LMFDB - Embedded newform 475.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,4,Mod(1,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("475.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	475.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:	$28.0259072527$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	475.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{3} -8.00000 q^{4} +22.0000 q^{7} -11.0000 q^{9} -12.0000 q^{11} +32.0000 q^{12} -8.00000 q^{13} +64.0000 q^{16} +66.0000 q^{17} +19.0000 q^{19} -88.0000 q^{21} +30.0000 q^{23} +152.000 q^{27} -176.000 q^{28} -6.00000 q^{29} -64.0000 q^{31} +48.0000 q^{33} +88.0000 q^{36} +16.0000 q^{37} +32.0000 q^{39} +54.0000 q^{41} -182.000 q^{43} +96.0000 q^{44} -594.000 q^{47} -256.000 q^{48} +141.000 q^{49} -264.000 q^{51} +64.0000 q^{52} -396.000 q^{53} -76.0000 q^{57} -564.000 q^{59} -706.000 q^{61} -242.000 q^{63} -512.000 q^{64} +628.000 q^{67} -528.000 q^{68} -120.000 q^{69} -984.000 q^{71} -14.0000 q^{73} -152.000 q^{76} -264.000 q^{77} -328.000 q^{79} -311.000 q^{81} +294.000 q^{83} +704.000 q^{84} +24.0000 q^{87} +918.000 q^{89} -176.000 q^{91} -240.000 q^{92} +256.000 q^{93} +1564.00 q^{97} +132.000 q^{99} +O(q^{100})$

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		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	−8.00000	−1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	22.0000	1.18789	0.593944	−	0.804506i	$-0.297570\pi$
$7$	22.0000	1.18789	0.593944	+	0.804506i	$0.297570\pi$
$8$	0	0
$9$	−11.0000	−0.407407
$10$	0	0
$11$	−12.0000	−0.328921	−0.164461	−	0.986384i	$-0.552588\pi$
$11$	−12.0000	−0.328921	−0.164461	+	0.986384i	$0.552588\pi$
$12$	32.0000	0.769800
$13$	−8.00000	−0.170677	−0.0853385	−	0.996352i	$-0.527197\pi$
$13$	−8.00000	−0.170677	−0.0853385	+	0.996352i	$0.527197\pi$
$14$	0	0
$15$	0	0
$16$	64.0000	1.00000
$17$	66.0000	0.941609	0.470804	−	0.882238i	$-0.343964\pi$
$17$	66.0000	0.941609	0.470804	+	0.882238i	$0.343964\pi$
$18$	0	0
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	0	0
$21$	−88.0000	−0.914437
$22$	0	0
$23$	30.0000	0.271975	0.135988	−	0.990711i	$-0.456579\pi$
$23$	30.0000	0.271975	0.135988	+	0.990711i	$0.456579\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	152.000	1.08342
$28$	−176.000	−1.18789
$29$	−6.00000	−0.0384197	−0.0192099	−	0.999815i	$-0.506115\pi$
$29$	−6.00000	−0.0384197	−0.0192099	+	0.999815i	$0.506115\pi$
$30$	0	0
$31$	−64.0000	−0.370798	−0.185399	−	0.982663i	$-0.559358\pi$
$31$	−64.0000	−0.370798	−0.185399	+	0.982663i	$0.559358\pi$
$32$	0	0
$33$	48.0000	0.253204
$34$	0	0
$35$	0	0
$36$	88.0000	0.407407
$37$	16.0000	0.0710915	0.0355457	−	0.999368i	$-0.488683\pi$
$37$	16.0000	0.0710915	0.0355457	+	0.999368i	$0.488683\pi$
$38$	0	0
$39$	32.0000	0.131387
$40$	0	0
$41$	54.0000	0.205692	0.102846	−	0.994697i	$-0.467205\pi$
$41$	54.0000	0.205692	0.102846	+	0.994697i	$0.467205\pi$
$42$	0	0
$43$	−182.000	−0.645459	−0.322730	−	0.946491i	$-0.604600\pi$
$43$	−182.000	−0.645459	−0.322730	+	0.946491i	$0.604600\pi$
$44$	96.0000	0.328921
$45$	0	0
$46$	0	0
$47$	−594.000	−1.84349	−0.921743	−	0.387802i	$-0.873234\pi$
$47$	−594.000	−1.84349	−0.921743	+	0.387802i	$0.873234\pi$
$48$	−256.000	−0.769800
$49$	141.000	0.411079
$50$	0	0
$51$	−264.000	−0.724851
$52$	64.0000	0.170677
$53$	−396.000	−1.02632	−0.513158	−	0.858294i	$-0.671525\pi$
$53$	−396.000	−1.02632	−0.513158	+	0.858294i	$0.671525\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−76.0000	−0.176604
$58$	0	0
$59$	−564.000	−1.24452	−0.622259	−	0.782812i	$-0.713785\pi$
$59$	−564.000	−1.24452	−0.622259	+	0.782812i	$0.713785\pi$
$60$	0	0
$61$	−706.000	−1.48187	−0.740935	−	0.671577i	$-0.765617\pi$
$61$	−706.000	−1.48187	−0.740935	+	0.671577i	$0.765617\pi$
$62$	0	0
$63$	−242.000	−0.483955
$64$	−512.000	−1.00000
$65$	0	0
$66$	0	0
$67$	628.000	1.14511	0.572555	−	0.819866i	$-0.305952\pi$
$67$	628.000	1.14511	0.572555	+	0.819866i	$0.305952\pi$
$68$	−528.000	−0.941609
$69$	−120.000	−0.209367
$70$	0	0
$71$	−984.000	−1.64478	−0.822390	−	0.568925i	$-0.807360\pi$
$71$	−984.000	−1.64478	−0.822390	+	0.568925i	$0.807360\pi$
$72$	0	0
$73$	−14.0000	−0.0224462	−0.0112231	−	0.999937i	$-0.503573\pi$
$73$	−14.0000	−0.0224462	−0.0112231	+	0.999937i	$0.503573\pi$
$74$	0	0
$75$	0	0
$76$	−152.000	−0.229416
$77$	−264.000	−0.390722
$78$	0	0
$79$	−328.000	−0.467125	−0.233563	−	0.972342i	$-0.575038\pi$
$79$	−328.000	−0.467125	−0.233563	+	0.972342i	$0.575038\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	0	0
$83$	294.000	0.388804	0.194402	−	0.980922i	$-0.437723\pi$
$83$	294.000	0.388804	0.194402	+	0.980922i	$0.437723\pi$
$84$	704.000	0.914437
$85$	0	0
$86$	0	0
$87$	24.0000	0.0295755
$88$	0	0
$89$	918.000	1.09335	0.546673	−	0.837346i	$-0.315894\pi$
$89$	918.000	1.09335	0.546673	+	0.837346i	$0.315894\pi$
$90$	0	0
$91$	−176.000	−0.202745
$92$	−240.000	−0.271975
$93$	256.000	0.285440
$94$	0	0
$95$	0	0
$96$	0	0
$97$	1564.00	1.63711	0.818557	−	0.574425i	$-0.194774\pi$
$97$	1564.00	1.63711	0.818557	+	0.574425i	$0.194774\pi$
$98$	0	0
$99$	132.000	0.134005
$100$	0	0
$101$	−294.000	−0.289644	−0.144822	−	0.989458i	$-0.546261\pi$
$101$	−294.000	−0.289644	−0.144822	+	0.989458i	$0.546261\pi$
$102$	0	0
$103$	−752.000	−0.719386	−0.359693	−	0.933071i	$-0.617119\pi$
$103$	−752.000	−0.719386	−0.359693	+	0.933071i	$0.617119\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	216.000	0.195154	0.0975771	−	0.995228i	$-0.468891\pi$
$107$	216.000	0.195154	0.0975771	+	0.995228i	$0.468891\pi$
$108$	−1216.00	−1.08342
$109$	−754.000	−0.662570	−0.331285	−	0.943531i	$-0.607482\pi$
$109$	−754.000	−0.662570	−0.331285	+	0.943531i	$0.607482\pi$
$110$	0	0
$111$	−64.0000	−0.0547262
$112$	1408.00	1.18789
$113$	12.0000	0.00998996	0.00499498	−	0.999988i	$-0.498410\pi$
$113$	12.0000	0.00998996	0.00499498	+	0.999988i	$0.498410\pi$
$114$	0	0
$115$	0	0
$116$	48.0000	0.0384197
$117$	88.0000	0.0695351
$118$	0	0
$119$	1452.00	1.11853
$120$	0	0
$121$	−1187.00	−0.891811
$122$	0	0
$123$	−216.000	−0.158342
$124$	512.000	0.370798
$125$	0	0
$126$	0	0
$127$	−344.000	−0.240355	−0.120177	−	0.992752i	$-0.538346\pi$
$127$	−344.000	−0.240355	−0.120177	+	0.992752i	$0.538346\pi$
$128$	0	0
$129$	728.000	0.496875
$130$	0	0
$131$	2520.00	1.68071	0.840357	−	0.542034i	$-0.182346\pi$
$131$	2520.00	1.68071	0.840357	+	0.542034i	$0.182346\pi$
$132$	−384.000	−0.253204
$133$	418.000	0.272520
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−654.000	−0.407847	−0.203923	−	0.978987i	$-0.565369\pi$
$137$	−654.000	−0.407847	−0.203923	+	0.978987i	$0.565369\pi$
$138$	0	0
$139$	−2392.00	−1.45962	−0.729809	−	0.683652i	$-0.760391\pi$
$139$	−2392.00	−1.45962	−0.729809	+	0.683652i	$0.760391\pi$
$140$	0	0
$141$	2376.00	1.41912
$142$	0	0
$143$	96.0000	0.0561393
$144$	−704.000	−0.407407
$145$	0	0
$146$	0	0
$147$	−564.000	−0.316449
$148$	−128.000	−0.0710915
$149$	−1266.00	−0.696072	−0.348036	−	0.937481i	$-0.613151\pi$
$149$	−1266.00	−0.696072	−0.348036	+	0.937481i	$0.613151\pi$
$150$	0	0
$151$	3080.00	1.65991	0.829956	−	0.557828i	$-0.188365\pi$
$151$	3080.00	1.65991	0.829956	+	0.557828i	$0.188365\pi$
$152$	0	0
$153$	−726.000	−0.383618
$154$	0	0
$155$	0	0
$156$	−256.000	−0.131387
$157$	−1838.00	−0.934321	−0.467160	−	0.884173i	$-0.654723\pi$
$157$	−1838.00	−0.934321	−0.467160	+	0.884173i	$0.654723\pi$
$158$	0	0
$159$	1584.00	0.790059
$160$	0	0
$161$	660.000	0.323076
$162$	0	0
$163$	850.000	0.408449	0.204224	−	0.978924i	$-0.434533\pi$
$163$	850.000	0.408449	0.204224	+	0.978924i	$0.434533\pi$
$164$	−432.000	−0.205692
$165$	0	0
$166$	0	0
$167$	−3804.00	−1.76265	−0.881324	−	0.472512i	$-0.843347\pi$
$167$	−3804.00	−1.76265	−0.881324	+	0.472512i	$0.843347\pi$
$168$	0	0
$169$	−2133.00	−0.970869
$170$	0	0
$171$	−209.000	−0.0934657
$172$	1456.00	0.645459
$173$	564.000	0.247862	0.123931	−	0.992291i	$-0.460450\pi$
$173$	564.000	0.247862	0.123931	+	0.992291i	$0.460450\pi$
$174$	0	0
$175$	0	0
$176$	−768.000	−0.328921
$177$	2256.00	0.958030
$178$	0	0
$179$	−1812.00	−0.756621	−0.378311	−	0.925679i	$-0.623495\pi$
$179$	−1812.00	−0.756621	−0.378311	+	0.925679i	$0.623495\pi$
$180$	0	0
$181$	−4498.00	−1.84715	−0.923574	−	0.383421i	$-0.874746\pi$
$181$	−4498.00	−1.84715	−0.923574	+	0.383421i	$0.874746\pi$
$182$	0	0
$183$	2824.00	1.14074
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−792.000	−0.309715
$188$	4752.00	1.84349
$189$	3344.00	1.28699
$190$	0	0
$191$	3588.00	1.35926	0.679630	−	0.733555i	$-0.262140\pi$
$191$	3588.00	1.35926	0.679630	+	0.733555i	$0.262140\pi$
$192$	2048.00	0.769800
$193$	4492.00	1.67534	0.837672	−	0.546174i	$-0.183916\pi$
$193$	4492.00	1.67534	0.837672	+	0.546174i	$0.183916\pi$
$194$	0	0
$195$	0	0
$196$	−1128.00	−0.411079
$197$	−2466.00	−0.891854	−0.445927	−	0.895069i	$-0.647126\pi$
$197$	−2466.00	−0.891854	−0.445927	+	0.895069i	$0.647126\pi$
$198$	0	0
$199$	824.000	0.293527	0.146763	−	0.989172i	$-0.453114\pi$
$199$	824.000	0.293527	0.146763	+	0.989172i	$0.453114\pi$
$200$	0	0
$201$	−2512.00	−0.881507
$202$	0	0
$203$	−132.000	−0.0456383
$204$	2112.00	0.724851
$205$	0	0
$206$	0	0
$207$	−330.000	−0.110805
$208$	−512.000	−0.170677
$209$	−228.000	−0.0754598
$210$	0	0
$211$	4244.00	1.38469	0.692344	−	0.721568i	$-0.256578\pi$
$211$	4244.00	1.38469	0.692344	+	0.721568i	$0.256578\pi$
$212$	3168.00	1.02632
$213$	3936.00	1.26615
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−1408.00	−0.440467
$218$	0	0
$219$	56.0000	0.0172791
$220$	0	0
$221$	−528.000	−0.160711
$222$	0	0
$223$	−5480.00	−1.64560	−0.822798	−	0.568334i	$-0.807588\pi$
$223$	−5480.00	−1.64560	−0.822798	+	0.568334i	$0.807588\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−5544.00	−1.62101	−0.810503	−	0.585735i	$-0.800806\pi$
$227$	−5544.00	−1.62101	−0.810503	+	0.585735i	$0.800806\pi$
$228$	608.000	0.176604
$229$	2930.00	0.845502	0.422751	−	0.906246i	$-0.361065\pi$
$229$	2930.00	0.845502	0.422751	+	0.906246i	$0.361065\pi$
$230$	0	0
$231$	1056.00	0.300778
$232$	0	0
$233$	4398.00	1.23658	0.618289	−	0.785951i	$-0.287826\pi$
$233$	4398.00	1.23658	0.618289	+	0.785951i	$0.287826\pi$
$234$	0	0
$235$	0	0
$236$	4512.00	1.24452
$237$	1312.00	0.359593
$238$	0	0
$239$	−6480.00	−1.75379	−0.876896	−	0.480680i	$-0.840390\pi$
$239$	−6480.00	−1.75379	−0.876896	+	0.480680i	$0.840390\pi$
$240$	0	0
$241$	−5770.00	−1.54223	−0.771117	−	0.636694i	$-0.780302\pi$
$241$	−5770.00	−1.54223	−0.771117	+	0.636694i	$0.780302\pi$
$242$	0	0
$243$	−2860.00	−0.755017
$244$	5648.00	1.48187
$245$	0	0
$246$	0	0
$247$	−152.000	−0.0391560
$248$	0	0
$249$	−1176.00	−0.299301
$250$	0	0
$251$	−624.000	−0.156918	−0.0784592	−	0.996917i	$-0.525000\pi$
$251$	−624.000	−0.156918	−0.0784592	+	0.996917i	$0.525000\pi$
$252$	1936.00	0.483955
$253$	−360.000	−0.0894585
$254$	0	0
$255$	0	0
$256$	4096.00	1.00000
$257$	−120.000	−0.0291260	−0.0145630	−	0.999894i	$-0.504636\pi$
$257$	−120.000	−0.0291260	−0.0145630	+	0.999894i	$0.504636\pi$
$258$	0	0
$259$	352.000	0.0844487
$260$	0	0
$261$	66.0000	0.0156525
$262$	0	0
$263$	−1842.00	−0.431873	−0.215936	−	0.976407i	$-0.569280\pi$
$263$	−1842.00	−0.431873	−0.215936	+	0.976407i	$0.569280\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−3672.00	−0.841658
$268$	−5024.00	−1.14511
$269$	−3234.00	−0.733013	−0.366506	−	0.930416i	$-0.619446\pi$
$269$	−3234.00	−0.733013	−0.366506	+	0.930416i	$0.619446\pi$
$270$	0	0
$271$	4664.00	1.04545	0.522727	−	0.852500i	$-0.324915\pi$
$271$	4664.00	1.04545	0.522727	+	0.852500i	$0.324915\pi$
$272$	4224.00	0.941609
$273$	704.000	0.156073
$274$	0	0
$275$	0	0
$276$	960.000	0.209367
$277$	−5222.00	−1.13271	−0.566353	−	0.824163i	$-0.691646\pi$
$277$	−5222.00	−1.13271	−0.566353	+	0.824163i	$0.691646\pi$
$278$	0	0
$279$	704.000	0.151066
$280$	0	0
$281$	7566.00	1.60623	0.803113	−	0.595826i	$-0.203175\pi$
$281$	7566.00	1.60623	0.803113	+	0.595826i	$0.203175\pi$
$282$	0	0
$283$	5614.00	1.17921	0.589607	−	0.807690i	$-0.299283\pi$
$283$	5614.00	1.17921	0.589607	+	0.807690i	$0.299283\pi$
$284$	7872.00	1.64478
$285$	0	0
$286$	0	0
$287$	1188.00	0.244339
$288$	0	0
$289$	−557.000	−0.113373
$290$	0	0
$291$	−6256.00	−1.26025
$292$	112.000	0.0224462
$293$	−924.000	−0.184234	−0.0921172	−	0.995748i	$-0.529363\pi$
$293$	−924.000	−0.184234	−0.0921172	+	0.995748i	$0.529363\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1824.00	−0.356361
$298$	0	0
$299$	−240.000	−0.0464199
$300$	0	0
$301$	−4004.00	−0.766733
$302$	0	0
$303$	1176.00	0.222968
$304$	1216.00	0.229416
$305$	0	0
$306$	0	0
$307$	4480.00	0.832857	0.416429	−	0.909168i	$-0.363282\pi$
$307$	4480.00	0.832857	0.416429	+	0.909168i	$0.363282\pi$
$308$	2112.00	0.390722
$309$	3008.00	0.553784
$310$	0	0
$311$	1272.00	0.231924	0.115962	−	0.993254i	$-0.463005\pi$
$311$	1272.00	0.231924	0.115962	+	0.993254i	$0.463005\pi$
$312$	0	0
$313$	−1370.00	−0.247402	−0.123701	−	0.992320i	$-0.539476\pi$
$313$	−1370.00	−0.247402	−0.123701	+	0.992320i	$0.539476\pi$
$314$	0	0
$315$	0	0
$316$	2624.00	0.467125
$317$	−3552.00	−0.629338	−0.314669	−	0.949201i	$-0.601894\pi$
$317$	−3552.00	−0.629338	−0.314669	+	0.949201i	$0.601894\pi$
$318$	0	0
$319$	72.0000	0.0126371
$320$	0	0
$321$	−864.000	−0.150230
$322$	0	0
$323$	1254.00	0.216020
$324$	2488.00	0.426612
$325$	0	0
$326$	0	0
$327$	3016.00	0.510046
$328$	0	0
$329$	−13068.0	−2.18985
$330$	0	0
$331$	4532.00	0.752572	0.376286	−	0.926504i	$-0.377201\pi$
$331$	4532.00	0.752572	0.376286	+	0.926504i	$0.377201\pi$
$332$	−2352.00	−0.388804
$333$	−176.000	−0.0289632
$334$	0	0
$335$	0	0
$336$	−5632.00	−0.914437
$337$	10036.0	1.62224	0.811121	−	0.584878i	$-0.198858\pi$
$337$	10036.0	1.62224	0.811121	+	0.584878i	$0.198858\pi$
$338$	0	0
$339$	−48.0000	−0.00769027
$340$	0	0
$341$	768.000	0.121963
$342$	0	0
$343$	−4444.00	−0.699573
$344$	0	0
$345$	0	0
$346$	0	0
$347$	2178.00	0.336949	0.168474	−	0.985706i	$-0.446116\pi$
$347$	2178.00	0.336949	0.168474	+	0.985706i	$0.446116\pi$
$348$	−192.000	−0.0295755
$349$	−10042.0	−1.54022	−0.770109	−	0.637913i	$-0.779798\pi$
$349$	−10042.0	−1.54022	−0.770109	+	0.637913i	$0.779798\pi$
$350$	0	0
$351$	−1216.00	−0.184915
$352$	0	0
$353$	−6102.00	−0.920047	−0.460024	−	0.887907i	$-0.652159\pi$
$353$	−6102.00	−0.920047	−0.460024	+	0.887907i	$0.652159\pi$
$354$	0	0
$355$	0	0
$356$	−7344.00	−1.09335
$357$	−5808.00	−0.861042
$358$	0	0
$359$	−1140.00	−0.167596	−0.0837979	−	0.996483i	$-0.526705\pi$
$359$	−1140.00	−0.167596	−0.0837979	+	0.996483i	$0.526705\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	0	0
$363$	4748.00	0.686516
$364$	1408.00	0.202745
$365$	0	0
$366$	0	0
$367$	5614.00	0.798497	0.399249	−	0.916843i	$-0.369271\pi$
$367$	5614.00	0.798497	0.399249	+	0.916843i	$0.369271\pi$
$368$	1920.00	0.271975
$369$	−594.000	−0.0838006
$370$	0	0
$371$	−8712.00	−1.21915
$372$	−2048.00	−0.285440
$373$	3652.00	0.506953	0.253476	−	0.967342i	$-0.418426\pi$
$373$	3652.00	0.506953	0.253476	+	0.967342i	$0.418426\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	48.0000	0.00655736
$378$	0	0
$379$	−316.000	−0.0428280	−0.0214140	−	0.999771i	$-0.506817\pi$
$379$	−316.000	−0.0428280	−0.0214140	+	0.999771i	$0.506817\pi$
$380$	0	0
$381$	1376.00	0.185025
$382$	0	0
$383$	8844.00	1.17991	0.589957	−	0.807434i	$-0.299145\pi$
$383$	8844.00	1.17991	0.589957	+	0.807434i	$0.299145\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	2002.00	0.262965
$388$	−12512.0	−1.63711
$389$	−7230.00	−0.942354	−0.471177	−	0.882039i	$-0.656171\pi$
$389$	−7230.00	−0.942354	−0.471177	+	0.882039i	$0.656171\pi$
$390$	0	0
$391$	1980.00	0.256094
$392$	0	0
$393$	−10080.0	−1.29381
$394$	0	0
$395$	0	0
$396$	−1056.00	−0.134005
$397$	−3446.00	−0.435642	−0.217821	−	0.975989i	$-0.569895\pi$
$397$	−3446.00	−0.435642	−0.217821	+	0.975989i	$0.569895\pi$
$398$	0	0
$399$	−1672.00	−0.209786
$400$	0	0
$401$	−14478.0	−1.80298	−0.901492	−	0.432795i	$-0.857527\pi$
$401$	−14478.0	−1.80298	−0.901492	+	0.432795i	$0.857527\pi$
$402$	0	0
$403$	512.000	0.0632867
$404$	2352.00	0.289644
$405$	0	0
$406$	0	0
$407$	−192.000	−0.0233835
$408$	0	0
$409$	9074.00	1.09702	0.548509	−	0.836145i	$-0.315196\pi$
$409$	9074.00	1.09702	0.548509	+	0.836145i	$0.315196\pi$
$410$	0	0
$411$	2616.00	0.313960
$412$	6016.00	0.719386
$413$	−12408.0	−1.47835
$414$	0	0
$415$	0	0
$416$	0	0
$417$	9568.00	1.12361
$418$	0	0
$419$	−7068.00	−0.824092	−0.412046	−	0.911163i	$-0.635186\pi$
$419$	−7068.00	−0.824092	−0.412046	+	0.911163i	$0.635186\pi$
$420$	0	0
$421$	−7342.00	−0.849946	−0.424973	−	0.905206i	$-0.639716\pi$
$421$	−7342.00	−0.849946	−0.424973	+	0.905206i	$0.639716\pi$
$422$	0	0
$423$	6534.00	0.751050
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−15532.0	−1.76030
$428$	−1728.00	−0.195154
$429$	−384.000	−0.0432161
$430$	0	0
$431$	2976.00	0.332596	0.166298	−	0.986076i	$-0.446819\pi$
$431$	2976.00	0.332596	0.166298	+	0.986076i	$0.446819\pi$
$432$	9728.00	1.08342
$433$	−3476.00	−0.385787	−0.192894	−	0.981220i	$-0.561787\pi$
$433$	−3476.00	−0.385787	−0.192894	+	0.981220i	$0.561787\pi$
$434$	0	0
$435$	0	0
$436$	6032.00	0.662570
$437$	570.000	0.0623954
$438$	0	0
$439$	6200.00	0.674054	0.337027	−	0.941495i	$-0.390579\pi$
$439$	6200.00	0.674054	0.337027	+	0.941495i	$0.390579\pi$
$440$	0	0
$441$	−1551.00	−0.167477
$442$	0	0
$443$	−16026.0	−1.71878	−0.859389	−	0.511323i	$-0.829156\pi$
$443$	−16026.0	−1.71878	−0.859389	+	0.511323i	$0.829156\pi$
$444$	512.000	0.0547262
$445$	0	0
$446$	0	0
$447$	5064.00	0.535837
$448$	−11264.0	−1.18789
$449$	−1830.00	−0.192345	−0.0961726	−	0.995365i	$-0.530660\pi$
$449$	−1830.00	−0.192345	−0.0961726	+	0.995365i	$0.530660\pi$
$450$	0	0
$451$	−648.000	−0.0676566
$452$	−96.0000	−0.00998996
$453$	−12320.0	−1.27780
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−12986.0	−1.32923	−0.664616	−	0.747185i	$-0.731405\pi$
$457$	−12986.0	−1.32923	−0.664616	+	0.747185i	$0.731405\pi$
$458$	0	0
$459$	10032.0	1.02016
$460$	0	0
$461$	−10506.0	−1.06142	−0.530708	−	0.847554i	$-0.678074\pi$
$461$	−10506.0	−1.06142	−0.530708	+	0.847554i	$0.678074\pi$
$462$	0	0
$463$	−1562.00	−0.156787	−0.0783934	−	0.996923i	$-0.524979\pi$
$463$	−1562.00	−0.156787	−0.0783934	+	0.996923i	$0.524979\pi$
$464$	−384.000	−0.0384197
$465$	0	0
$466$	0	0
$467$	−6.00000	−0.000594533 0	−0.000297266	−	1.00000i	$-0.500095\pi$
$467$	−6.00000	−0.000594533 0	−0.000297266		1.00000i	$0.500095\pi$
$468$	−704.000	−0.0695351
$469$	13816.0	1.36026
$470$	0	0
$471$	7352.00	0.719241
$472$	0	0
$473$	2184.00	0.212305
$474$	0	0
$475$	0	0
$476$	−11616.0	−1.11853
$477$	4356.00	0.418129
$478$	0	0
$479$	3132.00	0.298757	0.149379	−	0.988780i	$-0.452273\pi$
$479$	3132.00	0.298757	0.149379	+	0.988780i	$0.452273\pi$
$480$	0	0
$481$	−128.000	−0.0121337
$482$	0	0
$483$	−2640.00	−0.248704
$484$	9496.00	0.891811
$485$	0	0
$486$	0	0
$487$	12436.0	1.15714	0.578572	−	0.815631i	$-0.303610\pi$
$487$	12436.0	1.15714	0.578572	+	0.815631i	$0.303610\pi$
$488$	0	0
$489$	−3400.00	−0.314424
$490$	0	0
$491$	−7848.00	−0.721335	−0.360667	−	0.932695i	$-0.617451\pi$
$491$	−7848.00	−0.721335	−0.360667	+	0.932695i	$0.617451\pi$
$492$	1728.00	0.158342
$493$	−396.000	−0.0361764
$494$	0	0
$495$	0	0
$496$	−4096.00	−0.370798
$497$	−21648.0	−1.95381
$498$	0	0
$499$	17720.0	1.58969	0.794846	−	0.606811i	$-0.207552\pi$
$499$	17720.0	1.58969	0.794846	+	0.606811i	$0.207552\pi$
$500$	0	0
$501$	15216.0	1.35689
$502$	0	0
$503$	5094.00	0.451551	0.225776	−	0.974179i	$-0.427508\pi$
$503$	5094.00	0.451551	0.225776	+	0.974179i	$0.427508\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	8532.00	0.747376
$508$	2752.00	0.240355
$509$	−5670.00	−0.493749	−0.246875	−	0.969047i	$-0.579404\pi$
$509$	−5670.00	−0.493749	−0.246875	+	0.969047i	$0.579404\pi$
$510$	0	0
$511$	−308.000	−0.0266636
$512$	0	0
$513$	2888.00	0.248554
$514$	0	0
$515$	0	0
$516$	−5824.00	−0.496875
$517$	7128.00	0.606362
$518$	0	0
$519$	−2256.00	−0.190804
$520$	0	0
$521$	−20670.0	−1.73814	−0.869068	−	0.494692i	$-0.835281\pi$
$521$	−20670.0	−1.73814	−0.869068	+	0.494692i	$0.835281\pi$
$522$	0	0
$523$	16816.0	1.40595	0.702975	−	0.711214i	$-0.251854\pi$
$523$	16816.0	1.40595	0.702975	+	0.711214i	$0.251854\pi$
$524$	−20160.0	−1.68071
$525$	0	0
$526$	0	0
$527$	−4224.00	−0.349147
$528$	3072.00	0.253204
$529$	−11267.0	−0.926029
$530$	0	0
$531$	6204.00	0.507026
$532$	−3344.00	−0.272520
$533$	−432.000	−0.0351069
$534$	0	0
$535$	0	0
$536$	0	0
$537$	7248.00	0.582447
$538$	0	0
$539$	−1692.00	−0.135213
$540$	0	0
$541$	9530.00	0.757351	0.378675	−	0.925530i	$-0.376380\pi$
$541$	9530.00	0.757351	0.378675	+	0.925530i	$0.376380\pi$
$542$	0	0
$543$	17992.0	1.42193
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−5264.00	−0.411467	−0.205733	−	0.978608i	$-0.565958\pi$
$547$	−5264.00	−0.411467	−0.205733	+	0.978608i	$0.565958\pi$
$548$	5232.00	0.407847
$549$	7766.00	0.603725
$550$	0	0
$551$	−114.000	−0.00881409
$552$	0	0
$553$	−7216.00	−0.554892
$554$	0	0
$555$	0	0
$556$	19136.0	1.45962
$557$	−16542.0	−1.25836	−0.629180	−	0.777259i	$-0.716609\pi$
$557$	−16542.0	−1.25836	−0.629180	+	0.777259i	$0.716609\pi$
$558$	0	0
$559$	1456.00	0.110165
$560$	0	0
$561$	3168.00	0.238419
$562$	0	0
$563$	5232.00	0.391656	0.195828	−	0.980638i	$-0.437261\pi$
$563$	5232.00	0.391656	0.195828	+	0.980638i	$0.437261\pi$
$564$	−19008.0	−1.41912
$565$	0	0
$566$	0	0
$567$	−6842.00	−0.506767
$568$	0	0
$569$	15114.0	1.11355	0.556777	−	0.830662i	$-0.312038\pi$
$569$	15114.0	1.11355	0.556777	+	0.830662i	$0.312038\pi$
$570$	0	0
$571$	−11764.0	−0.862186	−0.431093	−	0.902308i	$-0.641872\pi$
$571$	−11764.0	−0.862186	−0.431093	+	0.902308i	$0.641872\pi$
$572$	−768.000	−0.0561393
$573$	−14352.0	−1.04636
$574$	0	0
$575$	0	0
$576$	5632.00	0.407407
$577$	25198.0	1.81804	0.909018	−	0.416757i	$-0.136834\pi$
$577$	25198.0	1.81804	0.909018	+	0.416757i	$0.136834\pi$
$578$	0	0
$579$	−17968.0	−1.28968
$580$	0	0
$581$	6468.00	0.461855
$582$	0	0
$583$	4752.00	0.337578
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−20190.0	−1.41964	−0.709822	−	0.704382i	$-0.751224\pi$
$587$	−20190.0	−1.41964	−0.709822	+	0.704382i	$0.751224\pi$
$588$	4512.00	0.316449
$589$	−1216.00	−0.0850669
$590$	0	0
$591$	9864.00	0.686549
$592$	1024.00	0.0710915
$593$	2886.00	0.199855	0.0999273	−	0.994995i	$-0.468139\pi$
$593$	2886.00	0.199855	0.0999273	+	0.994995i	$0.468139\pi$
$594$	0	0
$595$	0	0
$596$	10128.0	0.696072
$597$	−3296.00	−0.225957
$598$	0	0
$599$	−4464.00	−0.304498	−0.152249	−	0.988342i	$-0.548652\pi$
$599$	−4464.00	−0.304498	−0.152249	+	0.988342i	$0.548652\pi$
$600$	0	0
$601$	−15874.0	−1.07739	−0.538697	−	0.842499i	$-0.681083\pi$
$601$	−15874.0	−1.07739	−0.538697	+	0.842499i	$0.681083\pi$
$602$	0	0
$603$	−6908.00	−0.466527
$604$	−24640.0	−1.65991
$605$	0	0
$606$	0	0
$607$	18916.0	1.26487	0.632436	−	0.774613i	$-0.282055\pi$
$607$	18916.0	1.26487	0.632436	+	0.774613i	$0.282055\pi$
$608$	0	0
$609$	528.000	0.0351324
$610$	0	0
$611$	4752.00	0.314640
$612$	5808.00	0.383618
$613$	3058.00	0.201487	0.100743	−	0.994912i	$-0.467878\pi$
$613$	3058.00	0.201487	0.100743	+	0.994912i	$0.467878\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−4158.00	−0.271304	−0.135652	−	0.990757i	$-0.543313\pi$
$617$	−4158.00	−0.271304	−0.135652	+	0.990757i	$0.543313\pi$
$618$	0	0
$619$	−22864.0	−1.48462	−0.742312	−	0.670055i	$-0.766271\pi$
$619$	−22864.0	−1.48462	−0.742312	+	0.670055i	$0.766271\pi$
$620$	0	0
$621$	4560.00	0.294664
$622$	0	0
$623$	20196.0	1.29877
$624$	2048.00	0.131387
$625$	0	0
$626$	0	0
$627$	912.000	0.0580890
$628$	14704.0	0.934321
$629$	1056.00	0.0669403
$630$	0	0
$631$	18536.0	1.16942	0.584712	−	0.811241i	$-0.301208\pi$
$631$	18536.0	1.16942	0.584712	+	0.811241i	$0.301208\pi$
$632$	0	0
$633$	−16976.0	−1.06593
$634$	0	0
$635$	0	0
$636$	−12672.0	−0.790059
$637$	−1128.00	−0.0701617
$638$	0	0
$639$	10824.0	0.670095
$640$	0	0
$641$	15630.0	0.963101	0.481551	−	0.876418i	$-0.340074\pi$
$641$	15630.0	0.963101	0.481551	+	0.876418i	$0.340074\pi$
$642$	0	0
$643$	27574.0	1.69115	0.845577	−	0.533853i	$-0.179256\pi$
$643$	27574.0	1.69115	0.845577	+	0.533853i	$0.179256\pi$
$644$	−5280.00	−0.323076
$645$	0	0
$646$	0	0
$647$	8826.00	0.536300	0.268150	−	0.963377i	$-0.413588\pi$
$647$	8826.00	0.536300	0.268150	+	0.963377i	$0.413588\pi$
$648$	0	0
$649$	6768.00	0.409349
$650$	0	0
$651$	5632.00	0.339071
$652$	−6800.00	−0.408449
$653$	−18678.0	−1.11934	−0.559668	−	0.828717i	$-0.689071\pi$
$653$	−18678.0	−1.11934	−0.559668	+	0.828717i	$0.689071\pi$
$654$	0	0
$655$	0	0
$656$	3456.00	0.205692
$657$	154.000	0.00914477
$658$	0	0
$659$	16980.0	1.00371	0.501857	−	0.864951i	$-0.332651\pi$
$659$	16980.0	1.00371	0.501857	+	0.864951i	$0.332651\pi$
$660$	0	0
$661$	−9358.00	−0.550657	−0.275328	−	0.961350i	$-0.588787\pi$
$661$	−9358.00	−0.550657	−0.275328	+	0.961350i	$0.588787\pi$
$662$	0	0
$663$	2112.00	0.123715
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−180.000	−0.0104492
$668$	30432.0	1.76265
$669$	21920.0	1.26678
$670$	0	0
$671$	8472.00	0.487419
$672$	0	0
$673$	16120.0	0.923299	0.461650	−	0.887062i	$-0.347258\pi$
$673$	16120.0	0.923299	0.461650	+	0.887062i	$0.347258\pi$
$674$	0	0
$675$	0	0
$676$	17064.0	0.970869
$677$	−27876.0	−1.58251	−0.791257	−	0.611484i	$-0.790573\pi$
$677$	−27876.0	−1.58251	−0.791257	+	0.611484i	$0.790573\pi$
$678$	0	0
$679$	34408.0	1.94471
$680$	0	0
$681$	22176.0	1.24785
$682$	0	0
$683$	4872.00	0.272946	0.136473	−	0.990644i	$-0.456423\pi$
$683$	4872.00	0.272946	0.136473	+	0.990644i	$0.456423\pi$
$684$	1672.00	0.0934657
$685$	0	0
$686$	0	0
$687$	−11720.0	−0.650867
$688$	−11648.0	−0.645459
$689$	3168.00	0.175169
$690$	0	0
$691$	13412.0	0.738374	0.369187	−	0.929355i	$-0.379636\pi$
$691$	13412.0	0.738374	0.369187	+	0.929355i	$0.379636\pi$
$692$	−4512.00	−0.247862
$693$	2904.00	0.159183
$694$	0	0
$695$	0	0
$696$	0	0
$697$	3564.00	0.193682
$698$	0	0
$699$	−17592.0	−0.951918
$700$	0	0
$701$	1926.00	0.103772	0.0518859	−	0.998653i	$-0.483477\pi$
$701$	1926.00	0.103772	0.0518859	+	0.998653i	$0.483477\pi$
$702$	0	0
$703$	304.000	0.0163095
$704$	6144.00	0.328921
$705$	0	0
$706$	0	0
$707$	−6468.00	−0.344065
$708$	−18048.0	−0.958030
$709$	17534.0	0.928777	0.464389	−	0.885631i	$-0.346274\pi$
$709$	17534.0	0.928777	0.464389	+	0.885631i	$0.346274\pi$
$710$	0	0
$711$	3608.00	0.190310
$712$	0	0
$713$	−1920.00	−0.100848
$714$	0	0
$715$	0	0
$716$	14496.0	0.756621
$717$	25920.0	1.35007
$718$	0	0
$719$	−11220.0	−0.581969	−0.290984	−	0.956728i	$-0.593983\pi$
$719$	−11220.0	−0.581969	−0.290984	+	0.956728i	$0.593983\pi$
$720$	0	0
$721$	−16544.0	−0.854550
$722$	0	0
$723$	23080.0	1.18721
$724$	35984.0	1.84715
$725$	0	0
$726$	0	0
$727$	25078.0	1.27936	0.639678	−	0.768643i	$-0.279068\pi$
$727$	25078.0	1.27936	0.639678	+	0.768643i	$0.279068\pi$
$728$	0	0
$729$	19837.0	1.00782
$730$	0	0
$731$	−12012.0	−0.607770
$732$	−22592.0	−1.14074
$733$	−434.000	−0.0218692	−0.0109346	−	0.999940i	$-0.503481\pi$
$733$	−434.000	−0.0218692	−0.0109346	+	0.999940i	$0.503481\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−7536.00	−0.376651
$738$	0	0
$739$	2564.00	0.127630	0.0638148	−	0.997962i	$-0.479673\pi$
$739$	2564.00	0.127630	0.0638148	+	0.997962i	$0.479673\pi$
$740$	0	0
$741$	608.000	0.0301423
$742$	0	0
$743$	−21948.0	−1.08371	−0.541853	−	0.840473i	$-0.682277\pi$
$743$	−21948.0	−1.08371	−0.541853	+	0.840473i	$0.682277\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−3234.00	−0.158401
$748$	6336.00	0.309715
$749$	4752.00	0.231821
$750$	0	0
$751$	−7648.00	−0.371610	−0.185805	−	0.982587i	$-0.559489\pi$
$751$	−7648.00	−0.371610	−0.185805	+	0.982587i	$0.559489\pi$
$752$	−38016.0	−1.84349
$753$	2496.00	0.120796
$754$	0	0
$755$	0	0
$756$	−26752.0	−1.28699
$757$	30190.0	1.44950	0.724752	−	0.689010i	$-0.241954\pi$
$757$	30190.0	1.44950	0.724752	+	0.689010i	$0.241954\pi$
$758$	0	0
$759$	1440.00	0.0688652
$760$	0	0
$761$	−1242.00	−0.0591622	−0.0295811	−	0.999562i	$-0.509417\pi$
$761$	−1242.00	−0.0591622	−0.0295811	+	0.999562i	$0.509417\pi$
$762$	0	0
$763$	−16588.0	−0.787059
$764$	−28704.0	−1.35926
$765$	0	0
$766$	0	0
$767$	4512.00	0.212411
$768$	−16384.0	−0.769800
$769$	−28738.0	−1.34762	−0.673809	−	0.738905i	$-0.735343\pi$
$769$	−28738.0	−1.34762	−0.673809	+	0.738905i	$0.735343\pi$
$770$	0	0
$771$	480.000	0.0224212
$772$	−35936.0	−1.67534
$773$	40128.0	1.86715	0.933573	−	0.358387i	$-0.116673\pi$
$773$	40128.0	1.86715	0.933573	+	0.358387i	$0.116673\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−1408.00	−0.0650086
$778$	0	0
$779$	1026.00	0.0471890
$780$	0	0
$781$	11808.0	0.541003
$782$	0	0
$783$	−912.000	−0.0416248
$784$	9024.00	0.411079
$785$	0	0
$786$	0	0
$787$	15448.0	0.699697	0.349849	−	0.936806i	$-0.386233\pi$
$787$	15448.0	0.699697	0.349849	+	0.936806i	$0.386233\pi$
$788$	19728.0	0.891854
$789$	7368.00	0.332456
$790$	0	0
$791$	264.000	0.0118670
$792$	0	0
$793$	5648.00	0.252921
$794$	0	0
$795$	0	0
$796$	−6592.00	−0.293527
$797$	27324.0	1.21439	0.607193	−	0.794554i	$-0.292295\pi$
$797$	27324.0	1.21439	0.607193	+	0.794554i	$0.292295\pi$
$798$	0	0
$799$	−39204.0	−1.73584
$800$	0	0
$801$	−10098.0	−0.445437
$802$	0	0
$803$	168.000	0.00738305
$804$	20096.0	0.881507
$805$	0	0
$806$	0	0
$807$	12936.0	0.564274
$808$	0	0
$809$	−17766.0	−0.772088	−0.386044	−	0.922480i	$-0.626159\pi$
$809$	−17766.0	−0.772088	−0.386044	+	0.922480i	$0.626159\pi$
$810$	0	0
$811$	−7396.00	−0.320233	−0.160116	−	0.987098i	$-0.551187\pi$
$811$	−7396.00	−0.320233	−0.160116	+	0.987098i	$0.551187\pi$
$812$	1056.00	0.0456383
$813$	−18656.0	−0.804790
$814$	0	0
$815$	0	0
$816$	−16896.0	−0.724851
$817$	−3458.00	−0.148078
$818$	0	0
$819$	1936.00	0.0825999
$820$	0	0
$821$	26898.0	1.14342	0.571709	−	0.820456i	$-0.306281\pi$
$821$	26898.0	1.14342	0.571709	+	0.820456i	$0.306281\pi$
$822$	0	0
$823$	24442.0	1.03523	0.517615	−	0.855614i	$-0.326820\pi$
$823$	24442.0	1.03523	0.517615	+	0.855614i	$0.326820\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−13524.0	−0.568652	−0.284326	−	0.958728i	$-0.591770\pi$
$827$	−13524.0	−0.568652	−0.284326	+	0.958728i	$0.591770\pi$
$828$	2640.00	0.110805
$829$	−7714.00	−0.323183	−0.161591	−	0.986858i	$-0.551663\pi$
$829$	−7714.00	−0.323183	−0.161591	+	0.986858i	$0.551663\pi$
$830$	0	0
$831$	20888.0	0.871958
$832$	4096.00	0.170677
$833$	9306.00	0.387075
$834$	0	0
$835$	0	0
$836$	1824.00	0.0754598
$837$	−9728.00	−0.401731
$838$	0	0
$839$	−16248.0	−0.668586	−0.334293	−	0.942469i	$-0.608497\pi$
$839$	−16248.0	−0.668586	−0.334293	+	0.942469i	$0.608497\pi$
$840$	0	0
$841$	−24353.0	−0.998524
$842$	0	0
$843$	−30264.0	−1.23647
$844$	−33952.0	−1.38469
$845$	0	0
$846$	0	0
$847$	−26114.0	−1.05937
$848$	−25344.0	−1.02632
$849$	−22456.0	−0.907760
$850$	0	0
$851$	480.000	0.0193351
$852$	−31488.0	−1.26615
$853$	−35498.0	−1.42489	−0.712443	−	0.701730i	$-0.752411\pi$
$853$	−35498.0	−1.42489	−0.712443	+	0.701730i	$0.752411\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	40344.0	1.60808	0.804040	−	0.594575i	$-0.202680\pi$
$857$	40344.0	1.60808	0.804040	+	0.594575i	$0.202680\pi$
$858$	0	0
$859$	31484.0	1.25055	0.625274	−	0.780406i	$-0.284987\pi$
$859$	31484.0	1.25055	0.625274	+	0.780406i	$0.284987\pi$
$860$	0	0
$861$	−4752.00	−0.188093
$862$	0	0
$863$	28836.0	1.13741	0.568707	−	0.822540i	$-0.307444\pi$
$863$	28836.0	1.13741	0.568707	+	0.822540i	$0.307444\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	2228.00	0.0872743
$868$	11264.0	0.440467
$869$	3936.00	0.153647
$870$	0	0
$871$	−5024.00	−0.195444
$872$	0	0
$873$	−17204.0	−0.666973
$874$	0	0
$875$	0	0
$876$	−448.000	−0.0172791
$877$	−22796.0	−0.877727	−0.438863	−	0.898554i	$-0.644619\pi$
$877$	−22796.0	−0.877727	−0.438863	+	0.898554i	$0.644619\pi$
$878$	0	0
$879$	3696.00	0.141824
$880$	0	0
$881$	−18822.0	−0.719784	−0.359892	−	0.932994i	$-0.617186\pi$
$881$	−18822.0	−0.719784	−0.359892	+	0.932994i	$0.617186\pi$
$882$	0	0
$883$	−7526.00	−0.286829	−0.143415	−	0.989663i	$-0.545808\pi$
$883$	−7526.00	−0.286829	−0.143415	+	0.989663i	$0.545808\pi$
$884$	4224.00	0.160711
$885$	0	0
$886$	0	0
$887$	−33816.0	−1.28008	−0.640040	−	0.768342i	$-0.721082\pi$
$887$	−33816.0	−1.28008	−0.640040	+	0.768342i	$0.721082\pi$
$888$	0	0
$889$	−7568.00	−0.285515
$890$	0	0
$891$	3732.00	0.140322
$892$	43840.0	1.64560
$893$	−11286.0	−0.422925
$894$	0	0
$895$	0	0
$896$	0	0
$897$	960.000	0.0357341
$898$	0	0
$899$	384.000	0.0142460
$900$	0	0
$901$	−26136.0	−0.966389
$902$	0	0
$903$	16016.0	0.590232
$904$	0	0
$905$	0	0
$906$	0	0
$907$	33784.0	1.23680	0.618401	−	0.785863i	$-0.287781\pi$
$907$	33784.0	1.23680	0.618401	+	0.785863i	$0.287781\pi$
$908$	44352.0	1.62101
$909$	3234.00	0.118003
$910$	0	0
$911$	−15216.0	−0.553379	−0.276690	−	0.960959i	$-0.589237\pi$
$911$	−15216.0	−0.553379	−0.276690	+	0.960959i	$0.589237\pi$
$912$	−4864.00	−0.176604
$913$	−3528.00	−0.127886
$914$	0	0
$915$	0	0
$916$	−23440.0	−0.845502
$917$	55440.0	1.99650
$918$	0	0
$919$	19760.0	0.709273	0.354637	−	0.935004i	$-0.384605\pi$
$919$	19760.0	0.709273	0.354637	+	0.935004i	$0.384605\pi$
$920$	0	0
$921$	−17920.0	−0.641134
$922$	0	0
$923$	7872.00	0.280726
$924$	−8448.00	−0.300778
$925$	0	0
$926$	0	0
$927$	8272.00	0.293083
$928$	0	0
$929$	16278.0	0.574880	0.287440	−	0.957799i	$-0.407196\pi$
$929$	16278.0	0.574880	0.287440	+	0.957799i	$0.407196\pi$
$930$	0	0
$931$	2679.00	0.0943079
$932$	−35184.0	−1.23658
$933$	−5088.00	−0.178536
$934$	0	0
$935$	0	0
$936$	0	0
$937$	6994.00	0.243846	0.121923	−	0.992540i	$-0.461094\pi$
$937$	6994.00	0.243846	0.121923	+	0.992540i	$0.461094\pi$
$938$	0	0
$939$	5480.00	0.190451
$940$	0	0
$941$	32502.0	1.12597	0.562983	−	0.826468i	$-0.309653\pi$
$941$	32502.0	1.12597	0.562983	+	0.826468i	$0.309653\pi$
$942$	0	0
$943$	1620.00	0.0559432
$944$	−36096.0	−1.24452
$945$	0	0
$946$	0	0
$947$	−50358.0	−1.72800	−0.864000	−	0.503493i	$-0.832048\pi$
$947$	−50358.0	−1.72800	−0.864000	+	0.503493i	$0.832048\pi$
$948$	−10496.0	−0.359593
$949$	112.000	0.00383106
$950$	0	0
$951$	14208.0	0.484465
$952$	0	0
$953$	−39816.0	−1.35338	−0.676688	−	0.736270i	$-0.736585\pi$
$953$	−39816.0	−1.35338	−0.676688	+	0.736270i	$0.736585\pi$
$954$	0	0
$955$	0	0
$956$	51840.0	1.75379
$957$	−288.000	−0.00972802
$958$	0	0
$959$	−14388.0	−0.484476
$960$	0	0
$961$	−25695.0	−0.862509
$962$	0	0
$963$	−2376.00	−0.0795073
$964$	46160.0	1.54223
$965$	0	0
$966$	0	0
$967$	−590.000	−0.0196206	−0.00981030	−	0.999952i	$-0.503123\pi$
$967$	−590.000	−0.0196206	−0.00981030	+	0.999952i	$0.503123\pi$
$968$	0	0
$969$	−5016.00	−0.166292
$970$	0	0
$971$	26820.0	0.886400	0.443200	−	0.896423i	$-0.353843\pi$
$971$	26820.0	0.886400	0.443200	+	0.896423i	$0.353843\pi$
$972$	22880.0	0.755017
$973$	−52624.0	−1.73386
$974$	0	0
$975$	0	0
$976$	−45184.0	−1.48187
$977$	33312.0	1.09083	0.545417	−	0.838165i	$-0.316371\pi$
$977$	33312.0	1.09083	0.545417	+	0.838165i	$0.316371\pi$
$978$	0	0
$979$	−11016.0	−0.359625
$980$	0	0
$981$	8294.00	0.269936
$982$	0	0
$983$	−612.000	−0.0198573	−0.00992867	−	0.999951i	$-0.503160\pi$
$983$	−612.000	−0.0198573	−0.00992867	+	0.999951i	$0.503160\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	52272.0	1.68575
$988$	1216.00	0.0391560
$989$	−5460.00	−0.175549
$990$	0	0
$991$	39416.0	1.26346	0.631731	−	0.775188i	$-0.282345\pi$
$991$	39416.0	1.26346	0.631731	+	0.775188i	$0.282345\pi$
$992$	0	0
$993$	−18128.0	−0.579330
$994$	0	0
$995$	0	0
$996$	9408.00	0.299301
$997$	−36614.0	−1.16307	−0.581533	−	0.813523i	$-0.697547\pi$
$997$	−36614.0	−1.16307	−0.581533	+	0.813523i	$0.697547\pi$
$998$	0	0
$999$	2432.00	0.0770221

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.4.a.d.1.1		1
5.2	odd	4		475.4.b.e.324.2		2
5.3	odd	4		475.4.b.e.324.1		2
5.4	even	2		95.4.a.a.1.1	✓	1
15.14	odd	2		855.4.a.e.1.1		1
20.19	odd	2		1520.4.a.b.1.1		1
95.94	odd	2		1805.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.a.a.1.1	✓	1	5.4	even	2
475.4.a.d.1.1		1	1.1	even	1	trivial
475.4.b.e.324.1		2	5.3	odd	4
475.4.b.e.324.2		2	5.2	odd	4
855.4.a.e.1.1		1	15.14	odd	2
1520.4.a.b.1.1		1	20.19	odd	2
1805.4.a.f.1.1		1	95.94	odd	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	475.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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