LMFDB - Embedded newform 5796.2.a.l.1.1

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1932)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.618034 q^{5} -1.00000 q^{7} +O(q^{10})$	$q-0.618034 q^{5} -1.00000 q^{7} +3.00000 q^{11} -1.61803 q^{13} +6.70820 q^{17} +0.236068 q^{19} +1.00000 q^{23} -4.61803 q^{25} +6.23607 q^{29} -3.00000 q^{31} +0.618034 q^{35} +0.527864 q^{37} -5.94427 q^{41} +2.09017 q^{43} +4.76393 q^{47} +1.00000 q^{49} -6.32624 q^{53} -1.85410 q^{55} +7.38197 q^{59} -0.854102 q^{61} +1.00000 q^{65} -13.5623 q^{67} +2.38197 q^{71} +6.23607 q^{73} -3.00000 q^{77} +6.70820 q^{79} -1.47214 q^{83} -4.14590 q^{85} -7.79837 q^{89} +1.61803 q^{91} -0.145898 q^{95} +14.4164 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{5} - 2 q^{7}+O(q^{10}) $ 2 * q + q^5 - 2 * q^7	$ 2 q + q^{5} - 2 q^{7} + 6 q^{11} - q^{13} - 4 q^{19} + 2 q^{23} - 7 q^{25} + 8 q^{29} - 6 q^{31} - q^{35} + 10 q^{37} + 6 q^{41} - 7 q^{43} + 14 q^{47} + 2 q^{49} + 3 q^{53} + 3 q^{55} + 17 q^{59} + 5 q^{61} + 2 q^{65} - 7 q^{67} + 7 q^{71} + 8 q^{73} - 6 q^{77} + 6 q^{83} - 15 q^{85} + 9 q^{89} + q^{91} - 7 q^{95} + 2 q^{97}+O(q^{100}) $ 2 * q + q^5 - 2 * q^7 + 6 * q^11 - q^13 - 4 * q^19 + 2 * q^23 - 7 * q^25 + 8 * q^29 - 6 * q^31 - q^35 + 10 * q^37 + 6 * q^41 - 7 * q^43 + 14 * q^47 + 2 * q^49 + 3 * q^53 + 3 * q^55 + 17 * q^59 + 5 * q^61 + 2 * q^65 - 7 * q^67 + 7 * q^71 + 8 * q^73 - 6 * q^77 + 6 * q^83 - 15 * q^85 + 9 * q^89 + q^91 - 7 * q^95 + 2 * 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
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0	0
$9$	0	0
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	−1.61803	−0.448762	−0.224381	−	0.974502i	$-0.572036\pi$
$13$	−1.61803	−0.448762	−0.224381	+	0.974502i	$0.572036\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	6.70820	1.62698	0.813489	−	0.581580i	$-0.197565\pi$
$17$	6.70820	1.62698	0.813489	+	0.581580i	$0.197565\pi$
$18$	0	0
$19$	0.236068	0.0541577	0.0270789	−	0.999633i	$-0.491379\pi$
$19$	0.236068	0.0541577	0.0270789	+	0.999633i	$0.491379\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	−4.61803	−0.923607
$26$	0	0
$27$	0	0
$28$	0	0
$29$	6.23607	1.15801	0.579004	−	0.815324i	$-0.303441\pi$
$29$	6.23607	1.15801	0.579004	+	0.815324i	$0.303441\pi$
$30$	0	0
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	0.618034	0.104467
$36$	0	0
$37$	0.527864	0.0867803	0.0433902	−	0.999058i	$-0.486184\pi$
$37$	0.527864	0.0867803	0.0433902	+	0.999058i	$0.486184\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−5.94427	−0.928339	−0.464170	−	0.885746i	$-0.653647\pi$
$41$	−5.94427	−0.928339	−0.464170	+	0.885746i	$0.653647\pi$
$42$	0	0
$43$	2.09017	0.318748	0.159374	−	0.987218i	$-0.449052\pi$
$43$	2.09017	0.318748	0.159374	+	0.987218i	$0.449052\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	4.76393	0.694891	0.347445	−	0.937700i	$-0.387049\pi$
$47$	4.76393	0.694891	0.347445	+	0.937700i	$0.387049\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−6.32624	−0.868976	−0.434488	−	0.900678i	$-0.643071\pi$
$53$	−6.32624	−0.868976	−0.434488	+	0.900678i	$0.643071\pi$
$54$	0	0
$55$	−1.85410	−0.250007
$56$	0	0
$57$	0	0
$58$	0	0
$59$	7.38197	0.961050	0.480525	−	0.876981i	$-0.340446\pi$
$59$	7.38197	0.961050	0.480525	+	0.876981i	$0.340446\pi$
$60$	0	0
$61$	−0.854102	−0.109357	−0.0546783	−	0.998504i	$-0.517413\pi$
$61$	−0.854102	−0.109357	−0.0546783	+	0.998504i	$0.517413\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	1.00000	0.124035
$66$	0	0
$67$	−13.5623	−1.65690	−0.828450	−	0.560063i	$-0.810777\pi$
$67$	−13.5623	−1.65690	−0.828450	+	0.560063i	$0.810777\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	2.38197	0.282687	0.141344	−	0.989961i	$-0.454858\pi$
$71$	2.38197	0.282687	0.141344	+	0.989961i	$0.454858\pi$
$72$	0	0
$73$	6.23607	0.729877	0.364938	−	0.931032i	$-0.381090\pi$
$73$	6.23607	0.729877	0.364938	+	0.931032i	$0.381090\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−3.00000	−0.341882
$78$	0	0
$79$	6.70820	0.754732	0.377366	−	0.926064i	$-0.376830\pi$
$79$	6.70820	0.754732	0.377366	+	0.926064i	$0.376830\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	−1.47214	−0.161588	−0.0807940	−	0.996731i	$-0.525746\pi$
$83$	−1.47214	−0.161588	−0.0807940	+	0.996731i	$0.525746\pi$
$84$	0	0
$85$	−4.14590	−0.449686
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−7.79837	−0.826626	−0.413313	−	0.910589i	$-0.635628\pi$
$89$	−7.79837	−0.826626	−0.413313	+	0.910589i	$0.635628\pi$
$90$	0	0
$91$	1.61803	0.169616
$92$	0	0
$93$	0	0
$94$	0	0
$95$	−0.145898	−0.0149688
$96$	0	0
$97$	14.4164	1.46376	0.731882	−	0.681431i	$-0.238642\pi$
$97$	14.4164	1.46376	0.731882	+	0.681431i	$0.238642\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	10.3262	1.02750	0.513750	−	0.857940i	$-0.328256\pi$
$101$	10.3262	1.02750	0.513750	+	0.857940i	$0.328256\pi$
$102$	0	0
$103$	−7.41641	−0.730760	−0.365380	−	0.930858i	$-0.619061\pi$
$103$	−7.41641	−0.730760	−0.365380	+	0.930858i	$0.619061\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−8.38197	−0.810315	−0.405158	−	0.914247i	$-0.632783\pi$
$107$	−8.38197	−0.810315	−0.405158	+	0.914247i	$0.632783\pi$
$108$	0	0
$109$	9.09017	0.870680	0.435340	−	0.900266i	$-0.356628\pi$
$109$	9.09017	0.870680	0.435340	+	0.900266i	$0.356628\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	12.3262	1.15955	0.579777	−	0.814775i	$-0.303139\pi$
$113$	12.3262	1.15955	0.579777	+	0.814775i	$0.303139\pi$
$114$	0	0
$115$	−0.618034	−0.0576320
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−6.70820	−0.614940
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	0	0
$124$	0	0
$125$	5.94427	0.531672
$126$	0	0
$127$	−14.5623	−1.29220	−0.646098	−	0.763255i	$-0.723600\pi$
$127$	−14.5623	−1.29220	−0.646098	+	0.763255i	$0.723600\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	11.9443	1.04358	0.521788	−	0.853075i	$-0.325265\pi$
$131$	11.9443	1.04358	0.521788	+	0.853075i	$0.325265\pi$
$132$	0	0
$133$	−0.236068	−0.0204697
$134$	0	0
$135$	0	0
$136$	0	0
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	0	0
$139$	0.145898	0.0123749	0.00618745	−	0.999981i	$-0.498030\pi$
$139$	0.145898	0.0123749	0.00618745	+	0.999981i	$0.498030\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	−4.85410	−0.405920
$144$	0	0
$145$	−3.85410	−0.320066
$146$	0	0
$147$	0	0
$148$	0	0
$149$	−3.23607	−0.265109	−0.132555	−	0.991176i	$-0.542318\pi$
$149$	−3.23607	−0.265109	−0.132555	+	0.991176i	$0.542318\pi$
$150$	0	0
$151$	21.1246	1.71910	0.859548	−	0.511055i	$-0.170745\pi$
$151$	21.1246	1.71910	0.859548	+	0.511055i	$0.170745\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	1.85410	0.148925
$156$	0	0
$157$	13.2361	1.05635	0.528177	−	0.849135i	$-0.322876\pi$
$157$	13.2361	1.05635	0.528177	+	0.849135i	$0.322876\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	4.14590	0.324732	0.162366	−	0.986731i	$-0.448088\pi$
$163$	4.14590	0.324732	0.162366	+	0.986731i	$0.448088\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	19.4721	1.50680	0.753400	−	0.657563i	$-0.228413\pi$
$167$	19.4721	1.50680	0.753400	+	0.657563i	$0.228413\pi$
$168$	0	0
$169$	−10.3820	−0.798613
$170$	0	0
$171$	0	0
$172$	0	0
$173$	−4.52786	−0.344247	−0.172124	−	0.985075i	$-0.555063\pi$
$173$	−4.52786	−0.344247	−0.172124	+	0.985075i	$0.555063\pi$
$174$	0	0
$175$	4.61803	0.349091
$176$	0	0
$177$	0	0
$178$	0	0
$179$	18.0344	1.34796	0.673979	−	0.738751i	$-0.264584\pi$
$179$	18.0344	1.34796	0.673979	+	0.738751i	$0.264584\pi$
$180$	0	0
$181$	8.52786	0.633871	0.316936	−	0.948447i	$-0.397346\pi$
$181$	8.52786	0.633871	0.316936	+	0.948447i	$0.397346\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	−0.326238	−0.0239855
$186$	0	0
$187$	20.1246	1.47166
$188$	0	0
$189$	0	0
$190$	0	0
$191$	−10.6525	−0.770786	−0.385393	−	0.922753i	$-0.625934\pi$
$191$	−10.6525	−0.770786	−0.385393	+	0.922753i	$0.625934\pi$
$192$	0	0
$193$	7.70820	0.554849	0.277424	−	0.960747i	$-0.410519\pi$
$193$	7.70820	0.554849	0.277424	+	0.960747i	$0.410519\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−3.61803	−0.257774	−0.128887	−	0.991659i	$-0.541140\pi$
$197$	−3.61803	−0.257774	−0.128887	+	0.991659i	$0.541140\pi$
$198$	0	0
$199$	2.43769	0.172804	0.0864018	−	0.996260i	$-0.472463\pi$
$199$	2.43769	0.172804	0.0864018	+	0.996260i	$0.472463\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	−6.23607	−0.437686
$204$	0	0
$205$	3.67376	0.256587
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0.708204	0.0489875
$210$	0	0
$211$	14.1246	0.972378	0.486189	−	0.873854i	$-0.338387\pi$
$211$	14.1246	0.972378	0.486189	+	0.873854i	$0.338387\pi$
$212$	0	0
$213$	0	0
$214$	0	0
$215$	−1.29180	−0.0880998
$216$	0	0
$217$	3.00000	0.203653
$218$	0	0
$219$	0	0
$220$	0	0
$221$	−10.8541	−0.730126
$222$	0	0
$223$	−12.7984	−0.857043	−0.428521	−	0.903532i	$-0.640965\pi$
$223$	−12.7984	−0.857043	−0.428521	+	0.903532i	$0.640965\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	29.4508	1.95472	0.977361	−	0.211580i	$-0.0678608\pi$
$227$	29.4508	1.95472	0.977361	+	0.211580i	$0.0678608\pi$
$228$	0	0
$229$	−9.27051	−0.612613	−0.306306	−	0.951933i	$-0.599093\pi$
$229$	−9.27051	−0.612613	−0.306306	+	0.951933i	$0.599093\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0.909830	0.0596049	0.0298025	−	0.999556i	$-0.490512\pi$
$233$	0.909830	0.0596049	0.0298025	+	0.999556i	$0.490512\pi$
$234$	0	0
$235$	−2.94427	−0.192063
$236$	0	0
$237$	0	0
$238$	0	0
$239$	15.3820	0.994977	0.497488	−	0.867471i	$-0.334256\pi$
$239$	15.3820	0.994977	0.497488	+	0.867471i	$0.334256\pi$
$240$	0	0
$241$	21.0000	1.35273	0.676364	−	0.736567i	$-0.263554\pi$
$241$	21.0000	1.35273	0.676364	+	0.736567i	$0.263554\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	−0.618034	−0.0394847
$246$	0	0
$247$	−0.381966	−0.0243039
$248$	0	0
$249$	0	0
$250$	0	0
$251$	−8.65248	−0.546139	−0.273070	−	0.961994i	$-0.588039\pi$
$251$	−8.65248	−0.546139	−0.273070	+	0.961994i	$0.588039\pi$
$252$	0	0
$253$	3.00000	0.188608
$254$	0	0
$255$	0	0
$256$	0	0
$257$	14.6525	0.913996	0.456998	−	0.889468i	$-0.348925\pi$
$257$	14.6525	0.913996	0.456998	+	0.889468i	$0.348925\pi$
$258$	0	0
$259$	−0.527864	−0.0327999
$260$	0	0
$261$	0	0
$262$	0	0
$263$	7.18034	0.442759	0.221379	−	0.975188i	$-0.428944\pi$
$263$	7.18034	0.442759	0.221379	+	0.975188i	$0.428944\pi$
$264$	0	0
$265$	3.90983	0.240179
$266$	0	0
$267$	0	0
$268$	0	0
$269$	−1.79837	−0.109649	−0.0548244	−	0.998496i	$-0.517460\pi$
$269$	−1.79837	−0.109649	−0.0548244	+	0.998496i	$0.517460\pi$
$270$	0	0
$271$	1.18034	0.0717005	0.0358503	−	0.999357i	$-0.488586\pi$
$271$	1.18034	0.0717005	0.0358503	+	0.999357i	$0.488586\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	−13.8541	−0.835434
$276$	0	0
$277$	−5.03444	−0.302490	−0.151245	−	0.988496i	$-0.548328\pi$
$277$	−5.03444	−0.302490	−0.151245	+	0.988496i	$0.548328\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	17.2361	1.02822	0.514109	−	0.857725i	$-0.328123\pi$
$281$	17.2361	1.02822	0.514109	+	0.857725i	$0.328123\pi$
$282$	0	0
$283$	−8.14590	−0.484223	−0.242112	−	0.970248i	$-0.577840\pi$
$283$	−8.14590	−0.484223	−0.242112	+	0.970248i	$0.577840\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	5.94427	0.350879
$288$	0	0
$289$	28.0000	1.64706
$290$	0	0
$291$	0	0
$292$	0	0
$293$	−16.9443	−0.989895	−0.494947	−	0.868923i	$-0.664813\pi$
$293$	−16.9443	−0.989895	−0.494947	+	0.868923i	$0.664813\pi$
$294$	0	0
$295$	−4.56231	−0.265628
$296$	0	0
$297$	0	0
$298$	0	0
$299$	−1.61803	−0.0935733
$300$	0	0
$301$	−2.09017	−0.120475
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0.527864	0.0302254
$306$	0	0
$307$	−1.58359	−0.0903804	−0.0451902	−	0.998978i	$-0.514389\pi$
$307$	−1.58359	−0.0903804	−0.0451902	+	0.998978i	$0.514389\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−18.2705	−1.03603	−0.518013	−	0.855373i	$-0.673328\pi$
$311$	−18.2705	−1.03603	−0.518013	+	0.855373i	$0.673328\pi$
$312$	0	0
$313$	26.4721	1.49629	0.748147	−	0.663533i	$-0.230944\pi$
$313$	26.4721	1.49629	0.748147	+	0.663533i	$0.230944\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−3.38197	−0.189950	−0.0949751	−	0.995480i	$-0.530277\pi$
$317$	−3.38197	−0.189950	−0.0949751	+	0.995480i	$0.530277\pi$
$318$	0	0
$319$	18.7082	1.04746
$320$	0	0
$321$	0	0
$322$	0	0
$323$	1.58359	0.0881134
$324$	0	0
$325$	7.47214	0.414480
$326$	0	0
$327$	0	0
$328$	0	0
$329$	−4.76393	−0.262644
$330$	0	0
$331$	−27.8885	−1.53289	−0.766447	−	0.642308i	$-0.777977\pi$
$331$	−27.8885	−1.53289	−0.766447	+	0.642308i	$0.777977\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	8.38197	0.457956
$336$	0	0
$337$	−10.3820	−0.565542	−0.282771	−	0.959187i	$-0.591254\pi$
$337$	−10.3820	−0.565542	−0.282771	+	0.959187i	$0.591254\pi$
$338$	0	0
$339$	0	0
$340$	0	0
$341$	−9.00000	−0.487377
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	0	0
$345$	0	0
$346$	0	0
$347$	4.52786	0.243068	0.121534	−	0.992587i	$-0.461219\pi$
$347$	4.52786	0.243068	0.121534	+	0.992587i	$0.461219\pi$
$348$	0	0
$349$	19.8541	1.06277	0.531383	−	0.847132i	$-0.321673\pi$
$349$	19.8541	1.06277	0.531383	+	0.847132i	$0.321673\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	15.0000	0.798369	0.399185	−	0.916871i	$-0.369293\pi$
$353$	15.0000	0.798369	0.399185	+	0.916871i	$0.369293\pi$
$354$	0	0
$355$	−1.47214	−0.0781329
$356$	0	0
$357$	0	0
$358$	0	0
$359$	2.03444	0.107374	0.0536869	−	0.998558i	$-0.482903\pi$
$359$	2.03444	0.107374	0.0536869	+	0.998558i	$0.482903\pi$
$360$	0	0
$361$	−18.9443	−0.997067
$362$	0	0
$363$	0	0
$364$	0	0
$365$	−3.85410	−0.201733
$366$	0	0
$367$	−6.20163	−0.323722	−0.161861	−	0.986814i	$-0.551750\pi$
$367$	−6.20163	−0.323722	−0.161861	+	0.986814i	$0.551750\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	6.32624	0.328442
$372$	0	0
$373$	28.8885	1.49579	0.747896	−	0.663816i	$-0.231064\pi$
$373$	28.8885	1.49579	0.747896	+	0.663816i	$0.231064\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−10.0902	−0.519670
$378$	0	0
$379$	−5.52786	−0.283947	−0.141974	−	0.989870i	$-0.545345\pi$
$379$	−5.52786	−0.283947	−0.141974	+	0.989870i	$0.545345\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	−29.9443	−1.53008	−0.765040	−	0.643982i	$-0.777281\pi$
$383$	−29.9443	−1.53008	−0.765040	+	0.643982i	$0.777281\pi$
$384$	0	0
$385$	1.85410	0.0944938
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−9.65248	−0.489400	−0.244700	−	0.969599i	$-0.578689\pi$
$389$	−9.65248	−0.489400	−0.244700	+	0.969599i	$0.578689\pi$
$390$	0	0
$391$	6.70820	0.339248
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−4.14590	−0.208603
$396$	0	0
$397$	25.1246	1.26097	0.630484	−	0.776202i	$-0.282856\pi$
$397$	25.1246	1.26097	0.630484	+	0.776202i	$0.282856\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	11.7639	0.587463	0.293731	−	0.955888i	$-0.405103\pi$
$401$	11.7639	0.587463	0.293731	+	0.955888i	$0.405103\pi$
$402$	0	0
$403$	4.85410	0.241800
$404$	0	0
$405$	0	0
$406$	0	0
$407$	1.58359	0.0784957
$408$	0	0
$409$	9.58359	0.473878	0.236939	−	0.971525i	$-0.423856\pi$
$409$	9.58359	0.473878	0.236939	+	0.971525i	$0.423856\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	−7.38197	−0.363243
$414$	0	0
$415$	0.909830	0.0446618
$416$	0	0
$417$	0	0
$418$	0	0
$419$	24.2148	1.18297	0.591485	−	0.806316i	$-0.298542\pi$
$419$	24.2148	1.18297	0.591485	+	0.806316i	$0.298542\pi$
$420$	0	0
$421$	−15.6180	−0.761176	−0.380588	−	0.924745i	$-0.624278\pi$
$421$	−15.6180	−0.761176	−0.380588	+	0.924745i	$0.624278\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−30.9787	−1.50269
$426$	0	0
$427$	0.854102	0.0413329
$428$	0	0
$429$	0	0
$430$	0	0
$431$	−25.1459	−1.21124	−0.605618	−	0.795756i	$-0.707074\pi$
$431$	−25.1459	−1.21124	−0.605618	+	0.795756i	$0.707074\pi$
$432$	0	0
$433$	27.7082	1.33157	0.665786	−	0.746143i	$-0.268097\pi$
$433$	27.7082	1.33157	0.665786	+	0.746143i	$0.268097\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	0.236068	0.0112927
$438$	0	0
$439$	30.8885	1.47423	0.737115	−	0.675767i	$-0.236188\pi$
$439$	30.8885	1.47423	0.737115	+	0.675767i	$0.236188\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	19.4164	0.922501	0.461251	−	0.887270i	$-0.347401\pi$
$443$	19.4164	0.922501	0.461251	+	0.887270i	$0.347401\pi$
$444$	0	0
$445$	4.81966	0.228474
$446$	0	0
$447$	0	0
$448$	0	0
$449$	−0.909830	−0.0429375	−0.0214688	−	0.999770i	$-0.506834\pi$
$449$	−0.909830	−0.0429375	−0.0214688	+	0.999770i	$0.506834\pi$
$450$	0	0
$451$	−17.8328	−0.839714
$452$	0	0
$453$	0	0
$454$	0	0
$455$	−1.00000	−0.0468807
$456$	0	0
$457$	−6.97871	−0.326450	−0.163225	−	0.986589i	$-0.552190\pi$
$457$	−6.97871	−0.326450	−0.163225	+	0.986589i	$0.552190\pi$
$458$	0	0
$459$	0	0
$460$	0	0
$461$	−7.20163	−0.335413	−0.167707	−	0.985837i	$-0.553636\pi$
$461$	−7.20163	−0.335413	−0.167707	+	0.985837i	$0.553636\pi$
$462$	0	0
$463$	−37.8328	−1.75824	−0.879120	−	0.476600i	$-0.841869\pi$
$463$	−37.8328	−1.75824	−0.879120	+	0.476600i	$0.841869\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	24.8885	1.15170	0.575852	−	0.817554i	$-0.304670\pi$
$467$	24.8885	1.15170	0.575852	+	0.817554i	$0.304670\pi$
$468$	0	0
$469$	13.5623	0.626249
$470$	0	0
$471$	0	0
$472$	0	0
$473$	6.27051	0.288318
$474$	0	0
$475$	−1.09017	−0.0500204
$476$	0	0
$477$	0	0
$478$	0	0
$479$	−13.7639	−0.628890	−0.314445	−	0.949276i	$-0.601818\pi$
$479$	−13.7639	−0.628890	−0.314445	+	0.949276i	$0.601818\pi$
$480$	0	0
$481$	−0.854102	−0.0389437
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−8.90983	−0.404575
$486$	0	0
$487$	−29.0000	−1.31412	−0.657058	−	0.753840i	$-0.728199\pi$
$487$	−29.0000	−1.31412	−0.657058	+	0.753840i	$0.728199\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	−6.09017	−0.274846	−0.137423	−	0.990512i	$-0.543882\pi$
$491$	−6.09017	−0.274846	−0.137423	+	0.990512i	$0.543882\pi$
$492$	0	0
$493$	41.8328	1.88406
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−2.38197	−0.106846
$498$	0	0
$499$	34.5066	1.54473	0.772363	−	0.635181i	$-0.219075\pi$
$499$	34.5066	1.54473	0.772363	+	0.635181i	$0.219075\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	−40.2148	−1.79309	−0.896544	−	0.442954i	$-0.853930\pi$
$503$	−40.2148	−1.79309	−0.896544	+	0.442954i	$0.853930\pi$
$504$	0	0
$505$	−6.38197	−0.283994
$506$	0	0
$507$	0	0
$508$	0	0
$509$	−16.7639	−0.743048	−0.371524	−	0.928423i	$-0.621165\pi$
$509$	−16.7639	−0.743048	−0.371524	+	0.928423i	$0.621165\pi$
$510$	0	0
$511$	−6.23607	−0.275867
$512$	0	0
$513$	0	0
$514$	0	0
$515$	4.58359	0.201977
$516$	0	0
$517$	14.2918	0.628552
$518$	0	0
$519$	0	0
$520$	0	0
$521$	22.3607	0.979639	0.489820	−	0.871824i	$-0.337063\pi$
$521$	22.3607	0.979639	0.489820	+	0.871824i	$0.337063\pi$
$522$	0	0
$523$	18.0000	0.787085	0.393543	−	0.919306i	$-0.371249\pi$
$523$	18.0000	0.787085	0.393543	+	0.919306i	$0.371249\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−20.1246	−0.876642
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	0	0
$533$	9.61803	0.416603
$534$	0	0
$535$	5.18034	0.223966
$536$	0	0
$537$	0	0
$538$	0	0
$539$	3.00000	0.129219
$540$	0	0
$541$	37.1246	1.59611	0.798056	−	0.602583i	$-0.205862\pi$
$541$	37.1246	1.59611	0.798056	+	0.602583i	$0.205862\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−5.61803	−0.240650
$546$	0	0
$547$	−17.8541	−0.763386	−0.381693	−	0.924289i	$-0.624659\pi$
$547$	−17.8541	−0.763386	−0.381693	+	0.924289i	$0.624659\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	1.47214	0.0627151
$552$	0	0
$553$	−6.70820	−0.285262
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−18.7639	−0.795053	−0.397527	−	0.917591i	$-0.630131\pi$
$557$	−18.7639	−0.795053	−0.397527	+	0.917591i	$0.630131\pi$
$558$	0	0
$559$	−3.38197	−0.143042
$560$	0	0
$561$	0	0
$562$	0	0
$563$	28.3820	1.19616	0.598079	−	0.801437i	$-0.295931\pi$
$563$	28.3820	1.19616	0.598079	+	0.801437i	$0.295931\pi$
$564$	0	0
$565$	−7.61803	−0.320493
$566$	0	0
$567$	0	0
$568$	0	0
$569$	4.58359	0.192154	0.0960771	−	0.995374i	$-0.469370\pi$
$569$	4.58359	0.192154	0.0960771	+	0.995374i	$0.469370\pi$
$570$	0	0
$571$	0.708204	0.0296374	0.0148187	−	0.999890i	$-0.495283\pi$
$571$	0.708204	0.0296374	0.0148187	+	0.999890i	$0.495283\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−4.61803	−0.192585
$576$	0	0
$577$	37.7771	1.57268	0.786340	−	0.617794i	$-0.211973\pi$
$577$	37.7771	1.57268	0.786340	+	0.617794i	$0.211973\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	1.47214	0.0610745
$582$	0	0
$583$	−18.9787	−0.786018
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−22.3820	−0.923803	−0.461901	−	0.886931i	$-0.652833\pi$
$587$	−22.3820	−0.923803	−0.461901	+	0.886931i	$0.652833\pi$
$588$	0	0
$589$	−0.708204	−0.0291810
$590$	0	0
$591$	0	0
$592$	0	0
$593$	24.6525	1.01236	0.506178	−	0.862429i	$-0.331058\pi$
$593$	24.6525	1.01236	0.506178	+	0.862429i	$0.331058\pi$
$594$	0	0
$595$	4.14590	0.169965
$596$	0	0
$597$	0	0
$598$	0	0
$599$	8.74265	0.357215	0.178607	−	0.983920i	$-0.442841\pi$
$599$	8.74265	0.357215	0.178607	+	0.983920i	$0.442841\pi$
$600$	0	0
$601$	5.20163	0.212179	0.106089	−	0.994357i	$-0.466167\pi$
$601$	5.20163	0.212179	0.106089	+	0.994357i	$0.466167\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	1.23607	0.0502533
$606$	0	0
$607$	−4.56231	−0.185178	−0.0925891	−	0.995704i	$-0.529514\pi$
$607$	−4.56231	−0.185178	−0.0925891	+	0.995704i	$0.529514\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−7.70820	−0.311841
$612$	0	0
$613$	−9.29180	−0.375292	−0.187646	−	0.982237i	$-0.560086\pi$
$613$	−9.29180	−0.375292	−0.187646	+	0.982237i	$0.560086\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−22.8541	−0.920072	−0.460036	−	0.887900i	$-0.652163\pi$
$617$	−22.8541	−0.920072	−0.460036	+	0.887900i	$0.652163\pi$
$618$	0	0
$619$	−31.1459	−1.25186	−0.625930	−	0.779880i	$-0.715280\pi$
$619$	−31.1459	−1.25186	−0.625930	+	0.779880i	$0.715280\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	7.79837	0.312435
$624$	0	0
$625$	19.4164	0.776656
$626$	0	0
$627$	0	0
$628$	0	0
$629$	3.54102	0.141190
$630$	0	0
$631$	−40.7771	−1.62331	−0.811655	−	0.584137i	$-0.801433\pi$
$631$	−40.7771	−1.62331	−0.811655	+	0.584137i	$0.801433\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	9.00000	0.357154
$636$	0	0
$637$	−1.61803	−0.0641088
$638$	0	0
$639$	0	0
$640$	0	0
$641$	24.6738	0.974555	0.487278	−	0.873247i	$-0.337990\pi$
$641$	24.6738	0.974555	0.487278	+	0.873247i	$0.337990\pi$
$642$	0	0
$643$	7.32624	0.288919	0.144459	−	0.989511i	$-0.453856\pi$
$643$	7.32624	0.288919	0.144459	+	0.989511i	$0.453856\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−26.3951	−1.03770	−0.518850	−	0.854866i	$-0.673640\pi$
$647$	−26.3951	−1.03770	−0.518850	+	0.854866i	$0.673640\pi$
$648$	0	0
$649$	22.1459	0.869303
$650$	0	0
$651$	0	0
$652$	0	0
$653$	25.8541	1.01175	0.505875	−	0.862607i	$-0.331170\pi$
$653$	25.8541	1.01175	0.505875	+	0.862607i	$0.331170\pi$
$654$	0	0
$655$	−7.38197	−0.288437
$656$	0	0
$657$	0	0
$658$	0	0
$659$	−22.3050	−0.868878	−0.434439	−	0.900701i	$-0.643053\pi$
$659$	−22.3050	−0.868878	−0.434439	+	0.900701i	$0.643053\pi$
$660$	0	0
$661$	−28.7771	−1.11930	−0.559649	−	0.828729i	$-0.689064\pi$
$661$	−28.7771	−1.11930	−0.559649	+	0.828729i	$0.689064\pi$
$662$	0	0
$663$	0	0
$664$	0	0
$665$	0.145898	0.00565768
$666$	0	0
$667$	6.23607	0.241462
$668$	0	0
$669$	0	0
$670$	0	0
$671$	−2.56231	−0.0989167
$672$	0	0
$673$	−44.3050	−1.70783	−0.853915	−	0.520412i	$-0.825778\pi$
$673$	−44.3050	−1.70783	−0.853915	+	0.520412i	$0.825778\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−0.0901699	−0.00346551	−0.00173276	−	0.999998i	$-0.500552\pi$
$677$	−0.0901699	−0.00346551	−0.00173276	+	0.999998i	$0.500552\pi$
$678$	0	0
$679$	−14.4164	−0.553251
$680$	0	0
$681$	0	0
$682$	0	0
$683$	9.00000	0.344375	0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000	0.344375	0.172188	+	0.985064i	$0.444916\pi$
$684$	0	0
$685$	−5.56231	−0.212525
$686$	0	0
$687$	0	0
$688$	0	0
$689$	10.2361	0.389963
$690$	0	0
$691$	19.6180	0.746305	0.373153	−	0.927770i	$-0.378277\pi$
$691$	19.6180	0.746305	0.373153	+	0.927770i	$0.378277\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−0.0901699	−0.00342034
$696$	0	0
$697$	−39.8754	−1.51039
$698$	0	0
$699$	0	0
$700$	0	0
$701$	−13.0902	−0.494409	−0.247204	−	0.968963i	$-0.579512\pi$
$701$	−13.0902	−0.494409	−0.247204	+	0.968963i	$0.579512\pi$
$702$	0	0
$703$	0.124612	0.00469982
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−10.3262	−0.388358
$708$	0	0
$709$	0.0901699	0.00338640	0.00169320	−	0.999999i	$-0.499461\pi$
$709$	0.0901699	0.00338640	0.00169320	+	0.999999i	$0.499461\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−3.00000	−0.112351
$714$	0	0
$715$	3.00000	0.112194
$716$	0	0
$717$	0	0
$718$	0	0
$719$	3.65248	0.136214	0.0681072	−	0.997678i	$-0.478304\pi$
$719$	3.65248	0.136214	0.0681072	+	0.997678i	$0.478304\pi$
$720$	0	0
$721$	7.41641	0.276201
$722$	0	0
$723$	0	0
$724$	0	0
$725$	−28.7984	−1.06954
$726$	0	0
$727$	−19.2918	−0.715493	−0.357747	−	0.933819i	$-0.616455\pi$
$727$	−19.2918	−0.715493	−0.357747	+	0.933819i	$0.616455\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	14.0213	0.518596
$732$	0	0
$733$	−1.59675	−0.0589772	−0.0294886	−	0.999565i	$-0.509388\pi$
$733$	−1.59675	−0.0589772	−0.0294886	+	0.999565i	$0.509388\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−40.6869	−1.49872
$738$	0	0
$739$	15.2918	0.562518	0.281259	−	0.959632i	$-0.409248\pi$
$739$	15.2918	0.562518	0.281259	+	0.959632i	$0.409248\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	22.6180	0.829775	0.414888	−	0.909873i	$-0.363821\pi$
$743$	22.6180	0.829775	0.414888	+	0.909873i	$0.363821\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	0	0
$747$	0	0
$748$	0	0
$749$	8.38197	0.306270
$750$	0	0
$751$	4.72949	0.172582	0.0862908	−	0.996270i	$-0.472499\pi$
$751$	4.72949	0.172582	0.0862908	+	0.996270i	$0.472499\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−13.0557	−0.475147
$756$	0	0
$757$	−8.52786	−0.309950	−0.154975	−	0.987918i	$-0.549530\pi$
$757$	−8.52786	−0.309950	−0.154975	+	0.987918i	$0.549530\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	17.5279	0.635385	0.317692	−	0.948194i	$-0.397092\pi$
$761$	17.5279	0.635385	0.317692	+	0.948194i	$0.397092\pi$
$762$	0	0
$763$	−9.09017	−0.329086
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−11.9443	−0.431283
$768$	0	0
$769$	−35.1246	−1.26663	−0.633313	−	0.773896i	$-0.718305\pi$
$769$	−35.1246	−1.26663	−0.633313	+	0.773896i	$0.718305\pi$
$770$	0	0
$771$	0	0
$772$	0	0
$773$	33.9443	1.22089	0.610445	−	0.792058i	$-0.290991\pi$
$773$	33.9443	1.22089	0.610445	+	0.792058i	$0.290991\pi$
$774$	0	0
$775$	13.8541	0.497654
$776$	0	0
$777$	0	0
$778$	0	0
$779$	−1.40325	−0.0502767
$780$	0	0
$781$	7.14590	0.255700
$782$	0	0
$783$	0	0
$784$	0	0
$785$	−8.18034	−0.291969
$786$	0	0
$787$	12.9098	0.460186	0.230093	−	0.973169i	$-0.426097\pi$
$787$	12.9098	0.460186	0.230093	+	0.973169i	$0.426097\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	−12.3262	−0.438271
$792$	0	0
$793$	1.38197	0.0490751
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−44.1803	−1.56495	−0.782474	−	0.622683i	$-0.786043\pi$
$797$	−44.1803	−1.56495	−0.782474	+	0.622683i	$0.786043\pi$
$798$	0	0
$799$	31.9574	1.13057
$800$	0	0
$801$	0	0
$802$	0	0
$803$	18.7082	0.660198
$804$	0	0
$805$	0.618034	0.0217828
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−9.21478	−0.323974	−0.161987	−	0.986793i	$-0.551790\pi$
$809$	−9.21478	−0.323974	−0.161987	+	0.986793i	$0.551790\pi$
$810$	0	0
$811$	−27.2918	−0.958345	−0.479172	−	0.877721i	$-0.659063\pi$
$811$	−27.2918	−0.958345	−0.479172	+	0.877721i	$0.659063\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−2.56231	−0.0897537
$816$	0	0
$817$	0.493422	0.0172627
$818$	0	0
$819$	0	0
$820$	0	0
$821$	38.2918	1.33639	0.668196	−	0.743985i	$-0.267067\pi$
$821$	38.2918	1.33639	0.668196	+	0.743985i	$0.267067\pi$
$822$	0	0
$823$	−39.0902	−1.36260	−0.681299	−	0.732005i	$-0.738585\pi$
$823$	−39.0902	−1.36260	−0.681299	+	0.732005i	$0.738585\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	13.9230	0.484150	0.242075	−	0.970258i	$-0.422172\pi$
$827$	13.9230	0.484150	0.242075	+	0.970258i	$0.422172\pi$
$828$	0	0
$829$	7.00000	0.243120	0.121560	−	0.992584i	$-0.461210\pi$
$829$	7.00000	0.243120	0.121560	+	0.992584i	$0.461210\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	6.70820	0.232425
$834$	0	0
$835$	−12.0344	−0.416469
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−0.0901699	−0.00311301	−0.00155651	−	0.999999i	$-0.500495\pi$
$839$	−0.0901699	−0.00311301	−0.00155651	+	0.999999i	$0.500495\pi$
$840$	0	0
$841$	9.88854	0.340984
$842$	0	0
$843$	0	0
$844$	0	0
$845$	6.41641	0.220731
$846$	0	0
$847$	2.00000	0.0687208
$848$	0	0
$849$	0	0
$850$	0	0
$851$	0.527864	0.0180949
$852$	0	0
$853$	15.7082	0.537839	0.268919	−	0.963163i	$-0.413333\pi$
$853$	15.7082	0.537839	0.268919	+	0.963163i	$0.413333\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−10.1803	−0.347754	−0.173877	−	0.984767i	$-0.555629\pi$
$857$	−10.1803	−0.347754	−0.173877	+	0.984767i	$0.555629\pi$
$858$	0	0
$859$	27.3050	0.931633	0.465816	−	0.884881i	$-0.345761\pi$
$859$	27.3050	0.931633	0.465816	+	0.884881i	$0.345761\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−19.3475	−0.658597	−0.329299	−	0.944226i	$-0.606812\pi$
$863$	−19.3475	−0.658597	−0.329299	+	0.944226i	$0.606812\pi$
$864$	0	0
$865$	2.79837	0.0951476
$866$	0	0
$867$	0	0
$868$	0	0
$869$	20.1246	0.682681
$870$	0	0
$871$	21.9443	0.743553
$872$	0	0
$873$	0	0
$874$	0	0
$875$	−5.94427	−0.200953
$876$	0	0
$877$	23.4164	0.790716	0.395358	−	0.918527i	$-0.370621\pi$
$877$	23.4164	0.790716	0.395358	+	0.918527i	$0.370621\pi$
$878$	0	0
$879$	0	0
$880$	0	0
$881$	−3.70820	−0.124933	−0.0624663	−	0.998047i	$-0.519897\pi$
$881$	−3.70820	−0.124933	−0.0624663	+	0.998047i	$0.519897\pi$
$882$	0	0
$883$	−37.3262	−1.25613	−0.628064	−	0.778162i	$-0.716152\pi$
$883$	−37.3262	−1.25613	−0.628064	+	0.778162i	$0.716152\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−30.2705	−1.01638	−0.508192	−	0.861244i	$-0.669686\pi$
$887$	−30.2705	−1.01638	−0.508192	+	0.861244i	$0.669686\pi$
$888$	0	0
$889$	14.5623	0.488404
$890$	0	0
$891$	0	0
$892$	0	0
$893$	1.12461	0.0376337
$894$	0	0
$895$	−11.1459	−0.372566
$896$	0	0
$897$	0	0
$898$	0	0
$899$	−18.7082	−0.623954
$900$	0	0
$901$	−42.4377	−1.41380
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−5.27051	−0.175198
$906$	0	0
$907$	−32.4377	−1.07708	−0.538538	−	0.842601i	$-0.681023\pi$
$907$	−32.4377	−1.07708	−0.538538	+	0.842601i	$0.681023\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	56.1803	1.86134	0.930669	−	0.365863i	$-0.119226\pi$
$911$	56.1803	1.86134	0.930669	+	0.365863i	$0.119226\pi$
$912$	0	0
$913$	−4.41641	−0.146162
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−11.9443	−0.394435
$918$	0	0
$919$	36.3050	1.19759	0.598795	−	0.800902i	$-0.295646\pi$
$919$	36.3050	1.19759	0.598795	+	0.800902i	$0.295646\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	−3.85410	−0.126859
$924$	0	0
$925$	−2.43769	−0.0801509
$926$	0	0
$927$	0	0
$928$	0	0
$929$	36.0344	1.18225	0.591126	−	0.806579i	$-0.298684\pi$
$929$	36.0344	1.18225	0.591126	+	0.806579i	$0.298684\pi$
$930$	0	0
$931$	0.236068	0.00773682
$932$	0	0
$933$	0	0
$934$	0	0
$935$	−12.4377	−0.406756
$936$	0	0
$937$	−40.7082	−1.32988	−0.664940	−	0.746897i	$-0.731543\pi$
$937$	−40.7082	−1.32988	−0.664940	+	0.746897i	$0.731543\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	36.0000	1.17357	0.586783	−	0.809744i	$-0.300394\pi$
$941$	36.0000	1.17357	0.586783	+	0.809744i	$0.300394\pi$
$942$	0	0
$943$	−5.94427	−0.193572
$944$	0	0
$945$	0	0
$946$	0	0
$947$	55.3050	1.79717	0.898585	−	0.438800i	$-0.144596\pi$
$947$	55.3050	1.79717	0.898585	+	0.438800i	$0.144596\pi$
$948$	0	0
$949$	−10.0902	−0.327541
$950$	0	0
$951$	0	0
$952$	0	0
$953$	30.0902	0.974716	0.487358	−	0.873202i	$-0.337961\pi$
$953$	30.0902	0.974716	0.487358	+	0.873202i	$0.337961\pi$
$954$	0	0
$955$	6.58359	0.213040
$956$	0	0
$957$	0	0
$958$	0	0
$959$	−9.00000	−0.290625
$960$	0	0
$961$	−22.0000	−0.709677
$962$	0	0
$963$	0	0
$964$	0	0
$965$	−4.76393	−0.153356
$966$	0	0
$967$	−54.0000	−1.73652	−0.868261	−	0.496107i	$-0.834762\pi$
$967$	−54.0000	−1.73652	−0.868261	+	0.496107i	$0.834762\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−19.7984	−0.635360	−0.317680	−	0.948198i	$-0.602904\pi$
$971$	−19.7984	−0.635360	−0.317680	+	0.948198i	$0.602904\pi$
$972$	0	0
$973$	−0.145898	−0.00467728
$974$	0	0
$975$	0	0
$976$	0	0
$977$	59.2837	1.89665	0.948326	−	0.317297i	$-0.102775\pi$
$977$	59.2837	1.89665	0.948326	+	0.317297i	$0.102775\pi$
$978$	0	0
$979$	−23.3951	−0.747711
$980$	0	0
$981$	0	0
$982$	0	0
$983$	45.4721	1.45034	0.725168	−	0.688572i	$-0.241762\pi$
$983$	45.4721	1.45034	0.725168	+	0.688572i	$0.241762\pi$
$984$	0	0
$985$	2.23607	0.0712470
$986$	0	0
$987$	0	0
$988$	0	0
$989$	2.09017	0.0664635
$990$	0	0
$991$	−59.6869	−1.89602	−0.948009	−	0.318244i	$-0.896907\pi$
$991$	−59.6869	−1.89602	−0.948009	+	0.318244i	$0.896907\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−1.50658	−0.0477617
$996$	0	0
$997$	−15.4721	−0.490007	−0.245004	−	0.969522i	$-0.578789\pi$
$997$	−15.4721	−0.490007	−0.245004	+	0.969522i	$0.578789\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5796.2.a.l.1.1		2
3.2	odd	2		1932.2.a.g.1.2	✓	2
12.11	even	2		7728.2.a.ba.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1932.2.a.g.1.2	✓	2	3.2	odd	2
5796.2.a.l.1.1		2	1.1	even	1	trivial
7728.2.a.ba.1.2		2	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q-0.618034 q^{5} -1.00000 q^{7} +O(q^{10})\)	\(q-0.618034 q^{5} -1.00000 q^{7} +3.00000 q^{11} -1.61803 q^{13} +6.70820 q^{17} +0.236068 q^{19} +1.00000 q^{23} -4.61803 q^{25} +6.23607 q^{29} -3.00000 q^{31} +0.618034 q^{35} +0.527864 q^{37} -5.94427 q^{41} +2.09017 q^{43} +4.76393 q^{47} +1.00000 q^{49} -6.32624 q^{53} -1.85410 q^{55} +7.38197 q^{59} -0.854102 q^{61} +1.00000 q^{65} -13.5623 q^{67} +2.38197 q^{71} +6.23607 q^{73} -3.00000 q^{77} +6.70820 q^{79} -1.47214 q^{83} -4.14590 q^{85} -7.79837 q^{89} +1.61803 q^{91} -0.145898 q^{95} +14.4164 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{5} - 2 q^{7}+O(q^{10}) \) 2 * q + q^5 - 2 * q^7	\( 2 q + q^{5} - 2 q^{7} + 6 q^{11} - q^{13} - 4 q^{19} + 2 q^{23} - 7 q^{25} + 8 q^{29} - 6 q^{31} - q^{35} + 10 q^{37} + 6 q^{41} - 7 q^{43} + 14 q^{47} + 2 q^{49} + 3 q^{53} + 3 q^{55} + 17 q^{59} + 5 q^{61} + 2 q^{65} - 7 q^{67} + 7 q^{71} + 8 q^{73} - 6 q^{77} + 6 q^{83} - 15 q^{85} + 9 q^{89} + q^{91} - 7 q^{95} + 2 q^{97}+O(q^{100}) \) 2 * q + q^5 - 2 * q^7 + 6 * q^11 - q^13 - 4 * q^19 + 2 * q^23 - 7 * q^25 + 8 * q^29 - 6 * q^31 - q^35 + 10 * q^37 + 6 * q^41 - 7 * q^43 + 14 * q^47 + 2 * q^49 + 3 * q^53 + 3 * q^55 + 17 * q^59 + 5 * q^61 + 2 * q^65 - 7 * q^67 + 7 * q^71 + 8 * q^73 - 6 * q^77 + 6 * q^83 - 15 * q^85 + 9 * q^89 + q^91 - 7 * q^95 + 2 * q^97

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