LMFDB - Embedded newform 525.2.t.j.26.6

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			26.6
Character	$\chi$	$=$	525.26
Dual form			525.2.t.j.101.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.558418 - 0.322403i) q^{2} +(-0.358331 - 1.69458i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(-0.346239 + 1.06181i) q^{6} +(-0.105130 - 2.64366i) q^{7} +2.31113i q^{8} +(-2.74320 + 1.21444i) q^{9} +O(q^{10})$	\(q+(-0.558418 - 0.322403i) q^{2} +(-0.358331 - 1.69458i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(-0.346239 + 1.06181i) q^{6} +(-0.105130 - 2.64366i) q^{7} +2.31113i q^{8} +(-2.74320 + 1.21444i) q^{9} +(-3.51044 + 2.02675i) q^{11} +(-2.04109 + 1.83392i) q^{12} -4.21339i q^{13} +(-0.793618 + 1.51016i) q^{14} +(-0.839111 + 1.45338i) q^{16} +(-1.08830 - 1.88498i) q^{17} +(1.92339 + 0.206248i) q^{18} +(3.87634 + 2.23800i) q^{19} +(-4.44222 + 1.12546i) q^{21} +2.61372 q^{22} +(-0.558418 - 0.322403i) q^{23} +(3.91639 - 0.828150i) 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} +(4.69239 + 5.22247i) q^{33} +1.40348i q^{34} +(3.83911 + 2.80164i) q^{36} +(-2.13178 + 3.69236i) q^{37} +(-1.44308 - 2.49949i) q^{38} +(-7.13993 + 1.50979i) q^{39} -2.27971 q^{41} +(2.84347 + 0.803709i) 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} +(-2.80428 + 2.51965i) q^{51} +(-5.78069 + 3.33748i) q^{52} +(6.23667 - 3.60074i) q^{53} +(-0.339707 - 3.33324i) 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} +(3.49897 + 7.12441i) q^{63} -0.321779 q^{64} +(-0.936579 - 4.42916i) q^{66} +(-4.36870 - 7.56680i) q^{67} +(-1.72411 + 2.98624i) q^{68} +(-0.346239 + 1.06181i) q^{69} -8.13766i q^{71} +(-2.80673 - 6.33988i) 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} +(6.05026 - 6.66291i) q^{81} +(1.27303 + 0.734986i) q^{82} -5.27461 q^{83} +(5.06285 + 5.20315i) q^{84} +(3.65439 + 2.10987i) q^{86} +(1.98055 - 0.418802i) q^{87} +(-4.68409 - 8.11308i) q^{88} +(-0.447379 + 0.774883i) q^{89} +(-11.1388 + 0.442954i) q^{91} +1.02152i q^{92} +(0.453288 + 0.504494i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-6.60347 - 7.34943i) 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}+O(q^{10}) $ 24 * q + 12 * q^4 + 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.739877\pi$
$3$	−0.358331	−	1.69458i	−0.206883	−	0.978366i
$3$	−0.358331	−	1.69458i	−0.206883	−	0.978366i
$4$	−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
$9$	−2.74320	+	1.21444i	−0.914399	+	0.404814i
$10$		0			0
$11$	−3.51044	+	2.02675i	−1.05844	+	0.611089i	−0.924999	−	0.379968i	$-0.875935\pi$
$11$	−3.51044	+	2.02675i	−1.05844	+	0.611089i	−0.133437	+	0.991057i	$0.542602\pi$
$12$	−2.04109	+	1.83392i	−0.589212	+	0.529407i
$13$		−	4.21339i		−	1.16858i	−0.811543	−	0.584292i	$-0.801372\pi$
$13$		−	4.21339i		−	1.16858i	0.811543	−	0.584292i	$-0.198628\pi$
$14$	−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	$0.918359\pi$
$18$	1.92339	+	0.206248i	0.453348	+	0.0486132i
$19$	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
$21$	−4.44222	+	1.12546i	−0.969372	+	0.245595i
$22$	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	$0.688081\pi$
$24$	3.91639	−	0.828150i	0.799430	−	0.169045i
$25$		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	$0.0346099\pi$
$29$			1.16875i			0.217032i	−0.994095	+	0.108516i	$0.965390\pi$
$30$		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
$33$	4.69239	+	5.22247i	0.816841	+	0.909115i
$34$			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	−0.986331	−	0.164778i	$-0.947309\pi$
$37$	−2.13178	+	3.69236i	−0.350463	+	0.607020i	0.635868	+	0.771798i	$0.280642\pi$
$38$	−1.44308	−	2.49949i	−0.234098	−	0.405470i
$39$	−7.13993	+	1.50979i	−1.14330	+	0.241760i
$40$		0			0
$41$	−2.27971			−0.356031			−0.178016	−	0.984028i	$-0.556968\pi$
$41$	−2.27971			−0.356031			−0.178016	+	0.984028i	$0.556968\pi$
$42$	2.84347	+	0.803709i	0.438757	+	0.124015i
$43$	−6.54419			−0.997980			−0.498990	−	0.866608i	$-0.666295\pi$
$43$	−6.54419			−0.997980			−0.498990	+	0.866608i	$0.666295\pi$
$44$	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
$51$	−2.80428	+	2.51965i	−0.392678	+	0.352822i
$52$	−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	$0.168648\pi$
$54$	−0.339707	−	3.33324i	−0.0462283	−	0.453597i
$55$		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	$-0.902819\pi$
$59$	−5.66247	−	9.80768i	−0.737190	−	1.27685i	0.216566	−	0.976268i	$-0.430515\pi$
$60$		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
$63$	3.49897	+	7.12441i	0.440828	+	0.897591i
$64$	−0.321779			−0.0402224
$65$		0			0
$66$	−0.936579	−	4.42916i	−0.115285	−	0.545192i
$67$	−4.36870	−	7.56680i	−0.533721	−	0.924432i	−0.999224	−	0.0393859i	$-0.987460\pi$
$67$	−4.36870	−	7.56680i	−0.533721	−	0.924432i	0.465503	−	0.885046i	$-0.345873\pi$
$68$	−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	$-0.839590\pi$
$71$		−	8.13766i		−	0.965762i	0.875686	−	0.482881i	$-0.160410\pi$
$72$	−2.80673	−	6.33988i	−0.330777	−	0.747163i
$73$	−4.53525	+	2.61843i	−0.530810	+	0.306464i	−0.741346	−	0.671123i	$-0.765812\pi$
$73$	−4.53525	+	2.61843i	−0.530810	+	0.306464i	0.210536	+	0.977586i	$0.432479\pi$
$74$	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
$81$	6.05026	−	6.66291i	0.672251	−	0.740323i
$82$	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	$0.593483\pi$
$84$	5.06285	+	5.20315i	0.552402	+	0.567710i
$85$		0			0
$86$	3.65439	+	2.10987i	0.394064	+	0.227513i
$87$	1.98055	−	0.418802i	0.212337	−	0.0449002i
$88$	−4.68409	−	8.11308i	−0.499325	−	0.864857i
$89$	−0.447379	+	0.774883i	−0.0474221	+	0.0821375i	−0.888762	−	0.458369i	$-0.848434\pi$
$89$	−0.447379	+	0.774883i	−0.0474221	+	0.0821375i	0.841340	+	0.540506i	$0.181767\pi$
$90$		0			0
$91$	−11.1388	+	0.442954i	−1.16766	+	0.0464342i
$92$			1.02152i			0.106501i
$93$	0.453288	+	0.504494i	0.0470038	+	0.0523135i
$94$	4.35644	−	2.51519i	0.449333	−	0.259422i
$95$		0			0
$96$	−6.60347	−	7.34943i	−0.673964	−	0.750098i
$97$		−	3.89968i		−	0.395953i	−0.980207	−	0.197976i	$-0.936563\pi$
$97$		−	3.89968i		−	0.395953i	0.980207	−	0.197976i	$-0.0634370\pi$
$98$	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	0.982026	−	0.188745i	$-0.0604421\pi$
$101$	3.29188	+	5.70171i	0.327555	+	0.567341i	−0.654471	+	0.756087i	$0.727109\pi$
$102$	2.37831	−	0.502911i	0.235487	−	0.0497956i
$103$	−8.49954	−	4.90721i	−0.837485	−	0.483522i	0.0189238	−	0.999821i	$-0.493976\pi$
$103$	−8.49954	−	4.90721i	−0.837485	−	0.483522i	−0.856408	+	0.516299i	$0.827309\pi$
$104$	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	$-0.695527\pi$
$108$	3.37192	−	7.50959i	0.324463	−	0.722611i
$109$	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	$-0.136326\pi$
$114$	−3.71848	+	3.34105i	−0.348267	+	0.312918i
$115$		0			0
$116$	1.60351	−	0.925786i	0.148882	−	0.0859570i
$117$	5.11692	+	11.5582i	0.473059	+	1.06855i
$118$			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
$123$	0.816892	+	3.86315i	0.0736567	+	0.348329i
$124$	0.537228	+	0.310168i	0.0482445	+	0.0278540i
$125$		0			0
$126$	0.343045	−	5.10648i	0.0305609	−	0.454921i
$127$	−15.8249			−1.40424			−0.702118	−	0.712060i	$-0.747762\pi$
$127$	−15.8249			−1.40424			−0.702118	+	0.712060i	$0.747762\pi$
$128$	−9.70060	−	5.60064i	−0.857420	−	0.495032i
$129$	2.34499	+	11.0896i	0.206465	+	0.976389i
$130$		0			0
$131$	8.27814	−	14.3382i	0.723265	−	1.25273i	−0.236419	−	0.971651i	$-0.575974\pi$
$131$	8.27814	−	14.3382i	0.723265	−	1.25273i	0.959684	−	0.281080i	$-0.0906928\pi$
$132$	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	$0.0108721\pi$
$138$	0.535677	−	0.481306i	0.0455998	−	0.0409715i
$139$			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
$144$	0.536798	−	5.00596i	0.0447332	−	0.417164i
$145$		0			0
$146$	3.37675			0.279462
$147$	3.44234	+	11.6254i	0.283920	+	0.958848i
$148$	6.75445			0.555212
$149$	−8.62438	−	4.97929i	−0.706537	−	0.407919i	0.103240	−	0.994656i	$-0.467079\pi$
$149$	−8.62438	−	4.97929i	−0.706537	−	0.407919i	−0.809777	+	0.586737i	$0.800412\pi$
$150$		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
$156$	7.72703	+	8.59991i	0.618657	+	0.688544i
$157$	14.5956	−	8.42678i	1.16486	−	0.672531i	0.212394	−	0.977184i	$-0.431874\pi$
$157$	14.5956	−	8.42678i	1.16486	−	0.672531i	0.952463	+	0.304653i	$0.0985406\pi$
$158$	−2.09556	+	1.20987i	−0.166714	+	0.0962524i
$159$	−8.33653	−	9.27827i	−0.661130	−	0.735814i
$160$		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	−0.944668	−	0.328028i	$-0.893616\pi$
$163$	−2.40346	+	4.16292i	−0.188254	+	0.326065i	0.756414	+	0.654093i	$0.226949\pi$
$164$	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	$0.444909\pi$
$168$	−2.60108	−	10.2666i	−0.200678	−	0.792082i
$169$	−4.75268			−0.365590
$170$		0			0
$171$	−13.3515	−	1.43170i	−1.02101	−	0.109485i
$172$	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
$177$	−14.5908	+	13.1099i	−1.09672	+	0.985400i
$178$	0.499649	−	0.288473i	0.0374503	−	0.0216219i
$179$	9.04522	−	5.22226i	0.676071	−	0.390330i	−0.122302	−	0.992493i	$-0.539028\pi$
$179$	9.04522	−	5.22226i	0.676071	−	0.390330i	0.798373	+	0.602163i	$0.205694\pi$
$180$		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
$186$	−0.0904741	−	0.427860i	−0.00663389	−	0.0313722i
$187$	7.64079	+	4.41141i	0.558750	+	0.322594i
$188$	12.3592			0.901385
$189$	10.8191	−	8.48217i	0.786973	−	0.616987i
$190$		0			0
$191$	−12.2522	−	7.07383i	−0.886541	−	0.511844i	−0.0137312	−	0.999906i	$-0.504371\pi$
$191$	−12.2522	−	7.07383i	−0.886541	−	0.511844i	−0.872809	+	0.488061i	$0.837704\pi$
$192$	0.115303	+	0.545280i	0.00832131	+	0.0393522i
$193$	3.09566	+	5.36185i	0.222831	+	0.385954i	0.955666	−	0.294452i	$-0.0951369\pi$
$193$	3.09566	+	5.36185i	0.222831	+	0.385954i	−0.732836	+	0.680406i	$0.761804\pi$
$194$	−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	$-0.154227\pi$
$198$	−7.16996	+	3.17421i	−0.509547	+	0.225582i
$199$	−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
$201$	−11.2571	+	10.1145i	−0.794015	+	0.713424i
$202$		−	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
$207$	1.92339	+	0.206248i	0.133685	+	0.0143353i
$208$	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
$213$	−13.7899	+	2.91598i	−0.944869	+	0.199800i
$214$	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
$219$	6.06225	+	6.74707i	0.409649	+	0.455925i
$220$		0			0
$221$	−7.94218	+	4.58542i	−0.534249	+	0.308449i
$222$	−3.18248	−	3.54199i	−0.213594	−	0.237723i
$223$		−	0.627418i		−	0.0420150i	−0.999779	−	0.0210075i	$-0.993313\pi$
$223$		−	0.627418i		−	0.0420150i	0.999779	−	0.0210075i	$-0.00668739\pi$
$224$	−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	$0.775665\pi$
$228$	−12.0163	+	2.54093i	−0.795797	+	0.168277i
$229$	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
$231$	13.3131	−	12.9541i	0.875939	−	0.852320i
$232$	−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	$0.755725\pi$
$234$	0.869006	−	8.10400i	0.0568087	−	0.529775i
$235$		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	$0.0280230\pi$
$239$			2.71852i			0.175847i	−0.996127	+	0.0879233i	$0.971977\pi$
$240$		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
$243$	−13.4588	−	7.86512i	−0.863384	−	0.504548i
$244$		−	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
$249$	1.89006	+	8.93825i	0.119778	+	0.566439i
$250$		0			0
$251$	−8.81039			−0.556107			−0.278054	−	0.960566i	$-0.589689\pi$
$251$	−8.81039			−0.556107			−0.278054	+	0.960566i	$0.589689\pi$
$252$	7.00297	−	10.4438i	0.441146	−	0.657900i
$253$	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
$261$	−1.41938	−	3.20613i	−0.0878577	−	0.198454i
$262$	−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	$0.246291\pi$
$264$	−12.0698	+	10.8447i	−0.742845	+	0.667447i
$265$		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	$0.00958150\pi$
$269$	8.62438	+	14.9379i	0.525838	+	0.910778i	−0.473709	+	0.880681i	$0.657085\pi$
$270$		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
$273$	4.74200	+	18.7168i	0.286999	+	1.13279i
$274$	−12.8069			−0.773692
$275$		0			0
$276$	1.73104	−	0.366042i	0.104197	−	0.0220331i
$277$	−6.60561	−	11.4413i	−0.396893	−	0.687438i	0.596448	−	0.802652i	$-0.296578\pi$
$277$	−6.60561	−	11.4413i	−0.396893	−	0.687438i	−0.993341	+	0.115213i	$0.963245\pi$
$278$	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	$0.436940\pi$
$281$			32.8703i			1.96088i	−0.196817	+	0.980440i	$0.563060\pi$
$282$	−5.82324	−	6.48106i	−0.346769	−	0.385942i
$283$	13.6932	−	7.90575i	0.813974	−	0.469948i	−0.0343601	−	0.999410i	$-0.510939\pi$
$283$	13.6932	−	7.90575i	0.813974	−	0.469948i	0.848334	+	0.529462i	$0.177606\pi$
$284$	−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
$291$	−6.60832	+	1.39738i	−0.387387	+	0.0819158i
$292$	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	$0.707620\pi$
$294$	1.82580	−	7.60166i	0.106483	−	0.443338i
$295$		0			0
$296$	−8.53351	−	4.92683i	−0.496000	−	0.286366i
$297$	−19.2145	−	8.62762i	−1.11494	−	0.500625i
$298$	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
$303$	8.48241	−	7.62146i	0.487302	−	0.437841i
$304$	−6.50535	+	3.75587i	−0.373108	+	0.215414i
$305$		0			0
$306$	−1.70444	−	3.85002i	−0.0974366	−	0.220091i
$307$			12.9857i			0.741136i	0.928805	+	0.370568i	$0.120837\pi$
$307$			12.9857i			0.741136i	−0.928805	+	0.370568i	$0.879163\pi$
$308$	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	0.859465	−	0.511195i	$-0.170797\pi$
$311$	−0.228825	−	0.396337i	−0.0129755	−	0.0224742i	−0.872440	+	0.488721i	$0.837464\pi$
$312$	−3.48932	−	16.5013i	−0.197544	−	0.934202i
$313$	24.0252	+	13.8710i	1.35799	+	0.784033i	0.989352	−	0.145542i	$-0.0464925\pi$
$313$	24.0252	+	13.8710i	1.35799	+	0.784033i	0.368633	+	0.929575i	$0.379826\pi$
$314$	−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	$0.626122\pi$
$318$	1.66393	+	7.86888i	0.0933087	+	0.441265i
$319$	−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
$324$	−13.9339	−	3.02306i	−0.774103	−	0.167948i
$325$		0			0
$326$	2.68428	−	1.54977i	0.148668	−	0.0858337i
$327$	1.16728	−	1.04880i	0.0645508	−	0.0579989i
$328$		−	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
$333$	1.36375	−	12.7178i	0.0747330	−	0.696931i
$334$	−2.48546	−	1.43498i	−0.135998	−	0.0785186i
$335$		0			0
$336$	2.09180	−	7.40063i	0.114117	−	0.403738i
$337$	31.2616			1.70293			0.851464	−	0.524413i	$-0.175715\pi$
$337$	31.2616			1.70293			0.851464	+	0.524413i	$0.175715\pi$
$338$	2.65398	+	1.53228i	0.144358	+	0.0833449i
$339$	−14.9624	+	3.16390i	−0.812644	+	0.171840i
$340$		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	$0.309502\pi$
$348$	−2.14340	−	2.38553i	−0.114899	−	0.127878i
$349$		−	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	$0.861128\pi$
$354$	12.3745	−	2.61667i	0.657695	−	0.139075i
$355$		0			0
$356$	1.41750			0.0751273
$357$	6.95592	+	7.14869i	0.368147	+	0.378349i
$358$	−6.73469			−0.355939
$359$	−14.7282	−	8.50335i	−0.777326	−	0.448789i	0.0581557	−	0.998308i	$-0.481478\pi$
$359$	−14.7282	−	8.50335i	−0.777326	−	0.448789i	−0.835482	+	0.549518i	$0.814811\pi$
$360$		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
$366$	−5.80799	+	5.21849i	−0.303588	+	0.272775i
$367$	−14.8236	+	8.55840i	−0.773785	+	0.446745i	−0.834223	−	0.551427i	$-0.814084\pi$
$367$	−14.8236	+	8.55840i	−0.773785	+	0.446745i	0.0604381	+	0.998172i	$0.480750\pi$
$368$	0.937149	−	0.541063i	0.0488523	−	0.0282049i
$369$	6.25370	−	2.76858i	0.325555	−	0.144126i
$370$		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	$-0.564090\pi$
$373$	14.4567	−	25.0397i	0.748538	−	1.29651i	0.948524	−	0.316706i	$-0.102577\pi$
$374$	−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
$378$	−8.77626	+	1.24849i	−0.451402	+	0.0642156i
$379$	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
$381$	5.67057	+	26.8166i	0.290512	+	1.37386i
$382$	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
$387$	17.9520	−	7.94754i	0.912552	−	0.403996i
$388$	−5.35029	+	3.08899i	−0.271620	+	0.156820i
$389$	7.88909	−	4.55477i	0.399993	−	0.230936i	−0.286488	−	0.958084i	$-0.592488\pi$
$389$	7.88909	−	4.55477i	0.399993	−	0.230936i	0.686481	+	0.727148i	$0.259155\pi$
$390$		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
$396$	−19.1552	−	2.05404i	−0.962584	−	0.103219i
$397$	−20.9910	−	12.1191i	−1.05351	−	0.608242i	−0.129878	−	0.991530i	$-0.541458\pi$
$397$	−20.9910	−	12.1191i	−1.05351	−	0.608242i	−0.923629	+	0.383288i	$0.874792\pi$
$398$	10.9309			0.547914
$399$	−19.7383	−	5.57906i	−0.988153	−	0.279302i
$400$		0			0
$401$	26.1500	+	15.0977i	1.30587	+	0.753944i	0.981404	−	0.191953i	$-0.0614821\pi$
$401$	26.1500	+	15.0977i	1.30587	+	0.753944i	0.324466	+	0.945897i	$0.394815\pi$
$402$	9.54713	−	2.01881i	0.476167	−	0.100689i
$403$	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
$408$	−5.82324	−	6.48106i	−0.288294	−	0.320860i
$409$	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
$411$	−22.9921	−	25.5894i	−1.13412	−	1.26223i
$412$			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
$417$	0.387662	−	0.0819740i	0.0189839	−	0.00401428i
$418$	10.1317	+	5.84953i	0.495556	+	0.286110i
$419$	39.4615			1.92782			0.963911	−	0.266226i	$-0.0857766\pi$
$419$	39.4615			1.92782			0.963911	+	0.266226i	$0.0857766\pi$
$420$		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
$423$	2.49536	−	23.2708i	0.121329	−	1.13146i
$424$	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
$429$	22.0043	−	19.7709i	1.06238	−	0.954548i
$430$		0			0
$431$	26.6240	−	15.3713i	1.28243	−	0.740412i	0.305138	−	0.952308i	$-0.401297\pi$
$431$	26.6240	−	15.3713i	1.28243	−	0.740412i	0.977292	+	0.211896i	$0.0679639\pi$
$432$	−8.67536	+	0.884148i	−0.417393	+	0.0425386i
$433$			2.95856i			0.142179i	0.997470	+	0.0710896i	$0.0226476\pi$
$433$			2.95856i			0.142179i	−0.997470	+	0.0710896i	$0.977352\pi$
$434$	−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
$438$	−1.21000	−	5.72217i	−0.0578159	−	0.273416i
$439$	−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
$441$	18.4667	−	9.99907i	0.879366	−	0.476146i
$442$	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	$0.394163\pi$
$444$	−2.42033	−	11.4460i	−0.114864	−	0.543201i
$445$		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	$-0.977489\pi$
$449$		−	2.99461i		−	0.141324i	0.997500	−	0.0706621i	$-0.0225112\pi$
$450$		0			0
$451$	8.00279	−	4.62041i	0.376837	−	0.217567i
$452$	−12.1140	+	6.99400i	−0.569793	+	0.328970i
$453$	6.53784	−	5.87426i	0.307175	−	0.275997i
$454$		−	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	−0.950432	−	0.310932i	$-0.899359\pi$
$457$	−4.40252	+	7.62540i	−0.205941	+	0.356701i	0.744491	+	0.667633i	$0.232692\pi$
$458$	−4.63421	−	8.02669i	−0.216543	−	0.375063i
$459$	4.63273	−	10.3175i	0.216237	−	0.481582i
$460$		0			0
$461$	31.9710			1.48904			0.744519	−	0.667602i	$-0.232679\pi$
$461$	31.9710			1.48904			0.744519	+	0.667602i	$0.232679\pi$
$462$	−11.6107	+	2.94164i	−0.540181	+	0.136857i
$463$	6.94495			0.322759			0.161380	−	0.986892i	$-0.448406\pi$
$463$	6.94495			0.322759			0.161380	+	0.986892i	$0.448406\pi$
$464$	−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
$471$	−19.5099	−	21.7139i	−0.898970	−	1.00052i
$472$	22.6668	−	13.0867i	1.04332	−	0.602364i
$473$	22.9730	−	13.2635i	1.05630	−	0.609854i
$474$	2.80113	+	3.11756i	0.128660	+	0.143194i
$475$		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	$0.0205858\pi$
$479$	12.1451	+	21.0359i	0.554923	+	0.961156i	−0.442986	+	0.896529i	$0.646081\pi$
$480$		0			0
$481$	15.5573	+	8.98204i	0.709354	+	0.409546i
$482$	0.986217			0.0449209
$483$	2.84347	+	0.803709i	0.129382	+	0.0365700i
$484$	−8.60377			−0.391080
$485$		0			0
$486$	4.97991	+	8.73119i	0.225893	+	0.396055i
$487$	4.87823	+	8.44934i	0.221054	+	0.382876i	0.955128	−	0.296193i	$-0.0957171\pi$
$487$	4.87823	+	8.44934i	0.221054	+	0.382876i	−0.734075	+	0.679069i	$0.762384\pi$
$488$	−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	$-0.820658\pi$
$491$		−	23.6689i		−	1.06816i	0.845434	−	0.534080i	$-0.179342\pi$
$492$	4.65310	−	4.18081i	0.209778	−	0.188486i
$493$	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
$501$	−1.59489	−	7.54238i	−0.0712545	−	0.336969i
$502$	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	$0.622642\pi$
$504$	−16.4654	+	8.08656i	−0.733429	+	0.360204i
$505$		0			0
$506$	−1.45955	−	0.842672i	−0.0648849	−	0.0374613i
$507$	1.70303	+	8.05379i	0.0756343	+	0.357681i
$508$	12.5351	+	21.7115i	0.556157	+	0.963292i
$509$	1.47582	−	2.55620i	0.0654147	−	0.113302i	−0.831463	−	0.555580i	$-0.812496\pi$
$509$	1.47582	−	2.55620i	0.0654147	−	0.113302i	0.896878	+	0.442278i	$0.145830\pi$
$510$		0			0
$511$	7.39902	+	11.7144i	0.327313	+	0.518214i
$512$			17.3304i			0.765902i
$513$	2.35812	+	23.1382i	0.104114	+	1.02158i
$514$	11.2262	−	6.48142i	0.495164	−	0.285883i
$515$		0			0
$516$	13.3573	−	12.0015i	0.588021	−	0.528338i
$517$		−	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	0.638887	−	0.769300i	$-0.279395\pi$
$521$	−7.91563	−	13.7103i	−0.346790	−	0.600658i	−0.985677	+	0.168642i	$0.946062\pi$
$522$	−0.241054	+	2.24797i	−0.0105506	+	0.0983911i
$523$	−19.0179	−	10.9800i	−0.831595	−	0.480122i	0.0228034	−	0.999740i	$-0.492741\pi$
$523$	−19.0179	−	10.9800i	−0.831595	−	0.480122i	−0.854398	+	0.519618i	$0.826074\pi$
$524$	−26.2289			−1.14581
$525$		0			0
$526$	−5.64798			−0.246263
$527$	0.738105	+	0.426145i	0.0321524	+	0.0185632i
$528$	−11.5277	+	2.43761i	−0.501678	+	0.106083i
$529$	−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
$534$	−0.667880	−	0.743327i	−0.0289020	−	0.0321669i
$535$		0			0
$536$	17.4879	−	10.0966i	0.755361	−	0.436108i
$537$	−12.0907	−	13.4565i	−0.521753	−	0.580693i
$538$		−	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
$543$	−20.2698	+	4.28620i	−0.869860	+	0.183938i
$544$	−10.7527	−	6.20806i	−0.461017	−	0.266168i
$545$		0			0
$546$	3.38634	−	11.9807i	0.144922	−	0.512725i
$547$	−14.9485			−0.639151			−0.319575	−	0.947561i	$-0.603540\pi$
$547$	−14.9485			−0.639151			−0.319575	+	0.947561i	$0.603540\pi$
$548$	−27.2497	−	15.7326i	−1.16405	−	0.672065i
$549$	−20.8541	−	2.23622i	−0.890029	−	0.0954393i
$550$		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	$0.325044\pi$
$558$	−0.692623	+	0.306631i	−0.0293211	+	0.0129807i
$559$			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	$0.861593\pi$
$564$	−4.42868	−	20.9436i	−0.186481	−	0.881884i
$565$		0			0
$566$	−10.1953			−0.428542
$567$	−18.2505	−	15.2944i	−0.766450	−	0.642303i
$568$	18.8072			0.789132
$569$	22.3139	+	12.8829i	0.935447	+	0.540081i	0.888530	−	0.458818i	$-0.151727\pi$
$569$	22.3139	+	12.8829i	0.935447	+	0.540081i	0.0469169	+	0.998899i	$0.485060\pi$
$570$		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
$576$	0.882703	−	0.390782i	0.0367793	−	0.0162826i
$577$	−4.96565	+	2.86692i	−0.206723	+	0.119351i	−0.599787	−	0.800159i	$-0.704748\pi$
$577$	−4.96565	+	2.86692i	−0.206723	+	0.119351i	0.393065	+	0.919511i	$0.371415\pi$
$578$	−6.84757	+	3.95345i	−0.284822	+	0.164442i
$579$	7.97680	−	7.16716i	0.331504	−	0.297857i
$580$		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	$0.721336\pi$
$588$	13.2231	−	13.9315i	0.545312	−	0.574524i
$589$	−1.75268			−0.0722178
$590$		0			0
$591$	−22.1568	+	4.68522i	−0.911408	+	0.192724i
$592$	−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
$597$	19.6241	+	21.8409i	0.803159	+	0.893888i
$598$	1.51712	−	0.875911i	0.0620397	−	0.0358187i
$599$	−31.8553	+	18.3917i	−1.30157	+	0.751463i	−0.980674	−	0.195650i	$-0.937318\pi$
$599$	−31.8553	+	18.3917i	−1.30157	+	0.751463i	−0.320899	+	0.947113i	$0.603985\pi$
$600$		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
$606$	−7.19392	+	1.52121i	−0.292233	+	0.0617948i
$607$	14.6810	+	8.47607i	0.595883	+	0.344033i	0.767420	−	0.641144i	$-0.221540\pi$
$607$	14.6810	+	8.47607i	0.595883	+	0.344033i	−0.171537	+	0.985178i	$0.554873\pi$
$608$	25.5329			1.03550
$609$	−1.31538	−	5.19187i	−0.0533021	−	0.210385i
$610$		0			0
$611$	28.4666	+	16.4352i	1.15163	+	0.664896i
$612$	1.10295	−	10.2857i	0.0445841	−	0.415774i
$613$	−17.3421	−	30.0373i	−0.700439	−	1.21320i	−0.968312	−	0.249742i	$-0.919654\pi$
$613$	−17.3421	−	30.0373i	−0.700439	−	1.21320i	0.267873	−	0.963454i	$-0.413679\pi$
$614$	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	$0.628075\pi$
$618$	8.15340	−	7.32584i	0.327978	−	0.294689i
$619$	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
$621$	−0.339707	−	3.33324i	−0.0136320	−	0.133758i
$622$			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
$627$	6.50139	+	30.7456i	0.259641	+	1.22786i
$628$	−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
$633$	6.60437	+	31.2326i	0.262500	+	1.24139i
$634$	−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
$639$	9.88271	+	22.3232i	0.390954	+	0.883092i
$640$		0			0
$641$	−30.6083	+	17.6717i	−1.20896	+	0.697991i	−0.962531	−	0.271171i	$-0.912589\pi$
$641$	−30.6083	+	17.6717i	−1.20896	+	0.697991i	−0.246424	+	0.969162i	$0.579256\pi$
$642$	15.6012	−	14.0177i	0.615730	−	0.553234i
$643$			26.0538i			1.02746i	0.857951	+	0.513731i	$0.171737\pi$
$643$			26.0538i			1.02746i	−0.857951	+	0.513731i	$0.828263\pi$
$644$	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	$0.536653\pi$
$648$	15.3988	+	13.9829i	0.604924	+	0.549302i
$649$	39.7555	+	22.9528i	1.56054	+	0.900977i
$650$		0			0
$651$	1.28606	−	1.25138i	0.0504045	−	0.0490454i
$652$	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	$0.511008\pi$
$654$	−0.989968	+	0.209336i	−0.0387108	+	0.00818569i
$655$		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	$-0.727858\pi$
$659$		−	38.7398i		−	1.50909i	0.656248	−	0.754545i	$-0.272142\pi$
$660$		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
$663$	10.6163	+	11.8156i	0.412302	+	0.458878i
$664$		−	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
$669$	−1.06321	+	0.224823i	−0.0411060	+	0.00869218i
$670$		0			0
$671$	−28.3389			−1.09401
$672$	−18.7352	+	18.2300i	−0.722726	+	0.703238i
$673$	3.33192			0.128436			0.0642181	−	0.997936i	$-0.479545\pi$
$673$	3.33192			0.128436			0.0642181	+	0.997936i	$0.479545\pi$
$674$	−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
$681$	6.99514	−	6.28515i	0.268055	−	0.240847i
$682$	−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	$0.470102\pi$
$684$	8.61162	+	19.4520i	0.329273	+	0.743767i
$685$		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
$693$	−26.7223	−	17.9183i	−1.01510	−	0.680659i
$694$	−1.79689			−0.0682088
$695$		0			0
$696$	0.967905	+	4.57730i	0.0366883	+	0.173502i
$697$	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	$0.119005\pi$
$701$			19.3393i			0.730434i	−0.930922	+	0.365217i	$0.880995\pi$
$702$	−14.0443	+	1.43132i	−0.530067	+	0.0540217i
$703$	−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
$711$	−1.20034	+	11.1939i	−0.0450161	+	0.419802i
$712$	−1.79086	−	1.03395i	−0.0671152	−	0.0387490i
$713$	0.252487			0.00945573
$714$	−1.57956	−	6.23457i	−0.0591134	−	0.233323i
$715$		0			0
$716$	−14.3297	−	8.27324i	−0.535525	−	0.309185i
$717$	4.60675	−	0.974132i	0.172042	−	0.0363796i
$718$	5.48301	+	9.49685i	0.204624	+	0.354419i
$719$	−13.7118	+	23.7495i	−0.511363	+	0.885707i	0.488550	+	0.872536i	$0.337526\pi$
$719$	−13.7118	+	23.7495i	−0.511363	+	0.885707i	−0.999913	+	0.0131713i	$0.995807\pi$
$720$		0			0
$721$	−12.0795	+	22.9858i	−0.449862	+	0.856036i
$722$		−	0.667157i		−	0.0248290i
$723$	1.77055	+	1.97055i	0.0658473	+	0.0732857i
$724$	−16.4110	+	9.47490i	−0.609910	+	0.352132i
$725$		0			0
$726$	4.05382	+	4.51176i	0.150451	+	0.167447i
$727$		−	6.14612i		−	0.227947i	−0.993484	−	0.113973i	$-0.963642\pi$
$727$		−	6.14612i		−	0.227947i	0.993484	−	0.113973i	$-0.0363579\pi$
$728$	−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
$732$	−18.7686	+	3.96875i	−0.693706	+	0.146689i
$733$	−14.5795	−	8.41748i	−0.538506	−	0.310907i	0.205967	−	0.978559i	$-0.433966\pi$
$733$	−14.5795	−	8.41748i	−0.538506	−	0.310907i	−0.744473	+	0.667652i	$0.767299\pi$
$734$	11.0370			0.407384
$735$		0			0
$736$	−3.67822			−0.135581
$737$	30.6721	+	17.7085i	1.12982	+	0.652302i
$738$	−4.38478	−	0.470187i	−0.161406	−	0.0173078i
$739$	−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	$-0.256740\pi$
$744$	−1.16595	+	1.04761i	−0.0427458	+	0.0384072i
$745$		0			0
$746$	−16.1457	+	9.32174i	−0.591137	+	0.341293i
$747$	14.4693	−	6.40571i	0.529404	−	0.234373i
$748$		−	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
$753$	3.15704	+	14.9299i	0.115049	+	0.544076i
$754$	−2.74989	−	1.58765i	−0.100145	−	0.0578187i
$755$		0			0
$756$	−20.2073	−	8.12473i	−0.734933	−	0.295494i
$757$	−40.0667			−1.45625			−0.728124	−	0.685446i	$-0.759607\pi$
$757$	−40.0667			−1.45625			−0.728124	+	0.685446i	$0.759607\pi$
$758$	−0.312467	−	0.180403i	−0.0113493	−	0.00655252i
$759$	−0.936579	−	4.42916i	−0.0339957	−	0.160768i
$760$		0			0
$761$	−6.58977	+	11.4138i	−0.238879	+	0.413750i	−0.960393	−	0.278649i	$-0.910113\pi$
$761$	−6.58977	+	11.4138i	−0.238879	+	0.413750i	0.721514	+	0.692400i	$0.243447\pi$
$762$	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
$768$	10.1347	−	9.10604i	0.365704	−	0.328586i
$769$		−	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	$0.727262\pi$
$774$	−12.5870	−	1.34973i	−0.452432	−	0.0485150i
$775$		0			0
$776$	9.01267			0.323536
$777$	5.31426	−	18.8015i	0.190648	−	0.674500i
$778$	−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
$786$	12.3582	+	13.7543i	0.440803	+	0.490598i
$787$	1.07265	−	0.619297i	0.0382360	−	0.0220756i	−0.480760	−	0.876852i	$-0.659639\pi$
$787$	1.07265	−	0.619297i	0.0382360	−	0.0220756i	0.518996	+	0.854777i	$0.326306\pi$
$788$	−17.9388	+	10.3569i	−0.639042	+	0.368951i
$789$	−10.1398	−	11.2852i	−0.360985	−	0.401763i
$790$		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	$0.864748\pi$
$798$	9.22354	+	9.47915i	0.326510	+	0.335558i
$799$	16.9805			0.600725
$800$		0			0
$801$	0.286199	−	2.66897i	0.0101123	−	0.0943036i
$802$	−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
$807$	22.2230	−	19.9674i	0.782287	−	0.702886i
$808$	−13.1774	+	7.60797i	−0.463579	+	0.267647i
$809$	−2.44518	+	1.41172i	−0.0859679	+	0.0496336i	−0.542368	−	0.840141i	$-0.682472\pi$
$809$	−2.44518	+	1.41172i	−0.0859679	+	0.0496336i	0.456400	+	0.889775i	$0.349139\pi$
$810$		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
$816$	−1.30891	−	6.18996i	−0.0458211	−	0.216692i
$817$	−25.3675	−	14.6459i	−0.887496	−	0.512396i
$818$	−15.9051			−0.556108
$819$	30.0179	−	14.7425i	1.04891	−	0.515145i
$820$		0			0
$821$	−43.3765	−	25.0434i	−1.51385	−	0.874022i	−0.999868	−	0.0162217i	$-0.994836\pi$
$821$	−43.3765	−	25.0434i	−1.51385	−	0.874022i	−0.513983	−	0.857801i	$-0.671830\pi$
$822$	4.58911	+	21.7023i	0.160063	+	0.756954i
$823$	−19.1132	−	33.1050i	−0.666243	−	1.15397i	−0.978947	−	0.204116i	$-0.934568\pi$
$823$	−19.1132	−	33.1050i	−0.666243	−	1.15397i	0.312704	−	0.949851i	$-0.398765\pi$
$824$	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	$-0.0395680\pi$
$828$	−1.24057	−	2.80222i	−0.0431129	−	0.0973840i
$829$	−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
$831$	−17.0211	+	15.2935i	−0.590456	+	0.530525i
$832$			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
$837$	−1.85614	−	0.833433i	−0.0641575	−	0.0288077i
$838$	−22.0360	−	12.7225i	−0.761222	−	0.439492i
$839$	−29.5215			−1.01920			−0.509598	−	0.860412i	$-0.670206\pi$
$839$	−29.5215			−1.01920			−0.509598	+	0.860412i	$0.670206\pi$
$840$		0			0
$841$	27.6340			0.952897
$842$	17.2754	+	9.97394i	0.595348	+	0.343725i
$843$	55.7014	−	11.7785i	1.91846	−	0.405672i
$844$	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
$849$	−18.3036	−	20.3713i	−0.628178	−	0.699140i
$850$		0			0
$851$	2.38085	−	1.37459i	0.0816146	−	0.0471202i
$852$	14.9238	+	16.6097i	0.511282	+	0.569038i
$853$			22.0904i			0.756362i	0.925732	+	0.378181i	$0.123450\pi$
$853$			22.0904i			0.756362i	−0.925732	+	0.378181i	$0.876550\pi$
$854$	−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	$0.912046\pi$
$858$	−18.6618	+	3.94617i	−0.637103	+	0.134720i
$859$	−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
$861$	10.1270	−	2.56572i	0.345127	−	0.0874395i
$862$	−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	$0.577621\pi$
$864$	27.0401	+	12.1414i	0.919923	+	0.413059i
$865$		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
$873$	4.73594	+	10.6976i	0.160287	+	0.362059i
$874$			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	$-0.562807\pi$
$877$	22.2463	−	38.5317i	0.751204	−	1.30112i	0.947240	−	0.320527i	$-0.103860\pi$
$878$	5.61294	+	9.72189i	0.189427	+	0.328098i
$879$	7.44602	+	35.2129i	0.251148	+	1.18770i
$880$		0			0
$881$	0.841670			0.0283566			0.0141783	−	0.999899i	$-0.495487\pi$
$881$	0.841670			0.0283566			0.0141783	+	0.999899i	$0.495487\pi$
$882$	−13.5359	−	0.370050i	−0.455776	−	0.0124602i
$883$	−51.7706			−1.74222			−0.871110	−	0.491088i	$-0.836600\pi$
$883$	−51.7706			−1.74222			−0.871110	+	0.491088i	$0.836600\pi$
$884$	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
$891$	−7.73501	+	35.6521i	−0.259133	+	1.19439i
$892$	−0.860804	+	0.496986i	−0.0288219	+	0.0166403i
$893$	−30.2409	+	17.4596i	−1.01197	+	0.584262i
$894$	8.27316	−	7.43344i	0.276696	−	0.248612i
$895$		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
$903$	29.0707	−	7.36521i	0.967414	−	0.245099i
$904$	20.4062			0.678701
$905$		0			0
$906$	−5.54473	+	1.17247i	−0.184211	+	0.0389528i
$907$	18.1332	+	31.4075i	0.602102	+	1.04287i	0.992502	+	0.122226i	$0.0390031\pi$
$907$	18.1332	+	31.4075i	0.602102	+	1.04287i	−0.390401	+	0.920645i	$0.627664\pi$
$908$	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	$0.0282893\pi$
$911$			5.35784i			0.177513i	−0.996053	+	0.0887565i	$0.971711\pi$
$912$	8.69569	+	9.67799i	0.287943	+	0.320470i
$913$	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
$921$	22.0054	−	4.65320i	0.725102	−	0.153328i
$922$	−17.8532	−	10.3075i	−0.587963	−	0.339461i
$923$	−34.2872			−1.12858
$924$	−28.3183	−	8.00419i	−0.931604	−	0.263319i
$925$		0			0
$926$	−3.87818	−	2.23907i	−0.127445	−	0.0735804i
$927$	29.2754	+	3.13925i	0.961532	+	0.103107i
$928$	3.33351	+	5.77382i	0.109428	+	0.189535i
$929$	3.39903	−	5.88728i	0.111518	−	0.193156i	−0.804864	−	0.593459i	$-0.797762\pi$
$929$	3.39903	−	5.88728i	0.111518	−	0.193156i	0.916383	+	0.400303i	$0.131095\pi$
$930$		0			0
$931$	−28.2927	−	13.4619i	−0.927256	−	0.441195i
$932$			13.3558i			0.437483i
$933$	−0.589629	+	0.529783i	−0.0193036	+	0.0173443i
$934$	−13.6662	+	7.89021i	−0.447173	+	0.258176i
$935$		0			0
$936$	−26.7124	+	11.8259i	−0.873123	+	0.386540i
$937$			44.1327i			1.44175i	0.693063	+	0.720877i	$0.256261\pi$
$937$			44.1327i			1.44175i	−0.693063	+	0.720877i	$0.743739\pi$
$938$	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	0.930402	−	0.366540i	$-0.119458\pi$
$941$	4.53288	+	7.85118i	0.147768	+	0.255941i	−0.782634	+	0.622482i	$0.786125\pi$
$942$	3.89409	+	18.4155i	0.126876	+	0.600008i
$943$	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	$0.471048\pi$
$948$	2.13031	+	10.0744i	0.0691893	+	0.327202i
$949$	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	$0.943652\pi$
$954$	12.7382	−	5.63933i	0.412414	−	0.182580i
$955$		0			0
$956$	3.72976	−	2.15338i	0.120629	−	0.0696452i
$957$	−6.10378	+	5.48426i	−0.197307	+	0.177281i
$958$		−	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
$963$	56.0173	+	6.00683i	1.80513	+	0.193567i
$964$	2.09841	+	1.21152i	0.0675853	+	0.0390204i
$965$		0			0
$966$	−1.32873	−	1.36555i	−0.0427511	−	0.0439358i
$967$	21.3855			0.687711			0.343855	−	0.939023i	$-0.388267\pi$
$967$	21.3855			0.687711			0.343855	+	0.939023i	$0.388267\pi$
$968$	10.8699	+	6.27575i	0.349373	+	0.201710i
$969$	−16.5093	+	3.49102i	−0.530357	+	0.112148i
$970$		0			0
$971$	4.43174	−	7.67600i	0.142221	−	0.246335i	−0.786112	−	0.618085i	$-0.787909\pi$
$971$	4.43174	−	7.67600i	0.142221	−	0.246335i	0.928333	+	0.371750i	$0.121242\pi$
$972$	−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	$0.337056\pi$
$978$	−3.58806	−	3.99339i	−0.114734	−	0.127694i
$979$		−	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	$0.814377\pi$
$984$	−8.92825	+	1.88794i	−0.284622	+	0.0601855i
$985$		0			0
$986$	−1.64032			−0.0522385
$987$	9.72394	−	34.4027i	0.309516	−	1.09505i
$988$	−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
$996$	10.7660	−	9.67323i	0.341132	−	0.306508i
$997$	4.39264	−	2.53609i	0.139116	−	0.0803189i	−0.428826	−	0.903387i	$-0.641073\pi$
$997$	4.39264	−	2.53609i	0.139116	−	0.0803189i	0.567943	+	0.823068i	$0.307739\pi$
$998$	6.40544	−	3.69818i	0.202761	−	0.117064i
$999$	−22.0400	+	2.24620i	−0.697314	+	0.0710666i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.558418 - 0.322403i) q^{2} +(-0.358331 - 1.69458i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(-0.346239 + 1.06181i) q^{6} +(-0.105130 - 2.64366i) q^{7} +2.31113i q^{8} +(-2.74320 + 1.21444i) q^{9} +O(q^{10})\)	\(q+(-0.558418 - 0.322403i) q^{2} +(-0.358331 - 1.69458i) q^{3} +(-0.792113 - 1.37198i) q^{4} +(-0.346239 + 1.06181i) q^{6} +(-0.105130 - 2.64366i) q^{7} +2.31113i q^{8} +(-2.74320 + 1.21444i) q^{9} +(-3.51044 + 2.02675i) q^{11} +(-2.04109 + 1.83392i) q^{12} -4.21339i q^{13} +(-0.793618 + 1.51016i) q^{14} +(-0.839111 + 1.45338i) q^{16} +(-1.08830 - 1.88498i) q^{17} +(1.92339 + 0.206248i) q^{18} +(3.87634 + 2.23800i) q^{19} +(-4.44222 + 1.12546i) q^{21} +2.61372 q^{22} +(-0.558418 - 0.322403i) q^{23} +(3.91639 - 0.828150i) 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} +(4.69239 + 5.22247i) q^{33} +1.40348i q^{34} +(3.83911 + 2.80164i) q^{36} +(-2.13178 + 3.69236i) q^{37} +(-1.44308 - 2.49949i) q^{38} +(-7.13993 + 1.50979i) q^{39} -2.27971 q^{41} +(2.84347 + 0.803709i) 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} +(-2.80428 + 2.51965i) q^{51} +(-5.78069 + 3.33748i) q^{52} +(6.23667 - 3.60074i) q^{53} +(-0.339707 - 3.33324i) 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} +(3.49897 + 7.12441i) q^{63} -0.321779 q^{64} +(-0.936579 - 4.42916i) q^{66} +(-4.36870 - 7.56680i) q^{67} +(-1.72411 + 2.98624i) q^{68} +(-0.346239 + 1.06181i) q^{69} -8.13766i q^{71} +(-2.80673 - 6.33988i) 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} +(6.05026 - 6.66291i) q^{81} +(1.27303 + 0.734986i) q^{82} -5.27461 q^{83} +(5.06285 + 5.20315i) q^{84} +(3.65439 + 2.10987i) q^{86} +(1.98055 - 0.418802i) q^{87} +(-4.68409 - 8.11308i) q^{88} +(-0.447379 + 0.774883i) q^{89} +(-11.1388 + 0.442954i) q^{91} +1.02152i q^{92} +(0.453288 + 0.504494i) q^{93} +(4.35644 - 2.51519i) q^{94} +(-6.60347 - 7.34943i) q^{96} -3.89968i q^{97} +(4.07579 + 1.93929i) q^{98} +(7.16845 - 9.82300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^4 + 6 * q^9	\( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84} - 96 q^{91} + 72 q^{94} - 90 q^{96} + 48 q^{99}+O(q^{100}) \) 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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