LMFDB - Embedded newform 3420.2.bj.c.2629.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3420,2,Mod(1189,3420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3420, 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("3420.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3420.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.3088374913$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2629.2
Root			$-1.08802 + 0.628167i$ of defining polynomial
Character	$\chi$	$=$	3420.2629
Dual form			3420.2.bj.c.1189.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87507 + 1.21824i) q^{5} -4.97100i q^{7} +3.85491 q^{11} +(-2.31178 - 1.33470i) q^{13} +(-2.24337 + 1.29521i) q^{17} +(1.24479 - 4.17738i) q^{19} +(1.88243 + 1.08682i) q^{23} +(2.03180 - 4.56857i) q^{25} +(-1.29432 + 2.24183i) q^{29} +7.76610 q^{31} +(6.05586 + 9.32100i) q^{35} +2.75768i q^{37} +(-3.66243 - 6.34351i) q^{41} +(-1.55033 + 0.895083i) q^{43} +(1.47942 + 0.854141i) q^{47} -17.7109 q^{49} +(-6.89738 - 3.98220i) q^{53} +(-7.22823 + 4.69619i) q^{55} +(0.127300 + 0.220490i) q^{59} +(-1.66702 + 2.88737i) q^{61} +(5.96073 - 0.313624i) q^{65} +(-11.4356 - 6.60237i) q^{67} +(-3.85760 - 6.68156i) q^{71} +(3.90558 - 2.25489i) q^{73} -19.1628i q^{77} +(5.52715 + 9.57330i) q^{79} +3.04360i q^{83} +(2.62861 - 5.16157i) q^{85} +(-4.76212 + 8.24824i) q^{89} +(-6.63482 + 11.4918i) q^{91} +(2.75497 + 9.34934i) q^{95} +(9.72851 - 5.61676i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) $ 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times$.

$n$	$1711$	$1901$	$2737$	$3061$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.87507	+	1.21824i	−0.838558	+	0.544812i
$5$	−1.87507	+	1.21824i	−0.838558	+	0.544812i
$6$		0			0
$7$		−	4.97100i		−	1.87886i	−0.342736	−	0.939432i	$-0.611354\pi$
$7$		−	4.97100i		−	1.87886i	0.342736	−	0.939432i	$-0.388646\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.85491			1.16230			0.581149	−	0.813797i	$-0.302603\pi$
$11$	3.85491			1.16230			0.581149	+	0.813797i	$0.302603\pi$
$12$		0			0
$13$	−2.31178	−	1.33470i	−0.641171	−	0.370180i	0.143894	−	0.989593i	$-0.454037\pi$
$13$	−2.31178	−	1.33470i	−0.641171	−	0.370180i	−0.785066	+	0.619413i	$0.787371\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.24337	+	1.29521i	−0.544097	+	0.314135i	−0.746738	−	0.665118i	$-0.768381\pi$
$17$	−2.24337	+	1.29521i	−0.544097	+	0.314135i	0.202641	+	0.979253i	$0.435048\pi$
$18$		0			0
$19$	1.24479	−	4.17738i	0.285574	−	0.958357i
$19$	1.24479	−	4.17738i	0.285574	−	0.958357i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.88243	+	1.08682i	0.392514	+	0.226618i	0.683249	−	0.730186i	$-0.260566\pi$
$23$	1.88243	+	1.08682i	0.392514	+	0.226618i	−0.290735	+	0.956804i	$0.593900\pi$
$24$		0			0
$25$	2.03180	−	4.56857i	0.406359	−	0.913713i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.29432	+	2.24183i	−0.240350	+	0.416298i	−0.960814	−	0.277194i	$-0.910595\pi$
$29$	−1.29432	+	2.24183i	−0.240350	+	0.416298i	0.720464	+	0.693492i	$0.243929\pi$
$30$		0			0
$31$	7.76610			1.39483			0.697417	−	0.716666i	$-0.254333\pi$
$31$	7.76610			1.39483			0.697417	+	0.716666i	$0.254333\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.05586	+	9.32100i	1.02363	+	1.57554i
$36$		0			0
$37$			2.75768i			0.453359i	0.973969	+	0.226680i	$0.0727870\pi$
$37$			2.75768i			0.453359i	−0.973969	+	0.226680i	$0.927213\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.66243	−	6.34351i	−0.571975	−	0.990690i	−0.996363	−	0.0852097i	$-0.972844\pi$
$41$	−3.66243	−	6.34351i	−0.571975	−	0.990690i	0.424388	−	0.905481i	$-0.360489\pi$
$42$		0			0
$43$	−1.55033	+	0.895083i	−0.236423	+	0.136499i	−0.613532	−	0.789670i	$-0.710252\pi$
$43$	−1.55033	+	0.895083i	−0.236423	+	0.136499i	0.377109	+	0.926169i	$0.376918\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.47942	+	0.854141i	0.215795	+	0.124589i	0.604002	−	0.796983i	$-0.293572\pi$
$47$	1.47942	+	0.854141i	0.215795	+	0.124589i	−0.388207	+	0.921572i	$0.626905\pi$
$48$		0			0
$49$	−17.7109			−2.53013
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.89738	−	3.98220i	−0.947428	−	0.546998i	−0.0551469	−	0.998478i	$-0.517563\pi$
$53$	−6.89738	−	3.98220i	−0.947428	−	0.546998i	−0.892281	+	0.451480i	$0.850896\pi$
$54$		0			0
$55$	−7.22823	+	4.69619i	−0.974654	+	0.633234i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.127300	+	0.220490i	0.0165730	+	0.0287053i	0.874193	−	0.485579i	$-0.161391\pi$
$59$	0.127300	+	0.220490i	0.0165730	+	0.0287053i	−0.857620	+	0.514284i	$0.828058\pi$
$60$		0			0
$61$	−1.66702	+	2.88737i	−0.213441	+	0.369690i	−0.952789	−	0.303633i	$-0.901800\pi$
$61$	−1.66702	+	2.88737i	−0.213441	+	0.369690i	0.739349	+	0.673323i	$0.235134\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.96073	−	0.313624i	0.739338	−	0.0389002i
$66$		0			0
$67$	−11.4356	−	6.60237i	−1.39708	−	0.806607i	−0.402999	−	0.915201i	$-0.632032\pi$
$67$	−11.4356	−	6.60237i	−1.39708	−	0.806607i	−0.994086	+	0.108593i	$0.965365\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.85760	−	6.68156i	−0.457813	−	0.792955i	0.541032	−	0.841002i	$-0.318034\pi$
$71$	−3.85760	−	6.68156i	−0.457813	−	0.792955i	−0.998845	+	0.0480468i	$0.984700\pi$
$72$		0			0
$73$	3.90558	−	2.25489i	0.457114	−	0.263915i	−0.253716	−	0.967279i	$-0.581653\pi$
$73$	3.90558	−	2.25489i	0.457114	−	0.263915i	0.710830	+	0.703364i	$0.248320\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	19.1628i		−	2.18380i
$78$		0			0
$79$	5.52715	+	9.57330i	0.621852	+	1.07708i	0.989141	+	0.146973i	$0.0469530\pi$
$79$	5.52715	+	9.57330i	0.621852	+	1.07708i	−0.367288	+	0.930107i	$0.619714\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			3.04360i			0.334079i	0.985950	+	0.167040i	$0.0534207\pi$
$83$			3.04360i			0.334079i	−0.985950	+	0.167040i	$0.946579\pi$
$84$		0			0
$85$	2.62861	−	5.16157i	0.285113	−	0.559851i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.76212	+	8.24824i	−0.504784	+	0.874311i	0.495201	+	0.868779i	$0.335094\pi$
$89$	−4.76212	+	8.24824i	−0.504784	+	0.874311i	−0.999985	+	0.00553277i	$0.998239\pi$
$90$		0			0
$91$	−6.63482	+	11.4918i	−0.695518	+	1.20467i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.75497	+	9.34934i	0.282654	+	0.959222i
$96$		0			0
$97$	9.72851	−	5.61676i	0.987780	−	0.570295i	0.0831703	−	0.996535i	$-0.473495\pi$
$97$	9.72851	−	5.61676i	0.987780	−	0.570295i	0.904610	+	0.426240i	$0.140162\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.45345	+	9.44564i	−0.542638	+	0.939877i	0.456113	+	0.889922i	$0.349241\pi$
$101$	−5.45345	+	9.44564i	−0.542638	+	0.939877i	−0.998751	+	0.0499550i	$0.984092\pi$
$102$		0			0
$103$			11.4532i			1.12852i	0.825597	+	0.564260i	$0.190839\pi$
$103$			11.4532i			1.12852i	−0.825597	+	0.564260i	$0.809161\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	18.3401i		−	1.77300i	−0.462725	−	0.886502i	$-0.653128\pi$
$107$		−	18.3401i		−	1.77300i	0.462725	−	0.886502i	$-0.346872\pi$
$108$		0			0
$109$	−6.55467	−	11.3530i	−0.627824	−	1.08742i	−0.987988	−	0.154533i	$-0.950613\pi$
$109$	−6.55467	−	11.3530i	−0.627824	−	1.08742i	0.360164	−	0.932889i	$-0.382721\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	0.696954i		−	0.0655640i	−0.999463	−	0.0327820i	$-0.989563\pi$
$113$		−	0.696954i		−	0.0655640i	0.999463	−	0.0327820i	$-0.0104367\pi$
$114$		0			0
$115$	−4.85370	+	0.255377i	−0.452610	+	0.0238140i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.43850	+	11.1518i	0.590216	+	1.02228i
$120$		0			0
$121$	3.86029			0.350936
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.75583	+	11.0416i	0.157047	+	0.987591i
$126$		0			0
$127$	−11.9968	−	6.92636i	−1.06454	−	0.614615i	−0.137859	−	0.990452i	$-0.544022\pi$
$127$	−11.9968	−	6.92636i	−1.06454	−	0.614615i	−0.926686	+	0.375837i	$0.877355\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.11533	−	10.5921i	−0.534299	−	0.925433i	−0.999197	−	0.0400690i	$-0.987242\pi$
$131$	−6.11533	−	10.5921i	−0.534299	−	0.925433i	0.464898	−	0.885364i	$-0.346091\pi$
$132$		0			0
$133$	−20.7658	−	6.18785i	−1.80062	−	0.536554i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.96493	−	4.59855i	−0.680490	−	0.392881i	0.119550	−	0.992828i	$-0.461855\pi$
$137$	−7.96493	−	4.59855i	−0.680490	−	0.392881i	−0.800039	+	0.599947i	$0.795188\pi$
$138$		0			0
$139$	−3.22178	+	5.58028i	−0.273267	+	0.473313i	−0.969697	−	0.244312i	$-0.921438\pi$
$139$	−3.22178	+	5.58028i	−0.273267	+	0.473313i	0.696429	+	0.717626i	$0.254771\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.91168	−	5.14516i	−0.745232	−	0.430260i
$144$		0			0
$145$	−0.304135	−	5.78039i	−0.0252570	−	0.480036i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.5381	−	19.9846i	−0.945239	−	1.63720i	−0.755272	−	0.655411i	$-0.772495\pi$
$149$	−11.5381	−	19.9846i	−0.945239	−	1.63720i	−0.189966	−	0.981791i	$-0.560838\pi$
$150$		0			0
$151$	20.1613			1.64071			0.820353	−	0.571858i	$-0.193777\pi$
$151$	20.1613			1.64071			0.820353	+	0.571858i	$0.193777\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−14.5620	+	9.46096i	−1.16965	+	0.759922i
$156$		0			0
$157$	−10.2803	+	5.93532i	−0.820456	+	0.473690i	−0.850574	−	0.525856i	$-0.823745\pi$
$157$	−10.2803	+	5.93532i	−0.820456	+	0.473690i	0.0301179	+	0.999546i	$0.490412\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.40259	−	9.35757i	0.425784	−	0.737480i
$162$		0			0
$163$		−	13.1763i		−	1.03205i	−0.856575	−	0.516023i	$-0.827412\pi$
$163$		−	13.1763i		−	1.03205i	0.856575	−	0.516023i	$-0.172588\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.17459	−	1.83285i	−0.245657	−	0.141830i	0.372117	−	0.928186i	$-0.378632\pi$
$167$	−3.17459	−	1.83285i	−0.245657	−	0.141830i	−0.617774	+	0.786356i	$0.711965\pi$
$168$		0			0
$169$	−2.93713	−	5.08726i	−0.225933	−	0.391327i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.0739334	+	0.0426855i	−0.00562105	+	0.00324532i	−0.502808	−	0.864398i	$-0.667700\pi$
$173$	−0.0739334	+	0.0426855i	−0.00562105	+	0.00324532i	0.497187	+	0.867644i	$0.334366\pi$
$174$		0			0
$175$	−22.7104	−	10.1001i	−1.71674	−	0.763493i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.2256			−1.21276			−0.606380	−	0.795175i	$-0.707379\pi$
$179$	−16.2256			−1.21276			−0.606380	+	0.795175i	$0.707379\pi$
$180$		0			0
$181$	−10.1549	+	17.5888i	−0.754808	+	1.30737i	0.190662	+	0.981656i	$0.438937\pi$
$181$	−10.1549	+	17.5888i	−0.754808	+	1.30737i	−0.945470	+	0.325710i	$0.894397\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.35950	−	5.17084i	−0.246996	−	0.380168i
$186$		0			0
$187$	−8.64798	+	4.99291i	−0.632403	+	0.365118i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	21.9157			1.58576			0.792881	−	0.609377i	$-0.208580\pi$
$191$	21.9157			1.58576			0.792881	+	0.609377i	$0.208580\pi$
$192$		0			0
$193$	4.35575	−	2.51480i	0.313534	−	0.181019i	−0.334973	−	0.942228i	$-0.608727\pi$
$193$	4.35575	−	2.51480i	0.313534	−	0.181019i	0.648507	+	0.761209i	$0.275394\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			19.1189i			1.36217i	0.732205	+	0.681084i	$0.238491\pi$
$197$			19.1189i			1.36217i	−0.732205	+	0.681084i	$0.761509\pi$
$198$		0			0
$199$	9.04425	−	15.6651i	0.641130	−	1.11047i	−0.344051	−	0.938951i	$-0.611799\pi$
$199$	9.04425	−	15.6651i	0.641130	−	1.11047i	0.985181	−	0.171518i	$-0.0548672\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	11.1442	+	6.43409i	0.782167	+	0.451584i
$204$		0			0
$205$	14.5952	+	7.43284i	1.01937	+	0.519132i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.79854	−	16.1034i	0.331922	−	1.11390i
$210$		0			0
$211$	−8.03757	−	13.9215i	−0.553329	−	0.958394i	−0.998031	−	0.0627157i	$-0.980024\pi$
$211$	−8.03757	−	13.9215i	−0.553329	−	0.958394i	0.444702	−	0.895678i	$-0.353309\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.81656	−	3.56702i	0.123888	−	0.243268i
$216$		0			0
$217$		−	38.6053i		−	2.62070i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.91489			0.465146
$222$		0			0
$223$	15.0002	−	8.66036i	1.00449	−	0.579941i	0.0949140	−	0.995485i	$-0.469742\pi$
$223$	15.0002	−	8.66036i	1.00449	−	0.579941i	0.909573	+	0.415545i	$0.136409\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	23.7579i		−	1.57687i	−0.615120	−	0.788434i	$-0.710892\pi$
$227$		−	23.7579i		−	1.57687i	0.615120	−	0.788434i	$-0.289108\pi$
$228$		0			0
$229$	−0.732245			−0.0483881			−0.0241941	−	0.999707i	$-0.507702\pi$
$229$	−0.732245			−0.0483881			−0.0241941	+	0.999707i	$0.507702\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.2328	+	9.94933i	−1.12896	+	0.651803i	−0.943672	−	0.330883i	$-0.892654\pi$
$233$	−17.2328	+	9.94933i	−1.12896	+	0.651803i	−0.185283	+	0.982685i	$0.559320\pi$
$234$		0			0
$235$	−3.81456	+	0.200703i	−0.248834	+	0.0130924i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−28.9063			−1.86979			−0.934897	−	0.354919i	$-0.884508\pi$
$239$	−28.9063			−1.86979			−0.934897	+	0.354919i	$0.884508\pi$
$240$		0			0
$241$	11.8979	−	20.6077i	0.766409	−	1.32746i	−0.173090	−	0.984906i	$-0.555375\pi$
$241$	11.8979	−	20.6077i	0.766409	−	1.32746i	0.939499	−	0.342553i	$-0.111292\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	33.2092	−	21.5761i	2.12166	−	1.37844i
$246$		0			0
$247$	−8.45324	+	7.99574i	−0.537867	+	0.508757i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.44694	+	5.97028i	−0.217569	+	0.376840i	−0.954064	−	0.299602i	$-0.903146\pi$
$251$	−3.44694	+	5.97028i	−0.217569	+	0.376840i	0.736495	+	0.676443i	$0.236479\pi$
$252$		0			0
$253$	7.25659	+	4.18959i	0.456218	+	0.263397i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.9617	+	6.32874i	0.683772	+	0.394776i	0.801275	−	0.598296i	$-0.204155\pi$
$257$	10.9617	+	6.32874i	0.683772	+	0.394776i	−0.117502	+	0.993073i	$0.537489\pi$
$258$		0			0
$259$	13.7084			0.851800
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−21.6062	+	12.4743i	−1.33229	+	0.769200i	−0.985651	−	0.168797i	$-0.946012\pi$
$263$	−21.6062	+	12.4743i	−1.33229	+	0.769200i	−0.346643	+	0.937997i	$0.612678\pi$
$264$		0			0
$265$	17.7844	−	0.935723i	1.09248	−	0.0574810i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.54155	+	16.5265i	0.581759	+	1.00764i	0.995271	+	0.0971371i	$0.0309685\pi$
$269$	9.54155	+	16.5265i	0.581759	+	1.00764i	−0.413512	+	0.910499i	$0.635698\pi$
$270$		0			0
$271$	−1.48490	−	2.57192i	−0.0902012	−	0.156233i	0.817395	−	0.576078i	$-0.195418\pi$
$271$	−1.48490	−	2.57192i	−0.0902012	−	0.156233i	−0.907596	+	0.419845i	$0.862084\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.83238	−	17.6114i	0.472310	−	1.06201i
$276$		0			0
$277$			5.51535i			0.331385i	0.986177	+	0.165693i	$0.0529860\pi$
$277$			5.51535i			0.331385i	−0.986177	+	0.165693i	$0.947014\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.4800	+	21.6159i	−0.744493	+	1.28950i	0.205939	+	0.978565i	$0.433975\pi$
$281$	−12.4800	+	21.6159i	−0.744493	+	1.28950i	−0.950431	+	0.310934i	$0.899358\pi$
$282$		0			0
$283$	−11.6526	+	6.72761i	−0.692673	+	0.399915i	−0.804613	−	0.593800i	$-0.797627\pi$
$283$	−11.6526	+	6.72761i	−0.692673	+	0.399915i	0.111939	+	0.993715i	$0.464294\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−31.5336	+	18.2060i	−1.86137	+	1.07466i
$288$		0			0
$289$	−5.14486	+	8.91116i	−0.302639	+	0.524186i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	23.7710i		−	1.38871i	−0.719630	−	0.694357i	$-0.755689\pi$
$293$		−	23.7710i		−	1.38871i	0.719630	−	0.694357i	$-0.244311\pi$
$294$		0			0
$295$	−0.507305	−	0.258353i	−0.0295364	−	0.0150419i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.90117	−	5.02497i	−0.167779	−	0.290602i
$300$		0			0
$301$	4.44946	+	7.70670i	0.256463	+	0.444207i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.391711	−	7.44486i	−0.0224293	−	0.426291i
$306$		0			0
$307$	−5.84122	+	3.37243i	−0.333376	+	0.192475i	−0.657339	−	0.753595i	$-0.728318\pi$
$307$	−5.84122	+	3.37243i	−0.333376	+	0.192475i	0.323963	+	0.946070i	$0.394985\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.6908			0.662924			0.331462	−	0.943468i	$-0.392458\pi$
$311$	11.6908			0.662924			0.331462	+	0.943468i	$0.392458\pi$
$312$		0			0
$313$	−15.2101	−	8.78157i	−0.859727	−	0.496364i	0.00419387	−	0.999991i	$-0.498665\pi$
$313$	−15.2101	−	8.78157i	−0.859727	−	0.496364i	−0.863921	+	0.503628i	$0.831998\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	28.5399	+	16.4775i	1.60296	+	0.925469i	0.990891	+	0.134663i	$0.0429952\pi$
$317$	28.5399	+	16.4775i	1.60296	+	0.925469i	0.612067	+	0.790806i	$0.290338\pi$
$318$		0			0
$319$	−4.98949	+	8.64206i	−0.279358	+	0.483862i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.61807	+	10.9837i	0.145673	+	0.611148i
$324$		0			0
$325$	−10.7947	+	7.84966i	−0.598785	+	0.435421i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.24594	−	7.35418i	0.234086	−	0.405449i
$330$		0			0
$331$	−4.54726			−0.249940			−0.124970	−	0.992161i	$-0.539883\pi$
$331$	−4.54726			−0.249940			−0.124970	+	0.992161i	$0.539883\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	29.4859	−	1.55140i	1.61099	−	0.0847619i
$336$		0			0
$337$	19.0180	−	10.9801i	1.03598	−	0.598122i	0.117286	−	0.993098i	$-0.462581\pi$
$337$	19.0180	−	10.9801i	1.03598	−	0.598122i	0.918691	+	0.394976i	$0.129247\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	29.9376			1.62121
$342$		0			0
$343$			53.2439i			2.87490i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.28915	−	3.63104i	0.337619	−	0.194925i	−0.321599	−	0.946876i	$-0.604220\pi$
$347$	6.28915	−	3.63104i	0.337619	−	0.194925i	0.659219	+	0.751951i	$0.270887\pi$
$348$		0			0
$349$	16.0910			0.861329			0.430665	−	0.902512i	$-0.358279\pi$
$349$	16.0910			0.861329			0.430665	+	0.902512i	$0.358279\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	33.4331i		−	1.77947i	−0.456481	−	0.889733i	$-0.650890\pi$
$353$		−	33.4331i		−	1.77947i	0.456481	−	0.889733i	$-0.349110\pi$
$354$		0			0
$355$	15.3730	+	7.82894i	0.815914	+	0.415517i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.97814	−	17.2826i	−0.526626	−	0.912143i	−0.999519	−	0.0310231i	$-0.990123\pi$
$359$	−9.97814	−	17.2826i	−0.526626	−	0.912143i	0.472893	−	0.881120i	$-0.343210\pi$
$360$		0			0
$361$	−15.9010	−	10.3999i	−0.836895	−	0.547363i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.57626	+	8.98600i	−0.239532	+	0.470349i
$366$		0			0
$367$	6.60735	+	3.81476i	0.344901	+	0.199129i	0.662437	−	0.749117i	$-0.269522\pi$
$367$	6.60735	+	3.81476i	0.344901	+	0.199129i	−0.317536	+	0.948246i	$0.602856\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−19.7956	+	34.2869i	−1.02773	+	1.78009i
$372$		0			0
$373$		−	2.22095i		−	0.114996i	−0.998346	−	0.0574982i	$-0.981688\pi$
$373$		−	2.22095i		−	0.114996i	0.998346	−	0.0574982i	$-0.0183123\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.98437	−	3.45508i	0.308211	−	0.177946i
$378$		0			0
$379$	−6.92717			−0.355825			−0.177912	−	0.984046i	$-0.556934\pi$
$379$	−6.92717			−0.355825			−0.177912	+	0.984046i	$0.556934\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	16.6386	−	9.60631i	0.850193	−	0.490859i	−0.0105227	−	0.999945i	$-0.503350\pi$
$383$	16.6386	−	9.60631i	0.850193	−	0.490859i	0.860716	+	0.509085i	$0.170016\pi$
$384$		0			0
$385$	23.3448	+	35.9316i	1.18976	+	1.83124i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.4261	+	23.2547i	−0.680730	+	1.17906i	0.294029	+	0.955797i	$0.405004\pi$
$389$	−13.4261	+	23.2547i	−0.680730	+	1.17906i	−0.974758	+	0.223262i	$0.928329\pi$
$390$		0			0
$391$	−5.63065			−0.284754
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−22.0263	−	11.2173i	−1.10827	−	0.564401i
$396$		0			0
$397$	−6.42312	+	3.70839i	−0.322367	+	0.186119i	−0.652447	−	0.757834i	$-0.726258\pi$
$397$	−6.42312	+	3.70839i	−0.322367	+	0.186119i	0.330080	+	0.943953i	$0.392924\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.66556	−	4.61689i	−0.133112	−	0.230557i	0.791763	−	0.610829i	$-0.209164\pi$
$401$	−2.66556	−	4.61689i	−0.133112	−	0.230557i	−0.924875	+	0.380272i	$0.875830\pi$
$402$		0			0
$403$	−17.9535	−	10.3655i	−0.894327	−	0.516340i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			10.6306i			0.526938i
$408$		0			0
$409$	−5.70960	+	9.88933i	−0.282322	+	0.488996i	−0.971956	−	0.235162i	$-0.924438\pi$
$409$	−5.70960	+	9.88933i	−0.282322	+	0.488996i	0.689634	+	0.724158i	$0.257771\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.09605	−	0.632807i	0.0539333	−	0.0311384i
$414$		0			0
$415$	−3.70783	−	5.70698i	−0.182010	−	0.280145i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.2311			−0.597529			−0.298765	−	0.954327i	$-0.596575\pi$
$419$	−12.2311			−0.597529			−0.298765	+	0.954327i	$0.596575\pi$
$420$		0			0
$421$	6.63359	+	11.4897i	0.323301	+	0.559974i	0.981167	−	0.193161i	$-0.0618739\pi$
$421$	6.63359	+	11.4897i	0.323301	+	0.559974i	−0.657866	+	0.753135i	$0.728541\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.35919	+	12.8806i	0.0659302	+	0.624801i
$426$		0			0
$427$	14.3531	+	8.28678i	0.694597	+	0.401026i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.19094	−	14.1871i	0.394544	−	0.683370i	−0.598499	−	0.801124i	$-0.704236\pi$
$431$	8.19094	−	14.1871i	0.394544	−	0.683370i	0.993043	+	0.117754i	$0.0375693\pi$
$432$		0			0
$433$	13.0054	+	7.50864i	0.624997	+	0.360842i	0.778812	−	0.627257i	$-0.215823\pi$
$433$	13.0054	+	7.50864i	0.624997	+	0.360842i	−0.153815	+	0.988100i	$0.549156\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.88329	−	6.51076i	0.329272	−	0.311452i
$438$		0			0
$439$	7.68192	+	13.3055i	0.366638	+	0.635035i	0.989038	−	0.147664i	$-0.0471755\pi$
$439$	7.68192	+	13.3055i	0.366638	+	0.635035i	−0.622400	+	0.782700i	$0.713842\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.9890	−	12.1180i	−0.997219	−	0.575745i	−0.0897946	−	0.995960i	$-0.528621\pi$
$443$	−20.9890	−	12.1180i	−0.997219	−	0.575745i	−0.907424	+	0.420216i	$0.861954\pi$
$444$		0			0
$445$	−1.11898	−	21.2674i	−0.0530450	−	1.00817i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	16.8854			0.796873			0.398436	−	0.917196i	$-0.369553\pi$
$449$	16.8854			0.796873			0.398436	+	0.917196i	$0.369553\pi$
$450$		0			0
$451$	−14.1183	−	24.4536i	−0.664805	−	1.15148i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.55902	−	29.6308i	−0.0730882	−	1.38912i
$456$		0			0
$457$			29.1914i			1.36551i	0.730645	+	0.682757i	$0.239219\pi$
$457$			29.1914i			1.36551i	−0.730645	+	0.682757i	$0.760781\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.87254	+	3.24333i	0.0872127	+	0.151057i	0.906332	−	0.422566i	$-0.138871\pi$
$461$	1.87254	+	3.24333i	0.0872127	+	0.151057i	−0.819119	+	0.573623i	$0.805537\pi$
$462$		0			0
$463$		−	21.4714i		−	0.997860i	−0.866642	−	0.498930i	$-0.833727\pi$
$463$		−	21.4714i		−	0.997860i	0.866642	−	0.498930i	$-0.166273\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			29.1079i			1.34695i	0.739209	+	0.673476i	$0.235200\pi$
$467$			29.1079i			1.34695i	−0.739209	+	0.673476i	$0.764800\pi$
$468$		0			0
$469$	−32.8204	+	56.8466i	−1.51550	+	2.62493i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.97637	+	3.45046i	−0.274794	+	0.158652i
$474$		0			0
$475$	−16.5555	−	14.1745i	−0.759618	−	0.650370i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.258348	−	0.447471i	0.0118042	−	0.0204455i	−0.860063	−	0.510188i	$-0.829576\pi$
$479$	0.258348	−	0.447471i	0.0118042	−	0.0204455i	0.871867	+	0.489742i	$0.162909\pi$
$480$		0			0
$481$	3.68068	−	6.37513i	0.167825	−	0.290681i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.3991	+	22.3835i	−0.517607	+	1.01638i
$486$		0			0
$487$			10.6668i			0.483358i	0.970356	+	0.241679i	$0.0776981\pi$
$487$			10.6668i			0.483358i	−0.970356	+	0.241679i	$0.922302\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.0852	+	20.9322i	0.545398	+	0.944656i	0.998582	+	0.0532395i	$0.0169547\pi$
$491$	12.0852	+	20.9322i	0.545398	+	0.944656i	−0.453184	+	0.891417i	$0.649712\pi$
$492$		0			0
$493$		−	6.70569i		−	0.302009i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−33.2141	+	19.1761i	−1.48985	+	0.860168i
$498$		0			0
$499$	−2.38934	−	4.13846i	−0.106962	−	0.185263i	0.807576	−	0.589763i	$-0.200779\pi$
$499$	−2.38934	−	4.13846i	−0.106962	−	0.185263i	−0.914538	+	0.404500i	$0.867446\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	15.4577	+	8.92453i	0.689227	+	0.397925i	0.803322	−	0.595545i	$-0.203064\pi$
$503$	15.4577	+	8.92453i	0.689227	+	0.397925i	−0.114096	+	0.993470i	$0.536397\pi$
$504$		0			0
$505$	−1.28143	−	24.3549i	−0.0570229	−	1.08378i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.57492	+	6.19194i	−0.158455	+	0.274453i	−0.934312	−	0.356457i	$-0.883985\pi$
$509$	−3.57492	+	6.19194i	−0.158455	+	0.274453i	0.775856	+	0.630909i	$0.217318\pi$
$510$		0			0
$511$	−11.2091	−	19.4147i	−0.495860	−	0.858854i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−13.9528	−	21.4757i	−0.614832	−	0.946330i
$516$		0			0
$517$	5.70301	+	3.29263i	0.250818	+	0.144810i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	19.7280			0.864301			0.432151	−	0.901801i	$-0.357755\pi$
$521$	19.7280			0.864301			0.432151	+	0.901801i	$0.357755\pi$
$522$		0			0
$523$	31.4070	+	18.1328i	1.37333	+	0.792894i	0.991346	−	0.131274i	$-0.0419069\pi$
$523$	31.4070	+	18.1328i	1.37333	+	0.792894i	0.381986	+	0.924168i	$0.375240\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−17.4222	+	10.0587i	−0.758925	+	0.438166i
$528$		0			0
$529$	−9.13764	−	15.8269i	−0.397289	−	0.688124i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			19.5530i			0.846936i
$534$		0			0
$535$	22.3426	+	34.3890i	0.965954	+	1.48677i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−68.2738			−2.94076
$540$		0			0
$541$	11.4419	−	19.8180i	0.491927	−	0.852043i	−0.508029	−	0.861340i	$-0.669626\pi$
$541$	11.4419	−	19.8180i	0.491927	−	0.852043i	0.999957	+	0.00929658i	$0.00295924\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	26.1212	+	13.3026i	1.11891	+	0.569821i
$546$		0			0
$547$	−11.0134	−	6.35861i	−0.470901	−	0.271875i	0.245716	−	0.969342i	$-0.420977\pi$
$547$	−11.0134	−	6.35861i	−0.470901	−	0.271875i	−0.716617	+	0.697467i	$0.754310\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.75383	+	8.19749i	0.330324	+	0.349225i
$552$		0			0
$553$	47.5889	−	27.4755i	2.02369	−	1.16838i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.3648	+	11.1803i	0.820511	+	0.473722i	0.850593	−	0.525825i	$-0.176243\pi$
$557$	19.3648	+	11.1803i	0.820511	+	0.473722i	−0.0300814	+	0.999547i	$0.509577\pi$
$558$		0			0
$559$	4.77869			0.202117
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	10.6447i		−	0.448619i	−0.974518	−	0.224310i	$-0.927987\pi$
$563$		−	10.6447i		−	0.448619i	0.974518	−	0.224310i	$-0.0720127\pi$
$564$		0			0
$565$	0.849056	+	1.30684i	0.0357201	+	0.0549792i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.13498			−0.131425			−0.0657126	−	0.997839i	$-0.520932\pi$
$569$	−3.13498			−0.131425			−0.0657126	+	0.997839i	$0.520932\pi$
$570$		0			0
$571$	1.29260			0.0540938			0.0270469	−	0.999634i	$-0.491390\pi$
$571$	1.29260			0.0540938			0.0270469	+	0.999634i	$0.491390\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.78993	−	6.39181i	0.366565	−	0.266557i
$576$		0			0
$577$			8.18544i			0.340764i	0.985378	+	0.170382i	$0.0545002\pi$
$577$			8.18544i			0.340764i	−0.985378	+	0.170382i	$0.945500\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.1298			0.627689
$582$		0			0
$583$	−26.5887	−	15.3510i	−1.10119	−	0.635774i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.7359	−	9.08512i	0.649490	−	0.374983i	−0.138771	−	0.990325i	$-0.544315\pi$
$587$	15.7359	−	9.08512i	0.649490	−	0.374983i	0.788261	+	0.615341i	$0.210982\pi$
$588$		0			0
$589$	9.66715	−	32.4420i	0.398328	−	1.33675i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.69621	−	4.44341i	−0.316046	−	0.182469i	0.333583	−	0.942721i	$-0.391742\pi$
$593$	−7.69621	−	4.44341i	−0.316046	−	0.182469i	−0.649629	+	0.760252i	$0.725076\pi$
$594$		0			0
$595$	−25.6582	−	13.0668i	−1.05188	−	0.535688i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.18264	−	3.78044i	0.0891801	−	0.154465i	−0.817985	−	0.575240i	$-0.804909\pi$
$599$	2.18264	−	3.78044i	0.0891801	−	0.154465i	0.907165	+	0.420775i	$0.138242\pi$
$600$		0			0
$601$	−4.25303			−0.173485			−0.0867424	−	0.996231i	$-0.527646\pi$
$601$	−4.25303			−0.173485			−0.0867424	+	0.996231i	$0.527646\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.23833	+	4.70275i	−0.294280	+	0.191194i
$606$		0			0
$607$			23.5995i			0.957876i	0.877849	+	0.478938i	$0.158978\pi$
$607$			23.5995i			0.957876i	−0.877849	+	0.478938i	$0.841022\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.28005	−	3.94917i	−0.0922410	−	0.159766i
$612$		0			0
$613$	17.6090	−	10.1665i	0.711220	−	0.410623i	−0.100293	−	0.994958i	$-0.531978\pi$
$613$	17.6090	−	10.1665i	0.711220	−	0.410623i	0.811512	+	0.584335i	$0.198645\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.0932	+	15.6422i	1.09073	+	0.629733i	0.933771	−	0.357872i	$-0.116498\pi$
$617$	27.0932	+	15.6422i	1.09073	+	0.629733i	0.156959	+	0.987605i	$0.449831\pi$
$618$		0			0
$619$	−25.7635			−1.03552			−0.517761	−	0.855525i	$-0.673234\pi$
$619$	−25.7635			−1.03552			−0.517761	+	0.855525i	$0.673234\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	41.0020	+	23.6725i	1.64271	+	0.948420i
$624$		0			0
$625$	−16.7436	−	18.5648i	−0.669744	−	0.742592i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.57177	−	6.18649i	−0.142416	−	0.246671i
$630$		0			0
$631$	−10.6458	+	18.4391i	−0.423804	+	0.734050i	−0.996308	−	0.0858517i	$-0.972639\pi$
$631$	−10.6458	+	18.4391i	−0.423804	+	0.734050i	0.572504	+	0.819902i	$0.305972\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	30.9328	−	1.62753i	1.22753	−	0.0645865i
$636$		0			0
$637$	40.9436	+	23.6388i	1.62224	+	0.936603i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.5525	−	28.6698i	−0.653785	−	1.13239i	−0.982197	−	0.187854i	$-0.939847\pi$
$641$	−16.5525	−	28.6698i	−0.653785	−	1.13239i	0.328412	−	0.944535i	$-0.393487\pi$
$642$		0			0
$643$	26.1024	−	15.0702i	1.02938	−	0.594311i	0.112570	−	0.993644i	$-0.464092\pi$
$643$	26.1024	−	15.0702i	1.02938	−	0.594311i	0.916806	+	0.399333i	$0.130758\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			10.5273i			0.413870i	0.978355	+	0.206935i	$0.0663489\pi$
$647$			10.5273i			0.413870i	−0.978355	+	0.206935i	$0.933651\pi$
$648$		0			0
$649$	0.490728	+	0.849966i	0.0192628	+	0.0333641i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	14.9511i		−	0.585081i	−0.956253	−	0.292540i	$-0.905499\pi$
$653$		−	14.9511i		−	0.585081i	0.956253	−	0.292540i	$-0.0945006\pi$
$654$		0			0
$655$	24.3703	+	12.4110i	0.952228	+	0.484937i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.6909	−	28.9094i	0.650184	−	1.12615i	−0.332894	−	0.942964i	$-0.608025\pi$
$659$	16.6909	−	28.9094i	0.650184	−	1.12615i	0.983078	−	0.183187i	$-0.0586414\pi$
$660$		0			0
$661$	−12.7433	+	22.0720i	−0.495655	+	0.858501i	−0.999987	−	0.00500935i	$-0.998405\pi$
$661$	−12.7433	+	22.0720i	−0.495655	+	0.858501i	0.504332	+	0.863510i	$0.331739\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	46.4756	−	13.6950i	1.80225	−	0.531069i
$666$		0			0
$667$	−4.87295	+	2.81340i	−0.188681	+	0.108935i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−6.42622	+	11.1305i	−0.248081	+	0.429690i
$672$		0			0
$673$			9.87133i			0.380512i	0.981735	+	0.190256i	$0.0609318\pi$
$673$			9.87133i			0.380512i	−0.981735	+	0.190256i	$0.939068\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			11.8367i			0.454922i	0.973787	+	0.227461i	$0.0730424\pi$
$677$			11.8367i			0.454922i	−0.973787	+	0.227461i	$0.926958\pi$
$678$		0			0
$679$	−27.9209	−	48.3605i	−1.07151	−	1.85590i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			29.6716i			1.13535i	0.823253	+	0.567675i	$0.192157\pi$
$683$			29.6716i			1.13535i	−0.823253	+	0.567675i	$0.807843\pi$
$684$		0			0
$685$	20.5369	−	1.08055i	0.784676	−	0.0412857i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.6301	+	18.4119i	0.404976	+	0.701438i
$690$		0			0
$691$	9.73437			0.370313			0.185156	−	0.982709i	$-0.440721\pi$
$691$	9.73437			0.370313			0.185156	+	0.982709i	$0.440721\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.757040	−	14.3883i	−0.0287162	−	0.545780i
$696$		0			0
$697$	16.4324	+	9.48723i	0.622420	+	0.359355i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.3345	−	17.8999i	−0.390329	−	0.676070i	0.602164	−	0.798373i	$-0.294305\pi$
$701$	−10.3345	−	17.8999i	−0.390329	−	0.676070i	−0.992493	+	0.122303i	$0.960972\pi$
$702$		0			0
$703$	11.5199	+	3.43272i	0.434480	+	0.129468i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	46.9543	+	27.1091i	1.76590	+	1.01954i
$708$		0			0
$709$	10.0066	−	17.3319i	0.375806	−	0.650915i	−0.614641	−	0.788807i	$-0.710699\pi$
$709$	10.0066	−	17.3319i	0.375806	−	0.650915i	0.990447	+	0.137892i	$0.0440326\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.6191	+	8.44037i	0.547491	+	0.316094i
$714$		0			0
$715$	22.9781	−	1.20899i	0.859331	−	0.0452136i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.2807	−	19.5387i	−0.420698	−	0.728671i	0.575309	−	0.817936i	$-0.304882\pi$
$719$	−11.2807	−	19.5387i	−0.420698	−	0.728671i	−0.996008	+	0.0892647i	$0.971548\pi$
$720$		0			0
$721$	56.9341			2.12034
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.61217	+	10.4682i	0.282709	+	0.388777i
$726$		0			0
$727$	4.81051	−	2.77735i	0.178412	−	0.103006i	−0.408134	−	0.912922i	$-0.633821\pi$
$727$	4.81051	−	2.77735i	0.178412	−	0.103006i	0.586546	+	0.809916i	$0.300487\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.31864	−	4.01601i	0.0857581	−	0.148537i
$732$		0			0
$733$			45.3490i			1.67500i	0.546436	+	0.837501i	$0.315984\pi$
$733$			45.3490i			1.67500i	−0.546436	+	0.837501i	$0.684016\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−44.0833	−	25.4515i	−1.62383	−	0.937518i
$738$		0			0
$739$	−9.01081	−	15.6072i	−0.331468	−	0.574119i	0.651332	−	0.758793i	$-0.274211\pi$
$739$	−9.01081	−	15.6072i	−0.331468	−	0.574119i	−0.982800	+	0.184674i	$0.940877\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	36.9333	−	21.3235i	1.35495	−	0.782282i	0.366013	−	0.930610i	$-0.380723\pi$
$743$	36.9333	−	21.3235i	1.35495	−	0.782282i	0.988938	+	0.148328i	$0.0473892\pi$
$744$		0			0
$745$	45.9808	+	23.4164i	1.68461	+	0.857911i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−91.1687			−3.33123
$750$		0			0
$751$	−2.45338	+	4.24938i	−0.0895252	+	0.155062i	−0.907311	−	0.420461i	$-0.861868\pi$
$751$	−2.45338	+	4.24938i	−0.0895252	+	0.155062i	0.817785	+	0.575523i	$0.195202\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−37.8040	+	24.5613i	−1.37583	+	0.893876i
$756$		0			0
$757$	24.2213	−	13.9842i	0.880339	−	0.508264i	0.00956884	−	0.999954i	$-0.496954\pi$
$757$	24.2213	−	13.9842i	0.880339	−	0.508264i	0.870770	+	0.491690i	$0.163621\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.7443			0.425731			0.212866	−	0.977081i	$-0.431720\pi$
$761$	11.7443			0.425731			0.212866	+	0.977081i	$0.431720\pi$
$762$		0			0
$763$	−56.4359	+	32.5833i	−2.04312	+	1.17959i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	0.679630i		−	0.0245400i
$768$		0			0
$769$	8.22905	−	14.2531i	0.296747	−	0.513981i	−0.678643	−	0.734469i	$-0.737432\pi$
$769$	8.22905	−	14.2531i	0.296747	−	0.513981i	0.975390	+	0.220488i	$0.0707648\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−39.7578	−	22.9542i	−1.42999	−	0.825605i	−0.432871	−	0.901456i	$-0.642499\pi$
$773$	−39.7578	−	22.9542i	−1.42999	−	0.825605i	−0.997119	+	0.0758511i	$0.975833\pi$
$774$		0			0
$775$	15.7791	−	35.4800i	0.566803	−	1.27448i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−31.0582	+	7.40303i	−1.11278	+	0.265241i
$780$		0			0
$781$	−14.8707	−	25.7568i	−0.532115	−	0.921650i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.0456	−	23.6530i	0.429927	−	0.844211i
$786$		0			0
$787$			28.1763i			1.00438i	0.864758	+	0.502189i	$0.167472\pi$
$787$			28.1763i			1.00438i	−0.864758	+	0.502189i	$0.832528\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.46456			−0.123186
$792$		0			0
$793$	7.70757	−	4.44997i	0.273704	−	0.158023i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			1.18117i			0.0418394i	0.999781	+	0.0209197i	$0.00665943\pi$
$797$			1.18117i			0.0418394i	−0.999781	+	0.0209197i	$0.993341\pi$
$798$		0			0
$799$	−4.42517			−0.156551
$800$		0			0
$801$		0			0
$802$		0			0
$803$	15.0556	−	8.69238i	0.531302	−	0.306747i
$804$		0			0
$805$	1.26948	+	24.1278i	0.0447433	+	0.850392i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	4.72471			0.166112			0.0830561	−	0.996545i	$-0.473532\pi$
$809$	4.72471			0.166112			0.0830561	+	0.996545i	$0.473532\pi$
$810$		0			0
$811$	18.7800	−	32.5280i	0.659456	−	1.14221i	−0.321301	−	0.946977i	$-0.604120\pi$
$811$	18.7800	−	32.5280i	0.659456	−	1.14221i	0.980757	−	0.195234i	$-0.0625465\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.0518	+	24.7065i	0.562272	+	0.865431i
$816$		0			0
$817$	1.80927	+	7.59050i	0.0632984	+	0.265558i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	17.3453	−	30.0430i	0.605357	−	1.04851i	−0.386638	−	0.922231i	$-0.626364\pi$
$821$	17.3453	−	30.0430i	0.605357	−	1.04851i	0.991995	−	0.126277i	$-0.0403028\pi$
$822$		0			0
$823$	2.19067	+	1.26478i	0.0763620	+	0.0440876i	0.537695	−	0.843140i	$-0.319295\pi$
$823$	2.19067	+	1.26478i	0.0763620	+	0.0440876i	−0.461333	+	0.887227i	$0.652629\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−18.0721	−	10.4339i	−0.628428	−	0.362823i	0.151715	−	0.988424i	$-0.451520\pi$
$827$	−18.0721	−	10.4339i	−0.628428	−	0.362823i	−0.780143	+	0.625601i	$0.784854\pi$
$828$		0			0
$829$	−26.1170			−0.907081			−0.453540	−	0.891236i	$-0.649839\pi$
$829$	−26.1170			−0.907081			−0.453540	+	0.891236i	$0.649839\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	39.7321	−	22.9393i	1.37664	−	0.794801i
$834$		0			0
$835$	8.18544	−	0.430676i	0.283269	−	0.0149042i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.69792	+	9.86908i	0.196714	+	0.340719i	0.947461	−	0.319871i	$-0.103640\pi$
$839$	5.69792	+	9.86908i	0.196714	+	0.340719i	−0.750747	+	0.660590i	$0.770306\pi$
$840$		0			0
$841$	11.1495	+	19.3114i	0.384464	+	0.665911i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	11.7048	+	5.96086i	0.402658	+	0.205060i
$846$		0			0
$847$		−	19.1895i		−	0.659360i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.99710	+	5.19113i	−0.102739	+	0.177950i
$852$		0			0
$853$	5.39521	−	3.11493i	0.184728	−	0.106653i	−0.404784	−	0.914412i	$-0.632653\pi$
$853$	5.39521	−	3.11493i	0.184728	−	0.106653i	0.589512	+	0.807759i	$0.299320\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	43.9606	−	25.3807i	1.50166	−	0.866987i	0.501667	−	0.865061i	$-0.332720\pi$
$857$	43.9606	−	25.3807i	1.50166	−	0.866987i	0.999998	−	0.00192568i	$-0.000612963\pi$
$858$		0			0
$859$	−4.07445	+	7.05715i	−0.139018	+	0.240787i	−0.927125	−	0.374751i	$-0.877728\pi$
$859$	−4.07445	+	7.05715i	−0.139018	+	0.240787i	0.788107	+	0.615538i	$0.211061\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1.20591i			0.0410498i	0.999789	+	0.0205249i	$0.00653373\pi$
$863$			1.20591i			0.0410498i	−0.999789	+	0.0205249i	$0.993466\pi$
$864$		0			0
$865$	0.0866295	−	0.170107i	0.00294549	−	0.00578380i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	21.3066	+	36.9041i	0.722778	+	1.25189i
$870$		0			0
$871$	17.6244	+	30.5264i	0.597180	+	1.03435i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	54.8879	−	8.72826i	1.85555	−	0.295069i
$876$		0			0
$877$	14.2958	−	8.25368i	0.482735	−	0.278707i	−0.238821	−	0.971064i	$-0.576761\pi$
$877$	14.2958	−	8.25368i	0.482735	−	0.278707i	0.721555	+	0.692357i	$0.243428\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	22.9549			0.773370			0.386685	−	0.922212i	$-0.373620\pi$
$881$	22.9549			0.773370			0.386685	+	0.922212i	$0.373620\pi$
$882$		0			0
$883$	24.9234	+	14.3895i	0.838739	+	0.484246i	0.856835	−	0.515590i	$-0.172427\pi$
$883$	24.9234	+	14.3895i	0.838739	+	0.484246i	−0.0180963	+	0.999836i	$0.505761\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−26.4482	−	15.2699i	−0.888044	−	0.512712i	−0.0147418	−	0.999891i	$-0.504693\pi$
$887$	−26.4482	−	15.2699i	−0.888044	−	0.512712i	−0.873302	+	0.487179i	$0.838026\pi$
$888$		0			0
$889$	−34.4310	+	59.6362i	−1.15478	+	2.00013i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.40963	−	5.11686i	0.181026	−	0.171229i
$894$		0			0
$895$	30.4242	−	19.7667i	1.01697	−	0.660727i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−10.0518	+	17.4103i	−0.335248	+	0.580666i
$900$		0			0
$901$	20.6312			0.687324
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.38616	−	45.3514i	−0.0793186	−	1.50753i
$906$		0			0
$907$	−15.1811	+	8.76481i	−0.504080	+	0.291031i	−0.730397	−	0.683023i	$-0.760665\pi$
$907$	−15.1811	+	8.76481i	−0.504080	+	0.291031i	0.226317	+	0.974054i	$0.427332\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.25152			−0.0414648			−0.0207324	−	0.999785i	$-0.506600\pi$
$911$	−1.25152			−0.0414648			−0.0207324	+	0.999785i	$0.506600\pi$
$912$		0			0
$913$			11.7328i			0.388299i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−52.6532	+	30.3994i	−1.73876	+	1.00388i
$918$		0			0
$919$	−17.4588			−0.575912			−0.287956	−	0.957644i	$-0.592976\pi$
$919$	−17.4588			−0.575912			−0.287956	+	0.957644i	$0.592976\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			20.5950i			0.677893i
$924$		0			0
$925$	12.5986	+	5.60303i	0.414240	+	0.184227i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−28.6100	−	49.5540i	−0.938665	−	1.62582i	−0.767964	−	0.640493i	$-0.778730\pi$
$929$	−28.6100	−	49.5540i	−0.938665	−	1.62582i	−0.170701	−	0.985323i	$-0.554603\pi$
$930$		0			0
$931$	−22.0463	+	73.9851i	−0.722538	+	2.42476i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	10.1330	−	19.8974i	0.331386	−	0.650714i
$936$		0			0
$937$	−8.38001	−	4.83820i	−0.273763	−	0.158057i	0.356834	−	0.934168i	$-0.383856\pi$
$937$	−8.38001	−	4.83820i	−0.273763	−	0.158057i	−0.630596	+	0.776111i	$0.717190\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.0336	−	24.3069i	0.457482	−	0.792383i	−0.541345	−	0.840801i	$-0.682085\pi$
$941$	14.0336	−	24.3069i	0.457482	−	0.792383i	0.998827	+	0.0484179i	$0.0154179\pi$
$942$		0			0
$943$		−	15.9216i		−	0.518479i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.2228	−	15.1397i	0.852125	−	0.491975i	−0.00924220	−	0.999957i	$-0.502942\pi$
$947$	26.2228	−	15.1397i	0.852125	−	0.491975i	0.861367	+	0.507983i	$0.169609\pi$
$948$		0			0
$949$	−12.0384			−0.390784
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−5.82020	+	3.36029i	−0.188535	+	0.108851i	−0.591296	−	0.806454i	$-0.701384\pi$
$953$	−5.82020	+	3.36029i	−0.188535	+	0.108851i	0.402762	+	0.915305i	$0.368050\pi$
$954$		0			0
$955$	−41.0935	+	26.6985i	−1.32975	+	0.863942i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.8594	+	39.5937i	−0.738169	+	1.27855i
$960$		0			0
$961$	29.3124			0.945560
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.10374	+	10.0218i	−0.164295	+	0.322612i
$966$		0			0
$967$	−34.3960	+	19.8585i	−1.10610	+	0.638607i	−0.937817	−	0.347131i	$-0.887156\pi$
$967$	−34.3960	+	19.8585i	−1.10610	+	0.638607i	−0.168284	+	0.985739i	$0.553823\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	7.09379	+	12.2868i	0.227651	+	0.394302i	0.957111	−	0.289720i	$-0.0935623\pi$
$971$	7.09379	+	12.2868i	0.227651	+	0.394302i	−0.729461	+	0.684023i	$0.760229\pi$
$972$		0			0
$973$	27.7396	+	16.0155i	0.889291	+	0.513432i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	5.49394i		−	0.175767i	−0.996131	−	0.0878833i	$-0.971990\pi$
$977$		−	5.49394i		−	0.175767i	0.996131	−	0.0878833i	$-0.0280103\pi$
$978$		0			0
$979$	−18.3575	+	31.7962i	−0.586709	+	1.01621i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	32.7834	−	18.9275i	1.04563	−	0.603695i	0.124207	−	0.992256i	$-0.460361\pi$
$983$	32.7834	−	18.9275i	1.04563	−	0.603695i	0.921423	+	0.388562i	$0.127028\pi$
$984$		0			0
$985$	−23.2914	−	35.8494i	−0.742126	−	1.14226i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.89118			−0.123732
$990$		0			0
$991$	22.6116	+	39.1645i	0.718282	+	1.24410i	0.961680	+	0.274175i	$0.0884047\pi$
$991$	22.6116	+	39.1645i	0.718282	+	1.24410i	−0.243398	+	0.969927i	$0.578262\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	2.12518	+	40.3912i	0.0673728	+	1.28049i
$996$		0			0
$997$	42.8135	+	24.7184i	1.35592	+	0.782840i	0.989071	−	0.147441i	$-0.0471037\pi$
$997$	42.8135	+	24.7184i	1.35592	+	0.782840i	0.366848	+	0.930281i	$0.380437\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3420.2.bj.c.2629.2		20
3.2	odd	2		380.2.r.a.349.4	yes	20
5.4	even	2	inner	3420.2.bj.c.2629.9		20
15.2	even	4		1900.2.i.g.501.7		20
15.8	even	4		1900.2.i.g.501.4		20
15.14	odd	2		380.2.r.a.349.7	yes	20
19.11	even	3	inner	3420.2.bj.c.1189.9		20
57.11	odd	6		380.2.r.a.49.7	yes	20
95.49	even	6	inner	3420.2.bj.c.1189.2		20
285.68	even	12		1900.2.i.g.201.4		20
285.182	even	12		1900.2.i.g.201.7		20
285.239	odd	6		380.2.r.a.49.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.4	✓	20	285.239	odd	6
380.2.r.a.49.7	yes	20	57.11	odd	6
380.2.r.a.349.4	yes	20	3.2	odd	2
380.2.r.a.349.7	yes	20	15.14	odd	2
1900.2.i.g.201.4		20	285.68	even	12
1900.2.i.g.201.7		20	285.182	even	12
1900.2.i.g.501.4		20	15.8	even	4
1900.2.i.g.501.7		20	15.2	even	4
3420.2.bj.c.1189.2		20	95.49	even	6	inner
3420.2.bj.c.1189.9		20	19.11	even	3	inner
3420.2.bj.c.2629.2		20	1.1	even	1	trivial
3420.2.bj.c.2629.9		20	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87507 + 1.21824i) q^{5} -4.97100i q^{7} +3.85491 q^{11} +(-2.31178 - 1.33470i) q^{13} +(-2.24337 + 1.29521i) q^{17} +(1.24479 - 4.17738i) q^{19} +(1.88243 + 1.08682i) q^{23} +(2.03180 - 4.56857i) q^{25} +(-1.29432 + 2.24183i) q^{29} +7.76610 q^{31} +(6.05586 + 9.32100i) q^{35} +2.75768i q^{37} +(-3.66243 - 6.34351i) q^{41} +(-1.55033 + 0.895083i) q^{43} +(1.47942 + 0.854141i) q^{47} -17.7109 q^{49} +(-6.89738 - 3.98220i) q^{53} +(-7.22823 + 4.69619i) q^{55} +(0.127300 + 0.220490i) q^{59} +(-1.66702 + 2.88737i) q^{61} +(5.96073 - 0.313624i) q^{65} +(-11.4356 - 6.60237i) q^{67} +(-3.85760 - 6.68156i) q^{71} +(3.90558 - 2.25489i) q^{73} -19.1628i q^{77} +(5.52715 + 9.57330i) q^{79} +3.04360i q^{83} +(2.62861 - 5.16157i) q^{85} +(-4.76212 + 8.24824i) q^{89} +(-6.63482 + 11.4918i) q^{91} +(2.75497 + 9.34934i) q^{95} +(9.72851 - 5.61676i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) \) 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more