LMFDB - Embedded newform 98.15.b.c.97.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,15,Mod(97,98)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 15, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("98.97");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	98.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$121.842388789$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 65377122 x^{18} + \cdots + 55\!\cdots\!49 $ x^20 + 65377122x^18 + 1728832748767749x^16 + 23810004943987610752056x^14 + 184418085197043208636812761058x^12 + 821964230502026355382326768943559820x^10 + 2125212532386037161241520317573728788598450x^8 + 3120809352393783148047491941315355328441271841976x^6 + 2412583857914041729327770795122234431586294662017094365x^4 + 803880893410315142413979711089208500588142205522155883552546*x^2 + 55719138214665583379490595116442427075365693161320947770202688649
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{86}\cdot 3^{12}\cdot 7^{44} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			97.6
Root			$302.931i$ of defining polynomial
Character	$\chi$	$=$	98.97
Dual form			98.15.b.c.97.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-90.5097 q^{2} +302.931i q^{3} +8192.00 q^{4} +122619. i q^{5} -27418.1i q^{6} -741455. q^{8} +4.69120e6 q^{9} +O(q^{10})$	\(q-90.5097 q^{2} +302.931i q^{3} +8192.00 q^{4} +122619. i q^{5} -27418.1i q^{6} -741455. q^{8} +4.69120e6 q^{9} -1.10982e7i q^{10} -1.99797e7 q^{11} +2.48161e6i q^{12} -4.33468e7i q^{13} -3.71452e7 q^{15} +6.71089e7 q^{16} -5.18108e8i q^{17} -4.24599e8 q^{18} +9.74783e8i q^{19} +1.00450e9i q^{20} +1.80835e9 q^{22} +2.56578e9 q^{23} -2.24609e8i q^{24} -8.93201e9 q^{25} +3.92330e9i q^{26} +2.87002e9i q^{27} +3.33710e10 q^{29} +3.36200e9 q^{30} +4.56043e10i q^{31} -6.07400e9 q^{32} -6.05246e9i q^{33} +4.68938e10i q^{34} +3.84303e10 q^{36} +8.11009e10 q^{37} -8.82273e10i q^{38} +1.31311e10 q^{39} -9.09168e10i q^{40} +2.23592e11i q^{41} -3.64930e11 q^{43} -1.63674e11 q^{44} +5.75232e11i q^{45} -2.32228e11 q^{46} -4.09612e10i q^{47} +2.03293e10i q^{48} +8.08433e11 q^{50} +1.56951e11 q^{51} -3.55097e11i q^{52} +8.00859e11 q^{53} -2.59764e11i q^{54} -2.44990e12i q^{55} -2.95292e11 q^{57} -3.02040e12 q^{58} -1.00781e12i q^{59} -3.04293e11 q^{60} +1.35932e12i q^{61} -4.12763e12i q^{62} +5.49756e11 q^{64} +5.31516e12 q^{65} +5.47806e11i q^{66} +4.86524e12 q^{67} -4.24434e12i q^{68} +7.77254e11i q^{69} +4.67641e12 q^{71} -3.47832e12 q^{72} +5.46449e12i q^{73} -7.34042e12 q^{74} -2.70578e12i q^{75} +7.98543e12i q^{76} -1.18849e12 q^{78} +2.85798e12 q^{79} +8.22885e12i q^{80} +2.15685e13 q^{81} -2.02373e13i q^{82} +5.45017e12i q^{83} +6.35301e13 q^{85} +3.30297e13 q^{86} +1.01091e13i q^{87} +1.48140e13 q^{88} +3.76330e13i q^{89} -5.20641e13i q^{90} +2.10189e13 q^{92} -1.38149e13 q^{93} +3.70738e12i q^{94} -1.19527e14 q^{95} -1.84000e12i q^{96} -1.14678e14i q^{97} -9.37287e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 163840 q^{4} - 35094864 q^{9}+O(q^{10}) $ 20 * q + 163840 * q^4 - 35094864 * q^9	$ 20 q + 163840 q^{4} - 35094864 q^{9} - 16800852 q^{11} + 562720524 q^{15} + 1342177280 q^{16} + 503510016 q^{18} + 5394565632 q^{22} + 13810196772 q^{23} - 28330165288 q^{25} + 27884908704 q^{29} - 108207023616 q^{30} - 287497125888 q^{36} + 54052055852 q^{37} + 252250808760 q^{39} + 726682953656 q^{43} - 137632579584 q^{44} + 573329969664 q^{46} + 1161106642944 q^{50} + 4839219891204 q^{51} - 3092542975092 q^{53} + 14789884876092 q^{57} + 4731726081024 q^{58} + 4609806532608 q^{60} + 10995116277760 q^{64} - 15033407865672 q^{65} + 9311641526452 q^{67} + 96606137494152 q^{71} + 4124754051072 q^{72} + 1133064966144 q^{74} + 88663911671808 q^{78} + 121034948165956 q^{79} + 214360529022684 q^{81} + 416326699526124 q^{85} - 4726670349312 q^{86} + 44192281657344 q^{88} + 113133131956224 q^{92} + 188350136380260 q^{93} - 50405029030980 q^{95} + 10\!\cdots\!68 q^{99}+O(q^{100}) $ 20 * q + 163840 * q^4 - 35094864 * q^9 - 16800852 * q^11 + 562720524 * q^15 + 1342177280 * q^16 + 503510016 * q^18 + 5394565632 * q^22 + 13810196772 * q^23 - 28330165288 * q^25 + 27884908704 * q^29 - 108207023616 * q^30 - 287497125888 * q^36 + 54052055852 * q^37 + 252250808760 * q^39 + 726682953656 * q^43 - 137632579584 * q^44 + 573329969664 * q^46 + 1161106642944 * q^50 + 4839219891204 * q^51 - 3092542975092 * q^53 + 14789884876092 * q^57 + 4731726081024 * q^58 + 4609806532608 * q^60 + 10995116277760 * q^64 - 15033407865672 * q^65 + 9311641526452 * q^67 + 96606137494152 * q^71 + 4124754051072 * q^72 + 1133064966144 * q^74 + 88663911671808 * q^78 + 121034948165956 * q^79 + 214360529022684 * q^81 + 416326699526124 * q^85 - 4726670349312 * q^86 + 44192281657344 * q^88 + 113133131956224 * q^92 + 188350136380260 * q^93 - 50405029030980 * q^95 + 1056686373672768 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−90.5097	−0.707107
$2$	−90.5097	−0.707107
$3$	302.931i	0.138514i	0.997599	+	0.0692571i	$0.0220629\pi$
$3$	302.931i	0.138514i	−0.997599	+	0.0692571i	$0.977937\pi$
$4$	8192.00	0.500000
$5$	122619.i	1.56953i	0.619794	+	0.784764i	$0.287216\pi$
$5$	122619.i	1.56953i	−0.619794	+	0.784764i	$0.712784\pi$
$6$	− 27418.1i	− 0.0979443i
$7$	0	0
$7$	0	0
$8$	−741455.	−0.353553
$9$	4.69120e6	0.980814
$10$	− 1.10982e7i	− 1.10982i
$11$	−1.99797e7	−1.02527	−0.512637	−	0.858606i	$-0.671331\pi$
$11$	−1.99797e7	−1.02527	−0.512637	+	0.858606i	$0.671331\pi$
$12$	2.48161e6i	0.0692571i
$13$	− 4.33468e7i	− 0.690801i	−0.938455	−	0.345401i	$-0.887743\pi$
$13$	− 4.33468e7i	− 0.690801i	0.938455	−	0.345401i	$-0.112257\pi$
$14$	0	0
$15$	−3.71452e7	−0.217402
$16$	6.71089e7	0.250000
$17$	− 5.18108e8i	− 1.26263i	−0.775525	−	0.631317i	$-0.782515\pi$
$17$	− 5.18108e8i	− 1.26263i	0.775525	−	0.631317i	$-0.217485\pi$
$18$	−4.24599e8	−0.693540
$19$	9.74783e8i	1.09052i	0.838268	+	0.545259i	$0.183569\pi$
$19$	9.74783e8i	1.09052i	−0.838268	+	0.545259i	$0.816431\pi$
$20$	1.00450e9i	0.784764i
$21$	0	0
$22$	1.80835e9	0.724978
$23$	2.56578e9	0.753573	0.376786	−	0.926300i	$-0.377029\pi$
$23$	2.56578e9	0.753573	0.376786	+	0.926300i	$0.377029\pi$
$24$	− 2.24609e8i	− 0.0489722i
$25$	−8.93201e9	−1.46342
$26$	3.92330e9i	0.488470i
$27$	2.87002e9i	0.274371i
$28$	0	0
$29$	3.33710e10	1.93457	0.967283	−	0.253700i	$-0.0816476\pi$
$29$	3.33710e10	1.93457	0.967283	+	0.253700i	$0.0816476\pi$
$30$	3.36200e9	0.153726
$31$	4.56043e10i	1.65758i	0.559562	+	0.828788i	$0.310969\pi$
$31$	4.56043e10i	1.65758i	−0.559562	+	0.828788i	$0.689031\pi$
$32$	−6.07400e9	−0.176777
$33$	− 6.05246e9i	− 0.142015i
$34$	4.68938e10i	0.892817i
$35$	0	0
$36$	3.84303e10	0.490407
$37$	8.11009e10	0.854306	0.427153	−	0.904179i	$-0.359516\pi$
$37$	8.11009e10	0.854306	0.427153	+	0.904179i	$0.359516\pi$
$38$	− 8.82273e10i	− 0.771113i
$39$	1.31311e10	0.0956858
$40$	− 9.09168e10i	− 0.554912i
$41$	2.23592e11i	1.14807i	0.818830	+	0.574037i	$0.194623\pi$
$41$	2.23592e11i	1.14807i	−0.818830	+	0.574037i	$0.805377\pi$
$42$	0	0
$43$	−3.64930e11	−1.34255	−0.671275	−	0.741208i	$-0.734253\pi$
$43$	−3.64930e11	−1.34255	−0.671275	+	0.741208i	$0.734253\pi$
$44$	−1.63674e11	−0.512637
$45$	5.75232e11i	1.53942i
$46$	−2.32228e11	−0.532856
$47$	− 4.09612e10i	− 0.0808514i	−0.999183	−	0.0404257i	$-0.987129\pi$
$47$	− 4.09612e10i	− 0.0808514i	0.999183	−	0.0404257i	$-0.0128714\pi$
$48$	2.03293e10i	0.0346285i
$49$	0	0
$50$	8.08433e11	1.03479
$51$	1.56951e11	0.174893
$52$	− 3.55097e11i	− 0.345401i
$53$	8.00859e11	0.681750	0.340875	−	0.940109i	$-0.389277\pi$
$53$	8.00859e11	0.681750	0.340875	+	0.940109i	$0.389277\pi$
$54$	− 2.59764e11i	− 0.194009i
$55$	− 2.44990e12i	− 1.60920i
$56$	0	0
$57$	−2.95292e11	−0.151052
$58$	−3.02040e12	−1.36794
$59$	− 1.00781e12i	− 0.404963i	−0.979286	−	0.202481i	$-0.935099\pi$
$59$	− 1.00781e12i	− 0.404963i	0.979286	−	0.202481i	$-0.0649006\pi$
$60$	−3.04293e11	−0.108701
$61$	1.35932e12i	0.432527i	0.976335	+	0.216263i	$0.0693870\pi$
$61$	1.35932e12i	0.432527i	−0.976335	+	0.216263i	$0.930613\pi$
$62$	− 4.12763e12i	− 1.17208i
$63$	0	0
$64$	5.49756e11	0.125000
$65$	5.31516e12	1.08423
$66$	5.47806e11i	0.100420i
$67$	4.86524e12	0.802750	0.401375	−	0.915914i	$-0.368532\pi$
$67$	4.86524e12	0.802750	0.401375	+	0.915914i	$0.368532\pi$
$68$	− 4.24434e12i	− 0.631317i
$69$	7.77254e11i	0.104381i
$70$	0	0
$71$	4.67641e12	0.514167	0.257083	−	0.966389i	$-0.417238\pi$
$71$	4.67641e12	0.514167	0.257083	+	0.966389i	$0.417238\pi$
$72$	−3.47832e12	−0.346770
$73$	5.46449e12i	0.494640i	0.968934	+	0.247320i	$0.0795499\pi$
$73$	5.46449e12i	0.494640i	−0.968934	+	0.247320i	$0.920450\pi$
$74$	−7.34042e12	−0.604086
$75$	− 2.70578e12i	− 0.202704i
$76$	7.98543e12i	0.545259i
$77$	0	0
$78$	−1.18849e12	−0.0676601
$79$	2.85798e12	0.148823	0.0744113	−	0.997228i	$-0.476292\pi$
$79$	2.85798e12	0.148823	0.0744113	+	0.997228i	$0.476292\pi$
$80$	8.22885e12i	0.392382i
$81$	2.15685e13	0.942810
$82$	− 2.02373e13i	− 0.811811i
$83$	5.45017e12i	0.200846i	0.994945	+	0.100423i	$0.0320196\pi$
$83$	5.45017e12i	0.200846i	−0.994945	+	0.100423i	$0.967980\pi$
$84$	0	0
$85$	6.35301e13	1.98174
$86$	3.30297e13	0.949326
$87$	1.01091e13i	0.267965i
$88$	1.48140e13	0.362489
$89$	3.76330e13i	0.850823i	0.905000	+	0.425412i	$0.139871\pi$
$89$	3.76330e13i	0.850823i	−0.905000	+	0.425412i	$0.860129\pi$
$90$	− 5.20641e13i	− 1.08853i
$91$	0	0
$92$	2.10189e13	0.376786
$93$	−1.38149e13	−0.229598
$94$	3.70738e12i	0.0571706i
$95$	−1.19527e14	−1.71160
$96$	− 1.84000e12i	− 0.0244861i
$97$	− 1.14678e14i	− 1.41932i	−0.704547	−	0.709658i	$-0.748850\pi$
$97$	− 1.14678e14i	− 1.41932i	0.704547	−	0.709658i	$-0.251150\pi$
$98$	0	0
$99$	−9.37287e13	−1.00560
$100$	−7.31710e13	−0.731710
$101$	1.32157e13i	0.123265i	0.998099	+	0.0616324i	$0.0196306\pi$
$101$	1.32157e13i	0.123265i	−0.998099	+	0.0616324i	$0.980369\pi$
$102$	−1.42056e13	−0.123668
$103$	− 1.00928e14i	− 0.820639i	−0.911942	−	0.410320i	$-0.865417\pi$
$103$	− 1.00928e14i	− 0.820639i	0.911942	−	0.410320i	$-0.134583\pi$
$104$	3.21397e13i	0.244235i
$105$	0	0
$106$	−7.24855e13	−0.482070
$107$	−2.35851e14	−1.46876	−0.734382	−	0.678737i	$-0.762528\pi$
$107$	−2.35851e14	−1.46876	−0.734382	+	0.678737i	$0.762528\pi$
$108$	2.35112e13i	0.137185i
$109$	1.21153e14	0.662751	0.331375	−	0.943499i	$-0.392487\pi$
$109$	1.21153e14	0.662751	0.331375	+	0.943499i	$0.392487\pi$
$110$	2.21739e14i	1.13787i
$111$	2.45679e13i	0.118334i
$112$	0	0
$113$	−1.34624e14	−0.572235	−0.286117	−	0.958195i	$-0.592365\pi$
$113$	−1.34624e14	−0.572235	−0.286117	+	0.958195i	$0.592365\pi$
$114$	2.67268e13	0.106810
$115$	3.14615e14i	1.18275i
$116$	2.73375e14	0.967283
$117$	− 2.03348e14i	− 0.677548i
$118$	9.12167e13i	0.286352i
$119$	0	0
$120$	2.75415e13	0.0768632
$121$	1.94378e13	0.0511859
$122$	− 1.23032e14i	− 0.305843i
$123$	−6.77329e13	−0.159024
$124$	3.73590e14i	0.828788i
$125$	− 3.46828e14i	− 0.727351i
$126$	0	0
$127$	3.44488e14	0.646470	0.323235	−	0.946319i	$-0.395230\pi$
$127$	3.44488e14	0.646470	0.323235	+	0.946319i	$0.395230\pi$
$128$	−4.97582e13	−0.0883883
$129$	− 1.10548e14i	− 0.185962i
$130$	−4.81073e14	−0.766668
$131$	9.57758e14i	1.44663i	0.690520	+	0.723314i	$0.257382\pi$
$131$	9.57758e14i	1.44663i	−0.690520	+	0.723314i	$0.742618\pi$
$132$	− 4.95817e13i	− 0.0710075i
$133$	0	0
$134$	−4.40351e14	−0.567630
$135$	−3.51920e14	−0.430633
$136$	3.84154e14i	0.446409i
$137$	−1.13915e15	−1.25759	−0.628794	−	0.777572i	$-0.716451\pi$
$137$	−1.13915e15	−1.25759	−0.628794	+	0.777572i	$0.716451\pi$
$138$	− 7.03490e13i	− 0.0738082i
$139$	1.74371e15i	1.73928i	0.493686	+	0.869640i	$0.335649\pi$
$139$	1.74371e15i	1.73928i	−0.493686	+	0.869640i	$0.664351\pi$
$140$	0	0
$141$	1.24084e13	0.0111991
$142$	−4.23260e14	−0.363571
$143$	8.66055e14i	0.708260i
$144$	3.14821e14	0.245203
$145$	4.09194e15i	3.03636i
$146$	− 4.94589e14i	− 0.349763i
$147$	0	0
$148$	6.64379e14	0.427153
$149$	−2.86456e15	−1.75693	−0.878465	−	0.477808i	$-0.841432\pi$
$149$	−2.86456e15	−1.75693	−0.878465	+	0.477808i	$0.841432\pi$
$150$	2.44899e14i	0.143334i
$151$	9.76112e14	0.545332	0.272666	−	0.962109i	$-0.412095\pi$
$151$	9.76112e14	0.545332	0.272666	+	0.962109i	$0.412095\pi$
$152$	− 7.22758e14i	− 0.385556i
$153$	− 2.43055e15i	− 1.23841i
$154$	0	0
$155$	−5.59197e15	−2.60161
$156$	1.07570e14	0.0478429
$157$	6.04759e14i	0.257208i	0.991696	+	0.128604i	$0.0410496\pi$
$157$	6.04759e14i	0.257208i	−0.991696	+	0.128604i	$0.958950\pi$
$158$	−2.58674e14	−0.105233
$159$	2.42605e14i	0.0944320i
$160$	− 7.44790e14i	− 0.277456i
$161$	0	0
$162$	−1.95215e15	−0.666667
$163$	−3.31804e15	−1.08535	−0.542674	−	0.839944i	$-0.682588\pi$
$163$	−3.31804e15	−1.08535	−0.542674	+	0.839944i	$0.682588\pi$
$164$	1.83167e15i	0.574037i
$165$	7.42149e14	0.222896
$166$	− 4.93293e14i	− 0.142020i
$167$	7.57679e14i	0.209156i	0.994517	+	0.104578i	$0.0333492\pi$
$167$	7.57679e14i	0.209156i	−0.994517	+	0.104578i	$0.966651\pi$
$168$	0	0
$169$	2.05843e15	0.522793
$170$	−5.75009e15	−1.40130
$171$	4.57291e15i	1.06960i
$172$	−2.98951e15	−0.671275
$173$	− 1.31558e14i	− 0.0283659i	−0.999899	−	0.0141829i	$-0.995485\pi$
$173$	− 1.31558e14i	− 0.0283659i	0.999899	−	0.0141829i	$-0.00451472\pi$
$174$	− 9.14971e14i	− 0.189480i
$175$	0	0
$176$	−1.34081e15	−0.256318
$177$	3.05297e14	0.0560931
$178$	− 3.40615e15i	− 0.601623i
$179$	−2.38633e15	−0.405284	−0.202642	−	0.979253i	$-0.564953\pi$
$179$	−2.38633e15	−0.405284	−0.202642	+	0.979253i	$0.564953\pi$
$180$	4.71230e15i	0.769708i
$181$	− 6.33443e15i	− 0.995308i	−0.867376	−	0.497654i	$-0.834195\pi$
$181$	− 6.33443e15i	− 0.995308i	0.867376	−	0.497654i	$-0.165805\pi$
$182$	0	0
$183$	−4.11780e14	−0.0599111
$184$	−1.90241e15	−0.266428
$185$	9.94455e15i	1.34086i
$186$	1.25038e15	0.162350
$187$	1.03516e16i	1.29455i
$188$	− 3.35554e14i	− 0.0404257i
$189$	0	0
$190$	1.08184e16	1.21028
$191$	2.23433e15	0.240943	0.120471	−	0.992717i	$-0.461559\pi$
$191$	2.23433e15	0.240943	0.120471	+	0.992717i	$0.461559\pi$
$192$	1.66538e14i	0.0173143i
$193$	−1.03792e16	−1.04055	−0.520273	−	0.854000i	$-0.674170\pi$
$193$	−1.03792e16	−1.04055	−0.520273	+	0.854000i	$0.674170\pi$
$194$	1.03795e16i	1.00361i
$195$	1.61012e15i	0.150182i
$196$	0	0
$197$	7.07208e15	0.614163	0.307082	−	0.951683i	$-0.400648\pi$
$197$	7.07208e15	0.614163	0.307082	+	0.951683i	$0.400648\pi$
$198$	8.48336e15	0.711068
$199$	3.11527e15i	0.252072i	0.992026	+	0.126036i	$0.0402254\pi$
$199$	3.11527e15i	0.252072i	−0.992026	+	0.126036i	$0.959775\pi$
$200$	6.62268e15	0.517397
$201$	1.47383e15i	0.111192i
$202$	− 1.19614e15i	− 0.0871614i
$203$	0	0
$204$	1.28574e15	0.0874464
$205$	−2.74167e16	−1.80193
$206$	9.13498e15i	0.580279i
$207$	1.20366e16	0.739115
$208$	− 2.90895e15i	− 0.172700i
$209$	− 1.94759e16i	− 1.11808i
$210$	0	0
$211$	6.76121e15	0.363117	0.181559	−	0.983380i	$-0.441886\pi$
$211$	6.76121e15	0.363117	0.181559	+	0.983380i	$0.441886\pi$
$212$	6.56064e15	0.340875
$213$	1.41663e15i	0.0712194i
$214$	2.13468e16	1.03857
$215$	− 4.47475e16i	− 2.10717i
$216$	− 2.12799e15i	− 0.0970047i
$217$	0	0
$218$	−1.09656e16	−0.468636
$219$	−1.65536e15	−0.0685147
$220$	− 2.00696e16i	− 0.804598i
$221$	−2.24583e16	−0.872230
$222$	− 2.22364e15i	− 0.0836745i
$223$	1.24304e16i	0.453264i	0.973980	+	0.226632i	$0.0727715\pi$
$223$	1.24304e16i	0.453264i	−0.973980	+	0.226632i	$0.927228\pi$
$224$	0	0
$225$	−4.19018e16	−1.43534
$226$	1.21848e16	0.404631
$227$	2.39686e16i	0.771724i	0.922557	+	0.385862i	$0.126096\pi$
$227$	2.39686e16i	0.771724i	−0.922557	+	0.385862i	$0.873904\pi$
$228$	−2.41903e15	−0.0755261
$229$	3.51065e16i	1.06302i	0.847053	+	0.531508i	$0.178374\pi$
$229$	3.51065e16i	1.06302i	−0.847053	+	0.531508i	$0.821626\pi$
$230$	− 2.84757e16i	− 0.836333i
$231$	0	0
$232$	−2.47431e16	−0.683972
$233$	−3.49112e16	−0.936426	−0.468213	−	0.883616i	$-0.655102\pi$
$233$	−3.49112e16	−0.936426	−0.468213	+	0.883616i	$0.655102\pi$
$234$	1.84050e16i	0.479099i
$235$	5.02264e15	0.126899
$236$	− 8.25599e15i	− 0.202481i
$237$	8.65768e14i	0.0206140i
$238$	0	0
$239$	7.26933e16	1.63196	0.815979	−	0.578082i	$-0.196199\pi$
$239$	7.26933e16	1.63196	0.815979	+	0.578082i	$0.196199\pi$
$240$	−2.49277e15	−0.0543505
$241$	− 4.84983e16i	− 1.02709i	−0.858063	−	0.513544i	$-0.828332\pi$
$241$	− 4.84983e16i	− 1.02709i	0.858063	−	0.513544i	$-0.171668\pi$
$242$	−1.75931e15	−0.0361939
$243$	2.02609e16i	0.404963i
$244$	1.11355e16i	0.216263i
$245$	0	0
$246$	6.13048e15	0.112447
$247$	4.22537e16	0.753332
$248$	− 3.38135e16i	− 0.586042i
$249$	−1.65102e15	−0.0278200
$250$	3.13913e16i	0.514315i
$251$	9.46547e16i	1.50809i	0.656825	+	0.754043i	$0.271899\pi$
$251$	9.46547e16i	1.50809i	−0.656825	+	0.754043i	$0.728101\pi$
$252$	0	0
$253$	−5.12635e16	−0.772618
$254$	−3.11795e16	−0.457123
$255$	1.92452e16i	0.274499i
$256$	4.50360e15	0.0625000
$257$	− 7.51229e16i	− 1.01447i	−0.861807	−	0.507237i	$-0.830667\pi$
$257$	− 7.51229e16i	− 1.01447i	0.861807	−	0.507237i	$-0.169333\pi$
$258$	1.00057e16i	0.131495i
$259$	0	0
$260$	4.35418e16	0.542116
$261$	1.56550e17	1.89745
$262$	− 8.66864e16i	− 1.02292i
$263$	−1.57125e17	−1.80532	−0.902661	−	0.430352i	$-0.858390\pi$
$263$	−1.57125e17	−1.80532	−0.902661	+	0.430352i	$0.858390\pi$
$264$	4.48762e15i	0.0502099i
$265$	9.82009e16i	1.07003i
$266$	0	0
$267$	−1.14002e16	−0.117851
$268$	3.98560e16	0.401375
$269$	− 2.30468e16i	− 0.226123i	−0.993588	−	0.113061i	$-0.963934\pi$
$269$	− 2.30468e16i	− 0.226123i	0.993588	−	0.113061i	$-0.0360656\pi$
$270$	3.18521e16	0.304503
$271$	− 6.73386e16i	− 0.627306i	−0.949538	−	0.313653i	$-0.898447\pi$
$271$	− 6.73386e16i	− 0.627306i	0.949538	−	0.313653i	$-0.101553\pi$
$272$	− 3.47696e16i	− 0.315659i
$273$	0	0
$274$	1.03104e17	0.889249
$275$	1.78459e17	1.50041
$276$	6.36727e15i	0.0521903i
$277$	1.65914e17	1.32594	0.662970	−	0.748646i	$-0.269296\pi$
$277$	1.65914e17	1.32594	0.662970	+	0.748646i	$0.269296\pi$
$278$	− 1.57822e17i	− 1.22986i
$279$	2.13939e17i	1.62577i
$280$	0	0
$281$	−1.57534e17	−1.13875	−0.569376	−	0.822077i	$-0.692815\pi$
$281$	−1.57534e17	−1.13875	−0.569376	+	0.822077i	$0.692815\pi$
$282$	−1.12308e15	−0.00791894
$283$	4.83695e16i	0.332710i	0.986066	+	0.166355i	$0.0531998\pi$
$283$	4.83695e16i	0.332710i	−0.986066	+	0.166355i	$0.946800\pi$
$284$	3.83092e16	0.257083
$285$	− 3.62085e16i	− 0.237081i
$286$	− 7.83863e16i	− 0.500816i
$287$	0	0
$288$	−2.84944e16	−0.173385
$289$	−1.00058e17	−0.594246
$290$	− 3.70360e17i	− 2.14703i
$291$	3.47395e16	0.196595
$292$	4.47651e16i	0.247320i
$293$	− 1.19860e17i	− 0.646550i	−0.946305	−	0.323275i	$-0.895216\pi$
$293$	− 1.19860e17i	− 0.646550i	0.946305	−	0.323275i	$-0.104784\pi$
$294$	0	0
$295$	1.23577e17	0.635601
$296$	−6.01327e16	−0.302043
$297$	− 5.73420e16i	− 0.281305i
$298$	2.59270e17	1.24234
$299$	− 1.11218e17i	− 0.520569i
$300$	− 2.21657e16i	− 0.101352i
$301$	0	0
$302$	−8.83475e16	−0.385608
$303$	−4.00343e15	−0.0170739
$304$	6.54166e16i	0.272630i
$305$	−1.66679e17	−0.678863
$306$	2.19988e17i	0.875688i
$307$	− 1.36486e17i	− 0.531030i	−0.964107	−	0.265515i	$-0.914458\pi$
$307$	− 1.36486e17i	− 0.531030i	0.964107	−	0.265515i	$-0.0855419\pi$
$308$	0	0
$309$	3.05742e16	0.113670
$310$	5.06127e17	1.83962
$311$	− 9.30489e16i	− 0.330665i	−0.986238	−	0.165333i	$-0.947130\pi$
$311$	− 9.30489e16i	− 0.330665i	0.986238	−	0.165333i	$-0.0528698\pi$
$312$	−9.73609e15	−0.0338300
$313$	− 4.98958e17i	− 1.69533i	−0.530533	−	0.847664i	$-0.678008\pi$
$313$	− 4.98958e17i	− 1.69533i	0.530533	−	0.847664i	$-0.321992\pi$
$314$	− 5.47365e16i	− 0.181874i
$315$	0	0
$316$	2.34125e16	0.0744113
$317$	−4.43109e17	−1.37751	−0.688757	−	0.724992i	$-0.741843\pi$
$317$	−4.43109e17	−1.37751	−0.688757	+	0.724992i	$0.741843\pi$
$318$	− 2.19581e16i	− 0.0667735i
$319$	−6.66742e17	−1.98346
$320$	6.74107e16i	0.196191i
$321$	− 7.14465e16i	− 0.203445i
$322$	0	0
$323$	5.05043e17	1.37693
$324$	1.76689e17	0.471405
$325$	3.87174e17i	1.01093i
$326$	3.00315e17	0.767457
$327$	3.67011e16i	0.0918004i
$328$	− 1.65784e17i	− 0.405905i
$329$	0	0
$330$	−6.71716e16	−0.157612
$331$	5.48337e17	1.25965	0.629827	−	0.776735i	$-0.283126\pi$
$331$	5.48337e17	1.25965	0.629827	+	0.776735i	$0.283126\pi$
$332$	4.46478e16i	0.100423i
$333$	3.80461e17	0.837916
$334$	− 6.85773e16i	− 0.147896i
$335$	5.96573e17i	1.25994i
$336$	0	0
$337$	7.64047e16	0.154779	0.0773893	−	0.997001i	$-0.475342\pi$
$337$	7.64047e16	0.154779	0.0773893	+	0.997001i	$0.475342\pi$
$338$	−1.86308e17	−0.369671
$339$	− 4.07818e16i	− 0.0792626i
$340$	5.20438e17	0.990870
$341$	− 9.11159e17i	− 1.69947i
$342$	− 4.13892e17i	− 0.756318i
$343$	0	0
$344$	2.70579e17	0.474663
$345$	−9.53065e16	−0.163828
$346$	1.19073e16i	0.0200577i
$347$	−5.62425e17	−0.928449	−0.464224	−	0.885718i	$-0.653667\pi$
$347$	−5.62425e17	−0.928449	−0.464224	+	0.885718i	$0.653667\pi$
$348$	8.28138e16i	0.133982i
$349$	6.65335e17i	1.05502i	0.849547	+	0.527512i	$0.176875\pi$
$349$	6.65335e17i	1.05502i	−0.849547	+	0.527512i	$0.823125\pi$
$350$	0	0
$351$	1.24406e17	0.189536
$352$	1.21357e17	0.181244
$353$	7.18407e17i	1.05184i	0.850536	+	0.525918i	$0.176278\pi$
$353$	7.18407e17i	1.05184i	−0.850536	+	0.525918i	$0.823722\pi$
$354$	−2.76323e16	−0.0396638
$355$	5.73419e17i	0.807000i
$356$	3.08290e17i	0.425412i
$357$	0	0
$358$	2.15986e17	0.286579
$359$	−8.52465e17	−1.10921	−0.554607	−	0.832112i	$-0.687131\pi$
$359$	−8.52465e17	−1.10921	−0.554607	+	0.832112i	$0.687131\pi$
$360$	− 4.26509e17i	− 0.544265i
$361$	−1.51196e17	−0.189230
$362$	5.73327e17i	0.703789i
$363$	5.88831e15i	0.00708997i
$364$	0	0
$365$	−6.70052e17	−0.776352
$366$	3.72700e16	0.0423635
$367$	1.18712e18i	1.32383i	0.749580	+	0.661913i	$0.230255\pi$
$367$	1.18712e18i	1.32383i	−0.749580	+	0.661913i	$0.769745\pi$
$368$	1.72187e17	0.188393
$369$	1.04892e18i	1.12605i
$370$	− 9.00078e17i	− 0.948130i
$371$	0	0
$372$	−1.13172e17	−0.114799
$373$	3.79679e17	0.377968	0.188984	−	0.981980i	$-0.439481\pi$
$373$	3.79679e17	0.377968	0.188984	+	0.981980i	$0.439481\pi$
$374$	− 9.36922e17i	− 0.915382i
$375$	1.05065e17	0.100748
$376$	3.03709e16i	0.0285853i
$377$	− 1.44653e18i	− 1.33640i
$378$	0	0
$379$	−1.86804e18	−1.66307	−0.831537	−	0.555470i	$-0.812539\pi$
$379$	−1.86804e18	−1.66307	−0.831537	+	0.555470i	$0.812539\pi$
$380$	−9.79168e17	−0.855800
$381$	1.04356e17i	0.0895452i
$382$	−2.02228e17	−0.170372
$383$	1.42792e18i	1.18117i	0.806976	+	0.590584i	$0.201102\pi$
$383$	1.42792e18i	1.18117i	−0.806976	+	0.590584i	$0.798898\pi$
$384$	− 1.50733e16i	− 0.0122430i
$385$	0	0
$386$	9.39415e17	0.735778
$387$	−1.71196e18	−1.31679
$388$	− 9.39444e17i	− 0.709658i
$389$	−1.84381e18	−1.36795	−0.683974	−	0.729506i	$-0.739750\pi$
$389$	−1.84381e18	−1.36795	−0.683974	+	0.729506i	$0.739750\pi$
$390$	− 1.45732e17i	− 0.106194i
$391$	− 1.32935e18i	− 0.951487i
$392$	0	0
$393$	−2.90134e17	−0.200378
$394$	−6.40092e17	−0.434279
$395$	3.50443e17i	0.233581i
$396$	−7.67826e17	−0.502801
$397$	5.75536e17i	0.370287i	0.982711	+	0.185144i	$0.0592750\pi$
$397$	5.75536e17i	0.370287i	−0.982711	+	0.185144i	$0.940725\pi$
$398$	− 2.81962e17i	− 0.178242i
$399$	0	0
$400$	−5.99417e17	−0.365855
$401$	−6.47355e17	−0.388268	−0.194134	−	0.980975i	$-0.562190\pi$
$401$	−6.47355e17	−0.388268	−0.194134	+	0.980975i	$0.562190\pi$
$402$	− 1.33396e17i	− 0.0786248i
$403$	1.97680e18	1.14506
$404$	1.08263e17i	0.0616324i
$405$	2.64471e18i	1.47977i
$406$	0	0
$407$	−1.62037e18	−0.875898
$408$	−1.16372e17	−0.0618339
$409$	2.08311e18i	1.08805i	0.839069	+	0.544025i	$0.183100\pi$
$409$	2.08311e18i	1.08805i	−0.839069	+	0.544025i	$0.816900\pi$
$410$	2.48148e18	1.27416
$411$	− 3.45084e17i	− 0.174194i
$412$	− 8.26804e17i	− 0.410320i
$413$	0	0
$414$	−1.08943e18	−0.522633
$415$	−6.68297e17	−0.315234
$416$	2.63288e17i	0.122118i
$417$	−5.28222e17	−0.240915
$418$	1.76275e18i	0.790602i
$419$	5.16197e17i	0.227676i	0.993499	+	0.113838i	$0.0363145\pi$
$419$	5.16197e17i	0.227676i	−0.993499	+	0.113838i	$0.963686\pi$
$420$	0	0
$421$	1.69789e18	0.724328	0.362164	−	0.932114i	$-0.382038\pi$
$421$	1.69789e18	0.724328	0.362164	+	0.932114i	$0.382038\pi$
$422$	−6.11955e17	−0.256763
$423$	− 1.92157e17i	− 0.0793002i
$424$	−5.93801e17	−0.241035
$425$	4.62774e18i	1.84776i
$426$	− 1.28218e17i	− 0.0503597i
$427$	0	0
$428$	−1.93209e18	−0.734382
$429$	−2.62354e17	−0.0981041
$430$	4.05008e18i	1.48999i
$431$	−2.77287e18	−1.00366	−0.501832	−	0.864965i	$-0.667340\pi$
$431$	−2.77287e18	−1.00366	−0.501832	+	0.864965i	$0.667340\pi$
$432$	1.92603e17i	0.0685927i
$433$	5.15442e18i	1.80619i	0.429436	+	0.903097i	$0.358712\pi$
$433$	5.15442e18i	1.80619i	−0.429436	+	0.903097i	$0.641288\pi$
$434$	0	0
$435$	−1.23957e18	−0.420578
$436$	9.92489e17	0.331375
$437$	2.50108e18i	0.821785i
$438$	1.49826e17	0.0484472
$439$	− 4.71705e18i	− 1.50113i	−0.660796	−	0.750566i	$-0.729781\pi$
$439$	− 4.71705e18i	− 1.50113i	0.660796	−	0.750566i	$-0.270219\pi$
$440$	1.81649e18i	0.568937i
$441$	0	0
$442$	2.03269e18	0.616760
$443$	−1.99959e18	−0.597194	−0.298597	−	0.954379i	$-0.596519\pi$
$443$	−1.99959e18	−0.597194	−0.298597	+	0.954379i	$0.596519\pi$
$444$	2.01261e17i	0.0591668i
$445$	−4.61454e18	−1.33539
$446$	− 1.12507e18i	− 0.320506i
$447$	− 8.67763e17i	− 0.243360i
$448$	0	0
$449$	4.78871e18	1.30165	0.650825	−	0.759228i	$-0.274423\pi$
$449$	4.78871e18	1.30165	0.650825	+	0.759228i	$0.274423\pi$
$450$	3.79252e18	1.01494
$451$	− 4.46730e18i	− 1.17709i
$452$	−1.10284e18	−0.286117
$453$	2.95694e17i	0.0755362i
$454$	− 2.16939e18i	− 0.545691i
$455$	0	0
$456$	2.18946e17	0.0534050
$457$	−2.62913e18	−0.631537	−0.315768	−	0.948836i	$-0.602262\pi$
$457$	−2.62913e18	−0.631537	−0.315768	+	0.948836i	$0.602262\pi$
$458$	− 3.17748e18i	− 0.751665i
$459$	1.48698e18	0.346430
$460$	2.57733e18i	0.591377i
$461$	− 6.70171e18i	− 1.51453i	−0.653105	−	0.757267i	$-0.726534\pi$
$461$	− 6.70171e18i	− 1.51453i	0.653105	−	0.757267i	$-0.273466\pi$
$462$	0	0
$463$	1.64820e18	0.361363	0.180681	−	0.983542i	$-0.442170\pi$
$463$	1.64820e18	0.361363	0.180681	+	0.983542i	$0.442170\pi$
$464$	2.23949e18	0.483641
$465$	− 1.69398e18i	− 0.360361i
$466$	3.15980e18	0.662153
$467$	1.00428e17i	0.0207317i	0.999946	+	0.0103659i	$0.00329962\pi$
$467$	1.00428e17i	0.0207317i	−0.999946	+	0.0103659i	$0.996700\pi$
$468$	− 1.66583e18i	− 0.338774i
$469$	0	0
$470$	−4.54597e17	−0.0897309
$471$	−1.83200e17	−0.0356270
$472$	7.47247e17i	0.143176i
$473$	7.29119e18	1.37648
$474$	− 7.83604e16i	− 0.0145763i
$475$	− 8.70677e18i	− 1.59589i
$476$	0	0
$477$	3.75699e18	0.668670
$478$	−6.57944e18	−1.15397
$479$	9.97866e18i	1.72474i	0.506278	+	0.862370i	$0.331021\pi$
$479$	9.97866e18i	1.72474i	−0.506278	+	0.862370i	$0.668979\pi$
$480$	2.25620e17	0.0384316
$481$	− 3.51546e18i	− 0.590156i
$482$	4.38957e18i	0.726260i
$483$	0	0
$484$	1.59235e17	0.0255929
$485$	1.40618e19	2.22766
$486$	− 1.83381e18i	− 0.286352i
$487$	3.70788e18	0.570720	0.285360	−	0.958420i	$-0.407887\pi$
$487$	3.70788e18	0.570720	0.285360	+	0.958420i	$0.407887\pi$
$488$	− 1.00787e18i	− 0.152921i
$489$	− 1.00514e18i	− 0.150336i
$490$	0	0
$491$	−8.22467e18	−1.19550	−0.597748	−	0.801684i	$-0.703938\pi$
$491$	−8.22467e18	−1.19550	−0.597748	+	0.801684i	$0.703938\pi$
$492$	−5.54868e17	−0.0795122
$493$	− 1.72898e19i	− 2.44265i
$494$	−3.82437e18	−0.532686
$495$	− 1.14930e19i	− 1.57832i
$496$	3.06045e18i	0.414394i
$497$	0	0
$498$	1.49434e17	0.0196717
$499$	−1.31408e18	−0.170575	−0.0852877	−	0.996356i	$-0.527181\pi$
$499$	−1.31408e18	−0.170575	−0.0852877	+	0.996356i	$0.527181\pi$
$500$	− 2.84121e18i	− 0.363675i
$501$	−2.29524e17	−0.0289711
$502$	− 8.56716e18i	− 1.06638i
$503$	7.73353e18i	0.949297i	0.880175	+	0.474649i	$0.157425\pi$
$503$	7.73353e18i	0.949297i	−0.880175	+	0.474649i	$0.842575\pi$
$504$	0	0
$505$	−1.62050e18	−0.193468
$506$	4.63985e18	0.546324
$507$	6.23563e17i	0.0724143i
$508$	2.82205e18	0.323235
$509$	9.11502e17i	0.102975i	0.998674	+	0.0514877i	$0.0163963\pi$
$509$	9.11502e17i	0.102975i	−0.998674	+	0.0514877i	$0.983604\pi$
$510$	− 1.74188e18i	− 0.194100i
$511$	0	0
$512$	−4.07619e17	−0.0441942
$513$	−2.79764e18	−0.299206
$514$	6.79935e18i	0.717341i
$515$	1.23758e19	1.28802
$516$	− 9.05613e17i	− 0.0929811i
$517$	8.18392e17i	0.0828948i
$518$	0	0
$519$	3.98531e16	0.00392908
$520$	−3.94095e18	−0.383334
$521$	3.33336e18i	0.319903i	0.987125	+	0.159951i	$0.0511338\pi$
$521$	3.33336e18i	0.319903i	−0.987125	+	0.159951i	$0.948866\pi$
$522$	−1.41693e19	−1.34170
$523$	− 2.35875e18i	− 0.220379i	−0.993911	−	0.110190i	$-0.964854\pi$
$523$	− 2.35875e18i	− 0.220379i	0.993911	−	0.110190i	$-0.0351458\pi$
$524$	7.84595e18i	0.723314i
$525$	0	0
$526$	1.42213e19	1.27656
$527$	2.36279e19	2.09291
$528$	− 4.06173e17i	− 0.0355037i
$529$	−5.00959e18	−0.432128
$530$	− 8.88813e18i	− 0.756622i
$531$	− 4.72785e18i	− 0.397193i
$532$	0	0
$533$	9.69200e18	0.793091
$534$	1.03183e18	0.0833333
$535$	− 2.89199e19i	− 2.30527i
$536$	−3.60736e18	−0.283815
$537$	− 7.22893e17i	− 0.0561376i
$538$	2.08595e18i	0.159893i
$539$	0	0
$540$	−2.88293e18	−0.215316
$541$	2.43894e19	1.79813	0.899065	−	0.437816i	$-0.144248\pi$
$541$	2.43894e19	1.79813	0.899065	+	0.437816i	$0.144248\pi$
$542$	6.09480e18i	0.443572i
$543$	1.91889e18	0.137864
$544$	3.14699e18i	0.223204i
$545$	1.48558e19i	1.04021i
$546$	0	0
$547$	2.32496e19	1.58673	0.793367	−	0.608743i	$-0.208326\pi$
$547$	2.32496e19	1.58673	0.793367	+	0.608743i	$0.208326\pi$
$548$	−9.33195e18	−0.628794
$549$	6.37684e18i	0.424228i
$550$	−1.61522e19	−1.06095
$551$	3.25295e19i	2.10968i
$552$	− 5.76299e17i	− 0.0369041i
$553$	0	0
$554$	−1.50168e19	−0.937582
$555$	−3.01251e18	−0.185728
$556$	1.42844e19i	0.869640i
$557$	1.41842e19	0.852742	0.426371	−	0.904548i	$-0.359792\pi$
$557$	1.41842e19	0.852742	0.426371	+	0.904548i	$0.359792\pi$
$558$	− 1.93635e19i	− 1.14960i
$559$	1.58185e19i	0.927436i
$560$	0	0
$561$	−3.13582e18	−0.179313
$562$	1.42583e19	0.805219
$563$	− 1.91319e19i	− 1.06708i	−0.845773	−	0.533542i	$-0.820860\pi$
$563$	− 1.91319e19i	− 1.06708i	0.845773	−	0.533542i	$-0.179140\pi$
$564$	1.01650e17	0.00559953
$565$	− 1.65075e19i	− 0.898139i
$566$	− 4.37791e18i	− 0.235262i
$567$	0	0
$568$	−3.46735e18	−0.181785
$569$	−2.58658e19	−1.33949	−0.669746	−	0.742590i	$-0.733597\pi$
$569$	−2.58658e19	−1.33949	−0.669746	+	0.742590i	$0.733597\pi$
$570$	3.27722e18i	0.167641i
$571$	−1.25285e19	−0.633060	−0.316530	−	0.948582i	$-0.602518\pi$
$571$	−1.25285e19	−0.633060	−0.316530	+	0.948582i	$0.602518\pi$
$572$	7.09472e18i	0.354130i
$573$	6.76847e17i	0.0333740i
$574$	0	0
$575$	−2.29176e19	−1.10279
$576$	2.57902e18	0.122602
$577$	− 1.64236e19i	− 0.771326i	−0.922640	−	0.385663i	$-0.873973\pi$
$577$	− 1.64236e19i	− 0.771326i	0.922640	−	0.385663i	$-0.126027\pi$
$578$	9.05620e18	0.420195
$579$	− 3.14417e18i	− 0.144130i
$580$	3.35211e19i	1.51818i
$581$	0	0
$582$	−3.14426e18	−0.139014
$583$	−1.60009e19	−0.698980
$584$	− 4.05167e18i	− 0.174882i
$585$	2.49345e19	1.06343
$586$	1.08485e19i	0.457180i
$587$	− 3.59730e19i	− 1.49799i	−0.662574	−	0.748996i	$-0.730536\pi$
$587$	− 3.59730e19i	− 1.49799i	0.662574	−	0.748996i	$-0.269464\pi$
$588$	0	0
$589$	−4.44543e19	−1.80762
$590$	−1.11849e19	−0.449438
$591$	2.14235e18i	0.0850703i
$592$	5.44259e18	0.213577
$593$	− 1.34854e19i	− 0.522977i	−0.965207	−	0.261488i	$-0.915787\pi$
$593$	− 1.34854e19i	− 0.522977i	0.965207	−	0.261488i	$-0.0842133\pi$
$594$	5.19001e18i	0.198913i
$595$	0	0
$596$	−2.34665e19	−0.878465
$597$	−9.43710e17	−0.0349155
$598$	1.00663e19i	0.368098i
$599$	−7.03528e18	−0.254269	−0.127135	−	0.991885i	$-0.540578\pi$
$599$	−7.03528e18	−0.254269	−0.127135	+	0.991885i	$0.540578\pi$
$600$	2.00621e18i	0.0716668i
$601$	− 3.63144e19i	− 1.28220i	−0.767455	−	0.641102i	$-0.778477\pi$
$601$	− 3.63144e19i	− 1.28220i	0.767455	−	0.641102i	$-0.221523\pi$
$602$	0	0
$603$	2.28238e19	0.787348
$604$	7.99631e18	0.272666
$605$	2.38345e18i	0.0803377i
$606$	3.62349e17	0.0120731
$607$	1.22380e19i	0.403079i	0.979480	+	0.201539i	$0.0645944\pi$
$607$	1.22380e19i	0.403079i	−0.979480	+	0.201539i	$0.935406\pi$
$608$	− 5.92084e18i	− 0.192778i
$609$	0	0
$610$	1.50861e19	0.480029
$611$	−1.77554e18	−0.0558523
$612$	− 1.99110e19i	− 0.619205i
$613$	2.58809e19	0.795711	0.397856	−	0.917448i	$-0.369754\pi$
$613$	2.58809e19	0.795711	0.397856	+	0.917448i	$0.369754\pi$
$614$	1.23533e19i	0.375495i
$615$	− 8.30537e18i	− 0.249593i
$616$	0	0
$617$	1.38916e19	0.408091	0.204045	−	0.978961i	$-0.434591\pi$
$617$	1.38916e19	0.408091	0.204045	+	0.978961i	$0.434591\pi$
$618$	−2.76727e18	−0.0803769
$619$	1.37557e19i	0.395046i	0.980298	+	0.197523i	$0.0632897\pi$
$619$	1.37557e19i	0.395046i	−0.980298	+	0.197523i	$0.936710\pi$
$620$	−4.58094e19	−1.30081
$621$	7.36384e18i	0.206758i
$622$	8.42182e18i	0.233816i
$623$	0	0
$624$	8.81210e17	0.0239215
$625$	−1.19888e19	−0.321822
$626$	4.51605e19i	1.19878i
$627$	5.89983e18	0.154870
$628$	4.95418e18i	0.128604i
$629$	− 4.20190e19i	− 1.07868i
$630$	0	0
$631$	1.52607e19	0.383149	0.191575	−	0.981478i	$-0.438641\pi$
$631$	1.52607e19	0.383149	0.191575	+	0.981478i	$0.438641\pi$
$632$	−2.11906e18	−0.0526167
$633$	2.04818e18i	0.0502969i
$634$	4.01057e19	0.974049
$635$	4.22409e19i	1.01465i
$636$	1.98742e18i	0.0472160i
$637$	0	0
$638$	6.03466e19	1.40252
$639$	2.19380e19	0.504302
$640$	− 6.10132e18i	− 0.138728i
$641$	−7.42621e18	−0.167017	−0.0835086	−	0.996507i	$-0.526613\pi$
$641$	−7.42621e18	−0.167017	−0.0835086	+	0.996507i	$0.526613\pi$
$642$	6.46660e18i	0.143857i
$643$	7.17838e19i	1.57961i	0.613359	+	0.789804i	$0.289818\pi$
$643$	7.17838e19i	1.57961i	−0.613359	+	0.789804i	$0.710182\pi$
$644$	0	0
$645$	1.35554e19	0.291873
$646$	−4.57113e19	−0.973634
$647$	4.57440e19i	0.963839i	0.876216	+	0.481919i	$0.160060\pi$
$647$	4.57440e19i	0.963839i	−0.876216	+	0.481919i	$0.839940\pi$
$648$	−1.59920e19	−0.333334
$649$	2.01358e19i	0.415198i
$650$	− 3.50430e19i	− 0.714837i
$651$	0	0
$652$	−2.71814e19	−0.542674
$653$	−7.00787e19	−1.38418	−0.692092	−	0.721809i	$-0.743311\pi$
$653$	−7.00787e19	−1.38418	−0.692092	+	0.721809i	$0.743311\pi$
$654$	− 3.32180e18i	− 0.0649127i
$655$	−1.17440e20	−2.27052
$656$	1.50050e19i	0.287018i
$657$	2.56350e19i	0.485150i
$658$	0	0
$659$	8.31252e19	1.54005	0.770025	−	0.638014i	$-0.220244\pi$
$659$	8.31252e19	1.54005	0.770025	+	0.638014i	$0.220244\pi$
$660$	6.07968e18	0.111448
$661$	5.11197e19i	0.927211i	0.886042	+	0.463605i	$0.153444\pi$
$661$	5.11197e19i	0.927211i	−0.886042	+	0.463605i	$0.846556\pi$
$662$	−4.96298e19	−0.890710
$663$	− 6.80330e18i	− 0.120816i
$664$	− 4.04106e18i	− 0.0710098i
$665$	0	0
$666$	−3.44354e19	−0.592496
$667$	8.56228e19	1.45784
$668$	6.20691e18i	0.104578i
$669$	−3.76555e18	−0.0627835
$670$	− 5.39956e19i	− 0.890912i
$671$	− 2.71588e19i	− 0.443458i
$672$	0	0
$673$	−1.21090e20	−1.93644	−0.968219	−	0.250104i	$-0.919535\pi$
$673$	−1.21090e20	−1.93644	−0.968219	+	0.250104i	$0.919535\pi$
$674$	−6.91536e18	−0.109445
$675$	− 2.56350e19i	− 0.401520i
$676$	1.68627e19	0.261397
$677$	1.45438e18i	0.0223130i	0.999938	+	0.0111565i	$0.00355130\pi$
$677$	1.45438e18i	0.0223130i	−0.999938	+	0.0111565i	$0.996449\pi$
$678$	3.69115e18i	0.0560471i
$679$	0	0
$680$	−4.71047e19	−0.700651
$681$	−7.26082e18	−0.106895
$682$	8.24687e19i	1.20171i
$683$	1.29812e20	1.87228	0.936138	−	0.351634i	$-0.114374\pi$
$683$	1.29812e20	1.87228	0.936138	+	0.351634i	$0.114374\pi$
$684$	3.74612e19i	0.534798i
$685$	− 1.39682e20i	− 1.97382i
$686$	0	0
$687$	−1.06348e19	−0.147243
$688$	−2.44900e19	−0.335638
$689$	− 3.47146e19i	− 0.470954i
$690$	8.62616e18	0.115844
$691$	6.76787e19i	0.899716i	0.893100	+	0.449858i	$0.148525\pi$
$691$	6.76787e19i	0.899716i	−0.893100	+	0.449858i	$0.851475\pi$
$692$	− 1.07773e18i	− 0.0141829i
$693$	0	0
$694$	5.09049e19	0.656512
$695$	−2.13812e20	−2.72985
$696$	− 7.49545e18i	− 0.0947399i
$697$	1.15845e20	1.44960
$698$	− 6.02193e19i	− 0.746015i
$699$	− 1.05757e19i	− 0.129708i
$700$	0	0
$701$	3.16145e19	0.380067	0.190033	−	0.981778i	$-0.439140\pi$
$701$	3.16145e19	0.380067	0.190033	+	0.981778i	$0.439140\pi$
$702$	−1.12599e19	−0.134022
$703$	7.90558e19i	0.931637i
$704$	−1.09839e19	−0.128159
$705$	1.52151e18i	0.0175773i
$706$	− 6.50228e19i	− 0.743760i
$707$	0	0
$708$	2.50099e18	0.0280466
$709$	5.36783e19	0.596039	0.298020	−	0.954560i	$-0.403674\pi$
$709$	5.36783e19	0.596039	0.298020	+	0.954560i	$0.403674\pi$
$710$	− 5.18999e19i	− 0.570635i
$711$	1.34073e19	0.145967
$712$	− 2.79032e19i	− 0.300811i
$713$	1.17011e20i	1.24910i
$714$	0	0
$715$	−1.06195e20	−1.11164
$716$	−1.95488e19	−0.202642
$717$	2.20210e19i	0.226049i
$718$	7.71563e19	0.784333
$719$	− 4.11415e19i	− 0.414169i	−0.978323	−	0.207084i	$-0.933603\pi$
$719$	− 4.11415e19i	− 0.414169i	0.978323	−	0.207084i	$-0.0663975\pi$
$720$	3.86032e19i	0.384854i
$721$	0	0
$722$	1.36847e19	0.133806
$723$	1.46916e19	0.142266
$724$	− 5.18917e19i	− 0.497654i
$725$	−2.98070e20	−2.83108
$726$	− 5.32949e17i	− 0.00501336i
$727$	− 2.36120e19i	− 0.219985i	−0.993932	−	0.109992i	$-0.964917\pi$
$727$	− 2.36120e19i	− 0.219985i	0.993932	−	0.109992i	$-0.0350826\pi$
$728$	0	0
$729$	9.70236e19	0.886716
$730$	6.06462e19	0.548963
$731$	1.89073e20i	1.69515i
$732$	−3.37330e18	−0.0299555
$733$	1.52507e20i	1.34141i	0.741722	+	0.670707i	$0.234009\pi$
$733$	1.52507e20i	1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$734$	− 1.07446e20i	− 0.936087i
$735$	0	0
$736$	−1.55846e19	−0.133214
$737$	−9.72059e19	−0.823038
$738$	− 9.49371e19i	− 0.796235i
$739$	2.76859e19	0.230011	0.115005	−	0.993365i	$-0.463311\pi$
$739$	2.76859e19	0.230011	0.115005	+	0.993365i	$0.463311\pi$
$740$	8.14657e19i	0.670429i
$741$	1.27999e19i	0.104347i
$742$	0	0
$743$	−6.54827e19	−0.523848	−0.261924	−	0.965089i	$-0.584357\pi$
$743$	−6.54827e19	−0.523848	−0.261924	+	0.965089i	$0.584357\pi$
$744$	1.02431e19	0.0811751
$745$	− 3.51251e20i	− 2.75755i
$746$	−3.43646e19	−0.267263
$747$	2.55678e19i	0.196993i
$748$	8.48005e19i	0.647273i
$749$	0	0
$750$	−9.50937e18	−0.0712399
$751$	1.48042e20	1.09877	0.549384	−	0.835570i	$-0.314862\pi$
$751$	1.48042e20	1.09877	0.549384	+	0.835570i	$0.314862\pi$
$752$	− 2.74886e18i	− 0.0202129i
$753$	−2.86738e19	−0.208891
$754$	1.30925e20i	0.944978i
$755$	1.19690e20i	0.855914i
$756$	0	0
$757$	1.06274e19	0.0746029	0.0373014	−	0.999304i	$-0.488124\pi$
$757$	1.06274e19	0.0746029	0.0373014	+	0.999304i	$0.488124\pi$
$758$	1.69076e20	1.17597
$759$	− 1.55293e19i	− 0.107019i
$760$	8.86242e19	0.605142
$761$	− 1.43929e20i	− 0.973770i	−0.873466	−	0.486885i	$-0.838133\pi$
$761$	− 1.43929e20i	− 0.973770i	0.873466	−	0.486885i	$-0.161867\pi$
$762$	− 9.44522e18i	− 0.0633180i
$763$	0	0
$764$	1.83036e19	0.120471
$765$	2.98032e20	1.94372
$766$	− 1.29240e20i	− 0.835211i
$767$	−4.36854e19	−0.279749
$768$	1.36428e18i	0.00865714i
$769$	2.54467e20i	1.60010i	0.599934	+	0.800049i	$0.295193\pi$
$769$	2.54467e20i	1.60010i	−0.599934	+	0.800049i	$0.704807\pi$
$770$	0	0
$771$	2.27570e19	0.140519
$772$	−8.50262e19	−0.520273
$773$	1.78493e20i	1.08234i	0.840913	+	0.541170i	$0.182019\pi$
$773$	1.78493e20i	1.08234i	−0.840913	+	0.541170i	$0.817981\pi$
$774$	1.54949e20	0.931112
$775$	− 4.07338e20i	− 2.42573i
$776$	8.50288e19i	0.501804i
$777$	0	0
$778$	1.66883e20	0.967286
$779$	−2.17954e20	−1.25200
$780$	1.31901e19i	0.0750908i
$781$	−9.34332e19	−0.527162
$782$	1.20319e20i	0.672803i
$783$	9.57754e19i	0.530788i
$784$	0	0
$785$	−7.41552e19	−0.403695
$786$	2.62599e19	0.141689
$787$	1.85366e19i	0.0991305i	0.998771	+	0.0495652i	$0.0157836\pi$
$787$	1.85366e19i	0.0991305i	−0.998771	+	0.0495652i	$0.984216\pi$
$788$	5.79345e19	0.307082
$789$	− 4.75979e19i	− 0.250063i
$790$	− 3.17185e19i	− 0.165167i
$791$	0	0
$792$	6.94956e19	0.355534
$793$	5.89221e19	0.298790
$794$	− 5.20915e19i	− 0.261833i
$795$	−2.97480e19	−0.148214
$796$	2.55203e19i	0.126036i
$797$	1.10066e19i	0.0538824i	0.999637	+	0.0269412i	$0.00857669\pi$
$797$	1.10066e19i	0.0538824i	−0.999637	+	0.0269412i	$0.991423\pi$
$798$	0	0
$799$	−2.12223e19	−0.102086
$800$	5.42530e19	0.258699
$801$	1.76544e20i	0.834499i
$802$	5.85919e19	0.274547
$803$	− 1.09179e20i	− 0.507141i
$804$	1.20736e19i	0.0555961i
$805$	0	0
$806$	−1.78919e20	−0.809677
$807$	6.98157e18	0.0313212
$808$	− 9.79882e18i	− 0.0435807i
$809$	7.81519e19	0.344588	0.172294	−	0.985046i	$-0.444882\pi$
$809$	7.81519e19	0.344588	0.172294	+	0.985046i	$0.444882\pi$
$810$	− 2.39372e20i	− 1.04635i
$811$	− 7.50980e19i	− 0.325448i	−0.986672	−	0.162724i	$-0.947972\pi$
$811$	− 7.50980e19i	− 0.325448i	0.986672	−	0.162724i	$-0.0520281\pi$
$812$	0	0
$813$	2.03989e19	0.0868908
$814$	1.46659e20	0.619353
$815$	− 4.06857e20i	− 1.70348i
$816$	1.05328e19	0.0437232
$817$	− 3.55728e20i	− 1.46408i
$818$	− 1.88541e20i	− 0.769367i
$819$	0	0
$820$	−2.24598e20	−0.900967
$821$	1.18585e20	0.471660	0.235830	−	0.971794i	$-0.424219\pi$
$821$	1.18585e20	0.471660	0.235830	+	0.971794i	$0.424219\pi$
$822$	3.12335e19i	0.123174i
$823$	−1.85931e20	−0.727031	−0.363515	−	0.931588i	$-0.618424\pi$
$823$	−1.85931e20	−0.727031	−0.363515	+	0.931588i	$0.618424\pi$
$824$	7.48338e19i	0.290140i
$825$	5.40606e19i	0.207827i
$826$	0	0
$827$	−1.32871e20	−0.502218	−0.251109	−	0.967959i	$-0.580795\pi$
$827$	−1.32871e20	−0.502218	−0.251109	+	0.967959i	$0.580795\pi$
$828$	9.86039e19	0.369557
$829$	8.07218e19i	0.299992i	0.988687	+	0.149996i	$0.0479260\pi$
$829$	8.07218e19i	0.299992i	−0.988687	+	0.149996i	$0.952074\pi$
$830$	6.04873e19	0.222904
$831$	5.02603e19i	0.183662i
$832$	− 2.38301e19i	− 0.0863502i
$833$	0	0
$834$	4.78092e19	0.170353
$835$	−9.29062e19	−0.328276
$836$	− 1.59546e20i	− 0.559040i
$837$	−1.30885e20	−0.454791
$838$	− 4.67208e19i	− 0.160991i
$839$	− 1.89707e20i	− 0.648262i	−0.946012	−	0.324131i	$-0.894928\pi$
$839$	− 1.89707e20i	− 0.648262i	0.946012	−	0.324131i	$-0.105072\pi$
$840$	0	0
$841$	8.16067e20	2.74255
$842$	−1.53676e20	−0.512177
$843$	− 4.77218e19i	− 0.157733i
$844$	5.53878e19	0.181559
$845$	2.52404e20i	0.820539i
$846$	1.73921e19i	0.0560737i
$847$	0	0
$848$	5.37447e19	0.170437
$849$	−1.46526e19	−0.0460851
$850$	− 4.18855e20i	− 1.30657i
$851$	2.08087e20	0.643782
$852$	1.16050e19i	0.0356097i
$853$	1.23365e20i	0.375447i	0.982222	+	0.187724i	$0.0601109\pi$
$853$	1.23365e20i	0.375447i	−0.982222	+	0.187724i	$0.939889\pi$
$854$	0	0
$855$	−5.60727e20	−1.67876
$856$	1.74873e20	0.519286
$857$	3.23331e19i	0.0952316i	0.998866	+	0.0476158i	$0.0151623\pi$
$857$	3.23331e19i	0.0952316i	−0.998866	+	0.0476158i	$0.984838\pi$
$858$	2.37456e19	0.0693701
$859$	2.82580e20i	0.818821i	0.912350	+	0.409411i	$0.134266\pi$
$859$	2.82580e20i	0.818821i	−0.912350	+	0.409411i	$0.865734\pi$
$860$	− 3.66572e20i	− 1.05359i
$861$	0	0
$862$	2.50971e20	0.709697
$863$	2.28567e20	0.641118	0.320559	−	0.947229i	$-0.396129\pi$
$863$	2.28567e20	0.641118	0.320559	+	0.947229i	$0.396129\pi$
$864$	− 1.74325e19i	− 0.0485024i
$865$	1.61316e19	0.0445210
$866$	− 4.66525e20i	− 1.27717i
$867$	− 3.03106e19i	− 0.0823115i
$868$	0	0
$869$	−5.71014e19	−0.152584
$870$	1.12193e20	0.297394
$871$	− 2.10892e20i	− 0.554541i
$872$	−8.98298e19	−0.234318
$873$	− 5.37979e20i	− 1.39208i
$874$	− 2.26372e20i	− 0.581090i
$875$	0	0
$876$	−1.35607e19	−0.0342573
$877$	2.91024e20	0.729342	0.364671	−	0.931136i	$-0.381181\pi$
$877$	2.91024e20	0.729342	0.364671	+	0.931136i	$0.381181\pi$
$878$	4.26938e20i	1.06146i
$879$	3.63094e19	0.0895563
$880$	− 1.64410e20i	− 0.402299i
$881$	4.53668e20i	1.10130i	0.834735	+	0.550651i	$0.185621\pi$
$881$	4.53668e20i	1.10130i	−0.834735	+	0.550651i	$0.814379\pi$
$882$	0	0
$883$	6.73323e20	1.60879	0.804394	−	0.594096i	$-0.202490\pi$
$883$	6.73323e20	1.60879	0.804394	+	0.594096i	$0.202490\pi$
$884$	−1.83978e20	−0.436115
$885$	3.74353e19i	0.0880398i
$886$	1.80983e20	0.422280
$887$	6.39108e20i	1.47948i	0.672893	+	0.739740i	$0.265051\pi$
$887$	6.39108e20i	1.47948i	−0.672893	+	0.739740i	$0.734949\pi$
$888$	− 1.82160e19i	− 0.0418372i
$889$	0	0
$890$	4.17661e20	0.944264
$891$	−4.30931e20	−0.966638
$892$	1.01830e20i	0.226632i
$893$	3.99283e19	0.0881699
$894$	7.85409e19i	0.172081i
$895$	− 2.92611e20i	− 0.636106i
$896$	0	0
$897$	3.36915e19	0.0721062
$898$	−4.33425e20	−0.920406
$899$	1.52186e21i	3.20669i
$900$	−3.43260e20	−0.717671
$901$	− 4.14931e20i	− 0.860801i
$902$	4.04334e20i	0.832328i
$903$	0	0
$904$	9.98178e19	0.202315
$905$	7.76724e20	1.56216
$906$	− 2.67632e19i	− 0.0534122i
$907$	6.18936e20	1.22573	0.612865	−	0.790188i	$-0.290017\pi$
$907$	6.18936e20	1.22573	0.612865	+	0.790188i	$0.290017\pi$
$908$	1.96351e20i	0.385862i
$909$	6.19973e19i	0.120900i
$910$	0	0
$911$	−2.94910e20	−0.566319	−0.283160	−	0.959073i	$-0.591383\pi$
$911$	−2.94910e20	−0.566319	−0.283160	+	0.959073i	$0.591383\pi$
$912$	−1.98167e19	−0.0377631
$913$	− 1.08893e20i	− 0.205922i
$914$	2.37962e20	0.446564
$915$	− 5.04922e19i	− 0.0940321i
$916$	2.87593e20i	0.531508i
$917$	0	0
$918$	−1.34586e20	−0.244963
$919$	−3.54963e20	−0.641172	−0.320586	−	0.947219i	$-0.603880\pi$
$919$	−3.54963e20	−0.641172	−0.320586	+	0.947219i	$0.603880\pi$
$920$	− 2.33273e20i	− 0.418167i
$921$	4.13457e19	0.0735552
$922$	6.06569e20i	1.07094i
$923$	− 2.02707e20i	− 0.355187i
$924$	0	0
$925$	−7.24394e20	−1.25021
$926$	−1.49178e20	−0.255522
$927$	− 4.73475e20i	− 0.804894i
$928$	−2.02696e20	−0.341986
$929$	1.42975e20i	0.239415i	0.992809	+	0.119708i	$0.0381957\pi$
$929$	1.42975e20i	0.239415i	−0.992809	+	0.119708i	$0.961804\pi$
$930$	1.53321e20i	0.254813i
$931$	0	0
$932$	−2.85993e20	−0.468213
$933$	2.81873e19	0.0458018
$934$	− 9.08969e18i	− 0.0146596i
$935$	−1.26931e21	−2.03183
$936$	1.50774e20i	0.239549i
$937$	2.79349e20i	0.440524i	0.975441	+	0.220262i	$0.0706912\pi$
$937$	2.79349e20i	0.440524i	−0.975441	+	0.220262i	$0.929309\pi$
$938$	0	0
$939$	1.51150e20	0.234827
$940$	4.11455e19	0.0634493
$941$	− 5.48110e20i	− 0.838958i	−0.907765	−	0.419479i	$-0.862213\pi$
$941$	− 5.48110e20i	− 0.838958i	0.907765	−	0.419479i	$-0.137787\pi$
$942$	1.65814e19	0.0251921
$943$	5.73689e20i	0.865157i
$944$	− 6.76331e19i	− 0.101241i
$945$	0	0
$946$	−6.59923e20	−0.973319
$947$	−8.87681e20	−1.29959	−0.649796	−	0.760109i	$-0.725146\pi$
$947$	−8.87681e20	−1.29959	−0.649796	+	0.760109i	$0.725146\pi$
$948$	7.09237e18i	0.0103070i
$949$	2.36868e20	0.341698
$950$	7.88047e20i	1.12846i
$951$	− 1.34231e20i	− 0.190805i
$952$	0	0
$953$	−5.52988e20	−0.774578	−0.387289	−	0.921958i	$-0.626589\pi$
$953$	−5.52988e20	−0.774578	−0.387289	+	0.921958i	$0.626589\pi$
$954$	−3.40044e20	−0.472821
$955$	2.73972e20i	0.378166i
$956$	5.95503e20	0.815979
$957$	− 2.01977e20i	− 0.274737i
$958$	− 9.03166e20i	− 1.21958i
$959$	0	0
$960$	−2.04208e19	−0.0271752
$961$	−1.32281e21	−1.74756
$962$	3.18183e20i	0.417303i
$963$	−1.10643e21	−1.44058
$964$	− 3.97298e20i	− 0.513544i
$965$	− 1.27269e21i	− 1.63317i
$966$	0	0
$967$	−1.08872e20	−0.137700	−0.0688498	−	0.997627i	$-0.521933\pi$
$967$	−1.08872e20	−0.137700	−0.0688498	+	0.997627i	$0.521933\pi$
$968$	−1.44123e19	−0.0180969
$969$	1.52993e20i	0.190724i
$970$	−1.27273e21	−1.57519
$971$	9.88932e20i	1.21516i	0.794260	+	0.607578i	$0.207859\pi$
$971$	9.88932e20i	1.21516i	−0.794260	+	0.607578i	$0.792141\pi$
$972$	1.65978e20i	0.202482i
$973$	0	0
$974$	−3.35599e20	−0.403560
$975$	−1.17287e20	−0.140029
$976$	9.12224e19i	0.108132i
$977$	9.35940e20	1.10150	0.550752	−	0.834669i	$-0.314341\pi$
$977$	9.35940e20	1.10150	0.550752	+	0.834669i	$0.314341\pi$
$978$	9.09746e19i	0.106304i
$979$	− 7.51896e20i	− 0.872327i
$980$	0	0
$981$	5.68355e20	0.650035
$982$	7.44412e20	0.845343
$983$	1.24803e20i	0.140718i	0.997522	+	0.0703591i	$0.0224145\pi$
$983$	1.24803e20i	0.140718i	−0.997522	+	0.0703591i	$0.977585\pi$
$984$	5.02209e19	0.0562236
$985$	8.67175e20i	0.963947i
$986$	1.56489e21i	1.72721i
$987$	0	0
$988$	3.46142e20	0.376666
$989$	−9.36332e20	−1.01171
$990$	1.04022e21i	1.11604i
$991$	6.98882e20	0.744540	0.372270	−	0.928124i	$-0.378580\pi$
$991$	6.98882e20	0.744540	0.372270	+	0.928124i	$0.378580\pi$
$992$	− 2.77000e20i	− 0.293021i
$993$	1.66108e20i	0.174480i
$994$	0	0
$995$	−3.81992e20	−0.395634
$996$	−1.35252e19	−0.0139100
$997$	4.72520e20i	0.482563i	0.970455	+	0.241281i	$0.0775677\pi$
$997$	4.72520e20i	0.482563i	−0.970455	+	0.241281i	$0.922432\pi$
$998$	1.18937e20	0.120615
$999$	2.32761e20i	0.234397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.15.b.c.97.6		20
7.2	even	3		14.15.d.a.3.8	✓	20
7.3	odd	6		14.15.d.a.5.8	yes	20
7.4	even	3		98.15.d.b.19.8		20
7.5	odd	6		98.15.d.b.31.8		20
7.6	odd	2	inner	98.15.b.c.97.5		20
21.2	odd	6		126.15.n.b.73.1		20
21.17	even	6		126.15.n.b.19.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.8	✓	20	7.2	even	3
14.15.d.a.5.8	yes	20	7.3	odd	6
98.15.b.c.97.5		20	7.6	odd	2	inner
98.15.b.c.97.6		20	1.1	even	1	trivial
98.15.d.b.19.8		20	7.4	even	3
98.15.d.b.31.8		20	7.5	odd	6
126.15.n.b.19.1		20	21.17	even	6
126.15.n.b.73.1		20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	98.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-90.5097 q^{2} +302.931i q^{3} +8192.00 q^{4} +122619. i q^{5} -27418.1i q^{6} -741455. q^{8} +4.69120e6 q^{9} +O(q^{10})\)	\(q-90.5097 q^{2} +302.931i q^{3} +8192.00 q^{4} +122619. i q^{5} -27418.1i q^{6} -741455. q^{8} +4.69120e6 q^{9} -1.10982e7i q^{10} -1.99797e7 q^{11} +2.48161e6i q^{12} -4.33468e7i q^{13} -3.71452e7 q^{15} +6.71089e7 q^{16} -5.18108e8i q^{17} -4.24599e8 q^{18} +9.74783e8i q^{19} +1.00450e9i q^{20} +1.80835e9 q^{22} +2.56578e9 q^{23} -2.24609e8i q^{24} -8.93201e9 q^{25} +3.92330e9i q^{26} +2.87002e9i q^{27} +3.33710e10 q^{29} +3.36200e9 q^{30} +4.56043e10i q^{31} -6.07400e9 q^{32} -6.05246e9i q^{33} +4.68938e10i q^{34} +3.84303e10 q^{36} +8.11009e10 q^{37} -8.82273e10i q^{38} +1.31311e10 q^{39} -9.09168e10i q^{40} +2.23592e11i q^{41} -3.64930e11 q^{43} -1.63674e11 q^{44} +5.75232e11i q^{45} -2.32228e11 q^{46} -4.09612e10i q^{47} +2.03293e10i q^{48} +8.08433e11 q^{50} +1.56951e11 q^{51} -3.55097e11i q^{52} +8.00859e11 q^{53} -2.59764e11i q^{54} -2.44990e12i q^{55} -2.95292e11 q^{57} -3.02040e12 q^{58} -1.00781e12i q^{59} -3.04293e11 q^{60} +1.35932e12i q^{61} -4.12763e12i q^{62} +5.49756e11 q^{64} +5.31516e12 q^{65} +5.47806e11i q^{66} +4.86524e12 q^{67} -4.24434e12i q^{68} +7.77254e11i q^{69} +4.67641e12 q^{71} -3.47832e12 q^{72} +5.46449e12i q^{73} -7.34042e12 q^{74} -2.70578e12i q^{75} +7.98543e12i q^{76} -1.18849e12 q^{78} +2.85798e12 q^{79} +8.22885e12i q^{80} +2.15685e13 q^{81} -2.02373e13i q^{82} +5.45017e12i q^{83} +6.35301e13 q^{85} +3.30297e13 q^{86} +1.01091e13i q^{87} +1.48140e13 q^{88} +3.76330e13i q^{89} -5.20641e13i q^{90} +2.10189e13 q^{92} -1.38149e13 q^{93} +3.70738e12i q^{94} -1.19527e14 q^{95} -1.84000e12i q^{96} -1.14678e14i q^{97} -9.37287e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 163840 q^{4} - 35094864 q^{9}+O(q^{10}) \) 20 * q + 163840 * q^4 - 35094864 * q^9	\( 20 q + 163840 q^{4} - 35094864 q^{9} - 16800852 q^{11} + 562720524 q^{15} + 1342177280 q^{16} + 503510016 q^{18} + 5394565632 q^{22} + 13810196772 q^{23} - 28330165288 q^{25} + 27884908704 q^{29} - 108207023616 q^{30} - 287497125888 q^{36} + 54052055852 q^{37} + 252250808760 q^{39} + 726682953656 q^{43} - 137632579584 q^{44} + 573329969664 q^{46} + 1161106642944 q^{50} + 4839219891204 q^{51} - 3092542975092 q^{53} + 14789884876092 q^{57} + 4731726081024 q^{58} + 4609806532608 q^{60} + 10995116277760 q^{64} - 15033407865672 q^{65} + 9311641526452 q^{67} + 96606137494152 q^{71} + 4124754051072 q^{72} + 1133064966144 q^{74} + 88663911671808 q^{78} + 121034948165956 q^{79} + 214360529022684 q^{81} + 416326699526124 q^{85} - 4726670349312 q^{86} + 44192281657344 q^{88} + 113133131956224 q^{92} + 188350136380260 q^{93} - 50405029030980 q^{95} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q + 163840 * q^4 - 35094864 * q^9 - 16800852 * q^11 + 562720524 * q^15 + 1342177280 * q^16 + 503510016 * q^18 + 5394565632 * q^22 + 13810196772 * q^23 - 28330165288 * q^25 + 27884908704 * q^29 - 108207023616 * q^30 - 287497125888 * q^36 + 54052055852 * q^37 + 252250808760 * q^39 + 726682953656 * q^43 - 137632579584 * q^44 + 573329969664 * q^46 + 1161106642944 * q^50 + 4839219891204 * q^51 - 3092542975092 * q^53 + 14789884876092 * q^57 + 4731726081024 * q^58 + 4609806532608 * q^60 + 10995116277760 * q^64 - 15033407865672 * q^65 + 9311641526452 * q^67 + 96606137494152 * q^71 + 4124754051072 * q^72 + 1133064966144 * q^74 + 88663911671808 * q^78 + 121034948165956 * q^79 + 214360529022684 * q^81 + 416326699526124 * q^85 - 4726670349312 * q^86 + 44192281657344 * q^88 + 113133131956224 * q^92 + 188350136380260 * q^93 - 50405029030980 * q^95 + 1056686373672768 * q^99

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