LMFDB - Embedded newform 35.4.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,4,Mod(1,35)] 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("35.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment:select newform

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

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

Self dual:	yes
Analytic conductor:	$2.06506685020$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+1.00000 q^{2} -8.00000 q^{3} -7.00000 q^{4} -5.00000 q^{5} -8.00000 q^{6} +7.00000 q^{7} -15.0000 q^{8} +37.0000 q^{9} -5.00000 q^{10} +12.0000 q^{11} +56.0000 q^{12} -78.0000 q^{13} +7.00000 q^{14} +40.0000 q^{15} +41.0000 q^{16} -94.0000 q^{17} +37.0000 q^{18} +40.0000 q^{19} +35.0000 q^{20} -56.0000 q^{21} +12.0000 q^{22} +32.0000 q^{23} +120.000 q^{24} +25.0000 q^{25} -78.0000 q^{26} -80.0000 q^{27} -49.0000 q^{28} -50.0000 q^{29} +40.0000 q^{30} -248.000 q^{31} +161.000 q^{32} -96.0000 q^{33} -94.0000 q^{34} -35.0000 q^{35} -259.000 q^{36} -434.000 q^{37} +40.0000 q^{38} +624.000 q^{39} +75.0000 q^{40} +402.000 q^{41} -56.0000 q^{42} -68.0000 q^{43} -84.0000 q^{44} -185.000 q^{45} +32.0000 q^{46} +536.000 q^{47} -328.000 q^{48} +49.0000 q^{49} +25.0000 q^{50} +752.000 q^{51} +546.000 q^{52} +22.0000 q^{53} -80.0000 q^{54} -60.0000 q^{55} -105.000 q^{56} -320.000 q^{57} -50.0000 q^{58} -560.000 q^{59} -280.000 q^{60} -278.000 q^{61} -248.000 q^{62} +259.000 q^{63} -167.000 q^{64} +390.000 q^{65} -96.0000 q^{66} -164.000 q^{67} +658.000 q^{68} -256.000 q^{69} -35.0000 q^{70} +672.000 q^{71} -555.000 q^{72} +82.0000 q^{73} -434.000 q^{74} -200.000 q^{75} -280.000 q^{76} +84.0000 q^{77} +624.000 q^{78} -1000.00 q^{79} -205.000 q^{80} -359.000 q^{81} +402.000 q^{82} -448.000 q^{83} +392.000 q^{84} +470.000 q^{85} -68.0000 q^{86} +400.000 q^{87} -180.000 q^{88} -870.000 q^{89} -185.000 q^{90} -546.000 q^{91} -224.000 q^{92} +1984.00 q^{93} +536.000 q^{94} -200.000 q^{95} -1288.00 q^{96} +1026.00 q^{97} +49.0000 q^{98} +444.000 q^{99} +O(q^{100})\)

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	$-0.779644\pi$
$3$	−8.00000	−1.53960	−0.769800	+	0.638285i	$0.779644\pi$
$4$	−7.00000	−0.875000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−8.00000	−0.544331
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−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	$-0.812833\pi$
$13$	−78.0000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	7.00000	0.133631
$15$	40.0000	0.688530
$16$	41.0000	0.640625
$17$	−94.0000	−1.34108	−0.670540	−	0.741874i	$-0.733937\pi$
$17$	−94.0000	−1.34108	−0.670540	+	0.741874i	$0.733937\pi$
$18$	37.0000	0.484499
$19$	40.0000	0.482980	0.241490	−	0.970403i	$-0.422364\pi$
$19$	40.0000	0.482980	0.241490	+	0.970403i	$0.422364\pi$
$20$	35.0000	0.391312
$21$	−56.0000	−0.581914
$22$	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
$28$	−49.0000	−0.330719
$29$	−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	$-0.755135\pi$
$31$	−248.000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	161.000	0.889408
$33$	−96.0000	−0.506408
$34$	−94.0000	−0.474143
$35$	−35.0000	−0.169031
$36$	−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	$-0.222426\pi$
$41$	402.000	1.53126	0.765632	+	0.643278i	$0.222426\pi$
$42$	−56.0000	−0.205738
$43$	−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	$-0.187345\pi$
$47$	536.000	1.66348	0.831741	+	0.555164i	$0.187345\pi$
$48$	−328.000	−0.986307
$49$	49.0000	0.142857
$50$	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
$56$	−105.000	−0.250557
$57$	−320.000	−0.743597
$58$	−50.0000	−0.113195
$59$	−560.000	−1.23569	−0.617846	−	0.786299i	$-0.711994\pi$
$59$	−560.000	−1.23569	−0.617846	+	0.786299i	$0.711994\pi$
$60$	−280.000	−0.602464
$61$	−278.000	−0.583512	−0.291756	−	0.956493i	$-0.594240\pi$
$61$	−278.000	−0.583512	−0.291756	+	0.956493i	$0.594240\pi$
$62$	−248.000	−0.508001
$63$	259.000	0.517951
$64$	−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
$70$	−35.0000	−0.0597614
$71$	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	$-0.479061\pi$
$73$	82.0000	0.131471	0.0657354	+	0.997837i	$0.479061\pi$
$74$	−434.000	−0.681777
$75$	−200.000	−0.307920
$76$	−280.000	−0.422608
$77$	84.0000	0.124321
$78$	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	$-0.595730\pi$
$83$	−448.000	−0.592463	−0.296231	+	0.955116i	$0.595730\pi$
$84$	392.000	0.509175
$85$	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	$-0.673356\pi$
$89$	−870.000	−1.03618	−0.518089	+	0.855327i	$0.673356\pi$
$90$	−185.000	−0.216675
$91$	−546.000	−0.628971
$92$	−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	$-0.319564\pi$
$97$	1026.00	1.07396	0.536982	+	0.843594i	$0.319564\pi$
$98$	49.0000	0.0505076
$99$	444.000	0.450744
$100$	−175.000	−0.175000
$101$	482.000	0.474859	0.237430	−	0.971405i	$-0.423695\pi$
$101$	482.000	0.474859	0.237430	+	0.971405i	$0.423695\pi$
$102$	752.000	0.729991
$103$	272.000	0.260203	0.130102	−	0.991501i	$-0.458470\pi$
$103$	272.000	0.260203	0.130102	+	0.991501i	$0.458470\pi$
$104$	1170.00	1.10315
$105$	280.000	0.260240
$106$	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
$112$	287.000	0.242133
$113$	−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
$119$	−658.000	−0.506880
$120$	−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
$126$	259.000	0.183123
$127$	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	$-0.379075\pi$
$131$	1112.00	0.741648	0.370824	+	0.928703i	$0.379075\pi$
$132$	672.000	0.443107
$133$	280.000	0.182549
$134$	−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	$-0.464967\pi$
$139$	360.000	0.219675	0.109837	+	0.993950i	$0.464967\pi$
$140$	245.000	0.147902
$141$	−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
$147$	−392.000	−0.219943
$148$	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
$154$	84.0000	0.0439540
$155$	1240.00	0.642575
$156$	−4368.00	−2.24179
$157$	−734.000	−0.373118	−0.186559	−	0.982444i	$-0.559734\pi$
$157$	−734.000	−0.373118	−0.186559	+	0.982444i	$0.559734\pi$
$158$	−1000.00	−0.503517
$159$	−176.000	−0.0877843
$160$	−805.000	−0.397755
$161$	224.000	0.109650
$162$	−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	$-0.469273\pi$
$167$	416.000	0.192761	0.0963804	+	0.995345i	$0.469273\pi$
$168$	840.000	0.385758
$169$	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	$-0.266964\pi$
$173$	3042.00	1.33687	0.668436	+	0.743769i	$0.266964\pi$
$174$	400.000	0.174275
$175$	175.000	0.0755929
$176$	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	$-0.631697\pi$
$181$	−1958.00	−0.804072	−0.402036	+	0.915624i	$0.631697\pi$
$182$	−546.000	−0.222375
$183$	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
$189$	−560.000	−0.215524
$190$	−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
$196$	−343.000	−0.125000
$197$	−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	$-0.426787\pi$
$199$	1280.00	0.455964	0.227982	+	0.973665i	$0.426787\pi$
$200$	−375.000	−0.132583
$201$	1312.00	0.460405
$202$	482.000	0.167888
$203$	−350.000	−0.121011
$204$	−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
$210$	280.000	0.0920087
$211$	−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
$217$	−1736.00	−0.543075
$218$	−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	$-0.583542\pi$
$223$	−1728.00	−0.518903	−0.259452	+	0.965756i	$0.583542\pi$
$224$	1127.00	0.336165
$225$	925.000	0.274074
$226$	−798.000	−0.234877
$227$	−4864.00	−1.42218	−0.711090	−	0.703101i	$-0.751798\pi$
$227$	−4864.00	−1.42218	−0.711090	+	0.703101i	$0.751798\pi$
$228$	2240.00	0.650647
$229$	−5510.00	−1.59000	−0.795002	−	0.606606i	$-0.792530\pi$
$229$	−5510.00	−1.59000	−0.795002	+	0.606606i	$0.792530\pi$
$230$	−160.000	−0.0458699
$231$	−672.000	−0.191404
$232$	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
$238$	−658.000	−0.179209
$239$	−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	$-0.518643\pi$
$241$	−438.000	−0.117071	−0.0585354	+	0.998285i	$0.518643\pi$
$242$	−1187.00	−0.315303
$243$	5032.00	1.32841
$244$	1946.00	0.510573
$245$	−245.000	−0.0638877
$246$	−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	$-0.251792\pi$
$251$	5592.00	1.40623	0.703115	+	0.711076i	$0.251792\pi$
$252$	−1813.00	−0.453207
$253$	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	$-0.577004\pi$
$257$	−1974.00	−0.479123	−0.239562	+	0.970881i	$0.577004\pi$
$258$	544.000	0.131271
$259$	−3038.00	−0.728850
$260$	−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
$266$	280.000	0.0645410
$267$	6960.00	1.59530
$268$	1148.00	0.261661
$269$	5810.00	1.31688	0.658442	−	0.752631i	$-0.271216\pi$
$269$	5810.00	1.31688	0.658442	+	0.752631i	$0.271216\pi$
$270$	400.000	0.0901601
$271$	−6528.00	−1.46328	−0.731638	−	0.681693i	$-0.761244\pi$
$271$	−6528.00	−1.46328	−0.731638	+	0.681693i	$0.761244\pi$
$272$	−3854.00	−0.859129
$273$	4368.00	0.968364
$274$	−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
$280$	525.000	0.112053
$281$	−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	$-0.486892\pi$
$283$	392.000	0.0823392	0.0411696	+	0.999152i	$0.486892\pi$
$284$	−4704.00	−0.982856
$285$	1600.00	0.332547
$286$	−936.000	−0.193520
$287$	2814.00	0.578764
$288$	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	$-0.461764\pi$
$293$	1202.00	0.239664	0.119832	+	0.992794i	$0.461764\pi$
$294$	−392.000	−0.0777616
$295$	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
$301$	−476.000	−0.0911501
$302$	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	$-0.702219\pi$
$307$	−6384.00	−1.18682	−0.593411	+	0.804900i	$0.702219\pi$
$308$	−588.000	−0.108781
$309$	−2176.00	−0.400609
$310$	1240.00	0.227185
$311$	−4968.00	−0.905818	−0.452909	−	0.891557i	$-0.649614\pi$
$311$	−4968.00	−0.905818	−0.452909	+	0.891557i	$0.649614\pi$
$312$	−9360.00	−1.69842
$313$	−2758.00	−0.498056	−0.249028	−	0.968496i	$-0.580111\pi$
$313$	−2758.00	−0.498056	−0.249028	+	0.968496i	$0.580111\pi$
$314$	−734.000	−0.131917
$315$	−1295.00	−0.231635
$316$	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
$322$	224.000	0.0387672
$323$	−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
$329$	3752.00	0.628737
$330$	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
$336$	−2296.00	−0.372789
$337$	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
$343$	343.000	0.0539949
$344$	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	$-0.445790\pi$
$349$	2210.00	0.338964	0.169482	+	0.985533i	$0.445790\pi$
$350$	175.000	0.0267261
$351$	6240.00	0.948908
$352$	1932.00	0.292545
$353$	−2598.00	−0.391721	−0.195861	−	0.980632i	$-0.562750\pi$
$353$	−2598.00	−0.391721	−0.195861	+	0.980632i	$0.562750\pi$
$354$	4480.00	0.672625
$355$	−3360.00	−0.502339
$356$	6090.00	0.906655
$357$	5264.00	0.780393
$358$	−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
$364$	3822.00	0.550350
$365$	−410.000	−0.0587956
$366$	2224.00	0.317624
$367$	10816.0	1.53839	0.769197	−	0.639012i	$-0.220656\pi$
$367$	10816.0	1.53839	0.769197	+	0.639012i	$0.220656\pi$
$368$	1312.00	0.185850
$369$	14874.0	2.09840
$370$	2170.00	0.304900
$371$	154.000	0.0215506
$372$	−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
$378$	−560.000	−0.0761992
$379$	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	$-0.515464\pi$
$383$	−728.000	−0.0971255	−0.0485627	+	0.998820i	$0.515464\pi$
$384$	11640.0	1.54688
$385$	−420.000	−0.0555979
$386$	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
$392$	−735.000	−0.0947018
$393$	−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	$-0.511552\pi$
$397$	−574.000	−0.0725648	−0.0362824	+	0.999342i	$0.511552\pi$
$398$	1280.00	0.161208
$399$	−2240.00	−0.281053
$400$	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
$406$	−350.000	−0.0427838
$407$	−5208.00	−0.634278
$408$	−11280.0	−1.36873
$409$	8210.00	0.992563	0.496282	−	0.868162i	$-0.334698\pi$
$409$	8210.00	0.992563	0.496282	+	0.868162i	$0.334698\pi$
$410$	−2010.00	−0.242114
$411$	5552.00	0.666326
$412$	−1904.00	−0.227678
$413$	−3920.00	−0.467047
$414$	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	$-0.409723\pi$
$419$	4800.00	0.559655	0.279827	+	0.960050i	$0.409723\pi$
$420$	−1960.00	−0.227710
$421$	−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
$427$	−1946.00	−0.220547
$428$	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	$-0.519761\pi$
$433$	−1118.00	−0.124082	−0.0620412	+	0.998074i	$0.519761\pi$
$434$	−1736.00	−0.192006
$435$	−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	$-0.725288\pi$
$439$	−11960.0	−1.30027	−0.650136	+	0.759818i	$0.725288\pi$
$440$	900.000	0.0975132
$441$	1813.00	0.195767
$442$	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
$448$	−1169.00	−0.123281
$449$	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
$455$	2730.00	0.281284
$456$	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	$-0.638034\pi$
$461$	−8318.00	−0.840364	−0.420182	+	0.907440i	$0.638034\pi$
$462$	−672.000	−0.0676716
$463$	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	$-0.666158\pi$
$467$	−10064.0	−0.997230	−0.498615	+	0.866824i	$0.666158\pi$
$468$	20202.0	1.99538
$469$	−1148.00	−0.113027
$470$	−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
$476$	4606.00	0.443520
$477$	814.000	0.0781352
$478$	−1840.00	−0.176066
$479$	1400.00	0.133544	0.0667721	−	0.997768i	$-0.478730\pi$
$479$	1400.00	0.133544	0.0667721	+	0.997768i	$0.478730\pi$
$480$	6440.00	0.612384
$481$	33852.0	3.20898
$482$	−438.000	−0.0413908
$483$	−1792.00	−0.168817
$484$	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
$490$	−245.000	−0.0225877
$491$	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
$497$	4704.00	0.424554
$498$	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	$-0.564894\pi$
$503$	−4568.00	−0.404925	−0.202462	+	0.979290i	$0.564894\pi$
$504$	−3885.00	−0.343356
$505$	−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	$-0.168874\pi$
$509$	19810.0	1.72507	0.862537	+	0.505994i	$0.168874\pi$
$510$	−3760.00	−0.326462
$511$	574.000	0.0496913
$512$	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
$518$	−3038.00	−0.257687
$519$	−24336.0	−2.05825
$520$	−5850.00	−0.493345
$521$	−1838.00	−0.154557	−0.0772785	−	0.997010i	$-0.524623\pi$
$521$	−1838.00	−0.154557	−0.0772785	+	0.997010i	$0.524623\pi$
$522$	−1850.00	−0.155119
$523$	2072.00	0.173236	0.0866178	−	0.996242i	$-0.472394\pi$
$523$	2072.00	0.173236	0.0866178	+	0.996242i	$0.472394\pi$
$524$	−7784.00	−0.648942
$525$	−1400.00	−0.116383
$526$	−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
$532$	−1960.00	−0.159731
$533$	−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
$539$	588.000	0.0469888
$540$	−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
$546$	4368.00	0.342368
$547$	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
$553$	−7000.00	−0.538283
$554$	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
$560$	−1435.00	−0.108285
$561$	9024.00	0.679133
$562$	−2358.00	−0.176986
$563$	16072.0	1.20312	0.601558	−	0.798829i	$-0.294547\pi$
$563$	16072.0	1.20312	0.601558	+	0.798829i	$0.294547\pi$
$564$	30016.0	2.24096
$565$	3990.00	0.297098
$566$	392.000	0.0291113
$567$	−2513.00	−0.186131
$568$	−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
$574$	2814.00	0.204624
$575$	800.000	0.0580214
$576$	−6179.00	−0.446976
$577$	−20054.0	−1.44690	−0.723448	−	0.690379i	$-0.757444\pi$
$577$	−20054.0	−1.44690	−0.723448	+	0.690379i	$0.757444\pi$
$578$	3923.00	0.282310
$579$	−12816.0	−0.919887
$580$	−1750.00	−0.125284
$581$	−3136.00	−0.223930
$582$	−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	$-0.528508\pi$
$587$	−2544.00	−0.178879	−0.0894396	+	0.995992i	$0.528508\pi$
$588$	2744.00	0.192450
$589$	−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	$-0.336360\pi$
$593$	14202.0	0.983484	0.491742	+	0.870741i	$0.336360\pi$
$594$	−960.000	−0.0663119
$595$	3290.00	0.226684
$596$	−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	$-0.870932\pi$
$601$	−27078.0	−1.83783	−0.918914	+	0.394458i	$0.870932\pi$
$602$	−476.000	−0.0322264
$603$	−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	$-0.528816\pi$
$607$	−2704.00	−0.180811	−0.0904053	+	0.995905i	$0.528816\pi$
$608$	6440.00	0.429567
$609$	2800.00	0.186308
$610$	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
$616$	−1260.00	−0.0824137
$617$	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	$-0.490077\pi$
$619$	960.000	0.0623355	0.0311677	+	0.999514i	$0.490077\pi$
$620$	−8680.00	−0.562254
$621$	−2560.00	−0.165426
$622$	−4968.00	−0.320255
$623$	−6090.00	−0.391638
$624$	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
$630$	−1295.00	−0.0818953
$631$	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
$637$	−3822.00	−0.237729
$638$	−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	$-0.504764\pi$
$643$	−488.000	−0.0299298	−0.0149649	+	0.999888i	$0.504764\pi$
$644$	−1568.00	−0.0959439
$645$	−2720.00	−0.166046
$646$	−3760.00	−0.229002
$647$	−3984.00	−0.242082	−0.121041	−	0.992647i	$-0.538623\pi$
$647$	−3984.00	−0.242082	−0.121041	+	0.992647i	$0.538623\pi$
$648$	5385.00	0.326455
$649$	−6720.00	−0.406445
$650$	−1950.00	−0.117670
$651$	13888.0	0.836119
$652$	−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
$658$	3752.00	0.222292
$659$	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	$-0.685645\pi$
$661$	−18718.0	−1.10143	−0.550715	+	0.834693i	$0.685645\pi$
$662$	1932.00	0.113428
$663$	−58656.0	−3.43591
$664$	6720.00	0.392751
$665$	−1400.00	−0.0816386
$666$	−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
$672$	−9016.00	−0.517559
$673$	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	$-0.496874\pi$
$677$	346.000	0.0196423	0.00982117	+	0.999952i	$0.496874\pi$
$678$	6384.00	0.361617
$679$	7182.00	0.405920
$680$	−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
$686$	343.000	0.0190901
$687$	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	$-0.478324\pi$
$691$	2472.00	0.136092	0.0680458	+	0.997682i	$0.478324\pi$
$692$	−21294.0	−1.16976
$693$	3108.00	0.170365
$694$	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
$700$	−1225.00	−0.0661438
$701$	−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
$707$	3374.00	0.179480
$708$	−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
$714$	5264.00	0.275911
$715$	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	$-0.343530\pi$
$719$	18200.0	0.944013	0.472007	+	0.881595i	$0.343530\pi$
$720$	−7585.00	−0.392606
$721$	1904.00	0.0983477
$722$	−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	$-0.234282\pi$
$727$	29056.0	1.48229	0.741147	+	0.671343i	$0.234282\pi$
$728$	8190.00	0.416953
$729$	−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	$-0.442898\pi$
$733$	7082.00	0.356862	0.178431	+	0.983952i	$0.442898\pi$
$734$	10816.0	0.543904
$735$	1960.00	0.0983615
$736$	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
$742$	154.000	0.00761930
$743$	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
$749$	−3108.00	−0.151621
$750$	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
$756$	3920.00	0.188583
$757$	−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	$-0.679109\pi$
$761$	−22398.0	−1.06692	−0.533460	+	0.845825i	$0.679109\pi$
$762$	−6208.00	−0.295134
$763$	−8190.00	−0.388595
$764$	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	$-0.448352\pi$
$769$	6890.00	0.323095	0.161547	+	0.986865i	$0.448352\pi$
$770$	−420.000	−0.0196568
$771$	15792.0	0.737659
$772$	−11214.0	−0.522799
$773$	16722.0	0.778071	0.389035	−	0.921223i	$-0.372808\pi$
$773$	16722.0	0.778071	0.389035	+	0.921223i	$0.372808\pi$
$774$	−2516.00	−0.116842
$775$	−6200.00	−0.287368
$776$	−15390.0	−0.711944
$777$	24304.0	1.12214
$778$	−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
$784$	2009.00	0.0915179
$785$	3670.00	0.166864
$786$	−8896.00	−0.403702
$787$	−32624.0	−1.47766	−0.738831	−	0.673891i	$-0.764622\pi$
$787$	−32624.0	−1.47766	−0.738831	+	0.673891i	$0.764622\pi$
$788$	33558.0	1.51707
$789$	5824.00	0.262788
$790$	5000.00	0.225180
$791$	−5586.00	−0.251094
$792$	−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	$-0.418869\pi$
$797$	11346.0	0.504261	0.252130	+	0.967693i	$0.418869\pi$
$798$	−2240.00	−0.0993673
$799$	−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
$805$	−1120.00	−0.0490370
$806$	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	$-0.271054\pi$
$811$	30432.0	1.31765	0.658824	+	0.752297i	$0.271054\pi$
$812$	2450.00	0.105884
$813$	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
$819$	−20202.0	−0.861923
$820$	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
$826$	−3920.00	−0.165126
$827$	−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	$-0.314674\pi$
$829$	26250.0	1.09976	0.549879	+	0.835244i	$0.314674\pi$
$830$	2240.00	0.0936765
$831$	−41008.0	−1.71186
$832$	13026.0	0.542783
$833$	−4606.00	−0.191583
$834$	−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	$-0.602348\pi$
$839$	−15360.0	−0.632045	−0.316023	+	0.948752i	$0.602348\pi$
$840$	−4200.00	−0.172516
$841$	−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
$847$	−8309.00	−0.337073
$848$	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	$-0.433316\pi$
$853$	10362.0	0.415930	0.207965	+	0.978136i	$0.433316\pi$
$854$	−1946.00	−0.0779751
$855$	−7400.00	−0.295994
$856$	6660.00	0.265928
$857$	4506.00	0.179606	0.0898028	−	0.995960i	$-0.471376\pi$
$857$	4506.00	0.179606	0.0898028	+	0.995960i	$0.471376\pi$
$858$	7488.00	0.297944
$859$	24200.0	0.961226	0.480613	−	0.876933i	$-0.340414\pi$
$859$	24200.0	0.961226	0.480613	+	0.876933i	$0.340414\pi$
$860$	−2380.00	−0.0943690
$861$	−22512.0	−0.891065
$862$	−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
$868$	12152.0	0.475191
$869$	−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
$875$	−875.000	−0.0338062
$876$	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	$-0.599979\pi$
$881$	−16158.0	−0.617908	−0.308954	+	0.951077i	$0.599979\pi$
$882$	1813.00	0.0692142
$883$	−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	$-0.646748\pi$
$887$	−23504.0	−0.889726	−0.444863	+	0.895599i	$0.646748\pi$
$888$	−52080.0	−1.96812
$889$	5432.00	0.204931
$890$	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
$896$	−10185.0	−0.379751
$897$	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
$903$	3808.00	0.140335
$904$	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
$910$	2730.00	0.0994490
$911$	−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
$917$	7784.00	0.280317
$918$	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
$924$	4704.00	0.167479
$925$	−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	$-0.337893\pi$
$929$	27610.0	0.975086	0.487543	+	0.873099i	$0.337893\pi$
$930$	−9920.00	−0.349774
$931$	1960.00	0.0689972
$932$	−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	$-0.662912\pi$
$937$	−28094.0	−0.979499	−0.489750	+	0.871863i	$0.662912\pi$
$938$	−1148.00	−0.0399611
$939$	22064.0	0.766807
$940$	18760.0	0.650940
$941$	−12198.0	−0.422575	−0.211288	−	0.977424i	$-0.567766\pi$
$941$	−12198.0	−0.422575	−0.211288	+	0.977424i	$0.567766\pi$
$942$	5872.00	0.203100
$943$	12864.0	0.444231
$944$	−22960.0	−0.791615
$945$	2800.00	0.0963852
$946$	−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
$952$	9870.00	0.336017
$953$	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
$959$	−4858.00	−0.163580
$960$	−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
$966$	−1792.00	−0.0596860
$967$	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	$-0.497307\pi$
$971$	512.000	0.0169216	0.00846079	+	0.999964i	$0.497307\pi$
$972$	−35224.0	−1.16236
$973$	2520.00	0.0830293
$974$	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
$980$	1715.00	0.0559017
$981$	−43290.0	−1.40891
$982$	7092.00	0.230463
$983$	−61168.0	−1.98470	−0.992348	−	0.123472i	$-0.960597\pi$
$983$	−61168.0	−1.98470	−0.992348	+	0.123472i	$0.960597\pi$
$984$	48240.0	1.56284
$985$	23970.0	0.775378
$986$	4700.00	0.151804
$987$	−30016.0	−0.968004
$988$	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
$994$	4704.00	0.150102
$995$	−6400.00	−0.203913
$996$	−25088.0	−0.798136
$997$	−9454.00	−0.300312	−0.150156	−	0.988662i	$-0.547978\pi$
$997$	−9454.00	−0.300312	−0.150156	+	0.988662i	$0.547978\pi$
$998$	−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	35.4.a.a.1.1	✓	1
3.2	odd	2		315.4.a.c.1.1		1
4.3	odd	2		560.4.a.p.1.1		1
5.2	odd	4		175.4.b.a.99.2		2
5.3	odd	4		175.4.b.a.99.1		2
5.4	even	2		175.4.a.a.1.1		1
7.2	even	3		245.4.e.e.116.1		2
7.3	odd	6		245.4.e.b.226.1		2
7.4	even	3		245.4.e.e.226.1		2
7.5	odd	6		245.4.e.b.116.1		2
7.6	odd	2		245.4.a.d.1.1		1
8.3	odd	2		2240.4.a.b.1.1		1
8.5	even	2		2240.4.a.bk.1.1		1
15.14	odd	2		1575.4.a.g.1.1		1
21.20	even	2		2205.4.a.i.1.1		1
35.34	odd	2		1225.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.a.1.1	✓	1	1.1	even	1	trivial
175.4.a.a.1.1		1	5.4	even	2
175.4.b.a.99.1		2	5.3	odd	4
175.4.b.a.99.2		2	5.2	odd	4
245.4.a.d.1.1		1	7.6	odd	2
245.4.e.b.116.1		2	7.5	odd	6
245.4.e.b.226.1		2	7.3	odd	6
245.4.e.e.116.1		2	7.2	even	3
245.4.e.e.226.1		2	7.4	even	3
315.4.a.c.1.1		1	3.2	odd	2
560.4.a.p.1.1		1	4.3	odd	2
1225.4.a.e.1.1		1	35.34	odd	2
1575.4.a.g.1.1		1	15.14	odd	2
2205.4.a.i.1.1		1	21.20	even	2
2240.4.a.b.1.1		1	8.3	odd	2
2240.4.a.bk.1.1		1	8.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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