LMFDB - Embedded newform 175.10.b.d.99.1

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			99.1
Root			$4.96128i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.d.99.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-41.8019i q^{2} +0.232339i q^{3} -1235.40 q^{4} +9.71222 q^{6} -2401.00i q^{7} +30239.6i q^{8} +19682.9 q^{9} +17401.5 q^{11} -287.032i q^{12} -122541. i q^{13} -100366. q^{14} +631550. q^{16} -331933. i q^{17} -822785. i q^{18} -761707. q^{19} +557.846 q^{21} -727418. i q^{22} +1.23249e6i q^{23} -7025.85 q^{24} -5.12246e6 q^{26} +9146.25i q^{27} +2.96620e6i q^{28} -634604. q^{29} -5.38069e6 q^{31} -1.09173e7i q^{32} +4043.06i q^{33} -1.38754e7 q^{34} -2.43164e7 q^{36} +3.03611e6i q^{37} +3.18408e7i q^{38} +28471.1 q^{39} -7.37009e6 q^{41} -23319.1i q^{42} -2.06990e7i q^{43} -2.14979e7 q^{44} +5.15203e7 q^{46} -2.03632e7i q^{47} +146734. i q^{48} -5.76480e6 q^{49} +77120.9 q^{51} +1.51388e8i q^{52} -5.97380e7i q^{53} +382331. q^{54} +7.26054e7 q^{56} -176974. i q^{57} +2.65277e7i q^{58} -6.03461e7 q^{59} -9.44357e6 q^{61} +2.24923e8i q^{62} -4.72588e7i q^{63} -1.33012e8 q^{64} +169008. q^{66} +2.19187e8i q^{67} +4.10071e8i q^{68} -286355. q^{69} -5.58741e7 q^{71} +5.95205e8i q^{72} +4.54332e8i q^{73} +1.26915e8 q^{74} +9.41015e8 q^{76} -4.17811e7i q^{77} -1.19015e6i q^{78} -4.51057e7 q^{79} +3.87417e8 q^{81} +3.08084e8i q^{82} -3.34665e8i q^{83} -689165. q^{84} -8.65259e8 q^{86} -147443. i q^{87} +5.26216e8i q^{88} -6.51886e8 q^{89} -2.94221e8 q^{91} -1.52262e9i q^{92} -1.25014e6i q^{93} -8.51220e8 q^{94} +2.53652e6 q^{96} +1.42804e9i q^{97} +2.40980e8i q^{98} +3.42514e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 41.8019i	− 1.84740i	−0.383114	−	0.923701i	$-0.625148\pi$
$2$	− 41.8019i	− 1.84740i	0.383114	−	0.923701i	$-0.374852\pi$
$3$	0.232339i	0.00165606i	1.00000		0.000828031i	$0.000263570\pi$
$3$	0.232339i	0.00165606i	−1.00000		0.000828031i	$0.999736\pi$
$4$	−1235.40	−2.41290
$5$	0	0
$5$	0	0
$6$	9.71222	0.00305941
$7$	− 2401.00i	− 0.377964i
$7$	− 2401.00i	− 0.377964i
$8$	30239.6i	2.61019i
$9$	19682.9	0.999997
$10$	0	0
$11$	17401.5	0.358361	0.179180	−	0.983816i	$-0.442655\pi$
$11$	17401.5	0.358361	0.179180	+	0.983816i	$0.442655\pi$
$12$	− 287.032i	− 0.00399591i
$13$	− 122541.i	− 1.18997i	−0.803736	−	0.594986i	$-0.797158\pi$
$13$	− 122541.i	− 1.18997i	0.803736	−	0.594986i	$-0.202842\pi$
$14$	−100366.	−0.698253
$15$	0	0
$16$	631550.	2.40917
$17$	− 331933.i	− 0.963895i	−0.876200	−	0.481948i	$-0.839930\pi$
$17$	− 331933.i	− 0.963895i	0.876200	−	0.481948i	$-0.160070\pi$
$18$	− 822785.i	− 1.84740i
$19$	−761707.	−1.34090	−0.670450	−	0.741954i	$-0.733899\pi$
$19$	−761707.	−1.34090	−0.670450	+	0.741954i	$0.733899\pi$
$20$	0	0
$21$	557.846	0.000625933 0
$22$	− 727418.i	− 0.662037i
$23$	1.23249e6i	0.918347i	0.888347	+	0.459173i	$0.151854\pi$
$23$	1.23249e6i	0.918347i	−0.888347	+	0.459173i	$0.848146\pi$
$24$	−7025.85	−0.00432263
$25$	0	0
$26$	−5.12246e6	−2.19836
$27$	9146.25i	0.00331212i
$28$	2.96620e6i	0.911989i
$29$	−634604.	−0.166614	−0.0833071	−	0.996524i	$-0.526548\pi$
$29$	−634604.	−0.166614	−0.0833071	+	0.996524i	$0.526548\pi$
$30$	0	0
$31$	−5.38069e6	−1.04643	−0.523215	−	0.852201i	$-0.675268\pi$
$31$	−5.38069e6	−1.04643	−0.523215	+	0.852201i	$0.675268\pi$
$32$	− 1.09173e7i	− 1.84052i
$33$	4043.06i	0 0.000593468i
$34$	−1.38754e7	−1.78070
$35$	0	0
$36$	−2.43164e7	−2.41289
$37$	3.03611e6i	0.266324i	0.991094	+	0.133162i	$0.0425130\pi$
$37$	3.03611e6i	0.266324i	−0.991094	+	0.133162i	$0.957487\pi$
$38$	3.18408e7i	2.47718i
$39$	28471.1	0.00197067
$40$	0	0
$41$	−7.37009e6	−0.407329	−0.203665	−	0.979041i	$-0.565285\pi$
$41$	−7.37009e6	−0.407329	−0.203665	+	0.979041i	$0.565285\pi$
$42$	− 23319.1i	− 0.00115635i
$43$	− 2.06990e7i	− 0.923297i	−0.887063	−	0.461649i	$-0.847258\pi$
$43$	− 2.06990e7i	− 0.923297i	0.887063	−	0.461649i	$-0.152742\pi$
$44$	−2.14979e7	−0.864687
$45$	0	0
$46$	5.15203e7	1.69656
$47$	− 2.03632e7i	− 0.608702i	−0.952560	−	0.304351i	$-0.901560\pi$
$47$	− 2.03632e7i	− 0.608702i	0.952560	−	0.304351i	$-0.0984396\pi$
$48$	146734.i	0.00398974i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	77120.9	0.00159627
$52$	1.51388e8i	2.87128i
$53$	− 5.97380e7i	− 1.03994i	−0.854184	−	0.519971i	$-0.825943\pi$
$53$	− 5.97380e7i	− 1.03994i	0.854184	−	0.519971i	$-0.174057\pi$
$54$	382331.	0.00611882
$55$	0	0
$56$	7.26054e7	0.986558
$57$	− 176974.i	− 0.00222061i
$58$	2.65277e7i	0.307803i
$59$	−6.03461e7	−0.648358	−0.324179	−	0.945996i	$-0.605088\pi$
$59$	−6.03461e7	−0.648358	−0.324179	+	0.945996i	$0.605088\pi$
$60$	0	0
$61$	−9.44357e6	−0.0873277	−0.0436639	−	0.999046i	$-0.513903\pi$
$61$	−9.44357e6	−0.0873277	−0.0436639	+	0.999046i	$0.513903\pi$
$62$	2.24923e8i	1.93318i
$63$	− 4.72588e7i	− 0.377963i
$64$	−1.33012e8	−0.991013
$65$	0	0
$66$	169008.	0.00109637
$67$	2.19187e8i	1.32885i	0.747353	+	0.664427i	$0.231324\pi$
$67$	2.19187e8i	1.32885i	−0.747353	+	0.664427i	$0.768676\pi$
$68$	4.10071e8i	2.32578i
$69$	−286355.	−0.00152084
$70$	0	0
$71$	−5.58741e7	−0.260944	−0.130472	−	0.991452i	$-0.541649\pi$
$71$	−5.58741e7	−0.260944	−0.130472	+	0.991452i	$0.541649\pi$
$72$	5.95205e8i	2.61018i
$73$	4.54332e8i	1.87250i	0.351340	+	0.936248i	$0.385726\pi$
$73$	4.54332e8i	1.87250i	−0.351340	+	0.936248i	$0.614274\pi$
$74$	1.26915e8	0.492007
$75$	0	0
$76$	9.41015e8	3.23545
$77$	− 4.17811e7i	− 0.135448i
$78$	− 1.19015e6i	− 0.00364062i
$79$	−4.51057e7	−0.130289	−0.0651447	−	0.997876i	$-0.520751\pi$
$79$	−4.51057e7	−0.130289	−0.0651447	+	0.997876i	$0.520751\pi$
$80$	0	0
$81$	3.87417e8	0.999992
$82$	3.08084e8i	0.752501i
$83$	− 3.34665e8i	− 0.774031i	−0.922073	−	0.387016i	$-0.873506\pi$
$83$	− 3.34665e8i	− 0.774031i	0.922073	−	0.387016i	$-0.126494\pi$
$84$	−689165.	−0.00151031
$85$	0	0
$86$	−8.65259e8	−1.70570
$87$	− 147443.i	0 0.000275923i
$88$	5.26216e8i	0.935389i
$89$	−6.51886e8	−1.10133	−0.550664	−	0.834727i	$-0.685625\pi$
$89$	−6.51886e8	−1.10133	−0.550664	+	0.834727i	$0.685625\pi$
$90$	0	0
$91$	−2.94221e8	−0.449767
$92$	− 1.52262e9i	− 2.21588i
$93$	− 1.25014e6i	− 0.00173295i
$94$	−8.51220e8	−1.12452
$95$	0	0
$96$	2.53652e6	0.00304802
$97$	1.42804e9i	1.63783i	0.573916	+	0.818914i	$0.305424\pi$
$97$	1.42804e9i	1.63783i	−0.573916	+	0.818914i	$0.694576\pi$
$98$	2.40980e8i	0.263915i
$99$	3.42514e8	0.358360
$100$	0	0
$101$	8.91532e8	0.852493	0.426247	−	0.904607i	$-0.359836\pi$
$101$	8.91532e8	0.852493	0.426247	+	0.904607i	$0.359836\pi$
$102$	− 3.22380e6i	− 0.00294895i
$103$	− 7.12000e8i	− 0.623322i	−0.950193	−	0.311661i	$-0.899115\pi$
$103$	− 7.12000e8i	− 0.623322i	0.950193	−	0.311661i	$-0.100885\pi$
$104$	3.70560e9	3.10605
$105$	0	0
$106$	−2.49716e9	−1.92119
$107$	− 2.48598e9i	− 1.83346i	−0.399510	−	0.916729i	$-0.630820\pi$
$107$	− 2.48598e9i	− 1.83346i	0.399510	−	0.916729i	$-0.369180\pi$
$108$	− 1.12993e7i	− 0.00799180i
$109$	−3.83455e8	−0.260193	−0.130096	−	0.991501i	$-0.541529\pi$
$109$	−3.83455e8	−0.260193	−0.130096	+	0.991501i	$0.541529\pi$
$110$	0	0
$111$	−705407.	−0.000441048 0
$112$	− 1.51635e9i	− 0.910581i
$113$	2.39582e9i	1.38230i	0.722713	+	0.691148i	$0.242895\pi$
$113$	2.39582e9i	1.38230i	−0.722713	+	0.691148i	$0.757105\pi$
$114$	−7.39787e6	−0.00410237
$115$	0	0
$116$	7.83991e8	0.402023
$117$	− 2.41197e9i	− 1.18997i
$118$	2.52258e9i	1.19778i
$119$	−7.96970e8	−0.364318
$120$	0	0
$121$	−2.05513e9	−0.871578
$122$	3.94760e8i	0.161329i
$123$	− 1.71236e6i	0 0.000674562i
$124$	6.64732e9	2.52493
$125$	0	0
$126$	−1.97551e9	−0.698251
$127$	− 1.88261e9i	− 0.642161i	−0.947052	−	0.321080i	$-0.895954\pi$
$127$	− 1.88261e9i	− 0.642161i	0.947052	−	0.321080i	$-0.104046\pi$
$128$	− 2.95237e7i	− 0.00972134i
$129$	4.80919e6	0.00152904
$130$	0	0
$131$	−1.49241e9	−0.442760	−0.221380	−	0.975188i	$-0.571056\pi$
$131$	−1.49241e9	−0.442760	−0.221380	+	0.975188i	$0.571056\pi$
$132$	− 4.99480e6i	− 0.00143198i
$133$	1.82886e9i	0.506813i
$134$	9.16242e9	2.45493
$135$	0	0
$136$	1.00375e10	2.51595
$137$	3.21118e9i	0.778792i	0.921070	+	0.389396i	$0.127316\pi$
$137$	3.21118e9i	0.778792i	−0.921070	+	0.389396i	$0.872684\pi$
$138$	1.19702e7i	0.00280960i
$139$	3.03934e9	0.690577	0.345289	−	0.938497i	$-0.387781\pi$
$139$	3.03934e9	0.690577	0.345289	+	0.938497i	$0.387781\pi$
$140$	0	0
$141$	4.73116e6	0.00100805
$142$	2.33565e9i	0.482070i
$143$	− 2.13240e9i	− 0.426439i
$144$	1.24308e10	2.40917
$145$	0	0
$146$	1.89920e10	3.45925
$147$	− 1.33939e6i	0 0.000236580i
$148$	− 3.75082e9i	− 0.642611i
$149$	3.64286e9	0.605487	0.302743	−	0.953072i	$-0.402098\pi$
$149$	3.64286e9	0.605487	0.302743	+	0.953072i	$0.402098\pi$
$150$	0	0
$151$	5.05862e9	0.791837	0.395919	−	0.918286i	$-0.370426\pi$
$151$	5.05862e9	0.791837	0.395919	+	0.918286i	$0.370426\pi$
$152$	− 2.30337e10i	− 3.50000i
$153$	− 6.53341e9i	− 0.963893i
$154$	−1.74653e9	−0.250226
$155$	0	0
$156$	−3.51733e7	−0.00475502
$157$	1.19687e10i	1.57216i	0.618122	+	0.786082i	$0.287894\pi$
$157$	1.19687e10i	1.57216i	−0.618122	+	0.786082i	$0.712106\pi$
$158$	1.88551e9i	0.240697i
$159$	1.38795e7	0.00172221
$160$	0	0
$161$	2.95920e9	0.347102
$162$	− 1.61948e10i	− 1.84739i
$163$	1.40960e10i	1.56405i	0.623245	+	0.782027i	$0.285814\pi$
$163$	1.40960e10i	1.56405i	−0.623245	+	0.782027i	$0.714186\pi$
$164$	9.10503e9	0.982843
$165$	0	0
$166$	−1.39896e10	−1.42995
$167$	− 3.56028e9i	− 0.354210i	−0.984192	−	0.177105i	$-0.943327\pi$
$167$	− 3.56028e9i	− 0.354210i	0.984192	−	0.177105i	$-0.0566732\pi$
$168$	1.68691e7i	0.00163380i
$169$	−4.41184e9	−0.416034
$170$	0	0
$171$	−1.49926e10	−1.34090
$172$	2.55716e10i	2.22782i
$173$	2.64068e9i	0.224134i	0.993701	+	0.112067i	$0.0357471\pi$
$173$	2.64068e9i	0.224134i	−0.993701	+	0.112067i	$0.964253\pi$
$174$	−6.16342e6	−0.000509741 0
$175$	0	0
$176$	1.09899e10	0.863353
$177$	− 1.40208e7i	− 0.00107372i
$178$	2.72501e10i	2.03459i
$179$	−1.26973e9	−0.0924430	−0.0462215	−	0.998931i	$-0.514718\pi$
$179$	−1.26973e9	−0.0924430	−0.0462215	+	0.998931i	$0.514718\pi$
$180$	0	0
$181$	−2.17242e10	−1.50449	−0.752247	−	0.658881i	$-0.771030\pi$
$181$	−2.17242e10	−1.50449	−0.752247	+	0.658881i	$0.771030\pi$
$182$	1.22990e10i	0.830901i
$183$	− 2.19411e6i	0 0.000144620i
$184$	−3.72699e10	−2.39706
$185$	0	0
$186$	−5.22584e7	−0.00320146
$187$	− 5.77614e9i	− 0.345422i
$188$	2.51567e10i	1.46874i
$189$	2.19601e7	0.00125186
$190$	0	0
$191$	−1.07035e10	−0.581937	−0.290968	−	0.956733i	$-0.593977\pi$
$191$	−1.07035e10	−0.581937	−0.290968	+	0.956733i	$0.593977\pi$
$192$	− 3.09038e7i	− 0.00164118i
$193$	7.66063e9i	0.397426i	0.980058	+	0.198713i	$0.0636762\pi$
$193$	7.66063e9i	0.397426i	−0.980058	+	0.198713i	$0.936324\pi$
$194$	5.96950e10	3.02573
$195$	0	0
$196$	7.12185e9	0.344699
$197$	4.26160e9i	0.201592i	0.994907	+	0.100796i	$0.0321390\pi$
$197$	4.26160e9i	0.201592i	−0.994907	+	0.100796i	$0.967861\pi$
$198$	− 1.43177e10i	− 0.662035i
$199$	−3.16291e10	−1.42971	−0.714856	−	0.699272i	$-0.753508\pi$
$199$	−3.16291e10	−1.42971	−0.714856	+	0.699272i	$0.753508\pi$
$200$	0	0
$201$	−5.09256e7	−0.00220066
$202$	− 3.72678e10i	− 1.57490i
$203$	1.52368e9i	0.0629742i
$204$	−9.52754e7	−0.00385163
$205$	0	0
$206$	−2.97630e10	−1.15153
$207$	2.42590e10i	0.918344i
$208$	− 7.73909e10i	− 2.86685i
$209$	−1.32549e10	−0.480526
$210$	0	0
$211$	1.76561e10	0.613229	0.306615	−	0.951834i	$-0.400804\pi$
$211$	1.76561e10	0.613229	0.306615	+	0.951834i	$0.400804\pi$
$212$	7.38005e10i	2.50927i
$213$	− 1.29817e7i	0 0.000432140i
$214$	−1.03919e11	−3.38713
$215$	0	0
$216$	−2.76579e8	−0.00864525
$217$	1.29190e10i	0.395513i
$218$	1.60292e10i	0.480681i
$219$	−1.05559e8	−0.00310097
$220$	0	0
$221$	−4.06754e10	−1.14701
$222$	2.94874e7i	0 0.000814794i
$223$	− 1.04686e10i	− 0.283476i	−0.989904	−	0.141738i	$-0.954731\pi$
$223$	− 1.04686e10i	− 0.283476i	0.989904	−	0.141738i	$-0.0452690\pi$
$224$	−2.62125e10	−0.695652
$225$	0	0
$226$	1.00150e11	2.55366
$227$	− 1.95043e10i	− 0.487543i	−0.969833	−	0.243772i	$-0.921615\pi$
$227$	− 1.95043e10i	− 0.487543i	0.969833	−	0.243772i	$-0.0783848\pi$
$228$	2.18634e8i	0.00535811i
$229$	5.96135e10	1.43247	0.716234	−	0.697860i	$-0.245864\pi$
$229$	5.96135e10	1.43247	0.716234	+	0.697860i	$0.245864\pi$
$230$	0	0
$231$	9.70738e6	0.000224310 0
$232$	− 1.91902e10i	− 0.434894i
$233$	8.42619e10i	1.87296i	0.350716	+	0.936482i	$0.385938\pi$
$233$	8.42619e10i	1.87296i	−0.350716	+	0.936482i	$0.614062\pi$
$234$	−1.00825e11	−2.19835
$235$	0	0
$236$	7.45517e10	1.56442
$237$	− 1.04798e7i	0 0.000215767i
$238$	3.33149e10i	0.673042i
$239$	7.28353e10	1.44395	0.721974	−	0.691920i	$-0.243235\pi$
$239$	7.28353e10	1.44395	0.721974	+	0.691920i	$0.243235\pi$
$240$	0	0
$241$	4.45555e10	0.850795	0.425397	−	0.905007i	$-0.360134\pi$
$241$	4.45555e10	0.850795	0.425397	+	0.905007i	$0.360134\pi$
$242$	8.59086e10i	1.61015i
$243$	2.70038e8i	0.00496817i
$244$	1.16666e10	0.210713
$245$	0	0
$246$	−7.15800e7	−0.00124619
$247$	9.33404e10i	1.59564i
$248$	− 1.62710e11i	− 2.73138i
$249$	7.77557e7	0.00128184
$250$	0	0
$251$	−9.55068e10	−1.51881	−0.759404	−	0.650620i	$-0.774509\pi$
$251$	−9.55068e10	−1.51881	−0.759404	+	0.650620i	$0.774509\pi$
$252$	5.83836e10i	0.911987i
$253$	2.14472e10i	0.329100i
$254$	−7.86968e10	−1.18633
$255$	0	0
$256$	−6.93361e10	−1.00897
$257$	− 9.12794e10i	− 1.30519i	−0.757707	−	0.652595i	$-0.773680\pi$
$257$	− 9.12794e10i	− 1.30519i	0.757707	−	0.652595i	$-0.226320\pi$
$258$	− 2.01033e8i	− 0.00282475i
$259$	7.28970e9	0.100661
$260$	0	0
$261$	−1.24909e10	−0.166614
$262$	6.23858e10i	0.817956i
$263$	1.50976e11i	1.94584i	0.231138	+	0.972921i	$0.425755\pi$
$263$	1.50976e11i	1.94584i	−0.231138	+	0.972921i	$0.574245\pi$
$264$	−1.22261e8	−0.00154906
$265$	0	0
$266$	7.64498e10	0.936287
$267$	− 1.51458e8i	− 0.00182387i
$268$	− 2.70784e11i	− 3.20639i
$269$	−2.39622e10	−0.279024	−0.139512	−	0.990220i	$-0.544553\pi$
$269$	−2.39622e10	−0.279024	−0.139512	+	0.990220i	$0.544553\pi$
$270$	0	0
$271$	−5.51248e10	−0.620848	−0.310424	−	0.950598i	$-0.600471\pi$
$271$	−5.51248e10	−0.620848	−0.310424	+	0.950598i	$0.600471\pi$
$272$	− 2.09632e11i	− 2.32219i
$273$	− 6.83591e7i	0 0.000744842i
$274$	1.34233e11	1.43874
$275$	0	0
$276$	3.53763e8	0.00366963
$277$	− 2.19632e10i	− 0.224149i	−0.993700	−	0.112074i	$-0.964251\pi$
$277$	− 2.19632e10i	− 0.224149i	0.993700	−	0.112074i	$-0.0357495\pi$
$278$	− 1.27050e11i	− 1.27577i
$279$	−1.05908e11	−1.04643
$280$	0	0
$281$	−1.62670e10	−0.155643	−0.0778213	−	0.996967i	$-0.524796\pi$
$281$	−1.62670e10	−0.155643	−0.0778213	+	0.996967i	$0.524796\pi$
$282$	− 1.97772e8i	− 0.00186227i
$283$	1.35590e10i	0.125657i	0.998024	+	0.0628287i	$0.0200122\pi$
$283$	1.35590e10i	0.125657i	−0.998024	+	0.0628287i	$0.979988\pi$
$284$	6.90270e10	0.629632
$285$	0	0
$286$	−8.91387e10	−0.787805
$287$	1.76956e10i	0.153956i
$288$	− 2.14885e11i	− 1.84052i
$289$	8.40858e9	0.0709059
$290$	0	0
$291$	−3.31790e8	−0.00271235
$292$	− 5.61284e11i	− 4.51814i
$293$	5.41900e10i	0.429551i	0.976663	+	0.214776i	$0.0689021\pi$
$293$	5.41900e10i	0.429551i	−0.976663	+	0.214776i	$0.931098\pi$
$294$	−5.59890e7	−0.000437059 0
$295$	0	0
$296$	−9.18109e10	−0.695155
$297$	1.59159e8i	0.00118693i
$298$	− 1.52279e11i	− 1.11858i
$299$	1.51030e11	1.09281
$300$	0	0
$301$	−4.96983e10	−0.348974
$302$	− 2.11460e11i	− 1.46284i
$303$	2.07138e8i	0.00141178i
$304$	−4.81056e11	−3.23046
$305$	0	0
$306$	−2.73109e11	−1.78070
$307$	− 7.32498e10i	− 0.470634i	−0.971919	−	0.235317i	$-0.924387\pi$
$307$	− 7.32498e10i	− 0.470634i	0.971919	−	0.235317i	$-0.0756129\pi$
$308$	5.16165e10i	0.326821i
$309$	1.65425e8	0.00103226
$310$	0	0
$311$	−2.44502e11	−1.48204	−0.741021	−	0.671482i	$-0.765658\pi$
$311$	−2.44502e11	−1.48204	−0.741021	+	0.671482i	$0.765658\pi$
$312$	8.60956e8i	0.00514381i
$313$	− 4.39895e10i	− 0.259060i	−0.991576	−	0.129530i	$-0.958653\pi$
$313$	− 4.39895e10i	− 0.259060i	0.991576	−	0.129530i	$-0.0413468\pi$
$314$	5.00314e11	2.90442
$315$	0	0
$316$	5.57237e10	0.314375
$317$	2.17653e11i	1.21059i	0.795999	+	0.605297i	$0.206946\pi$
$317$	2.17653e11i	1.21059i	−0.795999	+	0.605297i	$0.793054\pi$
$318$	− 5.80189e8i	− 0.00318161i
$319$	−1.10431e10	−0.0597080
$320$	0	0
$321$	5.77591e8	0.00303632
$322$	− 1.23700e11i	− 0.641238i
$323$	2.52835e11i	1.29249i
$324$	−4.78616e11	−2.41288
$325$	0	0
$326$	5.89240e11	2.88944
$327$	− 8.90917e7i	0 0.000430896i
$328$	− 2.22869e11i	− 1.06321i
$329$	−4.88920e10	−0.230068
$330$	0	0
$331$	−3.66945e11	−1.68026	−0.840128	−	0.542389i	$-0.817520\pi$
$331$	−3.66945e11	−1.68026	−0.840128	+	0.542389i	$0.817520\pi$
$332$	4.13446e11i	1.86766i
$333$	5.97596e10i	0.266323i
$334$	−1.48827e11	−0.654368
$335$	0	0
$336$	3.52308e8	0.00150798
$337$	− 1.99451e11i	− 0.842367i	−0.906976	−	0.421183i	$-0.861615\pi$
$337$	− 1.99451e11i	− 0.842367i	0.906976	−	0.421183i	$-0.138385\pi$
$338$	1.84423e11i	0.768583i
$339$	−5.56642e8	−0.00228917
$340$	0	0
$341$	−9.36322e10	−0.374999
$342$	6.26721e11i	2.47718i
$343$	1.38413e10i	0.0539949i
$344$	6.25931e11	2.40998
$345$	0	0
$346$	1.10385e11	0.414066
$347$	− 6.63180e10i	− 0.245555i	−0.992434	−	0.122777i	$-0.960820\pi$
$347$	− 6.63180e10i	− 0.245555i	0.992434	−	0.122777i	$-0.0391801\pi$
$348$	1.82152e8i	0 0.000665774i
$349$	1.20301e11	0.434065	0.217033	−	0.976164i	$-0.430362\pi$
$349$	1.20301e11	0.434065	0.217033	+	0.976164i	$0.430362\pi$
$350$	0	0
$351$	1.12079e9	0.00394133
$352$	− 1.89978e11i	− 0.659571i
$353$	2.43060e11i	0.833159i	0.909099	+	0.416580i	$0.136771\pi$
$353$	2.43060e11i	0.833159i	−0.909099	+	0.416580i	$0.863229\pi$
$354$	−5.86095e8	−0.00198360
$355$	0	0
$356$	8.05341e11	2.65739
$357$	− 1.85167e8i	0 0.000603333i
$358$	5.30773e10i	0.170779i
$359$	−2.81654e11	−0.894933	−0.447466	−	0.894301i	$-0.647674\pi$
$359$	−2.81654e11	−0.894933	−0.447466	+	0.894301i	$0.647674\pi$
$360$	0	0
$361$	2.57510e11	0.798015
$362$	9.08115e11i	2.77941i
$363$	− 4.77488e8i	− 0.00144339i
$364$	3.63482e11	1.08524
$365$	0	0
$366$	−9.17181e7	−0.000267172 0
$367$	2.41000e11i	0.693458i	0.937965	+	0.346729i	$0.112708\pi$
$367$	2.41000e11i	0.693458i	−0.937965	+	0.346729i	$0.887292\pi$
$368$	7.78376e11i	2.21246i
$369$	−1.45065e11	−0.407328
$370$	0	0
$371$	−1.43431e11	−0.393061
$372$	1.54443e9i	0.00418143i
$373$	− 1.33921e11i	− 0.358227i	−0.983828	−	0.179114i	$-0.942677\pi$
$373$	− 1.33921e11i	− 0.358227i	0.983828	−	0.179114i	$-0.0573230\pi$
$374$	−2.41454e11	−0.638134
$375$	0	0
$376$	6.15775e11	1.58883
$377$	7.77651e10i	0.198266i
$378$	− 9.17976e8i	− 0.00231270i
$379$	−5.67201e11	−1.41208	−0.706042	−	0.708170i	$-0.749521\pi$
$379$	−5.67201e11	−1.41208	−0.706042	+	0.708170i	$0.749521\pi$
$380$	0	0
$381$	4.37404e8	0.00106346
$382$	4.47427e11i	1.07507i
$383$	− 1.03509e11i	− 0.245800i	−0.992419	−	0.122900i	$-0.960781\pi$
$383$	− 1.03509e11i	− 0.245800i	0.992419	−	0.122900i	$-0.0392194\pi$
$384$	6.85951e6	1.60991e−5 0
$385$	0	0
$386$	3.20229e11	0.734206
$387$	− 4.07417e11i	− 0.923295i
$388$	− 1.76421e12i	− 3.95191i
$389$	5.83600e11	1.29224	0.646119	−	0.763237i	$-0.276391\pi$
$389$	5.83600e11	1.29224	0.646119	+	0.763237i	$0.276391\pi$
$390$	0	0
$391$	4.09102e11	0.885190
$392$	− 1.74326e11i	− 0.372884i
$393$	− 3.46746e8i	0 0.000733238i
$394$	1.78143e11	0.372422
$395$	0	0
$396$	−4.23142e11	−0.864685
$397$	6.54542e10i	0.132245i	0.997812	+	0.0661226i	$0.0210629\pi$
$397$	6.54542e10i	0.132245i	−0.997812	+	0.0661226i	$0.978937\pi$
$398$	1.32216e12i	2.64125i
$399$	−4.24915e8	−0.000839313 0
$400$	0	0
$401$	4.06647e10	0.0785359	0.0392679	−	0.999229i	$-0.487497\pi$
$401$	4.06647e10	0.0785359	0.0392679	+	0.999229i	$0.487497\pi$
$402$	2.12879e9i	0.00406551i
$403$	6.59356e11i	1.24522i
$404$	−1.10140e12	−2.05698
$405$	0	0
$406$	6.36930e10	0.116339
$407$	5.28330e10i	0.0954400i
$408$	2.33211e9i	0.00416657i
$409$	−1.06163e12	−1.87594	−0.937970	−	0.346716i	$-0.887297\pi$
$409$	−1.06163e12	−1.87594	−0.937970	+	0.346716i	$0.887297\pi$
$410$	0	0
$411$	−7.46081e8	−0.00128973
$412$	8.79607e11i	1.50401i
$413$	1.44891e11i	0.245056i
$414$	1.01407e12	1.69655
$415$	0	0
$416$	−1.33782e12	−2.19017
$417$	7.06157e8i	0.00114364i
$418$	5.54079e11i	0.887726i
$419$	1.19335e12	1.89149	0.945744	−	0.324912i	$-0.105335\pi$
$419$	1.19335e12	1.89149	0.945744	+	0.324912i	$0.105335\pi$
$420$	0	0
$421$	−5.88397e11	−0.912853	−0.456427	−	0.889761i	$-0.650871\pi$
$421$	−5.88397e11	−0.912853	−0.456427	+	0.889761i	$0.650871\pi$
$422$	− 7.38058e11i	− 1.13288i
$423$	− 4.00807e11i	− 0.608701i
$424$	1.80646e12	2.71444
$425$	0	0
$426$	−5.42662e8	−0.000798337 0
$427$	2.26740e10i	0.0330068i
$428$	3.07119e12i	4.42394i
$429$	4.95441e8	0.000706210 0
$430$	0	0
$431$	−1.22932e12	−1.71599	−0.857997	−	0.513655i	$-0.828291\pi$
$431$	−1.22932e12	−1.71599	−0.857997	+	0.513655i	$0.828291\pi$
$432$	5.77631e9i	0.00797946i
$433$	− 4.73819e10i	− 0.0647764i	−0.999475	−	0.0323882i	$-0.989689\pi$
$433$	− 4.73819e10i	− 0.0647764i	0.999475	−	0.0323882i	$-0.0103113\pi$
$434$	5.40041e11	0.730672
$435$	0	0
$436$	4.73722e11	0.627819
$437$	− 9.38793e11i	− 1.23141i
$438$	4.41258e9i	0.00572874i
$439$	−6.14236e11	−0.789305	−0.394652	−	0.918830i	$-0.629135\pi$
$439$	−6.14236e11	−0.789305	−0.394652	+	0.918830i	$0.629135\pi$
$440$	0	0
$441$	−1.13468e11	−0.142857
$442$	1.70031e12i	2.11899i
$443$	− 8.19199e11i	− 1.01058i	−0.862948	−	0.505292i	$-0.831385\pi$
$443$	− 8.19199e11i	− 1.01058i	0.862948	−	0.505292i	$-0.168615\pi$
$444$	8.71462e8	0.00106420
$445$	0	0
$446$	−4.37607e11	−0.523694
$447$	8.46379e8i	0.00100272i
$448$	3.19361e11i	0.374568i
$449$	−4.81029e11	−0.558551	−0.279276	−	0.960211i	$-0.590094\pi$
$449$	−4.81029e11	−0.558551	−0.279276	+	0.960211i	$0.590094\pi$
$450$	0	0
$451$	−1.28251e11	−0.145971
$452$	− 2.95980e12i	− 3.33534i
$453$	1.17532e9i	0.00131133i
$454$	−8.15316e11	−0.900689
$455$	0	0
$456$	5.35164e9	0.00579622
$457$	− 1.15328e12i	− 1.23684i	−0.785849	−	0.618419i	$-0.787774\pi$
$457$	− 1.15328e12i	− 1.23684i	0.785849	−	0.618419i	$-0.212226\pi$
$458$	− 2.49196e12i	− 2.64635i
$459$	3.03594e9	0.00319254
$460$	0	0
$461$	−6.06986e11	−0.625928	−0.312964	−	0.949765i	$-0.601322\pi$
$461$	−6.06986e11	−0.625928	−0.312964	+	0.949765i	$0.601322\pi$
$462$	− 4.05787e8i	0 0.000414390i
$463$	− 8.87758e11i	− 0.897801i	−0.893582	−	0.448900i	$-0.851816\pi$
$463$	− 8.87758e11i	− 0.897801i	0.893582	−	0.448900i	$-0.148184\pi$
$464$	−4.00784e11	−0.401402
$465$	0	0
$466$	3.52231e12	3.46012
$467$	1.09779e12i	1.06806i	0.845466	+	0.534029i	$0.179323\pi$
$467$	1.09779e12i	1.06806i	−0.845466	+	0.534029i	$0.820677\pi$
$468$	2.97976e12i	2.87127i
$469$	5.26267e11	0.502260
$470$	0	0
$471$	−2.78079e9	−0.00260360
$472$	− 1.82484e12i	− 1.69234i
$473$	− 3.60195e11i	− 0.330874i
$474$	−4.38076e8	−0.000398609 0
$475$	0	0
$476$	9.84579e11	0.879062
$477$	− 1.17582e12i	− 1.03994i
$478$	− 3.04466e12i	− 2.66755i
$479$	3.12229e11	0.270996	0.135498	−	0.990778i	$-0.456737\pi$
$479$	3.12229e11	0.270996	0.135498	+	0.990778i	$0.456737\pi$
$480$	0	0
$481$	3.72048e11	0.316918
$482$	− 1.86251e12i	− 1.57176i
$483$	6.87537e8i	0 0.000574823i
$484$	2.53892e12	2.10303
$485$	0	0
$486$	1.12881e10	0.00917820
$487$	− 1.08377e12i	− 0.873088i	−0.899683	−	0.436544i	$-0.856202\pi$
$487$	− 1.08377e12i	− 0.873088i	0.899683	−	0.436544i	$-0.143798\pi$
$488$	− 2.85570e11i	− 0.227942i
$489$	−3.27505e9	−0.00259017
$490$	0	0
$491$	2.14702e12	1.66713	0.833567	−	0.552419i	$-0.186295\pi$
$491$	2.14702e12	1.66713	0.833567	+	0.552419i	$0.186295\pi$
$492$	2.11545e9i	0.00162765i
$493$	2.10646e11i	0.160599i
$494$	3.90181e12	2.94778
$495$	0	0
$496$	−3.39817e12	−2.52103
$497$	1.34154e11i	0.0986277i
$498$	− 3.25034e9i	− 0.00236808i
$499$	1.85705e12	1.34082	0.670411	−	0.741990i	$-0.266118\pi$
$499$	1.85705e12	1.34082	0.670411	+	0.741990i	$0.266118\pi$
$500$	0	0
$501$	8.27193e8	0.000586593 0
$502$	3.99237e12i	2.80585i
$503$	− 1.59040e12i	− 1.10777i	−0.832593	−	0.553885i	$-0.813145\pi$
$503$	− 1.59040e12i	− 1.10777i	0.832593	−	0.553885i	$-0.186855\pi$
$504$	1.42909e12	0.986556
$505$	0	0
$506$	8.96533e11	0.607979
$507$	− 1.02504e9i	0 0.000688979i
$508$	2.32578e12i	1.54947i
$509$	−2.32864e12	−1.53771	−0.768853	−	0.639426i	$-0.779172\pi$
$509$	−2.32864e12	−1.53771	−0.768853	+	0.639426i	$0.779172\pi$
$510$	0	0
$511$	1.09085e12	0.707737
$512$	2.88327e12i	1.85426i
$513$	− 6.96676e9i	− 0.00444122i
$514$	−3.81566e12	−2.41121
$515$	0	0
$516$	−5.94128e9	−0.00368941
$517$	− 3.54350e11i	− 0.218135i
$518$	− 3.04724e11i	− 0.185961i
$519$	−6.13532e8	−0.000371180 0
$520$	0	0
$521$	−1.48366e12	−0.882197	−0.441099	−	0.897459i	$-0.645411\pi$
$521$	−1.48366e12	−0.882197	−0.441099	+	0.897459i	$0.645411\pi$
$522$	5.22143e11i	0.307802i
$523$	− 1.95584e12i	− 1.14308i	−0.820574	−	0.571540i	$-0.806346\pi$
$523$	− 1.95584e12i	− 1.14308i	0.820574	−	0.571540i	$-0.193654\pi$
$524$	1.84373e12	1.06833
$525$	0	0
$526$	6.31110e12	3.59475
$527$	1.78603e12i	1.00865i
$528$	2.55339e9i	0.00142977i
$529$	2.82131e11	0.156639
$530$	0	0
$531$	−1.18779e12	−0.648357
$532$	− 2.25938e12i	− 1.22289i
$533$	9.03139e11i	0.484710i
$534$	−6.33126e9	−0.00336941
$535$	0	0
$536$	−6.62812e12	−3.46856
$537$	− 2.95009e8i	0 0.000153091i
$538$	1.00167e12i	0.515470i
$539$	−1.00316e11	−0.0511944
$540$	0	0
$541$	−1.34802e12	−0.676563	−0.338281	−	0.941045i	$-0.609846\pi$
$541$	−1.34802e12	−0.676563	−0.338281	+	0.941045i	$0.609846\pi$
$542$	2.30433e12i	1.14696i
$543$	− 5.04738e9i	− 0.00249154i
$544$	−3.62381e12	−1.77407
$545$	0	0
$546$	−2.85754e9	−0.00137602
$547$	− 1.02503e12i	− 0.489548i	−0.969580	−	0.244774i	$-0.921286\pi$
$547$	− 1.02503e12i	− 0.489548i	0.969580	−	0.244774i	$-0.0787137\pi$
$548$	− 3.96710e12i	− 1.87914i
$549$	−1.85877e11	−0.0873275
$550$	0	0
$551$	4.83382e11	0.223413
$552$	− 8.65926e9i	− 0.00396968i
$553$	1.08299e11i	0.0492448i
$554$	−9.18103e11	−0.414093
$555$	0	0
$556$	−3.75481e12	−1.66629
$557$	− 1.75343e12i	− 0.771864i	−0.922527	−	0.385932i	$-0.873880\pi$
$557$	− 1.75343e12i	− 0.771864i	0.922527	−	0.385932i	$-0.126120\pi$
$558$	4.42715e12i	1.93317i
$559$	−2.53648e12	−1.09870
$560$	0	0
$561$	1.34202e9	0.000572041 0
$562$	6.79991e11i	0.287535i
$563$	− 2.17456e12i	− 0.912185i	−0.889932	−	0.456092i	$-0.849249\pi$
$563$	− 2.17456e12i	− 0.912185i	0.889932	−	0.456092i	$-0.150751\pi$
$564$	−5.84489e9	−0.00243232
$565$	0	0
$566$	5.66792e11	0.232140
$567$	− 9.30189e11i	− 0.377961i
$568$	− 1.68961e12i	− 0.681114i
$569$	−3.13812e12	−1.25506	−0.627531	−	0.778592i	$-0.715934\pi$
$569$	−3.13812e12	−1.25506	−0.627531	+	0.778592i	$0.715934\pi$
$570$	0	0
$571$	2.05979e12	0.810887	0.405444	−	0.914120i	$-0.367117\pi$
$571$	2.05979e12	0.810887	0.405444	+	0.914120i	$0.367117\pi$
$572$	2.63438e12i	1.02895i
$573$	− 2.48684e9i	0 0.000963723i
$574$	7.39710e11	0.284419
$575$	0	0
$576$	−2.61806e12	−0.991011
$577$	− 3.94380e12i	− 1.48123i	−0.671927	−	0.740617i	$-0.734533\pi$
$577$	− 3.94380e12i	− 1.48123i	0.671927	−	0.740617i	$-0.265467\pi$
$578$	− 3.51495e11i	− 0.130992i
$579$	−1.77986e9	−0.000658162 0
$580$	0	0
$581$	−8.03530e11	−0.292556
$582$	1.38695e10i	0.00501079i
$583$	− 1.03953e12i	− 0.372675i
$584$	−1.37389e13	−4.88757
$585$	0	0
$586$	2.26525e12	0.793555
$587$	− 3.68239e12i	− 1.28014i	−0.768315	−	0.640071i	$-0.778905\pi$
$587$	− 3.68239e12i	− 1.28014i	0.768315	−	0.640071i	$-0.221095\pi$
$588$	1.65468e9i	0 0.000570844i
$589$	4.09851e12	1.40316
$590$	0	0
$591$	−9.90135e8	−0.000333850 0
$592$	1.91746e12i	0.641620i
$593$	− 1.17114e12i	− 0.388921i	−0.980910	−	0.194460i	$-0.937704\pi$
$593$	− 1.17114e12i	− 0.388921i	0.980910	−	0.194460i	$-0.0622956\pi$
$594$	6.65315e9	0.00219274
$595$	0	0
$596$	−4.50040e12	−1.46098
$597$	− 7.34868e9i	− 0.00236769i
$598$	− 6.31336e12i	− 2.01886i
$599$	−2.83757e12	−0.900586	−0.450293	−	0.892881i	$-0.648681\pi$
$599$	−2.83757e12	−0.900586	−0.450293	+	0.892881i	$0.648681\pi$
$600$	0	0
$601$	2.37066e12	0.741198	0.370599	−	0.928793i	$-0.379152\pi$
$601$	2.37066e12	0.741198	0.370599	+	0.928793i	$0.379152\pi$
$602$	2.07749e12i	0.644695i
$603$	4.31424e12i	1.32885i
$604$	−6.24943e12	−1.91062
$605$	0	0
$606$	8.65876e9	0.00260813
$607$	− 4.40080e12i	− 1.31578i	−0.753115	−	0.657889i	$-0.771450\pi$
$607$	− 4.40080e12i	− 1.31578i	0.753115	−	0.657889i	$-0.228550\pi$
$608$	8.31580e12i	2.46796i
$609$	−3.54011e8	−0.000104289 0
$610$	0	0
$611$	−2.49533e12	−0.724339
$612$	8.07140e12i	2.32577i
$613$	− 1.87570e12i	− 0.536527i	−0.963346	−	0.268264i	$-0.913550\pi$
$613$	− 1.87570e12i	− 0.536527i	0.963346	−	0.268264i	$-0.0864498\pi$
$614$	−3.06198e12	−0.869451
$615$	0	0
$616$	1.26345e12	0.353544
$617$	3.18170e12i	0.883845i	0.897053	+	0.441922i	$0.145703\pi$
$617$	3.18170e12i	0.883845i	−0.897053	+	0.441922i	$0.854297\pi$
$618$	− 6.91510e9i	− 0.00190700i
$619$	1.16476e11	0.0318880	0.0159440	−	0.999873i	$-0.494925\pi$
$619$	1.16476e11	0.0318880	0.0159440	+	0.999873i	$0.494925\pi$
$620$	0	0
$621$	−1.12726e10	−0.00304167
$622$	1.02207e13i	2.73793i
$623$	1.56518e12i	0.416263i
$624$	1.79809e10	0.00474768
$625$	0	0
$626$	−1.83885e12	−0.478587
$627$	− 3.07962e9i	0 0.000795781i
$628$	− 1.47861e13i	− 3.79347i
$629$	1.00778e12	0.256708
$630$	0	0
$631$	−3.71283e12	−0.932338	−0.466169	−	0.884696i	$-0.654366\pi$
$631$	−3.71283e12	−0.932338	−0.466169	+	0.884696i	$0.654366\pi$
$632$	− 1.36398e12i	− 0.340080i
$633$	4.10219e9i	0.00101555i
$634$	9.09834e12	2.23646
$635$	0	0
$636$	−1.71467e10	−0.00415551
$637$	7.06425e11i	0.169996i
$638$	4.61622e11i	0.110305i
$639$	−1.09977e12	−0.260944
$640$	0	0
$641$	2.93764e11	0.0687285	0.0343642	−	0.999409i	$-0.489059\pi$
$641$	2.93764e11	0.0687285	0.0343642	+	0.999409i	$0.489059\pi$
$642$	− 2.41444e10i	− 0.00560930i
$643$	5.27980e12i	1.21806i	0.793148	+	0.609029i	$0.208441\pi$
$643$	5.27980e12i	1.21806i	−0.793148	+	0.609029i	$0.791559\pi$
$644$	−3.65580e12	−0.837522
$645$	0	0
$646$	1.05690e13	2.38775
$647$	2.62000e12i	0.587804i	0.955836	+	0.293902i	$0.0949539\pi$
$647$	2.62000e12i	0.587804i	−0.955836	+	0.293902i	$0.905046\pi$
$648$	1.17154e13i	2.61017i
$649$	−1.05011e12	−0.232346
$650$	0	0
$651$	−3.00160e9	−0.000654995 0
$652$	− 1.74142e13i	− 3.77390i
$653$	3.15918e12i	0.679931i	0.940438	+	0.339965i	$0.110415\pi$
$653$	3.15918e12i	0.679931i	−0.940438	+	0.339965i	$0.889585\pi$
$654$	−3.72420e9	−0.000796038 0
$655$	0	0
$656$	−4.65458e12	−0.981326
$657$	8.94260e12i	1.87249i
$658$	2.04378e12i	0.425028i
$659$	−8.77292e11	−0.181201	−0.0906004	−	0.995887i	$-0.528879\pi$
$659$	−8.77292e11	−0.181201	−0.0906004	+	0.995887i	$0.528879\pi$
$660$	0	0
$661$	8.22108e12	1.67503	0.837514	−	0.546416i	$-0.184008\pi$
$661$	8.22108e12	1.67503	0.837514	+	0.546416i	$0.184008\pi$
$662$	1.53390e13i	3.10411i
$663$	− 9.45049e9i	− 0.00189952i
$664$	1.01201e13	2.02037
$665$	0	0
$666$	2.49807e12	0.492006
$667$	− 7.82140e11i	− 0.153010i
$668$	4.39838e12i	0.854671i
$669$	2.43226e9	0.000469454 0
$670$	0	0
$671$	−1.64333e11	−0.0312948
$672$	− 6.09018e9i	− 0.00115204i
$673$	− 7.47304e12i	− 1.40420i	−0.712077	−	0.702101i	$-0.752246\pi$
$673$	− 7.47304e12i	− 1.40420i	0.712077	−	0.702101i	$-0.247754\pi$
$674$	−8.33743e12	−1.55619
$675$	0	0
$676$	5.45039e12	1.00385
$677$	− 8.71309e12i	− 1.59413i	−0.603895	−	0.797064i	$-0.706386\pi$
$677$	− 8.71309e12i	− 1.59413i	0.603895	−	0.797064i	$-0.293614\pi$
$678$	2.32687e10i	0.00422901i
$679$	3.42873e12	0.619041
$680$	0	0
$681$	4.53160e9	0.000807402 0
$682$	3.91401e12i	0.692775i
$683$	− 3.73903e12i	− 0.657455i	−0.944425	−	0.328727i	$-0.893380\pi$
$683$	− 3.73903e12i	− 0.657455i	0.944425	−	0.328727i	$-0.106620\pi$
$684$	1.85219e13	3.23545
$685$	0	0
$686$	5.78593e11	0.0997504
$687$	1.38505e10i	0.00237226i
$688$	− 1.30725e13i	− 2.22438i
$689$	−7.32036e12	−1.23750
$690$	0	0
$691$	−6.26971e12	−1.04616	−0.523078	−	0.852285i	$-0.675216\pi$
$691$	−6.26971e12	−1.04616	−0.523078	+	0.852285i	$0.675216\pi$
$692$	− 3.26230e12i	− 0.540812i
$693$	− 8.22375e11i	− 0.135447i
$694$	−2.77222e12	−0.453639
$695$	0	0
$696$	4.45863e9	0.000720212 0
$697$	2.44637e12i	0.392623i
$698$	− 5.02882e12i	− 0.801893i
$699$	−1.95773e10	−0.00310174
$700$	0	0
$701$	−5.13904e12	−0.803805	−0.401903	−	0.915682i	$-0.631651\pi$
$701$	−5.13904e12	−0.803805	−0.401903	+	0.915682i	$0.631651\pi$
$702$	− 4.68513e10i	− 0.00728122i
$703$	− 2.31263e12i	− 0.357114i
$704$	−2.31461e12	−0.355140
$705$	0	0
$706$	1.01604e13	1.53918
$707$	− 2.14057e12i	− 0.322212i
$708$	1.73213e10i	0.00259078i
$709$	2.95438e12	0.439094	0.219547	−	0.975602i	$-0.429542\pi$
$709$	2.95438e12	0.439094	0.219547	+	0.975602i	$0.429542\pi$
$710$	0	0
$711$	−8.87813e11	−0.130289
$712$	− 1.97128e13i	− 2.87467i
$713$	− 6.63162e12i	− 0.960986i
$714$	−7.74035e9	−0.00111460
$715$	0	0
$716$	1.56863e12	0.223055
$717$	1.69225e10i	0.00239127i
$718$	1.17737e13i	1.65330i
$719$	1.21819e13	1.69994	0.849971	−	0.526829i	$-0.176619\pi$
$719$	1.21819e13	1.69994	0.849971	+	0.526829i	$0.176619\pi$
$720$	0	0
$721$	−1.70951e12	−0.235594
$722$	− 1.07644e13i	− 1.47426i
$723$	1.03520e10i	0.00140897i
$724$	2.68382e13	3.63019
$725$	0	0
$726$	−1.99599e10	−0.00266652
$727$	− 1.26291e13i	− 1.67675i	−0.545093	−	0.838376i	$-0.683506\pi$
$727$	− 1.26291e13i	− 1.67675i	0.545093	−	0.838376i	$-0.316494\pi$
$728$	− 8.89715e12i	− 1.17398i
$729$	7.62547e12	0.999984
$730$	0	0
$731$	−6.87068e12	−0.889962
$732$	2.71061e9i	0 0.000348953i
$733$	9.16594e12i	1.17276i	0.810036	+	0.586380i	$0.199447\pi$
$733$	9.16594e12i	1.17276i	−0.810036	+	0.586380i	$0.800553\pi$
$734$	1.00743e13	1.28110
$735$	0	0
$736$	1.34554e13	1.69024
$737$	3.81418e12i	0.476209i
$738$	6.06400e12i	0.752499i
$739$	−1.10658e13	−1.36484	−0.682420	−	0.730960i	$-0.739073\pi$
$739$	−1.10658e13	−1.36484	−0.682420	+	0.730960i	$0.739073\pi$
$740$	0	0
$741$	−2.16866e10	−0.00264247
$742$	5.99569e12i	0.726142i
$743$	1.84642e12i	0.222270i	0.993805	+	0.111135i	$0.0354486\pi$
$743$	1.84642e12i	0.222270i	−0.993805	+	0.111135i	$0.964551\pi$
$744$	3.78039e10	0.00452333
$745$	0	0
$746$	−5.59816e12	−0.661790
$747$	− 6.58719e12i	− 0.774029i
$748$	7.13586e12i	0.833468i
$749$	−5.96884e12	−0.692982
$750$	0	0
$751$	−9.19672e12	−1.05500	−0.527501	−	0.849555i	$-0.676871\pi$
$751$	−9.19672e12	−1.05500	−0.527501	+	0.849555i	$0.676871\pi$
$752$	− 1.28604e13i	− 1.46647i
$753$	− 2.21900e10i	− 0.00251524i
$754$	3.25073e12	0.366277
$755$	0	0
$756$	−2.71296e10	−0.00302062
$757$	− 8.81778e12i	− 0.975950i	−0.872858	−	0.487975i	$-0.837736\pi$
$757$	− 8.81778e12i	− 0.975950i	0.872858	−	0.487975i	$-0.162264\pi$
$758$	2.37101e13i	2.60869i
$759$	−4.98301e9	−0.000545009 0
$760$	0	0
$761$	−2.42043e12	−0.261614	−0.130807	−	0.991408i	$-0.541757\pi$
$761$	−2.42043e12	−0.261614	−0.130807	+	0.991408i	$0.541757\pi$
$762$	− 1.82843e10i	− 0.00196464i
$763$	9.20676e11i	0.0983437i
$764$	1.32231e13	1.40415
$765$	0	0
$766$	−4.32686e12	−0.454092
$767$	7.39488e12i	0.771528i
$768$	− 1.61095e10i	− 0.00167092i
$769$	−7.67945e12	−0.791885	−0.395942	−	0.918275i	$-0.629582\pi$
$769$	−7.67945e12	−0.791885	−0.395942	+	0.918275i	$0.629582\pi$
$770$	0	0
$771$	2.12078e10	0.00216148
$772$	− 9.46396e12i	− 0.958948i
$773$	1.04693e13i	1.05466i	0.849662	+	0.527328i	$0.176806\pi$
$773$	1.04693e13i	1.05466i	−0.849662	+	0.527328i	$0.823194\pi$
$774$	−1.70308e13	−1.70570
$775$	0	0
$776$	−4.31835e13	−4.27504
$777$	1.69368e9i	0 0.000166701i
$778$	− 2.43956e13i	− 2.38728i
$779$	5.61385e12	0.546188
$780$	0	0
$781$	−9.72296e11	−0.0935123
$782$	− 1.71013e13i	− 1.63530i
$783$	− 5.80424e9i	0 0.000551846i
$784$	−3.64076e12	−0.344167
$785$	0	0
$786$	−1.44947e10	−0.00135459
$787$	1.26490e13i	1.17535i	0.809095	+	0.587677i	$0.199958\pi$
$787$	1.26490e13i	1.17535i	−0.809095	+	0.587677i	$0.800042\pi$
$788$	− 5.26479e12i	− 0.486422i
$789$	−3.50777e10	−0.00322243
$790$	0	0
$791$	5.75236e12	0.522459
$792$	1.03575e13i	0.935387i
$793$	1.15723e12i	0.103918i
$794$	2.73611e12	0.244310
$795$	0	0
$796$	3.90747e13	3.44975
$797$	6.02337e11i	0.0528782i	0.999650	+	0.0264391i	$0.00841681\pi$
$797$	6.02337e11i	0.0528782i	−0.999650	+	0.0264391i	$0.991583\pi$
$798$	1.77623e10i	0.00155055i
$799$	−6.75920e12	−0.586725
$800$	0	0
$801$	−1.28310e13	−1.10132
$802$	− 1.69986e12i	− 0.145087i
$803$	7.90608e12i	0.671029i
$804$	6.29136e10	0.00530997
$805$	0	0
$806$	2.75624e13	2.30043
$807$	− 5.56736e9i	0 0.000462081i
$808$	2.69596e13i	2.22517i
$809$	7.72967e12	0.634443	0.317222	−	0.948351i	$-0.397250\pi$
$809$	7.72967e12	0.634443	0.317222	+	0.948351i	$0.397250\pi$
$810$	0	0
$811$	−1.20157e13	−0.975335	−0.487668	−	0.873029i	$-0.662152\pi$
$811$	−1.20157e13	−0.975335	−0.487668	+	0.873029i	$0.662152\pi$
$812$	− 1.88236e12i	− 0.151950i
$813$	− 1.28077e10i	− 0.00102816i
$814$	2.20852e12	0.176316
$815$	0	0
$816$	4.87057e10	0.00384569
$817$	1.57666e13i	1.23805i
$818$	4.43783e13i	3.46562i
$819$	−5.79114e12	−0.449766
$820$	0	0
$821$	1.39952e13	1.07507	0.537533	−	0.843243i	$-0.319356\pi$
$821$	1.39952e13	1.07507	0.537533	+	0.843243i	$0.319356\pi$
$822$	3.11877e10i	0.00238265i
$823$	1.61982e13i	1.23074i	0.788238	+	0.615371i	$0.210994\pi$
$823$	1.61982e13i	1.23074i	−0.788238	+	0.615371i	$0.789006\pi$
$824$	2.15306e13	1.62699
$825$	0	0
$826$	6.05672e12	0.452718
$827$	1.30127e13i	0.967374i	0.875241	+	0.483687i	$0.160703\pi$
$827$	1.30127e13i	0.967374i	−0.875241	+	0.483687i	$0.839297\pi$
$828$	− 2.99696e13i	− 2.21587i
$829$	1.31364e13	0.966007	0.483004	−	0.875618i	$-0.339546\pi$
$829$	1.31364e13	0.966007	0.483004	+	0.875618i	$0.339546\pi$
$830$	0	0
$831$	5.10290e9	0.000371204 0
$832$	1.62994e13i	1.17928i
$833$	1.91353e12i	0.137699i
$834$	2.95187e10	0.00211276
$835$	0	0
$836$	1.63751e13	1.15946
$837$	− 4.92131e10i	− 0.00346590i
$838$	− 4.98842e13i	− 3.49434i
$839$	5.22420e12	0.363991	0.181996	−	0.983299i	$-0.441744\pi$
$839$	5.22420e12	0.363991	0.181996	+	0.983299i	$0.441744\pi$
$840$	0	0
$841$	−1.41044e13	−0.972240
$842$	2.45961e13i	1.68641i
$843$	− 3.77945e9i	0 0.000257754i
$844$	−2.18124e13	−1.47966
$845$	0	0
$846$	−1.67545e13	−1.12452
$847$	4.93438e12i	0.329425i
$848$	− 3.77275e13i	− 2.50540i
$849$	−3.15028e9	−0.000208096 0
$850$	0	0
$851$	−3.74196e12	−0.244578
$852$	1.60377e10i	0.00104271i
$853$	− 5.65076e12i	− 0.365457i	−0.983163	−	0.182728i	$-0.941507\pi$
$853$	− 5.65076e12i	− 0.365457i	0.983163	−	0.182728i	$-0.0584929\pi$
$854$	9.47818e11	0.0609768
$855$	0	0
$856$	7.51752e13	4.78567
$857$	− 1.42516e12i	− 0.0902503i	−0.998981	−	0.0451251i	$-0.985631\pi$
$857$	− 1.42516e12i	− 0.0902503i	0.998981	−	0.0451251i	$-0.0143687\pi$
$858$	− 2.07104e10i	− 0.00130465i
$859$	−2.77961e13	−1.74186	−0.870932	−	0.491404i	$-0.836484\pi$
$859$	−2.77961e13	−1.74186	−0.870932	+	0.491404i	$0.836484\pi$
$860$	0	0
$861$	−4.11137e9	−0.000254960 0
$862$	5.13878e13i	3.17013i
$863$	− 1.14117e13i	− 0.700326i	−0.936689	−	0.350163i	$-0.886126\pi$
$863$	− 1.14117e13i	− 0.700326i	0.936689	−	0.350163i	$-0.113874\pi$
$864$	9.98525e10	0.00609603
$865$	0	0
$866$	−1.98066e12	−0.119668
$867$	1.95364e9i	0 0.000117425i
$868$	− 1.59602e13i	− 0.954333i
$869$	−7.84908e11	−0.0466906
$870$	0	0
$871$	2.68594e13	1.58130
$872$	− 1.15956e13i	− 0.679153i
$873$	2.81081e13i	1.63782i
$874$	−3.92434e13	−2.27491
$875$	0	0
$876$	1.30408e11	0.00748232
$877$	1.21188e13i	0.691769i	0.938277	+	0.345884i	$0.112421\pi$
$877$	1.21188e13i	0.691769i	−0.938277	+	0.345884i	$0.887579\pi$
$878$	2.56763e13i	1.45816i
$879$	−1.25905e10	−0.000711364 0
$880$	0	0
$881$	−4.60741e12	−0.257671	−0.128836	−	0.991666i	$-0.541124\pi$
$881$	−4.60741e12	−0.257671	−0.128836	+	0.991666i	$0.541124\pi$
$882$	4.74319e12i	0.263914i
$883$	1.04709e13i	0.579642i	0.957081	+	0.289821i	$0.0935958\pi$
$883$	1.04709e13i	0.579642i	−0.957081	+	0.289821i	$0.906404\pi$
$884$	5.02505e13	2.76761
$885$	0	0
$886$	−3.42441e13	−1.86696
$887$	3.68711e12i	0.200000i	0.994987	+	0.0999999i	$0.0318842\pi$
$887$	3.68711e12i	0.200000i	−0.994987	+	0.0999999i	$0.968116\pi$
$888$	− 2.13313e10i	− 0.00115122i
$889$	−4.52015e12	−0.242714
$890$	0	0
$891$	6.74166e12	0.358358
$892$	1.29329e13i	0.683998i
$893$	1.55108e13i	0.816209i
$894$	3.53803e10	0.00185243
$895$	0	0
$896$	−7.08864e10	−0.00367432
$897$	3.50902e10i	0.00180976i
$898$	2.01080e13i	1.03187i
$899$	3.41461e12	0.174350
$900$	0	0
$901$	−1.98290e13	−1.00240
$902$	5.36114e12i	0.269667i
$903$	− 1.15469e10i	0 0.000577922i
$904$	−7.24487e13	−3.60805
$905$	0	0
$906$	4.91305e10	0.00242256
$907$	6.05209e11i	0.0296943i	0.999890	+	0.0148471i	$0.00472616\pi$
$907$	6.05209e11i	0.0296943i	−0.999890	+	0.0148471i	$0.995274\pi$
$908$	2.40956e13i	1.17639i
$909$	1.75480e13	0.852491
$910$	0	0
$911$	−3.27450e12	−0.157512	−0.0787559	−	0.996894i	$-0.525095\pi$
$911$	−3.27450e12	−0.157512	−0.0787559	+	0.996894i	$0.525095\pi$
$912$	− 1.11768e11i	− 0.00534984i
$913$	− 5.82368e12i	− 0.277383i
$914$	−4.82094e13	−2.28494
$915$	0	0
$916$	−7.36467e13	−3.45640
$917$	3.58329e12i	0.167348i
$918$	− 1.26908e11i	− 0.00589790i
$919$	−2.21117e11	−0.0102259	−0.00511295	−	0.999987i	$-0.501628\pi$
$919$	−2.21117e11	−0.0102259	−0.00511295	+	0.999987i	$0.501628\pi$
$920$	0	0
$921$	1.70188e10	0.000779400 0
$922$	2.53732e13i	1.15634i
$923$	6.84688e12i	0.310517i
$924$	−1.19925e10	−0.000541236 0
$925$	0	0
$926$	−3.71100e13	−1.65860
$927$	− 1.40143e13i	− 0.623320i
$928$	6.92817e12i	0.306657i
$929$	4.00147e12	0.176258	0.0881290	−	0.996109i	$-0.471911\pi$
$929$	4.00147e12	0.176258	0.0881290	+	0.996109i	$0.471911\pi$
$930$	0	0
$931$	4.39109e12	0.191557
$932$	− 1.04097e14i	− 4.51927i
$933$	− 5.68073e10i	− 0.00245435i
$934$	4.58899e13	1.97313
$935$	0	0
$936$	7.29372e13	3.10604
$937$	3.76138e10i	0.00159411i	1.00000		0.000797056i	$0.000253711\pi$
$937$	3.76138e10i	0.00159411i	−1.00000		0.000797056i	$0.999746\pi$
$938$	− 2.19990e13i	− 0.927876i
$939$	1.02205e10	0.000429019 0
$940$	0	0
$941$	−2.21494e12	−0.0920894	−0.0460447	−	0.998939i	$-0.514662\pi$
$941$	−2.21494e12	−0.0920894	−0.0460447	+	0.998939i	$0.514662\pi$
$942$	1.16242e11i	0.00480990i
$943$	− 9.08353e12i	− 0.374069i
$944$	−3.81116e13	−1.56201
$945$	0	0
$946$	−1.50568e13	−0.611257
$947$	− 2.36266e13i	− 0.954610i	−0.878738	−	0.477305i	$-0.841614\pi$
$947$	− 2.36266e13i	− 0.954610i	0.878738	−	0.477305i	$-0.158386\pi$
$948$	1.29468e10i	0 0.000520624i
$949$	5.56744e13	2.22822
$950$	0	0
$951$	−5.05694e10	−0.00200482
$952$	− 2.41001e13i	− 0.950939i
$953$	− 1.15037e13i	− 0.451771i	−0.974154	−	0.225885i	$-0.927473\pi$
$953$	− 1.15037e13i	− 0.451771i	0.974154	−	0.225885i	$-0.0725274\pi$
$954$	−4.91516e13	−1.92119
$955$	0	0
$956$	−8.99810e13	−3.48410
$957$	− 2.56574e9i	0 9.88801e-5i
$958$	− 1.30518e13i	− 0.500639i
$959$	7.71003e12	0.294356
$960$	0	0
$961$	2.51218e12	0.0950156
$962$	− 1.55524e13i	− 0.585475i
$963$	− 4.89314e13i	− 1.83345i
$964$	−5.50440e13	−2.05288
$965$	0	0
$966$	2.87404e10	0.00106193
$967$	1.36863e13i	0.503346i	0.967812	+	0.251673i	$0.0809808\pi$
$967$	1.36863e13i	0.503346i	−0.967812	+	0.251673i	$0.919019\pi$
$968$	− 6.21465e13i	− 2.27498i
$969$	−5.87435e10	−0.00214044
$970$	0	0
$971$	9.95259e12	0.359294	0.179647	−	0.983731i	$-0.442504\pi$
$971$	9.95259e12	0.359294	0.179647	+	0.983731i	$0.442504\pi$
$972$	− 3.33605e11i	− 0.0119877i
$973$	− 7.29745e12i	− 0.261014i
$974$	−4.53038e13	−1.61295
$975$	0	0
$976$	−5.96409e12	−0.210387
$977$	− 1.51387e13i	− 0.531575i	−0.964032	−	0.265787i	$-0.914368\pi$
$977$	− 1.51387e13i	− 0.531575i	0.964032	−	0.265787i	$-0.0856319\pi$
$978$	1.36903e11i	0.00478508i
$979$	−1.13438e13	−0.394673
$980$	0	0
$981$	−7.54753e12	−0.260192
$982$	− 8.97498e13i	− 3.07987i
$983$	5.47141e13i	1.86899i	0.355970	+	0.934497i	$0.384151\pi$
$983$	5.47141e13i	1.86899i	−0.355970	+	0.934497i	$0.615849\pi$
$984$	5.17811e10	0.00176073
$985$	0	0
$986$	8.80540e12	0.296690
$987$	− 1.13595e10i	0 0.000381007i
$988$	− 1.15313e14i	− 3.85010i
$989$	2.55112e13	0.847907
$990$	0	0
$991$	4.86384e13	1.60195	0.800974	−	0.598699i	$-0.204316\pi$
$991$	4.86384e13	1.60195	0.800974	+	0.598699i	$0.204316\pi$
$992$	5.87427e13i	1.92598i
$993$	− 8.52557e10i	− 0.00278261i
$994$	5.60789e12	0.182205
$995$	0	0
$996$	−9.60596e10	−0.00309296
$997$	− 2.77758e13i	− 0.890304i	−0.895455	−	0.445152i	$-0.853150\pi$
$997$	− 2.77758e13i	− 0.890304i	0.895455	−	0.445152i	$-0.146850\pi$
$998$	− 7.76283e13i	− 2.47704i
$999$	−2.77690e10	−0.000882096 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.d.99.1		6
5.2	odd	4		7.10.a.b.1.3	✓	3
5.3	odd	4		175.10.a.d.1.1		3
5.4	even	2	inner	175.10.b.d.99.6		6
15.2	even	4		63.10.a.e.1.1		3
20.7	even	4		112.10.a.h.1.2		3
35.2	odd	12		49.10.c.d.18.1		6
35.12	even	12		49.10.c.e.18.1		6
35.17	even	12		49.10.c.e.30.1		6
35.27	even	4		49.10.a.c.1.3		3
35.32	odd	12		49.10.c.d.30.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.3	✓	3	5.2	odd	4
49.10.a.c.1.3		3	35.27	even	4
49.10.c.d.18.1		6	35.2	odd	12
49.10.c.d.30.1		6	35.32	odd	12
49.10.c.e.18.1		6	35.12	even	12
49.10.c.e.30.1		6	35.17	even	12
63.10.a.e.1.1		3	15.2	even	4
112.10.a.h.1.2		3	20.7	even	4
175.10.a.d.1.1		3	5.3	odd	4
175.10.b.d.99.1		6	1.1	even	1	trivial
175.10.b.d.99.6		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)

\(f(q)\)	\(=\)	\(q-41.8019i q^{2} +0.232339i q^{3} -1235.40 q^{4} +9.71222 q^{6} -2401.00i q^{7} +30239.6i q^{8} +19682.9 q^{9} +17401.5 q^{11} -287.032i q^{12} -122541. i q^{13} -100366. q^{14} +631550. q^{16} -331933. i q^{17} -822785. i q^{18} -761707. q^{19} +557.846 q^{21} -727418. i q^{22} +1.23249e6i q^{23} -7025.85 q^{24} -5.12246e6 q^{26} +9146.25i q^{27} +2.96620e6i q^{28} -634604. q^{29} -5.38069e6 q^{31} -1.09173e7i q^{32} +4043.06i q^{33} -1.38754e7 q^{34} -2.43164e7 q^{36} +3.03611e6i q^{37} +3.18408e7i q^{38} +28471.1 q^{39} -7.37009e6 q^{41} -23319.1i q^{42} -2.06990e7i q^{43} -2.14979e7 q^{44} +5.15203e7 q^{46} -2.03632e7i q^{47} +146734. i q^{48} -5.76480e6 q^{49} +77120.9 q^{51} +1.51388e8i q^{52} -5.97380e7i q^{53} +382331. q^{54} +7.26054e7 q^{56} -176974. i q^{57} +2.65277e7i q^{58} -6.03461e7 q^{59} -9.44357e6 q^{61} +2.24923e8i q^{62} -4.72588e7i q^{63} -1.33012e8 q^{64} +169008. q^{66} +2.19187e8i q^{67} +4.10071e8i q^{68} -286355. q^{69} -5.58741e7 q^{71} +5.95205e8i q^{72} +4.54332e8i q^{73} +1.26915e8 q^{74} +9.41015e8 q^{76} -4.17811e7i q^{77} -1.19015e6i q^{78} -4.51057e7 q^{79} +3.87417e8 q^{81} +3.08084e8i q^{82} -3.34665e8i q^{83} -689165. q^{84} -8.65259e8 q^{86} -147443. i q^{87} +5.26216e8i q^{88} -6.51886e8 q^{89} -2.94221e8 q^{91} -1.52262e9i q^{92} -1.25014e6i q^{93} -8.51220e8 q^{94} +2.53652e6 q^{96} +1.42804e9i q^{97} +2.40980e8i q^{98} +3.42514e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3114 q^{4} + 9828 q^{6} + 52002 q^{9} - 6888 q^{11} - 100842 q^{14} + 965922 q^{16} - 445704 q^{19} + 403368 q^{21} + 2899260 q^{24} - 17570112 q^{26} - 8163636 q^{29} + 5738880 q^{31} + 7963284 q^{34}+ \cdots + 3801958344 q^{99}+O(q^{100}) \) 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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