LMFDB - Embedded newform 2880.2.h.e.1151.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2880,2,Mod(1151,2880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2880, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2880.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2880 = 2^{6} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2880.h (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.18939904.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1151.6
Root			$0.500000 + 2.10607i$ of defining polynomial
Character	$\chi$	$=$	2880.1151
Dual form			2880.2.h.e.1151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{5} -1.63899i q^{7} +O(q^{10})$	$q+1.00000i q^{5} -1.63899i q^{7} -3.95687 q^{11} -0.585786 q^{13} -4.00000i q^{17} +7.91375i q^{19} +5.59587 q^{23} -1.00000 q^{25} -7.65685i q^{29} +5.59587i q^{31} +1.63899 q^{35} +9.07107 q^{37} -1.41421i q^{41} -7.91375i q^{43} -3.27798 q^{47} +4.31371 q^{49} -5.17157i q^{53} -3.95687i q^{55} +11.8706 q^{59} +0.828427 q^{61} -0.585786i q^{65} -11.1917i q^{67} -4.63577 q^{71} +8.82843 q^{73} +6.48528i q^{77} -10.2316i q^{79} -3.27798 q^{83} +4.00000 q^{85} -5.41421i q^{89} +0.960099i q^{91} -7.91375 q^{95} +14.4853 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 16 q^{13} - 8 q^{25} + 16 q^{37} - 56 q^{49} - 16 q^{61} + 48 q^{73} + 32 q^{85} + 48 q^{97}+O(q^{100}) $ 8 * q - 16 * q^13 - 8 * q^25 + 16 * q^37 - 56 * q^49 - 16 * q^61 + 48 * q^73 + 32 * q^85 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$577$	$641$	$901$	$2431$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	0	0
$3$	0	0
$4$	0	0
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	0	0
$7$	− 1.63899i	− 0.619480i	−0.950821	−	0.309740i	$-0.899758\pi$
$7$	− 1.63899i	− 0.619480i	0.950821	−	0.309740i	$-0.100242\pi$
$8$	0	0
$9$	0	0
$10$	0	0
$11$	−3.95687	−1.19304	−0.596521	−	0.802597i	$-0.703451\pi$
$11$	−3.95687	−1.19304	−0.596521	+	0.802597i	$0.703451\pi$
$12$	0	0
$13$	−0.585786	−0.162468	−0.0812340	−	0.996695i	$-0.525886\pi$
$13$	−0.585786	−0.162468	−0.0812340	+	0.996695i	$0.525886\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	− 4.00000i	− 0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$	− 4.00000i	− 0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$	0	0
$19$	7.91375i	1.81554i	0.419470	+	0.907769i	$0.362216\pi$
$19$	7.91375i	1.81554i	−0.419470	+	0.907769i	$0.637784\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	5.59587	1.16682	0.583409	−	0.812178i	$-0.301718\pi$
$23$	5.59587	1.16682	0.583409	+	0.812178i	$0.301718\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	0	0
$27$	0	0
$28$	0	0
$29$	− 7.65685i	− 1.42184i	−0.703272	−	0.710921i	$-0.748278\pi$
$29$	− 7.65685i	− 1.42184i	0.703272	−	0.710921i	$-0.251722\pi$
$30$	0	0
$31$	5.59587i	1.00505i	0.864564	+	0.502524i	$0.167595\pi$
$31$	5.59587i	1.00505i	−0.864564	+	0.502524i	$0.832405\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	1.63899	0.277040
$36$	0	0
$37$	9.07107	1.49127	0.745637	−	0.666352i	$-0.232145\pi$
$37$	9.07107	1.49127	0.745637	+	0.666352i	$0.232145\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	− 1.41421i	− 0.220863i	−0.993884	−	0.110432i	$-0.964777\pi$
$41$	− 1.41421i	− 0.220863i	0.993884	−	0.110432i	$-0.0352233\pi$
$42$	0	0
$43$	− 7.91375i	− 1.20684i	−0.797425	−	0.603418i	$-0.793805\pi$
$43$	− 7.91375i	− 1.20684i	0.797425	−	0.603418i	$-0.206195\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−3.27798	−0.478143	−0.239071	−	0.971002i	$-0.576843\pi$
$47$	−3.27798	−0.478143	−0.239071	+	0.971002i	$0.576843\pi$
$48$	0	0
$49$	4.31371	0.616244
$50$	0	0
$51$	0	0
$52$	0	0
$53$	− 5.17157i	− 0.710370i	−0.934796	−	0.355185i	$-0.884418\pi$
$53$	− 5.17157i	− 0.710370i	0.934796	−	0.355185i	$-0.115582\pi$
$54$	0	0
$55$	− 3.95687i	− 0.533545i
$56$	0	0
$57$	0	0
$58$	0	0
$59$	11.8706	1.54542	0.772712	−	0.634757i	$-0.218900\pi$
$59$	11.8706	1.54542	0.772712	+	0.634757i	$0.218900\pi$
$60$	0	0
$61$	0.828427	0.106069	0.0530346	−	0.998593i	$-0.483111\pi$
$61$	0.828427	0.106069	0.0530346	+	0.998593i	$0.483111\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	− 0.585786i	− 0.0726579i
$66$	0	0
$67$	− 11.1917i	− 1.36729i	−0.729816	−	0.683644i	$-0.760394\pi$
$67$	− 11.1917i	− 1.36729i	0.729816	−	0.683644i	$-0.239606\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−4.63577	−0.550164	−0.275082	−	0.961421i	$-0.588705\pi$
$71$	−4.63577	−0.550164	−0.275082	+	0.961421i	$0.588705\pi$
$72$	0	0
$73$	8.82843	1.03329	0.516645	−	0.856200i	$-0.327181\pi$
$73$	8.82843	1.03329	0.516645	+	0.856200i	$0.327181\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	6.48528i	0.739066i
$78$	0	0
$79$	− 10.2316i	− 1.15115i	−0.817750	−	0.575574i	$-0.804779\pi$
$79$	− 10.2316i	− 1.15115i	0.817750	−	0.575574i	$-0.195221\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	−3.27798	−0.359805	−0.179903	−	0.983684i	$-0.557578\pi$
$83$	−3.27798	−0.359805	−0.179903	+	0.983684i	$0.557578\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	0	0
$87$	0	0
$88$	0	0
$89$	− 5.41421i	− 0.573905i	−0.957945	−	0.286953i	$-0.907358\pi$
$89$	− 5.41421i	− 0.573905i	0.957945	−	0.286953i	$-0.0926423\pi$
$90$	0	0
$91$	0.960099i	0.100646i
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−7.91375	−0.811933
$96$	0	0
$97$	14.4853	1.47076	0.735379	−	0.677656i	$-0.237004\pi$
$97$	14.4853	1.47076	0.735379	+	0.677656i	$0.237004\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	− 7.17157i	− 0.713598i	−0.934181	−	0.356799i	$-0.883868\pi$
$101$	− 7.17157i	− 0.713598i	0.934181	−	0.356799i	$-0.116132\pi$
$102$	0	0
$103$	17.4665i	1.72102i	0.509430	+	0.860512i	$0.329856\pi$
$103$	17.4665i	1.72102i	−0.509430	+	0.860512i	$0.670144\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−3.27798	−0.316894	−0.158447	−	0.987367i	$-0.550649\pi$
$107$	−3.27798	−0.316894	−0.158447	+	0.987367i	$0.550649\pi$
$108$	0	0
$109$	4.82843	0.462479	0.231240	−	0.972897i	$-0.425722\pi$
$109$	4.82843	0.462479	0.231240	+	0.972897i	$0.425722\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	− 12.4853i	− 1.17452i	−0.809400	−	0.587258i	$-0.800207\pi$
$113$	− 12.4853i	− 1.17452i	0.809400	−	0.587258i	$-0.199793\pi$
$114$	0	0
$115$	5.59587i	0.521817i
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−6.55596	−0.600984
$120$	0	0
$121$	4.65685	0.423350
$122$	0	0
$123$	0	0
$124$	0	0
$125$	− 1.00000i	− 0.0894427i
$126$	0	0
$127$	− 1.63899i	− 0.145437i	−0.997353	−	0.0727185i	$-0.976833\pi$
$127$	− 1.63899i	− 0.145437i	0.997353	−	0.0727185i	$-0.0231675\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	−0.678892	−0.0593151	−0.0296575	−	0.999560i	$-0.509442\pi$
$131$	−0.678892	−0.0593151	−0.0296575	+	0.999560i	$0.509442\pi$
$132$	0	0
$133$	12.9706	1.12469
$134$	0	0
$135$	0	0
$136$	0	0
$137$	14.1421i	1.20824i	0.796892	+	0.604122i	$0.206476\pi$
$137$	14.1421i	1.20824i	−0.796892	+	0.604122i	$0.793524\pi$
$138$	0	0
$139$	2.31788i	0.196600i	0.995157	+	0.0983001i	$0.0313405\pi$
$139$	2.31788i	0.196600i	−0.995157	+	0.0983001i	$0.968659\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	2.31788	0.193831
$144$	0	0
$145$	7.65685	0.635867
$146$	0	0
$147$	0	0
$148$	0	0
$149$	− 6.48528i	− 0.531295i	−0.964070	−	0.265647i	$-0.914414\pi$
$149$	− 6.48528i	− 0.531295i	0.964070	−	0.265647i	$-0.0855857\pi$
$150$	0	0
$151$	− 2.31788i	− 0.188627i	−0.995543	−	0.0943133i	$-0.969934\pi$
$151$	− 2.31788i	− 0.188627i	0.995543	−	0.0943133i	$-0.0300656\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−5.59587	−0.449471
$156$	0	0
$157$	1.75736	0.140253	0.0701263	−	0.997538i	$-0.477660\pi$
$157$	1.75736	0.140253	0.0701263	+	0.997538i	$0.477660\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	− 9.17157i	− 0.722821i
$162$	0	0
$163$	7.91375i	0.619853i	0.950761	+	0.309926i	$0.100304\pi$
$163$	7.91375i	0.619853i	−0.950761	+	0.309926i	$0.899696\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	16.7876	1.29906	0.649532	−	0.760335i	$-0.274965\pi$
$167$	16.7876	1.29906	0.649532	+	0.760335i	$0.274965\pi$
$168$	0	0
$169$	−12.6569	−0.973604
$170$	0	0
$171$	0	0
$172$	0	0
$173$	− 4.48528i	− 0.341010i	−0.985357	−	0.170505i	$-0.945460\pi$
$173$	− 4.48528i	− 0.341010i	0.985357	−	0.170505i	$-0.0545398\pi$
$174$	0	0
$175$	1.63899i	0.123896i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−8.59264	−0.642244	−0.321122	−	0.947038i	$-0.604060\pi$
$179$	−8.59264	−0.642244	−0.321122	+	0.947038i	$0.604060\pi$
$180$	0	0
$181$	17.7990	1.32299	0.661494	−	0.749950i	$-0.269923\pi$
$181$	17.7990	1.32299	0.661494	+	0.749950i	$0.269923\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	9.07107i	0.666918i
$186$	0	0
$187$	15.8275i	1.15742i
$188$	0	0
$189$	0	0
$190$	0	0
$191$	19.1055	1.38242	0.691212	−	0.722652i	$-0.257077\pi$
$191$	19.1055	1.38242	0.691212	+	0.722652i	$0.257077\pi$
$192$	0	0
$193$	−4.34315	−0.312626	−0.156313	−	0.987708i	$-0.549961\pi$
$193$	−4.34315	−0.312626	−0.156313	+	0.987708i	$0.549961\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	− 8.34315i	− 0.594425i	−0.954811	−	0.297212i	$-0.903943\pi$
$197$	− 8.34315i	− 0.594425i	0.954811	−	0.297212i	$-0.0960569\pi$
$198$	0	0
$199$	− 4.23808i	− 0.300430i	−0.988653	−	0.150215i	$-0.952003\pi$
$199$	− 4.23808i	− 0.300430i	0.988653	−	0.150215i	$-0.0479965\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−12.5495	−0.880803
$204$	0	0
$205$	1.41421	0.0987730
$206$	0	0
$207$	0	0
$208$	0	0
$209$	− 31.3137i	− 2.16601i
$210$	0	0
$211$	− 8.87385i	− 0.610901i	−0.952208	−	0.305450i	$-0.901193\pi$
$211$	− 8.87385i	− 0.610901i	0.952208	−	0.305450i	$-0.0988070\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	7.91375	0.539713
$216$	0	0
$217$	9.17157	0.622607
$218$	0	0
$219$	0	0
$220$	0	0
$221$	2.34315i	0.157617i
$222$	0	0
$223$	− 16.1087i	− 1.07872i	−0.842076	−	0.539359i	$-0.818666\pi$
$223$	− 16.1087i	− 1.07872i	0.842076	−	0.539359i	$-0.181334\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	15.8275	1.05051	0.525254	−	0.850946i	$-0.323970\pi$
$227$	15.8275	1.05051	0.525254	+	0.850946i	$0.323970\pi$
$228$	0	0
$229$	1.31371	0.0868123	0.0434062	−	0.999058i	$-0.486179\pi$
$229$	1.31371	0.0868123	0.0434062	+	0.999058i	$0.486179\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	− 4.00000i	− 0.262049i	−0.991379	−	0.131024i	$-0.958173\pi$
$233$	− 4.00000i	− 0.262049i	0.991379	−	0.131024i	$-0.0418266\pi$
$234$	0	0
$235$	− 3.27798i	− 0.213832i
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−1.35778	−0.0878278	−0.0439139	−	0.999035i	$-0.513983\pi$
$239$	−1.35778	−0.0878278	−0.0439139	+	0.999035i	$0.513983\pi$
$240$	0	0
$241$	20.9706	1.35083	0.675416	−	0.737437i	$-0.263964\pi$
$241$	20.9706	1.35083	0.675416	+	0.737437i	$0.263964\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	4.31371i	0.275593i
$246$	0	0
$247$	− 4.63577i	− 0.294967i
$248$	0	0
$249$	0	0
$250$	0	0
$251$	7.23486	0.456660	0.228330	−	0.973584i	$-0.426673\pi$
$251$	7.23486	0.456660	0.228330	+	0.973584i	$0.426673\pi$
$252$	0	0
$253$	−22.1421	−1.39206
$254$	0	0
$255$	0	0
$256$	0	0
$257$	22.1421i	1.38119i	0.723242	+	0.690594i	$0.242651\pi$
$257$	22.1421i	1.38119i	−0.723242	+	0.690594i	$0.757349\pi$
$258$	0	0
$259$	− 14.8674i	− 0.923815i
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−21.4234	−1.32102	−0.660511	−	0.750817i	$-0.729660\pi$
$263$	−21.4234	−1.32102	−0.660511	+	0.750817i	$0.729660\pi$
$264$	0	0
$265$	5.17157	0.317687
$266$	0	0
$267$	0	0
$268$	0	0
$269$	− 2.00000i	− 0.121942i	−0.998140	−	0.0609711i	$-0.980580\pi$
$269$	− 2.00000i	− 0.121942i	0.998140	−	0.0609711i	$-0.0194197\pi$
$270$	0	0
$271$	2.31788i	0.140801i	0.997519	+	0.0704007i	$0.0224278\pi$
$271$	2.31788i	0.140801i	−0.997519	+	0.0704007i	$0.977572\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	3.95687	0.238608
$276$	0	0
$277$	14.2426	0.855757	0.427879	−	0.903836i	$-0.359261\pi$
$277$	14.2426	0.855757	0.427879	+	0.903836i	$0.359261\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	− 10.3848i	− 0.619504i	−0.950817	−	0.309752i	$-0.899754\pi$
$281$	− 10.3848i	− 0.619504i	0.950817	−	0.309752i	$-0.100246\pi$
$282$	0	0
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−2.31788	−0.136820
$288$	0	0
$289$	1.00000	0.0588235
$290$	0	0
$291$	0	0
$292$	0	0
$293$	− 3.65685i	− 0.213636i	−0.994279	−	0.106818i	$-0.965934\pi$
$293$	− 3.65685i	− 0.213636i	0.994279	−	0.106818i	$-0.0340662\pi$
$294$	0	0
$295$	11.8706i	0.691134i
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−3.27798	−0.189571
$300$	0	0
$301$	−12.9706	−0.747611
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0.828427i	0.0474356i
$306$	0	0
$307$	6.55596i	0.374169i	0.982344	+	0.187084i	$0.0599038\pi$
$307$	6.55596i	0.374169i	−0.982344	+	0.187084i	$0.940096\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−25.6614	−1.45513	−0.727563	−	0.686040i	$-0.759347\pi$
$311$	−25.6614	−1.45513	−0.727563	+	0.686040i	$0.759347\pi$
$312$	0	0
$313$	−23.6569	−1.33716	−0.668582	−	0.743638i	$-0.733099\pi$
$313$	−23.6569	−1.33716	−0.668582	+	0.743638i	$0.733099\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	26.9706i	1.51482i	0.652941	+	0.757409i	$0.273535\pi$
$317$	26.9706i	1.51482i	−0.652941	+	0.757409i	$0.726465\pi$
$318$	0	0
$319$	30.2972i	1.69632i
$320$	0	0
$321$	0	0
$322$	0	0
$323$	31.6550	1.76133
$324$	0	0
$325$	0.585786	0.0324936
$326$	0	0
$327$	0	0
$328$	0	0
$329$	5.37258i	0.296200i
$330$	0	0
$331$	12.5495i	0.689784i	0.938642	+	0.344892i	$0.112084\pi$
$331$	12.5495i	0.689784i	−0.938642	+	0.344892i	$0.887916\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	11.1917	0.611470
$336$	0	0
$337$	20.1421	1.09721	0.548606	−	0.836081i	$-0.315159\pi$
$337$	20.1421	1.09721	0.548606	+	0.836081i	$0.315159\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	− 22.1421i	− 1.19906i
$342$	0	0
$343$	− 18.5431i	− 1.00123i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−4.63577	−0.248861	−0.124430	−	0.992228i	$-0.539710\pi$
$347$	−4.63577	−0.248861	−0.124430	+	0.992228i	$0.539710\pi$
$348$	0	0
$349$	−30.4853	−1.63184	−0.815920	−	0.578165i	$-0.803769\pi$
$349$	−30.4853	−1.63184	−0.815920	+	0.578165i	$0.803769\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	− 11.3137i	− 0.602168i	−0.953598	−	0.301084i	$-0.902652\pi$
$353$	− 11.3137i	− 0.602168i	0.953598	−	0.301084i	$-0.0973484\pi$
$354$	0	0
$355$	− 4.63577i	− 0.246041i
$356$	0	0
$357$	0	0
$358$	0	0
$359$	19.1055	1.00835	0.504174	−	0.863602i	$-0.331797\pi$
$359$	19.1055	1.00835	0.504174	+	0.863602i	$0.331797\pi$
$360$	0	0
$361$	−43.6274	−2.29618
$362$	0	0
$363$	0	0
$364$	0	0
$365$	8.82843i	0.462101i
$366$	0	0
$367$	31.9362i	1.66706i	0.552477	+	0.833528i	$0.313683\pi$
$367$	31.9362i	1.66706i	−0.552477	+	0.833528i	$0.686317\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	−8.47616	−0.440060
$372$	0	0
$373$	15.4142	0.798118	0.399059	−	0.916925i	$-0.369337\pi$
$373$	15.4142	0.798118	0.399059	+	0.916925i	$0.369337\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	4.48528i	0.231004i
$378$	0	0
$379$	− 31.2573i	− 1.60558i	−0.596262	−	0.802790i	$-0.703348\pi$
$379$	− 31.2573i	− 1.60558i	0.596262	−	0.802790i	$-0.296652\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−3.27798	−0.167497	−0.0837485	−	0.996487i	$-0.526689\pi$
$383$	−3.27798	−0.167497	−0.0837485	+	0.996487i	$0.526689\pi$
$384$	0	0
$385$	−6.48528	−0.330521
$386$	0	0
$387$	0	0
$388$	0	0
$389$	− 38.9706i	− 1.97589i	−0.154818	−	0.987943i	$-0.549479\pi$
$389$	− 38.9706i	− 1.97589i	0.154818	−	0.987943i	$-0.450521\pi$
$390$	0	0
$391$	− 22.3835i	− 1.13198i
$392$	0	0
$393$	0	0
$394$	0	0
$395$	10.2316	0.514809
$396$	0	0
$397$	18.9289	0.950016	0.475008	−	0.879982i	$-0.342445\pi$
$397$	18.9289	0.950016	0.475008	+	0.879982i	$0.342445\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	21.2132i	1.05934i	0.848205	+	0.529668i	$0.177684\pi$
$401$	21.2132i	1.05934i	−0.848205	+	0.529668i	$0.822316\pi$
$402$	0	0
$403$	− 3.27798i	− 0.163288i
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−35.8931	−1.77915
$408$	0	0
$409$	−18.9706	−0.938034	−0.469017	−	0.883189i	$-0.655392\pi$
$409$	−18.9706	−0.938034	−0.469017	+	0.883189i	$0.655392\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	− 19.4558i	− 0.957360i
$414$	0	0
$415$	− 3.27798i	− 0.160910i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−30.9761	−1.51328	−0.756641	−	0.653831i	$-0.773161\pi$
$419$	−30.9761	−1.51328	−0.756641	+	0.653831i	$0.773161\pi$
$420$	0	0
$421$	−18.9706	−0.924569	−0.462284	−	0.886732i	$-0.652970\pi$
$421$	−18.9706	−0.924569	−0.462284	+	0.886732i	$0.652970\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	4.00000i	0.194029i
$426$	0	0
$427$	− 1.35778i	− 0.0657078i
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−21.0257	−1.01277	−0.506386	−	0.862307i	$-0.669019\pi$
$431$	−21.0257	−1.01277	−0.506386	+	0.862307i	$0.669019\pi$
$432$	0	0
$433$	19.4558	0.934988	0.467494	−	0.883996i	$-0.345157\pi$
$433$	19.4558	0.934988	0.467494	+	0.883996i	$0.345157\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	44.2843i	2.11840i
$438$	0	0
$439$	8.87385i	0.423526i	0.977321	+	0.211763i	$0.0679204\pi$
$439$	8.87385i	0.423526i	−0.977321	+	0.211763i	$0.932080\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	1.92020	0.0912313	0.0456157	−	0.998959i	$-0.485475\pi$
$443$	1.92020	0.0912313	0.0456157	+	0.998959i	$0.485475\pi$
$444$	0	0
$445$	5.41421	0.256658
$446$	0	0
$447$	0	0
$448$	0	0
$449$	− 9.21320i	− 0.434798i	−0.976083	−	0.217399i	$-0.930243\pi$
$449$	− 9.21320i	− 0.434798i	0.976083	−	0.217399i	$-0.0697573\pi$
$450$	0	0
$451$	5.59587i	0.263499i
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−0.960099	−0.0450101
$456$	0	0
$457$	−11.4558	−0.535882	−0.267941	−	0.963435i	$-0.586343\pi$
$457$	−11.4558	−0.535882	−0.267941	+	0.963435i	$0.586343\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	33.7990i	1.57418i	0.616841	+	0.787088i	$0.288412\pi$
$461$	33.7990i	1.57418i	−0.616841	+	0.787088i	$0.711588\pi$
$462$	0	0
$463$	− 31.9362i	− 1.48420i	−0.670289	−	0.742101i	$-0.733830\pi$
$463$	− 31.9362i	− 1.48420i	0.670289	−	0.742101i	$-0.266170\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−33.0128	−1.52765	−0.763825	−	0.645424i	$-0.776681\pi$
$467$	−33.0128	−1.52765	−0.763825	+	0.645424i	$0.776681\pi$
$468$	0	0
$469$	−18.3431	−0.847008
$470$	0	0
$471$	0	0
$472$	0	0
$473$	31.3137i	1.43981i
$474$	0	0
$475$	− 7.91375i	− 0.363108i
$476$	0	0
$477$	0	0
$478$	0	0
$479$	1.92020	0.0877361	0.0438680	−	0.999037i	$-0.486032\pi$
$479$	1.92020	0.0877361	0.0438680	+	0.999037i	$0.486032\pi$
$480$	0	0
$481$	−5.31371	−0.242284
$482$	0	0
$483$	0	0
$484$	0	0
$485$	14.4853i	0.657743i
$486$	0	0
$487$	1.63899i	0.0742698i	0.999310	+	0.0371349i	$0.0118231\pi$
$487$	1.63899i	0.0742698i	−0.999310	+	0.0371349i	$0.988177\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	27.6981	1.25000	0.624999	−	0.780625i	$-0.285099\pi$
$491$	27.6981	1.25000	0.624999	+	0.780625i	$0.285099\pi$
$492$	0	0
$493$	−30.6274	−1.37939
$494$	0	0
$495$	0	0
$496$	0	0
$497$	7.59798i	0.340816i
$498$	0	0
$499$	9.83395i	0.440228i	0.975474	+	0.220114i	$0.0706429\pi$
$499$	9.83395i	0.440228i	−0.975474	+	0.220114i	$0.929357\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	25.6614	1.14419	0.572094	−	0.820188i	$-0.306131\pi$
$503$	25.6614	1.14419	0.572094	+	0.820188i	$0.306131\pi$
$504$	0	0
$505$	7.17157	0.319131
$506$	0	0
$507$	0	0
$508$	0	0
$509$	11.8579i	0.525591i	0.964852	+	0.262795i	$0.0846444\pi$
$509$	11.8579i	0.525591i	−0.964852	+	0.262795i	$0.915356\pi$
$510$	0	0
$511$	− 14.4697i	− 0.640102i
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−17.4665	−0.769665
$516$	0	0
$517$	12.9706	0.570445
$518$	0	0
$519$	0	0
$520$	0	0
$521$	13.4142i	0.587687i	0.955853	+	0.293844i	$0.0949345\pi$
$521$	13.4142i	0.587687i	−0.955853	+	0.293844i	$0.905065\pi$
$522$	0	0
$523$	30.2972i	1.32480i	0.749148	+	0.662402i	$0.230463\pi$
$523$	30.2972i	1.32480i	−0.749148	+	0.662402i	$0.769537\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	22.3835	0.975039
$528$	0	0
$529$	8.31371	0.361466
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0.828427i	0.0358832i
$534$	0	0
$535$	− 3.27798i	− 0.141720i
$536$	0	0
$537$	0	0
$538$	0	0
$539$	−17.0688	−0.735205
$540$	0	0
$541$	−8.14214	−0.350058	−0.175029	−	0.984563i	$-0.556002\pi$
$541$	−8.14214	−0.350058	−0.175029	+	0.984563i	$0.556002\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	4.82843i	0.206827i
$546$	0	0
$547$	12.5495i	0.536579i	0.963338	+	0.268289i	$0.0864583\pi$
$547$	12.5495i	0.536579i	−0.963338	+	0.268289i	$0.913542\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	60.5944	2.58141
$552$	0	0
$553$	−16.7696	−0.713114
$554$	0	0
$555$	0	0
$556$	0	0
$557$	39.1127i	1.65726i	0.559798	+	0.828629i	$0.310879\pi$
$557$	39.1127i	1.65726i	−0.559798	+	0.828629i	$0.689121\pi$
$558$	0	0
$559$	4.63577i	0.196072i
$560$	0	0
$561$	0	0
$562$	0	0
$563$	4.63577	0.195374	0.0976871	−	0.995217i	$-0.468856\pi$
$563$	4.63577	0.195374	0.0976871	+	0.995217i	$0.468856\pi$
$564$	0	0
$565$	12.4853	0.525260
$566$	0	0
$567$	0	0
$568$	0	0
$569$	− 9.89949i	− 0.415008i	−0.978234	−	0.207504i	$-0.933466\pi$
$569$	− 9.89949i	− 0.415008i	0.978234	−	0.207504i	$-0.0665341\pi$
$570$	0	0
$571$	12.5495i	0.525181i	0.964907	+	0.262590i	$0.0845768\pi$
$571$	12.5495i	0.525181i	−0.964907	+	0.262590i	$0.915423\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−5.59587	−0.233364
$576$	0	0
$577$	−1.79899	−0.0748929	−0.0374465	−	0.999299i	$-0.511922\pi$
$577$	−1.79899	−0.0748929	−0.0374465	+	0.999299i	$0.511922\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	5.37258i	0.222892i
$582$	0	0
$583$	20.4633i	0.847502i
$584$	0	0
$585$	0	0
$586$	0	0
$587$	32.2174	1.32975	0.664877	−	0.746953i	$-0.268484\pi$
$587$	32.2174	1.32975	0.664877	+	0.746953i	$0.268484\pi$
$588$	0	0
$589$	−44.2843	−1.82470
$590$	0	0
$591$	0	0
$592$	0	0
$593$	− 38.1421i	− 1.56631i	−0.621827	−	0.783155i	$-0.713609\pi$
$593$	− 38.1421i	− 1.56631i	0.621827	−	0.783155i	$-0.286391\pi$
$594$	0	0
$595$	− 6.55596i	− 0.268768i
$596$	0	0
$597$	0	0
$598$	0	0
$599$	23.7412	0.970041	0.485021	−	0.874503i	$-0.338812\pi$
$599$	23.7412	0.970041	0.485021	+	0.874503i	$0.338812\pi$
$600$	0	0
$601$	−7.31371	−0.298332	−0.149166	−	0.988812i	$-0.547659\pi$
$601$	−7.31371	−0.298332	−0.149166	+	0.988812i	$0.547659\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	4.65685i	0.189328i
$606$	0	0
$607$	− 43.1279i	− 1.75051i	−0.483663	−	0.875254i	$-0.660694\pi$
$607$	− 43.1279i	− 1.75051i	0.483663	−	0.875254i	$-0.339306\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	1.92020	0.0776829
$612$	0	0
$613$	−8.38478	−0.338658	−0.169329	−	0.985560i	$-0.554160\pi$
$613$	−8.38478	−0.338658	−0.169329	+	0.985560i	$0.554160\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	40.0000i	1.61034i	0.593045	+	0.805170i	$0.297926\pi$
$617$	40.0000i	1.61034i	−0.593045	+	0.805170i	$0.702074\pi$
$618$	0	0
$619$	20.0656i	0.806504i	0.915089	+	0.403252i	$0.132120\pi$
$619$	20.0656i	0.806504i	−0.915089	+	0.403252i	$0.867880\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−8.87385	−0.355523
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	− 36.2843i	− 1.44675i
$630$	0	0
$631$	32.6151i	1.29839i	0.760624	+	0.649193i	$0.224893\pi$
$631$	32.6151i	1.29839i	−0.760624	+	0.649193i	$0.775107\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	1.63899	0.0650414
$636$	0	0
$637$	−2.52691	−0.100120
$638$	0	0
$639$	0	0
$640$	0	0
$641$	2.10051i	0.0829650i	0.999139	+	0.0414825i	$0.0132081\pi$
$641$	2.10051i	0.0829650i	−0.999139	+	0.0414825i	$0.986792\pi$
$642$	0	0
$643$	12.5495i	0.494905i	0.968900	+	0.247452i	$0.0795933\pi$
$643$	12.5495i	0.494905i	−0.968900	+	0.247452i	$0.920407\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−12.5495	−0.493372	−0.246686	−	0.969095i	$-0.579342\pi$
$647$	−12.5495	−0.493372	−0.246686	+	0.969095i	$0.579342\pi$
$648$	0	0
$649$	−46.9706	−1.84376
$650$	0	0
$651$	0	0
$652$	0	0
$653$	12.3431i	0.483025i	0.970398	+	0.241512i	$0.0776434\pi$
$653$	12.3431i	0.483025i	−0.970398	+	0.241512i	$0.922357\pi$
$654$	0	0
$655$	− 0.678892i	− 0.0265265i
$656$	0	0
$657$	0	0
$658$	0	0
$659$	47.3660	1.84512	0.922559	−	0.385856i	$-0.126094\pi$
$659$	47.3660	1.84512	0.922559	+	0.385856i	$0.126094\pi$
$660$	0	0
$661$	−9.51472	−0.370080	−0.185040	−	0.982731i	$-0.559241\pi$
$661$	−9.51472	−0.370080	−0.185040	+	0.982731i	$0.559241\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	12.9706i	0.502977i
$666$	0	0
$667$	− 42.8467i	− 1.65903i
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−3.27798	−0.126545
$672$	0	0
$673$	−49.7990	−1.91961	−0.959805	−	0.280668i	$-0.909444\pi$
$673$	−49.7990	−1.91961	−0.959805	+	0.280668i	$0.909444\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	− 17.3137i	− 0.665420i	−0.943029	−	0.332710i	$-0.892037\pi$
$677$	− 17.3137i	− 0.665420i	0.943029	−	0.332710i	$-0.107963\pi$
$678$	0	0
$679$	− 23.7412i	− 0.911105i
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−14.4697	−0.553668	−0.276834	−	0.960918i	$-0.589285\pi$
$683$	−14.4697	−0.553668	−0.276834	+	0.960918i	$0.589285\pi$
$684$	0	0
$685$	−14.1421	−0.540343
$686$	0	0
$687$	0	0
$688$	0	0
$689$	3.02944i	0.115412i
$690$	0	0
$691$	− 36.8532i	− 1.40196i	−0.713181	−	0.700980i	$-0.752746\pi$
$691$	− 36.8532i	− 1.40196i	0.713181	−	0.700980i	$-0.247254\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−2.31788	−0.0879223
$696$	0	0
$697$	−5.65685	−0.214269
$698$	0	0
$699$	0	0
$700$	0	0
$701$	4.14214i	0.156446i	0.996936	+	0.0782232i	$0.0249247\pi$
$701$	4.14214i	0.156446i	−0.996936	+	0.0782232i	$0.975075\pi$
$702$	0	0
$703$	71.7862i	2.70747i
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−11.7541	−0.442060
$708$	0	0
$709$	21.3137	0.800453	0.400227	−	0.916416i	$-0.368931\pi$
$709$	21.3137	0.800453	0.400227	+	0.916416i	$0.368931\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	31.3137i	1.17271i
$714$	0	0
$715$	2.31788i	0.0866839i
$716$	0	0
$717$	0	0
$718$	0	0
$719$	−41.4889	−1.54728	−0.773638	−	0.633628i	$-0.781565\pi$
$719$	−41.4889	−1.54728	−0.773638	+	0.633628i	$0.781565\pi$
$720$	0	0
$721$	28.6274	1.06614
$722$	0	0
$723$	0	0
$724$	0	0
$725$	7.65685i	0.284368i
$726$	0	0
$727$	− 8.19496i	− 0.303934i	−0.988386	−	0.151967i	$-0.951439\pi$
$727$	− 8.19496i	− 0.303934i	0.988386	−	0.151967i	$-0.0485608\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−31.6550	−1.17080
$732$	0	0
$733$	−18.9289	−0.699156	−0.349578	−	0.936907i	$-0.613675\pi$
$733$	−18.9289	−0.699156	−0.349578	+	0.936907i	$0.613675\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	44.2843i	1.63123i
$738$	0	0
$739$	5.99355i	0.220476i	0.993905	+	0.110238i	$0.0351614\pi$
$739$	5.99355i	0.220476i	−0.993905	+	0.110238i	$0.964839\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−34.9330	−1.28157	−0.640783	−	0.767722i	$-0.721390\pi$
$743$	−34.9330	−1.28157	−0.640783	+	0.767722i	$0.721390\pi$
$744$	0	0
$745$	6.48528	0.237602
$746$	0	0
$747$	0	0
$748$	0	0
$749$	5.37258i	0.196310i
$750$	0	0
$751$	0.960099i	0.0350345i	0.999847	+	0.0175172i	$0.00557620\pi$
$751$	0.960099i	0.0350345i	−0.999847	+	0.0175172i	$0.994424\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	2.31788	0.0843564
$756$	0	0
$757$	−6.04163	−0.219587	−0.109793	−	0.993954i	$-0.535019\pi$
$757$	−6.04163	−0.219587	−0.109793	+	0.993954i	$0.535019\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	− 14.3848i	− 0.521448i	−0.965413	−	0.260724i	$-0.916039\pi$
$761$	− 14.3848i	− 0.521448i	0.965413	−	0.260724i	$-0.0839612\pi$
$762$	0	0
$763$	− 7.91375i	− 0.286497i
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−6.95365	−0.251082
$768$	0	0
$769$	−46.6274	−1.68143	−0.840714	−	0.541480i	$-0.817864\pi$
$769$	−46.6274	−1.68143	−0.840714	+	0.541480i	$0.817864\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	14.2843i	0.513770i	0.966442	+	0.256885i	$0.0826961\pi$
$773$	14.2843i	0.513770i	−0.966442	+	0.256885i	$0.917304\pi$
$774$	0	0
$775$	− 5.59587i	− 0.201009i
$776$	0	0
$777$	0	0
$778$	0	0
$779$	11.1917	0.400985
$780$	0	0
$781$	18.3431	0.656369
$782$	0	0
$783$	0	0
$784$	0	0
$785$	1.75736i	0.0627228i
$786$	0	0
$787$	12.5495i	0.447342i	0.974665	+	0.223671i	$0.0718041\pi$
$787$	12.5495i	0.447342i	−0.974665	+	0.223671i	$0.928196\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	−20.4633	−0.727590
$792$	0	0
$793$	−0.485281	−0.0172328
$794$	0	0
$795$	0	0
$796$	0	0
$797$	37.4558i	1.32675i	0.748285	+	0.663377i	$0.230877\pi$
$797$	37.4558i	1.32675i	−0.748285	+	0.663377i	$0.769123\pi$
$798$	0	0
$799$	13.1119i	0.463867i
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−34.9330	−1.23276
$804$	0	0
$805$	9.17157	0.323255
$806$	0	0
$807$	0	0
$808$	0	0
$809$	− 46.8701i	− 1.64786i	−0.566689	−	0.823932i	$-0.691776\pi$
$809$	− 46.8701i	− 1.64786i	0.566689	−	0.823932i	$-0.308224\pi$
$810$	0	0
$811$	− 27.4169i	− 0.962738i	−0.876518	−	0.481369i	$-0.840140\pi$
$811$	− 27.4169i	− 0.962738i	0.876518	−	0.481369i	$-0.159860\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−7.91375	−0.277207
$816$	0	0
$817$	62.6274	2.19106
$818$	0	0
$819$	0	0
$820$	0	0
$821$	− 47.6569i	− 1.66324i	−0.555348	−	0.831618i	$-0.687415\pi$
$821$	− 47.6569i	− 1.66324i	0.555348	−	0.831618i	$-0.312585\pi$
$822$	0	0
$823$	− 3.55919i	− 0.124066i	−0.998074	−	0.0620328i	$-0.980242\pi$
$823$	− 3.55919i	− 0.124066i	0.998074	−	0.0620328i	$-0.0197583\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−8.47616	−0.294745	−0.147373	−	0.989081i	$-0.547082\pi$
$827$	−8.47616	−0.294745	−0.147373	+	0.989081i	$0.547082\pi$
$828$	0	0
$829$	−21.1127	−0.733274	−0.366637	−	0.930364i	$-0.619491\pi$
$829$	−21.1127	−0.733274	−0.366637	+	0.930364i	$0.619491\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	− 17.2548i	− 0.597845i
$834$	0	0
$835$	16.7876i	0.580959i
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−25.6614	−0.885931	−0.442966	−	0.896539i	$-0.646074\pi$
$839$	−25.6614	−0.885931	−0.442966	+	0.896539i	$0.646074\pi$
$840$	0	0
$841$	−29.6274	−1.02164
$842$	0	0
$843$	0	0
$844$	0	0
$845$	− 12.6569i	− 0.435409i
$846$	0	0
$847$	− 7.63254i	− 0.262257i
$848$	0	0
$849$	0	0
$850$	0	0
$851$	50.7605	1.74005
$852$	0	0
$853$	−20.1005	−0.688228	−0.344114	−	0.938928i	$-0.611821\pi$
$853$	−20.1005	−0.688228	−0.344114	+	0.938928i	$0.611821\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	32.9706i	1.12625i	0.826371	+	0.563126i	$0.190402\pi$
$857$	32.9706i	1.12625i	−0.826371	+	0.563126i	$0.809598\pi$
$858$	0	0
$859$	35.8931i	1.22466i	0.790604	+	0.612328i	$0.209767\pi$
$859$	35.8931i	1.22466i	−0.790604	+	0.612328i	$0.790233\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	19.5032	0.663895	0.331948	−	0.943298i	$-0.392294\pi$
$863$	19.5032	0.663895	0.331948	+	0.943298i	$0.392294\pi$
$864$	0	0
$865$	4.48528	0.152504
$866$	0	0
$867$	0	0
$868$	0	0
$869$	40.4853i	1.37337i
$870$	0	0
$871$	6.55596i	0.222140i
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−1.63899	−0.0554080
$876$	0	0
$877$	−21.0711	−0.711519	−0.355760	−	0.934577i	$-0.615778\pi$
$877$	−21.0711	−0.711519	−0.355760	+	0.934577i	$0.615778\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	− 39.7574i	− 1.33946i	−0.742605	−	0.669730i	$-0.766410\pi$
$881$	− 39.7574i	− 1.33946i	0.742605	−	0.669730i	$-0.233590\pi$
$882$	0	0
$883$	− 48.8403i	− 1.64361i	−0.569772	−	0.821803i	$-0.692968\pi$
$883$	− 48.8403i	− 1.64361i	0.569772	−	0.821803i	$-0.307032\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	10.2316	0.343545	0.171772	−	0.985137i	$-0.445051\pi$
$887$	10.2316	0.343545	0.171772	+	0.985137i	$0.445051\pi$
$888$	0	0
$889$	−2.68629	−0.0900953
$890$	0	0
$891$	0	0
$892$	0	0
$893$	− 25.9411i	− 0.868087i
$894$	0	0
$895$	− 8.59264i	− 0.287220i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	42.8467	1.42902
$900$	0	0
$901$	−20.6863	−0.689160
$902$	0	0
$903$	0	0
$904$	0	0
$905$	17.7990i	0.591658i
$906$	0	0
$907$	− 25.6614i	− 0.852074i	−0.904706	−	0.426037i	$-0.859909\pi$
$907$	− 25.6614i	− 0.852074i	0.904706	−	0.426037i	$-0.140091\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	13.1119	0.434418	0.217209	−	0.976125i	$-0.430305\pi$
$911$	13.1119	0.434418	0.217209	+	0.976125i	$0.430305\pi$
$912$	0	0
$913$	12.9706	0.429263
$914$	0	0
$915$	0	0
$916$	0	0
$917$	1.11270i	0.0367445i
$918$	0	0
$919$	− 18.7078i	− 0.617113i	−0.951206	−	0.308557i	$-0.900154\pi$
$919$	− 18.7078i	− 0.617113i	0.951206	−	0.308557i	$-0.0998459\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	2.71557	0.0893840
$924$	0	0
$925$	−9.07107	−0.298255
$926$	0	0
$927$	0	0
$928$	0	0
$929$	4.04163i	0.132602i	0.997800	+	0.0663008i	$0.0211197\pi$
$929$	4.04163i	0.132602i	−0.997800	+	0.0663008i	$0.978880\pi$
$930$	0	0
$931$	34.1376i	1.11881i
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−15.8275	−0.517615
$936$	0	0
$937$	−11.6569	−0.380813	−0.190406	−	0.981705i	$-0.560981\pi$
$937$	−11.6569	−0.380813	−0.190406	+	0.981705i	$0.560981\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	27.6569i	0.901588i	0.892628	+	0.450794i	$0.148859\pi$
$941$	27.6569i	0.901588i	−0.892628	+	0.450794i	$0.851141\pi$
$942$	0	0
$943$	− 7.91375i	− 0.257707i
$944$	0	0
$945$	0	0
$946$	0	0
$947$	17.7477	0.576723	0.288361	−	0.957522i	$-0.406890\pi$
$947$	17.7477	0.576723	0.288361	+	0.957522i	$0.406890\pi$
$948$	0	0
$949$	−5.17157	−0.167876
$950$	0	0
$951$	0	0
$952$	0	0
$953$	− 14.1421i	− 0.458109i	−0.973414	−	0.229054i	$-0.926437\pi$
$953$	− 14.1421i	− 0.458109i	0.973414	−	0.229054i	$-0.0735634\pi$
$954$	0	0
$955$	19.1055i	0.618239i
$956$	0	0
$957$	0	0
$958$	0	0
$959$	23.1788	0.748484
$960$	0	0
$961$	−0.313708	−0.0101196
$962$	0	0
$963$	0	0
$964$	0	0
$965$	− 4.34315i	− 0.139811i
$966$	0	0
$967$	51.0417i	1.64139i	0.571367	+	0.820695i	$0.306413\pi$
$967$	51.0417i	1.64139i	−0.571367	+	0.820695i	$0.693587\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−45.4458	−1.45843	−0.729213	−	0.684287i	$-0.760114\pi$
$971$	−45.4458	−1.45843	−0.729213	+	0.684287i	$0.760114\pi$
$972$	0	0
$973$	3.79899	0.121790
$974$	0	0
$975$	0	0
$976$	0	0
$977$	21.6569i	0.692864i	0.938075	+	0.346432i	$0.112607\pi$
$977$	21.6569i	0.692864i	−0.938075	+	0.346432i	$0.887393\pi$
$978$	0	0
$979$	21.4234i	0.684694i
$980$	0	0
$981$	0	0
$982$	0	0
$983$	41.4889	1.32329	0.661646	−	0.749816i	$-0.269858\pi$
$983$	41.4889	1.32329	0.661646	+	0.749816i	$0.269858\pi$
$984$	0	0
$985$	8.34315	0.265835
$986$	0	0
$987$	0	0
$988$	0	0
$989$	− 44.2843i	− 1.40816i
$990$	0	0
$991$	− 18.1454i	− 0.576407i	−0.957569	−	0.288204i	$-0.906942\pi$
$991$	− 18.1454i	− 0.576407i	0.957569	−	0.288204i	$-0.0930580\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	4.23808	0.134356
$996$	0	0
$997$	17.0711	0.540646	0.270323	−	0.962770i	$-0.412869\pi$
$997$	17.0711	0.540646	0.270323	+	0.962770i	$0.412869\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2880.2.h.e.1151.6		8
3.2	odd	2	inner	2880.2.h.e.1151.2		8
4.3	odd	2	inner	2880.2.h.e.1151.7		8
8.3	odd	2		180.2.e.a.71.7	yes	8
8.5	even	2		180.2.e.a.71.1	✓	8
12.11	even	2	inner	2880.2.h.e.1151.3		8
24.5	odd	2		180.2.e.a.71.8	yes	8
24.11	even	2		180.2.e.a.71.2	yes	8
40.3	even	4		900.2.h.c.899.2		8
40.13	odd	4		900.2.h.c.899.3		8
40.19	odd	2		900.2.e.d.251.2		8
40.27	even	4		900.2.h.b.899.7		8
40.29	even	2		900.2.e.d.251.8		8
40.37	odd	4		900.2.h.b.899.6		8
120.29	odd	2		900.2.e.d.251.1		8
120.53	even	4		900.2.h.b.899.5		8
120.59	even	2		900.2.e.d.251.7		8
120.77	even	4		900.2.h.c.899.4		8
120.83	odd	4		900.2.h.b.899.8		8
120.107	odd	4		900.2.h.c.899.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.e.a.71.1	✓	8	8.5	even	2
180.2.e.a.71.2	yes	8	24.11	even	2
180.2.e.a.71.7	yes	8	8.3	odd	2
180.2.e.a.71.8	yes	8	24.5	odd	2
900.2.e.d.251.1		8	120.29	odd	2
900.2.e.d.251.2		8	40.19	odd	2
900.2.e.d.251.7		8	120.59	even	2
900.2.e.d.251.8		8	40.29	even	2
900.2.h.b.899.5		8	120.53	even	4
900.2.h.b.899.6		8	40.37	odd	4
900.2.h.b.899.7		8	40.27	even	4
900.2.h.b.899.8		8	120.83	odd	4
900.2.h.c.899.1		8	120.107	odd	4
900.2.h.c.899.2		8	40.3	even	4
900.2.h.c.899.3		8	40.13	odd	4
900.2.h.c.899.4		8	120.77	even	4
2880.2.h.e.1151.2		8	3.2	odd	2	inner
2880.2.h.e.1151.3		8	12.11	even	2	inner
2880.2.h.e.1151.6		8	1.1	even	1	trivial
2880.2.h.e.1151.7		8	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2880.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{5} -1.63899i q^{7} +O(q^{10})\)	\(q+1.00000i q^{5} -1.63899i q^{7} -3.95687 q^{11} -0.585786 q^{13} -4.00000i q^{17} +7.91375i q^{19} +5.59587 q^{23} -1.00000 q^{25} -7.65685i q^{29} +5.59587i q^{31} +1.63899 q^{35} +9.07107 q^{37} -1.41421i q^{41} -7.91375i q^{43} -3.27798 q^{47} +4.31371 q^{49} -5.17157i q^{53} -3.95687i q^{55} +11.8706 q^{59} +0.828427 q^{61} -0.585786i q^{65} -11.1917i q^{67} -4.63577 q^{71} +8.82843 q^{73} +6.48528i q^{77} -10.2316i q^{79} -3.27798 q^{83} +4.00000 q^{85} -5.41421i q^{89} +0.960099i q^{91} -7.91375 q^{95} +14.4853 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 16 q^{13} - 8 q^{25} + 16 q^{37} - 56 q^{49} - 16 q^{61} + 48 q^{73} + 32 q^{85} + 48 q^{97}+O(q^{100}) \) 8 * q - 16 * q^13 - 8 * q^25 + 16 * q^37 - 56 * q^49 - 16 * q^61 + 48 * q^73 + 32 * q^85 + 48 * q^97

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