LMFDB - Embedded newform 525.2.t.j.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("525.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.5
Character	$\chi$	$=$	525.26
Dual form			525.2.t.j.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.558418 - 0.322403i) q^{2} +(-1.28838 - 1.15761i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(0.346239 + 1.06181i) q^{6} +(0.105130 + 2.64366i) q^{7} +2.31113i q^{8} +(0.319861 + 2.98290i) q^{9} +(3.51044 - 2.02675i) q^{11} +(-0.567678 + 2.68460i) q^{12} +4.21339i q^{13} +(0.793618 - 1.51016i) q^{14} +(-0.839111 + 1.45338i) q^{16} +(-1.08830 - 1.88498i) q^{17} +(0.783079 - 1.76883i) q^{18} +(3.87634 + 2.23800i) q^{19} +(2.92489 - 3.52775i) q^{21} -2.61372 q^{22} +(-0.558418 - 0.322403i) q^{23} +(2.67540 - 2.97762i) q^{24} +(1.35841 - 2.35284i) q^{26} +(3.04094 - 4.21339i) q^{27} +(3.54377 - 2.23831i) q^{28} -1.16875i q^{29} +(-0.339111 + 0.195786i) q^{31} +(4.94014 - 2.85219i) q^{32} +(-6.86898 - 1.45250i) q^{33} +1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +(2.13178 - 3.69236i) q^{37} +(-1.44308 - 2.49949i) q^{38} +(4.87748 - 5.42846i) q^{39} +2.27971 q^{41} +(-2.77067 + 1.02697i) q^{42} +6.54419 q^{43} +(-5.56132 - 3.21083i) q^{44} +(0.207887 + 0.360071i) q^{46} +(-3.90070 + 6.75621i) q^{47} +(2.76355 - 0.901147i) q^{48} +(-6.97790 + 0.555857i) q^{49} +(-0.779941 + 3.68841i) q^{51} +(5.78069 - 3.33748i) q^{52} +(6.23667 - 3.60074i) q^{53} +(-3.05653 + 1.37243i) q^{54} +(-6.10984 + 0.242969i) q^{56} +(-2.40346 - 7.37071i) q^{57} +(-0.376810 + 0.652654i) q^{58} +(5.66247 + 9.80768i) q^{59} +(6.05456 + 3.49560i) q^{61} +0.252487 q^{62} +(-7.85215 + 1.15920i) q^{63} -0.321779 q^{64} +(3.36748 + 3.02568i) q^{66} +(4.36870 + 7.56680i) q^{67} +(-1.72411 + 2.98624i) q^{68} +(0.346239 + 1.06181i) q^{69} +8.13766i q^{71} +(-6.89387 + 0.739241i) q^{72} +(4.53525 - 2.61843i) q^{73} +(-2.38085 + 1.37459i) q^{74} -7.09101i q^{76} +(5.72710 + 9.06734i) q^{77} +(-4.47383 + 1.45884i) q^{78} +(1.87634 - 3.24991i) q^{79} +(-8.79538 + 1.90823i) q^{81} +(-1.27303 - 0.734986i) q^{82} -5.27461 q^{83} +(-7.15684 - 1.21852i) q^{84} +(-3.65439 - 2.10987i) q^{86} +(-1.35297 + 1.50580i) q^{87} +(4.68409 + 8.11308i) q^{88} +(0.447379 - 0.774883i) q^{89} +(-11.1388 + 0.442954i) q^{91} +1.02152i q^{92} +(0.663548 + 0.140312i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-9.66653 - 2.04406i) q^{96} +3.89968i q^{97} +(4.07579 + 1.93929i) q^{98} +(7.16845 + 9.82300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^9 - 12 * q^16 - 6 * q^21 - 18 * q^24 + 84 * q^36 + 12 * q^39 + 36 * q^46 + 12 * q^49 - 12 * q^51 + 36 * q^54 + 36 * q^61 - 24 * q^64 - 72 * q^66 - 48 * q^79 - 6 * q^81 - 48 * q^84 - 96 * q^91 + 72 * q^94 - 90 * q^96 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.558418	−	0.322403i	−0.394861	−	0.227973i	0.289403	−	0.957207i	$-0.406543\pi$
$2$	−0.558418	−	0.322403i	−0.394861	−	0.227973i	−0.684264	+	0.729234i	$0.739877\pi$
$3$	−1.28838	−	1.15761i	−0.743848	−	0.668349i
$3$	−1.28838	−	1.15761i	−0.743848	−	0.668349i
$4$	−0.792113	−	1.37198i	−0.396056	−	0.685990i
$5$		0			0
$5$		0			0
$6$	0.346239	+	1.06181i	0.141351	+	0.433483i
$7$	0.105130	+	2.64366i	0.0397354	+	0.999210i
$7$	0.105130	+	2.64366i	0.0397354	+	0.999210i
$8$			2.31113i			0.817108i
$9$	0.319861	+	2.98290i	0.106620	+	0.994300i
$10$		0			0
$11$	3.51044	−	2.02675i	1.05844	−	0.611089i	0.133437	−	0.991057i	$-0.457398\pi$
$11$	3.51044	−	2.02675i	1.05844	−	0.611089i	0.924999	+	0.379968i	$0.124065\pi$
$12$	−0.567678	+	2.68460i	−0.163874	+	0.774976i
$13$			4.21339i			1.16858i	0.811543	+	0.584292i	$0.198628\pi$
$13$			4.21339i			1.16858i	−0.811543	+	0.584292i	$0.801372\pi$
$14$	0.793618	−	1.51016i	0.212103	−	0.403608i
$15$		0			0
$16$	−0.839111	+	1.45338i	−0.209778	+	0.363346i
$17$	−1.08830	−	1.88498i	−0.263951	−	0.457176i	0.703338	−	0.710856i	$-0.251692\pi$
$17$	−1.08830	−	1.88498i	−0.263951	−	0.457176i	−0.967288	+	0.253680i	$0.918359\pi$
$18$	0.783079	−	1.76883i	0.184574	−	0.416917i
$19$	3.87634	+	2.23800i	0.889293	+	0.513434i	0.873711	−	0.486445i	$-0.161707\pi$
$19$	3.87634	+	2.23800i	0.889293	+	0.513434i	0.0155818	+	0.999879i	$0.495040\pi$
$20$		0			0
$21$	2.92489	−	3.52775i	0.638264	−	0.769818i
$22$	−2.61372			−0.557248
$23$	−0.558418	−	0.322403i	−0.116438	−	0.0672257i	0.440650	−	0.897679i	$-0.354748\pi$
$23$	−0.558418	−	0.322403i	−0.116438	−	0.0672257i	−0.557088	+	0.830453i	$0.688081\pi$
$24$	2.67540	−	2.97762i	0.546113	−	0.607804i
$25$		0			0
$26$	1.35841	−	2.35284i	0.266406	−	0.461429i
$27$	3.04094	−	4.21339i	0.585229	−	0.810868i
$28$	3.54377	−	2.23831i	0.669710	−	0.423002i
$29$		−	1.16875i		−	0.217032i	−0.994095	−	0.108516i	$-0.965390\pi$
$29$		−	1.16875i		−	0.217032i	0.994095	−	0.108516i	$-0.0346099\pi$
$30$		0			0
$31$	−0.339111	+	0.195786i	−0.0609061	+	0.0351641i	−0.530144	−	0.847908i	$-0.677862\pi$
$31$	−0.339111	+	0.195786i	−0.0609061	+	0.0351641i	0.469238	+	0.883072i	$0.344529\pi$
$32$	4.94014	−	2.85219i	0.873302	−	0.504201i
$33$	−6.86898	−	1.45250i	−1.19574	−	0.252847i
$34$			1.40348i			0.240695i
$35$		0			0
$36$	3.83911	−	2.80164i	0.639852	−	0.466939i
$37$	2.13178	−	3.69236i	0.350463	−	0.607020i	−0.635868	−	0.771798i	$-0.719358\pi$
$37$	2.13178	−	3.69236i	0.350463	−	0.607020i	0.986331	+	0.164778i	$0.0526909\pi$
$38$	−1.44308	−	2.49949i	−0.234098	−	0.405470i
$39$	4.87748	−	5.42846i	0.781022	−	0.869250i
$40$		0			0
$41$	2.27971			0.356031			0.178016	−	0.984028i	$-0.443032\pi$
$41$	2.27971			0.356031			0.178016	+	0.984028i	$0.443032\pi$
$42$	−2.77067	+	1.02697i	−0.427524	+	0.158464i
$43$	6.54419			0.997980			0.498990	−	0.866608i	$-0.333705\pi$
$43$	6.54419			0.997980			0.498990	+	0.866608i	$0.333705\pi$
$44$	−5.56132	−	3.21083i	−0.838401	−	0.484051i
$45$		0			0
$46$	0.207887	+	0.360071i	0.0306513	+	0.0530896i
$47$	−3.90070	+	6.75621i	−0.568975	+	0.985494i	0.427692	+	0.903924i	$0.359327\pi$
$47$	−3.90070	+	6.75621i	−0.568975	+	0.985494i	−0.996668	+	0.0815698i	$0.974007\pi$
$48$	2.76355	−	0.901147i	0.398884	−	0.130069i
$49$	−6.97790	+	0.555857i	−0.996842	+	0.0794081i
$50$		0			0
$51$	−0.779941	+	3.68841i	−0.109214	+	0.516480i
$52$	5.78069	−	3.33748i	0.801637	−	0.462825i
$53$	6.23667	−	3.60074i	0.856672	−	0.494600i	−0.00622439	−	0.999981i	$-0.501981\pi$
$53$	6.23667	−	3.60074i	0.856672	−	0.494600i	0.862896	+	0.505381i	$0.168648\pi$
$54$	−3.05653	+	1.37243i	−0.415941	+	0.186764i
$55$		0			0
$56$	−6.10984	+	0.242969i	−0.816462	+	0.0324681i
$57$	−2.40346	−	7.37071i	−0.318346	−	0.976274i
$58$	−0.376810	+	0.652654i	−0.0494776	+	0.0856977i
$59$	5.66247	+	9.80768i	0.737190	+	1.27685i	0.953756	+	0.300583i	$0.0971812\pi$
$59$	5.66247	+	9.80768i	0.737190	+	1.27685i	−0.216566	+	0.976268i	$0.569485\pi$
$60$		0			0
$61$	6.05456	+	3.49560i	0.775207	+	0.447566i	0.834729	−	0.550661i	$-0.185624\pi$
$61$	6.05456	+	3.49560i	0.775207	+	0.447566i	−0.0595220	+	0.998227i	$0.518958\pi$
$62$	0.252487			0.0320659
$63$	−7.85215	+	1.15920i	−0.989278	+	0.146045i
$64$	−0.321779			−0.0402224
$65$		0			0
$66$	3.36748	+	3.02568i	0.414508	+	0.372436i
$67$	4.36870	+	7.56680i	0.533721	+	0.924432i	0.999224	+	0.0393859i	$0.0125402\pi$
$67$	4.36870	+	7.56680i	0.533721	+	0.924432i	−0.465503	+	0.885046i	$0.654127\pi$
$68$	−1.72411	+	2.98624i	−0.209079	+	0.362135i
$69$	0.346239	+	1.06181i	0.0416822	+	0.127827i
$70$		0			0
$71$			8.13766i			0.965762i	0.875686	+	0.482881i	$0.160410\pi$
$71$			8.13766i			0.965762i	−0.875686	+	0.482881i	$0.839590\pi$
$72$	−6.89387	+	0.739241i	−0.812450	+	0.0871204i
$73$	4.53525	−	2.61843i	0.530810	−	0.306464i	−0.210536	−	0.977586i	$-0.567521\pi$
$73$	4.53525	−	2.61843i	0.530810	−	0.306464i	0.741346	+	0.671123i	$0.234188\pi$
$74$	−2.38085	+	1.37459i	−0.276769	+	0.159792i
$75$		0			0
$76$		−	7.09101i		−	0.813394i
$77$	5.72710	+	9.06734i	0.652664	+	1.03332i
$78$	−4.47383	+	1.45884i	−0.506561	+	0.165181i
$79$	1.87634	−	3.24991i	0.211105	−	0.365644i	−0.740956	−	0.671554i	$-0.765627\pi$
$79$	1.87634	−	3.24991i	0.211105	−	0.365644i	0.952060	+	0.305910i	$0.0989606\pi$
$80$		0			0
$81$	−8.79538	+	1.90823i	−0.977264	+	0.212025i
$82$	−1.27303	−	0.734986i	−0.140583	−	0.0811656i
$83$	−5.27461			−0.578964			−0.289482	−	0.957183i	$-0.593483\pi$
$83$	−5.27461			−0.578964			−0.289482	+	0.957183i	$0.593483\pi$
$84$	−7.15684	−	1.21852i	−0.780876	−	0.132951i
$85$		0			0
$86$	−3.65439	−	2.10987i	−0.394064	−	0.227513i
$87$	−1.35297	+	1.50580i	−0.145053	+	0.161439i
$88$	4.68409	+	8.11308i	0.499325	+	0.864857i
$89$	0.447379	−	0.774883i	0.0474221	−	0.0821375i	−0.841340	−	0.540506i	$-0.818233\pi$
$89$	0.447379	−	0.774883i	0.0474221	−	0.0821375i	0.888762	+	0.458369i	$0.151566\pi$
$90$		0			0
$91$	−11.1388	+	0.442954i	−1.16766	+	0.0464342i
$92$			1.02152i			0.106501i
$93$	0.663548	+	0.140312i	0.0688068	+	0.0145497i
$94$	4.35644	−	2.51519i	0.449333	−	0.259422i
$95$		0			0
$96$	−9.66653	−	2.04406i	−0.986586	−	0.208621i
$97$			3.89968i			0.395953i	0.980207	+	0.197976i	$0.0634370\pi$
$97$			3.89968i			0.395953i	−0.980207	+	0.197976i	$0.936563\pi$
$98$	4.07579	+	1.93929i	0.411717	+	0.195898i
$99$	7.16845	+	9.82300i	0.720456	+	0.987249i
$100$		0			0
$101$	−3.29188	−	5.70171i	−0.327555	−	0.567341i	0.654471	−	0.756087i	$-0.272891\pi$
$101$	−3.29188	−	5.70171i	−0.327555	−	0.567341i	−0.982026	+	0.188745i	$0.939558\pi$
$102$	1.62469	−	1.80822i	0.160868	−	0.179040i
$103$	8.49954	+	4.90721i	0.837485	+	0.483522i	0.856408	−	0.516299i	$-0.172691\pi$
$103$	8.49954	+	4.90721i	0.837485	+	0.483522i	−0.0189238	+	0.999821i	$0.506024\pi$
$104$	−9.73770			−0.954860
$105$		0			0
$106$	−4.64356			−0.451022
$107$	−16.2635	−	9.38974i	−1.57225	−	0.907740i	−0.995892	−	0.0905447i	$-0.971139\pi$
$107$	−16.2635	−	9.38974i	−1.57225	−	0.907740i	−0.576360	−	0.817196i	$-0.695527\pi$
$108$	−8.18946	−	0.834627i	−0.788031	−	0.0803120i
$109$	0.453002	+	0.784623i	0.0433897	+	0.0751532i	0.886905	−	0.461952i	$-0.152851\pi$
$109$	0.453002	+	0.784623i	0.0433897	+	0.0751532i	−0.843515	+	0.537106i	$0.819518\pi$
$110$		0			0
$111$	−7.02088	+	2.28939i	−0.666392	+	0.217299i
$112$	−3.93047	−	2.06553i	−0.371394	−	0.195174i
$113$		−	8.82955i		−	0.830614i	−0.909681	−	0.415307i	$-0.863674\pi$
$113$		−	8.82955i		−	0.830614i	0.909681	−	0.415307i	$-0.136326\pi$
$114$	−1.03420	+	4.89082i	−0.0968618	+	0.458067i
$115$		0			0
$116$	−1.60351	+	0.925786i	−0.148882	+	0.0859570i
$117$	−12.5681	+	1.34770i	−1.16192	+	0.124595i
$118$		−	7.30238i		−	0.672239i
$119$	4.86885	−	3.07526i	0.446327	−	0.281908i
$120$		0			0
$121$	2.71545	−	4.70330i	0.246859	−	0.427572i
$122$	−2.25398	−	3.90402i	−0.204066	−	0.353453i
$123$	−2.93714	−	2.63903i	−0.264833	−	0.237953i
$124$	0.537228	+	0.310168i	0.0482445	+	0.0278540i
$125$		0			0
$126$	4.75851	+	1.88424i	0.423922	+	0.167861i
$127$	15.8249			1.40424			0.702118	−	0.712060i	$-0.252238\pi$
$127$	15.8249			1.40424			0.702118	+	0.712060i	$0.252238\pi$
$128$	−9.70060	−	5.60064i	−0.857420	−	0.495032i
$129$	−8.43142	−	7.57564i	−0.742345	−	0.666998i
$130$		0			0
$131$	−8.27814	+	14.3382i	−0.723265	+	1.25273i	0.236419	+	0.971651i	$0.424026\pi$
$131$	−8.27814	+	14.3382i	−0.723265	+	1.25273i	−0.959684	+	0.281080i	$0.909307\pi$
$132$	3.44821	+	10.5746i	0.300128	+	0.920405i
$133$	−5.50901	+	10.4830i	−0.477692	+	0.908992i
$134$		−	5.63392i		−	0.486697i
$135$		0			0
$136$	4.35644	−	2.51519i	0.373562	−	0.215676i
$137$	17.2007	−	9.93080i	1.46955	−	0.848446i	0.470135	−	0.882595i	$-0.344205\pi$
$137$	17.2007	−	9.93080i	1.46955	−	0.848446i	0.999417	+	0.0341490i	$0.0108721\pi$
$138$	0.148985	−	0.704563i	0.0126825	−	0.0599764i
$139$			0.228766i			0.0194037i	0.999953	+	0.00970183i	$0.00308824\pi$
$139$			0.228766i			0.0194037i	−0.999953	+	0.00970183i	$0.996912\pi$
$140$		0			0
$141$	12.8467	−	4.18908i	1.08188	−	0.352784i
$142$	2.62361	−	4.54422i	0.220168	−	0.381342i
$143$	8.53950	+	14.7909i	0.714109	+	1.23687i
$144$	−4.60369	−	2.03810i	−0.383641	−	0.169842i
$145$		0			0
$146$	−3.37675			−0.279462
$147$	9.63367	+	7.36155i	0.794572	+	0.607170i
$148$	−6.75445			−0.555212
$149$	8.62438	+	4.97929i	0.706537	+	0.407919i	0.809777	−	0.586737i	$-0.199588\pi$
$149$	8.62438	+	4.97929i	0.706537	+	0.407919i	−0.103240	+	0.994656i	$0.532921\pi$
$150$		0			0
$151$	2.53723	+	4.39461i	0.206477	+	0.357628i	0.950602	−	0.310412i	$-0.100467\pi$
$151$	2.53723	+	4.39461i	0.206477	+	0.357628i	−0.744126	+	0.668040i	$0.767134\pi$
$152$	−5.17232	+	8.95872i	−0.419530	+	0.726648i
$153$	5.27461	−	3.84921i	0.426427	−	0.311190i
$154$	−0.274781	−	6.90980i	−0.0221425	−	0.556808i
$155$		0			0
$156$	−11.3113	−	2.39185i	−0.905625	−	0.191501i
$157$	−14.5956	+	8.42678i	−1.16486	+	0.672531i	−0.952463	−	0.304653i	$-0.901459\pi$
$157$	−14.5956	+	8.42678i	−1.16486	+	0.672531i	−0.212394	+	0.977184i	$0.568126\pi$
$158$	−2.09556	+	1.20987i	−0.166714	+	0.0962524i
$159$	−12.2035	−	2.58052i	−0.967799	−	0.204648i
$160$		0			0
$161$	0.793618	−	1.51016i	0.0625458	−	0.119018i
$162$	5.52672	+	1.77007i	0.434220	+	0.139070i
$163$	2.40346	−	4.16292i	0.188254	−	0.326065i	−0.756414	−	0.654093i	$-0.773051\pi$
$163$	2.40346	−	4.16292i	0.188254	−	0.326065i	0.944668	+	0.328028i	$0.106384\pi$
$164$	−1.80579	−	3.12772i	−0.141008	−	0.244234i
$165$		0			0
$166$	2.94544	+	1.70055i	0.228611	+	0.131988i
$167$	4.45089			0.344420			0.172210	−	0.985060i	$-0.444909\pi$
$167$	4.45089			0.344420			0.172210	+	0.985060i	$0.444909\pi$
$168$	8.15308	+	6.75980i	0.629024	+	0.521530i
$169$	−4.75268			−0.365590
$170$		0			0
$171$	−5.43585	+	12.2786i	−0.415690	+	0.938966i
$172$	−5.18374	−	8.97849i	−0.395256	−	0.684604i
$173$	−5.72710	+	9.91963i	−0.435423	+	0.754175i	−0.997330	−	0.0730252i	$-0.976735\pi$
$173$	−5.72710	+	9.91963i	−0.435423	+	0.754175i	0.561907	+	0.827201i	$0.310068\pi$
$174$	1.24100	−	0.404668i	0.0940797	−	0.0306778i
$175$		0			0
$176$			6.80268i			0.512771i
$177$	4.05808	−	19.1910i	0.305024	−	1.44248i
$178$	−0.499649	+	0.288473i	−0.0374503	+	0.0216219i
$179$	−9.04522	+	5.22226i	−0.676071	+	0.390330i	−0.798373	−	0.602163i	$-0.794306\pi$
$179$	−9.04522	+	5.22226i	−0.676071	+	0.390330i	0.122302	+	0.992493i	$0.460972\pi$
$180$		0			0
$181$		−	11.9616i		−	0.889095i	−0.895755	−	0.444548i	$-0.853364\pi$
$181$		−	11.9616i		−	0.889095i	0.895755	−	0.444548i	$-0.146636\pi$
$182$	6.36291	+	3.34382i	0.471650	+	0.247861i
$183$	−3.75404	−	11.5125i	−0.277506	−	0.851030i
$184$	0.745115	−	1.29058i	0.0549306	−	0.0951426i
$185$		0			0
$186$	−0.325300	−	0.292283i	−0.0238522	−	0.0214312i
$187$	−7.64079	−	4.41141i	−0.558750	−	0.322594i
$188$	12.3592			0.901385
$189$	11.4585	+	7.59627i	0.833482	+	0.552547i
$190$		0			0
$191$	12.2522	+	7.07383i	0.886541	+	0.511844i	0.872809	−	0.488061i	$-0.162296\pi$
$191$	12.2522	+	7.07383i	0.886541	+	0.511844i	0.0137312	+	0.999906i	$0.495629\pi$
$192$	0.414574	+	0.372496i	0.0299193	+	0.0268826i
$193$	−3.09566	−	5.36185i	−0.222831	−	0.385954i	0.732836	−	0.680406i	$-0.238196\pi$
$193$	−3.09566	−	5.36185i	−0.222831	−	0.385954i	−0.955666	+	0.294452i	$0.904863\pi$
$194$	1.25727	−	2.17765i	0.0902667	−	0.156346i
$195$		0			0
$196$	6.28990	+	9.13323i	0.449279	+	0.652373i
$197$		−	13.0751i		−	0.931562i	−0.884900	−	0.465781i	$-0.845773\pi$
$197$		−	13.0751i		−	0.931562i	0.884900	−	0.465781i	$-0.154227\pi$
$198$	−0.836029	−	7.79647i	−0.0594140	−	0.554071i
$199$	−14.6810	+	8.47608i	−1.04071	+	0.600854i	−0.920034	−	0.391838i	$-0.871839\pi$
$199$	−14.6810	+	8.47608i	−1.04071	+	0.600854i	−0.120675	+	0.992692i	$0.538506\pi$
$200$		0			0
$201$	3.13088	−	14.8062i	0.220835	−	1.04435i
$202$			4.24525i			0.298695i
$203$	3.08979	−	0.122871i	0.216861	−	0.00862388i
$204$	5.67822	−	1.85157i	0.397555	−	0.129636i
$205$		0			0
$206$	−3.16420	−	5.48055i	−0.220460	−	0.381848i
$207$	0.783079	−	1.76883i	0.0544278	−	0.122942i
$208$	−6.12367	−	3.53550i	−0.424600	−	0.245143i
$209$	18.1435			1.25501
$210$		0			0
$211$	−18.4309			−1.26884			−0.634418	−	0.772990i	$-0.718760\pi$
$211$	−18.4309			−1.26884			−0.634418	+	0.772990i	$0.718760\pi$
$212$	−9.88029	−	5.70439i	−0.678581	−	0.391779i
$213$	9.42027	−	10.4844i	0.645466	−	0.718381i
$214$	6.05456	+	10.4868i	0.413881	+	0.716863i
$215$		0			0
$216$	9.73770	+	7.02801i	0.662566	+	0.478195i
$217$	−0.553242	−	0.875911i	−0.0375565	−	0.0594607i
$218$		−	0.584197i		−	0.0395668i
$219$	−8.87426	−	1.87653i	−0.599667	−	0.126804i
$220$		0			0
$221$	7.94218	−	4.58542i	0.534249	−	0.308449i
$222$	4.65869	+	0.985115i	0.312671	+	0.0661166i
$223$			0.627418i			0.0420150i	0.999779	+	0.0210075i	$0.00668739\pi$
$223$			0.627418i			0.0420150i	−0.999779	+	0.0210075i	$0.993313\pi$
$224$	8.05959	+	12.7602i	0.538504	+	0.852578i
$225$		0			0
$226$	−2.84667	+	4.93058i	−0.189358	+	0.327977i
$227$	2.71470	+	4.70200i	0.180181	+	0.312082i	0.941942	−	0.335776i	$-0.108998\pi$
$227$	2.71470	+	4.70200i	0.180181	+	0.312082i	−0.761761	+	0.647858i	$0.775665\pi$
$228$	−8.20865	+	9.13593i	−0.543631	+	0.605042i
$229$	12.4482	+	7.18699i	0.822602	+	0.474930i	0.851313	−	0.524658i	$-0.175807\pi$
$229$	12.4482	+	7.18699i	0.822602	+	0.474930i	−0.0287108	+	0.999588i	$0.509140\pi$
$230$		0			0
$231$	3.11778	−	18.3120i	0.205135	−	1.20484i
$232$	2.70114			0.177339
$233$	−7.30101	−	4.21524i	−0.478305	−	0.276150i	0.241405	−	0.970425i	$-0.422392\pi$
$233$	−7.30101	−	4.21524i	−0.478305	−	0.276150i	−0.719710	+	0.694275i	$0.755725\pi$
$234$	7.45277	+	3.29942i	0.487203	+	0.215690i
$235$		0			0
$236$	8.97062	−	15.5376i	0.583938	−	1.01141i
$237$	−6.17959	+	2.01506i	−0.401407	+	0.130892i
$238$	−3.71032	+	0.147548i	−0.240505	+	0.00956411i
$239$		−	2.71852i		−	0.175847i	−0.996127	−	0.0879233i	$-0.971977\pi$
$239$		−	2.71852i		−	0.175847i	0.996127	−	0.0879233i	$-0.0280230\pi$
$240$		0			0
$241$	−1.32457	+	0.764739i	−0.0853229	+	0.0492612i	−0.542054	−	0.840343i	$-0.682353\pi$
$241$	−1.32457	+	0.764739i	−0.0853229	+	0.0492612i	0.456732	+	0.889605i	$0.349020\pi$
$242$	−3.03271	+	1.75094i	−0.194950	+	0.112555i
$243$	13.5408	+	7.72312i	0.868643	+	0.495438i
$244$		−	11.0756i		−	0.709045i
$245$		0			0
$246$	0.789324	+	2.42062i	0.0503255	+	0.154333i
$247$	−9.42959	+	16.3325i	−0.599991	+	1.03921i
$248$	−0.452486	−	0.783728i	−0.0287329	−	0.0497668i
$249$	6.79572	+	6.10597i	0.430661	+	0.386950i
$250$		0			0
$251$	8.81039			0.556107			0.278054	−	0.960566i	$-0.410311\pi$
$251$	8.81039			0.556107			0.278054	+	0.960566i	$0.410311\pi$
$252$	7.81018	+	9.85477i	0.491995	+	0.620792i
$253$	−2.61372			−0.164323
$254$	−8.83694	−	5.10201i	−0.554479	−	0.320128i
$255$		0			0
$256$	3.93311	+	6.81234i	0.245819	+	0.425771i
$257$	−10.0517	+	17.4101i	−0.627011	+	1.08601i	0.361138	+	0.932512i	$0.382388\pi$
$257$	−10.0517	+	17.4101i	−0.627011	+	1.08601i	−0.988148	+	0.153502i	$0.950945\pi$
$258$	2.26585	+	6.94869i	0.141066	+	0.432607i
$259$	9.98546	+	5.24754i	0.620466	+	0.326066i
$260$		0			0
$261$	3.48628	−	0.373839i	0.215795	−	0.0231401i
$262$	9.24533	−	5.33780i	0.571179	−	0.329770i
$263$	7.58568	−	4.37959i	0.467753	−	0.270057i	−0.247546	−	0.968876i	$-0.579624\pi$
$263$	7.58568	−	4.37959i	0.467753	−	0.270057i	0.715299	+	0.698819i	$0.246291\pi$
$264$	3.35691	−	15.8751i	0.206604	−	0.977046i
$265$		0			0
$266$	6.45608	−	4.07778i	0.395848	−	0.250025i
$267$	−1.47341	+	0.480454i	−0.0901713	+	0.0294033i
$268$	6.92100	−	11.9875i	0.422767	−	0.732255i
$269$	−8.62438	−	14.9379i	−0.525838	−	0.910778i	−0.999547	−	0.0300966i	$-0.990419\pi$
$269$	−8.62438	−	14.9379i	−0.525838	−	0.910778i	0.473709	−	0.880681i	$-0.342915\pi$
$270$		0			0
$271$	19.6117	+	11.3228i	1.19132	+	0.687812i	0.958607	−	0.284733i	$-0.0919048\pi$
$271$	19.6117	+	11.3228i	1.19132	+	0.687812i	0.232718	+	0.972544i	$0.425238\pi$
$272$	3.65280			0.221484
$273$	14.8638	+	12.3237i	0.899598	+	0.745865i
$274$	−12.8069			−0.773692
$275$		0			0
$276$	1.18252	−	1.31611i	0.0711795	−	0.0792203i
$277$	6.60561	+	11.4413i	0.396893	+	0.687438i	0.993341	−	0.115213i	$-0.0367552\pi$
$277$	6.60561	+	11.4413i	0.396893	+	0.687438i	−0.596448	+	0.802652i	$0.703422\pi$
$278$	0.0737548	−	0.127747i	0.00442352	−	0.00766176i
$279$	−0.692477	−	0.948908i	−0.0414575	−	0.0568097i
$280$		0			0
$281$		−	32.8703i		−	1.96088i	−0.196817	−	0.980440i	$-0.563060\pi$
$281$		−	32.8703i		−	1.96088i	0.196817	−	0.980440i	$-0.436940\pi$
$282$	−8.52439	−	1.80255i	−0.507620	−	0.107340i
$283$	−13.6932	+	7.90575i	−0.813974	+	0.469948i	−0.848334	−	0.529462i	$-0.822394\pi$
$283$	−13.6932	+	7.90575i	−0.813974	+	0.469948i	0.0343601	+	0.999410i	$0.489061\pi$
$284$	11.1647	−	6.44594i	0.662503	−	0.382496i
$285$		0			0
$286$		−	11.0126i		−	0.651191i
$287$	0.239666	+	6.02679i	0.0141471	+	0.355750i
$288$	10.0880	+	13.8236i	0.594439	+	0.814566i
$289$	6.13122	−	10.6196i	0.360660	−	0.624682i
$290$		0			0
$291$	4.51433	−	5.02429i	0.264635	−	0.294529i
$292$	−7.18485	−	4.14818i	−0.420462	−	0.242754i
$293$	−20.7797			−1.21396			−0.606982	−	0.794716i	$-0.707620\pi$
$293$	−20.7797			−1.21396			−0.606982	+	0.794716i	$0.707620\pi$
$294$	−3.00623	−	7.21675i	−0.175327	−	0.420889i
$295$		0			0
$296$	8.53351	+	4.92683i	0.496000	+	0.286366i
$297$	2.13553	−	20.9541i	0.123916	−	1.21588i
$298$	−3.21068	−	5.56105i	−0.185989	−	0.322143i
$299$	1.35841	−	2.35284i	0.0785589	−	0.136068i
$300$		0			0
$301$	0.687991	+	17.3006i	0.0396552	+	0.997191i
$302$		−	3.27204i		−	0.188285i
$303$	−2.35917	+	11.1567i	−0.135531	+	0.640937i
$304$	−6.50535	+	3.75587i	−0.373108	+	0.215414i
$305$		0			0
$306$	−4.18644	+	0.448919i	−0.239323	+	0.0256630i
$307$		−	12.9857i		−	0.741136i	−0.928805	−	0.370568i	$-0.879163\pi$
$307$		−	12.9857i		−	0.741136i	0.928805	−	0.370568i	$-0.120837\pi$
$308$	7.90369	−	15.0398i	0.450355	−	0.856973i
$309$	−5.27001	−	16.1616i	−0.299800	−	0.919399i
$310$		0			0
$311$	0.228825	+	0.396337i	0.0129755	+	0.0224742i	0.872440	−	0.488721i	$-0.162536\pi$
$311$	0.228825	+	0.396337i	0.0129755	+	0.0224742i	−0.859465	+	0.511195i	$0.829203\pi$
$312$	12.5459	+	11.2725i	0.710271	+	0.638179i
$313$	−24.0252	−	13.8710i	−1.35799	−	0.784033i	−0.368633	−	0.929575i	$-0.620174\pi$
$313$	−24.0252	−	13.8710i	−1.35799	−	0.784033i	−0.989352	+	0.145542i	$0.953507\pi$
$314$	10.8673			0.613276
$315$		0			0
$316$	−5.94509			−0.334437
$317$	3.91737	+	2.26170i	0.220022	+	0.127030i	0.605960	−	0.795495i	$-0.292789\pi$
$317$	3.91737	+	2.26170i	0.220022	+	0.127030i	−0.385939	+	0.922524i	$0.626122\pi$
$318$	5.98268	+	5.37545i	0.335492	+	0.301440i
$319$	−2.36878	−	4.10284i	−0.132626	−	0.229715i
$320$		0			0
$321$	10.0839	+	30.9244i	0.562830	+	1.72603i
$322$	−0.930052	+	0.587438i	−0.0518297	+	0.0327366i
$323$		−	9.74245i		−	0.542084i
$324$	9.58498	+	10.5555i	0.532499	+	0.586419i
$325$		0			0
$326$	−2.68428	+	1.54977i	−0.148668	+	0.0858337i
$327$	0.324650	−	1.53530i	0.0179532	−	0.0849021i
$328$			5.26871i			0.290916i
$329$	−18.2712	−	9.60185i	−1.00732	−	0.529367i
$330$		0			0
$331$	11.4482	−	19.8289i	0.629252	−	1.08990i	−0.358451	−	0.933549i	$-0.616695\pi$
$331$	11.4482	−	19.8289i	0.629252	−	1.08990i	0.987702	−	0.156347i	$-0.0499718\pi$
$332$	4.17809	+	7.23666i	0.229302	+	0.397163i
$333$	11.6958	+	5.17785i	0.640926	+	0.283745i
$334$	−2.48546	−	1.43498i	−0.135998	−	0.0785186i
$335$		0			0
$336$	2.67286	+	7.21116i	0.145816	+	0.393401i
$337$	−31.2616			−1.70293			−0.851464	−	0.524413i	$-0.824285\pi$
$337$	−31.2616			−1.70293			−0.851464	+	0.524413i	$0.824285\pi$
$338$	2.65398	+	1.53228i	0.144358	+	0.0833449i
$339$	−10.2212	+	11.3758i	−0.555140	+	0.617851i
$340$		0			0
$341$	−0.793618	+	1.37459i	−0.0429768	+	0.0744380i
$342$	6.99413	−	5.10405i	0.378199	−	0.275995i
$343$	−2.20308	−	18.3888i	−0.118955	−	0.992900i
$344$			15.1245i			0.815457i
$345$		0			0
$346$	6.39623	−	3.69287i	0.343864	−	0.198530i
$347$	2.41336	−	1.39335i	0.129556	−	0.0747992i	−0.433821	−	0.900999i	$-0.642835\pi$
$347$	2.41336	−	1.39335i	0.129556	−	0.0747992i	0.563377	+	0.826200i	$0.309502\pi$
$348$	3.13763	+	0.663476i	0.168195	+	0.0355661i
$349$		−	16.5636i		−	0.886627i	−0.896367	−	0.443314i	$-0.853803\pi$
$349$		−	16.5636i		−	0.886627i	0.896367	−	0.443314i	$-0.146197\pi$
$350$		0			0
$351$	17.7527	+	12.8127i	0.947568	+	0.683890i
$352$	11.5614	−	20.0249i	0.616223	−	1.06733i
$353$	−1.63849	−	2.83794i	−0.0872078	−	0.151048i	0.819122	−	0.573619i	$-0.194461\pi$
$353$	−1.63849	−	2.83794i	−0.0872078	−	0.151048i	−0.906330	+	0.422571i	$0.861128\pi$
$354$	−8.45334	+	9.40826i	−0.449290	+	0.500044i
$355$		0			0
$356$	−1.41750			−0.0751273
$357$	−9.83290	−	1.67414i	−0.520412	−	0.0886048i
$358$	6.73469			0.355939
$359$	14.7282	+	8.50335i	0.777326	+	0.448789i	0.835482	−	0.549518i	$-0.185189\pi$
$359$	14.7282	+	8.50335i	0.777326	+	0.448789i	−0.0581557	+	0.998308i	$0.518522\pi$
$360$		0			0
$361$	0.517332	+	0.896045i	0.0272280	+	0.0471603i
$362$	−3.85644	+	6.67955i	−0.202690	+	0.351069i
$363$	−8.94314	+	2.91620i	−0.469393	+	0.153061i
$364$	9.43090	+	14.9313i	0.494313	+	0.782614i
$365$		0			0
$366$	−1.61535	+	7.63911i	−0.0844355	+	0.399303i
$367$	14.8236	−	8.55840i	0.773785	−	0.446745i	−0.0604381	−	0.998172i	$-0.519250\pi$
$367$	14.8236	−	8.55840i	0.773785	−	0.446745i	0.834223	+	0.551427i	$0.185916\pi$
$368$	0.937149	−	0.541063i	0.0488523	−	0.0282049i
$369$	0.729192	+	6.80015i	0.0379602	+	0.354002i
$370$		0			0
$371$	10.1748	+	16.1091i	0.528249	+	0.836342i
$372$	−0.333100	−	1.02152i	−0.0172704	−	0.0529632i
$373$	−14.4567	+	25.0397i	−0.748538	+	1.29651i	0.199986	+	0.979799i	$0.435910\pi$
$373$	−14.4567	+	25.0397i	−0.748538	+	1.29651i	−0.948524	+	0.316706i	$0.897423\pi$
$374$	2.84450	+	4.92683i	0.147086	+	0.254760i
$375$		0			0
$376$	−15.6145	−	9.01502i	−0.805255	−	0.464914i
$377$	4.92442			0.253621
$378$	−3.94957	−	7.93614i	−0.203144	−	0.408191i
$379$	0.559557			0.0287425			0.0143712	−	0.999897i	$-0.495425\pi$
$379$	0.559557			0.0287425			0.0143712	+	0.999897i	$0.495425\pi$
$380$		0			0
$381$	−20.3886	−	18.3192i	−1.04454	−	0.938519i
$382$	−4.56125	−	7.90031i	−0.233374	−	0.404215i
$383$	1.89920	−	3.28951i	0.0970447	−	0.168086i	−0.813415	−	0.581683i	$-0.802394\pi$
$383$	1.89920	−	3.28951i	0.0970447	−	0.168086i	0.910460	+	0.413597i	$0.135728\pi$
$384$	6.01470	+	18.4453i	0.306937	+	0.941284i
$385$		0			0
$386$			3.99220i			0.203198i
$387$	2.09323	+	19.5207i	0.106405	+	0.992291i
$388$	5.35029	−	3.08899i	0.271620	−	0.156820i
$389$	−7.88909	+	4.55477i	−0.399993	+	0.230936i	−0.686481	−	0.727148i	$-0.740845\pi$
$389$	−7.88909	+	4.55477i	−0.399993	+	0.230936i	0.286488	+	0.958084i	$0.407512\pi$
$390$		0			0
$391$			1.40348i			0.0709770i
$392$	−1.28466	−	16.1268i	−0.0648850	−	0.814527i
$393$	27.2635	−	8.89016i	1.37526	−	0.448449i
$394$	−4.21545	+	7.30137i	−0.212371	+	0.367838i
$395$		0			0
$396$	7.79874	−	17.6159i	0.391901	−	0.885232i
$397$	20.9910	+	12.1191i	1.05351	+	0.608242i	0.923629	−	0.383288i	$-0.125208\pi$
$397$	20.9910	+	12.1191i	1.05351	+	0.608242i	0.129878	+	0.991530i	$0.458542\pi$
$398$	10.9309			0.547914
$399$	19.2330	−	7.12883i	0.962854	−	0.356888i
$400$		0			0
$401$	−26.1500	−	15.0977i	−1.30587	−	0.753944i	−0.324466	−	0.945897i	$-0.605185\pi$
$401$	−26.1500	−	15.0977i	−1.30587	−	0.753944i	−0.981404	+	0.191953i	$0.938518\pi$
$402$	−6.52190	+	7.25865i	−0.325283	+	0.362028i
$403$	−0.824921	−	1.42881i	−0.0410923	−	0.0711739i
$404$	−5.21509	+	9.03279i	−0.259460	+	0.449398i
$405$		0			0
$406$	−1.76501	−	0.927545i	−0.0875960	−	0.0460333i
$407$		−	17.2824i		−	0.856656i
$408$	−8.52439	−	1.80255i	−0.422020	−	0.0892393i
$409$	21.3618	−	12.3332i	1.05627	−	0.609839i	0.131874	−	0.991267i	$-0.457901\pi$
$409$	21.3618	−	12.3332i	1.05627	−	0.609839i	0.924399	+	0.381427i	$0.124567\pi$
$410$		0			0
$411$	−33.6571	−	7.11704i	−1.66018	−	0.351058i
$412$		−	15.5483i		−	0.766008i
$413$	−25.3329	+	16.0007i	−1.24655	+	0.787344i
$414$	−1.00756	+	0.735280i	−0.0495189	+	0.0361370i
$415$		0			0
$416$	12.0174	+	20.8148i	0.589202	+	1.02053i
$417$	0.264822	−	0.294738i	0.0129684	−	0.0144334i
$418$	−10.1317	−	5.84953i	−0.495556	−	0.286110i
$419$	−39.4615			−1.92782			−0.963911	−	0.266226i	$-0.914223\pi$
$419$	−39.4615			−1.92782			−0.963911	+	0.266226i	$0.914223\pi$
$420$		0			0
$421$	−30.9363			−1.50774			−0.753870	−	0.657023i	$-0.771815\pi$
$421$	−30.9363			−1.50774			−0.753870	+	0.657023i	$0.771815\pi$
$422$	10.2921	+	5.94218i	0.501014	+	0.289261i
$423$	−21.4008	−	9.47434i	−1.04054	−	0.460658i
$424$	8.32178	+	14.4137i	0.404141	+	0.699993i
$425$		0			0
$426$	−8.64066	+	2.81757i	−0.418641	+	0.136512i
$427$	−8.60467	+	16.3737i	−0.416409	+	0.792379i
$428$			29.7509i			1.43807i
$429$	6.11994	−	28.9417i	0.295474	−	1.39732i
$430$		0			0
$431$	−26.6240	+	15.3713i	−1.28243	+	0.740412i	−0.977292	−	0.211896i	$-0.932036\pi$
$431$	−26.6240	+	15.3713i	−1.28243	+	0.740412i	−0.305138	+	0.952308i	$0.598703\pi$
$432$	3.57198	+	7.95515i	0.171857	+	0.382742i
$433$		−	2.95856i		−	0.142179i	−0.997470	−	0.0710896i	$-0.977352\pi$
$433$		−	2.95856i		−	0.142179i	0.997470	−	0.0710896i	$-0.0226476\pi$
$434$	0.0265440	+	0.667491i	0.00127415	+	0.0320406i
$435$		0			0
$436$	0.717658	−	1.24302i	0.0343696	−	0.0595298i
$437$	−1.44308	−	2.49949i	−0.0690318	−	0.119567i
$438$	4.35055	+	3.90897i	0.207877	+	0.186778i
$439$	−15.0772	−	8.70485i	−0.719598	−	0.415460i	0.0950070	−	0.995477i	$-0.469713\pi$
$439$	−15.0772	−	8.70485i	−0.719598	−	0.415460i	−0.814605	+	0.580017i	$0.803046\pi$
$440$		0			0
$441$	−3.89002	−	20.6366i	−0.185239	−	0.982693i
$442$	−5.91341			−0.281272
$443$	27.5344	+	15.8970i	1.30820	+	0.755288i	0.981795	−	0.189942i	$-0.0608301\pi$
$443$	27.5344	+	15.8970i	1.30820	+	0.755288i	0.326403	+	0.945231i	$0.394163\pi$
$444$	8.70232	+	7.81904i	0.412994	+	0.371075i
$445$		0			0
$446$	0.202281	−	0.350362i	0.00957830	−	0.0165901i
$447$	−5.34741	−	16.3989i	−0.252924	−	0.775643i
$448$	−0.0338286	−	0.850674i	−0.00159825	−	0.0401906i
$449$			2.99461i			0.141324i	0.997500	+	0.0706621i	$0.0225112\pi$
$449$			2.99461i			0.141324i	−0.997500	+	0.0706621i	$0.977489\pi$
$450$		0			0
$451$	8.00279	−	4.62041i	0.376837	−	0.217567i
$452$	−12.1140	+	6.99400i	−0.569793	+	0.328970i
$453$	1.81834	−	8.59907i	0.0854329	−	0.404019i
$454$		−	3.50091i		−	0.164306i
$455$		0			0
$456$	17.0347	−	5.55471i	0.797721	−	0.260123i
$457$	4.40252	−	7.62540i	0.205941	−	0.356701i	−0.744491	−	0.667633i	$-0.767308\pi$
$457$	4.40252	−	7.62540i	0.205941	−	0.356701i	0.950432	+	0.310932i	$0.100641\pi$
$458$	−4.63421	−	8.02669i	−0.216543	−	0.375063i
$459$	−11.2516	−	1.14671i	−0.525181	−	0.0535237i
$460$		0			0
$461$	−31.9710			−1.48904			−0.744519	−	0.667602i	$-0.767321\pi$
$461$	−31.9710			−1.48904			−0.744519	+	0.667602i	$0.767321\pi$
$462$	−7.64486	+	9.22056i	−0.355671	+	0.428979i
$463$	−6.94495			−0.322759			−0.161380	−	0.986892i	$-0.551594\pi$
$463$	−6.94495			−0.322759			−0.161380	+	0.986892i	$0.551594\pi$
$464$	1.69865	+	0.980715i	0.0788577	+	0.0455285i
$465$		0			0
$466$	2.71801	+	4.70774i	0.125910	+	0.218082i
$467$	12.2366	−	21.1944i	0.566241	−	0.980758i	−0.430692	−	0.902499i	$-0.641731\pi$
$467$	12.2366	−	21.1944i	0.566241	−	0.980758i	0.996933	−	0.0782589i	$-0.0249361\pi$
$468$	11.8044	+	16.1757i	0.545658	+	0.747721i
$469$	−19.5448	+	12.3449i	−0.902495	+	0.570032i
$470$		0			0
$471$	28.5597	+	6.03916i	1.31596	+	0.278270i
$472$	−22.6668	+	13.0867i	−1.04332	+	0.602364i
$473$	22.9730	−	13.2635i	1.05630	−	0.609854i
$474$	4.10045	+	0.867071i	0.188340	+	0.0398259i
$475$		0			0
$476$	−8.07586	−	4.24401i	−0.370157	−	0.194524i
$477$	12.7355	+	17.4516i	0.583119	+	0.799054i
$478$	−0.876459	+	1.51807i	−0.0400883	+	0.0694350i
$479$	−12.1451	−	21.0359i	−0.554923	−	0.961156i	−0.997909	−	0.0646271i	$-0.979414\pi$
$479$	−12.1451	−	21.0359i	−0.554923	−	0.961156i	0.442986	−	0.896529i	$-0.353919\pi$
$480$		0			0
$481$	15.5573	+	8.98204i	0.709354	+	0.409546i
$482$	0.986217			0.0449209
$483$	−2.77067	+	1.02697i	−0.126070	+	0.0467286i
$484$	−8.60377			−0.391080
$485$		0			0
$486$	−5.07148	−	8.67833i	−0.230047	−	0.393657i
$487$	−4.87823	−	8.44934i	−0.221054	−	0.382876i	0.734075	−	0.679069i	$-0.237616\pi$
$487$	−4.87823	−	8.44934i	−0.221054	−	0.382876i	−0.955128	+	0.296193i	$0.904283\pi$
$488$	−8.07879	+	13.9929i	−0.365710	+	0.633427i
$489$	−7.91563	+	2.58115i	−0.357957	+	0.116724i
$490$		0			0
$491$			23.6689i			1.06816i	0.845434	+	0.534080i	$0.179342\pi$
$491$			23.6689i			1.06816i	−0.845434	+	0.534080i	$0.820658\pi$
$492$	−1.29414	+	6.12011i	−0.0583444	+	0.275916i
$493$	−2.20308	+	1.27195i	−0.0992219	+	0.0572858i
$494$	10.5313	−	6.08026i	0.473826	−	0.273564i
$495$		0			0
$496$		−	0.657143i		−	0.0295066i
$497$	−21.5132	+	0.855513i	−0.965000	+	0.0383750i
$498$	−1.82627	−	5.60064i	−0.0818373	−	0.250971i
$499$	−5.73534	+	9.93391i	−0.256749	+	0.444703i	−0.965369	−	0.260888i	$-0.915985\pi$
$499$	−5.73534	+	9.93391i	−0.256749	+	0.444703i	0.708620	+	0.705590i	$0.249318\pi$
$500$		0			0
$501$	−5.73445	−	5.15241i	−0.256196	−	0.230193i
$502$	−4.91988	−	2.84050i	−0.219585	−	0.126778i
$503$	−16.8580			−0.751659			−0.375830	−	0.926689i	$-0.622642\pi$
$503$	−16.8580			−0.751659			−0.375830	+	0.926689i	$0.622642\pi$
$504$	−2.67906	−	18.1473i	−0.119335	−	0.808347i
$505$		0			0
$506$	1.45955	+	0.842672i	0.0648849	+	0.0374613i
$507$	6.12327	+	5.50176i	0.271944	+	0.244342i
$508$	−12.5351	−	21.7115i	−0.556157	−	0.963292i
$509$	−1.47582	+	2.55620i	−0.0654147	+	0.113302i	−0.896878	−	0.442278i	$-0.854170\pi$
$509$	−1.47582	+	2.55620i	−0.0654147	+	0.113302i	0.831463	+	0.555580i	$0.187504\pi$
$510$		0			0
$511$	7.39902	+	11.7144i	0.327313	+	0.518214i
$512$			17.3304i			0.765902i
$513$	21.2173	−	9.52689i	0.936767	−	0.420623i
$514$	11.2262	−	6.48142i	0.495164	−	0.285883i
$515$		0			0
$516$	−3.71499	+	17.5685i	−0.163543	+	0.773410i
$517$			31.6230i			1.39078i
$518$	−3.88424	−	6.14966i	−0.170664	−	0.270201i
$519$	18.8618	−	6.15051i	0.827941	−	0.269977i
$520$		0			0
$521$	7.91563	+	13.7103i	0.346790	+	0.600658i	0.985677	−	0.168642i	$-0.0539382\pi$
$521$	7.91563	+	13.7103i	0.346790	+	0.600658i	−0.638887	+	0.769300i	$0.720605\pi$
$522$	−2.06733	−	0.915228i	−0.0904845	−	0.0400584i
$523$	19.0179	+	10.9800i	0.831595	+	0.480122i	0.854398	−	0.519618i	$-0.173926\pi$
$523$	19.0179	+	10.9800i	0.831595	+	0.480122i	−0.0228034	+	0.999740i	$0.507259\pi$
$524$	26.2289			1.14581
$525$		0			0
$526$	−5.64798			−0.246263
$527$	0.738105	+	0.426145i	0.0321524	+	0.0185632i
$528$	7.87487	−	8.76445i	0.342710	−	0.381424i
$529$	−11.2921	−	19.5585i	−0.490961	−	0.850370i
$530$		0			0
$531$	−27.4441	+	20.0277i	−1.19097	+	0.869126i
$532$	18.7462	−	0.745479i	0.812752	−	0.0323206i
$533$			9.60532i			0.416053i
$534$	0.977680	+	0.206738i	0.0423083	+	0.00894641i
$535$		0			0
$536$	−17.4879	+	10.0966i	−0.755361	+	0.436108i
$537$	17.6991	+	3.74260i	0.763771	+	0.161505i
$538$			11.1221i			0.479508i
$539$	−23.3689	+	16.0938i	−1.00657	+	0.693208i
$540$		0			0
$541$	−2.34667	+	4.06456i	−0.100891	+	0.174749i	−0.912052	−	0.410074i	$-0.865503\pi$
$541$	−2.34667	+	4.06456i	−0.100891	+	0.174749i	0.811161	+	0.584823i	$0.198836\pi$
$542$	−7.30101	−	12.6457i	−0.313605	−	0.543181i
$543$	−13.8469	+	15.4111i	−0.594225	+	0.661352i
$544$	−10.7527	−	6.20806i	−0.461017	−	0.266168i
$545$		0			0
$546$	−4.32701	−	11.6739i	−0.185179	−	0.499597i
$547$	14.9485			0.639151			0.319575	−	0.947561i	$-0.396460\pi$
$547$	14.9485			0.639151			0.319575	+	0.947561i	$0.396460\pi$
$548$	−27.2497	−	15.7326i	−1.16405	−	0.672065i
$549$	−8.49041	+	19.1782i	−0.362362	+	0.818508i
$550$		0			0
$551$	2.61568	−	4.53049i	0.111432	−	0.193005i
$552$	−2.45398	+	0.800202i	−0.104448	+	0.0340589i
$553$	8.78893	+	4.61874i	0.373743	+	0.196409i
$554$		−	8.51867i		−	0.361924i
$555$		0			0
$556$	0.313862	−	0.181208i	0.0133107	−	0.00768494i
$557$	1.06435	−	0.614501i	0.0450979	−	0.0260373i	−0.477282	−	0.878750i	$-0.658378\pi$
$557$	1.06435	−	0.614501i	0.0450979	−	0.0260373i	0.522379	+	0.852713i	$0.325044\pi$
$558$	0.0807609	+	0.753144i	0.00341888	+	0.0318831i
$559$			27.5732i			1.16622i
$560$		0			0
$561$	4.73755	+	14.5287i	0.200020	+	0.613401i
$562$	−10.5975	+	18.3554i	−0.447028	+	0.774276i
$563$	−2.10379	−	3.64387i	−0.0886643	−	0.153571i	0.818282	−	0.574816i	$-0.194926\pi$
$563$	−2.10379	−	3.64387i	−0.0886643	−	0.153571i	−0.906947	+	0.421245i	$0.861593\pi$
$564$	−15.9233	−	14.3071i	−0.670494	−	0.602440i
$565$		0			0
$566$	10.1953			0.428542
$567$	−5.96937	−	23.0514i	−0.250690	−	0.968067i
$568$	−18.8072			−0.789132
$569$	−22.3139	−	12.8829i	−0.935447	−	0.540081i	−0.0469169	−	0.998899i	$-0.514940\pi$
$569$	−22.3139	−	12.8829i	−0.935447	−	0.540081i	−0.888530	+	0.458818i	$0.848273\pi$
$570$		0			0
$571$	−12.3419	−	21.3768i	−0.516492	−	0.894591i	−0.999817	−	0.0191497i	$-0.993904\pi$
$571$	−12.3419	−	21.3768i	−0.516492	−	0.894591i	0.483324	−	0.875441i	$-0.339429\pi$
$572$	13.5285	−	23.4320i	0.565655	−	0.979743i
$573$	−7.59681	−	23.2972i	−0.317361	−	0.973253i
$574$	1.80922	−	3.44274i	0.0755154	−	0.143697i
$575$		0			0
$576$	−0.102925	−	0.959834i	−0.00428852	−	0.0399931i
$577$	4.96565	−	2.86692i	0.206723	−	0.119351i	−0.393065	−	0.919511i	$-0.628585\pi$
$577$	4.96565	−	2.86692i	0.206723	−	0.119351i	0.599787	+	0.800159i	$0.295252\pi$
$578$	−6.84757	+	3.95345i	−0.284822	+	0.164442i
$579$	−2.21855	+	10.4917i	−0.0921996	+	0.436020i
$580$		0			0
$581$	−0.554521	−	13.9443i	−0.0230054	−	0.578507i
$582$	−4.14073	+	1.35022i	−0.171639	+	0.0559684i
$583$	14.5956	−	25.2804i	0.604489	−	1.04701i
$584$	6.05152	+	10.4815i	0.250414	+	0.433729i
$585$		0			0
$586$	11.6038	+	6.69944i	0.479347	+	0.276751i
$587$	−31.0435			−1.28130			−0.640652	−	0.767832i	$-0.721336\pi$
$587$	−31.0435			−1.28130			−0.640652	+	0.767832i	$0.721336\pi$
$588$	2.46894	−	19.0484i	0.101818	−	0.785542i
$589$	−1.75268			−0.0722178
$590$		0			0
$591$	−15.1359	+	16.8457i	−0.622608	+	0.692941i
$592$	3.57760	+	6.19659i	0.147039	+	0.254678i
$593$	16.2884	−	28.2124i	0.668885	−	1.15854i	−0.309331	−	0.950954i	$-0.600105\pi$
$593$	16.2884	−	28.2124i	0.668885	−	1.15854i	0.978216	−	0.207588i	$-0.0665614\pi$
$594$	−7.94818	+	11.0126i	−0.326118	+	0.451854i
$595$		0			0
$596$		−	15.7766i		−	0.646236i
$597$	28.7268	+	6.07449i	1.17571	+	0.248612i
$598$	−1.51712	+	0.875911i	−0.0620397	+	0.0358187i
$599$	31.8553	−	18.3917i	1.30157	−	0.751463i	0.320899	−	0.947113i	$-0.396015\pi$
$599$	31.8553	−	18.3917i	1.30157	−	0.751463i	0.980674	+	0.195650i	$0.0626817\pi$
$600$		0			0
$601$		−	42.5075i		−	1.73392i	−0.498380	−	0.866959i	$-0.666071\pi$
$601$		−	42.5075i		−	1.73392i	0.498380	−	0.866959i	$-0.333929\pi$
$602$	5.19358	−	9.88279i	0.211675	−	0.402793i
$603$	−21.1736	+	15.4517i	−0.862257	+	0.629242i
$604$	4.01954	−	6.96205i	0.163553	−	0.283282i
$605$		0			0
$606$	4.91436	−	5.46951i	0.199632	−	0.222184i
$607$	−14.6810	−	8.47607i	−0.595883	−	0.344033i	0.171537	−	0.985178i	$-0.445127\pi$
$607$	−14.6810	−	8.47607i	−0.595883	−	0.344033i	−0.767420	+	0.641144i	$0.778460\pi$
$608$	25.5329			1.03550
$609$	−4.12307	−	3.41848i	−0.167075	−	0.138524i
$610$		0			0
$611$	−28.4666	−	16.4352i	−1.15163	−	0.664896i
$612$	−9.45913	−	4.18765i	−0.382363	−	0.169276i
$613$	17.3421	+	30.0373i	0.700439	+	1.21320i	0.968312	+	0.249742i	$0.0803459\pi$
$613$	17.3421	+	30.0373i	0.700439	+	1.21320i	−0.267873	+	0.963454i	$0.586321\pi$
$614$	−4.18664	+	7.25148i	−0.168959	+	0.292646i
$615$		0			0
$616$	−20.9558	+	13.2361i	−0.844333	+	0.533296i
$617$			45.7116i			1.84028i	0.391590	+	0.920140i	$0.371925\pi$
$617$			45.7116i			1.84028i	−0.391590	+	0.920140i	$0.628075\pi$
$618$	−2.26766	+	10.7240i	−0.0912188	+	0.431381i
$619$	34.2356	−	19.7659i	1.37604	−	0.794459i	0.384363	−	0.923182i	$-0.374421\pi$
$619$	34.2356	−	19.7659i	1.37604	−	0.794459i	0.991681	+	0.128723i	$0.0410877\pi$
$620$		0			0
$621$	−3.05653	+	1.37243i	−0.122654	+	0.0550736i
$622$		−	0.295096i		−	0.0118323i
$623$	2.09556	+	1.10126i	0.0839570	+	0.0441209i
$624$	3.79689	+	11.6439i	0.151997	+	0.466130i
$625$		0			0
$626$	8.94408	+	15.4916i	0.357477	+	0.619169i
$627$	−23.3758	−	21.0032i	−0.933540	−	0.838787i
$628$	23.1228	+	13.3499i	0.922698	+	0.532720i
$629$	−9.28004			−0.370020
$630$		0			0
$631$	−21.1685			−0.842703			−0.421351	−	0.906897i	$-0.638444\pi$
$631$	−21.1685			−0.842703			−0.421351	+	0.906897i	$0.638444\pi$
$632$	7.51097	+	4.33646i	0.298770	+	0.172495i
$633$	23.7461	+	21.3359i	0.943821	+	0.848024i
$634$	−1.45835	−	2.52594i	−0.0579187	−	0.100318i
$635$		0			0
$636$	6.12612	+	18.7870i	0.242916	+	0.744952i
$637$	−2.34204	−	29.4006i	−0.0927951	−	1.16489i
$638$			3.05480i			0.120941i
$639$	−24.2738	+	2.60292i	−0.960257	+	0.102970i
$640$		0			0
$641$	30.6083	−	17.6717i	1.20896	−	0.697991i	0.246424	−	0.969162i	$-0.420744\pi$
$641$	30.6083	−	17.6717i	1.20896	−	0.697991i	0.962531	+	0.271171i	$0.0874109\pi$
$642$	4.33908	−	20.5199i	0.171250	−	0.809854i
$643$		−	26.0538i		−	1.02746i	−0.857951	−	0.513731i	$-0.828263\pi$
$643$		−	26.0538i		−	1.02746i	0.857951	−	0.513731i	$-0.171737\pi$
$644$	−2.70055	+	0.107392i	−0.106416	+	0.00423185i
$645$		0			0
$646$	−3.14099	+	5.44036i	−0.123581	+	0.214048i
$647$	20.4213	+	35.3707i	0.802844	+	1.39057i	0.917737	+	0.397188i	$0.130014\pi$
$647$	20.4213	+	35.3707i	0.802844	+	1.39057i	−0.114894	+	0.993378i	$0.536653\pi$
$648$	−4.41016	−	20.3273i	−0.173248	−	0.798530i
$649$	39.7555	+	22.9528i	1.56054	+	0.900977i
$650$		0			0
$651$	−0.301179	+	1.76895i	−0.0118041	+	0.0693306i
$652$	−7.61525			−0.298236
$653$	20.7918	+	12.0041i	0.813645	+	0.469758i	0.848220	−	0.529644i	$-0.177674\pi$
$653$	20.7918	+	12.0041i	0.813645	+	0.469758i	−0.0345747	+	0.999402i	$0.511008\pi$
$654$	−0.676274	+	0.752669i	−0.0264444	+	0.0294317i
$655$		0			0
$656$	−1.91293	+	3.31329i	−0.0746874	+	0.129362i
$657$	9.26115	+	12.6906i	0.361312	+	0.495109i
$658$	7.10731	+	11.2525i	0.277072	+	0.438670i
$659$			38.7398i			1.50909i	0.656248	+	0.754545i	$0.272142\pi$
$659$			38.7398i			1.50909i	−0.656248	+	0.754545i	$0.727858\pi$
$660$		0			0
$661$	44.0826	−	25.4511i	1.71461	−	0.989933i	0.786539	−	0.617541i	$-0.211871\pi$
$661$	44.0826	−	25.4511i	1.71461	−	0.989933i	0.928075	−	0.372392i	$-0.121462\pi$
$662$	−12.7858	+	7.38188i	−0.496934	+	0.286905i
$663$	−15.5407	−	3.28620i	−0.603551	−	0.127625i
$664$		−	12.1903i		−	0.473076i
$665$		0			0
$666$	−4.86179	−	6.66217i	−0.188391	−	0.258154i
$667$	−0.376810	+	0.652654i	−0.0145901	+	0.0252709i
$668$	−3.52560	−	6.10653i	−0.136410	−	0.236269i
$669$	0.726307	−	0.808354i	0.0280807	−	0.0312528i
$670$		0			0
$671$	28.3389			1.09401
$672$	4.38756	−	25.7699i	0.169254	−	0.994097i
$673$	−3.33192			−0.128436			−0.0642181	−	0.997936i	$-0.520455\pi$
$673$	−3.33192			−0.128436			−0.0642181	+	0.997936i	$0.520455\pi$
$674$	17.4570	+	10.0788i	0.672420	+	0.388222i
$675$		0			0
$676$	3.76466	+	6.52057i	0.144794	+	0.250791i
$677$	16.1861	−	28.0352i	0.622083	−	1.07748i	−0.367014	−	0.930215i	$-0.619620\pi$
$677$	16.1861	−	28.0352i	0.622083	−	1.07748i	0.989097	−	0.147264i	$-0.0470467\pi$
$678$	9.37531	−	3.05713i	0.360057	−	0.117408i
$679$	−10.3094	+	0.409974i	−0.395640	+	0.0157334i
$680$		0			0
$681$	1.94552	−	9.20055i	0.0745526	−	0.352566i
$682$	0.886341	−	0.511729i	0.0339398	−	0.0195951i
$683$	−18.8566	+	10.8868i	−0.721526	+	0.416573i	−0.815314	−	0.579019i	$-0.803436\pi$
$683$	−18.8566	+	10.8868i	−0.721526	+	0.416573i	0.0937881	+	0.995592i	$0.470102\pi$
$684$	21.1518	−	2.26814i	0.808758	−	0.0867245i
$685$		0			0
$686$	−4.69835	+	10.9789i	−0.179384	+	0.419176i
$687$	−7.71833	−	23.6698i	−0.294473	−	0.903060i
$688$	−5.49130	+	9.51121i	−0.209354	+	0.362611i
$689$	15.1713	+	26.2775i	0.577982	+	1.00109i
$690$		0			0
$691$	5.15554	+	2.97655i	0.196126	+	0.113233i	0.594847	−	0.803839i	$-0.297213\pi$
$691$	5.15554	+	2.97655i	0.196126	+	0.113233i	−0.398721	+	0.917072i	$0.630546\pi$
$692$	18.1460			0.689809
$693$	−25.2151	+	19.9837i	−0.957842	+	0.759116i
$694$	−1.79689			−0.0682088
$695$		0			0
$696$	−3.48011	−	3.12688i	−0.131913	−	0.118524i
$697$	−2.48100	−	4.29722i	−0.0939747	−	0.162769i
$698$	−5.34014	+	9.24939i	−0.202127	+	0.350095i
$699$	4.52688	+	13.8826i	0.171222	+	0.525088i
$700$		0			0
$701$		−	19.3393i		−	0.730434i	−0.930922	−	0.365217i	$-0.880995\pi$
$701$		−	19.3393i		−	0.730434i	0.930922	−	0.365217i	$-0.119005\pi$
$702$	−5.78257	−	12.8783i	−0.218249	−	0.486062i
$703$	16.5270	−	9.54188i	0.623329	−	0.359879i
$704$	−1.12958	+	0.652166i	−0.0425728	+	0.0245794i
$705$		0			0
$706$			2.11301i			0.0795242i
$707$	14.7273	−	9.30205i	0.553878	−	0.349840i
$708$	−29.5441	+	9.63383i	−1.11034	+	0.362061i
$709$	−16.9012	+	29.2738i	−0.634739	+	1.09940i	0.351831	+	0.936063i	$0.385559\pi$
$709$	−16.9012	+	29.2738i	−0.634739	+	1.09940i	−0.986570	+	0.163337i	$0.947774\pi$
$710$		0			0
$711$	10.2943	+	4.55741i	0.386068	+	0.170916i
$712$	1.79086	+	1.03395i	0.0671152	+	0.0387490i
$713$	0.252487			0.00945573
$714$	4.95112	+	4.10502i	0.185291	+	0.153627i
$715$		0			0
$716$	14.3297	+	8.27324i	0.535525	+	0.309185i
$717$	−3.14700	+	3.50250i	−0.117527	+	0.130803i
$718$	−5.48301	−	9.49685i	−0.204624	−	0.354419i
$719$	13.7118	−	23.7495i	0.511363	−	0.885707i	−0.488550	−	0.872536i	$-0.662474\pi$
$719$	13.7118	−	23.7495i	0.511363	−	0.885707i	0.999913	−	0.0131713i	$-0.00419267\pi$
$720$		0			0
$721$	−12.0795	+	22.9858i	−0.449862	+	0.856036i
$722$		−	0.667157i		−	0.0248290i
$723$	2.59182	+	0.548060i	0.0963909	+	0.0203826i
$724$	−16.4110	+	9.47490i	−0.609910	+	0.352132i
$725$		0			0
$726$	5.93420	+	1.25483i	0.220239	+	0.0465712i
$727$			6.14612i			0.227947i	0.993484	+	0.113973i	$0.0363579\pi$
$727$			6.14612i			0.227947i	−0.993484	+	0.113973i	$0.963642\pi$
$728$	−1.02372	−	25.7432i	−0.0379418	−	0.954105i
$729$	−8.50535	−	25.6254i	−0.315013	−	0.949087i
$730$		0			0
$731$	−7.12202	−	12.3357i	−0.263417	−	0.456252i
$732$	−12.8213	+	14.2697i	−0.473889	+	0.527422i
$733$	14.5795	+	8.41748i	0.538506	+	0.310907i	0.744473	−	0.667652i	$-0.232701\pi$
$733$	14.5795	+	8.41748i	0.538506	+	0.310907i	−0.205967	+	0.978559i	$0.566034\pi$
$734$	−11.0370			−0.407384
$735$		0			0
$736$	−3.67822			−0.135581
$737$	30.6721	+	17.7085i	1.12982	+	0.652302i
$738$	1.78520	−	4.03242i	0.0657139	−	0.148436i
$739$	−19.3419	−	33.5012i	−0.711503	−	1.23236i	−0.964293	−	0.264838i	$-0.914681\pi$
$739$	−19.3419	−	33.5012i	−0.711503	−	1.23236i	0.252790	−	0.967521i	$-0.418652\pi$
$740$		0			0
$741$	31.0557	−	10.1267i	1.14086	−	0.372015i
$742$	−0.488178	−	12.2760i	−0.0179216	−	0.450666i
$743$		−	39.3563i		−	1.44384i	−0.691976	−	0.721920i	$-0.743260\pi$
$743$		−	39.3563i		−	1.44384i	0.691976	−	0.721920i	$-0.256740\pi$
$744$	−0.324280	+	1.53355i	−0.0118887	+	0.0562225i
$745$		0			0
$746$	16.1457	−	9.32174i	0.591137	−	0.341293i
$747$	−1.68714	−	15.7336i	−0.0617294	−	0.575664i
$748$			13.9773i			0.511062i
$749$	23.1135	−	43.9824i	0.844549	−	1.60708i
$750$		0			0
$751$	−16.1416	+	27.9580i	−0.589014	+	1.02020i	0.405347	+	0.914163i	$0.367151\pi$
$751$	−16.1416	+	27.9580i	−0.589014	+	1.02020i	−0.994362	+	0.106040i	$0.966183\pi$
$752$	−6.54623	−	11.3384i	−0.238717	−	0.413469i
$753$	−11.3512	−	10.1990i	−0.413659	−	0.371673i
$754$	−2.74989	−	1.58765i	−0.100145	−	0.0578187i
$755$		0			0
$756$	1.34551	−	21.7379i	0.0489359	−	0.790600i
$757$	40.0667			1.45625			0.728124	−	0.685446i	$-0.240393\pi$
$757$	40.0667			1.45625			0.728124	+	0.685446i	$0.240393\pi$
$758$	−0.312467	−	0.180403i	−0.0113493	−	0.00655252i
$759$	3.36748	+	3.02568i	0.122232	+	0.109825i
$760$		0			0
$761$	6.58977	−	11.4138i	0.238879	−	0.413750i	−0.721514	−	0.692400i	$-0.756553\pi$
$761$	6.58977	−	11.4138i	0.238879	−	0.413750i	0.960393	+	0.278649i	$0.0898868\pi$
$762$	5.47920	+	16.8031i	0.198491	+	0.608712i
$763$	−2.02665	+	1.28007i	−0.0733698	+	0.0463417i
$764$		−	22.4131i		−	0.810877i
$765$		0			0
$766$	−2.12110	+	1.22462i	−0.0766384	+	0.0442472i
$767$	−41.3236	+	23.8582i	−1.49211	+	0.861469i
$768$	2.81871	−	13.3299i	0.101711	−	0.481002i
$769$		−	12.7709i		−	0.460530i	−0.973128	−	0.230265i	$-0.926041\pi$
$769$		−	12.7709i		−	0.460530i	0.973128	−	0.230265i	$-0.0739593\pi$
$770$		0			0
$771$	33.1047	−	10.7949i	1.19224	−	0.388768i
$772$	−4.90423	+	8.49437i	−0.176507	+	0.305719i
$773$	9.09428	+	15.7518i	0.327099	+	0.566551i	0.981935	−	0.189219i	$-0.0605957\pi$
$773$	9.09428	+	15.7518i	0.327099	+	0.566551i	−0.654836	+	0.755771i	$0.727262\pi$
$774$	5.12462	−	11.5756i	0.184201	−	0.416075i
$775$		0			0
$776$	−9.01267			−0.323536
$777$	−6.79047	−	18.3201i	−0.243607	−	0.657231i
$778$	5.87388			0.210589
$779$	8.83694	+	5.10201i	0.316616	+	0.182798i
$780$		0			0
$781$	16.4930	+	28.5667i	0.590167	+	1.02220i
$782$	0.452486	−	0.783728i	0.0161809	−	0.0280261i
$783$	−4.92442	−	3.55412i	−0.175985	−	0.127014i
$784$	5.04735	−	10.6080i	0.180263	−	0.378856i
$785$		0			0
$786$	−18.0906	−	3.82540i	−0.645272	−	0.136447i
$787$	−1.07265	+	0.619297i	−0.0382360	+	0.0220756i	−0.518996	−	0.854777i	$-0.673694\pi$
$787$	−1.07265	+	0.619297i	−0.0382360	+	0.0220756i	0.480760	+	0.876852i	$0.340361\pi$
$788$	−17.9388	+	10.3569i	−0.639042	+	0.368951i
$789$	−14.8431	−	3.13869i	−0.528430	−	0.111740i
$790$		0			0
$791$	23.3423	−	0.928251i	0.829958	−	0.0330048i
$792$	−22.7022	+	16.5672i	−0.806689	+	0.588690i
$793$	−14.7283	+	25.5102i	−0.523019	+	0.905895i
$794$	−7.81449	−	13.5351i	−0.277326	−	0.480343i
$795$		0			0
$796$	23.2580	+	13.4280i	0.824359	+	0.475944i
$797$	−51.4416			−1.82216			−0.911078	−	0.412235i	$-0.864748\pi$
$797$	−51.4416			−1.82216			−0.911078	+	0.412235i	$0.864748\pi$
$798$	−13.0384	−	2.21990i	−0.461555	−	0.0785837i
$799$	16.9805			0.600725
$800$		0			0
$801$	2.45450	+	1.08663i	0.0867254	+	0.0383942i
$802$	9.73510	+	16.8617i	0.343758	+	0.595407i
$803$	10.6138	−	18.3836i	0.374553	−	0.648745i
$804$	−22.7938	+	7.43268i	−0.803876	+	0.262130i
$805$		0			0
$806$			1.06383i			0.0374718i
$807$	−6.18077	+	29.2294i	−0.217574	+	1.02892i
$808$	13.1774	−	7.60797i	0.463579	−	0.267647i
$809$	2.44518	−	1.41172i	0.0859679	−	0.0496336i	−0.456400	−	0.889775i	$-0.650861\pi$
$809$	2.44518	−	1.41172i	0.0859679	−	0.0496336i	0.542368	+	0.840141i	$0.317528\pi$
$810$		0			0
$811$		−	0.162805i		−	0.00571687i	−0.999996	−	0.00285843i	$-0.999090\pi$
$811$		−	0.162805i		−	0.00571687i	0.999996	−	0.00285843i	$-0.000909869\pi$
$812$	−2.61604	−	4.14180i	−0.0918050	−	0.145349i
$813$	−12.1599	−	37.2909i	−0.426467	−	1.30785i
$814$	−5.57189	+	9.65080i	−0.195295	+	0.338260i
$815$		0			0
$816$	−4.70621	−	4.22853i	−0.164750	−	0.148028i
$817$	25.3675	+	14.6459i	0.887496	+	0.512396i
$818$	−15.9051			−0.556108
$819$	−4.88415	−	33.0842i	−0.170666	−	1.15606i
$820$		0			0
$821$	43.3765	+	25.0434i	1.51385	+	0.874022i	0.999868	+	0.0162217i	$0.00516375\pi$
$821$	43.3765	+	25.0434i	1.51385	+	0.874022i	0.513983	+	0.857801i	$0.328170\pi$
$822$	16.5002	+	14.8254i	0.575509	+	0.517096i
$823$	19.1132	+	33.1050i	0.666243	+	1.15397i	0.978947	+	0.204116i	$0.0654319\pi$
$823$	19.1132	+	33.1050i	0.666243	+	1.15397i	−0.312704	+	0.949851i	$0.601235\pi$
$824$	−11.3412	+	19.6435i	−0.395090	+	0.684315i
$825$		0			0
$826$	19.3050	−	0.767700i	0.671708	−	0.0267117i
$827$		−	7.13112i		−	0.247973i	−0.992284	−	0.123987i	$-0.960432\pi$
$827$		−	7.13112i		−	0.247973i	0.992284	−	0.123987i	$-0.0395680\pi$
$828$	−3.04708	+	0.326744i	−0.105894	+	0.0113551i
$829$	−0.876338	+	0.505954i	−0.0304365	+	0.0175725i	−0.515141	−	0.857105i	$-0.672260\pi$
$829$	−0.876338	+	0.505954i	−0.0304365	+	0.0175725i	0.484705	+	0.874678i	$0.338927\pi$
$830$		0			0
$831$	4.73399	−	22.3875i	0.164220	−	0.776612i
$832$		−	1.35578i		−	0.0470032i
$833$	8.64180	+	12.5483i	0.299421	+	0.434772i
$834$	−0.242906	+	0.0792075i	−0.00841115	+	0.00274273i
$835$		0			0
$836$	−14.3717	−	24.8925i	−0.497056	−	0.860927i
$837$	−0.206294	+	2.02418i	−0.00713056	+	0.0699658i
$838$	22.0360	+	12.7225i	0.761222	+	0.439492i
$839$	29.5215			1.01920			0.509598	−	0.860412i	$-0.329794\pi$
$839$	29.5215			1.01920			0.509598	+	0.860412i	$0.329794\pi$
$840$		0			0
$841$	27.6340			0.952897
$842$	17.2754	+	9.97394i	0.595348	+	0.343725i
$843$	−38.0512	+	42.3496i	−1.31055	+	1.45860i
$844$	14.5993	+	25.2868i	0.502530	+	0.870408i
$845$		0			0
$846$	8.89603	+	12.1903i	0.305852	+	0.419112i
$847$	12.7194	+	6.68427i	0.437044	+	0.229674i
$848$			12.0857i			0.415024i
$849$	26.7938	+	5.66576i	0.919562	+	0.194448i
$850$		0			0
$851$	−2.38085	+	1.37459i	−0.0816146	+	0.0471202i
$852$	−21.8463	−	4.61957i	−0.748443	−	0.158264i
$853$		−	22.0904i		−	0.756362i	−0.925732	−	0.378181i	$-0.876550\pi$
$853$		−	22.0904i		−	0.756362i	0.925732	−	0.378181i	$-0.123450\pi$
$854$	10.0839	−	6.36920i	0.345065	−	0.217950i
$855$		0			0
$856$	21.7009	−	37.5871i	0.741722	−	1.28470i
$857$	−7.16559	−	12.4112i	−0.244772	−	0.423957i	0.717296	−	0.696769i	$-0.245380\pi$
$857$	−7.16559	−	12.4112i	−0.244772	−	0.423957i	−0.962067	+	0.272812i	$0.912046\pi$
$858$	−12.7484	+	14.1885i	−0.435223	+	0.484387i
$859$	−23.7901	−	13.7352i	−0.811709	−	0.468640i	0.0358402	−	0.999358i	$-0.488589\pi$
$859$	−23.7901	−	13.7352i	−0.811709	−	0.468640i	−0.847549	+	0.530717i	$0.821923\pi$
$860$		0			0
$861$	6.66791	−	8.04225i	0.227242	−	0.274079i
$862$	19.8231			0.675176
$863$	14.0492	+	8.11130i	0.478240	+	0.276112i	0.719683	−	0.694303i	$-0.244287\pi$
$863$	14.0492	+	8.11130i	0.478240	+	0.276112i	−0.241443	+	0.970415i	$0.577621\pi$
$864$	3.00528	−	29.4881i	0.102242	−	1.00321i
$865$		0			0
$866$	−0.953847	+	1.65211i	−0.0324131	+	0.0561411i
$867$	−20.1927	+	6.58451i	−0.685782	+	0.223622i
$868$	−0.763502	+	1.45286i	−0.0259149	+	0.0493131i
$869$		−	15.2115i		−	0.516014i
$870$		0			0
$871$	−31.8819	+	18.4070i	−1.08028	+	0.623698i
$872$	−1.81336	+	1.04695i	−0.0614083	+	0.0354541i
$873$	−11.6324	+	1.24736i	−0.393696	+	0.0422167i
$874$			1.86101i			0.0629496i
$875$		0			0
$876$	4.45486	+	13.6617i	0.150516	+	0.461587i
$877$	−22.2463	+	38.5317i	−0.751204	+	1.30112i	0.196036	+	0.980597i	$0.437193\pi$
$877$	−22.2463	+	38.5317i	−0.751204	+	1.30112i	−0.947240	+	0.320527i	$0.896140\pi$
$878$	5.61294	+	9.72189i	0.189427	+	0.328098i
$879$	26.7722	+	24.0549i	0.903004	+	0.811351i
$880$		0			0
$881$	−0.841670			−0.0283566			−0.0141783	−	0.999899i	$-0.504513\pi$
$881$	−0.841670			−0.0283566			−0.0141783	+	0.999899i	$0.504513\pi$
$882$	−4.48103	+	12.7780i	−0.150884	+	0.430257i
$883$	51.7706			1.74222			0.871110	−	0.491088i	$-0.163400\pi$
$883$	51.7706			1.74222			0.871110	+	0.491088i	$0.163400\pi$
$884$	−12.5822	−	7.26434i	−0.423185	−	0.244326i
$885$		0			0
$886$	−10.2505	−	17.7543i	−0.344371	−	0.596468i
$887$	27.9867	−	48.4743i	0.939700	−	1.62761i	0.173669	−	0.984804i	$-0.444438\pi$
$887$	27.9867	−	48.4743i	0.939700	−	1.62761i	0.766031	−	0.642804i	$-0.222229\pi$
$888$	−5.29107	−	16.2262i	−0.177557	−	0.544514i
$889$	1.66368	+	41.8358i	0.0557980	+	1.40313i
$890$		0			0
$891$	−27.0081	+	24.5248i	−0.904806	+	0.821611i
$892$	0.860804	−	0.496986i	0.0288219	−	0.0166403i
$893$	−30.2409	+	17.4596i	−1.01197	+	0.584262i
$894$	−2.30097	+	10.8815i	−0.0769560	+	0.363931i
$895$		0			0
$896$	13.7864	−	26.2339i	0.460571	−	0.876413i
$897$	−4.47383	+	1.45884i	−0.149377	+	0.0487092i
$898$	0.965470	−	1.67224i	0.0322182	−	0.0558035i
$899$	0.228825	+	0.396337i	0.00763175	+	0.0132186i
$900$		0			0
$901$	−13.5747	−	7.83734i	−0.452238	−	0.261100i
$902$	−5.95854			−0.198398
$903$	19.1410	−	23.0863i	0.636974	−	0.768263i
$904$	20.4062			0.678701
$905$		0			0
$906$	−3.78776	+	4.21564i	−0.125840	+	0.140055i
$907$	−18.1332	−	31.4075i	−0.602102	−	1.04287i	−0.992502	−	0.122226i	$-0.960997\pi$
$907$	−18.1332	−	31.4075i	−0.602102	−	1.04287i	0.390401	−	0.920645i	$-0.372336\pi$
$908$	4.30070	−	7.44902i	0.142724	−	0.247205i
$909$	15.9547	−	11.6431i	0.529183	−	0.386178i
$910$		0			0
$911$		−	5.35784i		−	0.177513i	−0.996053	−	0.0887565i	$-0.971711\pi$
$911$		−	5.35784i		−	0.177513i	0.996053	−	0.0887565i	$-0.0282893\pi$
$912$	12.7292	+	2.69169i	0.421507	+	0.0891308i
$913$	−18.5162	+	10.6903i	−0.612797	+	0.353798i
$914$	−4.91690	+	2.83877i	−0.162637	+	0.0938983i
$915$		0			0
$916$		−	22.7716i		−	0.752396i
$917$	−38.7755	−	20.3772i	−1.28048	−	0.672916i
$918$	5.91341	+	4.26790i	0.195172	+	0.140862i
$919$	10.0571	−	17.4194i	0.331754	−	0.574615i	−0.651102	−	0.758990i	$-0.725693\pi$
$919$	10.0571	−	17.4194i	0.331754	−	0.574615i	0.982856	+	0.184376i	$0.0590263\pi$
$920$		0			0
$921$	−15.0325	+	16.7306i	−0.495337	+	0.551292i
$922$	17.8532	+	10.3075i	0.587963	+	0.339461i
$923$	−34.2872			−1.12858
$924$	−27.5933	+	10.2276i	−0.907752	+	0.336464i
$925$		0			0
$926$	3.87818	+	2.23907i	0.127445	+	0.0735804i
$927$	−11.9190	+	26.9229i	−0.391473	+	0.884264i
$928$	−3.33351	−	5.77382i	−0.109428	−	0.189535i
$929$	−3.39903	+	5.88728i	−0.111518	+	0.193156i	−0.916383	−	0.400303i	$-0.868905\pi$
$929$	−3.39903	+	5.88728i	−0.111518	+	0.193156i	0.804864	+	0.593459i	$0.202238\pi$
$930$		0			0
$931$	−28.2927	−	13.4619i	−0.927256	−	0.441195i
$932$			13.3558i			0.437483i
$933$	0.163991	−	0.775525i	0.00536881	−	0.0253896i
$934$	−13.6662	+	7.89021i	−0.447173	+	0.258176i
$935$		0			0
$936$	−3.11471	−	29.0466i	−0.101808	−	0.949417i
$937$		−	44.1327i		−	1.44175i	−0.693063	−	0.720877i	$-0.743739\pi$
$937$		−	44.1327i		−	1.44175i	0.693063	−	0.720877i	$-0.256261\pi$
$938$	14.8942	−	0.592295i	0.486312	−	0.0193391i
$939$	14.8965	+	45.6830i	0.486128	+	1.49081i
$940$		0			0
$941$	−4.53288	−	7.85118i	−0.147768	−	0.255941i	0.782634	−	0.622482i	$-0.213875\pi$
$941$	−4.53288	−	7.85118i	−0.147768	−	0.255941i	−0.930402	+	0.366540i	$0.880542\pi$
$942$	−14.0012	−	12.5801i	−0.456184	−	0.409882i
$943$	−1.27303	−	0.734986i	−0.0414557	−	0.0239344i
$944$	−19.0057			−0.618584
$945$		0			0
$946$	−17.1047			−0.556122
$947$	30.7330	+	17.7437i	0.998689	+	0.576593i	0.907860	−	0.419273i	$-0.137715\pi$
$947$	30.7330	+	17.7437i	0.998689	+	0.576593i	0.0908285	+	0.995867i	$0.471048\pi$
$948$	7.65955	+	6.88211i	0.248771	+	0.223521i
$949$	11.0325	+	19.1088i	0.358129	+	0.620297i
$950$		0			0
$951$	−2.42891	−	7.44873i	−0.0787627	−	0.241542i
$952$	7.10731	+	11.2525i	0.230349	+	0.364697i
$953$			10.8726i			0.352198i	0.984373	+	0.176099i	$0.0563478\pi$
$953$			10.8726i			0.352198i	−0.984373	+	0.176099i	$0.943652\pi$
$954$	−1.48529	−	13.8513i	−0.0480882	−	0.448451i
$955$		0			0
$956$	−3.72976	+	2.15338i	−0.120629	+	0.0696452i
$957$	−1.69761	+	8.02816i	−0.0548761	+	0.259514i
$958$			15.6625i			0.506031i
$959$	28.0620	+	44.4287i	0.906169	+	1.43468i
$960$		0			0
$961$	−15.4233	+	26.7140i	−0.497527	+	0.861742i
$962$	−5.79167	−	10.0315i	−0.186731	−	0.323428i
$963$	22.8066	−	51.5158i	0.734932	−	1.66007i
$964$	2.09841	+	1.21152i	0.0675853	+	0.0390204i
$965$		0			0
$966$	1.87829	+	0.319795i	0.0604330	+	0.0102892i
$967$	−21.3855			−0.687711			−0.343855	−	0.939023i	$-0.611733\pi$
$967$	−21.3855			−0.687711			−0.343855	+	0.939023i	$0.611733\pi$
$968$	10.8699	+	6.27575i	0.349373	+	0.201710i
$969$	−11.2780	+	12.5520i	−0.362301	+	0.403228i
$970$		0			0
$971$	−4.43174	+	7.67600i	−0.142221	+	0.246335i	−0.928333	−	0.371750i	$-0.878758\pi$
$971$	−4.43174	+	7.67600i	−0.142221	+	0.246335i	0.786112	+	0.618085i	$0.212091\pi$
$972$	−0.129881	−	24.6953i	−0.00416593	−	0.792102i
$973$	−0.604779	+	0.0240502i	−0.0193883	+	0.000771013i
$974$			6.29102i			0.201577i
$975$		0			0
$976$	−10.1609	+	5.86639i	−0.325242	+	0.187779i
$977$	−0.633128	+	0.365536i	−0.0202555	+	0.0116945i	−0.510094	−	0.860119i	$-0.670389\pi$
$977$	−0.633128	+	0.365536i	−0.0202555	+	0.0116945i	0.489838	+	0.871813i	$0.337056\pi$
$978$	5.25241	+	1.11066i	0.167953	+	0.0355150i
$979$		−	3.62691i		−	0.115916i
$980$		0			0
$981$	−2.19555	+	1.60223i	−0.0700986	+	0.0511553i
$982$	7.63091	−	13.2171i	0.243512	−	0.421775i
$983$	1.86607	+	3.23213i	0.0595184	+	0.103089i	0.894249	−	0.447569i	$-0.147710\pi$
$983$	1.86607	+	3.23213i	0.0595184	+	0.103089i	−0.834731	+	0.550658i	$0.814377\pi$
$984$	6.09913	−	6.78812i	0.194433	−	0.216397i
$985$		0			0
$986$	1.64032			0.0522385
$987$	12.4251	+	33.5219i	0.395495	+	1.06701i
$988$	29.8772			0.950520
$989$	−3.65439	−	2.10987i	−0.116203	−	0.0670898i
$990$		0			0
$991$	2.74255	+	4.75024i	0.0871200	+	0.150896i	0.906293	−	0.422651i	$-0.138900\pi$
$991$	2.74255	+	4.75024i	0.0871200	+	0.150896i	−0.819173	+	0.573547i	$0.805567\pi$
$992$	−1.11684	+	1.93442i	−0.0354596	+	0.0614178i
$993$	−37.7039	+	12.2946i	−1.19650	+	0.390158i
$994$	12.2892	+	6.45819i	0.389790	+	0.204841i
$995$		0			0
$996$	2.99428	−	14.1602i	0.0948774	−	0.448683i
$997$	−4.39264	+	2.53609i	−0.139116	+	0.0803189i	−0.567943	−	0.823068i	$-0.692261\pi$
$997$	−4.39264	+	2.53609i	−0.139116	+	0.0803189i	0.428826	+	0.903387i	$0.358927\pi$
$998$	6.40544	−	3.69818i	0.202761	−	0.117064i
$999$	−9.07472	−	20.2103i	−0.287111	−	0.639425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.j.26.5		24
3.2	odd	2	inner	525.2.t.j.26.7		24
5.2	odd	4		105.2.p.a.89.8	yes	24
5.3	odd	4		105.2.p.a.89.5	yes	24
5.4	even	2	inner	525.2.t.j.26.8		24
7.3	odd	6	inner	525.2.t.j.101.7		24
15.2	even	4		105.2.p.a.89.6	yes	24
15.8	even	4		105.2.p.a.89.7	yes	24
15.14	odd	2	inner	525.2.t.j.26.6		24
21.17	even	6	inner	525.2.t.j.101.5		24
35.2	odd	12		735.2.g.b.734.9		24
35.3	even	12		105.2.p.a.59.6	yes	24
35.12	even	12		735.2.g.b.734.12		24
35.13	even	4		735.2.p.f.509.6		24
35.17	even	12		105.2.p.a.59.7	yes	24
35.18	odd	12		735.2.p.f.374.5		24
35.23	odd	12		735.2.g.b.734.16		24
35.24	odd	6	inner	525.2.t.j.101.6		24
35.27	even	4		735.2.p.f.509.7		24
35.32	odd	12		735.2.p.f.374.8		24
35.33	even	12		735.2.g.b.734.13		24
105.2	even	12		735.2.g.b.734.14		24
105.17	odd	12		105.2.p.a.59.5	✓	24
105.23	even	12		735.2.g.b.734.11		24
105.32	even	12		735.2.p.f.374.6		24
105.38	odd	12		105.2.p.a.59.8	yes	24
105.47	odd	12		735.2.g.b.734.15		24
105.53	even	12		735.2.p.f.374.7		24
105.59	even	6	inner	525.2.t.j.101.8		24
105.62	odd	4		735.2.p.f.509.5		24
105.68	odd	12		735.2.g.b.734.10		24
105.83	odd	4		735.2.p.f.509.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.5	✓	24	105.17	odd	12
105.2.p.a.59.6	yes	24	35.3	even	12
105.2.p.a.59.7	yes	24	35.17	even	12
105.2.p.a.59.8	yes	24	105.38	odd	12
105.2.p.a.89.5	yes	24	5.3	odd	4
105.2.p.a.89.6	yes	24	15.2	even	4
105.2.p.a.89.7	yes	24	15.8	even	4
105.2.p.a.89.8	yes	24	5.2	odd	4
525.2.t.j.26.5		24	1.1	even	1	trivial
525.2.t.j.26.6		24	15.14	odd	2	inner
525.2.t.j.26.7		24	3.2	odd	2	inner
525.2.t.j.26.8		24	5.4	even	2	inner
525.2.t.j.101.5		24	21.17	even	6	inner
525.2.t.j.101.6		24	35.24	odd	6	inner
525.2.t.j.101.7		24	7.3	odd	6	inner
525.2.t.j.101.8		24	105.59	even	6	inner
735.2.g.b.734.9		24	35.2	odd	12
735.2.g.b.734.10		24	105.68	odd	12
735.2.g.b.734.11		24	105.23	even	12
735.2.g.b.734.12		24	35.12	even	12
735.2.g.b.734.13		24	35.33	even	12
735.2.g.b.734.14		24	105.2	even	12
735.2.g.b.734.15		24	105.47	odd	12
735.2.g.b.734.16		24	35.23	odd	12
735.2.p.f.374.5		24	35.18	odd	12
735.2.p.f.374.6		24	105.32	even	12
735.2.p.f.374.7		24	105.53	even	12
735.2.p.f.374.8		24	35.32	odd	12
735.2.p.f.509.5		24	105.62	odd	4
735.2.p.f.509.6		24	35.13	even	4
735.2.p.f.509.7		24	35.27	even	4
735.2.p.f.509.8		24	105.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.558418 - 0.322403i) q^{2} +(-1.28838 - 1.15761i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(0.346239 + 1.06181i) q^{6} +(0.105130 + 2.64366i) q^{7} +2.31113i q^{8} +(0.319861 + 2.98290i) q^{9} +(3.51044 - 2.02675i) q^{11} +(-0.567678 + 2.68460i) q^{12} +4.21339i q^{13} +(0.793618 - 1.51016i) q^{14} +(-0.839111 + 1.45338i) q^{16} +(-1.08830 - 1.88498i) q^{17} +(0.783079 - 1.76883i) q^{18} +(3.87634 + 2.23800i) q^{19} +(2.92489 - 3.52775i) q^{21} -2.61372 q^{22} +(-0.558418 - 0.322403i) q^{23} +(2.67540 - 2.97762i) q^{24} +(1.35841 - 2.35284i) q^{26} +(3.04094 - 4.21339i) q^{27} +(3.54377 - 2.23831i) q^{28} -1.16875i q^{29} +(-0.339111 + 0.195786i) q^{31} +(4.94014 - 2.85219i) q^{32} +(-6.86898 - 1.45250i) q^{33} +1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +(2.13178 - 3.69236i) q^{37} +(-1.44308 - 2.49949i) q^{38} +(4.87748 - 5.42846i) q^{39} +2.27971 q^{41} +(-2.77067 + 1.02697i) q^{42} +6.54419 q^{43} +(-5.56132 - 3.21083i) q^{44} +(0.207887 + 0.360071i) q^{46} +(-3.90070 + 6.75621i) q^{47} +(2.76355 - 0.901147i) q^{48} +(-6.97790 + 0.555857i) q^{49} +(-0.779941 + 3.68841i) q^{51} +(5.78069 - 3.33748i) q^{52} +(6.23667 - 3.60074i) q^{53} +(-3.05653 + 1.37243i) q^{54} +(-6.10984 + 0.242969i) q^{56} +(-2.40346 - 7.37071i) q^{57} +(-0.376810 + 0.652654i) q^{58} +(5.66247 + 9.80768i) q^{59} +(6.05456 + 3.49560i) q^{61} +0.252487 q^{62} +(-7.85215 + 1.15920i) q^{63} -0.321779 q^{64} +(3.36748 + 3.02568i) q^{66} +(4.36870 + 7.56680i) q^{67} +(-1.72411 + 2.98624i) q^{68} +(0.346239 + 1.06181i) q^{69} +8.13766i q^{71} +(-6.89387 + 0.739241i) q^{72} +(4.53525 - 2.61843i) q^{73} +(-2.38085 + 1.37459i) q^{74} -7.09101i q^{76} +(5.72710 + 9.06734i) q^{77} +(-4.47383 + 1.45884i) q^{78} +(1.87634 - 3.24991i) q^{79} +(-8.79538 + 1.90823i) q^{81} +(-1.27303 - 0.734986i) q^{82} -5.27461 q^{83} +(-7.15684 - 1.21852i) q^{84} +(-3.65439 - 2.10987i) q^{86} +(-1.35297 + 1.50580i) q^{87} +(4.68409 + 8.11308i) q^{88} +(0.447379 - 0.774883i) q^{89} +(-11.1388 + 0.442954i) q^{91} +1.02152i q^{92} +(0.663548 + 0.140312i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-9.66653 - 2.04406i) q^{96} +3.89968i q^{97} +(4.07579 + 1.93929i) q^{98} +(7.16845 + 9.82300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^9 - 12 * q^16 - 6 * q^21 - 18 * q^24 + 84 * q^36 + 12 * q^39 + 36 * q^46 + 12 * q^49 - 12 * q^51 + 36 * q^54 + 36 * q^61 - 24 * q^64 - 72 * q^66 - 48 * q^79 - 6 * q^81 - 48 * q^84 - 96 * q^91 + 72 * q^94 - 90 * q^96 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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