LMFDB - Embedded newform 490.4.a.m.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:	$1$
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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +1.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} +2.00000 q^{6} +8.00000 q^{8} -26.0000 q^{9} -10.0000 q^{10} -30.0000 q^{11} +4.00000 q^{12} +44.0000 q^{13} -5.00000 q^{15} +16.0000 q^{16} -24.0000 q^{17} -52.0000 q^{18} +2.00000 q^{19} -20.0000 q^{20} -60.0000 q^{22} -183.000 q^{23} +8.00000 q^{24} +25.0000 q^{25} +88.0000 q^{26} -53.0000 q^{27} -279.000 q^{29} -10.0000 q^{30} -40.0000 q^{31} +32.0000 q^{32} -30.0000 q^{33} -48.0000 q^{34} -104.000 q^{36} -76.0000 q^{37} +4.00000 q^{38} +44.0000 q^{39} -40.0000 q^{40} -423.000 q^{41} +305.000 q^{43} -120.000 q^{44} +130.000 q^{45} -366.000 q^{46} +456.000 q^{47} +16.0000 q^{48} +50.0000 q^{50} -24.0000 q^{51} +176.000 q^{52} -198.000 q^{53} -106.000 q^{54} +150.000 q^{55} +2.00000 q^{57} -558.000 q^{58} -462.000 q^{59} -20.0000 q^{60} +281.000 q^{61} -80.0000 q^{62} +64.0000 q^{64} -220.000 q^{65} -60.0000 q^{66} -499.000 q^{67} -96.0000 q^{68} -183.000 q^{69} -534.000 q^{71} -208.000 q^{72} +800.000 q^{73} -152.000 q^{74} +25.0000 q^{75} +8.00000 q^{76} +88.0000 q^{78} -790.000 q^{79} -80.0000 q^{80} +649.000 q^{81} -846.000 q^{82} -597.000 q^{83} +120.000 q^{85} +610.000 q^{86} -279.000 q^{87} -240.000 q^{88} +1017.00 q^{89} +260.000 q^{90} -732.000 q^{92} -40.0000 q^{93} +912.000 q^{94} -10.0000 q^{95} +32.0000 q^{96} -1330.00 q^{97} +780.000 q^{99} +O(q^{100})\)

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
$11$	−30.0000	−0.822304	−0.411152	−	0.911567i	$-0.634873\pi$
$11$	−30.0000	−0.822304	−0.411152	+	0.911567i	$0.634873\pi$
$12$	4.00000	0.0962250
$13$	44.0000	0.938723	0.469362	−	0.883006i	$-0.344484\pi$
$13$	44.0000	0.938723	0.469362	+	0.883006i	$0.344484\pi$
$14$	0	0
$15$	−5.00000	−0.0860663
$16$	16.0000	0.250000
$17$	−24.0000	−0.342403	−0.171202	−	0.985236i	$-0.554765\pi$
$17$	−24.0000	−0.342403	−0.171202	+	0.985236i	$0.554765\pi$
$18$	−52.0000	−0.680918
$19$	2.00000	0.0241490	0.0120745	−	0.999927i	$-0.496156\pi$
$19$	2.00000	0.0241490	0.0120745	+	0.999927i	$0.496156\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−60.0000	−0.581456
$23$	−183.000	−1.65905	−0.829525	−	0.558470i	$-0.811389\pi$
$23$	−183.000	−1.65905	−0.829525	+	0.558470i	$0.811389\pi$
$24$	8.00000	0.0680414
$25$	25.0000	0.200000
$26$	88.0000	0.663778
$27$	−53.0000	−0.377772
$28$	0	0
$29$	−279.000	−1.78652	−0.893259	−	0.449543i	$-0.851587\pi$
$29$	−279.000	−1.78652	−0.893259	+	0.449543i	$0.851587\pi$
$30$	−10.0000	−0.0608581
$31$	−40.0000	−0.231749	−0.115874	−	0.993264i	$-0.536967\pi$
$31$	−40.0000	−0.231749	−0.115874	+	0.993264i	$0.536967\pi$
$32$	32.0000	0.176777
$33$	−30.0000	−0.158252
$34$	−48.0000	−0.242116
$35$	0	0
$36$	−104.000	−0.481481
$37$	−76.0000	−0.337684	−0.168842	−	0.985643i	$-0.554003\pi$
$37$	−76.0000	−0.337684	−0.168842	+	0.985643i	$0.554003\pi$
$38$	4.00000	0.0170759
$39$	44.0000	0.180657
$40$	−40.0000	−0.158114
$41$	−423.000	−1.61126	−0.805628	−	0.592422i	$-0.798172\pi$
$41$	−423.000	−1.61126	−0.805628	+	0.592422i	$0.798172\pi$
$42$	0	0
$43$	305.000	1.08168	0.540838	−	0.841127i	$-0.318107\pi$
$43$	305.000	1.08168	0.540838	+	0.841127i	$0.318107\pi$
$44$	−120.000	−0.411152
$45$	130.000	0.430650
$46$	−366.000	−1.17313
$47$	456.000	1.41520	0.707600	−	0.706613i	$-0.249778\pi$
$47$	456.000	1.41520	0.707600	+	0.706613i	$0.249778\pi$
$48$	16.0000	0.0481125
$49$	0	0
$50$	50.0000	0.141421
$51$	−24.0000	−0.0658955
$52$	176.000	0.469362
$53$	−198.000	−0.513158	−0.256579	−	0.966523i	$-0.582595\pi$
$53$	−198.000	−0.513158	−0.256579	+	0.966523i	$0.582595\pi$
$54$	−106.000	−0.267125
$55$	150.000	0.367745
$56$	0	0
$57$	2.00000	0.00464748
$58$	−558.000	−1.26326
$59$	−462.000	−1.01945	−0.509723	−	0.860339i	$-0.670252\pi$
$59$	−462.000	−1.01945	−0.509723	+	0.860339i	$0.670252\pi$
$60$	−20.0000	−0.0430331
$61$	281.000	0.589809	0.294905	−	0.955527i	$-0.404712\pi$
$61$	281.000	0.589809	0.294905	+	0.955527i	$0.404712\pi$
$62$	−80.0000	−0.163871
$63$	0	0
$64$	64.0000	0.125000
$65$	−220.000	−0.419810
$66$	−60.0000	−0.111901
$67$	−499.000	−0.909889	−0.454944	−	0.890520i	$-0.650341\pi$
$67$	−499.000	−0.909889	−0.454944	+	0.890520i	$0.650341\pi$
$68$	−96.0000	−0.171202
$69$	−183.000	−0.319284
$70$	0	0
$71$	−534.000	−0.892594	−0.446297	−	0.894885i	$-0.647257\pi$
$71$	−534.000	−0.892594	−0.446297	+	0.894885i	$0.647257\pi$
$72$	−208.000	−0.340459
$73$	800.000	1.28264	0.641321	−	0.767272i	$-0.278387\pi$
$73$	800.000	1.28264	0.641321	+	0.767272i	$0.278387\pi$
$74$	−152.000	−0.238779
$75$	25.0000	0.0384900
$76$	8.00000	0.0120745
$77$	0	0
$78$	88.0000	0.127744
$79$	−790.000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−790.000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	−80.0000	−0.111803
$81$	649.000	0.890261
$82$	−846.000	−1.13933
$83$	−597.000	−0.789509	−0.394755	−	0.918787i	$-0.629170\pi$
$83$	−597.000	−0.789509	−0.394755	+	0.918787i	$0.629170\pi$
$84$	0	0
$85$	120.000	0.153127
$86$	610.000	0.764860
$87$	−279.000	−0.343815
$88$	−240.000	−0.290728
$89$	1017.00	1.21126	0.605628	−	0.795748i	$-0.292922\pi$
$89$	1017.00	1.21126	0.605628	+	0.795748i	$0.292922\pi$
$90$	260.000	0.304516
$91$	0	0
$92$	−732.000	−0.829525
$93$	−40.0000	−0.0446001
$94$	912.000	1.00070
$95$	−10.0000	−0.0107998
$96$	32.0000	0.0340207
$97$	−1330.00	−1.39218	−0.696088	−	0.717957i	$-0.745078\pi$
$97$	−1330.00	−1.39218	−0.696088	+	0.717957i	$0.745078\pi$
$98$	0	0
$99$	780.000	0.791848
$100$	100.000	0.100000
$101$	1035.00	1.01967	0.509833	−	0.860273i	$-0.329707\pi$
$101$	1035.00	1.01967	0.509833	+	0.860273i	$0.329707\pi$
$102$	−48.0000	−0.0465952
$103$	827.000	0.791133	0.395567	−	0.918437i	$-0.370548\pi$
$103$	827.000	0.791133	0.395567	+	0.918437i	$0.370548\pi$
$104$	352.000	0.331889
$105$	0	0
$106$	−396.000	−0.362858
$107$	81.0000	0.0731829	0.0365914	−	0.999330i	$-0.488350\pi$
$107$	81.0000	0.0731829	0.0365914	+	0.999330i	$0.488350\pi$
$108$	−212.000	−0.188886
$109$	215.000	0.188929	0.0944645	−	0.995528i	$-0.469886\pi$
$109$	215.000	0.188929	0.0944645	+	0.995528i	$0.469886\pi$
$110$	300.000	0.260035
$111$	−76.0000	−0.0649874
$112$	0	0
$113$	390.000	0.324674	0.162337	−	0.986735i	$-0.448097\pi$
$113$	390.000	0.324674	0.162337	+	0.986735i	$0.448097\pi$
$114$	4.00000	0.00328627
$115$	915.000	0.741949
$116$	−1116.00	−0.893259
$117$	−1144.00	−0.903956
$118$	−924.000	−0.720857
$119$	0	0
$120$	−40.0000	−0.0304290
$121$	−431.000	−0.323817
$122$	562.000	0.417058
$123$	−423.000	−0.310086
$124$	−160.000	−0.115874
$125$	−125.000	−0.0894427
$126$	0	0
$127$	2144.00	1.49803	0.749013	−	0.662556i	$-0.230528\pi$
$127$	2144.00	1.49803	0.749013	+	0.662556i	$0.230528\pi$
$128$	128.000	0.0883883
$129$	305.000	0.208169
$130$	−440.000	−0.296850
$131$	−2400.00	−1.60068	−0.800340	−	0.599547i	$-0.795347\pi$
$131$	−2400.00	−1.60068	−0.800340	+	0.599547i	$0.795347\pi$
$132$	−120.000	−0.0791262
$133$	0	0
$134$	−998.000	−0.643389
$135$	265.000	0.168945
$136$	−192.000	−0.121058
$137$	972.000	0.606157	0.303079	−	0.952966i	$-0.401985\pi$
$137$	972.000	0.606157	0.303079	+	0.952966i	$0.401985\pi$
$138$	−366.000	−0.225768
$139$	158.000	0.0964128	0.0482064	−	0.998837i	$-0.484649\pi$
$139$	158.000	0.0964128	0.0482064	+	0.998837i	$0.484649\pi$
$140$	0	0
$141$	456.000	0.272356
$142$	−1068.00	−0.631159
$143$	−1320.00	−0.771916
$144$	−416.000	−0.240741
$145$	1395.00	0.798955
$146$	1600.00	0.906965
$147$	0	0
$148$	−304.000	−0.168842
$149$	435.000	0.239172	0.119586	−	0.992824i	$-0.461843\pi$
$149$	435.000	0.239172	0.119586	+	0.992824i	$0.461843\pi$
$150$	50.0000	0.0272166
$151$	1316.00	0.709236	0.354618	−	0.935011i	$-0.384611\pi$
$151$	1316.00	0.709236	0.354618	+	0.935011i	$0.384611\pi$
$152$	16.0000	0.00853797
$153$	624.000	0.329722
$154$	0	0
$155$	200.000	0.103641
$156$	176.000	0.0903287
$157$	−3814.00	−1.93879	−0.969396	−	0.245502i	$-0.921047\pi$
$157$	−3814.00	−1.93879	−0.969396	+	0.245502i	$0.921047\pi$
$158$	−1580.00	−0.795557
$159$	−198.000	−0.0987574
$160$	−160.000	−0.0790569
$161$	0	0
$162$	1298.00	0.629509
$163$	2036.00	0.978355	0.489177	−	0.872184i	$-0.337297\pi$
$163$	2036.00	0.978355	0.489177	+	0.872184i	$0.337297\pi$
$164$	−1692.00	−0.805628
$165$	150.000	0.0707726
$166$	−1194.00	−0.558267
$167$	−303.000	−0.140400	−0.0702001	−	0.997533i	$-0.522364\pi$
$167$	−303.000	−0.140400	−0.0702001	+	0.997533i	$0.522364\pi$
$168$	0	0
$169$	−261.000	−0.118798
$170$	240.000	0.108277
$171$	−52.0000	−0.0232546
$172$	1220.00	0.540838
$173$	3816.00	1.67702	0.838512	−	0.544883i	$-0.183426\pi$
$173$	3816.00	1.67702	0.838512	+	0.544883i	$0.183426\pi$
$174$	−558.000	−0.243114
$175$	0	0
$176$	−480.000	−0.205576
$177$	−462.000	−0.196192
$178$	2034.00	0.856487
$179$	2256.00	0.942019	0.471009	−	0.882128i	$-0.343890\pi$
$179$	2256.00	0.942019	0.471009	+	0.882128i	$0.343890\pi$
$180$	520.000	0.215325
$181$	1895.00	0.778200	0.389100	−	0.921195i	$-0.372786\pi$
$181$	1895.00	0.778200	0.389100	+	0.921195i	$0.372786\pi$
$182$	0	0
$183$	281.000	0.113509
$184$	−1464.00	−0.586563
$185$	380.000	0.151017
$186$	−80.0000	−0.0315370
$187$	720.000	0.281559
$188$	1824.00	0.707600
$189$	0	0
$190$	−20.0000	−0.00763659
$191$	3930.00	1.48882	0.744411	−	0.667722i	$-0.232731\pi$
$191$	3930.00	1.48882	0.744411	+	0.667722i	$0.232731\pi$
$192$	64.0000	0.0240563
$193$	1370.00	0.510957	0.255479	−	0.966815i	$-0.417767\pi$
$193$	1370.00	0.510957	0.255479	+	0.966815i	$0.417767\pi$
$194$	−2660.00	−0.984417
$195$	−220.000	−0.0807924
$196$	0	0
$197$	−1326.00	−0.479561	−0.239781	−	0.970827i	$-0.577076\pi$
$197$	−1326.00	−0.479561	−0.239781	+	0.970827i	$0.577076\pi$
$198$	1560.00	0.559921
$199$	−1132.00	−0.403243	−0.201621	−	0.979464i	$-0.564621\pi$
$199$	−1132.00	−0.403243	−0.201621	+	0.979464i	$0.564621\pi$
$200$	200.000	0.0707107
$201$	−499.000	−0.175108
$202$	2070.00	0.721013
$203$	0	0
$204$	−96.0000	−0.0329478
$205$	2115.00	0.720576
$206$	1654.00	0.559416
$207$	4758.00	1.59760
$208$	704.000	0.234681
$209$	−60.0000	−0.0198578
$210$	0	0
$211$	−4138.00	−1.35010	−0.675051	−	0.737771i	$-0.735879\pi$
$211$	−4138.00	−1.35010	−0.675051	+	0.737771i	$0.735879\pi$
$212$	−792.000	−0.256579
$213$	−534.000	−0.171780
$214$	162.000	0.0517481
$215$	−1525.00	−0.483740
$216$	−424.000	−0.133563
$217$	0	0
$218$	430.000	0.133593
$219$	800.000	0.246845
$220$	600.000	0.183873
$221$	−1056.00	−0.321422
$222$	−152.000	−0.0459530
$223$	−484.000	−0.145341	−0.0726705	−	0.997356i	$-0.523152\pi$
$223$	−484.000	−0.145341	−0.0726705	+	0.997356i	$0.523152\pi$
$224$	0	0
$225$	−650.000	−0.192593
$226$	780.000	0.229579
$227$	−2676.00	−0.782433	−0.391217	−	0.920299i	$-0.627946\pi$
$227$	−2676.00	−0.782433	−0.391217	+	0.920299i	$0.627946\pi$
$228$	8.00000	0.00232374
$229$	1190.00	0.343395	0.171697	−	0.985150i	$-0.445075\pi$
$229$	1190.00	0.343395	0.171697	+	0.985150i	$0.445075\pi$
$230$	1830.00	0.524638
$231$	0	0
$232$	−2232.00	−0.631629
$233$	−5052.00	−1.42046	−0.710231	−	0.703969i	$-0.751409\pi$
$233$	−5052.00	−1.42046	−0.710231	+	0.703969i	$0.751409\pi$
$234$	−2288.00	−0.639193
$235$	−2280.00	−0.632897
$236$	−1848.00	−0.509723
$237$	−790.000	−0.216523
$238$	0	0
$239$	1140.00	0.308538	0.154269	−	0.988029i	$-0.450698\pi$
$239$	1140.00	0.308538	0.154269	+	0.988029i	$0.450698\pi$
$240$	−80.0000	−0.0215166
$241$	2018.00	0.539381	0.269690	−	0.962947i	$-0.413079\pi$
$241$	2018.00	0.539381	0.269690	+	0.962947i	$0.413079\pi$
$242$	−862.000	−0.228973
$243$	2080.00	0.549103
$244$	1124.00	0.294905
$245$	0	0
$246$	−846.000	−0.219264
$247$	88.0000	0.0226693
$248$	−320.000	−0.0819356
$249$	−597.000	−0.151941
$250$	−250.000	−0.0632456
$251$	7260.00	1.82569	0.912843	−	0.408311i	$-0.133882\pi$
$251$	7260.00	1.82569	0.912843	+	0.408311i	$0.133882\pi$
$252$	0	0
$253$	5490.00	1.36424
$254$	4288.00	1.05926
$255$	120.000	0.0294694
$256$	256.000	0.0625000
$257$	−6696.00	−1.62523	−0.812617	−	0.582798i	$-0.801958\pi$
$257$	−6696.00	−1.62523	−0.812617	+	0.582798i	$0.801958\pi$
$258$	610.000	0.147197
$259$	0	0
$260$	−880.000	−0.209905
$261$	7254.00	1.72035
$262$	−4800.00	−1.13185
$263$	2583.00	0.605607	0.302803	−	0.953053i	$-0.402077\pi$
$263$	2583.00	0.605607	0.302803	+	0.953053i	$0.402077\pi$
$264$	−240.000	−0.0559507
$265$	990.000	0.229491
$266$	0	0
$267$	1017.00	0.233106
$268$	−1996.00	−0.454944
$269$	−5685.00	−1.28855	−0.644276	−	0.764793i	$-0.722841\pi$
$269$	−5685.00	−1.28855	−0.644276	+	0.764793i	$0.722841\pi$
$270$	530.000	0.119462
$271$	6626.00	1.48524	0.742621	−	0.669711i	$-0.233582\pi$
$271$	6626.00	1.48524	0.742621	+	0.669711i	$0.233582\pi$
$272$	−384.000	−0.0856008
$273$	0	0
$274$	1944.00	0.428618
$275$	−750.000	−0.164461
$276$	−732.000	−0.159642
$277$	−4192.00	−0.909288	−0.454644	−	0.890673i	$-0.650234\pi$
$277$	−4192.00	−0.909288	−0.454644	+	0.890673i	$0.650234\pi$
$278$	316.000	0.0681742
$279$	1040.00	0.223165
$280$	0	0
$281$	−2502.00	−0.531163	−0.265582	−	0.964088i	$-0.585564\pi$
$281$	−2502.00	−0.531163	−0.265582	+	0.964088i	$0.585564\pi$
$282$	912.000	0.192584
$283$	1604.00	0.336918	0.168459	−	0.985709i	$-0.446121\pi$
$283$	1604.00	0.336918	0.168459	+	0.985709i	$0.446121\pi$
$284$	−2136.00	−0.446297
$285$	−10.0000	−0.00207842
$286$	−2640.00	−0.545827
$287$	0	0
$288$	−832.000	−0.170229
$289$	−4337.00	−0.882760
$290$	2790.00	0.564946
$291$	−1330.00	−0.267924
$292$	3200.00	0.641321
$293$	7692.00	1.53369	0.766845	−	0.641832i	$-0.221825\pi$
$293$	7692.00	1.53369	0.766845	+	0.641832i	$0.221825\pi$
$294$	0	0
$295$	2310.00	0.455910
$296$	−608.000	−0.119389
$297$	1590.00	0.310644
$298$	870.000	0.169120
$299$	−8052.00	−1.55739
$300$	100.000	0.0192450
$301$	0	0
$302$	2632.00	0.501505
$303$	1035.00	0.196235
$304$	32.0000	0.00603726
$305$	−1405.00	−0.263771
$306$	1248.00	0.233148
$307$	−6883.00	−1.27959	−0.639794	−	0.768546i	$-0.720980\pi$
$307$	−6883.00	−1.27959	−0.639794	+	0.768546i	$0.720980\pi$
$308$	0	0
$309$	827.000	0.152254
$310$	400.000	0.0732854
$311$	6966.00	1.27011	0.635057	−	0.772465i	$-0.280976\pi$
$311$	6966.00	1.27011	0.635057	+	0.772465i	$0.280976\pi$
$312$	352.000	0.0638720
$313$	−6736.00	−1.21643	−0.608213	−	0.793774i	$-0.708113\pi$
$313$	−6736.00	−1.21643	−0.608213	+	0.793774i	$0.708113\pi$
$314$	−7628.00	−1.37093
$315$	0	0
$316$	−3160.00	−0.562544
$317$	−3156.00	−0.559175	−0.279588	−	0.960120i	$-0.590198\pi$
$317$	−3156.00	−0.559175	−0.279588	+	0.960120i	$0.590198\pi$
$318$	−396.000	−0.0698320
$319$	8370.00	1.46906
$320$	−320.000	−0.0559017
$321$	81.0000	0.0140840
$322$	0	0
$323$	−48.0000	−0.00826870
$324$	2596.00	0.445130
$325$	1100.00	0.187745
$326$	4072.00	0.691801
$327$	215.000	0.0363594
$328$	−3384.00	−0.569665
$329$	0	0
$330$	300.000	0.0500438
$331$	10724.0	1.78080	0.890399	−	0.455180i	$-0.150425\pi$
$331$	10724.0	1.78080	0.890399	+	0.455180i	$0.150425\pi$
$332$	−2388.00	−0.394755
$333$	1976.00	0.325178
$334$	−606.000	−0.0992780
$335$	2495.00	0.406915
$336$	0	0
$337$	2786.00	0.450336	0.225168	−	0.974320i	$-0.427707\pi$
$337$	2786.00	0.450336	0.225168	+	0.974320i	$0.427707\pi$
$338$	−522.000	−0.0840031
$339$	390.000	0.0624835
$340$	480.000	0.0765637
$341$	1200.00	0.190568
$342$	−104.000	−0.0164435
$343$	0	0
$344$	2440.00	0.382430
$345$	915.000	0.142788
$346$	7632.00	1.18583
$347$	537.000	0.0830769	0.0415384	−	0.999137i	$-0.486774\pi$
$347$	537.000	0.0830769	0.0415384	+	0.999137i	$0.486774\pi$
$348$	−1116.00	−0.171908
$349$	−11491.0	−1.76246	−0.881231	−	0.472686i	$-0.843284\pi$
$349$	−11491.0	−1.76246	−0.881231	+	0.472686i	$0.843284\pi$
$350$	0	0
$351$	−2332.00	−0.354624
$352$	−960.000	−0.145364
$353$	6042.00	0.911001	0.455500	−	0.890236i	$-0.349460\pi$
$353$	6042.00	0.911001	0.455500	+	0.890236i	$0.349460\pi$
$354$	−924.000	−0.138729
$355$	2670.00	0.399180
$356$	4068.00	0.605628
$357$	0	0
$358$	4512.00	0.666108
$359$	−5616.00	−0.825630	−0.412815	−	0.910815i	$-0.635454\pi$
$359$	−5616.00	−0.825630	−0.412815	+	0.910815i	$0.635454\pi$
$360$	1040.00	0.152258
$361$	−6855.00	−0.999417
$362$	3790.00	0.550271
$363$	−431.000	−0.0623185
$364$	0	0
$365$	−4000.00	−0.573615
$366$	562.000	0.0802629
$367$	−10321.0	−1.46799	−0.733994	−	0.679156i	$-0.762346\pi$
$367$	−10321.0	−1.46799	−0.733994	+	0.679156i	$0.762346\pi$
$368$	−2928.00	−0.414762
$369$	10998.0	1.55158
$370$	760.000	0.106785
$371$	0	0
$372$	−160.000	−0.0223000
$373$	−9196.00	−1.27654	−0.638272	−	0.769811i	$-0.720350\pi$
$373$	−9196.00	−1.27654	−0.638272	+	0.769811i	$0.720350\pi$
$374$	1440.00	0.199093
$375$	−125.000	−0.0172133
$376$	3648.00	0.500349
$377$	−12276.0	−1.67705
$378$	0	0
$379$	−1978.00	−0.268082	−0.134041	−	0.990976i	$-0.542795\pi$
$379$	−1978.00	−0.268082	−0.134041	+	0.990976i	$0.542795\pi$
$380$	−40.0000	−0.00539989
$381$	2144.00	0.288295
$382$	7860.00	1.05276
$383$	−4587.00	−0.611971	−0.305985	−	0.952036i	$-0.598986\pi$
$383$	−4587.00	−0.611971	−0.305985	+	0.952036i	$0.598986\pi$
$384$	128.000	0.0170103
$385$	0	0
$386$	2740.00	0.361301
$387$	−7930.00	−1.04161
$388$	−5320.00	−0.696088
$389$	−12822.0	−1.67121	−0.835606	−	0.549330i	$-0.814883\pi$
$389$	−12822.0	−1.67121	−0.835606	+	0.549330i	$0.814883\pi$
$390$	−440.000	−0.0571289
$391$	4392.00	0.568064
$392$	0	0
$393$	−2400.00	−0.308051
$394$	−2652.00	−0.339101
$395$	3950.00	0.503155
$396$	3120.00	0.395924
$397$	−634.000	−0.0801500	−0.0400750	−	0.999197i	$-0.512760\pi$
$397$	−634.000	−0.0801500	−0.0400750	+	0.999197i	$0.512760\pi$
$398$	−2264.00	−0.285136
$399$	0	0
$400$	400.000	0.0500000
$401$	−4977.00	−0.619799	−0.309900	−	0.950769i	$-0.600295\pi$
$401$	−4977.00	−0.619799	−0.309900	+	0.950769i	$0.600295\pi$
$402$	−998.000	−0.123820
$403$	−1760.00	−0.217548
$404$	4140.00	0.509833
$405$	−3245.00	−0.398137
$406$	0	0
$407$	2280.00	0.277679
$408$	−192.000	−0.0232976
$409$	14627.0	1.76836	0.884179	−	0.467148i	$-0.154718\pi$
$409$	14627.0	1.76836	0.884179	+	0.467148i	$0.154718\pi$
$410$	4230.00	0.509524
$411$	972.000	0.116655
$412$	3308.00	0.395567
$413$	0	0
$414$	9516.00	1.12968
$415$	2985.00	0.353079
$416$	1408.00	0.165944
$417$	158.000	0.0185547
$418$	−120.000	−0.0140416
$419$	14160.0	1.65098	0.825491	−	0.564416i	$-0.190898\pi$
$419$	14160.0	1.65098	0.825491	+	0.564416i	$0.190898\pi$
$420$	0	0
$421$	−979.000	−0.113334	−0.0566669	−	0.998393i	$-0.518047\pi$
$421$	−979.000	−0.113334	−0.0566669	+	0.998393i	$0.518047\pi$
$422$	−8276.00	−0.954667
$423$	−11856.0	−1.36279
$424$	−1584.00	−0.181429
$425$	−600.000	−0.0684806
$426$	−1068.00	−0.121467
$427$	0	0
$428$	324.000	0.0365914
$429$	−1320.00	−0.148555
$430$	−3050.00	−0.342056
$431$	−12978.0	−1.45041	−0.725207	−	0.688531i	$-0.758256\pi$
$431$	−12978.0	−1.45041	−0.725207	+	0.688531i	$0.758256\pi$
$432$	−848.000	−0.0944431
$433$	−8902.00	−0.987997	−0.493999	−	0.869463i	$-0.664465\pi$
$433$	−8902.00	−0.987997	−0.493999	+	0.869463i	$0.664465\pi$
$434$	0	0
$435$	1395.00	0.153759
$436$	860.000	0.0944645
$437$	−366.000	−0.0400644
$438$	1600.00	0.174546
$439$	−6028.00	−0.655355	−0.327677	−	0.944790i	$-0.606266\pi$
$439$	−6028.00	−0.655355	−0.327677	+	0.944790i	$0.606266\pi$
$440$	1200.00	0.130018
$441$	0	0
$442$	−2112.00	−0.227280
$443$	11901.0	1.27637	0.638187	−	0.769881i	$-0.279685\pi$
$443$	11901.0	1.27637	0.638187	+	0.769881i	$0.279685\pi$
$444$	−304.000	−0.0324937
$445$	−5085.00	−0.541690
$446$	−968.000	−0.102772
$447$	435.000	0.0460286
$448$	0	0
$449$	−6513.00	−0.684560	−0.342280	−	0.939598i	$-0.611199\pi$
$449$	−6513.00	−0.684560	−0.342280	+	0.939598i	$0.611199\pi$
$450$	−1300.00	−0.136184
$451$	12690.0	1.32494
$452$	1560.00	0.162337
$453$	1316.00	0.136492
$454$	−5352.00	−0.553264
$455$	0	0
$456$	16.0000	0.00164313
$457$	−14296.0	−1.46332	−0.731662	−	0.681668i	$-0.761255\pi$
$457$	−14296.0	−1.46332	−0.731662	+	0.681668i	$0.761255\pi$
$458$	2380.00	0.242817
$459$	1272.00	0.129350
$460$	3660.00	0.370975
$461$	−2694.00	−0.272174	−0.136087	−	0.990697i	$-0.543453\pi$
$461$	−2694.00	−0.272174	−0.136087	+	0.990697i	$0.543453\pi$
$462$	0	0
$463$	−16105.0	−1.61655	−0.808275	−	0.588805i	$-0.799599\pi$
$463$	−16105.0	−1.61655	−0.808275	+	0.588805i	$0.799599\pi$
$464$	−4464.00	−0.446629
$465$	200.000	0.0199458
$466$	−10104.0	−1.00442
$467$	−8343.00	−0.826698	−0.413349	−	0.910573i	$-0.635641\pi$
$467$	−8343.00	−0.826698	−0.413349	+	0.910573i	$0.635641\pi$
$468$	−4576.00	−0.451978
$469$	0	0
$470$	−4560.00	−0.447526
$471$	−3814.00	−0.373121
$472$	−3696.00	−0.360428
$473$	−9150.00	−0.889466
$474$	−1580.00	−0.153105
$475$	50.0000	0.00482980
$476$	0	0
$477$	5148.00	0.494152
$478$	2280.00	0.218169
$479$	−10428.0	−0.994713	−0.497356	−	0.867546i	$-0.665696\pi$
$479$	−10428.0	−0.994713	−0.497356	+	0.867546i	$0.665696\pi$
$480$	−160.000	−0.0152145
$481$	−3344.00	−0.316992
$482$	4036.00	0.381400
$483$	0	0
$484$	−1724.00	−0.161908
$485$	6650.00	0.622600
$486$	4160.00	0.388275
$487$	−13672.0	−1.27215	−0.636075	−	0.771627i	$-0.719443\pi$
$487$	−13672.0	−1.27215	−0.636075	+	0.771627i	$0.719443\pi$
$488$	2248.00	0.208529
$489$	2036.00	0.188284
$490$	0	0
$491$	−2448.00	−0.225003	−0.112502	−	0.993652i	$-0.535886\pi$
$491$	−2448.00	−0.225003	−0.112502	+	0.993652i	$0.535886\pi$
$492$	−1692.00	−0.155043
$493$	6696.00	0.611709
$494$	176.000	0.0160296
$495$	−3900.00	−0.354125
$496$	−640.000	−0.0579372
$497$	0	0
$498$	−1194.00	−0.107439
$499$	−13846.0	−1.24215	−0.621074	−	0.783752i	$-0.713303\pi$
$499$	−13846.0	−1.24215	−0.621074	+	0.783752i	$0.713303\pi$
$500$	−500.000	−0.0447214
$501$	−303.000	−0.0270200
$502$	14520.0	1.29095
$503$	−5295.00	−0.469369	−0.234684	−	0.972072i	$-0.575406\pi$
$503$	−5295.00	−0.469369	−0.234684	+	0.972072i	$0.575406\pi$
$504$	0	0
$505$	−5175.00	−0.456009
$506$	10980.0	0.964665
$507$	−261.000	−0.0228628
$508$	8576.00	0.749013
$509$	6225.00	0.542079	0.271040	−	0.962568i	$-0.412633\pi$
$509$	6225.00	0.542079	0.271040	+	0.962568i	$0.412633\pi$
$510$	240.000	0.0208380
$511$	0	0
$512$	512.000	0.0441942
$513$	−106.000	−0.00912283
$514$	−13392.0	−1.14921
$515$	−4135.00	−0.353806
$516$	1220.00	0.104084
$517$	−13680.0	−1.16372
$518$	0	0
$519$	3816.00	0.322743
$520$	−1760.00	−0.148425
$521$	14862.0	1.24974	0.624871	−	0.780728i	$-0.285151\pi$
$521$	14862.0	1.24974	0.624871	+	0.780728i	$0.285151\pi$
$522$	14508.0	1.21647
$523$	4412.00	0.368878	0.184439	−	0.982844i	$-0.440953\pi$
$523$	4412.00	0.368878	0.184439	+	0.982844i	$0.440953\pi$
$524$	−9600.00	−0.800340
$525$	0	0
$526$	5166.00	0.428229
$527$	960.000	0.0793515
$528$	−480.000	−0.0395631
$529$	21322.0	1.75245
$530$	1980.00	0.162275
$531$	12012.0	0.981688
$532$	0	0
$533$	−18612.0	−1.51252
$534$	2034.00	0.164831
$535$	−405.000	−0.0327284
$536$	−3992.00	−0.321694
$537$	2256.00	0.181292
$538$	−11370.0	−0.911144
$539$	0	0
$540$	1060.00	0.0844725
$541$	−19045.0	−1.51351	−0.756755	−	0.653699i	$-0.773216\pi$
$541$	−19045.0	−1.51351	−0.756755	+	0.653699i	$0.773216\pi$
$542$	13252.0	1.05023
$543$	1895.00	0.149765
$544$	−768.000	−0.0605289
$545$	−1075.00	−0.0844916
$546$	0	0
$547$	8309.00	0.649483	0.324741	−	0.945803i	$-0.394723\pi$
$547$	8309.00	0.649483	0.324741	+	0.945803i	$0.394723\pi$
$548$	3888.00	0.303079
$549$	−7306.00	−0.567964
$550$	−1500.00	−0.116291
$551$	−558.000	−0.0431426
$552$	−1464.00	−0.112884
$553$	0	0
$554$	−8384.00	−0.642964
$555$	380.000	0.0290632
$556$	632.000	0.0482064
$557$	−15018.0	−1.14243	−0.571215	−	0.820801i	$-0.693528\pi$
$557$	−15018.0	−1.14243	−0.571215	+	0.820801i	$0.693528\pi$
$558$	2080.00	0.157802
$559$	13420.0	1.01539
$560$	0	0
$561$	720.000	0.0541861
$562$	−5004.00	−0.375589
$563$	−7677.00	−0.574684	−0.287342	−	0.957828i	$-0.592772\pi$
$563$	−7677.00	−0.574684	−0.287342	+	0.957828i	$0.592772\pi$
$564$	1824.00	0.136178
$565$	−1950.00	−0.145198
$566$	3208.00	0.238237
$567$	0	0
$568$	−4272.00	−0.315579
$569$	−2442.00	−0.179919	−0.0899595	−	0.995945i	$-0.528674\pi$
$569$	−2442.00	−0.179919	−0.0899595	+	0.995945i	$0.528674\pi$
$570$	−20.0000	−0.00146966
$571$	14570.0	1.06784	0.533919	−	0.845536i	$-0.320719\pi$
$571$	14570.0	1.06784	0.533919	+	0.845536i	$0.320719\pi$
$572$	−5280.00	−0.385958
$573$	3930.00	0.286524
$574$	0	0
$575$	−4575.00	−0.331810
$576$	−1664.00	−0.120370
$577$	−24622.0	−1.77648	−0.888239	−	0.459383i	$-0.848071\pi$
$577$	−24622.0	−1.77648	−0.888239	+	0.459383i	$0.848071\pi$
$578$	−8674.00	−0.624206
$579$	1370.00	0.0983338
$580$	5580.00	0.399477
$581$	0	0
$582$	−2660.00	−0.189451
$583$	5940.00	0.421972
$584$	6400.00	0.453483
$585$	5720.00	0.404261
$586$	15384.0	1.08448
$587$	9396.00	0.660672	0.330336	−	0.943863i	$-0.392838\pi$
$587$	9396.00	0.660672	0.330336	+	0.943863i	$0.392838\pi$
$588$	0	0
$589$	−80.0000	−0.00559651
$590$	4620.00	0.322377
$591$	−1326.00	−0.0922916
$592$	−1216.00	−0.0844211
$593$	−1314.00	−0.0909941	−0.0454971	−	0.998964i	$-0.514487\pi$
$593$	−1314.00	−0.0909941	−0.0454971	+	0.998964i	$0.514487\pi$
$594$	3180.00	0.219658
$595$	0	0
$596$	1740.00	0.119586
$597$	−1132.00	−0.0776041
$598$	−16104.0	−1.10124
$599$	924.000	0.0630277	0.0315139	−	0.999503i	$-0.489967\pi$
$599$	924.000	0.0630277	0.0315139	+	0.999503i	$0.489967\pi$
$600$	200.000	0.0136083
$601$	11618.0	0.788533	0.394266	−	0.918996i	$-0.370999\pi$
$601$	11618.0	0.788533	0.394266	+	0.918996i	$0.370999\pi$
$602$	0	0
$603$	12974.0	0.876189
$604$	5264.00	0.354618
$605$	2155.00	0.144815
$606$	2070.00	0.138759
$607$	−8845.00	−0.591446	−0.295723	−	0.955274i	$-0.595560\pi$
$607$	−8845.00	−0.591446	−0.295723	+	0.955274i	$0.595560\pi$
$608$	64.0000	0.00426898
$609$	0	0
$610$	−2810.00	−0.186514
$611$	20064.0	1.32848
$612$	2496.00	0.164861
$613$	4304.00	0.283584	0.141792	−	0.989896i	$-0.454714\pi$
$613$	4304.00	0.283584	0.141792	+	0.989896i	$0.454714\pi$
$614$	−13766.0	−0.904805
$615$	2115.00	0.138675
$616$	0	0
$617$	540.000	0.0352343	0.0176172	−	0.999845i	$-0.494392\pi$
$617$	540.000	0.0352343	0.0176172	+	0.999845i	$0.494392\pi$
$618$	1654.00	0.107660
$619$	3350.00	0.217525	0.108762	−	0.994068i	$-0.465311\pi$
$619$	3350.00	0.217525	0.108762	+	0.994068i	$0.465311\pi$
$620$	800.000	0.0518206
$621$	9699.00	0.626743
$622$	13932.0	0.898107
$623$	0	0
$624$	704.000	0.0451644
$625$	625.000	0.0400000
$626$	−13472.0	−0.860143
$627$	−60.0000	−0.00382164
$628$	−15256.0	−0.969396
$629$	1824.00	0.115624
$630$	0	0
$631$	23006.0	1.45143	0.725717	−	0.687994i	$-0.241508\pi$
$631$	23006.0	1.45143	0.725717	+	0.687994i	$0.241508\pi$
$632$	−6320.00	−0.397779
$633$	−4138.00	−0.259827
$634$	−6312.00	−0.395397
$635$	−10720.0	−0.669937
$636$	−792.000	−0.0493787
$637$	0	0
$638$	16740.0	1.03878
$639$	13884.0	0.859535
$640$	−640.000	−0.0395285
$641$	−15195.0	−0.936297	−0.468149	−	0.883650i	$-0.655079\pi$
$641$	−15195.0	−0.936297	−0.468149	+	0.883650i	$0.655079\pi$
$642$	162.000	0.00995893
$643$	15740.0	0.965358	0.482679	−	0.875797i	$-0.339664\pi$
$643$	15740.0	0.965358	0.482679	+	0.875797i	$0.339664\pi$
$644$	0	0
$645$	−1525.00	−0.0930958
$646$	−96.0000	−0.00584686
$647$	10647.0	0.646950	0.323475	−	0.946237i	$-0.395149\pi$
$647$	10647.0	0.646950	0.323475	+	0.946237i	$0.395149\pi$
$648$	5192.00	0.314755
$649$	13860.0	0.838294
$650$	2200.00	0.132756
$651$	0	0
$652$	8144.00	0.489177
$653$	−12264.0	−0.734958	−0.367479	−	0.930032i	$-0.619779\pi$
$653$	−12264.0	−0.734958	−0.367479	+	0.930032i	$0.619779\pi$
$654$	430.000	0.0257100
$655$	12000.0	0.715845
$656$	−6768.00	−0.402814
$657$	−20800.0	−1.23514
$658$	0	0
$659$	8550.00	0.505403	0.252702	−	0.967544i	$-0.418681\pi$
$659$	8550.00	0.505403	0.252702	+	0.967544i	$0.418681\pi$
$660$	600.000	0.0353863
$661$	15749.0	0.926725	0.463362	−	0.886169i	$-0.346643\pi$
$661$	15749.0	0.926725	0.463362	+	0.886169i	$0.346643\pi$
$662$	21448.0	1.25921
$663$	−1056.00	−0.0618577
$664$	−4776.00	−0.279134
$665$	0	0
$666$	3952.00	0.229935
$667$	51057.0	2.96392
$668$	−1212.00	−0.0702001
$669$	−484.000	−0.0279709
$670$	4990.00	0.287732
$671$	−8430.00	−0.485002
$672$	0	0
$673$	18320.0	1.04931	0.524654	−	0.851316i	$-0.324195\pi$
$673$	18320.0	1.04931	0.524654	+	0.851316i	$0.324195\pi$
$674$	5572.00	0.318435
$675$	−1325.00	−0.0755545
$676$	−1044.00	−0.0593992
$677$	−6924.00	−0.393074	−0.196537	−	0.980496i	$-0.562970\pi$
$677$	−6924.00	−0.393074	−0.196537	+	0.980496i	$0.562970\pi$
$678$	780.000	0.0441825
$679$	0	0
$680$	960.000	0.0541387
$681$	−2676.00	−0.150579
$682$	2400.00	0.134752
$683$	17025.0	0.953797	0.476899	−	0.878958i	$-0.341761\pi$
$683$	17025.0	0.953797	0.476899	+	0.878958i	$0.341761\pi$
$684$	−208.000	−0.0116273
$685$	−4860.00	−0.271082
$686$	0	0
$687$	1190.00	0.0660864
$688$	4880.00	0.270419
$689$	−8712.00	−0.481714
$690$	1830.00	0.100967
$691$	4010.00	0.220764	0.110382	−	0.993889i	$-0.464793\pi$
$691$	4010.00	0.220764	0.110382	+	0.993889i	$0.464793\pi$
$692$	15264.0	0.838512
$693$	0	0
$694$	1074.00	0.0587442
$695$	−790.000	−0.0431171
$696$	−2232.00	−0.121557
$697$	10152.0	0.551699
$698$	−22982.0	−1.24625
$699$	−5052.00	−0.273368
$700$	0	0
$701$	−29151.0	−1.57064	−0.785320	−	0.619091i	$-0.787501\pi$
$701$	−29151.0	−1.57064	−0.785320	+	0.619091i	$0.787501\pi$
$702$	−4664.00	−0.250757
$703$	−152.000	−0.00815475
$704$	−1920.00	−0.102788
$705$	−2280.00	−0.121801
$706$	12084.0	0.644175
$707$	0	0
$708$	−1848.00	−0.0980962
$709$	3269.00	0.173159	0.0865796	−	0.996245i	$-0.472406\pi$
$709$	3269.00	0.173159	0.0865796	+	0.996245i	$0.472406\pi$
$710$	5340.00	0.282263
$711$	20540.0	1.08342
$712$	8136.00	0.428244
$713$	7320.00	0.384483
$714$	0	0
$715$	6600.00	0.345211
$716$	9024.00	0.471009
$717$	1140.00	0.0593781
$718$	−11232.0	−0.583809
$719$	30.0000	0.00155607	0.000778033	−	1.00000i	$-0.499752\pi$
$719$	30.0000	0.00155607	0.000778033		1.00000i	$0.499752\pi$
$720$	2080.00	0.107663
$721$	0	0
$722$	−13710.0	−0.706694
$723$	2018.00	0.103804
$724$	7580.00	0.389100
$725$	−6975.00	−0.357303
$726$	−862.000	−0.0440659
$727$	−15583.0	−0.794968	−0.397484	−	0.917609i	$-0.630117\pi$
$727$	−15583.0	−0.794968	−0.397484	+	0.917609i	$0.630117\pi$
$728$	0	0
$729$	−15443.0	−0.784586
$730$	−8000.00	−0.405607
$731$	−7320.00	−0.370369
$732$	1124.00	0.0567544
$733$	−22858.0	−1.15181	−0.575907	−	0.817515i	$-0.695351\pi$
$733$	−22858.0	−1.15181	−0.575907	+	0.817515i	$0.695351\pi$
$734$	−20642.0	−1.03802
$735$	0	0
$736$	−5856.00	−0.293281
$737$	14970.0	0.748205
$738$	21996.0	1.09713
$739$	19802.0	0.985695	0.492847	−	0.870116i	$-0.335956\pi$
$739$	19802.0	0.985695	0.492847	+	0.870116i	$0.335956\pi$
$740$	1520.00	0.0755085
$741$	88.0000	0.00436270
$742$	0	0
$743$	−10029.0	−0.495193	−0.247596	−	0.968863i	$-0.579641\pi$
$743$	−10029.0	−0.495193	−0.247596	+	0.968863i	$0.579641\pi$
$744$	−320.000	−0.0157685
$745$	−2175.00	−0.106961
$746$	−18392.0	−0.902653
$747$	15522.0	0.760268
$748$	2880.00	0.140780
$749$	0	0
$750$	−250.000	−0.0121716
$751$	30404.0	1.47731	0.738654	−	0.674085i	$-0.235462\pi$
$751$	30404.0	1.47731	0.738654	+	0.674085i	$0.235462\pi$
$752$	7296.00	0.353800
$753$	7260.00	0.351353
$754$	−24552.0	−1.18585
$755$	−6580.00	−0.317180
$756$	0	0
$757$	24428.0	1.17285	0.586427	−	0.810002i	$-0.300534\pi$
$757$	24428.0	1.17285	0.586427	+	0.810002i	$0.300534\pi$
$758$	−3956.00	−0.189563
$759$	5490.00	0.262549
$760$	−80.0000	−0.00381830
$761$	4890.00	0.232933	0.116467	−	0.993195i	$-0.462843\pi$
$761$	4890.00	0.232933	0.116467	+	0.993195i	$0.462843\pi$
$762$	4288.00	0.203855
$763$	0	0
$764$	15720.0	0.744411
$765$	−3120.00	−0.147456
$766$	−9174.00	−0.432729
$767$	−20328.0	−0.956977
$768$	256.000	0.0120281
$769$	26306.0	1.23357	0.616787	−	0.787130i	$-0.288434\pi$
$769$	26306.0	1.23357	0.616787	+	0.787130i	$0.288434\pi$
$770$	0	0
$771$	−6696.00	−0.312776
$772$	5480.00	0.255479
$773$	−8724.00	−0.405926	−0.202963	−	0.979186i	$-0.565057\pi$
$773$	−8724.00	−0.405926	−0.202963	+	0.979186i	$0.565057\pi$
$774$	−15860.0	−0.736532
$775$	−1000.00	−0.0463498
$776$	−10640.0	−0.492208
$777$	0	0
$778$	−25644.0	−1.18172
$779$	−846.000	−0.0389103
$780$	−880.000	−0.0403962
$781$	16020.0	0.733983
$782$	8784.00	0.401682
$783$	14787.0	0.674897
$784$	0	0
$785$	19070.0	0.867054
$786$	−4800.00	−0.217825
$787$	−5443.00	−0.246534	−0.123267	−	0.992374i	$-0.539337\pi$
$787$	−5443.00	−0.246534	−0.123267	+	0.992374i	$0.539337\pi$
$788$	−5304.00	−0.239781
$789$	2583.00	0.116549
$790$	7900.00	0.355784
$791$	0	0
$792$	6240.00	0.279961
$793$	12364.0	0.553668
$794$	−1268.00	−0.0566746
$795$	990.000	0.0441656
$796$	−4528.00	−0.201621
$797$	22584.0	1.00372	0.501861	−	0.864948i	$-0.332649\pi$
$797$	22584.0	1.00372	0.501861	+	0.864948i	$0.332649\pi$
$798$	0	0
$799$	−10944.0	−0.484569
$800$	800.000	0.0353553
$801$	−26442.0	−1.16639
$802$	−9954.00	−0.438264
$803$	−24000.0	−1.05472
$804$	−1996.00	−0.0875541
$805$	0	0
$806$	−3520.00	−0.153830
$807$	−5685.00	−0.247982
$808$	8280.00	0.360507
$809$	−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
$811$	−21544.0	−0.932814	−0.466407	−	0.884570i	$-0.654452\pi$
$811$	−21544.0	−0.932814	−0.466407	+	0.884570i	$0.654452\pi$
$812$	0	0
$813$	6626.00	0.285835
$814$	4560.00	0.196349
$815$	−10180.0	−0.437534
$816$	−384.000	−0.0164739
$817$	610.000	0.0261214
$818$	29254.0	1.25042
$819$	0	0
$820$	8460.00	0.360288
$821$	−17802.0	−0.756753	−0.378376	−	0.925652i	$-0.623518\pi$
$821$	−17802.0	−0.756753	−0.378376	+	0.925652i	$0.623518\pi$
$822$	1944.00	0.0824876
$823$	28505.0	1.20732	0.603658	−	0.797243i	$-0.293709\pi$
$823$	28505.0	1.20732	0.603658	+	0.797243i	$0.293709\pi$
$824$	6616.00	0.279708
$825$	−750.000	−0.0316505
$826$	0	0
$827$	−11289.0	−0.474676	−0.237338	−	0.971427i	$-0.576275\pi$
$827$	−11289.0	−0.474676	−0.237338	+	0.971427i	$0.576275\pi$
$828$	19032.0	0.798802
$829$	10346.0	0.433452	0.216726	−	0.976233i	$-0.430462\pi$
$829$	10346.0	0.433452	0.216726	+	0.976233i	$0.430462\pi$
$830$	5970.00	0.249665
$831$	−4192.00	−0.174993
$832$	2816.00	0.117340
$833$	0	0
$834$	316.000	0.0131201
$835$	1515.00	0.0627889
$836$	−240.000	−0.00992892
$837$	2120.00	0.0875483
$838$	28320.0	1.16742
$839$	48138.0	1.98082	0.990410	−	0.138158i	$-0.0441182\pi$
$839$	48138.0	1.98082	0.990410	+	0.138158i	$0.0441182\pi$
$840$	0	0
$841$	53452.0	2.19164
$842$	−1958.00	−0.0801391
$843$	−2502.00	−0.102222
$844$	−16552.0	−0.675051
$845$	1305.00	0.0531282
$846$	−23712.0	−0.963635
$847$	0	0
$848$	−3168.00	−0.128290
$849$	1604.00	0.0648400
$850$	−1200.00	−0.0484231
$851$	13908.0	0.560235
$852$	−2136.00	−0.0858899
$853$	−13390.0	−0.537473	−0.268737	−	0.963214i	$-0.586606\pi$
$853$	−13390.0	−0.537473	−0.268737	+	0.963214i	$0.586606\pi$
$854$	0	0
$855$	260.000	0.0103998
$856$	648.000	0.0258740
$857$	38502.0	1.53466	0.767330	−	0.641253i	$-0.221585\pi$
$857$	38502.0	1.53466	0.767330	+	0.641253i	$0.221585\pi$
$858$	−2640.00	−0.105044
$859$	34040.0	1.35207	0.676036	−	0.736869i	$-0.263696\pi$
$859$	34040.0	1.35207	0.676036	+	0.736869i	$0.263696\pi$
$860$	−6100.00	−0.241870
$861$	0	0
$862$	−25956.0	−1.02560
$863$	−42993.0	−1.69583	−0.847914	−	0.530135i	$-0.822141\pi$
$863$	−42993.0	−1.69583	−0.847914	+	0.530135i	$0.822141\pi$
$864$	−1696.00	−0.0667814
$865$	−19080.0	−0.749988
$866$	−17804.0	−0.698620
$867$	−4337.00	−0.169887
$868$	0	0
$869$	23700.0	0.925164
$870$	2790.00	0.108724
$871$	−21956.0	−0.854134
$872$	1720.00	0.0667965
$873$	34580.0	1.34061
$874$	−732.000	−0.0283298
$875$	0	0
$876$	3200.00	0.123422
$877$	3962.00	0.152551	0.0762755	−	0.997087i	$-0.475697\pi$
$877$	3962.00	0.152551	0.0762755	+	0.997087i	$0.475697\pi$
$878$	−12056.0	−0.463406
$879$	7692.00	0.295159
$880$	2400.00	0.0919363
$881$	−1503.00	−0.0574771	−0.0287386	−	0.999587i	$-0.509149\pi$
$881$	−1503.00	−0.0574771	−0.0287386	+	0.999587i	$0.509149\pi$
$882$	0	0
$883$	17732.0	0.675798	0.337899	−	0.941182i	$-0.390284\pi$
$883$	17732.0	0.675798	0.337899	+	0.941182i	$0.390284\pi$
$884$	−4224.00	−0.160711
$885$	2310.00	0.0877399
$886$	23802.0	0.902533
$887$	−24177.0	−0.915202	−0.457601	−	0.889158i	$-0.651291\pi$
$887$	−24177.0	−0.915202	−0.457601	+	0.889158i	$0.651291\pi$
$888$	−608.000	−0.0229765
$889$	0	0
$890$	−10170.0	−0.383033
$891$	−19470.0	−0.732065
$892$	−1936.00	−0.0726705
$893$	912.000	0.0341757
$894$	870.000	0.0325472
$895$	−11280.0	−0.421284
$896$	0	0
$897$	−8052.00	−0.299720
$898$	−13026.0	−0.484057
$899$	11160.0	0.414023
$900$	−2600.00	−0.0962963
$901$	4752.00	0.175707
$902$	25380.0	0.936875
$903$	0	0
$904$	3120.00	0.114789
$905$	−9475.00	−0.348022
$906$	2632.00	0.0965147
$907$	18335.0	0.671228	0.335614	−	0.942000i	$-0.391056\pi$
$907$	18335.0	0.671228	0.335614	+	0.942000i	$0.391056\pi$
$908$	−10704.0	−0.391217
$909$	−26910.0	−0.981901
$910$	0	0
$911$	−30102.0	−1.09476	−0.547379	−	0.836885i	$-0.684374\pi$
$911$	−30102.0	−1.09476	−0.547379	+	0.836885i	$0.684374\pi$
$912$	32.0000	0.00116187
$913$	17910.0	0.649216
$914$	−28592.0	−1.03473
$915$	−1405.00	−0.0507627
$916$	4760.00	0.171697
$917$	0	0
$918$	2544.00	0.0914646
$919$	27614.0	0.991188	0.495594	−	0.868554i	$-0.334950\pi$
$919$	27614.0	0.991188	0.495594	+	0.868554i	$0.334950\pi$
$920$	7320.00	0.262319
$921$	−6883.00	−0.246257
$922$	−5388.00	−0.192456
$923$	−23496.0	−0.837898
$924$	0	0
$925$	−1900.00	−0.0675369
$926$	−32210.0	−1.14307
$927$	−21502.0	−0.761832
$928$	−8928.00	−0.315815
$929$	−10797.0	−0.381311	−0.190656	−	0.981657i	$-0.561061\pi$
$929$	−10797.0	−0.381311	−0.190656	+	0.981657i	$0.561061\pi$
$930$	400.000	0.0141038
$931$	0	0
$932$	−20208.0	−0.710231
$933$	6966.00	0.244434
$934$	−16686.0	−0.584564
$935$	−3600.00	−0.125917
$936$	−9152.00	−0.319597
$937$	−16732.0	−0.583362	−0.291681	−	0.956516i	$-0.594215\pi$
$937$	−16732.0	−0.583362	−0.291681	+	0.956516i	$0.594215\pi$
$938$	0	0
$939$	−6736.00	−0.234101
$940$	−9120.00	−0.316449
$941$	−35166.0	−1.21826	−0.609128	−	0.793072i	$-0.708480\pi$
$941$	−35166.0	−1.21826	−0.609128	+	0.793072i	$0.708480\pi$
$942$	−7628.00	−0.263836
$943$	77409.0	2.67315
$944$	−7392.00	−0.254861
$945$	0	0
$946$	−18300.0	−0.628947
$947$	−1851.00	−0.0635158	−0.0317579	−	0.999496i	$-0.510111\pi$
$947$	−1851.00	−0.0635158	−0.0317579	+	0.999496i	$0.510111\pi$
$948$	−3160.00	−0.108262
$949$	35200.0	1.20405
$950$	100.000	0.00341519
$951$	−3156.00	−0.107613
$952$	0	0
$953$	−35292.0	−1.19960	−0.599801	−	0.800149i	$-0.704753\pi$
$953$	−35292.0	−1.19960	−0.599801	+	0.800149i	$0.704753\pi$
$954$	10296.0	0.349419
$955$	−19650.0	−0.665821
$956$	4560.00	0.154269
$957$	8370.00	0.282721
$958$	−20856.0	−0.703368
$959$	0	0
$960$	−320.000	−0.0107583
$961$	−28191.0	−0.946293
$962$	−6688.00	−0.224147
$963$	−2106.00	−0.0704724
$964$	8072.00	0.269690
$965$	−6850.00	−0.228507
$966$	0	0
$967$	−21241.0	−0.706375	−0.353187	−	0.935553i	$-0.614902\pi$
$967$	−21241.0	−0.706375	−0.353187	+	0.935553i	$0.614902\pi$
$968$	−3448.00	−0.114486
$969$	−48.0000	−0.00159131
$970$	13300.0	0.440245
$971$	−7320.00	−0.241926	−0.120963	−	0.992657i	$-0.538598\pi$
$971$	−7320.00	−0.241926	−0.120963	+	0.992657i	$0.538598\pi$
$972$	8320.00	0.274552
$973$	0	0
$974$	−27344.0	−0.899546
$975$	1100.00	0.0361315
$976$	4496.00	0.147452
$977$	−38718.0	−1.26786	−0.633930	−	0.773391i	$-0.718559\pi$
$977$	−38718.0	−1.26786	−0.633930	+	0.773391i	$0.718559\pi$
$978$	4072.00	0.133137
$979$	−30510.0	−0.996020
$980$	0	0
$981$	−5590.00	−0.181932
$982$	−4896.00	−0.159101
$983$	15795.0	0.512495	0.256247	−	0.966611i	$-0.417514\pi$
$983$	15795.0	0.512495	0.256247	+	0.966611i	$0.417514\pi$
$984$	−3384.00	−0.109632
$985$	6630.00	0.214466
$986$	13392.0	0.432544
$987$	0	0
$988$	352.000	0.0113346
$989$	−55815.0	−1.79455
$990$	−7800.00	−0.250404
$991$	−35116.0	−1.12563	−0.562814	−	0.826584i	$-0.690281\pi$
$991$	−35116.0	−1.12563	−0.562814	+	0.826584i	$0.690281\pi$
$992$	−1280.00	−0.0409678
$993$	10724.0	0.342715
$994$	0	0
$995$	5660.00	0.180336
$996$	−2388.00	−0.0759706
$997$	46718.0	1.48403	0.742013	−	0.670386i	$-0.233871\pi$
$997$	46718.0	1.48403	0.742013	+	0.670386i	$0.233871\pi$
$998$	−27692.0	−0.878332
$999$	4028.00	0.127568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.m.1.1		1
5.4	even	2		2450.4.a.j.1.1		1
7.2	even	3		70.4.e.a.11.1	✓	2
7.3	odd	6		490.4.e.f.471.1		2
7.4	even	3		70.4.e.a.51.1	yes	2
7.5	odd	6		490.4.e.f.361.1		2
7.6	odd	2		490.4.a.k.1.1		1
21.2	odd	6		630.4.k.i.361.1		2
21.11	odd	6		630.4.k.i.541.1		2
28.11	odd	6		560.4.q.e.401.1		2
28.23	odd	6		560.4.q.e.81.1		2
35.2	odd	12		350.4.j.f.249.2		4
35.4	even	6		350.4.e.g.51.1		2
35.9	even	6		350.4.e.g.151.1		2
35.18	odd	12		350.4.j.f.149.2		4
35.23	odd	12		350.4.j.f.249.1		4
35.32	odd	12		350.4.j.f.149.1		4
35.34	odd	2		2450.4.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.a.11.1	✓	2	7.2	even	3
70.4.e.a.51.1	yes	2	7.4	even	3
350.4.e.g.51.1		2	35.4	even	6
350.4.e.g.151.1		2	35.9	even	6
350.4.j.f.149.1		4	35.32	odd	12
350.4.j.f.149.2		4	35.18	odd	12
350.4.j.f.249.1		4	35.23	odd	12
350.4.j.f.249.2		4	35.2	odd	12
490.4.a.k.1.1		1	7.6	odd	2
490.4.a.m.1.1		1	1.1	even	1	trivial
490.4.e.f.361.1		2	7.5	odd	6
490.4.e.f.471.1		2	7.3	odd	6
560.4.q.e.81.1		2	28.23	odd	6
560.4.q.e.401.1		2	28.11	odd	6
630.4.k.i.361.1		2	21.2	odd	6
630.4.k.i.541.1		2	21.11	odd	6
2450.4.a.j.1.1		1	5.4	even	2
2450.4.a.m.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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