LMFDB - Embedded newform 2100.2.bc.f.949.1

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			949.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2100.949
Dual form			2100.2.bc.f.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{3} +(-2.09077 - 1.62132i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{3} +(-2.09077 - 1.62132i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} +3.24264i q^{13} +(3.67423 + 2.12132i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(-3.67423 + 2.12132i) q^{23} -1.00000i q^{27} +1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(-3.67423 + 2.12132i) q^{33} +(-2.80821 + 1.62132i) q^{37} +(1.62132 - 2.80821i) q^{39} -4.24264 q^{41} +3.24264i q^{43} +(5.19615 - 3.00000i) q^{47} +(1.74264 + 6.77962i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(-7.34847 - 4.24264i) q^{53} +7.00000i q^{57} +(-5.12132 + 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(0.358719 - 2.62132i) q^{63} +(-4.54026 - 2.62132i) q^{67} +4.24264 q^{69} -12.7279 q^{71} +(-8.00436 - 4.62132i) q^{73} +(-10.3923 + 4.24264i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.2426i q^{83} +(-1.52192 - 0.878680i) q^{87} +(-5.12132 - 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(-8.21449 + 4.74264i) q^{93} +0.485281i q^{97} +4.24264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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
$7$	−2.09077	−	1.62132i	−0.790237	−	0.612801i
$7$	−2.09077	−	1.62132i	−0.790237	−	0.612801i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	−0.345918	−	0.938265i	$-0.612432\pi$
$11$	2.12132	−	3.67423i	0.639602	−	1.10782i	0.985520	−	0.169559i	$-0.0542342\pi$
$12$		0			0
$13$			3.24264i			0.899347i	0.893193	+	0.449673i	$0.148460\pi$
$13$			3.24264i			0.899347i	−0.893193	+	0.449673i	$0.851540\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.67423	+	2.12132i	0.891133	+	0.514496i	0.874313	−	0.485363i	$-0.161312\pi$
$17$	3.67423	+	2.12132i	0.891133	+	0.514496i	0.0168199	+	0.999859i	$0.494646\pi$
$18$		0			0
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−3.50000	−	6.06218i	−0.802955	−	1.39076i	0.114708	−	0.993399i	$-0.463407\pi$
$20$		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	$-0.812513\pi$
$23$	−3.67423	+	2.12132i	−0.766131	+	0.442326i	0.0653618	+	0.997862i	$0.479180\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	1.75736			0.326333			0.163167	−	0.986599i	$-0.447829\pi$
$29$	1.75736			0.326333			0.163167	+	0.986599i	$0.447829\pi$
$30$		0			0
$31$	4.74264	−	8.21449i	0.851803	−	1.47537i	−0.0277757	−	0.999614i	$-0.508842\pi$
$31$	4.74264	−	8.21449i	0.851803	−	1.47537i	0.879579	−	0.475753i	$-0.157824\pi$
$32$		0			0
$33$	−3.67423	+	2.12132i	−0.639602	+	0.369274i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.80821	+	1.62132i	−0.461667	+	0.266543i	−0.712745	−	0.701423i	$-0.752548\pi$
$37$	−2.80821	+	1.62132i	−0.461667	+	0.266543i	0.251078	+	0.967967i	$0.419215\pi$
$38$		0			0
$39$	1.62132	−	2.80821i	0.259619	−	0.449673i
$40$		0			0
$41$	−4.24264			−0.662589			−0.331295	−	0.943527i	$-0.607485\pi$
$41$	−4.24264			−0.662589			−0.331295	+	0.943527i	$0.607485\pi$
$42$		0			0
$43$			3.24264i			0.494498i	0.968952	+	0.247249i	$0.0795266\pi$
$43$			3.24264i			0.494498i	−0.968952	+	0.247249i	$0.920473\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$		0			0
$49$	1.74264	+	6.77962i	0.248949	+	0.968517i
$50$		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	$-0.531365\pi$
$53$	−7.34847	−	4.24264i	−1.00939	−	0.582772i	−0.911013	+	0.412378i	$0.864698\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			7.00000i			0.927173i
$58$		0			0
$59$	−5.12132	+	8.87039i	−0.666739	+	1.15483i	0.312072	+	0.950059i	$0.398977\pi$
$59$	−5.12132	+	8.87039i	−0.666739	+	1.15483i	−0.978811	+	0.204767i	$0.934356\pi$
$60$		0			0
$61$	−2.24264	−	3.88437i	−0.287141	−	0.497342i	0.685985	−	0.727615i	$-0.259371\pi$
$61$	−2.24264	−	3.88437i	−0.287141	−	0.497342i	−0.973126	+	0.230273i	$0.926038\pi$
$62$		0			0
$63$	0.358719	−	2.62132i	0.0451944	−	0.330255i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.54026	−	2.62132i	−0.554681	−	0.320245i	0.196327	−	0.980539i	$-0.437099\pi$
$67$	−4.54026	−	2.62132i	−0.554681	−	0.320245i	−0.751008	+	0.660293i	$0.770432\pi$
$68$		0			0
$69$	4.24264			0.510754
$70$		0			0
$71$	−12.7279			−1.51053			−0.755263	−	0.655422i	$-0.772491\pi$
$71$	−12.7279			−1.51053			−0.755263	+	0.655422i	$0.772491\pi$
$72$		0			0
$73$	−8.00436	−	4.62132i	−0.936840	−	0.540885i	−0.0478714	−	0.998854i	$-0.515244\pi$
$73$	−8.00436	−	4.62132i	−0.936840	−	0.540885i	−0.888968	+	0.457969i	$0.848577\pi$
$74$		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	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	10.2426i		−	1.12428i	−0.827043	−	0.562138i	$-0.809979\pi$
$83$		−	10.2426i		−	1.12428i	0.827043	−	0.562138i	$-0.190021\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.52192	−	0.878680i	−0.163167	−	0.0942043i
$88$		0			0
$89$	−5.12132	−	8.87039i	−0.542859	−	0.940259i	−0.998738	−	0.0502176i	$-0.984009\pi$
$89$	−5.12132	−	8.87039i	−0.542859	−	0.940259i	0.455879	−	0.890042i	$-0.349325\pi$
$90$		0			0
$91$	5.25736	−	6.77962i	0.551121	−	0.710697i
$92$		0			0
$93$	−8.21449	+	4.74264i	−0.851803	+	0.491789i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			0.485281i			0.0492729i	0.999696	+	0.0246364i	$0.00784281\pi$
$97$			0.485281i			0.0492729i	−0.999696	+	0.0246364i	$0.992157\pi$
$98$		0			0
$99$	4.24264			0.426401
$100$		0			0
$101$	3.87868	−	6.71807i	0.385943	−	0.668473i	−0.605956	−	0.795498i	$-0.707209\pi$
$101$	3.87868	−	6.71807i	0.385943	−	0.668473i	0.991900	+	0.127025i	$0.0405428\pi$
$102$		0			0
$103$	−14.9326	+	8.62132i	−1.47135	+	0.849484i	−0.999482	−	0.0321856i	$-0.989753\pi$
$103$	−14.9326	+	8.62132i	−1.47135	+	0.849484i	−0.471867	+	0.881670i	$0.656420\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.0227	+	6.36396i	−1.06561	+	0.615227i	−0.926977	−	0.375117i	$-0.877602\pi$
$107$	−11.0227	+	6.36396i	−1.06561	+	0.615227i	−0.138628	+	0.990345i	$0.544269\pi$
$108$		0			0
$109$	−4.74264	+	8.21449i	−0.454263	+	0.786806i	−0.998645	−	0.0520310i	$-0.983431\pi$
$109$	−4.74264	+	8.21449i	−0.454263	+	0.786806i	0.544383	+	0.838837i	$0.316764\pi$
$110$		0			0
$111$	3.24264			0.307778
$112$		0			0
$113$		−	18.0000i		−	1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$		−	18.0000i		−	1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.80821	+	1.62132i	−0.259619	+	0.149891i
$118$		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
$127$			2.75736i			0.244676i	0.992488	+	0.122338i	$0.0390392\pi$
$127$			2.75736i			0.244676i	−0.992488	+	0.122338i	$0.960961\pi$
$128$		0			0
$129$	1.62132	−	2.80821i	0.142749	−	0.247249i
$130$		0			0
$131$	−7.24264	−	12.5446i	−0.632792	−	1.09603i	−0.986978	−	0.160854i	$-0.948575\pi$
$131$	−7.24264	−	12.5446i	−0.632792	−	1.09603i	0.354186	−	0.935175i	$-0.384758\pi$
$132$		0			0
$133$	−2.51104	+	18.3492i	−0.217734	+	1.59108i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.67423	+	2.12132i	0.313911	+	0.181237i	0.648675	−	0.761065i	$-0.275323\pi$
$137$	3.67423	+	2.12132i	0.313911	+	0.181237i	−0.334764	+	0.942302i	$0.608657\pi$
$138$		0			0
$139$	15.4853			1.31344			0.656722	−	0.754133i	$-0.271942\pi$
$139$	15.4853			1.31344			0.656722	+	0.754133i	$0.271942\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	11.9142	+	6.87868i	0.996317	+	0.575224i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.88064	−	6.74264i	0.155112	−	0.556124i
$148$		0			0
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	0.508413	−	0.861113i	$-0.330232\pi$
$149$	−6.00000	−	10.3923i	−0.491539	−	0.851371i	−0.999953	+	0.00974235i	$0.996899\pi$
$150$		0			0
$151$	−11.2426	+	19.4728i	−0.914913	+	1.58468i	−0.107885	+	0.994163i	$0.534408\pi$
$151$	−11.2426	+	19.4728i	−0.914913	+	1.58468i	−0.807028	+	0.590513i	$0.798926\pi$
$152$		0			0
$153$			4.24264i			0.342997i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.61642	−	3.24264i	−0.448239	−	0.258791i	0.258847	−	0.965918i	$-0.416657\pi$
$157$	−5.61642	−	3.24264i	−0.448239	−	0.258791i	−0.707086	+	0.707127i	$0.749991\pi$
$158$		0			0
$159$	4.24264	+	7.34847i	0.336463	+	0.582772i
$160$		0			0
$161$	11.1213	+	1.52192i	0.876483	+	0.119944i
$162$		0			0
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	−0.203497	−	0.979076i	$-0.565231\pi$
$163$	6.92820	−	4.00000i	0.542659	−	0.313304i	0.746156	+	0.665771i	$0.231897\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	18.7279i		−	1.44921i	−0.689164	−	0.724605i	$-0.742022\pi$
$167$		−	18.7279i		−	1.44921i	0.689164	−	0.724605i	$-0.257978\pi$
$168$		0			0
$169$	2.48528			0.191175
$170$		0			0
$171$	3.50000	−	6.06218i	0.267652	−	0.463586i
$172$		0			0
$173$	−17.7408	+	10.2426i	−1.34881	+	0.778734i	−0.988080	−	0.153938i	$-0.950804\pi$
$173$	−17.7408	+	10.2426i	−1.34881	+	0.778734i	−0.360726	+	0.932672i	$0.617471\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.87039	−	5.12132i	0.666739	−	0.384942i
$178$		0			0
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	−0.956088	−	0.293079i	$-0.905320\pi$
$179$	−3.00000	+	5.19615i	−0.224231	+	0.388379i	0.731858	+	0.681457i	$0.238654\pi$
$180$		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
$183$			4.48528i			0.331562i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	15.5885	−	9.00000i	1.13994	−	0.658145i
$188$		0			0
$189$	−1.62132	+	2.09077i	−0.117934	+	0.152081i
$190$		0			0
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	0.736839	−	0.676068i	$-0.236317\pi$
$191$	−3.00000	−	5.19615i	−0.217072	−	0.375980i	−0.953912	+	0.300088i	$0.902984\pi$
$192$		0			0
$193$	−5.85204	−	3.37868i	−0.421239	−	0.243203i	0.274368	−	0.961625i	$-0.411531\pi$
$193$	−5.85204	−	3.37868i	−0.421239	−	0.243203i	−0.695607	+	0.718422i	$0.744865\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			16.2426i			1.15724i	0.815597	+	0.578620i	$0.196409\pi$
$197$			16.2426i			1.15724i	−0.815597	+	0.578620i	$0.803591\pi$
$198$		0			0
$199$	5.24264	−	9.08052i	0.371641	−	0.643701i	−0.618177	−	0.786039i	$-0.712129\pi$
$199$	5.24264	−	9.08052i	0.371641	−	0.643701i	0.989818	+	0.142338i	$0.0454619\pi$
$200$		0			0
$201$	2.62132	+	4.54026i	0.184894	+	0.320245i
$202$		0			0
$203$	−3.67423	−	2.84924i	−0.257881	−	0.199978i
$204$		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
$211$	22.4853			1.54795			0.773975	−	0.633216i	$-0.218265\pi$
$211$	22.4853			1.54795			0.773975	+	0.633216i	$0.218265\pi$
$212$		0			0
$213$	11.0227	+	6.36396i	0.755263	+	0.436051i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−23.2341	+	9.48528i	−1.57723	+	0.643903i
$218$		0			0
$219$	4.62132	+	8.00436i	0.312280	+	0.540885i
$220$		0			0
$221$	−6.87868	+	11.9142i	−0.462710	+	0.801437i
$222$		0			0
$223$		−	7.51472i		−	0.503223i	−0.967828	−	0.251611i	$-0.919040\pi$
$223$		−	7.51472i		−	0.503223i	0.967828	−	0.251611i	$-0.0809605\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.1750	−	7.60660i	−0.874457	−	0.504868i	−0.00563010	−	0.999984i	$-0.501792\pi$
$227$	−13.1750	−	7.60660i	−0.874457	−	0.504868i	−0.868827	+	0.495116i	$0.835125\pi$
$228$		0			0
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	0.726900	−	0.686743i	$-0.240960\pi$
$229$	−3.50000	−	6.06218i	−0.231287	−	0.400600i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$	11.1213	+	1.52192i	0.731729	+	0.100135i
$232$		0			0
$233$	12.5446	−	7.24264i	0.821825	−	0.474481i	−0.0292201	−	0.999573i	$-0.509302\pi$
$233$	12.5446	−	7.24264i	0.821825	−	0.474481i	0.851046	+	0.525092i	$0.175969\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	11.0000i		−	0.714527i
$238$		0			0
$239$	−10.9706			−0.709627			−0.354813	−	0.934937i	$-0.615456\pi$
$239$	−10.9706			−0.709627			−0.354813	+	0.934937i	$0.615456\pi$
$240$		0			0
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$242$		0			0
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	19.6575	−	11.3492i	1.25077	−	0.722135i
$248$		0			0
$249$	−5.12132	+	8.87039i	−0.324550	+	0.562138i
$250$		0			0
$251$	−18.7279			−1.18210			−0.591048	−	0.806636i	$-0.701286\pi$
$251$	−18.7279			−1.18210			−0.591048	+	0.806636i	$0.701286\pi$
$252$		0			0
$253$			18.0000i			1.13165i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.87039	+	5.12132i	−0.553320	+	0.319459i	−0.750460	−	0.660916i	$-0.770168\pi$
$257$	−8.87039	+	5.12132i	−0.553320	+	0.319459i	0.197140	+	0.980375i	$0.436835\pi$
$258$		0			0
$259$	8.50000	+	1.16320i	0.528164	+	0.0722776i
$260$		0			0
$261$	0.878680	+	1.52192i	0.0543889	+	0.0942043i
$262$		0			0
$263$	7.34847	+	4.24264i	0.453126	+	0.261612i	0.709150	−	0.705058i	$-0.249079\pi$
$263$	7.34847	+	4.24264i	0.453126	+	0.261612i	−0.256023	+	0.966671i	$0.582412\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			10.2426i			0.626839i
$268$		0			0
$269$	−1.24264	+	2.15232i	−0.0757651	+	0.131229i	−0.901419	−	0.432948i	$-0.857473\pi$
$269$	−1.24264	+	2.15232i	−0.0757651	+	0.131229i	0.825654	+	0.564177i	$0.190807\pi$
$270$		0			0
$271$	11.7279	+	20.3134i	0.712421	+	1.23395i	0.963946	+	0.266098i	$0.0857344\pi$
$271$	11.7279	+	20.3134i	0.712421	+	1.23395i	−0.251525	+	0.967851i	$0.580932\pi$
$272$		0			0
$273$	−7.94282	+	3.24264i	−0.480721	+	0.196254i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.3528	+	8.86396i	0.922462	+	0.532584i	0.884420	−	0.466692i	$-0.154554\pi$
$277$	15.3528	+	8.86396i	0.922462	+	0.532584i	0.0380425	+	0.999276i	$0.487888\pi$
$278$		0			0
$279$	9.48528			0.567869
$280$		0			0
$281$	28.9706			1.72824			0.864119	−	0.503287i	$-0.167876\pi$
$281$	28.9706			1.72824			0.864119	+	0.503287i	$0.167876\pi$
$282$		0			0
$283$	−20.5490	−	11.8640i	−1.22151	−	0.705239i	−0.256270	−	0.966605i	$-0.582494\pi$
$283$	−20.5490	−	11.8640i	−1.22151	−	0.705239i	−0.965240	+	0.261366i	$0.915827\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.87039	+	6.87868i	0.523602	+	0.406036i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	0.242641	−	0.420266i	0.0142238	−	0.0246364i
$292$		0			0
$293$		−	4.97056i		−	0.290383i	−0.989404	−	0.145192i	$-0.953620\pi$
$293$		−	4.97056i		−	0.290383i	0.989404	−	0.145192i	$-0.0463799\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.67423	−	2.12132i	−0.213201	−	0.123091i
$298$		0			0
$299$	−6.87868	−	11.9142i	−0.397804	−	0.689017i
$300$		0			0
$301$	5.25736	−	6.77962i	0.303029	−	0.390771i
$302$		0			0
$303$	−6.71807	+	3.87868i	−0.385943	+	0.222824i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	3.24264i		−	0.185067i	−0.995710	−	0.0925336i	$-0.970503\pi$
$307$		−	3.24264i		−	0.185067i	0.995710	−	0.0925336i	$-0.0294966\pi$
$308$		0			0
$309$	17.2426			0.980900
$310$		0			0
$311$	−10.6066	+	18.3712i	−0.601445	+	1.04173i	0.391157	+	0.920324i	$0.372075\pi$
$311$	−10.6066	+	18.3712i	−0.601445	+	1.04173i	−0.992602	+	0.121410i	$0.961258\pi$
$312$		0			0
$313$	20.5490	−	11.8640i	1.16150	−	0.670591i	0.209835	−	0.977737i	$-0.432707\pi$
$313$	20.5490	−	11.8640i	1.16150	−	0.670591i	0.951662	+	0.307146i	$0.0993740\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.4150	−	12.3640i	1.20279	−	0.694429i	0.241613	−	0.970373i	$-0.422324\pi$
$317$	21.4150	−	12.3640i	1.20279	−	0.694429i	0.961174	+	0.275943i	$0.0889903\pi$
$318$		0			0
$319$	3.72792	−	6.45695i	0.208724	−	0.361520i
$320$		0			0
$321$	12.7279			0.710403
$322$		0			0
$323$		−	29.6985i		−	1.65247i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.21449	−	4.74264i	0.454263	−	0.262269i
$328$		0			0
$329$	−15.7279	−	2.15232i	−0.867108	−	0.118661i
$330$		0			0
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$		0			0
$333$	−2.80821	−	1.62132i	−0.153889	−	0.0888478i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			13.7279i			0.747808i	0.927467	+	0.373904i	$0.121981\pi$
$337$			13.7279i			0.747808i	−0.927467	+	0.373904i	$0.878019\pi$
$338$		0			0
$339$	−9.00000	+	15.5885i	−0.488813	+	0.846649i
$340$		0			0
$341$	−20.1213	−	34.8511i	−1.08963	−	1.88730i
$342$		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	−0.175457	−	0.984487i	$-0.556140\pi$
$347$	−20.7846	−	12.0000i	−1.11578	−	0.644194i	−0.940319	+	0.340293i	$0.889474\pi$
$348$		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
$351$	3.24264			0.173079
$352$		0			0
$353$	8.87039	+	5.12132i	0.472123	+	0.272580i	0.717128	−	0.696941i	$-0.245456\pi$
$353$	8.87039	+	5.12132i	0.472123	+	0.272580i	−0.245005	+	0.969522i	$0.578790\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.52192	+	11.1213i	−0.0805484	+	0.588603i
$358$		0			0
$359$	0.878680	+	1.52192i	0.0463749	+	0.0803237i	0.888281	−	0.459300i	$-0.151900\pi$
$359$	0.878680	+	1.52192i	0.0463749	+	0.0803237i	−0.841906	+	0.539624i	$0.818566\pi$
$360$		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
$367$	30.9413	+	17.8640i	1.61512	+	0.932491i	0.988157	+	0.153443i	$0.0490363\pi$
$367$	30.9413	+	17.8640i	1.61512	+	0.932491i	0.626965	+	0.779048i	$0.284297\pi$
$368$		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
$373$	15.3528	−	8.86396i	0.794939	−	0.458959i	−0.0467591	−	0.998906i	$-0.514889\pi$
$373$	15.3528	−	8.86396i	0.794939	−	0.458959i	0.841699	+	0.539948i	$0.181556\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.69848i			0.293487i
$378$		0			0
$379$	20.4558			1.05075			0.525373	−	0.850872i	$-0.323926\pi$
$379$	20.4558			1.05075			0.525373	+	0.850872i	$0.323926\pi$
$380$		0			0
$381$	1.37868	−	2.38794i	0.0706319	−	0.122338i
$382$		0			0
$383$	22.0454	−	12.7279i	1.12647	−	0.650366i	0.183424	−	0.983034i	$-0.441282\pi$
$383$	22.0454	−	12.7279i	1.12647	−	0.650366i	0.943044	+	0.332668i	$0.107949\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.80821	+	1.62132i	−0.142749	+	0.0824163i
$388$		0			0
$389$	−10.6066	+	18.3712i	−0.537776	+	0.931455i	0.461247	+	0.887272i	$0.347402\pi$
$389$	−10.6066	+	18.3712i	−0.537776	+	0.931455i	−0.999023	+	0.0441839i	$0.985931\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$			14.4853i			0.730686i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	7.58410	−	4.37868i	0.380635	−	0.219760i	−0.297460	−	0.954734i	$-0.596139\pi$
$397$	7.58410	−	4.37868i	0.380635	−	0.219760i	0.678094	+	0.734975i	$0.262806\pi$
$398$		0			0
$399$	11.3492	−	14.6354i	0.568173	−	0.732686i
$400$		0			0
$401$	1.75736	+	3.04384i	0.0877583	+	0.152002i	0.906563	−	0.422070i	$-0.138696\pi$
$401$	1.75736	+	3.04384i	0.0877583	+	0.152002i	−0.818805	+	0.574072i	$0.805363\pi$
$402$		0			0
$403$	26.6367	+	15.3787i	1.32687	+	0.766067i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			13.7574i			0.681927i
$408$		0			0
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	−0.575670	−	0.817682i	$-0.695259\pi$
$409$	8.50000	−	14.7224i	0.420298	−	0.727977i	0.995968	+	0.0897044i	$0.0285922\pi$
$410$		0			0
$411$	−2.12132	−	3.67423i	−0.104637	−	0.181237i
$412$		0			0
$413$	25.0892	−	10.2426i	1.23456	−	0.504007i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−13.4106	−	7.74264i	−0.656722	−	0.379159i
$418$		0			0
$419$	14.4853			0.707652			0.353826	−	0.935311i	$-0.384880\pi$
$419$	14.4853			0.707652			0.353826	+	0.935311i	$0.384880\pi$
$420$		0			0
$421$	31.4853			1.53450			0.767249	−	0.641349i	$-0.221625\pi$
$421$	31.4853			1.53450			0.767249	+	0.641349i	$0.221625\pi$
$422$		0			0
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.60896	+	11.7574i	−0.0778629	+	0.568978i
$428$		0			0
$429$	−6.87868	−	11.9142i	−0.332106	−	0.575224i
$430$		0			0
$431$	−9.72792	+	16.8493i	−0.468578	+	0.811600i	−0.999355	−	0.0359112i	$-0.988567\pi$
$431$	−9.72792	+	16.8493i	−0.468578	+	0.811600i	0.530777	+	0.847511i	$0.321900\pi$
$432$		0			0
$433$			33.2426i			1.59754i	0.601637	+	0.798770i	$0.294515\pi$
$433$			33.2426i			1.59754i	−0.601637	+	0.798770i	$0.705485\pi$
$434$		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	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	−5.00000	+	4.89898i	−0.238095	+	0.233285i
$442$		0			0
$443$	17.7408	−	10.2426i	0.842890	−	0.486643i	−0.0153558	−	0.999882i	$-0.504888\pi$
$443$	17.7408	−	10.2426i	0.842890	−	0.486643i	0.858245	+	0.513240i	$0.171555\pi$
$444$		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
$453$	19.4728	−	11.2426i	0.914913	−	0.528225i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−27.8975	+	16.1066i	−1.30499	+	0.753435i	−0.981255	−	0.192714i	$-0.938271\pi$
$457$	−27.8975	+	16.1066i	−1.30499	+	0.753435i	−0.323733	+	0.946149i	$0.604938\pi$
$458$		0			0
$459$	2.12132	−	3.67423i	0.0990148	−	0.171499i
$460$		0			0
$461$	18.7279			0.872246			0.436123	−	0.899887i	$-0.356351\pi$
$461$	18.7279			0.872246			0.436123	+	0.899887i	$0.356351\pi$
$462$		0			0
$463$			10.2721i			0.477384i	0.971095	+	0.238692i	$0.0767186\pi$
$463$			10.2721i			0.477384i	−0.971095	+	0.238692i	$0.923281\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	9.50079	−	5.48528i	0.439644	−	0.253829i	−0.263803	−	0.964577i	$-0.584977\pi$
$467$	9.50079	−	5.48528i	0.439644	−	0.253829i	0.703447	+	0.710748i	$0.251643\pi$
$468$		0			0
$469$	5.24264	+	12.8418i	0.242083	+	0.592979i
$470$		0			0
$471$	3.24264	+	5.61642i	0.149413	+	0.258791i
$472$		0			0
$473$	11.9142	+	6.87868i	0.547817	+	0.316282i
$474$		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	−0.695773	−	0.718262i	$-0.744938\pi$
$479$	6.00000	−	10.3923i	0.274147	−	0.474837i	0.969920	+	0.243426i	$0.0782712\pi$
$480$		0			0
$481$	−5.25736	−	9.10601i	−0.239715	−	0.415198i
$482$		0			0
$483$	−8.87039	−	6.87868i	−0.403617	−	0.312991i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−32.6733	−	18.8640i	−1.48057	−	0.854808i	−0.480813	−	0.876823i	$-0.659658\pi$
$487$	−32.6733	−	18.8640i	−1.48057	−	0.854808i	−0.999758	+	0.0220157i	$0.992992\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	15.5147			0.700169			0.350085	−	0.936718i	$-0.386153\pi$
$491$	15.5147			0.700169			0.350085	+	0.936718i	$0.386153\pi$
$492$		0			0
$493$	6.45695	+	3.72792i	0.290806	+	0.167897i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	26.6112	+	20.6360i	1.19367	+	0.925653i
$498$		0			0
$499$	9.74264	+	16.8747i	0.436140	+	0.755417i	0.997388	−	0.0722305i	$-0.0230117\pi$
$499$	9.74264	+	16.8747i	0.436140	+	0.755417i	−0.561247	+	0.827648i	$0.689678\pi$
$500$		0			0
$501$	−9.36396	+	16.2189i	−0.418351	+	0.724605i
$502$		0			0
$503$		−	26.4853i		−	1.18092i	−0.807067	−	0.590460i	$-0.798946\pi$
$503$		−	26.4853i		−	1.18092i	0.807067	−	0.590460i	$-0.201054\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.15232	−	1.24264i	−0.0955877	−	0.0551876i
$508$		0			0
$509$	−9.72792	−	16.8493i	−0.431183	−	0.746830i	0.565793	−	0.824547i	$-0.308570\pi$
$509$	−9.72792	−	16.8493i	−0.431183	−	0.746830i	−0.996975	+	0.0777173i	$0.975237\pi$
$510$		0			0
$511$	9.24264	+	22.6398i	0.408870	+	1.00152i
$512$		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
$519$	20.4853			0.899204
$520$		0			0
$521$	6.72792	−	11.6531i	0.294756	−	0.510532i	−0.680172	−	0.733052i	$-0.738095\pi$
$521$	6.72792	−	11.6531i	0.294756	−	0.510532i	0.974928	+	0.222520i	$0.0714284\pi$
$522$		0			0
$523$	−4.54026	+	2.62132i	−0.198532	+	0.114622i	−0.595970	−	0.803006i	$-0.703232\pi$
$523$	−4.54026	+	2.62132i	−0.198532	+	0.114622i	0.397439	+	0.917629i	$0.369899\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	34.8511	−	20.1213i	1.51814	−	0.876498i
$528$		0			0
$529$	−2.50000	+	4.33013i	−0.108696	+	0.188266i
$530$		0			0
$531$	−10.2426			−0.444493
$532$		0			0
$533$		−	13.7574i		−	0.595897i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.19615	−	3.00000i	0.224231	−	0.129460i
$538$		0			0
$539$	28.6066	+	7.97887i	1.23217	+	0.343674i
$540$		0			0
$541$	20.4706	+	35.4561i	0.880098	+	1.52437i	0.851231	+	0.524792i	$0.175857\pi$
$541$	20.4706	+	35.4561i	0.880098	+	1.52437i	0.0288675	+	0.999583i	$0.490810\pi$
$542$		0			0
$543$	11.2583	+	6.50000i	0.483141	+	0.278942i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	33.4558i		−	1.43047i	−0.698885	−	0.715234i	$-0.746320\pi$
$547$		−	33.4558i		−	1.43047i	0.698885	−	0.715234i	$-0.253680\pi$
$548$		0			0
$549$	2.24264	−	3.88437i	0.0957136	−	0.165781i
$550$		0			0
$551$	−6.15076	−	10.6534i	−0.262031	−	0.453851i
$552$		0			0
$553$	3.94591	−	28.8345i	0.167797	−	1.22617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.9808	−	15.0000i	−1.10084	−	0.635570i	−0.164399	−	0.986394i	$-0.552568\pi$
$557$	−25.9808	−	15.0000i	−1.10084	−	0.635570i	−0.936442	+	0.350824i	$0.885902\pi$
$558$		0			0
$559$	−10.5147			−0.444725
$560$		0			0
$561$	−18.0000			−0.759961
$562$		0			0
$563$	5.19615	+	3.00000i	0.218992	+	0.126435i	0.605483	−	0.795858i	$-0.292980\pi$
$563$	5.19615	+	3.00000i	0.218992	+	0.126435i	−0.386492	+	0.922293i	$0.626313\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.44949	−	1.00000i	0.102869	−	0.0419961i
$568$		0			0
$569$	−20.8492	−	36.1119i	−0.874046	−	1.51389i	−0.857776	−	0.514024i	$-0.828154\pi$
$569$	−20.8492	−	36.1119i	−0.874046	−	1.51389i	−0.0162699	−	0.999868i	$-0.505179\pi$
$570$		0			0
$571$	14.4706	−	25.0637i	0.605574	−	1.04889i	−0.386386	−	0.922337i	$-0.626277\pi$
$571$	14.4706	−	25.0637i	0.605574	−	1.04889i	0.991960	−	0.126548i	$-0.0403898\pi$
$572$		0			0
$573$			6.00000i			0.250654i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	11.0482	+	6.37868i	0.459942	+	0.265548i	0.712020	−	0.702159i	$-0.247780\pi$
$577$	11.0482	+	6.37868i	0.459942	+	0.265548i	−0.252078	+	0.967707i	$0.581114\pi$
$578$		0			0
$579$	3.37868	+	5.85204i	0.140413	+	0.243203i
$580$		0			0
$581$	−16.6066	+	21.4150i	−0.688958	+	0.888444i
$582$		0			0
$583$	−31.1769	+	18.0000i	−1.29122	+	0.745484i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	45.2132i		−	1.86615i	−0.359684	−	0.933074i	$-0.617115\pi$
$587$		−	45.2132i		−	1.86615i	0.359684	−	0.933074i	$-0.382885\pi$
$588$		0			0
$589$	−66.3970			−2.73584
$590$		0			0
$591$	8.12132	−	14.0665i	0.334066	−	0.578620i
$592$		0			0
$593$	2.78272	−	1.60660i	0.114272	−	0.0659752i	−0.441774	−	0.897126i	$-0.645651\pi$
$593$	2.78272	−	1.60660i	0.114272	−	0.0659752i	0.556047	+	0.831151i	$0.312318\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−9.08052	+	5.24264i	−0.371641	+	0.214567i
$598$		0			0
$599$	−16.2426	+	28.1331i	−0.663656	+	1.14949i	0.315991	+	0.948762i	$0.397663\pi$
$599$	−16.2426	+	28.1331i	−0.663656	+	1.14949i	−0.979648	+	0.200724i	$0.935670\pi$
$600$		0			0
$601$	−3.48528			−0.142168			−0.0710838	−	0.997470i	$-0.522646\pi$
$601$	−3.48528			−0.142168			−0.0710838	+	0.997470i	$0.522646\pi$
$602$		0			0
$603$		−	5.24264i		−	0.213497i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	25.3249	−	14.6213i	1.02790	−	0.593461i	0.111521	−	0.993762i	$-0.464428\pi$
$607$	25.3249	−	14.6213i	1.02790	−	0.593461i	0.916384	+	0.400301i	$0.131094\pi$
$608$		0			0
$609$	1.75736	+	4.30463i	0.0712118	+	0.174433i
$610$		0			0
$611$	9.72792	+	16.8493i	0.393550	+	0.681648i
$612$		0			0
$613$	4.72490	+	2.72792i	0.190837	+	0.110180i	0.592374	−	0.805663i	$-0.298191\pi$
$613$	4.72490	+	2.72792i	0.190837	+	0.110180i	−0.401537	+	0.915843i	$0.631524\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			26.4853i			1.06626i	0.846034	+	0.533129i	$0.178984\pi$
$617$			26.4853i			1.06626i	−0.846034	+	0.533129i	$0.821016\pi$
$618$		0			0
$619$	−5.98528	+	10.3668i	−0.240569	+	0.416677i	−0.960876	−	0.276977i	$-0.910667\pi$
$619$	−5.98528	+	10.3668i	−0.240569	+	0.416677i	0.720308	+	0.693655i	$0.244001\pi$
$620$		0			0
$621$	2.12132	+	3.67423i	0.0851257	+	0.147442i
$622$		0			0
$623$	−3.67423	+	26.8492i	−0.147205	+	1.07569i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	25.7196	+	14.8492i	1.02714	+	0.593022i
$628$		0			0
$629$	−13.7574			−0.548542
$630$		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
$633$	−19.4728	−	11.2426i	−0.773975	−	0.446855i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−21.9839	+	5.65076i	−0.871032	+	0.223891i
$638$		0			0
$639$	−6.36396	−	11.0227i	−0.251754	−	0.436051i
$640$		0			0
$641$	−17.1213	+	29.6550i	−0.676251	+	1.17130i	0.299850	+	0.953986i	$0.403063\pi$
$641$	−17.1213	+	29.6550i	−0.676251	+	1.17130i	−0.976101	+	0.217316i	$0.930270\pi$
$642$		0			0
$643$		−	19.7279i		−	0.777993i	−0.921239	−	0.388997i	$-0.872822\pi$
$643$		−	19.7279i		−	0.777993i	0.921239	−	0.388997i	$-0.127178\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.87039	+	5.12132i	0.348731	+	0.201340i	0.664126	−	0.747621i	$-0.268804\pi$
$647$	8.87039	+	5.12132i	0.348731	+	0.201340i	−0.315395	+	0.948960i	$0.602137\pi$
$648$		0			0
$649$	21.7279	+	37.6339i	0.852896	+	1.47726i
$650$		0			0
$651$	24.8640	+	3.40256i	0.974495	+	0.133357i
$652$		0			0
$653$	8.87039	−	5.12132i	0.347125	−	0.200413i	−0.316293	−	0.948661i	$-0.602438\pi$
$653$	8.87039	−	5.12132i	0.347125	−	0.200413i	0.663418	+	0.748249i	$0.269105\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	9.24264i		−	0.360590i
$658$		0			0
$659$	−40.9706			−1.59599			−0.797993	−	0.602666i	$-0.794105\pi$
$659$	−40.9706			−1.59599			−0.797993	+	0.602666i	$0.794105\pi$
$660$		0			0
$661$	1.01472	−	1.75754i	0.0394680	−	0.0683605i	−0.845617	−	0.533791i	$-0.820767\pi$
$661$	1.01472	−	1.75754i	0.0394680	−	0.0683605i	0.885085	+	0.465430i	$0.154100\pi$
$662$		0			0
$663$	11.9142	−	6.87868i	0.462710	−	0.267146i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.45695	+	3.72792i	−0.250014	+	0.144346i
$668$		0			0
$669$	−3.75736	+	6.50794i	−0.145268	+	0.251611i
$670$		0			0
$671$	−19.0294			−0.734623
$672$		0			0
$673$			29.7279i			1.14593i	0.819581	+	0.572964i	$0.194206\pi$
$673$			29.7279i			1.14593i	−0.819581	+	0.572964i	$0.805794\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.0227	+	6.36396i	−0.423637	+	0.244587i	−0.696632	−	0.717428i	$-0.745319\pi$
$677$	−11.0227	+	6.36396i	−0.423637	+	0.244587i	0.272995	+	0.962015i	$0.411986\pi$
$678$		0			0
$679$	0.786797	−	1.01461i	0.0301945	−	0.0389372i
$680$		0			0
$681$	7.60660	+	13.1750i	0.291486	+	0.504868i
$682$		0			0
$683$	−28.7635	−	16.6066i	−1.10060	−	0.635434i	−0.164224	−	0.986423i	$-0.552512\pi$
$683$	−28.7635	−	16.6066i	−1.10060	−	0.635434i	−0.936380	+	0.350989i	$0.885845\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			7.00000i			0.267067i
$688$		0			0
$689$	13.7574	−	23.8284i	0.524114	−	0.907791i
$690$		0			0
$691$	−13.4706	−	23.3317i	−0.512444	−	0.887580i	−0.999896	−	0.0144296i	$-0.995407\pi$
$691$	−13.4706	−	23.3317i	−0.512444	−	0.887580i	0.487452	−	0.873150i	$-0.337927\pi$
$692$		0			0
$693$	−8.87039	−	6.87868i	−0.336958	−	0.261299i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−15.5885	−	9.00000i	−0.590455	−	0.340899i
$698$		0			0
$699$	−14.4853			−0.547884
$700$		0			0
$701$	8.78680			0.331873			0.165936	−	0.986136i	$-0.446935\pi$
$701$	8.78680			0.331873			0.165936	+	0.986136i	$0.446935\pi$
$702$		0			0
$703$	19.6575	+	11.3492i	0.741395	+	0.428045i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−19.0016	+	7.75736i	−0.714628	+	0.291746i
$708$		0			0
$709$	−18.2426	−	31.5972i	−0.685117	−	1.18666i	−0.973400	−	0.229112i	$-0.926418\pi$
$709$	−18.2426	−	31.5972i	−0.685117	−	1.18666i	0.288283	−	0.957545i	$-0.406915\pi$
$710$		0			0
$711$	−5.50000	+	9.52628i	−0.206266	+	0.357263i
$712$		0			0
$713$			40.2426i			1.50710i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	9.50079	+	5.48528i	0.354813	+	0.204852i
$718$		0			0
$719$	13.2426	+	22.9369i	0.493867	+	0.855403i	0.999975	−	0.00706717i	$-0.00224957\pi$
$719$	13.2426	+	22.9369i	0.493867	+	0.855403i	−0.506108	+	0.862470i	$0.668916\pi$
$720$		0			0
$721$	45.1985	+	6.18527i	1.68328	+	0.230352i
$722$		0			0
$723$	−3.46410	+	2.00000i	−0.128831	+	0.0743808i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	0.757359i		−	0.0280889i	−0.999901	−	0.0140445i	$-0.995529\pi$
$727$		−	0.757359i		−	0.0280889i	0.999901	−	0.0140445i	$-0.00447063\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−6.87868	+	11.9142i	−0.254417	+	0.440663i
$732$		0			0
$733$	1.54741	−	0.893398i	0.0571549	−	0.0329984i	−0.471150	−	0.882053i	$-0.656161\pi$
$733$	1.54741	−	0.893398i	0.0571549	−	0.0329984i	0.528305	+	0.849055i	$0.322828\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.2627	+	11.1213i	−0.709550	+	0.409659i
$738$		0			0
$739$	−7.74264	+	13.4106i	−0.284818	+	0.493319i	−0.972565	−	0.232632i	$-0.925266\pi$
$739$	−7.74264	+	13.4106i	−0.284818	+	0.493319i	0.687747	+	0.725950i	$0.258600\pi$
$740$		0			0
$741$	−22.6985			−0.833850
$742$		0			0
$743$			15.2132i			0.558118i	0.960274	+	0.279059i	$0.0900226\pi$
$743$			15.2132i			0.558118i	−0.960274	+	0.279059i	$0.909977\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	8.87039	−	5.12132i	0.324550	−	0.187379i
$748$		0			0
$749$	33.3640	+	4.56575i	1.21909	+	0.166829i
$750$		0			0
$751$	−22.4706	−	38.9202i	−0.819962	−	1.42022i	−0.905709	−	0.423900i	$-0.860661\pi$
$751$	−22.4706	−	38.9202i	−0.819962	−	1.42022i	0.0857467	−	0.996317i	$-0.472672\pi$
$752$		0			0
$753$	16.2189	+	9.36396i	0.591048	+	0.341242i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	9.02944i		−	0.328180i	−0.986445	−	0.164090i	$-0.947531\pi$
$757$		−	9.02944i		−	0.328180i	0.986445	−	0.164090i	$-0.0524688\pi$
$758$		0			0
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$		0			0
$761$	−23.1213	−	40.0473i	−0.838147	−	1.45171i	−0.891442	−	0.453135i	$-0.850306\pi$
$761$	−23.1213	−	40.0473i	−0.838147	−	1.45171i	0.0532948	−	0.998579i	$-0.483028\pi$
$762$		0			0
$763$	23.2341	−	9.48528i	0.841131	−	0.343390i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−28.7635	−	16.6066i	−1.03859	−	0.599630i
$768$		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
$771$	10.2426			0.368880
$772$		0			0
$773$	−10.1312	−	5.84924i	−0.364393	−	0.210383i	0.306613	−	0.951834i	$-0.400804\pi$
$773$	−10.1312	−	5.84924i	−0.364393	−	0.210383i	−0.671006	+	0.741452i	$0.734138\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−6.77962	−	5.25736i	−0.243217	−	0.188607i
$778$		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
$783$		−	1.75736i		−	0.0628029i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	24.6690	+	14.2426i	0.879354	+	0.507695i	0.870445	−	0.492265i	$-0.163831\pi$
$787$	24.6690	+	14.2426i	0.879354	+	0.507695i	0.00890869	+	0.999960i	$0.497164\pi$
$788$		0			0
$789$	−4.24264	−	7.34847i	−0.151042	−	0.261612i
$790$		0			0
$791$	−29.1838	+	37.6339i	−1.03766	+	1.33811i
$792$		0			0
$793$	12.5956	−	7.27208i	0.447283	−	0.258239i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			31.7574i			1.12490i	0.826830	+	0.562452i	$0.190142\pi$
$797$			31.7574i			1.12490i	−0.826830	+	0.562452i	$0.809858\pi$
$798$		0			0
$799$	25.4558			0.900563
$800$		0			0
$801$	5.12132	−	8.87039i	0.180953	−	0.313420i
$802$		0			0
$803$	−33.9596	+	19.6066i	−1.19841	+	0.691902i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.15232	−	1.24264i	0.0757651	−	0.0437430i
$808$		0			0
$809$	13.9706	−	24.1977i	0.491179	−	0.850747i	−0.508770	−	0.860903i	$-0.669899\pi$
$809$	13.9706	−	24.1977i	0.491179	−	0.850747i	0.999948	+	0.0101560i	$0.00323282\pi$
$810$		0			0
$811$	11.9411			0.419310			0.209655	−	0.977775i	$-0.432766\pi$
$811$	11.9411			0.419310			0.209655	+	0.977775i	$0.432766\pi$
$812$		0			0
$813$		−	23.4558i		−	0.822632i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	19.6575	−	11.3492i	0.687728	−	0.397060i
$818$		0			0
$819$	8.50000	+	1.16320i	0.297014	+	0.0406454i
$820$		0			0
$821$	−2.84924	−	4.93503i	−0.0994392	−	0.172234i	0.812013	−	0.583639i	$-0.198372\pi$
$821$	−2.84924	−	4.93503i	−0.0994392	−	0.172234i	−0.911453	+	0.411405i	$0.865038\pi$
$822$		0			0
$823$	33.7495	+	19.4853i	1.17643	+	0.679214i	0.955187	−	0.296004i	$-0.0956541\pi$
$823$	33.7495	+	19.4853i	1.17643	+	0.679214i	0.221247	+	0.975218i	$0.428987\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	43.4558i		−	1.51111i	−0.655087	−	0.755554i	$-0.727368\pi$
$827$		−	43.4558i		−	1.51111i	0.655087	−	0.755554i	$-0.272632\pi$
$828$		0			0
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	−0.754567	−	0.656223i	$-0.772153\pi$
$829$	5.50000	−	9.52628i	0.191023	−	0.330861i	0.945589	+	0.325362i	$0.105486\pi$
$830$		0			0
$831$	−8.86396	−	15.3528i	−0.307487	−	0.532584i
$832$		0			0
$833$	−7.97887	+	28.6066i	−0.276451	+	0.991160i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.21449	−	4.74264i	−0.283934	−	0.163930i
$838$		0			0
$839$	−25.7574			−0.889243			−0.444621	−	0.895719i	$-0.646662\pi$
$839$	−25.7574			−0.889243			−0.444621	+	0.895719i	$0.646662\pi$
$840$		0			0
$841$	−25.9117			−0.893506
$842$		0			0
$843$	−25.0892	−	14.4853i	−0.864119	−	0.498900i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.51104	+	18.3492i	−0.0862802	+	0.630487i
$848$		0			0
$849$	11.8640	+	20.5490i	0.407170	+	0.705239i
$850$		0			0
$851$	6.87868	−	11.9142i	0.235798	−	0.408414i
$852$		0			0
$853$		−	25.7279i		−	0.880907i	−0.897775	−	0.440454i	$-0.854818\pi$
$853$		−	25.7279i		−	0.880907i	0.897775	−	0.440454i	$-0.145182\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.67423	+	2.12132i	0.125509	+	0.0724629i	0.561440	−	0.827517i	$-0.310247\pi$
$857$	3.67423	+	2.12132i	0.125509	+	0.0724629i	−0.435931	+	0.899980i	$0.643581\pi$
$858$		0			0
$859$	−11.0000	−	19.0526i	−0.375315	−	0.650065i	0.615059	−	0.788481i	$-0.289132\pi$
$859$	−11.0000	−	19.0526i	−0.375315	−	0.650065i	−0.990374	+	0.138416i	$0.955799\pi$
$860$		0			0
$861$	−4.24264	−	10.3923i	−0.144589	−	0.354169i
$862$		0			0
$863$	−18.6323	+	10.7574i	−0.634251	+	0.366185i	−0.782396	−	0.622781i	$-0.786003\pi$
$863$	−18.6323	+	10.7574i	−0.634251	+	0.366185i	0.148146	+	0.988966i	$0.452670\pi$
$864$		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
$873$	−0.420266	+	0.242641i	−0.0142238	+	0.00821214i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	8.66025	−	5.00000i	0.292436	−	0.168838i	−0.346604	−	0.938012i	$-0.612665\pi$
$877$	8.66025	−	5.00000i	0.292436	−	0.168838i	0.639040	+	0.769174i	$0.279332\pi$
$878$		0			0
$879$	−2.48528	+	4.30463i	−0.0838265	+	0.145192i
$880$		0			0
$881$	40.9706			1.38033			0.690167	−	0.723650i	$-0.257537\pi$
$881$	40.9706			1.38033			0.690167	+	0.723650i	$0.257537\pi$
$882$		0			0
$883$			5.72792i			0.192760i	0.995345	+	0.0963800i	$0.0307264\pi$
$883$			5.72792i			0.192760i	−0.995345	+	0.0963800i	$0.969274\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.1750	+	7.60660i	−0.442374	+	0.255405i	−0.704604	−	0.709601i	$-0.748875\pi$
$887$	−13.1750	+	7.60660i	−0.442374	+	0.255405i	0.262230	+	0.965005i	$0.415542\pi$
$888$		0			0
$889$	4.47056	−	5.76500i	0.149938	−	0.193352i
$890$		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
$897$			13.7574i			0.459345i
$898$		0			0
$899$	8.33452	−	14.4358i	0.277972	−	0.481462i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$	−7.94282	+	3.24264i	−0.264320	+	0.107908i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−26.2164	−	15.1360i	−0.870501	−	0.502584i	−0.00298623	−	0.999996i	$-0.500951\pi$
$907$	−26.2164	−	15.1360i	−0.870501	−	0.502584i	−0.867515	+	0.497412i	$0.834284\pi$
$908$		0			0
$909$	7.75736			0.257295
$910$		0			0
$911$	51.2132			1.69677			0.848385	−	0.529380i	$-0.177576\pi$
$911$	51.2132			1.69677			0.848385	+	0.529380i	$0.177576\pi$
$912$		0			0
$913$	−37.6339	−	21.7279i	−1.24550	−	0.719089i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.19615	+	37.9706i	−0.171592	+	1.25390i
$918$		0			0
$919$	16.9853	+	29.4194i	0.560293	+	0.970455i	0.997471	+	0.0710804i	$0.0226447\pi$
$919$	16.9853	+	29.4194i	0.560293	+	0.970455i	−0.437178	+	0.899375i	$0.644022\pi$
$920$		0			0
$921$	−1.62132	+	2.80821i	−0.0534243	+	0.0925336i
$922$		0			0
$923$		−	41.2721i		−	1.35849i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−14.9326	−	8.62132i	−0.490450	−	0.283161i
$928$		0			0
$929$	18.3640	+	31.8073i	0.602502	+	1.04356i	0.992441	+	0.122723i	$0.0391628\pi$
$929$	18.3640	+	31.8073i	0.602502	+	1.04356i	−0.389939	+	0.920841i	$0.627504\pi$
$930$		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
$937$			18.6985i			0.610853i	0.952216	+	0.305426i	$0.0987990\pi$
$937$			18.6985i			0.610853i	−0.952216	+	0.305426i	$0.901201\pi$
$938$		0			0
$939$	−23.7279			−0.774331
$940$		0			0
$941$	23.8492	−	41.3081i	0.777463	−	1.34661i	−0.155937	−	0.987767i	$-0.549840\pi$
$941$	23.8492	−	41.3081i	0.777463	−	1.34661i	0.933400	−	0.358838i	$-0.116827\pi$
$942$		0			0
$943$	15.5885	−	9.00000i	0.507630	−	0.293080i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.78272	−	1.60660i	0.0904261	−	0.0522075i	−0.454105	−	0.890948i	$-0.650041\pi$
$947$	2.78272	−	1.60660i	0.0904261	−	0.0522075i	0.544531	+	0.838741i	$0.316708\pi$
$948$		0			0
$949$	14.9853	−	25.9553i	0.486443	−	0.842544i
$950$		0			0
$951$	−24.7279			−0.801858
$952$		0			0
$953$		−	27.5147i		−	0.891289i	−0.895210	−	0.445645i	$-0.852975\pi$
$953$		−	27.5147i		−	0.891289i	0.895210	−	0.445645i	$-0.147025\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−6.45695	+	3.72792i	−0.208724	+	0.120507i
$958$		0			0
$959$	−4.24264	−	10.3923i	−0.137002	−	0.335585i
$960$		0			0
$961$	−29.4853	−	51.0700i	−0.951138	−	1.64742i
$962$		0			0
$963$	−11.0227	−	6.36396i	−0.355202	−	0.205076i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			35.2426i			1.13333i	0.823949	+	0.566663i	$0.191766\pi$
$967$			35.2426i			1.13333i	−0.823949	+	0.566663i	$0.808234\pi$
$968$		0			0
$969$	−14.8492	+	25.7196i	−0.477026	+	0.826234i
$970$		0			0
$971$	−26.4853	−	45.8739i	−0.849953	−	1.47216i	−0.881249	−	0.472652i	$-0.843297\pi$
$971$	−26.4853	−	45.8739i	−0.849953	−	1.47216i	0.0312961	−	0.999510i	$-0.490037\pi$
$972$		0			0
$973$	−32.3762	−	25.1066i	−1.03793	−	0.804881i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.60959	−	4.39340i	−0.243452	−	0.140557i	0.373310	−	0.927707i	$-0.378223\pi$
$977$	−7.60959	−	4.39340i	−0.243452	−	0.140557i	−0.616762	+	0.787149i	$0.711556\pi$
$978$		0			0
$979$	−43.4558			−1.38885
$980$		0			0
$981$	−9.48528			−0.302842
$982$		0			0
$983$	36.1119	+	20.8492i	1.15179	+	0.664988i	0.949323	−	0.314301i	$-0.101770\pi$
$983$	36.1119	+	20.8492i	1.15179	+	0.664988i	0.202469	+	0.979289i	$0.435103\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	12.5446	+	9.72792i	0.399300	+	0.309643i
$988$		0			0
$989$	−6.87868	−	11.9142i	−0.218729	−	0.378850i
$990$		0			0
$991$	−7.47056	+	12.9394i	−0.237310	+	0.411033i	−0.959942	−	0.280200i	$-0.909599\pi$
$991$	−7.47056	+	12.9394i	−0.237310	+	0.411033i	0.722631	+	0.691234i	$0.242932\pi$
$992$		0			0
$993$			17.0000i			0.539479i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−22.2810	−	12.8640i	−0.705647	−	0.407406i	0.103800	−	0.994598i	$-0.466900\pi$
$997$	−22.2810	−	12.8640i	−0.705647	−	0.407406i	−0.809447	+	0.587192i	$0.800233\pi$
$998$		0			0
$999$	1.62132	+	2.80821i	0.0512963	+	0.0888478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.f.949.1		8
5.2	odd	4		420.2.q.d.361.2	yes	4
5.3	odd	4		2100.2.q.k.1201.1		4
5.4	even	2	inner	2100.2.bc.f.949.4		8
7.2	even	3	inner	2100.2.bc.f.1549.4		8
15.2	even	4		1260.2.s.e.361.2		4
20.7	even	4		1680.2.bg.t.1201.1		4
35.2	odd	12		420.2.q.d.121.2	✓	4
35.9	even	6	inner	2100.2.bc.f.1549.1		8
35.12	even	12		2940.2.q.q.961.2		4
35.17	even	12		2940.2.a.p.1.1		2
35.23	odd	12		2100.2.q.k.1801.1		4
35.27	even	4		2940.2.q.q.361.2		4
35.32	odd	12		2940.2.a.r.1.1		2
105.2	even	12		1260.2.s.e.541.2		4
105.17	odd	12		8820.2.a.bf.1.2		2
105.32	even	12		8820.2.a.bk.1.2		2
140.107	even	12		1680.2.bg.t.961.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.d.121.2	✓	4	35.2	odd	12
420.2.q.d.361.2	yes	4	5.2	odd	4
1260.2.s.e.361.2		4	15.2	even	4
1260.2.s.e.541.2		4	105.2	even	12
1680.2.bg.t.961.1		4	140.107	even	12
1680.2.bg.t.1201.1		4	20.7	even	4
2100.2.q.k.1201.1		4	5.3	odd	4
2100.2.q.k.1801.1		4	35.23	odd	12
2100.2.bc.f.949.1		8	1.1	even	1	trivial
2100.2.bc.f.949.4		8	5.4	even	2	inner
2100.2.bc.f.1549.1		8	35.9	even	6	inner
2100.2.bc.f.1549.4		8	7.2	even	3	inner
2940.2.a.p.1.1		2	35.17	even	12
2940.2.a.r.1.1		2	35.32	odd	12
2940.2.q.q.361.2		4	35.27	even	4
2940.2.q.q.961.2		4	35.12	even	12
8820.2.a.bf.1.2		2	105.17	odd	12
8820.2.a.bk.1.2		2	105.32	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-2.09077 - 1.62132i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{3} +(-2.09077 - 1.62132i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} +3.24264i q^{13} +(3.67423 + 2.12132i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(-3.67423 + 2.12132i) q^{23} -1.00000i q^{27} +1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(-3.67423 + 2.12132i) q^{33} +(-2.80821 + 1.62132i) q^{37} +(1.62132 - 2.80821i) q^{39} -4.24264 q^{41} +3.24264i q^{43} +(5.19615 - 3.00000i) q^{47} +(1.74264 + 6.77962i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(-7.34847 - 4.24264i) q^{53} +7.00000i q^{57} +(-5.12132 + 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(0.358719 - 2.62132i) q^{63} +(-4.54026 - 2.62132i) q^{67} +4.24264 q^{69} -12.7279 q^{71} +(-8.00436 - 4.62132i) q^{73} +(-10.3923 + 4.24264i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.2426i q^{83} +(-1.52192 - 0.878680i) q^{87} +(-5.12132 - 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(-8.21449 + 4.74264i) q^{93} +0.485281i q^{97} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 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

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