LMFDB - Embedded newform 525.2.m.c.118.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(118,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("525.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.m (of order $4$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.8
Character	$\chi$	$=$	525.118
Dual form			525.2.m.c.307.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.653796 - 0.653796i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.14510i q^{4} -0.924607i q^{6} +(-0.741188 + 2.53981i) q^{7} +(2.05625 + 2.05625i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.653796 - 0.653796i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.14510i q^{4} -0.924607i q^{6} +(-0.741188 + 2.53981i) q^{7} +(2.05625 + 2.05625i) q^{8} -1.00000i q^{9} -0.746568 q^{11} +(0.809710 + 0.809710i) q^{12} +(4.26864 - 4.26864i) q^{13} +(1.17593 + 2.14510i) q^{14} +0.398534 q^{16} +(5.29845 + 5.29845i) q^{17} +(-0.653796 - 0.653796i) q^{18} -1.17593 q^{19} +(1.27182 + 2.32002i) q^{21} +(-0.488103 + 0.488103i) q^{22} +(3.19815 + 3.19815i) q^{23} +2.90798 q^{24} -5.58164i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.90834 - 0.848736i) q^{28} +2.45636i q^{29} -4.87436i q^{31} +(-3.85195 + 3.85195i) q^{32} +(-0.527903 + 0.527903i) q^{33} +6.92820 q^{34} +1.14510 q^{36} +(-2.05625 + 2.05625i) q^{37} +(-0.768819 + 0.768819i) q^{38} -6.03677i q^{39} -6.92820i q^{41} +(2.34833 + 0.685307i) q^{42} +(-6.64484 - 6.64484i) q^{43} -0.854897i q^{44} +4.18188 q^{46} +(-5.29845 - 5.29845i) q^{47} +(0.281806 - 0.281806i) q^{48} +(-5.90128 - 3.76496i) q^{49} +7.49314 q^{51} +(4.88804 + 4.88804i) q^{52} +(4.89898 + 4.89898i) q^{53} -0.924607 q^{54} +(-6.74657 + 3.69843i) q^{56} +(-0.831509 + 0.831509i) q^{57} +(1.60596 + 1.60596i) q^{58} -12.5098 q^{59} +2.52249i q^{61} +(-3.18683 - 3.18683i) q^{62} +(2.53981 + 0.741188i) q^{63} +5.83384i q^{64} +0.690282i q^{66} +(6.47915 - 6.47915i) q^{67} +(-6.06727 + 6.06727i) q^{68} +4.52287 q^{69} -6.74657 q^{71} +(2.05625 - 2.05625i) q^{72} +(2.47002 - 2.47002i) q^{73} +2.68874i q^{74} -1.34656i q^{76} +(0.553347 - 1.89614i) q^{77} +(-3.94682 - 3.94682i) q^{78} -5.83384i q^{79} -1.00000 q^{81} +(-4.52963 - 4.52963i) q^{82} +(-0.768819 + 0.768819i) q^{83} +(-2.65666 + 1.45636i) q^{84} -8.68874 q^{86} +(1.73691 + 1.73691i) q^{87} +(-1.53513 - 1.53513i) q^{88} +3.69843 q^{89} +(7.67768 + 14.0054i) q^{91} +(-3.66221 + 3.66221i) q^{92} +(-3.44669 - 3.44669i) q^{93} -6.92820 q^{94} +5.44748i q^{96} +(-10.2839 - 10.2839i) q^{97} +(-6.31974 + 1.39672i) q^{98} +0.746568i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) $ 24 * q + 48 * q^11 + 24 * q^16 + 12 * q^21 - 24 * q^36 - 120 * q^46 + 48 * q^51 - 96 * q^56 - 96 * q^71 - 24 * q^81 - 120 * q^86 + 108 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.653796	−	0.653796i	0.462303	−	0.462303i	−0.437106	−	0.899410i	$-0.643997\pi$
$2$	0.653796	−	0.653796i	0.462303	−	0.462303i	0.899410	+	0.437106i	$0.143997\pi$
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.14510i			0.572551i
$5$		0			0
$5$		0			0
$6$		−	0.924607i		−	0.377469i
$7$	−0.741188	+	2.53981i	−0.280143	+	0.959958i
$7$	−0.741188	+	2.53981i	−0.280143	+	0.959958i
$8$	2.05625	+	2.05625i	0.726996	+	0.726996i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−0.746568			−0.225099			−0.112549	−	0.993646i	$-0.535902\pi$
$11$	−0.746568			−0.225099			−0.112549	+	0.993646i	$0.535902\pi$
$12$	0.809710	+	0.809710i	0.233743	+	0.233743i
$13$	4.26864	−	4.26864i	1.18391	−	1.18391i	0.205186	−	0.978723i	$-0.434220\pi$
$13$	4.26864	−	4.26864i	1.18391	−	1.18391i	0.978723	−	0.205186i	$-0.0657798\pi$
$14$	1.17593	+	2.14510i	0.314281	+	0.573303i
$15$		0			0
$16$	0.398534			0.0996336
$17$	5.29845	+	5.29845i	1.28506	+	1.28506i	0.937749	+	0.347313i	$0.112906\pi$
$17$	5.29845	+	5.29845i	1.28506	+	1.28506i	0.347313	+	0.937749i	$0.387094\pi$
$18$	−0.653796	−	0.653796i	−0.154101	−	0.154101i
$19$	−1.17593			−0.269777			−0.134889	−	0.990861i	$-0.543068\pi$
$19$	−1.17593			−0.269777			−0.134889	+	0.990861i	$0.543068\pi$
$20$		0			0
$21$	1.27182	+	2.32002i	0.277534	+	0.506269i
$22$	−0.488103	+	0.488103i	−0.104064	+	0.104064i
$23$	3.19815	+	3.19815i	0.666861	+	0.666861i	0.956988	−	0.290127i	$-0.0936976\pi$
$23$	3.19815	+	3.19815i	0.666861	+	0.666861i	−0.290127	+	0.956988i	$0.593698\pi$
$24$	2.90798			0.593589
$25$		0			0
$26$		−	5.58164i		−	1.09465i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−2.90834	−	0.848736i	−0.549625	−	0.160396i
$29$			2.45636i			0.456135i	0.973645	+	0.228068i	$0.0732407\pi$
$29$			2.45636i			0.456135i	−0.973645	+	0.228068i	$0.926759\pi$
$30$		0			0
$31$		−	4.87436i		−	0.875461i	−0.899106	−	0.437730i	$-0.855782\pi$
$31$		−	4.87436i		−	0.875461i	0.899106	−	0.437730i	$-0.144218\pi$
$32$	−3.85195	+	3.85195i	−0.680935	+	0.680935i
$33$	−0.527903	+	0.527903i	−0.0918962	+	0.0918962i
$34$	6.92820			1.18818
$35$		0			0
$36$	1.14510			0.190850
$37$	−2.05625	+	2.05625i	−0.338046	+	0.338046i	−0.855632	−	0.517585i	$-0.826831\pi$
$37$	−2.05625	+	2.05625i	−0.338046	+	0.338046i	0.517585	+	0.855632i	$0.326831\pi$
$38$	−0.768819	+	0.768819i	−0.124719	+	0.124719i
$39$		−	6.03677i		−	0.966657i
$40$		0			0
$41$		−	6.92820i		−	1.08200i	−0.841021	−	0.541002i	$-0.818045\pi$
$41$		−	6.92820i		−	1.08200i	0.841021	−	0.541002i	$-0.181955\pi$
$42$	2.34833	+	0.685307i	0.362355	+	0.105745i
$43$	−6.64484	−	6.64484i	−1.01333	−	1.01333i	−0.999910	−	0.0134193i	$-0.995728\pi$
$43$	−6.64484	−	6.64484i	−1.01333	−	1.01333i	−0.0134193	−	0.999910i	$-0.504272\pi$
$44$		−	0.854897i		−	0.128881i
$45$		0			0
$46$	4.18188			0.616584
$47$	−5.29845	−	5.29845i	−0.772858	−	0.772858i	0.205747	−	0.978605i	$-0.434038\pi$
$47$	−5.29845	−	5.29845i	−0.772858	−	0.772858i	−0.978605	+	0.205747i	$0.934038\pi$
$48$	0.281806	−	0.281806i	0.0406753	−	0.0406753i
$49$	−5.90128	−	3.76496i	−0.843040	−	0.537851i
$50$		0			0
$51$	7.49314			1.04925
$52$	4.88804	+	4.88804i	0.677849	+	0.677849i
$53$	4.89898	+	4.89898i	0.672927	+	0.672927i	0.958390	−	0.285463i	$-0.0921474\pi$
$53$	4.89898	+	4.89898i	0.672927	+	0.672927i	−0.285463	+	0.958390i	$0.592147\pi$
$54$	−0.924607			−0.125823
$55$		0			0
$56$	−6.74657	+	3.69843i	−0.901548	+	0.494223i
$57$	−0.831509	+	0.831509i	−0.110136	+	0.110136i
$58$	1.60596	+	1.60596i	0.210873	+	0.210873i
$59$	−12.5098			−1.62864			−0.814321	−	0.580414i	$-0.802891\pi$
$59$	−12.5098			−1.62864			−0.814321	+	0.580414i	$0.802891\pi$
$60$		0			0
$61$			2.52249i			0.322972i	0.986875	+	0.161486i	$0.0516287\pi$
$61$			2.52249i			0.322972i	−0.986875	+	0.161486i	$0.948371\pi$
$62$	−3.18683	−	3.18683i	−0.404728	−	0.404728i
$63$	2.53981	+	0.741188i	0.319986	+	0.0933809i
$64$			5.83384i			0.729230i
$65$		0			0
$66$			0.690282i			0.0849678i
$67$	6.47915	−	6.47915i	0.791554	−	0.791554i	−0.190192	−	0.981747i	$-0.560911\pi$
$67$	6.47915	−	6.47915i	0.791554	−	0.791554i	0.981747	+	0.190192i	$0.0609112\pi$
$68$	−6.06727	+	6.06727i	−0.735764	+	0.735764i
$69$	4.52287			0.544490
$70$		0			0
$71$	−6.74657			−0.800670			−0.400335	−	0.916369i	$-0.631106\pi$
$71$	−6.74657			−0.800670			−0.400335	+	0.916369i	$0.631106\pi$
$72$	2.05625	−	2.05625i	0.242332	−	0.242332i
$73$	2.47002	−	2.47002i	0.289094	−	0.289094i	−0.547628	−	0.836722i	$-0.684469\pi$
$73$	2.47002	−	2.47002i	0.289094	−	0.289094i	0.836722	+	0.547628i	$0.184469\pi$
$74$			2.68874i			0.312560i
$75$		0			0
$76$		−	1.34656i		−	0.154461i
$77$	0.553347	−	1.89614i	0.0630598	−	0.216085i
$78$	−3.94682	−	3.94682i	−0.446889	−	0.446889i
$79$		−	5.83384i		−	0.656359i	−0.944615	−	0.328179i	$-0.893565\pi$
$79$		−	5.83384i		−	0.656359i	0.944615	−	0.328179i	$-0.106435\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	−4.52963	−	4.52963i	−0.500214	−	0.500214i
$83$	−0.768819	+	0.768819i	−0.0843888	+	0.0843888i	−0.748041	−	0.663652i	$-0.769005\pi$
$83$	−0.768819	+	0.768819i	−0.0843888	+	0.0843888i	0.663652	+	0.748041i	$0.269005\pi$
$84$	−2.65666	+	1.45636i	−0.289865	+	0.158902i
$85$		0			0
$86$	−8.68874			−0.936931
$87$	1.73691	+	1.73691i	0.186216	+	0.186216i
$88$	−1.53513	−	1.53513i	−0.163646	−	0.163646i
$89$	3.69843			0.392032			0.196016	−	0.980601i	$-0.437199\pi$
$89$	3.69843			0.392032			0.196016	+	0.980601i	$0.437199\pi$
$90$		0			0
$91$	7.67768	+	14.0054i	0.804840	+	1.46817i
$92$	−3.66221	+	3.66221i	−0.381812	+	0.381812i
$93$	−3.44669	−	3.44669i	−0.357405	−	0.357405i
$94$	−6.92820			−0.714590
$95$		0			0
$96$			5.44748i			0.555981i
$97$	−10.2839	−	10.2839i	−1.04417	−	1.04417i	−0.998978	−	0.0451941i	$-0.985609\pi$
$97$	−10.2839	−	10.2839i	−1.04417	−	1.04417i	−0.0451941	−	0.998978i	$-0.514391\pi$
$98$	−6.31974	+	1.39672i	−0.638390	+	0.141090i
$99$			0.746568i			0.0750329i
$100$		0			0
$101$		−	3.69843i		−	0.368007i	−0.982926	−	0.184004i	$-0.941094\pi$
$101$		−	3.69843i		−	0.368007i	0.982926	−	0.184004i	$-0.0589058\pi$
$102$	4.89898	−	4.89898i	0.485071	−	0.485071i
$103$	−1.70120	+	1.70120i	−0.167624	+	0.167624i	−0.785934	−	0.618310i	$-0.787818\pi$
$103$	−1.70120	+	1.70120i	−0.167624	+	0.167624i	0.618310	+	0.785934i	$0.287818\pi$
$104$	17.5548			1.72139
$105$		0			0
$106$	6.40586			0.622192
$107$	11.2953	−	11.2953i	1.09196	−	1.09196i	0.0966367	−	0.995320i	$-0.469192\pi$
$107$	11.2953	−	11.2953i	1.09196	−	1.09196i	0.995320	−	0.0966367i	$-0.0308085\pi$
$108$	0.809710	−	0.809710i	0.0779144	−	0.0779144i
$109$			1.40586i			0.134657i	0.997731	+	0.0673286i	$0.0214476\pi$
$109$			1.40586i			0.134657i	−0.997731	+	0.0673286i	$0.978552\pi$
$110$		0			0
$111$			2.90798i			0.276013i
$112$	−0.295389	+	1.01220i	−0.0279116	+	0.0956441i
$113$	10.2813	+	10.2813i	0.967181	+	0.967181i	0.999478	−	0.0322977i	$-0.0102825\pi$
$113$	10.2813	+	10.2813i	0.967181	+	0.967181i	−0.0322977	+	0.999478i	$0.510282\pi$
$114$			1.08727i			0.101833i
$115$		0			0
$116$	−2.81279			−0.261161
$117$	−4.26864	−	4.26864i	−0.394636	−	0.394636i
$118$	−8.17888	+	8.17888i	−0.752927	+	0.752927i
$119$	−17.3842	+	9.52991i	−1.59361	+	0.873605i
$120$		0			0
$121$	−10.4426			−0.949331
$122$	1.64920	+	1.64920i	0.149311	+	0.149311i
$123$	−4.89898	−	4.89898i	−0.441726	−	0.441726i
$124$	5.58164			0.501246
$125$		0			0
$126$	2.14510	−	1.17593i	0.191101	−	0.104760i
$127$	5.48195	−	5.48195i	0.486444	−	0.486444i	−0.420738	−	0.907182i	$-0.638229\pi$
$127$	5.48195	−	5.48195i	0.486444	−	0.486444i	0.907182	+	0.420738i	$0.138229\pi$
$128$	−3.88976	−	3.88976i	−0.343809	−	0.343809i
$129$	−9.39723			−0.827380
$130$		0			0
$131$			15.3304i			1.33942i	0.742623	+	0.669710i	$0.233581\pi$
$131$			15.3304i			1.33942i	−0.742623	+	0.669710i	$0.766419\pi$
$132$	−0.604504	−	0.604504i	−0.0526153	−	0.0526153i
$133$	0.871587	−	2.98664i	0.0755761	−	0.258975i
$134$		−	8.47208i		−	0.731876i
$135$		0			0
$136$			21.7899i			1.86847i
$137$	−11.4610	+	11.4610i	−0.979177	+	0.979177i	−0.999788	−	0.0206102i	$-0.993439\pi$
$137$	−11.4610	+	11.4610i	−0.979177	+	0.979177i	0.0206102	+	0.999788i	$0.493439\pi$
$138$	2.95703	−	2.95703i	0.251719	−	0.251719i
$139$	12.5098			1.06107			0.530536	−	0.847663i	$-0.321991\pi$
$139$	12.5098			1.06107			0.530536	+	0.847663i	$0.321991\pi$
$140$		0			0
$141$	−7.49314			−0.631036
$142$	−4.41088	+	4.41088i	−0.370153	+	0.370153i
$143$	−3.18683	+	3.18683i	−0.266496	+	0.266496i
$144$		−	0.398534i		−	0.0332112i
$145$		0			0
$146$		−	3.22978i		−	0.267298i
$147$	−6.83506	+	1.51061i	−0.563746	+	0.124593i
$148$	−2.35462	−	2.35462i	−0.193549	−	0.193549i
$149$		−	2.45636i		−	0.201233i	−0.994925	−	0.100617i	$-0.967918\pi$
$149$		−	2.45636i		−	0.201233i	0.994925	−	0.100617i	$-0.0320815\pi$
$150$		0			0
$151$	−12.7833			−1.04029			−0.520147	−	0.854077i	$-0.674123\pi$
$151$	−12.7833			−1.04029			−0.520147	+	0.854077i	$0.674123\pi$
$152$	−2.41801	−	2.41801i	−0.196127	−	0.196127i
$153$	5.29845	−	5.29845i	0.428354	−	0.428354i
$154$	−0.877913	−	1.60147i	−0.0707443	−	0.129050i
$155$		0			0
$156$	6.91273			0.553461
$157$	9.56709	+	9.56709i	0.763537	+	0.763537i	0.976960	−	0.213423i	$-0.0684612\pi$
$157$	9.56709	+	9.56709i	0.763537	+	0.763537i	−0.213423	+	0.976960i	$0.568461\pi$
$158$	−3.81414	−	3.81414i	−0.303437	−	0.303437i
$159$	6.92820			0.549442
$160$		0			0
$161$	−10.4931	+	5.75227i	−0.826975	+	0.453342i
$162$	−0.653796	+	0.653796i	−0.0513670	+	0.0513670i
$163$	10.1744	+	10.1744i	0.796919	+	0.796919i	0.982608	−	0.185689i	$-0.0594518\pi$
$163$	10.1744	+	10.1744i	0.796919	+	0.796919i	−0.185689	+	0.982608i	$0.559452\pi$
$164$	7.93350			0.619503
$165$		0			0
$166$			1.00530i			0.0780265i
$167$	−16.6642	−	16.6642i	−1.28951	−	1.28951i	−0.935083	−	0.354428i	$-0.884675\pi$
$167$	−16.6642	−	16.6642i	−1.28951	−	1.28951i	−0.354428	−	0.935083i	$-0.615325\pi$
$168$	−2.15536	+	7.38573i	−0.166290	+	0.569821i
$169$		−	23.4426i		−	1.80328i
$170$		0			0
$171$			1.17593i			0.0899258i
$172$	7.60903	−	7.60903i	0.580183	−	0.580183i
$173$	6.83609	−	6.83609i	0.519738	−	0.519738i	−0.397754	−	0.917492i	$-0.630210\pi$
$173$	6.83609	−	6.83609i	0.519738	−	0.519738i	0.917492	+	0.397754i	$0.130210\pi$
$174$	2.27117			0.172177
$175$		0			0
$176$	−0.297533			−0.0224274
$177$	−8.84580	+	8.84580i	−0.664891	+	0.664891i
$178$	2.41801	−	2.41801i	0.181238	−	0.181238i
$179$			16.0735i			1.20139i	0.799477	+	0.600697i	$0.205110\pi$
$179$			16.0735i			1.20139i	−0.799477	+	0.600697i	$0.794890\pi$
$180$		0			0
$181$		−	26.6643i		−	1.98194i	−0.134086	−	0.990970i	$-0.542810\pi$
$181$		−	26.6643i		−	1.98194i	0.134086	−	0.990970i	$-0.457190\pi$
$182$	14.1763	+	4.13705i	1.05082	+	0.306658i
$183$	1.78367	+	1.78367i	0.131853	+	0.131853i
$184$			13.1524i			0.969610i
$185$		0			0
$186$	−4.50686			−0.330459
$187$	−3.95565	−	3.95565i	−0.289266	−	0.289266i
$188$	6.06727	−	6.06727i	0.442501	−	0.442501i
$189$	2.32002	−	1.27182i	0.168756	−	0.0925112i
$190$		0			0
$191$	1.89900			0.137407			0.0687034	−	0.997637i	$-0.478114\pi$
$191$	1.89900			0.137407			0.0687034	+	0.997637i	$0.478114\pi$
$192$	4.12515	+	4.12515i	0.297707	+	0.297707i
$193$	3.67423	+	3.67423i	0.264477	+	0.264477i	0.826870	−	0.562393i	$-0.190119\pi$
$193$	3.67423	+	3.67423i	0.264477	+	0.264477i	−0.562393	+	0.826870i	$0.690119\pi$
$194$	−13.4471			−0.965449
$195$		0			0
$196$	4.31126	−	6.75757i	0.307947	−	0.482684i
$197$	6.33446	−	6.33446i	0.451311	−	0.451311i	−0.444478	−	0.895790i	$-0.646611\pi$
$197$	6.33446	−	6.33446i	0.451311	−	0.451311i	0.895790	+	0.444478i	$0.146611\pi$
$198$	0.488103	+	0.488103i	0.0346880	+	0.0346880i
$199$	−8.98205			−0.636721			−0.318360	−	0.947970i	$-0.603132\pi$
$199$	−8.98205			−0.636721			−0.318360	+	0.947970i	$0.603132\pi$
$200$		0			0
$201$		−	9.16290i		−	0.646301i
$202$	−2.41801	−	2.41801i	−0.170131	−	0.170131i
$203$	−6.23870	−	1.82063i	−0.437871	−	0.127783i
$204$			8.58041i			0.600749i
$205$		0			0
$206$			2.22448i			0.154987i
$207$	3.19815	−	3.19815i	0.222287	−	0.222287i
$208$	1.70120	−	1.70120i	0.117957	−	0.117957i
$209$	0.877913			0.0607265
$210$		0			0
$211$	0.442636			0.0304723			0.0152362	−	0.999884i	$-0.495150\pi$
$211$	0.442636			0.0304723			0.0152362	+	0.999884i	$0.495150\pi$
$212$	−5.60983	+	5.60983i	−0.385285	+	0.385285i
$213$	−4.77054	+	4.77054i	−0.326872	+	0.326872i
$214$		−	14.7696i		−	1.00963i
$215$		0			0
$216$		−	2.90798i		−	0.197863i
$217$	12.3799	+	3.61282i	0.840406	+	0.245254i
$218$	0.919147	+	0.919147i	0.0622525	+	0.0622525i
$219$		−	3.49314i		−	0.236044i
$220$		0			0
$221$	45.2344			3.04279
$222$	1.90123	+	1.90123i	0.127602	+	0.127602i
$223$	6.32825	−	6.32825i	0.423771	−	0.423771i	−0.462729	−	0.886500i	$-0.653130\pi$
$223$	6.32825	−	6.32825i	0.423771	−	0.423771i	0.886500	+	0.462729i	$0.153130\pi$
$224$	−6.92820	−	12.6382i	−0.462910	−	0.844428i
$225$		0			0
$226$	13.4437			0.894262
$227$	3.95565	+	3.95565i	0.262546	+	0.262546i	0.826088	−	0.563542i	$-0.190562\pi$
$227$	3.95565	+	3.95565i	0.262546	+	0.262546i	−0.563542	+	0.826088i	$0.690562\pi$
$228$	−0.952164	−	0.952164i	−0.0630586	−	0.0630586i
$229$	14.1544			0.935351			0.467675	−	0.883900i	$-0.345092\pi$
$229$	14.1544			0.935351			0.467675	+	0.883900i	$0.345092\pi$
$230$		0			0
$231$	−0.949499	−	1.73205i	−0.0624725	−	0.113961i
$232$	−5.05091	+	5.05091i	−0.331608	+	0.331608i
$233$	−20.4106	−	20.4106i	−1.33714	−	1.33714i	−0.898814	−	0.438330i	$-0.855570\pi$
$233$	−20.4106	−	20.4106i	−1.33714	−	1.33714i	−0.438330	−	0.898814i	$-0.644430\pi$
$234$	−5.58164			−0.364883
$235$		0			0
$236$		−	14.3251i		−	0.932482i
$237$	−4.12515	−	4.12515i	−0.267957	−	0.267957i
$238$	−5.13510	+	17.5963i	−0.332859	+	1.14060i
$239$			14.9863i			0.969381i	0.874686	+	0.484691i	$0.161068\pi$
$239$			14.9863i			0.969381i	−0.874686	+	0.484691i	$0.838932\pi$
$240$		0			0
$241$		−	7.63549i		−	0.491845i	−0.969290	−	0.245922i	$-0.920909\pi$
$241$		−	7.63549i		−	0.491845i	0.969290	−	0.245922i	$-0.0790909\pi$
$242$	−6.82735	+	6.82735i	−0.438879	+	0.438879i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−2.88852			−0.184918
$245$		0			0
$246$	−6.40586			−0.408423
$247$	−5.01963	+	5.01963i	−0.319392	+	0.319392i
$248$	10.0229	−	10.0229i	0.636456	−	0.636456i
$249$			1.08727i			0.0689032i
$250$		0			0
$251$		−	15.3304i		−	0.967644i	−0.875167	−	0.483822i	$-0.839248\pi$
$251$		−	15.3304i		−	0.967644i	0.875167	−	0.483822i	$-0.160752\pi$
$252$	−0.848736	+	2.90834i	−0.0534654	+	0.183208i
$253$	−2.38764	−	2.38764i	−0.150110	−	0.150110i
$254$		−	7.16815i		−	0.449770i
$255$		0			0
$256$	−16.7539			−1.04712
$257$	19.0822	+	19.0822i	1.19031	+	1.19031i	0.976979	+	0.213334i	$0.0684323\pi$
$257$	19.0822	+	19.0822i	1.19031	+	1.19031i	0.213334	+	0.976979i	$0.431568\pi$
$258$	−6.14387	+	6.14387i	−0.382500	+	0.382500i
$259$	−3.69843	−	6.74657i	−0.229809	−	0.419211i
$260$		0			0
$261$	2.45636			0.152045
$262$	10.0229	+	10.0229i	0.619218	+	0.619218i
$263$	9.76015	+	9.76015i	0.601837	+	0.601837i	0.940800	−	0.338963i	$-0.110076\pi$
$263$	9.76015	+	9.76015i	0.601837	+	0.601837i	−0.338963	+	0.940800i	$0.610076\pi$
$264$	−2.17101			−0.133616
$265$		0			0
$266$	−1.38282	−	2.52249i	−0.0847859	−	0.154664i
$267$	2.61518	−	2.61518i	0.160047	−	0.160047i
$268$	7.41929	+	7.41929i	0.453206	+	0.453206i
$269$	−4.57634			−0.279024			−0.139512	−	0.990220i	$-0.544553\pi$
$269$	−4.57634			−0.279024			−0.139512	+	0.990220i	$0.544553\pi$
$270$		0			0
$271$		−	6.05029i		−	0.367529i	−0.982970	−	0.183764i	$-0.941172\pi$
$271$		−	6.05029i		−	0.367529i	0.982970	−	0.183764i	$-0.0588284\pi$
$272$	2.11161	+	2.11161i	0.128035	+	0.128035i
$273$	15.3323	+	4.47438i	0.927951	+	0.270802i
$274$			14.9863i			0.905354i
$275$		0			0
$276$			5.17915i			0.311748i
$277$	−11.3403	+	11.3403i	−0.681374	+	0.681374i	−0.960310	−	0.278936i	$-0.910018\pi$
$277$	−11.3403	+	11.3403i	−0.681374	+	0.681374i	0.278936	+	0.960310i	$0.410018\pi$
$278$	8.17888	−	8.17888i	0.490537	−	0.490537i
$279$	−4.87436			−0.291820
$280$		0			0
$281$	28.1976			1.68213			0.841064	−	0.540936i	$-0.181930\pi$
$281$	28.1976			1.68213			0.841064	+	0.540936i	$0.181930\pi$
$282$	−4.89898	+	4.89898i	−0.291730	+	0.291730i
$283$	−20.1120	+	20.1120i	−1.19553	+	1.19553i	−0.220043	+	0.975490i	$0.570620\pi$
$283$	−20.1120	+	20.1120i	−1.19553	+	1.19553i	−0.975490	+	0.220043i	$0.929380\pi$
$284$		−	7.72551i		−	0.458425i
$285$		0			0
$286$			4.16708i			0.246404i
$287$	17.5963	+	5.13510i	1.03868	+	0.303115i
$288$	3.85195	+	3.85195i	0.226978	+	0.226978i
$289$			39.1471i			2.30277i
$290$		0			0
$291$	−14.5436			−0.852563
$292$	2.82843	+	2.82843i	0.165521	+	0.165521i
$293$	3.18683	−	3.18683i	0.186177	−	0.186177i	−0.607864	−	0.794041i	$-0.707973\pi$
$293$	3.18683	−	3.18683i	0.186177	−	0.186177i	0.794041	+	0.607864i	$0.207973\pi$
$294$	−3.48110	+	5.45636i	−0.203022	+	0.318222i
$295$		0			0
$296$	−8.45636			−0.491516
$297$	0.527903	+	0.527903i	0.0306321	+	0.0306321i
$298$	−1.60596	−	1.60596i	−0.0930307	−	0.0930307i
$299$	27.3035			1.57901
$300$		0			0
$301$	21.8017	−	11.9516i	1.25663	−	0.688877i
$302$	−8.35769	+	8.35769i	−0.480931	+	0.480931i
$303$	−2.61518	−	2.61518i	−0.150238	−	0.150238i
$304$	−0.468649			−0.0268789
$305$		0			0
$306$		−	6.92820i		−	0.396059i
$307$	−3.49982	−	3.49982i	−0.199746	−	0.199746i	0.600145	−	0.799891i	$-0.295109\pi$
$307$	−3.49982	−	3.49982i	−0.199746	−	0.199746i	−0.799891	+	0.600145i	$0.795109\pi$
$308$	2.17128	+	0.633640i	0.123720	+	0.0361050i
$309$			2.40586i			0.136865i
$310$		0			0
$311$			17.6822i			1.00267i	0.865254	+	0.501333i	$0.167157\pi$
$311$			17.6822i			1.00267i	−0.865254	+	0.501333i	$0.832843\pi$
$312$	12.4131	−	12.4131i	0.702756	−	0.702756i
$313$	7.09707	−	7.09707i	0.401150	−	0.401150i	−0.477488	−	0.878638i	$-0.658453\pi$
$313$	7.09707	−	7.09707i	0.401150	−	0.401150i	0.878638	+	0.477488i	$0.158453\pi$
$314$	12.5098			0.705971
$315$		0			0
$316$	6.68035			0.375799
$317$	18.9133	−	18.9133i	1.06228	−	1.06228i	0.0643487	−	0.997927i	$-0.479503\pi$
$317$	18.9133	−	18.9133i	1.06228	−	1.06228i	0.997927	−	0.0643487i	$-0.0204970\pi$
$318$	4.52963	−	4.52963i	0.254009	−	0.254009i
$319$		−	1.83384i		−	0.102675i
$320$		0			0
$321$		−	15.9739i		−	0.891579i
$322$	−3.09956	+	10.6212i	−0.172732	+	0.591895i
$323$	−6.23061	−	6.23061i	−0.346681	−	0.346681i
$324$		−	1.14510i		−	0.0636168i
$325$		0			0
$326$	13.3039			0.736837
$327$	0.994095	+	0.994095i	0.0549736	+	0.0549736i
$328$	14.2461	−	14.2461i	0.786612	−	0.786612i
$329$	17.3842	−	9.52991i	0.958422	−	0.525401i
$330$		0			0
$331$	−19.2260			−1.05676			−0.528378	−	0.849009i	$-0.677199\pi$
$331$	−19.2260			−1.05676			−0.528378	+	0.849009i	$0.677199\pi$
$332$	−0.880377	−	0.880377i	−0.0483169	−	0.0483169i
$333$	2.05625	+	2.05625i	0.112682	+	0.112682i
$334$	−21.7899			−1.19229
$335$		0			0
$336$	0.506864	+	0.924607i	0.0276517	+	0.0504414i
$337$	−4.77833	+	4.77833i	−0.260292	+	0.260292i	−0.825173	−	0.564881i	$-0.808922\pi$
$337$	−4.77833	+	4.77833i	−0.260292	+	0.260292i	0.564881	+	0.825173i	$0.308922\pi$
$338$	−15.3267	−	15.3267i	−0.833662	−	0.833662i
$339$	14.5399			0.789700
$340$		0			0
$341$			3.63904i			0.197065i
$342$	0.768819	+	0.768819i	0.0415730	+	0.0415730i
$343$	13.9362	−	12.1976i	0.752486	−	0.658608i
$344$		−	27.3270i		−	1.47337i
$345$		0			0
$346$		−	8.93881i		−	0.480553i
$347$	−13.7826	+	13.7826i	−0.739888	+	0.739888i	−0.972556	−	0.232668i	$-0.925254\pi$
$347$	−13.7826	+	13.7826i	−0.739888	+	0.739888i	0.232668	+	0.972556i	$0.425254\pi$
$348$	−1.98894	+	1.98894i	−0.106618	+	0.106618i
$349$	14.3931			0.770443			0.385221	−	0.922824i	$-0.374125\pi$
$349$	14.3931			0.770443			0.385221	+	0.922824i	$0.374125\pi$
$350$		0			0
$351$	−6.03677			−0.322219
$352$	2.87574	−	2.87574i	0.153278	−	0.153278i
$353$	−9.82808	+	9.82808i	−0.523096	+	0.523096i	−0.918505	−	0.395409i	$-0.870603\pi$
$353$	−9.82808	+	9.82808i	−0.523096	+	0.523096i	0.395409	+	0.918505i	$0.370603\pi$
$354$			11.5667i			0.614762i
$355$		0			0
$356$			4.23508i			0.224459i
$357$	−5.55382	+	19.0312i	−0.293939	+	1.00724i
$358$	10.5088	+	10.5088i	0.555408	+	0.555408i
$359$		−	18.7466i		−	0.989406i	−0.869062	−	0.494703i	$-0.835277\pi$
$359$		−	18.7466i		−	0.989406i	0.869062	−	0.494703i	$-0.164723\pi$
$360$		0			0
$361$	−17.6172			−0.927220
$362$	−17.4330	−	17.4330i	−0.916257	−	0.916257i
$363$	−7.38406	+	7.38406i	−0.387563	+	0.387563i
$364$	−16.0376	+	8.79173i	−0.840601	+	0.460812i
$365$		0			0
$366$	2.33231			0.121912
$367$	−23.7612	−	23.7612i	−1.24033	−	1.24033i	−0.959865	−	0.280461i	$-0.909513\pi$
$367$	−23.7612	−	23.7612i	−1.24033	−	1.24033i	−0.280461	−	0.959865i	$-0.590487\pi$
$368$	1.27457	+	1.27457i	0.0664418	+	0.0664418i
$369$	−6.92820			−0.360668
$370$		0			0
$371$	−16.0735	+	8.81142i	−0.834497	+	0.457466i
$372$	3.94682	−	3.94682i	0.204633	−	0.204633i
$373$	5.83433	+	5.83433i	0.302090	+	0.302090i	0.841831	−	0.539741i	$-0.181478\pi$
$373$	5.83433	+	5.83433i	0.302090	+	0.302090i	−0.539741	+	0.841831i	$0.681478\pi$
$374$	−5.17238			−0.267457
$375$		0			0
$376$		−	21.7899i		−	1.12373i
$377$	10.4853	+	10.4853i	0.540022	+	0.540022i
$378$	0.685307	−	2.34833i	0.0352484	−	0.120785i
$379$		−	4.60879i		−	0.236738i	−0.992970	−	0.118369i	$-0.962233\pi$
$379$		−	4.60879i		−	0.236738i	0.992970	−	0.118369i	$-0.0377665\pi$
$380$		0			0
$381$		−	7.75265i		−	0.397180i
$382$	1.24156	−	1.24156i	0.0635236	−	0.0635236i
$383$	0.306401	−	0.306401i	0.0156564	−	0.0156564i	−0.699235	−	0.714892i	$-0.746476\pi$
$383$	0.306401	−	0.306401i	0.0156564	−	0.0156564i	0.714892	+	0.699235i	$0.246476\pi$
$384$	−5.50095			−0.280719
$385$		0			0
$386$	4.80440			0.244537
$387$	−6.64484	+	6.64484i	−0.337776	+	0.337776i
$388$	11.7761	−	11.7761i	0.597842	−	0.597842i
$389$		−	9.26809i		−	0.469911i	−0.972006	−	0.234955i	$-0.924506\pi$
$389$		−	9.26809i		−	0.469911i	0.972006	−	0.234955i	$-0.0754944\pi$
$390$		0			0
$391$			33.8905i			1.71392i
$392$	−4.39283	−	19.8762i	−0.221871	−	1.00390i
$393$	10.8402	+	10.8402i	0.546816	+	0.546816i
$394$		−	8.28288i		−	0.417285i
$395$		0			0
$396$	−0.854897			−0.0429602
$397$	20.1120	+	20.1120i	1.00939	+	1.00939i	0.999955	+	0.00943590i	$0.00300358\pi$
$397$	20.1120	+	20.1120i	1.00939	+	1.00939i	0.00943590	+	0.999955i	$0.496996\pi$
$398$	−5.87242	+	5.87242i	−0.294358	+	0.294358i
$399$	−1.49557	−	2.72818i	−0.0748722	−	0.136580i
$400$		0			0
$401$	5.03677			0.251524			0.125762	−	0.992060i	$-0.459862\pi$
$401$	5.03677			0.251524			0.125762	+	0.992060i	$0.459862\pi$
$402$	−5.99067	−	5.99067i	−0.298787	−	0.298787i
$403$	−20.8069	−	20.8069i	−1.03647	−	1.03647i
$404$	4.23508			0.210703
$405$		0			0
$406$	−5.26915	+	2.88852i	−0.261504	+	0.143355i
$407$	1.53513	−	1.53513i	0.0760938	−	0.0760938i
$408$	15.4078	+	15.4078i	0.762799	+	0.762799i
$409$	−19.7361			−0.975886			−0.487943	−	0.872876i	$-0.662253\pi$
$409$	−19.7361			−0.975886			−0.487943	+	0.872876i	$0.662253\pi$
$410$		0			0
$411$			16.2083i			0.799495i
$412$	−1.94805	−	1.94805i	−0.0959736	−	0.0959736i
$413$	9.27215	−	31.7726i	0.456252	−	1.56343i
$414$		−	4.18188i		−	0.205528i
$415$		0			0
$416$			32.8852i			1.61233i
$417$	8.84580	−	8.84580i	0.433180	−	0.433180i
$418$	0.573976	−	0.573976i	0.0280741	−	0.0280741i
$419$	−2.22448			−0.108673			−0.0543364	−	0.998523i	$-0.517304\pi$
$419$	−2.22448			−0.108673			−0.0543364	+	0.998523i	$0.517304\pi$
$420$		0			0
$421$	−22.0230			−1.07334			−0.536669	−	0.843793i	$-0.680318\pi$
$421$	−22.0230			−1.07334			−0.536669	+	0.843793i	$0.680318\pi$
$422$	0.289393	−	0.289393i	0.0140874	−	0.0140874i
$423$	−5.29845	+	5.29845i	−0.257619	+	0.257619i
$424$			20.1471i			0.978429i
$425$		0			0
$426$			6.23792i			0.302228i
$427$	−6.40666	−	1.86964i	−0.310040	−	0.0904784i
$428$	12.9343	+	12.9343i	0.625201	+	0.625201i
$429$			4.50686i			0.217593i
$430$		0			0
$431$	25.8990			1.24751			0.623755	−	0.781620i	$-0.285606\pi$
$431$	25.8990			1.24751			0.623755	+	0.781620i	$0.285606\pi$
$432$	−0.281806	−	0.281806i	−0.0135584	−	0.0135584i
$433$	−19.5900	+	19.5900i	−0.941436	+	0.941436i	−0.998378	−	0.0569417i	$-0.981865\pi$
$433$	−19.5900	+	19.5900i	−0.941436	+	0.941436i	0.0569417	+	0.998378i	$0.481865\pi$
$434$	10.4560	−	5.73191i	0.501904	−	0.275141i
$435$		0			0
$436$	−1.60986			−0.0770981
$437$	−3.76081	−	3.76081i	−0.179904	−	0.179904i
$438$	−2.28380	−	2.28380i	−0.109124	−	0.109124i
$439$	17.2568			0.823623			0.411811	−	0.911269i	$-0.364896\pi$
$439$	17.2568			0.823623			0.411811	+	0.911269i	$0.364896\pi$
$440$		0			0
$441$	−3.76496	+	5.90128i	−0.179284	+	0.281013i
$442$	29.5740	−	29.5740i	1.40669	−	1.40669i
$443$	−1.16594	−	1.16594i	−0.0553955	−	0.0553955i	0.678866	−	0.734262i	$-0.262472\pi$
$443$	−1.16594	−	1.16594i	−0.0553955	−	0.0553955i	−0.734262	+	0.678866i	$0.762472\pi$
$444$	−3.32994			−0.158032
$445$		0			0
$446$		−	8.27477i		−	0.391822i
$447$	−1.73691	−	1.73691i	−0.0821531	−	0.0821531i
$448$	−14.8169	−	4.32397i	−0.700031	−	0.204289i
$449$			17.0368i			0.804015i	0.915636	+	0.402008i	$0.131687\pi$
$449$			17.0368i			0.804015i	−0.915636	+	0.402008i	$0.868313\pi$
$450$		0			0
$451$			5.17238i			0.243558i
$452$	−11.7731	+	11.7731i	−0.553761	+	0.553761i
$453$	−9.03919	+	9.03919i	−0.424698	+	0.424698i
$454$	5.17238			0.242752
$455$		0			0
$456$	−3.41959			−0.160137
$457$	−26.8069	+	26.8069i	−1.25397	+	1.25397i	−0.300052	+	0.953923i	$0.597004\pi$
$457$	−26.8069	+	26.8069i	−1.25397	+	1.25397i	−0.953923	+	0.300052i	$0.902996\pi$
$458$	9.25410	−	9.25410i	0.432416	−	0.432416i
$459$		−	7.49314i		−	0.349750i
$460$		0			0
$461$			33.4218i			1.55661i	0.627886	+	0.778305i	$0.283920\pi$
$461$			33.4218i			1.55661i	−0.627886	+	0.778305i	$0.716080\pi$
$462$	−1.75319	−	0.511629i	−0.0815656	−	0.0238031i
$463$	−14.8626	−	14.8626i	−0.690725	−	0.690725i	0.271666	−	0.962391i	$-0.412425\pi$
$463$	−14.8626	−	14.8626i	−0.690725	−	0.690725i	−0.962391	+	0.271666i	$0.912425\pi$
$464$			0.978945i			0.0454464i
$465$		0			0
$466$	−26.6887			−1.23633
$467$	1.34279	+	1.34279i	0.0621371	+	0.0621371i	0.737492	−	0.675355i	$-0.236010\pi$
$467$	1.34279	+	1.34279i	0.0621371	+	0.0621371i	−0.675355	+	0.737492i	$0.736010\pi$
$468$	4.88804	−	4.88804i	0.225950	−	0.225950i
$469$	11.6536	+	21.2581i	0.538111	+	0.981607i
$470$		0			0
$471$	13.5299			0.623425
$472$	−25.7234	−	25.7234i	−1.18402	−	1.18402i
$473$	4.96083	+	4.96083i	0.228099	+	0.228099i
$474$	−5.39401			−0.247755
$475$		0			0
$476$	−10.9127	−	19.9067i	−0.500184	−	0.912422i
$477$	4.89898	−	4.89898i	0.224309	−	0.224309i
$478$	9.79796	+	9.79796i	0.448148	+	0.448148i
$479$	−17.2136			−0.786508			−0.393254	−	0.919430i	$-0.628651\pi$
$479$	−17.2136			−0.786508			−0.393254	+	0.919430i	$0.628651\pi$
$480$		0			0
$481$			17.5548i			0.800431i
$482$	−4.99205	−	4.99205i	−0.227381	−	0.227381i
$483$	−3.35230	+	11.4872i	−0.152535	+	0.522687i
$484$		−	11.9579i		−	0.543540i
$485$		0			0
$486$			0.924607i			0.0419410i
$487$	18.8923	−	18.8923i	0.856092	−	0.856092i	−0.134784	−	0.990875i	$-0.543034\pi$
$487$	18.8923	−	18.8923i	0.856092	−	0.856092i	0.990875	+	0.134784i	$0.0430339\pi$
$488$	−5.18689	+	5.18689i	−0.234799	+	0.234799i
$489$	14.3887			0.650682
$490$		0			0
$491$	−18.9947			−0.857217			−0.428609	−	0.903490i	$-0.640996\pi$
$491$	−18.9947			−0.857217			−0.428609	+	0.903490i	$0.640996\pi$
$492$	5.60983	−	5.60983i	0.252911	−	0.252911i
$493$	−13.0149	+	13.0149i	−0.586162	+	0.586162i
$494$			6.56363i			0.295312i
$495$		0			0
$496$		−	1.94260i		−	0.0872253i
$497$	5.00048	−	17.1350i	0.224302	−	0.768610i
$498$	0.710855	+	0.710855i	0.0318542	+	0.0318542i
$499$		−	5.52991i		−	0.247553i	−0.992310	−	0.123776i	$-0.960499\pi$
$499$		−	5.52991i		−	0.247553i	0.992310	−	0.123776i	$-0.0395006\pi$
$500$		0			0
$501$	−23.5667			−1.05288
$502$	−10.0229	−	10.0229i	−0.447345	−	0.447345i
$503$	−6.37367	+	6.37367i	−0.284188	+	0.284188i	−0.834777	−	0.550589i	$-0.814403\pi$
$503$	−6.37367	+	6.37367i	−0.284188	+	0.284188i	0.550589	+	0.834777i	$0.314403\pi$
$504$	3.69843	+	6.74657i	0.164741	+	0.300516i
$505$		0			0
$506$	−3.12206			−0.138792
$507$	−16.5764	−	16.5764i	−0.736186	−	0.736186i
$508$	6.27740	+	6.27740i	0.278514	+	0.278514i
$509$	−12.5098			−0.554489			−0.277245	−	0.960799i	$-0.589421\pi$
$509$	−12.5098			−0.554489			−0.277245	+	0.960799i	$0.589421\pi$
$510$		0			0
$511$	4.44264	+	8.10414i	0.196531	+	0.358506i
$512$	−3.17411	+	3.17411i	−0.140277	+	0.140277i
$513$	0.831509	+	0.831509i	0.0367120	+	0.0367120i
$514$	24.9517			1.10057
$515$		0			0
$516$		−	10.7608i		−	0.473717i
$517$	3.95565	+	3.95565i	0.173969	+	0.173969i
$518$	−6.82889	−	1.99286i	−0.300044	−	0.0875613i
$519$		−	9.66769i		−	0.424364i
$520$		0			0
$521$		−	16.2083i		−	0.710097i	−0.934848	−	0.355049i	$-0.884464\pi$
$521$		−	16.2083i		−	0.710097i	0.934848	−	0.355049i	$-0.115536\pi$
$522$	1.60596	−	1.60596i	0.0702909	−	0.0702909i
$523$	−15.2760	+	15.2760i	−0.667971	+	0.667971i	−0.957246	−	0.289275i	$-0.906586\pi$
$523$	−15.2760	+	15.2760i	−0.667971	+	0.667971i	0.289275	+	0.957246i	$0.406586\pi$
$524$	−17.5548			−0.766886
$525$		0			0
$526$	12.7623			0.556462
$527$	25.8265	−	25.8265i	1.12502	−	1.12502i
$528$	−0.210388	+	0.210388i	−0.00915595	+	0.00915595i
$529$		−	2.54364i		−	0.110593i
$530$		0			0
$531$			12.5098i			0.542881i
$532$	3.42001	+	0.998056i	0.148276	+	0.0432712i
$533$	−29.5740	−	29.5740i	−1.28099	−	1.28099i
$534$		−	3.41959i		−	0.147980i
$535$		0			0
$536$	26.6456			1.15091
$537$	11.3657	+	11.3657i	0.490467	+	0.490467i
$538$	−2.99199	+	2.99199i	−0.128994	+	0.128994i
$539$	4.40571	+	2.81080i	0.189767	+	0.121070i
$540$		0			0
$541$	18.7412			0.805749			0.402874	−	0.915255i	$-0.368011\pi$
$541$	18.7412			0.805749			0.402874	+	0.915255i	$0.368011\pi$
$542$	−3.95565	−	3.95565i	−0.169910	−	0.169910i
$543$	−18.8545	−	18.8545i	−0.809123	−	0.809123i
$544$	−40.8187			−1.75009
$545$		0			0
$546$	12.9495	−	7.09883i	0.554187	−	0.303802i
$547$	−13.6589	+	13.6589i	−0.584012	+	0.584012i	−0.936003	−	0.351992i	$-0.885505\pi$
$547$	−13.6589	+	13.6589i	−0.584012	+	0.584012i	0.351992	+	0.936003i	$0.385505\pi$
$548$	−13.1240	−	13.1240i	−0.560629	−	0.560629i
$549$	2.52249			0.107657
$550$		0			0
$551$		−	2.88852i		−	0.123055i
$552$	9.30017	+	9.30017i	0.395842	+	0.395842i
$553$	14.8169	+	4.32397i	0.630077	+	0.183874i
$554$			14.8285i			0.630003i
$555$		0			0
$556$			14.3251i			0.607518i
$557$	7.45231	−	7.45231i	0.315765	−	0.315765i	−0.531373	−	0.847138i	$-0.678324\pi$
$557$	7.45231	−	7.45231i	0.315765	−	0.315765i	0.847138	+	0.531373i	$0.178324\pi$
$558$	−3.18683	+	3.18683i	−0.134909	+	0.134909i
$559$	−56.7289			−2.39938
$560$		0			0
$561$	−5.59414			−0.236185
$562$	18.4355	−	18.4355i	0.777653	−	0.777653i
$563$	−31.9855	+	31.9855i	−1.34803	+	1.34803i	−0.460229	+	0.887800i	$0.652233\pi$
$563$	−31.9855	+	31.9855i	−1.34803	+	1.34803i	−0.887800	+	0.460229i	$0.847767\pi$
$564$		−	8.58041i		−	0.361300i
$565$		0			0
$566$			26.2982i			1.10540i
$567$	0.741188	−	2.53981i	0.0311270	−	0.106662i
$568$	−13.8727	−	13.8727i	−0.582084	−	0.582084i
$569$		−	3.13777i		−	0.131542i	−0.997835	−	0.0657712i	$-0.979049\pi$
$569$		−	3.13777i		−	0.131542i	0.997835	−	0.0657712i	$-0.0209507\pi$
$570$		0			0
$571$	11.5951			0.485238			0.242619	−	0.970122i	$-0.421993\pi$
$571$	11.5951			0.485238			0.242619	+	0.970122i	$0.421993\pi$
$572$	−3.64925	−	3.64925i	−0.152583	−	0.152583i
$573$	1.34279	−	1.34279i	0.0560961	−	0.0560961i
$574$	14.8617	−	8.14709i	0.620316	−	0.340053i
$575$		0			0
$576$	5.83384			0.243077
$577$	7.09707	+	7.09707i	0.295455	+	0.295455i	0.839231	−	0.543776i	$-0.183006\pi$
$577$	7.09707	+	7.09707i	0.295455	+	0.295455i	−0.543776	+	0.839231i	$0.683006\pi$
$578$	25.5942	+	25.5942i	1.06458	+	1.06458i
$579$	5.19615			0.215945
$580$		0			0
$581$	−1.38282	−	2.52249i	−0.0573689	−	0.104651i
$582$	−9.50857	+	9.50857i	−0.394143	+	0.394143i
$583$	−3.65742	−	3.65742i	−0.151475	−	0.151475i
$584$	10.1580			0.420340
$585$		0			0
$586$		−	4.16708i		−	0.172140i
$587$	10.9033	+	10.9033i	0.450027	+	0.450027i	0.895363	−	0.445336i	$-0.146916\pi$
$587$	10.9033	+	10.9033i	0.450027	+	0.450027i	−0.445336	+	0.895363i	$0.646916\pi$
$588$	−1.72980	−	7.82685i	−0.0713359	−	0.322774i
$589$			5.73191i			0.236179i
$590$		0			0
$591$		−	8.95827i		−	0.368494i
$592$	−0.819488	+	0.819488i	−0.0336808	+	0.0336808i
$593$	−10.5969	+	10.5969i	−0.435162	+	0.435162i	−0.890380	−	0.455218i	$-0.849561\pi$
$593$	−10.5969	+	10.5969i	−0.435162	+	0.435162i	0.455218	+	0.890380i	$0.349561\pi$
$594$	0.690282			0.0283226
$595$		0			0
$596$	2.81279			0.115216
$597$	−6.35127	+	6.35127i	−0.259940	+	0.259940i
$598$	17.8509	−	17.8509i	0.729979	−	0.729979i
$599$			0.0926102i			0.00378395i	0.999998	+	0.00189198i	$0.000602235\pi$
$599$			0.0926102i			0.00378395i	−0.999998	+	0.00189198i	$0.999398\pi$
$600$		0			0
$601$		−	25.6590i		−	1.04665i	−0.852133	−	0.523326i	$-0.824691\pi$
$601$		−	25.6590i		−	1.04665i	0.852133	−	0.523326i	$-0.175309\pi$
$602$	6.43999	−	22.0678i	0.262474	−	0.899415i
$603$	−6.47915	−	6.47915i	−0.263851	−	0.263851i
$604$		−	14.6382i		−	0.595622i
$605$		0			0
$606$	−3.41959			−0.138911
$607$	−11.0073	−	11.0073i	−0.446773	−	0.446773i	0.447507	−	0.894280i	$-0.352312\pi$
$607$	−11.0073	−	11.0073i	−0.446773	−	0.446773i	−0.894280	+	0.447507i	$0.852312\pi$
$608$	4.52963	−	4.52963i	0.183701	−	0.183701i
$609$	−5.69880	+	3.12405i	−0.230927	+	0.126593i
$610$		0			0
$611$	−45.2344			−1.82999
$612$	6.06727	+	6.06727i	0.245255	+	0.245255i
$613$	6.16876	+	6.16876i	0.249154	+	0.249154i	0.820623	−	0.571469i	$-0.193626\pi$
$613$	6.16876	+	6.16876i	0.249154	+	0.249154i	−0.571469	+	0.820623i	$0.693626\pi$
$614$	−4.57634			−0.184686
$615$		0			0
$616$	5.03677	−	2.76113i	0.202937	−	0.111249i
$617$	−27.9729	+	27.9729i	−1.12615	+	1.12615i	−0.135347	+	0.990798i	$0.543215\pi$
$617$	−27.9729	+	27.9729i	−1.12615	+	1.12615i	−0.990798	+	0.135347i	$0.956785\pi$
$618$	1.57294	+	1.57294i	0.0632730	+	0.0632730i
$619$	28.0788			1.12858			0.564292	−	0.825575i	$-0.309149\pi$
$619$	28.0788			1.12858			0.564292	+	0.825575i	$0.309149\pi$
$620$		0			0
$621$		−	4.52287i		−	0.181497i
$622$	11.5606	+	11.5606i	0.463536	+	0.463536i
$623$	−2.74123	+	9.39330i	−0.109825	+	0.376335i
$624$		−	2.40586i		−	0.0963116i
$625$		0			0
$626$		−	9.28007i		−	0.370906i
$627$	0.620778	−	0.620778i	0.0247915	−	0.0247915i
$628$	−10.9553	+	10.9553i	−0.437164	+	0.437164i
$629$	−21.7899			−0.868821
$630$		0			0
$631$	1.79707			0.0715402			0.0357701	−	0.999360i	$-0.488612\pi$
$631$	1.79707			0.0715402			0.0357701	+	0.999360i	$0.488612\pi$
$632$	11.9959	−	11.9959i	0.477170	−	0.477170i
$633$	0.312991	−	0.312991i	0.0124403	−	0.0124403i
$634$		−	24.7308i		−	0.982188i
$635$		0			0
$636$			7.93350i			0.314584i
$637$	−41.2617	+	9.11921i	−1.63485	+	0.361316i
$638$	−1.19896	−	1.19896i	−0.0474672	−	0.0474672i
$639$			6.74657i			0.266890i
$640$		0			0
$641$	−15.9220			−0.628883			−0.314441	−	0.949277i	$-0.601817\pi$
$641$	−15.9220			−0.628883			−0.314441	+	0.949277i	$0.601817\pi$
$642$	−10.4437	−	10.4437i	−0.412180	−	0.412180i
$643$	−4.94004	+	4.94004i	−0.194816	+	0.194816i	−0.797773	−	0.602957i	$-0.793989\pi$
$643$	−4.94004	+	4.94004i	−0.194816	+	0.194816i	0.602957	+	0.797773i	$0.293989\pi$
$644$	−6.58694	−	12.0157i	−0.259562	−	0.473486i
$645$		0			0
$646$	−8.14709			−0.320543
$647$	−18.5082	−	18.5082i	−0.727632	−	0.727632i	0.242515	−	0.970148i	$-0.422028\pi$
$647$	−18.5082	−	18.5082i	−0.727632	−	0.727632i	−0.970148	+	0.242515i	$0.922028\pi$
$648$	−2.05625	−	2.05625i	−0.0807773	−	0.0807773i
$649$	9.33945			0.366606
$650$		0			0
$651$	11.3086	−	6.19930i	0.443219	−	0.242970i
$652$	−11.6507	+	11.6507i	−0.456277	+	0.456277i
$653$	21.5903	+	21.5903i	0.844895	+	0.844895i	0.989491	−	0.144596i	$-0.0461883\pi$
$653$	21.5903	+	21.5903i	0.844895	+	0.844895i	−0.144596	+	0.989491i	$0.546188\pi$
$654$	1.29987			0.0508289
$655$		0			0
$656$		−	2.76113i		−	0.107804i
$657$	−2.47002	−	2.47002i	−0.0963647	−	0.0963647i
$658$	5.13510	−	17.5963i	0.200187	−	0.685976i
$659$			29.1608i			1.13594i	0.823048	+	0.567972i	$0.192272\pi$
$659$			29.1608i			1.13594i	−0.823048	+	0.567972i	$0.807728\pi$
$660$		0			0
$661$		−	5.92290i		−	0.230374i	−0.993344	−	0.115187i	$-0.963253\pi$
$661$		−	5.92290i		−	0.230374i	0.993344	−	0.115187i	$-0.0367468\pi$
$662$	−12.5699	+	12.5699i	−0.488541	+	0.488541i
$663$	31.9855	−	31.9855i	1.24222	−	1.24222i
$664$	−3.16177			−0.122701
$665$		0			0
$666$	2.68874			0.104187
$667$	−7.85582	+	7.85582i	−0.304179	+	0.304179i
$668$	19.0822	−	19.0822i	0.738312	−	0.738312i
$669$		−	8.94950i		−	0.346008i
$670$		0			0
$671$		−	1.88321i		−	0.0727007i
$672$	−13.8356	−	4.03761i	−0.533718	−	0.155754i
$673$	22.9220	+	22.9220i	0.883576	+	0.883576i	0.993896	−	0.110320i	$-0.0351875\pi$
$673$	22.9220	+	22.9220i	0.883576	+	0.883576i	−0.110320	+	0.993896i	$0.535187\pi$
$674$			6.24810i			0.240668i
$675$		0			0
$676$	26.8442			1.03247
$677$	21.3886	+	21.3886i	0.822032	+	0.822032i	0.986399	−	0.164367i	$-0.0525582\pi$
$677$	21.3886	+	21.3886i	0.822032	+	0.822032i	−0.164367	+	0.986399i	$0.552558\pi$
$678$	9.50613	−	9.50613i	0.365081	−	0.365081i
$679$	33.7415	−	18.4969i	1.29488	−	0.709845i
$680$		0			0
$681$	5.59414			0.214368
$682$	2.37919	+	2.37919i	0.0911039	+	0.0911039i
$683$	19.1030	+	19.1030i	0.730957	+	0.730957i	0.970809	−	0.239852i	$-0.0770991\pi$
$683$	19.1030	+	19.1030i	0.730957	+	0.730957i	−0.239852	+	0.970809i	$0.577099\pi$
$684$	−1.34656			−0.0514871
$685$		0			0
$686$	1.13671	−	17.0862i	0.0433999	−	0.652354i
$687$	10.0087	−	10.0087i	0.381855	−	0.381855i
$688$	−2.64820	−	2.64820i	−0.100962	−	0.100962i
$689$	41.8240			1.59337
$690$		0			0
$691$			6.58694i			0.250579i	0.992120	+	0.125290i	$0.0399860\pi$
$691$			6.58694i			0.250579i	−0.992120	+	0.125290i	$0.960014\pi$
$692$	7.82802	+	7.82802i	0.297577	+	0.297577i
$693$	−1.89614	−	0.553347i	−0.0720285	−	0.0210199i
$694$			18.0220i			0.684105i
$695$		0			0
$696$			7.14306i			0.270757i
$697$	36.7087	−	36.7087i	1.39044	−	1.39044i
$698$	9.41012	−	9.41012i	0.356178	−	0.356178i
$699$	−28.8650			−1.09177
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−3.94682	+	3.94682i	−0.148963	+	0.148963i
$703$	2.41801	−	2.41801i	0.0911972	−	0.0911972i
$704$		−	4.35536i		−	0.164149i
$705$		0			0
$706$			12.8511i			0.483658i
$707$	9.39330	+	2.74123i	0.353272	+	0.103095i
$708$	−10.1293	−	10.1293i	−0.380684	−	0.380684i
$709$		−	38.5897i		−	1.44927i	−0.689134	−	0.724634i	$-0.742009\pi$
$709$		−	38.5897i		−	1.44927i	0.689134	−	0.724634i	$-0.257991\pi$
$710$		0			0
$711$	−5.83384			−0.218786
$712$	7.60490	+	7.60490i	0.285006	+	0.285006i
$713$	15.5889	−	15.5889i	0.583810	−	0.583810i
$714$	8.81142	+	16.0735i	0.329759	+	0.601537i
$715$		0			0
$716$	−18.4059			−0.687859
$717$	10.5969	+	10.5969i	0.395748	+	0.395748i
$718$	−12.2564	−	12.2564i	−0.457406	−	0.457406i
$719$	−13.9838			−0.521508			−0.260754	−	0.965405i	$-0.583971\pi$
$719$	−13.9838			−0.521508			−0.260754	+	0.965405i	$0.583971\pi$
$720$		0			0
$721$	−3.05982	−	5.58164i	−0.113954	−	0.207871i
$722$	−11.5180	+	11.5180i	−0.428657	+	0.428657i
$723$	−5.39910	−	5.39910i	−0.200795	−	0.200795i
$724$	30.5333			1.13476
$725$		0			0
$726$			9.65533i			0.358343i
$727$	25.4104	+	25.4104i	0.942421	+	0.942421i	0.998430	−	0.0560096i	$-0.0178377\pi$
$727$	25.4104	+	25.4104i	0.942421	+	0.942421i	−0.0560096	+	0.998430i	$0.517838\pi$
$728$	−13.0114	+	44.5860i	−0.482236	+	1.65247i
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	70.4147i		−	2.60438i
$732$	−2.04249	+	2.04249i	−0.0754926	+	0.0754926i
$733$	25.5078	−	25.5078i	0.942154	−	0.942154i	−0.0562621	−	0.998416i	$-0.517918\pi$
$733$	25.5078	−	25.5078i	0.942154	−	0.942154i	0.998416	+	0.0562621i	$0.0179182\pi$
$734$	−31.0700			−1.14681
$735$		0			0
$736$	−24.6382			−0.908178
$737$	−4.83713	+	4.83713i	−0.178178	+	0.178178i
$738$	−4.52963	+	4.52963i	−0.166738	+	0.166738i
$739$			41.4005i			1.52294i	0.648198	+	0.761471i	$0.275523\pi$
$739$			41.4005i			1.52294i	−0.648198	+	0.761471i	$0.724477\pi$
$740$		0			0
$741$			7.09883i			0.260782i
$742$	−4.74795	+	16.2697i	−0.174303	+	0.597279i
$743$	17.9474	+	17.9474i	0.658425	+	0.658425i	0.955007	−	0.296582i	$-0.0958470\pi$
$743$	17.9474	+	17.9474i	0.658425	+	0.658425i	−0.296582	+	0.955007i	$0.595847\pi$
$744$		−	14.1745i		−	0.519664i
$745$		0			0
$746$	7.62892			0.279315
$747$	0.768819	+	0.768819i	0.0281296	+	0.0281296i
$748$	4.52963	−	4.52963i	0.165620	−	0.165620i
$749$	20.3160	+	37.0598i	0.742329	+	1.35414i
$750$		0			0
$751$	32.0000			1.16770			0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000			1.16770			0.583848	+	0.811863i	$0.301546\pi$
$752$	−2.11161	−	2.11161i	−0.0770026	−	0.0770026i
$753$	−10.8402	−	10.8402i	−0.395039	−	0.395039i
$754$	13.7105			0.499308
$755$		0			0
$756$	1.45636	+	2.65666i	0.0529674	+	0.0966217i
$757$	16.7226	−	16.7226i	0.607794	−	0.607794i	−0.334575	−	0.942369i	$-0.608593\pi$
$757$	16.7226	−	16.7226i	0.607794	−	0.607794i	0.942369	+	0.334575i	$0.108593\pi$
$758$	−3.01321	−	3.01321i	−0.109445	−	0.109445i
$759$	−3.37663			−0.122564
$760$		0			0
$761$			13.8564i			0.502294i	0.967949	+	0.251147i	$0.0808078\pi$
$761$			13.8564i			0.502294i	−0.967949	+	0.251147i	$0.919192\pi$
$762$	−5.06865	−	5.06865i	−0.183618	−	0.183618i
$763$	−3.57062	−	1.04201i	−0.129265	−	0.0377232i
$764$			2.17455i			0.0786724i
$765$		0			0
$766$		−	0.400647i		−	0.0144760i
$767$	−53.4001	+	53.4001i	−1.92816	+	1.92816i
$768$	−11.8468	+	11.8468i	−0.427484	+	0.427484i
$769$	−22.4972			−0.811270			−0.405635	−	0.914035i	$-0.632950\pi$
$769$	−22.4972			−0.811270			−0.405635	+	0.914035i	$0.632950\pi$
$770$		0			0
$771$	26.9863			0.971887
$772$	−4.20738	+	4.20738i	−0.151427	+	0.151427i
$773$	14.2461	−	14.2461i	0.512398	−	0.512398i	−0.402862	−	0.915261i	$-0.631985\pi$
$773$	14.2461	−	14.2461i	0.512398	−	0.512398i	0.915261	+	0.402862i	$0.131985\pi$
$774$			8.68874i			0.312310i
$775$		0			0
$776$		−	42.2926i		−	1.51822i
$777$	−7.38573	−	2.15536i	−0.264961	−	0.0773232i
$778$	−6.05943	−	6.05943i	−0.217241	−	0.217241i
$779$			8.14709i			0.291900i
$780$		0			0
$781$	5.03677			0.180230
$782$	22.1575	+	22.1575i	0.792349	+	0.792349i
$783$	1.73691	−	1.73691i	0.0620721	−	0.0620721i
$784$	−2.35186	−	1.50046i	−0.0839951	−	0.0535880i
$785$		0			0
$786$	14.1745			0.505589
$787$	19.8056	+	19.8056i	0.705993	+	0.705993i	0.965690	−	0.259697i	$-0.0836228\pi$
$787$	19.8056	+	19.8056i	0.705993	+	0.705993i	−0.259697	+	0.965690i	$0.583623\pi$
$788$	7.25360	+	7.25360i	0.258399	+	0.258399i
$789$	13.8029			0.491398
$790$		0			0
$791$	−33.7328	+	18.4921i	−1.19940	+	0.657504i
$792$	−1.53513	+	1.53513i	−0.0545486	+	0.0545486i
$793$	10.7676	+	10.7676i	0.382370	+	0.382370i
$794$	26.2982			0.933290
$795$		0			0
$796$		−	10.2854i		−	0.364555i
$797$	30.9103	+	30.9103i	1.09490	+	1.09490i	0.994997	+	0.0999020i	$0.0318529\pi$
$797$	30.9103	+	30.9103i	1.09490	+	1.09490i	0.0999020	+	0.994997i	$0.468147\pi$
$798$	−2.76147	−	0.805875i	−0.0977550	−	0.0285277i
$799$		−	56.1471i		−	1.98634i
$800$		0			0
$801$		−	3.69843i		−	0.130677i
$802$	3.29302	−	3.29302i	0.116281	−	0.116281i
$803$	−1.84404	+	1.84404i	−0.0650747	+	0.0650747i
$804$	10.4925			0.370041
$805$		0			0
$806$	−27.2069			−0.958323
$807$	−3.23596	+	3.23596i	−0.113911	+	0.113911i
$808$	7.60490	−	7.60490i	0.267540	−	0.267540i
$809$		−	6.15150i		−	0.216275i	−0.994136	−	0.108138i	$-0.965511\pi$
$809$		−	6.15150i		−	0.216275i	0.994136	−	0.108138i	$-0.0344887\pi$
$810$		0			0
$811$			34.4704i			1.21042i	0.796066	+	0.605209i	$0.206911\pi$
$811$			34.4704i			1.21042i	−0.796066	+	0.605209i	$0.793089\pi$
$812$	2.08480	−	7.14395i	0.0731623	−	0.250703i
$813$	−4.27820	−	4.27820i	−0.150043	−	0.150043i
$814$		−	2.00733i		−	0.0703568i
$815$		0			0
$816$	2.98627			0.104540
$817$	7.81388	+	7.81388i	0.273373	+	0.273373i
$818$	−12.9034	+	12.9034i	−0.451155	+	0.451155i
$819$	14.0054	−	7.67768i	0.489389	−	0.268280i
$820$		0			0
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$	10.5969	+	10.5969i	0.369609	+	0.369609i
$823$	−7.92839	−	7.92839i	−0.276366	−	0.276366i	0.555290	−	0.831657i	$-0.312607\pi$
$823$	−7.92839	−	7.92839i	−0.276366	−	0.276366i	−0.831657	+	0.555290i	$0.812607\pi$
$824$	−6.99621			−0.243724
$825$		0			0
$826$	−14.7107	−	26.8349i	−0.511852	−	0.933706i
$827$	3.24014	−	3.24014i	0.112671	−	0.112671i	−0.648524	−	0.761195i	$-0.724613\pi$
$827$	3.24014	−	3.24014i	0.112671	−	0.112671i	0.761195	+	0.648524i	$0.224613\pi$
$828$	3.66221	+	3.66221i	0.127271	+	0.127271i
$829$	−17.0862			−0.593428			−0.296714	−	0.954966i	$-0.595891\pi$
$829$	−17.0862			−0.593428			−0.296714	+	0.954966i	$0.595891\pi$
$830$		0			0
$831$			16.0376i			0.556340i
$832$	24.9026	+	24.9026i	0.863342	+	0.863342i
$833$	−11.3192	−	51.2160i	−0.392187	−	1.77453i
$834$		−	11.5667i		−	0.400522i
$835$		0			0
$836$			1.00530i			0.0347691i
$837$	−3.44669	+	3.44669i	−0.119135	+	0.119135i
$838$	−1.45435	+	1.45435i	−0.0502398	+	0.0502398i
$839$	−14.2657			−0.492506			−0.246253	−	0.969206i	$-0.579199\pi$
$839$	−14.2657			−0.492506			−0.246253	+	0.969206i	$0.579199\pi$
$840$		0			0
$841$	22.9663			0.791941
$842$	−14.3986	+	14.3986i	−0.496208	+	0.496208i
$843$	19.9387	−	19.9387i	0.686726	−	0.686726i
$844$			0.506864i			0.0174470i
$845$		0			0
$846$			6.92820i			0.238197i
$847$	7.73996	−	26.5223i	0.265948	−	0.911318i
$848$	1.95241	+	1.95241i	0.0670461	+	0.0670461i
$849$			28.4426i			0.976149i
$850$		0			0
$851$	−13.1524			−0.450860
$852$	−5.46276	−	5.46276i	−0.187151	−	0.187151i
$853$	7.45548	−	7.45548i	0.255271	−	0.255271i	−0.567857	−	0.823127i	$-0.692227\pi$
$853$	7.45548	−	7.45548i	0.255271	−	0.255271i	0.823127	+	0.567857i	$0.192227\pi$
$854$	−5.41101	+	2.96628i	−0.185161	+	0.101504i
$855$		0			0
$856$	46.4520			1.58770
$857$	−22.1575	−	22.1575i	−0.756884	−	0.756884i	0.218870	−	0.975754i	$-0.429763\pi$
$857$	−22.1575	−	22.1575i	−0.756884	−	0.756884i	−0.975754	+	0.218870i	$0.929763\pi$
$858$	2.94657	+	2.94657i	0.100594	+	0.100594i
$859$	27.3716			0.933905			0.466953	−	0.884282i	$-0.345352\pi$
$859$	27.3716			0.933905			0.466953	+	0.884282i	$0.345352\pi$
$860$		0			0
$861$	16.0735	−	8.81142i	0.547785	−	0.300292i
$862$	16.9327	−	16.9327i	0.576728	−	0.576728i
$863$	30.8534	+	30.8534i	1.05026	+	1.05026i	0.998668	+	0.0515936i	$0.0164301\pi$
$863$	30.8534	+	30.8534i	1.05026	+	1.05026i	0.0515936	+	0.998668i	$0.483570\pi$
$864$	5.44748			0.185327
$865$		0			0
$866$			25.6157i			0.870458i
$867$	27.6812	+	27.6812i	0.940102	+	0.940102i
$868$	−4.13705	+	14.1763i	−0.140420	+	0.481175i
$869$			4.35536i			0.147746i
$870$		0			0
$871$		−	55.3144i		−	1.87426i
$872$	−2.89081	+	2.89081i	−0.0978952	+	0.0978952i
$873$	−10.2839	+	10.2839i	−0.348057	+	0.348057i
$874$	−4.91760			−0.166340
$875$		0			0
$876$	4.00000			0.135147
$877$	1.54236	−	1.54236i	0.0520819	−	0.0520819i	−0.680586	−	0.732668i	$-0.738275\pi$
$877$	1.54236	−	1.54236i	0.0520819	−	0.0520819i	0.732668	+	0.680586i	$0.238275\pi$
$878$	11.2824	−	11.2824i	0.380764	−	0.380764i
$879$		−	4.50686i		−	0.152013i
$880$		0			0
$881$		−	14.3251i		−	0.482623i	−0.970448	−	0.241312i	$-0.922422\pi$
$881$		−	14.3251i		−	0.482623i	0.970448	−	0.241312i	$-0.0775776\pi$
$882$	1.39672	+	6.31974i	0.0470300	+	0.212797i
$883$	28.5666	+	28.5666i	0.961341	+	0.961341i	0.999280	−	0.0379391i	$-0.0120793\pi$
$883$	28.5666	+	28.5666i	0.961341	+	0.961341i	−0.0379391	+	0.999280i	$0.512079\pi$
$884$			51.7980i			1.74216i
$885$		0			0
$886$	−1.52457			−0.0512191
$887$	−38.9332	−	38.9332i	−1.30725	−	1.30725i	−0.923394	−	0.383854i	$-0.874596\pi$
$887$	−38.9332	−	38.9332i	−1.30725	−	1.30725i	−0.383854	−	0.923394i	$-0.625404\pi$
$888$	−5.97955	+	5.97955i	−0.200661	+	0.200661i
$889$	9.85996	+	17.9863i	0.330693	+	0.603240i
$890$		0			0
$891$	0.746568			0.0250110
$892$	7.24650	+	7.24650i	0.242631	+	0.242631i
$893$	6.23061	+	6.23061i	0.208500	+	0.208500i
$894$	−2.27117			−0.0759593
$895$		0			0
$896$	12.7623	−	6.99621i	0.426358	−	0.233727i
$897$	19.3065	−	19.3065i	0.644626	−	0.644626i
$898$	11.1386	+	11.1386i	0.371699	+	0.371699i
$899$	11.9732			0.399328
$900$		0			0
$901$			51.9140i			1.72951i
$902$	3.38168	+	3.38168i	0.112598	+	0.112598i
$903$	6.96511	−	23.8672i	0.231784	−	0.794250i
$904$			42.2818i			1.40627i
$905$		0			0
$906$			11.8196i			0.392679i
$907$	−14.5312	+	14.5312i	−0.482502	+	0.482502i	−0.905930	−	0.423428i	$-0.860827\pi$
$907$	−14.5312	+	14.5312i	−0.482502	+	0.482502i	0.423428	+	0.905930i	$0.360827\pi$
$908$	−4.52963	+	4.52963i	−0.150321	+	0.150321i
$909$	−3.69843			−0.122669
$910$		0			0
$911$	−18.3407			−0.607655			−0.303827	−	0.952727i	$-0.598265\pi$
$911$	−18.3407			−0.607655			−0.303827	+	0.952727i	$0.598265\pi$
$912$	−0.331385	+	0.331385i	−0.0109733	+	0.0109733i
$913$	0.573976	−	0.573976i	0.0189958	−	0.0189958i
$914$			35.0525i			1.15943i
$915$		0			0
$916$			16.2083i			0.535536i
$917$	−38.9362	−	11.3627i	−1.28579	−	0.375229i
$918$	−4.89898	−	4.89898i	−0.161690	−	0.161690i
$919$			7.36375i			0.242908i	0.992597	+	0.121454i	$0.0387557\pi$
$919$			7.36375i			0.242908i	−0.992597	+	0.121454i	$0.961244\pi$
$920$		0			0
$921$	−4.94950			−0.163092
$922$	21.8511	+	21.8511i	0.719626	+	0.719626i
$923$	−28.7987	+	28.7987i	−0.947921	+	0.947921i
$924$	1.98338	−	1.08727i	0.0652483	−	0.0357687i
$925$		0			0
$926$	−19.4342			−0.638649
$927$	1.70120	+	1.70120i	0.0558748	+	0.0558748i
$928$	−9.46178	−	9.46178i	−0.310598	−	0.310598i
$929$	−46.8010			−1.53549			−0.767745	−	0.640755i	$-0.778621\pi$
$929$	−46.8010			−1.53549			−0.767745	+	0.640755i	$0.778621\pi$
$930$		0			0
$931$	6.93950	+	4.42733i	0.227433	+	0.145100i
$932$	23.3723	−	23.3723i	0.765584	−	0.765584i
$933$	12.5032	+	12.5032i	0.409337	+	0.409337i
$934$	1.75583			0.0574524
$935$		0			0
$936$		−	17.5548i		−	0.573798i
$937$	3.80623	+	3.80623i	0.124344	+	0.124344i	0.766540	−	0.642196i	$-0.221977\pi$
$937$	3.80623	+	3.80623i	0.124344	+	0.124344i	−0.642196	+	0.766540i	$0.721977\pi$
$938$	21.5175	+	6.27941i	0.702571	+	0.205030i
$939$		−	10.0368i		−	0.327538i
$940$		0			0
$941$		−	42.6339i		−	1.38983i	−0.719094	−	0.694913i	$-0.755443\pi$
$941$		−	42.6339i		−	1.38983i	0.719094	−	0.694913i	$-0.244557\pi$
$942$	8.84580	−	8.84580i	0.288212	−	0.288212i
$943$	22.1575	−	22.1575i	0.721546	−	0.721546i
$944$	−4.98560			−0.162268
$945$		0			0
$946$	6.48674			0.210902
$947$	15.1940	−	15.1940i	0.493739	−	0.493739i	−0.415743	−	0.909482i	$-0.636478\pi$
$947$	15.1940	−	15.1940i	0.493739	−	0.493739i	0.909482	+	0.415743i	$0.136478\pi$
$948$	4.72372	−	4.72372i	0.153419	−	0.153419i
$949$		−	21.0873i		−	0.684522i
$950$		0			0
$951$		−	26.7474i		−	0.867345i
$952$	−55.3423	−	16.1504i	−1.79365	−	0.523438i
$953$	7.74170	+	7.74170i	0.250778	+	0.250778i	0.821290	−	0.570511i	$-0.193255\pi$
$953$	7.74170	+	7.74170i	0.250778	+	0.250778i	−0.570511	+	0.821290i	$0.693255\pi$
$954$		−	6.40586i		−	0.207397i
$955$		0			0
$956$	−17.1608			−0.555021
$957$	−1.29672	−	1.29672i	−0.0419171	−	0.0419171i
$958$	−11.2542	+	11.2542i	−0.363605	+	0.363605i
$959$	−20.6140	−	37.6035i	−0.665660	−	1.21428i
$960$		0			0
$961$	7.24063			0.233569
$962$	11.4773	+	11.4773i	0.370042	+	0.370042i
$963$	−11.2953	−	11.2953i	−0.363985	−	0.363985i
$964$	8.74342			0.281606
$965$		0			0
$966$	5.31859	+	9.70202i	0.171123	+	0.312157i
$967$	−18.8514	+	18.8514i	−0.606221	+	0.606221i	−0.941956	−	0.335735i	$-0.891015\pi$
$967$	−18.8514	+	18.8514i	−0.606221	+	0.606221i	0.335735	+	0.941956i	$0.391015\pi$
$968$	−21.4727	−	21.4727i	−0.690159	−	0.690159i
$969$	−8.81142			−0.283064
$970$		0			0
$971$		−	7.33747i		−	0.235471i	−0.993045	−	0.117735i	$-0.962437\pi$
$971$		−	7.33747i		−	0.235471i	0.993045	−	0.117735i	$-0.0375634\pi$
$972$	−0.809710	−	0.809710i	−0.0259715	−	0.0259715i
$973$	−9.27215	+	31.7726i	−0.297251	+	1.01858i
$974$		−	24.7034i		−	0.791548i
$975$		0			0
$976$			1.00530i			0.0321789i
$977$	18.0848	−	18.0848i	0.578585	−	0.578585i	−0.355928	−	0.934513i	$-0.615835\pi$
$977$	18.0848	−	18.0848i	0.578585	−	0.578585i	0.934513	+	0.355928i	$0.115835\pi$
$978$	9.40730	−	9.40730i	0.300812	−	0.300812i
$979$	−2.76113			−0.0882460
$980$		0			0
$981$	1.40586			0.0448857
$982$	−12.4186	+	12.4186i	−0.396294	+	0.396294i
$983$	7.87248	−	7.87248i	0.251093	−	0.251093i	−0.570326	−	0.821419i	$-0.693183\pi$
$983$	7.87248	−	7.87248i	0.251093	−	0.251093i	0.821419	+	0.570326i	$0.193183\pi$
$984$		−	20.1471i		−	0.642266i
$985$		0			0
$986$			17.0182i			0.541969i
$987$	5.55382	−	19.0312i	0.176780	−	0.605768i
$988$	−5.74800	−	5.74800i	−0.182868	−	0.182868i
$989$		−	42.5025i		−	1.35150i
$990$		0			0
$991$	4.85689			0.154284			0.0771421	−	0.997020i	$-0.475420\pi$
$991$	4.85689			0.154284			0.0771421	+	0.997020i	$0.475420\pi$
$992$	18.7758	+	18.7758i	0.596131	+	0.596131i
$993$	−13.5948	+	13.5948i	−0.431419	+	0.431419i
$994$	−7.93350	−	14.4721i	−0.251635	−	0.459027i
$995$		0			0
$996$	−1.24504			−0.0394506
$997$	−24.6275	−	24.6275i	−0.779960	−	0.779960i	0.199864	−	0.979824i	$-0.435950\pi$
$997$	−24.6275	−	24.6275i	−0.779960	−	0.779960i	−0.979824	+	0.199864i	$0.935950\pi$
$998$	−3.61543	−	3.61543i	−0.114444	−	0.114444i
$999$	2.90798			0.0920045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.c.118.8	yes	24
5.2	odd	4	inner	525.2.m.c.307.7	yes	24
5.3	odd	4	inner	525.2.m.c.307.6	yes	24
5.4	even	2	inner	525.2.m.c.118.5	✓	24
7.6	odd	2	inner	525.2.m.c.118.7	yes	24
35.13	even	4	inner	525.2.m.c.307.5	yes	24
35.27	even	4	inner	525.2.m.c.307.8	yes	24
35.34	odd	2	inner	525.2.m.c.118.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.m.c.118.5	✓	24	5.4	even	2	inner
525.2.m.c.118.6	yes	24	35.34	odd	2	inner
525.2.m.c.118.7	yes	24	7.6	odd	2	inner
525.2.m.c.118.8	yes	24	1.1	even	1	trivial
525.2.m.c.307.5	yes	24	35.13	even	4	inner
525.2.m.c.307.6	yes	24	5.3	odd	4	inner
525.2.m.c.307.7	yes	24	5.2	odd	4	inner
525.2.m.c.307.8	yes	24	35.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.653796 - 0.653796i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.14510i q^{4} -0.924607i q^{6} +(-0.741188 + 2.53981i) q^{7} +(2.05625 + 2.05625i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.653796 - 0.653796i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.14510i q^{4} -0.924607i q^{6} +(-0.741188 + 2.53981i) q^{7} +(2.05625 + 2.05625i) q^{8} -1.00000i q^{9} -0.746568 q^{11} +(0.809710 + 0.809710i) q^{12} +(4.26864 - 4.26864i) q^{13} +(1.17593 + 2.14510i) q^{14} +0.398534 q^{16} +(5.29845 + 5.29845i) q^{17} +(-0.653796 - 0.653796i) q^{18} -1.17593 q^{19} +(1.27182 + 2.32002i) q^{21} +(-0.488103 + 0.488103i) q^{22} +(3.19815 + 3.19815i) q^{23} +2.90798 q^{24} -5.58164i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.90834 - 0.848736i) q^{28} +2.45636i q^{29} -4.87436i q^{31} +(-3.85195 + 3.85195i) q^{32} +(-0.527903 + 0.527903i) q^{33} +6.92820 q^{34} +1.14510 q^{36} +(-2.05625 + 2.05625i) q^{37} +(-0.768819 + 0.768819i) q^{38} -6.03677i q^{39} -6.92820i q^{41} +(2.34833 + 0.685307i) q^{42} +(-6.64484 - 6.64484i) q^{43} -0.854897i q^{44} +4.18188 q^{46} +(-5.29845 - 5.29845i) q^{47} +(0.281806 - 0.281806i) q^{48} +(-5.90128 - 3.76496i) q^{49} +7.49314 q^{51} +(4.88804 + 4.88804i) q^{52} +(4.89898 + 4.89898i) q^{53} -0.924607 q^{54} +(-6.74657 + 3.69843i) q^{56} +(-0.831509 + 0.831509i) q^{57} +(1.60596 + 1.60596i) q^{58} -12.5098 q^{59} +2.52249i q^{61} +(-3.18683 - 3.18683i) q^{62} +(2.53981 + 0.741188i) q^{63} +5.83384i q^{64} +0.690282i q^{66} +(6.47915 - 6.47915i) q^{67} +(-6.06727 + 6.06727i) q^{68} +4.52287 q^{69} -6.74657 q^{71} +(2.05625 - 2.05625i) q^{72} +(2.47002 - 2.47002i) q^{73} +2.68874i q^{74} -1.34656i q^{76} +(0.553347 - 1.89614i) q^{77} +(-3.94682 - 3.94682i) q^{78} -5.83384i q^{79} -1.00000 q^{81} +(-4.52963 - 4.52963i) q^{82} +(-0.768819 + 0.768819i) q^{83} +(-2.65666 + 1.45636i) q^{84} -8.68874 q^{86} +(1.73691 + 1.73691i) q^{87} +(-1.53513 - 1.53513i) q^{88} +3.69843 q^{89} +(7.67768 + 14.0054i) q^{91} +(-3.66221 + 3.66221i) q^{92} +(-3.44669 - 3.44669i) q^{93} -6.92820 q^{94} +5.44748i q^{96} +(-10.2839 - 10.2839i) q^{97} +(-6.31974 + 1.39672i) q^{98} +0.746568i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) \) 24 * q + 48 * q^11 + 24 * q^16 + 12 * q^21 - 24 * q^36 - 120 * q^46 + 48 * q^51 - 96 * q^56 - 96 * q^71 - 24 * q^81 - 120 * q^86 + 108 * q^91

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