LMFDB - Embedded newform 840.2.da.b.89.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(89,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("840.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.da (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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.20
Character	$\chi$	$=$	840.89
Dual form			840.2.da.b.689.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58278 - 0.703435i) q^{3} +(-0.851635 + 2.06754i) q^{5} +(-1.08470 - 2.41318i) q^{7} +(2.01036 - 2.22676i) q^{9} +O(q^{10})$	\(q+(1.58278 - 0.703435i) q^{3} +(-0.851635 + 2.06754i) q^{5} +(-1.08470 - 2.41318i) q^{7} +(2.01036 - 2.22676i) q^{9} +(3.40398 - 1.96529i) q^{11} -2.95102 q^{13} +(0.106434 + 3.87152i) q^{15} +(2.29491 - 1.32497i) q^{17} +(6.11746 + 3.53192i) q^{19} +(-3.41435 - 3.05650i) q^{21} +(4.18989 - 7.25710i) q^{23} +(-3.54944 - 3.52158i) q^{25} +(1.61556 - 4.93862i) q^{27} -1.79956i q^{29} +(-5.96761 + 3.44540i) q^{31} +(4.00528 - 5.50509i) q^{33} +(5.91311 - 0.187521i) q^{35} +(8.34112 + 4.81575i) q^{37} +(-4.67080 + 2.07585i) q^{39} +3.41357 q^{41} -4.62710i q^{43} +(2.89183 + 6.05288i) q^{45} +(1.77400 + 1.02422i) q^{47} +(-4.64684 + 5.23516i) q^{49} +(2.70030 - 3.71144i) q^{51} +(-1.01300 - 1.75457i) q^{53} +(1.16436 + 8.71156i) q^{55} +(12.1670 + 1.28699i) q^{57} +(6.29445 + 10.9023i) q^{59} +(-4.88418 - 2.81988i) q^{61} +(-7.55421 - 2.43597i) q^{63} +(2.51319 - 6.10135i) q^{65} +(-8.62834 + 4.98157i) q^{67} +(1.52675 - 14.4337i) q^{69} -8.62351i q^{71} +(-4.14131 - 7.17295i) q^{73} +(-8.09516 - 3.07706i) q^{75} +(-8.43489 - 6.08264i) q^{77} +(-6.84071 + 11.8485i) q^{79} +(-0.916926 - 8.95317i) q^{81} +8.53557i q^{83} +(0.784996 + 5.87320i) q^{85} +(-1.26587 - 2.84830i) q^{87} +(-4.32867 + 7.49747i) q^{89} +(3.20098 + 7.12133i) q^{91} +(-7.02177 + 9.65112i) q^{93} +(-12.5122 + 9.64018i) q^{95} -5.65835 q^{97} +(2.46699 - 11.5308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{3} + 3 q^{5} - q^{9}+O(q^{10}) $ 48 * q + 3 * q^3 + 3 * q^5 - q^9	$ 48 q + 3 q^{3} + 3 q^{5} - q^{9} + 6 q^{15} + 5 q^{21} + 2 q^{23} + q^{25} + 6 q^{31} + 24 q^{33} - 4 q^{35} + 2 q^{39} - 21 q^{45} + 12 q^{51} - 6 q^{53} + 20 q^{57} + 18 q^{61} - 26 q^{63} + 10 q^{65} - 51 q^{75} + 2 q^{77} + 2 q^{79} - 9 q^{81} - 15 q^{87} + 24 q^{91} + 8 q^{93} + 6 q^{95} - 12 q^{99}+O(q^{100}) $ 48 * q + 3 * q^3 + 3 * q^5 - q^9 + 6 * q^15 + 5 * q^21 + 2 * q^23 + q^25 + 6 * q^31 + 24 * q^33 - 4 * q^35 + 2 * q^39 - 21 * q^45 + 12 * q^51 - 6 * q^53 + 20 * q^57 + 18 * q^61 - 26 * q^63 + 10 * q^65 - 51 * q^75 + 2 * q^77 + 2 * q^79 - 9 * q^81 - 15 * q^87 + 24 * q^91 + 8 * q^93 + 6 * q^95 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.58278	−	0.703435i	0.913816	−	0.406129i
$3$	1.58278	−	0.703435i	0.913816	−	0.406129i
$4$		0			0
$5$	−0.851635	+	2.06754i	−0.380863	+	0.924632i
$5$	−0.851635	+	2.06754i	−0.380863	+	0.924632i
$6$		0			0
$7$	−1.08470	−	2.41318i	−0.409979	−	0.912095i
$7$	−1.08470	−	2.41318i	−0.409979	−	0.912095i
$8$		0			0
$9$	2.01036	−	2.22676i	0.670119	−	0.742254i
$10$		0			0
$11$	3.40398	−	1.96529i	1.02634	−	0.592556i	0.110404	−	0.993887i	$-0.464785\pi$
$11$	3.40398	−	1.96529i	1.02634	−	0.592556i	0.915933	+	0.401330i	$0.131452\pi$
$12$		0			0
$13$	−2.95102			−0.818465			−0.409233	−	0.912430i	$-0.634204\pi$
$13$	−2.95102			−0.818465			−0.409233	+	0.912430i	$0.634204\pi$
$14$		0			0
$15$	0.106434	+	3.87152i	0.0274811	+	0.999622i
$16$		0			0
$17$	2.29491	−	1.32497i	0.556597	−	0.321352i	−0.195181	−	0.980767i	$-0.562530\pi$
$17$	2.29491	−	1.32497i	0.556597	−	0.321352i	0.751779	+	0.659416i	$0.229196\pi$
$18$		0			0
$19$	6.11746	+	3.53192i	1.40344	+	0.810277i	0.994744	−	0.102393i	$-0.0326498\pi$
$19$	6.11746	+	3.53192i	1.40344	+	0.810277i	0.408697	+	0.912670i	$0.365983\pi$
$20$		0			0
$21$	−3.41435	−	3.05650i	−0.745073	−	0.666983i
$22$		0			0
$23$	4.18989	−	7.25710i	0.873652	−	1.51321i	0.0154610	−	0.999880i	$-0.495078\pi$
$23$	4.18989	−	7.25710i	0.873652	−	1.51321i	0.858191	−	0.513330i	$-0.171588\pi$
$24$		0			0
$25$	−3.54944	−	3.52158i	−0.709887	−	0.704315i
$26$		0			0
$27$	1.61556	−	4.93862i	0.310915	−	0.950438i
$28$		0			0
$29$		−	1.79956i		−	0.334170i	−0.985942	−	0.167085i	$-0.946565\pi$
$29$		−	1.79956i		−	0.334170i	0.985942	−	0.167085i	$-0.0534354\pi$
$30$		0			0
$31$	−5.96761	+	3.44540i	−1.07181	+	0.618812i	−0.928677	−	0.370891i	$-0.879052\pi$
$31$	−5.96761	+	3.44540i	−1.07181	+	0.618812i	−0.143138	+	0.989703i	$0.545719\pi$
$32$		0			0
$33$	4.00528	−	5.50509i	0.697230	−	0.958312i
$34$		0			0
$35$	5.91311	−	0.187521i	0.999498	−	0.0316969i
$36$		0			0
$37$	8.34112	+	4.81575i	1.37127	+	0.791704i	0.991088	−	0.133207i	$-0.0425274\pi$
$37$	8.34112	+	4.81575i	1.37127	+	0.791704i	0.380184	+	0.924911i	$0.375861\pi$
$38$		0			0
$39$	−4.67080	+	2.07585i	−0.747927	+	0.332402i
$40$		0			0
$41$	3.41357			0.533111			0.266555	−	0.963820i	$-0.414114\pi$
$41$	3.41357			0.533111			0.266555	+	0.963820i	$0.414114\pi$
$42$		0			0
$43$		−	4.62710i		−	0.705627i	−0.935694	−	0.352813i	$-0.885225\pi$
$43$		−	4.62710i		−	0.705627i	0.935694	−	0.352813i	$-0.114775\pi$
$44$		0			0
$45$	2.89183	+	6.05288i	0.431088	+	0.902310i
$46$		0			0
$47$	1.77400	+	1.02422i	0.258765	+	0.149398i	0.623771	−	0.781607i	$-0.285600\pi$
$47$	1.77400	+	1.02422i	0.258765	+	0.149398i	−0.365006	+	0.931005i	$0.618933\pi$
$48$		0			0
$49$	−4.64684	+	5.23516i	−0.663834	+	0.747880i
$50$		0			0
$51$	2.70030	−	3.71144i	0.378117	−	0.519706i
$52$		0			0
$53$	−1.01300	−	1.75457i	−0.139146	−	0.241008i	0.788027	−	0.615640i	$-0.211102\pi$
$53$	−1.01300	−	1.75457i	−0.139146	−	0.241008i	−0.927174	+	0.374632i	$0.877769\pi$
$54$		0			0
$55$	1.16436	+	8.71156i	0.157003	+	1.17467i
$56$		0			0
$57$	12.1670	+	1.28699i	1.61156	+	0.170467i
$58$		0			0
$59$	6.29445	+	10.9023i	0.819468	+	1.41936i	0.906075	+	0.423118i	$0.139064\pi$
$59$	6.29445	+	10.9023i	0.819468	+	1.41936i	−0.0866065	+	0.996243i	$0.527602\pi$
$60$		0			0
$61$	−4.88418	−	2.81988i	−0.625355	−	0.361049i	0.153596	−	0.988134i	$-0.450915\pi$
$61$	−4.88418	−	2.81988i	−0.625355	−	0.361049i	−0.778951	+	0.627085i	$0.784248\pi$
$62$		0			0
$63$	−7.55421	−	2.43597i	−0.951741	−	0.306904i
$64$		0			0
$65$	2.51319	−	6.10135i	0.311723	−	0.756779i
$66$		0			0
$67$	−8.62834	+	4.98157i	−1.05412	+	0.608596i	−0.923800	−	0.382876i	$-0.874934\pi$
$67$	−8.62834	+	4.98157i	−1.05412	+	0.608596i	−0.130319	+	0.991472i	$0.541600\pi$
$68$		0			0
$69$	1.52675	−	14.4337i	0.183800	−	1.73761i
$70$		0			0
$71$		−	8.62351i		−	1.02342i	−0.859157	−	0.511711i	$-0.829012\pi$
$71$		−	8.62351i		−	1.02342i	0.859157	−	0.511711i	$-0.170988\pi$
$72$		0			0
$73$	−4.14131	−	7.17295i	−0.484703	−	0.839531i	0.515142	−	0.857105i	$-0.327739\pi$
$73$	−4.14131	−	7.17295i	−0.484703	−	0.839531i	−0.999846	+	0.0175739i	$0.994406\pi$
$74$		0			0
$75$	−8.09516	−	3.07706i	−0.934749	−	0.355309i
$76$		0			0
$77$	−8.43489	−	6.08264i	−0.961245	−	0.693182i
$78$		0			0
$79$	−6.84071	+	11.8485i	−0.769640	+	1.33306i	0.168118	+	0.985767i	$0.446231\pi$
$79$	−6.84071	+	11.8485i	−0.769640	+	1.33306i	−0.937758	+	0.347289i	$0.887102\pi$
$80$		0			0
$81$	−0.916926	−	8.95317i	−0.101881	−	0.994797i
$82$		0			0
$83$			8.53557i			0.936901i	0.883490	+	0.468450i	$0.155188\pi$
$83$			8.53557i			0.936901i	−0.883490	+	0.468450i	$0.844812\pi$
$84$		0			0
$85$	0.784996	+	5.87320i	0.0851448	+	0.637038i
$86$		0			0
$87$	−1.26587	−	2.84830i	−0.135716	−	0.305370i
$88$		0			0
$89$	−4.32867	+	7.49747i	−0.458838	+	0.794730i	−0.998900	−	0.0468948i	$-0.985067\pi$
$89$	−4.32867	+	7.49747i	−0.458838	+	0.794730i	0.540062	+	0.841625i	$0.318401\pi$
$90$		0			0
$91$	3.20098	+	7.12133i	0.335554	+	0.746518i
$92$		0			0
$93$	−7.02177	+	9.65112i	−0.728124	+	1.00077i
$94$		0			0
$95$	−12.5122	+	9.64018i	−1.28373	+	0.989062i
$96$		0			0
$97$	−5.65835			−0.574518			−0.287259	−	0.957853i	$-0.592744\pi$
$97$	−5.65835			−0.574518			−0.287259	+	0.957853i	$0.592744\pi$
$98$		0			0
$99$	2.46699	−	11.5308i	0.247941	−	1.15889i
$100$		0			0
$101$	−7.07114	−	12.2476i	−0.703605	−	1.21868i	−0.967193	−	0.254044i	$-0.918239\pi$
$101$	−7.07114	−	12.2476i	−0.703605	−	1.21868i	0.263587	−	0.964636i	$-0.415094\pi$
$102$		0			0
$103$	7.10289	−	12.3026i	0.699868	−	1.21221i	−0.268643	−	0.963240i	$-0.586575\pi$
$103$	7.10289	−	12.3026i	0.699868	−	1.21221i	0.968512	−	0.248968i	$-0.0800913\pi$
$104$		0			0
$105$	9.22721	−	4.45629i	0.900484	−	0.434890i
$106$		0			0
$107$	−2.42984	+	4.20861i	−0.234902	+	0.406862i	−0.959244	−	0.282579i	$-0.908810\pi$
$107$	−2.42984	+	4.20861i	−0.234902	+	0.406862i	0.724342	+	0.689440i	$0.242143\pi$
$108$		0			0
$109$	0.360008	+	0.623552i	0.0344825	+	0.0597254i	0.882752	−	0.469840i	$-0.155688\pi$
$109$	0.360008	+	0.623552i	0.0344825	+	0.0597254i	−0.848269	+	0.529565i	$0.822355\pi$
$110$		0			0
$111$	16.5897	+	1.75481i	1.57462	+	0.166559i
$112$		0			0
$113$	2.12266			0.199683			0.0998416	−	0.995003i	$-0.468166\pi$
$113$	2.12266			0.199683			0.0998416	+	0.995003i	$0.468166\pi$
$114$		0			0
$115$	11.4361	+	14.8432i	1.06642	+	1.38413i
$116$		0			0
$117$	−5.93260	+	6.57121i	−0.548469	+	0.607509i
$118$		0			0
$119$	−5.68667	−	4.10083i	−0.521296	−	0.375922i
$120$		0			0
$121$	2.22471	−	3.85330i	0.202246	−	0.350300i
$122$		0			0
$123$	5.40292	−	2.40123i	0.487165	−	0.216511i
$124$		0			0
$125$	10.3038	−	4.33950i	0.921602	−	0.388137i
$126$		0			0
$127$			5.91328i			0.524718i	0.964970	+	0.262359i	$0.0845005\pi$
$127$			5.91328i			0.524718i	−0.964970	+	0.262359i	$0.915499\pi$
$128$		0			0
$129$	−3.25487	−	7.32367i	−0.286575	−	0.644813i
$130$		0			0
$131$	−4.04460	+	7.00545i	−0.353378	+	0.612069i	−0.986839	−	0.161706i	$-0.948300\pi$
$131$	−4.04460	+	7.00545i	−0.353378	+	0.612069i	0.633461	+	0.773775i	$0.281634\pi$
$132$		0			0
$133$	1.88751	−	18.5936i	0.163668	−	1.61227i
$134$		0			0
$135$	8.83492	+	7.54614i	0.760389	+	0.649468i
$136$		0			0
$137$	0.00835570	+	0.0144725i	0.000713876	+	0.00123647i	0.866382	−	0.499382i	$-0.166439\pi$
$137$	0.00835570	+	0.0144725i	0.000713876	+	0.00123647i	−0.865668	+	0.500618i	$0.833106\pi$
$138$		0			0
$139$		−	7.93921i		−	0.673395i	−0.941613	−	0.336698i	$-0.890690\pi$
$139$		−	7.93921i		−	0.673395i	0.941613	−	0.336698i	$-0.109310\pi$
$140$		0			0
$141$	3.52832	+	0.373215i	0.297138	+	0.0314304i
$142$		0			0
$143$	−10.0452	+	5.79960i	−0.840022	+	0.484987i
$144$		0			0
$145$	3.72066	+	1.53257i	0.308984	+	0.127273i
$146$		0			0
$147$	−3.67231	+	11.5548i	−0.302887	+	0.953026i
$148$		0			0
$149$	10.6049	+	6.12276i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$149$	10.6049	+	6.12276i	0.868790	+	0.501596i	0.00184406	+	0.999998i	$0.499413\pi$
$150$		0			0
$151$	8.12863	+	14.0792i	0.661499	+	1.14575i	0.980222	+	0.197902i	$0.0634127\pi$
$151$	8.12863	+	14.0792i	0.661499	+	1.14575i	−0.318723	+	0.947848i	$0.603254\pi$
$152$		0			0
$153$	1.66320	−	7.77387i	0.134462	−	0.628480i
$154$		0			0
$155$	−2.04128	−	15.2725i	−0.163959	−	1.22672i
$156$		0			0
$157$	4.46980	+	7.74192i	0.356729	+	0.617873i	0.987412	−	0.158168i	$-0.0505586\pi$
$157$	4.46980	+	7.74192i	0.356729	+	0.617873i	−0.630683	+	0.776040i	$0.717225\pi$
$158$		0			0
$159$	−2.83758	−	2.06451i	−0.225034	−	0.163726i
$160$		0			0
$161$	−22.0575	−	2.23914i	−1.73837	−	0.176469i
$162$		0			0
$163$	−8.85883	−	5.11465i	−0.693877	−	0.400610i	0.111186	−	0.993800i	$-0.464535\pi$
$163$	−8.85883	−	5.11465i	−0.693877	−	0.400610i	−0.805063	+	0.593189i	$0.797869\pi$
$164$		0			0
$165$	7.97095	+	12.9694i	0.620537	+	1.00967i
$166$		0			0
$167$			21.6372i			1.67434i	0.546946	+	0.837168i	$0.315790\pi$
$167$			21.6372i			1.67434i	−0.546946	+	0.837168i	$0.684210\pi$
$168$		0			0
$169$	−4.29149			−0.330114
$170$		0			0
$171$	20.1630	−	6.52170i	1.54190	−	0.498727i
$172$		0			0
$173$	−6.28992	−	3.63149i	−0.478214	−	0.276097i	0.241458	−	0.970411i	$-0.422374\pi$
$173$	−6.28992	−	3.63149i	−0.478214	−	0.276097i	−0.719672	+	0.694314i	$0.755708\pi$
$174$		0			0
$175$	−4.64810	+	12.3853i	−0.351363	+	0.936239i
$176$		0			0
$177$	17.6318	+	12.8282i	1.32529	+	0.964225i
$178$		0			0
$179$	−2.97836	+	1.71956i	−0.222613	+	0.128526i	−0.607160	−	0.794580i	$-0.707691\pi$
$179$	−2.97836	+	1.71956i	−0.222613	+	0.128526i	0.384547	+	0.923106i	$0.374358\pi$
$180$		0			0
$181$			10.5865i			0.786886i	0.919349	+	0.393443i	$0.128716\pi$
$181$			10.5865i			0.786886i	−0.919349	+	0.393443i	$0.871284\pi$
$182$		0			0
$183$	−9.71417	−	1.02754i	−0.718092	−	0.0759577i
$184$		0			0
$185$	−17.0603	+	13.1443i	−1.25430	+	0.966391i
$186$		0			0
$187$	5.20788	−	9.02031i	0.380838	−	0.659630i
$188$		0			0
$189$	−13.6702	+	1.45830i	−0.994358	+	0.106075i
$190$		0			0
$191$	13.5893	+	7.84581i	0.983290	+	0.567703i	0.903262	−	0.429090i	$-0.141166\pi$
$191$	13.5893	+	7.84581i	0.983290	+	0.567703i	0.0800285	+	0.996793i	$0.474499\pi$
$192$		0			0
$193$	−13.0361	+	7.52638i	−0.938358	+	0.541761i	−0.889445	−	0.457042i	$-0.848909\pi$
$193$	−13.0361	+	7.52638i	−0.938358	+	0.541761i	−0.0489124	+	0.998803i	$0.515576\pi$
$194$		0			0
$195$	−0.314088	−	11.4249i	−0.0224923	−	0.818156i
$196$		0			0
$197$	−20.3934			−1.45297			−0.726485	−	0.687182i	$-0.758847\pi$
$197$	−20.3934			−1.45297			−0.726485	+	0.687182i	$0.758847\pi$
$198$		0			0
$199$	−7.43342	+	4.29169i	−0.526941	+	0.304230i	−0.739770	−	0.672860i	$-0.765066\pi$
$199$	−7.43342	+	4.29169i	−0.526941	+	0.304230i	0.212829	+	0.977089i	$0.431732\pi$
$200$		0			0
$201$	−10.1525	+	13.9542i	−0.716103	+	0.984252i
$202$		0			0
$203$	−4.34266	+	1.95199i	−0.304795	+	0.137003i
$204$		0			0
$205$	−2.90712	+	7.05770i	−0.203042	+	0.492931i
$206$		0			0
$207$	−7.73665	−	23.9193i	−0.537735	−	1.66250i
$208$		0			0
$209$	27.7649			1.92054
$210$		0			0
$211$	−8.30237			−0.571559			−0.285779	−	0.958295i	$-0.592252\pi$
$211$	−8.30237			−0.571559			−0.285779	+	0.958295i	$0.592252\pi$
$212$		0			0
$213$	−6.06608	−	13.6491i	−0.415641	−	0.935220i
$214$		0			0
$215$	9.56672	+	3.94060i	0.652445	+	0.268747i
$216$		0			0
$217$	14.7874	+	10.6637i	1.00384	+	0.723896i
$218$		0			0
$219$	−11.6005	−	8.44004i	−0.783887	−	0.570325i
$220$		0			0
$221$	−6.77232	+	3.91000i	−0.455556	+	0.263015i
$222$		0			0
$223$	−1.13362			−0.0759130			−0.0379565	−	0.999279i	$-0.512085\pi$
$223$	−1.13362			−0.0759130			−0.0379565	+	0.999279i	$0.512085\pi$
$224$		0			0
$225$	−14.9773	+	0.824121i	−0.998490	+	0.0549414i
$226$		0			0
$227$	11.3932	−	6.57787i	0.756193	−	0.436589i	−0.0717339	−	0.997424i	$-0.522853\pi$
$227$	11.3932	−	6.57787i	0.756193	−	0.436589i	0.827927	+	0.560835i	$0.189520\pi$
$228$		0			0
$229$	8.94517	+	5.16450i	0.591114	+	0.341280i	0.765538	−	0.643391i	$-0.222473\pi$
$229$	8.94517	+	5.16450i	0.591114	+	0.341280i	−0.174424	+	0.984671i	$0.555806\pi$
$230$		0			0
$231$	−17.6293	−	3.69406i	−1.15992	−	0.243052i
$232$		0			0
$233$	−2.63164	+	4.55814i	−0.172405	+	0.298614i	−0.939260	−	0.343206i	$-0.888487\pi$
$233$	−2.63164	+	4.55814i	−0.172405	+	0.298614i	0.766855	+	0.641820i	$0.221820\pi$
$234$		0			0
$235$	−3.62841	+	2.79555i	−0.236692	+	0.182362i
$236$		0			0
$237$	−2.49269	+	23.5654i	−0.161917	+	1.53074i
$238$		0			0
$239$		−	20.4664i		−	1.32386i	−0.749565	−	0.661931i	$-0.769737\pi$
$239$		−	20.4664i		−	1.32386i	0.749565	−	0.661931i	$-0.230263\pi$
$240$		0			0
$241$	1.05049	−	0.606500i	0.0676680	−	0.0390681i	−0.465784	−	0.884898i	$-0.654228\pi$
$241$	1.05049	−	0.606500i	0.0676680	−	0.0390681i	0.533452	+	0.845830i	$0.320894\pi$
$242$		0			0
$243$	−7.74926	−	13.5259i	−0.497116	−	0.867684i
$244$		0			0
$245$	−6.86649	−	14.0660i	−0.438684	−	0.898642i
$246$		0			0
$247$	−18.0527	−	10.4228i	−1.14867	−	0.663184i
$248$		0			0
$249$	6.00422	+	13.5099i	0.380502	+	0.856155i
$250$		0			0
$251$	10.9296			0.689873			0.344936	−	0.938626i	$-0.387900\pi$
$251$	10.9296			0.689873			0.344936	+	0.938626i	$0.387900\pi$
$252$		0			0
$253$		−	32.9373i		−	2.07075i
$254$		0			0
$255$	5.37389	+	8.74377i	0.336526	+	0.547556i
$256$		0			0
$257$	7.89770	+	4.55974i	0.492645	+	0.284429i	0.725671	−	0.688042i	$-0.241529\pi$
$257$	7.89770	+	4.55974i	0.492645	+	0.284429i	−0.233026	+	0.972470i	$0.574863\pi$
$258$		0			0
$259$	2.57361	−	25.3523i	0.159917	−	1.57531i
$260$		0			0
$261$	−4.00719	−	3.61776i	−0.248039	−	0.223934i
$262$		0			0
$263$	9.23403	+	15.9938i	0.569395	+	0.986221i	0.996626	+	0.0820781i	$0.0261557\pi$
$263$	9.23403	+	15.9938i	0.569395	+	0.986221i	−0.427231	+	0.904142i	$0.640511\pi$
$264$		0			0
$265$	4.49034	−	0.600167i	0.275839	−	0.0368680i
$266$		0			0
$267$	−1.57732	+	14.9118i	−0.0965306	+	0.912584i
$268$		0			0
$269$	7.45031	+	12.9043i	0.454253	+	0.786790i	0.998645	−	0.0520413i	$-0.0165727\pi$
$269$	7.45031	+	12.9043i	0.454253	+	0.786790i	−0.544392	+	0.838831i	$0.683239\pi$
$270$		0			0
$271$	−11.6404	−	6.72061i	−0.707106	−	0.408248i	0.102883	−	0.994693i	$-0.467193\pi$
$271$	−11.6404	−	6.72061i	−0.707106	−	0.408248i	−0.809988	+	0.586446i	$0.800527\pi$
$272$		0			0
$273$	10.0758	+	9.01978i	0.609817	+	0.545902i
$274$		0			0
$275$	−19.0031	−	5.01170i	−1.14593	−	0.302217i
$276$		0			0
$277$	−3.58231	+	2.06825i	−0.215240	+	0.124269i	−0.603744	−	0.797178i	$-0.706325\pi$
$277$	−3.58231	+	2.06825i	−0.215240	+	0.124269i	0.388504	+	0.921447i	$0.372992\pi$
$278$		0			0
$279$	−4.32494	+	20.2149i	−0.258928	+	1.21024i
$280$		0			0
$281$		−	16.7240i		−	0.997672i	−0.866696	−	0.498836i	$-0.833761\pi$
$281$		−	16.7240i		−	0.997672i	0.866696	−	0.498836i	$-0.166239\pi$
$282$		0			0
$283$	−0.888329	−	1.53863i	−0.0528057	−	0.0914622i	0.838414	−	0.545033i	$-0.183483\pi$
$283$	−0.888329	−	1.53863i	−0.0528057	−	0.0914622i	−0.891220	+	0.453571i	$0.850150\pi$
$284$		0			0
$285$	−13.0228	+	24.0598i	−0.771403	+	1.42518i
$286$		0			0
$287$	−3.70271	−	8.23756i	−0.218564	−	0.486248i
$288$		0			0
$289$	−4.98893	+	8.64108i	−0.293466	+	0.508299i
$290$		0			0
$291$	−8.95590	+	3.98028i	−0.525004	+	0.233328i
$292$		0			0
$293$		−	8.59767i		−	0.502281i	−0.967951	−	0.251141i	$-0.919194\pi$
$293$		−	8.59767i		−	0.502281i	0.967951	−	0.251141i	$-0.0808056\pi$
$294$		0			0
$295$	−27.9015	+	3.72924i	−1.62449	+	0.217125i
$296$		0			0
$297$	−4.20647	−	19.9860i	−0.244084	−	1.15970i
$298$		0			0
$299$	−12.3644	+	21.4158i	−0.715054	+	1.23851i
$300$		0			0
$301$	−11.1660	+	5.01903i	−0.643599	+	0.289292i
$302$		0			0
$303$	−19.8074	−	14.4111i	−1.13791	−	0.827895i
$304$		0			0
$305$	9.98976	−	7.69673i	0.572012	−	0.440713i
$306$		0			0
$307$	16.4849			0.940842			0.470421	−	0.882442i	$-0.344102\pi$
$307$	16.4849			0.940842			0.470421	+	0.882442i	$0.344102\pi$
$308$		0			0
$309$	2.58822	−	24.4686i	0.147239	−	1.39197i
$310$		0			0
$311$	16.7219	+	28.9632i	0.948214	+	1.64235i	0.749185	+	0.662361i	$0.230445\pi$
$311$	16.7219	+	28.9632i	0.948214	+	1.64235i	0.199029	+	0.979994i	$0.436221\pi$
$312$		0			0
$313$	−11.2653	+	19.5121i	−0.636754	+	1.10289i	0.349387	+	0.936978i	$0.386390\pi$
$313$	−11.2653	+	19.5121i	−0.636754	+	1.10289i	−0.986141	+	0.165911i	$0.946943\pi$
$314$		0			0
$315$	11.4699	−	13.5441i	0.646255	−	0.763121i
$316$		0			0
$317$	3.99907	−	6.92660i	0.224610	−	0.389036i	−0.731592	−	0.681743i	$-0.761222\pi$
$317$	3.99907	−	6.92660i	0.224610	−	0.389036i	0.956202	+	0.292706i	$0.0945558\pi$
$318$		0			0
$319$	−3.53665	−	6.12566i	−0.198015	−	0.342971i
$320$		0			0
$321$	−0.885410	+	8.37052i	−0.0494188	+	0.467197i
$322$		0			0
$323$	18.7187			1.04154
$324$		0			0
$325$	10.4745	+	10.3922i	0.581018	+	0.576458i
$326$		0			0
$327$	1.00844	+	0.733701i	0.0557669	+	0.0405737i
$328$		0			0
$329$	0.547359	−	5.39195i	0.0301769	−	0.297268i
$330$		0			0
$331$	17.0961	−	29.6113i	0.939686	−	1.62758i	0.173630	−	0.984811i	$-0.444450\pi$
$331$	17.0961	−	29.6113i	0.939686	−	1.62758i	0.766056	−	0.642774i	$-0.222216\pi$
$332$		0			0
$333$	27.4922	−	8.89231i	1.50656	−	0.487295i
$334$		0			0
$335$	−2.95141	−	22.0819i	−0.161253	−	1.20646i
$336$		0			0
$337$		−	18.9740i		−	1.03358i	−0.856113	−	0.516789i	$-0.827127\pi$
$337$		−	18.9740i		−	1.03358i	0.856113	−	0.516789i	$-0.172873\pi$
$338$		0			0
$339$	3.35970	−	1.49315i	0.182474	−	0.0810970i
$340$		0			0
$341$	−13.5424	+	23.4561i	−0.733362	+	1.27022i
$342$		0			0
$343$	17.6738	+	5.53505i	0.954295	+	0.298865i
$344$		0			0
$345$	28.5420	+	15.4488i	1.53665	+	0.831738i
$346$		0			0
$347$	−10.9257	−	18.9238i	−0.586520	−	1.01588i	−0.994684	−	0.102973i	$-0.967164\pi$
$347$	−10.9257	−	18.9238i	−0.586520	−	1.01588i	0.408164	−	0.912908i	$-0.366169\pi$
$348$		0			0
$349$			0.585198i			0.0313249i	0.999877	+	0.0156625i	$0.00498572\pi$
$349$			0.585198i			0.0313249i	−0.999877	+	0.0156625i	$0.995014\pi$
$350$		0			0
$351$	−4.76756	+	14.5740i	−0.254473	+	0.777900i
$352$		0			0
$353$	−20.8506	+	12.0381i	−1.10976	+	0.640722i	−0.938768	−	0.344549i	$-0.888032\pi$
$353$	−20.8506	+	12.0381i	−1.10976	+	0.640722i	−0.170996	+	0.985272i	$0.554698\pi$
$354$		0			0
$355$	17.8295	+	7.34408i	0.946289	+	0.389783i
$356$		0			0
$357$	−11.8854	−	2.49048i	−0.629042	−	0.131810i
$358$		0			0
$359$	14.5151	+	8.38032i	0.766080	+	0.442296i	0.831474	−	0.555563i	$-0.187497\pi$
$359$	14.5151	+	8.38032i	0.766080	+	0.442296i	−0.0653947	+	0.997859i	$0.520831\pi$
$360$		0			0
$361$	15.4489	+	26.7582i	0.813098	+	1.40833i
$362$		0			0
$363$	0.810660	−	7.66385i	0.0425486	−	0.402248i
$364$		0			0
$365$	18.3572	−	2.45358i	0.960862	−	0.128426i
$366$		0			0
$367$	13.6631	+	23.6652i	0.713209	+	1.23531i	0.963646	+	0.267181i	$0.0860921\pi$
$367$	13.6631	+	23.6652i	0.713209	+	1.23531i	−0.250438	+	0.968133i	$0.580575\pi$
$368$		0			0
$369$	6.86250	−	7.60121i	0.357248	−	0.395703i
$370$		0			0
$371$	−3.13528	+	4.34773i	−0.162775	+	0.225723i
$372$		0			0
$373$	9.36341	+	5.40597i	0.484819	+	0.279911i	0.722423	−	0.691452i	$-0.243029\pi$
$373$	9.36341	+	5.40597i	0.484819	+	0.279911i	−0.237603	+	0.971362i	$0.576362\pi$
$374$		0			0
$375$	13.2561	−	14.1165i	0.684541	−	0.728975i
$376$		0			0
$377$			5.31054i			0.273507i
$378$		0			0
$379$	26.0188			1.33650			0.668248	−	0.743938i	$-0.267044\pi$
$379$	26.0188			1.33650			0.668248	+	0.743938i	$0.267044\pi$
$380$		0			0
$381$	4.15961	+	9.35939i	0.213103	+	0.479496i
$382$		0			0
$383$	−5.91387	−	3.41437i	−0.302185	−	0.174466i	0.341239	−	0.939976i	$-0.389153\pi$
$383$	−5.91387	−	3.41437i	−0.302185	−	0.174466i	−0.643424	+	0.765510i	$0.722487\pi$
$384$		0			0
$385$	19.7595	−	12.2593i	1.00704	−	0.624790i
$386$		0			0
$387$	−10.3035	−	9.30213i	−0.523754	−	0.472854i
$388$		0			0
$389$	3.14675	−	1.81678i	0.159547	−	0.0921143i	−0.418101	−	0.908401i	$-0.637304\pi$
$389$	3.14675	−	1.81678i	0.159547	−	0.0921143i	0.577648	+	0.816286i	$0.303971\pi$
$390$		0			0
$391$		−	22.2059i		−	1.12300i
$392$		0			0
$393$	−1.47381	+	13.9332i	−0.0743439	+	0.702835i
$394$		0			0
$395$	−18.6714	−	24.2340i	−0.939458	−	1.21934i
$396$		0			0
$397$	−11.2860	+	19.5480i	−0.566431	+	0.981087i	0.430484	+	0.902598i	$0.358343\pi$
$397$	−11.2860	+	19.5480i	−0.566431	+	0.981087i	−0.996915	+	0.0784885i	$0.974991\pi$
$398$		0			0
$399$	−10.0919	−	30.7572i	−0.505226	−	1.53979i
$400$		0			0
$401$	−21.1988	−	12.2392i	−1.05862	−	0.611195i	−0.133570	−	0.991039i	$-0.542644\pi$
$401$	−21.1988	−	12.2392i	−1.05862	−	0.611195i	−0.925050	+	0.379845i	$0.875977\pi$
$402$		0			0
$403$	17.6105	−	10.1674i	0.877243	−	0.506476i
$404$		0			0
$405$	19.2919	+	5.72905i	0.958623	+	0.284679i
$406$		0			0
$407$	37.8573			1.87652
$408$		0			0
$409$	13.4224	−	7.74945i	0.663697	−	0.383186i	−0.129987	−	0.991516i	$-0.541494\pi$
$409$	13.4224	−	7.74945i	0.663697	−	0.383186i	0.793684	+	0.608330i	$0.208160\pi$
$410$		0			0
$411$	0.0234057	+	0.0170290i	0.00115452	+	0.000839980i
$412$		0			0
$413$	19.4816	−	27.0154i	0.958627	−	1.32934i
$414$		0			0
$415$	−17.6476	−	7.26919i	−0.866288	−	0.356830i
$416$		0			0
$417$	−5.58472	−	12.5660i	−0.273485	−	0.615359i
$418$		0			0
$419$	21.7751			1.06378			0.531891	−	0.846813i	$-0.321482\pi$
$419$	21.7751			1.06378			0.531891	+	0.846813i	$0.321482\pi$
$420$		0			0
$421$	18.2494			0.889422			0.444711	−	0.895674i	$-0.353306\pi$
$421$	18.2494			0.889422			0.444711	+	0.895674i	$0.353306\pi$
$422$		0			0
$423$	5.84707	−	1.89123i	0.284294	−	0.0919546i
$424$		0			0
$425$	−12.8116	−	3.37881i	−0.621454	−	0.163896i
$426$		0			0
$427$	−1.50699	+	14.8451i	−0.0729284	+	0.718406i
$428$		0			0
$429$	−11.8197	+	16.2456i	−0.570658	+	0.784346i
$430$		0			0
$431$	2.51876	−	1.45420i	0.121324	−	0.0700466i	−0.438110	−	0.898921i	$-0.644352\pi$
$431$	2.51876	−	1.45420i	0.121324	−	0.0700466i	0.559434	+	0.828875i	$0.311019\pi$
$432$		0			0
$433$	−32.1907			−1.54698			−0.773492	−	0.633806i	$-0.781492\pi$
$433$	−32.1907			−1.54698			−0.773492	+	0.633806i	$0.781492\pi$
$434$		0			0
$435$	6.96704	−	0.191534i	0.334044	−	0.00918335i
$436$		0			0
$437$	51.2630	−	29.5967i	2.45224	−	1.41580i
$438$		0			0
$439$	−18.2370	−	10.5291i	−0.870404	−	0.502528i	−0.00292144	−	0.999996i	$-0.500930\pi$
$439$	−18.2370	−	10.5291i	−0.870404	−	0.502528i	−0.867482	+	0.497468i	$0.834263\pi$
$440$		0			0
$441$	2.31563	+	20.8719i	0.110268	+	0.993902i
$442$		0			0
$443$	−2.49994	+	4.33002i	−0.118776	+	0.205725i	−0.919283	−	0.393598i	$-0.871230\pi$
$443$	−2.49994	+	4.33002i	−0.118776	+	0.205725i	0.800507	+	0.599323i	$0.204564\pi$
$444$		0			0
$445$	−11.8149	−	15.3348i	−0.560079	−	0.726939i
$446$		0			0
$447$	21.0922	+	2.23107i	0.997627	+	0.105526i
$448$		0			0
$449$			22.9527i			1.08321i	0.840634	+	0.541603i	$0.182182\pi$
$449$			22.9527i			1.08321i	−0.840634	+	0.541603i	$0.817818\pi$
$450$		0			0
$451$	11.6197	−	6.70865i	0.547151	−	0.315898i
$452$		0			0
$453$	22.7696	+	16.5663i	1.06981	+	0.778351i
$454$		0			0
$455$	−17.4497	+	0.553378i	−0.818054	+	0.0259428i
$456$		0			0
$457$	−14.2881	−	8.24924i	−0.668369	−	0.385883i	0.127089	−	0.991891i	$-0.459437\pi$
$457$	−14.2881	−	8.24924i	−0.668369	−	0.385883i	−0.795458	+	0.606008i	$0.792770\pi$
$458$		0			0
$459$	−2.83594	−	13.4742i	−0.132370	−	0.628924i
$460$		0			0
$461$	−6.69419			−0.311780			−0.155890	−	0.987774i	$-0.549824\pi$
$461$	−6.69419			−0.311780			−0.155890	+	0.987774i	$0.549824\pi$
$462$		0			0
$463$		−	26.4375i		−	1.22865i	−0.789052	−	0.614327i	$-0.789428\pi$
$463$		−	26.4375i		−	1.22865i	0.789052	−	0.614327i	$-0.210572\pi$
$464$		0			0
$465$	−13.9741	−	22.7370i	−0.648033	−	1.05440i
$466$		0			0
$467$	16.4994	+	9.52595i	0.763503	+	0.440809i	0.830552	−	0.556941i	$-0.188025\pi$
$467$	16.4994	+	9.52595i	0.763503	+	0.440809i	−0.0670492	+	0.997750i	$0.521358\pi$
$468$		0			0
$469$	21.3806	+	15.4182i	0.987264	+	0.711945i
$470$		0			0
$471$	12.5206	+	9.10951i	0.576920	+	0.419744i
$472$		0			0
$473$	−9.09359	−	15.7506i	−0.418124	−	0.724211i
$474$		0			0
$475$	−9.27562	−	34.0794i	−0.425595	−	1.56367i
$476$		0			0
$477$	−5.94349	−	1.27160i	−0.272134	−	0.0582225i
$478$		0			0
$479$	0.608489	+	1.05393i	0.0278026	+	0.0481554i	0.879592	−	0.475729i	$-0.157816\pi$
$479$	0.608489	+	1.05393i	0.0278026	+	0.0481554i	−0.851789	+	0.523884i	$0.824482\pi$
$480$		0			0
$481$	−24.6148	−	14.2114i	−1.12234	−	0.647983i
$482$		0			0
$483$	−36.4871	+	11.9719i	−1.66022	+	0.544742i
$484$		0			0
$485$	4.81885	−	11.6989i	0.218813	−	0.531218i
$486$		0			0
$487$	−14.9303	+	8.62003i	−0.676558	+	0.390611i	−0.798557	−	0.601919i	$-0.794403\pi$
$487$	−14.9303	+	8.62003i	−0.676558	+	0.390611i	0.121999	+	0.992530i	$0.461070\pi$
$488$		0			0
$489$	−17.6194	−	1.86373i	−0.796775	−	0.0842806i
$490$		0			0
$491$		−	33.3800i		−	1.50642i	−0.657780	−	0.753210i	$-0.728504\pi$
$491$		−	33.3800i		−	1.50642i	0.657780	−	0.753210i	$-0.271496\pi$
$492$		0			0
$493$	−2.38436	−	4.12983i	−0.107386	−	0.185998i
$494$		0			0
$495$	21.7393	+	14.9206i	0.977111	+	0.670631i
$496$		0			0
$497$	−20.8101	+	9.35395i	−0.933459	+	0.419582i
$498$		0			0
$499$	7.02003	−	12.1591i	0.314260	−	0.544314i	−0.665020	−	0.746826i	$-0.731577\pi$
$499$	7.02003	−	12.1591i	0.314260	−	0.544314i	0.979280	+	0.202511i	$0.0649103\pi$
$500$		0			0
$501$	15.2204	+	34.2468i	0.679995	+	1.53003i
$502$		0			0
$503$		−	23.1678i		−	1.03300i	−0.856287	−	0.516501i	$-0.827234\pi$
$503$		−	23.1678i		−	1.03300i	0.856287	−	0.516501i	$-0.172766\pi$
$504$		0			0
$505$	31.3444	−	4.18940i	1.39481	−	0.186426i
$506$		0			0
$507$	−6.79246	+	3.01878i	−0.301664	+	0.134069i
$508$		0			0
$509$	1.13912	−	1.97302i	0.0504907	−	0.0874525i	−0.839675	−	0.543089i	$-0.817255\pi$
$509$	1.13912	−	1.97302i	0.0504907	−	0.0874525i	0.890166	+	0.455636i	$0.150588\pi$
$510$		0			0
$511$	−12.8175	+	17.7742i	−0.567014	+	0.786286i
$512$		0			0
$513$	27.3259	−	24.5058i	1.20647	−	1.08196i
$514$		0			0
$515$	19.3870	+	25.1628i	0.854292	+	1.10880i
$516$		0			0
$517$	8.05154			0.354106
$518$		0			0
$519$	−12.5100	−	1.32328i	−0.549130	−	0.0580854i
$520$		0			0
$521$	−1.33810	−	2.31766i	−0.0586232	−	0.101538i	0.835224	−	0.549909i	$-0.185338\pi$
$521$	−1.33810	−	2.31766i	−0.0586232	−	0.101538i	−0.893848	+	0.448371i	$0.852004\pi$
$522$		0			0
$523$	−0.773728	+	1.34014i	−0.0338327	+	0.0586000i	−0.882446	−	0.470414i	$-0.844105\pi$
$523$	−0.773728	+	1.34014i	−0.0338327	+	0.0586000i	0.848613	+	0.529014i	$0.177438\pi$
$524$		0			0
$525$	1.35535	+	22.8728i	0.0591521	+	0.998249i
$526$		0			0
$527$	−9.13008	+	15.8138i	−0.397713	+	0.688858i
$528$		0			0
$529$	−23.6104	−	40.8943i	−1.02654	−	1.77801i
$530$		0			0
$531$	36.9309	+	7.90131i	1.60267	+	0.342887i
$532$		0			0
$533$	−10.0735			−0.436333
$534$		0			0
$535$	−6.63213	−	8.60799i	−0.286732	−	0.372156i
$536$		0			0
$537$	−3.50447	+	4.81675i	−0.151229	+	0.207858i
$538$		0			0
$539$	−5.52915	+	26.9527i	−0.238157	+	1.16094i
$540$		0			0
$541$	12.2069	−	21.1429i	0.524814	−	0.909005i	−0.474768	−	0.880111i	$-0.657468\pi$
$541$	12.2069	−	21.1429i	0.524814	−	0.909005i	0.999582	−	0.0288939i	$-0.00919848\pi$
$542$		0			0
$543$	7.44690	+	16.7560i	0.319577	+	0.719069i
$544$		0			0
$545$	−1.59581	+	0.213292i	−0.0683571	+	0.00913643i
$546$		0			0
$547$		−	5.82017i		−	0.248853i	−0.992229	−	0.124426i	$-0.960291\pi$
$547$		−	5.82017i		−	0.248853i	0.992229	−	0.124426i	$-0.0397090\pi$
$548$		0			0
$549$	−16.0982	+	5.20693i	−0.687053	+	0.222226i
$550$		0			0
$551$	6.35590	−	11.0087i	0.270770	−	0.468988i
$552$		0			0
$553$	36.0125	+	3.65578i	1.53141	+	0.155460i
$554$		0			0
$555$	−17.7565	+	32.8054i	−0.753721	+	1.39251i
$556$		0			0
$557$	−3.11728	−	5.39929i	−0.132083	−	0.228775i	0.792396	−	0.610007i	$-0.208833\pi$
$557$	−3.11728	−	5.39929i	−0.132083	−	0.228775i	−0.924480	+	0.381232i	$0.875500\pi$
$558$		0			0
$559$			13.6547i			0.577531i
$560$		0			0
$561$	1.89770	−	17.9405i	0.0801209	−	0.757450i
$562$		0			0
$563$	8.36154	−	4.82754i	0.352397	−	0.203456i	−0.313343	−	0.949640i	$-0.601449\pi$
$563$	8.36154	−	4.82754i	0.352397	−	0.203456i	0.665740	+	0.746183i	$0.268116\pi$
$564$		0			0
$565$	−1.80773	+	4.38869i	−0.0760518	+	0.184633i
$566$		0			0
$567$	−20.6110	+	11.9242i	−0.865580	+	0.500771i
$568$		0			0
$569$	10.2337	+	5.90844i	0.429020	+	0.247695i	0.698929	−	0.715191i	$-0.253660\pi$
$569$	10.2337	+	5.90844i	0.429020	+	0.247695i	−0.269909	+	0.962886i	$0.586994\pi$
$570$		0			0
$571$	−7.94370	−	13.7589i	−0.332434	−	0.575792i	0.650555	−	0.759459i	$-0.274536\pi$
$571$	−7.94370	−	13.7589i	−0.332434	−	0.575792i	−0.982988	+	0.183667i	$0.941203\pi$
$572$		0			0
$573$	27.0279	+	2.85893i	1.12911	+	0.119434i
$574$		0			0
$575$	−40.4282	+	11.0036i	−1.68597	+	0.458882i
$576$		0			0
$577$	−9.68169	−	16.7692i	−0.403054	−	0.698110i	0.591039	−	0.806643i	$-0.298718\pi$
$577$	−9.68169	−	16.7692i	−0.403054	−	0.698110i	−0.994093	+	0.108533i	$0.965385\pi$
$578$		0			0
$579$	−15.3389	+	21.0826i	−0.637461	+	0.876164i
$580$		0			0
$581$	20.5978	−	9.25856i	0.854542	−	0.384110i
$582$		0			0
$583$	−6.89646	−	3.98167i	−0.285622	−	0.164904i
$584$		0			0
$585$	−8.53383	−	17.8622i	−0.352830	−	0.738509i
$586$		0			0
$587$		−	18.3091i		−	0.755699i	−0.925867	−	0.377849i	$-0.876664\pi$
$587$		−	18.3091i		−	0.755699i	0.925867	−	0.377849i	$-0.123336\pi$
$588$		0			0
$589$	−48.6755			−2.00564
$590$		0			0
$591$	−32.2782	+	14.3454i	−1.32775	+	0.590093i
$592$		0			0
$593$	2.06686	+	1.19330i	0.0848759	+	0.0490031i	0.541837	−	0.840483i	$-0.317729\pi$
$593$	2.06686	+	1.19330i	0.0848759	+	0.0490031i	−0.456961	+	0.889487i	$0.651062\pi$
$594$		0			0
$595$	13.3216	−	8.26501i	0.546132	−	0.338832i
$596$		0			0
$597$	−8.74651	+	12.0217i	−0.357971	+	0.492016i
$598$		0			0
$599$	−14.4957	+	8.36909i	−0.592278	+	0.341952i	−0.765998	−	0.642843i	$-0.777755\pi$
$599$	−14.4957	+	8.36909i	−0.592278	+	0.341952i	0.173720	+	0.984795i	$0.444421\pi$
$600$		0			0
$601$		−	4.00150i		−	0.163225i	−0.996664	−	0.0816123i	$-0.973993\pi$
$601$		−	4.00150i		−	0.163225i	0.996664	−	0.0816123i	$-0.0260069\pi$
$602$		0			0
$603$	−6.25327	+	29.2280i	−0.254653	+	1.19026i
$604$		0			0
$605$	6.07222	+	7.88127i	0.246871	+	0.320419i
$606$		0			0
$607$	15.9171	−	27.5692i	0.646055	−	1.11900i	−0.338002	−	0.941146i	$-0.609751\pi$
$607$	15.9171	−	27.5692i	0.646055	−	1.11900i	0.984057	−	0.177855i	$-0.0569157\pi$
$608$		0			0
$609$	−5.50036	+	6.14434i	−0.222886	+	0.248981i
$610$		0			0
$611$	−5.23511	−	3.02249i	−0.211790	−	0.122277i
$612$		0			0
$613$	−31.1444	+	17.9812i	−1.25791	+	0.726255i	−0.972668	−	0.232200i	$-0.925408\pi$
$613$	−31.1444	+	17.9812i	−1.25791	+	0.726255i	−0.285243	+	0.958455i	$0.592074\pi$
$614$		0			0
$615$	0.363319	+	13.2157i	0.0146505	+	0.532909i
$616$		0			0
$617$	0.217492			0.00875590			0.00437795	−	0.999990i	$-0.498606\pi$
$617$	0.217492			0.00875590			0.00437795	+	0.999990i	$0.498606\pi$
$618$		0			0
$619$	−23.4686	+	13.5496i	−0.943284	+	0.544605i	−0.890988	−	0.454026i	$-0.849987\pi$
$619$	−23.4686	+	13.5496i	−0.943284	+	0.544605i	−0.0522960	+	0.998632i	$0.516654\pi$
$620$		0			0
$621$	−29.0710	−	32.4166i	−1.16658	−	1.30083i
$622$		0			0
$623$	22.7880	+	2.31331i	0.912983	+	0.0926808i
$624$		0			0
$625$	0.197008	+	24.9992i	0.00788030	+	0.999969i
$626$		0			0
$627$	43.9456	−	19.5308i	1.75502	−	0.779986i
$628$		0			0
$629$	25.5228			1.01766
$630$		0			0
$631$	36.0774			1.43622			0.718109	−	0.695930i	$-0.245008\pi$
$631$	36.0774			1.43622			0.718109	+	0.695930i	$0.245008\pi$
$632$		0			0
$633$	−13.1408	+	5.84018i	−0.522299	+	0.232126i
$634$		0			0
$635$	−12.2259	−	5.03595i	−0.485171	−	0.199846i
$636$		0			0
$637$	13.7129	−	15.4490i	0.543325	−	0.612114i
$638$		0			0
$639$	−19.2025	−	17.3363i	−0.759639	−	0.685815i
$640$		0			0
$641$	−34.8553	+	20.1237i	−1.37670	+	0.794840i	−0.991761	−	0.128101i	$-0.959112\pi$
$641$	−34.8553	+	20.1237i	−1.37670	+	0.794840i	−0.384942	+	0.922941i	$0.625778\pi$
$642$		0			0
$643$	24.0636			0.948975			0.474487	−	0.880262i	$-0.342633\pi$
$643$	24.0636			0.948975			0.474487	+	0.880262i	$0.342633\pi$
$644$		0			0
$645$	17.9139	−	0.492480i	0.705360	−	0.0193914i
$646$		0			0
$647$	−15.9816	+	9.22696i	−0.628300	+	0.362749i	−0.780094	−	0.625663i	$-0.784829\pi$
$647$	−15.9816	+	9.22696i	−0.628300	+	0.362749i	0.151793	+	0.988412i	$0.451495\pi$
$648$		0			0
$649$	42.8524	+	24.7408i	1.68210	+	0.971162i
$650$		0			0
$651$	30.9064	+	6.47617i	1.21132	+	0.253821i
$652$		0			0
$653$	2.74369	−	4.75222i	0.107369	−	0.185969i	−0.807335	−	0.590094i	$-0.799091\pi$
$653$	2.74369	−	4.75222i	0.107369	−	0.185969i	0.914704	+	0.404125i	$0.132424\pi$
$654$		0			0
$655$	−11.0395	−	14.3284i	−0.431350	−	0.559859i
$656$		0			0
$657$	−24.2980	−	5.19850i	−0.947954	−	0.202813i
$658$		0			0
$659$			28.4537i			1.10840i	0.832384	+	0.554199i	$0.186975\pi$
$659$			28.4537i			1.10840i	−0.832384	+	0.554199i	$0.813025\pi$
$660$		0			0
$661$	3.58946	−	2.07238i	0.139614	−	0.0806061i	−0.428566	−	0.903510i	$-0.640981\pi$
$661$	3.58946	−	2.07238i	0.139614	−	0.0806061i	0.568180	+	0.822904i	$0.307648\pi$
$662$		0			0
$663$	−7.96863	+	10.9525i	−0.309476	+	0.425362i
$664$		0			0
$665$	36.8355	+	19.7374i	1.42842	+	0.765385i
$666$		0			0
$667$	−13.0596	−	7.53996i	−0.505670	−	0.291948i
$668$		0			0
$669$	−1.79427	+	0.797431i	−0.0693705	+	0.0308305i
$670$		0			0
$671$	−22.1675			−0.855768
$672$		0			0
$673$			48.2923i			1.86153i	0.365616	+	0.930766i	$0.380858\pi$
$673$			48.2923i			1.86153i	−0.365616	+	0.930766i	$0.619142\pi$
$674$		0			0
$675$	−23.1261	+	11.8400i	−0.890122	+	0.455721i
$676$		0			0
$677$	−10.8496	−	6.26402i	−0.416984	−	0.240746i	0.276802	−	0.960927i	$-0.410725\pi$
$677$	−10.8496	−	6.26402i	−0.416984	−	0.240746i	−0.693786	+	0.720181i	$0.744059\pi$
$678$		0			0
$679$	6.13763	+	13.6546i	0.235541	+	0.524015i
$680$		0			0
$681$	13.4058	−	18.4257i	0.513711	−	0.706073i
$682$		0			0
$683$	−2.20645	−	3.82168i	−0.0844275	−	0.146233i	0.820720	−	0.571331i	$-0.193573\pi$
$683$	−2.20645	−	3.82168i	−0.0844275	−	0.146233i	−0.905147	+	0.425098i	$0.860239\pi$
$684$		0			0
$685$	−0.0370385	+	0.00495046i	−0.00141517	+	0.000189147i
$686$		0			0
$687$	17.7911	+	1.88189i	0.678773	+	0.0717986i
$688$		0			0
$689$	2.98938	+	5.17776i	0.113886	+	0.197257i
$690$		0			0
$691$	−20.8060	−	12.0123i	−0.791497	−	0.456971i	0.0489926	−	0.998799i	$-0.484399\pi$
$691$	−20.8060	−	12.0123i	−0.791497	−	0.456971i	−0.840489	+	0.541828i	$0.817732\pi$
$692$		0			0
$693$	−30.5017	+	6.55419i	−1.15866	+	0.248973i
$694$		0			0
$695$	16.4146	+	6.76131i	0.622642	+	0.256471i
$696$		0			0
$697$	7.83384	−	4.52287i	0.296728	−	0.171316i
$698$		0			0
$699$	−0.958944	+	9.06570i	−0.0362706	+	0.342896i
$700$		0			0
$701$		−	30.2717i		−	1.14335i	−0.820481	−	0.571674i	$-0.806294\pi$
$701$		−	30.2717i		−	1.14335i	0.820481	−	0.571674i	$-0.193706\pi$
$702$		0			0
$703$	34.0177	+	58.9203i	1.28300	+	2.22222i
$704$		0			0
$705$	−3.77647	+	6.97709i	−0.142230	+	0.262772i
$706$		0			0
$707$	−21.8855	+	30.3489i	−0.823088	+	1.14139i
$708$		0			0
$709$	11.8076	−	20.4514i	0.443444	−	0.768067i	−0.554499	−	0.832185i	$-0.687090\pi$
$709$	11.8076	−	20.4514i	0.443444	−	0.768067i	0.997942	+	0.0641175i	$0.0204232\pi$
$710$		0			0
$711$	12.6314	+	39.0523i	0.473715	+	1.46457i
$712$		0			0
$713$			57.7434i			2.16251i
$714$		0			0
$715$	−3.43606	−	25.7080i	−0.128501	−	0.961424i
$716$		0			0
$717$	−14.3968	−	32.3937i	−0.537658	−	1.20977i
$718$		0			0
$719$	19.4246	−	33.6445i	0.724417	−	1.25473i	−0.234797	−	0.972044i	$-0.575442\pi$
$719$	19.4246	−	33.6445i	0.724417	−	1.25473i	0.959214	−	0.282682i	$-0.0912242\pi$
$720$		0			0
$721$	−37.3928	−	3.79590i	−1.39258	−	0.141367i
$722$		0			0
$723$	1.23606	−	1.69891i	0.0459694	−	0.0631830i
$724$		0			0
$725$	−6.33729	+	6.38743i	−0.235361	+	0.237223i
$726$		0			0
$727$	−0.688436			−0.0255327			−0.0127663	−	0.999919i	$-0.504064\pi$
$727$	−0.688436			−0.0255327			−0.0127663	+	0.999919i	$0.504064\pi$
$728$		0			0
$729$	−21.7799	−	15.9573i	−0.806664	−	0.591011i
$730$		0			0
$731$	−6.13076	−	10.6188i	−0.226754	−	0.392750i
$732$		0			0
$733$	−15.4341	+	26.7326i	−0.570070	+	0.987391i	0.426488	+	0.904493i	$0.359751\pi$
$733$	−15.4341	+	26.7326i	−0.570070	+	0.987391i	−0.996558	+	0.0828976i	$0.973583\pi$
$734$		0			0
$735$	−20.7626	−	17.4331i	−0.765840	−	0.643031i
$736$		0			0
$737$	−19.5804	+	33.9143i	−0.721255	+	1.24925i
$738$		0			0
$739$	7.57159	+	13.1144i	0.278525	+	0.482420i	0.971018	−	0.239004i	$-0.0768210\pi$
$739$	7.57159	+	13.1144i	0.278525	+	0.482420i	−0.692493	+	0.721424i	$0.743488\pi$
$740$		0			0
$741$	−35.9052	−	3.79795i	−1.31901	−	0.139521i
$742$		0			0
$743$	−7.60770			−0.279100			−0.139550	−	0.990215i	$-0.544566\pi$
$743$	−7.60770			−0.279100			−0.139550	+	0.990215i	$0.544566\pi$
$744$		0			0
$745$	−21.6906	+	16.7118i	−0.794681	+	0.612272i
$746$		0			0
$747$	19.0067	+	17.1595i	0.695418	+	0.627835i
$748$		0			0
$749$	12.7918	+	1.29855i	0.467401	+	0.0474479i
$750$		0			0
$751$	10.3363	−	17.9031i	0.377179	−	0.653293i	−0.613472	−	0.789717i	$-0.710228\pi$
$751$	10.3363	−	17.9031i	0.377179	−	0.653293i	0.990651	+	0.136424i	$0.0435609\pi$
$752$		0			0
$753$	17.2992	−	7.68830i	0.630417	−	0.280177i
$754$		0			0
$755$	−36.0319	+	4.81593i	−1.31134	+	0.175270i
$756$		0			0
$757$		−	31.2760i		−	1.13675i	−0.822771	−	0.568374i	$-0.807573\pi$
$757$		−	31.2760i		−	1.13675i	0.822771	−	0.568374i	$-0.192427\pi$
$758$		0			0
$759$	−23.1693	−	52.1324i	−0.840992	−	1.89229i
$760$		0			0
$761$	22.5062	−	38.9818i	0.815847	−	1.41309i	−0.0928706	−	0.995678i	$-0.529604\pi$
$761$	22.5062	−	38.9818i	0.815847	−	1.41309i	0.908718	−	0.417411i	$-0.137062\pi$
$762$		0			0
$763$	1.11424	−	1.54513i	0.0403382	−	0.0559375i
$764$		0			0
$765$	14.6563	+	10.0592i	0.529901	+	0.363692i
$766$		0			0
$767$	−18.5751	−	32.1729i	−0.670706	−	1.16170i
$768$		0			0
$769$		−	46.0575i		−	1.66088i	−0.557110	−	0.830439i	$-0.688090\pi$
$769$		−	46.0575i		−	1.66088i	0.557110	−	0.830439i	$-0.311910\pi$
$770$		0			0
$771$	15.7078	+	1.66152i	0.565701	+	0.0598382i
$772$		0			0
$773$	−12.2491	+	7.07203i	−0.440570	+	0.254363i	−0.703839	−	0.710359i	$-0.748533\pi$
$773$	−12.2491	+	7.07203i	−0.440570	+	0.254363i	0.263269	+	0.964722i	$0.415199\pi$
$774$		0			0
$775$	33.3149	+	8.78615i	1.19671	+	0.315608i
$776$		0			0
$777$	−13.7602	−	41.9373i	−0.493645	−	1.50449i
$778$		0			0
$779$	20.8824	+	12.0565i	0.748190	+	0.431967i
$780$		0			0
$781$	−16.9477	−	29.3542i	−0.606436	−	1.05038i
$782$		0			0
$783$	−8.88735	−	2.90730i	−0.317608	−	0.103899i
$784$		0			0
$785$	−19.8134	+	2.64820i	−0.707169	+	0.0945183i
$786$		0			0
$787$	20.2209	+	35.0236i	0.720797	+	1.24846i	0.960681	+	0.277656i	$0.0895575\pi$
$787$	20.2209	+	35.0236i	0.720797	+	1.24846i	−0.239883	+	0.970802i	$0.577109\pi$
$788$		0			0
$789$	25.8660	+	18.8191i	0.920854	+	0.669977i
$790$		0			0
$791$	−2.30246	−	5.12236i	−0.0818659	−	0.182130i
$792$		0			0
$793$	14.4133	+	8.32153i	0.511832	+	0.295506i
$794$		0			0
$795$	6.68502	−	4.10859i	0.237093	−	0.145717i
$796$		0			0
$797$			25.4463i			0.901355i	0.892687	+	0.450677i	$0.148818\pi$
$797$			25.4463i			0.901355i	−0.892687	+	0.450677i	$0.851182\pi$
$798$		0			0
$799$	5.42823			0.192037
$800$		0			0
$801$	7.99291	+	24.7115i	0.282415	+	0.873138i
$802$		0			0
$803$	−28.1938	−	16.2777i	−0.994939	−	0.574428i
$804$		0			0
$805$	23.4144	−	43.6977i	0.825249	−	1.54014i
$806$		0			0
$807$	20.8695	+	15.1838i	0.734642	+	0.534496i
$808$		0			0
$809$	3.55412	−	2.05197i	0.124956	−	0.0721435i	−0.436219	−	0.899841i	$-0.643683\pi$
$809$	3.55412	−	2.05197i	0.124956	−	0.0721435i	0.561175	+	0.827697i	$0.310349\pi$
$810$		0			0
$811$			55.0385i			1.93266i	0.257300	+	0.966332i	$0.417167\pi$
$811$			55.0385i			1.93266i	−0.257300	+	0.966332i	$0.582833\pi$
$812$		0			0
$813$	−23.1517	−	2.44892i	−0.811966	−	0.0858874i
$814$		0			0
$815$	18.1192	−	13.9602i	0.634689	−	0.489004i
$816$		0			0
$817$	16.3425	−	28.3061i	0.571753	−	0.990306i
$818$		0			0
$819$	22.2926	+	7.18860i	0.778967	+	0.251190i
$820$		0			0
$821$	−20.7890	−	12.0025i	−0.725541	−	0.418891i	0.0912480	−	0.995828i	$-0.470914\pi$
$821$	−20.7890	−	12.0025i	−0.725541	−	0.418891i	−0.816789	+	0.576937i	$0.804248\pi$
$822$		0			0
$823$	−26.4790	+	15.2876i	−0.922999	+	0.532894i	−0.884591	−	0.466368i	$-0.845562\pi$
$823$	−26.4790	+	15.2876i	−0.922999	+	0.532894i	−0.0384087	+	0.999262i	$0.512229\pi$
$824$		0			0
$825$	−33.6031	+	5.43506i	−1.16991	+	0.189225i
$826$		0			0
$827$	−17.8478			−0.620629			−0.310314	−	0.950634i	$-0.600434\pi$
$827$	−17.8478			−0.620629			−0.310314	+	0.950634i	$0.600434\pi$
$828$		0			0
$829$	21.8248	−	12.6006i	0.758007	−	0.437636i	−0.0705726	−	0.997507i	$-0.522483\pi$
$829$	21.8248	−	12.6006i	0.758007	−	0.437636i	0.828580	+	0.559871i	$0.189149\pi$
$830$		0			0
$831$	−4.21511	+	5.79349i	−0.146221	+	0.200974i
$832$		0			0
$833$	−3.72767	+	18.1711i	−0.129156	+	0.629592i
$834$		0			0
$835$	−44.7357	−	18.4270i	−1.54814	−	0.637692i
$836$		0			0
$837$	7.37447	+	35.0380i	0.254899	+	1.21109i
$838$		0			0
$839$	−12.6110			−0.435379			−0.217690	−	0.976018i	$-0.569852\pi$
$839$	−12.6110			−0.435379			−0.217690	+	0.976018i	$0.569852\pi$
$840$		0			0
$841$	25.7616			0.888330
$842$		0			0
$843$	−11.7643	−	26.4704i	−0.405183	−	0.911688i
$844$		0			0
$845$	3.65478	−	8.87282i	0.125728	−	0.305234i
$846$		0			0
$847$	−11.7118	−	1.18892i	−0.402424	−	0.0408517i
$848$		0			0
$849$	−2.48835	−	1.81043i	−0.0854001	−	0.0621337i
$850$		0			0
$851$	69.8968	−	40.3549i	2.39603	−	1.38335i
$852$		0			0
$853$	3.75855			0.128690			0.0643452	−	0.997928i	$-0.479504\pi$
$853$	3.75855			0.128690			0.0643452	+	0.997928i	$0.479504\pi$
$854$		0			0
$855$	−3.68764	+	47.2419i	−0.126115	+	1.61564i
$856$		0			0
$857$	−23.2802	+	13.4408i	−0.795236	+	0.459130i	−0.841803	−	0.539785i	$-0.818505\pi$
$857$	−23.2802	+	13.4408i	−0.795236	+	0.459130i	0.0465666	+	0.998915i	$0.485172\pi$
$858$		0			0
$859$	16.8672	+	9.73831i	0.575503	+	0.332267i	0.759344	−	0.650689i	$-0.225520\pi$
$859$	16.8672	+	9.73831i	0.575503	+	0.332267i	−0.183841	+	0.982956i	$0.558853\pi$
$860$		0			0
$861$	−11.6552	−	10.4336i	−0.397206	−	0.355576i
$862$		0			0
$863$	−22.6071	+	39.1566i	−0.769554	+	1.33291i	0.168251	+	0.985744i	$0.446188\pi$
$863$	−22.6071	+	39.1566i	−0.769554	+	1.33291i	−0.937805	+	0.347163i	$0.887145\pi$
$864$		0			0
$865$	12.8650	−	9.91195i	0.437422	−	0.337017i
$866$		0			0
$867$	−1.81791	+	17.1863i	−0.0617396	+	0.583676i
$868$		0			0
$869$			53.7758i			1.82422i
$870$		0			0
$871$	25.4624	−	14.7007i	0.862760	−	0.498115i
$872$		0			0
$873$	−11.3753	+	12.5998i	−0.384996	+	0.426438i
$874$		0			0
$875$	−21.6486	−	20.1579i	−0.731855	−	0.681460i
$876$		0			0
$877$	22.1115	+	12.7661i	0.746651	+	0.431079i	0.824483	−	0.565887i	$-0.191466\pi$
$877$	22.1115	+	12.7661i	0.746651	+	0.431079i	−0.0778314	+	0.996967i	$0.524800\pi$
$878$		0			0
$879$	−6.04790	−	13.6082i	−0.203991	−	0.458993i
$880$		0			0
$881$	13.5218			0.455561			0.227781	−	0.973712i	$-0.426853\pi$
$881$	13.5218			0.455561			0.227781	+	0.973712i	$0.426853\pi$
$882$		0			0
$883$			33.9841i			1.14366i	0.820374	+	0.571828i	$0.193765\pi$
$883$			33.9841i			1.14366i	−0.820374	+	0.571828i	$0.806235\pi$
$884$		0			0
$885$	−41.5386	+	25.5295i	−1.39630	+	0.858164i
$886$		0			0
$887$	−18.3159	−	10.5747i	−0.614987	−	0.355063i	0.159927	−	0.987129i	$-0.448874\pi$
$887$	−18.3159	−	10.5747i	−0.614987	−	0.355063i	−0.774915	+	0.632066i	$0.782207\pi$
$888$		0			0
$889$	14.2698	−	6.41415i	0.478593	−	0.215124i
$890$		0			0
$891$	−20.7167	−	28.6744i	−0.694037	−	0.960627i
$892$		0			0
$893$	7.23492	+	12.5312i	0.242107	+	0.419342i
$894$		0			0
$895$	−1.01878	−	7.62230i	−0.0340539	−	0.254785i
$896$		0			0
$897$	−4.50548	+	42.5941i	−0.150434	+	1.42217i
$898$		0			0
$899$	6.20021	+	10.7391i	0.206789	+	0.358168i
$900$		0			0
$901$	−4.64948	−	2.68438i	−0.154897	−	0.0894297i
$902$		0			0
$903$	−14.1427	+	15.7986i	−0.470641	+	0.525744i
$904$		0			0
$905$	−21.8879	−	9.01580i	−0.727580	−	0.299695i
$906$		0			0
$907$	−45.7242	+	26.3989i	−1.51825	+	0.876560i	−0.518477	+	0.855091i	$0.673501\pi$
$907$	−45.7242	+	26.3989i	−1.51825	+	0.876560i	−0.999770	+	0.0214687i	$0.993166\pi$
$908$		0			0
$909$	−41.4880	−	8.87627i	−1.37607	−	0.294407i
$910$		0			0
$911$			39.7018i			1.31538i	0.753290	+	0.657689i	$0.228466\pi$
$911$			39.7018i			1.31538i	−0.753290	+	0.657689i	$0.771534\pi$
$912$		0			0
$913$	16.7748	+	29.0549i	0.555166	+	0.961576i
$914$		0			0
$915$	10.3974	−	19.2093i	0.343727	−	0.635041i
$916$		0			0
$917$	21.2926	+	2.16150i	0.703143	+	0.0713790i
$918$		0			0
$919$	−6.76375	+	11.7152i	−0.223116	+	0.386447i	−0.955752	−	0.294172i	$-0.904956\pi$
$919$	−6.76375	+	11.7152i	−0.223116	+	0.386447i	0.732637	+	0.680620i	$0.238289\pi$
$920$		0			0
$921$	26.0919	−	11.5960i	0.859756	−	0.382103i
$922$		0			0
$923$			25.4482i			0.837636i
$924$		0			0
$925$	−12.6473	−	46.4671i	−0.415839	−	1.52783i
$926$		0			0
$927$	−13.1155	−	40.5490i	−0.430770	−	1.33180i
$928$		0			0
$929$	−8.29852	+	14.3735i	−0.272266	+	0.471578i	−0.969442	−	0.245322i	$-0.921106\pi$
$929$	−8.29852	+	14.3735i	−0.272266	+	0.471578i	0.697176	+	0.716900i	$0.254440\pi$
$930$		0			0
$931$	−46.9170	+	15.6136i	−1.53764	+	0.511716i
$932$		0			0
$933$	46.8408	+	34.0795i	1.53350	+	1.11571i
$934$		0			0
$935$	14.2146	+	18.4495i	0.464868	+	0.603363i
$936$		0			0
$937$	−28.9791			−0.946705			−0.473352	−	0.880873i	$-0.656956\pi$
$937$	−28.9791			−0.946705			−0.473352	+	0.880873i	$0.656956\pi$
$938$		0			0
$939$	−4.10497	+	38.8077i	−0.133961	+	1.26644i
$940$		0			0
$941$	−12.5466	−	21.7314i	−0.409008	−	0.708423i	0.585770	−	0.810477i	$-0.300792\pi$
$941$	−12.5466	−	21.7314i	−0.409008	−	0.708423i	−0.994779	+	0.102054i	$0.967459\pi$
$942$		0			0
$943$	14.3025	−	24.7727i	0.465753	−	0.806709i
$944$		0			0
$945$	8.62690	−	29.5055i	0.280633	−	0.959815i
$946$		0			0
$947$	19.0315	−	32.9636i	0.618442	−	1.07117i	−0.371328	−	0.928502i	$-0.621098\pi$
$947$	19.0315	−	32.9636i	0.618442	−	1.07117i	0.989770	−	0.142671i	$-0.0455691\pi$
$948$		0			0
$949$	12.2211	+	21.1675i	0.396713	+	0.687127i
$950$		0			0
$951$	1.45722	−	13.7763i	0.0472536	−	0.446728i
$952$		0			0
$953$	54.0631			1.75127			0.875637	−	0.482970i	$-0.160442\pi$
$953$	54.0631			1.75127			0.875637	+	0.482970i	$0.160442\pi$
$954$		0			0
$955$	−27.7947	+	21.4147i	−0.899415	+	0.692965i
$956$		0			0
$957$	−9.90674	−	7.20774i	−0.320239	−	0.232993i
$958$		0			0
$959$	0.0258612	−	0.0358621i	0.000835103	−	0.00115805i
$960$		0			0
$961$	8.24157	−	14.2748i	0.265857	−	0.460478i
$962$		0			0
$963$	4.48672	+	13.8715i	0.144582	+	0.447002i
$964$		0			0
$965$	−4.45912	−	33.3623i	−0.143544	−	1.07397i
$966$		0			0
$967$		−	9.82808i		−	0.316050i	−0.987435	−	0.158025i	$-0.949487\pi$
$967$		−	9.82808i		−	0.316050i	0.987435	−	0.158025i	$-0.0505126\pi$
$968$		0			0
$969$	29.6275	−	13.1674i	0.951772	−	0.422997i
$970$		0			0
$971$	−4.49769	+	7.79022i	−0.144338	+	0.250000i	−0.929126	−	0.369764i	$-0.879438\pi$
$971$	−4.49769	+	7.79022i	−0.144338	+	0.250000i	0.784788	+	0.619764i	$0.212772\pi$
$972$		0			0
$973$	−19.1587	+	8.61168i	−0.614200	+	0.276078i
$974$		0			0
$975$	23.8890	+	9.08048i	0.765060	+	0.290808i
$976$		0			0
$977$	12.0131	+	20.8074i	0.384334	+	0.665687i	0.991677	−	0.128754i	$-0.0410977\pi$
$977$	12.0131	+	20.8074i	0.384334	+	0.665687i	−0.607342	+	0.794440i	$0.707764\pi$
$978$		0			0
$979$			34.0283i			1.08755i
$980$		0			0
$981$	2.11225	+	0.451911i	0.0674388	+	0.0144284i
$982$		0			0
$983$	29.5853	−	17.0811i	0.943626	−	0.544802i	0.0525306	−	0.998619i	$-0.483271\pi$
$983$	29.5853	−	17.0811i	0.943626	−	0.544802i	0.891095	+	0.453817i	$0.149938\pi$
$984$		0			0
$985$	17.3677	−	42.1642i	0.553382	−	1.34346i
$986$		0			0
$987$	−2.92654	−	8.91928i	−0.0931528	−	0.283904i
$988$		0			0
$989$	−33.5794	−	19.3871i	−1.06776	−	0.616473i
$990$		0			0
$991$	27.7678	+	48.0952i	0.882073	+	1.52779i	0.849033	+	0.528341i	$0.177186\pi$
$991$	27.7678	+	48.0952i	0.882073	+	1.52779i	0.0330401	+	0.999454i	$0.489481\pi$
$992$		0			0
$993$	6.22964	−	58.8940i	0.197692	−	1.86895i
$994$		0			0
$995$	−2.54267	−	19.0238i	−0.0806082	−	0.603096i
$996$		0			0
$997$	1.61931	+	2.80472i	0.0512840	+	0.0888265i	0.890528	−	0.454929i	$-0.150335\pi$
$997$	1.61931	+	2.80472i	0.0512840	+	0.0888265i	−0.839244	+	0.543755i	$0.817002\pi$
$998$		0			0
$999$	37.2588	−	33.4135i	1.17881	−	1.05716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.da.b.89.20	yes	48
3.2	odd	2		840.2.da.a.89.6	yes	48
5.4	even	2		840.2.da.a.89.5	✓	48
7.3	odd	6	inner	840.2.da.b.689.19	yes	48
15.14	odd	2	inner	840.2.da.b.89.19	yes	48
21.17	even	6		840.2.da.a.689.5	yes	48
35.24	odd	6		840.2.da.a.689.6	yes	48
105.59	even	6	inner	840.2.da.b.689.20	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.da.a.89.5	✓	48	5.4	even	2
840.2.da.a.89.6	yes	48	3.2	odd	2
840.2.da.a.689.5	yes	48	21.17	even	6
840.2.da.a.689.6	yes	48	35.24	odd	6
840.2.da.b.89.19	yes	48	15.14	odd	2	inner
840.2.da.b.89.20	yes	48	1.1	even	1	trivial
840.2.da.b.689.19	yes	48	7.3	odd	6	inner
840.2.da.b.689.20	yes	48	105.59	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.da (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58278 - 0.703435i) q^{3} +(-0.851635 + 2.06754i) q^{5} +(-1.08470 - 2.41318i) q^{7} +(2.01036 - 2.22676i) q^{9} +O(q^{10})\)	\(q+(1.58278 - 0.703435i) q^{3} +(-0.851635 + 2.06754i) q^{5} +(-1.08470 - 2.41318i) q^{7} +(2.01036 - 2.22676i) q^{9} +(3.40398 - 1.96529i) q^{11} -2.95102 q^{13} +(0.106434 + 3.87152i) q^{15} +(2.29491 - 1.32497i) q^{17} +(6.11746 + 3.53192i) q^{19} +(-3.41435 - 3.05650i) q^{21} +(4.18989 - 7.25710i) q^{23} +(-3.54944 - 3.52158i) q^{25} +(1.61556 - 4.93862i) q^{27} -1.79956i q^{29} +(-5.96761 + 3.44540i) q^{31} +(4.00528 - 5.50509i) q^{33} +(5.91311 - 0.187521i) q^{35} +(8.34112 + 4.81575i) q^{37} +(-4.67080 + 2.07585i) q^{39} +3.41357 q^{41} -4.62710i q^{43} +(2.89183 + 6.05288i) q^{45} +(1.77400 + 1.02422i) q^{47} +(-4.64684 + 5.23516i) q^{49} +(2.70030 - 3.71144i) q^{51} +(-1.01300 - 1.75457i) q^{53} +(1.16436 + 8.71156i) q^{55} +(12.1670 + 1.28699i) q^{57} +(6.29445 + 10.9023i) q^{59} +(-4.88418 - 2.81988i) q^{61} +(-7.55421 - 2.43597i) q^{63} +(2.51319 - 6.10135i) q^{65} +(-8.62834 + 4.98157i) q^{67} +(1.52675 - 14.4337i) q^{69} -8.62351i q^{71} +(-4.14131 - 7.17295i) q^{73} +(-8.09516 - 3.07706i) q^{75} +(-8.43489 - 6.08264i) q^{77} +(-6.84071 + 11.8485i) q^{79} +(-0.916926 - 8.95317i) q^{81} +8.53557i q^{83} +(0.784996 + 5.87320i) q^{85} +(-1.26587 - 2.84830i) q^{87} +(-4.32867 + 7.49747i) q^{89} +(3.20098 + 7.12133i) q^{91} +(-7.02177 + 9.65112i) q^{93} +(-12.5122 + 9.64018i) q^{95} -5.65835 q^{97} +(2.46699 - 11.5308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{3} + 3 q^{5} - q^{9}+O(q^{10}) \) 48 * q + 3 * q^3 + 3 * q^5 - q^9	\( 48 q + 3 q^{3} + 3 q^{5} - q^{9} + 6 q^{15} + 5 q^{21} + 2 q^{23} + q^{25} + 6 q^{31} + 24 q^{33} - 4 q^{35} + 2 q^{39} - 21 q^{45} + 12 q^{51} - 6 q^{53} + 20 q^{57} + 18 q^{61} - 26 q^{63} + 10 q^{65} - 51 q^{75} + 2 q^{77} + 2 q^{79} - 9 q^{81} - 15 q^{87} + 24 q^{91} + 8 q^{93} + 6 q^{95} - 12 q^{99}+O(q^{100}) \) 48 * q + 3 * q^3 + 3 * q^5 - q^9 + 6 * q^15 + 5 * q^21 + 2 * q^23 + q^25 + 6 * q^31 + 24 * q^33 - 4 * q^35 + 2 * q^39 - 21 * q^45 + 12 * q^51 - 6 * q^53 + 20 * q^57 + 18 * q^61 - 26 * q^63 + 10 * q^65 - 51 * q^75 + 2 * q^77 + 2 * q^79 - 9 * q^81 - 15 * q^87 + 24 * q^91 + 8 * q^93 + 6 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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