LMFDB - Embedded newform 5796.2.a.t.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5796,2,Mod(1,5796)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5796, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5796.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5796.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:	$46.2812930115$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.6963152.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 $ x^5 - 2x^4 - 10x^3 + 10x^2 + 29x + 10
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 644)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.76321$ of defining polynomial
Character	$\chi$	$=$	5796.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.11657 q^{5} -1.00000 q^{7} +O(q^{10})$	$q+3.11657 q^{5} -1.00000 q^{7} +5.23940 q^{11} +6.34832 q^{13} +0.585105 q^{17} +8.48889 q^{19} +1.00000 q^{23} +4.71298 q^{25} +1.59780 q^{29} -5.97640 q^{31} -3.11657 q^{35} +10.0153 q^{37} -1.17811 q^{41} -2.96247 q^{43} +2.55043 q^{47} +1.00000 q^{49} -8.27107 q^{53} +16.3289 q^{55} -14.6004 q^{59} +6.15410 q^{61} +19.7849 q^{65} -8.52015 q^{67} -8.38625 q^{71} -0.358396 q^{73} -5.23940 q^{77} -11.0216 q^{79} +10.7446 q^{83} +1.82352 q^{85} -18.1369 q^{89} -6.34832 q^{91} +26.4562 q^{95} -8.38723 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{5} - 5 q^{7}+O(q^{10}) $ 5 * q - 2 * q^5 - 5 * q^7	$ 5 q - 2 q^{5} - 5 q^{7} - 2 q^{11} + 13 q^{13} - 4 q^{17} + 12 q^{19} + 5 q^{23} + 19 q^{25} - 13 q^{29} - 3 q^{31} + 2 q^{35} - 4 q^{37} - q^{41} - 8 q^{43} - 5 q^{47} + 5 q^{49} + 8 q^{53} - 2 q^{55} - 12 q^{59} + 20 q^{61} + 12 q^{65} - 12 q^{67} - 9 q^{71} - 9 q^{73} + 2 q^{77} - 8 q^{79} + 28 q^{83} + 16 q^{85} - 32 q^{89} - 13 q^{91} + 36 q^{95} + 4 q^{97}+O(q^{100}) $ 5 * q - 2 * q^5 - 5 * q^7 - 2 * q^11 + 13 * q^13 - 4 * q^17 + 12 * q^19 + 5 * q^23 + 19 * q^25 - 13 * q^29 - 3 * q^31 + 2 * q^35 - 4 * q^37 - q^41 - 8 * q^43 - 5 * q^47 + 5 * q^49 + 8 * q^53 - 2 * q^55 - 12 * q^59 + 20 * q^61 + 12 * q^65 - 12 * q^67 - 9 * q^71 - 9 * q^73 + 2 * q^77 - 8 * q^79 + 28 * q^83 + 16 * q^85 - 32 * q^89 - 13 * q^91 + 36 * q^95 + 4 * q^97

Display 100 coefficients 10 coefficients

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
$5$	3.11657	1.39377	0.696885	−	0.717183i	$-0.254569\pi$
$5$	3.11657	1.39377	0.696885	+	0.717183i	$0.254569\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	0	0
$10$	0	0
$11$	5.23940	1.57974	0.789870	−	0.613274i	$-0.210148\pi$
$11$	5.23940	1.57974	0.789870	+	0.613274i	$0.210148\pi$
$12$	0	0
$13$	6.34832	1.76071	0.880353	−	0.474319i	$-0.157306\pi$
$13$	6.34832	1.76071	0.880353	+	0.474319i	$0.157306\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	0.585105	0.141909	0.0709544	−	0.997480i	$-0.477396\pi$
$17$	0.585105	0.141909	0.0709544	+	0.997480i	$0.477396\pi$
$18$	0	0
$19$	8.48889	1.94748	0.973742	−	0.227653i	$-0.0731051\pi$
$19$	8.48889	1.94748	0.973742	+	0.227653i	$0.0731051\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	4.71298	0.942597
$26$	0	0
$27$	0	0
$28$	0	0
$29$	1.59780	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$29$	1.59780	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$30$	0	0
$31$	−5.97640	−1.07339	−0.536696	−	0.843776i	$-0.680328\pi$
$31$	−5.97640	−1.07339	−0.536696	+	0.843776i	$0.680328\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−3.11657	−0.526796
$36$	0	0
$37$	10.0153	1.64651	0.823253	−	0.567674i	$-0.192157\pi$
$37$	10.0153	1.64651	0.823253	+	0.567674i	$0.192157\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−1.17811	−0.183989	−0.0919946	−	0.995760i	$-0.529324\pi$
$41$	−1.17811	−0.183989	−0.0919946	+	0.995760i	$0.529324\pi$
$42$	0	0
$43$	−2.96247	−0.451772	−0.225886	−	0.974154i	$-0.572528\pi$
$43$	−2.96247	−0.451772	−0.225886	+	0.974154i	$0.572528\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	2.55043	0.372018	0.186009	−	0.982548i	$-0.440445\pi$
$47$	2.55043	0.372018	0.186009	+	0.982548i	$0.440445\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−8.27107	−1.13612	−0.568059	−	0.822988i	$-0.692306\pi$
$53$	−8.27107	−1.13612	−0.568059	+	0.822988i	$0.692306\pi$
$54$	0	0
$55$	16.3289	2.20180
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−14.6004	−1.90081	−0.950406	−	0.311012i	$-0.899332\pi$
$59$	−14.6004	−1.90081	−0.950406	+	0.311012i	$0.899332\pi$
$60$	0	0
$61$	6.15410	0.787951	0.393976	−	0.919121i	$-0.371099\pi$
$61$	6.15410	0.787951	0.393976	+	0.919121i	$0.371099\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	19.7849	2.45402
$66$	0	0
$67$	−8.52015	−1.04090	−0.520451	−	0.853892i	$-0.674236\pi$
$67$	−8.52015	−1.04090	−0.520451	+	0.853892i	$0.674236\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	−8.38625	−0.995265	−0.497632	−	0.867388i	$-0.665797\pi$
$71$	−8.38625	−0.995265	−0.497632	+	0.867388i	$0.665797\pi$
$72$	0	0
$73$	−0.358396	−0.0419471	−0.0209735	−	0.999780i	$-0.506677\pi$
$73$	−0.358396	−0.0419471	−0.0209735	+	0.999780i	$0.506677\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−5.23940	−0.597086
$78$	0	0
$79$	−11.0216	−1.24002	−0.620012	−	0.784592i	$-0.712872\pi$
$79$	−11.0216	−1.24002	−0.620012	+	0.784592i	$0.712872\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	10.7446	1.17938	0.589689	−	0.807630i	$-0.299250\pi$
$83$	10.7446	1.17938	0.589689	+	0.807630i	$0.299250\pi$
$84$	0	0
$85$	1.82352	0.197788
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−18.1369	−1.92251	−0.961255	−	0.275662i	$-0.911103\pi$
$89$	−18.1369	−1.92251	−0.961255	+	0.275662i	$0.911103\pi$
$90$	0	0
$91$	−6.34832	−0.665484
$92$	0	0
$93$	0	0
$94$	0	0
$95$	26.4562	2.71435
$96$	0	0
$97$	−8.38723	−0.851594	−0.425797	−	0.904819i	$-0.640006\pi$
$97$	−8.38723	−0.851594	−0.425797	+	0.904819i	$0.640006\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	−6.79708	−0.676335	−0.338168	−	0.941086i	$-0.609807\pi$
$101$	−6.79708	−0.676335	−0.338168	+	0.941086i	$0.609807\pi$
$102$	0	0
$103$	−9.75955	−0.961637	−0.480819	−	0.876820i	$-0.659660\pi$
$103$	−9.75955	−0.961637	−0.480819	+	0.876820i	$0.659660\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	6.96247	0.673087	0.336544	−	0.941668i	$-0.390742\pi$
$107$	6.96247	0.673087	0.336544	+	0.941668i	$0.390742\pi$
$108$	0	0
$109$	−2.03794	−0.195199	−0.0975994	−	0.995226i	$-0.531116\pi$
$109$	−2.03794	−0.195199	−0.0975994	+	0.995226i	$0.531116\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−3.20815	−0.301797	−0.150898	−	0.988549i	$-0.548217\pi$
$113$	−3.20815	−0.301797	−0.150898	+	0.988549i	$0.548217\pi$
$114$	0	0
$115$	3.11657	0.290621
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−0.585105	−0.0536365
$120$	0	0
$121$	16.4514	1.49558
$122$	0	0
$123$	0	0
$124$	0	0
$125$	−0.894506	−0.0800070
$126$	0	0
$127$	4.83720	0.429232	0.214616	−	0.976698i	$-0.431150\pi$
$127$	4.83720	0.429232	0.214616	+	0.976698i	$0.431150\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	−13.9917	−1.22246	−0.611231	−	0.791453i	$-0.709325\pi$
$131$	−13.9917	−1.22246	−0.611231	+	0.791453i	$0.709325\pi$
$132$	0	0
$133$	−8.48889	−0.736080
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−3.65910	−0.312618	−0.156309	−	0.987708i	$-0.549960\pi$
$137$	−3.65910	−0.312618	−0.156309	+	0.987708i	$0.549960\pi$
$138$	0	0
$139$	16.4852	1.39826	0.699130	−	0.714995i	$-0.253571\pi$
$139$	16.4852	1.39826	0.699130	+	0.714995i	$0.253571\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	33.2614	2.78146
$144$	0	0
$145$	4.97965	0.413537
$146$	0	0
$147$	0	0
$148$	0	0
$149$	15.7596	1.29107	0.645536	−	0.763729i	$-0.276634\pi$
$149$	15.7596	1.29107	0.645536	+	0.763729i	$0.276634\pi$
$150$	0	0
$151$	6.13049	0.498892	0.249446	−	0.968389i	$-0.419751\pi$
$151$	6.13049	0.498892	0.249446	+	0.968389i	$0.419751\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−18.6258	−1.49606
$156$	0	0
$157$	3.65811	0.291949	0.145974	−	0.989288i	$-0.453368\pi$
$157$	3.65811	0.291949	0.145974	+	0.989288i	$0.453368\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	−17.9381	−1.40502	−0.702509	−	0.711675i	$-0.747937\pi$
$163$	−17.9381	−1.40502	−0.702509	+	0.711675i	$0.747937\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−0.419935	−0.0324956	−0.0162478	−	0.999868i	$-0.505172\pi$
$167$	−0.419935	−0.0324956	−0.0162478	+	0.999868i	$0.505172\pi$
$168$	0	0
$169$	27.3011	2.10009
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−2.48889	−0.189227	−0.0946134	−	0.995514i	$-0.530161\pi$
$173$	−2.48889	−0.189227	−0.0946134	+	0.995514i	$0.530161\pi$
$174$	0	0
$175$	−4.71298	−0.356268
$176$	0	0
$177$	0	0
$178$	0	0
$179$	2.64201	0.197473	0.0987365	−	0.995114i	$-0.468520\pi$
$179$	2.64201	0.197473	0.0987365	+	0.995114i	$0.468520\pi$
$180$	0	0
$181$	1.38950	0.103281	0.0516405	−	0.998666i	$-0.483555\pi$
$181$	1.38950	0.103281	0.0516405	+	0.998666i	$0.483555\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	31.2134	2.29485
$186$	0	0
$187$	3.06560	0.224179
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−13.0682	−0.945578	−0.472789	−	0.881176i	$-0.656753\pi$
$191$	−13.0682	−0.945578	−0.472789	+	0.881176i	$0.656753\pi$
$192$	0	0
$193$	21.5964	1.55454	0.777270	−	0.629167i	$-0.216604\pi$
$193$	21.5964	1.55454	0.777270	+	0.629167i	$0.216604\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−10.2410	−0.729643	−0.364822	−	0.931077i	$-0.618870\pi$
$197$	−10.2410	−0.729643	−0.364822	+	0.931077i	$0.618870\pi$
$198$	0	0
$199$	−21.6744	−1.53646	−0.768229	−	0.640175i	$-0.778862\pi$
$199$	−21.6744	−1.53646	−0.768229	+	0.640175i	$0.778862\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−1.59780	−0.112144
$204$	0	0
$205$	−3.67164	−0.256439
$206$	0	0
$207$	0	0
$208$	0	0
$209$	44.4767	3.07652
$210$	0	0
$211$	15.8499	1.09115	0.545577	−	0.838061i	$-0.316311\pi$
$211$	15.8499	1.09115	0.545577	+	0.838061i	$0.316311\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	−9.23273	−0.629667
$216$	0	0
$217$	5.97640	0.405704
$218$	0	0
$219$	0	0
$220$	0	0
$221$	3.71443	0.249860
$222$	0	0
$223$	1.04860	0.0702197	0.0351098	−	0.999383i	$-0.488822\pi$
$223$	1.04860	0.0702197	0.0351098	+	0.999383i	$0.488822\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−27.9455	−1.85481	−0.927403	−	0.374063i	$-0.877964\pi$
$227$	−27.9455	−1.85481	−0.927403	+	0.374063i	$0.877964\pi$
$228$	0	0
$229$	−17.8239	−1.17783	−0.588917	−	0.808193i	$-0.700446\pi$
$229$	−17.8239	−1.17783	−0.588917	+	0.808193i	$0.700446\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−9.53528	−0.624677	−0.312339	−	0.949971i	$-0.601112\pi$
$233$	−9.53528	−0.624677	−0.312339	+	0.949971i	$0.601112\pi$
$234$	0	0
$235$	7.94858	0.518508
$236$	0	0
$237$	0	0
$238$	0	0
$239$	−13.6190	−0.880939	−0.440469	−	0.897768i	$-0.645188\pi$
$239$	−13.6190	−0.880939	−0.440469	+	0.897768i	$0.645188\pi$
$240$	0	0
$241$	16.1115	1.03783	0.518917	−	0.854824i	$-0.326335\pi$
$241$	16.1115	1.03783	0.518917	+	0.854824i	$0.326335\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	3.11657	0.199110
$246$	0	0
$247$	53.8901	3.42895
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−17.7822	−1.12240	−0.561201	−	0.827680i	$-0.689660\pi$
$251$	−17.7822	−1.12240	−0.561201	+	0.827680i	$0.689660\pi$
$252$	0	0
$253$	5.23940	0.329399
$254$	0	0
$255$	0	0
$256$	0	0
$257$	11.3733	0.709447	0.354724	−	0.934971i	$-0.384575\pi$
$257$	11.3733	0.709447	0.354724	+	0.934971i	$0.384575\pi$
$258$	0	0
$259$	−10.0153	−0.622321
$260$	0	0
$261$	0	0
$262$	0	0
$263$	−8.22726	−0.507315	−0.253657	−	0.967294i	$-0.581634\pi$
$263$	−8.22726	−0.507315	−0.253657	+	0.967294i	$0.581634\pi$
$264$	0	0
$265$	−25.7773	−1.58349
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−3.31078	−0.201862	−0.100931	−	0.994893i	$-0.532182\pi$
$269$	−3.31078	−0.201862	−0.100931	+	0.994893i	$0.532182\pi$
$270$	0	0
$271$	24.3447	1.47883	0.739416	−	0.673248i	$-0.235102\pi$
$271$	24.3447	1.47883	0.739416	+	0.673248i	$0.235102\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	24.6932	1.48906
$276$	0	0
$277$	−14.1492	−0.850144	−0.425072	−	0.905160i	$-0.639751\pi$
$277$	−14.1492	−0.850144	−0.425072	+	0.905160i	$0.639751\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−10.2231	−0.609856	−0.304928	−	0.952375i	$-0.598632\pi$
$281$	−10.2231	−0.609856	−0.304928	+	0.952375i	$0.598632\pi$
$282$	0	0
$283$	5.80480	0.345060	0.172530	−	0.985004i	$-0.444806\pi$
$283$	5.80480	0.345060	0.172530	+	0.985004i	$0.444806\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	1.17811	0.0695414
$288$	0	0
$289$	−16.6577	−0.979862
$290$	0	0
$291$	0	0
$292$	0	0
$293$	31.1117	1.81757	0.908783	−	0.417269i	$-0.137013\pi$
$293$	31.1117	1.81757	0.908783	+	0.417269i	$0.137013\pi$
$294$	0	0
$295$	−45.5032	−2.64930
$296$	0	0
$297$	0	0
$298$	0	0
$299$	6.34832	0.367133
$300$	0	0
$301$	2.96247	0.170754
$302$	0	0
$303$	0	0
$304$	0	0
$305$	19.1797	1.09822
$306$	0	0
$307$	−4.55784	−0.260130	−0.130065	−	0.991505i	$-0.541519\pi$
$307$	−4.55784	−0.260130	−0.130065	+	0.991505i	$0.541519\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−1.08872	−0.0617358	−0.0308679	−	0.999523i	$-0.509827\pi$
$311$	−1.08872	−0.0617358	−0.0308679	+	0.999523i	$0.509827\pi$
$312$	0	0
$313$	16.9086	0.955731	0.477866	−	0.878433i	$-0.341411\pi$
$313$	16.9086	0.955731	0.477866	+	0.878433i	$0.341411\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	4.26439	0.239512	0.119756	−	0.992803i	$-0.461789\pi$
$317$	4.26439	0.239512	0.119756	+	0.992803i	$0.461789\pi$
$318$	0	0
$319$	8.37152	0.468715
$320$	0	0
$321$	0	0
$322$	0	0
$323$	4.96689	0.276365
$324$	0	0
$325$	29.9195	1.65964
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−2.55043	−0.140610
$330$	0	0
$331$	16.9450	0.931380	0.465690	−	0.884948i	$-0.345806\pi$
$331$	16.9450	0.931380	0.465690	+	0.884948i	$0.345806\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	−26.5536	−1.45078
$336$	0	0
$337$	10.7547	0.585847	0.292924	−	0.956136i	$-0.405372\pi$
$337$	10.7547	0.585847	0.292924	+	0.956136i	$0.405372\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	−31.3128	−1.69568
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−30.2105	−1.62178	−0.810892	−	0.585195i	$-0.801018\pi$
$347$	−30.2105	−1.62178	−0.810892	+	0.585195i	$0.801018\pi$
$348$	0	0
$349$	−20.2309	−1.08294	−0.541469	−	0.840721i	$-0.682132\pi$
$349$	−20.2309	−1.08294	−0.541469	+	0.840721i	$0.682132\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−14.0953	−0.750218	−0.375109	−	0.926981i	$-0.622395\pi$
$353$	−14.0953	−0.750218	−0.375109	+	0.926981i	$0.622395\pi$
$354$	0	0
$355$	−26.1363	−1.38717
$356$	0	0
$357$	0	0
$358$	0	0
$359$	16.0086	0.844903	0.422452	−	0.906385i	$-0.361170\pi$
$359$	16.0086	0.844903	0.422452	+	0.906385i	$0.361170\pi$
$360$	0	0
$361$	53.0612	2.79270
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−1.11696	−0.0584646
$366$	0	0
$367$	−28.8277	−1.50479	−0.752397	−	0.658710i	$-0.771102\pi$
$367$	−28.8277	−1.50479	−0.752397	+	0.658710i	$0.771102\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	8.27107	0.429412
$372$	0	0
$373$	−18.6273	−0.964484	−0.482242	−	0.876038i	$-0.660177\pi$
$373$	−18.6273	−0.964484	−0.482242	+	0.876038i	$0.660177\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	10.1433	0.522409
$378$	0	0
$379$	14.8138	0.760936	0.380468	−	0.924794i	$-0.375763\pi$
$379$	14.8138	0.760936	0.380468	+	0.924794i	$0.375763\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−0.611968	−0.0312701	−0.0156351	−	0.999878i	$-0.504977\pi$
$383$	−0.611968	−0.0312701	−0.0156351	+	0.999878i	$0.504977\pi$
$384$	0	0
$385$	−16.3289	−0.832200
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−11.4514	−0.580607	−0.290303	−	0.956935i	$-0.593756\pi$
$389$	−11.4514	−0.580607	−0.290303	+	0.956935i	$0.593756\pi$
$390$	0	0
$391$	0.585105	0.0295900
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−34.3495	−1.72831
$396$	0	0
$397$	15.9228	0.799140	0.399570	−	0.916703i	$-0.369159\pi$
$397$	15.9228	0.799140	0.399570	+	0.916703i	$0.369159\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	35.1157	1.75359	0.876797	−	0.480861i	$-0.159676\pi$
$401$	35.1157	1.75359	0.876797	+	0.480861i	$0.159676\pi$
$402$	0	0
$403$	−37.9400	−1.88993
$404$	0	0
$405$	0	0
$406$	0	0
$407$	52.4743	2.60105
$408$	0	0
$409$	24.6726	1.21998	0.609991	−	0.792408i	$-0.291173\pi$
$409$	24.6726	1.21998	0.609991	+	0.792408i	$0.291173\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	14.6004	0.718439
$414$	0	0
$415$	33.4864	1.64378
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−23.0411	−1.12563	−0.562816	−	0.826582i	$-0.690282\pi$
$419$	−23.0411	−1.12563	−0.562816	+	0.826582i	$0.690282\pi$
$420$	0	0
$421$	11.8048	0.575331	0.287665	−	0.957731i	$-0.407121\pi$
$421$	11.8048	0.575331	0.287665	+	0.957731i	$0.407121\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	2.75759	0.133763
$426$	0	0
$427$	−6.15410	−0.297818
$428$	0	0
$429$	0	0
$430$	0	0
$431$	3.56873	0.171899	0.0859497	−	0.996299i	$-0.472608\pi$
$431$	3.56873	0.171899	0.0859497	+	0.996299i	$0.472608\pi$
$432$	0	0
$433$	−41.0992	−1.97510	−0.987550	−	0.157305i	$-0.949719\pi$
$433$	−41.0992	−1.97510	−0.987550	+	0.157305i	$0.949719\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	8.48889	0.406079
$438$	0	0
$439$	31.6361	1.50991	0.754954	−	0.655778i	$-0.227659\pi$
$439$	31.6361	1.50991	0.754954	+	0.655778i	$0.227659\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−3.30070	−0.156821	−0.0784106	−	0.996921i	$-0.524985\pi$
$443$	−3.30070	−0.156821	−0.0784106	+	0.996921i	$0.524985\pi$
$444$	0	0
$445$	−56.5249	−2.67954
$446$	0	0
$447$	0	0
$448$	0	0
$449$	19.8820	0.938289	0.469145	−	0.883121i	$-0.344562\pi$
$449$	19.8820	0.938289	0.469145	+	0.883121i	$0.344562\pi$
$450$	0	0
$451$	−6.17257	−0.290655
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−19.7849	−0.927532
$456$	0	0
$457$	15.2707	0.714332	0.357166	−	0.934041i	$-0.383743\pi$
$457$	15.2707	0.714332	0.357166	+	0.934041i	$0.383743\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	8.68922	0.404697	0.202349	−	0.979314i	$-0.435143\pi$
$461$	8.68922	0.404697	0.202349	+	0.979314i	$0.435143\pi$
$462$	0	0
$463$	8.57355	0.398447	0.199223	−	0.979954i	$-0.436158\pi$
$463$	8.57355	0.398447	0.199223	+	0.979954i	$0.436158\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−30.1327	−1.39437	−0.697187	−	0.716889i	$-0.745565\pi$
$467$	−30.1327	−1.39437	−0.697187	+	0.716889i	$0.745565\pi$
$468$	0	0
$469$	8.52015	0.393424
$470$	0	0
$471$	0	0
$472$	0	0
$473$	−15.5216	−0.713683
$474$	0	0
$475$	40.0080	1.83569
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−4.74988	−0.217027	−0.108514	−	0.994095i	$-0.534609\pi$
$479$	−4.74988	−0.217027	−0.108514	+	0.994095i	$0.534609\pi$
$480$	0	0
$481$	63.5803	2.89901
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−26.1394	−1.18693
$486$	0	0
$487$	−18.9728	−0.859741	−0.429870	−	0.902891i	$-0.641441\pi$
$487$	−18.9728	−0.859741	−0.429870	+	0.902891i	$0.641441\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−6.18017	−0.278907	−0.139453	−	0.990229i	$-0.544535\pi$
$491$	−6.18017	−0.278907	−0.139453	+	0.990229i	$0.544535\pi$
$492$	0	0
$493$	0.934881	0.0421049
$494$	0	0
$495$	0	0
$496$	0	0
$497$	8.38625	0.376175
$498$	0	0
$499$	−20.9756	−0.938997	−0.469498	−	0.882933i	$-0.655565\pi$
$499$	−20.9756	−0.938997	−0.469498	+	0.882933i	$0.655565\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	3.42597	0.152756	0.0763782	−	0.997079i	$-0.475664\pi$
$503$	3.42597	0.152756	0.0763782	+	0.997079i	$0.475664\pi$
$504$	0	0
$505$	−21.1836	−0.942656
$506$	0	0
$507$	0	0
$508$	0	0
$509$	35.6250	1.57905	0.789526	−	0.613718i	$-0.210327\pi$
$509$	35.6250	1.57905	0.789526	+	0.613718i	$0.210327\pi$
$510$	0	0
$511$	0.358396	0.0158545
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−30.4163	−1.34030
$516$	0	0
$517$	13.3627	0.587692
$518$	0	0
$519$	0	0
$520$	0	0
$521$	28.6482	1.25510	0.627551	−	0.778576i	$-0.284058\pi$
$521$	28.6482	1.25510	0.627551	+	0.778576i	$0.284058\pi$
$522$	0	0
$523$	−14.7717	−0.645921	−0.322961	−	0.946412i	$-0.604678\pi$
$523$	−14.7717	−0.645921	−0.322961	+	0.946412i	$0.604678\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−3.49682	−0.152324
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	0	0
$533$	−7.47899	−0.323951
$534$	0	0
$535$	21.6990	0.938129
$536$	0	0
$537$	0	0
$538$	0	0
$539$	5.23940	0.225677
$540$	0	0
$541$	−12.3001	−0.528824	−0.264412	−	0.964410i	$-0.585178\pi$
$541$	−12.3001	−0.528824	−0.264412	+	0.964410i	$0.585178\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−6.35136	−0.272062
$546$	0	0
$547$	−20.4059	−0.872495	−0.436247	−	0.899827i	$-0.643693\pi$
$547$	−20.4059	−0.872495	−0.436247	+	0.899827i	$0.643693\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	13.5635	0.577827
$552$	0	0
$553$	11.0216	0.468685
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−13.9455	−0.590889	−0.295444	−	0.955360i	$-0.595468\pi$
$557$	−13.9455	−0.590889	−0.295444	+	0.955360i	$0.595468\pi$
$558$	0	0
$559$	−18.8067	−0.795438
$560$	0	0
$561$	0	0
$562$	0	0
$563$	22.3868	0.943492	0.471746	−	0.881734i	$-0.343624\pi$
$563$	22.3868	0.943492	0.471746	+	0.881734i	$0.343624\pi$
$564$	0	0
$565$	−9.99840	−0.420636
$566$	0	0
$567$	0	0
$568$	0	0
$569$	23.0581	0.966645	0.483322	−	0.875442i	$-0.339430\pi$
$569$	23.0581	0.966645	0.483322	+	0.875442i	$0.339430\pi$
$570$	0	0
$571$	0.606257	0.0253711	0.0126855	−	0.999920i	$-0.495962\pi$
$571$	0.606257	0.0253711	0.0126855	+	0.999920i	$0.495962\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	4.71298	0.196545
$576$	0	0
$577$	5.57828	0.232227	0.116113	−	0.993236i	$-0.462956\pi$
$577$	5.57828	0.232227	0.116113	+	0.993236i	$0.462956\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	−10.7446	−0.445763
$582$	0	0
$583$	−43.3355	−1.79477
$584$	0	0
$585$	0	0
$586$	0	0
$587$	15.5804	0.643071	0.321536	−	0.946898i	$-0.395801\pi$
$587$	15.5804	0.643071	0.321536	+	0.946898i	$0.395801\pi$
$588$	0	0
$589$	−50.7330	−2.09042
$590$	0	0
$591$	0	0
$592$	0	0
$593$	12.4788	0.512443	0.256222	−	0.966618i	$-0.417522\pi$
$593$	12.4788	0.512443	0.256222	+	0.966618i	$0.417522\pi$
$594$	0	0
$595$	−1.82352	−0.0747569
$596$	0	0
$597$	0	0
$598$	0	0
$599$	25.6897	1.04965	0.524827	−	0.851209i	$-0.324130\pi$
$599$	25.6897	1.04965	0.524827	+	0.851209i	$0.324130\pi$
$600$	0	0
$601$	14.1712	0.578055	0.289028	−	0.957321i	$-0.406668\pi$
$601$	14.1712	0.578055	0.289028	+	0.957321i	$0.406668\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	51.2717	2.08449
$606$	0	0
$607$	−38.6010	−1.56677	−0.783383	−	0.621539i	$-0.786508\pi$
$607$	−38.6010	−1.56677	−0.783383	+	0.621539i	$0.786508\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	16.1909	0.655015
$612$	0	0
$613$	−2.40423	−0.0971058	−0.0485529	−	0.998821i	$-0.515461\pi$
$613$	−2.40423	−0.0971058	−0.0485529	+	0.998821i	$0.515461\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−24.5675	−0.989051	−0.494526	−	0.869163i	$-0.664658\pi$
$617$	−24.5675	−0.989051	−0.494526	+	0.869163i	$0.664658\pi$
$618$	0	0
$619$	31.0657	1.24864	0.624318	−	0.781171i	$-0.285377\pi$
$619$	31.0657	1.24864	0.624318	+	0.781171i	$0.285377\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	18.1369	0.726640
$624$	0	0
$625$	−26.3527	−1.05411
$626$	0	0
$627$	0	0
$628$	0	0
$629$	5.86001	0.233654
$630$	0	0
$631$	−15.9461	−0.634805	−0.317402	−	0.948291i	$-0.602811\pi$
$631$	−15.9461	−0.634805	−0.317402	+	0.948291i	$0.602811\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	15.0755	0.598252
$636$	0	0
$637$	6.34832	0.251529
$638$	0	0
$639$	0	0
$640$	0	0
$641$	34.1109	1.34730	0.673650	−	0.739051i	$-0.264726\pi$
$641$	34.1109	1.34730	0.673650	+	0.739051i	$0.264726\pi$
$642$	0	0
$643$	22.7215	0.896050	0.448025	−	0.894021i	$-0.352128\pi$
$643$	22.7215	0.896050	0.448025	+	0.894021i	$0.352128\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	4.53740	0.178384	0.0891918	−	0.996014i	$-0.471572\pi$
$647$	4.53740	0.178384	0.0891918	+	0.996014i	$0.471572\pi$
$648$	0	0
$649$	−76.4975	−3.00279
$650$	0	0
$651$	0	0
$652$	0	0
$653$	38.9525	1.52433	0.762164	−	0.647384i	$-0.224137\pi$
$653$	38.9525	1.52433	0.762164	+	0.647384i	$0.224137\pi$
$654$	0	0
$655$	−43.6061	−1.70383
$656$	0	0
$657$	0	0
$658$	0	0
$659$	14.8983	0.580357	0.290179	−	0.956973i	$-0.406285\pi$
$659$	14.8983	0.580357	0.290179	+	0.956973i	$0.406285\pi$
$660$	0	0
$661$	17.2118	0.669461	0.334731	−	0.942314i	$-0.391355\pi$
$661$	17.2118	0.669461	0.334731	+	0.942314i	$0.391355\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	−26.4562	−1.02593
$666$	0	0
$667$	1.59780	0.0618671
$668$	0	0
$669$	0	0
$670$	0	0
$671$	32.2438	1.24476
$672$	0	0
$673$	19.7685	0.762018	0.381009	−	0.924571i	$-0.375577\pi$
$673$	19.7685	0.762018	0.381009	+	0.924571i	$0.375577\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	36.0117	1.38404	0.692020	−	0.721878i	$-0.256721\pi$
$677$	36.0117	1.38404	0.692020	+	0.721878i	$0.256721\pi$
$678$	0	0
$679$	8.38723	0.321872
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−11.0796	−0.423949	−0.211975	−	0.977275i	$-0.567989\pi$
$683$	−11.0796	−0.423949	−0.211975	+	0.977275i	$0.567989\pi$
$684$	0	0
$685$	−11.4038	−0.435718
$686$	0	0
$687$	0	0
$688$	0	0
$689$	−52.5073	−2.00037
$690$	0	0
$691$	−16.5328	−0.628936	−0.314468	−	0.949268i	$-0.601826\pi$
$691$	−16.5328	−0.628936	−0.314468	+	0.949268i	$0.601826\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	51.3773	1.94885
$696$	0	0
$697$	−0.689315	−0.0261097
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−17.2642	−0.652058	−0.326029	−	0.945360i	$-0.605711\pi$
$701$	−17.2642	−0.652058	−0.326029	+	0.945360i	$0.605711\pi$
$702$	0	0
$703$	85.0189	3.20655
$704$	0	0
$705$	0	0
$706$	0	0
$707$	6.79708	0.255631
$708$	0	0
$709$	−3.98260	−0.149570	−0.0747849	−	0.997200i	$-0.523827\pi$
$709$	−3.98260	−0.149570	−0.0747849	+	0.997200i	$0.523827\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−5.97640	−0.223818
$714$	0	0
$715$	103.661	3.87671
$716$	0	0
$717$	0	0
$718$	0	0
$719$	7.33439	0.273527	0.136763	−	0.990604i	$-0.456330\pi$
$719$	7.33439	0.273527	0.136763	+	0.990604i	$0.456330\pi$
$720$	0	0
$721$	9.75955	0.363465
$722$	0	0
$723$	0	0
$724$	0	0
$725$	7.53041	0.279672
$726$	0	0
$727$	4.06498	0.150762	0.0753809	−	0.997155i	$-0.475983\pi$
$727$	4.06498	0.150762	0.0753809	+	0.997155i	$0.475983\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−1.73335	−0.0641104
$732$	0	0
$733$	17.2247	0.636207	0.318104	−	0.948056i	$-0.396954\pi$
$733$	17.2247	0.636207	0.318104	+	0.948056i	$0.396954\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−44.6405	−1.64435
$738$	0	0
$739$	13.0829	0.481262	0.240631	−	0.970617i	$-0.422646\pi$
$739$	13.0829	0.481262	0.240631	+	0.970617i	$0.422646\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	9.58553	0.351659	0.175830	−	0.984421i	$-0.443739\pi$
$743$	9.58553	0.351659	0.175830	+	0.984421i	$0.443739\pi$
$744$	0	0
$745$	49.1157	1.79946
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−6.96247	−0.254403
$750$	0	0
$751$	39.3151	1.43463	0.717314	−	0.696750i	$-0.245371\pi$
$751$	39.3151	1.43463	0.717314	+	0.696750i	$0.245371\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	19.1061	0.695342
$756$	0	0
$757$	−30.7971	−1.11934	−0.559670	−	0.828716i	$-0.689072\pi$
$757$	−30.7971	−1.11934	−0.559670	+	0.828716i	$0.689072\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−19.0651	−0.691110	−0.345555	−	0.938399i	$-0.612309\pi$
$761$	−19.0651	−0.691110	−0.345555	+	0.938399i	$0.612309\pi$
$762$	0	0
$763$	2.03794	0.0737782
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−92.6880	−3.34677
$768$	0	0
$769$	14.0861	0.507959	0.253980	−	0.967210i	$-0.418260\pi$
$769$	14.0861	0.507959	0.253980	+	0.967210i	$0.418260\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	5.46538	0.196576	0.0982879	−	0.995158i	$-0.468663\pi$
$773$	5.46538	0.196576	0.0982879	+	0.995158i	$0.468663\pi$
$774$	0	0
$775$	−28.1667	−1.01178
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−10.0008	−0.358316
$780$	0	0
$781$	−43.9390	−1.57226
$782$	0	0
$783$	0	0
$784$	0	0
$785$	11.4007	0.406910
$786$	0	0
$787$	36.3921	1.29724	0.648618	−	0.761114i	$-0.275347\pi$
$787$	36.3921	1.29724	0.648618	+	0.761114i	$0.275347\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	3.20815	0.114069
$792$	0	0
$793$	39.0682	1.38735
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−43.5810	−1.54372	−0.771858	−	0.635794i	$-0.780673\pi$
$797$	−43.5810	−1.54372	−0.771858	+	0.635794i	$0.780673\pi$
$798$	0	0
$799$	1.49227	0.0527927
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−1.87778	−0.0662654
$804$	0	0
$805$	−3.11657	−0.109845
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−5.11013	−0.179663	−0.0898313	−	0.995957i	$-0.528633\pi$
$809$	−5.11013	−0.179663	−0.0898313	+	0.995957i	$0.528633\pi$
$810$	0	0
$811$	−2.06953	−0.0726712	−0.0363356	−	0.999340i	$-0.511569\pi$
$811$	−2.06953	−0.0726712	−0.0363356	+	0.999340i	$0.511569\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−55.9052	−1.95827
$816$	0	0
$817$	−25.1481	−0.879819
$818$	0	0
$819$	0	0
$820$	0	0
$821$	−2.87359	−0.100289	−0.0501446	−	0.998742i	$-0.515968\pi$
$821$	−2.87359	−0.100289	−0.0501446	+	0.998742i	$0.515968\pi$
$822$	0	0
$823$	3.81222	0.132886	0.0664428	−	0.997790i	$-0.478835\pi$
$823$	3.81222	0.132886	0.0664428	+	0.997790i	$0.478835\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	6.87210	0.238966	0.119483	−	0.992836i	$-0.461876\pi$
$827$	6.87210	0.238966	0.119483	+	0.992836i	$0.461876\pi$
$828$	0	0
$829$	5.53374	0.192195	0.0960973	−	0.995372i	$-0.469364\pi$
$829$	5.53374	0.192195	0.0960973	+	0.995372i	$0.469364\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	0.585105	0.0202727
$834$	0	0
$835$	−1.30876	−0.0452914
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−1.16338	−0.0401642	−0.0200821	−	0.999798i	$-0.506393\pi$
$839$	−1.16338	−0.0401642	−0.0200821	+	0.999798i	$0.506393\pi$
$840$	0	0
$841$	−26.4470	−0.911967
$842$	0	0
$843$	0	0
$844$	0	0
$845$	85.0857	2.92704
$846$	0	0
$847$	−16.4514	−0.565275
$848$	0	0
$849$	0	0
$850$	0	0
$851$	10.0153	0.343320
$852$	0	0
$853$	5.30694	0.181706	0.0908531	−	0.995864i	$-0.471041\pi$
$853$	5.30694	0.181706	0.0908531	+	0.995864i	$0.471041\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	1.84412	0.0629938	0.0314969	−	0.999504i	$-0.489973\pi$
$857$	1.84412	0.0629938	0.0314969	+	0.999504i	$0.489973\pi$
$858$	0	0
$859$	45.1077	1.53905	0.769527	−	0.638615i	$-0.220492\pi$
$859$	45.1077	1.53905	0.769527	+	0.638615i	$0.220492\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−2.75173	−0.0936701	−0.0468351	−	0.998903i	$-0.514914\pi$
$863$	−2.75173	−0.0936701	−0.0468351	+	0.998903i	$0.514914\pi$
$864$	0	0
$865$	−7.75679	−0.263739
$866$	0	0
$867$	0	0
$868$	0	0
$869$	−57.7465	−1.95892
$870$	0	0
$871$	−54.0886	−1.83272
$872$	0	0
$873$	0	0
$874$	0	0
$875$	0.894506	0.0302398
$876$	0	0
$877$	32.9340	1.11210	0.556052	−	0.831148i	$-0.312316\pi$
$877$	32.9340	1.11210	0.556052	+	0.831148i	$0.312316\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−40.6201	−1.36853	−0.684264	−	0.729235i	$-0.739876\pi$
$881$	−40.6201	−1.36853	−0.684264	+	0.729235i	$0.739876\pi$
$882$	0	0
$883$	0.817246	0.0275025	0.0137513	−	0.999905i	$-0.495623\pi$
$883$	0.817246	0.0275025	0.0137513	+	0.999905i	$0.495623\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−4.29164	−0.144099	−0.0720496	−	0.997401i	$-0.522954\pi$
$887$	−4.29164	−0.144099	−0.0720496	+	0.997401i	$0.522954\pi$
$888$	0	0
$889$	−4.83720	−0.162235
$890$	0	0
$891$	0	0
$892$	0	0
$893$	21.6503	0.724500
$894$	0	0
$895$	8.23399	0.275232
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−9.54909	−0.318480
$900$	0	0
$901$	−4.83944	−0.161225
$902$	0	0
$903$	0	0
$904$	0	0
$905$	4.33048	0.143950
$906$	0	0
$907$	−43.7845	−1.45384	−0.726920	−	0.686723i	$-0.759049\pi$
$907$	−43.7845	−1.45384	−0.726920	+	0.686723i	$0.759049\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	48.8009	1.61684	0.808422	−	0.588603i	$-0.200322\pi$
$911$	48.8009	1.61684	0.808422	+	0.588603i	$0.200322\pi$
$912$	0	0
$913$	56.2955	1.86311
$914$	0	0
$915$	0	0
$916$	0	0
$917$	13.9917	0.462047
$918$	0	0
$919$	10.5677	0.348596	0.174298	−	0.984693i	$-0.444234\pi$
$919$	10.5677	0.348596	0.174298	+	0.984693i	$0.444234\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	−53.2386	−1.75237
$924$	0	0
$925$	47.2020	1.55199
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−5.51933	−0.181083	−0.0905417	−	0.995893i	$-0.528860\pi$
$929$	−5.51933	−0.181083	−0.0905417	+	0.995893i	$0.528860\pi$
$930$	0	0
$931$	8.48889	0.278212
$932$	0	0
$933$	0	0
$934$	0	0
$935$	9.55415	0.312454
$936$	0	0
$937$	−51.4761	−1.68165	−0.840826	−	0.541305i	$-0.817930\pi$
$937$	−51.4761	−1.68165	−0.840826	+	0.541305i	$0.817930\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	−23.0595	−0.751718	−0.375859	−	0.926677i	$-0.622652\pi$
$941$	−23.0595	−0.751718	−0.375859	+	0.926677i	$0.622652\pi$
$942$	0	0
$943$	−1.17811	−0.0383644
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−27.0207	−0.878054	−0.439027	−	0.898474i	$-0.644677\pi$
$947$	−27.0207	−0.878054	−0.439027	+	0.898474i	$0.644677\pi$
$948$	0	0
$949$	−2.27521	−0.0738564
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−29.6466	−0.960348	−0.480174	−	0.877173i	$-0.659426\pi$
$953$	−29.6466	−0.960348	−0.480174	+	0.877173i	$0.659426\pi$
$954$	0	0
$955$	−40.7278	−1.31792
$956$	0	0
$957$	0	0
$958$	0	0
$959$	3.65910	0.118158
$960$	0	0
$961$	4.71731	0.152171
$962$	0	0
$963$	0	0
$964$	0	0
$965$	67.3065	2.16667
$966$	0	0
$967$	−41.6275	−1.33865	−0.669324	−	0.742970i	$-0.733416\pi$
$967$	−41.6275	−1.33865	−0.669324	+	0.742970i	$0.733416\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−37.4436	−1.20162	−0.600811	−	0.799391i	$-0.705155\pi$
$971$	−37.4436	−1.20162	−0.600811	+	0.799391i	$0.705155\pi$
$972$	0	0
$973$	−16.4852	−0.528492
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−25.8568	−0.827231	−0.413616	−	0.910452i	$-0.635734\pi$
$977$	−25.8568	−0.827231	−0.413616	+	0.910452i	$0.635734\pi$
$978$	0	0
$979$	−95.0266	−3.03706
$980$	0	0
$981$	0	0
$982$	0	0
$983$	−33.8201	−1.07869	−0.539347	−	0.842084i	$-0.681329\pi$
$983$	−33.8201	−1.07869	−0.539347	+	0.842084i	$0.681329\pi$
$984$	0	0
$985$	−31.9168	−1.01696
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−2.96247	−0.0942010
$990$	0	0
$991$	−26.9278	−0.855390	−0.427695	−	0.903923i	$-0.640674\pi$
$991$	−26.9278	−0.855390	−0.427695	+	0.903923i	$0.640674\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−67.5497	−2.14147
$996$	0	0
$997$	4.87456	0.154379	0.0771894	−	0.997016i	$-0.475405\pi$
$997$	4.87456	0.154379	0.0771894	+	0.997016i	$0.475405\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5796.2.a.t.1.5		5
3.2	odd	2		644.2.a.d.1.2	✓	5
12.11	even	2		2576.2.a.bb.1.4		5
21.20	even	2		4508.2.a.f.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.a.d.1.2	✓	5	3.2	odd	2
2576.2.a.bb.1.4		5	12.11	even	2
4508.2.a.f.1.4		5	21.20	even	2
5796.2.a.t.1.5		5	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5796 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5796.a (trivial)

\(f(q)\)	\(=\)	\(q+3.11657 q^{5} -1.00000 q^{7} +O(q^{10})\)	\(q+3.11657 q^{5} -1.00000 q^{7} +5.23940 q^{11} +6.34832 q^{13} +0.585105 q^{17} +8.48889 q^{19} +1.00000 q^{23} +4.71298 q^{25} +1.59780 q^{29} -5.97640 q^{31} -3.11657 q^{35} +10.0153 q^{37} -1.17811 q^{41} -2.96247 q^{43} +2.55043 q^{47} +1.00000 q^{49} -8.27107 q^{53} +16.3289 q^{55} -14.6004 q^{59} +6.15410 q^{61} +19.7849 q^{65} -8.52015 q^{67} -8.38625 q^{71} -0.358396 q^{73} -5.23940 q^{77} -11.0216 q^{79} +10.7446 q^{83} +1.82352 q^{85} -18.1369 q^{89} -6.34832 q^{91} +26.4562 q^{95} -8.38723 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{5} - 5 q^{7}+O(q^{10}) \) 5 * q - 2 * q^5 - 5 * q^7	\( 5 q - 2 q^{5} - 5 q^{7} - 2 q^{11} + 13 q^{13} - 4 q^{17} + 12 q^{19} + 5 q^{23} + 19 q^{25} - 13 q^{29} - 3 q^{31} + 2 q^{35} - 4 q^{37} - q^{41} - 8 q^{43} - 5 q^{47} + 5 q^{49} + 8 q^{53} - 2 q^{55} - 12 q^{59} + 20 q^{61} + 12 q^{65} - 12 q^{67} - 9 q^{71} - 9 q^{73} + 2 q^{77} - 8 q^{79} + 28 q^{83} + 16 q^{85} - 32 q^{89} - 13 q^{91} + 36 q^{95} + 4 q^{97}+O(q^{100}) \) 5 * q - 2 * q^5 - 5 * q^7 - 2 * q^11 + 13 * q^13 - 4 * q^17 + 12 * q^19 + 5 * q^23 + 19 * q^25 - 13 * q^29 - 3 * q^31 + 2 * q^35 - 4 * q^37 - q^41 - 8 * q^43 - 5 * q^47 + 5 * q^49 + 8 * q^53 - 2 * q^55 - 12 * q^59 + 20 * q^61 + 12 * q^65 - 12 * q^67 - 9 * q^71 - 9 * q^73 + 2 * q^77 - 8 * q^79 + 28 * q^83 + 16 * q^85 - 32 * q^89 - 13 * q^91 + 36 * q^95 + 4 * q^97

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