LMFDB - Embedded newform 961.2.d.r.628.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.5
Character	$\chi$	$=$	961.628
Dual form			961.2.d.r.531.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.384764 + 1.18418i) q^{2} +(-0.827744 - 2.54753i) q^{3} +(0.363788 + 0.264307i) q^{4} +2.61876 q^{5} +3.33523 q^{6} +(-0.974496 - 0.708013i) q^{7} +(-2.46761 + 1.79283i) q^{8} +(-3.37771 + 2.45405i) q^{9} +(-1.00760 + 3.10109i) q^{10} +(-3.55723 - 2.58448i) q^{11} +(0.372209 - 1.14554i) q^{12} +(0.376474 + 1.15867i) q^{13} +(1.21337 - 0.881563i) q^{14} +(-2.16766 - 6.67137i) q^{15} +(-0.895675 - 2.75661i) q^{16} +(2.95999 - 2.15056i) q^{17} +(-1.60642 - 4.94406i) q^{18} +(1.98691 - 6.11507i) q^{19} +(0.952672 + 0.692157i) q^{20} +(-0.997053 + 3.06861i) q^{21} +(4.42919 - 3.21800i) q^{22} +(3.19080 - 2.31825i) q^{23} +(6.60984 + 4.80233i) q^{24} +1.85789 q^{25} -1.51693 q^{26} +(2.54648 + 1.85013i) q^{27} +(-0.167377 - 0.515133i) q^{28} +(0.414206 - 1.27479i) q^{29} +8.73416 q^{30} -2.49133 q^{32} +(-3.63957 + 11.2014i) q^{33} +(1.40776 + 4.33263i) q^{34} +(-2.55197 - 1.85411i) q^{35} -1.87740 q^{36} -6.43574 q^{37} +(6.47687 + 4.70572i) q^{38} +(2.64012 - 1.91816i) q^{39} +(-6.46208 + 4.69498i) q^{40} +(0.645251 - 1.98588i) q^{41} +(-3.25017 - 2.36139i) q^{42} +(2.90880 - 8.95237i) q^{43} +(-0.610981 - 1.88040i) q^{44} +(-8.84541 + 6.42657i) q^{45} +(1.51753 + 4.67048i) q^{46} +(0.233002 + 0.717105i) q^{47} +(-6.28115 + 4.56353i) q^{48} +(-1.71476 - 5.27749i) q^{49} +(-0.714848 + 2.20008i) q^{50} +(-7.92873 - 5.76056i) q^{51} +(-0.169288 + 0.521015i) q^{52} +(-3.81371 + 2.77082i) q^{53} +(-3.17068 + 2.30364i) q^{54} +(-9.31552 - 6.76812i) q^{55} +3.67402 q^{56} -17.2230 q^{57} +(1.35022 + 0.980990i) q^{58} +(1.23338 + 3.79596i) q^{59} +(0.974724 - 2.99989i) q^{60} +2.21839 q^{61} +5.02907 q^{63} +(2.74992 - 8.46340i) q^{64} +(0.985895 + 3.03427i) q^{65} +(-11.8642 - 8.61984i) q^{66} +12.0098 q^{67} +1.64522 q^{68} +(-8.54699 - 6.20975i) q^{69} +(3.17751 - 2.30860i) q^{70} +(6.08610 - 4.42181i) q^{71} +(3.93520 - 12.1113i) q^{72} +(8.02884 + 5.83330i) q^{73} +(2.47624 - 7.62109i) q^{74} +(-1.53785 - 4.73302i) q^{75} +(2.33907 - 1.69944i) q^{76} +(1.63666 + 5.03713i) q^{77} +(1.25563 + 3.86443i) q^{78} +(-7.65399 + 5.56095i) q^{79} +(-2.34556 - 7.21888i) q^{80} +(-1.26509 + 3.89355i) q^{81} +(2.10337 + 1.52819i) q^{82} +(-1.73342 + 5.33490i) q^{83} +(-1.17377 + 0.852796i) q^{84} +(7.75149 - 5.63178i) q^{85} +(9.48204 + 6.88910i) q^{86} -3.59043 q^{87} +13.4114 q^{88} +(-11.2812 - 8.19625i) q^{89} +(-4.20683 - 12.9473i) q^{90} +(0.453480 - 1.39567i) q^{91} +1.77351 q^{92} -0.938835 q^{94} +(5.20323 - 16.0139i) q^{95} +(2.06218 + 6.34674i) q^{96} +(3.64843 + 2.65074i) q^{97} +6.90929 q^{98} +18.3578 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{4} + 32 q^{5} - 8 q^{7} - 12 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} + 48 q^{25} + 20 q^{28} + 96 q^{32} + 40 q^{33} - 56 q^{35} + 160 q^{36}+ \cdots + 16 q^{98}+O(q^{100}) $ 48 * q - 16 * q^4 + 32 * q^5 - 8 * q^7 - 12 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 + 48 * q^25 + 20 * q^28 + 96 * q^32 + 40 * q^33 - 56 * q^35 + 160 * q^36 - 36 * q^38 + 16 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 - 48 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 - 32 * q^56 - 40 * q^59 - 32 * q^63 + 28 * q^64 - 24 * q^66 + 64 * q^67 - 24 * q^69 - 12 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 + 104 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 + 256 * q^87 + 44 * q^90 + 64 * q^94 - 40 * q^95 + 8 * q^97 + 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.384764	+	1.18418i	−0.272070	+	0.837344i	0.717910	+	0.696136i	$0.245099\pi$
$2$	−0.384764	+	1.18418i	−0.272070	+	0.837344i	−0.989980	+	0.141208i	$0.954901\pi$
$3$	−0.827744	−	2.54753i	−0.477898	−	1.47082i	−0.842009	−	0.539463i	$-0.818627\pi$
$3$	−0.827744	−	2.54753i	−0.477898	−	1.47082i	0.364111	−	0.931356i	$-0.381373\pi$
$4$	0.363788	+	0.264307i	0.181894	+	0.132154i
$5$	2.61876			1.17114			0.585572	−	0.810621i	$-0.300870\pi$
$5$	2.61876			1.17114			0.585572	+	0.810621i	$0.300870\pi$
$6$	3.33523			1.36160
$7$	−0.974496	−	0.708013i	−0.368325	−	0.267604i	0.388191	−	0.921579i	$-0.373100\pi$
$7$	−0.974496	−	0.708013i	−0.368325	−	0.267604i	−0.756516	+	0.653975i	$0.773100\pi$
$8$	−2.46761	+	1.79283i	−0.872433	+	0.633860i
$9$	−3.37771	+	2.45405i	−1.12590	+	0.818018i
$10$	−1.00760	+	3.10109i	−0.318632	+	0.980650i
$11$	−3.55723	−	2.58448i	−1.07255	−	0.779250i	−0.0961772	−	0.995364i	$-0.530662\pi$
$11$	−3.55723	−	2.58448i	−1.07255	−	0.779250i	−0.976368	+	0.216115i	$0.930662\pi$
$12$	0.372209	−	1.14554i	0.107447	−	0.330689i
$13$	0.376474	+	1.15867i	0.104415	+	0.321357i	0.989593	−	0.143896i	$-0.0459632\pi$
$13$	0.376474	+	1.15867i	0.104415	+	0.321357i	−0.885178	+	0.465253i	$0.845963\pi$
$14$	1.21337	−	0.881563i	0.324286	−	0.235608i
$15$	−2.16766	−	6.67137i	−0.559687	−	1.72254i
$16$	−0.895675	−	2.75661i	−0.223919	−	0.689151i
$17$	2.95999	−	2.15056i	0.717902	−	0.521587i	−0.167811	−	0.985819i	$-0.553670\pi$
$17$	2.95999	−	2.15056i	0.717902	−	0.521587i	0.885713	+	0.464233i	$0.153670\pi$
$18$	−1.60642	−	4.94406i	−0.378638	−	1.16533i
$19$	1.98691	−	6.11507i	0.455828	−	1.40289i	−0.414333	−	0.910125i	$-0.635985\pi$
$19$	1.98691	−	6.11507i	0.455828	−	1.40289i	0.870161	−	0.492768i	$-0.164015\pi$
$20$	0.952672	+	0.692157i	0.213024	+	0.154771i
$21$	−0.997053	+	3.06861i	−0.217575	+	0.669626i
$22$	4.42919	−	3.21800i	0.944307	−	0.686079i
$23$	3.19080	−	2.31825i	0.665328	−	0.483389i	−0.203130	−	0.979152i	$-0.565111\pi$
$23$	3.19080	−	2.31825i	0.665328	−	0.483389i	0.868458	+	0.495763i	$0.165111\pi$
$24$	6.60984	+	4.80233i	1.34923	+	0.980271i
$25$	1.85789			0.371577
$26$	−1.51693			−0.297494
$27$	2.54648	+	1.85013i	0.490070	+	0.356057i
$28$	−0.167377	−	0.515133i	−0.0316313	−	0.0973510i
$29$	0.414206	−	1.27479i	0.0769160	−	0.236723i	−0.905205	−	0.424976i	$-0.860282\pi$
$29$	0.414206	−	1.27479i	0.0769160	−	0.236723i	0.982121	+	0.188253i	$0.0602825\pi$
$30$	8.73416			1.59463
$31$		0			0
$31$		0			0
$32$	−2.49133			−0.440409
$33$	−3.63957	+	11.2014i	−0.633568	+	1.94992i
$34$	1.40776	+	4.33263i	0.241428	+	0.743039i
$35$	−2.55197	−	1.85411i	−0.431361	−	0.313402i
$36$	−1.87740			−0.312899
$37$	−6.43574			−1.05803			−0.529014	−	0.848613i	$-0.677438\pi$
$37$	−6.43574			−1.05803			−0.529014	+	0.848613i	$0.677438\pi$
$38$	6.47687	+	4.70572i	1.05069	+	0.763369i
$39$	2.64012	−	1.91816i	0.422758	−	0.307152i
$40$	−6.46208	+	4.69498i	−1.02174	+	0.742341i
$41$	0.645251	−	1.98588i	0.100771	−	0.310142i	−0.887943	−	0.459953i	$-0.847866\pi$
$41$	0.645251	−	1.98588i	0.100771	−	0.310142i	0.988715	+	0.149811i	$0.0478664\pi$
$42$	−3.25017	−	2.36139i	−0.501512	−	0.364370i
$43$	2.90880	−	8.95237i	0.443588	−	1.36522i	−0.440437	−	0.897783i	$-0.645177\pi$
$43$	2.90880	−	8.95237i	0.443588	−	1.36522i	0.884025	−	0.467440i	$-0.154823\pi$
$44$	−0.610981	−	1.88040i	−0.0921088	−	0.283482i
$45$	−8.84541	+	6.42657i	−1.31860	+	0.958016i
$46$	1.51753	+	4.67048i	0.223748	+	0.688624i
$47$	0.233002	+	0.717105i	0.0339868	+	0.104601i	0.966611	−	0.256249i	$-0.0824867\pi$
$47$	0.233002	+	0.717105i	0.0339868	+	0.104601i	−0.932624	+	0.360850i	$0.882487\pi$
$48$	−6.28115	+	4.56353i	−0.906606	+	0.658688i
$49$	−1.71476	−	5.27749i	−0.244966	−	0.753926i
$50$	−0.714848	+	2.20008i	−0.101095	+	0.311138i
$51$	−7.92873	−	5.76056i	−1.11024	−	0.806639i
$52$	−0.169288	+	0.521015i	−0.0234760	+	0.0722518i
$53$	−3.81371	+	2.77082i	−0.523853	+	0.380602i	−0.818053	−	0.575142i	$-0.804947\pi$
$53$	−3.81371	+	2.77082i	−0.523853	+	0.380602i	0.294200	+	0.955744i	$0.404947\pi$
$54$	−3.17068	+	2.30364i	−0.431475	+	0.313485i
$55$	−9.31552	−	6.76812i	−1.25610	−	0.912613i
$56$	3.67402			0.490962
$57$	−17.2230			−2.28124
$58$	1.35022	+	0.980990i	0.177292	+	0.128810i
$59$	1.23338	+	3.79596i	0.160573	+	0.494192i	0.998683	−	0.0513091i	$-0.0163394\pi$
$59$	1.23338	+	3.79596i	0.160573	+	0.494192i	−0.838110	+	0.545501i	$0.816339\pi$
$60$	0.974724	−	2.99989i	0.125836	−	0.387284i
$61$	2.21839			0.284036			0.142018	−	0.989864i	$-0.454641\pi$
$61$	2.21839			0.284036			0.142018	+	0.989864i	$0.454641\pi$
$62$		0			0
$63$	5.02907			0.633603
$64$	2.74992	−	8.46340i	0.343741	−	1.05792i
$65$	0.985895	+	3.03427i	0.122285	+	0.376355i
$66$	−11.8642	−	8.61984i	−1.46038	−	1.06103i
$67$	12.0098			1.46723			0.733614	−	0.679567i	$-0.237832\pi$
$67$	12.0098			1.46723			0.733614	+	0.679567i	$0.237832\pi$
$68$	1.64522			0.199512
$69$	−8.54699	−	6.20975i	−1.02894	−	0.747567i
$70$	3.17751	−	2.30860i	0.379786	−	0.275930i
$71$	6.08610	−	4.42181i	0.722287	−	0.524772i	−0.164827	−	0.986322i	$-0.552707\pi$
$71$	6.08610	−	4.42181i	0.722287	−	0.524772i	0.887114	+	0.461550i	$0.152707\pi$
$72$	3.93520	−	12.1113i	0.463768	−	1.42733i
$73$	8.02884	+	5.83330i	0.939705	+	0.682736i	0.948350	−	0.317227i	$-0.102752\pi$
$73$	8.02884	+	5.83330i	0.939705	+	0.682736i	−0.00864451	+	0.999963i	$0.502752\pi$
$74$	2.47624	−	7.62109i	0.287857	−	0.885934i
$75$	−1.53785	−	4.73302i	−0.177576	−	0.546523i
$76$	2.33907	−	1.69944i	0.268310	−	0.194939i
$77$	1.63666	+	5.03713i	0.186515	+	0.574034i
$78$	1.25563	+	3.86443i	0.142172	+	0.437560i
$79$	−7.65399	+	5.56095i	−0.861141	+	0.625656i	−0.928195	−	0.372094i	$-0.878640\pi$
$79$	−7.65399	+	5.56095i	−0.861141	+	0.625656i	0.0670539	+	0.997749i	$0.478640\pi$
$80$	−2.34556	−	7.21888i	−0.262241	−	0.807095i
$81$	−1.26509	+	3.89355i	−0.140566	+	0.432617i
$82$	2.10337	+	1.52819i	0.232279	+	0.168760i
$83$	−1.73342	+	5.33490i	−0.190267	+	0.585582i	−0.999999	−	0.00121782i	$-0.999612\pi$
$83$	−1.73342	+	5.33490i	−0.190267	+	0.585582i	0.809732	+	0.586800i	$0.199612\pi$
$84$	−1.17377	+	0.852796i	−0.128069	+	0.0930477i
$85$	7.75149	−	5.63178i	0.840767	−	0.610853i
$86$	9.48204	+	6.88910i	1.02247	+	0.742871i
$87$	−3.59043			−0.384935
$88$	13.4114			1.42966
$89$	−11.2812	−	8.19625i	−1.19580	−	0.868800i	−0.201936	−	0.979399i	$-0.564723\pi$
$89$	−11.2812	−	8.19625i	−1.19580	−	0.868800i	−0.993865	+	0.110598i	$0.964723\pi$
$90$	−4.20683	−	12.9473i	−0.443439	−	1.36477i
$91$	0.453480	−	1.39567i	0.0475376	−	0.146306i
$92$	1.77351			0.184901
$93$		0			0
$94$	−0.938835			−0.0968334
$95$	5.20323	−	16.0139i	0.533840	−	1.64299i
$96$	2.06218	+	6.34674i	0.210470	+	0.647761i
$97$	3.64843	+	2.65074i	0.370441	+	0.269141i	0.757394	−	0.652958i	$-0.226472\pi$
$97$	3.64843	+	2.65074i	0.370441	+	0.269141i	−0.386953	+	0.922100i	$0.626472\pi$
$98$	6.90929			0.697943
$99$	18.3578			1.84502
$100$	0.675876	+	0.491053i	0.0675876	+	0.0491053i
$101$	−1.52813	+	1.11025i	−0.152055	+	0.110474i	−0.661211	−	0.750200i	$-0.729957\pi$
$101$	−1.52813	+	1.11025i	−0.152055	+	0.110474i	0.509157	+	0.860674i	$0.329957\pi$
$102$	9.87225	−	7.17261i	0.977498	−	0.710194i
$103$	3.48910	−	10.7383i	0.343791	−	1.05808i	−0.618437	−	0.785834i	$-0.712234\pi$
$103$	3.48910	−	10.7383i	0.343791	−	1.05808i	0.962228	−	0.272245i	$-0.0877661\pi$
$104$	−3.00629	−	2.18419i	−0.294791	−	0.214178i
$105$	−2.61104	+	8.03595i	−0.254811	+	0.784228i
$106$	−1.81378	−	5.58224i	−0.176170	−	0.542195i
$107$	−3.91749	+	2.84622i	−0.378718	+	0.275155i	−0.760817	−	0.648967i	$-0.775201\pi$
$107$	−3.91749	+	2.84622i	−0.378718	+	0.275155i	0.382099	+	0.924121i	$0.375201\pi$
$108$	0.437377	+	1.34611i	0.0420866	+	0.129529i
$109$	−3.93566	−	12.1127i	−0.376968	−	1.16019i	−0.942141	−	0.335216i	$-0.891191\pi$
$109$	−3.93566	−	12.1127i	−0.376968	−	1.16019i	0.565174	−	0.824972i	$-0.308809\pi$
$110$	11.5990	−	8.42715i	1.10592	−	0.803497i
$111$	5.32714	+	16.3953i	0.505630	+	1.55617i
$112$	−1.07888	+	3.32045i	−0.101945	+	0.313753i
$113$	−7.23424	−	5.25598i	−0.680540	−	0.494441i	0.192997	−	0.981199i	$-0.438179\pi$
$113$	−7.23424	−	5.25598i	−0.680540	−	0.494441i	−0.873537	+	0.486758i	$0.838179\pi$
$114$	6.62680	−	20.3952i	0.620656	−	1.91018i
$115$	8.35593	−	6.07094i	0.779195	−	0.566118i
$116$	0.487620	−	0.354277i	0.0452744	−	0.0328938i
$117$	−4.11506	−	2.98976i	−0.380437	−	0.276404i
$118$	−4.96967			−0.457496
$119$	−4.40712			−0.404000
$120$	17.3096	+	12.5761i	1.58014	+	1.14804i
$121$	2.57517	+	7.92555i	0.234106	+	0.720505i
$122$	−0.853558	+	2.62698i	−0.0772775	+	0.237836i
$123$	−5.59319			−0.504321
$124$		0			0
$125$	−8.22843			−0.735973
$126$	−1.93501	+	5.95534i	−0.172384	+	0.530544i
$127$	−1.57545	−	4.84875i	−0.139799	−	0.430257i	0.856507	−	0.516136i	$-0.172630\pi$
$127$	−1.57545	−	4.84875i	−0.139799	−	0.430257i	−0.996306	+	0.0858792i	$0.972630\pi$
$128$	4.93309	+	3.58410i	0.436027	+	0.316793i
$129$	−25.2142			−2.21999
$130$	−3.97247			−0.348409
$131$	−2.24460	−	1.63080i	−0.196111	−	0.142483i	0.485396	−	0.874294i	$-0.338675\pi$
$131$	−2.24460	−	1.63080i	−0.196111	−	0.142483i	−0.681508	+	0.731811i	$0.738675\pi$
$132$	−4.28466	+	3.11299i	−0.372932	+	0.270951i
$133$	−6.26578	+	4.55235i	−0.543312	+	0.394739i
$134$	−4.62093	+	14.2218i	−0.399188	+	1.22857i
$135$	6.66861	+	4.84503i	0.573943	+	0.416994i
$136$	−3.44853	+	10.6135i	−0.295709	+	0.910099i
$137$	3.19572	+	9.83542i	0.273029	+	0.840297i	0.989734	+	0.142921i	$0.0456493\pi$
$137$	3.19572	+	9.83542i	0.273029	+	0.840297i	−0.716705	+	0.697376i	$0.754351\pi$
$138$	10.6421	−	7.73191i	0.905913	−	0.658184i
$139$	0.0991287	+	0.305087i	0.00840799	+	0.0258771i	0.955172	−	0.296050i	$-0.0956694\pi$
$139$	0.0991287	+	0.305087i	0.00840799	+	0.0258771i	−0.946765	+	0.321927i	$0.895669\pi$
$140$	−0.438319	−	1.34901i	−0.0370447	−	0.114012i
$141$	1.63398	−	1.18716i	0.137606	−	0.0999768i
$142$	2.89452	+	8.90841i	0.242902	+	0.747577i
$143$	1.65535	−	5.09464i	0.138427	−	0.426035i
$144$	9.79019	+	7.11299i	0.815849	+	0.592749i
$145$	1.08470	−	3.33837i	0.0900797	−	0.277237i
$146$	−9.99691	+	7.26318i	−0.827350	+	0.601105i
$147$	−12.0252	+	8.73681i	−0.991821	+	0.720600i
$148$	−2.34124	−	1.70101i	−0.192449	−	0.139822i
$149$	21.8102			1.78676			0.893382	−	0.449298i	$-0.148326\pi$
$149$	21.8102			1.78676			0.893382	+	0.449298i	$0.148326\pi$
$150$	6.19648			0.505940
$151$	−2.89262	−	2.10161i	−0.235398	−	0.171027i	0.463832	−	0.885923i	$-0.346474\pi$
$151$	−2.89262	−	2.10161i	−0.235398	−	0.171027i	−0.699231	+	0.714896i	$0.746474\pi$
$152$	6.06034	+	18.6518i	0.491559	+	1.51286i
$153$	−4.72041	+	14.5279i	−0.381623	+	1.17451i
$154$	−6.59461			−0.531409
$155$		0			0
$156$	1.46743			0.117488
$157$	−5.60402	+	17.2474i	−0.447249	+	1.37649i	0.432749	+	0.901515i	$0.357544\pi$
$157$	−5.60402	+	17.2474i	−0.447249	+	1.37649i	−0.879998	+	0.474977i	$0.842456\pi$
$158$	−3.64020	−	11.2034i	−0.289599	−	0.891293i
$159$	10.2155	+	7.42202i	0.810145	+	0.588604i
$160$	−6.52418			−0.515782
$161$	−4.75078			−0.374414
$162$	−4.12392	−	2.99620i	−0.324005	−	0.235404i
$163$	6.36032	−	4.62104i	0.498179	−	0.361948i	−0.310142	−	0.950690i	$-0.600377\pi$
$163$	6.36032	−	4.62104i	0.498179	−	0.361948i	0.808321	+	0.588742i	$0.200377\pi$
$164$	0.759617	−	0.551894i	0.0593161	−	0.0430957i
$165$	−9.53115	+	29.3339i	−0.741999	+	2.28364i
$166$	−5.65055	−	4.10536i	−0.438567	−	0.318638i
$167$	−6.11036	+	18.8057i	−0.472834	+	1.45523i	0.376024	+	0.926610i	$0.377291\pi$
$167$	−6.11036	+	18.8057i	−0.472834	+	1.45523i	−0.848857	+	0.528622i	$0.822709\pi$
$168$	−3.04115	−	9.35969i	−0.234630	−	0.722116i
$169$	9.31644	−	6.76879i	0.716649	−	0.520676i
$170$	3.68657	+	11.3461i	0.282747	+	0.870205i
$171$	8.29550	+	25.5309i	0.634373	+	1.95240i
$172$	3.42436	−	2.48795i	0.261105	−	0.189704i
$173$	4.98949	+	15.3561i	0.379344	+	1.16750i	0.940501	+	0.339791i	$0.110356\pi$
$173$	4.98949	+	15.3561i	0.379344	+	1.16750i	−0.561157	+	0.827709i	$0.689644\pi$
$174$	1.38147	−	4.25173i	0.104729	−	0.322323i
$175$	−1.81050	−	1.31541i	−0.136861	−	0.0994354i
$176$	−3.93827	+	12.1207i	−0.296858	+	0.913635i
$177$	8.64941	−	6.28417i	0.650130	−	0.472347i
$178$	14.0464	−	10.2053i	1.05283	−	0.764923i
$179$	−3.20366	−	2.32760i	−0.239453	−	0.173973i	0.461587	−	0.887095i	$-0.347280\pi$
$179$	−3.20366	−	2.32760i	−0.239453	−	0.173973i	−0.701040	+	0.713122i	$0.747280\pi$
$180$	−4.91644			−0.366450
$181$	20.4021			1.51648			0.758239	−	0.651976i	$-0.226060\pi$
$181$	20.4021			1.51648			0.758239	+	0.651976i	$0.226060\pi$
$182$	1.47824	+	1.07401i	0.109575	+	0.0796106i
$183$	−1.83626	−	5.65142i	−0.135740	−	0.417765i
$184$	−3.71744	+	11.4411i	−0.274053	+	0.843450i
$185$	−16.8536			−1.23910
$186$		0			0
$187$	−16.0874			−1.17643
$188$	−0.104773	+	0.322458i	−0.00764136	+	0.0235177i
$189$	−1.17162	−	3.60588i	−0.0852229	−	0.262289i
$190$	16.9614	+	12.3231i	1.23051	+	0.894015i
$191$	19.0185			1.37613			0.688066	−	0.725648i	$-0.258460\pi$
$191$	19.0185			1.37613			0.688066	+	0.725648i	$0.258460\pi$
$192$	−23.8370			−1.72029
$193$	17.1006	+	12.4243i	1.23093	+	0.894320i	0.996959	−	0.0779244i	$-0.0248293\pi$
$193$	17.1006	+	12.4243i	1.23093	+	0.894320i	0.233967	+	0.972245i	$0.424829\pi$
$194$	−4.54274	+	3.30049i	−0.326150	+	0.236962i
$195$	6.91384	−	5.02320i	0.495110	−	0.359719i
$196$	0.771070	−	2.37311i	0.0550764	−	0.169508i
$197$	5.16285	+	3.75103i	0.367838	+	0.267250i	0.756314	−	0.654209i	$-0.226998\pi$
$197$	5.16285	+	3.75103i	0.367838	+	0.267250i	−0.388476	+	0.921459i	$0.626998\pi$
$198$	−7.06341	+	21.7389i	−0.501975	+	1.54492i
$199$	4.77766	+	14.7041i	0.338679	+	1.04235i	0.964881	+	0.262686i	$0.0846085\pi$
$199$	4.77766	+	14.7041i	0.338679	+	1.04235i	−0.626202	+	0.779661i	$0.715392\pi$
$200$	−4.58454	+	3.33087i	−0.324176	+	0.235528i
$201$	−9.94102	−	30.5953i	−0.701185	−	2.15803i
$202$	−0.726771	−	2.23677i	−0.0511354	−	0.157379i
$203$	−1.30621	+	0.949018i	−0.0916781	+	0.0666080i
$204$	−1.36182	−	4.19124i	−0.0953463	−	0.293446i
$205$	1.68975	−	5.20053i	0.118018	−	0.363221i
$206$	11.3737	+	8.26346i	0.792441	+	0.575742i
$207$	−5.08850	+	15.6608i	−0.353675	+	1.08850i
$208$	2.85679	−	2.07558i	0.198083	−	0.143916i
$209$	−22.8722	+	16.6176i	−1.58210	+	1.14946i
$210$	−8.51140	−	6.18390i	−0.587343	−	0.426729i
$211$	−26.6909			−1.83748			−0.918738	−	0.394869i	$-0.870790\pi$
$211$	−26.6909			−1.83748			−0.918738	+	0.394869i	$0.870790\pi$
$212$	−2.11973			−0.145584
$213$	−16.3024	−	11.8444i	−1.11702	−	0.811565i
$214$	−1.86314	−	5.73415i	−0.127361	−	0.391978i
$215$	7.61744	−	23.4441i	0.519505	−	1.59887i
$216$	−9.60068			−0.653244
$217$		0			0
$218$	15.8580			1.07404
$219$	8.21469	−	25.2822i	0.555097	−	1.70841i
$220$	−1.60001	−	4.92432i	−0.107873	−	0.331998i
$221$	3.60614	+	2.62002i	0.242575	+	0.176241i
$222$	−21.4647			−1.44061
$223$	12.6699			0.848437			0.424218	−	0.905560i	$-0.360549\pi$
$223$	12.6699			0.848437			0.424218	+	0.905560i	$0.360549\pi$
$224$	2.42779	+	1.76389i	0.162213	+	0.117855i
$225$	−6.27541	+	4.55935i	−0.418360	+	0.303957i
$226$	9.00752	−	6.54435i	0.599171	−	0.435323i
$227$	−3.57750	+	11.0104i	−0.237447	+	0.730788i	0.759340	+	0.650694i	$0.225522\pi$
$227$	−3.57750	+	11.0104i	−0.237447	+	0.730788i	−0.996787	+	0.0800936i	$0.974478\pi$
$228$	−6.26552	−	4.55217i	−0.414944	−	0.301475i
$229$	8.87846	−	27.3251i	0.586705	−	1.80569i	−0.00560705	−	0.999984i	$-0.501785\pi$
$229$	8.87846	−	27.3251i	0.586705	−	1.80569i	0.592312	−	0.805709i	$-0.298215\pi$
$230$	3.97404	+	12.2308i	0.262040	+	0.806478i
$231$	11.4775	−	8.33890i	0.755165	−	0.548659i
$232$	1.26338	+	3.88830i	0.0829452	+	0.255279i
$233$	3.53689	+	10.8854i	0.231709	+	0.713127i	0.997541	+	0.0700864i	$0.0223275\pi$
$233$	3.53689	+	10.8854i	0.231709	+	0.713127i	−0.765832	+	0.643041i	$0.777672\pi$
$234$	5.12376	−	3.72263i	0.334950	−	0.243356i
$235$	0.610175	+	1.87792i	0.0398034	+	0.122502i
$236$	−0.554611	+	1.70692i	−0.0361021	+	0.111111i
$237$	20.5022	+	14.8958i	1.33176	+	0.967583i
$238$	1.69570	−	5.21883i	0.109916	−	0.338287i
$239$	−20.3994	+	14.8210i	−1.31953	+	0.958691i	−0.319587	+	0.947557i	$0.603544\pi$
$239$	−20.3994	+	14.8210i	−1.31953	+	0.958691i	−0.999938	+	0.0111341i	$0.996456\pi$
$240$	−16.4488	+	11.9508i	−1.06177	+	0.771418i
$241$	8.39575	+	6.09987i	0.540818	+	0.392927i	0.824389	−	0.566024i	$-0.191519\pi$
$241$	8.39575	+	6.09987i	0.540818	+	0.392927i	−0.283571	+	0.958951i	$0.591519\pi$
$242$	−10.3761			−0.667003
$243$	20.4090			1.30924
$244$	0.807024	+	0.586337i	0.0516644	+	0.0375364i
$245$	−4.49054	−	13.8204i	−0.286890	−	0.882956i
$246$	2.15206	−	6.62336i	0.137210	−	0.422290i
$247$	7.83336			0.498425
$248$		0			0
$249$	15.0257			0.952213
$250$	3.16601	−	9.74397i	0.200236	−	0.616263i
$251$	−0.456437	−	1.40477i	−0.0288100	−	0.0886681i	0.935618	−	0.353015i	$-0.114844\pi$
$251$	−0.456437	−	1.40477i	−0.0288100	−	0.0886681i	−0.964428	+	0.264347i	$0.914844\pi$
$252$	1.82951	+	1.32922i	0.115249	+	0.0837330i
$253$	−17.3419			−1.09028
$254$	6.34798			0.398308
$255$	−20.7634	−	15.0855i	−1.30025	−	0.944690i
$256$	8.25649	−	5.99869i	0.516030	−	0.374918i
$257$	−13.6436	+	9.91262i	−0.851061	+	0.618332i	−0.925438	−	0.378898i	$-0.876303\pi$
$257$	−13.6436	+	9.91262i	−0.851061	+	0.618332i	0.0743771	+	0.997230i	$0.476303\pi$
$258$	9.70152	−	29.8582i	0.603990	−	1.85889i
$259$	6.27160	+	4.55658i	0.389698	+	0.283132i
$260$	−0.443324	+	1.36441i	−0.0274938	+	0.0846172i
$261$	1.72934	+	5.32237i	0.107044	+	0.329446i
$262$	2.79480	−	2.03054i	0.172664	−	0.125447i
$263$	7.25651	+	22.3332i	0.447455	+	1.37713i	0.879768	+	0.475403i	$0.157698\pi$
$263$	7.25651	+	22.3332i	0.447455	+	1.37713i	−0.432313	+	0.901724i	$0.642302\pi$
$264$	−11.1012	−	34.1660i	−0.683231	−	2.10277i
$265$	−9.98718	+	7.25611i	−0.613507	+	0.445739i
$266$	−2.97997	−	9.17141i	−0.182714	−	0.562335i
$267$	−11.5423	+	35.5235i	−0.706377	+	2.17400i
$268$	4.36901	+	3.17427i	0.266880	+	0.193900i
$269$	4.05522	−	12.4807i	0.247251	−	0.760961i	−0.748007	−	0.663691i	$-0.768989\pi$
$269$	4.05522	−	12.4807i	0.247251	−	0.760961i	0.995258	−	0.0972698i	$-0.0310110\pi$
$270$	−8.30325	+	6.03266i	−0.505319	+	0.367136i
$271$	9.11186	−	6.62016i	0.553506	−	0.402146i	−0.275570	−	0.961281i	$-0.588867\pi$
$271$	9.11186	−	6.62016i	0.553506	−	0.402146i	0.829077	+	0.559135i	$0.188867\pi$
$272$	−8.57942	−	6.23332i	−0.520204	−	0.377950i
$273$	−3.93087			−0.237907
$274$	−12.8765			−0.777900
$275$	−6.60893	−	4.80167i	−0.398533	−	0.289551i
$276$	−1.46801	−	4.51807i	−0.0883638	−	0.271956i
$277$	0.689671	−	2.12259i	0.0414383	−	0.127534i	−0.928197	−	0.372089i	$-0.878642\pi$
$277$	0.689671	−	2.12259i	0.0414383	−	0.127534i	0.969636	+	0.244555i	$0.0786417\pi$
$278$	−0.399420			−0.0239556
$279$		0			0
$280$	9.62137			0.574987
$281$	−1.64907	+	5.07532i	−0.0983754	+	0.302768i	−0.988119	−	0.153693i	$-0.950883\pi$
$281$	−1.64907	+	5.07532i	−0.0983754	+	0.302768i	0.889743	+	0.456461i	$0.150883\pi$
$282$	0.777115	+	2.39171i	0.0462765	+	0.142424i
$283$	−9.57350	−	6.95556i	−0.569086	−	0.413465i	0.265687	−	0.964059i	$-0.414401\pi$
$283$	−9.57350	−	6.95556i	−0.569086	−	0.413465i	−0.834773	+	0.550594i	$0.814401\pi$
$284$	3.38277			0.200730
$285$	−45.1028			−2.67166
$286$	5.39607	+	3.92047i	0.319076	+	0.231822i
$287$	−2.03482	+	1.47838i	−0.120112	+	0.0872662i
$288$	8.41499	−	6.11385i	0.495858	−	0.360262i
$289$	−1.11666	+	3.43672i	−0.0656857	+	0.202160i
$290$	3.53589	+	2.56898i	0.207635	+	0.150855i
$291$	3.73288	−	11.4886i	0.218825	−	0.673474i
$292$	1.37901	+	4.24417i	0.0807007	+	0.248371i
$293$	−21.6299	+	15.7150i	−1.26363	+	0.918081i	−0.998930	−	0.0462501i	$-0.985273\pi$
$293$	−21.6299	+	15.7150i	−1.26363	+	0.918081i	−0.264700	+	0.964331i	$0.585273\pi$
$294$	−5.71912	−	17.6016i	−0.333546	−	1.02655i
$295$	3.22993	+	9.94070i	0.188054	+	0.578770i
$296$	15.8809	−	11.5382i	0.923059	−	0.670642i
$297$	−4.27680	−	13.1626i	−0.248165	−	0.763774i
$298$	−8.39180	+	25.8273i	−0.486124	+	1.49614i
$299$	3.88734	+	2.82432i	0.224811	+	0.163335i
$300$	0.691521	−	2.12828i	0.0399250	−	0.122877i
$301$	−9.17300	+	6.66457i	−0.528723	+	0.384140i
$302$	3.60168	−	2.61677i	0.207253	−	0.150578i
$303$	4.09330	+	2.97396i	0.235154	+	0.170849i
$304$	−18.6365			−1.06887
$305$	5.80942			0.332647
$306$	−15.3875	−	11.1797i	−0.879644	−	0.639099i
$307$	−4.40400	−	13.5541i	−0.251350	−	0.773575i	−0.994527	−	0.104480i	$-0.966682\pi$
$307$	−4.40400	−	13.5541i	−0.251350	−	0.773575i	0.743177	−	0.669095i	$-0.233318\pi$
$308$	−0.735952	+	2.26503i	−0.0419348	+	0.129062i
$309$	−30.2443			−1.72054
$310$		0			0
$311$	20.2466			1.14808			0.574040	−	0.818827i	$-0.305375\pi$
$311$	20.2466			1.14808			0.574040	+	0.818827i	$0.305375\pi$
$312$	−3.07587	+	9.46656i	−0.174137	+	0.535939i
$313$	−2.79537	−	8.60326i	−0.158004	−	0.486285i	0.840449	−	0.541890i	$-0.182291\pi$
$313$	−2.79537	−	8.60326i	−0.158004	−	0.486285i	−0.998453	+	0.0556053i	$0.982291\pi$
$314$	−18.2678	−	13.2724i	−1.03091	−	0.749003i
$315$	13.1699			0.742040
$316$	−4.25423			−0.239319
$317$	24.3107	+	17.6628i	1.36543	+	0.992040i	0.998079	+	0.0619560i	$0.0197338\pi$
$317$	24.3107	+	17.6628i	1.36543	+	0.992040i	0.367347	+	0.930084i	$0.380266\pi$
$318$	−12.7196	+	9.24133i	−0.713280	+	0.518228i
$319$	−4.76810	+	3.46423i	−0.266962	+	0.193960i
$320$	7.20138	−	22.1636i	0.402570	−	1.23898i
$321$	10.4935	+	7.62399i	0.585691	+	0.425530i
$322$	1.82793	−	5.62579i	0.101867	−	0.313513i
$323$	−7.26959	−	22.3735i	−0.404491	−	1.24489i
$324$	−1.48932	+	1.08205i	−0.0827400	+	0.0601141i
$325$	0.699446	+	2.15267i	0.0387983	+	0.119409i
$326$	3.02494	+	9.30980i	0.167536	+	0.515622i
$327$	−27.5998	+	20.0524i	−1.52627	+	1.10890i
$328$	1.96810	+	6.05720i	0.108670	+	0.334453i
$329$	0.280660	−	0.863784i	0.0154733	−	0.0476220i
$330$	−31.0694	−	22.5733i	−1.71032	−	1.24262i
$331$	4.71765	−	14.5194i	0.259306	−	0.798061i	−0.733645	−	0.679533i	$-0.762182\pi$
$331$	4.71765	−	14.5194i	0.259306	−	0.798061i	0.992951	−	0.118528i	$-0.0378176\pi$
$332$	−2.04065	+	1.48262i	−0.111995	+	0.0813693i
$333$	21.7381	−	15.7936i	1.19124	−	0.865486i
$334$	−19.9184	−	14.4716i	−1.08989	−	0.791849i
$335$	31.4507			1.71833
$336$	9.35199			0.510193
$337$	6.65928	+	4.83825i	0.362754	+	0.263556i	0.754200	−	0.656645i	$-0.228025\pi$
$337$	6.65928	+	4.83825i	0.362754	+	0.263556i	−0.391446	+	0.920201i	$0.628025\pi$
$338$	4.43085	+	13.6368i	0.241007	+	0.741742i
$339$	−7.40169	+	22.7801i	−0.402005	+	1.23724i
$340$	4.30842			0.233657
$341$		0			0
$342$	−33.4251			−1.80742
$343$	−4.67107	+	14.3761i	−0.252214	+	0.776235i
$344$	8.87224	+	27.3060i	0.478359	+	1.47224i
$345$	−22.3825	−	16.2618i	−1.20503	−	0.875508i
$346$	−20.1042			−1.08081
$347$	3.48124			0.186883			0.0934413	−	0.995625i	$-0.470213\pi$
$347$	3.48124			0.186883			0.0934413	+	0.995625i	$0.470213\pi$
$348$	−1.30616	−	0.948979i	−0.0700174	−	0.0508706i
$349$	14.3592	−	10.4326i	0.768632	−	0.558444i	−0.132914	−	0.991128i	$-0.542433\pi$
$349$	14.3592	−	10.4326i	0.768632	−	0.558444i	0.901546	+	0.432684i	$0.142433\pi$
$350$	2.25430	−	1.63784i	0.120497	−	0.0875464i
$351$	−1.18500	+	3.64705i	−0.0632506	+	0.194665i
$352$	8.86222	+	6.43878i	0.472358	+	0.343188i
$353$	−1.57536	+	4.84846i	−0.0838480	+	0.258058i	−0.984187	−	0.177131i	$-0.943318\pi$
$353$	−1.57536	+	4.84846i	−0.0838480	+	0.258058i	0.900339	+	0.435189i	$0.143318\pi$
$354$	4.11362	+	12.6604i	0.218636	+	0.672893i
$355$	15.9380	−	11.5796i	0.845901	−	0.614583i
$356$	−1.93762	−	5.96339i	−0.102694	−	0.316059i
$357$	3.64796	+	11.2273i	0.193071	+	0.594210i
$358$	3.98896	−	2.89815i	0.210823	−	0.153172i
$359$	−2.39702	−	7.37727i	−0.126510	−	0.389357i	0.867663	−	0.497152i	$-0.165621\pi$
$359$	−2.39702	−	7.37727i	−0.126510	−	0.389357i	−0.994173	+	0.107795i	$0.965621\pi$
$360$	10.3053	−	31.7166i	0.543139	−	1.67161i
$361$	−18.0750	−	13.1322i	−0.951314	−	0.691170i
$362$	−7.85002	+	24.1599i	−0.412588	+	1.26981i
$363$	18.0590	−	13.1206i	0.947853	−	0.688655i
$364$	0.533855	−	0.387869i	0.0279816	−	0.0203298i
$365$	21.0256	+	15.2760i	1.10053	+	0.799582i
$366$	7.39885			0.386744
$367$	−30.2604			−1.57958			−0.789791	−	0.613376i	$-0.789811\pi$
$367$	−30.2604			−1.57958			−0.789791	+	0.613376i	$0.789811\pi$
$368$	−9.24843	−	6.71938i	−0.482108	−	0.350272i
$369$	2.69398	+	8.29120i	0.140243	+	0.431623i
$370$	6.48468	−	19.9578i	0.337122	−	1.03756i
$371$	5.67822			0.294798
$372$		0			0
$373$	−11.6354			−0.602458			−0.301229	−	0.953552i	$-0.597397\pi$
$373$	−11.6354			−0.602458			−0.301229	+	0.953552i	$0.597397\pi$
$374$	6.18987	−	19.0505i	0.320071	−	0.985076i
$375$	6.81103	+	20.9622i	0.351720	+	1.08248i
$376$	−1.86060	−	1.35181i	−0.0959533	−	0.0697141i
$377$	1.63300			0.0841039
$378$	4.72082			0.242813
$379$	−27.6304	−	20.0746i	−1.41928	−	1.03117i	−0.991890	−	0.127096i	$-0.959434\pi$
$379$	−27.6304	−	20.0746i	−1.41928	−	1.03117i	−0.427387	−	0.904069i	$-0.640566\pi$
$380$	6.12546	−	4.45041i	0.314229	−	0.228301i
$381$	−11.0483	+	8.02704i	−0.566020	+	0.411238i
$382$	−7.31765	+	22.5214i	−0.374403	+	1.15230i
$383$	0.474384	+	0.344660i	0.0242399	+	0.0176113i	0.599839	−	0.800121i	$-0.295231\pi$
$383$	0.474384	+	0.344660i	0.0242399	+	0.0176113i	−0.575599	+	0.817732i	$0.695231\pi$
$384$	5.04728	−	15.5339i	0.257568	−	0.792712i
$385$	4.28602	+	13.1910i	0.218436	+	0.672276i
$386$	−21.2923	+	15.4698i	−1.08375	+	0.787391i
$387$	12.1445	+	37.3769i	0.617339	+	1.89997i
$388$	0.626644	+	1.92861i	0.0318130	+	0.0979104i
$389$	15.0592	−	10.9412i	0.763532	−	0.554738i	−0.136460	−	0.990646i	$-0.543572\pi$
$389$	15.0592	−	10.9412i	0.763532	−	0.554738i	0.899992	+	0.435907i	$0.143572\pi$
$390$	3.28819	+	10.1200i	0.166504	+	0.512446i
$391$	4.45920	−	13.7240i	0.225511	−	0.694053i
$392$	13.6930	+	9.94853i	0.691600	+	0.502477i
$393$	−2.29656	+	7.06807i	−0.115846	+	0.356537i
$394$	−6.42838	+	4.67049i	−0.323857	+	0.235296i
$395$	−20.0439	+	14.5628i	−1.00852	+	0.732733i
$396$	6.67833	+	4.85209i	0.335599	+	0.243827i
$397$	13.9666			0.700964			0.350482	−	0.936569i	$-0.386018\pi$
$397$	13.9666			0.700964			0.350482	+	0.936569i	$0.386018\pi$
$398$	−19.2506			−0.964947
$399$	16.7837	+	12.1941i	0.840238	+	0.610468i
$400$	−1.66406	−	5.12146i	−0.0832031	−	0.256073i
$401$	1.09621	−	3.37379i	0.0547421	−	0.168479i	−0.919947	−	0.392042i	$-0.871769\pi$
$401$	1.09621	−	3.37379i	0.0547421	−	0.168479i	0.974690	+	0.223563i	$0.0717688\pi$
$402$	40.0554			1.99778
$403$		0			0
$404$	−0.849363			−0.0422574
$405$	−3.31297	+	10.1963i	−0.164623	+	0.506656i
$406$	−0.621228	−	1.91194i	−0.0308310	−	0.0948881i
$407$	22.8934	+	16.6330i	1.13478	+	0.824469i
$408$	29.8927			1.47991
$409$	17.1285			0.846951			0.423476	−	0.905907i	$-0.360810\pi$
$409$	17.1285			0.846951			0.423476	+	0.905907i	$0.360810\pi$
$410$	5.50822	+	4.00196i	0.272032	+	0.197643i
$411$	22.4108	−	16.2824i	1.10544	−	0.803152i
$412$	4.10751	−	2.98428i	0.202363	−	0.147025i
$413$	1.48566	−	4.57240i	0.0731047	−	0.224993i
$414$	−16.5874	−	12.0514i	−0.815225	−	0.592296i
$415$	−4.53939	+	13.9708i	−0.222830	+	0.685800i
$416$	−0.937921	−	2.88662i	−0.0459853	−	0.141528i
$417$	0.695166	−	0.505067i	0.0340424	−	0.0247333i
$418$	−10.8779	−	33.4787i	−0.532055	−	1.63750i
$419$	−5.62933	−	17.3253i	−0.275011	−	0.846396i	−0.989217	−	0.146461i	$-0.953212\pi$
$419$	−5.62933	−	17.3253i	−0.275011	−	0.846396i	0.714206	−	0.699936i	$-0.246788\pi$
$420$	−3.07383	+	2.23327i	−0.149987	+	0.108972i
$421$	−1.07784	−	3.31726i	−0.0525308	−	0.161673i	0.921349	−	0.388735i	$-0.127088\pi$
$421$	−1.07784	−	3.31726i	−0.0525308	−	0.161673i	−0.973880	+	0.227062i	$0.927088\pi$
$422$	10.2697	−	31.6069i	0.499921	−	1.53860i
$423$	−2.54683	−	1.85038i	−0.123831	−	0.0899685i
$424$	4.44316	−	13.6746i	0.215779	−	0.664099i
$425$	5.49932	−	3.99549i	0.266756	−	0.193810i
$426$	20.2985	−	14.7478i	0.983467	−	0.714531i
$427$	−2.16181	−	1.57065i	−0.104617	−	0.0760090i
$428$	−2.17741			−0.105249
$429$	−14.3490			−0.692775
$430$	24.8311	+	18.0409i	1.19746	+	0.870009i
$431$	4.39446	+	13.5247i	0.211674	+	0.651464i	0.999373	+	0.0354045i	$0.0112720\pi$
$431$	4.39446	+	13.5247i	0.211674	+	0.651464i	−0.787700	+	0.616060i	$0.788728\pi$
$432$	2.81925	−	8.67675i	0.135641	−	0.417460i
$433$	32.1386			1.54448			0.772242	−	0.635328i	$-0.219135\pi$
$433$	32.1386			1.54448			0.772242	+	0.635328i	$0.219135\pi$
$434$		0			0
$435$	−9.40247			−0.450814
$436$	1.76974	−	5.44668i	0.0847549	−	0.260849i
$437$	−7.83646	−	24.1181i	−0.374869	−	1.15373i
$438$	26.7781	+	19.4554i	1.27951	+	0.929615i
$439$	11.8608			0.566086			0.283043	−	0.959107i	$-0.408656\pi$
$439$	11.8608			0.566086			0.283043	+	0.959107i	$0.408656\pi$
$440$	35.1212			1.67434
$441$	18.7432	+	13.6177i	0.892533	+	0.648463i
$442$	−4.49009	+	3.26224i	−0.213572	+	0.155169i
$443$	27.5402	−	20.0091i	1.30847	−	0.950662i	0.308474	−	0.951233i	$-0.400182\pi$
$443$	27.5402	−	20.0091i	1.30847	−	0.950662i	1.00000		0.000570625i	$0.000181636\pi$
$444$	−2.39544	+	7.37240i	−0.113682	+	0.349879i
$445$	−29.5426	−	21.4640i	−1.40045	−	1.01749i
$446$	−4.87491	+	15.0034i	−0.230834	+	0.710433i
$447$	−18.0533	−	55.5623i	−0.853891	−	2.62801i
$448$	−8.67198	+	6.30056i	−0.409713	+	0.297674i
$449$	3.35187	+	10.3160i	0.158185	+	0.486842i	0.998470	−	0.0553026i	$-0.0176123\pi$
$449$	3.35187	+	10.3160i	0.158185	+	0.486842i	−0.840285	+	0.542145i	$0.817612\pi$
$450$	−2.98455	−	9.18551i	−0.140693	−	0.433009i
$451$	−7.42776	+	5.39658i	−0.349760	+	0.254115i
$452$	−1.24253	−	3.82413i	−0.0584439	−	0.179872i
$453$	−2.95958	+	9.10866i	−0.139053	+	0.427962i
$454$	−11.6619	−	8.47284i	−0.547318	−	0.397650i
$455$	1.18755	−	3.65491i	0.0556733	−	0.171345i
$456$	42.4997	−	30.8778i	1.99023	−	1.44599i
$457$	−9.47069	+	6.88086i	−0.443020	+	0.321873i	−0.786834	−	0.617165i	$-0.788281\pi$
$457$	−9.47069	+	6.88086i	−0.443020	+	0.321873i	0.343814	+	0.939038i	$0.388281\pi$
$458$	28.9418	+	21.0274i	1.35236	+	0.982548i
$459$	11.5164			0.537537
$460$	4.64438			0.216546
$461$	29.4551	+	21.4004i	1.37186	+	0.996716i	0.997589	+	0.0693975i	$0.0221077\pi$
$461$	29.4551	+	21.4004i	1.37186	+	0.996716i	0.374273	+	0.927319i	$0.377892\pi$
$462$	5.45865	+	16.8000i	0.253959	+	0.781606i
$463$	−5.61400	+	17.2781i	−0.260905	+	0.802983i	0.731704	+	0.681623i	$0.238726\pi$
$463$	−5.61400	+	17.2781i	−0.260905	+	0.802983i	−0.992609	+	0.121360i	$0.961274\pi$
$464$	−3.88510			−0.180361
$465$		0			0
$466$	−14.2512			−0.660174
$467$	−1.54490	+	4.75471i	−0.0714894	+	0.220022i	−0.980417	−	0.196932i	$-0.936902\pi$
$467$	−1.54490	+	4.75471i	−0.0714894	+	0.220022i	0.908928	+	0.416954i	$0.136902\pi$
$468$	−0.706792	−	2.17528i	−0.0326715	−	0.100552i
$469$	−11.7035	−	8.50307i	−0.540416	−	0.392635i
$470$	−2.45858			−0.113406
$471$	48.5770			2.23831
$472$	−9.84901	−	7.15572i	−0.453337	−	0.329369i
$473$	−33.4845	+	24.3279i	−1.53962	+	1.11860i
$474$	−25.5278	+	18.5471i	−1.17253	+	0.851895i
$475$	3.69145	−	11.3611i	0.169375	−	0.521283i
$476$	−1.60326	−	1.16483i	−0.0734851	−	0.0533901i
$477$	6.08188	−	18.7181i	0.278470	−	0.857042i
$478$	−9.70183	−	29.8592i	−0.443752	−	1.36573i
$479$	2.13890	−	1.55400i	0.0977289	−	0.0710042i	−0.537848	−	0.843042i	$-0.680762\pi$
$479$	2.13890	−	1.55400i	0.0977289	−	0.0710042i	0.635577	+	0.772038i	$0.280762\pi$
$480$	5.40035	+	16.6206i	0.246491	+	0.758621i
$481$	−2.42289	−	7.45689i	−0.110474	−	0.340005i
$482$	−10.4538	+	7.59510i	−0.476155	+	0.345947i
$483$	3.93242	+	12.1028i	0.178932	+	0.550695i
$484$	−1.15797	+	3.56386i	−0.0526349	+	0.161993i
$485$	9.55434	+	6.94163i	0.433840	+	0.315203i
$486$	−7.85265	+	24.1680i	−0.356204	+	1.09628i
$487$	18.9071	−	13.7368i	0.856760	−	0.622473i	−0.0702413	−	0.997530i	$-0.522377\pi$
$487$	18.9071	−	13.7368i	0.856760	−	0.622473i	0.927002	+	0.375057i	$0.122377\pi$
$488$	−5.47413	+	3.97719i	−0.247802	+	0.180039i
$489$	−17.0370	−	12.3781i	−0.770439	−	0.559756i
$490$	18.0937			0.817392
$491$	4.99687			0.225506			0.112753	−	0.993623i	$-0.464033\pi$
$491$	4.99687			0.225506			0.112753	+	0.993623i	$0.464033\pi$
$492$	−2.03474	−	1.47832i	−0.0917330	−	0.0666479i
$493$	−1.51547	−	4.66415i	−0.0682535	−	0.210063i
$494$	−3.01400	+	9.27613i	−0.135606	+	0.417353i
$495$	48.0745			2.16079
$496$		0			0
$497$	−9.06157			−0.406467
$498$	−5.78134	+	17.7931i	−0.259068	+	0.797330i
$499$	−5.36914	−	16.5245i	−0.240356	−	0.739739i	−0.996366	−	0.0851791i	$-0.972854\pi$
$499$	−5.36914	−	16.5245i	−0.240356	−	0.739739i	0.756010	−	0.654560i	$-0.227146\pi$
$500$	−2.99341	−	2.17484i	−0.133869	−	0.0972616i
$501$	52.9661			2.36635
$502$	1.83912			0.0820840
$503$	−3.14815	−	2.28727i	−0.140369	−	0.101984i	0.515385	−	0.856959i	$-0.327649\pi$
$503$	−3.14815	−	2.28727i	−0.140369	−	0.101984i	−0.655754	+	0.754975i	$0.727649\pi$
$504$	−12.4098	+	9.01625i	−0.552776	+	0.401616i
$505$	−4.00180	+	2.90748i	−0.178078	+	0.129381i
$506$	6.67254	−	20.5360i	0.296631	−	0.912936i
$507$	−24.9553	−	18.1311i	−1.10831	−	0.805231i
$508$	0.708429	−	2.18032i	0.0314315	−	0.0967361i
$509$	4.88449	+	15.0329i	0.216501	+	0.666322i	0.999044	+	0.0437250i	$0.0139225\pi$
$509$	4.88449	+	15.0329i	0.216501	+	0.666322i	−0.782542	+	0.622597i	$0.786077\pi$
$510$	25.8530	−	18.7833i	1.14479	−	0.831739i
$511$	−3.69403	−	11.3690i	−0.163414	−	0.502937i
$512$	7.69529	+	23.6837i	0.340087	+	1.04668i
$513$	16.3733	−	11.8959i	0.722898	−	0.525216i
$514$	−6.48880	−	19.9705i	−0.286209	−	0.880860i
$515$	9.13709	−	28.1211i	0.402628	−	1.23916i
$516$	−9.17262	−	6.66430i	−0.403802	−	0.293379i
$517$	1.02450	−	3.15310i	0.0450576	−	0.138673i
$518$	−7.80892	+	5.67351i	−0.343104	+	0.249280i
$519$	34.9901	−	25.4218i	1.53589	−	1.11589i
$520$	−7.87273	−	5.71987i	−0.345242	−	0.250833i
$521$	−30.8276			−1.35058			−0.675291	−	0.737552i	$-0.735982\pi$
$521$	−30.8276			−1.35058			−0.675291	+	0.737552i	$0.735982\pi$
$522$	−6.96805			−0.304983
$523$	1.04675	+	0.760508i	0.0457712	+	0.0332547i	0.610436	−	0.792066i	$-0.290994\pi$
$523$	1.04675	+	0.760508i	0.0457712	+	0.0332547i	−0.564664	+	0.825321i	$0.690994\pi$
$524$	−0.385526	−	1.18653i	−0.0168418	−	0.0518337i
$525$	−1.85241	+	5.70113i	−0.0808458	+	0.248818i
$526$	−29.2387			−1.27487
$527$		0			0
$528$	34.1378			1.48566
$529$	−2.30047	+	7.08012i	−0.100020	+	0.307831i
$530$	−4.74985	−	14.6185i	−0.206320	−	0.634989i
$531$	−13.4815	−	9.79489i	−0.585047	−	0.425062i
$532$	−3.48264			−0.150991
$533$	2.54389			0.110188
$534$	−37.6253	−	27.3364i	−1.62821	−	1.18296i
$535$	−10.2589	+	7.45356i	−0.443533	+	0.322246i
$536$	−29.6355	+	21.5314i	−1.28006	+	0.930017i
$537$	−3.27782	+	10.0881i	−0.141448	+	0.435333i
$538$	13.2191	+	9.60425i	0.569916	+	0.414068i
$539$	−7.53976	+	23.2050i	−0.324760	+	0.999510i
$540$	1.14538	+	3.52513i	0.0492894	+	0.151697i
$541$	10.6204	−	7.71615i	0.456605	−	0.331743i	−0.335593	−	0.942007i	$-0.608937\pi$
$541$	10.6204	−	7.71615i	0.456605	−	0.331743i	0.792198	+	0.610264i	$0.208937\pi$
$542$	4.33356	+	13.3373i	0.186142	+	0.572887i
$543$	−16.8877	−	51.9751i	−0.724722	−	2.23047i
$544$	−7.37430	+	5.35774i	−0.316170	+	0.229711i
$545$	−10.3065	−	31.7202i	−0.441483	−	1.35875i
$546$	1.51246	−	4.65487i	0.0647273	−	0.199210i
$547$	−24.3161	−	17.6667i	−1.03968	−	0.755372i	−0.0694570	−	0.997585i	$-0.522127\pi$
$547$	−24.3161	−	17.6667i	−1.03968	−	0.755372i	−0.970223	+	0.242213i	$0.922127\pi$
$548$	−1.43701	+	4.42266i	−0.0613860	+	0.188927i
$549$	−7.49309	+	5.44405i	−0.319797	+	0.232346i
$550$	8.22893	−	5.97867i	0.350883	−	0.254931i
$551$	−6.97247	−	5.06579i	−0.297037	−	0.215810i
$552$	32.2237			1.37153
$553$	11.3960			0.484607
$554$	2.24817	+	1.63339i	0.0955157	+	0.0693962i
$555$	13.9505	+	42.9352i	0.592165	+	1.82250i
$556$	−0.0445749	+	0.137187i	−0.00189040	+	0.00581804i
$557$	−12.8904			−0.546184			−0.273092	−	0.961988i	$-0.588046\pi$
$557$	−12.8904			−0.546184			−0.273092	+	0.961988i	$0.588046\pi$
$558$		0			0
$559$	11.4679			0.485041
$560$	−2.82532	+	8.69545i	−0.119392	+	0.367450i
$561$	13.3163	+	40.9833i	0.562213	+	1.73031i
$562$	−5.37561	−	3.90561i	−0.226756	−	0.164748i
$563$	12.7500			0.537348			0.268674	−	0.963231i	$-0.413415\pi$
$563$	12.7500			0.537348			0.268674	+	0.963231i	$0.413415\pi$
$564$	0.908199			0.0382421
$565$	−18.9447	−	13.7641i	−0.797010	−	0.579061i
$566$	11.9202	−	8.66053i	0.501043	−	0.364029i
$567$	3.98951	−	2.89855i	0.167544	−	0.121728i
$568$	−7.09060	+	21.8226i	−0.297515	+	0.915657i
$569$	2.71791	+	1.97468i	0.113941	+	0.0827828i	0.643296	−	0.765617i	$-0.277566\pi$
$569$	2.71791	+	1.97468i	0.113941	+	0.0827828i	−0.529356	+	0.848400i	$0.677566\pi$
$570$	17.3540	−	53.4100i	0.726878	−	2.23710i
$571$	2.49582	+	7.68134i	0.104447	+	0.321454i	0.989600	−	0.143845i	$-0.0459467\pi$
$571$	2.49582	+	7.68134i	0.104447	+	0.321454i	−0.885153	+	0.465299i	$0.845947\pi$
$572$	1.94875	−	1.41585i	0.0814813	−	0.0591996i
$573$	−15.7425	−	48.4503i	−0.657650	−	2.02404i
$574$	−0.967750	−	2.97843i	−0.0403931	−	0.124317i
$575$	5.92815	−	4.30705i	0.247221	−	0.179616i
$576$	11.4812	+	35.3354i	0.478382	+	1.47231i
$577$	5.58330	−	17.1836i	0.232436	−	0.715363i	−0.765016	−	0.644012i	$-0.777269\pi$
$577$	5.58330	−	17.1836i	0.232436	−	0.715363i	0.997451	−	0.0713516i	$-0.0227312\pi$
$578$	−3.64005	−	2.64465i	−0.151406	−	0.110003i
$579$	17.4964	−	53.8484i	0.727126	−	2.23786i
$580$	1.27696	−	0.927765i	0.0530228	−	0.0385234i
$581$	5.46638	−	3.97156i	0.226784	−	0.164768i
$582$	12.1683	+	8.84082i	0.504394	+	0.366464i
$583$	20.7274			0.858440
$584$	−30.2702			−1.25259
$585$	−10.7763	−	7.82947i	−0.445547	−	0.323709i
$586$	−10.2871	−	31.6603i	−0.424954	−	1.30787i
$587$	−5.14978	+	15.8494i	−0.212554	+	0.654174i	0.786764	+	0.617254i	$0.211755\pi$
$587$	−5.14978	+	15.8494i	−0.212554	+	0.654174i	−0.999318	+	0.0369204i	$0.988245\pi$
$588$	−6.68382			−0.275636
$589$		0			0
$590$	−13.0144			−0.535793
$591$	5.28235	−	16.2574i	0.217287	−	0.668741i
$592$	5.76433	+	17.7408i	0.236913	+	0.729142i
$593$	−26.4201	−	19.1953i	−1.08494	−	0.788258i	−0.106406	−	0.994323i	$-0.533934\pi$
$593$	−26.4201	−	19.1953i	−1.08494	−	0.788258i	−0.978538	+	0.206064i	$0.933934\pi$
$594$	17.2325			0.707060
$595$	−11.5412			−0.473142
$596$	7.93430	+	5.76461i	0.325002	+	0.236127i
$597$	33.5045	−	24.3425i	1.37125	−	0.996271i
$598$	−4.84022	+	3.51663i	−0.197931	+	0.143806i
$599$	6.49952	−	20.0035i	0.265563	−	0.817320i	−0.726000	−	0.687695i	$-0.758623\pi$
$599$	6.49952	−	20.0035i	0.265563	−	0.817320i	0.991563	−	0.129625i	$-0.0413774\pi$
$600$	12.2803	+	8.92217i	0.501342	+	0.364246i
$601$	−5.17088	+	15.9143i	−0.210925	+	0.649159i	0.788493	+	0.615043i	$0.210861\pi$
$601$	−5.17088	+	15.9143i	−0.210925	+	0.649159i	−0.999418	+	0.0341157i	$0.989139\pi$
$602$	−4.36263	−	13.4268i	−0.177808	−	0.547236i
$603$	−40.5656	+	29.4726i	−1.65196	+	1.20022i
$604$	−0.496830	−	1.52908i	−0.0202157	−	0.0622176i
$605$	6.74374	+	20.7551i	0.274172	+	0.843814i
$606$	−5.09667	+	3.70294i	−0.207038	+	0.150422i
$607$	−0.486941	−	1.49865i	−0.0197643	−	0.0608283i	0.940688	−	0.339273i	$-0.110181\pi$
$607$	−0.486941	−	1.49865i	−0.0197643	−	0.0608283i	−0.960452	+	0.278445i	$0.910181\pi$
$608$	−4.95004	+	15.2346i	−0.200750	+	0.617846i
$609$	3.49886	+	2.54207i	0.141781	+	0.103010i
$610$	−2.23526	+	6.87942i	−0.0905030	+	0.278540i
$611$	−0.743168	+	0.539944i	−0.0300654	+	0.0218438i
$612$	−5.55707	+	4.03745i	−0.224631	+	0.163204i
$613$	36.4269	+	26.4657i	1.47127	+	1.06894i	0.980244	+	0.197793i	$0.0633773\pi$
$613$	36.4269	+	26.4657i	1.47127	+	1.06894i	0.491024	+	0.871146i	$0.336623\pi$
$614$	17.7451			0.716133
$615$	−14.6472			−0.590632
$616$	−13.0693	−	9.49543i	−0.526579	−	0.382582i
$617$	−10.3321	−	31.7989i	−0.415955	−	1.28018i	−0.911394	−	0.411534i	$-0.864993\pi$
$617$	−10.3321	−	31.7989i	−0.415955	−	1.28018i	0.495440	−	0.868642i	$-0.335007\pi$
$618$	11.6369	−	35.8148i	0.468107	−	1.44068i
$619$	−10.7700			−0.432881			−0.216440	−	0.976296i	$-0.569445\pi$
$619$	−10.7700			−0.432881			−0.216440	+	0.976296i	$0.569445\pi$
$620$		0			0
$621$	12.4144			0.498172
$622$	−7.79017	+	23.9757i	−0.312357	+	0.961338i
$623$	5.19040	+	15.9744i	0.207949	+	0.640001i
$624$	−7.65231	−	5.55973i	−0.306337	−	0.222567i
$625$	−30.8377			−1.23351
$626$	11.2634			0.450176
$627$	61.2662	+	44.5125i	2.44673	+	1.77766i
$628$	−6.59729	+	4.79321i	−0.263260	+	0.191270i
$629$	−19.0497	+	13.8404i	−0.759561	+	0.551854i
$630$	−5.06731	+	15.5956i	−0.201887	+	0.621343i
$631$	14.9212	+	10.8409i	0.594005	+	0.431570i	0.843746	−	0.536743i	$-0.180345\pi$
$631$	14.9212	+	10.8409i	0.594005	+	0.431570i	−0.249741	+	0.968313i	$0.580345\pi$
$632$	8.91728	−	27.4446i	0.354710	−	1.09169i
$633$	22.0932	+	67.9959i	0.878126	+	2.70259i
$634$	−30.2699	+	21.9923i	−1.20217	+	0.873427i
$635$	−4.12573	−	12.6977i	−0.163725	−	0.503892i
$636$	1.75459	+	5.40008i	0.0695742	+	0.214127i
$637$	5.46930	−	3.97368i	0.216701	−	0.157443i
$638$	−2.26769	−	6.97922i	−0.0897785	−	0.276310i
$639$	−9.70574	+	29.8712i	−0.383953	+	1.18169i
$640$	12.9186	+	9.38588i	0.510651	+	0.371009i
$641$	−11.7314	+	36.1054i	−0.463361	+	1.42608i	0.397671	+	0.917528i	$0.369819\pi$
$641$	−11.7314	+	36.1054i	−0.463361	+	1.42608i	−0.861032	+	0.508551i	$0.830181\pi$
$642$	−13.0657	+	9.49281i	−0.515663	+	0.374651i
$643$	−13.0408	+	9.47467i	−0.514278	+	0.373645i	−0.814444	−	0.580242i	$-0.802958\pi$
$643$	−13.0408	+	9.47467i	−0.514278	+	0.373645i	0.300166	+	0.953887i	$0.402958\pi$
$644$	−1.72828	−	1.25567i	−0.0681036	−	0.0494802i
$645$	−66.0298			−2.59992
$646$	29.2914			1.15245
$647$	−5.58116	−	4.05495i	−0.219418	−	0.159416i	0.472647	−	0.881252i	$-0.343299\pi$
$647$	−5.58116	−	4.05495i	−0.219418	−	0.159416i	−0.692065	+	0.721836i	$0.743299\pi$
$648$	−3.85870	−	11.8759i	−0.151584	−	0.466528i
$649$	5.42316	−	16.6908i	0.212877	−	0.655170i
$650$	−2.81828			−0.110542
$651$		0			0
$652$	3.53518			0.138448
$653$	2.49784	−	7.68757i	0.0977481	−	0.300838i	−0.890212	−	0.455546i	$-0.849444\pi$
$653$	2.49784	−	7.68757i	0.0977481	−	0.300838i	0.987960	+	0.154709i	$0.0494439\pi$
$654$	−13.1263	−	40.3987i	−0.513280	−	1.57971i
$655$	−5.87806	−	4.27066i	−0.229675	−	0.166868i
$656$	−6.05221			−0.236299
$657$	−41.4344			−1.61651
$658$	0.914890	+	0.664707i	0.0356661	+	0.0259130i
$659$	−20.0393	+	14.5594i	−0.780621	+	0.567154i	−0.905165	−	0.425060i	$-0.860253\pi$
$659$	−20.0393	+	14.5594i	−0.780621	+	0.567154i	0.124544	+	0.992214i	$0.460253\pi$
$660$	−11.2205	+	8.15215i	−0.436756	+	0.317322i
$661$	12.2887	−	37.8207i	0.477974	−	1.47105i	−0.363930	−	0.931426i	$-0.618565\pi$
$661$	12.2887	−	37.8207i	0.477974	−	1.47105i	0.841904	−	0.539627i	$-0.181435\pi$
$662$	15.3785	+	11.1731i	0.597702	+	0.434256i
$663$	3.68962	−	11.3555i	0.143293	−	0.441010i
$664$	−5.28716	−	16.2722i	−0.205181	−	0.631484i
$665$	−16.4085	+	11.9215i	−0.636296	+	0.462296i
$666$	10.3385	+	31.8187i	0.400610	+	1.23295i
$667$	−1.63365	−	5.02785i	−0.0632551	−	0.194679i
$668$	−7.19337	+	5.22629i	−0.278320	+	0.202211i
$669$	−10.4874	−	32.2769i	−0.405466	−	1.24790i
$670$	−12.1011	+	37.2434i	−0.467506	+	1.43884i
$671$	−7.89132	−	5.73338i	−0.304641	−	0.221335i
$672$	2.48398	−	7.64492i	0.0958218	−	0.294909i
$673$	11.7795	−	8.55831i	0.454067	−	0.329899i	−0.337133	−	0.941457i	$-0.609457\pi$
$673$	11.7795	−	8.55831i	0.454067	−	0.329899i	0.791199	+	0.611558i	$0.209457\pi$
$674$	−8.29162	+	6.02422i	−0.319381	+	0.232044i
$675$	4.73107	+	3.43732i	0.182099	+	0.132303i
$676$	5.17825			0.199164
$677$	0.221019			0.00849445			0.00424722	−	0.999991i	$-0.498648\pi$
$677$	0.221019			0.00849445			0.00424722	+	0.999991i	$0.498648\pi$
$678$	−24.1279	−	17.5299i	−0.926625	−	0.673232i
$679$	−1.67862	−	5.16626i	−0.0644195	−	0.198263i
$680$	−9.03086	+	27.7941i	−0.346318	+	1.06586i
$681$	31.0107			1.18833
$682$		0			0
$683$	−16.3674			−0.626280			−0.313140	−	0.949707i	$-0.601381\pi$
$683$	−16.3674			−0.626280			−0.313140	+	0.949707i	$0.601381\pi$
$684$	−3.73021	+	11.4804i	−0.142628	+	0.438965i
$685$	8.36882	+	25.7566i	0.319756	+	0.984108i
$686$	−15.2266	−	11.0628i	−0.581356	−	0.422380i
$687$	−76.9607			−2.93623
$688$	−27.2835			−1.04017
$689$	−4.64623	−	3.37568i	−0.177007	−	0.128603i
$690$	27.8690	−	20.2480i	1.06095	−	0.770828i
$691$	38.2723	−	27.8064i	1.45595	−	1.05781i	0.471550	−	0.881839i	$-0.343695\pi$
$691$	38.2723	−	27.8064i	1.45595	−	1.05781i	0.984396	−	0.175967i	$-0.0563052\pi$
$692$	−2.24361	+	6.90511i	−0.0852891	+	0.262493i
$693$	−17.8896	−	12.9975i	−0.679568	−	0.493735i
$694$	−1.33946	+	4.12242i	−0.0508450	+	0.156485i
$695$	0.259594	+	0.798948i	0.00984696	+	0.0303058i
$696$	8.85981	−	6.43703i	0.335830	−	0.243995i
$697$	−2.36081	−	7.26582i	−0.0894220	−	0.275213i
$698$	6.82917	+	21.0180i	0.258488	+	0.795544i
$699$	24.8033	−	18.0207i	0.938148	−	0.681604i
$700$	−0.310967	−	0.957058i	−0.0117534	−	0.0361734i
$701$	7.51588	−	23.1315i	0.283871	−	0.873664i	−0.702864	−	0.711324i	$-0.748096\pi$
$701$	7.51588	−	23.1315i	0.283871	−	0.873664i	0.986735	−	0.162340i	$-0.0519042\pi$
$702$	−3.86283	−	2.80651i	−0.145793	−	0.105925i
$703$	−12.7872	+	39.3550i	−0.482279	+	1.48430i
$704$	−31.6556	+	22.9991i	−1.19306	+	0.866812i
$705$	4.27901	−	3.10888i	0.161157	−	0.117087i
$706$	−5.13533	−	3.73103i	−0.193271	−	0.140419i
$707$	2.27523			0.0855687
$708$	4.80750			0.180677
$709$	−14.5737	−	10.5884i	−0.547329	−	0.397657i	0.279471	−	0.960154i	$-0.409841\pi$
$709$	−14.5737	−	10.5884i	−0.547329	−	0.397657i	−0.826800	+	0.562497i	$0.809841\pi$
$710$	7.58003	+	23.3289i	0.284474	+	0.875520i
$711$	12.2061	−	37.5666i	0.457766	−	1.40886i
$712$	42.5320			1.59395
$713$		0			0
$714$	−14.6988			−0.550087
$715$	4.33496	−	13.3416i	0.162118	−	0.498949i
$716$	−0.550253	−	1.69350i	−0.0205639	−	0.0632892i
$717$	54.6424	+	39.7001i	2.04066	+	1.48263i
$718$	9.65832			0.360445
$719$	−31.3829			−1.17038			−0.585192	−	0.810895i	$-0.698981\pi$
$719$	−31.3829			−1.17038			−0.585192	+	0.810895i	$0.698981\pi$
$720$	25.6381	+	18.6272i	0.955477	+	0.694194i
$721$	−11.0030	+	7.99413i	−0.409772	+	0.297717i
$722$	22.5056	−	16.3513i	0.837571	−	0.608531i
$723$	8.59009	−	26.4376i	0.319469	−	0.983225i
$724$	7.42205	+	5.39244i	0.275838	+	0.200408i
$725$	0.769546	−	2.36842i	0.0285802	−	0.0879609i
$726$	8.58878	+	26.4336i	0.318760	+	0.981041i
$727$	3.76710	−	2.73696i	0.139714	−	0.101508i	−0.515733	−	0.856749i	$-0.672480\pi$
$727$	3.76710	−	2.73696i	0.139714	−	0.101508i	0.655447	+	0.755241i	$0.272480\pi$
$728$	1.38318	+	4.25698i	0.0512639	+	0.157774i
$729$	−13.0981	−	40.3119i	−0.485116	−	1.49303i
$730$	−26.1795	+	19.0205i	−0.968945	+	0.703980i
$731$	−10.6426	−	32.7544i	−0.393629	−	1.21147i
$732$	0.825704	−	2.54126i	0.0305189	−	0.0939275i
$733$	40.2769	+	29.2629i	1.48766	+	1.08085i	0.974986	+	0.222267i	$0.0713456\pi$
$733$	40.2769	+	29.2629i	1.48766	+	1.08085i	0.512675	+	0.858583i	$0.328654\pi$
$734$	11.6431	−	35.8339i	0.429756	−	1.32265i
$735$	−31.4910	+	22.8796i	−1.16156	+	0.843926i
$736$	−7.94933	+	5.77553i	−0.293016	+	0.212889i
$737$	−42.7215	−	31.0390i	−1.57367	−	1.14334i
$738$	−10.8548			−0.399573
$739$	−32.7194			−1.20360			−0.601802	−	0.798646i	$-0.705550\pi$
$739$	−32.7194			−1.20360			−0.601802	+	0.798646i	$0.705550\pi$
$740$	−6.13115	−	4.45454i	−0.225385	−	0.163752i
$741$	−6.48402	−	19.9557i	−0.238196	−	0.733093i
$742$	−2.18478	+	6.72405i	−0.0802057	+	0.246848i
$743$	−34.5763			−1.26848			−0.634241	−	0.773136i	$-0.718687\pi$
$743$	−34.5763			−1.26848			−0.634241	+	0.773136i	$0.718687\pi$
$744$		0			0
$745$	57.1157			2.09256
$746$	4.47689	−	13.7784i	0.163910	−	0.504464i
$747$	−7.23716	−	22.2737i	−0.264794	−	0.814951i
$748$	−5.85241	−	4.25203i	−0.213985	−	0.155470i
$749$	5.83274			0.213124
$750$	−27.4437			−1.00210
$751$	−13.1583	−	9.56006i	−0.480153	−	0.348852i	0.321232	−	0.947001i	$-0.395903\pi$
$751$	−13.1583	−	9.56006i	−0.480153	−	0.348852i	−0.801385	+	0.598149i	$0.795903\pi$
$752$	1.76808	−	1.28459i	0.0644753	−	0.0468441i
$753$	−3.20088	+	2.32557i	−0.116646	+	0.0847486i
$754$	−0.628321	+	1.93377i	−0.0228821	+	0.0704239i
$755$	−7.57508	−	5.50362i	−0.275685	−	0.200297i
$756$	0.526839	−	1.62144i	0.0191610	−	0.0589714i
$757$	−12.6590	−	38.9603i	−0.460098	−	1.41603i	−0.865045	−	0.501695i	$-0.832710\pi$
$757$	−12.6590	−	38.9603i	−0.460098	−	1.41603i	0.404947	−	0.914340i	$-0.367290\pi$
$758$	34.4032	−	24.9954i	1.24958	−	0.907874i
$759$	14.3546	+	44.1791i	0.521041	+	1.60360i
$760$	15.8706	+	48.8446i	0.575686	+	1.77178i
$761$	0.0510239	−	0.0370710i	0.00184961	−	0.00134382i	−0.586860	−	0.809688i	$-0.699636\pi$
$761$	0.0510239	−	0.0370710i	0.00184961	−	0.00134382i	0.588710	+	0.808345i	$0.299636\pi$
$762$	−5.25450	−	16.1717i	−0.190351	−	0.585839i
$763$	−4.74067	+	14.5903i	−0.171624	+	0.528204i
$764$	6.91871	+	5.02673i	0.250310	+	0.181861i
$765$	−12.3616	+	38.0451i	−0.446935	+	1.37552i
$766$	−0.590667	+	0.429144i	−0.0213417	+	0.0155056i
$767$	−3.93393	+	2.85816i	−0.142046	+	0.103202i
$768$	−22.1161	−	16.0683i	−0.798047	−	0.579815i
$769$	−40.4898			−1.46010			−0.730050	−	0.683393i	$-0.760503\pi$
$769$	−40.4898			−1.46010			−0.730050	+	0.683393i	$0.760503\pi$
$770$	−17.2697			−0.622356
$771$	36.5461	+	26.5523i	1.31618	+	0.956257i
$772$	2.93715	+	9.03962i	0.105710	+	0.325343i
$773$	11.3468	−	34.9218i	0.408115	−	1.25605i	−0.510150	−	0.860085i	$-0.670410\pi$
$773$	11.3468	−	34.9218i	0.408115	−	1.25605i	0.918266	−	0.395965i	$-0.129590\pi$
$774$	−48.9338			−1.75889
$775$		0			0
$776$	−13.7552			−0.493783
$777$	6.41677	−	19.7488i	0.230200	−	0.708484i
$778$	7.16208	+	22.0426i	0.256773	+	0.790266i
$779$	−10.8617	−	7.89151i	−0.389162	−	0.282743i
$780$	3.84284			0.137596
$781$	−33.0777			−1.18361
$782$	14.5360	+	10.5610i	0.519806	+	0.377661i
$783$	3.41329	−	2.47990i	0.121981	−	0.0886245i
$784$	−13.0121	+	9.45383i	−0.464717	+	0.337637i
$785$	−14.6756	+	45.1667i	−0.523793	+	1.61207i
$786$	−7.48626	−	5.43908i	−0.267026	−	0.194006i
$787$	2.08902	−	6.42934i	0.0744655	−	0.229181i	−0.906895	−	0.421356i	$-0.861554\pi$
$787$	2.08902	−	6.42934i	0.0744655	−	0.229181i	0.981361	+	0.192175i	$0.0615542\pi$
$788$	0.886757	+	2.72916i	0.0315894	+	0.0972222i
$789$	50.8881	−	36.9724i	1.81167	−	1.31625i
$790$	−9.53280	−	29.3389i	−0.339162	−	1.04383i
$791$	3.32843	+	10.2439i	0.118345	+	0.364230i
$792$	−45.2999	+	32.9123i	−1.60966	+	1.16949i
$793$	0.835167	+	2.57038i	0.0296576	+	0.0912769i
$794$	−5.37386	+	16.5390i	−0.190711	+	0.586948i
$795$	26.7520	+	19.4365i	0.948795	+	0.689340i
$796$	−2.14835	+	6.61195i	−0.0761464	+	0.234354i
$797$	−17.8628	+	12.9781i	−0.632733	+	0.459708i	−0.857346	−	0.514741i	$-0.827888\pi$
$797$	−17.8628	+	12.9781i	−0.632733	+	0.459708i	0.224613	+	0.974448i	$0.427888\pi$
$798$	−20.8978	+	15.1832i	−0.739775	+	0.537478i
$799$	2.23186	+	1.62154i	0.0789575	+	0.0573659i
$800$	−4.62860			−0.163646
$801$	58.2186			2.05705
$802$	3.57340	+	2.59623i	0.126181	+	0.0916760i
$803$	−13.4844	−	41.5008i	−0.475855	−	1.46453i
$804$	4.47014	−	13.7577i	0.157650	−	0.485196i
$805$	−12.4411			−0.438492
$806$		0			0
$807$	−35.1516			−1.23740
$808$	1.78035	−	5.47934i	0.0626324	−	0.192763i
$809$	−7.73045	−	23.7919i	−0.271788	−	0.836477i	−0.990051	−	0.140706i	$-0.955063\pi$
$809$	−7.73045	−	23.7919i	−0.271788	−	0.836477i	0.718263	−	0.695771i	$-0.244937\pi$
$810$	−10.7995	−	7.84632i	−0.379457	−	0.275692i
$811$	2.60138			0.0913468			0.0456734	−	0.998956i	$-0.485457\pi$
$811$	2.60138			0.0913468			0.0456734	+	0.998956i	$0.485457\pi$
$812$	−0.726017			−0.0254782
$813$	−24.4074	−	17.7330i	−0.856003	−	0.621923i
$814$	−28.5051	+	20.7102i	−0.999104	+	0.725891i
$815$	16.6561	−	12.1014i	0.583439	−	0.423893i
$816$	−8.77802	+	27.0160i	−0.307292	+	0.945748i
$817$	−48.9648	−	35.5750i	−1.71306	−	1.24461i
$818$	−6.59045	+	20.2833i	−0.230430	+	0.709189i
$819$	1.89332	+	5.82703i	0.0661578	+	0.203613i
$820$	1.98925	−	1.44528i	0.0694676	−	0.0504712i
$821$	−8.01153	−	24.6569i	−0.279604	−	0.860533i	−0.987964	−	0.154682i	$-0.950565\pi$
$821$	−8.01153	−	24.6569i	−0.279604	−	0.860533i	0.708360	−	0.705851i	$-0.249435\pi$
$822$	10.6585	+	32.8034i	0.371757	+	1.14415i
$823$	25.9612	−	18.8619i	0.904951	−	0.657485i	−0.0347819	−	0.999395i	$-0.511074\pi$
$823$	25.9612	−	18.8619i	0.904951	−	0.657485i	0.939733	+	0.341910i	$0.111074\pi$
$824$	10.6422	+	32.7534i	0.370739	+	1.14102i
$825$	−6.76191	+	20.8110i	−0.235419	+	0.724546i
$826$	4.84293	+	3.51859i	0.168507	+	0.122427i
$827$	6.71906	−	20.6791i	0.233644	−	0.719084i	−0.763654	−	0.645626i	$-0.776597\pi$
$827$	6.71906	−	20.6791i	0.233644	−	0.719084i	0.997298	−	0.0734579i	$-0.0234034\pi$
$828$	−5.99040	+	4.35228i	−0.208181	+	0.151252i
$829$	−16.6954	+	12.1299i	−0.579855	+	0.421289i	−0.838672	−	0.544637i	$-0.816667\pi$
$829$	−16.6954	+	12.1299i	−0.579855	+	0.421289i	0.258817	+	0.965926i	$0.416667\pi$
$830$	−14.7974	−	10.7509i	−0.513625	−	0.373171i
$831$	−5.97824			−0.207383
$832$	10.8416			0.375863
$833$	−16.4252	−	11.9336i	−0.569099	−	0.413475i
$834$	0.330617	+	1.01754i	0.0114483	+	0.0352344i
$835$	−16.0015	+	49.2477i	−0.553756	+	1.70429i
$836$	−12.7128			−0.439680
$837$		0			0
$838$	22.6823			0.783547
$839$	−2.37625	+	7.31334i	−0.0820372	+	0.252485i	−0.983659	−	0.180040i	$-0.942377\pi$
$839$	−2.37625	+	7.31334i	−0.0820372	+	0.252485i	0.901622	+	0.432525i	$0.142377\pi$
$840$	−7.96403	−	24.5108i	−0.274785	−	0.845702i
$841$	22.0080	+	15.9897i	0.758895	+	0.551370i
$842$	4.34296			0.149668
$843$	14.2946			0.492331
$844$	−9.70982	−	7.05460i	−0.334226	−	0.242829i
$845$	24.3975	−	17.7258i	0.839299	−	0.609786i
$846$	3.17112	−	2.30395i	0.109025	−	0.0792114i
$847$	3.10190	−	9.54667i	0.106583	−	0.328027i
$848$	11.0539	+	8.03113i	0.379593	+	0.275790i
$849$	−9.79511	+	30.1462i	−0.336167	+	1.03462i
$850$	2.61545	+	8.04952i	0.0897091	+	0.276096i
$851$	−20.5352	+	14.9197i	−0.703936	+	0.511440i
$852$	−2.80006	−	8.61771i	−0.0959286	−	0.295238i
$853$	−0.274664	−	0.845328i	−0.00940430	−	0.0289435i	0.946244	−	0.323453i	$-0.104844\pi$
$853$	−0.274664	−	0.845328i	−0.00940430	−	0.0289435i	−0.955649	+	0.294509i	$0.904844\pi$
$854$	2.69172	−	1.95565i	0.0921089	−	0.0669210i
$855$	21.7239	+	66.8593i	0.742942	+	2.28654i
$856$	4.56407	−	14.0468i	0.155997	−	0.480108i
$857$	−12.0188	−	8.73217i	−0.410554	−	0.298285i	0.363272	−	0.931683i	$-0.381660\pi$
$857$	−12.0188	−	8.73217i	−0.410554	−	0.298285i	−0.773826	+	0.633398i	$0.781660\pi$
$858$	5.52097	−	16.9918i	0.188483	−	0.580091i
$859$	33.5444	−	24.3714i	1.14452	−	0.831542i	0.156777	−	0.987634i	$-0.449890\pi$
$859$	33.5444	−	24.3714i	1.14452	−	0.831542i	0.987743	+	0.156092i	$0.0498896\pi$
$860$	8.96757	−	6.51532i	0.305792	−	0.222171i
$861$	5.45054	+	3.96005i	0.185754	+	0.134958i
$862$	−17.7066			−0.603089
$863$	22.3985			0.762453			0.381227	−	0.924482i	$-0.375502\pi$
$863$	22.3985			0.762453			0.381227	+	0.924482i	$0.375502\pi$
$864$	−6.34411	−	4.60927i	−0.215831	−	0.156811i
$865$	13.0663	+	40.2138i	0.444266	+	1.36731i
$866$	−12.3658	+	38.0580i	−0.420207	+	1.29327i
$867$	9.67946			0.328732
$868$		0			0
$869$	41.5992			1.41116
$870$	3.61774	−	11.1343i	0.122653	−	0.377486i
$871$	4.52137	+	13.9154i	0.153201	+	0.471504i
$872$	31.4277	+	22.8335i	1.06428	+	0.773241i
$873$	−18.8284			−0.637244
$874$	31.5755			1.06806
$875$	8.01857	+	5.82583i	0.271077	+	0.196949i
$876$	9.67069	−	7.02617i	0.326742	−	0.237392i
$877$	24.9093	−	18.0977i	0.841129	−	0.611116i	−0.0815570	−	0.996669i	$-0.525989\pi$
$877$	24.9093	−	18.0977i	0.841129	−	0.611116i	0.922686	+	0.385553i	$0.125989\pi$
$878$	−4.56362	+	14.0454i	−0.154015	+	0.474008i
$879$	57.9385	+	42.0948i	1.95422	+	1.41982i
$880$	−10.3134	+	31.7412i	−0.347663	+	1.07000i
$881$	0.883623	+	2.71951i	0.0297700	+	0.0916227i	0.964838	−	0.262847i	$-0.0846614\pi$
$881$	0.883623	+	2.71951i	0.0297700	+	0.0916227i	−0.935068	+	0.354470i	$0.884661\pi$
$882$	−23.3376	+	16.9558i	−0.785818	+	0.570930i
$883$	7.39527	+	22.7603i	0.248871	+	0.765945i	0.994976	+	0.100117i	$0.0319217\pi$
$883$	7.39527	+	22.7603i	0.248871	+	0.765945i	−0.746105	+	0.665828i	$0.768078\pi$
$884$	0.619382	+	1.90626i	0.0208321	+	0.0641145i
$885$	22.6507	−	16.4567i	0.761395	−	0.553186i
$886$	13.0980	+	40.3114i	0.440035	+	1.35429i
$887$	8.15348	−	25.0938i	0.273767	−	0.842568i	−0.715776	−	0.698330i	$-0.753927\pi$
$887$	8.15348	−	25.0938i	0.273767	−	0.842568i	0.989543	−	0.144238i	$-0.0460732\pi$
$888$	−42.5392	−	30.9065i	−1.42752	−	1.03715i
$889$	−1.89770	+	5.84053i	−0.0636469	+	0.195885i
$890$	36.7842	−	26.7253i	1.23301	−	0.895834i
$891$	14.5630	−	10.5807i	0.487880	−	0.354465i
$892$	4.60914	+	3.34874i	0.154326	+	0.112124i
$893$	4.84810			0.162236
$894$	72.7422			2.43286
$895$	−8.38961	−	6.09541i	−0.280434	−	0.203747i
$896$	−2.26969	−	6.98538i	−0.0758249	−	0.233365i
$897$	3.97733	−	12.2409i	0.132799	−	0.408713i
$898$	−13.5057			−0.450692
$899$		0			0
$900$	−3.48799			−0.116266
$901$	−5.32972	+	16.4032i	−0.177559	+	0.546470i
$902$	−3.53261	−	10.8722i	−0.117623	−	0.362006i
$903$	24.5711	+	17.8520i	0.817676	+	0.594076i
$904$	27.2744			0.907132
$905$	53.4282			1.77601
$906$	−9.64757	−	7.00937i	−0.320519	−	0.232871i
$907$	−8.26629	+	6.00581i	−0.274478	+	0.199420i	−0.716505	−	0.697582i	$-0.754259\pi$
$907$	−8.26629	+	6.00581i	−0.274478	+	0.199420i	0.442028	+	0.897001i	$0.354259\pi$
$908$	−4.21159	+	3.05990i	−0.139767	+	0.101546i
$909$	2.43697	−	7.50022i	0.0808292	−	0.248767i
$910$	3.87116	+	2.81256i	0.128328	+	0.0932354i
$911$	−1.97550	+	6.07995i	−0.0654511	+	0.201438i	−0.978434	−	0.206560i	$-0.933773\pi$
$911$	−1.97550	+	6.07995i	−0.0654511	+	0.201438i	0.912983	+	0.407998i	$0.133773\pi$
$912$	15.4262	+	47.4770i	0.510813	+	1.57212i
$913$	19.9541	−	14.4975i	0.660384	−	0.479797i
$914$	−4.50421	−	13.8625i	−0.148986	−	0.458532i
$915$	−4.80871	−	14.7997i	−0.158971	−	0.489263i
$916$	10.4521	−	7.59390i	0.345347	−	0.250909i
$917$	1.03273	+	3.17841i	0.0341037	+	0.104960i
$918$	−4.43108	+	13.6375i	−0.146247	+	0.450104i
$919$	22.0771	+	16.0400i	0.728258	+	0.529110i	0.889012	−	0.457884i	$-0.151393\pi$
$919$	22.0771	+	16.0400i	0.728258	+	0.529110i	−0.160754	+	0.986995i	$0.551393\pi$
$920$	−9.73507	+	29.9615i	−0.320956	+	0.987801i
$921$	−30.8842	+	22.4387i	−1.01767	+	0.739380i
$922$	−36.6753	+	26.6462i	−1.20784	+	0.877544i
$923$	7.41467	+	5.38707i	0.244057	+	0.177318i
$924$	6.37941			0.209867
$925$	−11.9569			−0.393139
$926$	−18.3004	−	13.2960i	−0.601388	−	0.436934i
$927$	14.5673	+	44.8334i	0.478452	+	1.47252i
$928$	−1.03192	+	3.17593i	−0.0338745	+	0.104255i
$929$	6.67079			0.218861			0.109431	−	0.993994i	$-0.465097\pi$
$929$	6.67079			0.218861			0.109431	+	0.993994i	$0.465097\pi$
$930$		0			0
$931$	−35.6793			−1.16934
$932$	−1.59042	+	4.89481i	−0.0520959	+	0.160335i
$933$	−16.7590	−	51.5789i	−0.548665	−	1.68862i
$934$	−5.03602	−	3.65889i	−0.164784	−	0.119722i
$935$	−42.1291			−1.37777
$936$	15.5145			0.507107
$937$	−0.375951	−	0.273144i	−0.0122818	−	0.00892324i	0.581627	−	0.813455i	$-0.302416\pi$
$937$	−0.375951	−	0.273144i	−0.0122818	−	0.00892324i	−0.593909	+	0.804532i	$0.702416\pi$
$938$	14.5723	−	10.5874i	0.475802	−	0.345690i
$939$	−19.6032	+	14.2426i	−0.639728	+	0.464789i
$940$	−0.274375	+	0.844440i	−0.00894913	+	0.0275426i
$941$	34.6502	+	25.1748i	1.12956	+	0.820675i	0.985631	−	0.168912i	$-0.0540255\pi$
$941$	34.6502	+	25.1748i	1.12956	+	0.820675i	0.143932	+	0.989588i	$0.454025\pi$
$942$	−18.6907	+	57.5241i	−0.608976	+	1.87423i
$943$	−2.54490	−	7.83239i	−0.0828733	−	0.255058i
$944$	9.35926	−	6.79990i	0.304618	−	0.221318i
$945$	−3.06819	−	9.44292i	−0.0998083	−	0.307178i
$946$	−15.9250	−	49.0123i	−0.517768	−	1.59353i
$947$	18.8646	−	13.7059i	0.613018	−	0.445384i	−0.237458	−	0.971398i	$-0.576314\pi$
$947$	18.8646	−	13.7059i	0.613018	−	0.445384i	0.850476	+	0.526014i	$0.176314\pi$
$948$	3.52141	+	10.8378i	0.114370	+	0.351995i
$949$	−3.73621	+	11.4989i	−0.121282	+	0.373269i
$950$	12.0333	+	8.74269i	0.390411	+	0.283650i
$951$	24.8734	−	76.5526i	0.806577	−	2.48239i
$952$	10.8751	−	7.90119i	0.352463	−	0.256079i
$953$	20.1582	−	14.6458i	0.652988	−	0.474424i	−0.211300	−	0.977421i	$-0.567770\pi$
$953$	20.1582	−	14.6458i	0.652988	−	0.474424i	0.864288	+	0.502998i	$0.167770\pi$
$954$	19.8256	+	14.4041i	0.641876	+	0.466350i
$955$	49.8049			1.61165
$956$	−11.3383			−0.366708
$957$	12.7720	+	9.27940i	0.412860	+	0.299961i
$958$	1.01725	+	3.13077i	0.0328659	+	0.101151i
$959$	3.84938	−	11.8472i	0.124303	−	0.382566i
$960$	−62.4234			−2.01470
$961$		0			0
$962$	9.76256			0.314758
$963$	6.24738	−	19.2275i	0.201319	−	0.619596i
$964$	1.44203	+	4.43812i	0.0464448	+	0.142942i
$965$	44.7822	+	32.5362i	1.44159	+	1.04738i
$966$	−15.8449			−0.509803
$967$	−22.5774			−0.726042			−0.363021	−	0.931781i	$-0.618255\pi$
$967$	−22.5774			−0.726042			−0.363021	+	0.931781i	$0.618255\pi$
$968$	−20.5637	−	14.9404i	−0.660941	−	0.480202i
$969$	−50.9799	+	37.0390i	−1.63771	+	1.18987i
$970$	−11.8963	+	8.64319i	−0.381968	+	0.277516i
$971$	−1.88383	+	5.79784i	−0.0604550	+	0.186061i	−0.976723	−	0.214504i	$-0.931186\pi$
$971$	−1.88383	+	5.79784i	−0.0604550	+	0.186061i	0.916268	+	0.400566i	$0.131186\pi$
$972$	7.42455	+	5.39425i	0.238142	+	0.173021i
$973$	0.119405	−	0.367490i	0.00382794	−	0.0117812i
$974$	8.99210	+	27.6748i	0.288125	+	0.886759i
$975$	4.90505	−	3.56372i	0.157087	−	0.114131i
$976$	−1.98696	−	6.11523i	−0.0636010	−	0.195744i
$977$	−4.16327	−	12.8132i	−0.133195	−	0.409932i	0.862110	−	0.506721i	$-0.169143\pi$
$977$	−4.16327	−	12.8132i	−0.133195	−	0.409932i	−0.995305	+	0.0967896i	$0.969143\pi$
$978$	21.2131	−	15.4122i	0.678321	−	0.492829i
$979$	18.9467	+	58.3119i	0.605538	+	1.86366i
$980$	2.01924	−	6.21460i	0.0645024	−	0.198518i
$981$	43.0188	+	31.2550i	1.37348	+	0.997894i
$982$	−1.92262	+	5.91721i	−0.0613532	+	0.188826i
$983$	15.1770	−	11.0268i	0.484072	−	0.351699i	−0.318828	−	0.947813i	$-0.603289\pi$
$983$	15.1770	−	11.0268i	0.484072	−	0.351699i	0.802900	+	0.596114i	$0.203289\pi$
$984$	13.8018	−	10.0276i	0.439986	−	0.319669i
$985$	13.5202	+	9.82303i	0.430791	+	0.312988i
$986$	6.10630			0.194464
$987$	−2.43283			−0.0774379
$988$	2.84968	+	2.07042i	0.0906605	+	0.0658687i
$989$	−11.4724	−	35.3086i	−0.364803	−	1.12275i
$990$	−18.4974	+	56.9290i	−0.587884	+	1.80932i
$991$	−57.0730			−1.81298			−0.906491	−	0.422225i	$-0.861249\pi$
$991$	−57.0730			−1.81298			−0.906491	+	0.422225i	$0.861249\pi$
$992$		0			0
$993$	−40.8938			−1.29773
$994$	3.48657	−	10.7306i	0.110587	−	0.340353i
$995$	12.5115	+	38.5065i	0.396642	+	1.22074i
$996$	5.46616	+	3.97140i	0.173202	+	0.125838i
$997$	−24.8889			−0.788239			−0.394119	−	0.919059i	$-0.628950\pi$
$997$	−24.8889			−0.788239			−0.394119	+	0.919059i	$0.628950\pi$
$998$	21.6339			0.684810
$999$	−16.3885	−	11.9069i	−0.518508	−	0.376718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.r.628.5		48
31.2	even	5		961.2.a.k.1.5	✓	12
31.3	odd	30		961.2.g.v.816.7		96
31.4	even	5	inner	961.2.d.r.531.5		48
31.5	even	3		961.2.g.v.448.5		96
31.6	odd	6		961.2.g.v.846.5		96
31.7	even	15		961.2.g.v.547.5		96
31.8	even	5	inner	961.2.d.r.388.8		48
31.9	even	15		961.2.g.v.338.8		96
31.10	even	15		961.2.c.k.521.6		24
31.11	odd	30		961.2.g.v.844.5		96
31.12	odd	30		961.2.c.k.439.5		24
31.13	odd	30		961.2.g.v.732.8		96
31.14	even	15		961.2.g.v.235.7		96
31.15	odd	10	inner	961.2.d.r.374.7		48
31.16	even	5	inner	961.2.d.r.374.8		48
31.17	odd	30		961.2.g.v.235.8		96
31.18	even	15		961.2.g.v.732.7		96
31.19	even	15		961.2.c.k.439.6		24
31.20	even	15		961.2.g.v.844.6		96
31.21	odd	30		961.2.c.k.521.5		24
31.22	odd	30		961.2.g.v.338.7		96
31.23	odd	10	inner	961.2.d.r.388.7		48
31.24	odd	30		961.2.g.v.547.6		96
31.25	even	3		961.2.g.v.846.6		96
31.26	odd	6		961.2.g.v.448.6		96
31.27	odd	10	inner	961.2.d.r.531.6		48
31.28	even	15		961.2.g.v.816.8		96
31.29	odd	10		961.2.a.k.1.6	yes	12
31.30	odd	2	inner	961.2.d.r.628.6		48
93.2	odd	10		8649.2.a.bp.1.7		12
93.29	even	10		8649.2.a.bp.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.5	✓	12	31.2	even	5
961.2.a.k.1.6	yes	12	31.29	odd	10
961.2.c.k.439.5		24	31.12	odd	30
961.2.c.k.439.6		24	31.19	even	15
961.2.c.k.521.5		24	31.21	odd	30
961.2.c.k.521.6		24	31.10	even	15
961.2.d.r.374.7		48	31.15	odd	10	inner
961.2.d.r.374.8		48	31.16	even	5	inner
961.2.d.r.388.7		48	31.23	odd	10	inner
961.2.d.r.388.8		48	31.8	even	5	inner
961.2.d.r.531.5		48	31.4	even	5	inner
961.2.d.r.531.6		48	31.27	odd	10	inner
961.2.d.r.628.5		48	1.1	even	1	trivial
961.2.d.r.628.6		48	31.30	odd	2	inner
961.2.g.v.235.7		96	31.14	even	15
961.2.g.v.235.8		96	31.17	odd	30
961.2.g.v.338.7		96	31.22	odd	30
961.2.g.v.338.8		96	31.9	even	15
961.2.g.v.448.5		96	31.5	even	3
961.2.g.v.448.6		96	31.26	odd	6
961.2.g.v.547.5		96	31.7	even	15
961.2.g.v.547.6		96	31.24	odd	30
961.2.g.v.732.7		96	31.18	even	15
961.2.g.v.732.8		96	31.13	odd	30
961.2.g.v.816.7		96	31.3	odd	30
961.2.g.v.816.8		96	31.28	even	15
961.2.g.v.844.5		96	31.11	odd	30
961.2.g.v.844.6		96	31.20	even	15
961.2.g.v.846.5		96	31.6	odd	6
961.2.g.v.846.6		96	31.25	even	3
8649.2.a.bp.1.7		12	93.2	odd	10
8649.2.a.bp.1.8		12	93.29	even	10

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.384764 + 1.18418i) q^{2} +(-0.827744 - 2.54753i) q^{3} +(0.363788 + 0.264307i) q^{4} +2.61876 q^{5} +3.33523 q^{6} +(-0.974496 - 0.708013i) q^{7} +(-2.46761 + 1.79283i) q^{8} +(-3.37771 + 2.45405i) q^{9} +(-1.00760 + 3.10109i) q^{10} +(-3.55723 - 2.58448i) q^{11} +(0.372209 - 1.14554i) q^{12} +(0.376474 + 1.15867i) q^{13} +(1.21337 - 0.881563i) q^{14} +(-2.16766 - 6.67137i) q^{15} +(-0.895675 - 2.75661i) q^{16} +(2.95999 - 2.15056i) q^{17} +(-1.60642 - 4.94406i) q^{18} +(1.98691 - 6.11507i) q^{19} +(0.952672 + 0.692157i) q^{20} +(-0.997053 + 3.06861i) q^{21} +(4.42919 - 3.21800i) q^{22} +(3.19080 - 2.31825i) q^{23} +(6.60984 + 4.80233i) q^{24} +1.85789 q^{25} -1.51693 q^{26} +(2.54648 + 1.85013i) q^{27} +(-0.167377 - 0.515133i) q^{28} +(0.414206 - 1.27479i) q^{29} +8.73416 q^{30} -2.49133 q^{32} +(-3.63957 + 11.2014i) q^{33} +(1.40776 + 4.33263i) q^{34} +(-2.55197 - 1.85411i) q^{35} -1.87740 q^{36} -6.43574 q^{37} +(6.47687 + 4.70572i) q^{38} +(2.64012 - 1.91816i) q^{39} +(-6.46208 + 4.69498i) q^{40} +(0.645251 - 1.98588i) q^{41} +(-3.25017 - 2.36139i) q^{42} +(2.90880 - 8.95237i) q^{43} +(-0.610981 - 1.88040i) q^{44} +(-8.84541 + 6.42657i) q^{45} +(1.51753 + 4.67048i) q^{46} +(0.233002 + 0.717105i) q^{47} +(-6.28115 + 4.56353i) q^{48} +(-1.71476 - 5.27749i) q^{49} +(-0.714848 + 2.20008i) q^{50} +(-7.92873 - 5.76056i) q^{51} +(-0.169288 + 0.521015i) q^{52} +(-3.81371 + 2.77082i) q^{53} +(-3.17068 + 2.30364i) q^{54} +(-9.31552 - 6.76812i) q^{55} +3.67402 q^{56} -17.2230 q^{57} +(1.35022 + 0.980990i) q^{58} +(1.23338 + 3.79596i) q^{59} +(0.974724 - 2.99989i) q^{60} +2.21839 q^{61} +5.02907 q^{63} +(2.74992 - 8.46340i) q^{64} +(0.985895 + 3.03427i) q^{65} +(-11.8642 - 8.61984i) q^{66} +12.0098 q^{67} +1.64522 q^{68} +(-8.54699 - 6.20975i) q^{69} +(3.17751 - 2.30860i) q^{70} +(6.08610 - 4.42181i) q^{71} +(3.93520 - 12.1113i) q^{72} +(8.02884 + 5.83330i) q^{73} +(2.47624 - 7.62109i) q^{74} +(-1.53785 - 4.73302i) q^{75} +(2.33907 - 1.69944i) q^{76} +(1.63666 + 5.03713i) q^{77} +(1.25563 + 3.86443i) q^{78} +(-7.65399 + 5.56095i) q^{79} +(-2.34556 - 7.21888i) q^{80} +(-1.26509 + 3.89355i) q^{81} +(2.10337 + 1.52819i) q^{82} +(-1.73342 + 5.33490i) q^{83} +(-1.17377 + 0.852796i) q^{84} +(7.75149 - 5.63178i) q^{85} +(9.48204 + 6.88910i) q^{86} -3.59043 q^{87} +13.4114 q^{88} +(-11.2812 - 8.19625i) q^{89} +(-4.20683 - 12.9473i) q^{90} +(0.453480 - 1.39567i) q^{91} +1.77351 q^{92} -0.938835 q^{94} +(5.20323 - 16.0139i) q^{95} +(2.06218 + 6.34674i) q^{96} +(3.64843 + 2.65074i) q^{97} +6.90929 q^{98} +18.3578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{4} + 32 q^{5} - 8 q^{7} - 12 q^{8} - 20 q^{9} - 20 q^{10} - 28 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{19} + 20 q^{20} + 48 q^{25} + 20 q^{28} + 96 q^{32} + 40 q^{33} - 56 q^{35} + 160 q^{36}+ \cdots + 16 q^{98}+O(q^{100}) \) 48 * q - 16 * q^4 + 32 * q^5 - 8 * q^7 - 12 * q^8 - 20 * q^9 - 20 * q^10 - 28 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^19 + 20 * q^20 + 48 * q^25 + 20 * q^28 + 96 * q^32 + 40 * q^33 - 56 * q^35 + 160 * q^36 - 36 * q^38 + 16 * q^39 + 16 * q^40 - 32 * q^41 - 16 * q^45 - 48 * q^47 + 20 * q^49 - 20 * q^50 - 16 * q^51 - 32 * q^56 - 40 * q^59 - 32 * q^63 + 28 * q^64 - 24 * q^66 + 64 * q^67 - 24 * q^69 - 12 * q^70 - 72 * q^71 - 36 * q^72 - 36 * q^76 + 104 * q^78 + 20 * q^80 + 36 * q^81 + 4 * q^82 + 256 * q^87 + 44 * q^90 + 64 * q^94 - 40 * q^95 + 8 * q^97 + 16 * q^98

Introduction

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