LMFDB - Embedded newform 2900.2.a.m.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2900,2,Mod(1,2900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2900, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2900.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2900 = 2^{2} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2900.a (trivial)

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:	yes
Analytic conductor:	$23.1566165862$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 22x^{8} + 149x^{6} - 324x^{4} + 252x^{2} - 64 $ x^10 - 22x^8 + 149x^6 - 324x^4 + 252x^2 - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 580)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$3.27452$ of defining polynomial
Character	$\chi$	$=$	2900.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.27452 q^{3} +1.44995 q^{7} +7.72245 q^{9} -1.39969 q^{11} +5.03427 q^{13} -3.10695 q^{17} -0.911344 q^{19} +4.74787 q^{21} -1.53426 q^{23} +15.4637 q^{27} +1.00000 q^{29} -7.29734 q^{31} -4.58329 q^{33} +9.65598 q^{37} +16.4848 q^{39} +11.0240 q^{41} +3.72549 q^{43} -6.34304 q^{47} -4.89766 q^{49} -10.1738 q^{51} +4.13231 q^{53} -2.98421 q^{57} -7.54724 q^{59} +4.92518 q^{61} +11.1971 q^{63} +10.5322 q^{67} -5.02397 q^{69} -10.5197 q^{71} +3.19127 q^{73} -2.02947 q^{77} -8.37216 q^{79} +27.4689 q^{81} -11.0675 q^{83} +3.27452 q^{87} -11.0989 q^{89} +7.29942 q^{91} -23.8953 q^{93} -18.7382 q^{97} -10.8090 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14 q^{9} + 4 q^{19} + 24 q^{21} + 10 q^{29} + 16 q^{31} + 4 q^{39} + 28 q^{41} + 26 q^{49} + 32 q^{51} - 24 q^{59} + 52 q^{61} + 32 q^{69} + 24 q^{71} + 8 q^{79} + 66 q^{81} + 20 q^{89} + 16 q^{91}+ \cdots - 20 q^{99}+O(q^{100}) $ 10 * q + 14 * q^9 + 4 * q^19 + 24 * q^21 + 10 * q^29 + 16 * q^31 + 4 * q^39 + 28 * q^41 + 26 * q^49 + 32 * q^51 - 24 * q^59 + 52 * q^61 + 32 * q^69 + 24 * q^71 + 8 * q^79 + 66 * q^81 + 20 * q^89 + 16 * q^91 - 20 * q^99

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
$3$	3.27452	1.89054	0.945271	−	0.326286i	$-0.105797\pi$
$3$	3.27452	1.89054	0.945271	+	0.326286i	$0.105797\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.44995	0.548028	0.274014	−	0.961726i	$-0.411648\pi$
$7$	1.44995	0.548028	0.274014	+	0.961726i	$0.411648\pi$
$8$	0	0
$9$	7.72245	2.57415
$10$	0	0
$11$	−1.39969	−0.422021	−0.211011	−	0.977484i	$-0.567675\pi$
$11$	−1.39969	−0.422021	−0.211011	+	0.977484i	$0.567675\pi$
$12$	0	0
$13$	5.03427	1.39625	0.698127	−	0.715974i	$-0.254017\pi$
$13$	5.03427	1.39625	0.698127	+	0.715974i	$0.254017\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−3.10695	−0.753546	−0.376773	−	0.926306i	$-0.622966\pi$
$17$	−3.10695	−0.753546	−0.376773	+	0.926306i	$0.622966\pi$
$18$	0	0
$19$	−0.911344	−0.209077	−0.104538	−	0.994521i	$-0.533337\pi$
$19$	−0.911344	−0.209077	−0.104538	+	0.994521i	$0.533337\pi$
$20$	0	0
$21$	4.74787	1.03607
$22$	0	0
$23$	−1.53426	−0.319916	−0.159958	−	0.987124i	$-0.551136\pi$
$23$	−1.53426	−0.319916	−0.159958	+	0.987124i	$0.551136\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	15.4637	2.97600
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−7.29734	−1.31064	−0.655321	−	0.755351i	$-0.727466\pi$
$31$	−7.29734	−1.31064	−0.655321	+	0.755351i	$0.727466\pi$
$32$	0	0
$33$	−4.58329	−0.797849
$34$	0	0
$35$	0	0
$36$	0	0
$37$	9.65598	1.58743	0.793717	−	0.608288i	$-0.208143\pi$
$37$	9.65598	1.58743	0.793717	+	0.608288i	$0.208143\pi$
$38$	0	0
$39$	16.4848	2.63968
$40$	0	0
$41$	11.0240	1.72166	0.860828	−	0.508897i	$-0.169946\pi$
$41$	11.0240	1.72166	0.860828	+	0.508897i	$0.169946\pi$
$42$	0	0
$43$	3.72549	0.568132	0.284066	−	0.958805i	$-0.408316\pi$
$43$	3.72549	0.568132	0.284066	+	0.958805i	$0.408316\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−6.34304	−0.925228	−0.462614	−	0.886560i	$-0.653088\pi$
$47$	−6.34304	−0.925228	−0.462614	+	0.886560i	$0.653088\pi$
$48$	0	0
$49$	−4.89766	−0.699665
$50$	0	0
$51$	−10.1738	−1.42461
$52$	0	0
$53$	4.13231	0.567617	0.283809	−	0.958881i	$-0.408402\pi$
$53$	4.13231	0.567617	0.283809	+	0.958881i	$0.408402\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−2.98421	−0.395268
$58$	0	0
$59$	−7.54724	−0.982567	−0.491284	−	0.871000i	$-0.663472\pi$
$59$	−7.54724	−0.982567	−0.491284	+	0.871000i	$0.663472\pi$
$60$	0	0
$61$	4.92518	0.630605	0.315303	−	0.948991i	$-0.397894\pi$
$61$	4.92518	0.630605	0.315303	+	0.948991i	$0.397894\pi$
$62$	0	0
$63$	11.1971	1.41071
$64$	0	0
$65$	0	0
$66$	0	0
$67$	10.5322	1.28671	0.643357	−	0.765566i	$-0.277541\pi$
$67$	10.5322	1.28671	0.643357	+	0.765566i	$0.277541\pi$
$68$	0	0
$69$	−5.02397	−0.604815
$70$	0	0
$71$	−10.5197	−1.24846	−0.624230	−	0.781240i	$-0.714587\pi$
$71$	−10.5197	−1.24846	−0.624230	+	0.781240i	$0.714587\pi$
$72$	0	0
$73$	3.19127	0.373510	0.186755	−	0.982407i	$-0.440203\pi$
$73$	3.19127	0.373510	0.186755	+	0.982407i	$0.440203\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−2.02947	−0.231279
$78$	0	0
$79$	−8.37216	−0.941941	−0.470971	−	0.882149i	$-0.656096\pi$
$79$	−8.37216	−0.941941	−0.470971	+	0.882149i	$0.656096\pi$
$80$	0	0
$81$	27.4689	3.05210
$82$	0	0
$83$	−11.0675	−1.21482	−0.607408	−	0.794390i	$-0.707791\pi$
$83$	−11.0675	−1.21482	−0.607408	+	0.794390i	$0.707791\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	3.27452	0.351065
$88$	0	0
$89$	−11.0989	−1.17649	−0.588243	−	0.808685i	$-0.700180\pi$
$89$	−11.0989	−1.17649	−0.588243	+	0.808685i	$0.700180\pi$
$90$	0	0
$91$	7.29942	0.765187
$92$	0	0
$93$	−23.8953	−2.47782
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−18.7382	−1.90258	−0.951290	−	0.308297i	$-0.900241\pi$
$97$	−18.7382	−1.90258	−0.951290	+	0.308297i	$0.900241\pi$
$98$	0	0
$99$	−10.8090	−1.08635
$100$	0	0
$101$	13.9492	1.38799	0.693996	−	0.719978i	$-0.255848\pi$
$101$	13.9492	1.38799	0.693996	+	0.719978i	$0.255848\pi$
$102$	0	0
$103$	−4.22866	−0.416662	−0.208331	−	0.978058i	$-0.566803\pi$
$103$	−4.22866	−0.416662	−0.208331	+	0.978058i	$0.566803\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−0.547993	−0.0529765	−0.0264882	−	0.999649i	$-0.508432\pi$
$107$	−0.547993	−0.0529765	−0.0264882	+	0.999649i	$0.508432\pi$
$108$	0	0
$109$	14.1992	1.36003	0.680017	−	0.733196i	$-0.261972\pi$
$109$	14.1992	1.36003	0.680017	+	0.733196i	$0.261972\pi$
$110$	0	0
$111$	31.6187	3.00111
$112$	0	0
$113$	−0.908845	−0.0854970	−0.0427485	−	0.999086i	$-0.513611\pi$
$113$	−0.908845	−0.0854970	−0.0427485	+	0.999086i	$0.513611\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	38.8769	3.59417
$118$	0	0
$119$	−4.50491	−0.412965
$120$	0	0
$121$	−9.04088	−0.821898
$122$	0	0
$123$	36.0982	3.25486
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−22.0523	−1.95682	−0.978411	−	0.206671i	$-0.933737\pi$
$127$	−22.0523	−1.95682	−0.978411	+	0.206671i	$0.933737\pi$
$128$	0	0
$129$	12.1992	1.07408
$130$	0	0
$131$	4.91134	0.429106	0.214553	−	0.976712i	$-0.431171\pi$
$131$	4.91134	0.429106	0.214553	+	0.976712i	$0.431171\pi$
$132$	0	0
$133$	−1.32140	−0.114580
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−3.44208	−0.294077	−0.147038	−	0.989131i	$-0.546974\pi$
$137$	−3.44208	−0.294077	−0.147038	+	0.989131i	$0.546974\pi$
$138$	0	0
$139$	13.4449	1.14038	0.570191	−	0.821512i	$-0.306869\pi$
$139$	13.4449	1.14038	0.570191	+	0.821512i	$0.306869\pi$
$140$	0	0
$141$	−20.7704	−1.74918
$142$	0	0
$143$	−7.04639	−0.589249
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−16.0374	−1.32275
$148$	0	0
$149$	−8.26969	−0.677480	−0.338740	−	0.940880i	$-0.610001\pi$
$149$	−8.26969	−0.677480	−0.338740	+	0.940880i	$0.610001\pi$
$150$	0	0
$151$	8.74787	0.711892	0.355946	−	0.934507i	$-0.384159\pi$
$151$	8.74787	0.711892	0.355946	+	0.934507i	$0.384159\pi$
$152$	0	0
$153$	−23.9933	−1.93974
$154$	0	0
$155$	0	0
$156$	0	0
$157$	5.64018	0.450136	0.225068	−	0.974343i	$-0.427740\pi$
$157$	5.64018	0.450136	0.225068	+	0.974343i	$0.427740\pi$
$158$	0	0
$159$	13.5313	1.07310
$160$	0	0
$161$	−2.22460	−0.175323
$162$	0	0
$163$	9.48842	0.743190	0.371595	−	0.928395i	$-0.378811\pi$
$163$	9.48842	0.743190	0.371595	+	0.928395i	$0.378811\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	14.5955	1.12943	0.564715	−	0.825286i	$-0.308986\pi$
$167$	14.5955	1.12943	0.564715	+	0.825286i	$0.308986\pi$
$168$	0	0
$169$	12.3439	0.949527
$170$	0	0
$171$	−7.03781	−0.538195
$172$	0	0
$173$	−19.7314	−1.50015	−0.750076	−	0.661352i	$-0.769983\pi$
$173$	−19.7314	−1.50015	−0.750076	+	0.661352i	$0.769983\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−24.7136	−1.85758
$178$	0	0
$179$	−22.5947	−1.68881	−0.844403	−	0.535709i	$-0.820045\pi$
$179$	−22.5947	−1.68881	−0.844403	+	0.535709i	$0.820045\pi$
$180$	0	0
$181$	19.6949	1.46391	0.731956	−	0.681352i	$-0.238608\pi$
$181$	19.6949	1.46391	0.731956	+	0.681352i	$0.238608\pi$
$182$	0	0
$183$	16.1276	1.19219
$184$	0	0
$185$	0	0
$186$	0	0
$187$	4.34875	0.318012
$188$	0	0
$189$	22.4216	1.63093
$190$	0	0
$191$	24.8846	1.80059	0.900294	−	0.435282i	$-0.143351\pi$
$191$	24.8846	1.80059	0.900294	+	0.435282i	$0.143351\pi$
$192$	0	0
$193$	−0.168053	−0.0120967	−0.00604836	−	0.999982i	$-0.501925\pi$
$193$	−0.168053	−0.0120967	−0.00604836	+	0.999982i	$0.501925\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−8.86831	−0.631841	−0.315921	−	0.948786i	$-0.602313\pi$
$197$	−8.86831	−0.631841	−0.315921	+	0.948786i	$0.602313\pi$
$198$	0	0
$199$	19.1504	1.35754	0.678769	−	0.734352i	$-0.262514\pi$
$199$	19.1504	1.35754	0.678769	+	0.734352i	$0.262514\pi$
$200$	0	0
$201$	34.4879	2.43259
$202$	0	0
$203$	1.44995	0.101766
$204$	0	0
$205$	0	0
$206$	0	0
$207$	−11.8483	−0.823512
$208$	0	0
$209$	1.27560	0.0882348
$210$	0	0
$211$	−0.0770445	−0.00530396	−0.00265198	−	0.999996i	$-0.500844\pi$
$211$	−0.0770445	−0.00530396	−0.00265198	+	0.999996i	$0.500844\pi$
$212$	0	0
$213$	−34.4470	−2.36027
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−10.5808	−0.718268
$218$	0	0
$219$	10.4499	0.706136
$220$	0	0
$221$	−15.6412	−1.05214
$222$	0	0
$223$	−12.1834	−0.815861	−0.407931	−	0.913013i	$-0.633750\pi$
$223$	−12.1834	−0.815861	−0.407931	+	0.913013i	$0.633750\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−3.81454	−0.253180	−0.126590	−	0.991955i	$-0.540403\pi$
$227$	−3.81454	−0.253180	−0.126590	+	0.991955i	$0.540403\pi$
$228$	0	0
$229$	20.9216	1.38254	0.691270	−	0.722597i	$-0.257052\pi$
$229$	20.9216	1.38254	0.691270	+	0.722597i	$0.257052\pi$
$230$	0	0
$231$	−6.64553	−0.437244
$232$	0	0
$233$	−21.6603	−1.41901	−0.709506	−	0.704699i	$-0.751082\pi$
$233$	−21.6603	−1.41901	−0.709506	+	0.704699i	$0.751082\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−27.4148	−1.78078
$238$	0	0
$239$	5.04299	0.326204	0.163102	−	0.986609i	$-0.447850\pi$
$239$	5.04299	0.326204	0.163102	+	0.986609i	$0.447850\pi$
$240$	0	0
$241$	−19.8729	−1.28013	−0.640063	−	0.768323i	$-0.721092\pi$
$241$	−19.8729	−1.28013	−0.640063	+	0.768323i	$0.721092\pi$
$242$	0	0
$243$	43.5560	2.79412
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−4.58795	−0.291924
$248$	0	0
$249$	−36.2407	−2.29666
$250$	0	0
$251$	9.34884	0.590094	0.295047	−	0.955483i	$-0.404665\pi$
$251$	9.34884	0.590094	0.295047	+	0.955483i	$0.404665\pi$
$252$	0	0
$253$	2.14749	0.135011
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−0.753905	−0.0470273	−0.0235137	−	0.999724i	$-0.507485\pi$
$257$	−0.753905	−0.0470273	−0.0235137	+	0.999724i	$0.507485\pi$
$258$	0	0
$259$	14.0007	0.869958
$260$	0	0
$261$	7.72245	0.478008
$262$	0	0
$263$	−7.20599	−0.444341	−0.222170	−	0.975008i	$-0.571314\pi$
$263$	−7.20599	−0.444341	−0.222170	+	0.975008i	$0.571314\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−36.3436	−2.22419
$268$	0	0
$269$	1.57907	0.0962779	0.0481389	−	0.998841i	$-0.484671\pi$
$269$	1.57907	0.0962779	0.0481389	+	0.998841i	$0.484671\pi$
$270$	0	0
$271$	−4.02620	−0.244574	−0.122287	−	0.992495i	$-0.539023\pi$
$271$	−4.02620	−0.244574	−0.122287	+	0.992495i	$0.539023\pi$
$272$	0	0
$273$	23.9021	1.44662
$274$	0	0
$275$	0	0
$276$	0	0
$277$	6.38787	0.383810	0.191905	−	0.981414i	$-0.438533\pi$
$277$	6.38787	0.383810	0.191905	+	0.981414i	$0.438533\pi$
$278$	0	0
$279$	−56.3533	−3.37379
$280$	0	0
$281$	−21.1907	−1.26413	−0.632065	−	0.774916i	$-0.717792\pi$
$281$	−21.1907	−1.26413	−0.632065	+	0.774916i	$0.717792\pi$
$282$	0	0
$283$	−19.0285	−1.13113	−0.565565	−	0.824704i	$-0.691342\pi$
$283$	−19.0285	−1.13113	−0.565565	+	0.824704i	$0.691342\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	15.9842	0.943516
$288$	0	0
$289$	−7.34686	−0.432168
$290$	0	0
$291$	−61.3587	−3.59691
$292$	0	0
$293$	−27.1050	−1.58349	−0.791745	−	0.610852i	$-0.790827\pi$
$293$	−27.1050	−1.58349	−0.791745	+	0.610852i	$0.790827\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−21.6444	−1.25593
$298$	0	0
$299$	−7.72390	−0.446685
$300$	0	0
$301$	5.40176	0.311352
$302$	0	0
$303$	45.6767	2.62406
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−22.0587	−1.25895	−0.629477	−	0.777019i	$-0.716731\pi$
$307$	−22.0587	−1.25895	−0.629477	+	0.777019i	$0.716731\pi$
$308$	0	0
$309$	−13.8468	−0.787718
$310$	0	0
$311$	11.9028	0.674948	0.337474	−	0.941335i	$-0.390428\pi$
$311$	11.9028	0.674948	0.337474	+	0.941335i	$0.390428\pi$
$312$	0	0
$313$	4.26195	0.240899	0.120450	−	0.992719i	$-0.461566\pi$
$313$	4.26195	0.240899	0.120450	+	0.992719i	$0.461566\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	3.59479	0.201903	0.100952	−	0.994891i	$-0.467811\pi$
$317$	3.59479	0.201903	0.100952	+	0.994891i	$0.467811\pi$
$318$	0	0
$319$	−1.39969	−0.0783673
$320$	0	0
$321$	−1.79441	−0.100154
$322$	0	0
$323$	2.83150	0.157549
$324$	0	0
$325$	0	0
$326$	0	0
$327$	46.4954	2.57120
$328$	0	0
$329$	−9.19707	−0.507051
$330$	0	0
$331$	−33.6912	−1.85184	−0.925919	−	0.377722i	$-0.876708\pi$
$331$	−33.6912	−1.85184	−0.925919	+	0.377722i	$0.876708\pi$
$332$	0	0
$333$	74.5678	4.08629
$334$	0	0
$335$	0	0
$336$	0	0
$337$	2.19655	0.119653	0.0598267	−	0.998209i	$-0.480945\pi$
$337$	2.19655	0.119653	0.0598267	+	0.998209i	$0.480945\pi$
$338$	0	0
$339$	−2.97603	−0.161636
$340$	0	0
$341$	10.2140	0.553118
$342$	0	0
$343$	−17.2510	−0.931464
$344$	0	0
$345$	0	0
$346$	0	0
$347$	11.0306	0.592156	0.296078	−	0.955164i	$-0.404321\pi$
$347$	11.0306	0.592156	0.296078	+	0.955164i	$0.404321\pi$
$348$	0	0
$349$	−7.76964	−0.415899	−0.207950	−	0.978140i	$-0.566679\pi$
$349$	−7.76964	−0.415899	−0.207950	+	0.978140i	$0.566679\pi$
$350$	0	0
$351$	77.8486	4.15525
$352$	0	0
$353$	35.9748	1.91475	0.957374	−	0.288852i	$-0.0932735\pi$
$353$	35.9748	1.91475	0.957374	+	0.288852i	$0.0932735\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−14.7514	−0.780727
$358$	0	0
$359$	20.4194	1.07770	0.538849	−	0.842403i	$-0.318859\pi$
$359$	20.4194	1.07770	0.538849	+	0.842403i	$0.318859\pi$
$360$	0	0
$361$	−18.1695	−0.956287
$362$	0	0
$363$	−29.6045	−1.55383
$364$	0	0
$365$	0	0
$366$	0	0
$367$	15.1703	0.791881	0.395941	−	0.918276i	$-0.370419\pi$
$367$	15.1703	0.791881	0.395941	+	0.918276i	$0.370419\pi$
$368$	0	0
$369$	85.1321	4.43180
$370$	0	0
$371$	5.99163	0.311070
$372$	0	0
$373$	−23.0617	−1.19409	−0.597045	−	0.802208i	$-0.703658\pi$
$373$	−23.0617	−1.19409	−0.597045	+	0.802208i	$0.703658\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	5.03427	0.259278
$378$	0	0
$379$	−6.68674	−0.343475	−0.171737	−	0.985143i	$-0.554938\pi$
$379$	−6.68674	−0.343475	−0.171737	+	0.985143i	$0.554938\pi$
$380$	0	0
$381$	−72.2104	−3.69945
$382$	0	0
$383$	−5.18873	−0.265132	−0.132566	−	0.991174i	$-0.542322\pi$
$383$	−5.18873	−0.265132	−0.132566	+	0.991174i	$0.542322\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	28.7699	1.46246
$388$	0	0
$389$	22.9413	1.16317	0.581585	−	0.813486i	$-0.302433\pi$
$389$	22.9413	1.16317	0.581585	+	0.813486i	$0.302433\pi$
$390$	0	0
$391$	4.76688	0.241072
$392$	0	0
$393$	16.0823	0.811243
$394$	0	0
$395$	0	0
$396$	0	0
$397$	1.14810	0.0576217	0.0288108	−	0.999585i	$-0.490828\pi$
$397$	1.14810	0.0576217	0.0288108	+	0.999585i	$0.490828\pi$
$398$	0	0
$399$	−4.32695	−0.216618
$400$	0	0
$401$	1.24993	0.0624184	0.0312092	−	0.999513i	$-0.490064\pi$
$401$	1.24993	0.0624184	0.0312092	+	0.999513i	$0.490064\pi$
$402$	0	0
$403$	−36.7368	−1.82999
$404$	0	0
$405$	0	0
$406$	0	0
$407$	−13.5153	−0.669930
$408$	0	0
$409$	2.50360	0.123795	0.0618976	−	0.998083i	$-0.480285\pi$
$409$	2.50360	0.123795	0.0618976	+	0.998083i	$0.480285\pi$
$410$	0	0
$411$	−11.2711	−0.555964
$412$	0	0
$413$	−10.9431	−0.538475
$414$	0	0
$415$	0	0
$416$	0	0
$417$	44.0255	2.15594
$418$	0	0
$419$	−38.3903	−1.87549	−0.937746	−	0.347323i	$-0.887091\pi$
$419$	−38.3903	−1.87549	−0.937746	+	0.347323i	$0.887091\pi$
$420$	0	0
$421$	10.7479	0.523819	0.261910	−	0.965092i	$-0.415648\pi$
$421$	10.7479	0.523819	0.261910	+	0.965092i	$0.415648\pi$
$422$	0	0
$423$	−48.9838	−2.38168
$424$	0	0
$425$	0	0
$426$	0	0
$427$	7.14125	0.345589
$428$	0	0
$429$	−23.0735	−1.11400
$430$	0	0
$431$	−31.4175	−1.51333	−0.756664	−	0.653804i	$-0.773172\pi$
$431$	−31.4175	−1.51333	−0.756664	+	0.653804i	$0.773172\pi$
$432$	0	0
$433$	2.77182	0.133205	0.0666026	−	0.997780i	$-0.478784\pi$
$433$	2.77182	0.133205	0.0666026	+	0.997780i	$0.478784\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1.39824	0.0668871
$438$	0	0
$439$	13.6216	0.650121	0.325061	−	0.945693i	$-0.394615\pi$
$439$	13.6216	0.650121	0.325061	+	0.945693i	$0.394615\pi$
$440$	0	0
$441$	−37.8219	−1.80104
$442$	0	0
$443$	−13.8288	−0.657026	−0.328513	−	0.944499i	$-0.606547\pi$
$443$	−13.8288	−0.657026	−0.328513	+	0.944499i	$0.606547\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−27.0792	−1.28080
$448$	0	0
$449$	−2.29891	−0.108492	−0.0542462	−	0.998528i	$-0.517276\pi$
$449$	−2.29891	−0.108492	−0.0542462	+	0.998528i	$0.517276\pi$
$450$	0	0
$451$	−15.4301	−0.726575
$452$	0	0
$453$	28.6450	1.34586
$454$	0	0
$455$	0	0
$456$	0	0
$457$	36.3121	1.69861	0.849305	−	0.527903i	$-0.177022\pi$
$457$	36.3121	1.69861	0.849305	+	0.527903i	$0.177022\pi$
$458$	0	0
$459$	−48.0450	−2.24255
$460$	0	0
$461$	−8.14963	−0.379566	−0.189783	−	0.981826i	$-0.560779\pi$
$461$	−8.14963	−0.379566	−0.189783	+	0.981826i	$0.560779\pi$
$462$	0	0
$463$	−19.5048	−0.906463	−0.453232	−	0.891393i	$-0.649729\pi$
$463$	−19.5048	−0.906463	−0.453232	+	0.891393i	$0.649729\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	12.4295	0.575168	0.287584	−	0.957755i	$-0.407148\pi$
$467$	12.4295	0.575168	0.287584	+	0.957755i	$0.407148\pi$
$468$	0	0
$469$	15.2711	0.705156
$470$	0	0
$471$	18.4689	0.851001
$472$	0	0
$473$	−5.21452	−0.239764
$474$	0	0
$475$	0	0
$476$	0	0
$477$	31.9116	1.46113
$478$	0	0
$479$	17.6249	0.805304	0.402652	−	0.915353i	$-0.368088\pi$
$479$	17.6249	0.805304	0.402652	+	0.915353i	$0.368088\pi$
$480$	0	0
$481$	48.6108	2.21646
$482$	0	0
$483$	−7.28449	−0.331456
$484$	0	0
$485$	0	0
$486$	0	0
$487$	2.53432	0.114841	0.0574205	−	0.998350i	$-0.481712\pi$
$487$	2.53432	0.114841	0.0574205	+	0.998350i	$0.481712\pi$
$488$	0	0
$489$	31.0700	1.40503
$490$	0	0
$491$	41.5387	1.87462	0.937308	−	0.348502i	$-0.113310\pi$
$491$	41.5387	1.87462	0.937308	+	0.348502i	$0.113310\pi$
$492$	0	0
$493$	−3.10695	−0.139930
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−15.2530	−0.684192
$498$	0	0
$499$	27.4928	1.23075	0.615374	−	0.788235i	$-0.289005\pi$
$499$	27.4928	1.23075	0.615374	+	0.788235i	$0.289005\pi$
$500$	0	0
$501$	47.7931	2.13524
$502$	0	0
$503$	−4.88671	−0.217888	−0.108944	−	0.994048i	$-0.534747\pi$
$503$	−4.88671	−0.217888	−0.108944	+	0.994048i	$0.534747\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	40.4201	1.79512
$508$	0	0
$509$	−11.0452	−0.489569	−0.244785	−	0.969577i	$-0.578717\pi$
$509$	−11.0452	−0.489569	−0.244785	+	0.969577i	$0.578717\pi$
$510$	0	0
$511$	4.62717	0.204694
$512$	0	0
$513$	−14.0928	−0.622212
$514$	0	0
$515$	0	0
$516$	0	0
$517$	8.87827	0.390466
$518$	0	0
$519$	−64.6108	−2.83610
$520$	0	0
$521$	−0.497193	−0.0217824	−0.0108912	−	0.999941i	$-0.503467\pi$
$521$	−0.497193	−0.0217824	−0.0108912	+	0.999941i	$0.503467\pi$
$522$	0	0
$523$	29.5250	1.29104	0.645518	−	0.763745i	$-0.276641\pi$
$523$	29.5250	1.29104	0.645518	+	0.763745i	$0.276641\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	22.6725	0.987629
$528$	0	0
$529$	−20.6460	−0.897654
$530$	0	0
$531$	−58.2832	−2.52928
$532$	0	0
$533$	55.4976	2.40387
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−73.9866	−3.19276
$538$	0	0
$539$	6.85518	0.295273
$540$	0	0
$541$	−10.8650	−0.467124	−0.233562	−	0.972342i	$-0.575038\pi$
$541$	−10.8650	−0.467124	−0.233562	+	0.972342i	$0.575038\pi$
$542$	0	0
$543$	64.4913	2.76759
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−20.5933	−0.880505	−0.440252	−	0.897874i	$-0.645111\pi$
$547$	−20.5933	−0.880505	−0.440252	+	0.897874i	$0.645111\pi$
$548$	0	0
$549$	38.0345	1.62327
$550$	0	0
$551$	−0.911344	−0.0388246
$552$	0	0
$553$	−12.1392	−0.516210
$554$	0	0
$555$	0	0
$556$	0	0
$557$	33.2467	1.40871	0.704355	−	0.709848i	$-0.251236\pi$
$557$	33.2467	1.40871	0.704355	+	0.709848i	$0.251236\pi$
$558$	0	0
$559$	18.7551	0.793257
$560$	0	0
$561$	14.2401	0.601216
$562$	0	0
$563$	−22.7530	−0.958923	−0.479462	−	0.877563i	$-0.659168\pi$
$563$	−22.7530	−0.958923	−0.479462	+	0.877563i	$0.659168\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	39.8284	1.67264
$568$	0	0
$569$	−15.9253	−0.667625	−0.333812	−	0.942640i	$-0.608335\pi$
$569$	−15.9253	−0.667625	−0.333812	+	0.942640i	$0.608335\pi$
$570$	0	0
$571$	−6.72820	−0.281567	−0.140783	−	0.990040i	$-0.544962\pi$
$571$	−6.72820	−0.281567	−0.140783	+	0.990040i	$0.544962\pi$
$572$	0	0
$573$	81.4851	3.40409
$574$	0	0
$575$	0	0
$576$	0	0
$577$	13.3167	0.554383	0.277191	−	0.960815i	$-0.410596\pi$
$577$	13.3167	0.554383	0.277191	+	0.960815i	$0.410596\pi$
$578$	0	0
$579$	−0.550292	−0.0228693
$580$	0	0
$581$	−16.0473	−0.665754
$582$	0	0
$583$	−5.78394	−0.239546
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−27.8990	−1.15152	−0.575758	−	0.817620i	$-0.695293\pi$
$587$	−27.8990	−1.15152	−0.575758	+	0.817620i	$0.695293\pi$
$588$	0	0
$589$	6.65039	0.274025
$590$	0	0
$591$	−29.0394	−1.19452
$592$	0	0
$593$	−29.8796	−1.22701	−0.613504	−	0.789692i	$-0.710241\pi$
$593$	−29.8796	−1.22701	−0.613504	+	0.789692i	$0.710241\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	62.7084	2.56648
$598$	0	0
$599$	−8.39983	−0.343208	−0.171604	−	0.985166i	$-0.554895\pi$
$599$	−8.39983	−0.343208	−0.171604	+	0.985166i	$0.554895\pi$
$600$	0	0
$601$	27.8658	1.13667	0.568335	−	0.822797i	$-0.307588\pi$
$601$	27.8658	1.13667	0.568335	+	0.822797i	$0.307588\pi$
$602$	0	0
$603$	81.3345	3.31220
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−42.5340	−1.72640	−0.863200	−	0.504861i	$-0.831544\pi$
$607$	−42.5340	−1.72640	−0.863200	+	0.504861i	$0.831544\pi$
$608$	0	0
$609$	4.74787	0.192393
$610$	0	0
$611$	−31.9326	−1.29185
$612$	0	0
$613$	−28.4792	−1.15026	−0.575132	−	0.818060i	$-0.695049\pi$
$613$	−28.4792	−1.15026	−0.575132	+	0.818060i	$0.695049\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−20.6087	−0.829675	−0.414837	−	0.909896i	$-0.636162\pi$
$617$	−20.6087	−0.829675	−0.414837	+	0.909896i	$0.636162\pi$
$618$	0	0
$619$	−27.5889	−1.10889	−0.554446	−	0.832220i	$-0.687070\pi$
$619$	−27.5889	−1.10889	−0.554446	+	0.832220i	$0.687070\pi$
$620$	0	0
$621$	−23.7255	−0.952070
$622$	0	0
$623$	−16.0929	−0.644747
$624$	0	0
$625$	0	0
$626$	0	0
$627$	4.17696	0.166812
$628$	0	0
$629$	−30.0007	−1.19620
$630$	0	0
$631$	22.6977	0.903580	0.451790	−	0.892124i	$-0.350786\pi$
$631$	22.6977	0.903580	0.451790	+	0.892124i	$0.350786\pi$
$632$	0	0
$633$	−0.252283	−0.0100274
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−24.6561	−0.976911
$638$	0	0
$639$	−81.2380	−3.21372
$640$	0	0
$641$	2.06630	0.0816141	0.0408070	−	0.999167i	$-0.487007\pi$
$641$	2.06630	0.0816141	0.0408070	+	0.999167i	$0.487007\pi$
$642$	0	0
$643$	−1.19914	−0.0472893	−0.0236446	−	0.999720i	$-0.507527\pi$
$643$	−1.19914	−0.0472893	−0.0236446	+	0.999720i	$0.507527\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	5.08530	0.199924	0.0999619	−	0.994991i	$-0.468128\pi$
$647$	5.08530	0.199924	0.0999619	+	0.994991i	$0.468128\pi$
$648$	0	0
$649$	10.5638	0.414664
$650$	0	0
$651$	−34.6468	−1.35792
$652$	0	0
$653$	−11.2713	−0.441081	−0.220541	−	0.975378i	$-0.570782\pi$
$653$	−11.2713	−0.441081	−0.220541	+	0.975378i	$0.570782\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	24.6444	0.961470
$658$	0	0
$659$	−26.5968	−1.03606	−0.518031	−	0.855362i	$-0.673335\pi$
$659$	−26.5968	−1.03606	−0.518031	+	0.855362i	$0.673335\pi$
$660$	0	0
$661$	23.0951	0.898297	0.449148	−	0.893457i	$-0.351727\pi$
$661$	23.0951	0.898297	0.449148	+	0.893457i	$0.351727\pi$
$662$	0	0
$663$	−51.2174	−1.98912
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−1.53426	−0.0594070
$668$	0	0
$669$	−39.8948	−1.54242
$670$	0	0
$671$	−6.89371	−0.266129
$672$	0	0
$673$	−33.5053	−1.29154	−0.645768	−	0.763534i	$-0.723463\pi$
$673$	−33.5053	−1.29154	−0.645768	+	0.763534i	$0.723463\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	16.1851	0.622044	0.311022	−	0.950403i	$-0.399329\pi$
$677$	16.1851	0.622044	0.311022	+	0.950403i	$0.399329\pi$
$678$	0	0
$679$	−27.1695	−1.04267
$680$	0	0
$681$	−12.4908	−0.478648
$682$	0	0
$683$	−0.270984	−0.0103689	−0.00518446	−	0.999987i	$-0.501650\pi$
$683$	−0.270984	−0.0103689	−0.00518446	+	0.999987i	$0.501650\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	68.5082	2.61375
$688$	0	0
$689$	20.8032	0.792538
$690$	0	0
$691$	21.9182	0.833808	0.416904	−	0.908950i	$-0.363115\pi$
$691$	21.9182	0.833808	0.416904	+	0.908950i	$0.363115\pi$
$692$	0	0
$693$	−15.6725	−0.595348
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−34.2509	−1.29735
$698$	0	0
$699$	−70.9269	−2.68270
$700$	0	0
$701$	10.5175	0.397239	0.198620	−	0.980077i	$-0.436354\pi$
$701$	10.5175	0.397239	0.198620	+	0.980077i	$0.436354\pi$
$702$	0	0
$703$	−8.79992	−0.331895
$704$	0	0
$705$	0	0
$706$	0	0
$707$	20.2255	0.760659
$708$	0	0
$709$	15.6045	0.586039	0.293020	−	0.956106i	$-0.405340\pi$
$709$	15.6045	0.586039	0.293020	+	0.956106i	$0.405340\pi$
$710$	0	0
$711$	−64.6536	−2.42470
$712$	0	0
$713$	11.1961	0.419295
$714$	0	0
$715$	0	0
$716$	0	0
$717$	16.5133	0.616702
$718$	0	0
$719$	−1.45261	−0.0541732	−0.0270866	−	0.999633i	$-0.508623\pi$
$719$	−1.45261	−0.0541732	−0.0270866	+	0.999633i	$0.508623\pi$
$720$	0	0
$721$	−6.13133	−0.228343
$722$	0	0
$723$	−65.0741	−2.42013
$724$	0	0
$725$	0	0
$726$	0	0
$727$	6.22294	0.230796	0.115398	−	0.993319i	$-0.463186\pi$
$727$	6.22294	0.230796	0.115398	+	0.993319i	$0.463186\pi$
$728$	0	0
$729$	60.2183	2.23031
$730$	0	0
$731$	−11.5749	−0.428114
$732$	0	0
$733$	17.3653	0.641400	0.320700	−	0.947181i	$-0.396082\pi$
$733$	17.3653	0.641400	0.320700	+	0.947181i	$0.396082\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−14.7418	−0.543021
$738$	0	0
$739$	35.9486	1.32239	0.661196	−	0.750213i	$-0.270049\pi$
$739$	35.9486	1.32239	0.661196	+	0.750213i	$0.270049\pi$
$740$	0	0
$741$	−15.0233	−0.551895
$742$	0	0
$743$	−16.5717	−0.607956	−0.303978	−	0.952679i	$-0.598315\pi$
$743$	−16.5717	−0.607956	−0.303978	+	0.952679i	$0.598315\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−85.4682	−3.12712
$748$	0	0
$749$	−0.794560	−0.0290326
$750$	0	0
$751$	−33.7738	−1.23242	−0.616211	−	0.787581i	$-0.711333\pi$
$751$	−33.7738	−1.23242	−0.616211	+	0.787581i	$0.711333\pi$
$752$	0	0
$753$	30.6129	1.11560
$754$	0	0
$755$	0	0
$756$	0	0
$757$	29.4033	1.06868	0.534341	−	0.845269i	$-0.320560\pi$
$757$	29.4033	1.06868	0.534341	+	0.845269i	$0.320560\pi$
$758$	0	0
$759$	7.03198	0.255245
$760$	0	0
$761$	−28.8518	−1.04588	−0.522938	−	0.852371i	$-0.675164\pi$
$761$	−28.8518	−1.04588	−0.522938	+	0.852371i	$0.675164\pi$
$762$	0	0
$763$	20.5880	0.745337
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−37.9948	−1.37191
$768$	0	0
$769$	11.6814	0.421243	0.210621	−	0.977568i	$-0.432451\pi$
$769$	11.6814	0.421243	0.210621	+	0.977568i	$0.432451\pi$
$770$	0	0
$771$	−2.46867	−0.0889071
$772$	0	0
$773$	51.1567	1.83998	0.919990	−	0.391943i	$-0.128197\pi$
$773$	51.1567	1.83998	0.919990	+	0.391943i	$0.128197\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	45.8454	1.64469
$778$	0	0
$779$	−10.0466	−0.359958
$780$	0	0
$781$	14.7243	0.526877
$782$	0	0
$783$	15.4637	0.552629
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−9.61117	−0.342601	−0.171301	−	0.985219i	$-0.554797\pi$
$787$	−9.61117	−0.342601	−0.171301	+	0.985219i	$0.554797\pi$
$788$	0	0
$789$	−23.5961	−0.840045
$790$	0	0
$791$	−1.31778	−0.0468548
$792$	0	0
$793$	24.7947	0.880485
$794$	0	0
$795$	0	0
$796$	0	0
$797$	19.7046	0.697973	0.348986	−	0.937128i	$-0.386526\pi$
$797$	19.7046	0.697973	0.348986	+	0.937128i	$0.386526\pi$
$798$	0	0
$799$	19.7075	0.697202
$800$	0	0
$801$	−85.7110	−3.02845
$802$	0	0
$803$	−4.46677	−0.157629
$804$	0	0
$805$	0	0
$806$	0	0
$807$	5.17070	0.182017
$808$	0	0
$809$	34.6616	1.21864	0.609319	−	0.792925i	$-0.291443\pi$
$809$	34.6616	1.21864	0.609319	+	0.792925i	$0.291443\pi$
$810$	0	0
$811$	−46.6192	−1.63702	−0.818510	−	0.574492i	$-0.805200\pi$
$811$	−46.6192	−1.63702	−0.818510	+	0.574492i	$0.805200\pi$
$812$	0	0
$813$	−13.1839	−0.462378
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−3.39521	−0.118783
$818$	0	0
$819$	56.3694	1.96971
$820$	0	0
$821$	−6.13288	−0.214039	−0.107019	−	0.994257i	$-0.534131\pi$
$821$	−6.13288	−0.214039	−0.107019	+	0.994257i	$0.534131\pi$
$822$	0	0
$823$	14.0997	0.491484	0.245742	−	0.969335i	$-0.420968\pi$
$823$	14.0997	0.491484	0.245742	+	0.969335i	$0.420968\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−20.9237	−0.727587	−0.363794	−	0.931480i	$-0.618519\pi$
$827$	−20.9237	−0.727587	−0.363794	+	0.931480i	$0.618519\pi$
$828$	0	0
$829$	29.9646	1.04071	0.520357	−	0.853949i	$-0.325799\pi$
$829$	29.9646	1.04071	0.520357	+	0.853949i	$0.325799\pi$
$830$	0	0
$831$	20.9172	0.725609
$832$	0	0
$833$	15.2168	0.527230
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−112.844	−3.90046
$838$	0	0
$839$	6.87642	0.237400	0.118700	−	0.992930i	$-0.462127\pi$
$839$	6.87642	0.237400	0.118700	+	0.992930i	$0.462127\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−69.3891	−2.38989
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−13.1088	−0.450423
$848$	0	0
$849$	−62.3092	−2.13845
$850$	0	0
$851$	−14.8148	−0.507846
$852$	0	0
$853$	−25.7698	−0.882341	−0.441170	−	0.897423i	$-0.645437\pi$
$853$	−25.7698	−0.882341	−0.441170	+	0.897423i	$0.645437\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−35.2927	−1.20557	−0.602787	−	0.797902i	$-0.705943\pi$
$857$	−35.2927	−1.20557	−0.602787	+	0.797902i	$0.705943\pi$
$858$	0	0
$859$	39.2111	1.33787	0.668933	−	0.743323i	$-0.266751\pi$
$859$	39.2111	1.33787	0.668933	+	0.743323i	$0.266751\pi$
$860$	0	0
$861$	52.3404	1.78376
$862$	0	0
$863$	26.1150	0.888966	0.444483	−	0.895787i	$-0.353387\pi$
$863$	26.1150	0.888966	0.444483	+	0.895787i	$0.353387\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−24.0574	−0.817032
$868$	0	0
$869$	11.7184	0.397519
$870$	0	0
$871$	53.0220	1.79658
$872$	0	0
$873$	−144.705	−4.89753
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−30.8669	−1.04230	−0.521150	−	0.853465i	$-0.674497\pi$
$877$	−30.8669	−1.04230	−0.521150	+	0.853465i	$0.674497\pi$
$878$	0	0
$879$	−88.7556	−2.99365
$880$	0	0
$881$	−23.8713	−0.804244	−0.402122	−	0.915586i	$-0.631727\pi$
$881$	−23.8713	−0.804244	−0.402122	+	0.915586i	$0.631727\pi$
$882$	0	0
$883$	42.0486	1.41505	0.707524	−	0.706690i	$-0.249812\pi$
$883$	42.0486	1.41505	0.707524	+	0.706690i	$0.249812\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−55.1261	−1.85095	−0.925477	−	0.378803i	$-0.876336\pi$
$887$	−55.1261	−1.85095	−0.925477	+	0.378803i	$0.876336\pi$
$888$	0	0
$889$	−31.9746	−1.07239
$890$	0	0
$891$	−38.4478	−1.28805
$892$	0	0
$893$	5.78070	0.193444
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−25.2920	−0.844476
$898$	0	0
$899$	−7.29734	−0.243380
$900$	0	0
$901$	−12.8389	−0.427726
$902$	0	0
$903$	17.6882	0.588625
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−6.81301	−0.226222	−0.113111	−	0.993582i	$-0.536082\pi$
$907$	−6.81301	−0.226222	−0.113111	+	0.993582i	$0.536082\pi$
$908$	0	0
$909$	107.722	3.57290
$910$	0	0
$911$	33.4675	1.10883	0.554415	−	0.832241i	$-0.312942\pi$
$911$	33.4675	1.10883	0.554415	+	0.832241i	$0.312942\pi$
$912$	0	0
$913$	15.4910	0.512678
$914$	0	0
$915$	0	0
$916$	0	0
$917$	7.12119	0.235162
$918$	0	0
$919$	−7.97743	−0.263151	−0.131576	−	0.991306i	$-0.542004\pi$
$919$	−7.97743	−0.263151	−0.131576	+	0.991306i	$0.542004\pi$
$920$	0	0
$921$	−72.2314	−2.38011
$922$	0	0
$923$	−52.9591	−1.74317
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−32.6556	−1.07255
$928$	0	0
$929$	0.440593	0.0144554	0.00722769	−	0.999974i	$-0.497699\pi$
$929$	0.440593	0.0144554	0.00722769	+	0.999974i	$0.497699\pi$
$930$	0	0
$931$	4.46345	0.146284
$932$	0	0
$933$	38.9760	1.27602
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−6.69858	−0.218833	−0.109417	−	0.993996i	$-0.534898\pi$
$937$	−6.69858	−0.218833	−0.109417	+	0.993996i	$0.534898\pi$
$938$	0	0
$939$	13.9558	0.455431
$940$	0	0
$941$	3.14308	0.102461	0.0512307	−	0.998687i	$-0.483686\pi$
$941$	3.14308	0.102461	0.0512307	+	0.998687i	$0.483686\pi$
$942$	0	0
$943$	−16.9137	−0.550786
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−36.7151	−1.19308	−0.596541	−	0.802583i	$-0.703459\pi$
$947$	−36.7151	−1.19308	−0.596541	+	0.802583i	$0.703459\pi$
$948$	0	0
$949$	16.0657	0.521515
$950$	0	0
$951$	11.7712	0.381707
$952$	0	0
$953$	6.34286	0.205465	0.102733	−	0.994709i	$-0.467241\pi$
$953$	6.34286	0.205465	0.102733	+	0.994709i	$0.467241\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−4.58329	−0.148157
$958$	0	0
$959$	−4.99083	−0.161162
$960$	0	0
$961$	22.2512	0.717780
$962$	0	0
$963$	−4.23185	−0.136369
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−14.9669	−0.481302	−0.240651	−	0.970612i	$-0.577361\pi$
$967$	−14.9669	−0.481302	−0.240651	+	0.970612i	$0.577361\pi$
$968$	0	0
$969$	9.27180	0.297853
$970$	0	0
$971$	25.0440	0.803699	0.401849	−	0.915706i	$-0.368368\pi$
$971$	25.0440	0.803699	0.401849	+	0.915706i	$0.368368\pi$
$972$	0	0
$973$	19.4944	0.624961
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−43.8796	−1.40383	−0.701917	−	0.712259i	$-0.747672\pi$
$977$	−43.8796	−1.40383	−0.701917	+	0.712259i	$0.747672\pi$
$978$	0	0
$979$	15.5350	0.496502
$980$	0	0
$981$	109.652	3.50093
$982$	0	0
$983$	7.18506	0.229168	0.114584	−	0.993414i	$-0.463447\pi$
$983$	7.18506	0.229168	0.114584	+	0.993414i	$0.463447\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−30.1160	−0.958602
$988$	0	0
$989$	−5.71589	−0.181755
$990$	0	0
$991$	0.349514	0.0111027	0.00555133	−	0.999985i	$-0.498233\pi$
$991$	0.349514	0.0111027	0.00555133	+	0.999985i	$0.498233\pi$
$992$	0	0
$993$	−110.322	−3.50098
$994$	0	0
$995$	0	0
$996$	0	0
$997$	55.7521	1.76569	0.882844	−	0.469666i	$-0.155626\pi$
$997$	55.7521	1.76569	0.882844	+	0.469666i	$0.155626\pi$
$998$	0	0
$999$	149.317	4.72420

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2900.2.a.m.1.10		10
5.2	odd	4		580.2.c.b.349.1	✓	10
5.3	odd	4		580.2.c.b.349.10	yes	10
5.4	even	2	inner	2900.2.a.m.1.1		10
15.2	even	4		5220.2.g.d.2089.2		10
15.8	even	4		5220.2.g.d.2089.1		10
20.3	even	4		2320.2.d.i.929.1		10
20.7	even	4		2320.2.d.i.929.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.c.b.349.1	✓	10	5.2	odd	4
580.2.c.b.349.10	yes	10	5.3	odd	4
2320.2.d.i.929.1		10	20.3	even	4
2320.2.d.i.929.10		10	20.7	even	4
2900.2.a.m.1.1		10	5.4	even	2	inner
2900.2.a.m.1.10		10	1.1	even	1	trivial
5220.2.g.d.2089.1		10	15.8	even	4
5220.2.g.d.2089.2		10	15.2	even	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:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2900.a (trivial)

\(f(q)\)	\(=\)	\(q+3.27452 q^{3} +1.44995 q^{7} +7.72245 q^{9} -1.39969 q^{11} +5.03427 q^{13} -3.10695 q^{17} -0.911344 q^{19} +4.74787 q^{21} -1.53426 q^{23} +15.4637 q^{27} +1.00000 q^{29} -7.29734 q^{31} -4.58329 q^{33} +9.65598 q^{37} +16.4848 q^{39} +11.0240 q^{41} +3.72549 q^{43} -6.34304 q^{47} -4.89766 q^{49} -10.1738 q^{51} +4.13231 q^{53} -2.98421 q^{57} -7.54724 q^{59} +4.92518 q^{61} +11.1971 q^{63} +10.5322 q^{67} -5.02397 q^{69} -10.5197 q^{71} +3.19127 q^{73} -2.02947 q^{77} -8.37216 q^{79} +27.4689 q^{81} -11.0675 q^{83} +3.27452 q^{87} -11.0989 q^{89} +7.29942 q^{91} -23.8953 q^{93} -18.7382 q^{97} -10.8090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{9} + 4 q^{19} + 24 q^{21} + 10 q^{29} + 16 q^{31} + 4 q^{39} + 28 q^{41} + 26 q^{49} + 32 q^{51} - 24 q^{59} + 52 q^{61} + 32 q^{69} + 24 q^{71} + 8 q^{79} + 66 q^{81} + 20 q^{89} + 16 q^{91}+ \cdots - 20 q^{99}+O(q^{100}) \) 10 * q + 14 * q^9 + 4 * q^19 + 24 * q^21 + 10 * q^29 + 16 * q^31 + 4 * q^39 + 28 * q^41 + 26 * q^49 + 32 * q^51 - 24 * q^59 + 52 * q^61 + 32 * q^69 + 24 * q^71 + 8 * q^79 + 66 * q^81 + 20 * q^89 + 16 * q^91 - 20 * q^99

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