LMFDB - Embedded newform 784.2.x.o.165.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.8
Character	$\chi$	$=$	784.165
Dual form			784.2.x.o.765.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.438190 + 1.34461i) q^{2} +(-0.0145698 - 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(0.337028 - 1.25781i) q^{5} +(0.0667293 - 0.0434174i) q^{6} +(-2.29259 - 1.65651i) q^{8} +(2.59533 - 1.49842i) q^{9} +O(q^{10})$	\(q+(0.438190 + 1.34461i) q^{2} +(-0.0145698 - 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(0.337028 - 1.25781i) q^{5} +(0.0667293 - 0.0434174i) q^{6} +(-2.29259 - 1.65651i) q^{8} +(2.59533 - 1.49842i) q^{9} +(1.83895 - 0.0979855i) q^{10} +(1.50355 - 0.402875i) q^{11} +(0.0876199 + 0.0707001i) q^{12} +(-1.59615 + 1.59615i) q^{13} -0.0733039 q^{15} +(1.22277 - 3.80852i) q^{16} +(-1.46910 + 2.54455i) q^{17} +(3.15204 + 2.83313i) q^{18} +(7.65147 + 2.05021i) q^{19} +(0.937562 + 2.42974i) q^{20} +(1.20055 + 1.84516i) q^{22} +(3.91784 - 2.26197i) q^{23} +(-0.0566703 + 0.148795i) q^{24} +(2.86164 + 1.65217i) q^{25} +(-2.84562 - 1.44679i) q^{26} +(-0.238706 - 0.238706i) q^{27} +(2.06234 - 2.06234i) q^{29} +(-0.0321210 - 0.0985654i) q^{30} +(3.14025 - 5.43908i) q^{31} +(5.65680 - 0.0246987i) q^{32} +(-0.0438128 - 0.0758861i) q^{33} +(-4.06519 - 0.860373i) q^{34} +(-2.42828 + 5.47973i) q^{36} +(-1.40616 + 5.24787i) q^{37} +(0.596064 + 11.1867i) q^{38} +(0.110046 + 0.0635352i) q^{39} +(-2.85623 + 2.32535i) q^{40} +7.34101i q^{41} +(-1.99391 - 1.99391i) q^{43} +(-1.95496 + 2.42282i) q^{44} +(-1.01002 - 3.76943i) q^{45} +(4.75824 + 4.27682i) q^{46} +(-0.979430 - 1.69642i) q^{47} +(-0.224904 - 0.0109992i) q^{48} +(-0.967587 + 4.57177i) q^{50} +(0.159765 + 0.0428089i) q^{51} +(0.698448 - 4.46023i) q^{52} +(-11.2146 + 3.00493i) q^{53} +(0.216369 - 0.425567i) q^{54} -2.02696i q^{55} -0.445921i q^{57} +(3.67676 + 1.86936i) q^{58} +(2.96105 - 0.793411i) q^{59} +(0.118457 - 0.0863809i) q^{60} +(9.72123 + 2.60480i) q^{61} +(8.68949 + 1.83908i) q^{62} +(2.51197 + 7.59540i) q^{64} +(1.46970 + 2.54559i) q^{65} +(0.0828392 - 0.0921640i) q^{66} +(0.566758 + 2.11517i) q^{67} +(-0.624456 - 5.84312i) q^{68} +(-0.180077 - 0.180077i) q^{69} -7.26378i q^{71} +(-8.43218 - 0.863930i) q^{72} +(-12.2392 - 7.06631i) q^{73} +(-7.67253 + 0.408819i) q^{74} +(0.0481435 - 0.179674i) q^{75} +(-14.7806 + 5.70337i) q^{76} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 - 1.66547i) q^{79} +(-4.37827 - 2.82159i) q^{80} +(4.48574 - 7.76954i) q^{81} +(-9.87083 + 3.21676i) q^{82} +(-8.82731 + 8.82731i) q^{83} +(2.70543 + 2.70543i) q^{85} +(1.80733 - 3.55475i) q^{86} +(-0.142188 - 0.0820924i) q^{87} +(-4.11440 - 1.56702i) q^{88} +(11.5526 - 6.66987i) q^{89} +(4.62586 - 3.00981i) q^{90} +(-3.66566 + 8.27206i) q^{92} +(-0.341503 - 0.0915056i) q^{93} +(1.85186 - 2.06031i) q^{94} +(5.15752 - 8.93309i) q^{95} +(-0.0837613 - 0.307230i) q^{96} +9.69578 q^{97} +(3.29854 - 3.29854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.438190	+	1.34461i	0.309847	+	0.950786i
$2$	0.438190	+	1.34461i	0.309847	+	0.950786i
$3$	−0.0145698	−	0.0543752i	−0.00841187	−	0.0313935i	0.961592	−	0.274482i	$-0.0885062\pi$
$3$	−0.0145698	−	0.0543752i	−0.00841187	−	0.0313935i	−0.970004	+	0.243088i	$0.921840\pi$
$4$	−1.61598	+	1.17839i	−0.807989	+	0.589197i
$5$	0.337028	−	1.25781i	0.150724	−	0.562508i	−0.848710	−	0.528858i	$-0.822620\pi$
$5$	0.337028	−	1.25781i	0.150724	−	0.562508i	0.999434	−	0.0336497i	$-0.0107130\pi$
$6$	0.0667293	−	0.0434174i	0.0272421	−	0.0177251i
$7$		0			0
$7$		0			0
$8$	−2.29259	−	1.65651i	−0.810554	−	0.585664i
$9$	2.59533	−	1.49842i	0.865111	−	0.499472i
$10$	1.83895	−	0.0979855i	0.581526	−	0.0309857i
$11$	1.50355	−	0.402875i	0.453338	−	0.121472i	−0.0249229	−	0.999689i	$-0.507934\pi$
$11$	1.50355	−	0.402875i	0.453338	−	0.121472i	0.478261	+	0.878218i	$0.341267\pi$
$12$	0.0876199	+	0.0707001i	0.0252937	+	0.0204094i
$13$	−1.59615	+	1.59615i	−0.442691	+	0.442691i	−0.892916	−	0.450224i	$-0.851344\pi$
$13$	−1.59615	+	1.59615i	−0.442691	+	0.442691i	0.450224	+	0.892916i	$0.351344\pi$
$14$		0			0
$15$	−0.0733039			−0.0189270
$16$	1.22277	−	3.80852i	0.305693	−	0.952130i
$17$	−1.46910	+	2.54455i	−0.356309	+	0.617145i	−0.987341	−	0.158612i	$-0.949298\pi$
$17$	−1.46910	+	2.54455i	−0.356309	+	0.617145i	0.631032	+	0.775757i	$0.282632\pi$
$18$	3.15204	+	2.83313i	0.742943	+	0.667775i
$19$	7.65147	+	2.05021i	1.75537	+	0.470350i	0.985759	−	0.168165i	$-0.0537841\pi$
$19$	7.65147	+	2.05021i	1.75537	+	0.470350i	0.769610	+	0.638514i	$0.220451\pi$
$20$	0.937562	+	2.42974i	0.209645	+	0.543306i
$21$		0			0
$22$	1.20055	+	1.84516i	0.255959	+	0.393390i
$23$	3.91784	−	2.26197i	0.816927	−	0.471653i	−0.0324286	−	0.999474i	$-0.510324\pi$
$23$	3.91784	−	2.26197i	0.816927	−	0.471653i	0.849356	+	0.527821i	$0.176991\pi$
$24$	−0.0566703	+	0.148795i	−0.0115678	+	0.0303727i
$25$	2.86164	+	1.65217i	0.572328	+	0.330434i
$26$	−2.84562	−	1.44679i	−0.558072	−	0.283738i
$27$	−0.238706	−	0.238706i	−0.0459390	−	0.0459390i
$28$		0			0
$29$	2.06234	−	2.06234i	0.382968	−	0.382968i	−0.489203	−	0.872170i	$-0.662712\pi$
$29$	2.06234	−	2.06234i	0.382968	−	0.382968i	0.872170	+	0.489203i	$0.162712\pi$
$30$	−0.0321210	−	0.0985654i	−0.00586447	−	0.0179955i
$31$	3.14025	−	5.43908i	0.564006	−	0.976887i	−0.433136	−	0.901329i	$-0.642593\pi$
$31$	3.14025	−	5.43908i	0.564006	−	0.976887i	0.997141	−	0.0755580i	$-0.0240738\pi$
$32$	5.65680	−	0.0246987i	0.999990	−	0.00436615i
$33$	−0.0438128	−	0.0758861i	−0.00762684	−	0.0132101i
$34$	−4.06519	−	0.860373i	−0.697174	−	0.147553i
$35$		0			0
$36$	−2.42828	+	5.47973i	−0.404713	+	0.913289i
$37$	−1.40616	+	5.24787i	−0.231172	+	0.862745i	0.748666	+	0.662948i	$0.230695\pi$
$37$	−1.40616	+	5.24787i	−0.231172	+	0.862745i	−0.979837	+	0.199797i	$0.935972\pi$
$38$	0.596064	+	11.1867i	0.0966944	+	1.81472i
$39$	0.110046	+	0.0635352i	0.0176215	+	0.0101738i
$40$	−2.85623	+	2.32535i	−0.451610	+	0.367670i
$41$			7.34101i			1.14647i	0.819390	+	0.573236i	$0.194312\pi$
$41$			7.34101i			1.14647i	−0.819390	+	0.573236i	$0.805688\pi$
$42$		0			0
$43$	−1.99391	−	1.99391i	−0.304068	−	0.304068i	0.538535	−	0.842603i	$-0.318978\pi$
$43$	−1.99391	−	1.99391i	−0.304068	−	0.304068i	−0.842603	+	0.538535i	$0.818978\pi$
$44$	−1.95496	+	2.42282i	−0.294721	+	0.365253i
$45$	−1.01002	−	3.76943i	−0.150564	−	0.561914i
$46$	4.75824	+	4.27682i	0.701564	+	0.630583i
$47$	−0.979430	−	1.69642i	−0.142865	−	0.247449i	0.785710	−	0.618596i	$-0.212298\pi$
$47$	−0.979430	−	1.69642i	−0.142865	−	0.247449i	−0.928574	+	0.371147i	$0.878965\pi$
$48$	−0.224904	−	0.0109992i	−0.0324622	−	0.00158759i
$49$		0			0
$50$	−0.967587	+	4.57177i	−0.136837	+	0.646545i
$51$	0.159765	+	0.0428089i	0.0223716	+	0.00599444i
$52$	0.698448	−	4.46023i	0.0968573	−	0.618523i
$53$	−11.2146	+	3.00493i	−1.54044	+	0.412759i	−0.926408	−	0.376522i	$-0.877120\pi$
$53$	−11.2146	+	3.00493i	−1.54044	+	0.412759i	−0.614031	+	0.789282i	$0.710453\pi$
$54$	0.216369	−	0.425567i	0.0294441	−	0.0579123i
$55$		−	2.02696i		−	0.273315i
$56$		0			0
$57$		−	0.445921i		−	0.0590637i
$58$	3.67676	+	1.86936i	0.482782	+	0.245459i
$59$	2.96105	−	0.793411i	0.385496	−	0.103293i	−0.0608657	−	0.998146i	$-0.519386\pi$
$59$	2.96105	−	0.793411i	0.385496	−	0.103293i	0.446362	+	0.894853i	$0.352719\pi$
$60$	0.118457	−	0.0863809i	0.0152928	−	0.0111517i
$61$	9.72123	+	2.60480i	1.24468	+	0.333510i	0.820277	−	0.571966i	$-0.193819\pi$
$61$	9.72123	+	2.60480i	1.24468	+	0.333510i	0.424398	+	0.905476i	$0.360486\pi$
$62$	8.68949	+	1.83908i	1.10357	+	0.233563i
$63$		0			0
$64$	2.51197	+	7.59540i	0.313996	+	0.949424i
$65$	1.46970	+	2.54559i	0.182293	+	0.315742i
$66$	0.0828392	−	0.0921640i	0.0101968	−	0.0113446i
$67$	0.566758	+	2.11517i	0.0692405	+	0.258409i	0.991866	−	0.127289i	$-0.0406274\pi$
$67$	0.566758	+	2.11517i	0.0692405	+	0.258409i	−0.922625	+	0.385698i	$0.873961\pi$
$68$	−0.624456	−	5.84312i	−0.0757264	−	0.708583i
$69$	−0.180077	−	0.180077i	−0.0216787	−	0.0216787i
$70$		0			0
$71$		−	7.26378i		−	0.862052i	−0.902340	−	0.431026i	$-0.858152\pi$
$71$		−	7.26378i		−	0.862052i	0.902340	−	0.431026i	$-0.141848\pi$
$72$	−8.43218	−	0.863930i	−0.993742	−	0.101815i
$73$	−12.2392	−	7.06631i	−1.43249	−	0.827049i	−0.435181	−	0.900343i	$-0.643316\pi$
$73$	−12.2392	−	7.06631i	−1.43249	−	0.827049i	−0.997310	+	0.0732936i	$0.976649\pi$
$74$	−7.67253	+	0.408819i	−0.891914	+	0.0475242i
$75$	0.0481435	−	0.179674i	0.00555913	−	0.0207469i
$76$	−14.7806	+	5.70337i	−1.69545	+	0.654221i
$77$		0			0
$78$	−0.0372092	+	0.175810i	−0.00421311	+	0.0199066i
$79$	−0.961559	−	1.66547i	−0.108184	−	0.187380i	0.806851	−	0.590755i	$-0.201170\pi$
$79$	−0.961559	−	1.66547i	−0.108184	−	0.187380i	−0.915035	+	0.403376i	$0.867837\pi$
$80$	−4.37827	−	2.82159i	−0.489506	−	0.315463i
$81$	4.48574	−	7.76954i	0.498416	−	0.863282i
$82$	−9.87083	+	3.21676i	−1.09005	+	0.355231i
$83$	−8.82731	+	8.82731i	−0.968923	+	0.968923i	−0.999531	−	0.0306086i	$-0.990255\pi$
$83$	−8.82731	+	8.82731i	−0.968923	+	0.968923i	0.0306086	+	0.999531i	$0.490255\pi$
$84$		0			0
$85$	2.70543	+	2.70543i	0.293445	+	0.293445i
$86$	1.80733	−	3.55475i	0.194889	−	0.383318i
$87$	−0.142188	−	0.0820924i	−0.0152442	−	0.00880123i
$88$	−4.11440	−	1.56702i	−0.438596	−	0.167044i
$89$	11.5526	−	6.66987i	1.22457	−	0.707005i	0.258680	−	0.965963i	$-0.416713\pi$
$89$	11.5526	−	6.66987i	1.22457	−	0.707005i	0.965888	+	0.258959i	$0.0833793\pi$
$90$	4.62586	−	3.00981i	0.487608	−	0.317262i
$91$		0			0
$92$	−3.66566	+	8.27206i	−0.382172	+	0.862422i
$93$	−0.341503	−	0.0915056i	−0.0354123	−	0.00948869i
$94$	1.85186	−	2.06031i	0.191005	−	0.212505i
$95$	5.15752	−	8.93309i	0.529151	−	0.916516i
$96$	−0.0837613	−	0.307230i	−0.00854886	−	0.0313565i
$97$	9.69578			0.984458			0.492229	−	0.870466i	$-0.336182\pi$
$97$	9.69578			0.984458			0.492229	+	0.870466i	$0.336182\pi$
$98$		0			0
$99$	3.29854	−	3.29854i	0.331516	−	0.331516i
$100$	−6.57125	+	0.702272i	−0.657125	+	0.0702272i
$101$	−10.2081	+	2.73526i	−1.01575	+	0.272168i	−0.728029	−	0.685547i	$-0.759563\pi$
$101$	−10.2081	+	2.73526i	−1.01575	+	0.272168i	−0.287718	+	0.957715i	$0.592897\pi$
$102$	0.0124460	+	0.233581i	0.00123234	+	0.0231279i
$103$	−2.96542	+	1.71209i	−0.292192	+	0.168697i	−0.638930	−	0.769265i	$-0.720623\pi$
$103$	−2.96542	+	1.71209i	−0.292192	+	0.168697i	0.346738	+	0.937962i	$0.387289\pi$
$104$	6.30334	−	1.01529i	0.618094	−	0.0995570i
$105$		0			0
$106$	−8.95459	−	13.7625i	−0.869747	−	1.33674i
$107$	2.96534	−	11.0668i	0.286670	−	1.06987i	−0.660940	−	0.750439i	$-0.729842\pi$
$107$	2.96534	−	11.0668i	0.286670	−	1.06987i	0.947610	−	0.319429i	$-0.103491\pi$
$108$	0.667034	+	0.104454i	0.0641854	+	0.0100511i
$109$	−0.811511	−	3.02860i	−0.0777287	−	0.290087i	0.916110	−	0.400928i	$-0.131312\pi$
$109$	−0.811511	−	3.02860i	−0.0777287	−	0.290087i	−0.993838	+	0.110841i	$0.964646\pi$
$110$	2.72548	−	0.888193i	0.259864	−	0.0846859i
$111$	0.305841			0.0290292
$112$		0			0
$113$	4.67963			0.440223			0.220111	−	0.975475i	$-0.429358\pi$
$113$	4.67963			0.440223			0.220111	+	0.975475i	$0.429358\pi$
$114$	0.599592	−	0.195398i	0.0561570	−	0.0183007i
$115$	−1.52469	−	5.69024i	−0.142178	−	0.530617i
$116$	−0.902448	+	5.76296i	−0.0837902	+	0.535077i
$117$	−1.75084	+	6.53422i	−0.161865	+	0.604089i
$118$	2.36434	+	3.63381i	0.217655	+	0.334519i
$119$		0			0
$120$	0.168056	+	0.121428i	0.0153413	+	0.0110848i
$121$	−7.42792	+	4.28851i	−0.675265	+	0.389865i
$122$	0.757302	+	14.2127i	0.0685629	+	1.28676i
$123$	0.399168	−	0.106957i	0.0359918	−	0.00964398i
$124$	1.33480	+	12.4899i	0.119868	+	1.12162i
$125$	7.64645	−	7.64645i	0.683919	−	0.683919i
$126$		0			0
$127$	5.63308			0.499855			0.249928	−	0.968265i	$-0.419593\pi$
$127$	5.63308			0.499855			0.249928	+	0.968265i	$0.419593\pi$
$128$	−9.11216	+	6.70586i	−0.805409	+	0.592719i
$129$	−0.0793683	+	0.137470i	−0.00698799	+	0.0121035i
$130$	−2.77883	+	3.09163i	−0.243720	+	0.271154i
$131$	2.00524	+	0.537304i	0.175199	+	0.0469444i	0.345352	−	0.938473i	$-0.387760\pi$
$131$	2.00524	+	0.537304i	0.175199	+	0.0469444i	−0.170153	+	0.985418i	$0.554426\pi$
$132$	0.160224	+	0.0710014i	0.0139457	+	0.00617988i
$133$		0			0
$134$	−2.59574	+	1.68892i	−0.224238	+	0.145900i
$135$	−0.380697	+	0.219795i	−0.0327652	+	0.0189170i
$136$	7.58312	−	3.40005i	0.650247	−	0.291552i
$137$	−2.68685	−	1.55125i	−0.229553	−	0.132532i	0.380813	−	0.924652i	$-0.375644\pi$
$137$	−2.68685	−	1.55125i	−0.229553	−	0.132532i	−0.610366	+	0.792120i	$0.708978\pi$
$138$	0.163226	−	0.321042i	0.0138947	−	0.0273289i
$139$	−12.7451	−	12.7451i	−1.08103	−	1.08103i	−0.996414	−	0.0846114i	$-0.973035\pi$
$139$	−12.7451	−	12.7451i	−1.08103	−	1.08103i	−0.0846114	−	0.996414i	$-0.526965\pi$
$140$		0			0
$141$	−0.0779732	+	0.0779732i	−0.00656653	+	0.00656653i
$142$	9.76698	−	3.18292i	0.819627	−	0.267104i
$143$	−1.75684	+	3.04294i	−0.146914	+	0.254463i
$144$	−2.53325	−	11.7166i	−0.211104	−	0.976383i
$145$	−1.89896	−	3.28910i	−0.157700	−	0.273145i
$146$	4.13836	−	19.5534i	0.342493	−	1.61825i
$147$		0			0
$148$	−3.91173	−	10.1375i	−0.321543	−	0.833294i
$149$	−3.89339	+	14.5303i	−0.318959	+	1.19037i	0.601288	+	0.799032i	$0.294654\pi$
$149$	−3.89339	+	14.5303i	−0.318959	+	1.19037i	−0.920247	+	0.391338i	$0.872012\pi$
$150$	0.262688	−	0.0139969i	0.0214484	−	0.00114284i
$151$	−15.7545	−	9.09588i	−1.28209	−	0.740212i	−0.304856	−	0.952398i	$-0.598608\pi$
$151$	−15.7545	−	9.09588i	−1.28209	−	0.740212i	−0.977229	+	0.212186i	$0.931942\pi$
$152$	−14.1455	−	17.3750i	−1.14735	−	1.40930i
$153$			8.80528i			0.711865i
$154$		0			0
$155$	−5.78295	−	5.78295i	−0.464498	−	0.464498i
$156$	−0.252702	+	0.0270063i	−0.0202323	+	0.00216224i
$157$	2.51651	+	9.39175i	0.200840	+	0.749544i	0.990678	+	0.136228i	$0.0434980\pi$
$157$	2.51651	+	9.39175i	0.200840	+	0.749544i	−0.789838	+	0.613316i	$0.789835\pi$
$158$	1.81807	−	2.02272i	0.144638	−	0.160919i
$159$	0.326788	+	0.566013i	0.0259159	+	0.0448877i
$160$	1.87543	−	7.12348i	0.148266	−	0.563161i
$161$		0			0
$162$	12.4126	+	2.62706i	0.975230	+	0.206402i
$163$	12.5602	+	3.36548i	0.983787	+	0.263605i	0.714639	−	0.699494i	$-0.246591\pi$
$163$	12.5602	+	3.36548i	0.983787	+	0.263605i	0.269148	+	0.963099i	$0.413258\pi$
$164$	−8.65060	−	11.8629i	−0.675498	−	0.926337i
$165$	−0.110216	+	0.0295323i	−0.00858031	+	0.00229909i
$166$	−15.7374	−	8.00129i	−1.22146	−	0.621020i
$167$		−	16.5417i		−	1.28004i	−0.768360	−	0.640018i	$-0.778927\pi$
$167$		−	16.5417i		−	1.28004i	0.768360	−	0.640018i	$-0.221073\pi$
$168$		0			0
$169$			7.90463i			0.608049i
$170$	−2.45227	+	4.82325i	−0.188080	+	0.369926i
$171$	22.9302	−	6.14412i	1.75351	−	0.469853i
$172$	5.57172	+	0.872502i	0.424840	+	0.0665276i
$173$	−20.8703	−	5.59219i	−1.58674	−	0.425166i	−0.645738	−	0.763559i	$-0.723450\pi$
$173$	−20.8703	−	5.59219i	−1.58674	−	0.425166i	−0.941005	+	0.338393i	$0.890117\pi$
$174$	0.0480771	−	0.227160i	0.00364472	−	0.0172210i
$175$		0			0
$176$	0.304142	−	6.21893i	0.0229256	−	0.468770i
$177$	−0.0862837	−	0.149448i	−0.00648548	−	0.0112332i
$178$	14.0306	+	12.6111i	1.05164	+	0.945239i
$179$	4.91053	+	18.3264i	0.367031	+	1.36978i	0.864647	+	0.502379i	$0.167542\pi$
$179$	4.91053	+	18.3264i	0.367031	+	1.36978i	−0.497617	+	0.867397i	$0.665791\pi$
$180$	6.07404	+	4.90112i	0.452732	+	0.365308i
$181$	−6.44222	−	6.44222i	−0.478846	−	0.478846i	0.425916	−	0.904763i	$-0.359952\pi$
$181$	−6.44222	−	6.44222i	−0.478846	−	0.478846i	−0.904763	+	0.425916i	$0.859952\pi$
$182$		0			0
$183$		−	0.566545i		−	0.0418802i
$184$	−12.7290	−	1.30417i	−0.938394	−	0.0961444i
$185$	6.12689	+	3.53736i	0.450458	+	0.260072i
$186$	−0.0266038	−	0.499287i	−0.00195068	−	0.0366095i
$187$	−1.18373	+	4.41773i	−0.0865627	+	0.323057i
$188$	3.58179	+	1.58723i	0.261229	+	0.115760i
$189$		0			0
$190$	14.2716	+	3.02049i	1.03537	+	0.219129i
$191$	−12.9567	−	22.4417i	−0.937515	−	1.62382i	−0.770086	−	0.637940i	$-0.779787\pi$
$191$	−12.9567	−	22.4417i	−0.937515	−	1.62382i	−0.167429	−	0.985884i	$-0.553546\pi$
$192$	0.376402	−	0.247252i	0.0271645	−	0.0178439i
$193$	−6.27389	+	10.8667i	−0.451604	+	0.782202i	−0.998486	−	0.0550082i	$-0.982481\pi$
$193$	−6.27389	+	10.8667i	−0.451604	+	0.782202i	0.546881	+	0.837210i	$0.315815\pi$
$194$	4.24860	+	13.0371i	0.305032	+	0.936009i
$195$	0.117004	−	0.117004i	0.00837881	−	0.00837881i
$196$		0			0
$197$	−8.31651	−	8.31651i	−0.592527	−	0.592527i	0.345786	−	0.938313i	$-0.387612\pi$
$197$	−8.31651	−	8.31651i	−0.592527	−	0.592527i	−0.938313	+	0.345786i	$0.887612\pi$
$198$	5.88066	+	2.98988i	0.417920	+	0.212481i
$199$	16.6783	+	9.62922i	1.18229	+	0.682597i	0.956544	−	0.291589i	$-0.0941838\pi$
$199$	16.6783	+	9.62922i	1.18229	+	0.682597i	0.225749	+	0.974186i	$0.427517\pi$
$200$	−3.82374	−	8.52807i	−0.270380	−	0.603026i
$201$	0.106755	−	0.0616352i	0.00752993	−	0.00434741i
$202$	−8.15097	−	12.5274i	−0.573501	−	0.881427i
$203$		0			0
$204$	−0.308623	+	0.119088i	−0.0216079	+	0.00833782i
$205$	9.23356	+	2.47413i	0.644900	+	0.172800i
$206$	−3.60151	−	3.23713i	−0.250929	−	0.225541i
$207$	6.77874	−	11.7411i	0.471155	−	0.816064i
$208$	4.12723	+	8.03068i	0.286172	+	0.556828i
$209$	12.3304			0.852909
$210$		0			0
$211$	−8.62222	+	8.62222i	−0.593578	+	0.593578i	−0.938596	−	0.345018i	$-0.887873\pi$
$211$	−8.62222	+	8.62222i	−0.593578	+	0.593578i	0.345018	+	0.938596i	$0.387873\pi$
$212$	14.5815	−	18.0711i	1.00146	−	1.24113i
$213$	−0.394969	+	0.105832i	−0.0270628	+	0.00725147i
$214$	16.1800	−	0.862124i	1.10604	−	0.0589336i
$215$	−3.17995	+	1.83595i	−0.216871	+	0.125211i
$216$	0.151838	+	0.942675i	0.0103312	+	0.0641409i
$217$		0			0
$218$	3.71670	−	2.41827i	0.251727	−	0.163786i
$219$	−0.205909	+	0.768464i	−0.0139141	+	0.0519280i
$220$	2.38856	+	3.27552i	0.161036	+	0.220835i
$221$	−1.71658	−	6.40638i	−0.115470	−	0.430940i
$222$	0.134017	+	0.411239i	0.00899461	+	0.0276005i
$223$	22.4402			1.50271			0.751354	−	0.659899i	$-0.229401\pi$
$223$	22.4402			1.50271			0.751354	+	0.659899i	$0.229401\pi$
$224$		0			0
$225$	9.90254			0.660169
$226$	2.05057	+	6.29230i	0.136402	+	0.418558i
$227$	−0.605377	−	2.25930i	−0.0401803	−	0.149955i	0.942921	−	0.333016i	$-0.108066\pi$
$227$	−0.605377	−	2.25930i	−0.0401803	−	0.149955i	−0.983102	+	0.183061i	$0.941400\pi$
$228$	0.525471	+	0.720599i	0.0348002	+	0.0477229i
$229$	−5.08653	+	18.9832i	−0.336127	+	1.25444i	0.566514	+	0.824052i	$0.308292\pi$
$229$	−5.08653	+	18.9832i	−0.336127	+	1.25444i	−0.902642	+	0.430393i	$0.858375\pi$
$230$	6.98307	−	4.54353i	0.460450	−	0.299592i
$231$		0			0
$232$	−8.14440	+	1.31183i	−0.534706	+	0.0861256i
$233$	3.35515	−	1.93710i	0.219803	−	0.126903i	−0.386056	−	0.922475i	$-0.626163\pi$
$233$	3.35515	−	1.93710i	0.219803	−	0.126903i	0.605859	+	0.795572i	$0.292829\pi$
$234$	−9.55321	+	0.509028i	−0.624513	+	0.0332762i
$235$	−2.46387	+	0.660191i	−0.160725	+	0.0430661i
$236$	−3.85004	+	4.77142i	−0.250616	+	0.310593i
$237$	−0.0765505	+	0.0765505i	−0.00497249	+	0.00497249i
$238$		0			0
$239$	−6.56774			−0.424832			−0.212416	−	0.977179i	$-0.568133\pi$
$239$	−6.56774			−0.424832			−0.212416	+	0.977179i	$0.568133\pi$
$240$	−0.0896339	+	0.279179i	−0.00578585	+	0.0180209i
$241$	−6.62647	+	11.4774i	−0.426849	+	0.739323i	−0.996591	−	0.0824998i	$-0.973710\pi$
$241$	−6.62647	+	11.4774i	−0.426849	+	0.739323i	0.569742	+	0.821823i	$0.307043\pi$
$242$	−9.02124	−	8.10851i	−0.579907	−	0.521235i
$243$	−1.46606	−	0.392830i	−0.0940479	−	0.0252001i
$244$	−18.7788	+	7.24615i	−1.20219	+	0.463887i
$245$		0			0
$246$	0.318728	+	0.489860i	0.0203213	+	0.0312324i
$247$	−15.4853	+	8.94045i	−0.985306	+	0.568867i
$248$	−16.2092	+	7.26774i	−1.02928	+	0.461502i
$249$	0.608598	+	0.351374i	0.0385683	+	0.0222674i
$250$	13.6321	+	6.93093i	0.862172	+	0.438350i
$251$	3.80916	+	3.80916i	0.240432	+	0.240432i	0.817029	−	0.576597i	$-0.195620\pi$
$251$	3.80916	+	3.80916i	0.240432	+	0.240432i	−0.576597	+	0.817029i	$0.695620\pi$
$252$		0			0
$253$	4.97939	−	4.97939i	0.313052	−	0.313052i
$254$	2.46836	+	7.57433i	0.154879	+	0.475256i
$255$	0.107691	−	0.186526i	0.00674385	−	0.0116807i
$256$	−13.0097	−	9.31391i	−0.813103	−	0.582119i
$257$	−11.8190	−	20.4712i	−0.737251	−	1.27696i	−0.953729	−	0.300669i	$-0.902790\pi$
$257$	−11.8190	−	20.4712i	−0.737251	−	1.27696i	0.216477	−	0.976288i	$-0.430543\pi$
$258$	−0.219622	−	0.0464818i	−0.0136731	−	0.00289383i
$259$		0			0
$260$	−5.37471	−	2.38174i	−0.333325	−	0.147709i
$261$	2.26222	−	8.44271i	0.140028	−	0.522591i
$262$	0.156212	+	2.93172i	0.00965083	+	0.181122i
$263$	15.4301	+	8.90857i	0.951460	+	0.549326i	0.893534	−	0.448995i	$-0.148218\pi$
$263$	15.4301	+	8.90857i	0.951460	+	0.549326i	0.0579260	+	0.998321i	$0.481551\pi$
$264$	−0.0252608	+	0.246552i	−0.00155470	+	0.0151742i
$265$			15.1185i			0.928722i
$266$		0			0
$267$	−0.530993	−	0.530993i	−0.0324963	−	0.0324963i
$268$	−3.40837	−	2.75021i	−0.208200	−	0.167996i
$269$	−1.65252	−	6.16728i	−0.100756	−	0.376026i	0.897073	−	0.441882i	$-0.145689\pi$
$269$	−1.65252	−	6.16728i	−0.100756	−	0.376026i	−0.997829	+	0.0658559i	$0.979022\pi$
$270$	−0.462358	−	0.415578i	−0.0281382	−	0.0252913i
$271$	−3.98703	−	6.90574i	−0.242195	−	0.419494i	0.719144	−	0.694861i	$-0.244534\pi$
$271$	−3.98703	−	6.90574i	−0.242195	−	0.419494i	−0.961339	+	0.275367i	$0.911201\pi$
$272$	7.89461	+	8.70650i	0.478681	+	0.527909i
$273$		0			0
$274$	0.908486	−	4.29252i	0.0548836	−	0.259320i
$275$	4.96824	+	1.33124i	0.299596	+	0.0802765i
$276$	0.503202	+	0.0787988i	0.0302892	+	0.00474313i
$277$	−12.3757	+	3.31607i	−0.743586	+	0.199243i	−0.610671	−	0.791884i	$-0.709100\pi$
$277$	−12.3757	+	3.31607i	−0.743586	+	0.199243i	−0.132915	+	0.991127i	$0.542434\pi$
$278$	11.5525	−	22.7220i	0.692871	−	1.36278i
$279$		−	18.8216i		−	1.12682i
$280$		0			0
$281$			13.0438i			0.778126i	0.921211	+	0.389063i	$0.127201\pi$
$281$			13.0438i			0.778126i	−0.921211	+	0.389063i	$0.872799\pi$
$282$	−0.139011	−	0.0706768i	−0.00827799	−	0.00420874i
$283$	−18.6171	+	4.98843i	−1.10667	+	0.296531i	−0.765478	−	0.643462i	$-0.777497\pi$
$283$	−18.6171	+	4.98843i	−1.10667	+	0.296531i	−0.341192	+	0.939994i	$0.610831\pi$
$284$	8.55960	+	11.7381i	0.507919	+	0.696529i
$285$	−0.560883	−	0.150288i	−0.0332238	−	0.00890229i
$286$	−4.86141	−	1.02889i	−0.287461	−	0.0608395i
$287$		0			0
$288$	14.6443	−	8.54034i	0.862922	−	0.503244i
$289$	4.18350	+	7.24603i	0.246088	+	0.426237i
$290$	3.59046	−	3.99462i	0.210839	−	0.234572i
$291$	−0.141265	−	0.527210i	−0.00828113	−	0.0309056i
$292$	28.1052	−	3.00361i	1.64473	−	0.175773i
$293$	−12.7021	−	12.7021i	−0.742067	−	0.742067i	0.230908	−	0.972975i	$-0.425830\pi$
$293$	−12.7021	−	12.7021i	−0.742067	−	0.742067i	−0.972975	+	0.230908i	$0.925830\pi$
$294$		0			0
$295$		−	3.99183i		−	0.232413i
$296$	11.9169	−	9.70191i	0.692655	−	0.563912i
$297$	−0.455076	−	0.262738i	−0.0264062	−	0.0152456i
$298$	−21.2437	+	1.13194i	−1.23062	+	0.0655715i
$299$	−2.64302	+	9.86389i	−0.152850	+	0.570443i
$300$	0.133928	+	0.347081i	0.00773233	+	0.0200387i
$301$		0			0
$302$	5.32697	−	25.1695i	0.306533	−	1.44834i
$303$	0.297460	+	0.515217i	0.0170887	+	0.0295984i
$304$	17.1643	−	26.6339i	0.984438	−	1.52756i
$305$	6.55265	−	11.3495i	0.375204	−	0.649872i
$306$	−11.8397	+	3.85839i	−0.676831	+	0.220569i
$307$	−15.5180	+	15.5180i	−0.885657	+	0.885657i	−0.994102	−	0.108446i	$-0.965413\pi$
$307$	−15.5180	+	15.5180i	−0.885657	+	0.885657i	0.108446	+	0.994102i	$0.465413\pi$
$308$		0			0
$309$	0.136300	+	0.136300i	0.00775386	+	0.00775386i
$310$	5.24181	−	10.3099i	0.297715	−	0.585561i
$311$	3.14576	+	1.81621i	0.178380	+	0.102988i	0.586531	−	0.809927i	$-0.300493\pi$
$311$	3.14576	+	1.81621i	0.178380	+	0.102988i	−0.408151	+	0.912914i	$0.633826\pi$
$312$	−0.147045	−	0.327953i	−0.00832477	−	0.0185667i
$313$	3.24479	−	1.87338i	0.183406	−	0.105890i	−0.405486	−	0.914101i	$-0.632898\pi$
$313$	3.24479	−	1.87338i	0.183406	−	0.105890i	0.588892	+	0.808212i	$0.299564\pi$
$314$	−11.5256	+	7.49912i	−0.650426	+	0.423200i
$315$		0			0
$316$	3.51644	+	1.55827i	0.197815	+	0.0876593i
$317$	−23.7647	−	6.36774i	−1.33476	−	0.357648i	−0.480272	−	0.877119i	$-0.659462\pi$
$317$	−23.7647	−	6.36774i	−1.33476	−	0.357648i	−0.854488	+	0.519472i	$0.826129\pi$
$318$	−0.617874	+	0.687425i	−0.0346486	+	0.0385489i
$319$	2.26997	−	3.93171i	0.127094	−	0.220133i
$320$	10.4001	−	0.599704i	0.581385	−	0.0335245i
$321$	−0.644963			−0.0359983
$322$		0			0
$323$	−16.4576	+	16.4576i	−0.915727	+	0.915727i
$324$	1.90671	+	17.8414i	0.105929	+	0.991188i
$325$	−7.20470	+	1.93049i	−0.399645	+	0.107084i
$326$	0.978459	+	18.3633i	0.0541919	+	1.01705i
$327$	−0.152857	+	0.0882521i	−0.00845302	+	0.00488035i
$328$	12.1604	−	16.8299i	0.671448	−	0.929278i
$329$		0			0
$330$	−0.0880053	−	0.135257i	−0.00484453	−	0.00744568i
$331$	−2.62451	+	9.79479i	−0.144256	+	0.538370i	0.855532	+	0.517751i	$0.173231\pi$
$331$	−2.62451	+	9.79479i	−0.144256	+	0.538370i	−0.999787	+	0.0206195i	$0.993436\pi$
$332$	3.86269	−	24.6668i	0.211993	−	1.35377i
$333$	4.21403	+	15.7270i	0.230928	+	0.861833i
$334$	22.2422	−	7.24842i	1.21704	−	0.396616i
$335$	2.85149			0.155793
$336$		0			0
$337$	−5.30745			−0.289115			−0.144558	−	0.989496i	$-0.546176\pi$
$337$	−5.30745			−0.289115			−0.144558	+	0.989496i	$0.546176\pi$
$338$	−10.6287	+	3.46373i	−0.578124	+	0.188402i
$339$	−0.0681812	−	0.254456i	−0.00370309	−	0.0138201i
$340$	−7.55997	−	1.18385i	−0.409997	−	0.0642034i
$341$	2.53026	−	9.44306i	0.137021	−	0.511370i
$342$	18.3093	+	28.1400i	0.990051	+	1.52163i
$343$		0			0
$344$	1.26830	+	7.87414i	0.0683819	+	0.424545i
$345$	−0.287193	+	0.165811i	−0.0154620	+	0.00892696i
$346$	−1.62584	−	30.5130i	−0.0874056	−	1.64039i
$347$	−3.98409	+	1.06753i	−0.213877	+	0.0573082i	−0.364166	−	0.931334i	$-0.618646\pi$
$347$	−3.98409	+	1.06753i	−0.213877	+	0.0573082i	0.150290	+	0.988642i	$0.451979\pi$
$348$	0.326510	−	0.0348942i	0.0175028	−	0.00187053i
$349$	−11.4637	+	11.4637i	−0.613639	+	0.613639i	−0.943892	−	0.330253i	$-0.892866\pi$
$349$	−11.4637	+	11.4637i	−0.613639	+	0.613639i	0.330253	+	0.943892i	$0.392866\pi$
$350$		0			0
$351$	0.762020			0.0406736
$352$	8.49534	−	2.31612i	0.452803	−	0.123450i
$353$	−1.93371	+	3.34929i	−0.102921	+	0.178265i	−0.912887	−	0.408212i	$-0.866152\pi$
$353$	−1.93371	+	3.34929i	−0.102921	+	0.178265i	0.809966	+	0.586477i	$0.199486\pi$
$354$	0.163141	−	0.181505i	0.00867085	−	0.00964688i
$355$	−9.13642	−	2.44810i	−0.484911	−	0.129932i
$356$	−10.8089	+	24.3918i	−0.572873	+	1.29276i
$357$		0			0
$358$	−22.4901	+	14.6332i	−1.18864	+	0.773389i
$359$	13.6977	−	7.90839i	0.722938	−	0.417389i	−0.0928949	−	0.995676i	$-0.529612\pi$
$359$	13.6977	−	7.90839i	0.722938	−	0.417389i	0.815833	+	0.578287i	$0.196279\pi$
$360$	−3.92854	+	10.3149i	−0.207052	+	0.543642i
$361$	37.8872	+	21.8742i	1.99407	+	1.15127i
$362$	5.83939	−	11.4852i	0.306911	−	0.603650i
$363$	0.341412	+	0.341412i	0.0179195	+	0.0179195i
$364$		0			0
$365$	−13.0130	+	13.0130i	−0.681132	+	0.681132i
$366$	0.761784	−	0.248254i	0.0398191	−	0.0129765i
$367$	−2.37345	+	4.11093i	−0.123893	+	0.214589i	−0.921300	−	0.388853i	$-0.872871\pi$
$367$	−2.37345	+	4.11093i	−0.123893	+	0.214589i	0.797407	+	0.603442i	$0.206205\pi$
$368$	−3.82412	−	17.6871i	−0.199346	−	0.922002i
$369$	10.9999	+	19.0523i	0.572631	+	0.991826i
$370$	−2.07164	+	9.78834i	−0.107700	+	0.508872i
$371$		0			0
$372$	0.659692	−	0.254555i	0.0342034	−	0.0131980i
$373$	−5.89711	+	22.0083i	−0.305341	+	1.13955i	0.627310	+	0.778769i	$0.284156\pi$
$373$	−5.89711	+	22.0083i	−0.305341	+	1.13955i	−0.932651	+	0.360779i	$0.882511\pi$
$374$	−6.45885	+	0.344150i	−0.333979	+	0.0177956i
$375$	−0.527184	−	0.304370i	−0.0272237	−	0.0157176i
$376$	−0.564703	+	5.51164i	−0.0291223	+	0.284241i
$377$			6.58360i			0.339073i
$378$		0			0
$379$	20.1030	+	20.1030i	1.03262	+	1.03262i	0.999450	+	0.0331705i	$0.0105604\pi$
$379$	20.1030	+	20.1030i	1.03262	+	1.03262i	0.0331705	+	0.999450i	$0.489440\pi$
$380$	2.19226	+	20.5133i	0.112461	+	1.05231i
$381$	−0.0820728	−	0.306300i	−0.00420472	−	0.0156922i
$382$	24.4979	−	27.2555i	1.25342	−	1.39451i
$383$	−11.7252	−	20.3087i	−0.599131	−	1.03773i	−0.992950	−	0.118537i	$-0.962180\pi$
$383$	−11.7252	−	20.3087i	−0.599131	−	1.03773i	0.393819	−	0.919188i	$-0.371154\pi$
$384$	0.497394	+	0.397773i	0.0253825	+	0.0202987i
$385$		0			0
$386$	−17.3607	−	3.67428i	−0.883635	−	0.187016i
$387$	−8.16255	−	2.18715i	−0.414926	−	0.111179i
$388$	−15.6682	+	11.4255i	−0.795431	+	0.580040i
$389$	−10.3510	+	2.77356i	−0.524819	+	0.140625i	−0.511495	−	0.859286i	$-0.670908\pi$
$389$	−10.3510	+	2.77356i	−0.524819	+	0.140625i	−0.0133242	+	0.999911i	$0.504241\pi$
$390$	0.208595	+	0.106055i	0.0105626	+	0.00537030i
$391$			13.2922i			0.672216i
$392$		0			0
$393$		−	0.116864i		−	0.00589500i
$394$	7.53829	−	14.8267i	0.379774	−	0.746959i
$395$	−2.41891	+	0.648145i	−0.121709	+	0.0326117i
$396$	−1.44339	+	9.21735i	−0.0725330	+	0.463189i
$397$	6.40226	+	1.71548i	0.321320	+	0.0860975i	0.415874	−	0.909422i	$-0.363476\pi$
$397$	6.40226	+	1.71548i	0.321320	+	0.0860975i	−0.0945536	+	0.995520i	$0.530142\pi$
$398$	−5.63932	+	26.6453i	−0.282674	+	1.33561i
$399$		0			0
$400$	9.79145	−	8.87838i	0.489572	−	0.443919i
$401$	−15.8657	−	27.4802i	−0.792294	−	1.37229i	−0.924543	−	0.381077i	$-0.875553\pi$
$401$	−15.8657	−	27.4802i	−0.792294	−	1.37229i	0.132250	−	0.991216i	$-0.457780\pi$
$402$	0.129655	+	0.116537i	0.00646659	+	0.00581232i
$403$	3.66926	+	13.6939i	0.182779	+	0.682140i
$404$	13.2729	−	16.4493i	0.660351	−	0.818384i
$405$	−8.26075	−	8.26075i	−0.410480	−	0.410480i
$406$		0			0
$407$			8.45695i			0.419196i
$408$	−0.295363	−	0.362795i	−0.0146226	−	0.0179610i
$409$	−1.11952	−	0.646353i	−0.0553565	−	0.0319601i	0.472066	−	0.881563i	$-0.343508\pi$
$409$	−1.11952	−	0.646353i	−0.0553565	−	0.0319601i	−0.527423	+	0.849603i	$0.676842\pi$
$410$	0.719312	+	13.4997i	0.0355243	+	0.666704i
$411$	−0.0452028	+	0.168699i	−0.00222969	+	0.00832131i
$412$	2.77454	−	6.26113i	0.136692	−	0.308464i
$413$		0			0
$414$	18.7577	+	3.96995i	0.921889	+	0.195112i
$415$	8.12799	+	14.0781i	0.398987	+	0.691066i
$416$	−8.98966	+	9.06851i	−0.440754	+	0.444620i
$417$	−0.507324	+	0.878710i	−0.0248437	+	0.0430306i
$418$	5.40305	+	16.5796i	0.264272	+	0.810935i
$419$	−17.2788	+	17.2788i	−0.844124	+	0.844124i	−0.989392	−	0.145269i	$-0.953595\pi$
$419$	−17.2788	+	17.2788i	−0.844124	+	0.844124i	0.145269	+	0.989392i	$0.453595\pi$
$420$		0			0
$421$	3.36245	+	3.36245i	0.163876	+	0.163876i	0.784281	−	0.620405i	$-0.213032\pi$
$421$	3.36245	+	3.36245i	0.163876	+	0.163876i	−0.620405	+	0.784281i	$0.713032\pi$
$422$	−15.3717	−	7.81539i	−0.748284	−	0.380447i
$423$	−5.08389	−	2.93519i	−0.247187	−	0.142714i
$424$	30.6881	+	11.6879i	1.49035	+	0.567616i
$425$	−8.40806	+	4.85440i	−0.407851	+	0.235473i
$426$	−0.315374	−	0.484707i	−0.0152799	−	0.0234841i
$427$		0			0
$428$	8.24913	+	21.3780i	0.398737	+	1.03335i
$429$	0.191057	+	0.0511936i	0.00922432	+	0.00247165i
$430$	−3.86207	−	3.47132i	−0.186245	−	0.167402i
$431$	−5.58722	+	9.67735i	−0.269127	+	0.466141i	−0.968637	−	0.248482i	$-0.920068\pi$
$431$	−5.58722	+	9.67735i	−0.269127	+	0.466141i	0.699510	+	0.714623i	$0.253402\pi$
$432$	−1.20100	+	0.617234i	−0.0577832	+	0.0296967i
$433$	17.3943			0.835916			0.417958	−	0.908466i	$-0.362746\pi$
$433$	17.3943			0.835916			0.417958	+	0.908466i	$0.362746\pi$
$434$		0			0
$435$	−0.151178	+	0.151178i	−0.00724842	+	0.00724842i
$436$	4.88027	+	3.93787i	0.233723	+	0.188590i
$437$	34.6148	−	9.27500i	1.65585	−	0.443684i
$438$	−1.12352	+	0.0598648i	−0.0536836	+	0.00286045i
$439$	−32.5115	+	18.7705i	−1.55169	+	0.895867i	−0.553683	+	0.832727i	$0.686778\pi$
$439$	−32.5115	+	18.7705i	−1.55169	+	0.895867i	−0.998005	+	0.0631399i	$0.979889\pi$
$440$	−3.35767	+	4.64699i	−0.160071	+	0.221536i
$441$		0			0
$442$	7.86192	−	5.11536i	0.373953	−	0.243313i
$443$	−1.84399	+	6.88186i	−0.0876106	+	0.326967i	−0.995796	−	0.0916015i	$-0.970801\pi$
$443$	−1.84399	+	6.88186i	−0.0876106	+	0.326967i	0.908185	+	0.418569i	$0.137468\pi$
$444$	−0.494233	+	0.360402i	−0.0234553	+	0.0171039i
$445$	−4.49587	−	16.7788i	−0.213125	−	0.795392i
$446$	9.83309	+	30.1734i	0.465610	+	1.42875i
$447$	0.846815			0.0400530
$448$		0			0
$449$	−7.84005			−0.369995			−0.184997	−	0.982739i	$-0.559228\pi$
$449$	−7.84005			−0.369995			−0.184997	+	0.982739i	$0.559228\pi$
$450$	4.33920	+	13.3151i	0.204552	+	0.627680i
$451$	2.95751	+	11.0376i	0.139264	+	0.519739i
$452$	−7.56218	+	5.51445i	−0.355695	+	0.259378i
$453$	−0.265050	+	0.989180i	−0.0124531	+	0.0464757i
$454$	2.77262	−	1.80400i	0.130125	−	0.0846660i
$455$		0			0
$456$	−0.738672	+	1.02232i	−0.0345915	+	0.0478743i
$457$	22.2821	−	12.8646i	1.04231	−	0.601780i	0.121826	−	0.992551i	$-0.461125\pi$
$457$	22.2821	−	12.8646i	1.04231	−	0.601780i	0.920488	+	0.390771i	$0.127792\pi$
$458$	−27.7539	+	1.47883i	−1.29686	+	0.0691010i
$459$	0.958084	−	0.256718i	0.0447195	−	0.0119826i
$460$	9.16922	+	7.39861i	0.427517	+	0.344962i
$461$	13.1661	−	13.1661i	0.613207	−	0.613207i	−0.330573	−	0.943780i	$-0.607242\pi$
$461$	13.1661	−	13.1661i	0.613207	−	0.613207i	0.943780	+	0.330573i	$0.107242\pi$
$462$		0			0
$463$	6.88821			0.320122			0.160061	−	0.987107i	$-0.448831\pi$
$463$	6.88821			0.320122			0.160061	+	0.987107i	$0.448831\pi$
$464$	−5.33270	−	10.3763i	−0.247564	−	0.481705i
$465$	−0.230193	+	0.398705i	−0.0106749	+	0.0184895i
$466$	4.07484	+	3.66257i	0.188764	+	0.169665i
$467$	38.2159	+	10.2399i	1.76842	+	0.473847i	0.988396	−	0.151902i	$-0.0485397\pi$
$467$	38.2159	+	10.2399i	1.76842	+	0.473847i	0.780025	+	0.625749i	$0.215206\pi$
$468$	−4.87057	−	12.6223i	−0.225142	−	0.583468i
$469$		0			0
$470$	−1.96735	−	3.02366i	−0.0907469	−	0.139471i
$471$	0.474013	−	0.273672i	0.0218414	−	0.0126101i
$472$	−8.10278	−	3.08603i	−0.372960	−	0.142046i
$473$	−3.80124	−	2.19465i	−0.174781	−	0.100910i
$474$	−0.136475	−	0.0693872i	−0.00626848	−	0.00318706i
$475$	18.5085	+	18.5085i	0.849227	+	0.849227i
$476$		0			0
$477$	−24.6029	+	24.6029i	−1.12649	+	1.12649i
$478$	−2.87792	−	8.83109i	−0.131633	−	0.403924i
$479$	−0.261991	+	0.453782i	−0.0119707	+	0.0207338i	−0.871949	−	0.489597i	$-0.837144\pi$
$479$	−0.261991	+	0.453782i	−0.0119707	+	0.0207338i	0.859978	+	0.510331i	$0.170477\pi$
$480$	−0.414665	+	0.00181051i	−0.0189268	+	8.26379e-5i
$481$	−6.13193	−	10.6208i	−0.279592	−	0.484267i
$482$	−18.3363	−	3.88077i	−0.835197	−	0.176764i
$483$		0			0
$484$	6.94980	−	15.6832i	0.315900	−	0.712871i
$485$	3.26775	−	12.1954i	0.148381	−	0.553765i
$486$	−0.114209	−	2.14342i	−0.00518063	−	0.0972277i
$487$	−2.46586	−	1.42366i	−0.111739	−	0.0645124i	0.443089	−	0.896478i	$-0.353883\pi$
$487$	−2.46586	−	1.42366i	−0.111739	−	0.0645124i	−0.554828	+	0.831965i	$0.687216\pi$
$488$	−17.9720	−	22.0750i	−0.813552	−	0.999289i
$489$		−	0.731995i		−	0.0331019i
$490$		0			0
$491$	−17.4826	−	17.4826i	−0.788977	−	0.788977i	0.192349	−	0.981327i	$-0.438389\pi$
$491$	−17.4826	−	17.4826i	−0.788977	−	0.788977i	−0.981327	+	0.192349i	$0.938389\pi$
$492$	−0.519010	+	0.643218i	−0.0233988	+	0.0289985i
$493$	2.21796	+	8.27753i	0.0998918	+	0.372801i
$494$	−18.8070	−	16.9042i	−0.846166	−	0.760554i
$495$	−3.03722	−	5.26063i	−0.136513	−	0.236448i
$496$	−16.8750	−	18.6105i	−0.757711	−	0.835635i
$497$		0			0
$498$	−0.205781	+	0.972299i	−0.00922128	+	0.0435698i
$499$	−1.30845	−	0.350599i	−0.0585743	−	0.0156949i	0.229413	−	0.973329i	$-0.426319\pi$
$499$	−1.30845	−	0.350599i	−0.0585743	−	0.0156949i	−0.287987	+	0.957634i	$0.592986\pi$
$500$	−3.34596	+	21.3670i	−0.149636	+	0.955563i
$501$	−0.899458	+	0.241009i	−0.0401848	+	0.0107675i
$502$	−3.45271	+	6.79098i	−0.154102	+	0.303096i
$503$			15.4389i			0.688388i	0.938899	+	0.344194i	$0.111848\pi$
$503$			15.4389i			0.688388i	−0.938899	+	0.344194i	$0.888152\pi$
$504$		0			0
$505$			13.7617i			0.612388i
$506$	8.87728	+	4.51344i	0.394643	+	0.200647i
$507$	0.429816	−	0.115169i	0.0190888	−	0.00511482i
$508$	−9.10294	+	6.63800i	−0.403878	+	0.294513i
$509$	−8.34301	−	2.23550i	−0.369797	−	0.0990869i	0.0691342	−	0.997607i	$-0.477976\pi$
$509$	−8.34301	−	2.23550i	−0.369797	−	0.0990869i	−0.438932	+	0.898520i	$0.644643\pi$
$510$	0.297994	+	0.0630687i	0.0131954	+	0.00279273i
$511$		0			0
$512$	6.82291	−	21.5742i	0.301533	−	0.953456i
$513$	−1.33706	−	2.31585i	−0.0590325	−	0.102247i
$514$	22.3469	−	24.8623i	0.985677	−	1.09663i
$515$	1.15404	+	4.30694i	0.0508532	+	0.189787i
$516$	−0.0337363	−	0.315675i	−0.00148516	−	0.0138968i
$517$	−2.15607	−	2.15607i	−0.0948239	−	0.0948239i
$518$		0			0
$519$			1.21631i			0.0533899i
$520$	0.847372	−	8.27056i	0.0371597	−	0.362688i
$521$	3.08690	+	1.78222i	0.135240	+	0.0780807i	0.566093	−	0.824341i	$-0.308454\pi$
$521$	3.08690	+	1.78222i	0.135240	+	0.0780807i	−0.430854	+	0.902422i	$0.641787\pi$
$522$	12.3435	−	0.657703i	0.540259	−	0.0287869i
$523$	5.23389	−	19.5332i	0.228862	−	0.854125i	−0.751958	−	0.659211i	$-0.770890\pi$
$523$	5.23389	−	19.5332i	0.228862	−	0.854125i	0.980820	−	0.194914i	$-0.0624429\pi$
$524$	−3.87359	+	1.49470i	−0.169218	+	0.0652962i
$525$		0			0
$526$	−5.21728	+	24.6512i	−0.227484	+	1.07484i
$527$	9.22668	+	15.9811i	0.401920	+	0.696147i
$528$	−0.342587	+	0.0740707i	−0.0149092	+	0.00322351i
$529$	−1.26700	+	2.19451i	−0.0550869	+	0.0954133i
$530$	−20.3286	+	6.62478i	−0.883016	+	0.287762i
$531$	6.49605	−	6.49605i	0.281905	−	0.281905i
$532$		0			0
$533$	−11.7173	−	11.7173i	−0.507534	−	0.507534i
$534$	0.481305	−	0.946658i	0.0208281	−	0.0409659i
$535$	−12.9205	−	7.45964i	−0.558601	−	0.322508i
$536$	2.20445	−	5.78806i	0.0952177	−	0.250006i
$537$	0.924954	−	0.534022i	0.0399147	−	0.0230448i
$538$	7.56850	−	4.92444i	0.326301	−	0.212308i
$539$		0			0
$540$	0.356192	−	0.803796i	0.0153281	−	0.0345899i
$541$	7.11973	+	1.90773i	0.306101	+	0.0820195i	0.408600	−	0.912714i	$-0.366017\pi$
$541$	7.11973	+	1.90773i	0.306101	+	0.0820195i	−0.102499	+	0.994733i	$0.532684\pi$
$542$	7.53849	−	8.38706i	0.323806	−	0.360255i
$543$	−0.256435	+	0.444159i	−0.0110047	+	0.0190607i
$544$	−8.24755	+	14.4303i	−0.353611	+	0.618695i
$545$	−4.08289			−0.174892
$546$		0			0
$547$	17.8464	−	17.8464i	0.763058	−	0.763058i	−0.213816	−	0.976874i	$-0.568589\pi$
$547$	17.8464	−	17.8464i	0.763058	−	0.763058i	0.976874	+	0.213816i	$0.0685893\pi$
$548$	6.16987	−	0.659376i	0.263564	−	0.0281671i
$549$	29.1329	−	7.80613i	1.24336	−	0.333158i
$550$	0.387035	+	7.26370i	0.0165032	+	0.309725i
$551$	20.0082	−	11.5517i	0.852378	−	0.492121i
$552$	0.114544	+	0.711142i	0.00487533	+	0.0302682i
$553$		0			0
$554$	−9.88177	−	15.1875i	−0.419836	−	0.645257i
$555$	0.103077	−	0.384689i	0.00437538	−	0.0163291i
$556$	35.6146	+	5.57705i	1.51039	+	0.236520i
$557$	3.86313	+	14.4174i	0.163686	+	0.610884i	0.998204	+	0.0599038i	$0.0190794\pi$
$557$	3.86313	+	14.4174i	0.163686	+	0.610884i	−0.834518	+	0.550980i	$0.814254\pi$
$558$	25.3078	−	8.24745i	1.07137	−	0.349142i
$559$	6.36514			0.269217
$560$		0			0
$561$	0.257462			0.0108700
$562$	−17.5388	+	5.71565i	−0.739831	+	0.241100i
$563$	2.06799	+	7.71786i	0.0871556	+	0.325269i	0.995714	−	0.0924895i	$-0.0294825\pi$
$563$	2.06799	+	7.71786i	0.0871556	+	0.325269i	−0.908558	+	0.417759i	$0.862816\pi$
$564$	0.0341198	−	0.217886i	0.00143670	−	0.00917467i
$565$	1.57717	−	5.88607i	0.0663519	−	0.247629i
$566$	−14.8653	−	22.8469i	−0.624837	−	0.960327i
$567$		0			0
$568$	−12.0325	+	16.6529i	−0.504873	+	0.698740i
$569$	12.1275	−	7.00179i	0.508409	−	0.293530i	−0.223770	−	0.974642i	$-0.571837\pi$
$569$	12.1275	−	7.00179i	0.508409	−	0.293530i	0.732180	+	0.681112i	$0.238503\pi$
$570$	−0.0436938	−	0.820026i	−0.00183013	−	0.0343471i
$571$	1.82494	−	0.488992i	0.0763715	−	0.0204637i	−0.220431	−	0.975403i	$-0.570746\pi$
$571$	1.82494	−	0.488992i	0.0763715	−	0.0204637i	0.296802	+	0.954939i	$0.404080\pi$
$572$	−0.746764	−	6.98757i	−0.0312238	−	0.292165i
$573$	−1.03149	+	1.03149i	−0.0430913	+	0.0430913i
$574$		0			0
$575$	14.9486			0.623400
$576$	17.9004	+	15.9486i	0.745852	+	0.664525i
$577$	8.81809	−	15.2734i	0.367102	−	0.635839i	−0.622009	−	0.783010i	$-0.713683\pi$
$577$	8.81809	−	15.2734i	0.367102	−	0.635839i	0.989111	+	0.147171i	$0.0470167\pi$
$578$	−7.90995	+	8.80034i	−0.329011	+	0.366046i
$579$	0.682288	+	0.182818i	0.0283549	+	0.00759767i
$580$	6.94453	+	3.07738i	0.288356	+	0.127781i
$581$		0			0
$582$	0.646993	−	0.420966i	0.0268187	−	0.0174496i
$583$	−15.6511	+	9.03615i	−0.648201	+	0.374239i
$584$	16.3541	+	36.4745i	0.676739	+	1.50933i
$585$	7.62870	+	4.40443i	0.315408	+	0.182101i
$586$	11.5135	−	22.6454i	0.475620	−	0.935475i
$587$	−18.5150	−	18.5150i	−0.764194	−	0.764194i	0.212883	−	0.977078i	$-0.431715\pi$
$587$	−18.5150	−	18.5150i	−0.764194	−	0.764194i	−0.977078	+	0.212883i	$0.931715\pi$
$588$		0			0
$589$	35.1788	−	35.1788i	1.44952	−	1.44952i
$590$	5.36747	−	1.74918i	0.220975	−	0.0720127i
$591$	−0.331042	+	0.573382i	−0.0136172	+	0.0235858i
$592$	18.2672	+	11.7724i	0.750777	+	0.483841i
$593$	3.95463	+	6.84963i	0.162397	+	0.281281i	0.935728	−	0.352722i	$-0.114744\pi$
$593$	3.95463	+	6.84963i	0.162397	+	0.281281i	−0.773331	+	0.634003i	$0.781411\pi$
$594$	0.153872	−	0.727031i	0.00631344	−	0.0298305i
$595$		0			0
$596$	−10.8308	−	28.0686i	−0.443648	−	1.14974i
$597$	0.280591	−	1.04718i	0.0114838	−	0.0428582i
$598$	−14.4213	+	0.768415i	−0.589730	+	0.0314228i
$599$	−18.5333	−	10.7002i	−0.757251	−	0.437199i	0.0710572	−	0.997472i	$-0.477363\pi$
$599$	−18.5333	−	10.7002i	−0.757251	−	0.437199i	−0.828308	+	0.560273i	$0.810696\pi$
$600$	−0.408004	+	0.332169i	−0.0166567	+	0.0135607i
$601$		−	0.974684i		−	0.0397582i	−0.999802	−	0.0198791i	$-0.993672\pi$
$601$		−	0.974684i		−	0.0397582i	0.999802	−	0.0198791i	$-0.00632813\pi$
$602$		0			0
$603$	4.64033	+	4.64033i	0.188969	+	0.188969i
$604$	36.1775	−	3.86630i	1.47204	−	0.157318i
$605$	2.89070	+	10.7882i	0.117524	+	0.438604i
$606$	−0.562424	+	0.625733i	−0.0228469	+	0.0254186i
$607$	3.01261	+	5.21800i	0.122278	+	0.211792i	0.920666	−	0.390352i	$-0.127647\pi$
$607$	3.01261	+	5.21800i	0.122278	+	0.211792i	−0.798388	+	0.602144i	$0.794313\pi$
$608$	43.3335	+	11.4086i	1.75741	+	0.462681i
$609$		0			0
$610$	18.1321	+	3.83754i	0.734146	+	0.155378i
$611$	4.27106	+	1.14443i	0.172788	+	0.0462985i
$612$	−10.3761	−	14.2291i	−0.419429	−	0.575179i
$613$	1.58990	−	0.426012i	0.0642155	−	0.0172065i	−0.226568	−	0.973995i	$-0.572751\pi$
$613$	1.58990	−	0.426012i	0.0642155	−	0.0172065i	0.290784	+	0.956789i	$0.406084\pi$
$614$	−27.6655	−	14.0659i	−1.11649	−	0.567652i
$615$		−	0.538124i		−	0.0216993i
$616$		0			0
$617$		−	34.0864i		−	1.37227i	−0.727476	−	0.686134i	$-0.759307\pi$
$617$		−	34.0864i		−	1.37227i	0.727476	−	0.686134i	$-0.240693\pi$
$618$	−0.123546	+	0.242997i	−0.00496975	+	0.00977478i
$619$	−32.3004	+	8.65485i	−1.29826	+	0.347868i	−0.840792	−	0.541358i	$-0.817910\pi$
$619$	−32.3004	+	8.65485i	−1.29826	+	0.347868i	−0.457469	+	0.889226i	$0.651244\pi$
$620$	16.1597	+	2.53053i	0.648990	+	0.101628i
$621$	−1.47516	−	0.395268i	−0.0591961	−	0.0158615i
$622$	−1.06366	+	5.02568i	−0.0426487	+	0.201512i
$623$		0			0
$624$	0.376537	−	0.341424i	0.0150735	−	0.0136679i
$625$	1.22016	+	2.11337i	0.0488063	+	0.0845349i
$626$	3.94081	+	3.54210i	0.157506	+	0.141571i
$627$	−0.179651	−	0.670466i	−0.00717456	−	0.0267758i
$628$	−15.1338	−	12.2114i	−0.603905	−	0.487289i
$629$	−11.2877	−	11.2877i	−0.450070	−	0.450070i
$630$		0			0
$631$			4.58799i			0.182645i	0.995821	+	0.0913225i	$0.0291094\pi$
$631$			4.58799i			0.182645i	−0.995821	+	0.0913225i	$0.970891\pi$
$632$	−0.554399	+	5.41107i	−0.0220528	+	0.215241i
$633$	0.594458	+	0.343211i	0.0236276	+	0.0136414i
$634$	−1.85132	−	34.7447i	−0.0735252	−	1.37989i
$635$	1.89851	−	7.08533i	0.0753400	−	0.281173i
$636$	−1.19507	−	0.529580i	−0.0473875	−	0.0209992i
$637$		0			0
$638$	6.28131	+	1.32940i	0.248680	+	0.0526315i
$639$	−10.8842	−	18.8519i	−0.430571	−	0.745770i
$640$	5.36361	+	13.7214i	0.212015	+	0.542386i
$641$	24.9135	−	43.1515i	0.984025	−	1.70438i	0.337835	−	0.941205i	$-0.390305\pi$
$641$	24.9135	−	43.1515i	0.984025	−	1.70438i	0.646190	−	0.763177i	$-0.276361\pi$
$642$	−0.282617	−	0.867227i	−0.0111540	−	0.0342267i
$643$	31.1050	−	31.1050i	1.22666	−	1.22666i	0.261443	−	0.965219i	$-0.415802\pi$
$643$	31.1050	−	31.1050i	1.22666	−	1.22666i	0.965219	−	0.261443i	$-0.0841985\pi$
$644$		0			0
$645$	0.146161	+	0.146161i	0.00575509	+	0.00575509i
$646$	−29.3408	−	14.9176i	−1.15440	−	0.586925i
$647$	−25.4255	−	14.6794i	−0.999579	−	0.577107i	−0.0914555	−	0.995809i	$-0.529152\pi$
$647$	−25.4255	−	14.6794i	−0.999579	−	0.577107i	−0.908124	+	0.418702i	$0.862485\pi$
$648$	−23.1543	+	10.3817i	−0.909586	+	0.407832i
$649$	4.13245	−	2.38587i	0.162213	−	0.0936536i
$650$	−5.75280	−	8.84162i	−0.225643	−	0.346797i
$651$		0			0
$652$	−24.2628	+	9.36227i	−0.950205	+	0.366655i
$653$	14.6954	+	3.93761i	0.575075	+	0.154091i	0.534623	−	0.845091i	$-0.320454\pi$
$653$	14.6954	+	3.93761i	0.575075	+	0.154091i	0.0404516	+	0.999181i	$0.487120\pi$
$654$	−0.185646	−	0.166863i	−0.00725932	−	0.00652485i
$655$	1.35165	−	2.34112i	0.0528132	−	0.0914752i
$656$	27.9584	+	8.97638i	1.09159	+	0.350469i
$657$	−42.3531			−1.65235
$658$		0			0
$659$	−8.45620	+	8.45620i	−0.329407	+	0.329407i	−0.852361	−	0.522954i	$-0.824830\pi$
$659$	−8.45620	+	8.45620i	−0.329407	+	0.329407i	0.522954	+	0.852361i	$0.324830\pi$
$660$	0.143306	−	0.177602i	0.00557819	−	0.00691314i
$661$	−13.0890	+	3.50720i	−0.509105	+	0.136414i	−0.504222	−	0.863574i	$-0.668221\pi$
$661$	−13.0890	+	3.50720i	−0.509105	+	0.136414i	−0.00488232	+	0.999988i	$0.501554\pi$
$662$	−14.3203	+	0.763032i	−0.556572	+	0.0296561i
$663$	−0.323338	+	0.186679i	−0.0125574	+	0.00725001i
$664$	34.8599	−	5.61492i	1.35283	−	0.217901i
$665$		0			0
$666$	−19.3002	+	12.5577i	−0.747867	+	0.486599i
$667$	3.41498	−	12.7449i	0.132229	−	0.493484i
$668$	19.4927	+	26.7310i	0.754194	+	1.03426i
$669$	−0.326949	−	1.22019i	−0.0126406	−	0.0471753i
$670$	1.24949	+	3.83415i	0.0482722	+	0.148126i
$671$	15.6658			0.604771
$672$		0			0
$673$	−15.5552			−0.599610			−0.299805	−	0.954000i	$-0.596922\pi$
$673$	−15.5552			−0.599610			−0.299805	+	0.954000i	$0.596922\pi$
$674$	−2.32567	−	7.13647i	−0.0895815	−	0.274887i
$675$	−0.288708	−	1.07747i	−0.0111124	−	0.0414720i
$676$	−9.31477	−	12.7737i	−0.358261	−	0.491297i
$677$	−10.6072	+	39.5868i	−0.407669	+	1.52144i	0.391410	+	0.920217i	$0.371988\pi$
$677$	−10.6072	+	39.5868i	−0.407669	+	1.52144i	−0.799079	+	0.601226i	$0.794679\pi$
$678$	0.312269	−	0.203178i	0.0119926	−	0.00780299i
$679$		0			0
$680$	−1.72088	−	10.6840i	−0.0659929	−	0.409713i
$681$	−0.114030	+	0.0658350i	−0.00436962	+	0.00252280i
$682$	13.8060	−	0.735632i	0.528660	−	0.0281688i
$683$	−11.9346	+	3.19786i	−0.456664	+	0.122363i	−0.479816	−	0.877369i	$-0.659296\pi$
$683$	−11.9346	+	3.19786i	−0.456664	+	0.122363i	0.0231521	+	0.999732i	$0.492630\pi$
$684$	−29.8145	+	36.9496i	−1.13998	+	1.41280i
$685$	−2.85672	+	2.85672i	−0.109150	+	0.109150i
$686$		0			0
$687$	1.10632			0.0422089
$688$	−10.0319	+	5.15574i	−0.382464	+	0.196561i
$689$	13.1038	−	22.6964i	0.499214	−	0.864664i
$690$	−0.348797	−	0.313507i	−0.0132785	−	0.0119350i
$691$	−5.37500	−	1.44023i	−0.204475	−	0.0547888i	0.155128	−	0.987894i	$-0.450421\pi$
$691$	−5.37500	−	1.44023i	−0.204475	−	0.0547888i	−0.359603	+	0.933106i	$0.617088\pi$
$692$	40.3158	−	15.5566i	1.53258	−	0.591375i
$693$		0			0
$694$	−3.18121	−	4.88928i	−0.120757	−	0.185594i
$695$	−20.3263	+	11.7354i	−0.771021	+	0.445149i
$696$	0.189993	+	0.423740i	0.00720166	+	0.0160618i
$697$	−18.6796	−	10.7847i	−0.707540	−	0.408498i
$698$	−20.4376	−	10.3910i	−0.773574	−	0.393305i
$699$	−0.154214	−	0.154214i	−0.00583290	−	0.00583290i
$700$		0			0
$701$	22.0458	−	22.0458i	0.832657	−	0.832657i	−0.155223	−	0.987880i	$-0.549609\pi$
$701$	22.0458	−	22.0458i	0.832657	−	0.832657i	0.987880	+	0.155223i	$0.0496095\pi$
$702$	0.333910	+	1.02462i	0.0126026	+	0.0386719i
$703$	−21.5184	+	37.2710i	−0.811583	+	1.40570i
$704$	6.83687	+	10.4081i	0.257674	+	0.392269i
$705$	0.0717960	+	0.124354i	0.00270399	+	0.00468346i
$706$	−5.35084	−	1.13247i	−0.201381	−	0.0426212i
$707$		0			0
$708$	0.315541	+	0.139828i	0.0118588	+	0.00525506i
$709$	3.20632	−	11.9661i	0.120416	−	0.449398i	−0.879219	−	0.476417i	$-0.841935\pi$
$709$	3.20632	−	11.9661i	0.120416	−	0.449398i	0.999635	+	0.0270200i	$0.00860177\pi$
$710$	−0.711745	−	13.3577i	−0.0267113	−	0.501306i
$711$	−4.99113	−	2.88163i	−0.187182	−	0.108070i
$712$	−37.5340	−	3.84559i	−1.40665	−	0.144120i
$713$		−	28.4126i		−	1.06406i
$714$		0			0
$715$	3.23532	+	3.23532i	0.120994	+	0.120994i
$716$	−29.5310	−	23.8285i	−1.10363	−	0.890511i
$717$	0.0956906	+	0.357122i	0.00357363	+	0.0133370i
$718$	16.6359	+	14.9528i	0.620848	+	0.558033i
$719$	7.64439	+	13.2405i	0.285088	+	0.493786i	0.972630	−	0.232358i	$-0.0746440\pi$
$719$	7.64439	+	13.2405i	0.285088	+	0.493786i	−0.687543	+	0.726144i	$0.741311\pi$
$720$	−15.5910	−	0.762491i	−0.581042	−	0.0284164i
$721$		0			0
$722$	−12.8106	+	60.5288i	−0.476760	+	2.25265i
$723$	0.720631	+	0.193093i	0.0268006	+	0.00718119i
$724$	18.0020	+	2.81901i	0.669038	+	0.104768i
$725$	9.30902	−	2.49434i	0.345728	−	0.0926376i
$726$	−0.309464	+	0.608671i	−0.0114853	+	0.0225899i
$727$		−	23.7860i		−	0.882173i	−0.897465	−	0.441086i	$-0.854593\pi$
$727$		−	23.7860i		−	0.882173i	0.897465	−	0.441086i	$-0.145407\pi$
$728$		0			0
$729$		−	26.8290i		−	0.993668i
$730$	−23.1997	−	11.7953i	−0.858658	−	0.436564i
$731$	8.00285	−	2.14436i	0.295996	−	0.0793119i
$732$	0.667613	+	0.915524i	0.0246757	+	0.0338387i
$733$	19.8871	+	5.32874i	0.734548	+	0.196822i	0.606654	−	0.794966i	$-0.292511\pi$
$733$	19.8871	+	5.32874i	0.734548	+	0.196822i	0.127894	+	0.991788i	$0.459178\pi$
$734$	−6.56764	−	1.39000i	−0.242416	−	0.0513059i
$735$		0			0
$736$	22.1066	−	12.8923i	0.814860	−	0.475215i
$737$	1.70430	+	2.95194i	0.0627787	+	0.108736i
$738$	−20.7980	+	23.1392i	−0.765586	+	0.851764i
$739$	−7.05306	−	26.3224i	−0.259451	−	0.968284i	−0.965560	−	0.260181i	$-0.916218\pi$
$739$	−7.05306	−	26.3224i	−0.259451	−	0.968284i	0.706109	−	0.708103i	$-0.250449\pi$
$740$	−14.0693	+	1.50359i	−0.517199	+	0.0552732i
$741$	0.711756	+	0.711756i	0.0261470	+	0.0261470i
$742$		0			0
$743$			12.8386i			0.471002i	0.971874	+	0.235501i	$0.0756731\pi$
$743$			12.8386i			0.471002i	−0.971874	+	0.235501i	$0.924327\pi$
$744$	0.631349	+	0.775488i	0.0231464	+	0.0284308i
$745$	16.9641	+	9.79426i	0.621518	+	0.358834i
$746$	−32.1768	+	1.71449i	−1.17808	+	0.0627719i
$747$	−9.68282	+	36.1368i	−0.354276	+	1.32218i
$748$	−3.29295	−	8.53386i	−0.120402	−	0.312029i
$749$		0			0
$750$	0.178253	−	0.842232i	0.00650889	−	0.0307539i
$751$	7.23318	+	12.5282i	0.263942	+	0.457162i	0.967286	−	0.253688i	$-0.0816438\pi$
$751$	7.23318	+	12.5282i	0.263942	+	0.457162i	−0.703344	+	0.710850i	$0.748310\pi$
$752$	−7.65848	+	1.65584i	−0.279276	+	0.0603823i
$753$	0.151625	−	0.262622i	0.00552552	−	0.00957048i
$754$	−8.85241	+	2.88487i	−0.322386	+	0.105061i
$755$	−16.7506	+	16.7506i	−0.609616	+	0.609616i
$756$		0			0
$757$	−2.16062	−	2.16062i	−0.0785291	−	0.0785291i	0.666751	−	0.745280i	$-0.267684\pi$
$757$	−2.16062	−	2.16062i	−0.0785291	−	0.0785291i	−0.745280	+	0.666751i	$0.767684\pi$
$758$	−18.2218	+	35.8397i	−0.661846	+	1.30176i
$759$	−0.343304	−	0.198207i	−0.0124611	−	0.00719444i
$760$	−26.6218	+	11.9365i	−0.965676	+	0.432981i
$761$	2.04136	−	1.17858i	0.0739994	−	0.0427236i	−0.462544	−	0.886596i	$-0.653063\pi$
$761$	2.04136	−	1.17858i	0.0739994	−	0.0427236i	0.536543	+	0.843873i	$0.319730\pi$
$762$	0.375892	−	0.244574i	0.0136171	−	0.00885998i
$763$		0			0
$764$	47.3829	+	20.9972i	1.71425	+	0.759651i
$765$	11.0753	+	2.96763i	0.400430	+	0.107295i
$766$	22.1695	−	24.6650i	0.801016	−	0.891182i
$767$	−3.45987	+	5.99267i	−0.124929	+	0.216383i
$768$	−0.316898	+	0.843104i	−0.0114351	+	0.0304229i
$769$	−7.96868			−0.287358			−0.143679	−	0.989624i	$-0.545893\pi$
$769$	−7.96868			−0.287358			−0.143679	+	0.989624i	$0.545893\pi$
$770$		0			0
$771$	−0.940923	+	0.940923i	−0.0338865	+	0.0338865i
$772$	−2.66678	−	24.9535i	−0.0959797	−	0.898095i
$773$	−21.2568	+	5.69575i	−0.764555	+	0.204862i	−0.619965	−	0.784630i	$-0.712853\pi$
$773$	−21.2568	+	5.69575i	−0.764555	+	0.204862i	−0.144590	+	0.989492i	$0.546186\pi$
$774$	−0.635878	−	11.9339i	−0.0228562	−	0.428954i
$775$	17.9725	−	10.3764i	0.645592	−	0.372733i
$776$	−22.2285	−	16.0611i	−0.797956	−	0.576561i
$777$		0			0
$778$	−8.26509	−	12.7028i	−0.296318	−	0.455418i
$779$	−15.0506	+	56.1695i	−0.539243	+	2.01248i
$780$	−0.0511989	+	0.326952i	−0.00183322	+	0.0117068i
$781$	−2.92640	−	10.9215i	−0.104715	−	0.390801i
$782$	−17.8729	+	5.82452i	−0.639134	+	0.208284i
$783$	−0.984588			−0.0351863
$784$		0			0
$785$	12.6611			0.451896
$786$	0.157137	−	0.0512086i	0.00560489	−	0.00182655i
$787$	−7.44405	−	27.7816i	−0.265352	−	0.990306i	−0.962035	−	0.272927i	$-0.912008\pi$
$787$	−7.44405	−	27.7816i	−0.265352	−	0.990306i	0.696683	−	0.717379i	$-0.254658\pi$
$788$	23.2394	+	3.63917i	0.827871	+	0.129640i
$789$	0.259592	−	0.968810i	0.00924171	−	0.0344905i
$790$	−1.93145	−	2.96849i	−0.0687178	−	0.105614i
$791$		0			0
$792$	−13.0263	+	2.09815i	−0.462868	+	0.0745547i
$793$	−19.6741	+	11.3589i	−0.698649	+	0.403365i
$794$	0.498748	+	9.36029i	0.0176999	+	0.332184i
$795$	0.822071	−	0.220273i	0.0291558	−	0.00781229i
$796$	−38.2988	+	4.09300i	−1.35746	+	0.145073i
$797$	22.0411	−	22.0411i	0.780736	−	0.780736i	−0.199219	−	0.979955i	$-0.563840\pi$
$797$	22.0411	−	22.0411i	0.780736	−	0.780736i	0.979955	+	0.199219i	$0.0638405\pi$
$798$		0			0
$799$	5.75552			0.203616
$800$	16.2285	+	9.27531i	0.573765	+	0.327932i
$801$	19.9885	−	34.6210i	0.706258	−	1.22327i
$802$	29.9980	−	33.3748i	1.05927	−	1.17850i
$803$	−21.2491	−	5.69369i	−0.749866	−	0.200926i
$804$	−0.0998836	+	0.225401i	−0.00352262	+	0.00794928i
$805$		0			0
$806$	−16.8051	+	10.9343i	−0.591936	+	0.385143i
$807$	−0.311270	+	0.179712i	−0.0109572	+	0.00632616i
$808$	27.9341	+	10.6390i	0.982717	+	0.374279i
$809$	−25.9855	−	15.0027i	−0.913600	−	0.527467i	−0.0320125	−	0.999487i	$-0.510192\pi$
$809$	−25.9855	−	15.0027i	−0.913600	−	0.527467i	−0.881588	+	0.472020i	$0.843525\pi$
$810$	7.48775	−	14.7273i	0.263093	−	0.517465i
$811$	20.2976	+	20.2976i	0.712746	+	0.712746i	0.967109	−	0.254363i	$-0.0818658\pi$
$811$	20.2976	+	20.2976i	0.712746	+	0.712746i	−0.254363	+	0.967109i	$0.581866\pi$
$812$		0			0
$813$	−0.317411	+	0.317411i	−0.0111321	+	0.0111321i
$814$	−11.3713	+	3.70576i	−0.398565	+	0.129887i
$815$	8.46625	−	14.6640i	0.296560	−	0.513657i
$816$	0.358395	−	0.556123i	0.0125463	−	0.0194682i
$817$	−11.1684	−	19.3443i	−0.390733	−	0.676770i
$818$	0.378535	−	1.78854i	0.0132351	−	0.0625349i
$819$		0			0
$820$	−17.8367	+	6.88265i	−0.622886	+	0.240352i
$821$	14.2176	−	53.0609i	0.496199	−	1.85184i	−0.0270111	−	0.999635i	$-0.508599\pi$
$821$	14.2176	−	53.0609i	0.496199	−	1.85184i	0.523210	−	0.852204i	$-0.324734\pi$
$822$	−0.246643	+	0.0131420i	−0.00860265	+	0.000458379i
$823$	−20.1906	−	11.6571i	−0.703800	−	0.406339i	0.104961	−	0.994476i	$-0.466528\pi$
$823$	−20.1906	−	11.6571i	−0.703800	−	0.406339i	−0.808761	+	0.588137i	$0.799862\pi$
$824$	9.63458	+	0.987124i	0.335637	+	0.0343881i
$825$		−	0.289545i		−	0.0100807i
$826$		0			0
$827$	4.26358	+	4.26358i	0.148259	+	0.148259i	0.777340	−	0.629081i	$-0.216568\pi$
$827$	4.26358	+	4.26358i	0.148259	+	0.148259i	−0.629081	+	0.777340i	$0.716568\pi$
$828$	2.88138	+	26.9614i	0.100135	+	0.936974i
$829$	−10.8606	−	40.5325i	−0.377206	−	1.40775i	−0.850095	−	0.526630i	$-0.823455\pi$
$829$	−10.8606	−	40.5325i	−0.377206	−	1.40775i	0.472889	−	0.881122i	$-0.343211\pi$
$830$	−15.3680	+	17.0979i	−0.533431	+	0.593477i
$831$	0.360624	+	0.624619i	0.0125099	+	0.0216678i
$832$	−16.1328	−	8.11390i	−0.559305	−	0.281299i
$833$		0			0
$834$	−1.40383	−	0.297113i	−0.0486107	−	0.0102882i
$835$	−20.8063	−	5.57502i	−0.720030	−	0.192932i
$836$	−19.9256	+	14.5300i	−0.689142	+	0.502532i
$837$	−2.04794	+	0.548743i	−0.0707871	+	0.0189673i
$838$	−30.8047	−	15.6619i	−1.06413	−	0.541032i
$839$			46.6970i			1.61216i	0.591806	+	0.806081i	$0.298415\pi$
$839$			46.6970i			1.61216i	−0.591806	+	0.806081i	$0.701585\pi$
$840$		0			0
$841$			20.4935i			0.706672i
$842$	−3.04781	+	5.99460i	−0.105034	+	0.206587i
$843$	0.709257	−	0.190045i	0.0244281	−	0.00654549i
$844$	3.77294	−	24.0937i	0.129870	−	0.829339i
$845$	9.94249	+	2.66408i	0.342032	+	0.0916472i
$846$	1.71898	−	8.12205i	0.0590999	−	0.279242i
$847$		0			0
$848$	−2.26851	+	46.3853i	−0.0779010	+	1.59288i
$849$	0.542493	+	0.939626i	0.0186183	+	0.0322479i
$850$	−10.2116	−	9.17845i	−0.350256	−	0.314818i
$851$	6.36139	+	23.7410i	0.218066	+	0.813832i
$852$	0.513550	−	0.636451i	0.0175939	−	0.0218045i
$853$	14.9036	+	14.9036i	0.510289	+	0.510289i	0.914615	−	0.404326i	$-0.132494\pi$
$853$	14.9036	+	14.9036i	0.510289	+	0.510289i	−0.404326	+	0.914615i	$0.632494\pi$
$854$		0			0
$855$		−	30.9125i		−	1.05718i
$856$	−25.1305	+	20.4595i	−0.858944	+	0.699293i
$857$	12.5881	+	7.26772i	0.430000	+	0.248261i	0.699347	−	0.714783i	$-0.253474\pi$
$857$	12.5881	+	7.26772i	0.430000	+	0.248261i	−0.269347	+	0.963043i	$0.586808\pi$
$858$	0.0148837	+	0.279331i	0.000508121	+	0.00953619i
$859$	10.1784	−	37.9861i	0.347281	−	1.29607i	−0.542644	−	0.839963i	$-0.682577\pi$
$859$	10.1784	−	37.9861i	0.347281	−	1.29607i	0.889925	−	0.456107i	$-0.150757\pi$
$860$	2.97527	−	6.71409i	0.101456	−	0.228949i
$861$		0			0
$862$	−15.4606	−	3.27214i	−0.526589	−	0.111449i
$863$	6.49230	+	11.2450i	0.221000	+	0.382784i	0.955112	−	0.296245i	$-0.0957345\pi$
$863$	6.49230	+	11.2450i	0.221000	+	0.382784i	−0.734112	+	0.679029i	$0.762401\pi$
$864$	−1.35621	−	1.34442i	−0.0461392	−	0.0457380i
$865$	−14.0678	+	24.3661i	−0.478319	+	0.828473i
$866$	7.62201	+	23.3886i	0.259006	+	0.794778i
$867$	0.333052	−	0.333052i	0.0113110	−	0.0113110i
$868$		0			0
$869$	−2.11673	−	2.11673i	−0.0718052	−	0.0718052i
$870$	−0.269520	−	0.137031i	−0.00913760	−	0.00464579i
$871$	−4.28075	−	2.47149i	−0.145048	−	0.0837434i
$872$	−3.15643	+	8.28762i	−0.106890	+	0.280654i
$873$	25.1638	−	14.5283i	0.851665	−	0.491709i
$874$	27.6392	+	42.4793i	0.934909	+	1.43689i
$875$		0			0
$876$	−0.572809	−	1.48446i	−0.0193534	−	0.0501554i
$877$	−21.6697	−	5.80637i	−0.731733	−	0.196067i	−0.126332	−	0.991988i	$-0.540321\pi$
$877$	−21.6697	−	5.80637i	−0.731733	−	0.196067i	−0.605401	+	0.795921i	$0.706987\pi$
$878$	−39.4853	−	35.4904i	−1.33256	−	1.19774i
$879$	−0.505614	+	0.875749i	−0.0170539	+	0.0295383i
$880$	−7.71971	−	2.47851i	−0.260231	−	0.0835505i
$881$	8.65332			0.291538			0.145769	−	0.989319i	$-0.453434\pi$
$881$	8.65332			0.291538			0.145769	+	0.989319i	$0.453434\pi$
$882$		0			0
$883$	30.6837	−	30.6837i	1.03259	−	1.03259i	0.0331374	−	0.999451i	$-0.489450\pi$
$883$	30.6837	−	30.6837i	1.03259	−	1.03259i	0.999451	−	0.0331374i	$-0.0105499\pi$
$884$	10.3232	+	8.32976i	0.347207	+	0.280160i
$885$	−0.217056	+	0.0581601i	−0.00729627	+	0.00195503i
$886$	−10.0615	+	0.536110i	−0.338022	+	0.0180110i
$887$	24.7803	−	14.3069i	0.832042	−	0.480380i	−0.0225091	−	0.999747i	$-0.507165\pi$
$887$	24.7803	−	14.3069i	0.832042	−	0.480380i	0.854551	+	0.519367i	$0.173832\pi$
$888$	−0.701170	−	0.506628i	−0.0235297	−	0.0170013i
$889$		0			0
$890$	20.5910	−	13.3975i	0.690211	−	0.449086i
$891$	3.61439	−	13.4891i	0.121087	−	0.451902i
$892$	−36.2629	+	26.4434i	−1.21417	+	0.885391i
$893$	−4.01607	−	14.9882i	−0.134393	−	0.501560i
$894$	0.371066	+	1.13864i	0.0124103	+	0.0380818i
$895$	24.7060			0.825830
$896$		0			0
$897$	0.574859			0.0191940
$898$	−3.43543	−	10.5418i	−0.114642	−	0.351786i
$899$	−4.74096	−	17.6935i	−0.158120	−	0.590112i
$900$	−16.0023	+	11.6691i	−0.533409	+	0.388970i
$901$	8.82909	−	32.9506i	0.294140	−	1.09774i
$902$	−13.5453	+	8.81328i	−0.451011	+	0.293450i
$903$		0			0
$904$	−10.7285	−	7.75184i	−0.356824	−	0.257822i
$905$	−10.2743	+	5.93185i	−0.341528	+	0.197182i
$906$	−1.44621	+	0.0770590i	−0.0480471	+	0.00256011i
$907$	−17.9969	+	4.82227i	−0.597579	+	0.160121i	−0.544915	−	0.838492i	$-0.683438\pi$
$907$	−17.9969	+	4.82227i	−0.597579	+	0.160121i	−0.0526640	+	0.998612i	$0.516771\pi$
$908$	3.64062	+	2.93760i	0.120818	+	0.0974878i
$909$	−22.3949	+	22.3949i	−0.742793	+	0.742793i
$910$		0			0
$911$	−12.2041			−0.404341			−0.202170	−	0.979350i	$-0.564799\pi$
$911$	−12.2041			−0.404341			−0.202170	+	0.979350i	$0.564799\pi$
$912$	−1.69830	−	0.545260i	−0.0562363	−	0.0180554i
$913$	−9.71601	+	16.8286i	−0.321553	+	0.556946i
$914$	27.0617	+	24.3237i	0.895123	+	0.804558i
$915$	−0.712603	−	0.190942i	−0.0235579	−	0.00631233i
$916$	−14.1500	−	36.6704i	−0.467528	−	1.21162i
$917$		0			0
$918$	0.765009	+	1.17576i	0.0252491	+	0.0388059i
$919$	3.57056	−	2.06146i	0.117782	−	0.0680014i	−0.439952	−	0.898021i	$-0.645004\pi$
$919$	3.57056	−	2.06146i	0.117782	−	0.0680014i	0.557734	+	0.830020i	$0.311671\pi$
$920$	−5.93042	+	15.5711i	−0.195520	+	0.513363i
$921$	1.06989	+	0.617699i	0.0352539	+	0.0203539i
$922$	23.4726	+	11.9341i	0.773030	+	0.393028i
$923$	11.5941	+	11.5941i	0.381623	+	0.381623i
$924$		0			0
$925$	−12.6943	+	12.6943i	−0.417386	+	0.417386i
$926$	3.01835	+	9.26199i	0.0991890	+	0.304368i
$927$	−5.13083	+	8.88686i	−0.168519	+	0.291883i
$928$	11.6153	−	11.7172i	0.381292	−	0.384636i
$929$	22.7002	+	39.3180i	0.744771	+	1.28998i	0.950302	+	0.311330i	$0.100775\pi$
$929$	22.7002	+	39.3180i	0.744771	+	1.28998i	−0.205531	+	0.978651i	$0.565892\pi$
$930$	−0.636973	−	0.134812i	−0.0208872	−	0.00442064i
$931$		0			0
$932$	−3.13919	+	7.08400i	−0.102827	+	0.232044i
$933$	0.0529235	−	0.197513i	0.00173264	−	0.00646629i
$934$	2.97709	+	55.8727i	0.0974133	+	1.82821i
$935$	5.15770	+	2.97780i	0.168675	+	0.0973845i
$936$	14.8379	−	12.0800i	0.484994	−	0.394848i
$937$		−	8.69727i		−	0.284127i	−0.989858	−	0.142064i	$-0.954626\pi$
$937$		−	8.69727i		−	0.284127i	0.989858	−	0.142064i	$-0.0453738\pi$
$938$		0			0
$939$	−0.149141	−	0.149141i	−0.00486704	−	0.00486704i
$940$	3.20359	−	3.97026i	0.104490	−	0.129496i
$941$	−3.11071	−	11.6093i	−0.101406	−	0.378454i	0.896506	−	0.443031i	$-0.146097\pi$
$941$	−3.11071	−	11.6093i	−0.101406	−	0.378454i	−0.997913	+	0.0645772i	$0.979430\pi$
$942$	0.575691	+	0.517445i	0.0187570	+	0.0168593i
$943$	16.6051	+	28.7609i	0.540737	+	0.936584i
$944$	0.598969	−	12.2474i	0.0194948	−	0.398618i
$945$		0			0
$946$	1.28529	−	6.07288i	0.0417883	−	0.197446i
$947$	55.5623	+	14.8879i	1.80553	+	0.483791i	0.994820	−	0.101652i	$-0.0324129\pi$
$947$	55.5623	+	14.8879i	1.80553	+	0.483791i	0.810713	+	0.585443i	$0.199080\pi$
$948$	0.0334972	−	0.213911i	0.00108794	−	0.00694749i
$949$	30.8145	−	8.25671i	1.00028	−	0.268024i
$950$	−16.7765	+	32.9970i	−0.544303	+	1.07056i
$951$			1.38499i			0.0449113i
$952$		0			0
$953$		−	8.69133i		−	0.281540i	−0.990042	−	0.140770i	$-0.955042\pi$
$953$		−	8.69133i		−	0.281540i	0.990042	−	0.140770i	$-0.0449578\pi$
$954$	−43.8621	−	22.3007i	−1.42009	−	0.722010i
$955$	−32.5941	+	8.73356i	−1.05472	+	0.282611i
$956$	10.6133	−	7.73939i	0.343260	−	0.250310i
$957$	−0.246860	−	0.0661460i	−0.00797986	−	0.00213820i
$958$	−0.724965	−	0.153434i	−0.0234225	−	0.00495724i
$959$		0			0
$960$	−0.184137	−	0.556772i	−0.00594299	−	0.0179697i
$961$	−4.22236	−	7.31334i	−0.136205	−	0.235914i
$962$	11.5940	−	12.8990i	0.373804	−	0.415881i
$963$	−8.88662	−	33.1653i	−0.286367	−	1.06874i
$964$	−2.81665	−	26.3558i	−0.0907183	−	0.848863i
$965$	11.5537	+	11.5537i	0.371927	+	0.371927i
$966$		0			0
$967$			28.1636i			0.905681i	0.891592	+	0.452840i	$0.149589\pi$
$967$			28.1636i			0.905681i	−0.891592	+	0.452840i	$0.850411\pi$
$968$	24.1331	+	2.47259i	0.775669	+	0.0794722i
$969$	1.13467	+	0.655102i	0.0364509	+	0.0210449i
$970$	17.8300	−	0.950046i	0.572488	−	0.0305041i
$971$	2.71368	−	10.1276i	0.0870862	−	0.325010i	−0.908615	−	0.417635i	$-0.862859\pi$
$971$	2.71368	−	10.1276i	0.0870862	−	0.325010i	0.995701	+	0.0926248i	$0.0295257\pi$
$972$	2.83203	−	1.09279i	0.0908375	−	0.0350514i
$973$		0			0
$974$	0.833765	−	3.93947i	0.0267155	−	0.126229i
$975$	0.209942	+	0.363630i	0.00672352	+	0.0116455i
$976$	21.8073	−	33.8384i	0.698034	−	1.08314i
$977$	−17.3812	+	30.1051i	−0.556073	+	0.963147i	0.441746	+	0.897140i	$0.354359\pi$
$977$	−17.3812	+	30.1051i	−0.556073	+	0.963147i	−0.997819	+	0.0660068i	$0.978974\pi$
$978$	0.984251	−	0.320753i	0.0314729	−	0.0102566i
$979$	14.6827	−	14.6827i	0.469262	−	0.469262i
$980$		0			0
$981$	−6.64424	−	6.64424i	−0.212134	−	0.212134i
$982$	15.8466	−	31.1680i	0.505686	−	0.994611i
$983$	2.48718	+	1.43597i	0.0793286	+	0.0458004i	0.539140	−	0.842216i	$-0.318750\pi$
$983$	2.48718	+	1.43597i	0.0793286	+	0.0458004i	−0.459811	+	0.888017i	$0.652083\pi$
$984$	−1.09231	−	0.416017i	−0.0348214	−	0.0132621i
$985$	−13.2635	+	7.65766i	−0.422609	+	0.243993i
$986$	−10.1582	+	6.60943i	−0.323503	+	0.210487i
$987$		0			0
$988$	14.4885	−	32.6954i	0.460942	−	1.04018i
$989$	−12.3220	−	3.30166i	−0.391816	−	0.104987i
$990$	5.74263	−	6.38905i	0.182513	−	0.203057i
$991$	15.8744	−	27.4952i	0.504266	−	0.873414i	−0.495722	−	0.868481i	$-0.665097\pi$
$991$	15.8744	−	27.4952i	0.504266	−	0.873414i	0.999988	−	0.00493273i	$-0.00157014\pi$
$992$	17.6294	−	30.8453i	0.559735	−	0.979340i
$993$	0.570832			0.0181148
$994$		0			0
$995$	17.7327	−	17.7327i	0.562166	−	0.562166i
$996$	−1.39754	+	0.149355i	−0.0442827	+	0.00473251i
$997$	19.7719	−	5.29788i	0.626184	−	0.167785i	0.0682464	−	0.997668i	$-0.478260\pi$
$997$	19.7719	−	5.29788i	0.626184	−	0.167785i	0.557937	+	0.829883i	$0.311593\pi$
$998$	−0.101931	−	1.91299i	−0.00322656	−	0.0605547i
$999$	1.58836	−	0.917039i	0.0502534	−	0.0290138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.165.8		48
7.2	even	3	inner	784.2.x.o.373.10		48
7.3	odd	6		784.2.m.j.197.1		24
7.4	even	3		784.2.m.k.197.1		24
7.5	odd	6		112.2.w.c.37.10	✓	48
7.6	odd	2		112.2.w.c.53.8	yes	48
16.13	even	4	inner	784.2.x.o.557.10		48
28.19	even	6		448.2.ba.c.177.7		48
28.27	even	2		448.2.ba.c.305.6		48
56.5	odd	6		896.2.ba.f.737.7		48
56.13	odd	2		896.2.ba.f.865.6		48
56.19	even	6		896.2.ba.e.737.6		48
56.27	even	2		896.2.ba.e.865.7		48
112.5	odd	12		896.2.ba.f.289.6		48
112.13	odd	4		112.2.w.c.109.10	yes	48
112.19	even	12		448.2.ba.c.401.6		48
112.27	even	4		896.2.ba.e.417.6		48
112.45	odd	12		784.2.m.j.589.1		24
112.61	odd	12		112.2.w.c.93.8	yes	48
112.69	odd	4		896.2.ba.f.417.7		48
112.75	even	12		896.2.ba.e.289.7		48
112.83	even	4		448.2.ba.c.81.7		48
112.93	even	12	inner	784.2.x.o.765.8		48
112.109	even	12		784.2.m.k.589.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.10	✓	48	7.5	odd	6
112.2.w.c.53.8	yes	48	7.6	odd	2
112.2.w.c.93.8	yes	48	112.61	odd	12
112.2.w.c.109.10	yes	48	112.13	odd	4
448.2.ba.c.81.7		48	112.83	even	4
448.2.ba.c.177.7		48	28.19	even	6
448.2.ba.c.305.6		48	28.27	even	2
448.2.ba.c.401.6		48	112.19	even	12
784.2.m.j.197.1		24	7.3	odd	6
784.2.m.j.589.1		24	112.45	odd	12
784.2.m.k.197.1		24	7.4	even	3
784.2.m.k.589.1		24	112.109	even	12
784.2.x.o.165.8		48	1.1	even	1	trivial
784.2.x.o.373.10		48	7.2	even	3	inner
784.2.x.o.557.10		48	16.13	even	4	inner
784.2.x.o.765.8		48	112.93	even	12	inner
896.2.ba.e.289.7		48	112.75	even	12
896.2.ba.e.417.6		48	112.27	even	4
896.2.ba.e.737.6		48	56.19	even	6
896.2.ba.e.865.7		48	56.27	even	2
896.2.ba.f.289.6		48	112.5	odd	12
896.2.ba.f.417.7		48	112.69	odd	4
896.2.ba.f.737.7		48	56.5	odd	6
896.2.ba.f.865.6		48	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.438190 + 1.34461i) q^{2} +(-0.0145698 - 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(0.337028 - 1.25781i) q^{5} +(0.0667293 - 0.0434174i) q^{6} +(-2.29259 - 1.65651i) q^{8} +(2.59533 - 1.49842i) q^{9} +O(q^{10})\)	\(q+(0.438190 + 1.34461i) q^{2} +(-0.0145698 - 0.0543752i) q^{3} +(-1.61598 + 1.17839i) q^{4} +(0.337028 - 1.25781i) q^{5} +(0.0667293 - 0.0434174i) q^{6} +(-2.29259 - 1.65651i) q^{8} +(2.59533 - 1.49842i) q^{9} +(1.83895 - 0.0979855i) q^{10} +(1.50355 - 0.402875i) q^{11} +(0.0876199 + 0.0707001i) q^{12} +(-1.59615 + 1.59615i) q^{13} -0.0733039 q^{15} +(1.22277 - 3.80852i) q^{16} +(-1.46910 + 2.54455i) q^{17} +(3.15204 + 2.83313i) q^{18} +(7.65147 + 2.05021i) q^{19} +(0.937562 + 2.42974i) q^{20} +(1.20055 + 1.84516i) q^{22} +(3.91784 - 2.26197i) q^{23} +(-0.0566703 + 0.148795i) q^{24} +(2.86164 + 1.65217i) q^{25} +(-2.84562 - 1.44679i) q^{26} +(-0.238706 - 0.238706i) q^{27} +(2.06234 - 2.06234i) q^{29} +(-0.0321210 - 0.0985654i) q^{30} +(3.14025 - 5.43908i) q^{31} +(5.65680 - 0.0246987i) q^{32} +(-0.0438128 - 0.0758861i) q^{33} +(-4.06519 - 0.860373i) q^{34} +(-2.42828 + 5.47973i) q^{36} +(-1.40616 + 5.24787i) q^{37} +(0.596064 + 11.1867i) q^{38} +(0.110046 + 0.0635352i) q^{39} +(-2.85623 + 2.32535i) q^{40} +7.34101i q^{41} +(-1.99391 - 1.99391i) q^{43} +(-1.95496 + 2.42282i) q^{44} +(-1.01002 - 3.76943i) q^{45} +(4.75824 + 4.27682i) q^{46} +(-0.979430 - 1.69642i) q^{47} +(-0.224904 - 0.0109992i) q^{48} +(-0.967587 + 4.57177i) q^{50} +(0.159765 + 0.0428089i) q^{51} +(0.698448 - 4.46023i) q^{52} +(-11.2146 + 3.00493i) q^{53} +(0.216369 - 0.425567i) q^{54} -2.02696i q^{55} -0.445921i q^{57} +(3.67676 + 1.86936i) q^{58} +(2.96105 - 0.793411i) q^{59} +(0.118457 - 0.0863809i) q^{60} +(9.72123 + 2.60480i) q^{61} +(8.68949 + 1.83908i) q^{62} +(2.51197 + 7.59540i) q^{64} +(1.46970 + 2.54559i) q^{65} +(0.0828392 - 0.0921640i) q^{66} +(0.566758 + 2.11517i) q^{67} +(-0.624456 - 5.84312i) q^{68} +(-0.180077 - 0.180077i) q^{69} -7.26378i q^{71} +(-8.43218 - 0.863930i) q^{72} +(-12.2392 - 7.06631i) q^{73} +(-7.67253 + 0.408819i) q^{74} +(0.0481435 - 0.179674i) q^{75} +(-14.7806 + 5.70337i) q^{76} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 - 1.66547i) q^{79} +(-4.37827 - 2.82159i) q^{80} +(4.48574 - 7.76954i) q^{81} +(-9.87083 + 3.21676i) q^{82} +(-8.82731 + 8.82731i) q^{83} +(2.70543 + 2.70543i) q^{85} +(1.80733 - 3.55475i) q^{86} +(-0.142188 - 0.0820924i) q^{87} +(-4.11440 - 1.56702i) q^{88} +(11.5526 - 6.66987i) q^{89} +(4.62586 - 3.00981i) q^{90} +(-3.66566 + 8.27206i) q^{92} +(-0.341503 - 0.0915056i) q^{93} +(1.85186 - 2.06031i) q^{94} +(5.15752 - 8.93309i) q^{95} +(-0.0837613 - 0.307230i) q^{96} +9.69578 q^{97} +(3.29854 - 3.29854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8}+O(q^{10}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 28 q^{31} + 16 q^{32} - 16 q^{33} + 44 q^{34} - 72 q^{36} - 24 q^{37} - 20 q^{38} - 26 q^{40} - 40 q^{43} + 6 q^{44} + 28 q^{45} - 14 q^{46} + 20 q^{47} - 56 q^{48} + 56 q^{50} + 24 q^{51} + 16 q^{52} - 16 q^{53} - 64 q^{54} - 6 q^{58} + 20 q^{59} + 46 q^{60} - 8 q^{61} - 24 q^{62} + 80 q^{64} + 8 q^{65} + 20 q^{66} + 48 q^{67} + 40 q^{69} - 32 q^{72} - 8 q^{74} + 4 q^{75} + 36 q^{76} + 116 q^{78} - 36 q^{79} + 28 q^{80} - 2 q^{82} + 8 q^{83} - 20 q^{86} - 42 q^{88} + 20 q^{90} + 76 q^{92} + 8 q^{93} + 72 q^{94} - 4 q^{95} + 120 q^{96} + 48 q^{97} - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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