LMFDB - Embedded newform 175.10.b.g.99.7

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 = [12,0,0,-6018] 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6045 x^{10} + 13278528 x^{8} + 12528585876 x^{6} + 4315564707360 x^{4} + 82968810446400 x^{2} + 360088576000000 $ x^12 + 6045x^10 + 13278528x^8 + 12528585876x^6 + 4315564707360x^4 + 82968810446400*x^2 + 360088576000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.7
Root			$3.69340i$ of defining polynomial
Character	$\chi$	$=$	175.99
Dual form			175.10.b.g.99.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.69340i q^{2} +266.960i q^{3} +509.132 q^{4} -452.070 q^{6} +2401.00i q^{7} +1729.19i q^{8} -51584.5 q^{9} +65231.2 q^{11} +135918. i q^{12} +29825.1i q^{13} -4065.86 q^{14} +257748. q^{16} +139801. i q^{17} -87353.4i q^{18} +487290. q^{19} -640971. q^{21} +110463. i q^{22} +2.19162e6i q^{23} -461624. q^{24} -50506.0 q^{26} -8.51643e6i q^{27} +1.22243e6i q^{28} -6.69055e6 q^{29} -5.38474e6 q^{31} +1.32181e6i q^{32} +1.74141e7i q^{33} -236740. q^{34} -2.62634e7 q^{36} +1.02850e7i q^{37} +825179. i q^{38} -7.96211e6 q^{39} +171768. q^{41} -1.08542e6i q^{42} -2.48723e7i q^{43} +3.32113e7 q^{44} -3.71130e6 q^{46} +1.56907e7i q^{47} +6.88082e7i q^{48} -5.76480e6 q^{49} -3.73214e7 q^{51} +1.51849e7i q^{52} +8.19930e7i q^{53} +1.44217e7 q^{54} -4.15178e6 q^{56} +1.30087e8i q^{57} -1.13298e7i q^{58} +3.68498e7 q^{59} -1.67161e8 q^{61} -9.11853e6i q^{62} -1.23854e8i q^{63} +1.29728e8 q^{64} -2.94891e7 q^{66} +2.76358e7i q^{67} +7.11774e7i q^{68} -5.85076e8 q^{69} +1.31934e7 q^{71} -8.91994e7i q^{72} -2.19922e8i q^{73} -1.74167e7 q^{74} +2.48095e8 q^{76} +1.56620e8i q^{77} -1.34831e7i q^{78} +3.18444e8 q^{79} +1.25821e9 q^{81} +290872. i q^{82} -5.31354e8i q^{83} -3.26339e8 q^{84} +4.21188e7 q^{86} -1.78611e9i q^{87} +1.12797e8i q^{88} +5.57591e8 q^{89} -7.16102e7 q^{91} +1.11583e9i q^{92} -1.43751e9i q^{93} -2.65707e7 q^{94} -3.52871e8 q^{96} +9.98409e8i q^{97} -9.76213e6i q^{98} -3.36492e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6018 q^{4} + 9776 q^{6} - 222180 q^{9} - 95592 q^{11} + 72030 q^{14} + 4742130 q^{16} - 722112 q^{19} + 595448 q^{21} - 9656152 q^{24} + 21695244 q^{26} - 32056368 q^{29} + 2725824 q^{31} + 18432588 q^{34}+ \cdots - 7143937568 q^{99}+O(q^{100}) $ 12 * q - 6018 * q^4 + 9776 * q^6 - 222180 * q^9 - 95592 * q^11 + 72030 * q^14 + 4742130 * q^16 - 722112 * q^19 + 595448 * q^21 - 9656152 * q^24 + 21695244 * q^26 - 32056368 * q^29 + 2725824 * q^31 + 18432588 * q^34 + 184639282 * q^36 + 40683736 * q^39 + 44905512 * q^41 + 188757456 * q^44 + 99179040 * q^46 - 69177612 * q^49 - 562676360 * q^51 + 580208616 * q^54 - 105840882 * q^56 - 240560784 * q^59 - 175387080 * q^61 - 1281294210 * q^64 - 2787941384 * q^66 - 2063267280 * q^69 + 507525024 * q^71 + 837612108 * q^74 - 1169438952 * q^76 - 1662159000 * q^79 + 3738629420 * q^81 - 2601032112 * q^84 + 1132399896 * q^86 - 1165159368 * q^89 - 490610736 * q^91 + 2231893320 * q^94 + 1978690504 * q^96 - 7143937568 * 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 $

$2$	1.69340i	0.0748385i	0.999300	+	0.0374193i	$0.0119137\pi$
$2$	1.69340i	0.0748385i	−0.999300	+	0.0374193i	$0.988086\pi$
$3$	266.960i	1.90283i	0.307910	+	0.951416i	$0.400370\pi$
$3$	266.960i	1.90283i	−0.307910	+	0.951416i	$0.599630\pi$
$4$	509.132	0.994399
$5$	0	0
$5$	0	0
$6$	−452.070	−0.142405
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	1729.19i	0.149258i
$9$	−51584.5	−2.62077
$10$	0	0
$11$	65231.2	1.34335	0.671674	−	0.740847i	$-0.265576\pi$
$11$	65231.2	1.34335	0.671674	+	0.740847i	$0.265576\pi$
$12$	135918.i	1.89217i
$13$	29825.1i	0.289626i	0.989459	+	0.144813i	$0.0462580\pi$
$13$	29825.1i	0.289626i	−0.989459	+	0.144813i	$0.953742\pi$
$14$	−4065.86	−0.0282863
$15$	0	0
$16$	257748.	0.983229
$17$	139801.i	0.405968i	0.979182	+	0.202984i	$0.0650639\pi$
$17$	139801.i	0.405968i	−0.979182	+	0.202984i	$0.934936\pi$
$18$	− 87353.4i	− 0.196134i
$19$	487290.	0.857821	0.428910	−	0.903347i	$-0.358898\pi$
$19$	487290.	0.857821	0.428910	+	0.903347i	$0.358898\pi$
$20$	0	0
$21$	−640971.	−0.719203
$22$	110463.i	0.100534i
$23$	2.19162e6i	1.63302i	0.577333	+	0.816509i	$0.304094\pi$
$23$	2.19162e6i	1.63302i	−0.577333	+	0.816509i	$0.695906\pi$
$24$	−461624.	−0.284013
$25$	0	0
$26$	−50506.0	−0.0216752
$27$	− 8.51643e6i	− 3.08404i
$28$	1.22243e6i	0.375848i
$29$	−6.69055e6	−1.75659	−0.878296	−	0.478116i	$-0.841320\pi$
$29$	−6.69055e6	−1.75659	−0.878296	+	0.478116i	$0.841320\pi$
$30$	0	0
$31$	−5.38474e6	−1.04722	−0.523609	−	0.851959i	$-0.675415\pi$
$31$	−5.38474e6	−1.04722	−0.523609	+	0.851959i	$0.675415\pi$
$32$	1.32181e6i	0.222841i
$33$	1.74141e7i	2.55616i
$34$	−236740.	−0.0303820
$35$	0	0
$36$	−2.62634e7	−2.60609
$37$	1.02850e7i	0.902188i	0.892476	+	0.451094i	$0.148966\pi$
$37$	1.02850e7i	0.902188i	−0.892476	+	0.451094i	$0.851034\pi$
$38$	825179.i	0.0641980i
$39$	−7.96211e6	−0.551109
$40$	0	0
$41$	171768.	0.00949324	0.00474662	−	0.999989i	$-0.498489\pi$
$41$	171768.	0.00949324	0.00474662	+	0.999989i	$0.498489\pi$
$42$	− 1.08542e6i	− 0.0538241i
$43$	− 2.48723e7i	− 1.10945i	−0.832034	−	0.554725i	$-0.812824\pi$
$43$	− 2.48723e7i	− 1.10945i	0.832034	−	0.554725i	$-0.187176\pi$
$44$	3.32113e7	1.33582
$45$	0	0
$46$	−3.71130e6	−0.122213
$47$	1.56907e7i	0.469033i	0.972112	+	0.234516i	$0.0753507\pi$
$47$	1.56907e7i	0.469033i	−0.972112	+	0.234516i	$0.924649\pi$
$48$	6.88082e7i	1.87092i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−3.73214e7	−0.772488
$52$	1.51849e7i	0.288004i
$53$	8.19930e7i	1.42737i	0.700469	+	0.713683i	$0.252974\pi$
$53$	8.19930e7i	1.42737i	−0.700469	+	0.713683i	$0.747026\pi$
$54$	1.44217e7	0.230805
$55$	0	0
$56$	−4.15178e6	−0.0564142
$57$	1.30087e8i	1.63229i
$58$	− 1.13298e7i	− 0.131461i
$59$	3.68498e7	0.395914	0.197957	−	0.980211i	$-0.436569\pi$
$59$	3.68498e7	0.395914	0.197957	+	0.980211i	$0.436569\pi$
$60$	0	0
$61$	−1.67161e8	−1.54579	−0.772896	−	0.634533i	$-0.781192\pi$
$61$	−1.67161e8	−1.54579	−0.772896	+	0.634533i	$0.781192\pi$
$62$	− 9.11853e6i	− 0.0783722i
$63$	− 1.23854e8i	− 0.990556i
$64$	1.29728e8	0.966552
$65$	0	0
$66$	−2.94891e7	−0.191299
$67$	2.76358e7i	0.167546i	0.996485	+	0.0837732i	$0.0266971\pi$
$67$	2.76358e7i	0.167546i	−0.996485	+	0.0837732i	$0.973303\pi$
$68$	7.11774e7i	0.403694i
$69$	−5.85076e8	−3.10736
$70$	0	0
$71$	1.31934e7	0.0616160	0.0308080	−	0.999525i	$-0.490192\pi$
$71$	1.31934e7	0.0616160	0.0308080	+	0.999525i	$0.490192\pi$
$72$	− 8.91994e7i	− 0.391170i
$73$	− 2.19922e8i	− 0.906392i	−0.891411	−	0.453196i	$-0.850284\pi$
$73$	− 2.19922e8i	− 0.906392i	0.891411	−	0.453196i	$-0.149716\pi$
$74$	−1.74167e7	−0.0675184
$75$	0	0
$76$	2.48095e8	0.853016
$77$	1.56620e8i	0.507738i
$78$	− 1.34831e7i	− 0.0412442i
$79$	3.18444e8	0.919838	0.459919	−	0.887961i	$-0.347878\pi$
$79$	3.18444e8	0.919838	0.459919	+	0.887961i	$0.347878\pi$
$80$	0	0
$81$	1.25821e9	3.24765
$82$	290872.i	0 0.000710460i
$83$	− 5.31354e8i	− 1.22895i	−0.788938	−	0.614473i	$-0.789369\pi$
$83$	− 5.31354e8i	− 1.22895i	0.788938	−	0.614473i	$-0.210631\pi$
$84$	−3.26339e8	−0.715174
$85$	0	0
$86$	4.21188e7	0.0830296
$87$	− 1.78611e9i	− 3.34250i
$88$	1.12797e8i	0.200505i
$89$	5.57591e8	0.942021	0.471011	−	0.882128i	$-0.343889\pi$
$89$	5.57591e8	0.942021	0.471011	+	0.882128i	$0.343889\pi$
$90$	0	0
$91$	−7.16102e7	−0.109468
$92$	1.11583e9i	1.62387i
$93$	− 1.43751e9i	− 1.99268i
$94$	−2.65707e7	−0.0351017
$95$	0	0
$96$	−3.52871e8	−0.424029
$97$	9.98409e8i	1.14508i	0.819877	+	0.572540i	$0.194042\pi$
$97$	9.98409e8i	1.14508i	−0.819877	+	0.572540i	$0.805958\pi$
$98$	− 9.76213e6i	− 0.0106912i
$99$	−3.36492e9	−3.52060
$100$	0	0
$101$	−5.25040e8	−0.502050	−0.251025	−	0.967981i	$-0.580768\pi$
$101$	−5.25040e8	−0.502050	−0.251025	+	0.967981i	$0.580768\pi$
$102$	− 6.32001e7i	− 0.0578119i
$103$	9.94810e8i	0.870908i	0.900211	+	0.435454i	$0.143412\pi$
$103$	9.94810e8i	0.870908i	−0.900211	+	0.435454i	$0.856588\pi$
$104$	−5.15733e7	−0.0432290
$105$	0	0
$106$	−1.38847e8	−0.106822
$107$	− 2.42972e9i	− 1.79197i	−0.444087	−	0.895984i	$-0.646472\pi$
$107$	− 2.42972e9i	− 1.79197i	0.444087	−	0.895984i	$-0.353528\pi$
$108$	− 4.33599e9i	− 3.06677i
$109$	−8.53072e8	−0.578851	−0.289425	−	0.957201i	$-0.593464\pi$
$109$	−8.53072e8	−0.578851	−0.289425	+	0.957201i	$0.593464\pi$
$110$	0	0
$111$	−2.74569e9	−1.71671
$112$	6.18852e8i	0.371626i
$113$	− 9.49056e7i	− 0.0547569i	−0.999625	−	0.0273784i	$-0.991284\pi$
$113$	− 9.49056e7i	− 0.0547569i	0.999625	−	0.0273784i	$-0.00871592\pi$
$114$	−2.20290e8	−0.122158
$115$	0	0
$116$	−3.40638e9	−1.74675
$117$	− 1.53852e9i	− 0.759042i
$118$	6.24016e7i	0.0296296i
$119$	−3.35663e8	−0.153441
$120$	0	0
$121$	1.89716e9	0.804582
$122$	− 2.83071e8i	− 0.115685i
$123$	4.58551e7i	0.0180640i
$124$	−2.74154e9	−1.04135
$125$	0	0
$126$	2.09736e8	0.0741318
$127$	2.24989e9i	0.767440i	0.923450	+	0.383720i	$0.125357\pi$
$127$	2.24989e9i	0.767440i	−0.923450	+	0.383720i	$0.874643\pi$
$128$	8.96452e8i	0.295177i
$129$	6.63990e9	2.11109
$130$	0	0
$131$	3.62125e8	0.107433	0.0537165	−	0.998556i	$-0.482893\pi$
$131$	3.62125e8	0.107433	0.0537165	+	0.998556i	$0.482893\pi$
$132$	8.86609e9i	2.54185i
$133$	1.16998e9i	0.324226i
$134$	−4.67985e7	−0.0125389
$135$	0	0
$136$	−2.41743e8	−0.0605939
$137$	2.65181e9i	0.643132i	0.946887	+	0.321566i	$0.104209\pi$
$137$	2.65181e9i	0.643132i	−0.946887	+	0.321566i	$0.895791\pi$
$138$	− 9.90769e8i	− 0.232550i
$139$	8.55002e8	0.194268	0.0971338	−	0.995271i	$-0.469033\pi$
$139$	8.55002e8	0.194268	0.0971338	+	0.995271i	$0.469033\pi$
$140$	0	0
$141$	−4.18880e9	−0.892490
$142$	2.23417e7i	0.00461125i
$143$	1.94553e9i	0.389068i
$144$	−1.32958e10	−2.57681
$145$	0	0
$146$	3.72417e8	0.0678331
$147$	− 1.53897e9i	− 0.271833i
$148$	5.23643e9i	0.897135i
$149$	−2.66821e9	−0.443489	−0.221744	−	0.975105i	$-0.571175\pi$
$149$	−2.66821e9	−0.443489	−0.221744	+	0.975105i	$0.571175\pi$
$150$	0	0
$151$	3.60329e9	0.564030	0.282015	−	0.959410i	$-0.408997\pi$
$151$	3.60329e9	0.564030	0.282015	+	0.959410i	$0.408997\pi$
$152$	8.42617e8i	0.128037i
$153$	− 7.21159e9i	− 1.06395i
$154$	−2.65221e8	−0.0379983
$155$	0	0
$156$	−4.05377e9	−0.548023
$157$	− 8.84712e9i	− 1.16213i	−0.813858	−	0.581063i	$-0.802637\pi$
$157$	− 8.84712e9i	− 1.16213i	0.813858	−	0.581063i	$-0.197363\pi$
$158$	5.39254e8i	0.0688393i
$159$	−2.18888e10	−2.71604
$160$	0	0
$161$	−5.26209e9	−0.617223
$162$	2.13065e9i	0.243049i
$163$	− 6.73119e8i	− 0.0746874i	−0.999302	−	0.0373437i	$-0.988110\pi$
$163$	− 6.73119e8i	− 0.0746874i	0.999302	−	0.0373437i	$-0.0118896\pi$
$164$	8.74525e7	0.00944007
$165$	0	0
$166$	8.99796e8	0.0919724
$167$	− 7.92632e9i	− 0.788583i	−0.918985	−	0.394292i	$-0.870990\pi$
$167$	− 7.92632e9i	− 0.788583i	0.918985	−	0.394292i	$-0.129010\pi$
$168$	− 1.10836e9i	− 0.107347i
$169$	9.71496e9	0.916117
$170$	0	0
$171$	−2.51366e10	−2.24815
$172$	− 1.26633e10i	− 1.10324i
$173$	− 9.38833e9i	− 0.796858i	−0.917199	−	0.398429i	$-0.869556\pi$
$173$	− 9.38833e9i	− 0.796858i	0.917199	−	0.398429i	$-0.130444\pi$
$174$	3.02460e9	0.250148
$175$	0	0
$176$	1.68132e10	1.32082
$177$	9.83742e9i	0.753358i
$178$	9.44226e8i	0.0704995i
$179$	−3.88868e9	−0.283116	−0.141558	−	0.989930i	$-0.545211\pi$
$179$	−3.88868e9	−0.283116	−0.141558	+	0.989930i	$0.545211\pi$
$180$	0	0
$181$	1.13851e10	0.788466	0.394233	−	0.919011i	$-0.371010\pi$
$181$	1.13851e10	0.788466	0.394233	+	0.919011i	$0.371010\pi$
$182$	− 1.21265e8i	− 0.00819245i
$183$	− 4.46253e10i	− 2.94138i
$184$	−3.78973e9	−0.243741
$185$	0	0
$186$	2.43428e9	0.149129
$187$	9.11942e9i	0.545356i
$188$	7.98867e9i	0.466406i
$189$	2.04479e10	1.16566
$190$	0	0
$191$	2.74058e10	1.49002	0.745009	−	0.667054i	$-0.232445\pi$
$191$	2.74058e10	1.49002	0.745009	+	0.667054i	$0.232445\pi$
$192$	3.46323e10i	1.83918i
$193$	− 8.42540e9i	− 0.437102i	−0.975826	−	0.218551i	$-0.929867\pi$
$193$	− 8.42540e9i	− 0.437102i	0.975826	−	0.218551i	$-0.0701330\pi$
$194$	−1.69071e9	−0.0856961
$195$	0	0
$196$	−2.93505e9	−0.142057
$197$	5.37976e9i	0.254486i	0.991872	+	0.127243i	$0.0406129\pi$
$197$	5.37976e9i	0.254486i	−0.991872	+	0.127243i	$0.959387\pi$
$198$	− 5.69817e9i	− 0.263476i
$199$	−4.28491e10	−1.93688	−0.968441	−	0.249245i	$-0.919818\pi$
$199$	−4.28491e10	−1.93688	−0.968441	+	0.249245i	$0.919818\pi$
$200$	0	0
$201$	−7.37764e9	−0.318812
$202$	− 8.89105e8i	− 0.0375727i
$203$	− 1.60640e10i	− 0.663930i
$204$	−1.90015e10	−0.768161
$205$	0	0
$206$	−1.68461e9	−0.0651775
$207$	− 1.13054e11i	− 4.27976i
$208$	7.68736e9i	0.284769i
$209$	3.17865e10	1.15235
$210$	0	0
$211$	−1.34847e10	−0.468350	−0.234175	−	0.972194i	$-0.575239\pi$
$211$	−1.34847e10	−0.468350	−0.234175	+	0.972194i	$0.575239\pi$
$212$	4.17453e10i	1.41937i
$213$	3.52210e9i	0.117245i
$214$	4.11450e9	0.134108
$215$	0	0
$216$	1.47265e10	0.460318
$217$	− 1.29288e10i	− 0.395811i
$218$	− 1.44459e9i	− 0.0433203i
$219$	5.87104e10	1.72471
$220$	0	0
$221$	−4.16960e9	−0.117579
$222$	− 4.64955e9i	− 0.128476i
$223$	− 3.90205e10i	− 1.05663i	−0.849050	−	0.528313i	$-0.822825\pi$
$223$	− 3.90205e10i	− 1.05663i	0.849050	−	0.528313i	$-0.177175\pi$
$224$	−3.17368e9	−0.0842261
$225$	0	0
$226$	1.60713e8	0.00409793
$227$	− 7.08123e8i	− 0.0177008i	−0.999961	−	0.00885038i	$-0.997183\pi$
$227$	− 7.08123e8i	− 0.0177008i	0.999961	−	0.00885038i	$-0.00281720\pi$
$228$	6.62315e10i	1.62315i
$229$	−4.83188e10	−1.16107	−0.580533	−	0.814237i	$-0.697156\pi$
$229$	−4.83188e10	−1.16107	−0.580533	+	0.814237i	$0.697156\pi$
$230$	0	0
$231$	−4.18113e10	−0.966139
$232$	− 1.15692e10i	− 0.262185i
$233$	1.38868e10i	0.308674i	0.988018	+	0.154337i	$0.0493241\pi$
$233$	1.38868e10i	0.308674i	−0.988018	+	0.154337i	$0.950676\pi$
$234$	2.60533e9	0.0568056
$235$	0	0
$236$	1.87614e10	0.393697
$237$	8.50118e10i	1.75030i
$238$	− 5.68413e8i	− 0.0114833i
$239$	8.52567e10	1.69020	0.845100	−	0.534608i	$-0.179541\pi$
$239$	8.52567e10	1.69020	0.845100	+	0.534608i	$0.179541\pi$
$240$	0	0
$241$	2.14186e10	0.408992	0.204496	−	0.978867i	$-0.434444\pi$
$241$	2.14186e10	0.408992	0.204496	+	0.978867i	$0.434444\pi$
$242$	3.21266e9i	0.0602137i
$243$	1.68262e11i	3.09568i
$244$	−8.51071e10	−1.53713
$245$	0	0
$246$	−7.76511e7	−0.00135188
$247$	1.45335e10i	0.248447i
$248$	− 9.31123e9i	− 0.156306i
$249$	1.41850e11	2.33847
$250$	0	0
$251$	−6.34876e10	−1.00962	−0.504809	−	0.863231i	$-0.668437\pi$
$251$	−6.34876e10	−1.00962	−0.504809	+	0.863231i	$0.668437\pi$
$252$	− 6.30583e10i	− 0.985009i
$253$	1.42962e11i	2.19371i
$254$	−3.80997e9	−0.0574341
$255$	0	0
$256$	6.49029e10	0.944461
$257$	6.20307e10i	0.886967i	0.896282	+	0.443484i	$0.146258\pi$
$257$	6.20307e10i	0.886967i	−0.896282	+	0.443484i	$0.853742\pi$
$258$	1.12440e10i	0.157991i
$259$	−2.46943e10	−0.340995
$260$	0	0
$261$	3.45129e11	4.60362
$262$	6.13224e8i	0.00804013i
$263$	3.41529e10i	0.440177i	0.975480	+	0.220088i	$0.0706346\pi$
$263$	3.41529e10i	0.440177i	−0.975480	+	0.220088i	$0.929365\pi$
$264$	−3.01123e10	−0.381528
$265$	0	0
$266$	−1.98125e9	−0.0242646
$267$	1.48854e11i	1.79251i
$268$	1.40703e10i	0.166608i
$269$	6.95076e10	0.809370	0.404685	−	0.914456i	$-0.367381\pi$
$269$	6.95076e10	0.809370	0.404685	+	0.914456i	$0.367381\pi$
$270$	0	0
$271$	−1.60754e11	−1.81050	−0.905252	−	0.424874i	$-0.860318\pi$
$271$	−1.60754e11	−1.81050	−0.905252	+	0.424874i	$0.860318\pi$
$272$	3.60335e10i	0.399159i
$273$	− 1.91170e10i	− 0.208300i
$274$	−4.49059e9	−0.0481311
$275$	0	0
$276$	−2.97881e11	−3.08995
$277$	− 5.68447e10i	− 0.580138i	−0.957006	−	0.290069i	$-0.906322\pi$
$277$	− 5.68447e10i	− 0.580138i	0.957006	−	0.290069i	$-0.0936782\pi$
$278$	1.44786e9i	0.0145387i
$279$	2.77769e11	2.74451
$280$	0	0
$281$	5.09457e10	0.487449	0.243725	−	0.969844i	$-0.421631\pi$
$281$	5.09457e10	0.487449	0.243725	+	0.969844i	$0.421631\pi$
$282$	− 7.09332e9i	− 0.0667927i
$283$	− 3.33397e10i	− 0.308974i	−0.987995	−	0.154487i	$-0.950627\pi$
$283$	− 3.33397e10i	− 0.308974i	0.987995	−	0.154487i	$-0.0493725\pi$
$284$	6.71717e9	0.0612709
$285$	0	0
$286$	−3.29457e9	−0.0291173
$287$	4.12414e8i	0.00358811i
$288$	− 6.81852e10i	− 0.584015i
$289$	9.90434e10	0.835190
$290$	0	0
$291$	−2.66535e11	−2.17889
$292$	− 1.11969e11i	− 0.901316i
$293$	6.23717e10i	0.494406i	0.968964	+	0.247203i	$0.0795114\pi$
$293$	6.23717e10i	0.494406i	−0.968964	+	0.247203i	$0.920489\pi$
$294$	2.60610e9	0.0203436
$295$	0	0
$296$	−1.77847e10	−0.134659
$297$	− 5.55537e11i	− 4.14294i
$298$	− 4.51836e9i	− 0.0331900i
$299$	−6.53655e10	−0.472964
$300$	0	0
$301$	5.97183e10	0.419332
$302$	6.10181e9i	0.0422112i
$303$	− 1.40165e11i	− 0.955315i
$304$	1.25598e11	0.843434
$305$	0	0
$306$	1.22121e10	0.0796242
$307$	2.60655e11i	1.67473i	0.546647	+	0.837363i	$0.315904\pi$
$307$	2.60655e11i	1.67473i	−0.546647	+	0.837363i	$0.684096\pi$
$308$	7.97404e10i	0.504894i
$309$	−2.65574e11	−1.65719
$310$	0	0
$311$	2.00531e10	0.121551	0.0607756	−	0.998151i	$-0.480643\pi$
$311$	2.00531e10	0.121551	0.0607756	+	0.998151i	$0.480643\pi$
$312$	− 1.37680e10i	− 0.0822574i
$313$	1.72221e11i	1.01423i	0.861878	+	0.507116i	$0.169288\pi$
$313$	1.72221e11i	1.01423i	−0.861878	+	0.507116i	$0.830712\pi$
$314$	1.49817e10	0.0869719
$315$	0	0
$316$	1.62130e11	0.914686
$317$	2.33991e11i	1.30147i	0.759306	+	0.650734i	$0.225539\pi$
$317$	2.33991e11i	1.30147i	−0.759306	+	0.650734i	$0.774461\pi$
$318$	− 3.70666e10i	− 0.203264i
$319$	−4.36433e11	−2.35971
$320$	0	0
$321$	6.48639e11	3.40981
$322$	− 8.91084e9i	− 0.0461920i
$323$	6.81239e10i	0.348247i
$324$	6.40593e11	3.22946
$325$	0	0
$326$	1.13986e9	0.00558950
$327$	− 2.27736e11i	− 1.10146i
$328$	2.97019e8i	0.00141694i
$329$	−3.76735e10	−0.177278
$330$	0	0
$331$	3.72261e11	1.70459	0.852297	−	0.523058i	$-0.175209\pi$
$331$	3.72261e11	1.70459	0.852297	+	0.523058i	$0.175209\pi$
$332$	− 2.70529e11i	− 1.22206i
$333$	− 5.30548e11i	− 2.36442i
$334$	1.34225e10	0.0590164
$335$	0	0
$336$	−1.65209e11	−0.707141
$337$	4.41686e11i	1.86543i	0.360612	+	0.932716i	$0.382568\pi$
$337$	4.41686e11i	1.86543i	−0.360612	+	0.932716i	$0.617432\pi$
$338$	1.64513e10i	0.0685608i
$339$	2.53360e10	0.104193
$340$	0	0
$341$	−3.51253e11	−1.40678
$342$	− 4.25665e10i	− 0.168248i
$343$	− 1.38413e10i	− 0.0539949i
$344$	4.30088e10	0.165594
$345$	0	0
$346$	1.58982e10	0.0596357
$347$	1.83989e11i	0.681256i	0.940198	+	0.340628i	$0.110640\pi$
$347$	1.83989e11i	0.681256i	−0.940198	+	0.340628i	$0.889360\pi$
$348$	− 9.09366e11i	− 3.32378i
$349$	−4.97480e11	−1.79499	−0.897493	−	0.441029i	$-0.854614\pi$
$349$	−4.97480e11	−1.79499	−0.897493	+	0.441029i	$0.854614\pi$
$350$	0	0
$351$	2.54004e11	0.893219
$352$	8.62236e10i	0.299353i
$353$	4.28742e11i	1.46964i	0.678265	+	0.734818i	$0.262732\pi$
$353$	4.28742e11i	1.46964i	−0.678265	+	0.734818i	$0.737268\pi$
$354$	−1.66587e10	−0.0563802
$355$	0	0
$356$	2.83888e11	0.936745
$357$	− 8.96086e10i	− 0.291973i
$358$	− 6.58511e9i	− 0.0211880i
$359$	−2.02484e11	−0.643378	−0.321689	−	0.946845i	$-0.604251\pi$
$359$	−2.02484e11	−0.643378	−0.321689	+	0.946845i	$0.604251\pi$
$360$	0	0
$361$	−8.52359e10	−0.264144
$362$	1.92795e10i	0.0590076i
$363$	5.06466e11i	1.53098i
$364$	−3.64591e10	−0.108855
$365$	0	0
$366$	7.55686e10	0.220128
$367$	− 1.15083e11i	− 0.331142i	−0.986198	−	0.165571i	$-0.947053\pi$
$367$	− 1.15083e11i	− 0.331142i	0.986198	−	0.165571i	$-0.0529467\pi$
$368$	5.64886e11i	1.60563i
$369$	−8.86056e9	−0.0248795
$370$	0	0
$371$	−1.96865e11	−0.539494
$372$	− 7.31882e11i	− 1.98152i
$373$	− 5.53723e11i	− 1.48116i	−0.671966	−	0.740582i	$-0.734550\pi$
$373$	− 5.53723e11i	− 1.48116i	0.671966	−	0.740582i	$-0.265450\pi$
$374$	−1.54428e10	−0.0408136
$375$	0	0
$376$	−2.71323e10	−0.0700069
$377$	− 1.99547e11i	− 0.508755i
$378$	3.46266e10i	0.0872362i
$379$	2.21458e11	0.551334	0.275667	−	0.961253i	$-0.411101\pi$
$379$	2.21458e11	0.551334	0.275667	+	0.961253i	$0.411101\pi$
$380$	0	0
$381$	−6.00630e11	−1.46031
$382$	4.64090e10i	0.111511i
$383$	− 2.51422e10i	− 0.0597048i	−0.999554	−	0.0298524i	$-0.990496\pi$
$383$	− 2.51422e10i	− 0.0597048i	0.999554	−	0.0298524i	$-0.00950372\pi$
$384$	−2.39317e11	−0.561671
$385$	0	0
$386$	1.42676e10	0.0327121
$387$	1.28302e12i	2.90761i
$388$	5.08322e11i	1.13867i
$389$	3.84801e11	0.852046	0.426023	−	0.904712i	$-0.359914\pi$
$389$	3.84801e11	0.852046	0.426023	+	0.904712i	$0.359914\pi$
$390$	0	0
$391$	−3.06392e11	−0.662952
$392$	− 9.96843e9i	− 0.0213226i
$393$	9.66729e10i	0.204427i
$394$	−9.11009e9	−0.0190454
$395$	0	0
$396$	−1.71319e12	−3.50088
$397$	2.83472e11i	0.572734i	0.958120	+	0.286367i	$0.0924477\pi$
$397$	2.83472e11i	0.572734i	−0.958120	+	0.286367i	$0.907552\pi$
$398$	− 7.25608e10i	− 0.144953i
$399$	−3.12339e11	−0.616947
$400$	0	0
$401$	6.37484e11	1.23118	0.615588	−	0.788069i	$-0.288919\pi$
$401$	6.37484e11	1.23118	0.615588	+	0.788069i	$0.288919\pi$
$402$	− 1.24933e10i	− 0.0238594i
$403$	− 1.60601e11i	− 0.303301i
$404$	−2.67315e11	−0.499238
$405$	0	0
$406$	2.72029e10	0.0496875
$407$	6.70904e11i	1.21195i
$408$	− 6.45357e10i	− 0.115300i
$409$	−1.02506e12	−1.81132	−0.905659	−	0.424006i	$-0.860623\pi$
$409$	−1.02506e12	−1.81132	−0.905659	+	0.424006i	$0.860623\pi$
$410$	0	0
$411$	−7.07927e11	−1.22377
$412$	5.06490e11i	0.866031i
$413$	8.84764e10i	0.149642i
$414$	1.91446e11	0.320291
$415$	0	0
$416$	−3.94233e10	−0.0645406
$417$	2.28251e11i	0.369658i
$418$	5.38274e10i	0.0862403i
$419$	7.04662e11	1.11691	0.558454	−	0.829535i	$-0.311395\pi$
$419$	7.04662e11	1.11691	0.558454	+	0.829535i	$0.311395\pi$
$420$	0	0
$421$	−1.74714e11	−0.271055	−0.135527	−	0.990774i	$-0.543273\pi$
$421$	−1.74714e11	−0.271055	−0.135527	+	0.990774i	$0.543273\pi$
$422$	− 2.28350e10i	− 0.0350506i
$423$	− 8.09400e11i	− 1.22923i
$424$	−1.41781e11	−0.213046
$425$	0	0
$426$	−5.96433e9	−0.00877443
$427$	− 4.01354e11i	− 0.584254i
$428$	− 1.23705e12i	− 1.78193i
$429$	−5.19378e11	−0.740331
$430$	0	0
$431$	6.66342e11	0.930142	0.465071	−	0.885273i	$-0.346029\pi$
$431$	6.66342e11	0.930142	0.465071	+	0.885273i	$0.346029\pi$
$432$	− 2.19509e12i	− 3.03232i
$433$	− 7.44020e11i	− 1.01716i	−0.861015	−	0.508580i	$-0.830171\pi$
$433$	− 7.44020e11i	− 1.01716i	0.861015	−	0.508580i	$-0.169829\pi$
$434$	2.18936e10	0.0296219
$435$	0	0
$436$	−4.34327e11	−0.575609
$437$	1.06796e12i	1.40084i
$438$	9.94203e10i	0.129075i
$439$	5.83899e11	0.750321	0.375161	−	0.926960i	$-0.377588\pi$
$439$	5.83899e11	0.750321	0.375161	+	0.926960i	$0.377588\pi$
$440$	0	0
$441$	2.97375e11	0.374395
$442$	− 7.06081e9i	− 0.00879942i
$443$	1.32106e12i	1.62969i	0.579677	+	0.814846i	$0.303179\pi$
$443$	1.32106e12i	1.62969i	−0.579677	+	0.814846i	$0.696821\pi$
$444$	−1.39792e12	−1.70710
$445$	0	0
$446$	6.60774e10	0.0790763
$447$	− 7.12306e11i	− 0.843884i
$448$	3.11478e11i	0.365322i
$449$	−1.30479e12	−1.51507	−0.757534	−	0.652795i	$-0.773596\pi$
$449$	−1.30479e12	−1.51507	−0.757534	+	0.652795i	$0.773596\pi$
$450$	0	0
$451$	1.12046e10	0.0127527
$452$	− 4.83195e10i	− 0.0544502i
$453$	9.61933e11i	1.07325i
$454$	1.19914e9	0.00132470
$455$	0	0
$456$	−2.24945e11	−0.243632
$457$	2.58261e11i	0.276972i	0.990364	+	0.138486i	$0.0442236\pi$
$457$	2.58261e11i	0.276972i	−0.990364	+	0.138486i	$0.955776\pi$
$458$	− 8.18233e10i	− 0.0868925i
$459$	1.19061e12	1.25202
$460$	0	0
$461$	−4.66547e11	−0.481106	−0.240553	−	0.970636i	$-0.577329\pi$
$461$	−4.66547e11	−0.481106	−0.240553	+	0.970636i	$0.577329\pi$
$462$	− 7.08033e10i	− 0.0723044i
$463$	− 3.16318e11i	− 0.319896i	−0.987125	−	0.159948i	$-0.948867\pi$
$463$	− 3.16318e11i	− 0.319896i	0.987125	−	0.159948i	$-0.0511327\pi$
$464$	−1.72447e12	−1.72713
$465$	0	0
$466$	−2.35159e10	−0.0231007
$467$	1.29338e12i	1.25835i	0.777265	+	0.629173i	$0.216606\pi$
$467$	1.29338e12i	1.25835i	−0.777265	+	0.629173i	$0.783394\pi$
$468$	− 7.83308e11i	− 0.754791i
$469$	−6.63535e10	−0.0633266
$470$	0	0
$471$	2.36183e12	2.21133
$472$	6.37203e10i	0.0590933i
$473$	− 1.62245e12i	− 1.49038i
$474$	−1.43959e11	−0.130990
$475$	0	0
$476$	−1.70897e11	−0.152582
$477$	− 4.22957e12i	− 3.74079i
$478$	1.44374e11i	0.126492i
$479$	−1.09778e12	−0.952806	−0.476403	−	0.879227i	$-0.658060\pi$
$479$	−1.09778e12	−0.952806	−0.476403	+	0.879227i	$0.658060\pi$
$480$	0	0
$481$	−3.06752e11	−0.261297
$482$	3.62704e10i	0.0306084i
$483$	− 1.40477e12i	− 1.17447i
$484$	9.65907e11	0.800076
$485$	0	0
$486$	−2.84934e11	−0.231676
$487$	5.90084e10i	0.0475372i	0.999717	+	0.0237686i	$0.00756649\pi$
$487$	5.90084e10i	0.0475372i	−0.999717	+	0.0237686i	$0.992434\pi$
$488$	− 2.89053e11i	− 0.230722i
$489$	1.79696e11	0.142118
$490$	0	0
$491$	1.36272e12	1.05813	0.529066	−	0.848580i	$-0.322542\pi$
$491$	1.36272e12	1.05813	0.529066	+	0.848580i	$0.322542\pi$
$492$	2.33463e10i	0.0179629i
$493$	− 9.35349e11i	− 0.713120i
$494$	−2.46111e10	−0.0185934
$495$	0	0
$496$	−1.38790e12	−1.02965
$497$	3.16773e10i	0.0232886i
$498$	2.40209e11i	0.175008i
$499$	1.75264e12	1.26544	0.632719	−	0.774381i	$-0.281939\pi$
$499$	1.75264e12	1.26544	0.632719	+	0.774381i	$0.281939\pi$
$500$	0	0
$501$	2.11601e12	1.50054
$502$	− 1.07510e11i	− 0.0755583i
$503$	1.41597e12i	0.986277i	0.869951	+	0.493139i	$0.164150\pi$
$503$	1.41597e12i	0.986277i	−0.869951	+	0.493139i	$0.835850\pi$
$504$	2.14168e11	0.147848
$505$	0	0
$506$	−2.42093e11	−0.164174
$507$	2.59350e12i	1.74322i
$508$	1.14549e12i	0.763141i
$509$	1.60342e12	1.05881	0.529404	−	0.848370i	$-0.322416\pi$
$509$	1.60342e12	1.05881	0.529404	+	0.848370i	$0.322416\pi$
$510$	0	0
$511$	5.28033e11	0.342584
$512$	5.68890e11i	0.365859i
$513$	− 4.14997e12i	− 2.64556i
$514$	−1.05043e11	−0.0663793
$515$	0	0
$516$	3.38059e12	2.09927
$517$	1.02353e12i	0.630074i
$518$	− 4.18174e10i	− 0.0255196i
$519$	2.50631e12	1.51629
$520$	0	0
$521$	2.45920e12	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$521$	2.45920e12	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$522$	5.84443e11i	0.344528i
$523$	− 1.84840e12i	− 1.08029i	−0.841573	−	0.540143i	$-0.818370\pi$
$523$	− 1.84840e12i	− 1.08029i	0.841573	−	0.540143i	$-0.181630\pi$
$524$	1.84370e11	0.106831
$525$	0	0
$526$	−5.78347e10	−0.0329422
$527$	− 7.52794e11i	− 0.425137i
$528$	4.48844e12i	2.51329i
$529$	−3.00207e12	−1.66675
$530$	0	0
$531$	−1.90088e12	−1.03760
$532$	5.95677e11i	0.322410i
$533$	5.12300e9i	0.00274949i
$534$	−2.52070e11	−0.134149
$535$	0	0
$536$	−4.77874e10	−0.0250076
$537$	− 1.03812e12i	− 0.538721i
$538$	1.17704e11i	0.0605721i
$539$	−3.76045e11	−0.191907
$540$	0	0
$541$	−2.18609e12	−1.09719	−0.548593	−	0.836090i	$-0.684836\pi$
$541$	−2.18609e12	−1.09719	−0.548593	+	0.836090i	$0.684836\pi$
$542$	− 2.72221e11i	− 0.135496i
$543$	3.03936e12i	1.50032i
$544$	−1.84792e11	−0.0904664
$545$	0	0
$546$	3.23728e10	0.0155888
$547$	3.84313e12i	1.83545i	0.397220	+	0.917723i	$0.369975\pi$
$547$	3.84313e12i	1.83545i	−0.397220	+	0.917723i	$0.630025\pi$
$548$	1.35012e12i	0.639530i
$549$	8.62292e12	4.05116
$550$	0	0
$551$	−3.26024e12	−1.50684
$552$	− 1.01171e12i	− 0.463798i
$553$	7.64584e11i	0.347666i
$554$	9.62610e10	0.0434166
$555$	0	0
$556$	4.35309e11	0.193180
$557$	− 2.62226e12i	− 1.15432i	−0.816629	−	0.577162i	$-0.804160\pi$
$557$	− 2.62226e12i	− 1.15432i	0.816629	−	0.577162i	$-0.195840\pi$
$558$	4.70375e11i	0.205395i
$559$	7.41819e11	0.321325
$560$	0	0
$561$	−2.43452e12	−1.03772
$562$	8.62716e10i	0.0364800i
$563$	− 1.28652e12i	− 0.539672i	−0.962906	−	0.269836i	$-0.913030\pi$
$563$	− 1.28652e12i	− 0.539672i	0.962906	−	0.269836i	$-0.0869696\pi$
$564$	−2.13265e12	−0.887492
$565$	0	0
$566$	5.64575e10	0.0231232
$567$	3.02095e12i	1.22750i
$568$	2.28138e10i	0.00919667i
$569$	−2.20765e12	−0.882926	−0.441463	−	0.897280i	$-0.645540\pi$
$569$	−2.20765e12	−0.882926	−0.441463	+	0.897280i	$0.645540\pi$
$570$	0	0
$571$	−2.20713e11	−0.0868891	−0.0434445	−	0.999056i	$-0.513833\pi$
$571$	−2.20713e11	−0.0868891	−0.0434445	+	0.999056i	$0.513833\pi$
$572$	9.90532e11i	0.386889i
$573$	7.31623e12i	2.83525i
$574$	−6.98384e8	−0.000268529 0
$575$	0	0
$576$	−6.69198e12	−2.53311
$577$	− 1.26604e12i	− 0.475505i	−0.971326	−	0.237752i	$-0.923589\pi$
$577$	− 1.26604e12i	− 0.475505i	0.971326	−	0.237752i	$-0.0764107\pi$
$578$	1.67720e11i	0.0625044i
$579$	2.24924e12	0.831731
$580$	0	0
$581$	1.27578e12	0.464498
$582$	− 4.51351e11i	− 0.163065i
$583$	5.34850e12i	1.91745i
$584$	3.80287e11	0.135286
$585$	0	0
$586$	−1.05620e11	−0.0370006
$587$	− 1.65238e12i	− 0.574430i	−0.957866	−	0.287215i	$-0.907271\pi$
$587$	− 1.65238e12i	− 0.574430i	0.957866	−	0.287215i	$-0.0927295\pi$
$588$	− 7.83540e11i	− 0.270311i
$589$	−2.62393e12	−0.898325
$590$	0	0
$591$	−1.43618e12	−0.484245
$592$	2.65094e12i	0.887058i
$593$	2.05437e12i	0.682233i	0.940021	+	0.341117i	$0.110805\pi$
$593$	2.05437e12i	0.682233i	−0.940021	+	0.341117i	$0.889195\pi$
$594$	9.40748e11	0.310052
$595$	0	0
$596$	−1.35847e12	−0.441005
$597$	− 1.14390e13i	− 3.68556i
$598$	− 1.10690e11i	− 0.0353960i
$599$	−2.33752e12	−0.741883	−0.370942	−	0.928656i	$-0.620965\pi$
$599$	−2.33752e12	−0.741883	−0.370942	+	0.928656i	$0.620965\pi$
$600$	0	0
$601$	2.09353e12	0.654553	0.327277	−	0.944929i	$-0.393869\pi$
$601$	2.09353e12	0.654553	0.327277	+	0.944929i	$0.393869\pi$
$602$	1.01127e11i	0.0313822i
$603$	− 1.42558e12i	− 0.439100i
$604$	1.83455e12	0.560871
$605$	0	0
$606$	2.37355e11	0.0714944
$607$	− 1.68850e12i	− 0.504838i	−0.967618	−	0.252419i	$-0.918774\pi$
$607$	− 1.68850e12i	− 0.504838i	0.967618	−	0.252419i	$-0.0812261\pi$
$608$	6.44107e11i	0.191158i
$609$	4.28845e12	1.26335
$610$	0	0
$611$	−4.67979e11	−0.135844
$612$	− 3.67166e12i	− 1.05799i
$613$	5.57278e12i	1.59404i	0.603951	+	0.797021i	$0.293592\pi$
$613$	5.57278e12i	1.59404i	−0.603951	+	0.797021i	$0.706408\pi$
$614$	−4.41394e11	−0.125334
$615$	0	0
$616$	−2.70826e11	−0.0757838
$617$	2.96764e12i	0.824381i	0.911098	+	0.412191i	$0.135236\pi$
$617$	2.96764e12i	0.824381i	−0.911098	+	0.412191i	$0.864764\pi$
$618$	− 4.49724e11i	− 0.124022i
$619$	5.71769e12	1.56536	0.782678	−	0.622427i	$-0.213853\pi$
$619$	5.71769e12	1.56536	0.782678	+	0.622427i	$0.213853\pi$
$620$	0	0
$621$	1.86648e13	5.03630
$622$	3.39580e10i	0.00909672i
$623$	1.33878e12i	0.356051i
$624$	−2.05222e12	−0.541867
$625$	0	0
$626$	−2.91640e11	−0.0759036
$627$	8.48573e12i	2.19273i
$628$	− 4.50436e12i	− 1.15562i
$629$	−1.43786e12	−0.366259
$630$	0	0
$631$	2.90694e12	0.729967	0.364984	−	0.931014i	$-0.381075\pi$
$631$	2.90694e12	0.729967	0.364984	+	0.931014i	$0.381075\pi$
$632$	5.50650e11i	0.137293i
$633$	− 3.59987e12i	− 0.891191i
$634$	−3.96242e11	−0.0973999
$635$	0	0
$636$	−1.11443e13	−2.70082
$637$	− 1.71936e11i	− 0.0413751i
$638$	− 7.39057e11i	− 0.176598i
$639$	−6.80574e11	−0.161481
$640$	0	0
$641$	5.82396e12	1.36256	0.681282	−	0.732021i	$-0.261423\pi$
$641$	5.82396e12	1.36256	0.681282	+	0.732021i	$0.261423\pi$
$642$	1.09841e12i	0.255185i
$643$	5.98350e11i	0.138040i	0.997615	+	0.0690202i	$0.0219873\pi$
$643$	5.98350e11i	0.138040i	−0.997615	+	0.0690202i	$0.978013\pi$
$644$	−2.67910e12	−0.613766
$645$	0	0
$646$	−1.15361e11	−0.0260623
$647$	4.75962e12i	1.06783i	0.845537	+	0.533916i	$0.179280\pi$
$647$	4.75962e12i	1.06783i	−0.845537	+	0.533916i	$0.820720\pi$
$648$	2.17567e12i	0.484737i
$649$	2.40376e12	0.531850
$650$	0	0
$651$	3.45146e12	0.753162
$652$	− 3.42707e11i	− 0.0742691i
$653$	− 7.21874e12i	− 1.55365i	−0.629719	−	0.776823i	$-0.716830\pi$
$653$	− 7.21874e12i	− 1.55365i	0.629719	−	0.776823i	$-0.283170\pi$
$654$	3.85649e11	0.0824313
$655$	0	0
$656$	4.42727e10	0.00933402
$657$	1.13446e13i	2.37544i
$658$	− 6.37964e10i	− 0.0132672i
$659$	2.24550e12	0.463797	0.231898	−	0.972740i	$-0.425506\pi$
$659$	2.24550e12	0.463797	0.231898	+	0.972740i	$0.425506\pi$
$660$	0	0
$661$	5.93233e12	1.20870	0.604351	−	0.796719i	$-0.293433\pi$
$661$	5.93233e12	1.20870	0.604351	+	0.796719i	$0.293433\pi$
$662$	6.30387e11i	0.127569i
$663$	− 1.11311e12i	− 0.223733i
$664$	9.18811e11	0.183430
$665$	0	0
$666$	8.98431e11	0.176950
$667$	− 1.46632e13i	− 2.86855i
$668$	− 4.03555e12i	− 0.784167i
$669$	1.04169e13	2.01058
$670$	0	0
$671$	−1.09041e13	−2.07653
$672$	− 8.47244e11i	− 0.160268i
$673$	− 3.87772e12i	− 0.728632i	−0.931275	−	0.364316i	$-0.881303\pi$
$673$	− 3.87772e12i	− 0.728632i	0.931275	−	0.364316i	$-0.118697\pi$
$674$	−7.47953e11	−0.139606
$675$	0	0
$676$	4.94620e12	0.910986
$677$	4.49780e12i	0.822907i	0.911431	+	0.411453i	$0.134979\pi$
$677$	4.49780e12i	0.822907i	−0.911431	+	0.411453i	$0.865021\pi$
$678$	4.29040e10i	0.00779766i
$679$	−2.39718e12	−0.432799
$680$	0	0
$681$	1.89040e11	0.0336816
$682$	− 5.94813e11i	− 0.105281i
$683$	5.74316e11i	0.100985i	0.998724	+	0.0504926i	$0.0160791\pi$
$683$	5.74316e11i	0.100985i	−0.998724	+	0.0504926i	$0.983921\pi$
$684$	−1.27979e13	−2.23556
$685$	0	0
$686$	2.34389e10	0.00404090
$687$	− 1.28992e13i	− 2.20931i
$688$	− 6.41077e12i	− 1.09084i
$689$	−2.44545e12	−0.413402
$690$	0	0
$691$	−2.00503e12	−0.334557	−0.167279	−	0.985910i	$-0.553498\pi$
$691$	−2.00503e12	−0.334557	−0.167279	+	0.985910i	$0.553498\pi$
$692$	− 4.77990e12i	− 0.792395i
$693$	− 8.07918e12i	− 1.33066i
$694$	−3.11568e11	−0.0509842
$695$	0	0
$696$	3.08852e12	0.498894
$697$	2.40134e10i	0.00385395i
$698$	− 8.42434e11i	− 0.134334i
$699$	−3.70721e12	−0.587355
$700$	0	0
$701$	7.81162e12	1.22183	0.610914	−	0.791697i	$-0.290802\pi$
$701$	7.81162e12	1.22183	0.610914	+	0.791697i	$0.290802\pi$
$702$	4.30131e11i	0.0668472i
$703$	5.01179e12i	0.773916i
$704$	8.46234e12	1.29841
$705$	0	0
$706$	−7.26032e11	−0.109985
$707$	− 1.26062e12i	− 0.189757i
$708$	5.00855e12i	0.749139i
$709$	−1.04951e13	−1.55984	−0.779919	−	0.625881i	$-0.784740\pi$
$709$	−1.04951e13	−1.55984	−0.779919	+	0.625881i	$0.784740\pi$
$710$	0	0
$711$	−1.64268e13	−2.41068
$712$	9.64180e11i	0.140604i
$713$	− 1.18013e13i	− 1.71012i
$714$	1.51743e11	0.0218508
$715$	0	0
$716$	−1.97985e12	−0.281530
$717$	2.27601e13i	3.21617i
$718$	− 3.42888e11i	− 0.0481495i
$719$	5.29073e12	0.738304	0.369152	−	0.929369i	$-0.379648\pi$
$719$	5.29073e12	0.738304	0.369152	+	0.929369i	$0.379648\pi$
$720$	0	0
$721$	−2.38854e12	−0.329172
$722$	− 1.44339e11i	− 0.0197681i
$723$	5.71791e12i	0.778243i
$724$	5.79652e12	0.784050
$725$	0	0
$726$	−8.57651e11	−0.114577
$727$	− 4.68319e12i	− 0.621780i	−0.950446	−	0.310890i	$-0.899373\pi$
$727$	− 4.68319e12i	− 0.621780i	0.950446	−	0.310890i	$-0.100627\pi$
$728$	− 1.23827e11i	− 0.0163390i
$729$	−2.01538e13	−2.64291
$730$	0	0
$731$	3.47718e12	0.450401
$732$	− 2.27202e13i	− 2.92491i
$733$	− 2.94394e12i	− 0.376670i	−0.982105	−	0.188335i	$-0.939691\pi$
$733$	− 2.94394e12i	− 0.376670i	0.982105	−	0.188335i	$-0.0603091\pi$
$734$	1.94882e11	0.0247822
$735$	0	0
$736$	−2.89692e12	−0.363904
$737$	1.80271e12i	0.225073i
$738$	− 1.50045e10i	− 0.00186195i
$739$	6.49705e12	0.801339	0.400670	−	0.916223i	$-0.368777\pi$
$739$	6.49705e12	0.801339	0.400670	+	0.916223i	$0.368777\pi$
$740$	0	0
$741$	−3.87986e12	−0.472753
$742$	− 3.33372e11i	− 0.0403749i
$743$	− 5.86507e12i	− 0.706031i	−0.935618	−	0.353015i	$-0.885156\pi$
$743$	− 5.86507e12i	− 0.706031i	0.935618	−	0.353015i	$-0.114844\pi$
$744$	2.48572e12	0.297423
$745$	0	0
$746$	9.37677e11	0.110848
$747$	2.74096e13i	3.22078i
$748$	4.64299e12i	0.542301i
$749$	5.83377e12	0.677300
$750$	0	0
$751$	−2.45932e12	−0.282121	−0.141060	−	0.990001i	$-0.545051\pi$
$751$	−2.45932e12	−0.282121	−0.141060	+	0.990001i	$0.545051\pi$
$752$	4.04425e12i	0.461167i
$753$	− 1.69486e13i	− 1.92113i
$754$	3.37913e11	0.0380745
$755$	0	0
$756$	1.04107e13	1.15913
$757$	1.42769e12i	0.158016i	0.996874	+	0.0790081i	$0.0251753\pi$
$757$	1.42769e12i	0.158016i	−0.996874	+	0.0790081i	$0.974825\pi$
$758$	3.75017e11i	0.0412610i
$759$	−3.81652e13	−4.17426
$760$	0	0
$761$	4.92744e12	0.532587	0.266294	−	0.963892i	$-0.414201\pi$
$761$	4.92744e12	0.532587	0.266294	+	0.963892i	$0.414201\pi$
$762$	− 1.01711e12i	− 0.109287i
$763$	− 2.04823e12i	− 0.218785i
$764$	1.39532e13	1.48167
$765$	0	0
$766$	4.25759e10	0.00446822
$767$	1.09905e12i	0.114667i
$768$	1.73265e13i	1.79715i
$769$	−6.15606e12	−0.634796	−0.317398	−	0.948292i	$-0.602809\pi$
$769$	−6.15606e12	−0.634796	−0.317398	+	0.948292i	$0.602809\pi$
$770$	0	0
$771$	−1.65597e13	−1.68775
$772$	− 4.28964e12i	− 0.434654i
$773$	1.37564e13i	1.38579i	0.721037	+	0.692897i	$0.243666\pi$
$773$	1.37564e13i	1.38579i	−0.721037	+	0.692897i	$0.756334\pi$
$774$	−2.17268e12	−0.217601
$775$	0	0
$776$	−1.72644e12	−0.170912
$777$	− 6.59239e12i	− 0.648856i
$778$	6.51623e11i	0.0637659i
$779$	8.37007e10	0.00814349
$780$	0	0
$781$	8.60620e11	0.0827716
$782$	− 5.18845e11i	− 0.0496144i
$783$	5.69796e13i	5.41741i
$784$	−1.48586e12	−0.140461
$785$	0	0
$786$	−1.63706e11	−0.0152990
$787$	− 1.84281e13i	− 1.71236i	−0.516677	−	0.856180i	$-0.672831\pi$
$787$	− 1.84281e13i	− 1.71236i	0.516677	−	0.856180i	$-0.327169\pi$
$788$	2.73901e12i	0.253061i
$789$	−9.11746e12	−0.837582
$790$	0	0
$791$	2.27868e11	0.0206962
$792$	− 5.81858e12i	− 0.525477i
$793$	− 4.98560e12i	− 0.447701i
$794$	−4.80032e11	−0.0428626
$795$	0	0
$796$	−2.18159e13	−1.92603
$797$	− 4.98632e12i	− 0.437742i	−0.975754	−	0.218871i	$-0.929763\pi$
$797$	− 4.98632e12i	− 0.437742i	0.975754	−	0.218871i	$-0.0702374\pi$
$798$	− 5.28915e11i	− 0.0461714i
$799$	−2.19359e12	−0.190412
$800$	0	0
$801$	−2.87631e13	−2.46882
$802$	1.07952e12i	0.0921393i
$803$	− 1.43458e13i	− 1.21760i
$804$	−3.75619e12	−0.317027
$805$	0	0
$806$	2.71961e11	0.0226986
$807$	1.85557e13i	1.54009i
$808$	− 9.07894e11i	− 0.0749349i
$809$	1.17441e12	0.0963940	0.0481970	−	0.998838i	$-0.484652\pi$
$809$	1.17441e12	0.0963940	0.0481970	+	0.998838i	$0.484652\pi$
$810$	0	0
$811$	−9.03042e12	−0.733017	−0.366509	−	0.930415i	$-0.619447\pi$
$811$	−9.03042e12	−0.733017	−0.366509	+	0.930415i	$0.619447\pi$
$812$	− 8.17871e12i	− 0.660211i
$813$	− 4.29148e13i	− 3.44508i
$814$	−1.13611e12	−0.0907007
$815$	0	0
$816$	−9.61949e12	−0.759533
$817$	− 1.21200e13i	− 0.951709i
$818$	− 1.73584e12i	− 0.135556i
$819$	3.69398e12	0.286891
$820$	0	0
$821$	4.14289e12	0.318243	0.159122	−	0.987259i	$-0.449134\pi$
$821$	4.14289e12	0.318243	0.159122	+	0.987259i	$0.449134\pi$
$822$	− 1.19881e12i	− 0.0915853i
$823$	1.66858e12i	0.126779i	0.997989	+	0.0633897i	$0.0201911\pi$
$823$	1.66858e12i	0.126779i	−0.997989	+	0.0633897i	$0.979809\pi$
$824$	−1.72021e12	−0.129990
$825$	0	0
$826$	−1.49826e11	−0.0111990
$827$	9.73830e12i	0.723950i	0.932188	+	0.361975i	$0.117897\pi$
$827$	9.73830e12i	0.723950i	−0.932188	+	0.361975i	$0.882103\pi$
$828$	− 5.75594e13i	− 4.25579i
$829$	6.26617e12	0.460794	0.230397	−	0.973097i	$-0.425997\pi$
$829$	6.26617e12	0.460794	0.230397	+	0.973097i	$0.425997\pi$
$830$	0	0
$831$	1.51752e13	1.10390
$832$	3.86917e12i	0.279938i
$833$	− 8.05927e11i	− 0.0579954i
$834$	−3.86521e11	−0.0276647
$835$	0	0
$836$	1.61836e13	1.14590
$837$	4.58587e13i	3.22967i
$838$	1.19328e12i	0.0835878i
$839$	1.10694e12	0.0771252	0.0385626	−	0.999256i	$-0.487722\pi$
$839$	1.10694e12	0.0771252	0.0385626	+	0.999256i	$0.487722\pi$
$840$	0	0
$841$	3.02564e13	2.08562
$842$	− 2.95860e11i	− 0.0202853i
$843$	1.36005e13i	0.927534i
$844$	−6.86550e12	−0.465727
$845$	0	0
$846$	1.37064e12	0.0919934
$847$	4.55509e12i	0.304103i
$848$	2.11335e13i	1.40343i
$849$	8.90035e12	0.587926
$850$	0	0
$851$	−2.25409e13	−1.47329
$852$	1.79322e12i	0.116588i
$853$	1.95944e13i	1.26725i	0.773641	+	0.633625i	$0.218434\pi$
$853$	1.95944e13i	1.26725i	−0.773641	+	0.633625i	$0.781566\pi$
$854$	6.79653e11	0.0437247
$855$	0	0
$856$	4.20145e12	0.267465
$857$	2.01160e11i	0.0127388i	0.999980	+	0.00636941i	$0.00202746\pi$
$857$	2.01160e11i	0.0127388i	−0.999980	+	0.00636941i	$0.997973\pi$
$858$	− 8.79517e11i	− 0.0554053i
$859$	−4.94473e12	−0.309866	−0.154933	−	0.987925i	$-0.549516\pi$
$859$	−4.94473e12	−0.309866	−0.154933	+	0.987925i	$0.549516\pi$
$860$	0	0
$861$	−1.10098e11	−0.00682756
$862$	1.12838e12i	0.0696105i
$863$	9.27855e12i	0.569418i	0.958614	+	0.284709i	$0.0918970\pi$
$863$	9.27855e12i	0.569418i	−0.958614	+	0.284709i	$0.908103\pi$
$864$	1.12571e13	0.687252
$865$	0	0
$866$	1.25993e12	0.0761228
$867$	2.64406e13i	1.58923i
$868$	− 6.58245e12i	− 0.393594i
$869$	2.07725e13	1.23566
$870$	0	0
$871$	−8.24241e11	−0.0485258
$872$	− 1.47512e12i	− 0.0863981i
$873$	− 5.15025e13i	− 3.00099i
$874$	−1.80848e12	−0.104837
$875$	0	0
$876$	2.98914e13	1.71505
$877$	− 1.62631e13i	− 0.928336i	−0.885747	−	0.464168i	$-0.846353\pi$
$877$	− 1.62631e13i	− 0.928336i	0.885747	−	0.464168i	$-0.153647\pi$
$878$	9.88775e11i	0.0561529i
$879$	−1.66507e13	−0.940771
$880$	0	0
$881$	2.88928e13	1.61584	0.807919	−	0.589294i	$-0.200594\pi$
$881$	2.88928e13	1.61584	0.807919	+	0.589294i	$0.200594\pi$
$882$	5.03575e11i	0.0280192i
$883$	1.17653e13i	0.651301i	0.945490	+	0.325650i	$0.105583\pi$
$883$	1.17653e13i	0.651301i	−0.945490	+	0.325650i	$0.894417\pi$
$884$	−2.12288e12	−0.116920
$885$	0	0
$886$	−2.23709e12	−0.121964
$887$	− 1.50357e13i	− 0.815582i	−0.913075	−	0.407791i	$-0.866299\pi$
$887$	− 1.50357e13i	− 0.815582i	0.913075	−	0.407791i	$-0.133701\pi$
$888$	− 4.74781e12i	− 0.256233i
$889$	−5.40198e12	−0.290065
$890$	0	0
$891$	8.20743e13	4.36272
$892$	− 1.98666e13i	− 1.05071i
$893$	7.64595e12i	0.402346i
$894$	1.20622e12	0.0631550
$895$	0	0
$896$	−2.15238e12	−0.111566
$897$	− 1.74500e13i	− 0.899971i
$898$	− 2.20954e12i	− 0.113386i
$899$	3.60269e13	1.83954
$900$	0	0
$901$	−1.14627e13	−0.579464
$902$	1.89739e10i	0 0.000954394i
$903$	1.59424e13i	0.797919i
$904$	1.64110e11	0.00817290
$905$	0	0
$906$	−1.62894e12	−0.0803208
$907$	− 2.81479e13i	− 1.38106i	−0.723302	−	0.690532i	$-0.757376\pi$
$907$	− 2.81479e13i	− 1.38106i	0.723302	−	0.690532i	$-0.242624\pi$
$908$	− 3.60528e11i	− 0.0176016i
$909$	2.70840e13	1.31575
$910$	0	0
$911$	1.34007e13	0.644608	0.322304	−	0.946636i	$-0.395543\pi$
$911$	1.34007e13	0.644608	0.322304	+	0.946636i	$0.395543\pi$
$912$	3.35296e13i	1.60491i
$913$	− 3.46609e13i	− 1.65090i
$914$	−4.37339e11	−0.0207282
$915$	0	0
$916$	−2.46007e13	−1.15456
$917$	8.69462e11i	0.0406059i
$918$	2.01618e12i	0.0936995i
$919$	1.00365e13	0.464156	0.232078	−	0.972697i	$-0.425447\pi$
$919$	1.00365e13	0.464156	0.232078	+	0.972697i	$0.425447\pi$
$920$	0	0
$921$	−6.95845e13	−3.18672
$922$	− 7.90051e11i	− 0.0360053i
$923$	3.93494e11i	0.0178456i
$924$	−2.12875e13	−0.960728
$925$	0	0
$926$	5.35654e11	0.0239406
$927$	− 5.13168e13i	− 2.28245i
$928$	− 8.84367e12i	− 0.391441i
$929$	−9.39494e12	−0.413831	−0.206916	−	0.978359i	$-0.566343\pi$
$929$	−9.39494e12	−0.413831	−0.206916	+	0.978359i	$0.566343\pi$
$930$	0	0
$931$	−2.80913e12	−0.122546
$932$	7.07021e12i	0.306945i
$933$	5.35337e12i	0.231292i
$934$	−2.19021e12	−0.0941728
$935$	0	0
$936$	2.66038e12	0.113293
$937$	− 3.95699e12i	− 0.167701i	−0.996478	−	0.0838506i	$-0.973278\pi$
$937$	− 3.95699e12i	− 0.167701i	0.996478	−	0.0838506i	$-0.0267219\pi$
$938$	− 1.12363e11i	− 0.00473927i
$939$	−4.59762e13	−1.92991
$940$	0	0
$941$	−5.99191e12	−0.249122	−0.124561	−	0.992212i	$-0.539752\pi$
$941$	−5.99191e12	−0.249122	−0.124561	+	0.992212i	$0.539752\pi$
$942$	3.99952e12i	0.165493i
$943$	3.76450e11i	0.0155026i
$944$	9.49795e12	0.389274
$945$	0	0
$946$	2.74746e12	0.111538
$947$	5.18688e12i	0.209571i	0.994495	+	0.104786i	$0.0334156\pi$
$947$	5.18688e12i	0.209571i	−0.994495	+	0.104786i	$0.966584\pi$
$948$	4.32822e13i	1.74049i
$949$	6.55921e12	0.262515
$950$	0	0
$951$	−6.24663e13	−2.47647
$952$	− 5.80425e11i	− 0.0229023i
$953$	− 2.37155e13i	− 0.931352i	−0.884955	−	0.465676i	$-0.845811\pi$
$953$	− 2.37155e13i	− 0.931352i	0.884955	−	0.465676i	$-0.154189\pi$
$954$	7.16237e12	0.279955
$955$	0	0
$956$	4.34070e13	1.68073
$957$	− 1.16510e14i	− 4.49014i
$958$	− 1.85898e12i	− 0.0713066i
$959$	−6.36700e12	−0.243081
$960$	0	0
$961$	2.55578e12	0.0966647
$962$	− 5.19455e11i	− 0.0195551i
$963$	1.25336e14i	4.69633i
$964$	1.09049e13	0.406702
$965$	0	0
$966$	2.37884e12	0.0878957
$967$	1.33577e13i	0.491263i	0.969363	+	0.245631i	$0.0789953\pi$
$967$	1.33577e13i	0.491263i	−0.969363	+	0.245631i	$0.921005\pi$
$968$	3.28055e12i	0.120090i
$969$	−1.81863e13	−0.662656
$970$	0	0
$971$	1.67122e13	0.603320	0.301660	−	0.953416i	$-0.402459\pi$
$971$	1.67122e13	0.603320	0.301660	+	0.953416i	$0.402459\pi$
$972$	8.56674e13i	3.07835i
$973$	2.05286e12i	0.0734262i
$974$	−9.99250e10	−0.00355761
$975$	0	0
$976$	−4.30853e13	−1.51987
$977$	3.02133e13i	1.06090i	0.847717	+	0.530449i	$0.177976\pi$
$977$	3.02133e13i	1.06090i	−0.847717	+	0.530449i	$0.822024\pi$
$978$	3.04297e11i	0.0106359i
$979$	3.63723e13	1.26546
$980$	0	0
$981$	4.40053e13	1.51703
$982$	2.30763e12i	0.0791891i
$983$	− 1.13956e13i	− 0.389265i	−0.980876	−	0.194633i	$-0.937649\pi$
$983$	− 1.13956e13i	− 0.389265i	0.980876	−	0.194633i	$-0.0623515\pi$
$984$	−7.92921e10	−0.00269620
$985$	0	0
$986$	1.58392e12	0.0533689
$987$	− 1.00573e13i	− 0.337330i
$988$	7.39948e12i	0.247056i
$989$	5.45107e13	1.81175
$990$	0	0
$991$	4.74563e12	0.156301	0.0781506	−	0.996942i	$-0.475099\pi$
$991$	4.74563e12	0.156301	0.0781506	+	0.996942i	$0.475099\pi$
$992$	− 7.11763e12i	− 0.233363i
$993$	9.93786e13i	3.24355i
$994$	−5.36424e10	−0.00174289
$995$	0	0
$996$	7.22205e13	2.32538
$997$	6.28978e12i	0.201608i	0.994906	+	0.100804i	$0.0321415\pi$
$997$	6.28978e12i	0.201608i	−0.994906	+	0.100804i	$0.967859\pi$
$998$	2.96793e12i	0.0947036i
$999$	8.75916e13	2.78239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.b.g.99.7		12
5.2	odd	4		35.10.a.e.1.3	✓	6
5.3	odd	4		175.10.a.g.1.4		6
5.4	even	2	inner	175.10.b.g.99.6		12
15.2	even	4		315.10.a.l.1.4		6
35.27	even	4		245.10.a.g.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.e.1.3	✓	6	5.2	odd	4
175.10.a.g.1.4		6	5.3	odd	4
175.10.b.g.99.6		12	5.4	even	2	inner
175.10.b.g.99.7		12	1.1	even	1	trivial
245.10.a.g.1.3		6	35.27	even	4
315.10.a.l.1.4		6	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+1.69340i q^{2} +266.960i q^{3} +509.132 q^{4} -452.070 q^{6} +2401.00i q^{7} +1729.19i q^{8} -51584.5 q^{9} +65231.2 q^{11} +135918. i q^{12} +29825.1i q^{13} -4065.86 q^{14} +257748. q^{16} +139801. i q^{17} -87353.4i q^{18} +487290. q^{19} -640971. q^{21} +110463. i q^{22} +2.19162e6i q^{23} -461624. q^{24} -50506.0 q^{26} -8.51643e6i q^{27} +1.22243e6i q^{28} -6.69055e6 q^{29} -5.38474e6 q^{31} +1.32181e6i q^{32} +1.74141e7i q^{33} -236740. q^{34} -2.62634e7 q^{36} +1.02850e7i q^{37} +825179. i q^{38} -7.96211e6 q^{39} +171768. q^{41} -1.08542e6i q^{42} -2.48723e7i q^{43} +3.32113e7 q^{44} -3.71130e6 q^{46} +1.56907e7i q^{47} +6.88082e7i q^{48} -5.76480e6 q^{49} -3.73214e7 q^{51} +1.51849e7i q^{52} +8.19930e7i q^{53} +1.44217e7 q^{54} -4.15178e6 q^{56} +1.30087e8i q^{57} -1.13298e7i q^{58} +3.68498e7 q^{59} -1.67161e8 q^{61} -9.11853e6i q^{62} -1.23854e8i q^{63} +1.29728e8 q^{64} -2.94891e7 q^{66} +2.76358e7i q^{67} +7.11774e7i q^{68} -5.85076e8 q^{69} +1.31934e7 q^{71} -8.91994e7i q^{72} -2.19922e8i q^{73} -1.74167e7 q^{74} +2.48095e8 q^{76} +1.56620e8i q^{77} -1.34831e7i q^{78} +3.18444e8 q^{79} +1.25821e9 q^{81} +290872. i q^{82} -5.31354e8i q^{83} -3.26339e8 q^{84} +4.21188e7 q^{86} -1.78611e9i q^{87} +1.12797e8i q^{88} +5.57591e8 q^{89} -7.16102e7 q^{91} +1.11583e9i q^{92} -1.43751e9i q^{93} -2.65707e7 q^{94} -3.52871e8 q^{96} +9.98409e8i q^{97} -9.76213e6i q^{98} -3.36492e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6018 q^{4} + 9776 q^{6} - 222180 q^{9} - 95592 q^{11} + 72030 q^{14} + 4742130 q^{16} - 722112 q^{19} + 595448 q^{21} - 9656152 q^{24} + 21695244 q^{26} - 32056368 q^{29} + 2725824 q^{31} + 18432588 q^{34}+ \cdots - 7143937568 q^{99}+O(q^{100}) \) 12 * q - 6018 * q^4 + 9776 * q^6 - 222180 * q^9 - 95592 * q^11 + 72030 * q^14 + 4742130 * q^16 - 722112 * q^19 + 595448 * q^21 - 9656152 * q^24 + 21695244 * q^26 - 32056368 * q^29 + 2725824 * q^31 + 18432588 * q^34 + 184639282 * q^36 + 40683736 * q^39 + 44905512 * q^41 + 188757456 * q^44 + 99179040 * q^46 - 69177612 * q^49 - 562676360 * q^51 + 580208616 * q^54 - 105840882 * q^56 - 240560784 * q^59 - 175387080 * q^61 - 1281294210 * q^64 - 2787941384 * q^66 - 2063267280 * q^69 + 507525024 * q^71 + 837612108 * q^74 - 1169438952 * q^76 - 1662159000 * q^79 + 3738629420 * q^81 - 2601032112 * q^84 + 1132399896 * q^86 - 1165159368 * q^89 - 490610736 * q^91 + 2231893320 * q^94 + 1978690504 * q^96 - 7143937568 * q^99

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