LMFDB - Embedded newform 490.4.a.n.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:	yes
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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.00000 q^{6} +8.00000 q^{8} -26.0000 q^{9} -10.0000 q^{10} -9.00000 q^{11} +4.00000 q^{12} +51.0000 q^{13} -5.00000 q^{15} +16.0000 q^{16} +81.0000 q^{17} -52.0000 q^{18} +86.0000 q^{19} -20.0000 q^{20} -18.0000 q^{22} +48.0000 q^{23} +8.00000 q^{24} +25.0000 q^{25} +102.000 q^{26} -53.0000 q^{27} +211.000 q^{29} -10.0000 q^{30} +254.000 q^{31} +32.0000 q^{32} -9.00000 q^{33} +162.000 q^{34} -104.000 q^{36} -20.0000 q^{37} +172.000 q^{38} +51.0000 q^{39} -40.0000 q^{40} +74.0000 q^{41} -318.000 q^{43} -36.0000 q^{44} +130.000 q^{45} +96.0000 q^{46} -167.000 q^{47} +16.0000 q^{48} +50.0000 q^{50} +81.0000 q^{51} +204.000 q^{52} -170.000 q^{53} -106.000 q^{54} +45.0000 q^{55} +86.0000 q^{57} +422.000 q^{58} +854.000 q^{59} -20.0000 q^{60} -580.000 q^{61} +508.000 q^{62} +64.0000 q^{64} -255.000 q^{65} -18.0000 q^{66} -58.0000 q^{67} +324.000 q^{68} +48.0000 q^{69} +152.000 q^{71} -208.000 q^{72} +702.000 q^{73} -40.0000 q^{74} +25.0000 q^{75} +344.000 q^{76} +102.000 q^{78} -419.000 q^{79} -80.0000 q^{80} +649.000 q^{81} +148.000 q^{82} +124.000 q^{83} -405.000 q^{85} -636.000 q^{86} +211.000 q^{87} -72.0000 q^{88} -768.000 q^{89} +260.000 q^{90} +192.000 q^{92} +254.000 q^{93} -334.000 q^{94} -430.000 q^{95} +32.0000 q^{96} +1085.00 q^{97} +234.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	1.00000	0.192450	0.0962250	−	0.995360i	$-0.469323\pi$
$3$	1.00000	0.192450	0.0962250	+	0.995360i	$0.469323\pi$
$4$	4.00000	0.500000
$5$	−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
$11$	−9.00000	−0.246691	−0.123346	−	0.992364i	$-0.539362\pi$
$11$	−9.00000	−0.246691	−0.123346	+	0.992364i	$0.539362\pi$
$12$	4.00000	0.0962250
$13$	51.0000	1.08807	0.544033	−	0.839064i	$-0.316897\pi$
$13$	51.0000	1.08807	0.544033	+	0.839064i	$0.316897\pi$
$14$	0	0
$15$	−5.00000	−0.0860663
$16$	16.0000	0.250000
$17$	81.0000	1.15561	0.577805	−	0.816175i	$-0.303909\pi$
$17$	81.0000	1.15561	0.577805	+	0.816175i	$0.303909\pi$
$18$	−52.0000	−0.680918
$19$	86.0000	1.03841	0.519204	−	0.854650i	$-0.326228\pi$
$19$	86.0000	1.03841	0.519204	+	0.854650i	$0.326228\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−18.0000	−0.174437
$23$	48.0000	0.435161	0.217580	−	0.976042i	$-0.430184\pi$
$23$	48.0000	0.435161	0.217580	+	0.976042i	$0.430184\pi$
$24$	8.00000	0.0680414
$25$	25.0000	0.200000
$26$	102.000	0.769379
$27$	−53.0000	−0.377772
$28$	0	0
$29$	211.000	1.35109	0.675547	−	0.737317i	$-0.263908\pi$
$29$	211.000	1.35109	0.675547	+	0.737317i	$0.263908\pi$
$30$	−10.0000	−0.0608581
$31$	254.000	1.47160	0.735802	−	0.677196i	$-0.236805\pi$
$31$	254.000	1.47160	0.735802	+	0.677196i	$0.236805\pi$
$32$	32.0000	0.176777
$33$	−9.00000	−0.0474757
$34$	162.000	0.817140
$35$	0	0
$36$	−104.000	−0.481481
$37$	−20.0000	−0.0888643	−0.0444322	−	0.999012i	$-0.514148\pi$
$37$	−20.0000	−0.0888643	−0.0444322	+	0.999012i	$0.514148\pi$
$38$	172.000	0.734265
$39$	51.0000	0.209398
$40$	−40.0000	−0.158114
$41$	74.0000	0.281875	0.140937	−	0.990019i	$-0.454988\pi$
$41$	74.0000	0.281875	0.140937	+	0.990019i	$0.454988\pi$
$42$	0	0
$43$	−318.000	−1.12778	−0.563890	−	0.825850i	$-0.690696\pi$
$43$	−318.000	−1.12778	−0.563890	+	0.825850i	$0.690696\pi$
$44$	−36.0000	−0.123346
$45$	130.000	0.430650
$46$	96.0000	0.307705
$47$	−167.000	−0.518286	−0.259143	−	0.965839i	$-0.583440\pi$
$47$	−167.000	−0.518286	−0.259143	+	0.965839i	$0.583440\pi$
$48$	16.0000	0.0481125
$49$	0	0
$50$	50.0000	0.141421
$51$	81.0000	0.222397
$52$	204.000	0.544033
$53$	−170.000	−0.440590	−0.220295	−	0.975433i	$-0.570702\pi$
$53$	−170.000	−0.440590	−0.220295	+	0.975433i	$0.570702\pi$
$54$	−106.000	−0.267125
$55$	45.0000	0.110324
$56$	0	0
$57$	86.0000	0.199842
$58$	422.000	0.955367
$59$	854.000	1.88443	0.942215	−	0.335010i	$-0.108740\pi$
$59$	854.000	1.88443	0.942215	+	0.335010i	$0.108740\pi$
$60$	−20.0000	−0.0430331
$61$	−580.000	−1.21740	−0.608700	−	0.793401i	$-0.708309\pi$
$61$	−580.000	−1.21740	−0.608700	+	0.793401i	$0.708309\pi$
$62$	508.000	1.04058
$63$	0	0
$64$	64.0000	0.125000
$65$	−255.000	−0.486598
$66$	−18.0000	−0.0335704
$67$	−58.0000	−0.105759	−0.0528793	−	0.998601i	$-0.516840\pi$
$67$	−58.0000	−0.105759	−0.0528793	+	0.998601i	$0.516840\pi$
$68$	324.000	0.577805
$69$	48.0000	0.0837467
$70$	0	0
$71$	152.000	0.254072	0.127036	−	0.991898i	$-0.459454\pi$
$71$	152.000	0.254072	0.127036	+	0.991898i	$0.459454\pi$
$72$	−208.000	−0.340459
$73$	702.000	1.12552	0.562759	−	0.826621i	$-0.309740\pi$
$73$	702.000	1.12552	0.562759	+	0.826621i	$0.309740\pi$
$74$	−40.0000	−0.0628366
$75$	25.0000	0.0384900
$76$	344.000	0.519204
$77$	0	0
$78$	102.000	0.148067
$79$	−419.000	−0.596724	−0.298362	−	0.954453i	$-0.596440\pi$
$79$	−419.000	−0.596724	−0.298362	+	0.954453i	$0.596440\pi$
$80$	−80.0000	−0.111803
$81$	649.000	0.890261
$82$	148.000	0.199315
$83$	124.000	0.163985	0.0819926	−	0.996633i	$-0.473872\pi$
$83$	124.000	0.163985	0.0819926	+	0.996633i	$0.473872\pi$
$84$	0	0
$85$	−405.000	−0.516805
$86$	−636.000	−0.797461
$87$	211.000	0.260018
$88$	−72.0000	−0.0872185
$89$	−768.000	−0.914695	−0.457347	−	0.889288i	$-0.651200\pi$
$89$	−768.000	−0.914695	−0.457347	+	0.889288i	$0.651200\pi$
$90$	260.000	0.304516
$91$	0	0
$92$	192.000	0.217580
$93$	254.000	0.283210
$94$	−334.000	−0.366484
$95$	−430.000	−0.464390
$96$	32.0000	0.0340207
$97$	1085.00	1.13572	0.567861	−	0.823124i	$-0.307771\pi$
$97$	1085.00	1.13572	0.567861	+	0.823124i	$0.307771\pi$
$98$	0	0
$99$	234.000	0.237554
$100$	100.000	0.100000
$101$	538.000	0.530030	0.265015	−	0.964244i	$-0.414623\pi$
$101$	538.000	0.530030	0.265015	+	0.964244i	$0.414623\pi$
$102$	162.000	0.157259
$103$	−1623.00	−1.55261	−0.776306	−	0.630357i	$-0.782909\pi$
$103$	−1623.00	−1.55261	−0.776306	+	0.630357i	$0.782909\pi$
$104$	408.000	0.384689
$105$	0	0
$106$	−340.000	−0.311545
$107$	1306.00	1.17996	0.589980	−	0.807418i	$-0.299135\pi$
$107$	1306.00	1.17996	0.589980	+	0.807418i	$0.299135\pi$
$108$	−212.000	−0.188886
$109$	−1395.00	−1.22584	−0.612921	−	0.790144i	$-0.710006\pi$
$109$	−1395.00	−1.22584	−0.612921	+	0.790144i	$0.710006\pi$
$110$	90.0000	0.0780106
$111$	−20.0000	−0.0171019
$112$	0	0
$113$	−996.000	−0.829166	−0.414583	−	0.910011i	$-0.636073\pi$
$113$	−996.000	−0.829166	−0.414583	+	0.910011i	$0.636073\pi$
$114$	172.000	0.141309
$115$	−240.000	−0.194610
$116$	844.000	0.675547
$117$	−1326.00	−1.04777
$118$	1708.00	1.33249
$119$	0	0
$120$	−40.0000	−0.0304290
$121$	−1250.00	−0.939144
$122$	−1160.00	−0.860832
$123$	74.0000	0.0542468
$124$	1016.00	0.735802
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1906.00	1.33173	0.665867	−	0.746071i	$-0.268062\pi$
$127$	1906.00	1.33173	0.665867	+	0.746071i	$0.268062\pi$
$128$	128.000	0.0883883
$129$	−318.000	−0.217041
$130$	−510.000	−0.344077
$131$	288.000	0.192082	0.0960408	−	0.995377i	$-0.469382\pi$
$131$	288.000	0.192082	0.0960408	+	0.995377i	$0.469382\pi$
$132$	−36.0000	−0.0237379
$133$	0	0
$134$	−116.000	−0.0747826
$135$	265.000	0.168945
$136$	648.000	0.408570
$137$	916.000	0.571235	0.285617	−	0.958344i	$-0.407801\pi$
$137$	916.000	0.571235	0.285617	+	0.958344i	$0.407801\pi$
$138$	96.0000	0.0592178
$139$	−640.000	−0.390533	−0.195267	−	0.980750i	$-0.562557\pi$
$139$	−640.000	−0.390533	−0.195267	+	0.980750i	$0.562557\pi$
$140$	0	0
$141$	−167.000	−0.0997442
$142$	304.000	0.179656
$143$	−459.000	−0.268416
$144$	−416.000	−0.240741
$145$	−1055.00	−0.604227
$146$	1404.00	0.795862
$147$	0	0
$148$	−80.0000	−0.0444322
$149$	330.000	0.181441	0.0907203	−	0.995876i	$-0.471083\pi$
$149$	330.000	0.181441	0.0907203	+	0.995876i	$0.471083\pi$
$150$	50.0000	0.0272166
$151$	2485.00	1.33925	0.669624	−	0.742700i	$-0.266455\pi$
$151$	2485.00	1.33925	0.669624	+	0.742700i	$0.266455\pi$
$152$	688.000	0.367133
$153$	−2106.00	−1.11281
$154$	0	0
$155$	−1270.00	−0.658122
$156$	204.000	0.104699
$157$	1114.00	0.566286	0.283143	−	0.959078i	$-0.408623\pi$
$157$	1114.00	0.566286	0.283143	+	0.959078i	$0.408623\pi$
$158$	−838.000	−0.421947
$159$	−170.000	−0.0847917
$160$	−160.000	−0.0790569
$161$	0	0
$162$	1298.00	0.629509
$163$	1448.00	0.695804	0.347902	−	0.937531i	$-0.386894\pi$
$163$	1448.00	0.695804	0.347902	+	0.937531i	$0.386894\pi$
$164$	296.000	0.140937
$165$	45.0000	0.0212318
$166$	248.000	0.115955
$167$	−4251.00	−1.96977	−0.984887	−	0.173198i	$-0.944590\pi$
$167$	−4251.00	−1.96977	−0.984887	+	0.173198i	$0.944590\pi$
$168$	0	0
$169$	404.000	0.183887
$170$	−810.000	−0.365436
$171$	−2236.00	−0.999949
$172$	−1272.00	−0.563890
$173$	2829.00	1.24327	0.621633	−	0.783309i	$-0.286470\pi$
$173$	2829.00	1.24327	0.621633	+	0.783309i	$0.286470\pi$
$174$	422.000	0.183861
$175$	0	0
$176$	−144.000	−0.0616728
$177$	854.000	0.362659
$178$	−1536.00	−0.646787
$179$	716.000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	716.000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	520.000	0.215325
$181$	−3614.00	−1.48412	−0.742062	−	0.670331i	$-0.766152\pi$
$181$	−3614.00	−1.48412	−0.742062	+	0.670331i	$0.766152\pi$
$182$	0	0
$183$	−580.000	−0.234289
$184$	384.000	0.153852
$185$	100.000	0.0397413
$186$	508.000	0.200260
$187$	−729.000	−0.285079
$188$	−668.000	−0.259143
$189$	0	0
$190$	−860.000	−0.328373
$191$	−4253.00	−1.61118	−0.805592	−	0.592470i	$-0.798153\pi$
$191$	−4253.00	−1.61118	−0.805592	+	0.592470i	$0.798153\pi$
$192$	64.0000	0.0240563
$193$	−4664.00	−1.73949	−0.869746	−	0.493499i	$-0.835718\pi$
$193$	−4664.00	−1.73949	−0.869746	+	0.493499i	$0.835718\pi$
$194$	2170.00	0.803077
$195$	−255.000	−0.0936458
$196$	0	0
$197$	3546.00	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	3546.00	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	468.000	0.167976
$199$	−54.0000	−0.0192360	−0.00961799	−	0.999954i	$-0.503062\pi$
$199$	−54.0000	−0.0192360	−0.00961799	+	0.999954i	$0.503062\pi$
$200$	200.000	0.0707107
$201$	−58.0000	−0.0203533
$202$	1076.00	0.374788
$203$	0	0
$204$	324.000	0.111199
$205$	−370.000	−0.126058
$206$	−3246.00	−1.09786
$207$	−1248.00	−0.419043
$208$	816.000	0.272016
$209$	−774.000	−0.256166
$210$	0	0
$211$	−4215.00	−1.37523	−0.687613	−	0.726078i	$-0.741341\pi$
$211$	−4215.00	−1.37523	−0.687613	+	0.726078i	$0.741341\pi$
$212$	−680.000	−0.220295
$213$	152.000	0.0488961
$214$	2612.00	0.834358
$215$	1590.00	0.504359
$216$	−424.000	−0.133563
$217$	0	0
$218$	−2790.00	−0.866801
$219$	702.000	0.216606
$220$	180.000	0.0551618
$221$	4131.00	1.25738
$222$	−40.0000	−0.0120929
$223$	−3179.00	−0.954626	−0.477313	−	0.878733i	$-0.658389\pi$
$223$	−3179.00	−0.954626	−0.477313	+	0.878733i	$0.658389\pi$
$224$	0	0
$225$	−650.000	−0.192593
$226$	−1992.00	−0.586309
$227$	−4951.00	−1.44762	−0.723809	−	0.690000i	$-0.757610\pi$
$227$	−4951.00	−1.44762	−0.723809	+	0.690000i	$0.757610\pi$
$228$	344.000	0.0999209
$229$	−266.000	−0.0767588	−0.0383794	−	0.999263i	$-0.512220\pi$
$229$	−266.000	−0.0767588	−0.0383794	+	0.999263i	$0.512220\pi$
$230$	−480.000	−0.137610
$231$	0	0
$232$	1688.00	0.477684
$233$	296.000	0.0832258	0.0416129	−	0.999134i	$-0.486750\pi$
$233$	296.000	0.0832258	0.0416129	+	0.999134i	$0.486750\pi$
$234$	−2652.00	−0.740883
$235$	835.000	0.231785
$236$	3416.00	0.942215
$237$	−419.000	−0.114840
$238$	0	0
$239$	6173.00	1.67070	0.835352	−	0.549716i	$-0.185264\pi$
$239$	6173.00	1.67070	0.835352	+	0.549716i	$0.185264\pi$
$240$	−80.0000	−0.0215166
$241$	3404.00	0.909838	0.454919	−	0.890533i	$-0.349668\pi$
$241$	3404.00	0.909838	0.454919	+	0.890533i	$0.349668\pi$
$242$	−2500.00	−0.664075
$243$	2080.00	0.549103
$244$	−2320.00	−0.608700
$245$	0	0
$246$	148.000	0.0383583
$247$	4386.00	1.12986
$248$	2032.00	0.520291
$249$	124.000	0.0315590
$250$	−250.000	−0.0632456
$251$	652.000	0.163960	0.0819798	−	0.996634i	$-0.473876\pi$
$251$	652.000	0.163960	0.0819798	+	0.996634i	$0.473876\pi$
$252$	0	0
$253$	−432.000	−0.107350
$254$	3812.00	0.941678
$255$	−405.000	−0.0994592
$256$	256.000	0.0625000
$257$	5554.00	1.34805	0.674025	−	0.738708i	$-0.264564\pi$
$257$	5554.00	1.34805	0.674025	+	0.738708i	$0.264564\pi$
$258$	−636.000	−0.153471
$259$	0	0
$260$	−1020.00	−0.243299
$261$	−5486.00	−1.30105
$262$	576.000	0.135822
$263$	−7070.00	−1.65762	−0.828812	−	0.559528i	$-0.810982\pi$
$263$	−7070.00	−1.65762	−0.828812	+	0.559528i	$0.810982\pi$
$264$	−72.0000	−0.0167852
$265$	850.000	0.197038
$266$	0	0
$267$	−768.000	−0.176033
$268$	−232.000	−0.0528793
$269$	−1856.00	−0.420678	−0.210339	−	0.977629i	$-0.567457\pi$
$269$	−1856.00	−0.420678	−0.210339	+	0.977629i	$0.567457\pi$
$270$	530.000	0.119462
$271$	1236.00	0.277054	0.138527	−	0.990359i	$-0.455763\pi$
$271$	1236.00	0.277054	0.138527	+	0.990359i	$0.455763\pi$
$272$	1296.00	0.288903
$273$	0	0
$274$	1832.00	0.403924
$275$	−225.000	−0.0493382
$276$	192.000	0.0418733
$277$	3844.00	0.833804	0.416902	−	0.908952i	$-0.363116\pi$
$277$	3844.00	0.833804	0.416902	+	0.908952i	$0.363116\pi$
$278$	−1280.00	−0.276149
$279$	−6604.00	−1.41710
$280$	0	0
$281$	−7605.00	−1.61451	−0.807253	−	0.590205i	$-0.799047\pi$
$281$	−7605.00	−1.61451	−0.807253	+	0.590205i	$0.799047\pi$
$282$	−334.000	−0.0705298
$283$	−4913.00	−1.03197	−0.515985	−	0.856598i	$-0.672574\pi$
$283$	−4913.00	−1.03197	−0.515985	+	0.856598i	$0.672574\pi$
$284$	608.000	0.127036
$285$	−430.000	−0.0893719
$286$	−918.000	−0.189799
$287$	0	0
$288$	−832.000	−0.170229
$289$	1648.00	0.335437
$290$	−2110.00	−0.427253
$291$	1085.00	0.218570
$292$	2808.00	0.562759
$293$	4633.00	0.923764	0.461882	−	0.886941i	$-0.347174\pi$
$293$	4633.00	0.923764	0.461882	+	0.886941i	$0.347174\pi$
$294$	0	0
$295$	−4270.00	−0.842742
$296$	−160.000	−0.0314183
$297$	477.000	0.0931931
$298$	660.000	0.128298
$299$	2448.00	0.473483
$300$	100.000	0.0192450
$301$	0	0
$302$	4970.00	0.946991
$303$	538.000	0.102004
$304$	1376.00	0.259602
$305$	2900.00	0.544438
$306$	−4212.00	−0.786876
$307$	271.000	0.0503804	0.0251902	−	0.999683i	$-0.491981\pi$
$307$	271.000	0.0503804	0.0251902	+	0.999683i	$0.491981\pi$
$308$	0	0
$309$	−1623.00	−0.298800
$310$	−2540.00	−0.465362
$311$	−6054.00	−1.10383	−0.551915	−	0.833901i	$-0.686103\pi$
$311$	−6054.00	−1.10383	−0.551915	+	0.833901i	$0.686103\pi$
$312$	408.000	0.0740335
$313$	−9529.00	−1.72080	−0.860401	−	0.509618i	$-0.829787\pi$
$313$	−9529.00	−1.72080	−0.860401	+	0.509618i	$0.829787\pi$
$314$	2228.00	0.400425
$315$	0	0
$316$	−1676.00	−0.298362
$317$	8506.00	1.50708	0.753540	−	0.657402i	$-0.228345\pi$
$317$	8506.00	1.50708	0.753540	+	0.657402i	$0.228345\pi$
$318$	−340.000	−0.0599568
$319$	−1899.00	−0.333303
$320$	−320.000	−0.0559017
$321$	1306.00	0.227084
$322$	0	0
$323$	6966.00	1.20000
$324$	2596.00	0.445130
$325$	1275.00	0.217613
$326$	2896.00	0.492008
$327$	−1395.00	−0.235913
$328$	592.000	0.0996577
$329$	0	0
$330$	90.0000	0.0150131
$331$	−10388.0	−1.72500	−0.862502	−	0.506054i	$-0.831104\pi$
$331$	−10388.0	−1.72500	−0.862502	+	0.506054i	$0.831104\pi$
$332$	496.000	0.0819926
$333$	520.000	0.0855730
$334$	−8502.00	−1.39284
$335$	290.000	0.0472967
$336$	0	0
$337$	11872.0	1.91902	0.959509	−	0.281678i	$-0.0908910\pi$
$337$	11872.0	1.91902	0.959509	+	0.281678i	$0.0908910\pi$
$338$	808.000	0.130028
$339$	−996.000	−0.159573
$340$	−1620.00	−0.258402
$341$	−2286.00	−0.363032
$342$	−4472.00	−0.707070
$343$	0	0
$344$	−2544.00	−0.398730
$345$	−240.000	−0.0374527
$346$	5658.00	0.879121
$347$	−5308.00	−0.821177	−0.410588	−	0.911821i	$-0.634677\pi$
$347$	−5308.00	−0.821177	−0.410588	+	0.911821i	$0.634677\pi$
$348$	844.000	0.130009
$349$	12470.0	1.91262	0.956309	−	0.292357i	$-0.0944396\pi$
$349$	12470.0	1.91262	0.956309	+	0.292357i	$0.0944396\pi$
$350$	0	0
$351$	−2703.00	−0.411041
$352$	−288.000	−0.0436092
$353$	−671.000	−0.101172	−0.0505860	−	0.998720i	$-0.516109\pi$
$353$	−671.000	−0.101172	−0.0505860	+	0.998720i	$0.516109\pi$
$354$	1708.00	0.256438
$355$	−760.000	−0.113624
$356$	−3072.00	−0.457347
$357$	0	0
$358$	1432.00	0.211407
$359$	1608.00	0.236398	0.118199	−	0.992990i	$-0.462288\pi$
$359$	1608.00	0.236398	0.118199	+	0.992990i	$0.462288\pi$
$360$	1040.00	0.152258
$361$	537.000	0.0782913
$362$	−7228.00	−1.04943
$363$	−1250.00	−0.180738
$364$	0	0
$365$	−3510.00	−0.503347
$366$	−1160.00	−0.165667
$367$	5681.00	0.808027	0.404013	−	0.914753i	$-0.367615\pi$
$367$	5681.00	0.808027	0.404013	+	0.914753i	$0.367615\pi$
$368$	768.000	0.108790
$369$	−1924.00	−0.271435
$370$	200.000	0.0281014
$371$	0	0
$372$	1016.00	0.141605
$373$	−3848.00	−0.534161	−0.267080	−	0.963674i	$-0.586059\pi$
$373$	−3848.00	−0.534161	−0.267080	+	0.963674i	$0.586059\pi$
$374$	−1458.00	−0.201581
$375$	−125.000	−0.0172133
$376$	−1336.00	−0.183242
$377$	10761.0	1.47008
$378$	0	0
$379$	5344.00	0.724282	0.362141	−	0.932123i	$-0.382046\pi$
$379$	5344.00	0.724282	0.362141	+	0.932123i	$0.382046\pi$
$380$	−1720.00	−0.232195
$381$	1906.00	0.256292
$382$	−8506.00	−1.13928
$383$	5920.00	0.789812	0.394906	−	0.918722i	$-0.370777\pi$
$383$	5920.00	0.789812	0.394906	+	0.918722i	$0.370777\pi$
$384$	128.000	0.0170103
$385$	0	0
$386$	−9328.00	−1.23001
$387$	8268.00	1.08601
$388$	4340.00	0.567861
$389$	−10743.0	−1.40024	−0.700118	−	0.714027i	$-0.746869\pi$
$389$	−10743.0	−1.40024	−0.700118	+	0.714027i	$0.746869\pi$
$390$	−510.000	−0.0662176
$391$	3888.00	0.502876
$392$	0	0
$393$	288.000	0.0369661
$394$	7092.00	0.906827
$395$	2095.00	0.266863
$396$	936.000	0.118777
$397$	−8663.00	−1.09517	−0.547586	−	0.836749i	$-0.684453\pi$
$397$	−8663.00	−1.09517	−0.547586	+	0.836749i	$0.684453\pi$
$398$	−108.000	−0.0136019
$399$	0	0
$400$	400.000	0.0500000
$401$	−4459.00	−0.555291	−0.277646	−	0.960684i	$-0.589554\pi$
$401$	−4459.00	−0.555291	−0.277646	+	0.960684i	$0.589554\pi$
$402$	−116.000	−0.0143919
$403$	12954.0	1.60120
$404$	2152.00	0.265015
$405$	−3245.00	−0.398137
$406$	0	0
$407$	180.000	0.0219220
$408$	648.000	0.0786294
$409$	13430.0	1.62364	0.811822	−	0.583904i	$-0.198476\pi$
$409$	13430.0	1.62364	0.811822	+	0.583904i	$0.198476\pi$
$410$	−740.000	−0.0891366
$411$	916.000	0.109934
$412$	−6492.00	−0.776306
$413$	0	0
$414$	−2496.00	−0.296308
$415$	−620.000	−0.0733364
$416$	1632.00	0.192345
$417$	−640.000	−0.0751581
$418$	−1548.00	−0.181137
$419$	11094.0	1.29350	0.646751	−	0.762701i	$-0.276127\pi$
$419$	11094.0	1.29350	0.646751	+	0.762701i	$0.276127\pi$
$420$	0	0
$421$	−12739.0	−1.47473	−0.737364	−	0.675495i	$-0.763930\pi$
$421$	−12739.0	−1.47473	−0.737364	+	0.675495i	$0.763930\pi$
$422$	−8430.00	−0.972431
$423$	4342.00	0.499090
$424$	−1360.00	−0.155772
$425$	2025.00	0.231122
$426$	304.000	0.0345748
$427$	0	0
$428$	5224.00	0.589980
$429$	−459.000	−0.0516567
$430$	3180.00	0.356635
$431$	7455.00	0.833166	0.416583	−	0.909098i	$-0.363227\pi$
$431$	7455.00	0.833166	0.416583	+	0.909098i	$0.363227\pi$
$432$	−848.000	−0.0944431
$433$	12210.0	1.35514	0.677569	−	0.735459i	$-0.263033\pi$
$433$	12210.0	1.35514	0.677569	+	0.735459i	$0.263033\pi$
$434$	0	0
$435$	−1055.00	−0.116284
$436$	−5580.00	−0.612921
$437$	4128.00	0.451874
$438$	1404.00	0.153164
$439$	−428.000	−0.0465315	−0.0232657	−	0.999729i	$-0.507406\pi$
$439$	−428.000	−0.0465315	−0.0232657	+	0.999729i	$0.507406\pi$
$440$	360.000	0.0390053
$441$	0	0
$442$	8262.00	0.889102
$443$	−7398.00	−0.793430	−0.396715	−	0.917942i	$-0.629850\pi$
$443$	−7398.00	−0.793430	−0.396715	+	0.917942i	$0.629850\pi$
$444$	−80.0000	−0.00855097
$445$	3840.00	0.409064
$446$	−6358.00	−0.675022
$447$	330.000	0.0349183
$448$	0	0
$449$	5807.00	0.610355	0.305177	−	0.952296i	$-0.401284\pi$
$449$	5807.00	0.610355	0.305177	+	0.952296i	$0.401284\pi$
$450$	−1300.00	−0.136184
$451$	−666.000	−0.0695360
$452$	−3984.00	−0.414583
$453$	2485.00	0.257738
$454$	−9902.00	−1.02362
$455$	0	0
$456$	688.000	0.0706547
$457$	18002.0	1.84267	0.921333	−	0.388775i	$-0.127102\pi$
$457$	18002.0	1.84267	0.921333	+	0.388775i	$0.127102\pi$
$458$	−532.000	−0.0542767
$459$	−4293.00	−0.436558
$460$	−960.000	−0.0973048
$461$	18964.0	1.91593	0.957963	−	0.286893i	$-0.0926224\pi$
$461$	18964.0	1.91593	0.957963	+	0.286893i	$0.0926224\pi$
$462$	0	0
$463$	2648.00	0.265795	0.132897	−	0.991130i	$-0.457572\pi$
$463$	2648.00	0.265795	0.132897	+	0.991130i	$0.457572\pi$
$464$	3376.00	0.337773
$465$	−1270.00	−0.126656
$466$	592.000	0.0588495
$467$	16395.0	1.62456	0.812281	−	0.583267i	$-0.198226\pi$
$467$	16395.0	1.62456	0.812281	+	0.583267i	$0.198226\pi$
$468$	−5304.00	−0.523884
$469$	0	0
$470$	1670.00	0.163897
$471$	1114.00	0.108982
$472$	6832.00	0.666246
$473$	2862.00	0.278213
$474$	−838.000	−0.0812038
$475$	2150.00	0.207682
$476$	0	0
$477$	4420.00	0.424272
$478$	12346.0	1.18137
$479$	−15804.0	−1.50752	−0.753761	−	0.657148i	$-0.771762\pi$
$479$	−15804.0	−1.50752	−0.753761	+	0.657148i	$0.771762\pi$
$480$	−160.000	−0.0152145
$481$	−1020.00	−0.0966902
$482$	6808.00	0.643352
$483$	0	0
$484$	−5000.00	−0.469572
$485$	−5425.00	−0.507910
$486$	4160.00	0.388275
$487$	132.000	0.0122823	0.00614116	−	0.999981i	$-0.498045\pi$
$487$	132.000	0.0122823	0.00614116	+	0.999981i	$0.498045\pi$
$488$	−4640.00	−0.430416
$489$	1448.00	0.133908
$490$	0	0
$491$	−15727.0	−1.44552	−0.722759	−	0.691100i	$-0.757126\pi$
$491$	−15727.0	−1.44552	−0.722759	+	0.691100i	$0.757126\pi$
$492$	296.000	0.0271234
$493$	17091.0	1.56134
$494$	8772.00	0.798929
$495$	−1170.00	−0.106238
$496$	4064.00	0.367901
$497$	0	0
$498$	248.000	0.0223156
$499$	−17213.0	−1.54421	−0.772104	−	0.635496i	$-0.780796\pi$
$499$	−17213.0	−1.54421	−0.772104	+	0.635496i	$0.780796\pi$
$500$	−500.000	−0.0447214
$501$	−4251.00	−0.379083
$502$	1304.00	0.115937
$503$	5583.00	0.494898	0.247449	−	0.968901i	$-0.420408\pi$
$503$	5583.00	0.494898	0.247449	+	0.968901i	$0.420408\pi$
$504$	0	0
$505$	−2690.00	−0.237036
$506$	−864.000	−0.0759081
$507$	404.000	0.0353891
$508$	7624.00	0.665867
$509$	4216.00	0.367133	0.183567	−	0.983007i	$-0.441236\pi$
$509$	4216.00	0.367133	0.183567	+	0.983007i	$0.441236\pi$
$510$	−810.000	−0.0703282
$511$	0	0
$512$	512.000	0.0441942
$513$	−4558.00	−0.392282
$514$	11108.0	0.953216
$515$	8115.00	0.694349
$516$	−1272.00	−0.108521
$517$	1503.00	0.127857
$518$	0	0
$519$	2829.00	0.239267
$520$	−2040.00	−0.172038
$521$	13378.0	1.12495	0.562477	−	0.826813i	$-0.309849\pi$
$521$	13378.0	1.12495	0.562477	+	0.826813i	$0.309849\pi$
$522$	−10972.0	−0.919984
$523$	3208.00	0.268214	0.134107	−	0.990967i	$-0.457183\pi$
$523$	3208.00	0.268214	0.134107	+	0.990967i	$0.457183\pi$
$524$	1152.00	0.0960408
$525$	0	0
$526$	−14140.0	−1.17212
$527$	20574.0	1.70060
$528$	−144.000	−0.0118689
$529$	−9863.00	−0.810635
$530$	1700.00	0.139327
$531$	−22204.0	−1.81464
$532$	0	0
$533$	3774.00	0.306698
$534$	−1536.00	−0.124474
$535$	−6530.00	−0.527694
$536$	−464.000	−0.0373913
$537$	716.000	0.0575376
$538$	−3712.00	−0.297464
$539$	0	0
$540$	1060.00	0.0844725
$541$	6351.00	0.504715	0.252358	−	0.967634i	$-0.418794\pi$
$541$	6351.00	0.504715	0.252358	+	0.967634i	$0.418794\pi$
$542$	2472.00	0.195907
$543$	−3614.00	−0.285620
$544$	2592.00	0.204285
$545$	6975.00	0.548213
$546$	0	0
$547$	2436.00	0.190413	0.0952064	−	0.995458i	$-0.469649\pi$
$547$	2436.00	0.190413	0.0952064	+	0.995458i	$0.469649\pi$
$548$	3664.00	0.285617
$549$	15080.0	1.17231
$550$	−450.000	−0.0348874
$551$	18146.0	1.40299
$552$	384.000	0.0296089
$553$	0	0
$554$	7688.00	0.589588
$555$	100.000	0.00764822
$556$	−2560.00	−0.195267
$557$	7508.00	0.571139	0.285569	−	0.958358i	$-0.407817\pi$
$557$	7508.00	0.571139	0.285569	+	0.958358i	$0.407817\pi$
$558$	−13208.0	−1.00204
$559$	−16218.0	−1.22710
$560$	0	0
$561$	−729.000	−0.0548635
$562$	−15210.0	−1.14163
$563$	−18996.0	−1.42200	−0.711000	−	0.703192i	$-0.751757\pi$
$563$	−18996.0	−1.42200	−0.711000	+	0.703192i	$0.751757\pi$
$564$	−668.000	−0.0498721
$565$	4980.00	0.370814
$566$	−9826.00	−0.729713
$567$	0	0
$568$	1216.00	0.0898279
$569$	−3982.00	−0.293382	−0.146691	−	0.989182i	$-0.546862\pi$
$569$	−3982.00	−0.293382	−0.146691	+	0.989182i	$0.546862\pi$
$570$	−860.000	−0.0631955
$571$	−14956.0	−1.09613	−0.548064	−	0.836436i	$-0.684635\pi$
$571$	−14956.0	−1.09613	−0.548064	+	0.836436i	$0.684635\pi$
$572$	−1836.00	−0.134208
$573$	−4253.00	−0.310073
$574$	0	0
$575$	1200.00	0.0870321
$576$	−1664.00	−0.120370
$577$	−1445.00	−0.104257	−0.0521284	−	0.998640i	$-0.516600\pi$
$577$	−1445.00	−0.104257	−0.0521284	+	0.998640i	$0.516600\pi$
$578$	3296.00	0.237189
$579$	−4664.00	−0.334766
$580$	−4220.00	−0.302114
$581$	0	0
$582$	2170.00	0.154552
$583$	1530.00	0.108690
$584$	5616.00	0.397931
$585$	6630.00	0.468576
$586$	9266.00	0.653200
$587$	6764.00	0.475605	0.237803	−	0.971314i	$-0.423573\pi$
$587$	6764.00	0.475605	0.237803	+	0.971314i	$0.423573\pi$
$588$	0	0
$589$	21844.0	1.52813
$590$	−8540.00	−0.595909
$591$	3546.00	0.246807
$592$	−320.000	−0.0222161
$593$	4895.00	0.338977	0.169489	−	0.985532i	$-0.445788\pi$
$593$	4895.00	0.338977	0.169489	+	0.985532i	$0.445788\pi$
$594$	954.000	0.0658975
$595$	0	0
$596$	1320.00	0.0907203
$597$	−54.0000	−0.00370196
$598$	4896.00	0.334803
$599$	−5677.00	−0.387239	−0.193619	−	0.981077i	$-0.562023\pi$
$599$	−5677.00	−0.387239	−0.193619	+	0.981077i	$0.562023\pi$
$600$	200.000	0.0136083
$601$	3330.00	0.226013	0.113006	−	0.993594i	$-0.463952\pi$
$601$	3330.00	0.226013	0.113006	+	0.993594i	$0.463952\pi$
$602$	0	0
$603$	1508.00	0.101842
$604$	9940.00	0.669624
$605$	6250.00	0.419998
$606$	1076.00	0.0721279
$607$	−1957.00	−0.130860	−0.0654301	−	0.997857i	$-0.520842\pi$
$607$	−1957.00	−0.130860	−0.0654301	+	0.997857i	$0.520842\pi$
$608$	2752.00	0.183566
$609$	0	0
$610$	5800.00	0.384976
$611$	−8517.00	−0.563930
$612$	−8424.00	−0.556405
$613$	7734.00	0.509581	0.254791	−	0.966996i	$-0.417993\pi$
$613$	7734.00	0.509581	0.254791	+	0.966996i	$0.417993\pi$
$614$	542.000	0.0356243
$615$	−370.000	−0.0242599
$616$	0	0
$617$	−19452.0	−1.26922	−0.634609	−	0.772833i	$-0.718839\pi$
$617$	−19452.0	−1.26922	−0.634609	+	0.772833i	$0.718839\pi$
$618$	−3246.00	−0.211284
$619$	−20884.0	−1.35606	−0.678028	−	0.735036i	$-0.737165\pi$
$619$	−20884.0	−1.35606	−0.678028	+	0.735036i	$0.737165\pi$
$620$	−5080.00	−0.329061
$621$	−2544.00	−0.164392
$622$	−12108.0	−0.780525
$623$	0	0
$624$	816.000	0.0523496
$625$	625.000	0.0400000
$626$	−19058.0	−1.21679
$627$	−774.000	−0.0492992
$628$	4456.00	0.283143
$629$	−1620.00	−0.102693
$630$	0	0
$631$	−18721.0	−1.18110	−0.590548	−	0.807003i	$-0.701088\pi$
$631$	−18721.0	−1.18110	−0.590548	+	0.807003i	$0.701088\pi$
$632$	−3352.00	−0.210974
$633$	−4215.00	−0.264662
$634$	17012.0	1.06567
$635$	−9530.00	−0.595569
$636$	−680.000	−0.0423958
$637$	0	0
$638$	−3798.00	−0.235681
$639$	−3952.00	−0.244662
$640$	−640.000	−0.0395285
$641$	−11562.0	−0.712436	−0.356218	−	0.934403i	$-0.615934\pi$
$641$	−11562.0	−0.712436	−0.356218	+	0.934403i	$0.615934\pi$
$642$	2612.00	0.160572
$643$	−23551.0	−1.44442	−0.722209	−	0.691675i	$-0.756873\pi$
$643$	−23551.0	−1.44442	−0.722209	+	0.691675i	$0.756873\pi$
$644$	0	0
$645$	1590.00	0.0970639
$646$	13932.0	0.848525
$647$	−22204.0	−1.34920	−0.674598	−	0.738186i	$-0.735683\pi$
$647$	−22204.0	−1.34920	−0.674598	+	0.738186i	$0.735683\pi$
$648$	5192.00	0.314755
$649$	−7686.00	−0.464872
$650$	2550.00	0.153876
$651$	0	0
$652$	5792.00	0.347902
$653$	1442.00	0.0864163	0.0432081	−	0.999066i	$-0.486242\pi$
$653$	1442.00	0.0864163	0.0432081	+	0.999066i	$0.486242\pi$
$654$	−2790.00	−0.166816
$655$	−1440.00	−0.0859015
$656$	1184.00	0.0704686
$657$	−18252.0	−1.08383
$658$	0	0
$659$	339.000	0.0200388	0.0100194	−	0.999950i	$-0.496811\pi$
$659$	339.000	0.0200388	0.0100194	+	0.999950i	$0.496811\pi$
$660$	180.000	0.0106159
$661$	−21372.0	−1.25760	−0.628801	−	0.777567i	$-0.716454\pi$
$661$	−21372.0	−1.25760	−0.628801	+	0.777567i	$0.716454\pi$
$662$	−20776.0	−1.21976
$663$	4131.00	0.241983
$664$	992.000	0.0579775
$665$	0	0
$666$	1040.00	0.0605093
$667$	10128.0	0.587943
$668$	−17004.0	−0.984887
$669$	−3179.00	−0.183718
$670$	580.000	0.0334438
$671$	5220.00	0.300322
$672$	0	0
$673$	6616.00	0.378942	0.189471	−	0.981886i	$-0.439323\pi$
$673$	6616.00	0.378942	0.189471	+	0.981886i	$0.439323\pi$
$674$	23744.0	1.35695
$675$	−1325.00	−0.0755545
$676$	1616.00	0.0919436
$677$	−8737.00	−0.495997	−0.247999	−	0.968760i	$-0.579773\pi$
$677$	−8737.00	−0.495997	−0.247999	+	0.968760i	$0.579773\pi$
$678$	−1992.00	−0.112835
$679$	0	0
$680$	−3240.00	−0.182718
$681$	−4951.00	−0.278594
$682$	−4572.00	−0.256702
$683$	1884.00	0.105548	0.0527740	−	0.998606i	$-0.483194\pi$
$683$	1884.00	0.105548	0.0527740	+	0.998606i	$0.483194\pi$
$684$	−8944.00	−0.499974
$685$	−4580.00	−0.255464
$686$	0	0
$687$	−266.000	−0.0147722
$688$	−5088.00	−0.281945
$689$	−8670.00	−0.479391
$690$	−480.000	−0.0264830
$691$	−33356.0	−1.83636	−0.918178	−	0.396168i	$-0.870340\pi$
$691$	−33356.0	−1.83636	−0.918178	+	0.396168i	$0.870340\pi$
$692$	11316.0	0.621633
$693$	0	0
$694$	−10616.0	−0.580660
$695$	3200.00	0.174652
$696$	1688.00	0.0919303
$697$	5994.00	0.325737
$698$	24940.0	1.35243
$699$	296.000	0.0160168
$700$	0	0
$701$	19107.0	1.02947	0.514737	−	0.857348i	$-0.327890\pi$
$701$	19107.0	1.02947	0.514737	+	0.857348i	$0.327890\pi$
$702$	−5406.00	−0.290650
$703$	−1720.00	−0.0922774
$704$	−576.000	−0.0308364
$705$	835.000	0.0446070
$706$	−1342.00	−0.0715394
$707$	0	0
$708$	3416.00	0.181329
$709$	−19117.0	−1.01263	−0.506315	−	0.862349i	$-0.668993\pi$
$709$	−19117.0	−1.01263	−0.506315	+	0.862349i	$0.668993\pi$
$710$	−1520.00	−0.0803445
$711$	10894.0	0.574623
$712$	−6144.00	−0.323393
$713$	12192.0	0.640384
$714$	0	0
$715$	2295.00	0.120039
$716$	2864.00	0.149487
$717$	6173.00	0.321527
$718$	3216.00	0.167159
$719$	36584.0	1.89757	0.948785	−	0.315922i	$-0.102314\pi$
$719$	36584.0	1.89757	0.948785	+	0.315922i	$0.102314\pi$
$720$	2080.00	0.107663
$721$	0	0
$722$	1074.00	0.0553603
$723$	3404.00	0.175098
$724$	−14456.0	−0.742062
$725$	5275.00	0.270219
$726$	−2500.00	−0.127801
$727$	−25040.0	−1.27742	−0.638709	−	0.769449i	$-0.720531\pi$
$727$	−25040.0	−1.27742	−0.638709	+	0.769449i	$0.720531\pi$
$728$	0	0
$729$	−15443.0	−0.784586
$730$	−7020.00	−0.355920
$731$	−25758.0	−1.30328
$732$	−2320.00	−0.117144
$733$	−13345.0	−0.672454	−0.336227	−	0.941781i	$-0.609151\pi$
$733$	−13345.0	−0.672454	−0.336227	+	0.941781i	$0.609151\pi$
$734$	11362.0	0.571361
$735$	0	0
$736$	1536.00	0.0769262
$737$	522.000	0.0260897
$738$	−3848.00	−0.191933
$739$	−15037.0	−0.748505	−0.374252	−	0.927327i	$-0.622101\pi$
$739$	−15037.0	−0.748505	−0.374252	+	0.927327i	$0.622101\pi$
$740$	400.000	0.0198707
$741$	4386.00	0.217441
$742$	0	0
$743$	29934.0	1.47802	0.739012	−	0.673692i	$-0.235293\pi$
$743$	29934.0	1.47802	0.739012	+	0.673692i	$0.235293\pi$
$744$	2032.00	0.100130
$745$	−1650.00	−0.0811427
$746$	−7696.00	−0.377709
$747$	−3224.00	−0.157912
$748$	−2916.00	−0.142539
$749$	0	0
$750$	−250.000	−0.0121716
$751$	8725.00	0.423941	0.211971	−	0.977276i	$-0.432012\pi$
$751$	8725.00	0.423941	0.211971	+	0.977276i	$0.432012\pi$
$752$	−2672.00	−0.129572
$753$	652.000	0.0315541
$754$	21522.0	1.03950
$755$	−12425.0	−0.598930
$756$	0	0
$757$	−13624.0	−0.654125	−0.327063	−	0.945003i	$-0.606059\pi$
$757$	−13624.0	−0.654125	−0.327063	+	0.945003i	$0.606059\pi$
$758$	10688.0	0.512145
$759$	−432.000	−0.0206596
$760$	−3440.00	−0.164187
$761$	24168.0	1.15123	0.575617	−	0.817719i	$-0.304762\pi$
$761$	24168.0	1.15123	0.575617	+	0.817719i	$0.304762\pi$
$762$	3812.00	0.181226
$763$	0	0
$764$	−17012.0	−0.805592
$765$	10530.0	0.497664
$766$	11840.0	0.558481
$767$	43554.0	2.05038
$768$	256.000	0.0120281
$769$	−12278.0	−0.575756	−0.287878	−	0.957667i	$-0.592950\pi$
$769$	−12278.0	−0.575756	−0.287878	+	0.957667i	$0.592950\pi$
$770$	0	0
$771$	5554.00	0.259432
$772$	−18656.0	−0.869746
$773$	4051.00	0.188492	0.0942460	−	0.995549i	$-0.469956\pi$
$773$	4051.00	0.188492	0.0942460	+	0.995549i	$0.469956\pi$
$774$	16536.0	0.767925
$775$	6350.00	0.294321
$776$	8680.00	0.401538
$777$	0	0
$778$	−21486.0	−0.990116
$779$	6364.00	0.292701
$780$	−1020.00	−0.0468229
$781$	−1368.00	−0.0626772
$782$	7776.00	0.355587
$783$	−11183.0	−0.510406
$784$	0	0
$785$	−5570.00	−0.253251
$786$	576.000	0.0261390
$787$	−30643.0	−1.38794	−0.693968	−	0.720006i	$-0.744139\pi$
$787$	−30643.0	−1.38794	−0.693968	+	0.720006i	$0.744139\pi$
$788$	14184.0	0.641223
$789$	−7070.00	−0.319010
$790$	4190.00	0.188701
$791$	0	0
$792$	1872.00	0.0839882
$793$	−29580.0	−1.32461
$794$	−17326.0	−0.774404
$795$	850.000	0.0379200
$796$	−216.000	−0.00961799
$797$	15549.0	0.691059	0.345529	−	0.938408i	$-0.387699\pi$
$797$	15549.0	0.691059	0.345529	+	0.938408i	$0.387699\pi$
$798$	0	0
$799$	−13527.0	−0.598937
$800$	800.000	0.0353553
$801$	19968.0	0.880817
$802$	−8918.00	−0.392650
$803$	−6318.00	−0.277656
$804$	−232.000	−0.0101766
$805$	0	0
$806$	25908.0	1.13222
$807$	−1856.00	−0.0809595
$808$	4304.00	0.187394
$809$	−12675.0	−0.550840	−0.275420	−	0.961324i	$-0.588817\pi$
$809$	−12675.0	−0.550840	−0.275420	+	0.961324i	$0.588817\pi$
$810$	−6490.00	−0.281525
$811$	−38008.0	−1.64567	−0.822837	−	0.568278i	$-0.807610\pi$
$811$	−38008.0	−1.64567	−0.822837	+	0.568278i	$0.807610\pi$
$812$	0	0
$813$	1236.00	0.0533191
$814$	360.000	0.0155012
$815$	−7240.00	−0.311173
$816$	1296.00	0.0555994
$817$	−27348.0	−1.17110
$818$	26860.0	1.14809
$819$	0	0
$820$	−1480.00	−0.0630291
$821$	5277.00	0.224322	0.112161	−	0.993690i	$-0.464223\pi$
$821$	5277.00	0.224322	0.112161	+	0.993690i	$0.464223\pi$
$822$	1832.00	0.0777352
$823$	−22350.0	−0.946625	−0.473312	−	0.880895i	$-0.656942\pi$
$823$	−22350.0	−0.946625	−0.473312	+	0.880895i	$0.656942\pi$
$824$	−12984.0	−0.548931
$825$	−225.000	−0.00949514
$826$	0	0
$827$	−33192.0	−1.39565	−0.697823	−	0.716270i	$-0.745848\pi$
$827$	−33192.0	−1.39565	−0.697823	+	0.716270i	$0.745848\pi$
$828$	−4992.00	−0.209522
$829$	−1694.00	−0.0709711	−0.0354856	−	0.999370i	$-0.511298\pi$
$829$	−1694.00	−0.0709711	−0.0354856	+	0.999370i	$0.511298\pi$
$830$	−1240.00	−0.0518567
$831$	3844.00	0.160466
$832$	3264.00	0.136008
$833$	0	0
$834$	−1280.00	−0.0531448
$835$	21255.0	0.880910
$836$	−3096.00	−0.128083
$837$	−13462.0	−0.555932
$838$	22188.0	0.914644
$839$	−17564.0	−0.722737	−0.361369	−	0.932423i	$-0.617690\pi$
$839$	−17564.0	−0.722737	−0.361369	+	0.932423i	$0.617690\pi$
$840$	0	0
$841$	20132.0	0.825454
$842$	−25478.0	−1.04279
$843$	−7605.00	−0.310712
$844$	−16860.0	−0.687613
$845$	−2020.00	−0.0822368
$846$	8684.00	0.352910
$847$	0	0
$848$	−2720.00	−0.110148
$849$	−4913.00	−0.198603
$850$	4050.00	0.163428
$851$	−960.000	−0.0386702
$852$	608.000	0.0244480
$853$	−10450.0	−0.419462	−0.209731	−	0.977759i	$-0.567259\pi$
$853$	−10450.0	−0.419462	−0.209731	+	0.977759i	$0.567259\pi$
$854$	0	0
$855$	11180.0	0.447191
$856$	10448.0	0.417179
$857$	30102.0	1.19984	0.599921	−	0.800059i	$-0.295199\pi$
$857$	30102.0	1.19984	0.599921	+	0.800059i	$0.295199\pi$
$858$	−918.000	−0.0365268
$859$	−22268.0	−0.884487	−0.442244	−	0.896895i	$-0.645817\pi$
$859$	−22268.0	−0.884487	−0.442244	+	0.896895i	$0.645817\pi$
$860$	6360.00	0.252179
$861$	0	0
$862$	14910.0	0.589138
$863$	−24842.0	−0.979874	−0.489937	−	0.871758i	$-0.662980\pi$
$863$	−24842.0	−0.979874	−0.489937	+	0.871758i	$0.662980\pi$
$864$	−1696.00	−0.0667814
$865$	−14145.0	−0.556005
$866$	24420.0	0.958228
$867$	1648.00	0.0645548
$868$	0	0
$869$	3771.00	0.147206
$870$	−2110.00	−0.0822249
$871$	−2958.00	−0.115072
$872$	−11160.0	−0.433401
$873$	−28210.0	−1.09366
$874$	8256.00	0.319523
$875$	0	0
$876$	2808.00	0.108303
$877$	24766.0	0.953579	0.476789	−	0.879018i	$-0.341800\pi$
$877$	24766.0	0.953579	0.476789	+	0.879018i	$0.341800\pi$
$878$	−856.000	−0.0329027
$879$	4633.00	0.177778
$880$	720.000	0.0275809
$881$	−9840.00	−0.376297	−0.188149	−	0.982141i	$-0.560249\pi$
$881$	−9840.00	−0.376297	−0.188149	+	0.982141i	$0.560249\pi$
$882$	0	0
$883$	−11500.0	−0.438285	−0.219143	−	0.975693i	$-0.570326\pi$
$883$	−11500.0	−0.438285	−0.219143	+	0.975693i	$0.570326\pi$
$884$	16524.0	0.628690
$885$	−4270.00	−0.162186
$886$	−14796.0	−0.561040
$887$	32768.0	1.24041	0.620204	−	0.784441i	$-0.287050\pi$
$887$	32768.0	1.24041	0.620204	+	0.784441i	$0.287050\pi$
$888$	−160.000	−0.00604645
$889$	0	0
$890$	7680.00	0.289252
$891$	−5841.00	−0.219619
$892$	−12716.0	−0.477313
$893$	−14362.0	−0.538193
$894$	660.000	0.0246909
$895$	−3580.00	−0.133705
$896$	0	0
$897$	2448.00	0.0911219
$898$	11614.0	0.431586
$899$	53594.0	1.98828
$900$	−2600.00	−0.0962963
$901$	−13770.0	−0.509151
$902$	−1332.00	−0.0491693
$903$	0	0
$904$	−7968.00	−0.293155
$905$	18070.0	0.663721
$906$	4970.00	0.182249
$907$	42548.0	1.55764	0.778822	−	0.627245i	$-0.215818\pi$
$907$	42548.0	1.55764	0.778822	+	0.627245i	$0.215818\pi$
$908$	−19804.0	−0.723809
$909$	−13988.0	−0.510399
$910$	0	0
$911$	29160.0	1.06050	0.530249	−	0.847842i	$-0.322098\pi$
$911$	29160.0	1.06050	0.530249	+	0.847842i	$0.322098\pi$
$912$	1376.00	0.0499604
$913$	−1116.00	−0.0404537
$914$	36004.0	1.30296
$915$	2900.00	0.104777
$916$	−1064.00	−0.0383794
$917$	0	0
$918$	−8586.00	−0.308693
$919$	−30731.0	−1.10307	−0.551535	−	0.834151i	$-0.685958\pi$
$919$	−30731.0	−1.10307	−0.551535	+	0.834151i	$0.685958\pi$
$920$	−1920.00	−0.0688049
$921$	271.000	0.00969572
$922$	37928.0	1.35476
$923$	7752.00	0.276447
$924$	0	0
$925$	−500.000	−0.0177729
$926$	5296.00	0.187945
$927$	42198.0	1.49511
$928$	6752.00	0.238842
$929$	−318.000	−0.0112306	−0.00561531	−	0.999984i	$-0.501787\pi$
$929$	−318.000	−0.0112306	−0.00561531	+	0.999984i	$0.501787\pi$
$930$	−2540.00	−0.0895590
$931$	0	0
$932$	1184.00	0.0416129
$933$	−6054.00	−0.212432
$934$	32790.0	1.14874
$935$	3645.00	0.127491
$936$	−10608.0	−0.370442
$937$	19689.0	0.686458	0.343229	−	0.939252i	$-0.388479\pi$
$937$	19689.0	0.686458	0.343229	+	0.939252i	$0.388479\pi$
$938$	0	0
$939$	−9529.00	−0.331168
$940$	3340.00	0.115892
$941$	45740.0	1.58457	0.792286	−	0.610150i	$-0.208891\pi$
$941$	45740.0	1.58457	0.792286	+	0.610150i	$0.208891\pi$
$942$	2228.00	0.0770617
$943$	3552.00	0.122661
$944$	13664.0	0.471107
$945$	0	0
$946$	5724.00	0.196727
$947$	−51474.0	−1.76629	−0.883147	−	0.469097i	$-0.844580\pi$
$947$	−51474.0	−1.76629	−0.883147	+	0.469097i	$0.844580\pi$
$948$	−1676.00	−0.0574198
$949$	35802.0	1.22464
$950$	4300.00	0.146853
$951$	8506.00	0.290038
$952$	0	0
$953$	−31554.0	−1.07254	−0.536272	−	0.844045i	$-0.680168\pi$
$953$	−31554.0	−1.07254	−0.536272	+	0.844045i	$0.680168\pi$
$954$	8840.00	0.300006
$955$	21265.0	0.720544
$956$	24692.0	0.835352
$957$	−1899.00	−0.0641442
$958$	−31608.0	−1.06598
$959$	0	0
$960$	−320.000	−0.0107583
$961$	34725.0	1.16562
$962$	−2040.00	−0.0683703
$963$	−33956.0	−1.13626
$964$	13616.0	0.454919
$965$	23320.0	0.777925
$966$	0	0
$967$	−20394.0	−0.678208	−0.339104	−	0.940749i	$-0.610124\pi$
$967$	−20394.0	−0.678208	−0.339104	+	0.940749i	$0.610124\pi$
$968$	−10000.0	−0.332037
$969$	6966.00	0.230939
$970$	−10850.0	−0.359147
$971$	−18562.0	−0.613474	−0.306737	−	0.951794i	$-0.599237\pi$
$971$	−18562.0	−0.613474	−0.306737	+	0.951794i	$0.599237\pi$
$972$	8320.00	0.274552
$973$	0	0
$974$	264.000	0.00868491
$975$	1275.00	0.0418797
$976$	−9280.00	−0.304350
$977$	−162.000	−0.00530485	−0.00265243	−	0.999996i	$-0.500844\pi$
$977$	−162.000	−0.00530485	−0.00265243	+	0.999996i	$0.500844\pi$
$978$	2896.00	0.0946870
$979$	6912.00	0.225647
$980$	0	0
$981$	36270.0	1.18044
$982$	−31454.0	−1.02214
$983$	52755.0	1.71172	0.855861	−	0.517206i	$-0.173028\pi$
$983$	52755.0	1.71172	0.855861	+	0.517206i	$0.173028\pi$
$984$	592.000	0.0191791
$985$	−17730.0	−0.573528
$986$	34182.0	1.10403
$987$	0	0
$988$	17544.0	0.564928
$989$	−15264.0	−0.490765
$990$	−2340.00	−0.0751213
$991$	−20836.0	−0.667888	−0.333944	−	0.942593i	$-0.608380\pi$
$991$	−20836.0	−0.667888	−0.333944	+	0.942593i	$0.608380\pi$
$992$	8128.00	0.260145
$993$	−10388.0	−0.331977
$994$	0	0
$995$	270.000	0.00860259
$996$	496.000	0.0157795
$997$	4221.00	0.134083	0.0670413	−	0.997750i	$-0.478644\pi$
$997$	4221.00	0.134083	0.0670413	+	0.997750i	$0.478644\pi$
$998$	−34426.0	−1.09192
$999$	1060.00	0.0335705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.n.1.1	yes	1
5.4	even	2		2450.4.a.k.1.1		1
7.2	even	3		490.4.e.d.361.1		2
7.3	odd	6		490.4.e.e.471.1		2
7.4	even	3		490.4.e.d.471.1		2
7.5	odd	6		490.4.e.e.361.1		2
7.6	odd	2		490.4.a.l.1.1	✓	1
35.34	odd	2		2450.4.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.l.1.1	✓	1	7.6	odd	2
490.4.a.n.1.1	yes	1	1.1	even	1	trivial
490.4.e.d.361.1		2	7.2	even	3
490.4.e.d.471.1		2	7.4	even	3
490.4.e.e.361.1		2	7.5	odd	6
490.4.e.e.471.1		2	7.3	odd	6
2450.4.a.k.1.1		1	5.4	even	2
2450.4.a.n.1.1		1	35.34	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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