0.299391	+	0.0879091i	0.427978	−	0.903789i	$-0.359226\pi$
$797$	8.45216	+	2.48178i	0.299391	+	0.0879091i	−0.128587	+	0.991698i	$0.541044\pi$
$798$	0.516515	+	3.59244i	0.0182844	+	0.127171i
$799$	30.1222	+	34.7628i	1.06565	+	1.22982i
$800$	4.02320	+	2.58555i	0.142241	+	0.0914130i
$801$	−4.72502	+	5.45297i	−0.166950	+	0.192671i
$802$	−17.0613	+	5.00966i	−0.602457	+	0.176897i
$803$	6.63597	+	14.5308i	0.234178	+	0.512779i
$804$	6.63793			0.234102
$805$	−14.1565	−	4.95864i	−0.498951	−	0.174769i
$806$	1.08735			0.0383003
$807$	10.4531	+	22.8892i	0.367968	+	0.805737i
$808$	−5.82768	+	1.71116i	−0.205017	+	0.0601984i
$809$	25.8682	−	29.8535i	0.909477	−	1.04959i	−0.0890873	−	0.996024i	$-0.528395\pi$
$809$	25.8682	−	29.8535i	0.909477	−	1.04959i	0.998564	−	0.0535684i	$-0.0170595\pi$
$810$	−2.63117	−	1.69095i	−0.0924500	−	0.0594140i
$811$	−21.3658	−	24.6575i	−0.750256	−	0.865841i	0.244338	−	0.969690i	$-0.421430\pi$
$811$	−21.3658	−	24.6575i	−0.750256	−	0.865841i	−0.994593	+	0.103849i	$0.966884\pi$
$812$	1.04311	+	7.25496i	0.0366058	+	0.254599i
$813$	−14.4170	−	4.23321i	−0.505626	−	0.148465i
$814$	12.1317	−	7.79657i	0.425216	−	0.273270i
$815$	1.46271	−	10.1734i	0.0512364	−	0.356357i
$816$	−1.94879	+	4.26725i	−0.0682212	+	0.149384i
$817$	12.3939	−	27.1389i	0.433608	−	0.949469i
$818$	−2.19045	+	15.2349i	−0.0765873	+	0.532677i
$819$	−1.04152	+	0.669346i	−0.0363938	+	0.0233888i
$820$	8.07998	+	2.37250i	0.282165	+	0.0828512i
$821$	−5.08395	−	35.3597i	−0.177431	−	1.23406i	−0.862680	−	0.505751i	$-0.831215\pi$
$821$	−5.08395	−	35.3597i	−0.177431	−	1.23406i	0.685248	−	0.728309i	$-0.259694\pi$
$822$	−4.42339	−	5.10486i	−0.154283	−	0.178052i
$823$	−29.1348	−	18.7238i	−1.01557	−	0.652670i	−0.0767439	−	0.997051i	$-0.524452\pi$
$823$	−29.1348	−	18.7238i	−1.01557	−	0.652670i	−0.938830	+	0.344381i	$0.888089\pi$
$824$	−1.82090	+	2.10144i	−0.0634342	+	0.0732070i
$825$	7.85611	−	2.30676i	0.273515	−	0.0803111i
$826$	1.43684	+	3.14624i	0.0499940	+	0.109472i
$827$	26.0911			0.907276			0.453638	−	0.891186i	$-0.350126\pi$
$827$	26.0911			0.907276			0.453638	+	0.891186i	$0.350126\pi$
$828$	−4.78952	−	0.246007i	−0.166447	−	0.00854933i
$829$	−28.5592			−0.991901			−0.495951	−	0.868351i	$-0.665180\pi$
$829$	−28.5592			−0.991901			−0.495951	+	0.868351i	$0.665180\pi$
$830$	−6.99735	−	15.3221i	−0.242882	−	0.531837i
$831$	18.0773	−	5.30798i	0.627095	−	0.184132i
$832$	0.810757	−	0.935664i	0.0281079	−	0.0324383i
$833$	−3.94647	−	2.53624i	−0.136737	−	0.0878756i
$834$	−3.93335	−	4.53933i	−0.136201	−	0.157184i
$835$	−1.30651	−	9.08698i	−0.0452136	−	0.314468i
$836$	−5.96205	−	1.75062i	−0.206202	−	0.0605464i
$837$	−0.738847	+	0.474828i	−0.0255383	+	0.0164125i
$838$	1.76935	−	12.3061i	0.0611212	−	0.425107i
$839$	−0.558345	+	1.22260i	−0.0192762	+	0.0422090i	−0.919025	−	0.394199i	$-0.871022\pi$
$839$	−0.558345	+	1.22260i	−0.0192762	+	0.0422090i	0.899749	+	0.436408i	$0.143749\pi$
$840$	−1.29929	+	2.84504i	−0.0448296	+	0.0981631i
$841$	−3.51838	+	24.4709i	−0.121323	+	0.843822i
$842$	0.481089	−	0.309177i	0.0165794	−	0.0106550i
$843$	−16.2071	−	4.75883i	−0.558202	−	0.163903i
$844$	1.97809	+	13.7579i	0.0680887	+	0.473568i
$845$	−23.4871	−	27.1055i	−0.807980	−	0.932458i
$846$	8.24863	+	5.30108i	0.283594	+	0.182255i
$847$	5.28395	−	6.09801i	0.181559	−	0.209530i
$848$	0.844331	−	0.247918i	0.0289944	−	0.00851354i
$849$	5.84336	+	12.7952i	0.200544	+	0.439130i
$850$	−22.4350			−0.769515
$851$	−24.8528	−	31.8460i	−0.851945	−	1.09167i
$852$	6.01883			0.206202
$853$	−13.4304	−	29.4085i	−0.459848	−	1.00693i	−0.987522	−	0.157480i	$-0.949663\pi$
$853$	−13.4304	−	29.4085i	−0.459848	−	1.00693i	0.527674	−	0.849447i	$-0.323064\pi$
$854$	−5.04182	+	1.48041i	−0.172528	+	0.0506587i
$855$	−7.43368	+	8.57893i	−0.254227	+	0.293393i
$856$	7.41565	+	4.76575i	0.253462	+	0.162890i
$857$	−6.15002	−	7.09751i	−0.210081	−	0.242446i	0.640924	−	0.767605i	$-0.278552\pi$
$857$	−6.15002	−	7.09751i	−0.210081	−	0.242446i	−0.851004	+	0.525158i	$0.824006\pi$
$858$	−0.301657	−	2.09807i	−0.0102984	−	0.0716269i
$859$	−8.39171	−	2.46403i	−0.286322	−	0.0840716i	0.135418	−	0.990789i	$-0.456762\pi$
$859$	−8.39171	−	2.46403i	−0.286322	−	0.0840716i	−0.421740	+	0.906717i	$0.638580\pi$
$860$	21.6293	−	13.9003i	0.737553	−	0.473997i
$861$	−0.383174	+	2.66504i	−0.0130585	+	0.0908242i
$862$	11.2734	−	24.6853i	0.383974	−	0.840785i
$863$	4.88583	−	10.6985i	0.166316	−	0.364181i	−0.808062	−	0.589097i	$-0.799484\pi$
$863$	4.88583	−	10.6985i	0.166316	−	0.364181i	0.974378	+	0.224916i	$0.0722109\pi$
$864$	−0.142315	+	0.989821i	−0.00484165	+	0.0336744i
$865$	63.4024	−	40.7463i	2.15575	−	1.38541i
$866$	3.66866	+	1.07722i	0.124666	+	0.0366053i
$867$	−0.712593	−	4.95619i	−0.0242009	−	0.168321i
$868$	0.575144	+	0.663751i	0.0195217	+	0.0225292i
$869$	−3.54465	−	2.27801i	−0.120244	−	0.0772761i
$870$	−15.0124	+	17.3252i	−0.508967	+	0.587379i
$871$	7.88526	−	2.31532i	0.267182	−	0.0784517i
$872$	3.17038	+	6.94215i	0.107362	+	0.235091i
$873$	9.95762			0.337014
$874$	−3.35762	+	17.0790i	−0.113573	+	0.577706i
$875$	0.680639			0.0230098
$876$	−3.87600	−	8.48725i	−0.130958	−	0.286757i
$877$	21.8432	−	6.41373i	0.737591	−	0.216576i	0.108705	−	0.994074i	$-0.465329\pi$
$877$	21.8432	−	6.41373i	0.737591	−	0.216576i	0.628886	+	0.777498i	$0.283511\pi$
$878$	−2.34980	+	2.71182i	−0.0793020	+	0.0915194i
$879$	14.2932	+	9.18569i	0.482098	+	0.309826i
$880$	−3.50665	−	4.04689i	−0.118209	−	0.136421i
$881$	0.105008	+	0.730346i	0.00353780	+	0.0246060i	0.991514	−	0.130001i	$-0.0414980\pi$
$881$	0.105008	+	0.730346i	0.00353780	+	0.0246060i	−0.987976	+	0.154607i	$0.950589\pi$
$882$	−0.959493	−	0.281733i	−0.0323078	−	0.00948643i
$883$	−24.7838	+	15.9276i	−0.834041	+	0.536006i	−0.886560	−	0.462614i	$-0.846911\pi$
$883$	−24.7838	+	15.9276i	−0.834041	+	0.536006i	0.0525186	+	0.998620i	$0.483275\pi$
$884$	−0.826559	+	5.74885i	−0.0278002	+	0.193355i
$885$	−4.49397	+	9.84042i	−0.151063	+	0.330782i
$886$	−6.41782	+	14.0531i	−0.215611	+	0.472122i
$887$	3.52200	−	24.4961i	0.118257	−	0.822498i	−0.841216	−	0.540699i	$-0.818160\pi$
$887$	3.52200	−	24.4961i	0.118257	−	0.822498i	0.959474	−	0.281799i	$-0.0909311\pi$
$888$	−7.08599	+	4.55389i	−0.237790	+	0.152818i
$889$	−15.3332	−	4.50223i	−0.514259	−	0.151000i
$890$	3.21164	+	22.3375i	0.107655	+	0.748754i
$891$	1.12117	+	1.29390i	0.0375605	+	0.0433471i
$892$	−12.4627	−	8.00926i	−0.417281	−	0.268170i
$893$	23.3043	−	26.8947i	0.779850	−	0.899995i
$894$	20.6125	−	6.05239i	0.689386	−	0.202422i
$895$	−7.29254	−	15.9684i	−0.243763	−	0.533766i
$896$	1.00000			0.0334077
$897$	−5.77533	+	1.37836i	−0.192832	+	0.0460221i
$898$	−28.6174			−0.954974
$899$	2.67416	+	5.85560i	0.0891883	+	0.195295i
$900$	−4.58866	+	1.34735i	−0.152955	+	0.0449118i
$901$	−2.70335	+	3.11983i	−0.0900616	+	0.103937i
$902$	−3.87788	−	2.49216i	−0.129119	−	0.0829799i
$903$	5.38322	+	6.21257i	0.179142	+	0.206741i
$904$	−1.34348	−	9.34414i	−0.0446836	−	0.310781i
$905$	−33.0785	−	9.71272i	−1.09957	−	0.322862i
$906$	7.05738	−	4.53550i	0.234466	−	0.150682i
$907$	2.74043	−	19.0601i	0.0909946	−	0.632882i	−0.892379	−	0.451287i	$-0.850965\pi$
$907$	2.74043	−	19.0601i	0.0909946	−	0.632882i	0.983373	−	0.181595i	$-0.0581259\pi$
$908$	−8.77489	+	19.2143i	−0.291205	+	0.637650i
$909$	2.52311	−	5.52484i	0.0836862	−	0.183247i
$910$	−0.551080	+	3.83284i	−0.0182681	+	0.127058i
$911$	14.2912	−	9.18443i	0.473490	−	0.304294i	−0.282046	−	0.959401i	$-0.591013\pi$
$911$	14.2912	−	9.18443i	0.473490	−	0.304294i	0.755536	+	0.655107i	$0.227377\pi$
$912$	3.48237	+	1.02252i	0.115313	+	0.0338589i
$913$	1.31220	+	9.12656i	0.0434275	+	0.302045i
$914$	20.7078	+	23.8981i	0.684954	+	0.790479i
$915$	−13.8260	−	8.88540i	−0.457072	−	0.293742i
$916$	10.3596	−	11.9556i	0.342291	−	0.395024i
$917$	−18.7783	+	5.51381i	−0.620115	+	0.182082i
$918$	−1.94879	−	4.26725i	−0.0643195	−	0.140840i
$919$	23.6273			0.779393			0.389696	−	0.920943i	$-0.372580\pi$
$919$	23.6273			0.779393			0.389696	+	0.920943i	$0.372580\pi$
$920$	−10.3914	+	10.8173i	−0.342593	+	0.356636i
$921$	13.7667			0.453628
$922$	−4.47522	−	9.79937i	−0.147384	−	0.322725i
$923$	7.14983	−	2.09938i	0.235339	−	0.0691019i
$924$	1.12117	−	1.29390i	0.0368837	−	0.0425660i
$925$	−33.8879	−	21.7784i	−1.11423	−	0.716070i
$926$	5.97201	+	6.89207i	0.196253	+	0.226487i
$927$	−0.395720	−	2.75230i	−0.0129972	−	0.0903972i
$928$	7.03266	+	2.06498i	0.230859	+	0.0677862i
$929$	−32.7414	+	21.0416i	−1.07421	+	0.690353i	−0.953213	−	0.302300i	$-0.902246\pi$
$929$	−32.7414	+	21.0416i	−1.07421	+	0.690353i	−0.120997	+	0.992653i	$0.538609\pi$
$930$	−0.390931	+	2.71898i	−0.0128191	+	0.0891590i
$931$	−1.50770	+	3.30140i	−0.0494129	+	0.108199i
$932$	−1.78497	+	3.90853i	−0.0584685	+	0.128028i
$933$	1.77782	−	12.3650i	0.0582032	−	0.404812i
$934$	14.4038	−	9.25675i	0.471306	−	0.302890i
$935$	24.1028	+	7.07722i	0.788246	+	0.231450i
$936$	0.176194	+	1.22546i	0.00575909	+	0.0400554i
$937$	−24.1636	−	27.8863i	−0.789390	−	0.911004i	0.208360	−	0.978052i	$-0.433187\pi$
$937$	−24.1636	−	27.8863i	−0.789390	−	0.911004i	−0.997750	+	0.0670480i	$0.978642\pi$
$938$	5.58418	+	3.58874i	0.182330	+	0.117176i
$939$	19.3107	−	22.2857i	0.630180	−	0.727266i
$940$	29.4252	−	8.64001i	0.959744	−	0.281806i
$941$	−23.9641	−	52.4741i	−0.781208	−	1.71061i	−0.700260	−	0.713888i	$-0.746933\pi$
$941$	−23.9641	−	52.4741i	−0.781208	−	1.71061i	−0.0809473	−	0.996718i	$-0.525795\pi$
$942$	−2.19031			−0.0713641
$943$	−5.95949	+	11.4550i	−0.194068	+	0.373026i
$944$	3.45880			0.112574
$945$	−1.29929	−	2.84504i	−0.0422658	−	0.0925491i
$946$	−13.5038	+	3.96508i	−0.439047	+	0.128916i
$947$	20.4202	−	23.5661i	0.663566	−	0.765796i	−0.319789	−	0.947489i	$-0.603612\pi$
$947$	20.4202	−	23.5661i	0.663566	−	0.765796i	0.983355	+	0.181693i	$0.0581576\pi$
$948$	2.07039	+	1.33056i	0.0672431	+	0.0432145i
$949$	−7.56470	−	8.73013i	−0.245561	−	0.283392i
$950$	2.47017	+	17.1804i	0.0801430	+	0.557407i
$951$	−30.3080	−	8.89923i	−0.982804	−	0.288577i
$952$	−3.94647	+	2.53624i	−0.127906	+	0.0822001i
$953$	7.83836	−	54.5170i	0.253909	−	1.76598i	−0.320344	−	0.947301i	$-0.603799\pi$
$953$	7.83836	−	54.5170i	0.253909	−	1.76598i	0.574254	−	0.818677i	$-0.305292\pi$
$954$	−0.365555	+	0.800455i	−0.0118353	+	0.0259157i
$955$	−31.0110	+	67.9046i	−1.00349	+	2.19734i
$956$	2.47680	−	17.2266i	0.0801056	−	0.557146i
$957$	10.5567	−	6.78435i	0.341248	−	0.219307i
$958$	−39.6265	−	11.6354i	−1.28027	−	0.375922i
$959$	−0.961293	−	6.68594i	−0.0310418	−	0.215900i
$960$	2.04819	+	2.36374i	0.0661052	+	0.0762895i
$961$	−25.4300	−	16.3428i	−0.820321	−	0.527188i
$962$	−6.82911	+	7.88122i	−0.220179	+	0.254101i
$963$	−8.45793	+	2.48347i	−0.272553	+	0.0800288i
$964$	−8.18206	−	17.9162i	−0.263527	−	0.577043i
$965$	−30.2915			−0.975117
$966$	−3.89620	−	2.79636i	−0.125358	−	0.0899715i
$967$	20.0128			0.643567			0.321784	−	0.946813i	$-0.395718\pi$
$967$	20.0128			0.643567			0.321784	+	0.946813i	$0.395718\pi$
$968$	−3.35191	−	7.33966i	−0.107734	−	0.235906i
$969$	−16.3364	+	4.79680i	−0.524801	+	0.154096i
$970$	20.3952	−	23.5373i	0.654849	−	0.755736i
$971$	−6.11365	−	3.92901i	−0.196196	−	0.126088i	0.438854	−	0.898558i	$-0.355384\pi$
$971$	−6.11365	−	3.92901i	−0.196196	−	0.126088i	−0.635051	+	0.772470i	$0.719021\pi$
$972$	−0.654861	−	0.755750i	−0.0210047	−	0.0242407i
$973$	−0.854799	−	5.94525i	−0.0274036	−	0.190596i
$974$	−30.7221	−	9.02081i	−0.984398	−	0.289045i
$975$	−4.98096	+	3.20107i	−0.159518	+	0.102516i
$976$	−0.747818	+	5.20119i	−0.0239371	+	0.166486i
$977$	23.1802	−	50.7575i	0.741599	−	1.62388i	−0.0393076	−	0.999227i	$-0.512515\pi$
$977$	23.1802	−	50.7575i	0.741599	−	1.62388i	0.780907	−	0.624648i	$-0.214758\pi$
$978$	1.36511	−	2.98917i	0.0436514	−	0.0955832i
$979$	1.75803	−	12.2274i	0.0561869	−	0.390788i
$980$	−2.63117	+	1.69095i	−0.0840497	+	0.0540155i
$981$	−7.32268	−	2.15013i	−0.233795	−	0.0686485i
$982$	0.0212646	+	0.147899i	0.000678581	+	0.00471964i
$983$	−2.23704	−	2.58169i	−0.0713506	−	0.0823430i	0.718952	−	0.695060i	$-0.244622\pi$
$983$	−2.23704	−	2.58169i	−0.0713506	−	0.0823430i	−0.790303	+	0.612717i	$0.790077\pi$
$984$	2.26503	+	1.45564i	0.0722064	+	0.0464042i
$985$	19.4502	−	22.4467i	0.619735	−	0.715213i
$986$	−32.9915	+	9.68717i	−1.05066	+	0.308502i
$987$	4.07321	+	8.91910i	0.129652	+	0.283898i
$988$	4.49340			0.142954
$989$	14.5161	+	36.6539i	0.461585	+	1.16553i
$990$	5.35480			0.170187
$991$	−22.4821	−	49.2289i	−0.714166	−	1.56381i	−0.821903	−	0.569627i	$-0.807088\pi$
$991$	−22.4821	−	49.2289i	−0.714166	−	1.56381i	0.107737	−	0.994179i	$-0.465640\pi$
$992$	0.842693	−	0.247437i	0.0267555	−	0.00785613i
$993$	−8.34432	+	9.62985i	−0.264799	+	0.305594i
$994$	5.06336	+	3.25402i	0.160600	+	0.103211i
$995$	31.1470	+	35.9455i	0.987425	+	1.13955i
$996$	−0.766442	−	5.33072i	−0.0242856	−	0.168910i
$997$	−21.2000	−	6.22488i	−0.671411	−	0.197144i	−0.0717795	−	0.997421i	$-0.522868\pi$
$997$	−21.2000	−	6.22488i	−0.671411	−	0.197144i	−0.599631	+	0.800277i	$0.704686\pi$
$998$	−21.2738	+	13.6719i	−0.673411	+	0.432775i
$999$	1.19874	−	8.33739i	0.0379263	−	0.263783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.i.211.1	✓	40
23.6	even	11	inner	966.2.q.i.673.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.i.211.1	✓	40	1.1	even	1	trivial
966.2.q.i.673.1	yes	40	23.6	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-2.63117 - 1.69095i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 + 0.909632i) q^{2} +(-0.959493 + 0.281733i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-2.63117 - 1.69095i) q^{5} +(-0.654861 - 0.755750i) q^{6} +(-0.142315 - 0.989821i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(0.841254 - 0.540641i) q^{9} +(0.445115 - 3.09584i) q^{10} +(-0.711219 + 1.55735i) q^{11} +(0.415415 - 0.909632i) q^{12} +(0.176194 - 1.22546i) q^{13} +(0.841254 - 0.540641i) q^{14} +(3.00099 + 0.881169i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(3.07207 + 3.54536i) q^{17} +(0.841254 + 0.540641i) q^{18} +(2.37674 - 2.74290i) q^{19} +(3.00099 - 0.881169i) q^{20} +(0.415415 + 0.909632i) q^{21} -1.71207 q^{22} +(0.438117 + 4.77578i) q^{23} +1.00000 q^{24} +(1.98667 + 4.35021i) q^{25} +(1.18791 - 0.348802i) q^{26} +(-0.654861 + 0.755750i) q^{27} +(0.841254 + 0.540641i) q^{28} +(4.79984 + 5.53931i) q^{29} +(0.445115 + 3.09584i) q^{30} +(0.842693 + 0.247437i) q^{31} +(0.841254 - 0.540641i) q^{32} +(0.243653 - 1.69464i) q^{33} +(-1.94879 + 4.26725i) q^{34} +(-1.29929 + 2.84504i) q^{35} +(-0.142315 + 0.989821i) q^{36} +(-7.08599 + 4.55389i) q^{37} +(3.48237 + 1.02252i) q^{38} +(0.176194 + 1.22546i) q^{39} +(2.04819 + 2.36374i) q^{40} +(2.26503 + 1.45564i) q^{41} +(-0.654861 + 0.755750i) q^{42} +(7.88742 - 2.31596i) q^{43} +(-0.711219 - 1.55735i) q^{44} -3.12768 q^{45} +(-4.16220 + 2.38245i) q^{46} +9.80517 q^{47} +(0.415415 + 0.909632i) q^{48} +(-0.959493 + 0.281733i) q^{49} +(-3.13179 + 3.61428i) q^{50} +(-3.94647 - 2.53624i) q^{51} +(0.810757 + 0.935664i) q^{52} +(0.125234 + 0.871019i) q^{53} +(-0.959493 - 0.281733i) q^{54} +(4.50475 - 2.89503i) q^{55} +(-0.142315 + 0.989821i) q^{56} +(-1.50770 + 3.30140i) q^{57} +(-3.04481 + 6.66720i) q^{58} +(-0.492239 + 3.42360i) q^{59} +(-2.63117 + 1.69095i) q^{60} +(-5.04182 - 1.48041i) q^{61} +(0.124991 + 0.869329i) q^{62} +(-0.654861 - 0.755750i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-2.53579 + 2.92646i) q^{65} +(1.64272 - 0.482346i) q^{66} +(2.75750 + 6.03807i) q^{67} -4.69118 q^{68} +(-1.76586 - 4.45889i) q^{69} -3.12768 q^{70} +(2.50031 + 5.47492i) q^{71} +(-0.959493 + 0.281733i) q^{72} +(6.11012 - 7.05146i) q^{73} +(-7.08599 - 4.55389i) q^{74} +(-3.13179 - 3.61428i) q^{75} +(0.516515 + 3.59244i) q^{76} +(1.64272 + 0.482346i) q^{77} +(-1.04152 + 0.669346i) q^{78} +(-0.350248 + 2.43603i) q^{79} +(-1.29929 + 2.84504i) q^{80} +(0.415415 - 0.909632i) q^{81} +(-0.383174 + 2.66504i) q^{82} +(4.53060 - 2.91164i) q^{83} +(-0.959493 - 0.281733i) q^{84} +(-2.08812 - 14.5232i) q^{85} +(5.38322 + 6.21257i) q^{86} +(-6.16602 - 3.96266i) q^{87} +(1.12117 - 1.29390i) q^{88} +(-6.92304 + 2.03279i) q^{89} +(-1.29929 - 2.84504i) q^{90} -1.23806 q^{91} +(-3.89620 - 2.79636i) q^{92} -0.878269 q^{93} +(4.07321 + 8.91910i) q^{94} +(-10.8917 + 3.19810i) q^{95} +(-0.654861 + 0.755750i) q^{96} +(8.37689 + 5.38350i) q^{97} +(-0.654861 - 0.755750i) q^{98} +(0.243653 + 1.69464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more