LMFDB - Embedded newform 630.2.bo.a.269.2

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			269.2
Root			$1.98669 - 1.02619i$ of defining polynomial
Character	$\chi$	$=$	630.269
Dual form			630.2.bo.a.89.2

$q$-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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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	0.277492	−	0.960728i	$-0.410497\pi$
$11$	−1.37897	−	0.796151i	−0.415776	−	0.240049i	−0.693269	+	0.720679i	$0.743830\pi$
$12$		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	0.854288	−	0.519799i	$-0.173993\pi$
$17$	3.42743	+	1.97883i	0.831273	+	0.479936i	−0.0230153	+	0.999735i	$0.507327\pi$
$18$		0			0
$19$	0.541679	−	0.312739i	0.124270	−	0.0717472i	−0.436577	−	0.899667i	$-0.643809\pi$
$19$	0.541679	−	0.312739i	0.124270	−	0.0717472i	0.560846	+	0.827920i	$0.310476\pi$
$20$	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	0.911667	+	0.410930i	$0.134796\pi$
$23$	3.89282	+	6.74256i	0.811709	+	1.40592i	−0.0999578	+	0.994992i	$0.531871\pi$
$24$		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	$-0.665441\pi$
$29$		−	9.34805i		−	1.73589i	0.496661	−	0.867945i	$-0.334559\pi$
$30$		0			0
$31$	8.94618	+	5.16508i	1.60678	+	0.927675i	0.990084	+	0.140474i	$0.0448626\pi$
$31$	8.94618	+	5.16508i	1.60678	+	0.927675i	0.616696	+	0.787201i	$0.288471\pi$
$32$	−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	−0.530046	−	0.847969i	$-0.677825\pi$
$37$	−0.369259	+	0.213192i	−0.0607058	+	0.0350485i	0.469340	+	0.883018i	$0.344492\pi$
$38$	−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	$-0.841295\pi$
$43$		−	6.27133i		−	0.956369i	0.878259	−	0.478184i	$-0.158705\pi$
$44$	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	−0.313934	−	0.949445i	$-0.601647\pi$
$47$	2.40868	−	1.39065i	0.351342	−	0.202847i	0.665276	+	0.746597i	$0.268314\pi$
$48$		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	−0.957854	−	0.287255i	$-0.907257\pi$
$53$	−1.67557	+	2.90217i	−0.230157	+	0.398644i	0.727697	+	0.685899i	$0.240591\pi$
$54$		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	−0.994260	−	0.106994i	$-0.965878\pi$
$59$	−3.10680	+	5.38113i	−0.404471	+	0.700564i	0.589789	+	0.807557i	$0.299211\pi$
$60$		0			0
$61$	9.52671	−	5.50025i	1.21977	−	0.704235i	0.254902	−	0.966967i	$-0.417957\pi$
$61$	9.52671	−	5.50025i	1.21977	−	0.704235i	0.964869	+	0.262732i	$0.0846236\pi$
$62$		−	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	0.481039	−	0.876699i	$-0.340259\pi$
$67$	−0.308459	−	0.178089i	−0.0376843	−	0.0217570i	−0.518724	+	0.854942i	$0.673593\pi$
$68$	−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	$0.181116\pi$
$71$			9.07975i			1.07757i	−0.842444	+	0.538784i	$0.818884\pi$
$72$		0			0
$73$	−3.41511	+	5.91515i	−0.399709	+	0.692316i	−0.993690	−	0.112163i	$-0.964222\pi$
$73$	−3.41511	+	5.91515i	−0.399709	+	0.692316i	0.593981	+	0.804479i	$0.297555\pi$
$74$	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	−0.999943	−	0.0106498i	$-0.996610\pi$
$79$	−4.52582	−	7.83895i	−0.509195	−	0.881951i	0.490749	−	0.871301i	$-0.336723\pi$
$80$	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	$-0.985847\pi$
$83$		−	0.809898i		−	0.0888978i	0.999012	−	0.0444489i	$-0.0141532\pi$
$84$		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	0.739815	−	0.672811i	$-0.234913\pi$
$89$	−2.00721	−	3.47659i	−0.212764	−	0.368518i	−0.952579	+	0.304293i	$0.901580\pi$
$90$		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	−0.990258	−	0.139241i	$-0.955534\pi$
$101$	−3.76411	+	6.51962i	−0.374543	+	0.648727i	0.615716	+	0.787968i	$0.288867\pi$
$102$		0			0
$103$	−0.831805	−	1.44073i	−0.0819601	−	0.141959i	0.822132	−	0.569297i	$-0.192785\pi$
$103$	−0.831805	−	1.44073i	−0.0819601	−	0.141959i	−0.904092	+	0.427338i	$0.859451\pi$
$104$	0.925091			0.0907127
$105$		0			0
$106$	3.35114			0.325492
$107$	9.70139	+	16.8033i	0.937869	+	1.62444i	0.769436	+	0.638724i	$0.220537\pi$
$107$	9.70139	+	16.8033i	0.937869	+	1.62444i	0.168433	+	0.985713i	$0.446129\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$	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	$-0.800535\pi$
$127$		−	13.2173i		−	1.17285i	0.810004	−	0.586424i	$-0.199465\pi$
$128$	−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	0.994968	−	0.100197i	$-0.0319472\pi$
$131$	4.70080	+	8.14203i	0.410711	+	0.711372i	−0.584257	+	0.811569i	$0.698614\pi$
$132$		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	−0.993772	−	0.111433i	$-0.964456\pi$
$137$	−4.68636	+	8.11701i	−0.400382	+	0.693483i	0.593390	+	0.804915i	$0.297789\pi$
$138$		0			0
$139$			14.1106i			1.19685i	0.801180	+	0.598423i	$0.204206\pi$
$139$			14.1106i			1.19685i	−0.801180	+	0.598423i	$0.795794\pi$
$140$	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	−0.585130	−	0.810940i	$-0.698956\pi$
$149$	−2.14103	+	1.23612i	−0.175400	+	0.101267i	0.409730	+	0.912207i	$0.365623\pi$
$150$		0			0
$151$	10.4425	−	18.0869i	0.849796	−	1.47189i	−0.0315949	−	0.999501i	$-0.510059\pi$
$151$	10.4425	−	18.0869i	0.849796	−	1.47189i	0.881391	−	0.472388i	$-0.156608\pi$
$152$	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	−0.297498	+	0.954723i	$0.596152\pi$
$157$	−12.2238	+	21.1722i	−0.975563	+	1.68972i	−0.678065	+	0.735002i	$0.737181\pi$
$158$	−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	−0.285780	−	0.958295i	$-0.592253\pi$
$163$	5.12267	−	2.95758i	0.401239	−	0.231655i	0.687018	+	0.726640i	$0.258919\pi$
$164$	−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	$-0.844302\pi$
$167$		−	12.1440i		−	0.939733i	0.882737	−	0.469867i	$-0.155698\pi$
$168$		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	−0.930819	−	0.365481i	$-0.880904\pi$
$173$	−14.2014	+	8.19918i	−1.07971	+	0.623372i	−0.148893	+	0.988853i	$0.547571\pi$
$174$		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	0.394334	−	0.918967i	$-0.370975\pi$
$179$	−2.73398	−	1.57846i	−0.204347	−	0.117980i	−0.598682	+	0.800987i	$0.704309\pi$
$180$		0			0
$181$			8.17916i			0.607952i	0.952680	+	0.303976i	$0.0983143\pi$
$181$			8.17916i			0.607952i	−0.952680	+	0.303976i	$0.901686\pi$
$182$	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	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	−15.3420	−	8.85772i	−1.10434	−	0.637593i	−0.166985	−	0.985959i	$-0.553403\pi$
$193$	−15.3420	−	8.85772i	−1.10434	−	0.637593i	−0.937358	+	0.348367i	$0.886736\pi$
$194$	−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	0.389885	−	0.920864i	$-0.372515\pi$
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	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	0.584360	−	0.811495i	$-0.301346\pi$
$227$	2.61803	+	1.51152i	0.173765	+	0.100323i	−0.410595	+	0.911818i	$0.634679\pi$
$228$		0			0
$229$	9.22014	−	5.32325i	0.609284	−	0.351770i	−0.163401	−	0.986560i	$-0.552246\pi$
$229$	9.22014	−	5.32325i	0.609284	−	0.351770i	0.772685	+	0.634789i	$0.218913\pi$
$230$	−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	0.793332	−	0.608789i	$-0.208345\pi$
$233$	−1.99293	−	3.45185i	−0.130561	−	0.226138i	−0.923893	+	0.382651i	$0.875011\pi$
$234$		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	$-0.914058\pi$
$239$		−	8.24699i		−	0.533453i	0.963772	−	0.266727i	$-0.0859421\pi$
$240$		0			0
$241$	−9.48785	−	5.47782i	−0.611166	−	0.352857i	0.162255	−	0.986749i	$-0.448123\pi$
$241$	−9.48785	−	5.47782i	−0.611166	−	0.352857i	−0.773422	+	0.633892i	$0.781456\pi$
$242$	−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	0.0513223	−	0.998682i	$-0.483656\pi$
$257$	15.0993	−	8.71758i	0.941868	−	0.543787i	0.890545	+	0.454895i	$0.150323\pi$
$258$		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	−0.431186	−	0.902263i	$-0.641905\pi$
$263$	9.17557	−	15.8926i	0.565790	−	0.979977i	0.996976	−	0.0777137i	$-0.0247620\pi$
$264$		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	−0.187117	−	0.982338i	$-0.559914\pi$
$269$	12.4185	−	21.5095i	0.757171	−	1.31146i	0.944288	−	0.329121i	$-0.106752\pi$
$270$		0			0
$271$	21.1663	−	12.2204i	1.28576	−	0.742335i	0.307867	−	0.951430i	$-0.400385\pi$
$271$	21.1663	−	12.2204i	1.28576	−	0.742335i	0.977895	+	0.209094i	$0.0670516\pi$
$272$		−	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	−0.244932	−	0.969540i	$-0.578766\pi$
$277$	−20.0892	−	11.5985i	−1.20704	−	0.696888i	−0.962113	+	0.272653i	$0.912099\pi$
$278$	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	$-0.862039\pi$
$281$		−	14.0801i		−	0.839949i	0.907536	−	0.419974i	$-0.137961\pi$
$282$		0			0
$283$	1.39910	−	2.42331i	0.0831677	−	0.144051i	−0.821441	−	0.570293i	$-0.806830\pi$
$283$	1.39910	−	2.42331i	0.0831677	−	0.144051i	0.904609	+	0.426242i	$0.140163\pi$
$284$	−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	$-0.731681\pi$
$293$		−	25.5598i		−	1.49322i	0.665263	−	0.746609i	$-0.268319\pi$
$294$		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	−0.716333	−	0.697759i	$-0.754181\pi$
$311$	4.34021	−	7.51746i	0.246110	−	0.426276i	0.962443	+	0.271483i	$0.0875141\pi$
$312$		0			0
$313$	15.0106	+	25.9992i	0.848452	+	1.46956i	0.882589	+	0.470145i	$0.155798\pi$
$313$	15.0106	+	25.9992i	0.848452	+	1.46956i	−0.0341376	+	0.999417i	$0.510868\pi$
$314$	24.4475			1.37965
$315$		0			0
$316$	9.05164			0.509195
$317$	13.8628	+	24.0111i	0.778613	+	1.34860i	0.932741	+	0.360547i	$0.117410\pi$
$317$	13.8628	+	24.0111i	0.778613	+	1.34860i	−0.154128	+	0.988051i	$0.549257\pi$
$318$		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	0.766314	−	0.642467i	$-0.222089\pi$
$331$	−3.15175	−	5.45899i	−0.173236	−	0.300053i	−0.939549	+	0.342414i	$0.888756\pi$
$332$	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	$0.268291\pi$
$337$			27.4097i			1.49310i	−0.665329	+	0.746550i	$0.731709\pi$
$338$	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	−0.735359	−	0.677677i	$-0.762987\pi$
$347$	4.08336	−	7.07258i	0.219206	−	0.379676i	0.954566	+	0.298001i	$0.0963199\pi$
$348$		0			0
$349$		−	27.5885i		−	1.47678i	−0.674374	−	0.738390i	$-0.735587\pi$
$349$		−	27.5885i		−	1.47678i	0.674374	−	0.738390i	$-0.264413\pi$
$350$	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	0.328823	−	0.944391i	$-0.393348\pi$
$353$	−6.09929	−	3.52142i	−0.324632	−	0.187426i	−0.653455	+	0.756965i	$0.726681\pi$
$354$		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	−0.0775782	−	0.996986i	$-0.524719\pi$
$359$	14.1545	−	8.17213i	0.747048	−	0.431308i	0.824626	+	0.565678i	$0.191385\pi$
$360$		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	−0.902606	−	0.430467i	$-0.858349\pi$
$367$	−1.50399	+	2.60498i	−0.0785076	+	0.135979i	0.824099	+	0.566446i	$0.191682\pi$
$368$	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	−0.919884	−	0.392189i	$-0.871718\pi$
$373$	−20.0892	+	11.5985i	−1.04018	+	0.600549i	−0.120296	+	0.992738i	$0.538384\pi$
$374$	−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	−0.402727	−	0.915320i	$-0.631938\pi$
$383$	3.69096	−	2.13098i	0.188599	−	0.108888i	0.591327	+	0.806432i	$0.298604\pi$
$384$		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	0.453600	−	0.891205i	$-0.350140\pi$
$389$	−1.80282	−	1.04086i	−0.0914066	−	0.0527736i	−0.545007	+	0.838432i	$0.683473\pi$
$390$		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	−0.997363	−	0.0725790i	$-0.976877\pi$
$397$	−11.1885	−	19.3791i	−0.561537	−	0.972610i	0.435826	−	0.900031i	$-0.356456\pi$
$398$			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	−0.0103787	−	0.999946i	$-0.503304\pi$
$401$	17.0295	−	9.83196i	0.850411	−	0.490985i	0.860789	+	0.508961i	$0.169970\pi$
$402$		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	0.553388	−	0.832923i	$-0.313335\pi$
$409$	2.19932	+	1.26978i	0.108750	+	0.0627866i	−0.444639	+	0.895710i	$0.646668\pi$
$410$	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	−0.409726	−	0.912209i	$-0.634376\pi$
$431$	−29.1599	−	16.8355i	−1.40458	−	0.810937i	−0.994859	+	0.101271i	$0.967709\pi$
$432$		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	−0.454887	−	0.890549i	$-0.650320\pi$
$439$	1.86282	−	1.07550i	0.0889074	−	0.0513307i	0.543795	+	0.839218i	$0.316987\pi$
$440$	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	0.760507	−	0.649330i	$-0.224950\pi$
$443$	−3.83239	−	6.63790i	−0.182082	−	0.315376i	−0.942590	+	0.333954i	$0.891617\pi$
$444$		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	$-0.853414\pi$
$449$		−	18.8337i		−	0.888817i	0.895824	−	0.444408i	$-0.146586\pi$
$450$		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	0.228258	−	0.973601i	$-0.426697\pi$
$457$	25.3442	−	14.6325i	1.18555	−	0.684478i	0.957292	+	0.289123i	$0.0933636\pi$
$458$	−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	$0.0569451\pi$
$463$			7.65787i			0.355891i	−0.984040	+	0.177946i	$0.943055\pi$
$464$	−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	−0.811023	−	0.585015i	$-0.801089\pi$
$467$	−15.3410	+	8.85713i	−0.709897	+	0.409859i	0.101126	+	0.994874i	$0.467755\pi$
$468$		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	−0.974596	−	0.223969i	$-0.928099\pi$
$479$	−6.41996	+	11.1197i	−0.293336	+	0.508072i	0.681261	+	0.732041i	$0.261432\pi$
$480$		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	0.424022	−	0.905652i	$-0.360618\pi$
$487$	−3.27235	−	1.88929i	−0.148284	−	0.0856119i	−0.572306	+	0.820040i	$0.693951\pi$
$488$	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	$0.258541\pi$
$491$			32.1664i			1.45165i	−0.687880	+	0.725824i	$0.741459\pi$
$492$		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	−0.963022	−	0.269424i	$-0.913167\pi$
$499$	−15.9683	−	27.6579i	−0.714839	−	1.23814i	0.248183	−	0.968713i	$-0.420167\pi$
$500$	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	$-0.962313\pi$
$503$		−	5.29834i		−	0.236241i	0.992999	−	0.118121i	$-0.0376870\pi$
$504$		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	0.901265	+	0.433269i	$0.142640\pi$
$509$	18.6321	+	32.2718i	0.825854	+	1.43042i	−0.0754100	+	0.997153i	$0.524027\pi$
$510$		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	−0.703919	−	0.710280i	$-0.748568\pi$
$521$	6.00676	−	10.4040i	0.263161	−	0.455808i	0.967080	+	0.254472i	$0.0819017\pi$
$522$		0			0
$523$	13.5178	+	23.4136i	0.591093	+	1.02380i	0.994085	+	0.108600i	$0.0346369\pi$
$523$	13.5178	+	23.4136i	0.591093	+	1.02380i	−0.402992	+	0.915203i	$0.632030\pi$
$524$	−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	0.963995	−	0.265919i	$-0.0856755\pi$
$541$	5.85450	+	10.1403i	0.251705	+	0.435965i	−0.712291	+	0.701885i	$0.752342\pi$
$542$	−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	$0.122827\pi$
$547$			17.6050i			0.752737i	−0.926470	+	0.376369i	$0.877173\pi$
$548$	−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	−0.571017	−	0.820938i	$-0.693451\pi$
$557$	10.0409	−	17.3913i	0.425445	−	0.736892i	0.996462	+	0.0840462i	$0.0267843\pi$
$558$		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	0.866998	−	0.498312i	$-0.166046\pi$
$563$	20.6180	+	11.9038i	0.868947	+	0.501687i	0.00194851	+	0.999998i	$0.499380\pi$
$564$		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	−0.504037	+	0.863682i	$0.668152\pi$
$569$	−35.8766	+	20.7134i	−1.50403	+	0.868350i	−0.999989	+	0.00466765i	$0.998514\pi$
$570$		0			0
$571$	−20.5784	+	35.6428i	−0.861177	+	1.49160i	0.00961607	+	0.999954i	$0.496939\pi$
$571$	−20.5784	+	35.6428i	−0.861177	+	1.49160i	−0.870793	+	0.491649i	$0.836394\pi$
$572$	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	−0.965829	−	0.259181i	$-0.916547\pi$
$577$	−6.20835	+	10.7532i	−0.258457	+	0.447661i	0.707372	+	0.706842i	$0.249881\pi$
$578$	−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	$-0.973563\pi$
$587$		−	4.01980i		−	0.165915i	0.996553	−	0.0829575i	$-0.0264366\pi$
$588$		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	−0.549914	+	0.835221i	$0.685340\pi$
$593$	−37.7010	+	21.7667i	−1.54819	+	0.893850i	−0.998280	+	0.0586292i	$0.981327\pi$
$594$		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	0.945629	−	0.325249i	$-0.105448\pi$
$599$	27.8218	+	16.0629i	1.13677	+	0.656314i	0.191141	+	0.981563i	$0.438781\pi$
$600$		0			0
$601$			8.21681i			0.335171i	0.985858	+	0.167585i	$0.0535970\pi$
$601$			8.21681i			0.335171i	−0.985858	+	0.167585i	$0.946403\pi$
$602$	−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	−0.996252	−	0.0864957i	$-0.972433\pi$
$607$	−14.1180	−	24.4532i	−0.573034	−	0.992523i	0.423219	−	0.906028i	$-0.360900\pi$
$608$			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	−0.146965	−	0.989142i	$-0.546950\pi$
$613$	−26.6670	−	15.3962i	−1.07707	−	0.621846i	−0.930104	+	0.367296i	$0.880284\pi$
$614$	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	0.678101	−	0.734969i	$-0.262803\pi$
$619$	9.47047	+	5.46778i	0.380650	+	0.219768i	−0.297451	+	0.954737i	$0.596136\pi$
$620$	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	−0.198671	−	0.980066i	$-0.563663\pi$
$641$	−29.0339	−	16.7627i	−1.14677	−	0.662088i	−0.948098	+	0.317979i	$0.896996\pi$
$642$		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	−0.321787	−	0.946812i	$-0.604284\pi$
$647$	−33.1343	−	19.1301i	−1.30264	−	0.752082i	−0.980857	+	0.194730i	$0.937617\pi$
$648$		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	−0.987004	−	0.160696i	$-0.948626\pi$
$653$	−16.1671	−	28.0023i	−0.632669	−	1.09581i	0.354335	−	0.935119i	$-0.384707\pi$
$654$		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	$0.103828\pi$
$659$			16.4516i			0.640865i	−0.947271	+	0.320433i	$0.896172\pi$
$660$		0			0
$661$	−2.14550	−	1.23870i	−0.0834502	−	0.0481800i	0.457694	−	0.889110i	$-0.348675\pi$
$661$	−2.14550	−	1.23870i	−0.0834502	−	0.0481800i	−0.541144	+	0.840930i	$0.682009\pi$
$662$	−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	$-0.893233\pi$
$673$		−	17.0784i		−	0.658326i	0.944273	−	0.329163i	$-0.106767\pi$
$674$	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	0.553276	−	0.832998i	$-0.313377\pi$
$677$	40.3639	−	23.3041i	1.55131	−	0.895650i	0.998035	−	0.0626524i	$-0.0199560\pi$
$678$		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	−0.842494	−	0.538706i	$-0.818913\pi$
$683$	1.18353	−	2.04994i	0.0452867	−	0.0784388i	0.887780	+	0.460268i	$0.152247\pi$
$684$		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	−0.816527	−	0.577308i	$-0.804103\pi$
$691$	−19.0534	+	11.0005i	−0.724826	+	0.418479i	0.0917001	+	0.995787i	$0.470770\pi$
$692$		−	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	$0.182980\pi$
$701$			28.7909i			1.08742i	−0.839274	+	0.543708i	$0.817020\pi$
$702$		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	0.973079	−	0.230472i	$-0.0740270\pi$
$709$	7.64049	+	13.2337i	0.286945	+	0.497003i	−0.686134	+	0.727475i	$0.740694\pi$
$710$	−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	0.667635	−	0.744489i	$-0.267307\pi$
$719$	−8.33730	−	14.4406i	−0.310929	−	0.538545i	−0.978564	+	0.205944i	$0.933973\pi$
$720$		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	−0.876115	−	0.482102i	$-0.839874\pi$
$733$	−23.1637	−	40.1207i	−0.855570	−	1.48189i	0.0205452	−	0.999789i	$-0.493460\pi$
$734$	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	−0.673815	−	0.738900i	$-0.735345\pi$
$739$	8.23689	−	14.2667i	0.302999	−	0.524809i	0.976814	+	0.214091i	$0.0686788\pi$
$740$	−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	−0.971773	−	0.235919i	$-0.924190\pi$
$751$	−18.9145	−	32.7608i	−0.690198	−	1.19546i	0.281574	−	0.959539i	$-0.409143\pi$
$752$	−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	$-0.935061\pi$
$757$		−	11.1485i		−	0.405197i	0.979262	−	0.202599i	$-0.0649387\pi$
$758$	−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	−0.999383	−	0.0351321i	$-0.988815\pi$
$761$	−14.6239	−	25.3294i	−0.530117	−	0.918189i	0.469266	−	0.883057i	$-0.344519\pi$
$762$		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	$0.00512438\pi$
$769$			0.892823i			0.0321960i	−0.999870	+	0.0160980i	$0.994876\pi$
$770$	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	0.775361	−	0.631519i	$-0.217568\pi$
$773$	17.1302	+	9.89011i	0.616130	+	0.355723i	−0.159231	+	0.987241i	$0.550901\pi$
$774$		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	−0.999557	−	0.0297473i	$-0.990530\pi$
$787$	−13.2978	+	23.0325i	−0.474017	+	0.821021i	0.525541	+	0.850769i	$0.323863\pi$
$788$	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	$0.124162\pi$
$797$			21.4698i			0.760499i	−0.924884	+	0.380250i	$0.875838\pi$
$798$		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	0.785827	−	0.618447i	$-0.212238\pi$
$809$	18.2930	+	10.5615i	0.643149	+	0.371322i	−0.142677	+	0.989769i	$0.545571\pi$
$810$		0			0
$811$			13.3784i			0.469779i	0.972022	+	0.234889i	$0.0754728\pi$
$811$			13.3784i			0.469779i	−0.972022	+	0.234889i	$0.924527\pi$
$812$	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	−0.397674	−	0.917527i	$-0.630182\pi$
$821$	5.67591	−	3.27699i	0.198091	−	0.114368i	0.595765	+	0.803159i	$0.296849\pi$
$822$		0			0
$823$	37.9915	+	21.9344i	1.32430	+	0.764585i	0.984412	−	0.175880i	$-0.0562772\pi$
$823$	37.9915	+	21.9344i	1.32430	+	0.764585i	0.339889	+	0.940466i	$0.389611\pi$
$824$	−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	0.732539	−	0.680725i	$-0.238335\pi$
$829$	14.6635	+	8.46597i	0.509284	+	0.294035i	−0.223255	+	0.974760i	$0.571668\pi$
$830$	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	0.133115	−	0.991101i	$-0.457502\pi$
$857$	−19.2816	−	11.1322i	−0.658646	−	0.380270i	−0.791761	+	0.610831i	$0.790835\pi$
$858$		0			0
$859$	26.7059	−	15.4187i	0.911195	−	0.526078i	0.0303793	−	0.999538i	$-0.490328\pi$
$859$	26.7059	−	15.4187i	0.911195	−	0.526078i	0.880815	+	0.473460i	$0.156995\pi$
$860$	−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	0.992900	−	0.118949i	$-0.0379525\pi$
$863$	11.5580	+	20.0190i	0.393437	+	0.681454i	−0.599463	+	0.800403i	$0.704619\pi$
$864$		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	−0.0837427	−	0.996487i	$-0.526687\pi$
$877$	21.8366	−	12.6074i	0.737369	−	0.425720i	0.821112	+	0.570767i	$0.193354\pi$
$878$	−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	$0.257864\pi$
$883$			43.0491i			1.44872i	−0.689424	+	0.724358i	$0.742136\pi$
$884$	−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	0.0714156	−	0.997447i	$-0.477248\pi$
$887$	28.9170	−	16.6952i	0.970938	−	0.560571i	0.899522	+	0.436876i	$0.143915\pi$
$888$		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	0.0516937	−	0.998663i	$-0.483538\pi$
$907$	−23.7115	−	13.6898i	−0.787327	−	0.454563i	−0.839021	+	0.544100i	$0.816871\pi$
$908$	−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	$-0.815630\pi$
$911$		−	33.0422i		−	1.09474i	0.836892	−	0.547368i	$-0.184370\pi$
$912$		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	0.997448	−	0.0713958i	$-0.0227453\pi$
$919$	13.2444	+	22.9400i	0.436893	+	0.756722i	−0.560555	+	0.828117i	$0.689412\pi$
$920$	−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	−0.999909	−	0.0135196i	$-0.995696\pi$
$929$	−15.5952	−	27.0117i	−0.511663	−	0.886226i	0.488246	−	0.872706i	$-0.337637\pi$
$930$		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	−0.904765	−	0.425911i	$-0.859954\pi$
$941$	−2.56243	+	4.43825i	−0.0835327	+	0.144683i	0.821232	+	0.570594i	$0.193287\pi$
$942$		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	−0.973101	−	0.230378i	$-0.926004\pi$
$947$	−21.1125	−	36.5679i	−0.686064	−	1.18830i	0.287037	−	0.957919i	$-0.407330\pi$
$948$		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	$0.318082\pi$
$967$			52.3097i			1.68217i	−0.540905	+	0.841084i	$0.681918\pi$
$968$	−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	0.970002	−	0.243097i	$-0.0781634\pi$
$971$	8.55280	+	14.8139i	0.274473	+	0.475400i	−0.695529	+	0.718498i	$0.744830\pi$
$972$		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	−0.412979	−	0.910741i	$-0.635512\pi$
$977$	18.1989	−	31.5215i	0.582235	−	1.00846i	0.995214	−	0.0977201i	$-0.0311550\pi$
$978$		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	0.100643	−	0.994923i	$-0.467910\pi$
$983$	−22.2813	−	12.8641i	−0.710664	−	0.410302i	−0.811307	+	0.584621i	$0.801243\pi$
$984$		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	−0.753284	−	0.657696i	$-0.771531\pi$
$991$	6.07375	−	10.5200i	0.192939	−	0.334180i	0.946223	+	0.323515i	$0.104865\pi$
$992$	−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	−0.969278	−	0.245968i	$-0.920894\pi$
$997$	−8.57663	+	14.8552i	−0.271625	+	0.470468i	0.697653	+	0.716435i	$0.254228\pi$
$998$	−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.269.2	yes	16
3.2	odd	2		630.2.bo.b.269.7	yes	16
5.2	odd	4		3150.2.bf.f.1151.15		32
5.3	odd	4		3150.2.bf.f.1151.6		32
5.4	even	2		630.2.bo.b.269.4	yes	16
7.3	odd	6		4410.2.d.b.4409.4		16
7.4	even	3		4410.2.d.b.4409.13		16
7.5	odd	6	inner	630.2.bo.a.89.5	yes	16
15.2	even	4		3150.2.bf.f.1151.5		32
15.8	even	4		3150.2.bf.f.1151.16		32
15.14	odd	2	inner	630.2.bo.a.269.5	yes	16
21.5	even	6		630.2.bo.b.89.4	yes	16
21.11	odd	6		4410.2.d.a.4409.4		16
21.17	even	6		4410.2.d.a.4409.13		16
35.4	even	6		4410.2.d.a.4409.14		16
35.12	even	12		3150.2.bf.f.1601.5		32
35.19	odd	6		630.2.bo.b.89.7	yes	16
35.24	odd	6		4410.2.d.a.4409.3		16
35.33	even	12		3150.2.bf.f.1601.14		32
105.47	odd	12		3150.2.bf.f.1601.13		32
105.59	even	6		4410.2.d.b.4409.14		16
105.68	odd	12		3150.2.bf.f.1601.6		32
105.74	odd	6		4410.2.d.b.4409.3		16
105.89	even	6	inner	630.2.bo.a.89.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.2	✓	16	105.89	even	6	inner
630.2.bo.a.89.5	yes	16	7.5	odd	6	inner
630.2.bo.a.269.2	yes	16	1.1	even	1	trivial
630.2.bo.a.269.5	yes	16	15.14	odd	2	inner
630.2.bo.b.89.4	yes	16	21.5	even	6
630.2.bo.b.89.7	yes	16	35.19	odd	6
630.2.bo.b.269.4	yes	16	5.4	even	2
630.2.bo.b.269.7	yes	16	3.2	odd	2
3150.2.bf.f.1151.5		32	15.2	even	4
3150.2.bf.f.1151.6		32	5.3	odd	4
3150.2.bf.f.1151.15		32	5.2	odd	4
3150.2.bf.f.1151.16		32	15.8	even	4
3150.2.bf.f.1601.5		32	35.12	even	12
3150.2.bf.f.1601.6		32	105.68	odd	12
3150.2.bf.f.1601.13		32	105.47	odd	12
3150.2.bf.f.1601.14		32	35.33	even	12
4410.2.d.a.4409.3		16	35.24	odd	6
4410.2.d.a.4409.4		16	21.11	odd	6
4410.2.d.a.4409.13		16	21.17	even	6
4410.2.d.a.4409.14		16	35.4	even	6
4410.2.d.b.4409.3		16	105.74	odd	6
4410.2.d.b.4409.4		16	7.3	odd	6
4410.2.d.b.4409.13		16	7.4	even	3
4410.2.d.b.4409.14		16	105.59	even	6

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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