LMFDB - Embedded newform 175.10.b.d.99.4

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			99.4
Root			$22.2358i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.d.99.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+13.3607i q^{2} -163.415i q^{3} +333.491 q^{4} +2183.34 q^{6} +2401.00i q^{7} +11296.4i q^{8} -7021.32 q^{9} -90199.9 q^{11} -54497.3i q^{12} +3199.89i q^{13} -32079.1 q^{14} +19819.7 q^{16} +116494. i q^{17} -93809.9i q^{18} +142449. q^{19} +392358. q^{21} -1.20514e6i q^{22} -1.27391e6i q^{23} +1.84599e6 q^{24} -42752.8 q^{26} -2.06910e6i q^{27} +800712. i q^{28} +1.42931e6 q^{29} +9.67494e6 q^{31} +6.04855e6i q^{32} +1.47400e7i q^{33} -1.55645e6 q^{34} -2.34155e6 q^{36} -8.67744e6i q^{37} +1.90323e6i q^{38} +522908. q^{39} +1.32544e7 q^{41} +5.24219e6i q^{42} +2.97554e7i q^{43} -3.00809e7 q^{44} +1.70204e7 q^{46} -1.07969e7i q^{47} -3.23882e6i q^{48} -5.76480e6 q^{49} +1.90369e7 q^{51} +1.06713e6i q^{52} -7.07399e7i q^{53} +2.76447e7 q^{54} -2.71226e7 q^{56} -2.32783e7i q^{57} +1.90966e7i q^{58} -6.40400e6 q^{59} +1.69190e8 q^{61} +1.29264e8i q^{62} -1.68582e7i q^{63} -7.06653e7 q^{64} -1.96937e8 q^{66} -1.16276e8i q^{67} +3.88498e7i q^{68} -2.08176e8 q^{69} +1.44496e8 q^{71} -7.93154e7i q^{72} -1.60155e8i q^{73} +1.15937e8 q^{74} +4.75056e7 q^{76} -2.16570e8i q^{77} +6.98643e6i q^{78} +4.89322e8 q^{79} -4.76322e8 q^{81} +1.77088e8i q^{82} +8.31590e7i q^{83} +1.30848e8 q^{84} -3.97553e8 q^{86} -2.33569e8i q^{87} -1.01893e9i q^{88} -2.08083e6 q^{89} -7.68292e6 q^{91} -4.24838e8i q^{92} -1.58103e9i q^{93} +1.44255e8 q^{94} +9.88421e8 q^{96} -3.15885e8i q^{97} -7.70219e7i q^{98} +6.33322e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	13.3607i	0.590466i	0.955425	+	0.295233i	$0.0953973\pi$
$2$	13.3607i	0.590466i	−0.955425	+	0.295233i	$0.904603\pi$
$3$	− 163.415i	− 1.16478i	−0.812908	−	0.582392i	$-0.802117\pi$
$3$	− 163.415i	− 1.16478i	0.812908	−	0.582392i	$-0.197883\pi$
$4$	333.491	0.651350
$5$	0	0
$5$	0	0
$6$	2183.34	0.687765
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	11296.4i	0.975066i
$9$	−7021.32	−0.356720
$10$	0	0
$11$	−90199.9	−1.85754	−0.928772	−	0.370652i	$-0.879134\pi$
$11$	−90199.9	−1.85754	−0.928772	+	0.370652i	$0.879134\pi$
$12$	− 54497.3i	− 0.758681i
$13$	3199.89i	0.0310734i	0.999879	+	0.0155367i	$0.00494569\pi$
$13$	3199.89i	0.0310734i	−0.999879	+	0.0155367i	$0.995054\pi$
$14$	−32079.1	−0.223175
$15$	0	0
$16$	19819.7	0.0756061
$17$	116494.i	0.338286i	0.985591	+	0.169143i	$0.0541000\pi$
$17$	116494.i	0.338286i	−0.985591	+	0.169143i	$0.945900\pi$
$18$	− 93809.9i	− 0.210631i
$19$	142449.	0.250767	0.125383	−	0.992108i	$-0.459984\pi$
$19$	142449.	0.250767	0.125383	+	0.992108i	$0.459984\pi$
$20$	0	0
$21$	392358.	0.440247
$22$	− 1.20514e6i	− 1.09682i
$23$	− 1.27391e6i	− 0.949213i	−0.880198	−	0.474606i	$-0.842590\pi$
$23$	− 1.27391e6i	− 0.949213i	0.880198	−	0.474606i	$-0.157410\pi$
$24$	1.84599e6	1.13574
$25$	0	0
$26$	−42752.8	−0.0183478
$27$	− 2.06910e6i	− 0.749282i
$28$	800712.i	0.246187i
$29$	1.42931e6	0.375262	0.187631	−	0.982240i	$-0.439919\pi$
$29$	1.42931e6	0.375262	0.187631	+	0.982240i	$0.439919\pi$
$30$	0	0
$31$	9.67494e6	1.88157	0.940786	−	0.339001i	$-0.110089\pi$
$31$	9.67494e6	1.88157	0.940786	+	0.339001i	$0.110089\pi$
$32$	6.04855e6i	1.01971i
$33$	1.47400e7i	2.16364i
$34$	−1.55645e6	−0.199747
$35$	0	0
$36$	−2.34155e6	−0.232349
$37$	− 8.67744e6i	− 0.761174i	−0.924745	−	0.380587i	$-0.875722\pi$
$37$	− 8.67744e6i	− 0.761174i	0.924745	−	0.380587i	$-0.124278\pi$
$38$	1.90323e6i	0.148069i
$39$	522908.	0.0361938
$40$	0	0
$41$	1.32544e7	0.732541	0.366271	−	0.930508i	$-0.380634\pi$
$41$	1.32544e7	0.732541	0.366271	+	0.930508i	$0.380634\pi$
$42$	5.24219e6i	0.259951i
$43$	2.97554e7i	1.32726i	0.748060	+	0.663632i	$0.230986\pi$
$43$	2.97554e7i	1.32726i	−0.748060	+	0.663632i	$0.769014\pi$
$44$	−3.00809e7	−1.20991
$45$	0	0
$46$	1.70204e7	0.560478
$47$	− 1.07969e7i	− 0.322745i	−0.986894	−	0.161373i	$-0.948408\pi$
$47$	− 1.07969e7i	− 0.322745i	0.986894	−	0.161373i	$-0.0515921\pi$
$48$	− 3.23882e6i	− 0.0880647i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	1.90369e7	0.394030
$52$	1.06713e6i	0.0202397i
$53$	− 7.07399e7i	− 1.23147i	−0.787954	−	0.615734i	$-0.788860\pi$
$53$	− 7.07399e7i	− 1.23147i	0.787954	−	0.615734i	$-0.211140\pi$
$54$	2.76447e7	0.442426
$55$	0	0
$56$	−2.71226e7	−0.368540
$57$	− 2.32783e7i	− 0.292089i
$58$	1.90966e7i	0.221579i
$59$	−6.40400e6	−0.0688046	−0.0344023	−	0.999408i	$-0.510953\pi$
$59$	−6.40400e6	−0.0688046	−0.0344023	+	0.999408i	$0.510953\pi$
$60$	0	0
$61$	1.69190e8	1.56455	0.782275	−	0.622933i	$-0.214059\pi$
$61$	1.69190e8	1.56455	0.782275	+	0.622933i	$0.214059\pi$
$62$	1.29264e8i	1.11100i
$63$	− 1.68582e7i	− 0.134827i
$64$	−7.06653e7	−0.526498
$65$	0	0
$66$	−1.96937e8	−1.27755
$67$	− 1.16276e8i	− 0.704943i	−0.935823	−	0.352471i	$-0.885341\pi$
$67$	− 1.16276e8i	− 0.704943i	0.935823	−	0.352471i	$-0.114659\pi$
$68$	3.88498e7i	0.220343i
$69$	−2.08176e8	−1.10563
$70$	0	0
$71$	1.44496e8	0.674826	0.337413	−	0.941357i	$-0.390448\pi$
$71$	1.44496e8	0.674826	0.337413	+	0.941357i	$0.390448\pi$
$72$	− 7.93154e7i	− 0.347825i
$73$	− 1.60155e8i	− 0.660066i	−0.943969	−	0.330033i	$-0.892940\pi$
$73$	− 1.60155e8i	− 0.660066i	0.943969	−	0.330033i	$-0.107060\pi$
$74$	1.15937e8	0.449447
$75$	0	0
$76$	4.75056e7	0.163337
$77$	− 2.16570e8i	− 0.702085i
$78$	6.98643e6i	0.0213712i
$79$	4.89322e8	1.41343	0.706713	−	0.707500i	$-0.250177\pi$
$79$	4.89322e8	1.41343	0.706713	+	0.707500i	$0.250177\pi$
$80$	0	0
$81$	−4.76322e8	−1.22947
$82$	1.77088e8i	0.432541i
$83$	8.31590e7i	0.192335i	0.995365	+	0.0961674i	$0.0306584\pi$
$83$	8.31590e7i	0.192335i	−0.995365	+	0.0961674i	$0.969342\pi$
$84$	1.30848e8	0.286755
$85$	0	0
$86$	−3.97553e8	−0.783704
$87$	− 2.33569e8i	− 0.437098i
$88$	− 1.01893e9i	− 1.81123i
$89$	−2.08083e6	−0.00351546	−0.00175773	−	0.999998i	$-0.500560\pi$
$89$	−2.08083e6	−0.00351546	−0.00175773	+	0.999998i	$0.500560\pi$
$90$	0	0
$91$	−7.68292e6	−0.0117447
$92$	− 4.24838e8i	− 0.618270i
$93$	− 1.58103e9i	− 2.19162i
$94$	1.44255e8	0.190570
$95$	0	0
$96$	9.88421e8	1.18774
$97$	− 3.15885e8i	− 0.362290i	−0.983456	−	0.181145i	$-0.942020\pi$
$97$	− 3.15885e8i	− 0.362290i	0.983456	−	0.181145i	$-0.0579803\pi$
$98$	− 7.70219e7i	− 0.0843523i
$99$	6.33322e8	0.662623
$100$	0	0
$101$	−5.74841e8	−0.549669	−0.274835	−	0.961492i	$-0.588623\pi$
$101$	−5.74841e8	−0.549669	−0.274835	+	0.961492i	$0.588623\pi$
$102$	2.54346e8i	0.232662i
$103$	1.51870e9i	1.32955i	0.747044	+	0.664775i	$0.231473\pi$
$103$	1.51870e9i	1.32955i	−0.747044	+	0.664775i	$0.768527\pi$
$104$	−3.61471e7	−0.0302987
$105$	0	0
$106$	9.45137e8	0.727140
$107$	− 2.01863e8i	− 0.148878i	−0.997226	−	0.0744390i	$-0.976283\pi$
$107$	− 2.01863e8i	− 0.148878i	0.997226	−	0.0744390i	$-0.0237166\pi$
$108$	− 6.90027e8i	− 0.488044i
$109$	8.73952e8	0.593019	0.296509	−	0.955030i	$-0.404177\pi$
$109$	8.73952e8	0.593019	0.296509	+	0.955030i	$0.404177\pi$
$110$	0	0
$111$	−1.41802e9	−0.886603
$112$	4.75871e7i	0.0285764i
$113$	− 1.52955e9i	− 0.882491i	−0.897386	−	0.441245i	$-0.854537\pi$
$113$	− 1.52955e9i	− 0.882491i	0.897386	−	0.441245i	$-0.145463\pi$
$114$	3.11015e8	0.172469
$115$	0	0
$116$	4.76661e8	0.244427
$117$	− 2.24674e7i	− 0.0110845i
$118$	− 8.55621e7i	− 0.0406268i
$119$	−2.79703e8	−0.127860
$120$	0	0
$121$	5.77807e9	2.45047
$122$	2.26050e9i	0.923814i
$123$	− 2.16596e9i	− 0.853252i
$124$	3.22651e9	1.22556
$125$	0	0
$126$	2.25238e8	0.0796110
$127$	− 8.71958e8i	− 0.297426i	−0.988880	−	0.148713i	$-0.952487\pi$
$127$	− 8.71958e8i	− 0.297426i	0.988880	−	0.148713i	$-0.0475130\pi$
$128$	2.15272e9i	0.708830i
$129$	4.86246e9	1.54597
$130$	0	0
$131$	2.24404e9	0.665747	0.332874	−	0.942971i	$-0.391982\pi$
$131$	2.24404e9	0.665747	0.332874	+	0.942971i	$0.391982\pi$
$132$	4.91565e9i	1.40928i
$133$	3.42021e8i	0.0947809i
$134$	1.55353e9	0.416245
$135$	0	0
$136$	−1.31596e9	−0.329852
$137$	4.16141e9i	1.00925i	0.863339	+	0.504624i	$0.168369\pi$
$137$	4.16141e9i	1.00925i	−0.863339	+	0.504624i	$0.831631\pi$
$138$	− 2.78138e9i	− 0.652836i
$139$	6.03383e9	1.37097	0.685483	−	0.728089i	$-0.259591\pi$
$139$	6.03383e9	1.37097	0.685483	+	0.728089i	$0.259591\pi$
$140$	0	0
$141$	−1.76438e9	−0.375928
$142$	1.93057e9i	0.398462i
$143$	− 2.88629e8i	− 0.0577203i
$144$	−1.39160e8	−0.0269702
$145$	0	0
$146$	2.13979e9	0.389747
$147$	9.42052e8i	0.166398i
$148$	− 2.89385e9i	− 0.495790i
$149$	4.37832e9	0.727728	0.363864	−	0.931452i	$-0.381457\pi$
$149$	4.37832e9	0.727728	0.363864	+	0.931452i	$0.381457\pi$
$150$	0	0
$151$	−2.69365e9	−0.421642	−0.210821	−	0.977525i	$-0.567614\pi$
$151$	−2.69365e9	−0.421642	−0.210821	+	0.977525i	$0.567614\pi$
$152$	1.60916e9i	0.244514i
$153$	− 8.17943e8i	− 0.120673i
$154$	2.89353e9	0.414558
$155$	0	0
$156$	1.74385e8	0.0235748
$157$	− 1.33044e9i	− 0.174762i	−0.996175	−	0.0873810i	$-0.972150\pi$
$157$	− 1.33044e9i	− 0.174762i	0.996175	−	0.0873810i	$-0.0278498\pi$
$158$	6.53770e9i	0.834580i
$159$	−1.15599e10	−1.43439
$160$	0	0
$161$	3.05866e9	0.358769
$162$	− 6.36401e9i	− 0.725961i
$163$	3.56094e9i	0.395112i	0.980292	+	0.197556i	$0.0633005\pi$
$163$	3.56094e9i	0.395112i	−0.980292	+	0.197556i	$0.936699\pi$
$164$	4.42022e9	0.477140
$165$	0	0
$166$	−1.11106e9	−0.113567
$167$	− 1.04285e10i	− 1.03752i	−0.854919	−	0.518762i	$-0.826393\pi$
$167$	− 1.04285e10i	− 1.03752i	0.854919	−	0.518762i	$-0.173607\pi$
$168$	4.43223e9i	0.429270i
$169$	1.05943e10	0.999034
$170$	0	0
$171$	−1.00018e9	−0.0894534
$172$	9.92314e9i	0.864512i
$173$	− 2.04717e10i	− 1.73759i	−0.495176	−	0.868793i	$-0.664896\pi$
$173$	− 2.04717e10i	− 1.73759i	0.495176	−	0.868793i	$-0.335104\pi$
$174$	3.12066e9	0.258092
$175$	0	0
$176$	−1.78773e9	−0.140442
$177$	1.04651e9i	0.0801424i
$178$	− 2.78014e7i	− 0.00207576i
$179$	−5.46705e9	−0.398029	−0.199014	−	0.979997i	$-0.563774\pi$
$179$	−5.46705e9	−0.398029	−0.199014	+	0.979997i	$0.563774\pi$
$180$	0	0
$181$	−2.11628e9	−0.146561	−0.0732807	−	0.997311i	$-0.523347\pi$
$181$	−2.11628e9	−0.146561	−0.0732807	+	0.997311i	$0.523347\pi$
$182$	− 1.02649e8i	− 0.00693482i
$183$	− 2.76481e10i	− 1.82236i
$184$	1.43906e10	0.925545
$185$	0	0
$186$	2.11237e10	1.29408
$187$	− 1.05078e10i	− 0.628381i
$188$	− 3.60068e9i	− 0.210220i
$189$	4.96792e9	0.283202
$190$	0	0
$191$	1.72421e10	0.937431	0.468715	−	0.883349i	$-0.344717\pi$
$191$	1.72421e10	0.937431	0.468715	+	0.883349i	$0.344717\pi$
$192$	1.15477e10i	0.613256i
$193$	− 2.02030e10i	− 1.04811i	−0.851684	−	0.524055i	$-0.824418\pi$
$193$	− 2.02030e10i	− 1.04811i	0.851684	−	0.524055i	$-0.175582\pi$
$194$	4.22045e9	0.213920
$195$	0	0
$196$	−1.92251e9	−0.0930500
$197$	− 2.22592e10i	− 1.05296i	−0.850187	−	0.526481i	$-0.823511\pi$
$197$	− 2.22592e10i	− 1.05296i	0.850187	−	0.526481i	$-0.176489\pi$
$198$	8.46164e9i	0.391256i
$199$	−1.70588e10	−0.771098	−0.385549	−	0.922687i	$-0.625988\pi$
$199$	−1.70588e10	−0.771098	−0.385549	+	0.922687i	$0.625988\pi$
$200$	0	0
$201$	−1.90012e10	−0.821105
$202$	− 7.68029e9i	− 0.324561i
$203$	3.43176e9i	0.141836i
$204$	6.34862e9	0.256651
$205$	0	0
$206$	−2.02909e10	−0.785054
$207$	8.94453e9i	0.338603i
$208$	6.34207e7i	0.00234934i
$209$	−1.28489e10	−0.465810
$210$	0	0
$211$	−3.19873e10	−1.11098	−0.555490	−	0.831523i	$-0.687469\pi$
$211$	−3.19873e10	−1.11098	−0.555490	+	0.831523i	$0.687469\pi$
$212$	− 2.35911e10i	− 0.802116i
$213$	− 2.36127e10i	− 0.786026i
$214$	2.69704e9	0.0879074
$215$	0	0
$216$	2.33734e10	0.730599
$217$	2.32295e10i	0.711167i
$218$	1.16766e10i	0.350157i
$219$	−2.61717e10	−0.768834
$220$	0	0
$221$	−3.72768e8	−0.0105117
$222$	− 1.89458e10i	− 0.523509i
$223$	2.30967e10i	0.625428i	0.949847	+	0.312714i	$0.101238\pi$
$223$	2.30967e10i	0.625428i	−0.949847	+	0.312714i	$0.898762\pi$
$224$	−1.45226e10	−0.385414
$225$	0	0
$226$	2.04359e10	0.521081
$227$	− 2.30894e10i	− 0.577160i	−0.957456	−	0.288580i	$-0.906817\pi$
$227$	− 2.30894e10i	− 0.577160i	0.957456	−	0.288580i	$-0.0931832\pi$
$228$	− 7.76311e9i	− 0.190252i
$229$	−4.25496e10	−1.02244	−0.511218	−	0.859451i	$-0.670805\pi$
$229$	−4.25496e10	−1.02244	−0.511218	+	0.859451i	$0.670805\pi$
$230$	0	0
$231$	−3.53907e10	−0.817777
$232$	1.61460e10i	0.365905i
$233$	1.26679e10i	0.281582i	0.990039	+	0.140791i	$0.0449645\pi$
$233$	1.26679e10i	0.281582i	−0.990039	+	0.140791i	$0.955036\pi$
$234$	3.00181e8	0.00654503
$235$	0	0
$236$	−2.13568e9	−0.0448158
$237$	− 7.99624e10i	− 1.64633i
$238$	− 3.73703e9i	− 0.0754971i
$239$	−6.37875e10	−1.26458	−0.632289	−	0.774733i	$-0.717884\pi$
$239$	−6.37875e10	−1.26458	−0.632289	+	0.774733i	$0.717884\pi$
$240$	0	0
$241$	−2.91604e10	−0.556823	−0.278412	−	0.960462i	$-0.589808\pi$
$241$	−2.91604e10	−0.556823	−0.278412	+	0.960462i	$0.589808\pi$
$242$	7.71992e10i	1.44692i
$243$	3.71118e10i	0.682785i
$244$	5.64232e10	1.01907
$245$	0	0
$246$	2.89388e10	0.503816
$247$	4.55822e8i	0.00779218i
$248$	1.09292e11i	1.83466i
$249$	1.35894e10	0.224028
$250$	0	0
$251$	6.28939e10	1.00018	0.500088	−	0.865974i	$-0.333301\pi$
$251$	6.28939e10	1.00018	0.500088	+	0.865974i	$0.333301\pi$
$252$	− 5.62205e9i	− 0.0878198i
$253$	1.14907e11i	1.76320i
$254$	1.16500e10	0.175620
$255$	0	0
$256$	−6.49425e10	−0.945038
$257$	1.14480e11i	1.63694i	0.574551	+	0.818469i	$0.305177\pi$
$257$	1.14480e11i	1.63694i	−0.574551	+	0.818469i	$0.694823\pi$
$258$	6.49660e10i	0.912845i
$259$	2.08345e10	0.287697
$260$	0	0
$261$	−1.00356e10	−0.133863
$262$	2.99820e10i	0.393101i
$263$	− 1.40705e10i	− 0.181346i	−0.995881	−	0.0906728i	$-0.971098\pi$
$263$	− 1.40705e10i	− 0.181346i	0.995881	−	0.0906728i	$-0.0289018\pi$
$264$	−1.66508e11	−2.10969
$265$	0	0
$266$	−4.56965e9	−0.0559649
$267$	3.40038e8i	0.00409475i
$268$	− 3.87770e10i	− 0.459164i
$269$	−8.39143e10	−0.977127	−0.488563	−	0.872528i	$-0.662479\pi$
$269$	−8.39143e10	−0.977127	−0.488563	+	0.872528i	$0.662479\pi$
$270$	0	0
$271$	1.98401e10	0.223451	0.111726	−	0.993739i	$-0.464362\pi$
$271$	1.98401e10	0.223451	0.111726	+	0.993739i	$0.464362\pi$
$272$	2.30888e9i	0.0255765i
$273$	1.25550e9i	0.0136800i
$274$	−5.55995e10	−0.595927
$275$	0	0
$276$	−6.94247e10	−0.720150
$277$	− 7.17911e10i	− 0.732675i	−0.930482	−	0.366338i	$-0.880611\pi$
$277$	− 7.17911e10i	− 0.732675i	0.930482	−	0.366338i	$-0.119389\pi$
$278$	8.06163e10i	0.809508i
$279$	−6.79308e10	−0.671194
$280$	0	0
$281$	1.02853e11	0.984101	0.492050	−	0.870567i	$-0.336248\pi$
$281$	1.02853e11	0.984101	0.492050	+	0.870567i	$0.336248\pi$
$282$	− 2.35733e10i	− 0.221973i
$283$	5.52883e10i	0.512382i	0.966626	+	0.256191i	$0.0824676\pi$
$283$	5.52883e10i	0.512382i	−0.966626	+	0.256191i	$0.917532\pi$
$284$	4.81880e10	0.439548
$285$	0	0
$286$	3.85630e9	0.0340819
$287$	3.18238e10i	0.276875i
$288$	− 4.24688e10i	− 0.363750i
$289$	1.05017e11	0.885562
$290$	0	0
$291$	−5.16202e10	−0.421989
$292$	− 5.34102e10i	− 0.429934i
$293$	− 1.05721e11i	− 0.838028i	−0.907980	−	0.419014i	$-0.862376\pi$
$293$	− 1.05721e11i	− 0.838028i	0.907980	−	0.419014i	$-0.137624\pi$
$294$	−1.25865e10	−0.0982522
$295$	0	0
$296$	9.80236e10	0.742195
$297$	1.86633e11i	1.39182i
$298$	5.84975e10i	0.429699i
$299$	4.07637e9	0.0294953
$300$	0	0
$301$	−7.14426e10	−0.501658
$302$	− 3.59891e10i	− 0.248966i
$303$	9.39374e10i	0.640246i
$304$	2.82330e9	0.0189595
$305$	0	0
$306$	1.09283e10	0.0712536
$307$	− 8.10064e10i	− 0.520471i	−0.965545	−	0.260236i	$-0.916200\pi$
$307$	− 8.10064e10i	− 0.520471i	0.965545	−	0.260236i	$-0.0838003\pi$
$308$	− 7.22241e10i	− 0.457303i
$309$	2.48178e11	1.54864
$310$	0	0
$311$	−3.18435e11	−1.93018	−0.965091	−	0.261913i	$-0.915647\pi$
$311$	−3.18435e11	−1.93018	−0.965091	+	0.261913i	$0.915647\pi$
$312$	5.90696e9i	0.0352914i
$313$	− 1.28876e11i	− 0.758965i	−0.925199	−	0.379483i	$-0.876102\pi$
$313$	− 1.28876e11i	− 0.758965i	0.925199	−	0.379483i	$-0.123898\pi$
$314$	1.77757e10	0.103191
$315$	0	0
$316$	1.63185e11	0.920635
$317$	− 7.44722e10i	− 0.414217i	−0.978318	−	0.207108i	$-0.933595\pi$
$317$	− 7.44722e10i	− 0.414217i	0.978318	−	0.207108i	$-0.0664053\pi$
$318$	− 1.54449e11i	− 0.846961i
$319$	−1.28923e11	−0.697065
$320$	0	0
$321$	−3.29874e10	−0.173411
$322$	4.08659e10i	0.211841i
$323$	1.65945e10i	0.0848309i
$324$	−1.58849e11	−0.800815
$325$	0	0
$326$	−4.75768e10	−0.233301
$327$	− 1.42816e11i	− 0.690738i
$328$	1.49726e11i	0.714276i
$329$	2.59234e10	0.121986
$330$	0	0
$331$	2.83840e11	1.29971	0.649857	−	0.760057i	$-0.274829\pi$
$331$	2.83840e11	1.29971	0.649857	+	0.760057i	$0.274829\pi$
$332$	2.77328e10i	0.125277i
$333$	6.09271e10i	0.271526i
$334$	1.39332e11	0.612623
$335$	0	0
$336$	7.77642e9	0.0332853
$337$	− 5.61414e9i	− 0.0237109i	−0.999930	−	0.0118555i	$-0.996226\pi$
$337$	− 5.61414e9i	− 0.0237109i	0.999930	−	0.0118555i	$-0.00377380\pi$
$338$	1.41547e11i	0.589896i
$339$	−2.49950e11	−1.02791
$340$	0	0
$341$	−8.72679e11	−3.49510
$342$	− 1.33632e10i	− 0.0528192i
$343$	− 1.38413e10i	− 0.0539949i
$344$	−3.36128e11	−1.29417
$345$	0	0
$346$	2.73517e11	1.02599
$347$	3.39846e11i	1.25834i	0.777267	+	0.629171i	$0.216606\pi$
$347$	3.39846e11i	1.25834i	−0.777267	+	0.629171i	$0.783394\pi$
$348$	− 7.78933e10i	− 0.284704i
$349$	−3.46718e10	−0.125101	−0.0625506	−	0.998042i	$-0.519923\pi$
$349$	−3.46718e10	−0.125101	−0.0625506	+	0.998042i	$0.519923\pi$
$350$	0	0
$351$	6.62089e9	0.0232828
$352$	− 5.45578e11i	− 1.89415i
$353$	3.46900e11i	1.18910i	0.804059	+	0.594550i	$0.202670\pi$
$353$	3.46900e11i	1.18910i	−0.804059	+	0.594550i	$0.797330\pi$
$354$	−1.39821e10	−0.0473214
$355$	0	0
$356$	−6.93939e8	−0.00228979
$357$	4.57075e10i	0.148929i
$358$	− 7.30438e10i	− 0.235023i
$359$	2.51011e11	0.797569	0.398785	−	0.917045i	$-0.369432\pi$
$359$	2.51011e11	0.797569	0.398785	+	0.917045i	$0.369432\pi$
$360$	0	0
$361$	−3.02396e11	−0.937116
$362$	− 2.82750e10i	− 0.0865396i
$363$	− 9.44221e11i	− 2.85426i
$364$	−2.56219e9	−0.00764988
$365$	0	0
$366$	3.69398e11	1.07604
$367$	4.79871e11i	1.38079i	0.723433	+	0.690394i	$0.242563\pi$
$367$	4.79871e11i	1.38079i	−0.723433	+	0.690394i	$0.757437\pi$
$368$	− 2.52485e10i	− 0.0717663i
$369$	−9.30632e10	−0.261312
$370$	0	0
$371$	1.69847e11	0.465451
$372$	− 5.27258e11i	− 1.42751i
$373$	1.84794e11i	0.494308i	0.968976	+	0.247154i	$0.0794954\pi$
$373$	1.84794e11i	0.494308i	−0.968976	+	0.247154i	$0.920505\pi$
$374$	1.40391e11	0.371038
$375$	0	0
$376$	1.21966e11	0.314698
$377$	4.57361e9i	0.0116607i
$378$	6.63750e10i	0.167221i
$379$	7.08908e11	1.76487	0.882437	−	0.470431i	$-0.155902\pi$
$379$	7.08908e11	1.76487	0.882437	+	0.470431i	$0.155902\pi$
$380$	0	0
$381$	−1.42491e11	−0.346437
$382$	2.30367e11i	0.553521i
$383$	− 1.23789e11i	− 0.293959i	−0.989140	−	0.146980i	$-0.953045\pi$
$383$	− 1.23789e11i	− 0.293959i	0.989140	−	0.146980i	$-0.0469552\pi$
$384$	3.51785e11	0.825633
$385$	0	0
$386$	2.69926e11	0.618874
$387$	− 2.08922e11i	− 0.473461i
$388$	− 1.05345e11i	− 0.235977i
$389$	2.97971e11	0.659782	0.329891	−	0.944019i	$-0.392988\pi$
$389$	2.97971e11	0.659782	0.329891	+	0.944019i	$0.392988\pi$
$390$	0	0
$391$	1.48403e11	0.321106
$392$	− 6.51213e10i	− 0.139295i
$393$	− 3.66708e11i	− 0.775451i
$394$	2.97400e11	0.621738
$395$	0	0
$396$	2.11207e11	0.431599
$397$	5.33426e11i	1.07775i	0.842387	+	0.538873i	$0.181150\pi$
$397$	5.33426e11i	1.07775i	−0.842387	+	0.538873i	$0.818850\pi$
$398$	− 2.27918e11i	− 0.455307i
$399$	5.58912e10	0.110399
$400$	0	0
$401$	4.15640e11	0.802726	0.401363	−	0.915919i	$-0.368537\pi$
$401$	4.15640e11	0.802726	0.401363	+	0.915919i	$0.368537\pi$
$402$	− 2.53870e11i	− 0.484835i
$403$	3.09587e10i	0.0584669i
$404$	−1.91704e11	−0.358027
$405$	0	0
$406$	−4.58508e10	−0.0837491
$407$	7.82704e11i	1.41391i
$408$	2.15047e11i	0.384206i
$409$	−1.07978e12	−1.90801	−0.954006	−	0.299788i	$-0.903084\pi$
$409$	−1.07978e12	−1.90801	−0.954006	+	0.299788i	$0.903084\pi$
$410$	0	0
$411$	6.80035e11	1.17556
$412$	5.06473e11i	0.866002i
$413$	− 1.53760e10i	− 0.0260057i
$414$	−1.19505e11	−0.199934
$415$	0	0
$416$	−1.93547e10	−0.0316859
$417$	− 9.86015e11i	− 1.59688i
$418$	− 1.71671e11i	− 0.275045i
$419$	2.20998e11	0.350289	0.175144	−	0.984543i	$-0.443961\pi$
$419$	2.20998e11	0.350289	0.175144	+	0.984543i	$0.443961\pi$
$420$	0	0
$421$	3.47478e11	0.539086	0.269543	−	0.962988i	$-0.413127\pi$
$421$	3.47478e11	0.539086	0.269543	+	0.962988i	$0.413127\pi$
$422$	− 4.27373e11i	− 0.655996i
$423$	7.58087e10i	0.115130i
$424$	7.99105e11	1.20076
$425$	0	0
$426$	3.15483e11	0.464122
$427$	4.06224e11i	0.591344i
$428$	− 6.73196e10i	− 0.0969716i
$429$	−4.71662e10	−0.0672316
$430$	0	0
$431$	1.23574e11	0.172496	0.0862479	−	0.996274i	$-0.472512\pi$
$431$	1.23574e11	0.172496	0.0862479	+	0.996274i	$0.472512\pi$
$432$	− 4.10090e10i	− 0.0566503i
$433$	7.27679e11i	0.994820i	0.867516	+	0.497410i	$0.165716\pi$
$433$	7.27679e11i	0.994820i	−0.867516	+	0.497410i	$0.834284\pi$
$434$	−3.10363e11	−0.419920
$435$	0	0
$436$	2.91455e11	0.386262
$437$	− 1.81468e11i	− 0.238031i
$438$	− 3.49672e11i	− 0.453970i
$439$	5.85966e11	0.752977	0.376489	−	0.926421i	$-0.377131\pi$
$439$	5.85966e11	0.752977	0.376489	+	0.926421i	$0.377131\pi$
$440$	0	0
$441$	4.04765e10	0.0509600
$442$	− 4.98045e9i	− 0.00620681i
$443$	2.11546e11i	0.260969i	0.991450	+	0.130484i	$0.0416533\pi$
$443$	2.11546e11i	0.260969i	−0.991450	+	0.130484i	$0.958347\pi$
$444$	−4.72897e11	−0.577488
$445$	0	0
$446$	−3.08588e11	−0.369294
$447$	− 7.15480e11i	− 0.847645i
$448$	− 1.69667e11i	− 0.198997i
$449$	9.21048e11	1.06948	0.534741	−	0.845016i	$-0.320409\pi$
$449$	9.21048e11	1.06948	0.534741	+	0.845016i	$0.320409\pi$
$450$	0	0
$451$	−1.19554e12	−1.36073
$452$	− 5.10091e11i	− 0.574810i
$453$	4.40181e11i	0.491122i
$454$	3.08491e11	0.340794
$455$	0	0
$456$	2.62961e11	0.284806
$457$	8.11185e11i	0.869955i	0.900441	+	0.434977i	$0.143244\pi$
$457$	8.11185e11i	0.869955i	−0.900441	+	0.434977i	$0.856756\pi$
$458$	− 5.68493e11i	− 0.603713i
$459$	2.41039e11	0.253472
$460$	0	0
$461$	−1.90069e11	−0.196001	−0.0980004	−	0.995186i	$-0.531245\pi$
$461$	−1.90069e11	−0.196001	−0.0980004	+	0.995186i	$0.531245\pi$
$462$	− 4.72845e11i	− 0.482870i
$463$	− 4.76945e11i	− 0.482341i	−0.970483	−	0.241170i	$-0.922469\pi$
$463$	− 4.76945e11i	− 0.482341i	0.970483	−	0.241170i	$-0.0775313\pi$
$464$	2.83284e10	0.0283721
$465$	0	0
$466$	−1.69253e11	−0.166264
$467$	1.06392e12i	1.03510i	0.855653	+	0.517549i	$0.173156\pi$
$467$	1.06392e12i	1.03510i	−0.855653	+	0.517549i	$0.826844\pi$
$468$	− 7.49268e9i	− 0.00721990i
$469$	2.79179e11	0.266443
$470$	0	0
$471$	−2.17413e11	−0.203560
$472$	− 7.23420e10i	− 0.0670890i
$473$	− 2.68393e12i	− 2.46545i
$474$	1.06836e12	0.972105
$475$	0	0
$476$	−9.32784e10	−0.0832817
$477$	4.96687e11i	0.439289i
$478$	− 8.52248e11i	− 0.746690i
$479$	8.43415e11	0.732034	0.366017	−	0.930608i	$-0.380721\pi$
$479$	8.43415e11	0.732034	0.366017	+	0.930608i	$0.380721\pi$
$480$	0	0
$481$	2.77668e10	0.0236523
$482$	− 3.89605e11i	− 0.328785i
$483$	− 4.99829e11i	− 0.417888i
$484$	1.92694e12	1.59611
$485$	0	0
$486$	−4.95841e11	−0.403162
$487$	1.15202e12i	0.928065i	0.885818	+	0.464032i	$0.153598\pi$
$487$	1.15202e12i	0.928065i	−0.885818	+	0.464032i	$0.846402\pi$
$488$	1.91123e12i	1.52554i
$489$	5.81910e11	0.460220
$490$	0	0
$491$	−9.68703e11	−0.752184	−0.376092	−	0.926582i	$-0.622732\pi$
$491$	−9.68703e11	−0.752184	−0.376092	+	0.926582i	$0.622732\pi$
$492$	− 7.22328e11i	− 0.555765i
$493$	1.66506e11i	0.126946i
$494$	−6.09011e9	−0.00460102
$495$	0	0
$496$	1.91754e11	0.142258
$497$	3.46934e11i	0.255060i
$498$	1.81564e11i	0.132281i
$499$	−2.62821e12	−1.89761	−0.948805	−	0.315863i	$-0.897706\pi$
$499$	−2.62821e12	−1.89761	−0.948805	+	0.315863i	$0.897706\pi$
$500$	0	0
$501$	−1.70417e12	−1.20849
$502$	8.40308e11i	0.590570i
$503$	− 3.95070e11i	− 0.275181i	−0.990489	−	0.137590i	$-0.956064\pi$
$503$	− 3.95070e11i	− 0.275181i	0.990489	−	0.137590i	$-0.0439358\pi$
$504$	1.90436e11	0.131466
$505$	0	0
$506$	−1.53524e12	−1.04111
$507$	− 1.73126e12i	− 1.16366i
$508$	− 2.90790e11i	− 0.193728i
$509$	−6.64157e11	−0.438572	−0.219286	−	0.975661i	$-0.570373\pi$
$509$	−6.64157e11	−0.438572	−0.219286	+	0.975661i	$0.570373\pi$
$510$	0	0
$511$	3.84532e11	0.249482
$512$	2.34512e11i	0.150817i
$513$	− 2.94743e11i	− 0.187895i
$514$	−1.52954e12	−0.966556
$515$	0	0
$516$	1.62159e12	1.00697
$517$	9.73882e11i	0.599513i
$518$	2.78364e11i	0.169875i
$519$	−3.34537e12	−2.02391
$520$	0	0
$521$	5.22766e11	0.310841	0.155420	−	0.987848i	$-0.450327\pi$
$521$	5.22766e11	0.310841	0.155420	+	0.987848i	$0.450327\pi$
$522$	− 1.34083e11i	− 0.0790417i
$523$	3.09135e12i	1.80672i	0.428882	+	0.903360i	$0.358907\pi$
$523$	3.09135e12i	1.80672i	−0.428882	+	0.903360i	$0.641093\pi$
$524$	7.48366e11	0.433634
$525$	0	0
$526$	1.87991e11	0.107078
$527$	1.12708e12i	0.636510i
$528$	2.92142e11i	0.163584i
$529$	1.78305e11	0.0989947
$530$	0	0
$531$	4.49645e10	0.0245440
$532$	1.14061e11i	0.0617355i
$533$	4.24125e10i	0.0227626i
$534$	−4.54316e9	−0.00241781
$535$	0	0
$536$	1.31350e12	0.687366
$537$	8.93396e11i	0.463617i
$538$	− 1.12116e12i	− 0.576960i
$539$	5.19984e11	0.265363
$540$	0	0
$541$	−1.47490e12	−0.740243	−0.370121	−	0.928983i	$-0.620684\pi$
$541$	−1.47490e12	−0.740243	−0.370121	+	0.928983i	$0.620684\pi$
$542$	2.65079e11i	0.131940i
$543$	3.45831e11i	0.170712i
$544$	−7.04621e11	−0.344954
$545$	0	0
$546$	−1.67744e10	−0.00807756
$547$	2.12294e12i	1.01390i	0.861976	+	0.506949i	$0.169227\pi$
$547$	2.12294e12i	1.01390i	−0.861976	+	0.506949i	$0.830773\pi$
$548$	1.38779e12i	0.657374i
$549$	−1.18793e12	−0.558106
$550$	0	0
$551$	2.03604e11	0.0941031
$552$	− 2.35163e12i	− 1.07806i
$553$	1.17486e12i	0.534225i
$554$	9.59181e11	0.432620
$555$	0	0
$556$	2.01223e12	0.892978
$557$	− 3.52857e12i	− 1.55328i	−0.629943	−	0.776641i	$-0.716922\pi$
$557$	− 3.52857e12i	− 1.55328i	0.629943	−	0.776641i	$-0.283078\pi$
$558$	− 9.07605e11i	− 0.396317i
$559$	−9.52137e10	−0.0412426
$560$	0	0
$561$	−1.71712e12	−0.731928
$562$	1.37419e12i	0.581078i
$563$	3.35280e12i	1.40644i	0.710974	+	0.703218i	$0.248254\pi$
$563$	3.35280e12i	1.40644i	−0.710974	+	0.703218i	$0.751746\pi$
$564$	−5.88403e11	−0.244861
$565$	0	0
$566$	−7.38691e11	−0.302544
$567$	− 1.14365e12i	− 0.464696i
$568$	1.63228e12i	0.658000i
$569$	−2.99364e12	−1.19727	−0.598637	−	0.801020i	$-0.704291\pi$
$569$	−2.99364e12	−1.19727	−0.598637	+	0.801020i	$0.704291\pi$
$570$	0	0
$571$	4.67267e12	1.83951	0.919756	−	0.392490i	$-0.128386\pi$
$571$	4.67267e12	1.83951	0.919756	+	0.392490i	$0.128386\pi$
$572$	− 9.62553e10i	− 0.0375961i
$573$	− 2.81761e12i	− 1.09190i
$574$	−4.25189e11	−0.163485
$575$	0	0
$576$	4.96164e11	0.187812
$577$	− 3.62799e12i	− 1.36262i	−0.731995	−	0.681310i	$-0.761411\pi$
$577$	− 3.62799e12i	− 1.36262i	0.731995	−	0.681310i	$-0.238589\pi$
$578$	1.40310e12i	0.522895i
$579$	−3.30146e12	−1.22082
$580$	0	0
$581$	−1.99665e11	−0.0726957
$582$	− 6.89683e11i	− 0.249170i
$583$	6.38073e12i	2.28751i
$584$	1.80917e12	0.643608
$585$	0	0
$586$	1.41252e12	0.494827
$587$	3.97200e12i	1.38082i	0.723417	+	0.690411i	$0.242570\pi$
$587$	3.97200e12i	1.38082i	−0.723417	+	0.690411i	$0.757430\pi$
$588$	3.14166e11i	0.108383i
$589$	1.37819e12	0.471835
$590$	0	0
$591$	−3.63748e12	−1.22647
$592$	− 1.71984e11i	− 0.0575494i
$593$	− 2.67436e12i	− 0.888123i	−0.895996	−	0.444061i	$-0.853537\pi$
$593$	− 2.67436e12i	− 0.888123i	0.895996	−	0.444061i	$-0.146463\pi$
$594$	−2.49355e12	−0.821825
$595$	0	0
$596$	1.46013e12	0.474005
$597$	2.78765e12i	0.898162i
$598$	5.44632e10i	0.0174160i
$599$	−4.84522e12	−1.53777	−0.768887	−	0.639384i	$-0.779189\pi$
$599$	−4.84522e12	−1.53777	−0.768887	+	0.639384i	$0.779189\pi$
$600$	0	0
$601$	−4.64764e12	−1.45311	−0.726553	−	0.687110i	$-0.758879\pi$
$601$	−4.64764e12	−1.45311	−0.726553	+	0.687110i	$0.758879\pi$
$602$	− 9.54525e11i	− 0.296212i
$603$	8.16411e11i	0.251467i
$604$	−8.98307e11	−0.274637
$605$	0	0
$606$	−1.25507e12	−0.378043
$607$	− 6.52447e12i	− 1.95073i	−0.220604	−	0.975363i	$-0.570803\pi$
$607$	− 6.52447e12i	− 1.95073i	0.220604	−	0.975363i	$-0.429197\pi$
$608$	8.61613e11i	0.255709i
$609$	5.60800e11	0.165208
$610$	0	0
$611$	3.45489e10	0.0100288
$612$	− 2.72777e11i	− 0.0786006i
$613$	9.54536e11i	0.273036i	0.990638	+	0.136518i	$0.0435912\pi$
$613$	9.54536e11i	0.273036i	−0.990638	+	0.136518i	$0.956409\pi$
$614$	1.08230e12	0.307321
$615$	0	0
$616$	2.44645e12	0.684580
$617$	− 4.50764e12i	− 1.25218i	−0.779752	−	0.626088i	$-0.784655\pi$
$617$	− 4.50764e12i	− 1.25218i	0.779752	−	0.626088i	$-0.215345\pi$
$618$	3.31583e12i	0.914418i
$619$	−3.64346e12	−0.997484	−0.498742	−	0.866750i	$-0.666204\pi$
$619$	−3.64346e12	−0.997484	−0.498742	+	0.866750i	$0.666204\pi$
$620$	0	0
$621$	−2.63585e12	−0.711228
$622$	− 4.25452e12i	− 1.13971i
$623$	− 4.99608e9i	− 0.00132872i
$624$	1.03639e10	0.00273647
$625$	0	0
$626$	1.72187e12	0.448143
$627$	2.09970e12i	0.542567i
$628$	− 4.43690e11i	− 0.113831i
$629$	1.01087e12	0.257495
$630$	0	0
$631$	3.61498e12	0.907766	0.453883	−	0.891061i	$-0.350038\pi$
$631$	3.61498e12	0.907766	0.453883	+	0.891061i	$0.350038\pi$
$632$	5.52757e12i	1.37818i
$633$	5.22718e12i	1.29405i
$634$	9.95003e11	0.244581
$635$	0	0
$636$	−3.85513e12	−0.934292
$637$	− 1.84467e10i	− 0.00443906i
$638$	− 1.72251e12i	− 0.411593i
$639$	−1.01455e12	−0.240724
$640$	0	0
$641$	−2.66304e12	−0.623041	−0.311521	−	0.950239i	$-0.600838\pi$
$641$	−2.66304e12	−0.623041	−0.311521	+	0.950239i	$0.600838\pi$
$642$	− 4.40736e11i	− 0.102393i
$643$	− 4.09899e12i	− 0.945644i	−0.881158	−	0.472822i	$-0.843235\pi$
$643$	− 4.09899e12i	− 0.945644i	0.881158	−	0.472822i	$-0.156765\pi$
$644$	1.02004e12	0.233684
$645$	0	0
$646$	−2.21715e11	−0.0500898
$647$	6.11325e12i	1.37152i	0.727827	+	0.685761i	$0.240531\pi$
$647$	6.11325e12i	1.37152i	−0.727827	+	0.685761i	$0.759469\pi$
$648$	− 5.38071e12i	− 1.19882i
$649$	5.77640e11	0.127807
$650$	0	0
$651$	3.79604e12	0.828356
$652$	1.18754e12i	0.257356i
$653$	− 7.66270e12i	− 1.64920i	−0.565719	−	0.824598i	$-0.691401\pi$
$653$	− 7.66270e12i	− 1.64920i	0.565719	−	0.824598i	$-0.308599\pi$
$654$	1.90813e12	0.407858
$655$	0	0
$656$	2.62698e11	0.0553846
$657$	1.12450e12i	0.235459i
$658$	3.46356e11i	0.0720287i
$659$	8.20110e9	0.00169390	0.000846950	−	1.00000i	$-0.499730\pi$
$659$	8.20110e9	0.00169390	0.000846950		1.00000i	$0.499730\pi$
$660$	0	0
$661$	3.20922e12	0.653872	0.326936	−	0.945046i	$-0.393984\pi$
$661$	3.20922e12	0.653872	0.326936	+	0.945046i	$0.393984\pi$
$662$	3.79231e12i	0.767437i
$663$	6.09158e10i	0.0122439i
$664$	−9.39395e11	−0.187539
$665$	0	0
$666$	−8.14030e11	−0.160327
$667$	− 1.82081e12i	− 0.356203i
$668$	− 3.47781e12i	− 0.675791i
$669$	3.77433e12	0.728488
$670$	0	0
$671$	−1.52609e13	−2.90622
$672$	2.37320e12i	0.448923i
$673$	4.91229e12i	0.923031i	0.887132	+	0.461515i	$0.152694\pi$
$673$	4.91229e12i	0.923031i	−0.887132	+	0.461515i	$0.847306\pi$
$674$	7.50089e10	0.0140005
$675$	0	0
$676$	3.53309e12	0.650721
$677$	− 3.11910e12i	− 0.570664i	−0.958429	−	0.285332i	$-0.907896\pi$
$677$	− 3.11910e12i	− 0.570664i	0.958429	−	0.285332i	$-0.0921038\pi$
$678$	− 3.33952e12i	− 0.606946i
$679$	7.58440e11	0.136933
$680$	0	0
$681$	−3.77315e12	−0.672267
$682$	− 1.16596e13i	− 2.06374i
$683$	− 2.91806e12i	− 0.513099i	−0.966531	−	0.256550i	$-0.917414\pi$
$683$	− 2.91806e12i	− 0.513099i	0.966531	−	0.256550i	$-0.0825857\pi$
$684$	−3.33552e11	−0.0582655
$685$	0	0
$686$	1.84930e11	0.0318822
$687$	6.95322e12i	1.19092i
$688$	5.89742e11i	0.100349i
$689$	2.26360e11	0.0382660
$690$	0	0
$691$	4.74697e12	0.792073	0.396037	−	0.918235i	$-0.370385\pi$
$691$	4.74697e12	0.792073	0.396037	+	0.918235i	$0.370385\pi$
$692$	− 6.82712e12i	− 1.13178i
$693$	1.52061e12i	0.250448i
$694$	−4.54058e12	−0.743009
$695$	0	0
$696$	2.63849e12	0.426200
$697$	1.54406e12i	0.247809i
$698$	− 4.63240e11i	− 0.0738680i
$699$	2.07013e12	0.327981
$700$	0	0
$701$	−2.24423e11	−0.0351023	−0.0175512	−	0.999846i	$-0.505587\pi$
$701$	−2.24423e11	−0.0351023	−0.0175512	+	0.999846i	$0.505587\pi$
$702$	8.84599e10i	0.0137477i
$703$	− 1.23610e12i	− 0.190877i
$704$	6.37400e12	0.977992
$705$	0	0
$706$	−4.63484e12	−0.702123
$707$	− 1.38019e12i	− 0.207755i
$708$	3.49001e11i	0.0522007i
$709$	−4.25463e12	−0.632344	−0.316172	−	0.948702i	$-0.602398\pi$
$709$	−4.25463e12	−0.632344	−0.316172	+	0.948702i	$0.602398\pi$
$710$	0	0
$711$	−3.43569e12	−0.504197
$712$	− 2.35059e10i	− 0.00342781i
$713$	− 1.23250e13i	− 1.78601i
$714$	−6.10685e11	−0.0879378
$715$	0	0
$716$	−1.82321e12	−0.259256
$717$	1.04238e13i	1.47296i
$718$	3.35369e12i	0.470938i
$719$	4.28931e12	0.598559	0.299280	−	0.954165i	$-0.403254\pi$
$719$	4.28931e12	0.598559	0.299280	+	0.954165i	$0.403254\pi$
$720$	0	0
$721$	−3.64640e12	−0.502523
$722$	− 4.04023e12i	− 0.553335i
$723$	4.76524e12i	0.648578i
$724$	−7.05761e11	−0.0954627
$725$	0	0
$726$	1.26155e13	1.68535
$727$	1.28935e13i	1.71185i	0.517098	+	0.855926i	$0.327012\pi$
$727$	1.28935e13i	1.71185i	−0.517098	+	0.855926i	$0.672988\pi$
$728$	− 8.67892e10i	− 0.0114518i
$729$	−3.31084e12	−0.434174
$730$	0	0
$731$	−3.46633e12	−0.448995
$732$	− 9.22038e12i	− 1.18699i
$733$	− 2.71447e12i	− 0.347310i	−0.984807	−	0.173655i	$-0.944442\pi$
$733$	− 2.71447e12i	− 0.347310i	0.984807	−	0.173655i	$-0.0555578\pi$
$734$	−6.41143e12	−0.815309
$735$	0	0
$736$	7.70531e12	0.967921
$737$	1.04881e13i	1.30946i
$738$	− 1.24339e12i	− 0.154296i
$739$	9.62579e12	1.18723	0.593617	−	0.804747i	$-0.297699\pi$
$739$	9.62579e12	1.18723	0.593617	+	0.804747i	$0.297699\pi$
$740$	0	0
$741$	7.44880e10	0.00907620
$742$	2.26927e12i	0.274833i
$743$	1.24362e13i	1.49706i	0.663103	+	0.748529i	$0.269239\pi$
$743$	1.24362e13i	1.49706i	−0.663103	+	0.748529i	$0.730761\pi$
$744$	1.78599e13	2.13698
$745$	0	0
$746$	−2.46898e12	−0.291872
$747$	− 5.83886e11i	− 0.0686097i
$748$	− 3.50425e12i	− 0.409296i
$749$	4.84674e11	0.0562706
$750$	0	0
$751$	4.26959e12	0.489786	0.244893	−	0.969550i	$-0.421247\pi$
$751$	4.26959e12	0.489786	0.244893	+	0.969550i	$0.421247\pi$
$752$	− 2.13992e11i	− 0.0244015i
$753$	− 1.02778e13i	− 1.16499i
$754$	−6.11068e10	−0.00688523
$755$	0	0
$756$	1.65676e12	0.184463
$757$	9.76840e12i	1.08116i	0.841291	+	0.540582i	$0.181796\pi$
$757$	9.76840e12i	1.08116i	−0.841291	+	0.540582i	$0.818204\pi$
$758$	9.47153e12i	1.04210i
$759$	1.87774e13	2.05375
$760$	0	0
$761$	1.23336e13	1.33309	0.666543	−	0.745466i	$-0.267773\pi$
$761$	1.23336e13	1.33309	0.666543	+	0.745466i	$0.267773\pi$
$762$	− 1.90378e12i	− 0.204559i
$763$	2.09836e12i	0.224140i
$764$	5.75008e12	0.610595
$765$	0	0
$766$	1.65391e12	0.173573
$767$	− 2.04921e10i	− 0.00213800i
$768$	1.06125e13i	1.10076i
$769$	1.68919e13	1.74185	0.870926	−	0.491415i	$-0.163520\pi$
$769$	1.68919e13	1.74185	0.870926	+	0.491415i	$0.163520\pi$
$770$	0	0
$771$	1.87078e13	1.90668
$772$	− 6.73751e12i	− 0.682687i
$773$	− 1.47186e13i	− 1.48272i	−0.671109	−	0.741359i	$-0.734182\pi$
$773$	− 1.47186e13i	− 1.48272i	0.671109	−	0.741359i	$-0.265818\pi$
$774$	2.79135e12	0.279563
$775$	0	0
$776$	3.56835e12	0.353257
$777$	− 3.40467e12i	− 0.335104i
$778$	3.98111e12i	0.389579i
$779$	1.88808e12	0.183697
$780$	0	0
$781$	−1.30335e13	−1.25352
$782$	1.98278e12i	0.189602i
$783$	− 2.95738e12i	− 0.281177i
$784$	−1.14257e11	−0.0108009
$785$	0	0
$786$	4.89949e12	0.457878
$787$	− 1.82466e13i	− 1.69549i	−0.530406	−	0.847744i	$-0.677960\pi$
$787$	− 1.82466e13i	− 1.69549i	0.530406	−	0.847744i	$-0.322040\pi$
$788$	− 7.42326e12i	− 0.685846i
$789$	−2.29932e12	−0.211228
$790$	0	0
$791$	3.67245e12	0.333550
$792$	7.15424e12i	0.646101i
$793$	5.41388e11i	0.0486160i
$794$	−7.12695e12	−0.636373
$795$	0	0
$796$	−5.68895e12	−0.502254
$797$	− 1.21558e13i	− 1.06714i	−0.845757	−	0.533568i	$-0.820851\pi$
$797$	− 1.21558e13i	− 1.06714i	0.845757	−	0.533568i	$-0.179149\pi$
$798$	7.46748e11i	0.0651870i
$799$	1.25778e12	0.109180
$800$	0	0
$801$	1.46102e10	0.00125403
$802$	5.55325e12i	0.473982i
$803$	1.44460e13i	1.22610i
$804$	−6.33673e12	−0.534827
$805$	0	0
$806$	−4.13631e11	−0.0345227
$807$	1.37128e13i	1.13814i
$808$	− 6.49362e12i	− 0.535964i
$809$	2.61893e12	0.214959	0.107479	−	0.994207i	$-0.465722\pi$
$809$	2.61893e12	0.214959	0.107479	+	0.994207i	$0.465722\pi$
$810$	0	0
$811$	1.16994e13	0.949662	0.474831	−	0.880077i	$-0.342509\pi$
$811$	1.16994e13	0.949662	0.474831	+	0.880077i	$0.342509\pi$
$812$	1.14446e12i	0.0923845i
$813$	− 3.24217e12i	− 0.260272i
$814$	−1.04575e13	−0.834868
$815$	0	0
$816$	3.77305e11	0.0297911
$817$	4.23863e12i	0.332833i
$818$	− 1.44267e13i	− 1.12662i
$819$	5.39443e10	0.00418955
$820$	0	0
$821$	5.17673e12	0.397659	0.198830	−	0.980034i	$-0.436286\pi$
$821$	5.17673e12	0.397659	0.198830	+	0.980034i	$0.436286\pi$
$822$	9.08577e12i	0.694126i
$823$	7.84017e12i	0.595698i	0.954613	+	0.297849i	$0.0962692\pi$
$823$	7.84017e12i	0.595698i	−0.954613	+	0.297849i	$0.903731\pi$
$824$	−1.71558e13	−1.29640
$825$	0	0
$826$	2.05435e11	0.0153555
$827$	− 1.43263e13i	− 1.06502i	−0.846422	−	0.532512i	$-0.821248\pi$
$827$	− 1.43263e13i	− 1.06502i	0.846422	−	0.532512i	$-0.178752\pi$
$828$	2.98292e12i	0.220549i
$829$	−4.95546e12	−0.364408	−0.182204	−	0.983261i	$-0.558323\pi$
$829$	−4.95546e12	−0.364408	−0.182204	+	0.983261i	$0.558323\pi$
$830$	0	0
$831$	−1.17317e13	−0.853408
$832$	− 2.26121e11i	− 0.0163601i
$833$	− 6.71566e11i	− 0.0483266i
$834$	1.31739e13	0.942902
$835$	0	0
$836$	−4.28500e12	−0.303405
$837$	− 2.00185e13i	− 1.40983i
$838$	2.95270e12i	0.206834i
$839$	−7.38235e12	−0.514358	−0.257179	−	0.966364i	$-0.582793\pi$
$839$	−7.38235e12	−0.514358	−0.257179	+	0.966364i	$0.582793\pi$
$840$	0	0
$841$	−1.24642e13	−0.859179
$842$	4.64256e12i	0.318312i
$843$	− 1.68077e13i	− 1.14626i
$844$	−1.06675e13	−0.723636
$845$	0	0
$846$	−1.01286e12	−0.0679802
$847$	1.38732e13i	0.926189i
$848$	− 1.40204e12i	− 0.0931065i
$849$	9.03491e12	0.596814
$850$	0	0
$851$	−1.10543e13	−0.722516
$852$	− 7.87462e12i	− 0.511978i
$853$	− 2.13356e13i	− 1.37985i	−0.723879	−	0.689927i	$-0.757643\pi$
$853$	− 2.13356e13i	− 1.37985i	0.723879	−	0.689927i	$-0.242357\pi$
$854$	−5.42745e12	−0.349169
$855$	0	0
$856$	2.28032e12	0.145166
$857$	1.65008e13i	1.04494i	0.852659	+	0.522468i	$0.174989\pi$
$857$	1.65008e13i	1.04494i	−0.852659	+	0.522468i	$0.825011\pi$
$858$	− 6.30175e11i	− 0.0396980i
$859$	1.94817e13	1.22083	0.610417	−	0.792080i	$-0.291002\pi$
$859$	1.94817e13	1.22083	0.610417	+	0.792080i	$0.291002\pi$
$860$	0	0
$861$	5.20047e12	0.322499
$862$	1.65103e12i	0.101853i
$863$	− 1.61059e13i	− 0.988411i	−0.869345	−	0.494205i	$-0.835459\pi$
$863$	− 1.61059e13i	− 0.988411i	0.869345	−	0.494205i	$-0.164541\pi$
$864$	1.25151e13	0.764049
$865$	0	0
$866$	−9.72232e12	−0.587408
$867$	− 1.71613e13i	− 1.03149i
$868$	7.74684e12i	0.463219i
$869$	−4.41368e13	−2.62550
$870$	0	0
$871$	3.72070e11	0.0219050
$872$	9.87249e12i	0.578232i
$873$	2.21793e12i	0.129236i
$874$	2.42454e12	0.140549
$875$	0	0
$876$	−8.72801e12	−0.500780
$877$	− 1.84919e13i	− 1.05556i	−0.849381	−	0.527780i	$-0.823025\pi$
$877$	− 1.84919e13i	− 1.05556i	0.849381	−	0.527780i	$-0.176975\pi$
$878$	7.82892e12i	0.444607i
$879$	−1.72764e13	−0.976121
$880$	0	0
$881$	−2.83078e13	−1.58312	−0.791562	−	0.611089i	$-0.790732\pi$
$881$	−2.83078e13	−1.58312	−0.791562	+	0.611089i	$0.790732\pi$
$882$	5.40795e11i	0.0300901i
$883$	7.32328e12i	0.405399i	0.979241	+	0.202700i	$0.0649715\pi$
$883$	7.32328e12i	0.405399i	−0.979241	+	0.202700i	$0.935029\pi$
$884$	−1.24315e11	−0.00684681
$885$	0	0
$886$	−2.82641e12	−0.154093
$887$	1.51372e13i	0.821087i	0.911841	+	0.410544i	$0.134661\pi$
$887$	1.51372e13i	0.821087i	−0.911841	+	0.410544i	$0.865339\pi$
$888$	− 1.60185e13i	− 0.864496i
$889$	2.09357e12	0.112416
$890$	0	0
$891$	4.29642e13	2.28380
$892$	7.70253e12i	0.407372i
$893$	− 1.53802e12i	− 0.0809337i
$894$	9.55934e12	0.500506
$895$	0	0
$896$	−5.16867e12	−0.267913
$897$	− 6.66138e11i	− 0.0343556i
$898$	1.23059e13i	0.631493i
$899$	1.38285e13	0.706082
$900$	0	0
$901$	8.24080e12	0.416589
$902$	− 1.59733e13i	− 0.803463i
$903$	1.16748e13i	0.584323i
$904$	1.72783e13	0.860487
$905$	0	0
$906$	−5.88114e12	−0.289991
$907$	− 2.24337e13i	− 1.10070i	−0.834935	−	0.550349i	$-0.814495\pi$
$907$	− 2.24337e13i	− 1.10070i	0.834935	−	0.550349i	$-0.185505\pi$
$908$	− 7.70011e12i	− 0.375933i
$909$	4.03614e12	0.196078
$910$	0	0
$911$	−6.34178e12	−0.305055	−0.152528	−	0.988299i	$-0.548741\pi$
$911$	−6.34178e12	−0.305055	−0.152528	+	0.988299i	$0.548741\pi$
$912$	− 4.61369e11i	− 0.0220837i
$913$	− 7.50094e12i	− 0.357270i
$914$	−1.08380e13	−0.513679
$915$	0	0
$916$	−1.41899e13	−0.665963
$917$	5.38793e12i	0.251629i
$918$	3.22045e12i	0.149667i
$919$	−9.04471e12	−0.418288	−0.209144	−	0.977885i	$-0.567068\pi$
$919$	−9.04471e12	−0.418288	−0.209144	+	0.977885i	$0.567068\pi$
$920$	0	0
$921$	−1.32376e13	−0.606236
$922$	− 2.53946e12i	− 0.115732i
$923$	4.62369e11i	0.0209692i
$924$	−1.18025e13	−0.532659
$925$	0	0
$926$	6.37233e12	0.284806
$927$	− 1.06633e13i	− 0.474277i
$928$	8.64522e12i	0.382658i
$929$	−8.50641e12	−0.374693	−0.187346	−	0.982294i	$-0.559989\pi$
$929$	−8.50641e12	−0.374693	−0.187346	+	0.982294i	$0.559989\pi$
$930$	0	0
$931$	−8.21193e11	−0.0358238
$932$	4.22464e12i	0.183408i
$933$	5.20368e13i	2.24824i
$934$	−1.42147e13	−0.611191
$935$	0	0
$936$	2.53800e11	0.0108081
$937$	− 3.00276e13i	− 1.27260i	−0.771442	−	0.636300i	$-0.780464\pi$
$937$	− 3.00276e13i	− 1.27260i	0.771442	−	0.636300i	$-0.219536\pi$
$938$	3.73003e12i	0.157326i
$939$	−2.10602e13	−0.884030
$940$	0	0
$941$	−3.15982e13	−1.31374	−0.656870	−	0.754004i	$-0.728120\pi$
$941$	−3.15982e13	−1.31374	−0.656870	+	0.754004i	$0.728120\pi$
$942$	− 2.90480e12i	− 0.120195i
$943$	− 1.68849e13i	− 0.695338i
$944$	−1.26925e11	−0.00520205
$945$	0	0
$946$	3.58592e13	1.45576
$947$	− 8.84885e12i	− 0.357529i	−0.983892	−	0.178765i	$-0.942790\pi$
$947$	− 8.84885e12i	− 0.357529i	0.983892	−	0.178765i	$-0.0572101\pi$
$948$	− 2.66667e13i	− 1.07234i
$949$	5.12477e11	0.0205105
$950$	0	0
$951$	−1.21698e13	−0.482473
$952$	− 3.15963e12i	− 0.124672i
$953$	4.90260e12i	0.192534i	0.995356	+	0.0962672i	$0.0306903\pi$
$953$	4.90260e12i	0.192534i	−0.995356	+	0.0962672i	$0.969310\pi$
$954$	−6.63610e12	−0.259385
$955$	0	0
$956$	−2.12726e13	−0.823682
$957$	2.10679e13i	0.811929i
$958$	1.12686e13i	0.432241i
$959$	−9.99155e12	−0.381460
$960$	0	0
$961$	6.71649e13	2.54031
$962$	3.70985e11i	0.0139659i
$963$	1.41735e12i	0.0531077i
$964$	−9.72475e12	−0.362687
$965$	0	0
$966$	6.67808e12	0.246749
$967$	1.55633e13i	0.572378i	0.958173	+	0.286189i	$0.0923885\pi$
$967$	1.55633e13i	0.572378i	−0.958173	+	0.286189i	$0.907612\pi$
$968$	6.52713e13i	2.38937i
$969$	2.71179e12	0.0988096
$970$	0	0
$971$	−2.49197e13	−0.899613	−0.449806	−	0.893126i	$-0.648507\pi$
$971$	−2.49197e13	−0.899613	−0.449806	+	0.893126i	$0.648507\pi$
$972$	1.23765e13i	0.444732i
$973$	1.44872e13i	0.518176i
$974$	−1.53918e13	−0.547991
$975$	0	0
$976$	3.35329e12	0.118290
$977$	4.47898e12i	0.157273i	0.996903	+	0.0786364i	$0.0250566\pi$
$977$	4.47898e12i	0.157273i	−0.996903	+	0.0786364i	$0.974943\pi$
$978$	7.77474e12i	0.271745i
$979$	1.87691e11	0.00653012
$980$	0	0
$981$	−6.13629e12	−0.211542
$982$	− 1.29426e13i	− 0.444139i
$983$	1.43233e13i	0.489275i	0.969615	+	0.244637i	$0.0786689\pi$
$983$	1.43233e13i	0.489275i	−0.969615	+	0.244637i	$0.921331\pi$
$984$	2.44675e13	0.831977
$985$	0	0
$986$	−2.22464e12	−0.0749572
$987$	− 4.23626e12i	− 0.142088i
$988$	1.52013e11i	0.00507543i
$989$	3.79057e13	1.25986
$990$	0	0
$991$	−2.28575e13	−0.752829	−0.376415	−	0.926451i	$-0.622843\pi$
$991$	−2.28575e13	−0.752829	−0.376415	+	0.926451i	$0.622843\pi$
$992$	5.85194e13i	1.91866i
$993$	− 4.63836e13i	− 1.51388i
$994$	−4.63529e12	−0.150605
$995$	0	0
$996$	4.53194e12	0.145921
$997$	− 2.67132e13i	− 0.856243i	−0.903721	−	0.428121i	$-0.859176\pi$
$997$	− 2.67132e13i	− 0.856243i	0.903721	−	0.428121i	$-0.140824\pi$
$998$	− 3.51147e13i	− 1.12047i
$999$	−1.79545e13	−0.570334

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.d.99.4		6
5.2	odd	4		175.10.a.d.1.2		3
5.3	odd	4		7.10.a.b.1.2	✓	3
5.4	even	2	inner	175.10.b.d.99.3		6
15.8	even	4		63.10.a.e.1.2		3
20.3	even	4		112.10.a.h.1.1		3
35.3	even	12		49.10.c.e.30.2		6
35.13	even	4		49.10.a.c.1.2		3
35.18	odd	12		49.10.c.d.30.2		6
35.23	odd	12		49.10.c.d.18.2		6
35.33	even	12		49.10.c.e.18.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.2	✓	3	5.3	odd	4
49.10.a.c.1.2		3	35.13	even	4
49.10.c.d.18.2		6	35.23	odd	12
49.10.c.d.30.2		6	35.18	odd	12
49.10.c.e.18.2		6	35.33	even	12
49.10.c.e.30.2		6	35.3	even	12
63.10.a.e.1.2		3	15.8	even	4
112.10.a.h.1.1		3	20.3	even	4
175.10.a.d.1.2		3	5.2	odd	4
175.10.b.d.99.3		6	5.4	even	2	inner
175.10.b.d.99.4		6	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+13.3607i q^{2} -163.415i q^{3} +333.491 q^{4} +2183.34 q^{6} +2401.00i q^{7} +11296.4i q^{8} -7021.32 q^{9} -90199.9 q^{11} -54497.3i q^{12} +3199.89i q^{13} -32079.1 q^{14} +19819.7 q^{16} +116494. i q^{17} -93809.9i q^{18} +142449. q^{19} +392358. q^{21} -1.20514e6i q^{22} -1.27391e6i q^{23} +1.84599e6 q^{24} -42752.8 q^{26} -2.06910e6i q^{27} +800712. i q^{28} +1.42931e6 q^{29} +9.67494e6 q^{31} +6.04855e6i q^{32} +1.47400e7i q^{33} -1.55645e6 q^{34} -2.34155e6 q^{36} -8.67744e6i q^{37} +1.90323e6i q^{38} +522908. q^{39} +1.32544e7 q^{41} +5.24219e6i q^{42} +2.97554e7i q^{43} -3.00809e7 q^{44} +1.70204e7 q^{46} -1.07969e7i q^{47} -3.23882e6i q^{48} -5.76480e6 q^{49} +1.90369e7 q^{51} +1.06713e6i q^{52} -7.07399e7i q^{53} +2.76447e7 q^{54} -2.71226e7 q^{56} -2.32783e7i q^{57} +1.90966e7i q^{58} -6.40400e6 q^{59} +1.69190e8 q^{61} +1.29264e8i q^{62} -1.68582e7i q^{63} -7.06653e7 q^{64} -1.96937e8 q^{66} -1.16276e8i q^{67} +3.88498e7i q^{68} -2.08176e8 q^{69} +1.44496e8 q^{71} -7.93154e7i q^{72} -1.60155e8i q^{73} +1.15937e8 q^{74} +4.75056e7 q^{76} -2.16570e8i q^{77} +6.98643e6i q^{78} +4.89322e8 q^{79} -4.76322e8 q^{81} +1.77088e8i q^{82} +8.31590e7i q^{83} +1.30848e8 q^{84} -3.97553e8 q^{86} -2.33569e8i q^{87} -1.01893e9i q^{88} -2.08083e6 q^{89} -7.68292e6 q^{91} -4.24838e8i q^{92} -1.58103e9i q^{93} +1.44255e8 q^{94} +9.88421e8 q^{96} -3.15885e8i q^{97} -7.70219e7i q^{98} +6.33322e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3114 q^{4} + 9828 q^{6} + 52002 q^{9} - 6888 q^{11} - 100842 q^{14} + 965922 q^{16} - 445704 q^{19} + 403368 q^{21} + 2899260 q^{24} - 17570112 q^{26} - 8163636 q^{29} + 5738880 q^{31} + 7963284 q^{34}+ \cdots + 3801958344 q^{99}+O(q^{100}) \) 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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