LMFDB - Embedded newform 5175.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5175,2,Mod(1,5175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5175, 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("5175.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5175 = 3^{2} \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5175.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:	$41.3225830460$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 575)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{4} -1.00000 q^{7} +3.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} -1.00000 q^{4} -1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{11} -1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -5.00000 q^{19} -1.00000 q^{22} +1.00000 q^{23} +1.00000 q^{26} +1.00000 q^{28} +5.00000 q^{29} -2.00000 q^{31} -5.00000 q^{32} +4.00000 q^{37} +5.00000 q^{38} +5.00000 q^{41} +9.00000 q^{43} -1.00000 q^{44} -1.00000 q^{46} -6.00000 q^{47} -6.00000 q^{49} +1.00000 q^{52} +2.00000 q^{53} -3.00000 q^{56} -5.00000 q^{58} -8.00000 q^{59} -8.00000 q^{61} +2.00000 q^{62} +7.00000 q^{64} -8.00000 q^{67} +10.0000 q^{71} +3.00000 q^{73} -4.00000 q^{74} +5.00000 q^{76} -1.00000 q^{77} -3.00000 q^{79} -5.00000 q^{82} +3.00000 q^{83} -9.00000 q^{86} +3.00000 q^{88} -10.0000 q^{89} +1.00000 q^{91} -1.00000 q^{92} +6.00000 q^{94} +2.00000 q^{97} +6.00000 q^{98} +O(q^{100})$

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 $

$2$	−1.00000	−0.707107	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	3.00000	1.06066
$9$	0	0
$10$	0	0
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	0	0
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	0	0
$22$	−1.00000	−0.213201
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0	0
$25$	0	0
$26$	1.00000	0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	0	0
$35$	0	0
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	5.00000	0.811107
$39$	0	0
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	0	0
$51$	0	0
$52$	1.00000	0.138675
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	0	0
$55$	0	0
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−5.00000	−0.656532
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	7.00000	0.875000
$65$	0	0
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	0	0
$73$	3.00000	0.351123	0.175562	−	0.984468i	$-0.443826\pi$
$73$	3.00000	0.351123	0.175562	+	0.984468i	$0.443826\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	5.00000	0.573539
$77$	−1.00000	−0.113961
$78$	0	0
$79$	−3.00000	−0.337526	−0.168763	−	0.985657i	$-0.553977\pi$
$79$	−3.00000	−0.337526	−0.168763	+	0.985657i	$0.553977\pi$
$80$	0	0
$81$	0	0
$82$	−5.00000	−0.552158
$83$	3.00000	0.329293	0.164646	−	0.986353i	$-0.447352\pi$
$83$	3.00000	0.329293	0.164646	+	0.986353i	$0.447352\pi$
$84$	0	0
$85$	0	0
$86$	−9.00000	−0.970495
$87$	0	0
$88$	3.00000	0.319801
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−1.00000	−0.104257
$93$	0	0
$94$	6.00000	0.618853
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	17.0000	1.67506	0.837530	−	0.546392i	$-0.183999\pi$
$103$	17.0000	1.67506	0.837530	+	0.546392i	$0.183999\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	−2.00000	−0.194257
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	0	0
$116$	−5.00000	−0.464238
$117$	0	0
$118$	8.00000	0.736460
$119$	0	0
$120$	0	0
$121$	−10.0000	−0.909091
$122$	8.00000	0.724286
$123$	0	0
$124$	2.00000	0.179605
$125$	0	0
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	3.00000	0.265165
$129$	0	0
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	0	0
$133$	5.00000	0.433555
$134$	8.00000	0.691095
$135$	0	0
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	0	0
$142$	−10.0000	−0.839181
$143$	−1.00000	−0.0836242
$144$	0	0
$145$	0	0
$146$	−3.00000	−0.248282
$147$	0	0
$148$	−4.00000	−0.328798
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	−15.0000	−1.21666
$153$	0	0
$154$	1.00000	0.0805823
$155$	0	0
$156$	0	0
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	3.00000	0.238667
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	0	0
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	−5.00000	−0.390434
$165$	0	0
$166$	−3.00000	−0.232845
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	0	0
$172$	−9.00000	−0.686244
$173$	15.0000	1.14043	0.570214	−	0.821496i	$-0.306860\pi$
$173$	15.0000	1.14043	0.570214	+	0.821496i	$0.306860\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	10.0000	0.749532
$179$	−6.00000	−0.448461	−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000	−0.448461	−0.224231	+	0.974536i	$0.571987\pi$
$180$	0	0
$181$	−20.0000	−1.48659	−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000	−1.48659	−0.743294	+	0.668965i	$0.766738\pi$
$182$	−1.00000	−0.0741249
$183$	0	0
$184$	3.00000	0.221163
$185$	0	0
$186$	0	0
$187$	0	0
$188$	6.00000	0.437595
$189$	0	0
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	6.00000	0.428571
$197$	−17.0000	−1.21120	−0.605600	−	0.795769i	$-0.707067\pi$
$197$	−17.0000	−1.21120	−0.605600	+	0.795769i	$0.707067\pi$
$198$	0	0
$199$	−7.00000	−0.496217	−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000	−0.496217	−0.248108	+	0.968732i	$0.579809\pi$
$200$	0	0
$201$	0	0
$202$	10.0000	0.703598
$203$	−5.00000	−0.350931
$204$	0	0
$205$	0	0
$206$	−17.0000	−1.18445
$207$	0	0
$208$	1.00000	0.0693375
$209$	−5.00000	−0.345857
$210$	0	0
$211$	−6.00000	−0.413057	−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000	−0.413057	−0.206529	+	0.978441i	$0.566217\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	−12.0000	−0.820303
$215$	0	0
$216$	0	0
$217$	2.00000	0.135769
$218$	4.00000	0.270914
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	6.00000	0.399114
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	0	0
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	0	0
$232$	15.0000	0.984798
$233$	−5.00000	−0.327561	−0.163780	−	0.986497i	$-0.552369\pi$
$233$	−5.00000	−0.327561	−0.163780	+	0.986497i	$0.552369\pi$
$234$	0	0
$235$	0	0
$236$	8.00000	0.520756
$237$	0	0
$238$	0	0
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	0	0
$241$	−30.0000	−1.93247	−0.966235	−	0.257663i	$-0.917048\pi$
$241$	−30.0000	−1.93247	−0.966235	+	0.257663i	$0.917048\pi$
$242$	10.0000	0.642824
$243$	0	0
$244$	8.00000	0.512148
$245$	0	0
$246$	0	0
$247$	5.00000	0.318142
$248$	−6.00000	−0.381000
$249$	0	0
$250$	0	0
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	0	0
$253$	1.00000	0.0628695
$254$	8.00000	0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	0	0
$261$	0	0
$262$	−6.00000	−0.370681
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	0	0
$266$	−5.00000	−0.306570
$267$	0	0
$268$	8.00000	0.488678
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	0	0
$271$	−14.0000	−0.850439	−0.425220	−	0.905090i	$-0.639803\pi$
$271$	−14.0000	−0.850439	−0.425220	+	0.905090i	$0.639803\pi$
$272$	0	0
$273$	0	0
$274$	−18.0000	−1.08742
$275$	0	0
$276$	0	0
$277$	33.0000	1.98278	0.991389	−	0.130950i	$-0.0418029\pi$
$277$	33.0000	1.98278	0.991389	+	0.130950i	$0.0418029\pi$
$278$	−20.0000	−1.19952
$279$	0	0
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−32.0000	−1.90220	−0.951101	−	0.308879i	$-0.900046\pi$
$283$	−32.0000	−1.90220	−0.951101	+	0.308879i	$0.900046\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	1.00000	0.0591312
$287$	−5.00000	−0.295141
$288$	0	0
$289$	−17.0000	−1.00000
$290$	0	0
$291$	0	0
$292$	−3.00000	−0.175562
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	0	0
$296$	12.0000	0.697486
$297$	0	0
$298$	−2.00000	−0.115857
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	−9.00000	−0.518751
$302$	−6.00000	−0.345261
$303$	0	0
$304$	5.00000	0.286770
$305$	0	0
$306$	0	0
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	1.00000	0.0569803
$309$	0	0
$310$	0	0
$311$	−28.0000	−1.58773	−0.793867	−	0.608091i	$-0.791935\pi$
$311$	−28.0000	−1.58773	−0.793867	+	0.608091i	$0.791935\pi$
$312$	0	0
$313$	12.0000	0.678280	0.339140	−	0.940736i	$-0.389864\pi$
$313$	12.0000	0.678280	0.339140	+	0.940736i	$0.389864\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	3.00000	0.168763
$317$	−33.0000	−1.85346	−0.926732	−	0.375722i	$-0.877395\pi$
$317$	−33.0000	−1.85346	−0.926732	+	0.375722i	$0.877395\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	0	0
$321$	0	0
$322$	1.00000	0.0557278
$323$	0	0
$324$	0	0
$325$	0	0
$326$	−6.00000	−0.332309
$327$	0	0
$328$	15.0000	0.828236
$329$	6.00000	0.330791
$330$	0	0
$331$	14.0000	0.769510	0.384755	−	0.923019i	$-0.374286\pi$
$331$	14.0000	0.769510	0.384755	+	0.923019i	$0.374286\pi$
$332$	−3.00000	−0.164646
$333$	0	0
$334$	−18.0000	−0.984916
$335$	0	0
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	−2.00000	−0.108306
$342$	0	0
$343$	13.0000	0.701934
$344$	27.0000	1.45574
$345$	0	0
$346$	−15.0000	−0.806405
$347$	−24.0000	−1.28839	−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000	−1.28839	−0.644194	+	0.764862i	$0.722807\pi$
$348$	0	0
$349$	−25.0000	−1.33822	−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000	−1.33822	−0.669110	+	0.743164i	$0.733324\pi$
$350$	0	0
$351$	0	0
$352$	−5.00000	−0.266501
$353$	−11.0000	−0.585471	−0.292735	−	0.956193i	$-0.594566\pi$
$353$	−11.0000	−0.585471	−0.292735	+	0.956193i	$0.594566\pi$
$354$	0	0
$355$	0	0
$356$	10.0000	0.529999
$357$	0	0
$358$	6.00000	0.317110
$359$	−33.0000	−1.74167	−0.870837	−	0.491572i	$-0.836422\pi$
$359$	−33.0000	−1.74167	−0.870837	+	0.491572i	$0.836422\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	20.0000	1.05118
$363$	0	0
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	0	0
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	−1.00000	−0.0521286
$369$	0	0
$370$	0	0
$371$	−2.00000	−0.103835
$372$	0	0
$373$	−20.0000	−1.03556	−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000	−1.03556	−0.517780	+	0.855514i	$0.673242\pi$
$374$	0	0
$375$	0	0
$376$	−18.0000	−0.928279
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	0	0
$381$	0	0
$382$	15.0000	0.767467
$383$	−19.0000	−0.970855	−0.485427	−	0.874277i	$-0.661336\pi$
$383$	−19.0000	−0.970855	−0.485427	+	0.874277i	$0.661336\pi$
$384$	0	0
$385$	0	0
$386$	10.0000	0.508987
$387$	0	0
$388$	−2.00000	−0.101535
$389$	14.0000	0.709828	0.354914	−	0.934899i	$-0.384510\pi$
$389$	14.0000	0.709828	0.354914	+	0.934899i	$0.384510\pi$
$390$	0	0
$391$	0	0
$392$	−18.0000	−0.909137
$393$	0	0
$394$	17.0000	0.856448
$395$	0	0
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	7.00000	0.350878
$399$	0	0
$400$	0	0
$401$	−32.0000	−1.59800	−0.799002	−	0.601329i	$-0.794638\pi$
$401$	−32.0000	−1.59800	−0.799002	+	0.601329i	$0.794638\pi$
$402$	0	0
$403$	2.00000	0.0996271
$404$	10.0000	0.497519
$405$	0	0
$406$	5.00000	0.248146
$407$	4.00000	0.198273
$408$	0	0
$409$	1.00000	0.0494468	0.0247234	−	0.999694i	$-0.492129\pi$
$409$	1.00000	0.0494468	0.0247234	+	0.999694i	$0.492129\pi$
$410$	0	0
$411$	0	0
$412$	−17.0000	−0.837530
$413$	8.00000	0.393654
$414$	0	0
$415$	0	0
$416$	5.00000	0.245145
$417$	0	0
$418$	5.00000	0.244558
$419$	−9.00000	−0.439679	−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000	−0.439679	−0.219839	+	0.975536i	$0.570553\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	6.00000	0.292075
$423$	0	0
$424$	6.00000	0.291386
$425$	0	0
$426$	0	0
$427$	8.00000	0.387147
$428$	−12.0000	−0.580042
$429$	0	0
$430$	0	0
$431$	8.00000	0.385346	0.192673	−	0.981263i	$-0.438284\pi$
$431$	8.00000	0.385346	0.192673	+	0.981263i	$0.438284\pi$
$432$	0	0
$433$	−32.0000	−1.53782	−0.768911	−	0.639356i	$-0.779201\pi$
$433$	−32.0000	−1.53782	−0.768911	+	0.639356i	$0.779201\pi$
$434$	−2.00000	−0.0960031
$435$	0	0
$436$	4.00000	0.191565
$437$	−5.00000	−0.239182
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−14.0000	−0.665160	−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000	−0.665160	−0.332580	+	0.943075i	$0.607919\pi$
$444$	0	0
$445$	0	0
$446$	2.00000	0.0947027
$447$	0	0
$448$	−7.00000	−0.330719
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	0	0
$451$	5.00000	0.235441
$452$	6.00000	0.282216
$453$	0	0
$454$	20.0000	0.938647
$455$	0	0
$456$	0	0
$457$	38.0000	1.77757	0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000	1.77757	0.888783	+	0.458329i	$0.151552\pi$
$458$	22.0000	1.02799
$459$	0	0
$460$	0	0
$461$	−7.00000	−0.326023	−0.163011	−	0.986624i	$-0.552121\pi$
$461$	−7.00000	−0.326023	−0.163011	+	0.986624i	$0.552121\pi$
$462$	0	0
$463$	28.0000	1.30127	0.650635	−	0.759390i	$-0.274503\pi$
$463$	28.0000	1.30127	0.650635	+	0.759390i	$0.274503\pi$
$464$	−5.00000	−0.232119
$465$	0	0
$466$	5.00000	0.231621
$467$	33.0000	1.52706	0.763529	−	0.645774i	$-0.223465\pi$
$467$	33.0000	1.52706	0.763529	+	0.645774i	$0.223465\pi$
$468$	0	0
$469$	8.00000	0.369406
$470$	0	0
$471$	0	0
$472$	−24.0000	−1.10469
$473$	9.00000	0.413820
$474$	0	0
$475$	0	0
$476$	0	0
$477$	0	0
$478$	10.0000	0.457389
$479$	9.00000	0.411220	0.205610	−	0.978634i	$-0.434082\pi$
$479$	9.00000	0.411220	0.205610	+	0.978634i	$0.434082\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	30.0000	1.36646
$483$	0	0
$484$	10.0000	0.454545
$485$	0	0
$486$	0	0
$487$	−14.0000	−0.634401	−0.317200	−	0.948359i	$-0.602743\pi$
$487$	−14.0000	−0.634401	−0.317200	+	0.948359i	$0.602743\pi$
$488$	−24.0000	−1.08643
$489$	0	0
$490$	0	0
$491$	−24.0000	−1.08310	−0.541552	−	0.840667i	$-0.682163\pi$
$491$	−24.0000	−1.08310	−0.541552	+	0.840667i	$0.682163\pi$
$492$	0	0
$493$	0	0
$494$	−5.00000	−0.224961
$495$	0	0
$496$	2.00000	0.0898027
$497$	−10.0000	−0.448561
$498$	0	0
$499$	10.0000	0.447661	0.223831	−	0.974628i	$-0.428144\pi$
$499$	10.0000	0.447661	0.223831	+	0.974628i	$0.428144\pi$
$500$	0	0
$501$	0	0
$502$	−8.00000	−0.357057
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	0	0
$506$	−1.00000	−0.0444554
$507$	0	0
$508$	8.00000	0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	−3.00000	−0.132712
$512$	11.0000	0.486136
$513$	0	0
$514$	2.00000	0.0882162
$515$	0	0
$516$	0	0
$517$	−6.00000	−0.263880
$518$	4.00000	0.175750
$519$	0	0
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	−5.00000	−0.218635	−0.109317	−	0.994007i	$-0.534866\pi$
$523$	−5.00000	−0.218635	−0.109317	+	0.994007i	$0.534866\pi$
$524$	−6.00000	−0.262111
$525$	0	0
$526$	−16.0000	−0.697633
$527$	0	0
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	0	0
$532$	−5.00000	−0.216777
$533$	−5.00000	−0.216574
$534$	0	0
$535$	0	0
$536$	−24.0000	−1.03664
$537$	0	0
$538$	3.00000	0.129339
$539$	−6.00000	−0.258438
$540$	0	0
$541$	31.0000	1.33279	0.666397	−	0.745597i	$-0.267836\pi$
$541$	31.0000	1.33279	0.666397	+	0.745597i	$0.267836\pi$
$542$	14.0000	0.601351
$543$	0	0
$544$	0	0
$545$	0	0
$546$	0	0
$547$	18.0000	0.769624	0.384812	−	0.922995i	$-0.374266\pi$
$547$	18.0000	0.769624	0.384812	+	0.922995i	$0.374266\pi$
$548$	−18.0000	−0.768922
$549$	0	0
$550$	0	0
$551$	−25.0000	−1.06504
$552$	0	0
$553$	3.00000	0.127573
$554$	−33.0000	−1.40204
$555$	0	0
$556$	−20.0000	−0.848189
$557$	−16.0000	−0.677942	−0.338971	−	0.940797i	$-0.610079\pi$
$557$	−16.0000	−0.677942	−0.338971	+	0.940797i	$0.610079\pi$
$558$	0	0
$559$	−9.00000	−0.380659
$560$	0	0
$561$	0	0
$562$	−30.0000	−1.26547
$563$	−41.0000	−1.72794	−0.863972	−	0.503540i	$-0.832031\pi$
$563$	−41.0000	−1.72794	−0.863972	+	0.503540i	$0.832031\pi$
$564$	0	0
$565$	0	0
$566$	32.0000	1.34506
$567$	0	0
$568$	30.0000	1.25877
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	0	0
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	1.00000	0.0418121
$573$	0	0
$574$	5.00000	0.208696
$575$	0	0
$576$	0	0
$577$	31.0000	1.29055	0.645273	−	0.763952i	$-0.276743\pi$
$577$	31.0000	1.29055	0.645273	+	0.763952i	$0.276743\pi$
$578$	17.0000	0.707107
$579$	0	0
$580$	0	0
$581$	−3.00000	−0.124461
$582$	0	0
$583$	2.00000	0.0828315
$584$	9.00000	0.372423
$585$	0	0
$586$	−24.0000	−0.991431
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	10.0000	0.412043
$590$	0	0
$591$	0	0
$592$	−4.00000	−0.164399
$593$	−25.0000	−1.02663	−0.513313	−	0.858201i	$-0.671582\pi$
$593$	−25.0000	−1.02663	−0.513313	+	0.858201i	$0.671582\pi$
$594$	0	0
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	0	0
$598$	1.00000	0.0408930
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	−30.0000	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$602$	9.00000	0.366813
$603$	0	0
$604$	−6.00000	−0.244137
$605$	0	0
$606$	0	0
$607$	−2.00000	−0.0811775	−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000	−0.0811775	−0.0405887	+	0.999176i	$0.512923\pi$
$608$	25.0000	1.01388
$609$	0	0
$610$	0	0
$611$	6.00000	0.242734
$612$	0	0
$613$	−28.0000	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$613$	−28.0000	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$614$	16.0000	0.645707
$615$	0	0
$616$	−3.00000	−0.120873
$617$	28.0000	1.12724	0.563619	−	0.826035i	$-0.309409\pi$
$617$	28.0000	1.12724	0.563619	+	0.826035i	$0.309409\pi$
$618$	0	0
$619$	36.0000	1.44696	0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000	1.44696	0.723481	+	0.690344i	$0.242541\pi$
$620$	0	0
$621$	0	0
$622$	28.0000	1.12270
$623$	10.0000	0.400642
$624$	0	0
$625$	0	0
$626$	−12.0000	−0.479616
$627$	0	0
$628$	14.0000	0.558661
$629$	0	0
$630$	0	0
$631$	7.00000	0.278666	0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000	0.278666	0.139333	+	0.990246i	$0.455504\pi$
$632$	−9.00000	−0.358001
$633$	0	0
$634$	33.0000	1.31060
$635$	0	0
$636$	0	0
$637$	6.00000	0.237729
$638$	−5.00000	−0.197952
$639$	0	0
$640$	0	0
$641$	16.0000	0.631962	0.315981	−	0.948766i	$-0.397666\pi$
$641$	16.0000	0.631962	0.315981	+	0.948766i	$0.397666\pi$
$642$	0	0
$643$	−31.0000	−1.22252	−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000	−1.22252	−0.611260	+	0.791430i	$0.709337\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	0	0
$647$	−38.0000	−1.49393	−0.746967	−	0.664861i	$-0.768491\pi$
$647$	−38.0000	−1.49393	−0.746967	+	0.664861i	$0.768491\pi$
$648$	0	0
$649$	−8.00000	−0.314027
$650$	0	0
$651$	0	0
$652$	−6.00000	−0.234978
$653$	−27.0000	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$653$	−27.0000	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$654$	0	0
$655$	0	0
$656$	−5.00000	−0.195217
$657$	0	0
$658$	−6.00000	−0.233904
$659$	3.00000	0.116863	0.0584317	−	0.998291i	$-0.481390\pi$
$659$	3.00000	0.116863	0.0584317	+	0.998291i	$0.481390\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	−14.0000	−0.544125
$663$	0	0
$664$	9.00000	0.349268
$665$	0	0
$666$	0	0
$667$	5.00000	0.193601
$668$	−18.0000	−0.696441
$669$	0	0
$670$	0	0
$671$	−8.00000	−0.308837
$672$	0	0
$673$	−19.0000	−0.732396	−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000	−0.732396	−0.366198	+	0.930537i	$0.619341\pi$
$674$	22.0000	0.847408
$675$	0	0
$676$	12.0000	0.461538
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	0	0
$682$	2.00000	0.0765840
$683$	2.00000	0.0765279	0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000	0.0765279	0.0382639	+	0.999268i	$0.487817\pi$
$684$	0	0
$685$	0	0
$686$	−13.0000	−0.496342
$687$	0	0
$688$	−9.00000	−0.343122
$689$	−2.00000	−0.0761939
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−15.0000	−0.570214
$693$	0	0
$694$	24.0000	0.911028
$695$	0	0
$696$	0	0
$697$	0	0
$698$	25.0000	0.946264
$699$	0	0
$700$	0	0
$701$	−36.0000	−1.35970	−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000	−1.35970	−0.679851	+	0.733351i	$0.737955\pi$
$702$	0	0
$703$	−20.0000	−0.754314
$704$	7.00000	0.263822
$705$	0	0
$706$	11.0000	0.413990
$707$	10.0000	0.376089
$708$	0	0
$709$	6.00000	0.225335	0.112667	−	0.993633i	$-0.464061\pi$
$709$	6.00000	0.225335	0.112667	+	0.993633i	$0.464061\pi$
$710$	0	0
$711$	0	0
$712$	−30.0000	−1.12430
$713$	−2.00000	−0.0749006
$714$	0	0
$715$	0	0
$716$	6.00000	0.224231
$717$	0	0
$718$	33.0000	1.23155
$719$	40.0000	1.49175	0.745874	−	0.666087i	$-0.232032\pi$
$719$	40.0000	1.49175	0.745874	+	0.666087i	$0.232032\pi$
$720$	0	0
$721$	−17.0000	−0.633113
$722$	−6.00000	−0.223297
$723$	0	0
$724$	20.0000	0.743294
$725$	0	0
$726$	0	0
$727$	32.0000	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$728$	3.00000	0.111187
$729$	0	0
$730$	0	0
$731$	0	0
$732$	0	0
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	17.0000	0.627481
$735$	0	0
$736$	−5.00000	−0.184302
$737$	−8.00000	−0.294684
$738$	0	0
$739$	−22.0000	−0.809283	−0.404642	−	0.914475i	$-0.632604\pi$
$739$	−22.0000	−0.809283	−0.404642	+	0.914475i	$0.632604\pi$
$740$	0	0
$741$	0	0
$742$	2.00000	0.0734223
$743$	−11.0000	−0.403551	−0.201775	−	0.979432i	$-0.564671\pi$
$743$	−11.0000	−0.403551	−0.201775	+	0.979432i	$0.564671\pi$
$744$	0	0
$745$	0	0
$746$	20.0000	0.732252
$747$	0	0
$748$	0	0
$749$	−12.0000	−0.438470
$750$	0	0
$751$	23.0000	0.839282	0.419641	−	0.907690i	$-0.362156\pi$
$751$	23.0000	0.839282	0.419641	+	0.907690i	$0.362156\pi$
$752$	6.00000	0.218797
$753$	0	0
$754$	5.00000	0.182089
$755$	0	0
$756$	0	0
$757$	−40.0000	−1.45382	−0.726912	−	0.686730i	$-0.759045\pi$
$757$	−40.0000	−1.45382	−0.726912	+	0.686730i	$0.759045\pi$
$758$	12.0000	0.435860
$759$	0	0
$760$	0	0
$761$	39.0000	1.41375	0.706874	−	0.707339i	$-0.250105\pi$
$761$	39.0000	1.41375	0.706874	+	0.707339i	$0.250105\pi$
$762$	0	0
$763$	4.00000	0.144810
$764$	15.0000	0.542681
$765$	0	0
$766$	19.0000	0.686498
$767$	8.00000	0.288863
$768$	0	0
$769$	−52.0000	−1.87517	−0.937584	−	0.347759i	$-0.886943\pi$
$769$	−52.0000	−1.87517	−0.937584	+	0.347759i	$0.886943\pi$
$770$	0	0
$771$	0	0
$772$	10.0000	0.359908
$773$	20.0000	0.719350	0.359675	−	0.933078i	$-0.382888\pi$
$773$	20.0000	0.719350	0.359675	+	0.933078i	$0.382888\pi$
$774$	0	0
$775$	0	0
$776$	6.00000	0.215387
$777$	0	0
$778$	−14.0000	−0.501924
$779$	−25.0000	−0.895718
$780$	0	0
$781$	10.0000	0.357828
$782$	0	0
$783$	0	0
$784$	6.00000	0.214286
$785$	0	0
$786$	0	0
$787$	43.0000	1.53278	0.766392	−	0.642373i	$-0.222050\pi$
$787$	43.0000	1.53278	0.766392	+	0.642373i	$0.222050\pi$
$788$	17.0000	0.605600
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	0	0
$793$	8.00000	0.284088
$794$	22.0000	0.780751
$795$	0	0
$796$	7.00000	0.248108
$797$	8.00000	0.283375	0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000	0.283375	0.141687	+	0.989911i	$0.454747\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	0	0
$802$	32.0000	1.12996
$803$	3.00000	0.105868
$804$	0	0
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	0	0
$808$	−30.0000	−1.05540
$809$	15.0000	0.527372	0.263686	−	0.964609i	$-0.415062\pi$
$809$	15.0000	0.527372	0.263686	+	0.964609i	$0.415062\pi$
$810$	0	0
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	5.00000	0.175466
$813$	0	0
$814$	−4.00000	−0.140200
$815$	0	0
$816$	0	0
$817$	−45.0000	−1.57435
$818$	−1.00000	−0.0349642
$819$	0	0
$820$	0	0
$821$	−1.00000	−0.0349002	−0.0174501	−	0.999848i	$-0.505555\pi$
$821$	−1.00000	−0.0349002	−0.0174501	+	0.999848i	$0.505555\pi$
$822$	0	0
$823$	−20.0000	−0.697156	−0.348578	−	0.937280i	$-0.613335\pi$
$823$	−20.0000	−0.697156	−0.348578	+	0.937280i	$0.613335\pi$
$824$	51.0000	1.77667
$825$	0	0
$826$	−8.00000	−0.278356
$827$	37.0000	1.28662	0.643308	−	0.765607i	$-0.277561\pi$
$827$	37.0000	1.28662	0.643308	+	0.765607i	$0.277561\pi$
$828$	0	0
$829$	15.0000	0.520972	0.260486	−	0.965478i	$-0.416117\pi$
$829$	15.0000	0.520972	0.260486	+	0.965478i	$0.416117\pi$
$830$	0	0
$831$	0	0
$832$	−7.00000	−0.242681
$833$	0	0
$834$	0	0
$835$	0	0
$836$	5.00000	0.172929
$837$	0	0
$838$	9.00000	0.310900
$839$	9.00000	0.310715	0.155357	−	0.987858i	$-0.450347\pi$
$839$	9.00000	0.310715	0.155357	+	0.987858i	$0.450347\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−22.0000	−0.758170
$843$	0	0
$844$	6.00000	0.206529
$845$	0	0
$846$	0	0
$847$	10.0000	0.343604
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	0	0
$851$	4.00000	0.137118
$852$	0	0
$853$	−37.0000	−1.26686	−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000	−1.26686	−0.633428	+	0.773802i	$0.718353\pi$
$854$	−8.00000	−0.273754
$855$	0	0
$856$	36.0000	1.23045
$857$	−26.0000	−0.888143	−0.444072	−	0.895991i	$-0.646466\pi$
$857$	−26.0000	−0.888143	−0.444072	+	0.895991i	$0.646466\pi$
$858$	0	0
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	0	0
$861$	0	0
$862$	−8.00000	−0.272481
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	0	0
$865$	0	0
$866$	32.0000	1.08740
$867$	0	0
$868$	−2.00000	−0.0678844
$869$	−3.00000	−0.101768
$870$	0	0
$871$	8.00000	0.271070
$872$	−12.0000	−0.406371
$873$	0	0
$874$	5.00000	0.169128
$875$	0	0
$876$	0	0
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	−20.0000	−0.674967
$879$	0	0
$880$	0	0
$881$	20.0000	0.673817	0.336909	−	0.941537i	$-0.390619\pi$
$881$	20.0000	0.673817	0.336909	+	0.941537i	$0.390619\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	0	0
$885$	0	0
$886$	14.0000	0.470339
$887$	28.0000	0.940148	0.470074	−	0.882627i	$-0.344227\pi$
$887$	28.0000	0.940148	0.470074	+	0.882627i	$0.344227\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	0	0
$891$	0	0
$892$	2.00000	0.0669650
$893$	30.0000	1.00391
$894$	0	0
$895$	0	0
$896$	−3.00000	−0.100223
$897$	0	0
$898$	−18.0000	−0.600668
$899$	−10.0000	−0.333519
$900$	0	0
$901$	0	0
$902$	−5.00000	−0.166482
$903$	0	0
$904$	−18.0000	−0.598671
$905$	0	0
$906$	0	0
$907$	−17.0000	−0.564476	−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000	−0.564476	−0.282238	+	0.959344i	$0.591077\pi$
$908$	20.0000	0.663723
$909$	0	0
$910$	0	0
$911$	55.0000	1.82223	0.911116	−	0.412151i	$-0.135222\pi$
$911$	55.0000	1.82223	0.911116	+	0.412151i	$0.135222\pi$
$912$	0	0
$913$	3.00000	0.0992855
$914$	−38.0000	−1.25693
$915$	0	0
$916$	22.0000	0.726900
$917$	−6.00000	−0.198137
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	0	0
$922$	7.00000	0.230533
$923$	−10.0000	−0.329154
$924$	0	0
$925$	0	0
$926$	−28.0000	−0.920137
$927$	0	0
$928$	−25.0000	−0.820665
$929$	45.0000	1.47640	0.738201	−	0.674581i	$-0.235676\pi$
$929$	45.0000	1.47640	0.738201	+	0.674581i	$0.235676\pi$
$930$	0	0
$931$	30.0000	0.983210
$932$	5.00000	0.163780
$933$	0	0
$934$	−33.0000	−1.07979
$935$	0	0
$936$	0	0
$937$	−26.0000	−0.849383	−0.424691	−	0.905338i	$-0.639617\pi$
$937$	−26.0000	−0.849383	−0.424691	+	0.905338i	$0.639617\pi$
$938$	−8.00000	−0.261209
$939$	0	0
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	0	0
$943$	5.00000	0.162822
$944$	8.00000	0.260378
$945$	0	0
$946$	−9.00000	−0.292615
$947$	−22.0000	−0.714904	−0.357452	−	0.933932i	$-0.616354\pi$
$947$	−22.0000	−0.714904	−0.357452	+	0.933932i	$0.616354\pi$
$948$	0	0
$949$	−3.00000	−0.0973841
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−28.0000	−0.907009	−0.453504	−	0.891254i	$-0.649826\pi$
$953$	−28.0000	−0.907009	−0.453504	+	0.891254i	$0.649826\pi$
$954$	0	0
$955$	0	0
$956$	10.0000	0.323423
$957$	0	0
$958$	−9.00000	−0.290777
$959$	−18.0000	−0.581250
$960$	0	0
$961$	−27.0000	−0.870968
$962$	4.00000	0.128965
$963$	0	0
$964$	30.0000	0.966235
$965$	0	0
$966$	0	0
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	−30.0000	−0.964237
$969$	0	0
$970$	0	0
$971$	15.0000	0.481373	0.240686	−	0.970603i	$-0.422627\pi$
$971$	15.0000	0.481373	0.240686	+	0.970603i	$0.422627\pi$
$972$	0	0
$973$	−20.0000	−0.641171
$974$	14.0000	0.448589
$975$	0	0
$976$	8.00000	0.256074
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	−10.0000	−0.319601
$980$	0	0
$981$	0	0
$982$	24.0000	0.765871
$983$	39.0000	1.24391	0.621953	−	0.783054i	$-0.286339\pi$
$983$	39.0000	1.24391	0.621953	+	0.783054i	$0.286339\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−5.00000	−0.159071
$989$	9.00000	0.286183
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	10.0000	0.317500
$993$	0	0
$994$	10.0000	0.317181
$995$	0	0
$996$	0	0
$997$	37.0000	1.17180	0.585901	−	0.810383i	$-0.300741\pi$
$997$	37.0000	1.17180	0.585901	+	0.810383i	$0.300741\pi$
$998$	−10.0000	−0.316544
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5175.2.a.e.1.1		1
3.2	odd	2		575.2.a.d.1.1	yes	1
5.4	even	2		5175.2.a.u.1.1		1
12.11	even	2		9200.2.a.u.1.1		1
15.2	even	4		575.2.b.b.24.2		2
15.8	even	4		575.2.b.b.24.1		2
15.14	odd	2		575.2.a.c.1.1	✓	1
60.59	even	2		9200.2.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.a.c.1.1	✓	1	15.14	odd	2
575.2.a.d.1.1	yes	1	3.2	odd	2
575.2.b.b.24.1		2	15.8	even	4
575.2.b.b.24.2		2	15.2	even	4
5175.2.a.e.1.1		1	1.1	even	1	trivial
5175.2.a.u.1.1		1	5.4	even	2
9200.2.a.r.1.1		1	60.59	even	2
9200.2.a.u.1.1		1	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:	\( N \)	\(=\)	\( 5175 = 3^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5175.a (trivial)

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