LMFDB - Embedded newform 350.10.c.d.99.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [350,10,Mod(99,350)] 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("350.99"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(350, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	350.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-512,0,5440] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$180.262542657$
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 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	350.99
Dual form			350.10.c.d.99.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-16.0000i q^{2} +170.000i q^{3} -256.000 q^{4} +2720.00 q^{6} +2401.00i q^{7} +4096.00i q^{8} -9217.00 q^{9} +48824.0 q^{11} -43520.0i q^{12} -15876.0i q^{13} +38416.0 q^{14} +65536.0 q^{16} +21418.0i q^{17} +147472. i q^{18} +716410. q^{19} -408170. q^{21} -781184. i q^{22} -2.47000e6i q^{23} -696320. q^{24} -254016. q^{26} +1.77922e6i q^{27} -614656. i q^{28} -5.55683e6 q^{29} +5.79935e6 q^{31} -1.04858e6i q^{32} +8.30008e6i q^{33} +342688. q^{34} +2.35955e6 q^{36} +3.89443e6i q^{37} -1.14626e7i q^{38} +2.69892e6 q^{39} -6.36086e6 q^{41} +6.53072e6i q^{42} -1.87013e7i q^{43} -1.24989e7 q^{44} -3.95200e7 q^{46} -5.65391e7i q^{47} +1.11411e7i q^{48} -5.76480e6 q^{49} -3.64106e6 q^{51} +4.06426e6i q^{52} -5.98947e7i q^{53} +2.84675e7 q^{54} -9.83450e6 q^{56} +1.21790e8i q^{57} +8.89092e7i q^{58} -1.65630e8 q^{59} +5.14190e7 q^{61} -9.27896e7i q^{62} -2.21300e7i q^{63} -1.67772e7 q^{64} +1.32801e8 q^{66} -9.35465e7i q^{67} -5.48301e6i q^{68} +4.19900e8 q^{69} -9.56335e7 q^{71} -3.77528e7i q^{72} +3.06496e8i q^{73} +6.23109e7 q^{74} -1.83401e8 q^{76} +1.17226e8i q^{77} -4.31827e7i q^{78} -4.96474e8 q^{79} -4.83886e8 q^{81} +1.01774e8i q^{82} -3.71487e8i q^{83} +1.04492e8 q^{84} -2.99221e8 q^{86} -9.44660e8i q^{87} +1.99983e8i q^{88} +1.65483e8 q^{89} +3.81183e7 q^{91} +6.32320e8i q^{92} +9.85889e8i q^{93} -9.04625e8 q^{94} +1.78258e8 q^{96} -7.58017e8i q^{97} +9.22368e7i q^{98} -4.50011e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 512 q^{4} + 5440 q^{6} - 18434 q^{9} + 97648 q^{11} + 76832 q^{14} + 131072 q^{16} + 1432820 q^{19} - 816340 q^{21} - 1392640 q^{24} - 508032 q^{26} - 11113652 q^{29} + 11598696 q^{31} + 685376 q^{34}+ \cdots - 900021616 q^{99}+O(q^{100}) $ 2 * q - 512 * q^4 + 5440 * q^6 - 18434 * q^9 + 97648 * q^11 + 76832 * q^14 + 131072 * q^16 + 1432820 * q^19 - 816340 * q^21 - 1392640 * q^24 - 508032 * q^26 - 11113652 * q^29 + 11598696 * q^31 + 685376 * q^34 + 4719104 * q^36 + 5397840 * q^39 - 12721716 * q^41 - 24997888 * q^44 - 79040000 * q^46 - 11529602 * q^49 - 7282120 * q^51 + 56935040 * q^54 - 19668992 * q^56 - 331259324 * q^59 + 102838032 * q^61 - 33554432 * q^64 + 265602560 * q^66 + 839800000 * q^69 - 191267072 * q^71 + 124621760 * q^74 - 366801920 * q^76 - 992948304 * q^79 - 967771222 * q^81 + 208983040 * q^84 - 598441472 * q^86 + 330965100 * q^89 + 76236552 * q^91 - 1809250176 * q^94 + 356515840 * q^96 - 900021616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 16.0000i	− 0.707107i
$2$	− 16.0000i	− 0.707107i
$3$	170.000i	1.21172i	0.795570	+	0.605861i	$0.207171\pi$
$3$	170.000i	1.21172i	−0.795570	+	0.605861i	$0.792829\pi$
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	2720.00	0.856817
$7$	2401.00i	0.377964i
$7$	2401.00i	0.377964i
$8$	4096.00i	0.353553i
$9$	−9217.00	−0.468272
$10$	0	0
$11$	48824.0	1.00546	0.502732	−	0.864442i	$-0.332328\pi$
$11$	48824.0	1.00546	0.502732	+	0.864442i	$0.332328\pi$
$12$	− 43520.0i	− 0.605861i
$13$	− 15876.0i	− 0.154169i	−0.997025	−	0.0770843i	$-0.975439\pi$
$13$	− 15876.0i	− 0.154169i	0.997025	−	0.0770843i	$-0.0245611\pi$
$14$	38416.0	0.267261
$15$	0	0
$16$	65536.0	0.250000
$17$	21418.0i	0.0621955i	0.999516	+	0.0310977i	$0.00990031\pi$
$17$	21418.0i	0.0621955i	−0.999516	+	0.0310977i	$0.990100\pi$
$18$	147472.i	0.331118i
$19$	716410.	1.26116	0.630580	−	0.776124i	$-0.282817\pi$
$19$	716410.	1.26116	0.630580	+	0.776124i	$0.282817\pi$
$20$	0	0
$21$	−408170.	−0.457988
$22$	− 781184.i	− 0.710970i
$23$	− 2.47000e6i	− 1.84044i	−0.391401	−	0.920220i	$-0.628010\pi$
$23$	− 2.47000e6i	− 1.84044i	0.391401	−	0.920220i	$-0.371990\pi$
$24$	−696320.	−0.428409
$25$	0	0
$26$	−254016.	−0.109014
$27$	1.77922e6i	0.644307i
$28$	− 614656.i	− 0.188982i
$29$	−5.55683e6	−1.45893	−0.729467	−	0.684016i	$-0.760232\pi$
$29$	−5.55683e6	−1.45893	−0.729467	+	0.684016i	$0.760232\pi$
$30$	0	0
$31$	5.79935e6	1.12785	0.563925	−	0.825826i	$-0.309291\pi$
$31$	5.79935e6	1.12785	0.563925	+	0.825826i	$0.309291\pi$
$32$	− 1.04858e6i	− 0.176777i
$33$	8.30008e6i	1.21834i
$34$	342688.	0.0439788
$35$	0	0
$36$	2.35955e6	0.234136
$37$	3.89443e6i	0.341614i	0.985304	+	0.170807i	$0.0546375\pi$
$37$	3.89443e6i	0.341614i	−0.985304	+	0.170807i	$0.945362\pi$
$38$	− 1.14626e7i	− 0.891775i
$39$	2.69892e6	0.186810
$40$	0	0
$41$	−6.36086e6	−0.351551	−0.175776	−	0.984430i	$-0.556243\pi$
$41$	−6.36086e6	−0.351551	−0.175776	+	0.984430i	$0.556243\pi$
$42$	6.53072e6i	0.323847i
$43$	− 1.87013e7i	− 0.834187i	−0.908863	−	0.417094i	$-0.863049\pi$
$43$	− 1.87013e7i	− 0.834187i	0.908863	−	0.417094i	$-0.136951\pi$
$44$	−1.24989e7	−0.502732
$45$	0	0
$46$	−3.95200e7	−1.30139
$47$	− 5.65391e7i	− 1.69008i	−0.534700	−	0.845042i	$-0.679575\pi$
$47$	− 5.65391e7i	− 1.69008i	0.534700	−	0.845042i	$-0.320425\pi$
$48$	1.11411e7i	0.302931i
$49$	−5.76480e6	−0.142857
$50$	0	0
$51$	−3.64106e6	−0.0753637
$52$	4.06426e6i	0.0770843i
$53$	− 5.98947e7i	− 1.04267i	−0.853352	−	0.521335i	$-0.825434\pi$
$53$	− 5.98947e7i	− 1.04267i	0.853352	−	0.521335i	$-0.174566\pi$
$54$	2.84675e7	0.455594
$55$	0	0
$56$	−9.83450e6	−0.133631
$57$	1.21790e8i	1.52818i
$58$	8.89092e7i	1.03162i
$59$	−1.65630e8	−1.77952	−0.889762	−	0.456424i	$-0.849130\pi$
$59$	−1.65630e8	−1.77952	−0.889762	+	0.456424i	$0.849130\pi$
$60$	0	0
$61$	5.14190e7	0.475488	0.237744	−	0.971328i	$-0.423592\pi$
$61$	5.14190e7	0.475488	0.237744	+	0.971328i	$0.423592\pi$
$62$	− 9.27896e7i	− 0.797511i
$63$	− 2.21300e7i	− 0.176990i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	1.32801e8	0.861499
$67$	− 9.35465e7i	− 0.567141i	−0.958951	−	0.283570i	$-0.908481\pi$
$67$	− 9.35465e7i	− 0.567141i	0.958951	−	0.283570i	$-0.0915190\pi$
$68$	− 5.48301e6i	− 0.0310977i
$69$	4.19900e8	2.23010
$70$	0	0
$71$	−9.56335e7	−0.446630	−0.223315	−	0.974746i	$-0.571688\pi$
$71$	−9.56335e7	−0.446630	−0.223315	+	0.974746i	$0.571688\pi$
$72$	− 3.77528e7i	− 0.165559i
$73$	3.06496e8i	1.26320i	0.775294	+	0.631601i	$0.217602\pi$
$73$	3.06496e8i	1.26320i	−0.775294	+	0.631601i	$0.782398\pi$
$74$	6.23109e7	0.241558
$75$	0	0
$76$	−1.83401e8	−0.630580
$77$	1.17226e8i	0.380029i
$78$	− 4.31827e7i	− 0.132094i
$79$	−4.96474e8	−1.43408	−0.717042	−	0.697030i	$-0.754505\pi$
$79$	−4.96474e8	−1.43408	−0.717042	+	0.697030i	$0.754505\pi$
$80$	0	0
$81$	−4.83886e8	−1.24899
$82$	1.01774e8i	0.248584i
$83$	− 3.71487e8i	− 0.859196i	−0.903020	−	0.429598i	$-0.858655\pi$
$83$	− 3.71487e8i	− 0.859196i	0.903020	−	0.429598i	$-0.141345\pi$
$84$	1.04492e8	0.228994
$85$	0	0
$86$	−2.99221e8	−0.589860
$87$	− 9.44660e8i	− 1.76782i
$88$	1.99983e8i	0.355485i
$89$	1.65483e8	0.279574	0.139787	−	0.990182i	$-0.455358\pi$
$89$	1.65483e8	0.279574	0.139787	+	0.990182i	$0.455358\pi$
$90$	0	0
$91$	3.81183e7	0.0582703
$92$	6.32320e8i	0.920220i
$93$	9.85889e8i	1.36664i
$94$	−9.04625e8	−1.19507
$95$	0	0
$96$	1.78258e8	0.214204
$97$	− 7.58017e8i	− 0.869373i	−0.900582	−	0.434686i	$-0.856859\pi$
$97$	− 7.58017e8i	− 0.869373i	0.900582	−	0.434686i	$-0.143141\pi$
$98$	9.22368e7i	0.101015i
$99$	−4.50011e8	−0.470830
$100$	0	0
$101$	−9.04212e8	−0.864618	−0.432309	−	0.901726i	$-0.642301\pi$
$101$	−9.04212e8	−0.864618	−0.432309	+	0.901726i	$0.642301\pi$
$102$	5.82570e7i	0.0532902i
$103$	1.98157e9i	1.73477i	0.497639	+	0.867384i	$0.334200\pi$
$103$	1.98157e9i	1.73477i	−0.497639	+	0.867384i	$0.665800\pi$
$104$	6.50281e7	0.0545068
$105$	0	0
$106$	−9.58315e8	−0.737279
$107$	− 4.16379e8i	− 0.307087i	−0.988142	−	0.153544i	$-0.950931\pi$
$107$	− 4.16379e8i	− 0.307087i	0.988142	−	0.153544i	$-0.0490686\pi$
$108$	− 4.55480e8i	− 0.322153i
$109$	1.26921e9	0.861220	0.430610	−	0.902538i	$-0.358299\pi$
$109$	1.26921e9	0.861220	0.430610	+	0.902538i	$0.358299\pi$
$110$	0	0
$111$	−6.62053e8	−0.413942
$112$	1.57352e8i	0.0944911i
$113$	− 2.83528e9i	− 1.63585i	−0.575328	−	0.817923i	$-0.695126\pi$
$113$	− 2.83528e9i	− 1.63585i	0.575328	−	0.817923i	$-0.304874\pi$
$114$	1.94864e9	1.08058
$115$	0	0
$116$	1.42255e9	0.729467
$117$	1.46329e8i	0.0721929i
$118$	2.65007e9i	1.25831i
$119$	−5.14246e7	−0.0235077
$120$	0	0
$121$	2.58353e7	0.0109567
$122$	− 8.22704e8i	− 0.336221i
$123$	− 1.08135e9i	− 0.425982i
$124$	−1.48463e9	−0.563925
$125$	0	0
$126$	−3.54080e8	−0.125151
$127$	− 5.44282e9i	− 1.85655i	−0.371889	−	0.928277i	$-0.621290\pi$
$127$	− 5.44282e9i	− 1.85655i	0.371889	−	0.928277i	$-0.378710\pi$
$128$	2.68435e8i	0.0883883i
$129$	3.17922e9	1.01080
$130$	0	0
$131$	−6.44057e8	−0.191075	−0.0955374	−	0.995426i	$-0.530457\pi$
$131$	−6.44057e8	−0.191075	−0.0955374	+	0.995426i	$0.530457\pi$
$132$	− 2.12482e9i	− 0.609171i
$133$	1.72010e9i	0.476674i
$134$	−1.49674e9	−0.401029
$135$	0	0
$136$	−8.77281e7	−0.0219894
$137$	− 1.67376e9i	− 0.405928i	−0.979186	−	0.202964i	$-0.934942\pi$
$137$	− 1.67376e9i	− 0.405928i	0.979186	−	0.202964i	$-0.0650575\pi$
$138$	− 6.71840e9i	− 1.57692i
$139$	4.17330e9	0.948229	0.474115	−	0.880463i	$-0.342768\pi$
$139$	4.17330e9	0.948229	0.474115	+	0.880463i	$0.342768\pi$
$140$	0	0
$141$	9.61164e9	2.04791
$142$	1.53014e9i	0.315815i
$143$	− 7.75130e8i	− 0.155011i
$144$	−6.04045e8	−0.117068
$145$	0	0
$146$	4.90394e9	0.893218
$147$	− 9.80016e8i	− 0.173103i
$148$	− 9.96974e8i	− 0.170807i
$149$	4.64096e8	0.0771382	0.0385691	−	0.999256i	$-0.487720\pi$
$149$	4.64096e8	0.0771382	0.0385691	+	0.999256i	$0.487720\pi$
$150$	0	0
$151$	7.31929e9	1.14571	0.572853	−	0.819658i	$-0.305837\pi$
$151$	7.31929e9	1.14571	0.572853	+	0.819658i	$0.305837\pi$
$152$	2.93442e9i	0.445888i
$153$	− 1.97410e8i	− 0.0291244i
$154$	1.87562e9	0.268721
$155$	0	0
$156$	−6.90924e8	−0.0934048
$157$	4.43050e9i	0.581975i	0.956727	+	0.290987i	$0.0939838\pi$
$157$	4.43050e9i	0.581975i	−0.956727	+	0.290987i	$0.906016\pi$
$158$	7.94359e9i	1.01405i
$159$	1.01821e10	1.26343
$160$	0	0
$161$	5.93047e9	0.695621
$162$	7.74217e9i	0.883172i
$163$	− 1.33645e10i	− 1.48289i	−0.671013	−	0.741446i	$-0.734140\pi$
$163$	− 1.33645e10i	− 1.48289i	0.671013	−	0.741446i	$-0.265860\pi$
$164$	1.62838e9	0.175776
$165$	0	0
$166$	−5.94379e9	−0.607543
$167$	1.24456e10i	1.23821i	0.785310	+	0.619103i	$0.212504\pi$
$167$	1.24456e10i	1.23821i	−0.785310	+	0.619103i	$0.787496\pi$
$168$	− 1.67186e9i	− 0.161923i
$169$	1.03525e10	0.976232
$170$	0	0
$171$	−6.60315e9	−0.590566
$172$	4.78753e9i	0.417094i
$173$	1.04544e10i	0.887345i	0.896189	+	0.443672i	$0.146325\pi$
$173$	1.04544e10i	0.887345i	−0.896189	+	0.443672i	$0.853675\pi$
$174$	−1.51146e10	−1.25004
$175$	0	0
$176$	3.19973e9	0.251366
$177$	− 2.81570e10i	− 2.15629i
$178$	− 2.64772e9i	− 0.197689i
$179$	4.04391e9	0.294417	0.147208	−	0.989105i	$-0.452971\pi$
$179$	4.04391e9	0.294417	0.147208	+	0.989105i	$0.452971\pi$
$180$	0	0
$181$	1.24735e10	0.863843	0.431922	−	0.901911i	$-0.357836\pi$
$181$	1.24735e10	0.863843	0.431922	+	0.901911i	$0.357836\pi$
$182$	− 6.09892e8i	− 0.0412033i
$183$	8.74123e9i	0.576160i
$184$	1.01171e10	0.650694
$185$	0	0
$186$	1.57742e10	0.966362
$187$	1.04571e9i	0.0625353i
$188$	1.44740e10i	0.845042i
$189$	−4.27191e9	−0.243525
$190$	0	0
$191$	−3.81947e9	−0.207660	−0.103830	−	0.994595i	$-0.533110\pi$
$191$	−3.81947e9	−0.207660	−0.103830	+	0.994595i	$0.533110\pi$
$192$	− 2.85213e9i	− 0.151465i
$193$	− 2.41193e10i	− 1.25129i	−0.780109	−	0.625644i	$-0.784836\pi$
$193$	− 2.41193e10i	− 1.25129i	0.780109	−	0.625644i	$-0.215164\pi$
$194$	−1.21283e10	−0.614739
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	1.24798e10i	0.590351i	0.955443	+	0.295176i	$0.0953782\pi$
$197$	1.24798e10i	0.590351i	−0.955443	+	0.295176i	$0.904622\pi$
$198$	7.20017e9i	0.332927i
$199$	2.93127e9	0.132500	0.0662502	−	0.997803i	$-0.478896\pi$
$199$	2.93127e9	0.132500	0.0662502	+	0.997803i	$0.478896\pi$
$200$	0	0
$201$	1.59029e10	0.687218
$202$	1.44674e10i	0.611377i
$203$	− 1.33419e10i	− 0.551425i
$204$	9.32111e8	0.0376818
$205$	0	0
$206$	3.17051e10	1.22667
$207$	2.27660e10i	0.861827i
$208$	− 1.04045e9i	− 0.0385422i
$209$	3.49780e10	1.26805
$210$	0	0
$211$	3.36978e10	1.17039	0.585195	−	0.810892i	$-0.301018\pi$
$211$	3.36978e10	1.17039	0.585195	+	0.810892i	$0.301018\pi$
$212$	1.53330e10i	0.521335i
$213$	− 1.62577e10i	− 0.541191i
$214$	−6.66206e9	−0.217143
$215$	0	0
$216$	−7.28769e9	−0.227797
$217$	1.39242e10i	0.426287i
$218$	− 2.03073e10i	− 0.608974i
$219$	−5.21044e10	−1.53065
$220$	0	0
$221$	3.40032e8	0.00958859
$222$	1.05928e10i	0.292701i
$223$	− 3.87208e10i	− 1.04851i	−0.851561	−	0.524255i	$-0.824344\pi$
$223$	− 3.87208e10i	− 1.04851i	0.851561	−	0.524255i	$-0.175656\pi$
$224$	2.51763e9	0.0668153
$225$	0	0
$226$	−4.53644e10	−1.15672
$227$	− 7.69011e10i	− 1.92228i	−0.276063	−	0.961139i	$-0.589030\pi$
$227$	− 7.69011e10i	− 1.92228i	0.276063	−	0.961139i	$-0.410970\pi$
$228$	− 3.11782e10i	− 0.764089i
$229$	−4.35114e10	−1.04555	−0.522773	−	0.852472i	$-0.675103\pi$
$229$	−4.35114e10	−1.04555	−0.522773	+	0.852472i	$0.675103\pi$
$230$	0	0
$231$	−1.99285e10	−0.460490
$232$	− 2.27608e10i	− 0.515811i
$233$	− 2.07043e10i	− 0.460213i	−0.973165	−	0.230107i	$-0.926093\pi$
$233$	− 2.07043e10i	− 0.460213i	0.973165	−	0.230107i	$-0.0739075\pi$
$234$	2.34127e9	0.0510481
$235$	0	0
$236$	4.24012e10	0.889762
$237$	− 8.44006e10i	− 1.73771i
$238$	8.22794e8i	0.0166224i
$239$	−2.16220e10	−0.428653	−0.214326	−	0.976762i	$-0.568756\pi$
$239$	−2.16220e10	−0.428653	−0.214326	+	0.976762i	$0.568756\pi$
$240$	0	0
$241$	6.77789e10	1.29425	0.647124	−	0.762385i	$-0.275971\pi$
$241$	6.77789e10	1.29425	0.647124	+	0.762385i	$0.275971\pi$
$242$	− 4.13365e8i	− 0.00774754i
$243$	− 4.72402e10i	− 0.869127i
$244$	−1.31633e10	−0.237744
$245$	0	0
$246$	−1.73015e10	−0.301215
$247$	− 1.13737e10i	− 0.194431i
$248$	2.37541e10i	0.398755i
$249$	6.31528e10	1.04111
$250$	0	0
$251$	4.87895e9	0.0775881	0.0387940	−	0.999247i	$-0.487648\pi$
$251$	4.87895e9	0.0775881	0.0387940	+	0.999247i	$0.487648\pi$
$252$	5.66528e9i	0.0884951i
$253$	− 1.20595e11i	− 1.85050i
$254$	−8.70852e10	−1.31278
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	2.75029e10i	0.393259i	0.980478	+	0.196630i	$0.0629997\pi$
$257$	2.75029e10i	0.393259i	−0.980478	+	0.196630i	$0.937000\pi$
$258$	− 5.08675e10i	− 0.714746i
$259$	−9.35053e9	−0.129118
$260$	0	0
$261$	5.12173e10	0.683178
$262$	1.03049e10i	0.135110i
$263$	− 2.22595e10i	− 0.286889i	−0.989658	−	0.143445i	$-0.954182\pi$
$263$	− 2.22595e10i	− 0.286889i	0.989658	−	0.143445i	$-0.0458179\pi$
$264$	−3.39971e10	−0.430749
$265$	0	0
$266$	2.75216e10	0.337059
$267$	2.81320e10i	0.338766i
$268$	2.39479e10i	0.283570i
$269$	−1.73017e10	−0.201466	−0.100733	−	0.994913i	$-0.532119\pi$
$269$	−1.73017e10	−0.201466	−0.100733	+	0.994913i	$0.532119\pi$
$270$	0	0
$271$	4.81901e10	0.542745	0.271372	−	0.962474i	$-0.412523\pi$
$271$	4.81901e10	0.542745	0.271372	+	0.962474i	$0.412523\pi$
$272$	1.40365e9i	0.0155489i
$273$	6.48011e9i	0.0706074i
$274$	−2.67801e10	−0.287035
$275$	0	0
$276$	−1.07494e11	−1.11505
$277$	− 8.03834e10i	− 0.820365i	−0.912003	−	0.410183i	$-0.865465\pi$
$277$	− 8.03834e10i	− 0.820365i	0.912003	−	0.410183i	$-0.134535\pi$
$278$	− 6.67728e10i	− 0.670499i
$279$	−5.34526e10	−0.528141
$280$	0	0
$281$	−1.95595e11	−1.87146	−0.935729	−	0.352719i	$-0.885257\pi$
$281$	−1.95595e11	−1.87146	−0.935729	+	0.352719i	$0.885257\pi$
$282$	− 1.53786e11i	− 1.44809i
$283$	− 6.02802e10i	− 0.558645i	−0.960197	−	0.279322i	$-0.909890\pi$
$283$	− 6.02802e10i	− 0.558645i	0.960197	−	0.279322i	$-0.0901098\pi$
$284$	2.44822e10	0.223315
$285$	0	0
$286$	−1.24021e10	−0.109609
$287$	− 1.52724e10i	− 0.132874i
$288$	9.66472e9i	0.0827796i
$289$	1.18129e11	0.996132
$290$	0	0
$291$	1.28863e11	1.05344
$292$	− 7.84631e10i	− 0.631601i
$293$	− 4.86743e10i	− 0.385830i	−0.981216	−	0.192915i	$-0.938206\pi$
$293$	− 4.86743e10i	− 0.385830i	0.981216	−	0.192915i	$-0.0617941\pi$
$294$	−1.56803e10	−0.122402
$295$	0	0
$296$	−1.59516e10	−0.120779
$297$	8.68686e10i	0.647827i
$298$	− 7.42553e9i	− 0.0545449i
$299$	−3.92137e10	−0.283738
$300$	0	0
$301$	4.49018e10	0.315293
$302$	− 1.17109e11i	− 0.810136i
$303$	− 1.53716e11i	− 1.04768i
$304$	4.69506e10	0.315290
$305$	0	0
$306$	−3.15856e9	−0.0205941
$307$	− 2.75178e11i	− 1.76804i	−0.467453	−	0.884018i	$-0.654828\pi$
$307$	− 2.75178e11i	− 1.76804i	0.467453	−	0.884018i	$-0.345172\pi$
$308$	− 3.00100e10i	− 0.190015i
$309$	−3.36867e11	−2.10206
$310$	0	0
$311$	1.12322e11	0.680835	0.340418	−	0.940274i	$-0.389432\pi$
$311$	1.12322e11	0.680835	0.340418	+	0.940274i	$0.389432\pi$
$312$	1.10548e10i	0.0660472i
$313$	− 1.06140e11i	− 0.625069i	−0.949906	−	0.312535i	$-0.898822\pi$
$313$	− 1.06140e11i	− 0.625069i	0.949906	−	0.312535i	$-0.101178\pi$
$314$	7.08880e10	0.411518
$315$	0	0
$316$	1.27097e11	0.717042
$317$	− 2.31358e9i	− 0.0128682i	−0.999979	−	0.00643409i	$-0.997952\pi$
$317$	− 2.31358e9i	− 0.0128682i	0.999979	−	0.00643409i	$-0.00204805\pi$
$318$	− 1.62914e11i	− 0.893378i
$319$	−2.71306e11	−1.46691
$320$	0	0
$321$	7.07844e10	0.372105
$322$	− 9.48875e10i	− 0.491878i
$323$	1.53441e10i	0.0784385i
$324$	1.23875e11	0.624497
$325$	0	0
$326$	−2.13832e11	−1.04856
$327$	2.15766e11i	1.04356i
$328$	− 2.60541e10i	− 0.124292i
$329$	1.35750e11	0.638792
$330$	0	0
$331$	−2.16185e11	−0.989921	−0.494960	−	0.868916i	$-0.664817\pi$
$331$	−2.16185e11	−0.989921	−0.494960	+	0.868916i	$0.664817\pi$
$332$	9.51007e10i	0.429598i
$333$	− 3.58950e10i	− 0.159968i
$334$	1.99130e11	0.875544
$335$	0	0
$336$	−2.67498e10	−0.114497
$337$	− 5.00291e10i	− 0.211294i	−0.994404	−	0.105647i	$-0.966309\pi$
$337$	− 5.00291e10i	− 0.211294i	0.994404	−	0.105647i	$-0.0336914\pi$
$338$	− 1.65639e11i	− 0.690300i
$339$	4.81997e11	1.98219
$340$	0	0
$341$	2.83147e11	1.13401
$342$	1.05650e11i	0.417594i
$343$	− 1.38413e10i	− 0.0539949i
$344$	7.66005e10	0.294930
$345$	0	0
$346$	1.67271e11	0.627448
$347$	1.84606e11i	0.683541i	0.939784	+	0.341770i	$0.111026\pi$
$347$	1.84606e11i	0.683541i	−0.939784	+	0.341770i	$0.888974\pi$
$348$	2.41833e11i	0.883912i
$349$	−2.74666e11	−0.991039	−0.495520	−	0.868597i	$-0.665022\pi$
$349$	−2.74666e11	−0.991039	−0.495520	+	0.868597i	$0.665022\pi$
$350$	0	0
$351$	2.82469e10	0.0993319
$352$	− 5.11957e10i	− 0.177743i
$353$	− 1.58053e11i	− 0.541774i	−0.962611	−	0.270887i	$-0.912683\pi$
$353$	− 1.58053e11i	− 0.541774i	0.962611	−	0.270887i	$-0.0873169\pi$
$354$	−4.50513e11	−1.52473
$355$	0	0
$356$	−4.23635e10	−0.139787
$357$	− 8.74219e9i	− 0.0284848i
$358$	− 6.47025e10i	− 0.208184i
$359$	−3.40759e11	−1.08274	−0.541368	−	0.840786i	$-0.682093\pi$
$359$	−3.40759e11	−1.08274	−0.541368	+	0.840786i	$0.682093\pi$
$360$	0	0
$361$	1.90556e11	0.590526
$362$	− 1.99576e11i	− 0.610829i
$363$	4.39200e9i	0.0132765i
$364$	−9.75828e9	−0.0291351
$365$	0	0
$366$	1.39860e11	0.407406
$367$	6.10216e11i	1.75584i	0.478803	+	0.877922i	$0.341071\pi$
$367$	6.10216e11i	1.75584i	−0.478803	+	0.877922i	$0.658929\pi$
$368$	− 1.61874e11i	− 0.460110i
$369$	5.86280e10	0.164622
$370$	0	0
$371$	1.43807e11	0.394092
$372$	− 2.52388e11i	− 0.683321i
$373$	4.34930e11i	1.16340i	0.813402	+	0.581701i	$0.197613\pi$
$373$	4.34930e11i	1.16340i	−0.813402	+	0.581701i	$0.802387\pi$
$374$	1.67314e10	0.0442191
$375$	0	0
$376$	2.31584e11	0.597535
$377$	8.82202e10i	0.224922i
$378$	6.83505e10i	0.172198i
$379$	7.30677e11	1.81907	0.909534	−	0.415630i	$-0.136439\pi$
$379$	7.30677e11	1.81907	0.909534	+	0.415630i	$0.136439\pi$
$380$	0	0
$381$	9.25280e11	2.24963
$382$	6.11115e10i	0.146838i
$383$	2.11074e11i	0.501233i	0.968086	+	0.250617i	$0.0806333\pi$
$383$	2.11074e11i	0.501233i	−0.968086	+	0.250617i	$0.919367\pi$
$384$	−4.56340e10	−0.107102
$385$	0	0
$386$	−3.85909e11	−0.884794
$387$	1.72370e11i	0.390627i
$388$	1.94052e11i	0.434686i
$389$	−7.21857e9	−0.0159837	−0.00799186	−	0.999968i	$-0.502544\pi$
$389$	−7.21857e9	−0.0159837	−0.00799186	+	0.999968i	$0.502544\pi$
$390$	0	0
$391$	5.29025e10	0.114467
$392$	− 2.36126e10i	− 0.0505076i
$393$	− 1.09490e11i	− 0.231530i
$394$	1.99677e11	0.417441
$395$	0	0
$396$	1.15203e11	0.235415
$397$	6.99387e11i	1.41306i	0.707684	+	0.706529i	$0.249740\pi$
$397$	6.99387e11i	1.41306i	−0.707684	+	0.706529i	$0.750260\pi$
$398$	− 4.69004e10i	− 0.0936920i
$399$	−2.92417e11	−0.577597
$400$	0	0
$401$	6.40644e11	1.23728	0.618638	−	0.785676i	$-0.287685\pi$
$401$	6.40644e11	1.23728	0.618638	+	0.785676i	$0.287685\pi$
$402$	− 2.54447e11i	− 0.485936i
$403$	− 9.20704e10i	− 0.173879i
$404$	2.31478e11	0.432309
$405$	0	0
$406$	−2.13471e11	−0.389917
$407$	1.90142e11i	0.343481i
$408$	− 1.49138e10i	− 0.0266451i
$409$	1.31500e10	0.0232365	0.0116182	−	0.999933i	$-0.496302\pi$
$409$	1.31500e10	0.0232365	0.0116182	+	0.999933i	$0.496302\pi$
$410$	0	0
$411$	2.84538e11	0.491873
$412$	− 5.07281e11i	− 0.867384i
$413$	− 3.97677e11i	− 0.672597i
$414$	3.64256e11	0.609404
$415$	0	0
$416$	−1.66472e10	−0.0272534
$417$	7.09461e11i	1.14899i
$418$	− 5.59648e11i	− 0.896647i
$419$	5.79915e11	0.919182	0.459591	−	0.888131i	$-0.347996\pi$
$419$	5.79915e11	0.919182	0.459591	+	0.888131i	$0.347996\pi$
$420$	0	0
$421$	1.66175e11	0.257808	0.128904	−	0.991657i	$-0.458854\pi$
$421$	1.66175e11	0.257808	0.128904	+	0.991657i	$0.458854\pi$
$422$	− 5.39165e11i	− 0.827591i
$423$	5.21121e11i	0.791419i
$424$	2.45329e11	0.368639
$425$	0	0
$426$	−2.60123e11	−0.382680
$427$	1.23457e11i	0.179718i
$428$	1.06593e11i	0.153544i
$429$	1.31772e11	0.187830
$430$	0	0
$431$	7.57723e11	1.05770	0.528850	−	0.848715i	$-0.322623\pi$
$431$	7.57723e11	1.05770	0.528850	+	0.848715i	$0.322623\pi$
$432$	1.16603e11i	0.161077i
$433$	− 1.07485e12i	− 1.46944i	−0.678371	−	0.734719i	$-0.737314\pi$
$433$	− 1.07485e12i	− 1.46944i	0.678371	−	0.734719i	$-0.262686\pi$
$434$	2.22788e11	0.301431
$435$	0	0
$436$	−3.24918e11	−0.430610
$437$	− 1.76953e12i	− 2.32109i
$438$	8.33670e11i	1.08233i
$439$	−1.70418e11	−0.218991	−0.109496	−	0.993987i	$-0.534924\pi$
$439$	−1.70418e11	−0.218991	−0.109496	+	0.993987i	$0.534924\pi$
$440$	0	0
$441$	5.31342e10	0.0668960
$442$	− 5.44051e9i	− 0.00678016i
$443$	1.22937e12i	1.51658i	0.651918	+	0.758290i	$0.273965\pi$
$443$	1.22937e12i	1.51658i	−0.651918	+	0.758290i	$0.726035\pi$
$444$	1.69486e11	0.206971
$445$	0	0
$446$	−6.19533e11	−0.741409
$447$	7.88963e10i	0.0934701i
$448$	− 4.02821e10i	− 0.0472456i
$449$	7.25792e10	0.0842759	0.0421380	−	0.999112i	$-0.486583\pi$
$449$	7.25792e10	0.0842759	0.0421380	+	0.999112i	$0.486583\pi$
$450$	0	0
$451$	−3.10563e11	−0.353472
$452$	7.25831e11i	0.817923i
$453$	1.24428e12i	1.38828i
$454$	−1.23042e12	−1.35926
$455$	0	0
$456$	−4.98851e11	−0.540292
$457$	6.64172e11i	0.712291i	0.934431	+	0.356146i	$0.115909\pi$
$457$	6.64172e11i	0.712291i	−0.934431	+	0.356146i	$0.884091\pi$
$458$	6.96183e11i	0.739313i
$459$	−3.81073e10	−0.0400730
$460$	0	0
$461$	−1.21501e12	−1.25293	−0.626463	−	0.779451i	$-0.715498\pi$
$461$	−1.21501e12	−1.25293	−0.626463	+	0.779451i	$0.715498\pi$
$462$	3.18856e11i	0.325616i
$463$	2.93878e11i	0.297202i	0.988897	+	0.148601i	$0.0474771\pi$
$463$	2.93878e11i	0.297202i	−0.988897	+	0.148601i	$0.952523\pi$
$464$	−3.64172e11	−0.364734
$465$	0	0
$466$	−3.31269e11	−0.325420
$467$	− 4.73112e11i	− 0.460297i	−0.973155	−	0.230149i	$-0.926079\pi$
$467$	− 4.73112e11i	− 0.460297i	0.973155	−	0.230149i	$-0.0739212\pi$
$468$	− 3.74602e10i	− 0.0360964i
$469$	2.24605e11	0.214359
$470$	0	0
$471$	−7.53185e11	−0.705192
$472$	− 6.78419e11i	− 0.629157i
$473$	− 9.13072e11i	− 0.838745i
$474$	−1.35041e12	−1.22875
$475$	0	0
$476$	1.31647e10	0.0117538
$477$	5.52049e11i	0.488253i
$478$	3.45952e11i	0.303103i
$479$	2.05945e12	1.78748	0.893742	−	0.448582i	$-0.148071\pi$
$479$	2.05945e12	1.78748	0.893742	+	0.448582i	$0.148071\pi$
$480$	0	0
$481$	6.18280e10	0.0526662
$482$	− 1.08446e12i	− 0.915172i
$483$	1.00818e12i	0.842900i
$484$	−6.61383e9	−0.00547834
$485$	0	0
$486$	−7.55843e11	−0.614566
$487$	1.22247e12i	0.984821i	0.870363	+	0.492411i	$0.163884\pi$
$487$	1.22247e12i	0.984821i	−0.870363	+	0.492411i	$0.836116\pi$
$488$	2.10612e11i	0.168110i
$489$	2.27197e12	1.79685
$490$	0	0
$491$	1.98225e11	0.153918	0.0769592	−	0.997034i	$-0.475479\pi$
$491$	1.98225e11	0.153918	0.0769592	+	0.997034i	$0.475479\pi$
$492$	2.76825e11i	0.212991i
$493$	− 1.19016e11i	− 0.0907391i
$494$	−1.81980e11	−0.137484
$495$	0	0
$496$	3.80066e11	0.281963
$497$	− 2.29616e11i	− 0.168810i
$498$	− 1.01044e12i	− 0.736174i
$499$	3.00745e11	0.217143	0.108571	−	0.994089i	$-0.465372\pi$
$499$	3.00745e11	0.217143	0.108571	+	0.994089i	$0.465372\pi$
$500$	0	0
$501$	−2.11576e12	−1.50036
$502$	− 7.80633e10i	− 0.0548631i
$503$	3.30194e11i	0.229993i	0.993366	+	0.114996i	$0.0366856\pi$
$503$	3.30194e11i	0.229993i	−0.993366	+	0.114996i	$0.963314\pi$
$504$	9.06445e10	0.0625755
$505$	0	0
$506$	−1.92952e12	−1.30850
$507$	1.75992e12i	1.18292i
$508$	1.39336e12i	0.928277i
$509$	6.32399e10	0.0417600	0.0208800	−	0.999782i	$-0.493353\pi$
$509$	6.32399e10	0.0417600	0.0208800	+	0.999782i	$0.493353\pi$
$510$	0	0
$511$	−7.35898e11	−0.477445
$512$	− 6.87195e10i	− 0.0441942i
$513$	1.27465e12i	0.812574i
$514$	4.40046e11	0.278076
$515$	0	0
$516$	−8.13880e11	−0.505402
$517$	− 2.76046e12i	− 1.69932i
$518$	1.49608e11i	0.0913003i
$519$	−1.77725e12	−1.07522
$520$	0	0
$521$	−1.88994e12	−1.12377	−0.561886	−	0.827215i	$-0.689924\pi$
$521$	−1.88994e12	−1.12377	−0.561886	+	0.827215i	$0.689924\pi$
$522$	− 8.19476e11i	− 0.483080i
$523$	8.95863e11i	0.523581i	0.965125	+	0.261791i	$0.0843130\pi$
$523$	8.95863e11i	0.523581i	−0.965125	+	0.261791i	$0.915687\pi$
$524$	1.64879e11	0.0955374
$525$	0	0
$526$	−3.56152e11	−0.202861
$527$	1.24210e11i	0.0701472i
$528$	5.43954e11i	0.304586i
$529$	−4.29975e12	−2.38722
$530$	0	0
$531$	1.52661e12	0.833302
$532$	− 4.40346e11i	− 0.238337i
$533$	1.00985e11i	0.0541981i
$534$	4.50113e11	0.239544
$535$	0	0
$536$	3.83166e11	0.200515
$537$	6.87464e11i	0.356752i
$538$	2.76826e11i	0.142458i
$539$	−2.81461e11	−0.143638
$540$	0	0
$541$	1.00221e12	0.503005	0.251502	−	0.967857i	$-0.419075\pi$
$541$	1.00221e12	0.503005	0.251502	+	0.967857i	$0.419075\pi$
$542$	− 7.71041e11i	− 0.383778i
$543$	2.12050e12i	1.04674i
$544$	2.24584e10	0.0109947
$545$	0	0
$546$	1.03682e11	0.0499270
$547$	− 2.73436e12i	− 1.30591i	−0.757396	−	0.652955i	$-0.773529\pi$
$547$	− 2.73436e12i	− 1.30591i	0.757396	−	0.652955i	$-0.226471\pi$
$548$	4.28481e11i	0.202964i
$549$	−4.73929e11	−0.222658
$550$	0	0
$551$	−3.98097e12	−1.83995
$552$	1.71991e12i	0.788461i
$553$	− 1.19203e12i	− 0.542033i
$554$	−1.28613e12	−0.580086
$555$	0	0
$556$	−1.06837e12	−0.474115
$557$	4.22359e12i	1.85923i	0.368534	+	0.929614i	$0.379860\pi$
$557$	4.22359e12i	1.85923i	−0.368534	+	0.929614i	$0.620140\pi$
$558$	8.55241e11i	0.373452i
$559$	−2.96902e11	−0.128606
$560$	0	0
$561$	−1.77771e11	−0.0757754
$562$	3.12953e12i	1.32332i
$563$	− 3.08311e12i	− 1.29330i	−0.762785	−	0.646652i	$-0.776169\pi$
$563$	− 3.08311e12i	− 1.29330i	0.762785	−	0.646652i	$-0.223831\pi$
$564$	−2.46058e12	−1.02396
$565$	0	0
$566$	−9.64483e11	−0.395021
$567$	− 1.16181e12i	− 0.472075i
$568$	− 3.91715e11i	− 0.157907i
$569$	2.74669e11	0.109851	0.0549256	−	0.998490i	$-0.482508\pi$
$569$	2.74669e11	0.109851	0.0549256	+	0.998490i	$0.482508\pi$
$570$	0	0
$571$	2.82499e12	1.11213	0.556064	−	0.831140i	$-0.312311\pi$
$571$	2.82499e12	1.11213	0.556064	+	0.831140i	$0.312311\pi$
$572$	1.98433e11i	0.0775055i
$573$	− 6.49310e11i	− 0.251626i
$574$	−2.44359e11	−0.0939560
$575$	0	0
$576$	1.54636e11	0.0585340
$577$	− 3.76585e12i	− 1.41440i	−0.707014	−	0.707199i	$-0.749958\pi$
$577$	− 3.76585e12i	− 1.41440i	0.707014	−	0.707199i	$-0.250042\pi$
$578$	− 1.89007e12i	− 0.704371i
$579$	4.10028e12	1.51621
$580$	0	0
$581$	8.91940e11	0.324745
$582$	− 2.06181e12i	− 0.744894i
$583$	− 2.92430e12i	− 1.04837i
$584$	−1.25541e12	−0.446609
$585$	0	0
$586$	−7.78789e11	−0.272823
$587$	3.00831e12i	1.04580i	0.852393	+	0.522902i	$0.175151\pi$
$587$	3.00831e12i	1.04580i	−0.852393	+	0.522902i	$0.824849\pi$
$588$	2.50884e11i	0.0865516i
$589$	4.15471e12	1.42240
$590$	0	0
$591$	−2.12157e12	−0.715342
$592$	2.55225e11i	0.0854036i
$593$	3.64775e12i	1.21138i	0.795703	+	0.605688i	$0.207102\pi$
$593$	3.64775e12i	1.21138i	−0.795703	+	0.605688i	$0.792898\pi$
$594$	1.38990e12	0.458083
$595$	0	0
$596$	−1.18809e11	−0.0385691
$597$	4.98316e11i	0.160554i
$598$	6.27420e11i	0.200633i
$599$	−4.17778e12	−1.32594	−0.662972	−	0.748644i	$-0.730705\pi$
$599$	−4.17778e12	−1.32594	−0.662972	+	0.748644i	$0.730705\pi$
$600$	0	0
$601$	4.84445e12	1.51464	0.757321	−	0.653043i	$-0.226508\pi$
$601$	4.84445e12	1.51464	0.757321	+	0.653043i	$0.226508\pi$
$602$	− 7.18429e11i	− 0.222946i
$603$	8.62218e11i	0.265576i
$604$	−1.87374e12	−0.572853
$605$	0	0
$606$	−2.45946e12	−0.740819
$607$	1.58444e12i	0.473726i	0.971543	+	0.236863i	$0.0761193\pi$
$607$	1.58444e12i	0.473726i	−0.971543	+	0.236863i	$0.923881\pi$
$608$	− 7.51210e11i	− 0.222944i
$609$	2.26813e12	0.668175
$610$	0	0
$611$	−8.97614e11	−0.260558
$612$	5.05369e10i	0.0145622i
$613$	− 2.79203e11i	− 0.0798635i	−0.999202	−	0.0399318i	$-0.987286\pi$
$613$	− 2.79203e11i	− 0.0798635i	0.999202	−	0.0399318i	$-0.0127141\pi$
$614$	−4.40285e12	−1.25019
$615$	0	0
$616$	−4.80159e11	−0.134361
$617$	5.55576e12i	1.54333i	0.636027	+	0.771667i	$0.280577\pi$
$617$	5.55576e12i	1.54333i	−0.636027	+	0.771667i	$0.719423\pi$
$618$	5.38986e12i	1.48638i
$619$	2.70437e12	0.740385	0.370192	−	0.928955i	$-0.379292\pi$
$619$	2.70437e12	0.740385	0.370192	+	0.928955i	$0.379292\pi$
$620$	0	0
$621$	4.39467e12	1.18581
$622$	− 1.79715e12i	− 0.481423i
$623$	3.97324e11i	0.105669i
$624$	1.76876e11	0.0467024
$625$	0	0
$626$	−1.69823e12	−0.441991
$627$	5.94626e12i	1.53653i
$628$	− 1.13421e12i	− 0.290987i
$629$	−8.34109e10	−0.0212469
$630$	0	0
$631$	−4.73158e12	−1.18816	−0.594078	−	0.804407i	$-0.702483\pi$
$631$	−4.73158e12	−1.18816	−0.594078	+	0.804407i	$0.702483\pi$
$632$	− 2.03356e12i	− 0.507025i
$633$	5.72863e12i	1.41819i
$634$	−3.70172e10	−0.00909918
$635$	0	0
$636$	−2.60662e12	−0.631713
$637$	9.15220e10i	0.0220241i
$638$	4.34090e12i	1.03726i
$639$	8.81454e11	0.209144
$640$	0	0
$641$	1.38865e12	0.324887	0.162444	−	0.986718i	$-0.448062\pi$
$641$	1.38865e12	0.324887	0.162444	+	0.986718i	$0.448062\pi$
$642$	− 1.13255e12i	− 0.263118i
$643$	3.09398e12i	0.713786i	0.934145	+	0.356893i	$0.116164\pi$
$643$	3.09398e12i	0.713786i	−0.934145	+	0.356893i	$0.883836\pi$
$644$	−1.51820e12	−0.347810
$645$	0	0
$646$	2.45505e11	0.0554644
$647$	− 2.31453e12i	− 0.519270i	−0.965707	−	0.259635i	$-0.916398\pi$
$647$	− 2.31453e12i	− 0.519270i	0.965707	−	0.259635i	$-0.0836022\pi$
$648$	− 1.98200e12i	− 0.441586i
$649$	−8.08670e12	−1.78925
$650$	0	0
$651$	−2.36712e12	−0.516542
$652$	3.42132e12i	0.741446i
$653$	− 8.10575e11i	− 0.174455i	−0.996188	−	0.0872276i	$-0.972199\pi$
$653$	− 8.10575e11i	− 0.174455i	0.996188	−	0.0872276i	$-0.0278007\pi$
$654$	3.45225e12	0.737908
$655$	0	0
$656$	−4.16865e11	−0.0878878
$657$	− 2.82498e12i	− 0.591522i
$658$	− 2.17200e12i	− 0.451694i
$659$	−4.57355e11	−0.0944645	−0.0472323	−	0.998884i	$-0.515040\pi$
$659$	−4.57355e11	−0.0944645	−0.0472323	+	0.998884i	$0.515040\pi$
$660$	0	0
$661$	7.94557e12	1.61889	0.809447	−	0.587193i	$-0.199767\pi$
$661$	7.94557e12	1.61889	0.809447	+	0.587193i	$0.199767\pi$
$662$	3.45897e12i	0.699980i
$663$	5.78055e10i	0.0116187i
$664$	1.52161e12	0.303772
$665$	0	0
$666$	−5.74319e11	−0.113115
$667$	1.37254e13i	2.68508i
$668$	− 3.18608e12i	− 0.619103i
$669$	6.58254e12	1.27050
$670$	0	0
$671$	2.51048e12	0.478086
$672$	4.27997e11i	0.0809616i
$673$	− 8.92805e12i	− 1.67760i	−0.544439	−	0.838801i	$-0.683257\pi$
$673$	− 8.92805e12i	− 1.67760i	0.544439	−	0.838801i	$-0.316743\pi$
$674$	−8.00465e11	−0.149408
$675$	0	0
$676$	−2.65023e12	−0.488116
$677$	8.01730e12i	1.46683i	0.679782	+	0.733414i	$0.262074\pi$
$677$	8.01730e12i	1.46683i	−0.679782	+	0.733414i	$0.737926\pi$
$678$	− 7.71195e12i	− 1.40162i
$679$	1.82000e12	0.328592
$680$	0	0
$681$	1.30732e13	2.32927
$682$	− 4.53036e12i	− 0.801868i
$683$	4.14724e12i	0.729233i	0.931158	+	0.364617i	$0.118800\pi$
$683$	4.14724e12i	0.729233i	−0.931158	+	0.364617i	$0.881200\pi$
$684$	1.69041e12	0.295283
$685$	0	0
$686$	−2.21461e11	−0.0381802
$687$	− 7.39694e12i	− 1.26691i
$688$	− 1.22561e12i	− 0.208547i
$689$	−9.50888e11	−0.160747
$690$	0	0
$691$	−6.05580e12	−1.01046	−0.505231	−	0.862984i	$-0.668593\pi$
$691$	−6.05580e12	−1.01046	−0.505231	+	0.862984i	$0.668593\pi$
$692$	− 2.67633e12i	− 0.443672i
$693$	− 1.08048e12i	− 0.177957i
$694$	2.95370e12	0.483336
$695$	0	0
$696$	3.86933e12	0.625020
$697$	− 1.36237e11i	− 0.0218649i
$698$	4.39466e12i	0.700771i
$699$	3.51973e12	0.557651
$700$	0	0
$701$	1.88599e12	0.294990	0.147495	−	0.989063i	$-0.452879\pi$
$701$	1.88599e12	0.294990	0.147495	+	0.989063i	$0.452879\pi$
$702$	− 4.51950e11i	− 0.0702383i
$703$	2.79001e12i	0.430831i
$704$	−8.19131e11	−0.125683
$705$	0	0
$706$	−2.52886e12	−0.383092
$707$	− 2.17101e12i	− 0.326795i
$708$	7.20820e12i	1.07815i
$709$	4.76210e12	0.707767	0.353884	−	0.935289i	$-0.384861\pi$
$709$	4.76210e12	0.707767	0.353884	+	0.935289i	$0.384861\pi$
$710$	0	0
$711$	4.57600e12	0.671542
$712$	6.77817e11i	0.0988444i
$713$	− 1.43244e13i	− 2.07574i
$714$	−1.39875e11	−0.0201418
$715$	0	0
$716$	−1.03524e12	−0.147208
$717$	− 3.67574e12i	− 0.519408i
$718$	5.45215e12i	0.765610i
$719$	−5.34893e12	−0.746427	−0.373213	−	0.927746i	$-0.621744\pi$
$719$	−5.34893e12	−0.746427	−0.373213	+	0.927746i	$0.621744\pi$
$720$	0	0
$721$	−4.75774e12	−0.655681
$722$	− 3.04889e12i	− 0.417565i
$723$	1.15224e13i	1.56827i
$724$	−3.19322e12	−0.431922
$725$	0	0
$726$	7.02720e10	0.00938788
$727$	− 9.08222e12i	− 1.20583i	−0.797804	−	0.602917i	$-0.794005\pi$
$727$	− 9.08222e12i	− 1.20583i	0.797804	−	0.602917i	$-0.205995\pi$
$728$	1.56132e11i	0.0206016i
$729$	−1.49349e12	−0.195852
$730$	0	0
$731$	4.00544e11	0.0518827
$732$	− 2.23776e12i	− 0.288080i
$733$	− 1.20547e13i	− 1.54237i	−0.636611	−	0.771185i	$-0.719664\pi$
$733$	− 1.20547e13i	− 1.54237i	0.636611	−	0.771185i	$-0.280336\pi$
$734$	9.76345e12	1.24157
$735$	0	0
$736$	−2.58998e12	−0.325347
$737$	− 4.56731e12i	− 0.570239i
$738$	− 9.38048e11i	− 0.116405i
$739$	−1.08128e13	−1.33364	−0.666822	−	0.745217i	$-0.732346\pi$
$739$	−1.08128e13	−1.33364	−0.666822	+	0.745217i	$0.732346\pi$
$740$	0	0
$741$	1.93353e12	0.235597
$742$	− 2.30091e12i	− 0.278665i
$743$	6.39433e12i	0.769742i	0.922970	+	0.384871i	$0.125754\pi$
$743$	6.39433e12i	0.769742i	−0.922970	+	0.384871i	$0.874246\pi$
$744$	−4.03820e12	−0.483181
$745$	0	0
$746$	6.95889e12	0.822650
$747$	3.42400e12i	0.402337i
$748$	− 2.67702e11i	− 0.0312676i
$749$	9.99726e11	0.116068
$750$	0	0
$751$	−2.30580e12	−0.264510	−0.132255	−	0.991216i	$-0.542222\pi$
$751$	−2.30580e12	−0.264510	−0.132255	+	0.991216i	$0.542222\pi$
$752$	− 3.70534e12i	− 0.422521i
$753$	8.29422e11i	0.0940152i
$754$	1.41152e12	0.159044
$755$	0	0
$756$	1.09361e12	0.121763
$757$	6.85316e12i	0.758507i	0.925293	+	0.379253i	$0.123819\pi$
$757$	6.85316e12i	0.758507i	−0.925293	+	0.379253i	$0.876181\pi$
$758$	− 1.16908e13i	− 1.28628i
$759$	2.05012e13	2.24229
$760$	0	0
$761$	−1.55520e12	−0.168095	−0.0840474	−	0.996462i	$-0.526785\pi$
$761$	−1.55520e12	−0.168095	−0.0840474	+	0.996462i	$0.526785\pi$
$762$	− 1.48045e13i	− 1.59073i
$763$	3.04737e12i	0.325510i
$764$	9.77784e11	0.103830
$765$	0	0
$766$	3.37718e12	0.354425
$767$	2.62954e12i	0.274347i
$768$	7.30144e11i	0.0757327i
$769$	1.31148e12	0.135236	0.0676179	−	0.997711i	$-0.478460\pi$
$769$	1.31148e12	0.135236	0.0676179	+	0.997711i	$0.478460\pi$
$770$	0	0
$771$	−4.67549e12	−0.476521
$772$	6.17454e12i	0.625644i
$773$	− 9.82010e12i	− 0.989255i	−0.869105	−	0.494627i	$-0.835305\pi$
$773$	− 9.82010e12i	− 0.989255i	0.869105	−	0.494627i	$-0.164695\pi$
$774$	2.75792e12	0.276215
$775$	0	0
$776$	3.10484e12	0.307370
$777$	− 1.58959e12i	− 0.156455i
$778$	1.15497e11i	0.0113022i
$779$	−4.55698e12	−0.443362
$780$	0	0
$781$	−4.66921e12	−0.449070
$782$	− 8.46439e11i	− 0.0809404i
$783$	− 9.88682e12i	− 0.940001i
$784$	−3.77802e11	−0.0357143
$785$	0	0
$786$	−1.75184e12	−0.163716
$787$	4.81658e12i	0.447562i	0.974639	+	0.223781i	$0.0718400\pi$
$787$	4.81658e12i	0.447562i	−0.974639	+	0.223781i	$0.928160\pi$
$788$	− 3.19484e12i	− 0.295176i
$789$	3.78411e12	0.347630
$790$	0	0
$791$	6.80750e12	0.618292
$792$	− 1.84324e12i	− 0.166464i
$793$	− 8.16328e11i	− 0.0733053i
$794$	1.11902e13	0.999183
$795$	0	0
$796$	−7.50406e11	−0.0662502
$797$	− 7.71344e12i	− 0.677151i	−0.940939	−	0.338575i	$-0.890055\pi$
$797$	− 7.71344e12i	− 0.677151i	0.940939	−	0.338575i	$-0.109945\pi$
$798$	4.67867e12i	0.408423i
$799$	1.21095e12	0.105116
$800$	0	0
$801$	−1.52525e12	−0.130917
$802$	− 1.02503e13i	− 0.874887i
$803$	1.49644e13i	1.27010i
$804$	−4.07114e12	−0.343609
$805$	0	0
$806$	−1.47313e12	−0.122951
$807$	− 2.94128e12i	− 0.244121i
$808$	− 3.70365e12i	− 0.305688i
$809$	−2.12869e13	−1.74721	−0.873604	−	0.486637i	$-0.838223\pi$
$809$	−2.12869e13	−1.74721	−0.873604	+	0.486637i	$0.838223\pi$
$810$	0	0
$811$	2.45053e13	1.98914	0.994570	−	0.104067i	$-0.0331856\pi$
$811$	2.45053e13	1.98914	0.994570	+	0.104067i	$0.0331856\pi$
$812$	3.41554e12i	0.275713i
$813$	8.19231e12i	0.657656i
$814$	3.04227e12	0.242878
$815$	0	0
$816$	−2.38621e11	−0.0188409
$817$	− 1.33978e13i	− 1.05204i
$818$	− 2.10400e11i	− 0.0164307i
$819$	−3.51336e11	−0.0272863
$820$	0	0
$821$	−9.72826e12	−0.747293	−0.373646	−	0.927571i	$-0.621893\pi$
$821$	−9.72826e12	−0.747293	−0.373646	+	0.927571i	$0.621893\pi$
$822$	− 4.55261e12i	− 0.347807i
$823$	− 8.28745e11i	− 0.0629683i	−0.999504	−	0.0314841i	$-0.989977\pi$
$823$	− 8.28745e11i	− 0.0629683i	0.999504	−	0.0314841i	$-0.0100234\pi$
$824$	−8.11650e12	−0.613333
$825$	0	0
$826$	−6.36283e12	−0.475598
$827$	− 2.42842e13i	− 1.80530i	−0.430376	−	0.902649i	$-0.641619\pi$
$827$	− 2.42842e13i	− 1.80530i	0.430376	−	0.902649i	$-0.358381\pi$
$828$	− 5.82809e12i	− 0.430913i
$829$	−1.95570e13	−1.43816	−0.719078	−	0.694929i	$-0.755436\pi$
$829$	−1.95570e13	−1.43816	−0.719078	+	0.694929i	$0.755436\pi$
$830$	0	0
$831$	1.36652e13	0.994055
$832$	2.66355e11i	0.0192711i
$833$	− 1.23471e11i	− 0.00888507i
$834$	1.13514e13	0.812459
$835$	0	0
$836$	−8.95437e12	−0.634025
$837$	1.03183e13i	0.726682i
$838$	− 9.27865e12i	− 0.649960i
$839$	7.69577e12	0.536196	0.268098	−	0.963392i	$-0.413605\pi$
$839$	7.69577e12	0.536196	0.268098	+	0.963392i	$0.413605\pi$
$840$	0	0
$841$	1.63712e13	1.12849
$842$	− 2.65880e12i	− 0.182298i
$843$	− 3.32512e13i	− 2.26769i
$844$	−8.62664e12	−0.585195
$845$	0	0
$846$	8.33793e12	0.559618
$847$	6.20305e10i	0.00414124i
$848$	− 3.92526e12i	− 0.260667i
$849$	1.02476e13	0.676923
$850$	0	0
$851$	9.61924e12	0.628721
$852$	4.16197e12i	0.270596i
$853$	− 2.79895e12i	− 0.181019i	−0.995896	−	0.0905097i	$-0.971150\pi$
$853$	− 2.79895e12i	− 0.181019i	0.995896	−	0.0905097i	$-0.0288496\pi$
$854$	1.97531e12	0.127079
$855$	0	0
$856$	1.70549e12	0.108572
$857$	5.56141e12i	0.352185i	0.984374	+	0.176093i	$0.0563459\pi$
$857$	5.56141e12i	0.352185i	−0.984374	+	0.176093i	$0.943654\pi$
$858$	− 2.10835e12i	− 0.132816i
$859$	−3.51052e12	−0.219989	−0.109995	−	0.993932i	$-0.535083\pi$
$859$	−3.51052e12	−0.219989	−0.109995	+	0.993932i	$0.535083\pi$
$860$	0	0
$861$	2.59631e12	0.161006
$862$	− 1.21236e13i	− 0.747908i
$863$	1.43838e13i	0.882721i	0.897330	+	0.441361i	$0.145504\pi$
$863$	1.43838e13i	0.882721i	−0.897330	+	0.441361i	$0.854496\pi$
$864$	1.86565e12	0.113898
$865$	0	0
$866$	−1.71976e13	−1.03905
$867$	2.00820e13i	1.20704i
$868$	− 3.56460e12i	− 0.213144i
$869$	−2.42399e13	−1.44192
$870$	0	0
$871$	−1.48514e12	−0.0874353
$872$	5.19868e12i	0.304487i
$873$	6.98664e12i	0.407103i
$874$	−2.83125e13	−1.64126
$875$	0	0
$876$	1.33387e13	0.765325
$877$	6.34278e12i	0.362061i	0.983477	+	0.181030i	$0.0579433\pi$
$877$	6.34278e12i	0.362061i	−0.983477	+	0.181030i	$0.942057\pi$
$878$	2.72670e12i	0.154850i
$879$	8.27463e12	0.467519
$880$	0	0
$881$	−2.89282e13	−1.61782	−0.808910	−	0.587933i	$-0.799942\pi$
$881$	−2.89282e13	−1.61782	−0.808910	+	0.587933i	$0.799942\pi$
$882$	− 8.50147e11i	− 0.0473026i
$883$	− 7.17154e12i	− 0.396999i	−0.980101	−	0.198500i	$-0.936393\pi$
$883$	− 7.17154e12i	− 0.396999i	0.980101	−	0.198500i	$-0.0636068\pi$
$884$	−8.70482e10	−0.00479430
$885$	0	0
$886$	1.96699e13	1.07238
$887$	1.68020e13i	0.911389i	0.890136	+	0.455695i	$0.150609\pi$
$887$	1.68020e13i	0.911389i	−0.890136	+	0.455695i	$0.849391\pi$
$888$	− 2.71177e12i	− 0.146351i
$889$	1.30682e13	0.701711
$890$	0	0
$891$	−2.36252e13	−1.25582
$892$	9.91254e12i	0.524255i
$893$	− 4.05052e13i	− 2.13147i
$894$	1.26234e12	0.0660933
$895$	0	0
$896$	−6.44514e11	−0.0334077
$897$	− 6.66633e12i	− 0.343812i
$898$	− 1.16127e12i	− 0.0595921i
$899$	−3.22260e13	−1.64546
$900$	0	0
$901$	1.28282e12	0.0648493
$902$	4.96900e12i	0.249942i
$903$	7.63331e12i	0.382048i
$904$	1.16133e13	0.578359
$905$	0	0
$906$	1.99085e13	0.981660
$907$	1.87924e13i	0.922038i	0.887390	+	0.461019i	$0.152516\pi$
$907$	1.87924e13i	0.922038i	−0.887390	+	0.461019i	$0.847484\pi$
$908$	1.96867e13i	0.961139i
$909$	8.33412e12	0.404876
$910$	0	0
$911$	−3.39496e13	−1.63306	−0.816529	−	0.577304i	$-0.804105\pi$
$911$	−3.39496e13	−1.63306	−0.816529	+	0.577304i	$0.804105\pi$
$912$	7.98161e12i	0.382044i
$913$	− 1.81375e13i	− 0.863890i
$914$	1.06267e13	0.503666
$915$	0	0
$916$	1.11389e13	0.522773
$917$	− 1.54638e12i	− 0.0722195i
$918$	6.09717e11i	0.0283359i
$919$	−1.03287e13	−0.477667	−0.238833	−	0.971061i	$-0.576765\pi$
$919$	−1.03287e13	−0.477667	−0.238833	+	0.971061i	$0.576765\pi$
$920$	0	0
$921$	4.67803e13	2.14237
$922$	1.94401e13i	0.885952i
$923$	1.51828e12i	0.0688563i
$924$	5.10169e12	0.230245
$925$	0	0
$926$	4.70205e12	0.210154
$927$	− 1.82641e13i	− 0.812344i
$928$	5.82675e12i	0.257906i
$929$	2.79767e13	1.23233	0.616163	−	0.787619i	$-0.288686\pi$
$929$	2.79767e13	1.23233	0.616163	+	0.787619i	$0.288686\pi$
$930$	0	0
$931$	−4.12996e12	−0.180166
$932$	5.30030e12i	0.230107i
$933$	1.90947e13i	0.824984i
$934$	−7.56980e12	−0.325479
$935$	0	0
$936$	−5.99364e11	−0.0255240
$937$	− 3.31649e13i	− 1.40556i	−0.711406	−	0.702782i	$-0.751941\pi$
$937$	− 3.31649e13i	− 1.40556i	0.711406	−	0.702782i	$-0.248059\pi$
$938$	− 3.59368e12i	− 0.151575i
$939$	1.80437e13	0.757411
$940$	0	0
$941$	3.19309e13	1.32757	0.663786	−	0.747923i	$-0.268949\pi$
$941$	3.19309e13	1.32757	0.663786	+	0.747923i	$0.268949\pi$
$942$	1.20510e13i	0.498646i
$943$	1.57113e13i	0.647009i
$944$	−1.08547e13	−0.444881
$945$	0	0
$946$	−1.46092e13	−0.593082
$947$	− 3.56921e13i	− 1.44210i	−0.692881	−	0.721052i	$-0.743659\pi$
$947$	− 3.56921e13i	− 1.44210i	0.692881	−	0.721052i	$-0.256341\pi$
$948$	2.16066e13i	0.868856i
$949$	4.86594e12	0.194746
$950$	0	0
$951$	3.93308e11	0.0155927
$952$	− 2.10635e11i	− 0.00831122i
$953$	− 3.04923e13i	− 1.19749i	−0.800940	−	0.598745i	$-0.795666\pi$
$953$	− 3.04923e13i	− 1.19749i	0.800940	−	0.598745i	$-0.204334\pi$
$954$	8.83279e12	0.345247
$955$	0	0
$956$	5.53524e12	0.214326
$957$	− 4.61221e13i	− 1.77748i
$958$	− 3.29512e13i	− 1.26394i
$959$	4.01869e12	0.153427
$960$	0	0
$961$	7.19282e12	0.272047
$962$	− 9.89248e11i	− 0.0372406i
$963$	3.83776e12i	0.143800i
$964$	−1.73514e13	−0.647124
$965$	0	0
$966$	1.61309e13	0.596020
$967$	3.45533e13i	1.27078i	0.772192	+	0.635389i	$0.219160\pi$
$967$	3.45533e13i	1.27078i	−0.772192	+	0.635389i	$0.780840\pi$
$968$	1.05821e11i	0.00387377i
$969$	−2.60849e12	−0.0950457
$970$	0	0
$971$	−2.06708e13	−0.746225	−0.373112	−	0.927786i	$-0.621709\pi$
$971$	−2.06708e13	−0.746225	−0.373112	+	0.927786i	$0.621709\pi$
$972$	1.20935e13i	0.434563i
$973$	1.00201e13i	0.358397i
$974$	1.95595e13	0.696374
$975$	0	0
$976$	3.36980e12	0.118872
$977$	− 1.78789e11i	− 0.00627791i	−0.999995	−	0.00313896i	$-0.999001\pi$
$977$	− 1.78789e11i	− 0.00627791i	0.999995	−	0.00313896i	$-0.000999163\pi$
$978$	− 3.63515e13i	− 1.27057i
$979$	8.07952e12	0.281102
$980$	0	0
$981$	−1.16983e13	−0.403285
$982$	− 3.17159e12i	− 0.108837i
$983$	− 1.42657e13i	− 0.487305i	−0.969863	−	0.243652i	$-0.921654\pi$
$983$	− 1.42657e13i	− 0.487305i	0.969863	−	0.243652i	$-0.0783456\pi$
$984$	4.42919e12	0.150608
$985$	0	0
$986$	−1.90426e12	−0.0641622
$987$	2.30776e13i	0.774038i
$988$	2.91167e12i	0.0972157i
$989$	−4.61922e13	−1.53527
$990$	0	0
$991$	−2.71296e13	−0.893537	−0.446768	−	0.894650i	$-0.647425\pi$
$991$	−2.71296e13	−0.893537	−0.446768	+	0.894650i	$0.647425\pi$
$992$	− 6.08106e12i	− 0.199378i
$993$	− 3.67515e13i	− 1.19951i
$994$	−3.67386e12	−0.119367
$995$	0	0
$996$	−1.61671e13	−0.520554
$997$	3.86723e12i	0.123957i	0.998077	+	0.0619787i	$0.0197411\pi$
$997$	3.86723e12i	0.123957i	−0.998077	+	0.0619787i	$0.980259\pi$
$998$	− 4.81191e12i	− 0.153543i
$999$	−6.92905e12	−0.220104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.10.c.d.99.1		2
5.2	odd	4		14.10.a.b.1.1	✓	1
5.3	odd	4		350.10.a.a.1.1		1
5.4	even	2	inner	350.10.c.d.99.2		2
15.2	even	4		126.10.a.a.1.1		1
20.7	even	4		112.10.a.a.1.1		1
35.2	odd	12		98.10.c.a.67.1		2
35.12	even	12		98.10.c.d.67.1		2
35.17	even	12		98.10.c.d.79.1		2
35.27	even	4		98.10.a.b.1.1		1
35.32	odd	12		98.10.c.a.79.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.b.1.1	✓	1	5.2	odd	4
98.10.a.b.1.1		1	35.27	even	4
98.10.c.a.67.1		2	35.2	odd	12
98.10.c.a.79.1		2	35.32	odd	12
98.10.c.d.67.1		2	35.12	even	12
98.10.c.d.79.1		2	35.17	even	12
112.10.a.a.1.1		1	20.7	even	4
126.10.a.a.1.1		1	15.2	even	4
350.10.a.a.1.1		1	5.3	odd	4
350.10.c.d.99.1		2	1.1	even	1	trivial
350.10.c.d.99.2		2	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	350.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-16.0000i q^{2} +170.000i q^{3} -256.000 q^{4} +2720.00 q^{6} +2401.00i q^{7} +4096.00i q^{8} -9217.00 q^{9} +48824.0 q^{11} -43520.0i q^{12} -15876.0i q^{13} +38416.0 q^{14} +65536.0 q^{16} +21418.0i q^{17} +147472. i q^{18} +716410. q^{19} -408170. q^{21} -781184. i q^{22} -2.47000e6i q^{23} -696320. q^{24} -254016. q^{26} +1.77922e6i q^{27} -614656. i q^{28} -5.55683e6 q^{29} +5.79935e6 q^{31} -1.04858e6i q^{32} +8.30008e6i q^{33} +342688. q^{34} +2.35955e6 q^{36} +3.89443e6i q^{37} -1.14626e7i q^{38} +2.69892e6 q^{39} -6.36086e6 q^{41} +6.53072e6i q^{42} -1.87013e7i q^{43} -1.24989e7 q^{44} -3.95200e7 q^{46} -5.65391e7i q^{47} +1.11411e7i q^{48} -5.76480e6 q^{49} -3.64106e6 q^{51} +4.06426e6i q^{52} -5.98947e7i q^{53} +2.84675e7 q^{54} -9.83450e6 q^{56} +1.21790e8i q^{57} +8.89092e7i q^{58} -1.65630e8 q^{59} +5.14190e7 q^{61} -9.27896e7i q^{62} -2.21300e7i q^{63} -1.67772e7 q^{64} +1.32801e8 q^{66} -9.35465e7i q^{67} -5.48301e6i q^{68} +4.19900e8 q^{69} -9.56335e7 q^{71} -3.77528e7i q^{72} +3.06496e8i q^{73} +6.23109e7 q^{74} -1.83401e8 q^{76} +1.17226e8i q^{77} -4.31827e7i q^{78} -4.96474e8 q^{79} -4.83886e8 q^{81} +1.01774e8i q^{82} -3.71487e8i q^{83} +1.04492e8 q^{84} -2.99221e8 q^{86} -9.44660e8i q^{87} +1.99983e8i q^{88} +1.65483e8 q^{89} +3.81183e7 q^{91} +6.32320e8i q^{92} +9.85889e8i q^{93} -9.04625e8 q^{94} +1.78258e8 q^{96} -7.58017e8i q^{97} +9.22368e7i q^{98} -4.50011e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 512 q^{4} + 5440 q^{6} - 18434 q^{9} + 97648 q^{11} + 76832 q^{14} + 131072 q^{16} + 1432820 q^{19} - 816340 q^{21} - 1392640 q^{24} - 508032 q^{26} - 11113652 q^{29} + 11598696 q^{31} + 685376 q^{34}+ \cdots - 900021616 q^{99}+O(q^{100}) \) 2 * q - 512 * q^4 + 5440 * q^6 - 18434 * q^9 + 97648 * q^11 + 76832 * q^14 + 131072 * q^16 + 1432820 * q^19 - 816340 * q^21 - 1392640 * q^24 - 508032 * q^26 - 11113652 * q^29 + 11598696 * q^31 + 685376 * q^34 + 4719104 * q^36 + 5397840 * q^39 - 12721716 * q^41 - 24997888 * q^44 - 79040000 * q^46 - 11529602 * q^49 - 7282120 * q^51 + 56935040 * q^54 - 19668992 * q^56 - 331259324 * q^59 + 102838032 * q^61 - 33554432 * q^64 + 265602560 * q^66 + 839800000 * q^69 - 191267072 * q^71 + 124621760 * q^74 - 366801920 * q^76 - 992948304 * q^79 - 967771222 * q^81 + 208983040 * q^84 - 598441472 * q^86 + 330965100 * q^89 + 76236552 * q^91 - 1809250176 * q^94 + 356515840 * q^96 - 900021616 * q^99

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