LMFDB - Embedded newform 2880.2.bc.a.593.2

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			593.2
Character	$\chi$	$=$	2880.593
Dual form			2880.2.bc.a.1457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23368 + 0.103242i) q^{5} +(-1.05564 - 1.05564i) q^{7} +O(q^{10})$	$q+(-2.23368 + 0.103242i) q^{5} +(-1.05564 - 1.05564i) q^{7} +(1.51428 + 1.51428i) q^{11} -2.65415i q^{13} +(0.254280 + 0.254280i) q^{17} +(-3.23203 + 3.23203i) q^{19} +(4.80800 + 4.80800i) q^{23} +(4.97868 - 0.461221i) q^{25} +(1.90168 + 1.90168i) q^{29} -5.16972 q^{31} +(2.46696 + 2.24898i) q^{35} -2.11437i q^{37} +8.70551 q^{41} -2.75804 q^{43} +(-7.38909 - 7.38909i) q^{47} -4.77124i q^{49} -10.4747i q^{53} +(-3.53875 - 3.22607i) q^{55} +(-3.57121 + 3.57121i) q^{59} +(-8.66887 - 8.66887i) q^{61} +(0.274020 + 5.92852i) q^{65} -1.21905 q^{67} +8.38170 q^{71} +(3.75046 - 3.75046i) q^{73} -3.19707i q^{77} -1.72981i q^{79} +9.30525 q^{83} +(-0.594233 - 0.541728i) q^{85} -7.87524i q^{89} +(-2.80183 + 2.80183i) q^{91} +(6.88566 - 7.55302i) q^{95} +(-9.69875 + 9.69875i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.23368	+	0.103242i	−0.998934	+	0.0461713i
$5$	−2.23368	+	0.103242i	−0.998934	+	0.0461713i
$6$		0			0
$7$	−1.05564	−	1.05564i	−0.398995	−	0.398995i	0.478883	−	0.877879i	$-0.341042\pi$
$7$	−1.05564	−	1.05564i	−0.398995	−	0.398995i	−0.877879	+	0.478883i	$0.841042\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.51428	+	1.51428i	0.456571	+	0.456571i	0.897528	−	0.440957i	$-0.145361\pi$
$11$	1.51428	+	1.51428i	0.456571	+	0.456571i	−0.440957	+	0.897528i	$0.645361\pi$
$12$		0			0
$13$		−	2.65415i		−	0.736128i	−0.929801	−	0.368064i	$-0.880021\pi$
$13$		−	2.65415i		−	0.736128i	0.929801	−	0.368064i	$-0.119979\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.254280	+	0.254280i	0.0616719	+	0.0616719i	0.737270	−	0.675598i	$-0.236115\pi$
$17$	0.254280	+	0.254280i	0.0616719	+	0.0616719i	−0.675598	+	0.737270i	$0.736115\pi$
$18$		0			0
$19$	−3.23203	+	3.23203i	−0.741480	+	0.741480i	−0.972863	−	0.231383i	$-0.925675\pi$
$19$	−3.23203	+	3.23203i	−0.741480	+	0.741480i	0.231383	+	0.972863i	$0.425675\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.80800	+	4.80800i	1.00254	+	1.00254i	0.999997	+	0.00254003i	$0.000808517\pi$
$23$	4.80800	+	4.80800i	1.00254	+	1.00254i	0.00254003	+	0.999997i	$0.499191\pi$
$24$		0			0
$25$	4.97868	−	0.461221i	0.995736	−	0.0922441i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.90168	+	1.90168i	0.353133	+	0.353133i	0.861274	−	0.508141i	$-0.169667\pi$
$29$	1.90168	+	1.90168i	0.353133	+	0.353133i	−0.508141	+	0.861274i	$0.669667\pi$
$30$		0			0
$31$	−5.16972			−0.928509			−0.464254	−	0.885702i	$-0.653678\pi$
$31$	−5.16972			−0.928509			−0.464254	+	0.885702i	$0.653678\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.46696	+	2.24898i	0.416992	+	0.380148i
$36$		0			0
$37$		−	2.11437i		−	0.347601i	−0.984781	−	0.173801i	$-0.944395\pi$
$37$		−	2.11437i		−	0.347601i	0.984781	−	0.173801i	$-0.0556048\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.70551			1.35957			0.679786	−	0.733410i	$-0.262073\pi$
$41$	8.70551			1.35957			0.679786	+	0.733410i	$0.262073\pi$
$42$		0			0
$43$	−2.75804			−0.420597			−0.210298	−	0.977637i	$-0.567444\pi$
$43$	−2.75804			−0.420597			−0.210298	+	0.977637i	$0.567444\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.38909	−	7.38909i	−1.07781	−	1.07781i	−0.996706	−	0.0811038i	$-0.974155\pi$
$47$	−7.38909	−	7.38909i	−1.07781	−	1.07781i	−0.0811038	−	0.996706i	$-0.525845\pi$
$48$		0			0
$49$		−	4.77124i		−	0.681606i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	10.4747i		−	1.43882i	−0.694588	−	0.719408i	$-0.744413\pi$
$53$		−	10.4747i		−	1.43882i	0.694588	−	0.719408i	$-0.255587\pi$
$54$		0			0
$55$	−3.53875	−	3.22607i	−0.477165	−	0.435004i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.57121	+	3.57121i	−0.464932	+	0.464932i	−0.900268	−	0.435336i	$-0.856630\pi$
$59$	−3.57121	+	3.57121i	−0.464932	+	0.464932i	0.435336	+	0.900268i	$0.356630\pi$
$60$		0			0
$61$	−8.66887	−	8.66887i	−1.10994	−	1.10994i	−0.993158	−	0.116777i	$-0.962744\pi$
$61$	−8.66887	−	8.66887i	−1.10994	−	1.10994i	−0.116777	−	0.993158i	$-0.537256\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.274020	+	5.92852i	0.0339880	+	0.735343i
$66$		0			0
$67$	−1.21905			−0.148931			−0.0744656	−	0.997224i	$-0.523725\pi$
$67$	−1.21905			−0.148931			−0.0744656	+	0.997224i	$0.523725\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	8.38170			0.994724			0.497362	−	0.867543i	$-0.334302\pi$
$71$	8.38170			0.994724			0.497362	+	0.867543i	$0.334302\pi$
$72$		0			0
$73$	3.75046	−	3.75046i	0.438959	−	0.438959i	−0.452703	−	0.891661i	$-0.649540\pi$
$73$	3.75046	−	3.75046i	0.438959	−	0.438959i	0.891661	+	0.452703i	$0.149540\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	3.19707i		−	0.364340i
$78$		0			0
$79$		−	1.72981i		−	0.194618i	−0.995254	−	0.0973092i	$-0.968976\pi$
$79$		−	1.72981i		−	0.194618i	0.995254	−	0.0973092i	$-0.0310236\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	9.30525			1.02138			0.510692	−	0.859764i	$-0.329389\pi$
$83$	9.30525			1.02138			0.510692	+	0.859764i	$0.329389\pi$
$84$		0			0
$85$	−0.594233	−	0.541728i	−0.0644536	−	0.0587587i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	7.87524i		−	0.834774i	−0.908729	−	0.417387i	$-0.862946\pi$
$89$		−	7.87524i		−	0.834774i	0.908729	−	0.417387i	$-0.137054\pi$
$90$		0			0
$91$	−2.80183	+	2.80183i	−0.293711	+	0.293711i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	6.88566	−	7.55302i	0.706454	−	0.774924i
$96$		0			0
$97$	−9.69875	+	9.69875i	−0.984759	+	0.984759i	−0.999886	−	0.0151266i	$-0.995185\pi$
$97$	−9.69875	+	9.69875i	−0.984759	+	0.984759i	0.0151266	+	0.999886i	$0.495185\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.53348	−	4.53348i	−0.451098	−	0.451098i	0.444621	−	0.895719i	$-0.353338\pi$
$101$	−4.53348	−	4.53348i	−0.451098	−	0.451098i	−0.895719	+	0.444621i	$0.853338\pi$
$102$		0			0
$103$	10.9422	−	10.9422i	1.07816	−	1.07816i	0.0814886	−	0.996674i	$-0.474033\pi$
$103$	10.9422	−	10.9422i	1.07816	−	1.07816i	0.996674	−	0.0814886i	$-0.0259674\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.56175			0.344328			0.172164	−	0.985068i	$-0.444924\pi$
$107$	3.56175			0.344328			0.172164	+	0.985068i	$0.444924\pi$
$108$		0			0
$109$	8.89026	−	8.89026i	0.851532	−	0.851532i	−0.138790	−	0.990322i	$-0.544321\pi$
$109$	8.89026	−	8.89026i	0.851532	−	0.851532i	0.990322	+	0.138790i	$0.0443212\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.81674	−	5.81674i	0.547193	−	0.547193i	−0.378435	−	0.925628i	$-0.623538\pi$
$113$	5.81674	−	5.81674i	0.547193	−	0.547193i	0.925628	+	0.378435i	$0.123538\pi$
$114$		0			0
$115$	−11.2359	−	10.2432i	−1.04776	−	0.955179i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		−	0.536857i		−	0.0492136i
$120$		0			0
$121$		−	6.41394i		−	0.583085i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.0732	+	1.54423i	−0.990415	+	0.138120i
$126$		0			0
$127$	13.5826	−	13.5826i	1.20526	−	1.20526i	0.232714	−	0.972545i	$-0.425239\pi$
$127$	13.5826	−	13.5826i	1.20526	−	1.20526i	0.972545	−	0.232714i	$-0.0747607\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.9431	+	11.9431i	−1.04347	+	1.04347i	−0.0444609	+	0.999011i	$0.514157\pi$
$131$	−11.9431	+	11.9431i	−1.04347	+	1.04347i	−0.999011	+	0.0444609i	$0.985843\pi$
$132$		0			0
$133$	6.82375			0.591694
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.8098	−	14.8098i	1.26529	−	1.26529i	0.316790	−	0.948496i	$-0.397395\pi$
$137$	14.8098	−	14.8098i	1.26529	−	1.26529i	0.948496	−	0.316790i	$-0.102605\pi$
$138$		0			0
$139$	1.30878	+	1.30878i	0.111009	+	0.111009i	0.760430	−	0.649420i	$-0.224988\pi$
$139$	1.30878	+	1.30878i	0.111009	+	0.111009i	−0.649420	+	0.760430i	$0.724988\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	4.01911	−	4.01911i	0.336095	−	0.336095i
$144$		0			0
$145$	−4.44408	−	4.05141i	−0.369061	−	0.336451i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.96235	+	9.96235i	−0.816148	+	0.816148i	−0.985547	−	0.169400i	$-0.945817\pi$
$149$	−9.96235	+	9.96235i	−0.816148	+	0.816148i	0.169400	+	0.985547i	$0.445817\pi$
$150$		0			0
$151$			8.27525i			0.673431i	0.941606	+	0.336715i	$0.109316\pi$
$151$			8.27525i			0.673431i	−0.941606	+	0.336715i	$0.890684\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.5475	−	0.533733i	0.927518	−	0.0428705i
$156$		0			0
$157$	−14.0605			−1.12215			−0.561073	−	0.827766i	$-0.689611\pi$
$157$	−14.0605			−1.12215			−0.561073	+	0.827766i	$0.689611\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	10.1511i		−	0.800015i
$162$		0			0
$163$		−	17.6493i		−	1.38240i	−0.722662	−	0.691201i	$-0.757082\pi$
$163$		−	17.6493i		−	1.38240i	0.722662	−	0.691201i	$-0.242918\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.39133	−	2.39133i	0.185047	−	0.185047i	−0.608504	−	0.793551i	$-0.708230\pi$
$167$	2.39133	−	2.39133i	0.185047	−	0.185047i	0.793551	+	0.608504i	$0.208230\pi$
$168$		0			0
$169$	5.95551			0.458116
$170$		0			0
$171$		0			0
$172$		0			0
$173$	15.4240			1.17266			0.586331	−	0.810071i	$-0.300572\pi$
$173$	15.4240			1.17266			0.586331	+	0.810071i	$0.300572\pi$
$174$		0			0
$175$	−5.74259	−	4.76882i	−0.434099	−	0.360489i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.30612	+	4.30612i	0.321854	+	0.321854i	0.849478	−	0.527624i	$-0.176917\pi$
$179$	4.30612	+	4.30612i	0.321854	+	0.321854i	−0.527624	+	0.849478i	$0.676917\pi$
$180$		0			0
$181$	11.4990	−	11.4990i	0.854712	−	0.854712i	−0.135997	−	0.990709i	$-0.543424\pi$
$181$	11.4990	−	11.4990i	0.854712	−	0.854712i	0.990709	+	0.135997i	$0.0434237\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.218293	+	4.72284i	0.0160492	+	0.347230i
$186$		0			0
$187$			0.770099i			0.0563152i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	17.6550i		−	1.27747i	−0.769426	−	0.638736i	$-0.779458\pi$
$191$		−	17.6550i		−	1.27747i	0.769426	−	0.638736i	$-0.220542\pi$
$192$		0			0
$193$	6.16818	+	6.16818i	0.443996	+	0.443996i	0.893352	−	0.449357i	$-0.148347\pi$
$193$	6.16818	+	6.16818i	0.443996	+	0.443996i	−0.449357	+	0.893352i	$0.648347\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.99067			−0.711806			−0.355903	−	0.934523i	$-0.615827\pi$
$197$	−9.99067			−0.711806			−0.355903	+	0.934523i	$0.615827\pi$
$198$		0			0
$199$	−3.67453			−0.260480			−0.130240	−	0.991482i	$-0.541575\pi$
$199$	−3.67453			−0.260480			−0.130240	+	0.991482i	$0.541575\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	4.01498i		−	0.281797i
$204$		0			0
$205$	−19.4454	+	0.898776i	−1.35812	+	0.0627732i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.78838			−0.677076
$210$		0			0
$211$	−14.5199	−	14.5199i	−0.999591	−	0.999591i	0.000408671	−	1.00000i	$-0.499870\pi$
$211$	−14.5199	−	14.5199i	−0.999591	−	0.999591i	−1.00000		0.000408671i	$0.999870\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.16058	−	0.284746i	0.420148	−	0.0194195i
$216$		0			0
$217$	5.45737	+	5.45737i	0.370471	+	0.370471i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.674896	−	0.674896i	0.0453984	−	0.0453984i
$222$		0			0
$223$	9.67263	+	9.67263i	0.647727	+	0.647727i	0.952443	−	0.304716i	$-0.0985616\pi$
$223$	9.67263	+	9.67263i	0.647727	+	0.647727i	−0.304716	+	0.952443i	$0.598562\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			4.60247i			0.305477i	0.988267	+	0.152738i	$0.0488092\pi$
$227$			4.60247i			0.305477i	−0.988267	+	0.152738i	$0.951191\pi$
$228$		0			0
$229$	−9.02771	−	9.02771i	−0.596568	−	0.596568i	0.342829	−	0.939398i	$-0.388615\pi$
$229$	−9.02771	−	9.02771i	−0.596568	−	0.596568i	−0.939398	+	0.342829i	$0.888615\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.19060	+	5.19060i	0.340047	+	0.340047i	0.856385	−	0.516338i	$-0.172705\pi$
$233$	5.19060	+	5.19060i	0.340047	+	0.340047i	−0.516338	+	0.856385i	$0.672705\pi$
$234$		0			0
$235$	17.2678	+	15.7420i	1.12642	+	1.02690i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−28.8788			−1.86801			−0.934007	−	0.357254i	$-0.883713\pi$
$239$	−28.8788			−1.86801			−0.934007	+	0.357254i	$0.883713\pi$
$240$		0			0
$241$	−25.4602			−1.64003			−0.820016	−	0.572340i	$-0.806036\pi$
$241$	−25.4602			−1.64003			−0.820016	+	0.572340i	$0.806036\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.492593	+	10.6574i	0.0314706	+	0.680879i
$246$		0			0
$247$	8.57829	+	8.57829i	0.545824	+	0.545824i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.6822	+	18.6822i	1.17921	+	1.17921i	0.979946	+	0.199265i	$0.0638556\pi$
$251$	18.6822	+	18.6822i	1.17921	+	1.17921i	0.199265	+	0.979946i	$0.436144\pi$
$252$		0			0
$253$			14.5613i			0.915459i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.64788	−	1.64788i	−0.102792	−	0.102792i	0.653841	−	0.756632i	$-0.273157\pi$
$257$	−1.64788	−	1.64788i	−0.102792	−	0.102792i	−0.756632	+	0.653841i	$0.773157\pi$
$258$		0			0
$259$	−2.23202	+	2.23202i	−0.138691	+	0.138691i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.57958	−	1.57958i	−0.0974014	−	0.0974014i	0.656727	−	0.754128i	$-0.271940\pi$
$263$	−1.57958	−	1.57958i	−0.0974014	−	0.0974014i	−0.754128	+	0.656727i	$0.771940\pi$
$264$		0			0
$265$	1.08143	+	23.3972i	0.0664320	+	1.43728i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.1676	+	13.1676i	0.802842	+	0.802842i	0.983539	−	0.180697i	$-0.0578353\pi$
$269$	13.1676	+	13.1676i	0.802842	+	0.802842i	−0.180697	+	0.983539i	$0.557835\pi$
$270$		0			0
$271$	5.17418			0.314309			0.157155	−	0.987574i	$-0.449768\pi$
$271$	5.17418			0.314309			0.157155	+	0.987574i	$0.449768\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.23751	+	6.84068i	0.496741	+	0.412509i
$276$		0			0
$277$		−	11.7509i		−	0.706044i	−0.935615	−	0.353022i	$-0.885154\pi$
$277$		−	11.7509i		−	0.706044i	0.935615	−	0.353022i	$-0.114846\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	26.7311			1.59464			0.797322	−	0.603554i	$-0.206249\pi$
$281$	26.7311			1.59464			0.797322	+	0.603554i	$0.206249\pi$
$282$		0			0
$283$	−16.8169			−0.999660			−0.499830	−	0.866123i	$-0.666604\pi$
$283$	−16.8169			−0.999660			−0.499830	+	0.866123i	$0.666604\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−9.18990	−	9.18990i	−0.542463	−	0.542463i
$288$		0			0
$289$		−	16.8707i		−	0.992393i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			7.41502i			0.433190i	0.976262	+	0.216595i	$0.0694951\pi$
$293$			7.41502i			0.433190i	−0.976262	+	0.216595i	$0.930505\pi$
$294$		0			0
$295$	7.60826	−	8.34566i	0.442970	−	0.485903i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.7611	−	12.7611i	0.737995	−	0.737995i
$300$		0			0
$301$	2.91150	+	2.91150i	0.167816	+	0.167816i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	20.2585	+	18.4685i	1.16000	+	1.05750i
$306$		0			0
$307$	−2.77175			−0.158192			−0.0790961	−	0.996867i	$-0.525203\pi$
$307$	−2.77175			−0.158192			−0.0790961	+	0.996867i	$0.525203\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−21.7089			−1.23100			−0.615500	−	0.788137i	$-0.711046\pi$
$311$	−21.7089			−1.23100			−0.615500	+	0.788137i	$0.711046\pi$
$312$		0			0
$313$	−22.7143	+	22.7143i	−1.28389	+	1.28389i	−0.345453	+	0.938436i	$0.612275\pi$
$313$	−22.7143	+	22.7143i	−1.28389	+	1.28389i	−0.938436	+	0.345453i	$0.887725\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			10.1890i			0.572271i	0.958189	+	0.286135i	$0.0923707\pi$
$317$			10.1890i			0.572271i	−0.958189	+	0.286135i	$0.907629\pi$
$318$		0			0
$319$			5.75933i			0.322460i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.64368			−0.0914569
$324$		0			0
$325$	−1.22415	−	13.2141i	−0.0679035	−	0.732989i
$326$		0			0
$327$		0			0
$328$		0			0
$329$			15.6005i			0.860082i
$330$		0			0
$331$	14.6826	−	14.6826i	0.807030	−	0.807030i	−0.177154	−	0.984183i	$-0.556689\pi$
$331$	14.6826	−	14.6826i	0.807030	−	0.807030i	0.984183	+	0.177154i	$0.0566889\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.72298	−	0.125858i	0.148772	−	0.00687635i
$336$		0			0
$337$	8.11842	−	8.11842i	0.442238	−	0.442238i	−0.450525	−	0.892764i	$-0.648763\pi$
$337$	8.11842	−	8.11842i	0.442238	−	0.442238i	0.892764	+	0.450525i	$0.148763\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.82838	−	7.82838i	−0.423930	−	0.423930i
$342$		0			0
$343$	−12.4262	+	12.4262i	−0.670953	+	0.670953i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−28.5941			−1.53501			−0.767506	−	0.641042i	$-0.778502\pi$
$347$	−28.5941			−1.53501			−0.767506	+	0.641042i	$0.778502\pi$
$348$		0			0
$349$	17.7724	−	17.7724i	0.951336	−	0.951336i	−0.0475336	−	0.998870i	$-0.515136\pi$
$349$	17.7724	−	17.7724i	0.951336	−	0.951336i	0.998870	+	0.0475336i	$0.0151361\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.30550	−	5.30550i	0.282383	−	0.282383i	−0.551675	−	0.834059i	$-0.686011\pi$
$353$	5.30550	−	5.30550i	0.282383	−	0.282383i	0.834059	+	0.551675i	$0.186011\pi$
$354$		0			0
$355$	−18.7221	+	0.865345i	−0.993664	+	0.0459277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	27.1306i		−	1.43190i	−0.698152	−	0.715950i	$-0.745994\pi$
$359$		−	27.1306i		−	1.43190i	0.698152	−	0.715950i	$-0.254006\pi$
$360$		0			0
$361$		−	1.89210i		−	0.0995840i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.99014	+	8.76455i	−0.418223	+	0.458758i
$366$		0			0
$367$	24.8356	−	24.8356i	1.29641	−	1.29641i	0.365657	−	0.930750i	$-0.380844\pi$
$367$	24.8356	−	24.8356i	1.29641	−	1.29641i	0.930750	−	0.365657i	$-0.119156\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−11.0576	+	11.0576i	−0.574081	+	0.574081i
$372$		0			0
$373$	16.3161			0.844817			0.422408	−	0.906406i	$-0.361185\pi$
$373$	16.3161			0.844817			0.422408	+	0.906406i	$0.361185\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	5.04733	−	5.04733i	0.259951	−	0.259951i
$378$		0			0
$379$	−8.69282	−	8.69282i	−0.446520	−	0.446520i	0.447676	−	0.894196i	$-0.352252\pi$
$379$	−8.69282	−	8.69282i	−0.446520	−	0.446520i	−0.894196	+	0.447676i	$0.852252\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.8954	−	14.8954i	0.761118	−	0.761118i	−0.215406	−	0.976525i	$-0.569108\pi$
$383$	14.8954	−	14.8954i	0.761118	−	0.761118i	0.976525	+	0.215406i	$0.0691075\pi$
$384$		0			0
$385$	0.330072	+	7.14123i	0.0168220	+	0.363951i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.34275	+	8.34275i	−0.422994	+	0.422994i	−0.886233	−	0.463239i	$-0.846687\pi$
$389$	−8.34275	+	8.34275i	−0.422994	+	0.422994i	0.463239	+	0.886233i	$0.346687\pi$
$390$		0			0
$391$			2.44515i			0.123657i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.178589	+	3.86384i	0.00898579	+	0.194411i
$396$		0			0
$397$	−8.37843			−0.420501			−0.210251	−	0.977647i	$-0.567428\pi$
$397$	−8.37843			−0.420501			−0.210251	+	0.977647i	$0.567428\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			10.6568i			0.532176i	0.963949	+	0.266088i	$0.0857312\pi$
$401$			10.6568i			0.532176i	−0.963949	+	0.266088i	$0.914269\pi$
$402$		0			0
$403$			13.7212i			0.683501i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.20175	−	3.20175i	0.158705	−	0.158705i
$408$		0			0
$409$	8.23834			0.407360			0.203680	−	0.979038i	$-0.434710\pi$
$409$	8.23834			0.407360			0.203680	+	0.979038i	$0.434710\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.53985			0.371012
$414$		0			0
$415$	−20.7850	+	0.960695i	−1.02029	+	0.0471586i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−27.9688	−	27.9688i	−1.36637	−	1.36637i	−0.865559	−	0.500807i	$-0.833037\pi$
$419$	−27.9688	−	27.9688i	−1.36637	−	1.36637i	−0.500807	−	0.865559i	$-0.666963\pi$
$420$		0			0
$421$	−20.9868	+	20.9868i	−1.02283	+	1.02283i	−0.0231012	+	0.999733i	$0.507354\pi$
$421$	−20.9868	+	20.9868i	−1.02283	+	1.02283i	−0.999733	+	0.0231012i	$0.992646\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.38326	+	1.14870i	0.0670979	+	0.0557201i
$426$		0			0
$427$			18.3025i			0.885718i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			17.3162i			0.834090i	0.908886	+	0.417045i	$0.136934\pi$
$431$			17.3162i			0.834090i	−0.908886	+	0.417045i	$0.863066\pi$
$432$		0			0
$433$	13.6354	+	13.6354i	0.655277	+	0.655277i	0.954259	−	0.298982i	$-0.0966471\pi$
$433$	13.6354	+	13.6354i	0.655277	+	0.655277i	−0.298982	+	0.954259i	$0.596647\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−31.0792			−1.48672
$438$		0			0
$439$	0.504459			0.0240765			0.0120383	−	0.999928i	$-0.496168\pi$
$439$	0.504459			0.0240765			0.0120383	+	0.999928i	$0.496168\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	30.5844i		−	1.45311i	−0.687110	−	0.726553i	$-0.741121\pi$
$443$		−	30.5844i		−	1.45311i	0.687110	−	0.726553i	$-0.258879\pi$
$444$		0			0
$445$	0.813057	+	17.5908i	0.0385426	+	0.833883i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.04269			0.190786			0.0953931	−	0.995440i	$-0.469589\pi$
$449$	4.04269			0.190786			0.0953931	+	0.995440i	$0.469589\pi$
$450$		0			0
$451$	13.1825	+	13.1825i	0.620741	+	0.620741i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.96913	−	6.54767i	0.279837	−	0.306959i
$456$		0			0
$457$	4.55921	+	4.55921i	0.213271	+	0.213271i	0.805655	−	0.592384i	$-0.201813\pi$
$457$	4.55921	+	4.55921i	0.213271	+	0.213271i	−0.592384	+	0.805655i	$0.701813\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−27.8106	+	27.8106i	−1.29527	+	1.29527i	−0.363784	+	0.931483i	$0.618515\pi$
$461$	−27.8106	+	27.8106i	−1.29527	+	1.29527i	−0.931483	+	0.363784i	$0.881485\pi$
$462$		0			0
$463$	18.4748	+	18.4748i	0.858595	+	0.858595i	0.991173	−	0.132578i	$-0.0423254\pi$
$463$	18.4748	+	18.4748i	0.858595	+	0.858595i	−0.132578	+	0.991173i	$0.542325\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			11.3664i			0.525976i	0.964799	+	0.262988i	$0.0847080\pi$
$467$			11.3664i			0.525976i	−0.964799	+	0.262988i	$0.915292\pi$
$468$		0			0
$469$	1.28689	+	1.28689i	0.0594229	+	0.0594229i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.17643	−	4.17643i	−0.192032	−	0.192032i
$474$		0			0
$475$	−14.6006	+	17.5820i	−0.669921	+	0.806715i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−24.5489			−1.12167			−0.560835	−	0.827928i	$-0.689520\pi$
$479$	−24.5489			−1.12167			−0.560835	+	0.827928i	$0.689520\pi$
$480$		0			0
$481$	−5.61186			−0.255879
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.6626	−	22.6653i	0.938241	−	1.02918i
$486$		0			0
$487$	−3.31613	−	3.31613i	−0.150268	−	0.150268i	0.627970	−	0.778238i	$-0.283886\pi$
$487$	−3.31613	−	3.31613i	−0.150268	−	0.150268i	−0.778238	+	0.627970i	$0.783886\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.3132	+	12.3132i	0.555689	+	0.555689i	0.928077	−	0.372388i	$-0.121461\pi$
$491$	12.3132	+	12.3132i	0.555689	+	0.555689i	−0.372388	+	0.928077i	$0.621461\pi$
$492$		0			0
$493$			0.967117i			0.0435567i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.84807	−	8.84807i	−0.396890	−	0.396890i
$498$		0			0
$499$	−2.46597	+	2.46597i	−0.110392	+	0.110392i	−0.760145	−	0.649753i	$-0.774872\pi$
$499$	−2.46597	+	2.46597i	−0.110392	+	0.110392i	0.649753	+	0.760145i	$0.274872\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	7.33425	+	7.33425i	0.327018	+	0.327018i	0.851451	−	0.524434i	$-0.175723\pi$
$503$	7.33425	+	7.33425i	0.327018	+	0.327018i	−0.524434	+	0.851451i	$0.675723\pi$
$504$		0			0
$505$	10.5944	+	9.65831i	0.471445	+	0.429789i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.05717	−	9.05717i	−0.401452	−	0.401452i	0.477292	−	0.878745i	$-0.341618\pi$
$509$	−9.05717	−	9.05717i	−0.401452	−	0.401452i	−0.878745	+	0.477292i	$0.841618\pi$
$510$		0			0
$511$	−7.91830			−0.350285
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−23.3116	+	25.5710i	−1.02723	+	1.12679i
$516$		0			0
$517$		−	22.3782i		−	0.984194i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.71018			−0.0749242			−0.0374621	−	0.999298i	$-0.511927\pi$
$521$	−1.71018			−0.0749242			−0.0374621	+	0.999298i	$0.511927\pi$
$522$		0			0
$523$	22.9286			1.00260			0.501298	−	0.865275i	$-0.332856\pi$
$523$	22.9286			1.00260			0.501298	+	0.865275i	$0.332856\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.31455	−	1.31455i	−0.0572629	−	0.0572629i
$528$		0			0
$529$			23.2337i			1.01016i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	23.1057i		−	1.00082i
$534$		0			0
$535$	−7.95583	+	0.367723i	−0.343960	+	0.0158981i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	7.22497	−	7.22497i	0.311201	−	0.311201i
$540$		0			0
$541$	23.2938	+	23.2938i	1.00148	+	1.00148i	0.999999	+	0.00148102i	$0.000471425\pi$
$541$	23.2938	+	23.2938i	1.00148	+	1.00148i	0.00148102	+	0.999999i	$0.499529\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.9402	+	20.7759i	−0.811308	+	0.889940i
$546$		0			0
$547$	30.8130			1.31747			0.658735	−	0.752375i	$-0.271092\pi$
$547$	30.8130			1.31747			0.658735	+	0.752375i	$0.271092\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.2926			−0.523681
$552$		0			0
$553$	−1.82606	+	1.82606i	−0.0776518	+	0.0776518i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	38.7018i		−	1.63985i	−0.572474	−	0.819923i	$-0.694016\pi$
$557$		−	38.7018i		−	1.63985i	0.572474	−	0.819923i	$-0.305984\pi$
$558$		0			0
$559$			7.32023i			0.309613i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	25.9486			1.09361			0.546803	−	0.837262i	$-0.315845\pi$
$563$	25.9486			1.09361			0.546803	+	0.837262i	$0.315845\pi$
$564$		0			0
$565$	−12.3922	+	13.5933i	−0.521344	+	0.571874i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	40.2656i		−	1.68802i	−0.536325	−	0.844012i	$-0.680188\pi$
$569$		−	40.2656i		−	1.68802i	0.536325	−	0.844012i	$-0.319812\pi$
$570$		0			0
$571$	−0.756446	+	0.756446i	−0.0316563	+	0.0316563i	−0.722758	−	0.691101i	$-0.757126\pi$
$571$	−0.756446	+	0.756446i	−0.0316563	+	0.0316563i	0.691101	+	0.722758i	$0.257126\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	26.1550	+	21.7199i	1.09074	+	0.905784i
$576$		0			0
$577$	23.1618	−	23.1618i	0.964240	−	0.964240i	−0.0351420	−	0.999382i	$-0.511188\pi$
$577$	23.1618	−	23.1618i	0.964240	−	0.964240i	0.999382	+	0.0351420i	$0.0111883\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9.82302	−	9.82302i	−0.407527	−	0.407527i
$582$		0			0
$583$	15.8616	−	15.8616i	0.656922	−	0.656922i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.7508			0.691379			0.345689	−	0.938349i	$-0.387645\pi$
$587$	16.7508			0.691379			0.345689	+	0.938349i	$0.387645\pi$
$588$		0			0
$589$	16.7087	−	16.7087i	0.688470	−	0.688470i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.48968	−	1.48968i	0.0611737	−	0.0611737i	−0.675858	−	0.737032i	$-0.736227\pi$
$593$	1.48968	−	1.48968i	0.0611737	−	0.0611737i	0.737032	+	0.675858i	$0.236227\pi$
$594$		0			0
$595$	0.0554263	+	1.19917i	0.00227226	+	0.0491611i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			20.8334i			0.851228i	0.904905	+	0.425614i	$0.139942\pi$
$599$			20.8334i			0.851228i	−0.904905	+	0.425614i	$0.860058\pi$
$600$		0			0
$601$		−	11.7390i		−	0.478844i	−0.970916	−	0.239422i	$-0.923042\pi$
$601$		−	11.7390i		−	0.478844i	0.970916	−	0.239422i	$-0.0769580\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.662189	+	14.3267i	0.0269218	+	0.582464i
$606$		0			0
$607$	−0.700123	+	0.700123i	−0.0284171	+	0.0284171i	−0.721173	−	0.692755i	$-0.756397\pi$
$607$	−0.700123	+	0.700123i	−0.0284171	+	0.0284171i	0.692755	+	0.721173i	$0.256397\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−19.6117	+	19.6117i	−0.793405	+	0.793405i
$612$		0			0
$613$	7.85869			0.317410			0.158705	−	0.987326i	$-0.449268\pi$
$613$	7.85869			0.317410			0.158705	+	0.987326i	$0.449268\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.93604	+	9.93604i	−0.400010	+	0.400010i	−0.878237	−	0.478226i	$-0.841280\pi$
$617$	−9.93604	+	9.93604i	−0.400010	+	0.400010i	0.478226	+	0.878237i	$0.341280\pi$
$618$		0			0
$619$	−19.5066	−	19.5066i	−0.784036	−	0.784036i	0.196474	−	0.980509i	$-0.437051\pi$
$619$	−19.5066	−	19.5066i	−0.784036	−	0.784036i	−0.980509	+	0.196474i	$0.937051\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.31343	+	8.31343i	−0.333071	+	0.333071i
$624$		0			0
$625$	24.5746	−	4.59254i	0.982982	−	0.183702i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.537643	−	0.537643i	0.0214372	−	0.0214372i
$630$		0			0
$631$			39.0187i			1.55331i	0.629927	+	0.776655i	$0.283085\pi$
$631$			39.0187i			1.55331i	−0.629927	+	0.776655i	$0.716915\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−28.9369	+	31.7415i	−1.14833	+	1.25962i
$636$		0			0
$637$	−12.6636			−0.501749
$638$		0			0
$639$		0			0
$640$		0			0
$641$			21.3772i			0.844350i	0.906514	+	0.422175i	$0.138733\pi$
$641$			21.3772i			0.844350i	−0.906514	+	0.422175i	$0.861267\pi$
$642$		0			0
$643$			47.0098i			1.85389i	0.375203	+	0.926943i	$0.377573\pi$
$643$			47.0098i			1.85389i	−0.375203	+	0.926943i	$0.622427\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.90326	+	3.90326i	−0.153453	+	0.153453i	−0.779658	−	0.626205i	$-0.784607\pi$
$647$	−3.90326	+	3.90326i	−0.153453	+	0.153453i	0.626205	+	0.779658i	$0.284607\pi$
$648$		0			0
$649$	−10.8156			−0.424550
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−12.2545			−0.479557			−0.239778	−	0.970828i	$-0.577075\pi$
$653$	−12.2545			−0.479557			−0.239778	+	0.970828i	$0.577075\pi$
$654$		0			0
$655$	25.4440	−	27.9101i	0.994181	−	1.09054i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.65088	+	6.65088i	0.259081	+	0.259081i	0.824680	−	0.565599i	$-0.191355\pi$
$659$	6.65088	+	6.65088i	0.259081	+	0.259081i	−0.565599	+	0.824680i	$0.691355\pi$
$660$		0			0
$661$	−1.93445	+	1.93445i	−0.0752413	+	0.0752413i	−0.743726	−	0.668485i	$-0.766943\pi$
$661$	−1.93445	+	1.93445i	−0.0752413	+	0.0752413i	0.668485	+	0.743726i	$0.266943\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.2421	+	0.704498i	−0.591063	+	0.0273193i
$666$		0			0
$667$			18.2865i			0.708057i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	26.2541i		−	1.01353i
$672$		0			0
$673$	30.4208	+	30.4208i	1.17264	+	1.17264i	0.981579	+	0.191058i	$0.0611917\pi$
$673$	30.4208	+	30.4208i	1.17264	+	1.17264i	0.191058	+	0.981579i	$0.438808\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.8366			0.570215			0.285108	−	0.958496i	$-0.407971\pi$
$677$	14.8366			0.570215			0.285108	+	0.958496i	$0.407971\pi$
$678$		0			0
$679$	20.4768			0.785828
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	18.0535i		−	0.690796i	−0.938456	−	0.345398i	$-0.887744\pi$
$683$		−	18.0535i		−	0.690796i	0.938456	−	0.345398i	$-0.112256\pi$
$684$		0			0
$685$	−31.5514	+	34.6094i	−1.20552	+	1.32236i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−27.8015			−1.05915
$690$		0			0
$691$	31.1909	+	31.1909i	1.18656	+	1.18656i	0.978012	+	0.208547i	$0.0668735\pi$
$691$	31.1909	+	31.1909i	1.18656	+	1.18656i	0.208547	+	0.978012i	$0.433126\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.05852	−	2.78828i	−0.116016	−	0.105765i
$696$		0			0
$697$	2.21364	+	2.21364i	0.0838474	+	0.0838474i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.5826	+	23.5826i	−0.890703	+	0.890703i	−0.994589	−	0.103886i	$-0.966872\pi$
$701$	−23.5826	+	23.5826i	−0.890703	+	0.890703i	0.103886	+	0.994589i	$0.466872\pi$
$702$		0			0
$703$	6.83373	+	6.83373i	0.257739	+	0.257739i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			9.57147i			0.359972i
$708$		0			0
$709$	9.17660	+	9.17660i	0.344635	+	0.344635i	0.858106	−	0.513472i	$-0.171641\pi$
$709$	9.17660	+	9.17660i	0.344635	+	0.344635i	−0.513472	+	0.858106i	$0.671641\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.8560	−	24.8560i	−0.930864	−	0.930864i
$714$		0			0
$715$	−8.56247	+	9.39236i	−0.320218	+	0.351254i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.14349			−0.303701			−0.151850	−	0.988403i	$-0.548523\pi$
$719$	−8.14349			−0.303701			−0.151850	+	0.988403i	$0.548523\pi$
$720$		0			0
$721$	−23.1020			−0.860364
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.3449	+	8.59076i	0.384201	+	0.319053i
$726$		0			0
$727$	−4.93800	−	4.93800i	−0.183140	−	0.183140i	0.609582	−	0.792723i	$-0.291337\pi$
$727$	−4.93800	−	4.93800i	−0.183140	−	0.183140i	−0.792723	+	0.609582i	$0.791337\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.701313	−	0.701313i	−0.0259390	−	0.0259390i
$732$		0			0
$733$		−	19.8468i		−	0.733057i	−0.930407	−	0.366528i	$-0.880546\pi$
$733$		−	19.8468i		−	0.733057i	0.930407	−	0.366528i	$-0.119454\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.84598	−	1.84598i	−0.0679977	−	0.0679977i
$738$		0			0
$739$	3.73527	−	3.73527i	0.137404	−	0.137404i	−0.635059	−	0.772463i	$-0.719024\pi$
$739$	3.73527	−	3.73527i	0.137404	−	0.137404i	0.772463	+	0.635059i	$0.219024\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	13.8239	+	13.8239i	0.507151	+	0.507151i	0.913651	−	0.406500i	$-0.133251\pi$
$743$	13.8239	+	13.8239i	0.507151	+	0.507151i	−0.406500	+	0.913651i	$0.633251\pi$
$744$		0			0
$745$	21.2242	−	23.2813i	0.777595	−	0.852960i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.75994	−	3.75994i	−0.137385	−	0.137385i
$750$		0			0
$751$	−17.5053			−0.638778			−0.319389	−	0.947624i	$-0.603478\pi$
$751$	−17.5053			−0.638778			−0.319389	+	0.947624i	$0.603478\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.854355	−	18.4843i	−0.0310932	−	0.672712i
$756$		0			0
$757$			27.6804i			1.00606i	0.864269	+	0.503030i	$0.167782\pi$
$757$			27.6804i			1.00606i	−0.864269	+	0.503030i	$0.832218\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.83070			−0.0663629			−0.0331815	−	0.999449i	$-0.510564\pi$
$761$	−1.83070			−0.0663629			−0.0331815	+	0.999449i	$0.510564\pi$
$762$		0			0
$763$	−18.7699			−0.679515
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.47852	+	9.47852i	0.342250	+	0.342250i
$768$		0			0
$769$			1.64717i			0.0593983i	0.999559	+	0.0296992i	$0.00945493\pi$
$769$			1.64717i			0.0593983i	−0.999559	+	0.0296992i	$0.990545\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	4.29765i		−	0.154576i	−0.997009	−	0.0772878i	$-0.975374\pi$
$773$		−	4.29765i		−	0.154576i	0.997009	−	0.0772878i	$-0.0246260\pi$
$774$		0			0
$775$	−25.7384	+	2.38438i	−0.924550	+	0.0856495i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−28.1365	+	28.1365i	−1.00809	+	1.00809i
$780$		0			0
$781$	12.6922	+	12.6922i	0.454163	+	0.454163i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	31.4066	−	1.45163i	1.12095	−	0.0518110i
$786$		0			0
$787$	−3.84308			−0.136991			−0.0684955	−	0.997651i	$-0.521820\pi$
$787$	−3.84308			−0.136991			−0.0684955	+	0.997651i	$0.521820\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.2808			−0.436654
$792$		0			0
$793$	−23.0085	+	23.0085i	−0.817054	+	0.817054i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	39.4795i		−	1.39843i	−0.714909	−	0.699217i	$-0.753532\pi$
$797$		−	39.4795i		−	1.39843i	0.714909	−	0.699217i	$-0.246468\pi$
$798$		0			0
$799$		−	3.75779i		−	0.132941i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	11.3585			0.400832
$804$		0			0
$805$	1.04802	+	22.6742i	0.0369377	+	0.799162i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	21.9084i		−	0.770258i	−0.922863	−	0.385129i	$-0.874157\pi$
$809$		−	21.9084i		−	0.770258i	0.922863	−	0.385129i	$-0.125843\pi$
$810$		0			0
$811$	31.3248	−	31.3248i	1.09996	−	1.09996i	0.105548	−	0.994414i	$-0.466340\pi$
$811$	31.3248	−	31.3248i	1.09996	−	1.09996i	0.994414	−	0.105548i	$-0.0336597\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.82216	+	39.4230i	0.0638273	+	1.38093i
$816$		0			0
$817$	8.91407	−	8.91407i	0.311864	−	0.311864i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	23.9130	+	23.9130i	0.834568	+	0.834568i	0.988138	−	0.153570i	$-0.0490770\pi$
$821$	23.9130	+	23.9130i	0.834568	+	0.834568i	−0.153570	+	0.988138i	$0.549077\pi$
$822$		0			0
$823$	−27.5965	+	27.5965i	−0.961952	+	0.961952i	−0.999302	−	0.0373504i	$-0.988108\pi$
$823$	−27.5965	+	27.5965i	−0.961952	+	0.961952i	0.0373504	+	0.999302i	$0.488108\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.14227			−0.213588			−0.106794	−	0.994281i	$-0.534058\pi$
$827$	−6.14227			−0.213588			−0.106794	+	0.994281i	$0.534058\pi$
$828$		0			0
$829$	−8.35295	+	8.35295i	−0.290110	+	0.290110i	−0.837124	−	0.547014i	$-0.815765\pi$
$829$	−8.35295	+	8.35295i	−0.290110	+	0.290110i	0.547014	+	0.837124i	$0.315765\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.21323	−	1.21323i	0.0420359	−	0.0420359i
$834$		0			0
$835$	−5.09458	+	5.58836i	−0.176305	+	0.193393i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			40.3000i			1.39131i	0.718375	+	0.695656i	$0.244886\pi$
$839$			40.3000i			1.39131i	−0.718375	+	0.695656i	$0.755114\pi$
$840$		0			0
$841$		−	21.7672i		−	0.750595i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.3027	+	0.614860i	−0.457628	+	0.0211518i
$846$		0			0
$847$	−6.77083	+	6.77083i	−0.232648	+	0.232648i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.1659	−	10.1659i	0.348483	−	0.348483i
$852$		0			0
$853$	−29.4952			−1.00990			−0.504948	−	0.863150i	$-0.668488\pi$
$853$	−29.4952			−1.00990			−0.504948	+	0.863150i	$0.668488\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−39.5931	+	39.5931i	−1.35247	+	1.35247i	−0.469586	+	0.882887i	$0.655597\pi$
$857$	−39.5931	+	39.5931i	−1.35247	+	1.35247i	−0.882887	+	0.469586i	$0.844403\pi$
$858$		0			0
$859$	−27.4482	−	27.4482i	−0.936519	−	0.936519i	0.0615827	−	0.998102i	$-0.480385\pi$
$859$	−27.4482	−	27.4482i	−0.936519	−	0.936519i	−0.998102	+	0.0615827i	$0.980385\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	31.7237	−	31.7237i	1.07989	−	1.07989i	0.0833696	−	0.996519i	$-0.473432\pi$
$863$	31.7237	−	31.7237i	1.07989	−	1.07989i	0.996519	−	0.0833696i	$-0.0265682\pi$
$864$		0			0
$865$	−34.4523	+	1.59240i	−1.17141	+	0.0541434i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.61940	−	2.61940i	0.0888572	−	0.0888572i
$870$		0			0
$871$			3.23555i			0.109632i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	13.3195	+	10.0592i	0.450280	+	0.340062i
$876$		0			0
$877$	41.6552			1.40660			0.703298	−	0.710896i	$-0.251710\pi$
$877$	41.6552			1.40660			0.703298	+	0.710896i	$0.251710\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	3.26244i		−	0.109914i	−0.998489	−	0.0549571i	$-0.982498\pi$
$881$		−	3.26244i		−	0.109914i	0.998489	−	0.0549571i	$-0.0175022\pi$
$882$		0			0
$883$		−	40.1719i		−	1.35189i	−0.736951	−	0.675946i	$-0.763735\pi$
$883$		−	40.1719i		−	1.35189i	0.736951	−	0.675946i	$-0.236265\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.45279	+	3.45279i	−0.115933	+	0.115933i	−0.762693	−	0.646760i	$-0.776123\pi$
$887$	−3.45279	+	3.45279i	−0.115933	+	0.115933i	0.646760	+	0.762693i	$0.276123\pi$
$888$		0			0
$889$	−28.6767			−0.961786
$890$		0			0
$891$		0			0
$892$		0			0
$893$	47.7636			1.59835
$894$		0			0
$895$	−10.0631	−	9.17393i	−0.336372	−	0.306651i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.83114	−	9.83114i	−0.327887	−	0.327887i
$900$		0			0
$901$	2.66351	−	2.66351i	0.0887345	−	0.0887345i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.4979	+	26.8723i	−0.814338	+	0.893264i
$906$		0			0
$907$		−	49.4914i		−	1.64333i	−0.569967	−	0.821667i	$-0.693044\pi$
$907$		−	49.4914i		−	1.64333i	0.569967	−	0.821667i	$-0.306956\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			5.73068i			0.189866i	0.995484	+	0.0949330i	$0.0302637\pi$
$911$			5.73068i			0.189866i	−0.995484	+	0.0949330i	$0.969736\pi$
$912$		0			0
$913$	14.0907	+	14.0907i	0.466335	+	0.466335i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	25.2152			0.832681
$918$		0			0
$919$	−38.8811			−1.28257			−0.641284	−	0.767304i	$-0.721598\pi$
$919$	−38.8811			−1.28257			−0.641284	+	0.767304i	$0.721598\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	22.2462i		−	0.732244i
$924$		0			0
$925$	−0.975193	−	10.5268i	−0.0320642	−	0.346119i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.16998			−0.202430			−0.101215	−	0.994865i	$-0.532273\pi$
$929$	−6.16998			−0.202430			−0.101215	+	0.994865i	$0.532273\pi$
$930$		0			0
$931$	15.4208	+	15.4208i	0.505397	+	0.505397i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.0795067	−	1.72016i	−0.00260015	−	0.0562552i
$936$		0			0
$937$	20.2894	+	20.2894i	0.662826	+	0.662826i	0.956045	−	0.293219i	$-0.0947266\pi$
$937$	20.2894	+	20.2894i	0.662826	+	0.662826i	−0.293219	+	0.956045i	$0.594727\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.553875	+	0.553875i	−0.0180558	+	0.0180558i	−0.716077	−	0.698021i	$-0.754064\pi$
$941$	−0.553875	+	0.553875i	−0.0180558	+	0.0180558i	0.698021	+	0.716077i	$0.254064\pi$
$942$		0			0
$943$	41.8561	+	41.8561i	1.36302	+	1.36302i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	37.2488i		−	1.21042i	−0.796064	−	0.605212i	$-0.793088\pi$
$947$		−	37.2488i		−	1.21042i	0.796064	−	0.605212i	$-0.206912\pi$
$948$		0			0
$949$	−9.95428	−	9.95428i	−0.323130	−	0.323130i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.23104	−	8.23104i	−0.266630	−	0.266630i	0.561111	−	0.827741i	$-0.310374\pi$
$953$	−8.23104	−	8.23104i	−0.266630	−	0.266630i	−0.827741	+	0.561111i	$0.810374\pi$
$954$		0			0
$955$	1.82274	+	39.4357i	0.0589826	+	1.27611i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−31.2677			−1.00969
$960$		0			0
$961$	−4.27402			−0.137872
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.4146	−	13.1410i	−0.464022	−	0.423022i
$966$		0			0
$967$	2.07290	+	2.07290i	0.0666601	+	0.0666601i	0.739651	−	0.672991i	$-0.234991\pi$
$967$	2.07290	+	2.07290i	0.0666601	+	0.0666601i	−0.672991	+	0.739651i	$0.734991\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.72632	+	6.72632i	0.215858	+	0.215858i	0.806750	−	0.590892i	$-0.201224\pi$
$971$	6.72632	+	6.72632i	0.215858	+	0.215858i	−0.590892	+	0.806750i	$0.701224\pi$
$972$		0			0
$973$		−	2.76320i		−	0.0885843i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−29.5596	−	29.5596i	−0.945694	−	0.945694i	0.0529057	−	0.998600i	$-0.483152\pi$
$977$	−29.5596	−	29.5596i	−0.945694	−	0.945694i	−0.998600	+	0.0529057i	$0.983152\pi$
$978$		0			0
$979$	11.9253	−	11.9253i	0.381134	−	0.381134i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.57048	−	5.57048i	−0.177671	−	0.177671i	0.612669	−	0.790340i	$-0.290096\pi$
$983$	−5.57048	−	5.57048i	−0.177671	−	0.177671i	−0.790340	+	0.612669i	$0.790096\pi$
$984$		0			0
$985$	22.3160	−	1.03146i	0.711047	−	0.0328650i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−13.2606	−	13.2606i	−0.421664	−	0.421664i
$990$		0			0
$991$	−60.6866			−1.92777			−0.963887	−	0.266310i	$-0.914195\pi$
$991$	−60.6866			−1.92777			−0.963887	+	0.266310i	$0.914195\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.20773	−	0.379366i	0.260202	−	0.0120267i
$996$		0			0
$997$		−	19.1258i		−	0.605720i	−0.953035	−	0.302860i	$-0.902058\pi$
$997$		−	19.1258i		−	0.605720i	0.953035	−	0.302860i	$-0.0979415\pi$
$998$		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.593.2		96
3.2	odd	2	inner	2880.2.bc.a.593.47		96
4.3	odd	2		720.2.bc.a.413.22	yes	96
5.2	odd	4		2880.2.bg.a.17.26		96
12.11	even	2		720.2.bc.a.413.27	yes	96
15.2	even	4		2880.2.bg.a.17.23		96
16.5	even	4		2880.2.bg.a.2033.23		96
16.11	odd	4		720.2.bg.a.53.46	yes	96
20.7	even	4		720.2.bg.a.557.3	yes	96
48.5	odd	4		2880.2.bg.a.2033.26		96
48.11	even	4		720.2.bg.a.53.3	yes	96
60.47	odd	4		720.2.bg.a.557.46	yes	96
80.27	even	4		720.2.bc.a.197.27	yes	96
80.37	odd	4	inner	2880.2.bc.a.1457.47		96
240.107	odd	4		720.2.bc.a.197.22	✓	96
240.197	even	4	inner	2880.2.bc.a.1457.2		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bc.a.197.22	✓	96	240.107	odd	4
720.2.bc.a.197.27	yes	96	80.27	even	4
720.2.bc.a.413.22	yes	96	4.3	odd	2
720.2.bc.a.413.27	yes	96	12.11	even	2
720.2.bg.a.53.3	yes	96	48.11	even	4
720.2.bg.a.53.46	yes	96	16.11	odd	4
720.2.bg.a.557.3	yes	96	20.7	even	4
720.2.bg.a.557.46	yes	96	60.47	odd	4
2880.2.bc.a.593.2		96	1.1	even	1	trivial
2880.2.bc.a.593.47		96	3.2	odd	2	inner
2880.2.bc.a.1457.2		96	240.197	even	4	inner
2880.2.bc.a.1457.47		96	80.37	odd	4	inner
2880.2.bg.a.17.23		96	15.2	even	4
2880.2.bg.a.17.26		96	5.2	odd	4
2880.2.bg.a.2033.23		96	16.5	even	4
2880.2.bg.a.2033.26		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)

\(f(q)\)	\(=\)	\(q+(-2.23368 + 0.103242i) q^{5} +(-1.05564 - 1.05564i) q^{7} +O(q^{10})\)	\(q+(-2.23368 + 0.103242i) q^{5} +(-1.05564 - 1.05564i) q^{7} +(1.51428 + 1.51428i) q^{11} -2.65415i q^{13} +(0.254280 + 0.254280i) q^{17} +(-3.23203 + 3.23203i) q^{19} +(4.80800 + 4.80800i) q^{23} +(4.97868 - 0.461221i) q^{25} +(1.90168 + 1.90168i) q^{29} -5.16972 q^{31} +(2.46696 + 2.24898i) q^{35} -2.11437i q^{37} +8.70551 q^{41} -2.75804 q^{43} +(-7.38909 - 7.38909i) q^{47} -4.77124i q^{49} -10.4747i q^{53} +(-3.53875 - 3.22607i) q^{55} +(-3.57121 + 3.57121i) q^{59} +(-8.66887 - 8.66887i) q^{61} +(0.274020 + 5.92852i) q^{65} -1.21905 q^{67} +8.38170 q^{71} +(3.75046 - 3.75046i) q^{73} -3.19707i q^{77} -1.72981i q^{79} +9.30525 q^{83} +(-0.594233 - 0.541728i) q^{85} -7.87524i q^{89} +(-2.80183 + 2.80183i) q^{91} +(6.88566 - 7.55302i) q^{95} +(-9.69875 + 9.69875i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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