LMFDB - Embedded newform 2880.2.u.a.719.44

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(719,2880)]

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([2, 1, 2, 2]))

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

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

chi := DirichletCharacter("2880.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.u (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.9969157821$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 720)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			719.44
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18619 + 0.469629i) q^{5} -2.94937i q^{7} +O(q^{10})$	$q+(2.18619 + 0.469629i) q^{5} -2.94937i q^{7} +(-3.81783 - 3.81783i) q^{11} +(-0.772847 - 0.772847i) q^{13} +2.27916 q^{17} +(5.18129 + 5.18129i) q^{19} +2.63370 q^{23} +(4.55890 + 2.05340i) q^{25} +(3.25626 + 3.25626i) q^{29} -1.93666i q^{31} +(1.38511 - 6.44789i) q^{35} +(-2.66367 + 2.66367i) q^{37} -1.01630 q^{41} +(-4.46535 - 4.46535i) q^{43} -6.93871i q^{47} -1.69876 q^{49} +(-9.01752 - 9.01752i) q^{53} +(-6.55356 - 10.1395i) q^{55} +(-2.82309 - 2.82309i) q^{59} +(10.8603 - 10.8603i) q^{61} +(-1.32664 - 2.05255i) q^{65} +(7.21414 - 7.21414i) q^{67} -8.03085i q^{71} -1.58003 q^{73} +(-11.2602 + 11.2602i) q^{77} +0.288222i q^{79} +(-8.90062 - 8.90062i) q^{83} +(4.98270 + 1.07036i) q^{85} +6.44258 q^{89} +(-2.27941 + 2.27941i) q^{91} +(8.89402 + 13.7606i) q^{95} -18.1267i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) $ 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	2.18619	+	0.469629i	0.977696	+	0.210025i
$5$	2.18619	+	0.469629i	0.977696	+	0.210025i
$6$		0			0
$7$		−	2.94937i		−	1.11476i	−0.830259	−	0.557378i	$-0.811807\pi$
$7$		−	2.94937i		−	1.11476i	0.830259	−	0.557378i	$-0.188193\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.81783	−	3.81783i	−1.15112	−	1.15112i	−0.986328	−	0.164792i	$-0.947305\pi$
$11$	−3.81783	−	3.81783i	−1.15112	−	1.15112i	−0.164792	−	0.986328i	$-0.552695\pi$
$12$		0			0
$13$	−0.772847	−	0.772847i	−0.214349	−	0.214349i	0.591763	−	0.806112i	$-0.298432\pi$
$13$	−0.772847	−	0.772847i	−0.214349	−	0.214349i	−0.806112	+	0.591763i	$0.798432\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.27916			0.552778			0.276389	−	0.961046i	$-0.410862\pi$
$17$	2.27916			0.552778			0.276389	+	0.961046i	$0.410862\pi$
$18$		0			0
$19$	5.18129	+	5.18129i	1.18867	+	1.18867i	0.977436	+	0.211233i	$0.0677477\pi$
$19$	5.18129	+	5.18129i	1.18867	+	1.18867i	0.211233	+	0.977436i	$0.432252\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.63370			0.549164			0.274582	−	0.961564i	$-0.411461\pi$
$23$	2.63370			0.549164			0.274582	+	0.961564i	$0.411461\pi$
$24$		0			0
$25$	4.55890	+	2.05340i	0.911779	+	0.410681i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.25626	+	3.25626i	0.604673	+	0.604673i	0.941549	−	0.336876i	$-0.109370\pi$
$29$	3.25626	+	3.25626i	0.604673	+	0.604673i	−0.336876	+	0.941549i	$0.609370\pi$
$30$		0			0
$31$		−	1.93666i		−	0.347835i	−0.984760	−	0.173917i	$-0.944357\pi$
$31$		−	1.93666i		−	0.347835i	0.984760	−	0.173917i	$-0.0556426\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.38511	−	6.44789i	0.234126	−	1.08989i
$36$		0			0
$37$	−2.66367	+	2.66367i	−0.437904	+	0.437904i	−0.891306	−	0.453402i	$-0.850210\pi$
$37$	−2.66367	+	2.66367i	−0.437904	+	0.437904i	0.453402	+	0.891306i	$0.350210\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.01630			−0.158719			−0.0793596	−	0.996846i	$-0.525288\pi$
$41$	−1.01630			−0.158719			−0.0793596	+	0.996846i	$0.525288\pi$
$42$		0			0
$43$	−4.46535	−	4.46535i	−0.680959	−	0.680959i	0.279257	−	0.960216i	$-0.409912\pi$
$43$	−4.46535	−	4.46535i	−0.680959	−	0.680959i	−0.960216	+	0.279257i	$0.909912\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	6.93871i		−	1.01211i	−0.862500	−	0.506057i	$-0.831102\pi$
$47$		−	6.93871i		−	1.01211i	0.862500	−	0.506057i	$-0.168898\pi$
$48$		0			0
$49$	−1.69876			−0.242680
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−9.01752	−	9.01752i	−1.23865	−	1.23865i	−0.960552	−	0.278099i	$-0.910296\pi$
$53$	−9.01752	−	9.01752i	−1.23865	−	1.23865i	−0.278099	−	0.960552i	$-0.589704\pi$
$54$		0			0
$55$	−6.55356	−	10.1395i	−0.883682	−	1.36721i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.82309	−	2.82309i	−0.367536	−	0.367536i	0.499042	−	0.866578i	$-0.333685\pi$
$59$	−2.82309	−	2.82309i	−0.367536	−	0.367536i	−0.866578	+	0.499042i	$0.833685\pi$
$60$		0			0
$61$	10.8603	−	10.8603i	1.39052	−	1.39052i	0.566365	−	0.824154i	$-0.308349\pi$
$61$	10.8603	−	10.8603i	1.39052	−	1.39052i	0.824154	−	0.566365i	$-0.191651\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.32664	−	2.05255i	−0.164550	−	0.254587i
$66$		0			0
$67$	7.21414	−	7.21414i	0.881347	−	0.881347i	−0.112324	−	0.993672i	$-0.535830\pi$
$67$	7.21414	−	7.21414i	0.881347	−	0.881347i	0.993672	+	0.112324i	$0.0358296\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.03085i		−	0.953087i	−0.879151	−	0.476543i	$-0.841890\pi$
$71$		−	8.03085i		−	0.953087i	0.879151	−	0.476543i	$-0.158110\pi$
$72$		0			0
$73$	−1.58003			−0.184929			−0.0924645	−	0.995716i	$-0.529474\pi$
$73$	−1.58003			−0.184929			−0.0924645	+	0.995716i	$0.529474\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.2602	+	11.2602i	−1.28322	+	1.28322i
$78$		0			0
$79$			0.288222i			0.0324275i	0.999869	+	0.0162137i	$0.00516122\pi$
$79$			0.288222i			0.0324275i	−0.999869	+	0.0162137i	$0.994839\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.90062	−	8.90062i	−0.976970	−	0.976970i	0.0227710	−	0.999741i	$-0.492751\pi$
$83$	−8.90062	−	8.90062i	−0.976970	−	0.976970i	−0.999741	+	0.0227710i	$0.992751\pi$
$84$		0			0
$85$	4.98270	+	1.07036i	0.540449	+	0.116097i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.44258			0.682912			0.341456	−	0.939898i	$-0.389080\pi$
$89$	6.44258			0.682912			0.341456	+	0.939898i	$0.389080\pi$
$90$		0			0
$91$	−2.27941	+	2.27941i	−0.238947	+	0.238947i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.89402	+	13.7606i	0.912507	+	1.41181i
$96$		0			0
$97$		−	18.1267i		−	1.84049i	−0.391342	−	0.920245i	$-0.627989\pi$
$97$		−	18.1267i		−	1.84049i	0.391342	−	0.920245i	$-0.372011\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.2655	+	11.2655i	−1.12096	+	1.12096i	−0.129357	+	0.991598i	$0.541291\pi$
$101$	−11.2655	+	11.2655i	−1.12096	+	1.12096i	−0.991598	+	0.129357i	$0.958709\pi$
$102$		0			0
$103$			4.58275i			0.451552i	0.974179	+	0.225776i	$0.0724918\pi$
$103$			4.58275i			0.451552i	−0.974179	+	0.225776i	$0.927508\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.70168	+	2.70168i	−0.261181	+	0.261181i	−0.825534	−	0.564353i	$-0.809126\pi$
$107$	−2.70168	+	2.70168i	−0.261181	+	0.261181i	0.564353	+	0.825534i	$0.309126\pi$
$108$		0			0
$109$	5.05700	−	5.05700i	0.484372	−	0.484372i	−0.422152	−	0.906525i	$-0.638725\pi$
$109$	5.05700	−	5.05700i	0.484372	−	0.484372i	0.906525	+	0.422152i	$0.138725\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.0909			−1.04334			−0.521672	−	0.853146i	$-0.674691\pi$
$113$	−11.0909			−1.04334			−0.521672	+	0.853146i	$0.674691\pi$
$114$		0			0
$115$	5.75778	+	1.23686i	0.536915	+	0.115338i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	6.72209i		−	0.616213i
$120$		0			0
$121$			18.1517i			1.65016i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.00230	+	6.63013i	0.805190	+	0.593017i
$126$		0			0
$127$	10.4288			0.925403			0.462701	−	0.886514i	$-0.346880\pi$
$127$	10.4288			0.925403			0.462701	+	0.886514i	$0.346880\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.5532	+	13.5532i	−1.18415	+	1.18415i	−0.205491	+	0.978659i	$0.565879\pi$
$131$	−13.5532	+	13.5532i	−1.18415	+	1.18415i	−0.978659	+	0.205491i	$0.934121\pi$
$132$		0			0
$133$	15.2815	−	15.2815i	1.32507	−	1.32507i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	7.61130i		−	0.650278i	−0.945666	−	0.325139i	$-0.894589\pi$
$137$		−	7.61130i		−	0.650278i	0.945666	−	0.325139i	$-0.105411\pi$
$138$		0			0
$139$	−1.68008	+	1.68008i	−0.142502	+	0.142502i	−0.774759	−	0.632257i	$-0.782129\pi$
$139$	−1.68008	+	1.68008i	−0.142502	+	0.142502i	0.632257	+	0.774759i	$0.282129\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			5.90120i			0.493484i
$144$		0			0
$145$	5.58959	+	8.64807i	0.464190	+	0.718183i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	13.1900	−	13.1900i	1.08057	−	1.08057i	0.0841097	−	0.996456i	$-0.473195\pi$
$149$	13.1900	−	13.1900i	1.08057	−	1.08057i	0.996456	−	0.0841097i	$-0.0268046\pi$
$150$		0			0
$151$	14.8005			1.20444			0.602222	−	0.798329i	$-0.294282\pi$
$151$	14.8005			1.20444			0.602222	+	0.798329i	$0.294282\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.909513	−	4.23392i	0.0730539	−	0.340077i
$156$		0			0
$157$	10.2112	+	10.2112i	0.814942	+	0.814942i	0.985370	−	0.170428i	$-0.0545151\pi$
$157$	10.2112	+	10.2112i	0.814942	+	0.814942i	−0.170428	+	0.985370i	$0.554515\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	7.76774i		−	0.612184i
$162$		0			0
$163$	−11.3893	+	11.3893i	−0.892077	+	0.892077i	−0.994718	−	0.102641i	$-0.967271\pi$
$163$	−11.3893	+	11.3893i	−0.892077	+	0.892077i	0.102641	+	0.994718i	$0.467271\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.0783			−0.779880			−0.389940	−	0.920840i	$-0.627504\pi$
$167$	−10.0783			−0.779880			−0.389940	+	0.920840i	$0.627504\pi$
$168$		0			0
$169$		−	11.8054i		−	0.908109i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.02442	+	9.02442i	−0.686114	+	0.686114i	−0.961371	−	0.275257i	$-0.911237\pi$
$173$	−9.02442	+	9.02442i	−0.686114	+	0.686114i	0.275257	+	0.961371i	$0.411237\pi$
$174$		0			0
$175$	6.05624	−	13.4459i	0.457809	−	1.01641i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.3226	+	10.3226i	−0.771547	+	0.771547i	−0.978377	−	0.206830i	$-0.933685\pi$
$179$	−10.3226	+	10.3226i	−0.771547	+	0.771547i	0.206830	+	0.978377i	$0.433685\pi$
$180$		0			0
$181$	13.9184	+	13.9184i	1.03455	+	1.03455i	0.999381	+	0.0351674i	$0.0111964\pi$
$181$	13.9184	+	13.9184i	1.03455	+	1.03455i	0.0351674	+	0.999381i	$0.488804\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.07423	+	4.57236i	−0.520108	+	0.336167i
$186$		0			0
$187$	−8.70147	−	8.70147i	−0.636314	−	0.636314i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.3885			0.896403			0.448202	−	0.893932i	$-0.352065\pi$
$191$	12.3885			0.896403			0.448202	+	0.893932i	$0.352065\pi$
$192$		0			0
$193$		−	23.2784i		−	1.67562i	−0.545965	−	0.837808i	$-0.683837\pi$
$193$		−	23.2784i		−	1.67562i	0.545965	−	0.837808i	$-0.316163\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.494769	+	0.494769i	0.0352508	+	0.0352508i	0.724513	−	0.689262i	$-0.242065\pi$
$197$	0.494769	+	0.494769i	0.0352508	+	0.0352508i	−0.689262	+	0.724513i	$0.742065\pi$
$198$		0			0
$199$	−2.97860			−0.211147			−0.105574	−	0.994411i	$-0.533668\pi$
$199$	−2.97860			−0.211147			−0.105574	+	0.994411i	$0.533668\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	9.60392	−	9.60392i	0.674063	−	0.674063i
$204$		0			0
$205$	−2.22183	−	0.477284i	−0.155179	−	0.0333349i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	39.5626i		−	2.73660i
$210$		0			0
$211$	9.97252	+	9.97252i	0.686537	+	0.686537i	0.961465	−	0.274928i	$-0.0886540\pi$
$211$	9.97252	+	9.97252i	0.686537	+	0.686537i	−0.274928	+	0.961465i	$0.588654\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−7.66506	−	11.8592i	−0.522753	−	0.808790i
$216$		0			0
$217$	−5.71192			−0.387751
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.76144	−	1.76144i	−0.118488	−	0.118488i
$222$		0			0
$223$	1.35577			0.0907889			0.0453945	−	0.998969i	$-0.485546\pi$
$223$	1.35577			0.0907889			0.0453945	+	0.998969i	$0.485546\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.282506	+	0.282506i	0.0187506	+	0.0187506i	0.716420	−	0.697669i	$-0.245780\pi$
$227$	0.282506	+	0.282506i	0.0187506	+	0.0187506i	−0.697669	+	0.716420i	$0.745780\pi$
$228$		0			0
$229$	3.61973	+	3.61973i	0.239199	+	0.239199i	0.816518	−	0.577320i	$-0.195901\pi$
$229$	3.61973	+	3.61973i	0.239199	+	0.239199i	−0.577320	+	0.816518i	$0.695901\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	19.3142i		−	1.26531i	−0.774432	−	0.632657i	$-0.781964\pi$
$233$		−	19.3142i		−	1.26531i	0.774432	−	0.632657i	$-0.218036\pi$
$234$		0			0
$235$	3.25862	−	15.1694i	0.212569	−	0.989540i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	12.7616			0.825481			0.412740	−	0.910849i	$-0.364572\pi$
$239$	12.7616			0.825481			0.412740	+	0.910849i	$0.364572\pi$
$240$		0			0
$241$	−9.03963			−0.582294			−0.291147	−	0.956678i	$-0.594037\pi$
$241$	−9.03963			−0.582294			−0.291147	+	0.956678i	$0.594037\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.71382	−	0.797788i	−0.237267	−	0.0509688i
$246$		0			0
$247$		−	8.00868i		−	0.509580i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.63101	+	7.63101i	0.481665	+	0.481665i	0.905663	−	0.423998i	$-0.139374\pi$
$251$	7.63101	+	7.63101i	0.481665	+	0.481665i	−0.423998	+	0.905663i	$0.639374\pi$
$252$		0			0
$253$	−10.0550	−	10.0550i	−0.632154	−	0.632154i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.14111			0.570207			0.285103	−	0.958497i	$-0.407972\pi$
$257$	9.14111			0.570207			0.285103	+	0.958497i	$0.407972\pi$
$258$		0			0
$259$	7.85613	+	7.85613i	0.488156	+	0.488156i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.35127			0.329974			0.164987	−	0.986296i	$-0.447242\pi$
$263$	5.35127			0.329974			0.164987	+	0.986296i	$0.447242\pi$
$264$		0			0
$265$	−15.4792	−	23.9489i	−0.950877	−	1.47117i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	17.5132	+	17.5132i	1.06780	+	1.06780i	0.997528	+	0.0702731i	$0.0223871\pi$
$269$	17.5132	+	17.5132i	1.06780	+	1.06780i	0.0702731	+	0.997528i	$0.477613\pi$
$270$		0			0
$271$			14.8401i			0.901471i	0.892657	+	0.450736i	$0.148838\pi$
$271$			14.8401i			0.901471i	−0.892657	+	0.450736i	$0.851162\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.56556	−	25.2447i	−0.576825	−	1.52231i
$276$		0			0
$277$	−9.59587	+	9.59587i	−0.576560	+	0.576560i	−0.933954	−	0.357394i	$-0.883665\pi$
$277$	−9.59587	+	9.59587i	−0.576560	+	0.576560i	0.357394	+	0.933954i	$0.383665\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−24.1743			−1.44212			−0.721059	−	0.692874i	$-0.756344\pi$
$281$	−24.1743			−1.44212			−0.721059	+	0.692874i	$0.756344\pi$
$282$		0			0
$283$	22.5338	+	22.5338i	1.33950	+	1.33950i	0.896546	+	0.442950i	$0.146068\pi$
$283$	22.5338	+	22.5338i	1.33950	+	1.33950i	0.442950	+	0.896546i	$0.353932\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			2.99744i			0.176933i
$288$		0			0
$289$	−11.8054			−0.694436
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.21485	−	2.21485i	−0.129393	−	0.129393i	0.639445	−	0.768837i	$-0.279164\pi$
$293$	−2.21485	−	2.21485i	−0.129393	−	0.129393i	−0.768837	+	0.639445i	$0.779164\pi$
$294$		0			0
$295$	−4.84603	−	7.49764i	−0.282147	−	0.436530i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.03545	−	2.03545i	−0.117713	−	0.117713i
$300$		0			0
$301$	−13.1699	+	13.1699i	−0.759103	+	0.759103i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	28.8431	−	18.6424i	1.65155	−	1.06746i
$306$		0			0
$307$	−12.5025	+	12.5025i	−0.713556	+	0.713556i	−0.967277	−	0.253722i	$-0.918345\pi$
$307$	−12.5025	+	12.5025i	−0.713556	+	0.713556i	0.253722	+	0.967277i	$0.418345\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		−	3.75997i		−	0.213209i	−0.994302	−	0.106604i	$-0.966002\pi$
$311$		−	3.75997i		−	0.213209i	0.994302	−	0.106604i	$-0.0339978\pi$
$312$		0			0
$313$	6.19979			0.350433			0.175216	−	0.984530i	$-0.443938\pi$
$313$	6.19979			0.350433			0.175216	+	0.984530i	$0.443938\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.6244	−	13.6244i	0.765221	−	0.765221i	−0.212040	−	0.977261i	$-0.568011\pi$
$317$	13.6244	−	13.6244i	0.765221	−	0.765221i	0.977261	+	0.212040i	$0.0680108\pi$
$318$		0			0
$319$		−	24.8638i		−	1.39210i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	11.8090	+	11.8090i	0.657070	+	0.657070i
$324$		0			0
$325$	−1.93636	−	5.11030i	−0.107410	−	0.283468i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.4648			−1.12826
$330$		0			0
$331$	−11.4420	+	11.4420i	−0.628910	+	0.628910i	−0.947794	−	0.318884i	$-0.896692\pi$
$331$	−11.4420	+	11.4420i	−0.628910	+	0.628910i	0.318884	+	0.947794i	$0.396692\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	19.1595	−	12.3835i	1.04679	−	0.676585i
$336$		0			0
$337$		−	9.70392i		−	0.528606i	−0.964440	−	0.264303i	$-0.914858\pi$
$337$		−	9.70392i		−	0.528606i	0.964440	−	0.264303i	$-0.0851419\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.39385	+	7.39385i	−0.400400	+	0.400400i
$342$		0			0
$343$		−	15.6353i		−	0.844227i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.6678	+	16.6678i	−0.894776	+	0.894776i	−0.994968	−	0.100192i	$-0.968054\pi$
$347$	−16.6678	+	16.6678i	−0.894776	+	0.894776i	0.100192	+	0.994968i	$0.468054\pi$
$348$		0			0
$349$	0.985320	−	0.985320i	0.0527430	−	0.0527430i	−0.680243	−	0.732986i	$-0.738126\pi$
$349$	0.985320	−	0.985320i	0.0527430	−	0.0527430i	0.732986	+	0.680243i	$0.238126\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.6331			0.991742			0.495871	−	0.868396i	$-0.334849\pi$
$353$	18.6331			0.991742			0.495871	+	0.868396i	$0.334849\pi$
$354$		0			0
$355$	3.77152	−	17.5570i	0.200172	−	0.931829i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			15.6789i			0.827503i	0.910390	+	0.413751i	$0.135782\pi$
$359$			15.6789i			0.827503i	−0.910390	+	0.413751i	$0.864218\pi$
$360$		0			0
$361$			34.6914i			1.82586i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.45426	−	0.742031i	−0.180804	−	0.0388397i
$366$		0			0
$367$	24.8012			1.29461			0.647305	−	0.762231i	$-0.275896\pi$
$367$	24.8012			1.29461			0.647305	+	0.762231i	$0.275896\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−26.5960	+	26.5960i	−1.38079	+	1.38079i
$372$		0			0
$373$	−7.99818	+	7.99818i	−0.414130	+	0.414130i	−0.883175	−	0.469045i	$-0.844598\pi$
$373$	−7.99818	+	7.99818i	−0.414130	+	0.414130i	0.469045	+	0.883175i	$0.344598\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	5.03319i		−	0.259222i
$378$		0			0
$379$	5.54375	−	5.54375i	0.284763	−	0.284763i	−0.550242	−	0.835005i	$-0.685464\pi$
$379$	5.54375	−	5.54375i	0.284763	−	0.284763i	0.835005	+	0.550242i	$0.185464\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			35.2874i			1.80310i	0.432675	+	0.901550i	$0.357570\pi$
$383$			35.2874i			1.80310i	−0.432675	+	0.901550i	$0.642430\pi$
$384$		0			0
$385$	−29.9051	+	19.3289i	−1.52410	+	0.985090i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.5078	+	10.5078i	−0.532767	+	0.532767i	−0.921395	−	0.388628i	$-0.872949\pi$
$389$	−10.5078	+	10.5078i	−0.532767	+	0.532767i	0.388628	+	0.921395i	$0.372949\pi$
$390$		0			0
$391$	6.00263			0.303566
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.135357	+	0.630109i	−0.00681057	+	0.0317042i
$396$		0			0
$397$	10.4175	+	10.4175i	0.522838	+	0.522838i	0.918427	−	0.395589i	$-0.129460\pi$
$397$	10.4175	+	10.4175i	0.522838	+	0.522838i	−0.395589	+	0.918427i	$0.629460\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			15.4212i			0.770099i	0.922896	+	0.385049i	$0.125816\pi$
$401$			15.4212i			0.770099i	−0.922896	+	0.385049i	$0.874184\pi$
$402$		0			0
$403$	−1.49674	+	1.49674i	−0.0745581	+	0.0745581i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.3389			1.00816
$408$		0			0
$409$			5.10228i			0.252291i	0.992012	+	0.126146i	$0.0402607\pi$
$409$			5.10228i			0.252291i	−0.992012	+	0.126146i	$0.959739\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.32634	+	8.32634i	−0.409712	+	0.409712i
$414$		0			0
$415$	−15.2785	−	23.6385i	−0.749992	−	1.16037i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.0584508	−	0.0584508i	0.00285551	−	0.00285551i	−0.705678	−	0.708533i	$-0.749357\pi$
$419$	0.0584508	−	0.0584508i	0.00285551	−	0.00285551i	0.708533	+	0.705678i	$0.249357\pi$
$420$		0			0
$421$	−6.66123	−	6.66123i	−0.324648	−	0.324648i	0.525899	−	0.850547i	$-0.323729\pi$
$421$	−6.66123	−	6.66123i	−0.324648	−	0.324648i	−0.850547	+	0.525899i	$0.823729\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.3905	+	4.68004i	0.504012	+	0.227015i
$426$		0			0
$427$	−32.0310	−	32.0310i	−1.55009	−	1.55009i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.3929			−0.596946			−0.298473	−	0.954418i	$-0.596477\pi$
$431$	−12.3929			−0.596946			−0.298473	+	0.954418i	$0.596477\pi$
$432$		0			0
$433$		−	6.31623i		−	0.303539i	−0.988416	−	0.151769i	$-0.951503\pi$
$433$		−	6.31623i		−	0.303539i	0.988416	−	0.151769i	$-0.0484971\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.6459	+	13.6459i	0.652774	+	0.652774i
$438$		0			0
$439$	5.22876			0.249555			0.124778	−	0.992185i	$-0.460178\pi$
$439$	5.22876			0.249555			0.124778	+	0.992185i	$0.460178\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.30848	−	4.30848i	0.204702	−	0.204702i	−0.597309	−	0.802011i	$-0.703763\pi$
$443$	4.30848	−	4.30848i	0.204702	−	0.204702i	0.802011	+	0.597309i	$0.203763\pi$
$444$		0			0
$445$	14.0847	+	3.02562i	0.667680	+	0.143428i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.8023i			1.07611i	0.842911	+	0.538053i	$0.180840\pi$
$449$			22.8023i			1.07611i	−0.842911	+	0.538053i	$0.819160\pi$
$450$		0			0
$451$	3.88006	+	3.88006i	0.182705	+	0.182705i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.05371	+	3.91276i	−0.283802	+	0.183433i
$456$		0			0
$457$	23.8294			1.11469			0.557345	−	0.830281i	$-0.311820\pi$
$457$	23.8294			1.11469			0.557345	+	0.830281i	$0.311820\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.75855	+	7.75855i	0.361352	+	0.361352i	0.864310	−	0.502959i	$-0.167755\pi$
$461$	7.75855	+	7.75855i	0.361352	+	0.361352i	−0.502959	+	0.864310i	$0.667755\pi$
$462$		0			0
$463$	−9.96705			−0.463208			−0.231604	−	0.972810i	$-0.574397\pi$
$463$	−9.96705			−0.463208			−0.231604	+	0.972810i	$0.574397\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.6782	−	25.6782i	−1.18824	−	1.18824i	−0.977553	−	0.210692i	$-0.932428\pi$
$467$	−25.6782	−	25.6782i	−1.18824	−	1.18824i	−0.210692	−	0.977553i	$-0.567572\pi$
$468$		0			0
$469$	−21.2771	−	21.2771i	−0.982487	−	0.982487i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			34.0959i			1.56773i
$474$		0			0
$475$	12.9817	+	34.2602i	0.595640	+	1.57197i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	19.8901			0.908803			0.454402	−	0.890797i	$-0.349853\pi$
$479$	19.8901			0.908803			0.454402	+	0.890797i	$0.349853\pi$
$480$		0			0
$481$	4.11722			0.187729
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.51284	−	39.6286i	0.386548	−	1.79944i
$486$		0			0
$487$			24.3871i			1.10508i	0.833485	+	0.552541i	$0.186342\pi$
$487$			24.3871i			1.10508i	−0.833485	+	0.552541i	$0.813658\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−16.7013	−	16.7013i	−0.753719	−	0.753719i	0.221452	−	0.975171i	$-0.428920\pi$
$491$	−16.7013	−	16.7013i	−0.753719	−	0.753719i	−0.975171	+	0.221452i	$0.928920\pi$
$492$		0			0
$493$	7.42156	+	7.42156i	0.334250	+	0.334250i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−23.6859			−1.06246
$498$		0			0
$499$	−6.16191	−	6.16191i	−0.275845	−	0.275845i	0.555603	−	0.831448i	$-0.312488\pi$
$499$	−6.16191	−	6.16191i	−0.275845	−	0.275845i	−0.831448	+	0.555603i	$0.812488\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	15.6520			0.697889			0.348945	−	0.937143i	$-0.386540\pi$
$503$	15.6520			0.697889			0.348945	+	0.937143i	$0.386540\pi$
$504$		0			0
$505$	−29.9191	+	19.3379i	−1.33138	+	0.860525i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.0382	−	13.0382i	−0.577908	−	0.577908i	0.356418	−	0.934326i	$-0.383998\pi$
$509$	−13.0382	−	13.0382i	−0.577908	−	0.577908i	−0.934326	+	0.356418i	$0.883998\pi$
$510$		0			0
$511$			4.66010i			0.206151i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.15220	+	10.0188i	−0.0948371	+	0.441481i
$516$		0			0
$517$	−26.4908	+	26.4908i	−1.16507	+	1.16507i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−11.6740			−0.511445			−0.255723	−	0.966750i	$-0.582313\pi$
$521$	−11.6740			−0.511445			−0.255723	+	0.966750i	$0.582313\pi$
$522$		0			0
$523$	12.7738	+	12.7738i	0.558559	+	0.558559i	0.928897	−	0.370338i	$-0.120758\pi$
$523$	12.7738	+	12.7738i	0.558559	+	0.558559i	−0.370338	+	0.928897i	$0.620758\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	4.41397i		−	0.192275i
$528$		0			0
$529$	−16.0636			−0.698419
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.785444	+	0.785444i	0.0340213	+	0.0340213i
$534$		0			0
$535$	−7.17518	+	4.63761i	−0.310210	+	0.200501i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.48559	+	6.48559i	0.279354	+	0.279354i
$540$		0			0
$541$	23.1601	−	23.1601i	0.995729	−	0.995729i	−0.00426226	−	0.999991i	$-0.501357\pi$
$541$	23.1601	−	23.1601i	0.995729	−	0.995729i	0.999991	+	0.00426226i	$0.00135673\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.4305	−	8.68066i	0.575299	−	0.371839i
$546$		0			0
$547$	−32.6697	+	32.6697i	−1.39686	+	1.39686i	−0.587983	+	0.808873i	$0.700078\pi$
$547$	−32.6697	+	32.6697i	−1.39686	+	1.39686i	−0.808873	+	0.587983i	$0.799922\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			33.7433i			1.43751i
$552$		0			0
$553$	0.850072			0.0361487
$554$		0			0
$555$		0			0
$556$		0			0
$557$	27.6869	−	27.6869i	1.17313	−	1.17313i	0.191673	−	0.981459i	$-0.438609\pi$
$557$	27.6869	−	27.6869i	1.17313	−	1.17313i	0.981459	−	0.191673i	$-0.0613912\pi$
$558$		0			0
$559$			6.90206i			0.291926i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	12.9042	+	12.9042i	0.543845	+	0.543845i	0.924654	−	0.380809i	$-0.124354\pi$
$563$	12.9042	+	12.9042i	0.543845	+	0.543845i	−0.380809	+	0.924654i	$0.624354\pi$
$564$		0			0
$565$	−24.2469	−	5.20861i	−1.02007	−	0.219128i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	39.4363			1.65326			0.826628	−	0.562749i	$-0.190256\pi$
$569$	39.4363			1.65326			0.826628	+	0.562749i	$0.190256\pi$
$570$		0			0
$571$	1.54757	−	1.54757i	0.0647637	−	0.0647637i	−0.673983	−	0.738747i	$-0.735418\pi$
$571$	1.54757	−	1.54757i	0.0647637	−	0.0647637i	0.738747	+	0.673983i	$0.235418\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.0068	+	5.40804i	0.500716	+	0.225531i
$576$		0			0
$577$			26.5133i			1.10376i	0.833923	+	0.551881i	$0.186090\pi$
$577$			26.5133i			1.10376i	−0.833923	+	0.551881i	$0.813910\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−26.2512	+	26.2512i	−1.08908	+	1.08908i
$582$		0			0
$583$			68.8548i			2.85167i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.43417	+	4.43417i	−0.183018	+	0.183018i	−0.792669	−	0.609652i	$-0.791309\pi$
$587$	−4.43417	+	4.43417i	−0.183018	+	0.183018i	0.609652	+	0.792669i	$0.291309\pi$
$588$		0			0
$589$	10.0344	−	10.0344i	0.413460	−	0.413460i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.0418			0.823019			0.411510	−	0.911405i	$-0.365002\pi$
$593$	20.0418			0.823019			0.411510	+	0.911405i	$0.365002\pi$
$594$		0			0
$595$	3.15689	−	14.6958i	0.129420	−	0.602469i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	30.5731i		−	1.24918i	−0.780951	−	0.624592i	$-0.785265\pi$
$599$		−	30.5731i		−	1.24918i	0.780951	−	0.624592i	$-0.214735\pi$
$600$		0			0
$601$		−	36.4715i		−	1.48770i	−0.668344	−	0.743852i	$-0.732997\pi$
$601$		−	36.4715i		−	1.48770i	0.668344	−	0.743852i	$-0.267003\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.52458	+	39.6832i	−0.346573	+	1.61335i
$606$		0			0
$607$	18.5659			0.753566			0.376783	−	0.926302i	$-0.377030\pi$
$607$	18.5659			0.753566			0.376783	+	0.926302i	$0.377030\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−5.36256	+	5.36256i	−0.216946	+	0.216946i
$612$		0			0
$613$	17.3170	−	17.3170i	0.699425	−	0.699425i	−0.264861	−	0.964286i	$-0.585326\pi$
$613$	17.3170	−	17.3170i	0.699425	−	0.699425i	0.964286	+	0.264861i	$0.0853262\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			1.18526i			0.0477167i	0.999715	+	0.0238584i	$0.00759508\pi$
$617$			1.18526i			0.0477167i	−0.999715	+	0.0238584i	$0.992405\pi$
$618$		0			0
$619$	0.522478	−	0.522478i	0.0210002	−	0.0210002i	−0.696529	−	0.717529i	$-0.745273\pi$
$619$	0.522478	−	0.522478i	0.0210002	−	0.0210002i	0.717529	+	0.696529i	$0.245273\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	19.0015i		−	0.761280i
$624$		0			0
$625$	16.5671	+	18.7225i	0.662683	+	0.748900i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.07093	+	6.07093i	−0.242064	+	0.242064i
$630$		0			0
$631$	−33.4437			−1.33137			−0.665687	−	0.746231i	$-0.731861\pi$
$631$	−33.4437			−1.33137			−0.665687	+	0.746231i	$0.731861\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	22.7993	+	4.89765i	0.904763	+	0.194357i
$636$		0			0
$637$	1.31288	+	1.31288i	0.0520183	+	0.0520183i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	0.0475126i		−	0.00187664i	−1.00000		0.000938318i	$-0.999701\pi$
$641$		−	0.0475126i		−	0.00187664i	1.00000		0.000938318i	$-0.000298676\pi$
$642$		0			0
$643$	−6.27347	+	6.27347i	−0.247402	+	0.247402i	−0.819903	−	0.572502i	$-0.805973\pi$
$643$	−6.27347	+	6.27347i	−0.247402	+	0.247402i	0.572502	+	0.819903i	$0.305973\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	30.1491			1.18529			0.592643	−	0.805465i	$-0.298085\pi$
$647$	30.1491			1.18529			0.592643	+	0.805465i	$0.298085\pi$
$648$		0			0
$649$			21.5562i			0.846155i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.4196	+	19.4196i	−0.759947	+	0.759947i	−0.976312	−	0.216365i	$-0.930580\pi$
$653$	−19.4196	+	19.4196i	−0.759947	+	0.759947i	0.216365	+	0.976312i	$0.430580\pi$
$654$		0			0
$655$	−35.9950	+	23.2650i	−1.40644	+	0.909038i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	29.1034	−	29.1034i	1.13371	−	1.13371i	0.144153	−	0.989555i	$-0.453954\pi$
$659$	29.1034	−	29.1034i	1.13371	−	1.13371i	0.989555	−	0.144153i	$-0.0460457\pi$
$660$		0			0
$661$	27.9971	+	27.9971i	1.08896	+	1.08896i	0.995636	+	0.0933236i	$0.0297491\pi$
$661$	27.9971	+	27.9971i	1.08896	+	1.08896i	0.0933236	+	0.995636i	$0.470251\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	40.5850	−	26.2317i	1.57382	−	1.01722i
$666$		0			0
$667$	8.57602	+	8.57602i	0.332065	+	0.332065i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−82.9257			−3.20131
$672$		0			0
$673$			24.1910i			0.932495i	0.884654	+	0.466248i	$0.154394\pi$
$673$			24.1910i			0.932495i	−0.884654	+	0.466248i	$0.845606\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	22.7749	+	22.7749i	0.875311	+	0.875311i	0.993045	−	0.117734i	$-0.0375631\pi$
$677$	22.7749	+	22.7749i	0.875311	+	0.875311i	−0.117734	+	0.993045i	$0.537563\pi$
$678$		0			0
$679$	−53.4624			−2.05170
$680$		0			0
$681$		0			0
$682$		0			0
$683$	11.1813	−	11.1813i	0.427842	−	0.427842i	−0.460051	−	0.887893i	$-0.652169\pi$
$683$	11.1813	−	11.1813i	0.427842	−	0.427842i	0.887893	+	0.460051i	$0.152169\pi$
$684$		0			0
$685$	3.57449	−	16.6398i	0.136574	−	0.635774i
$686$		0			0
$687$		0			0
$688$		0			0
$689$			13.9383i			0.531008i
$690$		0			0
$691$	30.4888	+	30.4888i	1.15985	+	1.15985i	0.984507	+	0.175343i	$0.0561035\pi$
$691$	30.4888	+	30.4888i	1.15985	+	1.15985i	0.175343	+	0.984507i	$0.443897\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.46199	+	2.88397i	−0.169253	+	0.109395i
$696$		0			0
$697$	−2.31631			−0.0877365
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.1167	−	10.1167i	−0.382102	−	0.382102i	0.489757	−	0.871859i	$-0.337086\pi$
$701$	−10.1167	−	10.1167i	−0.382102	−	0.382102i	−0.871859	+	0.489757i	$0.837086\pi$
$702$		0			0
$703$	−27.6024			−1.04105
$704$		0			0
$705$		0			0
$706$		0			0
$707$	33.2260	+	33.2260i	1.24959	+	1.24959i
$708$		0			0
$709$	10.9333	+	10.9333i	0.410608	+	0.410608i	0.881950	−	0.471342i	$-0.156230\pi$
$709$	10.9333	+	10.9333i	0.410608	+	0.410608i	−0.471342	+	0.881950i	$0.656230\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	5.10058i		−	0.191018i
$714$		0			0
$715$	−2.77138	+	12.9012i	−0.103644	+	0.482477i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	17.0081			0.634295			0.317148	−	0.948376i	$-0.397275\pi$
$719$	17.0081			0.634295			0.317148	+	0.948376i	$0.397275\pi$
$720$		0			0
$721$	13.5162			0.503370
$722$		0			0
$723$		0			0
$724$		0			0
$725$	8.15855	+	21.5314i	0.303001	+	0.799656i
$726$		0			0
$727$		−	9.36040i		−	0.347158i	−0.984820	−	0.173579i	$-0.944467\pi$
$727$		−	9.36040i		−	0.347158i	0.984820	−	0.173579i	$-0.0555332\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.1773	−	10.1773i	−0.376420	−	0.376420i
$732$		0			0
$733$	0.534164	+	0.534164i	0.0197298	+	0.0197298i	0.716903	−	0.697173i	$-0.245559\pi$
$733$	0.534164	+	0.534164i	0.0197298	+	0.0197298i	−0.697173	+	0.716903i	$0.745559\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−55.0848			−2.02907
$738$		0			0
$739$	−29.8329	−	29.8329i	−1.09742	−	1.09742i	−0.994712	−	0.102708i	$-0.967249\pi$
$739$	−29.8329	−	29.8329i	−1.09742	−	1.09742i	−0.102708	−	0.994712i	$-0.532751\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	18.5297			0.679788			0.339894	−	0.940464i	$-0.389609\pi$
$743$	18.5297			0.679788			0.339894	+	0.940464i	$0.389609\pi$
$744$		0			0
$745$	35.0303	−	22.6415i	1.28341	−	0.829520i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.96824	+	7.96824i	0.291153	+	0.291153i
$750$		0			0
$751$		−	14.3204i		−	0.522560i	−0.965263	−	0.261280i	$-0.915855\pi$
$751$		−	14.3204i		−	0.522560i	0.965263	−	0.261280i	$-0.0841446\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	32.3567	+	6.95073i	1.17758	+	0.252963i
$756$		0			0
$757$	−19.9592	+	19.9592i	−0.725431	+	0.725431i	−0.969706	−	0.244275i	$-0.921450\pi$
$757$	−19.9592	+	19.9592i	−0.725431	+	0.725431i	0.244275	+	0.969706i	$0.421450\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−44.8390			−1.62541			−0.812706	−	0.582674i	$-0.802006\pi$
$761$	−44.8390			−1.62541			−0.812706	+	0.582674i	$0.802006\pi$
$762$		0			0
$763$	−14.9149	−	14.9149i	−0.539957	−	0.539957i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			4.36364i			0.157562i
$768$		0			0
$769$	7.94970			0.286673			0.143337	−	0.989674i	$-0.454217\pi$
$769$	7.94970			0.286673			0.143337	+	0.989674i	$0.454217\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−6.73346	−	6.73346i	−0.242186	−	0.242186i	0.575568	−	0.817754i	$-0.304781\pi$
$773$	−6.73346	−	6.73346i	−0.242186	−	0.242186i	−0.817754	+	0.575568i	$0.804781\pi$
$774$		0			0
$775$	3.97675	−	8.82904i	0.142849	−	0.317148i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.26573	−	5.26573i	−0.188664	−	0.188664i
$780$		0			0
$781$	−30.6605	+	30.6605i	−1.09712	+	1.09712i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	17.5282	+	27.1191i	0.625608	+	0.967923i
$786$		0			0
$787$	2.03543	−	2.03543i	0.0725554	−	0.0725554i	−0.669898	−	0.742453i	$-0.733662\pi$
$787$	2.03543	−	2.03543i	0.0725554	−	0.0725554i	0.742453	+	0.669898i	$0.233662\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			32.7111i			1.16307i
$792$		0			0
$793$	−16.7867			−0.596114
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.7768	+	14.7768i	−0.523422	+	0.523422i	−0.918603	−	0.395181i	$-0.870682\pi$
$797$	−14.7768	+	14.7768i	−0.523422	+	0.523422i	0.395181	+	0.918603i	$0.370682\pi$
$798$		0			0
$799$		−	15.8144i		−	0.559475i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.03231	+	6.03231i	0.212876	+	0.212876i
$804$		0			0
$805$	3.64796	−	16.9818i	0.128574	−	0.598530i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.77033			−0.238032			−0.119016	−	0.992892i	$-0.537974\pi$
$809$	−6.77033			−0.238032			−0.119016	+	0.992892i	$0.537974\pi$
$810$		0			0
$811$	18.8412	−	18.8412i	0.661604	−	0.661604i	−0.294154	−	0.955758i	$-0.595038\pi$
$811$	18.8412	−	18.8412i	0.661604	−	0.661604i	0.955758	+	0.294154i	$0.0950378\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−30.2479	+	19.5504i	−1.05954	+	0.684822i
$816$		0			0
$817$		−	46.2725i		−	1.61887i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.33164	+	4.33164i	−0.151175	+	0.151175i	−0.778643	−	0.627467i	$-0.784092\pi$
$821$	−4.33164	+	4.33164i	−0.151175	+	0.151175i	0.627467	+	0.778643i	$0.284092\pi$
$822$		0			0
$823$		−	22.3521i		−	0.779144i	−0.920996	−	0.389572i	$-0.872623\pi$
$823$		−	22.3521i		−	0.779144i	0.920996	−	0.389572i	$-0.127377\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.1708	−	33.1708i	1.15346	−	1.15346i	0.167609	−	0.985854i	$-0.446395\pi$
$827$	33.1708	−	33.1708i	1.15346	−	1.15346i	0.985854	−	0.167609i	$-0.0536047\pi$
$828$		0			0
$829$	−22.9388	+	22.9388i	−0.796696	+	0.796696i	−0.982573	−	0.185877i	$-0.940488\pi$
$829$	−22.9388	+	22.9388i	−0.796696	+	0.796696i	0.185877	+	0.982573i	$0.440488\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.87175			−0.134148
$834$		0			0
$835$	−22.0331	−	4.73305i	−0.762485	−	0.163794i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	19.8135i		−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$839$		−	19.8135i		−	0.684040i	0.939693	−	0.342020i	$-0.111111\pi$
$840$		0			0
$841$		−	7.79349i		−	0.268741i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.54417	−	25.8089i	0.190725	−	0.887854i
$846$		0			0
$847$	53.5360			1.83952
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.01530	+	7.01530i	−0.240481	+	0.240481i
$852$		0			0
$853$	21.6771	−	21.6771i	0.742211	−	0.742211i	−0.230792	−	0.973003i	$-0.574132\pi$
$853$	21.6771	−	21.6771i	0.742211	−	0.742211i	0.973003	+	0.230792i	$0.0741318\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	9.66909i		−	0.330290i	−0.986269	−	0.165145i	$-0.947191\pi$
$857$		−	9.66909i		−	0.330290i	0.986269	−	0.165145i	$-0.0528092\pi$
$858$		0			0
$859$	−24.3747	+	24.3747i	−0.831652	+	0.831652i	−0.987743	−	0.156090i	$-0.950111\pi$
$859$	−24.3747	+	24.3747i	−0.831652	+	0.831652i	0.156090	+	0.987743i	$0.450111\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	11.2656i		−	0.383485i	−0.981445	−	0.191742i	$-0.938586\pi$
$863$		−	11.2656i		−	0.383485i	0.981445	−	0.191742i	$-0.0614138\pi$
$864$		0			0
$865$	−23.9673	+	15.4910i	−0.814912	+	0.526710i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.10038	−	1.10038i	0.0373279	−	0.0373279i
$870$		0			0
$871$	−11.1509			−0.377832
$872$		0			0
$873$		0			0
$874$		0			0
$875$	19.5547	−	26.5511i	0.661069	−	0.897590i
$876$		0			0
$877$	−14.2210	−	14.2210i	−0.480210	−	0.480210i	0.424989	−	0.905199i	$-0.360278\pi$
$877$	−14.2210	−	14.2210i	−0.480210	−	0.480210i	−0.905199	+	0.424989i	$0.860278\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			43.8480i			1.47728i	0.674103	+	0.738638i	$0.264531\pi$
$881$			43.8480i			1.47728i	−0.674103	+	0.738638i	$0.735469\pi$
$882$		0			0
$883$	23.8519	−	23.8519i	0.802681	−	0.802681i	−0.180833	−	0.983514i	$-0.557879\pi$
$883$	23.8519	−	23.8519i	0.802681	−	0.802681i	0.983514	+	0.180833i	$0.0578792\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.2892			−0.412632			−0.206316	−	0.978485i	$-0.566148\pi$
$887$	−12.2892			−0.412632			−0.206316	+	0.978485i	$0.566148\pi$
$888$		0			0
$889$		−	30.7582i		−	1.03160i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	35.9514	−	35.9514i	1.20307	−	1.20307i
$894$		0			0
$895$	−27.4150	+	17.7194i	−0.916383	+	0.592295i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.30628	−	6.30628i	0.210326	−	0.210326i
$900$		0			0
$901$	−20.5524	−	20.5524i	−0.684700	−	0.684700i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.8919	+	36.9649i	0.794194	+	1.22876i
$906$		0			0
$907$	−31.4979	−	31.4979i	−1.04587	−	1.04587i	−0.998896	−	0.0469745i	$-0.985042\pi$
$907$	−31.4979	−	31.4979i	−1.04587	−	1.04587i	−0.0469745	−	0.998896i	$-0.514958\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.04962			0.299827			0.149914	−	0.988699i	$-0.452100\pi$
$911$	9.04962			0.299827			0.149914	+	0.988699i	$0.452100\pi$
$912$		0			0
$913$			67.9622i			2.24922i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	39.9734	+	39.9734i	1.32004	+	1.32004i
$918$		0			0
$919$	−4.82428			−0.159138			−0.0795692	−	0.996829i	$-0.525354\pi$
$919$	−4.82428			−0.159138			−0.0795692	+	0.996829i	$0.525354\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.20662	+	6.20662i	−0.204293	+	0.204293i
$924$		0			0
$925$	−17.6130	+	6.67380i	−0.579111	+	0.219433i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			15.4281i			0.506180i	0.967443	+	0.253090i	$0.0814468\pi$
$929$			15.4281i			0.506180i	−0.967443	+	0.253090i	$0.918553\pi$
$930$		0			0
$931$	−8.80177	−	8.80177i	−0.288466	−	0.288466i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−14.9366	−	23.1096i	−0.488480	−	0.755764i
$936$		0			0
$937$	12.7904			0.417845			0.208923	−	0.977932i	$-0.433004\pi$
$937$	12.7904			0.417845			0.208923	+	0.977932i	$0.433004\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.02632	+	3.02632i	0.0986553	+	0.0986553i	0.754712	−	0.656056i	$-0.227777\pi$
$941$	3.02632	+	3.02632i	0.0986553	+	0.0986553i	−0.656056	+	0.754712i	$0.727777\pi$
$942$		0			0
$943$	−2.67662			−0.0871629
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.2910	+	13.2910i	0.431898	+	0.431898i	0.889274	−	0.457375i	$-0.151210\pi$
$947$	13.2910	+	13.2910i	0.431898	+	0.431898i	−0.457375	+	0.889274i	$0.651210\pi$
$948$		0			0
$949$	1.22113	+	1.22113i	0.0396394	+	0.0396394i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	24.7645i		−	0.802200i	−0.916034	−	0.401100i	$-0.868628\pi$
$953$		−	24.7645i		−	0.802200i	0.916034	−	0.401100i	$-0.131372\pi$
$954$		0			0
$955$	27.0838	+	5.81802i	0.876410	+	0.188267i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−22.4485			−0.724901
$960$		0			0
$961$	27.2493			0.879011
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.9322	−	50.8911i	0.351921	−	1.63824i
$966$		0			0
$967$			50.8732i			1.63597i	0.575238	+	0.817986i	$0.304909\pi$
$967$			50.8732i			1.63597i	−0.575238	+	0.817986i	$0.695091\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.95162	−	9.95162i	−0.319363	−	0.319363i	0.529160	−	0.848522i	$-0.322507\pi$
$971$	−9.95162	−	9.95162i	−0.319363	−	0.319363i	−0.848522	+	0.529160i	$0.822507\pi$
$972$		0			0
$973$	4.95517	+	4.95517i	0.158855	+	0.158855i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.29541			0.169415			0.0847076	−	0.996406i	$-0.473004\pi$
$977$	5.29541			0.169415			0.0847076	+	0.996406i	$0.473004\pi$
$978$		0			0
$979$	−24.5967	−	24.5967i	−0.786114	−	0.786114i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−42.1592			−1.34467			−0.672335	−	0.740247i	$-0.734709\pi$
$983$	−42.1592			−1.34467			−0.672335	+	0.740247i	$0.734709\pi$
$984$		0			0
$985$	0.849304	+	1.31402i	0.0270611	+	0.0418682i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.7604	−	11.7604i	−0.373958	−	0.373958i
$990$		0			0
$991$			40.3299i			1.28112i	0.767907	+	0.640561i	$0.221298\pi$
$991$			40.3299i			1.28112i	−0.767907	+	0.640561i	$0.778702\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.51180	−	1.39884i	−0.206438	−	0.0443461i
$996$		0			0
$997$	−35.3041	+	35.3041i	−1.11809	+	1.11809i	−0.126069	+	0.992021i	$0.540236\pi$
$997$	−35.3041	+	35.3041i	−1.11809	+	1.11809i	−0.992021	+	0.126069i	$0.959764\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.u.a.719.44		96
3.2	odd	2	inner	2880.2.u.a.719.5		96
4.3	odd	2		720.2.u.a.539.12	yes	96
5.4	even	2	inner	2880.2.u.a.719.20		96
12.11	even	2		720.2.u.a.539.37	yes	96
15.14	odd	2	inner	2880.2.u.a.719.29		96
16.3	odd	4	inner	2880.2.u.a.2159.29		96
16.13	even	4		720.2.u.a.179.11	✓	96
20.19	odd	2		720.2.u.a.539.38	yes	96
48.29	odd	4		720.2.u.a.179.38	yes	96
48.35	even	4	inner	2880.2.u.a.2159.20		96
60.59	even	2		720.2.u.a.539.11	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.5		96
80.29	even	4		720.2.u.a.179.37	yes	96
240.29	odd	4		720.2.u.a.179.12	yes	96
240.179	even	4	inner	2880.2.u.a.2159.44		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.11	✓	96	16.13	even	4
720.2.u.a.179.12	yes	96	240.29	odd	4
720.2.u.a.179.37	yes	96	80.29	even	4
720.2.u.a.179.38	yes	96	48.29	odd	4
720.2.u.a.539.11	yes	96	60.59	even	2
720.2.u.a.539.12	yes	96	4.3	odd	2
720.2.u.a.539.37	yes	96	12.11	even	2
720.2.u.a.539.38	yes	96	20.19	odd	2
2880.2.u.a.719.5		96	3.2	odd	2	inner
2880.2.u.a.719.20		96	5.4	even	2	inner
2880.2.u.a.719.29		96	15.14	odd	2	inner
2880.2.u.a.719.44		96	1.1	even	1	trivial
2880.2.u.a.2159.5		96	80.19	odd	4	inner
2880.2.u.a.2159.20		96	48.35	even	4	inner
2880.2.u.a.2159.29		96	16.3	odd	4	inner
2880.2.u.a.2159.44		96	240.179	even	4	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.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.18619 + 0.469629i) q^{5} -2.94937i q^{7} +O(q^{10})\)	\(q+(2.18619 + 0.469629i) q^{5} -2.94937i q^{7} +(-3.81783 - 3.81783i) q^{11} +(-0.772847 - 0.772847i) q^{13} +2.27916 q^{17} +(5.18129 + 5.18129i) q^{19} +2.63370 q^{23} +(4.55890 + 2.05340i) q^{25} +(3.25626 + 3.25626i) q^{29} -1.93666i q^{31} +(1.38511 - 6.44789i) q^{35} +(-2.66367 + 2.66367i) q^{37} -1.01630 q^{41} +(-4.46535 - 4.46535i) q^{43} -6.93871i q^{47} -1.69876 q^{49} +(-9.01752 - 9.01752i) q^{53} +(-6.55356 - 10.1395i) q^{55} +(-2.82309 - 2.82309i) q^{59} +(10.8603 - 10.8603i) q^{61} +(-1.32664 - 2.05255i) q^{65} +(7.21414 - 7.21414i) q^{67} -8.03085i q^{71} -1.58003 q^{73} +(-11.2602 + 11.2602i) q^{77} +0.288222i q^{79} +(-8.90062 - 8.90062i) q^{83} +(4.98270 + 1.07036i) q^{85} +6.44258 q^{89} +(-2.27941 + 2.27941i) q^{91} +(8.89402 + 13.7606i) q^{95} -18.1267i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q + 16 q^{19} - 96 q^{49} - 64 q^{55} - 32 q^{61}+O(q^{100}) \) 96 * q + 16 * q^19 - 96 * q^49 - 64 * q^55 - 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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