LMFDB - Embedded newform 490.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, 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("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.9109359028$
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	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -2.00000 q^{6} -8.00000 q^{8} -26.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -2.00000 q^{6} -8.00000 q^{8} -26.0000 q^{9} -10.0000 q^{10} -65.0000 q^{11} +4.00000 q^{12} -13.0000 q^{13} +5.00000 q^{15} +16.0000 q^{16} +73.0000 q^{17} +52.0000 q^{18} +142.000 q^{19} +20.0000 q^{20} +130.000 q^{22} +130.000 q^{23} -8.00000 q^{24} +25.0000 q^{25} +26.0000 q^{26} -53.0000 q^{27} +111.000 q^{29} -10.0000 q^{30} -256.000 q^{31} -32.0000 q^{32} -65.0000 q^{33} -146.000 q^{34} -104.000 q^{36} -266.000 q^{37} -284.000 q^{38} -13.0000 q^{39} -40.0000 q^{40} +424.000 q^{41} +534.000 q^{43} -260.000 q^{44} -130.000 q^{45} -260.000 q^{46} +269.000 q^{47} +16.0000 q^{48} -50.0000 q^{50} +73.0000 q^{51} -52.0000 q^{52} -132.000 q^{53} +106.000 q^{54} -325.000 q^{55} +142.000 q^{57} -222.000 q^{58} +224.000 q^{59} +20.0000 q^{60} +572.000 q^{61} +512.000 q^{62} +64.0000 q^{64} -65.0000 q^{65} +130.000 q^{66} -108.000 q^{67} +292.000 q^{68} +130.000 q^{69} +560.000 q^{71} +208.000 q^{72} -586.000 q^{73} +532.000 q^{74} +25.0000 q^{75} +568.000 q^{76} +26.0000 q^{78} +57.0000 q^{79} +80.0000 q^{80} +649.000 q^{81} -848.000 q^{82} -252.000 q^{83} +365.000 q^{85} -1068.00 q^{86} +111.000 q^{87} +520.000 q^{88} +184.000 q^{89} +260.000 q^{90} +520.000 q^{92} -256.000 q^{93} -538.000 q^{94} +710.000 q^{95} -32.0000 q^{96} +605.000 q^{97} +1690.00 q^{99} +O(q^{100})\)

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
$3$	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
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−2.00000	−0.136083
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	−26.0000	−0.962963
$10$	−10.0000	−0.316228
$11$	−65.0000	−1.78166	−0.890829	−	0.454339i	$-0.849876\pi$
$11$	−65.0000	−1.78166	−0.890829	+	0.454339i	$0.849876\pi$
$12$	4.00000	0.0962250
$13$	−13.0000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−13.0000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	0	0
$15$	5.00000	0.0860663
$16$	16.0000	0.250000
$17$	73.0000	1.04148	0.520738	−	0.853716i	$-0.325657\pi$
$17$	73.0000	1.04148	0.520738	+	0.853716i	$0.325657\pi$
$18$	52.0000	0.680918
$19$	142.000	1.71458	0.857290	−	0.514833i	$-0.172146\pi$
$19$	142.000	1.71458	0.857290	+	0.514833i	$0.172146\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	130.000	1.25982
$23$	130.000	1.17856	0.589280	−	0.807929i	$-0.299412\pi$
$23$	130.000	1.17856	0.589280	+	0.807929i	$0.299412\pi$
$24$	−8.00000	−0.0680414
$25$	25.0000	0.200000
$26$	26.0000	0.196116
$27$	−53.0000	−0.377772
$28$	0	0
$29$	111.000	0.710765	0.355382	−	0.934721i	$-0.384351\pi$
$29$	111.000	0.710765	0.355382	+	0.934721i	$0.384351\pi$
$30$	−10.0000	−0.0608581
$31$	−256.000	−1.48319	−0.741596	−	0.670847i	$-0.765931\pi$
$31$	−256.000	−1.48319	−0.741596	+	0.670847i	$0.765931\pi$
$32$	−32.0000	−0.176777
$33$	−65.0000	−0.342880
$34$	−146.000	−0.736435
$35$	0	0
$36$	−104.000	−0.481481
$37$	−266.000	−1.18190	−0.590948	−	0.806710i	$-0.701246\pi$
$37$	−266.000	−1.18190	−0.590948	+	0.806710i	$0.701246\pi$
$38$	−284.000	−1.21239
$39$	−13.0000	−0.0533761
$40$	−40.0000	−0.158114
$41$	424.000	1.61507	0.807533	−	0.589823i	$-0.200802\pi$
$41$	424.000	1.61507	0.807533	+	0.589823i	$0.200802\pi$
$42$	0	0
$43$	534.000	1.89382	0.946910	−	0.321500i	$-0.104187\pi$
$43$	534.000	1.89382	0.946910	+	0.321500i	$0.104187\pi$
$44$	−260.000	−0.890829
$45$	−130.000	−0.430650
$46$	−260.000	−0.833368
$47$	269.000	0.834844	0.417422	−	0.908713i	$-0.362934\pi$
$47$	269.000	0.834844	0.417422	+	0.908713i	$0.362934\pi$
$48$	16.0000	0.0481125
$49$	0	0
$50$	−50.0000	−0.141421
$51$	73.0000	0.200432
$52$	−52.0000	−0.138675
$53$	−132.000	−0.342106	−0.171053	−	0.985262i	$-0.554717\pi$
$53$	−132.000	−0.342106	−0.171053	+	0.985262i	$0.554717\pi$
$54$	106.000	0.267125
$55$	−325.000	−0.796782
$56$	0	0
$57$	142.000	0.329971
$58$	−222.000	−0.502587
$59$	224.000	0.494277	0.247138	−	0.968980i	$-0.420510\pi$
$59$	224.000	0.494277	0.247138	+	0.968980i	$0.420510\pi$
$60$	20.0000	0.0430331
$61$	572.000	1.20061	0.600304	−	0.799772i	$-0.295046\pi$
$61$	572.000	1.20061	0.600304	+	0.799772i	$0.295046\pi$
$62$	512.000	1.04878
$63$	0	0
$64$	64.0000	0.125000
$65$	−65.0000	−0.124035
$66$	130.000	0.242453
$67$	−108.000	−0.196930	−0.0984649	−	0.995141i	$-0.531393\pi$
$67$	−108.000	−0.196930	−0.0984649	+	0.995141i	$0.531393\pi$
$68$	292.000	0.520738
$69$	130.000	0.226814
$70$	0	0
$71$	560.000	0.936053	0.468027	−	0.883714i	$-0.344965\pi$
$71$	560.000	0.936053	0.468027	+	0.883714i	$0.344965\pi$
$72$	208.000	0.340459
$73$	−586.000	−0.939536	−0.469768	−	0.882790i	$-0.655662\pi$
$73$	−586.000	−0.939536	−0.469768	+	0.882790i	$0.655662\pi$
$74$	532.000	0.835726
$75$	25.0000	0.0384900
$76$	568.000	0.857290
$77$	0	0
$78$	26.0000	0.0377426
$79$	57.0000	0.0811772	0.0405886	−	0.999176i	$-0.487077\pi$
$79$	57.0000	0.0811772	0.0405886	+	0.999176i	$0.487077\pi$
$80$	80.0000	0.111803
$81$	649.000	0.890261
$82$	−848.000	−1.14202
$83$	−252.000	−0.333260	−0.166630	−	0.986019i	$-0.553289\pi$
$83$	−252.000	−0.333260	−0.166630	+	0.986019i	$0.553289\pi$
$84$	0	0
$85$	365.000	0.465762
$86$	−1068.00	−1.33913
$87$	111.000	0.136787
$88$	520.000	0.629911
$89$	184.000	0.219146	0.109573	−	0.993979i	$-0.465052\pi$
$89$	184.000	0.219146	0.109573	+	0.993979i	$0.465052\pi$
$90$	260.000	0.304516
$91$	0	0
$92$	520.000	0.589280
$93$	−256.000	−0.285440
$94$	−538.000	−0.590324
$95$	710.000	0.766784
$96$	−32.0000	−0.0340207
$97$	605.000	0.633283	0.316641	−	0.948545i	$-0.397445\pi$
$97$	605.000	0.633283	0.316641	+	0.948545i	$0.397445\pi$
$98$	0	0
$99$	1690.00	1.71567
$100$	100.000	0.100000
$101$	750.000	0.738889	0.369445	−	0.929253i	$-0.379548\pi$
$101$	750.000	0.738889	0.369445	+	0.929253i	$0.379548\pi$
$102$	−146.000	−0.141727
$103$	337.000	0.322384	0.161192	−	0.986923i	$-0.448466\pi$
$103$	337.000	0.322384	0.161192	+	0.986923i	$0.448466\pi$
$104$	104.000	0.0980581
$105$	0	0
$106$	264.000	0.241905
$107$	634.000	0.572814	0.286407	−	0.958108i	$-0.407539\pi$
$107$	634.000	0.572814	0.286407	+	0.958108i	$0.407539\pi$
$108$	−212.000	−0.188886
$109$	−827.000	−0.726718	−0.363359	−	0.931649i	$-0.618370\pi$
$109$	−827.000	−0.726718	−0.363359	+	0.931649i	$0.618370\pi$
$110$	650.000	0.563410
$111$	−266.000	−0.227456
$112$	0	0
$113$	−1862.00	−1.55011	−0.775054	−	0.631895i	$-0.782277\pi$
$113$	−1862.00	−1.55011	−0.775054	+	0.631895i	$0.782277\pi$
$114$	−284.000	−0.233325
$115$	650.000	0.527068
$116$	444.000	0.355382
$117$	338.000	0.267078
$118$	−448.000	−0.349506
$119$	0	0
$120$	−40.0000	−0.0304290
$121$	2894.00	2.17431
$122$	−1144.00	−0.848958
$123$	424.000	0.310819
$124$	−1024.00	−0.741596
$125$	125.000	0.0894427
$126$	0	0
$127$	48.0000	0.0335379	0.0167689	−	0.999859i	$-0.494662\pi$
$127$	48.0000	0.0335379	0.0167689	+	0.999859i	$0.494662\pi$
$128$	−128.000	−0.0883883
$129$	534.000	0.364466
$130$	130.000	0.0877058
$131$	582.000	0.388165	0.194082	−	0.980985i	$-0.437827\pi$
$131$	582.000	0.388165	0.194082	+	0.980985i	$0.437827\pi$
$132$	−260.000	−0.171440
$133$	0	0
$134$	216.000	0.139250
$135$	−265.000	−0.168945
$136$	−584.000	−0.368218
$137$	−344.000	−0.214525	−0.107262	−	0.994231i	$-0.534209\pi$
$137$	−344.000	−0.214525	−0.107262	+	0.994231i	$0.534209\pi$
$138$	−260.000	−0.160382
$139$	1894.00	1.15573	0.577867	−	0.816131i	$-0.303885\pi$
$139$	1894.00	1.15573	0.577867	+	0.816131i	$0.303885\pi$
$140$	0	0
$141$	269.000	0.160666
$142$	−1120.00	−0.661890
$143$	845.000	0.494143
$144$	−416.000	−0.240741
$145$	555.000	0.317864
$146$	1172.00	0.664352
$147$	0	0
$148$	−1064.00	−0.590948
$149$	618.000	0.339789	0.169894	−	0.985462i	$-0.445657\pi$
$149$	618.000	0.339789	0.169894	+	0.985462i	$0.445657\pi$
$150$	−50.0000	−0.0272166
$151$	233.000	0.125571	0.0627857	−	0.998027i	$-0.480002\pi$
$151$	233.000	0.125571	0.0627857	+	0.998027i	$0.480002\pi$
$152$	−1136.00	−0.606196
$153$	−1898.00	−1.00290
$154$	0	0
$155$	−1280.00	−0.663304
$156$	−52.0000	−0.0266880
$157$	2218.00	1.12749	0.563744	−	0.825949i	$-0.309360\pi$
$157$	2218.00	1.12749	0.563744	+	0.825949i	$0.309360\pi$
$158$	−114.000	−0.0574010
$159$	−132.000	−0.0658382
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−1298.00	−0.629509
$163$	−2298.00	−1.10425	−0.552127	−	0.833760i	$-0.686183\pi$
$163$	−2298.00	−1.10425	−0.552127	+	0.833760i	$0.686183\pi$
$164$	1696.00	0.807533
$165$	−325.000	−0.153341
$166$	504.000	0.235651
$167$	−311.000	−0.144107	−0.0720536	−	0.997401i	$-0.522955\pi$
$167$	−311.000	−0.144107	−0.0720536	+	0.997401i	$0.522955\pi$
$168$	0	0
$169$	−2028.00	−0.923077
$170$	−730.000	−0.329344
$171$	−3692.00	−1.65108
$172$	2136.00	0.946910
$173$	1081.00	0.475069	0.237534	−	0.971379i	$-0.423661\pi$
$173$	1081.00	0.475069	0.237534	+	0.971379i	$0.423661\pi$
$174$	−222.000	−0.0967229
$175$	0	0
$176$	−1040.00	−0.445414
$177$	224.000	0.0951236
$178$	−368.000	−0.154959
$179$	−908.000	−0.379146	−0.189573	−	0.981867i	$-0.560710\pi$
$179$	−908.000	−0.379146	−0.189573	+	0.981867i	$0.560710\pi$
$180$	−520.000	−0.215325
$181$	460.000	0.188903	0.0944517	−	0.995529i	$-0.469890\pi$
$181$	460.000	0.188903	0.0944517	+	0.995529i	$0.469890\pi$
$182$	0	0
$183$	572.000	0.231057
$184$	−1040.00	−0.416684
$185$	−1330.00	−0.528560
$186$	512.000	0.201837
$187$	−4745.00	−1.85555
$188$	1076.00	0.417422
$189$	0	0
$190$	−1420.00	−0.542198
$191$	4679.00	1.77257	0.886284	−	0.463142i	$-0.153278\pi$
$191$	4679.00	1.77257	0.886284	+	0.463142i	$0.153278\pi$
$192$	64.0000	0.0240563
$193$	−2528.00	−0.942847	−0.471423	−	0.881907i	$-0.656260\pi$
$193$	−2528.00	−0.942847	−0.471423	+	0.881907i	$0.656260\pi$
$194$	−1210.00	−0.447799
$195$	−65.0000	−0.0238705
$196$	0	0
$197$	4404.00	1.59275	0.796376	−	0.604802i	$-0.206748\pi$
$197$	4404.00	1.59275	0.796376	+	0.604802i	$0.206748\pi$
$198$	−3380.00	−1.21316
$199$	1240.00	0.441715	0.220857	−	0.975306i	$-0.429114\pi$
$199$	1240.00	0.441715	0.220857	+	0.975306i	$0.429114\pi$
$200$	−200.000	−0.0707107
$201$	−108.000	−0.0378992
$202$	−1500.00	−0.522473
$203$	0	0
$204$	292.000	0.100216
$205$	2120.00	0.722279
$206$	−674.000	−0.227960
$207$	−3380.00	−1.13491
$208$	−208.000	−0.0693375
$209$	−9230.00	−3.05480
$210$	0	0
$211$	−2959.00	−0.965431	−0.482716	−	0.875777i	$-0.660349\pi$
$211$	−2959.00	−0.965431	−0.482716	+	0.875777i	$0.660349\pi$
$212$	−528.000	−0.171053
$213$	560.000	0.180144
$214$	−1268.00	−0.405041
$215$	2670.00	0.846942
$216$	424.000	0.133563
$217$	0	0
$218$	1654.00	0.513867
$219$	−586.000	−0.180814
$220$	−1300.00	−0.398391
$221$	−949.000	−0.288854
$222$	532.000	0.160836
$223$	−5559.00	−1.66932	−0.834660	−	0.550766i	$-0.814336\pi$
$223$	−5559.00	−1.66932	−0.834660	+	0.550766i	$0.814336\pi$
$224$	0	0
$225$	−650.000	−0.192593
$226$	3724.00	1.09609
$227$	5109.00	1.49382	0.746908	−	0.664927i	$-0.231538\pi$
$227$	5109.00	1.49382	0.746908	+	0.664927i	$0.231538\pi$
$228$	568.000	0.164986
$229$	−3184.00	−0.918798	−0.459399	−	0.888230i	$-0.651935\pi$
$229$	−3184.00	−0.918798	−0.459399	+	0.888230i	$0.651935\pi$
$230$	−1300.00	−0.372693
$231$	0	0
$232$	−888.000	−0.251293
$233$	4552.00	1.27988	0.639939	−	0.768426i	$-0.278960\pi$
$233$	4552.00	1.27988	0.639939	+	0.768426i	$0.278960\pi$
$234$	−676.000	−0.188853
$235$	1345.00	0.373354
$236$	896.000	0.247138
$237$	57.0000	0.0156226
$238$	0	0
$239$	−1819.00	−0.492307	−0.246153	−	0.969231i	$-0.579167\pi$
$239$	−1819.00	−0.492307	−0.246153	+	0.969231i	$0.579167\pi$
$240$	80.0000	0.0215166
$241$	4470.00	1.19476	0.597382	−	0.801957i	$-0.296208\pi$
$241$	4470.00	1.19476	0.597382	+	0.801957i	$0.296208\pi$
$242$	−5788.00	−1.53747
$243$	2080.00	0.549103
$244$	2288.00	0.600304
$245$	0	0
$246$	−848.000	−0.219783
$247$	−1846.00	−0.475539
$248$	2048.00	0.524388
$249$	−252.000	−0.0641359
$250$	−250.000	−0.0632456
$251$	5258.00	1.32224	0.661120	−	0.750281i	$-0.270082\pi$
$251$	5258.00	1.32224	0.661120	+	0.750281i	$0.270082\pi$
$252$	0	0
$253$	−8450.00	−2.09979
$254$	−96.0000	−0.0237149
$255$	365.000	0.0896360
$256$	256.000	0.0625000
$257$	−6566.00	−1.59368	−0.796840	−	0.604190i	$-0.793497\pi$
$257$	−6566.00	−1.59368	−0.796840	+	0.604190i	$0.793497\pi$
$258$	−1068.00	−0.257716
$259$	0	0
$260$	−260.000	−0.0620174
$261$	−2886.00	−0.684440
$262$	−1164.00	−0.274474
$263$	2730.00	0.640072	0.320036	−	0.947405i	$-0.396305\pi$
$263$	2730.00	0.640072	0.320036	+	0.947405i	$0.396305\pi$
$264$	520.000	0.121226
$265$	−660.000	−0.152994
$266$	0	0
$267$	184.000	0.0421746
$268$	−432.000	−0.0984649
$269$	−6762.00	−1.53266	−0.766332	−	0.642445i	$-0.777920\pi$
$269$	−6762.00	−1.53266	−0.766332	+	0.642445i	$0.777920\pi$
$270$	530.000	0.119462
$271$	6276.00	1.40679	0.703395	−	0.710800i	$-0.251667\pi$
$271$	6276.00	1.40679	0.703395	+	0.710800i	$0.251667\pi$
$272$	1168.00	0.260369
$273$	0	0
$274$	688.000	0.151692
$275$	−1625.00	−0.356332
$276$	520.000	0.113407
$277$	−3610.00	−0.783046	−0.391523	−	0.920168i	$-0.628052\pi$
$277$	−3610.00	−0.783046	−0.391523	+	0.920168i	$0.628052\pi$
$278$	−3788.00	−0.817227
$279$	6656.00	1.42826
$280$	0	0
$281$	−3821.00	−0.811181	−0.405590	−	0.914055i	$-0.632934\pi$
$281$	−3821.00	−0.811181	−0.405590	+	0.914055i	$0.632934\pi$
$282$	−538.000	−0.113608
$283$	931.000	0.195555	0.0977777	−	0.995208i	$-0.468827\pi$
$283$	931.000	0.195555	0.0977777	+	0.995208i	$0.468827\pi$
$284$	2240.00	0.468027
$285$	710.000	0.147568
$286$	−1690.00	−0.349412
$287$	0	0
$288$	832.000	0.170229
$289$	416.000	0.0846733
$290$	−1110.00	−0.224764
$291$	605.000	0.121875
$292$	−2344.00	−0.469768
$293$	1773.00	0.353515	0.176757	−	0.984254i	$-0.443439\pi$
$293$	1773.00	0.353515	0.176757	+	0.984254i	$0.443439\pi$
$294$	0	0
$295$	1120.00	0.221047
$296$	2128.00	0.417863
$297$	3445.00	0.673061
$298$	−1236.00	−0.240267
$299$	−1690.00	−0.326874
$300$	100.000	0.0192450
$301$	0	0
$302$	−466.000	−0.0887923
$303$	750.000	0.142199
$304$	2272.00	0.428645
$305$	2860.00	0.536928
$306$	3796.00	0.709160
$307$	−7469.00	−1.38853	−0.694264	−	0.719720i	$-0.744270\pi$
$307$	−7469.00	−1.38853	−0.694264	+	0.719720i	$0.744270\pi$
$308$	0	0
$309$	337.000	0.0620429
$310$	2560.00	0.469027
$311$	1174.00	0.214056	0.107028	−	0.994256i	$-0.465867\pi$
$311$	1174.00	0.214056	0.107028	+	0.994256i	$0.465867\pi$
$312$	104.000	0.0188713
$313$	−7945.00	−1.43475	−0.717377	−	0.696685i	$-0.754657\pi$
$313$	−7945.00	−1.43475	−0.717377	+	0.696685i	$0.754657\pi$
$314$	−4436.00	−0.797255
$315$	0	0
$316$	228.000	0.0405886
$317$	−2578.00	−0.456766	−0.228383	−	0.973571i	$-0.573344\pi$
$317$	−2578.00	−0.456766	−0.228383	+	0.973571i	$0.573344\pi$
$318$	264.000	0.0465547
$319$	−7215.00	−1.26634
$320$	320.000	0.0559017
$321$	634.000	0.110238
$322$	0	0
$323$	10366.0	1.78570
$324$	2596.00	0.445130
$325$	−325.000	−0.0554700
$326$	4596.00	0.780825
$327$	−827.000	−0.139857
$328$	−3392.00	−0.571012
$329$	0	0
$330$	650.000	0.108428
$331$	28.0000	0.00464960	0.00232480	−	0.999997i	$-0.499260\pi$
$331$	28.0000	0.00464960	0.00232480	+	0.999997i	$0.499260\pi$
$332$	−1008.00	−0.166630
$333$	6916.00	1.13812
$334$	622.000	0.101899
$335$	−540.000	−0.0880697
$336$	0	0
$337$	398.000	0.0643337	0.0321668	−	0.999483i	$-0.489759\pi$
$337$	398.000	0.0643337	0.0321668	+	0.999483i	$0.489759\pi$
$338$	4056.00	0.652714
$339$	−1862.00	−0.298318
$340$	1460.00	0.232881
$341$	16640.0	2.64254
$342$	7384.00	1.16749
$343$	0	0
$344$	−4272.00	−0.669566
$345$	650.000	0.101434
$346$	−2162.00	−0.335924
$347$	2142.00	0.331379	0.165690	−	0.986178i	$-0.447015\pi$
$347$	2142.00	0.331379	0.165690	+	0.986178i	$0.447015\pi$
$348$	444.000	0.0683934
$349$	7282.00	1.11690	0.558448	−	0.829540i	$-0.311397\pi$
$349$	7282.00	1.11690	0.558448	+	0.829540i	$0.311397\pi$
$350$	0	0
$351$	689.000	0.104775
$352$	2080.00	0.314956
$353$	−5739.00	−0.865315	−0.432657	−	0.901558i	$-0.642424\pi$
$353$	−5739.00	−0.865315	−0.432657	+	0.901558i	$0.642424\pi$
$354$	−448.000	−0.0672625
$355$	2800.00	0.418616
$356$	736.000	0.109573
$357$	0	0
$358$	1816.00	0.268097
$359$	904.000	0.132901	0.0664503	−	0.997790i	$-0.478833\pi$
$359$	904.000	0.132901	0.0664503	+	0.997790i	$0.478833\pi$
$360$	1040.00	0.152258
$361$	13305.0	1.93979
$362$	−920.000	−0.133575
$363$	2894.00	0.418445
$364$	0	0
$365$	−2930.00	−0.420173
$366$	−1144.00	−0.163382
$367$	−9451.00	−1.34425	−0.672123	−	0.740440i	$-0.734617\pi$
$367$	−9451.00	−1.34425	−0.672123	+	0.740440i	$0.734617\pi$
$368$	2080.00	0.294640
$369$	−11024.0	−1.55525
$370$	2660.00	0.373748
$371$	0	0
$372$	−1024.00	−0.142720
$373$	−10888.0	−1.51142	−0.755709	−	0.654907i	$-0.772708\pi$
$373$	−10888.0	−1.51142	−0.755709	+	0.654907i	$0.772708\pi$
$374$	9490.00	1.31208
$375$	125.000	0.0172133
$376$	−2152.00	−0.295162
$377$	−1443.00	−0.197131
$378$	0	0
$379$	1276.00	0.172939	0.0864693	−	0.996255i	$-0.472442\pi$
$379$	1276.00	0.172939	0.0864693	+	0.996255i	$0.472442\pi$
$380$	2840.00	0.383392
$381$	48.0000	0.00645437
$382$	−9358.00	−1.25340
$383$	−588.000	−0.0784475	−0.0392238	−	0.999230i	$-0.512489\pi$
$383$	−588.000	−0.0784475	−0.0392238	+	0.999230i	$0.512489\pi$
$384$	−128.000	−0.0170103
$385$	0	0
$386$	5056.00	0.666693
$387$	−13884.0	−1.82368
$388$	2420.00	0.316641
$389$	2577.00	0.335885	0.167942	−	0.985797i	$-0.446288\pi$
$389$	2577.00	0.335885	0.167942	+	0.985797i	$0.446288\pi$
$390$	130.000	0.0168790
$391$	9490.00	1.22744
$392$	0	0
$393$	582.000	0.0747023
$394$	−8808.00	−1.12625
$395$	285.000	0.0363036
$396$	6760.00	0.857835
$397$	−8575.00	−1.08405	−0.542024	−	0.840363i	$-0.682342\pi$
$397$	−8575.00	−1.08405	−0.542024	+	0.840363i	$0.682342\pi$
$398$	−2480.00	−0.312340
$399$	0	0
$400$	400.000	0.0500000
$401$	5217.00	0.649687	0.324844	−	0.945768i	$-0.394688\pi$
$401$	5217.00	0.649687	0.324844	+	0.945768i	$0.394688\pi$
$402$	216.000	0.0267988
$403$	3328.00	0.411363
$404$	3000.00	0.369445
$405$	3245.00	0.398137
$406$	0	0
$407$	17290.0	2.10573
$408$	−584.000	−0.0708635
$409$	5594.00	0.676297	0.338149	−	0.941093i	$-0.390199\pi$
$409$	5594.00	0.676297	0.338149	+	0.941093i	$0.390199\pi$
$410$	−4240.00	−0.510728
$411$	−344.000	−0.0412853
$412$	1348.00	0.161192
$413$	0	0
$414$	6760.00	0.802502
$415$	−1260.00	−0.149038
$416$	416.000	0.0490290
$417$	1894.00	0.222421
$418$	18460.0	2.16007
$419$	6036.00	0.703766	0.351883	−	0.936044i	$-0.385542\pi$
$419$	6036.00	0.703766	0.351883	+	0.936044i	$0.385542\pi$
$420$	0	0
$421$	−14915.0	−1.72663	−0.863317	−	0.504663i	$-0.831617\pi$
$421$	−14915.0	−1.72663	−0.863317	+	0.504663i	$0.831617\pi$
$422$	5918.00	0.682663
$423$	−6994.00	−0.803924
$424$	1056.00	0.120953
$425$	1825.00	0.208295
$426$	−1120.00	−0.127381
$427$	0	0
$428$	2536.00	0.286407
$429$	845.000	0.0950979
$430$	−5340.00	−0.598878
$431$	3219.00	0.359754	0.179877	−	0.983689i	$-0.442430\pi$
$431$	3219.00	0.359754	0.179877	+	0.983689i	$0.442430\pi$
$432$	−848.000	−0.0944431
$433$	6942.00	0.770465	0.385232	−	0.922820i	$-0.374121\pi$
$433$	6942.00	0.770465	0.385232	+	0.922820i	$0.374121\pi$
$434$	0	0
$435$	555.000	0.0611729
$436$	−3308.00	−0.363359
$437$	18460.0	2.02074
$438$	1172.00	0.127855
$439$	1978.00	0.215045	0.107523	−	0.994203i	$-0.465708\pi$
$439$	1978.00	0.215045	0.107523	+	0.994203i	$0.465708\pi$
$440$	2600.00	0.281705
$441$	0	0
$442$	1898.00	0.204250
$443$	6254.00	0.670737	0.335369	−	0.942087i	$-0.391139\pi$
$443$	6254.00	0.670737	0.335369	+	0.942087i	$0.391139\pi$
$444$	−1064.00	−0.113728
$445$	920.000	0.0980049
$446$	11118.0	1.18039
$447$	618.000	0.0653924
$448$	0	0
$449$	14287.0	1.50166	0.750830	−	0.660496i	$-0.229654\pi$
$449$	14287.0	1.50166	0.750830	+	0.660496i	$0.229654\pi$
$450$	1300.00	0.136184
$451$	−27560.0	−2.87749
$452$	−7448.00	−0.775054
$453$	233.000	0.0241662
$454$	−10218.0	−1.05629
$455$	0	0
$456$	−1136.00	−0.116662
$457$	−6860.00	−0.702182	−0.351091	−	0.936341i	$-0.614189\pi$
$457$	−6860.00	−0.702182	−0.351091	+	0.936341i	$0.614189\pi$
$458$	6368.00	0.649688
$459$	−3869.00	−0.393441
$460$	2600.00	0.263534
$461$	−8552.00	−0.864005	−0.432003	−	0.901872i	$-0.642193\pi$
$461$	−8552.00	−0.864005	−0.432003	+	0.901872i	$0.642193\pi$
$462$	0	0
$463$	2876.00	0.288680	0.144340	−	0.989528i	$-0.453894\pi$
$463$	2876.00	0.288680	0.144340	+	0.989528i	$0.453894\pi$
$464$	1776.00	0.177691
$465$	−1280.00	−0.127653
$466$	−9104.00	−0.905010
$467$	9287.00	0.920238	0.460119	−	0.887857i	$-0.347807\pi$
$467$	9287.00	0.920238	0.460119	+	0.887857i	$0.347807\pi$
$468$	1352.00	0.133539
$469$	0	0
$470$	−2690.00	−0.264001
$471$	2218.00	0.216985
$472$	−1792.00	−0.174753
$473$	−34710.0	−3.37414
$474$	−114.000	−0.0110468
$475$	3550.00	0.342916
$476$	0	0
$477$	3432.00	0.329435
$478$	3638.00	0.348113
$479$	−11466.0	−1.09373	−0.546863	−	0.837222i	$-0.684178\pi$
$479$	−11466.0	−1.09373	−0.546863	+	0.837222i	$0.684178\pi$
$480$	−160.000	−0.0152145
$481$	3458.00	0.327799
$482$	−8940.00	−0.844825
$483$	0	0
$484$	11576.0	1.08715
$485$	3025.00	0.283213
$486$	−4160.00	−0.388275
$487$	17898.0	1.66537	0.832686	−	0.553746i	$-0.186802\pi$
$487$	17898.0	1.66537	0.832686	+	0.553746i	$0.186802\pi$
$488$	−4576.00	−0.424479
$489$	−2298.00	−0.212514
$490$	0	0
$491$	3333.00	0.306347	0.153173	−	0.988199i	$-0.451051\pi$
$491$	3333.00	0.306347	0.153173	+	0.988199i	$0.451051\pi$
$492$	1696.00	0.155410
$493$	8103.00	0.740245
$494$	3692.00	0.336257
$495$	8450.00	0.767271
$496$	−4096.00	−0.370798
$497$	0	0
$498$	504.000	0.0453510
$499$	−14141.0	−1.26861	−0.634307	−	0.773081i	$-0.718714\pi$
$499$	−14141.0	−1.26861	−0.634307	+	0.773081i	$0.718714\pi$
$500$	500.000	0.0447214
$501$	−311.000	−0.0277334
$502$	−10516.0	−0.934964
$503$	17735.0	1.57210	0.786048	−	0.618165i	$-0.212124\pi$
$503$	17735.0	1.57210	0.786048	+	0.618165i	$0.212124\pi$
$504$	0	0
$505$	3750.00	0.330441
$506$	16900.0	1.48478
$507$	−2028.00	−0.177646
$508$	192.000	0.0167689
$509$	1246.00	0.108503	0.0542515	−	0.998527i	$-0.482723\pi$
$509$	1246.00	0.108503	0.0542515	+	0.998527i	$0.482723\pi$
$510$	−730.000	−0.0633822
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−7526.00	−0.647721
$514$	13132.0	1.12690
$515$	1685.00	0.144175
$516$	2136.00	0.182233
$517$	−17485.0	−1.48741
$518$	0	0
$519$	1081.00	0.0914270
$520$	520.000	0.0438529
$521$	−14346.0	−1.20635	−0.603176	−	0.797608i	$-0.706098\pi$
$521$	−14346.0	−1.20635	−0.603176	+	0.797608i	$0.706098\pi$
$522$	5772.00	0.483972
$523$	−15596.0	−1.30395	−0.651975	−	0.758241i	$-0.726059\pi$
$523$	−15596.0	−1.30395	−0.651975	+	0.758241i	$0.726059\pi$
$524$	2328.00	0.194082
$525$	0	0
$526$	−5460.00	−0.452599
$527$	−18688.0	−1.54471
$528$	−1040.00	−0.0857201
$529$	4733.00	0.389003
$530$	1320.00	0.108183
$531$	−5824.00	−0.475970
$532$	0	0
$533$	−5512.00	−0.447939
$534$	−368.000	−0.0298219
$535$	3170.00	0.256170
$536$	864.000	0.0696252
$537$	−908.000	−0.0729667
$538$	13524.0	1.08376
$539$	0	0
$540$	−1060.00	−0.0844725
$541$	23.0000	0.00182781	0.000913907	−	1.00000i	$-0.499709\pi$
$541$	23.0000	0.00182781	0.000913907		1.00000i	$0.499709\pi$
$542$	−12552.0	−0.994750
$543$	460.000	0.0363545
$544$	−2336.00	−0.184109
$545$	−4135.00	−0.324998
$546$	0	0
$547$	12076.0	0.943935	0.471968	−	0.881616i	$-0.343544\pi$
$547$	12076.0	0.943935	0.471968	+	0.881616i	$0.343544\pi$
$548$	−1376.00	−0.107262
$549$	−14872.0	−1.15614
$550$	3250.00	0.251964
$551$	15762.0	1.21866
$552$	−1040.00	−0.0801908
$553$	0	0
$554$	7220.00	0.553697
$555$	−1330.00	−0.101721
$556$	7576.00	0.577867
$557$	−23528.0	−1.78979	−0.894895	−	0.446276i	$-0.852750\pi$
$557$	−23528.0	−1.78979	−0.894895	+	0.446276i	$0.852750\pi$
$558$	−13312.0	−1.00993
$559$	−6942.00	−0.525251
$560$	0	0
$561$	−4745.00	−0.357102
$562$	7642.00	0.573591
$563$	420.000	0.0314403	0.0157202	−	0.999876i	$-0.494996\pi$
$563$	420.000	0.0314403	0.0157202	+	0.999876i	$0.494996\pi$
$564$	1076.00	0.0803329
$565$	−9310.00	−0.693229
$566$	−1862.00	−0.138279
$567$	0	0
$568$	−4480.00	−0.330945
$569$	3234.00	0.238271	0.119136	−	0.992878i	$-0.461988\pi$
$569$	3234.00	0.238271	0.119136	+	0.992878i	$0.461988\pi$
$570$	−1420.00	−0.104346
$571$	19372.0	1.41978	0.709889	−	0.704314i	$-0.248745\pi$
$571$	19372.0	1.41978	0.709889	+	0.704314i	$0.248745\pi$
$572$	3380.00	0.247072
$573$	4679.00	0.341131
$574$	0	0
$575$	3250.00	0.235712
$576$	−1664.00	−0.120370
$577$	5011.00	0.361544	0.180772	−	0.983525i	$-0.442140\pi$
$577$	5011.00	0.361544	0.180772	+	0.983525i	$0.442140\pi$
$578$	−832.000	−0.0598731
$579$	−2528.00	−0.181451
$580$	2220.00	0.158932
$581$	0	0
$582$	−1210.00	−0.0861789
$583$	8580.00	0.609515
$584$	4688.00	0.332176
$585$	1690.00	0.119441
$586$	−3546.00	−0.249973
$587$	5904.00	0.415135	0.207567	−	0.978221i	$-0.433445\pi$
$587$	5904.00	0.415135	0.207567	+	0.978221i	$0.433445\pi$
$588$	0	0
$589$	−36352.0	−2.54305
$590$	−2240.00	−0.156304
$591$	4404.00	0.306525
$592$	−4256.00	−0.295474
$593$	14883.0	1.03064	0.515322	−	0.856997i	$-0.327672\pi$
$593$	14883.0	1.03064	0.515322	+	0.856997i	$0.327672\pi$
$594$	−6890.00	−0.475926
$595$	0	0
$596$	2472.00	0.169894
$597$	1240.00	0.0850081
$598$	3380.00	0.231135
$599$	−7021.00	−0.478915	−0.239458	−	0.970907i	$-0.576970\pi$
$599$	−7021.00	−0.478915	−0.239458	+	0.970907i	$0.576970\pi$
$600$	−200.000	−0.0136083
$601$	10474.0	0.710887	0.355444	−	0.934698i	$-0.384330\pi$
$601$	10474.0	0.710887	0.355444	+	0.934698i	$0.384330\pi$
$602$	0	0
$603$	2808.00	0.189636
$604$	932.000	0.0627857
$605$	14470.0	0.972379
$606$	−1500.00	−0.100550
$607$	−9609.00	−0.642533	−0.321266	−	0.946989i	$-0.604108\pi$
$607$	−9609.00	−0.642533	−0.321266	+	0.946989i	$0.604108\pi$
$608$	−4544.00	−0.303098
$609$	0	0
$610$	−5720.00	−0.379666
$611$	−3497.00	−0.231544
$612$	−7592.00	−0.501452
$613$	−934.000	−0.0615398	−0.0307699	−	0.999526i	$-0.509796\pi$
$613$	−934.000	−0.0615398	−0.0307699	+	0.999526i	$0.509796\pi$
$614$	14938.0	0.981838
$615$	2120.00	0.139003
$616$	0	0
$617$	−25358.0	−1.65458	−0.827289	−	0.561777i	$-0.810118\pi$
$617$	−25358.0	−1.65458	−0.827289	+	0.561777i	$0.810118\pi$
$618$	−674.000	−0.0438710
$619$	11486.0	0.745818	0.372909	−	0.927868i	$-0.378360\pi$
$619$	11486.0	0.745818	0.372909	+	0.927868i	$0.378360\pi$
$620$	−5120.00	−0.331652
$621$	−6890.00	−0.445227
$622$	−2348.00	−0.151360
$623$	0	0
$624$	−208.000	−0.0133440
$625$	625.000	0.0400000
$626$	15890.0	1.01452
$627$	−9230.00	−0.587896
$628$	8872.00	0.563744
$629$	−19418.0	−1.23092
$630$	0	0
$631$	12459.0	0.786030	0.393015	−	0.919532i	$-0.371432\pi$
$631$	12459.0	0.786030	0.393015	+	0.919532i	$0.371432\pi$
$632$	−456.000	−0.0287005
$633$	−2959.00	−0.185797
$634$	5156.00	0.322983
$635$	240.000	0.0149986
$636$	−528.000	−0.0329191
$637$	0	0
$638$	14430.0	0.895438
$639$	−14560.0	−0.901385
$640$	−640.000	−0.0395285
$641$	5442.00	0.335329	0.167665	−	0.985844i	$-0.446377\pi$
$641$	5442.00	0.335329	0.167665	+	0.985844i	$0.446377\pi$
$642$	−1268.00	−0.0779501
$643$	11513.0	0.706109	0.353055	−	0.935603i	$-0.385143\pi$
$643$	11513.0	0.706109	0.353055	+	0.935603i	$0.385143\pi$
$644$	0	0
$645$	2670.00	0.162994
$646$	−20732.0	−1.26268
$647$	29744.0	1.80735	0.903676	−	0.428216i	$-0.140858\pi$
$647$	29744.0	1.80735	0.903676	+	0.428216i	$0.140858\pi$
$648$	−5192.00	−0.314755
$649$	−14560.0	−0.880632
$650$	650.000	0.0392232
$651$	0	0
$652$	−9192.00	−0.552127
$653$	27254.0	1.63328	0.816640	−	0.577148i	$-0.195834\pi$
$653$	27254.0	1.63328	0.816640	+	0.577148i	$0.195834\pi$
$654$	1654.00	0.0988938
$655$	2910.00	0.173593
$656$	6784.00	0.403766
$657$	15236.0	0.904738
$658$	0	0
$659$	−11861.0	−0.701121	−0.350561	−	0.936540i	$-0.614009\pi$
$659$	−11861.0	−0.701121	−0.350561	+	0.936540i	$0.614009\pi$
$660$	−1300.00	−0.0766704
$661$	5320.00	0.313047	0.156523	−	0.987674i	$-0.449971\pi$
$661$	5320.00	0.313047	0.156523	+	0.987674i	$0.449971\pi$
$662$	−56.0000	−0.00328777
$663$	−949.000	−0.0555899
$664$	2016.00	0.117825
$665$	0	0
$666$	−13832.0	−0.804773
$667$	14430.0	0.837679
$668$	−1244.00	−0.0720536
$669$	−5559.00	−0.321261
$670$	1080.00	0.0622747
$671$	−37180.0	−2.13907
$672$	0	0
$673$	1688.00	0.0966829	0.0483415	−	0.998831i	$-0.484606\pi$
$673$	1688.00	0.0966829	0.0483415	+	0.998831i	$0.484606\pi$
$674$	−796.000	−0.0454908
$675$	−1325.00	−0.0755545
$676$	−8112.00	−0.461538
$677$	−23061.0	−1.30917	−0.654584	−	0.755990i	$-0.727156\pi$
$677$	−23061.0	−1.30917	−0.654584	+	0.755990i	$0.727156\pi$
$678$	3724.00	0.210943
$679$	0	0
$680$	−2920.00	−0.164672
$681$	5109.00	0.287485
$682$	−33280.0	−1.86856
$683$	14804.0	0.829369	0.414685	−	0.909965i	$-0.363892\pi$
$683$	14804.0	0.829369	0.414685	+	0.909965i	$0.363892\pi$
$684$	−14768.0	−0.825539
$685$	−1720.00	−0.0959384
$686$	0	0
$687$	−3184.00	−0.176823
$688$	8544.00	0.473455
$689$	1716.00	0.0948830
$690$	−1300.00	−0.0717249
$691$	1196.00	0.0658437	0.0329218	−	0.999458i	$-0.489519\pi$
$691$	1196.00	0.0658437	0.0329218	+	0.999458i	$0.489519\pi$
$692$	4324.00	0.237534
$693$	0	0
$694$	−4284.00	−0.234320
$695$	9470.00	0.516860
$696$	−888.000	−0.0483614
$697$	30952.0	1.68205
$698$	−14564.0	−0.789764
$699$	4552.00	0.246313
$700$	0	0
$701$	−18237.0	−0.982599	−0.491300	−	0.870991i	$-0.663478\pi$
$701$	−18237.0	−0.982599	−0.491300	+	0.870991i	$0.663478\pi$
$702$	−1378.00	−0.0740873
$703$	−37772.0	−2.02646
$704$	−4160.00	−0.222707
$705$	1345.00	0.0718520
$706$	11478.0	0.611870
$707$	0	0
$708$	896.000	0.0475618
$709$	16351.0	0.866114	0.433057	−	0.901367i	$-0.357435\pi$
$709$	16351.0	0.866114	0.433057	+	0.901367i	$0.357435\pi$
$710$	−5600.00	−0.296006
$711$	−1482.00	−0.0781707
$712$	−1472.00	−0.0774797
$713$	−33280.0	−1.74803
$714$	0	0
$715$	4225.00	0.220987
$716$	−3632.00	−0.189573
$717$	−1819.00	−0.0947445
$718$	−1808.00	−0.0939749
$719$	13902.0	0.721081	0.360540	−	0.932744i	$-0.382592\pi$
$719$	13902.0	0.721081	0.360540	+	0.932744i	$0.382592\pi$
$720$	−2080.00	−0.107663
$721$	0	0
$722$	−26610.0	−1.37164
$723$	4470.00	0.229932
$724$	1840.00	0.0944517
$725$	2775.00	0.142153
$726$	−5788.00	−0.295885
$727$	4992.00	0.254667	0.127334	−	0.991860i	$-0.459358\pi$
$727$	4992.00	0.254667	0.127334	+	0.991860i	$0.459358\pi$
$728$	0	0
$729$	−15443.0	−0.784586
$730$	5860.00	0.297107
$731$	38982.0	1.97237
$732$	2288.00	0.115529
$733$	−38505.0	−1.94027	−0.970133	−	0.242575i	$-0.922008\pi$
$733$	−38505.0	−1.94027	−0.970133	+	0.242575i	$0.922008\pi$
$734$	18902.0	0.950525
$735$	0	0
$736$	−4160.00	−0.208342
$737$	7020.00	0.350862
$738$	22048.0	1.09973
$739$	−5649.00	−0.281193	−0.140597	−	0.990067i	$-0.544902\pi$
$739$	−5649.00	−0.281193	−0.140597	+	0.990067i	$0.544902\pi$
$740$	−5320.00	−0.264280
$741$	−1846.00	−0.0915175
$742$	0	0
$743$	−25308.0	−1.24961	−0.624805	−	0.780781i	$-0.714822\pi$
$743$	−25308.0	−1.24961	−0.624805	+	0.780781i	$0.714822\pi$
$744$	2048.00	0.100918
$745$	3090.00	0.151958
$746$	21776.0	1.06873
$747$	6552.00	0.320917
$748$	−18980.0	−0.927777
$749$	0	0
$750$	−250.000	−0.0121716
$751$	−335.000	−0.0162774	−0.00813870	−	0.999967i	$-0.502591\pi$
$751$	−335.000	−0.0162774	−0.00813870	+	0.999967i	$0.502591\pi$
$752$	4304.00	0.208711
$753$	5258.00	0.254465
$754$	2886.00	0.139392
$755$	1165.00	0.0561572
$756$	0	0
$757$	7304.00	0.350685	0.175342	−	0.984508i	$-0.443897\pi$
$757$	7304.00	0.350685	0.175342	+	0.984508i	$0.443897\pi$
$758$	−2552.00	−0.122286
$759$	−8450.00	−0.404105
$760$	−5680.00	−0.271099
$761$	−31082.0	−1.48058	−0.740290	−	0.672288i	$-0.765312\pi$
$761$	−31082.0	−1.48058	−0.740290	+	0.672288i	$0.765312\pi$
$762$	−96.0000	−0.00456393
$763$	0	0
$764$	18716.0	0.886284
$765$	−9490.00	−0.448512
$766$	1176.00	0.0554708
$767$	−2912.00	−0.137088
$768$	256.000	0.0120281
$769$	16994.0	0.796904	0.398452	−	0.917189i	$-0.369548\pi$
$769$	16994.0	0.796904	0.398452	+	0.917189i	$0.369548\pi$
$770$	0	0
$771$	−6566.00	−0.306704
$772$	−10112.0	−0.471423
$773$	33083.0	1.53934	0.769672	−	0.638440i	$-0.220420\pi$
$773$	33083.0	1.53934	0.769672	+	0.638440i	$0.220420\pi$
$774$	27768.0	1.28954
$775$	−6400.00	−0.296638
$776$	−4840.00	−0.223899
$777$	0	0
$778$	−5154.00	−0.237506
$779$	60208.0	2.76916
$780$	−260.000	−0.0119352
$781$	−36400.0	−1.66773
$782$	−18980.0	−0.867933
$783$	−5883.00	−0.268507
$784$	0	0
$785$	11090.0	0.504228
$786$	−1164.00	−0.0528225
$787$	41269.0	1.86923	0.934613	−	0.355666i	$-0.115746\pi$
$787$	41269.0	1.86923	0.934613	+	0.355666i	$0.115746\pi$
$788$	17616.0	0.796376
$789$	2730.00	0.123182
$790$	−570.000	−0.0256705
$791$	0	0
$792$	−13520.0	−0.606581
$793$	−7436.00	−0.332989
$794$	17150.0	0.766537
$795$	−660.000	−0.0294438
$796$	4960.00	0.220857
$797$	−40431.0	−1.79691	−0.898456	−	0.439063i	$-0.855311\pi$
$797$	−40431.0	−1.79691	−0.898456	+	0.439063i	$0.855311\pi$
$798$	0	0
$799$	19637.0	0.869471
$800$	−800.000	−0.0353553
$801$	−4784.00	−0.211029
$802$	−10434.0	−0.459398
$803$	38090.0	1.67393
$804$	−432.000	−0.0189496
$805$	0	0
$806$	−6656.00	−0.290878
$807$	−6762.00	−0.294961
$808$	−6000.00	−0.261237
$809$	−31991.0	−1.39029	−0.695144	−	0.718870i	$-0.744660\pi$
$809$	−31991.0	−1.39029	−0.695144	+	0.718870i	$0.744660\pi$
$810$	−6490.00	−0.281525
$811$	18498.0	0.800928	0.400464	−	0.916312i	$-0.368849\pi$
$811$	18498.0	0.800928	0.400464	+	0.916312i	$0.368849\pi$
$812$	0	0
$813$	6276.00	0.270737
$814$	−34580.0	−1.48898
$815$	−11490.0	−0.493837
$816$	1168.00	0.0501081
$817$	75828.0	3.24711
$818$	−11188.0	−0.478214
$819$	0	0
$820$	8480.00	0.361140
$821$	9601.00	0.408133	0.204067	−	0.978957i	$-0.434584\pi$
$821$	9601.00	0.408133	0.204067	+	0.978957i	$0.434584\pi$
$822$	688.000	0.0291931
$823$	−22640.0	−0.958907	−0.479454	−	0.877567i	$-0.659165\pi$
$823$	−22640.0	−0.958907	−0.479454	+	0.877567i	$0.659165\pi$
$824$	−2696.00	−0.113980
$825$	−1625.00	−0.0685760
$826$	0	0
$827$	28818.0	1.21173	0.605865	−	0.795568i	$-0.292827\pi$
$827$	28818.0	1.21173	0.605865	+	0.795568i	$0.292827\pi$
$828$	−13520.0	−0.567455
$829$	−20384.0	−0.853999	−0.427000	−	0.904252i	$-0.640429\pi$
$829$	−20384.0	−0.853999	−0.427000	+	0.904252i	$0.640429\pi$
$830$	2520.00	0.105386
$831$	−3610.00	−0.150697
$832$	−832.000	−0.0346688
$833$	0	0
$834$	−3788.00	−0.157275
$835$	−1555.00	−0.0644467
$836$	−36920.0	−1.52740
$837$	13568.0	0.560309
$838$	−12072.0	−0.497638
$839$	28842.0	1.18681	0.593407	−	0.804903i	$-0.297783\pi$
$839$	28842.0	1.18681	0.593407	+	0.804903i	$0.297783\pi$
$840$	0	0
$841$	−12068.0	−0.494813
$842$	29830.0	1.22091
$843$	−3821.00	−0.156112
$844$	−11836.0	−0.482716
$845$	−10140.0	−0.412813
$846$	13988.0	0.568460
$847$	0	0
$848$	−2112.00	−0.0855264
$849$	931.000	0.0376347
$850$	−3650.00	−0.147287
$851$	−34580.0	−1.39293
$852$	2240.00	0.0900718
$853$	11618.0	0.466346	0.233173	−	0.972435i	$-0.425089\pi$
$853$	11618.0	0.466346	0.233173	+	0.972435i	$0.425089\pi$
$854$	0	0
$855$	−18460.0	−0.738384
$856$	−5072.00	−0.202520
$857$	14926.0	0.594939	0.297469	−	0.954731i	$-0.403857\pi$
$857$	14926.0	0.594939	0.297469	+	0.954731i	$0.403857\pi$
$858$	−1690.00	−0.0672443
$859$	2764.00	0.109786	0.0548932	−	0.998492i	$-0.482518\pi$
$859$	2764.00	0.109786	0.0548932	+	0.998492i	$0.482518\pi$
$860$	10680.0	0.423471
$861$	0	0
$862$	−6438.00	−0.254384
$863$	−4332.00	−0.170873	−0.0854363	−	0.996344i	$-0.527228\pi$
$863$	−4332.00	−0.170873	−0.0854363	+	0.996344i	$0.527228\pi$
$864$	1696.00	0.0667814
$865$	5405.00	0.212457
$866$	−13884.0	−0.544801
$867$	416.000	0.0162954
$868$	0	0
$869$	−3705.00	−0.144630
$870$	−1110.00	−0.0432558
$871$	1404.00	0.0546185
$872$	6616.00	0.256934
$873$	−15730.0	−0.609828
$874$	−36920.0	−1.42888
$875$	0	0
$876$	−2344.00	−0.0904069
$877$	−24274.0	−0.934635	−0.467317	−	0.884090i	$-0.654779\pi$
$877$	−24274.0	−0.934635	−0.467317	+	0.884090i	$0.654779\pi$
$878$	−3956.00	−0.152060
$879$	1773.00	0.0680339
$880$	−5200.00	−0.199195
$881$	−5136.00	−0.196409	−0.0982044	−	0.995166i	$-0.531310\pi$
$881$	−5136.00	−0.196409	−0.0982044	+	0.995166i	$0.531310\pi$
$882$	0	0
$883$	6280.00	0.239342	0.119671	−	0.992814i	$-0.461816\pi$
$883$	6280.00	0.239342	0.119671	+	0.992814i	$0.461816\pi$
$884$	−3796.00	−0.144427
$885$	1120.00	0.0425406
$886$	−12508.0	−0.474283
$887$	20312.0	0.768895	0.384448	−	0.923147i	$-0.374392\pi$
$887$	20312.0	0.768895	0.384448	+	0.923147i	$0.374392\pi$
$888$	2128.00	0.0804178
$889$	0	0
$890$	−1840.00	−0.0692999
$891$	−42185.0	−1.58614
$892$	−22236.0	−0.834660
$893$	38198.0	1.43141
$894$	−1236.00	−0.0462394
$895$	−4540.00	−0.169559
$896$	0	0
$897$	−1690.00	−0.0629069
$898$	−28574.0	−1.06183
$899$	−28416.0	−1.05420
$900$	−2600.00	−0.0962963
$901$	−9636.00	−0.356295
$902$	55120.0	2.03470
$903$	0	0
$904$	14896.0	0.548046
$905$	2300.00	0.0844802
$906$	−466.000	−0.0170881
$907$	42618.0	1.56021	0.780103	−	0.625651i	$-0.215166\pi$
$907$	42618.0	1.56021	0.780103	+	0.625651i	$0.215166\pi$
$908$	20436.0	0.746908
$909$	−19500.0	−0.711523
$910$	0	0
$911$	47808.0	1.73869	0.869347	−	0.494203i	$-0.164540\pi$
$911$	47808.0	1.73869	0.869347	+	0.494203i	$0.164540\pi$
$912$	2272.00	0.0824928
$913$	16380.0	0.593756
$914$	13720.0	0.496518
$915$	2860.00	0.103332
$916$	−12736.0	−0.459399
$917$	0	0
$918$	7738.00	0.278205
$919$	−34211.0	−1.22798	−0.613992	−	0.789312i	$-0.710437\pi$
$919$	−34211.0	−1.22798	−0.613992	+	0.789312i	$0.710437\pi$
$920$	−5200.00	−0.186347
$921$	−7469.00	−0.267222
$922$	17104.0	0.610944
$923$	−7280.00	−0.259614
$924$	0	0
$925$	−6650.00	−0.236379
$926$	−5752.00	−0.204128
$927$	−8762.00	−0.310444
$928$	−3552.00	−0.125647
$929$	−19084.0	−0.673978	−0.336989	−	0.941509i	$-0.609409\pi$
$929$	−19084.0	−0.673978	−0.336989	+	0.941509i	$0.609409\pi$
$930$	2560.00	0.0902642
$931$	0	0
$932$	18208.0	0.639939
$933$	1174.00	0.0411951
$934$	−18574.0	−0.650706
$935$	−23725.0	−0.829829
$936$	−2704.00	−0.0944263
$937$	381.000	0.0132836	0.00664180	−	0.999978i	$-0.497886\pi$
$937$	381.000	0.0132836	0.00664180	+	0.999978i	$0.497886\pi$
$938$	0	0
$939$	−7945.00	−0.276119
$940$	5380.00	0.186677
$941$	−11196.0	−0.387863	−0.193932	−	0.981015i	$-0.562124\pi$
$941$	−11196.0	−0.387863	−0.193932	+	0.981015i	$0.562124\pi$
$942$	−4436.00	−0.153432
$943$	55120.0	1.90345
$944$	3584.00	0.123569
$945$	0	0
$946$	69420.0	2.38588
$947$	28908.0	0.991958	0.495979	−	0.868335i	$-0.334809\pi$
$947$	28908.0	0.991958	0.495979	+	0.868335i	$0.334809\pi$
$948$	228.000	0.00781128
$949$	7618.00	0.260580
$950$	−7100.00	−0.242478
$951$	−2578.00	−0.0879047
$952$	0	0
$953$	4068.00	0.138274	0.0691372	−	0.997607i	$-0.477975\pi$
$953$	4068.00	0.138274	0.0691372	+	0.997607i	$0.477975\pi$
$954$	−6864.00	−0.232946
$955$	23395.0	0.792717
$956$	−7276.00	−0.246153
$957$	−7215.00	−0.243707
$958$	22932.0	0.773381
$959$	0	0
$960$	320.000	0.0107583
$961$	35745.0	1.19986
$962$	−6916.00	−0.231789
$963$	−16484.0	−0.551599
$964$	17880.0	0.597382
$965$	−12640.0	−0.421654
$966$	0	0
$967$	−9026.00	−0.300162	−0.150081	−	0.988674i	$-0.547953\pi$
$967$	−9026.00	−0.300162	−0.150081	+	0.988674i	$0.547953\pi$
$968$	−23152.0	−0.768733
$969$	10366.0	0.343657
$970$	−6050.00	−0.200262
$971$	−38844.0	−1.28379	−0.641897	−	0.766791i	$-0.721852\pi$
$971$	−38844.0	−1.28379	−0.641897	+	0.766791i	$0.721852\pi$
$972$	8320.00	0.274552
$973$	0	0
$974$	−35796.0	−1.17760
$975$	−325.000	−0.0106752
$976$	9152.00	0.300152
$977$	−1302.00	−0.0426353	−0.0213176	−	0.999773i	$-0.506786\pi$
$977$	−1302.00	−0.0426353	−0.0213176	+	0.999773i	$0.506786\pi$
$978$	4596.00	0.150270
$979$	−11960.0	−0.390443
$980$	0	0
$981$	21502.0	0.699802
$982$	−6666.00	−0.216620
$983$	−31337.0	−1.01678	−0.508390	−	0.861127i	$-0.669759\pi$
$983$	−31337.0	−1.01678	−0.508390	+	0.861127i	$0.669759\pi$
$984$	−3392.00	−0.109891
$985$	22020.0	0.712300
$986$	−16206.0	−0.523432
$987$	0	0
$988$	−7384.00	−0.237770
$989$	69420.0	2.23198
$990$	−16900.0	−0.542543
$991$	−24296.0	−0.778797	−0.389399	−	0.921069i	$-0.627317\pi$
$991$	−24296.0	−0.778797	−0.389399	+	0.921069i	$0.627317\pi$
$992$	8192.00	0.262194
$993$	28.0000	0.000894817 0
$994$	0	0
$995$	6200.00	0.197541
$996$	−1008.00	−0.0320680
$997$	−46931.0	−1.49079	−0.745396	−	0.666622i	$-0.767740\pi$
$997$	−46931.0	−1.49079	−0.745396	+	0.666622i	$0.767740\pi$
$998$	28282.0	0.897045
$999$	14098.0	0.446487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.d.1.1		1
5.4	even	2		2450.4.a.bc.1.1		1
7.2	even	3		490.4.e.n.361.1		2
7.3	odd	6		490.4.e.o.471.1		2
7.4	even	3		490.4.e.n.471.1		2
7.5	odd	6		490.4.e.o.361.1		2
7.6	odd	2		70.4.a.c.1.1	✓	1
21.20	even	2		630.4.a.x.1.1		1
28.27	even	2		560.4.a.i.1.1		1
35.13	even	4		350.4.c.h.99.2		2
35.27	even	4		350.4.c.h.99.1		2
35.34	odd	2		350.4.a.r.1.1		1
56.13	odd	2		2240.4.a.v.1.1		1
56.27	even	2		2240.4.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.c.1.1	✓	1	7.6	odd	2
350.4.a.r.1.1		1	35.34	odd	2
350.4.c.h.99.1		2	35.27	even	4
350.4.c.h.99.2		2	35.13	even	4
490.4.a.d.1.1		1	1.1	even	1	trivial
490.4.e.n.361.1		2	7.2	even	3
490.4.e.n.471.1		2	7.4	even	3
490.4.e.o.361.1		2	7.5	odd	6
490.4.e.o.471.1		2	7.3	odd	6
560.4.a.i.1.1		1	28.27	even	2
630.4.a.x.1.1		1	21.20	even	2
2240.4.a.r.1.1		1	56.27	even	2
2240.4.a.v.1.1		1	56.13	odd	2
2450.4.a.bc.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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