LMFDB - Embedded newform 630.2.p.b.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(307,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("630.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.p (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$2.16053i$ of defining polynomial
Character	$\chi$	$=$	630.307
Dual form			630.2.p.b.433.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(0.781409 + 2.52773i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(0.781409 + 2.52773i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.63280 - 1.52773i) q^{10} -4.90685 q^{11} +(-3.41421 - 3.41421i) q^{13} +(-1.23483 + 2.33991i) q^{14} -1.00000 q^{16} +(-2.74632 + 2.74632i) q^{17} +1.26561 q^{19} +(-0.0743018 - 2.23483i) q^{20} +(-3.46967 - 3.46967i) q^{22} +(1.05545 - 1.05545i) q^{23} +(4.98896 - 0.332104i) q^{25} -4.82843i q^{26} +(-2.52773 + 0.781409i) q^{28} +4.76687i q^{29} +7.05545i q^{31} +(-0.707107 - 0.707107i) q^{32} -3.88388 q^{34} +(-1.93413 - 5.59099i) q^{35} +(-4.74632 - 4.74632i) q^{37} +(0.894921 + 0.894921i) q^{38} +(1.52773 - 1.63280i) q^{40} -5.44670i q^{41} +(-7.58667 + 7.58667i) q^{43} -4.90685i q^{44} +1.49264 q^{46} +(-0.734390 + 0.734390i) q^{47} +(-5.77880 + 3.95037i) q^{49} +(3.76256 + 3.29289i) q^{50} +(3.41421 - 3.41421i) q^{52} +(-1.26561 + 1.26561i) q^{53} +(10.9660 - 0.364588i) q^{55} +(-2.33991 - 1.23483i) q^{56} +(-3.37069 + 3.37069i) q^{58} -1.39735 q^{59} +2.29721i q^{61} +(-4.98896 + 4.98896i) q^{62} -1.00000i q^{64} +(7.88388 + 7.37652i) q^{65} +(3.05545 + 3.05545i) q^{67} +(-2.74632 - 2.74632i) q^{68} +(2.58579 - 5.32106i) q^{70} +13.0334 q^{71} +(5.04441 + 5.04441i) q^{73} -6.71231i q^{74} +1.26561i q^{76} +(-3.83425 - 12.4032i) q^{77} -14.8063i q^{79} +(2.23483 - 0.0743018i) q^{80} +(3.85140 - 3.85140i) q^{82} +(9.29809 + 9.29809i) q^{83} +(5.93351 - 6.34162i) q^{85} -10.7292 q^{86} +(3.46967 - 3.46967i) q^{88} +15.3596 q^{89} +(5.96230 - 11.2981i) q^{91} +(1.05545 + 1.05545i) q^{92} -1.03858 q^{94} +(-2.82843 + 0.0940371i) q^{95} +(-8.42614 + 8.42614i) q^{97} +(-6.87957 - 1.29289i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 4 q^{10} - 8 q^{11} - 16 q^{13} + 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 4 q^{20} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 8 q^{28} + 16 q^{34} - 8 q^{35} - 28 q^{37} + 4 q^{38} - 8 q^{46} - 24 q^{47} + 4 q^{49} + 16 q^{52} + 8 q^{53} + 28 q^{55} - 4 q^{56} - 12 q^{58} - 8 q^{59} + 4 q^{62} + 16 q^{65} - 12 q^{68} + 32 q^{70} - 8 q^{71} - 28 q^{73} + 44 q^{77} + 24 q^{82} + 16 q^{83} + 28 q^{85} - 8 q^{86} - 8 q^{88} + 64 q^{89} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^11 - 16 * q^13 + 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 4 * q^20 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 8 * q^28 + 16 * q^34 - 8 * q^35 - 28 * q^37 + 4 * q^38 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^52 + 8 * q^53 + 28 * q^55 - 4 * q^56 - 12 * q^58 - 8 * q^59 + 4 * q^62 + 16 * q^65 - 12 * q^68 + 32 * q^70 - 8 * q^71 - 28 * q^73 + 44 * q^77 + 24 * q^82 + 16 * q^83 + 28 * q^85 - 8 * q^86 - 8 * q^88 + 64 * q^89 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−2.23483	+	0.0743018i	−0.999448	+	0.0332288i
$5$	−2.23483	+	0.0743018i	−0.999448	+	0.0332288i
$6$		0			0
$7$	0.781409	+	2.52773i	0.295345	+	0.955391i
$7$	0.781409	+	2.52773i	0.295345	+	0.955391i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.63280	−	1.52773i	−0.516338	−	0.483109i
$11$	−4.90685			−1.47947			−0.739735	−	0.672898i	$-0.765049\pi$
$11$	−4.90685			−1.47947			−0.739735	+	0.672898i	$0.765049\pi$
$12$		0			0
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	0.0517287	−	0.998661i	$-0.483527\pi$
$13$	−3.41421	−	3.41421i	−0.946932	−	0.946932i	−0.998661	+	0.0517287i	$0.983527\pi$
$14$	−1.23483	+	2.33991i	−0.330023	+	0.625368i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.74632	+	2.74632i	−0.666080	+	0.666080i	−0.956806	−	0.290726i	$-0.906103\pi$
$17$	−2.74632	+	2.74632i	−0.666080	+	0.666080i	0.290726	+	0.956806i	$0.406103\pi$
$18$		0			0
$19$	1.26561			0.290351			0.145175	−	0.989406i	$-0.453625\pi$
$19$	1.26561			0.290351			0.145175	+	0.989406i	$0.453625\pi$
$20$	−0.0743018	−	2.23483i	−0.0166144	−	0.499724i
$21$		0			0
$22$	−3.46967	−	3.46967i	−0.739735	−	0.739735i
$23$	1.05545	−	1.05545i	0.220077	−	0.220077i	−0.588454	−	0.808531i	$-0.700263\pi$
$23$	1.05545	−	1.05545i	0.220077	−	0.220077i	0.808531	+	0.588454i	$0.200263\pi$
$24$		0			0
$25$	4.98896	−	0.332104i	0.997792	−	0.0664208i
$26$		−	4.82843i		−	0.946932i
$27$		0			0
$28$	−2.52773	+	0.781409i	−0.477695	+	0.147672i
$29$			4.76687i			0.885186i	0.896723	+	0.442593i	$0.145941\pi$
$29$			4.76687i			0.885186i	−0.896723	+	0.442593i	$0.854059\pi$
$30$		0			0
$31$			7.05545i			1.26720i	0.773662	+	0.633598i	$0.218423\pi$
$31$			7.05545i			1.26720i	−0.773662	+	0.633598i	$0.781577\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	−3.88388			−0.666080
$35$	−1.93413	−	5.59099i	−0.326928	−	0.945049i
$36$		0			0
$37$	−4.74632	−	4.74632i	−0.780290	−	0.780290i	0.199590	−	0.979880i	$-0.436039\pi$
$37$	−4.74632	−	4.74632i	−0.780290	−	0.780290i	−0.979880	+	0.199590i	$0.936039\pi$
$38$	0.894921	+	0.894921i	0.145175	+	0.145175i
$39$		0			0
$40$	1.52773	−	1.63280i	0.241555	−	0.258169i
$41$		−	5.44670i		−	0.850631i	−0.905045	−	0.425316i	$-0.860163\pi$
$41$		−	5.44670i		−	0.850631i	0.905045	−	0.425316i	$-0.139837\pi$
$42$		0			0
$43$	−7.58667	+	7.58667i	−1.15696	+	1.15696i	−0.171830	+	0.985127i	$0.554968\pi$
$43$	−7.58667	+	7.58667i	−1.15696	+	1.15696i	−0.985127	+	0.171830i	$0.945032\pi$
$44$		−	4.90685i		−	0.739735i
$45$		0			0
$46$	1.49264			0.220077
$47$	−0.734390	+	0.734390i	−0.107122	+	0.107122i	−0.758636	−	0.651514i	$-0.774134\pi$
$47$	−0.734390	+	0.734390i	−0.107122	+	0.107122i	0.651514	+	0.758636i	$0.274134\pi$
$48$		0			0
$49$	−5.77880	+	3.95037i	−0.825543	+	0.564339i
$50$	3.76256	+	3.29289i	0.532106	+	0.465685i
$51$		0			0
$52$	3.41421	−	3.41421i	0.473466	−	0.473466i
$53$	−1.26561	+	1.26561i	−0.173845	+	0.173845i	−0.788666	−	0.614821i	$-0.789228\pi$
$53$	−1.26561	+	1.26561i	−0.173845	+	0.173845i	0.614821	+	0.788666i	$0.289228\pi$
$54$		0			0
$55$	10.9660	−	0.364588i	1.47865	−	0.0491610i
$56$	−2.33991	−	1.23483i	−0.312684	−	0.165012i
$57$		0			0
$58$	−3.37069	+	3.37069i	−0.442593	+	0.442593i
$59$	−1.39735			−0.181919			−0.0909594	−	0.995855i	$-0.528993\pi$
$59$	−1.39735			−0.181919			−0.0909594	+	0.995855i	$0.528993\pi$
$60$		0			0
$61$			2.29721i			0.294127i	0.989127	+	0.147064i	$0.0469822\pi$
$61$			2.29721i			0.294127i	−0.989127	+	0.147064i	$0.953018\pi$
$62$	−4.98896	+	4.98896i	−0.633598	+	0.633598i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	7.88388	+	7.37652i	0.977875	+	0.914944i
$66$		0			0
$67$	3.05545	+	3.05545i	0.373283	+	0.373283i	0.868672	−	0.495389i	$-0.164974\pi$
$67$	3.05545	+	3.05545i	0.373283	+	0.373283i	−0.495389	+	0.868672i	$0.664974\pi$
$68$	−2.74632	−	2.74632i	−0.333040	−	0.333040i
$69$		0			0
$70$	2.58579	−	5.32106i	0.309061	−	0.635989i
$71$	13.0334			1.54678			0.773388	−	0.633933i	$-0.218560\pi$
$71$	13.0334			1.54678			0.773388	+	0.633933i	$0.218560\pi$
$72$		0			0
$73$	5.04441	+	5.04441i	0.590404	+	0.590404i	0.937740	−	0.347337i	$-0.112914\pi$
$73$	5.04441	+	5.04441i	0.590404	+	0.590404i	−0.347337	+	0.937740i	$0.612914\pi$
$74$		−	6.71231i		−	0.780290i
$75$		0			0
$76$			1.26561i			0.145175i
$77$	−3.83425	−	12.4032i	−0.436954	−	1.41347i
$78$		0			0
$79$		−	14.8063i		−	1.66584i	−0.553391	−	0.832922i	$-0.686666\pi$
$79$		−	14.8063i		−	1.66584i	0.553391	−	0.832922i	$-0.313334\pi$
$80$	2.23483	−	0.0743018i	0.249862	−	0.00830719i
$81$		0			0
$82$	3.85140	−	3.85140i	0.425316	−	0.425316i
$83$	9.29809	+	9.29809i	1.02060	+	1.02060i	0.999783	+	0.0208150i	$0.00662610\pi$
$83$	9.29809	+	9.29809i	1.02060	+	1.02060i	0.0208150	+	0.999783i	$0.493374\pi$
$84$		0			0
$85$	5.93351	−	6.34162i	0.643579	−	0.687845i
$86$	−10.7292			−1.15696
$87$		0			0
$88$	3.46967	−	3.46967i	0.369868	−	0.369868i
$89$	15.3596			1.62812			0.814060	−	0.580781i	$-0.197253\pi$
$89$	15.3596			1.62812			0.814060	+	0.580781i	$0.197253\pi$
$90$		0			0
$91$	5.96230	−	11.2981i	0.625019	−	1.18436i
$92$	1.05545	+	1.05545i	0.110039	+	0.110039i
$93$		0			0
$94$	−1.03858			−0.107122
$95$	−2.82843	+	0.0940371i	−0.290191	+	0.00964800i
$96$		0			0
$97$	−8.42614	+	8.42614i	−0.855545	+	0.855545i	−0.990810	−	0.135264i	$-0.956812\pi$
$97$	−8.42614	+	8.42614i	−0.855545	+	0.855545i	0.135264	+	0.990810i	$0.456812\pi$
$98$	−6.87957	−	1.29289i	−0.694941	−	0.130602i
$99$		0			0
$100$	0.332104	+	4.98896i	0.0332104	+	0.498896i
$101$			18.1504i			1.80603i	0.429609	+	0.903015i	$0.358651\pi$
$101$			18.1504i			1.80603i	−0.429609	+	0.903015i	$0.641349\pi$
$102$		0			0
$103$	8.36459	+	8.36459i	0.824187	+	0.824187i	0.986706	−	0.162518i	$-0.0519616\pi$
$103$	8.36459	+	8.36459i	0.824187	+	0.824187i	−0.162518	+	0.986706i	$0.551962\pi$
$104$	4.82843			0.473466
$105$		0			0
$106$	−1.78984			−0.173845
$107$	−3.77297	−	3.77297i	−0.364747	−	0.364747i	0.500810	−	0.865557i	$-0.333036\pi$
$107$	−3.77297	−	3.77297i	−0.364747	−	0.364747i	−0.865557	+	0.500810i	$0.833036\pi$
$108$		0			0
$109$			0.0870500i			0.00833787i	0.999991	+	0.00416894i	$0.00132702\pi$
$109$			0.0870500i			0.00833787i	−0.999991	+	0.00416894i	$0.998673\pi$
$110$	8.01193	+	7.49632i	0.763907	+	0.714746i
$111$		0			0
$112$	−0.781409	−	2.52773i	−0.0738362	−	0.238848i
$113$	−2.03248	+	2.03248i	−0.191200	+	0.191200i	−0.796214	−	0.605014i	$-0.793167\pi$
$113$	−2.03248	+	2.03248i	−0.191200	+	0.191200i	0.605014	+	0.796214i	$0.293167\pi$
$114$		0			0
$115$	−2.28034	+	2.43718i	−0.212643	+	0.227268i
$116$	−4.76687			−0.442593
$117$		0			0
$118$	−0.988072	−	0.988072i	−0.0909594	−	0.0909594i
$119$	−9.08794	−	4.79594i	−0.833090	−	0.439643i
$120$		0			0
$121$	13.0772			1.18883
$122$	−1.62437	+	1.62437i	−0.147064	+	0.147064i
$123$		0			0
$124$	−7.05545			−0.633598
$125$	−11.1248	+	1.11289i	−0.995034	+	0.0995396i
$126$		0			0
$127$	−11.1761	−	11.1761i	−0.991723	−	0.991723i	0.00824340	−	0.999966i	$-0.497376\pi$
$127$	−11.1761	−	11.1761i	−0.991723	−	0.991723i	−0.999966	+	0.00824340i	$0.997376\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	0.358761	+	10.7907i	0.0314654	+	0.946410i
$131$		−	12.8367i		−	1.12154i	−0.827970	−	0.560772i	$-0.810504\pi$
$131$		−	12.8367i		−	1.12154i	0.827970	−	0.560772i	$-0.189496\pi$
$132$		0			0
$133$	0.988958	+	3.19912i	0.0857536	+	0.277399i
$134$			4.32106i			0.373283i
$135$		0			0
$136$		−	3.88388i		−	0.333040i
$137$	3.62437	+	3.62437i	0.309651	+	0.309651i	0.844774	−	0.535123i	$-0.179735\pi$
$137$	3.62437	+	3.62437i	0.309651	+	0.309651i	−0.535123	+	0.844774i	$0.679735\pi$
$138$		0			0
$139$	3.90596			0.331299			0.165650	−	0.986185i	$-0.447028\pi$
$139$	3.90596			0.331299			0.165650	+	0.986185i	$0.447028\pi$
$140$	5.59099	−	1.93413i	0.472525	−	0.163464i
$141$		0			0
$142$	9.21598	+	9.21598i	0.773388	+	0.773388i
$143$	16.7530	+	16.7530i	1.40096	+	1.40096i
$144$		0			0
$145$	−0.354187	−	10.6532i	−0.0294137	−	0.884697i
$146$			7.13387i			0.590404i
$147$		0			0
$148$	4.74632	−	4.74632i	0.390145	−	0.390145i
$149$			5.64124i			0.462148i	0.972936	+	0.231074i	$0.0742240\pi$
$149$			5.64124i			0.462148i	−0.972936	+	0.231074i	$0.925776\pi$
$150$		0			0
$151$	−11.7678			−0.957647			−0.478823	−	0.877911i	$-0.658937\pi$
$151$	−11.7678			−0.957647			−0.478823	+	0.877911i	$0.658937\pi$
$152$	−0.894921	+	0.894921i	−0.0725877	+	0.0725877i
$153$		0			0
$154$	6.05914	−	11.4816i	0.488259	−	0.925213i
$155$	−0.524233	−	15.7678i	−0.0421074	−	1.26650i
$156$		0			0
$157$	−13.7132	+	13.7132i	−1.09443	+	1.09443i	−0.0993827	+	0.995049i	$0.531687\pi$
$157$	−13.7132	+	13.7132i	−1.09443	+	1.09443i	−0.995049	+	0.0993827i	$0.968313\pi$
$158$	10.4697	−	10.4697i	0.832922	−	0.832922i
$159$		0			0
$160$	1.63280	+	1.52773i	0.129085	+	0.120777i
$161$	3.49264	+	1.84316i	0.275258	+	0.145261i
$162$		0			0
$163$	−7.21967	+	7.21967i	−0.565488	+	0.565488i	−0.930861	−	0.365373i	$-0.880941\pi$
$163$	−7.21967	+	7.21967i	−0.565488	+	0.565488i	0.365373	+	0.930861i	$0.380941\pi$
$164$	5.44670			0.425316
$165$		0			0
$166$			13.1495i			1.02060i
$167$	6.73439	−	6.73439i	0.521123	−	0.521123i	−0.396788	−	0.917910i	$-0.629875\pi$
$167$	6.73439	−	6.73439i	0.521123	−	0.521123i	0.917910	+	0.396788i	$0.129875\pi$
$168$		0			0
$169$			10.3137i			0.793362i
$170$	8.67982	−	0.288579i	0.665712	−	0.0221330i
$171$		0			0
$172$	−7.58667	−	7.58667i	−0.578478	−	0.578478i
$173$	−14.1605	−	14.1605i	−1.07661	−	1.07661i	−0.996811	−	0.0797939i	$-0.974574\pi$
$173$	−14.1605	−	14.1605i	−1.07661	−	1.07661i	−0.0797939	−	0.996811i	$-0.525426\pi$
$174$		0			0
$175$	4.73788	+	12.3512i	0.358150	+	0.933664i
$176$	4.90685			0.369868
$177$		0			0
$178$	10.8609	+	10.8609i	0.814060	+	0.814060i
$179$		−	3.28123i		−	0.245250i	−0.992453	−	0.122625i	$-0.960869\pi$
$179$		−	3.28123i		−	0.245250i	0.992453	−	0.122625i	$-0.0391313\pi$
$180$		0			0
$181$		−	19.3934i		−	1.44150i	−0.693196	−	0.720749i	$-0.743798\pi$
$181$		−	19.3934i		−	1.44150i	0.693196	−	0.720749i	$-0.256202\pi$
$182$	12.2049	−	3.77297i	0.904691	−	0.279671i
$183$		0			0
$184$			1.49264i			0.110039i
$185$	10.9599	+	10.2546i	0.805787	+	0.753931i
$186$		0			0
$187$	13.4758	−	13.4758i	0.985446	−	0.985446i
$188$	−0.734390	−	0.734390i	−0.0535609	−	0.0535609i
$189$		0			0
$190$	−2.06649	−	1.93351i	−0.149919	−	0.140271i
$191$	16.8453			1.21888			0.609441	−	0.792831i	$-0.291394\pi$
$191$	16.8453			1.21888			0.609441	+	0.792831i	$0.291394\pi$
$192$		0			0
$193$	−4.81370	+	4.81370i	−0.346498	+	0.346498i	−0.858803	−	0.512306i	$-0.828792\pi$
$193$	−4.81370	+	4.81370i	−0.346498	+	0.346498i	0.512306	+	0.858803i	$0.328792\pi$
$194$	−11.9164			−0.855545
$195$		0			0
$196$	−3.95037	−	5.77880i	−0.282170	−	0.412772i
$197$	−13.0334	−	13.0334i	−0.928589	−	0.928589i	0.0690257	−	0.997615i	$-0.478011\pi$
$197$	−13.0334	−	13.0334i	−0.928589	−	0.928589i	−0.997615	+	0.0690257i	$0.978011\pi$
$198$		0			0
$199$	11.7509			0.832999			0.416499	−	0.909136i	$-0.363257\pi$
$199$	11.7509			0.832999			0.416499	+	0.909136i	$0.363257\pi$
$200$	−3.29289	+	3.76256i	−0.232843	+	0.266053i
$201$		0			0
$202$	−12.8343	+	12.8343i	−0.903015	+	0.903015i
$203$	−12.0494	+	3.72488i	−0.845699	+	0.261435i
$204$		0			0
$205$	0.404699	+	12.1725i	0.0282654	+	0.850161i
$206$			11.8293i			0.824187i
$207$		0			0
$208$	3.41421	+	3.41421i	0.236733	+	0.236733i
$209$	−6.21016			−0.429566
$210$		0			0
$211$	16.5502			1.13937			0.569683	−	0.821864i	$-0.307066\pi$
$211$	16.5502			1.13937			0.569683	+	0.821864i	$0.307066\pi$
$212$	−1.26561	−	1.26561i	−0.0869224	−	0.0869224i
$213$		0			0
$214$		−	5.33579i		−	0.364747i
$215$	16.3912	−	17.5187i	1.11787	−	1.19476i
$216$		0			0
$217$	−17.8343	+	5.51319i	−1.21067	+	0.374260i
$218$	−0.0615536	+	0.0615536i	−0.00416894	+	0.00416894i
$219$		0			0
$220$	0.364588	+	10.9660i	0.0245805	+	0.739327i
$221$	18.7530			1.26147
$222$		0			0
$223$	−8.26067	−	8.26067i	−0.553175	−	0.553175i	0.374181	−	0.927356i	$-0.377924\pi$
$223$	−8.26067	−	8.26067i	−0.553175	−	0.553175i	−0.927356	+	0.374181i	$0.877924\pi$
$224$	1.23483	−	2.33991i	0.0825058	−	0.156342i
$225$		0			0
$226$	−2.87437			−0.191200
$227$	−5.91295	+	5.91295i	−0.392456	+	0.392456i	−0.875562	−	0.483106i	$-0.839509\pi$
$227$	−5.91295	+	5.91295i	−0.392456	+	0.392456i	0.483106	+	0.875562i	$0.339509\pi$
$228$		0			0
$229$	−9.31371			−0.615467			−0.307734	−	0.951473i	$-0.599571\pi$
$229$	−9.31371			−0.615467			−0.307734	+	0.951473i	$0.599571\pi$
$230$	−3.33579	+	0.110906i	−0.219956	+	0.00731289i
$231$		0			0
$232$	−3.37069	−	3.37069i	−0.221297	−	0.221297i
$233$	−16.0563	+	16.0563i	−1.05189	+	1.05189i	−0.0533076	+	0.998578i	$0.516976\pi$
$233$	−16.0563	+	16.0563i	−1.05189	+	1.05189i	−0.998578	+	0.0533076i	$0.983024\pi$
$234$		0			0
$235$	1.58667	−	1.69581i	0.103503	−	0.110622i
$236$		−	1.39735i		−	0.0909594i
$237$		0			0
$238$	−3.03490	−	9.81739i	−0.196723	−	0.636367i
$239$			1.68592i			0.109053i	0.998512	+	0.0545267i	$0.0173650\pi$
$239$			1.68592i			0.109053i	−0.998512	+	0.0545267i	$0.982635\pi$
$240$		0			0
$241$			3.61574i			0.232910i	0.993196	+	0.116455i	$0.0371532\pi$
$241$			3.61574i			0.232910i	−0.993196	+	0.116455i	$0.962847\pi$
$242$	9.24695	+	9.24695i	0.594417	+	0.594417i
$243$		0			0
$244$	−2.29721			−0.147064
$245$	12.6211	−	9.25780i	0.806335	−	0.591459i
$246$		0			0
$247$	−4.32106	−	4.32106i	−0.274943	−	0.274943i
$248$	−4.98896	−	4.98896i	−0.316799	−	0.316799i
$249$		0			0
$250$	−8.65336	−	7.07950i	−0.547287	−	0.447747i
$251$			4.78896i			0.302276i	0.988513	+	0.151138i	$0.0482938\pi$
$251$			4.78896i			0.302276i	−0.988513	+	0.151138i	$0.951706\pi$
$252$		0			0
$253$	−5.17895	+	5.17895i	−0.325598	+	0.325598i
$254$		−	15.8055i		−	0.991723i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−20.8113	+	20.8113i	−1.29817	+	1.29817i	−0.368574	+	0.929599i	$0.620154\pi$
$257$	−20.8113	+	20.8113i	−1.29817	+	1.29817i	−0.929599	+	0.368574i	$0.879846\pi$
$258$		0			0
$259$	8.28858	−	15.7062i	0.515027	−	0.975936i
$260$	−7.37652	+	7.88388i	−0.457472	+	0.488937i
$261$		0			0
$262$	9.07689	−	9.07689i	0.560772	−	0.560772i
$263$	−6.61827	+	6.61827i	−0.408100	+	0.408100i	−0.881076	−	0.472976i	$-0.843180\pi$
$263$	−6.61827	+	6.61827i	−0.408100	+	0.408100i	0.472976	+	0.881076i	$0.343180\pi$
$264$		0			0
$265$	2.73439	−	2.92246i	0.167972	−	0.179526i
$266$	−1.56282	+	2.96142i	−0.0958225	+	0.181576i
$267$		0			0
$268$	−3.05545	+	3.05545i	−0.186641	+	0.186641i
$269$	−13.1192			−0.799890			−0.399945	−	0.916539i	$-0.630971\pi$
$269$	−13.1192			−0.799890			−0.399945	+	0.916539i	$0.630971\pi$
$270$		0			0
$271$		−	18.0836i		−	1.09850i	−0.835658	−	0.549250i	$-0.814913\pi$
$271$		−	18.0836i		−	1.09850i	0.835658	−	0.549250i	$-0.185087\pi$
$272$	2.74632	−	2.74632i	0.166520	−	0.166520i
$273$		0			0
$274$			5.12563i			0.309651i
$275$	−24.4801	+	1.62959i	−1.47620	+	0.0982677i
$276$		0			0
$277$	2.63541	+	2.63541i	0.158347	+	0.158347i	0.781834	−	0.623487i	$-0.214285\pi$
$277$	2.63541	+	2.63541i	0.158347	+	0.158347i	−0.623487	+	0.781834i	$0.714285\pi$
$278$	2.76193	+	2.76193i	0.165650	+	0.165650i
$279$		0			0
$280$	5.32106	+	2.58579i	0.317994	+	0.154530i
$281$	−20.4558			−1.22029			−0.610146	−	0.792289i	$-0.708889\pi$
$281$	−20.4558			−1.22029			−0.610146	+	0.792289i	$0.708889\pi$
$282$		0			0
$283$	10.7751	+	10.7751i	0.640514	+	0.640514i	0.950682	−	0.310168i	$-0.100385\pi$
$283$	10.7751	+	10.7751i	0.640514	+	0.640514i	−0.310168	+	0.950682i	$0.600385\pi$
$284$			13.0334i			0.773388i
$285$		0			0
$286$			23.6924i			1.40096i
$287$	13.7678	−	4.25610i	0.812685	−	0.251229i
$288$		0			0
$289$			1.91548i			0.112675i
$290$	7.28248	−	7.78337i	0.427642	−	0.457056i
$291$		0			0
$292$	−5.04441	+	5.04441i	−0.295202	+	0.295202i
$293$	3.15965	+	3.15965i	0.184588	+	0.184588i	0.793352	−	0.608763i	$-0.208334\pi$
$293$	3.15965	+	3.15965i	0.184588	+	0.184588i	−0.608763	+	0.793352i	$0.708334\pi$
$294$		0			0
$295$	3.12283	−	0.103825i	0.181818	−	0.00604494i
$296$	6.71231			0.390145
$297$		0			0
$298$	−3.98896	+	3.98896i	−0.231074	+	0.231074i
$299$	−7.20708			−0.416796
$300$		0			0
$301$	−25.1053	−	13.2487i	−1.44705	−	0.763645i
$302$	−8.32106	−	8.32106i	−0.478823	−	0.478823i
$303$		0			0
$304$	−1.26561			−0.0725877
$305$	−0.170687	−	5.13387i	−0.00977349	−	0.293965i
$306$		0			0
$307$	20.8011	−	20.8011i	1.18718	−	1.18718i	0.209340	−	0.977843i	$-0.432868\pi$
$307$	20.8011	−	20.8011i	1.18718	−	1.18718i	0.977843	−	0.209340i	$-0.0671316\pi$
$308$	12.4032	−	3.83425i	0.706736	−	0.218477i
$309$		0			0
$310$	10.7788	−	11.5202i	0.612195	−	0.654302i
$311$		−	11.4706i		−	0.650435i	−0.945639	−	0.325218i	$-0.894562\pi$
$311$		−	11.4706i		−	0.650435i	0.945639	−	0.325218i	$-0.105438\pi$
$312$		0			0
$313$	0.612443	+	0.612443i	0.0346173	+	0.0346173i	0.724204	−	0.689586i	$-0.242208\pi$
$313$	0.612443	+	0.612443i	0.0346173	+	0.0346173i	−0.689586	+	0.724204i	$0.742208\pi$
$314$	−19.3934			−1.09443
$315$		0			0
$316$	14.8063			0.832922
$317$	−7.03984	−	7.03984i	−0.395397	−	0.395397i	0.481209	−	0.876606i	$-0.340198\pi$
$317$	−7.03984	−	7.03984i	−0.395397	−	0.395397i	−0.876606	+	0.481209i	$0.840198\pi$
$318$		0			0
$319$		−	23.3903i		−	1.30961i
$320$	0.0743018	+	2.23483i	0.00415360	+	0.124931i
$321$		0			0
$322$	1.16636	+	3.77297i	0.0649986	+	0.210260i
$323$	−3.47577	+	3.47577i	−0.193397	+	0.193397i
$324$		0			0
$325$	−18.1672	−	15.8995i	−1.00774	−	0.881945i
$326$	−10.2102			−0.565488
$327$		0			0
$328$	3.85140	+	3.85140i	0.212658	+	0.212658i
$329$	−2.43020	−	1.28248i	−0.133981	−	0.0707053i
$330$		0			0
$331$	10.1759			0.559317			0.279658	−	0.960100i	$-0.409779\pi$
$331$	10.1759			0.559317			0.279658	+	0.960100i	$0.409779\pi$
$332$	−9.29809	+	9.29809i	−0.510299	+	0.510299i
$333$		0			0
$334$	9.52387			0.521123
$335$	−7.05545	−	6.60140i	−0.385481	−	0.360673i
$336$		0			0
$337$	16.8137	+	16.8137i	0.915901	+	0.915901i	0.996728	−	0.0808276i	$-0.0257563\pi$
$337$	16.8137	+	16.8137i	0.915901	+	0.915901i	−0.0808276	+	0.996728i	$0.525756\pi$
$338$	−7.29289	+	7.29289i	−0.396681	+	0.396681i
$339$		0			0
$340$	6.34162	+	5.93351i	0.343923	+	0.321790i
$341$		−	34.6200i		−	1.87478i
$342$		0			0
$343$	−14.5011	−	11.5204i	−0.782984	−	0.622042i
$344$		−	10.7292i		−	0.578478i
$345$		0			0
$346$		−	20.0260i		−	1.07661i
$347$	7.83919	+	7.83919i	0.420830	+	0.420830i	0.885489	−	0.464659i	$-0.153823\pi$
$347$	7.83919	+	7.83919i	0.420830	+	0.420830i	−0.464659	+	0.885489i	$0.653823\pi$
$348$		0			0
$349$	−5.10838			−0.273445			−0.136723	−	0.990609i	$-0.543657\pi$
$349$	−5.10838			−0.273445			−0.136723	+	0.990609i	$0.543657\pi$
$350$	−5.38344	+	12.0838i	−0.287757	+	0.645907i
$351$		0			0
$352$	3.46967	+	3.46967i	0.184934	+	0.184934i
$353$	−12.0821	−	12.0821i	−0.643066	−	0.643066i	0.308242	−	0.951308i	$-0.400259\pi$
$353$	−12.0821	−	12.0821i	−0.643066	−	0.643066i	−0.951308	+	0.308242i	$0.900259\pi$
$354$		0			0
$355$	−29.1274	+	0.968403i	−1.54592	+	0.0513975i
$356$			15.3596i			0.814060i
$357$		0			0
$358$	2.32018	−	2.32018i	0.122625	−	0.122625i
$359$		−	3.90596i		−	0.206149i	−0.994674	−	0.103074i	$-0.967132\pi$
$359$		−	3.90596i		−	0.206149i	0.994674	−	0.103074i	$-0.0328680\pi$
$360$		0			0
$361$	−17.3982			−0.915696
$362$	13.7132	−	13.7132i	0.720749	−	0.720749i
$363$		0			0
$364$	11.2981	+	5.96230i	0.592181	+	0.312510i
$365$	−11.6482	−	10.8986i	−0.609696	−	0.570459i
$366$		0			0
$367$	−3.98072	+	3.98072i	−0.207792	+	0.207792i	−0.803328	−	0.595536i	$-0.796940\pi$
$367$	−3.98072	+	3.98072i	−0.207792	+	0.207792i	0.595536	+	0.803328i	$0.296940\pi$
$368$	−1.05545	+	1.05545i	−0.0550193	+	0.0550193i
$369$		0			0
$370$	0.498736	+	15.0009i	0.0259281	+	0.779859i
$371$	−4.18807	−	2.21016i	−0.217434	−	0.114746i
$372$		0			0
$373$	−8.95648	+	8.95648i	−0.463749	+	0.463749i	−0.899882	−	0.436133i	$-0.856348\pi$
$373$	−8.95648	+	8.95648i	−0.463749	+	0.463749i	0.436133	+	0.899882i	$0.356348\pi$
$374$	19.0576			0.985446
$375$		0			0
$376$		−	1.03858i		−	0.0535609i
$377$	16.2751	−	16.2751i	0.838212	−	0.838212i
$378$		0			0
$379$			14.0190i			0.720109i	0.932931	+	0.360055i	$0.117242\pi$
$379$			14.0190i			0.720109i	−0.932931	+	0.360055i	$0.882758\pi$
$380$	−0.0940371	−	2.82843i	−0.00482400	−	0.145095i
$381$		0			0
$382$	11.9114	+	11.9114i	0.609441	+	0.609441i
$383$	−7.00951	−	7.00951i	−0.358169	−	0.358169i	0.504968	−	0.863138i	$-0.331504\pi$
$383$	−7.00951	−	7.00951i	−0.358169	−	0.358169i	−0.863138	+	0.504968i	$0.831504\pi$
$384$		0			0
$385$	9.49050	+	27.4341i	0.483680	+	1.39817i
$386$	−6.80760			−0.346498
$387$		0			0
$388$	−8.42614	−	8.42614i	−0.427773	−	0.427773i
$389$			18.6560i			0.945895i	0.881091	+	0.472948i	$0.156810\pi$
$389$			18.6560i			0.945895i	−0.881091	+	0.472948i	$0.843190\pi$
$390$		0			0
$391$			5.79722i			0.293178i
$392$	1.29289	−	6.87957i	0.0653010	−	0.347471i
$393$		0			0
$394$		−	18.4320i		−	0.928589i
$395$	1.10014	+	33.0897i	0.0553539	+	1.66492i
$396$		0			0
$397$	19.3683	−	19.3683i	0.972066	−	0.972066i	−0.0275544	−	0.999620i	$-0.508772\pi$
$397$	19.3683	−	19.3683i	0.972066	−	0.972066i	0.999620	+	0.0275544i	$0.00877196\pi$
$398$	8.30913	+	8.30913i	0.416499	+	0.416499i
$399$		0			0
$400$	−4.98896	+	0.332104i	−0.249448	+	0.0166052i
$401$	27.9099			1.39375			0.696877	−	0.717191i	$-0.254572\pi$
$401$	27.9099			1.39375			0.696877	+	0.717191i	$0.254572\pi$
$402$		0			0
$403$	24.0888	−	24.0888i	1.19995	−	1.19995i
$404$	−18.1504			−0.903015
$405$		0			0
$406$	−11.1541	−	5.88629i	−0.553567	−	0.292132i
$407$	23.2895	+	23.2895i	1.15442	+	1.15442i
$408$		0			0
$409$	−18.3211			−0.905918			−0.452959	−	0.891531i	$-0.649632\pi$
$409$	−18.3211			−0.905918			−0.452959	+	0.891531i	$0.649632\pi$
$410$	−8.32106	+	8.89339i	−0.410948	+	0.439213i
$411$		0			0
$412$	−8.36459	+	8.36459i	−0.412094	+	0.412094i
$413$	−1.09190	−	3.53211i	−0.0537288	−	0.173804i
$414$		0			0
$415$	−21.4706	−	20.0888i	−1.05395	−	0.986122i
$416$			4.82843i			0.236733i
$417$		0			0
$418$	−4.39124	−	4.39124i	−0.214783	−	0.214783i
$419$	5.49605			0.268500			0.134250	−	0.990948i	$-0.457138\pi$
$419$	5.49605			0.268500			0.134250	+	0.990948i	$0.457138\pi$
$420$		0			0
$421$	24.5863			1.19826			0.599132	−	0.800651i	$-0.295513\pi$
$421$	24.5863			1.19826			0.599132	+	0.800651i	$0.295513\pi$
$422$	11.7028	+	11.7028i	0.569683	+	0.569683i
$423$		0			0
$424$		−	1.78984i		−	0.0869224i
$425$	−12.7892	+	14.6133i	−0.620367	+	0.708851i
$426$		0			0
$427$	−5.80671	+	1.79506i	−0.281006	+	0.0868689i
$428$	3.77297	−	3.77297i	0.182374	−	0.182374i
$429$		0			0
$430$	23.9779	−	0.797197i	1.15632	−	0.0384443i
$431$	−22.8133			−1.09888			−0.549440	−	0.835533i	$-0.685159\pi$
$431$	−22.8133			−1.09888			−0.549440	+	0.835533i	$0.685159\pi$
$432$		0			0
$433$	17.1216	+	17.1216i	0.822811	+	0.822811i	0.986510	−	0.163700i	$-0.0523428\pi$
$433$	17.1216	+	17.1216i	0.822811	+	0.822811i	−0.163700	+	0.986510i	$0.552343\pi$
$434$	−16.5091	−	8.71231i	−0.792464	−	0.418204i
$435$		0			0
$436$	−0.0870500			−0.00416894
$437$	1.33579	−	1.33579i	0.0638996	−	0.0638996i
$438$		0			0
$439$	−35.8323			−1.71018			−0.855092	−	0.518476i	$-0.826500\pi$
$439$	−35.8323			−1.71018			−0.855092	+	0.518476i	$0.826500\pi$
$440$	−7.49632	+	8.01193i	−0.357373	+	0.381954i
$441$		0			0
$442$	13.2604	+	13.2604i	0.630733	+	0.630733i
$443$	−2.93109	+	2.93109i	−0.139260	+	0.139260i	−0.773300	−	0.634040i	$-0.781395\pi$
$443$	−2.93109	+	2.93109i	−0.139260	+	0.139260i	0.634040	+	0.773300i	$0.281395\pi$
$444$		0			0
$445$	−34.3262	+	1.14125i	−1.62722	+	0.0541004i
$446$		−	11.6824i		−	0.553175i
$447$		0			0
$448$	2.52773	−	0.781409i	0.119424	−	0.0369181i
$449$		−	1.70279i		−	0.0803598i	−0.999192	−	0.0401799i	$-0.987207\pi$
$449$		−	1.70279i		−	0.0803598i	0.999192	−	0.0401799i	$-0.0127931\pi$
$450$		0			0
$451$			26.7261i			1.25848i
$452$	−2.03248	−	2.03248i	−0.0956000	−	0.0956000i
$453$		0			0
$454$	−8.36217			−0.392456
$455$	−12.4853	+	25.6924i	−0.585319	+	1.20448i
$456$		0			0
$457$	−5.34315	−	5.34315i	−0.249942	−	0.249942i	0.571005	−	0.820947i	$-0.306554\pi$
$457$	−5.34315	−	5.34315i	−0.249942	−	0.249942i	−0.820947	+	0.571005i	$0.806554\pi$
$458$	−6.58579	−	6.58579i	−0.307734	−	0.307734i
$459$		0			0
$460$	−2.43718	−	2.28034i	−0.113634	−	0.106321i
$461$		−	0.858751i		−	0.0399960i	−0.999800	−	0.0199980i	$-0.993634\pi$
$461$		−	0.858751i		−	0.0399960i	0.999800	−	0.0199980i	$-0.00636599\pi$
$462$		0			0
$463$	−20.3594	+	20.3594i	−0.946180	+	0.946180i	−0.998624	−	0.0524436i	$-0.983299\pi$
$463$	−20.3594	+	20.3594i	−0.946180	+	0.946180i	0.0524436	+	0.998624i	$0.483299\pi$
$464$		−	4.76687i		−	0.221297i
$465$		0			0
$466$	−22.7071			−1.05189
$467$	−8.77908	+	8.77908i	−0.406247	+	0.406247i	−0.880428	−	0.474181i	$-0.842744\pi$
$467$	−8.77908	+	8.77908i	−0.406247	+	0.406247i	0.474181	+	0.880428i	$0.342744\pi$
$468$		0			0
$469$	−5.33579	+	10.1109i	−0.246384	+	0.466878i
$470$	2.32106	−	0.0771687i	0.107063	−	0.00355953i
$471$		0			0
$472$	0.988072	−	0.988072i	0.0454797	−	0.0454797i
$473$	37.2267	−	37.2267i	1.71168	−	1.71168i
$474$		0			0
$475$	6.31408	−	0.420314i	0.289710	−	0.0192853i
$476$	4.79594	−	9.08794i	0.219822	−	0.416545i
$477$		0			0
$478$	−1.19213	+	1.19213i	−0.0545267	+	0.0545267i
$479$	1.17157			0.0535305			0.0267653	−	0.999642i	$-0.491479\pi$
$479$	1.17157			0.0535305			0.0267653	+	0.999642i	$0.491479\pi$
$480$		0			0
$481$			32.4099i			1.47776i
$482$	−2.55672	+	2.55672i	−0.116455	+	0.116455i
$483$		0			0
$484$			13.0772i			0.594417i
$485$	18.2049	−	19.4571i	0.826644	−	0.883501i
$486$		0			0
$487$	9.70737	+	9.70737i	0.439883	+	0.439883i	0.891972	−	0.452090i	$-0.149321\pi$
$487$	9.70737	+	9.70737i	0.439883	+	0.439883i	−0.452090	+	0.891972i	$0.649321\pi$
$488$	−1.62437	−	1.62437i	−0.0735318	−	0.0735318i
$489$		0			0
$490$	15.4707	+	2.37824i	0.698897	+	0.107438i
$491$	16.9381			0.764405			0.382202	−	0.924079i	$-0.375166\pi$
$491$	16.9381			0.764405			0.382202	+	0.924079i	$0.375166\pi$
$492$		0			0
$493$	−13.0913	−	13.0913i	−0.589605	−	0.589605i
$494$		−	6.11091i		−	0.274943i
$495$		0			0
$496$		−	7.05545i		−	0.316799i
$497$	10.1844	+	32.9448i	0.456832	+	1.47778i
$498$		0			0
$499$			30.4117i			1.36141i	0.732556	+	0.680706i	$0.238327\pi$
$499$			30.4117i			1.36141i	−0.732556	+	0.680706i	$0.761673\pi$
$500$	−1.11289	−	11.1248i	−0.0497698	−	0.497517i
$501$		0			0
$502$	−3.38630	+	3.38630i	−0.151138	+	0.151138i
$503$	4.75825	+	4.75825i	0.212160	+	0.212160i	0.805184	−	0.593025i	$-0.202066\pi$
$503$	4.75825	+	4.75825i	0.212160	+	0.212160i	−0.593025	+	0.805184i	$0.702066\pi$
$504$		0			0
$505$	−1.34861	−	40.5631i	−0.0600122	−	1.80503i
$506$	−7.32414			−0.325598
$507$		0			0
$508$	11.1761	−	11.1761i	0.495861	−	0.495861i
$509$	40.3501			1.78849			0.894243	−	0.447581i	$-0.147714\pi$
$509$	40.3501			1.78849			0.894243	+	0.447581i	$0.147714\pi$
$510$		0			0
$511$	−8.80915	+	16.6926i	−0.389694	+	0.738439i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−29.4316			−1.29817
$515$	−19.3150	−	18.0720i	−0.851119	−	0.796345i
$516$		0			0
$517$	3.60354	−	3.60354i	0.158484	−	0.158484i
$518$	16.9669	−	5.24505i	0.745482	−	0.230454i
$519$		0			0
$520$	−10.7907	+	0.358761i	−0.473205	+	0.0157327i
$521$		−	8.96879i		−	0.392930i	−0.980511	−	0.196465i	$-0.937054\pi$
$521$		−	8.96879i		−	0.392930i	0.980511	−	0.196465i	$-0.0629462\pi$
$522$		0			0
$523$	−8.40290	−	8.40290i	−0.367433	−	0.367433i	0.499107	−	0.866540i	$-0.333661\pi$
$523$	−8.40290	−	8.40290i	−0.367433	−	0.367433i	−0.866540	+	0.499107i	$0.833661\pi$
$524$	12.8367			0.560772
$525$		0			0
$526$	−9.35965			−0.408100
$527$	−19.3765	−	19.3765i	−0.844054	−	0.844054i
$528$		0			0
$529$			20.7720i			0.903132i
$530$	4.00000	−	0.132989i	0.173749	−	0.00577665i
$531$		0			0
$532$	−3.19912	+	0.988958i	−0.138699	+	0.0428768i
$533$	−18.5962	+	18.5962i	−0.805490	+	0.805490i
$534$		0			0
$535$	8.71231	+	8.15163i	0.376666	+	0.352426i
$536$	−4.32106			−0.186641
$537$		0			0
$538$	−9.27665	−	9.27665i	−0.399945	−	0.399945i
$539$	28.3557	−	19.3839i	1.22137	−	0.834923i
$540$		0			0
$541$	27.1611			1.16775			0.583874	−	0.811844i	$-0.301536\pi$
$541$	27.1611			1.16775			0.583874	+	0.811844i	$0.301536\pi$
$542$	12.7870	−	12.7870i	0.549250	−	0.549250i
$543$		0			0
$544$	3.88388			0.166520
$545$	−0.00646797	−	0.194542i	−0.000277057	−	0.00833327i
$546$		0			0
$547$	−16.8471	−	16.8471i	−0.720329	−	0.720329i	0.248343	−	0.968672i	$-0.420114\pi$
$547$	−16.8471	−	16.8471i	−0.720329	−	0.720329i	−0.968672	+	0.248343i	$0.920114\pi$
$548$	−3.62437	+	3.62437i	−0.154825	+	0.154825i
$549$		0			0
$550$	−18.4623	−	16.1577i	−0.787236	−	0.688968i
$551$			6.03300i			0.257015i
$552$		0			0
$553$	37.4264	−	11.5698i	1.59153	−	0.491998i
$554$			3.72704i			0.158347i
$555$		0			0
$556$			3.90596i			0.165650i
$557$	0.0529257	+	0.0529257i	0.00224253	+	0.00224253i	0.708227	−	0.705985i	$-0.249495\pi$
$557$	0.0529257	+	0.0529257i	0.00224253	+	0.00224253i	−0.705985	+	0.708227i	$0.749495\pi$
$558$		0			0
$559$	51.8050			2.19112
$560$	1.93413	+	5.59099i	0.0817320	+	0.236262i
$561$		0			0
$562$	−14.4645	−	14.4645i	−0.610146	−	0.610146i
$563$	7.84316	+	7.84316i	0.330550	+	0.330550i	0.852795	−	0.522246i	$-0.174906\pi$
$563$	7.84316	+	7.84316i	0.330550	+	0.330550i	−0.522246	+	0.852795i	$0.674906\pi$
$564$		0			0
$565$	4.39124	−	4.69328i	0.184741	−	0.197448i
$566$			15.2383i			0.640514i
$567$		0			0
$568$	−9.21598	+	9.21598i	−0.386694	+	0.386694i
$569$		−	6.12311i		−	0.256694i	−0.991729	−	0.128347i	$-0.959033\pi$
$569$		−	6.12311i		−	0.256694i	0.991729	−	0.128347i	$-0.0409671\pi$
$570$		0			0
$571$	30.4896			1.27595			0.637974	−	0.770058i	$-0.279773\pi$
$571$	30.4896			1.27595			0.637974	+	0.770058i	$0.279773\pi$
$572$	−16.7530	+	16.7530i	−0.700479	+	0.700479i
$573$		0			0
$574$	12.7448	+	6.72576i	0.531957	+	0.280728i
$575$	4.91509	−	5.61613i	0.204973	−	0.234209i
$576$		0			0
$577$	−11.5444	+	11.5444i	−0.480600	+	0.480600i	−0.905323	−	0.424723i	$-0.860371\pi$
$577$	−11.5444	+	11.5444i	−0.480600	+	0.480600i	0.424723	+	0.905323i	$0.360371\pi$
$578$	−1.35445	+	1.35445i	−0.0563376	+	0.0563376i
$579$		0			0
$580$	10.6532	−	0.354187i	0.442349	−	0.0147068i
$581$	−16.2374	+	30.7686i	−0.673642	+	1.27650i
$582$		0			0
$583$	6.21016	−	6.21016i	0.257198	−	0.257198i
$584$	−7.13387			−0.295202
$585$		0			0
$586$			4.46841i			0.184588i
$587$	7.24478	−	7.24478i	0.299024	−	0.299024i	−0.541607	−	0.840632i	$-0.682184\pi$
$587$	7.24478	−	7.24478i	0.299024	−	0.299024i	0.840632	+	0.541607i	$0.182184\pi$
$588$		0			0
$589$			8.92945i			0.367932i
$590$	2.28159	+	2.13476i	0.0939317	+	0.0878867i
$591$		0			0
$592$	4.74632	+	4.74632i	0.195072	+	0.195072i
$593$	6.67652	+	6.67652i	0.274172	+	0.274172i	0.830777	−	0.556605i	$-0.187896\pi$
$593$	6.67652	+	6.67652i	0.274172	+	0.274172i	−0.556605	+	0.830777i	$0.687896\pi$
$594$		0			0
$595$	20.6664	+	10.0429i	0.847239	+	0.411718i
$596$	−5.64124			−0.231074
$597$		0			0
$598$	−5.09618	−	5.09618i	−0.208398	−	0.208398i
$599$			2.62526i			0.107265i	0.998561	+	0.0536325i	$0.0170800\pi$
$599$			2.62526i			0.107265i	−0.998561	+	0.0536325i	$0.982920\pi$
$600$		0			0
$601$		−	11.7003i		−	0.477265i	−0.971110	−	0.238632i	$-0.923301\pi$
$601$		−	11.7003i		−	0.477265i	0.971110	−	0.238632i	$-0.0766991\pi$
$602$	−8.38387	−	27.1204i	−0.341701	−	1.10535i
$603$		0			0
$604$		−	11.7678i		−	0.478823i
$605$	−29.2253	+	0.971657i	−1.18818	+	0.0395035i
$606$		0			0
$607$	23.2749	−	23.2749i	0.944697	−	0.944697i	−0.0538519	−	0.998549i	$-0.517150\pi$
$607$	23.2749	−	23.2749i	0.944697	−	0.944697i	0.998549	+	0.0538519i	$0.0171499\pi$
$608$	−0.894921	−	0.894921i	−0.0362939	−	0.0362939i
$609$		0			0
$610$	3.50950	−	3.75089i	0.142096	−	0.151869i
$611$	5.01473			0.202874
$612$		0			0
$613$	18.1372	−	18.1372i	0.732554	−	0.732554i	−0.238571	−	0.971125i	$-0.576679\pi$
$613$	18.1372	−	18.1372i	0.732554	−	0.732554i	0.971125	+	0.238571i	$0.0766789\pi$
$614$	29.4172			1.18718
$615$		0			0
$616$	11.4816	+	6.05914i	0.462607	+	0.244130i
$617$	−1.59063	−	1.59063i	−0.0640365	−	0.0640365i	0.674363	−	0.738400i	$-0.264418\pi$
$617$	−1.59063	−	1.59063i	−0.0640365	−	0.0640365i	−0.738400	+	0.674363i	$0.764418\pi$
$618$		0			0
$619$	39.2232			1.57651			0.788257	−	0.615346i	$-0.210984\pi$
$619$	39.2232			1.57651			0.788257	+	0.615346i	$0.210984\pi$
$620$	15.7678	−	0.524233i	0.633248	−	0.0210537i
$621$		0			0
$622$	8.11091	−	8.11091i	0.325218	−	0.325218i
$623$	12.0022	+	38.8250i	0.480856	+	1.55549i
$624$		0			0
$625$	24.7794	−	3.31371i	0.991177	−	0.132548i
$626$			0.866125i			0.0346173i
$627$		0			0
$628$	−13.7132	−	13.7132i	−0.547216	−	0.547216i
$629$	26.0698			1.03947
$630$		0			0
$631$	−1.69542			−0.0674935			−0.0337468	−	0.999430i	$-0.510744\pi$
$631$	−1.69542			−0.0674935			−0.0337468	+	0.999430i	$0.510744\pi$
$632$	10.4697	+	10.4697i	0.416461	+	0.416461i
$633$		0			0
$634$		−	9.95583i		−	0.395397i
$635$	25.8072	+	24.1464i	1.02413	+	0.958221i
$636$		0			0
$637$	33.2175	+	6.24264i	1.31612	+	0.247342i
$638$	16.5395	−	16.5395i	0.654804	−	0.654804i
$639$		0			0
$640$	−1.52773	+	1.63280i	−0.0603887	+	0.0645423i
$641$	−23.0043			−0.908615			−0.454308	−	0.890845i	$-0.650113\pi$
$641$	−23.0043			−0.908615			−0.454308	+	0.890845i	$0.650113\pi$
$642$		0			0
$643$	−13.9948	−	13.9948i	−0.551900	−	0.551900i	0.375089	−	0.926989i	$-0.377612\pi$
$643$	−13.9948	−	13.9948i	−0.551900	−	0.551900i	−0.926989	+	0.375089i	$0.877612\pi$
$644$	−1.84316	+	3.49264i	−0.0726305	+	0.137629i
$645$		0			0
$646$	−4.91548			−0.193397
$647$	−5.22955	+	5.22955i	−0.205595	+	0.205595i	−0.802392	−	0.596797i	$-0.796440\pi$
$647$	−5.22955	+	5.22955i	−0.205595	+	0.205595i	0.596797	+	0.802392i	$0.296440\pi$
$648$		0			0
$649$	6.85656			0.269144
$650$	−1.60354	−	24.0888i	−0.0628961	−	0.944841i
$651$		0			0
$652$	−7.21967	−	7.21967i	−0.282744	−	0.282744i
$653$	−1.74516	+	1.74516i	−0.0682933	+	0.0682933i	−0.740428	−	0.672135i	$-0.765377\pi$
$653$	−1.74516	+	1.74516i	−0.0682933	+	0.0682933i	0.672135	+	0.740428i	$0.265377\pi$
$654$		0			0
$655$	0.953787	+	28.6878i	0.0372676	+	1.12093i
$656$			5.44670i			0.212658i
$657$		0			0
$658$	−0.811559	−	2.62526i	−0.0316379	−	0.102343i
$659$			21.4234i			0.834536i	0.908784	+	0.417268i	$0.137012\pi$
$659$			21.4234i			0.834536i	−0.908784	+	0.417268i	$0.862988\pi$
$660$		0			0
$661$			15.6881i			0.610196i	0.952321	+	0.305098i	$0.0986892\pi$
$661$			15.6881i			0.610196i	−0.952321	+	0.305098i	$0.901311\pi$
$662$	7.19543	+	7.19543i	0.279658	+	0.279658i
$663$		0			0
$664$	−13.1495			−0.510299
$665$	−2.44786	−	7.07601i	−0.0949238	−	0.274396i
$666$		0			0
$667$	5.03121	+	5.03121i	0.194809	+	0.194809i
$668$	6.73439	+	6.73439i	0.260561	+	0.260561i
$669$		0			0
$670$	−0.321063	−	9.65685i	−0.0124037	−	0.373077i
$671$		−	11.2720i		−	0.435153i
$672$		0			0
$673$	26.0502	−	26.0502i	1.00416	−	1.00416i	0.00417159	−	0.999991i	$-0.498672\pi$
$673$	26.0502	−	26.0502i	1.00416	−	1.00416i	0.999991	−	0.00417159i	$-0.00132786\pi$
$674$			23.7782i			0.915901i
$675$		0			0
$676$	−10.3137			−0.396681
$677$	3.99149	−	3.99149i	0.153405	−	0.153405i	−0.626232	−	0.779637i	$-0.715404\pi$
$677$	3.99149	−	3.99149i	0.153405	−	0.153405i	0.779637	+	0.626232i	$0.215404\pi$
$678$		0			0
$679$	−27.8832	−	14.7147i	−1.07006	−	0.564699i
$680$	0.288579	+	8.67982i	0.0110665	+	0.332856i
$681$		0			0
$682$	24.4801	−	24.4801i	0.937390	−	0.937390i
$683$	28.2530	−	28.2530i	1.08107	−	1.08107i	0.0846629	−	0.996410i	$-0.473019\pi$
$683$	28.2530	−	28.2530i	1.08107	−	1.08107i	0.996410	−	0.0846629i	$-0.0269813\pi$
$684$		0			0
$685$	−8.36916	−	7.83057i	−0.319769	−	0.299191i
$686$	−2.10767	−	18.3999i	−0.0804713	−	0.702513i
$687$		0			0
$688$	7.58667	−	7.58667i	0.289239	−	0.289239i
$689$	8.64213			0.329239
$690$		0			0
$691$			2.45366i			0.0933418i	0.998910	+	0.0466709i	$0.0148612\pi$
$691$			2.45366i			0.0933418i	−0.998910	+	0.0466709i	$0.985139\pi$
$692$	14.1605	−	14.1605i	0.538303	−	0.538303i
$693$		0			0
$694$			11.0863i			0.420830i
$695$	−8.72918	+	0.290220i	−0.331116	+	0.0110087i
$696$		0			0
$697$	14.9584	+	14.9584i	0.566588	+	0.566588i
$698$	−3.61217	−	3.61217i	−0.136723	−	0.136723i
$699$		0			0
$700$	−12.3512	+	4.73788i	−0.466832	+	0.179075i
$701$	6.34833			0.239773			0.119887	−	0.992788i	$-0.461747\pi$
$701$	6.34833			0.239773			0.119887	+	0.992788i	$0.461747\pi$
$702$		0			0
$703$	−6.00699	−	6.00699i	−0.226558	−	0.226558i
$704$			4.90685i			0.184934i
$705$		0			0
$706$		−	17.0867i		−	0.643066i
$707$	−45.8792	+	14.1829i	−1.72546	+	0.533401i
$708$		0			0
$709$			20.3645i			0.764805i	0.923996	+	0.382402i	$0.124903\pi$
$709$			20.3645i			0.764805i	−0.923996	+	0.382402i	$0.875097\pi$
$710$	−21.2810	−	19.9114i	−0.798660	−	0.747262i
$711$		0			0
$712$	−10.8609	+	10.8609i	−0.407030	+	0.407030i
$713$	7.44670	+	7.44670i	0.278881	+	0.278881i
$714$		0			0
$715$	−38.6850	−	36.1954i	−1.44674	−	1.35363i
$716$	3.28123			0.122625
$717$		0			0
$718$	2.76193	−	2.76193i	0.103074	−	0.103074i
$719$	−25.9031			−0.966021			−0.483011	−	0.875614i	$-0.660457\pi$
$719$	−25.9031			−0.966021			−0.483011	+	0.875614i	$0.660457\pi$
$720$		0			0
$721$	−14.6072	+	27.6795i	−0.544002	+	1.03084i
$722$	−12.3024	−	12.3024i	−0.457848	−	0.457848i
$723$		0			0
$724$	19.3934			0.720749
$725$	1.58310	+	23.7817i	0.0587948	+	0.883231i
$726$		0			0
$727$	−36.3373	+	36.3373i	−1.34768	+	1.34768i	−0.459495	+	0.888180i	$0.651970\pi$
$727$	−36.3373	+	36.3373i	−1.34768	+	1.34768i	−0.888180	+	0.459495i	$0.848030\pi$
$728$	3.77297	+	12.2049i	0.139836	+	0.452345i
$729$		0			0
$730$	−0.530060	−	15.9430i	−0.0196184	−	0.590078i
$731$		−	41.6708i		−	1.54125i
$732$		0			0
$733$	18.3535	+	18.3535i	0.677904	+	0.677904i	0.959525	−	0.281622i	$-0.0908723\pi$
$733$	18.3535	+	18.3535i	0.677904	+	0.677904i	−0.281622	+	0.959525i	$0.590872\pi$
$734$	−5.62959			−0.207792
$735$		0			0
$736$	−1.49264			−0.0550193
$737$	−14.9926	−	14.9926i	−0.552261	−	0.552261i
$738$		0			0
$739$			21.3934i			0.786968i	0.919331	+	0.393484i	$0.128730\pi$
$739$			21.3934i			0.786968i	−0.919331	+	0.393484i	$0.871270\pi$
$740$	−10.2546	+	10.9599i	−0.376965	+	0.402894i
$741$		0			0
$742$	−1.39860	−	4.52423i	−0.0513442	−	0.166090i
$743$	29.9264	−	29.9264i	1.09789	−	1.09789i	0.103235	−	0.994657i	$-0.467081\pi$
$743$	29.9264	−	29.9264i	1.09789	−	1.09789i	0.994657	−	0.103235i	$-0.0329195\pi$
$744$		0			0
$745$	−0.419154	−	12.6072i	−0.0153566	−	0.461893i
$746$	−12.6664			−0.463749
$747$		0			0
$748$	13.4758	+	13.4758i	0.492723	+	0.492723i
$749$	6.58881	−	12.4853i	0.240750	−	0.456202i
$750$		0			0
$751$	−19.3081			−0.704563			−0.352281	−	0.935894i	$-0.614594\pi$
$751$	−19.3081			−0.704563			−0.352281	+	0.935894i	$0.614594\pi$
$752$	0.734390	−	0.734390i	0.0267804	−	0.0267804i
$753$		0			0
$754$	23.0165			0.838212
$755$	26.2990	−	0.874366i	0.957118	−	0.0318214i
$756$		0			0
$757$	−30.9872	−	30.9872i	−1.12625	−	1.12625i	−0.990782	−	0.135465i	$-0.956747\pi$
$757$	−30.9872	−	30.9872i	−1.12625	−	1.12625i	−0.135465	−	0.990782i	$-0.543253\pi$
$758$	−9.91295	+	9.91295i	−0.360055	+	0.360055i
$759$		0			0
$760$	1.93351	−	2.06649i	0.0701356	−	0.0749596i
$761$			47.3418i			1.71614i	0.513532	+	0.858070i	$0.328337\pi$
$761$			47.3418i			1.71614i	−0.513532	+	0.858070i	$0.671663\pi$
$762$		0			0
$763$	−0.220039	+	0.0680216i	−0.00796593	+	0.00246255i
$764$			16.8453i			0.609441i
$765$		0			0
$766$		−	9.91295i		−	0.358169i
$767$	4.77083	+	4.77083i	0.172265	+	0.172265i
$768$		0			0
$769$	44.0520			1.58856			0.794278	−	0.607554i	$-0.207849\pi$
$769$	44.0520			1.58856			0.794278	+	0.607554i	$0.207849\pi$
$770$	−12.6881	+	26.1097i	−0.457246	+	0.940927i
$771$		0			0
$772$	−4.81370	−	4.81370i	−0.173249	−	0.173249i
$773$	−11.1336	−	11.1336i	−0.400448	−	0.400448i	0.477943	−	0.878391i	$-0.341383\pi$
$773$	−11.1336	−	11.1336i	−0.400448	−	0.400448i	−0.878391	+	0.477943i	$0.841383\pi$
$774$		0			0
$775$	2.34315	+	35.1994i	0.0841683	+	1.26440i
$776$		−	11.9164i		−	0.427773i
$777$		0			0
$778$	−13.1918	+	13.1918i	−0.472948	+	0.472948i
$779$		−	6.89339i		−	0.246981i
$780$		0			0
$781$	−63.9528			−2.28841
$782$	−4.09925	+	4.09925i	−0.146589	+	0.146589i
$783$		0			0
$784$	5.77880	−	3.95037i	0.206386	−	0.141085i
$785$	29.6278	−	31.6656i	1.05746	−	1.13019i
$786$		0			0
$787$	11.7098	−	11.7098i	0.417409	−	0.417409i	−0.466901	−	0.884310i	$-0.654630\pi$
$787$	11.7098	−	11.7098i	0.417409	−	0.417409i	0.884310	+	0.466901i	$0.154630\pi$
$788$	13.0334	−	13.0334i	0.464295	−	0.464295i
$789$		0			0
$790$	−22.6200	+	24.1759i	−0.804785	+	0.860139i
$791$	−6.72576	−	3.54936i	−0.239141	−	0.126201i
$792$		0			0
$793$	7.84316	−	7.84316i	0.278519	−	0.278519i
$794$	27.3909			0.972066
$795$		0			0
$796$			11.7509i			0.416499i
$797$	−12.7255	+	12.7255i	−0.450760	+	0.450760i	−0.895607	−	0.444847i	$-0.853258\pi$
$797$	−12.7255	+	12.7255i	−0.450760	+	0.450760i	0.444847	+	0.895607i	$0.353258\pi$
$798$		0			0
$799$		−	4.03374i		−	0.142703i
$800$	−3.76256	−	3.29289i	−0.133027	−	0.116421i
$801$		0			0
$802$	19.7353	+	19.7353i	0.696877	+	0.696877i
$803$	−24.7522	−	24.7522i	−0.873485	−	0.873485i
$804$		0			0
$805$	−7.94241	−	3.85964i	−0.279933	−	0.136034i
$806$	34.0667			1.19995
$807$		0			0
$808$	−12.8343	−	12.8343i	−0.451507	−	0.451507i
$809$			22.8744i			0.804220i	0.915591	+	0.402110i	$0.131723\pi$
$809$			22.8744i			0.804220i	−0.915591	+	0.402110i	$0.868277\pi$
$810$		0			0
$811$		−	0.722188i		−	0.0253595i	−0.999920	−	0.0126797i	$-0.995964\pi$
$811$		−	0.722188i		−	0.0253595i	0.999920	−	0.0126797i	$-0.00403619\pi$
$812$	−3.72488	−	12.0494i	−0.130718	−	0.422849i
$813$		0			0
$814$			32.9363i			1.15442i
$815$	15.5983	−	16.6712i	0.546386	−	0.583967i
$816$		0			0
$817$	−9.60177	+	9.60177i	−0.335923	+	0.335923i
$818$	−12.9549	−	12.9549i	−0.452959	−	0.452959i
$819$		0			0
$820$	−12.1725	+	0.404699i	−0.425081	+	0.0141327i
$821$	−21.2417			−0.741341			−0.370671	−	0.928764i	$-0.620872\pi$
$821$	−21.2417			−0.741341			−0.370671	+	0.928764i	$0.620872\pi$
$822$		0			0
$823$	10.3066	−	10.3066i	0.359266	−	0.359266i	−0.504276	−	0.863542i	$-0.668241\pi$
$823$	10.3066	−	10.3066i	0.359266	−	0.359266i	0.863542	+	0.504276i	$0.168241\pi$
$824$	−11.8293			−0.412094
$825$		0			0
$826$	1.72549	−	3.26966i	0.0600374	−	0.113766i
$827$	26.1746	+	26.1746i	0.910181	+	0.910181i	0.996286	−	0.0861054i	$-0.0274422\pi$
$827$	26.1746	+	26.1746i	0.910181	+	0.910181i	−0.0861054	+	0.996286i	$0.527442\pi$
$828$		0			0
$829$	−21.0061			−0.729571			−0.364786	−	0.931092i	$-0.618858\pi$
$829$	−21.0061			−0.729571			−0.364786	+	0.931092i	$0.618858\pi$
$830$	−0.977031	−	29.3869i	−0.0339132	−	1.02003i
$831$		0			0
$832$	−3.41421	+	3.41421i	−0.118367	+	0.118367i
$833$	5.02144	−	26.7194i	0.173983	−	0.925773i
$834$		0			0
$835$	−14.5499	+	15.5506i	−0.503519	+	0.538151i
$836$		−	6.21016i		−	0.214783i
$837$		0			0
$838$	3.88629	+	3.88629i	0.134250	+	0.134250i
$839$	−50.2886			−1.73615			−0.868077	−	0.496430i	$-0.834644\pi$
$839$	−50.2886			−1.73615			−0.868077	+	0.496430i	$0.834644\pi$
$840$		0			0
$841$	6.27692			0.216445
$842$	17.3851	+	17.3851i	0.599132	+	0.599132i
$843$		0			0
$844$			16.5502i			0.569683i
$845$	−0.766327	−	23.0494i	−0.0263625	−	0.792924i
$846$		0			0
$847$	10.2186	+	33.0555i	0.351116	+	1.13580i
$848$	1.26561	−	1.26561i	0.0434612	−	0.0434612i
$849$		0			0
$850$	−19.3765	+	1.28985i	−0.664609	+	0.0442416i
$851$	−10.0190			−0.343448
$852$		0			0
$853$	−13.1647	−	13.1647i	−0.450751	−	0.450751i	0.444853	−	0.895604i	$-0.353256\pi$
$853$	−13.1647	−	13.1647i	−0.450751	−	0.450751i	−0.895604	+	0.444853i	$0.853256\pi$
$854$	−5.37526	−	2.83667i	−0.183938	−	0.0970688i
$855$		0			0
$856$	5.33579			0.182374
$857$	19.5839	−	19.5839i	0.668973	−	0.668973i	−0.288505	−	0.957478i	$-0.593158\pi$
$857$	19.5839	−	19.5839i	0.668973	−	0.668973i	0.957478	+	0.288505i	$0.0931583\pi$
$858$		0			0
$859$	7.58185			0.258689			0.129345	−	0.991600i	$-0.458713\pi$
$859$	7.58185			0.258689			0.129345	+	0.991600i	$0.458713\pi$
$860$	17.5187	+	16.3912i	0.597381	+	0.558937i
$861$		0			0
$862$	−16.1315	−	16.1315i	−0.549440	−	0.549440i
$863$	22.1829	−	22.1829i	0.755113	−	0.755113i	−0.220315	−	0.975429i	$-0.570709\pi$
$863$	22.1829	−	22.1829i	0.755113	−	0.755113i	0.975429	+	0.220315i	$0.0707086\pi$
$864$		0			0
$865$	32.6986	+	30.5943i	1.11179	+	1.04024i
$866$			24.2136i			0.822811i
$867$		0			0
$868$	−5.51319	−	17.8343i	−0.187130	−	0.605334i
$869$			72.6525i			2.46457i
$870$		0			0
$871$		−	20.8639i		−	0.706948i
$872$	−0.0615536	−	0.0615536i	−0.00208447	−	0.00208447i
$873$		0			0
$874$	1.88909			0.0638996
$875$	−11.5061	−	27.2509i	−0.388977	−	0.921247i
$876$		0			0
$877$	−5.71511	−	5.71511i	−0.192985	−	0.192985i	0.603999	−	0.796985i	$-0.293573\pi$
$877$	−5.71511	−	5.71511i	−0.192985	−	0.192985i	−0.796985	+	0.603999i	$0.793573\pi$
$878$	−25.3373	−	25.3373i	−0.855092	−	0.855092i
$879$		0			0
$880$	−10.9660	+	0.364588i	−0.369663	+	0.0122902i
$881$			31.8033i			1.07148i	0.844383	+	0.535740i	$0.179967\pi$
$881$			31.8033i			1.07148i	−0.844383	+	0.535740i	$0.820033\pi$
$882$		0			0
$883$	−16.9653	+	16.9653i	−0.570929	+	0.570929i	−0.932388	−	0.361459i	$-0.882279\pi$
$883$	−16.9653	+	16.9653i	−0.570929	+	0.570929i	0.361459	+	0.932388i	$0.382279\pi$
$884$			18.7530i			0.630733i
$885$		0			0
$886$	−4.14519			−0.139260
$887$	7.70801	−	7.70801i	0.258810	−	0.258810i	−0.565760	−	0.824570i	$-0.691417\pi$
$887$	7.70801	−	7.70801i	0.258810	−	0.258810i	0.824570	+	0.565760i	$0.191417\pi$
$888$		0			0
$889$	19.5171	−	36.9834i	0.654583	−	1.24038i
$890$	−25.0793	−	23.4653i	−0.840660	−	0.786560i
$891$		0			0
$892$	8.26067	−	8.26067i	0.276588	−	0.276588i
$893$	−0.929451	+	0.929451i	−0.0311029	+	0.0311029i
$894$		0			0
$895$	0.243801	+	7.33299i	0.00814937	+	0.245115i
$896$	2.33991	+	1.23483i	0.0781710	+	0.0412529i
$897$		0			0
$898$	1.20406	−	1.20406i	0.0401799	−	0.0401799i
$899$	−33.6325			−1.12171
$900$		0			0
$901$		−	6.95153i		−	0.231589i
$902$	−18.8982	+	18.8982i	−0.629242	+	0.629242i
$903$		0			0
$904$		−	2.87437i		−	0.0956000i
$905$	1.44096	+	43.3410i	0.0478992	+	1.44070i
$906$		0			0
$907$	0.997860	+	0.997860i	0.0331334	+	0.0331334i	0.723479	−	0.690346i	$-0.242542\pi$
$907$	0.997860	+	0.997860i	0.0331334	+	0.0331334i	−0.690346	+	0.723479i	$0.742542\pi$
$908$	−5.91295	−	5.91295i	−0.196228	−	0.196228i
$909$		0			0
$910$	−26.9957	+	9.33882i	−0.894898	+	0.309579i
$911$	21.9623			0.727643			0.363821	−	0.931469i	$-0.381472\pi$
$911$	21.9623			0.727643			0.363821	+	0.931469i	$0.381472\pi$
$912$		0			0
$913$	−45.6243	−	45.6243i	−1.50995	−	1.50995i
$914$		−	7.55635i		−	0.249942i
$915$		0			0
$916$		−	9.31371i		−	0.307734i
$917$	32.4476	−	10.0307i	1.07151	−	0.331242i
$918$		0			0
$919$			32.6954i			1.07852i	0.842138	+	0.539262i	$0.181297\pi$
$919$			32.6954i			1.07852i	−0.842138	+	0.539262i	$0.818703\pi$
$920$	−0.110906	−	3.33579i	−0.00365645	−	0.109978i
$921$		0			0
$922$	0.607228	−	0.607228i	0.0199980	−	0.0199980i
$923$	−44.4987	−	44.4987i	−1.46469	−	1.46469i
$924$		0			0
$925$	−25.2555	−	22.1029i	−0.830394	−	0.726739i
$926$	−28.7925			−0.946180
$927$		0			0
$928$	3.37069	−	3.37069i	0.110648	−	0.110648i
$929$	10.8063			0.354545			0.177272	−	0.984162i	$-0.443273\pi$
$929$	10.8063			0.354545			0.177272	+	0.984162i	$0.443273\pi$
$930$		0			0
$931$	−7.31371	+	4.99963i	−0.239697	+	0.163856i
$932$	−16.0563	−	16.0563i	−0.525943	−	0.525943i
$933$		0			0
$934$	−12.4155			−0.406247
$935$	−29.1148	+	31.1174i	−0.952156	+	1.01765i
$936$		0			0
$937$	−3.51804	+	3.51804i	−0.114929	+	0.114929i	−0.762233	−	0.647303i	$-0.775897\pi$
$937$	−3.51804	+	3.51804i	−0.114929	+	0.114929i	0.647303	+	0.762233i	$0.275897\pi$
$938$	−10.9225	+	3.37652i	−0.356631	+	0.110247i
$939$		0			0
$940$	1.69581	+	1.58667i	0.0553111	+	0.0517516i
$941$		−	54.9021i		−	1.78976i	−0.446309	−	0.894879i	$-0.647262\pi$
$941$		−	54.9021i		−	1.78976i	0.446309	−	0.894879i	$-0.352738\pi$
$942$		0			0
$943$	−5.74873	−	5.74873i	−0.187204	−	0.187204i
$944$	1.39735			0.0454797
$945$		0			0
$946$	52.6464			1.71168
$947$	30.4494	+	30.4494i	0.989471	+	0.989471i	0.999945	−	0.0104740i	$-0.00333405\pi$
$947$	30.4494	+	30.4494i	0.989471	+	0.989471i	−0.0104740	+	0.999945i	$0.503334\pi$
$948$		0			0
$949$		−	34.4454i		−	1.11814i
$950$	4.76193	+	4.16752i	0.154498	+	0.135212i
$951$		0			0
$952$	9.81739	−	3.03490i	0.318183	−	0.0983616i
$953$	−40.3553	+	40.3553i	−1.30724	+	1.30724i	−0.383836	+	0.923401i	$0.625397\pi$
$953$	−40.3553	+	40.3553i	−1.30724	+	1.30724i	−0.923401	+	0.383836i	$0.874603\pi$
$954$		0			0
$955$	−37.6464	+	1.25164i	−1.21821	+	0.0405020i
$956$	−1.68592			−0.0545267
$957$		0			0
$958$	0.828427	+	0.828427i	0.0267653	+	0.0267653i
$959$	−6.32930	+	11.9935i	−0.204384	+	0.387291i
$960$		0			0
$961$	−18.7794			−0.605788
$962$	−22.9172	+	22.9172i	−0.738882	+	0.738882i
$963$		0			0
$964$	−3.61574			−0.116455
$965$	10.4001	−	11.1155i	0.334793	−	0.357820i
$966$		0			0
$967$	30.6566	+	30.6566i	0.985849	+	0.985849i	0.999901	−	0.0140521i	$-0.00447307\pi$
$967$	30.6566	+	30.6566i	0.985849	+	0.985849i	−0.0140521	+	0.999901i	$0.504473\pi$
$968$	−9.24695	+	9.24695i	−0.297208	+	0.297208i
$969$		0			0
$970$	26.6311	−	0.885407i	0.855073	−	0.0284287i
$971$			46.5248i			1.49305i	0.665357	+	0.746525i	$0.268279\pi$
$971$			46.5248i			1.49305i	−0.665357	+	0.746525i	$0.731721\pi$
$972$		0			0
$973$	3.05215	+	9.87321i	0.0978475	+	0.316520i
$974$			13.7283i			0.439883i
$975$		0			0
$976$		−	2.29721i		−	0.0735318i
$977$	−42.6690	−	42.6690i	−1.36510	−	1.36510i	−0.867278	−	0.497825i	$-0.834132\pi$
$977$	−42.6690	−	42.6690i	−1.36510	−	1.36510i	−0.497825	−	0.867278i	$-0.665868\pi$
$978$		0			0
$979$	−75.3675			−2.40875
$980$	9.25780	+	12.6211i	0.295730	+	0.403167i
$981$		0			0
$982$	11.9770	+	11.9770i	0.382202	+	0.382202i
$983$	−1.34529	−	1.34529i	−0.0429079	−	0.0429079i	0.685327	−	0.728235i	$-0.259659\pi$
$983$	−1.34529	−	1.34529i	−0.0429079	−	0.0429079i	−0.728235	+	0.685327i	$0.759659\pi$
$984$		0			0
$985$	30.0958	+	28.1590i	0.958932	+	0.897220i
$986$		−	18.5140i		−	0.589605i
$987$		0			0
$988$	4.32106	−	4.32106i	0.137471	−	0.137471i
$989$			16.0147i			0.509239i
$990$		0			0
$991$	3.44975			0.109585			0.0547925	−	0.998498i	$-0.482550\pi$
$991$	3.44975			0.109585			0.0547925	+	0.998498i	$0.482550\pi$
$992$	4.98896	−	4.98896i	0.158400	−	0.158400i
$993$		0			0
$994$	−16.0940	+	30.4969i	−0.510472	+	0.967304i
$995$	−26.2613	+	0.873112i	−0.832539	+	0.0276795i
$996$		0			0
$997$	31.5368	−	31.5368i	0.998780	−	0.998780i	−0.00121964	−	0.999999i	$-0.500388\pi$
$997$	31.5368	−	31.5368i	0.998780	−	0.998780i	0.999999	+	0.00121964i	$0.000388223\pi$
$998$	−21.5043	+	21.5043i	−0.680706	+	0.680706i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.p.b.307.3		8
3.2	odd	2		210.2.m.a.97.2	yes	8
5.3	odd	4		630.2.p.c.433.4		8
7.6	odd	2		630.2.p.c.307.4		8
12.11	even	2		1680.2.cz.b.97.4		8
15.2	even	4		1050.2.m.a.643.3		8
15.8	even	4		210.2.m.b.13.1	yes	8
15.14	odd	2		1050.2.m.b.307.4		8
21.20	even	2		210.2.m.b.97.1	yes	8
35.13	even	4	inner	630.2.p.b.433.3		8
60.23	odd	4		1680.2.cz.a.433.1		8
84.83	odd	2		1680.2.cz.a.97.1		8
105.62	odd	4		1050.2.m.b.643.4		8
105.83	odd	4		210.2.m.a.13.2	✓	8
105.104	even	2		1050.2.m.a.307.3		8
420.83	even	4		1680.2.cz.b.433.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.2	✓	8	105.83	odd	4
210.2.m.a.97.2	yes	8	3.2	odd	2
210.2.m.b.13.1	yes	8	15.8	even	4
210.2.m.b.97.1	yes	8	21.20	even	2
630.2.p.b.307.3		8	1.1	even	1	trivial
630.2.p.b.433.3		8	35.13	even	4	inner
630.2.p.c.307.4		8	7.6	odd	2
630.2.p.c.433.4		8	5.3	odd	4
1050.2.m.a.307.3		8	105.104	even	2
1050.2.m.a.643.3		8	15.2	even	4
1050.2.m.b.307.4		8	15.14	odd	2
1050.2.m.b.643.4		8	105.62	odd	4
1680.2.cz.a.97.1		8	84.83	odd	2
1680.2.cz.a.433.1		8	60.23	odd	4
1680.2.cz.b.97.4		8	12.11	even	2
1680.2.cz.b.433.4		8	420.83	even	4

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(0.781409 + 2.52773i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-2.23483 + 0.0743018i) q^{5} +(0.781409 + 2.52773i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.63280 - 1.52773i) q^{10} -4.90685 q^{11} +(-3.41421 - 3.41421i) q^{13} +(-1.23483 + 2.33991i) q^{14} -1.00000 q^{16} +(-2.74632 + 2.74632i) q^{17} +1.26561 q^{19} +(-0.0743018 - 2.23483i) q^{20} +(-3.46967 - 3.46967i) q^{22} +(1.05545 - 1.05545i) q^{23} +(4.98896 - 0.332104i) q^{25} -4.82843i q^{26} +(-2.52773 + 0.781409i) q^{28} +4.76687i q^{29} +7.05545i q^{31} +(-0.707107 - 0.707107i) q^{32} -3.88388 q^{34} +(-1.93413 - 5.59099i) q^{35} +(-4.74632 - 4.74632i) q^{37} +(0.894921 + 0.894921i) q^{38} +(1.52773 - 1.63280i) q^{40} -5.44670i q^{41} +(-7.58667 + 7.58667i) q^{43} -4.90685i q^{44} +1.49264 q^{46} +(-0.734390 + 0.734390i) q^{47} +(-5.77880 + 3.95037i) q^{49} +(3.76256 + 3.29289i) q^{50} +(3.41421 - 3.41421i) q^{52} +(-1.26561 + 1.26561i) q^{53} +(10.9660 - 0.364588i) q^{55} +(-2.33991 - 1.23483i) q^{56} +(-3.37069 + 3.37069i) q^{58} -1.39735 q^{59} +2.29721i q^{61} +(-4.98896 + 4.98896i) q^{62} -1.00000i q^{64} +(7.88388 + 7.37652i) q^{65} +(3.05545 + 3.05545i) q^{67} +(-2.74632 - 2.74632i) q^{68} +(2.58579 - 5.32106i) q^{70} +13.0334 q^{71} +(5.04441 + 5.04441i) q^{73} -6.71231i q^{74} +1.26561i q^{76} +(-3.83425 - 12.4032i) q^{77} -14.8063i q^{79} +(2.23483 - 0.0743018i) q^{80} +(3.85140 - 3.85140i) q^{82} +(9.29809 + 9.29809i) q^{83} +(5.93351 - 6.34162i) q^{85} -10.7292 q^{86} +(3.46967 - 3.46967i) q^{88} +15.3596 q^{89} +(5.96230 - 11.2981i) q^{91} +(1.05545 + 1.05545i) q^{92} -1.03858 q^{94} +(-2.82843 + 0.0940371i) q^{95} +(-8.42614 + 8.42614i) q^{97} +(-6.87957 - 1.29289i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 4 q^{10} - 8 q^{11} - 16 q^{13} + 8 q^{14} - 8 q^{16} - 12 q^{17} - 8 q^{19} - 4 q^{20} + 8 q^{22} - 16 q^{23} - 4 q^{25} - 8 q^{28} + 16 q^{34} - 8 q^{35} - 28 q^{37} + 4 q^{38} - 8 q^{46} - 24 q^{47} + 4 q^{49} + 16 q^{52} + 8 q^{53} + 28 q^{55} - 4 q^{56} - 12 q^{58} - 8 q^{59} + 4 q^{62} + 16 q^{65} - 12 q^{68} + 32 q^{70} - 8 q^{71} - 28 q^{73} + 44 q^{77} + 24 q^{82} + 16 q^{83} + 28 q^{85} - 8 q^{86} - 8 q^{88} + 64 q^{89} - 8 q^{91} - 16 q^{92} + 8 q^{94} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^11 - 16 * q^13 + 8 * q^14 - 8 * q^16 - 12 * q^17 - 8 * q^19 - 4 * q^20 + 8 * q^22 - 16 * q^23 - 4 * q^25 - 8 * q^28 + 16 * q^34 - 8 * q^35 - 28 * q^37 + 4 * q^38 - 8 * q^46 - 24 * q^47 + 4 * q^49 + 16 * q^52 + 8 * q^53 + 28 * q^55 - 4 * q^56 - 12 * q^58 - 8 * q^59 + 4 * q^62 + 16 * q^65 - 12 * q^68 + 32 * q^70 - 8 * q^71 - 28 * q^73 + 44 * q^77 + 24 * q^82 + 16 * q^83 + 28 * q^85 - 8 * q^86 - 8 * q^88 + 64 * q^89 - 8 * q^91 - 16 * q^92 + 8 * q^94 - 28 * q^97

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