LMFDB - Embedded newform 630.2.bo.a.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(89,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("630.89");

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.bo (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.2
Root			$1.98669 + 1.02619i$ of defining polynomial
Character	$\chi$	$=$	630.89
Dual form			630.2.bo.a.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.98669 + 1.02619i) q^{5} +(1.39924 - 2.24547i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.98669 + 1.02619i) q^{5} +(1.39924 - 2.24547i) q^{7} +1.00000 q^{8} +(0.104634 - 2.23362i) q^{10} +(-1.37897 + 0.796151i) q^{11} +0.925091 q^{13} +(1.24501 + 2.33451i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.42743 - 1.97883i) q^{17} +(0.541679 + 0.312739i) q^{19} +(1.88205 + 1.20743i) q^{20} -1.59230i q^{22} +(3.89282 - 6.74256i) q^{23} +(2.89385 - 4.07745i) q^{25} +(-0.462546 + 0.801153i) q^{26} +(-2.64425 - 0.0890445i) q^{28} +9.34805i q^{29} +(8.94618 - 5.16508i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.95765i q^{34} +(-0.475571 + 5.89693i) q^{35} +(-0.369259 - 0.213192i) q^{37} +(-0.541679 + 0.312739i) q^{38} +(-1.98669 + 1.02619i) q^{40} +8.35463 q^{41} +6.27133i q^{43} +(1.37897 + 0.796151i) q^{44} +(3.89282 + 6.74256i) q^{46} +(2.40868 + 1.39065i) q^{47} +(-3.08425 - 6.28390i) q^{49} +(2.08425 + 4.54488i) q^{50} +(-0.462546 - 0.801153i) q^{52} +(-1.67557 - 2.90217i) q^{53} +(1.92259 - 2.99680i) q^{55} +(1.39924 - 2.24547i) q^{56} +(-8.09565 - 4.67403i) q^{58} +(-3.10680 - 5.38113i) q^{59} +(9.52671 + 5.50025i) q^{61} +10.3302i q^{62} +1.00000 q^{64} +(-1.83787 + 0.949323i) q^{65} +(-0.308459 + 0.178089i) q^{67} +(-3.42743 - 1.97883i) q^{68} +(-4.86911 - 3.36032i) q^{70} -9.07975i q^{71} +(-3.41511 - 5.91515i) q^{73} +(0.369259 - 0.213192i) q^{74} -0.625477i q^{76} +(-0.141786 + 4.21045i) q^{77} +(-4.52582 + 7.83895i) q^{79} +(0.104634 - 2.23362i) q^{80} +(-4.17731 + 7.23532i) q^{82} +0.809898i q^{83} +(-4.77857 + 7.44851i) q^{85} +(-5.43113 - 3.13566i) q^{86} +(-1.37897 + 0.796151i) q^{88} +(-2.00721 + 3.47659i) q^{89} +(1.29443 - 2.07726i) q^{91} -7.78564 q^{92} +(-2.40868 + 1.39065i) q^{94} +(-1.39708 - 0.0654463i) q^{95} +7.87721 q^{97} +(6.98414 + 0.470912i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8	$ 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50} + 16 q^{53} + 24 q^{61} + 16 q^{64} - 20 q^{65} - 14 q^{70} - 88 q^{77} + 4 q^{79} + 6 q^{80} + 64 q^{85} - 28 q^{91} + 16 q^{92} - 60 q^{94} - 12 q^{95} + 20 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 - 8 * q^23 - 6 * q^25 + 12 * q^31 - 8 * q^32 + 4 * q^35 - 24 * q^38 - 6 * q^40 - 8 * q^46 + 60 * q^47 - 28 * q^49 + 12 * q^50 + 16 * q^53 + 24 * q^61 + 16 * q^64 - 20 * q^65 - 14 * q^70 - 88 * q^77 + 4 * q^79 + 6 * q^80 + 64 * q^85 - 28 * q^91 + 16 * q^92 - 60 * q^94 - 12 * q^95 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.98669	+	1.02619i	−0.888474	+	0.458928i
$5$	−1.98669	+	1.02619i	−0.888474	+	0.458928i
$6$		0			0
$7$	1.39924	−	2.24547i	0.528863	−	0.848707i
$7$	1.39924	−	2.24547i	0.528863	−	0.848707i
$8$	1.00000			0.353553
$9$		0			0
$10$	0.104634	−	2.23362i	0.0330883	−	0.706332i
$11$	−1.37897	+	0.796151i	−0.415776	+	0.240049i	−0.693269	−	0.720679i	$-0.743830\pi$
$11$	−1.37897	+	0.796151i	−0.415776	+	0.240049i	0.277492	+	0.960728i	$0.410497\pi$
$12$		0			0
$13$	0.925091			0.256574			0.128287	−	0.991737i	$-0.459052\pi$
$13$	0.925091			0.256574			0.128287	+	0.991737i	$0.459052\pi$
$14$	1.24501	+	2.33451i	0.332743	+	0.623925i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.42743	−	1.97883i	0.831273	−	0.479936i	−0.0230153	−	0.999735i	$-0.507327\pi$
$17$	3.42743	−	1.97883i	0.831273	−	0.479936i	0.854288	+	0.519799i	$0.173993\pi$
$18$		0			0
$19$	0.541679	+	0.312739i	0.124270	+	0.0717472i	0.560846	−	0.827920i	$-0.310476\pi$
$19$	0.541679	+	0.312739i	0.124270	+	0.0717472i	−0.436577	+	0.899667i	$0.643809\pi$
$20$	1.88205	+	1.20743i	0.420840	+	0.269988i
$21$		0			0
$22$		−	1.59230i		−	0.339480i
$23$	3.89282	−	6.74256i	0.811709	−	1.40592i	−0.0999578	−	0.994992i	$-0.531871\pi$
$23$	3.89282	−	6.74256i	0.811709	−	1.40592i	0.911667	−	0.410930i	$-0.134796\pi$
$24$		0			0
$25$	2.89385	−	4.07745i	0.578771	−	0.815490i
$26$	−0.462546	+	0.801153i	−0.0907127	+	0.157119i
$27$		0			0
$28$	−2.64425	−	0.0890445i	−0.499717	−	0.0168278i
$29$			9.34805i			1.73589i	0.496661	+	0.867945i	$0.334559\pi$
$29$			9.34805i			1.73589i	−0.496661	+	0.867945i	$0.665441\pi$
$30$		0			0
$31$	8.94618	−	5.16508i	1.60678	−	0.927675i	0.616696	−	0.787201i	$-0.288471\pi$
$31$	8.94618	−	5.16508i	1.60678	−	0.927675i	0.990084	−	0.140474i	$-0.0448626\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$			3.95765i			0.678732i
$35$	−0.475571	+	5.89693i	−0.0803862	+	0.996764i
$36$		0			0
$37$	−0.369259	−	0.213192i	−0.0607058	−	0.0350485i	0.469340	−	0.883018i	$-0.344492\pi$
$37$	−0.369259	−	0.213192i	−0.0607058	−	0.0350485i	−0.530046	+	0.847969i	$0.677825\pi$
$38$	−0.541679	+	0.312739i	−0.0878720	+	0.0507329i
$39$		0			0
$40$	−1.98669	+	1.02619i	−0.314123	+	0.162255i
$41$	8.35463			1.30477			0.652387	−	0.757886i	$-0.273768\pi$
$41$	8.35463			1.30477			0.652387	+	0.757886i	$0.273768\pi$
$42$		0			0
$43$			6.27133i			0.956369i	0.878259	+	0.478184i	$0.158705\pi$
$43$			6.27133i			0.956369i	−0.878259	+	0.478184i	$0.841295\pi$
$44$	1.37897	+	0.796151i	0.207888	+	0.120024i
$45$		0			0
$46$	3.89282	+	6.74256i	0.573965	+	0.994137i
$47$	2.40868	+	1.39065i	0.351342	+	0.202847i	0.665276	−	0.746597i	$-0.268314\pi$
$47$	2.40868	+	1.39065i	0.351342	+	0.202847i	−0.313934	+	0.949445i	$0.601647\pi$
$48$		0			0
$49$	−3.08425	−	6.28390i	−0.440607	−	0.897700i
$50$	2.08425	+	4.54488i	0.294757	+	0.642743i
$51$		0			0
$52$	−0.462546	−	0.801153i	−0.0641435	−	0.111100i
$53$	−1.67557	−	2.90217i	−0.230157	−	0.398644i	0.727697	−	0.685899i	$-0.240591\pi$
$53$	−1.67557	−	2.90217i	−0.230157	−	0.398644i	−0.957854	+	0.287255i	$0.907257\pi$
$54$		0			0
$55$	1.92259	−	2.99680i	0.259241	−	0.404088i
$56$	1.39924	−	2.24547i	0.186981	−	0.300063i
$57$		0			0
$58$	−8.09565	−	4.67403i	−1.06301	−	0.613730i
$59$	−3.10680	−	5.38113i	−0.404471	−	0.700564i	0.589789	−	0.807557i	$-0.299211\pi$
$59$	−3.10680	−	5.38113i	−0.404471	−	0.700564i	−0.994260	+	0.106994i	$0.965878\pi$
$60$		0			0
$61$	9.52671	+	5.50025i	1.21977	+	0.704235i	0.964869	−	0.262732i	$-0.0846236\pi$
$61$	9.52671	+	5.50025i	1.21977	+	0.704235i	0.254902	+	0.966967i	$0.417957\pi$
$62$			10.3302i			1.31193i
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.83787	+	0.949323i	−0.227959	+	0.117749i
$66$		0			0
$67$	−0.308459	+	0.178089i	−0.0376843	+	0.0217570i	−0.518724	−	0.854942i	$-0.673593\pi$
$67$	−0.308459	+	0.178089i	−0.0376843	+	0.0217570i	0.481039	+	0.876699i	$0.340259\pi$
$68$	−3.42743	−	1.97883i	−0.415637	−	0.239968i
$69$		0			0
$70$	−4.86911	−	3.36032i	−0.581970	−	0.401635i
$71$		−	9.07975i		−	1.07757i	−0.842444	−	0.538784i	$-0.818884\pi$
$71$		−	9.07975i		−	1.07757i	0.842444	−	0.538784i	$-0.181116\pi$
$72$		0			0
$73$	−3.41511	−	5.91515i	−0.399709	−	0.692316i	0.593981	−	0.804479i	$-0.297555\pi$
$73$	−3.41511	−	5.91515i	−0.399709	−	0.692316i	−0.993690	+	0.112163i	$0.964222\pi$
$74$	0.369259	−	0.213192i	0.0429255	−	0.0247830i
$75$		0			0
$76$		−	0.625477i		−	0.0717472i
$77$	−0.141786	+	4.21045i	−0.0161580	+	0.479825i
$78$		0			0
$79$	−4.52582	+	7.83895i	−0.509195	+	0.881951i	0.490749	+	0.871301i	$0.336723\pi$
$79$	−4.52582	+	7.83895i	−0.509195	+	0.881951i	−0.999943	+	0.0106498i	$0.996610\pi$
$80$	0.104634	−	2.23362i	0.0116985	−	0.249726i
$81$		0			0
$82$	−4.17731	+	7.23532i	−0.461307	+	0.799007i
$83$			0.809898i			0.0888978i	0.999012	+	0.0444489i	$0.0141532\pi$
$83$			0.809898i			0.0888978i	−0.999012	+	0.0444489i	$0.985847\pi$
$84$		0			0
$85$	−4.77857	+	7.44851i	−0.518308	+	0.807904i
$86$	−5.43113	−	3.13566i	−0.585654	−	0.338127i
$87$		0			0
$88$	−1.37897	+	0.796151i	−0.146999	+	0.0848700i
$89$	−2.00721	+	3.47659i	−0.212764	+	0.368518i	−0.952579	−	0.304293i	$-0.901580\pi$
$89$	−2.00721	+	3.47659i	−0.212764	+	0.368518i	0.739815	+	0.672811i	$0.234913\pi$
$90$		0			0
$91$	1.29443	−	2.07726i	0.135693	−	0.217756i
$92$	−7.78564			−0.811709
$93$		0			0
$94$	−2.40868	+	1.39065i	−0.248436	+	0.143435i
$95$	−1.39708	−	0.0654463i	−0.143337	−	0.00671465i
$96$		0			0
$97$	7.87721			0.799809			0.399905	−	0.916557i	$-0.369043\pi$
$97$	7.87721			0.799809			0.399905	+	0.916557i	$0.369043\pi$
$98$	6.98414	+	0.470912i	0.705505	+	0.0475693i
$99$		0			0
$100$	−4.97810	−	0.467426i	−0.497810	−	0.0467426i
$101$	−3.76411	−	6.51962i	−0.374543	−	0.648727i	0.615716	−	0.787968i	$-0.288867\pi$
$101$	−3.76411	−	6.51962i	−0.374543	−	0.648727i	−0.990258	+	0.139241i	$0.955534\pi$
$102$		0			0
$103$	−0.831805	+	1.44073i	−0.0819601	+	0.141959i	−0.904092	−	0.427338i	$-0.859451\pi$
$103$	−0.831805	+	1.44073i	−0.0819601	+	0.141959i	0.822132	+	0.569297i	$0.192785\pi$
$104$	0.925091			0.0907127
$105$		0			0
$106$	3.35114			0.325492
$107$	9.70139	−	16.8033i	0.937869	−	1.62444i	0.168433	−	0.985713i	$-0.446129\pi$
$107$	9.70139	−	16.8033i	0.937869	−	1.62444i	0.769436	−	0.638724i	$-0.220537\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$	1.63401	+	3.16341i	0.155797	+	0.301619i
$111$		0			0
$112$	1.24501	+	2.33451i	0.117643	+	0.220591i
$113$	−16.0750			−1.51221			−0.756104	−	0.654451i	$-0.772900\pi$
$113$	−16.0750			−1.51221			−0.756104	+	0.654451i	$0.772900\pi$
$114$		0			0
$115$	−0.814645	+	17.3902i	−0.0759660	+	1.62164i
$116$	8.09565	−	4.67403i	0.751662	−	0.433972i
$117$		0			0
$118$	6.21360			0.572008
$119$	0.352407	−	10.4650i	0.0323051	−	0.959328i
$120$		0			0
$121$	−4.23229	+	7.33053i	−0.384753	+	0.666412i
$122$	−9.52671	+	5.50025i	−0.862508	+	0.497969i
$123$		0			0
$124$	−8.94618	−	5.16508i	−0.803390	−	0.463838i
$125$	−1.56493	+	11.0703i	−0.139972	+	0.990156i
$126$		0			0
$127$			13.2173i			1.17285i	0.810004	+	0.586424i	$0.199465\pi$
$127$			13.2173i			1.17285i	−0.810004	+	0.586424i	$0.800535\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	0.0967962	−	2.06630i	0.00848959	−	0.181227i
$131$	4.70080	−	8.14203i	0.410711	−	0.711372i	−0.584257	−	0.811569i	$-0.698614\pi$
$131$	4.70080	−	8.14203i	0.410711	−	0.711372i	0.994968	+	0.100197i	$0.0319472\pi$
$132$		0			0
$133$	1.46018	−	0.778726i	0.126614	−	0.0675241i
$134$		−	0.356178i		−	0.0307691i
$135$		0			0
$136$	3.42743	−	1.97883i	0.293899	−	0.169683i
$137$	−4.68636	−	8.11701i	−0.400382	−	0.693483i	0.593390	−	0.804915i	$-0.297789\pi$
$137$	−4.68636	−	8.11701i	−0.400382	−	0.693483i	−0.993772	+	0.111433i	$0.964456\pi$
$138$		0			0
$139$		−	14.1106i		−	1.19685i	−0.801180	−	0.598423i	$-0.795794\pi$
$139$		−	14.1106i		−	1.19685i	0.801180	−	0.598423i	$-0.204206\pi$
$140$	5.34468	−	2.53661i	0.451708	−	0.214383i
$141$		0			0
$142$	7.86330	+	4.53988i	0.659873	+	0.380978i
$143$	−1.27568	+	0.736513i	−0.106678	+	0.0615903i
$144$		0			0
$145$	−9.59291	−	18.5717i	−0.796648	−	1.54229i
$146$	6.83023			0.565274
$147$		0			0
$148$			0.426383i			0.0350485i
$149$	−2.14103	−	1.23612i	−0.175400	−	0.101267i	0.409730	−	0.912207i	$-0.365623\pi$
$149$	−2.14103	−	1.23612i	−0.175400	−	0.101267i	−0.585130	+	0.810940i	$0.698956\pi$
$150$		0			0
$151$	10.4425	+	18.0869i	0.849796	+	1.47189i	0.881391	+	0.472388i	$0.156608\pi$
$151$	10.4425	+	18.0869i	0.849796	+	1.47189i	−0.0315949	+	0.999501i	$0.510059\pi$
$152$	0.541679	+	0.312739i	0.0439360	+	0.0253664i
$153$		0			0
$154$	−3.57546	−	2.22802i	−0.288119	−	0.179539i
$155$	−12.4729	+	19.4419i	−1.00185	+	1.56161i
$156$		0			0
$157$	−12.2238	−	21.1722i	−0.975563	−	1.68972i	−0.678065	−	0.735002i	$-0.737181\pi$
$157$	−12.2238	−	21.1722i	−0.975563	−	1.68972i	−0.297498	−	0.954723i	$-0.596152\pi$
$158$	−4.52582	−	7.83895i	−0.360055	−	0.623634i
$159$		0			0
$160$	1.88205	+	1.20743i	0.148789	+	0.0954553i
$161$	−9.69321	−	18.1757i	−0.763932	−	1.43244i
$162$		0			0
$163$	5.12267	+	2.95758i	0.401239	+	0.231655i	0.687018	−	0.726640i	$-0.258919\pi$
$163$	5.12267	+	2.95758i	0.401239	+	0.231655i	−0.285780	+	0.958295i	$0.592253\pi$
$164$	−4.17731	−	7.23532i	−0.326193	−	0.564983i
$165$		0			0
$166$	−0.701392	−	0.404949i	−0.0544386	−	0.0314301i
$167$			12.1440i			0.939733i	0.882737	+	0.469867i	$0.155698\pi$
$167$			12.1440i			0.939733i	−0.882737	+	0.469867i	$0.844302\pi$
$168$		0			0
$169$	−12.1442			−0.934170
$170$	−4.06132	−	7.86262i	−0.311489	−	0.603035i
$171$		0			0
$172$	5.43113	−	3.13566i	0.414120	−	0.239092i
$173$	−14.2014	−	8.19918i	−1.07971	−	0.623372i	−0.148893	−	0.988853i	$-0.547571\pi$
$173$	−14.2014	−	8.19918i	−1.07971	−	0.623372i	−0.930819	+	0.365481i	$0.880904\pi$
$174$		0			0
$175$	−5.10658	−	12.2034i	−0.386021	−	0.922490i
$176$		−	1.59230i		−	0.120024i
$177$		0			0
$178$	−2.00721	−	3.47659i	−0.150447	−	0.260581i
$179$	−2.73398	+	1.57846i	−0.204347	+	0.117980i	−0.598682	−	0.800987i	$-0.704309\pi$
$179$	−2.73398	+	1.57846i	−0.204347	+	0.117980i	0.394334	+	0.918967i	$0.370975\pi$
$180$		0			0
$181$		−	8.17916i		−	0.607952i	−0.952680	−	0.303976i	$-0.901686\pi$
$181$		−	8.17916i		−	0.607952i	0.952680	−	0.303976i	$-0.0983143\pi$
$182$	1.15175	+	2.15964i	0.0853733	+	0.160083i
$183$		0			0
$184$	3.89282	−	6.74256i	0.286983	−	0.497068i
$185$	0.952378	+	0.0446143i	0.0700202	+	0.00328011i
$186$		0			0
$187$	−3.15089	+	5.45750i	−0.230416	+	0.399092i
$188$		−	2.78130i		−	0.202847i
$189$		0			0
$190$	0.755217	−	1.17718i	0.0547892	−	0.0854017i
$191$	−2.44949	−	1.41421i	−0.177239	−	0.102329i	0.408756	−	0.912644i	$-0.365963\pi$
$191$	−2.44949	−	1.41421i	−0.177239	−	0.102329i	−0.585995	+	0.810315i	$0.699296\pi$
$192$		0			0
$193$	−15.3420	+	8.85772i	−1.10434	+	0.637593i	−0.937358	−	0.348367i	$-0.886736\pi$
$193$	−15.3420	+	8.85772i	−1.10434	+	0.637593i	−0.166985	+	0.985959i	$0.553403\pi$
$194$	−3.93860	+	6.82186i	−0.282775	+	0.489781i
$195$		0			0
$196$	−3.89989	+	5.81299i	−0.278564	+	0.415213i
$197$	−4.30350			−0.306612			−0.153306	−	0.988179i	$-0.548992\pi$
$197$	−4.30350			−0.306612			−0.153306	+	0.988179i	$0.548992\pi$
$198$		0			0
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−3.00000	+	1.73205i	−0.212664	+	0.122782i	0.389885	+	0.920864i	$0.372515\pi$
$200$	2.89385	−	4.07745i	0.204626	−	0.288319i
$201$		0			0
$202$	7.52821			0.529683
$203$	20.9907	+	13.0802i	1.47326	+	0.918048i
$204$		0			0
$205$	−16.5980	+	8.57346i	−1.15926	+	0.598797i
$206$	−0.831805	−	1.44073i	−0.0579546	−	0.100380i
$207$		0			0
$208$	−0.462546	+	0.801153i	−0.0320718	+	0.0555499i
$209$	−0.995949			−0.0688912
$210$		0			0
$211$	10.3886			0.715183			0.357592	−	0.933878i	$-0.383598\pi$
$211$	10.3886			0.715183			0.357592	+	0.933878i	$0.383598\pi$
$212$	−1.67557	+	2.90217i	−0.115079	+	0.199322i
$213$		0			0
$214$	9.70139	+	16.8033i	0.663173	+	1.14865i
$215$	−6.43560	−	12.4592i	−0.438904	−	0.849708i
$216$		0			0
$217$	0.919844	−	27.3155i	0.0624431	−	1.85430i
$218$	2.00000			0.135457
$219$		0			0
$220$	−3.55660	−	0.166609i	−0.239786	−	0.0112328i
$221$	3.17068	−	1.83059i	0.213283	−	0.123139i
$222$		0			0
$223$	18.3555			1.22918			0.614589	−	0.788848i	$-0.289322\pi$
$223$	18.3555			1.22918			0.614589	+	0.788848i	$0.289322\pi$
$224$	−2.64425	−	0.0890445i	−0.176677	−	0.00594954i
$225$		0			0
$226$	8.03750	−	13.9214i	0.534646	−	0.926035i
$227$	2.61803	−	1.51152i	0.173765	−	0.100323i	−0.410595	−	0.911818i	$-0.634679\pi$
$227$	2.61803	−	1.51152i	0.173765	−	0.100323i	0.584360	+	0.811495i	$0.301346\pi$
$228$		0			0
$229$	9.22014	+	5.32325i	0.609284	+	0.351770i	0.772685	−	0.634789i	$-0.218913\pi$
$229$	9.22014	+	5.32325i	0.609284	+	0.351770i	−0.163401	+	0.986560i	$0.552246\pi$
$230$	−14.6530	−	9.40058i	−0.966190	−	0.619856i
$231$		0			0
$232$			9.34805i			0.613730i
$233$	−1.99293	+	3.45185i	−0.130561	+	0.226138i	−0.923893	−	0.382651i	$-0.875011\pi$
$233$	−1.99293	+	3.45185i	−0.130561	+	0.226138i	0.793332	+	0.608789i	$0.208345\pi$
$234$		0			0
$235$	−6.21237	−	0.291019i	−0.405250	−	0.0189840i
$236$	−3.10680	+	5.38113i	−0.202235	+	0.350282i
$237$		0			0
$238$	8.88678	+	5.53771i	0.576044	+	0.358956i
$239$			8.24699i			0.533453i	0.963772	+	0.266727i	$0.0859421\pi$
$239$			8.24699i			0.533453i	−0.963772	+	0.266727i	$0.914058\pi$
$240$		0			0
$241$	−9.48785	+	5.47782i	−0.611166	+	0.352857i	−0.773422	−	0.633892i	$-0.781456\pi$
$241$	−9.48785	+	5.47782i	−0.611166	+	0.352857i	0.162255	+	0.986749i	$0.448123\pi$
$242$	−4.23229	−	7.33053i	−0.272062	−	0.471225i
$243$		0			0
$244$		−	11.0005i		−	0.704235i
$245$	12.5759	+	9.31911i	0.803447	+	0.595376i
$246$		0			0
$247$	0.501103	+	0.289312i	0.0318844	+	0.0184085i
$248$	8.94618	−	5.16508i	0.568083	−	0.327983i
$249$		0			0
$250$	−8.80467	−	6.89041i	−0.556856	−	0.435788i
$251$	21.7369			1.37202			0.686012	−	0.727590i	$-0.259360\pi$
$251$	21.7369			1.37202			0.686012	+	0.727590i	$0.259360\pi$
$252$		0			0
$253$			12.3971i			0.779399i
$254$	−11.4465	−	6.60867i	−0.718220	−	0.414665i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0993	+	8.71758i	0.941868	+	0.543787i	0.890545	−	0.454895i	$-0.150323\pi$
$257$	15.0993	+	8.71758i	0.941868	+	0.543787i	0.0513223	+	0.998682i	$0.483656\pi$
$258$		0			0
$259$	−0.995397	+	0.530852i	−0.0618510	+	0.0329856i
$260$	1.74107	+	1.11698i	0.107977	+	0.0692721i
$261$		0			0
$262$	4.70080	+	8.14203i	0.290417	+	0.503016i
$263$	9.17557	+	15.8926i	0.565790	+	0.979977i	0.996976	+	0.0777137i	$0.0247620\pi$
$263$	9.17557	+	15.8926i	0.565790	+	0.979977i	−0.431186	+	0.902263i	$0.641905\pi$
$264$		0			0
$265$	6.30703	+	4.04625i	0.387438	+	0.248559i
$266$	−0.0556953	+	1.65392i	−0.00341490	+	0.101408i
$267$		0			0
$268$	0.308459	+	0.178089i	0.0188422	+	0.0108785i
$269$	12.4185	+	21.5095i	0.757171	+	1.31146i	0.944288	+	0.329121i	$0.106752\pi$
$269$	12.4185	+	21.5095i	0.757171	+	1.31146i	−0.187117	+	0.982338i	$0.559914\pi$
$270$		0			0
$271$	21.1663	+	12.2204i	1.28576	+	0.742335i	0.977895	−	0.209094i	$-0.0670516\pi$
$271$	21.1663	+	12.2204i	1.28576	+	0.742335i	0.307867	+	0.951430i	$0.400385\pi$
$272$			3.95765i			0.239968i
$273$		0			0
$274$	9.37271			0.566226
$275$	−0.744284	+	7.92665i	−0.0448820	+	0.477995i
$276$		0			0
$277$	−20.0892	+	11.5985i	−1.20704	+	0.696888i	−0.962113	−	0.272653i	$-0.912099\pi$
$277$	−20.0892	+	11.5985i	−1.20704	+	0.696888i	−0.244932	+	0.969540i	$0.578766\pi$
$278$	12.2201	+	7.05530i	0.732915	+	0.423149i
$279$		0			0
$280$	−0.475571	+	5.89693i	−0.0284208	+	0.352409i
$281$			14.0801i			0.839949i	0.907536	+	0.419974i	$0.137961\pi$
$281$			14.0801i			0.839949i	−0.907536	+	0.419974i	$0.862039\pi$
$282$		0			0
$283$	1.39910	+	2.42331i	0.0831677	+	0.144051i	0.904609	−	0.426242i	$-0.140163\pi$
$283$	1.39910	+	2.42331i	0.0831677	+	0.144051i	−0.821441	+	0.570293i	$0.806830\pi$
$284$	−7.86330	+	4.53988i	−0.466601	+	0.269392i
$285$		0			0
$286$		−	1.47303i		−	0.0871018i
$287$	11.6901	−	18.7600i	0.690047	−	1.10737i
$288$		0			0
$289$	−0.668498	+	1.15787i	−0.0393234	+	0.0681101i
$290$	20.8800	+	0.978126i	1.22611	+	0.0574376i
$291$		0			0
$292$	−3.41511	+	5.91515i	−0.199854	+	0.346158i
$293$			25.5598i			1.49322i	0.665263	+	0.746609i	$0.268319\pi$
$293$			25.5598i			1.49322i	−0.665263	+	0.746609i	$0.731681\pi$
$294$		0			0
$295$	11.6943	+	7.50245i	0.680870	+	0.436810i
$296$	−0.369259	−	0.213192i	−0.0214627	−	0.0123915i
$297$		0			0
$298$	2.14103	−	1.23612i	0.124027	−	0.0716068i
$299$	3.60121	−	6.23749i	0.208264	−	0.360723i
$300$		0			0
$301$	14.0821	+	8.77510i	0.811677	+	0.505788i
$302$	−20.8849			−1.20179
$303$		0			0
$304$	−0.541679	+	0.312739i	−0.0310674	+	0.0179368i
$305$	−24.5709	−	1.15103i	−1.40693	−	0.0659077i
$306$		0			0
$307$	−34.2860			−1.95681			−0.978403	−	0.206704i	$-0.933726\pi$
$307$	−34.2860			−1.95681			−0.978403	+	0.206704i	$0.933726\pi$
$308$	3.71725	−	1.98243i	0.211810	−	0.112960i
$309$		0			0
$310$	−10.6007	−	20.5228i	−0.602081	−	1.16562i
$311$	4.34021	+	7.51746i	0.246110	+	0.426276i	0.962443	−	0.271483i	$-0.0875141\pi$
$311$	4.34021	+	7.51746i	0.246110	+	0.426276i	−0.716333	+	0.697759i	$0.754181\pi$
$312$		0			0
$313$	15.0106	−	25.9992i	0.848452	−	1.46956i	−0.0341376	−	0.999417i	$-0.510868\pi$
$313$	15.0106	−	25.9992i	0.848452	−	1.46956i	0.882589	−	0.470145i	$-0.155798\pi$
$314$	24.4475			1.37965
$315$		0			0
$316$	9.05164			0.509195
$317$	13.8628	−	24.0111i	0.778613	−	1.34860i	−0.154128	−	0.988051i	$-0.549257\pi$
$317$	13.8628	−	24.0111i	0.778613	−	1.34860i	0.932741	−	0.360547i	$-0.117410\pi$
$318$		0			0
$319$	−7.44246	−	12.8907i	−0.416698	−	0.721742i
$320$	−1.98669	+	1.02619i	−0.111059	+	0.0573660i
$321$		0			0
$322$	20.5872	+	0.693269i	1.14728	+	0.0386344i
$323$	2.47542			0.137736
$324$		0			0
$325$	2.67708	−	3.77201i	0.148498	−	0.209234i
$326$	−5.12267	+	2.95758i	−0.283719	+	0.163805i
$327$		0			0
$328$	8.35463			0.461307
$329$	6.49298	−	3.46275i	0.357970	−	0.190908i
$330$		0			0
$331$	−3.15175	+	5.45899i	−0.173236	+	0.300053i	−0.939549	−	0.342414i	$-0.888756\pi$
$331$	−3.15175	+	5.45899i	−0.173236	+	0.300053i	0.766314	+	0.642467i	$0.222089\pi$
$332$	0.701392	−	0.404949i	0.0384939	−	0.0222245i
$333$		0			0
$334$	−10.5170	−	6.07201i	−0.575467	−	0.332246i
$335$	0.430058	−	0.670346i	0.0234966	−	0.0366249i
$336$		0			0
$337$		−	27.4097i		−	1.49310i	−0.665329	−	0.746550i	$-0.731709\pi$
$337$		−	27.4097i		−	1.49310i	0.665329	−	0.746550i	$-0.268291\pi$
$338$	6.07210	−	10.5172i	0.330279	−	0.572060i
$339$		0			0
$340$	8.83988	+	0.414106i	0.479410	+	0.0224580i
$341$	−8.22437	+	14.2450i	−0.445374	+	0.771411i
$342$		0			0
$343$	−18.4259	−	1.86711i	−0.994905	−	0.100815i
$344$			6.27133i			0.338127i
$345$		0			0
$346$	14.2014	−	8.19918i	0.763472	−	0.440791i
$347$	4.08336	+	7.07258i	0.219206	+	0.379676i	0.954566	−	0.298001i	$-0.0963199\pi$
$347$	4.08336	+	7.07258i	0.219206	+	0.379676i	−0.735359	+	0.677677i	$0.762987\pi$
$348$		0			0
$349$			27.5885i			1.47678i	0.674374	+	0.738390i	$0.264413\pi$
$349$			27.5885i			1.47678i	−0.674374	+	0.738390i	$0.735587\pi$
$350$	13.1217	+	1.67927i	0.701387	+	0.0897605i
$351$		0			0
$352$	1.37897	+	0.796151i	0.0734996	+	0.0424350i
$353$	−6.09929	+	3.52142i	−0.324632	+	0.187426i	−0.653455	−	0.756965i	$-0.726681\pi$
$353$	−6.09929	+	3.52142i	−0.324632	+	0.187426i	0.328823	+	0.944391i	$0.393348\pi$
$354$		0			0
$355$	9.31758	+	18.0386i	0.494526	+	0.957391i
$356$	4.01442			0.212764
$357$		0			0
$358$		−	3.15693i		−	0.166849i
$359$	14.1545	+	8.17213i	0.747048	+	0.431308i	0.824626	−	0.565678i	$-0.191385\pi$
$359$	14.1545	+	8.17213i	0.747048	+	0.431308i	−0.0775782	+	0.996986i	$0.524719\pi$
$360$		0			0
$361$	−9.30439	−	16.1157i	−0.489705	−	0.848193i
$362$	7.08336	+	4.08958i	0.372293	+	0.214943i
$363$		0			0
$364$	−2.44618	−	0.0823743i	−0.128214	−	0.00431759i
$365$	12.8549	+	8.24699i	0.672854	+	0.431667i
$366$		0			0
$367$	−1.50399	−	2.60498i	−0.0785076	−	0.135979i	0.824099	−	0.566446i	$-0.191682\pi$
$367$	−1.50399	−	2.60498i	−0.0785076	−	0.135979i	−0.902606	+	0.430467i	$0.858349\pi$
$368$	3.89282	+	6.74256i	0.202927	+	0.351480i
$369$		0			0
$370$	−0.514826	+	0.802476i	−0.0267645	+	0.0417188i
$371$	−8.86126	−	0.298401i	−0.460054	−	0.0154922i
$372$		0			0
$373$	−20.0892	−	11.5985i	−1.04018	−	0.600549i	−0.120296	−	0.992738i	$-0.538384\pi$
$373$	−20.0892	−	11.5985i	−1.04018	−	0.600549i	−0.919884	+	0.392189i	$0.871718\pi$
$374$	−3.15089	−	5.45750i	−0.162929	−	0.282201i
$375$		0			0
$376$	2.40868	+	1.39065i	0.124218	+	0.0717174i
$377$			8.64780i			0.445384i
$378$		0			0
$379$	27.2718			1.40086			0.700429	−	0.713722i	$-0.252992\pi$
$379$	27.2718			1.40086			0.700429	+	0.713722i	$0.252992\pi$
$380$	0.641860	+	1.24263i	0.0329267	+	0.0637455i
$381$		0			0
$382$	2.44949	−	1.41421i	0.125327	−	0.0723575i
$383$	3.69096	+	2.13098i	0.188599	+	0.108888i	0.591327	−	0.806432i	$-0.298604\pi$
$383$	3.69096	+	2.13098i	0.188599	+	0.108888i	−0.402727	+	0.915320i	$0.631938\pi$
$384$		0			0
$385$	−4.03905	−	8.51035i	−0.205849	−	0.433728i
$386$		−	17.7154i		−	0.901692i
$387$		0			0
$388$	−3.93860	−	6.82186i	−0.199952	−	0.346327i
$389$	−1.80282	+	1.04086i	−0.0914066	+	0.0527736i	−0.545007	−	0.838432i	$-0.683473\pi$
$389$	−1.80282	+	1.04086i	−0.0914066	+	0.0527736i	0.453600	+	0.891205i	$0.350140\pi$
$390$		0			0
$391$		−	30.8129i		−	1.55827i
$392$	−3.08425	−	6.28390i	−0.155778	−	0.317385i
$393$		0			0
$394$	2.15175	−	3.72694i	0.108404	−	0.187760i
$395$	0.947112	−	20.2179i	0.0476544	−	1.01727i
$396$		0			0
$397$	−11.1885	+	19.3791i	−0.561537	+	0.972610i	0.435826	+	0.900031i	$0.356456\pi$
$397$	−11.1885	+	19.3791i	−0.561537	+	0.972610i	−0.997363	+	0.0725790i	$0.976877\pi$
$398$		−	3.46410i		−	0.173640i
$399$		0			0
$400$	2.08425	+	4.54488i	0.104212	+	0.227244i
$401$	17.0295	+	9.83196i	0.850411	+	0.490985i	0.860789	−	0.508961i	$-0.169970\pi$
$401$	17.0295	+	9.83196i	0.850411	+	0.490985i	−0.0103787	+	0.999946i	$0.503304\pi$
$402$		0			0
$403$	8.27603	−	4.77817i	0.412258	−	0.238017i
$404$	−3.76411	+	6.51962i	−0.187271	+	0.324363i
$405$		0			0
$406$	−21.8231	+	11.6384i	−1.08306	+	0.577606i
$407$	0.678932			0.0336534
$408$		0			0
$409$	2.19932	−	1.26978i	0.108750	−	0.0627866i	−0.444639	−	0.895710i	$-0.646668\pi$
$409$	2.19932	−	1.26978i	0.108750	−	0.0627866i	0.553388	+	0.832923i	$0.313335\pi$
$410$	0.874180	−	18.6610i	0.0431727	−	0.921604i
$411$		0			0
$412$	1.66361			0.0819601
$413$	−16.4303	−	0.553287i	−0.808483	−	0.0272255i
$414$		0			0
$415$	−0.831112	−	1.60901i	−0.0407977	−	0.0789834i
$416$	−0.462546	−	0.801153i	−0.0226782	−	0.0392797i
$417$		0			0
$418$	0.497974	−	0.862517i	0.0243567	−	0.0421871i
$419$	−32.0568			−1.56608			−0.783039	−	0.621973i	$-0.786331\pi$
$419$	−32.0568			−1.56608			−0.783039	+	0.621973i	$0.786331\pi$
$420$		0			0
$421$	−25.2201			−1.22915			−0.614577	−	0.788857i	$-0.710673\pi$
$421$	−25.2201			−1.22915			−0.614577	+	0.788857i	$0.710673\pi$
$422$	−5.19432	+	8.99682i	−0.252855	+	0.437959i
$423$		0			0
$424$	−1.67557	−	2.90217i	−0.0813729	−	0.140942i
$425$	1.84991	−	19.7016i	0.0897338	−	0.955668i
$426$		0			0
$427$	25.6808	−	13.6957i	1.24278	−	0.662784i
$428$	−19.4028			−0.937869
$429$		0			0
$430$	14.0078	+	0.656196i	0.675514	+	0.0316446i
$431$	−29.1599	+	16.8355i	−1.40458	+	0.810937i	−0.994859	−	0.101271i	$-0.967709\pi$
$431$	−29.1599	+	16.8355i	−1.40458	+	0.810937i	−0.409726	+	0.912209i	$0.634376\pi$
$432$		0			0
$433$	22.7610			1.09382			0.546912	−	0.837190i	$-0.315803\pi$
$433$	22.7610			1.09382			0.546912	+	0.837190i	$0.315803\pi$
$434$	23.1960	+	14.4544i	1.11344	+	0.693832i
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	4.21732	−	2.43487i	0.201742	−	0.116476i
$438$		0			0
$439$	1.86282	+	1.07550i	0.0889074	+	0.0513307i	0.543795	−	0.839218i	$-0.316987\pi$
$439$	1.86282	+	1.07550i	0.0889074	+	0.0513307i	−0.454887	+	0.890549i	$0.650320\pi$
$440$	1.92259	−	2.99680i	0.0916557	−	0.142867i
$441$		0			0
$442$			3.66119i			0.174145i
$443$	−3.83239	+	6.63790i	−0.182082	+	0.315376i	−0.942590	−	0.333954i	$-0.891617\pi$
$443$	−3.83239	+	6.63790i	−0.182082	+	0.315376i	0.760507	+	0.649330i	$0.224950\pi$
$444$		0			0
$445$	0.420046	−	8.96669i	0.0199121	−	0.425062i
$446$	−9.17777	+	15.8964i	−0.434580	+	0.752715i
$447$		0			0
$448$	1.39924	−	2.24547i	0.0661079	−	0.106088i
$449$			18.8337i			0.888817i	0.895824	+	0.444408i	$0.146586\pi$
$449$			18.8337i			0.888817i	−0.895824	+	0.444408i	$0.853414\pi$
$450$		0			0
$451$	−11.5208	+	6.65155i	−0.542494	+	0.313209i
$452$	8.03750	+	13.9214i	0.378052	+	0.654805i
$453$		0			0
$454$			3.02304i			0.141879i
$455$	−0.439947	+	5.45520i	−0.0206250	+	0.255744i
$456$		0			0
$457$	25.3442	+	14.6325i	1.18555	+	0.684478i	0.957292	−	0.289123i	$-0.0933636\pi$
$457$	25.3442	+	14.6325i	1.18555	+	0.684478i	0.228258	+	0.973601i	$0.426697\pi$
$458$	−9.22014	+	5.32325i	−0.430829	+	0.248739i
$459$		0			0
$460$	15.4676	−	7.98957i	0.721182	−	0.372516i
$461$	14.1963			0.661188			0.330594	−	0.943773i	$-0.392751\pi$
$461$	14.1963			0.661188			0.330594	+	0.943773i	$0.392751\pi$
$462$		0			0
$463$		−	7.65787i		−	0.355891i	−0.984040	−	0.177946i	$-0.943055\pi$
$463$		−	7.65787i		−	0.355891i	0.984040	−	0.177946i	$-0.0569451\pi$
$464$	−8.09565	−	4.67403i	−0.375831	−	0.216986i
$465$		0			0
$466$	−1.99293	−	3.45185i	−0.0923206	−	0.159904i
$467$	−15.3410	−	8.85713i	−0.709897	−	0.409859i	0.101126	−	0.994874i	$-0.467755\pi$
$467$	−15.3410	−	8.85713i	−0.709897	−	0.409859i	−0.811023	+	0.585015i	$0.801089\pi$
$468$		0			0
$469$	−0.0317157	+	0.941825i	−0.00146450	+	0.0434894i
$470$	3.35821	−	5.23456i	0.154903	−	0.241452i
$471$		0			0
$472$	−3.10680	−	5.38113i	−0.143002	−	0.247687i
$473$	−4.99293	−	8.64800i	−0.229575	−	0.397636i
$474$		0			0
$475$	2.84272	−	1.30365i	0.130433	−	0.0598156i
$476$	−9.23918	+	4.92732i	−0.423477	+	0.225843i
$477$		0			0
$478$	−7.14210	−	4.12349i	−0.326672	−	0.188604i
$479$	−6.41996	−	11.1197i	−0.293336	−	0.508072i	0.681261	−	0.732041i	$-0.261432\pi$
$479$	−6.41996	−	11.1197i	−0.293336	−	0.508072i	−0.974596	+	0.223969i	$0.928099\pi$
$480$		0			0
$481$	−0.341598	−	0.197222i	−0.0155755	−	0.00899254i
$482$		−	10.9556i		−	0.499015i
$483$		0			0
$484$	8.46457			0.384753
$485$	−15.6495	+	8.08354i	−0.710609	+	0.367054i
$486$		0			0
$487$	−3.27235	+	1.88929i	−0.148284	+	0.0856119i	−0.572306	−	0.820040i	$-0.693951\pi$
$487$	−3.27235	+	1.88929i	−0.148284	+	0.0856119i	0.424022	+	0.905652i	$0.360618\pi$
$488$	9.52671	+	5.50025i	0.431254	+	0.248985i
$489$		0			0
$490$	−14.3586	+	6.23152i	−0.648653	+	0.281512i
$491$		−	32.1664i		−	1.45165i	−0.687880	−	0.725824i	$-0.741459\pi$
$491$		−	32.1664i		−	1.45165i	0.687880	−	0.725824i	$-0.258541\pi$
$492$		0			0
$493$	18.4982	+	32.0398i	0.833115	+	1.44300i
$494$	−0.501103	+	0.289312i	−0.0225457	+	0.0130168i
$495$		0			0
$496$			10.3302i			0.463838i
$497$	−20.3883	−	12.7048i	−0.914540	−	0.569886i
$498$		0			0
$499$	−15.9683	+	27.6579i	−0.714839	+	1.23814i	0.248183	+	0.968713i	$0.420167\pi$
$499$	−15.9683	+	27.6579i	−0.714839	+	1.23814i	−0.963022	+	0.269424i	$0.913167\pi$
$500$	10.3696	−	4.17987i	0.463743	−	0.186929i
$501$		0			0
$502$	−10.8685	+	18.8247i	−0.485084	+	0.840190i
$503$			5.29834i			0.236241i	0.992999	+	0.118121i	$0.0376870\pi$
$503$			5.29834i			0.236241i	−0.992999	+	0.118121i	$0.962313\pi$
$504$		0			0
$505$	14.1685	+	9.08975i	0.630490	+	0.404489i
$506$	−10.7362	−	6.19855i	−0.477282	−	0.275559i
$507$		0			0
$508$	11.4465	−	6.60867i	0.507858	−	0.293212i
$509$	18.6321	−	32.2718i	0.825854	−	1.43042i	−0.0754100	−	0.997153i	$-0.524027\pi$
$509$	18.6321	−	32.2718i	0.825854	−	1.43042i	0.901265	−	0.433269i	$-0.142640\pi$
$510$		0			0
$511$	−18.0608	−	0.608195i	−0.798965	−	0.0269049i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−15.0993	+	8.71758i	−0.666001	+	0.384516i
$515$	0.174070	−	3.71587i	0.00767046	−	0.163741i
$516$		0			0
$517$	−4.42867			−0.194773
$518$	0.0379671	−	1.12747i	0.00166818	−	0.0495380i
$519$		0			0
$520$	−1.83787	+	0.949323i	−0.0805958	+	0.0416305i
$521$	6.00676	+	10.4040i	0.263161	+	0.455808i	0.967080	−	0.254472i	$-0.0819017\pi$
$521$	6.00676	+	10.4040i	0.263161	+	0.455808i	−0.703919	+	0.710280i	$0.748568\pi$
$522$		0			0
$523$	13.5178	−	23.4136i	0.591093	−	1.02380i	−0.402992	−	0.915203i	$-0.632030\pi$
$523$	13.5178	−	23.4136i	0.591093	−	1.02380i	0.994085	−	0.108600i	$-0.0346369\pi$
$524$	−9.40160			−0.410711
$525$		0			0
$526$	−18.3511			−0.800148
$527$	20.4416	−	35.4058i	0.890449	−	1.54230i
$528$		0			0
$529$	−18.8081	−	32.5766i	−0.817744	−	1.41637i
$530$	−6.65767	+	3.43892i	−0.289191	+	0.149377i
$531$		0			0
$532$	−1.40449	−	0.875193i	−0.0608923	−	0.0379444i
$533$	7.72879			0.334771
$534$		0			0
$535$	−2.03020	+	43.3384i	−0.0877730	+	1.87368i
$536$	−0.308459	+	0.178089i	−0.0133234	+	0.00769228i
$537$		0			0
$538$	−24.8371			−1.07080
$539$	9.25604	+	6.20981i	0.398686	+	0.267475i
$540$		0			0
$541$	5.85450	−	10.1403i	0.251705	−	0.435965i	−0.712291	−	0.701885i	$-0.752342\pi$
$541$	5.85450	−	10.1403i	0.251705	−	0.435965i	0.963995	+	0.265919i	$0.0856755\pi$
$542$	−21.1663	+	12.2204i	−0.909171	+	0.524910i
$543$		0			0
$544$	−3.42743	−	1.97883i	−0.146950	−	0.0848415i
$545$	3.76411	+	2.41485i	0.161237	+	0.103441i
$546$		0			0
$547$		−	17.6050i		−	0.752737i	−0.926470	−	0.376369i	$-0.877173\pi$
$547$		−	17.6050i		−	0.752737i	0.926470	−	0.376369i	$-0.122827\pi$
$548$	−4.68636	+	8.11701i	−0.200191	+	0.346741i
$549$		0			0
$550$	−6.49254	−	4.60789i	−0.276843	−	0.196481i
$551$	−2.92350	+	5.06364i	−0.124545	+	0.215718i
$552$		0			0
$553$	11.2694	+	21.1312i	0.479224	+	0.898589i
$554$		−	23.1970i		−	0.985548i
$555$		0			0
$556$	−12.2201	+	7.05530i	−0.518249	+	0.299211i
$557$	10.0409	+	17.3913i	0.425445	+	0.736892i	0.996462	−	0.0840462i	$-0.0267843\pi$
$557$	10.0409	+	17.3913i	0.425445	+	0.736892i	−0.571017	+	0.820938i	$0.693451\pi$
$558$		0			0
$559$			5.80155i			0.245380i
$560$	−4.86911	−	3.36032i	−0.205757	−	0.142000i
$561$		0			0
$562$	−12.1937	−	7.04005i	−0.514361	−	0.296967i
$563$	20.6180	−	11.9038i	0.868947	−	0.501687i	0.00194851	−	0.999998i	$-0.499380\pi$
$563$	20.6180	−	11.9038i	0.868947	−	0.501687i	0.866998	+	0.498312i	$0.166046\pi$
$564$		0			0
$565$	31.9360	−	16.4961i	1.34356	−	0.693994i
$566$	−2.79820			−0.117617
$567$		0			0
$568$		−	9.07975i		−	0.380978i
$569$	−35.8766	−	20.7134i	−1.50403	−	0.868350i	−0.999989	−	0.00466765i	$-0.998514\pi$
$569$	−35.8766	−	20.7134i	−1.50403	−	0.868350i	−0.504037	−	0.863682i	$-0.668152\pi$
$570$		0			0
$571$	−20.5784	−	35.6428i	−0.861177	−	1.49160i	−0.870793	−	0.491649i	$-0.836394\pi$
$571$	−20.5784	−	35.6428i	−0.861177	−	1.49160i	0.00961607	−	0.999954i	$-0.496939\pi$
$572$	1.27568	+	0.736513i	0.0533388	+	0.0307951i
$573$		0			0
$574$	10.4016	+	19.5040i	0.434155	+	0.814080i
$575$	−16.2272	−	35.3848i	−0.676722	−	1.47565i
$576$		0			0
$577$	−6.20835	−	10.7532i	−0.258457	−	0.447661i	0.707372	−	0.706842i	$-0.249881\pi$
$577$	−6.20835	−	10.7532i	−0.258457	−	0.447661i	−0.965829	+	0.259181i	$0.916547\pi$
$578$	−0.668498	−	1.15787i	−0.0278058	−	0.0481611i
$579$		0			0
$580$	−11.2871	+	17.5935i	−0.468670	+	0.730532i
$581$	1.81860	+	1.13324i	0.0754482	+	0.0470148i
$582$		0			0
$583$	4.62114	+	2.66802i	0.191388	+	0.110498i
$584$	−3.41511	−	5.91515i	−0.141318	−	0.244771i
$585$		0			0
$586$	−22.1354	−	12.7799i	−0.914406	−	0.527932i
$587$			4.01980i			0.165915i	0.996553	+	0.0829575i	$0.0264366\pi$
$587$			4.01980i			0.165915i	−0.996553	+	0.0829575i	$0.973563\pi$
$588$		0			0
$589$	6.46127			0.266232
$590$	−12.3445	+	6.37635i	−0.508214	+	0.262510i
$591$		0			0
$592$	0.369259	−	0.213192i	0.0151764	−	0.00876213i
$593$	−37.7010	−	21.7667i	−1.54819	−	0.893850i	−0.998280	−	0.0586292i	$-0.981327\pi$
$593$	−37.7010	−	21.7667i	−1.54819	−	0.893850i	−0.549914	−	0.835221i	$-0.685340\pi$
$594$		0			0
$595$	10.0390	+	21.1524i	0.411560	+	0.867163i
$596$			2.47225i			0.101267i
$597$		0			0
$598$	3.60121	+	6.23749i	0.147265	+	0.255070i
$599$	27.8218	−	16.0629i	1.13677	−	0.656314i	0.191141	−	0.981563i	$-0.438781\pi$
$599$	27.8218	−	16.0629i	1.13677	−	0.656314i	0.945629	+	0.325249i	$0.105448\pi$
$600$		0			0
$601$		−	8.21681i		−	0.335171i	−0.985858	−	0.167585i	$-0.946403\pi$
$601$		−	8.21681i		−	0.335171i	0.985858	−	0.167585i	$-0.0535970\pi$
$602$	−14.6405	+	7.80788i	−0.596702	+	0.318225i
$603$		0			0
$604$	10.4425	−	18.0869i	0.424898	−	0.735945i
$605$	0.885684	−	18.9066i	0.0360082	−	0.768664i
$606$		0			0
$607$	−14.1180	+	24.4532i	−0.573034	+	0.992523i	0.423219	+	0.906028i	$0.360900\pi$
$607$	−14.1180	+	24.4532i	−0.573034	+	0.992523i	−0.996252	+	0.0864957i	$0.972433\pi$
$608$		−	0.625477i		−	0.0253664i
$609$		0			0
$610$	13.2823	−	20.7035i	0.537784	−	0.838261i
$611$	2.22825	+	1.28648i	0.0901452	+	0.0520454i
$612$		0			0
$613$	−26.6670	+	15.3962i	−1.07707	+	0.621846i	−0.930104	−	0.367296i	$-0.880284\pi$
$613$	−26.6670	+	15.3962i	−1.07707	+	0.621846i	−0.146965	+	0.989142i	$0.546950\pi$
$614$	17.1430	−	29.6926i	0.691836	−	1.19829i
$615$		0			0
$616$	−0.141786	+	4.21045i	−0.00571272	+	0.169644i
$617$	4.42613			0.178189			0.0890947	−	0.996023i	$-0.471603\pi$
$617$	4.42613			0.178189			0.0890947	+	0.996023i	$0.471603\pi$
$618$		0			0
$619$	9.47047	−	5.46778i	0.380650	−	0.219768i	−0.297451	−	0.954737i	$-0.596136\pi$
$619$	9.47047	−	5.46778i	0.380650	−	0.219768i	0.678101	+	0.734969i	$0.262803\pi$
$620$	23.0736	+	1.08089i	0.926659	+	0.0434095i
$621$		0			0
$622$	−8.68041			−0.348053
$623$	4.99800	+	9.37171i	0.200241	+	0.375470i
$624$		0			0
$625$	−8.25121	−	23.5991i	−0.330049	−	0.943964i
$626$	15.0106	+	25.9992i	0.599946	+	1.03914i
$627$		0			0
$628$	−12.2238	+	21.1722i	−0.487781	+	0.844862i
$629$	−1.68748			−0.0672841
$630$		0			0
$631$	−38.2293			−1.52189			−0.760943	−	0.648819i	$-0.775263\pi$
$631$	−38.2293			−1.52189			−0.760943	+	0.648819i	$0.775263\pi$
$632$	−4.52582	+	7.83895i	−0.180028	+	0.311817i
$633$		0			0
$634$	13.8628	+	24.0111i	0.550563	+	0.953603i
$635$	−13.5635	−	26.2587i	−0.538253	−	1.04205i
$636$		0			0
$637$	−2.85321	−	5.81318i	−0.113048	−	0.230327i
$638$	14.8849			0.589300
$639$		0			0
$640$	0.104634	−	2.23362i	0.00413603	−	0.0882915i
$641$	−29.0339	+	16.7627i	−1.14677	+	0.662088i	−0.948098	−	0.317979i	$-0.896996\pi$
$641$	−29.0339	+	16.7627i	−1.14677	+	0.662088i	−0.198671	+	0.980066i	$0.563663\pi$
$642$		0			0
$643$	−17.4072			−0.686474			−0.343237	−	0.939249i	$-0.611523\pi$
$643$	−17.4072			−0.686474			−0.343237	+	0.939249i	$0.611523\pi$
$644$	−10.8940	+	17.4824i	−0.429283	+	0.688903i
$645$		0			0
$646$	−1.23771	+	2.14378i	−0.0486971	+	0.0843458i
$647$	−33.1343	+	19.1301i	−1.30264	+	0.752082i	−0.980857	−	0.194730i	$-0.937617\pi$
$647$	−33.1343	+	19.1301i	−1.30264	+	0.752082i	−0.321787	+	0.946812i	$0.604284\pi$
$648$		0			0
$649$	8.56839	+	4.94696i	0.336339	+	0.194185i
$650$	1.92812	+	4.20443i	0.0756271	+	0.164911i
$651$		0			0
$652$		−	5.91515i		−	0.231655i
$653$	−16.1671	+	28.0023i	−0.632669	+	1.09581i	0.354335	+	0.935119i	$0.384707\pi$
$653$	−16.1671	+	28.0023i	−0.632669	+	1.09581i	−0.987004	+	0.160696i	$0.948626\pi$
$654$		0			0
$655$	−0.983730	+	20.9996i	−0.0384375	+	0.820522i
$656$	−4.17731	+	7.23532i	−0.163097	+	0.282492i
$657$		0			0
$658$	−0.247660	+	7.35446i	−0.00965478	+	0.286707i
$659$		−	16.4516i		−	0.640865i	−0.947271	−	0.320433i	$-0.896172\pi$
$659$		−	16.4516i		−	0.640865i	0.947271	−	0.320433i	$-0.103828\pi$
$660$		0			0
$661$	−2.14550	+	1.23870i	−0.0834502	+	0.0481800i	−0.541144	−	0.840930i	$-0.682009\pi$
$661$	−2.14550	+	1.23870i	−0.0834502	+	0.0481800i	0.457694	+	0.889110i	$0.348675\pi$
$662$	−3.15175	−	5.45899i	−0.122496	−	0.212170i
$663$		0			0
$664$			0.809898i			0.0314301i
$665$	−2.10181	+	3.04552i	−0.0815045	+	0.118100i
$666$		0			0
$667$	63.0298	+	36.3903i	2.44052	+	1.40904i
$668$	10.5170	−	6.07201i	0.406916	−	0.234933i
$669$		0			0
$670$	0.365508	+	0.707615i	0.0141208	+	0.0273375i
$671$	−17.5161			−0.676202
$672$		0			0
$673$			17.0784i			0.658326i	0.944273	+	0.329163i	$0.106767\pi$
$673$			17.0784i			0.658326i	−0.944273	+	0.329163i	$0.893233\pi$
$674$	23.7375	+	13.7048i	0.914333	+	0.527891i
$675$		0			0
$676$	6.07210	+	10.5172i	0.233542	+	0.404507i
$677$	40.3639	+	23.3041i	1.55131	+	0.895650i	0.998035	+	0.0626524i	$0.0199560\pi$
$677$	40.3639	+	23.3041i	1.55131	+	0.895650i	0.553276	+	0.832998i	$0.313377\pi$
$678$		0			0
$679$	11.0221	−	17.6880i	0.422990	−	0.678803i
$680$	−4.77857	+	7.44851i	−0.183250	+	0.285637i
$681$		0			0
$682$	−8.22437	−	14.2450i	−0.314927	−	0.545470i
$683$	1.18353	+	2.04994i	0.0452867	+	0.0784388i	0.887780	−	0.460268i	$-0.152247\pi$
$683$	1.18353	+	2.04994i	0.0452867	+	0.0784388i	−0.842494	+	0.538706i	$0.818913\pi$
$684$		0			0
$685$	17.6399	+	11.3168i	0.673988	+	0.432395i
$686$	10.8299	−	15.0237i	0.413488	−	0.573609i
$687$		0			0
$688$	−5.43113	−	3.13566i	−0.207060	−	0.119546i
$689$	−1.55006	−	2.68478i	−0.0590524	−	0.102282i
$690$		0			0
$691$	−19.0534	−	11.0005i	−0.724826	−	0.418479i	0.0917001	−	0.995787i	$-0.470770\pi$
$691$	−19.0534	−	11.0005i	−0.724826	−	0.418479i	−0.816527	+	0.577308i	$0.804103\pi$
$692$			16.3984i			0.623372i
$693$		0			0
$694$	−8.16672			−0.310004
$695$	14.4802	+	28.0334i	0.549266	+	1.06337i
$696$		0			0
$697$	28.6349	−	16.5323i	1.08462	−	0.626207i
$698$	−23.8924	−	13.7943i	−0.904339	−	0.522120i
$699$		0			0
$700$	−8.01516	+	10.5241i	−0.302944	+	0.397775i
$701$		−	28.7909i		−	1.08742i	−0.839274	−	0.543708i	$-0.817020\pi$
$701$		−	28.7909i		−	1.08742i	0.839274	−	0.543708i	$-0.182980\pi$
$702$		0			0
$703$	−0.133347	−	0.230963i	−0.00502926	−	0.00871094i
$704$	−1.37897	+	0.796151i	−0.0519721	+	0.0300061i
$705$		0			0
$706$		−	7.04285i		−	0.265061i
$707$	−19.9065	−	0.670346i	−0.748661	−	0.0252110i
$708$		0			0
$709$	7.64049	−	13.2337i	0.286945	−	0.497003i	−0.686134	−	0.727475i	$-0.740694\pi$
$709$	7.64049	−	13.2337i	0.286945	−	0.497003i	0.973079	+	0.230472i	$0.0740270\pi$
$710$	−20.2807	−	0.950053i	−0.761121	−	0.0356549i
$711$		0			0
$712$	−2.00721	+	3.47659i	−0.0752234	+	0.130291i
$713$		−	80.4269i		−	3.01201i
$714$		0			0
$715$	1.77857	−	2.77231i	0.0665147	−	0.103679i
$716$	2.73398	+	1.57846i	0.102174	+	0.0589900i
$717$		0			0
$718$	−14.1545	+	8.17213i	−0.528243	+	0.304981i
$719$	−8.33730	+	14.4406i	−0.310929	+	0.538545i	−0.978564	−	0.205944i	$-0.933973\pi$
$719$	−8.33730	+	14.4406i	−0.310929	+	0.538545i	0.667635	+	0.744489i	$0.267307\pi$
$720$		0			0
$721$	2.07121	+	3.88372i	0.0771360	+	0.144637i
$722$	18.6088			0.692547
$723$		0			0
$724$	−7.08336	+	4.08958i	−0.263251	+	0.151988i
$725$	38.1162	+	27.0519i	1.41560	+	1.00468i
$726$		0			0
$727$	−32.4228			−1.20250			−0.601248	−	0.799062i	$-0.705330\pi$
$727$	−32.4228			−1.20250			−0.601248	+	0.799062i	$0.705330\pi$
$728$	1.29443	−	2.07726i	0.0479746	−	0.0769885i
$729$		0			0
$730$	−13.5695	+	7.00913i	−0.502231	+	0.259420i
$731$	12.4099	+	21.4945i	0.458996	+	0.795004i
$732$		0			0
$733$	−23.1637	+	40.1207i	−0.855570	+	1.48189i	0.0205452	+	0.999789i	$0.493460\pi$
$733$	−23.1637	+	40.1207i	−0.855570	+	1.48189i	−0.876115	+	0.482102i	$0.839874\pi$
$734$	3.00798			0.111026
$735$		0			0
$736$	−7.78564			−0.286983
$737$	0.283572	−	0.491161i	0.0104455	−	0.0180921i
$738$		0			0
$739$	8.23689	+	14.2667i	0.302999	+	0.524809i	0.976814	−	0.214091i	$-0.0686788\pi$
$739$	8.23689	+	14.2667i	0.302999	+	0.524809i	−0.673815	+	0.738900i	$0.735345\pi$
$740$	−0.437552	−	0.847091i	−0.0160847	−	0.0311397i
$741$		0			0
$742$	4.68905	−	7.52488i	0.172141	−	0.276247i
$743$	38.4778			1.41161			0.705806	−	0.708405i	$-0.250585\pi$
$743$	38.4778			1.41161			0.705806	+	0.708405i	$0.250585\pi$
$744$		0			0
$745$	5.52206	+	0.258682i	0.202313	+	0.00947737i
$746$	20.0892	−	11.5985i	0.735519	−	0.424652i
$747$		0			0
$748$	6.30178			0.230416
$749$	−24.1567	−	45.2960i	−0.882666	−	1.65508i
$750$		0			0
$751$	−18.9145	+	32.7608i	−0.690198	+	1.19546i	0.281574	+	0.959539i	$0.409143\pi$
$751$	−18.9145	+	32.7608i	−0.690198	+	1.19546i	−0.971773	+	0.235919i	$0.924190\pi$
$752$	−2.40868	+	1.39065i	−0.0878355	+	0.0507118i
$753$		0			0
$754$	−7.48922	−	4.32390i	−0.272741	−	0.157467i
$755$	−39.3065	−	25.2170i	−1.43051	−	0.917740i
$756$		0			0
$757$			11.1485i			0.405197i	0.979262	+	0.202599i	$0.0649387\pi$
$757$			11.1485i			0.405197i	−0.979262	+	0.202599i	$0.935061\pi$
$758$	−13.6359	+	23.6181i	−0.495278	+	0.857846i
$759$		0			0
$760$	−1.39708	−	0.0654463i	−0.0506773	−	0.00237399i
$761$	−14.6239	+	25.3294i	−0.530117	+	0.918189i	0.469266	+	0.883057i	$0.344519\pi$
$761$	−14.6239	+	25.3294i	−0.530117	+	0.918189i	−0.999383	+	0.0351321i	$0.988815\pi$
$762$		0			0
$763$	−5.28850	−	0.178089i	−0.191457	−	0.00644726i
$764$			2.82843i			0.102329i
$765$		0			0
$766$	−3.69096	+	2.13098i	−0.133360	+	0.0769953i
$767$	−2.87407	−	4.97804i	−0.103777	−	0.179747i
$768$		0			0
$769$		−	0.892823i		−	0.0321960i	−0.999870	−	0.0160980i	$-0.994876\pi$
$769$		−	0.892823i		−	0.0321960i	0.999870	−	0.0160980i	$-0.00512438\pi$
$770$	9.38970	+	0.757253i	0.338381	+	0.0272895i
$771$		0			0
$772$	15.3420	+	8.85772i	0.552172	+	0.318796i
$773$	17.1302	−	9.89011i	0.616130	−	0.355723i	−0.159231	−	0.987241i	$-0.550901\pi$
$773$	17.1302	−	9.89011i	0.616130	−	0.355723i	0.775361	+	0.631519i	$0.217568\pi$
$774$		0			0
$775$	4.82858	−	51.4246i	0.173448	−	1.84723i
$776$	7.87721			0.282775
$777$		0			0
$778$		−	2.08172i		−	0.0746332i
$779$	4.52553	+	2.61281i	0.162144	+	0.0936138i
$780$		0			0
$781$	7.22886	+	12.5207i	0.258669	+	0.448028i
$782$	26.6847	+	15.4064i	0.954243	+	0.550933i
$783$		0			0
$784$	6.98414	+	0.470912i	0.249434	+	0.0168183i
$785$	46.0116	+	29.5186i	1.64222	+	1.05356i
$786$		0			0
$787$	−13.2978	−	23.0325i	−0.474017	−	0.821021i	0.525541	−	0.850769i	$-0.323863\pi$
$787$	−13.2978	−	23.0325i	−0.474017	−	0.821021i	−0.999557	+	0.0297473i	$0.990530\pi$
$788$	2.15175	+	3.72694i	0.0766529	+	0.132767i
$789$		0			0
$790$	17.0357	+	10.9292i	0.606102	+	0.388843i
$791$	−22.4928	+	36.0959i	−0.799752	+	1.28342i
$792$		0			0
$793$	8.81308	+	5.08823i	0.312962	+	0.180688i
$794$	−11.1885	−	19.3791i	−0.397066	−	0.687739i
$795$		0			0
$796$	3.00000	+	1.73205i	0.106332	+	0.0613909i
$797$		−	21.4698i		−	0.760499i	−0.924884	−	0.380250i	$-0.875838\pi$
$797$		−	21.4698i		−	0.760499i	0.924884	−	0.380250i	$-0.124162\pi$
$798$		0			0
$799$	11.0074			0.389415
$800$	−4.97810	−	0.467426i	−0.176003	−	0.0165260i
$801$		0			0
$802$	−17.0295	+	9.83196i	−0.601331	+	0.347179i
$803$	9.41871	+	5.43790i	0.332379	+	0.191899i
$804$		0			0
$805$	37.9091	+	26.1623i	1.33612	+	0.922099i
$806$			9.55634i			0.336608i
$807$		0			0
$808$	−3.76411	−	6.51962i	−0.132421	−	0.229360i
$809$	18.2930	−	10.5615i	0.643149	−	0.371322i	−0.142677	−	0.989769i	$-0.545571\pi$
$809$	18.2930	−	10.5615i	0.643149	−	0.371322i	0.785827	+	0.618447i	$0.212238\pi$
$810$		0			0
$811$		−	13.3784i		−	0.469779i	−0.972022	−	0.234889i	$-0.924527\pi$
$811$		−	13.3784i		−	0.469779i	0.972022	−	0.234889i	$-0.0754728\pi$
$812$	0.832393	−	24.7186i	0.0292113	−	0.867453i
$813$		0			0
$814$	−0.339466	+	0.587972i	−0.0118983	+	0.0206084i
$815$	−13.2122	−	0.618927i	−0.462803	−	0.0216801i
$816$		0			0
$817$	−1.96129	+	3.39705i	−0.0686167	+	0.118848i
$818$			2.53956i			0.0887936i
$819$		0			0
$820$	15.7239	+	10.0876i	0.549101	+	0.352274i
$821$	5.67591	+	3.27699i	0.198091	+	0.114368i	0.595765	−	0.803159i	$-0.296849\pi$
$821$	5.67591	+	3.27699i	0.198091	+	0.114368i	−0.397674	+	0.917527i	$0.630182\pi$
$822$		0			0
$823$	37.9915	−	21.9344i	1.32430	−	0.764585i	0.339889	−	0.940466i	$-0.389611\pi$
$823$	37.9915	−	21.9344i	1.32430	−	0.764585i	0.984412	+	0.175880i	$0.0562772\pi$
$824$	−0.831805	+	1.44073i	−0.0289773	+	0.0501901i
$825$		0			0
$826$	8.69432	−	13.9524i	0.302514	−	0.485467i
$827$	−19.1611			−0.666296			−0.333148	−	0.942875i	$-0.608111\pi$
$827$	−19.1611			−0.666296			−0.333148	+	0.942875i	$0.608111\pi$
$828$		0			0
$829$	14.6635	−	8.46597i	0.509284	−	0.294035i	−0.223255	−	0.974760i	$-0.571668\pi$
$829$	14.6635	−	8.46597i	0.509284	−	0.294035i	0.732539	+	0.680725i	$0.238335\pi$
$830$	1.80900	+	0.0847430i	0.0627914	+	0.00294147i
$831$		0			0
$832$	0.925091			0.0320718
$833$	−23.0058	−	15.4344i	−0.797103	−	0.534771i
$834$		0			0
$835$	−12.4621	−	24.1264i	−0.431269	−	0.834928i
$836$	0.497974	+	0.862517i	0.0172228	+	0.0298308i
$837$		0			0
$838$	16.0284	−	27.7620i	0.553692	−	0.959023i
$839$	−10.5028			−0.362596			−0.181298	−	0.983428i	$-0.558030\pi$
$839$	−10.5028			−0.362596			−0.181298	+	0.983428i	$0.558030\pi$
$840$		0			0
$841$	−58.3861			−2.01331
$842$	12.6101	−	21.8413i	0.434572	−	0.752700i
$843$		0			0
$844$	−5.19432	−	8.99682i	−0.178796	−	0.309683i
$845$	24.1267	−	12.4623i	0.829985	−	0.428716i
$846$		0			0
$847$	10.5385	+	19.7606i	0.362107	+	0.678984i
$848$	3.35114			0.115079
$849$		0			0
$850$	16.1371	+	11.4529i	0.553499	+	0.392830i
$851$	−2.87492	+	1.65983i	−0.0985509	+	0.0568984i
$852$		0			0
$853$	−30.2419			−1.03546			−0.517731	−	0.855544i	$-0.673223\pi$
$853$	−30.2419			−1.03546			−0.517731	+	0.855544i	$0.673223\pi$
$854$	−0.979534	+	29.0881i	−0.0335190	+	0.995374i
$855$		0			0
$856$	9.70139	−	16.8033i	0.331587	−	0.574325i
$857$	−19.2816	+	11.1322i	−0.658646	+	0.380270i	−0.791761	−	0.610831i	$-0.790835\pi$
$857$	−19.2816	+	11.1322i	−0.658646	+	0.380270i	0.133115	+	0.991101i	$0.457502\pi$
$858$		0			0
$859$	26.7059	+	15.4187i	0.911195	+	0.526078i	0.880815	−	0.473460i	$-0.156995\pi$
$859$	26.7059	+	15.4187i	0.911195	+	0.526078i	0.0303793	+	0.999538i	$0.490328\pi$
$860$	−7.57216	+	11.8030i	−0.258209	+	0.402478i
$861$		0			0
$862$		−	33.6710i		−	1.14684i
$863$	11.5580	−	20.0190i	0.393437	−	0.681454i	−0.599463	−	0.800403i	$-0.704619\pi$
$863$	11.5580	−	20.0190i	0.393437	−	0.681454i	0.992900	+	0.118949i	$0.0379525\pi$
$864$		0			0
$865$	36.6277	+	1.71583i	1.24538	+	0.0583400i
$866$	−11.3805	+	19.7116i	−0.386725	+	0.669828i
$867$		0			0
$868$	−24.1159	+	12.8612i	−0.818546	+	0.436536i
$869$		−	14.4130i		−	0.488926i
$870$		0			0
$871$	−0.285353	+	0.164749i	−0.00966882	+	0.00558230i
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$		0			0
$874$			4.86974i			0.164721i
$875$	22.6682	+	19.0040i	0.766326	+	0.642452i
$876$		0			0
$877$	21.8366	+	12.6074i	0.737369	+	0.425720i	0.821112	−	0.570767i	$-0.193354\pi$
$877$	21.8366	+	12.6074i	0.737369	+	0.425720i	−0.0837427	+	0.996487i	$0.526687\pi$
$878$	−1.86282	+	1.07550i	−0.0628670	+	0.0362963i
$879$		0			0
$880$	1.63401	+	3.16341i	0.0550825	+	0.106638i
$881$	−20.5142			−0.691140			−0.345570	−	0.938393i	$-0.612314\pi$
$881$	−20.5142			−0.691140			−0.345570	+	0.938393i	$0.612314\pi$
$882$		0			0
$883$		−	43.0491i		−	1.44872i	−0.689424	−	0.724358i	$-0.742136\pi$
$883$		−	43.0491i		−	1.44872i	0.689424	−	0.724358i	$-0.257864\pi$
$884$	−3.17068	−	1.83059i	−0.106642	−	0.0615696i
$885$		0			0
$886$	−3.83239	−	6.63790i	−0.128752	−	0.223005i
$887$	28.9170	+	16.6952i	0.970938	+	0.560571i	0.899522	−	0.436876i	$-0.143915\pi$
$887$	28.9170	+	16.6952i	0.970938	+	0.560571i	0.0714156	+	0.997447i	$0.477248\pi$
$888$		0			0
$889$	29.6791	+	18.4942i	0.995405	+	0.620277i
$890$	7.55535	+	4.84711i	0.253256	+	0.162476i
$891$		0			0
$892$	−9.17777	−	15.8964i	−0.307294	−	0.532250i
$893$	0.869820	+	1.50657i	0.0291074	+	0.0504156i
$894$		0			0
$895$	3.81176	−	5.94151i	0.127413	−	0.198603i
$896$	1.24501	+	2.33451i	0.0415929	+	0.0779906i
$897$		0			0
$898$	−16.3104	−	9.41684i	−0.544287	−	0.314244i
$899$	48.2834	+	83.6293i	1.61034	+	2.78919i
$900$		0			0
$901$	−11.4858	−	6.63132i	−0.382647	−	0.220921i
$902$		−	13.3031i		−	0.442945i
$903$		0			0
$904$	−16.0750			−0.534646
$905$	8.39340	+	16.2494i	0.279006	+	0.540149i
$906$		0			0
$907$	−23.7115	+	13.6898i	−0.787327	+	0.454563i	−0.839021	−	0.544100i	$-0.816871\pi$
$907$	−23.7115	+	13.6898i	−0.787327	+	0.454563i	0.0516937	+	0.998663i	$0.483538\pi$
$908$	−2.61803	−	1.51152i	−0.0868825	−	0.0501616i
$909$		0			0
$910$	−4.50437	−	3.10861i	−0.149318	−	0.103049i
$911$			33.0422i			1.09474i	0.836892	+	0.547368i	$0.184370\pi$
$911$			33.0422i			1.09474i	−0.836892	+	0.547368i	$0.815630\pi$
$912$		0			0
$913$	−0.644801	−	1.11683i	−0.0213398	−	0.0369616i
$914$	−25.3442	+	14.6325i	−0.838311	+	0.483999i
$915$		0			0
$916$		−	10.6465i		−	0.351770i
$917$	−11.7051	−	21.9482i	−0.386537	−	0.724792i
$918$		0			0
$919$	13.2444	−	22.9400i	0.436893	−	0.756722i	−0.560555	−	0.828117i	$-0.689412\pi$
$919$	13.2444	−	22.9400i	0.436893	−	0.756722i	0.997448	+	0.0713958i	$0.0227453\pi$
$920$	−0.814645	+	17.3902i	−0.0268580	+	0.573336i
$921$		0			0
$922$	−7.09815	+	12.2944i	−0.233765	+	0.404893i
$923$		−	8.39960i		−	0.276476i
$924$		0			0
$925$	−1.93786	+	0.888689i	−0.0637165	+	0.0292199i
$926$	6.63191	+	3.82893i	0.217938	+	0.125827i
$927$		0			0
$928$	8.09565	−	4.67403i	0.265753	−	0.153432i
$929$	−15.5952	+	27.0117i	−0.511663	+	0.886226i	0.488246	+	0.872706i	$0.337637\pi$
$929$	−15.5952	+	27.0117i	−0.511663	+	0.886226i	−0.999909	+	0.0135196i	$0.995696\pi$
$930$		0			0
$931$	0.294545	−	4.36842i	0.00965332	−	0.143169i
$932$	3.98585			0.130561
$933$		0			0
$934$	15.3410	−	8.85713i	0.501973	−	0.289814i
$935$	0.659382	−	14.0758i	0.0215641	−	0.460327i
$936$		0			0
$937$	6.40017			0.209084			0.104542	−	0.994520i	$-0.466662\pi$
$937$	6.40017			0.209084			0.104542	+	0.994520i	$0.466662\pi$
$938$	−0.799787	−	0.498379i	−0.0261140	−	0.0162727i
$939$		0			0
$940$	2.85415	+	5.52558i	0.0930922	+	0.180224i
$941$	−2.56243	−	4.43825i	−0.0835327	−	0.144683i	0.821232	−	0.570594i	$-0.193287\pi$
$941$	−2.56243	−	4.43825i	−0.0835327	−	0.144683i	−0.904765	+	0.425911i	$0.859954\pi$
$942$		0			0
$943$	32.5231	−	56.3316i	1.05910	−	1.83441i
$944$	6.21360			0.202235
$945$		0			0
$946$	9.98585			0.324668
$947$	−21.1125	+	36.5679i	−0.686064	+	1.18830i	0.287037	+	0.957919i	$0.407330\pi$
$947$	−21.1125	+	36.5679i	−0.686064	+	1.18830i	−0.973101	+	0.230378i	$0.926004\pi$
$948$		0			0
$949$	−3.15929	−	5.47206i	−0.102555	−	0.177630i
$950$	−0.292364	+	3.11369i	−0.00948555	+	0.101021i
$951$		0			0
$952$	0.352407	−	10.4650i	0.0114216	−	0.339174i
$953$	−8.12428			−0.263171			−0.131586	−	0.991305i	$-0.542007\pi$
$953$	−8.12428			−0.263171			−0.131586	+	0.991305i	$0.542007\pi$
$954$		0			0
$955$	6.31763	+	0.295950i	0.204434	+	0.00957673i
$956$	7.14210	−	4.12349i	0.230992	−	0.133363i
$957$		0			0
$958$	12.8399			0.414839
$959$	−24.7838	−	0.834589i	−0.800311	−	0.0269503i
$960$		0			0
$961$	37.8560	−	65.5686i	1.22116	−	2.11512i
$962$	0.341598	−	0.197222i	0.0110136	−	0.00635869i
$963$		0			0
$964$	9.48785	+	5.47782i	0.305583	+	0.176429i
$965$	21.3901	−	33.3414i	0.688571	−	1.07330i
$966$		0			0
$967$		−	52.3097i		−	1.68217i	−0.540905	−	0.841084i	$-0.681918\pi$
$967$		−	52.3097i		−	1.68217i	0.540905	−	0.841084i	$-0.318082\pi$
$968$	−4.23229	+	7.33053i	−0.136031	+	0.235612i
$969$		0			0
$970$	0.824225	−	17.5947i	0.0264643	−	0.564931i
$971$	8.55280	−	14.8139i	0.274473	−	0.475400i	−0.695529	−	0.718498i	$-0.744830\pi$
$971$	8.55280	−	14.8139i	0.274473	−	0.475400i	0.970002	+	0.243097i	$0.0781634\pi$
$972$		0			0
$973$	−31.6849	−	19.7441i	−1.01577	−	0.632968i
$974$		−	3.77858i		−	0.121073i
$975$		0			0
$976$	−9.52671	+	5.50025i	−0.304943	+	0.176059i
$977$	18.1989	+	31.5215i	0.582235	+	1.00846i	0.995214	+	0.0977201i	$0.0311550\pi$
$977$	18.1989	+	31.5215i	0.582235	+	1.00846i	−0.412979	+	0.910741i	$0.635512\pi$
$978$		0			0
$979$		−	6.39217i		−	0.204295i
$980$	1.78262	−	15.5506i	0.0569437	−	0.496747i
$981$		0			0
$982$	27.8569	+	16.0832i	0.888950	+	0.513235i
$983$	−22.2813	+	12.8641i	−0.710664	+	0.410302i	−0.811307	−	0.584621i	$-0.801243\pi$
$983$	−22.2813	+	12.8641i	−0.710664	+	0.410302i	0.100643	+	0.994923i	$0.467910\pi$
$984$		0			0
$985$	8.54971	−	4.41622i	0.272416	−	0.140713i
$986$	−36.9963			−1.17820
$987$		0			0
$988$		−	0.578623i		−	0.0184085i
$989$	42.2848	+	24.4132i	1.34458	+	0.776293i
$990$		0			0
$991$	6.07375	+	10.5200i	0.192939	+	0.334180i	0.946223	−	0.323515i	$-0.104865\pi$
$991$	6.07375	+	10.5200i	0.192939	+	0.334180i	−0.753284	+	0.657696i	$0.771531\pi$
$992$	−8.94618	−	5.16508i	−0.284041	−	0.163991i
$993$		0			0
$994$	21.1968	−	11.3044i	0.672321	−	0.358554i
$995$	4.18264	−	6.51962i	0.132599	−	0.206686i
$996$		0			0
$997$	−8.57663	−	14.8552i	−0.271625	−	0.470468i	0.697653	−	0.716435i	$-0.254228\pi$
$997$	−8.57663	−	14.8552i	−0.271625	−	0.470468i	−0.969278	+	0.245968i	$0.920894\pi$
$998$	−15.9683	−	27.6579i	−0.505467	−	0.875495i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bo.a.89.2	✓	16
3.2	odd	2		630.2.bo.b.89.7	yes	16
5.2	odd	4		3150.2.bf.f.1601.6		32
5.3	odd	4		3150.2.bf.f.1601.13		32
5.4	even	2		630.2.bo.b.89.4	yes	16
7.2	even	3		4410.2.d.b.4409.14		16
7.3	odd	6	inner	630.2.bo.a.269.5	yes	16
7.5	odd	6		4410.2.d.b.4409.3		16
15.2	even	4		3150.2.bf.f.1601.14		32
15.8	even	4		3150.2.bf.f.1601.5		32
15.14	odd	2	inner	630.2.bo.a.89.5	yes	16
21.2	odd	6		4410.2.d.a.4409.3		16
21.5	even	6		4410.2.d.a.4409.14		16
21.17	even	6		630.2.bo.b.269.4	yes	16
35.3	even	12		3150.2.bf.f.1151.5		32
35.9	even	6		4410.2.d.a.4409.13		16
35.17	even	12		3150.2.bf.f.1151.16		32
35.19	odd	6		4410.2.d.a.4409.4		16
35.24	odd	6		630.2.bo.b.269.7	yes	16
105.17	odd	12		3150.2.bf.f.1151.6		32
105.38	odd	12		3150.2.bf.f.1151.15		32
105.44	odd	6		4410.2.d.b.4409.4		16
105.59	even	6	inner	630.2.bo.a.269.2	yes	16
105.89	even	6		4410.2.d.b.4409.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.2	✓	16	1.1	even	1	trivial
630.2.bo.a.89.5	yes	16	15.14	odd	2	inner
630.2.bo.a.269.2	yes	16	105.59	even	6	inner
630.2.bo.a.269.5	yes	16	7.3	odd	6	inner
630.2.bo.b.89.4	yes	16	5.4	even	2
630.2.bo.b.89.7	yes	16	3.2	odd	2
630.2.bo.b.269.4	yes	16	21.17	even	6
630.2.bo.b.269.7	yes	16	35.24	odd	6
3150.2.bf.f.1151.5		32	35.3	even	12
3150.2.bf.f.1151.6		32	105.17	odd	12
3150.2.bf.f.1151.15		32	105.38	odd	12
3150.2.bf.f.1151.16		32	35.17	even	12
3150.2.bf.f.1601.5		32	15.8	even	4
3150.2.bf.f.1601.6		32	5.2	odd	4
3150.2.bf.f.1601.13		32	5.3	odd	4
3150.2.bf.f.1601.14		32	15.2	even	4
4410.2.d.a.4409.3		16	21.2	odd	6
4410.2.d.a.4409.4		16	35.19	odd	6
4410.2.d.a.4409.13		16	35.9	even	6
4410.2.d.a.4409.14		16	21.5	even	6
4410.2.d.b.4409.3		16	7.5	odd	6
4410.2.d.b.4409.4		16	105.44	odd	6
4410.2.d.b.4409.13		16	105.89	even	6
4410.2.d.b.4409.14		16	7.2	even	3

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.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.98669 + 1.02619i) q^{5} +(1.39924 - 2.24547i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.98669 + 1.02619i) q^{5} +(1.39924 - 2.24547i) q^{7} +1.00000 q^{8} +(0.104634 - 2.23362i) q^{10} +(-1.37897 + 0.796151i) q^{11} +0.925091 q^{13} +(1.24501 + 2.33451i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.42743 - 1.97883i) q^{17} +(0.541679 + 0.312739i) q^{19} +(1.88205 + 1.20743i) q^{20} -1.59230i q^{22} +(3.89282 - 6.74256i) q^{23} +(2.89385 - 4.07745i) q^{25} +(-0.462546 + 0.801153i) q^{26} +(-2.64425 - 0.0890445i) q^{28} +9.34805i q^{29} +(8.94618 - 5.16508i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.95765i q^{34} +(-0.475571 + 5.89693i) q^{35} +(-0.369259 - 0.213192i) q^{37} +(-0.541679 + 0.312739i) q^{38} +(-1.98669 + 1.02619i) q^{40} +8.35463 q^{41} +6.27133i q^{43} +(1.37897 + 0.796151i) q^{44} +(3.89282 + 6.74256i) q^{46} +(2.40868 + 1.39065i) q^{47} +(-3.08425 - 6.28390i) q^{49} +(2.08425 + 4.54488i) q^{50} +(-0.462546 - 0.801153i) q^{52} +(-1.67557 - 2.90217i) q^{53} +(1.92259 - 2.99680i) q^{55} +(1.39924 - 2.24547i) q^{56} +(-8.09565 - 4.67403i) q^{58} +(-3.10680 - 5.38113i) q^{59} +(9.52671 + 5.50025i) q^{61} +10.3302i q^{62} +1.00000 q^{64} +(-1.83787 + 0.949323i) q^{65} +(-0.308459 + 0.178089i) q^{67} +(-3.42743 - 1.97883i) q^{68} +(-4.86911 - 3.36032i) q^{70} -9.07975i q^{71} +(-3.41511 - 5.91515i) q^{73} +(0.369259 - 0.213192i) q^{74} -0.625477i q^{76} +(-0.141786 + 4.21045i) q^{77} +(-4.52582 + 7.83895i) q^{79} +(0.104634 - 2.23362i) q^{80} +(-4.17731 + 7.23532i) q^{82} +0.809898i q^{83} +(-4.77857 + 7.44851i) q^{85} +(-5.43113 - 3.13566i) q^{86} +(-1.37897 + 0.796151i) q^{88} +(-2.00721 + 3.47659i) q^{89} +(1.29443 - 2.07726i) q^{91} -7.78564 q^{92} +(-2.40868 + 1.39065i) q^{94} +(-1.39708 - 0.0654463i) q^{95} +7.87721 q^{97} +(6.98414 + 0.470912i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8	\( 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50} + 16 q^{53} + 24 q^{61} + 16 q^{64} - 20 q^{65} - 14 q^{70} - 88 q^{77} + 4 q^{79} + 6 q^{80} + 64 q^{85} - 28 q^{91} + 16 q^{92} - 60 q^{94} - 12 q^{95} + 20 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 - 8 * q^23 - 6 * q^25 + 12 * q^31 - 8 * q^32 + 4 * q^35 - 24 * q^38 - 6 * q^40 - 8 * q^46 + 60 * q^47 - 28 * q^49 + 12 * q^50 + 16 * q^53 + 24 * q^61 + 16 * q^64 - 20 * q^65 - 14 * q^70 - 88 * q^77 + 4 * q^79 + 6 * q^80 + 64 * q^85 - 28 * q^91 + 16 * q^92 - 60 * q^94 - 12 * q^95 + 20 * q^98

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