LMFDB - Embedded newform 2880.2.bj.f.1313.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(737,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 1]))

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

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

chi := DirichletCharacter("2880.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.bj (of order $4$, 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:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1313.5
Character	$\chi$	$=$	2880.1313
Dual form			2880.2.bj.f.737.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27770 - 1.83507i) q^{5} +(-0.254252 + 0.254252i) q^{7} +O(q^{10})$	$q+(-1.27770 - 1.83507i) q^{5} +(-0.254252 + 0.254252i) q^{7} -1.83080 q^{11} +(-0.689567 + 0.689567i) q^{13} +(2.00475 + 2.00475i) q^{17} -4.78955 q^{19} +(4.64533 - 4.64533i) q^{23} +(-1.73495 + 4.68935i) q^{25} -1.83628i q^{29} -3.61389 q^{31} +(0.791427 + 0.141711i) q^{35} +(5.09169 + 5.09169i) q^{37} -0.516552i q^{41} +(-4.20041 + 4.20041i) q^{43} +(1.22065 + 1.22065i) q^{47} +6.87071i q^{49} +(-3.36642 - 3.36642i) q^{53} +(2.33922 + 3.35964i) q^{55} +12.6782i q^{59} -2.95560i q^{61} +(2.14647 + 0.384340i) q^{65} +(-6.25944 - 6.25944i) q^{67} +1.95039i q^{71} +(7.15481 + 7.15481i) q^{73} +(0.465483 - 0.465483i) q^{77} +6.76682i q^{79} +(0.933138 + 0.933138i) q^{83} +(1.11738 - 6.24034i) q^{85} +13.7800 q^{89} -0.350647i q^{91} +(6.11963 + 8.78915i) q^{95} +(-7.21384 + 7.21384i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 32 q^{19} - 32 q^{43} + 96 q^{67} + 48 q^{73} + 144 q^{97}+O(q^{100}) $ 32 * q + 32 * q^19 - 32 * q^43 + 96 * q^67 + 48 * q^73 + 144 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$1$

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
$5$	−1.27770	−	1.83507i	−0.571406	−	0.820667i
$5$	−1.27770	−	1.83507i	−0.571406	−	0.820667i
$6$		0			0
$7$	−0.254252	+	0.254252i	−0.0960981	+	0.0960981i	−0.753521	−	0.657423i	$-0.771646\pi$
$7$	−0.254252	+	0.254252i	−0.0960981	+	0.0960981i	0.657423	+	0.753521i	$0.271646\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.83080			−0.552007			−0.276003	−	0.961157i	$-0.589010\pi$
$11$	−1.83080			−0.552007			−0.276003	+	0.961157i	$0.589010\pi$
$12$		0			0
$13$	−0.689567	+	0.689567i	−0.191252	+	0.191252i	−0.796237	−	0.604985i	$-0.793179\pi$
$13$	−0.689567	+	0.689567i	−0.191252	+	0.191252i	0.604985	+	0.796237i	$0.293179\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.00475	+	2.00475i	0.486224	+	0.486224i	0.907113	−	0.420888i	$-0.138281\pi$
$17$	2.00475	+	2.00475i	0.486224	+	0.486224i	−0.420888	+	0.907113i	$0.638281\pi$
$18$		0			0
$19$	−4.78955			−1.09880			−0.549399	−	0.835560i	$-0.685143\pi$
$19$	−4.78955			−1.09880			−0.549399	+	0.835560i	$0.685143\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.64533	−	4.64533i	0.968618	−	0.968618i	−0.0309039	−	0.999522i	$-0.509839\pi$
$23$	4.64533	−	4.64533i	0.968618	−	0.968618i	0.999522	+	0.0309039i	$0.00983858\pi$
$24$		0			0
$25$	−1.73495	+	4.68935i	−0.346989	+	0.937869i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	1.83628i		−	0.340988i	−0.985359	−	0.170494i	$-0.945464\pi$
$29$		−	1.83628i		−	0.340988i	0.985359	−	0.170494i	$-0.0545363\pi$
$30$		0			0
$31$	−3.61389			−0.649074			−0.324537	−	0.945873i	$-0.605208\pi$
$31$	−3.61389			−0.649074			−0.324537	+	0.945873i	$0.605208\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.791427	+	0.141711i	0.133776	+	0.0239535i
$36$		0			0
$37$	5.09169	+	5.09169i	0.837069	+	0.837069i	0.988472	−	0.151403i	$-0.0483792\pi$
$37$	5.09169	+	5.09169i	0.837069	+	0.837069i	−0.151403	+	0.988472i	$0.548379\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	0.516552i		−	0.0806719i	−0.999186	−	0.0403360i	$-0.987157\pi$
$41$		−	0.516552i		−	0.0806719i	0.999186	−	0.0403360i	$-0.0128428\pi$
$42$		0			0
$43$	−4.20041	+	4.20041i	−0.640556	+	0.640556i	−0.950692	−	0.310136i	$-0.899625\pi$
$43$	−4.20041	+	4.20041i	−0.640556	+	0.640556i	0.310136	+	0.950692i	$0.399625\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.22065	+	1.22065i	0.178049	+	0.178049i	0.790505	−	0.612456i	$-0.209818\pi$
$47$	1.22065	+	1.22065i	0.178049	+	0.178049i	−0.612456	+	0.790505i	$0.709818\pi$
$48$		0			0
$49$			6.87071i			0.981530i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.36642	−	3.36642i	−0.462413	−	0.462413i	0.437032	−	0.899446i	$-0.356029\pi$
$53$	−3.36642	−	3.36642i	−0.462413	−	0.462413i	−0.899446	+	0.437032i	$0.856029\pi$
$54$		0			0
$55$	2.33922	+	3.35964i	0.315420	+	0.453014i
$56$		0			0
$57$		0			0
$58$		0			0
$59$			12.6782i			1.65057i	0.564719	+	0.825283i	$0.308985\pi$
$59$			12.6782i			1.65057i	−0.564719	+	0.825283i	$0.691015\pi$
$60$		0			0
$61$		−	2.95560i		−	0.378426i	−0.981936	−	0.189213i	$-0.939406\pi$
$61$		−	2.95560i		−	0.378426i	0.981936	−	0.189213i	$-0.0605936\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.14647	+	0.384340i	0.266236	+	0.0476715i
$66$		0			0
$67$	−6.25944	−	6.25944i	−0.764713	−	0.764713i	0.212458	−	0.977170i	$-0.431853\pi$
$67$	−6.25944	−	6.25944i	−0.764713	−	0.764713i	−0.977170	+	0.212458i	$0.931853\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.95039i			0.231469i	0.993280	+	0.115734i	$0.0369222\pi$
$71$			1.95039i			0.231469i	−0.993280	+	0.115734i	$0.963078\pi$
$72$		0			0
$73$	7.15481	+	7.15481i	0.837407	+	0.837407i	0.988517	−	0.151110i	$-0.0482848\pi$
$73$	7.15481	+	7.15481i	0.837407	+	0.837407i	−0.151110	+	0.988517i	$0.548285\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.465483	−	0.465483i	0.0530468	−	0.0530468i
$78$		0			0
$79$			6.76682i			0.761327i	0.924714	+	0.380663i	$0.124304\pi$
$79$			6.76682i			0.761327i	−0.924714	+	0.380663i	$0.875696\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.933138	+	0.933138i	0.102425	+	0.102425i	0.756462	−	0.654037i	$-0.226926\pi$
$83$	0.933138	+	0.933138i	0.102425	+	0.102425i	−0.654037	+	0.756462i	$0.726926\pi$
$84$		0			0
$85$	1.11738	−	6.24034i	0.121197	−	0.676860i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	13.7800			1.46068			0.730340	−	0.683084i	$-0.239362\pi$
$89$	13.7800			1.46068			0.730340	+	0.683084i	$0.239362\pi$
$90$		0			0
$91$		−	0.350647i		−	0.0367578i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.11963	+	8.78915i	0.627860	+	0.901748i
$96$		0			0
$97$	−7.21384	+	7.21384i	−0.732455	+	0.732455i	−0.971105	−	0.238651i	$-0.923295\pi$
$97$	−7.21384	+	7.21384i	−0.732455	+	0.732455i	0.238651	+	0.971105i	$0.423295\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.05879			0.702376			0.351188	−	0.936305i	$-0.385778\pi$
$101$	7.05879			0.702376			0.351188	+	0.936305i	$0.385778\pi$
$102$		0			0
$103$	5.08589	+	5.08589i	0.501128	+	0.501128i	0.911788	−	0.410660i	$-0.134702\pi$
$103$	5.08589	+	5.08589i	0.501128	+	0.501128i	−0.410660	+	0.911788i	$0.634702\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.60425	+	8.60425i	−0.831804	+	0.831804i	−0.987763	−	0.155960i	$-0.950153\pi$
$107$	−8.60425	+	8.60425i	−0.831804	+	0.831804i	0.155960	+	0.987763i	$0.450153\pi$
$108$		0			0
$109$	19.3463			1.85304			0.926522	−	0.376241i	$-0.122784\pi$
$109$	19.3463			1.85304			0.926522	+	0.376241i	$0.122784\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.36399	−	7.36399i	0.692746	−	0.692746i	−0.270090	−	0.962835i	$-0.587053\pi$
$113$	7.36399	−	7.36399i	0.692746	−	0.692746i	0.962835	+	0.270090i	$0.0870533\pi$
$114$		0			0
$115$	−14.4599	−	2.58914i	−1.34839	−	0.241439i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.01942			−0.0934505
$120$		0			0
$121$	−7.64818			−0.695289
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.8220	−	2.80785i	0.967950	−	0.251142i
$126$		0			0
$127$	−12.0141	+	12.0141i	−1.06608	+	1.06608i	−0.0684223	+	0.997656i	$0.521797\pi$
$127$	−12.0141	+	12.0141i	−1.06608	+	1.06608i	−0.997656	+	0.0684223i	$0.978203\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	13.4279			1.17320			0.586602	−	0.809876i	$-0.300465\pi$
$131$	13.4279			1.17320			0.586602	+	0.809876i	$0.300465\pi$
$132$		0			0
$133$	1.21775	−	1.21775i	0.105592	−	0.105592i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.42848	+	7.42848i	0.634658	+	0.634658i	0.949233	−	0.314575i	$-0.101862\pi$
$137$	7.42848	+	7.42848i	0.634658	+	0.634658i	−0.314575	+	0.949233i	$0.601862\pi$
$138$		0			0
$139$	−7.77951			−0.659849			−0.329925	−	0.944007i	$-0.607023\pi$
$139$	−7.77951			−0.659849			−0.329925	+	0.944007i	$0.607023\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.26246	−	1.26246i	0.105572	−	0.105572i
$144$		0			0
$145$	−3.36969	+	2.34622i	−0.279837	+	0.194843i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			5.40869i			0.443097i	0.975149	+	0.221549i	$0.0711112\pi$
$149$			5.40869i			0.443097i	−0.975149	+	0.221549i	$0.928889\pi$
$150$		0			0
$151$	20.4143			1.66129			0.830646	−	0.556801i	$-0.187971\pi$
$151$	20.4143			1.66129			0.830646	+	0.556801i	$0.187971\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.61748	+	6.63174i	0.370885	+	0.532674i
$156$		0			0
$157$	1.47780	+	1.47780i	0.117941	+	0.117941i	0.763614	−	0.645673i	$-0.223423\pi$
$157$	1.47780	+	1.47780i	0.117941	+	0.117941i	−0.645673	+	0.763614i	$0.723423\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			2.36217i			0.186165i
$162$		0			0
$163$	−6.20041	+	6.20041i	−0.485654	+	0.485654i	−0.906932	−	0.421278i	$-0.861582\pi$
$163$	−6.20041	+	6.20041i	−0.485654	+	0.485654i	0.421278	+	0.906932i	$0.361582\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.70865	−	8.70865i	−0.673895	−	0.673895i	0.284716	−	0.958612i	$-0.408101\pi$
$167$	−8.70865	−	8.70865i	−0.673895	−	0.673895i	−0.958612	+	0.284716i	$0.908101\pi$
$168$		0			0
$169$			12.0490i			0.926846i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−11.2164	−	11.2164i	−0.852767	−	0.852767i	0.137706	−	0.990473i	$-0.456027\pi$
$173$	−11.2164	−	11.2164i	−0.852767	−	0.852767i	−0.990473	+	0.137706i	$0.956027\pi$
$174$		0			0
$175$	−0.751160	−	1.63339i	−0.0567824	−	0.123472i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			4.10948i			0.307157i	0.988136	+	0.153578i	$0.0490797\pi$
$179$			4.10948i			0.307157i	−0.988136	+	0.153578i	$0.950920\pi$
$180$		0			0
$181$			0.00341534i			0.000253860i	1.00000		0.000126930i	$4.04031e-5\pi$
$181$			0.00341534i			0.000253860i	−1.00000		0.000126930i	$0.999960\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.83793	−	15.8493i	0.208648	−	1.16526i
$186$		0			0
$187$	−3.67030	−	3.67030i	−0.268399	−	0.268399i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			15.3997i			1.11428i	0.830418	+	0.557141i	$0.188102\pi$
$191$			15.3997i			1.11428i	−0.830418	+	0.557141i	$0.811898\pi$
$192$		0			0
$193$	11.7895	+	11.7895i	0.848630	+	0.848630i	0.989962	−	0.141332i	$-0.0451385\pi$
$193$	11.7895	+	11.7895i	0.848630	+	0.848630i	−0.141332	+	0.989962i	$0.545138\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.0500670	−	0.0500670i	0.00356713	−	0.00356713i	−0.705321	−	0.708888i	$-0.749197\pi$
$197$	0.0500670	−	0.0500670i	0.00356713	−	0.00356713i	0.708888	+	0.705321i	$0.249197\pi$
$198$		0			0
$199$			21.0367i			1.49125i	0.666367	+	0.745624i	$0.267849\pi$
$199$			21.0367i			1.49125i	−0.666367	+	0.745624i	$0.732151\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.466876	+	0.466876i	0.0327683	+	0.0327683i
$204$		0			0
$205$	−0.947908	+	0.660001i	−0.0662048	+	0.0460965i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.76870			0.606544
$210$		0			0
$211$		−	6.97787i		−	0.480377i	−0.970726	−	0.240188i	$-0.922791\pi$
$211$		−	6.97787i		−	0.480377i	0.970726	−	0.240188i	$-0.0772092\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	13.0749	+	2.34116i	0.891702	+	0.159666i
$216$		0			0
$217$	0.918838	−	0.918838i	0.0623748	−	0.0623748i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.76483			−0.185982
$222$		0			0
$223$	−17.5156	−	17.5156i	−1.17293	−	1.17293i	−0.981507	−	0.191426i	$-0.938689\pi$
$223$	−17.5156	−	17.5156i	−1.17293	−	1.17293i	−0.191426	−	0.981507i	$-0.561311\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−12.4948	+	12.4948i	−0.829308	+	0.829308i	−0.987421	−	0.158113i	$-0.949459\pi$
$227$	−12.4948	+	12.4948i	−0.829308	+	0.829308i	0.158113	+	0.987421i	$0.449459\pi$
$228$		0			0
$229$	10.7394			0.709681			0.354841	−	0.934927i	$-0.384535\pi$
$229$	10.7394			0.709681			0.354841	+	0.934927i	$0.384535\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−14.9848	+	14.9848i	−0.981687	+	0.981687i	−0.999835	−	0.0181481i	$-0.994223\pi$
$233$	−14.9848	+	14.9848i	−0.981687	+	0.981687i	0.0181481	+	0.999835i	$0.494223\pi$
$234$		0			0
$235$	0.680344	−	3.79959i	0.0443808	−	0.247858i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.22643			−0.0793311			−0.0396656	−	0.999213i	$-0.512629\pi$
$239$	−1.22643			−0.0793311			−0.0396656	+	0.999213i	$0.512629\pi$
$240$		0			0
$241$	1.90880			0.122956			0.0614782	−	0.998108i	$-0.480419\pi$
$241$	1.90880			0.122956			0.0614782	+	0.998108i	$0.480419\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.6082	−	8.77873i	0.805510	−	0.560853i
$246$		0			0
$247$	3.30272	−	3.30272i	0.210147	−	0.210147i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.9617			−0.818133			−0.409067	−	0.912505i	$-0.634146\pi$
$251$	−12.9617			−0.818133			−0.409067	+	0.912505i	$0.634146\pi$
$252$		0			0
$253$	−8.50467	+	8.50467i	−0.534684	+	0.534684i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.79714	+	6.79714i	0.423994	+	0.423994i	0.886576	−	0.462582i	$-0.153077\pi$
$257$	6.79714	+	6.79714i	0.423994	+	0.423994i	−0.462582	+	0.886576i	$0.653077\pi$
$258$		0			0
$259$	−2.58914			−0.160881
$260$		0			0
$261$		0			0
$262$		0			0
$263$	21.3880	−	21.3880i	1.31884	−	1.31884i	0.404142	−	0.914696i	$-0.367570\pi$
$263$	21.3880	−	21.3880i	1.31884	−	1.31884i	0.914696	−	0.404142i	$-0.132430\pi$
$264$		0			0
$265$	−1.87632	+	10.4789i	−0.115262	+	0.643713i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			8.79735i			0.536384i	0.963366	+	0.268192i	$0.0864261\pi$
$269$			8.79735i			0.536384i	−0.963366	+	0.268192i	$0.913574\pi$
$270$		0			0
$271$	−20.7139			−1.25828			−0.629139	−	0.777293i	$-0.716593\pi$
$271$	−20.7139			−1.25828			−0.629139	+	0.777293i	$0.716593\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.17634	−	8.58525i	0.191540	−	0.517710i
$276$		0			0
$277$	3.64175	+	3.64175i	0.218812	+	0.218812i	0.807997	−	0.589186i	$-0.200551\pi$
$277$	3.64175	+	3.64175i	0.218812	+	0.218812i	−0.589186	+	0.807997i	$0.700551\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	7.96873i		−	0.475375i	−0.971342	−	0.237687i	$-0.923611\pi$
$281$		−	7.96873i		−	0.475375i	0.971342	−	0.237687i	$-0.0763893\pi$
$282$		0			0
$283$	−15.1783	+	15.1783i	−0.902255	+	0.902255i	−0.995631	−	0.0933758i	$-0.970234\pi$
$283$	−15.1783	+	15.1783i	−0.902255	+	0.902255i	0.0933758	+	0.995631i	$0.470234\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.131334	+	0.131334i	0.00775241	+	0.00775241i
$288$		0			0
$289$		−	8.96192i		−	0.527172i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−19.2504	−	19.2504i	−1.12462	−	1.12462i	−0.991038	−	0.133582i	$-0.957352\pi$
$293$	−19.2504	−	19.2504i	−1.12462	−	1.12462i	−0.133582	−	0.991038i	$-0.542648\pi$
$294$		0			0
$295$	23.2654	−	16.1990i	1.35457	−	0.943145i
$296$		0			0
$297$		0			0
$298$		0			0
$299$			6.40654i			0.370500i
$300$		0			0
$301$		−	2.13592i		−	0.123112i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.42372	+	3.77638i	−0.310561	+	0.216235i
$306$		0			0
$307$	14.0590	+	14.0590i	0.802391	+	0.802391i	0.983469	−	0.181077i	$-0.0579584\pi$
$307$	14.0590	+	14.0590i	0.802391	+	0.802391i	−0.181077	+	0.983469i	$0.557958\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	24.3949i		−	1.38331i	−0.722230	−	0.691653i	$-0.756883\pi$
$311$		−	24.3949i		−	1.38331i	0.722230	−	0.691653i	$-0.243117\pi$
$312$		0			0
$313$	−3.49794	−	3.49794i	−0.197715	−	0.197715i	0.601305	−	0.799020i	$-0.294648\pi$
$313$	−3.49794	−	3.49794i	−0.197715	−	0.197715i	−0.799020	+	0.601305i	$0.794648\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.1877	+	16.1877i	−0.909191	+	0.909191i	−0.996207	−	0.0870160i	$-0.972267\pi$
$317$	−16.1877	+	16.1877i	−0.909191	+	0.909191i	0.0870160	+	0.996207i	$0.472267\pi$
$318$		0			0
$319$			3.36185i			0.188228i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.60187	−	9.60187i	−0.534263	−	0.534263i
$324$		0			0
$325$	−2.03726	−	4.42998i	−0.113007	−	0.245731i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.620702			−0.0342204
$330$		0			0
$331$		−	7.02804i		−	0.386296i	−0.981170	−	0.193148i	$-0.938130\pi$
$331$		−	7.02804i		−	0.386296i	0.981170	−	0.193148i	$-0.0618698\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.48879	+	19.4842i	−0.190613	+	1.06454i
$336$		0			0
$337$	1.44642	−	1.44642i	0.0787915	−	0.0787915i	−0.666613	−	0.745404i	$-0.732256\pi$
$337$	1.44642	−	1.44642i	0.0787915	−	0.0787915i	0.745404	+	0.666613i	$0.232256\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.61631			0.358293
$342$		0			0
$343$	−3.52665	−	3.52665i	−0.190421	−	0.190421i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	21.9677	−	21.9677i	1.17929	−	1.17929i	0.199361	−	0.979926i	$-0.436113\pi$
$347$	21.9677	−	21.9677i	1.17929	−	1.17929i	0.979926	−	0.199361i	$-0.0638866\pi$
$348$		0			0
$349$	−19.8467			−1.06237			−0.531184	−	0.847257i	$-0.678253\pi$
$349$	−19.8467			−1.06237			−0.531184	+	0.847257i	$0.678253\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.3280	+	17.3280i	−0.922275	+	0.922275i	−0.997190	−	0.0749150i	$-0.976131\pi$
$353$	−17.3280	+	17.3280i	−0.922275	+	0.922275i	0.0749150	+	0.997190i	$0.476131\pi$
$354$		0			0
$355$	3.57910	−	2.49202i	0.189959	−	0.132263i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−19.0838			−1.00720			−0.503602	−	0.863936i	$-0.667992\pi$
$359$	−19.0838			−1.00720			−0.503602	+	0.863936i	$0.667992\pi$
$360$		0			0
$361$	3.93979			0.207357
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.98783	−	22.2713i	0.208733	−	1.16573i
$366$		0			0
$367$	−16.9049	+	16.9049i	−0.882427	+	0.882427i	−0.993781	−	0.111354i	$-0.964481\pi$
$367$	−16.9049	+	16.9049i	−0.882427	+	0.882427i	0.111354	+	0.993781i	$0.464481\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.71184			0.0888740
$372$		0			0
$373$	−16.1898	+	16.1898i	−0.838278	+	0.838278i	−0.988632	−	0.150355i	$-0.951958\pi$
$373$	−16.1898	+	16.1898i	−0.838278	+	0.838278i	0.150355	+	0.988632i	$0.451958\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.26624	+	1.26624i	0.0652144	+	0.0652144i
$378$		0			0
$379$	18.0180			0.925523			0.462761	−	0.886483i	$-0.346859\pi$
$379$	18.0180			0.925523			0.462761	+	0.886483i	$0.346859\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.69204	−	9.69204i	0.495240	−	0.495240i	−0.414712	−	0.909953i	$-0.636118\pi$
$383$	9.69204	−	9.69204i	0.495240	−	0.495240i	0.909953	+	0.414712i	$0.136118\pi$
$384$		0			0
$385$	−1.44894	−	0.259444i	−0.0738450	−	0.0132225i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			12.0298i			0.609937i	0.952363	+	0.304968i	$0.0986459\pi$
$389$			12.0298i			0.609937i	−0.952363	+	0.304968i	$0.901354\pi$
$390$		0			0
$391$	18.6255			0.941932
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.4176	−	8.64599i	0.624796	−	0.435027i
$396$		0			0
$397$	14.2547	+	14.2547i	0.715420	+	0.715420i	0.967664	−	0.252243i	$-0.0811684\pi$
$397$	14.2547	+	14.2547i	0.715420	+	0.715420i	−0.252243	+	0.967664i	$0.581168\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	27.8873i		−	1.39263i	−0.717739	−	0.696313i	$-0.754823\pi$
$401$		−	27.8873i		−	1.39263i	0.717739	−	0.696313i	$-0.245177\pi$
$402$		0			0
$403$	2.49202	−	2.49202i	0.124136	−	0.124136i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.32186	−	9.32186i	−0.462068	−	0.462068i
$408$		0			0
$409$		−	25.0490i		−	1.23859i	−0.785157	−	0.619297i	$-0.787418\pi$
$409$		−	25.0490i		−	1.23859i	0.785157	−	0.619297i	$-0.212582\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−3.22346	−	3.22346i	−0.158616	−	0.158616i
$414$		0			0
$415$	0.520097	−	2.90464i	0.0255306	−	0.142583i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			6.04215i			0.295178i	0.989049	+	0.147589i	$0.0471513\pi$
$419$			6.04215i			0.295178i	−0.989049	+	0.147589i	$0.952849\pi$
$420$		0			0
$421$		−	16.2560i		−	0.792267i	−0.918193	−	0.396134i	$-0.870352\pi$
$421$		−	16.2560i		−	0.792267i	0.918193	−	0.396134i	$-0.129648\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.8791	+	5.92284i	−0.624730	+	0.287300i
$426$		0			0
$427$	0.751466	+	0.751466i	0.0363660	+	0.0363660i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			39.5991i			1.90742i	0.300725	+	0.953711i	$0.402771\pi$
$431$			39.5991i			1.90742i	−0.300725	+	0.953711i	$0.597229\pi$
$432$		0			0
$433$	−6.87071	−	6.87071i	−0.330185	−	0.330185i	0.522471	−	0.852657i	$-0.325010\pi$
$433$	−6.87071	−	6.87071i	−0.330185	−	0.330185i	−0.852657	+	0.522471i	$0.825010\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.2490	+	22.2490i	−1.06432	+	1.06432i
$438$		0			0
$439$		−	4.51705i		−	0.215587i	−0.994173	−	0.107794i	$-0.965621\pi$
$439$		−	4.51705i		−	0.215587i	0.994173	−	0.107794i	$-0.0343786\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−28.0369	−	28.0369i	−1.33208	−	1.33208i	−0.903512	−	0.428564i	$-0.859020\pi$
$443$	−28.0369	−	28.0369i	−1.33208	−	1.33208i	−0.428564	−	0.903512i	$-0.640980\pi$
$444$		0			0
$445$	−17.6068	−	25.2873i	−0.834642	−	1.19873i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.00946			0.0948321			0.0474161	−	0.998875i	$-0.484901\pi$
$449$	2.00946			0.0948321			0.0474161	+	0.998875i	$0.484901\pi$
$450$		0			0
$451$			0.945703i			0.0445314i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.643461	+	0.448023i	−0.0301659	+	0.0210036i
$456$		0			0
$457$	18.6837	−	18.6837i	0.873988	−	0.873988i	−0.118916	−	0.992904i	$-0.537942\pi$
$457$	18.6837	−	18.6837i	0.873988	−	0.873988i	0.992904	+	0.118916i	$0.0379419\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	30.8230			1.43557			0.717785	−	0.696265i	$-0.245156\pi$
$461$	30.8230			1.43557			0.717785	+	0.696265i	$0.245156\pi$
$462$		0			0
$463$	−25.6582	−	25.6582i	−1.19244	−	1.19244i	−0.976381	−	0.216055i	$-0.930681\pi$
$463$	−25.6582	−	25.6582i	−1.19244	−	1.19244i	−0.216055	−	0.976381i	$-0.569319\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.7321	+	20.7321i	−0.959368	+	0.959368i	−0.999206	−	0.0398377i	$-0.987316\pi$
$467$	−20.7321	+	20.7321i	−0.959368	+	0.959368i	0.0398377	+	0.999206i	$0.487316\pi$
$468$		0			0
$469$	3.18295			0.146975
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.69010	−	7.69010i	0.353591	−	0.353591i
$474$		0			0
$475$	8.30961	−	22.4599i	0.381271	−	1.03053i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−34.4211			−1.57274			−0.786369	−	0.617757i	$-0.788042\pi$
$479$	−34.4211			−1.57274			−0.786369	+	0.617757i	$0.788042\pi$
$480$		0			0
$481$	−7.02213			−0.320181
$482$		0			0
$483$		0			0
$484$		0			0
$485$	22.4550	+	4.02074i	1.01963	+	0.182572i
$486$		0			0
$487$	16.4836	−	16.4836i	0.746944	−	0.746944i	−0.226960	−	0.973904i	$-0.572879\pi$
$487$	16.4836	−	16.4836i	0.746944	−	0.746944i	0.973904	+	0.226960i	$0.0728788\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	28.4583			1.28431			0.642153	−	0.766576i	$-0.278041\pi$
$491$	28.4583			1.28431			0.642153	+	0.766576i	$0.278041\pi$
$492$		0			0
$493$	3.68128	−	3.68128i	0.165797	−	0.165797i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.495890	−	0.495890i	−0.0222437	−	0.0222437i
$498$		0			0
$499$	32.7252			1.46498			0.732491	−	0.680777i	$-0.238358\pi$
$499$	32.7252			1.46498			0.732491	+	0.680777i	$0.238358\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.29645	−	9.29645i	0.414508	−	0.414508i	−0.468798	−	0.883306i	$-0.655313\pi$
$503$	9.29645	−	9.29645i	0.414508	−	0.414508i	0.883306	+	0.468798i	$0.155313\pi$
$504$		0			0
$505$	−9.01904	−	12.9534i	−0.401342	−	0.576417i
$506$		0			0
$507$		0			0
$508$		0			0
$509$			42.2217i			1.87145i	0.352736	+	0.935723i	$0.385251\pi$
$509$			42.2217i			1.87145i	−0.352736	+	0.935723i	$0.614749\pi$
$510$		0			0
$511$	−3.63824			−0.160946
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.83469	−	15.8312i	0.124912	−	0.697607i
$516$		0			0
$517$	−2.23476	−	2.23476i	−0.0982845	−	0.0982845i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			20.2056i			0.885222i	0.896714	+	0.442611i	$0.145948\pi$
$521$			20.2056i			0.885222i	−0.896714	+	0.442611i	$0.854052\pi$
$522$		0			0
$523$	12.0770	−	12.0770i	0.528092	−	0.528092i	−0.391911	−	0.920003i	$-0.628186\pi$
$523$	12.0770	−	12.0770i	0.528092	−	0.528092i	0.920003	+	0.391911i	$0.128186\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.24497	−	7.24497i	−0.315596	−	0.315596i
$528$		0			0
$529$		−	20.1582i		−	0.876443i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.356198	+	0.356198i	0.0154286	+	0.0154286i
$534$		0			0
$535$	26.7830	+	4.79570i	1.15793	+	0.207336i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	12.5789i		−	0.541811i
$540$		0			0
$541$		−	1.64277i		−	0.0706282i	−0.999376	−	0.0353141i	$-0.988757\pi$
$541$		−	1.64277i		−	0.0706282i	0.999376	−	0.0353141i	$-0.0112432\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−24.7189	−	35.5018i	−1.05884	−	1.52073i
$546$		0			0
$547$	30.1302	+	30.1302i	1.28827	+	1.28827i	0.935836	+	0.352437i	$0.114647\pi$
$547$	30.1302	+	30.1302i	1.28827	+	1.28827i	0.352437	+	0.935836i	$0.385353\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			8.79493i			0.374677i
$552$		0			0
$553$	−1.72047	−	1.72047i	−0.0731620	−	0.0731620i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.13608	−	6.13608i	0.259994	−	0.259994i	−0.565058	−	0.825051i	$-0.691146\pi$
$557$	6.13608	−	6.13608i	0.259994	−	0.259994i	0.825051	+	0.565058i	$0.191146\pi$
$558$		0			0
$559$		−	5.79293i		−	0.245015i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.8286	+	11.8286i	0.498516	+	0.498516i	0.910976	−	0.412460i	$-0.135330\pi$
$563$	11.8286	+	11.8286i	0.498516	+	0.498516i	−0.412460	+	0.910976i	$0.635330\pi$
$564$		0			0
$565$	−22.9224	−	4.10442i	−0.964353	−	0.172674i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.00956			−0.251934			−0.125967	−	0.992034i	$-0.540203\pi$
$569$	−6.00956			−0.251934			−0.125967	+	0.992034i	$0.540203\pi$
$570$		0			0
$571$			22.6691i			0.948673i	0.880344	+	0.474337i	$0.157312\pi$
$571$			22.6691i			0.948673i	−0.880344	+	0.474337i	$0.842688\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	13.7242	+	29.8430i	0.572337	+	1.24454i
$576$		0			0
$577$	22.5469	−	22.5469i	0.938641	−	0.938641i	−0.0595824	−	0.998223i	$-0.518977\pi$
$577$	22.5469	−	22.5469i	0.938641	−	0.938641i	0.998223	+	0.0595824i	$0.0189769\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.474503			−0.0196857
$582$		0			0
$583$	6.16324	+	6.16324i	0.255255	+	0.255255i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.28298	−	9.28298i	0.383149	−	0.383149i	−0.489086	−	0.872236i	$-0.662670\pi$
$587$	9.28298	−	9.28298i	0.383149	−	0.383149i	0.872236	+	0.489086i	$0.162670\pi$
$588$		0			0
$589$	17.3089			0.713201
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−20.4256	+	20.4256i	−0.838780	+	0.838780i	−0.988698	−	0.149919i	$-0.952099\pi$
$593$	−20.4256	+	20.4256i	−0.838780	+	0.838780i	0.149919	+	0.988698i	$0.452099\pi$
$594$		0			0
$595$	1.30252	+	1.87071i	0.0533982	+	0.0766917i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−32.3981			−1.32375			−0.661876	−	0.749613i	$-0.730239\pi$
$599$	−32.3981			−1.32375			−0.661876	+	0.749613i	$0.730239\pi$
$600$		0			0
$601$	−18.6924			−0.762480			−0.381240	−	0.924476i	$-0.624503\pi$
$601$	−18.6924			−0.762480			−0.381240	+	0.924476i	$0.624503\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.77210	+	14.0349i	0.397292	+	0.570601i
$606$		0			0
$607$	−5.49215	+	5.49215i	−0.222919	+	0.222919i	−0.809727	−	0.586807i	$-0.800385\pi$
$607$	−5.49215	+	5.49215i	−0.222919	+	0.222919i	0.586807	+	0.809727i	$0.300385\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.68343			−0.0681045
$612$		0			0
$613$	−23.9411	+	23.9411i	−0.966973	+	0.966973i	−0.999472	−	0.0324989i	$-0.989653\pi$
$613$	−23.9411	+	23.9411i	−0.966973	+	0.966973i	0.0324989	+	0.999472i	$0.489653\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−25.4369	−	25.4369i	−1.02405	−	1.02405i	−0.999704	−	0.0243492i	$-0.992249\pi$
$617$	−25.4369	−	25.4369i	−1.02405	−	1.02405i	−0.0243492	−	0.999704i	$-0.507751\pi$
$618$		0			0
$619$	29.9418			1.20346			0.601732	−	0.798698i	$-0.294478\pi$
$619$	29.9418			1.20346			0.601732	+	0.798698i	$0.294478\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.50359	+	3.50359i	−0.140368	+	0.140368i
$624$		0			0
$625$	−18.9799	−	16.2715i	−0.759197	−	0.650861i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			20.4152i			0.814007i
$630$		0			0
$631$	46.4833			1.85047			0.925236	−	0.379391i	$-0.123867\pi$
$631$	46.4833			1.85047			0.925236	+	0.379391i	$0.123867\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	37.3971	+	6.69623i	1.48406	+	0.265732i
$636$		0			0
$637$	−4.73782	−	4.73782i	−0.187719	−	0.187719i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			10.9516i			0.432562i	0.976331	+	0.216281i	$0.0693927\pi$
$641$			10.9516i			0.432562i	−0.976331	+	0.216281i	$0.930607\pi$
$642$		0			0
$643$	23.5469	−	23.5469i	0.928600	−	0.928600i	−0.0690153	−	0.997616i	$-0.521986\pi$
$643$	23.5469	−	23.5469i	0.928600	−	0.928600i	0.997616	+	0.0690153i	$0.0219857\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−30.3239	−	30.3239i	−1.19216	−	1.19216i	−0.976461	−	0.215694i	$-0.930799\pi$
$647$	−30.3239	−	30.3239i	−1.19216	−	1.19216i	−0.215694	−	0.976461i	$-0.569201\pi$
$648$		0			0
$649$		−	23.2113i		−	0.911124i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.3657	−	21.3657i	−0.836106	−	0.836106i	0.152238	−	0.988344i	$-0.451352\pi$
$653$	−21.3657	−	21.3657i	−0.836106	−	0.836106i	−0.988344	+	0.152238i	$0.951352\pi$
$654$		0			0
$655$	−17.1569	−	24.6412i	−0.670376	−	0.962810i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	16.9067i		−	0.658591i	−0.944227	−	0.329295i	$-0.893189\pi$
$659$		−	16.9067i		−	0.658591i	0.944227	−	0.329295i	$-0.106811\pi$
$660$		0			0
$661$		−	5.28919i		−	0.205726i	−0.994696	−	0.102863i	$-0.967200\pi$
$661$		−	5.28919i		−	0.205726i	0.994696	−	0.102863i	$-0.0328003\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.79058	−	0.678730i	−0.146992	−	0.0263200i
$666$		0			0
$667$	−8.53011	−	8.53011i	−0.330287	−	0.330287i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			5.41111i			0.208893i
$672$		0			0
$673$	9.93979	+	9.93979i	0.383151	+	0.383151i	0.872236	−	0.489085i	$-0.162669\pi$
$673$	9.93979	+	9.93979i	0.383151	+	0.383151i	−0.489085	+	0.872236i	$0.662669\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.23998	+	8.23998i	−0.316688	+	0.316688i	−0.847494	−	0.530805i	$-0.821889\pi$
$677$	−8.23998	+	8.23998i	−0.316688	+	0.316688i	0.530805	+	0.847494i	$0.321889\pi$
$678$		0			0
$679$		−	3.66826i		−	0.140775i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−30.8299	−	30.8299i	−1.17967	−	1.17967i	−0.979827	−	0.199846i	$-0.935956\pi$
$683$	−30.8299	−	30.8299i	−1.17967	−	1.17967i	−0.199846	−	0.979827i	$-0.564044\pi$
$684$		0			0
$685$	4.14037	−	23.1232i	0.158195	−	0.883490i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.64275			0.176875
$690$		0			0
$691$		−	22.2506i		−	0.846452i	−0.906024	−	0.423226i	$-0.860898\pi$
$691$		−	22.2506i		−	0.846452i	0.906024	−	0.423226i	$-0.139102\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	9.93991	+	14.2759i	0.377042	+	0.541517i
$696$		0			0
$697$	1.03556	−	1.03556i	0.0392247	−	0.0392247i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	6.59065			0.248925			0.124463	−	0.992224i	$-0.460279\pi$
$701$	6.59065			0.248925			0.124463	+	0.992224i	$0.460279\pi$
$702$		0			0
$703$	−24.3869	−	24.3869i	−0.919770	−	0.919770i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.79471	+	1.79471i	−0.0674970	+	0.0674970i
$708$		0			0
$709$	20.7255			0.778362			0.389181	−	0.921161i	$-0.372758\pi$
$709$	20.7255			0.778362			0.389181	+	0.921161i	$0.372758\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−16.7877	+	16.7877i	−0.628705	+	0.628705i
$714$		0			0
$715$	−3.92975	−	0.703649i	−0.146964	−	0.0263150i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.2992			−0.645152			−0.322576	−	0.946543i	$-0.604549\pi$
$719$	−17.2992			−0.645152			−0.322576	+	0.946543i	$0.604549\pi$
$720$		0			0
$721$	−2.58619			−0.0963149
$722$		0			0
$723$		0			0
$724$		0			0
$725$	8.61093	+	3.18584i	0.319802	+	0.118319i
$726$		0			0
$727$	−7.70255	+	7.70255i	−0.285672	+	0.285672i	−0.835366	−	0.549694i	$-0.814744\pi$
$727$	−7.70255	+	7.70255i	−0.285672	+	0.285672i	0.549694	+	0.835366i	$0.314744\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.8416			−0.622908
$732$		0			0
$733$	−37.9043	+	37.9043i	−1.40003	+	1.40003i	−0.600106	+	0.799920i	$0.704875\pi$
$733$	−37.9043	+	37.9043i	−1.40003	+	1.40003i	−0.799920	+	0.600106i	$0.795125\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.4598	+	11.4598i	0.422127	+	0.422127i
$738$		0			0
$739$	4.01209			0.147587			0.0737935	−	0.997274i	$-0.476489\pi$
$739$	4.01209			0.147587			0.0737935	+	0.997274i	$0.476489\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	32.0857	−	32.0857i	1.17711	−	1.17711i	0.196633	−	0.980477i	$-0.436999\pi$
$743$	32.0857	−	32.0857i	1.17711	−	1.17711i	0.980477	−	0.196633i	$-0.0630006\pi$
$744$		0			0
$745$	9.92532	−	6.91070i	0.363635	−	0.253189i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	4.37529i		−	0.159869i
$750$		0			0
$751$	−26.1166			−0.953007			−0.476504	−	0.879172i	$-0.658096\pi$
$751$	−26.1166			−0.953007			−0.476504	+	0.879172i	$0.658096\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−26.0834	−	37.4616i	−0.949273	−	1.36337i
$756$		0			0
$757$	−15.7046	−	15.7046i	−0.570793	−	0.570793i	0.361557	−	0.932350i	$-0.382245\pi$
$757$	−15.7046	−	15.7046i	−0.570793	−	0.570793i	−0.932350	+	0.361557i	$0.882245\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	39.0720i		−	1.41636i	−0.706032	−	0.708180i	$-0.749517\pi$
$761$		−	39.0720i		−	1.41636i	0.706032	−	0.708180i	$-0.250483\pi$
$762$		0			0
$763$	−4.91884	+	4.91884i	−0.178074	+	0.178074i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.74250	−	8.74250i	−0.315674	−	0.315674i
$768$		0			0
$769$		−	43.8064i		−	1.57970i	−0.613301	−	0.789849i	$-0.710159\pi$
$769$		−	43.8064i		−	1.57970i	0.613301	−	0.789849i	$-0.289841\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−12.8154	−	12.8154i	−0.460939	−	0.460939i	0.438024	−	0.898963i	$-0.355678\pi$
$773$	−12.8154	−	12.8154i	−0.460939	−	0.460939i	−0.898963	+	0.438024i	$0.855678\pi$
$774$		0			0
$775$	6.26991	−	16.9468i	0.225222	−	0.608746i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			2.47405i			0.0886421i
$780$		0			0
$781$		−	3.57077i		−	0.127772i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.823672	−	4.60005i	0.0293981	−	0.164183i
$786$		0			0
$787$	21.4879	+	21.4879i	0.765961	+	0.765961i	0.977393	−	0.211432i	$-0.0678127\pi$
$787$	21.4879	+	21.4879i	0.765961	+	0.765961i	−0.211432	+	0.977393i	$0.567813\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			3.74461i			0.133143i
$792$		0			0
$793$	2.03808	+	2.03808i	0.0723745	+	0.0723745i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−23.2719	+	23.2719i	−0.824333	+	0.824333i	−0.986726	−	0.162393i	$-0.948079\pi$
$797$	−23.2719	+	23.2719i	−0.824333	+	0.824333i	0.162393	+	0.986726i	$0.448079\pi$
$798$		0			0
$799$			4.89419i			0.173144i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−13.0990	−	13.0990i	−0.462254	−	0.462254i
$804$		0			0
$805$	4.33473	−	3.01815i	0.152779	−	0.106376i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.3594			−0.504850			−0.252425	−	0.967617i	$-0.581228\pi$
$809$	−14.3594			−0.504850			−0.252425	+	0.967617i	$0.581228\pi$
$810$		0			0
$811$			4.03808i			0.141796i	0.997484	+	0.0708982i	$0.0225865\pi$
$811$			4.03808i			0.141796i	−0.997484	+	0.0708982i	$0.977413\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	19.3005	+	3.45589i	0.676065	+	0.121054i
$816$		0			0
$817$	20.1181	−	20.1181i	0.703842	−	0.703842i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.45799			−0.190485			−0.0952426	−	0.995454i	$-0.530363\pi$
$821$	−5.45799			−0.190485			−0.0952426	+	0.995454i	$0.530363\pi$
$822$		0			0
$823$	−12.0732	−	12.0732i	−0.420846	−	0.420846i	0.464649	−	0.885495i	$-0.346181\pi$
$823$	−12.0732	−	12.0732i	−0.420846	−	0.420846i	−0.885495	+	0.464649i	$0.846181\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	5.37343	−	5.37343i	0.186853	−	0.186853i	−0.607481	−	0.794334i	$-0.707820\pi$
$827$	5.37343	−	5.37343i	0.186853	−	0.186853i	0.794334	+	0.607481i	$0.207820\pi$
$828$		0			0
$829$	−25.2343			−0.876425			−0.438213	−	0.898871i	$-0.644388\pi$
$829$	−25.2343			−0.876425			−0.438213	+	0.898871i	$0.644388\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−13.7741	+	13.7741i	−0.477244	+	0.477244i
$834$		0			0
$835$	−4.85389	+	27.1080i	−0.167976	+	0.938112i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.7466			0.750775			0.375388	−	0.926868i	$-0.377510\pi$
$839$	21.7466			0.750775			0.375388	+	0.926868i	$0.377510\pi$
$840$		0			0
$841$	25.6281			0.883727
$842$		0			0
$843$		0			0
$844$		0			0
$845$	22.1107	−	15.3950i	0.760632	−	0.529606i
$846$		0			0
$847$	1.94456	−	1.94456i	0.0668159	−	0.0668159i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	47.3052			1.62160
$852$		0			0
$853$	−13.0763	+	13.0763i	−0.447723	+	0.447723i	−0.894597	−	0.446874i	$-0.852537\pi$
$853$	−13.0763	+	13.0763i	−0.447723	+	0.447723i	0.446874	+	0.894597i	$0.352537\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	17.8777	+	17.8777i	0.610691	+	0.610691i	0.943126	−	0.332435i	$-0.107870\pi$
$857$	17.8777	+	17.8777i	0.610691	+	0.610691i	−0.332435	+	0.943126i	$0.607870\pi$
$858$		0			0
$859$	26.9017			0.917874			0.458937	−	0.888469i	$-0.348230\pi$
$859$	26.9017			0.917874			0.458937	+	0.888469i	$0.348230\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.00388	+	2.00388i	−0.0682129	+	0.0682129i	−0.740390	−	0.672177i	$-0.765359\pi$
$863$	−2.00388	+	2.00388i	−0.0682129	+	0.0682129i	0.672177	+	0.740390i	$0.265359\pi$
$864$		0			0
$865$	−6.25162	+	34.9141i	−0.212561	+	1.18711i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	12.3887i		−	0.420257i
$870$		0			0
$871$	8.63262			0.292505
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.03761	+	3.46541i	−0.0688839	+	0.117152i
$876$		0			0
$877$	12.9778	+	12.9778i	0.438228	+	0.438228i	0.891415	−	0.453187i	$-0.149713\pi$
$877$	12.9778	+	12.9778i	0.438228	+	0.438228i	−0.453187	+	0.891415i	$0.649713\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			24.4446i			0.823561i	0.911283	+	0.411780i	$0.135093\pi$
$881$			24.4446i			0.823561i	−0.911283	+	0.411780i	$0.864907\pi$
$882$		0			0
$883$	−25.2583	+	25.2583i	−0.850008	+	0.850008i	−0.990134	−	0.140125i	$-0.955249\pi$
$883$	−25.2583	+	25.2583i	−0.850008	+	0.850008i	0.140125	+	0.990134i	$0.455249\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−30.8856	−	30.8856i	−1.03704	−	1.03704i	−0.999287	−	0.0377508i	$-0.987981\pi$
$887$	−30.8856	−	30.8856i	−1.03704	−	1.03704i	−0.0377508	−	0.999287i	$-0.512019\pi$
$888$		0			0
$889$		−	6.10921i		−	0.204896i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.84634	−	5.84634i	−0.195640	−	0.195640i
$894$		0			0
$895$	7.54117	−	5.25069i	0.252073	−	0.175511i
$896$		0			0
$897$		0			0
$898$		0			0
$899$			6.63610i			0.221326i
$900$		0			0
$901$		−	13.4977i		−	0.449673i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.00626738	−	0.00436379i	0.000208335	−	0.000145057i
$906$		0			0
$907$	5.41677	+	5.41677i	0.179861	+	0.179861i	0.791295	−	0.611434i	$-0.209407\pi$
$907$	5.41677	+	5.41677i	0.179861	+	0.179861i	−0.611434	+	0.791295i	$0.709407\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			5.68534i			0.188364i	0.995555	+	0.0941819i	$0.0300235\pi$
$911$			5.68534i			0.188364i	−0.995555	+	0.0941819i	$0.969976\pi$
$912$		0			0
$913$	−1.70839	−	1.70839i	−0.0565394	−	0.0565394i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.41407	+	3.41407i	−0.112743	+	0.112743i
$918$		0			0
$919$			0.556042i			0.0183421i	0.999958	+	0.00917107i	$0.00291928\pi$
$919$			0.556042i			0.0183421i	−0.999958	+	0.00917107i	$0.997081\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.34493	−	1.34493i	−0.0442688	−	0.0442688i
$924$		0			0
$925$	−32.7105	+	15.0429i	−1.07551	+	0.494607i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.82202			−0.158205			−0.0791026	−	0.996866i	$-0.525205\pi$
$929$	−4.82202			−0.158205			−0.0791026	+	0.996866i	$0.525205\pi$
$930$		0			0
$931$		−	32.9076i		−	1.07850i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.04570	+	11.4248i	−0.0669014	+	0.373631i
$936$		0			0
$937$	−21.4658	+	21.4658i	−0.701256	+	0.701256i	−0.964680	−	0.263424i	$-0.915148\pi$
$937$	−21.4658	+	21.4658i	−0.701256	+	0.701256i	0.263424	+	0.964680i	$0.415148\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−44.7844			−1.45993			−0.729965	−	0.683485i	$-0.760464\pi$
$941$	−44.7844			−1.45993			−0.729965	+	0.683485i	$0.760464\pi$
$942$		0			0
$943$	−2.39956	−	2.39956i	−0.0781403	−	0.0781403i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.2492	+	19.2492i	−0.625516	+	0.625516i	−0.946937	−	0.321420i	$-0.895840\pi$
$947$	−19.2492	+	19.2492i	−0.625516	+	0.625516i	0.321420	+	0.946937i	$0.395840\pi$
$948$		0			0
$949$	−9.86744			−0.320311
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−17.3612	+	17.3612i	−0.562383	+	0.562383i	−0.929984	−	0.367600i	$-0.880179\pi$
$953$	−17.3612	+	17.3612i	−0.562383	+	0.562383i	0.367600	+	0.929984i	$0.380179\pi$
$954$		0			0
$955$	28.2594	−	19.6762i	0.914454	−	0.636707i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.77740			−0.121979
$960$		0			0
$961$	−17.9398			−0.578703
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.57107	−	36.6982i	0.211530	−	1.18136i
$966$		0			0
$967$	9.61454	−	9.61454i	0.309183	−	0.309183i	−0.535410	−	0.844592i	$-0.679843\pi$
$967$	9.61454	−	9.61454i	0.309183	−	0.309183i	0.844592	+	0.535410i	$0.179843\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−41.6838			−1.33770			−0.668848	−	0.743399i	$-0.733212\pi$
$971$	−41.6838			−1.33770			−0.668848	+	0.743399i	$0.733212\pi$
$972$		0			0
$973$	1.97795	−	1.97795i	0.0634102	−	0.0634102i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−22.3061	−	22.3061i	−0.713635	−	0.713635i	0.253659	−	0.967294i	$-0.418366\pi$
$977$	−22.3061	−	22.3061i	−0.713635	−	0.713635i	−0.967294	+	0.253659i	$0.918366\pi$
$978$		0			0
$979$	−25.2285			−0.806305
$980$		0			0
$981$		0			0
$982$		0			0
$983$	15.3658	−	15.3658i	0.490093	−	0.490093i	−0.418242	−	0.908336i	$-0.637354\pi$
$983$	15.3658	−	15.3658i	0.490093	−	0.490093i	0.908336	+	0.418242i	$0.137354\pi$
$984$		0			0
$985$	−0.155847	−	0.0279056i	−0.00496571	−	0.000889145i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			39.0246i			1.24091i
$990$		0			0
$991$	−14.1016			−0.447953			−0.223976	−	0.974595i	$-0.571904\pi$
$991$	−14.1016			−0.447953			−0.223976	+	0.974595i	$0.571904\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	38.6037	−	26.8786i	1.22382	−	0.852109i
$996$		0			0
$997$	44.5052	+	44.5052i	1.40949	+	1.40949i	0.762466	+	0.647029i	$0.223989\pi$
$997$	44.5052	+	44.5052i	1.40949	+	1.40949i	0.647029	+	0.762466i	$0.276011\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.bj.f.1313.5	yes	32
3.2	odd	2	inner	2880.2.bj.f.1313.11	yes	32
4.3	odd	2		2880.2.bj.e.1313.6	yes	32
5.2	odd	4		2880.2.bj.e.737.5	✓	32
8.3	odd	2	inner	2880.2.bj.f.1313.12	yes	32
8.5	even	2		2880.2.bj.e.1313.11	yes	32
12.11	even	2		2880.2.bj.e.1313.12	yes	32
15.2	even	4		2880.2.bj.e.737.11	yes	32
20.7	even	4	inner	2880.2.bj.f.737.6	yes	32
24.5	odd	2		2880.2.bj.e.1313.5	yes	32
24.11	even	2	inner	2880.2.bj.f.1313.6	yes	32
40.27	even	4		2880.2.bj.e.737.12	yes	32
40.37	odd	4	inner	2880.2.bj.f.737.11	yes	32
60.47	odd	4	inner	2880.2.bj.f.737.12	yes	32
120.77	even	4	inner	2880.2.bj.f.737.5	yes	32
120.107	odd	4		2880.2.bj.e.737.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2880.2.bj.e.737.5	✓	32	5.2	odd	4
2880.2.bj.e.737.6	yes	32	120.107	odd	4
2880.2.bj.e.737.11	yes	32	15.2	even	4
2880.2.bj.e.737.12	yes	32	40.27	even	4
2880.2.bj.e.1313.5	yes	32	24.5	odd	2
2880.2.bj.e.1313.6	yes	32	4.3	odd	2
2880.2.bj.e.1313.11	yes	32	8.5	even	2
2880.2.bj.e.1313.12	yes	32	12.11	even	2
2880.2.bj.f.737.5	yes	32	120.77	even	4	inner
2880.2.bj.f.737.6	yes	32	20.7	even	4	inner
2880.2.bj.f.737.11	yes	32	40.37	odd	4	inner
2880.2.bj.f.737.12	yes	32	60.47	odd	4	inner
2880.2.bj.f.1313.5	yes	32	1.1	even	1	trivial
2880.2.bj.f.1313.6	yes	32	24.11	even	2	inner
2880.2.bj.f.1313.11	yes	32	3.2	odd	2	inner
2880.2.bj.f.1313.12	yes	32	8.3	odd	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:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27770 - 1.83507i) q^{5} +(-0.254252 + 0.254252i) q^{7} +O(q^{10})\)	\(q+(-1.27770 - 1.83507i) q^{5} +(-0.254252 + 0.254252i) q^{7} -1.83080 q^{11} +(-0.689567 + 0.689567i) q^{13} +(2.00475 + 2.00475i) q^{17} -4.78955 q^{19} +(4.64533 - 4.64533i) q^{23} +(-1.73495 + 4.68935i) q^{25} -1.83628i q^{29} -3.61389 q^{31} +(0.791427 + 0.141711i) q^{35} +(5.09169 + 5.09169i) q^{37} -0.516552i q^{41} +(-4.20041 + 4.20041i) q^{43} +(1.22065 + 1.22065i) q^{47} +6.87071i q^{49} +(-3.36642 - 3.36642i) q^{53} +(2.33922 + 3.35964i) q^{55} +12.6782i q^{59} -2.95560i q^{61} +(2.14647 + 0.384340i) q^{65} +(-6.25944 - 6.25944i) q^{67} +1.95039i q^{71} +(7.15481 + 7.15481i) q^{73} +(0.465483 - 0.465483i) q^{77} +6.76682i q^{79} +(0.933138 + 0.933138i) q^{83} +(1.11738 - 6.24034i) q^{85} +13.7800 q^{89} -0.350647i q^{91} +(6.11963 + 8.78915i) q^{95} +(-7.21384 + 7.21384i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 32 q^{19} - 32 q^{43} + 96 q^{67} + 48 q^{73} + 144 q^{97}+O(q^{100}) \) 32 * q + 32 * q^19 - 32 * q^43 + 96 * q^67 + 48 * q^73 + 144 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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