LMFDB - Embedded newform 1260.2.s.e.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(361,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1260.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1260.361
Dual form			1260.2.s.e.541.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +(-2.12132 + 3.67423i) q^{11} +3.24264 q^{13} +(2.12132 - 3.67423i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-2.12132 - 3.67423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(-2.62132 - 0.358719i) q^{35} +(-1.62132 - 2.80821i) q^{37} +4.24264 q^{41} +3.24264 q^{43} +(-3.00000 - 5.19615i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(4.24264 - 7.34847i) q^{53} +4.24264 q^{55} +(-5.12132 + 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(-1.62132 - 2.80821i) q^{65} +(2.62132 - 4.54026i) q^{67} +12.7279 q^{71} +(-4.62132 + 8.00436i) q^{73} +(4.24264 + 10.3923i) q^{77} +(-5.50000 - 9.52628i) q^{79} +10.2426 q^{83} -4.24264 q^{85} +(-5.12132 - 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(3.50000 - 6.06218i) q^{95} -0.485281 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q - 2 * q^5 - 2 * q^7	$ 4 q - 2 q^{5} - 2 q^{7} - 4 q^{13} + 14 q^{19} - 2 q^{25} + 24 q^{29} + 2 q^{31} - 2 q^{35} + 2 q^{37} - 4 q^{43} - 12 q^{47} + 10 q^{49} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 2 q^{67} - 10 q^{73} - 22 q^{79} + 24 q^{83} - 12 q^{89} + 38 q^{91} + 14 q^{95} + 32 q^{97}+O(q^{100}) $ 4 * q - 2 * q^5 - 2 * q^7 - 4 * q^13 + 14 * q^19 - 2 * q^25 + 24 * q^29 + 2 * q^31 - 2 * q^35 + 2 * q^37 - 4 * q^43 - 12 * q^47 + 10 * q^49 - 12 * q^59 + 8 * q^61 + 2 * q^65 + 2 * q^67 - 10 * q^73 - 22 * q^79 + 24 * q^83 - 12 * q^89 + 38 * q^91 + 14 * q^95 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$3$		0			0
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$		0			0
$13$	3.24264			0.899347			0.449673	−	0.893193i	$-0.351540\pi$
$13$	3.24264			0.899347			0.449673	+	0.893193i	$0.351540\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.12132	−	3.67423i	0.514496	−	0.891133i	−0.485363	−	0.874313i	$-0.661312\pi$
$17$	2.12132	−	3.67423i	0.514496	−	0.891133i	0.999859	−	0.0168199i	$-0.00535420\pi$
$18$		0			0
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.12132	−	3.67423i	−0.442326	−	0.766131i	0.555536	−	0.831493i	$-0.312513\pi$
$23$	−2.12132	−	3.67423i	−0.442326	−	0.766131i	−0.997862	+	0.0653618i	$0.979180\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		0			0
$28$		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
$33$		0			0
$34$		0			0
$35$	−2.62132	−	0.358719i	−0.443084	−	0.0606347i
$36$		0			0
$37$	−1.62132	−	2.80821i	−0.266543	−	0.461667i	0.701423	−	0.712745i	$-0.252548\pi$
$37$	−1.62132	−	2.80821i	−0.266543	−	0.461667i	−0.967967	+	0.251078i	$0.919215\pi$
$38$		0			0
$39$		0			0
$40$		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
$43$	3.24264			0.494498			0.247249	−	0.968952i	$-0.420473\pi$
$43$	3.24264			0.494498			0.247249	+	0.968952i	$0.420473\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.24264	−	7.34847i	0.582772	−	1.00939i	−0.412378	−	0.911013i	$-0.635302\pi$
$53$	4.24264	−	7.34847i	0.582772	−	1.00939i	0.995149	−	0.0983769i	$-0.0313651\pi$
$54$		0			0
$55$	4.24264			0.572078
$56$		0			0
$57$		0			0
$58$		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			0
$64$		0			0
$65$	−1.62132	−	2.80821i	−0.201100	−	0.348315i
$66$		0			0
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	−0.660293	−	0.751008i	$-0.729568\pi$
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	0.980539	+	0.196327i	$0.0629013\pi$
$68$		0			0
$69$		0			0
$70$		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
$73$	−4.62132	+	8.00436i	−0.540885	+	0.936840i	0.457969	+	0.888968i	$0.348577\pi$
$73$	−4.62132	+	8.00436i	−0.540885	+	0.936840i	−0.998854	+	0.0478714i	$0.984756\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.24264	+	10.3923i	0.483494	+	1.18431i
$78$		0			0
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	10.2426			1.12428			0.562138	−	0.827043i	$-0.309979\pi$
$83$	10.2426			1.12428			0.562138	+	0.827043i	$0.309979\pi$
$84$		0			0
$85$	−4.24264			−0.460179
$86$		0			0
$87$		0			0
$88$		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
$93$		0			0
$94$		0			0
$95$	3.50000	−	6.06218i	0.359092	−	0.621966i
$96$		0			0
$97$	−0.485281			−0.0492729			−0.0246364	−	0.999696i	$-0.507843\pi$
$97$	−0.485281			−0.0492729			−0.0246364	+	0.999696i	$0.507843\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.87868	+	6.71807i	−0.385943	+	0.668473i	−0.991900	−	0.127025i	$-0.959457\pi$
$101$	−3.87868	+	6.71807i	−0.385943	+	0.668473i	0.605956	+	0.795498i	$0.292791\pi$
$102$		0			0
$103$	8.62132	+	14.9326i	0.849484	+	1.47135i	0.881670	+	0.471867i	$0.156420\pi$
$103$	8.62132	+	14.9326i	0.849484	+	1.47135i	−0.0321856	+	0.999482i	$0.510247\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.36396	+	11.0227i	0.615227	+	1.06561i	0.990345	+	0.138628i	$0.0442691\pi$
$107$	6.36396	+	11.0227i	0.615227	+	1.06561i	−0.375117	+	0.926977i	$0.622398\pi$
$108$		0			0
$109$	4.74264	−	8.21449i	0.454263	−	0.786806i	−0.544383	−	0.838837i	$-0.683236\pi$
$109$	4.74264	−	8.21449i	0.454263	−	0.786806i	0.998645	+	0.0520310i	$0.0165695\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$		0			0
$115$	−2.12132	+	3.67423i	−0.197814	+	0.342624i
$116$		0			0
$117$		0			0
$118$		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
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.75736			−0.244676			−0.122338	−	0.992488i	$-0.539039\pi$
$127$	−2.75736			−0.244676			−0.122338	+	0.992488i	$0.539039\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	7.24264	+	12.5446i	0.632792	+	1.09603i	0.986978	+	0.160854i	$0.0514247\pi$
$131$	7.24264	+	12.5446i	0.632792	+	1.09603i	−0.354186	+	0.935175i	$0.615242\pi$
$132$		0			0
$133$	18.3492	+	2.51104i	1.59108	+	0.217734i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.12132	−	3.67423i	0.181237	−	0.313911i	−0.761065	−	0.648675i	$-0.775323\pi$
$137$	2.12132	−	3.67423i	0.181237	−	0.313911i	0.942302	+	0.334764i	$0.108657\pi$
$138$		0			0
$139$	−15.4853			−1.31344			−0.656722	−	0.754133i	$-0.728058\pi$
$139$	−15.4853			−1.31344			−0.656722	+	0.754133i	$0.728058\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.87868	+	11.9142i	−0.575224	+	0.996317i
$144$		0			0
$145$	−0.878680	−	1.52192i	−0.0729704	−	0.126388i
$146$		0			0
$147$		0			0
$148$		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
$153$		0			0
$154$		0			0
$155$	−9.48528			−0.761876
$156$		0			0
$157$	3.24264	−	5.61642i	0.258791	−	0.448239i	−0.707127	−	0.707086i	$-0.750009\pi$
$157$	3.24264	−	5.61642i	0.258791	−	0.448239i	0.965918	+	0.258847i	$0.0833426\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−11.1213	−	1.52192i	−0.876483	−	0.119944i
$162$		0			0
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	0.665771	−	0.746156i	$-0.268103\pi$
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	−0.979076	+	0.203497i	$0.934769\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.7279			−1.44921			−0.724605	−	0.689164i	$-0.757978\pi$
$167$	−18.7279			−1.44921			−0.724605	+	0.689164i	$0.757978\pi$
$168$		0			0
$169$	−2.48528			−0.191175
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.2426	−	17.7408i	−0.778734	−	1.34881i	−0.932672	−	0.360726i	$-0.882529\pi$
$173$	−10.2426	−	17.7408i	−0.778734	−	1.34881i	0.153938	−	0.988080i	$-0.450804\pi$
$174$		0			0
$175$	1.00000	+	2.44949i	0.0755929	+	0.185164i
$176$		0			0
$177$		0			0
$178$		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
$183$		0			0
$184$		0			0
$185$	−1.62132	+	2.80821i	−0.119202	+	0.206464i
$186$		0			0
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$		0			0
$193$	−3.37868	+	5.85204i	−0.243203	+	0.421239i	−0.961625	−	0.274368i	$-0.911531\pi$
$193$	−3.37868	+	5.85204i	−0.243203	+	0.421239i	0.718422	+	0.695607i	$0.244865\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	16.2426			1.15724			0.578620	−	0.815597i	$-0.303591\pi$
$197$	16.2426			1.15724			0.578620	+	0.815597i	$0.303591\pi$
$198$		0			0
$199$	−5.24264	+	9.08052i	−0.371641	+	0.643701i	−0.989818	−	0.142338i	$-0.954538\pi$
$199$	−5.24264	+	9.08052i	−0.371641	+	0.643701i	0.618177	+	0.786039i	$0.287871\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.84924	−	3.67423i	0.199978	−	0.257881i
$204$		0			0
$205$	−2.12132	−	3.67423i	−0.148159	−	0.256620i
$206$		0			0
$207$		0			0
$208$		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
$213$		0			0
$214$		0			0
$215$	−1.62132	−	2.80821i	−0.110573	−	0.191518i
$216$		0			0
$217$	−9.48528	−	23.2341i	−0.643903	−	1.57723i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.87868	−	11.9142i	0.462710	−	0.801437i
$222$		0			0
$223$	−7.51472			−0.503223			−0.251611	−	0.967828i	$-0.580960\pi$
$223$	−7.51472			−0.503223			−0.251611	+	0.967828i	$0.580960\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.60660	+	13.1750i	−0.504868	+	0.874457i	0.495116	+	0.868827i	$0.335125\pi$
$227$	−7.60660	+	13.1750i	−0.504868	+	0.874457i	−0.999984	+	0.00563010i	$0.998208\pi$
$228$		0			0
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.24264	+	12.5446i	0.474481	+	0.821825i	0.999573	−	0.0292201i	$-0.00930237\pi$
$233$	7.24264	+	12.5446i	0.474481	+	0.821825i	−0.525092	+	0.851046i	$0.675969\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$		0			0
$238$		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			0
$244$		0			0
$245$	−5.00000	+	4.89898i	−0.319438	+	0.312984i
$246$		0			0
$247$	11.3492	+	19.6575i	0.722135	+	1.25077i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.7279			1.18210			0.591048	−	0.806636i	$-0.298714\pi$
$251$	18.7279			1.18210			0.591048	+	0.806636i	$0.298714\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.12132	+	8.87039i	0.319459	+	0.553320i	0.980375	−	0.197140i	$-0.0631654\pi$
$257$	5.12132	+	8.87039i	0.319459	+	0.553320i	−0.660916	+	0.750460i	$0.729832\pi$
$258$		0			0
$259$	−8.50000	−	1.16320i	−0.528164	−	0.0722776i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−4.24264	+	7.34847i	−0.261612	+	0.453126i	−0.966671	−	0.256023i	$-0.917588\pi$
$263$	−4.24264	+	7.34847i	−0.261612	+	0.453126i	0.705058	+	0.709150i	$0.250921\pi$
$264$		0			0
$265$	−8.48528			−0.521247
$266$		0			0
$267$		0			0
$268$		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
$273$		0			0
$274$		0			0
$275$	−2.12132	−	3.67423i	−0.127920	−	0.221565i
$276$		0			0
$277$	−8.86396	+	15.3528i	−0.532584	+	0.922462i	0.466692	+	0.884420i	$0.345446\pi$
$277$	−8.86396	+	15.3528i	−0.532584	+	0.922462i	−0.999276	+	0.0380425i	$0.987888\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−28.9706			−1.72824			−0.864119	−	0.503287i	$-0.832124\pi$
$281$	−28.9706			−1.72824			−0.864119	+	0.503287i	$0.832124\pi$
$282$		0			0
$283$	−11.8640	+	20.5490i	−0.705239	+	1.22151i	0.261366	+	0.965240i	$0.415827\pi$
$283$	−11.8640	+	20.5490i	−0.705239	+	1.22151i	−0.966605	+	0.256270i	$0.917506\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.87868	−	8.87039i	0.406036	−	0.523602i
$288$		0			0
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.97056			0.290383			0.145192	−	0.989404i	$-0.453620\pi$
$293$	4.97056			0.290383			0.145192	+	0.989404i	$0.453620\pi$
$294$		0			0
$295$	10.2426			0.596350
$296$		0			0
$297$		0			0
$298$		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
$303$		0			0
$304$		0			0
$305$	−2.24264	+	3.88437i	−0.128413	+	0.222418i
$306$		0			0
$307$	3.24264			0.185067			0.0925336	−	0.995710i	$-0.470503\pi$
$307$	3.24264			0.185067			0.0925336	+	0.995710i	$0.470503\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	10.6066	−	18.3712i	0.601445	−	1.04173i	−0.391157	−	0.920324i	$-0.627925\pi$
$311$	10.6066	−	18.3712i	0.601445	−	1.04173i	0.992602	−	0.121410i	$-0.0387415\pi$
$312$		0			0
$313$	−11.8640	−	20.5490i	−0.670591	−	1.16150i	−0.977737	−	0.209835i	$-0.932707\pi$
$313$	−11.8640	−	20.5490i	−0.670591	−	1.16150i	0.307146	−	0.951662i	$-0.400626\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.3640	−	21.4150i	−0.694429	−	1.20279i	−0.970373	−	0.241613i	$-0.922324\pi$
$317$	−12.3640	−	21.4150i	−0.694429	−	1.20279i	0.275943	−	0.961174i	$-0.411010\pi$
$318$		0			0
$319$	−3.72792	+	6.45695i	−0.208724	+	0.361520i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	29.6985			1.65247
$324$		0			0
$325$	−1.62132	+	2.80821i	−0.0899347	+	0.155771i
$326$		0			0
$327$		0			0
$328$		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
$333$		0			0
$334$		0			0
$335$	−5.24264			−0.286436
$336$		0			0
$337$	−13.7279			−0.747808			−0.373904	−	0.927467i	$-0.621981\pi$
$337$	−13.7279			−0.747808			−0.373904	+	0.927467i	$0.621981\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	20.1213	+	34.8511i	1.08963	+	1.88730i
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	0.340293	+	0.940319i	$0.389474\pi$
$347$	−12.0000	+	20.7846i	−0.644194	+	1.11578i	−0.984487	+	0.175457i	$0.943860\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.12132	+	8.87039i	−0.272580	+	0.472123i	−0.969522	−	0.245005i	$-0.921210\pi$
$353$	−5.12132	+	8.87039i	−0.272580	+	0.472123i	0.696941	+	0.717128i	$0.254544\pi$
$354$		0			0
$355$	−6.36396	−	11.0227i	−0.337764	−	0.585024i
$356$		0			0
$357$		0			0
$358$		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
$363$		0			0
$364$		0			0
$365$	9.24264			0.483782
$366$		0			0
$367$	−17.8640	+	30.9413i	−0.932491	+	1.61512i	−0.153443	+	0.988157i	$0.549036\pi$
$367$	−17.8640	+	30.9413i	−0.932491	+	1.61512i	−0.779048	+	0.626965i	$0.784297\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.48528	−	20.7846i	−0.440534	−	1.07908i
$372$		0			0
$373$	−8.86396	−	15.3528i	−0.458959	−	0.794939i	0.539948	−	0.841699i	$-0.318444\pi$
$373$	−8.86396	−	15.3528i	−0.458959	−	0.794939i	−0.998906	+	0.0467591i	$0.985111\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.69848			0.293487
$378$		0			0
$379$	−20.4558			−1.05075			−0.525373	−	0.850872i	$-0.676074\pi$
$379$	−20.4558			−1.05075			−0.525373	+	0.850872i	$0.676074\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.7279	+	22.0454i	0.650366	+	1.12647i	0.983034	+	0.183424i	$0.0587180\pi$
$383$	12.7279	+	22.0454i	0.650366	+	1.12647i	−0.332668	+	0.943044i	$0.607949\pi$
$384$		0			0
$385$	6.87868	−	8.87039i	0.350570	−	0.452077i
$386$		0			0
$387$		0			0
$388$		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
$393$		0			0
$394$		0			0
$395$	−5.50000	+	9.52628i	−0.276735	+	0.479319i
$396$		0			0
$397$	4.37868	+	7.58410i	0.219760	+	0.380635i	0.954734	−	0.297460i	$-0.0961394\pi$
$397$	4.37868	+	7.58410i	0.219760	+	0.380635i	−0.734975	+	0.678094i	$0.762806\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.75736	−	3.04384i	−0.0877583	−	0.152002i	0.818805	−	0.574072i	$-0.194637\pi$
$401$	−1.75736	−	3.04384i	−0.0877583	−	0.152002i	−0.906563	+	0.422070i	$0.861304\pi$
$402$		0			0
$403$	15.3787	−	26.6367i	0.766067	−	1.32687i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	13.7574			0.681927
$408$		0			0
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	−0.995968	−	0.0897044i	$-0.971408\pi$
$409$	−8.50000	+	14.7224i	−0.420298	+	0.727977i	0.575670	+	0.817682i	$0.304741\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.2426	+	25.0892i	0.504007	+	1.23456i
$414$		0			0
$415$	−5.12132	−	8.87039i	−0.251396	−	0.435430i
$416$		0			0
$417$		0			0
$418$		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
$423$		0			0
$424$		0			0
$425$	2.12132	+	3.67423i	0.102899	+	0.178227i
$426$		0			0
$427$	−11.7574	−	1.60896i	−0.568978	−	0.0778629i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.72792	−	16.8493i	0.468578	−	0.811600i	−0.530777	−	0.847511i	$-0.678100\pi$
$431$	9.72792	−	16.8493i	0.468578	−	0.811600i	0.999355	+	0.0359112i	$0.0114333\pi$
$432$		0			0
$433$	33.2426			1.59754			0.798770	−	0.601637i	$-0.205485\pi$
$433$	33.2426			1.59754			0.798770	+	0.601637i	$0.205485\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.8492	−	25.7196i	0.710336	−	1.23034i
$438$		0			0
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.2426	+	17.7408i	0.486643	+	0.842890i	0.999882	−	0.0153558i	$-0.00488809\pi$
$443$	10.2426	+	17.7408i	0.486643	+	0.842890i	−0.513240	+	0.858245i	$0.671555\pi$
$444$		0			0
$445$	−5.12132	+	8.87039i	−0.242774	+	0.420497i
$446$		0			0
$447$		0			0
$448$		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
$453$		0			0
$454$		0			0
$455$	−8.50000	−	1.16320i	−0.398486	−	0.0545316i
$456$		0			0
$457$	−16.1066	−	27.8975i	−0.753435	−	1.30499i	−0.946149	−	0.323733i	$-0.895062\pi$
$457$	−16.1066	−	27.8975i	−0.753435	−	1.30499i	0.192714	−	0.981255i	$-0.438271\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.7279			−0.872246			−0.436123	−	0.899887i	$-0.643649\pi$
$461$	−18.7279			−0.872246			−0.436123	+	0.899887i	$0.643649\pi$
$462$		0			0
$463$	10.2721			0.477384			0.238692	−	0.971095i	$-0.423281\pi$
$463$	10.2721			0.477384			0.238692	+	0.971095i	$0.423281\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.48528	−	9.50079i	−0.253829	−	0.439644i	0.710748	−	0.703447i	$-0.248357\pi$
$467$	−5.48528	−	9.50079i	−0.253829	−	0.439644i	−0.964577	+	0.263803i	$0.915023\pi$
$468$		0			0
$469$	−5.24264	−	12.8418i	−0.242083	−	0.592979i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.87868	+	11.9142i	−0.316282	+	0.547817i
$474$		0			0
$475$	−7.00000			−0.321182
$476$		0			0
$477$		0			0
$478$		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
$483$		0			0
$484$		0			0
$485$	0.242641	+	0.420266i	0.0110177	+	0.0190833i
$486$		0			0
$487$	18.8640	−	32.6733i	0.854808	−	1.48057i	−0.0220157	−	0.999758i	$-0.507008\pi$
$487$	18.8640	−	32.6733i	0.854808	−	1.48057i	0.876823	−	0.480813i	$-0.159658\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−15.5147			−0.700169			−0.350085	−	0.936718i	$-0.613847\pi$
$491$	−15.5147			−0.700169			−0.350085	+	0.936718i	$0.613847\pi$
$492$		0			0
$493$	3.72792	−	6.45695i	0.167897	−	0.290806i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	20.6360	−	26.6112i	0.925653	−	1.19367i
$498$		0			0
$499$	−9.74264	−	16.8747i	−0.436140	−	0.755417i	0.561247	−	0.827648i	$-0.310322\pi$
$499$	−9.74264	−	16.8747i	−0.436140	−	0.755417i	−0.997388	+	0.0722305i	$0.976988\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	26.4853			1.18092			0.590460	−	0.807067i	$-0.298946\pi$
$503$	26.4853			1.18092			0.590460	+	0.807067i	$0.298946\pi$
$504$		0			0
$505$	7.75736			0.345198
$506$		0			0
$507$		0			0
$508$		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
$513$		0			0
$514$		0			0
$515$	8.62132	−	14.9326i	0.379901	−	0.658007i
$516$		0			0
$517$	25.4558			1.11955
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.72792	+	11.6531i	−0.294756	+	0.510532i	−0.974928	−	0.222520i	$-0.928572\pi$
$521$	−6.72792	+	11.6531i	−0.294756	+	0.510532i	0.680172	+	0.733052i	$0.261905\pi$
$522$		0			0
$523$	2.62132	+	4.54026i	0.114622	+	0.198532i	0.917629	−	0.397439i	$-0.130101\pi$
$523$	2.62132	+	4.54026i	0.114622	+	0.198532i	−0.803006	+	0.595970i	$0.796768\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−20.1213	−	34.8511i	−0.876498	−	1.51814i
$528$		0			0
$529$	2.50000	−	4.33013i	0.108696	−	0.188266i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	13.7574			0.595897
$534$		0			0
$535$	6.36396	−	11.0227i	0.275138	−	0.476553i
$536$		0			0
$537$		0			0
$538$		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
$543$		0			0
$544$		0			0
$545$	−9.48528			−0.406305
$546$		0			0
$547$	33.4558			1.43047			0.715234	−	0.698885i	$-0.246320\pi$
$547$	33.4558			1.43047			0.715234	+	0.698885i	$0.246320\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.15076	+	10.6534i	0.262031	+	0.453851i
$552$		0			0
$553$	−28.8345	−	3.94591i	−1.22617	−	0.167797i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	0.350824	+	0.936442i	$0.385902\pi$
$557$	−15.0000	+	25.9808i	−0.635570	+	1.10084i	−0.986394	+	0.164399i	$0.947432\pi$
$558$		0			0
$559$	10.5147			0.444725
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	−0.922293	−	0.386492i	$-0.873687\pi$
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	0.795858	+	0.605483i	$0.207020\pi$
$564$		0			0
$565$	−9.00000	−	15.5885i	−0.378633	−	0.655811i
$566$		0			0
$567$		0			0
$568$		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
$573$		0			0
$574$		0			0
$575$	4.24264			0.176930
$576$		0			0
$577$	−6.37868	+	11.0482i	−0.265548	+	0.459942i	−0.967707	−	0.252078i	$-0.918886\pi$
$577$	−6.37868	+	11.0482i	−0.265548	+	0.459942i	0.702159	+	0.712020i	$0.252220\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.6066	−	21.4150i	0.688958	−	0.888444i
$582$		0			0
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−45.2132			−1.86615			−0.933074	−	0.359684i	$-0.882885\pi$
$587$	−45.2132			−1.86615			−0.933074	+	0.359684i	$0.882885\pi$
$588$		0			0
$589$	66.3970			2.73584
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.60660	+	2.78272i	0.0659752	+	0.114272i	0.897126	−	0.441774i	$-0.145651\pi$
$593$	1.60660	+	2.78272i	0.0659752	+	0.114272i	−0.831151	+	0.556047i	$0.812318\pi$
$594$		0			0
$595$	−6.87868	+	8.87039i	−0.281998	+	0.363650i
$596$		0			0
$597$		0			0
$598$		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
$603$		0			0
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	14.6213	+	25.3249i	0.593461	+	1.02790i	0.993762	+	0.111521i	$0.0355722\pi$
$607$	14.6213	+	25.3249i	0.593461	+	1.02790i	−0.400301	+	0.916384i	$0.631094\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.72792	−	16.8493i	−0.393550	−	0.681648i
$612$		0			0
$613$	2.72792	−	4.72490i	0.110180	−	0.190837i	−0.805663	−	0.592374i	$-0.798191\pi$
$613$	2.72792	−	4.72490i	0.110180	−	0.190837i	0.915843	+	0.401537i	$0.131524\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	26.4853			1.06626			0.533129	−	0.846034i	$-0.321016\pi$
$617$	26.4853			1.06626			0.533129	+	0.846034i	$0.321016\pi$
$618$		0			0
$619$	5.98528	−	10.3668i	0.240569	−	0.416677i	−0.720308	−	0.693655i	$-0.755999\pi$
$619$	5.98528	−	10.3668i	0.240569	−	0.416677i	0.960876	+	0.276977i	$0.0893327\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−26.8492	−	3.67423i	−1.07569	−	0.147205i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$		0			0
$628$		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
$633$		0			0
$634$		0			0
$635$	1.37868	+	2.38794i	0.0547112	+	0.0947626i
$636$		0			0
$637$	−5.65076	−	21.9839i	−0.223891	−	0.871032i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.1213	−	29.6550i	0.676251	−	1.17130i	−0.299850	−	0.953986i	$-0.596937\pi$
$641$	17.1213	−	29.6550i	0.676251	−	1.17130i	0.976101	−	0.217316i	$-0.0697301\pi$
$642$		0			0
$643$	−19.7279			−0.777993			−0.388997	−	0.921239i	$-0.627178\pi$
$643$	−19.7279			−0.777993			−0.388997	+	0.921239i	$0.627178\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.12132	−	8.87039i	0.201340	−	0.348731i	−0.747621	−	0.664126i	$-0.768804\pi$
$647$	5.12132	−	8.87039i	0.201340	−	0.348731i	0.948960	+	0.315395i	$0.102137\pi$
$648$		0			0
$649$	−21.7279	−	37.6339i	−0.852896	−	1.47726i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.12132	+	8.87039i	0.200413	+	0.347125i	0.948661	−	0.316293i	$-0.102438\pi$
$653$	5.12132	+	8.87039i	0.200413	+	0.347125i	−0.748249	+	0.663418i	$0.769105\pi$
$654$		0			0
$655$	7.24264	−	12.5446i	0.282993	−	0.490159i
$656$		0			0
$657$		0			0
$658$		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
$663$		0			0
$664$		0			0
$665$	−7.00000	−	17.1464i	−0.271448	−	0.664910i
$666$		0			0
$667$	−3.72792	−	6.45695i	−0.144346	−	0.250014i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	19.0294			0.734623
$672$		0			0
$673$	29.7279			1.14593			0.572964	−	0.819581i	$-0.305794\pi$
$673$	29.7279			1.14593			0.572964	+	0.819581i	$0.305794\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	0.962015	−	0.272995i	$-0.0880143\pi$
$677$	6.36396	+	11.0227i	0.244587	+	0.423637i	−0.717428	+	0.696632i	$0.754681\pi$
$678$		0			0
$679$	−0.786797	+	1.01461i	−0.0301945	+	0.0389372i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.6066	−	28.7635i	0.635434	−	1.10060i	−0.350989	−	0.936380i	$-0.614155\pi$
$683$	16.6066	−	28.7635i	0.635434	−	1.10060i	0.986423	−	0.164224i	$-0.0525121\pi$
$684$		0			0
$685$	−4.24264			−0.162103
$686$		0			0
$687$		0			0
$688$		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
$693$		0			0
$694$		0			0
$695$	7.74264	+	13.4106i	0.293695	+	0.508695i
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.78680			−0.331873			−0.165936	−	0.986136i	$-0.553065\pi$
$701$	−8.78680			−0.331873			−0.165936	+	0.986136i	$0.553065\pi$
$702$		0			0
$703$	11.3492	−	19.6575i	0.428045	−	0.741395i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.75736	+	19.0016i	0.291746	+	0.714628i
$708$		0			0
$709$	18.2426	+	31.5972i	0.685117	+	1.18666i	0.973400	+	0.229112i	$0.0735822\pi$
$709$	18.2426	+	31.5972i	0.685117	+	1.18666i	−0.288283	+	0.957545i	$0.593085\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−40.2426			−1.50710
$714$		0			0
$715$	13.7574			0.514496
$716$		0			0
$717$		0			0
$718$		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
$723$		0			0
$724$		0			0
$725$	−0.878680	+	1.52192i	−0.0326333	+	0.0565226i
$726$		0			0
$727$	0.757359			0.0280889			0.0140445	−	0.999901i	$-0.495529\pi$
$727$	0.757359			0.0280889			0.0140445	+	0.999901i	$0.495529\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.87868	−	11.9142i	0.254417	−	0.440663i
$732$		0			0
$733$	−0.893398	−	1.54741i	−0.0329984	−	0.0571549i	0.849055	−	0.528305i	$-0.177172\pi$
$733$	−0.893398	−	1.54741i	−0.0329984	−	0.0571549i	−0.882053	+	0.471150i	$0.843839\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.1213	+	19.2627i	0.409659	+	0.709550i
$738$		0			0
$739$	7.74264	−	13.4106i	0.284818	−	0.493319i	−0.687747	−	0.725950i	$-0.741400\pi$
$739$	7.74264	−	13.4106i	0.284818	−	0.493319i	0.972565	+	0.232632i	$0.0747336\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−15.2132			−0.558118			−0.279059	−	0.960274i	$-0.590023\pi$
$743$	−15.2132			−0.558118			−0.279059	+	0.960274i	$0.590023\pi$
$744$		0			0
$745$	−6.00000	+	10.3923i	−0.219823	+	0.380745i
$746$		0			0
$747$		0			0
$748$		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
$753$		0			0
$754$		0			0
$755$	22.4853			0.818323
$756$		0			0
$757$	9.02944			0.328180			0.164090	−	0.986445i	$-0.447531\pi$
$757$	9.02944			0.328180			0.164090	+	0.986445i	$0.447531\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	23.1213	+	40.0473i	0.838147	+	1.45171i	0.891442	+	0.453135i	$0.149694\pi$
$761$	23.1213	+	40.0473i	0.838147	+	1.45171i	−0.0532948	+	0.998579i	$0.516972\pi$
$762$		0			0
$763$	−9.48528	−	23.2341i	−0.343390	−	0.841131i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.6066	+	28.7635i	−0.599630	+	1.03859i
$768$		0			0
$769$	5.00000			0.180305			0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000			0.180305			0.0901523	+	0.995928i	$0.471265\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.84924	−	10.1312i	0.210383	−	0.364393i	−0.741452	−	0.671006i	$-0.765862\pi$
$773$	5.84924	−	10.1312i	0.210383	−	0.364393i	0.951834	+	0.306613i	$0.0991957\pi$
$774$		0			0
$775$	4.74264	+	8.21449i	0.170361	+	0.295073i
$776$		0			0
$777$		0			0
$778$		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
$783$		0			0
$784$		0			0
$785$	−6.48528			−0.231470
$786$		0			0
$787$	−14.2426	+	24.6690i	−0.507695	+	0.879354i	0.492265	+	0.870445i	$0.336169\pi$
$787$	−14.2426	+	24.6690i	−0.507695	+	0.879354i	−0.999960	+	0.00890869i	$0.997164\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	29.1838	−	37.6339i	1.03766	−	1.33811i
$792$		0			0
$793$	−7.27208	−	12.5956i	−0.258239	−	0.447283i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	31.7574			1.12490			0.562452	−	0.826830i	$-0.309858\pi$
$797$	31.7574			1.12490			0.562452	+	0.826830i	$0.309858\pi$
$798$		0			0
$799$	−25.4558			−0.900563
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−19.6066	−	33.9596i	−0.691902	−	1.19841i
$804$		0			0
$805$	4.24264	+	10.3923i	0.149533	+	0.366281i
$806$		0			0
$807$		0			0
$808$		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
$813$		0			0
$814$		0			0
$815$	−4.00000	+	6.92820i	−0.140114	+	0.242684i
$816$		0			0
$817$	11.3492	+	19.6575i	0.397060	+	0.687728i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.84924	+	4.93503i	0.0994392	+	0.172234i	0.911453	−	0.411405i	$-0.134962\pi$
$821$	2.84924	+	4.93503i	0.0994392	+	0.172234i	−0.812013	+	0.583639i	$0.801628\pi$
$822$		0			0
$823$	19.4853	−	33.7495i	0.679214	−	1.17643i	−0.296004	−	0.955187i	$-0.595654\pi$
$823$	19.4853	−	33.7495i	0.679214	−	1.17643i	0.975218	−	0.221247i	$-0.0710126\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−43.4558			−1.51111			−0.755554	−	0.655087i	$-0.772632\pi$
$827$	−43.4558			−1.51111			−0.755554	+	0.655087i	$0.772632\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−28.6066	−	7.97887i	−0.991160	−	0.276451i
$834$		0			0
$835$	9.36396	+	16.2189i	0.324053	+	0.561277i
$836$		0			0
$837$		0			0
$838$		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
$843$		0			0
$844$		0			0
$845$	1.24264	+	2.15232i	0.0427481	+	0.0740419i
$846$		0			0
$847$	−18.3492	−	2.51104i	−0.630487	−	0.0862802i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.87868	+	11.9142i	−0.235798	+	0.408414i
$852$		0			0
$853$	−25.7279			−0.880907			−0.440454	−	0.897775i	$-0.645182\pi$
$853$	−25.7279			−0.880907			−0.440454	+	0.897775i	$0.645182\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.12132	−	3.67423i	0.0724629	−	0.125509i	−0.827517	−	0.561440i	$-0.810247\pi$
$857$	2.12132	−	3.67423i	0.0724629	−	0.125509i	0.899980	+	0.435931i	$0.143581\pi$
$858$		0			0
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	0.990374	−	0.138416i	$-0.0442012\pi$
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	−0.615059	+	0.788481i	$0.710868\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−10.7574	−	18.6323i	−0.366185	−	0.634251i	0.622781	−	0.782396i	$-0.286003\pi$
$863$	−10.7574	−	18.6323i	−0.366185	−	0.634251i	−0.988966	+	0.148146i	$0.952670\pi$
$864$		0			0
$865$	−10.2426	+	17.7408i	−0.348260	+	0.603204i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	46.6690			1.58314
$870$		0			0
$871$	8.50000	−	14.7224i	0.288012	−	0.498851i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.62132	−	2.09077i	0.0548106	−	0.0706809i
$876$		0			0
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	0.938012	−	0.346604i	$-0.112665\pi$
$877$	5.00000	+	8.66025i	0.168838	+	0.292436i	−0.769174	+	0.639040i	$0.779332\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−40.9706			−1.38033			−0.690167	−	0.723650i	$-0.742463\pi$
$881$	−40.9706			−1.38033			−0.690167	+	0.723650i	$0.742463\pi$
$882$		0			0
$883$	5.72792			0.192760			0.0963800	−	0.995345i	$-0.469274\pi$
$883$	5.72792			0.192760			0.0963800	+	0.995345i	$0.469274\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.60660	+	13.1750i	0.255405	+	0.442374i	0.965005	−	0.262230i	$-0.0844580\pi$
$887$	7.60660	+	13.1750i	0.255405	+	0.442374i	−0.709601	+	0.704604i	$0.751125\pi$
$888$		0			0
$889$	−4.47056	+	5.76500i	−0.149938	+	0.193352i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	21.0000	−	36.3731i	0.702738	−	1.21718i
$894$		0			0
$895$	6.00000			0.200558
$896$		0			0
$897$		0			0
$898$		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
$903$		0			0
$904$		0			0
$905$	6.50000	+	11.2583i	0.216067	+	0.374240i
$906$		0			0
$907$	15.1360	−	26.2164i	0.502584	−	0.870501i	−0.497412	−	0.867515i	$-0.665716\pi$
$907$	15.1360	−	26.2164i	0.502584	−	0.870501i	0.999996	−	0.00298623i	$-0.000950549\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−51.2132			−1.69677			−0.848385	−	0.529380i	$-0.822424\pi$
$911$	−51.2132			−1.69677			−0.848385	+	0.529380i	$0.822424\pi$
$912$		0			0
$913$	−21.7279	+	37.6339i	−0.719089	+	1.24550i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	37.9706	+	5.19615i	1.25390	+	0.171592i
$918$		0			0
$919$	−16.9853	−	29.4194i	−0.560293	−	0.970455i	−0.997471	−	0.0710804i	$-0.977355\pi$
$919$	−16.9853	−	29.4194i	−0.560293	−	0.970455i	0.437178	−	0.899375i	$-0.355978\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	41.2721			1.35849
$924$		0			0
$925$	3.24264			0.106617
$926$		0			0
$927$		0			0
$928$		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
$933$		0			0
$934$		0			0
$935$	9.00000	−	15.5885i	0.294331	−	0.509797i
$936$		0			0
$937$	−18.6985			−0.610853			−0.305426	−	0.952216i	$-0.598799\pi$
$937$	−18.6985			−0.610853			−0.305426	+	0.952216i	$0.598799\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−23.8492	+	41.3081i	−0.777463	+	1.34661i	0.155937	+	0.987767i	$0.450160\pi$
$941$	−23.8492	+	41.3081i	−0.777463	+	1.34661i	−0.933400	+	0.358838i	$0.883173\pi$
$942$		0			0
$943$	−9.00000	−	15.5885i	−0.293080	−	0.507630i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.60660	−	2.78272i	−0.0522075	−	0.0904261i	0.838741	−	0.544531i	$-0.183292\pi$
$947$	−1.60660	−	2.78272i	−0.0522075	−	0.0904261i	−0.890948	+	0.454105i	$0.849959\pi$
$948$		0			0
$949$	−14.9853	+	25.9553i	−0.486443	+	0.842544i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	27.5147			0.891289			0.445645	−	0.895210i	$-0.352975\pi$
$953$	27.5147			0.891289			0.445645	+	0.895210i	$0.352975\pi$
$954$		0			0
$955$	3.00000	−	5.19615i	0.0970777	−	0.168144i
$956$		0			0
$957$		0			0
$958$		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
$963$		0			0
$964$		0			0
$965$	6.75736			0.217527
$966$		0			0
$967$	−35.2426			−1.13333			−0.566663	−	0.823949i	$-0.691766\pi$
$967$	−35.2426			−1.13333			−0.566663	+	0.823949i	$0.691766\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	26.4853	+	45.8739i	0.849953	+	1.47216i	0.881249	+	0.472652i	$0.156703\pi$
$971$	26.4853	+	45.8739i	0.849953	+	1.47216i	−0.0312961	+	0.999510i	$0.509963\pi$
$972$		0			0
$973$	−25.1066	+	32.3762i	−0.804881	+	1.03793i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.39340	+	7.60959i	−0.140557	+	0.243452i	−0.927707	−	0.373310i	$-0.878223\pi$
$977$	−4.39340	+	7.60959i	−0.140557	+	0.243452i	0.787149	+	0.616762i	$0.211556\pi$
$978$		0			0
$979$	43.4558			1.38885
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.8492	+	36.1119i	−0.664988	+	1.15179i	0.314301	+	0.949323i	$0.398230\pi$
$983$	−20.8492	+	36.1119i	−0.664988	+	1.15179i	−0.979289	+	0.202469i	$0.935103\pi$
$984$		0			0
$985$	−8.12132	−	14.0665i	−0.258767	−	0.448197i
$986$		0			0
$987$		0			0
$988$		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
$993$		0			0
$994$		0			0
$995$	10.4853			0.332406
$996$		0			0
$997$	12.8640	−	22.2810i	0.407406	−	0.705647i	−0.587192	−	0.809447i	$-0.699767\pi$
$997$	12.8640	−	22.2810i	0.407406	−	0.705647i	0.994598	+	0.103800i	$0.0331002\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.s.e.361.2		4
3.2	odd	2		420.2.q.d.361.2	yes	4
7.2	even	3	inner	1260.2.s.e.541.2		4
7.3	odd	6		8820.2.a.bf.1.2		2
7.4	even	3		8820.2.a.bk.1.2		2
12.11	even	2		1680.2.bg.t.1201.1		4
15.2	even	4		2100.2.bc.f.949.4		8
15.8	even	4		2100.2.bc.f.949.1		8
15.14	odd	2		2100.2.q.k.1201.1		4
21.2	odd	6		420.2.q.d.121.2	✓	4
21.5	even	6		2940.2.q.q.961.2		4
21.11	odd	6		2940.2.a.r.1.1		2
21.17	even	6		2940.2.a.p.1.1		2
21.20	even	2		2940.2.q.q.361.2		4
84.23	even	6		1680.2.bg.t.961.1		4
105.2	even	12		2100.2.bc.f.1549.1		8
105.23	even	12		2100.2.bc.f.1549.4		8
105.44	odd	6		2100.2.q.k.1801.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.d.121.2	✓	4	21.2	odd	6
420.2.q.d.361.2	yes	4	3.2	odd	2
1260.2.s.e.361.2		4	1.1	even	1	trivial
1260.2.s.e.541.2		4	7.2	even	3	inner
1680.2.bg.t.961.1		4	84.23	even	6
1680.2.bg.t.1201.1		4	12.11	even	2
2100.2.q.k.1201.1		4	15.14	odd	2
2100.2.q.k.1801.1		4	105.44	odd	6
2100.2.bc.f.949.1		8	15.8	even	4
2100.2.bc.f.949.4		8	15.2	even	4
2100.2.bc.f.1549.1		8	105.2	even	12
2100.2.bc.f.1549.4		8	105.23	even	12
2940.2.a.p.1.1		2	21.17	even	6
2940.2.a.r.1.1		2	21.11	odd	6
2940.2.q.q.361.2		4	21.20	even	2
2940.2.q.q.961.2		4	21.5	even	6
8820.2.a.bf.1.2		2	7.3	odd	6
8820.2.a.bk.1.2		2	7.4	even	3

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +(-2.12132 + 3.67423i) q^{11} +3.24264 q^{13} +(2.12132 - 3.67423i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-2.12132 - 3.67423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(-2.62132 - 0.358719i) q^{35} +(-1.62132 - 2.80821i) q^{37} +4.24264 q^{41} +3.24264 q^{43} +(-3.00000 - 5.19615i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(4.24264 - 7.34847i) q^{53} +4.24264 q^{55} +(-5.12132 + 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(-1.62132 - 2.80821i) q^{65} +(2.62132 - 4.54026i) q^{67} +12.7279 q^{71} +(-4.62132 + 8.00436i) q^{73} +(4.24264 + 10.3923i) q^{77} +(-5.50000 - 9.52628i) q^{79} +10.2426 q^{83} -4.24264 q^{85} +(-5.12132 - 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(3.50000 - 6.06218i) q^{95} -0.485281 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q - 2 * q^5 - 2 * q^7	\( 4 q - 2 q^{5} - 2 q^{7} - 4 q^{13} + 14 q^{19} - 2 q^{25} + 24 q^{29} + 2 q^{31} - 2 q^{35} + 2 q^{37} - 4 q^{43} - 12 q^{47} + 10 q^{49} - 12 q^{59} + 8 q^{61} + 2 q^{65} + 2 q^{67} - 10 q^{73} - 22 q^{79} + 24 q^{83} - 12 q^{89} + 38 q^{91} + 14 q^{95} + 32 q^{97}+O(q^{100}) \) 4 * q - 2 * q^5 - 2 * q^7 - 4 * q^13 + 14 * q^19 - 2 * q^25 + 24 * q^29 + 2 * q^31 - 2 * q^35 + 2 * q^37 - 4 * q^43 - 12 * q^47 + 10 * q^49 - 12 * q^59 + 8 * q^61 + 2 * q^65 + 2 * q^67 - 10 * q^73 - 22 * q^79 + 24 * q^83 - 12 * q^89 + 38 * q^91 + 14 * q^95 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more