LMFDB - Embedded newform 2880.2.bc.a.593.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(593,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("2880.593");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.bc (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			593.15
Character	$\chi$	$=$	2880.593
Dual form			2880.2.bc.a.1457.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29201 + 1.82503i) q^{5} +(2.02860 + 2.02860i) q^{7} +O(q^{10})$	$q+(-1.29201 + 1.82503i) q^{5} +(2.02860 + 2.02860i) q^{7} +(-3.30349 - 3.30349i) q^{11} -1.32263i q^{13} +(-1.37324 - 1.37324i) q^{17} +(3.52013 - 3.52013i) q^{19} +(2.72908 + 2.72908i) q^{23} +(-1.66144 - 4.71589i) q^{25} +(-5.39873 - 5.39873i) q^{29} -0.163297 q^{31} +(-6.32321 + 1.08128i) q^{35} +4.06899i q^{37} -8.10945 q^{41} -6.10902 q^{43} +(3.28261 + 3.28261i) q^{47} +1.23042i q^{49} -11.5149i q^{53} +(10.2971 - 1.76083i) q^{55} +(8.29599 - 8.29599i) q^{59} +(-5.11708 - 5.11708i) q^{61} +(2.41384 + 1.70885i) q^{65} +10.8288 q^{67} +2.20918 q^{71} +(3.31187 - 3.31187i) q^{73} -13.4029i q^{77} +6.43519i q^{79} +8.28920 q^{83} +(4.28042 - 0.731962i) q^{85} -10.1147i q^{89} +(2.68309 - 2.68309i) q^{91} +(1.87630 + 10.9723i) q^{95} +(-7.10602 + 7.10602i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) $ 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−1.29201	+	1.82503i	−0.577803	+	0.816176i
$5$	−1.29201	+	1.82503i	−0.577803	+	0.816176i
$6$		0			0
$7$	2.02860	+	2.02860i	0.766738	+	0.766738i	0.977531	−	0.210793i	$-0.0676045\pi$
$7$	2.02860	+	2.02860i	0.766738	+	0.766738i	−0.210793	+	0.977531i	$0.567604\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.30349	−	3.30349i	−0.996041	−	0.996041i	0.00395115	−	0.999992i	$-0.498742\pi$
$11$	−3.30349	−	3.30349i	−0.996041	−	0.996041i	−0.999992	+	0.00395115i	$0.998742\pi$
$12$		0			0
$13$		−	1.32263i		−	0.366832i	−0.983035	−	0.183416i	$-0.941284\pi$
$13$		−	1.32263i		−	0.366832i	0.983035	−	0.183416i	$-0.0587156\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.37324	−	1.37324i	−0.333059	−	0.333059i	0.520688	−	0.853747i	$-0.325675\pi$
$17$	−1.37324	−	1.37324i	−0.333059	−	0.333059i	−0.853747	+	0.520688i	$0.825675\pi$
$18$		0			0
$19$	3.52013	−	3.52013i	0.807573	−	0.807573i	−0.176693	−	0.984266i	$-0.556540\pi$
$19$	3.52013	−	3.52013i	0.807573	−	0.807573i	0.984266	+	0.176693i	$0.0565401\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.72908	+	2.72908i	0.569052	+	0.569052i	0.931863	−	0.362811i	$-0.118183\pi$
$23$	2.72908	+	2.72908i	0.569052	+	0.569052i	−0.362811	+	0.931863i	$0.618183\pi$
$24$		0			0
$25$	−1.66144	−	4.71589i	−0.332288	−	0.943178i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.39873	−	5.39873i	−1.00252	−	1.00252i	−0.999997	−	0.00252292i	$-0.999197\pi$
$29$	−5.39873	−	5.39873i	−1.00252	−	1.00252i	−0.00252292	−	0.999997i	$-0.500803\pi$
$30$		0			0
$31$	−0.163297			−0.0293289			−0.0146645	−	0.999892i	$-0.504668\pi$
$31$	−0.163297			−0.0293289			−0.0146645	+	0.999892i	$0.504668\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.32321	+	1.08128i	−1.06882	+	0.182770i
$36$		0			0
$37$			4.06899i			0.668938i	0.942407	+	0.334469i	$0.108557\pi$
$37$			4.06899i			0.668938i	−0.942407	+	0.334469i	$0.891443\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−8.10945			−1.26648			−0.633241	−	0.773954i	$-0.718276\pi$
$41$	−8.10945			−1.26648			−0.633241	+	0.773954i	$0.718276\pi$
$42$		0			0
$43$	−6.10902			−0.931617			−0.465808	−	0.884886i	$-0.654236\pi$
$43$	−6.10902			−0.931617			−0.465808	+	0.884886i	$0.654236\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.28261	+	3.28261i	0.478819	+	0.478819i	0.904754	−	0.425935i	$-0.140055\pi$
$47$	3.28261	+	3.28261i	0.478819	+	0.478819i	−0.425935	+	0.904754i	$0.640055\pi$
$48$		0			0
$49$			1.23042i			0.175775i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	11.5149i		−	1.58170i	−0.612012	−	0.790849i	$-0.709639\pi$
$53$		−	11.5149i		−	1.58170i	0.612012	−	0.790849i	$-0.290361\pi$
$54$		0			0
$55$	10.2971	−	1.76083i	1.38846	−	0.237430i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.29599	−	8.29599i	1.08005	−	1.08005i	0.0835415	−	0.996504i	$-0.473377\pi$
$59$	8.29599	−	8.29599i	1.08005	−	1.08005i	0.996504	−	0.0835415i	$-0.0266231\pi$
$60$		0			0
$61$	−5.11708	−	5.11708i	−0.655175	−	0.655175i	0.299059	−	0.954234i	$-0.403327\pi$
$61$	−5.11708	−	5.11708i	−0.655175	−	0.655175i	−0.954234	+	0.299059i	$0.903327\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.41384	+	1.70885i	0.299400	+	0.211957i
$66$		0			0
$67$	10.8288			1.32295			0.661476	−	0.749966i	$-0.269930\pi$
$67$	10.8288			1.32295			0.661476	+	0.749966i	$0.269930\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.20918			0.262181			0.131090	−	0.991370i	$-0.458152\pi$
$71$	2.20918			0.262181			0.131090	+	0.991370i	$0.458152\pi$
$72$		0			0
$73$	3.31187	−	3.31187i	0.387625	−	0.387625i	−0.486215	−	0.873839i	$-0.661623\pi$
$73$	3.31187	−	3.31187i	0.387625	−	0.387625i	0.873839	+	0.486215i	$0.161623\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	13.4029i		−	1.52741i
$78$		0			0
$79$			6.43519i			0.724016i	0.932175	+	0.362008i	$0.117909\pi$
$79$			6.43519i			0.724016i	−0.932175	+	0.362008i	$0.882091\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.28920			0.909858			0.454929	−	0.890528i	$-0.349665\pi$
$83$	8.28920			0.909858			0.454929	+	0.890528i	$0.349665\pi$
$84$		0			0
$85$	4.28042	−	0.731962i	0.464277	−	0.0793924i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	10.1147i		−	1.07215i	−0.844169	−	0.536077i	$-0.819906\pi$
$89$		−	10.1147i		−	1.07215i	0.844169	−	0.536077i	$-0.180094\pi$
$90$		0			0
$91$	2.68309	−	2.68309i	0.281264	−	0.281264i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.87630	+	10.9723i	0.192504	+	1.12574i
$96$		0			0
$97$	−7.10602	+	7.10602i	−0.721507	+	0.721507i	−0.968912	−	0.247405i	$-0.920422\pi$
$97$	−7.10602	+	7.10602i	−0.721507	+	0.721507i	0.247405	+	0.968912i	$0.420422\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.74768	+	5.74768i	0.571916	+	0.571916i	0.932663	−	0.360748i	$-0.117478\pi$
$101$	5.74768	+	5.74768i	0.571916	+	0.571916i	−0.360748	+	0.932663i	$0.617478\pi$
$102$		0			0
$103$	11.7463	−	11.7463i	1.15740	−	1.15740i	0.172362	−	0.985034i	$-0.444860\pi$
$103$	11.7463	−	11.7463i	1.15740	−	1.15740i	0.985034	−	0.172362i	$-0.0551398\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.5402			−1.11563			−0.557814	−	0.829966i	$-0.688360\pi$
$107$	−11.5402			−1.11563			−0.557814	+	0.829966i	$0.688360\pi$
$108$		0			0
$109$	11.7772	−	11.7772i	1.12805	−	1.12805i	0.137561	−	0.990493i	$-0.456074\pi$
$109$	11.7772	−	11.7772i	1.12805	−	1.12805i	0.990493	−	0.137561i	$-0.0439262\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.3930	+	14.3930i	−1.35398	+	1.35398i	−0.472812	+	0.881163i	$0.656761\pi$
$113$	−14.3930	+	14.3930i	−1.35398	+	1.35398i	−0.881163	+	0.472812i	$0.843239\pi$
$114$		0			0
$115$	−8.50662	+	1.45465i	−0.793246	+	0.135647i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	5.57149i		−	0.510737i
$120$		0			0
$121$			10.8262i			0.984196i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.7532	+	3.06079i	0.961797	+	0.273765i
$126$		0			0
$127$	4.36365	−	4.36365i	0.387211	−	0.387211i	−0.486480	−	0.873692i	$-0.661719\pi$
$127$	4.36365	−	4.36365i	0.387211	−	0.387211i	0.873692	+	0.486480i	$0.161719\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.23684	+	9.23684i	−0.807027	+	0.807027i	−0.984183	−	0.177156i	$-0.943310\pi$
$131$	−9.23684	+	9.23684i	−0.807027	+	0.807027i	0.177156	+	0.984183i	$0.443310\pi$
$132$		0			0
$133$	14.2818			1.23839
$134$		0			0
$135$		0			0
$136$		0			0
$137$	8.76531	−	8.76531i	0.748871	−	0.748871i	−0.225396	−	0.974267i	$-0.572368\pi$
$137$	8.76531	−	8.76531i	0.748871	−	0.748871i	0.974267	+	0.225396i	$0.0723675\pi$
$138$		0			0
$139$	6.90118	+	6.90118i	0.585350	+	0.585350i	0.936369	−	0.351018i	$-0.114165\pi$
$139$	6.90118	+	6.90118i	0.585350	+	0.585350i	−0.351018	+	0.936369i	$0.614165\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.36931	+	4.36931i	−0.365380	+	0.365380i
$144$		0			0
$145$	16.8280	−	2.87763i	1.39749	−	0.238974i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.07872	−	7.07872i	0.579911	−	0.579911i	−0.354968	−	0.934879i	$-0.615508\pi$
$149$	7.07872	−	7.07872i	0.579911	−	0.579911i	0.934879	+	0.354968i	$0.115508\pi$
$150$		0			0
$151$		−	20.3002i		−	1.65201i	−0.563665	−	0.826004i	$-0.690609\pi$
$151$		−	20.3002i		−	1.65201i	0.563665	−	0.826004i	$-0.309391\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.210980	−	0.298021i	0.0169463	−	0.0239376i
$156$		0			0
$157$	−11.9083			−0.950386			−0.475193	−	0.879882i	$-0.657622\pi$
$157$	−11.9083			−0.950386			−0.475193	+	0.879882i	$0.657622\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			11.0724i			0.872627i
$162$		0			0
$163$		−	20.0121i		−	1.56747i	−0.621094	−	0.783736i	$-0.713312\pi$
$163$		−	20.0121i		−	1.56747i	0.621094	−	0.783736i	$-0.286688\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.214521	+	0.214521i	−0.0166001	+	0.0166001i	−0.715358	−	0.698758i	$-0.753736\pi$
$167$	−0.214521	+	0.214521i	−0.0166001	+	0.0166001i	0.698758	+	0.715358i	$0.253736\pi$
$168$		0			0
$169$	11.2506			0.865434
$170$		0			0
$171$		0			0
$172$		0			0
$173$	20.9078			1.58959			0.794794	−	0.606880i	$-0.207579\pi$
$173$	20.9078			1.58959			0.794794	+	0.606880i	$0.207579\pi$
$174$		0			0
$175$	6.19625	−	12.9370i	0.468393	−	0.977948i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−11.0326	−	11.0326i	−0.824618	−	0.824618i	0.162148	−	0.986766i	$-0.448158\pi$
$179$	−11.0326	−	11.0326i	−0.824618	−	0.824618i	−0.986766	+	0.162148i	$0.948158\pi$
$180$		0			0
$181$	−12.0226	+	12.0226i	−0.893633	+	0.893633i	−0.994863	−	0.101230i	$-0.967722\pi$
$181$	−12.0226	+	12.0226i	−0.893633	+	0.893633i	0.101230	+	0.994863i	$0.467722\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−7.42602	−	5.25716i	−0.545972	−	0.386514i
$186$		0			0
$187$			9.07295i			0.663480i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	8.67589i		−	0.627765i	−0.949462	−	0.313883i	$-0.898370\pi$
$191$		−	8.67589i		−	0.627765i	0.949462	−	0.313883i	$-0.101630\pi$
$192$		0			0
$193$	0.197253	+	0.197253i	0.0141986	+	0.0141986i	0.714170	−	0.699972i	$-0.246804\pi$
$193$	0.197253	+	0.197253i	0.0141986	+	0.0141986i	−0.699972	+	0.714170i	$0.746804\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.6104			−0.969700			−0.484850	−	0.874597i	$-0.661126\pi$
$197$	−13.6104			−0.969700			−0.484850	+	0.874597i	$0.661126\pi$
$198$		0			0
$199$	−10.3148			−0.731196			−0.365598	−	0.930773i	$-0.619135\pi$
$199$	−10.3148			−0.731196			−0.365598	+	0.930773i	$0.619135\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	21.9037i		−	1.53734i
$204$		0			0
$205$	10.4775	−	14.8000i	0.731777	−	1.03367i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−23.2574			−1.60875
$210$		0			0
$211$	8.23573	+	8.23573i	0.566971	+	0.566971i	0.931279	−	0.364308i	$-0.118694\pi$
$211$	8.23573	+	8.23573i	0.566971	+	0.566971i	−0.364308	+	0.931279i	$0.618694\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.89289	−	11.1491i	0.538291	−	0.760364i
$216$		0			0
$217$	−0.331263	−	0.331263i	−0.0224876	−	0.0224876i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.81629	+	1.81629i	−0.122177	+	0.122177i
$222$		0			0
$223$	−6.03653	−	6.03653i	−0.404236	−	0.404236i	0.475487	−	0.879723i	$-0.342272\pi$
$223$	−6.03653	−	6.03653i	−0.404236	−	0.404236i	−0.879723	+	0.475487i	$0.842272\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	9.05713i		−	0.601143i	−0.953759	−	0.300571i	$-0.902823\pi$
$227$		−	9.05713i		−	0.601143i	0.953759	−	0.300571i	$-0.0971773\pi$
$228$		0			0
$229$	−13.6898	−	13.6898i	−0.904649	−	0.904649i	0.0911851	−	0.995834i	$-0.470935\pi$
$229$	−13.6898	−	13.6898i	−0.904649	−	0.904649i	−0.995834	+	0.0911851i	$0.970935\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.31459	−	6.31459i	−0.413683	−	0.413683i	0.469337	−	0.883019i	$-0.344493\pi$
$233$	−6.31459	−	6.31459i	−0.413683	−	0.413683i	−0.883019	+	0.469337i	$0.844493\pi$
$234$		0			0
$235$	−10.2320	+	1.74970i	−0.667463	+	0.114138i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−10.5908			−0.685060			−0.342530	−	0.939507i	$-0.611284\pi$
$239$	−10.5908			−0.685060			−0.342530	+	0.939507i	$0.611284\pi$
$240$		0			0
$241$	25.8811			1.66715			0.833574	−	0.552408i	$-0.186291\pi$
$241$	25.8811			1.66715			0.833574	+	0.552408i	$0.186291\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.24555	−	1.58971i	−0.143463	−	0.101563i
$246$		0			0
$247$	−4.65584	−	4.65584i	−0.296244	−	0.296244i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.3065	−	12.3065i	−0.776778	−	0.776778i	0.202504	−	0.979281i	$-0.435092\pi$
$251$	−12.3065	−	12.3065i	−0.776778	−	0.776778i	−0.979281	+	0.202504i	$0.935092\pi$
$252$		0			0
$253$		−	18.0310i		−	1.13360i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.8942	+	13.8942i	0.866695	+	0.866695i	0.992105	−	0.125410i	$-0.0400248\pi$
$257$	13.8942	+	13.8942i	0.866695	+	0.866695i	−0.125410	+	0.992105i	$0.540025\pi$
$258$		0			0
$259$	−8.25435	+	8.25435i	−0.512900	+	0.512900i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.57250	+	9.57250i	0.590265	+	0.590265i	0.937703	−	0.347438i	$-0.112948\pi$
$263$	9.57250	+	9.57250i	0.590265	+	0.590265i	−0.347438	+	0.937703i	$0.612948\pi$
$264$		0			0
$265$	21.0151	+	14.8774i	1.29094	+	0.913909i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.87070	+	5.87070i	0.357943	+	0.357943i	0.863054	−	0.505111i	$-0.168549\pi$
$269$	5.87070	+	5.87070i	0.357943	+	0.357943i	−0.505111	+	0.863054i	$0.668549\pi$
$270$		0			0
$271$	13.6589			0.829718			0.414859	−	0.909886i	$-0.363831\pi$
$271$	13.6589			0.829718			0.414859	+	0.909886i	$0.363831\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−10.0904	+	21.0675i	−0.608471	+	1.27042i
$276$		0			0
$277$		−	2.46783i		−	0.148278i	−0.997248	−	0.0741389i	$-0.976379\pi$
$277$		−	2.46783i		−	0.148278i	0.997248	−	0.0741389i	$-0.0236208\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−22.7084			−1.35467			−0.677335	−	0.735675i	$-0.736865\pi$
$281$	−22.7084			−1.35467			−0.677335	+	0.735675i	$0.736865\pi$
$282$		0			0
$283$	−3.21667			−0.191211			−0.0956056	−	0.995419i	$-0.530479\pi$
$283$	−3.21667			−0.191211			−0.0956056	+	0.995419i	$0.530479\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−16.4508	−	16.4508i	−0.971061	−	0.971061i
$288$		0			0
$289$		−	13.2284i		−	0.778144i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	18.4166i		−	1.07591i	−0.842973	−	0.537955i	$-0.819197\pi$
$293$		−	18.4166i		−	1.07591i	0.842973	−	0.537955i	$-0.180803\pi$
$294$		0			0
$295$	4.42193	+	25.8589i	0.257455	+	1.50556i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.60956	−	3.60956i	0.208746	−	0.208746i
$300$		0			0
$301$	−12.3927	−	12.3927i	−0.714306	−	0.714306i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15.9501	−	2.72751i	0.913300	−	0.156177i
$306$		0			0
$307$	−16.5626			−0.945277			−0.472638	−	0.881256i	$-0.656698\pi$
$307$	−16.5626			−0.945277			−0.472638	+	0.881256i	$0.656698\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	20.6119			1.16879			0.584397	−	0.811468i	$-0.301331\pi$
$311$	20.6119			1.16879			0.584397	+	0.811468i	$0.301331\pi$
$312$		0			0
$313$	−4.41531	+	4.41531i	−0.249568	+	0.249568i	−0.820793	−	0.571225i	$-0.806468\pi$
$313$	−4.41531	+	4.41531i	−0.249568	+	0.249568i	0.571225	+	0.820793i	$0.306468\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			3.21460i			0.180550i	0.995917	+	0.0902750i	$0.0287746\pi$
$317$			3.21460i			0.180550i	−0.995917	+	0.0902750i	$0.971225\pi$
$318$		0			0
$319$			35.6694i			1.99710i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.66793			−0.537938
$324$		0			0
$325$	−6.23739	+	2.19748i	−0.345988	+	0.121894i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			13.3182i			0.734257i
$330$		0			0
$331$	−23.1909	+	23.1909i	−1.27469	+	1.27469i	−0.331089	+	0.943600i	$0.607416\pi$
$331$	−23.1909	+	23.1909i	−1.27469	+	1.27469i	−0.943600	+	0.331089i	$0.892584\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−13.9909	+	19.7629i	−0.764405	+	1.07976i
$336$		0			0
$337$	−12.5067	+	12.5067i	−0.681285	+	0.681285i	−0.960290	−	0.279005i	$-0.909995\pi$
$337$	−12.5067	+	12.5067i	−0.681285	+	0.681285i	0.279005	+	0.960290i	$0.409995\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.539450	+	0.539450i	0.0292128	+	0.0292128i
$342$		0			0
$343$	11.7042	−	11.7042i	0.631965	−	0.631965i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	11.9538			0.641716			0.320858	−	0.947127i	$-0.396029\pi$
$347$	11.9538			0.641716			0.320858	+	0.947127i	$0.396029\pi$
$348$		0			0
$349$	−17.0082	+	17.0082i	−0.910429	+	0.910429i	−0.996306	−	0.0858769i	$-0.972631\pi$
$349$	−17.0082	+	17.0082i	−0.910429	+	0.910429i	0.0858769	+	0.996306i	$0.472631\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.0137	−	14.0137i	0.745872	−	0.745872i	−0.227829	−	0.973701i	$-0.573163\pi$
$353$	14.0137	−	14.0137i	0.745872	−	0.745872i	0.973701	+	0.227829i	$0.0731627\pi$
$354$		0			0
$355$	−2.85427	+	4.03180i	−0.151489	+	0.213986i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			19.4255i			1.02524i	0.858616	+	0.512620i	$0.171325\pi$
$359$			19.4255i			1.02524i	−0.858616	+	0.512620i	$0.828675\pi$
$360$		0			0
$361$		−	5.78259i		−	0.304347i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.76529	+	10.3232i	0.0923996	+	0.540341i
$366$		0			0
$367$	8.99308	−	8.99308i	0.469435	−	0.469435i	−0.432296	−	0.901732i	$-0.642297\pi$
$367$	8.99308	−	8.99308i	0.469435	−	0.469435i	0.901732	+	0.432296i	$0.142297\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	23.3592	−	23.3592i	1.21275	−	1.21275i
$372$		0			0
$373$	3.75511			0.194432			0.0972160	−	0.995263i	$-0.469006\pi$
$373$	3.75511			0.194432			0.0972160	+	0.995263i	$0.469006\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.14054	+	7.14054i	−0.367757	+	0.367757i
$378$		0			0
$379$	11.2095	+	11.2095i	0.575794	+	0.575794i	0.933742	−	0.357948i	$-0.116523\pi$
$379$	11.2095	+	11.2095i	0.575794	+	0.575794i	−0.357948	+	0.933742i	$0.616523\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.22015	−	7.22015i	0.368932	−	0.368932i	−0.498155	−	0.867088i	$-0.665989\pi$
$383$	7.22015	−	7.22015i	0.368932	−	0.368932i	0.867088	+	0.498155i	$0.165989\pi$
$384$		0			0
$385$	24.4607	+	17.3167i	1.24663	+	0.882539i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−24.5313	+	24.5313i	−1.24379	+	1.24379i	−0.285369	+	0.958418i	$0.592116\pi$
$389$	−24.5313	+	24.5313i	−1.24379	+	1.24379i	−0.958418	+	0.285369i	$0.907884\pi$
$390$		0			0
$391$		−	7.49533i		−	0.379055i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.7444	−	8.31431i	−0.590924	−	0.418338i
$396$		0			0
$397$	−5.77500			−0.289839			−0.144919	−	0.989443i	$-0.546292\pi$
$397$	−5.77500			−0.289839			−0.144919	+	0.989443i	$0.546292\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			19.4666i			0.972116i	0.873927	+	0.486058i	$0.161566\pi$
$401$			19.4666i			0.972116i	−0.873927	+	0.486058i	$0.838434\pi$
$402$		0			0
$403$			0.215982i			0.0107588i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	13.4419	−	13.4419i	0.666290	−	0.666290i
$408$		0			0
$409$	−24.6895			−1.22081			−0.610407	−	0.792088i	$-0.708994\pi$
$409$	−24.6895			−1.22081			−0.610407	+	0.792088i	$0.708994\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	33.6585			1.65622
$414$		0			0
$415$	−10.7097	+	15.1280i	−0.525718	+	0.742605i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.5085	−	12.5085i	−0.611082	−	0.611082i	0.332146	−	0.943228i	$-0.392227\pi$
$419$	−12.5085	−	12.5085i	−0.611082	−	0.611082i	−0.943228	+	0.332146i	$0.892227\pi$
$420$		0			0
$421$	−3.90394	+	3.90394i	−0.190266	+	0.190266i	−0.795811	−	0.605545i	$-0.792955\pi$
$421$	−3.90394	+	3.90394i	−0.190266	+	0.190266i	0.605545	+	0.795811i	$0.292955\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.19448	+	8.75758i	−0.203462	+	0.424805i
$426$		0			0
$427$		−	20.7610i		−	1.00470i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			33.5433i			1.61572i	0.589371	+	0.807862i	$0.299376\pi$
$431$			33.5433i			1.61572i	−0.589371	+	0.807862i	$0.700624\pi$
$432$		0			0
$433$	−24.0797	−	24.0797i	−1.15720	−	1.15720i	−0.985076	−	0.172121i	$-0.944938\pi$
$433$	−24.0797	−	24.0797i	−1.15720	−	1.15720i	−0.172121	−	0.985076i	$-0.555062\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	19.2134			0.919101
$438$		0			0
$439$	1.80454			0.0861261			0.0430630	−	0.999072i	$-0.486288\pi$
$439$	1.80454			0.0861261			0.0430630	+	0.999072i	$0.486288\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	7.99522i		−	0.379865i	−0.981797	−	0.189932i	$-0.939173\pi$
$443$		−	7.99522i		−	0.379865i	0.981797	−	0.189932i	$-0.0608268\pi$
$444$		0			0
$445$	18.4596	+	13.0682i	0.875067	+	0.619494i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−23.9985			−1.13256			−0.566279	−	0.824214i	$-0.691617\pi$
$449$	−23.9985			−1.13256			−0.566279	+	0.824214i	$0.691617\pi$
$450$		0			0
$451$	26.7895	+	26.7895i	1.26147	+	1.26147i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.43014	+	8.36328i	0.0670460	+	0.392077i
$456$		0			0
$457$	0.921521	+	0.921521i	0.0431069	+	0.0431069i	0.728332	−	0.685225i	$-0.240296\pi$
$457$	0.921521	+	0.921521i	0.0431069	+	0.0431069i	−0.685225	+	0.728332i	$0.740296\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.71477	+	7.71477i	−0.359313	+	0.359313i	−0.863560	−	0.504247i	$-0.831770\pi$
$461$	−7.71477	+	7.71477i	−0.359313	+	0.359313i	0.504247	+	0.863560i	$0.331770\pi$
$462$		0			0
$463$	−10.7374	−	10.7374i	−0.499009	−	0.499009i	0.412120	−	0.911129i	$-0.364788\pi$
$463$	−10.7374	−	10.7374i	−0.499009	−	0.499009i	−0.911129	+	0.412120i	$0.864788\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	11.8647i		−	0.549033i	−0.961582	−	0.274516i	$-0.911482\pi$
$467$		−	11.8647i		−	0.549033i	0.961582	−	0.274516i	$-0.0885178\pi$
$468$		0			0
$469$	21.9673	+	21.9673i	1.01436	+	1.01436i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	20.1811	+	20.1811i	0.927929	+	0.927929i
$474$		0			0
$475$	−22.4490	−	10.7521i	−1.03003	−	0.493338i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.6761			0.670568			0.335284	−	0.942117i	$-0.391168\pi$
$479$	14.6761			0.670568			0.335284	+	0.942117i	$0.391168\pi$
$480$		0			0
$481$	5.38178			0.245388
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.78765	−	22.1497i	−0.171988	−	1.00577i
$486$		0			0
$487$	−15.8046	−	15.8046i	−0.716177	−	0.716177i	0.251643	−	0.967820i	$-0.419029\pi$
$487$	−15.8046	−	15.8046i	−0.716177	−	0.716177i	−0.967820	+	0.251643i	$0.919029\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.5216	+	12.5216i	0.565091	+	0.565091i	0.930749	−	0.365658i	$-0.119156\pi$
$491$	12.5216	+	12.5216i	0.565091	+	0.565091i	−0.365658	+	0.930749i	$0.619156\pi$
$492$		0			0
$493$			14.8275i			0.667796i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.48153	+	4.48153i	0.201024	+	0.201024i
$498$		0			0
$499$	−16.6276	+	16.6276i	−0.744356	+	0.744356i	−0.973413	−	0.229057i	$-0.926436\pi$
$499$	−16.6276	+	16.6276i	−0.744356	+	0.744356i	0.229057	+	0.973413i	$0.426436\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	25.0801	+	25.0801i	1.11827	+	1.11827i	0.991996	+	0.126269i	$0.0403003\pi$
$503$	25.0801	+	25.0801i	1.11827	+	1.11827i	0.126269	+	0.991996i	$0.459700\pi$
$504$		0			0
$505$	−17.9157	+	3.06363i	−0.797239	+	0.136330i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.37812	−	1.37812i	−0.0610839	−	0.0610839i	0.675905	−	0.736989i	$-0.263753\pi$
$509$	−1.37812	−	1.37812i	−0.0610839	−	0.0610839i	−0.736989	+	0.675905i	$0.763753\pi$
$510$		0			0
$511$	13.4369			0.594414
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.26100	+	36.6135i	0.275893	+	1.61339i
$516$		0			0
$517$		−	21.6882i		−	0.953846i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.2515			0.755802			0.377901	−	0.925846i	$-0.376646\pi$
$521$	17.2515			0.755802			0.377901	+	0.925846i	$0.376646\pi$
$522$		0			0
$523$	−24.4981			−1.07123			−0.535613	−	0.844464i	$-0.679919\pi$
$523$	−24.4981			−1.07123			−0.535613	+	0.844464i	$0.679919\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.224245	+	0.224245i	0.00976826	+	0.00976826i
$528$		0			0
$529$		−	8.10430i		−	0.352361i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			10.7258i			0.464587i
$534$		0			0
$535$	14.9100	−	21.0611i	0.644613	−	0.910550i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.06470	−	4.06470i	0.175079	−	0.175079i
$540$		0			0
$541$	3.53300	+	3.53300i	0.151896	+	0.151896i	0.778964	−	0.627068i	$-0.215745\pi$
$541$	3.53300	+	3.53300i	0.151896	+	0.151896i	−0.627068	+	0.778964i	$0.715745\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.27750	+	36.7100i	0.268898	+	1.57248i
$546$		0			0
$547$	−8.27786			−0.353936			−0.176968	−	0.984217i	$-0.556629\pi$
$547$	−8.27786			−0.353936			−0.176968	+	0.984217i	$0.556629\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−38.0085			−1.61921
$552$		0			0
$553$	−13.0544	+	13.0544i	−0.555130	+	0.555130i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	41.4835i		−	1.75771i	−0.477088	−	0.878855i	$-0.658308\pi$
$557$		−	41.4835i		−	1.75771i	0.477088	−	0.878855i	$-0.341692\pi$
$558$		0			0
$559$			8.07999i			0.341747i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	21.7731			0.917628			0.458814	−	0.888532i	$-0.348274\pi$
$563$	21.7731			0.917628			0.458814	+	0.888532i	$0.348274\pi$
$564$		0			0
$565$	−7.67173	−	44.8633i	−0.322752	−	1.88741i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	10.0468i		−	0.421182i	−0.977574	−	0.210591i	$-0.932461\pi$
$569$		−	10.0468i		−	0.421182i	0.977574	−	0.210591i	$-0.0675388\pi$
$570$		0			0
$571$	9.72264	−	9.72264i	0.406880	−	0.406880i	−0.473769	−	0.880649i	$-0.657107\pi$
$571$	9.72264	−	9.72264i	0.406880	−	0.406880i	0.880649	+	0.473769i	$0.157107\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.33582	−	17.4042i	0.347628	−	0.725806i
$576$		0			0
$577$	−7.38116	+	7.38116i	−0.307282	+	0.307282i	−0.843854	−	0.536572i	$-0.819719\pi$
$577$	−7.38116	+	7.38116i	−0.307282	+	0.307282i	0.536572	+	0.843854i	$0.319719\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.8155	+	16.8155i	0.697623	+	0.697623i
$582$		0			0
$583$	−38.0395	+	38.0395i	−1.57544	+	1.57544i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−39.8451			−1.64458			−0.822292	−	0.569066i	$-0.807305\pi$
$587$	−39.8451			−1.64458			−0.822292	+	0.569066i	$0.807305\pi$
$588$		0			0
$589$	−0.574825	+	0.574825i	−0.0236853	+	0.0236853i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	10.3163	−	10.3163i	0.423641	−	0.423641i	−0.462814	−	0.886455i	$-0.653160\pi$
$593$	10.3163	−	10.3163i	0.423641	−	0.423641i	0.886455	+	0.462814i	$0.153160\pi$
$594$		0			0
$595$	10.1681	+	7.19840i	0.416852	+	0.295105i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			4.32724i			0.176806i	0.996085	+	0.0884030i	$0.0281763\pi$
$599$			4.32724i			0.176806i	−0.996085	+	0.0884030i	$0.971824\pi$
$600$		0			0
$601$		−	35.7850i		−	1.45970i	−0.683607	−	0.729851i	$-0.739590\pi$
$601$		−	35.7850i		−	1.45970i	0.683607	−	0.729851i	$-0.260410\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.7580	−	13.9875i	−0.803277	−	0.568671i
$606$		0			0
$607$	−10.5879	+	10.5879i	−0.429748	+	0.429748i	−0.888543	−	0.458794i	$-0.848282\pi$
$607$	−10.5879	+	10.5879i	−0.429748	+	0.429748i	0.458794	+	0.888543i	$0.348282\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.34169	−	4.34169i	0.175646	−	0.175646i
$612$		0			0
$613$	−9.05654			−0.365790			−0.182895	−	0.983132i	$-0.558547\pi$
$613$	−9.05654			−0.365790			−0.182895	+	0.983132i	$0.558547\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.00692	−	8.00692i	0.322346	−	0.322346i	−0.527320	−	0.849667i	$-0.676803\pi$
$617$	8.00692	−	8.00692i	0.322346	−	0.322346i	0.849667	+	0.527320i	$0.176803\pi$
$618$		0			0
$619$	−16.5160	−	16.5160i	−0.663834	−	0.663834i	0.292448	−	0.956281i	$-0.405530\pi$
$619$	−16.5160	−	16.5160i	−0.663834	−	0.663834i	−0.956281	+	0.292448i	$0.905530\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	20.5186	−	20.5186i	0.822061	−	0.822061i
$624$		0			0
$625$	−19.4792	+	15.6703i	−0.779169	+	0.626813i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.58768	−	5.58768i	0.222796	−	0.222796i
$630$		0			0
$631$			1.83078i			0.0728822i	0.999336	+	0.0364411i	$0.0116021\pi$
$631$			1.83078i			0.0728822i	−0.999336	+	0.0364411i	$0.988398\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.32591	+	13.6016i	0.0923010	+	0.539765i
$636$		0			0
$637$	1.62740			0.0644799
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	14.7618i		−	0.583058i	−0.956562	−	0.291529i	$-0.905836\pi$
$641$		−	14.7618i		−	0.583058i	0.956562	−	0.291529i	$-0.0941640\pi$
$642$		0			0
$643$		−	17.1777i		−	0.677421i	−0.940891	−	0.338710i	$-0.890009\pi$
$643$		−	17.1777i		−	0.677421i	0.940891	−	0.338710i	$-0.109991\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	15.7483	−	15.7483i	0.619130	−	0.619130i	−0.326178	−	0.945308i	$-0.605761\pi$
$647$	15.7483	−	15.7483i	0.619130	−	0.619130i	0.945308	+	0.326178i	$0.105761\pi$
$648$		0			0
$649$	−54.8115			−2.15154
$650$		0			0
$651$		0			0
$652$		0			0
$653$	34.1501			1.33640			0.668199	−	0.743983i	$-0.267065\pi$
$653$	34.1501			1.33640			0.668199	+	0.743983i	$0.267065\pi$
$654$		0			0
$655$	−4.92342	−	28.7915i	−0.192374	−	1.12498i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.91488	+	3.91488i	0.152502	+	0.152502i	0.779234	−	0.626732i	$-0.215608\pi$
$659$	3.91488	+	3.91488i	0.152502	+	0.152502i	−0.626732	+	0.779234i	$0.715608\pi$
$660$		0			0
$661$	−33.0265	+	33.0265i	−1.28458	+	1.28458i	−0.346548	+	0.938032i	$0.612646\pi$
$661$	−33.0265	+	33.0265i	−1.28458	+	1.28458i	−0.938032	+	0.346548i	$0.887354\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−18.4522	+	26.0647i	−0.715547	+	1.01075i
$666$		0			0
$667$		−	29.4671i		−	1.14097i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			33.8085i			1.30516i
$672$		0			0
$673$	13.0734	+	13.0734i	0.503942	+	0.503942i	0.912660	−	0.408719i	$-0.134024\pi$
$673$	13.0734	+	13.0734i	0.503942	+	0.503942i	−0.408719	+	0.912660i	$0.634024\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.97260			0.152679			0.0763397	−	0.997082i	$-0.475677\pi$
$677$	3.97260			0.152679			0.0763397	+	0.997082i	$0.475677\pi$
$678$		0			0
$679$	−28.8305			−1.10641
$680$		0			0
$681$		0			0
$682$		0			0
$683$			18.7686i			0.718161i	0.933307	+	0.359081i	$0.116910\pi$
$683$			18.7686i			0.718161i	−0.933307	+	0.359081i	$0.883090\pi$
$684$		0			0
$685$	4.67209	+	27.3218i	0.178511	+	1.04391i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.2300			−0.580218
$690$		0			0
$691$	13.2261	+	13.2261i	0.503144	+	0.503144i	0.912413	−	0.409270i	$-0.134216\pi$
$691$	13.2261	+	13.2261i	0.503144	+	0.503144i	−0.409270	+	0.912413i	$0.634216\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−21.5112	+	3.67846i	−0.815966	+	0.139532i
$696$		0			0
$697$	11.1362	+	11.1362i	0.421813	+	0.421813i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	5.85188	−	5.85188i	0.221022	−	0.221022i	−0.587906	−	0.808929i	$-0.700048\pi$
$701$	5.85188	−	5.85188i	0.221022	−	0.221022i	0.808929	+	0.587906i	$0.200048\pi$
$702$		0			0
$703$	14.3234	+	14.3234i	0.540216	+	0.540216i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			23.3195i			0.877019i
$708$		0			0
$709$	11.1418	+	11.1418i	0.418438	+	0.418438i	0.884665	−	0.466227i	$-0.154387\pi$
$709$	11.1418	+	11.1418i	0.418438	+	0.418438i	−0.466227	+	0.884665i	$0.654387\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.445649	−	0.445649i	−0.0166897	−	0.0166897i
$714$		0			0
$715$	−2.32893	−	13.6193i	−0.0870970	−	0.509332i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.83653			−0.329547			−0.164773	−	0.986331i	$-0.552689\pi$
$719$	−8.83653			−0.329547			−0.164773	+	0.986331i	$0.552689\pi$
$720$		0			0
$721$	47.6570			1.77484
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−16.4902	+	34.4295i	−0.612429	+	1.27868i
$726$		0			0
$727$	21.8860	+	21.8860i	0.811708	+	0.811708i	0.984890	−	0.173182i	$-0.0554048\pi$
$727$	21.8860	+	21.8860i	0.811708	+	0.811708i	−0.173182	+	0.984890i	$0.555405\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	8.38912	+	8.38912i	0.310283	+	0.310283i
$732$		0			0
$733$		−	9.81906i		−	0.362675i	−0.983421	−	0.181338i	$-0.941957\pi$
$733$		−	9.81906i		−	0.362675i	0.983421	−	0.181338i	$-0.0580427\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−35.7730	−	35.7730i	−1.31771	−	1.31771i
$738$		0			0
$739$	28.7826	−	28.7826i	1.05879	−	1.05879i	0.0606259	−	0.998161i	$-0.480690\pi$
$739$	28.7826	−	28.7826i	1.05879	−	1.05879i	0.998161	−	0.0606259i	$-0.0193097\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	33.6714	+	33.6714i	1.23528	+	1.23528i	0.961907	+	0.273376i	$0.0881404\pi$
$743$	33.6714	+	33.6714i	1.23528	+	1.23528i	0.273376	+	0.961907i	$0.411860\pi$
$744$		0			0
$745$	3.77310	+	22.0646i	0.138236	+	0.808384i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−23.4103	−	23.4103i	−0.855395	−	0.855395i
$750$		0			0
$751$	0.304020			0.0110939			0.00554693	−	0.999985i	$-0.498234\pi$
$751$	0.304020			0.0110939			0.00554693	+	0.999985i	$0.498234\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	37.0484	+	26.2280i	1.34833	+	0.954534i
$756$		0			0
$757$			33.6193i			1.22191i	0.791664	+	0.610956i	$0.209215\pi$
$757$			33.6193i			1.22191i	−0.791664	+	0.610956i	$0.790785\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.6846			0.967317			0.483659	−	0.875257i	$-0.339308\pi$
$761$	26.6846			0.967317			0.483659	+	0.875257i	$0.339308\pi$
$762$		0			0
$763$	47.7825			1.72984
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.9725	−	10.9725i	−0.396196	−	0.396196i
$768$		0			0
$769$		−	2.66538i		−	0.0961159i	−0.998845	−	0.0480580i	$-0.984697\pi$
$769$		−	2.66538i		−	0.0961159i	0.998845	−	0.0480580i	$-0.0153032\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	0.126666i		−	0.00455587i	−0.999997	−	0.00227793i	$-0.999275\pi$
$773$		−	0.126666i		−	0.00455587i	0.999997	−	0.00227793i	$-0.000725089\pi$
$774$		0			0
$775$	0.271308	+	0.770089i	0.00974566	+	0.0276624i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−28.5463	+	28.5463i	−1.02278	+	1.02278i
$780$		0			0
$781$	−7.29800	−	7.29800i	−0.261143	−	0.261143i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	15.3856	−	21.7330i	0.549136	−	0.775683i
$786$		0			0
$787$	−43.9684			−1.56731			−0.783653	−	0.621199i	$-0.786646\pi$
$787$	−43.9684			−1.56731			−0.783653	+	0.621199i	$0.786646\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−58.3950			−2.07629
$792$		0			0
$793$	−6.76802	+	6.76802i	−0.240339	+	0.240339i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			40.6870i			1.44121i	0.693347	+	0.720604i	$0.256135\pi$
$797$			40.6870i			1.44121i	−0.693347	+	0.720604i	$0.743865\pi$
$798$		0			0
$799$		−	9.01561i		−	0.318949i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−21.8815			−0.772181
$804$		0			0
$805$	−20.2074	−	14.3056i	−0.712218	−	0.504206i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	9.49678i		−	0.333889i	−0.985966	−	0.166944i	$-0.946610\pi$
$809$		−	9.49678i		−	0.333889i	0.985966	−	0.166944i	$-0.0533900\pi$
$810$		0			0
$811$	6.57198	−	6.57198i	0.230773	−	0.230773i	−0.582242	−	0.813015i	$-0.697824\pi$
$811$	6.57198	−	6.57198i	0.230773	−	0.230773i	0.813015	+	0.582242i	$0.197824\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	36.5227	+	25.8558i	1.27933	+	0.905689i
$816$		0			0
$817$	−21.5045	+	21.5045i	−0.752348	+	0.752348i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−6.14199	−	6.14199i	−0.214357	−	0.214357i	0.591758	−	0.806115i	$-0.298434\pi$
$821$	−6.14199	−	6.14199i	−0.214357	−	0.214357i	−0.806115	+	0.591758i	$0.798434\pi$
$822$		0			0
$823$	−31.1801	+	31.1801i	−1.08687	+	1.08687i	−0.0910195	+	0.995849i	$0.529013\pi$
$823$	−31.1801	+	31.1801i	−1.08687	+	1.08687i	−0.995849	+	0.0910195i	$0.970987\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.501217			−0.0174290			−0.00871451	−	0.999962i	$-0.502774\pi$
$827$	−0.501217			−0.0174290			−0.00871451	+	0.999962i	$0.502774\pi$
$828$		0			0
$829$	−19.4306	+	19.4306i	−0.674851	+	0.674851i	−0.958830	−	0.283979i	$-0.908345\pi$
$829$	−19.4306	+	19.4306i	−0.674851	+	0.674851i	0.283979	+	0.958830i	$0.408345\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.68966	−	1.68966i	0.0585433	−	0.0585433i
$834$		0			0
$835$	−0.114344	−	0.668668i	−0.00395703	−	0.0231402i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			14.2054i			0.490424i	0.969469	+	0.245212i	$0.0788576\pi$
$839$			14.2054i			0.490424i	−0.969469	+	0.245212i	$0.921142\pi$
$840$		0			0
$841$			29.2927i			1.01009i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−14.5359	+	20.5327i	−0.500050	+	0.706347i
$846$		0			0
$847$	−21.9619	+	21.9619i	−0.754620	+	0.754620i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−11.1046	+	11.1046i	−0.380660	+	0.380660i
$852$		0			0
$853$	0.980294			0.0335646			0.0167823	−	0.999859i	$-0.494658\pi$
$853$	0.980294			0.0335646			0.0167823	+	0.999859i	$0.494658\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.66573	+	1.66573i	−0.0569003	+	0.0569003i	−0.734984	−	0.678084i	$-0.762811\pi$
$857$	−1.66573	+	1.66573i	−0.0569003	+	0.0569003i	0.678084	+	0.734984i	$0.262811\pi$
$858$		0			0
$859$	35.4006	+	35.4006i	1.20785	+	1.20785i	0.971721	+	0.236133i	$0.0758801\pi$
$859$	35.4006	+	35.4006i	1.20785	+	1.20785i	0.236133	+	0.971721i	$0.424120\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	32.0987	−	32.0987i	1.09265	−	1.09265i	0.0974086	−	0.995244i	$-0.468945\pi$
$863$	32.0987	−	32.0987i	1.09265	−	1.09265i	0.995244	−	0.0974086i	$-0.0310554\pi$
$864$		0			0
$865$	−27.0129	+	38.1572i	−0.918468	+	1.29738i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	21.2586	−	21.2586i	0.721149	−	0.721149i
$870$		0			0
$871$		−	14.3226i		−	0.485301i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	15.6048	+	28.0231i	0.527540	+	0.947352i
$876$		0			0
$877$	−10.3966			−0.351069			−0.175534	−	0.984473i	$-0.556165\pi$
$877$	−10.3966			−0.351069			−0.175534	+	0.984473i	$0.556165\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	41.2431i		−	1.38951i	−0.719245	−	0.694757i	$-0.755512\pi$
$881$		−	41.2431i		−	1.38951i	0.719245	−	0.694757i	$-0.244488\pi$
$882$		0			0
$883$		−	22.8134i		−	0.767732i	−0.923389	−	0.383866i	$-0.874593\pi$
$883$		−	22.8134i		−	0.767732i	0.923389	−	0.383866i	$-0.125407\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.9633	−	15.9633i	0.535996	−	0.535996i	−0.386354	−	0.922350i	$-0.626266\pi$
$887$	15.9633	−	15.9633i	0.535996	−	0.535996i	0.922350	+	0.386354i	$0.126266\pi$
$888$		0			0
$889$	17.7042			0.593779
$890$		0			0
$891$		0			0
$892$		0			0
$893$	23.1104			0.773361
$894$		0			0
$895$	34.3891	−	5.88062i	1.14950	−	0.196567i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.881595	+	0.881595i	0.0294028	+	0.0294028i
$900$		0			0
$901$	−15.8127	+	15.8127i	−0.526798	+	0.526798i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.40829	−	37.4748i	−0.213019	−	1.24571i
$906$		0			0
$907$			33.6267i			1.11656i	0.829654	+	0.558278i	$0.188538\pi$
$907$			33.6267i			1.11656i	−0.829654	+	0.558278i	$0.811462\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	16.3069i		−	0.540272i	−0.962822	−	0.270136i	$-0.912931\pi$
$911$		−	16.3069i		−	0.540272i	0.962822	−	0.270136i	$-0.0870687\pi$
$912$		0			0
$913$	−27.3833	−	27.3833i	−0.906256	−	0.906256i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−37.4757			−1.23756
$918$		0			0
$919$	−25.5350			−0.842323			−0.421162	−	0.906986i	$-0.638377\pi$
$919$	−25.5350			−0.842323			−0.421162	+	0.906986i	$0.638377\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	2.92193i		−	0.0961765i
$924$		0			0
$925$	19.1889	−	6.76039i	0.630928	−	0.222280i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−14.3973			−0.472360			−0.236180	−	0.971709i	$-0.575895\pi$
$929$	−14.3973			−0.472360			−0.236180	+	0.971709i	$0.575895\pi$
$930$		0			0
$931$	4.33125	+	4.33125i	0.141951	+	0.141951i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.5584	−	11.7223i	−0.541517	−	0.383361i
$936$		0			0
$937$	−41.3301	−	41.3301i	−1.35020	−	1.35020i	−0.885438	−	0.464757i	$-0.846142\pi$
$937$	−41.3301	−	41.3301i	−1.35020	−	1.35020i	−0.464757	−	0.885438i	$-0.653858\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−32.9564	+	32.9564i	−1.07435	+	1.07435i	−0.0773431	+	0.997005i	$0.524644\pi$
$941$	−32.9564	+	32.9564i	−1.07435	+	1.07435i	−0.997005	+	0.0773431i	$0.975356\pi$
$942$		0			0
$943$	−22.1313	−	22.1313i	−0.720694	−	0.720694i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	5.80564i		−	0.188658i	−0.995541	−	0.0943290i	$-0.969929\pi$
$947$		−	5.80564i		−	0.188658i	0.995541	−	0.0943290i	$-0.0300706\pi$
$948$		0			0
$949$	−4.38039	−	4.38039i	−0.142193	−	0.142193i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	31.6012	+	31.6012i	1.02366	+	1.02366i	0.999713	+	0.0239501i	$0.00762429\pi$
$953$	31.6012	+	31.6012i	1.02366	+	1.02366i	0.0239501	+	0.999713i	$0.492376\pi$
$954$		0			0
$955$	15.8337	+	11.2093i	0.512367	+	0.362725i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	35.5626			1.14838
$960$		0			0
$961$	−30.9733			−0.999140
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.614843	+	0.105140i	−0.0197925	+	0.00338456i
$966$		0			0
$967$	30.6886	+	30.6886i	0.986878	+	0.986878i	0.999915	−	0.0130369i	$-0.00414988\pi$
$967$	30.6886	+	30.6886i	0.986878	+	0.986878i	−0.0130369	+	0.999915i	$0.504150\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.02162	+	5.02162i	0.161151	+	0.161151i	0.783077	−	0.621925i	$-0.213649\pi$
$971$	5.02162	+	5.02162i	0.161151	+	0.161151i	−0.621925	+	0.783077i	$0.713649\pi$
$972$		0			0
$973$			27.9994i			0.897620i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.2983	+	21.2983i	0.681392	+	0.681392i	0.960314	−	0.278922i	$-0.0899770\pi$
$977$	21.2983	+	21.2983i	0.681392	+	0.681392i	−0.278922	+	0.960314i	$0.589977\pi$
$978$		0			0
$979$	−33.4138	+	33.4138i	−1.06791	+	1.06791i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−33.5737	−	33.5737i	−1.07084	−	1.07084i	−0.997292	−	0.0735434i	$-0.976569\pi$
$983$	−33.5737	−	33.5737i	−1.07084	−	1.07084i	−0.0735434	−	0.997292i	$-0.523431\pi$
$984$		0			0
$985$	17.5847	−	24.8393i	0.560295	−	0.791446i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.6720	−	16.6720i	−0.530138	−	0.530138i
$990$		0			0
$991$	−29.9874			−0.952580			−0.476290	−	0.879288i	$-0.658019\pi$
$991$	−29.9874			−0.952580			−0.476290	+	0.879288i	$0.658019\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	13.3268	−	18.8248i	0.422487	−	0.596785i
$996$		0			0
$997$		−	34.1815i		−	1.08254i	−0.840849	−	0.541270i	$-0.817944\pi$
$997$		−	34.1815i		−	1.08254i	0.840849	−	0.541270i	$-0.182056\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.bc.a.593.15		96
3.2	odd	2	inner	2880.2.bc.a.593.34		96
4.3	odd	2		720.2.bc.a.413.3	yes	96
5.2	odd	4		2880.2.bg.a.17.39		96
12.11	even	2		720.2.bc.a.413.46	yes	96
15.2	even	4		2880.2.bg.a.17.10		96
16.5	even	4		2880.2.bg.a.2033.10		96
16.11	odd	4		720.2.bg.a.53.27	yes	96
20.7	even	4		720.2.bg.a.557.22	yes	96
48.5	odd	4		2880.2.bg.a.2033.39		96
48.11	even	4		720.2.bg.a.53.22	yes	96
60.47	odd	4		720.2.bg.a.557.27	yes	96
80.27	even	4		720.2.bc.a.197.46	yes	96
80.37	odd	4	inner	2880.2.bc.a.1457.34		96
240.107	odd	4		720.2.bc.a.197.3	✓	96
240.197	even	4	inner	2880.2.bc.a.1457.15		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.3	✓	96	240.107	odd	4
720.2.bc.a.197.46	yes	96	80.27	even	4
720.2.bc.a.413.3	yes	96	4.3	odd	2
720.2.bc.a.413.46	yes	96	12.11	even	2
720.2.bg.a.53.22	yes	96	48.11	even	4
720.2.bg.a.53.27	yes	96	16.11	odd	4
720.2.bg.a.557.22	yes	96	20.7	even	4
720.2.bg.a.557.27	yes	96	60.47	odd	4
2880.2.bc.a.593.15		96	1.1	even	1	trivial
2880.2.bc.a.593.34		96	3.2	odd	2	inner
2880.2.bc.a.1457.15		96	240.197	even	4	inner
2880.2.bc.a.1457.34		96	80.37	odd	4	inner
2880.2.bg.a.17.10		96	15.2	even	4
2880.2.bg.a.17.39		96	5.2	odd	4
2880.2.bg.a.2033.10		96	16.5	even	4
2880.2.bg.a.2033.39		96	48.5	odd	4

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.bc (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29201 + 1.82503i) q^{5} +(2.02860 + 2.02860i) q^{7} +O(q^{10})\)	\(q+(-1.29201 + 1.82503i) q^{5} +(2.02860 + 2.02860i) q^{7} +(-3.30349 - 3.30349i) q^{11} -1.32263i q^{13} +(-1.37324 - 1.37324i) q^{17} +(3.52013 - 3.52013i) q^{19} +(2.72908 + 2.72908i) q^{23} +(-1.66144 - 4.71589i) q^{25} +(-5.39873 - 5.39873i) q^{29} -0.163297 q^{31} +(-6.32321 + 1.08128i) q^{35} +4.06899i q^{37} -8.10945 q^{41} -6.10902 q^{43} +(3.28261 + 3.28261i) q^{47} +1.23042i q^{49} -11.5149i q^{53} +(10.2971 - 1.76083i) q^{55} +(8.29599 - 8.29599i) q^{59} +(-5.11708 - 5.11708i) q^{61} +(2.41384 + 1.70885i) q^{65} +10.8288 q^{67} +2.20918 q^{71} +(3.31187 - 3.31187i) q^{73} -13.4029i q^{77} +6.43519i q^{79} +8.28920 q^{83} +(4.28042 - 0.731962i) q^{85} -10.1147i q^{89} +(2.68309 - 2.68309i) q^{91} +(1.87630 + 10.9723i) q^{95} +(-7.10602 + 7.10602i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 16 q^{19} - 64 q^{43} + 32 q^{61}+O(q^{100}) \) 96 * q - 16 * q^19 - 64 * q^43 + 32 * q^61

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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