LMFDB - Embedded newform 175.8.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,8,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("175.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	175.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:	$54.6673794597$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+6.00000 q^{2} +42.0000 q^{3} -92.0000 q^{4} +252.000 q^{6} -343.000 q^{7} -1320.00 q^{8} -423.000 q^{9} +O(q^{10})$

\(q+6.00000 q^{2} +42.0000 q^{3} -92.0000 q^{4} +252.000 q^{6} -343.000 q^{7} -1320.00 q^{8} -423.000 q^{9} -5568.00 q^{11} -3864.00 q^{12} +5152.00 q^{13} -2058.00 q^{14} +3856.00 q^{16} +13986.0 q^{17} -2538.00 q^{18} +55370.0 q^{19} -14406.0 q^{21} -33408.0 q^{22} +91272.0 q^{23} -55440.0 q^{24} +30912.0 q^{26} -109620. q^{27} +31556.0 q^{28} +41610.0 q^{29} +150332. q^{31} +192096. q^{32} -233856. q^{33} +83916.0 q^{34} +38916.0 q^{36} +136366. q^{37} +332220. q^{38} +216384. q^{39} -510258. q^{41} -86436.0 q^{42} +172072. q^{43} +512256. q^{44} +547632. q^{46} +519036. q^{47} +161952. q^{48} +117649. q^{49} +587412. q^{51} -473984. q^{52} +59202.0 q^{53} -657720. q^{54} +452760. q^{56} +2.32554e6 q^{57} +249660. q^{58} +1.97925e6 q^{59} -2.98875e6 q^{61} +901992. q^{62} +145089. q^{63} +659008. q^{64} -1.40314e6 q^{66} -2.40940e6 q^{67} -1.28671e6 q^{68} +3.83342e6 q^{69} +1.50451e6 q^{71} +558360. q^{72} +1.82102e6 q^{73} +818196. q^{74} -5.09404e6 q^{76} +1.90982e6 q^{77} +1.29830e6 q^{78} -1.66924e6 q^{79} -3.67894e6 q^{81} -3.06155e6 q^{82} -696738. q^{83} +1.32535e6 q^{84} +1.03243e6 q^{86} +1.74762e6 q^{87} +7.34976e6 q^{88} +5.55849e6 q^{89} -1.76714e6 q^{91} -8.39702e6 q^{92} +6.31394e6 q^{93} +3.11422e6 q^{94} +8.06803e6 q^{96} -9.87673e6 q^{97} +705894. q^{98} +2.35526e6 q^{99} +O(q^{100})\)

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 $

$2$	6.00000	0.530330	0.265165	−	0.964203i	$-0.414574\pi$
$2$	6.00000	0.530330	0.265165	+	0.964203i	$0.414574\pi$
$3$	42.0000	0.898100	0.449050	−	0.893507i	$-0.351762\pi$
$3$	42.0000	0.898100	0.449050	+	0.893507i	$0.351762\pi$
$4$	−92.0000	−0.718750
$5$	0	0
$5$	0	0
$6$	252.000	0.476290
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	−1320.00	−0.911505
$9$	−423.000	−0.193416
$10$	0	0
$11$	−5568.00	−1.26132	−0.630659	−	0.776060i	$-0.717215\pi$
$11$	−5568.00	−1.26132	−0.630659	+	0.776060i	$0.717215\pi$
$12$	−3864.00	−0.645510
$13$	5152.00	0.650390	0.325195	−	0.945647i	$-0.394570\pi$
$13$	5152.00	0.650390	0.325195	+	0.945647i	$0.394570\pi$
$14$	−2058.00	−0.200446
$15$	0	0
$16$	3856.00	0.235352
$17$	13986.0	0.690434	0.345217	−	0.938523i	$-0.387805\pi$
$17$	13986.0	0.690434	0.345217	+	0.938523i	$0.387805\pi$
$18$	−2538.00	−0.102574
$19$	55370.0	1.85198	0.925991	−	0.377545i	$-0.123232\pi$
$19$	55370.0	1.85198	0.925991	+	0.377545i	$0.123232\pi$
$20$	0	0
$21$	−14406.0	−0.339450
$22$	−33408.0	−0.668915
$23$	91272.0	1.56419	0.782096	−	0.623158i	$-0.214151\pi$
$23$	91272.0	1.56419	0.782096	+	0.623158i	$0.214151\pi$
$24$	−55440.0	−0.818623
$25$	0	0
$26$	30912.0	0.344922
$27$	−109620.	−1.07181
$28$	31556.0	0.271662
$29$	41610.0	0.316814	0.158407	−	0.987374i	$-0.449364\pi$
$29$	41610.0	0.316814	0.158407	+	0.987374i	$0.449364\pi$
$30$	0	0
$31$	150332.	0.906328	0.453164	−	0.891427i	$-0.350295\pi$
$31$	150332.	0.906328	0.453164	+	0.891427i	$0.350295\pi$
$32$	192096.	1.03632
$33$	−233856.	−1.13279
$34$	83916.0	0.366158
$35$	0	0
$36$	38916.0	0.139017
$37$	136366.	0.442588	0.221294	−	0.975207i	$-0.428972\pi$
$37$	136366.	0.442588	0.221294	+	0.975207i	$0.428972\pi$
$38$	332220.	0.982162
$39$	216384.	0.584116
$40$	0	0
$41$	−510258.	−1.15624	−0.578118	−	0.815953i	$-0.696213\pi$
$41$	−510258.	−1.15624	−0.578118	+	0.815953i	$0.696213\pi$
$42$	−86436.0	−0.180021
$43$	172072.	0.330043	0.165022	−	0.986290i	$-0.447231\pi$
$43$	172072.	0.330043	0.165022	+	0.986290i	$0.447231\pi$
$44$	512256.	0.906573
$45$	0	0
$46$	547632.	0.829538
$47$	519036.	0.729214	0.364607	−	0.931162i	$-0.381203\pi$
$47$	519036.	0.729214	0.364607	+	0.931162i	$0.381203\pi$
$48$	161952.	0.211369
$49$	117649.	0.142857
$50$	0	0
$51$	587412.	0.620079
$52$	−473984.	−0.467468
$53$	59202.0	0.0546224	0.0273112	−	0.999627i	$-0.491305\pi$
$53$	59202.0	0.0546224	0.0273112	+	0.999627i	$0.491305\pi$
$54$	−657720.	−0.568412
$55$	0	0
$56$	452760.	0.344516
$57$	2.32554e6	1.66327
$58$	249660.	0.168016
$59$	1.97925e6	1.25464	0.627319	−	0.778762i	$-0.284152\pi$
$59$	1.97925e6	1.25464	0.627319	+	0.778762i	$0.284152\pi$
$60$	0	0
$61$	−2.98875e6	−1.68591	−0.842956	−	0.537983i	$-0.819187\pi$
$61$	−2.98875e6	−1.68591	−0.842956	+	0.537983i	$0.819187\pi$
$62$	901992.	0.480653
$63$	145089.	0.0731042
$64$	659008.	0.314240
$65$	0	0
$66$	−1.40314e6	−0.600753
$67$	−2.40940e6	−0.978696	−0.489348	−	0.872089i	$-0.662765\pi$
$67$	−2.40940e6	−0.978696	−0.489348	+	0.872089i	$0.662765\pi$
$68$	−1.28671e6	−0.496250
$69$	3.83342e6	1.40480
$70$	0	0
$71$	1.50451e6	0.498875	0.249437	−	0.968391i	$-0.419754\pi$
$71$	1.50451e6	0.498875	0.249437	+	0.968391i	$0.419754\pi$
$72$	558360.	0.176299
$73$	1.82102e6	0.547880	0.273940	−	0.961747i	$-0.411673\pi$
$73$	1.82102e6	0.547880	0.273940	+	0.961747i	$0.411673\pi$
$74$	818196.	0.234718
$75$	0	0
$76$	−5.09404e6	−1.33111
$77$	1.90982e6	0.476734
$78$	1.29830e6	0.309774
$79$	−1.66924e6	−0.380911	−0.190456	−	0.981696i	$-0.560997\pi$
$79$	−1.66924e6	−0.380911	−0.190456	+	0.981696i	$0.560997\pi$
$80$	0	0
$81$	−3.67894e6	−0.769175
$82$	−3.06155e6	−0.613187
$83$	−696738.	−0.133751	−0.0668754	−	0.997761i	$-0.521303\pi$
$83$	−696738.	−0.133751	−0.0668754	+	0.997761i	$0.521303\pi$
$84$	1.32535e6	0.243980
$85$	0	0
$86$	1.03243e6	0.175032
$87$	1.74762e6	0.284531
$88$	7.34976e6	1.14970
$89$	5.55849e6	0.835780	0.417890	−	0.908498i	$-0.362770\pi$
$89$	5.55849e6	0.835780	0.417890	+	0.908498i	$0.362770\pi$
$90$	0	0
$91$	−1.76714e6	−0.245824
$92$	−8.39702e6	−1.12426
$93$	6.31394e6	0.813974
$94$	3.11422e6	0.386724
$95$	0	0
$96$	8.06803e6	0.930718
$97$	−9.87673e6	−1.09878	−0.549392	−	0.835565i	$-0.685141\pi$
$97$	−9.87673e6	−1.09878	−0.549392	+	0.835565i	$0.685141\pi$
$98$	705894.	0.0757614
$99$	2.35526e6	0.243959
$100$	0	0
$101$	−2.16359e6	−0.208954	−0.104477	−	0.994527i	$-0.533317\pi$
$101$	−2.16359e6	−0.208954	−0.104477	+	0.994527i	$0.533317\pi$
$102$	3.52447e6	0.328847
$103$	1.15657e7	1.04289	0.521447	−	0.853284i	$-0.325393\pi$
$103$	1.15657e7	1.04289	0.521447	+	0.853284i	$0.325393\pi$
$104$	−6.80064e6	−0.592834
$105$	0	0
$106$	355212.	0.0289679
$107$	1.82564e7	1.44069	0.720346	−	0.693615i	$-0.243983\pi$
$107$	1.82564e7	1.44069	0.720346	+	0.693615i	$0.243983\pi$
$108$	1.00850e7	0.770361
$109$	2.34053e7	1.73110	0.865550	−	0.500823i	$-0.166969\pi$
$109$	2.34053e7	1.73110	0.865550	+	0.500823i	$0.166969\pi$
$110$	0	0
$111$	5.72737e6	0.397489
$112$	−1.32261e6	−0.0889545
$113$	2.53040e7	1.64973	0.824867	−	0.565327i	$-0.191250\pi$
$113$	2.53040e7	1.64973	0.824867	+	0.565327i	$0.191250\pi$
$114$	1.39532e7	0.882080
$115$	0	0
$116$	−3.82812e6	−0.227710
$117$	−2.17930e6	−0.125796
$118$	1.18755e7	0.665373
$119$	−4.79720e6	−0.260960
$120$	0	0
$121$	1.15155e7	0.590925
$122$	−1.79325e7	−0.894090
$123$	−2.14308e7	−1.03842
$124$	−1.38305e7	−0.651423
$125$	0	0
$126$	870534.	0.0387694
$127$	2.65646e6	0.115077	0.0575386	−	0.998343i	$-0.481675\pi$
$127$	2.65646e6	0.115077	0.0575386	+	0.998343i	$0.481675\pi$
$128$	−2.06342e7	−0.869668
$129$	7.22702e6	0.296412
$130$	0	0
$131$	−3.01946e7	−1.17349	−0.586745	−	0.809771i	$-0.699591\pi$
$131$	−3.01946e7	−1.17349	−0.586745	+	0.809771i	$0.699591\pi$
$132$	2.15148e7	0.814193
$133$	−1.89919e7	−0.699984
$134$	−1.44564e7	−0.519032
$135$	0	0
$136$	−1.84615e7	−0.629334
$137$	1.58504e7	0.526647	0.263323	−	0.964708i	$-0.415181\pi$
$137$	1.58504e7	0.526647	0.263323	+	0.964708i	$0.415181\pi$
$138$	2.30005e7	0.745009
$139$	−1.02518e7	−0.323780	−0.161890	−	0.986809i	$-0.551759\pi$
$139$	−1.02518e7	−0.323780	−0.161890	+	0.986809i	$0.551759\pi$
$140$	0	0
$141$	2.17995e7	0.654907
$142$	9.02707e6	0.264568
$143$	−2.86863e7	−0.820350
$144$	−1.63109e6	−0.0455207
$145$	0	0
$146$	1.09261e7	0.290557
$147$	4.94126e6	0.128300
$148$	−1.25457e7	−0.318110
$149$	2.21020e7	0.547368	0.273684	−	0.961820i	$-0.411758\pi$
$149$	2.21020e7	0.547368	0.273684	+	0.961820i	$0.411758\pi$
$150$	0	0
$151$	1.48011e6	0.0349845	0.0174922	−	0.999847i	$-0.494432\pi$
$151$	1.48011e6	0.0349845	0.0174922	+	0.999847i	$0.494432\pi$
$152$	−7.30884e7	−1.68809
$153$	−5.91608e6	−0.133541
$154$	1.14589e7	0.252826
$155$	0	0
$156$	−1.99073e7	−0.419833
$157$	4.73086e7	0.975643	0.487822	−	0.872943i	$-0.337792\pi$
$157$	4.73086e7	0.975643	0.487822	+	0.872943i	$0.337792\pi$
$158$	−1.00154e7	−0.202009
$159$	2.48648e6	0.0490564
$160$	0	0
$161$	−3.13063e7	−0.591209
$162$	−2.20736e7	−0.407917
$163$	−1.32133e6	−0.0238976	−0.0119488	−	0.999929i	$-0.503804\pi$
$163$	−1.32133e6	−0.0238976	−0.0119488	+	0.999929i	$0.503804\pi$
$164$	4.69437e7	0.831044
$165$	0	0
$166$	−4.18043e6	−0.0709320
$167$	3.56294e7	0.591971	0.295985	−	0.955192i	$-0.404352\pi$
$167$	3.56294e7	0.591971	0.295985	+	0.955192i	$0.404352\pi$
$168$	1.90159e7	0.309410
$169$	−3.62054e7	−0.576992
$170$	0	0
$171$	−2.34215e7	−0.358202
$172$	−1.58306e7	−0.237218
$173$	−9.17248e7	−1.34687	−0.673435	−	0.739247i	$-0.735182\pi$
$173$	−9.17248e7	−1.34687	−0.673435	+	0.739247i	$0.735182\pi$
$174$	1.04857e7	0.150895
$175$	0	0
$176$	−2.14702e7	−0.296853
$177$	8.31285e7	1.12679
$178$	3.33509e7	0.443239
$179$	−9.83043e7	−1.28111	−0.640556	−	0.767912i	$-0.721296\pi$
$179$	−9.83043e7	−1.28111	−0.640556	+	0.767912i	$0.721296\pi$
$180$	0	0
$181$	8.75015e7	1.09683	0.548417	−	0.836205i	$-0.315231\pi$
$181$	8.75015e7	1.09683	0.548417	+	0.836205i	$0.315231\pi$
$182$	−1.06028e7	−0.130368
$183$	−1.25527e8	−1.51412
$184$	−1.20479e8	−1.42577
$185$	0	0
$186$	3.78837e7	0.431675
$187$	−7.78740e7	−0.870858
$188$	−4.77513e7	−0.524123
$189$	3.75997e7	0.405105
$190$	0	0
$191$	1.61682e8	1.67898	0.839490	−	0.543375i	$-0.182854\pi$
$191$	1.61682e8	1.67898	0.839490	+	0.543375i	$0.182854\pi$
$192$	2.76783e7	0.282219
$193$	1.10526e7	0.110666	0.0553328	−	0.998468i	$-0.482378\pi$
$193$	1.10526e7	0.110666	0.0553328	+	0.998468i	$0.482378\pi$
$194$	−5.92604e7	−0.582718
$195$	0	0
$196$	−1.08237e7	−0.102679
$197$	3.32668e7	0.310013	0.155006	−	0.987913i	$-0.450460\pi$
$197$	3.32668e7	0.310013	0.155006	+	0.987913i	$0.450460\pi$
$198$	1.41316e7	0.129379
$199$	2.36571e7	0.212802	0.106401	−	0.994323i	$-0.466067\pi$
$199$	2.36571e7	0.212802	0.106401	+	0.994323i	$0.466067\pi$
$200$	0	0
$201$	−1.01195e8	−0.878967
$202$	−1.29815e7	−0.110814
$203$	−1.42722e7	−0.119745
$204$	−5.40419e7	−0.445682
$205$	0	0
$206$	6.93939e7	0.553078
$207$	−3.86081e7	−0.302539
$208$	1.98661e7	0.153070
$209$	−3.08300e8	−2.33594
$210$	0	0
$211$	1.59342e7	0.116773	0.0583863	−	0.998294i	$-0.481404\pi$
$211$	1.59342e7	0.116773	0.0583863	+	0.998294i	$0.481404\pi$
$212$	−5.44658e6	−0.0392599
$213$	6.31895e7	0.448040
$214$	1.09538e8	0.764042
$215$	0	0
$216$	1.44698e8	0.976957
$217$	−5.15639e7	−0.342560
$218$	1.40432e8	0.918054
$219$	7.64829e7	0.492051
$220$	0	0
$221$	7.20559e7	0.449052
$222$	3.43642e7	0.210800
$223$	1.22028e8	0.736871	0.368436	−	0.929653i	$-0.379894\pi$
$223$	1.22028e8	0.736871	0.368436	+	0.929653i	$0.379894\pi$
$224$	−6.58889e7	−0.391692
$225$	0	0
$226$	1.51824e8	0.874904
$227$	−3.03605e8	−1.72274	−0.861368	−	0.507981i	$-0.830392\pi$
$227$	−3.03605e8	−1.72274	−0.861368	+	0.507981i	$0.830392\pi$
$228$	−2.13950e8	−1.19547
$229$	−1.14364e8	−0.629309	−0.314655	−	0.949206i	$-0.601889\pi$
$229$	−1.14364e8	−0.629309	−0.314655	+	0.949206i	$0.601889\pi$
$230$	0	0
$231$	8.02126e7	0.428155
$232$	−5.49252e7	−0.288778
$233$	−1.39403e7	−0.0721982	−0.0360991	−	0.999348i	$-0.511493\pi$
$233$	−1.39403e7	−0.0721982	−0.0360991	+	0.999348i	$0.511493\pi$
$234$	−1.30758e7	−0.0667132
$235$	0	0
$236$	−1.82091e8	−0.901771
$237$	−7.01081e7	−0.342097
$238$	−2.87832e7	−0.138395
$239$	−2.64328e8	−1.25242	−0.626210	−	0.779655i	$-0.715395\pi$
$239$	−2.64328e8	−1.25242	−0.626210	+	0.779655i	$0.715395\pi$
$240$	0	0
$241$	−3.64932e8	−1.67939	−0.839696	−	0.543056i	$-0.817267\pi$
$241$	−3.64932e8	−1.67939	−0.839696	+	0.543056i	$0.817267\pi$
$242$	6.90927e7	0.313385
$243$	8.52235e7	0.381011
$244$	2.74965e8	1.21175
$245$	0	0
$246$	−1.28585e8	−0.550703
$247$	2.85266e8	1.20451
$248$	−1.98438e8	−0.826123
$249$	−2.92630e7	−0.120122
$250$	0	0
$251$	4.55058e7	0.181639	0.0908194	−	0.995867i	$-0.471051\pi$
$251$	4.55058e7	0.181639	0.0908194	+	0.995867i	$0.471051\pi$
$252$	−1.33482e7	−0.0525437
$253$	−5.08202e8	−1.97294
$254$	1.59387e7	0.0610289
$255$	0	0
$256$	−2.08158e8	−0.775451
$257$	−5.04016e7	−0.185216	−0.0926079	−	0.995703i	$-0.529520\pi$
$257$	−5.04016e7	−0.185216	−0.0926079	+	0.995703i	$0.529520\pi$
$258$	4.33621e7	0.157196
$259$	−4.67735e7	−0.167283
$260$	0	0
$261$	−1.76010e7	−0.0612768
$262$	−1.81168e8	−0.622338
$263$	2.21310e8	0.750163	0.375082	−	0.926992i	$-0.377615\pi$
$263$	2.21310e8	0.750163	0.375082	+	0.926992i	$0.377615\pi$
$264$	3.08690e8	1.03254
$265$	0	0
$266$	−1.13951e8	−0.371222
$267$	2.33457e8	0.750614
$268$	2.21665e8	0.703438
$269$	3.38343e8	1.05980	0.529900	−	0.848060i	$-0.322229\pi$
$269$	3.38343e8	1.05980	0.529900	+	0.848060i	$0.322229\pi$
$270$	0	0
$271$	3.79683e8	1.15885	0.579427	−	0.815024i	$-0.303276\pi$
$271$	3.79683e8	1.15885	0.579427	+	0.815024i	$0.303276\pi$
$272$	5.39300e7	0.162495
$273$	−7.42197e7	−0.220775
$274$	9.51027e7	0.279297
$275$	0	0
$276$	−3.52675e8	−1.00970
$277$	−2.18056e8	−0.616437	−0.308219	−	0.951316i	$-0.599733\pi$
$277$	−2.18056e8	−0.616437	−0.308219	+	0.951316i	$0.599733\pi$
$278$	−6.15111e7	−0.171710
$279$	−6.35904e7	−0.175298
$280$	0	0
$281$	3.60144e8	0.968286	0.484143	−	0.874989i	$-0.339131\pi$
$281$	3.60144e8	0.968286	0.484143	+	0.874989i	$0.339131\pi$
$282$	1.30797e8	0.347317
$283$	5.44384e8	1.42775	0.713876	−	0.700272i	$-0.246938\pi$
$283$	5.44384e8	1.42775	0.713876	+	0.700272i	$0.246938\pi$
$284$	−1.38415e8	−0.358566
$285$	0	0
$286$	−1.72118e8	−0.435056
$287$	1.75018e8	0.437016
$288$	−8.12566e7	−0.200440
$289$	−2.14730e8	−0.523301
$290$	0	0
$291$	−4.14823e8	−0.986818
$292$	−1.67534e8	−0.393789
$293$	−1.17983e8	−0.274020	−0.137010	−	0.990570i	$-0.543749\pi$
$293$	−1.17983e8	−0.274020	−0.137010	+	0.990570i	$0.543749\pi$
$294$	2.96475e7	0.0680414
$295$	0	0
$296$	−1.80003e8	−0.403422
$297$	6.10364e8	1.35189
$298$	1.32612e8	0.290286
$299$	4.70233e8	1.01734
$300$	0	0
$301$	−5.90207e7	−0.124745
$302$	8.88067e6	0.0185533
$303$	−9.08707e7	−0.187661
$304$	2.13507e8	0.435867
$305$	0	0
$306$	−3.54965e7	−0.0708207
$307$	−1.46606e8	−0.289180	−0.144590	−	0.989492i	$-0.546186\pi$
$307$	−1.46606e8	−0.289180	−0.144590	+	0.989492i	$0.546186\pi$
$308$	−1.75704e8	−0.342652
$309$	4.85757e8	0.936623
$310$	0	0
$311$	6.85655e8	1.29254	0.646270	−	0.763109i	$-0.276328\pi$
$311$	6.85655e8	1.29254	0.646270	+	0.763109i	$0.276328\pi$
$312$	−2.85627e8	−0.532424
$313$	5.41169e8	0.997533	0.498767	−	0.866736i	$-0.333786\pi$
$313$	5.41169e8	0.997533	0.498767	+	0.866736i	$0.333786\pi$
$314$	2.83851e8	0.517413
$315$	0	0
$316$	1.53570e8	0.273780
$317$	2.68477e8	0.473369	0.236684	−	0.971587i	$-0.423939\pi$
$317$	2.68477e8	0.473369	0.236684	+	0.971587i	$0.423939\pi$
$318$	1.49189e7	0.0260161
$319$	−2.31684e8	−0.399604
$320$	0	0
$321$	7.66767e8	1.29389
$322$	−1.87838e8	−0.313536
$323$	7.74405e8	1.27867
$324$	3.38462e8	0.552844
$325$	0	0
$326$	−7.92797e6	−0.0126736
$327$	9.83024e8	1.55470
$328$	6.73541e8	1.05391
$329$	−1.78029e8	−0.275617
$330$	0	0
$331$	−1.33832e7	−0.0202844	−0.0101422	−	0.999949i	$-0.503228\pi$
$331$	−1.33832e7	−0.0202844	−0.0101422	+	0.999949i	$0.503228\pi$
$332$	6.40999e7	0.0961333
$333$	−5.76828e7	−0.0856035
$334$	2.13776e8	0.313940
$335$	0	0
$336$	−5.55495e7	−0.0798901
$337$	6.98606e8	0.994323	0.497162	−	0.867658i	$-0.334376\pi$
$337$	6.98606e8	0.994323	0.497162	+	0.867658i	$0.334376\pi$
$338$	−2.17232e8	−0.305996
$339$	1.06277e9	1.48163
$340$	0	0
$341$	−8.37049e8	−1.14317
$342$	−1.40529e8	−0.189966
$343$	−4.03536e7	−0.0539949
$344$	−2.27135e8	−0.300836
$345$	0	0
$346$	−5.50349e8	−0.714285
$347$	−4.25461e8	−0.546647	−0.273323	−	0.961922i	$-0.588123\pi$
$347$	−4.25461e8	−0.546647	−0.273323	+	0.961922i	$0.588123\pi$
$348$	−1.60781e8	−0.204507
$349$	2.83399e8	0.356869	0.178435	−	0.983952i	$-0.442897\pi$
$349$	2.83399e8	0.356869	0.178435	+	0.983952i	$0.442897\pi$
$350$	0	0
$351$	−5.64762e8	−0.697093
$352$	−1.06959e9	−1.30713
$353$	1.20608e9	1.45937	0.729684	−	0.683784i	$-0.239667\pi$
$353$	1.20608e9	1.45937	0.729684	+	0.683784i	$0.239667\pi$
$354$	4.98771e8	0.597571
$355$	0	0
$356$	−5.11381e8	−0.600717
$357$	−2.01482e8	−0.234368
$358$	−5.89826e8	−0.679412
$359$	5.68486e8	0.648469	0.324235	−	0.945977i	$-0.394893\pi$
$359$	5.68486e8	0.648469	0.324235	+	0.945977i	$0.394893\pi$
$360$	0	0
$361$	2.17197e9	2.42984
$362$	5.25009e8	0.581684
$363$	4.83649e8	0.530710
$364$	1.62577e8	0.176686
$365$	0	0
$366$	−7.53164e8	−0.802982
$367$	−1.28228e9	−1.35410	−0.677051	−	0.735936i	$-0.736742\pi$
$367$	−1.28228e9	−1.35410	−0.677051	+	0.735936i	$0.736742\pi$
$368$	3.51945e8	0.368135
$369$	2.15839e8	0.223634
$370$	0	0
$371$	−2.03063e7	−0.0206453
$372$	−5.80883e8	−0.585044
$373$	9.80232e7	0.0978020	0.0489010	−	0.998804i	$-0.484428\pi$
$373$	9.80232e7	0.0978020	0.0489010	+	0.998804i	$0.484428\pi$
$374$	−4.67244e8	−0.461842
$375$	0	0
$376$	−6.85128e8	−0.664682
$377$	2.14375e8	0.206053
$378$	2.25598e8	0.214839
$379$	−8.04985e8	−0.759539	−0.379770	−	0.925081i	$-0.623997\pi$
$379$	−8.04985e8	−0.759539	−0.379770	+	0.925081i	$0.623997\pi$
$380$	0	0
$381$	1.11571e8	0.103351
$382$	9.70094e8	0.890414
$383$	−1.80572e9	−1.64231	−0.821155	−	0.570705i	$-0.806670\pi$
$383$	−1.80572e9	−1.64231	−0.821155	+	0.570705i	$0.806670\pi$
$384$	−8.66638e8	−0.781049
$385$	0	0
$386$	6.63154e7	0.0586893
$387$	−7.27865e7	−0.0638355
$388$	9.08660e8	0.789751
$389$	−1.60994e9	−1.38672	−0.693358	−	0.720593i	$-0.743869\pi$
$389$	−1.60994e9	−1.38672	−0.693358	+	0.720593i	$0.743869\pi$
$390$	0	0
$391$	1.27653e9	1.07997
$392$	−1.55297e8	−0.130215
$393$	−1.26817e9	−1.05391
$394$	1.99601e8	0.164409
$395$	0	0
$396$	−2.16684e8	−0.175345
$397$	3.69718e8	0.296554	0.148277	−	0.988946i	$-0.452627\pi$
$397$	3.69718e8	0.296554	0.148277	+	0.988946i	$0.452627\pi$
$398$	1.41942e8	0.112855
$399$	−7.97660e8	−0.628656
$400$	0	0
$401$	−2.16035e9	−1.67309	−0.836545	−	0.547898i	$-0.815428\pi$
$401$	−2.16035e9	−1.67309	−0.836545	+	0.547898i	$0.815428\pi$
$402$	−6.07170e8	−0.466143
$403$	7.74510e8	0.589467
$404$	1.99050e8	0.150185
$405$	0	0
$406$	−8.56334e7	−0.0635041
$407$	−7.59286e8	−0.558245
$408$	−7.75384e8	−0.565205
$409$	−4.97539e8	−0.359580	−0.179790	−	0.983705i	$-0.557542\pi$
$409$	−4.97539e8	−0.359580	−0.179790	+	0.983705i	$0.557542\pi$
$410$	0	0
$411$	6.65719e8	0.472982
$412$	−1.06404e9	−0.749579
$413$	−6.78883e8	−0.474209
$414$	−2.31648e8	−0.160446
$415$	0	0
$416$	9.89679e8	0.674012
$417$	−4.30578e8	−0.290787
$418$	−1.84980e9	−1.23882
$419$	7.04012e8	0.467553	0.233777	−	0.972290i	$-0.424892\pi$
$419$	7.04012e8	0.467553	0.233777	+	0.972290i	$0.424892\pi$
$420$	0	0
$421$	−1.07019e9	−0.698995	−0.349497	−	0.936937i	$-0.613648\pi$
$421$	−1.07019e9	−0.698995	−0.349497	+	0.936937i	$0.613648\pi$
$422$	9.56050e7	0.0619280
$423$	−2.19552e8	−0.141041
$424$	−7.81466e7	−0.0497886
$425$	0	0
$426$	3.79137e8	0.237609
$427$	1.02514e9	0.637215
$428$	−1.67958e9	−1.03550
$429$	−1.20483e9	−0.736756
$430$	0	0
$431$	1.36893e9	0.823587	0.411793	−	0.911277i	$-0.364903\pi$
$431$	1.36893e9	0.823587	0.411793	+	0.911277i	$0.364903\pi$
$432$	−4.22695e8	−0.252251
$433$	7.83027e8	0.463521	0.231760	−	0.972773i	$-0.425551\pi$
$433$	7.83027e8	0.463521	0.231760	+	0.972773i	$0.425551\pi$
$434$	−3.09383e8	−0.181670
$435$	0	0
$436$	−2.15329e9	−1.24423
$437$	5.05373e9	2.89686
$438$	4.58898e8	0.260949
$439$	−1.52936e9	−0.862747	−0.431373	−	0.902173i	$-0.641971\pi$
$439$	−1.52936e9	−0.862747	−0.431373	+	0.902173i	$0.641971\pi$
$440$	0	0
$441$	−4.97655e7	−0.0276308
$442$	4.32335e8	0.238146
$443$	−3.44970e8	−0.188525	−0.0942624	−	0.995547i	$-0.530049\pi$
$443$	−3.44970e8	−0.188525	−0.0942624	+	0.995547i	$0.530049\pi$
$444$	−5.26918e8	−0.285695
$445$	0	0
$446$	7.32167e8	0.390785
$447$	9.28284e8	0.491591
$448$	−2.26040e8	−0.118771
$449$	1.20565e9	0.628580	0.314290	−	0.949327i	$-0.398234\pi$
$449$	1.20565e9	0.628580	0.314290	+	0.949327i	$0.398234\pi$
$450$	0	0
$451$	2.84112e9	1.45838
$452$	−2.32796e9	−1.18575
$453$	6.21647e7	0.0314196
$454$	−1.82163e9	−0.913619
$455$	0	0
$456$	−3.06971e9	−1.51608
$457$	−2.85702e9	−1.40026	−0.700128	−	0.714018i	$-0.746874\pi$
$457$	−2.85702e9	−1.40026	−0.700128	+	0.714018i	$0.746874\pi$
$458$	−6.86183e8	−0.333742
$459$	−1.53315e9	−0.740012
$460$	0	0
$461$	2.73931e9	1.30223	0.651115	−	0.758979i	$-0.274302\pi$
$461$	2.73931e9	1.30223	0.651115	+	0.758979i	$0.274302\pi$
$462$	4.81276e8	0.227063
$463$	−7.27885e8	−0.340823	−0.170412	−	0.985373i	$-0.554510\pi$
$463$	−7.27885e8	−0.340823	−0.170412	+	0.985373i	$0.554510\pi$
$464$	1.60448e8	0.0745627
$465$	0	0
$466$	−8.36418e7	−0.0382889
$467$	1.37399e9	0.624275	0.312138	−	0.950037i	$-0.398955\pi$
$467$	1.37399e9	0.624275	0.312138	+	0.950037i	$0.398955\pi$
$468$	2.00495e8	0.0904156
$469$	8.26426e8	0.369912
$470$	0	0
$471$	1.98696e9	0.876226
$472$	−2.61261e9	−1.14361
$473$	−9.58097e8	−0.416289
$474$	−4.20648e8	−0.181424
$475$	0	0
$476$	4.41342e8	0.187565
$477$	−2.50424e7	−0.0105648
$478$	−1.58597e9	−0.664196
$479$	−2.49370e8	−0.103674	−0.0518369	−	0.998656i	$-0.516508\pi$
$479$	−2.49370e8	−0.103674	−0.0518369	+	0.998656i	$0.516508\pi$
$480$	0	0
$481$	7.02558e8	0.287855
$482$	−2.18959e9	−0.890632
$483$	−1.31486e9	−0.530965
$484$	−1.05942e9	−0.424727
$485$	0	0
$486$	5.11341e8	0.202062
$487$	2.18907e9	0.858830	0.429415	−	0.903107i	$-0.358720\pi$
$487$	2.18907e9	0.858830	0.429415	+	0.903107i	$0.358720\pi$
$488$	3.94515e9	1.53672
$489$	−5.54958e7	−0.0214624
$490$	0	0
$491$	1.39900e9	0.533375	0.266688	−	0.963783i	$-0.414071\pi$
$491$	1.39900e9	0.533375	0.266688	+	0.963783i	$0.414071\pi$
$492$	1.97164e9	0.746361
$493$	5.81957e8	0.218739
$494$	1.71160e9	0.638789
$495$	0	0
$496$	5.79680e8	0.213306
$497$	−5.16048e8	−0.188557
$498$	−1.75578e8	−0.0637041
$499$	1.55162e9	0.559027	0.279514	−	0.960142i	$-0.409827\pi$
$499$	1.55162e9	0.559027	0.279514	+	0.960142i	$0.409827\pi$
$500$	0	0
$501$	1.49643e9	0.531649
$502$	2.73035e8	0.0963285
$503$	4.95456e9	1.73587	0.867934	−	0.496679i	$-0.165447\pi$
$503$	4.95456e9	1.73587	0.867934	+	0.496679i	$0.165447\pi$
$504$	−1.91517e8	−0.0666349
$505$	0	0
$506$	−3.04921e9	−1.04631
$507$	−1.52063e9	−0.518197
$508$	−2.44394e8	−0.0827118
$509$	−3.58960e9	−1.20652	−0.603260	−	0.797545i	$-0.706132\pi$
$509$	−3.58960e9	−1.20652	−0.603260	+	0.797545i	$0.706132\pi$
$510$	0	0
$511$	−6.24611e8	−0.207079
$512$	1.39223e9	0.458423
$513$	−6.06966e9	−1.98497
$514$	−3.02409e8	−0.0982255
$515$	0	0
$516$	−6.64886e8	−0.213046
$517$	−2.88999e9	−0.919771
$518$	−2.80641e8	−0.0887151
$519$	−3.85244e9	−1.20962
$520$	0	0
$521$	−2.44223e9	−0.756580	−0.378290	−	0.925687i	$-0.623488\pi$
$521$	−2.44223e9	−0.756580	−0.378290	+	0.925687i	$0.623488\pi$
$522$	−1.05606e8	−0.0324969
$523$	−6.22285e8	−0.190210	−0.0951050	−	0.995467i	$-0.530319\pi$
$523$	−6.22285e8	−0.190210	−0.0951050	+	0.995467i	$0.530319\pi$
$524$	2.77790e9	0.843447
$525$	0	0
$526$	1.32786e9	0.397834
$527$	2.10254e9	0.625760
$528$	−9.01749e8	−0.266604
$529$	4.92575e9	1.44670
$530$	0	0
$531$	−8.37223e8	−0.242667
$532$	1.74726e9	0.503113
$533$	−2.62885e9	−0.752005
$534$	1.40074e9	0.398073
$535$	0	0
$536$	3.18041e9	0.892086
$537$	−4.12878e9	−1.15057
$538$	2.03006e9	0.562044
$539$	−6.55070e8	−0.180188
$540$	0	0
$541$	−5.56421e9	−1.51082	−0.755411	−	0.655251i	$-0.772563\pi$
$541$	−5.56421e9	−1.51082	−0.755411	+	0.655251i	$0.772563\pi$
$542$	2.27810e9	0.614575
$543$	3.67506e9	0.985066
$544$	2.68665e9	0.715510
$545$	0	0
$546$	−4.45318e8	−0.117084
$547$	2.01375e9	0.526077	0.263038	−	0.964785i	$-0.415275\pi$
$547$	2.01375e9	0.526077	0.263038	+	0.964785i	$0.415275\pi$
$548$	−1.45824e9	−0.378527
$549$	1.26424e9	0.326082
$550$	0	0
$551$	2.30395e9	0.586735
$552$	−5.06012e9	−1.28048
$553$	5.72549e8	0.143971
$554$	−1.30834e9	−0.326915
$555$	0	0
$556$	9.43170e8	0.232717
$557$	5.59246e9	1.37123	0.685614	−	0.727965i	$-0.259534\pi$
$557$	5.59246e9	1.37123	0.685614	+	0.727965i	$0.259534\pi$
$558$	−3.81543e8	−0.0929658
$559$	8.86515e8	0.214657
$560$	0	0
$561$	−3.27071e9	−0.782118
$562$	2.16086e9	0.513511
$563$	5.44186e7	0.0128519	0.00642596	−	0.999979i	$-0.497955\pi$
$563$	5.44186e7	0.0128519	0.00642596	+	0.999979i	$0.497955\pi$
$564$	−2.00556e9	−0.470715
$565$	0	0
$566$	3.26630e9	0.757180
$567$	1.26188e9	0.290721
$568$	−1.98596e9	−0.454727
$569$	−2.67749e9	−0.609304	−0.304652	−	0.952464i	$-0.598540\pi$
$569$	−2.67749e9	−0.609304	−0.304652	+	0.952464i	$0.598540\pi$
$570$	0	0
$571$	−3.65014e9	−0.820510	−0.410255	−	0.911971i	$-0.634560\pi$
$571$	−3.65014e9	−0.820510	−0.410255	+	0.911971i	$0.634560\pi$
$572$	2.63914e9	0.589626
$573$	6.79066e9	1.50789
$574$	1.05011e9	0.231763
$575$	0	0
$576$	−2.78760e8	−0.0607788
$577$	1.07847e9	0.233718	0.116859	−	0.993149i	$-0.462717\pi$
$577$	1.07847e9	0.233718	0.116859	+	0.993149i	$0.462717\pi$
$578$	−1.28838e9	−0.277522
$579$	4.64208e8	0.0993888
$580$	0	0
$581$	2.38981e8	0.0505530
$582$	−2.48894e9	−0.523339
$583$	−3.29637e8	−0.0688963
$584$	−2.40375e9	−0.499395
$585$	0	0
$586$	−7.07897e8	−0.145321
$587$	−4.20971e9	−0.859051	−0.429525	−	0.903055i	$-0.641319\pi$
$587$	−4.20971e9	−0.859051	−0.429525	+	0.903055i	$0.641319\pi$
$588$	−4.54596e8	−0.0922157
$589$	8.32388e9	1.67850
$590$	0	0
$591$	1.39721e9	0.278423
$592$	5.25827e8	0.104164
$593$	−5.74388e9	−1.13113	−0.565567	−	0.824702i	$-0.691343\pi$
$593$	−5.74388e9	−1.13113	−0.565567	+	0.824702i	$0.691343\pi$
$594$	3.66218e9	0.716948
$595$	0	0
$596$	−2.03338e9	−0.393421
$597$	9.93597e8	0.191117
$598$	2.82140e9	0.539524
$599$	9.33394e8	0.177448	0.0887240	−	0.996056i	$-0.471721\pi$
$599$	9.33394e8	0.177448	0.0887240	+	0.996056i	$0.471721\pi$
$600$	0	0
$601$	3.35934e9	0.631239	0.315619	−	0.948886i	$-0.397788\pi$
$601$	3.35934e9	0.631239	0.315619	+	0.948886i	$0.397788\pi$
$602$	−3.54124e8	−0.0661558
$603$	1.01918e9	0.189295
$604$	−1.36170e8	−0.0251451
$605$	0	0
$606$	−5.45224e8	−0.0995224
$607$	−4.15281e9	−0.753670	−0.376835	−	0.926280i	$-0.622988\pi$
$607$	−4.15281e9	−0.753670	−0.376835	+	0.926280i	$0.622988\pi$
$608$	1.06364e10	1.91924
$609$	−5.99434e8	−0.107543
$610$	0	0
$611$	2.67407e9	0.474274
$612$	5.44279e8	0.0959824
$613$	7.50640e9	1.31620	0.658098	−	0.752933i	$-0.271361\pi$
$613$	7.50640e9	1.31620	0.658098	+	0.752933i	$0.271361\pi$
$614$	−8.79639e8	−0.153361
$615$	0	0
$616$	−2.52097e9	−0.434545
$617$	3.00913e9	0.515754	0.257877	−	0.966178i	$-0.416977\pi$
$617$	3.00913e9	0.515754	0.257877	+	0.966178i	$0.416977\pi$
$618$	2.91454e9	0.496719
$619$	3.76275e8	0.0637659	0.0318830	−	0.999492i	$-0.489850\pi$
$619$	3.76275e8	0.0637659	0.0318830	+	0.999492i	$0.489850\pi$
$620$	0	0
$621$	−1.00052e10	−1.67651
$622$	4.11393e9	0.685473
$623$	−1.90656e9	−0.315895
$624$	8.34377e8	0.137473
$625$	0	0
$626$	3.24701e9	0.529022
$627$	−1.29486e10	−2.09791
$628$	−4.35239e9	−0.701244
$629$	1.90721e9	0.305578
$630$	0	0
$631$	−1.14466e10	−1.81373	−0.906866	−	0.421418i	$-0.861532\pi$
$631$	−1.14466e10	−1.81373	−0.906866	+	0.421418i	$0.861532\pi$
$632$	2.20340e9	0.347203
$633$	6.69235e8	0.104874
$634$	1.61086e9	0.251042
$635$	0	0
$636$	−2.28757e8	−0.0352593
$637$	6.06128e8	0.0929129
$638$	−1.39011e9	−0.211922
$639$	−6.36409e8	−0.0964902
$640$	0	0
$641$	5.64297e9	0.846261	0.423131	−	0.906069i	$-0.360931\pi$
$641$	5.64297e9	0.846261	0.423131	+	0.906069i	$0.360931\pi$
$642$	4.60060e9	0.686186
$643$	−1.28092e9	−0.190013	−0.0950063	−	0.995477i	$-0.530287\pi$
$643$	−1.28092e9	−0.190013	−0.0950063	+	0.995477i	$0.530287\pi$
$644$	2.88018e9	0.424932
$645$	0	0
$646$	4.64643e9	0.678118
$647$	−2.91819e9	−0.423593	−0.211797	−	0.977314i	$-0.567931\pi$
$647$	−2.91819e9	−0.423593	−0.211797	+	0.977314i	$0.567931\pi$
$648$	4.85620e9	0.701107
$649$	−1.10205e10	−1.58250
$650$	0	0
$651$	−2.16568e9	−0.307653
$652$	1.21562e8	0.0171764
$653$	−7.26090e9	−1.02046	−0.510228	−	0.860039i	$-0.670439\pi$
$653$	−7.26090e9	−1.02046	−0.510228	+	0.860039i	$0.670439\pi$
$654$	5.89814e9	0.824505
$655$	0	0
$656$	−1.96755e9	−0.272122
$657$	−7.70292e8	−0.105968
$658$	−1.06818e9	−0.146168
$659$	5.72191e8	0.0778828	0.0389414	−	0.999241i	$-0.487601\pi$
$659$	5.72191e8	0.0778828	0.0389414	+	0.999241i	$0.487601\pi$
$660$	0	0
$661$	3.74993e9	0.505031	0.252515	−	0.967593i	$-0.418742\pi$
$661$	3.74993e9	0.505031	0.252515	+	0.967593i	$0.418742\pi$
$662$	−8.02992e7	−0.0107574
$663$	3.02635e9	0.403294
$664$	9.19694e8	0.121914
$665$	0	0
$666$	−3.46097e8	−0.0453981
$667$	3.79783e9	0.495558
$668$	−3.27790e9	−0.425479
$669$	5.12517e9	0.661784
$670$	0	0
$671$	1.66413e10	2.12647
$672$	−2.76733e9	−0.351778
$673$	2.63426e9	0.333124	0.166562	−	0.986031i	$-0.446733\pi$
$673$	2.63426e9	0.333124	0.166562	+	0.986031i	$0.446733\pi$
$674$	4.19164e9	0.527320
$675$	0	0
$676$	3.33090e9	0.414713
$677$	3.95251e9	0.489568	0.244784	−	0.969578i	$-0.421283\pi$
$677$	3.95251e9	0.489568	0.244784	+	0.969578i	$0.421283\pi$
$678$	6.37660e9	0.785751
$679$	3.38772e9	0.415301
$680$	0	0
$681$	−1.27514e10	−1.54719
$682$	−5.02229e9	−0.606257
$683$	1.18389e10	1.42180	0.710898	−	0.703295i	$-0.248289\pi$
$683$	1.18389e10	1.42180	0.710898	+	0.703295i	$0.248289\pi$
$684$	2.15478e9	0.257458
$685$	0	0
$686$	−2.42122e8	−0.0286351
$687$	−4.80328e9	−0.565183
$688$	6.63510e8	0.0776762
$689$	3.05009e8	0.0355259
$690$	0	0
$691$	−1.41598e10	−1.63261	−0.816306	−	0.577620i	$-0.803982\pi$
$691$	−1.41598e10	−1.63261	−0.816306	+	0.577620i	$0.803982\pi$
$692$	8.43868e9	0.968062
$693$	−8.07856e8	−0.0922077
$694$	−2.55277e9	−0.289903
$695$	0	0
$696$	−2.30686e9	−0.259351
$697$	−7.13647e9	−0.798305
$698$	1.70039e9	0.189259
$699$	−5.85493e8	−0.0648412
$700$	0	0
$701$	−8.54644e9	−0.937070	−0.468535	−	0.883445i	$-0.655218\pi$
$701$	−8.54644e9	−0.937070	−0.468535	+	0.883445i	$0.655218\pi$
$702$	−3.38857e9	−0.369689
$703$	7.55059e9	0.819666
$704$	−3.66936e9	−0.396356
$705$	0	0
$706$	7.23649e9	0.773947
$707$	7.42111e8	0.0789770
$708$	−7.64782e9	−0.809881
$709$	−4.02549e9	−0.424187	−0.212093	−	0.977249i	$-0.568028\pi$
$709$	−4.02549e9	−0.424187	−0.212093	+	0.977249i	$0.568028\pi$
$710$	0	0
$711$	7.06089e8	0.0736742
$712$	−7.33721e9	−0.761817
$713$	1.37211e10	1.41767
$714$	−1.20889e9	−0.124292
$715$	0	0
$716$	9.04400e9	0.920799
$717$	−1.11018e10	−1.12480
$718$	3.41092e9	0.343903
$719$	1.86141e10	1.86763	0.933816	−	0.357754i	$-0.116457\pi$
$719$	1.86141e10	1.86763	0.933816	+	0.357754i	$0.116457\pi$
$720$	0	0
$721$	−3.96702e9	−0.394177
$722$	1.30318e10	1.28862
$723$	−1.53271e10	−1.50826
$724$	−8.05014e9	−0.788349
$725$	0	0
$726$	2.90189e9	0.281451
$727$	−1.65695e9	−0.159934	−0.0799668	−	0.996798i	$-0.525481\pi$
$727$	−1.65695e9	−0.159934	−0.0799668	+	0.996798i	$0.525481\pi$
$728$	2.33262e9	0.224070
$729$	1.16252e10	1.11136
$730$	0	0
$731$	2.40660e9	0.227873
$732$	1.15485e10	1.08827
$733$	−1.54861e10	−1.45237	−0.726187	−	0.687498i	$-0.758709\pi$
$733$	−1.54861e10	−1.45237	−0.726187	+	0.687498i	$0.758709\pi$
$734$	−7.69368e9	−0.718121
$735$	0	0
$736$	1.75330e10	1.62100
$737$	1.34156e10	1.23445
$738$	1.29503e9	0.118600
$739$	1.33359e10	1.21553	0.607766	−	0.794117i	$-0.292066\pi$
$739$	1.33359e10	1.21553	0.607766	+	0.794117i	$0.292066\pi$
$740$	0	0
$741$	1.19812e10	1.08177
$742$	−1.21838e8	−0.0109488
$743$	−3.28409e9	−0.293734	−0.146867	−	0.989156i	$-0.546919\pi$
$743$	−3.28409e9	−0.293734	−0.146867	+	0.989156i	$0.546919\pi$
$744$	−8.33441e9	−0.741941
$745$	0	0
$746$	5.88139e8	0.0518674
$747$	2.94720e8	0.0258695
$748$	7.16441e9	0.625929
$749$	−6.26193e9	−0.544530
$750$	0	0
$751$	−5.69946e9	−0.491014	−0.245507	−	0.969395i	$-0.578954\pi$
$751$	−5.69946e9	−0.491014	−0.245507	+	0.969395i	$0.578954\pi$
$752$	2.00140e9	0.171622
$753$	1.91124e9	0.163130
$754$	1.28625e9	0.109276
$755$	0	0
$756$	−3.45917e9	−0.291169
$757$	1.13301e9	0.0949287	0.0474643	−	0.998873i	$-0.484886\pi$
$757$	1.13301e9	0.0949287	0.0474643	+	0.998873i	$0.484886\pi$
$758$	−4.82991e9	−0.402807
$759$	−2.13445e10	−1.77190
$760$	0	0
$761$	7.00776e9	0.576412	0.288206	−	0.957568i	$-0.406941\pi$
$761$	7.00776e9	0.576412	0.288206	+	0.957568i	$0.406941\pi$
$762$	6.69427e8	0.0548101
$763$	−8.02803e9	−0.654294
$764$	−1.48748e10	−1.20677
$765$	0	0
$766$	−1.08343e10	−0.870967
$767$	1.01971e10	0.816005
$768$	−8.74266e9	−0.696433
$769$	1.53891e9	0.122031	0.0610155	−	0.998137i	$-0.480566\pi$
$769$	1.53891e9	0.122031	0.0610155	+	0.998137i	$0.480566\pi$
$770$	0	0
$771$	−2.11687e9	−0.166342
$772$	−1.01684e9	−0.0795409
$773$	−2.26463e10	−1.76347	−0.881737	−	0.471741i	$-0.843626\pi$
$773$	−2.26463e10	−1.76347	−0.881737	+	0.471741i	$0.843626\pi$
$774$	−4.36719e8	−0.0338539
$775$	0	0
$776$	1.30373e10	1.00155
$777$	−1.96449e9	−0.150237
$778$	−9.65967e9	−0.735417
$779$	−2.82530e10	−2.14133
$780$	0	0
$781$	−8.37712e9	−0.629240
$782$	7.65918e9	0.572742
$783$	−4.56129e9	−0.339564
$784$	4.53655e8	0.0336217
$785$	0	0
$786$	−7.60904e9	−0.558922
$787$	−3.90403e9	−0.285497	−0.142748	−	0.989759i	$-0.545594\pi$
$787$	−3.90403e9	−0.285497	−0.142748	+	0.989759i	$0.545594\pi$
$788$	−3.06055e9	−0.222822
$789$	9.29502e9	0.673722
$790$	0	0
$791$	−8.67926e9	−0.623541
$792$	−3.10895e9	−0.222370
$793$	−1.53980e10	−1.09650
$794$	2.21831e9	0.157272
$795$	0	0
$796$	−2.17645e9	−0.152951
$797$	−1.47537e10	−1.03228	−0.516138	−	0.856505i	$-0.672631\pi$
$797$	−1.47537e10	−1.03228	−0.516138	+	0.856505i	$0.672631\pi$
$798$	−4.78596e9	−0.333395
$799$	7.25924e9	0.503474
$800$	0	0
$801$	−2.35124e9	−0.161653
$802$	−1.29621e10	−0.887290
$803$	−1.01395e10	−0.691051
$804$	9.30994e9	0.631758
$805$	0	0
$806$	4.64706e9	0.312612
$807$	1.42104e10	0.951807
$808$	2.85594e9	0.190462
$809$	−1.79877e10	−1.19442	−0.597209	−	0.802085i	$-0.703724\pi$
$809$	−1.79877e10	−1.19442	−0.597209	+	0.802085i	$0.703724\pi$
$810$	0	0
$811$	−3.52168e9	−0.231834	−0.115917	−	0.993259i	$-0.536981\pi$
$811$	−3.52168e9	−0.231834	−0.115917	+	0.993259i	$0.536981\pi$
$812$	1.31305e9	0.0860664
$813$	1.59467e10	1.04077
$814$	−4.55572e9	−0.296054
$815$	0	0
$816$	2.26506e9	0.145937
$817$	9.52763e9	0.611234
$818$	−2.98524e9	−0.190696
$819$	7.47499e8	0.0475463
$820$	0	0
$821$	2.51068e10	1.58340	0.791699	−	0.610911i	$-0.209197\pi$
$821$	2.51068e10	1.58340	0.791699	+	0.610911i	$0.209197\pi$
$822$	3.99431e9	0.250836
$823$	−1.28188e10	−0.801584	−0.400792	−	0.916169i	$-0.631265\pi$
$823$	−1.28188e10	−0.801584	−0.400792	+	0.916169i	$0.631265\pi$
$824$	−1.52667e10	−0.950602
$825$	0	0
$826$	−4.07330e9	−0.251487
$827$	8.04747e9	0.494755	0.247377	−	0.968919i	$-0.420431\pi$
$827$	8.04747e9	0.494755	0.247377	+	0.968919i	$0.420431\pi$
$828$	3.55194e9	0.217450
$829$	1.39485e10	0.850330	0.425165	−	0.905116i	$-0.360216\pi$
$829$	1.39485e10	0.850330	0.425165	+	0.905116i	$0.360216\pi$
$830$	0	0
$831$	−9.15836e9	−0.553623
$832$	3.39521e9	0.204378
$833$	1.64544e9	0.0986335
$834$	−2.58347e9	−0.154213
$835$	0	0
$836$	2.83636e10	1.67896
$837$	−1.64794e10	−0.971409
$838$	4.22407e9	0.247958
$839$	−2.03937e10	−1.19215	−0.596074	−	0.802930i	$-0.703273\pi$
$839$	−2.03937e10	−1.19215	−0.596074	+	0.802930i	$0.703273\pi$
$840$	0	0
$841$	−1.55185e10	−0.899629
$842$	−6.42114e9	−0.370698
$843$	1.51260e10	0.869618
$844$	−1.46594e9	−0.0839303
$845$	0	0
$846$	−1.31731e9	−0.0747985
$847$	−3.94980e9	−0.223349
$848$	2.28283e8	0.0128555
$849$	2.28641e10	1.28226
$850$	0	0
$851$	1.24464e10	0.692293
$852$	−5.81343e9	−0.322028
$853$	3.20572e10	1.76850	0.884248	−	0.467018i	$-0.154672\pi$
$853$	3.20572e10	1.76850	0.884248	+	0.467018i	$0.154672\pi$
$854$	6.15084e9	0.337934
$855$	0	0
$856$	−2.40984e10	−1.31320
$857$	−4.54985e9	−0.246925	−0.123462	−	0.992349i	$-0.539400\pi$
$857$	−4.54985e9	−0.246925	−0.123462	+	0.992349i	$0.539400\pi$
$858$	−7.22896e9	−0.390724
$859$	−3.07832e10	−1.65706	−0.828530	−	0.559945i	$-0.810822\pi$
$859$	−3.07832e10	−1.65706	−0.828530	+	0.559945i	$0.810822\pi$
$860$	0	0
$861$	7.35078e9	0.392484
$862$	8.21355e9	0.436773
$863$	−9.27058e9	−0.490986	−0.245493	−	0.969398i	$-0.578950\pi$
$863$	−9.27058e9	−0.490986	−0.245493	+	0.969398i	$0.578950\pi$
$864$	−2.10576e10	−1.11073
$865$	0	0
$866$	4.69816e9	0.245819
$867$	−9.01868e9	−0.469976
$868$	4.74388e9	0.246215
$869$	9.29433e9	0.480451
$870$	0	0
$871$	−1.24132e10	−0.636534
$872$	−3.08950e10	−1.57791
$873$	4.17786e9	0.212522
$874$	3.03224e10	1.53629
$875$	0	0
$876$	−7.03643e9	−0.353662
$877$	−2.02698e10	−1.01473	−0.507365	−	0.861731i	$-0.669380\pi$
$877$	−2.02698e10	−1.01473	−0.507365	+	0.861731i	$0.669380\pi$
$878$	−9.17615e9	−0.457541
$879$	−4.95528e9	−0.246097
$880$	0	0
$881$	−1.20420e10	−0.593312	−0.296656	−	0.954984i	$-0.595871\pi$
$881$	−1.20420e10	−0.593312	−0.296656	+	0.954984i	$0.595871\pi$
$882$	−2.98593e8	−0.0146534
$883$	−4.07501e10	−1.99189	−0.995946	−	0.0899511i	$-0.971329\pi$
$883$	−4.07501e10	−1.99189	−0.995946	+	0.0899511i	$0.971329\pi$
$884$	−6.62914e9	−0.322756
$885$	0	0
$886$	−2.06982e9	−0.0999804
$887$	−6.25298e9	−0.300853	−0.150426	−	0.988621i	$-0.548065\pi$
$887$	−6.25298e9	−0.300853	−0.150426	+	0.988621i	$0.548065\pi$
$888$	−7.56013e9	−0.362313
$889$	−9.11164e8	−0.0434951
$890$	0	0
$891$	2.04843e10	0.970174
$892$	−1.12266e10	−0.529626
$893$	2.87390e10	1.35049
$894$	5.56970e9	0.260706
$895$	0	0
$896$	7.07754e9	0.328704
$897$	1.97498e10	0.913670
$898$	7.23392e9	0.333355
$899$	6.25531e9	0.287138
$900$	0	0
$901$	8.27999e8	0.0377132
$902$	1.70467e10	0.773424
$903$	−2.47887e9	−0.112033
$904$	−3.34012e10	−1.50374
$905$	0	0
$906$	3.72988e8	0.0166627
$907$	−9.81994e9	−0.437002	−0.218501	−	0.975837i	$-0.570117\pi$
$907$	−9.81994e9	−0.437002	−0.218501	+	0.975837i	$0.570117\pi$
$908$	2.79317e10	1.23822
$909$	9.15198e8	0.0404149
$910$	0	0
$911$	9.73056e9	0.426406	0.213203	−	0.977008i	$-0.431610\pi$
$911$	9.73056e9	0.426406	0.213203	+	0.977008i	$0.431610\pi$
$912$	8.96728e9	0.391452
$913$	3.87944e9	0.168702
$914$	−1.71421e10	−0.742598
$915$	0	0
$916$	1.05215e10	0.452316
$917$	1.03567e10	0.443538
$918$	−9.19887e9	−0.392451
$919$	−4.29536e9	−0.182556	−0.0912778	−	0.995825i	$-0.529095\pi$
$919$	−4.29536e9	−0.182556	−0.0912778	+	0.995825i	$0.529095\pi$
$920$	0	0
$921$	−6.15747e9	−0.259713
$922$	1.64358e10	0.690612
$923$	7.75125e9	0.324463
$924$	−7.37956e9	−0.307736
$925$	0	0
$926$	−4.36731e9	−0.180749
$927$	−4.89227e9	−0.201712
$928$	7.99311e9	0.328321
$929$	2.64304e10	1.08155	0.540777	−	0.841166i	$-0.318130\pi$
$929$	2.64304e10	1.08155	0.540777	+	0.841166i	$0.318130\pi$
$930$	0	0
$931$	6.51423e9	0.264569
$932$	1.28251e9	0.0518925
$933$	2.87975e10	1.16083
$934$	8.24397e9	0.331072
$935$	0	0
$936$	2.87667e9	0.114663
$937$	−2.42536e10	−0.963136	−0.481568	−	0.876409i	$-0.659933\pi$
$937$	−2.42536e10	−0.963136	−0.481568	+	0.876409i	$0.659933\pi$
$938$	4.95855e9	0.196176
$939$	2.27291e10	0.895885
$940$	0	0
$941$	−2.13011e10	−0.833370	−0.416685	−	0.909051i	$-0.636808\pi$
$941$	−2.13011e10	−0.833370	−0.416685	+	0.909051i	$0.636808\pi$
$942$	1.19218e10	0.464689
$943$	−4.65723e10	−1.80857
$944$	7.63199e9	0.295281
$945$	0	0
$946$	−5.74858e9	−0.220771
$947$	2.55846e9	0.0978934	0.0489467	−	0.998801i	$-0.484414\pi$
$947$	2.55846e9	0.0978934	0.0489467	+	0.998801i	$0.484414\pi$
$948$	6.44994e9	0.245882
$949$	9.38191e9	0.356336
$950$	0	0
$951$	1.12760e10	0.425133
$952$	6.33230e9	0.237866
$953$	4.10738e10	1.53723	0.768616	−	0.639711i	$-0.220946\pi$
$953$	4.10738e10	1.53723	0.768616	+	0.639711i	$0.220946\pi$
$954$	−1.50255e8	−0.00560285
$955$	0	0
$956$	2.43181e10	0.900177
$957$	−9.73075e9	−0.358884
$958$	−1.49622e9	−0.0549813
$959$	−5.43670e9	−0.199054
$960$	0	0
$961$	−4.91290e9	−0.178569
$962$	4.21535e9	0.152658
$963$	−7.72244e9	−0.278652
$964$	3.35737e10	1.20706
$965$	0	0
$966$	−7.88919e9	−0.281587
$967$	−3.87008e10	−1.37634	−0.688172	−	0.725548i	$-0.741587\pi$
$967$	−3.87008e10	−1.37634	−0.688172	+	0.725548i	$0.741587\pi$
$968$	−1.52004e10	−0.538631
$969$	3.25250e10	1.14838
$970$	0	0
$971$	−1.86478e9	−0.0653672	−0.0326836	−	0.999466i	$-0.510405\pi$
$971$	−1.86478e9	−0.0653672	−0.0326836	+	0.999466i	$0.510405\pi$
$972$	−7.84056e9	−0.273852
$973$	3.51638e9	0.122377
$974$	1.31344e10	0.455464
$975$	0	0
$976$	−1.15246e10	−0.396782
$977$	4.44026e10	1.52327	0.761635	−	0.648006i	$-0.224397\pi$
$977$	4.44026e10	1.52327	0.761635	+	0.648006i	$0.224397\pi$
$978$	−3.32975e8	−0.0113822
$979$	−3.09497e10	−1.05418
$980$	0	0
$981$	−9.90045e9	−0.334822
$982$	8.39401e9	0.282865
$983$	5.42112e10	1.82034	0.910169	−	0.414238i	$-0.135952\pi$
$983$	5.42112e10	1.82034	0.910169	+	0.414238i	$0.135952\pi$
$984$	2.82887e10	0.946521
$985$	0	0
$986$	3.49174e9	0.116004
$987$	−7.47723e9	−0.247532
$988$	−2.62445e10	−0.865743
$989$	1.57054e10	0.516251
$990$	0	0
$991$	−2.64475e9	−0.0863230	−0.0431615	−	0.999068i	$-0.513743\pi$
$991$	−2.64475e9	−0.0863230	−0.0431615	+	0.999068i	$0.513743\pi$
$992$	2.88782e10	0.939245
$993$	−5.62095e8	−0.0182174
$994$	−3.09629e9	−0.0999974
$995$	0	0
$996$	2.69220e9	0.0863374
$997$	4.58169e10	1.46417	0.732087	−	0.681211i	$-0.238547\pi$
$997$	4.58169e10	1.46417	0.732087	+	0.681211i	$0.238547\pi$
$998$	9.30971e9	0.296469
$999$	−1.49484e10	−0.474369

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.8.a.a.1.1		1
5.2	odd	4		175.8.b.a.99.2		2
5.3	odd	4		175.8.b.a.99.1		2
5.4	even	2		7.8.a.a.1.1	✓	1
15.14	odd	2		63.8.a.b.1.1		1
20.19	odd	2		112.8.a.c.1.1		1
35.4	even	6		49.8.c.b.30.1		2
35.9	even	6		49.8.c.b.18.1		2
35.19	odd	6		49.8.c.a.18.1		2
35.24	odd	6		49.8.c.a.30.1		2
35.34	odd	2		49.8.a.b.1.1		1
40.19	odd	2		448.8.a.d.1.1		1
40.29	even	2		448.8.a.g.1.1		1
105.104	even	2		441.8.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.8.a.a.1.1	✓	1	5.4	even	2
49.8.a.b.1.1		1	35.34	odd	2
49.8.c.a.18.1		2	35.19	odd	6
49.8.c.a.30.1		2	35.24	odd	6
49.8.c.b.18.1		2	35.9	even	6
49.8.c.b.30.1		2	35.4	even	6
63.8.a.b.1.1		1	15.14	odd	2
112.8.a.c.1.1		1	20.19	odd	2
175.8.a.a.1.1		1	1.1	even	1	trivial
175.8.b.a.99.1		2	5.3	odd	4
175.8.b.a.99.2		2	5.2	odd	4
441.8.a.e.1.1		1	105.104	even	2
448.8.a.d.1.1		1	40.19	odd	2
448.8.a.g.1.1		1	40.29	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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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