LMFDB - Embedded newform 245.4.a.d.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,4,Mod(1,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,1,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} +8.00000 q^{3} -7.00000 q^{4} +5.00000 q^{5} +8.00000 q^{6} -15.0000 q^{8} +37.0000 q^{9} +5.00000 q^{10} +12.0000 q^{11} -56.0000 q^{12} +78.0000 q^{13} +40.0000 q^{15} +41.0000 q^{16} +94.0000 q^{17} +37.0000 q^{18} -40.0000 q^{19} -35.0000 q^{20} +12.0000 q^{22} +32.0000 q^{23} -120.000 q^{24} +25.0000 q^{25} +78.0000 q^{26} +80.0000 q^{27} -50.0000 q^{29} +40.0000 q^{30} +248.000 q^{31} +161.000 q^{32} +96.0000 q^{33} +94.0000 q^{34} -259.000 q^{36} -434.000 q^{37} -40.0000 q^{38} +624.000 q^{39} -75.0000 q^{40} -402.000 q^{41} -68.0000 q^{43} -84.0000 q^{44} +185.000 q^{45} +32.0000 q^{46} -536.000 q^{47} +328.000 q^{48} +25.0000 q^{50} +752.000 q^{51} -546.000 q^{52} +22.0000 q^{53} +80.0000 q^{54} +60.0000 q^{55} -320.000 q^{57} -50.0000 q^{58} +560.000 q^{59} -280.000 q^{60} +278.000 q^{61} +248.000 q^{62} -167.000 q^{64} +390.000 q^{65} +96.0000 q^{66} -164.000 q^{67} -658.000 q^{68} +256.000 q^{69} +672.000 q^{71} -555.000 q^{72} -82.0000 q^{73} -434.000 q^{74} +200.000 q^{75} +280.000 q^{76} +624.000 q^{78} -1000.00 q^{79} +205.000 q^{80} -359.000 q^{81} -402.000 q^{82} +448.000 q^{83} +470.000 q^{85} -68.0000 q^{86} -400.000 q^{87} -180.000 q^{88} +870.000 q^{89} +185.000 q^{90} -224.000 q^{92} +1984.00 q^{93} -536.000 q^{94} -200.000 q^{95} +1288.00 q^{96} -1026.00 q^{97} +444.000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	8.00000	1.53960	0.769800	−	0.638285i	$-0.220356\pi$
$3$	8.00000	1.53960	0.769800	+	0.638285i	$0.220356\pi$
$4$	−7.00000	−0.875000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	8.00000	0.544331
$7$	0	0
$7$	0	0
$8$	−15.0000	−0.662913
$9$	37.0000	1.37037
$10$	5.00000	0.158114
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	−56.0000	−1.34715
$13$	78.0000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	78.0000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	40.0000	0.688530
$16$	41.0000	0.640625
$17$	94.0000	1.34108	0.670540	−	0.741874i	$-0.266063\pi$
$17$	94.0000	1.34108	0.670540	+	0.741874i	$0.266063\pi$
$18$	37.0000	0.484499
$19$	−40.0000	−0.482980	−0.241490	−	0.970403i	$-0.577636\pi$
$19$	−40.0000	−0.482980	−0.241490	+	0.970403i	$0.577636\pi$
$20$	−35.0000	−0.391312
$21$	0	0
$22$	12.0000	0.116291
$23$	32.0000	0.290107	0.145054	−	0.989424i	$-0.453665\pi$
$23$	32.0000	0.290107	0.145054	+	0.989424i	$0.453665\pi$
$24$	−120.000	−1.02062
$25$	25.0000	0.200000
$26$	78.0000	0.588348
$27$	80.0000	0.570222
$28$	0	0
$29$	−50.0000	−0.320164	−0.160082	−	0.987104i	$-0.551176\pi$
$29$	−50.0000	−0.320164	−0.160082	+	0.987104i	$0.551176\pi$
$30$	40.0000	0.243432
$31$	248.000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	248.000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	161.000	0.889408
$33$	96.0000	0.506408
$34$	94.0000	0.474143
$35$	0	0
$36$	−259.000	−1.19907
$37$	−434.000	−1.92836	−0.964178	−	0.265257i	$-0.914543\pi$
$37$	−434.000	−1.92836	−0.964178	+	0.265257i	$0.914543\pi$
$38$	−40.0000	−0.170759
$39$	624.000	2.56205
$40$	−75.0000	−0.296464
$41$	−402.000	−1.53126	−0.765632	−	0.643278i	$-0.777574\pi$
$41$	−402.000	−1.53126	−0.765632	+	0.643278i	$0.777574\pi$
$42$	0	0
$43$	−68.0000	−0.241161	−0.120580	−	0.992704i	$-0.538476\pi$
$43$	−68.0000	−0.241161	−0.120580	+	0.992704i	$0.538476\pi$
$44$	−84.0000	−0.287806
$45$	185.000	0.612848
$46$	32.0000	0.102568
$47$	−536.000	−1.66348	−0.831741	−	0.555164i	$-0.812655\pi$
$47$	−536.000	−1.66348	−0.831741	+	0.555164i	$0.812655\pi$
$48$	328.000	0.986307
$49$	0	0
$50$	25.0000	0.0707107
$51$	752.000	2.06473
$52$	−546.000	−1.45609
$53$	22.0000	0.0570176	0.0285088	−	0.999594i	$-0.490924\pi$
$53$	22.0000	0.0570176	0.0285088	+	0.999594i	$0.490924\pi$
$54$	80.0000	0.201604
$55$	60.0000	0.147098
$56$	0	0
$57$	−320.000	−0.743597
$58$	−50.0000	−0.113195
$59$	560.000	1.23569	0.617846	−	0.786299i	$-0.288006\pi$
$59$	560.000	1.23569	0.617846	+	0.786299i	$0.288006\pi$
$60$	−280.000	−0.602464
$61$	278.000	0.583512	0.291756	−	0.956493i	$-0.405760\pi$
$61$	278.000	0.583512	0.291756	+	0.956493i	$0.405760\pi$
$62$	248.000	0.508001
$63$	0	0
$64$	−167.000	−0.326172
$65$	390.000	0.744208
$66$	96.0000	0.179042
$67$	−164.000	−0.299042	−0.149521	−	0.988759i	$-0.547773\pi$
$67$	−164.000	−0.299042	−0.149521	+	0.988759i	$0.547773\pi$
$68$	−658.000	−1.17344
$69$	256.000	0.446649
$70$	0	0
$71$	672.000	1.12326	0.561632	−	0.827387i	$-0.310174\pi$
$71$	672.000	1.12326	0.561632	+	0.827387i	$0.310174\pi$
$72$	−555.000	−0.908436
$73$	−82.0000	−0.131471	−0.0657354	−	0.997837i	$-0.520939\pi$
$73$	−82.0000	−0.131471	−0.0657354	+	0.997837i	$0.520939\pi$
$74$	−434.000	−0.681777
$75$	200.000	0.307920
$76$	280.000	0.422608
$77$	0	0
$78$	624.000	0.905822
$79$	−1000.00	−1.42416	−0.712081	−	0.702097i	$-0.752247\pi$
$79$	−1000.00	−1.42416	−0.712081	+	0.702097i	$0.752247\pi$
$80$	205.000	0.286496
$81$	−359.000	−0.492455
$82$	−402.000	−0.541384
$83$	448.000	0.592463	0.296231	−	0.955116i	$-0.404270\pi$
$83$	448.000	0.592463	0.296231	+	0.955116i	$0.404270\pi$
$84$	0	0
$85$	470.000	0.599749
$86$	−68.0000	−0.0852631
$87$	−400.000	−0.492925
$88$	−180.000	−0.218046
$89$	870.000	1.03618	0.518089	−	0.855327i	$-0.326644\pi$
$89$	870.000	1.03618	0.518089	+	0.855327i	$0.326644\pi$
$90$	185.000	0.216675
$91$	0	0
$92$	−224.000	−0.253844
$93$	1984.00	2.21216
$94$	−536.000	−0.588130
$95$	−200.000	−0.215995
$96$	1288.00	1.36933
$97$	−1026.00	−1.07396	−0.536982	−	0.843594i	$-0.680436\pi$
$97$	−1026.00	−1.07396	−0.536982	+	0.843594i	$0.680436\pi$
$98$	0	0
$99$	444.000	0.450744
$100$	−175.000	−0.175000
$101$	−482.000	−0.474859	−0.237430	−	0.971405i	$-0.576305\pi$
$101$	−482.000	−0.474859	−0.237430	+	0.971405i	$0.576305\pi$
$102$	752.000	0.729991
$103$	−272.000	−0.260203	−0.130102	−	0.991501i	$-0.541530\pi$
$103$	−272.000	−0.260203	−0.130102	+	0.991501i	$0.541530\pi$
$104$	−1170.00	−1.10315
$105$	0	0
$106$	22.0000	0.0201588
$107$	−444.000	−0.401150	−0.200575	−	0.979678i	$-0.564281\pi$
$107$	−444.000	−0.401150	−0.200575	+	0.979678i	$0.564281\pi$
$108$	−560.000	−0.498945
$109$	−1170.00	−1.02813	−0.514063	−	0.857753i	$-0.671860\pi$
$109$	−1170.00	−1.02813	−0.514063	+	0.857753i	$0.671860\pi$
$110$	60.0000	0.0520071
$111$	−3472.00	−2.96890
$112$	0	0
$113$	−798.000	−0.664332	−0.332166	−	0.943221i	$-0.607779\pi$
$113$	−798.000	−0.664332	−0.332166	+	0.943221i	$0.607779\pi$
$114$	−320.000	−0.262901
$115$	160.000	0.129740
$116$	350.000	0.280144
$117$	2886.00	2.28043
$118$	560.000	0.436883
$119$	0	0
$120$	−600.000	−0.456435
$121$	−1187.00	−0.891811
$122$	278.000	0.206303
$123$	−3216.00	−2.35754
$124$	−1736.00	−1.25724
$125$	125.000	0.0894427
$126$	0	0
$127$	776.000	0.542196	0.271098	−	0.962552i	$-0.412613\pi$
$127$	776.000	0.542196	0.271098	+	0.962552i	$0.412613\pi$
$128$	−1455.00	−1.00473
$129$	−544.000	−0.371291
$130$	390.000	0.263117
$131$	−1112.00	−0.741648	−0.370824	−	0.928703i	$-0.620925\pi$
$131$	−1112.00	−0.741648	−0.370824	+	0.928703i	$0.620925\pi$
$132$	−672.000	−0.443107
$133$	0	0
$134$	−164.000	−0.105727
$135$	400.000	0.255011
$136$	−1410.00	−0.889018
$137$	−694.000	−0.432791	−0.216396	−	0.976306i	$-0.569430\pi$
$137$	−694.000	−0.432791	−0.216396	+	0.976306i	$0.569430\pi$
$138$	256.000	0.157914
$139$	−360.000	−0.219675	−0.109837	−	0.993950i	$-0.535033\pi$
$139$	−360.000	−0.219675	−0.109837	+	0.993950i	$0.535033\pi$
$140$	0	0
$141$	−4288.00	−2.56110
$142$	672.000	0.397134
$143$	936.000	0.547358
$144$	1517.00	0.877894
$145$	−250.000	−0.143182
$146$	−82.0000	−0.0464820
$147$	0	0
$148$	3038.00	1.68731
$149$	2270.00	1.24809	0.624046	−	0.781388i	$-0.285488\pi$
$149$	2270.00	1.24809	0.624046	+	0.781388i	$0.285488\pi$
$150$	200.000	0.108866
$151$	632.000	0.340606	0.170303	−	0.985392i	$-0.445525\pi$
$151$	632.000	0.340606	0.170303	+	0.985392i	$0.445525\pi$
$152$	600.000	0.320174
$153$	3478.00	1.83778
$154$	0	0
$155$	1240.00	0.642575
$156$	−4368.00	−2.24179
$157$	734.000	0.373118	0.186559	−	0.982444i	$-0.440266\pi$
$157$	734.000	0.373118	0.186559	+	0.982444i	$0.440266\pi$
$158$	−1000.00	−0.503517
$159$	176.000	0.0877843
$160$	805.000	0.397755
$161$	0	0
$162$	−359.000	−0.174109
$163$	2532.00	1.21670	0.608348	−	0.793670i	$-0.291832\pi$
$163$	2532.00	1.21670	0.608348	+	0.793670i	$0.291832\pi$
$164$	2814.00	1.33986
$165$	480.000	0.226472
$166$	448.000	0.209467
$167$	−416.000	−0.192761	−0.0963804	−	0.995345i	$-0.530727\pi$
$167$	−416.000	−0.192761	−0.0963804	+	0.995345i	$0.530727\pi$
$168$	0	0
$169$	3887.00	1.76923
$170$	470.000	0.212043
$171$	−1480.00	−0.661862
$172$	476.000	0.211015
$173$	−3042.00	−1.33687	−0.668436	−	0.743769i	$-0.733036\pi$
$173$	−3042.00	−1.33687	−0.668436	+	0.743769i	$0.733036\pi$
$174$	−400.000	−0.174275
$175$	0	0
$176$	492.000	0.210715
$177$	4480.00	1.90247
$178$	870.000	0.366344
$179$	−180.000	−0.0751611	−0.0375805	−	0.999294i	$-0.511965\pi$
$179$	−180.000	−0.0751611	−0.0375805	+	0.999294i	$0.511965\pi$
$180$	−1295.00	−0.536242
$181$	1958.00	0.804072	0.402036	−	0.915624i	$-0.368303\pi$
$181$	1958.00	0.804072	0.402036	+	0.915624i	$0.368303\pi$
$182$	0	0
$183$	2224.00	0.898376
$184$	−480.000	−0.192316
$185$	−2170.00	−0.862387
$186$	1984.00	0.782118
$187$	1128.00	0.441110
$188$	3752.00	1.45555
$189$	0	0
$190$	−200.000	−0.0763659
$191$	−2888.00	−1.09408	−0.547038	−	0.837108i	$-0.684245\pi$
$191$	−2888.00	−1.09408	−0.547038	+	0.837108i	$0.684245\pi$
$192$	−1336.00	−0.502174
$193$	1602.00	0.597484	0.298742	−	0.954334i	$-0.403433\pi$
$193$	1602.00	0.597484	0.298742	+	0.954334i	$0.403433\pi$
$194$	−1026.00	−0.379704
$195$	3120.00	1.14578
$196$	0	0
$197$	−4794.00	−1.73380	−0.866899	−	0.498483i	$-0.833891\pi$
$197$	−4794.00	−1.73380	−0.866899	+	0.498483i	$0.833891\pi$
$198$	444.000	0.159362
$199$	−1280.00	−0.455964	−0.227982	−	0.973665i	$-0.573213\pi$
$199$	−1280.00	−0.455964	−0.227982	+	0.973665i	$0.573213\pi$
$200$	−375.000	−0.132583
$201$	−1312.00	−0.460405
$202$	−482.000	−0.167888
$203$	0	0
$204$	−5264.00	−1.80664
$205$	−2010.00	−0.684802
$206$	−272.000	−0.0919958
$207$	1184.00	0.397554
$208$	3198.00	1.06606
$209$	−480.000	−0.158863
$210$	0	0
$211$	−68.0000	−0.0221863	−0.0110932	−	0.999938i	$-0.503531\pi$
$211$	−68.0000	−0.0221863	−0.0110932	+	0.999938i	$0.503531\pi$
$212$	−154.000	−0.0498904
$213$	5376.00	1.72938
$214$	−444.000	−0.141828
$215$	−340.000	−0.107850
$216$	−1200.00	−0.378008
$217$	0	0
$218$	−1170.00	−0.363497
$219$	−656.000	−0.202413
$220$	−420.000	−0.128711
$221$	7332.00	2.23169
$222$	−3472.00	−1.04966
$223$	1728.00	0.518903	0.259452	−	0.965756i	$-0.416458\pi$
$223$	1728.00	0.518903	0.259452	+	0.965756i	$0.416458\pi$
$224$	0	0
$225$	925.000	0.274074
$226$	−798.000	−0.234877
$227$	4864.00	1.42218	0.711090	−	0.703101i	$-0.248202\pi$
$227$	4864.00	1.42218	0.711090	+	0.703101i	$0.248202\pi$
$228$	2240.00	0.650647
$229$	5510.00	1.59000	0.795002	−	0.606606i	$-0.207470\pi$
$229$	5510.00	1.59000	0.795002	+	0.606606i	$0.207470\pi$
$230$	160.000	0.0458699
$231$	0	0
$232$	750.000	0.212241
$233$	5322.00	1.49638	0.748188	−	0.663486i	$-0.230924\pi$
$233$	5322.00	1.49638	0.748188	+	0.663486i	$0.230924\pi$
$234$	2886.00	0.806255
$235$	−2680.00	−0.743932
$236$	−3920.00	−1.08123
$237$	−8000.00	−2.19264
$238$	0	0
$239$	−1840.00	−0.497990	−0.248995	−	0.968505i	$-0.580100\pi$
$239$	−1840.00	−0.497990	−0.248995	+	0.968505i	$0.580100\pi$
$240$	1640.00	0.441090
$241$	438.000	0.117071	0.0585354	−	0.998285i	$-0.481357\pi$
$241$	438.000	0.117071	0.0585354	+	0.998285i	$0.481357\pi$
$242$	−1187.00	−0.315303
$243$	−5032.00	−1.32841
$244$	−1946.00	−0.510573
$245$	0	0
$246$	−3216.00	−0.833515
$247$	−3120.00	−0.803728
$248$	−3720.00	−0.952501
$249$	3584.00	0.912156
$250$	125.000	0.0316228
$251$	−5592.00	−1.40623	−0.703115	−	0.711076i	$-0.748208\pi$
$251$	−5592.00	−1.40623	−0.703115	+	0.711076i	$0.748208\pi$
$252$	0	0
$253$	384.000	0.0954224
$254$	776.000	0.191695
$255$	3760.00	0.923374
$256$	−119.000	−0.0290527
$257$	1974.00	0.479123	0.239562	−	0.970881i	$-0.422996\pi$
$257$	1974.00	0.479123	0.239562	+	0.970881i	$0.422996\pi$
$258$	−544.000	−0.131271
$259$	0	0
$260$	−2730.00	−0.651182
$261$	−1850.00	−0.438744
$262$	−1112.00	−0.262212
$263$	−728.000	−0.170686	−0.0853430	−	0.996352i	$-0.527199\pi$
$263$	−728.000	−0.170686	−0.0853430	+	0.996352i	$0.527199\pi$
$264$	−1440.00	−0.335704
$265$	110.000	0.0254990
$266$	0	0
$267$	6960.00	1.59530
$268$	1148.00	0.261661
$269$	−5810.00	−1.31688	−0.658442	−	0.752631i	$-0.728784\pi$
$269$	−5810.00	−1.31688	−0.658442	+	0.752631i	$0.728784\pi$
$270$	400.000	0.0901601
$271$	6528.00	1.46328	0.731638	−	0.681693i	$-0.238756\pi$
$271$	6528.00	1.46328	0.731638	+	0.681693i	$0.238756\pi$
$272$	3854.00	0.859129
$273$	0	0
$274$	−694.000	−0.153015
$275$	300.000	0.0657843
$276$	−1792.00	−0.390818
$277$	5126.00	1.11188	0.555941	−	0.831222i	$-0.312358\pi$
$277$	5126.00	1.11188	0.555941	+	0.831222i	$0.312358\pi$
$278$	−360.000	−0.0776668
$279$	9176.00	1.96901
$280$	0	0
$281$	−2358.00	−0.500592	−0.250296	−	0.968169i	$-0.580528\pi$
$281$	−2358.00	−0.500592	−0.250296	+	0.968169i	$0.580528\pi$
$282$	−4288.00	−0.905485
$283$	−392.000	−0.0823392	−0.0411696	−	0.999152i	$-0.513108\pi$
$283$	−392.000	−0.0823392	−0.0411696	+	0.999152i	$0.513108\pi$
$284$	−4704.00	−0.982856
$285$	−1600.00	−0.332547
$286$	936.000	0.193520
$287$	0	0
$288$	5957.00	1.21882
$289$	3923.00	0.798494
$290$	−250.000	−0.0506224
$291$	−8208.00	−1.65348
$292$	574.000	0.115037
$293$	−1202.00	−0.239664	−0.119832	−	0.992794i	$-0.538236\pi$
$293$	−1202.00	−0.239664	−0.119832	+	0.992794i	$0.538236\pi$
$294$	0	0
$295$	2800.00	0.552618
$296$	6510.00	1.27833
$297$	960.000	0.187558
$298$	2270.00	0.441267
$299$	2496.00	0.482767
$300$	−1400.00	−0.269430
$301$	0	0
$302$	632.000	0.120422
$303$	−3856.00	−0.731094
$304$	−1640.00	−0.309409
$305$	1390.00	0.260955
$306$	3478.00	0.649752
$307$	6384.00	1.18682	0.593411	−	0.804900i	$-0.297781\pi$
$307$	6384.00	1.18682	0.593411	+	0.804900i	$0.297781\pi$
$308$	0	0
$309$	−2176.00	−0.400609
$310$	1240.00	0.227185
$311$	4968.00	0.905818	0.452909	−	0.891557i	$-0.350386\pi$
$311$	4968.00	0.905818	0.452909	+	0.891557i	$0.350386\pi$
$312$	−9360.00	−1.69842
$313$	2758.00	0.498056	0.249028	−	0.968496i	$-0.419889\pi$
$313$	2758.00	0.498056	0.249028	+	0.968496i	$0.419889\pi$
$314$	734.000	0.131917
$315$	0	0
$316$	7000.00	1.24614
$317$	−6274.00	−1.11162	−0.555809	−	0.831310i	$-0.687591\pi$
$317$	−6274.00	−1.11162	−0.555809	+	0.831310i	$0.687591\pi$
$318$	176.000	0.0310364
$319$	−600.000	−0.105309
$320$	−835.000	−0.145868
$321$	−3552.00	−0.617612
$322$	0	0
$323$	−3760.00	−0.647715
$324$	2513.00	0.430898
$325$	1950.00	0.332820
$326$	2532.00	0.430167
$327$	−9360.00	−1.58290
$328$	6030.00	1.01509
$329$	0	0
$330$	480.000	0.0800701
$331$	1932.00	0.320823	0.160411	−	0.987050i	$-0.448718\pi$
$331$	1932.00	0.320823	0.160411	+	0.987050i	$0.448718\pi$
$332$	−3136.00	−0.518405
$333$	−16058.0	−2.64256
$334$	−416.000	−0.0681512
$335$	−820.000	−0.133735
$336$	0	0
$337$	2386.00	0.385679	0.192839	−	0.981230i	$-0.438230\pi$
$337$	2386.00	0.385679	0.192839	+	0.981230i	$0.438230\pi$
$338$	3887.00	0.625518
$339$	−6384.00	−1.02281
$340$	−3290.00	−0.524780
$341$	2976.00	0.472608
$342$	−1480.00	−0.234004
$343$	0	0
$344$	1020.00	0.159868
$345$	1280.00	0.199747
$346$	−3042.00	−0.472656
$347$	6076.00	0.939991	0.469995	−	0.882669i	$-0.344256\pi$
$347$	6076.00	0.939991	0.469995	+	0.882669i	$0.344256\pi$
$348$	2800.00	0.431310
$349$	−2210.00	−0.338964	−0.169482	−	0.985533i	$-0.554210\pi$
$349$	−2210.00	−0.338964	−0.169482	+	0.985533i	$0.554210\pi$
$350$	0	0
$351$	6240.00	0.948908
$352$	1932.00	0.292545
$353$	2598.00	0.391721	0.195861	−	0.980632i	$-0.437250\pi$
$353$	2598.00	0.391721	0.195861	+	0.980632i	$0.437250\pi$
$354$	4480.00	0.672625
$355$	3360.00	0.502339
$356$	−6090.00	−0.906655
$357$	0	0
$358$	−180.000	−0.0265735
$359$	−13320.0	−1.95822	−0.979112	−	0.203320i	$-0.934827\pi$
$359$	−13320.0	−1.95822	−0.979112	+	0.203320i	$0.934827\pi$
$360$	−2775.00	−0.406265
$361$	−5259.00	−0.766730
$362$	1958.00	0.284282
$363$	−9496.00	−1.37303
$364$	0	0
$365$	−410.000	−0.0587956
$366$	2224.00	0.317624
$367$	−10816.0	−1.53839	−0.769197	−	0.639012i	$-0.779344\pi$
$367$	−10816.0	−1.53839	−0.769197	+	0.639012i	$0.779344\pi$
$368$	1312.00	0.185850
$369$	−14874.0	−2.09840
$370$	−2170.00	−0.304900
$371$	0	0
$372$	−13888.0	−1.93564
$373$	−11098.0	−1.54057	−0.770285	−	0.637700i	$-0.779886\pi$
$373$	−11098.0	−1.54057	−0.770285	+	0.637700i	$0.779886\pi$
$374$	1128.00	0.155956
$375$	1000.00	0.137706
$376$	8040.00	1.10274
$377$	−3900.00	−0.532786
$378$	0	0
$379$	7100.00	0.962276	0.481138	−	0.876645i	$-0.340224\pi$
$379$	7100.00	0.962276	0.481138	+	0.876645i	$0.340224\pi$
$380$	1400.00	0.188996
$381$	6208.00	0.834765
$382$	−2888.00	−0.386814
$383$	728.000	0.0971255	0.0485627	−	0.998820i	$-0.484536\pi$
$383$	728.000	0.0971255	0.0485627	+	0.998820i	$0.484536\pi$
$384$	−11640.0	−1.54688
$385$	0	0
$386$	1602.00	0.211243
$387$	−2516.00	−0.330479
$388$	7182.00	0.939719
$389$	−6810.00	−0.887611	−0.443806	−	0.896123i	$-0.646372\pi$
$389$	−6810.00	−0.887611	−0.443806	+	0.896123i	$0.646372\pi$
$390$	3120.00	0.405096
$391$	3008.00	0.389057
$392$	0	0
$393$	−8896.00	−1.14184
$394$	−4794.00	−0.612990
$395$	−5000.00	−0.636905
$396$	−3108.00	−0.394401
$397$	574.000	0.0725648	0.0362824	−	0.999342i	$-0.488448\pi$
$397$	574.000	0.0725648	0.0362824	+	0.999342i	$0.488448\pi$
$398$	−1280.00	−0.161208
$399$	0	0
$400$	1025.00	0.128125
$401$	6162.00	0.767371	0.383685	−	0.923464i	$-0.374655\pi$
$401$	6162.00	0.767371	0.383685	+	0.923464i	$0.374655\pi$
$402$	−1312.00	−0.162778
$403$	19344.0	2.39105
$404$	3374.00	0.415502
$405$	−1795.00	−0.220233
$406$	0	0
$407$	−5208.00	−0.634278
$408$	−11280.0	−1.36873
$409$	−8210.00	−0.992563	−0.496282	−	0.868162i	$-0.665302\pi$
$409$	−8210.00	−0.992563	−0.496282	+	0.868162i	$0.665302\pi$
$410$	−2010.00	−0.242114
$411$	−5552.00	−0.666326
$412$	1904.00	0.227678
$413$	0	0
$414$	1184.00	0.140557
$415$	2240.00	0.264957
$416$	12558.0	1.48006
$417$	−2880.00	−0.338212
$418$	−480.000	−0.0561664
$419$	−4800.00	−0.559655	−0.279827	−	0.960050i	$-0.590277\pi$
$419$	−4800.00	−0.559655	−0.279827	+	0.960050i	$0.590277\pi$
$420$	0	0
$421$	−9938.00	−1.15047	−0.575236	−	0.817988i	$-0.695090\pi$
$421$	−9938.00	−1.15047	−0.575236	+	0.817988i	$0.695090\pi$
$422$	−68.0000	−0.00784405
$423$	−19832.0	−2.27959
$424$	−330.000	−0.0377977
$425$	2350.00	0.268216
$426$	5376.00	0.611427
$427$	0	0
$428$	3108.00	0.351007
$429$	7488.00	0.842713
$430$	−340.000	−0.0381308
$431$	−9248.00	−1.03355	−0.516776	−	0.856121i	$-0.672868\pi$
$431$	−9248.00	−1.03355	−0.516776	+	0.856121i	$0.672868\pi$
$432$	3280.00	0.365299
$433$	1118.00	0.124082	0.0620412	−	0.998074i	$-0.480239\pi$
$433$	1118.00	0.124082	0.0620412	+	0.998074i	$0.480239\pi$
$434$	0	0
$435$	−2000.00	−0.220443
$436$	8190.00	0.899610
$437$	−1280.00	−0.140116
$438$	−656.000	−0.0715637
$439$	11960.0	1.30027	0.650136	−	0.759818i	$-0.274712\pi$
$439$	11960.0	1.30027	0.650136	+	0.759818i	$0.274712\pi$
$440$	−900.000	−0.0975132
$441$	0	0
$442$	7332.00	0.789022
$443$	7332.00	0.786352	0.393176	−	0.919463i	$-0.371376\pi$
$443$	7332.00	0.786352	0.393176	+	0.919463i	$0.371376\pi$
$444$	24304.0	2.59779
$445$	4350.00	0.463393
$446$	1728.00	0.183460
$447$	18160.0	1.92156
$448$	0	0
$449$	1890.00	0.198652	0.0993259	−	0.995055i	$-0.468331\pi$
$449$	1890.00	0.198652	0.0993259	+	0.995055i	$0.468331\pi$
$450$	925.000	0.0968998
$451$	−4824.00	−0.503666
$452$	5586.00	0.581291
$453$	5056.00	0.524396
$454$	4864.00	0.502817
$455$	0	0
$456$	4800.00	0.492940
$457$	−7014.00	−0.717945	−0.358973	−	0.933348i	$-0.616873\pi$
$457$	−7014.00	−0.717945	−0.358973	+	0.933348i	$0.616873\pi$
$458$	5510.00	0.562152
$459$	7520.00	0.764714
$460$	−1120.00	−0.113522
$461$	8318.00	0.840364	0.420182	−	0.907440i	$-0.361966\pi$
$461$	8318.00	0.840364	0.420182	+	0.907440i	$0.361966\pi$
$462$	0	0
$463$	6432.00	0.645616	0.322808	−	0.946464i	$-0.395373\pi$
$463$	6432.00	0.645616	0.322808	+	0.946464i	$0.395373\pi$
$464$	−2050.00	−0.205105
$465$	9920.00	0.989310
$466$	5322.00	0.529049
$467$	10064.0	0.997230	0.498615	−	0.866824i	$-0.333842\pi$
$467$	10064.0	0.997230	0.498615	+	0.866824i	$0.333842\pi$
$468$	−20202.0	−1.99538
$469$	0	0
$470$	−2680.00	−0.263020
$471$	5872.00	0.574453
$472$	−8400.00	−0.819155
$473$	−816.000	−0.0793229
$474$	−8000.00	−0.775216
$475$	−1000.00	−0.0965961
$476$	0	0
$477$	814.000	0.0781352
$478$	−1840.00	−0.176066
$479$	−1400.00	−0.133544	−0.0667721	−	0.997768i	$-0.521270\pi$
$479$	−1400.00	−0.133544	−0.0667721	+	0.997768i	$0.521270\pi$
$480$	6440.00	0.612384
$481$	−33852.0	−3.20898
$482$	438.000	0.0413908
$483$	0	0
$484$	8309.00	0.780334
$485$	−5130.00	−0.480291
$486$	−5032.00	−0.469663
$487$	13376.0	1.24461	0.622304	−	0.782775i	$-0.286197\pi$
$487$	13376.0	1.24461	0.622304	+	0.782775i	$0.286197\pi$
$488$	−4170.00	−0.386818
$489$	20256.0	1.87323
$490$	0	0
$491$	7092.00	0.651848	0.325924	−	0.945396i	$-0.394325\pi$
$491$	7092.00	0.651848	0.325924	+	0.945396i	$0.394325\pi$
$492$	22512.0	2.06284
$493$	−4700.00	−0.429366
$494$	−3120.00	−0.284161
$495$	2220.00	0.201579
$496$	10168.0	0.920477
$497$	0	0
$498$	3584.00	0.322496
$499$	−820.000	−0.0735636	−0.0367818	−	0.999323i	$-0.511711\pi$
$499$	−820.000	−0.0735636	−0.0367818	+	0.999323i	$0.511711\pi$
$500$	−875.000	−0.0782624
$501$	−3328.00	−0.296775
$502$	−5592.00	−0.497178
$503$	4568.00	0.404925	0.202462	−	0.979290i	$-0.435106\pi$
$503$	4568.00	0.404925	0.202462	+	0.979290i	$0.435106\pi$
$504$	0	0
$505$	−2410.00	−0.212364
$506$	384.000	0.0337369
$507$	31096.0	2.72391
$508$	−5432.00	−0.474421
$509$	−19810.0	−1.72507	−0.862537	−	0.505994i	$-0.831126\pi$
$509$	−19810.0	−1.72507	−0.862537	+	0.505994i	$0.831126\pi$
$510$	3760.00	0.326462
$511$	0	0
$512$	11521.0	0.994455
$513$	−3200.00	−0.275406
$514$	1974.00	0.169396
$515$	−1360.00	−0.116367
$516$	3808.00	0.324880
$517$	−6432.00	−0.547155
$518$	0	0
$519$	−24336.0	−2.05825
$520$	−5850.00	−0.493345
$521$	1838.00	0.154557	0.0772785	−	0.997010i	$-0.475377\pi$
$521$	1838.00	0.154557	0.0772785	+	0.997010i	$0.475377\pi$
$522$	−1850.00	−0.155119
$523$	−2072.00	−0.173236	−0.0866178	−	0.996242i	$-0.527606\pi$
$523$	−2072.00	−0.173236	−0.0866178	+	0.996242i	$0.527606\pi$
$524$	7784.00	0.648942
$525$	0	0
$526$	−728.000	−0.0603466
$527$	23312.0	1.92692
$528$	3936.00	0.324417
$529$	−11143.0	−0.915838
$530$	110.000	0.00901527
$531$	20720.0	1.69335
$532$	0	0
$533$	−31356.0	−2.54818
$534$	6960.00	0.564024
$535$	−2220.00	−0.179400
$536$	2460.00	0.198238
$537$	−1440.00	−0.115718
$538$	−5810.00	−0.465589
$539$	0	0
$540$	−2800.00	−0.223135
$541$	−3498.00	−0.277987	−0.138993	−	0.990293i	$-0.544387\pi$
$541$	−3498.00	−0.277987	−0.138993	+	0.990293i	$0.544387\pi$
$542$	6528.00	0.517346
$543$	15664.0	1.23795
$544$	15134.0	1.19277
$545$	−5850.00	−0.459792
$546$	0	0
$547$	5076.00	0.396772	0.198386	−	0.980124i	$-0.436430\pi$
$547$	5076.00	0.396772	0.198386	+	0.980124i	$0.436430\pi$
$548$	4858.00	0.378692
$549$	10286.0	0.799628
$550$	300.000	0.0232583
$551$	2000.00	0.154633
$552$	−3840.00	−0.296089
$553$	0	0
$554$	5126.00	0.393110
$555$	−17360.0	−1.32773
$556$	2520.00	0.192215
$557$	−8674.00	−0.659837	−0.329918	−	0.944009i	$-0.607021\pi$
$557$	−8674.00	−0.659837	−0.329918	+	0.944009i	$0.607021\pi$
$558$	9176.00	0.696149
$559$	−5304.00	−0.401315
$560$	0	0
$561$	9024.00	0.679133
$562$	−2358.00	−0.176986
$563$	−16072.0	−1.20312	−0.601558	−	0.798829i	$-0.705453\pi$
$563$	−16072.0	−1.20312	−0.601558	+	0.798829i	$0.705453\pi$
$564$	30016.0	2.24096
$565$	−3990.00	−0.297098
$566$	−392.000	−0.0291113
$567$	0	0
$568$	−10080.0	−0.744626
$569$	2730.00	0.201138	0.100569	−	0.994930i	$-0.467934\pi$
$569$	2730.00	0.201138	0.100569	+	0.994930i	$0.467934\pi$
$570$	−1600.00	−0.117573
$571$	19932.0	1.46082	0.730410	−	0.683009i	$-0.239329\pi$
$571$	19932.0	1.46082	0.730410	+	0.683009i	$0.239329\pi$
$572$	−6552.00	−0.478939
$573$	−23104.0	−1.68444
$574$	0	0
$575$	800.000	0.0580214
$576$	−6179.00	−0.446976
$577$	20054.0	1.44690	0.723448	−	0.690379i	$-0.242556\pi$
$577$	20054.0	1.44690	0.723448	+	0.690379i	$0.242556\pi$
$578$	3923.00	0.282310
$579$	12816.0	0.919887
$580$	1750.00	0.125284
$581$	0	0
$582$	−8208.00	−0.584592
$583$	264.000	0.0187543
$584$	1230.00	0.0871537
$585$	14430.0	1.01984
$586$	−1202.00	−0.0847341
$587$	2544.00	0.178879	0.0894396	−	0.995992i	$-0.471492\pi$
$587$	2544.00	0.178879	0.0894396	+	0.995992i	$0.471492\pi$
$588$	0	0
$589$	−9920.00	−0.693967
$590$	2800.00	0.195380
$591$	−38352.0	−2.66936
$592$	−17794.0	−1.23535
$593$	−14202.0	−0.983484	−0.491742	−	0.870741i	$-0.663640\pi$
$593$	−14202.0	−0.983484	−0.491742	+	0.870741i	$0.663640\pi$
$594$	960.000	0.0663119
$595$	0	0
$596$	−15890.0	−1.09208
$597$	−10240.0	−0.702002
$598$	2496.00	0.170684
$599$	−19600.0	−1.33695	−0.668476	−	0.743734i	$-0.733053\pi$
$599$	−19600.0	−1.33695	−0.668476	+	0.743734i	$0.733053\pi$
$600$	−3000.00	−0.204124
$601$	27078.0	1.83783	0.918914	−	0.394458i	$-0.129068\pi$
$601$	27078.0	1.83783	0.918914	+	0.394458i	$0.129068\pi$
$602$	0	0
$603$	−6068.00	−0.409798
$604$	−4424.00	−0.298030
$605$	−5935.00	−0.398830
$606$	−3856.00	−0.258481
$607$	2704.00	0.180811	0.0904053	−	0.995905i	$-0.471184\pi$
$607$	2704.00	0.180811	0.0904053	+	0.995905i	$0.471184\pi$
$608$	−6440.00	−0.429567
$609$	0	0
$610$	1390.00	0.0922614
$611$	−41808.0	−2.76820
$612$	−24346.0	−1.60805
$613$	12702.0	0.836915	0.418458	−	0.908236i	$-0.362571\pi$
$613$	12702.0	0.836915	0.418458	+	0.908236i	$0.362571\pi$
$614$	6384.00	0.419605
$615$	−16080.0	−1.05432
$616$	0	0
$617$	12666.0	0.826441	0.413220	−	0.910631i	$-0.364404\pi$
$617$	12666.0	0.826441	0.413220	+	0.910631i	$0.364404\pi$
$618$	−2176.00	−0.141637
$619$	−960.000	−0.0623355	−0.0311677	−	0.999514i	$-0.509923\pi$
$619$	−960.000	−0.0623355	−0.0311677	+	0.999514i	$0.509923\pi$
$620$	−8680.00	−0.562254
$621$	2560.00	0.165426
$622$	4968.00	0.320255
$623$	0	0
$624$	25584.0	1.64131
$625$	625.000	0.0400000
$626$	2758.00	0.176089
$627$	−3840.00	−0.244585
$628$	−5138.00	−0.326479
$629$	−40796.0	−2.58608
$630$	0	0
$631$	23232.0	1.46569	0.732846	−	0.680395i	$-0.238192\pi$
$631$	23232.0	1.46569	0.732846	+	0.680395i	$0.238192\pi$
$632$	15000.0	0.944095
$633$	−544.000	−0.0341581
$634$	−6274.00	−0.393016
$635$	3880.00	0.242477
$636$	−1232.00	−0.0768113
$637$	0	0
$638$	−600.000	−0.0372323
$639$	24864.0	1.53929
$640$	−7275.00	−0.449328
$641$	12162.0	0.749407	0.374704	−	0.927145i	$-0.377744\pi$
$641$	12162.0	0.749407	0.374704	+	0.927145i	$0.377744\pi$
$642$	−3552.00	−0.218359
$643$	488.000	0.0299298	0.0149649	−	0.999888i	$-0.495236\pi$
$643$	488.000	0.0299298	0.0149649	+	0.999888i	$0.495236\pi$
$644$	0	0
$645$	−2720.00	−0.166046
$646$	−3760.00	−0.229002
$647$	3984.00	0.242082	0.121041	−	0.992647i	$-0.461377\pi$
$647$	3984.00	0.242082	0.121041	+	0.992647i	$0.461377\pi$
$648$	5385.00	0.326455
$649$	6720.00	0.406445
$650$	1950.00	0.117670
$651$	0	0
$652$	−17724.0	−1.06461
$653$	−30538.0	−1.83008	−0.915042	−	0.403360i	$-0.867842\pi$
$653$	−30538.0	−1.83008	−0.915042	+	0.403360i	$0.867842\pi$
$654$	−9360.00	−0.559641
$655$	−5560.00	−0.331675
$656$	−16482.0	−0.980966
$657$	−3034.00	−0.180164
$658$	0	0
$659$	22740.0	1.34420	0.672098	−	0.740463i	$-0.265394\pi$
$659$	22740.0	1.34420	0.672098	+	0.740463i	$0.265394\pi$
$660$	−3360.00	−0.198163
$661$	18718.0	1.10143	0.550715	−	0.834693i	$-0.314355\pi$
$661$	18718.0	1.10143	0.550715	+	0.834693i	$0.314355\pi$
$662$	1932.00	0.113428
$663$	58656.0	3.43591
$664$	−6720.00	−0.392751
$665$	0	0
$666$	−16058.0	−0.934287
$667$	−1600.00	−0.0928819
$668$	2912.00	0.168666
$669$	13824.0	0.798904
$670$	−820.000	−0.0472826
$671$	3336.00	0.191930
$672$	0	0
$673$	10802.0	0.618702	0.309351	−	0.950948i	$-0.399888\pi$
$673$	10802.0	0.618702	0.309351	+	0.950948i	$0.399888\pi$
$674$	2386.00	0.136358
$675$	2000.00	0.114044
$676$	−27209.0	−1.54808
$677$	−346.000	−0.0196423	−0.00982117	−	0.999952i	$-0.503126\pi$
$677$	−346.000	−0.0196423	−0.00982117	+	0.999952i	$0.503126\pi$
$678$	−6384.00	−0.361617
$679$	0	0
$680$	−7050.00	−0.397581
$681$	38912.0	2.18959
$682$	2976.00	0.167092
$683$	−11628.0	−0.651439	−0.325720	−	0.945466i	$-0.605607\pi$
$683$	−11628.0	−0.651439	−0.325720	+	0.945466i	$0.605607\pi$
$684$	10360.0	0.579129
$685$	−3470.00	−0.193550
$686$	0	0
$687$	44080.0	2.44797
$688$	−2788.00	−0.154493
$689$	1716.00	0.0948830
$690$	1280.00	0.0706214
$691$	−2472.00	−0.136092	−0.0680458	−	0.997682i	$-0.521676\pi$
$691$	−2472.00	−0.136092	−0.0680458	+	0.997682i	$0.521676\pi$
$692$	21294.0	1.16976
$693$	0	0
$694$	6076.00	0.332337
$695$	−1800.00	−0.0982416
$696$	6000.00	0.326766
$697$	−37788.0	−2.05355
$698$	−2210.00	−0.119842
$699$	42576.0	2.30382
$700$	0	0
$701$	−2018.00	−0.108729	−0.0543643	−	0.998521i	$-0.517313\pi$
$701$	−2018.00	−0.108729	−0.0543643	+	0.998521i	$0.517313\pi$
$702$	6240.00	0.335489
$703$	17360.0	0.931358
$704$	−2004.00	−0.107285
$705$	−21440.0	−1.14536
$706$	2598.00	0.138494
$707$	0	0
$708$	−31360.0	−1.66466
$709$	790.000	0.0418464	0.0209232	−	0.999781i	$-0.493339\pi$
$709$	790.000	0.0418464	0.0209232	+	0.999781i	$0.493339\pi$
$710$	3360.00	0.177604
$711$	−37000.0	−1.95163
$712$	−13050.0	−0.686895
$713$	7936.00	0.416838
$714$	0	0
$715$	4680.00	0.244786
$716$	1260.00	0.0657659
$717$	−14720.0	−0.766706
$718$	−13320.0	−0.692337
$719$	−18200.0	−0.944013	−0.472007	−	0.881595i	$-0.656470\pi$
$719$	−18200.0	−0.944013	−0.472007	+	0.881595i	$0.656470\pi$
$720$	7585.00	0.392606
$721$	0	0
$722$	−5259.00	−0.271080
$723$	3504.00	0.180242
$724$	−13706.0	−0.703563
$725$	−1250.00	−0.0640329
$726$	−9496.00	−0.485440
$727$	−29056.0	−1.48229	−0.741147	−	0.671343i	$-0.765718\pi$
$727$	−29056.0	−1.48229	−0.741147	+	0.671343i	$0.765718\pi$
$728$	0	0
$729$	−30563.0	−1.55276
$730$	−410.000	−0.0207874
$731$	−6392.00	−0.323415
$732$	−15568.0	−0.786079
$733$	−7082.00	−0.356862	−0.178431	−	0.983952i	$-0.557102\pi$
$733$	−7082.00	−0.356862	−0.178431	+	0.983952i	$0.557102\pi$
$734$	−10816.0	−0.543904
$735$	0	0
$736$	5152.00	0.258023
$737$	−1968.00	−0.0983612
$738$	−14874.0	−0.741896
$739$	11060.0	0.550539	0.275270	−	0.961367i	$-0.411233\pi$
$739$	11060.0	0.550539	0.275270	+	0.961367i	$0.411233\pi$
$740$	15190.0	0.754589
$741$	−24960.0	−1.23742
$742$	0	0
$743$	33072.0	1.63297	0.816483	−	0.577369i	$-0.195921\pi$
$743$	33072.0	1.63297	0.816483	+	0.577369i	$0.195921\pi$
$744$	−29760.0	−1.46647
$745$	11350.0	0.558164
$746$	−11098.0	−0.544674
$747$	16576.0	0.811893
$748$	−7896.00	−0.385971
$749$	0	0
$750$	1000.00	0.0486864
$751$	29072.0	1.41259	0.706293	−	0.707919i	$-0.250366\pi$
$751$	29072.0	1.41259	0.706293	+	0.707919i	$0.250366\pi$
$752$	−21976.0	−1.06567
$753$	−44736.0	−2.16503
$754$	−3900.00	−0.188368
$755$	3160.00	0.152323
$756$	0	0
$757$	−13234.0	−0.635400	−0.317700	−	0.948191i	$-0.602911\pi$
$757$	−13234.0	−0.635400	−0.317700	+	0.948191i	$0.602911\pi$
$758$	7100.00	0.340216
$759$	3072.00	0.146912
$760$	3000.00	0.143186
$761$	22398.0	1.06692	0.533460	−	0.845825i	$-0.320891\pi$
$761$	22398.0	1.06692	0.533460	+	0.845825i	$0.320891\pi$
$762$	6208.00	0.295134
$763$	0	0
$764$	20216.0	0.957316
$765$	17390.0	0.821878
$766$	728.000	0.0343390
$767$	43680.0	2.05631
$768$	−952.000	−0.0447296
$769$	−6890.00	−0.323095	−0.161547	−	0.986865i	$-0.551648\pi$
$769$	−6890.00	−0.323095	−0.161547	+	0.986865i	$0.551648\pi$
$770$	0	0
$771$	15792.0	0.737659
$772$	−11214.0	−0.522799
$773$	−16722.0	−0.778071	−0.389035	−	0.921223i	$-0.627192\pi$
$773$	−16722.0	−0.778071	−0.389035	+	0.921223i	$0.627192\pi$
$774$	−2516.00	−0.116842
$775$	6200.00	0.287368
$776$	15390.0	0.711944
$777$	0	0
$778$	−6810.00	−0.313818
$779$	16080.0	0.739571
$780$	−21840.0	−1.00256
$781$	8064.00	0.369466
$782$	3008.00	0.137552
$783$	−4000.00	−0.182565
$784$	0	0
$785$	3670.00	0.166864
$786$	−8896.00	−0.403702
$787$	32624.0	1.47766	0.738831	−	0.673891i	$-0.235378\pi$
$787$	32624.0	1.47766	0.738831	+	0.673891i	$0.235378\pi$
$788$	33558.0	1.51707
$789$	−5824.00	−0.262788
$790$	−5000.00	−0.225180
$791$	0	0
$792$	−6660.00	−0.298804
$793$	21684.0	0.971023
$794$	574.000	0.0256555
$795$	880.000	0.0392583
$796$	8960.00	0.398968
$797$	−11346.0	−0.504261	−0.252130	−	0.967693i	$-0.581131\pi$
$797$	−11346.0	−0.504261	−0.252130	+	0.967693i	$0.581131\pi$
$798$	0	0
$799$	−50384.0	−2.23086
$800$	4025.00	0.177882
$801$	32190.0	1.41995
$802$	6162.00	0.271306
$803$	−984.000	−0.0432436
$804$	9184.00	0.402854
$805$	0	0
$806$	19344.0	0.845364
$807$	−46480.0	−2.02748
$808$	7230.00	0.314790
$809$	−35190.0	−1.52931	−0.764657	−	0.644438i	$-0.777091\pi$
$809$	−35190.0	−1.52931	−0.764657	+	0.644438i	$0.777091\pi$
$810$	−1795.00	−0.0778640
$811$	−30432.0	−1.31765	−0.658824	−	0.752297i	$-0.728946\pi$
$811$	−30432.0	−1.31765	−0.658824	+	0.752297i	$0.728946\pi$
$812$	0	0
$813$	52224.0	2.25286
$814$	−5208.00	−0.224251
$815$	12660.0	0.544123
$816$	30832.0	1.32272
$817$	2720.00	0.116476
$818$	−8210.00	−0.350924
$819$	0	0
$820$	14070.0	0.599202
$821$	12702.0	0.539955	0.269977	−	0.962867i	$-0.412984\pi$
$821$	12702.0	0.539955	0.269977	+	0.962867i	$0.412984\pi$
$822$	−5552.00	−0.235582
$823$	16952.0	0.717995	0.358997	−	0.933339i	$-0.383119\pi$
$823$	16952.0	0.717995	0.358997	+	0.933339i	$0.383119\pi$
$824$	4080.00	0.172492
$825$	2400.00	0.101282
$826$	0	0
$827$	−25404.0	−1.06818	−0.534089	−	0.845428i	$-0.679345\pi$
$827$	−25404.0	−1.06818	−0.534089	+	0.845428i	$0.679345\pi$
$828$	−8288.00	−0.347860
$829$	−26250.0	−1.09976	−0.549879	−	0.835244i	$-0.685326\pi$
$829$	−26250.0	−1.09976	−0.549879	+	0.835244i	$0.685326\pi$
$830$	2240.00	0.0936765
$831$	41008.0	1.71186
$832$	−13026.0	−0.542783
$833$	0	0
$834$	−2880.00	−0.119576
$835$	−2080.00	−0.0862052
$836$	3360.00	0.139005
$837$	19840.0	0.819320
$838$	−4800.00	−0.197868
$839$	15360.0	0.632045	0.316023	−	0.948752i	$-0.397652\pi$
$839$	15360.0	0.632045	0.316023	+	0.948752i	$0.397652\pi$
$840$	0	0
$841$	−21889.0	−0.897495
$842$	−9938.00	−0.406753
$843$	−18864.0	−0.770713
$844$	476.000	0.0194130
$845$	19435.0	0.791224
$846$	−19832.0	−0.805955
$847$	0	0
$848$	902.000	0.0365269
$849$	−3136.00	−0.126769
$850$	2350.00	0.0948286
$851$	−13888.0	−0.559430
$852$	−37632.0	−1.51321
$853$	−10362.0	−0.415930	−0.207965	−	0.978136i	$-0.566684\pi$
$853$	−10362.0	−0.415930	−0.207965	+	0.978136i	$0.566684\pi$
$854$	0	0
$855$	−7400.00	−0.295994
$856$	6660.00	0.265928
$857$	−4506.00	−0.179606	−0.0898028	−	0.995960i	$-0.528624\pi$
$857$	−4506.00	−0.179606	−0.0898028	+	0.995960i	$0.528624\pi$
$858$	7488.00	0.297944
$859$	−24200.0	−0.961226	−0.480613	−	0.876933i	$-0.659586\pi$
$859$	−24200.0	−0.961226	−0.480613	+	0.876933i	$0.659586\pi$
$860$	2380.00	0.0943690
$861$	0	0
$862$	−9248.00	−0.365415
$863$	−37008.0	−1.45975	−0.729877	−	0.683579i	$-0.760422\pi$
$863$	−37008.0	−1.45975	−0.729877	+	0.683579i	$0.760422\pi$
$864$	12880.0	0.507160
$865$	−15210.0	−0.597868
$866$	1118.00	0.0438697
$867$	31384.0	1.22936
$868$	0	0
$869$	−12000.0	−0.468437
$870$	−2000.00	−0.0779383
$871$	−12792.0	−0.497635
$872$	17550.0	0.681557
$873$	−37962.0	−1.47173
$874$	−1280.00	−0.0495385
$875$	0	0
$876$	4592.00	0.177111
$877$	3446.00	0.132683	0.0663416	−	0.997797i	$-0.478867\pi$
$877$	3446.00	0.132683	0.0663416	+	0.997797i	$0.478867\pi$
$878$	11960.0	0.459716
$879$	−9616.00	−0.368987
$880$	2460.00	0.0942348
$881$	16158.0	0.617908	0.308954	−	0.951077i	$-0.400021\pi$
$881$	16158.0	0.617908	0.308954	+	0.951077i	$0.400021\pi$
$882$	0	0
$883$	−44708.0	−1.70390	−0.851950	−	0.523623i	$-0.824580\pi$
$883$	−44708.0	−1.70390	−0.851950	+	0.523623i	$0.824580\pi$
$884$	−51324.0	−1.95273
$885$	22400.0	0.850811
$886$	7332.00	0.278017
$887$	23504.0	0.889726	0.444863	−	0.895599i	$-0.353252\pi$
$887$	23504.0	0.889726	0.444863	+	0.895599i	$0.353252\pi$
$888$	52080.0	1.96812
$889$	0	0
$890$	4350.00	0.163834
$891$	−4308.00	−0.161979
$892$	−12096.0	−0.454040
$893$	21440.0	0.803429
$894$	18160.0	0.679375
$895$	−900.000	−0.0336131
$896$	0	0
$897$	19968.0	0.743269
$898$	1890.00	0.0702340
$899$	−12400.0	−0.460026
$900$	−6475.00	−0.239815
$901$	2068.00	0.0764651
$902$	−4824.00	−0.178073
$903$	0	0
$904$	11970.0	0.440394
$905$	9790.00	0.359592
$906$	5056.00	0.185402
$907$	42436.0	1.55354	0.776772	−	0.629782i	$-0.216856\pi$
$907$	42436.0	1.55354	0.776772	+	0.629782i	$0.216856\pi$
$908$	−34048.0	−1.24441
$909$	−17834.0	−0.650733
$910$	0	0
$911$	−7968.00	−0.289782	−0.144891	−	0.989448i	$-0.546283\pi$
$911$	−7968.00	−0.289782	−0.144891	+	0.989448i	$0.546283\pi$
$912$	−13120.0	−0.476367
$913$	5376.00	0.194874
$914$	−7014.00	−0.253832
$915$	11120.0	0.401766
$916$	−38570.0	−1.39125
$917$	0	0
$918$	7520.00	0.270367
$919$	14880.0	0.534109	0.267054	−	0.963681i	$-0.413950\pi$
$919$	14880.0	0.534109	0.267054	+	0.963681i	$0.413950\pi$
$920$	−2400.00	−0.0860061
$921$	51072.0	1.82723
$922$	8318.00	0.297114
$923$	52416.0	1.86922
$924$	0	0
$925$	−10850.0	−0.385671
$926$	6432.00	0.228260
$927$	−10064.0	−0.356575
$928$	−8050.00	−0.284757
$929$	−27610.0	−0.975086	−0.487543	−	0.873099i	$-0.662107\pi$
$929$	−27610.0	−0.975086	−0.487543	+	0.873099i	$0.662107\pi$
$930$	9920.00	0.349774
$931$	0	0
$932$	−37254.0	−1.30933
$933$	39744.0	1.39460
$934$	10064.0	0.352574
$935$	5640.00	0.197270
$936$	−43290.0	−1.51173
$937$	28094.0	0.979499	0.489750	−	0.871863i	$-0.337088\pi$
$937$	28094.0	0.979499	0.489750	+	0.871863i	$0.337088\pi$
$938$	0	0
$939$	22064.0	0.766807
$940$	18760.0	0.650940
$941$	12198.0	0.422575	0.211288	−	0.977424i	$-0.432234\pi$
$941$	12198.0	0.422575	0.211288	+	0.977424i	$0.432234\pi$
$942$	5872.00	0.203100
$943$	−12864.0	−0.444231
$944$	22960.0	0.791615
$945$	0	0
$946$	−816.000	−0.0280449
$947$	31316.0	1.07459	0.537293	−	0.843396i	$-0.319447\pi$
$947$	31316.0	1.07459	0.537293	+	0.843396i	$0.319447\pi$
$948$	56000.0	1.91856
$949$	−6396.00	−0.218781
$950$	−1000.00	−0.0341519
$951$	−50192.0	−1.71145
$952$	0	0
$953$	27322.0	0.928695	0.464348	−	0.885653i	$-0.346289\pi$
$953$	27322.0	0.928695	0.464348	+	0.885653i	$0.346289\pi$
$954$	814.000	0.0276250
$955$	−14440.0	−0.489285
$956$	12880.0	0.435742
$957$	−4800.00	−0.162134
$958$	−1400.00	−0.0472150
$959$	0	0
$960$	−6680.00	−0.224579
$961$	31713.0	1.06452
$962$	−33852.0	−1.13454
$963$	−16428.0	−0.549725
$964$	−3066.00	−0.102437
$965$	8010.00	0.267203
$966$	0	0
$967$	5296.00	0.176120	0.0880599	−	0.996115i	$-0.471933\pi$
$967$	5296.00	0.176120	0.0880599	+	0.996115i	$0.471933\pi$
$968$	17805.0	0.591193
$969$	−30080.0	−0.997223
$970$	−5130.00	−0.169809
$971$	−512.000	−0.0169216	−0.00846079	−	0.999964i	$-0.502693\pi$
$971$	−512.000	−0.0169216	−0.00846079	+	0.999964i	$0.502693\pi$
$972$	35224.0	1.16236
$973$	0	0
$974$	13376.0	0.440036
$975$	15600.0	0.512410
$976$	11398.0	0.373813
$977$	−20734.0	−0.678955	−0.339478	−	0.940614i	$-0.610250\pi$
$977$	−20734.0	−0.678955	−0.339478	+	0.940614i	$0.610250\pi$
$978$	20256.0	0.662286
$979$	10440.0	0.340821
$980$	0	0
$981$	−43290.0	−1.40891
$982$	7092.00	0.230463
$983$	61168.0	1.98470	0.992348	−	0.123472i	$-0.0394030\pi$
$983$	61168.0	1.98470	0.992348	+	0.123472i	$0.0394030\pi$
$984$	48240.0	1.56284
$985$	−23970.0	−0.775378
$986$	−4700.00	−0.151804
$987$	0	0
$988$	21840.0	0.703262
$989$	−2176.00	−0.0699624
$990$	2220.00	0.0712689
$991$	−47928.0	−1.53631	−0.768155	−	0.640264i	$-0.778825\pi$
$991$	−47928.0	−1.53631	−0.768155	+	0.640264i	$0.778825\pi$
$992$	39928.0	1.27794
$993$	15456.0	0.493939
$994$	0	0
$995$	−6400.00	−0.203913
$996$	−25088.0	−0.798136
$997$	9454.00	0.300312	0.150156	−	0.988662i	$-0.452022\pi$
$997$	9454.00	0.300312	0.150156	+	0.988662i	$0.452022\pi$
$998$	−820.000	−0.0260087
$999$	−34720.0	−1.09959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.a.d.1.1		1
3.2	odd	2		2205.4.a.i.1.1		1
5.4	even	2		1225.4.a.e.1.1		1
7.2	even	3		245.4.e.b.116.1		2
7.3	odd	6		245.4.e.e.226.1		2
7.4	even	3		245.4.e.b.226.1		2
7.5	odd	6		245.4.e.e.116.1		2
7.6	odd	2		35.4.a.a.1.1	✓	1
21.20	even	2		315.4.a.c.1.1		1
28.27	even	2		560.4.a.p.1.1		1
35.13	even	4		175.4.b.a.99.1		2
35.27	even	4		175.4.b.a.99.2		2
35.34	odd	2		175.4.a.a.1.1		1
56.13	odd	2		2240.4.a.bk.1.1		1
56.27	even	2		2240.4.a.b.1.1		1
105.104	even	2		1575.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.a.1.1	✓	1	7.6	odd	2
175.4.a.a.1.1		1	35.34	odd	2
175.4.b.a.99.1		2	35.13	even	4
175.4.b.a.99.2		2	35.27	even	4
245.4.a.d.1.1		1	1.1	even	1	trivial
245.4.e.b.116.1		2	7.2	even	3
245.4.e.b.226.1		2	7.4	even	3
245.4.e.e.116.1		2	7.5	odd	6
245.4.e.e.226.1		2	7.3	odd	6
315.4.a.c.1.1		1	21.20	even	2
560.4.a.p.1.1		1	28.27	even	2
1225.4.a.e.1.1		1	5.4	even	2
1575.4.a.g.1.1		1	105.104	even	2
2205.4.a.i.1.1		1	3.2	odd	2
2240.4.a.b.1.1		1	56.27	even	2
2240.4.a.bk.1.1		1	56.13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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