LMFDB - Embedded newform 175.10.b.f.99.3

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} + 2 x^{8} - 2016 x^{7} + 425617 x^{6} - 2170178 x^{5} + 5521250 x^{4} + \cdots + 231472080000 $ x^10 - 2x^9 + 2x^8 - 2016x^7 + 425617x^6 - 2170178x^5 + 5521250x^4 - 35024640x^3 + 21285642816x^2 - 99267638400*x + 231472080000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.3
Root			$11.3831 - 11.3831i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.f.99.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-22.7661i q^{2} -239.496i q^{3} -6.29742 q^{4} -5452.41 q^{6} -2401.00i q^{7} -11512.9i q^{8} -37675.5 q^{9} -21227.5 q^{11} +1508.21i q^{12} +47399.7i q^{13} -54661.5 q^{14} -265329. q^{16} -569500. i q^{17} +857725. i q^{18} -1.08959e6 q^{19} -575031. q^{21} +483268. i q^{22} -1.34776e6i q^{23} -2.75730e6 q^{24} +1.07911e6 q^{26} +4.30913e6i q^{27} +15120.1i q^{28} +6.23203e6 q^{29} -413669. q^{31} +145906. i q^{32} +5.08391e6i q^{33} -1.29653e7 q^{34} +237258. q^{36} -1.28411e7i q^{37} +2.48057e7i q^{38} +1.13520e7 q^{39} +3.90722e6 q^{41} +1.30912e7i q^{42} +1.27760e7i q^{43} +133678. q^{44} -3.06834e7 q^{46} +3.61213e7i q^{47} +6.35452e7i q^{48} -5.76480e6 q^{49} -1.36393e8 q^{51} -298496. i q^{52} +1.10032e8i q^{53} +9.81022e7 q^{54} -2.76425e7 q^{56} +2.60952e8i q^{57} -1.41879e8i q^{58} +8.68650e6 q^{59} +1.06957e8 q^{61} +9.41766e6i q^{62} +9.04588e7i q^{63} -1.32527e8 q^{64} +1.15741e8 q^{66} -1.89423e8i q^{67} +3.58638e6i q^{68} -3.22784e8 q^{69} +9.10989e7 q^{71} +4.33754e8i q^{72} -9.84572e7i q^{73} -2.92341e8 q^{74} +6.86157e6 q^{76} +5.09672e7i q^{77} -2.58442e8i q^{78} +2.41368e8 q^{79} +2.90454e8 q^{81} -8.89525e7i q^{82} +4.28456e8i q^{83} +3.62121e6 q^{84} +2.90861e8 q^{86} -1.49255e9i q^{87} +2.44390e8i q^{88} -5.29736e7 q^{89} +1.13807e8 q^{91} +8.48743e6i q^{92} +9.90722e7i q^{93} +8.22342e8 q^{94} +3.49439e7 q^{96} -3.01374e8i q^{97} +1.31242e8i q^{98} +7.99756e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 1664 q^{4} - 288 q^{6} - 135594 q^{9} + 20624 q^{11} - 9604 q^{14} - 1053392 q^{16} - 3310752 q^{19} + 672280 q^{21} - 13009152 q^{24} + 20438120 q^{26} + 6707452 q^{29} + 5356240 q^{31} - 43097224 q^{34}+ \cdots - 1396625336 q^{99}+O(q^{100}) $ 10 * q - 1664 * q^4 - 288 * q^6 - 135594 * q^9 + 20624 * q^11 - 9604 * q^14 - 1053392 * q^16 - 3310752 * q^19 + 672280 * q^21 - 13009152 * q^24 + 20438120 * q^26 + 6707452 * q^29 + 5356240 * q^31 - 43097224 * q^34 + 30780920 * q^36 + 36248 * q^39 + 12660388 * q^41 + 142451784 * q^44 - 285690944 * q^46 - 57648010 * q^49 - 35940424 * q^51 + 226558656 * q^54 - 67881072 * q^56 + 304670336 * q^59 + 514031396 * q^61 + 387976864 * q^64 + 366483328 * q^66 + 383914672 * q^69 + 1045577920 * q^71 + 488357736 * q^74 - 690113232 * q^76 - 928349800 * q^79 + 1730301978 * q^81 - 304389176 * q^84 + 1389121232 * q^86 + 2213416652 * q^89 + 761779676 * q^91 + 7205003488 * q^94 - 5304257280 * q^96 - 1396625336 * 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 $

$2$	− 22.7661i	− 1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$2$	− 22.7661i	− 1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$3$	− 239.496i	− 1.70708i	−0.521030	−	0.853538i	$-0.674452\pi$
$3$	− 239.496i	− 1.70708i	0.521030	−	0.853538i	$-0.325548\pi$
$4$	−6.29742	−0.0122996
$5$	0	0
$5$	0	0
$6$	−5452.41	−1.71754
$7$	− 2401.00i	− 0.377964i
$7$	− 2401.00i	− 0.377964i
$8$	− 11512.9i	− 0.993756i
$9$	−37675.5	−1.91411
$10$	0	0
$11$	−21227.5	−0.437151	−0.218576	−	0.975820i	$-0.570141\pi$
$11$	−21227.5	−0.437151	−0.218576	+	0.975820i	$0.570141\pi$
$12$	1508.21i	0.0209964i
$13$	47399.7i	0.460289i	0.973156	+	0.230144i	$0.0739198\pi$
$13$	47399.7i	0.460289i	−0.973156	+	0.230144i	$0.926080\pi$
$14$	−54661.5	−0.380282
$15$	0	0
$16$	−265329.	−1.01215
$17$	− 569500.i	− 1.65376i	−0.562376	−	0.826882i	$-0.690113\pi$
$17$	− 569500.i	− 1.65376i	0.562376	−	0.826882i	$-0.309887\pi$
$18$	857725.i	1.92585i
$19$	−1.08959e6	−1.91810	−0.959048	−	0.283245i	$-0.908589\pi$
$19$	−1.08959e6	−1.91810	−0.959048	+	0.283245i	$0.908589\pi$
$20$	0	0
$21$	−575031.	−0.645214
$22$	483268.i	0.439831i
$23$	− 1.34776e6i	− 1.00424i	−0.864797	−	0.502121i	$-0.832553\pi$
$23$	− 1.34776e6i	− 1.00424i	0.864797	−	0.502121i	$-0.167447\pi$
$24$	−2.75730e6	−1.69642
$25$	0	0
$26$	1.07911e6	0.463111
$27$	4.30913e6i	1.56046i
$28$	15120.1i	0.00464883i
$29$	6.23203e6	1.63621	0.818104	−	0.575071i	$-0.195026\pi$
$29$	6.23203e6	1.63621	0.818104	+	0.575071i	$0.195026\pi$
$30$	0	0
$31$	−413669.	−0.0804499	−0.0402250	−	0.999191i	$-0.512807\pi$
$31$	−413669.	−0.0804499	−0.0402250	+	0.999191i	$0.512807\pi$
$32$	145906.i	0.0245979i
$33$	5.08391e6i	0.746251i
$34$	−1.29653e7	−1.66390
$35$	0	0
$36$	237258.	0.0235429
$37$	− 1.28411e7i	− 1.12640i	−0.826320	−	0.563200i	$-0.809570\pi$
$37$	− 1.28411e7i	− 1.12640i	0.826320	−	0.563200i	$-0.190430\pi$
$38$	2.48057e7i	1.92986i
$39$	1.13520e7	0.785748
$40$	0	0
$41$	3.90722e6	0.215944	0.107972	−	0.994154i	$-0.465564\pi$
$41$	3.90722e6	0.215944	0.107972	+	0.994154i	$0.465564\pi$
$42$	1.30912e7i	0.649170i
$43$	1.27760e7i	0.569886i	0.958544	+	0.284943i	$0.0919747\pi$
$43$	1.27760e7i	0.569886i	−0.958544	+	0.284943i	$0.908025\pi$
$44$	133678.	0.00537680
$45$	0	0
$46$	−3.06834e7	−1.01040
$47$	3.61213e7i	1.07975i	0.841746	+	0.539874i	$0.181528\pi$
$47$	3.61213e7i	1.07975i	−0.841746	+	0.539874i	$0.818472\pi$
$48$	6.35452e7i	1.72782i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−1.36393e8	−2.82310
$52$	− 298496.i	− 0.00566139i
$53$	1.10032e8i	1.91548i	0.287635	+	0.957740i	$0.407131\pi$
$53$	1.10032e8i	1.91548i	−0.287635	+	0.957740i	$0.592869\pi$
$54$	9.81022e7	1.57003
$55$	0	0
$56$	−2.76425e7	−0.375604
$57$	2.60952e8i	3.27434i
$58$	− 1.41879e8i	− 1.64624i
$59$	8.68650e6	0.0933277	0.0466639	−	0.998911i	$-0.485141\pi$
$59$	8.68650e6	0.0933277	0.0466639	+	0.998911i	$0.485141\pi$
$60$	0	0
$61$	1.06957e8	0.989066	0.494533	−	0.869159i	$-0.335339\pi$
$61$	1.06957e8	0.989066	0.494533	+	0.869159i	$0.335339\pi$
$62$	9.41766e6i	0.0809432i
$63$	9.04588e7i	0.723466i
$64$	−1.32527e8	−0.987400
$65$	0	0
$66$	1.15741e8	0.750826
$67$	− 1.89423e8i	− 1.14841i	−0.818712	−	0.574204i	$-0.805312\pi$
$67$	− 1.89423e8i	− 1.14841i	0.818712	−	0.574204i	$-0.194688\pi$
$68$	3.58638e6i	0.0203407i
$69$	−3.22784e8	−1.71432
$70$	0	0
$71$	9.10989e7	0.425452	0.212726	−	0.977112i	$-0.431766\pi$
$71$	9.10989e7	0.425452	0.212726	+	0.977112i	$0.431766\pi$
$72$	4.33754e8i	1.90216i
$73$	− 9.84572e7i	− 0.405784i	−0.979201	−	0.202892i	$-0.934966\pi$
$73$	− 9.84572e7i	− 0.405784i	0.979201	−	0.202892i	$-0.0650340\pi$
$74$	−2.92341e8	−1.13331
$75$	0	0
$76$	6.86157e6	0.0235919
$77$	5.09672e7i	0.165228i
$78$	− 2.58442e8i	− 0.790566i
$79$	2.41368e8	0.697200	0.348600	−	0.937272i	$-0.386657\pi$
$79$	2.41368e8	0.697200	0.348600	+	0.937272i	$0.386657\pi$
$80$	0	0
$81$	2.90454e8	0.749712
$82$	− 8.89525e7i	− 0.217268i
$83$	4.28456e8i	0.990956i	0.868620	+	0.495478i	$0.165007\pi$
$83$	4.28456e8i	0.990956i	−0.868620	+	0.495478i	$0.834993\pi$
$84$	3.62121e6	0.00793591
$85$	0	0
$86$	2.90861e8	0.573380
$87$	− 1.49255e9i	− 2.79313i
$88$	2.44390e8i	0.434422i
$89$	−5.29736e7	−0.0894962	−0.0447481	−	0.998998i	$-0.514249\pi$
$89$	−5.29736e7	−0.0894962	−0.0447481	+	0.998998i	$0.514249\pi$
$90$	0	0
$91$	1.13807e8	0.173973
$92$	8.48743e6i	0.0123518i
$93$	9.90722e7i	0.137334i
$94$	8.22342e8	1.08637
$95$	0	0
$96$	3.49439e7	0.0419905
$97$	− 3.01374e8i	− 0.345647i	−0.984953	−	0.172824i	$-0.944711\pi$
$97$	− 3.01374e8i	− 0.345647i	0.984953	−	0.172824i	$-0.0552890\pi$
$98$	1.31242e8i	0.143733i
$99$	7.99756e8	0.836756
$100$	0	0
$101$	1.68070e9	1.60710	0.803552	−	0.595234i	$-0.202941\pi$
$101$	1.68070e9	1.60710	0.803552	+	0.595234i	$0.202941\pi$
$102$	3.10514e9i	2.84041i
$103$	4.68604e8i	0.410241i	0.978737	+	0.205120i	$0.0657586\pi$
$103$	4.68604e8i	0.410241i	−0.978737	+	0.205120i	$0.934241\pi$
$104$	5.45708e8	0.457415
$105$	0	0
$106$	2.50500e9	1.92722
$107$	− 5.15481e8i	− 0.380177i	−0.981767	−	0.190089i	$-0.939123\pi$
$107$	− 5.15481e8i	− 0.380177i	0.981767	−	0.190089i	$-0.0608775\pi$
$108$	− 2.71364e7i	− 0.0191931i
$109$	−5.36760e8	−0.364218	−0.182109	−	0.983278i	$-0.558292\pi$
$109$	−5.36760e8	−0.364218	−0.182109	+	0.983278i	$0.558292\pi$
$110$	0	0
$111$	−3.07538e9	−1.92285
$112$	6.37054e8i	0.382556i
$113$	− 5.40168e8i	− 0.311656i	−0.987784	−	0.155828i	$-0.950195\pi$
$113$	− 5.40168e8i	− 0.311656i	0.987784	−	0.155828i	$-0.0498046\pi$
$114$	5.94086e9	3.29441
$115$	0	0
$116$	−3.92457e7	−0.0201248
$117$	− 1.78581e9i	− 0.881044i
$118$	− 1.97758e8i	− 0.0938999i
$119$	−1.36737e9	−0.625064
$120$	0	0
$121$	−1.90734e9	−0.808899
$122$	− 2.43500e9i	− 0.995130i
$123$	− 9.35766e8i	− 0.368633i
$124$	2.60505e6	0.000989505 0
$125$	0	0
$126$	2.05940e9	0.727902
$127$	− 8.96674e8i	− 0.305857i	−0.988237	−	0.152928i	$-0.951130\pi$
$127$	− 8.96674e8i	− 0.305857i	0.988237	−	0.152928i	$-0.0488704\pi$
$128$	3.09182e9i	1.01805i
$129$	3.05981e9	0.972839
$130$	0	0
$131$	−2.92350e9	−0.867325	−0.433663	−	0.901075i	$-0.642779\pi$
$131$	−2.92350e9	−0.867325	−0.433663	+	0.901075i	$0.642779\pi$
$132$	− 3.20155e7i	− 0.00917862i
$133$	2.61610e9i	0.724972i
$134$	−4.31243e9	−1.15545
$135$	0	0
$136$	−6.55659e9	−1.64344
$137$	− 4.52069e9i	− 1.09638i	−0.836353	−	0.548191i	$-0.815317\pi$
$137$	− 4.52069e9i	− 1.09638i	0.836353	−	0.548191i	$-0.184683\pi$
$138$	7.34856e9i	1.72483i
$139$	7.23687e9	1.64431	0.822156	−	0.569262i	$-0.192771\pi$
$139$	7.23687e9	1.64431	0.822156	+	0.569262i	$0.192771\pi$
$140$	0	0
$141$	8.65091e9	1.84321
$142$	− 2.07397e9i	− 0.428061i
$143$	− 1.00618e9i	− 0.201216i
$144$	9.99638e9	1.93736
$145$	0	0
$146$	−2.24149e9	−0.408272
$147$	1.38065e9i	0.243868i
$148$	8.08655e7i	0.0138543i
$149$	−3.83905e9	−0.638096	−0.319048	−	0.947739i	$-0.603363\pi$
$149$	−3.83905e9	−0.638096	−0.319048	+	0.947739i	$0.603363\pi$
$150$	0	0
$151$	−6.14269e9	−0.961528	−0.480764	−	0.876850i	$-0.659641\pi$
$151$	−6.14269e9	−0.961528	−0.480764	+	0.876850i	$0.659641\pi$
$152$	1.25443e10i	1.90612i
$153$	2.14562e10i	3.16549i
$154$	1.16033e9	0.166241
$155$	0	0
$156$	−7.14886e7	−0.00966442
$157$	− 9.31680e9i	− 1.22382i	−0.790926	−	0.611911i	$-0.790401\pi$
$157$	− 9.31680e9i	− 1.22382i	0.790926	−	0.611911i	$-0.209599\pi$
$158$	− 5.49501e9i	− 0.701474i
$159$	2.63523e10	3.26987
$160$	0	0
$161$	−3.23598e9	−0.379568
$162$	− 6.61251e9i	− 0.754308i
$163$	6.53147e9i	0.724714i	0.932039	+	0.362357i	$0.118028\pi$
$163$	6.53147e9i	0.724714i	−0.932039	+	0.362357i	$0.881972\pi$
$164$	−2.46054e7	−0.00265603
$165$	0	0
$166$	9.75429e9	0.997032
$167$	− 2.73053e9i	− 0.271659i	−0.990732	−	0.135829i	$-0.956630\pi$
$167$	− 2.73053e9i	− 0.271659i	0.990732	−	0.135829i	$-0.0433699\pi$
$168$	6.62027e9i	0.641186i
$169$	8.35777e9	0.788134
$170$	0	0
$171$	4.10506e10	3.67145
$172$	− 8.04560e7i	− 0.00700939i
$173$	3.68616e8i	0.0312872i	0.999878	+	0.0156436i	$0.00497971\pi$
$173$	3.68616e8i	0.0312872i	−0.999878	+	0.0156436i	$0.995020\pi$
$174$	−3.39795e10	−2.81026
$175$	0	0
$176$	5.63226e9	0.442462
$177$	− 2.08038e9i	− 0.159318i
$178$	1.20600e9i	0.0900449i
$179$	1.97250e10	1.43608	0.718040	−	0.696001i	$-0.245039\pi$
$179$	1.97250e10	1.43608	0.718040	+	0.696001i	$0.245039\pi$
$180$	0	0
$181$	−3.11426e9	−0.215676	−0.107838	−	0.994168i	$-0.534393\pi$
$181$	−3.11426e9	−0.215676	−0.107838	+	0.994168i	$0.534393\pi$
$182$	− 2.59094e9i	− 0.175039i
$183$	− 2.56158e10i	− 1.68841i
$184$	−1.55167e10	−0.997972
$185$	0	0
$186$	2.25549e9	0.138176
$187$	1.20891e10i	0.722945i
$188$	− 2.27471e8i	− 0.0132805i
$189$	1.03462e10	0.589798
$190$	0	0
$191$	−3.17752e10	−1.72758	−0.863790	−	0.503852i	$-0.831916\pi$
$191$	−3.17752e10	−1.72758	−0.863790	+	0.503852i	$0.831916\pi$
$192$	3.17396e10i	1.68557i
$193$	− 2.21167e10i	− 1.14739i	−0.819068	−	0.573696i	$-0.805509\pi$
$193$	− 2.21167e10i	− 1.14739i	0.819068	−	0.573696i	$-0.194491\pi$
$194$	−6.86112e9	−0.347766
$195$	0	0
$196$	3.63034e7	0.00175709
$197$	− 2.15871e10i	− 1.02116i	−0.859829	−	0.510582i	$-0.829430\pi$
$197$	− 2.15871e10i	− 1.02116i	0.859829	−	0.510582i	$-0.170570\pi$
$198$	− 1.82074e10i	− 0.841886i
$199$	−2.78732e10	−1.25993	−0.629966	−	0.776622i	$-0.716931\pi$
$199$	−2.78732e10	−1.25993	−0.629966	+	0.776622i	$0.716931\pi$
$200$	0	0
$201$	−4.53661e10	−1.96042
$202$	− 3.82631e10i	− 1.61696i
$203$	− 1.49631e10i	− 0.618428i
$204$	8.58924e8	0.0347231
$205$	0	0
$206$	1.06683e10	0.412756
$207$	5.07776e10i	1.92223i
$208$	− 1.25765e10i	− 0.465881i
$209$	2.31292e10	0.838498
$210$	0	0
$211$	1.31458e10	0.456579	0.228290	−	0.973593i	$-0.426687\pi$
$211$	1.31458e10	0.456579	0.228290	+	0.973593i	$0.426687\pi$
$212$	− 6.92917e8i	− 0.0235597i
$213$	− 2.18179e10i	− 0.726280i
$214$	−1.17355e10	−0.382508
$215$	0	0
$216$	4.96105e10	1.55072
$217$	9.93220e8i	0.0304072i
$218$	1.22200e10i	0.366451i
$219$	−2.35801e10	−0.692704
$220$	0	0
$221$	2.69941e10	0.761209
$222$	7.00146e10i	1.93464i
$223$	5.58951e10i	1.51357i	0.653665	+	0.756784i	$0.273231\pi$
$223$	5.58951e10i	1.51357i	−0.653665	+	0.756784i	$0.726769\pi$
$224$	3.50320e8	0.00929713
$225$	0	0
$226$	−1.22975e10	−0.313567
$227$	5.98856e10i	1.49695i	0.663165	+	0.748473i	$0.269213\pi$
$227$	5.98856e10i	1.49695i	−0.663165	+	0.748473i	$0.730787\pi$
$228$	− 1.64332e9i	− 0.0402732i
$229$	−6.62019e10	−1.59078	−0.795391	−	0.606097i	$-0.792734\pi$
$229$	−6.62019e10	−1.59078	−0.795391	+	0.606097i	$0.792734\pi$
$230$	0	0
$231$	1.22065e10	0.282056
$232$	− 7.17487e10i	− 1.62599i
$233$	6.50041e10i	1.44490i	0.691421	+	0.722452i	$0.256985\pi$
$233$	6.50041e10i	1.44490i	−0.691421	+	0.722452i	$0.743015\pi$
$234$	−4.06559e10	−0.886446
$235$	0	0
$236$	−5.47025e7	−0.00114790
$237$	− 5.78067e10i	− 1.19017i
$238$	3.11297e10i	0.628896i
$239$	−9.18633e9	−0.182117	−0.0910587	−	0.995846i	$-0.529025\pi$
$239$	−9.18633e9	−0.182117	−0.0910587	+	0.995846i	$0.529025\pi$
$240$	0	0
$241$	1.49904e10	0.286244	0.143122	−	0.989705i	$-0.454286\pi$
$241$	1.49904e10	0.286244	0.143122	+	0.989705i	$0.454286\pi$
$242$	4.34228e10i	0.813858i
$243$	1.52540e10i	0.280643i
$244$	−6.73553e8	−0.0121652
$245$	0	0
$246$	−2.13038e10	−0.370893
$247$	− 5.16460e10i	− 0.882878i
$248$	4.76253e9i	0.0799476i
$249$	1.02614e11	1.69164
$250$	0	0
$251$	−1.03095e11	−1.63947	−0.819737	−	0.572741i	$-0.805880\pi$
$251$	−1.03095e11	−1.63947	−0.819737	+	0.572741i	$0.805880\pi$
$252$	− 5.69657e8i	− 0.00889837i
$253$	2.86097e10i	0.439006i
$254$	−2.04138e10	−0.307732
$255$	0	0
$256$	2.53529e9	0.0368934
$257$	− 7.34759e10i	− 1.05062i	−0.850911	−	0.525310i	$-0.823949\pi$
$257$	− 7.34759e10i	− 1.05062i	0.850911	−	0.525310i	$-0.176051\pi$
$258$	− 6.96601e10i	− 0.978804i
$259$	−3.08314e10	−0.425739
$260$	0	0
$261$	−2.34794e11	−3.13188
$262$	6.65568e10i	0.872643i
$263$	− 8.95222e10i	− 1.15380i	−0.816815	−	0.576899i	$-0.804263\pi$
$263$	− 8.95222e10i	− 1.15380i	0.816815	−	0.576899i	$-0.195737\pi$
$264$	5.85305e10	0.741591
$265$	0	0
$266$	5.95584e10	0.729417
$267$	1.26870e10i	0.152777i
$268$	1.19288e9i	0.0141250i
$269$	−1.00270e11	−1.16758	−0.583791	−	0.811904i	$-0.698431\pi$
$269$	−1.00270e11	−1.16758	−0.583791	+	0.811904i	$0.698431\pi$
$270$	0	0
$271$	1.05822e11	1.19183	0.595915	−	0.803048i	$-0.296790\pi$
$271$	1.05822e11	1.19183	0.595915	+	0.803048i	$0.296790\pi$
$272$	1.51105e11i	1.67385i
$273$	− 2.72563e10i	− 0.296985i
$274$	−1.02919e11	−1.10310
$275$	0	0
$276$	2.03271e9	0.0210855
$277$	1.20160e10i	0.122631i	0.998118	+	0.0613156i	$0.0195296\pi$
$277$	1.20160e10i	0.122631i	−0.998118	+	0.0613156i	$0.980470\pi$
$278$	− 1.64756e11i	− 1.65439i
$279$	1.55852e10	0.153990
$280$	0	0
$281$	−2.03641e11	−1.94844	−0.974218	−	0.225610i	$-0.927563\pi$
$281$	−2.03641e11	−1.94844	−0.974218	+	0.225610i	$0.927563\pi$
$282$	− 1.96948e11i	− 1.85451i
$283$	1.52674e11i	1.41490i	0.706765	+	0.707449i	$0.250154\pi$
$283$	1.52674e11i	1.41490i	−0.706765	+	0.707449i	$0.749846\pi$
$284$	−5.73688e8	−0.00523291
$285$	0	0
$286$	−2.29068e10	−0.202449
$287$	− 9.38125e9i	− 0.0816191i
$288$	− 5.49707e9i	− 0.0470831i
$289$	−2.05742e11	−1.73493
$290$	0	0
$291$	−7.21779e10	−0.590046
$292$	6.20026e8i	0.00499099i
$293$	− 1.91313e11i	− 1.51649i	−0.651970	−	0.758244i	$-0.726057\pi$
$293$	− 1.91313e11i	− 1.51649i	0.651970	−	0.758244i	$-0.273943\pi$
$294$	3.14320e10	0.245363
$295$	0	0
$296$	−1.47838e11	−1.11937
$297$	− 9.14720e10i	− 0.682157i
$298$	8.74004e10i	0.642008i
$299$	6.38836e10	0.462242
$300$	0	0
$301$	3.06753e10	0.215397
$302$	1.39845e11i	0.967423i
$303$	− 4.02522e11i	− 2.74345i
$304$	2.89098e11	1.94140
$305$	0	0
$306$	4.88474e11	3.18490
$307$	7.89027e10i	0.506955i	0.967341	+	0.253477i	$0.0815743\pi$
$307$	7.89027e10i	0.506955i	−0.967341	+	0.253477i	$0.918426\pi$
$308$	− 3.20962e8i	− 0.00203224i
$309$	1.12229e11	0.700312
$310$	0	0
$311$	1.17336e11	0.711230	0.355615	−	0.934633i	$-0.384271\pi$
$311$	1.17336e11	0.711230	0.355615	+	0.934633i	$0.384271\pi$
$312$	− 1.30695e11i	− 0.780842i
$313$	− 1.77136e11i	− 1.04318i	−0.853198	−	0.521588i	$-0.825340\pi$
$313$	− 1.77136e11i	− 1.04318i	0.853198	−	0.521588i	$-0.174660\pi$
$314$	−2.12108e11	−1.23133
$315$	0	0
$316$	−1.51999e9	−0.00857531
$317$	− 3.17183e11i	− 1.76418i	−0.471080	−	0.882091i	$-0.656136\pi$
$317$	− 3.17183e11i	− 1.76418i	0.471080	−	0.882091i	$-0.343864\pi$
$318$	− 5.99939e11i	− 3.28992i
$319$	−1.32290e11	−0.715270
$320$	0	0
$321$	−1.23456e11	−0.648991
$322$	7.36708e10i	0.381895i
$323$	6.20519e11i	3.17208i
$324$	−1.82911e9	−0.00922118
$325$	0	0
$326$	1.48696e11	0.729157
$327$	1.28552e11i	0.621747i
$328$	− 4.49835e10i	− 0.214596i
$329$	8.67272e10	0.408107
$330$	0	0
$331$	−7.29998e10	−0.334269	−0.167134	−	0.985934i	$-0.553451\pi$
$331$	−7.29998e10	−0.334269	−0.167134	+	0.985934i	$0.553451\pi$
$332$	− 2.69816e9i	− 0.0121884i
$333$	4.83793e11i	2.15606i
$334$	−6.21637e10	−0.273324
$335$	0	0
$336$	1.52572e11	0.653053
$337$	1.07231e11i	0.452882i	0.974025	+	0.226441i	$0.0727091\pi$
$337$	1.07231e11i	0.452882i	−0.974025	+	0.226441i	$0.927291\pi$
$338$	− 1.90274e11i	− 0.792966i
$339$	−1.29368e11	−0.532021
$340$	0	0
$341$	8.78116e9	0.0351688
$342$	− 9.34565e11i	− 3.69396i
$343$	1.38413e10i	0.0539949i
$344$	1.47089e11	0.566328
$345$	0	0
$346$	8.39196e9	0.0314790
$347$	2.66192e11i	0.985627i	0.870135	+	0.492813i	$0.164031\pi$
$347$	2.66192e11i	0.985627i	−0.870135	+	0.492813i	$0.835969\pi$
$348$	9.39919e9i	0.0343545i
$349$	−7.30078e10	−0.263424	−0.131712	−	0.991288i	$-0.542047\pi$
$349$	−7.30078e10	−0.263424	−0.131712	+	0.991288i	$0.542047\pi$
$350$	0	0
$351$	−2.04251e11	−0.718262
$352$	− 3.09722e9i	− 0.0107530i
$353$	1.03915e11i	0.356198i	0.984013	+	0.178099i	$0.0569948\pi$
$353$	1.03915e11i	0.356198i	−0.984013	+	0.178099i	$0.943005\pi$
$354$	−4.73623e10	−0.160294
$355$	0	0
$356$	3.33597e8	0.00110077
$357$	3.27480e11i	1.06703i
$358$	− 4.49063e11i	− 1.44489i
$359$	−8.28712e10	−0.263317	−0.131658	−	0.991295i	$-0.542030\pi$
$359$	−8.28712e10	−0.263317	−0.131658	+	0.991295i	$0.542030\pi$
$360$	0	0
$361$	8.64509e11	2.67909
$362$	7.08997e10i	0.216998i
$363$	4.56801e11i	1.38085i
$364$	−7.16688e8	−0.00213980
$365$	0	0
$366$	−5.83173e11	−1.69876
$367$	1.99606e11i	0.574348i	0.957878	+	0.287174i	$0.0927158\pi$
$367$	1.99606e11i	0.574348i	−0.957878	+	0.287174i	$0.907284\pi$
$368$	3.57600e11i	1.01644i
$369$	−1.47206e11	−0.413341
$370$	0	0
$371$	2.64187e11	0.723983
$372$	− 6.23899e8i	− 0.00168916i
$373$	4.49796e10i	0.120317i	0.998189	+	0.0601583i	$0.0191606\pi$
$373$	4.49796e10i	0.120317i	−0.998189	+	0.0601583i	$0.980839\pi$
$374$	2.75221e11	0.727377
$375$	0	0
$376$	4.15861e11	1.07301
$377$	2.95396e11i	0.753128i
$378$	− 2.35543e11i	− 0.593414i
$379$	1.89077e9	0.00470718	0.00235359	−	0.999997i	$-0.499251\pi$
$379$	1.89077e9	0.00470718	0.00235359	+	0.999997i	$0.499251\pi$
$380$	0	0
$381$	−2.14750e11	−0.522121
$382$	7.23399e11i	1.73817i
$383$	3.12549e11i	0.742205i	0.928592	+	0.371103i	$0.121020\pi$
$383$	3.12549e11i	0.742205i	−0.928592	+	0.371103i	$0.878980\pi$
$384$	7.40480e11	1.73789
$385$	0	0
$386$	−5.03511e11	−1.15443
$387$	− 4.81343e11i	− 1.09083i
$388$	1.89788e9i	0.00425134i
$389$	−2.84599e11	−0.630173	−0.315086	−	0.949063i	$-0.602033\pi$
$389$	−2.84599e11	−0.630173	−0.315086	+	0.949063i	$0.602033\pi$
$390$	0	0
$391$	−7.67551e11	−1.66078
$392$	6.63696e10i	0.141965i
$393$	7.00167e11i	1.48059i
$394$	−4.91454e11	−1.02742
$395$	0	0
$396$	−5.03639e9	−0.0102918
$397$	7.92352e11i	1.60089i	0.599408	+	0.800444i	$0.295403\pi$
$397$	7.92352e11i	1.60089i	−0.599408	+	0.800444i	$0.704597\pi$
$398$	6.34564e11i	1.26766i
$399$	6.26545e11	1.23758
$400$	0	0
$401$	6.62180e11	1.27887	0.639435	−	0.768845i	$-0.279168\pi$
$401$	6.62180e11	1.27887	0.639435	+	0.768845i	$0.279168\pi$
$402$	1.03281e12i	1.97244i
$403$	− 1.96078e10i	− 0.0370302i
$404$	−1.05841e10	−0.0197668
$405$	0	0
$406$	−3.40652e11	−0.622220
$407$	2.72583e11i	0.492407i
$408$	1.57028e12i	2.80547i
$409$	−1.09286e12	−1.93112	−0.965560	−	0.260182i	$-0.916217\pi$
$409$	−1.09286e12	−1.93112	−0.965560	+	0.260182i	$0.916217\pi$
$410$	0	0
$411$	−1.08269e12	−1.87161
$412$	− 2.95100e9i	− 0.00504581i
$413$	− 2.08563e10i	− 0.0352746i
$414$	1.15601e12	1.93402
$415$	0	0
$416$	−6.91589e9	−0.0113221
$417$	− 1.73320e12i	− 2.80697i
$418$	− 5.26562e11i	− 0.843639i
$419$	−3.74698e11	−0.593907	−0.296953	−	0.954892i	$-0.595971\pi$
$419$	−3.74698e11	−0.593907	−0.296953	+	0.954892i	$0.595971\pi$
$420$	0	0
$421$	7.35051e11	1.14038	0.570188	−	0.821514i	$-0.306870\pi$
$421$	7.35051e11	1.14038	0.570188	+	0.821514i	$0.306870\pi$
$422$	− 2.99279e11i	− 0.459379i
$423$	− 1.36089e12i	− 2.06676i
$424$	1.26679e12	1.90352
$425$	0	0
$426$	−4.96709e11	−0.730732
$427$	− 2.56804e11i	− 0.373832i
$428$	3.24620e9i	0.00467604i
$429$	−2.40976e11	−0.343491
$430$	0	0
$431$	−5.29788e11	−0.739528	−0.369764	−	0.929126i	$-0.620561\pi$
$431$	−5.29788e11	−0.739528	−0.369764	+	0.929126i	$0.620561\pi$
$432$	− 1.14333e12i	− 1.57942i
$433$	1.82162e11i	0.249036i	0.992217	+	0.124518i	$0.0397384\pi$
$433$	1.82162e11i	0.249036i	−0.992217	+	0.124518i	$0.960262\pi$
$434$	2.26118e10	0.0305936
$435$	0	0
$436$	3.38020e9	0.00447975
$437$	1.46850e12i	1.92623i
$438$	5.36829e11i	0.696951i
$439$	8.13895e11	1.04587	0.522936	−	0.852372i	$-0.324837\pi$
$439$	8.13895e11	1.04587	0.522936	+	0.852372i	$0.324837\pi$
$440$	0	0
$441$	2.17192e11	0.273445
$442$	− 6.14552e11i	− 0.765876i
$443$	− 5.65176e11i	− 0.697215i	−0.937269	−	0.348607i	$-0.886655\pi$
$443$	− 5.65176e11i	− 0.697215i	0.937269	−	0.348607i	$-0.113345\pi$
$444$	1.93670e10	0.0236504
$445$	0	0
$446$	1.27252e12	1.52285
$447$	9.19439e11i	1.08928i
$448$	3.18196e11i	0.373202i
$449$	5.86919e11	0.681506	0.340753	−	0.940153i	$-0.389318\pi$
$449$	5.86919e11	0.681506	0.340753	+	0.940153i	$0.389318\pi$
$450$	0	0
$451$	−8.29406e10	−0.0944002
$452$	3.40166e9i	0.00383326i
$453$	1.47115e12i	1.64140i
$454$	1.36337e12	1.50612
$455$	0	0
$456$	3.00431e12	3.25389
$457$	2.06593e10i	0.0221561i	0.999939	+	0.0110781i	$0.00352633\pi$
$457$	2.06593e10i	0.0221561i	−0.999939	+	0.0110781i	$0.996474\pi$
$458$	1.50716e12i	1.60054i
$459$	2.45405e12	2.58063
$460$	0	0
$461$	2.59983e11	0.268096	0.134048	−	0.990975i	$-0.457202\pi$
$461$	2.59983e11	0.268096	0.134048	+	0.990975i	$0.457202\pi$
$462$	− 2.77894e11i	− 0.283786i
$463$	− 6.62434e11i	− 0.669928i	−0.942231	−	0.334964i	$-0.891276\pi$
$463$	− 6.62434e11i	− 0.669928i	0.942231	−	0.334964i	$-0.108724\pi$
$464$	−1.65353e12	−1.65608
$465$	0	0
$466$	1.47989e12	1.45376
$467$	5.78561e11i	0.562890i	0.959577	+	0.281445i	$0.0908137\pi$
$467$	5.78561e11i	0.562890i	−0.959577	+	0.281445i	$0.909186\pi$
$468$	1.12460e10i	0.0108365i
$469$	−4.54805e11	−0.434058
$470$	0	0
$471$	−2.23134e12	−2.08916
$472$	− 1.00007e11i	− 0.0927450i
$473$	− 2.71203e11i	− 0.249126i
$474$	−1.31604e12	−1.19747
$475$	0	0
$476$	8.61089e9	0.00768806
$477$	− 4.14551e12i	− 3.66644i
$478$	2.09137e11i	0.183234i
$479$	−1.30509e12	−1.13274	−0.566370	−	0.824151i	$-0.691653\pi$
$479$	−1.30509e12	−1.13274	−0.566370	+	0.824151i	$0.691653\pi$
$480$	0	0
$481$	6.08662e11	0.518470
$482$	− 3.41274e11i	− 0.287999i
$483$	7.75006e11i	0.647952i
$484$	1.20113e10	0.00994916
$485$	0	0
$486$	3.47274e11	0.282364
$487$	− 2.26035e12i	− 1.82094i	−0.413579	−	0.910468i	$-0.635722\pi$
$487$	− 2.26035e12i	− 1.82094i	0.413579	−	0.910468i	$-0.364278\pi$
$488$	− 1.23139e12i	− 0.982890i
$489$	1.56426e12	1.23714
$490$	0	0
$491$	−2.05833e11	−0.159827	−0.0799133	−	0.996802i	$-0.525464\pi$
$491$	−2.05833e11	−0.159827	−0.0799133	+	0.996802i	$0.525464\pi$
$492$	5.89291e9i	0.00453405i
$493$	− 3.54914e12i	− 2.70590i
$494$	−1.17578e12	−0.888291
$495$	0	0
$496$	1.09758e11	0.0814273
$497$	− 2.18729e11i	− 0.160806i
$498$	− 2.33612e12i	− 1.70201i
$499$	2.10713e11	0.152139	0.0760693	−	0.997103i	$-0.475763\pi$
$499$	2.10713e11	0.152139	0.0760693	+	0.997103i	$0.475763\pi$
$500$	0	0
$501$	−6.53952e11	−0.463742
$502$	2.34707e12i	1.64953i
$503$	7.30487e10i	0.0508811i	0.999676	+	0.0254406i	$0.00809886\pi$
$503$	7.30487e10i	0.0508811i	−0.999676	+	0.0254406i	$0.991901\pi$
$504$	1.04144e12	0.718949
$505$	0	0
$506$	6.51332e11	0.441697
$507$	− 2.00165e12i	− 1.34541i
$508$	5.64673e9i	0.00376193i
$509$	1.52888e11	0.100958	0.0504792	−	0.998725i	$-0.483925\pi$
$509$	1.52888e11	0.100958	0.0504792	+	0.998725i	$0.483925\pi$
$510$	0	0
$511$	−2.36396e11	−0.153372
$512$	1.52529e12i	0.980932i
$513$	− 4.69516e12i	− 2.99311i
$514$	−1.67276e12	−1.05706
$515$	0	0
$516$	−1.92689e10	−0.0119656
$517$	− 7.66764e11i	− 0.472014i
$518$	7.01911e11i	0.428350i
$519$	8.82820e10	0.0534096
$520$	0	0
$521$	−3.12005e11	−0.185520	−0.0927601	−	0.995688i	$-0.529569\pi$
$521$	−3.12005e11	−0.185520	−0.0927601	+	0.995688i	$0.529569\pi$
$522$	5.34536e12i	3.15108i
$523$	7.13578e11i	0.417046i	0.978017	+	0.208523i	$0.0668656\pi$
$523$	7.13578e11i	0.417046i	−0.978017	+	0.208523i	$0.933134\pi$
$524$	1.84105e10	0.0106678
$525$	0	0
$526$	−2.03808e12	−1.16087
$527$	2.35585e11i	0.133045i
$528$	− 1.34891e12i	− 0.755317i
$529$	−1.53155e10	−0.00850315
$530$	0	0
$531$	−3.27268e11	−0.178640
$532$	− 1.64746e10i	− 0.00891689i
$533$	1.85201e11i	0.0993966i
$534$	2.88834e11	0.153713
$535$	0	0
$536$	−2.18081e12	−1.14124
$537$	− 4.72407e12i	− 2.45150i
$538$	2.28277e12i	1.17474i
$539$	1.22372e11	0.0624502
$540$	0	0
$541$	−7.80203e9	−0.00391580	−0.00195790	−	0.999998i	$-0.500623\pi$
$541$	−7.80203e9	−0.00391580	−0.00195790	+	0.999998i	$0.500623\pi$
$542$	− 2.40916e12i	− 1.19914i
$543$	7.45854e11i	0.368175i
$544$	8.30934e10	0.0406791
$545$	0	0
$546$	−6.20520e11	−0.298806
$547$	2.00379e12i	0.956994i	0.878089	+	0.478497i	$0.158818\pi$
$547$	2.00379e12i	0.956994i	−0.878089	+	0.478497i	$0.841182\pi$
$548$	2.84687e10i	0.0134851i
$549$	−4.02966e12	−1.89318
$550$	0	0
$551$	−6.79033e12	−3.13840
$552$	3.71618e12i	1.70362i
$553$	− 5.79524e11i	− 0.263517i
$554$	2.73558e11	0.123383
$555$	0	0
$556$	−4.55736e10	−0.0202245
$557$	− 6.30817e11i	− 0.277687i	−0.990314	−	0.138843i	$-0.955662\pi$
$557$	− 6.30817e11i	− 0.277687i	0.990314	−	0.138843i	$-0.0443385\pi$
$558$	− 3.54815e11i	− 0.154934i
$559$	−6.05580e11	−0.262312
$560$	0	0
$561$	2.89528e12	1.23412
$562$	4.63611e12i	1.96038i
$563$	2.72592e12i	1.14347i	0.820438	+	0.571736i	$0.193730\pi$
$563$	2.72592e12i	1.14347i	−0.820438	+	0.571736i	$0.806270\pi$
$564$	−5.44784e10	−0.0226709
$565$	0	0
$566$	3.47579e12	1.42357
$567$	− 6.97379e11i	− 0.283364i
$568$	− 1.04881e12i	− 0.422796i
$569$	3.54264e12	1.41684	0.708422	−	0.705789i	$-0.249408\pi$
$569$	3.54264e12	1.41684	0.708422	+	0.705789i	$0.249408\pi$
$570$	0	0
$571$	3.74623e12	1.47480	0.737398	−	0.675458i	$-0.236054\pi$
$571$	3.74623e12	1.47480	0.737398	+	0.675458i	$0.236054\pi$
$572$	6.33631e9i	0.00247488i
$573$	7.61004e12i	2.94911i
$574$	−2.13575e11	−0.0821196
$575$	0	0
$576$	4.99300e12	1.88999
$577$	− 3.74243e12i	− 1.40560i	−0.711386	−	0.702802i	$-0.751932\pi$
$577$	− 3.74243e12i	− 1.40560i	0.711386	−	0.702802i	$-0.248068\pi$
$578$	4.68396e12i	1.74557i
$579$	−5.29686e12	−1.95869
$580$	0	0
$581$	1.02872e12	0.374546
$582$	1.64321e12i	0.593664i
$583$	− 2.33570e12i	− 0.837354i
$584$	−1.13353e12	−0.403250
$585$	0	0
$586$	−4.35545e12	−1.52579
$587$	2.19633e12i	0.763532i	0.924259	+	0.381766i	$0.124684\pi$
$587$	2.19633e12i	0.763532i	−0.924259	+	0.381766i	$0.875316\pi$
$588$	− 8.69452e9i	− 0.00299949i
$589$	4.50728e11	0.154311
$590$	0	0
$591$	−5.17002e12	−1.74321
$592$	3.40710e12i	1.14008i
$593$	− 5.88312e12i	− 1.95372i	−0.213884	−	0.976859i	$-0.568611\pi$
$593$	− 5.88312e12i	− 1.95372i	0.213884	−	0.976859i	$-0.431389\pi$
$594$	−2.08246e12	−0.686339
$595$	0	0
$596$	2.41761e10	0.00784835
$597$	6.67552e12i	2.15080i
$598$	− 1.45438e12i	− 0.465076i
$599$	1.32770e12	0.421385	0.210692	−	0.977552i	$-0.432428\pi$
$599$	1.32770e12	0.421385	0.210692	+	0.977552i	$0.432428\pi$
$600$	0	0
$601$	−5.90463e11	−0.184611	−0.0923055	−	0.995731i	$-0.529424\pi$
$601$	−5.90463e11	−0.184611	−0.0923055	+	0.995731i	$0.529424\pi$
$602$	− 6.98357e11i	− 0.216717i
$603$	7.13660e12i	2.19818i
$604$	3.86830e10	0.0118265
$605$	0	0
$606$	−9.16386e12	−2.76027
$607$	− 1.15860e12i	− 0.346404i	−0.984886	−	0.173202i	$-0.944589\pi$
$607$	− 1.15860e12i	− 0.346404i	0.984886	−	0.173202i	$-0.0554114\pi$
$608$	− 1.58977e11i	− 0.0471811i
$609$	−3.58361e12	−1.05570
$610$	0	0
$611$	−1.71214e12	−0.496996
$612$	− 1.35118e11i	− 0.0389344i
$613$	− 4.56114e12i	− 1.30467i	−0.757929	−	0.652337i	$-0.773789\pi$
$613$	− 4.56114e12i	− 1.30467i	0.757929	−	0.652337i	$-0.226211\pi$
$614$	1.79631e12	0.510063
$615$	0	0
$616$	5.86781e11	0.164196
$617$	5.85962e10i	0.0162774i	0.999967	+	0.00813872i	$0.00259066\pi$
$617$	5.85962e10i	0.0162774i	−0.999967	+	0.00813872i	$0.997409\pi$
$618$	− 2.55502e12i	− 0.704606i
$619$	−2.31615e12	−0.634101	−0.317050	−	0.948409i	$-0.602692\pi$
$619$	−2.31615e12	−0.634101	−0.317050	+	0.948409i	$0.602692\pi$
$620$	0	0
$621$	5.80769e12	1.56708
$622$	− 2.67129e12i	− 0.715590i
$623$	1.27190e11i	0.0338264i
$624$	−3.01202e12	−0.795294
$625$	0	0
$626$	−4.03271e12	−1.04957
$627$	− 5.53935e12i	− 1.43138i
$628$	5.86718e10i	0.0150526i
$629$	−7.31298e12	−1.86280
$630$	0	0
$631$	1.36072e12	0.341693	0.170847	−	0.985298i	$-0.445350\pi$
$631$	1.36072e12	0.341693	0.170847	+	0.985298i	$0.445350\pi$
$632$	− 2.77884e12i	− 0.692847i
$633$	− 3.14837e12i	− 0.779416i
$634$	−7.22103e12	−1.77500
$635$	0	0
$636$	−1.65951e11	−0.0402182
$637$	− 2.73250e11i	− 0.0657555i
$638$	3.01174e12i	0.719655i
$639$	−3.43219e12	−0.814363
$640$	0	0
$641$	−5.19542e12	−1.21551	−0.607756	−	0.794124i	$-0.707930\pi$
$641$	−5.19542e12	−1.21551	−0.607756	+	0.794124i	$0.707930\pi$
$642$	2.81061e12i	0.652970i
$643$	− 5.15183e12i	− 1.18854i	−0.804267	−	0.594268i	$-0.797442\pi$
$643$	− 5.15183e12i	− 1.18854i	0.804267	−	0.594268i	$-0.202558\pi$
$644$	2.03783e10	0.00466855
$645$	0	0
$646$	1.41268e13	3.19152
$647$	9.10873e11i	0.204357i	0.994766	+	0.102178i	$0.0325812\pi$
$647$	9.10873e11i	0.204357i	−0.994766	+	0.102178i	$0.967419\pi$
$648$	− 3.34396e12i	− 0.745030i
$649$	−1.84393e11	−0.0407983
$650$	0	0
$651$	2.37872e11	0.0519075
$652$	− 4.11314e10i	− 0.00891372i
$653$	− 3.27767e12i	− 0.705433i	−0.935730	−	0.352717i	$-0.885258\pi$
$653$	− 3.27767e12i	− 0.705433i	0.935730	−	0.352717i	$-0.114742\pi$
$654$	2.92663e12	0.625559
$655$	0	0
$656$	−1.03670e12	−0.218567
$657$	3.70942e12i	0.776715i
$658$	− 1.97444e12i	− 0.410609i
$659$	−2.27024e12	−0.468907	−0.234453	−	0.972127i	$-0.575330\pi$
$659$	−2.27024e12	−0.468907	−0.234453	+	0.972127i	$0.575330\pi$
$660$	0	0
$661$	−3.17394e12	−0.646684	−0.323342	−	0.946282i	$-0.604806\pi$
$661$	−3.17394e12	−0.646684	−0.323342	+	0.946282i	$0.604806\pi$
$662$	1.66192e12i	0.336318i
$663$	− 6.46499e12i	− 1.29944i
$664$	4.93277e12	0.984769
$665$	0	0
$666$	1.10141e13	2.16928
$667$	− 8.39930e12i	− 1.64315i
$668$	1.71953e10i	0.00334130i
$669$	1.33867e13	2.58378
$670$	0	0
$671$	−2.27043e12	−0.432371
$672$	− 8.39003e10i	− 0.0158709i
$673$	− 4.96227e12i	− 0.932423i	−0.884673	−	0.466212i	$-0.845619\pi$
$673$	− 4.96227e12i	− 0.932423i	0.884673	−	0.466212i	$-0.154381\pi$
$674$	2.44124e12	0.455659
$675$	0	0
$676$	−5.26324e10	−0.00969377
$677$	− 6.67904e12i	− 1.22198i	−0.791638	−	0.610991i	$-0.790771\pi$
$677$	− 6.67904e12i	− 1.22198i	0.791638	−	0.610991i	$-0.209229\pi$
$678$	2.94522e12i	0.535283i
$679$	−7.23599e11	−0.130642
$680$	0	0
$681$	1.43424e13	2.55540
$682$	− 1.99913e11i	− 0.0353844i
$683$	5.75109e12i	1.01125i	0.862755	+	0.505623i	$0.168737\pi$
$683$	5.75109e12i	1.01125i	−0.862755	+	0.505623i	$0.831263\pi$
$684$	−2.58513e11	−0.0451575
$685$	0	0
$686$	3.15113e11	0.0543260
$687$	1.58551e13i	2.71559i
$688$	− 3.38985e12i	− 0.576809i
$689$	−5.21548e12	−0.881674
$690$	0	0
$691$	4.84476e12	0.808391	0.404196	−	0.914673i	$-0.367552\pi$
$691$	4.84476e12	0.808391	0.404196	+	0.914673i	$0.367552\pi$
$692$	− 2.32133e9i	0 0.000384821i
$693$	− 1.92021e12i	− 0.316264i
$694$	6.06017e12	0.991669
$695$	0	0
$696$	−1.71835e13	−2.77569
$697$	− 2.22516e12i	− 0.357120i
$698$	1.66211e12i	0.265039i
$699$	1.55682e13	2.46656
$700$	0	0
$701$	−2.61772e12	−0.409441	−0.204721	−	0.978820i	$-0.565629\pi$
$701$	−2.61772e12	−0.409441	−0.204721	+	0.978820i	$0.565629\pi$
$702$	4.65001e12i	0.722665i
$703$	1.39914e13i	2.16054i
$704$	2.81321e12	0.431643
$705$	0	0
$706$	2.36574e12	0.358382
$707$	− 4.03536e12i	− 0.607429i
$708$	1.31010e10i	0.00195955i
$709$	−2.83866e12	−0.421897	−0.210948	−	0.977497i	$-0.567655\pi$
$709$	−2.83866e12	−0.421897	−0.210948	+	0.977497i	$0.567655\pi$
$710$	0	0
$711$	−9.09364e12	−1.33452
$712$	6.09880e11i	0.0889373i
$713$	5.57529e11i	0.0807912i
$714$	7.45545e12	1.07357
$715$	0	0
$716$	−1.24217e11	−0.0176633
$717$	2.20009e12i	0.310889i
$718$	1.88666e12i	0.264931i
$719$	3.57178e12	0.498430	0.249215	−	0.968448i	$-0.419827\pi$
$719$	3.57178e12	0.498430	0.249215	+	0.968448i	$0.419827\pi$
$720$	0	0
$721$	1.12512e12	0.155056
$722$	− 1.96815e13i	− 2.69552i
$723$	− 3.59015e12i	− 0.488641i
$724$	1.96118e10	0.00265273
$725$	0	0
$726$	1.03996e13	1.38932
$727$	− 2.44104e12i	− 0.324094i	−0.986783	−	0.162047i	$-0.948190\pi$
$727$	− 2.44104e12i	− 0.324094i	0.986783	−	0.162047i	$-0.0518096\pi$
$728$	− 1.31024e12i	− 0.172887i
$729$	9.37027e12	1.22879
$730$	0	0
$731$	7.27595e12	0.942457
$732$	1.61313e11i	0.0207669i
$733$	− 2.05203e12i	− 0.262553i	−0.991346	−	0.131276i	$-0.958092\pi$
$733$	− 2.05203e12i	− 0.262553i	0.991346	−	0.131276i	$-0.0419075\pi$
$734$	4.54425e12	0.577870
$735$	0	0
$736$	1.96647e11	0.0247023
$737$	4.02098e12i	0.502028i
$738$	3.35132e12i	0.415875i
$739$	−5.67988e12	−0.700550	−0.350275	−	0.936647i	$-0.613912\pi$
$739$	−5.67988e12	−0.700550	−0.350275	+	0.936647i	$0.613912\pi$
$740$	0	0
$741$	−1.23690e13	−1.50714
$742$	− 6.01452e12i	− 0.728422i
$743$	− 1.78018e12i	− 0.214296i	−0.994243	−	0.107148i	$-0.965828\pi$
$743$	− 1.78018e12i	− 0.214296i	0.994243	−	0.107148i	$-0.0341719\pi$
$744$	1.14061e12	0.136477
$745$	0	0
$746$	1.02401e12	0.121054
$747$	− 1.61423e13i	− 1.89680i
$748$	− 7.61298e10i	− 0.00889196i
$749$	−1.23767e12	−0.143693
$750$	0	0
$751$	4.66195e12	0.534796	0.267398	−	0.963586i	$-0.413836\pi$
$751$	4.66195e12	0.534796	0.267398	+	0.963586i	$0.413836\pi$
$752$	− 9.58401e12i	− 1.09287i
$753$	2.46908e13i	2.79871i
$754$	6.72503e12	0.757745
$755$	0	0
$756$	−6.51544e10	−0.00725430
$757$	− 6.36622e12i	− 0.704612i	−0.935885	−	0.352306i	$-0.885398\pi$
$757$	− 6.36622e12i	− 0.704612i	0.935885	−	0.352306i	$-0.114602\pi$
$758$	− 4.30454e10i	− 0.00473604i
$759$	6.85191e12	0.749417
$760$	0	0
$761$	−9.79260e12	−1.05844	−0.529221	−	0.848484i	$-0.677516\pi$
$761$	−9.79260e12	−1.05844	−0.529221	+	0.848484i	$0.677516\pi$
$762$	4.88903e12i	0.525322i
$763$	1.28876e12i	0.137661i
$764$	2.00102e11	0.0212486
$765$	0	0
$766$	7.11554e12	0.746756
$767$	4.11737e11i	0.0429577i
$768$	− 6.07193e11i	− 0.0629798i
$769$	−1.05064e13	−1.08339	−0.541696	−	0.840575i	$-0.682217\pi$
$769$	−1.05064e13	−1.08339	−0.541696	+	0.840575i	$0.682217\pi$
$770$	0	0
$771$	−1.75972e13	−1.79349
$772$	1.39278e11i	0.0141125i
$773$	6.50971e12i	0.655774i	0.944717	+	0.327887i	$0.106337\pi$
$773$	6.50971e12i	0.655774i	−0.944717	+	0.327887i	$0.893663\pi$
$774$	−1.09583e13	−1.09751
$775$	0	0
$776$	−3.46969e12	−0.343489
$777$	7.38400e12i	0.726770i
$778$	6.47921e12i	0.634036i
$779$	−4.25726e12	−0.414201
$780$	0	0
$781$	−1.93380e12	−0.185987
$782$	1.74742e13i	1.67096i
$783$	2.68546e13i	2.55323i
$784$	1.52957e12	0.144593
$785$	0	0
$786$	1.59401e13	1.48967
$787$	1.85396e13i	1.72272i	0.507996	+	0.861359i	$0.330386\pi$
$787$	1.85396e13i	1.72272i	−0.507996	+	0.861359i	$0.669614\pi$
$788$	1.35943e11i	0.0125599i
$789$	−2.14402e13	−1.96962
$790$	0	0
$791$	−1.29694e12	−0.117795
$792$	− 9.20751e12i	− 0.831532i
$793$	5.06973e12i	0.455256i
$794$	1.80388e13	1.61070
$795$	0	0
$796$	1.75529e11	0.0154967
$797$	4.13989e12i	0.363435i	0.983351	+	0.181718i	$0.0581656\pi$
$797$	4.13989e12i	0.363435i	−0.983351	+	0.181718i	$0.941834\pi$
$798$	− 1.42640e13i	− 1.24517i
$799$	2.05711e13	1.78565
$800$	0	0
$801$	1.99580e12	0.171306
$802$	− 1.50753e13i	− 1.28671i
$803$	2.09000e12i	0.177389i
$804$	2.85689e11	0.0241125
$805$	0	0
$806$	−4.46394e11	−0.0372572
$807$	2.40144e13i	1.99315i
$808$	− 1.93497e13i	− 1.59707i
$809$	1.06411e13	0.873408	0.436704	−	0.899605i	$-0.356146\pi$
$809$	1.06411e13	0.873408	0.436704	+	0.899605i	$0.356146\pi$
$810$	0	0
$811$	1.16080e11	0.00942244	0.00471122	−	0.999989i	$-0.498500\pi$
$811$	1.16080e11	0.00942244	0.00471122	+	0.999989i	$0.498500\pi$
$812$	9.42288e10i	0.00760644i
$813$	− 2.53440e13i	− 2.03455i
$814$	6.20567e12	0.495426
$815$	0	0
$816$	3.61890e13	2.85740
$817$	− 1.39206e13i	− 1.09310i
$818$	2.48802e13i	1.94296i
$819$	−4.28772e12	−0.333003
$820$	0	0
$821$	−2.47649e13	−1.90236	−0.951179	−	0.308641i	$-0.900126\pi$
$821$	−2.47649e13	−1.90236	−0.951179	+	0.308641i	$0.900126\pi$
$822$	2.46486e13i	1.88308i
$823$	7.59942e12i	0.577406i	0.957419	+	0.288703i	$0.0932240\pi$
$823$	7.59942e12i	0.577406i	−0.957419	+	0.288703i	$0.906776\pi$
$824$	5.39499e12	0.407679
$825$	0	0
$826$	−4.74817e11	−0.0354908
$827$	9.92558e12i	0.737872i	0.929455	+	0.368936i	$0.120278\pi$
$827$	9.92558e12i	0.737872i	−0.929455	+	0.368936i	$0.879722\pi$
$828$	− 3.19768e11i	− 0.0236428i
$829$	−2.17549e12	−0.159978	−0.0799891	−	0.996796i	$-0.525489\pi$
$829$	−2.17549e12	−0.159978	−0.0799891	+	0.996796i	$0.525489\pi$
$830$	0	0
$831$	2.87779e12	0.209341
$832$	− 6.28172e12i	− 0.454489i
$833$	3.28305e12i	0.236252i
$834$	−3.94584e13	−2.82418
$835$	0	0
$836$	−1.45654e11	−0.0103132
$837$	− 1.78255e12i	− 0.125539i
$838$	8.53043e12i	0.597548i
$839$	8.79323e12	0.612660	0.306330	−	0.951925i	$-0.400899\pi$
$839$	8.79323e12	0.612660	0.306330	+	0.951925i	$0.400899\pi$
$840$	0	0
$841$	2.43310e13	1.67717
$842$	− 1.67343e13i	− 1.14737i
$843$	4.87712e13i	3.32613i
$844$	−8.27846e10	−0.00561576
$845$	0	0
$846$	−3.09821e13	−2.07943
$847$	4.57953e12i	0.305735i
$848$	− 2.91946e13i	− 1.93875i
$849$	3.65647e13	2.41534
$850$	0	0
$851$	−1.73067e13	−1.13118
$852$	1.37396e11i	0.00893298i
$853$	− 2.98980e13i	− 1.93362i	−0.255494	−	0.966811i	$-0.582238\pi$
$853$	− 2.98980e13i	− 1.93362i	0.255494	−	0.966811i	$-0.417762\pi$
$854$	−5.84643e12	−0.376124
$855$	0	0
$856$	−5.93468e12	−0.377803
$857$	− 1.46014e13i	− 0.924654i	−0.886709	−	0.462327i	$-0.847015\pi$
$857$	− 1.46014e13i	− 0.924654i	0.886709	−	0.462327i	$-0.152985\pi$
$858$	5.48609e12i	0.345597i
$859$	6.23914e11	0.0390981	0.0195490	−	0.999809i	$-0.493777\pi$
$859$	6.23914e11	0.0390981	0.0195490	+	0.999809i	$0.493777\pi$
$860$	0	0
$861$	−2.24677e12	−0.139330
$862$	1.20612e13i	0.744062i
$863$	2.27436e12i	0.139576i	0.997562	+	0.0697879i	$0.0222322\pi$
$863$	2.27436e12i	0.139576i	−0.997562	+	0.0697879i	$0.977768\pi$
$864$	−6.28727e11	−0.0383840
$865$	0	0
$866$	4.14712e12	0.250563
$867$	4.92745e13i	2.96167i
$868$	− 6.25472e9i	0 0.000373998i
$869$	−5.12363e12	−0.304782
$870$	0	0
$871$	8.97860e12	0.528600
$872$	6.17966e12i	0.361943i
$873$	1.13544e13i	0.661607i
$874$	3.34322e13	1.93804
$875$	0	0
$876$	1.48494e11	0.00852001
$877$	− 2.75045e13i	− 1.57002i	−0.619482	−	0.785011i	$-0.712657\pi$
$877$	− 2.75045e13i	− 1.57002i	0.619482	−	0.785011i	$-0.287343\pi$
$878$	− 1.85293e13i	− 1.05228i
$879$	−4.58186e13	−2.58876
$880$	0	0
$881$	−1.54100e13	−0.861809	−0.430904	−	0.902398i	$-0.641805\pi$
$881$	−1.54100e13	−0.861809	−0.430904	+	0.902398i	$0.641805\pi$
$882$	− 4.94461e12i	− 0.275121i
$883$	− 1.77905e13i	− 0.984838i	−0.870358	−	0.492419i	$-0.836113\pi$
$883$	− 1.77905e13i	− 0.984838i	0.870358	−	0.492419i	$-0.163887\pi$
$884$	−1.69993e11	−0.00936260
$885$	0	0
$886$	−1.28669e13	−0.701489
$887$	1.07061e13i	0.580734i	0.956915	+	0.290367i	$0.0937773\pi$
$887$	1.07061e13i	0.580734i	−0.956915	+	0.290367i	$0.906223\pi$
$888$	3.54066e13i	1.91085i
$889$	−2.15292e12	−0.115603
$890$	0	0
$891$	−6.16560e12	−0.327737
$892$	− 3.51995e11i	− 0.0186163i
$893$	− 3.93572e13i	− 2.07106i
$894$	2.09321e13	1.09596
$895$	0	0
$896$	7.42347e12	0.384787
$897$	− 1.52999e13i	− 0.789082i
$898$	− 1.33619e13i	− 0.685684i
$899$	−2.57800e12	−0.131633
$900$	0	0
$901$	6.26632e13	3.16775
$902$	1.88824e12i	0.0949789i
$903$	− 7.34661e12i	− 0.367699i
$904$	−6.21890e12	−0.309710
$905$	0	0
$906$	3.34924e13	1.65147
$907$	9.46109e12i	0.464203i	0.972692	+	0.232102i	$0.0745602\pi$
$907$	9.46109e12i	0.464203i	−0.972692	+	0.232102i	$0.925440\pi$
$908$	− 3.77125e11i	− 0.0184119i
$909$	−6.33212e13	−3.07618
$910$	0	0
$911$	3.69156e13	1.77573	0.887865	−	0.460104i	$-0.152188\pi$
$911$	3.69156e13	1.77573	0.887865	+	0.460104i	$0.152188\pi$
$912$	− 6.92380e13i	− 3.31411i
$913$	− 9.09504e12i	− 0.433198i
$914$	4.70334e11	0.0222920
$915$	0	0
$916$	4.16901e11	0.0195660
$917$	7.01932e12i	0.327818i
$918$	− 5.58692e13i	− 2.59645i
$919$	−2.21297e13	−1.02343	−0.511713	−	0.859156i	$-0.670989\pi$
$919$	−2.21297e13	−1.02343	−0.511713	+	0.859156i	$0.670989\pi$
$920$	0	0
$921$	1.88969e13	0.865411
$922$	− 5.91882e12i	− 0.269740i
$923$	4.31806e12i	0.195831i
$924$	−7.68692e10	−0.00346919
$925$	0	0
$926$	−1.50811e13	−0.674035
$927$	− 1.76549e13i	− 0.785246i
$928$	9.09289e11i	0.0402472i
$929$	−1.24192e13	−0.547043	−0.273521	−	0.961866i	$-0.588188\pi$
$929$	−1.24192e13	−0.547043	−0.273521	+	0.961866i	$0.588188\pi$
$930$	0	0
$931$	6.28124e12	0.274014
$932$	− 4.09358e11i	− 0.0177718i
$933$	− 2.81016e13i	− 1.21412i
$934$	1.31716e13	0.566341
$935$	0	0
$936$	−2.05598e13	−0.875543
$937$	3.54355e13i	1.50179i	0.660420	+	0.750896i	$0.270378\pi$
$937$	3.54355e13i	1.50179i	−0.660420	+	0.750896i	$0.729622\pi$
$938$	1.03542e13i	0.436719i
$939$	−4.24234e13	−1.78078
$940$	0	0
$941$	1.16327e13	0.483646	0.241823	−	0.970320i	$-0.422255\pi$
$941$	1.16327e13	0.483646	0.241823	+	0.970320i	$0.422255\pi$
$942$	5.07990e13i	2.10197i
$943$	− 5.26602e12i	− 0.216860i
$944$	−2.30478e12	−0.0944615
$945$	0	0
$946$	−6.17425e12	−0.250654
$947$	− 3.20915e13i	− 1.29663i	−0.761373	−	0.648314i	$-0.775474\pi$
$947$	− 3.20915e13i	− 1.29663i	0.761373	−	0.648314i	$-0.224526\pi$
$948$	3.64033e11i	0.0146387i
$949$	4.66684e12	0.186778
$950$	0	0
$951$	−7.59641e13	−3.01159
$952$	1.57424e13i	0.621161i
$953$	3.35135e12i	0.131614i	0.997832	+	0.0658069i	$0.0209621\pi$
$953$	3.35135e12i	0.131614i	−0.997832	+	0.0658069i	$0.979038\pi$
$954$	−9.43772e13	−3.68892
$955$	0	0
$956$	5.78502e10	0.00223998
$957$	3.16830e13i	1.22102i
$958$	2.97118e13i	1.13968i
$959$	−1.08542e13	−0.414394
$960$	0	0
$961$	−2.62685e13	−0.993528
$962$	− 1.38569e13i	− 0.521648i
$963$	1.94210e13i	0.727701i
$964$	−9.44009e10	−0.00352070
$965$	0	0
$966$	1.76439e13	0.651924
$967$	− 3.10299e13i	− 1.14120i	−0.821229	−	0.570599i	$-0.806711\pi$
$967$	− 3.10299e13i	− 1.14120i	0.821229	−	0.570599i	$-0.193289\pi$
$968$	2.19590e13i	0.803848i
$969$	1.48612e14	5.41498
$970$	0	0
$971$	−1.95452e13	−0.705591	−0.352796	−	0.935700i	$-0.614769\pi$
$971$	−1.95452e13	−0.705591	−0.352796	+	0.935700i	$0.614769\pi$
$972$	− 9.60606e10i	− 0.00345181i
$973$	− 1.73757e13i	− 0.621492i
$974$	−5.14594e13	−1.83210
$975$	0	0
$976$	−2.83788e13	−1.00108
$977$	2.92875e13i	1.02839i	0.857674	+	0.514194i	$0.171909\pi$
$977$	2.92875e13i	1.02839i	−0.857674	+	0.514194i	$0.828091\pi$
$978$	− 3.56122e13i	− 1.24473i
$979$	1.12450e12	0.0391234
$980$	0	0
$981$	2.02227e13	0.697153
$982$	4.68603e12i	0.160806i
$983$	2.28350e13i	0.780029i	0.920809	+	0.390014i	$0.127530\pi$
$983$	2.28350e13i	0.780029i	−0.920809	+	0.390014i	$0.872470\pi$
$984$	−1.07734e13	−0.366331
$985$	0	0
$986$	−8.08002e13	−2.72249
$987$	− 2.07708e13i	− 0.696669i
$988$	3.25236e11i	0.0108591i
$989$	1.72191e13	0.572304
$990$	0	0
$991$	−9.28345e11	−0.0305758	−0.0152879	−	0.999883i	$-0.504866\pi$
$991$	−9.28345e11	−0.0305758	−0.0152879	+	0.999883i	$0.504866\pi$
$992$	− 6.03568e10i	− 0.00197890i
$993$	1.74832e13i	0.570622i
$994$	−4.97961e12	−0.161792
$995$	0	0
$996$	−6.46200e11	−0.0208066
$997$	3.95911e13i	1.26902i	0.772914	+	0.634511i	$0.218798\pi$
$997$	3.95911e13i	1.26902i	−0.772914	+	0.634511i	$0.781202\pi$
$998$	− 4.79713e12i	− 0.153071i
$999$	5.53337e13	1.75770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.f.99.3		10
5.2	odd	4		35.10.a.d.1.4	✓	5
5.3	odd	4		175.10.a.f.1.2		5
5.4	even	2	inner	175.10.b.f.99.8		10
15.2	even	4		315.10.a.j.1.2		5
35.27	even	4		245.10.a.f.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.d.1.4	✓	5	5.2	odd	4
175.10.a.f.1.2		5	5.3	odd	4
175.10.b.f.99.3		10	1.1	even	1	trivial
175.10.b.f.99.8		10	5.4	even	2	inner
245.10.a.f.1.4		5	35.27	even	4
315.10.a.j.1.2		5	15.2	even	4

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)

\(f(q)\)	\(=\)	\(q-22.7661i q^{2} -239.496i q^{3} -6.29742 q^{4} -5452.41 q^{6} -2401.00i q^{7} -11512.9i q^{8} -37675.5 q^{9} -21227.5 q^{11} +1508.21i q^{12} +47399.7i q^{13} -54661.5 q^{14} -265329. q^{16} -569500. i q^{17} +857725. i q^{18} -1.08959e6 q^{19} -575031. q^{21} +483268. i q^{22} -1.34776e6i q^{23} -2.75730e6 q^{24} +1.07911e6 q^{26} +4.30913e6i q^{27} +15120.1i q^{28} +6.23203e6 q^{29} -413669. q^{31} +145906. i q^{32} +5.08391e6i q^{33} -1.29653e7 q^{34} +237258. q^{36} -1.28411e7i q^{37} +2.48057e7i q^{38} +1.13520e7 q^{39} +3.90722e6 q^{41} +1.30912e7i q^{42} +1.27760e7i q^{43} +133678. q^{44} -3.06834e7 q^{46} +3.61213e7i q^{47} +6.35452e7i q^{48} -5.76480e6 q^{49} -1.36393e8 q^{51} -298496. i q^{52} +1.10032e8i q^{53} +9.81022e7 q^{54} -2.76425e7 q^{56} +2.60952e8i q^{57} -1.41879e8i q^{58} +8.68650e6 q^{59} +1.06957e8 q^{61} +9.41766e6i q^{62} +9.04588e7i q^{63} -1.32527e8 q^{64} +1.15741e8 q^{66} -1.89423e8i q^{67} +3.58638e6i q^{68} -3.22784e8 q^{69} +9.10989e7 q^{71} +4.33754e8i q^{72} -9.84572e7i q^{73} -2.92341e8 q^{74} +6.86157e6 q^{76} +5.09672e7i q^{77} -2.58442e8i q^{78} +2.41368e8 q^{79} +2.90454e8 q^{81} -8.89525e7i q^{82} +4.28456e8i q^{83} +3.62121e6 q^{84} +2.90861e8 q^{86} -1.49255e9i q^{87} +2.44390e8i q^{88} -5.29736e7 q^{89} +1.13807e8 q^{91} +8.48743e6i q^{92} +9.90722e7i q^{93} +8.22342e8 q^{94} +3.49439e7 q^{96} -3.01374e8i q^{97} +1.31242e8i q^{98} +7.99756e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 1664 q^{4} - 288 q^{6} - 135594 q^{9} + 20624 q^{11} - 9604 q^{14} - 1053392 q^{16} - 3310752 q^{19} + 672280 q^{21} - 13009152 q^{24} + 20438120 q^{26} + 6707452 q^{29} + 5356240 q^{31} - 43097224 q^{34}+ \cdots - 1396625336 q^{99}+O(q^{100}) \) 10 * q - 1664 * q^4 - 288 * q^6 - 135594 * q^9 + 20624 * q^11 - 9604 * q^14 - 1053392 * q^16 - 3310752 * q^19 + 672280 * q^21 - 13009152 * q^24 + 20438120 * q^26 + 6707452 * q^29 + 5356240 * q^31 - 43097224 * q^34 + 30780920 * q^36 + 36248 * q^39 + 12660388 * q^41 + 142451784 * q^44 - 285690944 * q^46 - 57648010 * q^49 - 35940424 * q^51 + 226558656 * q^54 - 67881072 * q^56 + 304670336 * q^59 + 514031396 * q^61 + 387976864 * q^64 + 366483328 * q^66 + 383914672 * q^69 + 1045577920 * q^71 + 488357736 * q^74 - 690113232 * q^76 - 928349800 * q^79 + 1730301978 * q^81 - 304389176 * q^84 + 1389121232 * q^86 + 2213416652 * q^89 + 761779676 * q^91 + 7205003488 * q^94 - 5304257280 * q^96 - 1396625336 * q^99

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