LMFDB - Embedded newform 2880.2.u.a.719.18

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			719.18
Character	$\chi$	$=$	2880.719
Dual form			2880.2.u.a.2159.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +O(q^{10})$	$q+(-1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(-3.34421 - 3.34421i) q^{11} +(2.90349 + 2.90349i) q^{13} -4.56733 q^{17} +(-0.0693845 - 0.0693845i) q^{19} -1.07695 q^{23} +(-2.52593 + 4.31505i) q^{25} +(-1.23988 - 1.23988i) q^{29} -8.56612i q^{31} +(-3.46816 + 1.98849i) q^{35} +(-7.62458 + 7.62458i) q^{37} +7.91601 q^{41} +(-2.35179 - 2.35179i) q^{43} +6.32188i q^{47} +3.80356 q^{49} +(-3.61429 - 3.61429i) q^{53} +(-2.76772 + 10.2067i) q^{55} +(-2.25080 - 2.25080i) q^{59} +(4.29893 - 4.29893i) q^{61} +(2.40297 - 8.86160i) q^{65} +(-5.85271 + 5.85271i) q^{67} +15.1431i q^{71} +6.88118 q^{73} +(-5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-6.88840 - 6.88840i) q^{83} +(5.07987 + 8.85986i) q^{85} +6.31609 q^{89} +(5.19103 - 5.19103i) q^{91} +(-0.0574238 + 0.211766i) q^{95} +4.56728i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.11222	−	1.93984i	−0.497400	−	0.867521i
$5$	−1.11222	−	1.93984i	−0.497400	−	0.867521i
$6$		0			0
$7$		−	1.78786i		−	0.675747i	−0.941191	−	0.337874i	$-0.890292\pi$
$7$		−	1.78786i		−	0.675747i	0.941191	−	0.337874i	$-0.109708\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.34421	−	3.34421i	−1.00832	−	1.00832i	−0.999965	−	0.00835103i	$-0.997342\pi$
$11$	−3.34421	−	3.34421i	−1.00832	−	1.00832i	−0.00835103	−	0.999965i	$-0.502658\pi$
$12$		0			0
$13$	2.90349	+	2.90349i	0.805282	+	0.805282i	0.983916	−	0.178634i	$-0.0571677\pi$
$13$	2.90349	+	2.90349i	0.805282	+	0.805282i	−0.178634	+	0.983916i	$0.557168\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.56733			−1.10774			−0.553870	−	0.832603i	$-0.686849\pi$
$17$	−4.56733			−1.10774			−0.553870	+	0.832603i	$0.686849\pi$
$18$		0			0
$19$	−0.0693845	−	0.0693845i	−0.0159179	−	0.0159179i	0.699103	−	0.715021i	$-0.253583\pi$
$19$	−0.0693845	−	0.0693845i	−0.0159179	−	0.0159179i	−0.715021	+	0.699103i	$0.753583\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.07695			−0.224560			−0.112280	−	0.993677i	$-0.535815\pi$
$23$	−1.07695			−0.224560			−0.112280	+	0.993677i	$0.535815\pi$
$24$		0			0
$25$	−2.52593	+	4.31505i	−0.505186	+	0.863010i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.23988	−	1.23988i	−0.230239	−	0.230239i	0.582553	−	0.812792i	$-0.302054\pi$
$29$	−1.23988	−	1.23988i	−0.230239	−	0.230239i	−0.812792	+	0.582553i	$0.802054\pi$
$30$		0			0
$31$		−	8.56612i		−	1.53852i	−0.638935	−	0.769261i	$-0.720625\pi$
$31$		−	8.56612i		−	1.53852i	0.638935	−	0.769261i	$-0.279375\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.46816	+	1.98849i	−0.586225	+	0.336117i
$36$		0			0
$37$	−7.62458	+	7.62458i	−1.25347	+	1.25347i	−0.299321	+	0.954153i	$0.596760\pi$
$37$	−7.62458	+	7.62458i	−1.25347	+	1.25347i	−0.954153	+	0.299321i	$0.903240\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.91601			1.23627			0.618137	−	0.786071i	$-0.287888\pi$
$41$	7.91601			1.23627			0.618137	+	0.786071i	$0.287888\pi$
$42$		0			0
$43$	−2.35179	−	2.35179i	−0.358645	−	0.358645i	0.504668	−	0.863313i	$-0.331615\pi$
$43$	−2.35179	−	2.35179i	−0.358645	−	0.358645i	−0.863313	+	0.504668i	$0.831615\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			6.32188i			0.922141i	0.887364	+	0.461070i	$0.152534\pi$
$47$			6.32188i			0.922141i	−0.887364	+	0.461070i	$0.847466\pi$
$48$		0			0
$49$	3.80356			0.543365
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.61429	−	3.61429i	−0.496461	−	0.496461i	0.413874	−	0.910334i	$-0.364176\pi$
$53$	−3.61429	−	3.61429i	−0.496461	−	0.496461i	−0.910334	+	0.413874i	$0.864176\pi$
$54$		0			0
$55$	−2.76772	+	10.2067i	−0.373199	+	1.37627i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.25080	−	2.25080i	−0.293030	−	0.293030i	0.545246	−	0.838276i	$-0.316436\pi$
$59$	−2.25080	−	2.25080i	−0.293030	−	0.293030i	−0.838276	+	0.545246i	$0.816436\pi$
$60$		0			0
$61$	4.29893	−	4.29893i	0.550421	−	0.550421i	−0.376141	−	0.926562i	$-0.622749\pi$
$61$	4.29893	−	4.29893i	0.550421	−	0.550421i	0.926562	+	0.376141i	$0.122749\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.40297	−	8.86160i	0.298052	−	1.09915i
$66$		0			0
$67$	−5.85271	+	5.85271i	−0.715022	+	0.715022i	−0.967581	−	0.252559i	$-0.918728\pi$
$67$	−5.85271	+	5.85271i	−0.715022	+	0.715022i	0.252559	+	0.967581i	$0.418728\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			15.1431i			1.79716i	0.438812	+	0.898579i	$0.355399\pi$
$71$			15.1431i			1.79716i	−0.438812	+	0.898579i	$0.644601\pi$
$72$		0			0
$73$	6.88118			0.805381			0.402691	−	0.915336i	$-0.368075\pi$
$73$	6.88118			0.805381			0.402691	+	0.915336i	$0.368075\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.97897	+	5.97897i	−0.681367	+	0.681367i
$78$		0			0
$79$			12.9721i			1.45947i	0.683730	+	0.729735i	$0.260357\pi$
$79$			12.9721i			1.45947i	−0.683730	+	0.729735i	$0.739643\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.88840	−	6.88840i	−0.756100	−	0.756100i	0.219510	−	0.975610i	$-0.429554\pi$
$83$	−6.88840	−	6.88840i	−0.756100	−	0.756100i	−0.975610	+	0.219510i	$0.929554\pi$
$84$		0			0
$85$	5.07987	+	8.85986i	0.550989	+	0.960987i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.31609			0.669504			0.334752	−	0.942306i	$-0.391347\pi$
$89$	6.31609			0.669504			0.334752	+	0.942306i	$0.391347\pi$
$90$		0			0
$91$	5.19103	−	5.19103i	0.544167	−	0.544167i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0574238	+	0.211766i	−0.00589155	+	0.0217267i
$96$		0			0
$97$			4.56728i			0.463737i	0.972747	+	0.231869i	$0.0744839\pi$
$97$			4.56728i			0.463737i	−0.972747	+	0.231869i	$0.925516\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.24690	+	6.24690i	−0.621589	+	0.621589i	−0.945938	−	0.324348i	$-0.894855\pi$
$101$	−6.24690	+	6.24690i	−0.621589	+	0.621589i	0.324348	+	0.945938i	$0.394855\pi$
$102$		0			0
$103$			13.8548i			1.36515i	0.730815	+	0.682576i	$0.239140\pi$
$103$			13.8548i			1.36515i	−0.730815	+	0.682576i	$0.760860\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.922209	−	0.922209i	0.0891533	−	0.0891533i	−0.661124	−	0.750277i	$-0.729920\pi$
$107$	0.922209	−	0.922209i	0.0891533	−	0.0891533i	0.750277	+	0.661124i	$0.229920\pi$
$108$		0			0
$109$	−2.28662	+	2.28662i	−0.219019	+	0.219019i	−0.808085	−	0.589066i	$-0.799496\pi$
$109$	−2.28662	+	2.28662i	−0.219019	+	0.219019i	0.589066	+	0.808085i	$0.299496\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.53772			−0.709089			−0.354544	−	0.935039i	$-0.615364\pi$
$113$	−7.53772			−0.709089			−0.354544	+	0.935039i	$0.615364\pi$
$114$		0			0
$115$	1.19781	+	2.08911i	0.111696	+	0.194811i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			8.16574i			0.748552i
$120$		0			0
$121$			11.3674i			1.03340i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.1799	+	0.100608i	0.999960	+	0.00899866i
$126$		0			0
$127$	0.00277854			0.000246555			0.000123278	−	1.00000i	$-0.499961\pi$
$127$	0.00277854			0.000246555			0.000123278		1.00000i	$0.499961\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.71989	+	8.71989i	−0.761860	+	0.761860i	−0.976658	−	0.214798i	$-0.931091\pi$
$131$	−8.71989	+	8.71989i	−0.761860	+	0.761860i	0.214798	+	0.976658i	$0.431091\pi$
$132$		0			0
$133$	−0.124050	+	0.124050i	−0.0107565	+	0.0107565i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	23.1771i		−	1.98016i	−0.140516	−	0.990078i	$-0.544876\pi$
$137$		−	23.1771i		−	1.98016i	0.140516	−	0.990078i	$-0.455124\pi$
$138$		0			0
$139$	7.85331	−	7.85331i	0.666109	−	0.666109i	−0.290704	−	0.956813i	$-0.593889\pi$
$139$	7.85331	−	7.85331i	0.666109	−	0.666109i	0.956813	+	0.290704i	$0.0938894\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	19.4197i		−	1.62396i
$144$		0			0
$145$	−1.02614	+	3.78417i	−0.0852164	+	0.314258i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−13.6076	+	13.6076i	−1.11478	+	1.11478i	−0.122285	+	0.992495i	$0.539022\pi$
$149$	−13.6076	+	13.6076i	−1.11478	+	1.11478i	−0.992495	+	0.122285i	$0.960978\pi$
$150$		0			0
$151$	−15.2447			−1.24059			−0.620297	−	0.784367i	$-0.712988\pi$
$151$	−15.2447			−1.24059			−0.620297	+	0.784367i	$0.712988\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−16.6169	+	9.52742i	−1.33470	+	0.765261i
$156$		0			0
$157$	5.76894	+	5.76894i	0.460411	+	0.460411i	0.898790	−	0.438379i	$-0.144447\pi$
$157$	5.76894	+	5.76894i	0.460411	+	0.460411i	−0.438379	+	0.898790i	$0.644447\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.92544i			0.151746i
$162$		0			0
$163$	−10.4511	+	10.4511i	−0.818594	+	0.818594i	−0.985904	−	0.167311i	$-0.946492\pi$
$163$	−10.4511	+	10.4511i	−0.818594	+	0.818594i	0.167311	+	0.985904i	$0.446492\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.41872			−0.728842			−0.364421	−	0.931234i	$-0.618733\pi$
$167$	−9.41872			−0.728842			−0.364421	+	0.931234i	$0.618733\pi$
$168$		0			0
$169$			3.86046i			0.296958i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.21995	+	6.21995i	−0.472894	+	0.472894i	−0.902850	−	0.429956i	$-0.858529\pi$
$173$	−6.21995	+	6.21995i	−0.472894	+	0.472894i	0.429956	+	0.902850i	$0.358529\pi$
$174$		0			0
$175$	7.71471	+	4.51601i	0.583177	+	0.341378i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	18.4020	−	18.4020i	1.37543	−	1.37543i	0.523251	−	0.852179i	$-0.324719\pi$
$179$	18.4020	−	18.4020i	1.37543	−	1.37543i	0.852179	−	0.523251i	$-0.175281\pi$
$180$		0			0
$181$	−18.5731	−	18.5731i	−1.38053	−	1.38053i	−0.843677	−	0.536851i	$-0.819614\pi$
$181$	−18.5731	−	18.5731i	−1.38053	−	1.38053i	−0.536851	−	0.843677i	$-0.680386\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	23.2707	+	6.31023i	1.71089	+	0.463937i
$186$		0			0
$187$	15.2741	+	15.2741i	1.11695	+	1.11695i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.73383			−0.342528			−0.171264	−	0.985225i	$-0.554785\pi$
$191$	−4.73383			−0.342528			−0.171264	+	0.985225i	$0.554785\pi$
$192$		0			0
$193$			16.7218i			1.20366i	0.798625	+	0.601829i	$0.205561\pi$
$193$			16.7218i			1.20366i	−0.798625	+	0.601829i	$0.794439\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.93066	+	7.93066i	0.565036	+	0.565036i	0.930734	−	0.365698i	$-0.119170\pi$
$197$	7.93066	+	7.93066i	0.565036	+	0.565036i	−0.365698	+	0.930734i	$0.619170\pi$
$198$		0			0
$199$	2.34717			0.166386			0.0831932	−	0.996533i	$-0.473488\pi$
$199$	2.34717			0.166386			0.0831932	+	0.996533i	$0.473488\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.21672	+	2.21672i	−0.155583	+	0.155583i
$204$		0			0
$205$	−8.80435	−	15.3558i	−0.614922	−	1.07249i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			0.464072i			0.0321006i
$210$		0			0
$211$	3.00077	+	3.00077i	0.206581	+	0.206581i	0.802813	−	0.596231i	$-0.203336\pi$
$211$	3.00077	+	3.00077i	0.206581	+	0.206581i	−0.596231	+	0.802813i	$0.703336\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.94638	+	7.17781i	−0.132742	+	0.489522i
$216$		0			0
$217$	−15.3150			−1.03965
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−13.2612	−	13.2612i	−0.892042	−	0.892042i
$222$		0			0
$223$	−24.6842			−1.65298			−0.826489	−	0.562952i	$-0.809665\pi$
$223$	−24.6842			−1.65298			−0.826489	+	0.562952i	$0.809665\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.05360	−	5.05360i	−0.335419	−	0.335419i	0.519221	−	0.854640i	$-0.326222\pi$
$227$	−5.05360	−	5.05360i	−0.335419	−	0.335419i	−0.854640	+	0.519221i	$0.826222\pi$
$228$		0			0
$229$	−13.4816	−	13.4816i	−0.890886	−	0.890886i	0.103720	−	0.994606i	$-0.466925\pi$
$229$	−13.4816	−	13.4816i	−0.890886	−	0.890886i	−0.994606	+	0.103720i	$0.966925\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			11.8466i			0.776096i	0.921639	+	0.388048i	$0.126851\pi$
$233$			11.8466i			0.776096i	−0.921639	+	0.388048i	$0.873149\pi$
$234$		0			0
$235$	12.2634	−	7.03132i	0.799977	−	0.458673i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	24.8620			1.60819			0.804093	−	0.594503i	$-0.202651\pi$
$239$	24.8620			1.60819			0.804093	+	0.594503i	$0.202651\pi$
$240$		0			0
$241$	18.8396			1.21356			0.606782	−	0.794868i	$-0.292460\pi$
$241$	18.8396			1.21356			0.606782	+	0.794868i	$0.292460\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.23039	−	7.37828i	−0.270270	−	0.471381i
$246$		0			0
$247$		−	0.402914i		−	0.0256368i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−21.6723	−	21.6723i	−1.36795	−	1.36795i	−0.863364	−	0.504582i	$-0.831647\pi$
$251$	−21.6723	−	21.6723i	−1.36795	−	1.36795i	−0.504582	−	0.863364i	$-0.668353\pi$
$252$		0			0
$253$	3.60155	+	3.60155i	0.226428	+	0.226428i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.914423			−0.0570402			−0.0285201	−	0.999593i	$-0.509079\pi$
$257$	−0.914423			−0.0570402			−0.0285201	+	0.999593i	$0.509079\pi$
$258$		0			0
$259$	13.6317	+	13.6317i	0.847031	+	0.847031i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.19643			0.0737752			0.0368876	−	0.999319i	$-0.488256\pi$
$263$	1.19643			0.0737752			0.0368876	+	0.999319i	$0.488256\pi$
$264$		0			0
$265$	−2.99124	+	11.0310i	−0.183751	+	0.677630i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.54542	−	7.54542i	−0.460053	−	0.460053i	0.438620	−	0.898673i	$-0.355467\pi$
$269$	−7.54542	−	7.54542i	−0.460053	−	0.460053i	−0.898673	+	0.438620i	$0.855467\pi$
$270$		0			0
$271$			4.45852i			0.270836i	0.990789	+	0.135418i	$0.0432377\pi$
$271$			4.45852i			0.270836i	−0.990789	+	0.135418i	$0.956762\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	22.8777	−	5.98318i	1.37957	−	0.360800i
$276$		0			0
$277$	5.28152	−	5.28152i	0.317336	−	0.317336i	−0.530407	−	0.847743i	$-0.677961\pi$
$277$	5.28152	−	5.28152i	0.317336	−	0.317336i	0.847743	+	0.530407i	$0.177961\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−26.3280			−1.57060			−0.785298	−	0.619118i	$-0.787490\pi$
$281$	−26.3280			−1.57060			−0.785298	+	0.619118i	$0.787490\pi$
$282$		0			0
$283$	−13.6186	−	13.6186i	−0.809540	−	0.809540i	0.175024	−	0.984564i	$-0.444000\pi$
$283$	−13.6186	−	13.6186i	−0.809540	−	0.809540i	−0.984564	+	0.175024i	$0.944000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	14.1527i		−	0.835409i
$288$		0			0
$289$	3.86046			0.227086
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.23746	+	9.23746i	0.539658	+	0.539658i	0.923429	−	0.383770i	$-0.125375\pi$
$293$	9.23746	+	9.23746i	0.539658	+	0.539658i	−0.383770	+	0.923429i	$0.625375\pi$
$294$		0			0
$295$	−1.86280	+	6.86958i	−0.108457	+	0.399962i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.12692	−	3.12692i	−0.180834	−	0.180834i
$300$		0			0
$301$	−4.20468	+	4.20468i	−0.242353	+	0.242353i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−13.1206	−	3.55786i	−0.751282	−	0.203723i
$306$		0			0
$307$	−2.37148	+	2.37148i	−0.135348	+	0.135348i	−0.771535	−	0.636187i	$-0.780511\pi$
$307$	−2.37148	+	2.37148i	−0.135348	+	0.135348i	0.636187	+	0.771535i	$0.280511\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$			14.5352i			0.824214i	0.911135	+	0.412107i	$0.135207\pi$
$311$			14.5352i			0.824214i	−0.911135	+	0.412107i	$0.864793\pi$
$312$		0			0
$313$	21.2104			1.19888			0.599442	−	0.800418i	$-0.295389\pi$
$313$	21.2104			1.19888			0.599442	+	0.800418i	$0.295389\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.575423	+	0.575423i	−0.0323190	+	0.0323190i	−0.723082	−	0.690763i	$-0.757275\pi$
$317$	−0.575423	+	0.575423i	−0.0323190	+	0.0323190i	0.690763	+	0.723082i	$0.257275\pi$
$318$		0			0
$319$			8.29280i			0.464308i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.316902	+	0.316902i	0.0176329	+	0.0176329i
$324$		0			0
$325$	−19.8627	+	5.19468i	−1.10178	+	0.288149i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.3026			0.623134
$330$		0			0
$331$	−5.54595	+	5.54595i	−0.304833	+	0.304833i	−0.842901	−	0.538068i	$-0.819154\pi$
$331$	−5.54595	+	5.54595i	−0.304833	+	0.304833i	0.538068	+	0.842901i	$0.319154\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.8628	+	4.84380i	0.975949	+	0.264645i
$336$		0			0
$337$		−	16.3650i		−	0.891460i	−0.895167	−	0.445730i	$-0.852944\pi$
$337$		−	16.3650i		−	0.891460i	0.895167	−	0.445730i	$-0.147056\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−28.6469	+	28.6469i	−1.55132	+	1.55132i
$342$		0			0
$343$		−	19.3152i		−	1.04293i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−18.6768	+	18.6768i	−1.00262	+	1.00262i	−0.00262421	+	0.999997i	$0.500835\pi$
$347$	−18.6768	+	18.6768i	−1.00262	+	1.00262i	−0.999997	+	0.00262421i	$0.999165\pi$
$348$		0			0
$349$	15.2350	−	15.2350i	0.815511	−	0.815511i	−0.169943	−	0.985454i	$-0.554358\pi$
$349$	15.2350	−	15.2350i	0.815511	−	0.815511i	0.985454	+	0.169943i	$0.0543583\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.23255			−0.438175			−0.219087	−	0.975705i	$-0.570308\pi$
$353$	−8.23255			−0.438175			−0.219087	+	0.975705i	$0.570308\pi$
$354$		0			0
$355$	29.3752	−	16.8425i	1.55907	−	0.893906i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	4.96843i		−	0.262224i	−0.991368	−	0.131112i	$-0.958145\pi$
$359$		−	4.96843i		−	0.262224i	0.991368	−	0.131112i	$-0.0418547\pi$
$360$		0			0
$361$		−	18.9904i		−	0.999493i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.65339	−	13.3484i	−0.400597	−	0.698685i
$366$		0			0
$367$	25.3790			1.32477			0.662385	−	0.749163i	$-0.269544\pi$
$367$	25.3790			1.32477			0.662385	+	0.749163i	$0.269544\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.46184	+	6.46184i	−0.335482	+	0.335482i
$372$		0			0
$373$	−2.85715	+	2.85715i	−0.147938	+	0.147938i	−0.777196	−	0.629259i	$-0.783359\pi$
$373$	−2.85715	+	2.85715i	−0.147938	+	0.147938i	0.629259	+	0.777196i	$0.283359\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	7.19992i		−	0.370815i
$378$		0			0
$379$	8.96148	−	8.96148i	0.460320	−	0.460320i	−0.438440	−	0.898760i	$-0.644469\pi$
$379$	8.96148	−	8.96148i	0.460320	−	0.460320i	0.898760	+	0.438440i	$0.144469\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$			9.83688i			0.502641i	0.967904	+	0.251321i	$0.0808648\pi$
$383$			9.83688i			0.502641i	−0.967904	+	0.251321i	$0.919135\pi$
$384$		0			0
$385$	18.2482	+	4.94829i	0.930012	+	0.252188i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.69886	+	8.69886i	−0.441050	+	0.441050i	−0.892365	−	0.451315i	$-0.850955\pi$
$389$	−8.69886	+	8.69886i	−0.441050	+	0.441050i	0.451315	+	0.892365i	$0.350955\pi$
$390$		0			0
$391$	4.91879			0.248754
$392$		0			0
$393$		0			0
$394$		0			0
$395$	25.1637	−	14.4278i	1.26612	−	0.725941i
$396$		0			0
$397$	2.52696	+	2.52696i	0.126824	+	0.126824i	0.767670	−	0.640845i	$-0.221416\pi$
$397$	2.52696	+	2.52696i	0.126824	+	0.126824i	−0.640845	+	0.767670i	$0.721416\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			11.5176i			0.575161i	0.957757	+	0.287580i	$0.0928508\pi$
$401$			11.5176i			0.575161i	−0.957757	+	0.287580i	$0.907149\pi$
$402$		0			0
$403$	24.8716	−	24.8716i	1.23894	−	1.23894i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	50.9963			2.52779
$408$		0			0
$409$			17.5055i			0.865591i	0.901492	+	0.432795i	$0.142473\pi$
$409$			17.5055i			0.865591i	−0.901492	+	0.432795i	$0.857527\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.02412	+	4.02412i	−0.198014	+	0.198014i
$414$		0			0
$415$	−5.70095	+	21.0238i	−0.279849	+	1.03202i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.30068	−	3.30068i	0.161249	−	0.161249i	−0.621871	−	0.783120i	$-0.713627\pi$
$419$	3.30068	−	3.30068i	0.161249	−	0.161249i	0.783120	+	0.621871i	$0.213627\pi$
$420$		0			0
$421$	−6.14311	−	6.14311i	−0.299397	−	0.299397i	0.541381	−	0.840778i	$-0.317902\pi$
$421$	−6.14311	−	6.14311i	−0.299397	−	0.299397i	−0.840778	+	0.541381i	$0.817902\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	11.5368	−	19.7082i	0.559615	−	0.955990i
$426$		0			0
$427$	−7.68588	−	7.68588i	−0.371946	−	0.371946i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.73359			−0.420682			−0.210341	−	0.977628i	$-0.567457\pi$
$431$	−8.73359			−0.420682			−0.210341	+	0.977628i	$0.567457\pi$
$432$		0			0
$433$		−	2.28479i		−	0.109800i	−0.998492	−	0.0548999i	$-0.982516\pi$
$433$		−	2.28479i		−	0.109800i	0.998492	−	0.0548999i	$-0.0174840\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.0747238	+	0.0747238i	0.00357452	+	0.00357452i
$438$		0			0
$439$	−27.7235			−1.32317			−0.661585	−	0.749870i	$-0.730116\pi$
$439$	−27.7235			−1.32317			−0.661585	+	0.749870i	$0.730116\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.8575	−	15.8575i	0.753410	−	0.753410i	−0.221704	−	0.975114i	$-0.571162\pi$
$443$	15.8575	−	15.8575i	0.753410	−	0.753410i	0.975114	+	0.221704i	$0.0711618\pi$
$444$		0			0
$445$	−7.02488	−	12.2522i	−0.333011	−	0.580809i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	22.7098i		−	1.07174i	−0.844301	−	0.535870i	$-0.819984\pi$
$449$		−	22.7098i		−	1.07174i	0.844301	−	0.535870i	$-0.180016\pi$
$450$		0			0
$451$	−26.4728	−	26.4728i	−1.24655	−	1.24655i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−15.8433	−	4.29618i	−0.742746	−	0.201408i
$456$		0			0
$457$	−23.3185			−1.09079			−0.545397	−	0.838178i	$-0.683621\pi$
$457$	−23.3185			−1.09079			−0.545397	+	0.838178i	$0.683621\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.98422	+	6.98422i	0.325288	+	0.325288i	0.850791	−	0.525504i	$-0.176123\pi$
$461$	6.98422	+	6.98422i	0.325288	+	0.325288i	−0.525504	+	0.850791i	$0.676123\pi$
$462$		0			0
$463$	0.177929			0.00826905			0.00413453	−	0.999991i	$-0.498684\pi$
$463$	0.177929			0.00826905			0.00413453	+	0.999991i	$0.498684\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.8586	−	25.8586i	−1.19659	−	1.19659i	−0.975180	−	0.221414i	$-0.928933\pi$
$467$	−25.8586	−	25.8586i	−1.19659	−	1.19659i	−0.221414	−	0.975180i	$-0.571067\pi$
$468$		0			0
$469$	10.4638	+	10.4638i	0.483175	+	0.483175i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			15.7298i			0.723255i
$474$		0			0
$475$	0.474658	−	0.124137i	0.0217788	−	0.00569581i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.74528			0.308200			0.154100	−	0.988055i	$-0.450752\pi$
$479$	6.74528			0.308200			0.154100	+	0.988055i	$0.450752\pi$
$480$		0			0
$481$	−44.2757			−2.01880
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.85978	−	5.07982i	0.402302	−	0.230663i
$486$		0			0
$487$		−	27.5084i		−	1.24652i	−0.782014	−	0.623261i	$-0.785807\pi$
$487$		−	27.5084i		−	1.24652i	0.782014	−	0.623261i	$-0.214193\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.96277	+	1.96277i	0.0885786	+	0.0885786i	0.750008	−	0.661429i	$-0.230050\pi$
$491$	1.96277	+	1.96277i	0.0885786	+	0.0885786i	−0.661429	+	0.750008i	$0.730050\pi$
$492$		0			0
$493$	5.66291	+	5.66291i	0.255045	+	0.255045i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	27.0738			1.21442
$498$		0			0
$499$	10.0400	+	10.0400i	0.449452	+	0.449452i	0.895172	−	0.445720i	$-0.147052\pi$
$499$	10.0400	+	10.0400i	0.449452	+	0.449452i	−0.445720	+	0.895172i	$0.647052\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	15.8104			0.704952			0.352476	−	0.935821i	$-0.385340\pi$
$503$	15.8104			0.704952			0.352476	+	0.935821i	$0.385340\pi$
$504$		0			0
$505$	19.0659	+	5.17003i	0.848421	+	0.230063i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.6015	+	16.6015i	0.735849	+	0.735849i	0.971772	−	0.235922i	$-0.0758111\pi$
$509$	16.6015	+	16.6015i	0.735849	+	0.735849i	−0.235922	+	0.971772i	$0.575811\pi$
$510$		0			0
$511$		−	12.3026i		−	0.544234i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	26.8760	−	15.4096i	1.18430	−	0.679027i
$516$		0			0
$517$	21.1417	−	21.1417i	0.929809	−	0.929809i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.96468			0.348939			0.174469	−	0.984663i	$-0.444179\pi$
$521$	7.96468			0.348939			0.174469	+	0.984663i	$0.444179\pi$
$522$		0			0
$523$	−15.2514	−	15.2514i	−0.666897	−	0.666897i	0.290099	−	0.956997i	$-0.406312\pi$
$523$	−15.2514	−	15.2514i	−0.666897	−	0.666897i	−0.956997	+	0.290099i	$0.906312\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			39.1243i			1.70428i
$528$		0			0
$529$	−21.8402			−0.949573
$530$		0			0
$531$		0			0
$532$		0			0
$533$	22.9840	+	22.9840i	0.995549	+	0.995549i
$534$		0			0
$535$	−2.81463	−	0.763235i	−0.121687	−	0.0329975i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−12.7199	−	12.7199i	−0.547884	−	0.547884i
$540$		0			0
$541$	−6.80924	+	6.80924i	−0.292752	+	0.292752i	−0.838167	−	0.545414i	$-0.816372\pi$
$541$	−6.80924	+	6.80924i	−0.292752	+	0.292752i	0.545414	+	0.838167i	$0.316372\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.97890	+	1.89245i	0.298943	+	0.0810635i
$546$		0			0
$547$	−24.8809	+	24.8809i	−1.06383	+	1.06383i	−0.0660132	+	0.997819i	$0.521028\pi$
$547$	−24.8809	+	24.8809i	−1.06383	+	1.06383i	−0.997819	+	0.0660132i	$0.978972\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			0.172056i			0.00732985i
$552$		0			0
$553$	23.1922			0.986233
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.05959	−	3.05959i	0.129639	−	0.129639i	−0.639310	−	0.768949i	$-0.720780\pi$
$557$	3.05959	−	3.05959i	0.129639	−	0.129639i	0.768949	+	0.639310i	$0.220780\pi$
$558$		0			0
$559$		−	13.6568i		−	0.577621i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	32.0945	+	32.0945i	1.35262	+	1.35262i	0.882716	+	0.469906i	$0.155712\pi$
$563$	32.0945	+	32.0945i	1.35262	+	1.35262i	0.469906	+	0.882716i	$0.344288\pi$
$564$		0			0
$565$	8.38360	+	14.6219i	0.352701	+	0.615150i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	28.4585			1.19304			0.596521	−	0.802597i	$-0.296549\pi$
$569$	28.4585			1.19304			0.596521	+	0.802597i	$0.296549\pi$
$570$		0			0
$571$	26.7837	−	26.7837i	1.12086	−	1.12086i	0.129250	−	0.991612i	$-0.458743\pi$
$571$	26.7837	−	26.7837i	1.12086	−	1.12086i	0.991612	−	0.129250i	$-0.0412571\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.72031	−	4.64710i	0.113445	−	0.193798i
$576$		0			0
$577$		−	33.4904i		−	1.39423i	−0.716962	−	0.697113i	$-0.754468\pi$
$577$		−	33.4904i		−	1.39423i	0.716962	−	0.697113i	$-0.245532\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−12.3155	+	12.3155i	−0.510933	+	0.510933i
$582$		0			0
$583$			24.1738i			1.00118i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.3666	+	12.3666i	−0.510425	+	0.510425i	−0.914657	−	0.404232i	$-0.867539\pi$
$587$	−12.3666	+	12.3666i	−0.510425	+	0.510425i	0.404232	+	0.914657i	$0.367539\pi$
$588$		0			0
$589$	−0.594357	+	0.594357i	−0.0244900	+	0.0244900i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	24.1105			0.990099			0.495050	−	0.868865i	$-0.335150\pi$
$593$	24.1105			0.990099			0.495050	+	0.868865i	$0.335150\pi$
$594$		0			0
$595$	15.8402	−	9.08210i	0.649385	−	0.372330i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			18.0184i			0.736213i	0.929784	+	0.368107i	$0.119994\pi$
$599$			18.0184i			0.736213i	−0.929784	+	0.368107i	$0.880006\pi$
$600$		0			0
$601$		−	18.8361i		−	0.768342i	−0.923262	−	0.384171i	$-0.874487\pi$
$601$		−	18.8361i		−	0.768342i	0.923262	−	0.384171i	$-0.125513\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	22.0510	−	12.6431i	0.896499	−	0.514015i
$606$		0			0
$607$	10.4336			0.423486			0.211743	−	0.977325i	$-0.432086\pi$
$607$	10.4336			0.423486			0.211743	+	0.977325i	$0.432086\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−18.3555	+	18.3555i	−0.742583	+	0.742583i
$612$		0			0
$613$	9.35631	−	9.35631i	0.377898	−	0.377898i	−0.492445	−	0.870343i	$-0.663897\pi$
$613$	9.35631	−	9.35631i	0.377898	−	0.377898i	0.870343	+	0.492445i	$0.163897\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			22.8927i			0.921626i	0.887497	+	0.460813i	$0.152442\pi$
$617$			22.8927i			0.921626i	−0.887497	+	0.460813i	$0.847558\pi$
$618$		0			0
$619$	−32.9542	+	32.9542i	−1.32454	+	1.32454i	−0.414484	+	0.910057i	$0.636038\pi$
$619$	−32.9542	+	32.9542i	−1.32454	+	1.32454i	−0.910057	+	0.414484i	$0.863962\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		−	11.2923i		−	0.452415i
$624$		0			0
$625$	−12.2393	−	21.7991i	−0.489573	−	0.871962i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	34.8239	−	34.8239i	1.38852	−	1.38852i
$630$		0			0
$631$	−14.9668			−0.595817			−0.297908	−	0.954594i	$-0.596289\pi$
$631$	−14.9668			−0.595817			−0.297908	+	0.954594i	$0.596289\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.00309035	−	0.00538991i	−0.000122637	−	0.000213892i
$636$		0			0
$637$	11.0436	+	11.0436i	0.437562	+	0.437562i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	3.08889i		−	0.122004i	−0.998138	−	0.0610019i	$-0.980570\pi$
$641$		−	3.08889i		−	0.122004i	0.998138	−	0.0610019i	$-0.0194296\pi$
$642$		0			0
$643$	−18.1306	+	18.1306i	−0.715001	+	0.715001i	−0.967577	−	0.252576i	$-0.918722\pi$
$643$	−18.1306	+	18.1306i	−0.715001	+	0.715001i	0.252576	+	0.967577i	$0.418722\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.79255			0.267043			0.133521	−	0.991046i	$-0.457372\pi$
$647$	6.79255			0.267043			0.133521	+	0.991046i	$0.457372\pi$
$648$		0			0
$649$			15.0543i			0.590933i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.2088	−	12.2088i	0.477769	−	0.477769i	−0.426649	−	0.904417i	$-0.640306\pi$
$653$	12.2088	−	12.2088i	0.477769	−	0.477769i	0.904417	+	0.426649i	$0.140306\pi$
$654$		0			0
$655$	26.6136	+	7.21672i	1.03988	+	0.281981i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−24.8761	+	24.8761i	−0.969034	+	0.969034i	−0.999535	−	0.0305007i	$-0.990290\pi$
$659$	−24.8761	+	24.8761i	−0.969034	+	0.969034i	0.0305007	+	0.999535i	$0.490290\pi$
$660$		0			0
$661$	−21.1349	−	21.1349i	−0.822052	−	0.822052i	0.164350	−	0.986402i	$-0.447447\pi$
$661$	−21.1349	−	21.1349i	−0.822052	−	0.822052i	−0.986402	+	0.164350i	$0.947447\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.378607	+	0.102666i	0.0146818	+	0.00398120i
$666$		0			0
$667$	1.33529	+	1.33529i	0.0517025	+	0.0517025i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.7530			−1.11000
$672$		0			0
$673$		−	48.6471i		−	1.87521i	−0.347705	−	0.937604i	$-0.613039\pi$
$673$		−	48.6471i		−	1.87521i	0.347705	−	0.937604i	$-0.386961\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.69556	−	8.69556i	−0.334197	−	0.334197i	0.519981	−	0.854178i	$-0.325939\pi$
$677$	−8.69556	−	8.69556i	−0.334197	−	0.334197i	−0.854178	+	0.519981i	$0.825939\pi$
$678$		0			0
$679$	8.16566			0.313369
$680$		0			0
$681$		0			0
$682$		0			0
$683$	26.4514	−	26.4514i	1.01213	−	1.01213i	0.0122093	−	0.999925i	$-0.496114\pi$
$683$	26.4514	−	26.4514i	1.01213	−	1.01213i	0.999925	−	0.0122093i	$-0.00388645\pi$
$684$		0			0
$685$	−44.9599	+	25.7781i	−1.71783	+	0.984930i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		−	20.9881i		−	0.799582i
$690$		0			0
$691$	−8.89820	−	8.89820i	−0.338503	−	0.338503i	0.517301	−	0.855804i	$-0.326937\pi$
$691$	−8.89820	−	8.89820i	−0.338503	−	0.338503i	−0.855804	+	0.517301i	$0.826937\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−23.9688	−	6.49953i	−0.909187	−	0.246541i
$696$		0			0
$697$	−36.1550			−1.36947
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−15.7989	−	15.7989i	−0.596716	−	0.596716i	0.342721	−	0.939437i	$-0.388651\pi$
$701$	−15.7989	−	15.7989i	−0.596716	−	0.596716i	−0.939437	+	0.342721i	$0.888651\pi$
$702$		0			0
$703$	1.05806			0.0399053
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.1686	+	11.1686i	0.420037	+	0.420037i
$708$		0			0
$709$	18.9259	+	18.9259i	0.710776	+	0.710776i	0.966697	−	0.255922i	$-0.0823790\pi$
$709$	18.9259	+	18.9259i	0.710776	+	0.710776i	−0.255922	+	0.966697i	$0.582379\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			9.22531i			0.345490i
$714$		0			0
$715$	−37.6711	+	21.5990i	−1.40882	+	0.807757i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−10.6789			−0.398256			−0.199128	−	0.979973i	$-0.563811\pi$
$719$	−10.6789			−0.398256			−0.199128	+	0.979973i	$0.563811\pi$
$720$		0			0
$721$	24.7704			0.922498
$722$		0			0
$723$		0			0
$724$		0			0
$725$	8.48197	−	2.21828i	0.315012	−	0.0823850i
$726$		0			0
$727$		−	32.2573i		−	1.19636i	−0.801363	−	0.598179i	$-0.795891\pi$
$727$		−	32.2573i		−	1.19636i	0.801363	−	0.598179i	$-0.204109\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.7414	+	10.7414i	0.397285	+	0.397285i
$732$		0			0
$733$	−29.6986	−	29.6986i	−1.09694	−	1.09694i	−0.994766	−	0.102175i	$-0.967420\pi$
$733$	−29.6986	−	29.6986i	−1.09694	−	1.09694i	−0.102175	−	0.994766i	$-0.532580\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	39.1453			1.44194
$738$		0			0
$739$	−19.7806	−	19.7806i	−0.727640	−	0.727640i	0.242509	−	0.970149i	$-0.422030\pi$
$739$	−19.7806	−	19.7806i	−0.727640	−	0.727640i	−0.970149	+	0.242509i	$0.922030\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−34.3449			−1.25999			−0.629996	−	0.776598i	$-0.716944\pi$
$743$	−34.3449			−1.25999			−0.629996	+	0.776598i	$0.716944\pi$
$744$		0			0
$745$	41.5312	+	11.2619i	1.52159	+	0.412604i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.64878	−	1.64878i	−0.0602451	−	0.0602451i
$750$		0			0
$751$		−	48.4556i		−	1.76817i	−0.467326	−	0.884085i	$-0.654783\pi$
$751$		−	48.4556i		−	1.76817i	0.467326	−	0.884085i	$-0.345217\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.9554	+	29.5722i	0.617071	+	1.07624i
$756$		0			0
$757$	24.8358	−	24.8358i	0.902672	−	0.902672i	−0.0929947	−	0.995667i	$-0.529644\pi$
$757$	24.8358	−	24.8358i	0.902672	−	0.902672i	0.995667	+	0.0929947i	$0.0296440\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−26.2421			−0.951274			−0.475637	−	0.879642i	$-0.657782\pi$
$761$	−26.2421			−0.951274			−0.475637	+	0.879642i	$0.657782\pi$
$762$		0			0
$763$	4.08816	+	4.08816i	0.148001	+	0.148001i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	13.0704i		−	0.471943i
$768$		0			0
$769$	25.4168			0.916552			0.458276	−	0.888810i	$-0.348467\pi$
$769$	25.4168			0.916552			0.458276	+	0.888810i	$0.348467\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−30.1984	−	30.1984i	−1.08616	−	1.08616i	−0.995920	−	0.0902412i	$-0.971236\pi$
$773$	−30.1984	−	30.1984i	−1.08616	−	1.08616i	−0.0902412	−	0.995920i	$-0.528764\pi$
$774$		0			0
$775$	36.9633	+	21.6374i	1.32776	+	0.777240i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.549249	−	0.549249i	−0.0196789	−	0.0196789i
$780$		0			0
$781$	50.6417	−	50.6417i	1.81210	−	1.81210i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.77447	−	17.6071i	0.170408	−	0.628425i
$786$		0			0
$787$	19.3428	−	19.3428i	0.689496	−	0.689496i	−0.272625	−	0.962120i	$-0.587892\pi$
$787$	19.3428	−	19.3428i	0.689496	−	0.689496i	0.962120	+	0.272625i	$0.0878917\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			13.4764i			0.479165i
$792$		0			0
$793$	24.9637			0.886489
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−32.3328	+	32.3328i	−1.14529	+	1.14529i	−0.157820	+	0.987468i	$0.550447\pi$
$797$	−32.3328	+	32.3328i	−1.14529	+	1.14529i	−0.987468	+	0.157820i	$0.949553\pi$
$798$		0			0
$799$		−	28.8741i		−	1.02149i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−23.0121	−	23.0121i	−0.812079	−	0.812079i
$804$		0			0
$805$	3.73504	−	2.14151i	0.131643	−	0.0754784i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.09587			−0.144003			−0.0720015	−	0.997405i	$-0.522939\pi$
$809$	−4.09587			−0.144003			−0.0720015	+	0.997405i	$0.522939\pi$
$810$		0			0
$811$	−1.34586	+	1.34586i	−0.0472594	+	0.0472594i	−0.730342	−	0.683082i	$-0.760639\pi$
$811$	−1.34586	+	1.34586i	−0.0472594	+	0.0472594i	0.683082	+	0.730342i	$0.260639\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	31.8974	+	8.64950i	1.11732	+	0.302979i
$816$		0			0
$817$			0.326356i			0.0114178i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.3658	−	16.3658i	0.571171	−	0.571171i	−0.361285	−	0.932456i	$-0.617662\pi$
$821$	16.3658	−	16.3658i	0.571171	−	0.571171i	0.932456	+	0.361285i	$0.117662\pi$
$822$		0			0
$823$		−	33.6816i		−	1.17407i	−0.809562	−	0.587034i	$-0.800295\pi$
$823$		−	33.6816i		−	1.17407i	0.809562	−	0.587034i	$-0.199705\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.94113	−	1.94113i	0.0674997	−	0.0674997i	−0.672551	−	0.740051i	$-0.734801\pi$
$827$	1.94113	−	1.94113i	0.0674997	−	0.0674997i	0.740051	+	0.672551i	$0.234801\pi$
$828$		0			0
$829$	−31.5836	+	31.5836i	−1.09695	+	1.09695i	−0.102179	+	0.994766i	$0.532581\pi$
$829$	−31.5836	+	31.5836i	−1.09695	+	1.09695i	−0.994766	+	0.102179i	$0.967419\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−17.3721			−0.601907
$834$		0			0
$835$	10.4757	+	18.2708i	0.362526	+	0.632286i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	25.0492i		−	0.864795i	−0.901683	−	0.432398i	$-0.857668\pi$
$839$		−	25.0492i		−	0.864795i	0.901683	−	0.432398i	$-0.142332\pi$
$840$		0			0
$841$		−	25.9254i		−	0.893980i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.48866	−	4.29368i	0.257618	−	0.147707i
$846$		0			0
$847$	20.3234			0.698319
$848$		0			0
$849$		0			0
$850$		0			0
$851$	8.21131	−	8.21131i	0.281480	−	0.281480i
$852$		0			0
$853$	−5.21199	+	5.21199i	−0.178455	+	0.178455i	−0.790682	−	0.612227i	$-0.790274\pi$
$853$	−5.21199	+	5.21199i	−0.178455	+	0.178455i	0.612227	+	0.790682i	$0.290274\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	42.7298i		−	1.45962i	−0.683649	−	0.729811i	$-0.739608\pi$
$857$		−	42.7298i		−	1.45962i	0.683649	−	0.729811i	$-0.260392\pi$
$858$		0			0
$859$	12.0244	−	12.0244i	0.410268	−	0.410268i	−0.471564	−	0.881832i	$-0.656310\pi$
$859$	12.0244	−	12.0244i	0.410268	−	0.410268i	0.881832	+	0.471564i	$0.156310\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			2.21809i			0.0755047i	0.999287	+	0.0377523i	$0.0120198\pi$
$863$			2.21809i			0.0755047i	−0.999287	+	0.0377523i	$0.987980\pi$
$864$		0			0
$865$	18.9836	+	5.14773i	0.645463	+	0.175028i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	43.3812	−	43.3812i	1.47161	−	1.47161i
$870$		0			0
$871$	−33.9865			−1.15159
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.179873	−	19.9881i	0.00608082	−	0.675720i
$876$		0			0
$877$	37.6890	+	37.6890i	1.27267	+	1.27267i	0.944683	+	0.327984i	$0.106369\pi$
$877$	37.6890	+	37.6890i	1.27267	+	1.27267i	0.327984	+	0.944683i	$0.393631\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			16.4850i			0.555395i	0.960669	+	0.277698i	$0.0895713\pi$
$881$			16.4850i			0.555395i	−0.960669	+	0.277698i	$0.910429\pi$
$882$		0			0
$883$	25.2952	−	25.2952i	0.851251	−	0.851251i	−0.139036	−	0.990287i	$-0.544400\pi$
$883$	25.2952	−	25.2952i	0.851251	−	0.851251i	0.990287	+	0.139036i	$0.0444004\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	51.1894			1.71877			0.859386	−	0.511327i	$-0.170846\pi$
$887$	51.1894			1.71877			0.859386	+	0.511327i	$0.170846\pi$
$888$		0			0
$889$		−	0.00496763i		−	0.000166609i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.438641	−	0.438641i	0.0146785	−	0.0146785i
$894$		0			0
$895$	−56.1639	−	15.2298i	−1.87735	−	0.509076i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−10.6209	+	10.6209i	−0.354228	+	0.354228i
$900$		0			0
$901$	16.5076	+	16.5076i	0.549949	+	0.549949i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−15.3714	+	56.6862i	−0.510963	+	1.88431i
$906$		0			0
$907$	−12.4729	−	12.4729i	−0.414156	−	0.414156i	0.469028	−	0.883183i	$-0.344604\pi$
$907$	−12.4729	−	12.4729i	−0.414156	−	0.414156i	−0.883183	+	0.469028i	$0.844604\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−41.2168			−1.36557			−0.682786	−	0.730618i	$-0.739232\pi$
$911$	−41.2168			−1.36557			−0.682786	+	0.730618i	$0.739232\pi$
$912$		0			0
$913$			46.0725i			1.52478i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	15.5899	+	15.5899i	0.514825	+	0.514825i
$918$		0			0
$919$	36.4592			1.20268			0.601339	−	0.798994i	$-0.294634\pi$
$919$	36.4592			1.20268			0.601339	+	0.798994i	$0.294634\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−43.9678	+	43.9678i	−1.44722	+	1.44722i
$924$		0			0
$925$	−13.6413	−	52.1596i	−0.448523	−	1.71500i
$926$		0			0
$927$		0			0
$928$		0			0
$929$			23.1770i			0.760413i	0.924902	+	0.380206i	$0.124147\pi$
$929$			23.1770i			0.760413i	−0.924902	+	0.380206i	$0.875853\pi$
$930$		0			0
$931$	−0.263908	−	0.263908i	−0.00864924	−	0.00864924i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12.6411	−	46.6174i	0.413407	−	1.52455i
$936$		0			0
$937$	−33.1100			−1.08166			−0.540829	−	0.841133i	$-0.681889\pi$
$937$	−33.1100			−1.08166			−0.540829	+	0.841133i	$0.681889\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.7810	+	11.7810i	0.384050	+	0.384050i	0.872559	−	0.488509i	$-0.162459\pi$
$941$	11.7810	+	11.7810i	0.384050	+	0.384050i	−0.488509	+	0.872559i	$0.662459\pi$
$942$		0			0
$943$	−8.52517			−0.277618
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.78760	+	3.78760i	0.123080	+	0.123080i	0.765964	−	0.642884i	$-0.222262\pi$
$947$	3.78760	+	3.78760i	0.123080	+	0.123080i	−0.642884	+	0.765964i	$0.722262\pi$
$948$		0			0
$949$	19.9794	+	19.9794i	0.648559	+	0.648559i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	33.8756i		−	1.09734i	−0.836039	−	0.548670i	$-0.815134\pi$
$953$		−	33.8756i		−	1.09734i	0.836039	−	0.548670i	$-0.184866\pi$
$954$		0			0
$955$	5.26506	+	9.18286i	0.170373	+	0.297150i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−41.4375			−1.33809
$960$		0			0
$961$	−42.3785			−1.36705
$962$		0			0
$963$		0			0
$964$		0			0
$965$	32.4375	−	18.5983i	1.04420	−	0.598700i
$966$		0			0
$967$		−	39.8455i		−	1.28134i	−0.767814	−	0.640672i	$-0.778656\pi$
$967$		−	39.8455i		−	1.28134i	0.767814	−	0.640672i	$-0.221344\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	10.4598	+	10.4598i	0.335670	+	0.335670i	0.854735	−	0.519065i	$-0.173720\pi$
$971$	10.4598	+	10.4598i	0.335670	+	0.335670i	−0.519065	+	0.854735i	$0.673720\pi$
$972$		0			0
$973$	−14.0406	−	14.0406i	−0.450122	−	0.450122i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.8272			−1.05024			−0.525118	−	0.851030i	$-0.675979\pi$
$977$	−32.8272			−1.05024			−0.525118	+	0.851030i	$0.675979\pi$
$978$		0			0
$979$	−21.1223	−	21.1223i	−0.675071	−	0.675071i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4.96088			0.158227			0.0791137	−	0.996866i	$-0.474791\pi$
$983$	4.96088			0.158227			0.0791137	+	0.996866i	$0.474791\pi$
$984$		0			0
$985$	6.56354	−	24.2048i	0.209132	−	0.771229i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.53277	+	2.53277i	0.0805373	+	0.0805373i
$990$		0			0
$991$			53.9675i			1.71433i	0.515039	+	0.857166i	$0.327777\pi$
$991$			53.9675i			1.71433i	−0.515039	+	0.857166i	$0.672223\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.61057	−	4.55312i	−0.0827606	−	0.144344i
$996$		0			0
$997$	3.14670	−	3.14670i	0.0996570	−	0.0996570i	−0.655520	−	0.755177i	$-0.727551\pi$
$997$	3.14670	−	3.14670i	0.0996570	−	0.0996570i	0.755177	+	0.655520i	$0.227551\pi$
$998$		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.719.18		96
3.2	odd	2	inner	2880.2.u.a.719.31		96
4.3	odd	2		720.2.u.a.539.36	yes	96
5.4	even	2	inner	2880.2.u.a.719.42		96
12.11	even	2		720.2.u.a.539.13	yes	96
15.14	odd	2	inner	2880.2.u.a.719.7		96
16.3	odd	4	inner	2880.2.u.a.2159.7		96
16.13	even	4		720.2.u.a.179.35	yes	96
20.19	odd	2		720.2.u.a.539.14	yes	96
48.29	odd	4		720.2.u.a.179.14	yes	96
48.35	even	4	inner	2880.2.u.a.2159.42		96
60.59	even	2		720.2.u.a.539.35	yes	96
80.19	odd	4	inner	2880.2.u.a.2159.31		96
80.29	even	4		720.2.u.a.179.13	✓	96
240.29	odd	4		720.2.u.a.179.36	yes	96
240.179	even	4	inner	2880.2.u.a.2159.18		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.13	✓	96	80.29	even	4
720.2.u.a.179.14	yes	96	48.29	odd	4
720.2.u.a.179.35	yes	96	16.13	even	4
720.2.u.a.179.36	yes	96	240.29	odd	4
720.2.u.a.539.13	yes	96	12.11	even	2
720.2.u.a.539.14	yes	96	20.19	odd	2
720.2.u.a.539.35	yes	96	60.59	even	2
720.2.u.a.539.36	yes	96	4.3	odd	2
2880.2.u.a.719.7		96	15.14	odd	2	inner
2880.2.u.a.719.18		96	1.1	even	1	trivial
2880.2.u.a.719.31		96	3.2	odd	2	inner
2880.2.u.a.719.42		96	5.4	even	2	inner
2880.2.u.a.2159.7		96	16.3	odd	4	inner
2880.2.u.a.2159.18		96	240.179	even	4	inner
2880.2.u.a.2159.31		96	80.19	odd	4	inner
2880.2.u.a.2159.42		96	48.35	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)

\(f(q)\)	\(=\)	\(q+(-1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +O(q^{10})\)	\(q+(-1.11222 - 1.93984i) q^{5} -1.78786i q^{7} +(-3.34421 - 3.34421i) q^{11} +(2.90349 + 2.90349i) q^{13} -4.56733 q^{17} +(-0.0693845 - 0.0693845i) q^{19} -1.07695 q^{23} +(-2.52593 + 4.31505i) q^{25} +(-1.23988 - 1.23988i) q^{29} -8.56612i q^{31} +(-3.46816 + 1.98849i) q^{35} +(-7.62458 + 7.62458i) q^{37} +7.91601 q^{41} +(-2.35179 - 2.35179i) q^{43} +6.32188i q^{47} +3.80356 q^{49} +(-3.61429 - 3.61429i) q^{53} +(-2.76772 + 10.2067i) q^{55} +(-2.25080 - 2.25080i) q^{59} +(4.29893 - 4.29893i) q^{61} +(2.40297 - 8.86160i) q^{65} +(-5.85271 + 5.85271i) q^{67} +15.1431i q^{71} +6.88118 q^{73} +(-5.97897 + 5.97897i) q^{77} +12.9721i q^{79} +(-6.88840 - 6.88840i) q^{83} +(5.07987 + 8.85986i) q^{85} +6.31609 q^{89} +(5.19103 - 5.19103i) q^{91} +(-0.0574238 + 0.211766i) q^{95} +4.56728i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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