LMFDB - Embedded newform 525.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(1,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("525.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.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:	$30.9760027530$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	525.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{6} +7.00000 q^{7} +21.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-3.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +9.00000 q^{6} +7.00000 q^{7} +21.0000 q^{8} +9.00000 q^{9} -6.00000 q^{11} -3.00000 q^{12} +41.0000 q^{13} -21.0000 q^{14} -71.0000 q^{16} +27.0000 q^{17} -27.0000 q^{18} -4.00000 q^{19} -21.0000 q^{21} +18.0000 q^{22} +75.0000 q^{23} -63.0000 q^{24} -123.000 q^{26} -27.0000 q^{27} +7.00000 q^{28} -123.000 q^{29} -205.000 q^{31} +45.0000 q^{32} +18.0000 q^{33} -81.0000 q^{34} +9.00000 q^{36} -262.000 q^{37} +12.0000 q^{38} -123.000 q^{39} +57.0000 q^{41} +63.0000 q^{42} +407.000 q^{43} -6.00000 q^{44} -225.000 q^{46} -60.0000 q^{47} +213.000 q^{48} +49.0000 q^{49} -81.0000 q^{51} +41.0000 q^{52} +327.000 q^{53} +81.0000 q^{54} +147.000 q^{56} +12.0000 q^{57} +369.000 q^{58} +33.0000 q^{59} -427.000 q^{61} +615.000 q^{62} +63.0000 q^{63} +433.000 q^{64} -54.0000 q^{66} -628.000 q^{67} +27.0000 q^{68} -225.000 q^{69} +300.000 q^{71} +189.000 q^{72} +98.0000 q^{73} +786.000 q^{74} -4.00000 q^{76} -42.0000 q^{77} +369.000 q^{78} +686.000 q^{79} +81.0000 q^{81} -171.000 q^{82} +1401.00 q^{83} -21.0000 q^{84} -1221.00 q^{86} +369.000 q^{87} -126.000 q^{88} +714.000 q^{89} +287.000 q^{91} +75.0000 q^{92} +615.000 q^{93} +180.000 q^{94} -135.000 q^{96} +494.000 q^{97} -147.000 q^{98} -54.0000 q^{99} +O(q^{100})\)

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 $

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	9.00000	0.612372
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	21.0000	0.928078
$9$	9.00000	0.333333
$10$	0	0
$11$	−6.00000	−0.164461	−0.0822304	−	0.996613i	$-0.526204\pi$
$11$	−6.00000	−0.164461	−0.0822304	+	0.996613i	$0.526204\pi$
$12$	−3.00000	−0.0721688
$13$	41.0000	0.874720	0.437360	−	0.899287i	$-0.355914\pi$
$13$	41.0000	0.874720	0.437360	+	0.899287i	$0.355914\pi$
$14$	−21.0000	−0.400892
$15$	0	0
$16$	−71.0000	−1.10938
$17$	27.0000	0.385204	0.192602	−	0.981277i	$-0.438307\pi$
$17$	27.0000	0.385204	0.192602	+	0.981277i	$0.438307\pi$
$18$	−27.0000	−0.353553
$19$	−4.00000	−0.0482980	−0.0241490	−	0.999708i	$-0.507688\pi$
$19$	−4.00000	−0.0482980	−0.0241490	+	0.999708i	$0.507688\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	18.0000	0.174437
$23$	75.0000	0.679938	0.339969	−	0.940437i	$-0.389583\pi$
$23$	75.0000	0.679938	0.339969	+	0.940437i	$0.389583\pi$
$24$	−63.0000	−0.535826
$25$	0	0
$26$	−123.000	−0.927780
$27$	−27.0000	−0.192450
$28$	7.00000	0.0472456
$29$	−123.000	−0.787604	−0.393802	−	0.919195i	$-0.628841\pi$
$29$	−123.000	−0.787604	−0.393802	+	0.919195i	$0.628841\pi$
$30$	0	0
$31$	−205.000	−1.18771	−0.593856	−	0.804571i	$-0.702395\pi$
$31$	−205.000	−1.18771	−0.593856	+	0.804571i	$0.702395\pi$
$32$	45.0000	0.248592
$33$	18.0000	0.0949514
$34$	−81.0000	−0.408570
$35$	0	0
$36$	9.00000	0.0416667
$37$	−262.000	−1.16412	−0.582061	−	0.813145i	$-0.697754\pi$
$37$	−262.000	−1.16412	−0.582061	+	0.813145i	$0.697754\pi$
$38$	12.0000	0.0512278
$39$	−123.000	−0.505020
$40$	0	0
$41$	57.0000	0.217120	0.108560	−	0.994090i	$-0.465376\pi$
$41$	57.0000	0.217120	0.108560	+	0.994090i	$0.465376\pi$
$42$	63.0000	0.231455
$43$	407.000	1.44342	0.721708	−	0.692197i	$-0.243357\pi$
$43$	407.000	1.44342	0.721708	+	0.692197i	$0.243357\pi$
$44$	−6.00000	−0.0205576
$45$	0	0
$46$	−225.000	−0.721183
$47$	−60.0000	−0.186211	−0.0931053	−	0.995656i	$-0.529679\pi$
$47$	−60.0000	−0.186211	−0.0931053	+	0.995656i	$0.529679\pi$
$48$	213.000	0.640498
$49$	49.0000	0.142857
$50$	0	0
$51$	−81.0000	−0.222397
$52$	41.0000	0.109340
$53$	327.000	0.847489	0.423744	−	0.905782i	$-0.360715\pi$
$53$	327.000	0.847489	0.423744	+	0.905782i	$0.360715\pi$
$54$	81.0000	0.204124
$55$	0	0
$56$	147.000	0.350780
$57$	12.0000	0.0278849
$58$	369.000	0.835381
$59$	33.0000	0.0728175	0.0364088	−	0.999337i	$-0.488408\pi$
$59$	33.0000	0.0728175	0.0364088	+	0.999337i	$0.488408\pi$
$60$	0	0
$61$	−427.000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−427.000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	615.000	1.25976
$63$	63.0000	0.125988
$64$	433.000	0.845703
$65$	0	0
$66$	−54.0000	−0.100711
$67$	−628.000	−1.14511	−0.572555	−	0.819866i	$-0.694048\pi$
$67$	−628.000	−1.14511	−0.572555	+	0.819866i	$0.694048\pi$
$68$	27.0000	0.0481505
$69$	−225.000	−0.392563
$70$	0	0
$71$	300.000	0.501457	0.250729	−	0.968057i	$-0.419330\pi$
$71$	300.000	0.501457	0.250729	+	0.968057i	$0.419330\pi$
$72$	189.000	0.309359
$73$	98.0000	0.157124	0.0785619	−	0.996909i	$-0.474967\pi$
$73$	98.0000	0.157124	0.0785619	+	0.996909i	$0.474967\pi$
$74$	786.000	1.23474
$75$	0	0
$76$	−4.00000	−0.00603726
$77$	−42.0000	−0.0621603
$78$	369.000	0.535654
$79$	686.000	0.976975	0.488488	−	0.872571i	$-0.337549\pi$
$79$	686.000	0.976975	0.488488	+	0.872571i	$0.337549\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−171.000	−0.230290
$83$	1401.00	1.85277	0.926384	−	0.376580i	$-0.122900\pi$
$83$	1401.00	1.85277	0.926384	+	0.376580i	$0.122900\pi$
$84$	−21.0000	−0.0272772
$85$	0	0
$86$	−1221.00	−1.53097
$87$	369.000	0.454724
$88$	−126.000	−0.152632
$89$	714.000	0.850380	0.425190	−	0.905104i	$-0.360207\pi$
$89$	714.000	0.850380	0.425190	+	0.905104i	$0.360207\pi$
$90$	0	0
$91$	287.000	0.330613
$92$	75.0000	0.0849923
$93$	615.000	0.685726
$94$	180.000	0.197506
$95$	0	0
$96$	−135.000	−0.143525
$97$	494.000	0.517094	0.258547	−	0.965999i	$-0.416756\pi$
$97$	494.000	0.517094	0.258547	+	0.965999i	$0.416756\pi$
$98$	−147.000	−0.151523
$99$	−54.0000	−0.0548202
$100$	0	0
$101$	624.000	0.614756	0.307378	−	0.951588i	$-0.400548\pi$
$101$	624.000	0.614756	0.307378	+	0.951588i	$0.400548\pi$
$102$	243.000	0.235888
$103$	−769.000	−0.735649	−0.367824	−	0.929895i	$-0.619897\pi$
$103$	−769.000	−0.735649	−0.367824	+	0.929895i	$0.619897\pi$
$104$	861.000	0.811808
$105$	0	0
$106$	−981.000	−0.898898
$107$	1662.00	1.50160	0.750802	−	0.660527i	$-0.229667\pi$
$107$	1662.00	1.50160	0.750802	+	0.660527i	$0.229667\pi$
$108$	−27.0000	−0.0240563
$109$	188.000	0.165203	0.0826015	−	0.996583i	$-0.473677\pi$
$109$	188.000	0.165203	0.0826015	+	0.996583i	$0.473677\pi$
$110$	0	0
$111$	786.000	0.672106
$112$	−497.000	−0.419304
$113$	−18.0000	−0.0149849	−0.00749247	−	0.999972i	$-0.502385\pi$
$113$	−18.0000	−0.0149849	−0.00749247	+	0.999972i	$0.502385\pi$
$114$	−36.0000	−0.0295764
$115$	0	0
$116$	−123.000	−0.0984505
$117$	369.000	0.291573
$118$	−99.0000	−0.0772347
$119$	189.000	0.145593
$120$	0	0
$121$	−1295.00	−0.972953
$122$	1281.00	0.950625
$123$	−171.000	−0.125354
$124$	−205.000	−0.148464
$125$	0	0
$126$	−189.000	−0.133631
$127$	−1450.00	−1.01312	−0.506562	−	0.862204i	$-0.669084\pi$
$127$	−1450.00	−1.01312	−0.506562	+	0.862204i	$0.669084\pi$
$128$	−1659.00	−1.14560
$129$	−1221.00	−0.833357
$130$	0	0
$131$	2664.00	1.77675	0.888377	−	0.459115i	$-0.151833\pi$
$131$	2664.00	1.77675	0.888377	+	0.459115i	$0.151833\pi$
$132$	18.0000	0.0118689
$133$	−28.0000	−0.0182549
$134$	1884.00	1.21457
$135$	0	0
$136$	567.000	0.357499
$137$	1692.00	1.05516	0.527581	−	0.849504i	$-0.323099\pi$
$137$	1692.00	1.05516	0.527581	+	0.849504i	$0.323099\pi$
$138$	675.000	0.416375
$139$	1268.00	0.773744	0.386872	−	0.922134i	$-0.373556\pi$
$139$	1268.00	0.773744	0.386872	+	0.922134i	$0.373556\pi$
$140$	0	0
$141$	180.000	0.107509
$142$	−900.000	−0.531876
$143$	−246.000	−0.143857
$144$	−639.000	−0.369792
$145$	0	0
$146$	−294.000	−0.166655
$147$	−147.000	−0.0824786
$148$	−262.000	−0.145515
$149$	2169.00	1.19256	0.596280	−	0.802777i	$-0.296645\pi$
$149$	2169.00	1.19256	0.596280	+	0.802777i	$0.296645\pi$
$150$	0	0
$151$	518.000	0.279167	0.139584	−	0.990210i	$-0.455424\pi$
$151$	518.000	0.279167	0.139584	+	0.990210i	$0.455424\pi$
$152$	−84.0000	−0.0448243
$153$	243.000	0.128401
$154$	126.000	0.0659310
$155$	0	0
$156$	−123.000	−0.0631274
$157$	−886.000	−0.450385	−0.225193	−	0.974314i	$-0.572301\pi$
$157$	−886.000	−0.450385	−0.225193	+	0.974314i	$0.572301\pi$
$158$	−2058.00	−1.03624
$159$	−981.000	−0.489298
$160$	0	0
$161$	525.000	0.256993
$162$	−243.000	−0.117851
$163$	3893.00	1.87070	0.935348	−	0.353730i	$-0.115087\pi$
$163$	3893.00	1.87070	0.935348	+	0.353730i	$0.115087\pi$
$164$	57.0000	0.0271400
$165$	0	0
$166$	−4203.00	−1.96516
$167$	2046.00	0.948049	0.474025	−	0.880512i	$-0.342801\pi$
$167$	2046.00	0.948049	0.474025	+	0.880512i	$0.342801\pi$
$168$	−441.000	−0.202523
$169$	−516.000	−0.234866
$170$	0	0
$171$	−36.0000	−0.0160993
$172$	407.000	0.180427
$173$	−3540.00	−1.55573	−0.777865	−	0.628432i	$-0.783697\pi$
$173$	−3540.00	−1.55573	−0.777865	+	0.628432i	$0.783697\pi$
$174$	−1107.00	−0.482307
$175$	0	0
$176$	426.000	0.182449
$177$	−99.0000	−0.0420412
$178$	−2142.00	−0.901965
$179$	−3246.00	−1.35540	−0.677702	−	0.735336i	$-0.737024\pi$
$179$	−3246.00	−1.35540	−0.677702	+	0.735336i	$0.737024\pi$
$180$	0	0
$181$	1334.00	0.547820	0.273910	−	0.961755i	$-0.411683\pi$
$181$	1334.00	0.547820	0.273910	+	0.961755i	$0.411683\pi$
$182$	−861.000	−0.350668
$183$	1281.00	0.517455
$184$	1575.00	0.631036
$185$	0	0
$186$	−1845.00	−0.727322
$187$	−162.000	−0.0633509
$188$	−60.0000	−0.0232763
$189$	−189.000	−0.0727393
$190$	0	0
$191$	−873.000	−0.330723	−0.165361	−	0.986233i	$-0.552879\pi$
$191$	−873.000	−0.330723	−0.165361	+	0.986233i	$0.552879\pi$
$192$	−1299.00	−0.488267
$193$	−1006.00	−0.375199	−0.187600	−	0.982246i	$-0.560071\pi$
$193$	−1006.00	−0.375199	−0.187600	+	0.982246i	$0.560071\pi$
$194$	−1482.00	−0.548461
$195$	0	0
$196$	49.0000	0.0178571
$197$	591.000	0.213741	0.106871	−	0.994273i	$-0.465917\pi$
$197$	591.000	0.213741	0.106871	+	0.994273i	$0.465917\pi$
$198$	162.000	0.0581456
$199$	−2584.00	−0.920477	−0.460238	−	0.887795i	$-0.652236\pi$
$199$	−2584.00	−0.920477	−0.460238	+	0.887795i	$0.652236\pi$
$200$	0	0
$201$	1884.00	0.661130
$202$	−1872.00	−0.652047
$203$	−861.000	−0.297686
$204$	−81.0000	−0.0277997
$205$	0	0
$206$	2307.00	0.780273
$207$	675.000	0.226646
$208$	−2911.00	−0.970392
$209$	24.0000	0.00794313
$210$	0	0
$211$	−1441.00	−0.470154	−0.235077	−	0.971977i	$-0.575534\pi$
$211$	−1441.00	−0.470154	−0.235077	+	0.971977i	$0.575534\pi$
$212$	327.000	0.105936
$213$	−900.000	−0.289516
$214$	−4986.00	−1.59269
$215$	0	0
$216$	−567.000	−0.178609
$217$	−1435.00	−0.448913
$218$	−564.000	−0.175224
$219$	−294.000	−0.0907154
$220$	0	0
$221$	1107.00	0.336945
$222$	−2358.00	−0.712877
$223$	3827.00	1.14921	0.574607	−	0.818429i	$-0.305155\pi$
$223$	3827.00	1.14921	0.574607	+	0.818429i	$0.305155\pi$
$224$	315.000	0.0939590
$225$	0	0
$226$	54.0000	0.0158939
$227$	−5421.00	−1.58504	−0.792521	−	0.609845i	$-0.791232\pi$
$227$	−5421.00	−1.58504	−0.792521	+	0.609845i	$0.791232\pi$
$228$	12.0000	0.00348561
$229$	−5290.00	−1.52652	−0.763260	−	0.646092i	$-0.776402\pi$
$229$	−5290.00	−1.52652	−0.763260	+	0.646092i	$0.776402\pi$
$230$	0	0
$231$	126.000	0.0358883
$232$	−2583.00	−0.730958
$233$	4908.00	1.37997	0.689987	−	0.723822i	$-0.257616\pi$
$233$	4908.00	1.37997	0.689987	+	0.723822i	$0.257616\pi$
$234$	−1107.00	−0.309260
$235$	0	0
$236$	33.0000	0.00910219
$237$	−2058.00	−0.564057
$238$	−567.000	−0.154425
$239$	1056.00	0.285803	0.142902	−	0.989737i	$-0.454357\pi$
$239$	1056.00	0.285803	0.142902	+	0.989737i	$0.454357\pi$
$240$	0	0
$241$	5342.00	1.42784	0.713918	−	0.700229i	$-0.246919\pi$
$241$	5342.00	1.42784	0.713918	+	0.700229i	$0.246919\pi$
$242$	3885.00	1.03197
$243$	−243.000	−0.0641500
$244$	−427.000	−0.112032
$245$	0	0
$246$	513.000	0.132958
$247$	−164.000	−0.0422472
$248$	−4305.00	−1.10229
$249$	−4203.00	−1.06970
$250$	0	0
$251$	5805.00	1.45979	0.729897	−	0.683557i	$-0.239568\pi$
$251$	5805.00	1.45979	0.729897	+	0.683557i	$0.239568\pi$
$252$	63.0000	0.0157485
$253$	−450.000	−0.111823
$254$	4350.00	1.07458
$255$	0	0
$256$	1513.00	0.369385
$257$	543.000	0.131795	0.0658977	−	0.997826i	$-0.479009\pi$
$257$	543.000	0.131795	0.0658977	+	0.997826i	$0.479009\pi$
$258$	3663.00	0.883909
$259$	−1834.00	−0.439997
$260$	0	0
$261$	−1107.00	−0.262535
$262$	−7992.00	−1.88453
$263$	−5193.00	−1.21754	−0.608772	−	0.793345i	$-0.708338\pi$
$263$	−5193.00	−1.21754	−0.608772	+	0.793345i	$0.708338\pi$
$264$	378.000	0.0881223
$265$	0	0
$266$	84.0000	0.0193623
$267$	−2142.00	−0.490967
$268$	−628.000	−0.143139
$269$	2154.00	0.488222	0.244111	−	0.969747i	$-0.421504\pi$
$269$	2154.00	0.488222	0.244111	+	0.969747i	$0.421504\pi$
$270$	0	0
$271$	2396.00	0.537072	0.268536	−	0.963270i	$-0.413460\pi$
$271$	2396.00	0.537072	0.268536	+	0.963270i	$0.413460\pi$
$272$	−1917.00	−0.427335
$273$	−861.000	−0.190879
$274$	−5076.00	−1.11917
$275$	0	0
$276$	−225.000	−0.0490703
$277$	4286.00	0.929678	0.464839	−	0.885395i	$-0.346112\pi$
$277$	4286.00	0.929678	0.464839	+	0.885395i	$0.346112\pi$
$278$	−3804.00	−0.820679
$279$	−1845.00	−0.395904
$280$	0	0
$281$	2208.00	0.468748	0.234374	−	0.972146i	$-0.424696\pi$
$281$	2208.00	0.468748	0.234374	+	0.972146i	$0.424696\pi$
$282$	−540.000	−0.114030
$283$	3620.00	0.760377	0.380188	−	0.924909i	$-0.375859\pi$
$283$	3620.00	0.760377	0.380188	+	0.924909i	$0.375859\pi$
$284$	300.000	0.0626821
$285$	0	0
$286$	738.000	0.152583
$287$	399.000	0.0820635
$288$	405.000	0.0828641
$289$	−4184.00	−0.851618
$290$	0	0
$291$	−1482.00	−0.298544
$292$	98.0000	0.0196405
$293$	−1392.00	−0.277548	−0.138774	−	0.990324i	$-0.544316\pi$
$293$	−1392.00	−0.277548	−0.138774	+	0.990324i	$0.544316\pi$
$294$	441.000	0.0874818
$295$	0	0
$296$	−5502.00	−1.08040
$297$	162.000	0.0316505
$298$	−6507.00	−1.26490
$299$	3075.00	0.594755
$300$	0	0
$301$	2849.00	0.545560
$302$	−1554.00	−0.296101
$303$	−1872.00	−0.354929
$304$	284.000	0.0535806
$305$	0	0
$306$	−729.000	−0.136190
$307$	9002.00	1.67352	0.836761	−	0.547568i	$-0.184446\pi$
$307$	9002.00	1.67352	0.836761	+	0.547568i	$0.184446\pi$
$308$	−42.0000	−0.00777004
$309$	2307.00	0.424727
$310$	0	0
$311$	6666.00	1.21542	0.607708	−	0.794161i	$-0.292089\pi$
$311$	6666.00	1.21542	0.607708	+	0.794161i	$0.292089\pi$
$312$	−2583.00	−0.468697
$313$	−2878.00	−0.519726	−0.259863	−	0.965646i	$-0.583677\pi$
$313$	−2878.00	−0.519726	−0.259863	+	0.965646i	$0.583677\pi$
$314$	2658.00	0.477706
$315$	0	0
$316$	686.000	0.122122
$317$	4611.00	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$317$	4611.00	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$318$	2943.00	0.518979
$319$	738.000	0.129530
$320$	0	0
$321$	−4986.00	−0.866951
$322$	−1575.00	−0.272582
$323$	−108.000	−0.0186046
$324$	81.0000	0.0138889
$325$	0	0
$326$	−11679.0	−1.98417
$327$	−564.000	−0.0953800
$328$	1197.00	0.201504
$329$	−420.000	−0.0703810
$330$	0	0
$331$	−7459.00	−1.23862	−0.619311	−	0.785146i	$-0.712588\pi$
$331$	−7459.00	−1.23862	−0.619311	+	0.785146i	$0.712588\pi$
$332$	1401.00	0.231596
$333$	−2358.00	−0.388041
$334$	−6138.00	−1.00556
$335$	0	0
$336$	1491.00	0.242085
$337$	5843.00	0.944476	0.472238	−	0.881471i	$-0.343446\pi$
$337$	5843.00	0.944476	0.472238	+	0.881471i	$0.343446\pi$
$338$	1548.00	0.249113
$339$	54.0000	0.00865156
$340$	0	0
$341$	1230.00	0.195332
$342$	108.000	0.0170759
$343$	343.000	0.0539949
$344$	8547.00	1.33960
$345$	0	0
$346$	10620.0	1.65010
$347$	2346.00	0.362939	0.181470	−	0.983397i	$-0.441915\pi$
$347$	2346.00	0.362939	0.181470	+	0.983397i	$0.441915\pi$
$348$	369.000	0.0568404
$349$	5807.00	0.890664	0.445332	−	0.895366i	$-0.353086\pi$
$349$	5807.00	0.890664	0.445332	+	0.895366i	$0.353086\pi$
$350$	0	0
$351$	−1107.00	−0.168340
$352$	−270.000	−0.0408837
$353$	−5190.00	−0.782538	−0.391269	−	0.920276i	$-0.627964\pi$
$353$	−5190.00	−0.782538	−0.391269	+	0.920276i	$0.627964\pi$
$354$	297.000	0.0445914
$355$	0	0
$356$	714.000	0.106298
$357$	−567.000	−0.0840583
$358$	9738.00	1.43762
$359$	8883.00	1.30592	0.652962	−	0.757391i	$-0.273526\pi$
$359$	8883.00	1.30592	0.652962	+	0.757391i	$0.273526\pi$
$360$	0	0
$361$	−6843.00	−0.997667
$362$	−4002.00	−0.581051
$363$	3885.00	0.561734
$364$	287.000	0.0413266
$365$	0	0
$366$	−3843.00	−0.548844
$367$	9965.00	1.41735	0.708677	−	0.705533i	$-0.249292\pi$
$367$	9965.00	1.41735	0.708677	+	0.705533i	$0.249292\pi$
$368$	−5325.00	−0.754307
$369$	513.000	0.0723732
$370$	0	0
$371$	2289.00	0.320321
$372$	615.000	0.0857158
$373$	11660.0	1.61858	0.809292	−	0.587406i	$-0.199851\pi$
$373$	11660.0	1.61858	0.809292	+	0.587406i	$0.199851\pi$
$374$	486.000	0.0671937
$375$	0	0
$376$	−1260.00	−0.172818
$377$	−5043.00	−0.688933
$378$	567.000	0.0771517
$379$	3203.00	0.434108	0.217054	−	0.976160i	$-0.430355\pi$
$379$	3203.00	0.434108	0.217054	+	0.976160i	$0.430355\pi$
$380$	0	0
$381$	4350.00	0.584927
$382$	2619.00	0.350785
$383$	−8220.00	−1.09666	−0.548332	−	0.836261i	$-0.684737\pi$
$383$	−8220.00	−1.09666	−0.548332	+	0.836261i	$0.684737\pi$
$384$	4977.00	0.661410
$385$	0	0
$386$	3018.00	0.397959
$387$	3663.00	0.481139
$388$	494.000	0.0646367
$389$	−2226.00	−0.290135	−0.145068	−	0.989422i	$-0.546340\pi$
$389$	−2226.00	−0.290135	−0.145068	+	0.989422i	$0.546340\pi$
$390$	0	0
$391$	2025.00	0.261915
$392$	1029.00	0.132583
$393$	−7992.00	−1.02581
$394$	−1773.00	−0.226707
$395$	0	0
$396$	−54.0000	−0.00685253
$397$	10451.0	1.32121	0.660605	−	0.750733i	$-0.270300\pi$
$397$	10451.0	1.32121	0.660605	+	0.750733i	$0.270300\pi$
$398$	7752.00	0.976313
$399$	84.0000	0.0105395
$400$	0	0
$401$	−1320.00	−0.164383	−0.0821916	−	0.996617i	$-0.526192\pi$
$401$	−1320.00	−0.164383	−0.0821916	+	0.996617i	$0.526192\pi$
$402$	−5652.00	−0.701234
$403$	−8405.00	−1.03892
$404$	624.000	0.0768445
$405$	0	0
$406$	2583.00	0.315744
$407$	1572.00	0.191452
$408$	−1701.00	−0.206402
$409$	2402.00	0.290394	0.145197	−	0.989403i	$-0.453618\pi$
$409$	2402.00	0.290394	0.145197	+	0.989403i	$0.453618\pi$
$410$	0	0
$411$	−5076.00	−0.609199
$412$	−769.000	−0.0919561
$413$	231.000	0.0275224
$414$	−2025.00	−0.240394
$415$	0	0
$416$	1845.00	0.217448
$417$	−3804.00	−0.446721
$418$	−72.0000	−0.00842496
$419$	−3333.00	−0.388610	−0.194305	−	0.980941i	$-0.562245\pi$
$419$	−3333.00	−0.388610	−0.194305	+	0.980941i	$0.562245\pi$
$420$	0	0
$421$	−1462.00	−0.169248	−0.0846241	−	0.996413i	$-0.526969\pi$
$421$	−1462.00	−0.169248	−0.0846241	+	0.996413i	$0.526969\pi$
$422$	4323.00	0.498674
$423$	−540.000	−0.0620702
$424$	6867.00	0.786535
$425$	0	0
$426$	2700.00	0.307078
$427$	−2989.00	−0.338754
$428$	1662.00	0.187700
$429$	738.000	0.0830559
$430$	0	0
$431$	−10089.0	−1.12754	−0.563770	−	0.825932i	$-0.690650\pi$
$431$	−10089.0	−1.12754	−0.563770	+	0.825932i	$0.690650\pi$
$432$	1917.00	0.213499
$433$	3242.00	0.359817	0.179908	−	0.983683i	$-0.442420\pi$
$433$	3242.00	0.359817	0.179908	+	0.983683i	$0.442420\pi$
$434$	4305.00	0.476144
$435$	0	0
$436$	188.000	0.0206504
$437$	−300.000	−0.0328397
$438$	882.000	0.0962182
$439$	1799.00	0.195584	0.0977922	−	0.995207i	$-0.468822\pi$
$439$	1799.00	0.195584	0.0977922	+	0.995207i	$0.468822\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	−3321.00	−0.357384
$443$	8772.00	0.940791	0.470395	−	0.882456i	$-0.344111\pi$
$443$	8772.00	0.940791	0.470395	+	0.882456i	$0.344111\pi$
$444$	786.000	0.0840133
$445$	0	0
$446$	−11481.0	−1.21893
$447$	−6507.00	−0.688525
$448$	3031.00	0.319646
$449$	1560.00	0.163966	0.0819832	−	0.996634i	$-0.473875\pi$
$449$	1560.00	0.163966	0.0819832	+	0.996634i	$0.473875\pi$
$450$	0	0
$451$	−342.000	−0.0357077
$452$	−18.0000	−0.00187312
$453$	−1554.00	−0.161177
$454$	16263.0	1.68119
$455$	0	0
$456$	252.000	0.0258793
$457$	11615.0	1.18890	0.594449	−	0.804133i	$-0.297370\pi$
$457$	11615.0	1.18890	0.594449	+	0.804133i	$0.297370\pi$
$458$	15870.0	1.61912
$459$	−729.000	−0.0741325
$460$	0	0
$461$	6960.00	0.703166	0.351583	−	0.936157i	$-0.385644\pi$
$461$	6960.00	0.703166	0.351583	+	0.936157i	$0.385644\pi$
$462$	−378.000	−0.0380653
$463$	13052.0	1.31010	0.655052	−	0.755584i	$-0.272647\pi$
$463$	13052.0	1.31010	0.655052	+	0.755584i	$0.272647\pi$
$464$	8733.00	0.873749
$465$	0	0
$466$	−14724.0	−1.46368
$467$	14013.0	1.38853	0.694266	−	0.719719i	$-0.255729\pi$
$467$	14013.0	1.38853	0.694266	+	0.719719i	$0.255729\pi$
$468$	369.000	0.0364466
$469$	−4396.00	−0.432811
$470$	0	0
$471$	2658.00	0.260030
$472$	693.000	0.0675803
$473$	−2442.00	−0.237385
$474$	6174.00	0.598273
$475$	0	0
$476$	189.000	0.0181992
$477$	2943.00	0.282496
$478$	−3168.00	−0.303140
$479$	1056.00	0.100730	0.0503652	−	0.998731i	$-0.483961\pi$
$479$	1056.00	0.100730	0.0503652	+	0.998731i	$0.483961\pi$
$480$	0	0
$481$	−10742.0	−1.01828
$482$	−16026.0	−1.51445
$483$	−1575.00	−0.148375
$484$	−1295.00	−0.121619
$485$	0	0
$486$	729.000	0.0680414
$487$	7886.00	0.733776	0.366888	−	0.930265i	$-0.380423\pi$
$487$	7886.00	0.733776	0.366888	+	0.930265i	$0.380423\pi$
$488$	−8967.00	−0.831797
$489$	−11679.0	−1.08005
$490$	0	0
$491$	10590.0	0.973361	0.486680	−	0.873580i	$-0.338208\pi$
$491$	10590.0	0.973361	0.486680	+	0.873580i	$0.338208\pi$
$492$	−171.000	−0.0156693
$493$	−3321.00	−0.303388
$494$	492.000	0.0448100
$495$	0	0
$496$	14555.0	1.31762
$497$	2100.00	0.189533
$498$	12609.0	1.13458
$499$	−14899.0	−1.33661	−0.668307	−	0.743885i	$-0.732981\pi$
$499$	−14899.0	−1.33661	−0.668307	+	0.743885i	$0.732981\pi$
$500$	0	0
$501$	−6138.00	−0.547357
$502$	−17415.0	−1.54835
$503$	21558.0	1.91098	0.955491	−	0.295021i	$-0.0953267\pi$
$503$	21558.0	1.91098	0.955491	+	0.295021i	$0.0953267\pi$
$504$	1323.00	0.116927
$505$	0	0
$506$	1350.00	0.118606
$507$	1548.00	0.135600
$508$	−1450.00	−0.126640
$509$	−15240.0	−1.32711	−0.663557	−	0.748126i	$-0.730954\pi$
$509$	−15240.0	−1.32711	−0.663557	+	0.748126i	$0.730954\pi$
$510$	0	0
$511$	686.000	0.0593872
$512$	8733.00	0.753804
$513$	108.000	0.00929496
$514$	−1629.00	−0.139790
$515$	0	0
$516$	−1221.00	−0.104170
$517$	360.000	0.0306243
$518$	5502.00	0.466687
$519$	10620.0	0.898201
$520$	0	0
$521$	−16797.0	−1.41246	−0.706228	−	0.707984i	$-0.749605\pi$
$521$	−16797.0	−1.41246	−0.706228	+	0.707984i	$0.749605\pi$
$522$	3321.00	0.278460
$523$	22520.0	1.88285	0.941425	−	0.337222i	$-0.109487\pi$
$523$	22520.0	1.88285	0.941425	+	0.337222i	$0.109487\pi$
$524$	2664.00	0.222094
$525$	0	0
$526$	15579.0	1.29140
$527$	−5535.00	−0.457511
$528$	−1278.00	−0.105337
$529$	−6542.00	−0.537684
$530$	0	0
$531$	297.000	0.0242725
$532$	−28.0000	−0.00228187
$533$	2337.00	0.189919
$534$	6426.00	0.520749
$535$	0	0
$536$	−13188.0	−1.06275
$537$	9738.00	0.782543
$538$	−6462.00	−0.517838
$539$	−294.000	−0.0234944
$540$	0	0
$541$	−12004.0	−0.953960	−0.476980	−	0.878914i	$-0.658269\pi$
$541$	−12004.0	−0.953960	−0.476980	+	0.878914i	$0.658269\pi$
$542$	−7188.00	−0.569651
$543$	−4002.00	−0.316284
$544$	1215.00	0.0957586
$545$	0	0
$546$	2583.00	0.202458
$547$	−16423.0	−1.28372	−0.641862	−	0.766820i	$-0.721838\pi$
$547$	−16423.0	−1.28372	−0.641862	+	0.766820i	$0.721838\pi$
$548$	1692.00	0.131895
$549$	−3843.00	−0.298753
$550$	0	0
$551$	492.000	0.0380398
$552$	−4725.00	−0.364329
$553$	4802.00	0.369262
$554$	−12858.0	−0.986072
$555$	0	0
$556$	1268.00	0.0967179
$557$	714.000	0.0543145	0.0271572	−	0.999631i	$-0.491355\pi$
$557$	714.000	0.0543145	0.0271572	+	0.999631i	$0.491355\pi$
$558$	5535.00	0.419920
$559$	16687.0	1.26258
$560$	0	0
$561$	486.000	0.0365756
$562$	−6624.00	−0.497183
$563$	16293.0	1.21966	0.609830	−	0.792533i	$-0.291238\pi$
$563$	16293.0	1.21966	0.609830	+	0.792533i	$0.291238\pi$
$564$	180.000	0.0134386
$565$	0	0
$566$	−10860.0	−0.806501
$567$	567.000	0.0419961
$568$	6300.00	0.465391
$569$	−17370.0	−1.27977	−0.639884	−	0.768471i	$-0.721018\pi$
$569$	−17370.0	−1.27977	−0.639884	+	0.768471i	$0.721018\pi$
$570$	0	0
$571$	−12589.0	−0.922650	−0.461325	−	0.887231i	$-0.652626\pi$
$571$	−12589.0	−0.922650	−0.461325	+	0.887231i	$0.652626\pi$
$572$	−246.000	−0.0179821
$573$	2619.00	0.190943
$574$	−1197.00	−0.0870415
$575$	0	0
$576$	3897.00	0.281901
$577$	−13318.0	−0.960894	−0.480447	−	0.877024i	$-0.659525\pi$
$577$	−13318.0	−0.960894	−0.480447	+	0.877024i	$0.659525\pi$
$578$	12552.0	0.903277
$579$	3018.00	0.216621
$580$	0	0
$581$	9807.00	0.700280
$582$	4446.00	0.316654
$583$	−1962.00	−0.139379
$584$	2058.00	0.145823
$585$	0	0
$586$	4176.00	0.294384
$587$	−7551.00	−0.530942	−0.265471	−	0.964119i	$-0.585528\pi$
$587$	−7551.00	−0.530942	−0.265471	+	0.964119i	$0.585528\pi$
$588$	−147.000	−0.0103098
$589$	820.000	0.0573642
$590$	0	0
$591$	−1773.00	−0.123404
$592$	18602.0	1.29145
$593$	−6402.00	−0.443337	−0.221668	−	0.975122i	$-0.571150\pi$
$593$	−6402.00	−0.443337	−0.221668	+	0.975122i	$0.571150\pi$
$594$	−486.000	−0.0335704
$595$	0	0
$596$	2169.00	0.149070
$597$	7752.00	0.531438
$598$	−9225.00	−0.630833
$599$	−15753.0	−1.07454	−0.537271	−	0.843410i	$-0.680545\pi$
$599$	−15753.0	−1.07454	−0.537271	+	0.843410i	$0.680545\pi$
$600$	0	0
$601$	9764.00	0.662699	0.331349	−	0.943508i	$-0.392496\pi$
$601$	9764.00	0.662699	0.331349	+	0.943508i	$0.392496\pi$
$602$	−8547.00	−0.578654
$603$	−5652.00	−0.381704
$604$	518.000	0.0348959
$605$	0	0
$606$	5616.00	0.376459
$607$	7772.00	0.519696	0.259848	−	0.965649i	$-0.416327\pi$
$607$	7772.00	0.519696	0.259848	+	0.965649i	$0.416327\pi$
$608$	−180.000	−0.0120065
$609$	2583.00	0.171869
$610$	0	0
$611$	−2460.00	−0.162882
$612$	243.000	0.0160502
$613$	−24262.0	−1.59859	−0.799293	−	0.600942i	$-0.794792\pi$
$613$	−24262.0	−1.59859	−0.799293	+	0.600942i	$0.794792\pi$
$614$	−27006.0	−1.77504
$615$	0	0
$616$	−882.000	−0.0576896
$617$	−25818.0	−1.68459	−0.842296	−	0.539015i	$-0.818797\pi$
$617$	−25818.0	−1.68459	−0.842296	+	0.539015i	$0.818797\pi$
$618$	−6921.00	−0.450491
$619$	22430.0	1.45644	0.728221	−	0.685342i	$-0.240347\pi$
$619$	22430.0	1.45644	0.728221	+	0.685342i	$0.240347\pi$
$620$	0	0
$621$	−2025.00	−0.130854
$622$	−19998.0	−1.28914
$623$	4998.00	0.321414
$624$	8733.00	0.560256
$625$	0	0
$626$	8634.00	0.551252
$627$	−72.0000	−0.00458597
$628$	−886.000	−0.0562982
$629$	−7074.00	−0.448424
$630$	0	0
$631$	−2830.00	−0.178543	−0.0892714	−	0.996007i	$-0.528454\pi$
$631$	−2830.00	−0.178543	−0.0892714	+	0.996007i	$0.528454\pi$
$632$	14406.0	0.906709
$633$	4323.00	0.271444
$634$	−13833.0	−0.866528
$635$	0	0
$636$	−981.000	−0.0611622
$637$	2009.00	0.124960
$638$	−2214.00	−0.137387
$639$	2700.00	0.167152
$640$	0	0
$641$	−5202.00	−0.320541	−0.160270	−	0.987073i	$-0.551237\pi$
$641$	−5202.00	−0.320541	−0.160270	+	0.987073i	$0.551237\pi$
$642$	14958.0	0.919541
$643$	−22030.0	−1.35113	−0.675566	−	0.737299i	$-0.736101\pi$
$643$	−22030.0	−1.35113	−0.675566	+	0.737299i	$0.736101\pi$
$644$	525.000	0.0321241
$645$	0	0
$646$	324.000	0.0197331
$647$	−20370.0	−1.23775	−0.618877	−	0.785488i	$-0.712412\pi$
$647$	−20370.0	−1.23775	−0.618877	+	0.785488i	$0.712412\pi$
$648$	1701.00	0.103120
$649$	−198.000	−0.0119756
$650$	0	0
$651$	4305.00	0.259180
$652$	3893.00	0.233837
$653$	−31626.0	−1.89528	−0.947642	−	0.319333i	$-0.896541\pi$
$653$	−31626.0	−1.89528	−0.947642	+	0.319333i	$0.896541\pi$
$654$	1692.00	0.101166
$655$	0	0
$656$	−4047.00	−0.240867
$657$	882.000	0.0523746
$658$	1260.00	0.0746503
$659$	−11142.0	−0.658620	−0.329310	−	0.944222i	$-0.606816\pi$
$659$	−11142.0	−0.658620	−0.329310	+	0.944222i	$0.606816\pi$
$660$	0	0
$661$	−5518.00	−0.324698	−0.162349	−	0.986733i	$-0.551907\pi$
$661$	−5518.00	−0.324698	−0.162349	+	0.986733i	$0.551907\pi$
$662$	22377.0	1.31376
$663$	−3321.00	−0.194535
$664$	29421.0	1.71951
$665$	0	0
$666$	7074.00	0.411579
$667$	−9225.00	−0.535522
$668$	2046.00	0.118506
$669$	−11481.0	−0.663499
$670$	0	0
$671$	2562.00	0.147399
$672$	−945.000	−0.0542473
$673$	−12517.0	−0.716931	−0.358466	−	0.933543i	$-0.616700\pi$
$673$	−12517.0	−0.716931	−0.358466	+	0.933543i	$0.616700\pi$
$674$	−17529.0	−1.00177
$675$	0	0
$676$	−516.000	−0.0293582
$677$	−2604.00	−0.147828	−0.0739142	−	0.997265i	$-0.523549\pi$
$677$	−2604.00	−0.147828	−0.0739142	+	0.997265i	$0.523549\pi$
$678$	−162.000	−0.00917636
$679$	3458.00	0.195443
$680$	0	0
$681$	16263.0	0.915124
$682$	−3690.00	−0.207181
$683$	25986.0	1.45582	0.727911	−	0.685671i	$-0.240491\pi$
$683$	25986.0	1.45582	0.727911	+	0.685671i	$0.240491\pi$
$684$	−36.0000	−0.00201242
$685$	0	0
$686$	−1029.00	−0.0572703
$687$	15870.0	0.881337
$688$	−28897.0	−1.60129
$689$	13407.0	0.741315
$690$	0	0
$691$	−24610.0	−1.35486	−0.677430	−	0.735587i	$-0.736906\pi$
$691$	−24610.0	−1.35486	−0.677430	+	0.735587i	$0.736906\pi$
$692$	−3540.00	−0.194466
$693$	−378.000	−0.0207201
$694$	−7038.00	−0.384955
$695$	0	0
$696$	7749.00	0.422019
$697$	1539.00	0.0836353
$698$	−17421.0	−0.944691
$699$	−14724.0	−0.796728
$700$	0	0
$701$	10725.0	0.577857	0.288928	−	0.957351i	$-0.406701\pi$
$701$	10725.0	0.577857	0.288928	+	0.957351i	$0.406701\pi$
$702$	3321.00	0.178551
$703$	1048.00	0.0562248
$704$	−2598.00	−0.139085
$705$	0	0
$706$	15570.0	0.830007
$707$	4368.00	0.232356
$708$	−99.0000	−0.00525515
$709$	−34516.0	−1.82832	−0.914158	−	0.405359i	$-0.867147\pi$
$709$	−34516.0	−1.82832	−0.914158	+	0.405359i	$0.867147\pi$
$710$	0	0
$711$	6174.00	0.325658
$712$	14994.0	0.789219
$713$	−15375.0	−0.807571
$714$	1701.00	0.0891573
$715$	0	0
$716$	−3246.00	−0.169426
$717$	−3168.00	−0.165009
$718$	−26649.0	−1.38514
$719$	17958.0	0.931461	0.465730	−	0.884927i	$-0.345792\pi$
$719$	17958.0	0.931461	0.465730	+	0.884927i	$0.345792\pi$
$720$	0	0
$721$	−5383.00	−0.278049
$722$	20529.0	1.05819
$723$	−16026.0	−0.824361
$724$	1334.00	0.0684775
$725$	0	0
$726$	−11655.0	−0.595809
$727$	2255.00	0.115039	0.0575195	−	0.998344i	$-0.481681\pi$
$727$	2255.00	0.115039	0.0575195	+	0.998344i	$0.481681\pi$
$728$	6027.00	0.306834
$729$	729.000	0.0370370
$730$	0	0
$731$	10989.0	0.556009
$732$	1281.00	0.0646819
$733$	9539.00	0.480670	0.240335	−	0.970690i	$-0.422743\pi$
$733$	9539.00	0.480670	0.240335	+	0.970690i	$0.422743\pi$
$734$	−29895.0	−1.50333
$735$	0	0
$736$	3375.00	0.169027
$737$	3768.00	0.188326
$738$	−1539.00	−0.0767634
$739$	37979.0	1.89050	0.945250	−	0.326346i	$-0.105817\pi$
$739$	37979.0	1.89050	0.945250	+	0.326346i	$0.105817\pi$
$740$	0	0
$741$	492.000	0.0243915
$742$	−6867.00	−0.339751
$743$	−20535.0	−1.01394	−0.506969	−	0.861964i	$-0.669234\pi$
$743$	−20535.0	−1.01394	−0.506969	+	0.861964i	$0.669234\pi$
$744$	12915.0	0.636407
$745$	0	0
$746$	−34980.0	−1.71677
$747$	12609.0	0.617589
$748$	−162.000	−0.00791886
$749$	11634.0	0.567553
$750$	0	0
$751$	−2452.00	−0.119141	−0.0595704	−	0.998224i	$-0.518973\pi$
$751$	−2452.00	−0.119141	−0.0595704	+	0.998224i	$0.518973\pi$
$752$	4260.00	0.206577
$753$	−17415.0	−0.842813
$754$	15129.0	0.730724
$755$	0	0
$756$	−189.000	−0.00909241
$757$	−36850.0	−1.76927	−0.884634	−	0.466286i	$-0.845592\pi$
$757$	−36850.0	−1.76927	−0.884634	+	0.466286i	$0.845592\pi$
$758$	−9609.00	−0.460441
$759$	1350.00	0.0645611
$760$	0	0
$761$	30258.0	1.44133	0.720665	−	0.693284i	$-0.243837\pi$
$761$	30258.0	1.44133	0.720665	+	0.693284i	$0.243837\pi$
$762$	−13050.0	−0.620409
$763$	1316.00	0.0624409
$764$	−873.000	−0.0413404
$765$	0	0
$766$	24660.0	1.16319
$767$	1353.00	0.0636949
$768$	−4539.00	−0.213264
$769$	29288.0	1.37341	0.686705	−	0.726936i	$-0.259056\pi$
$769$	29288.0	1.37341	0.686705	+	0.726936i	$0.259056\pi$
$770$	0	0
$771$	−1629.00	−0.0760921
$772$	−1006.00	−0.0468999
$773$	40668.0	1.89227	0.946136	−	0.323769i	$-0.104950\pi$
$773$	40668.0	1.89227	0.946136	+	0.323769i	$0.104950\pi$
$774$	−10989.0	−0.510325
$775$	0	0
$776$	10374.0	0.479903
$777$	5502.00	0.254032
$778$	6678.00	0.307735
$779$	−228.000	−0.0104865
$780$	0	0
$781$	−1800.00	−0.0824700
$782$	−6075.00	−0.277803
$783$	3321.00	0.151575
$784$	−3479.00	−0.158482
$785$	0	0
$786$	23976.0	1.08804
$787$	13118.0	0.594163	0.297081	−	0.954852i	$-0.403987\pi$
$787$	13118.0	0.594163	0.297081	+	0.954852i	$0.403987\pi$
$788$	591.000	0.0267176
$789$	15579.0	0.702949
$790$	0	0
$791$	−126.000	−0.00566377
$792$	−1134.00	−0.0508774
$793$	−17507.0	−0.783975
$794$	−31353.0	−1.40136
$795$	0	0
$796$	−2584.00	−0.115060
$797$	−37278.0	−1.65678	−0.828391	−	0.560151i	$-0.810743\pi$
$797$	−37278.0	−1.65678	−0.828391	+	0.560151i	$0.810743\pi$
$798$	−252.000	−0.0111788
$799$	−1620.00	−0.0717290
$800$	0	0
$801$	6426.00	0.283460
$802$	3960.00	0.174355
$803$	−588.000	−0.0258407
$804$	1884.00	0.0826412
$805$	0	0
$806$	25215.0	1.10194
$807$	−6462.00	−0.281875
$808$	13104.0	0.570541
$809$	5268.00	0.228941	0.114470	−	0.993427i	$-0.463483\pi$
$809$	5268.00	0.228941	0.114470	+	0.993427i	$0.463483\pi$
$810$	0	0
$811$	34994.0	1.51517	0.757587	−	0.652735i	$-0.226378\pi$
$811$	34994.0	1.51517	0.757587	+	0.652735i	$0.226378\pi$
$812$	−861.000	−0.0372108
$813$	−7188.00	−0.310079
$814$	−4716.00	−0.203066
$815$	0	0
$816$	5751.00	0.246722
$817$	−1628.00	−0.0697142
$818$	−7206.00	−0.308010
$819$	2583.00	0.110204
$820$	0	0
$821$	28818.0	1.22504	0.612518	−	0.790456i	$-0.290157\pi$
$821$	28818.0	1.22504	0.612518	+	0.790456i	$0.290157\pi$
$822$	15228.0	0.646153
$823$	−20962.0	−0.887836	−0.443918	−	0.896067i	$-0.646412\pi$
$823$	−20962.0	−0.887836	−0.443918	+	0.896067i	$0.646412\pi$
$824$	−16149.0	−0.682739
$825$	0	0
$826$	−693.000	−0.0291920
$827$	−28266.0	−1.18852	−0.594259	−	0.804273i	$-0.702555\pi$
$827$	−28266.0	−1.18852	−0.594259	+	0.804273i	$0.702555\pi$
$828$	675.000	0.0283308
$829$	42491.0	1.78019	0.890093	−	0.455780i	$-0.150640\pi$
$829$	42491.0	1.78019	0.890093	+	0.455780i	$0.150640\pi$
$830$	0	0
$831$	−12858.0	−0.536750
$832$	17753.0	0.739753
$833$	1323.00	0.0550291
$834$	11412.0	0.473819
$835$	0	0
$836$	24.0000	0.000992892 0
$837$	5535.00	0.228575
$838$	9999.00	0.412183
$839$	−40512.0	−1.66702	−0.833510	−	0.552505i	$-0.813672\pi$
$839$	−40512.0	−1.66702	−0.833510	+	0.552505i	$0.813672\pi$
$840$	0	0
$841$	−9260.00	−0.379679
$842$	4386.00	0.179515
$843$	−6624.00	−0.270632
$844$	−1441.00	−0.0587693
$845$	0	0
$846$	1620.00	0.0658354
$847$	−9065.00	−0.367742
$848$	−23217.0	−0.940183
$849$	−10860.0	−0.439004
$850$	0	0
$851$	−19650.0	−0.791532
$852$	−900.000	−0.0361895
$853$	−40525.0	−1.62667	−0.813335	−	0.581796i	$-0.802350\pi$
$853$	−40525.0	−1.62667	−0.813335	+	0.581796i	$0.802350\pi$
$854$	8967.00	0.359303
$855$	0	0
$856$	34902.0	1.39360
$857$	−7182.00	−0.286269	−0.143134	−	0.989703i	$-0.545718\pi$
$857$	−7182.00	−0.286269	−0.143134	+	0.989703i	$0.545718\pi$
$858$	−2214.00	−0.0880941
$859$	−7864.00	−0.312359	−0.156179	−	0.987729i	$-0.549918\pi$
$859$	−7864.00	−0.312359	−0.156179	+	0.987729i	$0.549918\pi$
$860$	0	0
$861$	−1197.00	−0.0473794
$862$	30267.0	1.19594
$863$	28872.0	1.13883	0.569417	−	0.822049i	$-0.307169\pi$
$863$	28872.0	1.13883	0.569417	+	0.822049i	$0.307169\pi$
$864$	−1215.00	−0.0478416
$865$	0	0
$866$	−9726.00	−0.381643
$867$	12552.0	0.491682
$868$	−1435.00	−0.0561141
$869$	−4116.00	−0.160674
$870$	0	0
$871$	−25748.0	−1.00165
$872$	3948.00	0.153321
$873$	4446.00	0.172365
$874$	900.000	0.0348318
$875$	0	0
$876$	−294.000	−0.0113394
$877$	−47392.0	−1.82476	−0.912380	−	0.409345i	$-0.865757\pi$
$877$	−47392.0	−1.82476	−0.912380	+	0.409345i	$0.865757\pi$
$878$	−5397.00	−0.207449
$879$	4176.00	0.160242
$880$	0	0
$881$	17769.0	0.679515	0.339758	−	0.940513i	$-0.389655\pi$
$881$	17769.0	0.679515	0.339758	+	0.940513i	$0.389655\pi$
$882$	−1323.00	−0.0505076
$883$	32549.0	1.24050	0.620250	−	0.784404i	$-0.287031\pi$
$883$	32549.0	1.24050	0.620250	+	0.784404i	$0.287031\pi$
$884$	1107.00	0.0421181
$885$	0	0
$886$	−26316.0	−0.997859
$887$	6714.00	0.254153	0.127077	−	0.991893i	$-0.459441\pi$
$887$	6714.00	0.254153	0.127077	+	0.991893i	$0.459441\pi$
$888$	16506.0	0.623767
$889$	−10150.0	−0.382925
$890$	0	0
$891$	−486.000	−0.0182734
$892$	3827.00	0.143652
$893$	240.000	0.00899361
$894$	19521.0	0.730291
$895$	0	0
$896$	−11613.0	−0.432995
$897$	−9225.00	−0.343382
$898$	−4680.00	−0.173913
$899$	25215.0	0.935448
$900$	0	0
$901$	8829.00	0.326456
$902$	1026.00	0.0378737
$903$	−8547.00	−0.314979
$904$	−378.000	−0.0139072
$905$	0	0
$906$	4662.00	0.170954
$907$	29693.0	1.08703	0.543517	−	0.839398i	$-0.317092\pi$
$907$	29693.0	1.08703	0.543517	+	0.839398i	$0.317092\pi$
$908$	−5421.00	−0.198130
$909$	5616.00	0.204919
$910$	0	0
$911$	−8199.00	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−8199.00	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	−852.000	−0.0309348
$913$	−8406.00	−0.304708
$914$	−34845.0	−1.26102
$915$	0	0
$916$	−5290.00	−0.190815
$917$	18648.0	0.671550
$918$	2187.00	0.0786294
$919$	−15388.0	−0.552343	−0.276172	−	0.961108i	$-0.589066\pi$
$919$	−15388.0	−0.552343	−0.276172	+	0.961108i	$0.589066\pi$
$920$	0	0
$921$	−27006.0	−0.966208
$922$	−20880.0	−0.745820
$923$	12300.0	0.438634
$924$	126.000	0.00448603
$925$	0	0
$926$	−39156.0	−1.38957
$927$	−6921.00	−0.245216
$928$	−5535.00	−0.195792
$929$	−411.000	−0.0145150	−0.00725752	−	0.999974i	$-0.502310\pi$
$929$	−411.000	−0.0145150	−0.00725752	+	0.999974i	$0.502310\pi$
$930$	0	0
$931$	−196.000	−0.00689972
$932$	4908.00	0.172497
$933$	−19998.0	−0.701720
$934$	−42039.0	−1.47276
$935$	0	0
$936$	7749.00	0.270603
$937$	26066.0	0.908793	0.454397	−	0.890800i	$-0.349855\pi$
$937$	26066.0	0.908793	0.454397	+	0.890800i	$0.349855\pi$
$938$	13188.0	0.459066
$939$	8634.00	0.300064
$940$	0	0
$941$	24048.0	0.833095	0.416548	−	0.909114i	$-0.363240\pi$
$941$	24048.0	0.833095	0.416548	+	0.909114i	$0.363240\pi$
$942$	−7974.00	−0.275804
$943$	4275.00	0.147628
$944$	−2343.00	−0.0807819
$945$	0	0
$946$	7326.00	0.251785
$947$	−22968.0	−0.788131	−0.394065	−	0.919082i	$-0.628932\pi$
$947$	−22968.0	−0.788131	−0.394065	+	0.919082i	$0.628932\pi$
$948$	−2058.00	−0.0705071
$949$	4018.00	0.137439
$950$	0	0
$951$	−13833.0	−0.471678
$952$	3969.00	0.135122
$953$	−10248.0	−0.348337	−0.174169	−	0.984716i	$-0.555724\pi$
$953$	−10248.0	−0.348337	−0.174169	+	0.984716i	$0.555724\pi$
$954$	−8829.00	−0.299633
$955$	0	0
$956$	1056.00	0.0357254
$957$	−2214.00	−0.0747842
$958$	−3168.00	−0.106841
$959$	11844.0	0.398814
$960$	0	0
$961$	12234.0	0.410661
$962$	32226.0	1.08005
$963$	14958.0	0.500535
$964$	5342.00	0.178479
$965$	0	0
$966$	4725.00	0.157375
$967$	−43060.0	−1.43197	−0.715986	−	0.698115i	$-0.754022\pi$
$967$	−43060.0	−1.43197	−0.715986	+	0.698115i	$0.754022\pi$
$968$	−27195.0	−0.902976
$969$	324.000	0.0107414
$970$	0	0
$971$	−12348.0	−0.408101	−0.204051	−	0.978960i	$-0.565411\pi$
$971$	−12348.0	−0.408101	−0.204051	+	0.978960i	$0.565411\pi$
$972$	−243.000	−0.00801875
$973$	8876.00	0.292448
$974$	−23658.0	−0.778287
$975$	0	0
$976$	30317.0	0.994286
$977$	−44190.0	−1.44705	−0.723523	−	0.690301i	$-0.757478\pi$
$977$	−44190.0	−1.44705	−0.723523	+	0.690301i	$0.757478\pi$
$978$	35037.0	1.14556
$979$	−4284.00	−0.139854
$980$	0	0
$981$	1692.00	0.0550677
$982$	−31770.0	−1.03240
$983$	60168.0	1.95225	0.976125	−	0.217211i	$-0.0696959\pi$
$983$	60168.0	1.95225	0.976125	+	0.217211i	$0.0696959\pi$
$984$	−3591.00	−0.116338
$985$	0	0
$986$	9963.00	0.321792
$987$	1260.00	0.0406345
$988$	−164.000	−0.00528091
$989$	30525.0	0.981434
$990$	0	0
$991$	8804.00	0.282208	0.141104	−	0.989995i	$-0.454935\pi$
$991$	8804.00	0.282208	0.141104	+	0.989995i	$0.454935\pi$
$992$	−9225.00	−0.295256
$993$	22377.0	0.715118
$994$	−6300.00	−0.201030
$995$	0	0
$996$	−4203.00	−0.133712
$997$	15302.0	0.486077	0.243039	−	0.970017i	$-0.421856\pi$
$997$	15302.0	0.486077	0.243039	+	0.970017i	$0.421856\pi$
$998$	44697.0	1.41769
$999$	7074.00	0.224035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.a.c.1.1	✓	1
3.2	odd	2		1575.4.a.j.1.1		1
5.2	odd	4		525.4.d.d.274.1		2
5.3	odd	4		525.4.d.d.274.2		2
5.4	even	2		525.4.a.h.1.1	yes	1
15.14	odd	2		1575.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.c.1.1	✓	1	1.1	even	1	trivial
525.4.a.h.1.1	yes	1	5.4	even	2
525.4.d.d.274.1		2	5.2	odd	4
525.4.d.d.274.2		2	5.3	odd	4
1575.4.a.a.1.1		1	15.14	odd	2
1575.4.a.j.1.1		1	3.2	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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