LMFDB - Embedded newform 98.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,4,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	98.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:	$5.78218718056$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} +12.0000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +2.00000 q^{3} +4.00000 q^{4} +12.0000 q^{5} +4.00000 q^{6} +8.00000 q^{8} -23.0000 q^{9} +24.0000 q^{10} +48.0000 q^{11} +8.00000 q^{12} -56.0000 q^{13} +24.0000 q^{15} +16.0000 q^{16} +114.000 q^{17} -46.0000 q^{18} -2.00000 q^{19} +48.0000 q^{20} +96.0000 q^{22} -120.000 q^{23} +16.0000 q^{24} +19.0000 q^{25} -112.000 q^{26} -100.000 q^{27} -54.0000 q^{29} +48.0000 q^{30} -236.000 q^{31} +32.0000 q^{32} +96.0000 q^{33} +228.000 q^{34} -92.0000 q^{36} +146.000 q^{37} -4.00000 q^{38} -112.000 q^{39} +96.0000 q^{40} -126.000 q^{41} -376.000 q^{43} +192.000 q^{44} -276.000 q^{45} -240.000 q^{46} +12.0000 q^{47} +32.0000 q^{48} +38.0000 q^{50} +228.000 q^{51} -224.000 q^{52} +174.000 q^{53} -200.000 q^{54} +576.000 q^{55} -4.00000 q^{57} -108.000 q^{58} -138.000 q^{59} +96.0000 q^{60} -380.000 q^{61} -472.000 q^{62} +64.0000 q^{64} -672.000 q^{65} +192.000 q^{66} -484.000 q^{67} +456.000 q^{68} -240.000 q^{69} +576.000 q^{71} -184.000 q^{72} +1150.00 q^{73} +292.000 q^{74} +38.0000 q^{75} -8.00000 q^{76} -224.000 q^{78} +776.000 q^{79} +192.000 q^{80} +421.000 q^{81} -252.000 q^{82} -378.000 q^{83} +1368.00 q^{85} -752.000 q^{86} -108.000 q^{87} +384.000 q^{88} +390.000 q^{89} -552.000 q^{90} -480.000 q^{92} -472.000 q^{93} +24.0000 q^{94} -24.0000 q^{95} +64.0000 q^{96} +1330.00 q^{97} -1104.00 q^{99} +O(q^{100})\)

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
$3$	2.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	2.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	4.00000	0.500000
$5$	12.0000	1.07331	0.536656	−	0.843801i	$-0.319687\pi$
$5$	12.0000	1.07331	0.536656	+	0.843801i	$0.319687\pi$
$6$	4.00000	0.272166
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	−23.0000	−0.851852
$10$	24.0000	0.758947
$11$	48.0000	1.31569	0.657843	−	0.753155i	$-0.271469\pi$
$11$	48.0000	1.31569	0.657843	+	0.753155i	$0.271469\pi$
$12$	8.00000	0.192450
$13$	−56.0000	−1.19474	−0.597369	−	0.801966i	$-0.703787\pi$
$13$	−56.0000	−1.19474	−0.597369	+	0.801966i	$0.703787\pi$
$14$	0	0
$15$	24.0000	0.413118
$16$	16.0000	0.250000
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	−46.0000	−0.602350
$19$	−2.00000	−0.0241490	−0.0120745	−	0.999927i	$-0.503844\pi$
$19$	−2.00000	−0.0241490	−0.0120745	+	0.999927i	$0.503844\pi$
$20$	48.0000	0.536656
$21$	0	0
$22$	96.0000	0.930330
$23$	−120.000	−1.08790	−0.543951	−	0.839117i	$-0.683072\pi$
$23$	−120.000	−1.08790	−0.543951	+	0.839117i	$0.683072\pi$
$24$	16.0000	0.136083
$25$	19.0000	0.152000
$26$	−112.000	−0.844808
$27$	−100.000	−0.712778
$28$	0	0
$29$	−54.0000	−0.345778	−0.172889	−	0.984941i	$-0.555310\pi$
$29$	−54.0000	−0.345778	−0.172889	+	0.984941i	$0.555310\pi$
$30$	48.0000	0.292119
$31$	−236.000	−1.36732	−0.683659	−	0.729802i	$-0.739612\pi$
$31$	−236.000	−1.36732	−0.683659	+	0.729802i	$0.739612\pi$
$32$	32.0000	0.176777
$33$	96.0000	0.506408
$34$	228.000	1.15005
$35$	0	0
$36$	−92.0000	−0.425926
$37$	146.000	0.648710	0.324355	−	0.945936i	$-0.394853\pi$
$37$	146.000	0.648710	0.324355	+	0.945936i	$0.394853\pi$
$38$	−4.00000	−0.0170759
$39$	−112.000	−0.459855
$40$	96.0000	0.379473
$41$	−126.000	−0.479949	−0.239974	−	0.970779i	$-0.577139\pi$
$41$	−126.000	−0.479949	−0.239974	+	0.970779i	$0.577139\pi$
$42$	0	0
$43$	−376.000	−1.33348	−0.666738	−	0.745292i	$-0.732310\pi$
$43$	−376.000	−1.33348	−0.666738	+	0.745292i	$0.732310\pi$
$44$	192.000	0.657843
$45$	−276.000	−0.914303
$46$	−240.000	−0.769262
$47$	12.0000	0.0372421	0.0186211	−	0.999827i	$-0.494072\pi$
$47$	12.0000	0.0372421	0.0186211	+	0.999827i	$0.494072\pi$
$48$	32.0000	0.0962250
$49$	0	0
$50$	38.0000	0.107480
$51$	228.000	0.626008
$52$	−224.000	−0.597369
$53$	174.000	0.450957	0.225479	−	0.974248i	$-0.427605\pi$
$53$	174.000	0.450957	0.225479	+	0.974248i	$0.427605\pi$
$54$	−200.000	−0.504010
$55$	576.000	1.41214
$56$	0	0
$57$	−4.00000	−0.00929496
$58$	−108.000	−0.244502
$59$	−138.000	−0.304510	−0.152255	−	0.988341i	$-0.548653\pi$
$59$	−138.000	−0.304510	−0.152255	+	0.988341i	$0.548653\pi$
$60$	96.0000	0.206559
$61$	−380.000	−0.797607	−0.398803	−	0.917036i	$-0.630574\pi$
$61$	−380.000	−0.797607	−0.398803	+	0.917036i	$0.630574\pi$
$62$	−472.000	−0.966840
$63$	0	0
$64$	64.0000	0.125000
$65$	−672.000	−1.28233
$66$	192.000	0.358084
$67$	−484.000	−0.882537	−0.441269	−	0.897375i	$-0.645471\pi$
$67$	−484.000	−0.882537	−0.441269	+	0.897375i	$0.645471\pi$
$68$	456.000	0.813208
$69$	−240.000	−0.418733
$70$	0	0
$71$	576.000	0.962798	0.481399	−	0.876502i	$-0.340129\pi$
$71$	576.000	0.962798	0.481399	+	0.876502i	$0.340129\pi$
$72$	−184.000	−0.301175
$73$	1150.00	1.84380	0.921899	−	0.387429i	$-0.126637\pi$
$73$	1150.00	1.84380	0.921899	+	0.387429i	$0.126637\pi$
$74$	292.000	0.458707
$75$	38.0000	0.0585048
$76$	−8.00000	−0.0120745
$77$	0	0
$78$	−224.000	−0.325167
$79$	776.000	1.10515	0.552575	−	0.833463i	$-0.313645\pi$
$79$	776.000	1.10515	0.552575	+	0.833463i	$0.313645\pi$
$80$	192.000	0.268328
$81$	421.000	0.577503
$82$	−252.000	−0.339375
$83$	−378.000	−0.499890	−0.249945	−	0.968260i	$-0.580413\pi$
$83$	−378.000	−0.499890	−0.249945	+	0.968260i	$0.580413\pi$
$84$	0	0
$85$	1368.00	1.74565
$86$	−752.000	−0.942910
$87$	−108.000	−0.133090
$88$	384.000	0.465165
$89$	390.000	0.464493	0.232247	−	0.972657i	$-0.425392\pi$
$89$	390.000	0.464493	0.232247	+	0.972657i	$0.425392\pi$
$90$	−552.000	−0.646510
$91$	0	0
$92$	−480.000	−0.543951
$93$	−472.000	−0.526281
$94$	24.0000	0.0263342
$95$	−24.0000	−0.0259195
$96$	64.0000	0.0680414
$97$	1330.00	1.39218	0.696088	−	0.717957i	$-0.254922\pi$
$97$	1330.00	1.39218	0.696088	+	0.717957i	$0.254922\pi$
$98$	0	0
$99$	−1104.00	−1.12077
$100$	76.0000	0.0760000
$101$	1500.00	1.47778	0.738889	−	0.673827i	$-0.235351\pi$
$101$	1500.00	1.47778	0.738889	+	0.673827i	$0.235351\pi$
$102$	456.000	0.442654
$103$	−380.000	−0.363520	−0.181760	−	0.983343i	$-0.558179\pi$
$103$	−380.000	−0.363520	−0.181760	+	0.983343i	$0.558179\pi$
$104$	−448.000	−0.422404
$105$	0	0
$106$	348.000	0.318875
$107$	636.000	0.574621	0.287310	−	0.957838i	$-0.407239\pi$
$107$	636.000	0.574621	0.287310	+	0.957838i	$0.407239\pi$
$108$	−400.000	−0.356389
$109$	146.000	0.128296	0.0641480	−	0.997940i	$-0.479567\pi$
$109$	146.000	0.128296	0.0641480	+	0.997940i	$0.479567\pi$
$110$	1152.00	0.998535
$111$	292.000	0.249688
$112$	0	0
$113$	198.000	0.164834	0.0824171	−	0.996598i	$-0.473736\pi$
$113$	198.000	0.164834	0.0824171	+	0.996598i	$0.473736\pi$
$114$	−8.00000	−0.00657253
$115$	−1440.00	−1.16766
$116$	−216.000	−0.172889
$117$	1288.00	1.01774
$118$	−276.000	−0.215321
$119$	0	0
$120$	192.000	0.146059
$121$	973.000	0.731029
$122$	−760.000	−0.563993
$123$	−252.000	−0.184732
$124$	−944.000	−0.683659
$125$	−1272.00	−0.910169
$126$	0	0
$127$	−376.000	−0.262713	−0.131357	−	0.991335i	$-0.541933\pi$
$127$	−376.000	−0.262713	−0.131357	+	0.991335i	$0.541933\pi$
$128$	128.000	0.0883883
$129$	−752.000	−0.513255
$130$	−1344.00	−0.906743
$131$	−2130.00	−1.42060	−0.710301	−	0.703898i	$-0.751441\pi$
$131$	−2130.00	−1.42060	−0.710301	+	0.703898i	$0.751441\pi$
$132$	384.000	0.253204
$133$	0	0
$134$	−968.000	−0.624048
$135$	−1200.00	−0.765034
$136$	912.000	0.575025
$137$	−78.0000	−0.0486423	−0.0243211	−	0.999704i	$-0.507742\pi$
$137$	−78.0000	−0.0486423	−0.0243211	+	0.999704i	$0.507742\pi$
$138$	−480.000	−0.296089
$139$	2338.00	1.42667	0.713333	−	0.700825i	$-0.247185\pi$
$139$	2338.00	1.42667	0.713333	+	0.700825i	$0.247185\pi$
$140$	0	0
$141$	24.0000	0.0143345
$142$	1152.00	0.680801
$143$	−2688.00	−1.57190
$144$	−368.000	−0.212963
$145$	−648.000	−0.371127
$146$	2300.00	1.30376
$147$	0	0
$148$	584.000	0.324355
$149$	−1002.00	−0.550920	−0.275460	−	0.961313i	$-0.588830\pi$
$149$	−1002.00	−0.550920	−0.275460	+	0.961313i	$0.588830\pi$
$150$	76.0000	0.0413692
$151$	−2752.00	−1.48314	−0.741571	−	0.670874i	$-0.765919\pi$
$151$	−2752.00	−1.48314	−0.741571	+	0.670874i	$0.765919\pi$
$152$	−16.0000	−0.00853797
$153$	−2622.00	−1.38546
$154$	0	0
$155$	−2832.00	−1.46756
$156$	−448.000	−0.229928
$157$	520.000	0.264335	0.132167	−	0.991227i	$-0.457806\pi$
$157$	520.000	0.264335	0.132167	+	0.991227i	$0.457806\pi$
$158$	1552.00	0.781459
$159$	348.000	0.173574
$160$	384.000	0.189737
$161$	0	0
$162$	842.000	0.408357
$163$	1280.00	0.615076	0.307538	−	0.951536i	$-0.400495\pi$
$163$	1280.00	0.615076	0.307538	+	0.951536i	$0.400495\pi$
$164$	−504.000	−0.239974
$165$	1152.00	0.543534
$166$	−756.000	−0.353476
$167$	−1764.00	−0.817380	−0.408690	−	0.912673i	$-0.634014\pi$
$167$	−1764.00	−0.817380	−0.408690	+	0.912673i	$0.634014\pi$
$168$	0	0
$169$	939.000	0.427401
$170$	2736.00	1.23436
$171$	46.0000	0.0205714
$172$	−1504.00	−0.666738
$173$	768.000	0.337514	0.168757	−	0.985658i	$-0.446025\pi$
$173$	768.000	0.337514	0.168757	+	0.985658i	$0.446025\pi$
$174$	−216.000	−0.0941087
$175$	0	0
$176$	768.000	0.328921
$177$	−276.000	−0.117206
$178$	780.000	0.328446
$179$	1812.00	0.756621	0.378311	−	0.925679i	$-0.376505\pi$
$179$	1812.00	0.756621	0.378311	+	0.925679i	$0.376505\pi$
$180$	−1104.00	−0.457152
$181$	448.000	0.183976	0.0919878	−	0.995760i	$-0.470678\pi$
$181$	448.000	0.183976	0.0919878	+	0.995760i	$0.470678\pi$
$182$	0	0
$183$	−760.000	−0.306999
$184$	−960.000	−0.384631
$185$	1752.00	0.696268
$186$	−944.000	−0.372137
$187$	5472.00	2.13985
$188$	48.0000	0.0186211
$189$	0	0
$190$	−48.0000	−0.0183278
$191$	−2136.00	−0.809191	−0.404596	−	0.914496i	$-0.632588\pi$
$191$	−2136.00	−0.809191	−0.404596	+	0.914496i	$0.632588\pi$
$192$	128.000	0.0481125
$193$	4430.00	1.65222	0.826110	−	0.563509i	$-0.190549\pi$
$193$	4430.00	1.65222	0.826110	+	0.563509i	$0.190549\pi$
$194$	2660.00	0.984417
$195$	−1344.00	−0.493568
$196$	0	0
$197$	198.000	0.0716087	0.0358044	−	0.999359i	$-0.488601\pi$
$197$	198.000	0.0716087	0.0358044	+	0.999359i	$0.488601\pi$
$198$	−2208.00	−0.792504
$199$	2284.00	0.813610	0.406805	−	0.913515i	$-0.366643\pi$
$199$	2284.00	0.813610	0.406805	+	0.913515i	$0.366643\pi$
$200$	152.000	0.0537401
$201$	−968.000	−0.339689
$202$	3000.00	1.04495
$203$	0	0
$204$	912.000	0.313004
$205$	−1512.00	−0.515135
$206$	−760.000	−0.257047
$207$	2760.00	0.926731
$208$	−896.000	−0.298685
$209$	−96.0000	−0.0317725
$210$	0	0
$211$	4412.00	1.43950	0.719750	−	0.694233i	$-0.244256\pi$
$211$	4412.00	1.43950	0.719750	+	0.694233i	$0.244256\pi$
$212$	696.000	0.225479
$213$	1152.00	0.370581
$214$	1272.00	0.406318
$215$	−4512.00	−1.43124
$216$	−800.000	−0.252005
$217$	0	0
$218$	292.000	0.0907190
$219$	2300.00	0.709679
$220$	2304.00	0.706071
$221$	−6384.00	−1.94314
$222$	584.000	0.176556
$223$	−2072.00	−0.622204	−0.311102	−	0.950377i	$-0.600698\pi$
$223$	−2072.00	−0.622204	−0.311102	+	0.950377i	$0.600698\pi$
$224$	0	0
$225$	−437.000	−0.129481
$226$	396.000	0.116555
$227$	366.000	0.107014	0.0535072	−	0.998567i	$-0.482960\pi$
$227$	366.000	0.107014	0.0535072	+	0.998567i	$0.482960\pi$
$228$	−16.0000	−0.00464748
$229$	376.000	0.108501	0.0542506	−	0.998527i	$-0.482723\pi$
$229$	376.000	0.108501	0.0542506	+	0.998527i	$0.482723\pi$
$230$	−2880.00	−0.825659
$231$	0	0
$232$	−432.000	−0.122251
$233$	−2262.00	−0.636002	−0.318001	−	0.948090i	$-0.603012\pi$
$233$	−2262.00	−0.636002	−0.318001	+	0.948090i	$0.603012\pi$
$234$	2576.00	0.719651
$235$	144.000	0.0399724
$236$	−552.000	−0.152255
$237$	1552.00	0.425372
$238$	0	0
$239$	2592.00	0.701517	0.350758	−	0.936466i	$-0.385924\pi$
$239$	2592.00	0.701517	0.350758	+	0.936466i	$0.385924\pi$
$240$	384.000	0.103280
$241$	−110.000	−0.0294013	−0.0147007	−	0.999892i	$-0.504680\pi$
$241$	−110.000	−0.0294013	−0.0147007	+	0.999892i	$0.504680\pi$
$242$	1946.00	0.516916
$243$	3542.00	0.935059
$244$	−1520.00	−0.398803
$245$	0	0
$246$	−504.000	−0.130625
$247$	112.000	0.0288518
$248$	−1888.00	−0.483420
$249$	−756.000	−0.192408
$250$	−2544.00	−0.643587
$251$	1890.00	0.475282	0.237641	−	0.971353i	$-0.423626\pi$
$251$	1890.00	0.475282	0.237641	+	0.971353i	$0.423626\pi$
$252$	0	0
$253$	−5760.00	−1.43134
$254$	−752.000	−0.185766
$255$	2736.00	0.671902
$256$	256.000	0.0625000
$257$	−2130.00	−0.516987	−0.258494	−	0.966013i	$-0.583226\pi$
$257$	−2130.00	−0.516987	−0.258494	+	0.966013i	$0.583226\pi$
$258$	−1504.00	−0.362926
$259$	0	0
$260$	−2688.00	−0.641164
$261$	1242.00	0.294551
$262$	−4260.00	−1.00452
$263$	−4992.00	−1.17042	−0.585209	−	0.810883i	$-0.698988\pi$
$263$	−4992.00	−1.17042	−0.585209	+	0.810883i	$0.698988\pi$
$264$	768.000	0.179042
$265$	2088.00	0.484018
$266$	0	0
$267$	780.000	0.178784
$268$	−1936.00	−0.441269
$269$	−6816.00	−1.54490	−0.772451	−	0.635074i	$-0.780970\pi$
$269$	−6816.00	−1.54490	−0.772451	+	0.635074i	$0.780970\pi$
$270$	−2400.00	−0.540961
$271$	−8192.00	−1.83627	−0.918134	−	0.396270i	$-0.870304\pi$
$271$	−8192.00	−1.83627	−0.918134	+	0.396270i	$0.870304\pi$
$272$	1824.00	0.406604
$273$	0	0
$274$	−156.000	−0.0343953
$275$	912.000	0.199984
$276$	−960.000	−0.209367
$277$	2414.00	0.523622	0.261811	−	0.965119i	$-0.415680\pi$
$277$	2414.00	0.523622	0.261811	+	0.965119i	$0.415680\pi$
$278$	4676.00	1.00881
$279$	5428.00	1.16475
$280$	0	0
$281$	1962.00	0.416524	0.208262	−	0.978073i	$-0.433219\pi$
$281$	1962.00	0.416524	0.208262	+	0.978073i	$0.433219\pi$
$282$	48.0000	0.0101360
$283$	−5402.00	−1.13468	−0.567342	−	0.823482i	$-0.692028\pi$
$283$	−5402.00	−1.13468	−0.567342	+	0.823482i	$0.692028\pi$
$284$	2304.00	0.481399
$285$	−48.0000	−0.00997640
$286$	−5376.00	−1.11150
$287$	0	0
$288$	−736.000	−0.150588
$289$	8083.00	1.64523
$290$	−1296.00	−0.262427
$291$	2660.00	0.535849
$292$	4600.00	0.921899
$293$	4788.00	0.954669	0.477334	−	0.878722i	$-0.341603\pi$
$293$	4788.00	0.954669	0.477334	+	0.878722i	$0.341603\pi$
$294$	0	0
$295$	−1656.00	−0.326834
$296$	1168.00	0.229353
$297$	−4800.00	−0.937792
$298$	−2004.00	−0.389559
$299$	6720.00	1.29976
$300$	152.000	0.0292524
$301$	0	0
$302$	−5504.00	−1.04874
$303$	3000.00	0.568797
$304$	−32.0000	−0.00603726
$305$	−4560.00	−0.856081
$306$	−5244.00	−0.979672
$307$	574.000	0.106710	0.0533549	−	0.998576i	$-0.483009\pi$
$307$	574.000	0.106710	0.0533549	+	0.998576i	$0.483009\pi$
$308$	0	0
$309$	−760.000	−0.139919
$310$	−5664.00	−1.03772
$311$	8808.00	1.60597	0.802984	−	0.596001i	$-0.203245\pi$
$311$	8808.00	1.60597	0.802984	+	0.596001i	$0.203245\pi$
$312$	−896.000	−0.162583
$313$	2770.00	0.500223	0.250111	−	0.968217i	$-0.419533\pi$
$313$	2770.00	0.500223	0.250111	+	0.968217i	$0.419533\pi$
$314$	1040.00	0.186913
$315$	0	0
$316$	3104.00	0.552575
$317$	7566.00	1.34053	0.670266	−	0.742121i	$-0.266180\pi$
$317$	7566.00	1.34053	0.670266	+	0.742121i	$0.266180\pi$
$318$	696.000	0.122735
$319$	−2592.00	−0.454935
$320$	768.000	0.134164
$321$	1272.00	0.221172
$322$	0	0
$323$	−228.000	−0.0392763
$324$	1684.00	0.288752
$325$	−1064.00	−0.181600
$326$	2560.00	0.434924
$327$	292.000	0.0493812
$328$	−1008.00	−0.169687
$329$	0	0
$330$	2304.00	0.384336
$331$	−11320.0	−1.87977	−0.939884	−	0.341493i	$-0.889068\pi$
$331$	−11320.0	−1.87977	−0.939884	+	0.341493i	$0.889068\pi$
$332$	−1512.00	−0.249945
$333$	−3358.00	−0.552604
$334$	−3528.00	−0.577975
$335$	−5808.00	−0.947239
$336$	0	0
$337$	−4786.00	−0.773620	−0.386810	−	0.922159i	$-0.626423\pi$
$337$	−4786.00	−0.773620	−0.386810	+	0.922159i	$0.626423\pi$
$338$	1878.00	0.302218
$339$	396.000	0.0634447
$340$	5472.00	0.872826
$341$	−11328.0	−1.79896
$342$	92.0000	0.0145462
$343$	0	0
$344$	−3008.00	−0.471455
$345$	−2880.00	−0.449432
$346$	1536.00	0.238659
$347$	12648.0	1.95672	0.978358	−	0.206921i	$-0.0663443\pi$
$347$	12648.0	1.95672	0.978358	+	0.206921i	$0.0663443\pi$
$348$	−432.000	−0.0665449
$349$	−9632.00	−1.47733	−0.738666	−	0.674071i	$-0.764544\pi$
$349$	−9632.00	−1.47733	−0.738666	+	0.674071i	$0.764544\pi$
$350$	0	0
$351$	5600.00	0.851584
$352$	1536.00	0.232583
$353$	3390.00	0.511137	0.255569	−	0.966791i	$-0.417737\pi$
$353$	3390.00	0.511137	0.255569	+	0.966791i	$0.417737\pi$
$354$	−552.000	−0.0828770
$355$	6912.00	1.03338
$356$	1560.00	0.232247
$357$	0	0
$358$	3624.00	0.535012
$359$	−10704.0	−1.57364	−0.786818	−	0.617185i	$-0.788273\pi$
$359$	−10704.0	−1.57364	−0.786818	+	0.617185i	$0.788273\pi$
$360$	−2208.00	−0.323255
$361$	−6855.00	−0.999417
$362$	896.000	0.130090
$363$	1946.00	0.281373
$364$	0	0
$365$	13800.0	1.97897
$366$	−1520.00	−0.217081
$367$	8584.00	1.22093	0.610465	−	0.792043i	$-0.290983\pi$
$367$	8584.00	1.22093	0.610465	+	0.792043i	$0.290983\pi$
$368$	−1920.00	−0.271975
$369$	2898.00	0.408845
$370$	3504.00	0.492336
$371$	0	0
$372$	−1888.00	−0.263140
$373$	−2122.00	−0.294566	−0.147283	−	0.989094i	$-0.547053\pi$
$373$	−2122.00	−0.294566	−0.147283	+	0.989094i	$0.547053\pi$
$374$	10944.0	1.51310
$375$	−2544.00	−0.350324
$376$	96.0000	0.0131671
$377$	3024.00	0.413114
$378$	0	0
$379$	−4912.00	−0.665732	−0.332866	−	0.942974i	$-0.608016\pi$
$379$	−4912.00	−0.665732	−0.332866	+	0.942974i	$0.608016\pi$
$380$	−96.0000	−0.0129597
$381$	−752.000	−0.101118
$382$	−4272.00	−0.572185
$383$	−9060.00	−1.20873	−0.604366	−	0.796707i	$-0.706574\pi$
$383$	−9060.00	−1.20873	−0.604366	+	0.796707i	$0.706574\pi$
$384$	256.000	0.0340207
$385$	0	0
$386$	8860.00	1.16830
$387$	8648.00	1.13592
$388$	5320.00	0.696088
$389$	8994.00	1.17227	0.586136	−	0.810213i	$-0.300648\pi$
$389$	8994.00	1.17227	0.586136	+	0.810213i	$0.300648\pi$
$390$	−2688.00	−0.349006
$391$	−13680.0	−1.76938
$392$	0	0
$393$	−4260.00	−0.546790
$394$	396.000	0.0506350
$395$	9312.00	1.18617
$396$	−4416.00	−0.560385
$397$	12976.0	1.64042	0.820210	−	0.572062i	$-0.193857\pi$
$397$	12976.0	1.64042	0.820210	+	0.572062i	$0.193857\pi$
$398$	4568.00	0.575309
$399$	0	0
$400$	304.000	0.0380000
$401$	−3522.00	−0.438604	−0.219302	−	0.975657i	$-0.570378\pi$
$401$	−3522.00	−0.438604	−0.219302	+	0.975657i	$0.570378\pi$
$402$	−1936.00	−0.240196
$403$	13216.0	1.63359
$404$	6000.00	0.738889
$405$	5052.00	0.619842
$406$	0	0
$407$	7008.00	0.853498
$408$	1824.00	0.221327
$409$	−12710.0	−1.53660	−0.768300	−	0.640090i	$-0.778897\pi$
$409$	−12710.0	−1.53660	−0.768300	+	0.640090i	$0.778897\pi$
$410$	−3024.00	−0.364255
$411$	−156.000	−0.0187224
$412$	−1520.00	−0.181760
$413$	0	0
$414$	5520.00	0.655298
$415$	−4536.00	−0.536539
$416$	−1792.00	−0.211202
$417$	4676.00	0.549124
$418$	−192.000	−0.0224666
$419$	−1638.00	−0.190982	−0.0954911	−	0.995430i	$-0.530442\pi$
$419$	−1638.00	−0.190982	−0.0954911	+	0.995430i	$0.530442\pi$
$420$	0	0
$421$	−12850.0	−1.48758	−0.743789	−	0.668414i	$-0.766973\pi$
$421$	−12850.0	−1.48758	−0.743789	+	0.668414i	$0.766973\pi$
$422$	8824.00	1.01788
$423$	−276.000	−0.0317248
$424$	1392.00	0.159437
$425$	2166.00	0.247215
$426$	2304.00	0.262040
$427$	0	0
$428$	2544.00	0.287310
$429$	−5376.00	−0.605025
$430$	−9024.00	−1.01204
$431$	−8016.00	−0.895863	−0.447932	−	0.894068i	$-0.647839\pi$
$431$	−8016.00	−0.895863	−0.447932	+	0.894068i	$0.647839\pi$
$432$	−1600.00	−0.178195
$433$	−2198.00	−0.243947	−0.121974	−	0.992533i	$-0.538922\pi$
$433$	−2198.00	−0.243947	−0.121974	+	0.992533i	$0.538922\pi$
$434$	0	0
$435$	−1296.00	−0.142847
$436$	584.000	0.0641480
$437$	240.000	0.0262718
$438$	4600.00	0.501818
$439$	376.000	0.0408781	0.0204391	−	0.999791i	$-0.493494\pi$
$439$	376.000	0.0408781	0.0204391	+	0.999791i	$0.493494\pi$
$440$	4608.00	0.499268
$441$	0	0
$442$	−12768.0	−1.37401
$443$	7188.00	0.770908	0.385454	−	0.922727i	$-0.374045\pi$
$443$	7188.00	0.770908	0.385454	+	0.922727i	$0.374045\pi$
$444$	1168.00	0.124844
$445$	4680.00	0.498547
$446$	−4144.00	−0.439964
$447$	−2004.00	−0.212049
$448$	0	0
$449$	−14670.0	−1.54192	−0.770958	−	0.636886i	$-0.780222\pi$
$449$	−14670.0	−1.54192	−0.770958	+	0.636886i	$0.780222\pi$
$450$	−874.000	−0.0915572
$451$	−6048.00	−0.631462
$452$	792.000	0.0824171
$453$	−5504.00	−0.570862
$454$	732.000	0.0756706
$455$	0	0
$456$	−32.0000	−0.00328627
$457$	−5146.00	−0.526739	−0.263370	−	0.964695i	$-0.584834\pi$
$457$	−5146.00	−0.526739	−0.263370	+	0.964695i	$0.584834\pi$
$458$	752.000	0.0767219
$459$	−11400.0	−1.15927
$460$	−5760.00	−0.583829
$461$	1512.00	0.152757	0.0763784	−	0.997079i	$-0.475664\pi$
$461$	1512.00	0.152757	0.0763784	+	0.997079i	$0.475664\pi$
$462$	0	0
$463$	7184.00	0.721099	0.360549	−	0.932740i	$-0.382589\pi$
$463$	7184.00	0.721099	0.360549	+	0.932740i	$0.382589\pi$
$464$	−864.000	−0.0864444
$465$	−5664.00	−0.564864
$466$	−4524.00	−0.449722
$467$	16518.0	1.63675	0.818375	−	0.574685i	$-0.194875\pi$
$467$	16518.0	1.63675	0.818375	+	0.574685i	$0.194875\pi$
$468$	5152.00	0.508870
$469$	0	0
$470$	288.000	0.0282648
$471$	1040.00	0.101742
$472$	−1104.00	−0.107660
$473$	−18048.0	−1.75444
$474$	3104.00	0.300784
$475$	−38.0000	−0.00367065
$476$	0	0
$477$	−4002.00	−0.384149
$478$	5184.00	0.496047
$479$	−10092.0	−0.962662	−0.481331	−	0.876539i	$-0.659847\pi$
$479$	−10092.0	−0.962662	−0.481331	+	0.876539i	$0.659847\pi$
$480$	768.000	0.0730297
$481$	−8176.00	−0.775038
$482$	−220.000	−0.0207899
$483$	0	0
$484$	3892.00	0.365515
$485$	15960.0	1.49424
$486$	7084.00	0.661187
$487$	7832.00	0.728751	0.364376	−	0.931252i	$-0.381282\pi$
$487$	7832.00	0.728751	0.364376	+	0.931252i	$0.381282\pi$
$488$	−3040.00	−0.281997
$489$	2560.00	0.236743
$490$	0	0
$491$	−6732.00	−0.618759	−0.309380	−	0.950939i	$-0.600121\pi$
$491$	−6732.00	−0.618759	−0.309380	+	0.950939i	$0.600121\pi$
$492$	−1008.00	−0.0923662
$493$	−6156.00	−0.562378
$494$	224.000	0.0204013
$495$	−13248.0	−1.20294
$496$	−3776.00	−0.341829
$497$	0	0
$498$	−1512.00	−0.136053
$499$	18668.0	1.67474	0.837369	−	0.546638i	$-0.184093\pi$
$499$	18668.0	1.67474	0.837369	+	0.546638i	$0.184093\pi$
$500$	−5088.00	−0.455085
$501$	−3528.00	−0.314610
$502$	3780.00	0.336075
$503$	6048.00	0.536117	0.268059	−	0.963403i	$-0.413618\pi$
$503$	6048.00	0.536117	0.268059	+	0.963403i	$0.413618\pi$
$504$	0	0
$505$	18000.0	1.58612
$506$	−11520.0	−1.01211
$507$	1878.00	0.164507
$508$	−1504.00	−0.131357
$509$	−11328.0	−0.986453	−0.493227	−	0.869901i	$-0.664183\pi$
$509$	−11328.0	−0.986453	−0.493227	+	0.869901i	$0.664183\pi$
$510$	5472.00	0.475106
$511$	0	0
$512$	512.000	0.0441942
$513$	200.000	0.0172129
$514$	−4260.00	−0.365565
$515$	−4560.00	−0.390170
$516$	−3008.00	−0.256628
$517$	576.000	0.0489989
$518$	0	0
$519$	1536.00	0.129909
$520$	−5376.00	−0.453372
$521$	4146.00	0.348636	0.174318	−	0.984689i	$-0.444228\pi$
$521$	4146.00	0.348636	0.174318	+	0.984689i	$0.444228\pi$
$522$	2484.00	0.208279
$523$	1006.00	0.0841096	0.0420548	−	0.999115i	$-0.486610\pi$
$523$	1006.00	0.0841096	0.0420548	+	0.999115i	$0.486610\pi$
$524$	−8520.00	−0.710301
$525$	0	0
$526$	−9984.00	−0.827610
$527$	−26904.0	−2.22383
$528$	1536.00	0.126602
$529$	2233.00	0.183529
$530$	4176.00	0.342253
$531$	3174.00	0.259397
$532$	0	0
$533$	7056.00	0.573413
$534$	1560.00	0.126419
$535$	7632.00	0.616748
$536$	−3872.00	−0.312024
$537$	3624.00	0.291224
$538$	−13632.0	−1.09241
$539$	0	0
$540$	−4800.00	−0.382517
$541$	−14722.0	−1.16996	−0.584980	−	0.811048i	$-0.698898\pi$
$541$	−14722.0	−1.16996	−0.584980	+	0.811048i	$0.698898\pi$
$542$	−16384.0	−1.29844
$543$	896.000	0.0708122
$544$	3648.00	0.287512
$545$	1752.00	0.137702
$546$	0	0
$547$	−13480.0	−1.05368	−0.526840	−	0.849964i	$-0.676623\pi$
$547$	−13480.0	−1.05368	−0.526840	+	0.849964i	$0.676623\pi$
$548$	−312.000	−0.0243211
$549$	8740.00	0.679443
$550$	1824.00	0.141410
$551$	108.000	0.00835019
$552$	−1920.00	−0.148045
$553$	0	0
$554$	4828.00	0.370256
$555$	3504.00	0.267994
$556$	9352.00	0.713333
$557$	6222.00	0.473312	0.236656	−	0.971594i	$-0.423949\pi$
$557$	6222.00	0.473312	0.236656	+	0.971594i	$0.423949\pi$
$558$	10856.0	0.823604
$559$	21056.0	1.59316
$560$	0	0
$561$	10944.0	0.823629
$562$	3924.00	0.294527
$563$	−4926.00	−0.368750	−0.184375	−	0.982856i	$-0.559026\pi$
$563$	−4926.00	−0.368750	−0.184375	+	0.982856i	$0.559026\pi$
$564$	96.0000	0.00716725
$565$	2376.00	0.176919
$566$	−10804.0	−0.802343
$567$	0	0
$568$	4608.00	0.340400
$569$	22182.0	1.63430	0.817151	−	0.576424i	$-0.195552\pi$
$569$	22182.0	1.63430	0.817151	+	0.576424i	$0.195552\pi$
$570$	−96.0000	−0.00705438
$571$	3296.00	0.241564	0.120782	−	0.992679i	$-0.461460\pi$
$571$	3296.00	0.241564	0.120782	+	0.992679i	$0.461460\pi$
$572$	−10752.0	−0.785951
$573$	−4272.00	−0.311458
$574$	0	0
$575$	−2280.00	−0.165361
$576$	−1472.00	−0.106481
$577$	24334.0	1.75570	0.877849	−	0.478938i	$-0.158978\pi$
$577$	24334.0	1.75570	0.877849	+	0.478938i	$0.158978\pi$
$578$	16166.0	1.16335
$579$	8860.00	0.635940
$580$	−2592.00	−0.185564
$581$	0	0
$582$	5320.00	0.378902
$583$	8352.00	0.593318
$584$	9200.00	0.651881
$585$	15456.0	1.09235
$586$	9576.00	0.675053
$587$	−1638.00	−0.115175	−0.0575873	−	0.998340i	$-0.518341\pi$
$587$	−1638.00	−0.115175	−0.0575873	+	0.998340i	$0.518341\pi$
$588$	0	0
$589$	472.000	0.0330194
$590$	−3312.00	−0.231107
$591$	396.000	0.0275622
$592$	2336.00	0.162177
$593$	7446.00	0.515633	0.257817	−	0.966194i	$-0.416997\pi$
$593$	7446.00	0.515633	0.257817	+	0.966194i	$0.416997\pi$
$594$	−9600.00	−0.663119
$595$	0	0
$596$	−4008.00	−0.275460
$597$	4568.00	0.313159
$598$	13440.0	0.919068
$599$	−6504.00	−0.443650	−0.221825	−	0.975087i	$-0.571201\pi$
$599$	−6504.00	−0.443650	−0.221825	+	0.975087i	$0.571201\pi$
$600$	304.000	0.0206846
$601$	−16058.0	−1.08988	−0.544941	−	0.838474i	$-0.683448\pi$
$601$	−16058.0	−1.08988	−0.544941	+	0.838474i	$0.683448\pi$
$602$	0	0
$603$	11132.0	0.751791
$604$	−11008.0	−0.741571
$605$	11676.0	0.784623
$606$	6000.00	0.402200
$607$	−10208.0	−0.682586	−0.341293	−	0.939957i	$-0.610865\pi$
$607$	−10208.0	−0.682586	−0.341293	+	0.939957i	$0.610865\pi$
$608$	−64.0000	−0.00426898
$609$	0	0
$610$	−9120.00	−0.605341
$611$	−672.000	−0.0444946
$612$	−10488.0	−0.692732
$613$	−14974.0	−0.986614	−0.493307	−	0.869855i	$-0.664212\pi$
$613$	−14974.0	−0.986614	−0.493307	+	0.869855i	$0.664212\pi$
$614$	1148.00	0.0754552
$615$	−3024.00	−0.198276
$616$	0	0
$617$	7254.00	0.473314	0.236657	−	0.971593i	$-0.423948\pi$
$617$	7254.00	0.473314	0.236657	+	0.971593i	$0.423948\pi$
$618$	−1520.00	−0.0989375
$619$	−12458.0	−0.808933	−0.404466	−	0.914553i	$-0.632543\pi$
$619$	−12458.0	−0.808933	−0.404466	+	0.914553i	$0.632543\pi$
$620$	−11328.0	−0.733780
$621$	12000.0	0.775432
$622$	17616.0	1.13559
$623$	0	0
$624$	−1792.00	−0.114964
$625$	−17639.0	−1.12890
$626$	5540.00	0.353711
$627$	−192.000	−0.0122293
$628$	2080.00	0.132167
$629$	16644.0	1.05507
$630$	0	0
$631$	28352.0	1.78871	0.894354	−	0.447359i	$-0.147635\pi$
$631$	28352.0	1.78871	0.894354	+	0.447359i	$0.147635\pi$
$632$	6208.00	0.390729
$633$	8824.00	0.554064
$634$	15132.0	0.947900
$635$	−4512.00	−0.281974
$636$	1392.00	0.0867868
$637$	0	0
$638$	−5184.00	−0.321687
$639$	−13248.0	−0.820161
$640$	1536.00	0.0948683
$641$	27390.0	1.68774	0.843869	−	0.536549i	$-0.180272\pi$
$641$	27390.0	1.68774	0.843869	+	0.536549i	$0.180272\pi$
$642$	2544.00	0.156392
$643$	21490.0	1.31801	0.659007	−	0.752137i	$-0.270977\pi$
$643$	21490.0	1.31801	0.659007	+	0.752137i	$0.270977\pi$
$644$	0	0
$645$	−9024.00	−0.550883
$646$	−456.000	−0.0277726
$647$	−17652.0	−1.07260	−0.536300	−	0.844028i	$-0.680178\pi$
$647$	−17652.0	−1.07260	−0.536300	+	0.844028i	$0.680178\pi$
$648$	3368.00	0.204178
$649$	−6624.00	−0.400639
$650$	−2128.00	−0.128411
$651$	0	0
$652$	5120.00	0.307538
$653$	−4782.00	−0.286576	−0.143288	−	0.989681i	$-0.545768\pi$
$653$	−4782.00	−0.286576	−0.143288	+	0.989681i	$0.545768\pi$
$654$	584.000	0.0349177
$655$	−25560.0	−1.52475
$656$	−2016.00	−0.119987
$657$	−26450.0	−1.57064
$658$	0	0
$659$	−27144.0	−1.60452	−0.802261	−	0.596973i	$-0.796370\pi$
$659$	−27144.0	−1.60452	−0.802261	+	0.596973i	$0.796370\pi$
$660$	4608.00	0.271767
$661$	11860.0	0.697883	0.348941	−	0.937145i	$-0.386541\pi$
$661$	11860.0	0.697883	0.348941	+	0.937145i	$0.386541\pi$
$662$	−22640.0	−1.32920
$663$	−12768.0	−0.747916
$664$	−3024.00	−0.176738
$665$	0	0
$666$	−6716.00	−0.390750
$667$	6480.00	0.376172
$668$	−7056.00	−0.408690
$669$	−4144.00	−0.239486
$670$	−11616.0	−0.669799
$671$	−18240.0	−1.04940
$672$	0	0
$673$	5546.00	0.317656	0.158828	−	0.987306i	$-0.449228\pi$
$673$	5546.00	0.317656	0.158828	+	0.987306i	$0.449228\pi$
$674$	−9572.00	−0.547032
$675$	−1900.00	−0.108342
$676$	3756.00	0.213701
$677$	14880.0	0.844734	0.422367	−	0.906425i	$-0.361199\pi$
$677$	14880.0	0.844734	0.422367	+	0.906425i	$0.361199\pi$
$678$	792.000	0.0448622
$679$	0	0
$680$	10944.0	0.617181
$681$	732.000	0.0411899
$682$	−22656.0	−1.27206
$683$	20964.0	1.17447	0.587237	−	0.809415i	$-0.300216\pi$
$683$	20964.0	1.17447	0.587237	+	0.809415i	$0.300216\pi$
$684$	184.000	0.0102857
$685$	−936.000	−0.0522084
$686$	0	0
$687$	752.000	0.0417621
$688$	−6016.00	−0.333369
$689$	−9744.00	−0.538776
$690$	−5760.00	−0.317796
$691$	−13106.0	−0.721528	−0.360764	−	0.932657i	$-0.617484\pi$
$691$	−13106.0	−0.721528	−0.360764	+	0.932657i	$0.617484\pi$
$692$	3072.00	0.168757
$693$	0	0
$694$	25296.0	1.38361
$695$	28056.0	1.53126
$696$	−864.000	−0.0470544
$697$	−14364.0	−0.780596
$698$	−19264.0	−1.04463
$699$	−4524.00	−0.244797
$700$	0	0
$701$	−4590.00	−0.247307	−0.123653	−	0.992325i	$-0.539461\pi$
$701$	−4590.00	−0.247307	−0.123653	+	0.992325i	$0.539461\pi$
$702$	11200.0	0.602161
$703$	−292.000	−0.0156657
$704$	3072.00	0.164461
$705$	288.000	0.0153854
$706$	6780.00	0.361429
$707$	0	0
$708$	−1104.00	−0.0586029
$709$	−862.000	−0.0456602	−0.0228301	−	0.999739i	$-0.507268\pi$
$709$	−862.000	−0.0456602	−0.0228301	+	0.999739i	$0.507268\pi$
$710$	13824.0	0.730712
$711$	−17848.0	−0.941424
$712$	3120.00	0.164223
$713$	28320.0	1.48751
$714$	0	0
$715$	−32256.0	−1.68714
$716$	7248.00	0.378311
$717$	5184.00	0.270014
$718$	−21408.0	−1.11273
$719$	3540.00	0.183616	0.0918079	−	0.995777i	$-0.470735\pi$
$719$	3540.00	0.183616	0.0918079	+	0.995777i	$0.470735\pi$
$720$	−4416.00	−0.228576
$721$	0	0
$722$	−13710.0	−0.706694
$723$	−220.000	−0.0113166
$724$	1792.00	0.0919878
$725$	−1026.00	−0.0525582
$726$	3892.00	0.198961
$727$	4228.00	0.215692	0.107846	−	0.994168i	$-0.465605\pi$
$727$	4228.00	0.215692	0.107846	+	0.994168i	$0.465605\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	27600.0	1.39934
$731$	−42864.0	−2.16879
$732$	−3040.00	−0.153499
$733$	−5420.00	−0.273114	−0.136557	−	0.990632i	$-0.543604\pi$
$733$	−5420.00	−0.273114	−0.136557	+	0.990632i	$0.543604\pi$
$734$	17168.0	0.863328
$735$	0	0
$736$	−3840.00	−0.192316
$737$	−23232.0	−1.16114
$738$	5796.00	0.289097
$739$	1280.00	0.0637152	0.0318576	−	0.999492i	$-0.489858\pi$
$739$	1280.00	0.0637152	0.0318576	+	0.999492i	$0.489858\pi$
$740$	7008.00	0.348134
$741$	224.000	0.0111051
$742$	0	0
$743$	−35712.0	−1.76332	−0.881660	−	0.471886i	$-0.843573\pi$
$743$	−35712.0	−1.76332	−0.881660	+	0.471886i	$0.843573\pi$
$744$	−3776.00	−0.186068
$745$	−12024.0	−0.591309
$746$	−4244.00	−0.208289
$747$	8694.00	0.425832
$748$	21888.0	1.06993
$749$	0	0
$750$	−5088.00	−0.247717
$751$	24464.0	1.18869	0.594344	−	0.804211i	$-0.297412\pi$
$751$	24464.0	1.18869	0.594344	+	0.804211i	$0.297412\pi$
$752$	192.000	0.00931053
$753$	3780.00	0.182936
$754$	6048.00	0.292116
$755$	−33024.0	−1.59188
$756$	0	0
$757$	30242.0	1.45200	0.726000	−	0.687695i	$-0.241377\pi$
$757$	30242.0	1.45200	0.726000	+	0.687695i	$0.241377\pi$
$758$	−9824.00	−0.470744
$759$	−11520.0	−0.550922
$760$	−192.000	−0.00916391
$761$	2154.00	0.102605	0.0513025	−	0.998683i	$-0.483663\pi$
$761$	2154.00	0.102605	0.0513025	+	0.998683i	$0.483663\pi$
$762$	−1504.00	−0.0715015
$763$	0	0
$764$	−8544.00	−0.404596
$765$	−31464.0	−1.48704
$766$	−18120.0	−0.854703
$767$	7728.00	0.363810
$768$	512.000	0.0240563
$769$	−10262.0	−0.481219	−0.240609	−	0.970622i	$-0.577347\pi$
$769$	−10262.0	−0.481219	−0.240609	+	0.970622i	$0.577347\pi$
$770$	0	0
$771$	−4260.00	−0.198989
$772$	17720.0	0.826110
$773$	−9084.00	−0.422676	−0.211338	−	0.977413i	$-0.567782\pi$
$773$	−9084.00	−0.422676	−0.211338	+	0.977413i	$0.567782\pi$
$774$	17296.0	0.803219
$775$	−4484.00	−0.207832
$776$	10640.0	0.492208
$777$	0	0
$778$	17988.0	0.828922
$779$	252.000	0.0115903
$780$	−5376.00	−0.246784
$781$	27648.0	1.26674
$782$	−27360.0	−1.25114
$783$	5400.00	0.246463
$784$	0	0
$785$	6240.00	0.283714
$786$	−8520.00	−0.386639
$787$	19798.0	0.896725	0.448362	−	0.893852i	$-0.352007\pi$
$787$	19798.0	0.896725	0.448362	+	0.893852i	$0.352007\pi$
$788$	792.000	0.0358044
$789$	−9984.00	−0.450494
$790$	18624.0	0.838750
$791$	0	0
$792$	−8832.00	−0.396252
$793$	21280.0	0.952932
$794$	25952.0	1.15995
$795$	4176.00	0.186299
$796$	9136.00	0.406805
$797$	−30240.0	−1.34398	−0.671992	−	0.740558i	$-0.734561\pi$
$797$	−30240.0	−1.34398	−0.671992	+	0.740558i	$0.734561\pi$
$798$	0	0
$799$	1368.00	0.0605712
$800$	608.000	0.0268701
$801$	−8970.00	−0.395680
$802$	−7044.00	−0.310140
$803$	55200.0	2.42586
$804$	−3872.00	−0.169844
$805$	0	0
$806$	26432.0	1.15512
$807$	−13632.0	−0.594633
$808$	12000.0	0.522473
$809$	−2346.00	−0.101954	−0.0509771	−	0.998700i	$-0.516234\pi$
$809$	−2346.00	−0.101954	−0.0509771	+	0.998700i	$0.516234\pi$
$810$	10104.0	0.438294
$811$	29806.0	1.29054	0.645271	−	0.763953i	$-0.276744\pi$
$811$	29806.0	1.29054	0.645271	+	0.763953i	$0.276744\pi$
$812$	0	0
$813$	−16384.0	−0.706780
$814$	14016.0	0.603514
$815$	15360.0	0.660169
$816$	3648.00	0.156502
$817$	752.000	0.0322021
$818$	−25420.0	−1.08654
$819$	0	0
$820$	−6048.00	−0.257567
$821$	−1506.00	−0.0640192	−0.0320096	−	0.999488i	$-0.510191\pi$
$821$	−1506.00	−0.0640192	−0.0320096	+	0.999488i	$0.510191\pi$
$822$	−312.000	−0.0132387
$823$	−20392.0	−0.863694	−0.431847	−	0.901947i	$-0.642138\pi$
$823$	−20392.0	−0.863694	−0.431847	+	0.901947i	$0.642138\pi$
$824$	−3040.00	−0.128524
$825$	1824.00	0.0769740
$826$	0	0
$827$	36108.0	1.51826	0.759128	−	0.650941i	$-0.225626\pi$
$827$	36108.0	1.51826	0.759128	+	0.650941i	$0.225626\pi$
$828$	11040.0	0.463365
$829$	13876.0	0.581343	0.290672	−	0.956823i	$-0.406121\pi$
$829$	13876.0	0.581343	0.290672	+	0.956823i	$0.406121\pi$
$830$	−9072.00	−0.379390
$831$	4828.00	0.201542
$832$	−3584.00	−0.149342
$833$	0	0
$834$	9352.00	0.388289
$835$	−21168.0	−0.877304
$836$	−384.000	−0.0158863
$837$	23600.0	0.974594
$838$	−3276.00	−0.135045
$839$	−23436.0	−0.964363	−0.482182	−	0.876071i	$-0.660155\pi$
$839$	−23436.0	−0.964363	−0.482182	+	0.876071i	$0.660155\pi$
$840$	0	0
$841$	−21473.0	−0.880438
$842$	−25700.0	−1.05188
$843$	3924.00	0.160320
$844$	17648.0	0.719750
$845$	11268.0	0.458735
$846$	−552.000	−0.0224328
$847$	0	0
$848$	2784.00	0.112739
$849$	−10804.0	−0.436740
$850$	4332.00	0.174807
$851$	−17520.0	−0.705732
$852$	4608.00	0.185290
$853$	−8120.00	−0.325936	−0.162968	−	0.986631i	$-0.552107\pi$
$853$	−8120.00	−0.325936	−0.162968	+	0.986631i	$0.552107\pi$
$854$	0	0
$855$	552.000	0.0220795
$856$	5088.00	0.203159
$857$	50010.0	1.99336	0.996680	−	0.0814218i	$-0.0259461\pi$
$857$	50010.0	1.99336	0.996680	+	0.0814218i	$0.0259461\pi$
$858$	−10752.0	−0.427817
$859$	−34526.0	−1.37138	−0.685688	−	0.727896i	$-0.740499\pi$
$859$	−34526.0	−1.37138	−0.685688	+	0.727896i	$0.740499\pi$
$860$	−18048.0	−0.715618
$861$	0	0
$862$	−16032.0	−0.633471
$863$	−17256.0	−0.680650	−0.340325	−	0.940308i	$-0.610537\pi$
$863$	−17256.0	−0.680650	−0.340325	+	0.940308i	$0.610537\pi$
$864$	−3200.00	−0.126003
$865$	9216.00	0.362258
$866$	−4396.00	−0.172497
$867$	16166.0	0.633248
$868$	0	0
$869$	37248.0	1.45403
$870$	−2592.00	−0.101008
$871$	27104.0	1.05440
$872$	1168.00	0.0453595
$873$	−30590.0	−1.18593
$874$	480.000	0.0185769
$875$	0	0
$876$	9200.00	0.354839
$877$	8714.00	0.335520	0.167760	−	0.985828i	$-0.446347\pi$
$877$	8714.00	0.335520	0.167760	+	0.985828i	$0.446347\pi$
$878$	752.000	0.0289052
$879$	9576.00	0.367452
$880$	9216.00	0.353036
$881$	22806.0	0.872138	0.436069	−	0.899913i	$-0.356370\pi$
$881$	22806.0	0.872138	0.436069	+	0.899913i	$0.356370\pi$
$882$	0	0
$883$	40196.0	1.53194	0.765970	−	0.642876i	$-0.222259\pi$
$883$	40196.0	1.53194	0.765970	+	0.642876i	$0.222259\pi$
$884$	−25536.0	−0.971571
$885$	−3312.00	−0.125798
$886$	14376.0	0.545114
$887$	−40812.0	−1.54491	−0.772454	−	0.635071i	$-0.780971\pi$
$887$	−40812.0	−1.54491	−0.772454	+	0.635071i	$0.780971\pi$
$888$	2336.00	0.0882782
$889$	0	0
$890$	9360.00	0.352526
$891$	20208.0	0.759813
$892$	−8288.00	−0.311102
$893$	−24.0000	−0.000899361 0
$894$	−4008.00	−0.149941
$895$	21744.0	0.812091
$896$	0	0
$897$	13440.0	0.500277
$898$	−29340.0	−1.09030
$899$	12744.0	0.472788
$900$	−1748.00	−0.0647407
$901$	19836.0	0.733444
$902$	−12096.0	−0.446511
$903$	0	0
$904$	1584.00	0.0582777
$905$	5376.00	0.197463
$906$	−11008.0	−0.403660
$907$	−13588.0	−0.497444	−0.248722	−	0.968575i	$-0.580011\pi$
$907$	−13588.0	−0.497444	−0.248722	+	0.968575i	$0.580011\pi$
$908$	1464.00	0.0535072
$909$	−34500.0	−1.25885
$910$	0	0
$911$	−47304.0	−1.72036	−0.860182	−	0.509987i	$-0.829650\pi$
$911$	−47304.0	−1.72036	−0.860182	+	0.509987i	$0.829650\pi$
$912$	−64.0000	−0.00232374
$913$	−18144.0	−0.657699
$914$	−10292.0	−0.372461
$915$	−9120.00	−0.329506
$916$	1504.00	0.0542506
$917$	0	0
$918$	−22800.0	−0.819730
$919$	1784.00	0.0640356	0.0320178	−	0.999487i	$-0.489807\pi$
$919$	1784.00	0.0640356	0.0320178	+	0.999487i	$0.489807\pi$
$920$	−11520.0	−0.412830
$921$	1148.00	0.0410726
$922$	3024.00	0.108015
$923$	−32256.0	−1.15029
$924$	0	0
$925$	2774.00	0.0986038
$926$	14368.0	0.509894
$927$	8740.00	0.309665
$928$	−1728.00	−0.0611254
$929$	35922.0	1.26864	0.634318	−	0.773072i	$-0.281281\pi$
$929$	35922.0	1.26864	0.634318	+	0.773072i	$0.281281\pi$
$930$	−11328.0	−0.399419
$931$	0	0
$932$	−9048.00	−0.318001
$933$	17616.0	0.618137
$934$	33036.0	1.15736
$935$	65664.0	2.29673
$936$	10304.0	0.359826
$937$	26782.0	0.933756	0.466878	−	0.884322i	$-0.345379\pi$
$937$	26782.0	0.933756	0.466878	+	0.884322i	$0.345379\pi$
$938$	0	0
$939$	5540.00	0.192536
$940$	576.000	0.0199862
$941$	−4044.00	−0.140096	−0.0700482	−	0.997544i	$-0.522315\pi$
$941$	−4044.00	−0.140096	−0.0700482	+	0.997544i	$0.522315\pi$
$942$	2080.00	0.0719427
$943$	15120.0	0.522137
$944$	−2208.00	−0.0761274
$945$	0	0
$946$	−36096.0	−1.24057
$947$	−2136.00	−0.0732953	−0.0366477	−	0.999328i	$-0.511668\pi$
$947$	−2136.00	−0.0732953	−0.0366477	+	0.999328i	$0.511668\pi$
$948$	6208.00	0.212686
$949$	−64400.0	−2.20286
$950$	−76.0000	−0.00259554
$951$	15132.0	0.515971
$952$	0	0
$953$	−15174.0	−0.515776	−0.257888	−	0.966175i	$-0.583026\pi$
$953$	−15174.0	−0.515776	−0.257888	+	0.966175i	$0.583026\pi$
$954$	−8004.00	−0.271634
$955$	−25632.0	−0.868515
$956$	10368.0	0.350758
$957$	−5184.00	−0.175104
$958$	−20184.0	−0.680705
$959$	0	0
$960$	1536.00	0.0516398
$961$	25905.0	0.869558
$962$	−16352.0	−0.548035
$963$	−14628.0	−0.489492
$964$	−440.000	−0.0147007
$965$	53160.0	1.77335
$966$	0	0
$967$	25832.0	0.859050	0.429525	−	0.903055i	$-0.358681\pi$
$967$	25832.0	0.859050	0.429525	+	0.903055i	$0.358681\pi$
$968$	7784.00	0.258458
$969$	−456.000	−0.0151175
$970$	31920.0	1.05659
$971$	37686.0	1.24552	0.622761	−	0.782412i	$-0.286011\pi$
$971$	37686.0	1.24552	0.622761	+	0.782412i	$0.286011\pi$
$972$	14168.0	0.467530
$973$	0	0
$974$	15664.0	0.515305
$975$	−2128.00	−0.0698980
$976$	−6080.00	−0.199402
$977$	−54006.0	−1.76848	−0.884240	−	0.467033i	$-0.845323\pi$
$977$	−54006.0	−1.76848	−0.884240	+	0.467033i	$0.845323\pi$
$978$	5120.00	0.167402
$979$	18720.0	0.611127
$980$	0	0
$981$	−3358.00	−0.109289
$982$	−13464.0	−0.437529
$983$	−33276.0	−1.07969	−0.539847	−	0.841763i	$-0.681518\pi$
$983$	−33276.0	−1.07969	−0.539847	+	0.841763i	$0.681518\pi$
$984$	−2016.00	−0.0653127
$985$	2376.00	0.0768585
$986$	−12312.0	−0.397661
$987$	0	0
$988$	448.000	0.0144259
$989$	45120.0	1.45069
$990$	−26496.0	−0.850604
$991$	−3760.00	−0.120525	−0.0602625	−	0.998183i	$-0.519194\pi$
$991$	−3760.00	−0.120525	−0.0602625	+	0.998183i	$0.519194\pi$
$992$	−7552.00	−0.241710
$993$	−22640.0	−0.723523
$994$	0	0
$995$	27408.0	0.873258
$996$	−3024.00	−0.0962039
$997$	−36524.0	−1.16021	−0.580104	−	0.814543i	$-0.696988\pi$
$997$	−36524.0	−1.16021	−0.580104	+	0.814543i	$0.696988\pi$
$998$	37336.0	1.18422
$999$	−14600.0	−0.462386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.4.a.e.1.1		1
3.2	odd	2		882.4.a.b.1.1		1
4.3	odd	2		784.4.a.h.1.1		1
5.4	even	2		2450.4.a.i.1.1		1
7.2	even	3		98.4.c.b.67.1		2
7.3	odd	6		98.4.c.c.79.1		2
7.4	even	3		98.4.c.b.79.1		2
7.5	odd	6		98.4.c.c.67.1		2
7.6	odd	2		14.4.a.b.1.1	✓	1
21.2	odd	6		882.4.g.v.361.1		2
21.5	even	6		882.4.g.p.361.1		2
21.11	odd	6		882.4.g.v.667.1		2
21.17	even	6		882.4.g.p.667.1		2
21.20	even	2		126.4.a.d.1.1		1
28.27	even	2		112.4.a.e.1.1		1
35.13	even	4		350.4.c.g.99.1		2
35.27	even	4		350.4.c.g.99.2		2
35.34	odd	2		350.4.a.f.1.1		1
56.13	odd	2		448.4.a.k.1.1		1
56.27	even	2		448.4.a.g.1.1		1
77.76	even	2		1694.4.a.b.1.1		1
84.83	odd	2		1008.4.a.r.1.1		1
91.90	odd	2		2366.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.a.b.1.1	✓	1	7.6	odd	2
98.4.a.e.1.1		1	1.1	even	1	trivial
98.4.c.b.67.1		2	7.2	even	3
98.4.c.b.79.1		2	7.4	even	3
98.4.c.c.67.1		2	7.5	odd	6
98.4.c.c.79.1		2	7.3	odd	6
112.4.a.e.1.1		1	28.27	even	2
126.4.a.d.1.1		1	21.20	even	2
350.4.a.f.1.1		1	35.34	odd	2
350.4.c.g.99.1		2	35.13	even	4
350.4.c.g.99.2		2	35.27	even	4
448.4.a.g.1.1		1	56.27	even	2
448.4.a.k.1.1		1	56.13	odd	2
784.4.a.h.1.1		1	4.3	odd	2
882.4.a.b.1.1		1	3.2	odd	2
882.4.g.p.361.1		2	21.5	even	6
882.4.g.p.667.1		2	21.17	even	6
882.4.g.v.361.1		2	21.2	odd	6
882.4.g.v.667.1		2	21.11	odd	6
1008.4.a.r.1.1		1	84.83	odd	2
1694.4.a.b.1.1		1	77.76	even	2
2366.4.a.c.1.1		1	91.90	odd	2
2450.4.a.i.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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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