LMFDB - Embedded newform 175.10.b.d.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(99,175)]

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([1, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("175.99");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 853x^{4} + 185508x^{2} + 4064256 $ x^6 + 853x^4 + 185508x^2 + 4064256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 7)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$-18.2745i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.d.99.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-34.1627i q^{2} +79.6469i q^{3} -655.088 q^{4} +2720.95 q^{6} +2401.00i q^{7} +4888.28i q^{8} +13339.4 q^{9} +69354.4 q^{11} -52175.7i q^{12} -105959. i q^{13} +82024.6 q^{14} -168409. q^{16} +568267. i q^{17} -455709. i q^{18} +396405. q^{19} -191232. q^{21} -2.36933e6i q^{22} +620765. i q^{23} -389336. q^{24} -3.61984e6 q^{26} +2.63013e6i q^{27} -1.57287e6i q^{28} -4.87652e6 q^{29} -1.42482e6 q^{31} +8.25609e6i q^{32} +5.52386e6i q^{33} +1.94135e7 q^{34} -8.73846e6 q^{36} +1.31092e7i q^{37} -1.35423e7i q^{38} +8.43931e6 q^{39} -2.03049e7 q^{41} +6.53300e6i q^{42} +1.11768e7i q^{43} -4.54332e7 q^{44} +2.12070e7 q^{46} -1.99352e7i q^{47} -1.34132e7i q^{48} -5.76480e6 q^{49} -4.52607e7 q^{51} +6.94125e7i q^{52} -5.65007e7i q^{53} +8.98523e7 q^{54} -1.17367e7 q^{56} +3.15725e7i q^{57} +1.66595e8i q^{58} +1.09340e8 q^{59} +3.20008e7 q^{61} +4.86755e7i q^{62} +3.20278e7i q^{63} +1.95825e8 q^{64} +1.88710e8 q^{66} +8.02869e7i q^{67} -3.72265e8i q^{68} -4.94420e7 q^{69} +2.07893e8 q^{71} +6.52065e7i q^{72} +2.70274e8i q^{73} +4.47844e8 q^{74} -2.59680e8 q^{76} +1.66520e8i q^{77} -2.88309e8i q^{78} +5.16196e8 q^{79} +5.30772e7 q^{81} +6.93671e8i q^{82} +6.82693e8i q^{83} +1.25274e8 q^{84} +3.81830e8 q^{86} -3.88400e8i q^{87} +3.39023e8i q^{88} +1.47150e8 q^{89} +2.54408e8 q^{91} -4.06656e8i q^{92} -1.13482e8i q^{93} -6.81040e8 q^{94} -6.57572e8 q^{96} +1.09643e9i q^{97} +1.96941e8i q^{98} +9.25144e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3114 q^{4} + 9828 q^{6} + 52002 q^{9} - 6888 q^{11} - 100842 q^{14} + 965922 q^{16} - 445704 q^{19} + 403368 q^{21} + 2899260 q^{24} - 17570112 q^{26} - 8163636 q^{29} + 5738880 q^{31} + 7963284 q^{34}+ \cdots + 3801958344 q^{99}+O(q^{100}) $ 6 * q - 3114 * q^4 + 9828 * q^6 + 52002 * q^9 - 6888 * q^11 - 100842 * q^14 + 965922 * q^16 - 445704 * q^19 + 403368 * q^21 + 2899260 * q^24 - 17570112 * q^26 - 8163636 * q^29 + 5738880 * q^31 + 7963284 * q^34 - 70792758 * q^36 + 17981376 * q^39 - 28841316 * q^41 - 194023968 * q^44 + 179495328 * q^46 - 34588806 * q^49 - 52293456 * q^51 + 235758600 * q^54 + 67492110 * q^56 + 85180200 * q^59 + 383493684 * q^61 - 15704322 * q^64 - 16115904 * q^66 - 515807712 * q^69 + 593029008 * q^71 + 1381392924 * q^74 + 1457679972 * q^76 + 1920825312 * q^79 - 71655354 * q^81 + 510865572 * q^84 - 1761964512 * q^86 - 1013632956 * q^89 - 94993164 * q^91 - 2776009656 * q^94 + 666771588 * q^96 + 3801958344 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 34.1627i	− 1.50979i	−0.655845	−	0.754896i	$-0.727688\pi$
$2$	− 34.1627i	− 1.50979i	0.655845	−	0.754896i	$-0.272312\pi$
$3$	79.6469i	0.567706i	0.958868	+	0.283853i	$0.0916127\pi$
$3$	79.6469i	0.567706i	−0.958868	+	0.283853i	$0.908387\pi$
$4$	−655.088	−1.27947
$5$	0	0
$5$	0	0
$6$	2720.95	0.857117
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	4888.28i	0.421940i
$9$	13339.4	0.677710
$10$	0	0
$11$	69354.4	1.42826	0.714129	−	0.700014i	$-0.246823\pi$
$11$	69354.4	1.42826	0.714129	+	0.700014i	$0.246823\pi$
$12$	− 52175.7i	− 0.726362i
$13$	− 105959.i	− 1.02895i	−0.857506	−	0.514473i	$-0.827987\pi$
$13$	− 105959.i	− 1.02895i	0.857506	−	0.514473i	$-0.172013\pi$
$14$	82024.6	0.570647
$15$	0	0
$16$	−168409.	−0.642428
$17$	568267.i	1.65018i	0.564998	+	0.825092i	$0.308877\pi$
$17$	568267.i	1.65018i	−0.564998	+	0.825092i	$0.691123\pi$
$18$	− 455709.i	− 1.02320i
$19$	396405.	0.697828	0.348914	−	0.937155i	$-0.386551\pi$
$19$	396405.	0.697828	0.348914	+	0.937155i	$0.386551\pi$
$20$	0	0
$21$	−191232.	−0.214573
$22$	− 2.36933e6i	− 2.15637i
$23$	620765.i	0.462543i	0.972889	+	0.231271i	$0.0742885\pi$
$23$	620765.i	0.462543i	−0.972889	+	0.231271i	$0.925712\pi$
$24$	−389336.	−0.239538
$25$	0	0
$26$	−3.61984e6	−1.55349
$27$	2.63013e6i	0.952446i
$28$	− 1.57287e6i	− 0.483594i
$29$	−4.87652e6	−1.28032	−0.640161	−	0.768241i	$-0.721132\pi$
$29$	−4.87652e6	−1.28032	−0.640161	+	0.768241i	$0.721132\pi$
$30$	0	0
$31$	−1.42482e6	−0.277096	−0.138548	−	0.990356i	$-0.544244\pi$
$31$	−1.42482e6	−0.277096	−0.138548	+	0.990356i	$0.544244\pi$
$32$	8.25609e6i	1.39187i
$33$	5.52386e6i	0.810830i
$34$	1.94135e7	2.49143
$35$	0	0
$36$	−8.73846e6	−0.867109
$37$	1.31092e7i	1.14992i	0.818182	+	0.574960i	$0.194982\pi$
$37$	1.31092e7i	1.14992i	−0.818182	+	0.574960i	$0.805018\pi$
$38$	− 1.35423e7i	− 1.05357i
$39$	8.43931e6	0.584139
$40$	0	0
$41$	−2.03049e7	−1.12221	−0.561105	−	0.827744i	$-0.689624\pi$
$41$	−2.03049e7	−1.12221	−0.561105	+	0.827744i	$0.689624\pi$
$42$	6.53300e6i	0.323960i
$43$	1.11768e7i	0.498551i	0.968433	+	0.249276i	$0.0801925\pi$
$43$	1.11768e7i	0.498551i	−0.968433	+	0.249276i	$0.919807\pi$
$44$	−4.54332e7	−1.82741
$45$	0	0
$46$	2.12070e7	0.698343
$47$	− 1.99352e7i	− 0.595909i	−0.954580	−	0.297955i	$-0.903696\pi$
$47$	− 1.99352e7i	− 0.595909i	0.954580	−	0.297955i	$-0.0963044\pi$
$48$	− 1.34132e7i	− 0.364710i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−4.52607e7	−0.936819
$52$	6.94125e7i	1.31651i
$53$	− 5.65007e7i	− 0.983586i	−0.870712	−	0.491793i	$-0.836342\pi$
$53$	− 5.65007e7i	− 0.983586i	0.870712	−	0.491793i	$-0.163658\pi$
$54$	8.98523e7	1.43799
$55$	0	0
$56$	−1.17367e7	−0.159478
$57$	3.15725e7i	0.396161i
$58$	1.66595e8i	1.93302i
$59$	1.09340e8	1.17475	0.587375	−	0.809315i	$-0.300161\pi$
$59$	1.09340e8	1.17475	0.587375	+	0.809315i	$0.300161\pi$
$60$	0	0
$61$	3.20008e7	0.295921	0.147961	−	0.988993i	$-0.452729\pi$
$61$	3.20008e7	0.295921	0.147961	+	0.988993i	$0.452729\pi$
$62$	4.86755e7i	0.418358i
$63$	3.20278e7i	0.256150i
$64$	1.95825e8	1.45901
$65$	0	0
$66$	1.88710e8	1.22418
$67$	8.02869e7i	0.486752i	0.969932	+	0.243376i	$0.0782549\pi$
$67$	8.02869e7i	0.486752i	−0.969932	+	0.243376i	$0.921745\pi$
$68$	− 3.72265e8i	− 2.11136i
$69$	−4.94420e7	−0.262588
$70$	0	0
$71$	2.07893e8	0.970906	0.485453	−	0.874263i	$-0.338655\pi$
$71$	2.07893e8	0.970906	0.485453	+	0.874263i	$0.338655\pi$
$72$	6.52065e7i	0.285953i
$73$	2.70274e8i	1.11391i	0.830541	+	0.556957i	$0.188031\pi$
$73$	2.70274e8i	1.11391i	−0.830541	+	0.556957i	$0.811969\pi$
$74$	4.47844e8	1.73614
$75$	0	0
$76$	−2.59680e8	−0.892849
$77$	1.66520e8i	0.539831i
$78$	− 2.88309e8i	− 0.881928i
$79$	5.16196e8	1.49105	0.745526	−	0.666477i	$-0.232198\pi$
$79$	5.16196e8	1.49105	0.745526	+	0.666477i	$0.232198\pi$
$80$	0	0
$81$	5.30772e7	0.137002
$82$	6.93671e8i	1.69430i
$83$	6.82693e8i	1.57897i	0.613769	+	0.789486i	$0.289653\pi$
$83$	6.82693e8i	1.57897i	−0.613769	+	0.789486i	$0.710347\pi$
$84$	1.25274e8	0.274539
$85$	0	0
$86$	3.81830e8	0.752708
$87$	− 3.88400e8i	− 0.726846i
$88$	3.39023e8i	0.602639i
$89$	1.47150e8	0.248602	0.124301	−	0.992245i	$-0.460331\pi$
$89$	1.47150e8	0.248602	0.124301	+	0.992245i	$0.460331\pi$
$90$	0	0
$91$	2.54408e8	0.388905
$92$	− 4.06656e8i	− 0.591809i
$93$	− 1.13482e8i	− 0.157309i
$94$	−6.81040e8	−0.899699
$95$	0	0
$96$	−6.57572e8	−0.790174
$97$	1.09643e9i	1.25750i	0.777608	+	0.628750i	$0.216433\pi$
$97$	1.09643e9i	1.25750i	−0.777608	+	0.628750i	$0.783567\pi$
$98$	1.96941e8i	0.215684i
$99$	9.25144e8	0.967945
$100$	0	0
$101$	2.08683e8	0.199545	0.0997727	−	0.995010i	$-0.468188\pi$
$101$	2.08683e8	0.199545	0.0997727	+	0.995010i	$0.468188\pi$
$102$	1.54623e9i	1.41440i
$103$	− 6.78194e8i	− 0.593727i	−0.954920	−	0.296863i	$-0.904059\pi$
$103$	− 6.78194e8i	− 0.593727i	0.954920	−	0.296863i	$-0.0959406\pi$
$104$	5.17957e8	0.434154
$105$	0	0
$106$	−1.93021e9	−1.48501
$107$	− 4.59542e8i	− 0.338921i	−0.985537	−	0.169461i	$-0.945797\pi$
$107$	− 4.59542e8i	− 0.338921i	0.985537	−	0.169461i	$-0.0542025\pi$
$108$	− 1.72297e9i	− 1.21862i
$109$	−5.21086e8	−0.353582	−0.176791	−	0.984248i	$-0.556572\pi$
$109$	−5.21086e8	−0.353582	−0.176791	+	0.984248i	$0.556572\pi$
$110$	0	0
$111$	−1.04410e9	−0.652816
$112$	− 4.04349e8i	− 0.242815i
$113$	− 4.45612e8i	− 0.257101i	−0.991703	−	0.128551i	$-0.958968\pi$
$113$	− 4.45612e8i	− 0.257101i	0.991703	−	0.128551i	$-0.0410325\pi$
$114$	1.07860e9	0.598120
$115$	0	0
$116$	3.19455e9	1.63813
$117$	− 1.41343e9i	− 0.697328i
$118$	− 3.73535e9i	− 1.77363i
$119$	−1.36441e9	−0.623711
$120$	0	0
$121$	2.45208e9	1.03992
$122$	− 1.09323e9i	− 0.446779i
$123$	− 1.61723e9i	− 0.637086i
$124$	9.33380e8	0.354536
$125$	0	0
$126$	1.09416e9	0.386734
$127$	9.28626e8i	0.316755i	0.987379	+	0.158378i	$0.0506264\pi$
$127$	9.28626e8i	0.316755i	−0.987379	+	0.158378i	$0.949374\pi$
$128$	− 2.46278e9i	− 0.810925i
$129$	−8.90198e8	−0.283030
$130$	0	0
$131$	2.57694e9	0.764509	0.382255	−	0.924057i	$-0.375148\pi$
$131$	2.57694e9	0.764509	0.382255	+	0.924057i	$0.375148\pi$
$132$	− 3.61862e9i	− 1.03743i
$133$	9.51769e8i	0.263754i
$134$	2.74281e9	0.734894
$135$	0	0
$136$	−2.77785e9	−0.696279
$137$	− 4.44116e9i	− 1.07710i	−0.842595	−	0.538548i	$-0.818973\pi$
$137$	− 4.44116e9i	− 1.07710i	0.842595	−	0.538548i	$-0.181027\pi$
$138$	1.68907e9i	0.396453i
$139$	7.28389e9	1.65499	0.827497	−	0.561470i	$-0.189764\pi$
$139$	7.28389e9	1.65499	0.827497	+	0.561470i	$0.189764\pi$
$140$	0	0
$141$	1.58778e9	0.338301
$142$	− 7.10218e9i	− 1.46587i
$143$	− 7.34872e9i	− 1.46960i
$144$	−2.24647e9	−0.435380
$145$	0	0
$146$	9.23328e9	1.68178
$147$	− 4.59149e8i	− 0.0811008i
$148$	− 8.58766e9i	− 1.47129i
$149$	−4.87355e9	−0.810042	−0.405021	−	0.914307i	$-0.632736\pi$
$149$	−4.87355e9	−0.810042	−0.405021	+	0.914307i	$0.632736\pi$
$150$	0	0
$151$	−8.63776e9	−1.35209	−0.676044	−	0.736861i	$-0.736307\pi$
$151$	−8.63776e9	−1.35209	−0.676044	+	0.736861i	$0.736307\pi$
$152$	1.93774e9i	0.294442i
$153$	7.58033e9i	1.11835i
$154$	5.68876e9	0.815032
$155$	0	0
$156$	−5.52849e9	−0.747388
$157$	− 9.34170e9i	− 1.22709i	−0.789659	−	0.613546i	$-0.789742\pi$
$157$	− 9.34170e9i	− 1.22709i	0.789659	−	0.613546i	$-0.210258\pi$
$158$	− 1.76346e10i	− 2.25118i
$159$	4.50010e9	0.558387
$160$	0	0
$161$	−1.49046e9	−0.174825
$162$	− 1.81326e9i	− 0.206844i
$163$	2.10680e9i	0.233765i	0.993146	+	0.116883i	$0.0372901\pi$
$163$	2.10680e9i	0.233765i	−0.993146	+	0.116883i	$0.962710\pi$
$164$	1.33015e10	1.43583
$165$	0	0
$166$	2.33226e10	2.38392
$167$	1.39800e10i	1.39086i	0.718593	+	0.695431i	$0.244787\pi$
$167$	1.39800e10i	1.39086i	−0.718593	+	0.695431i	$0.755213\pi$
$168$	− 9.34796e8i	− 0.0905367i
$169$	−6.22820e8	−0.0587316
$170$	0	0
$171$	5.28780e9	0.472925
$172$	− 7.32180e9i	− 0.637881i
$173$	1.24435e10i	1.05618i	0.849190	+	0.528088i	$0.177091\pi$
$173$	1.24435e10i	1.05618i	−0.849190	+	0.528088i	$0.822909\pi$
$174$	−1.32688e10	−1.09739
$175$	0	0
$176$	−1.16799e10	−0.917553
$177$	8.70861e9i	0.666913i
$178$	− 5.02704e9i	− 0.375338i
$179$	−7.30178e9	−0.531606	−0.265803	−	0.964027i	$-0.585637\pi$
$179$	−7.30178e9	−0.531606	−0.265803	+	0.964027i	$0.585637\pi$
$180$	0	0
$181$	−1.27074e10	−0.880038	−0.440019	−	0.897988i	$-0.645028\pi$
$181$	−1.27074e10	−0.880038	−0.440019	+	0.897988i	$0.645028\pi$
$182$	− 8.69125e9i	− 0.587166i
$183$	2.54876e9i	0.167996i
$184$	−3.03447e9	−0.195165
$185$	0	0
$186$	−3.87685e9	−0.237504
$187$	3.94118e10i	2.35689i
$188$	1.30593e10i	0.762448i
$189$	−6.31494e9	−0.359991
$190$	0	0
$191$	1.61547e10	0.878311	0.439155	−	0.898411i	$-0.355278\pi$
$191$	1.61547e10	0.878311	0.439155	+	0.898411i	$0.355278\pi$
$192$	1.55968e10i	0.828287i
$193$	1.52841e10i	0.792924i	0.918051	+	0.396462i	$0.129762\pi$
$193$	1.52841e10i	0.792924i	−0.918051	+	0.396462i	$0.870238\pi$
$194$	3.74570e10	1.89856
$195$	0	0
$196$	3.77645e9	0.182781
$197$	2.33886e10i	1.10639i	0.833053	+	0.553193i	$0.186591\pi$
$197$	2.33886e10i	1.10639i	−0.833053	+	0.553193i	$0.813409\pi$
$198$	− 3.16054e10i	− 1.46139i
$199$	2.53610e10	1.14638	0.573189	−	0.819423i	$-0.305706\pi$
$199$	2.53610e10	1.14638	0.573189	+	0.819423i	$0.305706\pi$
$200$	0	0
$201$	−6.39460e9	−0.276332
$202$	− 7.12918e9i	− 0.301272i
$203$	− 1.17085e10i	− 0.483916i
$204$	2.96498e10	1.19863
$205$	0	0
$206$	−2.31689e10	−0.896403
$207$	8.28061e9i	0.313470i
$208$	1.78444e10i	0.661024i
$209$	2.74924e10	0.996678
$210$	0	0
$211$	−9.23757e8	−0.0320838	−0.0160419	−	0.999871i	$-0.505107\pi$
$211$	−9.23757e8	−0.0320838	−0.0160419	+	0.999871i	$0.505107\pi$
$212$	3.70129e10i	1.25847i
$213$	1.65580e10i	0.551189i
$214$	−1.56992e10	−0.511700
$215$	0	0
$216$	−1.28568e10	−0.401875
$217$	− 3.42098e9i	− 0.104733i
$218$	1.78017e10i	0.533835i
$219$	−2.15265e10	−0.632375
$220$	0	0
$221$	6.02130e10	1.69795
$222$	3.56694e10i	0.985615i
$223$	− 6.68635e9i	− 0.181058i	−0.995894	−	0.0905290i	$-0.971144\pi$
$223$	− 6.68635e9i	− 0.181058i	0.995894	−	0.0905290i	$-0.0288558\pi$
$224$	−1.98229e10	−0.526078
$225$	0	0
$226$	−1.52233e10	−0.388169
$227$	− 4.82876e10i	− 1.20703i	−0.797351	−	0.603516i	$-0.793766\pi$
$227$	− 4.82876e10i	− 1.20703i	0.797351	−	0.603516i	$-0.206234\pi$
$228$	− 2.06827e10i	− 0.506876i
$229$	2.34264e10	0.562918	0.281459	−	0.959573i	$-0.409182\pi$
$229$	2.34264e10	0.562918	0.281459	+	0.959573i	$0.409182\pi$
$230$	0	0
$231$	−1.32628e10	−0.306465
$232$	− 2.38378e10i	− 0.540219i
$233$	3.29140e10i	0.731609i	0.930692	+	0.365805i	$0.119206\pi$
$233$	3.29140e10i	0.731609i	−0.930692	+	0.365805i	$0.880794\pi$
$234$	−4.82864e10	−1.05282
$235$	0	0
$236$	−7.16275e10	−1.50306
$237$	4.11134e10i	0.846479i
$238$	4.66119e10i	0.941673i
$239$	−2.51973e10	−0.499533	−0.249766	−	0.968306i	$-0.580354\pi$
$239$	−2.51973e10	−0.499533	−0.249766	+	0.968306i	$0.580354\pi$
$240$	0	0
$241$	7.00815e10	1.33822	0.669109	−	0.743165i	$-0.266676\pi$
$241$	7.00815e10	1.33822	0.669109	+	0.743165i	$0.266676\pi$
$242$	− 8.37696e10i	− 1.57006i
$243$	5.59963e10i	1.03022i
$244$	−2.09633e10	−0.378622
$245$	0	0
$246$	−5.52488e10	−0.961866
$247$	− 4.20027e10i	− 0.718028i
$248$	− 6.96489e9i	− 0.116918i
$249$	−5.43744e10	−0.896391
$250$	0	0
$251$	4.19681e10	0.667401	0.333701	−	0.942679i	$-0.391703\pi$
$251$	4.19681e10	0.667401	0.333701	+	0.942679i	$0.391703\pi$
$252$	− 2.09811e10i	− 0.327737i
$253$	4.30527e10i	0.660630i
$254$	3.17243e10	0.478235
$255$	0	0
$256$	1.61271e10	0.234680
$257$	8.37595e10i	1.19766i	0.800875	+	0.598832i	$0.204368\pi$
$257$	8.37595e10i	1.19766i	−0.800875	+	0.598832i	$0.795632\pi$
$258$	3.04116e10i	0.427317i
$259$	−3.14751e10	−0.434629
$260$	0	0
$261$	−6.50497e10	−0.867687
$262$	− 8.80350e10i	− 1.15425i
$263$	2.34604e9i	0.0302367i	0.999886	+	0.0151184i	$0.00481251\pi$
$263$	2.34604e9i	0.0302367i	−0.999886	+	0.0151184i	$0.995187\pi$
$264$	−2.70021e10	−0.342122
$265$	0	0
$266$	3.25150e10	0.398214
$267$	1.17200e10i	0.141133i
$268$	− 5.25950e10i	− 0.622784i
$269$	6.44659e10	0.750663	0.375332	−	0.926891i	$-0.377529\pi$
$269$	6.44659e10	0.750663	0.375332	+	0.926891i	$0.377529\pi$
$270$	0	0
$271$	−1.40530e10	−0.158273	−0.0791365	−	0.996864i	$-0.525216\pi$
$271$	−1.40530e10	−0.158273	−0.0791365	+	0.996864i	$0.525216\pi$
$272$	− 9.57011e10i	− 1.06012i
$273$	2.02628e10i	0.220784i
$274$	−1.51722e11	−1.62619
$275$	0	0
$276$	3.23889e10	0.335973
$277$	− 7.52768e10i	− 0.768249i	−0.923281	−	0.384124i	$-0.874503\pi$
$277$	− 7.52768e10i	− 0.768249i	0.923281	−	0.384124i	$-0.125497\pi$
$278$	− 2.48837e11i	− 2.49870i
$279$	−1.90061e10	−0.187791
$280$	0	0
$281$	9.56085e10	0.914783	0.457391	−	0.889266i	$-0.348784\pi$
$281$	9.56085e10	0.914783	0.457391	+	0.889266i	$0.348784\pi$
$282$	− 5.42427e10i	− 0.510764i
$283$	− 4.82806e10i	− 0.447439i	−0.974654	−	0.223719i	$-0.928180\pi$
$283$	− 4.82806e10i	− 0.447439i	0.974654	−	0.223719i	$-0.0718199\pi$
$284$	−1.36188e11	−1.24224
$285$	0	0
$286$	−2.51052e11	−2.21879
$287$	− 4.87522e10i	− 0.424156i
$288$	1.10131e11i	0.943286i
$289$	−2.04340e11	−1.72311
$290$	0	0
$291$	−8.73272e10	−0.713890
$292$	− 1.77053e11i	− 1.42522i
$293$	7.07439e10i	0.560770i	0.959888	+	0.280385i	$0.0904621\pi$
$293$	7.07439e10i	0.560770i	−0.959888	+	0.280385i	$0.909538\pi$
$294$	−1.56857e10	−0.122445
$295$	0	0
$296$	−6.40812e10	−0.485197
$297$	1.82411e11i	1.36034i
$298$	1.66494e11i	1.22299i
$299$	6.57756e10	0.475932
$300$	0	0
$301$	−2.68355e10	−0.188435
$302$	2.95089e11i	2.04137i
$303$	1.66210e10i	0.113283i
$304$	−6.67581e10	−0.448304
$305$	0	0
$306$	2.58964e11	1.68847
$307$	1.30493e11i	0.838429i	0.907887	+	0.419214i	$0.137694\pi$
$307$	1.30493e11i	0.838429i	−0.907887	+	0.419214i	$0.862306\pi$
$308$	− 1.09085e11i	− 0.690697i
$309$	5.40161e10	0.337062
$310$	0	0
$311$	8.51715e10	0.516265	0.258132	−	0.966110i	$-0.416893\pi$
$311$	8.51715e10	0.516265	0.258132	+	0.966110i	$0.416893\pi$
$312$	4.12537e10i	0.246472i
$313$	1.21745e11i	0.716969i	0.933536	+	0.358484i	$0.116706\pi$
$313$	1.21745e11i	0.716969i	−0.933536	+	0.358484i	$0.883294\pi$
$314$	−3.19137e11	−1.85265
$315$	0	0
$316$	−3.38154e11	−1.90775
$317$	− 2.14595e11i	− 1.19358i	−0.802397	−	0.596791i	$-0.796442\pi$
$317$	− 2.14595e11i	− 1.19358i	0.802397	−	0.596791i	$-0.203558\pi$
$318$	− 1.53736e11i	− 0.843048i
$319$	−3.38208e11	−1.82863
$320$	0	0
$321$	3.66011e10	0.192407
$322$	5.09180e10i	0.263949i
$323$	2.25264e11i	1.15154i
$324$	−3.47703e10	−0.175289
$325$	0	0
$326$	7.19740e10	0.352936
$327$	− 4.15029e10i	− 0.200731i
$328$	− 9.92562e10i	− 0.473506i
$329$	4.78644e10	0.225233
$330$	0	0
$331$	−5.48000e10	−0.250931	−0.125466	−	0.992098i	$-0.540042\pi$
$331$	−5.48000e10	−0.250931	−0.125466	+	0.992098i	$0.540042\pi$
$332$	− 4.47224e11i	− 2.02025i
$333$	1.74868e11i	0.779312i
$334$	4.77595e11	2.09991
$335$	0	0
$336$	3.22051e10	0.137847
$337$	− 2.34297e11i	− 0.989538i	−0.869025	−	0.494769i	$-0.835253\pi$
$337$	− 2.34297e11i	− 0.989538i	0.869025	−	0.494769i	$-0.164747\pi$
$338$	2.12772e10i	0.0886725i
$339$	3.54916e10	0.145958
$340$	0	0
$341$	−9.88172e10	−0.395765
$342$	− 1.80645e11i	− 0.714018i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−5.46353e10	−0.210359
$345$	0	0
$346$	4.25104e11	1.59460
$347$	3.43449e10i	0.127169i	0.997976	+	0.0635843i	$0.0202532\pi$
$347$	3.43449e10i	0.127169i	−0.997976	+	0.0635843i	$0.979747\pi$
$348$	2.54436e11i	0.929977i
$349$	2.13485e11	0.770288	0.385144	−	0.922856i	$-0.374152\pi$
$349$	2.13485e11	0.770288	0.385144	+	0.922856i	$0.374152\pi$
$350$	0	0
$351$	2.78686e11	0.980016
$352$	5.72595e11i	1.98795i
$353$	− 2.75882e11i	− 0.945664i	−0.881153	−	0.472832i	$-0.843232\pi$
$353$	− 2.75882e11i	− 0.945664i	0.881153	−	0.472832i	$-0.156768\pi$
$354$	2.97509e11	1.00690
$355$	0	0
$356$	−9.63962e10	−0.318079
$357$	− 1.08671e11i	− 0.354084i
$358$	2.49448e11i	0.802614i
$359$	3.46238e11	1.10015	0.550073	−	0.835117i	$-0.314600\pi$
$359$	3.46238e11	1.10015	0.550073	+	0.835117i	$0.314600\pi$
$360$	0	0
$361$	−1.65550e11	−0.513036
$362$	4.34117e11i	1.32867i
$363$	1.95300e11i	0.590369i
$364$	−1.66659e11	−0.497592
$365$	0	0
$366$	8.70725e10	0.253639
$367$	3.56842e11i	1.02678i	0.858155	+	0.513391i	$0.171611\pi$
$367$	3.56842e11i	1.02678i	−0.858155	+	0.513391i	$0.828389\pi$
$368$	− 1.04542e11i	− 0.297150i
$369$	−2.70855e11	−0.760534
$370$	0	0
$371$	1.35658e11	0.371760
$372$	7.43408e10i	0.201272i
$373$	− 6.73833e11i	− 1.80245i	−0.433354	−	0.901224i	$-0.642670\pi$
$373$	− 6.73833e11i	− 1.80245i	0.433354	−	0.901224i	$-0.357330\pi$
$374$	1.34641e12	3.55841
$375$	0	0
$376$	9.74487e10	0.251438
$377$	5.16711e11i	1.31738i
$378$	2.15735e11i	0.543511i
$379$	−5.90163e11	−1.46925	−0.734625	−	0.678473i	$-0.762642\pi$
$379$	−5.90163e11	−1.46925	−0.734625	+	0.678473i	$0.762642\pi$
$380$	0	0
$381$	−7.39622e10	−0.179824
$382$	− 5.51887e11i	− 1.32607i
$383$	1.58931e11i	0.377412i	0.982034	+	0.188706i	$0.0604293\pi$
$383$	1.58931e11i	0.377412i	−0.982034	+	0.188706i	$0.939571\pi$
$384$	1.96153e11	0.460367
$385$	0	0
$386$	5.22145e11	1.19715
$387$	1.49092e11i	0.337873i
$388$	− 7.18258e11i	− 1.60893i
$389$	3.75434e11	0.831304	0.415652	−	0.909524i	$-0.363553\pi$
$389$	3.75434e11	0.831304	0.415652	+	0.909524i	$0.363553\pi$
$390$	0	0
$391$	−3.52760e11	−0.763280
$392$	− 2.81799e10i	− 0.0602771i
$393$	2.05245e11i	0.434016i
$394$	7.99018e11	1.67041
$395$	0	0
$396$	−6.06051e11	−1.23846
$397$	− 4.33507e11i	− 0.875869i	−0.899007	−	0.437935i	$-0.855710\pi$
$397$	− 4.33507e11i	− 0.875869i	0.899007	−	0.437935i	$-0.144290\pi$
$398$	− 8.66400e11i	− 1.73079i
$399$	−7.58055e10	−0.149735
$400$	0	0
$401$	−1.77805e11	−0.343395	−0.171698	−	0.985150i	$-0.554925\pi$
$401$	−1.77805e11	−0.343395	−0.171698	+	0.985150i	$0.554925\pi$
$402$	2.18457e11i	0.417203i
$403$	1.50972e11i	0.285118i
$404$	−1.36706e11	−0.255312
$405$	0	0
$406$	−3.99994e11	−0.730612
$407$	9.09178e11i	1.64238i
$408$	− 2.21247e11i	− 0.395281i
$409$	7.67870e11	1.35685	0.678427	−	0.734668i	$-0.262662\pi$
$409$	7.67870e11	1.35685	0.678427	+	0.734668i	$0.262662\pi$
$410$	0	0
$411$	3.53725e11	0.611473
$412$	4.44277e11i	0.759655i
$413$	2.62526e11i	0.444014i
$414$	2.82888e11	0.473274
$415$	0	0
$416$	8.74807e11	1.43216
$417$	5.80139e11i	0.939550i
$418$	− 9.39215e11i	− 1.50478i
$419$	−4.96552e11	−0.787048	−0.393524	−	0.919314i	$-0.628744\pi$
$419$	−4.96552e11	−0.787048	−0.393524	+	0.919314i	$0.628744\pi$
$420$	0	0
$421$	−4.48514e11	−0.695835	−0.347917	−	0.937525i	$-0.613111\pi$
$421$	−4.48514e11	−0.695835	−0.347917	+	0.937525i	$0.613111\pi$
$422$	3.15580e10i	0.0484399i
$423$	− 2.65923e11i	− 0.403854i
$424$	2.76191e11	0.415014
$425$	0	0
$426$	5.65667e11	0.832180
$427$	7.68338e10i	0.111848i
$428$	3.01041e11i	0.433639i
$429$	5.85303e11	0.834301
$430$	0	0
$431$	−1.65940e11	−0.231635	−0.115817	−	0.993271i	$-0.536949\pi$
$431$	−1.65940e11	−0.231635	−0.115817	+	0.993271i	$0.536949\pi$
$432$	− 4.42936e11i	− 0.611878i
$433$	4.10674e11i	0.561438i	0.959790	+	0.280719i	$0.0905730\pi$
$433$	4.10674e11i	0.561438i	−0.959790	+	0.280719i	$0.909427\pi$
$434$	−1.16870e11	−0.158124
$435$	0	0
$436$	3.41358e11	0.452398
$437$	2.46074e11i	0.322775i
$438$	7.35402e11i	0.954754i
$439$	3.29593e11	0.423534	0.211767	−	0.977320i	$-0.432078\pi$
$439$	3.29593e11	0.423534	0.211767	+	0.977320i	$0.432078\pi$
$440$	0	0
$441$	−7.68988e10	−0.0968158
$442$	− 2.05704e12i	− 2.56355i
$443$	− 5.09091e11i	− 0.628027i	−0.949418	−	0.314014i	$-0.898326\pi$
$443$	− 5.09091e11i	− 0.628027i	0.949418	−	0.314014i	$-0.101674\pi$
$444$	6.83981e11	0.835258
$445$	0	0
$446$	−2.28424e11	−0.273360
$447$	− 3.88163e11i	− 0.459865i
$448$	4.70175e11i	0.551453i
$449$	−1.49596e12	−1.73705	−0.868525	−	0.495646i	$-0.834931\pi$
$449$	−1.49596e12	−1.73705	−0.868525	+	0.495646i	$0.834931\pi$
$450$	0	0
$451$	−1.40824e12	−1.60281
$452$	2.91915e11i	0.328953i
$453$	− 6.87971e11i	− 0.767588i
$454$	−1.64963e12	−1.82237
$455$	0	0
$456$	−1.54335e11	−0.167156
$457$	1.43920e12i	1.54347i	0.635944	+	0.771735i	$0.280611\pi$
$457$	1.43920e12i	1.54347i	−0.635944	+	0.771735i	$0.719389\pi$
$458$	− 8.00307e11i	− 0.849889i
$459$	−1.49462e12	−1.57171
$460$	0	0
$461$	−1.37741e12	−1.42039	−0.710195	−	0.704005i	$-0.751393\pi$
$461$	−1.37741e12	−1.42039	−0.710195	+	0.704005i	$0.751393\pi$
$462$	4.53092e11i	0.462698i
$463$	− 1.76612e12i	− 1.78610i	−0.449960	−	0.893049i	$-0.648562\pi$
$463$	− 1.76612e12i	− 1.78610i	0.449960	−	0.893049i	$-0.351438\pi$
$464$	8.21248e11	0.822514
$465$	0	0
$466$	1.12443e12	1.10458
$467$	− 1.17323e12i	− 1.14145i	−0.821140	−	0.570727i	$-0.806661\pi$
$467$	− 1.17323e12i	− 1.14145i	0.821140	−	0.570727i	$-0.193339\pi$
$468$	9.25919e11i	0.892209i
$469$	−1.92769e11	−0.183975
$470$	0	0
$471$	7.44037e11	0.696627
$472$	5.34485e11i	0.495674i
$473$	7.75161e11i	0.712060i
$474$	1.40454e12	1.27801
$475$	0	0
$476$	8.93808e11	0.798019
$477$	− 7.53683e11i	− 0.666586i
$478$	8.60808e11i	0.754190i
$479$	1.98723e12	1.72480	0.862401	−	0.506225i	$-0.168960\pi$
$479$	1.98723e12	1.72480	0.862401	+	0.506225i	$0.168960\pi$
$480$	0	0
$481$	1.38903e12	1.18321
$482$	− 2.39417e12i	− 2.02043i
$483$	− 1.18710e11i	− 0.0992489i
$484$	−1.60633e12	−1.33055
$485$	0	0
$486$	1.91298e12	1.55542
$487$	− 1.23240e12i	− 0.992825i	−0.868087	−	0.496413i	$-0.834650\pi$
$487$	− 1.23240e12i	− 0.992825i	0.868087	−	0.496413i	$-0.165350\pi$
$488$	1.56428e11i	0.124861i
$489$	−1.67800e11	−0.132710
$490$	0	0
$491$	−2.03763e12	−1.58219	−0.791095	−	0.611693i	$-0.790489\pi$
$491$	−2.03763e12	−1.58219	−0.791095	+	0.611693i	$0.790489\pi$
$492$	1.05943e12i	0.815131i
$493$	− 2.77117e12i	− 2.11277i
$494$	−1.43493e12	−1.08407
$495$	0	0
$496$	2.39951e11	0.178014
$497$	4.99151e11i	0.366968i
$498$	1.85758e12i	1.35336i
$499$	3.26299e11	0.235594	0.117797	−	0.993038i	$-0.462417\pi$
$499$	3.26299e11	0.235594	0.117797	+	0.993038i	$0.462417\pi$
$500$	0	0
$501$	−1.11347e12	−0.789601
$502$	− 1.43374e12i	− 1.00764i
$503$	4.46869e11i	0.311261i	0.987815	+	0.155630i	$0.0497409\pi$
$503$	4.46869e11i	0.311261i	−0.987815	+	0.155630i	$0.950259\pi$
$504$	−1.56561e11	−0.108080
$505$	0	0
$506$	1.47080e12	0.997413
$507$	− 4.96056e10i	− 0.0333423i
$508$	− 6.08332e11i	− 0.405279i
$509$	−1.34100e12	−0.885523	−0.442761	−	0.896639i	$-0.646001\pi$
$509$	−1.34100e12	−0.885523	−0.442761	+	0.896639i	$0.646001\pi$
$510$	0	0
$511$	−6.48928e11	−0.421020
$512$	− 1.81189e12i	− 1.16524i
$513$	1.04260e12i	0.664643i
$514$	2.86145e12	1.80822
$515$	0	0
$516$	5.83158e11	0.362129
$517$	− 1.38259e12i	− 0.851112i
$518$	1.07527e12i	0.656199i
$519$	−9.91089e11	−0.599597
$520$	0	0
$521$	2.98523e12	1.77504	0.887520	−	0.460769i	$-0.152426\pi$
$521$	2.98523e12	1.77504	0.887520	+	0.460769i	$0.152426\pi$
$522$	2.22227e12i	1.31003i
$523$	− 1.64651e12i	− 0.962289i	−0.876641	−	0.481145i	$-0.840221\pi$
$523$	− 1.64651e12i	− 0.962289i	0.876641	−	0.481145i	$-0.159779\pi$
$524$	−1.68812e12	−0.978166
$525$	0	0
$526$	8.01470e10	0.0456511
$527$	− 8.09676e11i	− 0.457260i
$528$	− 9.30265e11i	− 0.520900i
$529$	1.41580e12	0.786054
$530$	0	0
$531$	1.45853e12	0.796141
$532$	− 6.23493e11i	− 0.337465i
$533$	2.15149e12i	1.15470i
$534$	4.00388e11	0.213081
$535$	0	0
$536$	−3.92464e11	−0.205380
$537$	− 5.81564e11i	− 0.301796i
$538$	− 2.20233e12i	− 1.13334i
$539$	−3.99814e11	−0.204037
$540$	0	0
$541$	−4.57968e11	−0.229852	−0.114926	−	0.993374i	$-0.536663\pi$
$541$	−4.57968e11	−0.229852	−0.114926	+	0.993374i	$0.536663\pi$
$542$	4.80087e11i	0.238959i
$543$	− 1.01210e12i	− 0.499603i
$544$	−4.69166e12	−2.29684
$545$	0	0
$546$	6.92231e11	0.333337
$547$	2.39624e12i	1.14443i	0.820105	+	0.572213i	$0.193915\pi$
$547$	2.39624e12i	1.14443i	−0.820105	+	0.572213i	$0.806085\pi$
$548$	2.90935e12i	1.37811i
$549$	4.26870e11	0.200549
$550$	0	0
$551$	−1.93308e12	−0.893444
$552$	− 2.41686e11i	− 0.110796i
$553$	1.23939e12i	0.563565i
$554$	−2.57166e12	−1.15990
$555$	0	0
$556$	−4.77159e12	−2.11751
$557$	1.07863e12i	0.474814i	0.971410	+	0.237407i	$0.0762976\pi$
$557$	1.07863e12i	0.474814i	−0.971410	+	0.237407i	$0.923702\pi$
$558$	6.49301e11i	0.283525i
$559$	1.18428e12	0.512983
$560$	0	0
$561$	−3.13903e12	−1.33802
$562$	− 3.26624e12i	− 1.38113i
$563$	− 2.33140e11i	− 0.0977976i	−0.998804	−	0.0488988i	$-0.984429\pi$
$563$	− 2.33140e11i	− 0.0977976i	0.998804	−	0.0488988i	$-0.0155712\pi$
$564$	−1.04013e12	−0.432846
$565$	0	0
$566$	−1.64939e12	−0.675539
$567$	1.27438e11i	0.0517817i
$568$	1.01624e12i	0.409664i
$569$	−4.50535e11	−0.180187	−0.0900934	−	0.995933i	$-0.528717\pi$
$569$	−4.50535e11	−0.180187	−0.0900934	+	0.995933i	$0.528717\pi$
$570$	0	0
$571$	−4.38839e12	−1.72760	−0.863800	−	0.503835i	$-0.831922\pi$
$571$	−4.38839e12	−1.72760	−0.863800	+	0.503835i	$0.831922\pi$
$572$	4.81406e12i	1.88031i
$573$	1.28667e12i	0.498622i
$574$	−1.66550e12	−0.640387
$575$	0	0
$576$	2.61218e12	0.988785
$577$	3.13994e12i	1.17932i	0.807653	+	0.589658i	$0.200737\pi$
$577$	3.13994e12i	1.17932i	−0.807653	+	0.589658i	$0.799263\pi$
$578$	6.98079e12i	2.60153i
$579$	−1.21733e12	−0.450148
$580$	0	0
$581$	−1.63915e12	−0.596795
$582$	2.98333e12i	1.07782i
$583$	− 3.91857e12i	− 1.40481i
$584$	−1.32117e12	−0.470005
$585$	0	0
$586$	2.41680e12	0.846645
$587$	2.52512e12i	0.877829i	0.898529	+	0.438915i	$0.144637\pi$
$587$	2.52512e12i	0.877829i	−0.898529	+	0.438915i	$0.855363\pi$
$588$	3.00783e11i	0.103766i
$589$	−5.64805e11	−0.193366
$590$	0	0
$591$	−1.86283e12	−0.628102
$592$	− 2.20770e12i	− 0.738740i
$593$	9.35417e11i	0.310641i	0.987864	+	0.155321i	$0.0496410\pi$
$593$	9.35417e11i	0.310641i	−0.987864	+	0.155321i	$0.950359\pi$
$594$	6.23165e12	2.05383
$595$	0	0
$596$	3.19261e12	1.03642
$597$	2.01993e12i	0.650805i
$598$	− 2.24707e12i	− 0.718557i
$599$	−4.73586e12	−1.50307	−0.751534	−	0.659694i	$-0.770686\pi$
$599$	−4.73586e12	−1.50307	−0.751534	+	0.659694i	$0.770686\pi$
$600$	0	0
$601$	−5.99855e12	−1.87548	−0.937738	−	0.347344i	$-0.887084\pi$
$601$	−5.99855e12	−1.87548	−0.937738	+	0.347344i	$0.887084\pi$
$602$	9.16773e11i	0.284497i
$603$	1.07098e12i	0.329877i
$604$	5.65850e12	1.72995
$605$	0	0
$606$	5.67817e11	0.171034
$607$	3.43715e12i	1.02766i	0.857892	+	0.513830i	$0.171774\pi$
$607$	3.43715e12i	1.02766i	−0.857892	+	0.513830i	$0.828226\pi$
$608$	3.27276e12i	0.971287i
$609$	9.32548e11	0.274722
$610$	0	0
$611$	−2.11231e12	−0.613159
$612$	− 4.96578e12i	− 1.43089i
$613$	− 4.15273e12i	− 1.18785i	−0.804520	−	0.593925i	$-0.797577\pi$
$613$	− 4.15273e12i	− 1.18785i	0.804520	−	0.593925i	$-0.202423\pi$
$614$	4.45801e12	1.26585
$615$	0	0
$616$	−8.13995e11	−0.227776
$617$	− 1.12196e12i	− 0.311669i	−0.987783	−	0.155834i	$-0.950193\pi$
$617$	− 1.12196e12i	− 0.311669i	0.987783	−	0.155834i	$-0.0498066\pi$
$618$	− 1.84533e12i	− 0.508893i
$619$	5.98940e12	1.63974	0.819871	−	0.572549i	$-0.194045\pi$
$619$	5.98940e12	1.63974	0.819871	+	0.572549i	$0.194045\pi$
$620$	0	0
$621$	−1.63269e12	−0.440547
$622$	− 2.90969e12i	− 0.779452i
$623$	3.53307e11i	0.0939628i
$624$	−1.42125e12	−0.375267
$625$	0	0
$626$	4.15912e12	1.08247
$627$	2.18969e12i	0.565820i
$628$	6.11963e12i	1.57003i
$629$	−7.44951e12	−1.89758
$630$	0	0
$631$	4.97135e12	1.24837	0.624184	−	0.781277i	$-0.285432\pi$
$631$	4.97135e12	1.24837	0.624184	+	0.781277i	$0.285432\pi$
$632$	2.52331e12i	0.629134i
$633$	− 7.35743e10i	− 0.0182142i
$634$	−7.33113e12	−1.80206
$635$	0	0
$636$	−2.94796e12	−0.714439
$637$	6.10833e11i	0.146992i
$638$	1.15541e13i	2.76085i
$639$	2.77316e12	0.657993
$640$	0	0
$641$	−2.41181e12	−0.564263	−0.282131	−	0.959376i	$-0.591041\pi$
$641$	−2.41181e12	−0.564263	−0.282131	+	0.959376i	$0.591041\pi$
$642$	− 1.25039e12i	− 0.290495i
$643$	− 6.86804e12i	− 1.58447i	−0.610217	−	0.792234i	$-0.708918\pi$
$643$	− 6.86804e12i	− 1.58447i	0.610217	−	0.792234i	$-0.291082\pi$
$644$	9.76380e11	0.223683
$645$	0	0
$646$	7.69562e12	1.73859
$647$	− 1.73394e12i	− 0.389013i	−0.980901	−	0.194506i	$-0.937690\pi$
$647$	− 1.73394e12i	− 0.389013i	0.980901	−	0.194506i	$-0.0623105\pi$
$648$	2.59456e11i	0.0578064i
$649$	7.58322e12	1.67785
$650$	0	0
$651$	2.72471e11	0.0594573
$652$	− 1.38014e12i	− 0.299095i
$653$	− 2.86440e10i	− 0.00616488i	−0.999995	−	0.00308244i	$-0.999019\pi$
$653$	− 2.86440e10i	− 0.00616488i	0.999995	−	0.00308244i	$-0.000981173\pi$
$654$	−1.41785e12	−0.303061
$655$	0	0
$656$	3.41953e12	0.720940
$657$	3.60529e12i	0.754911i
$658$	− 1.63518e12i	− 0.340054i
$659$	6.31728e12	1.30481	0.652403	−	0.757872i	$-0.273761\pi$
$659$	6.31728e12	1.30481	0.652403	+	0.757872i	$0.273761\pi$
$660$	0	0
$661$	−3.49558e12	−0.712217	−0.356109	−	0.934445i	$-0.615897\pi$
$661$	−3.49558e12	−0.712217	−0.356109	+	0.934445i	$0.615897\pi$
$662$	1.87212e12i	0.378854i
$663$	4.79578e12i	0.963937i
$664$	−3.33719e12	−0.666231
$665$	0	0
$666$	5.97396e12	1.17660
$667$	− 3.02717e12i	− 0.592203i
$668$	− 9.15816e12i	− 1.77957i
$669$	5.32547e11	0.102788
$670$	0	0
$671$	2.21939e12	0.422652
$672$	− 1.57883e12i	− 0.298658i
$673$	8.02535e12i	1.50798i	0.656885	+	0.753991i	$0.271874\pi$
$673$	8.02535e12i	1.50798i	−0.656885	+	0.753991i	$0.728126\pi$
$674$	−8.00422e12	−1.49400
$675$	0	0
$676$	4.08002e11	0.0751453
$677$	1.17163e12i	0.214358i	0.994240	+	0.107179i	$0.0341818\pi$
$677$	1.17163e12i	0.214358i	−0.994240	+	0.107179i	$0.965818\pi$
$678$	− 1.21249e12i	− 0.220366i
$679$	−2.63253e12	−0.475290
$680$	0	0
$681$	3.84596e12	0.685239
$682$	3.37586e12i	0.597523i
$683$	− 4.69754e12i	− 0.825995i	−0.910732	−	0.412997i	$-0.864482\pi$
$683$	− 4.69754e12i	− 0.825995i	0.910732	−	0.412997i	$-0.135518\pi$
$684$	−3.46397e12	−0.605093
$685$	0	0
$686$	−4.72855e11	−0.0815211
$687$	1.86584e12i	0.319572i
$688$	− 1.88227e12i	− 0.320283i
$689$	−5.98676e12	−1.01206
$690$	0	0
$691$	−7.83193e12	−1.30683	−0.653413	−	0.757001i	$-0.726664\pi$
$691$	−7.83193e12	−1.30683	−0.653413	+	0.757001i	$0.726664\pi$
$692$	− 8.15161e12i	− 1.35134i
$693$	2.22127e12i	0.365849i
$694$	1.17332e12	0.191998
$695$	0	0
$696$	1.89860e12	0.306685
$697$	− 1.15386e13i	− 1.85185i
$698$	− 7.29322e12i	− 1.16297i
$699$	−2.62150e12	−0.415339
$700$	0	0
$701$	7.13243e12	1.11559	0.557797	−	0.829977i	$-0.311647\pi$
$701$	7.13243e12	1.11559	0.557797	+	0.829977i	$0.311647\pi$
$702$	− 9.52066e12i	− 1.47962i
$703$	5.19655e12i	0.802446i
$704$	1.35813e13	2.08384
$705$	0	0
$706$	−9.42486e12	−1.42776
$707$	5.01049e11i	0.0754211i
$708$	− 5.70491e12i	− 0.853294i
$709$	−8.65274e12	−1.28601	−0.643007	−	0.765861i	$-0.722313\pi$
$709$	−8.65274e12	−1.28601	−0.643007	+	0.765861i	$0.722313\pi$
$710$	0	0
$711$	6.88573e12	1.01050
$712$	7.19310e11i	0.104895i
$713$	− 8.84475e11i	− 0.128169i
$714$	−3.71249e12	−0.534593
$715$	0	0
$716$	4.78331e12	0.680174
$717$	− 2.00689e12i	− 0.283588i
$718$	− 1.18284e13i	− 1.66099i
$719$	−4.58446e11	−0.0639747	−0.0319873	−	0.999488i	$-0.510184\pi$
$719$	−4.58446e11	−0.0639747	−0.0319873	+	0.999488i	$0.510184\pi$
$720$	0	0
$721$	1.62834e12	0.224408
$722$	5.65565e12i	0.774577i
$723$	5.58177e12i	0.759713i
$724$	8.32444e12	1.12598
$725$	0	0
$726$	6.67199e12	0.891334
$727$	− 2.53850e12i	− 0.337033i	−0.985699	−	0.168517i	$-0.946102\pi$
$727$	− 2.53850e12i	− 0.337033i	0.985699	−	0.168517i	$-0.0538977\pi$
$728$	1.24361e12i	0.164095i
$729$	−3.41521e12	−0.447861
$730$	0	0
$731$	−6.35141e12	−0.822701
$732$	− 1.66966e12i	− 0.214946i
$733$	− 1.09361e13i	− 1.39925i	−0.714511	−	0.699624i	$-0.753351\pi$
$733$	− 1.09361e13i	− 1.39925i	0.714511	−	0.699624i	$-0.246649\pi$
$734$	1.21907e13	1.55023
$735$	0	0
$736$	−5.12509e12	−0.643800
$737$	5.56824e12i	0.695208i
$738$	9.25314e12i	1.14825i
$739$	−7.34996e12	−0.906536	−0.453268	−	0.891374i	$-0.649742\pi$
$739$	−7.34996e12	−0.906536	−0.453268	+	0.891374i	$0.649742\pi$
$740$	0	0
$741$	3.34539e12	0.407628
$742$	− 4.63444e12i	− 0.561281i
$743$	1.60813e12i	0.193584i	0.995305	+	0.0967922i	$0.0308582\pi$
$743$	1.60813e12i	0.193584i	−0.995305	+	0.0967922i	$0.969142\pi$
$744$	5.54732e11	0.0663751
$745$	0	0
$746$	−2.30199e13	−2.72132
$747$	9.10670e12i	1.07009i
$748$	− 2.58182e13i	− 3.01557i
$749$	1.10336e12	0.128100
$750$	0	0
$751$	−2.95903e12	−0.339446	−0.169723	−	0.985492i	$-0.554287\pi$
$751$	−2.95903e12	−0.339446	−0.169723	+	0.985492i	$0.554287\pi$
$752$	3.35726e12i	0.382829i
$753$	3.34263e12i	0.378888i
$754$	1.76522e13	1.98897
$755$	0	0
$756$	4.13684e12	0.460597
$757$	− 4.83223e12i	− 0.534830i	−0.963581	−	0.267415i	$-0.913830\pi$
$757$	− 4.83223e12i	− 0.534830i	0.963581	−	0.267415i	$-0.0861695\pi$
$758$	2.01616e13i	2.21826i
$759$	−3.42902e12	−0.375043
$760$	0	0
$761$	3.15213e12	0.340701	0.170350	−	0.985384i	$-0.445510\pi$
$761$	3.15213e12	0.340701	0.170350	+	0.985384i	$0.445510\pi$
$762$	2.52675e12i	0.271496i
$763$	− 1.25113e12i	− 0.133642i
$764$	−1.05827e13	−1.12377
$765$	0	0
$766$	5.42952e12	0.569813
$767$	− 1.15856e13i	− 1.20876i
$768$	1.28447e12i	0.133229i
$769$	6.87650e12	0.709086	0.354543	−	0.935040i	$-0.384636\pi$
$769$	6.87650e12	0.709086	0.354543	+	0.935040i	$0.384636\pi$
$770$	0	0
$771$	−6.67118e12	−0.679920
$772$	− 1.00124e13i	− 1.01452i
$773$	− 1.16083e13i	− 1.16939i	−0.811253	−	0.584696i	$-0.801214\pi$
$773$	− 1.16083e13i	− 1.16939i	0.811253	−	0.584696i	$-0.198786\pi$
$774$	5.09337e12	0.510118
$775$	0	0
$776$	−5.35965e12	−0.530590
$777$	− 2.50690e12i	− 0.246741i
$778$	− 1.28258e13i	− 1.25510i
$779$	−8.04899e12	−0.783110
$780$	0	0
$781$	1.44183e13	1.38670
$782$	1.20512e13i	1.15239i
$783$	− 1.28259e13i	− 1.21944i
$784$	9.70842e11	0.0917754
$785$	0	0
$786$	7.01171e12	0.655274
$787$	− 2.50005e12i	− 0.232307i	−0.993231	−	0.116154i	$-0.962943\pi$
$787$	− 2.50005e12i	− 0.232307i	0.993231	−	0.116154i	$-0.0370565\pi$
$788$	− 1.53216e13i	− 1.41559i
$789$	−1.86855e11	−0.0171656
$790$	0	0
$791$	1.06991e12	0.0971751
$792$	4.52236e12i	0.408415i
$793$	− 3.39077e12i	− 0.304487i
$794$	−1.48098e13	−1.32238
$795$	0	0
$796$	−1.66137e13	−1.46675
$797$	2.77023e12i	0.243194i	0.992580	+	0.121597i	$0.0388016\pi$
$797$	2.77023e12i	0.243194i	−0.992580	+	0.121597i	$0.961198\pi$
$798$	2.58972e12i	0.226068i
$799$	1.13285e13	0.983360
$800$	0	0
$801$	1.96289e12	0.168480
$802$	6.07429e12i	0.518455i
$803$	1.87447e13i	1.59096i
$804$	4.18903e12	0.353558
$805$	0	0
$806$	5.15761e12	0.430468
$807$	5.13451e12i	0.426156i
$808$	1.02010e12i	0.0841962i
$809$	2.96640e12	0.243479	0.121739	−	0.992562i	$-0.461153\pi$
$809$	2.96640e12	0.243479	0.121739	+	0.992562i	$0.461153\pi$
$810$	0	0
$811$	−9.01447e12	−0.731722	−0.365861	−	0.930669i	$-0.619225\pi$
$811$	−9.01447e12	−0.731722	−0.365861	+	0.930669i	$0.619225\pi$
$812$	7.67012e12i	0.619156i
$813$	− 1.11928e12i	− 0.0898524i
$814$	3.10599e13	2.47965
$815$	0	0
$816$	7.62229e12	0.601838
$817$	4.43055e12i	0.347903i
$818$	− 2.62325e13i	− 2.04857i
$819$	3.39364e12	0.263565
$820$	0	0
$821$	1.25176e13	0.961563	0.480782	−	0.876840i	$-0.340353\pi$
$821$	1.25176e13	0.961563	0.480782	+	0.876840i	$0.340353\pi$
$822$	− 1.20842e13i	− 0.923197i
$823$	1.50348e13i	1.14234i	0.820830	+	0.571172i	$0.193511\pi$
$823$	1.50348e13i	1.14234i	−0.820830	+	0.571172i	$0.806489\pi$
$824$	3.31520e12	0.250517
$825$	0	0
$826$	8.96858e12	0.670369
$827$	2.31522e13i	1.72115i	0.509325	+	0.860574i	$0.329895\pi$
$827$	2.31522e13i	1.72115i	−0.509325	+	0.860574i	$0.670105\pi$
$828$	− 5.42453e12i	− 0.401075i
$829$	−4.88071e12	−0.358912	−0.179456	−	0.983766i	$-0.557434\pi$
$829$	−4.88071e12	−0.358912	−0.179456	+	0.983766i	$0.557434\pi$
$830$	0	0
$831$	5.99556e12	0.436139
$832$	− 2.07494e13i	− 1.50124i
$833$	− 3.27595e12i	− 0.235741i
$834$	1.98191e13	1.41852
$835$	0	0
$836$	−1.80100e13	−1.27522
$837$	− 3.74745e12i	− 0.263919i
$838$	1.69635e13i	1.18828i
$839$	1.18015e13	0.822258	0.411129	−	0.911577i	$-0.365135\pi$
$839$	1.18015e13	0.822258	0.411129	+	0.911577i	$0.365135\pi$
$840$	0	0
$841$	9.27330e12	0.639223
$842$	1.53224e13i	1.05057i
$843$	7.61492e12i	0.519327i
$844$	6.05142e11	0.0410503
$845$	0	0
$846$	−9.08464e12	−0.609735
$847$	5.88744e12i	0.393053i
$848$	9.51520e12i	0.631883i
$849$	3.84540e12	0.254014
$850$	0	0
$851$	−8.13771e12	−0.531887
$852$	− 1.08470e13i	− 0.705229i
$853$	2.54707e13i	1.64729i	0.567104	+	0.823646i	$0.308064\pi$
$853$	2.54707e13i	1.64729i	−0.567104	+	0.823646i	$0.691936\pi$
$854$	2.62485e12	0.168867
$855$	0	0
$856$	2.24637e12	0.143004
$857$	1.26584e13i	0.801615i	0.916162	+	0.400807i	$0.131270\pi$
$857$	1.26584e13i	0.801615i	−0.916162	+	0.400807i	$0.868730\pi$
$858$	− 1.99955e13i	− 1.25962i
$859$	−2.01387e13	−1.26201	−0.631004	−	0.775779i	$-0.717357\pi$
$859$	−2.01387e13	−1.26201	−0.631004	+	0.775779i	$0.717357\pi$
$860$	0	0
$861$	3.88296e12	0.240796
$862$	5.66896e12i	0.349720i
$863$	1.44977e13i	0.889716i	0.895601	+	0.444858i	$0.146746\pi$
$863$	1.44977e13i	0.889716i	−0.895601	+	0.444858i	$0.853254\pi$
$864$	−2.17146e13	−1.32568
$865$	0	0
$866$	1.40297e13	0.847655
$867$	− 1.62750e13i	− 0.978217i
$868$	2.24104e12i	0.134002i
$869$	3.58004e13	2.12961
$870$	0	0
$871$	8.50712e12	0.500842
$872$	− 2.54721e12i	− 0.149191i
$873$	1.46257e13i	0.852221i
$874$	8.40656e12	0.487323
$875$	0	0
$876$	1.41018e13	0.809104
$877$	1.83297e13i	1.04630i	0.852241	+	0.523150i	$0.175243\pi$
$877$	1.83297e13i	1.04630i	−0.852241	+	0.523150i	$0.824757\pi$
$878$	− 1.12598e13i	− 0.639448i
$879$	−5.63453e12	−0.318352
$880$	0	0
$881$	4.57369e12	0.255785	0.127892	−	0.991788i	$-0.459179\pi$
$881$	4.57369e12	0.255785	0.127892	+	0.991788i	$0.459179\pi$
$882$	2.62707e12i	0.146172i
$883$	− 3.07854e13i	− 1.70420i	−0.523377	−	0.852101i	$-0.675328\pi$
$883$	− 3.07854e13i	− 1.70420i	0.523377	−	0.852101i	$-0.324672\pi$
$884$	−3.94448e13	−2.17248
$885$	0	0
$886$	−1.73919e13	−0.948190
$887$	− 2.58803e13i	− 1.40382i	−0.712264	−	0.701911i	$-0.752330\pi$
$887$	− 2.58803e13i	− 1.40382i	0.712264	−	0.701911i	$-0.247670\pi$
$888$	− 5.10387e12i	− 0.275449i
$889$	−2.22963e12	−0.119722
$890$	0	0
$891$	3.68114e12	0.195674
$892$	4.38015e12i	0.231658i
$893$	− 7.90242e12i	− 0.415842i
$894$	−1.32607e13	−0.694301
$895$	0	0
$896$	5.91314e12	0.306501
$897$	5.23882e12i	0.270189i
$898$	5.11061e13i	2.62258i
$899$	6.94814e12	0.354773
$900$	0	0
$901$	3.21075e13	1.62310
$902$	4.81091e13i	2.41990i
$903$	− 2.13737e12i	− 0.106975i
$904$	2.17827e12	0.108481
$905$	0	0
$906$	−2.35029e13	−1.15890
$907$	9.64118e12i	0.473040i	0.971627	+	0.236520i	$0.0760068\pi$
$907$	9.64118e12i	0.473040i	−0.971627	+	0.236520i	$0.923993\pi$
$908$	3.16326e13i	1.54436i
$909$	2.78371e12	0.135234
$910$	0	0
$911$	7.28746e12	0.350545	0.175272	−	0.984520i	$-0.443919\pi$
$911$	7.28746e12	0.350545	0.175272	+	0.984520i	$0.443919\pi$
$912$	− 5.31707e12i	− 0.254505i
$913$	4.73478e13i	2.25518i
$914$	4.91669e13	2.33032
$915$	0	0
$916$	−1.53463e13	−0.720236
$917$	6.18722e12i	0.288957i
$918$	5.10601e13i	2.37295i
$919$	−2.73276e13	−1.26381	−0.631906	−	0.775045i	$-0.717727\pi$
$919$	−2.73276e13	−1.26381	−0.631906	+	0.775045i	$0.717727\pi$
$920$	0	0
$921$	−1.03934e13	−0.475981
$922$	4.70559e13i	2.14449i
$923$	− 2.20281e13i	− 0.999011i
$924$	8.68829e12	0.392112
$925$	0	0
$926$	−6.03353e13	−2.69663
$927$	− 9.04668e12i	− 0.402375i
$928$	− 4.02610e13i	− 1.78204i
$929$	7.21805e12	0.317943	0.158971	−	0.987283i	$-0.449182\pi$
$929$	7.21805e12	0.317943	0.158971	+	0.987283i	$0.449182\pi$
$930$	0	0
$931$	−2.28520e12	−0.0996897
$932$	− 2.15616e13i	− 0.936071i
$933$	6.78365e12i	0.293087i
$934$	−4.00808e13	−1.72336
$935$	0	0
$936$	6.90922e12	0.294231
$937$	1.41988e13i	0.601761i	0.953662	+	0.300880i	$0.0972805\pi$
$937$	1.41988e13i	0.601761i	−0.953662	+	0.300880i	$0.902719\pi$
$938$	6.58550e12i	0.277764i
$939$	−9.69658e12	−0.407027
$940$	0	0
$941$	−2.53242e13	−1.05289	−0.526445	−	0.850209i	$-0.676475\pi$
$941$	−2.53242e13	−1.05289	−0.526445	+	0.850209i	$0.676475\pi$
$942$	− 2.54183e13i	− 1.05176i
$943$	− 1.26046e13i	− 0.519070i
$944$	−1.84138e13	−0.754693
$945$	0	0
$946$	2.64816e13	1.07506
$947$	− 1.37160e13i	− 0.554182i	−0.960844	−	0.277091i	$-0.910630\pi$
$947$	− 1.37160e13i	− 0.554182i	0.960844	−	0.277091i	$-0.0893703\pi$
$948$	− 2.69329e13i	− 1.08304i
$949$	2.86380e13	1.14616
$950$	0	0
$951$	1.70918e13	0.677604
$952$	− 6.66961e12i	− 0.263169i
$953$	− 2.44096e13i	− 0.958610i	−0.877648	−	0.479305i	$-0.840889\pi$
$953$	− 2.44096e13i	− 0.958610i	0.877648	−	0.479305i	$-0.159111\pi$
$954$	−2.57478e13	−1.00641
$955$	0	0
$956$	1.65065e13	0.639137
$957$	− 2.69372e13i	− 1.03812i
$958$	− 6.78892e13i	− 2.60409i
$959$	1.06632e13	0.407104
$960$	0	0
$961$	−2.44095e13	−0.923218
$962$	− 4.74531e13i	− 1.78639i
$963$	− 6.13001e12i	− 0.229690i
$964$	−4.59096e13	−1.71221
$965$	0	0
$966$	−4.05546e12	−0.149845
$967$	− 4.19850e13i	− 1.54410i	−0.635563	−	0.772049i	$-0.719232\pi$
$967$	− 4.19850e13i	− 1.54410i	0.635563	−	0.772049i	$-0.280768\pi$
$968$	1.19864e13i	0.438784i
$969$	−1.79416e13	−0.653738
$970$	0	0
$971$	3.13254e12	0.113086	0.0565432	−	0.998400i	$-0.481992\pi$
$971$	3.13254e12	0.113086	0.0565432	+	0.998400i	$0.481992\pi$
$972$	− 3.66825e13i	− 1.31814i
$973$	1.74886e13i	0.625529i
$974$	−4.21022e13	−1.49896
$975$	0	0
$976$	−5.38920e12	−0.190108
$977$	4.53124e13i	1.59108i	0.605902	+	0.795539i	$0.292812\pi$
$977$	4.53124e13i	1.59108i	−0.605902	+	0.795539i	$0.707188\pi$
$978$	5.73251e12i	0.200364i
$979$	1.02055e13	0.355068
$980$	0	0
$981$	−6.95097e12	−0.239626
$982$	6.96109e13i	2.38878i
$983$	2.54481e13i	0.869290i	0.900602	+	0.434645i	$0.143126\pi$
$983$	2.54481e13i	0.869290i	−0.900602	+	0.434645i	$0.856874\pi$
$984$	7.90545e12	0.268812
$985$	0	0
$986$	−9.46704e13	−3.18983
$987$	3.81225e12i	0.127866i
$988$	2.75155e13i	0.918694i
$989$	−6.93817e12	−0.230601
$990$	0	0
$991$	−5.41691e13	−1.78410	−0.892052	−	0.451933i	$-0.850734\pi$
$991$	−5.41691e13	−1.78410	−0.892052	+	0.451933i	$0.850734\pi$
$992$	− 1.17634e13i	− 0.385683i
$993$	− 4.36465e12i	− 0.142455i
$994$	1.70523e13	0.554045
$995$	0	0
$996$	3.56200e13	1.14690
$997$	− 4.29329e13i	− 1.37614i	−0.725646	−	0.688069i	$-0.758459\pi$
$997$	− 4.29329e13i	− 1.37614i	0.725646	−	0.688069i	$-0.241541\pi$
$998$	− 1.11473e13i	− 0.355697i
$999$	−3.44788e13	−1.09524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.d.99.2		6
5.2	odd	4		175.10.a.d.1.3		3
5.3	odd	4		7.10.a.b.1.1	✓	3
5.4	even	2	inner	175.10.b.d.99.5		6
15.8	even	4		63.10.a.e.1.3		3
20.3	even	4		112.10.a.h.1.3		3
35.3	even	12		49.10.c.e.30.3		6
35.13	even	4		49.10.a.c.1.1		3
35.18	odd	12		49.10.c.d.30.3		6
35.23	odd	12		49.10.c.d.18.3		6
35.33	even	12		49.10.c.e.18.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.1	✓	3	5.3	odd	4
49.10.a.c.1.1		3	35.13	even	4
49.10.c.d.18.3		6	35.23	odd	12
49.10.c.d.30.3		6	35.18	odd	12
49.10.c.e.18.3		6	35.33	even	12
49.10.c.e.30.3		6	35.3	even	12
63.10.a.e.1.3		3	15.8	even	4
112.10.a.h.1.3		3	20.3	even	4
175.10.a.d.1.3		3	5.2	odd	4
175.10.b.d.99.2		6	1.1	even	1	trivial
175.10.b.d.99.5		6	5.4	even	2	inner

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-34.1627i q^{2} +79.6469i q^{3} -655.088 q^{4} +2720.95 q^{6} +2401.00i q^{7} +4888.28i q^{8} +13339.4 q^{9} +69354.4 q^{11} -52175.7i q^{12} -105959. i q^{13} +82024.6 q^{14} -168409. q^{16} +568267. i q^{17} -455709. i q^{18} +396405. q^{19} -191232. q^{21} -2.36933e6i q^{22} +620765. i q^{23} -389336. q^{24} -3.61984e6 q^{26} +2.63013e6i q^{27} -1.57287e6i q^{28} -4.87652e6 q^{29} -1.42482e6 q^{31} +8.25609e6i q^{32} +5.52386e6i q^{33} +1.94135e7 q^{34} -8.73846e6 q^{36} +1.31092e7i q^{37} -1.35423e7i q^{38} +8.43931e6 q^{39} -2.03049e7 q^{41} +6.53300e6i q^{42} +1.11768e7i q^{43} -4.54332e7 q^{44} +2.12070e7 q^{46} -1.99352e7i q^{47} -1.34132e7i q^{48} -5.76480e6 q^{49} -4.52607e7 q^{51} +6.94125e7i q^{52} -5.65007e7i q^{53} +8.98523e7 q^{54} -1.17367e7 q^{56} +3.15725e7i q^{57} +1.66595e8i q^{58} +1.09340e8 q^{59} +3.20008e7 q^{61} +4.86755e7i q^{62} +3.20278e7i q^{63} +1.95825e8 q^{64} +1.88710e8 q^{66} +8.02869e7i q^{67} -3.72265e8i q^{68} -4.94420e7 q^{69} +2.07893e8 q^{71} +6.52065e7i q^{72} +2.70274e8i q^{73} +4.47844e8 q^{74} -2.59680e8 q^{76} +1.66520e8i q^{77} -2.88309e8i q^{78} +5.16196e8 q^{79} +5.30772e7 q^{81} +6.93671e8i q^{82} +6.82693e8i q^{83} +1.25274e8 q^{84} +3.81830e8 q^{86} -3.88400e8i q^{87} +3.39023e8i q^{88} +1.47150e8 q^{89} +2.54408e8 q^{91} -4.06656e8i q^{92} -1.13482e8i q^{93} -6.81040e8 q^{94} -6.57572e8 q^{96} +1.09643e9i q^{97} +1.96941e8i q^{98} +9.25144e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3114 q^{4} + 9828 q^{6} + 52002 q^{9} - 6888 q^{11} - 100842 q^{14} + 965922 q^{16} - 445704 q^{19} + 403368 q^{21} + 2899260 q^{24} - 17570112 q^{26} - 8163636 q^{29} + 5738880 q^{31} + 7963284 q^{34}+ \cdots + 3801958344 q^{99}+O(q^{100}) \) 6 * q - 3114 * q^4 + 9828 * q^6 + 52002 * q^9 - 6888 * q^11 - 100842 * q^14 + 965922 * q^16 - 445704 * q^19 + 403368 * q^21 + 2899260 * q^24 - 17570112 * q^26 - 8163636 * q^29 + 5738880 * q^31 + 7963284 * q^34 - 70792758 * q^36 + 17981376 * q^39 - 28841316 * q^41 - 194023968 * q^44 + 179495328 * q^46 - 34588806 * q^49 - 52293456 * q^51 + 235758600 * q^54 + 67492110 * q^56 + 85180200 * q^59 + 383493684 * q^61 - 15704322 * q^64 - 16115904 * q^66 - 515807712 * q^69 + 593029008 * q^71 + 1381392924 * q^74 + 1457679972 * q^76 + 1920825312 * q^79 - 71655354 * q^81 + 510865572 * q^84 - 1761964512 * q^86 - 1013632956 * q^89 - 94993164 * q^91 - 2776009656 * q^94 + 666771588 * q^96 + 3801958344 * q^99

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