LMFDB - Embedded newform 525.2.m.c.118.7

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			118.7
Character	$\chi$	$=$	525.118
Dual form			525.2.m.c.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.653796 - 0.653796i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.14510i q^{4} +0.924607i q^{6} +(-2.53981 + 0.741188i) q^{7} +(2.05625 + 2.05625i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.653796 - 0.653796i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.14510i q^{4} +0.924607i q^{6} +(-2.53981 + 0.741188i) q^{7} +(2.05625 + 2.05625i) q^{8} -1.00000i q^{9} -0.746568 q^{11} +(-0.809710 - 0.809710i) q^{12} +(-4.26864 + 4.26864i) q^{13} +(-1.17593 + 2.14510i) q^{14} +0.398534 q^{16} +(-5.29845 - 5.29845i) q^{17} +(-0.653796 - 0.653796i) q^{18} +1.17593 q^{19} +(1.27182 - 2.32002i) q^{21} +(-0.488103 + 0.488103i) q^{22} +(3.19815 + 3.19815i) q^{23} -2.90798 q^{24} +5.58164i q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.848736 - 2.90834i) q^{28} +2.45636i q^{29} +4.87436i q^{31} +(-3.85195 + 3.85195i) q^{32} +(0.527903 - 0.527903i) q^{33} -6.92820 q^{34} +1.14510 q^{36} +(-2.05625 + 2.05625i) q^{37} +(0.768819 - 0.768819i) q^{38} -6.03677i q^{39} +6.92820i q^{41} +(-0.685307 - 2.34833i) q^{42} +(-6.64484 - 6.64484i) q^{43} -0.854897i q^{44} +4.18188 q^{46} +(5.29845 + 5.29845i) q^{47} +(-0.281806 + 0.281806i) q^{48} +(5.90128 - 3.76496i) q^{49} +7.49314 q^{51} +(-4.88804 - 4.88804i) q^{52} +(4.89898 + 4.89898i) q^{53} +0.924607 q^{54} +(-6.74657 - 3.69843i) q^{56} +(-0.831509 + 0.831509i) q^{57} +(1.60596 + 1.60596i) q^{58} +12.5098 q^{59} -2.52249i q^{61} +(3.18683 + 3.18683i) q^{62} +(0.741188 + 2.53981i) q^{63} +5.83384i q^{64} -0.690282i q^{66} +(6.47915 - 6.47915i) q^{67} +(6.06727 - 6.06727i) q^{68} -4.52287 q^{69} -6.74657 q^{71} +(2.05625 - 2.05625i) q^{72} +(-2.47002 + 2.47002i) q^{73} +2.68874i q^{74} +1.34656i q^{76} +(1.89614 - 0.553347i) q^{77} +(-3.94682 - 3.94682i) q^{78} -5.83384i q^{79} -1.00000 q^{81} +(4.52963 + 4.52963i) q^{82} +(0.768819 - 0.768819i) q^{83} +(2.65666 + 1.45636i) q^{84} -8.68874 q^{86} +(-1.73691 - 1.73691i) q^{87} +(-1.53513 - 1.53513i) q^{88} -3.69843 q^{89} +(7.67768 - 14.0054i) q^{91} +(-3.66221 + 3.66221i) q^{92} +(-3.44669 - 3.44669i) q^{93} +6.92820 q^{94} -5.44748i q^{96} +(10.2839 + 10.2839i) q^{97} +(1.39672 - 6.31974i) q^{98} +0.746568i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2.53981	+	0.741188i	−0.959958	+	0.280143i
$7$	−2.53981	+	0.741188i	−0.959958	+	0.280143i
$8$	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	$0.565780\pi$
$13$	−4.26864	+	4.26864i	−1.18391	+	1.18391i	−0.978723	+	0.205186i	$0.934220\pi$
$14$	−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	$-0.887094\pi$
$17$	−5.29845	−	5.29845i	−1.28506	−	1.28506i	−0.347313	−	0.937749i	$-0.612906\pi$
$18$	−0.653796	−	0.653796i	−0.154101	−	0.154101i
$19$	1.17593			0.269777			0.134889	−	0.990861i	$-0.456932\pi$
$19$	1.17593			0.269777			0.134889	+	0.990861i	$0.456932\pi$
$20$		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
$28$	−0.848736	−	2.90834i	−0.160396	−	0.549625i
$29$			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	$0.144218\pi$
$31$			4.87436i			0.875461i	−0.899106	+	0.437730i	$0.855782\pi$
$32$	−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	$0.181955\pi$
$41$			6.92820i			1.08200i	−0.841021	+	0.541002i	$0.818045\pi$
$42$	−0.685307	−	2.34833i	−0.105745	−	0.362355i
$43$	−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	0.978605	−	0.205747i	$-0.0659624\pi$
$47$	5.29845	+	5.29845i	0.772858	+	0.772858i	−0.205747	+	0.978605i	$0.565962\pi$
$48$	−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	$-0.197109\pi$
$59$	12.5098			1.62864			0.814321	+	0.580414i	$0.197109\pi$
$60$		0			0
$61$		−	2.52249i		−	0.322972i	−0.986875	−	0.161486i	$-0.948371\pi$
$61$		−	2.52249i		−	0.322972i	0.986875	−	0.161486i	$-0.0516287\pi$
$62$	3.18683	+	3.18683i	0.404728	+	0.404728i
$63$	0.741188	+	2.53981i	0.0933809	+	0.319986i
$64$			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	−0.836722	−	0.547628i	$-0.815531\pi$
$73$	−2.47002	+	2.47002i	−0.289094	+	0.289094i	0.547628	+	0.836722i	$0.315531\pi$
$74$			2.68874i			0.312560i
$75$		0			0
$76$			1.34656i			0.154461i
$77$	1.89614	−	0.553347i	0.216085	−	0.0630598i
$78$	−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	−0.663652	−	0.748041i	$-0.730995\pi$
$83$	0.768819	−	0.768819i	0.0843888	−	0.0843888i	0.748041	+	0.663652i	$0.230995\pi$
$84$	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	$-0.562801\pi$
$89$	−3.69843			−0.392032			−0.196016	+	0.980601i	$0.562801\pi$
$90$		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	$0.0143906\pi$
$97$	10.2839	+	10.2839i	1.04417	+	1.04417i	0.0451941	+	0.998978i	$0.485609\pi$
$98$	1.39672	−	6.31974i	0.141090	−	0.638390i
$99$			0.746568i			0.0750329i
$100$		0			0
$101$			3.69843i			0.368007i	0.982926	+	0.184004i	$0.0589058\pi$
$101$			3.69843i			0.368007i	−0.982926	+	0.184004i	$0.941094\pi$
$102$	4.89898	−	4.89898i	0.485071	−	0.485071i
$103$	1.70120	−	1.70120i	0.167624	−	0.167624i	−0.618310	−	0.785934i	$-0.712182\pi$
$103$	1.70120	−	1.70120i	0.167624	−	0.167624i	0.785934	+	0.618310i	$0.212182\pi$
$104$	−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
$112$	−1.01220	+	0.295389i	−0.0956441	+	0.0279116i
$113$	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	$-0.766419\pi$
$131$		−	15.3304i		−	1.33942i	0.742623	−	0.669710i	$-0.233581\pi$
$132$	0.604504	+	0.604504i	0.0526153	+	0.0526153i
$133$	−2.98664	+	0.871587i	−0.258975	+	0.0755761i
$134$		−	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	$-0.678009\pi$
$139$	−12.5098			−1.06107			−0.530536	+	0.847663i	$0.678009\pi$
$140$		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
$147$	−1.51061	+	6.83506i	−0.124593	+	0.563746i
$148$	−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	0.213423	−	0.976960i	$-0.431539\pi$
$157$	−9.56709	−	9.56709i	−0.763537	−	0.763537i	−0.976960	+	0.213423i	$0.931539\pi$
$158$	−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	$0.115325\pi$
$167$	16.6642	+	16.6642i	1.28951	+	1.28951i	0.354428	+	0.935083i	$0.384675\pi$
$168$	7.38573	−	2.15536i	0.569821	−	0.166290i
$169$		−	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	−0.917492	−	0.397754i	$-0.869790\pi$
$173$	−6.83609	+	6.83609i	−0.519738	+	0.519738i	0.397754	+	0.917492i	$0.369790\pi$
$174$	−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	$0.457190\pi$
$181$			26.6643i			1.98194i	−0.134086	+	0.990970i	$0.542810\pi$
$182$	−4.13705	−	14.1763i	−0.306658	−	1.05082i
$183$	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	$-0.396868\pi$
$199$	8.98205			0.636721			0.318360	+	0.947970i	$0.396868\pi$
$200$		0			0
$201$			9.16290i			0.646301i
$202$	2.41801	+	2.41801i	0.170131	+	0.170131i
$203$	−1.82063	−	6.23870i	−0.127783	−	0.437871i
$204$			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
$217$	−3.61282	−	12.3799i	−0.245254	−	0.840406i
$218$	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	−0.886500	−	0.462729i	$-0.846870\pi$
$223$	−6.32825	+	6.32825i	−0.423771	+	0.423771i	0.462729	+	0.886500i	$0.346870\pi$
$224$	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	0.563542	−	0.826088i	$-0.309438\pi$
$227$	−3.95565	−	3.95565i	−0.262546	−	0.262546i	−0.826088	+	0.563542i	$0.809438\pi$
$228$	−0.952164	−	0.952164i	−0.0630586	−	0.0630586i
$229$	−14.1544			−0.935351			−0.467675	−	0.883900i	$-0.654908\pi$
$229$	−14.1544			−0.935351			−0.467675	+	0.883900i	$0.654908\pi$
$230$		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
$238$	17.5963	−	5.13510i	1.14060	−	0.332859i
$239$			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	$0.0790909\pi$
$241$			7.63549i			0.491845i	−0.969290	+	0.245922i	$0.920909\pi$
$242$	−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	$0.160752\pi$
$251$			15.3304i			0.967644i	−0.875167	+	0.483822i	$0.839248\pi$
$252$	−2.90834	+	0.848736i	−0.183208	+	0.0534654i
$253$	−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	$-0.931568\pi$
$257$	−19.0822	−	19.0822i	−1.19031	−	1.19031i	−0.213334	−	0.976979i	$-0.568432\pi$
$258$	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	$-0.455447\pi$
$269$	4.57634			0.279024			0.139512	+	0.990220i	$0.455447\pi$
$270$		0			0
$271$			6.05029i			0.367529i	0.982970	+	0.183764i	$0.0588284\pi$
$271$			6.05029i			0.367529i	−0.982970	+	0.183764i	$0.941172\pi$
$272$	−2.11161	−	2.11161i	−0.128035	−	0.128035i
$273$	4.47438	+	15.3323i	0.270802	+	0.927951i
$274$			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	$-0.429380\pi$
$283$	20.1120	−	20.1120i	1.19553	−	1.19553i	0.975490	−	0.220043i	$-0.0706198\pi$
$284$		−	7.72551i		−	0.458425i
$285$		0			0
$286$		−	4.16708i		−	0.246404i
$287$	−5.13510	−	17.5963i	−0.303115	−	1.03868i
$288$	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	−0.794041	−	0.607864i	$-0.792027\pi$
$293$	−3.18683	+	3.18683i	−0.186177	+	0.186177i	0.607864	+	0.794041i	$0.292027\pi$
$294$	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	0.799891	−	0.600145i	$-0.204891\pi$
$307$	3.49982	+	3.49982i	0.199746	+	0.199746i	−0.600145	+	0.799891i	$0.704891\pi$
$308$	0.633640	+	2.17128i	0.0361050	+	0.123720i
$309$			2.40586i			0.136865i
$310$		0			0
$311$		−	17.6822i		−	1.00267i	−0.865254	−	0.501333i	$-0.832843\pi$
$311$		−	17.6822i		−	1.00267i	0.865254	−	0.501333i	$-0.167157\pi$
$312$	12.4131	−	12.4131i	0.702756	−	0.702756i
$313$	−7.09707	+	7.09707i	−0.401150	+	0.401150i	−0.878638	−	0.477488i	$-0.841547\pi$
$313$	−7.09707	+	7.09707i	−0.401150	+	0.401150i	0.477488	+	0.878638i	$0.341547\pi$
$314$	−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
$322$	−10.6212	+	3.09956i	−0.591895	+	0.172732i
$323$	−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
$343$	−12.1976	+	13.9362i	−0.658608	+	0.752486i
$344$		−	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	$-0.625875\pi$
$349$	−14.3931			−0.770443			−0.385221	+	0.922824i	$0.625875\pi$
$350$		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	−0.395409	−	0.918505i	$-0.629397\pi$
$353$	9.82808	−	9.82808i	0.523096	−	0.523096i	0.918505	+	0.395409i	$0.129397\pi$
$354$			11.5667i			0.614762i
$355$		0			0
$356$		−	4.23508i		−	0.224459i
$357$	−19.0312	+	5.55382i	−1.00724	+	0.293939i
$358$	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	$0.0904873\pi$
$367$	23.7612	+	23.7612i	1.24033	+	1.24033i	0.280461	+	0.959865i	$0.409513\pi$
$368$	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
$378$	−2.34833	+	0.685307i	−0.120785	+	0.0352484i
$379$		−	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	−0.714892	−	0.699235i	$-0.753524\pi$
$383$	−0.306401	+	0.306401i	−0.0156564	+	0.0156564i	0.699235	+	0.714892i	$0.253524\pi$
$384$	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
$392$	19.8762	+	4.39283i	1.00390	+	0.221871i
$393$	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	$-0.996996\pi$
$397$	−20.1120	−	20.1120i	−1.00939	−	1.00939i	−0.00943590	−	0.999955i	$-0.503004\pi$
$398$	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	$-0.337747\pi$
$409$	19.7361			0.975886			0.487943	+	0.872876i	$0.337747\pi$
$410$		0			0
$411$		−	16.2083i		−	0.799495i
$412$	1.94805	+	1.94805i	0.0959736	+	0.0959736i
$413$	−31.7726	+	9.27215i	−1.56343	+	0.456252i
$414$		−	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	$-0.482696\pi$
$419$	2.22448			0.108673			0.0543364	+	0.998523i	$0.482696\pi$
$420$		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
$427$	1.86964	+	6.40666i	0.0904784	+	0.310040i
$428$	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	−0.0569417	−	0.998378i	$-0.518135\pi$
$433$	19.5900	−	19.5900i	0.941436	−	0.941436i	0.998378	+	0.0569417i	$0.0181349\pi$
$434$	−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	$-0.635104\pi$
$439$	−17.2568			−0.823623			−0.411811	+	0.911269i	$0.635104\pi$
$440$		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
$448$	−4.32397	−	14.8169i	−0.204289	−	0.700031i
$449$			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	$-0.716080\pi$
$461$		−	33.4218i		−	1.55661i	0.627886	−	0.778305i	$-0.283920\pi$
$462$	0.511629	+	1.75319i	0.0238031	+	0.0815656i
$463$	−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	0.675355	−	0.737492i	$-0.263990\pi$
$467$	−1.34279	−	1.34279i	−0.0621371	−	0.0621371i	−0.737492	+	0.675355i	$0.763990\pi$
$468$	−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	$-0.371349\pi$
$479$	17.2136			0.786508			0.393254	+	0.919430i	$0.371349\pi$
$480$		0			0
$481$		−	17.5548i		−	0.800431i
$482$	4.99205	+	4.99205i	0.227381	+	0.227381i
$483$	11.4872	−	3.35230i	0.522687	−	0.152535i
$484$		−	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
$497$	17.1350	−	5.00048i	0.768610	−	0.224302i
$498$	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	−0.550589	−	0.834777i	$-0.685597\pi$
$503$	6.37367	−	6.37367i	0.284188	−	0.284188i	0.834777	+	0.550589i	$0.185597\pi$
$504$	−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	$-0.410579\pi$
$509$	12.5098			0.554489			0.277245	+	0.960799i	$0.410579\pi$
$510$		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
$518$	−1.99286	−	6.82889i	−0.0875613	−	0.300044i
$519$		−	9.66769i		−	0.424364i
$520$		0			0
$521$			16.2083i			0.710097i	0.934848	+	0.355049i	$0.115536\pi$
$521$			16.2083i			0.710097i	−0.934848	+	0.355049i	$0.884464\pi$
$522$	1.60596	−	1.60596i	0.0702909	−	0.0702909i
$523$	15.2760	−	15.2760i	0.667971	−	0.667971i	−0.289275	−	0.957246i	$-0.593414\pi$
$523$	15.2760	−	15.2760i	0.667971	−	0.667971i	0.957246	+	0.289275i	$0.0934143\pi$
$524$	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
$532$	−0.998056	−	3.42001i	−0.0432712	−	0.148276i
$533$	−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
$553$	4.32397	+	14.8169i	0.183874	+	0.630077i
$554$			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	$-0.347767\pi$
$563$	31.9855	−	31.9855i	1.34803	−	1.34803i	0.887800	−	0.460229i	$-0.152233\pi$
$564$		−	8.58041i		−	0.361300i
$565$		0			0
$566$		−	26.2982i		−	1.10540i
$567$	2.53981	−	0.741188i	0.106662	−	0.0311270i
$568$	−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	0.543776	−	0.839231i	$-0.316994\pi$
$577$	−7.09707	−	7.09707i	−0.295455	−	0.295455i	−0.839231	+	0.543776i	$0.816994\pi$
$578$	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	0.445336	−	0.895363i	$-0.353084\pi$
$587$	−10.9033	−	10.9033i	−0.450027	−	0.450027i	−0.895363	+	0.445336i	$0.853084\pi$
$588$	−7.82685	−	1.72980i	−0.322774	−	0.0713359i
$589$			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	−0.455218	−	0.890380i	$-0.650439\pi$
$593$	10.5969	−	10.5969i	0.435162	−	0.435162i	0.890380	+	0.455218i	$0.150439\pi$
$594$	−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	$0.175309\pi$
$601$			25.6590i			1.04665i	−0.852133	+	0.523326i	$0.824691\pi$
$602$	22.0678	−	6.43999i	0.899415	−	0.262474i
$603$	−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	0.894280	−	0.447507i	$-0.147688\pi$
$607$	11.0073	+	11.0073i	0.446773	+	0.446773i	−0.447507	+	0.894280i	$0.647688\pi$
$608$	−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	$-0.690851\pi$
$619$	−28.0788			−1.12858			−0.564292	+	0.825575i	$0.690851\pi$
$620$		0			0
$621$			4.52287i			0.181497i
$622$	−11.5606	−	11.5606i	−0.463536	−	0.463536i
$623$	9.39330	−	2.74123i	0.376335	−	0.109825i
$624$		−	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
$637$	−9.11921	+	41.2617i	−0.361316	+	1.63485i
$638$	−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	−0.602957	−	0.797773i	$-0.706011\pi$
$643$	4.94004	−	4.94004i	0.194816	−	0.194816i	0.797773	+	0.602957i	$0.206011\pi$
$644$	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	0.970148	−	0.242515i	$-0.0779724\pi$
$647$	18.5082	+	18.5082i	0.727632	+	0.727632i	−0.242515	+	0.970148i	$0.577972\pi$
$648$	−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
$658$	−17.5963	+	5.13510i	−0.685976	+	0.200187i
$659$			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	$0.0367468\pi$
$661$			5.92290i			0.230374i	−0.993344	+	0.115187i	$0.963253\pi$
$662$	−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
$672$	4.03761	+	13.8356i	0.155754	+	0.533718i
$673$	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	0.164367	−	0.986399i	$-0.447442\pi$
$677$	−21.3886	−	21.3886i	−0.822032	−	0.822032i	−0.986399	+	0.164367i	$0.947442\pi$
$678$	−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	$-0.960014\pi$
$691$		−	6.58694i		−	0.250579i	0.992120	−	0.125290i	$-0.0399860\pi$
$692$	−7.82802	−	7.82802i	−0.297577	−	0.297577i
$693$	−0.553347	−	1.89614i	−0.0210199	−	0.0720285i
$694$			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
$707$	−2.74123	−	9.39330i	−0.103095	−	0.353272i
$708$	−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	$-0.416029\pi$
$719$	13.9838			0.521508			0.260754	+	0.965405i	$0.416029\pi$
$720$		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	0.0560096	−	0.998430i	$-0.482162\pi$
$727$	−25.4104	−	25.4104i	−0.942421	−	0.942421i	−0.998430	+	0.0560096i	$0.982162\pi$
$728$	44.5860	−	13.0114i	1.65247	−	0.482236i
$729$			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	−0.998416	−	0.0562621i	$-0.982082\pi$
$733$	−25.5078	+	25.5078i	−0.942154	+	0.942154i	0.0562621	+	0.998416i	$0.482082\pi$
$734$	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
$742$	−16.2697	+	4.74795i	−0.597279	+	0.174303i
$743$	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	$-0.919192\pi$
$761$		−	13.8564i		−	0.502294i	0.967949	−	0.251147i	$-0.0808078\pi$
$762$	5.06865	+	5.06865i	0.183618	+	0.183618i
$763$	−1.04201	−	3.57062i	−0.0377232	−	0.129265i
$764$			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	$-0.367050\pi$
$769$	22.4972			0.811270			0.405635	+	0.914035i	$0.367050\pi$
$770$		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	−0.915261	−	0.402862i	$-0.868015\pi$
$773$	−14.2461	+	14.2461i	−0.512398	+	0.512398i	0.402862	+	0.915261i	$0.368015\pi$
$774$			8.68874i			0.312310i
$775$		0			0
$776$			42.2926i			1.51822i
$777$	2.15536	+	7.38573i	0.0773232	+	0.264961i
$778$	−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	0.259697	−	0.965690i	$-0.416377\pi$
$787$	−19.8056	−	19.8056i	−0.705993	−	0.705993i	−0.965690	+	0.259697i	$0.916377\pi$
$788$	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	$-0.968147\pi$
$797$	−30.9103	−	30.9103i	−1.09490	−	1.09490i	−0.0999020	−	0.994997i	$-0.531853\pi$
$798$	−0.805875	−	2.76147i	−0.0285277	−	0.0977550i
$799$		−	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	$-0.793089\pi$
$811$		−	34.4704i		−	1.21042i	0.796066	−	0.605209i	$-0.206911\pi$
$812$	7.14395	−	2.08480i	0.250703	−	0.0731623i
$813$	−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	$-0.404109\pi$
$829$	17.0862			0.593428			0.296714	+	0.954966i	$0.404109\pi$
$830$		0			0
$831$		−	16.0376i		−	0.556340i
$832$	−24.9026	−	24.9026i	−0.863342	−	0.863342i
$833$	−51.2160	−	11.3192i	−1.77453	−	0.392187i
$834$		−	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	$-0.420801\pi$
$839$	14.2657			0.492506			0.246253	+	0.969206i	$0.420801\pi$
$840$		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
$847$	26.5223	−	7.73996i	0.911318	−	0.265948i
$848$	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	−0.823127	−	0.567857i	$-0.807773\pi$
$853$	−7.45548	+	7.45548i	−0.255271	+	0.255271i	0.567857	+	0.823127i	$0.307773\pi$
$854$	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	0.975754	−	0.218870i	$-0.0702370\pi$
$857$	22.1575	+	22.1575i	0.756884	+	0.756884i	−0.218870	+	0.975754i	$0.570237\pi$
$858$	2.94657	+	2.94657i	0.100594	+	0.100594i
$859$	−27.3716			−0.933905			−0.466953	−	0.884282i	$-0.654648\pi$
$859$	−27.3716			−0.933905			−0.466953	+	0.884282i	$0.654648\pi$
$860$		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
$868$	14.1763	−	4.13705i	0.481175	−	0.140420i
$869$			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	$0.0775776\pi$
$881$			14.3251i			0.482623i	−0.970448	+	0.241312i	$0.922422\pi$
$882$	−6.31974	−	1.39672i	−0.212797	−	0.0470300i
$883$	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	$0.125404\pi$
$887$	38.9332	+	38.9332i	1.30725	+	1.30725i	0.383854	+	0.923394i	$0.374596\pi$
$888$	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
$903$	−23.8672	+	6.96511i	−0.794250	+	0.231784i
$904$			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
$917$	11.3627	+	38.9362i	0.375229	+	1.28579i
$918$	−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	$-0.221379\pi$
$929$	46.8010			1.53549			0.767745	+	0.640755i	$0.221379\pi$
$930$		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	0.642196	−	0.766540i	$-0.278023\pi$
$937$	−3.80623	−	3.80623i	−0.124344	−	0.124344i	−0.766540	+	0.642196i	$0.778023\pi$
$938$	6.27941	+	21.5175i	0.205030	+	0.702571i
$939$		−	10.0368i		−	0.327538i
$940$		0			0
$941$			42.6339i			1.38983i	0.719094	+	0.694913i	$0.244557\pi$
$941$			42.6339i			1.38983i	−0.719094	+	0.694913i	$0.755443\pi$
$942$	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
$952$	16.1504	+	55.3423i	0.523438	+	1.79365i
$953$	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	$0.0375634\pi$
$971$			7.33747i			0.235471i	−0.993045	+	0.117735i	$0.962437\pi$
$972$	0.809710	+	0.809710i	0.0259715	+	0.0259715i
$973$	31.7726	−	9.27215i	1.01858	−	0.297251i
$974$		−	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	−0.821419	−	0.570326i	$-0.806817\pi$
$983$	−7.87248	+	7.87248i	−0.251093	+	0.251093i	0.570326	+	0.821419i	$0.306817\pi$
$984$		−	20.1471i		−	0.642266i
$985$		0			0
$986$		−	17.0182i		−	0.541969i
$987$	19.0312	−	5.55382i	0.605768	−	0.176780i
$988$	−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	0.979824	−	0.199864i	$-0.0640500\pi$
$997$	24.6275	+	24.6275i	0.779960	+	0.779960i	−0.199864	+	0.979824i	$0.564050\pi$
$998$	−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.118.7	yes	24
5.2	odd	4	inner	525.2.m.c.307.8	yes	24
5.3	odd	4	inner	525.2.m.c.307.5	yes	24
5.4	even	2	inner	525.2.m.c.118.6	yes	24
7.6	odd	2	inner	525.2.m.c.118.8	yes	24
35.13	even	4	inner	525.2.m.c.307.6	yes	24
35.27	even	4	inner	525.2.m.c.307.7	yes	24
35.34	odd	2	inner	525.2.m.c.118.5	✓	24

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

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