LMFDB - Embedded newform 2450.4.a.bh.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,4,Mod(1,2450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2450, 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("2450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2450.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:	$144.554679514$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} +2.00000 q^{6} +8.00000 q^{8} -26.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} +2.00000 q^{6} +8.00000 q^{8} -26.0000 q^{9} +35.0000 q^{11} +4.00000 q^{12} -66.0000 q^{13} +16.0000 q^{16} -59.0000 q^{17} -52.0000 q^{18} +137.000 q^{19} +70.0000 q^{22} +7.00000 q^{23} +8.00000 q^{24} -132.000 q^{26} -53.0000 q^{27} +106.000 q^{29} +75.0000 q^{31} +32.0000 q^{32} +35.0000 q^{33} -118.000 q^{34} -104.000 q^{36} -11.0000 q^{37} +274.000 q^{38} -66.0000 q^{39} -498.000 q^{41} -260.000 q^{43} +140.000 q^{44} +14.0000 q^{46} +171.000 q^{47} +16.0000 q^{48} -59.0000 q^{51} -264.000 q^{52} +417.000 q^{53} -106.000 q^{54} +137.000 q^{57} +212.000 q^{58} -17.0000 q^{59} +51.0000 q^{61} +150.000 q^{62} +64.0000 q^{64} +70.0000 q^{66} -439.000 q^{67} -236.000 q^{68} +7.00000 q^{69} -784.000 q^{71} -208.000 q^{72} -295.000 q^{73} -22.0000 q^{74} +548.000 q^{76} -132.000 q^{78} -495.000 q^{79} +649.000 q^{81} -996.000 q^{82} -932.000 q^{83} -520.000 q^{86} +106.000 q^{87} +280.000 q^{88} -873.000 q^{89} +28.0000 q^{92} +75.0000 q^{93} +342.000 q^{94} +32.0000 q^{96} +290.000 q^{97} -910.000 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	1.00000	0.192450	0.0962250	−	0.995360i	$-0.469323\pi$
$3$	1.00000	0.192450	0.0962250	+	0.995360i	$0.469323\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	2.00000	0.136083
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−26.0000	−0.962963
$10$	0	0
$11$	35.0000	0.959354	0.479677	−	0.877445i	$-0.340754\pi$
$11$	35.0000	0.959354	0.479677	+	0.877445i	$0.340754\pi$
$12$	4.00000	0.0962250
$13$	−66.0000	−1.40809	−0.704043	−	0.710158i	$-0.748624\pi$
$13$	−66.0000	−1.40809	−0.704043	+	0.710158i	$0.748624\pi$
$14$	0	0
$15$	0	0
$16$	16.0000	0.250000
$17$	−59.0000	−0.841741	−0.420871	−	0.907121i	$-0.638275\pi$
$17$	−59.0000	−0.841741	−0.420871	+	0.907121i	$0.638275\pi$
$18$	−52.0000	−0.680918
$19$	137.000	1.65421	0.827104	−	0.562049i	$-0.189987\pi$
$19$	137.000	1.65421	0.827104	+	0.562049i	$0.189987\pi$
$20$	0	0
$21$	0	0
$22$	70.0000	0.678366
$23$	7.00000	0.0634609	0.0317305	−	0.999496i	$-0.489898\pi$
$23$	7.00000	0.0634609	0.0317305	+	0.999496i	$0.489898\pi$
$24$	8.00000	0.0680414
$25$	0	0
$26$	−132.000	−0.995667
$27$	−53.0000	−0.377772
$28$	0	0
$29$	106.000	0.678748	0.339374	−	0.940651i	$-0.389785\pi$
$29$	106.000	0.678748	0.339374	+	0.940651i	$0.389785\pi$
$30$	0	0
$31$	75.0000	0.434529	0.217264	−	0.976113i	$-0.430287\pi$
$31$	75.0000	0.434529	0.217264	+	0.976113i	$0.430287\pi$
$32$	32.0000	0.176777
$33$	35.0000	0.184628
$34$	−118.000	−0.595201
$35$	0	0
$36$	−104.000	−0.481481
$37$	−11.0000	−0.0488754	−0.0244377	−	0.999701i	$-0.507780\pi$
$37$	−11.0000	−0.0488754	−0.0244377	+	0.999701i	$0.507780\pi$
$38$	274.000	1.16970
$39$	−66.0000	−0.270986
$40$	0	0
$41$	−498.000	−1.89694	−0.948470	−	0.316867i	$-0.897369\pi$
$41$	−498.000	−1.89694	−0.948470	+	0.316867i	$0.897369\pi$
$42$	0	0
$43$	−260.000	−0.922084	−0.461042	−	0.887378i	$-0.652524\pi$
$43$	−260.000	−0.922084	−0.461042	+	0.887378i	$0.652524\pi$
$44$	140.000	0.479677
$45$	0	0
$46$	14.0000	0.0448736
$47$	171.000	0.530700	0.265350	−	0.964152i	$-0.414512\pi$
$47$	171.000	0.530700	0.265350	+	0.964152i	$0.414512\pi$
$48$	16.0000	0.0481125
$49$	0	0
$50$	0	0
$51$	−59.0000	−0.161993
$52$	−264.000	−0.704043
$53$	417.000	1.08074	0.540371	−	0.841427i	$-0.318284\pi$
$53$	417.000	1.08074	0.540371	+	0.841427i	$0.318284\pi$
$54$	−106.000	−0.267125
$55$	0	0
$56$	0	0
$57$	137.000	0.318353
$58$	212.000	0.479948
$59$	−17.0000	−0.0375121	−0.0187560	−	0.999824i	$-0.505971\pi$
$59$	−17.0000	−0.0375121	−0.0187560	+	0.999824i	$0.505971\pi$
$60$	0	0
$61$	51.0000	0.107047	0.0535236	−	0.998567i	$-0.482955\pi$
$61$	51.0000	0.107047	0.0535236	+	0.998567i	$0.482955\pi$
$62$	150.000	0.307258
$63$	0	0
$64$	64.0000	0.125000
$65$	0	0
$66$	70.0000	0.130552
$67$	−439.000	−0.800483	−0.400242	−	0.916410i	$-0.631074\pi$
$67$	−439.000	−0.800483	−0.400242	+	0.916410i	$0.631074\pi$
$68$	−236.000	−0.420871
$69$	7.00000	0.0122131
$70$	0	0
$71$	−784.000	−1.31047	−0.655237	−	0.755423i	$-0.727431\pi$
$71$	−784.000	−1.31047	−0.655237	+	0.755423i	$0.727431\pi$
$72$	−208.000	−0.340459
$73$	−295.000	−0.472974	−0.236487	−	0.971635i	$-0.575996\pi$
$73$	−295.000	−0.472974	−0.236487	+	0.971635i	$0.575996\pi$
$74$	−22.0000	−0.0345601
$75$	0	0
$76$	548.000	0.827104
$77$	0	0
$78$	−132.000	−0.191616
$79$	−495.000	−0.704960	−0.352480	−	0.935819i	$-0.614662\pi$
$79$	−495.000	−0.704960	−0.352480	+	0.935819i	$0.614662\pi$
$80$	0	0
$81$	649.000	0.890261
$82$	−996.000	−1.34134
$83$	−932.000	−1.23253	−0.616267	−	0.787537i	$-0.711356\pi$
$83$	−932.000	−1.23253	−0.616267	+	0.787537i	$0.711356\pi$
$84$	0	0
$85$	0	0
$86$	−520.000	−0.652012
$87$	106.000	0.130625
$88$	280.000	0.339183
$89$	−873.000	−1.03975	−0.519875	−	0.854242i	$-0.674022\pi$
$89$	−873.000	−1.03975	−0.519875	+	0.854242i	$0.674022\pi$
$90$	0	0
$91$	0	0
$92$	28.0000	0.0317305
$93$	75.0000	0.0836251
$94$	342.000	0.375262
$95$	0	0
$96$	32.0000	0.0340207
$97$	290.000	0.303557	0.151779	−	0.988415i	$-0.451500\pi$
$97$	290.000	0.303557	0.151779	+	0.988415i	$0.451500\pi$
$98$	0	0
$99$	−910.000	−0.923823
$100$	0	0
$101$	−1085.00	−1.06893	−0.534463	−	0.845192i	$-0.679486\pi$
$101$	−1085.00	−1.06893	−0.534463	+	0.845192i	$0.679486\pi$
$102$	−118.000	−0.114546
$103$	−1553.00	−1.48565	−0.742823	−	0.669487i	$-0.766514\pi$
$103$	−1553.00	−1.48565	−0.742823	+	0.669487i	$0.766514\pi$
$104$	−528.000	−0.497833
$105$	0	0
$106$	834.000	0.764200
$107$	−129.000	−0.116550	−0.0582752	−	0.998301i	$-0.518560\pi$
$107$	−129.000	−0.116550	−0.0582752	+	0.998301i	$0.518560\pi$
$108$	−212.000	−0.188886
$109$	−965.000	−0.847984	−0.423992	−	0.905666i	$-0.639372\pi$
$109$	−965.000	−0.847984	−0.423992	+	0.905666i	$0.639372\pi$
$110$	0	0
$111$	−11.0000	−0.00940607
$112$	0	0
$113$	50.0000	0.0416248	0.0208124	−	0.999783i	$-0.493375\pi$
$113$	50.0000	0.0416248	0.0208124	+	0.999783i	$0.493375\pi$
$114$	274.000	0.225109
$115$	0	0
$116$	424.000	0.339374
$117$	1716.00	1.35593
$118$	−34.0000	−0.0265250
$119$	0	0
$120$	0	0
$121$	−106.000	−0.0796394
$122$	102.000	0.0756938
$123$	−498.000	−0.365066
$124$	300.000	0.217264
$125$	0	0
$126$	0	0
$127$	−936.000	−0.653989	−0.326994	−	0.945026i	$-0.606036\pi$
$127$	−936.000	−0.653989	−0.326994	+	0.945026i	$0.606036\pi$
$128$	128.000	0.0883883
$129$	−260.000	−0.177455
$130$	0	0
$131$	−755.000	−0.503547	−0.251773	−	0.967786i	$-0.581014\pi$
$131$	−755.000	−0.503547	−0.251773	+	0.967786i	$0.581014\pi$
$132$	140.000	0.0923139
$133$	0	0
$134$	−878.000	−0.566027
$135$	0	0
$136$	−472.000	−0.297600
$137$	2357.00	1.46987	0.734935	−	0.678138i	$-0.237213\pi$
$137$	2357.00	1.46987	0.734935	+	0.678138i	$0.237213\pi$
$138$	14.0000	0.00863594
$139$	28.0000	0.0170858	0.00854291	−	0.999964i	$-0.497281\pi$
$139$	28.0000	0.0170858	0.00854291	+	0.999964i	$0.497281\pi$
$140$	0	0
$141$	171.000	0.102133
$142$	−1568.00	−0.926645
$143$	−2310.00	−1.35085
$144$	−416.000	−0.240741
$145$	0	0
$146$	−590.000	−0.334443
$147$	0	0
$148$	−44.0000	−0.0244377
$149$	2295.00	1.26184	0.630919	−	0.775849i	$-0.282678\pi$
$149$	2295.00	1.26184	0.630919	+	0.775849i	$0.282678\pi$
$150$	0	0
$151$	−1109.00	−0.597676	−0.298838	−	0.954304i	$-0.596599\pi$
$151$	−1109.00	−0.597676	−0.298838	+	0.954304i	$0.596599\pi$
$152$	1096.00	0.584851
$153$	1534.00	0.810566
$154$	0	0
$155$	0	0
$156$	−264.000	−0.135493
$157$	−1559.00	−0.792495	−0.396248	−	0.918144i	$-0.629688\pi$
$157$	−1559.00	−0.792495	−0.396248	+	0.918144i	$0.629688\pi$
$158$	−990.000	−0.498482
$159$	417.000	0.207989
$160$	0	0
$161$	0	0
$162$	1298.00	0.629509
$163$	2251.00	1.08167	0.540834	−	0.841129i	$-0.318109\pi$
$163$	2251.00	1.08167	0.540834	+	0.841129i	$0.318109\pi$
$164$	−1992.00	−0.948470
$165$	0	0
$166$	−1864.00	−0.871533
$167$	−2788.00	−1.29187	−0.645934	−	0.763393i	$-0.723532\pi$
$167$	−2788.00	−1.29187	−0.645934	+	0.763393i	$0.723532\pi$
$168$	0	0
$169$	2159.00	0.982704
$170$	0	0
$171$	−3562.00	−1.59294
$172$	−1040.00	−0.461042
$173$	−1579.00	−0.693926	−0.346963	−	0.937879i	$-0.612787\pi$
$173$	−1579.00	−0.693926	−0.346963	+	0.937879i	$0.612787\pi$
$174$	212.000	0.0923660
$175$	0	0
$176$	560.000	0.239839
$177$	−17.0000	−0.00721920
$178$	−1746.00	−0.735215
$179$	2451.00	1.02344	0.511722	−	0.859151i	$-0.329008\pi$
$179$	2451.00	1.02344	0.511722	+	0.859151i	$0.329008\pi$
$180$	0	0
$181$	−1170.00	−0.480472	−0.240236	−	0.970715i	$-0.577225\pi$
$181$	−1170.00	−0.480472	−0.240236	+	0.970715i	$0.577225\pi$
$182$	0	0
$183$	51.0000	0.0206012
$184$	56.0000	0.0224368
$185$	0	0
$186$	150.000	0.0591319
$187$	−2065.00	−0.807528
$188$	684.000	0.265350
$189$	0	0
$190$	0	0
$191$	−1275.00	−0.483014	−0.241507	−	0.970399i	$-0.577642\pi$
$191$	−1275.00	−0.483014	−0.241507	+	0.970399i	$0.577642\pi$
$192$	64.0000	0.0240563
$193$	−35.0000	−0.0130537	−0.00652683	−	0.999979i	$-0.502078\pi$
$193$	−35.0000	−0.0130537	−0.00652683	+	0.999979i	$0.502078\pi$
$194$	580.000	0.214647
$195$	0	0
$196$	0	0
$197$	2734.00	0.988779	0.494389	−	0.869241i	$-0.335392\pi$
$197$	2734.00	0.988779	0.494389	+	0.869241i	$0.335392\pi$
$198$	−1820.00	−0.653241
$199$	2243.00	0.799005	0.399503	−	0.916732i	$-0.369183\pi$
$199$	2243.00	0.799005	0.399503	+	0.916732i	$0.369183\pi$
$200$	0	0
$201$	−439.000	−0.154053
$202$	−2170.00	−0.755845
$203$	0	0
$204$	−236.000	−0.0809966
$205$	0	0
$206$	−3106.00	−1.05051
$207$	−182.000	−0.0611105
$208$	−1056.00	−0.352021
$209$	4795.00	1.58697
$210$	0	0
$211$	1172.00	0.382388	0.191194	−	0.981552i	$-0.438764\pi$
$211$	1172.00	0.382388	0.191194	+	0.981552i	$0.438764\pi$
$212$	1668.00	0.540371
$213$	−784.000	−0.252201
$214$	−258.000	−0.0824136
$215$	0	0
$216$	−424.000	−0.133563
$217$	0	0
$218$	−1930.00	−0.599615
$219$	−295.000	−0.0910240
$220$	0	0
$221$	3894.00	1.18524
$222$	−22.0000	−0.00665110
$223$	−2024.00	−0.607790	−0.303895	−	0.952706i	$-0.598287\pi$
$223$	−2024.00	−0.607790	−0.303895	+	0.952706i	$0.598287\pi$
$224$	0	0
$225$	0	0
$226$	100.000	0.0294332
$227$	−2571.00	−0.751732	−0.375866	−	0.926674i	$-0.622655\pi$
$227$	−2571.00	−0.751732	−0.375866	+	0.926674i	$0.622655\pi$
$228$	548.000	0.159176
$229$	895.000	0.258268	0.129134	−	0.991627i	$-0.458780\pi$
$229$	895.000	0.258268	0.129134	+	0.991627i	$0.458780\pi$
$230$	0	0
$231$	0	0
$232$	848.000	0.239974
$233$	−1787.00	−0.502447	−0.251224	−	0.967929i	$-0.580833\pi$
$233$	−1787.00	−0.502447	−0.251224	+	0.967929i	$0.580833\pi$
$234$	3432.00	0.958790
$235$	0	0
$236$	−68.0000	−0.0187560
$237$	−495.000	−0.135670
$238$	0	0
$239$	−5100.00	−1.38030	−0.690150	−	0.723667i	$-0.742455\pi$
$239$	−5100.00	−1.38030	−0.690150	+	0.723667i	$0.742455\pi$
$240$	0	0
$241$	−4177.00	−1.11645	−0.558225	−	0.829690i	$-0.688517\pi$
$241$	−4177.00	−1.11645	−0.558225	+	0.829690i	$0.688517\pi$
$242$	−212.000	−0.0563135
$243$	2080.00	0.549103
$244$	204.000	0.0535236
$245$	0	0
$246$	−996.000	−0.258141
$247$	−9042.00	−2.32927
$248$	600.000	0.153629
$249$	−932.000	−0.237201
$250$	0	0
$251$	−4680.00	−1.17689	−0.588444	−	0.808538i	$-0.700259\pi$
$251$	−4680.00	−1.17689	−0.588444	+	0.808538i	$0.700259\pi$
$252$	0	0
$253$	245.000	0.0608815
$254$	−1872.00	−0.462440
$255$	0	0
$256$	256.000	0.0625000
$257$	1749.00	0.424512	0.212256	−	0.977214i	$-0.431919\pi$
$257$	1749.00	0.424512	0.212256	+	0.977214i	$0.431919\pi$
$258$	−520.000	−0.125480
$259$	0	0
$260$	0	0
$261$	−2756.00	−0.653610
$262$	−1510.00	−0.356061
$263$	4473.00	1.04873	0.524367	−	0.851492i	$-0.324302\pi$
$263$	4473.00	1.04873	0.524367	+	0.851492i	$0.324302\pi$
$264$	280.000	0.0652758
$265$	0	0
$266$	0	0
$267$	−873.000	−0.200100
$268$	−1756.00	−0.400242
$269$	1975.00	0.447650	0.223825	−	0.974629i	$-0.428146\pi$
$269$	1975.00	0.447650	0.223825	+	0.974629i	$0.428146\pi$
$270$	0	0
$271$	−8439.00	−1.89163	−0.945817	−	0.324701i	$-0.894736\pi$
$271$	−8439.00	−1.89163	−0.945817	+	0.324701i	$0.894736\pi$
$272$	−944.000	−0.210435
$273$	0	0
$274$	4714.00	1.03935
$275$	0	0
$276$	28.0000	0.00610653
$277$	−527.000	−0.114312	−0.0571559	−	0.998365i	$-0.518203\pi$
$277$	−527.000	−0.114312	−0.0571559	+	0.998365i	$0.518203\pi$
$278$	56.0000	0.0120815
$279$	−1950.00	−0.418435
$280$	0	0
$281$	−202.000	−0.0428837	−0.0214418	−	0.999770i	$-0.506826\pi$
$281$	−202.000	−0.0428837	−0.0214418	+	0.999770i	$0.506826\pi$
$282$	342.000	0.0722192
$283$	7949.00	1.66968	0.834839	−	0.550494i	$-0.185561\pi$
$283$	7949.00	1.66968	0.834839	+	0.550494i	$0.185561\pi$
$284$	−3136.00	−0.655237
$285$	0	0
$286$	−4620.00	−0.955197
$287$	0	0
$288$	−832.000	−0.170229
$289$	−1432.00	−0.291472
$290$	0	0
$291$	290.000	0.0584196
$292$	−1180.00	−0.236487
$293$	−318.000	−0.0634053	−0.0317027	−	0.999497i	$-0.510093\pi$
$293$	−318.000	−0.0634053	−0.0317027	+	0.999497i	$0.510093\pi$
$294$	0	0
$295$	0	0
$296$	−88.0000	−0.0172801
$297$	−1855.00	−0.362418
$298$	4590.00	0.892254
$299$	−462.000	−0.0893584
$300$	0	0
$301$	0	0
$302$	−2218.00	−0.422621
$303$	−1085.00	−0.205715
$304$	2192.00	0.413552
$305$	0	0
$306$	3068.00	0.573156
$307$	8132.00	1.51178	0.755892	−	0.654696i	$-0.227203\pi$
$307$	8132.00	1.51178	0.755892	+	0.654696i	$0.227203\pi$
$308$	0	0
$309$	−1553.00	−0.285913
$310$	0	0
$311$	−929.000	−0.169385	−0.0846925	−	0.996407i	$-0.526991\pi$
$311$	−929.000	−0.169385	−0.0846925	+	0.996407i	$0.526991\pi$
$312$	−528.000	−0.0958081
$313$	209.000	0.0377424	0.0188712	−	0.999822i	$-0.493993\pi$
$313$	209.000	0.0377424	0.0188712	+	0.999822i	$0.493993\pi$
$314$	−3118.00	−0.560379
$315$	0	0
$316$	−1980.00	−0.352480
$317$	−7131.00	−1.26346	−0.631730	−	0.775188i	$-0.717655\pi$
$317$	−7131.00	−1.26346	−0.631730	+	0.775188i	$0.717655\pi$
$318$	834.000	0.147070
$319$	3710.00	0.651160
$320$	0	0
$321$	−129.000	−0.0224301
$322$	0	0
$323$	−8083.00	−1.39242
$324$	2596.00	0.445130
$325$	0	0
$326$	4502.00	0.764855
$327$	−965.000	−0.163195
$328$	−3984.00	−0.670670
$329$	0	0
$330$	0	0
$331$	−6571.00	−1.09116	−0.545581	−	0.838058i	$-0.683691\pi$
$331$	−6571.00	−1.09116	−0.545581	+	0.838058i	$0.683691\pi$
$332$	−3728.00	−0.616267
$333$	286.000	0.0470652
$334$	−5576.00	−0.913488
$335$	0	0
$336$	0	0
$337$	11466.0	1.85339	0.926696	−	0.375813i	$-0.122636\pi$
$337$	11466.0	1.85339	0.926696	+	0.375813i	$0.122636\pi$
$338$	4318.00	0.694876
$339$	50.0000	0.00801070
$340$	0	0
$341$	2625.00	0.416867
$342$	−7124.00	−1.12638
$343$	0	0
$344$	−2080.00	−0.326006
$345$	0	0
$346$	−3158.00	−0.490680
$347$	9777.00	1.51256	0.756278	−	0.654251i	$-0.227016\pi$
$347$	9777.00	1.51256	0.756278	+	0.654251i	$0.227016\pi$
$348$	424.000	0.0653126
$349$	11914.0	1.82734	0.913670	−	0.406456i	$-0.133236\pi$
$349$	11914.0	1.82734	0.913670	+	0.406456i	$0.133236\pi$
$350$	0	0
$351$	3498.00	0.531936
$352$	1120.00	0.169591
$353$	−9123.00	−1.37555	−0.687774	−	0.725925i	$-0.741412\pi$
$353$	−9123.00	−1.37555	−0.687774	+	0.725925i	$0.741412\pi$
$354$	−34.0000	−0.00510474
$355$	0	0
$356$	−3492.00	−0.519875
$357$	0	0
$358$	4902.00	0.723684
$359$	8149.00	1.19802	0.599008	−	0.800743i	$-0.295562\pi$
$359$	8149.00	1.19802	0.599008	+	0.800743i	$0.295562\pi$
$360$	0	0
$361$	11910.0	1.73640
$362$	−2340.00	−0.339745
$363$	−106.000	−0.0153266
$364$	0	0
$365$	0	0
$366$	102.000	0.0145673
$367$	−9671.00	−1.37554	−0.687769	−	0.725930i	$-0.741410\pi$
$367$	−9671.00	−1.37554	−0.687769	+	0.725930i	$0.741410\pi$
$368$	112.000	0.0158652
$369$	12948.0	1.82668
$370$	0	0
$371$	0	0
$372$	300.000	0.0418126
$373$	4109.00	0.570391	0.285196	−	0.958469i	$-0.407941\pi$
$373$	4109.00	0.570391	0.285196	+	0.958469i	$0.407941\pi$
$374$	−4130.00	−0.571009
$375$	0	0
$376$	1368.00	0.187631
$377$	−6996.00	−0.955736
$378$	0	0
$379$	−3488.00	−0.472735	−0.236367	−	0.971664i	$-0.575957\pi$
$379$	−3488.00	−0.472735	−0.236367	+	0.971664i	$0.575957\pi$
$380$	0	0
$381$	−936.000	−0.125860
$382$	−2550.00	−0.341543
$383$	−8717.00	−1.16297	−0.581485	−	0.813557i	$-0.697528\pi$
$383$	−8717.00	−1.16297	−0.581485	+	0.813557i	$0.697528\pi$
$384$	128.000	0.0170103
$385$	0	0
$386$	−70.0000	−0.00923033
$387$	6760.00	0.887933
$388$	1160.00	0.151779
$389$	163.000	0.0212453	0.0106227	−	0.999944i	$-0.496619\pi$
$389$	163.000	0.0212453	0.0106227	+	0.999944i	$0.496619\pi$
$390$	0	0
$391$	−413.000	−0.0534177
$392$	0	0
$393$	−755.000	−0.0969077
$394$	5468.00	0.699172
$395$	0	0
$396$	−3640.00	−0.461911
$397$	−999.000	−0.126293	−0.0631466	−	0.998004i	$-0.520114\pi$
$397$	−999.000	−0.126293	−0.0631466	+	0.998004i	$0.520114\pi$
$398$	4486.00	0.564982
$399$	0	0
$400$	0	0
$401$	−14757.0	−1.83773	−0.918865	−	0.394573i	$-0.870893\pi$
$401$	−14757.0	−1.83773	−0.918865	+	0.394573i	$0.870893\pi$
$402$	−878.000	−0.108932
$403$	−4950.00	−0.611854
$404$	−4340.00	−0.534463
$405$	0	0
$406$	0	0
$407$	−385.000	−0.0468888
$408$	−472.000	−0.0572732
$409$	−133.000	−0.0160793	−0.00803964	−	0.999968i	$-0.502559\pi$
$409$	−133.000	−0.0160793	−0.00803964	+	0.999968i	$0.502559\pi$
$410$	0	0
$411$	2357.00	0.282876
$412$	−6212.00	−0.742823
$413$	0	0
$414$	−364.000	−0.0432117
$415$	0	0
$416$	−2112.00	−0.248917
$417$	28.0000	0.00328817
$418$	9590.00	1.12216
$419$	−6420.00	−0.748538	−0.374269	−	0.927320i	$-0.622106\pi$
$419$	−6420.00	−0.748538	−0.374269	+	0.927320i	$0.622106\pi$
$420$	0	0
$421$	10266.0	1.18844	0.594221	−	0.804302i	$-0.297460\pi$
$421$	10266.0	1.18844	0.594221	+	0.804302i	$0.297460\pi$
$422$	2344.00	0.270389
$423$	−4446.00	−0.511045
$424$	3336.00	0.382100
$425$	0	0
$426$	−1568.00	−0.178333
$427$	0	0
$428$	−516.000	−0.0582752
$429$	−2310.00	−0.259972
$430$	0	0
$431$	−15213.0	−1.70020	−0.850098	−	0.526625i	$-0.823457\pi$
$431$	−15213.0	−1.70020	−0.850098	+	0.526625i	$0.823457\pi$
$432$	−848.000	−0.0944431
$433$	1378.00	0.152939	0.0764693	−	0.997072i	$-0.475635\pi$
$433$	1378.00	0.152939	0.0764693	+	0.997072i	$0.475635\pi$
$434$	0	0
$435$	0	0
$436$	−3860.00	−0.423992
$437$	959.000	0.104978
$438$	−590.000	−0.0643637
$439$	−2763.00	−0.300389	−0.150195	−	0.988656i	$-0.547990\pi$
$439$	−2763.00	−0.300389	−0.150195	+	0.988656i	$0.547990\pi$
$440$	0	0
$441$	0	0
$442$	7788.00	0.838094
$443$	−5849.00	−0.627301	−0.313651	−	0.949538i	$-0.601552\pi$
$443$	−5849.00	−0.627301	−0.313651	+	0.949538i	$0.601552\pi$
$444$	−44.0000	−0.00470304
$445$	0	0
$446$	−4048.00	−0.429772
$447$	2295.00	0.242841
$448$	0	0
$449$	4582.00	0.481599	0.240799	−	0.970575i	$-0.422590\pi$
$449$	4582.00	0.481599	0.240799	+	0.970575i	$0.422590\pi$
$450$	0	0
$451$	−17430.0	−1.81984
$452$	200.000	0.0208124
$453$	−1109.00	−0.115023
$454$	−5142.00	−0.531555
$455$	0	0
$456$	1096.00	0.112555
$457$	−11551.0	−1.18235	−0.591174	−	0.806544i	$-0.701335\pi$
$457$	−11551.0	−1.18235	−0.591174	+	0.806544i	$0.701335\pi$
$458$	1790.00	0.182623
$459$	3127.00	0.317987
$460$	0	0
$461$	−9494.00	−0.959175	−0.479587	−	0.877494i	$-0.659214\pi$
$461$	−9494.00	−0.959175	−0.479587	+	0.877494i	$0.659214\pi$
$462$	0	0
$463$	10160.0	1.01982	0.509908	−	0.860229i	$-0.329679\pi$
$463$	10160.0	1.01982	0.509908	+	0.860229i	$0.329679\pi$
$464$	1696.00	0.169687
$465$	0	0
$466$	−3574.00	−0.355284
$467$	1307.00	0.129509	0.0647545	−	0.997901i	$-0.479374\pi$
$467$	1307.00	0.129509	0.0647545	+	0.997901i	$0.479374\pi$
$468$	6864.00	0.677967
$469$	0	0
$470$	0	0
$471$	−1559.00	−0.152516
$472$	−136.000	−0.0132625
$473$	−9100.00	−0.884606
$474$	−990.000	−0.0959329
$475$	0	0
$476$	0	0
$477$	−10842.0	−1.04072
$478$	−10200.0	−0.976019
$479$	18287.0	1.74437	0.872186	−	0.489174i	$-0.162702\pi$
$479$	18287.0	1.74437	0.872186	+	0.489174i	$0.162702\pi$
$480$	0	0
$481$	726.000	0.0688207
$482$	−8354.00	−0.789449
$483$	0	0
$484$	−424.000	−0.0398197
$485$	0	0
$486$	4160.00	0.388275
$487$	14953.0	1.39135	0.695673	−	0.718359i	$-0.255106\pi$
$487$	14953.0	1.39135	0.695673	+	0.718359i	$0.255106\pi$
$488$	408.000	0.0378469
$489$	2251.00	0.208167
$490$	0	0
$491$	14352.0	1.31914	0.659569	−	0.751644i	$-0.270739\pi$
$491$	14352.0	1.31914	0.659569	+	0.751644i	$0.270739\pi$
$492$	−1992.00	−0.182533
$493$	−6254.00	−0.571331
$494$	−18084.0	−1.64704
$495$	0	0
$496$	1200.00	0.108632
$497$	0	0
$498$	−1864.00	−0.167727
$499$	−5531.00	−0.496196	−0.248098	−	0.968735i	$-0.579805\pi$
$499$	−5531.00	−0.496196	−0.248098	+	0.968735i	$0.579805\pi$
$500$	0	0
$501$	−2788.00	−0.248620
$502$	−9360.00	−0.832186
$503$	−8400.00	−0.744607	−0.372304	−	0.928111i	$-0.621432\pi$
$503$	−8400.00	−0.744607	−0.372304	+	0.928111i	$0.621432\pi$
$504$	0	0
$505$	0	0
$506$	490.000	0.0430497
$507$	2159.00	0.189121
$508$	−3744.00	−0.326994
$509$	−2385.00	−0.207688	−0.103844	−	0.994594i	$-0.533114\pi$
$509$	−2385.00	−0.207688	−0.103844	+	0.994594i	$0.533114\pi$
$510$	0	0
$511$	0	0
$512$	512.000	0.0441942
$513$	−7261.00	−0.624914
$514$	3498.00	0.300175
$515$	0	0
$516$	−1040.00	−0.0887276
$517$	5985.00	0.509130
$518$	0	0
$519$	−1579.00	−0.133546
$520$	0	0
$521$	−9153.00	−0.769674	−0.384837	−	0.922985i	$-0.625742\pi$
$521$	−9153.00	−0.769674	−0.384837	+	0.922985i	$0.625742\pi$
$522$	−5512.00	−0.462172
$523$	13807.0	1.15437	0.577187	−	0.816612i	$-0.304150\pi$
$523$	13807.0	1.15437	0.577187	+	0.816612i	$0.304150\pi$
$524$	−3020.00	−0.251773
$525$	0	0
$526$	8946.00	0.741567
$527$	−4425.00	−0.365761
$528$	560.000	0.0461570
$529$	−12118.0	−0.995973
$530$	0	0
$531$	442.000	0.0361227
$532$	0	0
$533$	32868.0	2.67105
$534$	−1746.00	−0.141492
$535$	0	0
$536$	−3512.00	−0.283014
$537$	2451.00	0.196962
$538$	3950.00	0.316536
$539$	0	0
$540$	0	0
$541$	8175.00	0.649669	0.324834	−	0.945771i	$-0.394691\pi$
$541$	8175.00	0.649669	0.324834	+	0.945771i	$0.394691\pi$
$542$	−16878.0	−1.33759
$543$	−1170.00	−0.0924669
$544$	−1888.00	−0.148800
$545$	0	0
$546$	0	0
$547$	−4656.00	−0.363942	−0.181971	−	0.983304i	$-0.558248\pi$
$547$	−4656.00	−0.363942	−0.181971	+	0.983304i	$0.558248\pi$
$548$	9428.00	0.734935
$549$	−1326.00	−0.103083
$550$	0	0
$551$	14522.0	1.12279
$552$	56.0000	0.00431797
$553$	0	0
$554$	−1054.00	−0.0808306
$555$	0	0
$556$	112.000	0.00854291
$557$	−7003.00	−0.532723	−0.266361	−	0.963873i	$-0.585821\pi$
$557$	−7003.00	−0.532723	−0.266361	+	0.963873i	$0.585821\pi$
$558$	−3900.00	−0.295878
$559$	17160.0	1.29837
$560$	0	0
$561$	−2065.00	−0.155409
$562$	−404.000	−0.0303233
$563$	19753.0	1.47867	0.739334	−	0.673339i	$-0.235141\pi$
$563$	19753.0	1.47867	0.739334	+	0.673339i	$0.235141\pi$
$564$	684.000	0.0510667
$565$	0	0
$566$	15898.0	1.18064
$567$	0	0
$568$	−6272.00	−0.463323
$569$	−6897.00	−0.508150	−0.254075	−	0.967185i	$-0.581771\pi$
$569$	−6897.00	−0.508150	−0.254075	+	0.967185i	$0.581771\pi$
$570$	0	0
$571$	24915.0	1.82603	0.913013	−	0.407932i	$-0.133750\pi$
$571$	24915.0	1.82603	0.913013	+	0.407932i	$0.133750\pi$
$572$	−9240.00	−0.675426
$573$	−1275.00	−0.0929562
$574$	0	0
$575$	0	0
$576$	−1664.00	−0.120370
$577$	−127.000	−0.00916305	−0.00458152	−	0.999990i	$-0.501458\pi$
$577$	−127.000	−0.00916305	−0.00458152	+	0.999990i	$0.501458\pi$
$578$	−2864.00	−0.206102
$579$	−35.0000	−0.00251218
$580$	0	0
$581$	0	0
$582$	580.000	0.0413089
$583$	14595.0	1.03681
$584$	−2360.00	−0.167222
$585$	0	0
$586$	−636.000	−0.0448343
$587$	−9044.00	−0.635921	−0.317961	−	0.948104i	$-0.602998\pi$
$587$	−9044.00	−0.635921	−0.317961	+	0.948104i	$0.602998\pi$
$588$	0	0
$589$	10275.0	0.718801
$590$	0	0
$591$	2734.00	0.190291
$592$	−176.000	−0.0122188
$593$	10701.0	0.741041	0.370521	−	0.928824i	$-0.379179\pi$
$593$	10701.0	0.741041	0.370521	+	0.928824i	$0.379179\pi$
$594$	−3710.00	−0.256268
$595$	0	0
$596$	9180.00	0.630919
$597$	2243.00	0.153769
$598$	−924.000	−0.0631859
$599$	20799.0	1.41874	0.709369	−	0.704837i	$-0.248980\pi$
$599$	20799.0	1.41874	0.709369	+	0.704837i	$0.248980\pi$
$600$	0	0
$601$	−1402.00	−0.0951560	−0.0475780	−	0.998868i	$-0.515150\pi$
$601$	−1402.00	−0.0951560	−0.0475780	+	0.998868i	$0.515150\pi$
$602$	0	0
$603$	11414.0	0.770836
$604$	−4436.00	−0.298838
$605$	0	0
$606$	−2170.00	−0.145462
$607$	−6525.00	−0.436312	−0.218156	−	0.975914i	$-0.570004\pi$
$607$	−6525.00	−0.436312	−0.218156	+	0.975914i	$0.570004\pi$
$608$	4384.00	0.292425
$609$	0	0
$610$	0	0
$611$	−11286.0	−0.747271
$612$	6136.00	0.405283
$613$	−15051.0	−0.991687	−0.495844	−	0.868412i	$-0.665141\pi$
$613$	−15051.0	−0.991687	−0.495844	+	0.868412i	$0.665141\pi$
$614$	16264.0	1.06899
$615$	0	0
$616$	0	0
$617$	−11150.0	−0.727524	−0.363762	−	0.931492i	$-0.618508\pi$
$617$	−11150.0	−0.727524	−0.363762	+	0.931492i	$0.618508\pi$
$618$	−3106.00	−0.202171
$619$	3415.00	0.221745	0.110873	−	0.993835i	$-0.464635\pi$
$619$	3415.00	0.221745	0.110873	+	0.993835i	$0.464635\pi$
$620$	0	0
$621$	−371.000	−0.0239738
$622$	−1858.00	−0.119773
$623$	0	0
$624$	−1056.00	−0.0677465
$625$	0	0
$626$	418.000	0.0266879
$627$	4795.00	0.305413
$628$	−6236.00	−0.396248
$629$	649.000	0.0411404
$630$	0	0
$631$	−21184.0	−1.33648	−0.668242	−	0.743944i	$-0.732953\pi$
$631$	−21184.0	−1.33648	−0.668242	+	0.743944i	$0.732953\pi$
$632$	−3960.00	−0.249241
$633$	1172.00	0.0735905
$634$	−14262.0	−0.893401
$635$	0	0
$636$	1668.00	0.103995
$637$	0	0
$638$	7420.00	0.460440
$639$	20384.0	1.26194
$640$	0	0
$641$	−10705.0	−0.659629	−0.329814	−	0.944046i	$-0.606986\pi$
$641$	−10705.0	−0.659629	−0.329814	+	0.944046i	$0.606986\pi$
$642$	−258.000	−0.0158605
$643$	−6860.00	−0.420734	−0.210367	−	0.977622i	$-0.567466\pi$
$643$	−6860.00	−0.420734	−0.210367	+	0.977622i	$0.567466\pi$
$644$	0	0
$645$	0	0
$646$	−16166.0	−0.984586
$647$	−14463.0	−0.878824	−0.439412	−	0.898286i	$-0.644813\pi$
$647$	−14463.0	−0.878824	−0.439412	+	0.898286i	$0.644813\pi$
$648$	5192.00	0.314755
$649$	−595.000	−0.0359874
$650$	0	0
$651$	0	0
$652$	9004.00	0.540834
$653$	−5979.00	−0.358310	−0.179155	−	0.983821i	$-0.557336\pi$
$653$	−5979.00	−0.358310	−0.179155	+	0.983821i	$0.557336\pi$
$654$	−1930.00	−0.115396
$655$	0	0
$656$	−7968.00	−0.474235
$657$	7670.00	0.455457
$658$	0	0
$659$	−6940.00	−0.410234	−0.205117	−	0.978737i	$-0.565757\pi$
$659$	−6940.00	−0.410234	−0.205117	+	0.978737i	$0.565757\pi$
$660$	0	0
$661$	13399.0	0.788443	0.394221	−	0.919015i	$-0.371014\pi$
$661$	13399.0	0.788443	0.394221	+	0.919015i	$0.371014\pi$
$662$	−13142.0	−0.771568
$663$	3894.00	0.228100
$664$	−7456.00	−0.435766
$665$	0	0
$666$	572.000	0.0332801
$667$	742.000	0.0430740
$668$	−11152.0	−0.645934
$669$	−2024.00	−0.116969
$670$	0	0
$671$	1785.00	0.102696
$672$	0	0
$673$	−29510.0	−1.69023	−0.845117	−	0.534582i	$-0.820469\pi$
$673$	−29510.0	−1.69023	−0.845117	+	0.534582i	$0.820469\pi$
$674$	22932.0	1.31055
$675$	0	0
$676$	8636.00	0.491352
$677$	26001.0	1.47607	0.738035	−	0.674762i	$-0.235754\pi$
$677$	26001.0	1.47607	0.738035	+	0.674762i	$0.235754\pi$
$678$	100.000	0.00566442
$679$	0	0
$680$	0	0
$681$	−2571.00	−0.144671
$682$	5250.00	0.294770
$683$	8805.00	0.493285	0.246643	−	0.969106i	$-0.420673\pi$
$683$	8805.00	0.493285	0.246643	+	0.969106i	$0.420673\pi$
$684$	−14248.0	−0.796471
$685$	0	0
$686$	0	0
$687$	895.000	0.0497036
$688$	−4160.00	−0.230521
$689$	−27522.0	−1.52178
$690$	0	0
$691$	28685.0	1.57920	0.789601	−	0.613620i	$-0.210287\pi$
$691$	28685.0	1.57920	0.789601	+	0.613620i	$0.210287\pi$
$692$	−6316.00	−0.346963
$693$	0	0
$694$	19554.0	1.06954
$695$	0	0
$696$	848.000	0.0461830
$697$	29382.0	1.59673
$698$	23828.0	1.29212
$699$	−1787.00	−0.0966961
$700$	0	0
$701$	−3146.00	−0.169505	−0.0847523	−	0.996402i	$-0.527010\pi$
$701$	−3146.00	−0.169505	−0.0847523	+	0.996402i	$0.527010\pi$
$702$	6996.00	0.376135
$703$	−1507.00	−0.0808500
$704$	2240.00	0.119919
$705$	0	0
$706$	−18246.0	−0.972659
$707$	0	0
$708$	−68.0000	−0.00360960
$709$	1259.00	0.0666893	0.0333447	−	0.999444i	$-0.489384\pi$
$709$	1259.00	0.0666893	0.0333447	+	0.999444i	$0.489384\pi$
$710$	0	0
$711$	12870.0	0.678851
$712$	−6984.00	−0.367607
$713$	525.000	0.0275756
$714$	0	0
$715$	0	0
$716$	9804.00	0.511722
$717$	−5100.00	−0.265639
$718$	16298.0	0.847125
$719$	16425.0	0.851946	0.425973	−	0.904736i	$-0.359932\pi$
$719$	16425.0	0.851946	0.425973	+	0.904736i	$0.359932\pi$
$720$	0	0
$721$	0	0
$722$	23820.0	1.22782
$723$	−4177.00	−0.214861
$724$	−4680.00	−0.240236
$725$	0	0
$726$	−212.000	−0.0108375
$727$	6032.00	0.307723	0.153861	−	0.988092i	$-0.450829\pi$
$727$	6032.00	0.307723	0.153861	+	0.988092i	$0.450829\pi$
$728$	0	0
$729$	−15443.0	−0.784586
$730$	0	0
$731$	15340.0	0.776156
$732$	204.000	0.0103006
$733$	−15243.0	−0.768094	−0.384047	−	0.923314i	$-0.625470\pi$
$733$	−15243.0	−0.768094	−0.384047	+	0.923314i	$0.625470\pi$
$734$	−19342.0	−0.972652
$735$	0	0
$736$	224.000	0.0112184
$737$	−15365.0	−0.767947
$738$	25896.0	1.29166
$739$	−10053.0	−0.500414	−0.250207	−	0.968192i	$-0.580499\pi$
$739$	−10053.0	−0.500414	−0.250207	+	0.968192i	$0.580499\pi$
$740$	0	0
$741$	−9042.00	−0.448267
$742$	0	0
$743$	−24384.0	−1.20399	−0.601993	−	0.798501i	$-0.705627\pi$
$743$	−24384.0	−1.20399	−0.601993	+	0.798501i	$0.705627\pi$
$744$	600.000	0.0295660
$745$	0	0
$746$	8218.00	0.403328
$747$	24232.0	1.18688
$748$	−8260.00	−0.403764
$749$	0	0
$750$	0	0
$751$	11589.0	0.563101	0.281550	−	0.959546i	$-0.409151\pi$
$751$	11589.0	0.563101	0.281550	+	0.959546i	$0.409151\pi$
$752$	2736.00	0.132675
$753$	−4680.00	−0.226492
$754$	−13992.0	−0.675807
$755$	0	0
$756$	0	0
$757$	−14562.0	−0.699161	−0.349581	−	0.936906i	$-0.613676\pi$
$757$	−14562.0	−0.699161	−0.349581	+	0.936906i	$0.613676\pi$
$758$	−6976.00	−0.334274
$759$	245.000	0.0117166
$760$	0	0
$761$	−22765.0	−1.08440	−0.542201	−	0.840249i	$-0.682409\pi$
$761$	−22765.0	−1.08440	−0.542201	+	0.840249i	$0.682409\pi$
$762$	−1872.00	−0.0889966
$763$	0	0
$764$	−5100.00	−0.241507
$765$	0	0
$766$	−17434.0	−0.822345
$767$	1122.00	0.0528202
$768$	256.000	0.0120281
$769$	3766.00	0.176600	0.0883000	−	0.996094i	$-0.471857\pi$
$769$	3766.00	0.176600	0.0883000	+	0.996094i	$0.471857\pi$
$770$	0	0
$771$	1749.00	0.0816974
$772$	−140.000	−0.00652683
$773$	26861.0	1.24984	0.624918	−	0.780691i	$-0.285132\pi$
$773$	26861.0	1.24984	0.624918	+	0.780691i	$0.285132\pi$
$774$	13520.0	0.627864
$775$	0	0
$776$	2320.00	0.107324
$777$	0	0
$778$	326.000	0.0150227
$779$	−68226.0	−3.13793
$780$	0	0
$781$	−27440.0	−1.25721
$782$	−826.000	−0.0377720
$783$	−5618.00	−0.256412
$784$	0	0
$785$	0	0
$786$	−1510.00	−0.0685241
$787$	2097.00	0.0949809	0.0474905	−	0.998872i	$-0.484878\pi$
$787$	2097.00	0.0949809	0.0474905	+	0.998872i	$0.484878\pi$
$788$	10936.0	0.494389
$789$	4473.00	0.201829
$790$	0	0
$791$	0	0
$792$	−7280.00	−0.326621
$793$	−3366.00	−0.150732
$794$	−1998.00	−0.0893027
$795$	0	0
$796$	8972.00	0.399503
$797$	35334.0	1.57038	0.785191	−	0.619254i	$-0.212565\pi$
$797$	35334.0	1.57038	0.785191	+	0.619254i	$0.212565\pi$
$798$	0	0
$799$	−10089.0	−0.446712
$800$	0	0
$801$	22698.0	1.00124
$802$	−29514.0	−1.29947
$803$	−10325.0	−0.453750
$804$	−1756.00	−0.0770265
$805$	0	0
$806$	−9900.00	−0.432646
$807$	1975.00	0.0861503
$808$	−8680.00	−0.377922
$809$	42535.0	1.84852	0.924259	−	0.381766i	$-0.124684\pi$
$809$	42535.0	1.84852	0.924259	+	0.381766i	$0.124684\pi$
$810$	0	0
$811$	30676.0	1.32821	0.664106	−	0.747638i	$-0.268812\pi$
$811$	30676.0	1.32821	0.664106	+	0.747638i	$0.268812\pi$
$812$	0	0
$813$	−8439.00	−0.364045
$814$	−770.000	−0.0331554
$815$	0	0
$816$	−944.000	−0.0404983
$817$	−35620.0	−1.52532
$818$	−266.000	−0.0113698
$819$	0	0
$820$	0	0
$821$	37343.0	1.58743	0.793715	−	0.608290i	$-0.208144\pi$
$821$	37343.0	1.58743	0.793715	+	0.608290i	$0.208144\pi$
$822$	4714.00	0.200024
$823$	−2815.00	−0.119228	−0.0596141	−	0.998222i	$-0.518987\pi$
$823$	−2815.00	−0.119228	−0.0596141	+	0.998222i	$0.518987\pi$
$824$	−12424.0	−0.525256
$825$	0	0
$826$	0	0
$827$	9276.00	0.390034	0.195017	−	0.980800i	$-0.437524\pi$
$827$	9276.00	0.390034	0.195017	+	0.980800i	$0.437524\pi$
$828$	−728.000	−0.0305553
$829$	18571.0	0.778043	0.389021	−	0.921229i	$-0.372813\pi$
$829$	18571.0	0.778043	0.389021	+	0.921229i	$0.372813\pi$
$830$	0	0
$831$	−527.000	−0.0219993
$832$	−4224.00	−0.176011
$833$	0	0
$834$	56.0000	0.00232509
$835$	0	0
$836$	19180.0	0.793486
$837$	−3975.00	−0.164153
$838$	−12840.0	−0.529296
$839$	29048.0	1.19529	0.597645	−	0.801761i	$-0.296103\pi$
$839$	29048.0	1.19529	0.597645	+	0.801761i	$0.296103\pi$
$840$	0	0
$841$	−13153.0	−0.539301
$842$	20532.0	0.840356
$843$	−202.000	−0.00825297
$844$	4688.00	0.191194
$845$	0	0
$846$	−8892.00	−0.361363
$847$	0	0
$848$	6672.00	0.270186
$849$	7949.00	0.321330
$850$	0	0
$851$	−77.0000	−0.00310168
$852$	−3136.00	−0.126100
$853$	−32090.0	−1.28809	−0.644045	−	0.764988i	$-0.722745\pi$
$853$	−32090.0	−1.28809	−0.644045	+	0.764988i	$0.722745\pi$
$854$	0	0
$855$	0	0
$856$	−1032.00	−0.0412068
$857$	24537.0	0.978026	0.489013	−	0.872277i	$-0.337357\pi$
$857$	24537.0	0.978026	0.489013	+	0.872277i	$0.337357\pi$
$858$	−4620.00	−0.183828
$859$	20825.0	0.827171	0.413585	−	0.910465i	$-0.364276\pi$
$859$	20825.0	0.827171	0.413585	+	0.910465i	$0.364276\pi$
$860$	0	0
$861$	0	0
$862$	−30426.0	−1.20222
$863$	22847.0	0.901183	0.450591	−	0.892730i	$-0.351213\pi$
$863$	22847.0	0.901183	0.450591	+	0.892730i	$0.351213\pi$
$864$	−1696.00	−0.0667814
$865$	0	0
$866$	2756.00	0.108144
$867$	−1432.00	−0.0560937
$868$	0	0
$869$	−17325.0	−0.676307
$870$	0	0
$871$	28974.0	1.12715
$872$	−7720.00	−0.299808
$873$	−7540.00	−0.292314
$874$	1918.00	0.0742303
$875$	0	0
$876$	−1180.00	−0.0455120
$877$	42737.0	1.64553	0.822763	−	0.568385i	$-0.192432\pi$
$877$	42737.0	1.64553	0.822763	+	0.568385i	$0.192432\pi$
$878$	−5526.00	−0.212407
$879$	−318.000	−0.0122024
$880$	0	0
$881$	6162.00	0.235645	0.117822	−	0.993035i	$-0.462409\pi$
$881$	6162.00	0.235645	0.117822	+	0.993035i	$0.462409\pi$
$882$	0	0
$883$	−7748.00	−0.295290	−0.147645	−	0.989040i	$-0.547169\pi$
$883$	−7748.00	−0.295290	−0.147645	+	0.989040i	$0.547169\pi$
$884$	15576.0	0.592622
$885$	0	0
$886$	−11698.0	−0.443569
$887$	25923.0	0.981296	0.490648	−	0.871358i	$-0.336760\pi$
$887$	25923.0	0.981296	0.490648	+	0.871358i	$0.336760\pi$
$888$	−88.0000	−0.00332555
$889$	0	0
$890$	0	0
$891$	22715.0	0.854075
$892$	−8096.00	−0.303895
$893$	23427.0	0.877889
$894$	4590.00	0.171714
$895$	0	0
$896$	0	0
$897$	−462.000	−0.0171970
$898$	9164.00	0.340542
$899$	7950.00	0.294936
$900$	0	0
$901$	−24603.0	−0.909706
$902$	−34860.0	−1.28682
$903$	0	0
$904$	400.000	0.0147166
$905$	0	0
$906$	−2218.00	−0.0813335
$907$	−31935.0	−1.16911	−0.584556	−	0.811353i	$-0.698731\pi$
$907$	−31935.0	−1.16911	−0.584556	+	0.811353i	$0.698731\pi$
$908$	−10284.0	−0.375866
$909$	28210.0	1.02934
$910$	0	0
$911$	3408.00	0.123943	0.0619715	−	0.998078i	$-0.480261\pi$
$911$	3408.00	0.123943	0.0619715	+	0.998078i	$0.480261\pi$
$912$	2192.00	0.0795881
$913$	−32620.0	−1.18244
$914$	−23102.0	−0.836046
$915$	0	0
$916$	3580.00	0.129134
$917$	0	0
$918$	6254.00	0.224850
$919$	13909.0	0.499255	0.249628	−	0.968342i	$-0.419692\pi$
$919$	13909.0	0.499255	0.249628	+	0.968342i	$0.419692\pi$
$920$	0	0
$921$	8132.00	0.290943
$922$	−18988.0	−0.678239
$923$	51744.0	1.84526
$924$	0	0
$925$	0	0
$926$	20320.0	0.721119
$927$	40378.0	1.43062
$928$	3392.00	0.119987
$929$	−24537.0	−0.866559	−0.433279	−	0.901260i	$-0.642644\pi$
$929$	−24537.0	−0.866559	−0.433279	+	0.901260i	$0.642644\pi$
$930$	0	0
$931$	0	0
$932$	−7148.00	−0.251224
$933$	−929.000	−0.0325982
$934$	2614.00	0.0915768
$935$	0	0
$936$	13728.0	0.479395
$937$	32758.0	1.14211	0.571055	−	0.820912i	$-0.306534\pi$
$937$	32758.0	1.14211	0.571055	+	0.820912i	$0.306534\pi$
$938$	0	0
$939$	209.000	0.00726353
$940$	0	0
$941$	−38561.0	−1.33587	−0.667934	−	0.744220i	$-0.732821\pi$
$941$	−38561.0	−1.33587	−0.667934	+	0.744220i	$0.732821\pi$
$942$	−3118.00	−0.107845
$943$	−3486.00	−0.120382
$944$	−272.000	−0.00937801
$945$	0	0
$946$	−18200.0	−0.625511
$947$	−39661.0	−1.36094	−0.680470	−	0.732776i	$-0.738224\pi$
$947$	−39661.0	−1.36094	−0.680470	+	0.732776i	$0.738224\pi$
$948$	−1980.00	−0.0678348
$949$	19470.0	0.665988
$950$	0	0
$951$	−7131.00	−0.243153
$952$	0	0
$953$	46618.0	1.58458	0.792290	−	0.610144i	$-0.208889\pi$
$953$	46618.0	1.58458	0.792290	+	0.610144i	$0.208889\pi$
$954$	−21684.0	−0.735897
$955$	0	0
$956$	−20400.0	−0.690150
$957$	3710.00	0.125316
$958$	36574.0	1.23346
$959$	0	0
$960$	0	0
$961$	−24166.0	−0.811185
$962$	1452.00	0.0486636
$963$	3354.00	0.112234
$964$	−16708.0	−0.558225
$965$	0	0
$966$	0	0
$967$	−14816.0	−0.492710	−0.246355	−	0.969180i	$-0.579233\pi$
$967$	−14816.0	−0.492710	−0.246355	+	0.969180i	$0.579233\pi$
$968$	−848.000	−0.0281568
$969$	−8083.00	−0.267970
$970$	0	0
$971$	−16875.0	−0.557718	−0.278859	−	0.960332i	$-0.589956\pi$
$971$	−16875.0	−0.557718	−0.278859	+	0.960332i	$0.589956\pi$
$972$	8320.00	0.274552
$973$	0	0
$974$	29906.0	0.983830
$975$	0	0
$976$	816.000	0.0267618
$977$	15837.0	0.518598	0.259299	−	0.965797i	$-0.416508\pi$
$977$	15837.0	0.518598	0.259299	+	0.965797i	$0.416508\pi$
$978$	4502.00	0.147196
$979$	−30555.0	−0.997489
$980$	0	0
$981$	25090.0	0.816577
$982$	28704.0	0.932771
$983$	−9915.00	−0.321708	−0.160854	−	0.986978i	$-0.551425\pi$
$983$	−9915.00	−0.321708	−0.160854	+	0.986978i	$0.551425\pi$
$984$	−3984.00	−0.129070
$985$	0	0
$986$	−12508.0	−0.403992
$987$	0	0
$988$	−36168.0	−1.16463
$989$	−1820.00	−0.0585163
$990$	0	0
$991$	−43681.0	−1.40017	−0.700087	−	0.714057i	$-0.746856\pi$
$991$	−43681.0	−1.40017	−0.700087	+	0.714057i	$0.746856\pi$
$992$	2400.00	0.0768146
$993$	−6571.00	−0.209994
$994$	0	0
$995$	0	0
$996$	−3728.00	−0.118601
$997$	47113.0	1.49657	0.748287	−	0.663375i	$-0.230877\pi$
$997$	47113.0	1.49657	0.748287	+	0.663375i	$0.230877\pi$
$998$	−11062.0	−0.350863
$999$	583.000	0.0184638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2450.4.a.bh.1.1		1
5.4	even	2		98.4.a.b.1.1		1
7.2	even	3		350.4.e.b.151.1		2
7.4	even	3		350.4.e.b.51.1		2
7.6	odd	2		2450.4.a.bf.1.1		1
15.14	odd	2		882.4.a.k.1.1		1
20.19	odd	2		784.4.a.l.1.1		1
35.2	odd	12		350.4.j.d.249.2		4
35.4	even	6		14.4.c.b.9.1	✓	2
35.9	even	6		14.4.c.b.11.1	yes	2
35.18	odd	12		350.4.j.d.149.2		4
35.19	odd	6		98.4.c.e.67.1		2
35.23	odd	12		350.4.j.d.249.1		4
35.24	odd	6		98.4.c.e.79.1		2
35.32	odd	12		350.4.j.d.149.1		4
35.34	odd	2		98.4.a.c.1.1		1
105.44	odd	6		126.4.g.c.109.1		2
105.59	even	6		882.4.g.d.667.1		2
105.74	odd	6		126.4.g.c.37.1		2
105.89	even	6		882.4.g.d.361.1		2
105.104	even	2		882.4.a.p.1.1		1
140.39	odd	6		112.4.i.b.65.1		2
140.79	odd	6		112.4.i.b.81.1		2
140.139	even	2		784.4.a.j.1.1		1
280.109	even	6		448.4.i.c.65.1		2
280.149	even	6		448.4.i.c.193.1		2
280.179	odd	6		448.4.i.d.65.1		2
280.219	odd	6		448.4.i.d.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.b.9.1	✓	2	35.4	even	6
14.4.c.b.11.1	yes	2	35.9	even	6
98.4.a.b.1.1		1	5.4	even	2
98.4.a.c.1.1		1	35.34	odd	2
98.4.c.e.67.1		2	35.19	odd	6
98.4.c.e.79.1		2	35.24	odd	6
112.4.i.b.65.1		2	140.39	odd	6
112.4.i.b.81.1		2	140.79	odd	6
126.4.g.c.37.1		2	105.74	odd	6
126.4.g.c.109.1		2	105.44	odd	6
350.4.e.b.51.1		2	7.4	even	3
350.4.e.b.151.1		2	7.2	even	3
350.4.j.d.149.1		4	35.32	odd	12
350.4.j.d.149.2		4	35.18	odd	12
350.4.j.d.249.1		4	35.23	odd	12
350.4.j.d.249.2		4	35.2	odd	12
448.4.i.c.65.1		2	280.109	even	6
448.4.i.c.193.1		2	280.149	even	6
448.4.i.d.65.1		2	280.179	odd	6
448.4.i.d.193.1		2	280.219	odd	6
784.4.a.j.1.1		1	140.139	even	2
784.4.a.l.1.1		1	20.19	odd	2
882.4.a.k.1.1		1	15.14	odd	2
882.4.a.p.1.1		1	105.104	even	2
882.4.g.d.361.1		2	105.89	even	6
882.4.g.d.667.1		2	105.59	even	6
2450.4.a.bf.1.1		1	7.6	odd	2
2450.4.a.bh.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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