LMFDB - Embedded newform 720.2.cf.a.11.64

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.64
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.64

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.734399 + 1.20858i) q^{2} +(-1.13524 + 1.30814i) q^{3} +(-0.921316 + 1.77516i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-2.41471 - 0.411329i) q^{6} +(-2.44759 + 4.23936i) q^{7} +(-2.82203 + 0.190190i) q^{8} +(-0.422459 - 2.97011i) q^{9} +O(q^{10})$	\(q+(0.734399 + 1.20858i) q^{2} +(-1.13524 + 1.30814i) q^{3} +(-0.921316 + 1.77516i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-2.41471 - 0.411329i) q^{6} +(-2.44759 + 4.23936i) q^{7} +(-2.82203 + 0.190190i) q^{8} +(-0.422459 - 2.97011i) q^{9} +(0.396572 + 1.35747i) q^{10} +(-2.73683 + 0.733331i) q^{11} +(-1.27624 - 3.22044i) q^{12} +(4.66270 + 1.24937i) q^{13} +(-6.92110 + 0.155274i) q^{14} +(-1.43513 + 0.969744i) q^{15} +(-2.30235 - 3.27096i) q^{16} -3.56813i q^{17} +(3.27935 - 2.69182i) q^{18} +(0.879841 + 0.879841i) q^{19} +(-1.34937 + 1.47621i) q^{20} +(-2.76706 - 8.01448i) q^{21} +(-2.89621 - 2.76911i) q^{22} +(3.76921 - 2.17615i) q^{23} +(2.95488 - 3.90752i) q^{24} +(0.866025 + 0.500000i) q^{25} +(1.91433 + 6.55277i) q^{26} +(4.36491 + 2.81915i) q^{27} +(-5.27051 - 8.25065i) q^{28} +(-5.87239 + 1.57350i) q^{29} +(-2.22597 - 1.02229i) q^{30} +(-6.43671 + 3.71624i) q^{31} +(2.26236 - 5.18476i) q^{32} +(2.14766 - 4.41266i) q^{33} +(4.31236 - 2.62043i) q^{34} +(-3.46142 + 3.46142i) q^{35} +(5.66162 + 1.98648i) q^{36} +(-0.0686124 - 0.0686124i) q^{37} +(-0.417201 + 1.70951i) q^{38} +(-6.92763 + 4.68113i) q^{39} +(-2.77509 - 0.546684i) q^{40} +(4.11233 + 7.12276i) q^{41} +(7.65399 - 9.23004i) q^{42} +(-1.78402 - 6.65805i) q^{43} +(1.21971 - 5.53393i) q^{44} +(0.360656 - 2.97824i) q^{45} +(5.39815 + 2.95721i) q^{46} +(0.0739339 - 0.128057i) q^{47} +(6.89259 + 0.701526i) q^{48} +(-8.48143 - 14.6903i) q^{49} +(0.0317197 + 1.41386i) q^{50} +(4.66761 + 4.05068i) q^{51} +(-6.51364 + 7.12596i) q^{52} +(-2.14497 + 2.14497i) q^{53} +(-0.201575 + 7.34570i) q^{54} -2.83337 q^{55} +(6.10089 - 12.4291i) q^{56} +(-2.14979 + 0.152124i) q^{57} +(-6.21438 - 5.94166i) q^{58} +(1.59422 - 5.94972i) q^{59} +(-0.399238 - 3.44102i) q^{60} +(3.69698 + 13.7973i) q^{61} +(-9.21848 - 5.05006i) q^{62} +(13.6253 + 5.47866i) q^{63} +(7.92766 - 1.07344i) q^{64} +(4.18046 + 2.41359i) q^{65} +(6.91028 - 0.645043i) q^{66} +(0.871616 - 3.25291i) q^{67} +(6.33398 + 3.28738i) q^{68} +(-1.43224 + 7.40111i) q^{69} +(-6.72546 - 1.64133i) q^{70} +5.68898i q^{71} +(1.75708 + 8.30137i) q^{72} +11.8331i q^{73} +(0.0325345 - 0.133312i) q^{74} +(-1.63722 + 0.565262i) q^{75} +(-2.37247 + 0.751242i) q^{76} +(3.58979 - 13.3973i) q^{77} +(-10.7452 - 4.93476i) q^{78} +(-6.04358 - 3.48926i) q^{79} +(-1.37731 - 3.75540i) q^{80} +(-8.64306 + 2.50950i) q^{81} +(-5.58832 + 10.2010i) q^{82} +(-2.81000 - 10.4871i) q^{83} +(16.7763 + 2.47191i) q^{84} +(0.923500 - 3.44655i) q^{85} +(6.73658 - 7.04579i) q^{86} +(4.60821 - 9.46821i) q^{87} +(7.58393 - 2.59000i) q^{88} -2.82877 q^{89} +(3.86430 - 1.75134i) q^{90} +(-16.7089 + 16.7089i) q^{91} +(0.390377 + 8.69586i) q^{92} +(2.44586 - 12.6389i) q^{93} +(0.209064 - 0.00469032i) q^{94} +(0.622141 + 1.07758i) q^{95} +(4.21407 + 8.84543i) q^{96} +(-8.20341 + 14.2087i) q^{97} +(11.5256 - 21.0390i) q^{98} +(3.33427 + 7.81887i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.734399	+	1.20858i	0.519298	+	0.854593i
$2$	0.734399	+	1.20858i	0.519298	+	0.854593i
$3$	−1.13524	+	1.30814i	−0.655431	+	0.755255i
$3$	−1.13524	+	1.30814i	−0.655431	+	0.755255i
$4$	−0.921316	+	1.77516i	−0.460658	+	0.887578i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−2.41471	−	0.411329i	−0.985800	−	0.167924i
$7$	−2.44759	+	4.23936i	−0.925104	+	1.60233i	−0.133709	+	0.991021i	$0.542689\pi$
$7$	−2.44759	+	4.23936i	−0.925104	+	1.60233i	−0.791394	+	0.611306i	$0.790645\pi$
$8$	−2.82203	+	0.190190i	−0.997737	+	0.0672425i
$9$	−0.422459	−	2.97011i	−0.140820	−	0.990035i
$10$	0.396572	+	1.35747i	0.125407	+	0.429270i
$11$	−2.73683	+	0.733331i	−0.825185	+	0.221108i	−0.646612	−	0.762819i	$-0.723815\pi$
$11$	−2.73683	+	0.733331i	−0.825185	+	0.221108i	−0.178573	+	0.983927i	$0.557148\pi$
$12$	−1.27624	−	3.22044i	−0.368417	−	0.929660i
$13$	4.66270	+	1.24937i	1.29320	+	0.346512i	0.838875	−	0.544324i	$-0.183214\pi$
$13$	4.66270	+	1.24937i	1.29320	+	0.346512i	0.454326	+	0.890836i	$0.349880\pi$
$14$	−6.92110	+	0.155274i	−1.84974	+	0.0414987i
$15$	−1.43513	+	0.969744i	−0.370549	+	0.250387i
$16$	−2.30235	−	3.27096i	−0.575588	−	0.817740i
$17$		−	3.56813i		−	0.865398i	−0.901538	−	0.432699i	$-0.857561\pi$
$17$		−	3.56813i		−	0.865398i	0.901538	−	0.432699i	$-0.142439\pi$
$18$	3.27935	−	2.69182i	0.772950	−	0.634467i
$19$	0.879841	+	0.879841i	0.201849	+	0.201849i	0.800792	−	0.598943i	$-0.204412\pi$
$19$	0.879841	+	0.879841i	0.201849	+	0.201849i	−0.598943	+	0.800792i	$0.704412\pi$
$20$	−1.34937	+	1.47621i	−0.301728	+	0.330091i
$21$	−2.76706	−	8.01448i	−0.603823	−	1.74890i
$22$	−2.89621	−	2.76911i	−0.617474	−	0.590376i
$23$	3.76921	−	2.17615i	0.785935	−	0.453759i	−0.0525948	−	0.998616i	$-0.516749\pi$
$23$	3.76921	−	2.17615i	0.785935	−	0.453759i	0.838529	+	0.544856i	$0.183416\pi$
$24$	2.95488	−	3.90752i	0.603163	−	0.797618i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	1.91433	+	6.55277i	0.375430	+	1.28510i
$27$	4.36491	+	2.81915i	0.840027	+	0.542545i
$28$	−5.27051	−	8.25065i	−0.996033	−	1.55923i
$29$	−5.87239	+	1.57350i	−1.09048	+	0.292192i	−0.758881	−	0.651230i	$-0.774253\pi$
$29$	−5.87239	+	1.57350i	−1.09048	+	0.292192i	−0.331595	+	0.943422i	$0.607587\pi$
$30$	−2.22597	−	1.02229i	−0.406404	−	0.186643i
$31$	−6.43671	+	3.71624i	−1.15607	+	0.667456i	−0.950359	−	0.311157i	$-0.899284\pi$
$31$	−6.43671	+	3.71624i	−1.15607	+	0.667456i	−0.205709	+	0.978613i	$0.565950\pi$
$32$	2.26236	−	5.18476i	0.399933	−	0.916545i
$33$	2.14766	−	4.41266i	0.373859	−	0.768146i
$34$	4.31236	−	2.62043i	0.739563	−	0.449400i
$35$	−3.46142	+	3.46142i	−0.585087	+	0.585087i
$36$	5.66162	+	1.98648i	0.943603	+	0.331079i
$37$	−0.0686124	−	0.0686124i	−0.0112798	−	0.0112798i	0.701444	−	0.712724i	$-0.252539\pi$
$37$	−0.0686124	−	0.0686124i	−0.0112798	−	0.0112798i	−0.712724	+	0.701444i	$0.752539\pi$
$38$	−0.417201	+	1.70951i	−0.0676790	+	0.277319i
$39$	−6.92763	+	4.68113i	−1.10931	+	0.749581i
$40$	−2.77509	−	0.546684i	−0.438781	−	0.0864384i
$41$	4.11233	+	7.12276i	0.642238	+	1.11239i	0.984932	+	0.172942i	$0.0553273\pi$
$41$	4.11233	+	7.12276i	0.642238	+	1.11239i	−0.342694	+	0.939447i	$0.611339\pi$
$42$	7.65399	−	9.23004i	1.18104	−	1.42423i
$43$	−1.78402	−	6.65805i	−0.272060	−	1.01534i	−0.957786	−	0.287483i	$-0.907182\pi$
$43$	−1.78402	−	6.65805i	−0.272060	−	1.01534i	0.685725	−	0.727860i	$-0.259485\pi$
$44$	1.21971	−	5.53393i	0.183878	−	0.834271i
$45$	0.360656	−	2.97824i	0.0537634	−	0.443970i
$46$	5.39815	+	2.95721i	0.795914	+	0.436017i
$47$	0.0739339	−	0.128057i	0.0107844	−	0.0186791i	−0.860583	−	0.509310i	$-0.829900\pi$
$47$	0.0739339	−	0.128057i	0.0107844	−	0.0186791i	0.871367	+	0.490631i	$0.163234\pi$
$48$	6.89259	+	0.701526i	0.994860	+	0.101257i
$49$	−8.48143	−	14.6903i	−1.21163	−	2.09861i
$50$	0.0317197	+	1.41386i	0.00448584	+	0.199950i
$51$	4.66761	+	4.05068i	0.653596	+	0.567209i
$52$	−6.51364	+	7.12596i	−0.903280	+	0.988192i
$53$	−2.14497	+	2.14497i	−0.294634	+	0.294634i	−0.838908	−	0.544274i	$-0.816805\pi$
$53$	−2.14497	+	2.14497i	−0.294634	+	0.294634i	0.544274	+	0.838908i	$0.316805\pi$
$54$	−0.201575	+	7.34570i	−0.0274309	+	0.999624i
$55$	−2.83337			−0.382052
$56$	6.10089	−	12.4291i	0.815265	−	1.66091i
$57$	−2.14979	+	0.152124i	−0.284746	+	0.0201493i
$58$	−6.21438	−	5.94166i	−0.815988	−	0.780178i
$59$	1.59422	−	5.94972i	0.207550	−	0.774588i	−0.781107	−	0.624397i	$-0.785345\pi$
$59$	1.59422	−	5.94972i	0.207550	−	0.774588i	0.988657	−	0.150190i	$-0.0479886\pi$
$60$	−0.399238	−	3.44102i	−0.0515414	−	0.444234i
$61$	3.69698	+	13.7973i	0.473350	+	1.76657i	0.627600	+	0.778536i	$0.284037\pi$
$61$	3.69698	+	13.7973i	0.473350	+	1.76657i	−0.154250	+	0.988032i	$0.549296\pi$
$62$	−9.21848	−	5.05006i	−1.17075	−	0.641359i
$63$	13.6253	+	5.47866i	1.71663	+	0.690246i
$64$	7.92766	−	1.07344i	0.990957	−	0.134181i
$65$	4.18046	+	2.41359i	0.518523	+	0.299369i
$66$	6.91028	−	0.645043i	0.850597	−	0.0793993i
$67$	0.871616	−	3.25291i	0.106485	−	0.397407i	−0.892025	−	0.451987i	$-0.850715\pi$
$67$	0.871616	−	3.25291i	0.106485	−	0.397407i	0.998509	+	0.0545802i	$0.0173820\pi$
$68$	6.33398	+	3.28738i	0.768108	+	0.398653i
$69$	−1.43224	+	7.40111i	−0.172422	+	0.890989i
$70$	−6.72546	−	1.64133i	−0.803846	−	0.196176i
$71$			5.68898i			0.675158i	0.941297	+	0.337579i	$0.109608\pi$
$71$			5.68898i			0.675158i	−0.941297	+	0.337579i	$0.890392\pi$
$72$	1.75708	+	8.30137i	0.207073	+	0.978325i
$73$			11.8331i			1.38496i	0.721437	+	0.692480i	$0.243482\pi$
$73$			11.8331i			1.38496i	−0.721437	+	0.692480i	$0.756518\pi$
$74$	0.0325345	−	0.133312i	0.00378206	−	0.0154972i
$75$	−1.63722	+	0.565262i	−0.189050	+	0.0652708i
$76$	−2.37247	+	0.751242i	−0.272140	+	0.0861734i
$77$	3.58979	−	13.3973i	0.409095	−	1.52676i
$78$	−10.7452	−	4.93476i	−1.21665	−	0.558751i
$79$	−6.04358	−	3.48926i	−0.679956	−	0.392573i	0.119882	−	0.992788i	$-0.461748\pi$
$79$	−6.04358	−	3.48926i	−0.679956	−	0.392573i	−0.799838	+	0.600215i	$0.795082\pi$
$80$	−1.37731	−	3.75540i	−0.153988	−	0.419866i
$81$	−8.64306	+	2.50950i	−0.960340	+	0.278833i
$82$	−5.58832	+	10.2010i	−0.617126	+	1.12651i
$83$	−2.81000	−	10.4871i	−0.308437	−	1.15110i	−0.929946	−	0.367696i	$-0.880147\pi$
$83$	−2.81000	−	10.4871i	−0.308437	−	1.15110i	0.621508	−	0.783407i	$-0.286520\pi$
$84$	16.7763	+	2.47191i	1.83044	+	0.269707i
$85$	0.923500	−	3.44655i	0.100168	−	0.373831i
$86$	6.73658	−	7.04579i	0.726424	−	0.759767i
$87$	4.60821	−	9.46821i	0.494052	−	1.01510i
$88$	7.58393	−	2.59000i	0.808449	−	0.276095i
$89$	−2.82877			−0.299849			−0.149924	−	0.988697i	$-0.547903\pi$
$89$	−2.82877			−0.299849			−0.149924	+	0.988697i	$0.547903\pi$
$90$	3.86430	−	1.75134i	0.407333	−	0.184607i
$91$	−16.7089	+	16.7089i	−1.75157	+	1.75157i
$92$	0.390377	+	8.69586i	0.0406996	+	0.906606i
$93$	2.44586	−	12.6389i	0.253624	−	1.31060i
$94$	0.209064	−	0.00469032i	0.0215633	−	0.000483769i
$95$	0.622141	+	1.07758i	0.0638304	+	0.110557i
$96$	4.21407	+	8.84543i	0.430096	+	0.902783i
$97$	−8.20341	+	14.2087i	−0.832931	+	1.44268i	0.0627738	+	0.998028i	$0.480005\pi$
$97$	−8.20341	+	14.2087i	−0.832931	+	1.44268i	−0.895704	+	0.444650i	$0.853328\pi$
$98$	11.5256	−	21.0390i	1.16426	−	2.12526i
$99$	3.33427	+	7.81887i	0.335107	+	0.785826i
$100$	−1.68546	+	1.07667i	−0.168546	+	0.107667i
$101$	−2.86374	−	10.6876i	−0.284952	−	1.06346i	−0.948874	−	0.315655i	$-0.897776\pi$
$101$	−2.86374	−	10.6876i	−0.284952	−	1.06346i	0.663922	−	0.747802i	$-0.268891\pi$
$102$	−1.46767	+	8.61599i	−0.145321	+	0.853110i
$103$	7.56704	+	13.1065i	0.745602	+	1.29142i	0.949913	+	0.312515i	$0.101172\pi$
$103$	7.56704	+	13.1065i	0.745602	+	1.29142i	−0.204310	+	0.978906i	$0.565495\pi$
$104$	−13.3959	−	2.63895i	−1.31357	−	0.258770i
$105$	−0.598478	−	8.45757i	−0.0584055	−	0.825374i
$106$	−4.16762	−	1.01710i	−0.404795	−	0.0987891i
$107$	11.6274	+	11.6274i	1.12406	+	1.12406i	0.991125	+	0.132935i	$0.0424401\pi$
$107$	11.6274	+	11.6274i	1.12406	+	1.12406i	0.132935	+	0.991125i	$0.457560\pi$
$108$	−9.02589	+	5.15106i	−0.868516	+	0.495661i
$109$	3.41100	−	3.41100i	0.326714	−	0.326714i	−0.524621	−	0.851336i	$-0.675793\pi$
$109$	3.41100	−	3.41100i	0.326714	−	0.326714i	0.851336	+	0.524621i	$0.175793\pi$
$110$	−2.08083	−	3.42435i	−0.198399	−	0.326499i
$111$	0.167646	−	0.0118630i	0.0159123	−	0.00112599i
$112$	19.5020	−	1.75451i	1.84276	−	0.165786i
$113$	−8.22270	+	4.74738i	−0.773527	+	0.446596i	−0.834131	−	0.551566i	$-0.814030\pi$
$113$	−8.22270	+	4.74738i	−0.773527	+	0.446596i	0.0606045	+	0.998162i	$0.480697\pi$
$114$	−1.76265	−	2.48646i	−0.165088	−	0.232878i
$115$	4.20401	−	1.12646i	0.392026	−	0.105043i
$116$	2.61712	−	11.8741i	0.242993	−	1.10248i
$117$	1.74095	−	14.3765i	0.160951	−	1.32911i
$118$	8.36149	−	2.44273i	0.769737	−	0.224871i
$119$	15.1266	+	8.73333i	1.38665	+	0.800583i
$120$	3.86554	−	3.00959i	0.352874	−	0.274737i
$121$	−2.57382	+	1.48600i	−0.233984	+	0.135091i
$122$	−13.9601	+	14.6008i	−1.26389	+	1.32190i
$123$	−13.9861	−	2.70655i	−1.26108	−	0.244041i
$124$	−0.666650	−	14.8500i	−0.0598670	−	1.33357i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	3.38506	+	20.4908i	0.301565	+	1.82547i
$127$			12.3696i			1.09762i	0.835946	+	0.548811i	$0.184919\pi$
$127$			12.3696i			1.09762i	−0.835946	+	0.548811i	$0.815081\pi$
$128$	7.11940	+	8.79285i	0.629272	+	0.777185i
$129$	10.7349	+	5.22474i	0.945160	+	0.460013i
$130$	0.153117	+	6.82495i	0.0134292	+	0.598588i
$131$	12.3160	+	3.30007i	1.07606	+	0.288329i	0.752979	−	0.658044i	$-0.228616\pi$
$131$	12.3160	+	3.30007i	1.07606	+	0.288329i	0.323077	+	0.946373i	$0.395283\pi$
$132$	5.85449	+	7.87788i	0.509568	+	0.685682i
$133$	−5.88345	+	1.57647i	−0.510160	+	0.136697i
$134$	4.57151	−	1.33552i	0.394918	−	0.115372i
$135$	3.48653	+	3.85281i	0.300072	+	0.331597i
$136$	0.678624	+	10.0694i	0.0581915	+	0.863440i
$137$	−5.41174	+	9.37341i	−0.462356	+	0.800824i	−0.999078	−	0.0429350i	$-0.986329\pi$
$137$	−5.41174	+	9.37341i	−0.462356	+	0.800824i	0.536722	+	0.843759i	$0.319662\pi$
$138$	−9.99665	+	3.70439i	−0.850971	+	0.315339i
$139$	−19.7916	−	5.30313i	−1.67870	−	0.449806i	−0.711264	−	0.702925i	$-0.751877\pi$
$139$	−19.7916	−	5.30313i	−1.67870	−	0.449806i	−0.967435	+	0.253119i	$0.918543\pi$
$140$	−2.95550	−	9.33362i	−0.249785	−	0.788835i
$141$	0.0835840	+	0.242092i	0.00703905	+	0.0203878i
$142$	−6.87557	+	4.17798i	−0.576985	+	0.350608i
$143$	−13.6772			−1.14375
$144$	−8.74245	+	8.22008i	−0.728537	+	0.685006i
$145$	−6.07955			−0.504879
$146$	−14.3012	+	8.69022i	−1.18358	+	0.719208i
$147$	28.8454	+	5.58209i	2.37913	+	0.460403i
$148$	0.185011	−	0.0585839i	0.0152078	−	0.00481557i
$149$	15.0128	+	4.02267i	1.22990	+	0.329550i	0.814540	−	0.580108i	$-0.196990\pi$
$149$	15.0128	+	4.02267i	1.22990	+	0.329550i	0.415358	+	0.909658i	$0.363656\pi$
$150$	−1.88553	−	1.56357i	−0.153953	−	0.127665i
$151$	−7.26880	+	12.5899i	−0.591526	+	1.02455i	0.402501	+	0.915420i	$0.368141\pi$
$151$	−7.26880	+	12.5899i	−0.591526	+	1.02455i	−0.994027	+	0.109134i	$0.965192\pi$
$152$	−2.65027	−	2.31560i	−0.214965	−	0.187820i
$153$	−10.5977	+	1.50739i	−0.856775	+	0.121865i
$154$	18.8280	−	5.50042i	1.51720	−	0.443236i
$155$	−7.17922	+	1.92367i	−0.576649	+	0.154513i
$156$	−1.92720	−	16.6104i	−0.154299	−	1.32990i
$157$	7.15548	+	1.91730i	0.571069	+	0.153018i	0.532787	−	0.846249i	$-0.321145\pi$
$157$	7.15548	+	1.91730i	0.571069	+	0.153018i	0.0382823	+	0.999267i	$0.487811\pi$
$158$	−0.221357	−	9.86664i	−0.0176102	−	0.784948i
$159$	−0.370864	−	5.24097i	−0.0294114	−	0.415636i
$160$	3.52719	−	4.42255i	0.278849	−	0.349633i
$161$			21.3054i			1.67910i
$162$	−9.38037	−	8.60283i	−0.736992	−	0.675902i
$163$	3.91789	+	3.91789i	0.306873	+	0.306873i	0.843695	−	0.536823i	$-0.180376\pi$
$163$	3.91789	+	3.91789i	0.306873	+	0.306873i	−0.536823	+	0.843695i	$0.680376\pi$
$164$	−16.4328	+	0.737704i	−1.28318	+	0.0576050i
$165$	3.21656	−	3.70645i	0.250409	−	0.288547i
$166$	10.6108	−	11.0978i	0.823554	−	0.861355i
$167$	10.5218	−	6.07479i	0.814205	−	0.470082i	−0.0342090	−	0.999415i	$-0.510891\pi$
$167$	10.5218	−	6.07479i	0.814205	−	0.470082i	0.848414	+	0.529333i	$0.177558\pi$
$168$	9.33300	+	22.0908i	0.720057	+	1.70434i
$169$	8.92154	+	5.15085i	0.686272	+	0.396220i
$170$	4.84364	−	1.41502i	0.371490	−	0.108527i
$171$	2.24152	−	2.98492i	0.171414	−	0.228262i
$172$	13.4627	+	2.96726i	1.02652	+	0.226251i
$173$	6.49280	−	1.73974i	0.493639	−	0.132270i	−0.00340740	−	0.999994i	$-0.501085\pi$
$173$	6.49280	−	1.73974i	0.493639	−	0.132270i	0.497046	+	0.867724i	$0.334418\pi$
$174$	14.8273	−	1.38406i	1.12406	−	0.104926i
$175$	−4.23936	+	2.44759i	−0.320465	+	0.185021i
$176$	8.69984	+	7.26367i	0.655775	+	0.547520i
$177$	5.97324	+	8.83983i	0.448976	+	0.664442i
$178$	−2.07744	−	3.41878i	−0.155711	−	0.256249i
$179$	−8.97996	+	8.97996i	−0.671194	+	0.671194i	−0.957991	−	0.286798i	$-0.907409\pi$
$179$	−8.97996	+	8.97996i	−0.671194	+	0.671194i	0.286798	+	0.957991i	$0.407409\pi$
$180$	4.95456	+	3.38412i	0.369291	+	0.252238i
$181$	−6.04226	−	6.04226i	−0.449118	−	0.449118i	0.445943	−	0.895061i	$-0.352868\pi$
$181$	−6.04226	−	6.04226i	−0.449118	−	0.449118i	−0.895061	+	0.445943i	$0.852868\pi$
$182$	−32.4650	−	7.92300i	−2.40647	−	0.587292i
$183$	−22.2458	−	10.8271i	−1.64446	−	0.800364i
$184$	−10.2229	+	6.85803i	−0.753644	+	0.505581i
$185$	−0.0485163	−	0.0840327i	−0.00356699	−	0.00617820i
$186$	17.0714	−	6.32602i	1.25173	−	0.463846i
$187$	2.61662	+	9.76536i	0.191346	+	0.714114i
$188$	0.159205	+	0.249225i	0.0116112	+	0.0181766i
$189$	−22.6349	+	11.6043i	−1.64645	+	0.844086i
$190$	−0.845439	+	1.54328i	−0.0613346	+	0.111961i
$191$	5.64638	−	9.77982i	0.408558	−	0.707643i	−0.586170	−	0.810188i	$-0.699365\pi$
$191$	5.64638	−	9.77982i	0.408558	−	0.707643i	0.994728	+	0.102545i	$0.0326984\pi$
$192$	−7.59558	+	11.5891i	−0.548164	+	0.836371i
$193$	−4.28783	−	7.42675i	−0.308645	−	0.534589i	0.669421	−	0.742883i	$-0.266542\pi$
$193$	−4.28783	−	7.42675i	−0.308645	−	0.534589i	−0.978066	+	0.208294i	$0.933209\pi$
$194$	−23.1969	+	0.520419i	−1.66544	+	0.0373639i
$195$	−7.90315	+	2.72862i	−0.565956	+	0.195401i
$196$	33.8916	−	1.52147i	2.42083	−	0.108677i
$197$	16.4297	−	16.4297i	1.17057	−	1.17057i	0.188495	−	0.982074i	$-0.439639\pi$
$197$	16.4297	−	16.4297i	1.17057	−	1.17057i	0.982074	−	0.188495i	$-0.0603608\pi$
$198$	−7.00102	+	9.77189i	−0.497541	+	0.694458i
$199$	−2.16837			−0.153712			−0.0768560	−	0.997042i	$-0.524488\pi$
$199$	−2.16837			−0.153712			−0.0768560	+	0.997042i	$0.524488\pi$
$200$	−2.53904	−	1.24630i	−0.179537	−	0.0881269i
$201$	3.26577	+	4.83303i	0.230350	+	0.340896i
$202$	10.8137	−	11.3100i	0.760847	−	0.795770i
$203$	7.70259	−	28.7465i	0.540616	−	2.01761i
$204$	−11.4909	+	4.55377i	−0.804527	+	0.318828i
$205$	2.12870	+	7.94441i	0.148675	+	0.554862i
$206$	−10.2830	+	18.7707i	−0.716449	+	1.30782i
$207$	−8.05574	−	10.2756i	−0.559913	−	0.714205i
$208$	−6.64855	−	18.1280i	−0.460994	−	1.25695i
$209$	−3.05319	−	1.76276i	−0.211193	−	0.121933i
$210$	9.78210	−	6.93453i	0.675029	−	0.478528i
$211$	1.07617	−	4.01631i	0.0740863	−	0.276494i	−0.918938	−	0.394401i	$-0.870952\pi$
$211$	1.07617	−	4.01631i	0.0740863	−	0.276494i	0.993025	+	0.117907i	$0.0376186\pi$
$212$	−1.83146	−	5.78384i	−0.125785	−	0.397236i
$213$	−7.44198	−	6.45836i	−0.509916	−	0.442519i
$214$	−5.51344	+	22.5917i	−0.376891	+	1.54434i
$215$		−	6.89292i		−	0.470093i
$216$	−12.8541	−	7.12554i	−0.874607	−	0.484832i
$217$		−	36.3834i		−	2.46986i
$218$	6.62749	+	1.61742i	0.448870	+	0.109546i
$219$	−15.4794	−	13.4334i	−1.04600	−	0.907746i
$220$	2.61043	−	5.02968i	0.175995	−	0.339101i
$221$	4.45790	−	16.6371i	0.299871	−	1.11913i
$222$	0.137457	+	0.193901i	0.00922548	+	0.0130138i
$223$	8.42169	+	4.86226i	0.563958	+	0.325601i	0.754732	−	0.656033i	$-0.227767\pi$
$223$	8.42169	+	4.86226i	0.563958	+	0.325601i	−0.190775	+	0.981634i	$0.561100\pi$
$224$	16.4427	+	22.2811i	1.09862	+	1.48872i
$225$	1.11919	−	2.78342i	0.0746128	−	0.185561i
$226$	−11.7763	−	6.45130i	−0.783349	−	0.429134i
$227$	−1.91658	−	7.15276i	−0.127208	−	0.474745i	0.872701	−	0.488255i	$-0.162366\pi$
$227$	−1.91658	−	7.15276i	−0.127208	−	0.474745i	−0.999909	+	0.0135096i	$0.995700\pi$
$228$	1.71059	−	3.95636i	0.113286	−	0.262016i
$229$	4.50341	−	16.8069i	0.297593	−	1.11063i	−0.641542	−	0.767088i	$-0.721705\pi$
$229$	4.50341	−	16.8069i	0.297593	−	1.11063i	0.939136	−	0.343546i	$-0.111628\pi$
$230$	4.44883	+	4.25359i	0.293347	+	0.280474i
$231$	13.4503	+	19.9051i	0.884962	+	1.30966i
$232$	16.2728	−	5.55734i	1.06836	−	0.364857i
$233$	−8.09477			−0.530306			−0.265153	−	0.964206i	$-0.585422\pi$
$233$	−8.09477			−0.530306			−0.265153	+	0.964206i	$0.585422\pi$
$234$	18.6537	−	8.45403i	1.21943	−	0.552657i
$235$	0.104558	−	0.104558i	0.00682063	−	0.00682063i
$236$	9.09289	+	8.31157i	0.591897	+	0.541037i
$237$	11.4254	−	3.94470i	0.742157	−	0.256236i
$238$	0.554037	+	24.6954i	0.0359129	+	1.60076i
$239$	−1.92246	−	3.32979i	−0.124353	−	0.215387i	0.797127	−	0.603812i	$-0.206352\pi$
$239$	−1.92246	−	3.32979i	−0.124353	−	0.215387i	−0.921480	+	0.388426i	$0.873019\pi$
$240$	6.47617	+	2.46156i	0.418035	+	0.158893i
$241$	−4.08600	+	7.07715i	−0.263202	+	0.455880i	−0.967091	−	0.254431i	$-0.918112\pi$
$241$	−4.08600	+	7.07715i	−0.263202	+	0.455880i	0.703889	+	0.710310i	$0.251445\pi$
$242$	−3.68615	−	2.01935i	−0.236955	−	0.129809i
$243$	6.52917	−	14.1552i	0.418847	−	0.908057i
$244$	−27.8985	−	6.14899i	−1.78602	−	0.393649i
$245$	−4.39031	−	16.3849i	−0.280487	−	1.04679i
$246$	−7.00027	−	18.8909i	−0.446321	−	1.20444i
$247$	3.00319	+	5.20168i	0.191088	+	0.330975i
$248$	17.4578	−	11.7115i	1.10857	−	0.743682i
$249$	16.9086	+	8.22946i	1.07154	+	0.521521i
$250$	−0.335294	+	1.37389i	−0.0212059	+	0.0868925i
$251$	7.21390	+	7.21390i	0.455338	+	0.455338i	0.897121	−	0.441784i	$-0.145654\pi$
$251$	7.21390	+	7.21390i	0.455338	+	0.455338i	−0.441784	+	0.897121i	$0.645654\pi$
$252$	−22.2787	+	19.1395i	−1.40343	+	1.20568i
$253$	−8.71984	+	8.71984i	−0.548212	+	0.548212i
$254$	−14.9496	+	9.08420i	−0.938020	+	0.569993i
$255$	3.46017	+	5.12073i	0.216684	+	0.320672i
$256$	−5.39835	+	15.0618i	−0.337397	+	0.941363i
$257$	6.37428	−	3.68019i	0.397617	−	0.229564i	−0.287838	−	0.957679i	$-0.592937\pi$
$257$	6.37428	−	3.68019i	0.397617	−	0.229564i	0.685455	+	0.728115i	$0.259603\pi$
$258$	1.56924	+	16.8111i	0.0976963	+	1.04661i
$259$	0.458808	−	0.122937i	0.0285089	−	0.00763894i
$260$	−8.13603	+	5.19729i	−0.504575	+	0.322322i
$261$	7.15431	+	16.7769i	0.442841	+	1.03846i
$262$	5.05649	+	17.3084i	0.312391	+	1.06932i
$263$	8.66310	+	5.00164i	0.534190	+	0.308415i	0.742721	−	0.669601i	$-0.233535\pi$
$263$	8.66310	+	5.00164i	0.534190	+	0.308415i	−0.208531	+	0.978016i	$0.566868\pi$
$264$	−5.22150	+	12.8611i	−0.321361	+	0.791546i
$265$	−2.62704	+	1.51672i	−0.161378	+	0.0931714i
$266$	−6.22608	−	5.95285i	−0.381746	−	0.364993i
$267$	3.21133	−	3.70042i	0.196530	−	0.226462i
$268$	4.97139	+	4.54422i	0.303676	+	0.277582i
$269$	18.1059	+	18.1059i	1.10394	+	1.10394i	0.993931	+	0.110005i	$0.0350868\pi$
$269$	18.1059	+	18.1059i	1.10394	+	1.10394i	0.110005	+	0.993931i	$0.464913\pi$
$270$	−2.09591	+	7.04323i	−0.127553	+	0.428638i
$271$		−	9.96334i		−	0.605230i	−0.953113	−	0.302615i	$-0.902140\pi$
$271$		−	9.96334i		−	0.605230i	0.953113	−	0.302615i	$-0.0978596\pi$
$272$	−11.6712	+	8.21509i	−0.707671	+	0.498113i
$273$	−2.88896	−	40.8262i	−0.174848	−	2.47092i
$274$	−15.3029	+	0.343317i	−0.924480	+	0.0207406i
$275$	−2.73683	−	0.733331i	−0.165037	−	0.0442215i
$276$	−11.8186	−	9.36122i	−0.711394	−	0.563479i
$277$	19.0316	−	5.09949i	1.14350	−	0.306399i	0.363140	−	0.931735i	$-0.381705\pi$
$277$	19.0316	−	5.09949i	1.14350	−	0.306399i	0.780356	+	0.625336i	$0.215038\pi$
$278$	−8.12566	−	27.8142i	−0.487345	−	1.66819i
$279$	13.7569	+	17.5478i	0.823602	+	1.05056i
$280$	9.10989	−	10.4265i	0.544420	−	0.623105i
$281$	−2.89822	+	5.01986i	−0.172893	+	0.299460i	−0.939430	−	0.342740i	$-0.888645\pi$
$281$	−2.89822	+	5.01986i	−0.172893	+	0.299460i	0.766537	+	0.642200i	$0.221978\pi$
$282$	−0.231202	+	0.278810i	−0.0137679	+	0.0166029i
$283$	−1.47671	−	0.395682i	−0.0877811	−	0.0235209i	0.214661	−	0.976689i	$-0.431135\pi$
$283$	−1.47671	−	0.395682i	−0.0877811	−	0.0235209i	−0.302442	+	0.953168i	$0.597802\pi$
$284$	−10.0988	−	5.24135i	−0.599255	−	0.311017i
$285$	−2.11591	−	0.409465i	−0.125335	−	0.0242546i
$286$	−10.0445	−	16.5300i	−0.593946	−	0.977438i
$287$	−40.2613			−2.37655
$288$	−16.3550	−	4.52910i	−0.963730	−	0.266880i
$289$	4.26846			0.251086
$290$	−4.46481	−	7.34760i	−0.262183	−	0.431466i
$291$	−9.27416	−	26.8615i	−0.543661	−	1.57465i
$292$	−21.0056	−	10.9020i	−1.22926	−	0.637993i
$293$	−8.91105	−	2.38771i	−0.520589	−	0.139491i	−0.0110500	−	0.999939i	$-0.503517\pi$
$293$	−8.91105	−	2.38771i	−0.520589	−	0.139491i	−0.509539	+	0.860448i	$0.670184\pi$
$294$	14.4376	+	38.9614i	0.842021	+	2.27227i
$295$	3.07980	−	5.33437i	0.179313	−	0.310579i
$296$	0.206675	+	0.180576i	0.0120128	+	0.0104958i
$297$	−14.0134	−	4.51460i	−0.813138	−	0.261964i
$298$	6.16369	+	21.0984i	0.357053	+	1.22220i
$299$	20.2935	−	5.43763i	1.17360	−	0.314466i
$300$	0.504967	−	3.42710i	0.0291543	−	0.197864i
$301$	32.5924	+	8.73311i	1.87860	+	0.503368i
$302$	−20.5541	+	0.461128i	−1.18276	+	0.0265349i
$303$	17.2319	+	8.38684i	0.989947	+	0.481811i
$304$	0.852220	−	4.90363i	0.0488782	−	0.281242i
$305$			14.2841i			0.817902i
$306$	−9.60475	−	11.7011i	−0.549067	−	0.668909i
$307$	4.34072	+	4.34072i	0.247738	+	0.247738i	0.820042	−	0.572304i	$-0.193950\pi$
$307$	4.34072	+	4.34072i	0.247738	+	0.247738i	−0.572304	+	0.820042i	$0.693950\pi$
$308$	20.4749	+	18.7156i	1.16667	+	1.06642i
$309$	−25.7355	−	4.98028i	−1.46404	−	0.283318i
$310$	−7.59731	−	7.26390i	−0.431498	−	0.412562i
$311$	−0.397929	+	0.229744i	−0.0225645	+	0.0130276i	−0.511240	−	0.859438i	$-0.670814\pi$
$311$	−0.397929	+	0.229744i	−0.0225645	+	0.0130276i	0.488675	+	0.872466i	$0.337480\pi$
$312$	18.6597	−	14.5278i	1.05639	−	0.822477i
$313$	−22.6285	−	13.0646i	−1.27904	−	0.738454i	−0.302368	−	0.953191i	$-0.597777\pi$
$313$	−22.6285	−	13.0646i	−1.27904	−	0.738454i	−0.976672	+	0.214737i	$0.931111\pi$
$314$	2.93776	+	10.0560i	0.165788	+	0.567493i
$315$	11.7431	+	8.81848i	0.661648	+	0.496865i
$316$	11.7620	−	7.51358i	0.661666	−	0.422672i
$317$	−3.51260	+	0.941199i	−0.197287	+	0.0528630i	−0.356110	−	0.934444i	$-0.615897\pi$
$317$	−3.51260	+	0.941199i	−0.197287	+	0.0528630i	0.158822	+	0.987307i	$0.449230\pi$
$318$	6.06175	−	4.29718i	0.339926	−	0.240974i
$319$	14.9178	−	8.61281i	0.835238	−	0.482225i
$320$	7.93535	+	1.01496i	0.443600	+	0.0567380i
$321$	−28.4101	+	2.01036i	−1.58570	+	0.112208i
$322$	−25.7492	+	15.6466i	−1.43495	+	0.871953i
$323$	3.13939	−	3.13939i	0.174680	−	0.174680i
$324$	3.50824	−	17.6548i	0.194902	−	0.980823i
$325$	3.41333	+	3.41333i	0.189338	+	0.189338i
$326$	−1.85778	+	7.61236i	−0.102893	+	0.421610i
$327$	0.589760	+	8.33436i	0.0326138	+	0.460891i
$328$	−12.9598	−	19.3185i	−0.715584	−	1.06669i
$329$	0.361920	+	0.626864i	0.0199533	+	0.0345601i
$330$	6.84177	+	1.16545i	0.376627	+	0.0641558i
$331$	3.86757	+	14.4340i	0.212581	+	0.793363i	0.987004	+	0.160695i	$0.0513735\pi$
$331$	3.86757	+	14.4340i	0.212581	+	0.793363i	−0.774423	+	0.632668i	$0.781960\pi$
$332$	21.2050	+	4.67371i	1.16378	+	0.256503i
$333$	−0.174800	+	0.232772i	−0.00957899	+	0.0127558i
$334$	15.0691	+	8.25514i	0.824544	+	0.451701i
$335$	1.68383	−	2.91648i	0.0919976	−	0.159344i
$336$	−19.8443	+	27.5031i	−1.08260	+	1.50042i
$337$	7.45234	+	12.9078i	0.405955	+	0.703135i	0.994432	−	0.105379i	$-0.0336056\pi$
$337$	7.45234	+	12.9078i	0.405955	+	0.703135i	−0.588477	+	0.808514i	$0.700272\pi$
$338$	0.326767	+	14.5651i	0.0177738	+	0.792240i
$339$	3.12451	−	16.1459i	0.169700	−	0.876923i
$340$	5.26732	+	4.81472i	0.285661	+	0.261115i
$341$	14.8910	−	14.8910i	0.806390	−	0.806390i
$342$	5.25367	+	0.516934i	0.284086	+	0.0279526i
$343$	48.7701			2.63334
$344$	6.30084	+	18.4499i	0.339719	+	0.994751i
$345$	−3.29899	+	6.77823i	−0.177612	+	0.364928i
$346$	6.87092	+	6.56939i	0.369383	+	0.353173i
$347$	1.59648	−	5.95816i	0.0857038	−	0.319851i	−0.909743	−	0.415172i	$-0.863721\pi$
$347$	1.59648	−	5.95816i	0.0857038	−	0.319851i	0.995447	+	0.0953215i	$0.0303879\pi$
$348$	12.5619	+	16.9035i	0.673390	+	0.906123i
$349$	−5.15472	−	19.2377i	−0.275926	−	1.02977i	−0.955219	−	0.295901i	$-0.904380\pi$
$349$	−5.15472	−	19.2377i	−0.275926	−	1.02977i	0.679293	−	0.733867i	$-0.262287\pi$
$350$	−6.07149	−	3.32608i	−0.324535	−	0.177786i
$351$	16.8301	+	18.5982i	0.898324	+	0.992699i
$352$	−2.38955	+	15.8489i	−0.127363	+	0.844747i
$353$	25.1226	+	14.5045i	1.33714	+	0.771998i	0.986382	−	0.164468i	$-0.0525909\pi$
$353$	25.1226	+	14.5045i	1.33714	+	0.771998i	0.350757	+	0.936466i	$0.385924\pi$
$354$	−6.29687	+	13.7111i	−0.334675	+	0.728736i
$355$	−1.47242	+	5.49513i	−0.0781477	+	0.291651i
$356$	2.60619	−	5.02150i	0.138128	−	0.266139i
$357$	−28.5967	+	9.87324i	−1.51350	+	0.522547i
$358$	−17.4478	−	4.25810i	−0.922147	−	0.225048i
$359$		−	22.6503i		−	1.19544i	−0.801706	−	0.597718i	$-0.796074\pi$
$359$		−	22.6503i		−	1.19544i	0.801706	−	0.597718i	$-0.203926\pi$
$360$	−0.451347	+	8.47327i	−0.0237881	+	0.446580i
$361$		−	17.4518i		−	0.918514i
$362$	2.86511	−	11.7400i	0.150587	−	0.617039i
$363$	0.978015	−	5.05388i	0.0513325	−	0.265260i
$364$	−14.2667	−	45.0551i	−0.747779	−	2.36153i
$365$	−3.06263	+	11.4299i	−0.160306	+	0.598268i
$366$	−3.25189	−	34.8372i	−0.169979	−	1.82097i
$367$	25.4367	+	14.6859i	1.32779	+	0.766598i	0.984957	−	0.172800i	$-0.0552813\pi$
$367$	25.4367	+	14.6859i	1.32779	+	0.766598i	0.342830	+	0.939398i	$0.388615\pi$
$368$	−15.7962	−	7.31866i	−0.823432	−	0.381511i
$369$	19.4181	−	15.2231i	1.01086	−	0.792485i
$370$	0.0659296	−	0.120349i	0.00342752	−	0.00625665i
$371$	−3.84327	−	14.3433i	−0.199533	−	0.744666i
$372$	20.1827	+	15.9862i	1.04642	+	0.828848i
$373$	−3.03439	+	11.3245i	−0.157115	+	0.586360i	0.841800	+	0.539789i	$0.181496\pi$
$373$	−3.03439	+	11.3245i	−0.157115	+	0.586360i	−0.998915	+	0.0465711i	$0.985171\pi$
$374$	−9.88054	+	10.3341i	−0.510911	+	0.534361i
$375$	−1.72773	+	0.122258i	−0.0892196	+	0.00631340i
$376$	−0.184288	+	0.375442i	−0.00950393	+	0.0193620i
$377$	−29.3471			−1.51145
$378$	−30.6477	−	18.8339i	−1.57635	−	0.968709i
$379$	3.15994	−	3.15994i	0.162315	−	0.162315i	−0.621276	−	0.783592i	$-0.713386\pi$
$379$	3.15994	−	3.15994i	0.162315	−	0.162315i	0.783592	+	0.621276i	$0.213386\pi$
$380$	−2.48606	+	0.111605i	−0.127532	+	0.00572521i
$381$	−16.1811	−	14.0424i	−0.828984	−	0.719416i
$382$	15.9664	−	0.358203i	0.816910	−	0.0183273i
$383$	−2.04373	−	3.53984i	−0.104430	−	0.180878i	0.809075	−	0.587705i	$-0.199968\pi$
$383$	−2.04373	−	3.53984i	−0.104430	−	0.180878i	−0.913505	+	0.406827i	$0.866635\pi$
$384$	−19.5845	−	0.668820i	−0.999417	−	0.0341306i
$385$	6.93495	−	12.0117i	0.353438	−	0.612172i
$386$	5.82681	−	10.6364i	0.296577	−	0.541377i
$387$	−19.0214	+	8.11148i	−0.966914	+	0.412330i
$388$	−17.6648	−	27.6531i	−0.896792	−	1.40387i
$389$	2.17205	+	8.10622i	0.110128	+	0.411001i	0.998876	−	0.0473931i	$-0.0150913\pi$
$389$	2.17205	+	8.10622i	0.110128	+	0.411001i	−0.888749	+	0.458395i	$0.848425\pi$
$390$	−9.10182	−	7.54766i	−0.460888	−	0.382191i
$391$	−7.76480	−	13.4490i	−0.392683	−	0.680146i
$392$	26.7288	+	39.8432i	1.35001	+	2.01239i
$393$	−18.2986	+	12.3647i	−0.923043	+	0.623717i
$394$	31.9225	+	7.79061i	1.60823	+	0.392485i
$395$	−4.93456	−	4.93456i	−0.248285	−	0.248285i
$396$	−16.9516	−	1.28481i	−0.851851	−	0.0645640i
$397$	20.9845	−	20.9845i	1.05318	−	1.05318i	0.0546772	−	0.998504i	$-0.482587\pi$
$397$	20.9845	−	20.9845i	1.05318	−	1.05318i	0.998504	−	0.0546772i	$-0.0174130\pi$
$398$	−1.59245	−	2.62065i	−0.0798224	−	0.131361i
$399$	4.61689	−	9.48605i	0.231134	−	0.474896i
$400$	−0.358416	−	3.98391i	−0.0179208	−	0.199195i
$401$	7.10219	−	4.10045i	0.354666	−	0.204767i	−0.312072	−	0.950058i	$-0.601023\pi$
$401$	7.10219	−	4.10045i	0.354666	−	0.204767i	0.666739	+	0.745292i	$0.267690\pi$
$402$	−3.44271	+	7.49631i	−0.171707	+	0.373882i
$403$	−34.6554	+	9.28589i	−1.72631	+	0.462563i
$404$	21.6106	+	4.76309i	1.07517	+	0.236973i
$405$	−8.99806	+	0.186999i	−0.447117	+	0.00929208i
$406$	40.3991	−	11.8022i	2.00497	−	0.585733i
$407$	0.238096	+	0.137465i	0.0118020	+	0.00681387i
$408$	−13.9425	−	10.5434i	−0.690258	−	0.521976i
$409$	13.2939	−	7.67526i	0.657343	−	0.379517i	−0.133921	−	0.990992i	$-0.542757\pi$
$409$	13.2939	−	7.67526i	0.657343	−	0.379517i	0.791264	+	0.611475i	$0.209423\pi$
$410$	−8.03812	+	8.40706i	−0.396974	+	0.415195i
$411$	−6.11810	−	17.7204i	−0.301784	−	0.874082i
$412$	−30.2377	+	1.35744i	−1.48970	+	0.0668762i
$413$	21.3210	+	21.3210i	1.04914	+	1.04914i
$414$	6.50274	−	17.2824i	0.319592	−	0.849383i
$415$		−	10.8570i		−	0.532949i
$416$	17.0264	−	21.3485i	0.834787	−	1.04669i
$417$	29.4054	−	19.8698i	1.43999	−	0.973028i
$418$	−0.111828	−	4.98458i	−0.00546970	−	0.243804i
$419$	−24.3166	−	6.51563i	−1.18795	−	0.318309i	−0.389872	−	0.920869i	$-0.627481\pi$
$419$	−24.3166	−	6.51563i	−1.18795	−	0.318309i	−0.798074	+	0.602560i	$0.794148\pi$
$420$	15.5649	+	6.72970i	0.759488	+	0.328376i
$421$	−16.3239	+	4.37398i	−0.795580	+	0.213175i	−0.633642	−	0.773626i	$-0.718441\pi$
$421$	−16.3239	+	4.37398i	−0.795580	+	0.213175i	−0.161937	+	0.986801i	$0.551774\pi$
$422$	5.64435	−	1.64894i	0.274763	−	0.0802692i
$423$	−0.411578	−	0.165492i	−0.0200116	−	0.00804652i
$424$	5.64520	−	6.46110i	0.274155	−	0.313779i
$425$	1.78406	−	3.09009i	0.0865398	−	0.149891i
$426$	2.34004	−	13.7372i	0.113375	−	0.665570i
$427$	−67.5406	−	18.0974i	−3.26852	−	0.875796i
$428$	−31.3529	+	9.92789i	−1.51550	+	0.479883i
$429$	15.5269	−	17.8917i	0.749647	−	0.863820i
$430$	8.33062	−	5.06215i	0.401738	−	0.244119i
$431$	22.2414			1.07133			0.535664	−	0.844431i	$-0.320061\pi$
$431$	22.2414			1.07133			0.535664	+	0.844431i	$0.320061\pi$
$432$	−0.828232	−	20.7681i	−0.0398483	−	0.999206i
$433$	11.0962			0.533249			0.266625	−	0.963800i	$-0.414092\pi$
$433$	11.0962			0.533249			0.266625	+	0.963800i	$0.414092\pi$
$434$	43.9721	−	26.7199i	2.11073	−	1.28260i
$435$	6.90175	−	7.95290i	0.330913	−	0.381312i
$436$	2.91244	+	9.19766i	0.139481	+	0.440488i
$437$	5.23097	+	1.40163i	0.250231	+	0.0670493i
$438$	4.86730	−	28.5735i	0.232568	−	1.36529i
$439$	−2.14581	+	3.71665i	−0.102414	+	0.177386i	−0.912679	−	0.408678i	$-0.865990\pi$
$439$	−2.14581	+	3.71665i	−0.102414	+	0.177386i	0.810265	+	0.586064i	$0.199323\pi$
$440$	7.99585	−	0.538880i	0.381187	−	0.0256901i
$441$	−40.0486	+	31.3968i	−1.90708	+	1.49509i
$442$	23.3811	−	6.83057i	1.11213	−	0.324897i
$443$	−10.2275	+	2.74044i	−0.485922	+	0.130202i	−0.493459	−	0.869769i	$-0.664268\pi$
$443$	−10.2275	+	2.74044i	−0.485922	+	0.130202i	0.00753673	+	0.999972i	$0.497601\pi$
$444$	−0.133396	+	0.308527i	−0.00633071	+	0.0146421i
$445$	−2.73238	−	0.732139i	−0.129527	−	0.0347067i
$446$	0.308459	+	13.7491i	0.0146059	+	0.651038i
$447$	−22.3054	+	15.0722i	−1.05501	+	0.712889i
$448$	−14.8530	+	36.2355i	−0.701737	+	1.71197i
$449$			2.35873i			0.111315i	0.998450	+	0.0556577i	$0.0177255\pi$
$449$			2.35873i			0.111315i	−0.998450	+	0.0556577i	$0.982274\pi$
$450$	4.18591	−	0.691508i	0.197326	−	0.0325980i
$451$	−16.4781	−	16.4781i	−0.775923	−	0.775923i
$452$	−0.851625	−	18.9704i	−0.0400571	−	0.892293i
$453$	−8.21755	−	23.8012i	−0.386094	−	1.11828i
$454$	7.23712	−	7.56930i	0.339655	−	0.355245i
$455$	−20.4642	+	11.8150i	−0.959375	+	0.553895i
$456$	6.03782	−	0.838166i	0.282747	−	0.0392507i
$457$	13.0110	+	7.51189i	0.608628	+	0.351391i	0.772428	−	0.635102i	$-0.219042\pi$
$457$	13.0110	+	7.51189i	0.608628	+	0.351391i	−0.163800	+	0.986493i	$0.552375\pi$
$458$	23.6198	−	6.90028i	1.10368	−	0.322429i
$459$	10.0591	−	15.5745i	0.469518	−	0.726958i
$460$	−1.87358	+	8.50059i	−0.0873561	+	0.396342i
$461$	−32.8546	+	8.80336i	−1.53019	+	0.410013i	−0.923081	−	0.384605i	$-0.874338\pi$
$461$	−32.8546	+	8.80336i	−1.53019	+	0.410013i	−0.607109	+	0.794618i	$0.707671\pi$
$462$	−14.1790	+	30.8739i	−0.659666	+	1.43639i
$463$	0.865378	−	0.499626i	0.0402175	−	0.0232196i	−0.479756	−	0.877402i	$-0.659275\pi$
$463$	0.865378	−	0.499626i	0.0402175	−	0.0232196i	0.519974	+	0.854182i	$0.325942\pi$
$464$	18.6672	+	15.5856i	0.866602	+	0.723543i
$465$	5.63372	−	11.5752i	0.261257	−	0.536789i
$466$	−5.94479	−	9.78315i	−0.275387	−	0.453196i
$467$	21.5161	−	21.5161i	0.995647	−	0.995647i	−0.00434388	−	0.999991i	$-0.501383\pi$
$467$	21.5161	−	21.5161i	0.995647	−	0.995647i	0.999991	+	0.00434388i	$0.00138270\pi$
$468$	23.9166	+	16.3358i	1.10554	+	0.755122i
$469$	11.6569	+	11.6569i	0.538266	+	0.538266i
$470$	0.203154	+	0.0495792i	0.00937081	+	0.00228692i
$471$	−10.6313	+	7.18376i	−0.489864	+	0.331010i
$472$	−3.36736	+	17.0935i	−0.154995	+	0.786791i
$473$	9.76511	+	16.9137i	0.449000	+	0.777691i
$474$	13.1582	+	10.9114i	0.604378	+	0.501179i
$475$	0.322044	+	1.20188i	0.0147764	+	0.0551463i
$476$	−29.4394	+	18.8059i	−1.34935	+	0.861965i
$477$	7.27694	+	5.46462i	0.333188	+	0.250208i
$478$	2.61246	−	4.76884i	0.119491	−	0.218121i
$479$	13.8795	−	24.0401i	0.634173	−	1.09842i	−0.352517	−	0.935805i	$-0.614674\pi$
$479$	13.8795	−	24.0401i	0.634173	−	1.09842i	0.986690	−	0.162614i	$-0.0519924\pi$
$480$	1.78111	+	9.63471i	0.0812961	+	0.439762i
$481$	−0.234197	−	0.405641i	−0.0106785	−	0.0184956i
$482$	−11.5540	+	0.259213i	−0.526272	+	0.0118068i
$483$	−27.8704	−	24.1867i	−1.26815	−	1.10053i
$484$	−0.266571	−	5.93801i	−0.0121168	−	0.269909i
$485$	−11.6014	+	11.6014i	−0.526792	+	0.526792i
$486$	21.9027	−	2.50456i	0.993526	−	0.113609i
$487$	2.94197			0.133313			0.0666567	−	0.997776i	$-0.478767\pi$
$487$	2.94197			0.133313			0.0666567	+	0.997776i	$0.478767\pi$
$488$	−13.0571	−	38.2333i	−0.591067	−	1.73074i
$489$	−9.57289	+	0.677401i	−0.432901	+	0.0306331i
$490$	16.5781	−	17.3391i	0.748924	−	0.783299i
$491$	−2.00064	+	7.46649i	−0.0902877	+	0.336958i	−0.996263	−	0.0863725i	$-0.972472\pi$
$491$	−2.00064	+	7.46649i	−0.0902877	+	0.336958i	0.905975	+	0.423331i	$0.139139\pi$
$492$	17.6901	−	22.3338i	0.797532	−	1.00689i
$493$	5.61446	+	20.9534i	0.252863	+	0.943696i
$494$	−4.08109	+	7.44969i	−0.183617	+	0.335178i
$495$	1.19698	+	8.41542i	0.0538004	+	0.378245i
$496$	26.9752	+	12.4981i	1.21122	+	0.561183i
$497$	−24.1176	−	13.9243i	−1.08182	−	0.624591i
$498$	2.47169	+	26.4790i	0.110759	+	1.18655i
$499$	−8.07683	+	30.1431i	−0.361569	+	1.34939i	0.510445	+	0.859911i	$0.329481\pi$
$499$	−8.07683	+	30.1431i	−0.361569	+	1.34939i	−0.872013	+	0.489482i	$0.837186\pi$
$500$	−1.90669	+	0.603755i	−0.0852699	+	0.0270008i
$501$	−3.99815	+	20.6604i	−0.178624	+	0.923038i
$502$	−3.42067	+	14.0164i	−0.152672	+	0.625584i
$503$			9.79790i			0.436867i	0.975852	+	0.218433i	$0.0700946\pi$
$503$			9.79790i			0.436867i	−0.975852	+	0.218433i	$0.929905\pi$
$504$	−39.4931	−	12.8695i	−1.75916	−	0.573253i
$505$		−	11.0646i		−	0.492369i
$506$	−16.9424	−	4.13476i	−0.753183	−	0.183812i
$507$	−16.8661	+	5.82316i	−0.749051	+	0.258616i
$508$	−21.9579	−	11.3963i	−0.974225	−	0.505629i
$509$	−8.89275	+	33.1882i	−0.394164	+	1.47104i	0.429035	+	0.903288i	$0.358854\pi$
$509$	−8.89275	+	33.1882i	−0.394164	+	1.47104i	−0.823199	+	0.567753i	$0.807813\pi$
$510$	−3.64765	+	7.94254i	−0.161520	+	0.351702i
$511$	−50.1648	−	28.9626i	−2.21916	−	1.28123i
$512$	−22.1679	+	4.53705i	−0.979691	+	0.200511i
$513$	1.36002	+	6.32082i	0.0600464	+	0.279071i
$514$	9.12906	+	5.00108i	0.402666	+	0.220588i
$515$	3.91699	+	14.6184i	0.172603	+	0.644164i
$516$	−19.1650	+	14.2426i	−0.843692	+	0.626994i
$517$	−0.108436	+	0.404689i	−0.00476901	+	0.0177982i
$518$	0.485527	+	0.464219i	0.0213328	+	0.0203966i
$519$	−5.09507	+	10.4685i	−0.223649	+	0.459517i
$520$	−12.2564	−	6.01613i	−0.537479	−	0.263825i
$521$	−27.2730			−1.19485			−0.597426	−	0.801924i	$-0.703810\pi$
$521$	−27.2730			−1.19485			−0.597426	+	0.801924i	$0.703810\pi$
$522$	−15.0220	+	20.9675i	−0.657496	+	0.917721i
$523$	2.76773	−	2.76773i	0.121025	−	0.121025i	−0.644001	−	0.765025i	$-0.722727\pi$
$523$	2.76773	−	2.76773i	0.121025	−	0.121025i	0.765025	+	0.644001i	$0.222727\pi$
$524$	−17.2051	+	18.8225i	−0.751608	+	0.822263i
$525$	1.61089	−	8.32428i	0.0703052	−	0.363301i
$526$	0.317301	+	14.1432i	0.0138350	+	0.616674i
$527$	13.2600	+	22.9670i	0.577615	+	1.00046i
$528$	−19.3783	+	3.13460i	−0.843332	+	0.136416i
$529$	−2.02871	+	3.51382i	−0.0882046	+	0.152775i
$530$	−3.76237	−	2.06110i	−0.163427	−	0.0895284i
$531$	−18.3448	−	2.22150i	−0.796096	−	0.0964047i
$532$	2.62205	−	11.8965i	0.113680	−	0.515777i
$533$	10.2756	+	38.3491i	0.445087	+	1.66109i
$534$	6.83064	+	1.16355i	0.295591	+	0.0503519i
$535$	8.22179	+	14.2406i	0.355459	+	0.615673i
$536$	−1.84105	+	9.34558i	−0.0795212	+	0.403668i
$537$	−1.55263	−	21.9415i	−0.0670009	−	0.946844i
$538$	−8.58542	+	35.1793i	−0.370144	+	1.51669i
$539$	33.9851	+	33.9851i	1.46384	+	1.46384i
$540$	−10.0515	+	2.63947i	−0.432549	+	0.113585i
$541$	−25.0455	+	25.0455i	−1.07679	+	1.07679i	−0.0799969	+	0.996795i	$0.525491\pi$
$541$	−25.0455	+	25.0455i	−1.07679	+	1.07679i	−0.996795	+	0.0799969i	$0.974509\pi$
$542$	12.0415	−	7.31707i	0.517225	−	0.314295i
$543$	14.7635	−	1.04470i	0.633564	−	0.0448325i
$544$	−18.4999	−	8.07240i	−0.793176	−	0.346101i
$545$	4.17760	−	2.41194i	0.178949	−	0.103316i
$546$	47.2200	−	33.4743i	2.02083	−	1.43257i
$547$	−32.2110	+	8.63091i	−1.37724	+	0.369031i	−0.870119	−	0.492842i	$-0.835958\pi$
$547$	−32.2110	+	8.63091i	−1.37724	+	0.369031i	−0.507124	+	0.861873i	$0.669292\pi$
$548$	−11.6533	−	18.2426i	−0.497806	−	0.779283i
$549$	39.4177	−	16.8092i	1.68231	−	0.717401i
$550$	−1.12364	−	3.84623i	−0.0479120	−	0.164004i
$551$	−6.55120	−	3.78234i	−0.279090	−	0.161133i
$552$	2.63421	−	21.1585i	0.112119	−	0.900566i
$553$	29.5845	−	17.0806i	1.25806	−	0.726341i
$554$	20.1399	+	19.2560i	0.855662	+	0.818111i
$555$	0.165004	+	0.0319312i	0.00700403	+	0.00135540i
$556$	27.6482	−	30.2472i	1.17254	−	1.28277i
$557$	6.30361	+	6.30361i	0.267092	+	0.267092i	0.827928	−	0.560835i	$-0.189520\pi$
$557$	6.30361	+	6.30361i	0.267092	+	0.267092i	−0.560835	+	0.827928i	$0.689520\pi$
$558$	−11.1048	+	29.5133i	−0.470103	+	1.24940i
$559$		−	33.2734i		−	1.40731i
$560$	19.2916	+	3.35276i	0.815218	+	0.141680i
$561$	−15.7449	−	7.66312i	−0.664752	−	0.323537i
$562$	−8.19534	+	0.183861i	−0.345699	+	0.00775571i
$563$	−9.08508	−	2.43434i	−0.382891	−	0.102595i	0.0622393	−	0.998061i	$-0.480176\pi$
$563$	−9.08508	−	2.43434i	−0.382891	−	0.102595i	−0.445130	+	0.895466i	$0.646842\pi$
$564$	−0.506757	−	0.0746683i	−0.0213383	−	0.00314410i
$565$	−9.17123	+	2.45742i	−0.385837	+	0.103385i
$566$	−0.606279	−	2.07530i	−0.0254838	−	0.0872315i
$567$	10.5160	−	42.7832i	0.441632	−	1.79673i
$568$	−1.08199	−	16.0544i	−0.0453993	−	0.673630i
$569$	4.68820	−	8.12021i	0.196540	−	0.340417i	−0.750864	−	0.660456i	$-0.770363\pi$
$569$	4.68820	−	8.12021i	0.196540	−	0.340417i	0.947404	+	0.320039i	$0.103696\pi$
$570$	−1.05905	−	2.85795i	−0.0443587	−	0.119706i
$571$	−9.63374	−	2.58135i	−0.403159	−	0.108026i	0.0515406	−	0.998671i	$-0.483587\pi$
$571$	−9.63374	−	2.58135i	−0.403159	−	0.108026i	−0.454700	+	0.890645i	$0.650254\pi$
$572$	12.6010	−	24.2792i	0.526876	−	1.01516i
$573$	6.38337	+	18.4887i	0.266669	+	0.772377i
$574$	−29.5678	−	48.6588i	−1.23414	−	2.03098i
$575$	4.35231			0.181504
$576$	−6.53735	−	23.0925i	−0.272390	−	0.962187i
$577$	−20.7642			−0.864426			−0.432213	−	0.901772i	$-0.642267\pi$
$577$	−20.7642			−0.864426			−0.432213	+	0.901772i	$0.642267\pi$
$578$	3.13475	+	5.15876i	0.130388	+	0.214576i
$579$	14.5829	+	2.82206i	0.606046	+	0.117281i
$580$	5.60119	−	10.7921i	0.232577	−	0.448119i
$581$	51.3361	+	13.7555i	2.12978	+	0.570673i
$582$	25.6533	−	30.9356i	1.06336	−	1.28232i
$583$	4.29744	−	7.44338i	0.177982	−	0.308273i
$584$	−2.25054	−	33.3933i	−0.0931281	−	1.38183i
$585$	5.40255	−	13.4361i	0.223368	−	0.555513i
$586$	−3.65854	−	12.5232i	−0.151133	−	0.517329i
$587$	24.3560	−	6.52617i	1.00528	−	0.269364i	0.281624	−	0.959525i	$-0.409127\pi$
$587$	24.3560	−	6.52617i	1.00528	−	0.269364i	0.723656	+	0.690161i	$0.242460\pi$
$588$	−36.4848	+	46.0622i	−1.50461	+	1.89957i
$589$	−8.93298	−	2.39358i	−0.368077	−	0.0986259i
$590$	8.70880	−	0.195381i	0.358536	−	0.00804369i
$591$	2.84069	+	40.1440i	0.116850	+	1.65131i
$592$	−0.0664584	+	0.382398i	−0.00273142	+	0.0157165i
$593$		−	18.7439i		−	0.769718i	−0.922975	−	0.384859i	$-0.874250\pi$
$593$		−	18.7439i		−	0.769718i	0.922975	−	0.384859i	$-0.125750\pi$
$594$	−4.83516	−	20.2518i	−0.198389	−	0.830940i
$595$	12.3508	+	12.3508i	0.506333	+	0.506333i
$596$	−20.9724	+	22.9439i	−0.859064	+	0.939820i
$597$	2.46162	−	2.83654i	0.100748	−	0.116092i
$598$	21.4753	+	20.5329i	0.878192	+	0.839652i
$599$	−31.9192	+	18.4286i	−1.30418	+	0.752971i	−0.981119	−	0.193406i	$-0.938047\pi$
$599$	−31.9192	+	18.4286i	−1.30418	+	0.752971i	−0.323065	+	0.946377i	$0.604713\pi$
$600$	4.51276	−	1.90657i	0.184233	−	0.0778353i
$601$	22.5318	+	13.0087i	0.919091	+	0.530637i	0.883345	−	0.468723i	$-0.155286\pi$
$601$	22.5318	+	13.0087i	0.919091	+	0.530637i	0.0357460	+	0.999361i	$0.488619\pi$
$602$	13.3812	+	45.8040i	0.545377	+	1.86683i
$603$	−10.0297	−	1.21457i	−0.408442	−	0.0494610i
$604$	−15.6522	−	24.5026i	−0.636880	−	0.996995i
$605$	−2.87073	+	0.769209i	−0.116712	+	0.0312728i
$606$	2.51896	+	26.9854i	0.102326	+	1.09621i
$607$	−6.43241	+	3.71375i	−0.261083	+	0.150737i	−0.624829	−	0.780762i	$-0.714831\pi$
$607$	−6.43241	+	3.71375i	−0.261083	+	0.150737i	0.363745	+	0.931498i	$0.381498\pi$
$608$	6.55228	−	2.57124i	0.265730	−	0.104278i
$609$	28.8601	+	42.7102i	1.16947	+	1.73070i
$610$	−17.2634	+	10.4902i	−0.698974	+	0.424735i
$611$	0.504722	−	0.504722i	0.0204189	−	0.0204189i
$612$	7.08801	−	20.2014i	0.286516	−	0.816592i
$613$	20.4044	+	20.4044i	0.824128	+	0.824128i	0.986697	−	0.162569i	$-0.0519781\pi$
$613$	20.4044	+	20.4044i	0.824128	+	0.824128i	−0.162569	+	0.986697i	$0.551978\pi$
$614$	−2.05827	+	8.43391i	−0.0830651	+	0.340365i
$615$	−12.8090	−	6.23418i	−0.516508	−	0.251386i
$616$	−7.58245	+	38.4902i	−0.305506	+	1.55082i
$617$	9.04802	+	15.6716i	0.364260	+	0.630916i	0.988657	−	0.150191i	$-0.0479888\pi$
$617$	9.04802	+	15.6716i	0.364260	+	0.630916i	−0.624397	+	0.781107i	$0.714655\pi$
$618$	−12.8811	−	34.7609i	−0.518154	−	1.39829i
$619$	−4.69688	−	17.5290i	−0.188784	−	0.704551i	−0.993789	−	0.111283i	$-0.964504\pi$
$619$	−4.69688	−	17.5290i	−0.188784	−	0.704551i	0.805005	−	0.593268i	$-0.202163\pi$
$620$	3.19953	−	14.5165i	0.128496	−	0.582998i
$621$	22.5871	+	1.12725i	0.906391	+	0.0452351i
$622$	−0.569903	−	0.312204i	−0.0228510	−	0.0125182i
$623$	6.92367	−	11.9922i	0.277391	−	0.480456i
$624$	31.2617	+	11.8824i	1.25147	+	0.475676i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−0.828809	−	36.9429i	−0.0331259	−	1.47654i
$627$	5.77204	−	1.99284i	0.230513	−	0.0795864i
$628$	−9.99597	+	10.9356i	−0.398883	+	0.436379i
$629$	−0.244818	+	0.244818i	−0.00976153	+	0.00976153i
$630$	−2.03369	+	20.6687i	−0.0810242	+	0.823461i
$631$	22.0627			0.878304			0.439152	−	0.898413i	$-0.355279\pi$
$631$	22.0627			0.878304			0.439152	+	0.898413i	$0.355279\pi$
$632$	17.7188	+	8.69736i	0.704815	+	0.345962i
$633$	4.03218	+	5.96725i	0.160265	+	0.237177i
$634$	−3.71716	−	3.55404i	−0.147627	−	0.141149i
$635$	−3.20148	+	11.9481i	−0.127047	+	0.474145i
$636$	9.64522	+	4.17025i	0.382458	+	0.165361i
$637$	−21.1929	−	79.0928i	−0.839691	−	3.13377i
$638$	21.3649	+	11.7041i	0.845844	+	0.463370i
$639$	16.8969	−	2.40336i	0.668430	−	0.0950755i
$640$	4.60106	+	10.3359i	0.181873	+	0.408561i
$641$	31.5243	+	18.2005i	1.24513	+	0.718878i	0.970135	−	0.242567i	$-0.0779893\pi$
$641$	31.5243	+	18.2005i	1.24513	+	0.718878i	0.274998	+	0.961445i	$0.411323\pi$
$642$	−23.2940	−	32.8593i	−0.919341	−	1.29685i
$643$	7.28368	−	27.1831i	0.287240	−	1.07200i	−0.659946	−	0.751313i	$-0.729421\pi$
$643$	7.28368	−	27.1831i	0.287240	−	1.07200i	0.947187	−	0.320683i	$-0.103912\pi$
$644$	−37.8203	−	19.6290i	−1.49033	−	0.773490i
$645$	9.01690	+	7.82512i	0.355040	+	0.308114i
$646$	6.09975	+	1.48863i	0.239991	+	0.0585693i
$647$			24.9360i			0.980334i	0.871629	+	0.490167i	$0.163064\pi$
$647$			24.9360i			0.980334i	−0.871629	+	0.490167i	$0.836936\pi$
$648$	23.9136	−	8.72569i	0.939417	−	0.342777i
$649$			17.4525i			0.685069i
$650$	−1.61853	+	6.63203i	−0.0634839	+	0.260129i
$651$	47.5945	+	41.3039i	1.86538	+	1.61883i
$652$	−10.5645	+	3.34524i	−0.413737	+	0.131010i
$653$	−3.48014	+	12.9880i	−0.136188	+	0.508262i	0.863802	+	0.503832i	$0.168077\pi$
$653$	−3.48014	+	12.9880i	−0.136188	+	0.508262i	−0.999990	+	0.00442996i	$0.998590\pi$
$654$	−9.63960	+	6.83352i	−0.376938	+	0.267212i
$655$	11.0423	+	6.37525i	0.431456	+	0.249102i
$656$	13.8302	−	29.8504i	0.539980	−	1.16546i
$657$	35.1456	−	4.99900i	1.37116	−	0.195030i
$658$	−0.491820	+	0.897777i	−0.0191731	+	0.0349990i
$659$	−3.41761	−	12.7547i	−0.133131	−	0.496853i	0.866867	−	0.498539i	$-0.166130\pi$
$659$	−3.41761	−	12.7547i	−0.133131	−	0.496853i	−0.999999	+	0.00168619i	$0.999463\pi$
$660$	3.61605	+	9.12470i	0.140755	+	0.355179i
$661$	−4.13609	+	15.4361i	−0.160875	+	0.600395i	0.837655	+	0.546200i	$0.183926\pi$
$661$	−4.13609	+	15.4361i	−0.160875	+	0.600395i	−0.998530	+	0.0541952i	$0.982741\pi$
$662$	−14.6042	+	15.2745i	−0.567609	+	0.593662i
$663$	16.7029	+	24.7187i	0.648686	+	0.959994i
$664$	9.92442	+	29.0603i	0.385142	+	1.12776i
$665$	−6.09100			−0.236199
$666$	−0.409696	−	0.0403119i	−0.0158754	−	0.00156205i
$667$	−18.7101	+	18.7101i	−0.724457	+	0.724457i
$668$	1.08975	+	24.2747i	0.0421636	+	0.939217i
$669$	−15.9212	+	5.49691i	−0.615547	+	0.212523i
$670$	4.76140	−	0.106821i	0.183949	−	0.00412686i
$671$	−20.2360	−	35.0498i	−0.781203	−	1.35308i
$672$	−47.8133	−	3.78509i	−1.84444	−	0.146013i
$673$	12.9879	−	22.4956i	0.500645	−	0.867143i	−0.499355	−	0.866398i	$-0.666430\pi$
$673$	12.9879	−	22.4956i	0.500645	−	0.867143i	1.00000		0.000744938i	$-0.000237121\pi$
$674$	−10.1271	+	18.4862i	−0.390082	+	0.712063i
$675$	2.37055	+	4.62391i	0.0912423	+	0.177974i
$676$	−17.3631	+	11.0916i	−0.667813	+	0.426598i
$677$	−9.40525	−	35.1009i	−0.361473	−	1.34904i	−0.872140	−	0.489257i	$-0.837268\pi$
$677$	−9.40525	−	35.1009i	−0.361473	−	1.34904i	0.510667	−	0.859779i	$-0.329399\pi$
$678$	21.8081	−	8.08129i	0.837537	−	0.310360i
$679$	−40.1573	−	69.5544i	−1.54109	−	2.66925i
$680$	−1.95064	+	9.90189i	−0.0748036	+	0.379720i
$681$	11.5326	+	5.61295i	0.441929	+	0.215089i
$682$	28.9328	+	7.06096i	1.10789	+	0.270378i
$683$	25.8204	+	25.8204i	0.987990	+	0.987990i	0.999929	−	0.0119383i	$-0.00380016\pi$
$683$	25.8204	+	25.8204i	0.987990	+	0.987990i	−0.0119383	+	0.999929i	$0.503800\pi$
$684$	3.23354	+	6.72910i	0.123637	+	0.257294i
$685$	−7.65336	+	7.65336i	−0.292420	+	0.292420i
$686$	35.8167	+	58.9424i	1.36749	+	2.25043i
$687$	16.8734	+	24.9710i	0.643759	+	0.952703i
$688$	−17.6708	+	21.1646i	−0.673692	+	0.806894i
$689$	−12.6812	+	7.32149i	−0.483115	+	0.278927i
$690$	−10.6148	+	0.990842i	−0.404098	+	0.0377207i
$691$	41.6922	−	11.1714i	1.58605	−	0.424980i	0.645254	−	0.763968i	$-0.276751\pi$
$691$	41.6922	−	11.1714i	1.58605	−	0.424980i	0.940791	+	0.338988i	$0.110085\pi$
$692$	−2.89362	+	13.1286i	−0.109999	+	0.499074i
$693$	−41.3079	−	5.00226i	−1.56916	−	0.190020i
$694$	8.37335	−	2.44619i	0.317848	−	0.0928562i
$695$	−17.7446	−	10.2449i	−0.673092	−	0.388610i
$696$	−11.2037	+	27.5960i	−0.424676	+	1.04602i
$697$	25.4149	−	14.6733i	0.962660	−	0.555792i
$698$	19.4646	−	20.3580i	0.736745	−	0.770561i
$699$	9.18951	−	10.5891i	0.347579	−	0.400516i
$700$	−0.439070	−	9.78053i	−0.0165953	−	0.369669i
$701$	−17.0795	−	17.0795i	−0.645085	−	0.645085i	0.306716	−	0.951801i	$-0.400770\pi$
$701$	−17.0795	−	17.0795i	−0.645085	−	0.645085i	−0.951801	+	0.306716i	$0.900770\pi$
$702$	−10.1174	+	33.9990i	−0.381855	+	1.28321i
$703$		−	0.120736i		−	0.00455364i
$704$	−20.9094	+	8.75143i	−0.788054	+	0.329832i
$705$	0.0180781	+	0.255476i	0.000680860	+	0.00962177i
$706$	0.920157	+	41.0147i	0.0346306	+	1.54361i
$707$	52.3179	+	14.0185i	1.96762	+	0.527221i
$708$	−21.1953	+	2.45915i	−0.796568	+	0.0924205i
$709$	34.8242	−	9.33111i	1.30785	−	0.350437i	0.463437	−	0.886130i	$-0.346616\pi$
$709$	34.8242	−	9.33111i	1.30785	−	0.350437i	0.844413	+	0.535693i	$0.179949\pi$
$710$	−7.72263	+	2.25609i	−0.289825	+	0.0846696i
$711$	−7.81031	+	19.4241i	−0.292910	+	0.728462i
$712$	7.98285	−	0.538004i	0.299170	−	0.0201626i
$713$	−16.1742	+	28.0146i	−0.605729	+	1.04915i
$714$	−32.9340	−	27.3104i	−1.23252	−	1.02207i
$715$	−13.2112	−	3.53992i	−0.494070	−	0.132386i
$716$	−7.66744	−	24.2142i	−0.286546	−	0.904927i
$717$	6.53829	+	1.26527i	0.244177	+	0.0472525i
$718$	27.3746	−	16.6343i	1.02161	−	0.620788i
$719$	−34.0233			−1.26886			−0.634428	−	0.772982i	$-0.718764\pi$
$719$	−34.0233			−1.26886			−0.634428	+	0.772982i	$0.718764\pi$
$720$	−10.5721	+	5.67727i	−0.393998	+	0.211579i
$721$	−74.0842			−2.75904
$722$	21.0918	−	12.8166i	0.784955	−	0.476983i
$723$	−4.61932	−	13.3793i	−0.171794	−	0.497583i
$724$	16.2928	−	5.15912i	0.605516	−	0.191737i
$725$	−5.87239	−	1.57350i	−0.218095	−	0.0584384i
$726$	6.82626	−	2.52956i	0.253346	−	0.0938808i
$727$	−16.7205	+	28.9608i	−0.620130	+	1.07410i	0.369331	+	0.929298i	$0.379587\pi$
$727$	−16.7205	+	28.9608i	−0.620130	+	1.07410i	−0.989461	+	0.144799i	$0.953746\pi$
$728$	43.9751	−	50.3309i	1.62983	−	1.86539i
$729$	11.1048	+	24.6106i	0.411289	+	0.911505i
$730$	−16.0631	+	4.69268i	−0.594522	+	0.173684i
$731$	−23.7568	+	6.36561i	−0.878676	+	0.235441i
$732$	39.7152	−	29.5146i	1.46792	−	1.09089i
$733$	19.9464	+	5.34463i	0.736739	+	0.197409i	0.607628	−	0.794222i	$-0.292121\pi$
$733$	19.9464	+	5.34463i	0.736739	+	0.197409i	0.129111	+	0.991630i	$0.458788\pi$
$734$	0.931664	+	41.5276i	0.0343884	+	1.53281i
$735$	26.4178	+	12.8576i	0.974434	+	0.474261i
$736$	−2.75552	−	24.4657i	−0.101570	−	0.901817i
$737$			9.54185i			0.351479i
$738$	32.6589	+	12.2884i	1.20219	+	0.452342i
$739$	18.5144	+	18.5144i	0.681062	+	0.681062i	0.960240	−	0.279177i	$-0.0900617\pi$
$739$	18.5144	+	18.5144i	0.681062	+	0.681062i	−0.279177	+	0.960240i	$0.590062\pi$
$740$	0.193870	−	0.00870326i	0.00712680	−	0.000319938i
$741$	−10.2139	−	1.97656i	−0.375216	−	0.0726108i
$742$	14.5125	−	15.1786i	0.532770	−	0.557223i
$743$	31.3442	−	18.0966i	1.14991	−	0.663899i	0.201043	−	0.979582i	$-0.435567\pi$
$743$	31.3442	−	18.0966i	1.14991	−	0.663899i	0.948865	+	0.315683i	$0.102234\pi$
$744$	−4.49847	+	36.1326i	−0.164922	+	1.32469i
$745$	13.4601	+	7.77121i	0.493141	+	0.284715i
$746$	−15.9150	+	4.64941i	−0.582689	+	0.170227i
$747$	−29.9606	+	12.7763i	−1.09620	+	0.467462i
$748$	−19.7458	−	4.35208i	−0.721977	−	0.159128i
$749$	−77.7516	+	20.8335i	−2.84098	+	0.761239i
$750$	−1.41660	−	1.99831i	−0.0517270	−	0.0729679i
$751$	−3.12952	+	1.80683i	−0.114198	+	0.0659321i	−0.556011	−	0.831175i	$-0.687669\pi$
$751$	−3.12952	+	1.80683i	−0.114198	+	0.0659321i	0.441813	+	0.897107i	$0.354335\pi$
$752$	−0.589092	+	0.0529981i	−0.0214820	+	0.00193264i
$753$	−17.6263	+	1.24728i	−0.642338	+	0.0454534i
$754$	−21.5525	−	35.4682i	−0.784895	−	1.29168i
$755$	−10.2796	+	10.2796i	−0.374114	+	0.374114i
$756$	0.254527	−	50.8717i	0.00925707	−	1.85018i
$757$	18.0110	+	18.0110i	0.654621	+	0.654621i	0.954102	−	0.299481i	$-0.0968137\pi$
$757$	18.0110	+	18.0110i	0.654621	+	0.654621i	−0.299481	+	0.954102i	$0.596814\pi$
$758$	6.13970	+	1.49838i	0.223004	+	0.0544235i
$759$	−1.50766	−	21.3059i	−0.0547244	−	0.773354i
$760$	−1.96064	−	2.92263i	−0.0711200	−	0.106015i
$761$	13.5486	+	23.4668i	0.491136	+	0.850672i	0.999948	−	0.0102053i	$-0.00324850\pi$
$761$	13.5486	+	23.4668i	0.491136	+	0.850672i	−0.508812	+	0.860878i	$0.669915\pi$
$762$	5.08796	−	29.8689i	0.184317	−	1.08204i
$763$	6.11170	+	22.8092i	0.221258	+	0.825748i
$764$	12.1586	+	19.0335i	0.439883	+	0.688609i
$765$	−10.6268	−	1.28687i	−0.384211	−	0.0465268i
$766$	2.77726	−	5.06966i	0.100347	−	0.183174i
$767$	14.8668	−	25.7500i	0.536808	−	0.929779i
$768$	−13.5745	−	24.1606i	−0.489828	−	0.871819i
$769$	25.3967	+	43.9884i	0.915828	+	1.58626i	0.805685	+	0.592345i	$0.201798\pi$
$769$	25.3967	+	43.9884i	0.915828	+	1.58626i	0.110143	+	0.993916i	$0.464869\pi$
$770$	19.6101	−	0.439949i	0.706698	−	0.0158546i
$771$	−2.42213	+	12.5164i	−0.0872310	+	0.450765i
$772$	17.1341	−	0.769188i	0.616669	−	0.0276837i
$773$	27.2157	−	27.2157i	0.978880	−	0.978880i	−0.0209013	−	0.999782i	$-0.506654\pi$
$773$	27.2157	−	27.2157i	0.978880	−	0.978880i	0.999782	+	0.0209013i	$0.00665358\pi$
$774$	−23.7727	−	17.0318i	−0.854491	−	0.612196i
$775$	−7.43248			−0.266982
$776$	20.4479	−	41.6576i	0.734036	−	1.49542i
$777$	−0.360038	+	0.739748i	−0.0129163	+	0.0265383i
$778$	−8.20183	+	8.57829i	−0.294050	+	0.307547i
$779$	−2.64870	+	9.88509i	−0.0948996	+	0.354170i
$780$	2.43757	−	16.5432i	0.0872789	−	0.592343i
$781$	−4.17191	−	15.5698i	−0.149283	−	0.557130i
$782$	10.5517	−	19.2613i	0.377329	−	0.688783i
$783$	−30.0684	−	9.68695i	−1.07456	−	0.346183i
$784$	−28.5240	+	61.5646i	−1.01872	+	2.19874i
$785$	6.41542	+	3.70395i	0.228976	+	0.132200i
$786$	−28.3822	−	13.0346i	−1.01236	−	0.464930i
$787$	−0.509361	+	1.90096i	−0.0181567	+	0.0677619i	−0.974410	−	0.224779i	$-0.927834\pi$
$787$	−0.509361	+	1.90096i	−0.0181567	+	0.0677619i	0.956253	+	0.292541i	$0.0945007\pi$
$788$	14.0283	+	44.3023i	0.499739	+	1.57820i
$789$	−16.3776	+	5.65448i	−0.583056	+	0.201305i
$790$	2.33986	−	9.58774i	0.0832485	−	0.341116i
$791$		−	46.4786i		−	1.65259i
$792$	−10.8965	−	21.4309i	−0.387189	−	0.761514i
$793$			68.9518i			2.44855i
$794$	40.7724	+	9.95038i	1.44696	+	0.353126i
$795$	0.998236	−	5.15837i	0.0354038	−	0.182949i
$796$	1.99776	−	3.84920i	0.0708086	−	0.136431i
$797$	−0.193006	+	0.720309i	−0.00683663	+	0.0255147i	−0.969260	−	0.246039i	$-0.920871\pi$
$797$	−0.193006	+	0.720309i	−0.00683663	+	0.0255147i	0.962423	+	0.271554i	$0.0875375\pi$
$798$	14.8553	−	1.38667i	0.525870	−	0.0490876i
$799$	−0.456925	−	0.263806i	−0.0161648	−	0.00933277i
$800$	4.55164	−	3.35895i	0.160925	−	0.118757i
$801$	1.19504	+	8.40174i	0.0422246	+	0.296861i
$802$	10.1715	+	5.57217i	0.359170	+	0.196760i
$803$	−8.67758	−	32.3852i	−0.306225	−	1.14285i
$804$	−11.5882	+	1.34450i	−0.408684	+	0.0474169i
$805$	−5.51424	+	20.5794i	−0.194351	+	0.725329i
$806$	−36.6736	−	35.0642i	−1.29177	−	1.23508i
$807$	−44.2396	+	3.13050i	−1.55731	+	0.110199i
$808$	10.1142	+	29.6160i	0.355817	+	1.04189i
$809$	−22.4317			−0.788655			−0.394328	−	0.918970i	$-0.629022\pi$
$809$	−22.4317			−0.788655			−0.394328	+	0.918970i	$0.629022\pi$
$810$	−6.83417	−	10.7375i	−0.240128	−	0.377278i
$811$	26.6687	−	26.6687i	0.936464	−	0.936464i	−0.0616347	−	0.998099i	$-0.519631\pi$
$811$	26.6687	−	26.6687i	0.936464	−	0.936464i	0.998099	+	0.0616347i	$0.0196314\pi$
$812$	43.9329	+	40.1579i	1.54174	+	1.40927i
$813$	13.0334	+	11.3108i	0.457103	+	0.396687i
$814$	0.00872067	+	0.388711i	0.000305659	+	0.0136243i
$815$	2.77036	+	4.79841i	0.0970416	+	0.168081i
$816$	2.50314	−	24.5937i	0.0876273	−	0.860951i
$817$	4.28837	−	7.42768i	0.150031	−	0.259861i
$818$	19.0392	+	10.4301i	0.665690	+	0.364678i
$819$	56.6861	+	42.5684i	1.98077	+	1.48746i
$820$	−16.0638	−	3.54055i	−0.560971	−	0.123641i
$821$	−4.61739	−	17.2323i	−0.161148	−	0.601412i	−0.998500	−	0.0547484i	$-0.982564\pi$
$821$	−4.61739	−	17.2323i	−0.161148	−	0.601412i	0.837352	−	0.546664i	$-0.184102\pi$
$822$	16.9233	−	20.4080i	0.590268	−	0.711812i
$823$	3.03290	+	5.25314i	0.105720	+	0.183113i	0.914032	−	0.405641i	$-0.132952\pi$
$823$	3.03290	+	5.25314i	0.105720	+	0.183113i	−0.808312	+	0.588754i	$0.799618\pi$
$824$	−23.8471	−	35.5477i	−0.830753	−	1.23836i
$825$	4.06626	−	2.74765i	0.141569	−	0.0956608i
$826$	−10.1099	+	41.4261i	−0.351770	+	1.44140i
$827$	−2.89413	−	2.89413i	−0.100639	−	0.100639i	0.654995	−	0.755633i	$-0.272671\pi$
$827$	−2.89413	−	2.89413i	−0.100639	−	0.100639i	−0.755633	+	0.654995i	$0.772671\pi$
$828$	25.6627	−	4.83310i	0.891841	−	0.167962i
$829$	−20.3880	+	20.3880i	−0.708103	+	0.708103i	−0.966136	−	0.258033i	$-0.916926\pi$
$829$	−20.3880	+	20.3880i	−0.708103	+	0.708103i	0.258033	+	0.966136i	$0.416926\pi$
$830$	13.1215	−	7.97337i	0.455455	−	0.276760i
$831$	−14.9346	+	30.6851i	−0.518074	+	1.06445i
$832$	38.3054	+	4.89940i	1.32800	+	0.169856i
$833$	−52.4168	+	30.2629i	−1.81613	+	1.04855i
$834$	45.6095	+	20.9464i	1.57933	+	0.725313i
$835$	11.7356	−	3.14454i	0.406127	−	0.108821i
$836$	5.94212	−	3.79582i	0.205513	−	0.131281i
$837$	−38.5723	−	1.92502i	−1.33325	−	0.0665384i
$838$	−9.98349	−	34.1736i	−0.344874	−	1.18051i
$839$	−22.0012	−	12.7024i	−0.759567	−	0.438536i	0.0695730	−	0.997577i	$-0.477836\pi$
$839$	−22.0012	−	12.7024i	−0.759567	−	0.438536i	−0.829140	+	0.559040i	$0.811170\pi$
$840$	3.29747	+	23.7536i	0.113773	+	0.819579i
$841$	6.89432	−	3.98044i	0.237735	−	0.137256i
$842$	−17.2746	−	16.5165i	−0.595321	−	0.569195i
$843$	−3.27651	−	9.49002i	−0.112849	−	0.326854i
$844$	6.13808	+	5.61065i	0.211281	+	0.193127i
$845$	7.28441	+	7.28441i	0.250591	+	0.250591i
$846$	−0.102252	−	0.618961i	−0.00351549	−	0.0212803i
$847$		−	14.5485i		−	0.499891i
$848$	11.9546	+	2.07763i	0.410522	+	0.0713461i
$849$	2.19402	−	1.48254i	0.0752987	−	0.0508808i
$850$	5.04483	−	0.113180i	0.173036	−	0.00388204i
$851$	−0.407926	−	0.109303i	−0.0139835	−	0.00374687i
$852$	18.3210	−	7.26048i	0.627667	−	0.248740i
$853$	32.8762	−	8.80915i	1.12566	−	0.301620i	0.352488	−	0.935816i	$-0.385336\pi$
$853$	32.8762	−	8.80915i	1.12566	−	0.301620i	0.773172	+	0.634197i	$0.218669\pi$
$854$	−27.7296	−	94.9187i	−0.948886	−	3.24805i
$855$	2.93770	−	2.30306i	0.100467	−	0.0787630i
$856$	−35.0241	−	30.6013i	−1.19710	−	1.04593i
$857$	−6.23034	+	10.7913i	−0.212824	+	0.368623i	−0.952597	−	0.304234i	$-0.901600\pi$
$857$	−6.23034	+	10.7913i	−0.212824	+	0.368623i	0.739773	+	0.672857i	$0.234933\pi$
$858$	33.0265	+	5.62583i	1.12750	+	0.192063i
$859$	31.3354	+	8.39629i	1.06915	+	0.286478i	0.750144	−	0.661275i	$-0.229984\pi$
$859$	31.3354	+	8.39629i	1.06915	+	0.286478i	0.319006	+	0.947753i	$0.396651\pi$
$860$	12.2360	+	6.35056i	0.417244	+	0.216552i
$861$	45.7062	−	52.6674i	1.55766	−	1.79490i
$862$	16.3340	+	26.8804i	0.556339	+	0.915550i
$863$	−42.0828			−1.43252			−0.716258	−	0.697836i	$-0.754147\pi$
$863$	−42.0828			−1.43252			−0.716258	+	0.697836i	$0.754147\pi$
$864$	24.4916	−	16.2531i	0.833221	−	0.552940i
$865$	6.72185			0.228550
$866$	8.14904	+	13.4106i	0.276916	+	0.455711i
$867$	−4.84572	+	5.58374i	−0.164569	+	0.189634i
$868$	64.5861	+	33.5206i	2.19220	+	1.13776i
$869$	19.0990	+	5.11757i	0.647890	+	0.173602i
$870$	14.6803	+	2.50069i	0.497709	+	0.0847814i
$871$	8.12817	−	14.0784i	0.275412	−	0.477028i
$872$	−8.97718	+	10.2747i	−0.304006	+	0.347944i
$873$	45.6670	+	18.3624i	1.54560	+	0.621473i
$874$	2.14764	+	7.35139i	0.0726449	+	0.248665i
$875$	−4.72839	+	1.26697i	−0.159849	+	0.0428313i
$876$	38.1078	−	15.1018i	1.28754	−	0.510244i
$877$	−7.40403	−	1.98390i	−0.250016	−	0.0669917i	0.131634	−	0.991298i	$-0.457978\pi$
$877$	−7.40403	−	1.98390i	−0.250016	−	0.0669917i	−0.381651	+	0.924307i	$0.624644\pi$
$878$	−6.06773	+	0.136129i	−0.204776	+	0.00459412i
$879$	13.2396	−	8.94627i	0.446562	−	0.301750i
$880$	6.52342	+	9.26785i	0.219905	+	0.312419i
$881$		−	5.23030i		−	0.176213i	−0.996111	−	0.0881066i	$-0.971918\pi$
$881$		−	5.23030i		−	0.176213i	0.996111	−	0.0881066i	$-0.0280816\pi$
$882$	−67.3571	−	25.3441i	−2.26803	−	0.853379i
$883$	18.2230	+	18.2230i	0.613254	+	0.613254i	0.943792	−	0.330539i	$-0.107230\pi$
$883$	18.2230	+	18.2230i	0.613254	+	0.613254i	−0.330539	+	0.943792i	$0.607230\pi$
$884$	25.4263	+	23.2415i	0.855180	+	0.781697i
$885$	3.48179	+	10.0846i	0.117039	+	0.338990i
$886$	−10.8231	−	10.3481i	−0.363609	−	0.347652i
$887$	29.9754	−	17.3063i	1.00648	−	0.581089i	0.0963176	−	0.995351i	$-0.469294\pi$
$887$	29.9754	−	17.3063i	1.00648	−	0.581089i	0.910158	+	0.414262i	$0.135960\pi$
$888$	−0.470845	+	0.0653625i	−0.0158005	+	0.00219342i
$889$	−52.4390	−	30.2757i	−1.75875	−	1.01541i
$890$	−1.12181	−	3.83997i	−0.0376032	−	0.128716i
$891$	21.8143	−	13.2063i	0.730806	−	0.442427i
$892$	−16.3903	+	10.4701i	−0.548788	+	0.350565i
$893$	0.177720	−	0.0476199i	0.00594717	−	0.00159354i
$894$	−34.5969	−	15.8888i	−1.15709	−	0.531400i
$895$	−10.9982	+	6.34979i	−0.367628	+	0.212250i
$896$	−54.7014	+	8.66037i	−1.82745	+	0.289323i
$897$	−15.9248	+	32.7198i	−0.531715	+	1.09248i
$898$	−2.85071	+	1.73225i	−0.0951293	+	0.0578059i
$899$	31.9514	−	31.9514i	1.06564	−	1.06564i
$900$	3.90987	+	4.55115i	0.130329	+	0.151705i
$901$	7.65352	+	7.65352i	0.254976	+	0.254976i
$902$	7.81355	−	32.0165i	0.260163	−	1.06603i
$903$	−48.4243	+	32.7212i	−1.61146	+	1.08889i
$904$	22.3018	−	14.9611i	0.741746	−	0.497599i
$905$	−4.27252	−	7.40023i	−0.142023	−	0.245992i
$906$	22.7306	−	27.4111i	0.755174	−	0.910673i
$907$	5.30752	+	19.8079i	0.176233	+	0.657712i	0.996338	+	0.0854985i	$0.0272483\pi$
$907$	5.30752	+	19.8079i	0.176233	+	0.657712i	−0.820105	+	0.572213i	$0.806085\pi$
$908$	14.4630	+	3.18773i	0.479972	+	0.105789i
$909$	−30.5335	+	13.0207i	−1.01273	+	0.431869i
$910$	−29.3082	−	16.0556i	−0.971557	−	0.532238i
$911$	−28.1536	+	48.7635i	−0.932770	+	1.61561i	−0.154208	+	0.988038i	$0.549283\pi$
$911$	−28.1536	+	48.7635i	−0.932770	+	1.61561i	−0.778562	+	0.627567i	$0.784051\pi$
$912$	5.44715	+	6.68162i	0.180373	+	0.221250i
$913$	15.3810	+	26.6406i	0.509036	+	0.881676i
$914$	0.476549	+	21.2415i	0.0157628	+	0.702606i
$915$	−18.6855	−	16.2158i	−0.617725	−	0.536079i
$916$	25.6859	+	23.4787i	0.848685	+	0.775760i
$917$	−44.1348	+	44.1348i	−1.45746	+	1.45746i
$918$	26.2104	+	0.719247i	0.865073	+	0.0237387i
$919$	17.9498			0.592108			0.296054	−	0.955171i	$-0.404329\pi$
$919$	17.9498			0.592108			0.296054	+	0.955171i	$0.404329\pi$
$920$	−11.6496	+	3.97846i	−0.384075	+	0.131166i
$921$	−10.6060	+	0.750507i	−0.349480	+	0.0247301i
$922$	−34.7679	−	33.2421i	−1.14502	−	1.09477i
$923$	−7.10762	+	26.5260i	−0.233950	+	0.873114i
$924$	−47.7266	+	5.53739i	−1.57009	+	0.182167i
$925$	−0.0251139	−	0.0937262i	−0.000825739	−	0.00308170i
$926$	1.23937	+	0.678951i	0.0407282	+	0.0223117i
$927$	35.7309	−	28.0119i	1.17356	−	0.920030i
$928$	−5.12724	+	34.0068i	−0.168310	+	1.11633i
$929$	−26.9612	−	15.5661i	−0.884569	−	0.510706i	−0.0124069	−	0.999923i	$-0.503949\pi$
$929$	−26.9612	−	15.5661i	−0.884569	−	0.510706i	−0.872162	+	0.489217i	$0.837283\pi$
$930$	18.1270	−	1.69207i	0.594407	−	0.0554852i
$931$	5.46279	−	20.3874i	0.179036	−	0.668170i
$932$	7.45785	−	14.3695i	0.244290	−	0.470688i
$933$	0.151207	−	0.781362i	0.00495030	−	0.0255806i
$934$	41.8053	+	10.2025i	1.36791	+	0.333835i
$935$			10.1098i			0.330627i
$936$	−2.17873	+	40.9020i	−0.0712142	+	1.33692i
$937$		−	29.3486i		−	0.958776i	−0.877603	−	0.479388i	$-0.840859\pi$
$937$		−	29.3486i		−	0.958776i	0.877603	−	0.479388i	$-0.159141\pi$
$938$	−5.52745	+	22.6491i	−0.180478	+	0.739519i
$939$	42.7791	−	14.7698i	1.39604	−	0.481995i
$940$	0.0892759	+	0.281938i	0.00291186	+	0.00919582i
$941$	6.84477	−	25.5450i	0.223133	−	0.832744i	−0.760011	−	0.649910i	$-0.774806\pi$
$941$	6.84477	−	25.5450i	0.223133	−	0.832744i	0.983144	−	0.182834i	$-0.0585269\pi$
$942$	−16.4897	−	7.57298i	−0.537265	−	0.246741i
$943$	31.0005	+	17.8981i	1.00951	+	0.582843i
$944$	−23.1318	+	8.48371i	−0.752874	+	0.276121i
$945$	−24.8670	+	5.35052i	−0.808925	+	0.174052i
$946$	−13.2700	+	24.2233i	−0.431444	+	0.787566i
$947$	1.16563	+	4.35018i	0.0378778	+	0.141362i	0.982275	−	0.187444i	$-0.0600204\pi$
$947$	1.16563	+	4.35018i	0.0378778	+	0.141362i	−0.944397	+	0.328806i	$0.893354\pi$
$948$	−3.52392	+	23.9161i	−0.114452	+	0.776759i
$949$	−14.7839	+	55.1742i	−0.479905	+	1.79103i
$950$	−1.21606	+	1.27188i	−0.0394542	+	0.0412652i
$951$	2.75643	−	5.66346i	0.0893833	−	0.183650i
$952$	−44.3486	−	21.7688i	−1.43735	−	0.705529i
$953$	−30.9788			−1.00350			−0.501751	−	0.865012i	$-0.667311\pi$
$953$	−30.9788			−1.00350			−0.501751	+	0.865012i	$0.667311\pi$
$954$	−1.26023	+	12.8079i	−0.0408016	+	0.414673i
$955$	7.98519	−	7.98519i	0.258395	−	0.258395i
$956$	7.68210	−	0.344867i	0.248457	−	0.0111538i
$957$	−5.66856	+	29.2922i	−0.183238	+	0.946883i
$958$	39.2474	−	0.880509i	1.26803	−	0.0284480i
$959$	−26.4915	−	45.8846i	−0.855455	−	1.48169i
$960$	−10.3362	+	9.22833i	−0.333601	+	0.297843i
$961$	12.1209	−	20.9939i	0.390995	−	0.677224i
$962$	0.318254	−	0.580948i	0.0102609	−	0.0187305i
$963$	29.6224	−	39.4466i	0.954569	−	1.27115i
$964$	−8.79855	−	13.7736i	−0.283382	−	0.443617i
$965$	−2.21955	−	8.28346i	−0.0714497	−	0.266654i
$966$	8.76351	−	51.4462i	0.281961	−	1.65525i
$967$	17.0674	+	29.5617i	0.548851	+	0.950639i	0.998354	+	0.0573593i	$0.0182681\pi$
$967$	17.0674	+	29.5617i	0.548851	+	0.950639i	−0.449502	+	0.893279i	$0.648399\pi$
$968$	6.98077	−	4.68304i	0.224370	−	0.150519i
$969$	0.542798	+	7.67071i	0.0174372	+	0.246419i
$970$	−22.5412	−	5.50112i	−0.723754	−	0.176630i
$971$	−31.6617	−	31.6617i	−1.01607	−	1.01607i	−0.999869	−	0.0162050i	$-0.994842\pi$
$971$	−31.6617	−	31.6617i	−1.01607	−	1.01607i	−0.0162050	−	0.999869i	$-0.505158\pi$
$972$	19.1123	+	24.6317i	0.613026	+	0.790063i
$973$	70.9236	−	70.9236i	2.27371	−	2.27371i
$974$	2.16058	+	3.55560i	0.0692294	+	0.113929i
$975$	−8.34007	+	0.590164i	−0.267096	+	0.0189004i
$976$	36.6188	−	43.8590i	1.17214	−	1.40389i
$977$	14.0820	−	8.13027i	0.450525	−	0.260111i	−0.257527	−	0.966271i	$-0.582908\pi$
$977$	14.0820	−	8.13027i	0.450525	−	0.260111i	0.708052	+	0.706161i	$0.249574\pi$
$978$	−7.84901	−	11.0721i	−0.250984	−	0.354046i
$979$	7.74185	−	2.07442i	0.247431	−	0.0662988i
$980$	33.1306	+	7.30216i	1.05832	+	0.233259i
$981$	−11.5720	−	8.69002i	−0.369467	−	0.277451i
$982$	−10.4931	+	3.06546i	−0.334848	+	0.0978227i
$983$	−29.0134	−	16.7509i	−0.925384	−	0.534271i	−0.0400355	−	0.999198i	$-0.512747\pi$
$983$	−29.0134	−	16.7509i	−0.925384	−	0.534271i	−0.885349	+	0.464927i	$0.846080\pi$
$984$	39.9838	+	4.97793i	1.27464	+	0.158691i
$985$	20.1222	−	11.6176i	0.641147	−	0.370166i
$986$	−21.2006	+	22.1737i	−0.675165	+	0.706154i
$987$	−1.23089	−	0.238199i	−0.0391797	−	0.00758197i
$988$	−12.0007	+	0.538738i	−0.381792	+	0.0171395i
$989$	−21.2133	−	21.2133i	−0.674543	−	0.674543i
$990$	−9.29162	+	7.62692i	−0.295307	+	0.242400i
$991$		−	27.8920i		−	0.886017i	−0.896517	−	0.443009i	$-0.853911\pi$
$991$		−	27.8920i		−	0.886017i	0.896517	−	0.443009i	$-0.146089\pi$
$992$	4.70563	+	41.7803i	0.149404	+	1.32653i
$993$	−23.2723	−	11.3267i	−0.738523	−	0.359442i
$994$	−0.883349	−	39.3740i	−0.0280181	−	1.24887i
$995$	−2.09449	−	0.561216i	−0.0663997	−	0.0177918i
$996$	−30.1867	+	22.4334i	−0.956502	+	0.710829i
$997$	−31.1232	+	8.33944i	−0.985682	+	0.264113i	−0.715436	−	0.698678i	$-0.753772\pi$
$997$	−31.1232	+	8.33944i	−0.985682	+	0.264113i	−0.270247	+	0.962791i	$0.587105\pi$
$998$	−42.3619	+	12.3756i	−1.34094	+	0.391743i
$999$	−0.106058	−	0.492915i	−0.00335553	−	0.0155951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.64	✓	384
9.5	odd	6	inner	720.2.cf.a.491.94	yes	384
16.3	odd	4	inner	720.2.cf.a.371.94	yes	384
144.131	even	12	inner	720.2.cf.a.131.64	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.64	✓	384	1.1	even	1	trivial
720.2.cf.a.131.64	yes	384	144.131	even	12	inner
720.2.cf.a.371.94	yes	384	16.3	odd	4	inner
720.2.cf.a.491.94	yes	384	9.5	odd	6	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.734399 + 1.20858i) q^{2} +(-1.13524 + 1.30814i) q^{3} +(-0.921316 + 1.77516i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-2.41471 - 0.411329i) q^{6} +(-2.44759 + 4.23936i) q^{7} +(-2.82203 + 0.190190i) q^{8} +(-0.422459 - 2.97011i) q^{9} +O(q^{10})\)	\(q+(0.734399 + 1.20858i) q^{2} +(-1.13524 + 1.30814i) q^{3} +(-0.921316 + 1.77516i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-2.41471 - 0.411329i) q^{6} +(-2.44759 + 4.23936i) q^{7} +(-2.82203 + 0.190190i) q^{8} +(-0.422459 - 2.97011i) q^{9} +(0.396572 + 1.35747i) q^{10} +(-2.73683 + 0.733331i) q^{11} +(-1.27624 - 3.22044i) q^{12} +(4.66270 + 1.24937i) q^{13} +(-6.92110 + 0.155274i) q^{14} +(-1.43513 + 0.969744i) q^{15} +(-2.30235 - 3.27096i) q^{16} -3.56813i q^{17} +(3.27935 - 2.69182i) q^{18} +(0.879841 + 0.879841i) q^{19} +(-1.34937 + 1.47621i) q^{20} +(-2.76706 - 8.01448i) q^{21} +(-2.89621 - 2.76911i) q^{22} +(3.76921 - 2.17615i) q^{23} +(2.95488 - 3.90752i) q^{24} +(0.866025 + 0.500000i) q^{25} +(1.91433 + 6.55277i) q^{26} +(4.36491 + 2.81915i) q^{27} +(-5.27051 - 8.25065i) q^{28} +(-5.87239 + 1.57350i) q^{29} +(-2.22597 - 1.02229i) q^{30} +(-6.43671 + 3.71624i) q^{31} +(2.26236 - 5.18476i) q^{32} +(2.14766 - 4.41266i) q^{33} +(4.31236 - 2.62043i) q^{34} +(-3.46142 + 3.46142i) q^{35} +(5.66162 + 1.98648i) q^{36} +(-0.0686124 - 0.0686124i) q^{37} +(-0.417201 + 1.70951i) q^{38} +(-6.92763 + 4.68113i) q^{39} +(-2.77509 - 0.546684i) q^{40} +(4.11233 + 7.12276i) q^{41} +(7.65399 - 9.23004i) q^{42} +(-1.78402 - 6.65805i) q^{43} +(1.21971 - 5.53393i) q^{44} +(0.360656 - 2.97824i) q^{45} +(5.39815 + 2.95721i) q^{46} +(0.0739339 - 0.128057i) q^{47} +(6.89259 + 0.701526i) q^{48} +(-8.48143 - 14.6903i) q^{49} +(0.0317197 + 1.41386i) q^{50} +(4.66761 + 4.05068i) q^{51} +(-6.51364 + 7.12596i) q^{52} +(-2.14497 + 2.14497i) q^{53} +(-0.201575 + 7.34570i) q^{54} -2.83337 q^{55} +(6.10089 - 12.4291i) q^{56} +(-2.14979 + 0.152124i) q^{57} +(-6.21438 - 5.94166i) q^{58} +(1.59422 - 5.94972i) q^{59} +(-0.399238 - 3.44102i) q^{60} +(3.69698 + 13.7973i) q^{61} +(-9.21848 - 5.05006i) q^{62} +(13.6253 + 5.47866i) q^{63} +(7.92766 - 1.07344i) q^{64} +(4.18046 + 2.41359i) q^{65} +(6.91028 - 0.645043i) q^{66} +(0.871616 - 3.25291i) q^{67} +(6.33398 + 3.28738i) q^{68} +(-1.43224 + 7.40111i) q^{69} +(-6.72546 - 1.64133i) q^{70} +5.68898i q^{71} +(1.75708 + 8.30137i) q^{72} +11.8331i q^{73} +(0.0325345 - 0.133312i) q^{74} +(-1.63722 + 0.565262i) q^{75} +(-2.37247 + 0.751242i) q^{76} +(3.58979 - 13.3973i) q^{77} +(-10.7452 - 4.93476i) q^{78} +(-6.04358 - 3.48926i) q^{79} +(-1.37731 - 3.75540i) q^{80} +(-8.64306 + 2.50950i) q^{81} +(-5.58832 + 10.2010i) q^{82} +(-2.81000 - 10.4871i) q^{83} +(16.7763 + 2.47191i) q^{84} +(0.923500 - 3.44655i) q^{85} +(6.73658 - 7.04579i) q^{86} +(4.60821 - 9.46821i) q^{87} +(7.58393 - 2.59000i) q^{88} -2.82877 q^{89} +(3.86430 - 1.75134i) q^{90} +(-16.7089 + 16.7089i) q^{91} +(0.390377 + 8.69586i) q^{92} +(2.44586 - 12.6389i) q^{93} +(0.209064 - 0.00469032i) q^{94} +(0.622141 + 1.07758i) q^{95} +(4.21407 + 8.84543i) q^{96} +(-8.20341 + 14.2087i) q^{97} +(11.5256 - 21.0390i) q^{98} +(3.33427 + 7.81887i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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