LMFDB - Embedded newform 350.4.a.v.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:	no (minimal twist has level 70)
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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +8.00000 q^{3} +4.00000 q^{4} +16.0000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +37.0000 q^{9} +68.0000 q^{11} +32.0000 q^{12} -34.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -74.0000 q^{17} +74.0000 q^{18} -128.000 q^{19} +56.0000 q^{21} +136.000 q^{22} +80.0000 q^{23} +64.0000 q^{24} -68.0000 q^{26} +80.0000 q^{27} +28.0000 q^{28} +286.000 q^{29} -24.0000 q^{31} +32.0000 q^{32} +544.000 q^{33} -148.000 q^{34} +148.000 q^{36} -294.000 q^{37} -256.000 q^{38} -272.000 q^{39} +66.0000 q^{41} +112.000 q^{42} +124.000 q^{43} +272.000 q^{44} +160.000 q^{46} -312.000 q^{47} +128.000 q^{48} +49.0000 q^{49} -592.000 q^{51} -136.000 q^{52} +34.0000 q^{53} +160.000 q^{54} +56.0000 q^{56} -1024.00 q^{57} +572.000 q^{58} +168.000 q^{59} +170.000 q^{61} -48.0000 q^{62} +259.000 q^{63} +64.0000 q^{64} +1088.00 q^{66} -564.000 q^{67} -296.000 q^{68} +640.000 q^{69} +616.000 q^{71} +296.000 q^{72} -250.000 q^{73} -588.000 q^{74} -512.000 q^{76} +476.000 q^{77} -544.000 q^{78} -944.000 q^{79} -359.000 q^{81} +132.000 q^{82} -672.000 q^{83} +224.000 q^{84} +248.000 q^{86} +2288.00 q^{87} +544.000 q^{88} -1430.00 q^{89} -238.000 q^{91} +320.000 q^{92} -192.000 q^{93} -624.000 q^{94} +256.000 q^{96} +1270.00 q^{97} +98.0000 q^{98} +2516.00 q^{99} +O(q^{100})\)

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
$11$	68.0000	1.86389	0.931944	−	0.362602i	$-0.118111\pi$
$11$	68.0000	1.86389	0.931944	+	0.362602i	$0.118111\pi$
$12$	32.0000	0.769800
$13$	−34.0000	−0.725377	−0.362689	−	0.931910i	$-0.618141\pi$
$13$	−34.0000	−0.725377	−0.362689	+	0.931910i	$0.618141\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−74.0000	−1.05574	−0.527872	−	0.849324i	$-0.677010\pi$
$17$	−74.0000	−1.05574	−0.527872	+	0.849324i	$0.677010\pi$
$18$	74.0000	0.968998
$19$	−128.000	−1.54554	−0.772769	−	0.634688i	$-0.781129\pi$
$19$	−128.000	−1.54554	−0.772769	+	0.634688i	$0.781129\pi$
$20$	0	0
$21$	56.0000	0.581914
$22$	136.000	1.31797
$23$	80.0000	0.725268	0.362634	−	0.931932i	$-0.381878\pi$
$23$	80.0000	0.725268	0.362634	+	0.931932i	$0.381878\pi$
$24$	64.0000	0.544331
$25$	0	0
$26$	−68.0000	−0.512919
$27$	80.0000	0.570222
$28$	28.0000	0.188982
$29$	286.000	1.83134	0.915670	−	0.401931i	$-0.131661\pi$
$29$	286.000	1.83134	0.915670	+	0.401931i	$0.131661\pi$
$30$	0	0
$31$	−24.0000	−0.139049	−0.0695246	−	0.997580i	$-0.522148\pi$
$31$	−24.0000	−0.139049	−0.0695246	+	0.997580i	$0.522148\pi$
$32$	32.0000	0.176777
$33$	544.000	2.86964
$34$	−148.000	−0.746523
$35$	0	0
$36$	148.000	0.685185
$37$	−294.000	−1.30631	−0.653153	−	0.757226i	$-0.726554\pi$
$37$	−294.000	−1.30631	−0.653153	+	0.757226i	$0.726554\pi$
$38$	−256.000	−1.09286
$39$	−272.000	−1.11679
$40$	0	0
$41$	66.0000	0.251402	0.125701	−	0.992068i	$-0.459882\pi$
$41$	66.0000	0.251402	0.125701	+	0.992068i	$0.459882\pi$
$42$	112.000	0.411476
$43$	124.000	0.439763	0.219882	−	0.975527i	$-0.429433\pi$
$43$	124.000	0.439763	0.219882	+	0.975527i	$0.429433\pi$
$44$	272.000	0.931944
$45$	0	0
$46$	160.000	0.512842
$47$	−312.000	−0.968295	−0.484148	−	0.874986i	$-0.660870\pi$
$47$	−312.000	−0.968295	−0.484148	+	0.874986i	$0.660870\pi$
$48$	128.000	0.384900
$49$	49.0000	0.142857
$50$	0	0
$51$	−592.000	−1.62542
$52$	−136.000	−0.362689
$53$	34.0000	0.0881181	0.0440590	−	0.999029i	$-0.485971\pi$
$53$	34.0000	0.0881181	0.0440590	+	0.999029i	$0.485971\pi$
$54$	160.000	0.403208
$55$	0	0
$56$	56.0000	0.133631
$57$	−1024.00	−2.37951
$58$	572.000	1.29495
$59$	168.000	0.370707	0.185354	−	0.982672i	$-0.440657\pi$
$59$	168.000	0.370707	0.185354	+	0.982672i	$0.440657\pi$
$60$	0	0
$61$	170.000	0.356824	0.178412	−	0.983956i	$-0.442904\pi$
$61$	170.000	0.356824	0.178412	+	0.983956i	$0.442904\pi$
$62$	−48.0000	−0.0983227
$63$	259.000	0.517951
$64$	64.0000	0.125000
$65$	0	0
$66$	1088.00	2.02914
$67$	−564.000	−1.02841	−0.514206	−	0.857667i	$-0.671913\pi$
$67$	−564.000	−1.02841	−0.514206	+	0.857667i	$0.671913\pi$
$68$	−296.000	−0.527872
$69$	640.000	1.11662
$70$	0	0
$71$	616.000	1.02966	0.514829	−	0.857293i	$-0.327855\pi$
$71$	616.000	1.02966	0.514829	+	0.857293i	$0.327855\pi$
$72$	296.000	0.484499
$73$	−250.000	−0.400826	−0.200413	−	0.979712i	$-0.564228\pi$
$73$	−250.000	−0.400826	−0.200413	+	0.979712i	$0.564228\pi$
$74$	−588.000	−0.923697
$75$	0	0
$76$	−512.000	−0.772769
$77$	476.000	0.704484
$78$	−544.000	−0.789691
$79$	−944.000	−1.34441	−0.672204	−	0.740366i	$-0.734652\pi$
$79$	−944.000	−1.34441	−0.672204	+	0.740366i	$0.734652\pi$
$80$	0	0
$81$	−359.000	−0.492455
$82$	132.000	0.177768
$83$	−672.000	−0.888694	−0.444347	−	0.895855i	$-0.646564\pi$
$83$	−672.000	−0.888694	−0.444347	+	0.895855i	$0.646564\pi$
$84$	224.000	0.290957
$85$	0	0
$86$	248.000	0.310960
$87$	2288.00	2.81953
$88$	544.000	0.658984
$89$	−1430.00	−1.70314	−0.851571	−	0.524239i	$-0.824350\pi$
$89$	−1430.00	−1.70314	−0.851571	+	0.524239i	$0.824350\pi$
$90$	0	0
$91$	−238.000	−0.274167
$92$	320.000	0.362634
$93$	−192.000	−0.214080
$94$	−624.000	−0.684688
$95$	0	0
$96$	256.000	0.272166
$97$	1270.00	1.32937	0.664685	−	0.747123i	$-0.268566\pi$
$97$	1270.00	1.32937	0.664685	+	0.747123i	$0.268566\pi$
$98$	98.0000	0.101015
$99$	2516.00	2.55422
$100$	0	0
$101$	930.000	0.916222	0.458111	−	0.888895i	$-0.348526\pi$
$101$	930.000	0.916222	0.458111	+	0.888895i	$0.348526\pi$
$102$	−1184.00	−1.14935
$103$	−160.000	−0.153061	−0.0765304	−	0.997067i	$-0.524384\pi$
$103$	−160.000	−0.153061	−0.0765304	+	0.997067i	$0.524384\pi$
$104$	−272.000	−0.256460
$105$	0	0
$106$	68.0000	0.0623089
$107$	−1404.00	−1.26850	−0.634251	−	0.773127i	$-0.718692\pi$
$107$	−1404.00	−1.26850	−0.634251	+	0.773127i	$0.718692\pi$
$108$	320.000	0.285111
$109$	−274.000	−0.240775	−0.120387	−	0.992727i	$-0.538414\pi$
$109$	−274.000	−0.240775	−0.120387	+	0.992727i	$0.538414\pi$
$110$	0	0
$111$	−2352.00	−2.01119
$112$	112.000	0.0944911
$113$	798.000	0.664332	0.332166	−	0.943221i	$-0.392221\pi$
$113$	798.000	0.664332	0.332166	+	0.943221i	$0.392221\pi$
$114$	−2048.00	−1.68257
$115$	0	0
$116$	1144.00	0.915670
$117$	−1258.00	−0.994035
$118$	336.000	0.262130
$119$	−518.000	−0.399033
$120$	0	0
$121$	3293.00	2.47408
$122$	340.000	0.252313
$123$	528.000	0.387058
$124$	−96.0000	−0.0695246
$125$	0	0
$126$	518.000	0.366247
$127$	904.000	0.631630	0.315815	−	0.948821i	$-0.397722\pi$
$127$	904.000	0.631630	0.315815	+	0.948821i	$0.397722\pi$
$128$	128.000	0.0883883
$129$	992.000	0.677060
$130$	0	0
$131$	−2080.00	−1.38726	−0.693628	−	0.720334i	$-0.743989\pi$
$131$	−2080.00	−1.38726	−0.693628	+	0.720334i	$0.743989\pi$
$132$	2176.00	1.43482
$133$	−896.000	−0.584158
$134$	−1128.00	−0.727197
$135$	0	0
$136$	−592.000	−0.373262
$137$	−2218.00	−1.38319	−0.691593	−	0.722287i	$-0.743091\pi$
$137$	−2218.00	−1.38319	−0.691593	+	0.722287i	$0.743091\pi$
$138$	1280.00	0.789571
$139$	2432.00	1.48403	0.742013	−	0.670386i	$-0.233871\pi$
$139$	2432.00	1.48403	0.742013	+	0.670386i	$0.233871\pi$
$140$	0	0
$141$	−2496.00	−1.49079
$142$	1232.00	0.728078
$143$	−2312.00	−1.35202
$144$	592.000	0.342593
$145$	0	0
$146$	−500.000	−0.283427
$147$	392.000	0.219943
$148$	−1176.00	−0.653153
$149$	1598.00	0.878612	0.439306	−	0.898337i	$-0.355224\pi$
$149$	1598.00	0.878612	0.439306	+	0.898337i	$0.355224\pi$
$150$	0	0
$151$	−2672.00	−1.44003	−0.720014	−	0.693959i	$-0.755865\pi$
$151$	−2672.00	−1.44003	−0.720014	+	0.693959i	$0.755865\pi$
$152$	−1024.00	−0.546430
$153$	−2738.00	−1.44676
$154$	952.000	0.498145
$155$	0	0
$156$	−1088.00	−0.558396
$157$	−1170.00	−0.594753	−0.297376	−	0.954760i	$-0.596112\pi$
$157$	−1170.00	−0.594753	−0.297376	+	0.954760i	$0.596112\pi$
$158$	−1888.00	−0.950641
$159$	272.000	0.135667
$160$	0	0
$161$	560.000	0.274125
$162$	−718.000	−0.348219
$163$	−1580.00	−0.759234	−0.379617	−	0.925144i	$-0.623944\pi$
$163$	−1580.00	−0.759234	−0.379617	+	0.925144i	$0.623944\pi$
$164$	264.000	0.125701
$165$	0	0
$166$	−1344.00	−0.628401
$167$	704.000	0.326211	0.163105	−	0.986609i	$-0.447849\pi$
$167$	704.000	0.326211	0.163105	+	0.986609i	$0.447849\pi$
$168$	448.000	0.205738
$169$	−1041.00	−0.473828
$170$	0	0
$171$	−4736.00	−2.11796
$172$	496.000	0.219882
$173$	−18.0000	−0.00791049	−0.00395524	−	0.999992i	$-0.501259\pi$
$173$	−18.0000	−0.00791049	−0.00395524	+	0.999992i	$0.501259\pi$
$174$	4576.00	1.99371
$175$	0	0
$176$	1088.00	0.465972
$177$	1344.00	0.570741
$178$	−2860.00	−1.20430
$179$	−4268.00	−1.78215	−0.891076	−	0.453854i	$-0.850049\pi$
$179$	−4268.00	−1.78215	−0.891076	+	0.453854i	$0.850049\pi$
$180$	0	0
$181$	282.000	0.115806	0.0579030	−	0.998322i	$-0.481559\pi$
$181$	282.000	0.115806	0.0579030	+	0.998322i	$0.481559\pi$
$182$	−476.000	−0.193865
$183$	1360.00	0.549367
$184$	640.000	0.256421
$185$	0	0
$186$	−384.000	−0.151378
$187$	−5032.00	−1.96779
$188$	−1248.00	−0.484148
$189$	560.000	0.215524
$190$	0	0
$191$	1424.00	0.539461	0.269730	−	0.962936i	$-0.413065\pi$
$191$	1424.00	0.539461	0.269730	+	0.962936i	$0.413065\pi$
$192$	512.000	0.192450
$193$	1870.00	0.697438	0.348719	−	0.937227i	$-0.386617\pi$
$193$	1870.00	0.697438	0.348719	+	0.937227i	$0.386617\pi$
$194$	2540.00	0.940007
$195$	0	0
$196$	196.000	0.0714286
$197$	3618.00	1.30849	0.654243	−	0.756284i	$-0.272987\pi$
$197$	3618.00	1.30849	0.654243	+	0.756284i	$0.272987\pi$
$198$	5032.00	1.80610
$199$	2736.00	0.974623	0.487311	−	0.873228i	$-0.337978\pi$
$199$	2736.00	0.974623	0.487311	+	0.873228i	$0.337978\pi$
$200$	0	0
$201$	−4512.00	−1.58334
$202$	1860.00	0.647867
$203$	2002.00	0.692182
$204$	−2368.00	−0.812712
$205$	0	0
$206$	−320.000	−0.108230
$207$	2960.00	0.993885
$208$	−544.000	−0.181344
$209$	−8704.00	−2.88071
$210$	0	0
$211$	−348.000	−0.113542	−0.0567709	−	0.998387i	$-0.518080\pi$
$211$	−348.000	−0.113542	−0.0567709	+	0.998387i	$0.518080\pi$
$212$	136.000	0.0440590
$213$	4928.00	1.58526
$214$	−2808.00	−0.896967
$215$	0	0
$216$	640.000	0.201604
$217$	−168.000	−0.0525557
$218$	−548.000	−0.170253
$219$	−2000.00	−0.617112
$220$	0	0
$221$	2516.00	0.765812
$222$	−4704.00	−1.42213
$223$	−5888.00	−1.76811	−0.884057	−	0.467378i	$-0.845199\pi$
$223$	−5888.00	−1.76811	−0.884057	+	0.467378i	$0.845199\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	1596.00	0.469754
$227$	4304.00	1.25844	0.629221	−	0.777226i	$-0.283374\pi$
$227$	4304.00	1.25844	0.629221	+	0.777226i	$0.283374\pi$
$228$	−4096.00	−1.18976
$229$	3674.00	1.06020	0.530098	−	0.847937i	$-0.322155\pi$
$229$	3674.00	1.06020	0.530098	+	0.847937i	$0.322155\pi$
$230$	0	0
$231$	3808.00	1.08462
$232$	2288.00	0.647477
$233$	838.000	0.235619	0.117809	−	0.993036i	$-0.462413\pi$
$233$	838.000	0.235619	0.117809	+	0.993036i	$0.462413\pi$
$234$	−2516.00	−0.702889
$235$	0	0
$236$	672.000	0.185354
$237$	−7552.00	−2.06985
$238$	−1036.00	−0.282159
$239$	5832.00	1.57841	0.789207	−	0.614128i	$-0.210492\pi$
$239$	5832.00	1.57841	0.789207	+	0.614128i	$0.210492\pi$
$240$	0	0
$241$	1690.00	0.451711	0.225856	−	0.974161i	$-0.427482\pi$
$241$	1690.00	0.451711	0.225856	+	0.974161i	$0.427482\pi$
$242$	6586.00	1.74944
$243$	−5032.00	−1.32841
$244$	680.000	0.178412
$245$	0	0
$246$	1056.00	0.273691
$247$	4352.00	1.12110
$248$	−192.000	−0.0491613
$249$	−5376.00	−1.36823
$250$	0	0
$251$	5760.00	1.44848	0.724239	−	0.689549i	$-0.242191\pi$
$251$	5760.00	1.44848	0.724239	+	0.689549i	$0.242191\pi$
$252$	1036.00	0.258976
$253$	5440.00	1.35182
$254$	1808.00	0.446630
$255$	0	0
$256$	256.000	0.0625000
$257$	350.000	0.0849510	0.0424755	−	0.999098i	$-0.486476\pi$
$257$	350.000	0.0849510	0.0424755	+	0.999098i	$0.486476\pi$
$258$	1984.00	0.478754
$259$	−2058.00	−0.493737
$260$	0	0
$261$	10582.0	2.50961
$262$	−4160.00	−0.980938
$263$	2968.00	0.695873	0.347937	−	0.937518i	$-0.386882\pi$
$263$	2968.00	0.695873	0.347937	+	0.937518i	$0.386882\pi$
$264$	4352.00	1.01457
$265$	0	0
$266$	−1792.00	−0.413062
$267$	−11440.0	−2.62216
$268$	−2256.00	−0.514206
$269$	−4494.00	−1.01860	−0.509301	−	0.860588i	$-0.670096\pi$
$269$	−4494.00	−1.01860	−0.509301	+	0.860588i	$0.670096\pi$
$270$	0	0
$271$	1312.00	0.294090	0.147045	−	0.989130i	$-0.453024\pi$
$271$	1312.00	0.294090	0.147045	+	0.989130i	$0.453024\pi$
$272$	−1184.00	−0.263936
$273$	−1904.00	−0.422107
$274$	−4436.00	−0.978060
$275$	0	0
$276$	2560.00	0.558311
$277$	5234.00	1.13531	0.567654	−	0.823267i	$-0.307851\pi$
$277$	5234.00	1.13531	0.567654	+	0.823267i	$0.307851\pi$
$278$	4864.00	1.04936
$279$	−888.000	−0.190549
$280$	0	0
$281$	−5718.00	−1.21390	−0.606952	−	0.794738i	$-0.707608\pi$
$281$	−5718.00	−1.21390	−0.606952	+	0.794738i	$0.707608\pi$
$282$	−4992.00	−1.05415
$283$	3752.00	0.788103	0.394052	−	0.919088i	$-0.371073\pi$
$283$	3752.00	0.788103	0.394052	+	0.919088i	$0.371073\pi$
$284$	2464.00	0.514829
$285$	0	0
$286$	−4624.00	−0.956024
$287$	462.000	0.0950209
$288$	1184.00	0.242250
$289$	563.000	0.114594
$290$	0	0
$291$	10160.0	2.04670
$292$	−1000.00	−0.200413
$293$	−7698.00	−1.53489	−0.767444	−	0.641116i	$-0.778472\pi$
$293$	−7698.00	−1.53489	−0.767444	+	0.641116i	$0.778472\pi$
$294$	784.000	0.155523
$295$	0	0
$296$	−2352.00	−0.461849
$297$	5440.00	1.06283
$298$	3196.00	0.621273
$299$	−2720.00	−0.526093
$300$	0	0
$301$	868.000	0.166215
$302$	−5344.00	−1.01825
$303$	7440.00	1.41062
$304$	−2048.00	−0.386384
$305$	0	0
$306$	−5476.00	−1.02301
$307$	1456.00	0.270679	0.135339	−	0.990799i	$-0.456788\pi$
$307$	1456.00	0.270679	0.135339	+	0.990799i	$0.456788\pi$
$308$	1904.00	0.352242
$309$	−1280.00	−0.235653
$310$	0	0
$311$	9592.00	1.74891	0.874457	−	0.485103i	$-0.161218\pi$
$311$	9592.00	1.74891	0.874457	+	0.485103i	$0.161218\pi$
$312$	−2176.00	−0.394845
$313$	−3570.00	−0.644691	−0.322346	−	0.946622i	$-0.604471\pi$
$313$	−3570.00	−0.644691	−0.322346	+	0.946622i	$0.604471\pi$
$314$	−2340.00	−0.420554
$315$	0	0
$316$	−3776.00	−0.672204
$317$	3866.00	0.684972	0.342486	−	0.939523i	$-0.388731\pi$
$317$	3866.00	0.684972	0.342486	+	0.939523i	$0.388731\pi$
$318$	544.000	0.0959308
$319$	19448.0	3.41341
$320$	0	0
$321$	−11232.0	−1.95299
$322$	1120.00	0.193836
$323$	9472.00	1.63169
$324$	−1436.00	−0.246228
$325$	0	0
$326$	−3160.00	−0.536860
$327$	−2192.00	−0.370697
$328$	528.000	0.0888839
$329$	−2184.00	−0.365981
$330$	0	0
$331$	−2940.00	−0.488209	−0.244104	−	0.969749i	$-0.578494\pi$
$331$	−2940.00	−0.488209	−0.244104	+	0.969749i	$0.578494\pi$
$332$	−2688.00	−0.444347
$333$	−10878.0	−1.79012
$334$	1408.00	0.230666
$335$	0	0
$336$	896.000	0.145479
$337$	414.000	0.0669199	0.0334600	−	0.999440i	$-0.489347\pi$
$337$	414.000	0.0669199	0.0334600	+	0.999440i	$0.489347\pi$
$338$	−2082.00	−0.335047
$339$	6384.00	1.02281
$340$	0	0
$341$	−1632.00	−0.259172
$342$	−9472.00	−1.49762
$343$	343.000	0.0539949
$344$	992.000	0.155480
$345$	0	0
$346$	−36.0000	−0.00559356
$347$	5068.00	0.784048	0.392024	−	0.919955i	$-0.371775\pi$
$347$	5068.00	0.784048	0.392024	+	0.919955i	$0.371775\pi$
$348$	9152.00	1.40977
$349$	2882.00	0.442034	0.221017	−	0.975270i	$-0.429062\pi$
$349$	2882.00	0.442034	0.221017	+	0.975270i	$0.429062\pi$
$350$	0	0
$351$	−2720.00	−0.413626
$352$	2176.00	0.329492
$353$	6350.00	0.957440	0.478720	−	0.877968i	$-0.341101\pi$
$353$	6350.00	0.957440	0.478720	+	0.877968i	$0.341101\pi$
$354$	2688.00	0.403575
$355$	0	0
$356$	−5720.00	−0.851571
$357$	−4144.00	−0.614352
$358$	−8536.00	−1.26017
$359$	4656.00	0.684497	0.342248	−	0.939610i	$-0.388812\pi$
$359$	4656.00	0.684497	0.342248	+	0.939610i	$0.388812\pi$
$360$	0	0
$361$	9525.00	1.38869
$362$	564.000	0.0818872
$363$	26344.0	3.80909
$364$	−952.000	−0.137083
$365$	0	0
$366$	2720.00	0.388461
$367$	8336.00	1.18566	0.592828	−	0.805329i	$-0.298011\pi$
$367$	8336.00	1.18566	0.592828	+	0.805329i	$0.298011\pi$
$368$	1280.00	0.181317
$369$	2442.00	0.344513
$370$	0	0
$371$	238.000	0.0333055
$372$	−768.000	−0.107040
$373$	−4862.00	−0.674919	−0.337460	−	0.941340i	$-0.609568\pi$
$373$	−4862.00	−0.674919	−0.337460	+	0.941340i	$0.609568\pi$
$374$	−10064.0	−1.39144
$375$	0	0
$376$	−2496.00	−0.342344
$377$	−9724.00	−1.32841
$378$	1120.00	0.152398
$379$	−3932.00	−0.532911	−0.266456	−	0.963847i	$-0.585853\pi$
$379$	−3932.00	−0.532911	−0.266456	+	0.963847i	$0.585853\pi$
$380$	0	0
$381$	7232.00	0.972458
$382$	2848.00	0.381456
$383$	8120.00	1.08332	0.541661	−	0.840597i	$-0.317796\pi$
$383$	8120.00	1.08332	0.541661	+	0.840597i	$0.317796\pi$
$384$	1024.00	0.136083
$385$	0	0
$386$	3740.00	0.493163
$387$	4588.00	0.602639
$388$	5080.00	0.664685
$389$	−4346.00	−0.566455	−0.283227	−	0.959053i	$-0.591405\pi$
$389$	−4346.00	−0.566455	−0.283227	+	0.959053i	$0.591405\pi$
$390$	0	0
$391$	−5920.00	−0.765696
$392$	392.000	0.0505076
$393$	−16640.0	−2.13582
$394$	7236.00	0.925240
$395$	0	0
$396$	10064.0	1.27711
$397$	4494.00	0.568129	0.284065	−	0.958805i	$-0.408317\pi$
$397$	4494.00	0.568129	0.284065	+	0.958805i	$0.408317\pi$
$398$	5472.00	0.689162
$399$	−7168.00	−0.899371
$400$	0	0
$401$	2578.00	0.321045	0.160523	−	0.987032i	$-0.448682\pi$
$401$	2578.00	0.321045	0.160523	+	0.987032i	$0.448682\pi$
$402$	−9024.00	−1.11959
$403$	816.000	0.100863
$404$	3720.00	0.458111
$405$	0	0
$406$	4004.00	0.489446
$407$	−19992.0	−2.43481
$408$	−4736.00	−0.574674
$409$	3730.00	0.450945	0.225473	−	0.974249i	$-0.427607\pi$
$409$	3730.00	0.450945	0.225473	+	0.974249i	$0.427607\pi$
$410$	0	0
$411$	−17744.0	−2.12955
$412$	−640.000	−0.0765304
$413$	1176.00	0.140114
$414$	5920.00	0.702783
$415$	0	0
$416$	−1088.00	−0.128230
$417$	19456.0	2.28481
$418$	−17408.0	−2.03697
$419$	−2872.00	−0.334860	−0.167430	−	0.985884i	$-0.553547\pi$
$419$	−2872.00	−0.334860	−0.167430	+	0.985884i	$0.553547\pi$
$420$	0	0
$421$	−2210.00	−0.255840	−0.127920	−	0.991784i	$-0.540830\pi$
$421$	−2210.00	−0.255840	−0.127920	+	0.991784i	$0.540830\pi$
$422$	−696.000	−0.0802861
$423$	−11544.0	−1.32692
$424$	272.000	0.0311545
$425$	0	0
$426$	9856.00	1.12095
$427$	1190.00	0.134867
$428$	−5616.00	−0.634251
$429$	−18496.0	−2.08157
$430$	0	0
$431$	−456.000	−0.0509623	−0.0254811	−	0.999675i	$-0.508112\pi$
$431$	−456.000	−0.0509623	−0.0254811	+	0.999675i	$0.508112\pi$
$432$	1280.00	0.142556
$433$	5318.00	0.590223	0.295112	−	0.955463i	$-0.404643\pi$
$433$	5318.00	0.590223	0.295112	+	0.955463i	$0.404643\pi$
$434$	−336.000	−0.0371625
$435$	0	0
$436$	−1096.00	−0.120387
$437$	−10240.0	−1.12093
$438$	−4000.00	−0.436364
$439$	16264.0	1.76820	0.884098	−	0.467301i	$-0.154774\pi$
$439$	16264.0	1.76820	0.884098	+	0.467301i	$0.154774\pi$
$440$	0	0
$441$	1813.00	0.195767
$442$	5032.00	0.541511
$443$	−4812.00	−0.516084	−0.258042	−	0.966134i	$-0.583077\pi$
$443$	−4812.00	−0.516084	−0.258042	+	0.966134i	$0.583077\pi$
$444$	−9408.00	−1.00559
$445$	0	0
$446$	−11776.0	−1.25025
$447$	12784.0	1.35271
$448$	448.000	0.0472456
$449$	−2590.00	−0.272226	−0.136113	−	0.990693i	$-0.543461\pi$
$449$	−2590.00	−0.272226	−0.136113	+	0.990693i	$0.543461\pi$
$450$	0	0
$451$	4488.00	0.468585
$452$	3192.00	0.332166
$453$	−21376.0	−2.21707
$454$	8608.00	0.889853
$455$	0	0
$456$	−8192.00	−0.841284
$457$	14294.0	1.46312	0.731559	−	0.681778i	$-0.238793\pi$
$457$	14294.0	1.46312	0.731559	+	0.681778i	$0.238793\pi$
$458$	7348.00	0.749671
$459$	−5920.00	−0.602009
$460$	0	0
$461$	8258.00	0.834302	0.417151	−	0.908837i	$-0.363029\pi$
$461$	8258.00	0.834302	0.417151	+	0.908837i	$0.363029\pi$
$462$	7616.00	0.766945
$463$	7344.00	0.737159	0.368580	−	0.929596i	$-0.379844\pi$
$463$	7344.00	0.737159	0.368580	+	0.929596i	$0.379844\pi$
$464$	4576.00	0.457835
$465$	0	0
$466$	1676.00	0.166608
$467$	−6288.00	−0.623071	−0.311535	−	0.950235i	$-0.600843\pi$
$467$	−6288.00	−0.623071	−0.311535	+	0.950235i	$0.600843\pi$
$468$	−5032.00	−0.497018
$469$	−3948.00	−0.388703
$470$	0	0
$471$	−9360.00	−0.915682
$472$	1344.00	0.131065
$473$	8432.00	0.819670
$474$	−15104.0	−1.46361
$475$	0	0
$476$	−2072.00	−0.199517
$477$	1258.00	0.120754
$478$	11664.0	1.11611
$479$	392.000	0.0373924	0.0186962	−	0.999825i	$-0.494048\pi$
$479$	392.000	0.0373924	0.0186962	+	0.999825i	$0.494048\pi$
$480$	0	0
$481$	9996.00	0.947564
$482$	3380.00	0.319408
$483$	4480.00	0.422044
$484$	13172.0	1.23704
$485$	0	0
$486$	−10064.0	−0.939326
$487$	512.000	0.0476405	0.0238203	−	0.999716i	$-0.492417\pi$
$487$	512.000	0.0476405	0.0238203	+	0.999716i	$0.492417\pi$
$488$	1360.00	0.126156
$489$	−12640.0	−1.16892
$490$	0	0
$491$	13308.0	1.22318	0.611590	−	0.791175i	$-0.290530\pi$
$491$	13308.0	1.22318	0.611590	+	0.791175i	$0.290530\pi$
$492$	2112.00	0.193529
$493$	−21164.0	−1.93343
$494$	8704.00	0.792736
$495$	0	0
$496$	−384.000	−0.0347623
$497$	4312.00	0.389174
$498$	−10752.0	−0.967487
$499$	−6252.00	−0.560878	−0.280439	−	0.959872i	$-0.590480\pi$
$499$	−6252.00	−0.560878	−0.280439	+	0.959872i	$0.590480\pi$
$500$	0	0
$501$	5632.00	0.502234
$502$	11520.0	1.02423
$503$	−12568.0	−1.11407	−0.557037	−	0.830488i	$-0.688062\pi$
$503$	−12568.0	−1.11407	−0.557037	+	0.830488i	$0.688062\pi$
$504$	2072.00	0.183123
$505$	0	0
$506$	10880.0	0.955879
$507$	−8328.00	−0.729506
$508$	3616.00	0.315815
$509$	−5502.00	−0.479120	−0.239560	−	0.970882i	$-0.577003\pi$
$509$	−5502.00	−0.479120	−0.239560	+	0.970882i	$0.577003\pi$
$510$	0	0
$511$	−1750.00	−0.151498
$512$	512.000	0.0441942
$513$	−10240.0	−0.881300
$514$	700.000	0.0600694
$515$	0	0
$516$	3968.00	0.338530
$517$	−21216.0	−1.80479
$518$	−4116.00	−0.349125
$519$	−144.000	−0.0121790
$520$	0	0
$521$	−19086.0	−1.60494	−0.802469	−	0.596694i	$-0.796481\pi$
$521$	−19086.0	−1.60494	−0.802469	+	0.596694i	$0.796481\pi$
$522$	21164.0	1.77457
$523$	16184.0	1.35311	0.676555	−	0.736392i	$-0.263472\pi$
$523$	16184.0	1.35311	0.676555	+	0.736392i	$0.263472\pi$
$524$	−8320.00	−0.693628
$525$	0	0
$526$	5936.00	0.492057
$527$	1776.00	0.146800
$528$	8704.00	0.717411
$529$	−5767.00	−0.473987
$530$	0	0
$531$	6216.00	0.508006
$532$	−3584.00	−0.292079
$533$	−2244.00	−0.182361
$534$	−22880.0	−1.85415
$535$	0	0
$536$	−4512.00	−0.363598
$537$	−34144.0	−2.74380
$538$	−8988.00	−0.720261
$539$	3332.00	0.266270
$540$	0	0
$541$	−16042.0	−1.27486	−0.637430	−	0.770508i	$-0.720003\pi$
$541$	−16042.0	−1.27486	−0.637430	+	0.770508i	$0.720003\pi$
$542$	2624.00	0.207953
$543$	2256.00	0.178295
$544$	−2368.00	−0.186631
$545$	0	0
$546$	−3808.00	−0.298475
$547$	6180.00	0.483067	0.241534	−	0.970392i	$-0.422350\pi$
$547$	6180.00	0.483067	0.241534	+	0.970392i	$0.422350\pi$
$548$	−8872.00	−0.691593
$549$	6290.00	0.488981
$550$	0	0
$551$	−36608.0	−2.83041
$552$	5120.00	0.394786
$553$	−6608.00	−0.508139
$554$	10468.0	0.802785
$555$	0	0
$556$	9728.00	0.742013
$557$	−9078.00	−0.690569	−0.345285	−	0.938498i	$-0.612218\pi$
$557$	−9078.00	−0.690569	−0.345285	+	0.938498i	$0.612218\pi$
$558$	−1776.00	−0.134738
$559$	−4216.00	−0.318994
$560$	0	0
$561$	−40256.0	−3.02961
$562$	−11436.0	−0.858360
$563$	−9464.00	−0.708455	−0.354227	−	0.935159i	$-0.615256\pi$
$563$	−9464.00	−0.708455	−0.354227	+	0.935159i	$0.615256\pi$
$564$	−9984.00	−0.745394
$565$	0	0
$566$	7504.00	0.557273
$567$	−2513.00	−0.186131
$568$	4928.00	0.364039
$569$	15722.0	1.15835	0.579174	−	0.815204i	$-0.303375\pi$
$569$	15722.0	1.15835	0.579174	+	0.815204i	$0.303375\pi$
$570$	0	0
$571$	−17084.0	−1.25209	−0.626045	−	0.779787i	$-0.715327\pi$
$571$	−17084.0	−1.25209	−0.626045	+	0.779787i	$0.715327\pi$
$572$	−9248.00	−0.676011
$573$	11392.0	0.830554
$574$	924.000	0.0671899
$575$	0	0
$576$	2368.00	0.171296
$577$	16526.0	1.19235	0.596175	−	0.802854i	$-0.296686\pi$
$577$	16526.0	1.19235	0.596175	+	0.802854i	$0.296686\pi$
$578$	1126.00	0.0810301
$579$	14960.0	1.07378
$580$	0	0
$581$	−4704.00	−0.335895
$582$	20320.0	1.44724
$583$	2312.00	0.164242
$584$	−2000.00	−0.141713
$585$	0	0
$586$	−15396.0	−1.08533
$587$	−2832.00	−0.199130	−0.0995649	−	0.995031i	$-0.531745\pi$
$587$	−2832.00	−0.199130	−0.0995649	+	0.995031i	$0.531745\pi$
$588$	1568.00	0.109971
$589$	3072.00	0.214906
$590$	0	0
$591$	28944.0	2.01455
$592$	−4704.00	−0.326576
$593$	−9666.00	−0.669368	−0.334684	−	0.942330i	$-0.608630\pi$
$593$	−9666.00	−0.669368	−0.334684	+	0.942330i	$0.608630\pi$
$594$	10880.0	0.751535
$595$	0	0
$596$	6392.00	0.439306
$597$	21888.0	1.50053
$598$	−5440.00	−0.372004
$599$	4536.00	0.309409	0.154704	−	0.987961i	$-0.450557\pi$
$599$	4536.00	0.309409	0.154704	+	0.987961i	$0.450557\pi$
$600$	0	0
$601$	−15542.0	−1.05486	−0.527430	−	0.849598i	$-0.676844\pi$
$601$	−15542.0	−1.05486	−0.527430	+	0.849598i	$0.676844\pi$
$602$	1736.00	0.117532
$603$	−20868.0	−1.40930
$604$	−10688.0	−0.720014
$605$	0	0
$606$	14880.0	0.997457
$607$	23648.0	1.58129	0.790645	−	0.612275i	$-0.209746\pi$
$607$	23648.0	1.58129	0.790645	+	0.612275i	$0.209746\pi$
$608$	−4096.00	−0.273215
$609$	16016.0	1.06568
$610$	0	0
$611$	10608.0	0.702379
$612$	−10952.0	−0.723380
$613$	906.000	0.0596949	0.0298475	−	0.999554i	$-0.490498\pi$
$613$	906.000	0.0596949	0.0298475	+	0.999554i	$0.490498\pi$
$614$	2912.00	0.191399
$615$	0	0
$616$	3808.00	0.249073
$617$	−26666.0	−1.73992	−0.869962	−	0.493119i	$-0.835857\pi$
$617$	−26666.0	−1.73992	−0.869962	+	0.493119i	$0.835857\pi$
$618$	−2560.00	−0.166632
$619$	−3352.00	−0.217655	−0.108827	−	0.994061i	$-0.534710\pi$
$619$	−3352.00	−0.217655	−0.108827	+	0.994061i	$0.534710\pi$
$620$	0	0
$621$	6400.00	0.413564
$622$	19184.0	1.23667
$623$	−10010.0	−0.643727
$624$	−4352.00	−0.279198
$625$	0	0
$626$	−7140.00	−0.455865
$627$	−69632.0	−4.43514
$628$	−4680.00	−0.297376
$629$	21756.0	1.37912
$630$	0	0
$631$	2792.00	0.176145	0.0880727	−	0.996114i	$-0.471929\pi$
$631$	2792.00	0.176145	0.0880727	+	0.996114i	$0.471929\pi$
$632$	−7552.00	−0.475320
$633$	−2784.00	−0.174809
$634$	7732.00	0.484348
$635$	0	0
$636$	1088.00	0.0678333
$637$	−1666.00	−0.103625
$638$	38896.0	2.41365
$639$	22792.0	1.41101
$640$	0	0
$641$	19330.0	1.19109	0.595545	−	0.803322i	$-0.296936\pi$
$641$	19330.0	1.19109	0.595545	+	0.803322i	$0.296936\pi$
$642$	−22464.0	−1.38097
$643$	15160.0	0.929785	0.464893	−	0.885367i	$-0.346093\pi$
$643$	15160.0	0.929785	0.464893	+	0.885367i	$0.346093\pi$
$644$	2240.00	0.137063
$645$	0	0
$646$	18944.0	1.15378
$647$	23472.0	1.42624	0.713122	−	0.701040i	$-0.247281\pi$
$647$	23472.0	1.42624	0.713122	+	0.701040i	$0.247281\pi$
$648$	−2872.00	−0.174109
$649$	11424.0	0.690957
$650$	0	0
$651$	−1344.00	−0.0809148
$652$	−6320.00	−0.379617
$653$	−542.000	−0.0324810	−0.0162405	−	0.999868i	$-0.505170\pi$
$653$	−542.000	−0.0324810	−0.0162405	+	0.999868i	$0.505170\pi$
$654$	−4384.00	−0.262122
$655$	0	0
$656$	1056.00	0.0628504
$657$	−9250.00	−0.549280
$658$	−4368.00	−0.258788
$659$	−19764.0	−1.16828	−0.584140	−	0.811653i	$-0.698568\pi$
$659$	−19764.0	−1.16828	−0.584140	+	0.811653i	$0.698568\pi$
$660$	0	0
$661$	4130.00	0.243023	0.121512	−	0.992590i	$-0.461226\pi$
$661$	4130.00	0.243023	0.121512	+	0.992590i	$0.461226\pi$
$662$	−5880.00	−0.345216
$663$	20128.0	1.17904
$664$	−5376.00	−0.314201
$665$	0	0
$666$	−21756.0	−1.26581
$667$	22880.0	1.32821
$668$	2816.00	0.163105
$669$	−47104.0	−2.72219
$670$	0	0
$671$	11560.0	0.665080
$672$	1792.00	0.102869
$673$	24366.0	1.39560	0.697801	−	0.716292i	$-0.254162\pi$
$673$	24366.0	1.39560	0.697801	+	0.716292i	$0.254162\pi$
$674$	828.000	0.0473195
$675$	0	0
$676$	−4164.00	−0.236914
$677$	16790.0	0.953164	0.476582	−	0.879130i	$-0.341876\pi$
$677$	16790.0	0.953164	0.476582	+	0.879130i	$0.341876\pi$
$678$	12768.0	0.723233
$679$	8890.00	0.502455
$680$	0	0
$681$	34432.0	1.93750
$682$	−3264.00	−0.183262
$683$	7764.00	0.434965	0.217483	−	0.976064i	$-0.430215\pi$
$683$	7764.00	0.434965	0.217483	+	0.976064i	$0.430215\pi$
$684$	−18944.0	−1.05898
$685$	0	0
$686$	686.000	0.0381802
$687$	29392.0	1.63228
$688$	1984.00	0.109941
$689$	−1156.00	−0.0639189
$690$	0	0
$691$	−2064.00	−0.113630	−0.0568149	−	0.998385i	$-0.518095\pi$
$691$	−2064.00	−0.113630	−0.0568149	+	0.998385i	$0.518095\pi$
$692$	−72.0000	−0.00395524
$693$	17612.0	0.965403
$694$	10136.0	0.554405
$695$	0	0
$696$	18304.0	0.996855
$697$	−4884.00	−0.265416
$698$	5764.00	0.312565
$699$	6704.00	0.362759
$700$	0	0
$701$	1230.00	0.0662717	0.0331358	−	0.999451i	$-0.489451\pi$
$701$	1230.00	0.0662717	0.0331358	+	0.999451i	$0.489451\pi$
$702$	−5440.00	−0.292478
$703$	37632.0	2.01894
$704$	4352.00	0.232986
$705$	0	0
$706$	12700.0	0.677012
$707$	6510.00	0.346300
$708$	5376.00	0.285371
$709$	5158.00	0.273220	0.136610	−	0.990625i	$-0.456379\pi$
$709$	5158.00	0.273220	0.136610	+	0.990625i	$0.456379\pi$
$710$	0	0
$711$	−34928.0	−1.84234
$712$	−11440.0	−0.602152
$713$	−1920.00	−0.100848
$714$	−8288.00	−0.434413
$715$	0	0
$716$	−17072.0	−0.891076
$717$	46656.0	2.43013
$718$	9312.00	0.484012
$719$	−23800.0	−1.23448	−0.617239	−	0.786775i	$-0.711749\pi$
$719$	−23800.0	−1.23448	−0.617239	+	0.786775i	$0.711749\pi$
$720$	0	0
$721$	−1120.00	−0.0578516
$722$	19050.0	0.981950
$723$	13520.0	0.695455
$724$	1128.00	0.0579030
$725$	0	0
$726$	52688.0	2.69344
$727$	12832.0	0.654625	0.327313	−	0.944916i	$-0.393857\pi$
$727$	12832.0	0.654625	0.327313	+	0.944916i	$0.393857\pi$
$728$	−1904.00	−0.0969326
$729$	−30563.0	−1.55276
$730$	0	0
$731$	−9176.00	−0.464277
$732$	5440.00	0.274683
$733$	−15370.0	−0.774494	−0.387247	−	0.921976i	$-0.626574\pi$
$733$	−15370.0	−0.774494	−0.387247	+	0.921976i	$0.626574\pi$
$734$	16672.0	0.838385
$735$	0	0
$736$	2560.00	0.128210
$737$	−38352.0	−1.91684
$738$	4884.00	0.243608
$739$	16940.0	0.843231	0.421616	−	0.906775i	$-0.361463\pi$
$739$	16940.0	0.843231	0.421616	+	0.906775i	$0.361463\pi$
$740$	0	0
$741$	34816.0	1.72604
$742$	476.000	0.0235506
$743$	−39792.0	−1.96477	−0.982387	−	0.186858i	$-0.940169\pi$
$743$	−39792.0	−1.96477	−0.982387	+	0.186858i	$0.940169\pi$
$744$	−1536.00	−0.0756888
$745$	0	0
$746$	−9724.00	−0.477240
$747$	−24864.0	−1.21784
$748$	−20128.0	−0.983894
$749$	−9828.00	−0.479449
$750$	0	0
$751$	−776.000	−0.0377052	−0.0188526	−	0.999822i	$-0.506001\pi$
$751$	−776.000	−0.0377052	−0.0188526	+	0.999822i	$0.506001\pi$
$752$	−4992.00	−0.242074
$753$	46080.0	2.23008
$754$	−19448.0	−0.939329
$755$	0	0
$756$	2240.00	0.107762
$757$	17882.0	0.858563	0.429282	−	0.903171i	$-0.358767\pi$
$757$	17882.0	0.858563	0.429282	+	0.903171i	$0.358767\pi$
$758$	−7864.00	−0.376825
$759$	43520.0	2.08126
$760$	0	0
$761$	6946.00	0.330870	0.165435	−	0.986221i	$-0.447097\pi$
$761$	6946.00	0.330870	0.165435	+	0.986221i	$0.447097\pi$
$762$	14464.0	0.687632
$763$	−1918.00	−0.0910043
$764$	5696.00	0.269730
$765$	0	0
$766$	16240.0	0.766025
$767$	−5712.00	−0.268903
$768$	2048.00	0.0962250
$769$	35002.0	1.64136	0.820679	−	0.571389i	$-0.193595\pi$
$769$	35002.0	1.64136	0.820679	+	0.571389i	$0.193595\pi$
$770$	0	0
$771$	2800.00	0.130791
$772$	7480.00	0.348719
$773$	14414.0	0.670680	0.335340	−	0.942097i	$-0.391149\pi$
$773$	14414.0	0.670680	0.335340	+	0.942097i	$0.391149\pi$
$774$	9176.00	0.426130
$775$	0	0
$776$	10160.0	0.470004
$777$	−16464.0	−0.760158
$778$	−8692.00	−0.400544
$779$	−8448.00	−0.388551
$780$	0	0
$781$	41888.0	1.91917
$782$	−11840.0	−0.541429
$783$	22880.0	1.04427
$784$	784.000	0.0357143
$785$	0	0
$786$	−33280.0	−1.51025
$787$	7312.00	0.331188	0.165594	−	0.986194i	$-0.447046\pi$
$787$	7312.00	0.331188	0.165594	+	0.986194i	$0.447046\pi$
$788$	14472.0	0.654243
$789$	23744.0	1.07137
$790$	0	0
$791$	5586.00	0.251094
$792$	20128.0	0.903052
$793$	−5780.00	−0.258832
$794$	8988.00	0.401728
$795$	0	0
$796$	10944.0	0.487311
$797$	−4290.00	−0.190664	−0.0953322	−	0.995446i	$-0.530391\pi$
$797$	−4290.00	−0.190664	−0.0953322	+	0.995446i	$0.530391\pi$
$798$	−14336.0	−0.635951
$799$	23088.0	1.02227
$800$	0	0
$801$	−52910.0	−2.33394
$802$	5156.00	0.227013
$803$	−17000.0	−0.747095
$804$	−18048.0	−0.791671
$805$	0	0
$806$	1632.00	0.0713210
$807$	−35952.0	−1.56824
$808$	7440.00	0.323934
$809$	−28246.0	−1.22754	−0.613768	−	0.789487i	$-0.710347\pi$
$809$	−28246.0	−1.22754	−0.613768	+	0.789487i	$0.710347\pi$
$810$	0	0
$811$	−15656.0	−0.677875	−0.338937	−	0.940809i	$-0.610067\pi$
$811$	−15656.0	−0.677875	−0.338937	+	0.940809i	$0.610067\pi$
$812$	8008.00	0.346091
$813$	10496.0	0.452781
$814$	−39984.0	−1.72167
$815$	0	0
$816$	−9472.00	−0.406356
$817$	−15872.0	−0.679671
$818$	7460.00	0.318866
$819$	−8806.00	−0.375710
$820$	0	0
$821$	−27506.0	−1.16926	−0.584632	−	0.811298i	$-0.698761\pi$
$821$	−27506.0	−1.16926	−0.584632	+	0.811298i	$0.698761\pi$
$822$	−35488.0	−1.50582
$823$	−36552.0	−1.54814	−0.774072	−	0.633097i	$-0.781783\pi$
$823$	−36552.0	−1.54814	−0.774072	+	0.633097i	$0.781783\pi$
$824$	−1280.00	−0.0541152
$825$	0	0
$826$	2352.00	0.0990757
$827$	−18892.0	−0.794364	−0.397182	−	0.917740i	$-0.630012\pi$
$827$	−18892.0	−0.794364	−0.397182	+	0.917740i	$0.630012\pi$
$828$	11840.0	0.496943
$829$	−19446.0	−0.814701	−0.407351	−	0.913272i	$-0.633547\pi$
$829$	−19446.0	−0.814701	−0.407351	+	0.913272i	$0.633547\pi$
$830$	0	0
$831$	41872.0	1.74792
$832$	−2176.00	−0.0906721
$833$	−3626.00	−0.150820
$834$	38912.0	1.61560
$835$	0	0
$836$	−34816.0	−1.44035
$837$	−1920.00	−0.0792890
$838$	−5744.00	−0.236782
$839$	12416.0	0.510903	0.255452	−	0.966822i	$-0.417776\pi$
$839$	12416.0	0.510903	0.255452	+	0.966822i	$0.417776\pi$
$840$	0	0
$841$	57407.0	2.35381
$842$	−4420.00	−0.180906
$843$	−45744.0	−1.86893
$844$	−1392.00	−0.0567709
$845$	0	0
$846$	−23088.0	−0.938276
$847$	23051.0	0.935114
$848$	544.000	0.0220295
$849$	30016.0	1.21336
$850$	0	0
$851$	−23520.0	−0.947421
$852$	19712.0	0.792631
$853$	−19210.0	−0.771088	−0.385544	−	0.922689i	$-0.625986\pi$
$853$	−19210.0	−0.771088	−0.385544	+	0.922689i	$0.625986\pi$
$854$	2380.00	0.0953652
$855$	0	0
$856$	−11232.0	−0.448483
$857$	−530.000	−0.0211254	−0.0105627	−	0.999944i	$-0.503362\pi$
$857$	−530.000	−0.0211254	−0.0105627	+	0.999944i	$0.503362\pi$
$858$	−36992.0	−1.47190
$859$	−2624.00	−0.104226	−0.0521128	−	0.998641i	$-0.516596\pi$
$859$	−2624.00	−0.104226	−0.0521128	+	0.998641i	$0.516596\pi$
$860$	0	0
$861$	3696.00	0.146294
$862$	−912.000	−0.0360358
$863$	−37136.0	−1.46480	−0.732401	−	0.680874i	$-0.761600\pi$
$863$	−37136.0	−1.46480	−0.732401	+	0.680874i	$0.761600\pi$
$864$	2560.00	0.100802
$865$	0	0
$866$	10636.0	0.417351
$867$	4504.00	0.176429
$868$	−672.000	−0.0262778
$869$	−64192.0	−2.50583
$870$	0	0
$871$	19176.0	0.745986
$872$	−2192.00	−0.0851267
$873$	46990.0	1.82173
$874$	−20480.0	−0.792616
$875$	0	0
$876$	−8000.00	−0.308556
$877$	−44606.0	−1.71749	−0.858744	−	0.512404i	$-0.828755\pi$
$877$	−44606.0	−1.71749	−0.858744	+	0.512404i	$0.828755\pi$
$878$	32528.0	1.25030
$879$	−61584.0	−2.36311
$880$	0	0
$881$	−41806.0	−1.59873	−0.799364	−	0.600847i	$-0.794830\pi$
$881$	−41806.0	−1.59873	−0.799364	+	0.600847i	$0.794830\pi$
$882$	3626.00	0.138428
$883$	−8324.00	−0.317242	−0.158621	−	0.987340i	$-0.550705\pi$
$883$	−8324.00	−0.317242	−0.158621	+	0.987340i	$0.550705\pi$
$884$	10064.0	0.382906
$885$	0	0
$886$	−9624.00	−0.364926
$887$	6592.00	0.249535	0.124768	−	0.992186i	$-0.460181\pi$
$887$	6592.00	0.249535	0.124768	+	0.992186i	$0.460181\pi$
$888$	−18816.0	−0.711063
$889$	6328.00	0.238734
$890$	0	0
$891$	−24412.0	−0.917882
$892$	−23552.0	−0.884057
$893$	39936.0	1.49654
$894$	25568.0	0.956512
$895$	0	0
$896$	896.000	0.0334077
$897$	−21760.0	−0.809972
$898$	−5180.00	−0.192493
$899$	−6864.00	−0.254647
$900$	0	0
$901$	−2516.00	−0.0930301
$902$	8976.00	0.331339
$903$	6944.00	0.255905
$904$	6384.00	0.234877
$905$	0	0
$906$	−42752.0	−1.56770
$907$	−43948.0	−1.60890	−0.804448	−	0.594023i	$-0.797539\pi$
$907$	−43948.0	−1.60890	−0.804448	+	0.594023i	$0.797539\pi$
$908$	17216.0	0.629221
$909$	34410.0	1.25556
$910$	0	0
$911$	14936.0	0.543196	0.271598	−	0.962411i	$-0.412448\pi$
$911$	14936.0	0.543196	0.271598	+	0.962411i	$0.412448\pi$
$912$	−16384.0	−0.594878
$913$	−45696.0	−1.65643
$914$	28588.0	1.03458
$915$	0	0
$916$	14696.0	0.530098
$917$	−14560.0	−0.524333
$918$	−11840.0	−0.425684
$919$	8104.00	0.290888	0.145444	−	0.989366i	$-0.453539\pi$
$919$	8104.00	0.290888	0.145444	+	0.989366i	$0.453539\pi$
$920$	0	0
$921$	11648.0	0.416737
$922$	16516.0	0.589941
$923$	−20944.0	−0.746891
$924$	15232.0	0.542312
$925$	0	0
$926$	14688.0	0.521250
$927$	−5920.00	−0.209750
$928$	9152.00	0.323738
$929$	−43622.0	−1.54057	−0.770286	−	0.637699i	$-0.779887\pi$
$929$	−43622.0	−1.54057	−0.770286	+	0.637699i	$0.779887\pi$
$930$	0	0
$931$	−6272.00	−0.220791
$932$	3352.00	0.117809
$933$	76736.0	2.69263
$934$	−12576.0	−0.440577
$935$	0	0
$936$	−10064.0	−0.351445
$937$	30278.0	1.05564	0.527822	−	0.849355i	$-0.323009\pi$
$937$	30278.0	1.05564	0.527822	+	0.849355i	$0.323009\pi$
$938$	−7896.00	−0.274855
$939$	−28560.0	−0.992567
$940$	0	0
$941$	45594.0	1.57951	0.789757	−	0.613420i	$-0.210207\pi$
$941$	45594.0	1.57951	0.789757	+	0.613420i	$0.210207\pi$
$942$	−18720.0	−0.647485
$943$	5280.00	0.182333
$944$	2688.00	0.0926769
$945$	0	0
$946$	16864.0	0.579594
$947$	−5836.00	−0.200258	−0.100129	−	0.994974i	$-0.531926\pi$
$947$	−5836.00	−0.200258	−0.100129	+	0.994974i	$0.531926\pi$
$948$	−30208.0	−1.03493
$949$	8500.00	0.290750
$950$	0	0
$951$	30928.0	1.05458
$952$	−4144.00	−0.141080
$953$	−7274.00	−0.247249	−0.123624	−	0.992329i	$-0.539452\pi$
$953$	−7274.00	−0.247249	−0.123624	+	0.992329i	$0.539452\pi$
$954$	2516.00	0.0853863
$955$	0	0
$956$	23328.0	0.789207
$957$	155584.	5.25529
$958$	784.000	0.0264404
$959$	−15526.0	−0.522795
$960$	0	0
$961$	−29215.0	−0.980665
$962$	19992.0	0.670029
$963$	−51948.0	−1.73832
$964$	6760.00	0.225856
$965$	0	0
$966$	8960.00	0.298430
$967$	2432.00	0.0808768	0.0404384	−	0.999182i	$-0.487125\pi$
$967$	2432.00	0.0808768	0.0404384	+	0.999182i	$0.487125\pi$
$968$	26344.0	0.874719
$969$	75776.0	2.51215
$970$	0	0
$971$	−7496.00	−0.247743	−0.123871	−	0.992298i	$-0.539531\pi$
$971$	−7496.00	−0.247743	−0.123871	+	0.992298i	$0.539531\pi$
$972$	−20128.0	−0.664204
$973$	17024.0	0.560909
$974$	1024.00	0.0336869
$975$	0	0
$976$	2720.00	0.0892060
$977$	56574.0	1.85257	0.926286	−	0.376822i	$-0.122983\pi$
$977$	56574.0	1.85257	0.926286	+	0.376822i	$0.122983\pi$
$978$	−25280.0	−0.826549
$979$	−97240.0	−3.17447
$980$	0	0
$981$	−10138.0	−0.329950
$982$	26616.0	0.864919
$983$	25776.0	0.836345	0.418172	−	0.908368i	$-0.362671\pi$
$983$	25776.0	0.836345	0.418172	+	0.908368i	$0.362671\pi$
$984$	4224.00	0.136846
$985$	0	0
$986$	−42328.0	−1.36714
$987$	−17472.0	−0.563465
$988$	17408.0	0.560549
$989$	9920.00	0.318946
$990$	0	0
$991$	−60080.0	−1.92584	−0.962918	−	0.269793i	$-0.913045\pi$
$991$	−60080.0	−1.92584	−0.962918	+	0.269793i	$0.913045\pi$
$992$	−768.000	−0.0245807
$993$	−23520.0	−0.751646
$994$	8624.00	0.275188
$995$	0	0
$996$	−21504.0	−0.684117
$997$	−49906.0	−1.58529	−0.792647	−	0.609680i	$-0.791298\pi$
$997$	−49906.0	−1.58529	−0.792647	+	0.609680i	$0.791298\pi$
$998$	−12504.0	−0.396600
$999$	−23520.0	−0.744885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.4.a.v.1.1		1
5.2	odd	4		350.4.c.n.99.2		2
5.3	odd	4		350.4.c.n.99.1		2
5.4	even	2		70.4.a.a.1.1	✓	1
7.6	odd	2		2450.4.a.x.1.1		1
15.14	odd	2		630.4.a.s.1.1		1
20.19	odd	2		560.4.a.q.1.1		1
35.4	even	6		490.4.e.r.471.1		2
35.9	even	6		490.4.e.r.361.1		2
35.19	odd	6		490.4.e.j.361.1		2
35.24	odd	6		490.4.e.j.471.1		2
35.34	odd	2		490.4.a.g.1.1		1
40.19	odd	2		2240.4.a.d.1.1		1
40.29	even	2		2240.4.a.bi.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.a.1.1	✓	1	5.4	even	2
350.4.a.v.1.1		1	1.1	even	1	trivial
350.4.c.n.99.1		2	5.3	odd	4
350.4.c.n.99.2		2	5.2	odd	4
490.4.a.g.1.1		1	35.34	odd	2
490.4.e.j.361.1		2	35.19	odd	6
490.4.e.j.471.1		2	35.24	odd	6
490.4.e.r.361.1		2	35.9	even	6
490.4.e.r.471.1		2	35.4	even	6
560.4.a.q.1.1		1	20.19	odd	2
630.4.a.s.1.1		1	15.14	odd	2
2240.4.a.d.1.1		1	40.19	odd	2
2240.4.a.bi.1.1		1	40.29	even	2
2450.4.a.x.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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