LMFDB - Embedded newform 98.7.b.c.97.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,7,Mod(97,98)] 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("98.97"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	98.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,256,0,0,0,0,-1512] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$22.5453001947$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 $ x^8 - 2x^7 + 285x^6 + 282x^5 + 62091x^4 + 29260x^3 + 4838750x^2 + 2401000*x + 294122500
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.5
Root			$-4.86132 + 8.42006i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.7.b.c.97.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+5.65685 q^{2} -31.8814i q^{3} +32.0000 q^{4} +129.137i q^{5} -180.349i q^{6} +181.019 q^{8} -287.425 q^{9} +730.512i q^{10} +2378.46 q^{11} -1020.21i q^{12} -820.701i q^{13} +4117.09 q^{15} +1024.00 q^{16} +2637.36i q^{17} -1625.92 q^{18} -5559.80i q^{19} +4132.40i q^{20} +13454.6 q^{22} +11392.7 q^{23} -5771.15i q^{24} -1051.49 q^{25} -4642.58i q^{26} -14078.0i q^{27} -32822.6 q^{29} +23289.8 q^{30} -46906.7i q^{31} +5792.62 q^{32} -75828.7i q^{33} +14919.2i q^{34} -9197.60 q^{36} +21725.5 q^{37} -31451.0i q^{38} -26165.1 q^{39} +23376.4i q^{40} +85846.0i q^{41} +113977. q^{43} +76110.8 q^{44} -37117.3i q^{45} +64447.0 q^{46} +38529.3i q^{47} -32646.6i q^{48} -5948.11 q^{50} +84082.8 q^{51} -26262.4i q^{52} +33240.7 q^{53} -79637.4i q^{54} +307149. i q^{55} -177254. q^{57} -185672. q^{58} +334749. i q^{59} +131747. q^{60} -168408. i q^{61} -265344. i q^{62} +32768.0 q^{64} +105983. q^{65} -428952. i q^{66} -322522. q^{67} +84395.6i q^{68} -363217. i q^{69} +325510. q^{71} -52029.5 q^{72} -107854. i q^{73} +122898. q^{74} +33522.9i q^{75} -177914. i q^{76} -148012. q^{78} -339049. q^{79} +132237. i q^{80} -658361. q^{81} +485619. i q^{82} +224674. i q^{83} -340582. q^{85} +644752. q^{86} +1.04643e6i q^{87} +430548. q^{88} +383231. i q^{89} -209967. i q^{90} +364567. q^{92} -1.49545e6 q^{93} +217955. i q^{94} +717978. q^{95} -184677. i q^{96} -32664.1i q^{97} -683629. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 256 q^{4} - 1512 q^{9} + 2712 q^{11} + 27144 q^{15} + 8192 q^{16} + 13632 q^{18} + 25248 q^{22} + 8256 q^{23} - 9328 q^{25} - 30312 q^{29} - 19296 q^{30} - 48384 q^{36} + 12248 q^{37} - 201528 q^{39}+ \cdots - 4625928 q^{99}+O(q^{100}) $ 8 * q + 256 * q^4 - 1512 * q^9 + 2712 * q^11 + 27144 * q^15 + 8192 * q^16 + 13632 * q^18 + 25248 * q^22 + 8256 * q^23 - 9328 * q^25 - 30312 * q^29 - 19296 * q^30 - 48384 * q^36 + 12248 * q^37 - 201528 * q^39 - 297376 * q^43 + 86784 * q^44 + 388128 * q^46 + 38784 * q^50 - 507384 * q^51 - 556968 * q^53 - 81288 * q^57 + 339648 * q^58 + 868608 * q^60 + 262144 * q^64 - 16632 * q^65 - 1297616 * q^67 + 190128 * q^71 + 436224 * q^72 + 2316288 * q^74 + 1122432 * q^78 - 140192 * q^79 - 2355840 * q^81 + 2190984 * q^85 + 1146048 * q^86 + 807936 * q^88 + 264192 * q^92 + 46728 * q^93 - 1451280 * q^95 - 4625928 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	5.65685	0.707107
$2$	5.65685	0.707107
$3$	− 31.8814i	− 1.18079i	−0.807113	−	0.590397i	$-0.798971\pi$
$3$	− 31.8814i	− 1.18079i	0.807113	−	0.590397i	$-0.201029\pi$
$4$	32.0000	0.500000
$5$	129.137i	1.03310i	0.856257	+	0.516550i	$0.172784\pi$
$5$	129.137i	1.03310i	−0.856257	+	0.516550i	$0.827216\pi$
$6$	− 180.349i	− 0.834947i
$7$	0	0
$7$	0	0
$8$	181.019	0.353553
$9$	−287.425	−0.394273
$10$	730.512i	0.730512i
$11$	2378.46	1.78697	0.893487	−	0.449090i	$-0.148252\pi$
$11$	2378.46	1.78697	0.893487	+	0.449090i	$0.148252\pi$
$12$	− 1020.21i	− 0.590397i
$13$	− 820.701i	− 0.373555i	−0.982402	−	0.186778i	$-0.940196\pi$
$13$	− 820.701i	− 0.373555i	0.982402	−	0.186778i	$-0.0598044\pi$
$14$	0	0
$15$	4117.09	1.21988
$16$	1024.00	0.250000
$17$	2637.36i	0.536813i	0.963306	+	0.268406i	$0.0864970\pi$
$17$	2637.36i	0.536813i	−0.963306	+	0.268406i	$0.913503\pi$
$18$	−1625.92	−0.278793
$19$	− 5559.80i	− 0.810584i	−0.914187	−	0.405292i	$-0.867170\pi$
$19$	− 5559.80i	− 0.810584i	0.914187	−	0.405292i	$-0.132830\pi$
$20$	4132.40i	0.516550i
$21$	0	0
$22$	13454.6	1.26358
$23$	11392.7	0.936363	0.468182	−	0.883632i	$-0.344909\pi$
$23$	11392.7	0.936363	0.468182	+	0.883632i	$0.344909\pi$
$24$	− 5771.15i	− 0.417474i
$25$	−1051.49	−0.0672951
$26$	− 4642.58i	− 0.264143i
$27$	− 14078.0i	− 0.715238i
$28$	0	0
$29$	−32822.6	−1.34579	−0.672897	−	0.739736i	$-0.734950\pi$
$29$	−32822.6	−1.34579	−0.672897	+	0.739736i	$0.734950\pi$
$30$	23289.8	0.862584
$31$	− 46906.7i	− 1.57453i	−0.616617	−	0.787263i	$-0.711497\pi$
$31$	− 46906.7i	− 1.57453i	0.616617	−	0.787263i	$-0.288503\pi$
$32$	5792.62	0.176777
$33$	− 75828.7i	− 2.11005i
$34$	14919.2i	0.379584i
$35$	0	0
$36$	−9197.60	−0.197136
$37$	21725.5	0.428909	0.214454	−	0.976734i	$-0.431203\pi$
$37$	21725.5	0.428909	0.214454	+	0.976734i	$0.431203\pi$
$38$	− 31451.0i	− 0.573170i
$39$	−26165.1	−0.441091
$40$	23376.4i	0.365256i
$41$	85846.0i	1.24557i	0.782392	+	0.622786i	$0.213999\pi$
$41$	85846.0i	1.24557i	−0.782392	+	0.622786i	$0.786001\pi$
$42$	0	0
$43$	113977.	1.43355	0.716774	−	0.697305i	$-0.245618\pi$
$43$	113977.	1.43355	0.716774	+	0.697305i	$0.245618\pi$
$44$	76110.8	0.893487
$45$	− 37117.3i	− 0.407323i
$46$	64447.0	0.662109
$47$	38529.3i	0.371105i	0.982634	+	0.185553i	$0.0594076\pi$
$47$	38529.3i	0.371105i	−0.982634	+	0.185553i	$0.940592\pi$
$48$	− 32646.6i	− 0.295198i
$49$	0	0
$50$	−5948.11	−0.0475849
$51$	84082.8	0.633865
$52$	− 26262.4i	− 0.186778i
$53$	33240.7	0.223277	0.111638	−	0.993749i	$-0.464390\pi$
$53$	33240.7	0.223277	0.111638	+	0.993749i	$0.464390\pi$
$54$	− 79637.4i	− 0.505750i
$55$	307149.i	1.84612i
$56$	0	0
$57$	−177254.	−0.957133
$58$	−185672.	−0.951620
$59$	334749.i	1.62991i	0.579527	+	0.814953i	$0.303237\pi$
$59$	334749.i	1.62991i	−0.579527	+	0.814953i	$0.696763\pi$
$60$	131747.	0.609939
$61$	− 168408.i	− 0.741946i	−0.928644	−	0.370973i	$-0.879024\pi$
$61$	− 168408.i	− 0.741946i	0.928644	−	0.370973i	$-0.120976\pi$
$62$	− 265344.i	− 1.11336i
$63$	0	0
$64$	32768.0	0.125000
$65$	105983.	0.385920
$66$	− 428952.i	− 1.49203i
$67$	−322522.	−1.07235	−0.536173	−	0.844108i	$-0.680131\pi$
$67$	−322522.	−1.07235	−0.536173	+	0.844108i	$0.680131\pi$
$68$	84395.6i	0.268406i
$69$	− 363217.i	− 1.10565i
$70$	0	0
$71$	325510.	0.909473	0.454737	−	0.890626i	$-0.349733\pi$
$71$	325510.	0.909473	0.454737	+	0.890626i	$0.349733\pi$
$72$	−52029.5	−0.139397
$73$	− 107854.i	− 0.277247i	−0.990345	−	0.138624i	$-0.955732\pi$
$73$	− 107854.i	− 0.277247i	0.990345	−	0.138624i	$-0.0442679\pi$
$74$	122898.	0.303284
$75$	33522.9i	0.0794617i
$76$	− 177914.i	− 0.405292i
$77$	0	0
$78$	−148012.	−0.311899
$79$	−339049.	−0.687672	−0.343836	−	0.939030i	$-0.611726\pi$
$79$	−339049.	−0.687672	−0.343836	+	0.939030i	$0.611726\pi$
$80$	132237.i	0.258275i
$81$	−658361.	−1.23882
$82$	485619.i	0.880752i
$83$	224674.i	0.392934i	0.980510	+	0.196467i	$0.0629468\pi$
$83$	224674.i	0.392934i	−0.980510	+	0.196467i	$0.937053\pi$
$84$	0	0
$85$	−340582.	−0.554581
$86$	644752.	1.01367
$87$	1.04643e6i	1.58910i
$88$	430548.	0.631791
$89$	383231.i	0.543614i	0.962352	+	0.271807i	$0.0876212\pi$
$89$	383231.i	0.543614i	−0.962352	+	0.271807i	$0.912379\pi$
$90$	− 209967.i	− 0.288021i
$91$	0	0
$92$	364567.	0.468182
$93$	−1.49545e6	−1.85919
$94$	217955.i	0.262411i
$95$	717978.	0.837415
$96$	− 184677.i	− 0.208737i
$97$	− 32664.1i	− 0.0357895i	−0.999840	−	0.0178948i	$-0.994304\pi$
$97$	− 32664.1i	− 0.0357895i	0.999840	−	0.0178948i	$-0.00569638\pi$
$98$	0	0
$99$	−683629.	−0.704555
$100$	−33647.6	−0.0336476
$101$	499988.i	0.485284i	0.970116	+	0.242642i	$0.0780140\pi$
$101$	499988.i	0.485284i	−0.970116	+	0.242642i	$0.921986\pi$
$102$	475644.	0.448210
$103$	446002.i	0.408155i	0.978955	+	0.204077i	$0.0654194\pi$
$103$	446002.i	0.408155i	−0.978955	+	0.204077i	$0.934581\pi$
$104$	− 148563.i	− 0.132072i
$105$	0	0
$106$	188038.	0.157880
$107$	−1.88947e6	−1.54237	−0.771186	−	0.636610i	$-0.780336\pi$
$107$	−1.88947e6	−1.54237	−0.771186	+	0.636610i	$0.780336\pi$
$108$	− 450497.i	− 0.357619i
$109$	−1.92186e6	−1.48403	−0.742014	−	0.670384i	$-0.766129\pi$
$109$	−1.92186e6	−1.48403	−0.742014	+	0.670384i	$0.766129\pi$
$110$	1.73749e6i	1.30541i
$111$	− 692640.i	− 0.506453i
$112$	0	0
$113$	−472481.	−0.327453	−0.163726	−	0.986506i	$-0.552351\pi$
$113$	−472481.	−0.327453	−0.163726	+	0.986506i	$0.552351\pi$
$114$	−1.00270e6	−0.676795
$115$	1.47123e6i	0.967357i
$116$	−1.05032e6	−0.672897
$117$	235890.i	0.147283i
$118$	1.89362e6i	1.15252i
$119$	0	0
$120$	745272.	0.431292
$121$	3.88552e6	2.19327
$122$	− 952658.i	− 0.524635i
$123$	2.73689e6	1.47076
$124$	− 1.50101e6i	− 0.787263i
$125$	1.88199e6i	0.963577i
$126$	0	0
$127$	−632211.	−0.308639	−0.154319	−	0.988021i	$-0.549319\pi$
$127$	−632211.	−0.308639	−0.154319	+	0.988021i	$0.549319\pi$
$128$	185364.	0.0883883
$129$	− 3.63375e6i	− 1.69272i
$130$	599531.	0.272886
$131$	129243.i	0.0574901i	0.999587	+	0.0287451i	$0.00915110\pi$
$131$	129243.i	0.0574901i	−0.999587	+	0.0287451i	$0.990849\pi$
$132$	− 2.42652e6i	− 1.05502i
$133$	0	0
$134$	−1.82446e6	−0.758263
$135$	1.81800e6	0.738913
$136$	477413.i	0.189792i
$137$	−1.59601e6	−0.620688	−0.310344	−	0.950624i	$-0.600444\pi$
$137$	−1.59601e6	−0.620688	−0.310344	+	0.950624i	$0.600444\pi$
$138$	− 2.05466e6i	− 0.781814i
$139$	688428.i	0.256339i	0.991752	+	0.128169i	$0.0409101\pi$
$139$	688428.i	0.256339i	−0.991752	+	0.128169i	$0.959090\pi$
$140$	0	0
$141$	1.22837e6	0.438199
$142$	1.84137e6	0.643095
$143$	− 1.95200e6i	− 0.667533i
$144$	−294323.	−0.0985682
$145$	− 4.23862e6i	− 1.39034i
$146$	− 610114.i	− 0.196044i
$147$	0	0
$148$	695217.	0.214454
$149$	633490.	0.191505	0.0957527	−	0.995405i	$-0.469474\pi$
$149$	633490.	0.191505	0.0957527	+	0.995405i	$0.469474\pi$
$150$	189634.i	0.0561879i
$151$	−2.49392e6	−0.724356	−0.362178	−	0.932109i	$-0.617967\pi$
$151$	−2.49392e6	−0.724356	−0.362178	+	0.932109i	$0.617967\pi$
$152$	− 1.00643e6i	− 0.286585i
$153$	− 758044.i	− 0.211651i
$154$	0	0
$155$	6.05741e6	1.62664
$156$	−837283.	−0.220546
$157$	− 2.57542e6i	− 0.665502i	−0.943015	−	0.332751i	$-0.892023\pi$
$157$	− 2.57542e6i	− 0.665502i	0.943015	−	0.332751i	$-0.107977\pi$
$158$	−1.91795e6	−0.486258
$159$	− 1.05976e6i	− 0.263643i
$160$	748044.i	0.182628i
$161$	0	0
$162$	−3.72425e6	−0.875979
$163$	−875715.	−0.202209	−0.101104	−	0.994876i	$-0.532238\pi$
$163$	−875715.	−0.202209	−0.101104	+	0.994876i	$0.532238\pi$
$164$	2.74707e6i	0.622786i
$165$	9.79233e6	2.17989
$166$	1.27095e6i	0.277846i
$167$	− 4.20699e6i	− 0.903280i	−0.892200	−	0.451640i	$-0.850839\pi$
$167$	− 4.20699e6i	− 0.903280i	0.892200	−	0.451640i	$-0.149161\pi$
$168$	0	0
$169$	4.15326e6	0.860457
$170$	−1.92662e6	−0.392148
$171$	1.59803e6i	0.319592i
$172$	3.64727e6	0.716774
$173$	− 3.79488e6i	− 0.732926i	−0.930433	−	0.366463i	$-0.880569\pi$
$173$	− 3.79488e6i	− 0.732926i	0.930433	−	0.366463i	$-0.119431\pi$
$174$	5.91950e6i	1.12367i
$175$	0	0
$176$	2.43554e6	0.446743
$177$	1.06723e7	1.92458
$178$	2.16788e6i	0.384393i
$179$	1.32520e6	0.231059	0.115530	−	0.993304i	$-0.463143\pi$
$179$	1.32520e6	0.231059	0.115530	+	0.993304i	$0.463143\pi$
$180$	− 1.18775e6i	− 0.203662i
$181$	4.90685e6i	0.827499i	0.910391	+	0.413749i	$0.135781\pi$
$181$	4.90685e6i	0.827499i	−0.910391	+	0.413749i	$0.864219\pi$
$182$	0	0
$183$	−5.36908e6	−0.876085
$184$	2.06230e6	0.331054
$185$	2.80558e6i	0.443106i
$186$	−8.45956e6	−1.31465
$187$	6.27286e6i	0.959270i
$188$	1.23294e6i	0.185553i
$189$	0	0
$190$	4.06150e6	0.592142
$191$	−6.30782e6	−0.905272	−0.452636	−	0.891695i	$-0.649516\pi$
$191$	−6.30782e6	−0.905272	−0.452636	+	0.891695i	$0.649516\pi$
$192$	− 1.04469e6i	− 0.147599i
$193$	874910.	0.121700	0.0608501	−	0.998147i	$-0.480619\pi$
$193$	874910.	0.121700	0.0608501	+	0.998147i	$0.480619\pi$
$194$	− 184776.i	− 0.0253070i
$195$	− 3.37889e6i	− 0.455691i
$196$	0	0
$197$	−6.85421e6	−0.896518	−0.448259	−	0.893904i	$-0.647956\pi$
$197$	−6.85421e6	−0.896518	−0.448259	+	0.893904i	$0.647956\pi$
$198$	−3.86719e6	−0.498196
$199$	− 9.52040e6i	− 1.20808i	−0.796954	−	0.604040i	$-0.793557\pi$
$199$	− 9.52040e6i	− 1.20808i	0.796954	−	0.604040i	$-0.206443\pi$
$200$	−190339.	−0.0237924
$201$	1.02825e7i	1.26622i
$202$	2.82836e6i	0.343148i
$203$	0	0
$204$	2.69065e6	0.316932
$205$	−1.10859e7	−1.28680
$206$	2.52297e6i	0.288609i
$207$	−3.27456e6	−0.369183
$208$	− 840397.i	− 0.0933888i
$209$	− 1.32238e7i	− 1.44849i
$210$	0	0
$211$	−1.02482e7	−1.09094	−0.545469	−	0.838131i	$-0.683649\pi$
$211$	−1.02482e7	−1.09094	−0.545469	+	0.838131i	$0.683649\pi$
$212$	1.06370e6	0.111638
$213$	− 1.03777e7i	− 1.07390i
$214$	−1.06885e7	−1.09062
$215$	1.47187e7i	1.48100i
$216$	− 2.54840e6i	− 0.252875i
$217$	0	0
$218$	−1.08717e7	−1.04937
$219$	−3.43854e6	−0.327372
$220$	9.82875e6i	0.923061i
$221$	2.16448e6	0.200529
$222$	− 3.91817e6i	− 0.358116i
$223$	− 1.75966e6i	− 0.158677i	−0.996848	−	0.0793385i	$-0.974719\pi$
$223$	− 1.75966e6i	− 0.158677i	0.996848	−	0.0793385i	$-0.0252808\pi$
$224$	0	0
$225$	302224.	0.0265327
$226$	−2.67275e6	−0.231544
$227$	9.75221e6i	0.833730i	0.908968	+	0.416865i	$0.136871\pi$
$227$	9.75221e6i	0.833730i	−0.908968	+	0.416865i	$0.863129\pi$
$228$	−5.67214e6	−0.478566
$229$	− 2.03025e7i	− 1.69061i	−0.534283	−	0.845306i	$-0.679418\pi$
$229$	− 2.03025e7i	− 1.69061i	0.534283	−	0.845306i	$-0.320582\pi$
$230$	8.32253e6i	0.684025i
$231$	0	0
$232$	−5.94152e6	−0.475810
$233$	−5.42907e6	−0.429198	−0.214599	−	0.976702i	$-0.568844\pi$
$233$	−5.42907e6	−0.429198	−0.214599	+	0.976702i	$0.568844\pi$
$234$	1.33439e6i	0.104145i
$235$	−4.97557e6	−0.383389
$236$	1.07120e7i	0.814953i
$237$	1.08094e7i	0.811999i
$238$	0	0
$239$	−920423.	−0.0674208	−0.0337104	−	0.999432i	$-0.510732\pi$
$239$	−920423.	−0.0674208	−0.0337104	+	0.999432i	$0.510732\pi$
$240$	4.21590e6	0.304969
$241$	2.49292e7i	1.78098i	0.455007	+	0.890488i	$0.349637\pi$
$241$	2.49292e7i	1.78098i	−0.455007	+	0.890488i	$0.650363\pi$
$242$	2.19798e7	1.55088
$243$	1.07266e7i	0.747554i
$244$	− 5.38905e6i	− 0.370973i
$245$	0	0
$246$	1.54822e7	1.03999
$247$	−4.56293e6	−0.302798
$248$	− 8.49102e6i	− 0.556679i
$249$	7.16294e6	0.463973
$250$	1.06461e7i	0.681352i
$251$	− 9.00977e6i	− 0.569761i	−0.958563	−	0.284880i	$-0.908046\pi$
$251$	− 9.00977e6i	− 0.569761i	0.958563	−	0.284880i	$-0.0919539\pi$
$252$	0	0
$253$	2.70972e7	1.67326
$254$	−3.57632e6	−0.218241
$255$	1.08582e7i	0.654846i
$256$	1.04858e6	0.0625000
$257$	1.75554e7i	1.03422i	0.855920	+	0.517109i	$0.172992\pi$
$257$	1.75554e7i	1.03422i	−0.855920	+	0.517109i	$0.827008\pi$
$258$	− 2.05556e7i	− 1.19694i
$259$	0	0
$260$	3.39146e6	0.192960
$261$	9.43402e6	0.530610
$262$	731109.i	0.0406517i
$263$	−8.04157e6	−0.442052	−0.221026	−	0.975268i	$-0.570941\pi$
$263$	−8.04157e6	−0.442052	−0.221026	+	0.975268i	$0.570941\pi$
$264$	− 1.37265e7i	− 0.746014i
$265$	4.29263e6i	0.230667i
$266$	0	0
$267$	1.22179e7	0.641895
$268$	−1.03207e7	−0.536173
$269$	− 1.63018e7i	− 0.837488i	−0.908104	−	0.418744i	$-0.862470\pi$
$269$	− 1.63018e7i	− 0.837488i	0.908104	−	0.418744i	$-0.137530\pi$
$270$	1.02842e7	0.522490
$271$	− 3.09382e7i	− 1.55449i	−0.629201	−	0.777243i	$-0.716618\pi$
$271$	− 3.09382e7i	− 1.55449i	0.629201	−	0.777243i	$-0.283382\pi$
$272$	2.70066e6i	0.134203i
$273$	0	0
$274$	−9.02839e6	−0.438893
$275$	−2.50092e6	−0.120255
$276$	− 1.16229e7i	− 0.552826i
$277$	−1.34160e7	−0.631224	−0.315612	−	0.948888i	$-0.602210\pi$
$277$	−1.34160e7	−0.631224	−0.315612	+	0.948888i	$0.602210\pi$
$278$	3.89434e6i	0.181259i
$279$	1.34822e7i	0.620793i
$280$	0	0
$281$	−1.17351e6	−0.0528895	−0.0264447	−	0.999650i	$-0.508419\pi$
$281$	−1.17351e6	−0.0528895	−0.0264447	+	0.999650i	$0.508419\pi$
$282$	6.94870e6	0.309853
$283$	2.82751e7i	1.24751i	0.781619	+	0.623756i	$0.214394\pi$
$283$	2.82751e7i	1.24751i	−0.781619	+	0.623756i	$0.785606\pi$
$284$	1.04163e7	0.454737
$285$	− 2.28902e7i	− 0.988814i
$286$	− 1.10422e7i	− 0.472017i
$287$	0	0
$288$	−1.66494e6	−0.0696983
$289$	1.71819e7	0.711832
$290$	− 2.39773e7i	− 0.983118i
$291$	−1.04138e6	−0.0422600
$292$	− 3.45133e6i	− 0.138624i
$293$	− 5.58159e6i	− 0.221899i	−0.993826	−	0.110949i	$-0.964611\pi$
$293$	− 5.58159e6i	− 0.221899i	0.993826	−	0.110949i	$-0.0353892\pi$
$294$	0	0
$295$	−4.32286e7	−1.68386
$296$	3.93274e6	0.151642
$297$	− 3.34841e7i	− 1.27811i
$298$	3.58356e6	0.135415
$299$	− 9.35002e6i	− 0.349783i
$300$	1.07273e6i	0.0397308i
$301$	0	0
$302$	−1.41078e7	−0.512197
$303$	1.59403e7	0.573020
$304$	− 5.69323e6i	− 0.202646i
$305$	2.17477e7	0.766505
$306$	− 4.28814e6i	− 0.149660i
$307$	4.40807e7i	1.52347i	0.647891	+	0.761733i	$0.275651\pi$
$307$	4.40807e7i	1.52347i	−0.647891	+	0.761733i	$0.724349\pi$
$308$	0	0
$309$	1.42192e7	0.481946
$310$	3.42659e7	1.15021
$311$	− 2.82022e7i	− 0.937566i	−0.883313	−	0.468783i	$-0.844693\pi$
$311$	− 2.82022e7i	− 0.937566i	0.883313	−	0.468783i	$-0.155307\pi$
$312$	−4.73639e6	−0.155949
$313$	− 5.92894e6i	− 0.193350i	−0.995316	−	0.0966750i	$-0.969179\pi$
$313$	− 5.92894e6i	− 0.193350i	0.995316	−	0.0966750i	$-0.0308207\pi$
$314$	− 1.45688e7i	− 0.470581i
$315$	0	0
$316$	−1.08496e7	−0.343836
$317$	4.52982e7	1.42201	0.711007	−	0.703185i	$-0.248240\pi$
$317$	4.52982e7	1.42201	0.711007	+	0.703185i	$0.248240\pi$
$318$	− 5.99492e6i	− 0.186424i
$319$	−7.80672e7	−2.40490
$320$	4.23158e6i	0.129137i
$321$	6.02390e7i	1.82122i
$322$	0	0
$323$	1.46632e7	0.435132
$324$	−2.10675e7	−0.619411
$325$	862956.i	0.0251384i
$326$	−4.95379e6	−0.142983
$327$	6.12716e7i	1.75233i
$328$	1.55398e7i	0.440376i
$329$	0	0
$330$	5.53938e7	1.54141
$331$	−6.69014e7	−1.84481	−0.922404	−	0.386227i	$-0.873778\pi$
$331$	−6.69014e7	−1.84481	−0.922404	+	0.386227i	$0.873778\pi$
$332$	7.18958e6i	0.196467i
$333$	−6.24446e6	−0.169107
$334$	− 2.37984e7i	− 0.638716i
$335$	− 4.16497e7i	− 1.10784i
$336$	0	0
$337$	−3.67215e7	−0.959469	−0.479735	−	0.877414i	$-0.659267\pi$
$337$	−3.67215e7	−0.959469	−0.479735	+	0.877414i	$0.659267\pi$
$338$	2.34944e7	0.608435
$339$	1.50634e7i	0.386654i
$340$	−1.08986e7	−0.277291
$341$	− 1.11566e8i	− 2.81364i
$342$	9.03980e6i	0.225985i
$343$	0	0
$344$	2.06321e7	0.506836
$345$	4.69049e7	1.14225
$346$	− 2.14671e7i	− 0.518257i
$347$	6.63547e7	1.58812	0.794059	−	0.607840i	$-0.207964\pi$
$347$	6.63547e7	1.58812	0.794059	+	0.607840i	$0.207964\pi$
$348$	3.34858e7i	0.794552i
$349$	9.44163e6i	0.222111i	0.993814	+	0.111056i	$0.0354232\pi$
$349$	9.44163e6i	0.222111i	−0.993814	+	0.111056i	$0.964577\pi$
$350$	0	0
$351$	−1.15539e7	−0.267181
$352$	1.37775e7	0.315895
$353$	− 1.10060e7i	− 0.250211i	−0.992143	−	0.125105i	$-0.960073\pi$
$353$	− 1.10060e7i	− 0.250211i	0.992143	−	0.125105i	$-0.0399269\pi$
$354$	6.03714e7	1.36089
$355$	4.20356e7i	0.939576i
$356$	1.22634e7i	0.271807i
$357$	0	0
$358$	7.49648e6	0.163384
$359$	−5.47275e7	−1.18283	−0.591415	−	0.806367i	$-0.701431\pi$
$359$	−5.47275e7	−1.18283	−0.591415	+	0.806367i	$0.701431\pi$
$360$	− 6.71896e6i	− 0.144011i
$361$	1.61345e7	0.342953
$362$	2.77574e7i	0.585130i
$363$	− 1.23876e8i	− 2.58980i
$364$	0	0
$365$	1.39280e7	0.286424
$366$	−3.03721e7	−0.619486
$367$	9.53851e7i	1.92967i	0.262861	+	0.964834i	$0.415334\pi$
$367$	9.53851e7i	1.92967i	−0.262861	+	0.964834i	$0.584666\pi$
$368$	1.16662e7	0.234091
$369$	− 2.46743e7i	− 0.491095i
$370$	1.58708e7i	0.313323i
$371$	0	0
$372$	−4.78545e7	−0.929595
$373$	−4.22508e7	−0.814157	−0.407078	−	0.913393i	$-0.633452\pi$
$373$	−4.22508e7	−0.814157	−0.407078	+	0.913393i	$0.633452\pi$
$374$	3.54847e7i	0.678306i
$375$	6.00004e7	1.13779
$376$	6.97455e6i	0.131206i
$377$	2.69375e7i	0.502728i
$378$	0	0
$379$	2.92437e7	0.537173	0.268587	−	0.963256i	$-0.413443\pi$
$379$	2.92437e7	0.537173	0.268587	+	0.963256i	$0.413443\pi$
$380$	2.29753e7	0.418707
$381$	2.01558e7i	0.364439i
$382$	−3.56824e7	−0.640124
$383$	2.93257e7i	0.521979i	0.965342	+	0.260989i	$0.0840487\pi$
$383$	2.93257e7i	0.521979i	−0.965342	+	0.260989i	$0.915951\pi$
$384$	− 5.90966e6i	− 0.104368i
$385$	0	0
$386$	4.94924e6	0.0860550
$387$	−3.27599e7	−0.565209
$388$	− 1.04525e6i	− 0.0178948i
$389$	−1.04066e8	−1.76791	−0.883957	−	0.467568i	$-0.845130\pi$
$389$	−1.04066e8	−1.76791	−0.883957	+	0.467568i	$0.845130\pi$
$390$	− 1.91139e7i	− 0.322222i
$391$	3.00468e7i	0.502652i
$392$	0	0
$393$	4.12045e6	0.0678840
$394$	−3.87733e7	−0.633934
$395$	− 4.37840e7i	− 0.710434i
$396$	−2.18761e7	−0.352278
$397$	7.00576e7i	1.11965i	0.828609	+	0.559827i	$0.189132\pi$
$397$	7.00576e7i	1.11965i	−0.828609	+	0.559827i	$0.810868\pi$
$398$	− 5.38555e7i	− 0.854242i
$399$	0	0
$400$	−1.07672e6	−0.0168238
$401$	7.69480e7	1.19334	0.596670	−	0.802487i	$-0.296490\pi$
$401$	7.69480e7	1.19334	0.596670	+	0.802487i	$0.296490\pi$
$402$	5.81664e7i	0.895352i
$403$	−3.84964e7	−0.588172
$404$	1.59996e7i	0.242642i
$405$	− 8.50190e7i	− 1.27983i
$406$	0	0
$407$	5.16733e7	0.766449
$408$	1.52206e7	0.224105
$409$	− 4.04869e7i	− 0.591759i	−0.955225	−	0.295880i	$-0.904387\pi$
$409$	− 4.04869e7i	− 0.591759i	0.955225	−	0.295880i	$-0.0956127\pi$
$410$	−6.27115e7	−0.909905
$411$	5.08830e7i	0.732905i
$412$	1.42721e7i	0.204077i
$413$	0	0
$414$	−1.85237e7	−0.261052
$415$	−2.90139e7	−0.405940
$416$	− 4.75401e6i	− 0.0660358i
$417$	2.19481e7	0.302683
$418$	− 7.48049e7i	− 1.02424i
$419$	5.02960e7i	0.683741i	0.939747	+	0.341870i	$0.111060\pi$
$419$	5.02960e7i	0.683741i	−0.939747	+	0.341870i	$0.888940\pi$
$420$	0	0
$421$	1.61043e6	0.0215822	0.0107911	−	0.999942i	$-0.496565\pi$
$421$	1.61043e6	0.0215822	0.0107911	+	0.999942i	$0.496565\pi$
$422$	−5.79726e7	−0.771410
$423$	− 1.10743e7i	− 0.146317i
$424$	6.01722e6	0.0789402
$425$	− 2.77315e6i	− 0.0361249i
$426$	− 5.87053e7i	− 0.759362i
$427$	0	0
$428$	−6.04631e7	−0.771186
$429$	−6.22327e7	−0.788219
$430$	8.32617e7i	1.04722i
$431$	6.90302e7	0.862199	0.431099	−	0.902304i	$-0.358126\pi$
$431$	6.90302e7	0.862199	0.431099	+	0.902304i	$0.358126\pi$
$432$	− 1.44159e7i	− 0.178810i
$433$	7.91462e7i	0.974915i	0.873147	+	0.487457i	$0.162076\pi$
$433$	7.91462e7i	0.974915i	−0.873147	+	0.487457i	$0.837924\pi$
$434$	0	0
$435$	−1.35133e8	−1.64170
$436$	−6.14995e7	−0.742014
$437$	− 6.33413e7i	− 0.759002i
$438$	−1.94513e7	−0.231487
$439$	2.41373e7i	0.285296i	0.989774	+	0.142648i	$0.0455616\pi$
$439$	2.41373e7i	0.285296i	−0.989774	+	0.142648i	$0.954438\pi$
$440$	5.55998e7i	0.652703i
$441$	0	0
$442$	1.22442e7	0.141796
$443$	4.71007e7	0.541772	0.270886	−	0.962611i	$-0.412683\pi$
$443$	4.71007e7	0.541772	0.270886	+	0.962611i	$0.412683\pi$
$444$	− 2.21645e7i	− 0.253226i
$445$	−4.94895e7	−0.561607
$446$	− 9.95413e6i	− 0.112202i
$447$	− 2.01966e7i	− 0.226128i
$448$	0	0
$449$	−4.69720e6	−0.0518920	−0.0259460	−	0.999663i	$-0.508260\pi$
$449$	−4.69720e6	−0.0518920	−0.0259460	+	0.999663i	$0.508260\pi$
$450$	1.70963e6	0.0187614
$451$	2.04182e8i	2.22580i
$452$	−1.51194e7	−0.163726
$453$	7.95098e7i	0.855315i
$454$	5.51668e7i	0.589536i
$455$	0	0
$456$	−3.20865e7	−0.338398
$457$	1.18297e8	1.23944	0.619718	−	0.784824i	$-0.287247\pi$
$457$	1.18297e8	1.23944	0.619718	+	0.784824i	$0.287247\pi$
$458$	− 1.14849e8i	− 1.19544i
$459$	3.71289e7	0.383949
$460$	4.70793e7i	0.483678i
$461$	− 1.71817e8i	− 1.75373i	−0.480733	−	0.876867i	$-0.659629\pi$
$461$	− 1.71817e8i	− 1.75373i	0.480733	−	0.876867i	$-0.340371\pi$
$462$	0	0
$463$	4.58717e7	0.462170	0.231085	−	0.972934i	$-0.425772\pi$
$463$	4.58717e7	0.462170	0.231085	+	0.972934i	$0.425772\pi$
$464$	−3.36103e7	−0.336448
$465$	− 1.93119e8i	− 1.92073i
$466$	−3.07114e7	−0.303489
$467$	1.29756e7i	0.127402i	0.997969	+	0.0637010i	$0.0202904\pi$
$467$	1.29756e7i	0.127402i	−0.997969	+	0.0637010i	$0.979710\pi$
$468$	7.54848e6i	0.0736413i
$469$	0	0
$470$	−2.81461e7	−0.271097
$471$	−8.21081e7	−0.785821
$472$	6.05960e7i	0.576259i
$473$	2.71090e8	2.56171
$474$	6.11471e7i	0.574170i
$475$	5.84605e6i	0.0545484i
$476$	0	0
$477$	−9.55422e6	−0.0880319
$478$	−5.20670e6	−0.0476737
$479$	2.30962e7i	0.210152i	0.994464	+	0.105076i	$0.0335086\pi$
$479$	2.30962e7i	0.210152i	−0.994464	+	0.105076i	$0.966491\pi$
$480$	2.38487e7	0.215646
$481$	− 1.78301e7i	− 0.160221i
$482$	1.41021e8i	1.25934i
$483$	0	0
$484$	1.24337e8	1.09664
$485$	4.21816e6	0.0369741
$486$	6.06787e7i	0.528601i
$487$	−3.34171e7	−0.289322	−0.144661	−	0.989481i	$-0.546209\pi$
$487$	−3.34171e7	−0.289322	−0.144661	+	0.989481i	$0.546209\pi$
$488$	− 3.04851e7i	− 0.262318i
$489$	2.79190e7i	0.238767i
$490$	0	0
$491$	1.96184e8	1.65737	0.828686	−	0.559714i	$-0.189089\pi$
$491$	1.96184e8	1.65737	0.828686	+	0.559714i	$0.189089\pi$
$492$	8.75806e7	0.735381
$493$	− 8.65649e7i	− 0.722439i
$494$	−2.58118e7	−0.214110
$495$	− 8.82822e7i	− 0.727876i
$496$	− 4.80325e7i	− 0.393631i
$497$	0	0
$498$	4.05197e7	0.328079
$499$	9.27394e7	0.746385	0.373192	−	0.927754i	$-0.378263\pi$
$499$	9.27394e7	0.746385	0.373192	+	0.927754i	$0.378263\pi$
$500$	6.02236e7i	0.481789i
$501$	−1.34125e8	−1.06659
$502$	− 5.09670e7i	− 0.402882i
$503$	1.26998e8i	0.997914i	0.866627	+	0.498957i	$0.166283\pi$
$503$	1.26998e8i	0.997914i	−0.866627	+	0.498957i	$0.833717\pi$
$504$	0	0
$505$	−6.45673e7	−0.501347
$506$	1.53285e8	1.18317
$507$	− 1.32412e8i	− 1.01602i
$508$	−2.02307e7	−0.154319
$509$	− 1.43688e8i	− 1.08960i	−0.838567	−	0.544799i	$-0.816606\pi$
$509$	− 1.43688e8i	− 1.08960i	0.838567	−	0.544799i	$-0.183394\pi$
$510$	6.14235e7i	0.463046i
$511$	0	0
$512$	5.93164e6	0.0441942
$513$	−7.82711e7	−0.579761
$514$	9.93085e7i	0.731303i
$515$	−5.75955e7	−0.421665
$516$	− 1.16280e8i	− 0.846362i
$517$	9.16404e7i	0.663156i
$518$	0	0
$519$	−1.20986e8	−0.865434
$520$	1.91850e7	0.136443
$521$	1.29474e8i	0.915523i	0.889075	+	0.457761i	$0.151349\pi$
$521$	1.29474e8i	0.915523i	−0.889075	+	0.457761i	$0.848651\pi$
$522$	5.33669e7	0.375198
$523$	− 2.44399e8i	− 1.70842i	−0.519928	−	0.854210i	$-0.674041\pi$
$523$	− 2.44399e8i	− 1.70842i	0.519928	−	0.854210i	$-0.325959\pi$
$524$	4.13578e6i	0.0287451i
$525$	0	0
$526$	−4.54900e7	−0.312578
$527$	1.23710e8	0.845226
$528$	− 7.76486e7i	− 0.527512i
$529$	−1.82415e7	−0.123224
$530$	2.42828e7i	0.163106i
$531$	− 9.62151e7i	− 0.642628i
$532$	0	0
$533$	7.04539e7	0.465290
$534$	6.91151e7	0.453889
$535$	− 2.44002e8i	− 1.59342i
$536$	−5.83827e7	−0.379132
$537$	− 4.22494e7i	− 0.272833i
$538$	− 9.22169e7i	− 0.592194i
$539$	0	0
$540$	5.81761e7	0.369456
$541$	−4.43418e6	−0.0280041	−0.0140020	−	0.999902i	$-0.504457\pi$
$541$	−4.43418e6	−0.0280041	−0.0140020	+	0.999902i	$0.504457\pi$
$542$	− 1.75013e8i	− 1.09919i
$543$	1.56437e8	0.977105
$544$	1.52772e7i	0.0948960i
$545$	− 2.48184e8i	− 1.53315i
$546$	0	0
$547$	−7.96292e7	−0.486531	−0.243265	−	0.969960i	$-0.578219\pi$
$547$	−7.96292e7	−0.486531	−0.243265	+	0.969960i	$0.578219\pi$
$548$	−5.10723e7	−0.310344
$549$	4.84046e7i	0.292529i
$550$	−1.41473e7	−0.0850329
$551$	1.82487e8i	1.09088i
$552$	− 6.57492e7i	− 0.390907i
$553$	0	0
$554$	−7.58924e7	−0.446343
$555$	8.94458e7	0.523216
$556$	2.20297e7i	0.128169i
$557$	2.92691e7	0.169373	0.0846865	−	0.996408i	$-0.473011\pi$
$557$	2.92691e7	0.169373	0.0846865	+	0.996408i	$0.473011\pi$
$558$	7.62666e7i	0.438967i
$559$	− 9.35411e7i	− 0.535509i
$560$	0	0
$561$	1.99988e8	1.13270
$562$	−6.63840e6	−0.0373985
$563$	− 1.87109e8i	− 1.04850i	−0.851564	−	0.524251i	$-0.824345\pi$
$563$	− 1.87109e8i	− 1.04850i	0.851564	−	0.524251i	$-0.175655\pi$
$564$	3.93078e7	0.219099
$565$	− 6.10150e7i	− 0.338291i
$566$	1.59948e8i	0.882124i
$567$	0	0
$568$	5.89237e7	0.321547
$569$	6.36799e7	0.345673	0.172837	−	0.984950i	$-0.444707\pi$
$569$	6.36799e7	0.345673	0.172837	+	0.984950i	$0.444707\pi$
$570$	− 1.29486e8i	− 0.699197i
$571$	−1.54842e8	−0.831726	−0.415863	−	0.909427i	$-0.636520\pi$
$571$	−1.54842e8	−0.831726	−0.415863	+	0.909427i	$0.636520\pi$
$572$	− 6.24642e7i	− 0.333767i
$573$	2.01102e8i	1.06894i
$574$	0	0
$575$	−1.19793e7	−0.0630127
$576$	−9.41834e6	−0.0492841
$577$	3.15507e8i	1.64241i	0.570633	+	0.821205i	$0.306698\pi$
$577$	3.15507e8i	1.64241i	−0.570633	+	0.821205i	$0.693302\pi$
$578$	9.71955e7	0.503341
$579$	− 2.78934e7i	− 0.143703i
$580$	− 1.35636e8i	− 0.695170i
$581$	0	0
$582$	−5.89093e6	−0.0298823
$583$	7.90618e7	0.398989
$584$	− 1.95237e7i	− 0.0980218i
$585$	−3.04622e7	−0.152158
$586$	− 3.15743e7i	− 0.156906i
$587$	5.57952e7i	0.275856i	0.990442	+	0.137928i	$0.0440443\pi$
$587$	5.57952e7i	0.275856i	−0.990442	+	0.137928i	$0.955956\pi$
$588$	0	0
$589$	−2.60792e8	−1.27629
$590$	−2.44538e8	−1.19067
$591$	2.18522e8i	1.05860i
$592$	2.22469e7	0.107227
$593$	2.76982e8i	1.32827i	0.747611	+	0.664137i	$0.231201\pi$
$593$	2.76982e8i	1.32827i	−0.747611	+	0.664137i	$0.768799\pi$
$594$	− 1.89415e8i	− 0.903762i
$595$	0	0
$596$	2.02717e7	0.0957527
$597$	−3.03524e8	−1.42649
$598$	− 5.28917e7i	− 0.247334i
$599$	−1.86519e8	−0.867845	−0.433923	−	0.900950i	$-0.642871\pi$
$599$	−1.86519e8	−0.867845	−0.433923	+	0.900950i	$0.642871\pi$
$600$	6.06829e6i	0.0280939i
$601$	2.43621e8i	1.12226i	0.827729	+	0.561128i	$0.189632\pi$
$601$	2.43621e8i	1.12226i	−0.827729	+	0.561128i	$0.810368\pi$
$602$	0	0
$603$	9.27009e7	0.422797
$604$	−7.98055e7	−0.362178
$605$	5.01766e8i	2.26587i
$606$	9.01722e7	0.405186
$607$	1.04114e8i	0.465523i	0.972534	+	0.232762i	$0.0747762\pi$
$607$	1.04114e8i	0.465523i	−0.972534	+	0.232762i	$0.925224\pi$
$608$	− 3.22058e7i	− 0.143292i
$609$	0	0
$610$	1.23024e8	0.542001
$611$	3.16210e7	0.138628
$612$	− 2.42574e7i	− 0.105825i
$613$	2.84295e8	1.23421	0.617103	−	0.786882i	$-0.288306\pi$
$613$	2.84295e8	1.23421	0.617103	+	0.786882i	$0.288306\pi$
$614$	2.49358e8i	1.07725i
$615$	3.53436e8i	1.51944i
$616$	0	0
$617$	−1.78930e8	−0.761776	−0.380888	−	0.924621i	$-0.624382\pi$
$617$	−1.78930e8	−0.761776	−0.380888	+	0.924621i	$0.624382\pi$
$618$	8.04358e7	0.340788
$619$	− 2.36361e8i	− 0.996562i	−0.867016	−	0.498281i	$-0.833965\pi$
$619$	− 2.36361e8i	− 0.996562i	0.867016	−	0.498281i	$-0.166035\pi$
$620$	1.93837e8	0.813321
$621$	− 1.60387e8i	− 0.669723i
$622$	− 1.59536e8i	− 0.662959i
$623$	0	0
$624$	−2.67931e7	−0.110273
$625$	−2.59464e8	−1.06277
$626$	− 3.35392e7i	− 0.136719i
$627$	−4.21593e8	−1.71037
$628$	− 8.24135e7i	− 0.332751i
$629$	5.72980e7i	0.230244i
$630$	0	0
$631$	1.51341e8	0.602378	0.301189	−	0.953564i	$-0.402616\pi$
$631$	1.51341e8	0.602378	0.301189	+	0.953564i	$0.402616\pi$
$632$	−6.13745e7	−0.243129
$633$	3.26727e8i	1.28817i
$634$	2.56246e8	1.00552
$635$	− 8.16421e7i	− 0.318855i
$636$	− 3.39124e7i	− 0.131822i
$637$	0	0
$638$	−4.41615e8	−1.70052
$639$	−9.35598e7	−0.358581
$640$	2.39374e7i	0.0913140i
$641$	−2.30663e8	−0.875798	−0.437899	−	0.899024i	$-0.644277\pi$
$641$	−2.30663e8	−0.875798	−0.437899	+	0.899024i	$0.644277\pi$
$642$	3.40763e8i	1.28780i
$643$	− 1.68539e8i	− 0.633967i	−0.948431	−	0.316983i	$-0.897330\pi$
$643$	− 1.68539e8i	− 0.633967i	0.948431	−	0.316983i	$-0.102670\pi$
$644$	0	0
$645$	4.69254e8	1.74875
$646$	8.29476e7	0.307685
$647$	1.66139e8i	0.613422i	0.951803	+	0.306711i	$0.0992285\pi$
$647$	1.66139e8i	0.613422i	−0.951803	+	0.306711i	$0.900772\pi$
$648$	−1.19176e8	−0.437990
$649$	7.96187e8i	2.91260i
$650$	4.88161e6i	0.0177756i
$651$	0	0
$652$	−2.80229e7	−0.101104
$653$	−2.37608e8	−0.853339	−0.426670	−	0.904408i	$-0.640313\pi$
$653$	−2.37608e8	−0.853339	−0.426670	+	0.904408i	$0.640313\pi$
$654$	3.46605e8i	1.23908i
$655$	−1.66901e7	−0.0593930
$656$	8.79063e7i	0.311393i
$657$	3.09999e7i	0.109311i
$658$	0	0
$659$	−3.19568e8	−1.11662	−0.558312	−	0.829631i	$-0.688551\pi$
$659$	−3.19568e8	−1.11662	−0.558312	+	0.829631i	$0.688551\pi$
$660$	3.13355e8	1.08994
$661$	− 4.23109e8i	− 1.46503i	−0.680749	−	0.732517i	$-0.738345\pi$
$661$	− 4.23109e8i	− 1.46503i	0.680749	−	0.732517i	$-0.261655\pi$
$662$	−3.78451e8	−1.30448
$663$	− 6.90068e7i	− 0.236783i
$664$	4.06704e7i	0.138923i
$665$	0	0
$666$	−3.53240e7	−0.119577
$667$	−3.73939e8	−1.26015
$668$	− 1.34624e8i	− 0.451640i
$669$	−5.61004e7	−0.187365
$670$	− 2.35606e8i	− 0.783362i
$671$	− 4.00551e8i	− 1.32584i
$672$	0	0
$673$	−2.60395e8	−0.854256	−0.427128	−	0.904191i	$-0.640475\pi$
$673$	−2.60395e8	−0.854256	−0.427128	+	0.904191i	$0.640475\pi$
$674$	−2.07728e8	−0.678447
$675$	1.48029e7i	0.0481321i
$676$	1.32904e8	0.430228
$677$	− 2.80949e8i	− 0.905445i	−0.891651	−	0.452723i	$-0.850453\pi$
$677$	− 2.80949e8i	− 0.905445i	0.891651	−	0.452723i	$-0.149547\pi$
$678$	8.52112e7i	0.273406i
$679$	0	0
$680$	−6.16520e7	−0.196074
$681$	3.10914e8	0.984463
$682$	− 6.31111e8i	− 1.98954i
$683$	2.17162e8	0.681587	0.340794	−	0.940138i	$-0.389304\pi$
$683$	2.17162e8	0.681587	0.340794	+	0.940138i	$0.389304\pi$
$684$	5.11368e7i	0.159796i
$685$	− 2.06105e8i	− 0.641233i
$686$	0	0
$687$	−6.47274e8	−1.99626
$688$	1.16713e8	0.358387
$689$	− 2.72807e7i	− 0.0834061i
$690$	2.65334e8	0.807692
$691$	− 5.22047e8i	− 1.58225i	−0.611653	−	0.791126i	$-0.709495\pi$
$691$	− 5.22047e8i	− 1.58225i	0.611653	−	0.791126i	$-0.290505\pi$
$692$	− 1.21436e8i	− 0.366463i
$693$	0	0
$694$	3.75359e8	1.12297
$695$	−8.89019e7	−0.264824
$696$	1.89424e8i	0.561833i
$697$	−2.26407e8	−0.668639
$698$	5.34099e7i	0.157056i
$699$	1.73086e8i	0.506794i
$700$	0	0
$701$	3.81338e8	1.10702	0.553511	−	0.832842i	$-0.313288\pi$
$701$	3.81338e8	1.10702	0.553511	+	0.832842i	$0.313288\pi$
$702$	−6.53585e7	−0.188925
$703$	− 1.20790e8i	− 0.347667i
$704$	7.79374e7	0.223372
$705$	1.58628e8i	0.452703i
$706$	− 6.22595e7i	− 0.176926i
$707$	0	0
$708$	3.41512e8	0.962291
$709$	2.39532e8	0.672085	0.336043	−	0.941847i	$-0.390911\pi$
$709$	2.39532e8	0.672085	0.336043	+	0.941847i	$0.390911\pi$
$710$	2.37789e8i	0.664381i
$711$	9.74513e7	0.271131
$712$	6.93722e7i	0.192196i
$713$	− 5.34396e8i	− 1.47433i
$714$	0	0
$715$	2.52077e8	0.689628
$716$	4.24065e7	0.115530
$717$	2.93444e7i	0.0796100i
$718$	−3.09586e8	−0.836387
$719$	− 4.82685e8i	− 1.29860i	−0.760531	−	0.649302i	$-0.775061\pi$
$719$	− 4.82685e8i	− 1.29860i	0.760531	−	0.649302i	$-0.224939\pi$
$720$	− 3.80082e7i	− 0.101831i
$721$	0	0
$722$	9.12706e7	0.242504
$723$	7.94780e8	2.10296
$724$	1.57019e8i	0.413749i
$725$	3.45125e7	0.0905654
$726$	− 7.00748e8i	− 1.83127i
$727$	5.49464e8i	1.43000i	0.699124	+	0.715000i	$0.253574\pi$
$727$	5.49464e8i	1.43000i	−0.699124	+	0.715000i	$0.746426\pi$
$728$	0	0
$729$	−1.37966e8	−0.356115
$730$	7.87886e7	0.202533
$731$	3.00599e8i	0.769547i
$732$	−1.71810e8	−0.438043
$733$	5.88105e8i	1.49329i	0.665225	+	0.746643i	$0.268336\pi$
$733$	5.88105e8i	1.49329i	−0.665225	+	0.746643i	$0.731664\pi$
$734$	5.39580e8i	1.36448i
$735$	0	0
$736$	6.59938e7	0.165527
$737$	−7.67106e8	−1.91625
$738$	− 1.39579e8i	− 0.347257i
$739$	7.85636e8	1.94665	0.973325	−	0.229429i	$-0.0736858\pi$
$739$	7.85636e8	1.94665	0.973325	+	0.229429i	$0.0736858\pi$
$740$	8.97785e7i	0.221553i
$741$	1.45473e8i	0.357542i
$742$	0	0
$743$	5.34716e8	1.30364	0.651819	−	0.758375i	$-0.274006\pi$
$743$	5.34716e8	1.30364	0.651819	+	0.758375i	$0.274006\pi$
$744$	−2.70706e8	−0.657323
$745$	8.18073e7i	0.197844i
$746$	−2.39006e8	−0.575696
$747$	− 6.45770e7i	− 0.154923i
$748$	2.00732e8i	0.479635i
$749$	0	0
$750$	3.39414e8	0.804536
$751$	6.73060e8	1.58904	0.794518	−	0.607240i	$-0.207723\pi$
$751$	6.73060e8	1.58904	0.794518	+	0.607240i	$0.207723\pi$
$752$	3.94540e7i	0.0927764i
$753$	−2.87244e8	−0.672770
$754$	1.52381e8i	0.355482i
$755$	− 3.22059e8i	− 0.748332i
$756$	0	0
$757$	−4.17395e8	−0.962188	−0.481094	−	0.876669i	$-0.659760\pi$
$757$	−4.17395e8	−0.962188	−0.481094	+	0.876669i	$0.659760\pi$
$758$	1.65427e8	0.379839
$759$	− 8.63897e8i	− 1.97577i
$760$	1.29968e8	0.296071
$761$	− 4.58321e8i	− 1.03996i	−0.854179	−	0.519980i	$-0.825940\pi$
$761$	− 4.58321e8i	− 1.03996i	0.854179	−	0.519980i	$-0.174060\pi$
$762$	1.14018e8i	0.257697i
$763$	0	0
$764$	−2.01850e8	−0.452636
$765$	9.78918e7	0.218656
$766$	1.65891e8i	0.369095i
$767$	2.74728e8	0.608860
$768$	− 3.34301e7i	− 0.0737996i
$769$	− 4.67013e8i	− 1.02695i	−0.858104	−	0.513475i	$-0.828358\pi$
$769$	− 4.67013e8i	− 1.02695i	0.858104	−	0.513475i	$-0.171642\pi$
$770$	0	0
$771$	5.59692e8	1.22120
$772$	2.79971e7	0.0608501
$773$	5.47247e7i	0.118480i	0.998244	+	0.0592400i	$0.0188677\pi$
$773$	5.47247e7i	0.118480i	−0.998244	+	0.0592400i	$0.981132\pi$
$774$	−1.85318e8	−0.399663
$775$	4.93218e7i	0.105958i
$776$	− 5.91284e6i	− 0.0126535i
$777$	0	0
$778$	−5.88688e8	−1.25010
$779$	4.77287e8	1.00964
$780$	− 1.08125e8i	− 0.227846i
$781$	7.74214e8	1.62520
$782$	1.69970e8i	0.355429i
$783$	4.62077e8i	0.962563i
$784$	0	0
$785$	3.32584e8	0.687530
$786$	2.33088e7	0.0480012
$787$	− 3.52741e8i	− 0.723656i	−0.932245	−	0.361828i	$-0.882153\pi$
$787$	− 3.52741e8i	− 0.723656i	0.932245	−	0.361828i	$-0.117847\pi$
$788$	−2.19335e8	−0.448259
$789$	2.56377e8i	0.521972i
$790$	− 2.47680e8i	− 0.502353i
$791$	0	0
$792$	−1.23750e8	−0.249098
$793$	−1.38212e8	−0.277158
$794$	3.96306e8i	0.791715i
$795$	1.36855e8	0.272370
$796$	− 3.04653e8i	− 0.604040i
$797$	6.57525e8i	1.29879i	0.760453	+	0.649393i	$0.224977\pi$
$797$	6.57525e8i	1.29879i	−0.760453	+	0.649393i	$0.775023\pi$
$798$	0	0
$799$	−1.01616e8	−0.199214
$800$	−6.09086e6	−0.0118962
$801$	− 1.10150e8i	− 0.214332i
$802$	4.35284e8	0.843819
$803$	− 2.56527e8i	− 0.495434i
$804$	3.29039e8i	0.633110i
$805$	0	0
$806$	−2.17768e8	−0.415901
$807$	−5.19725e8	−0.988901
$808$	9.05076e7i	0.171574i
$809$	−6.88528e8	−1.30040	−0.650198	−	0.759765i	$-0.725314\pi$
$809$	−6.88528e8	−1.30040	−0.650198	+	0.759765i	$0.725314\pi$
$810$	− 4.80940e8i	− 0.904974i
$811$	− 4.12718e8i	− 0.773732i	−0.922136	−	0.386866i	$-0.873558\pi$
$811$	− 4.12718e8i	− 0.773732i	0.922136	−	0.386866i	$-0.126442\pi$
$812$	0	0
$813$	−9.86353e8	−1.83553
$814$	2.92308e8	0.541961
$815$	− 1.13088e8i	− 0.208902i
$816$	8.61008e7	0.158466
$817$	− 6.33690e8i	− 1.16201i
$818$	− 2.29029e8i	− 0.418437i
$819$	0	0
$820$	−3.54750e8	−0.643400
$821$	−3.97678e8	−0.718624	−0.359312	−	0.933217i	$-0.616989\pi$
$821$	−3.97678e8	−0.718624	−0.359312	+	0.933217i	$0.616989\pi$
$822$	2.87838e8i	0.518242i
$823$	−2.16423e8	−0.388242	−0.194121	−	0.980978i	$-0.562186\pi$
$823$	−2.16423e8	−0.388242	−0.194121	+	0.980978i	$0.562186\pi$
$824$	8.07349e7i	0.144305i
$825$	7.97329e7i	0.141996i
$826$	0	0
$827$	4.58785e8	0.811134	0.405567	−	0.914065i	$-0.367074\pi$
$827$	4.58785e8	0.811134	0.405567	+	0.914065i	$0.367074\pi$
$828$	−1.04786e8	−0.184591
$829$	− 8.03257e8i	− 1.40991i	−0.709253	−	0.704954i	$-0.750968\pi$
$829$	− 8.03257e8i	− 1.40991i	0.709253	−	0.704954i	$-0.249032\pi$
$830$	−1.64127e8	−0.287043
$831$	4.27721e8i	0.745346i
$832$	− 2.68927e7i	− 0.0466944i
$833$	0	0
$834$	1.24157e8	0.214029
$835$	5.43281e8	0.933179
$836$	− 4.23161e8i	− 0.724246i
$837$	−6.60354e8	−1.12616
$838$	2.84517e8i	0.483478i
$839$	1.09867e9i	1.86030i	0.367185	+	0.930148i	$0.380322\pi$
$839$	1.09867e9i	1.86030i	−0.367185	+	0.930148i	$0.619678\pi$
$840$	0	0
$841$	4.82497e8	0.811160
$842$	9.10997e6	0.0152609
$843$	3.74133e7i	0.0624515i
$844$	−3.27943e8	−0.545469
$845$	5.36341e8i	0.888938i
$846$	− 6.26456e7i	− 0.103462i
$847$	0	0
$848$	3.40385e7	0.0558191
$849$	9.01450e8	1.47305
$850$	− 1.56873e7i	− 0.0255442i
$851$	2.47513e8	0.401615
$852$	− 3.32088e8i	− 0.536950i
$853$	− 8.99416e8i	− 1.44915i	−0.689196	−	0.724575i	$-0.742036\pi$
$853$	− 8.99416e8i	− 1.44915i	0.689196	−	0.724575i	$-0.257964\pi$
$854$	0	0
$855$	−2.06365e8	−0.330170
$856$	−3.42031e8	−0.545311
$857$	− 9.34161e8i	− 1.48416i	−0.670314	−	0.742078i	$-0.733840\pi$
$857$	− 9.34161e8i	− 1.48416i	0.670314	−	0.742078i	$-0.266160\pi$
$858$	−3.52041e8	−0.557355
$859$	4.50145e8i	0.710188i	0.934831	+	0.355094i	$0.115551\pi$
$859$	4.50145e8i	0.710188i	−0.934831	+	0.355094i	$0.884449\pi$
$860$	4.70999e8i	0.740499i
$861$	0	0
$862$	3.90494e8	0.609667
$863$	4.65913e8	0.724890	0.362445	−	0.932005i	$-0.381942\pi$
$863$	4.65913e8	0.724890	0.362445	+	0.932005i	$0.381942\pi$
$864$	− 8.15487e7i	− 0.126437i
$865$	4.90062e8	0.757186
$866$	4.47719e8i	0.689369i
$867$	− 5.47783e8i	− 0.840527i
$868$	0	0
$869$	−8.06416e8	−1.22885
$870$	−7.64429e8	−1.16086
$871$	2.64694e8i	0.400580i
$872$	−3.47894e8	−0.524683
$873$	9.38848e6i	0.0141108i
$874$	− 3.58313e8i	− 0.536695i
$875$	0	0
$876$	−1.10033e8	−0.163686
$877$	3.75527e8	0.556727	0.278363	−	0.960476i	$-0.410208\pi$
$877$	3.75527e8	0.556727	0.278363	+	0.960476i	$0.410208\pi$
$878$	1.36541e8i	0.201735i
$879$	−1.77949e8	−0.262017
$880$	3.14520e8i	0.461530i
$881$	− 6.74362e8i	− 0.986201i	−0.869972	−	0.493101i	$-0.835863\pi$
$881$	− 6.74362e8i	− 0.986201i	0.869972	−	0.493101i	$-0.164137\pi$
$882$	0	0
$883$	1.23657e9	1.79612	0.898061	−	0.439871i	$-0.144976\pi$
$883$	1.23657e9	1.79612	0.898061	+	0.439871i	$0.144976\pi$
$884$	6.92635e7	0.100265
$885$	1.37819e9i	1.98829i
$886$	2.66442e8	0.383091
$887$	4.79766e8i	0.687478i	0.939065	+	0.343739i	$0.111694\pi$
$887$	4.79766e8i	0.687478i	−0.939065	+	0.343739i	$0.888306\pi$
$888$	− 1.25381e8i	− 0.179058i
$889$	0	0
$890$	−2.79955e8	−0.397116
$891$	−1.56589e9	−2.21374
$892$	− 5.63091e7i	− 0.0793385i
$893$	2.14215e8	0.300812
$894$	− 1.14249e8i	− 0.159897i
$895$	1.71133e8i	0.238707i
$896$	0	0
$897$	−2.98092e8	−0.413022
$898$	−2.65714e7	−0.0366932
$899$	1.53960e9i	2.11899i
$900$	9.67115e6	0.0132663
$901$	8.76679e7i	0.119858i
$902$	1.15503e9i	1.57388i
$903$	0	0
$904$	−8.55281e7	−0.115772
$905$	−6.33659e8	−0.854889
$906$	4.49775e8i	0.604799i
$907$	−4.32323e6	−0.00579411	−0.00289705	−	0.999996i	$-0.500922\pi$
$907$	−4.32323e6	−0.00579411	−0.00289705	+	0.999996i	$0.500922\pi$
$908$	3.12071e8i	0.416865i
$909$	− 1.43709e8i	− 0.191334i
$910$	0	0
$911$	−4.54738e8	−0.601459	−0.300730	−	0.953709i	$-0.597230\pi$
$911$	−4.54738e8	−0.601459	−0.300730	+	0.953709i	$0.597230\pi$
$912$	−1.81508e8	−0.239283
$913$	5.34379e8i	0.702162i
$914$	6.69188e8	0.876414
$915$	− 6.93349e8i	− 0.905084i
$916$	− 6.49681e8i	− 0.845306i
$917$	0	0
$918$	2.10033e8	0.271493
$919$	−6.17813e8	−0.795996	−0.397998	−	0.917386i	$-0.630295\pi$
$919$	−6.17813e8	−0.795996	−0.397998	+	0.917386i	$0.630295\pi$
$920$	2.66321e8i	0.342012i
$921$	1.40535e9	1.79890
$922$	− 9.71945e8i	− 1.24008i
$923$	− 2.67147e8i	− 0.339738i
$924$	0	0
$925$	−2.28441e7	−0.0288635
$926$	2.59489e8	0.326803
$927$	− 1.28192e8i	− 0.160924i
$928$	−1.90129e8	−0.237905
$929$	− 7.02942e8i	− 0.876743i	−0.898794	−	0.438371i	$-0.855555\pi$
$929$	− 7.02942e8i	− 0.876743i	0.898794	−	0.438371i	$-0.144445\pi$
$930$	− 1.09245e9i	− 1.35816i
$931$	0	0
$932$	−1.73730e8	−0.214599
$933$	−8.99126e8	−1.10707
$934$	7.34009e7i	0.0900867i
$935$	−8.10062e8	−0.991022
$936$	4.27006e7i	0.0520723i
$937$	2.35920e8i	0.286779i	0.989666	+	0.143389i	$0.0458001\pi$
$937$	2.35920e8i	0.286779i	−0.989666	+	0.143389i	$0.954200\pi$
$938$	0	0
$939$	−1.89023e8	−0.228306
$940$	−1.59218e8	−0.191694
$941$	3.68227e8i	0.441923i	0.975282	+	0.220962i	$0.0709196\pi$
$941$	3.68227e8i	0.441923i	−0.975282	+	0.220962i	$0.929080\pi$
$942$	−4.64474e8	−0.555659
$943$	9.78021e8i	1.16631i
$944$	3.42783e8i	0.407477i
$945$	0	0
$946$	1.53352e9	1.81140
$947$	6.03662e8	0.710794	0.355397	−	0.934715i	$-0.384346\pi$
$947$	6.03662e8	0.710794	0.355397	+	0.934715i	$0.384346\pi$
$948$	3.45900e8i	0.406000i
$949$	−8.85158e7	−0.103567
$950$	3.30703e7i	0.0385715i
$951$	− 1.44417e9i	− 1.67910i
$952$	0	0
$953$	2.87119e8	0.331729	0.165864	−	0.986149i	$-0.446959\pi$
$953$	2.87119e8	0.331729	0.165864	+	0.986149i	$0.446959\pi$
$954$	−5.40468e7	−0.0622480
$955$	− 8.14576e8i	− 0.935236i
$956$	−2.94535e7	−0.0337104
$957$	2.48889e9i	2.83969i
$958$	1.30652e8i	0.148600i
$959$	0	0
$960$	1.34909e8	0.152485
$961$	−1.31273e9	−1.47913
$962$	− 1.00863e8i	− 0.113293i
$963$	5.43081e8	0.608115
$964$	7.97736e8i	0.890488i
$965$	1.12984e8i	0.125728i
$966$	0	0
$967$	−7.68357e8	−0.849735	−0.424868	−	0.905256i	$-0.639679\pi$
$967$	−7.68357e8	−0.849735	−0.424868	+	0.905256i	$0.639679\pi$
$968$	7.03354e8	0.775440
$969$	− 4.67484e8i	− 0.513801i
$970$	2.38615e7	0.0261447
$971$	− 8.26140e8i	− 0.902394i	−0.892424	−	0.451197i	$-0.850997\pi$
$971$	− 8.26140e8i	− 0.902394i	0.892424	−	0.451197i	$-0.149003\pi$
$972$	3.43251e8i	0.373777i
$973$	0	0
$974$	−1.89036e8	−0.204582
$975$	2.75123e7	0.0296833
$976$	− 1.72450e8i	− 0.185487i
$977$	−8.35715e8	−0.896137	−0.448068	−	0.893999i	$-0.647888\pi$
$977$	−8.35715e8	−0.896137	−0.448068	+	0.893999i	$0.647888\pi$
$978$	1.57934e8i	0.168834i
$979$	9.11500e8i	0.971423i
$980$	0	0
$981$	5.52390e8	0.585112
$982$	1.10979e9	1.17194
$983$	− 2.20836e8i	− 0.232493i	−0.993220	−	0.116247i	$-0.962914\pi$
$983$	− 2.20836e8i	− 0.232493i	0.993220	−	0.116247i	$-0.0370863\pi$
$984$	4.95431e8	0.519993
$985$	− 8.85136e8i	− 0.926192i
$986$	− 4.89685e8i	− 0.510842i
$987$	0	0
$988$	−1.46014e8	−0.151399
$989$	1.29851e9	1.34232
$990$	− 4.99399e8i	− 0.514686i
$991$	−7.28293e8	−0.748317	−0.374158	−	0.927365i	$-0.622068\pi$
$991$	−7.28293e8	−0.748317	−0.374158	+	0.927365i	$0.622068\pi$
$992$	− 2.71713e8i	− 0.278339i
$993$	2.13291e9i	2.17834i
$994$	0	0
$995$	1.22944e9	1.24807
$996$	2.29214e8	0.231987
$997$	1.69809e8i	0.171347i	0.996323	+	0.0856735i	$0.0273042\pi$
$997$	1.69809e8i	0.171347i	−0.996323	+	0.0856735i	$0.972696\pi$
$998$	5.24613e8	0.527774
$999$	− 3.05853e8i	− 0.306772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.7.b.c.97.5		8
7.2	even	3		14.7.d.a.3.2	✓	8
7.3	odd	6		14.7.d.a.5.2	yes	8
7.4	even	3		98.7.d.c.19.1		8
7.5	odd	6		98.7.d.c.31.1		8
7.6	odd	2	inner	98.7.b.c.97.8		8
21.2	odd	6		126.7.n.c.73.3		8
21.17	even	6		126.7.n.c.19.3		8
28.3	even	6		112.7.s.c.33.1		8
28.23	odd	6		112.7.s.c.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.d.a.3.2	✓	8	7.2	even	3
14.7.d.a.5.2	yes	8	7.3	odd	6
98.7.b.c.97.5		8	1.1	even	1	trivial
98.7.b.c.97.8		8	7.6	odd	2	inner
98.7.d.c.19.1		8	7.4	even	3
98.7.d.c.31.1		8	7.5	odd	6
112.7.s.c.17.1		8	28.23	odd	6
112.7.s.c.33.1		8	28.3	even	6
126.7.n.c.19.3		8	21.17	even	6
126.7.n.c.73.3		8	21.2	odd	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685 q^{2} -31.8814i q^{3} +32.0000 q^{4} +129.137i q^{5} -180.349i q^{6} +181.019 q^{8} -287.425 q^{9} +730.512i q^{10} +2378.46 q^{11} -1020.21i q^{12} -820.701i q^{13} +4117.09 q^{15} +1024.00 q^{16} +2637.36i q^{17} -1625.92 q^{18} -5559.80i q^{19} +4132.40i q^{20} +13454.6 q^{22} +11392.7 q^{23} -5771.15i q^{24} -1051.49 q^{25} -4642.58i q^{26} -14078.0i q^{27} -32822.6 q^{29} +23289.8 q^{30} -46906.7i q^{31} +5792.62 q^{32} -75828.7i q^{33} +14919.2i q^{34} -9197.60 q^{36} +21725.5 q^{37} -31451.0i q^{38} -26165.1 q^{39} +23376.4i q^{40} +85846.0i q^{41} +113977. q^{43} +76110.8 q^{44} -37117.3i q^{45} +64447.0 q^{46} +38529.3i q^{47} -32646.6i q^{48} -5948.11 q^{50} +84082.8 q^{51} -26262.4i q^{52} +33240.7 q^{53} -79637.4i q^{54} +307149. i q^{55} -177254. q^{57} -185672. q^{58} +334749. i q^{59} +131747. q^{60} -168408. i q^{61} -265344. i q^{62} +32768.0 q^{64} +105983. q^{65} -428952. i q^{66} -322522. q^{67} +84395.6i q^{68} -363217. i q^{69} +325510. q^{71} -52029.5 q^{72} -107854. i q^{73} +122898. q^{74} +33522.9i q^{75} -177914. i q^{76} -148012. q^{78} -339049. q^{79} +132237. i q^{80} -658361. q^{81} +485619. i q^{82} +224674. i q^{83} -340582. q^{85} +644752. q^{86} +1.04643e6i q^{87} +430548. q^{88} +383231. i q^{89} -209967. i q^{90} +364567. q^{92} -1.49545e6 q^{93} +217955. i q^{94} +717978. q^{95} -184677. i q^{96} -32664.1i q^{97} -683629. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{4} - 1512 q^{9} + 2712 q^{11} + 27144 q^{15} + 8192 q^{16} + 13632 q^{18} + 25248 q^{22} + 8256 q^{23} - 9328 q^{25} - 30312 q^{29} - 19296 q^{30} - 48384 q^{36} + 12248 q^{37} - 201528 q^{39}+ \cdots - 4625928 q^{99}+O(q^{100}) \) 8 * q + 256 * q^4 - 1512 * q^9 + 2712 * q^11 + 27144 * q^15 + 8192 * q^16 + 13632 * q^18 + 25248 * q^22 + 8256 * q^23 - 9328 * q^25 - 30312 * q^29 - 19296 * q^30 - 48384 * q^36 + 12248 * q^37 - 201528 * q^39 - 297376 * q^43 + 86784 * q^44 + 388128 * q^46 + 38784 * q^50 - 507384 * q^51 - 556968 * q^53 - 81288 * q^57 + 339648 * q^58 + 868608 * q^60 + 262144 * q^64 - 16632 * q^65 - 1297616 * q^67 + 190128 * q^71 + 436224 * q^72 + 2316288 * q^74 + 1122432 * q^78 - 140192 * q^79 - 2355840 * q^81 + 2190984 * q^85 + 1146048 * q^86 + 807936 * q^88 + 264192 * q^92 + 46728 * q^93 - 1451280 * q^95 - 4625928 * q^99

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