LMFDB - Embedded newform 1035.2.j.b.737.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1035,2,Mod(323,1035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1035, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1035.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1035 = 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1035.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.26451660920$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.19
Character	$\chi$	$=$	1035.737
Dual form			1035.2.j.b.323.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56692 - 1.56692i) q^{2} -2.91045i q^{4} +(-2.12072 + 0.708917i) q^{5} +(1.66463 + 1.66463i) q^{7} +(-1.42659 - 1.42659i) q^{8} +O(q^{10})$	\(q+(1.56692 - 1.56692i) q^{2} -2.91045i q^{4} +(-2.12072 + 0.708917i) q^{5} +(1.66463 + 1.66463i) q^{7} +(-1.42659 - 1.42659i) q^{8} +(-2.21217 + 4.43380i) q^{10} -6.00605i q^{11} +(0.950336 - 0.950336i) q^{13} +5.21668 q^{14} +1.35019 q^{16} +(3.39083 - 3.39083i) q^{17} -4.77009i q^{19} +(2.06327 + 6.17223i) q^{20} +(-9.41097 - 9.41097i) q^{22} +(0.707107 + 0.707107i) q^{23} +(3.99487 - 3.00682i) q^{25} -2.97819i q^{26} +(4.84483 - 4.84483i) q^{28} -8.39840 q^{29} -6.12842 q^{31} +(4.96882 - 4.96882i) q^{32} -10.6263i q^{34} +(-4.71031 - 2.35013i) q^{35} +(8.08840 + 8.08840i) q^{37} +(-7.47432 - 7.47432i) q^{38} +(4.03674 + 2.01406i) q^{40} -3.39575i q^{41} +(-3.81628 + 3.81628i) q^{43} -17.4803 q^{44} +2.21595 q^{46} +(4.67549 - 4.67549i) q^{47} -1.45798i q^{49} +(1.54819 - 10.9711i) q^{50} +(-2.76590 - 2.76590i) q^{52} +(1.97254 + 1.97254i) q^{53} +(4.25779 + 12.7371i) q^{55} -4.74951i q^{56} +(-13.1596 + 13.1596i) q^{58} +0.951199 q^{59} +13.6040 q^{61} +(-9.60272 + 9.60272i) q^{62} -12.8711i q^{64} +(-1.34168 + 2.68910i) q^{65} +(4.40059 + 4.40059i) q^{67} +(-9.86883 - 9.86883i) q^{68} +(-11.0631 + 3.69820i) q^{70} +16.3971i q^{71} +(-8.01005 + 8.01005i) q^{73} +25.3477 q^{74} -13.8831 q^{76} +(9.99787 - 9.99787i) q^{77} +6.34641i q^{79} +(-2.86337 + 0.957174i) q^{80} +(-5.32085 - 5.32085i) q^{82} +(-3.16809 - 3.16809i) q^{83} +(-4.78717 + 9.59481i) q^{85} +11.9596i q^{86} +(-8.56819 + 8.56819i) q^{88} -4.16819 q^{89} +3.16392 q^{91} +(2.05800 - 2.05800i) q^{92} -14.6522i q^{94} +(3.38160 + 10.1160i) q^{95} +(-3.80049 - 3.80049i) q^{97} +(-2.28453 - 2.28453i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{7}+O(q^{10}) $ 44 * q + 12 * q^7	$ 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) $ 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1035\mathbb{Z}\right)^\times$.

$n$	$461$	$622$	$856$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.56692	−	1.56692i	1.10798	−	1.10798i	0.114560	−	0.993416i	$-0.463454\pi$
$2$	1.56692	−	1.56692i	1.10798	−	1.10798i	0.993416	−	0.114560i	$-0.0365459\pi$
$3$		0			0
$3$		0			0
$4$		−	2.91045i		−	1.45522i
$5$	−2.12072	+	0.708917i	−0.948413	+	0.317037i
$5$	−2.12072	+	0.708917i	−0.948413	+	0.317037i
$6$		0			0
$7$	1.66463	+	1.66463i	0.629173	+	0.629173i	0.947860	−	0.318687i	$-0.103242\pi$
$7$	1.66463	+	1.66463i	0.629173	+	0.629173i	−0.318687	+	0.947860i	$0.603242\pi$
$8$	−1.42659	−	1.42659i	−0.504377	−	0.504377i
$9$		0			0
$10$	−2.21217	+	4.43380i	−0.699549	+	1.40209i
$11$		−	6.00605i		−	1.81089i	−0.424462	−	0.905446i	$-0.639537\pi$
$11$		−	6.00605i		−	1.81089i	0.424462	−	0.905446i	$-0.360463\pi$
$12$		0			0
$13$	0.950336	−	0.950336i	0.263576	−	0.263576i	−0.562929	−	0.826505i	$-0.690326\pi$
$13$	0.950336	−	0.950336i	0.263576	−	0.263576i	0.826505	+	0.562929i	$0.190326\pi$
$14$	5.21668			1.39422
$15$		0			0
$16$	1.35019			0.337548
$17$	3.39083	−	3.39083i	0.822397	−	0.822397i	−0.164054	−	0.986451i	$-0.552457\pi$
$17$	3.39083	−	3.39083i	0.822397	−	0.822397i	0.986451	+	0.164054i	$0.0524571\pi$
$18$		0			0
$19$		−	4.77009i		−	1.09433i	−0.837024	−	0.547167i	$-0.815706\pi$
$19$		−	4.77009i		−	1.09433i	0.837024	−	0.547167i	$-0.184294\pi$
$20$	2.06327	+	6.17223i	0.461360	+	1.38015i
$21$		0			0
$22$	−9.41097	−	9.41097i	−2.00642	−	2.00642i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	3.99487	−	3.00682i	0.798975	−	0.601365i
$26$		−	2.97819i		−	0.584071i
$27$		0			0
$28$	4.84483	−	4.84483i	0.915587	−	0.915587i
$29$	−8.39840			−1.55954			−0.779772	−	0.626063i	$-0.784665\pi$
$29$	−8.39840			−1.55954			−0.779772	+	0.626063i	$0.784665\pi$
$30$		0			0
$31$	−6.12842			−1.10070			−0.550349	−	0.834935i	$-0.685505\pi$
$31$	−6.12842			−1.10070			−0.550349	+	0.834935i	$0.685505\pi$
$32$	4.96882	−	4.96882i	0.878372	−	0.878372i
$33$		0			0
$34$		−	10.6263i		−	1.82239i
$35$	−4.71031	−	2.35013i	−0.796187	−	0.397244i
$36$		0			0
$37$	8.08840	+	8.08840i	1.32973	+	1.32973i	0.905606	+	0.424119i	$0.139416\pi$
$37$	8.08840	+	8.08840i	1.32973	+	1.32973i	0.424119	+	0.905606i	$0.360584\pi$
$38$	−7.47432	−	7.47432i	−1.21250	−	1.21250i
$39$		0			0
$40$	4.03674	+	2.01406i	0.638264	+	0.318451i
$41$		−	3.39575i		−	0.530327i	−0.964204	−	0.265163i	$-0.914574\pi$
$41$		−	3.39575i		−	0.530327i	0.964204	−	0.265163i	$-0.0854259\pi$
$42$		0			0
$43$	−3.81628	+	3.81628i	−0.581977	+	0.581977i	−0.935446	−	0.353469i	$-0.885002\pi$
$43$	−3.81628	+	3.81628i	−0.581977	+	0.581977i	0.353469	+	0.935446i	$0.385002\pi$
$44$	−17.4803			−2.63525
$45$		0			0
$46$	2.21595			0.326724
$47$	4.67549	−	4.67549i	0.681990	−	0.681990i	−0.278458	−	0.960448i	$-0.589823\pi$
$47$	4.67549	−	4.67549i	0.681990	−	0.681990i	0.960448	+	0.278458i	$0.0898235\pi$
$48$		0			0
$49$		−	1.45798i		−	0.208283i
$50$	1.54819	−	10.9711i	0.218947	−	1.55154i
$51$		0			0
$52$	−2.76590	−	2.76590i	−0.383562	−	0.383562i
$53$	1.97254	+	1.97254i	0.270949	+	0.270949i	0.829482	−	0.558533i	$-0.188636\pi$
$53$	1.97254	+	1.97254i	0.270949	+	0.270949i	−0.558533	+	0.829482i	$0.688636\pi$
$54$		0			0
$55$	4.25779	+	12.7371i	0.574120	+	1.71747i
$56$		−	4.74951i		−	0.634681i
$57$		0			0
$58$	−13.1596	+	13.1596i	−1.72794	+	1.72794i
$59$	0.951199			0.123835			0.0619177	−	0.998081i	$-0.480278\pi$
$59$	0.951199			0.123835			0.0619177	+	0.998081i	$0.480278\pi$
$60$		0			0
$61$	13.6040			1.74181			0.870907	−	0.491449i	$-0.163532\pi$
$61$	13.6040			1.74181			0.870907	+	0.491449i	$0.163532\pi$
$62$	−9.60272	+	9.60272i	−1.21955	+	1.21955i
$63$		0			0
$64$		−	12.8711i		−	1.60888i
$65$	−1.34168	+	2.68910i	−0.166415	+	0.333542i
$66$		0			0
$67$	4.40059	+	4.40059i	0.537617	+	0.537617i	0.922828	−	0.385211i	$-0.125871\pi$
$67$	4.40059	+	4.40059i	0.537617	+	0.537617i	−0.385211	+	0.922828i	$0.625871\pi$
$68$	−9.86883	−	9.86883i	−1.19677	−	1.19677i
$69$		0			0
$70$	−11.0631	+	3.69820i	−1.32229	+	0.442019i
$71$			16.3971i			1.94597i	0.230859	+	0.972987i	$0.425846\pi$
$71$			16.3971i			1.94597i	−0.230859	+	0.972987i	$0.574154\pi$
$72$		0			0
$73$	−8.01005	+	8.01005i	−0.937505	+	0.937505i	−0.998159	−	0.0606535i	$-0.980682\pi$
$73$	−8.01005	+	8.01005i	−0.937505	+	0.937505i	0.0606535	+	0.998159i	$0.480682\pi$
$74$	25.3477			2.94661
$75$		0			0
$76$	−13.8831			−1.59250
$77$	9.99787	−	9.99787i	1.13936	−	1.13936i
$78$		0			0
$79$			6.34641i			0.714026i	0.934099	+	0.357013i	$0.116205\pi$
$79$			6.34641i			0.714026i	−0.934099	+	0.357013i	$0.883795\pi$
$80$	−2.86337	+	0.957174i	−0.320135	+	0.107015i
$81$		0			0
$82$	−5.32085	−	5.32085i	−0.587589	−	0.587589i
$83$	−3.16809	−	3.16809i	−0.347743	−	0.347743i	0.511525	−	0.859268i	$-0.329081\pi$
$83$	−3.16809	−	3.16809i	−0.347743	−	0.347743i	−0.859268	+	0.511525i	$0.829081\pi$
$84$		0			0
$85$	−4.78717	+	9.59481i	−0.519242	+	1.04070i
$86$			11.9596i			1.28963i
$87$		0			0
$88$	−8.56819	+	8.56819i	−0.913372	+	0.913372i
$89$	−4.16819			−0.441828			−0.220914	−	0.975293i	$-0.570904\pi$
$89$	−4.16819			−0.441828			−0.220914	+	0.975293i	$0.570904\pi$
$90$		0			0
$91$	3.16392			0.331669
$92$	2.05800	−	2.05800i	0.214561	−	0.214561i
$93$		0			0
$94$		−	14.6522i		−	1.51126i
$95$	3.38160	+	10.1160i	0.346944	+	1.03788i
$96$		0			0
$97$	−3.80049	−	3.80049i	−0.385881	−	0.385881i	0.487334	−	0.873215i	$-0.337969\pi$
$97$	−3.80049	−	3.80049i	−0.385881	−	0.385881i	−0.873215	+	0.487334i	$0.837969\pi$
$98$	−2.28453	−	2.28453i	−0.230773	−	0.230773i
$99$		0			0
$100$	−8.75120	−	11.6269i	−0.875120	−	1.16269i
$101$		−	14.4050i		−	1.43335i	−0.697409	−	0.716673i	$-0.745664\pi$
$101$		−	14.4050i		−	1.43335i	0.697409	−	0.716673i	$-0.254336\pi$
$102$		0			0
$103$	−1.53829	+	1.53829i	−0.151572	+	0.151572i	−0.778820	−	0.627248i	$-0.784181\pi$
$103$	−1.53829	+	1.53829i	−0.151572	+	0.151572i	0.627248	+	0.778820i	$0.284181\pi$
$104$	−2.71149			−0.265883
$105$		0			0
$106$	6.18161			0.600411
$107$	4.95243	−	4.95243i	0.478769	−	0.478769i	−0.425969	−	0.904738i	$-0.640067\pi$
$107$	4.95243	−	4.95243i	0.478769	−	0.478769i	0.904738	+	0.425969i	$0.140067\pi$
$108$		0			0
$109$			10.7680i			1.03138i	0.856774	+	0.515692i	$0.172465\pi$
$109$			10.7680i			1.03138i	−0.856774	+	0.515692i	$0.827535\pi$
$110$	26.6296	+	13.2864i	2.53903	+	1.26681i
$111$		0			0
$112$	2.24758	+	2.24758i	0.212376	+	0.212376i
$113$	−1.45473	−	1.45473i	−0.136850	−	0.136850i	0.635363	−	0.772213i	$-0.280850\pi$
$113$	−1.45473	−	1.45473i	−0.136850	−	0.136850i	−0.772213	+	0.635363i	$0.780850\pi$
$114$		0			0
$115$	−2.00085	−	0.998293i	−0.186580	−	0.0930913i
$116$			24.4431i			2.26949i
$117$		0			0
$118$	1.49045	−	1.49045i	0.137207	−	0.137207i
$119$	11.2890			1.03486
$120$		0			0
$121$	−25.0726			−2.27933
$122$	21.3163	−	21.3163i	1.92989	−	1.92989i
$123$		0			0
$124$			17.8364i			1.60176i
$125$	−6.34040	+	9.20865i	−0.567103	+	0.823647i
$126$		0			0
$127$	−2.38975	−	2.38975i	−0.212056	−	0.212056i	0.593084	−	0.805140i	$-0.297910\pi$
$127$	−2.38975	−	2.38975i	−0.212056	−	0.212056i	−0.805140	+	0.593084i	$0.797910\pi$
$128$	−10.2302	−	10.2302i	−0.904233	−	0.904233i
$129$		0			0
$130$	2.11129	+	6.31590i	0.185172	+	0.553941i
$131$			13.2515i			1.15779i	0.815403	+	0.578894i	$0.196515\pi$
$131$			13.2515i			1.15779i	−0.815403	+	0.578894i	$0.803485\pi$
$132$		0			0
$133$	7.94045	−	7.94045i	0.688525	−	0.688525i
$134$	13.7907			1.19133
$135$		0			0
$136$	−9.67467			−0.829597
$137$	−8.96400	+	8.96400i	−0.765846	+	0.765846i	−0.977372	−	0.211526i	$-0.932157\pi$
$137$	−8.96400	+	8.96400i	−0.765846	+	0.765846i	0.211526	+	0.977372i	$0.432157\pi$
$138$		0			0
$139$		−	10.9831i		−	0.931576i	−0.884896	−	0.465788i	$-0.845771\pi$
$139$		−	10.9831i		−	0.931576i	0.884896	−	0.465788i	$-0.154229\pi$
$140$	−6.83993	+	13.7091i	−0.578080	+	1.15863i
$141$		0			0
$142$	25.6928	+	25.6928i	2.15609	+	2.15609i
$143$	−5.70776	−	5.70776i	−0.477307	−	0.477307i
$144$		0			0
$145$	17.8106	−	5.95377i	1.47909	−	0.494434i
$146$			25.1021i			2.07747i
$147$		0			0
$148$	23.5409	−	23.5409i	1.93505	−	1.93505i
$149$	17.3893			1.42459			0.712294	−	0.701881i	$-0.247656\pi$
$149$	17.3893			1.42459			0.712294	+	0.701881i	$0.247656\pi$
$150$		0			0
$151$	−9.41270			−0.765995			−0.382997	−	0.923749i	$-0.625108\pi$
$151$	−9.41270			−0.765995			−0.382997	+	0.923749i	$0.625108\pi$
$152$	−6.80498	+	6.80498i	−0.551956	+	0.551956i
$153$		0			0
$154$		−	31.3316i		−	2.52478i
$155$	12.9966	−	4.34454i	1.04392	−	0.348962i
$156$		0			0
$157$	3.12863	+	3.12863i	0.249692	+	0.249692i	0.820844	−	0.571152i	$-0.193503\pi$
$157$	3.12863	+	3.12863i	0.249692	+	0.249692i	−0.571152	+	0.820844i	$0.693503\pi$
$158$	9.94428	+	9.94428i	0.791124	+	0.791124i
$159$		0			0
$160$	−7.01498	+	14.0599i	−0.554583	+	1.11154i
$161$			2.35415i			0.185533i
$162$		0			0
$163$	−9.57659	+	9.57659i	−0.750096	+	0.750096i	−0.974497	−	0.224401i	$-0.927958\pi$
$163$	−9.57659	+	9.57659i	−0.750096	+	0.750096i	0.224401	+	0.974497i	$0.427958\pi$
$164$	−9.88314			−0.771744
$165$		0			0
$166$	−9.92825			−0.770581
$167$	1.81755	−	1.81755i	0.140646	−	0.140646i	−0.633278	−	0.773924i	$-0.718291\pi$
$167$	1.81755	−	1.81755i	0.140646	−	0.140646i	0.773924	+	0.633278i	$0.218291\pi$
$168$		0			0
$169$			11.1937i			0.861056i
$170$	7.53316	+	22.5353i	0.577767	+	1.72838i
$171$		0			0
$172$	11.1071	+	11.1071i	0.846906	+	0.846906i
$173$	−8.52007	−	8.52007i	−0.647769	−	0.647769i	0.304685	−	0.952453i	$-0.401449\pi$
$173$	−8.52007	−	8.52007i	−0.647769	−	0.647769i	−0.952453	+	0.304685i	$0.901449\pi$
$174$		0			0
$175$	11.6553	+	1.64474i	0.881056	+	0.124331i
$176$		−	8.10932i		−	0.611263i
$177$		0			0
$178$	−6.53121	+	6.53121i	−0.489535	+	0.489535i
$179$	0.952495			0.0711928			0.0355964	−	0.999366i	$-0.488667\pi$
$179$	0.952495			0.0711928			0.0355964	+	0.999366i	$0.488667\pi$
$180$		0			0
$181$	21.7129			1.61391			0.806953	−	0.590615i	$-0.201115\pi$
$181$	21.7129			1.61391			0.806953	+	0.590615i	$0.201115\pi$
$182$	4.95760	−	4.95760i	0.367482	−	0.367482i
$183$		0			0
$184$		−	2.01751i		−	0.148733i
$185$	−22.8872	−	11.4192i	−1.68270	−	0.839556i
$186$		0			0
$187$	−20.3655	−	20.3655i	−1.48927	−	1.48927i
$188$	−13.6078	−	13.6078i	−0.992448	−	0.992448i
$189$		0			0
$190$	21.1496	+	10.5522i	1.53435	+	0.765540i
$191$			8.30254i			0.600751i	0.953821	+	0.300375i	$0.0971119\pi$
$191$			8.30254i			0.600751i	−0.953821	+	0.300375i	$0.902888\pi$
$192$		0			0
$193$	7.02762	−	7.02762i	0.505859	−	0.505859i	−0.407394	−	0.913253i	$-0.633562\pi$
$193$	7.02762	−	7.02762i	0.505859	−	0.505859i	0.913253	+	0.407394i	$0.133562\pi$
$194$	−11.9101			−0.855094
$195$		0			0
$196$	−4.24338			−0.303098
$197$	−0.203911	+	0.203911i	−0.0145280	+	0.0145280i	−0.714333	−	0.699805i	$-0.753270\pi$
$197$	−0.203911	+	0.203911i	−0.0145280	+	0.0145280i	0.699805	+	0.714333i	$0.253270\pi$
$198$		0			0
$199$			23.7590i			1.68423i	0.539300	+	0.842114i	$0.318689\pi$
$199$			23.7590i			1.68423i	−0.539300	+	0.842114i	$0.681311\pi$
$200$	−9.98857	−	1.40955i	−0.706299	−	0.0996699i
$201$		0			0
$202$	−22.5713	−	22.5713i	−1.58811	−	1.58811i
$203$	−13.9803	−	13.9803i	−0.981223	−	0.981223i
$204$		0			0
$205$	2.40730	+	7.20142i	0.168133	+	0.502969i
$206$			4.82072i			0.335876i
$207$		0			0
$208$	1.28314	−	1.28314i	0.0889695	−	0.0889695i
$209$	−28.6494			−1.98172
$210$		0			0
$211$	8.53087			0.587289			0.293645	−	0.955915i	$-0.405132\pi$
$211$	8.53087			0.587289			0.293645	+	0.955915i	$0.405132\pi$
$212$	5.74098	−	5.74098i	0.394292	−	0.394292i
$213$		0			0
$214$		−	15.5201i		−	1.06093i
$215$	5.38781	−	10.7987i	0.367446	−	0.736462i
$216$		0			0
$217$	−10.2016	−	10.2016i	−0.692529	−	0.692529i
$218$	16.8725	+	16.8725i	1.14275	+	1.14275i
$219$		0			0
$220$	37.0707	−	12.3921i	2.49931	−	0.835473i
$221$		−	6.44486i		−	0.433528i
$222$		0			0
$223$	1.56240	−	1.56240i	0.104626	−	0.104626i	−0.652856	−	0.757482i	$-0.726429\pi$
$223$	1.56240	−	1.56240i	0.104626	−	0.104626i	0.757482	+	0.652856i	$0.226429\pi$
$224$	16.5426			1.10530
$225$		0			0
$226$	−4.55889			−0.303253
$227$	5.42400	−	5.42400i	0.360003	−	0.360003i	−0.503811	−	0.863814i	$-0.668069\pi$
$227$	5.42400	−	5.42400i	0.360003	−	0.360003i	0.863814	+	0.503811i	$0.168069\pi$
$228$		0			0
$229$		−	13.7696i		−	0.909920i	−0.890512	−	0.454960i	$-0.849654\pi$
$229$		−	13.7696i		−	0.909920i	0.890512	−	0.454960i	$-0.150346\pi$
$230$	−4.69941	+	1.57093i	−0.309870	+	0.103584i
$231$		0			0
$232$	11.9811	+	11.9811i	0.786598	+	0.786598i
$233$	13.2712	+	13.2712i	0.869428	+	0.869428i	0.992409	−	0.122981i	$-0.0392453\pi$
$233$	13.2712	+	13.2712i	0.869428	+	0.869428i	−0.122981	+	0.992409i	$0.539245\pi$
$234$		0			0
$235$	−6.60085	+	13.2299i	−0.430592	+	0.863024i
$236$		−	2.76841i		−	0.180208i
$237$		0			0
$238$	17.6889	−	17.6889i	1.14660	−	1.14660i
$239$	−22.3103			−1.44313			−0.721566	−	0.692346i	$-0.756577\pi$
$239$	−22.3103			−1.44313			−0.721566	+	0.692346i	$0.756577\pi$
$240$		0			0
$241$	0.970182			0.0624949			0.0312474	−	0.999512i	$-0.490052\pi$
$241$	0.970182			0.0624949			0.0312474	+	0.999512i	$0.490052\pi$
$242$	−39.2866	+	39.2866i	−2.52544	+	2.52544i
$243$		0			0
$244$		−	39.5937i		−	2.53473i
$245$	1.03359	+	3.09196i	0.0660335	+	0.197538i
$246$		0			0
$247$	−4.53318	−	4.53318i	−0.288440	−	0.288440i
$248$	8.74277	+	8.74277i	0.555166	+	0.555166i
$249$		0			0
$250$	4.49430	+	24.3641i	0.284245	+	1.54092i
$251$			7.71515i			0.486976i	0.969904	+	0.243488i	$0.0782916\pi$
$251$			7.71515i			0.486976i	−0.969904	+	0.243488i	$0.921708\pi$
$252$		0			0
$253$	4.24692	−	4.24692i	0.267001	−	0.267001i
$254$	−7.48906			−0.469906
$255$		0			0
$256$	−6.31766			−0.394854
$257$	−15.4180	+	15.4180i	−0.961750	+	0.961750i	−0.999295	−	0.0375453i	$-0.988046\pi$
$257$	−15.4180	+	15.4180i	−0.961750	+	0.961750i	0.0375453	+	0.999295i	$0.488046\pi$
$258$		0			0
$259$			26.9285i			1.67325i
$260$	7.82649	+	3.90490i	0.485378	+	0.242171i
$261$		0			0
$262$	20.7639	+	20.7639i	1.28280	+	1.28280i
$263$	−9.43769	−	9.43769i	−0.581953	−	0.581953i	0.353486	−	0.935440i	$-0.384996\pi$
$263$	−9.43769	−	9.43769i	−0.581953	−	0.581953i	−0.935440	+	0.353486i	$0.884996\pi$
$264$		0			0
$265$	−5.58157	−	2.78483i	−0.342873	−	0.171071i
$266$		−	24.8840i		−	1.52574i
$267$		0			0
$268$	12.8077	−	12.8077i	0.782353	−	0.782353i
$269$	−13.7635			−0.839177			−0.419589	−	0.907714i	$-0.637826\pi$
$269$	−13.7635			−0.839177			−0.419589	+	0.907714i	$0.637826\pi$
$270$		0			0
$271$	3.01214			0.182974			0.0914871	−	0.995806i	$-0.470838\pi$
$271$	3.01214			0.182974			0.0914871	+	0.995806i	$0.470838\pi$
$272$	4.57827	−	4.57827i	0.277599	−	0.277599i
$273$		0			0
$274$			28.0917i			1.69708i
$275$	−18.0591	−	23.9934i	−1.08901	−	1.44686i
$276$		0			0
$277$	2.48730	+	2.48730i	0.149448	+	0.149448i	0.777871	−	0.628424i	$-0.216300\pi$
$277$	2.48730	+	2.48730i	0.149448	+	0.149448i	−0.628424	+	0.777871i	$0.716300\pi$
$278$	−17.2096	−	17.2096i	−1.03216	−	1.03216i
$279$		0			0
$280$	3.36701	+	10.0724i	0.201217	+	0.601939i
$281$			19.9292i			1.18888i	0.804141	+	0.594438i	$0.202626\pi$
$281$			19.9292i			1.18888i	−0.804141	+	0.594438i	$0.797374\pi$
$282$		0			0
$283$	11.0428	−	11.0428i	0.656427	−	0.656427i	−0.298106	−	0.954533i	$-0.596355\pi$
$283$	11.0428	−	11.0428i	0.656427	−	0.656427i	0.954533	+	0.298106i	$0.0963549\pi$
$284$	47.7228			2.83183
$285$		0			0
$286$	−17.8872			−1.05769
$287$	5.65268	−	5.65268i	0.333667	−	0.333667i
$288$		0			0
$289$		−	5.99547i		−	0.352675i
$290$	18.5787	−	37.2368i	1.09098	−	2.18662i
$291$		0			0
$292$	23.3128	+	23.3128i	1.36428	+	1.36428i
$293$	12.4743	+	12.4743i	0.728754	+	0.728754i	0.970372	−	0.241618i	$-0.0776779\pi$
$293$	12.4743	+	12.4743i	0.728754	+	0.728754i	−0.241618	+	0.970372i	$0.577678\pi$
$294$		0			0
$295$	−2.01722	+	0.674321i	−0.117447	+	0.0392605i
$296$		−	23.0777i		−	1.34137i
$297$		0			0
$298$	27.2476	−	27.2476i	1.57841	−	1.57841i
$299$	1.34398			0.0777242
$300$		0			0
$301$	−12.7054			−0.732328
$302$	−14.7489	+	14.7489i	−0.848704	+	0.848704i
$303$		0			0
$304$		−	6.44053i		−	0.369390i
$305$	−28.8502	+	9.64410i	−1.65196	+	0.552220i
$306$		0			0
$307$	−15.5581	−	15.5581i	−0.887945	−	0.887945i	0.106380	−	0.994326i	$-0.466074\pi$
$307$	−15.5581	−	15.5581i	−0.887945	−	0.887945i	−0.994326	+	0.106380i	$0.966074\pi$
$308$	−29.0983	−	29.0983i	−1.65803	−	1.65803i
$309$		0			0
$310$	13.5571	−	27.1722i	0.769992	−	1.54328i
$311$			13.2040i			0.748733i	0.927281	+	0.374366i	$0.122140\pi$
$311$			13.2040i			0.748733i	−0.927281	+	0.374366i	$0.877860\pi$
$312$		0			0
$313$	−5.47026	+	5.47026i	−0.309198	+	0.309198i	−0.844598	−	0.535401i	$-0.820161\pi$
$313$	−5.47026	+	5.47026i	−0.309198	+	0.309198i	0.535401	+	0.844598i	$0.320161\pi$
$314$	9.80461			0.553306
$315$		0			0
$316$	18.4709			1.03907
$317$	−3.53094	+	3.53094i	−0.198317	+	0.198317i	−0.799278	−	0.600961i	$-0.794785\pi$
$317$	−3.53094	+	3.53094i	−0.198317	+	0.198317i	0.600961	+	0.799278i	$0.294785\pi$
$318$		0			0
$319$			50.4412i			2.82416i
$320$	9.12452	+	27.2959i	0.510076	+	1.52589i
$321$		0			0
$322$	3.68875	+	3.68875i	0.205566	+	0.205566i
$323$	−16.1746	−	16.1746i	−0.899977	−	0.899977i
$324$		0			0
$325$	0.938979	−	6.65396i	0.0520852	−	0.369095i
$326$			30.0114i			1.66218i
$327$		0			0
$328$	−4.84435	+	4.84435i	−0.267485	+	0.267485i
$329$	15.5660			0.858179
$330$		0			0
$331$	13.7092			0.753523			0.376762	−	0.926310i	$-0.377038\pi$
$331$	13.7092			0.753523			0.376762	+	0.926310i	$0.377038\pi$
$332$	−9.22055	+	9.22055i	−0.506043	+	0.506043i
$333$		0			0
$334$		−	5.69589i		−	0.311665i
$335$	−12.4520	−	6.21274i	−0.680328	−	0.339438i
$336$		0			0
$337$	14.4217	+	14.4217i	0.785602	+	0.785602i	0.980770	−	0.195168i	$-0.0625251\pi$
$337$	14.4217	+	14.4217i	0.785602	+	0.785602i	−0.195168	+	0.980770i	$0.562525\pi$
$338$	17.5396	+	17.5396i	0.954029	+	0.954029i
$339$		0			0
$340$	27.9252	+	13.9328i	1.51446	+	0.755613i
$341$			36.8076i			1.99324i
$342$		0			0
$343$	14.0795	−	14.0795i	0.760219	−	0.760219i
$344$	10.8885			0.587071
$345$		0			0
$346$	−26.7004			−1.43542
$347$	−9.49276	+	9.49276i	−0.509598	+	0.509598i	−0.914403	−	0.404805i	$-0.867339\pi$
$347$	−9.49276	+	9.49276i	−0.509598	+	0.509598i	0.404805	+	0.914403i	$0.367339\pi$
$348$		0			0
$349$		−	0.326538i		−	0.0174792i	−0.999962	−	0.00873960i	$-0.997218\pi$
$349$		−	0.326538i		−	0.0174792i	0.999962	−	0.00873960i	$-0.00278194\pi$
$350$	20.8400	−	15.6856i	1.11394	−	0.838433i
$351$		0			0
$352$	−29.8430	−	29.8430i	−1.59064	−	1.59064i
$353$	24.7661	+	24.7661i	1.31817	+	1.31817i	0.915227	+	0.402939i	$0.132011\pi$
$353$	24.7661	+	24.7661i	1.31817	+	1.31817i	0.402939	+	0.915227i	$0.367989\pi$
$354$		0			0
$355$	−11.6242	−	34.7735i	−0.616947	−	1.84559i
$356$			12.1313i			0.642958i
$357$		0			0
$358$	1.49248	−	1.49248i	0.0788799	−	0.0788799i
$359$	19.7773			1.04381			0.521904	−	0.853004i	$-0.325222\pi$
$359$	19.7773			1.04381			0.521904	+	0.853004i	$0.325222\pi$
$360$		0			0
$361$	−3.75374			−0.197565
$362$	34.0223	−	34.0223i	1.78817	−	1.78817i
$363$		0			0
$364$		−	9.20843i		−	0.482653i
$365$	11.3086	−	22.6655i	0.591918	−	1.18637i
$366$		0			0
$367$	−5.12016	−	5.12016i	−0.267270	−	0.267270i	0.560729	−	0.827999i	$-0.310521\pi$
$367$	−5.12016	−	5.12016i	−0.267270	−	0.267270i	−0.827999	+	0.560729i	$0.810521\pi$
$368$	0.954730	+	0.954730i	0.0497687	+	0.0497687i
$369$		0			0
$370$	−53.7553	+	17.9694i	−2.79460	+	0.934185i
$371$			6.56712i			0.340948i
$372$		0			0
$373$	20.8115	−	20.8115i	1.07758	−	1.07758i	0.0808522	−	0.996726i	$-0.474236\pi$
$373$	20.8115	−	20.8115i	1.07758	−	1.07758i	0.996726	−	0.0808522i	$-0.0257642\pi$
$374$	−63.8220			−3.30016
$375$		0			0
$376$	−13.3400			−0.687960
$377$	−7.98130	+	7.98130i	−0.411058	+	0.411058i
$378$		0			0
$379$		−	23.5409i		−	1.20921i	−0.796524	−	0.604606i	$-0.793330\pi$
$379$		−	23.5409i		−	1.20921i	0.796524	−	0.604606i	$-0.206670\pi$
$380$	29.4421	−	9.84196i	1.51035	−	0.504882i
$381$		0			0
$382$	13.0094	+	13.0094i	0.665618	+	0.665618i
$383$	11.2611	+	11.2611i	0.575413	+	0.575413i	0.933636	−	0.358223i	$-0.116617\pi$
$383$	11.2611	+	11.2611i	0.575413	+	0.575413i	−0.358223	+	0.933636i	$0.616617\pi$
$384$		0			0
$385$	−14.1150	+	28.2903i	−0.719366	+	1.44181i
$386$		−	22.0234i		−	1.12096i
$387$		0			0
$388$	−11.0611	+	11.0611i	−0.561543	+	0.561543i
$389$	4.84770			0.245788			0.122894	−	0.992420i	$-0.460782\pi$
$389$	4.84770			0.245788			0.122894	+	0.992420i	$0.460782\pi$
$390$		0			0
$391$	4.79536			0.242512
$392$	−2.07995	+	2.07995i	−0.105053	+	0.105053i
$393$		0			0
$394$			0.639021i			0.0321934i
$395$	−4.49907	−	13.4589i	−0.226373	−	0.677192i
$396$		0			0
$397$	−17.1306	−	17.1306i	−0.859759	−	0.859759i	0.131550	−	0.991309i	$-0.458005\pi$
$397$	−17.1306	−	17.1306i	−0.859759	−	0.859759i	−0.991309	+	0.131550i	$0.958005\pi$
$398$	37.2283	+	37.2283i	1.86608	+	1.86608i
$399$		0			0
$400$	5.39385	−	4.05979i	0.269692	−	0.202989i
$401$		−	2.99675i		−	0.149650i	−0.997197	−	0.0748252i	$-0.976160\pi$
$401$		−	2.99675i		−	0.149650i	0.997197	−	0.0748252i	$-0.0238399\pi$
$402$		0			0
$403$	−5.82406	+	5.82406i	−0.290117	+	0.290117i
$404$	−41.9248			−2.08584
$405$		0			0
$406$	−43.8118			−2.17434
$407$	48.5793	−	48.5793i	2.40799	−	2.40799i
$408$		0			0
$409$		−	28.4823i		−	1.40836i	−0.710021	−	0.704180i	$-0.751315\pi$
$409$		−	28.4823i		−	1.40836i	0.710021	−	0.704180i	$-0.248685\pi$
$410$	15.0560	+	7.51197i	0.743565	+	0.370990i
$411$		0			0
$412$	4.47710	+	4.47710i	0.220571	+	0.220571i
$413$	1.58340	+	1.58340i	0.0779139	+	0.0779139i
$414$		0			0
$415$	8.96452	+	4.47270i	0.440051	+	0.219556i
$416$		−	9.44410i		−	0.463035i
$417$		0			0
$418$	−44.8911	+	44.8911i	−2.19570	+	2.19570i
$419$	29.8295			1.45726			0.728632	−	0.684905i	$-0.240156\pi$
$419$	29.8295			1.45726			0.728632	+	0.684905i	$0.240156\pi$
$420$		0			0
$421$	−8.98527			−0.437915			−0.218958	−	0.975734i	$-0.570266\pi$
$421$	−8.98527			−0.437915			−0.218958	+	0.975734i	$0.570266\pi$
$422$	13.3671	−	13.3671i	0.650702	−	0.650702i
$423$		0			0
$424$		−	5.62803i		−	0.273321i
$425$	3.35031	−	23.7416i	0.162514	−	1.15164i
$426$		0			0
$427$	22.6457	+	22.6457i	1.09590	+	1.09590i
$428$	−14.4138	−	14.4138i	−0.696716	−	0.696716i
$429$		0			0
$430$	−8.47834	−	25.3628i	−0.408862	−	1.22310i
$431$			0.814544i			0.0392352i	0.999808	+	0.0196176i	$0.00624488\pi$
$431$			0.814544i			0.0392352i	−0.999808	+	0.0196176i	$0.993755\pi$
$432$		0			0
$433$	9.42170	−	9.42170i	0.452778	−	0.452778i	−0.443498	−	0.896276i	$-0.646263\pi$
$433$	9.42170	−	9.42170i	0.452778	−	0.452778i	0.896276	+	0.443498i	$0.146263\pi$
$434$	−31.9700			−1.53461
$435$		0			0
$436$	31.3396			1.50089
$437$	3.37296	−	3.37296i	0.161351	−	0.161351i
$438$		0			0
$439$			5.59329i			0.266953i	0.991052	+	0.133477i	$0.0426141\pi$
$439$			5.59329i			0.266953i	−0.991052	+	0.133477i	$0.957386\pi$
$440$	12.0966	−	24.2448i	0.576681	−	1.15583i
$441$		0			0
$442$	−10.0985	−	10.0985i	−0.480339	−	0.480339i
$443$	1.57689	+	1.57689i	0.0749203	+	0.0749203i	0.743574	−	0.668654i	$-0.233129\pi$
$443$	1.57689	+	1.57689i	0.0749203	+	0.0749203i	−0.668654	+	0.743574i	$0.733129\pi$
$444$		0			0
$445$	8.83956	−	2.95490i	0.419035	−	0.140076i
$446$		−	4.89629i		−	0.231846i
$447$		0			0
$448$	21.4256	−	21.4256i	1.01227	−	1.01227i
$449$	8.19073			0.386545			0.193272	−	0.981145i	$-0.438090\pi$
$449$	8.19073			0.386545			0.193272	+	0.981145i	$0.438090\pi$
$450$		0			0
$451$	−20.3950			−0.960364
$452$	−4.23393	+	4.23393i	−0.199147	+	0.199147i
$453$		0			0
$454$		−	16.9979i		−	0.797750i
$455$	−6.70979	+	2.24296i	−0.314560	+	0.105152i
$456$		0			0
$457$	−2.22860	−	2.22860i	−0.104250	−	0.104250i	0.653058	−	0.757308i	$-0.273486\pi$
$457$	−2.22860	−	2.22860i	−0.104250	−	0.104250i	−0.757308	+	0.653058i	$0.773486\pi$
$458$	−21.5758	−	21.5758i	−1.00817	−	1.00817i
$459$		0			0
$460$	−2.90548	+	5.82338i	−0.135469	+	0.271516i
$461$			15.1228i			0.704338i	0.935936	+	0.352169i	$0.114556\pi$
$461$			15.1228i			0.704338i	−0.935936	+	0.352169i	$0.885444\pi$
$462$		0			0
$463$	−7.82664	+	7.82664i	−0.363735	+	0.363735i	−0.865186	−	0.501451i	$-0.832800\pi$
$463$	−7.82664	+	7.82664i	−0.363735	+	0.363735i	0.501451	+	0.865186i	$0.332800\pi$
$464$	−11.3395			−0.526421
$465$		0			0
$466$	41.5898			1.92661
$467$	−9.29552	+	9.29552i	−0.430146	+	0.430146i	−0.888678	−	0.458532i	$-0.848375\pi$
$467$	−9.29552	+	9.29552i	−0.430146	+	0.430146i	0.458532	+	0.888678i	$0.348375\pi$
$468$		0			0
$469$			14.6507i			0.676508i
$470$	10.3872	+	31.0731i	0.479125	+	1.43330i
$471$		0			0
$472$	−1.35697	−	1.35697i	−0.0624598	−	0.0624598i
$473$	22.9207	+	22.9207i	1.05390	+	1.05390i
$474$		0			0
$475$	−14.3428	−	19.0559i	−0.658093	−	0.874344i
$476$		−	32.8560i		−	1.50595i
$477$		0			0
$478$	−34.9583	+	34.9583i	−1.59896	+	1.59896i
$479$	−39.4992			−1.80476			−0.902381	−	0.430939i	$-0.858183\pi$
$479$	−39.4992			−1.80476			−0.902381	+	0.430939i	$0.858183\pi$
$480$		0			0
$481$	15.3734			0.700967
$482$	1.52019	−	1.52019i	0.0692429	−	0.0692429i
$483$		0			0
$484$			72.9724i			3.31693i
$485$	10.7540	+	5.36553i	0.488313	+	0.243636i
$486$		0			0
$487$	−3.74404	−	3.74404i	−0.169658	−	0.169658i	0.617171	−	0.786829i	$-0.288279\pi$
$487$	−3.74404	−	3.74404i	−0.169658	−	0.169658i	−0.786829	+	0.617171i	$0.788279\pi$
$488$	−19.4074	−	19.4074i	−0.878530	−	0.878530i
$489$		0			0
$490$	6.46439	+	3.22530i	0.292031	+	0.145704i
$491$		−	24.0463i		−	1.08519i	−0.839993	−	0.542597i	$-0.817441\pi$
$491$		−	24.0463i		−	1.08519i	0.839993	−	0.542597i	$-0.182559\pi$
$492$		0			0
$493$	−28.4776	+	28.4776i	−1.28257	+	1.28257i
$494$	−14.2062			−0.639169
$495$		0			0
$496$	−8.27455			−0.371538
$497$	−27.2951	+	27.2951i	−1.22435	+	1.22435i
$498$		0			0
$499$		−	33.0257i		−	1.47843i	−0.673467	−	0.739217i	$-0.735196\pi$
$499$		−	33.0257i		−	1.47843i	0.673467	−	0.739217i	$-0.264804\pi$
$500$	26.8013	+	18.4534i	1.19859	+	0.825262i
$501$		0			0
$502$	12.0890	+	12.0890i	0.539558	+	0.539558i
$503$	−27.3808	−	27.3808i	−1.22085	−	1.22085i	−0.967330	−	0.253521i	$-0.918411\pi$
$503$	−27.3808	−	27.3808i	−1.22085	−	1.22085i	−0.253521	−	0.967330i	$-0.581589\pi$
$504$		0			0
$505$	10.2119	+	30.5488i	0.454424	+	1.35940i
$506$		−	13.3091i		−	0.591662i
$507$		0			0
$508$	−6.95523	+	6.95523i	−0.308589	+	0.308589i
$509$	−17.4276			−0.772467			−0.386233	−	0.922401i	$-0.626224\pi$
$509$	−17.4276			−0.772467			−0.386233	+	0.922401i	$0.626224\pi$
$510$		0			0
$511$	−26.6676			−1.17971
$512$	10.5612	−	10.5612i	0.466744	−	0.466744i
$513$		0			0
$514$			48.3175i			2.13119i
$515$	2.17175	−	4.35278i	0.0956987	−	0.191807i
$516$		0			0
$517$	−28.0812	−	28.0812i	−1.23501	−	1.23501i
$518$	42.1947	+	42.1947i	1.85393	+	1.85393i
$519$		0			0
$520$	5.75029	−	1.92222i	0.252167	−	0.0842948i
$521$			6.94025i			0.304058i	0.988376	+	0.152029i	$0.0485807\pi$
$521$			6.94025i			0.304058i	−0.988376	+	0.152029i	$0.951419\pi$
$522$		0			0
$523$	12.5498	−	12.5498i	0.548765	−	0.548765i	−0.377319	−	0.926084i	$-0.623154\pi$
$523$	12.5498	−	12.5498i	0.548765	−	0.548765i	0.926084	+	0.377319i	$0.123154\pi$
$524$	38.5677			1.68484
$525$		0			0
$526$	−29.5761			−1.28958
$527$	−20.7804	+	20.7804i	−0.905210	+	0.905210i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$	−13.1094	+	4.38225i	−0.569438	+	0.190353i
$531$		0			0
$532$	−23.1103	−	23.1103i	−1.00196	−	1.00196i
$533$	−3.22710	−	3.22710i	−0.139781	−	0.139781i
$534$		0			0
$535$	−6.99183	+	14.0136i	−0.302283	+	0.605859i
$536$		−	12.5557i		−	0.542323i
$537$		0			0
$538$	−21.5663	+	21.5663i	−0.929788	+	0.929788i
$539$	−8.75670			−0.377178
$540$		0			0
$541$	4.13258			0.177674			0.0888368	−	0.996046i	$-0.471685\pi$
$541$	4.13258			0.177674			0.0888368	+	0.996046i	$0.471685\pi$
$542$	4.71976	−	4.71976i	0.202731	−	0.202731i
$543$		0			0
$544$		−	33.6969i		−	1.44474i
$545$	−7.63360	−	22.8358i	−0.326987	−	0.978178i
$546$		0			0
$547$	−16.2225	−	16.2225i	−0.693623	−	0.693623i	0.269404	−	0.963027i	$-0.413173\pi$
$547$	−16.2225	−	16.2225i	−0.693623	−	0.693623i	−0.963027	+	0.269404i	$0.913173\pi$
$548$	26.0893	+	26.0893i	1.11448	+	1.11448i
$549$		0			0
$550$	−65.8927	−	9.29851i	−2.80968	−	0.396490i
$551$			40.0611i			1.70666i
$552$		0			0
$553$	−10.5644	+	10.5644i	−0.449246	+	0.449246i
$554$	7.79479			0.331169
$555$		0			0
$556$	−31.9658			−1.35565
$557$	−28.5140	+	28.5140i	−1.20818	+	1.20818i	−0.236558	+	0.971617i	$0.576019\pi$
$557$	−28.5140	+	28.5140i	−1.20818	+	1.20818i	−0.971617	+	0.236558i	$0.923981\pi$
$558$		0			0
$559$			7.25349i			0.306790i
$560$	−6.35982	−	3.17313i	−0.268751	−	0.134089i
$561$		0			0
$562$	31.2274	+	31.2274i	1.31725	+	1.31725i
$563$	−24.4895	−	24.4895i	−1.03211	−	1.03211i	−0.999467	−	0.0326442i	$-0.989607\pi$
$563$	−24.4895	−	24.4895i	−1.03211	−	1.03211i	−0.0326442	−	0.999467i	$-0.510393\pi$
$564$		0			0
$565$	4.11636	+	2.05379i	0.173177	+	0.0864037i
$566$		−	34.6063i		−	1.45461i
$567$		0			0
$568$	23.3920	−	23.3920i	0.981505	−	0.981505i
$569$	−12.9818			−0.544225			−0.272113	−	0.962265i	$-0.587722\pi$
$569$	−12.9818			−0.544225			−0.272113	+	0.962265i	$0.587722\pi$
$570$		0			0
$571$	−20.3493			−0.851591			−0.425796	−	0.904819i	$-0.640006\pi$
$571$	−20.3493			−0.851591			−0.425796	+	0.904819i	$0.640006\pi$
$572$	−16.6121	+	16.6121i	−0.694588	+	0.694588i
$573$		0			0
$574$		−	17.7145i		−	0.739391i
$575$	4.95095	+	0.698657i	0.206469	+	0.0291360i
$576$		0			0
$577$	10.5531	+	10.5531i	0.439331	+	0.439331i	0.891787	−	0.452456i	$-0.149452\pi$
$577$	10.5531	+	10.5531i	0.439331	+	0.439331i	−0.452456	+	0.891787i	$0.649452\pi$
$578$	−9.39440	−	9.39440i	−0.390755	−	0.390755i
$579$		0			0
$580$	−17.3281	−	51.8369i	−0.719512	−	2.15241i
$581$		−	10.5474i		−	0.437581i
$582$		0			0
$583$	11.8472	−	11.8472i	0.490660	−	0.490660i
$584$	22.8542			0.945712
$585$		0			0
$586$	39.0922			1.61488
$587$	15.6706	−	15.6706i	0.646795	−	0.646795i	−0.305422	−	0.952217i	$-0.598798\pi$
$587$	15.6706	−	15.6706i	0.646795	−	0.646795i	0.952217	+	0.305422i	$0.0987976\pi$
$588$		0			0
$589$			29.2331i			1.20453i
$590$	−2.10421	+	4.21742i	−0.0866291	+	0.173628i
$591$		0			0
$592$	10.9209	+	10.9209i	0.448846	+	0.448846i
$593$	33.6024	+	33.6024i	1.37988	+	1.37988i	0.844796	+	0.535088i	$0.179721\pi$
$593$	33.6024	+	33.6024i	1.37988	+	1.37988i	0.535088	+	0.844796i	$0.320279\pi$
$594$		0			0
$595$	−23.9407	+	8.00296i	−0.981475	+	0.328089i
$596$		−	50.6107i		−	2.07309i
$597$		0			0
$598$	2.10590	−	2.10590i	0.0861166	−	0.0861166i
$599$	−33.6307			−1.37411			−0.687056	−	0.726604i	$-0.741097\pi$
$599$	−33.6307			−1.37411			−0.687056	+	0.726604i	$0.741097\pi$
$600$		0			0
$601$	12.2355			0.499097			0.249549	−	0.968362i	$-0.419718\pi$
$601$	12.2355			0.499097			0.249549	+	0.968362i	$0.419718\pi$
$602$	−19.9083	+	19.9083i	−0.811402	+	0.811402i
$603$		0			0
$604$			27.3952i			1.11469i
$605$	53.1718	−	17.7744i	2.16174	−	0.722632i
$606$		0			0
$607$	11.6236	+	11.6236i	0.471789	+	0.471789i	0.902493	−	0.430704i	$-0.141735\pi$
$607$	11.6236	+	11.6236i	0.471789	+	0.471789i	−0.430704	+	0.902493i	$0.641735\pi$
$608$	−23.7017	−	23.7017i	−0.961232	−	0.961232i
$609$		0			0
$610$	−30.0943	+	60.3173i	−1.21848	+	2.44218i
$611$		−	8.88656i		−	0.359512i
$612$		0			0
$613$	3.32566	−	3.32566i	0.134322	−	0.134322i	−0.636749	−	0.771071i	$-0.719721\pi$
$613$	3.32566	−	3.32566i	0.134322	−	0.134322i	0.771071	+	0.636749i	$0.219721\pi$
$614$	−48.7563			−1.96765
$615$		0			0
$616$	−28.5258			−1.14934
$617$	12.9698	−	12.9698i	0.522145	−	0.522145i	−0.396073	−	0.918219i	$-0.629627\pi$
$617$	12.9698	−	12.9698i	0.522145	−	0.522145i	0.918219	+	0.396073i	$0.129627\pi$
$618$		0			0
$619$		−	3.75521i		−	0.150935i	−0.997148	−	0.0754673i	$-0.975955\pi$
$619$		−	3.75521i		−	0.150935i	0.997148	−	0.0754673i	$-0.0240449\pi$
$620$	−12.6446	−	37.8260i	−0.507818	−	1.51913i
$621$		0			0
$622$	20.6896	+	20.6896i	0.829578	+	0.829578i
$623$	−6.93852	−	6.93852i	−0.277986	−	0.277986i
$624$		0			0
$625$	6.91803	−	24.0238i	0.276721	−	0.960950i
$626$			17.1429i			0.685167i
$627$		0			0
$628$	9.10572	−	9.10572i	0.363358	−	0.363358i
$629$	54.8528			2.18713
$630$		0			0
$631$	−13.5466			−0.539281			−0.269640	−	0.962961i	$-0.586905\pi$
$631$	−13.5466			−0.539281			−0.269640	+	0.962961i	$0.586905\pi$
$632$	9.05374	−	9.05374i	0.360138	−	0.360138i
$633$		0			0
$634$			11.0654i			0.439462i
$635$	6.76211	+	3.37384i	0.268346	+	0.133887i
$636$		0			0
$637$	−1.38557	−	1.38557i	−0.0548984	−	0.0548984i
$638$	79.0371	+	79.0371i	3.12911	+	3.12911i
$639$		0			0
$640$	28.9478	+	14.4430i	1.14426	+	0.570911i
$641$			9.25186i			0.365426i	0.983166	+	0.182713i	$0.0584880\pi$
$641$			9.25186i			0.365426i	−0.983166	+	0.182713i	$0.941512\pi$
$642$		0			0
$643$	6.02539	−	6.02539i	0.237618	−	0.237618i	−0.578245	−	0.815863i	$-0.696262\pi$
$643$	6.02539	−	6.02539i	0.237618	−	0.237618i	0.815863	+	0.578245i	$0.196262\pi$
$644$	6.85163			0.269992
$645$		0			0
$646$	−50.6883			−1.99431
$647$	6.98974	−	6.98974i	0.274795	−	0.274795i	−0.556232	−	0.831027i	$-0.687753\pi$
$647$	6.98974	−	6.98974i	0.274795	−	0.274795i	0.831027	+	0.556232i	$0.187753\pi$
$648$		0			0
$649$		−	5.71294i		−	0.224253i
$650$	−8.95490	−	11.8975i	−0.351240	−	0.466658i
$651$		0			0
$652$	27.8721	+	27.8721i	1.09156	+	1.09156i
$653$	10.3962	+	10.3962i	0.406834	+	0.406834i	0.880633	−	0.473799i	$-0.157118\pi$
$653$	10.3962	+	10.3962i	0.406834	+	0.406834i	−0.473799	+	0.880633i	$0.657118\pi$
$654$		0			0
$655$	−9.39420	−	28.1026i	−0.367062	−	1.09806i
$656$		−	4.58491i		−	0.179011i
$657$		0			0
$658$	24.3905	−	24.3905i	0.950842	−	0.950842i
$659$	−13.3265			−0.519126			−0.259563	−	0.965726i	$-0.583579\pi$
$659$	−13.3265			−0.519126			−0.259563	+	0.965726i	$0.583579\pi$
$660$		0			0
$661$	−16.1751			−0.629139			−0.314570	−	0.949234i	$-0.601860\pi$
$661$	−16.1751			−0.629139			−0.314570	+	0.949234i	$0.601860\pi$
$662$	21.4811	−	21.4811i	0.834886	−	0.834886i
$663$		0			0
$664$			9.03914i			0.350787i
$665$	−11.2103	+	22.4686i	−0.434718	+	0.871294i
$666$		0			0
$667$	−5.93857	−	5.93857i	−0.229942	−	0.229942i
$668$	−5.28988	−	5.28988i	−0.204672	−	0.204672i
$669$		0			0
$670$	−29.2461	+	9.77645i	−1.12988	+	0.377697i
$671$		−	81.7062i		−	3.15423i
$672$		0			0
$673$	23.6148	−	23.6148i	0.910284	−	0.910284i	−0.0860100	−	0.996294i	$-0.527412\pi$
$673$	23.6148	−	23.6148i	0.910284	−	0.910284i	0.996294	+	0.0860100i	$0.0274117\pi$
$674$	45.1953			1.74086
$675$		0			0
$676$	32.5787			1.25303
$677$	−4.04226	+	4.04226i	−0.155357	+	0.155357i	−0.780505	−	0.625149i	$-0.785038\pi$
$677$	−4.04226	+	4.04226i	−0.155357	+	0.155357i	0.625149	+	0.780505i	$0.285038\pi$
$678$		0			0
$679$		−	12.6529i		−	0.485572i
$680$	20.5172	−	6.85854i	0.786800	−	0.263013i
$681$		0			0
$682$	57.6744	+	57.6744i	2.20847	+	2.20847i
$683$	17.5938	+	17.5938i	0.673206	+	0.673206i	0.958454	−	0.285248i	$-0.0920758\pi$
$683$	17.5938	+	17.5938i	0.673206	+	0.673206i	−0.285248	+	0.958454i	$0.592076\pi$
$684$		0			0
$685$	12.6554	−	25.3648i	0.483537	−	0.969141i
$686$		−	44.1226i		−	1.68461i
$687$		0			0
$688$	−5.15271	+	5.15271i	−0.196445	+	0.196445i
$689$	3.74915			0.142831
$690$		0			0
$691$	−31.5706			−1.20100			−0.600501	−	0.799624i	$-0.705032\pi$
$691$	−31.5706			−1.20100			−0.600501	+	0.799624i	$0.705032\pi$
$692$	−24.7972	+	24.7972i	−0.942648	+	0.942648i
$693$		0			0
$694$			29.7487i			1.12925i
$695$	7.78612	+	23.2921i	0.295344	+	0.883519i
$696$		0			0
$697$	−11.5144	−	11.5144i	−0.436139	−	0.436139i
$698$	−0.511658	−	0.511658i	−0.0193665	−	0.0193665i
$699$		0			0
$700$	4.78694	−	33.9220i	0.180929	−	1.28213i
$701$		−	31.4129i		−	1.18645i	−0.805038	−	0.593224i	$-0.797855\pi$
$701$		−	31.4129i		−	1.18645i	0.805038	−	0.593224i	$-0.202145\pi$
$702$		0			0
$703$	38.5824	−	38.5824i	1.45516	−	1.45516i
$704$	−77.3042			−2.91351
$705$		0			0
$706$	77.6127			2.92099
$707$	23.9790	−	23.9790i	0.901822	−	0.901822i
$708$		0			0
$709$			3.18902i			0.119766i	0.998205	+	0.0598831i	$0.0190728\pi$
$709$			3.18902i			0.119766i	−0.998205	+	0.0598831i	$0.980927\pi$
$710$	−72.7013	−	36.2731i	−2.72843	−	1.36131i
$711$		0			0
$712$	5.94632	+	5.94632i	0.222848	+	0.222848i
$713$	−4.33345	−	4.33345i	−0.162289	−	0.162289i
$714$		0			0
$715$	16.1509	+	8.05821i	0.604008	+	0.301360i
$716$		−	2.77218i		−	0.103601i
$717$		0			0
$718$	30.9894	−	30.9894i	1.15651	−	1.15651i
$719$	−10.2056			−0.380606			−0.190303	−	0.981725i	$-0.560947\pi$
$719$	−10.2056			−0.380606			−0.190303	+	0.981725i	$0.560947\pi$
$720$		0			0
$721$	−5.12137			−0.190730
$722$	−5.88179	+	5.88179i	−0.218897	+	0.218897i
$723$		0			0
$724$		−	63.1942i		−	2.34859i
$725$	−33.5506	+	25.2525i	−1.24604	+	0.937855i
$726$		0			0
$727$	−36.1852	−	36.1852i	−1.34203	−	1.34203i	−0.894033	−	0.448002i	$-0.852136\pi$
$727$	−36.1852	−	36.1852i	−1.34203	−	1.34203i	−0.448002	−	0.894033i	$-0.647864\pi$
$728$	−4.51363	−	4.51363i	−0.167286	−	0.167286i
$729$		0			0
$730$	−17.7953	−	53.2345i	−0.658635	−	1.97030i
$731$			25.8807i			0.957232i
$732$		0			0
$733$	17.3576	−	17.3576i	0.641117	−	0.641117i	−0.309713	−	0.950830i	$-0.600233\pi$
$733$	17.3576	−	17.3576i	0.641117	−	0.641117i	0.950830	+	0.309713i	$0.100233\pi$
$734$	−16.0457			−0.592258
$735$		0			0
$736$	7.02698			0.259018
$737$	26.4301	−	26.4301i	0.973566	−	0.973566i
$738$		0			0
$739$		−	8.37363i		−	0.308029i	−0.988069	−	0.154015i	$-0.950780\pi$
$739$		−	8.37363i		−	0.308029i	0.988069	−	0.154015i	$-0.0492203\pi$
$740$	−33.2350	+	66.6120i	−1.22174	+	2.44871i
$741$		0			0
$742$	10.2901	+	10.2901i	0.377762	+	0.377762i
$743$	−30.2618	−	30.2618i	−1.11020	−	1.11020i	−0.993123	−	0.117074i	$-0.962648\pi$
$743$	−30.2618	−	30.2618i	−1.11020	−	1.11020i	−0.117074	−	0.993123i	$-0.537352\pi$
$744$		0			0
$745$	−36.8778	+	12.3276i	−1.35110	+	0.451647i
$746$		−	65.2197i		−	2.38786i
$747$		0			0
$748$	−59.2727	+	59.2727i	−2.16722	+	2.16722i
$749$	16.4880			0.602457
$750$		0			0
$751$	−39.7222			−1.44948			−0.724742	−	0.689020i	$-0.758041\pi$
$751$	−39.7222			−1.44948			−0.724742	+	0.689020i	$0.758041\pi$
$752$	6.31280	−	6.31280i	0.230204	−	0.230204i
$753$		0			0
$754$			25.0121i			0.910885i
$755$	19.9617	−	6.67282i	0.726480	−	0.242849i
$756$		0			0
$757$	0.0816915	+	0.0816915i	0.00296913	+	0.00296913i	0.708590	−	0.705621i	$-0.249332\pi$
$757$	0.0816915	+	0.0816915i	0.00296913	+	0.00296913i	−0.705621	+	0.708590i	$0.749332\pi$
$758$	−36.8865	−	36.8865i	−1.33978	−	1.33978i
$759$		0			0
$760$	9.60726	−	19.2556i	0.348492	−	0.698473i
$761$			3.74643i			0.135808i	0.997692	+	0.0679040i	$0.0216312\pi$
$761$			3.74643i			0.135808i	−0.997692	+	0.0679040i	$0.978369\pi$
$762$		0			0
$763$	−17.9247	+	17.9247i	−0.648919	+	0.648919i
$764$	24.1641			0.874227
$765$		0			0
$766$	35.2902			1.27509
$767$	0.903958	−	0.903958i	0.0326400	−	0.0326400i
$768$		0			0
$769$			11.6541i			0.420257i	0.977674	+	0.210128i	$0.0673882\pi$
$769$			11.6541i			0.420257i	−0.977674	+	0.210128i	$0.932612\pi$
$770$	22.2115	+	66.4455i	0.800448	+	2.39453i
$771$		0			0
$772$	−20.4535	−	20.4535i	−0.736138	−	0.736138i
$773$	26.2938	+	26.2938i	0.945724	+	0.945724i	0.998601	−	0.0528770i	$-0.0168391\pi$
$773$	26.2938	+	26.2938i	0.945724	+	0.945724i	−0.0528770	+	0.998601i	$0.516839\pi$
$774$		0			0
$775$	−24.4823	+	18.4271i	−0.879429	+	0.661920i
$776$			10.8435i			0.389259i
$777$		0			0
$778$	7.59593	−	7.59593i	0.272327	−	0.272327i
$779$	−16.1980			−0.580354
$780$		0			0
$781$	98.4816			3.52395
$782$	7.51392	−	7.51392i	0.268697	−	0.268697i
$783$		0			0
$784$		−	1.96855i		−	0.0703055i
$785$	−8.85288	−	4.41700i	−0.315973	−	0.157650i
$786$		0			0
$787$	35.9900	+	35.9900i	1.28290	+	1.28290i	0.939008	+	0.343896i	$0.111747\pi$
$787$	35.9900	+	35.9900i	1.28290	+	1.28290i	0.343896	+	0.939008i	$0.388253\pi$
$788$	0.593471	+	0.593471i	0.0211415	+	0.0211415i
$789$		0			0
$790$	−28.1387	−	14.0393i	−1.00113	−	0.499497i
$791$		−	4.84320i		−	0.172204i
$792$		0			0
$793$	12.9284	−	12.9284i	0.459100	−	0.459100i
$794$	−53.6843			−1.90519
$795$		0			0
$796$	69.1492			2.45093
$797$	−24.8449	+	24.8449i	−0.880051	+	0.880051i	−0.993539	−	0.113489i	$-0.963797\pi$
$797$	−24.8449	+	24.8449i	−0.880051	+	0.880051i	0.113489	+	0.993539i	$0.463797\pi$
$798$		0			0
$799$		−	31.7076i		−	1.12173i
$800$	4.90945	−	34.7902i	0.173575	−	1.23002i
$801$		0			0
$802$	−4.69565	−	4.69565i	−0.165809	−	0.165809i
$803$	48.1087	+	48.1087i	1.69772	+	1.69772i
$804$		0			0
$805$	−1.66890	−	4.99248i	−0.0588209	−	0.175962i
$806$			18.2516i			0.642886i
$807$		0			0
$808$	−20.5500	+	20.5500i	−0.722947	+	0.722947i
$809$	5.44548			0.191453			0.0957265	−	0.995408i	$-0.469483\pi$
$809$	5.44548			0.191453			0.0957265	+	0.995408i	$0.469483\pi$
$810$		0			0
$811$	9.14088			0.320980			0.160490	−	0.987037i	$-0.448693\pi$
$811$	9.14088			0.320980			0.160490	+	0.987037i	$0.448693\pi$
$812$	−40.6888	+	40.6888i	−1.42790	+	1.42790i
$813$		0			0
$814$		−	152.239i		−	5.33599i
$815$	13.5202	−	27.0982i	0.473593	−	0.949210i
$816$		0			0
$817$	18.2040	+	18.2040i	0.636876	+	0.636876i
$818$	−44.6294	−	44.6294i	−1.56043	−	1.56043i
$819$		0			0
$820$	20.9593	−	7.00633i	0.731932	−	0.244672i
$821$			19.9719i			0.697025i	0.937304	+	0.348513i	$0.113313\pi$
$821$			19.9719i			0.697025i	−0.937304	+	0.348513i	$0.886687\pi$
$822$		0			0
$823$	7.66461	−	7.66461i	0.267171	−	0.267171i	−0.560788	−	0.827959i	$-0.689502\pi$
$823$	7.66461	−	7.66461i	0.267171	−	0.267171i	0.827959	+	0.560788i	$0.189502\pi$
$824$	4.38901			0.152899
$825$		0			0
$826$	4.96210			0.172654
$827$	21.2918	−	21.2918i	0.740388	−	0.740388i	−0.232265	−	0.972653i	$-0.574614\pi$
$827$	21.2918	−	21.2918i	0.740388	−	0.740388i	0.972653	+	0.232265i	$0.0746136\pi$
$828$		0			0
$829$			11.5523i			0.401227i	0.979670	+	0.200614i	$0.0642936\pi$
$829$			11.5523i			0.401227i	−0.979670	+	0.200614i	$0.935706\pi$
$830$	21.0550	−	7.03830i	0.730830	−	0.244303i
$831$		0			0
$832$	−12.2318	−	12.2318i	−0.424063	−	0.424063i
$833$	−4.94377	−	4.94377i	−0.171291	−	0.171291i
$834$		0			0
$835$	−2.56602	+	5.14300i	−0.0888006	+	0.177981i
$836$			83.3825i			2.88384i
$837$		0			0
$838$	46.7402	−	46.7402i	1.61461	−	1.61461i
$839$	27.7576			0.958299			0.479150	−	0.877733i	$-0.340945\pi$
$839$	27.7576			0.958299			0.479150	+	0.877733i	$0.340945\pi$
$840$		0			0
$841$	41.5332			1.43218
$842$	−14.0792	+	14.0792i	−0.485200	+	0.485200i
$843$		0			0
$844$		−	24.8286i		−	0.854637i
$845$	−7.93542	−	23.7387i	−0.272987	−	0.816636i
$846$		0			0
$847$	−41.7367	−	41.7367i	−1.43409	−	1.43409i
$848$	2.66331	+	2.66331i	0.0914584	+	0.0914584i
$849$		0			0
$850$	−31.9514	−	42.4507i	−1.09592	−	1.45605i
$851$			11.4387i			0.392115i
$852$		0			0
$853$	−7.78380	+	7.78380i	−0.266512	+	0.266512i	−0.827693	−	0.561181i	$-0.810347\pi$
$853$	−7.78380	+	7.78380i	−0.266512	+	0.266512i	0.561181	+	0.827693i	$0.310347\pi$
$854$	70.9677			2.42847
$855$		0			0
$856$	−14.1302			−0.482960
$857$	−16.6497	+	16.6497i	−0.568744	+	0.568744i	−0.931777	−	0.363032i	$-0.881741\pi$
$857$	−16.6497	+	16.6497i	−0.568744	+	0.568744i	0.363032	+	0.931777i	$0.381741\pi$
$858$		0			0
$859$			14.2358i			0.485719i	0.970061	+	0.242859i	$0.0780854\pi$
$859$			14.2358i			0.485719i	−0.970061	+	0.242859i	$0.921915\pi$
$860$	−31.4289	−	15.6809i	−1.07172	−	0.534716i
$861$		0			0
$862$	1.27632	+	1.27632i	0.0434717	+	0.0434717i
$863$	23.7251	+	23.7251i	0.807611	+	0.807611i	0.984272	−	0.176661i	$-0.0565295\pi$
$863$	23.7251	+	23.7251i	0.807611	+	0.807611i	−0.176661	+	0.984272i	$0.556530\pi$
$864$		0			0
$865$	24.1087	+	12.0286i	0.819719	+	0.408985i
$866$		−	29.5260i		−	1.00333i
$867$		0			0
$868$	−29.6912	+	29.6912i	−1.00778	+	1.00778i
$869$	38.1168			1.29302
$870$		0			0
$871$	8.36407			0.283406
$872$	15.3615	−	15.3615i	0.520207	−	0.520207i
$873$		0			0
$874$		−	10.5703i		−	0.357545i
$875$	−25.8835	+	4.77459i	−0.875022	+	0.161410i
$876$		0			0
$877$	40.2981	+	40.2981i	1.36077	+	1.36077i	0.872936	+	0.487834i	$0.162213\pi$
$877$	40.2981	+	40.2981i	1.36077	+	1.36077i	0.487834	+	0.872936i	$0.337787\pi$
$878$	8.76422	+	8.76422i	0.295778	+	0.295778i
$879$		0			0
$880$	5.74883	+	17.1976i	0.193793	+	0.579730i
$881$			38.8908i			1.31026i	0.755514	+	0.655132i	$0.227387\pi$
$881$			38.8908i			1.31026i	−0.755514	+	0.655132i	$0.772613\pi$
$882$		0			0
$883$	13.8005	−	13.8005i	0.464424	−	0.464424i	−0.435678	−	0.900103i	$-0.643491\pi$
$883$	13.8005	−	13.8005i	0.464424	−	0.464424i	0.900103	+	0.435678i	$0.143491\pi$
$884$	−18.7574			−0.630880
$885$		0			0
$886$	4.94171			0.166020
$887$	−23.7187	+	23.7187i	−0.796396	+	0.796396i	−0.982525	−	0.186129i	$-0.940406\pi$
$887$	−23.7187	+	23.7187i	−0.796396	+	0.796396i	0.186129	+	0.982525i	$0.440406\pi$
$888$		0			0
$889$		−	7.95611i		−	0.266840i
$890$	9.22075	−	18.4809i	0.309080	−	0.619482i
$891$		0			0
$892$	−4.54728	−	4.54728i	−0.152254	−	0.152254i
$893$	−22.3025	−	22.3025i	−0.746324	−	0.746324i
$894$		0			0
$895$	−2.01997	+	0.675240i	−0.0675202	+	0.0225708i
$896$		−	34.0592i		−	1.13784i
$897$		0			0
$898$	12.8342	−	12.8342i	0.428282	−	0.428282i
$899$	51.4690			1.71659
$900$		0			0
$901$	13.3771			0.445656
$902$	−31.9573	+	31.9573i	−1.06406	+	1.06406i
$903$		0			0
$904$			4.15063i			0.138048i
$905$	−46.0469	+	15.3926i	−1.53065	+	0.511669i
$906$		0			0
$907$	13.2487	+	13.2487i	0.439915	+	0.439915i	0.891983	−	0.452068i	$-0.149314\pi$
$907$	13.2487	+	13.2487i	0.439915	+	0.439915i	−0.452068	+	0.891983i	$0.649314\pi$
$908$	−15.7863	−	15.7863i	−0.523885	−	0.523885i
$909$		0			0
$910$	−6.99914	+	14.0282i	−0.232019	+	0.465030i
$911$		−	11.4305i		−	0.378708i	−0.981909	−	0.189354i	$-0.939361\pi$
$911$		−	11.4305i		−	0.378708i	0.981909	−	0.189354i	$-0.0606395\pi$
$912$		0			0
$913$	−19.0277	+	19.0277i	−0.629724	+	0.629724i
$914$	−6.98406			−0.231012
$915$		0			0
$916$	−40.0757			−1.32414
$917$	−22.0589	+	22.0589i	−0.728448	+	0.728448i
$918$		0			0
$919$			59.1330i			1.95062i	0.220842	+	0.975310i	$0.429119\pi$
$919$			59.1330i			1.95062i	−0.220842	+	0.975310i	$0.570881\pi$
$920$	1.43025	+	4.27856i	0.0471538	+	0.141060i
$921$		0			0
$922$	23.6961	+	23.6961i	0.780390	+	0.780390i
$923$	15.5827	+	15.5827i	0.512912	+	0.512912i
$924$		0			0
$925$	56.6326	+	7.99175i	1.86207	+	0.262767i
$926$			24.5274i			0.806019i
$927$		0			0
$928$	−41.7302	+	41.7302i	−1.36986	+	1.36986i
$929$	1.03367			0.0339136			0.0169568	−	0.999856i	$-0.494602\pi$
$929$	1.03367			0.0339136			0.0169568	+	0.999856i	$0.494602\pi$
$930$		0			0
$931$	−6.95470			−0.227931
$932$	38.6253	−	38.6253i	1.26521	−	1.26521i
$933$		0			0
$934$			29.1306i			0.953182i
$935$	57.6269	+	28.7520i	1.88460	+	0.940290i
$936$		0			0
$937$	−26.0566	−	26.0566i	−0.851233	−	0.851233i	0.139052	−	0.990285i	$-0.455594\pi$
$937$	−26.0566	−	26.0566i	−0.851233	−	0.851233i	−0.990285	+	0.139052i	$0.955594\pi$
$938$	22.9565	+	22.9565i	0.749555	+	0.749555i
$939$		0			0
$940$	38.5050	+	19.2114i	1.25589	+	0.626607i
$941$		−	30.3947i		−	0.990838i	−0.868654	−	0.495419i	$-0.835015\pi$
$941$		−	30.3947i		−	0.990838i	0.868654	−	0.495419i	$-0.164985\pi$
$942$		0			0
$943$	2.40116	−	2.40116i	0.0781924	−	0.0781924i
$944$	1.28430			0.0418004
$945$		0			0
$946$	71.8297			2.33538
$947$	−7.70544	+	7.70544i	−0.250393	+	0.250393i	−0.821132	−	0.570739i	$-0.806657\pi$
$947$	−7.70544	+	7.70544i	−0.250393	+	0.250393i	0.570739	+	0.821132i	$0.306657\pi$
$948$		0			0
$949$			15.2245i			0.494207i
$950$	−52.3329	−	7.38501i	−1.69790	−	0.239601i
$951$		0			0
$952$	−16.1048	−	16.1048i	−0.521960	−	0.521960i
$953$	−12.2701	−	12.2701i	−0.397469	−	0.397469i	0.479870	−	0.877339i	$-0.340684\pi$
$953$	−12.2701	−	12.2701i	−0.397469	−	0.397469i	−0.877339	+	0.479870i	$0.840684\pi$
$954$		0			0
$955$	−5.88581	−	17.6073i	−0.190460	−	0.569760i
$956$			64.9328i			2.10008i
$957$		0			0
$958$	−61.8918	+	61.8918i	−1.99963	+	1.99963i
$959$	−29.8436			−0.963699
$960$		0			0
$961$	6.55755			0.211534
$962$	24.0888	−	24.0888i	0.776655	−	0.776655i
$963$		0			0
$964$		−	2.82366i		−	0.0909440i
$965$	−9.92158	+	19.8856i	−0.319387	+	0.640139i
$966$		0			0
$967$	−28.9305	−	28.9305i	−0.930342	−	0.930342i	0.0673854	−	0.997727i	$-0.478534\pi$
$967$	−28.9305	−	28.9305i	−0.930342	−	0.930342i	−0.997727	+	0.0673854i	$0.978534\pi$
$968$	35.7684	+	35.7684i	1.14964	+	1.14964i
$969$		0			0
$970$	25.2579	−	8.44326i	0.810983	−	0.271097i
$971$		−	50.0506i		−	1.60620i	−0.595844	−	0.803100i	$-0.703182\pi$
$971$		−	50.0506i		−	1.60620i	0.595844	−	0.803100i	$-0.296818\pi$
$972$		0			0
$973$	18.2829	−	18.2829i	0.586123	−	0.586123i
$974$	−11.7332			−0.375955
$975$		0			0
$976$	18.3680			0.587946
$977$	37.8802	−	37.8802i	1.21190	−	1.21190i	0.241494	−	0.970402i	$-0.422363\pi$
$977$	37.8802	−	37.8802i	1.21190	−	1.21190i	0.970402	−	0.241494i	$-0.0776374\pi$
$978$		0			0
$979$			25.0344i			0.800102i
$980$	8.99900	−	3.00820i	0.287462	−	0.0960935i
$981$		0			0
$982$	−37.6785	−	37.6785i	−1.20237	−	1.20237i
$983$	26.9103	+	26.9103i	0.858305	+	0.858305i	0.991138	−	0.132833i	$-0.0424074\pi$
$983$	26.9103	+	26.9103i	0.858305	+	0.858305i	−0.132833	+	0.991138i	$0.542407\pi$
$984$		0			0
$985$	0.287881	−	0.576992i	0.00917265	−	0.0183845i
$986$			89.2439i			2.84210i
$987$		0			0
$988$	−13.1936	+	13.1936i	−0.419744	+	0.419744i
$989$	−5.39703			−0.171616
$990$		0			0
$991$	45.9550			1.45981			0.729905	−	0.683548i	$-0.239564\pi$
$991$	45.9550			1.45981			0.729905	+	0.683548i	$0.239564\pi$
$992$	−30.4510	+	30.4510i	−0.966822	+	0.966822i
$993$		0			0
$994$			85.5383i			2.71311i
$995$	−16.8431	−	50.3860i	−0.533963	−	1.59734i
$996$		0			0
$997$	−32.5808	−	32.5808i	−1.03184	−	1.03184i	−0.999476	−	0.0323668i	$-0.989696\pi$
$997$	−32.5808	−	32.5808i	−1.03184	−	1.03184i	−0.0323668	−	0.999476i	$-0.510304\pi$
$998$	−51.7485	−	51.7485i	−1.63807	−	1.63807i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1035.2.j.b.737.19	yes	44
3.2	odd	2	inner	1035.2.j.b.737.4	yes	44
5.3	odd	4	inner	1035.2.j.b.323.4	✓	44
15.8	even	4	inner	1035.2.j.b.323.19	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1035.2.j.b.323.4	✓	44	5.3	odd	4	inner
1035.2.j.b.323.19	yes	44	15.8	even	4	inner
1035.2.j.b.737.4	yes	44	3.2	odd	2	inner
1035.2.j.b.737.19	yes	44	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1035.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56692 - 1.56692i) q^{2} -2.91045i q^{4} +(-2.12072 + 0.708917i) q^{5} +(1.66463 + 1.66463i) q^{7} +(-1.42659 - 1.42659i) q^{8} +O(q^{10})\)	\(q+(1.56692 - 1.56692i) q^{2} -2.91045i q^{4} +(-2.12072 + 0.708917i) q^{5} +(1.66463 + 1.66463i) q^{7} +(-1.42659 - 1.42659i) q^{8} +(-2.21217 + 4.43380i) q^{10} -6.00605i q^{11} +(0.950336 - 0.950336i) q^{13} +5.21668 q^{14} +1.35019 q^{16} +(3.39083 - 3.39083i) q^{17} -4.77009i q^{19} +(2.06327 + 6.17223i) q^{20} +(-9.41097 - 9.41097i) q^{22} +(0.707107 + 0.707107i) q^{23} +(3.99487 - 3.00682i) q^{25} -2.97819i q^{26} +(4.84483 - 4.84483i) q^{28} -8.39840 q^{29} -6.12842 q^{31} +(4.96882 - 4.96882i) q^{32} -10.6263i q^{34} +(-4.71031 - 2.35013i) q^{35} +(8.08840 + 8.08840i) q^{37} +(-7.47432 - 7.47432i) q^{38} +(4.03674 + 2.01406i) q^{40} -3.39575i q^{41} +(-3.81628 + 3.81628i) q^{43} -17.4803 q^{44} +2.21595 q^{46} +(4.67549 - 4.67549i) q^{47} -1.45798i q^{49} +(1.54819 - 10.9711i) q^{50} +(-2.76590 - 2.76590i) q^{52} +(1.97254 + 1.97254i) q^{53} +(4.25779 + 12.7371i) q^{55} -4.74951i q^{56} +(-13.1596 + 13.1596i) q^{58} +0.951199 q^{59} +13.6040 q^{61} +(-9.60272 + 9.60272i) q^{62} -12.8711i q^{64} +(-1.34168 + 2.68910i) q^{65} +(4.40059 + 4.40059i) q^{67} +(-9.86883 - 9.86883i) q^{68} +(-11.0631 + 3.69820i) q^{70} +16.3971i q^{71} +(-8.01005 + 8.01005i) q^{73} +25.3477 q^{74} -13.8831 q^{76} +(9.99787 - 9.99787i) q^{77} +6.34641i q^{79} +(-2.86337 + 0.957174i) q^{80} +(-5.32085 - 5.32085i) q^{82} +(-3.16809 - 3.16809i) q^{83} +(-4.78717 + 9.59481i) q^{85} +11.9596i q^{86} +(-8.56819 + 8.56819i) q^{88} -4.16819 q^{89} +3.16392 q^{91} +(2.05800 - 2.05800i) q^{92} -14.6522i q^{94} +(3.38160 + 10.1160i) q^{95} +(-3.80049 - 3.80049i) q^{97} +(-2.28453 - 2.28453i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{7}+O(q^{10}) \) 44 * q + 12 * q^7	\( 44 q + 12 q^{7} - 20 q^{10} + 4 q^{13} - 44 q^{16} + 16 q^{22} - 8 q^{25} + 40 q^{28} - 32 q^{31} + 56 q^{37} - 16 q^{40} + 72 q^{43} - 4 q^{46} + 76 q^{52} + 56 q^{55} - 12 q^{58} - 96 q^{61} + 12 q^{67} - 48 q^{70} + 68 q^{73} - 112 q^{76} + 52 q^{82} + 32 q^{85} + 56 q^{88} - 176 q^{91} + 76 q^{97}+O(q^{100}) \) 44 * q + 12 * q^7 - 20 * q^10 + 4 * q^13 - 44 * q^16 + 16 * q^22 - 8 * q^25 + 40 * q^28 - 32 * q^31 + 56 * q^37 - 16 * q^40 + 72 * q^43 - 4 * q^46 + 76 * q^52 + 56 * q^55 - 12 * q^58 - 96 * q^61 + 12 * q^67 - 48 * q^70 + 68 * q^73 - 112 * q^76 + 52 * q^82 + 32 * q^85 + 56 * q^88 - 176 * q^91 + 76 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more