LMFDB - Embedded newform 2100.2.bc.f.1549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(949,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("2100.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bc (of order $6$, degree $2$, not 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1549.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2100.1549
Dual form			2100.2.bc.f.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(0.358719 - 2.62132i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{3} +(0.358719 - 2.62132i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{11} +5.24264i q^{13} +(-3.67423 + 2.12132i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(3.67423 + 2.12132i) q^{23} +1.00000i q^{27} +10.2426 q^{29} +(-3.74264 - 6.48244i) q^{31} +(3.67423 + 2.12132i) q^{33} +(4.54026 + 2.62132i) q^{37} +(-2.62132 - 4.54026i) q^{39} +4.24264 q^{41} +5.24264i q^{43} +(5.19615 + 3.00000i) q^{47} +(-6.74264 - 1.88064i) q^{49} +(2.12132 - 3.67423i) q^{51} +(7.34847 - 4.24264i) q^{53} -7.00000i q^{57} +(-0.878680 - 1.52192i) q^{59} +(6.24264 - 10.8126i) q^{61} +(-2.09077 - 1.62132i) q^{63} +(2.80821 - 1.62132i) q^{67} -4.24264 q^{69} +12.7279 q^{71} +(-0.655892 + 0.378680i) q^{73} +(-10.3923 + 4.24264i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +1.75736i q^{83} +(-8.87039 + 5.12132i) q^{87} +(-0.878680 + 1.52192i) q^{89} +(13.7426 + 1.88064i) q^{91} +(6.48244 + 3.74264i) q^{93} +16.4853i q^{97} -4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} - 28 q^{19} + 8 q^{21} + 48 q^{29} + 4 q^{31} - 4 q^{39} - 20 q^{49} - 24 q^{59} + 16 q^{61} + 44 q^{79} - 4 q^{81} - 24 q^{89} + 76 q^{91}+O(q^{100}) $ 8 * q + 4 * q^9 - 28 * q^19 + 8 * q^21 + 48 * q^29 + 4 * q^31 - 4 * q^39 - 20 * q^49 - 24 * q^59 + 16 * q^61 + 44 * q^79 - 4 * q^81 - 24 * q^89 + 76 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.358719	−	2.62132i	0.135583	−	0.990766i
$7$	0.358719	−	2.62132i	0.135583	−	0.990766i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	−0.985520	−	0.169559i	$-0.945766\pi$
$11$	−2.12132	−	3.67423i	−0.639602	−	1.10782i	0.345918	−	0.938265i	$-0.387568\pi$
$12$		0			0
$13$			5.24264i			1.45405i	0.686613	+	0.727023i	$0.259097\pi$
$13$			5.24264i			1.45405i	−0.686613	+	0.727023i	$0.740903\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.67423	+	2.12132i	−0.891133	+	0.514496i	−0.874313	−	0.485363i	$-0.838688\pi$
$17$	−3.67423	+	2.12132i	−0.891133	+	0.514496i	−0.0168199	+	0.999859i	$0.505354\pi$
$18$		0			0
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	0.114708	+	0.993399i	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	1.00000	+	2.44949i	0.218218	+	0.534522i
$22$		0			0
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	0.831493	−	0.555536i	$-0.187487\pi$
$23$	3.67423	+	2.12132i	0.766131	+	0.442326i	−0.0653618	+	0.997862i	$0.520820\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	10.2426			1.90201			0.951005	−	0.309175i	$-0.100053\pi$
$29$	10.2426			1.90201			0.951005	+	0.309175i	$0.100053\pi$
$30$		0			0
$31$	−3.74264	−	6.48244i	−0.672198	−	1.16428i	−0.977279	−	0.211955i	$-0.932017\pi$
$31$	−3.74264	−	6.48244i	−0.672198	−	1.16428i	0.305081	−	0.952326i	$-0.401316\pi$
$32$		0			0
$33$	3.67423	+	2.12132i	0.639602	+	0.369274i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.54026	+	2.62132i	0.746414	+	0.430942i	0.824397	−	0.566012i	$-0.191515\pi$
$37$	4.54026	+	2.62132i	0.746414	+	0.430942i	−0.0779826	+	0.996955i	$0.524848\pi$
$38$		0			0
$39$	−2.62132	−	4.54026i	−0.419747	−	0.727023i
$40$		0			0
$41$	4.24264			0.662589			0.331295	−	0.943527i	$-0.392515\pi$
$41$	4.24264			0.662589			0.331295	+	0.943527i	$0.392515\pi$
$42$		0			0
$43$			5.24264i			0.799495i	0.916625	+	0.399748i	$0.130902\pi$
$43$			5.24264i			0.799495i	−0.916625	+	0.399748i	$0.869098\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	0.828554	−	0.559908i	$-0.189164\pi$
$47$	5.19615	+	3.00000i	0.757937	+	0.437595i	−0.0706177	+	0.997503i	$0.522497\pi$
$48$		0			0
$49$	−6.74264	−	1.88064i	−0.963234	−	0.268662i
$50$		0			0
$51$	2.12132	−	3.67423i	0.297044	−	0.514496i
$52$		0			0
$53$	7.34847	−	4.24264i	1.00939	−	0.582772i	0.0983769	−	0.995149i	$-0.468635\pi$
$53$	7.34847	−	4.24264i	1.00939	−	0.582772i	0.911013	+	0.412378i	$0.135302\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	7.00000i		−	0.927173i
$58$		0			0
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	0.803143	−	0.595786i	$-0.203159\pi$
$59$	−0.878680	−	1.52192i	−0.114394	−	0.198137i	−0.917537	+	0.397649i	$0.869826\pi$
$60$		0			0
$61$	6.24264	−	10.8126i	0.799288	−	1.38441i	−0.120792	−	0.992678i	$-0.538543\pi$
$61$	6.24264	−	10.8126i	0.799288	−	1.38441i	0.920080	−	0.391730i	$-0.128123\pi$
$62$		0			0
$63$	−2.09077	−	1.62132i	−0.263412	−	0.204267i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.80821	−	1.62132i	0.343077	−	0.198076i	−0.318555	−	0.947904i	$-0.603197\pi$
$67$	2.80821	−	1.62132i	0.343077	−	0.198076i	0.661632	+	0.749829i	$0.269864\pi$
$68$		0			0
$69$	−4.24264			−0.510754
$70$		0			0
$71$	12.7279			1.51053			0.755263	−	0.655422i	$-0.227509\pi$
$71$	12.7279			1.51053			0.755263	+	0.655422i	$0.227509\pi$
$72$		0			0
$73$	−0.655892	+	0.378680i	−0.0767664	+	0.0443211i	−0.537892	−	0.843014i	$-0.680779\pi$
$73$	−0.655892	+	0.378680i	−0.0767664	+	0.0443211i	0.461125	+	0.887335i	$0.347446\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.3923	+	4.24264i	−1.18431	+	0.483494i
$78$		0			0
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	−0.370907	−	0.928670i	$-0.620953\pi$
$79$	5.50000	−	9.52628i	0.618798	−	1.07179i	0.989705	−	0.143120i	$-0.0457135\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			1.75736i			0.192895i	0.995338	+	0.0964476i	$0.0307480\pi$
$83$			1.75736i			0.192895i	−0.995338	+	0.0964476i	$0.969252\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.87039	+	5.12132i	−0.951005	+	0.549063i
$88$		0			0
$89$	−0.878680	+	1.52192i	−0.0931399	+	0.161323i	−0.908831	−	0.417165i	$-0.863024\pi$
$89$	−0.878680	+	1.52192i	−0.0931399	+	0.161323i	0.815691	+	0.578488i	$0.196357\pi$
$90$		0			0
$91$	13.7426	+	1.88064i	1.44062	+	0.197144i
$92$		0			0
$93$	6.48244	+	3.74264i	0.672198	+	0.388094i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			16.4853i			1.67383i	0.547335	+	0.836913i	$0.315642\pi$
$97$			16.4853i			1.67383i	−0.547335	+	0.836913i	$0.684358\pi$
$98$		0			0
$99$	−4.24264			−0.426401
$100$		0			0
$101$	8.12132	+	14.0665i	0.808102	+	1.39967i	0.914177	+	0.405315i	$0.132838\pi$
$101$	8.12132	+	14.0665i	0.808102	+	1.39967i	−0.106076	+	0.994358i	$0.533829\pi$
$102$		0			0
$103$	−7.58410	−	4.37868i	−0.747283	−	0.431444i	0.0774283	−	0.996998i	$-0.475329\pi$
$103$	−7.58410	−	4.37868i	−0.747283	−	0.431444i	−0.824711	+	0.565554i	$0.808662\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.0227	+	6.36396i	1.06561	+	0.615227i	0.926977	−	0.375117i	$-0.122398\pi$
$107$	11.0227	+	6.36396i	1.06561	+	0.615227i	0.138628	+	0.990345i	$0.455731\pi$
$108$		0			0
$109$	3.74264	+	6.48244i	0.358480	+	0.620906i	0.987707	−	0.156316i	$-0.0499618\pi$
$109$	3.74264	+	6.48244i	0.358480	+	0.620906i	−0.629227	+	0.777221i	$0.716628\pi$
$110$		0			0
$111$	−5.24264			−0.497609
$112$		0			0
$113$			18.0000i			1.69330i	0.532152	+	0.846649i	$0.321383\pi$
$113$			18.0000i			1.69330i	−0.532152	+	0.846649i	$0.678617\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4.54026	+	2.62132i	0.419747	+	0.242341i
$118$		0			0
$119$	4.24264	+	10.3923i	0.388922	+	0.952661i
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		0			0
$123$	−3.67423	+	2.12132i	−0.331295	+	0.191273i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	11.2426i		−	0.997623i	−0.866710	−	0.498812i	$-0.833770\pi$
$127$		−	11.2426i		−	0.997623i	0.866710	−	0.498812i	$-0.166230\pi$
$128$		0			0
$129$	−2.62132	−	4.54026i	−0.230794	−	0.399748i
$130$		0			0
$131$	1.24264	−	2.15232i	0.108570	−	0.188049i	−0.806621	−	0.591069i	$-0.798706\pi$
$131$	1.24264	−	2.15232i	0.108570	−	0.188049i	0.915191	+	0.403020i	$0.132039\pi$
$132$		0			0
$133$	14.6354	+	11.3492i	1.26905	+	0.984104i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.67423	+	2.12132i	−0.313911	+	0.181237i	−0.648675	−	0.761065i	$-0.724677\pi$
$137$	−3.67423	+	2.12132i	−0.313911	+	0.181237i	0.334764	+	0.942302i	$0.391343\pi$
$138$		0			0
$139$	−1.48528			−0.125980			−0.0629900	−	0.998014i	$-0.520064\pi$
$139$	−1.48528			−0.125980			−0.0629900	+	0.998014i	$0.520064\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	19.2627	−	11.1213i	1.61083	−	0.930012i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.77962	−	1.74264i	0.559173	−	0.143731i
$148$		0			0
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$		0			0
$151$	−2.75736	−	4.77589i	−0.224391	−	0.388656i	0.731746	−	0.681578i	$-0.238706\pi$
$151$	−2.75736	−	4.77589i	−0.224391	−	0.388656i	−0.956136	+	0.292922i	$0.905373\pi$
$152$		0			0
$153$			4.24264i			0.342997i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	9.08052	−	5.24264i	0.724704	−	0.418408i	−0.0917773	−	0.995780i	$-0.529255\pi$
$157$	9.08052	−	5.24264i	0.724704	−	0.418408i	0.816482	+	0.577371i	$0.195921\pi$
$158$		0			0
$159$	−4.24264	+	7.34847i	−0.336463	+	0.582772i
$160$		0			0
$161$	6.87868	−	8.87039i	0.542116	−	0.699084i
$162$		0			0
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	0.746156	−	0.665771i	$-0.231897\pi$
$163$	6.92820	+	4.00000i	0.542659	+	0.313304i	−0.203497	+	0.979076i	$0.565231\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	6.72792i		−	0.520622i	−0.965525	−	0.260311i	$-0.916175\pi$
$167$		−	6.72792i		−	0.520622i	0.965525	−	0.260311i	$-0.0838251\pi$
$168$		0			0
$169$	−14.4853			−1.11425
$170$		0			0
$171$	3.50000	+	6.06218i	0.267652	+	0.463586i
$172$		0			0
$173$	−3.04384	−	1.75736i	−0.231419	−	0.133610i	0.379808	−	0.925065i	$-0.375990\pi$
$173$	−3.04384	−	1.75736i	−0.231419	−	0.133610i	−0.611226	+	0.791456i	$0.709323\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.52192	+	0.878680i	0.114394	+	0.0660456i
$178$		0			0
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	−13.0000			−0.966282			−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000			−0.966282			−0.483141	+	0.875542i	$0.660504\pi$
$182$		0			0
$183$			12.4853i			0.922939i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	15.5885	+	9.00000i	1.13994	+	0.658145i
$188$		0			0
$189$	2.62132	+	0.358719i	0.190673	+	0.0260930i
$190$		0			0
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	−0.953912	−	0.300088i	$-0.902984\pi$
$191$	−3.00000	+	5.19615i	−0.217072	+	0.375980i	0.736839	+	0.676068i	$0.236317\pi$
$192$		0			0
$193$	−13.2005	+	7.62132i	−0.950194	+	0.548595i	−0.893141	−	0.449777i	$-0.851504\pi$
$193$	−13.2005	+	7.62132i	−0.950194	+	0.548595i	−0.0570527	+	0.998371i	$0.518170\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.75736i		−	0.552689i	−0.961059	−	0.276344i	$-0.910877\pi$
$197$		−	7.75736i		−	0.552689i	0.961059	−	0.276344i	$-0.0891231\pi$
$198$		0			0
$199$	−3.24264	−	5.61642i	−0.229865	−	0.398137i	0.727903	−	0.685680i	$-0.240495\pi$
$199$	−3.24264	−	5.61642i	−0.229865	−	0.398137i	−0.957768	+	0.287543i	$0.907162\pi$
$200$		0			0
$201$	−1.62132	+	2.80821i	−0.114359	+	0.198076i
$202$		0			0
$203$	3.67423	−	26.8492i	0.257881	−	1.88445i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.67423	−	2.12132i	0.255377	−	0.147442i
$208$		0			0
$209$	29.6985			2.05429
$210$		0			0
$211$	5.51472			0.379649			0.189824	−	0.981818i	$-0.439208\pi$
$211$	5.51472			0.379649			0.189824	+	0.981818i	$0.439208\pi$
$212$		0			0
$213$	−11.0227	+	6.36396i	−0.755263	+	0.436051i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−18.3351	+	7.48528i	−1.24467	+	0.508134i
$218$		0			0
$219$	0.378680	−	0.655892i	0.0255888	−	0.0443211i
$220$		0			0
$221$	−11.1213	−	19.2627i	−0.748101	−	1.29575i
$222$		0			0
$223$			24.4853i			1.63966i	0.572610	+	0.819828i	$0.305931\pi$
$223$			24.4853i			1.63966i	−0.572610	+	0.819828i	$0.694069\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	23.5673	−	13.6066i	1.56422	−	0.903102i	0.567396	−	0.823445i	$-0.307951\pi$
$227$	23.5673	−	13.6066i	1.56422	−	0.903102i	0.996822	−	0.0796568i	$-0.0253824\pi$
$228$		0			0
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	6.87868	−	8.87039i	0.452584	−	0.583629i
$232$		0			0
$233$	−2.15232	−	1.24264i	−0.141003	−	0.0814081i	0.427839	−	0.903855i	$-0.359275\pi$
$233$	−2.15232	−	1.24264i	−0.141003	−	0.0814081i	−0.568842	+	0.822447i	$0.692608\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			11.0000i			0.714527i
$238$		0			0
$239$	22.9706			1.48584			0.742921	−	0.669379i	$-0.233440\pi$
$239$	22.9706			1.48584			0.742921	+	0.669379i	$0.233440\pi$
$240$		0			0
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	0.923224	−	0.384262i	$-0.125544\pi$
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	−0.794393	+	0.607404i	$0.792211\pi$
$242$		0			0
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−31.7818	−	18.3492i	−2.02223	−	1.16753i
$248$		0			0
$249$	−0.878680	−	1.52192i	−0.0556841	−	0.0964476i
$250$		0			0
$251$	6.72792			0.424663			0.212331	−	0.977198i	$-0.431894\pi$
$251$	6.72792			0.424663			0.212331	+	0.977198i	$0.431894\pi$
$252$		0			0
$253$		−	18.0000i		−	1.13165i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.52192	−	0.878680i	−0.0949346	−	0.0548105i	0.451781	−	0.892129i	$-0.350789\pi$
$257$	−1.52192	−	0.878680i	−0.0949346	−	0.0548105i	−0.546716	+	0.837318i	$0.684122\pi$
$258$		0			0
$259$	8.50000	−	10.9612i	0.528164	−	0.681093i
$260$		0			0
$261$	5.12132	−	8.87039i	0.317002	−	0.549063i
$262$		0			0
$263$	−7.34847	+	4.24264i	−0.453126	+	0.261612i	−0.709150	−	0.705058i	$-0.750921\pi$
$263$	−7.34847	+	4.24264i	−0.453126	+	0.261612i	0.256023	+	0.966671i	$0.417588\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	1.75736i		−	0.107549i
$268$		0			0
$269$	7.24264	+	12.5446i	0.441592	+	0.764859i	0.997808	−	0.0661785i	$-0.0210807\pi$
$269$	7.24264	+	12.5446i	0.441592	+	0.764859i	−0.556216	+	0.831038i	$0.687747\pi$
$270$		0			0
$271$	−13.7279	+	23.7775i	−0.833912	+	1.44438i	0.0610014	+	0.998138i	$0.480571\pi$
$271$	−13.7279	+	23.7775i	−0.833912	+	1.44438i	−0.894913	+	0.446240i	$0.852763\pi$
$272$		0			0
$273$	−12.8418	+	5.24264i	−0.777221	+	0.317299i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.69258	+	3.86396i	−0.402118	+	0.232163i	−0.687397	−	0.726281i	$-0.741247\pi$
$277$	−6.69258	+	3.86396i	−0.402118	+	0.232163i	0.285279	+	0.958444i	$0.407914\pi$
$278$		0			0
$279$	−7.48528			−0.448132
$280$		0			0
$281$	−4.97056			−0.296519			−0.148259	−	0.988948i	$-0.547367\pi$
$281$	−4.97056			−0.296519			−0.148259	+	0.988948i	$0.547367\pi$
$282$		0			0
$283$	1.49642	−	0.863961i	0.0889532	−	0.0513572i	−0.454864	−	0.890561i	$-0.650312\pi$
$283$	1.49642	−	0.863961i	0.0889532	−	0.0513572i	0.543817	+	0.839204i	$0.316979\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.52192	−	11.1213i	0.0898360	−	0.656471i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−8.24264	−	14.2767i	−0.483192	−	0.836913i
$292$		0			0
$293$		−	28.9706i		−	1.69248i	−0.532803	−	0.846239i	$-0.678861\pi$
$293$		−	28.9706i		−	1.69248i	0.532803	−	0.846239i	$-0.321139\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.67423	−	2.12132i	0.213201	−	0.123091i
$298$		0			0
$299$	−11.1213	+	19.2627i	−0.643163	+	1.11399i
$300$		0			0
$301$	13.7426	+	1.88064i	0.792113	+	0.108398i
$302$		0			0
$303$	−14.0665	−	8.12132i	−0.808102	−	0.466558i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	5.24264i		−	0.299213i	−0.988746	−	0.149607i	$-0.952199\pi$
$307$		−	5.24264i		−	0.299213i	0.988746	−	0.149607i	$-0.0478007\pi$
$308$		0			0
$309$	8.75736			0.498189
$310$		0			0
$311$	10.6066	+	18.3712i	0.601445	+	1.04173i	0.992602	+	0.121410i	$0.0387415\pi$
$311$	10.6066	+	18.3712i	0.601445	+	1.04173i	−0.391157	+	0.920324i	$0.627925\pi$
$312$		0			0
$313$	−1.49642	−	0.863961i	−0.0845829	−	0.0488340i	0.457112	−	0.889409i	$-0.348884\pi$
$313$	−1.49642	−	0.863961i	−0.0845829	−	0.0488340i	−0.541695	+	0.840575i	$0.682217\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.630399	−	0.363961i	−0.0354067	−	0.0204421i	0.482192	−	0.876065i	$-0.339841\pi$
$317$	−0.630399	−	0.363961i	−0.0354067	−	0.0204421i	−0.517599	+	0.855623i	$0.673174\pi$
$318$		0			0
$319$	−21.7279	−	37.6339i	−1.21653	−	2.10709i
$320$		0			0
$321$	−12.7279			−0.710403
$322$		0			0
$323$		−	29.6985i		−	1.65247i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.48244	−	3.74264i	−0.358480	−	0.206969i
$328$		0			0
$329$	9.72792	−	12.5446i	0.536318	−	0.691607i
$330$		0			0
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	−0.999298	−	0.0374662i	$-0.988071\pi$
$331$	−8.50000	+	14.7224i	−0.467202	+	0.809218i	0.532096	+	0.846684i	$0.321405\pi$
$332$		0			0
$333$	4.54026	−	2.62132i	0.248805	−	0.143647i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			11.7279i			0.638861i	0.947610	+	0.319430i	$0.103492\pi$
$337$			11.7279i			0.638861i	−0.947610	+	0.319430i	$0.896508\pi$
$338$		0			0
$339$	−9.00000	−	15.5885i	−0.488813	−	0.846649i
$340$		0			0
$341$	−15.8787	+	27.5027i	−0.859879	+	1.48935i
$342$		0			0
$343$	−7.34847	+	17.0000i	−0.396780	+	0.917914i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.7846	+	12.0000i	−1.11578	+	0.644194i	−0.940319	−	0.340293i	$-0.889474\pi$
$347$	−20.7846	+	12.0000i	−1.11578	+	0.644194i	−0.175457	+	0.984487i	$0.556140\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−5.24264			−0.279831
$352$		0			0
$353$	1.52192	−	0.878680i	0.0810035	−	0.0467674i	−0.458951	−	0.888462i	$-0.651775\pi$
$353$	1.52192	−	0.878680i	0.0810035	−	0.0467674i	0.539955	+	0.841694i	$0.318441\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−8.87039	−	6.87868i	−0.469471	−	0.364058i
$358$		0			0
$359$	5.12132	−	8.87039i	0.270293	−	0.468161i	−0.698644	−	0.715470i	$-0.746213\pi$
$359$	5.12132	−	8.87039i	0.270293	−	0.468161i	0.968937	+	0.247309i	$0.0795461\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$		0			0
$363$		−	7.00000i		−	0.367405i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	8.89588	−	5.13604i	0.464361	−	0.268099i	−0.249515	−	0.968371i	$-0.580271\pi$
$367$	8.89588	−	5.13604i	0.464361	−	0.268099i	0.713876	+	0.700272i	$0.246938\pi$
$368$		0			0
$369$	2.12132	−	3.67423i	0.110432	−	0.191273i
$370$		0			0
$371$	−8.48528	−	20.7846i	−0.440534	−	1.07908i
$372$		0			0
$373$	−6.69258	−	3.86396i	−0.346528	−	0.200068i	0.316627	−	0.948550i	$-0.397450\pi$
$373$	−6.69258	−	3.86396i	−0.346528	−	0.200068i	−0.663155	+	0.748482i	$0.730783\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			53.6985i			2.76561i
$378$		0			0
$379$	−30.4558			−1.56441			−0.782206	−	0.623020i	$-0.785905\pi$
$379$	−30.4558			−1.56441			−0.782206	+	0.623020i	$0.785905\pi$
$380$		0			0
$381$	5.62132	+	9.73641i	0.287989	+	0.498812i
$382$		0			0
$383$	−22.0454	−	12.7279i	−1.12647	−	0.650366i	−0.183424	−	0.983034i	$-0.558718\pi$
$383$	−22.0454	−	12.7279i	−1.12647	−	0.650366i	−0.943044	+	0.332668i	$0.892051\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.54026	+	2.62132i	0.230794	+	0.133249i
$388$		0			0
$389$	10.6066	+	18.3712i	0.537776	+	0.931455i	0.999023	+	0.0441839i	$0.0140687\pi$
$389$	10.6066	+	18.3712i	0.537776	+	0.931455i	−0.461247	+	0.887272i	$0.652598\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$			2.48528i			0.125366i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	14.9326	+	8.62132i	0.749444	+	0.432692i	0.825493	−	0.564412i	$-0.190897\pi$
$397$	14.9326	+	8.62132i	0.749444	+	0.432692i	−0.0760490	+	0.997104i	$0.524231\pi$
$398$		0			0
$399$	−18.3492	−	2.51104i	−0.918611	−	0.125709i
$400$		0			0
$401$	10.2426	−	17.7408i	0.511493	−	0.885932i	−0.488418	−	0.872610i	$-0.662426\pi$
$401$	10.2426	−	17.7408i	0.511493	−	0.885932i	0.999911	−	0.0133223i	$-0.00424074\pi$
$402$		0			0
$403$	33.9851	−	19.6213i	1.69292	−	0.977408i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	22.2426i		−	1.10253i
$408$		0			0
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	0.995968	−	0.0897044i	$-0.0285922\pi$
$409$	8.50000	+	14.7224i	0.420298	+	0.727977i	−0.575670	+	0.817682i	$0.695259\pi$
$410$		0			0
$411$	2.12132	−	3.67423i	0.104637	−	0.181237i
$412$		0			0
$413$	−4.30463	+	1.75736i	−0.211817	+	0.0864740i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.28629	−	0.742641i	0.0629900	−	0.0363673i
$418$		0			0
$419$	−2.48528			−0.121414			−0.0607070	−	0.998156i	$-0.519336\pi$
$419$	−2.48528			−0.121414			−0.0607070	+	0.998156i	$0.519336\pi$
$420$		0			0
$421$	14.5147			0.707404			0.353702	−	0.935358i	$-0.384923\pi$
$421$	14.5147			0.707404			0.353702	+	0.935358i	$0.384923\pi$
$422$		0			0
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−26.1039	−	20.2426i	−1.26325	−	0.979610i
$428$		0			0
$429$	−11.1213	+	19.2627i	−0.536942	+	0.930012i
$430$		0			0
$431$	15.7279	+	27.2416i	0.757587	+	1.31218i	0.944078	+	0.329723i	$0.106955\pi$
$431$	15.7279	+	27.2416i	0.757587	+	1.31218i	−0.186490	+	0.982457i	$0.559711\pi$
$432$		0			0
$433$		−	24.7574i		−	1.18976i	−0.803814	−	0.594881i	$-0.797199\pi$
$433$		−	24.7574i		−	1.18976i	0.803814	−	0.594881i	$-0.202801\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−25.7196	+	14.8492i	−1.23034	+	0.710336i
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$		0			0
$443$	3.04384	+	1.75736i	0.144617	+	0.0834947i	0.570563	−	0.821254i	$-0.306725\pi$
$443$	3.04384	+	1.75736i	0.144617	+	0.0834947i	−0.425946	+	0.904749i	$0.640059\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	12.0000i		−	0.567581i
$448$		0			0
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$		0			0
$453$	4.77589	+	2.75736i	0.224391	+	0.129552i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	8.84489	+	5.10660i	0.413747	+	0.238877i	0.692398	−	0.721516i	$-0.256554\pi$
$457$	8.84489	+	5.10660i	0.413747	+	0.238877i	−0.278652	+	0.960392i	$0.589887\pi$
$458$		0			0
$459$	−2.12132	−	3.67423i	−0.0990148	−	0.171499i
$460$		0			0
$461$	−6.72792			−0.313351			−0.156675	−	0.987650i	$-0.550078\pi$
$461$	−6.72792			−0.313351			−0.156675	+	0.987650i	$0.550078\pi$
$462$		0			0
$463$		−	35.7279i		−	1.66042i	−0.557453	−	0.830209i	$-0.688221\pi$
$463$		−	35.7279i		−	1.66042i	0.557453	−	0.830209i	$-0.311779\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.8931	−	11.4853i	−0.920542	−	0.531475i	−0.0367344	−	0.999325i	$-0.511696\pi$
$467$	−19.8931	−	11.4853i	−0.920542	−	0.531475i	−0.883808	+	0.467850i	$0.845029\pi$
$468$		0			0
$469$	−3.24264	−	7.94282i	−0.149731	−	0.366765i
$470$		0			0
$471$	−5.24264	+	9.08052i	−0.241568	+	0.418408i
$472$		0			0
$473$	19.2627	−	11.1213i	0.885700	−	0.511359i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	8.48528i		−	0.388514i
$478$		0			0
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	−13.7426	+	23.8030i	−0.626610	+	1.08532i
$482$		0			0
$483$	−1.52192	+	11.1213i	−0.0692497	+	0.506038i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−10.6279	+	6.13604i	−0.481598	+	0.278050i	−0.721082	−	0.692850i	$-0.756355\pi$
$487$	−10.6279	+	6.13604i	−0.481598	+	0.278050i	0.239484	+	0.970900i	$0.423022\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	32.4853			1.46604			0.733020	−	0.680207i	$-0.238110\pi$
$491$	32.4853			1.46604			0.733020	+	0.680207i	$0.238110\pi$
$492$		0			0
$493$	−37.6339	+	21.7279i	−1.69494	+	0.978576i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.56575	−	33.3640i	0.204802	−	1.49658i
$498$		0			0
$499$	1.25736	−	2.17781i	0.0562871	−	0.0974922i	−0.836509	−	0.547953i	$-0.815407\pi$
$499$	1.25736	−	2.17781i	0.0562871	−	0.0974922i	0.892796	+	0.450461i	$0.148740\pi$
$500$		0			0
$501$	3.36396	+	5.82655i	0.150291	+	0.260311i
$502$		0			0
$503$			9.51472i			0.424240i	0.977244	+	0.212120i	$0.0680368\pi$
$503$			9.51472i			0.424240i	−0.977244	+	0.212120i	$0.931963\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.5446	−	7.24264i	0.557126	−	0.321657i
$508$		0			0
$509$	15.7279	−	27.2416i	0.697128	−	1.20746i	−0.272330	−	0.962204i	$-0.587794\pi$
$509$	15.7279	−	27.2416i	0.697128	−	1.20746i	0.969458	−	0.245257i	$-0.0788724\pi$
$510$		0			0
$511$	0.757359	+	1.85514i	0.0335036	+	0.0820667i
$512$		0			0
$513$	−6.06218	−	3.50000i	−0.267652	−	0.154529i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	25.4558i		−	1.11955i
$518$		0			0
$519$	3.51472			0.154279
$520$		0			0
$521$	−18.7279	−	32.4377i	−0.820485	−	1.42112i	−0.905321	−	0.424727i	$-0.860370\pi$
$521$	−18.7279	−	32.4377i	−0.820485	−	1.42112i	0.0848363	−	0.996395i	$-0.472963\pi$
$522$		0			0
$523$	2.80821	+	1.62132i	0.122794	+	0.0708954i	0.560139	−	0.828399i	$-0.310748\pi$
$523$	2.80821	+	1.62132i	0.122794	+	0.0708954i	−0.437345	+	0.899294i	$0.644081\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	27.5027	+	15.8787i	1.19804	+	0.691686i
$528$		0			0
$529$	−2.50000	−	4.33013i	−0.108696	−	0.188266i
$530$		0			0
$531$	−1.75736			−0.0762629
$532$		0			0
$533$			22.2426i			0.963436i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.19615	+	3.00000i	0.224231	+	0.129460i
$538$		0			0
$539$	7.39340	+	28.7635i	0.318456	+	1.23893i
$540$		0			0
$541$	−13.4706	+	23.3317i	−0.579145	+	1.00311i	0.416433	+	0.909166i	$0.363280\pi$
$541$	−13.4706	+	23.3317i	−0.579145	+	1.00311i	−0.995578	+	0.0939417i	$0.970053\pi$
$542$		0			0
$543$	11.2583	−	6.50000i	0.483141	−	0.278942i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	17.4558i		−	0.746358i	−0.927759	−	0.373179i	$-0.878268\pi$
$547$		−	17.4558i		−	0.746358i	0.927759	−	0.373179i	$-0.121732\pi$
$548$		0			0
$549$	−6.24264	−	10.8126i	−0.266429	−	0.461469i
$550$		0			0
$551$	−35.8492	+	62.0927i	−1.52723	+	2.64524i
$552$		0			0
$553$	−22.9985	−	17.8345i	−0.977995	−	0.758401i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.9808	+	15.0000i	−1.10084	+	0.635570i	−0.936442	−	0.350824i	$-0.885902\pi$
$557$	−25.9808	+	15.0000i	−1.10084	+	0.635570i	−0.164399	+	0.986394i	$0.552568\pi$
$558$		0			0
$559$	−27.4853			−1.16250
$560$		0			0
$561$	−18.0000			−0.759961
$562$		0			0
$563$	5.19615	−	3.00000i	0.218992	−	0.126435i	−0.386492	−	0.922293i	$-0.626313\pi$
$563$	5.19615	−	3.00000i	0.218992	−	0.126435i	0.605483	+	0.795858i	$0.292980\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.44949	+	1.00000i	−0.102869	+	0.0419961i
$568$		0			0
$569$	8.84924	−	15.3273i	0.370980	−	0.642555i	−0.618737	−	0.785598i	$-0.712355\pi$
$569$	8.84924	−	15.3273i	0.370980	−	0.642555i	0.989717	+	0.143043i	$0.0456887\pi$
$570$		0			0
$571$	−19.4706	−	33.7240i	−0.814818	−	1.41131i	−0.909459	−	0.415794i	$-0.863504\pi$
$571$	−19.4706	−	33.7240i	−0.814818	−	1.41131i	0.0946410	−	0.995511i	$-0.469830\pi$
$572$		0			0
$573$		−	6.00000i		−	0.250654i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	18.3967	−	10.6213i	0.765863	−	0.442171i	−0.0655337	−	0.997850i	$-0.520875\pi$
$577$	18.3967	−	10.6213i	0.765863	−	0.442171i	0.831397	+	0.555679i	$0.187542\pi$
$578$		0			0
$579$	7.62132	−	13.2005i	0.316731	−	0.548595i
$580$		0			0
$581$	4.60660	+	0.630399i	0.191114	+	0.0261534i
$582$		0			0
$583$	−31.1769	−	18.0000i	−1.29122	−	0.745484i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			2.78680i			0.115023i	0.998345	+	0.0575117i	$0.0183167\pi$
$587$			2.78680i			0.115023i	−0.998345	+	0.0575117i	$0.981683\pi$
$588$		0			0
$589$	52.3970			2.15898
$590$		0			0
$591$	3.87868	+	6.71807i	0.159548	+	0.276344i
$592$		0			0
$593$	−33.9596	−	19.6066i	−1.39455	−	0.805147i	−0.400740	−	0.916192i	$-0.631247\pi$
$593$	−33.9596	−	19.6066i	−1.39455	−	0.805147i	−0.993815	+	0.111045i	$0.964580\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.61642	+	3.24264i	0.229865	+	0.132712i
$598$		0			0
$599$	−7.75736	−	13.4361i	−0.316957	−	0.548986i	0.662894	−	0.748713i	$-0.269328\pi$
$599$	−7.75736	−	13.4361i	−0.316957	−	0.548986i	−0.979852	+	0.199727i	$0.935994\pi$
$600$		0			0
$601$	13.4853			0.550076			0.275038	−	0.961433i	$-0.411310\pi$
$601$	13.4853			0.550076			0.275038	+	0.961433i	$0.411310\pi$
$602$		0			0
$603$		−	3.24264i		−	0.132051i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	17.9764	+	10.3787i	0.729640	+	0.421258i	0.818290	−	0.574805i	$-0.194922\pi$
$607$	17.9764	+	10.3787i	0.729640	+	0.421258i	−0.0886507	+	0.996063i	$0.528255\pi$
$608$		0			0
$609$	10.2426	+	25.0892i	0.415053	+	1.01667i
$610$		0			0
$611$	−15.7279	+	27.2416i	−0.636284	+	1.10208i
$612$		0			0
$613$	−39.3659	+	22.7279i	−1.58997	+	0.917972i	−0.596665	+	0.802491i	$0.703508\pi$
$613$	−39.3659	+	22.7279i	−1.58997	+	0.917972i	−0.993310	+	0.115482i	$0.963159\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	9.51472i		−	0.383048i	−0.981488	−	0.191524i	$-0.938657\pi$
$617$		−	9.51472i		−	0.383048i	0.981488	−	0.191524i	$-0.0613430\pi$
$618$		0			0
$619$	10.9853	+	19.0271i	0.441536	+	0.764762i	0.997804	−	0.0662407i	$-0.0211005\pi$
$619$	10.9853	+	19.0271i	0.441536	+	0.764762i	−0.556268	+	0.831003i	$0.687767\pi$
$620$		0			0
$621$	−2.12132	+	3.67423i	−0.0851257	+	0.147442i
$622$		0			0
$623$	3.67423	+	2.84924i	0.147205	+	0.114152i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−25.7196	+	14.8492i	−1.02714	+	0.593022i
$628$		0			0
$629$	−22.2426			−0.886872
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$	−4.77589	+	2.75736i	−0.189824	+	0.109595i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	9.85951	−	35.3492i	0.390648	−	1.40059i
$638$		0			0
$639$	6.36396	−	11.0227i	0.251754	−	0.436051i
$640$		0			0
$641$	−12.8787	−	22.3065i	−0.508677	−	0.881055i	−0.999950	−	0.0100488i	$-0.996801\pi$
$641$	−12.8787	−	22.3065i	−0.508677	−	0.881055i	0.491272	−	0.871006i	$-0.336532\pi$
$642$		0			0
$643$		−	5.72792i		−	0.225887i	−0.993601	−	0.112944i	$-0.963972\pi$
$643$		−	5.72792i		−	0.225887i	0.993601	−	0.112944i	$-0.0360279\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.52192	−	0.878680i	0.0598328	−	0.0345445i	−0.469785	−	0.882781i	$-0.655669\pi$
$647$	1.52192	−	0.878680i	0.0598328	−	0.0345445i	0.529618	+	0.848236i	$0.322335\pi$
$648$		0			0
$649$	−3.72792	+	6.45695i	−0.146334	+	0.253457i
$650$		0			0
$651$	12.1360	−	15.6500i	0.475649	−	0.613372i
$652$		0			0
$653$	1.52192	+	0.878680i	0.0595572	+	0.0343854i	0.529483	−	0.848321i	$-0.322386\pi$
$653$	1.52192	+	0.878680i	0.0595572	+	0.0343854i	−0.469926	+	0.882706i	$0.655719\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			0.757359i			0.0295474i
$658$		0			0
$659$	−7.02944			−0.273828			−0.136914	−	0.990583i	$-0.543718\pi$
$659$	−7.02944			−0.273828			−0.136914	+	0.990583i	$0.543718\pi$
$660$		0			0
$661$	17.9853	+	31.1514i	0.699546	+	1.21165i	0.968624	+	0.248531i	$0.0799479\pi$
$661$	17.9853	+	31.1514i	0.699546	+	1.21165i	−0.269077	+	0.963119i	$0.586719\pi$
$662$		0			0
$663$	19.2627	+	11.1213i	0.748101	+	0.431916i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	37.6339	+	21.7279i	1.45719	+	0.841309i
$668$		0			0
$669$	−12.2426	−	21.2049i	−0.473328	−	0.819828i
$670$		0			0
$671$	−52.9706			−2.04491
$672$		0			0
$673$		−	4.27208i		−	0.164677i	−0.996604	−	0.0823383i	$-0.973761\pi$
$673$		−	4.27208i		−	0.164677i	0.996604	−	0.0823383i	$-0.0262388\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.0227	+	6.36396i	0.423637	+	0.244587i	0.696632	−	0.717428i	$-0.254681\pi$
$677$	11.0227	+	6.36396i	0.423637	+	0.244587i	−0.272995	+	0.962015i	$0.588014\pi$
$678$		0			0
$679$	43.2132	+	5.91359i	1.65837	+	0.226943i
$680$		0			0
$681$	−13.6066	+	23.5673i	−0.521406	+	0.903102i
$682$		0			0
$683$	7.97887	−	4.60660i	0.305303	−	0.176267i	−0.339520	−	0.940599i	$-0.610265\pi$
$683$	7.97887	−	4.60660i	0.305303	−	0.176267i	0.644823	+	0.764332i	$0.276931\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	7.00000i		−	0.267067i
$688$		0			0
$689$	22.2426	+	38.5254i	0.847377	+	1.46770i
$690$		0			0
$691$	20.4706	−	35.4561i	0.778737	−	1.34881i	−0.153933	−	0.988081i	$-0.549194\pi$
$691$	20.4706	−	35.4561i	0.778737	−	1.34881i	0.932670	−	0.360731i	$-0.117473\pi$
$692$		0			0
$693$	−1.52192	+	11.1213i	−0.0578129	+	0.422464i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−15.5885	+	9.00000i	−0.590455	+	0.340899i
$698$		0			0
$699$	2.48528			0.0940020
$700$		0			0
$701$	51.2132			1.93430			0.967148	−	0.254214i	$-0.0818167\pi$
$701$	51.2132			1.93430			0.967148	+	0.254214i	$0.0818167\pi$
$702$		0			0
$703$	−31.7818	+	18.3492i	−1.19867	+	0.692055i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	39.7862	−	16.2426i	1.49631	−	0.610867i
$708$		0			0
$709$	−9.75736	+	16.9002i	−0.366445	+	0.634702i	−0.989007	−	0.147869i	$-0.952759\pi$
$709$	−9.75736	+	16.9002i	−0.366445	+	0.634702i	0.622562	+	0.782571i	$0.286092\pi$
$710$		0			0
$711$	−5.50000	−	9.52628i	−0.206266	−	0.357263i
$712$		0			0
$713$		−	31.7574i		−	1.18932i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−19.8931	+	11.4853i	−0.742921	+	0.428926i
$718$		0			0
$719$	4.75736	−	8.23999i	0.177420	−	0.307300i	−0.763576	−	0.645718i	$-0.776558\pi$
$719$	4.75736	−	8.23999i	0.177420	−	0.307300i	0.940996	+	0.338418i	$0.109892\pi$
$720$		0			0
$721$	−14.1985	+	18.3096i	−0.528779	+	0.681886i
$722$		0			0
$723$	−3.46410	−	2.00000i	−0.128831	−	0.0743808i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			9.24264i			0.342791i	0.985202	+	0.171395i	$0.0548275\pi$
$727$			9.24264i			0.342791i	−0.985202	+	0.171395i	$0.945172\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−11.1213	−	19.2627i	−0.411337	−	0.712456i
$732$		0			0
$733$	38.2898	+	22.1066i	1.41426	+	0.816526i	0.995787	−	0.0917010i	$-0.0292304\pi$
$733$	38.2898	+	22.1066i	1.41426	+	0.816526i	0.418478	+	0.908227i	$0.362564\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−11.9142	−	6.87868i	−0.438866	−	0.253379i
$738$		0			0
$739$	0.742641	+	1.28629i	0.0273185	+	0.0473170i	0.879361	−	0.476155i	$-0.157970\pi$
$739$	0.742641	+	1.28629i	0.0273185	+	0.0473170i	−0.852043	+	0.523472i	$0.824637\pi$
$740$		0			0
$741$	36.6985			1.34815
$742$		0			0
$743$			27.2132i			0.998356i	0.866500	+	0.499178i	$0.166365\pi$
$743$			27.2132i			0.998356i	−0.866500	+	0.499178i	$0.833635\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.52192	+	0.878680i	0.0556841	+	0.0321492i
$748$		0			0
$749$	20.6360	−	26.6112i	0.754024	−	0.972351i
$750$		0			0
$751$	11.4706	−	19.8676i	0.418567	−	0.724979i	−0.577229	−	0.816582i	$-0.695866\pi$
$751$	11.4706	−	19.8676i	0.418567	−	0.724979i	0.995796	+	0.0916035i	$0.0291992\pi$
$752$		0			0
$753$	−5.82655	+	3.36396i	−0.212331	+	0.122590i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			42.9706i			1.56179i	0.624661	+	0.780896i	$0.285237\pi$
$757$			42.9706i			1.56179i	−0.624661	+	0.780896i	$0.714763\pi$
$758$		0			0
$759$	9.00000	+	15.5885i	0.326679	+	0.565825i
$760$		0			0
$761$	−18.8787	+	32.6988i	−0.684352	+	1.18533i	0.289288	+	0.957242i	$0.406581\pi$
$761$	−18.8787	+	32.6988i	−0.684352	+	1.18533i	−0.973640	+	0.228090i	$0.926752\pi$
$762$		0			0
$763$	18.3351	−	7.48528i	0.663776	−	0.270985i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.97887	−	4.60660i	0.288100	−	0.166335i
$768$		0			0
$769$	−5.00000			−0.180305			−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000			−0.180305			−0.0901523	+	0.995928i	$0.528735\pi$
$770$		0			0
$771$	1.75736			0.0632897
$772$		0			0
$773$	41.3081	−	23.8492i	1.48575	−	0.857798i	0.485881	−	0.874025i	$-0.338499\pi$
$773$	41.3081	−	23.8492i	1.48575	−	0.857798i	0.999868	+	0.0162275i	$0.00516560\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.88064	+	13.7426i	−0.0674675	+	0.493014i
$778$		0			0
$779$	−14.8492	+	25.7196i	−0.532029	+	0.921502i
$780$		0			0
$781$	−27.0000	−	46.7654i	−0.966136	−	1.67340i
$782$		0			0
$783$			10.2426i			0.366042i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	9.97204	−	5.75736i	0.355465	−	0.205228i	−0.311625	−	0.950205i	$-0.600873\pi$
$787$	9.97204	−	5.75736i	0.355465	−	0.205228i	0.667090	+	0.744978i	$0.267540\pi$
$788$		0			0
$789$	4.24264	−	7.34847i	0.151042	−	0.261612i
$790$		0			0
$791$	47.1838	+	6.45695i	1.67766	+	0.229583i
$792$		0			0
$793$	56.6864	+	32.7279i	2.01299	+	1.16220i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	40.2426i		−	1.42547i	−0.701435	−	0.712734i	$-0.747457\pi$
$797$		−	40.2426i		−	1.42547i	0.701435	−	0.712734i	$-0.252543\pi$
$798$		0			0
$799$	−25.4558			−0.900563
$800$		0			0
$801$	0.878680	+	1.52192i	0.0310466	+	0.0537743i
$802$		0			0
$803$	2.78272	+	1.60660i	0.0981999	+	0.0566957i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.5446	−	7.24264i	−0.441592	−	0.254953i
$808$		0			0
$809$	−19.9706	−	34.5900i	−0.702128	−	1.21612i	−0.967718	−	0.252035i	$-0.918900\pi$
$809$	−19.9706	−	34.5900i	−0.702128	−	1.21612i	0.265591	−	0.964086i	$-0.414433\pi$
$810$		0			0
$811$	−55.9411			−1.96436			−0.982179	−	0.187946i	$-0.939817\pi$
$811$	−55.9411			−1.96436			−0.982179	+	0.187946i	$0.939817\pi$
$812$		0			0
$813$		−	27.4558i		−	0.962918i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−31.7818	−	18.3492i	−1.11191	−	0.641959i
$818$		0			0
$819$	8.50000	−	10.9612i	0.297014	−	0.383014i
$820$		0			0
$821$	26.8492	−	46.5043i	0.937045	−	1.62301i	0.166099	−	0.986109i	$-0.446883\pi$
$821$	26.8492	−	46.5043i	0.937045	−	1.62301i	0.770946	−	0.636901i	$-0.219784\pi$
$822$		0			0
$823$	4.35562	−	2.51472i	0.151827	−	0.0876576i	−0.422162	−	0.906521i	$-0.638729\pi$
$823$	4.35562	−	2.51472i	0.151827	−	0.0876576i	0.573989	+	0.818863i	$0.305395\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	7.45584i		−	0.259265i	−0.991562	−	0.129633i	$-0.958620\pi$
$827$		−	7.45584i		−	0.259265i	0.991562	−	0.129633i	$-0.0413798\pi$
$828$		0			0
$829$	5.50000	+	9.52628i	0.191023	+	0.330861i	0.945589	−	0.325362i	$-0.105486\pi$
$829$	5.50000	+	9.52628i	0.191023	+	0.330861i	−0.754567	+	0.656223i	$0.772153\pi$
$830$		0			0
$831$	3.86396	−	6.69258i	0.134039	−	0.232163i
$832$		0			0
$833$	28.7635	−	7.39340i	0.996595	−	0.256166i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	6.48244	−	3.74264i	0.224066	−	0.129365i
$838$		0			0
$839$	−34.2426			−1.18219			−0.591094	−	0.806603i	$-0.701304\pi$
$839$	−34.2426			−1.18219			−0.591094	+	0.806603i	$0.701304\pi$
$840$		0			0
$841$	75.9117			2.61764
$842$		0			0
$843$	4.30463	−	2.48528i	0.148259	−	0.0855976i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	14.6354	+	11.3492i	0.502878	+	0.389965i
$848$		0			0
$849$	−0.863961	+	1.49642i	−0.0296511	+	0.0513572i
$850$		0			0
$851$	11.1213	+	19.2627i	0.381234	+	0.660317i
$852$		0			0
$853$			0.272078i			0.00931577i	0.999989	+	0.00465789i	$0.00148266\pi$
$853$			0.272078i			0.00931577i	−0.999989	+	0.00465789i	$0.998517\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.67423	+	2.12132i	−0.125509	+	0.0724629i	−0.561440	−	0.827517i	$-0.689753\pi$
$857$	−3.67423	+	2.12132i	−0.125509	+	0.0724629i	0.435931	+	0.899980i	$0.356419\pi$
$858$		0			0
$859$	−11.0000	+	19.0526i	−0.375315	+	0.650065i	−0.990374	−	0.138416i	$-0.955799\pi$
$859$	−11.0000	+	19.0526i	−0.375315	+	0.650065i	0.615059	+	0.788481i	$0.289132\pi$
$860$		0			0
$861$	4.24264	+	10.3923i	0.144589	+	0.354169i
$862$		0			0
$863$	−33.3292	−	19.2426i	−1.13454	−	0.655027i	−0.189467	−	0.981887i	$-0.560676\pi$
$863$	−33.3292	−	19.2426i	−1.13454	−	0.655027i	−0.945073	+	0.326860i	$0.894009\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			1.00000i			0.0339618i
$868$		0			0
$869$	−46.6690			−1.58314
$870$		0			0
$871$	8.50000	+	14.7224i	0.288012	+	0.498851i
$872$		0			0
$873$	14.2767	+	8.24264i	0.483192	+	0.278971i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	0.639040	−	0.769174i	$-0.279332\pi$
$877$	8.66025	+	5.00000i	0.292436	+	0.168838i	−0.346604	+	0.938012i	$0.612665\pi$
$878$		0			0
$879$	14.4853	+	25.0892i	0.488576	+	0.846239i
$880$		0			0
$881$	7.02944			0.236828			0.118414	−	0.992964i	$-0.462219\pi$
$881$	7.02944			0.236828			0.118414	+	0.992964i	$0.462219\pi$
$882$		0			0
$883$			19.7279i			0.663897i	0.943297	+	0.331949i	$0.107706\pi$
$883$			19.7279i			0.663897i	−0.943297	+	0.331949i	$0.892294\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.5673	+	13.6066i	0.791313	+	0.456865i	0.840425	−	0.541928i	$-0.182306\pi$
$887$	23.5673	+	13.6066i	0.791313	+	0.456865i	−0.0491114	+	0.998793i	$0.515639\pi$
$888$		0			0
$889$	−29.4706	−	4.03295i	−0.988411	−	0.135261i
$890$		0			0
$891$	−2.12132	+	3.67423i	−0.0710669	+	0.123091i
$892$		0			0
$893$	−36.3731	+	21.0000i	−1.21718	+	0.702738i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	22.2426i		−	0.742660i
$898$		0			0
$899$	−38.3345	−	66.3973i	−1.27853	−	2.21448i
$900$		0			0
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$	−12.8418	+	5.24264i	−0.427348	+	0.174464i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−48.2618	+	27.8640i	−1.60251	+	0.925208i	−0.611523	+	0.791227i	$0.709443\pi$
$907$	−48.2618	+	27.8640i	−1.60251	+	0.925208i	−0.990984	+	0.133981i	$0.957224\pi$
$908$		0			0
$909$	16.2426			0.538734
$910$		0			0
$911$	8.78680			0.291120			0.145560	−	0.989349i	$-0.453502\pi$
$911$	8.78680			0.291120			0.145560	+	0.989349i	$0.453502\pi$
$912$		0			0
$913$	6.45695	−	3.72792i	0.213694	−	0.123376i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.19615	−	4.02944i	−0.171592	−	0.133064i
$918$		0			0
$919$	0.0147186	−	0.0254934i	0.000485523	−	0.000840950i	−0.865783	−	0.500420i	$-0.833179\pi$
$919$	0.0147186	−	0.0254934i	0.000485523	−	0.000840950i	0.866268	+	0.499579i	$0.166512\pi$
$920$		0			0
$921$	2.62132	+	4.54026i	0.0863754	+	0.149607i
$922$		0			0
$923$			66.7279i			2.19638i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−7.58410	+	4.37868i	−0.249094	+	0.143815i
$928$		0			0
$929$	5.63604	−	9.76191i	0.184912	−	0.320278i	−0.758635	−	0.651516i	$-0.774133\pi$
$929$	5.63604	−	9.76191i	0.184912	−	0.320278i	0.943547	+	0.331239i	$0.107467\pi$
$930$		0			0
$931$	35.0000	−	34.2929i	1.14708	−	1.12390i
$932$		0			0
$933$	−18.3712	−	10.6066i	−0.601445	−	0.347245i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			40.6985i			1.32956i	0.747039	+	0.664781i	$0.231475\pi$
$937$			40.6985i			1.32956i	−0.747039	+	0.664781i	$0.768525\pi$
$938$		0			0
$939$	1.72792			0.0563886
$940$		0			0
$941$	−5.84924	−	10.1312i	−0.190680	−	0.330267i	0.754796	−	0.655960i	$-0.227736\pi$
$941$	−5.84924	−	10.1312i	−0.190680	−	0.330267i	−0.945476	+	0.325693i	$0.894403\pi$
$942$		0			0
$943$	15.5885	+	9.00000i	0.507630	+	0.293080i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−33.9596	−	19.6066i	−1.10354	−	0.637129i	−0.166391	−	0.986060i	$-0.553211\pi$
$947$	−33.9596	−	19.6066i	−1.10354	−	0.637129i	−0.937148	+	0.348931i	$0.886545\pi$
$948$		0			0
$949$	−1.98528	−	3.43861i	−0.0644450	−	0.111622i
$950$		0			0
$951$	0.727922			0.0236045
$952$		0			0
$953$			44.4853i			1.44102i	0.693445	+	0.720510i	$0.256092\pi$
$953$			44.4853i			1.44102i	−0.693445	+	0.720510i	$0.743908\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	37.6339	+	21.7279i	1.21653	+	0.702364i
$958$		0			0
$959$	4.24264	+	10.3923i	0.137002	+	0.335585i
$960$		0			0
$961$	−12.5147	+	21.6761i	−0.403701	+	0.699230i
$962$		0			0
$963$	11.0227	−	6.36396i	0.355202	−	0.205076i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	26.7574i		−	0.860459i	−0.902720	−	0.430229i	$-0.858433\pi$
$967$		−	26.7574i		−	0.860459i	0.902720	−	0.430229i	$-0.141567\pi$
$968$		0			0
$969$	14.8492	+	25.7196i	0.477026	+	0.826234i
$970$		0			0
$971$	−9.51472	+	16.4800i	−0.305342	+	0.528868i	−0.977337	−	0.211688i	$-0.932104\pi$
$971$	−9.51472	+	16.4800i	−0.305342	+	0.528868i	0.671996	+	0.740555i	$0.265437\pi$
$972$		0			0
$973$	−0.532799	+	3.89340i	−0.0170808	+	0.124817i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−44.3519	+	25.6066i	−1.41894	+	0.819228i	−0.996206	−	0.0870242i	$-0.972264\pi$
$977$	−44.3519	+	25.6066i	−1.41894	+	0.819228i	−0.422738	+	0.906252i	$0.638931\pi$
$978$		0			0
$979$	7.45584			0.238290
$980$		0			0
$981$	7.48528			0.238987
$982$		0			0
$983$	−15.3273	+	8.84924i	−0.488866	+	0.282247i	−0.724104	−	0.689691i	$-0.757746\pi$
$983$	−15.3273	+	8.84924i	−0.488866	+	0.282247i	0.235238	+	0.971938i	$0.424413\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−2.15232	+	15.7279i	−0.0685090	+	0.500625i
$988$		0			0
$989$	−11.1213	+	19.2627i	−0.353637	+	0.612518i
$990$		0			0
$991$	26.4706	+	45.8484i	0.840865	+	1.45642i	0.889164	+	0.457588i	$0.151287\pi$
$991$	26.4706	+	45.8484i	0.840865	+	1.45642i	−0.0482991	+	0.998833i	$0.515380\pi$
$992$		0			0
$993$		−	17.0000i		−	0.539479i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.235626	+	0.136039i	−0.00746236	+	0.00430840i	−0.503727	−	0.863863i	$-0.668038\pi$
$997$	−0.235626	+	0.136039i	−0.00746236	+	0.00430840i	0.496264	+	0.868172i	$0.334705\pi$
$998$		0			0
$999$	−2.62132	+	4.54026i	−0.0829349	+	0.143647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.f.1549.2		8
5.2	odd	4		2100.2.q.k.1801.2		4
5.3	odd	4		420.2.q.d.121.1	✓	4
5.4	even	2	inner	2100.2.bc.f.1549.3		8
7.4	even	3	inner	2100.2.bc.f.949.3		8
15.8	even	4		1260.2.s.e.541.1		4
20.3	even	4		1680.2.bg.t.961.2		4
35.3	even	12		2940.2.q.q.361.1		4
35.4	even	6	inner	2100.2.bc.f.949.2		8
35.13	even	4		2940.2.q.q.961.1		4
35.18	odd	12		420.2.q.d.361.1	yes	4
35.23	odd	12		2940.2.a.r.1.2		2
35.32	odd	12		2100.2.q.k.1201.2		4
35.33	even	12		2940.2.a.p.1.2		2
105.23	even	12		8820.2.a.bk.1.1		2
105.53	even	12		1260.2.s.e.361.1		4
105.68	odd	12		8820.2.a.bf.1.1		2
140.123	even	12		1680.2.bg.t.1201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.d.121.1	✓	4	5.3	odd	4
420.2.q.d.361.1	yes	4	35.18	odd	12
1260.2.s.e.361.1		4	105.53	even	12
1260.2.s.e.541.1		4	15.8	even	4
1680.2.bg.t.961.2		4	20.3	even	4
1680.2.bg.t.1201.2		4	140.123	even	12
2100.2.q.k.1201.2		4	35.32	odd	12
2100.2.q.k.1801.2		4	5.2	odd	4
2100.2.bc.f.949.2		8	35.4	even	6	inner
2100.2.bc.f.949.3		8	7.4	even	3	inner
2100.2.bc.f.1549.2		8	1.1	even	1	trivial
2100.2.bc.f.1549.3		8	5.4	even	2	inner
2940.2.a.p.1.2		2	35.33	even	12
2940.2.a.r.1.2		2	35.23	odd	12
2940.2.q.q.361.1		4	35.3	even	12
2940.2.q.q.961.1		4	35.13	even	4
8820.2.a.bf.1.1		2	105.68	odd	12
8820.2.a.bk.1.1		2	105.23	even	12

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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.358719 - 2.62132i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.358719 - 2.62132i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-2.12132 - 3.67423i) q^{11} +5.24264i q^{13} +(-3.67423 + 2.12132i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(3.67423 + 2.12132i) q^{23} +1.00000i q^{27} +10.2426 q^{29} +(-3.74264 - 6.48244i) q^{31} +(3.67423 + 2.12132i) q^{33} +(4.54026 + 2.62132i) q^{37} +(-2.62132 - 4.54026i) q^{39} +4.24264 q^{41} +5.24264i q^{43} +(5.19615 + 3.00000i) q^{47} +(-6.74264 - 1.88064i) q^{49} +(2.12132 - 3.67423i) q^{51} +(7.34847 - 4.24264i) q^{53} -7.00000i q^{57} +(-0.878680 - 1.52192i) q^{59} +(6.24264 - 10.8126i) q^{61} +(-2.09077 - 1.62132i) q^{63} +(2.80821 - 1.62132i) q^{67} -4.24264 q^{69} +12.7279 q^{71} +(-0.655892 + 0.378680i) q^{73} +(-10.3923 + 4.24264i) q^{77} +(5.50000 - 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +1.75736i q^{83} +(-8.87039 + 5.12132i) q^{87} +(-0.878680 + 1.52192i) q^{89} +(13.7426 + 1.88064i) q^{91} +(6.48244 + 3.74264i) q^{93} +16.4853i q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} - 28 q^{19} + 8 q^{21} + 48 q^{29} + 4 q^{31} - 4 q^{39} - 20 q^{49} - 24 q^{59} + 16 q^{61} + 44 q^{79} - 4 q^{81} - 24 q^{89} + 76 q^{91}+O(q^{100}) \) 8 * q + 4 * q^9 - 28 * q^19 + 8 * q^21 + 48 * q^29 + 4 * q^31 - 4 * q^39 - 20 * q^49 - 24 * q^59 + 16 * q^61 + 44 * q^79 - 4 * q^81 - 24 * q^89 + 76 * q^91

Introduction

L-functions

Modular forms

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