LMFDB - Embedded newform 175.10.b.a.99.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,10,Mod(99,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,0,0,-544] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$90.1312713287$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.a.99.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+28.0000i q^{2} +116.000i q^{3} -272.000 q^{4} -3248.00 q^{6} +2401.00i q^{7} +6720.00i q^{8} +6227.00 q^{9} -25548.0 q^{11} -31552.0i q^{12} +42306.0i q^{13} -67228.0 q^{14} -327424. q^{16} -526342. i q^{17} +174356. i q^{18} +350060. q^{19} -278516. q^{21} -715344. i q^{22} +621976. i q^{23} -779520. q^{24} -1.18457e6 q^{26} +3.00556e6i q^{27} -653072. i q^{28} -6.72043e6 q^{29} -6.41221e6 q^{31} -5.72723e6i q^{32} -2.96357e6i q^{33} +1.47376e7 q^{34} -1.69374e6 q^{36} -2.31768e6i q^{37} +9.80168e6i q^{38} -4.90750e6 q^{39} -1.02247e7 q^{41} -7.79845e6i q^{42} -3.01140e7i q^{43} +6.94906e6 q^{44} -1.74153e7 q^{46} -2.36449e7i q^{47} -3.79812e7i q^{48} -5.76480e6 q^{49} +6.10557e7 q^{51} -1.15072e7i q^{52} -5.72927e7i q^{53} -8.41557e7 q^{54} -1.61347e7 q^{56} +4.06070e7i q^{57} -1.88172e8i q^{58} -8.49348e7 q^{59} +1.46778e7 q^{61} -1.79542e8i q^{62} +1.49510e7i q^{63} -7.27859e6 q^{64} +8.29799e7 q^{66} -2.44558e8i q^{67} +1.43165e8i q^{68} -7.21492e7 q^{69} +6.19020e7 q^{71} +4.18454e7i q^{72} +2.83764e8i q^{73} +6.48951e7 q^{74} -9.52163e7 q^{76} -6.13407e7i q^{77} -1.37410e8i q^{78} -2.76107e8 q^{79} -2.26079e8 q^{81} -2.86291e8i q^{82} +7.29960e7i q^{83} +7.57564e7 q^{84} +8.43192e8 q^{86} -7.79570e8i q^{87} -1.71683e8i q^{88} +8.96368e8 q^{89} -1.01577e8 q^{91} -1.69177e8i q^{92} -7.43816e8i q^{93} +6.62058e8 q^{94} +6.64359e8 q^{96} +1.20581e9i q^{97} -1.61414e8i q^{98} -1.59087e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 544 q^{4} - 6496 q^{6} + 12454 q^{9} - 51096 q^{11} - 134456 q^{14} - 654848 q^{16} + 700120 q^{19} - 557032 q^{21} - 1559040 q^{24} - 2369136 q^{26} - 13440860 q^{29} - 12824416 q^{31} + 29475152 q^{34}+ \cdots - 318174792 q^{99}+O(q^{100}) $ 2 * q - 544 * q^4 - 6496 * q^6 + 12454 * q^9 - 51096 * q^11 - 134456 * q^14 - 654848 * q^16 + 700120 * q^19 - 557032 * q^21 - 1559040 * q^24 - 2369136 * q^26 - 13440860 * q^29 - 12824416 * q^31 + 29475152 * q^34 - 3387488 * q^36 - 9814992 * q^39 - 20449356 * q^41 + 13898112 * q^44 - 34830656 * q^46 - 11529602 * q^49 + 122111344 * q^51 - 168311360 * q^54 - 32269440 * q^56 - 169869560 * q^59 + 29355644 * q^61 - 14557184 * q^64 + 165959808 * q^66 - 144298432 * q^69 + 123803904 * q^71 + 129790192 * q^74 - 190432640 * q^76 - 552214960 * q^79 - 452157838 * q^81 + 151512704 * q^84 + 1686384224 * q^86 + 1792736940 * q^89 - 203153412 * q^91 + 1324115072 * q^94 + 1328717824 * q^96 - 318174792 * 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 $

$2$	28.0000i	1.23744i	0.785613	+	0.618718i	$0.212348\pi$
$2$	28.0000i	1.23744i	−0.785613	+	0.618718i	$0.787652\pi$
$3$	116.000i	0.826823i	0.910544	+	0.413411i	$0.135663\pi$
$3$	116.000i	0.826823i	−0.910544	+	0.413411i	$0.864337\pi$
$4$	−272.000	−0.531250
$5$	0	0
$5$	0	0
$6$	−3248.00	−1.02314
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	6720.00i	0.580049i
$9$	6227.00	0.316364
$10$	0	0
$11$	−25548.0	−0.526126	−0.263063	−	0.964779i	$-0.584733\pi$
$11$	−25548.0	−0.526126	−0.263063	+	0.964779i	$0.584733\pi$
$12$	− 31552.0i	− 0.439250i
$13$	42306.0i	0.410825i	0.978675	+	0.205413i	$0.0658536\pi$
$13$	42306.0i	0.410825i	−0.978675	+	0.205413i	$0.934146\pi$
$14$	−67228.0	−0.467707
$15$	0	0
$16$	−327424.	−1.24902
$17$	− 526342.i	− 1.52844i	−0.644957	−	0.764219i	$-0.723125\pi$
$17$	− 526342.i	− 1.52844i	0.644957	−	0.764219i	$-0.276875\pi$
$18$	174356.i	0.391481i
$19$	350060.	0.616242	0.308121	−	0.951347i	$-0.400300\pi$
$19$	350060.	0.616242	0.308121	+	0.951347i	$0.400300\pi$
$20$	0	0
$21$	−278516.	−0.312510
$22$	− 715344.i	− 0.651048i
$23$	621976.i	0.463445i	0.972782	+	0.231723i	$0.0744362\pi$
$23$	621976.i	0.463445i	−0.972782	+	0.231723i	$0.925564\pi$
$24$	−779520.	−0.479597
$25$	0	0
$26$	−1.18457e6	−0.508370
$27$	3.00556e6i	1.08840i
$28$	− 653072.i	− 0.200794i
$29$	−6.72043e6	−1.76444	−0.882218	−	0.470841i	$-0.843951\pi$
$29$	−6.72043e6	−1.76444	−0.882218	+	0.470841i	$0.843951\pi$
$30$	0	0
$31$	−6.41221e6	−1.24704	−0.623519	−	0.781808i	$-0.714298\pi$
$31$	−6.41221e6	−1.24704	−0.623519	+	0.781808i	$0.714298\pi$
$32$	− 5.72723e6i	− 0.965539i
$33$	− 2.96357e6i	− 0.435013i
$34$	1.47376e7	1.89135
$35$	0	0
$36$	−1.69374e6	−0.168069
$37$	− 2.31768e6i	− 0.203304i	−0.994820	−	0.101652i	$-0.967587\pi$
$37$	− 2.31768e6i	− 0.203304i	0.994820	−	0.101652i	$-0.0324128\pi$
$38$	9.80168e6i	0.762561i
$39$	−4.90750e6	−0.339679
$40$	0	0
$41$	−1.02247e7	−0.565096	−0.282548	−	0.959253i	$-0.591180\pi$
$41$	−1.02247e7	−0.565096	−0.282548	+	0.959253i	$0.591180\pi$
$42$	− 7.79845e6i	− 0.386711i
$43$	− 3.01140e7i	− 1.34326i	−0.740886	−	0.671631i	$-0.765594\pi$
$43$	− 3.01140e7i	− 1.34326i	0.740886	−	0.671631i	$-0.234406\pi$
$44$	6.94906e6	0.279504
$45$	0	0
$46$	−1.74153e7	−0.573484
$47$	− 2.36449e7i	− 0.706801i	−0.935472	−	0.353401i	$-0.885025\pi$
$47$	− 2.36449e7i	− 0.706801i	0.935472	−	0.353401i	$-0.114975\pi$
$48$	− 3.79812e7i	− 1.03272i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	6.10557e7	1.26375
$52$	− 1.15072e7i	− 0.218251i
$53$	− 5.72927e7i	− 0.997373i	−0.866782	−	0.498686i	$-0.833816\pi$
$53$	− 5.72927e7i	− 0.997373i	0.866782	−	0.498686i	$-0.166184\pi$
$54$	−8.41557e7	−1.34683
$55$	0	0
$56$	−1.61347e7	−0.219238
$57$	4.06070e7i	0.509523i
$58$	− 1.88172e8i	− 2.18338i
$59$	−8.49348e7	−0.912539	−0.456270	−	0.889842i	$-0.650815\pi$
$59$	−8.49348e7	−0.912539	−0.456270	+	0.889842i	$0.650815\pi$
$60$	0	0
$61$	1.46778e7	0.135730	0.0678652	−	0.997694i	$-0.478381\pi$
$61$	1.46778e7	0.135730	0.0678652	+	0.997694i	$0.478381\pi$
$62$	− 1.79542e8i	− 1.54313i
$63$	1.49510e7i	0.119574i
$64$	−7.27859e6	−0.0542297
$65$	0	0
$66$	8.29799e7	0.538301
$67$	− 2.44558e8i	− 1.48267i	−0.671134	−	0.741336i	$-0.734193\pi$
$67$	− 2.44558e8i	− 1.48267i	0.671134	−	0.741336i	$-0.265807\pi$
$68$	1.43165e8i	0.811983i
$69$	−7.21492e7	−0.383187
$70$	0	0
$71$	6.19020e7	0.289096	0.144548	−	0.989498i	$-0.453827\pi$
$71$	6.19020e7	0.289096	0.144548	+	0.989498i	$0.453827\pi$
$72$	4.18454e7i	0.183507i
$73$	2.83764e8i	1.16951i	0.811210	+	0.584755i	$0.198809\pi$
$73$	2.83764e8i	1.16951i	−0.811210	+	0.584755i	$0.801191\pi$
$74$	6.48951e7	0.251576
$75$	0	0
$76$	−9.52163e7	−0.327379
$77$	− 6.13407e7i	− 0.198857i
$78$	− 1.37410e8i	− 0.420332i
$79$	−2.76107e8	−0.797547	−0.398773	−	0.917049i	$-0.630564\pi$
$79$	−2.76107e8	−0.797547	−0.398773	+	0.917049i	$0.630564\pi$
$80$	0	0
$81$	−2.26079e8	−0.583549
$82$	− 2.86291e8i	− 0.699271i
$83$	7.29960e7i	0.168829i	0.996431	+	0.0844146i	$0.0269020\pi$
$83$	7.29960e7i	0.168829i	−0.996431	+	0.0844146i	$0.973098\pi$
$84$	7.57564e7	0.166021
$85$	0	0
$86$	8.43192e8	1.66220
$87$	− 7.79570e8i	− 1.45888i
$88$	− 1.71683e8i	− 0.305179i
$89$	8.96368e8	1.51437	0.757184	−	0.653201i	$-0.226575\pi$
$89$	8.96368e8	1.51437	0.757184	+	0.653201i	$0.226575\pi$
$90$	0	0
$91$	−1.01577e8	−0.155277
$92$	− 1.69177e8i	− 0.246205i
$93$	− 7.43816e8i	− 1.03108i
$94$	6.62058e8	0.874622
$95$	0	0
$96$	6.64359e8	0.798330
$97$	1.20581e9i	1.38295i	0.722401	+	0.691474i	$0.243038\pi$
$97$	1.20581e9i	1.38295i	−0.722401	+	0.691474i	$0.756962\pi$
$98$	− 1.61414e8i	− 0.176777i
$99$	−1.59087e8	−0.166448
$100$	0	0
$101$	−1.46021e9	−1.39627	−0.698136	−	0.715965i	$-0.745987\pi$
$101$	−1.46021e9	−1.39627	−0.698136	+	0.715965i	$0.745987\pi$
$102$	1.70956e9i	1.56381i
$103$	− 1.08009e9i	− 0.945563i	−0.881180	−	0.472782i	$-0.843250\pi$
$103$	− 1.08009e9i	− 0.945563i	0.881180	−	0.472782i	$-0.156750\pi$
$104$	−2.84296e8	−0.238298
$105$	0	0
$106$	1.60419e9	1.23419
$107$	3.35949e8i	0.247769i	0.992297	+	0.123884i	$0.0395352\pi$
$107$	3.35949e8i	0.247769i	−0.992297	+	0.123884i	$0.960465\pi$
$108$	− 8.17512e8i	− 0.578212i
$109$	1.42521e9	0.967072	0.483536	−	0.875324i	$-0.339352\pi$
$109$	1.42521e9	0.967072	0.483536	+	0.875324i	$0.339352\pi$
$110$	0	0
$111$	2.68851e8	0.168096
$112$	− 7.86145e8i	− 0.472086i
$113$	2.84178e9i	1.63960i	0.572651	+	0.819799i	$0.305915\pi$
$113$	2.84178e9i	1.63960i	−0.572651	+	0.819799i	$0.694085\pi$
$114$	−1.13699e9	−0.630502
$115$	0	0
$116$	1.82796e9	0.937357
$117$	2.63439e8i	0.129970i
$118$	− 2.37817e9i	− 1.12921i
$119$	1.26375e9	0.577695
$120$	0	0
$121$	−1.70525e9	−0.723191
$122$	4.10979e8i	0.167958i
$123$	− 1.18606e9i	− 0.467234i
$124$	1.74412e9	0.662489
$125$	0	0
$126$	−4.18629e8	−0.147966
$127$	3.49339e9i	1.19160i	0.803133	+	0.595800i	$0.203165\pi$
$127$	3.49339e9i	1.19160i	−0.803133	+	0.595800i	$0.796835\pi$
$128$	− 3.13614e9i	− 1.03264i
$129$	3.49322e9	1.11064
$130$	0	0
$131$	−1.84697e9	−0.547946	−0.273973	−	0.961737i	$-0.588338\pi$
$131$	−1.84697e9	−0.547946	−0.273973	+	0.961737i	$0.588338\pi$
$132$	8.06090e8i	0.231101i
$133$	8.40494e8i	0.232918i
$134$	6.84762e9	1.83471
$135$	0	0
$136$	3.53702e9	0.886568
$137$	1.17238e9i	0.284331i	0.989843	+	0.142166i	$0.0454066\pi$
$137$	1.17238e9i	0.284331i	−0.989843	+	0.142166i	$0.954593\pi$
$138$	− 2.02018e9i	− 0.474170i
$139$	4.89001e9	1.11108	0.555538	−	0.831491i	$-0.312512\pi$
$139$	4.89001e9	1.11108	0.555538	+	0.831491i	$0.312512\pi$
$140$	0	0
$141$	2.74281e9	0.584399
$142$	1.73325e9i	0.357738i
$143$	− 1.08083e9i	− 0.216146i
$144$	−2.03887e9	−0.395147
$145$	0	0
$146$	−7.94538e9	−1.44720
$147$	− 6.68717e8i	− 0.118118i
$148$	6.30410e8i	0.108005i
$149$	8.61488e9	1.43189	0.715947	−	0.698155i	$-0.245995\pi$
$149$	8.61488e9	1.43189	0.715947	+	0.698155i	$0.245995\pi$
$150$	0	0
$151$	5.48905e9	0.859213	0.429607	−	0.903016i	$-0.358652\pi$
$151$	5.48905e9	0.859213	0.429607	+	0.903016i	$0.358652\pi$
$152$	2.35240e9i	0.357450i
$153$	− 3.27753e9i	− 0.483543i
$154$	1.71754e9	0.246073
$155$	0	0
$156$	1.33484e9	0.180455
$157$	− 1.33110e9i	− 0.174849i	−0.996171	−	0.0874246i	$-0.972136\pi$
$157$	− 1.33110e9i	− 0.174849i	0.996171	−	0.0874246i	$-0.0278637\pi$
$158$	− 7.73101e9i	− 0.986914i
$159$	6.64595e9	0.824650
$160$	0	0
$161$	−1.49336e9	−0.175166
$162$	− 6.33021e9i	− 0.722105i
$163$	− 1.41097e9i	− 0.156557i	−0.996932	−	0.0782786i	$-0.975058\pi$
$163$	− 1.41097e9i	− 0.156557i	0.996932	−	0.0782786i	$-0.0249424\pi$
$164$	2.78111e9	0.300207
$165$	0	0
$166$	−2.04389e9	−0.208915
$167$	2.48555e8i	0.0247285i	0.999924	+	0.0123642i	$0.00393576\pi$
$167$	2.48555e8i	0.0247285i	−0.999924	+	0.0123642i	$0.996064\pi$
$168$	− 1.87163e9i	− 0.181271i
$169$	8.81470e9	0.831223
$170$	0	0
$171$	2.17982e9	0.194957
$172$	8.19101e9i	0.713607i
$173$	− 1.66522e10i	− 1.41340i	−0.707515	−	0.706699i	$-0.750184\pi$
$173$	− 1.66522e10i	− 1.41340i	0.707515	−	0.706699i	$-0.249816\pi$
$174$	2.18280e10	1.80527
$175$	0	0
$176$	8.36503e9	0.657144
$177$	− 9.85243e9i	− 0.754508i
$178$	2.50983e10i	1.87394i
$179$	−2.02956e10	−1.47762	−0.738811	−	0.673913i	$-0.764612\pi$
$179$	−2.02956e10	−1.47762	−0.738811	+	0.673913i	$0.764612\pi$
$180$	0	0
$181$	−1.36159e10	−0.942960	−0.471480	−	0.881877i	$-0.656280\pi$
$181$	−1.36159e10	−0.942960	−0.471480	+	0.881877i	$0.656280\pi$
$182$	− 2.84415e9i	− 0.192146i
$183$	1.70263e9i	0.112225i
$184$	−4.17968e9	−0.268821
$185$	0	0
$186$	2.08269e10	1.27590
$187$	1.34470e10i	0.804151i
$188$	6.43142e9i	0.375488i
$189$	−7.21635e9	−0.411376
$190$	0	0
$191$	1.82357e9	0.0991453	0.0495726	−	0.998771i	$-0.484214\pi$
$191$	1.82357e9	0.0991453	0.0495726	+	0.998771i	$0.484214\pi$
$192$	− 8.44317e8i	− 0.0448384i
$193$	− 1.23747e10i	− 0.641989i	−0.947081	−	0.320995i	$-0.895983\pi$
$193$	− 1.23747e10i	− 0.641989i	0.947081	−	0.320995i	$-0.104017\pi$
$194$	−3.37627e10	−1.71131
$195$	0	0
$196$	1.56803e9	0.0758929
$197$	1.93137e10i	0.913626i	0.889563	+	0.456813i	$0.151009\pi$
$197$	1.93137e10i	0.913626i	−0.889563	+	0.456813i	$0.848991\pi$
$198$	− 4.45445e9i	− 0.205968i
$199$	−1.52145e10	−0.687733	−0.343867	−	0.939019i	$-0.611737\pi$
$199$	−1.52145e10	−0.687733	−0.343867	+	0.939019i	$0.611737\pi$
$200$	0	0
$201$	2.83687e10	1.22591
$202$	− 4.08860e10i	− 1.72780i
$203$	− 1.61358e10i	− 0.666894i
$204$	−1.66071e10	−0.671366
$205$	0	0
$206$	3.02424e10	1.17007
$207$	3.87304e9i	0.146618i
$208$	− 1.38520e10i	− 0.513130i
$209$	−8.94333e9	−0.324221
$210$	0	0
$211$	−3.89626e10	−1.35325	−0.676624	−	0.736329i	$-0.736558\pi$
$211$	−3.89626e10	−1.35325	−0.676624	+	0.736329i	$0.736558\pi$
$212$	1.55836e10i	0.529854i
$213$	7.18063e9i	0.239031i
$214$	−9.40658e9	−0.306598
$215$	0	0
$216$	−2.01974e10	−0.631325
$217$	− 1.53957e10i	− 0.471336i
$218$	3.99058e10i	1.19669i
$219$	−3.29166e10	−0.966977
$220$	0	0
$221$	2.22674e10	0.627921
$222$	7.52783e9i	0.208009i
$223$	− 1.08324e9i	− 0.0293328i	−0.999892	−	0.0146664i	$-0.995331\pi$
$223$	− 1.08324e9i	− 0.0293328i	0.999892	−	0.0146664i	$-0.00466863\pi$
$224$	1.37511e10	0.364939
$225$	0	0
$226$	−7.95698e10	−2.02890
$227$	− 4.94618e10i	− 1.23639i	−0.786027	−	0.618193i	$-0.787865\pi$
$227$	− 4.94618e10i	− 1.23639i	0.786027	−	0.618193i	$-0.212135\pi$
$228$	− 1.10451e10i	− 0.270684i
$229$	4.32776e10	1.03993	0.519965	−	0.854188i	$-0.325945\pi$
$229$	4.32776e10	1.03993	0.519965	+	0.854188i	$0.325945\pi$
$230$	0	0
$231$	7.11553e9	0.164419
$232$	− 4.51613e10i	− 1.02346i
$233$	7.55367e9i	0.167902i	0.996470	+	0.0839511i	$0.0267539\pi$
$233$	7.55367e9i	0.167902i	−0.996470	+	0.0839511i	$0.973246\pi$
$234$	−7.37630e9	−0.160830
$235$	0	0
$236$	2.31023e10	0.484786
$237$	− 3.20285e10i	− 0.659430i
$238$	3.53849e10i	0.714862i
$239$	2.76516e10	0.548188	0.274094	−	0.961703i	$-0.411622\pi$
$239$	2.76516e10	0.548188	0.274094	+	0.961703i	$0.411622\pi$
$240$	0	0
$241$	−8.26006e10	−1.57727	−0.788635	−	0.614861i	$-0.789212\pi$
$241$	−8.26006e10	−1.57727	−0.788635	+	0.614861i	$0.789212\pi$
$242$	− 4.77469e10i	− 0.894904i
$243$	3.29333e10i	0.605908i
$244$	−3.99237e9	−0.0721068
$245$	0	0
$246$	3.32098e10	0.578173
$247$	1.48096e10i	0.253168i
$248$	− 4.30900e10i	− 0.723343i
$249$	−8.46753e9	−0.139592
$250$	0	0
$251$	2.01817e10	0.320942	0.160471	−	0.987041i	$-0.448699\pi$
$251$	2.01817e10	0.320942	0.160471	+	0.987041i	$0.448699\pi$
$252$	− 4.06668e9i	− 0.0635240i
$253$	− 1.58902e10i	− 0.243831i
$254$	−9.78150e10	−1.47453
$255$	0	0
$256$	8.40854e10	1.22360
$257$	2.82781e10i	0.404344i	0.979350	+	0.202172i	$0.0648000\pi$
$257$	2.82781e10i	0.404344i	−0.979350	+	0.202172i	$0.935200\pi$
$258$	9.78103e10i	1.37435i
$259$	5.56475e9	0.0768417
$260$	0	0
$261$	−4.18481e10	−0.558205
$262$	− 5.17150e10i	− 0.678049i
$263$	− 1.39139e11i	− 1.79328i	−0.442756	−	0.896642i	$-0.645999\pi$
$263$	− 1.39139e11i	− 1.79328i	0.442756	−	0.896642i	$-0.354001\pi$
$264$	1.99152e10	0.252329
$265$	0	0
$266$	−2.35338e10	−0.288221
$267$	1.03979e11i	1.25211i
$268$	6.65197e10i	0.787669i
$269$	−5.78883e9	−0.0674071	−0.0337035	−	0.999432i	$-0.510730\pi$
$269$	−5.78883e9	−0.0674071	−0.0337035	+	0.999432i	$0.510730\pi$
$270$	0	0
$271$	−7.46910e10	−0.841214	−0.420607	−	0.907243i	$-0.638183\pi$
$271$	−7.46910e10	−0.841214	−0.420607	+	0.907243i	$0.638183\pi$
$272$	1.72337e11i	1.90906i
$273$	− 1.17829e10i	− 0.128387i
$274$	−3.28265e10	−0.351842
$275$	0	0
$276$	1.96246e10	0.203568
$277$	2.22355e10i	0.226928i	0.993542	+	0.113464i	$0.0361947\pi$
$277$	2.22355e10i	0.226928i	−0.993542	+	0.113464i	$0.963805\pi$
$278$	1.36920e11i	1.37489i
$279$	−3.99288e10	−0.394519
$280$	0	0
$281$	−1.36058e11	−1.30180	−0.650901	−	0.759162i	$-0.725609\pi$
$281$	−1.36058e11	−1.30180	−0.650901	+	0.759162i	$0.725609\pi$
$282$	7.67987e10i	0.723157i
$283$	1.71084e11i	1.58551i	0.609538	+	0.792757i	$0.291355\pi$
$283$	1.71084e11i	1.58551i	−0.609538	+	0.792757i	$0.708645\pi$
$284$	−1.68373e10	−0.153582
$285$	0	0
$286$	3.02633e10	0.267467
$287$	− 2.45495e10i	− 0.213586i
$288$	− 3.56635e10i	− 0.305462i
$289$	−1.58448e11	−1.33612
$290$	0	0
$291$	−1.39874e11	−1.14345
$292$	− 7.71837e10i	− 0.621302i
$293$	− 1.05732e11i	− 0.838115i	−0.907960	−	0.419058i	$-0.862361\pi$
$293$	− 1.05732e11i	− 0.838115i	0.907960	−	0.419058i	$-0.137639\pi$
$294$	1.87241e10	0.146163
$295$	0	0
$296$	1.55748e10	0.117926
$297$	− 7.67860e10i	− 0.572636i
$298$	2.41217e11i	1.77188i
$299$	−2.63133e10	−0.190395
$300$	0	0
$301$	7.23037e10	0.507705
$302$	1.53693e11i	1.06322i
$303$	− 1.69385e11i	− 1.15447i
$304$	−1.14618e11	−0.769701
$305$	0	0
$306$	9.17709e10	0.598354
$307$	1.74144e11i	1.11889i	0.828869	+	0.559443i	$0.188985\pi$
$307$	1.74144e11i	1.11889i	−0.828869	+	0.559443i	$0.811015\pi$
$308$	1.66847e10i	0.105643i
$309$	1.25290e11	0.781813
$310$	0	0
$311$	−1.05907e11	−0.641954	−0.320977	−	0.947087i	$-0.604011\pi$
$311$	−1.05907e11	−0.641954	−0.320977	+	0.947087i	$0.604011\pi$
$312$	− 3.29784e10i	− 0.197031i
$313$	2.43558e11i	1.43434i	0.696897	+	0.717171i	$0.254563\pi$
$313$	2.43558e11i	1.43434i	−0.696897	+	0.717171i	$0.745437\pi$
$314$	3.72709e10	0.216365
$315$	0	0
$316$	7.51012e10	0.423697
$317$	1.83776e11i	1.02217i	0.859531	+	0.511083i	$0.170755\pi$
$317$	1.83776e11i	1.02217i	−0.859531	+	0.511083i	$0.829245\pi$
$318$	1.86087e11i	1.02045i
$319$	1.71694e11	0.928316
$320$	0	0
$321$	−3.89701e10	−0.204861
$322$	− 4.18142e10i	− 0.216757i
$323$	− 1.84251e11i	− 0.941888i
$324$	6.14935e10	0.310011
$325$	0	0
$326$	3.95071e10	0.193730
$327$	1.65324e11i	0.799597i
$328$	− 6.87098e10i	− 0.327783i
$329$	5.67714e10	0.267146
$330$	0	0
$331$	−5.81760e10	−0.266390	−0.133195	−	0.991090i	$-0.542524\pi$
$331$	−5.81760e10	−0.266390	−0.133195	+	0.991090i	$0.542524\pi$
$332$	− 1.98549e10i	− 0.0896905i
$333$	− 1.44322e10i	− 0.0643182i
$334$	−6.95953e9	−0.0305999
$335$	0	0
$336$	9.11928e10	0.390332
$337$	− 3.40267e11i	− 1.43709i	−0.695478	−	0.718547i	$-0.744807\pi$
$337$	− 3.40267e11i	− 1.43709i	0.695478	−	0.718547i	$-0.255193\pi$
$338$	2.46812e11i	1.02859i
$339$	−3.29646e11	−1.35566
$340$	0	0
$341$	1.63819e11	0.656100
$342$	6.10351e10i	0.241247i
$343$	− 1.38413e10i	− 0.0539949i
$344$	2.02366e11	0.779157
$345$	0	0
$346$	4.66262e11	1.74899
$347$	− 5.02625e11i	− 1.86107i	−0.366208	−	0.930533i	$-0.619344\pi$
$347$	− 5.02625e11i	− 1.86107i	0.366208	−	0.930533i	$-0.380656\pi$
$348$	2.12043e11i	0.775028i
$349$	−7.14710e10	−0.257879	−0.128939	−	0.991652i	$-0.541157\pi$
$349$	−7.14710e10	−0.257879	−0.128939	+	0.991652i	$0.541157\pi$
$350$	0	0
$351$	−1.27153e11	−0.447142
$352$	1.46319e11i	0.507995i
$353$	2.55096e10i	0.0874414i	0.999044	+	0.0437207i	$0.0139212\pi$
$353$	2.55096e10i	0.0874414i	−0.999044	+	0.0437207i	$0.986079\pi$
$354$	2.75868e11	0.933656
$355$	0	0
$356$	−2.43812e11	−0.804508
$357$	1.46595e11i	0.477652i
$358$	− 5.68277e11i	− 1.82846i
$359$	−1.49816e11	−0.476029	−0.238014	−	0.971262i	$-0.576497\pi$
$359$	−1.49816e11	−0.476029	−0.238014	+	0.971262i	$0.576497\pi$
$360$	0	0
$361$	−2.00146e11	−0.620246
$362$	− 3.81246e11i	− 1.16685i
$363$	− 1.97809e11i	− 0.597951i
$364$	2.76289e10	0.0824910
$365$	0	0
$366$	−4.76736e10	−0.138871
$367$	− 4.59514e11i	− 1.32221i	−0.750291	−	0.661107i	$-0.770087\pi$
$367$	− 4.59514e11i	− 1.32221i	0.750291	−	0.661107i	$-0.229913\pi$
$368$	− 2.03650e11i	− 0.578854i
$369$	−6.36691e10	−0.178776
$370$	0	0
$371$	1.37560e11	0.376971
$372$	2.02318e11i	0.547761i
$373$	5.04230e11i	1.34877i	0.738379	+	0.674386i	$0.235592\pi$
$373$	5.04230e11i	1.34877i	−0.738379	+	0.674386i	$0.764408\pi$
$374$	−3.76516e11	−0.995086
$375$	0	0
$376$	1.58894e11	0.409979
$377$	− 2.84315e11i	− 0.724875i
$378$	− 2.02058e11i	− 0.509052i
$379$	9.63136e10	0.239779	0.119889	−	0.992787i	$-0.461746\pi$
$379$	9.63136e10	0.239779	0.119889	+	0.992787i	$0.461746\pi$
$380$	0	0
$381$	−4.05234e11	−0.985242
$382$	5.10599e10i	0.122686i
$383$	− 6.10835e11i	− 1.45054i	−0.688465	−	0.725269i	$-0.741715\pi$
$383$	− 6.10835e11i	− 1.45054i	0.688465	−	0.725269i	$-0.258285\pi$
$384$	3.63793e11	0.853814
$385$	0	0
$386$	3.46492e11	0.794421
$387$	− 1.87520e11i	− 0.424960i
$388$	− 3.27980e11i	− 0.734691i
$389$	6.49908e11	1.43906	0.719530	−	0.694461i	$-0.244357\pi$
$389$	6.49908e11	1.43906	0.719530	+	0.694461i	$0.244357\pi$
$390$	0	0
$391$	3.27372e11	0.708347
$392$	− 3.87395e10i	− 0.0828641i
$393$	− 2.14248e11i	− 0.453054i
$394$	−5.40785e11	−1.13055
$395$	0	0
$396$	4.32718e10	0.0884253
$397$	− 3.67168e11i	− 0.741836i	−0.928666	−	0.370918i	$-0.879043\pi$
$397$	− 3.67168e11i	− 0.741836i	0.928666	−	0.370918i	$-0.120957\pi$
$398$	− 4.26007e11i	− 0.851026i
$399$	−9.74973e10	−0.192582
$400$	0	0
$401$	−9.73985e11	−1.88106	−0.940530	−	0.339712i	$-0.889670\pi$
$401$	−9.73985e11	−1.88106	−0.940530	+	0.339712i	$0.889670\pi$
$402$	7.94324e11i	1.51698i
$403$	− 2.71275e11i	− 0.512315i
$404$	3.97178e11	0.741770
$405$	0	0
$406$	4.51801e11	0.825240
$407$	5.92121e10i	0.106964i
$408$	4.10294e11i	0.733035i
$409$	−3.58196e11	−0.632944	−0.316472	−	0.948602i	$-0.602498\pi$
$409$	−3.58196e11	−0.632944	−0.316472	+	0.948602i	$0.602498\pi$
$410$	0	0
$411$	−1.35996e11	−0.235091
$412$	2.93783e11i	0.502330i
$413$	− 2.03928e11i	− 0.344907i
$414$	−1.08445e11	−0.181430
$415$	0	0
$416$	2.42296e11	0.396668
$417$	5.67242e11i	0.918662i
$418$	− 2.50413e11i	− 0.401203i
$419$	−4.84712e11	−0.768283	−0.384141	−	0.923274i	$-0.625502\pi$
$419$	−4.84712e11	−0.768283	−0.384141	+	0.923274i	$0.625502\pi$
$420$	0	0
$421$	7.18298e11	1.11438	0.557192	−	0.830384i	$-0.311879\pi$
$421$	7.18298e11	1.11438	0.557192	+	0.830384i	$0.311879\pi$
$422$	− 1.09095e12i	− 1.67456i
$423$	− 1.47237e11i	− 0.223607i
$424$	3.85007e11	0.578525
$425$	0	0
$426$	−2.01058e11	−0.295786
$427$	3.52415e10i	0.0513013i
$428$	− 9.13782e10i	− 0.131627i
$429$	1.25377e11	0.178714
$430$	0	0
$431$	8.27297e11	1.15482	0.577409	−	0.816455i	$-0.304064\pi$
$431$	8.27297e11	1.15482	0.577409	+	0.816455i	$0.304064\pi$
$432$	− 9.84092e11i	− 1.35944i
$433$	− 8.73032e11i	− 1.19353i	−0.802415	−	0.596767i	$-0.796452\pi$
$433$	− 8.73032e11i	− 1.19353i	0.802415	−	0.596767i	$-0.203548\pi$
$434$	4.31080e11	0.583249
$435$	0	0
$436$	−3.87657e11	−0.513757
$437$	2.17729e11i	0.285594i
$438$	− 9.21665e11i	− 1.19657i
$439$	−7.15061e11	−0.918867	−0.459433	−	0.888212i	$-0.651947\pi$
$439$	−7.15061e11	−0.918867	−0.459433	+	0.888212i	$0.651947\pi$
$440$	0	0
$441$	−3.58974e10	−0.0451949
$442$	6.23488e11i	0.777012i
$443$	− 5.89691e11i	− 0.727457i	−0.931505	−	0.363729i	$-0.881504\pi$
$443$	− 5.89691e11i	− 0.727457i	0.931505	−	0.363729i	$-0.118496\pi$
$444$	−7.31275e10	−0.0893012
$445$	0	0
$446$	3.03308e10	0.0362975
$447$	9.99326e11i	1.18392i
$448$	− 1.74759e10i	− 0.0204969i
$449$	1.06477e12	1.23636	0.618181	−	0.786036i	$-0.287870\pi$
$449$	1.06477e12	1.23636	0.618181	+	0.786036i	$0.287870\pi$
$450$	0	0
$451$	2.61220e11	0.297312
$452$	− 7.72964e11i	− 0.871037i
$453$	6.36730e11i	0.710417i
$454$	1.38493e12	1.52995
$455$	0	0
$456$	−2.72879e11	−0.295548
$457$	1.54296e12i	1.65475i	0.561651	+	0.827374i	$0.310166\pi$
$457$	1.54296e12i	1.65475i	−0.561651	+	0.827374i	$0.689834\pi$
$458$	1.21177e12i	1.28685i
$459$	1.58195e12	1.66355
$460$	0	0
$461$	−8.38680e11	−0.864852	−0.432426	−	0.901669i	$-0.642342\pi$
$461$	−8.38680e11	−0.864852	−0.432426	+	0.901669i	$0.642342\pi$
$462$	1.99235e11i	0.203459i
$463$	8.61819e11i	0.871569i	0.900051	+	0.435784i	$0.143529\pi$
$463$	8.61819e11i	0.871569i	−0.900051	+	0.435784i	$0.856471\pi$
$464$	2.20043e12	2.20382
$465$	0	0
$466$	−2.11503e11	−0.207768
$467$	1.46986e12i	1.43005i	0.699101	+	0.715023i	$0.253584\pi$
$467$	1.46986e12i	1.43005i	−0.699101	+	0.715023i	$0.746416\pi$
$468$	− 7.16555e10i	− 0.0690468i
$469$	5.87183e11	0.560397
$470$	0	0
$471$	1.54408e11	0.144569
$472$	− 5.70762e11i	− 0.529317i
$473$	7.69353e11i	0.706725i
$474$	8.96797e11	0.816003
$475$	0	0
$476$	−3.43739e11	−0.306901
$477$	− 3.56761e11i	− 0.315533i
$478$	7.74245e11i	0.678348i
$479$	−2.20227e12	−1.91144	−0.955721	−	0.294275i	$-0.904922\pi$
$479$	−2.20227e12	−1.91144	−0.955721	+	0.294275i	$0.904922\pi$
$480$	0	0
$481$	9.80519e10	0.0835224
$482$	− 2.31282e12i	− 1.95177i
$483$	− 1.73230e11i	− 0.144831i
$484$	4.63827e11	0.384195
$485$	0	0
$486$	−9.22132e11	−0.749773
$487$	1.30073e12i	1.04786i	0.851760	+	0.523932i	$0.175536\pi$
$487$	1.30073e12i	1.04786i	−0.851760	+	0.523932i	$0.824464\pi$
$488$	9.86350e10i	0.0787303i
$489$	1.63672e11	0.129445
$490$	0	0
$491$	6.88947e11	0.534957	0.267479	−	0.963564i	$-0.413810\pi$
$491$	6.88947e11	0.534957	0.267479	+	0.963564i	$0.413810\pi$
$492$	3.22609e11i	0.248218i
$493$	3.53724e12i	2.69683i
$494$	−4.14670e11	−0.313279
$495$	0	0
$496$	2.09951e12	1.55758
$497$	1.48627e11i	0.109268i
$498$	− 2.37091e11i	− 0.172736i
$499$	−1.76710e12	−1.27588	−0.637939	−	0.770087i	$-0.720213\pi$
$499$	−1.76710e12	−1.27588	−0.637939	+	0.770087i	$0.720213\pi$
$500$	0	0
$501$	−2.88323e10	−0.0204461
$502$	5.65088e11i	0.397145i
$503$	− 2.63527e12i	− 1.83556i	−0.397089	−	0.917780i	$-0.629980\pi$
$503$	− 2.63527e12i	− 1.83556i	0.397089	−	0.917780i	$-0.370020\pi$
$504$	−1.00471e11	−0.0693590
$505$	0	0
$506$	4.44927e11	0.301725
$507$	1.02251e12i	0.687274i
$508$	− 9.50203e11i	− 0.633038i
$509$	−2.22151e12	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$509$	−2.22151e12	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$510$	0	0
$511$	−6.81317e11	−0.442033
$512$	7.48685e11i	0.481487i
$513$	1.05213e12i	0.670718i
$514$	−7.91786e11	−0.500350
$515$	0	0
$516$	−9.50157e11	−0.590027
$517$	6.04080e11i	0.371867i
$518$	1.55813e11i	0.0950868i
$519$	1.93166e12	1.16863
$520$	0	0
$521$	−1.87441e12	−1.11454	−0.557269	−	0.830332i	$-0.688151\pi$
$521$	−1.87441e12	−1.11454	−0.557269	+	0.830332i	$0.688151\pi$
$522$	− 1.17175e12i	− 0.690743i
$523$	1.58412e12i	0.925828i	0.886403	+	0.462914i	$0.153196\pi$
$523$	1.58412e12i	0.925828i	−0.886403	+	0.462914i	$0.846804\pi$
$524$	5.02375e11	0.291096
$525$	0	0
$526$	3.89590e12	2.21908
$527$	3.37501e12i	1.90602i
$528$	9.70343e11i	0.543341i
$529$	1.41430e12	0.785219
$530$	0	0
$531$	−5.28889e11	−0.288695
$532$	− 2.28614e11i	− 0.123737i
$533$	− 4.32565e11i	− 0.232156i
$534$	−2.91140e12	−1.54941
$535$	0	0
$536$	1.64343e12	0.860021
$537$	− 2.35429e12i	− 1.22173i
$538$	− 1.62087e11i	− 0.0834120i
$539$	1.47279e11	0.0751609
$540$	0	0
$541$	2.79888e12	1.40474	0.702370	−	0.711812i	$-0.252125\pi$
$541$	2.79888e12	1.40474	0.702370	+	0.711812i	$0.252125\pi$
$542$	− 2.09135e12i	− 1.04095i
$543$	− 1.57945e12i	− 0.779660i
$544$	−3.01448e12	−1.47577
$545$	0	0
$546$	3.29921e11	0.158870
$547$	1.16606e12i	0.556901i	0.960451	+	0.278451i	$0.0898209\pi$
$547$	1.16606e12i	0.556901i	−0.960451	+	0.278451i	$0.910179\pi$
$548$	− 3.18886e11i	− 0.151051i
$549$	9.13988e10	0.0429403
$550$	0	0
$551$	−2.35255e12	−1.08732
$552$	− 4.84843e11i	− 0.222267i
$553$	− 6.62934e11i	− 0.301444i
$554$	−6.22594e11	−0.280809
$555$	0	0
$556$	−1.33008e12	−0.590259
$557$	3.29033e12i	1.44841i	0.689586	+	0.724204i	$0.257793\pi$
$557$	3.29033e12i	1.44841i	−0.689586	+	0.724204i	$0.742207\pi$
$558$	− 1.11801e12i	− 0.488192i
$559$	1.27400e12	0.551845
$560$	0	0
$561$	−1.55985e12	−0.664890
$562$	− 3.80962e12i	− 1.61090i
$563$	3.63871e12i	1.52637i	0.646179	+	0.763186i	$0.276366\pi$
$563$	3.63871e12i	1.52637i	−0.646179	+	0.763186i	$0.723634\pi$
$564$	−7.46044e11	−0.310462
$565$	0	0
$566$	−4.79035e12	−1.96197
$567$	− 5.42815e11i	− 0.220561i
$568$	4.15981e11i	0.167690i
$569$	−4.35009e12	−1.73978	−0.869888	−	0.493250i	$-0.835809\pi$
$569$	−4.35009e12	−1.73978	−0.869888	+	0.493250i	$0.835809\pi$
$570$	0	0
$571$	−4.91136e12	−1.93348	−0.966739	−	0.255767i	$-0.917672\pi$
$571$	−4.91136e12	−1.93348	−0.966739	+	0.255767i	$0.917672\pi$
$572$	2.93987e11i	0.114827i
$573$	2.11534e11i	0.0819756i
$574$	6.87385e11	0.264299
$575$	0	0
$576$	−4.53238e10	−0.0171564
$577$	− 1.68758e12i	− 0.633830i	−0.948454	−	0.316915i	$-0.897353\pi$
$577$	− 1.68758e12i	− 0.633830i	0.948454	−	0.316915i	$-0.102647\pi$
$578$	− 4.43654e12i	− 1.65337i
$579$	1.43547e12	0.530811
$580$	0	0
$581$	−1.75263e11	−0.0638114
$582$	− 3.91647e12i	− 1.41495i
$583$	1.46371e12i	0.524744i
$584$	−1.90689e12	−0.678373
$585$	0	0
$586$	2.96051e12	1.03711
$587$	− 4.82739e12i	− 1.67819i	−0.543987	−	0.839094i	$-0.683086\pi$
$587$	− 4.82739e12i	− 1.67819i	0.543987	−	0.839094i	$-0.316914\pi$
$588$	1.81891e11i	0.0627499i
$589$	−2.24466e12	−0.768478
$590$	0	0
$591$	−2.24039e12	−0.755407
$592$	7.58865e11i	0.253932i
$593$	1.12076e12i	0.372193i	0.982532	+	0.186096i	$0.0595837\pi$
$593$	1.12076e12i	0.372193i	−0.982532	+	0.186096i	$0.940416\pi$
$594$	2.15001e12	0.708600
$595$	0	0
$596$	−2.34325e12	−0.760694
$597$	− 1.76489e12i	− 0.568633i
$598$	− 7.36773e11i	− 0.235602i
$599$	−1.35944e12	−0.431460	−0.215730	−	0.976453i	$-0.569213\pi$
$599$	−1.35944e12	−0.431460	−0.215730	+	0.976453i	$0.569213\pi$
$600$	0	0
$601$	9.50421e11	0.297153	0.148577	−	0.988901i	$-0.452531\pi$
$601$	9.50421e11	0.297153	0.148577	+	0.988901i	$0.452531\pi$
$602$	2.02450e12i	0.628253i
$603$	− 1.52286e12i	− 0.469064i
$604$	−1.49302e12	−0.456457
$605$	0	0
$606$	4.74277e12	1.42858
$607$	3.35939e12i	1.00441i	0.864749	+	0.502205i	$0.167478\pi$
$607$	3.35939e12i	1.00441i	−0.864749	+	0.502205i	$0.832522\pi$
$608$	− 2.00487e12i	− 0.595006i
$609$	1.87175e12	0.551403
$610$	0	0
$611$	1.00032e12	0.290372
$612$	8.91489e11i	0.256882i
$613$	2.62257e12i	0.750162i	0.926992	+	0.375081i	$0.122385\pi$
$613$	2.62257e12i	0.750162i	−0.926992	+	0.375081i	$0.877615\pi$
$614$	−4.87603e12	−1.38455
$615$	0	0
$616$	4.12210e11	0.115347
$617$	− 3.35285e10i	− 0.00931388i	−0.999989	−	0.00465694i	$-0.998518\pi$
$617$	− 3.35285e10i	− 0.00931388i	0.999989	−	0.00465694i	$-0.00148236\pi$
$618$	3.50812e12i	0.967444i
$619$	−5.51587e12	−1.51010	−0.755051	−	0.655666i	$-0.772388\pi$
$619$	−5.51587e12	−1.51010	−0.755051	+	0.655666i	$0.772388\pi$
$620$	0	0
$621$	−1.86939e12	−0.504414
$622$	− 2.96540e12i	− 0.794377i
$623$	2.15218e12i	0.572377i
$624$	1.60683e12	0.424268
$625$	0	0
$626$	−6.81962e12	−1.77491
$627$	− 1.03743e12i	− 0.268073i
$628$	3.62060e11i	0.0928886i
$629$	−1.21989e12	−0.310738
$630$	0	0
$631$	2.72456e12	0.684170	0.342085	−	0.939669i	$-0.388867\pi$
$631$	2.72456e12	0.684170	0.342085	+	0.939669i	$0.388867\pi$
$632$	− 1.85544e12i	− 0.462616i
$633$	− 4.51966e12i	− 1.11890i
$634$	−5.14572e12	−1.26487
$635$	0	0
$636$	−1.80770e12	−0.438096
$637$	− 2.43886e11i	− 0.0586893i
$638$	4.80742e12i	1.14873i
$639$	3.85463e11	0.0914596
$640$	0	0
$641$	3.79136e11	0.0887022	0.0443511	−	0.999016i	$-0.485878\pi$
$641$	3.79136e11	0.0887022	0.0443511	+	0.999016i	$0.485878\pi$
$642$	− 1.09116e12i	− 0.253502i
$643$	5.15446e12i	1.18914i	0.804043	+	0.594571i	$0.202678\pi$
$643$	5.15446e12i	1.18914i	−0.804043	+	0.594571i	$0.797322\pi$
$644$	4.06195e11	0.0930568
$645$	0	0
$646$	5.15904e12	1.16553
$647$	− 2.68059e12i	− 0.601397i	−0.953719	−	0.300699i	$-0.902780\pi$
$647$	− 2.68059e12i	− 0.601397i	0.953719	−	0.300699i	$-0.0972198\pi$
$648$	− 1.51925e12i	− 0.338487i
$649$	2.16991e12	0.480111
$650$	0	0
$651$	1.78590e12	0.389712
$652$	3.83783e11i	0.0831710i
$653$	6.44986e12i	1.38816i	0.719896	+	0.694082i	$0.244190\pi$
$653$	6.44986e12i	1.38816i	−0.719896	+	0.694082i	$0.755810\pi$
$654$	−4.62908e12	−0.989451
$655$	0	0
$656$	3.34780e12	0.705818
$657$	1.76700e12i	0.369991i
$658$	1.58960e12i	0.330576i
$659$	2.79549e12	0.577396	0.288698	−	0.957420i	$-0.406778\pi$
$659$	2.79549e12	0.577396	0.288698	+	0.957420i	$0.406778\pi$
$660$	0	0
$661$	−4.93691e11	−0.100589	−0.0502943	−	0.998734i	$-0.516016\pi$
$661$	−4.93691e11	−0.100589	−0.0502943	+	0.998734i	$0.516016\pi$
$662$	− 1.62893e12i	− 0.329641i
$663$	2.58302e12i	0.519179i
$664$	−4.90533e11	−0.0979291
$665$	0	0
$666$	4.04102e11	0.0795897
$667$	− 4.17995e12i	− 0.817720i
$668$	− 6.76068e10i	− 0.0131370i
$669$	1.25656e11	0.0242530
$670$	0	0
$671$	−3.74989e11	−0.0714113
$672$	1.59513e12i	0.301740i
$673$	− 2.83805e12i	− 0.533277i	−0.963797	−	0.266638i	$-0.914087\pi$
$673$	− 2.83805e12i	− 0.533277i	0.963797	−	0.266638i	$-0.0859130\pi$
$674$	9.52747e12	1.77831
$675$	0	0
$676$	−2.39760e12	−0.441587
$677$	7.71236e12i	1.41104i	0.708691	+	0.705519i	$0.249286\pi$
$677$	7.71236e12i	1.41104i	−0.708691	+	0.705519i	$0.750714\pi$
$678$	− 9.23010e12i	− 1.67754i
$679$	−2.89515e12	−0.522705
$680$	0	0
$681$	5.73757e12	1.02227
$682$	4.58693e12i	0.811882i
$683$	− 1.07677e13i	− 1.89334i	−0.322204	−	0.946670i	$-0.604424\pi$
$683$	− 1.07677e13i	− 1.89334i	0.322204	−	0.946670i	$-0.395576\pi$
$684$	−5.92912e11	−0.103571
$685$	0	0
$686$	3.87556e11	0.0668153
$687$	5.02021e12i	0.859837i
$688$	9.86005e12i	1.67776i
$689$	2.42382e12	0.409746
$690$	0	0
$691$	2.02298e12	0.337552	0.168776	−	0.985654i	$-0.446019\pi$
$691$	2.02298e12	0.337552	0.168776	+	0.985654i	$0.446019\pi$
$692$	4.52940e12i	0.750867i
$693$	− 3.81969e11i	− 0.0629113i
$694$	1.40735e13	2.30295
$695$	0	0
$696$	5.23871e12	0.846219
$697$	5.38168e12i	0.863714i
$698$	− 2.00119e12i	− 0.319109i
$699$	−8.76226e11	−0.138825
$700$	0	0
$701$	8.66031e11	0.135457	0.0677286	−	0.997704i	$-0.478425\pi$
$701$	8.66031e11	0.135457	0.0677286	+	0.997704i	$0.478425\pi$
$702$	− 3.56029e12i	− 0.553310i
$703$	− 8.11328e11i	− 0.125285i
$704$	1.85953e11	0.0285317
$705$	0	0
$706$	−7.14268e11	−0.108203
$707$	− 3.50597e12i	− 0.527741i
$708$	2.67986e12i	0.400832i
$709$	3.78834e12	0.563042	0.281521	−	0.959555i	$-0.409161\pi$
$709$	3.78834e12	0.563042	0.281521	+	0.959555i	$0.409161\pi$
$710$	0	0
$711$	−1.71932e12	−0.252315
$712$	6.02360e12i	0.878407i
$713$	− 3.98824e12i	− 0.577934i
$714$	−4.10465e12	−0.591064
$715$	0	0
$716$	5.52040e12	0.784986
$717$	3.20758e12i	0.453254i
$718$	− 4.19485e12i	− 0.589056i
$719$	−8.16972e11	−0.114006	−0.0570029	−	0.998374i	$-0.518154\pi$
$719$	−8.16972e11	−0.114006	−0.0570029	+	0.998374i	$0.518154\pi$
$720$	0	0
$721$	2.59328e12	0.357389
$722$	− 5.60408e12i	− 0.767515i
$723$	− 9.58166e12i	− 1.30412i
$724$	3.70353e12	0.500947
$725$	0	0
$726$	5.53864e12	0.739927
$727$	3.13227e12i	0.415867i	0.978143	+	0.207933i	$0.0666737\pi$
$727$	3.13227e12i	0.415867i	−0.978143	+	0.207933i	$0.933326\pi$
$728$	− 6.82595e11i	− 0.0900683i
$729$	−8.27017e12	−1.08453
$730$	0	0
$731$	−1.58503e13	−2.05309
$732$	− 4.63115e11i	− 0.0596195i
$733$	1.33197e13i	1.70422i	0.523360	+	0.852112i	$0.324678\pi$
$733$	1.33197e13i	1.70422i	−0.523360	+	0.852112i	$0.675322\pi$
$734$	1.28664e13	1.63616
$735$	0	0
$736$	3.56220e12	0.447474
$737$	6.24796e12i	0.780072i
$738$	− 1.78273e12i	− 0.221224i
$739$	1.56702e13	1.93274	0.966371	−	0.257154i	$-0.0827847\pi$
$739$	1.56702e13	1.93274	0.966371	+	0.257154i	$0.0827847\pi$
$740$	0	0
$741$	−1.71792e12	−0.209325
$742$	3.85167e12i	0.466478i
$743$	− 7.91108e12i	− 0.952327i	−0.879357	−	0.476164i	$-0.842027\pi$
$743$	− 7.91108e12i	− 0.952327i	0.879357	−	0.476164i	$-0.157973\pi$
$744$	4.99844e12	0.598076
$745$	0	0
$746$	−1.41184e13	−1.66902
$747$	4.54546e11i	0.0534115i
$748$	− 3.65758e12i	− 0.427205i
$749$	−8.06614e11	−0.0936478
$750$	0	0
$751$	−4.01514e12	−0.460597	−0.230299	−	0.973120i	$-0.573970\pi$
$751$	−4.01514e12	−0.460597	−0.230299	+	0.973120i	$0.573970\pi$
$752$	7.74191e12i	0.882811i
$753$	2.34108e12i	0.265362i
$754$	7.96081e12	0.896987
$755$	0	0
$756$	1.96285e12	0.218544
$757$	2.84075e12i	0.314414i	0.987566	+	0.157207i	$0.0502489\pi$
$757$	2.84075e12i	0.314414i	−0.987566	+	0.157207i	$0.949751\pi$
$758$	2.69678e12i	0.296711i
$759$	1.84327e12	0.201605
$760$	0	0
$761$	−7.10439e12	−0.767884	−0.383942	−	0.923357i	$-0.625434\pi$
$761$	−7.10439e12	−0.767884	−0.383942	+	0.923357i	$0.625434\pi$
$762$	− 1.13465e13i	− 1.21918i
$763$	3.42192e12i	0.365519i
$764$	−4.96011e11	−0.0526709
$765$	0	0
$766$	1.71034e13	1.79495
$767$	− 3.59325e12i	− 0.374894i
$768$	9.75390e12i	1.01170i
$769$	4.97052e12	0.512546	0.256273	−	0.966604i	$-0.417505\pi$
$769$	4.97052e12	0.512546	0.256273	+	0.966604i	$0.417505\pi$
$770$	0	0
$771$	−3.28026e12	−0.334321
$772$	3.36593e12i	0.341057i
$773$	− 1.11565e13i	− 1.12388i	−0.827179	−	0.561939i	$-0.810056\pi$
$773$	− 1.11565e13i	− 1.12388i	0.827179	−	0.561939i	$-0.189944\pi$
$774$	5.25056e12	0.525861
$775$	0	0
$776$	−8.10304e12	−0.802177
$777$	6.45512e11i	0.0635345i
$778$	1.81974e13i	1.78075i
$779$	−3.57925e12	−0.348236
$780$	0	0
$781$	−1.58147e12	−0.152101
$782$	9.16642e12i	0.876535i
$783$	− 2.01987e13i	− 1.92041i
$784$	1.88753e12	0.178432
$785$	0	0
$786$	5.99894e12	0.560626
$787$	− 6.23763e12i	− 0.579607i	−0.957086	−	0.289803i	$-0.906410\pi$
$787$	− 6.23763e12i	− 0.579607i	0.957086	−	0.289803i	$-0.0935899\pi$
$788$	− 5.25334e12i	− 0.485364i
$789$	1.61402e13	1.48273
$790$	0	0
$791$	−6.82311e12	−0.619710
$792$	− 1.06907e12i	− 0.0965477i
$793$	6.20960e11i	0.0557615i
$794$	1.02807e13	0.917975
$795$	0	0
$796$	4.13835e12	0.365358
$797$	− 1.83799e12i	− 0.161355i	−0.996740	−	0.0806773i	$-0.974292\pi$
$797$	− 1.83799e12i	− 0.161355i	0.996740	−	0.0806773i	$-0.0257083\pi$
$798$	− 2.72992e12i	− 0.238307i
$799$	−1.24453e13	−1.08030
$800$	0	0
$801$	5.58169e12	0.479092
$802$	− 2.72716e13i	− 2.32769i
$803$	− 7.24960e12i	− 0.615310i
$804$	−7.71629e12	−0.651263
$805$	0	0
$806$	7.59570e12	0.633957
$807$	− 6.71504e11i	− 0.0557337i
$808$	− 9.81263e12i	− 0.809906i
$809$	−1.92205e13	−1.57760	−0.788801	−	0.614649i	$-0.789298\pi$
$809$	−1.92205e13	−1.57760	−0.788801	+	0.614649i	$0.789298\pi$
$810$	0	0
$811$	−1.70316e13	−1.38249	−0.691246	−	0.722620i	$-0.742938\pi$
$811$	−1.70316e13	−1.38249	−0.691246	+	0.722620i	$0.742938\pi$
$812$	4.38892e12i	0.354288i
$813$	− 8.66416e12i	− 0.695535i
$814$	−1.65794e12	−0.132361
$815$	0	0
$816$	−1.99911e13	−1.57845
$817$	− 1.05417e13i	− 0.827774i
$818$	− 1.00295e13i	− 0.783228i
$819$	−6.32518e11	−0.0491242
$820$	0	0
$821$	1.33485e13	1.02539	0.512694	−	0.858572i	$-0.328648\pi$
$821$	1.33485e13	1.02539	0.512694	+	0.858572i	$0.328648\pi$
$822$	− 3.80788e12i	− 0.290911i
$823$	1.72858e13i	1.31338i	0.754161	+	0.656689i	$0.228044\pi$
$823$	1.72858e13i	1.31338i	−0.754161	+	0.656689i	$0.771956\pi$
$824$	7.25817e12	0.548473
$825$	0	0
$826$	5.71000e12	0.426801
$827$	1.64651e13i	1.22402i	0.790849	+	0.612012i	$0.209639\pi$
$827$	1.64651e13i	1.22402i	−0.790849	+	0.612012i	$0.790361\pi$
$828$	− 1.05347e12i	− 0.0778906i
$829$	5.91786e12	0.435181	0.217590	−	0.976040i	$-0.430180\pi$
$829$	5.91786e12	0.435181	0.217590	+	0.976040i	$0.430180\pi$
$830$	0	0
$831$	−2.57932e12	−0.187629
$832$	− 3.07928e11i	− 0.0222789i
$833$	3.03426e12i	0.218348i
$834$	−1.58828e13	−1.13679
$835$	0	0
$836$	2.43259e12	0.172242
$837$	− 1.92723e13i	− 1.35728i
$838$	− 1.35719e13i	− 0.950701i
$839$	−2.40380e13	−1.67483	−0.837414	−	0.546569i	$-0.815934\pi$
$839$	−2.40380e13	−1.67483	−0.837414	+	0.546569i	$0.815934\pi$
$840$	0	0
$841$	3.06570e13	2.11324
$842$	2.01123e13i	1.37898i
$843$	− 1.57827e13i	− 1.07636i
$844$	1.05978e13	0.718913
$845$	0	0
$846$	4.12263e12	0.276699
$847$	− 4.09430e12i	− 0.273341i
$848$	1.87590e13i	1.24574i
$849$	−1.98457e13	−1.31094
$850$	0	0
$851$	1.44154e12	0.0942203
$852$	− 1.95313e12i	− 0.126985i
$853$	− 2.26446e13i	− 1.46452i	−0.681027	−	0.732258i	$-0.738466\pi$
$853$	− 2.26446e13i	− 1.46452i	0.681027	−	0.732258i	$-0.261534\pi$
$854$	−9.86761e11	−0.0634821
$855$	0	0
$856$	−2.25758e12	−0.143718
$857$	− 1.20223e13i	− 0.761334i	−0.924712	−	0.380667i	$-0.875694\pi$
$857$	− 1.20223e13i	− 0.761334i	0.924712	−	0.380667i	$-0.124306\pi$
$858$	3.51055e12i	0.221148i
$859$	9.44258e12	0.591727	0.295864	−	0.955230i	$-0.404393\pi$
$859$	9.44258e12	0.591727	0.295864	+	0.955230i	$0.404393\pi$
$860$	0	0
$861$	2.84774e12	0.176598
$862$	2.31643e13i	1.42901i
$863$	− 8.80380e12i	− 0.540283i	−0.962821	−	0.270142i	$-0.912929\pi$
$863$	− 8.80380e12i	− 0.540283i	0.962821	−	0.270142i	$-0.0870705\pi$
$864$	1.72135e13	1.05089
$865$	0	0
$866$	2.44449e13	1.47692
$867$	− 1.83800e13i	− 1.10474i
$868$	4.18763e12i	0.250397i
$869$	7.05399e12	0.419610
$870$	0	0
$871$	1.03463e13	0.609119
$872$	9.57740e12i	0.560949i
$873$	7.50858e12i	0.437516i
$874$	−6.09641e12	−0.353405
$875$	0	0
$876$	8.95331e12	0.513707
$877$	6.73513e12i	0.384457i	0.981350	+	0.192229i	$0.0615715\pi$
$877$	6.73513e12i	0.384457i	−0.981350	+	0.192229i	$0.938429\pi$
$878$	− 2.00217e13i	− 1.13704i
$879$	1.22650e13	0.692973
$880$	0	0
$881$	−7.58474e12	−0.424179	−0.212089	−	0.977250i	$-0.568027\pi$
$881$	−7.58474e12	−0.424179	−0.212089	+	0.977250i	$0.568027\pi$
$882$	− 1.00513e12i	− 0.0559258i
$883$	1.78234e13i	0.986662i	0.869842	+	0.493331i	$0.164221\pi$
$883$	1.78234e13i	0.986662i	−0.869842	+	0.493331i	$0.835779\pi$
$884$	−6.05674e12	−0.333583
$885$	0	0
$886$	1.65113e13	0.900182
$887$	− 2.45177e13i	− 1.32991i	−0.746882	−	0.664956i	$-0.768450\pi$
$887$	− 2.45177e13i	− 1.32991i	0.746882	−	0.664956i	$-0.231550\pi$
$888$	1.80668e12i	0.0975041i
$889$	−8.38764e12	−0.450383
$890$	0	0
$891$	5.77586e12	0.307020
$892$	2.94642e11i	0.0155830i
$893$	− 8.27714e12i	− 0.435561i
$894$	−2.79811e13	−1.46503
$895$	0	0
$896$	7.52988e12	0.390303
$897$	− 3.05234e12i	− 0.157423i
$898$	2.98134e13i	1.52992i
$899$	4.30928e13	2.20032
$900$	0	0
$901$	−3.01555e13	−1.52442
$902$	7.31416e12i	0.367905i
$903$	8.38723e12i	0.419782i
$904$	−1.90968e13	−0.951047
$905$	0	0
$906$	−1.78284e13	−0.879096
$907$	− 8.14231e12i	− 0.399498i	−0.979847	−	0.199749i	$-0.935987\pi$
$907$	− 8.14231e12i	− 0.399498i	0.979847	−	0.199749i	$-0.0640127\pi$
$908$	1.34536e13i	0.656830i
$909$	−9.09275e12	−0.441731
$910$	0	0
$911$	−1.26965e13	−0.610733	−0.305367	−	0.952235i	$-0.598779\pi$
$911$	−1.26965e13	−0.610733	−0.305367	+	0.952235i	$0.598779\pi$
$912$	− 1.32957e13i	− 0.636406i
$913$	− 1.86490e12i	− 0.0888254i
$914$	−4.32029e13	−2.04765
$915$	0	0
$916$	−1.17715e13	−0.552463
$917$	− 4.43456e12i	− 0.207104i
$918$	4.42947e13i	2.05854i
$919$	2.53575e13	1.17270	0.586350	−	0.810058i	$-0.300564\pi$
$919$	2.53575e13	1.17270	0.586350	+	0.810058i	$0.300564\pi$
$920$	0	0
$921$	−2.02007e13	−0.925120
$922$	− 2.34830e13i	− 1.07020i
$923$	2.61882e12i	0.118768i
$924$	−1.93542e12	−0.0873478
$925$	0	0
$926$	−2.41309e13	−1.07851
$927$	− 6.72569e12i	− 0.299143i
$928$	3.84895e13i	1.70363i
$929$	−1.89611e13	−0.835203	−0.417602	−	0.908630i	$-0.637129\pi$
$929$	−1.89611e13	−0.835203	−0.417602	+	0.908630i	$0.637129\pi$
$930$	0	0
$931$	−2.01803e12	−0.0880346
$932$	− 2.05460e12i	− 0.0891980i
$933$	− 1.22852e13i	− 0.530782i
$934$	−4.11561e13	−1.76959
$935$	0	0
$936$	−1.77031e12	−0.0753891
$937$	8.65559e12i	0.366833i	0.983035	+	0.183416i	$0.0587157\pi$
$937$	8.65559e12i	0.366833i	−0.983035	+	0.183416i	$0.941284\pi$
$938$	1.64411e13i	0.693456i
$939$	−2.82527e13	−1.18595
$940$	0	0
$941$	3.42336e13	1.42331	0.711654	−	0.702530i	$-0.247946\pi$
$941$	3.42336e13	1.42331	0.711654	+	0.702530i	$0.247946\pi$
$942$	4.32343e12i	0.178895i
$943$	− 6.35950e12i	− 0.261891i
$944$	2.78097e13	1.13978
$945$	0	0
$946$	−2.15419e13	−0.874527
$947$	2.38597e13i	0.964030i	0.876163	+	0.482015i	$0.160095\pi$
$947$	2.38597e13i	0.964030i	−0.876163	+	0.482015i	$0.839905\pi$
$948$	8.71174e12i	0.350322i
$949$	−1.20049e13	−0.480464
$950$	0	0
$951$	−2.13180e13	−0.845150
$952$	8.49238e12i	0.335091i
$953$	4.83481e13i	1.89872i	0.314189	+	0.949360i	$0.398267\pi$
$953$	4.83481e13i	1.89872i	−0.314189	+	0.949360i	$0.601733\pi$
$954$	9.98932e12	0.390452
$955$	0	0
$956$	−7.52123e12	−0.291225
$957$	1.99165e13i	0.767553i
$958$	− 6.16636e13i	− 2.36529i
$959$	−2.81488e12	−0.107467
$960$	0	0
$961$	1.46768e13	0.555106
$962$	2.74545e12i	0.103354i
$963$	2.09196e12i	0.0783852i
$964$	2.24674e13	0.837925
$965$	0	0
$966$	4.85045e12	0.179219
$967$	− 2.28025e13i	− 0.838617i	−0.907844	−	0.419308i	$-0.862273\pi$
$967$	− 2.28025e13i	− 0.838617i	0.907844	−	0.419308i	$-0.137727\pi$
$968$	− 1.14593e13i	− 0.419486i
$969$	2.13731e13	0.778774
$970$	0	0
$971$	7.62385e12	0.275225	0.137612	−	0.990486i	$-0.456057\pi$
$971$	7.62385e12	0.275225	0.137612	+	0.990486i	$0.456057\pi$
$972$	− 8.95785e12i	− 0.321889i
$973$	1.17409e13i	0.419947i
$974$	−3.64203e13	−1.29667
$975$	0	0
$976$	−4.80587e12	−0.169531
$977$	2.97018e13i	1.04293i	0.853272	+	0.521467i	$0.174615\pi$
$977$	2.97018e13i	1.04293i	−0.853272	+	0.521467i	$0.825385\pi$
$978$	4.58282e12i	0.160180i
$979$	−2.29004e13	−0.796749
$980$	0	0
$981$	8.87477e12	0.305947
$982$	1.92905e13i	0.661976i
$983$	1.08292e13i	0.369917i	0.982746	+	0.184958i	$0.0592150\pi$
$983$	1.08292e13i	0.369917i	−0.982746	+	0.184958i	$0.940785\pi$
$984$	7.97034e12	0.271019
$985$	0	0
$986$	−9.90428e13	−3.33716
$987$	6.58549e12i	0.220882i
$988$	− 4.02822e12i	− 0.134495i
$989$	1.87302e13	0.622528
$990$	0	0
$991$	5.29514e12	0.174400	0.0871999	−	0.996191i	$-0.472208\pi$
$991$	5.29514e12	0.174400	0.0871999	+	0.996191i	$0.472208\pi$
$992$	3.67242e13i	1.20406i
$993$	− 6.74842e12i	− 0.220257i
$994$	−4.16154e12	−0.135212
$995$	0	0
$996$	2.30317e12	0.0741581
$997$	1.64214e13i	0.526360i	0.964747	+	0.263180i	$0.0847712\pi$
$997$	1.64214e13i	0.526360i	−0.964747	+	0.263180i	$0.915229\pi$
$998$	− 4.94788e13i	− 1.57882i
$999$	6.96593e12	0.221276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.a.99.2		2
5.2	odd	4		175.10.a.a.1.1		1
5.3	odd	4		35.10.a.a.1.1	✓	1
5.4	even	2	inner	175.10.b.a.99.1		2
15.8	even	4		315.10.a.a.1.1		1
35.13	even	4		245.10.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.a.1.1	✓	1	5.3	odd	4
175.10.a.a.1.1		1	5.2	odd	4
175.10.b.a.99.1		2	5.4	even	2	inner
175.10.b.a.99.2		2	1.1	even	1	trivial
245.10.a.b.1.1		1	35.13	even	4
315.10.a.a.1.1		1	15.8	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+28.0000i q^{2} +116.000i q^{3} -272.000 q^{4} -3248.00 q^{6} +2401.00i q^{7} +6720.00i q^{8} +6227.00 q^{9} -25548.0 q^{11} -31552.0i q^{12} +42306.0i q^{13} -67228.0 q^{14} -327424. q^{16} -526342. i q^{17} +174356. i q^{18} +350060. q^{19} -278516. q^{21} -715344. i q^{22} +621976. i q^{23} -779520. q^{24} -1.18457e6 q^{26} +3.00556e6i q^{27} -653072. i q^{28} -6.72043e6 q^{29} -6.41221e6 q^{31} -5.72723e6i q^{32} -2.96357e6i q^{33} +1.47376e7 q^{34} -1.69374e6 q^{36} -2.31768e6i q^{37} +9.80168e6i q^{38} -4.90750e6 q^{39} -1.02247e7 q^{41} -7.79845e6i q^{42} -3.01140e7i q^{43} +6.94906e6 q^{44} -1.74153e7 q^{46} -2.36449e7i q^{47} -3.79812e7i q^{48} -5.76480e6 q^{49} +6.10557e7 q^{51} -1.15072e7i q^{52} -5.72927e7i q^{53} -8.41557e7 q^{54} -1.61347e7 q^{56} +4.06070e7i q^{57} -1.88172e8i q^{58} -8.49348e7 q^{59} +1.46778e7 q^{61} -1.79542e8i q^{62} +1.49510e7i q^{63} -7.27859e6 q^{64} +8.29799e7 q^{66} -2.44558e8i q^{67} +1.43165e8i q^{68} -7.21492e7 q^{69} +6.19020e7 q^{71} +4.18454e7i q^{72} +2.83764e8i q^{73} +6.48951e7 q^{74} -9.52163e7 q^{76} -6.13407e7i q^{77} -1.37410e8i q^{78} -2.76107e8 q^{79} -2.26079e8 q^{81} -2.86291e8i q^{82} +7.29960e7i q^{83} +7.57564e7 q^{84} +8.43192e8 q^{86} -7.79570e8i q^{87} -1.71683e8i q^{88} +8.96368e8 q^{89} -1.01577e8 q^{91} -1.69177e8i q^{92} -7.43816e8i q^{93} +6.62058e8 q^{94} +6.64359e8 q^{96} +1.20581e9i q^{97} -1.61414e8i q^{98} -1.59087e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 544 q^{4} - 6496 q^{6} + 12454 q^{9} - 51096 q^{11} - 134456 q^{14} - 654848 q^{16} + 700120 q^{19} - 557032 q^{21} - 1559040 q^{24} - 2369136 q^{26} - 13440860 q^{29} - 12824416 q^{31} + 29475152 q^{34}+ \cdots - 318174792 q^{99}+O(q^{100}) \) 2 * q - 544 * q^4 - 6496 * q^6 + 12454 * q^9 - 51096 * q^11 - 134456 * q^14 - 654848 * q^16 + 700120 * q^19 - 557032 * q^21 - 1559040 * q^24 - 2369136 * q^26 - 13440860 * q^29 - 12824416 * q^31 + 29475152 * q^34 - 3387488 * q^36 - 9814992 * q^39 - 20449356 * q^41 + 13898112 * q^44 - 34830656 * q^46 - 11529602 * q^49 + 122111344 * q^51 - 168311360 * q^54 - 32269440 * q^56 - 169869560 * q^59 + 29355644 * q^61 - 14557184 * q^64 + 165959808 * q^66 - 144298432 * q^69 + 123803904 * q^71 + 129790192 * q^74 - 190432640 * q^76 - 552214960 * q^79 - 452157838 * q^81 + 151512704 * q^84 + 1686384224 * q^86 + 1792736940 * q^89 - 203153412 * q^91 + 1324115072 * q^94 + 1328717824 * q^96 - 318174792 * q^99

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