LMFDB - Embedded newform 350.4.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,4,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, 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("350.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.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:	$20.6506685020$
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	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +8.00000 q^{3} +4.00000 q^{4} +16.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +37.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +8.00000 q^{3} +4.00000 q^{4} +16.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +37.0000 q^{9} -7.00000 q^{11} +32.0000 q^{12} +26.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -44.0000 q^{17} +74.0000 q^{18} +142.000 q^{19} +56.0000 q^{21} -14.0000 q^{22} -115.000 q^{23} +64.0000 q^{24} +52.0000 q^{26} +80.0000 q^{27} +28.0000 q^{28} +1.00000 q^{29} +6.00000 q^{31} +32.0000 q^{32} -56.0000 q^{33} -88.0000 q^{34} +148.000 q^{36} +411.000 q^{37} +284.000 q^{38} +208.000 q^{39} -444.000 q^{41} +112.000 q^{42} -221.000 q^{43} -28.0000 q^{44} -230.000 q^{46} +258.000 q^{47} +128.000 q^{48} +49.0000 q^{49} -352.000 q^{51} +104.000 q^{52} -626.000 q^{53} +160.000 q^{54} +56.0000 q^{56} +1136.00 q^{57} +2.00000 q^{58} -162.000 q^{59} -820.000 q^{61} +12.0000 q^{62} +259.000 q^{63} +64.0000 q^{64} -112.000 q^{66} -519.000 q^{67} -176.000 q^{68} -920.000 q^{69} +61.0000 q^{71} +296.000 q^{72} +1160.00 q^{73} +822.000 q^{74} +568.000 q^{76} -49.0000 q^{77} +416.000 q^{78} -809.000 q^{79} -359.000 q^{81} -888.000 q^{82} +678.000 q^{83} +224.000 q^{84} -442.000 q^{86} +8.00000 q^{87} -56.0000 q^{88} +370.000 q^{89} +182.000 q^{91} -460.000 q^{92} +48.0000 q^{93} +516.000 q^{94} +256.000 q^{96} +310.000 q^{97} +98.0000 q^{98} -259.000 q^{99} +O(q^{100})\)

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
$3$	8.00000	1.53960	0.769800	−	0.638285i	$-0.220356\pi$
$3$	8.00000	1.53960	0.769800	+	0.638285i	$0.220356\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	16.0000	1.08866
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	37.0000	1.37037
$10$	0	0
$11$	−7.00000	−0.191871	−0.0959354	−	0.995388i	$-0.530584\pi$
$11$	−7.00000	−0.191871	−0.0959354	+	0.995388i	$0.530584\pi$
$12$	32.0000	0.769800
$13$	26.0000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	26.0000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−44.0000	−0.627739	−0.313870	−	0.949466i	$-0.601625\pi$
$17$	−44.0000	−0.627739	−0.313870	+	0.949466i	$0.601625\pi$
$18$	74.0000	0.968998
$19$	142.000	1.71458	0.857290	−	0.514833i	$-0.172146\pi$
$19$	142.000	1.71458	0.857290	+	0.514833i	$0.172146\pi$
$20$	0	0
$21$	56.0000	0.581914
$22$	−14.0000	−0.135673
$23$	−115.000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−115.000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	64.0000	0.544331
$25$	0	0
$26$	52.0000	0.392232
$27$	80.0000	0.570222
$28$	28.0000	0.188982
$29$	1.00000	0.00640329	0.00320164	−	0.999995i	$-0.498981\pi$
$29$	1.00000	0.00640329	0.00320164	+	0.999995i	$0.498981\pi$
$30$	0	0
$31$	6.00000	0.0347623	0.0173812	−	0.999849i	$-0.494467\pi$
$31$	6.00000	0.0347623	0.0173812	+	0.999849i	$0.494467\pi$
$32$	32.0000	0.176777
$33$	−56.0000	−0.295405
$34$	−88.0000	−0.443879
$35$	0	0
$36$	148.000	0.685185
$37$	411.000	1.82616	0.913081	−	0.407779i	$-0.133696\pi$
$37$	411.000	1.82616	0.913081	+	0.407779i	$0.133696\pi$
$38$	284.000	1.21239
$39$	208.000	0.854017
$40$	0	0
$41$	−444.000	−1.69125	−0.845624	−	0.533779i	$-0.820771\pi$
$41$	−444.000	−1.69125	−0.845624	+	0.533779i	$0.820771\pi$
$42$	112.000	0.411476
$43$	−221.000	−0.783772	−0.391886	−	0.920014i	$-0.628177\pi$
$43$	−221.000	−0.783772	−0.391886	+	0.920014i	$0.628177\pi$
$44$	−28.0000	−0.0959354
$45$	0	0
$46$	−230.000	−0.737210
$47$	258.000	0.800706	0.400353	−	0.916361i	$-0.368888\pi$
$47$	258.000	0.800706	0.400353	+	0.916361i	$0.368888\pi$
$48$	128.000	0.384900
$49$	49.0000	0.142857
$50$	0	0
$51$	−352.000	−0.966468
$52$	104.000	0.277350
$53$	−626.000	−1.62241	−0.811205	−	0.584762i	$-0.801188\pi$
$53$	−626.000	−1.62241	−0.811205	+	0.584762i	$0.801188\pi$
$54$	160.000	0.403208
$55$	0	0
$56$	56.0000	0.133631
$57$	1136.00	2.63977
$58$	2.00000	0.00452781
$59$	−162.000	−0.357468	−0.178734	−	0.983897i	$-0.557200\pi$
$59$	−162.000	−0.357468	−0.178734	+	0.983897i	$0.557200\pi$
$60$	0	0
$61$	−820.000	−1.72115	−0.860576	−	0.509322i	$-0.829896\pi$
$61$	−820.000	−1.72115	−0.860576	+	0.509322i	$0.829896\pi$
$62$	12.0000	0.0245807
$63$	259.000	0.517951
$64$	64.0000	0.125000
$65$	0	0
$66$	−112.000	−0.208883
$67$	−519.000	−0.946357	−0.473179	−	0.880966i	$-0.656893\pi$
$67$	−519.000	−0.946357	−0.473179	+	0.880966i	$0.656893\pi$
$68$	−176.000	−0.313870
$69$	−920.000	−1.60514
$70$	0	0
$71$	61.0000	0.101963	0.0509815	−	0.998700i	$-0.483765\pi$
$71$	61.0000	0.101963	0.0509815	+	0.998700i	$0.483765\pi$
$72$	296.000	0.484499
$73$	1160.00	1.85983	0.929916	−	0.367772i	$-0.119879\pi$
$73$	1160.00	1.85983	0.929916	+	0.367772i	$0.119879\pi$
$74$	822.000	1.29129
$75$	0	0
$76$	568.000	0.857290
$77$	−49.0000	−0.0725204
$78$	416.000	0.603881
$79$	−809.000	−1.15215	−0.576073	−	0.817398i	$-0.695416\pi$
$79$	−809.000	−1.15215	−0.576073	+	0.817398i	$0.695416\pi$
$80$	0	0
$81$	−359.000	−0.492455
$82$	−888.000	−1.19589
$83$	678.000	0.896629	0.448314	−	0.893876i	$-0.352025\pi$
$83$	678.000	0.896629	0.448314	+	0.893876i	$0.352025\pi$
$84$	224.000	0.290957
$85$	0	0
$86$	−442.000	−0.554210
$87$	8.00000	0.00985851
$88$	−56.0000	−0.0678366
$89$	370.000	0.440673	0.220337	−	0.975424i	$-0.429284\pi$
$89$	370.000	0.440673	0.220337	+	0.975424i	$0.429284\pi$
$90$	0	0
$91$	182.000	0.209657
$92$	−460.000	−0.521286
$93$	48.0000	0.0535201
$94$	516.000	0.566184
$95$	0	0
$96$	256.000	0.272166
$97$	310.000	0.324492	0.162246	−	0.986750i	$-0.448126\pi$
$97$	310.000	0.324492	0.162246	+	0.986750i	$0.448126\pi$
$98$	98.0000	0.101015
$99$	−259.000	−0.262934
$100$	0	0
$101$	420.000	0.413778	0.206889	−	0.978364i	$-0.433666\pi$
$101$	420.000	0.413778	0.206889	+	0.978364i	$0.433666\pi$
$102$	−704.000	−0.683396
$103$	−610.000	−0.583545	−0.291772	−	0.956488i	$-0.594245\pi$
$103$	−610.000	−0.583545	−0.291772	+	0.956488i	$0.594245\pi$
$104$	208.000	0.196116
$105$	0	0
$106$	−1252.00	−1.14722
$107$	−1284.00	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−1284.00	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	320.000	0.285111
$109$	1661.00	1.45959	0.729793	−	0.683668i	$-0.239616\pi$
$109$	1661.00	1.45959	0.729793	+	0.683668i	$0.239616\pi$
$110$	0	0
$111$	3288.00	2.81156
$112$	112.000	0.0944911
$113$	1413.00	1.17632	0.588159	−	0.808746i	$-0.299853\pi$
$113$	1413.00	1.17632	0.588159	+	0.808746i	$0.299853\pi$
$114$	2272.00	1.86660
$115$	0	0
$116$	4.00000	0.00320164
$117$	962.000	0.760145
$118$	−324.000	−0.252768
$119$	−308.000	−0.237263
$120$	0	0
$121$	−1282.00	−0.963186
$122$	−1640.00	−1.21704
$123$	−3552.00	−2.60385
$124$	24.0000	0.0173812
$125$	0	0
$126$	518.000	0.366247
$127$	1189.00	0.830761	0.415381	−	0.909648i	$-0.363648\pi$
$127$	1189.00	0.830761	0.415381	+	0.909648i	$0.363648\pi$
$128$	128.000	0.0883883
$129$	−1768.00	−1.20670
$130$	0	0
$131$	−2380.00	−1.58734	−0.793670	−	0.608348i	$-0.791832\pi$
$131$	−2380.00	−1.58734	−0.793670	+	0.608348i	$0.791832\pi$
$132$	−224.000	−0.147702
$133$	994.000	0.648051
$134$	−1038.00	−0.669176
$135$	0	0
$136$	−352.000	−0.221939
$137$	−1618.00	−1.00902	−0.504508	−	0.863407i	$-0.668326\pi$
$137$	−1618.00	−1.00902	−0.504508	+	0.863407i	$0.668326\pi$
$138$	−1840.00	−1.13501
$139$	−3148.00	−1.92093	−0.960467	−	0.278393i	$-0.910198\pi$
$139$	−3148.00	−1.92093	−0.960467	+	0.278393i	$0.910198\pi$
$140$	0	0
$141$	2064.00	1.23277
$142$	122.000	0.0720987
$143$	−182.000	−0.106431
$144$	592.000	0.342593
$145$	0	0
$146$	2320.00	1.31510
$147$	392.000	0.219943
$148$	1644.00	0.913081
$149$	1883.00	1.03531	0.517656	−	0.855589i	$-0.326805\pi$
$149$	1883.00	1.03531	0.517656	+	0.855589i	$0.326805\pi$
$150$	0	0
$151$	733.000	0.395038	0.197519	−	0.980299i	$-0.436712\pi$
$151$	733.000	0.395038	0.197519	+	0.980299i	$0.436712\pi$
$152$	1136.00	0.606196
$153$	−1628.00	−0.860235
$154$	−98.0000	−0.0512796
$155$	0	0
$156$	832.000	0.427008
$157$	720.000	0.366002	0.183001	−	0.983113i	$-0.441419\pi$
$157$	720.000	0.366002	0.183001	+	0.983113i	$0.441419\pi$
$158$	−1618.00	−0.814691
$159$	−5008.00	−2.49786
$160$	0	0
$161$	−805.000	−0.394055
$162$	−718.000	−0.348219
$163$	880.000	0.422865	0.211432	−	0.977393i	$-0.432187\pi$
$163$	880.000	0.422865	0.211432	+	0.977393i	$0.432187\pi$
$164$	−1776.00	−0.845624
$165$	0	0
$166$	1356.00	0.634012
$167$	−2866.00	−1.32801	−0.664005	−	0.747728i	$-0.731145\pi$
$167$	−2866.00	−1.32801	−0.664005	+	0.747728i	$0.731145\pi$
$168$	448.000	0.205738
$169$	−1521.00	−0.692308
$170$	0	0
$171$	5254.00	2.34961
$172$	−884.000	−0.391886
$173$	−1698.00	−0.746223	−0.373111	−	0.927787i	$-0.621709\pi$
$173$	−1698.00	−0.746223	−0.373111	+	0.927787i	$0.621709\pi$
$174$	16.0000	0.00697102
$175$	0	0
$176$	−112.000	−0.0479677
$177$	−1296.00	−0.550358
$178$	740.000	0.311603
$179$	292.000	0.121928	0.0609640	−	0.998140i	$-0.480583\pi$
$179$	292.000	0.121928	0.0609640	+	0.998140i	$0.480583\pi$
$180$	0	0
$181$	−2388.00	−0.980655	−0.490328	−	0.871538i	$-0.663123\pi$
$181$	−2388.00	−0.980655	−0.490328	+	0.871538i	$0.663123\pi$
$182$	364.000	0.148250
$183$	−6560.00	−2.64989
$184$	−920.000	−0.368605
$185$	0	0
$186$	96.0000	0.0378444
$187$	308.000	0.120445
$188$	1032.00	0.400353
$189$	560.000	0.215524
$190$	0	0
$191$	464.000	0.175779	0.0878897	−	0.996130i	$-0.471988\pi$
$191$	464.000	0.175779	0.0878897	+	0.996130i	$0.471988\pi$
$192$	512.000	0.192450
$193$	−1595.00	−0.594874	−0.297437	−	0.954742i	$-0.596132\pi$
$193$	−1595.00	−0.594874	−0.297437	+	0.954742i	$0.596132\pi$
$194$	620.000	0.229451
$195$	0	0
$196$	196.000	0.0714286
$197$	2733.00	0.988417	0.494209	−	0.869343i	$-0.335458\pi$
$197$	2733.00	0.988417	0.494209	+	0.869343i	$0.335458\pi$
$198$	−518.000	−0.185923
$199$	−324.000	−0.115416	−0.0577079	−	0.998334i	$-0.518379\pi$
$199$	−324.000	−0.115416	−0.0577079	+	0.998334i	$0.518379\pi$
$200$	0	0
$201$	−4152.00	−1.45701
$202$	840.000	0.292585
$203$	7.00000	0.00242022
$204$	−1408.00	−0.483234
$205$	0	0
$206$	−1220.00	−0.412628
$207$	−4255.00	−1.42871
$208$	416.000	0.138675
$209$	−994.000	−0.328978
$210$	0	0
$211$	2172.00	0.708657	0.354329	−	0.935121i	$-0.384709\pi$
$211$	2172.00	0.708657	0.354329	+	0.935121i	$0.384709\pi$
$212$	−2504.00	−0.811205
$213$	488.000	0.156982
$214$	−2568.00	−0.820303
$215$	0	0
$216$	640.000	0.201604
$217$	42.0000	0.0131389
$218$	3322.00	1.03208
$219$	9280.00	2.86340
$220$	0	0
$221$	−1144.00	−0.348207
$222$	6576.00	1.98807
$223$	5332.00	1.60115	0.800577	−	0.599231i	$-0.204527\pi$
$223$	5332.00	1.60115	0.800577	+	0.599231i	$0.204527\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	2826.00	0.831782
$227$	−226.000	−0.0660799	−0.0330400	−	0.999454i	$-0.510519\pi$
$227$	−226.000	−0.0660799	−0.0330400	+	0.999454i	$0.510519\pi$
$228$	4544.00	1.31988
$229$	−4006.00	−1.15600	−0.578000	−	0.816037i	$-0.696167\pi$
$229$	−4006.00	−1.15600	−0.578000	+	0.816037i	$0.696167\pi$
$230$	0	0
$231$	−392.000	−0.111652
$232$	8.00000	0.00226390
$233$	6403.00	1.80032	0.900160	−	0.435560i	$-0.143450\pi$
$233$	6403.00	1.80032	0.900160	+	0.435560i	$0.143450\pi$
$234$	1924.00	0.537503
$235$	0	0
$236$	−648.000	−0.178734
$237$	−6472.00	−1.77385
$238$	−616.000	−0.167770
$239$	5412.00	1.46474	0.732371	−	0.680906i	$-0.238414\pi$
$239$	5412.00	1.46474	0.732371	+	0.680906i	$0.238414\pi$
$240$	0	0
$241$	−410.000	−0.109587	−0.0547934	−	0.998498i	$-0.517450\pi$
$241$	−410.000	−0.109587	−0.0547934	+	0.998498i	$0.517450\pi$
$242$	−2564.00	−0.681075
$243$	−5032.00	−1.32841
$244$	−3280.00	−0.860576
$245$	0	0
$246$	−7104.00	−1.84120
$247$	3692.00	0.951078
$248$	48.0000	0.0122903
$249$	5424.00	1.38045
$250$	0	0
$251$	−2520.00	−0.633709	−0.316855	−	0.948474i	$-0.602627\pi$
$251$	−2520.00	−0.633709	−0.316855	+	0.948474i	$0.602627\pi$
$252$	1036.00	0.258976
$253$	805.000	0.200039
$254$	2378.00	0.587437
$255$	0	0
$256$	256.000	0.0625000
$257$	−1450.00	−0.351940	−0.175970	−	0.984396i	$-0.556306\pi$
$257$	−1450.00	−0.351940	−0.175970	+	0.984396i	$0.556306\pi$
$258$	−3536.00	−0.853263
$259$	2877.00	0.690224
$260$	0	0
$261$	37.0000	0.00877488
$262$	−4760.00	−1.12242
$263$	8203.00	1.92326	0.961632	−	0.274341i	$-0.0884598\pi$
$263$	8203.00	1.92326	0.961632	+	0.274341i	$0.0884598\pi$
$264$	−448.000	−0.104441
$265$	0	0
$266$	1988.00	0.458241
$267$	2960.00	0.678461
$268$	−2076.00	−0.473179
$269$	6306.00	1.42931	0.714654	−	0.699479i	$-0.246584\pi$
$269$	6306.00	1.42931	0.714654	+	0.699479i	$0.246584\pi$
$270$	0	0
$271$	2122.00	0.475654	0.237827	−	0.971307i	$-0.423565\pi$
$271$	2122.00	0.475654	0.237827	+	0.971307i	$0.423565\pi$
$272$	−704.000	−0.156935
$273$	1456.00	0.322788
$274$	−3236.00	−0.713481
$275$	0	0
$276$	−3680.00	−0.802572
$277$	254.000	0.0550952	0.0275476	−	0.999620i	$-0.491230\pi$
$277$	254.000	0.0550952	0.0275476	+	0.999620i	$0.491230\pi$
$278$	−6296.00	−1.35831
$279$	222.000	0.0476372
$280$	0	0
$281$	−5163.00	−1.09608	−0.548040	−	0.836452i	$-0.684626\pi$
$281$	−5163.00	−1.09608	−0.548040	+	0.836452i	$0.684626\pi$
$282$	4128.00	0.871698
$283$	2162.00	0.454126	0.227063	−	0.973880i	$-0.427088\pi$
$283$	2162.00	0.454126	0.227063	+	0.973880i	$0.427088\pi$
$284$	244.000	0.0509815
$285$	0	0
$286$	−364.000	−0.0752579
$287$	−3108.00	−0.639231
$288$	1184.00	0.242250
$289$	−2977.00	−0.605943
$290$	0	0
$291$	2480.00	0.499588
$292$	4640.00	0.929916
$293$	−6558.00	−1.30759	−0.653793	−	0.756674i	$-0.726823\pi$
$293$	−6558.00	−1.30759	−0.653793	+	0.756674i	$0.726823\pi$
$294$	784.000	0.155523
$295$	0	0
$296$	3288.00	0.645646
$297$	−560.000	−0.109409
$298$	3766.00	0.732076
$299$	−2990.00	−0.578315
$300$	0	0
$301$	−1547.00	−0.296238
$302$	1466.00	0.279334
$303$	3360.00	0.637053
$304$	2272.00	0.428645
$305$	0	0
$306$	−3256.00	−0.608278
$307$	1696.00	0.315296	0.157648	−	0.987495i	$-0.449609\pi$
$307$	1696.00	0.315296	0.157648	+	0.987495i	$0.449609\pi$
$308$	−196.000	−0.0362602
$309$	−4880.00	−0.898426
$310$	0	0
$311$	2632.00	0.479894	0.239947	−	0.970786i	$-0.422870\pi$
$311$	2632.00	0.479894	0.239947	+	0.970786i	$0.422870\pi$
$312$	1664.00	0.301941
$313$	7890.00	1.42482	0.712411	−	0.701763i	$-0.247603\pi$
$313$	7890.00	1.42482	0.712411	+	0.701763i	$0.247603\pi$
$314$	1440.00	0.258802
$315$	0	0
$316$	−3236.00	−0.576073
$317$	1361.00	0.241140	0.120570	−	0.992705i	$-0.461528\pi$
$317$	1361.00	0.241140	0.120570	+	0.992705i	$0.461528\pi$
$318$	−10016.0	−1.76626
$319$	−7.00000	−0.00122860
$320$	0	0
$321$	−10272.0	−1.78607
$322$	−1610.00	−0.278639
$323$	−6248.00	−1.07631
$324$	−1436.00	−0.246228
$325$	0	0
$326$	1760.00	0.299010
$327$	13288.0	2.24718
$328$	−3552.00	−0.597946
$329$	1806.00	0.302638
$330$	0	0
$331$	3255.00	0.540517	0.270258	−	0.962788i	$-0.412891\pi$
$331$	3255.00	0.540517	0.270258	+	0.962788i	$0.412891\pi$
$332$	2712.00	0.448314
$333$	15207.0	2.50252
$334$	−5732.00	−0.939045
$335$	0	0
$336$	896.000	0.145479
$337$	5634.00	0.910693	0.455346	−	0.890314i	$-0.349515\pi$
$337$	5634.00	0.910693	0.455346	+	0.890314i	$0.349515\pi$
$338$	−3042.00	−0.489535
$339$	11304.0	1.81106
$340$	0	0
$341$	−42.0000	−0.00666988
$342$	10508.0	1.66143
$343$	343.000	0.0539949
$344$	−1768.00	−0.277105
$345$	0	0
$346$	−3396.00	−0.527659
$347$	12463.0	1.92809	0.964047	−	0.265730i	$-0.0856131\pi$
$347$	12463.0	1.92809	0.964047	+	0.265730i	$0.0856131\pi$
$348$	32.0000	0.00492925
$349$	−2578.00	−0.395407	−0.197704	−	0.980262i	$-0.563348\pi$
$349$	−2578.00	−0.395407	−0.197704	+	0.980262i	$0.563348\pi$
$350$	0	0
$351$	2080.00	0.316303
$352$	−224.000	−0.0339183
$353$	890.000	0.134192	0.0670962	−	0.997747i	$-0.478627\pi$
$353$	890.000	0.134192	0.0670962	+	0.997747i	$0.478627\pi$
$354$	−2592.00	−0.389162
$355$	0	0
$356$	1480.00	0.220337
$357$	−2464.00	−0.365291
$358$	584.000	0.0862161
$359$	−3639.00	−0.534983	−0.267492	−	0.963560i	$-0.586195\pi$
$359$	−3639.00	−0.534983	−0.267492	+	0.963560i	$0.586195\pi$
$360$	0	0
$361$	13305.0	1.93979
$362$	−4776.00	−0.693428
$363$	−10256.0	−1.48292
$364$	728.000	0.104828
$365$	0	0
$366$	−13120.0	−1.87375
$367$	7976.00	1.13445	0.567226	−	0.823562i	$-0.308017\pi$
$367$	7976.00	1.13445	0.567226	+	0.823562i	$0.308017\pi$
$368$	−1840.00	−0.260643
$369$	−16428.0	−2.31764
$370$	0	0
$371$	−4382.00	−0.613213
$372$	192.000	0.0267600
$373$	11413.0	1.58430	0.792148	−	0.610328i	$-0.208963\pi$
$373$	11413.0	1.58430	0.792148	+	0.610328i	$0.208963\pi$
$374$	616.000	0.0851674
$375$	0	0
$376$	2064.00	0.283092
$377$	26.0000	0.00355190
$378$	1120.00	0.152398
$379$	5503.00	0.745831	0.372916	−	0.927865i	$-0.378358\pi$
$379$	5503.00	0.745831	0.372916	+	0.927865i	$0.378358\pi$
$380$	0	0
$381$	9512.00	1.27904
$382$	928.000	0.124295
$383$	1550.00	0.206792	0.103396	−	0.994640i	$-0.467029\pi$
$383$	1550.00	0.206792	0.103396	+	0.994640i	$0.467029\pi$
$384$	1024.00	0.136083
$385$	0	0
$386$	−3190.00	−0.420639
$387$	−8177.00	−1.07406
$388$	1240.00	0.162246
$389$	14089.0	1.83635	0.918176	−	0.396174i	$-0.129662\pi$
$389$	14089.0	1.83635	0.918176	+	0.396174i	$0.129662\pi$
$390$	0	0
$391$	5060.00	0.654463
$392$	392.000	0.0505076
$393$	−19040.0	−2.44387
$394$	5466.00	0.698917
$395$	0	0
$396$	−1036.00	−0.131467
$397$	2334.00	0.295063	0.147532	−	0.989057i	$-0.452867\pi$
$397$	2334.00	0.295063	0.147532	+	0.989057i	$0.452867\pi$
$398$	−648.000	−0.0816113
$399$	7952.00	0.997739
$400$	0	0
$401$	1933.00	0.240722	0.120361	−	0.992730i	$-0.461595\pi$
$401$	1933.00	0.240722	0.120361	+	0.992730i	$0.461595\pi$
$402$	−8304.00	−1.03026
$403$	156.000	0.0192827
$404$	1680.00	0.206889
$405$	0	0
$406$	14.0000	0.00171135
$407$	−2877.00	−0.350387
$408$	−2816.00	−0.341698
$409$	−350.000	−0.0423139	−0.0211570	−	0.999776i	$-0.506735\pi$
$409$	−350.000	−0.0423139	−0.0211570	+	0.999776i	$0.506735\pi$
$410$	0	0
$411$	−12944.0	−1.55348
$412$	−2440.00	−0.291772
$413$	−1134.00	−0.135110
$414$	−8510.00	−1.01025
$415$	0	0
$416$	832.000	0.0980581
$417$	−25184.0	−2.95747
$418$	−1988.00	−0.232623
$419$	11618.0	1.35460	0.677299	−	0.735708i	$-0.263150\pi$
$419$	11618.0	1.35460	0.677299	+	0.735708i	$0.263150\pi$
$420$	0	0
$421$	−4085.00	−0.472900	−0.236450	−	0.971644i	$-0.575984\pi$
$421$	−4085.00	−0.472900	−0.236450	+	0.971644i	$0.575984\pi$
$422$	4344.00	0.501096
$423$	9546.00	1.09726
$424$	−5008.00	−0.573608
$425$	0	0
$426$	976.000	0.111003
$427$	−5740.00	−0.650534
$428$	−5136.00	−0.580042
$429$	−1456.00	−0.163861
$430$	0	0
$431$	15024.0	1.67907	0.839537	−	0.543303i	$-0.182827\pi$
$431$	15024.0	1.67907	0.839537	+	0.543303i	$0.182827\pi$
$432$	1280.00	0.142556
$433$	−8212.00	−0.911417	−0.455708	−	0.890129i	$-0.650614\pi$
$433$	−8212.00	−0.911417	−0.455708	+	0.890129i	$0.650614\pi$
$434$	84.0000	0.00929062
$435$	0	0
$436$	6644.00	0.729793
$437$	−16330.0	−1.78757
$438$	18560.0	2.02473
$439$	−6086.00	−0.661660	−0.330830	−	0.943690i	$-0.607329\pi$
$439$	−6086.00	−0.661660	−0.330830	+	0.943690i	$0.607329\pi$
$440$	0	0
$441$	1813.00	0.195767
$442$	−2288.00	−0.246220
$443$	−9552.00	−1.02445	−0.512223	−	0.858853i	$-0.671178\pi$
$443$	−9552.00	−1.02445	−0.512223	+	0.858853i	$0.671178\pi$
$444$	13152.0	1.40578
$445$	0	0
$446$	10664.0	1.13219
$447$	15064.0	1.59397
$448$	448.000	0.0472456
$449$	−4885.00	−0.513446	−0.256723	−	0.966485i	$-0.582643\pi$
$449$	−4885.00	−0.513446	−0.256723	+	0.966485i	$0.582643\pi$
$450$	0	0
$451$	3108.00	0.324501
$452$	5652.00	0.588159
$453$	5864.00	0.608200
$454$	−452.000	−0.0467256
$455$	0	0
$456$	9088.00	0.933300
$457$	−14551.0	−1.48942	−0.744712	−	0.667386i	$-0.767413\pi$
$457$	−14551.0	−1.48942	−0.744712	+	0.667386i	$0.767413\pi$
$458$	−8012.00	−0.817415
$459$	−3520.00	−0.357951
$460$	0	0
$461$	−12442.0	−1.25701	−0.628505	−	0.777805i	$-0.716333\pi$
$461$	−12442.0	−1.25701	−0.628505	+	0.777805i	$0.716333\pi$
$462$	−784.000	−0.0789502
$463$	7704.00	0.773294	0.386647	−	0.922228i	$-0.373633\pi$
$463$	7704.00	0.773294	0.386647	+	0.922228i	$0.373633\pi$
$464$	16.0000	0.00160082
$465$	0	0
$466$	12806.0	1.27302
$467$	4422.00	0.438171	0.219085	−	0.975706i	$-0.429693\pi$
$467$	4422.00	0.438171	0.219085	+	0.975706i	$0.429693\pi$
$468$	3848.00	0.380072
$469$	−3633.00	−0.357689
$470$	0	0
$471$	5760.00	0.563496
$472$	−1296.00	−0.126384
$473$	1547.00	0.150383
$474$	−12944.0	−1.25430
$475$	0	0
$476$	−1232.00	−0.118632
$477$	−23162.0	−2.22330
$478$	10824.0	1.03573
$479$	2762.00	0.263463	0.131732	−	0.991285i	$-0.457946\pi$
$479$	2762.00	0.263463	0.131732	+	0.991285i	$0.457946\pi$
$480$	0	0
$481$	10686.0	1.01297
$482$	−820.000	−0.0774896
$483$	−6440.00	−0.606688
$484$	−5128.00	−0.481593
$485$	0	0
$486$	−10064.0	−0.939326
$487$	10967.0	1.02046	0.510228	−	0.860039i	$-0.329561\pi$
$487$	10967.0	1.02046	0.510228	+	0.860039i	$0.329561\pi$
$488$	−6560.00	−0.608519
$489$	7040.00	0.651043
$490$	0	0
$491$	−9387.00	−0.862789	−0.431394	−	0.902163i	$-0.641978\pi$
$491$	−9387.00	−0.862789	−0.431394	+	0.902163i	$0.641978\pi$
$492$	−14208.0	−1.30192
$493$	−44.0000	−0.00401960
$494$	7384.00	0.672514
$495$	0	0
$496$	96.0000	0.00869058
$497$	427.000	0.0385384
$498$	10848.0	0.976126
$499$	5028.00	0.451071	0.225535	−	0.974235i	$-0.427587\pi$
$499$	5028.00	0.451071	0.225535	+	0.974235i	$0.427587\pi$
$500$	0	0
$501$	−22928.0	−2.04461
$502$	−5040.00	−0.448100
$503$	1442.00	0.127824	0.0639121	−	0.997956i	$-0.479642\pi$
$503$	1442.00	0.127824	0.0639121	+	0.997956i	$0.479642\pi$
$504$	2072.00	0.183123
$505$	0	0
$506$	1610.00	0.141449
$507$	−12168.0	−1.06588
$508$	4756.00	0.415381
$509$	−12642.0	−1.10088	−0.550439	−	0.834875i	$-0.685540\pi$
$509$	−12642.0	−1.10088	−0.550439	+	0.834875i	$0.685540\pi$
$510$	0	0
$511$	8120.00	0.702950
$512$	512.000	0.0441942
$513$	11360.0	0.977693
$514$	−2900.00	−0.248859
$515$	0	0
$516$	−7072.00	−0.603348
$517$	−1806.00	−0.153632
$518$	5754.00	0.488062
$519$	−13584.0	−1.14889
$520$	0	0
$521$	−22146.0	−1.86225	−0.931127	−	0.364696i	$-0.881173\pi$
$521$	−22146.0	−1.86225	−0.931127	+	0.364696i	$0.881173\pi$
$522$	74.0000	0.00620477
$523$	−21016.0	−1.75710	−0.878552	−	0.477646i	$-0.841490\pi$
$523$	−21016.0	−1.75710	−0.878552	+	0.477646i	$0.841490\pi$
$524$	−9520.00	−0.793670
$525$	0	0
$526$	16406.0	1.35995
$527$	−264.000	−0.0218217
$528$	−896.000	−0.0738511
$529$	1058.00	0.0869565
$530$	0	0
$531$	−5994.00	−0.489863
$532$	3976.00	0.324025
$533$	−11544.0	−0.938135
$534$	5920.00	0.479744
$535$	0	0
$536$	−4152.00	−0.334588
$537$	2336.00	0.187720
$538$	12612.0	1.01067
$539$	−343.000	−0.0274101
$540$	0	0
$541$	17543.0	1.39415	0.697073	−	0.717001i	$-0.254486\pi$
$541$	17543.0	1.39415	0.697073	+	0.717001i	$0.254486\pi$
$542$	4244.00	0.336338
$543$	−19104.0	−1.50982
$544$	−1408.00	−0.110970
$545$	0	0
$546$	2912.00	0.228246
$547$	16785.0	1.31202	0.656010	−	0.754752i	$-0.272243\pi$
$547$	16785.0	1.31202	0.656010	+	0.754752i	$0.272243\pi$
$548$	−6472.00	−0.504508
$549$	−30340.0	−2.35862
$550$	0	0
$551$	142.000	0.0109790
$552$	−7360.00	−0.567504
$553$	−5663.00	−0.435471
$554$	508.000	0.0389582
$555$	0	0
$556$	−12592.0	−0.960467
$557$	−9483.00	−0.721378	−0.360689	−	0.932686i	$-0.617458\pi$
$557$	−9483.00	−0.721378	−0.360689	+	0.932686i	$0.617458\pi$
$558$	444.000	0.0336846
$559$	−5746.00	−0.434758
$560$	0	0
$561$	2464.00	0.185437
$562$	−10326.0	−0.775046
$563$	9586.00	0.717587	0.358794	−	0.933417i	$-0.383188\pi$
$563$	9586.00	0.717587	0.358794	+	0.933417i	$0.383188\pi$
$564$	8256.00	0.616384
$565$	0	0
$566$	4324.00	0.321115
$567$	−2513.00	−0.186131
$568$	488.000	0.0360493
$569$	−3163.00	−0.233040	−0.116520	−	0.993188i	$-0.537174\pi$
$569$	−3163.00	−0.233040	−0.116520	+	0.993188i	$0.537174\pi$
$570$	0	0
$571$	−10469.0	−0.767275	−0.383637	−	0.923484i	$-0.625329\pi$
$571$	−10469.0	−0.767275	−0.383637	+	0.923484i	$0.625329\pi$
$572$	−728.000	−0.0532154
$573$	3712.00	0.270630
$574$	−6216.00	−0.452005
$575$	0	0
$576$	2368.00	0.171296
$577$	18686.0	1.34819	0.674097	−	0.738643i	$-0.264533\pi$
$577$	18686.0	1.34819	0.674097	+	0.738643i	$0.264533\pi$
$578$	−5954.00	−0.428467
$579$	−12760.0	−0.915868
$580$	0	0
$581$	4746.00	0.338894
$582$	4960.00	0.353262
$583$	4382.00	0.311293
$584$	9280.00	0.657550
$585$	0	0
$586$	−13116.0	−0.924602
$587$	−7572.00	−0.532419	−0.266209	−	0.963915i	$-0.585771\pi$
$587$	−7572.00	−0.532419	−0.266209	+	0.963915i	$0.585771\pi$
$588$	1568.00	0.109971
$589$	852.000	0.0596028
$590$	0	0
$591$	21864.0	1.52177
$592$	6576.00	0.456540
$593$	−23736.0	−1.64371	−0.821856	−	0.569696i	$-0.807061\pi$
$593$	−23736.0	−1.64371	−0.821856	+	0.569696i	$0.807061\pi$
$594$	−1120.00	−0.0773639
$595$	0	0
$596$	7532.00	0.517656
$597$	−2592.00	−0.177694
$598$	−5980.00	−0.408930
$599$	−9849.00	−0.671818	−0.335909	−	0.941894i	$-0.609044\pi$
$599$	−9849.00	−0.671818	−0.335909	+	0.941894i	$0.609044\pi$
$600$	0	0
$601$	2848.00	0.193298	0.0966492	−	0.995319i	$-0.469188\pi$
$601$	2848.00	0.193298	0.0966492	+	0.995319i	$0.469188\pi$
$602$	−3094.00	−0.209472
$603$	−19203.0	−1.29686
$604$	2932.00	0.197519
$605$	0	0
$606$	6720.00	0.450464
$607$	12818.0	0.857111	0.428556	−	0.903515i	$-0.359023\pi$
$607$	12818.0	0.857111	0.428556	+	0.903515i	$0.359023\pi$
$608$	4544.00	0.303098
$609$	56.0000	0.00372617
$610$	0	0
$611$	6708.00	0.444152
$612$	−6512.00	−0.430118
$613$	1371.00	0.0903331	0.0451665	−	0.998979i	$-0.485618\pi$
$613$	1371.00	0.0903331	0.0451665	+	0.998979i	$0.485618\pi$
$614$	3392.00	0.222948
$615$	0	0
$616$	−392.000	−0.0256398
$617$	13159.0	0.858608	0.429304	−	0.903160i	$-0.358759\pi$
$617$	13159.0	0.858608	0.429304	+	0.903160i	$0.358759\pi$
$618$	−9760.00	−0.635283
$619$	−18142.0	−1.17801	−0.589005	−	0.808129i	$-0.700480\pi$
$619$	−18142.0	−1.17801	−0.589005	+	0.808129i	$0.700480\pi$
$620$	0	0
$621$	−9200.00	−0.594498
$622$	5264.00	0.339336
$623$	2590.00	0.166559
$624$	3328.00	0.213504
$625$	0	0
$626$	15780.0	1.00750
$627$	−7952.00	−0.506495
$628$	2880.00	0.183001
$629$	−18084.0	−1.14635
$630$	0	0
$631$	9347.00	0.589696	0.294848	−	0.955544i	$-0.404731\pi$
$631$	9347.00	0.589696	0.294848	+	0.955544i	$0.404731\pi$
$632$	−6472.00	−0.407345
$633$	17376.0	1.09105
$634$	2722.00	0.170512
$635$	0	0
$636$	−20032.0	−1.24893
$637$	1274.00	0.0792429
$638$	−14.0000	−0.000868754 0
$639$	2257.00	0.139727
$640$	0	0
$641$	−12455.0	−0.767462	−0.383731	−	0.923445i	$-0.625361\pi$
$641$	−12455.0	−0.767462	−0.383731	+	0.923445i	$0.625361\pi$
$642$	−20544.0	−1.26294
$643$	15940.0	0.977624	0.488812	−	0.872389i	$-0.337430\pi$
$643$	15940.0	0.977624	0.488812	+	0.872389i	$0.337430\pi$
$644$	−3220.00	−0.197028
$645$	0	0
$646$	−12496.0	−0.761066
$647$	14562.0	0.884840	0.442420	−	0.896808i	$-0.354120\pi$
$647$	14562.0	0.884840	0.442420	+	0.896808i	$0.354120\pi$
$648$	−2872.00	−0.174109
$649$	1134.00	0.0685877
$650$	0	0
$651$	336.000	0.0202287
$652$	3520.00	0.211432
$653$	538.000	0.0322413	0.0161206	−	0.999870i	$-0.494868\pi$
$653$	538.000	0.0322413	0.0161206	+	0.999870i	$0.494868\pi$
$654$	26576.0	1.58900
$655$	0	0
$656$	−7104.00	−0.422812
$657$	42920.0	2.54866
$658$	3612.00	0.213998
$659$	15276.0	0.902987	0.451494	−	0.892274i	$-0.350891\pi$
$659$	15276.0	0.902987	0.451494	+	0.892274i	$0.350891\pi$
$660$	0	0
$661$	−5650.00	−0.332465	−0.166233	−	0.986087i	$-0.553160\pi$
$661$	−5650.00	−0.332465	−0.166233	+	0.986087i	$0.553160\pi$
$662$	6510.00	0.382203
$663$	−9152.00	−0.536100
$664$	5424.00	0.317006
$665$	0	0
$666$	30414.0	1.76955
$667$	−115.000	−0.00667589
$668$	−11464.0	−0.664005
$669$	42656.0	2.46514
$670$	0	0
$671$	5740.00	0.330239
$672$	1792.00	0.102869
$673$	16326.0	0.935098	0.467549	−	0.883967i	$-0.345137\pi$
$673$	16326.0	0.935098	0.467549	+	0.883967i	$0.345137\pi$
$674$	11268.0	0.643957
$675$	0	0
$676$	−6084.00	−0.346154
$677$	−16030.0	−0.910019	−0.455010	−	0.890487i	$-0.650364\pi$
$677$	−16030.0	−0.910019	−0.455010	+	0.890487i	$0.650364\pi$
$678$	22608.0	1.28061
$679$	2170.00	0.122646
$680$	0	0
$681$	−1808.00	−0.101737
$682$	−84.0000	−0.00471631
$683$	−29721.0	−1.66507	−0.832535	−	0.553973i	$-0.813111\pi$
$683$	−29721.0	−1.66507	−0.832535	+	0.553973i	$0.813111\pi$
$684$	21016.0	1.17481
$685$	0	0
$686$	686.000	0.0381802
$687$	−32048.0	−1.77978
$688$	−3536.00	−0.195943
$689$	−16276.0	−0.899951
$690$	0	0
$691$	27036.0	1.48842	0.744210	−	0.667946i	$-0.232826\pi$
$691$	27036.0	1.48842	0.744210	+	0.667946i	$0.232826\pi$
$692$	−6792.00	−0.373111
$693$	−1813.00	−0.0993798
$694$	24926.0	1.36337
$695$	0	0
$696$	64.0000	0.00348551
$697$	19536.0	1.06166
$698$	−5156.00	−0.279595
$699$	51224.0	2.77177
$700$	0	0
$701$	−36450.0	−1.96391	−0.981953	−	0.189127i	$-0.939434\pi$
$701$	−36450.0	−1.96391	−0.981953	+	0.189127i	$0.939434\pi$
$702$	4160.00	0.223660
$703$	58362.0	3.13110
$704$	−448.000	−0.0239839
$705$	0	0
$706$	1780.00	0.0948884
$707$	2940.00	0.156393
$708$	−5184.00	−0.275179
$709$	26158.0	1.38559	0.692796	−	0.721134i	$-0.256379\pi$
$709$	26158.0	1.38559	0.692796	+	0.721134i	$0.256379\pi$
$710$	0	0
$711$	−29933.0	−1.57887
$712$	2960.00	0.155802
$713$	−690.000	−0.0362422
$714$	−4928.00	−0.258299
$715$	0	0
$716$	1168.00	0.0609640
$717$	43296.0	2.25512
$718$	−7278.00	−0.378290
$719$	7880.00	0.408727	0.204363	−	0.978895i	$-0.434488\pi$
$719$	7880.00	0.408727	0.204363	+	0.978895i	$0.434488\pi$
$720$	0	0
$721$	−4270.00	−0.220559
$722$	26610.0	1.37164
$723$	−3280.00	−0.168720
$724$	−9552.00	−0.490328
$725$	0	0
$726$	−20512.0	−1.04858
$727$	6352.00	0.324048	0.162024	−	0.986787i	$-0.448198\pi$
$727$	6352.00	0.324048	0.162024	+	0.986787i	$0.448198\pi$
$728$	1456.00	0.0741249
$729$	−30563.0	−1.55276
$730$	0	0
$731$	9724.00	0.492004
$732$	−26240.0	−1.32494
$733$	20900.0	1.05315	0.526575	−	0.850129i	$-0.323476\pi$
$733$	20900.0	1.05315	0.526575	+	0.850129i	$0.323476\pi$
$734$	15952.0	0.802179
$735$	0	0
$736$	−3680.00	−0.184302
$737$	3633.00	0.181578
$738$	−32856.0	−1.63882
$739$	15845.0	0.788725	0.394362	−	0.918955i	$-0.370965\pi$
$739$	15845.0	0.788725	0.394362	+	0.918955i	$0.370965\pi$
$740$	0	0
$741$	29536.0	1.46428
$742$	−8764.00	−0.433607
$743$	29388.0	1.45106	0.725532	−	0.688188i	$-0.241594\pi$
$743$	29388.0	1.45106	0.725532	+	0.688188i	$0.241594\pi$
$744$	384.000	0.0189222
$745$	0	0
$746$	22826.0	1.12027
$747$	25086.0	1.22871
$748$	1232.00	0.0602224
$749$	−8988.00	−0.438470
$750$	0	0
$751$	1564.00	0.0759936	0.0379968	−	0.999278i	$-0.487902\pi$
$751$	1564.00	0.0759936	0.0379968	+	0.999278i	$0.487902\pi$
$752$	4128.00	0.200176
$753$	−20160.0	−0.975659
$754$	52.0000	0.00251158
$755$	0	0
$756$	2240.00	0.107762
$757$	−14593.0	−0.700649	−0.350325	−	0.936628i	$-0.613929\pi$
$757$	−14593.0	−0.700649	−0.350325	+	0.936628i	$0.613929\pi$
$758$	11006.0	0.527382
$759$	6440.00	0.307980
$760$	0	0
$761$	−1184.00	−0.0563994	−0.0281997	−	0.999602i	$-0.508977\pi$
$761$	−1184.00	−0.0563994	−0.0281997	+	0.999602i	$0.508977\pi$
$762$	19024.0	0.904418
$763$	11627.0	0.551672
$764$	1856.00	0.0878897
$765$	0	0
$766$	3100.00	0.146224
$767$	−4212.00	−0.198287
$768$	2048.00	0.0962250
$769$	−34328.0	−1.60975	−0.804876	−	0.593443i	$-0.797768\pi$
$769$	−34328.0	−1.60975	−0.804876	+	0.593443i	$0.797768\pi$
$770$	0	0
$771$	−11600.0	−0.541847
$772$	−6380.00	−0.297437
$773$	31814.0	1.48030	0.740149	−	0.672443i	$-0.234755\pi$
$773$	31814.0	1.48030	0.740149	+	0.672443i	$0.234755\pi$
$774$	−16354.0	−0.759473
$775$	0	0
$776$	2480.00	0.114725
$777$	23016.0	1.06267
$778$	28178.0	1.29850
$779$	−63048.0	−2.89978
$780$	0	0
$781$	−427.000	−0.0195637
$782$	10120.0	0.462776
$783$	80.0000	0.00365130
$784$	784.000	0.0357143
$785$	0	0
$786$	−38080.0	−1.72808
$787$	−32108.0	−1.45429	−0.727145	−	0.686484i	$-0.759153\pi$
$787$	−32108.0	−1.45429	−0.727145	+	0.686484i	$0.759153\pi$
$788$	10932.0	0.494209
$789$	65624.0	2.96106
$790$	0	0
$791$	9891.00	0.444606
$792$	−2072.00	−0.0929613
$793$	−21320.0	−0.954723
$794$	4668.00	0.208641
$795$	0	0
$796$	−1296.00	−0.0577079
$797$	11520.0	0.511994	0.255997	−	0.966678i	$-0.417596\pi$
$797$	11520.0	0.511994	0.255997	+	0.966678i	$0.417596\pi$
$798$	15904.0	0.705508
$799$	−11352.0	−0.502634
$800$	0	0
$801$	13690.0	0.603886
$802$	3866.00	0.170216
$803$	−8120.00	−0.356848
$804$	−16608.0	−0.728506
$805$	0	0
$806$	312.000	0.0136349
$807$	50448.0	2.20056
$808$	3360.00	0.146293
$809$	18479.0	0.803074	0.401537	−	0.915843i	$-0.368476\pi$
$809$	18479.0	0.803074	0.401537	+	0.915843i	$0.368476\pi$
$810$	0	0
$811$	13354.0	0.578203	0.289101	−	0.957299i	$-0.406644\pi$
$811$	13354.0	0.578203	0.289101	+	0.957299i	$0.406644\pi$
$812$	28.0000	0.00121011
$813$	16976.0	0.732318
$814$	−5754.00	−0.247761
$815$	0	0
$816$	−5632.00	−0.241617
$817$	−31382.0	−1.34384
$818$	−700.000	−0.0299204
$819$	6734.00	0.287308
$820$	0	0
$821$	−20366.0	−0.865747	−0.432874	−	0.901455i	$-0.642500\pi$
$821$	−20366.0	−0.865747	−0.432874	+	0.901455i	$0.642500\pi$
$822$	−25888.0	−1.09848
$823$	−41247.0	−1.74700	−0.873499	−	0.486825i	$-0.838155\pi$
$823$	−41247.0	−1.74700	−0.873499	+	0.486825i	$0.838155\pi$
$824$	−4880.00	−0.206314
$825$	0	0
$826$	−2268.00	−0.0955373
$827$	−27877.0	−1.17216	−0.586081	−	0.810252i	$-0.699330\pi$
$827$	−27877.0	−1.17216	−0.586081	+	0.810252i	$0.699330\pi$
$828$	−17020.0	−0.714355
$829$	3984.00	0.166912	0.0834560	−	0.996511i	$-0.473404\pi$
$829$	3984.00	0.166912	0.0834560	+	0.996511i	$0.473404\pi$
$830$	0	0
$831$	2032.00	0.0848247
$832$	1664.00	0.0693375
$833$	−2156.00	−0.0896770
$834$	−50368.0	−2.09125
$835$	0	0
$836$	−3976.00	−0.164489
$837$	480.000	0.0198223
$838$	23236.0	0.957845
$839$	−6424.00	−0.264340	−0.132170	−	0.991227i	$-0.542194\pi$
$839$	−6424.00	−0.264340	−0.132170	+	0.991227i	$0.542194\pi$
$840$	0	0
$841$	−24388.0	−0.999959
$842$	−8170.00	−0.334390
$843$	−41304.0	−1.68753
$844$	8688.00	0.354329
$845$	0	0
$846$	19092.0	0.775882
$847$	−8974.00	−0.364050
$848$	−10016.0	−0.405602
$849$	17296.0	0.699172
$850$	0	0
$851$	−47265.0	−1.90391
$852$	1952.00	0.0784911
$853$	−35200.0	−1.41293	−0.706463	−	0.707750i	$-0.749710\pi$
$853$	−35200.0	−1.41293	−0.706463	+	0.707750i	$0.749710\pi$
$854$	−11480.0	−0.459997
$855$	0	0
$856$	−10272.0	−0.410152
$857$	30220.0	1.20455	0.602273	−	0.798290i	$-0.294262\pi$
$857$	30220.0	1.20455	0.602273	+	0.798290i	$0.294262\pi$
$858$	−2912.00	−0.115867
$859$	−11294.0	−0.448599	−0.224299	−	0.974520i	$-0.572009\pi$
$859$	−11294.0	−0.448599	−0.224299	+	0.974520i	$0.572009\pi$
$860$	0	0
$861$	−24864.0	−0.984161
$862$	30048.0	1.18728
$863$	−19901.0	−0.784980	−0.392490	−	0.919756i	$-0.628386\pi$
$863$	−19901.0	−0.784980	−0.392490	+	0.919756i	$0.628386\pi$
$864$	2560.00	0.100802
$865$	0	0
$866$	−16424.0	−0.644469
$867$	−23816.0	−0.932911
$868$	168.000	0.00656946
$869$	5663.00	0.221063
$870$	0	0
$871$	−13494.0	−0.524945
$872$	13288.0	0.516042
$873$	11470.0	0.444674
$874$	−32660.0	−1.26401
$875$	0	0
$876$	37120.0	1.43170
$877$	21634.0	0.832985	0.416493	−	0.909139i	$-0.363259\pi$
$877$	21634.0	0.832985	0.416493	+	0.909139i	$0.363259\pi$
$878$	−12172.0	−0.467865
$879$	−52464.0	−2.01316
$880$	0	0
$881$	−21526.0	−0.823189	−0.411594	−	0.911367i	$-0.635028\pi$
$881$	−21526.0	−0.823189	−0.411594	+	0.911367i	$0.635028\pi$
$882$	3626.00	0.138428
$883$	961.000	0.0366254	0.0183127	−	0.999832i	$-0.494171\pi$
$883$	961.000	0.0366254	0.0183127	+	0.999832i	$0.494171\pi$
$884$	−4576.00	−0.174104
$885$	0	0
$886$	−19104.0	−0.724392
$887$	−31628.0	−1.19725	−0.598627	−	0.801028i	$-0.704287\pi$
$887$	−31628.0	−1.19725	−0.598627	+	0.801028i	$0.704287\pi$
$888$	26304.0	0.994037
$889$	8323.00	0.313998
$890$	0	0
$891$	2513.00	0.0944878
$892$	21328.0	0.800577
$893$	36636.0	1.37287
$894$	30128.0	1.12710
$895$	0	0
$896$	896.000	0.0334077
$897$	−23920.0	−0.890374
$898$	−9770.00	−0.363061
$899$	6.00000	0.000222593 0
$900$	0	0
$901$	27544.0	1.01845
$902$	6216.00	0.229457
$903$	−12376.0	−0.456088
$904$	11304.0	0.415891
$905$	0	0
$906$	11728.0	0.430063
$907$	−988.000	−0.0361698	−0.0180849	−	0.999836i	$-0.505757\pi$
$907$	−988.000	−0.0361698	−0.0180849	+	0.999836i	$0.505757\pi$
$908$	−904.000	−0.0330400
$909$	15540.0	0.567029
$910$	0	0
$911$	−39169.0	−1.42451	−0.712254	−	0.701922i	$-0.752326\pi$
$911$	−39169.0	−1.42451	−0.712254	+	0.701922i	$0.752326\pi$
$912$	18176.0	0.659942
$913$	−4746.00	−0.172037
$914$	−29102.0	−1.05318
$915$	0	0
$916$	−16024.0	−0.578000
$917$	−16660.0	−0.599958
$918$	−7040.00	−0.253110
$919$	−38681.0	−1.38843	−0.694216	−	0.719767i	$-0.744249\pi$
$919$	−38681.0	−1.38843	−0.694216	+	0.719767i	$0.744249\pi$
$920$	0	0
$921$	13568.0	0.485430
$922$	−24884.0	−0.888840
$923$	1586.00	0.0565589
$924$	−1568.00	−0.0558262
$925$	0	0
$926$	15408.0	0.546802
$927$	−22570.0	−0.799672
$928$	32.0000	0.00113195
$929$	21028.0	0.742633	0.371317	−	0.928506i	$-0.378906\pi$
$929$	21028.0	0.742633	0.371317	+	0.928506i	$0.378906\pi$
$930$	0	0
$931$	6958.00	0.244940
$932$	25612.0	0.900160
$933$	21056.0	0.738845
$934$	8844.00	0.309834
$935$	0	0
$936$	7696.00	0.268752
$937$	−19972.0	−0.696325	−0.348163	−	0.937434i	$-0.613194\pi$
$937$	−19972.0	−0.696325	−0.348163	+	0.937434i	$0.613194\pi$
$938$	−7266.00	−0.252925
$939$	63120.0	2.19366
$940$	0	0
$941$	29754.0	1.03077	0.515384	−	0.856959i	$-0.327649\pi$
$941$	29754.0	1.03077	0.515384	+	0.856959i	$0.327649\pi$
$942$	11520.0	0.398452
$943$	51060.0	1.76325
$944$	−2592.00	−0.0893670
$945$	0	0
$946$	3094.00	0.106337
$947$	−20836.0	−0.714973	−0.357486	−	0.933918i	$-0.616366\pi$
$947$	−20836.0	−0.714973	−0.357486	+	0.933918i	$0.616366\pi$
$948$	−25888.0	−0.886923
$949$	30160.0	1.03165
$950$	0	0
$951$	10888.0	0.371259
$952$	−2464.00	−0.0838852
$953$	−13319.0	−0.452723	−0.226361	−	0.974043i	$-0.572683\pi$
$953$	−13319.0	−0.452723	−0.226361	+	0.974043i	$0.572683\pi$
$954$	−46324.0	−1.57211
$955$	0	0
$956$	21648.0	0.732371
$957$	−56.0000	−0.00189156
$958$	5524.00	0.186297
$959$	−11326.0	−0.381372
$960$	0	0
$961$	−29755.0	−0.998792
$962$	21372.0	0.716280
$963$	−47508.0	−1.58974
$964$	−1640.00	−0.0547934
$965$	0	0
$966$	−12880.0	−0.428993
$967$	17192.0	0.571724	0.285862	−	0.958271i	$-0.407720\pi$
$967$	17192.0	0.571724	0.285862	+	0.958271i	$0.407720\pi$
$968$	−10256.0	−0.340538
$969$	−49984.0	−1.65709
$970$	0	0
$971$	−2726.00	−0.0900942	−0.0450471	−	0.998985i	$-0.514344\pi$
$971$	−2726.00	−0.0900942	−0.0450471	+	0.998985i	$0.514344\pi$
$972$	−20128.0	−0.664204
$973$	−22036.0	−0.726045
$974$	21934.0	0.721572
$975$	0	0
$976$	−13120.0	−0.430288
$977$	−43161.0	−1.41335	−0.706675	−	0.707538i	$-0.749806\pi$
$977$	−43161.0	−1.41335	−0.706675	+	0.707538i	$0.749806\pi$
$978$	14080.0	0.460357
$979$	−2590.00	−0.0845524
$980$	0	0
$981$	61457.0	2.00017
$982$	−18774.0	−0.610084
$983$	33306.0	1.08067	0.540334	−	0.841451i	$-0.318298\pi$
$983$	33306.0	1.08067	0.540334	+	0.841451i	$0.318298\pi$
$984$	−28416.0	−0.920599
$985$	0	0
$986$	−88.0000	−0.00284228
$987$	14448.0	0.465942
$988$	14768.0	0.475539
$989$	25415.0	0.817139
$990$	0	0
$991$	11155.0	0.357568	0.178784	−	0.983888i	$-0.442784\pi$
$991$	11155.0	0.357568	0.178784	+	0.983888i	$0.442784\pi$
$992$	192.000	0.00614517
$993$	26040.0	0.832180
$994$	854.000	0.0272507
$995$	0	0
$996$	21696.0	0.690225
$997$	−34186.0	−1.08594	−0.542970	−	0.839752i	$-0.682700\pi$
$997$	−34186.0	−1.08594	−0.542970	+	0.839752i	$0.682700\pi$
$998$	10056.0	0.318955
$999$	32880.0	1.04132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.a.u.1.1	yes	1
5.2	odd	4		350.4.c.m.99.2		2
5.3	odd	4		350.4.c.m.99.1		2
5.4	even	2		350.4.a.a.1.1	✓	1
7.6	odd	2		2450.4.a.w.1.1		1
35.34	odd	2		2450.4.a.u.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.4.a.a.1.1	✓	1	5.4	even	2
350.4.a.u.1.1	yes	1	1.1	even	1	trivial
350.4.c.m.99.1		2	5.3	odd	4
350.4.c.m.99.2		2	5.2	odd	4
2450.4.a.u.1.1		1	35.34	odd	2
2450.4.a.w.1.1		1	7.6	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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