LMFDB - Embedded newform 465.2.n.d.376.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(16,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 7 x^{13} + 168 x^{12} - 290 x^{11} + 2849 x^{10} - 4031 x^{9} + \cdots + 259081 $ x^16 - 6x^15 + 18x^14 - 7x^13 + 168x^12 - 290x^11 + 2849x^10 - 4031x^9 + 17808x^8 - 13133x^7 + 83911x^6 + 72289x^5 + 228578x^4 + 298284x^3 + 484502x^2 + 341539*x + 259081
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			376.2
Root			$-0.316962 - 0.975510i$ of defining polynomial
Character	$\chi$	$=$	465.376
Dual form			465.2.n.d.256.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.147481 - 0.453901i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.43376 - 1.04169i) q^{4} -1.00000 q^{5} -0.477260 q^{6} +(3.67861 - 2.67266i) q^{7} +(-1.45650 - 1.05821i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.147481 + 0.453901i) q^{10} +(1.13088 - 0.821630i) q^{11} +(-0.547647 - 1.68548i) q^{12} +(-1.47966 + 4.55393i) q^{13} +(-1.75565 - 1.27556i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.829779 - 2.55380i) q^{16} +(-3.14174 - 2.28261i) q^{17} +(-0.147481 + 0.453901i) q^{18} +(1.62065 + 4.98786i) q^{19} +(-1.43376 + 1.04169i) q^{20} +(-1.40510 - 4.32446i) q^{21} +(-0.539722 - 0.392131i) q^{22} +(1.31202 + 0.953235i) q^{23} +(-1.45650 + 1.05821i) q^{24} +1.00000 q^{25} +2.28525 q^{26} +(-0.809017 + 0.587785i) q^{27} +(2.49016 - 7.66391i) q^{28} +(-2.24589 - 6.91214i) q^{29} +0.477260 q^{30} +(5.46517 + 1.06393i) q^{31} -4.88221 q^{32} +(-0.431957 - 1.32943i) q^{33} +(-0.572731 + 1.76268i) q^{34} +(-3.67861 + 2.67266i) q^{35} -1.77222 q^{36} -8.88900 q^{37} +(2.02498 - 1.47123i) q^{38} +(3.87380 + 2.81448i) q^{39} +(1.45650 + 1.05821i) q^{40} +(3.94410 + 12.1387i) q^{41} +(-1.75565 + 1.27556i) q^{42} +(-2.07995 - 6.40143i) q^{43} +(0.765523 - 2.35604i) q^{44} +(0.809017 + 0.587785i) q^{45} +(0.239177 - 0.736110i) q^{46} +(1.98523 - 6.10991i) q^{47} +(-2.17239 - 1.57833i) q^{48} +(4.22590 - 13.0060i) q^{49} +(-0.147481 - 0.453901i) q^{50} +(-3.14174 + 2.28261i) q^{51} +(2.62229 + 8.07057i) q^{52} +(4.29291 + 3.11898i) q^{53} +(0.386111 + 0.280526i) q^{54} +(-1.13088 + 0.821630i) q^{55} -8.18612 q^{56} +5.24454 q^{57} +(-2.80620 + 2.03883i) q^{58} +(-3.91334 + 12.0440i) q^{59} +(0.547647 + 1.68548i) q^{60} -10.1665 q^{61} +(-0.323092 - 2.63756i) q^{62} -4.54701 q^{63} +(-0.939522 - 2.89155i) q^{64} +(1.47966 - 4.55393i) q^{65} +(-0.539722 + 0.392131i) q^{66} +4.42957 q^{67} -6.88226 q^{68} +(1.31202 - 0.953235i) q^{69} +(1.75565 + 1.27556i) q^{70} +(12.2127 + 8.87308i) q^{71} +(0.556333 + 1.71222i) q^{72} +(8.39868 - 6.10200i) q^{73} +(1.31096 + 4.03473i) q^{74} +(0.309017 - 0.951057i) q^{75} +(7.51941 + 5.46317i) q^{76} +(1.96411 - 6.04491i) q^{77} +(0.706183 - 2.17341i) q^{78} +(1.17325 + 0.852419i) q^{79} +(-0.829779 + 2.55380i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.92809 - 3.58047i) q^{82} +(-1.03556 - 3.18713i) q^{83} +(-6.51931 - 4.73656i) q^{84} +(3.14174 + 2.28261i) q^{85} +(-2.59886 + 1.88819i) q^{86} -7.26786 q^{87} -2.51658 q^{88} +(5.25175 - 3.81562i) q^{89} +(0.147481 - 0.453901i) q^{90} +(6.72803 + 20.7067i) q^{91} +2.87409 q^{92} +(2.70069 - 4.86891i) q^{93} -3.06608 q^{94} +(-1.62065 - 4.98786i) q^{95} +(-1.50869 + 4.64326i) q^{96} +(1.77134 - 1.28695i) q^{97} -6.52667 q^{98} -1.39784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} + 4 q^{6} + 7 q^{7} - 8 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} + 6 q^{12} + 8 q^{13} - q^{14} + 4 q^{15} + 8 q^{16} + 4 q^{17} + 4 q^{18} + 17 q^{19} + 4 q^{20}+ \cdots + 14 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 + 4 * q^6 + 7 * q^7 - 8 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 + 6 * q^12 + 8 * q^13 - q^14 + 4 * q^15 + 8 * q^16 + 4 * q^17 + 4 * q^18 + 17 * q^19 + 4 * q^20 - 8 * q^21 - 11 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 10 * q^26 - 4 * q^27 + 10 * q^28 + 3 * q^29 - 4 * q^30 - 5 * q^31 - 32 * q^32 - 11 * q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 + 44 * q^37 - 7 * q^38 - 7 * q^39 + 8 * q^40 + 14 * q^41 - q^42 - 10 * q^43 + 13 * q^44 + 4 * q^45 - 5 * q^46 + 34 * q^47 - 2 * q^48 + 33 * q^49 + 4 * q^50 + 4 * q^51 - 13 * q^52 - 6 * q^54 - 4 * q^55 - 20 * q^56 - 8 * q^57 - 25 * q^58 - 26 * q^59 - 6 * q^60 + 30 * q^61 - 15 * q^62 + 2 * q^63 - 52 * q^64 - 8 * q^65 - 11 * q^66 + 30 * q^67 - 60 * q^68 - 14 * q^69 + q^70 + 10 * q^71 + 2 * q^72 + 40 * q^73 + 2 * q^74 - 4 * q^75 - 13 * q^76 - 16 * q^77 + 15 * q^78 + 3 * q^79 - 8 * q^80 - 4 * q^81 - 9 * q^82 + 6 * q^83 - 10 * q^84 - 4 * q^85 + 18 * q^86 + 8 * q^87 + 6 * q^88 + 20 * q^89 - 4 * q^90 - 7 * q^91 + 14 * q^92 + 30 * q^93 + 34 * q^94 - 17 * q^95 - 32 * q^96 - 27 * q^97 + 80 * q^98 + 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.147481	−	0.453901i	−0.104285	−	0.320957i	0.885277	−	0.465064i	$-0.153969\pi$
$2$	−0.147481	−	0.453901i	−0.104285	−	0.320957i	−0.989562	+	0.144108i	$0.953969\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	1.43376	−	1.04169i	0.716879	−	0.520843i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.477260			−0.194841
$7$	3.67861	−	2.67266i	1.39038	−	1.01017i	0.394560	−	0.918870i	$-0.370897\pi$
$7$	3.67861	−	2.67266i	1.39038	−	1.01017i	0.995823	−	0.0913021i	$-0.0291029\pi$
$8$	−1.45650	−	1.05821i	−0.514950	−	0.374133i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	0.147481	+	0.453901i	0.0466377	+	0.143536i
$11$	1.13088	−	0.821630i	0.340972	−	0.247731i	−0.404100	−	0.914715i	$-0.632415\pi$
$11$	1.13088	−	0.821630i	0.340972	−	0.247731i	0.745072	+	0.666984i	$0.232415\pi$
$12$	−0.547647	−	1.68548i	−0.158092	−	0.486557i
$13$	−1.47966	+	4.55393i	−0.410384	+	1.26303i	0.505931	+	0.862574i	$0.331149\pi$
$13$	−1.47966	+	4.55393i	−0.410384	+	1.26303i	−0.916315	+	0.400458i	$0.868851\pi$
$14$	−1.75565	−	1.27556i	−0.469218	−	0.340907i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	0.829779	−	2.55380i	0.207445	−	0.638449i
$17$	−3.14174	−	2.28261i	−0.761985	−	0.553614i	0.137534	−	0.990497i	$-0.456082\pi$
$17$	−3.14174	−	2.28261i	−0.761985	−	0.553614i	−0.899518	+	0.436883i	$0.856082\pi$
$18$	−0.147481	+	0.453901i	−0.0347617	+	0.106986i
$19$	1.62065	+	4.98786i	0.371803	+	1.14429i	0.945610	+	0.325302i	$0.105466\pi$
$19$	1.62065	+	4.98786i	0.371803	+	1.14429i	−0.573807	+	0.818991i	$0.694534\pi$
$20$	−1.43376	+	1.04169i	−0.320598	+	0.232928i
$21$	−1.40510	−	4.32446i	−0.306619	−	0.943675i
$22$	−0.539722	−	0.392131i	−0.115069	−	0.0836027i
$23$	1.31202	+	0.953235i	0.273574	+	0.198763i	0.716110	−	0.697988i	$-0.245921\pi$
$23$	1.31202	+	0.953235i	0.273574	+	0.198763i	−0.442536	+	0.896751i	$0.645921\pi$
$24$	−1.45650	+	1.05821i	−0.297306	+	0.216006i
$25$	1.00000			0.200000
$26$	2.28525			0.448175
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	2.49016	−	7.66391i	0.470595	−	1.44834i
$29$	−2.24589	−	6.91214i	−0.417052	−	1.28355i	−0.910403	−	0.413723i	$-0.864228\pi$
$29$	−2.24589	−	6.91214i	−0.417052	−	1.28355i	0.493351	−	0.869830i	$-0.335772\pi$
$30$	0.477260			0.0871354
$31$	5.46517	+	1.06393i	0.981573	+	0.191087i
$31$	5.46517	+	1.06393i	0.981573	+	0.191087i
$32$	−4.88221			−0.863061
$33$	−0.431957	−	1.32943i	−0.0751940	−	0.231423i
$34$	−0.572731	+	1.76268i	−0.0982225	+	0.302298i
$35$	−3.67861	+	2.67266i	−0.621798	+	0.451763i
$36$	−1.77222			−0.295370
$37$	−8.88900			−1.46134			−0.730671	−	0.682729i	$-0.760793\pi$
$37$	−8.88900			−1.46134			−0.730671	+	0.682729i	$0.760793\pi$
$38$	2.02498	−	1.47123i	0.328495	−	0.238665i
$39$	3.87380	+	2.81448i	0.620305	+	0.450678i
$40$	1.45650	+	1.05821i	0.230293	+	0.167317i
$41$	3.94410	+	12.1387i	0.615966	+	1.89575i	0.385728	+	0.922613i	$0.373950\pi$
$41$	3.94410	+	12.1387i	0.615966	+	1.89575i	0.230238	+	0.973134i	$0.426050\pi$
$42$	−1.75565	+	1.27556i	−0.270903	+	0.196823i
$43$	−2.07995	−	6.40143i	−0.317190	−	0.976210i	−0.974844	−	0.222889i	$-0.928451\pi$
$43$	−2.07995	−	6.40143i	−0.317190	−	0.976210i	0.657654	−	0.753320i	$-0.271549\pi$
$44$	0.765523	−	2.35604i	0.115407	−	0.355186i
$45$	0.809017	+	0.587785i	0.120601	+	0.0876219i
$46$	0.239177	−	0.736110i	0.0352647	−	0.108534i
$47$	1.98523	−	6.10991i	0.289576	−	0.891222i	−0.695414	−	0.718609i	$-0.744779\pi$
$47$	1.98523	−	6.10991i	0.289576	−	0.891222i	0.984990	−	0.172613i	$-0.0552209\pi$
$48$	−2.17239	−	1.57833i	−0.313557	−	0.227813i
$49$	4.22590	−	13.0060i	0.603700	−	1.85800i
$50$	−0.147481	−	0.453901i	−0.0208570	−	0.0641913i
$51$	−3.14174	+	2.28261i	−0.439932	+	0.319629i
$52$	2.62229	+	8.07057i	0.363646	+	1.11919i
$53$	4.29291	+	3.11898i	0.589677	+	0.428425i	0.842200	−	0.539165i	$-0.181260\pi$
$53$	4.29291	+	3.11898i	0.589677	+	0.428425i	−0.252523	+	0.967591i	$0.581260\pi$
$54$	0.386111	+	0.280526i	0.0525431	+	0.0381748i
$55$	−1.13088	+	0.821630i	−0.152487	+	0.110789i
$56$	−8.18612			−1.09392
$57$	5.24454			0.694657
$58$	−2.80620	+	2.03883i	−0.368473	+	0.267711i
$59$	−3.91334	+	12.0440i	−0.509473	+	1.56800i	0.283645	+	0.958929i	$0.408456\pi$
$59$	−3.91334	+	12.0440i	−0.509473	+	1.56800i	−0.793118	+	0.609068i	$0.791544\pi$
$60$	0.547647	+	1.68548i	0.0707009	+	0.217595i
$61$	−10.1665			−1.30169			−0.650845	−	0.759211i	$-0.725585\pi$
$61$	−10.1665			−1.30169			−0.650845	+	0.759211i	$0.725585\pi$
$62$	−0.323092	−	2.63756i	−0.0410327	−	0.334970i
$63$	−4.54701			−0.572869
$64$	−0.939522	−	2.89155i	−0.117440	−	0.361444i
$65$	1.47966	−	4.55393i	0.183529	−	0.564845i
$66$	−0.539722	+	0.392131i	−0.0664352	+	0.0482680i
$67$	4.42957			0.541158			0.270579	−	0.962698i	$-0.412785\pi$
$67$	4.42957			0.541158			0.270579	+	0.962698i	$0.412785\pi$
$68$	−6.88226			−0.834597
$69$	1.31202	−	0.953235i	0.157948	−	0.114756i
$70$	1.75565	+	1.27556i	0.209841	+	0.152458i
$71$	12.2127	+	8.87308i	1.44939	+	1.05304i	0.985974	+	0.166897i	$0.0533749\pi$
$71$	12.2127	+	8.87308i	1.44939	+	1.05304i	0.463412	+	0.886143i	$0.346625\pi$
$72$	0.556333	+	1.71222i	0.0655645	+	0.201787i
$73$	8.39868	−	6.10200i	0.982991	−	0.714185i	0.0246157	−	0.999697i	$-0.492164\pi$
$73$	8.39868	−	6.10200i	0.982991	−	0.714185i	0.958375	+	0.285512i	$0.0921638\pi$
$74$	1.31096	+	4.03473i	0.152396	+	0.469028i
$75$	0.309017	−	0.951057i	0.0356822	−	0.109819i
$76$	7.51941	+	5.46317i	0.862535	+	0.626668i
$77$	1.96411	−	6.04491i	0.223831	−	0.688882i
$78$	0.706183	−	2.17341i	0.0799594	−	0.246090i
$79$	1.17325	+	0.852419i	0.132001	+	0.0959046i	0.651827	−	0.758368i	$-0.274003\pi$
$79$	1.17325	+	0.852419i	0.132001	+	0.0959046i	−0.519825	+	0.854273i	$0.674003\pi$
$80$	−0.829779	+	2.55380i	−0.0927721	+	0.285523i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	4.92809	−	3.58047i	0.544217	−	0.395396i
$83$	−1.03556	−	3.18713i	−0.113667	−	0.349833i	0.877999	−	0.478662i	$-0.158878\pi$
$83$	−1.03556	−	3.18713i	−0.113667	−	0.349833i	−0.991667	+	0.128829i	$0.958878\pi$
$84$	−6.51931	−	4.73656i	−0.711315	−	0.516801i
$85$	3.14174	+	2.28261i	0.340770	+	0.247584i
$86$	−2.59886	+	1.88819i	−0.280243	+	0.203608i
$87$	−7.26786			−0.779196
$88$	−2.51658			−0.268268
$89$	5.25175	−	3.81562i	0.556685	−	0.404455i	−0.273559	−	0.961855i	$-0.588201\pi$
$89$	5.25175	−	3.81562i	0.556685	−	0.404455i	0.830244	+	0.557400i	$0.188201\pi$
$90$	0.147481	−	0.453901i	0.0155459	−	0.0478454i
$91$	6.72803	+	20.7067i	0.705289	+	2.17066i
$92$	2.87409			0.299644
$93$	2.70069	−	4.86891i	0.280048	−	0.504883i
$94$	−3.06608			−0.316242
$95$	−1.62065	−	4.98786i	−0.166275	−	0.511743i
$96$	−1.50869	+	4.64326i	−0.153980	+	0.473901i
$97$	1.77134	−	1.28695i	0.179852	−	0.130670i	−0.494217	−	0.869339i	$-0.664545\pi$
$97$	1.77134	−	1.28695i	0.179852	−	0.130670i	0.674069	+	0.738668i	$0.264545\pi$
$98$	−6.52667			−0.659293
$99$	−1.39784			−0.140488
$100$	1.43376	−	1.04169i	0.143376	−	0.104169i
$101$	12.0169	+	8.73081i	1.19573	+	0.868748i	0.993858	−	0.110664i	$-0.0352978\pi$
$101$	12.0169	+	8.73081i	1.19573	+	0.868748i	0.201871	+	0.979412i	$0.435298\pi$
$102$	1.49943	+	1.08940i	0.148466	+	0.107867i
$103$	4.68809	+	14.4285i	0.461931	+	1.42168i	0.862801	+	0.505543i	$0.168708\pi$
$103$	4.68809	+	14.4285i	0.461931	+	1.42168i	−0.400870	+	0.916135i	$0.631292\pi$
$104$	6.97412	−	5.06700i	0.683869	−	0.496860i
$105$	1.40510	+	4.32446i	0.137124	+	0.422024i
$106$	0.782586	−	2.40855i	0.0760114	−	0.233939i
$107$	−1.48157	−	1.07643i	−0.143229	−	0.104062i	0.513863	−	0.857872i	$-0.328214\pi$
$107$	−1.48157	−	1.07643i	−0.143229	−	0.104062i	−0.657092	+	0.753810i	$0.728214\pi$
$108$	−0.547647	+	1.68548i	−0.0526974	+	0.162186i
$109$	−2.08909	+	6.42955i	−0.200098	+	0.615839i	0.799781	+	0.600292i	$0.204949\pi$
$109$	−2.08909	+	6.42955i	−0.200098	+	0.615839i	−0.999879	+	0.0155472i	$0.995051\pi$
$110$	0.539722	+	0.392131i	0.0514605	+	0.0373882i
$111$	−2.74685	+	8.45394i	−0.260720	+	0.802413i
$112$	−3.77301	−	11.6121i	−0.356516	−	1.09724i
$113$	−10.1556	+	7.37850i	−0.955361	+	0.694111i	−0.952069	−	0.305884i	$-0.901048\pi$
$113$	−10.1556	+	7.37850i	−0.955361	+	0.694111i	−0.00329260	+	0.999995i	$0.501048\pi$
$114$	−0.773473	−	2.38050i	−0.0724423	−	0.222955i
$115$	−1.31202	−	0.953235i	−0.122346	−	0.0888897i
$116$	−10.4204	−	7.57083i	−0.967505	−	0.702934i
$117$	3.87380	−	2.81448i	0.358133	−	0.260199i
$118$	6.04394			0.556390
$119$	−17.6579			−1.61870
$120$	1.45650	−	1.05821i	0.132960	−	0.0966007i
$121$	−2.79538	+	8.60330i	−0.254125	+	0.782118i
$122$	1.49937	+	4.61460i	0.135747	+	0.417786i
$123$	12.7634			1.15084
$124$	8.94401	−	4.16757i	0.803196	−	0.374259i
$125$	−1.00000			−0.0894427
$126$	0.670599	+	2.06389i	0.0597418	+	0.183866i
$127$	−0.850526	+	2.61765i	−0.0754719	+	0.232279i	−0.981675	−	0.190565i	$-0.938968\pi$
$127$	−0.850526	+	2.61765i	−0.0754719	+	0.232279i	0.906203	+	0.422844i	$0.138968\pi$
$128$	−9.07350	+	6.59228i	−0.801992	+	0.582681i
$129$	−6.73087			−0.592620
$130$	−2.28525			−0.200430
$131$	10.8871	−	7.90994i	0.951210	−	0.691095i	0.000117556	−	1.00000i	$-0.499963\pi$
$131$	10.8871	−	7.90994i	0.951210	−	0.691095i	0.951093	+	0.308905i	$0.0999626\pi$
$132$	−2.00417	−	1.45611i	−0.174440	−	0.126738i
$133$	19.2926	+	14.0169i	1.67288	+	1.21542i
$134$	−0.653279	−	2.01059i	−0.0564347	−	0.173688i
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$	2.16047	+	6.64924i	0.185259	+	0.570167i
$137$	−4.37200	+	13.4556i	−0.373525	+	1.14959i	0.570943	+	0.820990i	$0.306578\pi$
$137$	−4.37200	+	13.4556i	−0.373525	+	1.14959i	−0.944468	+	0.328603i	$0.893422\pi$
$138$	−0.626173	−	0.454941i	−0.0533034	−	0.0387272i
$139$	1.17382	−	3.61265i	0.0995622	−	0.306421i	−0.888854	−	0.458191i	$-0.848497\pi$
$139$	1.17382	−	3.61265i	0.0995622	−	0.306421i	0.988416	+	0.151770i	$0.0484974\pi$
$140$	−2.49016	+	7.66391i	−0.210457	+	0.647719i
$141$	−5.19740	−	3.77613i	−0.437700	−	0.318008i
$142$	2.22635	−	6.85199i	0.186831	−	0.575007i
$143$	2.06833	+	6.36566i	0.172962	+	0.532324i
$144$	−2.17239	+	1.57833i	−0.181032	+	0.131528i
$145$	2.24589	+	6.91214i	0.186511	+	0.574022i
$146$	−4.00835	−	2.91224i	−0.331734	−	0.241019i
$147$	−11.0635	−	8.03813i	−0.912506	−	0.662974i
$148$	−12.7447	+	9.25955i	−1.04761	+	0.761131i
$149$	7.68303			0.629418			0.314709	−	0.949188i	$-0.398093\pi$
$149$	7.68303			0.629418			0.314709	+	0.949188i	$0.398093\pi$
$150$	−0.477260			−0.0389681
$151$	−4.00381	+	2.90894i	−0.325826	+	0.236726i	−0.738657	−	0.674081i	$-0.764540\pi$
$151$	−4.00381	+	2.90894i	−0.325826	+	0.236726i	0.412832	+	0.910807i	$0.364540\pi$
$152$	2.91771	−	8.97979i	0.236658	−	0.728357i
$153$	1.20004	+	3.69334i	0.0970174	+	0.298589i
$154$	−3.03346			−0.244443
$155$	−5.46517	−	1.06393i	−0.438973	−	0.0854569i
$156$	8.48590			0.679416
$157$	1.41784	+	4.36367i	0.113156	+	0.348259i	0.991558	−	0.129664i	$-0.0413899\pi$
$157$	1.41784	+	4.36367i	0.113156	+	0.348259i	−0.878402	+	0.477923i	$0.841390\pi$
$158$	0.213881	−	0.658257i	0.0170154	−	0.0523682i
$159$	4.29291	−	3.11898i	0.340450	−	0.247352i
$160$	4.88221			0.385973
$161$	7.37407			0.581158
$162$	0.386111	−	0.280526i	0.0303358	−	0.0220402i
$163$	−14.4284	−	10.4829i	−1.13012	−	0.821080i	−0.144408	−	0.989518i	$-0.546128\pi$
$163$	−14.4284	−	10.4829i	−1.13012	−	0.821080i	−0.985712	+	0.168438i	$0.946128\pi$
$164$	18.2996	+	13.2954i	1.42896	+	1.03820i
$165$	0.431957	+	1.32943i	0.0336278	+	0.103496i
$166$	−1.29391	+	0.940084i	−0.100427	+	0.0729647i
$167$	−3.86871	−	11.9067i	−0.299370	−	0.921366i	−0.981718	−	0.190339i	$-0.939041\pi$
$167$	−3.86871	−	11.9067i	−0.299370	−	0.921366i	0.682349	−	0.731027i	$-0.260959\pi$
$168$	−2.52965	+	7.78546i	−0.195167	+	0.600662i
$169$	−8.03162	−	5.83532i	−0.617817	−	0.448870i
$170$	0.572731	−	1.76268i	0.0439264	−	0.135192i
$171$	1.62065	−	4.98786i	0.123934	−	0.381431i
$172$	−9.65044	−	7.01145i	−0.735839	−	0.534618i
$173$	1.83780	−	5.65617i	0.139725	−	0.430031i	−0.856570	−	0.516031i	$-0.827409\pi$
$173$	1.83780	−	5.65617i	0.139725	−	0.430031i	0.996295	+	0.0860009i	$0.0274088\pi$
$174$	1.07187	+	3.29889i	0.0812586	+	0.250088i
$175$	3.67861	−	2.67266i	0.278077	−	0.202034i
$176$	−1.15990	−	3.56980i	−0.0874306	−	0.269084i
$177$	10.2453	+	7.44361i	0.770080	+	0.559496i
$178$	−2.50645	−	1.82104i	−0.187867	−	0.136493i
$179$	9.73247	−	7.07105i	0.727439	−	0.528515i	−0.161313	−	0.986903i	$-0.551573\pi$
$179$	9.73247	−	7.07105i	0.727439	−	0.528515i	0.888752	+	0.458388i	$0.151573\pi$
$180$	1.77222			0.132094
$181$	−14.6090			−1.08588			−0.542941	−	0.839771i	$-0.682689\pi$
$181$	−14.6090			−1.08588			−0.542941	+	0.839771i	$0.682689\pi$
$182$	8.40656	−	6.10772i	0.623135	−	0.452734i
$183$	−3.14163	+	9.66894i	−0.232236	+	0.714748i
$184$	−0.902228	−	2.77677i	−0.0665131	−	0.204706i
$185$	8.88900			0.653532
$186$	−2.60831	−	0.507771i	−0.191250	−	0.0372316i
$187$	−5.42839			−0.396963
$188$	−3.51827	−	10.8281i	−0.256596	−	0.789722i
$189$	−1.40510	+	4.32446i	−0.102206	+	0.314558i
$190$	−2.02498	+	1.47123i	−0.146907	+	0.106734i
$191$	2.33541			0.168984			0.0844920	−	0.996424i	$-0.473073\pi$
$191$	2.33541			0.168984			0.0844920	+	0.996424i	$0.473073\pi$
$192$	−3.04036			−0.219419
$193$	−1.39270	+	1.01186i	−0.100249	+	0.0728351i	−0.636780	−	0.771045i	$-0.719734\pi$
$193$	−1.39270	+	1.01186i	−0.100249	+	0.0728351i	0.536532	+	0.843880i	$0.319734\pi$
$194$	−0.845389	−	0.614211i	−0.0606954	−	0.0440978i
$195$	−3.87380	−	2.81448i	−0.277409	−	0.201549i
$196$	−7.48923	−	23.0495i	−0.534945	−	1.64639i
$197$	−3.68204	+	2.67516i	−0.262335	+	0.190597i	−0.711176	−	0.703014i	$-0.751837\pi$
$197$	−3.68204	+	2.67516i	−0.262335	+	0.190597i	0.448841	+	0.893612i	$0.351837\pi$
$198$	0.206156	+	0.634482i	0.0146508	+	0.0450907i
$199$	8.27839	−	25.4783i	0.586839	−	1.80611i	−0.00491515	−	0.999988i	$-0.501565\pi$
$199$	8.27839	−	25.4783i	0.586839	−	1.80611i	0.591755	−	0.806118i	$-0.298435\pi$
$200$	−1.45650	−	1.05821i	−0.102990	−	0.0748266i
$201$	1.36881	−	4.21277i	0.0965486	−	0.297146i
$202$	2.19065	−	6.74213i	0.154134	−	0.474375i
$203$	−26.7356	−	19.4245i	−1.87647	−	1.36334i
$204$	−2.12674	+	6.54542i	−0.148901	+	0.458271i
$205$	−3.94410	−	12.1387i	−0.275468	−	0.847804i
$206$	5.85769	−	4.25586i	0.408124	−	0.296520i
$207$	−0.501145	−	1.54237i	−0.0348320	−	0.107202i
$208$	10.4020	+	7.55750i	0.721249	+	0.524018i
$209$	5.93093	+	4.30907i	0.410251	+	0.298065i
$210$	1.75565	−	1.27556i	0.121152	−	0.0880217i
$211$	−18.8334			−1.29654			−0.648272	−	0.761409i	$-0.724508\pi$
$211$	−18.8334			−1.29654			−0.648272	+	0.761409i	$0.724508\pi$
$212$	9.40401			0.645870
$213$	12.2127	−	8.87308i	0.836803	−	0.607973i
$214$	−0.270087	+	0.831241i	−0.0184627	+	0.0568225i
$215$	2.07995	+	6.40143i	0.141852	+	0.436574i
$216$	1.80033			0.122497
$217$	22.9477	−	10.6928i	1.55779	−	0.725873i
$218$	3.22648			0.218525
$219$	−3.20801	−	9.87324i	−0.216777	−	0.667172i
$220$	−0.765523	+	2.35604i	−0.0516116	+	0.158844i
$221$	15.0435	−	10.9298i	1.01194	−	0.735216i
$222$	4.24237			0.284729
$223$	11.4126			0.764244			0.382122	−	0.924112i	$-0.375193\pi$
$223$	11.4126			0.764244			0.382122	+	0.924112i	$0.375193\pi$
$224$	−17.9597	+	13.0485i	−1.19999	+	0.871840i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	4.84688	+	3.52146i	0.322409	+	0.234244i
$227$	−4.60991	−	14.1878i	−0.305971	−	0.941681i	−0.979313	−	0.202350i	$-0.935142\pi$
$227$	−4.60991	−	14.1878i	−0.305971	−	0.941681i	0.673343	−	0.739331i	$-0.264858\pi$
$228$	7.51941	−	5.46317i	0.497985	−	0.361807i
$229$	−2.73806	−	8.42689i	−0.180936	−	0.556864i	0.818918	−	0.573910i	$-0.194574\pi$
$229$	−2.73806	−	8.42689i	−0.180936	−	0.556864i	−0.999855	+	0.0170454i	$0.994574\pi$
$230$	−0.239177	+	0.736110i	−0.0157708	+	0.0485377i
$231$	−5.14211	−	3.73596i	−0.338326	−	0.245808i
$232$	−4.04335	+	12.4441i	−0.265459	+	0.816998i
$233$	2.80340	−	8.62799i	0.183657	−	0.565238i	−0.816266	−	0.577677i	$-0.803959\pi$
$233$	2.80340	−	8.62799i	0.183657	−	0.565238i	0.999923	+	0.0124384i	$0.00395937\pi$
$234$	−1.84881	−	1.34324i	−0.120860	−	0.0878103i
$235$	−1.98523	+	6.10991i	−0.129502	+	0.398567i
$236$	6.93531	+	21.3447i	0.451450	+	1.38942i
$237$	1.17325	−	0.852419i	0.0762110	−	0.0553706i
$238$	2.60421	+	8.01494i	0.168806	+	0.519531i
$239$	−13.0457	−	9.47822i	−0.843853	−	0.613095i	0.0795913	−	0.996828i	$-0.474638\pi$
$239$	−13.0457	−	9.47822i	−0.843853	−	0.613095i	−0.923444	+	0.383732i	$0.874638\pi$
$240$	2.17239	+	1.57833i	0.140227	+	0.101881i
$241$	0.469873	−	0.341383i	0.0302672	−	0.0219904i	−0.572549	−	0.819871i	$-0.694045\pi$
$241$	0.469873	−	0.341383i	0.0302672	−	0.0219904i	0.602816	+	0.797880i	$0.294045\pi$
$242$	4.31731			0.277527
$243$	1.00000			0.0641500
$244$	−14.5763	+	10.5903i	−0.933154	+	0.677976i
$245$	−4.22590	+	13.0060i	−0.269983	+	0.830921i
$246$	−1.88236	−	5.79332i	−0.120015	−	0.369368i
$247$	−25.1123			−1.59786
$248$	−6.83415	−	7.33290i	−0.433969	−	0.465639i
$249$	−3.35114			−0.212370
$250$	0.147481	+	0.453901i	0.00932755	+	0.0287072i
$251$	−6.43259	+	19.7975i	−0.406022	+	1.24961i	0.514017	+	0.857780i	$0.328157\pi$
$251$	−6.43259	+	19.7975i	−0.406022	+	1.24961i	−0.920039	+	0.391827i	$0.871843\pi$
$252$	−6.51931	+	4.73656i	−0.410678	+	0.298375i
$253$	2.26694			0.142521
$254$	1.31359			0.0824220
$255$	3.14174	−	2.28261i	0.196744	−	0.142943i
$256$	−0.588982	−	0.427920i	−0.0368113	−	0.0267450i
$257$	−12.0054	−	8.72246i	−0.748879	−	0.544092i	0.146600	−	0.989196i	$-0.453167\pi$
$257$	−12.0054	−	8.72246i	−0.748879	−	0.544092i	−0.895479	+	0.445104i	$0.853167\pi$
$258$	0.992678	+	3.05515i	0.0618014	+	0.190205i
$259$	−32.6992	+	23.7573i	−2.03183	+	1.47621i
$260$	−2.62229	−	8.07057i	−0.162627	−	0.500516i
$261$	−2.24589	+	6.91214i	−0.139017	+	0.427851i
$262$	−5.19598	−	3.77510i	−0.321009	−	0.233226i
$263$	−1.24370	+	3.82772i	−0.0766900	+	0.236028i	−0.982051	−	0.188615i	$-0.939600\pi$
$263$	−1.24370	+	3.82772i	−0.0766900	+	0.236028i	0.905361	+	0.424642i	$0.139600\pi$
$264$	−0.777665	+	2.39341i	−0.0478620	+	0.147304i
$265$	−4.29291	−	3.11898i	−0.263712	−	0.191598i
$266$	3.51699	−	10.8242i	0.215640	−	0.663673i
$267$	−2.00599	−	6.17381i	−0.122765	−	0.377831i
$268$	6.35093	−	4.61422i	0.387945	−	0.281858i
$269$	1.26572	+	3.89549i	0.0771725	+	0.237512i	0.982199	−	0.187842i	$-0.0601494\pi$
$269$	1.26572	+	3.89549i	0.0771725	+	0.237512i	−0.905027	+	0.425355i	$0.860149\pi$
$270$	−0.386111	−	0.280526i	−0.0234980	−	0.0170723i
$271$	4.07412	+	2.96002i	0.247485	+	0.179809i	0.704612	−	0.709593i	$-0.251121\pi$
$271$	4.07412	+	2.96002i	0.247485	+	0.179809i	−0.457126	+	0.889402i	$0.651121\pi$
$272$	−8.43627	+	6.12931i	−0.511524	+	0.371644i
$273$	21.7724			1.31772
$274$	6.75232			0.407922
$275$	1.13088	−	0.821630i	0.0681945	−	0.0495462i
$276$	0.888142	−	2.73342i	0.0534598	−	0.164532i
$277$	6.29951	+	19.3879i	0.378501	+	1.16491i	0.941086	+	0.338167i	$0.109807\pi$
$277$	6.29951	+	19.3879i	0.378501	+	1.16491i	−0.562585	+	0.826739i	$0.690193\pi$
$278$	−1.81290			−0.108731
$279$	−3.79605	−	4.07308i	−0.227264	−	0.243849i
$280$	8.18612			0.489214
$281$	−4.44575	−	13.6826i	−0.265211	−	0.816236i	−0.991645	−	0.128999i	$-0.958823\pi$
$281$	−4.44575	−	13.6826i	−0.265211	−	0.816236i	0.726433	−	0.687237i	$-0.241177\pi$
$282$	−0.947471	+	2.91602i	−0.0564211	+	0.173646i
$283$	−13.8960	+	10.0960i	−0.826029	+	0.600145i	−0.918433	−	0.395576i	$-0.870545\pi$
$283$	−13.8960	+	10.0960i	−0.826029	+	0.600145i	0.0924042	+	0.995722i	$0.470545\pi$
$284$	26.7531			1.58750
$285$	−5.24454			−0.310660
$286$	2.58434	−	1.87763i	0.152815	−	0.111027i
$287$	46.9515	+	34.1123i	2.77146	+	2.01358i
$288$	3.94979	+	2.86969i	0.232744	+	0.169098i
$289$	−0.593048	−	1.82521i	−0.0348852	−	0.107366i
$290$	2.80620	−	2.03883i	0.164786	−	0.119724i
$291$	−0.676591	−	2.08233i	−0.0396625	−	0.122069i
$292$	5.68531	−	17.4976i	0.332707	−	1.02397i
$293$	−17.9361	−	13.0314i	−1.04784	−	0.761301i	−0.0760402	−	0.997105i	$-0.524228\pi$
$293$	−17.9361	−	13.0314i	−1.04784	−	0.761301i	−0.971801	+	0.235804i	$0.924228\pi$
$294$	−2.01685	+	6.20723i	−0.117625	+	0.362013i
$295$	3.91334	−	12.0440i	0.227843	−	0.701230i
$296$	12.9468	+	9.40641i	0.752518	+	0.546737i
$297$	−0.431957	+	1.32943i	−0.0250647	+	0.0771411i
$298$	−1.13310	−	3.48734i	−0.0656390	−	0.202016i
$299$	−6.28230	+	4.56436i	−0.363315	+	0.263964i
$300$	−0.547647	−	1.68548i	−0.0316184	−	0.0973115i
$301$	−24.7602	−	17.9894i	−1.42716	−	1.03689i
$302$	1.91086	+	1.38832i	0.109958	+	0.0798889i
$303$	12.0169	−	8.73081i	0.690354	−	0.501572i
$304$	14.0827			0.807701
$305$	10.1665			0.582133
$306$	1.49943	−	1.08940i	0.0857166	−	0.0622768i
$307$	−1.88044	+	5.78741i	−0.107323	+	0.330305i	−0.990269	−	0.139170i	$-0.955557\pi$
$307$	−1.88044	+	5.78741i	−0.107323	+	0.330305i	0.882946	+	0.469475i	$0.155557\pi$
$308$	−3.48084	−	10.7129i	−0.198339	−	0.610426i
$309$	15.1710			0.863047
$310$	0.323092	+	2.63756i	0.0183504	+	0.149803i
$311$	−21.3656			−1.21153			−0.605766	−	0.795643i	$-0.707133\pi$
$311$	−21.3656			−1.21153			−0.605766	+	0.795643i	$0.707133\pi$
$312$	−2.66388	−	8.19857i	−0.150812	−	0.464153i
$313$	3.27362	−	10.0752i	0.185036	−	0.569482i	−0.814913	−	0.579583i	$-0.803215\pi$
$313$	3.27362	−	10.0752i	0.185036	−	0.569482i	0.999949	+	0.0101011i	$0.00321534\pi$
$314$	1.77157	−	1.28712i	0.0999754	−	0.0726364i
$315$	4.54701			0.256195
$316$	2.57012			0.144580
$317$	5.75128	−	4.17855i	0.323024	−	0.234691i	−0.414441	−	0.910076i	$-0.636023\pi$
$317$	5.75128	−	4.17855i	0.323024	−	0.234691i	0.737465	+	0.675386i	$0.236023\pi$
$318$	−2.04884	−	1.48857i	−0.114893	−	0.0834747i
$319$	−8.21905	−	5.97149i	−0.460179	−	0.334339i
$320$	0.939522	+	2.89155i	0.0525209	+	0.161643i
$321$	−1.48157	+	1.07643i	−0.0826934	+	0.0600803i
$322$	−1.08754	−	3.34710i	−0.0606062	−	0.186527i
$323$	6.29365	−	19.3699i	0.350188	−	1.07777i
$324$	1.43376	+	1.04169i	0.0796532	+	0.0578715i
$325$	−1.47966	+	4.55393i	−0.0820768	+	0.252606i
$326$	−2.63026	+	8.09510i	−0.145676	+	0.448346i
$327$	5.46930	+	3.97368i	0.302453	+	0.219745i
$328$	7.10069	−	21.8537i	0.392070	−	1.20667i
$329$	−9.02686	−	27.7818i	−0.497667	−	1.53166i
$330$	0.539722	−	0.392131i	0.0297107	−	0.0215861i
$331$	−3.09775	−	9.53388i	−0.170268	−	0.524030i	0.829118	−	0.559073i	$-0.188843\pi$
$331$	−3.09775	−	9.53388i	−0.170268	−	0.524030i	−0.999386	+	0.0350437i	$0.988843\pi$
$332$	−4.80473	−	3.49084i	−0.263694	−	0.191585i
$333$	7.19135	+	5.22482i	0.394084	+	0.286319i
$334$	−4.83389	+	3.51203i	−0.264499	+	0.192169i
$335$	−4.42957			−0.242013
$336$	−12.2097			−0.666095
$337$	−14.0698	+	10.2223i	−0.766432	+	0.556845i	−0.900876	−	0.434076i	$-0.857075\pi$
$337$	−14.0698	+	10.2223i	−0.766432	+	0.556845i	0.134444	+	0.990921i	$0.457075\pi$
$338$	−1.46414	+	4.50616i	−0.0796388	+	0.245103i
$339$	3.87911	+	11.9387i	0.210684	+	0.648419i
$340$	6.88226			0.373243
$341$	7.05459	−	3.28717i	0.382027	−	0.178010i
$342$	−2.50301			−0.135347
$343$	−9.37947	−	28.8670i	−0.506444	−	1.55867i
$344$	−3.74460	+	11.5247i	−0.201895	+	0.621370i
$345$	−1.31202	+	0.953235i	−0.0706366	+	0.0513205i
$346$	−2.83838			−0.152592
$347$	−0.0194964			−0.00104662			−0.000523310	−	1.00000i	$-0.500167\pi$
$347$	−0.0194964			−0.00104662			−0.000523310		1.00000i	$0.500167\pi$
$348$	−10.4204	+	7.57083i	−0.558590	+	0.405839i
$349$	−3.17308	−	2.30538i	−0.169851	−	0.123404i	0.499612	−	0.866249i	$-0.333476\pi$
$349$	−3.17308	−	2.30538i	−0.169851	−	0.123404i	−0.669463	+	0.742845i	$0.733476\pi$
$350$	−1.75565	−	1.27556i	−0.0938436	−	0.0681813i
$351$	−1.47966	−	4.55393i	−0.0789784	−	0.243071i
$352$	−5.52118	+	4.01137i	−0.294280	+	0.213807i
$353$	8.50884	+	26.1875i	0.452880	+	1.39382i	0.873607	+	0.486633i	$0.161775\pi$
$353$	8.50884	+	26.1875i	0.452880	+	1.39382i	−0.420727	+	0.907187i	$0.638225\pi$
$354$	1.86768	−	5.74813i	0.0992661	−	0.305510i
$355$	−12.2127	−	8.87308i	−0.648185	−	0.470934i
$356$	3.55506	−	10.9414i	0.188418	−	0.579891i
$357$	−5.45659	+	16.7937i	−0.288793	+	0.888814i
$358$	−4.64492	−	3.37473i	−0.245492	−	0.178360i
$359$	−5.66681	+	17.4407i	−0.299083	+	0.920483i	0.682736	+	0.730665i	$0.260790\pi$
$359$	−5.66681	+	17.4407i	−0.299083	+	0.920483i	−0.981819	+	0.189818i	$0.939210\pi$
$360$	−0.556333	−	1.71222i	−0.0293213	−	0.0902417i
$361$	−6.88087	+	4.99924i	−0.362151	+	0.263118i
$362$	2.15456	+	6.63106i	0.113241	+	0.348521i
$363$	7.31840	+	5.31713i	0.384116	+	0.279077i
$364$	31.2163	+	22.6800i	1.63618	+	1.18875i
$365$	−8.39868	+	6.10200i	−0.439607	+	0.319393i
$366$	4.85207			0.253622
$367$	−19.4025			−1.01280			−0.506400	−	0.862299i	$-0.669024\pi$
$367$	−19.4025			−1.01280			−0.506400	+	0.862299i	$0.669024\pi$
$368$	3.52305	−	2.55965i	0.183652	−	0.133431i
$369$	3.94410	−	12.1387i	0.205322	−	0.631916i
$370$	−1.31096	−	4.03473i	−0.0681537	−	0.209756i
$371$	24.1279			1.25266
$372$	−1.19975	−	9.79411i	−0.0622039	−	0.507801i
$373$	33.9064			1.75561			0.877804	−	0.479019i	$-0.159008\pi$
$373$	33.9064			1.75561			0.877804	+	0.479019i	$0.159008\pi$
$374$	0.800586	+	2.46395i	0.0413973	+	0.127408i
$375$	−0.309017	+	0.951057i	−0.0159576	+	0.0491123i
$376$	−9.35704	+	6.79829i	−0.482553	+	0.350595i
$377$	34.8005			1.79232
$378$	2.17011			0.111618
$379$	−12.7159	+	9.23861i	−0.653169	+	0.474555i	−0.864349	−	0.502892i	$-0.832269\pi$
$379$	−12.7159	+	9.23861i	−0.653169	+	0.474555i	0.211180	+	0.977447i	$0.432269\pi$
$380$	−7.51941	−	5.46317i	−0.385737	−	0.280255i
$381$	2.22671	+	1.61780i	0.114078	+	0.0828822i
$382$	−0.344429	−	1.06004i	−0.0176225	−	0.0542366i
$383$	−3.89922	+	2.83295i	−0.199241	+	0.144757i	−0.682933	−	0.730481i	$-0.739296\pi$
$383$	−3.89922	+	2.83295i	−0.199241	+	0.144757i	0.483691	+	0.875239i	$0.339296\pi$
$384$	3.46577	+	10.6665i	0.176862	+	0.544324i
$385$	−1.96411	+	6.04491i	−0.100100	+	0.308077i
$386$	0.664681	+	0.482919i	0.0338314	+	0.0245799i
$387$	−2.07995	+	6.40143i	−0.105730	+	0.325403i
$388$	1.19907	−	3.69036i	0.0608736	−	0.187350i
$389$	6.87526	+	4.99517i	0.348590	+	0.253265i	0.748277	−	0.663386i	$-0.230881\pi$
$389$	6.87526	+	4.99517i	0.348590	+	0.253265i	−0.399687	+	0.916651i	$0.630881\pi$
$390$	−0.706183	+	2.17341i	−0.0357589	+	0.110055i
$391$	−1.94615	−	5.98964i	−0.0984212	−	0.302909i
$392$	−19.9180	+	14.4713i	−1.00601	+	0.730911i
$393$	−4.15850	−	12.7986i	−0.209769	−	0.645602i
$394$	1.75729	+	1.27675i	0.0885311	+	0.0643216i
$395$	−1.17325	−	0.852419i	−0.0590328	−	0.0428899i
$396$	−2.00417	+	1.45611i	−0.100713	+	0.0731724i
$397$	−20.0547			−1.00652			−0.503259	−	0.864136i	$-0.667866\pi$
$397$	−20.0547			−1.00652			−0.503259	+	0.864136i	$0.667866\pi$
$398$	−12.7855			−0.640880
$399$	19.2926	−	14.0169i	0.965839	−	0.701723i
$400$	0.829779	−	2.55380i	0.0414889	−	0.127690i
$401$	5.66372	+	17.4311i	0.282833	+	0.870470i	0.987040	+	0.160475i	$0.0513026\pi$
$401$	5.66372	+	17.4311i	0.282833	+	0.870470i	−0.704207	+	0.709995i	$0.748697\pi$
$402$	−2.11406			−0.105440
$403$	−12.9316	+	23.3137i	−0.644171	+	1.16134i
$404$	26.3241			1.30967
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−4.87382	+	15.0001i	−0.241884	+	0.744441i
$407$	−10.0524	+	7.30347i	−0.498277	+	0.362020i
$408$	6.99142			0.346127
$409$	−2.43248			−0.120279			−0.0601393	−	0.998190i	$-0.519154\pi$
$409$	−2.43248			−0.120279			−0.0601393	+	0.998190i	$0.519154\pi$
$410$	−4.92809	+	3.58047i	−0.243381	+	0.176827i
$411$	11.4460	+	8.31604i	0.564592	+	0.410200i
$412$	21.7515	+	15.8034i	1.07162	+	0.778578i
$413$	17.7940	+	54.7643i	0.875585	+	2.69477i
$414$	−0.626173	+	0.454941i	−0.0307747	+	0.0223591i
$415$	1.03556	+	3.18713i	0.0508336	+	0.156450i
$416$	7.22401	−	22.2332i	0.354186	−	1.09007i
$417$	−3.07310	−	2.23274i	−0.150491	−	0.109338i
$418$	1.08119	−	3.32757i	0.0528828	−	0.162757i
$419$	−2.02150	+	6.22155i	−0.0987569	+	0.303943i	−0.988215	−	0.153075i	$-0.951082\pi$
$419$	−2.02150	+	6.22155i	−0.0987569	+	0.303943i	0.889458	+	0.457018i	$0.151082\pi$
$420$	6.51931	+	4.73656i	0.318110	+	0.231120i
$421$	4.26583	−	13.1289i	0.207904	−	0.639862i	−0.791678	−	0.610939i	$-0.790792\pi$
$421$	4.26583	−	13.1289i	0.207904	−	0.639862i	0.999582	−	0.0289235i	$-0.00920791\pi$
$422$	2.77758	+	8.54850i	0.135210	+	0.416135i
$423$	−5.19740	+	3.77613i	−0.252706	+	0.183602i
$424$	−2.95209	−	9.08559i	−0.143366	−	0.441235i
$425$	−3.14174	−	2.28261i	−0.152397	−	0.110723i
$426$	−5.82865	−	4.23476i	−0.282399	−	0.205175i
$427$	−37.3986	+	27.1717i	−1.80985	+	1.31493i
$428$	−3.24552			−0.156878
$429$	6.69325			0.323153
$430$	2.59886	−	1.88819i	0.125328	−	0.0910564i
$431$	10.9261	−	33.6272i	0.526294	−	1.61977i	−0.235449	−	0.971887i	$-0.575656\pi$
$431$	10.9261	−	33.6272i	0.526294	−	1.61977i	0.761743	−	0.647879i	$-0.224344\pi$
$432$	0.829779	+	2.55380i	0.0399227	+	0.122870i
$433$	15.3086			0.735685			0.367843	−	0.929888i	$-0.380097\pi$
$433$	15.3086			0.735685			0.367843	+	0.929888i	$0.380097\pi$
$434$	−8.23783	−	8.83902i	−0.395429	−	0.424286i
$435$	7.26786			0.348467
$436$	3.70233	+	11.3946i	0.177309	+	0.545702i
$437$	−2.62828	+	8.08901i	−0.125728	+	0.386950i
$438$	−4.00835	+	2.91224i	−0.191526	+	0.139152i
$439$	12.6240			0.602510			0.301255	−	0.953544i	$-0.402595\pi$
$439$	12.6240			0.602510			0.301255	+	0.953544i	$0.402595\pi$
$440$	2.51658			0.119973
$441$	−11.0635	+	8.03813i	−0.526835	+	0.382768i
$442$	−7.17968	−	5.21635i	−0.341503	−	0.248116i
$443$	−3.25428	−	2.36437i	−0.154615	−	0.112335i	0.507788	−	0.861482i	$-0.330463\pi$
$443$	−3.25428	−	2.36437i	−0.154615	−	0.112335i	−0.662403	+	0.749148i	$0.730463\pi$
$444$	4.86804	+	14.9823i	0.231027	+	0.711027i
$445$	−5.25175	+	3.81562i	−0.248957	+	0.180878i
$446$	−1.68315	−	5.18019i	−0.0796993	−	0.245289i
$447$	2.37419	−	7.30699i	0.112295	−	0.345609i
$448$	−11.1843	−	8.12585i	−0.528407	−	0.383910i
$449$	−1.01515	+	3.12433i	−0.0479081	+	0.147446i	−0.972149	−	0.234364i	$-0.924699\pi$
$449$	−1.01515	+	3.12433i	−0.0479081	+	0.147446i	0.924241	+	0.381810i	$0.124699\pi$
$450$	−0.147481	+	0.453901i	−0.00695234	+	0.0213971i
$451$	14.4338	+	10.4868i	0.679662	+	0.493804i
$452$	−6.87464	+	21.1580i	−0.323356	+	0.995187i
$453$	1.52932	+	4.70676i	0.0718537	+	0.221143i
$454$	−5.76001	+	4.18489i	−0.270330	+	0.196407i
$455$	−6.72803	−	20.7067i	−0.315415	−	0.970747i
$456$	−7.63867	−	5.54982i	−0.357713	−	0.259894i
$457$	8.17275	+	5.93785i	0.382305	+	0.277761i	0.762295	−	0.647230i	$-0.224073\pi$
$457$	8.17275	+	5.93785i	0.382305	+	0.277761i	−0.379990	+	0.924991i	$0.624073\pi$
$458$	−3.42116	+	2.48562i	−0.159860	+	0.116145i
$459$	3.88341			0.181262
$460$	−2.87409			−0.134005
$461$	10.6615	−	7.74606i	0.496557	−	0.360770i	−0.311143	−	0.950363i	$-0.600712\pi$
$461$	10.6615	−	7.74606i	0.496557	−	0.360770i	0.807700	+	0.589593i	$0.200712\pi$
$462$	−0.937391	+	2.88499i	−0.0436114	+	0.134222i
$463$	9.99890	+	30.7735i	0.464688	+	1.43016i	0.859374	+	0.511348i	$0.170854\pi$
$463$	9.99890	+	30.7735i	0.464688	+	1.43016i	−0.394685	+	0.918816i	$0.629146\pi$
$464$	−19.5158			−0.905998
$465$	−2.70069	+	4.86891i	−0.125241	+	0.225790i
$466$	−4.32971			−0.200570
$467$	5.25057	+	16.1596i	0.242967	+	0.747777i	0.995964	+	0.0897525i	$0.0286076\pi$
$467$	5.25057	+	16.1596i	0.242967	+	0.747777i	−0.752997	+	0.658024i	$0.771392\pi$
$468$	2.62229	−	8.07057i	0.121215	−	0.373062i
$469$	16.2946	−	11.8388i	0.752417	−	0.546663i
$470$	3.06608			0.141428
$471$	4.58823			0.211415
$472$	18.4448	−	13.4010i	0.848993	−	0.616829i
$473$	−7.61178	−	5.53028i	−0.349990	−	0.254283i
$474$	−0.559947	−	0.406825i	−0.0257192	−	0.0186861i
$475$	1.62065	+	4.98786i	0.0743606	+	0.228859i
$476$	−25.3171	+	18.3940i	−1.16041	+	0.843087i
$477$	−1.63975	−	5.04662i	−0.0750789	−	0.231069i
$478$	−2.37818	+	7.31930i	−0.108776	+	0.334777i
$479$	−24.6335	−	17.8973i	−1.12553	−	0.817746i	−0.140493	−	0.990082i	$-0.544869\pi$
$479$	−24.6335	−	17.8973i	−1.12553	−	0.817746i	−0.985038	+	0.172335i	$0.944869\pi$
$480$	1.50869	−	4.64326i	0.0688618	−	0.211935i
$481$	13.1527	−	40.4799i	0.599712	−	1.84572i
$482$	−0.224252	−	0.162928i	−0.0102144	−	0.00742118i
$483$	2.27871	−	7.01316i	0.103685	−	0.319110i
$484$	4.95404	+	15.2470i	0.225183	+	0.693044i
$485$	−1.77134	+	1.28695i	−0.0804323	+	0.0584375i
$486$	−0.147481	−	0.453901i	−0.00668989	−	0.0205894i
$487$	−7.72584	−	5.61315i	−0.350091	−	0.254356i	0.398816	−	0.917031i	$-0.369421\pi$
$487$	−7.72584	−	5.61315i	−0.350091	−	0.254356i	−0.748907	+	0.662675i	$0.769421\pi$
$488$	14.8075	+	10.7583i	0.670305	+	0.487005i
$489$	−14.4284	+	10.4829i	−0.652475	+	0.474051i
$490$	6.52667			0.294845
$491$	−2.18355			−0.0985422			−0.0492711	−	0.998785i	$-0.515690\pi$
$491$	−2.18355			−0.0985422			−0.0492711	+	0.998785i	$0.515690\pi$
$492$	18.2996	−	13.2954i	0.825010	−	0.599405i
$493$	−8.72171	+	26.8427i	−0.392806	+	1.20893i
$494$	3.70360	+	11.3985i	0.166633	+	0.512844i
$495$	1.39784			0.0628283
$496$	7.25194	−	13.0741i	0.325622	−	0.587044i
$497$	68.6407			3.07895
$498$	0.494231	+	1.52109i	0.0221470	+	0.0681616i
$499$	−7.76270	+	23.8911i	−0.347506	+	1.06951i	0.612722	+	0.790298i	$0.290074\pi$
$499$	−7.76270	+	23.8911i	−0.347506	+	1.06951i	−0.960228	+	0.279216i	$0.909926\pi$
$500$	−1.43376	+	1.04169i	−0.0641196	+	0.0465856i
$501$	−12.5194			−0.559326
$502$	9.93479			0.443412
$503$	−6.15933	+	4.47501i	−0.274631	+	0.199531i	−0.716572	−	0.697513i	$-0.754290\pi$
$503$	−6.15933	+	4.47501i	−0.274631	+	0.199531i	0.441941	+	0.897044i	$0.354290\pi$
$504$	6.62271	+	4.81168i	0.294999	+	0.214329i
$505$	−12.0169	−	8.73081i	−0.534746	−	0.388516i
$506$	−0.334331	−	1.02896i	−0.0148628	−	0.0457431i
$507$	−8.03162	+	5.83532i	−0.356697	+	0.259155i
$508$	1.50732	+	4.63906i	0.0668766	+	0.205825i
$509$	3.02971	−	9.32450i	0.134290	−	0.413301i	−0.861189	−	0.508285i	$-0.830280\pi$
$509$	3.02971	−	9.32450i	0.134290	−	0.413301i	0.995479	+	0.0949833i	$0.0302798\pi$
$510$	−1.49943	−	1.08940i	−0.0663958	−	0.0482394i
$511$	14.5868	−	44.8937i	0.645284	−	1.98598i
$512$	−7.03891	+	21.6635i	−0.311079	+	0.957402i
$513$	−4.24292	−	3.08266i	−0.187330	−	0.136103i
$514$	−2.18856	+	6.73568i	−0.0965331	+	0.297098i
$515$	−4.68809	−	14.4285i	−0.206582	−	0.635794i
$516$	−9.65044	+	7.01145i	−0.424837	+	0.308662i
$517$	−2.77504	−	8.54068i	−0.122046	−	0.375619i
$518$	15.6060	+	11.3384i	0.685688	+	0.498182i
$519$	−4.81142	−	3.49570i	−0.211198	−	0.153444i
$520$	−6.97412	+	5.06700i	−0.305836	+	0.222203i
$521$	−30.3004			−1.32749			−0.663743	−	0.747961i	$-0.731033\pi$
$521$	−30.3004			−1.32749			−0.663743	+	0.747961i	$0.731033\pi$
$522$	3.46866			0.151819
$523$	−26.3273	+	19.1279i	−1.15121	+	0.836406i	−0.988642	−	0.150290i	$-0.951979\pi$
$523$	−26.3273	+	19.1279i	−1.15121	+	0.836406i	−0.162573	+	0.986697i	$0.551979\pi$
$524$	7.36979	−	22.6819i	0.321951	−	0.990863i
$525$	−1.40510	−	4.32446i	−0.0613237	−	0.188735i
$526$	1.92083			0.0837522
$527$	−14.7416	−	15.8174i	−0.642155	−	0.689018i
$528$	−3.75351			−0.163351
$529$	−6.29466	−	19.3730i	−0.273681	−	0.842303i
$530$	−0.782586	+	2.40855i	−0.0339934	+	0.104621i
$531$	10.2453	−	7.44361i	0.444606	−	0.323025i
$532$	42.2622			1.83230
$533$	−61.1147			−2.64717
$534$	−2.50645	+	1.82104i	−0.108465	+	0.0788043i
$535$	1.48157	+	1.07643i	0.0640540	+	0.0465380i
$536$	−6.45166	−	4.68741i	−0.278669	−	0.202465i
$537$	−3.71747	−	11.4412i	−0.160421	−	0.493725i
$538$	1.58150	−	1.14903i	0.0681833	−	0.0495380i
$539$	−5.90713	−	18.1803i	−0.254438	−	0.783080i
$540$	0.547647	−	1.68548i	0.0235670	−	0.0725317i
$541$	−0.663405	−	0.481992i	−0.0285220	−	0.0207225i	0.573433	−	0.819253i	$-0.305611\pi$
$541$	−0.663405	−	0.481992i	−0.0285220	−	0.0207225i	−0.601955	+	0.798530i	$0.705611\pi$
$542$	0.742700	−	2.28580i	0.0319017	−	0.0981834i
$543$	−4.51444	+	13.8940i	−0.193733	+	0.596250i
$544$	15.3386	+	11.1442i	0.657639	+	0.477803i
$545$	2.08909	−	6.42955i	0.0894867	−	0.275412i
$546$	−3.21102	−	9.88250i	−0.137419	−	0.422932i
$547$	−13.1849	+	9.57938i	−0.563745	+	0.409585i	−0.832828	−	0.553532i	$-0.813279\pi$
$547$	−13.1849	+	9.57938i	−0.563745	+	0.409585i	0.269083	+	0.963117i	$0.413279\pi$
$548$	7.74816	+	23.8464i	0.330985	+	1.01867i
$549$	8.22489	+	5.97573i	0.351030	+	0.255038i
$550$	−0.539722	−	0.392131i	−0.0230138	−	0.0167205i
$551$	30.8370	−	22.4044i	1.31370	−	0.954458i
$552$	−2.91967			−0.124269
$553$	6.59417			0.280413
$554$	7.87113	−	5.71871i	0.334412	−	0.242965i
$555$	2.74685	−	8.45394i	0.116597	−	0.358850i
$556$	−2.08027	−	6.40242i	−0.0882232	−	0.271523i
$557$	−17.4588			−0.739752			−0.369876	−	0.929081i	$-0.620600\pi$
$557$	−17.4588			−0.739752			−0.369876	+	0.929081i	$0.620600\pi$
$558$	−1.28893	+	2.32374i	−0.0545647	+	0.0983716i
$559$	32.2293			1.36315
$560$	3.77301	+	11.6121i	0.159439	+	0.490702i
$561$	−1.67746	+	5.16270i	−0.0708226	+	0.217969i
$562$	−5.55489	+	4.03586i	−0.234319	+	0.170243i
$563$	4.35918			0.183718			0.0918588	−	0.995772i	$-0.470719\pi$
$563$	4.35918			0.183718			0.0918588	+	0.995772i	$0.470719\pi$
$564$	−11.3854			−0.479410
$565$	10.1556	−	7.37850i	0.427251	−	0.310416i
$566$	6.63198	+	4.81842i	0.278763	+	0.202533i
$567$	3.67861	+	2.67266i	0.154487	+	0.112241i
$568$	−8.39828	−	25.8472i	−0.352384	−	1.08453i
$569$	−9.03976	+	6.56777i	−0.378967	+	0.275335i	−0.760919	−	0.648847i	$-0.775252\pi$
$569$	−9.03976	+	6.56777i	−0.378967	+	0.275335i	0.381953	+	0.924182i	$0.375252\pi$
$570$	0.773473	+	2.38050i	0.0323972	+	0.0997083i
$571$	−2.24737	+	6.91671i	−0.0940497	+	0.289455i	−0.987005	−	0.160690i	$-0.948628\pi$
$571$	−2.24737	+	6.91671i	−0.0940497	+	0.289455i	0.892955	+	0.450146i	$0.148628\pi$
$572$	9.59651	+	6.97227i	0.401250	+	0.291525i
$573$	0.721680	−	2.22110i	0.0301486	−	0.0927879i
$574$	8.55912	−	26.3423i	0.357251	−	1.09951i
$575$	1.31202	+	0.953235i	0.0547148	+	0.0397527i
$576$	−0.939522	+	2.89155i	−0.0391467	+	0.120481i
$577$	3.10718	+	9.56293i	0.129354	+	0.398110i	0.994669	−	0.103118i	$-0.0328819\pi$
$577$	3.10718	+	9.56293i	0.129354	+	0.398110i	−0.865315	+	0.501228i	$0.832882\pi$
$578$	−0.741004	+	0.538371i	−0.0308217	+	0.0223933i
$579$	0.531965	+	1.63722i	0.0221077	+	0.0680405i
$580$	10.4204	+	7.57083i	0.432682	+	0.314362i
$581$	−12.3275	−	8.95648i	−0.511432	−	0.371577i
$582$	−0.845389	+	0.614211i	−0.0350425	+	0.0254599i
$583$	7.41741			0.307198
$584$	−18.6898			−0.773391
$585$	−3.87380	+	2.81448i	−0.160162	+	0.116364i
$586$	−3.26971	+	10.0631i	−0.135070	+	0.415704i
$587$	−2.42426	−	7.46110i	−0.100060	−	0.307952i	0.888479	−	0.458916i	$-0.151762\pi$
$587$	−2.42426	−	7.46110i	−0.100060	−	0.307952i	−0.988539	+	0.150964i	$0.951762\pi$
$588$	−24.2357			−0.999462
$589$	3.55041	+	28.9837i	0.146292	+	1.19425i
$590$	−6.04394			−0.248825
$591$	1.40642	+	4.32850i	0.0578522	+	0.178051i
$592$	−7.37590	+	22.7007i	−0.303148	+	0.932993i
$593$	−16.3159	+	11.8542i	−0.670016	+	0.486795i	−0.870030	−	0.492998i	$-0.835901\pi$
$593$	−16.3159	+	11.8542i	−0.670016	+	0.486795i	0.200015	+	0.979793i	$0.435901\pi$
$594$	0.667134			0.0273728
$595$	17.6579			0.723903
$596$	11.0156	−	8.00331i	0.451217	−	0.327828i
$597$	−21.6731	−	15.7464i	−0.887021	−	0.644459i
$598$	2.99829	+	2.17839i	0.122609	+	0.0890808i
$599$	−8.73406	−	26.8807i	−0.356864	−	1.09831i	−0.954921	−	0.296861i	$-0.904060\pi$
$599$	−8.73406	−	26.8807i	−0.356864	−	1.09831i	0.598057	−	0.801454i	$-0.295940\pi$
$600$	−1.45650	+	1.05821i	−0.0594613	+	0.0432012i
$601$	−4.11582	−	12.6672i	−0.167888	−	0.516705i	0.831350	−	0.555750i	$-0.187569\pi$
$601$	−4.11582	−	12.6672i	−0.167888	−	0.516705i	−0.999237	+	0.0390442i	$0.987569\pi$
$602$	−4.51372	+	13.8918i	−0.183965	+	0.566187i
$603$	−3.58360	−	2.60364i	−0.145935	−	0.106028i
$604$	−2.71030	+	8.34143i	−0.110280	+	0.339408i
$605$	2.79538	−	8.60330i	0.113648	−	0.349774i
$606$	−5.73520	−	4.16687i	−0.232976	−	0.169267i
$607$	4.83106	−	14.8685i	0.196087	−	0.603493i	−0.803876	−	0.594798i	$-0.797232\pi$
$607$	4.83106	−	14.8685i	0.196087	−	0.603493i	0.999962	−	0.00869519i	$-0.00276780\pi$
$608$	−7.91237	−	24.3518i	−0.320889	−	0.987594i
$609$	−26.7356	+	19.4245i	−1.08338	+	0.787122i
$610$	−1.49937	−	4.61460i	−0.0607078	−	0.186840i
$611$	24.8866	+	18.0812i	1.00680	+	0.731486i
$612$	5.56787	+	4.04529i	0.225068	+	0.163521i
$613$	32.0106	−	23.2571i	1.29290	−	0.939345i	0.293037	−	0.956101i	$-0.405334\pi$
$613$	32.0106	−	23.2571i	1.29290	−	0.939345i	0.999860	+	0.0167565i	$0.00533400\pi$
$614$	2.90424			0.117206
$615$	−12.7634			−0.514670
$616$	−9.25750	+	6.72597i	−0.372995	+	0.270997i
$617$	1.48208	−	4.56137i	0.0596662	−	0.183634i	−0.916781	−	0.399390i	$-0.869222\pi$
$617$	1.48208	−	4.56137i	0.0596662	−	0.183634i	0.976447	+	0.215757i	$0.0692218\pi$
$618$	−2.23744	−	6.88612i	−0.0900029	−	0.277001i
$619$	−6.74571			−0.271133			−0.135566	−	0.990768i	$-0.543285\pi$
$619$	−6.74571			−0.271133			−0.135566	+	0.990768i	$0.543285\pi$
$620$	−8.94401	+	4.16757i	−0.359200	+	0.167374i
$621$	−1.62174			−0.0650782
$622$	3.15103	+	9.69787i	0.126345	+	0.388849i
$623$	9.12126	−	28.0724i	0.365436	−	1.12470i
$624$	10.4020	−	7.55750i	0.416413	−	0.302542i
$625$	1.00000			0.0400000
$626$	−5.05593			−0.202076
$627$	5.93093	−	4.30907i	0.236859	−	0.172088i
$628$	6.57842	+	4.77950i	0.262507	+	0.190723i
$629$	27.9270	+	20.2901i	1.11352	+	0.809020i
$630$	−0.670599	−	2.06389i	−0.0267173	−	0.0822275i
$631$	−20.3126	+	14.7580i	−0.808631	+	0.587505i	−0.913433	−	0.406988i	$-0.866579\pi$
$631$	−20.3126	+	14.7580i	−0.808631	+	0.587505i	0.104802	+	0.994493i	$0.466579\pi$
$632$	−0.806806	−	2.48309i	−0.0320930	−	0.0987722i
$633$	−5.81984	+	17.9116i	−0.231318	+	0.711923i
$634$	−2.74485	−	1.99425i	−0.109012	−	0.0792019i
$635$	0.850526	−	2.61765i	0.0337521	−	0.103878i
$636$	2.90600	−	8.94374i	0.115230	−	0.354642i
$637$	52.9753	+	38.4888i	2.09896	+	1.52498i
$638$	−1.49831	+	4.61132i	−0.0593186	+	0.182564i
$639$	−4.66485	−	14.3569i	−0.184539	−	0.567952i
$640$	9.07350	−	6.59228i	0.358662	−	0.260583i
$641$	−5.91863	−	18.2157i	−0.233772	−	0.719475i	−0.997282	−	0.0736797i	$-0.976526\pi$
$641$	−5.91863	−	18.2157i	−0.233772	−	0.719475i	0.763510	−	0.645796i	$-0.223474\pi$
$642$	0.707096	+	0.513735i	0.0279069	+	0.0202755i
$643$	17.2927	+	12.5639i	0.681957	+	0.495471i	0.874006	−	0.485914i	$-0.161513\pi$
$643$	17.2927	+	12.5639i	0.681957	+	0.495471i	−0.192049	+	0.981385i	$0.561513\pi$
$644$	10.5726	−	7.68147i	0.416620	−	0.302692i
$645$	6.73087			0.265028
$646$	−9.72021			−0.382436
$647$	1.22360	−	0.888994i	0.0481045	−	0.0349500i	−0.563473	−	0.826134i	$-0.690535\pi$
$647$	1.22360	−	0.888994i	0.0481045	−	0.0349500i	0.611578	+	0.791184i	$0.290535\pi$
$648$	0.556333	−	1.71222i	0.0218548	−	0.0672622i
$649$	5.47023	+	16.8356i	0.214725	+	0.660856i
$650$	2.28525			0.0896351
$651$	−3.07820	−	25.1288i	−0.120644	−	0.984877i
$652$	−31.6067			−1.23781
$653$	−9.78738	−	30.1225i	−0.383010	−	1.17878i	−0.937914	−	0.346869i	$-0.887245\pi$
$653$	−9.78738	−	30.1225i	−0.383010	−	1.17878i	0.554904	−	0.831914i	$-0.312755\pi$
$654$	0.997038	−	3.06857i	0.0389873	−	0.119990i
$655$	−10.8871	+	7.90994i	−0.425394	+	0.309067i
$656$	34.2725			1.33812
$657$	−10.3813			−0.405014
$658$	−11.2789	+	8.19460i	−0.439698	+	0.319459i
$659$	−22.5273	−	16.3670i	−0.877539	−	0.637569i	0.0550603	−	0.998483i	$-0.482465\pi$
$659$	−22.5273	−	16.3670i	−0.877539	−	0.637569i	−0.932599	+	0.360914i	$0.882465\pi$
$660$	2.00417	+	1.45611i	0.0780121	+	0.0566791i
$661$	1.29872	+	3.99704i	0.0505143	+	0.155467i	0.973132	−	0.230250i	$-0.0739543\pi$
$661$	1.29872	+	3.99704i	0.0505143	+	0.155467i	−0.922617	+	0.385717i	$0.873954\pi$
$662$	−3.87058	+	2.81214i	−0.150434	+	0.109297i
$663$	−5.74612	−	17.6848i	−0.223161	−	0.686819i
$664$	−1.86435	+	5.73788i	−0.0723508	+	0.222673i
$665$	−19.2926	−	14.0169i	−0.748135	−	0.543552i
$666$	1.31096	−	4.03473i	0.0507988	−	0.156343i
$667$	3.64225	−	11.2097i	0.141029	−	0.434042i
$668$	−17.9498	−	13.0413i	−0.694499	−	0.504583i
$669$	3.52669	−	10.8540i	0.136350	−	0.419641i
$670$	0.653279	+	2.01059i	0.0252384	+	0.0776757i
$671$	−11.4971	+	8.35312i	−0.443840	+	0.322469i
$672$	6.86001	+	21.1129i	0.264631	+	0.814449i
$673$	−20.1201	−	14.6181i	−0.775574	−	0.563487i	0.128074	−	0.991765i	$-0.459121\pi$
$673$	−20.1201	−	14.6181i	−0.775574	−	0.563487i	−0.903647	+	0.428277i	$0.859121\pi$
$674$	6.71496	+	4.87871i	0.258651	+	0.187921i
$675$	−0.809017	+	0.587785i	−0.0311391	+	0.0226239i
$676$	−17.5940			−0.676691
$677$	−21.7483			−0.835856			−0.417928	−	0.908480i	$-0.637244\pi$
$677$	−21.7483			−0.835856			−0.417928	+	0.908480i	$0.637244\pi$
$678$	4.84688	−	3.52146i	0.186143	−	0.135241i
$679$	3.07647	−	9.46839i	0.118064	−	0.363363i
$680$	−2.16047	−	6.64924i	−0.0828501	−	0.254987i
$681$	−14.9180			−0.571658
$682$	−2.53247	−	2.71729i	−0.0969734	−	0.104050i
$683$	−1.62172			−0.0620533			−0.0310266	−	0.999519i	$-0.509878\pi$
$683$	−1.62172			−0.0620533			−0.0310266	+	0.999519i	$0.509878\pi$
$684$	−2.87216	−	8.83959i	−0.109820	−	0.337990i
$685$	4.37200	−	13.4556i	0.167046	−	0.514113i
$686$	−11.7195	+	8.51471i	−0.447452	+	0.325093i
$687$	−8.86055			−0.338051
$688$	−18.0739			−0.689059
$689$	−20.5557	+	14.9346i	−0.783109	+	0.568962i
$690$	0.626173	+	0.454941i	0.0238380	+	0.0173193i
$691$	−15.3794	−	11.1738i	−0.585059	−	0.425070i	0.255485	−	0.966813i	$-0.417765\pi$
$691$	−15.3794	−	11.1738i	−0.585059	−	0.425070i	−0.840544	+	0.541743i	$0.817765\pi$
$692$	−3.25699	−	10.0240i	−0.123812	−	0.381055i
$693$	−5.14211	+	3.73596i	−0.195333	+	0.141917i
$694$	0.00287535	+	0.00884942i	0.000109147	+	0.000335919i
$695$	−1.17382	+	3.61265i	−0.0445256	+	0.137036i
$696$	10.5856	+	7.69091i	0.401247	+	0.291523i
$697$	15.3166	−	47.1395i	0.580156	−	1.78554i
$698$	−0.578444	+	1.78027i	−0.0218944	+	0.0673841i
$699$	−7.33941	−	5.33239i	−0.277602	−	0.201690i
$700$	2.49016	−	7.66391i	0.0941190	−	0.289669i
$701$	4.20184	+	12.9319i	0.158701	+	0.488433i	0.998517	−	0.0544388i	$-0.0173370\pi$
$701$	4.20184	+	12.9319i	0.158701	+	0.488433i	−0.839816	+	0.542872i	$0.817337\pi$
$702$	−1.84881	+	1.34324i	−0.0697788	+	0.0506973i
$703$	−14.4060	−	44.3371i	−0.543332	−	1.67220i
$704$	−3.43827	−	2.49805i	−0.129585	−	0.0941487i
$705$	5.19740	+	3.77613i	0.195745	+	0.142217i
$706$	10.6316	−	7.72434i	0.400127	−	0.290709i
$707$	67.5401			2.54011
$708$	22.4431			0.843464
$709$	39.9162	−	29.0008i	1.49908	−	1.08915i	0.528340	−	0.849033i	$-0.322815\pi$
$709$	39.9162	−	29.0008i	1.49908	−	1.08915i	0.970744	−	0.240115i	$-0.0771852\pi$
$710$	−2.22635	+	6.85199i	−0.0835533	+	0.257151i
$711$	−0.448143	−	1.37924i	−0.0168067	−	0.0517256i
$712$	−11.6869			−0.437985
$713$	6.15621	+	6.60548i	0.230552	+	0.247377i
$714$	8.42740			0.315388
$715$	−2.06833	−	6.36566i	−0.0773511	−	0.238062i
$716$	6.58819	−	20.2764i	0.246212	−	0.757763i
$717$	−13.0457	+	9.47822i	−0.487199	+	0.353971i
$718$	8.75208			0.326625
$719$	46.9465			1.75081			0.875405	−	0.483391i	$-0.160595\pi$
$719$	46.9465			1.75081			0.875405	+	0.483391i	$0.160595\pi$
$720$	2.17239	−	1.57833i	0.0809601	−	0.0588210i
$721$	55.8081	+	40.5469i	2.07840	+	1.51005i
$722$	3.28396	+	2.38594i	0.122216	+	0.0887954i
$723$	−0.179475	−	0.552369i	−0.00667477	−	0.0205428i
$724$	−20.9458	+	15.2180i	−0.778446	+	0.565574i
$725$	−2.24589	−	6.91214i	−0.0834103	−	0.256711i
$726$	1.33412	−	4.10601i	0.0495140	−	0.152388i
$727$	26.8298	+	19.4930i	0.995061	+	0.722954i	0.961024	−	0.276466i	$-0.0891634\pi$
$727$	26.8298	+	19.4930i	0.995061	+	0.722954i	0.0340375	+	0.999421i	$0.489163\pi$
$728$	12.1127	−	37.2790i	0.448926	−	1.38165i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	4.00835	+	2.91224i	0.148356	+	0.107787i
$731$	−8.07730	+	24.8594i	−0.298750	+	0.919457i
$732$	5.56766	+	17.1355i	0.205787	+	0.633347i
$733$	9.12059	−	6.62650i	0.336877	−	0.244755i	−0.406466	−	0.913666i	$-0.633239\pi$
$733$	9.12059	−	6.62650i	0.336877	−	0.244755i	0.743343	+	0.668911i	$0.233239\pi$
$734$	2.86150	+	8.80680i	0.105620	+	0.325065i
$735$	11.0635	+	8.03813i	0.408085	+	0.296491i
$736$	−6.40554	−	4.65390i	−0.236111	−	0.171545i
$737$	5.00930	−	3.63947i	0.184520	−	0.134062i
$738$	−6.09145			−0.224230
$739$	−8.32078			−0.306085			−0.153042	−	0.988220i	$-0.548907\pi$
$739$	−8.32078			−0.306085			−0.153042	+	0.988220i	$0.548907\pi$
$740$	12.7447	−	9.25955i	0.468504	−	0.340388i
$741$	−7.76014	+	23.8833i	−0.285076	+	0.877373i
$742$	−3.55842	−	10.9517i	−0.130634	−	0.402050i
$743$	47.7537			1.75191			0.875957	−	0.482388i	$-0.160231\pi$
$743$	47.7537			1.75191			0.875957	+	0.482388i	$0.160231\pi$
$744$	−9.08587	+	4.23367i	−0.333104	+	0.155214i
$745$	−7.68303			−0.281484
$746$	−5.00057	−	15.3902i	−0.183084	−	0.563474i
$747$	−1.03556	+	3.18713i	−0.0378892	+	0.116611i
$748$	−7.78299	+	5.65468i	−0.284574	+	0.206755i
$749$	−8.32706			−0.304264
$750$	0.477260			0.0174271
$751$	6.17543	−	4.48671i	0.225345	−	0.163722i	−0.469385	−	0.882994i	$-0.655524\pi$
$751$	6.17543	−	4.48671i	0.225345	−	0.163722i	0.694729	+	0.719271i	$0.255524\pi$
$752$	−13.9562	−	10.1397i	−0.508929	−	0.369758i
$753$	16.8408	+	12.2355i	0.613711	+	0.445887i
$754$	−5.13243	−	15.7960i	−0.186912	−	0.575257i
$755$	4.00381	−	2.90894i	0.145714	−	0.105867i
$756$	2.49016	+	7.66391i	0.0905661	+	0.278734i
$757$	4.12905	−	12.7079i	0.150073	−	0.461877i	−0.847555	−	0.530707i	$-0.821927\pi$
$757$	4.12905	−	12.7079i	0.150073	−	0.461877i	0.997628	+	0.0688297i	$0.0219265\pi$
$758$	6.06877	+	4.40922i	0.220428	+	0.160150i
$759$	0.700522	−	2.15598i	0.0254273	−	0.0782573i
$760$	−2.91771	+	8.97979i	−0.105837	+	0.325731i
$761$	−31.2508	−	22.7050i	−1.13284	−	0.823057i	−0.146735	−	0.989176i	$-0.546876\pi$
$761$	−31.2508	−	22.7050i	−1.13284	−	0.823057i	−0.986106	+	0.166119i	$0.946876\pi$
$762$	0.405922	−	1.24930i	0.0147050	−	0.0452573i
$763$	9.49910	+	29.2352i	0.343891	+	1.05839i
$764$	3.34841	−	2.43276i	0.121141	−	0.0880142i
$765$	−1.20004	−	3.69334i	−0.0433875	−	0.133533i
$766$	1.86094	+	1.35205i	0.0672386	+	0.0488517i
$767$	−49.0572	−	35.6421i	−1.77135	−	1.28696i
$768$	−0.588982	+	0.427920i	−0.0212530	+	0.0154412i
$769$	−22.0989			−0.796908			−0.398454	−	0.917188i	$-0.630453\pi$
$769$	−22.0989			−0.796908			−0.398454	+	0.917188i	$0.630453\pi$
$770$	3.03346			0.109318
$771$	−12.0054	+	8.72246i	−0.432365	+	0.314132i
$772$	−0.942760	+	2.90152i	−0.0339307	+	0.104428i
$773$	7.71921	+	23.7573i	0.277641	+	0.854490i	0.988509	+	0.151164i	$0.0483023\pi$
$773$	7.71921	+	23.7573i	0.277641	+	0.854490i	−0.710868	+	0.703325i	$0.751698\pi$
$774$	3.21237			0.115466
$775$	5.46517	+	1.06393i	0.196315	+	0.0382175i
$776$	−3.94182			−0.141503
$777$	12.4900	+	38.4402i	0.448075	+	1.37903i
$778$	1.25334	−	3.85739i	0.0449344	−	0.138294i
$779$	−54.1541	+	39.3452i	−1.94027	+	1.40969i
$780$	−8.48590			−0.303844
$781$	21.1015			0.755071
$782$	−2.43168	+	1.76672i	−0.0869568	+	0.0631778i
$783$	5.87982	+	4.27194i	0.210128	+	0.152667i
$784$	−29.7080	−	21.5842i	−1.06100	−	0.770863i
$785$	−1.41784	−	4.36367i	−0.0506049	−	0.155746i
$786$	−5.19598	+	3.77510i	−0.185334	+	0.134653i
$787$	−10.5268	−	32.3981i	−0.375239	−	1.15487i	−0.943317	−	0.331892i	$-0.892313\pi$
$787$	−10.5268	−	32.3981i	−0.375239	−	1.15487i	0.568078	−	0.822974i	$-0.307687\pi$
$788$	−2.49248	+	7.67107i	−0.0887910	+	0.273270i
$789$	3.25606	+	2.36566i	0.115919	+	0.0842198i
$790$	−0.213881	+	0.658257i	−0.00760954	+	0.0234197i
$791$	−17.6383	+	54.2852i	−0.627147	+	1.93016i
$792$	2.03595	+	1.47921i	0.0723444	+	0.0525613i
$793$	15.0430	−	46.2976i	0.534192	−	1.64408i
$794$	2.95770	+	9.10286i	0.104965	+	0.323048i
$795$	−4.29291	+	3.11898i	−0.152254	+	0.110619i
$796$	−14.6712	−	45.1532i	−0.520005	−	1.60041i
$797$	18.8955	+	13.7284i	0.669314	+	0.486285i	0.869795	−	0.493413i	$-0.164251\pi$
$797$	18.8955	+	13.7284i	0.669314	+	0.486285i	−0.200482	+	0.979697i	$0.564251\pi$
$798$	−9.20759	−	6.68971i	−0.325945	−	0.236813i
$799$	−20.1836	+	14.6643i	−0.714045	+	0.518784i
$800$	−4.88221			−0.172612
$801$	−6.49153			−0.229367
$802$	7.07672	−	5.14154i	0.249888	−	0.181554i
$803$	4.48429	−	13.8012i	0.158247	−	0.487034i
$804$	−2.42584	−	7.46597i	−0.0855528	−	0.263304i
$805$	−7.37407			−0.259902
$806$	12.4893	+	2.43135i	0.439917	+	0.0856406i
$807$	4.09596			0.144185
$808$	−8.26362	−	25.4328i	−0.290713	−	0.894723i
$809$	−8.54873	+	26.3103i	−0.300557	+	0.925021i	0.680740	+	0.732525i	$0.261658\pi$
$809$	−8.54873	+	26.3103i	−0.300557	+	0.925021i	−0.981298	+	0.192496i	$0.938342\pi$
$810$	−0.386111	+	0.280526i	−0.0135666	+	0.00985669i
$811$	−9.97579			−0.350297			−0.175149	−	0.984542i	$-0.556041\pi$
$811$	−9.97579			−0.350297			−0.175149	+	0.984542i	$0.556041\pi$
$812$	−58.5667			−2.05529
$813$	4.07412	−	2.96002i	0.142886	−	0.103813i
$814$	4.79759	+	3.48566i	0.168156	+	0.122172i
$815$	14.4284	+	10.4829i	0.505405	+	0.367198i
$816$	3.22237	+	9.91743i	0.112805	+	0.347180i
$817$	28.5586	−	20.7490i	0.999137	−	0.725916i
$818$	0.358746	+	1.10411i	0.0125433	+	0.0386042i
$819$	6.72803	−	20.7067i	0.235096	−	0.723552i
$820$	−18.2996	−	13.2954i	−0.639050	−	0.464297i
$821$	6.99159	−	21.5179i	0.244008	−	0.750980i	−0.751790	−	0.659403i	$-0.770809\pi$
$821$	6.99159	−	21.5179i	0.244008	−	0.750980i	0.995798	−	0.0915770i	$-0.0291908\pi$
$822$	2.08658	−	6.42184i	0.0727779	−	0.223987i
$823$	31.1706	+	22.6468i	1.08654	+	0.789416i	0.978811	−	0.204764i	$-0.0656428\pi$
$823$	31.1706	+	22.6468i	1.08654	+	0.789416i	0.107727	+	0.994181i	$0.465643\pi$
$824$	8.44011	−	25.9760i	0.294025	−	0.904917i
$825$	−0.431957	−	1.32943i	−0.0150388	−	0.0462847i
$826$	22.2333	−	16.1534i	0.773595	−	0.562050i
$827$	−5.42376	−	16.6926i	−0.188603	−	0.580459i	0.811389	−	0.584506i	$-0.198712\pi$
$827$	−5.42376	−	16.6926i	−0.188603	−	0.580459i	−0.999992	+	0.00404704i	$0.998712\pi$
$828$	−2.32518	−	1.68935i	−0.0808058	−	0.0587088i
$829$	−28.1722	−	20.4683i	−0.978459	−	0.710892i	−0.0210957	−	0.999777i	$-0.506715\pi$
$829$	−28.1722	−	20.4683i	−0.978459	−	0.710892i	−0.957364	+	0.288885i	$0.906715\pi$
$830$	1.29391	−	0.940084i	0.0449124	−	0.0326308i
$831$	20.3856			0.707170
$832$	14.5581			0.504711
$833$	−42.9642	+	31.2154i	−1.48862	+	1.08155i
$834$	−0.560218	+	1.72417i	−0.0193988	+	0.0597033i
$835$	3.86871	+	11.9067i	0.133882	+	0.412047i
$836$	12.9922			0.449346
$837$	−5.04678	+	2.35161i	−0.174442	+	0.0812835i
$838$	3.12210			0.107851
$839$	15.0571	+	46.3411i	0.519830	+	1.59987i	0.774318	+	0.632796i	$0.218093\pi$
$839$	15.0571	+	46.3411i	0.519830	+	1.59987i	−0.254488	+	0.967076i	$0.581907\pi$
$840$	2.52965	−	7.78546i	0.0872812	−	0.268624i
$841$	−19.2722	+	14.0021i	−0.664559	+	0.482830i
$842$	−6.58835			−0.227049
$843$	−14.3867			−0.495506
$844$	−27.0025	+	19.6185i	−0.929466	+	0.675297i
$845$	8.03162	+	5.83532i	0.276296	+	0.200741i
$846$	2.48051	+	1.80220i	0.0852817	+	0.0619608i
$847$	12.7106	+	39.1193i	0.436742	+	1.34415i
$848$	11.5274	−	8.37516i	0.395853	−	0.287604i
$849$	5.30778	+	16.3357i	0.182163	+	0.560639i
$850$	−0.572731	+	1.76268i	−0.0196445	+	0.0604595i
$851$	−11.6625	−	8.47331i	−0.399786	−	0.290461i
$852$	8.26716	−	25.4437i	0.283228	−	0.871687i
$853$	6.52182	−	20.0721i	0.223303	−	0.687256i	−0.775157	−	0.631769i	$-0.782329\pi$
$853$	6.52182	−	20.0721i	0.223303	−	0.687256i	0.998459	−	0.0554864i	$-0.0176709\pi$
$854$	17.8489	+	12.9680i	0.610776	+	0.443755i
$855$	−1.62065	+	4.98786i	−0.0554251	+	0.170581i
$856$	1.01883	+	3.13563i	0.0348228	+	0.107174i
$857$	−19.4294	+	14.1163i	−0.663696	+	0.482203i	−0.867909	−	0.496723i	$-0.834536\pi$
$857$	−19.4294	+	14.1163i	−0.663696	+	0.482203i	0.204213	+	0.978926i	$0.434536\pi$
$858$	−0.987131	−	3.03808i	−0.0337001	−	0.103718i
$859$	24.5569	+	17.8417i	0.837872	+	0.608749i	0.921775	−	0.387724i	$-0.126739\pi$
$859$	24.5569	+	17.8417i	0.837872	+	0.608749i	−0.0839036	+	0.996474i	$0.526739\pi$
$860$	9.65044	+	7.01145i	0.329077	+	0.239089i
$861$	46.9515	−	34.1123i	1.60010	−	1.16254i
$862$	−16.8748			−0.574759
$863$	24.5331			0.835116			0.417558	−	0.908650i	$-0.362886\pi$
$863$	24.5331			0.835116			0.417558	+	0.908650i	$0.362886\pi$
$864$	3.94979	−	2.86969i	0.134375	−	0.0976289i
$865$	−1.83780	+	5.65617i	−0.0624871	+	0.192315i
$866$	−2.25774	−	6.94860i	−0.0767210	−	0.236123i
$867$	−1.91914			−0.0651776
$868$	21.7630	−	39.2352i	0.738684	−	1.33173i
$869$	2.02718			0.0687674
$870$	−1.07187	−	3.29889i	−0.0363399	−	0.111843i
$871$	−6.55426	+	20.1719i	−0.222082	+	0.683500i
$872$	9.84656	−	7.15394i	0.333446	−	0.242263i
$873$	−2.18949			−0.0741032
$874$	4.05923			0.137306
$875$	−3.67861	+	2.67266i	−0.124360	+	0.0903526i
$876$	−14.8843	−	10.8141i	−0.502895	−	0.365374i
$877$	14.1664	+	10.2925i	0.478365	+	0.347553i	0.800692	−	0.599076i	$-0.204465\pi$
$877$	14.1664	+	10.2925i	0.478365	+	0.347553i	−0.322327	+	0.946628i	$0.604465\pi$
$878$	−1.86180	−	5.73004i	−0.0628328	−	0.193379i
$879$	−17.9361	+	13.0314i	−0.604971	+	0.439537i
$880$	1.15990	+	3.56980i	0.0391002	+	0.120338i
$881$	−3.18798	+	9.81158i	−0.107406	+	0.330561i	−0.990288	−	0.139035i	$-0.955600\pi$
$881$	−3.18798	+	9.81158i	−0.107406	+	0.330561i	0.882882	+	0.469595i	$0.155600\pi$
$882$	5.28019	+	3.83628i	0.177793	+	0.129174i
$883$	−17.8063	+	54.8022i	−0.599231	+	1.84424i	−0.0668034	+	0.997766i	$0.521280\pi$
$883$	−17.8063	+	54.8022i	−0.599231	+	1.84424i	−0.532427	+	0.846476i	$0.678720\pi$
$884$	10.1834	−	31.3413i	0.342505	−	1.05412i
$885$	−10.2453	−	7.44361i	−0.344390	−	0.250214i
$886$	−0.593245	+	1.82582i	−0.0199305	+	0.0613397i
$887$	−6.89934	−	21.2340i	−0.231657	−	0.712967i	−0.997547	−	0.0699960i	$-0.977701\pi$
$887$	−6.89934	−	21.2340i	−0.231657	−	0.712967i	0.765890	−	0.642972i	$-0.222299\pi$
$888$	12.9468	−	9.40641i	0.434467	−	0.315659i
$889$	3.86735	+	11.9025i	0.129707	+	0.399196i
$890$	2.50645	+	1.82104i	0.0840165	+	0.0610415i
$891$	1.13088	+	0.821630i	0.0378858	+	0.0275257i
$892$	16.3629	−	11.8884i	0.547871	−	0.398051i
$893$	33.6927			1.12748
$894$	−3.66680			−0.122636
$895$	−9.73247	+	7.07105i	−0.325321	+	0.236359i
$896$	−15.7589	+	48.5008i	−0.526467	+	1.62030i
$897$	2.39963	+	7.38529i	0.0801212	+	0.246588i
$898$	1.56785			0.0523199
$899$	−4.92014	−	40.1655i	−0.164096	−	1.33959i
$900$	−1.77222			−0.0590741
$901$	−6.36781	−	19.5981i	−0.212142	−	0.652907i
$902$	2.63124	−	8.09814i	0.0876108	−	0.269638i
$903$	−24.7602	+	17.9894i	−0.823968	+	0.598648i
$904$	22.5996			0.751653
$905$	14.6090			0.485621
$906$	1.91086	−	1.38832i	0.0634840	−	0.0461239i
$907$	12.6623	+	9.19971i	0.420445	+	0.305471i	0.777817	−	0.628491i	$-0.216327\pi$
$907$	12.6623	+	9.19971i	0.420445	+	0.305471i	−0.357372	+	0.933962i	$0.616327\pi$
$908$	−21.3888	−	15.5399i	−0.709812	−	0.515709i
$909$	−4.59006	−	14.1267i	−0.152243	−	0.468555i
$910$	−8.40656	+	6.10772i	−0.278675	+	0.202469i
$911$	−13.7697	−	42.3787i	−0.456209	−	1.40407i	−0.869709	−	0.493564i	$-0.835694\pi$
$911$	−13.7697	−	42.3787i	−0.456209	−	1.40407i	0.413500	−	0.910504i	$-0.364306\pi$
$912$	4.35181	−	13.3935i	0.144103	−	0.443503i
$913$	−3.78973	−	2.75340i	−0.125422	−	0.0911243i
$914$	1.48987	−	4.58534i	0.0492805	−	0.151670i
$915$	3.14163	−	9.66894i	0.103859	−	0.319645i
$916$	−12.7039	−	9.22992i	−0.419749	−	0.304965i
$917$	18.9087	−	58.1951i	0.624422	−	1.92177i
$918$	−0.572731	−	1.76268i	−0.0189029	−	0.0581772i
$919$	−10.6589	+	7.74416i	−0.351606	+	0.255456i	−0.749542	−	0.661956i	$-0.769726\pi$
$919$	−10.6589	+	7.74416i	−0.351606	+	0.255456i	0.397937	+	0.917413i	$0.369726\pi$
$920$	0.902228	+	2.77677i	0.0297456	+	0.0915475i
$921$	4.92307	+	3.57682i	0.162221	+	0.117860i
$922$	−5.08832	−	3.69688i	−0.167575	−	0.121750i
$923$	−58.4780	+	42.4868i	−1.92483	+	1.39847i
$924$	−11.2642			−0.370566
$925$	−8.88900			−0.292269
$926$	12.4935	−	9.07703i	0.410561	−	0.298290i
$927$	4.68809	−	14.4285i	0.153977	−	0.473893i
$928$	10.9649	+	33.7465i	0.359941	+	1.10778i
$929$	20.9246			0.686514			0.343257	−	0.939241i	$-0.388470\pi$
$929$	20.9246			0.686514			0.343257	+	0.939241i	$0.388470\pi$
$930$	2.60831	+	0.507771i	0.0855297	+	0.0166505i
$931$	71.7206			2.35055
$932$	−4.96826	−	15.2907i	−0.162741	−	0.500864i
$933$	−6.60233	+	20.3199i	−0.216151	+	0.665243i
$934$	6.56050	−	4.76648i	0.214666	−	0.155964i
$935$	5.42839			0.177527
$936$	−8.62049			−0.281770
$937$	−23.9166	+	17.3764i	−0.781320	+	0.567662i	−0.905375	−	0.424613i	$-0.860410\pi$
$937$	−23.9166	+	17.3764i	−0.781320	+	0.567662i	0.124055	+	0.992275i	$0.460410\pi$
$938$	−7.77678	−	5.65016i	−0.253921	−	0.184484i
$939$	−8.57045	−	6.22680i	−0.279686	−	0.203204i
$940$	3.51827	+	10.8281i	0.114753	+	0.353174i
$941$	−35.9410	+	26.1126i	−1.17164	+	0.851248i	−0.991205	−	0.132339i	$-0.957751\pi$
$941$	−35.9410	+	26.1126i	−1.17164	+	0.851248i	−0.180437	+	0.983586i	$0.557751\pi$
$942$	−0.676679	−	2.08260i	−0.0220474	−	0.0678549i
$943$	−6.39631	+	19.6858i	−0.208293	+	0.641059i
$944$	27.5108	+	19.9877i	0.895399	+	0.650545i
$945$	1.40510	−	4.32446i	0.0457080	−	0.140675i
$946$	−1.38761	+	4.27061i	−0.0451150	+	0.138850i
$947$	−27.3522	−	19.8726i	−0.888829	−	0.645772i	0.0467437	−	0.998907i	$-0.485116\pi$
$947$	−27.3522	−	19.8726i	−0.888829	−	0.645772i	−0.935572	+	0.353135i	$0.885116\pi$
$948$	0.794210	−	2.44433i	0.0257947	−	0.0793880i
$949$	15.3608	+	47.2758i	0.498634	+	1.53464i
$950$	2.02498	−	1.47123i	0.0656989	−	0.0477331i
$951$	−2.19679	−	6.76103i	−0.0712359	−	0.219241i
$952$	25.7187	+	18.6857i	0.833548	+	0.605608i
$953$	−43.1306	−	31.3362i	−1.39714	−	1.01508i	−0.995039	−	0.0994839i	$-0.968281\pi$
$953$	−43.1306	−	31.3362i	−1.39714	−	1.01508i	−0.402099	−	0.915596i	$-0.631719\pi$
$954$	−2.04884	+	1.48857i	−0.0663335	+	0.0481941i
$955$	−2.33541			−0.0755720
$956$	−28.5776			−0.924267
$957$	−8.21905	+	5.97149i	−0.265684	+	0.193031i
$958$	−4.49061	+	13.8207i	−0.145085	+	0.446526i
$959$	19.8795	+	61.1829i	0.641943	+	1.97570i
$960$	3.04036			0.0981271
$961$	28.7361	+	11.6291i	0.926971	+	0.375132i
$962$	−20.3136			−0.654938
$963$	0.565911	+	1.74169i	0.0182362	+	0.0561253i
$964$	0.318071	−	0.978921i	0.0102444	−	0.0315289i
$965$	1.39270	−	1.01186i	0.0448327	−	0.0325728i
$966$	−3.51935			−0.113233
$967$	−10.6153			−0.341364			−0.170682	−	0.985326i	$-0.554597\pi$
$967$	−10.6153			−0.341364			−0.170682	+	0.985326i	$0.554597\pi$
$968$	13.1755	−	9.57259i	0.423478	−	0.307675i
$969$	−16.4770	−	11.9712i	−0.529318	−	0.384572i
$970$	0.845389	+	0.614211i	0.0271438	+	0.0197211i
$971$	1.99908	+	6.15253i	0.0641534	+	0.197444i	0.977996	−	0.208626i	$-0.0668990\pi$
$971$	1.99908	+	6.15253i	0.0641534	+	0.197444i	−0.913842	+	0.406070i	$0.866899\pi$
$972$	1.43376	−	1.04169i	0.0459878	−	0.0334121i
$973$	−5.33738	−	16.4268i	−0.171108	−	0.526618i
$974$	−1.40840	+	4.33460i	−0.0451280	+	0.138890i
$975$	3.87380	+	2.81448i	0.124061	+	0.0901355i
$976$	−8.43596	+	25.9632i	−0.270029	+	0.831062i
$977$	4.74512	−	14.6040i	0.151810	−	0.467223i	−0.846014	−	0.533161i	$-0.821004\pi$
$977$	4.74512	−	14.6040i	0.151810	−	0.467223i	0.997824	+	0.0659381i	$0.0210040\pi$
$978$	6.88610	+	5.00305i	0.220193	+	0.159980i
$979$	2.80406	−	8.63000i	0.0896181	−	0.275816i
$980$	7.48923	+	23.0495i	0.239235	+	0.736289i
$981$	5.46930	−	3.97368i	0.174621	−	0.126870i
$982$	0.322033	+	0.991116i	0.0102765	+	0.0316278i
$983$	14.3274	+	10.4094i	0.456972	+	0.332009i	0.792342	−	0.610077i	$-0.208861\pi$
$983$	14.3274	+	10.4094i	0.456972	+	0.332009i	−0.335370	+	0.942086i	$0.608861\pi$
$984$	−18.5899	−	13.5063i	−0.592623	−	0.430566i
$985$	3.68204	−	2.67516i	0.117320	−	0.0852377i
$986$	13.4702			0.428979
$987$	−29.2115			−0.929813
$988$	−36.0050	+	26.1592i	−1.14547	+	0.832234i
$989$	3.37314	−	10.3815i	0.107260	−	0.330111i
$990$	−0.206156	−	0.634482i	−0.00655206	−	0.0201652i
$991$	10.7789			0.342402			0.171201	−	0.985236i	$-0.445235\pi$
$991$	10.7789			0.342402			0.171201	+	0.985236i	$0.445235\pi$
$992$	−26.6821	−	5.19433i	−0.847157	−	0.164920i
$993$	−10.0245			−0.318118
$994$	−10.1232	−	31.1561i	−0.321089	−	0.988211i
$995$	−8.27839	+	25.4783i	−0.262443	+	0.807715i
$996$	−4.80473	+	3.49084i	−0.152244	+	0.110611i
$997$	0.781811			0.0247602			0.0123801	−	0.999923i	$-0.496059\pi$
$997$	0.781811			0.0247602			0.0123801	+	0.999923i	$0.496059\pi$
$998$	11.9891			0.379507
$999$	7.19135	−	5.22482i	0.227524	−	0.165306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.n.d.376.2	yes	16
31.8	even	5	inner	465.2.n.d.256.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.n.d.256.2	✓	16	31.8	even	5	inner
465.2.n.d.376.2	yes	16	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.147481 - 0.453901i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.43376 - 1.04169i) q^{4} -1.00000 q^{5} -0.477260 q^{6} +(3.67861 - 2.67266i) q^{7} +(-1.45650 - 1.05821i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.147481 + 0.453901i) q^{10} +(1.13088 - 0.821630i) q^{11} +(-0.547647 - 1.68548i) q^{12} +(-1.47966 + 4.55393i) q^{13} +(-1.75565 - 1.27556i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.829779 - 2.55380i) q^{16} +(-3.14174 - 2.28261i) q^{17} +(-0.147481 + 0.453901i) q^{18} +(1.62065 + 4.98786i) q^{19} +(-1.43376 + 1.04169i) q^{20} +(-1.40510 - 4.32446i) q^{21} +(-0.539722 - 0.392131i) q^{22} +(1.31202 + 0.953235i) q^{23} +(-1.45650 + 1.05821i) q^{24} +1.00000 q^{25} +2.28525 q^{26} +(-0.809017 + 0.587785i) q^{27} +(2.49016 - 7.66391i) q^{28} +(-2.24589 - 6.91214i) q^{29} +0.477260 q^{30} +(5.46517 + 1.06393i) q^{31} -4.88221 q^{32} +(-0.431957 - 1.32943i) q^{33} +(-0.572731 + 1.76268i) q^{34} +(-3.67861 + 2.67266i) q^{35} -1.77222 q^{36} -8.88900 q^{37} +(2.02498 - 1.47123i) q^{38} +(3.87380 + 2.81448i) q^{39} +(1.45650 + 1.05821i) q^{40} +(3.94410 + 12.1387i) q^{41} +(-1.75565 + 1.27556i) q^{42} +(-2.07995 - 6.40143i) q^{43} +(0.765523 - 2.35604i) q^{44} +(0.809017 + 0.587785i) q^{45} +(0.239177 - 0.736110i) q^{46} +(1.98523 - 6.10991i) q^{47} +(-2.17239 - 1.57833i) q^{48} +(4.22590 - 13.0060i) q^{49} +(-0.147481 - 0.453901i) q^{50} +(-3.14174 + 2.28261i) q^{51} +(2.62229 + 8.07057i) q^{52} +(4.29291 + 3.11898i) q^{53} +(0.386111 + 0.280526i) q^{54} +(-1.13088 + 0.821630i) q^{55} -8.18612 q^{56} +5.24454 q^{57} +(-2.80620 + 2.03883i) q^{58} +(-3.91334 + 12.0440i) q^{59} +(0.547647 + 1.68548i) q^{60} -10.1665 q^{61} +(-0.323092 - 2.63756i) q^{62} -4.54701 q^{63} +(-0.939522 - 2.89155i) q^{64} +(1.47966 - 4.55393i) q^{65} +(-0.539722 + 0.392131i) q^{66} +4.42957 q^{67} -6.88226 q^{68} +(1.31202 - 0.953235i) q^{69} +(1.75565 + 1.27556i) q^{70} +(12.2127 + 8.87308i) q^{71} +(0.556333 + 1.71222i) q^{72} +(8.39868 - 6.10200i) q^{73} +(1.31096 + 4.03473i) q^{74} +(0.309017 - 0.951057i) q^{75} +(7.51941 + 5.46317i) q^{76} +(1.96411 - 6.04491i) q^{77} +(0.706183 - 2.17341i) q^{78} +(1.17325 + 0.852419i) q^{79} +(-0.829779 + 2.55380i) q^{80} +(0.309017 + 0.951057i) q^{81} +(4.92809 - 3.58047i) q^{82} +(-1.03556 - 3.18713i) q^{83} +(-6.51931 - 4.73656i) q^{84} +(3.14174 + 2.28261i) q^{85} +(-2.59886 + 1.88819i) q^{86} -7.26786 q^{87} -2.51658 q^{88} +(5.25175 - 3.81562i) q^{89} +(0.147481 - 0.453901i) q^{90} +(6.72803 + 20.7067i) q^{91} +2.87409 q^{92} +(2.70069 - 4.86891i) q^{93} -3.06608 q^{94} +(-1.62065 - 4.98786i) q^{95} +(-1.50869 + 4.64326i) q^{96} +(1.77134 - 1.28695i) q^{97} -6.52667 q^{98} -1.39784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} + 4 q^{6} + 7 q^{7} - 8 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} + 6 q^{12} + 8 q^{13} - q^{14} + 4 q^{15} + 8 q^{16} + 4 q^{17} + 4 q^{18} + 17 q^{19} + 4 q^{20}+ \cdots + 14 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 + 4 * q^6 + 7 * q^7 - 8 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 + 6 * q^12 + 8 * q^13 - q^14 + 4 * q^15 + 8 * q^16 + 4 * q^17 + 4 * q^18 + 17 * q^19 + 4 * q^20 - 8 * q^21 - 11 * q^22 - 14 * q^23 - 8 * q^24 + 16 * q^25 - 10 * q^26 - 4 * q^27 + 10 * q^28 + 3 * q^29 - 4 * q^30 - 5 * q^31 - 32 * q^32 - 11 * q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 + 44 * q^37 - 7 * q^38 - 7 * q^39 + 8 * q^40 + 14 * q^41 - q^42 - 10 * q^43 + 13 * q^44 + 4 * q^45 - 5 * q^46 + 34 * q^47 - 2 * q^48 + 33 * q^49 + 4 * q^50 + 4 * q^51 - 13 * q^52 - 6 * q^54 - 4 * q^55 - 20 * q^56 - 8 * q^57 - 25 * q^58 - 26 * q^59 - 6 * q^60 + 30 * q^61 - 15 * q^62 + 2 * q^63 - 52 * q^64 - 8 * q^65 - 11 * q^66 + 30 * q^67 - 60 * q^68 - 14 * q^69 + q^70 + 10 * q^71 + 2 * q^72 + 40 * q^73 + 2 * q^74 - 4 * q^75 - 13 * q^76 - 16 * q^77 + 15 * q^78 + 3 * q^79 - 8 * q^80 - 4 * q^81 - 9 * q^82 + 6 * q^83 - 10 * q^84 - 4 * q^85 + 18 * q^86 + 8 * q^87 + 6 * q^88 + 20 * q^89 - 4 * q^90 - 7 * q^91 + 14 * q^92 + 30 * q^93 + 34 * q^94 - 17 * q^95 - 32 * q^96 - 27 * q^97 + 80 * q^98 + 14 * q^99

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