LMFDB - Embedded newform 50.26.b.f.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not 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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 13801761x^{2} + 47622144774400 $ x^4 + 13801761*x^2 + 47622144774400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.3
Root			$2627.45i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.26.b.f.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4096.00i q^{2} -1.63785e6i q^{3} -1.67772e7 q^{4} +6.70863e9 q^{6} +2.07876e10i q^{7} -6.87195e10i q^{8} -1.83526e12 q^{9} +4.14605e12 q^{11} +2.74785e13i q^{12} -1.30955e14i q^{13} -8.51459e13 q^{14} +2.81475e14 q^{16} +4.62477e15i q^{17} -7.51722e15i q^{18} +5.62727e15 q^{19} +3.40469e16 q^{21} +1.69822e16i q^{22} -2.45654e16i q^{23} -1.12552e17 q^{24} +5.36390e17 q^{26} +1.61815e18i q^{27} -3.48758e17i q^{28} +1.86225e18 q^{29} +7.10276e17 q^{31} +1.15292e18i q^{32} -6.79060e18i q^{33} -1.89431e19 q^{34} +3.07905e19 q^{36} -5.29105e19i q^{37} +2.30493e19i q^{38} -2.14484e20 q^{39} -2.57715e20 q^{41} +1.39456e20i q^{42} -1.94678e19i q^{43} -6.95591e19 q^{44} +1.00620e20 q^{46} -1.05479e21i q^{47} -4.61013e20i q^{48} +9.08945e20 q^{49} +7.57467e21 q^{51} +2.19705e21i q^{52} +1.71922e21i q^{53} -6.62792e21 q^{54} +1.42851e21 q^{56} -9.21661e21i q^{57} +7.62780e21i q^{58} +2.29629e22 q^{59} -9.00207e20 q^{61} +2.90929e21i q^{62} -3.81506e22i q^{63} -4.72237e21 q^{64} +2.78143e22 q^{66} +1.50272e22i q^{67} -7.75908e22i q^{68} -4.02345e22 q^{69} +2.23447e23 q^{71} +1.26118e23i q^{72} -3.25252e23i q^{73} +2.16721e23 q^{74} -9.44099e22 q^{76} +8.61863e22i q^{77} -8.78525e23i q^{78} -6.06979e23 q^{79} +1.09528e24 q^{81} -1.05560e24i q^{82} -7.26128e23i q^{83} -5.71212e23 q^{84} +7.97403e22 q^{86} -3.05009e24i q^{87} -2.84914e23i q^{88} -1.91182e24 q^{89} +2.72223e24 q^{91} +4.12140e23i q^{92} -1.16332e24i q^{93} +4.32043e24 q^{94} +1.88831e24 q^{96} +1.71656e24i q^{97} +3.72304e24i q^{98} -7.60907e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 67108864 q^{4} + 3592912896 q^{6} - 4852391719572 q^{9} + 38689365583968 q^{11} - 278598423642112 q^{14} + 11\!\cdots\!24 q^{16} - 27069564790640 q^{19} + 36\!\cdots\!68 q^{21} - 60\!\cdots\!36 q^{24}+ \cdots - 33\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 67108864 * q^4 + 3592912896 * q^6 - 4852391719572 * q^9 + 38689365583968 * q^11 - 278598423642112 * q^14 + 1125899906842624 * q^16 - 27069564790640 * q^19 + 36382943373231168 * q^21 - 60279075725377536 * q^24 + 1046905225491152896 * q^26 + 3352194974618066760 * q^29 + 14251730312692753328 * q^31 - 24566644208258875392 * q^34 + 81409623995870871552 * q^36 - 436543015316491576944 * q^39 - 557953890277086019512 * q^41 - 649099843305197273088 * q^44 + 1448349866251256365056 * q^46 + 4150436861800468606332 * q^49 + 19049132675049275084688 * q^51 - 15774334415689015296000 * q^54 + 4674105930703219720192 * q^56 + 7531122243979537536720 * q^59 + 2177681218008805632248 * q^61 - 18889465931478580854784 * q^64 - 93688004873690155450368 * q^66 + 284670059282373004612416 * q^69 + 242975004103174569736848 * q^71 + 688208474290658872229888 * q^74 + 454151935518562058240 * q^76 - 1642777411067289683461280 * q^79 + 451795166977848570924804 * q^81 - 610404499688467923468288 * q^84 - 3493737291012689868652544 * q^86 - 10118439858808991441985960 * q^89 + 5360939619520672539104368 * q^91 + 9073628451972583753678848 * q^94 + 1011315073725015603019776 * q^96 - 33181012666288372472905824 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	4096.00i	0.707107i
$2$	4096.00i	0.707107i
$3$	− 1.63785e6i	− 1.77934i	−0.456608	−	0.889668i	$-0.650936\pi$
$3$	− 1.63785e6i	− 1.77934i	0.456608	−	0.889668i	$-0.349064\pi$
$4$	−1.67772e7	−0.500000
$5$	0	0
$5$	0	0
$6$	6.70863e9	1.25818
$7$	2.07876e10i	0.567647i	0.958877	+	0.283824i	$0.0916030\pi$
$7$	2.07876e10i	0.567647i	−0.958877	+	0.283824i	$0.908397\pi$
$8$	− 6.87195e10i	− 0.353553i
$9$	−1.83526e12	−2.16604
$10$	0	0
$11$	4.14605e12	0.398314	0.199157	−	0.979968i	$-0.436180\pi$
$11$	4.14605e12	0.398314	0.199157	+	0.979968i	$0.436180\pi$
$12$	2.74785e13i	0.889668i
$13$	− 1.30955e14i	− 1.55894i	−0.626441	−	0.779469i	$-0.715489\pi$
$13$	− 1.30955e14i	− 1.55894i	0.626441	−	0.779469i	$-0.284511\pi$
$14$	−8.51459e13	−0.401387
$15$	0	0
$16$	2.81475e14	0.250000
$17$	4.62477e15i	1.92521i	0.270904	+	0.962606i	$0.412677\pi$
$17$	4.62477e15i	1.92521i	−0.270904	+	0.962606i	$0.587323\pi$
$18$	− 7.51722e15i	− 1.53162i
$19$	5.62727e15	0.583280	0.291640	−	0.956528i	$-0.405799\pi$
$19$	5.62727e15	0.583280	0.291640	+	0.956528i	$0.405799\pi$
$20$	0	0
$21$	3.40469e16	1.01004
$22$	1.69822e16i	0.281651i
$23$	− 2.45654e16i	− 0.233737i	−0.993147	−	0.116868i	$-0.962714\pi$
$23$	− 2.45654e16i	− 0.233737i	0.993147	−	0.116868i	$-0.0372855\pi$
$24$	−1.12552e17	−0.629090
$25$	0	0
$26$	5.36390e17	1.10234
$27$	1.61815e18i	2.07477i
$28$	− 3.48758e17i	− 0.283824i
$29$	1.86225e18	0.977382	0.488691	−	0.872457i	$-0.337475\pi$
$29$	1.86225e18	0.977382	0.488691	+	0.872457i	$0.337475\pi$
$30$	0	0
$31$	7.10276e17	0.161959	0.0809796	−	0.996716i	$-0.474195\pi$
$31$	7.10276e17	0.161959	0.0809796	+	0.996716i	$0.474195\pi$
$32$	1.15292e18i	0.176777i
$33$	− 6.79060e18i	− 0.708735i
$34$	−1.89431e19	−1.36133
$35$	0	0
$36$	3.07905e19	1.08302
$37$	− 5.29105e19i	− 1.32136i	−0.750669	−	0.660679i	$-0.770269\pi$
$37$	− 5.29105e19i	− 1.32136i	0.750669	−	0.660679i	$-0.229731\pi$
$38$	2.30493e19i	0.412442i
$39$	−2.14484e20	−2.77387
$40$	0	0
$41$	−2.57715e20	−1.78378	−0.891892	−	0.452249i	$-0.850622\pi$
$41$	−2.57715e20	−1.78378	−0.891892	+	0.452249i	$0.850622\pi$
$42$	1.39456e20i	0.714203i
$43$	− 1.94678e19i	− 0.0742954i	−0.999310	−	0.0371477i	$-0.988173\pi$
$43$	− 1.94678e19i	− 0.0742954i	0.999310	−	0.0371477i	$-0.0118272\pi$
$44$	−6.95591e19	−0.199157
$45$	0	0
$46$	1.00620e20	0.165277
$47$	− 1.05479e21i	− 1.32417i	−0.749428	−	0.662085i	$-0.769672\pi$
$47$	− 1.05479e21i	− 1.32417i	0.749428	−	0.662085i	$-0.230328\pi$
$48$	− 4.61013e20i	− 0.444834i
$49$	9.08945e20	0.677777
$50$	0	0
$51$	7.57467e21	3.42560
$52$	2.19705e21i	0.779469i
$53$	1.71922e21i	0.480709i	0.970685	+	0.240354i	$0.0772636\pi$
$53$	1.71922e21i	0.480709i	−0.970685	+	0.240354i	$0.922736\pi$
$54$	−6.62792e21	−1.46709
$55$	0	0
$56$	1.42851e21	0.200694
$57$	− 9.21661e21i	− 1.03785i
$58$	7.62780e21i	0.691113i
$59$	2.29629e22	1.68026	0.840130	−	0.542386i	$-0.182479\pi$
$59$	2.29629e22	1.68026	0.840130	+	0.542386i	$0.182479\pi$
$60$	0	0
$61$	−9.00207e20	−0.0434230	−0.0217115	−	0.999764i	$-0.506912\pi$
$61$	−9.00207e20	−0.0434230	−0.0217115	+	0.999764i	$0.506912\pi$
$62$	2.90929e21i	0.114523i
$63$	− 3.81506e22i	− 1.22955i
$64$	−4.72237e21	−0.125000
$65$	0	0
$66$	2.78143e22	0.501151
$67$	1.50272e22i	0.224358i	0.993688	+	0.112179i	$0.0357831\pi$
$67$	1.50272e22i	0.224358i	−0.993688	+	0.112179i	$0.964217\pi$
$68$	− 7.75908e22i	− 0.962606i
$69$	−4.02345e22	−0.415896
$70$	0	0
$71$	2.23447e23	1.61602	0.808008	−	0.589172i	$-0.200546\pi$
$71$	2.23447e23	1.61602	0.808008	+	0.589172i	$0.200546\pi$
$72$	1.26118e23i	0.765810i
$73$	− 3.25252e23i	− 1.66220i	−0.556122	−	0.831101i	$-0.687711\pi$
$73$	− 3.25252e23i	− 1.66220i	0.556122	−	0.831101i	$-0.312289\pi$
$74$	2.16721e23	0.934341
$75$	0	0
$76$	−9.44099e22	−0.291640
$77$	8.61863e22i	0.226102i
$78$	− 8.78525e23i	− 1.96142i
$79$	−6.06979e23	−1.15567	−0.577837	−	0.816152i	$-0.696103\pi$
$79$	−6.06979e23	−1.15567	−0.577837	+	0.816152i	$0.696103\pi$
$80$	0	0
$81$	1.09528e24	1.52568
$82$	− 1.05560e24i	− 1.26133i
$83$	− 7.26128e23i	− 0.745653i	−0.927901	−	0.372827i	$-0.878389\pi$
$83$	− 7.26128e23i	− 0.745653i	0.927901	−	0.372827i	$-0.121611\pi$
$84$	−5.71212e23	−0.505018
$85$	0	0
$86$	7.97403e22	0.0525348
$87$	− 3.05009e24i	− 1.73909i
$88$	− 2.84914e23i	− 0.140825i
$89$	−1.91182e24	−0.820488	−0.410244	−	0.911976i	$-0.634556\pi$
$89$	−1.91182e24	−0.820488	−0.410244	+	0.911976i	$0.634556\pi$
$90$	0	0
$91$	2.72223e24	0.884926
$92$	4.12140e23i	0.116868i
$93$	− 1.16332e24i	− 0.288180i
$94$	4.32043e24	0.936330
$95$	0	0
$96$	1.88831e24	0.314545
$97$	1.71656e24i	0.251195i	0.992081	+	0.125598i	$0.0400849\pi$
$97$	1.71656e24i	0.251195i	−0.992081	+	0.125598i	$0.959915\pi$
$98$	3.72304e24i	0.479260i
$99$	−7.60907e24	−0.862763
$100$	0	0
$101$	1.34215e25	1.18518	0.592590	−	0.805504i	$-0.298105\pi$
$101$	1.34215e25	1.18518	0.592590	+	0.805504i	$0.298105\pi$
$102$	3.10259e25i	2.42227i
$103$	2.08010e25i	1.43754i	0.695249	+	0.718769i	$0.255294\pi$
$103$	2.08010e25i	1.43754i	−0.695249	+	0.718769i	$0.744706\pi$
$104$	−8.99913e24	−0.551168
$105$	0	0
$106$	−7.04191e24	−0.339912
$107$	− 2.98949e25i	− 1.28322i	−0.767032	−	0.641609i	$-0.778267\pi$
$107$	− 2.98949e25i	− 1.28322i	0.767032	−	0.641609i	$-0.221733\pi$
$108$	− 2.71480e25i	− 1.03739i
$109$	−5.99753e24	−0.204240	−0.102120	−	0.994772i	$-0.532563\pi$
$109$	−5.99753e24	−0.204240	−0.102120	+	0.994772i	$0.532563\pi$
$110$	0	0
$111$	−8.66594e25	−2.35114
$112$	5.85118e24i	0.141912i
$113$	− 3.21651e25i	− 0.698080i	−0.937108	−	0.349040i	$-0.886508\pi$
$113$	− 3.21651e25i	− 0.698080i	0.937108	−	0.349040i	$-0.113492\pi$
$114$	3.77512e25	0.733872
$115$	0	0
$116$	−3.12435e25	−0.488691
$117$	2.40335e26i	3.37672i
$118$	9.40560e25i	1.18812i
$119$	−9.61378e25	−1.09284
$120$	0	0
$121$	−9.11573e25	−0.841346
$122$	− 3.68725e24i	− 0.0307047i
$123$	4.22099e26i	3.17395i
$124$	−1.19165e25	−0.0809796
$125$	0	0
$126$	1.56265e26	0.869420
$127$	1.12460e26i	0.566829i	0.958998	+	0.283414i	$0.0914671\pi$
$127$	1.12460e26i	0.566829i	−0.958998	+	0.283414i	$0.908533\pi$
$128$	− 1.93428e25i	− 0.0883883i
$129$	−3.18854e25	−0.132197
$130$	0	0
$131$	2.26749e26	0.775630	0.387815	−	0.921737i	$-0.373230\pi$
$131$	2.26749e26	0.775630	0.387815	+	0.921737i	$0.373230\pi$
$132$	1.13927e26i	0.354367i
$133$	1.16977e26i	0.331098i
$134$	−6.15513e25	−0.158645
$135$	0	0
$136$	3.17812e26	0.680665
$137$	− 6.81423e26i	− 1.33171i	−0.746081	−	0.665855i	$-0.768067\pi$
$137$	− 6.81423e26i	− 1.33171i	0.746081	−	0.665855i	$-0.231933\pi$
$138$	− 1.64800e26i	− 0.294083i
$139$	−5.03091e26	−0.820279	−0.410140	−	0.912023i	$-0.634520\pi$
$139$	−5.03091e26	−0.820279	−0.410140	+	0.912023i	$0.634520\pi$
$140$	0	0
$141$	−1.72759e27	−2.35614
$142$	9.15240e26i	1.14270i
$143$	− 5.42944e26i	− 0.620947i
$144$	−5.16579e26	−0.541509
$145$	0	0
$146$	1.33223e27	1.17535
$147$	− 1.48871e27i	− 1.20599i
$148$	8.87691e26i	0.660679i
$149$	−7.27393e26	−0.497669	−0.248835	−	0.968546i	$-0.580048\pi$
$149$	−7.27393e26	−0.497669	−0.248835	+	0.968546i	$0.580048\pi$
$150$	0	0
$151$	9.92827e25	0.0574992	0.0287496	−	0.999587i	$-0.490847\pi$
$151$	9.92827e25	0.0574992	0.0287496	+	0.999587i	$0.490847\pi$
$152$	− 3.86703e26i	− 0.206221i
$153$	− 8.48765e27i	− 4.17008i
$154$	−3.53019e26	−0.159878
$155$	0	0
$156$	3.59844e27	1.38694
$157$	2.27168e26i	0.0808355i	0.999183	+	0.0404177i	$0.0128689\pi$
$157$	2.27168e26i	0.0808355i	−0.999183	+	0.0404177i	$0.987131\pi$
$158$	− 2.48619e27i	− 0.817184i
$159$	2.81581e27	0.855342
$160$	0	0
$161$	5.10656e26	0.132680
$162$	4.48628e27i	1.07882i
$163$	5.17654e27i	1.15264i	0.817223	+	0.576322i	$0.195512\pi$
$163$	5.17654e27i	1.15264i	−0.817223	+	0.576322i	$0.804488\pi$
$164$	4.32375e27	0.891892
$165$	0	0
$166$	2.97422e27	0.527256
$167$	− 1.02965e27i	− 0.169330i	−0.996409	−	0.0846652i	$-0.973018\pi$
$167$	− 1.02965e27i	− 0.169330i	0.996409	−	0.0846652i	$-0.0269821\pi$
$168$	− 2.33969e27i	− 0.357101i
$169$	−1.00927e28	−1.43029
$170$	0	0
$171$	−1.03275e28	−1.26341
$172$	3.26616e26i	0.0371477i
$173$	1.24548e28i	1.31753i	0.752348	+	0.658766i	$0.228921\pi$
$173$	1.24548e28i	1.31753i	−0.752348	+	0.658766i	$0.771079\pi$
$174$	1.24932e28	1.22972
$175$	0	0
$176$	1.16701e27	0.0995785
$177$	− 3.76097e28i	− 2.98975i
$178$	− 7.83082e27i	− 0.580173i
$179$	−4.58615e27	−0.316800	−0.158400	−	0.987375i	$-0.550634\pi$
$179$	−4.58615e27	−0.316800	−0.158400	+	0.987375i	$0.550634\pi$
$180$	0	0
$181$	−1.24754e28	−0.750019	−0.375010	−	0.927021i	$-0.622361\pi$
$181$	−1.24754e28	−0.750019	−0.375010	+	0.927021i	$0.622361\pi$
$182$	1.11502e28i	0.625737i
$183$	1.47440e27i	0.0772641i
$184$	−1.68812e27	−0.0826384
$185$	0	0
$186$	4.76498e27	0.203774
$187$	1.91745e28i	0.766839i
$188$	1.76965e28i	0.662085i
$189$	−3.36373e28	−1.17774
$190$	0	0
$191$	−5.82809e28	−1.78900	−0.894498	−	0.447072i	$-0.852467\pi$
$191$	−5.82809e28	−1.78900	−0.894498	+	0.447072i	$0.852467\pi$
$192$	7.73452e27i	0.222417i
$193$	− 2.07224e28i	− 0.558437i	−0.960228	−	0.279218i	$-0.909925\pi$
$193$	− 2.07224e28i	− 0.558437i	0.960228	−	0.279218i	$-0.0900753\pi$
$194$	−7.03102e27	−0.177622
$195$	0	0
$196$	−1.52496e28	−0.338888
$197$	− 2.21753e28i	− 0.462425i	−0.972903	−	0.231213i	$-0.925731\pi$
$197$	− 2.21753e28i	− 0.462425i	0.972903	−	0.231213i	$-0.0742693\pi$
$198$	− 3.11668e28i	− 0.610066i
$199$	2.56881e28	0.472138	0.236069	−	0.971736i	$-0.424141\pi$
$199$	2.56881e28	0.472138	0.236069	+	0.971736i	$0.424141\pi$
$200$	0	0
$201$	2.46122e28	0.399209
$202$	5.49745e28i	0.838049i
$203$	3.87118e28i	0.554808i
$204$	−1.27082e29	−1.71280
$205$	0	0
$206$	−8.52010e28	−1.01649
$207$	4.50839e28i	0.506282i
$208$	− 3.68604e28i	− 0.389734i
$209$	2.33309e28	0.232329
$210$	0	0
$211$	−1.69750e29	−1.50065	−0.750323	−	0.661072i	$-0.770102\pi$
$211$	−1.69750e29	−1.50065	−0.750323	+	0.661072i	$0.770102\pi$
$212$	− 2.88437e28i	− 0.240354i
$213$	− 3.65973e29i	− 2.87543i
$214$	1.22450e29	0.907372
$215$	0	0
$216$	1.11198e29	0.733543
$217$	1.47649e28i	0.0919357i
$218$	− 2.45659e28i	− 0.144420i
$219$	−5.32713e29	−2.95762
$220$	0	0
$221$	6.05635e29	3.00129
$222$	− 3.54957e29i	− 1.66251i
$223$	− 1.64686e29i	− 0.729197i	−0.931165	−	0.364598i	$-0.881206\pi$
$223$	− 1.64686e29i	− 0.729197i	0.931165	−	0.364598i	$-0.118794\pi$
$224$	−2.39665e28	−0.100347
$225$	0	0
$226$	1.31748e29	0.493617
$227$	5.10933e29i	1.81151i	0.423803	+	0.905754i	$0.360695\pi$
$227$	5.10933e29i	1.81151i	−0.423803	+	0.905754i	$0.639305\pi$
$228$	1.54629e29i	0.518926i
$229$	−1.25023e29	−0.397235	−0.198617	−	0.980077i	$-0.563645\pi$
$229$	−1.25023e29	−0.397235	−0.198617	+	0.980077i	$0.563645\pi$
$230$	0	0
$231$	1.41160e29	0.402311
$232$	− 1.27973e29i	− 0.345557i
$233$	− 5.70548e29i	− 1.45997i	−0.683464	−	0.729984i	$-0.739528\pi$
$233$	− 5.70548e29i	− 1.45997i	0.683464	−	0.729984i	$-0.260472\pi$
$234$	−9.84414e29	−2.38770
$235$	0	0
$236$	−3.85253e29	−0.840130
$237$	9.94140e29i	2.05633i
$238$	− 3.93780e29i	− 0.772756i
$239$	−6.05498e29	−1.12756	−0.563780	−	0.825925i	$-0.690653\pi$
$239$	−6.05498e29	−1.12756	−0.563780	+	0.825925i	$0.690653\pi$
$240$	0	0
$241$	−5.11295e29	−0.857943	−0.428972	−	0.903318i	$-0.641124\pi$
$241$	−5.11295e29	−0.857943	−0.428972	+	0.903318i	$0.641124\pi$
$242$	− 3.73380e29i	− 0.594921i
$243$	− 4.22872e29i	− 0.639927i
$244$	1.51030e28	0.0217115
$245$	0	0
$246$	−1.72892e30	−2.24432
$247$	− 7.36916e29i	− 0.909298i
$248$	− 4.88098e28i	− 0.0572613i
$249$	−1.18929e30	−1.32677
$250$	0	0
$251$	2.51767e29	0.254142	0.127071	−	0.991894i	$-0.459442\pi$
$251$	2.51767e29	0.254142	0.127071	+	0.991894i	$0.459442\pi$
$252$	6.40061e29i	0.614773i
$253$	− 1.01850e29i	− 0.0931006i
$254$	−4.60636e29	−0.400808
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	− 4.32516e29i	− 0.324967i	−0.986711	−	0.162483i	$-0.948050\pi$
$257$	− 4.32516e29i	− 0.324967i	0.986711	−	0.162483i	$-0.0519503\pi$
$258$	− 1.30603e29i	− 0.0934771i
$259$	1.09988e30	0.750065
$260$	0	0
$261$	−3.41772e30	−2.11705
$262$	9.28765e29i	0.548454i
$263$	3.00951e30i	1.69453i	0.531171	+	0.847265i	$0.321752\pi$
$263$	3.00951e30i	1.69453i	−0.531171	+	0.847265i	$0.678248\pi$
$264$	−4.66646e29	−0.250576
$265$	0	0
$266$	−4.79139e29	−0.234121
$267$	3.13127e30i	1.45992i
$268$	− 2.52114e29i	− 0.112179i
$269$	−5.09495e29	−0.216390	−0.108195	−	0.994130i	$-0.534507\pi$
$269$	−5.09495e29	−0.216390	−0.108195	+	0.994130i	$0.534507\pi$
$270$	0	0
$271$	1.05937e30	0.410140	0.205070	−	0.978747i	$-0.434258\pi$
$271$	1.05937e30	0.410140	0.205070	+	0.978747i	$0.434258\pi$
$272$	1.30176e30i	0.481303i
$273$	− 4.45860e30i	− 1.57458i
$274$	2.79111e30	0.941661
$275$	0	0
$276$	6.75022e29	0.207948
$277$	− 5.67674e30i	− 1.67148i	−0.549124	−	0.835741i	$-0.685039\pi$
$277$	− 5.67674e30i	− 1.67148i	0.549124	−	0.835741i	$-0.314961\pi$
$278$	− 2.06066e30i	− 0.580025i
$279$	−1.30354e30	−0.350810
$280$	0	0
$281$	−1.50424e30	−0.370245	−0.185122	−	0.982715i	$-0.559268\pi$
$281$	−1.50424e30	−0.370245	−0.185122	+	0.982715i	$0.559268\pi$
$282$	− 7.07621e30i	− 1.66605i
$283$	− 4.46973e30i	− 1.00682i	−0.864048	−	0.503409i	$-0.832079\pi$
$283$	− 4.46973e30i	− 1.00682i	0.864048	−	0.503409i	$-0.167921\pi$
$284$	−3.74882e30	−0.808008
$285$	0	0
$286$	2.22390e30	0.439076
$287$	− 5.35728e30i	− 1.01256i
$288$	− 2.11591e30i	− 0.382905i
$289$	−1.56179e31	−2.70644
$290$	0	0
$291$	2.81146e30	0.446961
$292$	5.45682e30i	0.831101i
$293$	4.32602e30i	0.631311i	0.948874	+	0.315655i	$0.102224\pi$
$293$	4.32602e30i	0.631311i	−0.948874	+	0.315655i	$0.897776\pi$
$294$	6.09777e30	0.852766
$295$	0	0
$296$	−3.63598e30	−0.467170
$297$	6.70891e30i	0.826411i
$298$	− 2.97940e30i	− 0.351905i
$299$	−3.21696e30	−0.364381
$300$	0	0
$301$	4.04689e29	0.0421736
$302$	4.06662e29i	0.0406581i
$303$	− 2.19824e31i	− 2.10883i
$304$	1.58393e30	0.145820
$305$	0	0
$306$	3.47654e31	2.94869
$307$	− 1.40982e31i	− 1.14798i	−0.818862	−	0.573991i	$-0.805395\pi$
$307$	− 1.40982e31i	− 1.14798i	0.818862	−	0.573991i	$-0.194605\pi$
$308$	− 1.44597e30i	− 0.113051i
$309$	3.40689e31	2.55786
$310$	0	0
$311$	−4.30946e30	−0.298482	−0.149241	−	0.988801i	$-0.547683\pi$
$311$	−4.30946e30	−0.298482	−0.149241	+	0.988801i	$0.547683\pi$
$312$	1.47392e31i	0.980712i
$313$	− 2.24958e30i	− 0.143813i	−0.997411	−	0.0719065i	$-0.977092\pi$
$313$	− 2.24958e30i	− 0.143813i	0.997411	−	0.0719065i	$-0.0229083\pi$
$314$	−9.30481e29	−0.0571593
$315$	0	0
$316$	1.01834e31	0.577837
$317$	− 7.47129e30i	− 0.407525i	−0.979020	−	0.203763i	$-0.934683\pi$
$317$	− 7.47129e30i	− 0.407525i	0.979020	−	0.203763i	$-0.0653171\pi$
$318$	1.15336e31i	0.604818i
$319$	7.72100e30	0.389305
$320$	0	0
$321$	−4.89634e31	−2.28328
$322$	2.09165e30i	0.0938189i
$323$	2.60248e31i	1.12294i
$324$	−1.83758e31	−0.762840
$325$	0	0
$326$	−2.12031e31	−0.815042
$327$	9.82304e30i	0.363412i
$328$	1.77101e31i	0.630663i
$329$	2.19266e31	0.751662
$330$	0	0
$331$	−1.01412e31	−0.322286	−0.161143	−	0.986931i	$-0.551518\pi$
$331$	−1.01412e31	−0.322286	−0.161143	+	0.986931i	$0.551518\pi$
$332$	1.21824e31i	0.372827i
$333$	9.71045e31i	2.86211i
$334$	4.21746e30	0.119735
$335$	0	0
$336$	9.58335e30	0.252509
$337$	4.27054e31i	1.08420i	0.840315	+	0.542099i	$0.182370\pi$
$337$	4.27054e31i	1.08420i	−0.840315	+	0.542099i	$0.817630\pi$
$338$	− 4.13396e31i	− 1.01136i
$339$	−5.26816e31	−1.24212
$340$	0	0
$341$	2.94484e30	0.0645107
$342$	− 4.23014e31i	− 0.893364i
$343$	4.67723e31i	0.952385i
$344$	−1.33782e30	−0.0262674
$345$	0	0
$346$	−5.10149e31	−0.931636
$347$	− 1.42992e30i	− 0.0251880i	−0.999921	−	0.0125940i	$-0.995991\pi$
$347$	− 1.42992e30i	− 0.0251880i	0.999921	−	0.0125940i	$-0.00400890\pi$
$348$	5.11720e31i	0.869545i
$349$	−3.55571e30	−0.0582920	−0.0291460	−	0.999575i	$-0.509279\pi$
$349$	−3.55571e30	−0.0582920	−0.0291460	+	0.999575i	$0.509279\pi$
$350$	0	0
$351$	2.11903e32	3.23444
$352$	4.78007e30i	0.0704127i
$353$	6.63973e31i	0.943988i	0.881602	+	0.471994i	$0.156466\pi$
$353$	6.63973e31i	0.943988i	−0.881602	+	0.471994i	$0.843534\pi$
$354$	1.54049e32	2.11407
$355$	0	0
$356$	3.20750e31	0.410244
$357$	1.57459e32i	1.94453i
$358$	− 1.87849e31i	− 0.224012i
$359$	1.86335e31	0.214593	0.107296	−	0.994227i	$-0.465781\pi$
$359$	1.86335e31	0.214593	0.107296	+	0.994227i	$0.465781\pi$
$360$	0	0
$361$	−6.14104e31	−0.659784
$362$	− 5.10992e31i	− 0.530344i
$363$	1.49302e32i	1.49704i
$364$	−4.56714e31	−0.442463
$365$	0	0
$366$	−6.03915e30	−0.0546339
$367$	− 8.66272e31i	− 0.757406i	−0.925518	−	0.378703i	$-0.876370\pi$
$367$	− 8.66272e31i	− 0.757406i	0.925518	−	0.378703i	$-0.123630\pi$
$368$	− 6.91456e30i	− 0.0584341i
$369$	4.72975e32	3.86374
$370$	0	0
$371$	−3.57383e31	−0.272873
$372$	1.95173e31i	0.144090i
$373$	− 2.52885e32i	− 1.80536i	−0.430316	−	0.902678i	$-0.641598\pi$
$373$	− 2.52885e32i	− 1.80536i	0.430316	−	0.902678i	$-0.358402\pi$
$374$	−7.85388e31	−0.542237
$375$	0	0
$376$	−7.24848e31	−0.468165
$377$	− 2.43871e32i	− 1.52368i
$378$	− 1.37779e32i	− 0.832787i
$379$	7.89983e31	0.461985	0.230992	−	0.972956i	$-0.425803\pi$
$379$	7.89983e31	0.461985	0.230992	+	0.972956i	$0.425803\pi$
$380$	0	0
$381$	1.84192e32	1.00858
$382$	− 2.38719e32i	− 1.26501i
$383$	2.10109e32i	1.07761i	0.842432	+	0.538803i	$0.181123\pi$
$383$	2.10109e32i	1.07761i	−0.842432	+	0.538803i	$0.818877\pi$
$384$	−3.16806e31	−0.157273
$385$	0	0
$386$	8.48790e31	0.394874
$387$	3.57285e31i	0.160927i
$388$	− 2.87991e31i	− 0.125598i
$389$	−1.39534e32	−0.589264	−0.294632	−	0.955611i	$-0.595197\pi$
$389$	−1.39534e32	−0.589264	−0.294632	+	0.955611i	$0.595197\pi$
$390$	0	0
$391$	1.13610e32	0.449993
$392$	− 6.24622e31i	− 0.239630i
$393$	− 3.71381e32i	− 1.38011i
$394$	9.08300e31	0.326984
$395$	0	0
$396$	1.27659e32	0.431382
$397$	1.58963e32i	0.520494i	0.965542	+	0.260247i	$0.0838040\pi$
$397$	1.58963e32i	0.520494i	−0.965542	+	0.260247i	$0.916196\pi$
$398$	1.05219e32i	0.333852i
$399$	1.91591e32	0.589134
$400$	0	0
$401$	4.43370e32	1.28074	0.640371	−	0.768066i	$-0.278781\pi$
$401$	4.43370e32	1.28074	0.640371	+	0.768066i	$0.278781\pi$
$402$	1.00812e32i	0.282283i
$403$	− 9.30138e31i	− 0.252484i
$404$	−2.25176e32	−0.592590
$405$	0	0
$406$	−1.58563e32	−0.392308
$407$	− 2.19369e32i	− 0.526315i
$408$	− 5.20528e32i	− 1.21113i
$409$	1.41371e32	0.319021	0.159510	−	0.987196i	$-0.449008\pi$
$409$	1.41371e32	0.319021	0.159510	+	0.987196i	$0.449008\pi$
$410$	0	0
$411$	−1.11607e33	−2.36956
$412$	− 3.48983e32i	− 0.718769i
$413$	4.77343e32i	0.953795i
$414$	−1.84664e32	−0.357996
$415$	0	0
$416$	1.50980e32	0.275584
$417$	8.23987e32i	1.45955i
$418$	9.55634e31i	0.164281i
$419$	−5.65693e32	−0.943856	−0.471928	−	0.881637i	$-0.656442\pi$
$419$	−5.65693e32	−0.943856	−0.471928	+	0.881637i	$0.656442\pi$
$420$	0	0
$421$	−9.28896e32	−1.46030	−0.730148	−	0.683289i	$-0.760549\pi$
$421$	−9.28896e32	−1.46030	−0.730148	+	0.683289i	$0.760549\pi$
$422$	− 6.95294e32i	− 1.06112i
$423$	1.93582e33i	2.86820i
$424$	1.18144e32	0.169956
$425$	0	0
$426$	1.49902e33	2.03324
$427$	− 1.87131e31i	− 0.0246489i
$428$	5.01554e32i	0.641609i
$429$	−8.89260e32	−1.10487
$430$	0	0
$431$	−1.00278e33	−1.17555	−0.587773	−	0.809026i	$-0.699995\pi$
$431$	−1.00278e33	−1.17555	−0.587773	+	0.809026i	$0.699995\pi$
$432$	4.55467e32i	0.518693i
$433$	− 5.32205e31i	− 0.0588817i	−0.999567	−	0.0294408i	$-0.990627\pi$
$433$	− 5.32205e31i	− 0.0588817i	0.999567	−	0.0294408i	$-0.00937266\pi$
$434$	−6.04771e31	−0.0650084
$435$	0	0
$436$	1.00622e32	0.102120
$437$	− 1.38236e32i	− 0.136334i
$438$	− 2.18199e33i	− 2.09135i
$439$	4.95347e32	0.461427	0.230714	−	0.973022i	$-0.425894\pi$
$439$	4.95347e32	0.461427	0.230714	+	0.973022i	$0.425894\pi$
$440$	0	0
$441$	−1.66815e33	−1.46809
$442$	2.48068e33i	2.12223i
$443$	− 6.00200e32i	− 0.499171i	−0.968353	−	0.249585i	$-0.919706\pi$
$443$	− 6.00200e32i	− 0.499171i	0.968353	−	0.249585i	$-0.0802943\pi$
$444$	1.45390e33	1.17557
$445$	0	0
$446$	6.74552e32	0.515620
$447$	1.19136e33i	0.885521i
$448$	− 9.81666e31i	− 0.0709559i
$449$	−2.44542e31	−0.0171899	−0.00859497	−	0.999963i	$-0.502736\pi$
$449$	−2.44542e31	−0.0171899	−0.00859497	+	0.999963i	$0.502736\pi$
$450$	0	0
$451$	−1.06850e33	−0.710506
$452$	5.39642e32i	0.349040i
$453$	− 1.62610e32i	− 0.102310i
$454$	−2.09278e33	−1.28093
$455$	0	0
$456$	−6.33361e32	−0.366936
$457$	1.65246e33i	0.931492i	0.884918	+	0.465746i	$0.154214\pi$
$457$	1.65246e33i	0.931492i	−0.884918	+	0.465746i	$0.845786\pi$
$458$	− 5.12095e32i	− 0.280887i
$459$	−7.48355e33	−3.99438
$460$	0	0
$461$	1.16768e33	0.590284	0.295142	−	0.955453i	$-0.404633\pi$
$461$	1.16768e33	0.590284	0.295142	+	0.955453i	$0.404633\pi$
$462$	5.78192e32i	0.284477i
$463$	− 2.39229e33i	− 1.14565i	−0.819679	−	0.572823i	$-0.805848\pi$
$463$	− 2.39229e33i	− 1.14565i	0.819679	−	0.572823i	$-0.194152\pi$
$464$	5.24178e32	0.244345
$465$	0	0
$466$	2.33697e33	1.03235
$467$	− 4.47360e33i	− 1.92396i	−0.273116	−	0.961981i	$-0.588054\pi$
$467$	− 4.47360e33i	− 1.92396i	0.273116	−	0.961981i	$-0.411946\pi$
$468$	− 4.03216e33i	− 1.68836i
$469$	−3.12379e32	−0.127356
$470$	0	0
$471$	3.72067e32	0.143834
$472$	− 1.57800e33i	− 0.594061i
$473$	− 8.07146e31i	− 0.0295929i
$474$	−4.07200e33	−1.45405
$475$	0	0
$476$	1.61292e33	0.546421
$477$	− 3.15521e33i	− 1.04123i
$478$	− 2.48012e33i	− 0.797305i
$479$	−2.33765e33	−0.732127	−0.366064	−	0.930590i	$-0.619295\pi$
$479$	−2.33765e33	−0.732127	−0.366064	+	0.930590i	$0.619295\pi$
$480$	0	0
$481$	−6.92887e33	−2.05991
$482$	− 2.09426e33i	− 0.606657i
$483$	− 8.36377e32i	− 0.236082i
$484$	1.52937e33	0.420673
$485$	0	0
$486$	1.73208e33	0.452496
$487$	1.27777e33i	0.325343i	0.986680	+	0.162672i	$0.0520111\pi$
$487$	1.27777e33i	0.325343i	−0.986680	+	0.162672i	$0.947989\pi$
$488$	6.18618e31i	0.0153523i
$489$	8.47839e33	2.05094
$490$	0	0
$491$	5.48118e33	1.25996	0.629978	−	0.776613i	$-0.283064\pi$
$491$	5.48118e33	1.25996	0.629978	+	0.776613i	$0.283064\pi$
$492$	− 7.08164e33i	− 1.58698i
$493$	8.61250e33i	1.88167i
$494$	3.01841e33	0.642970
$495$	0	0
$496$	1.99925e32	0.0404898
$497$	4.64493e33i	0.917327i
$498$	− 4.87132e33i	− 0.938167i
$499$	−3.23941e33	−0.608429	−0.304214	−	0.952604i	$-0.598394\pi$
$499$	−3.23941e33	−0.608429	−0.304214	+	0.952604i	$0.598394\pi$
$500$	0	0
$501$	−1.68642e33	−0.301296
$502$	1.03124e33i	0.179706i
$503$	− 4.70148e33i	− 0.799162i	−0.916698	−	0.399581i	$-0.869156\pi$
$503$	− 4.70148e33i	− 0.799162i	0.916698	−	0.399581i	$-0.130844\pi$
$504$	−2.62169e33	−0.434710
$505$	0	0
$506$	4.17176e32	0.0658321
$507$	1.65303e34i	2.54496i
$508$	− 1.88677e33i	− 0.283414i
$509$	7.74677e32	0.113540	0.0567699	−	0.998387i	$-0.481920\pi$
$509$	7.74677e32	0.113540	0.0567699	+	0.998387i	$0.481920\pi$
$510$	0	0
$511$	6.76120e33	0.943544
$512$	3.24519e32i	0.0441942i
$513$	9.10574e33i	1.21017i
$514$	1.77159e33	0.229786
$515$	0	0
$516$	5.34948e32	0.0660983
$517$	− 4.37322e33i	− 0.527436i
$518$	4.50512e33i	0.530376i
$519$	2.03991e34	2.34433
$520$	0	0
$521$	−7.09925e33	−0.777573	−0.388786	−	0.921328i	$-0.627106\pi$
$521$	−7.09925e33	−0.777573	−0.388786	+	0.921328i	$0.627106\pi$
$522$	− 1.39990e34i	− 1.49698i
$523$	− 8.65615e33i	− 0.903761i	−0.892079	−	0.451880i	$-0.850753\pi$
$523$	− 8.65615e33i	− 0.903761i	0.892079	−	0.451880i	$-0.149247\pi$
$524$	−3.80422e33	−0.387815
$525$	0	0
$526$	−1.23270e34	−1.19821
$527$	3.28486e33i	0.311806i
$528$	− 1.91138e33i	− 0.177184i
$529$	1.04423e34	0.945367
$530$	0	0
$531$	−4.21428e34	−3.63950
$532$	− 1.96255e33i	− 0.165549i
$533$	3.37490e34i	2.78081i
$534$	−1.28257e34	−1.03232
$535$	0	0
$536$	1.03266e33	0.0793226
$537$	7.51142e33i	0.563694i
$538$	− 2.08689e33i	− 0.153011i
$539$	3.76853e33	0.269968
$540$	0	0
$541$	2.82575e34	1.93272	0.966358	−	0.257202i	$-0.0828007\pi$
$541$	2.82575e34	1.93272	0.966358	+	0.257202i	$0.0828007\pi$
$542$	4.33918e33i	0.290013i
$543$	2.04328e34i	1.33454i
$544$	−5.33200e33	−0.340333
$545$	0	0
$546$	1.82624e34	1.11340
$547$	− 1.70002e34i	− 1.01300i	−0.862239	−	0.506502i	$-0.830938\pi$
$547$	− 1.70002e34i	− 1.01300i	0.862239	−	0.506502i	$-0.169062\pi$
$548$	1.14324e34i	0.665855i
$549$	1.65211e33	0.0940558
$550$	0	0
$551$	1.04794e34	0.570088
$552$	2.76489e33i	0.147041i
$553$	− 1.26176e34i	− 0.656015i
$554$	2.32519e34	1.18192
$555$	0	0
$556$	8.44047e33	0.410140
$557$	− 1.04504e34i	− 0.496529i	−0.968692	−	0.248264i	$-0.920140\pi$
$557$	− 1.04504e34i	− 0.496529i	0.968692	−	0.248264i	$-0.0798602\pi$
$558$	− 5.33930e33i	− 0.248060i
$559$	−2.54940e33	−0.115822
$560$	0	0
$561$	3.14050e34	1.36447
$562$	− 6.16138e33i	− 0.261803i
$563$	− 1.28118e34i	− 0.532421i	−0.963915	−	0.266211i	$-0.914228\pi$
$563$	− 1.28118e34i	− 0.532421i	0.963915	−	0.266211i	$-0.0857717\pi$
$564$	2.89842e34	1.17807
$565$	0	0
$566$	1.83080e34	0.711927
$567$	2.27683e34i	0.866048i
$568$	− 1.53552e34i	− 0.571348i
$569$	6.19441e33	0.225474	0.112737	−	0.993625i	$-0.464038\pi$
$569$	6.19441e33	0.225474	0.112737	+	0.993625i	$0.464038\pi$
$570$	0	0
$571$	5.43372e32	0.0189298	0.00946490	−	0.999955i	$-0.496987\pi$
$571$	5.43372e32	0.0189298	0.00946490	+	0.999955i	$0.496987\pi$
$572$	9.10908e33i	0.310473i
$573$	9.54553e34i	3.18322i
$574$	2.19434e34	0.715988
$575$	0	0
$576$	8.66677e33	0.270755
$577$	− 1.51288e34i	− 0.462495i	−0.972895	−	0.231248i	$-0.925719\pi$
$577$	− 1.51288e34i	− 0.462495i	0.972895	−	0.231248i	$-0.0742808\pi$
$578$	− 6.39708e34i	− 1.91374i
$579$	−3.39402e34	−0.993646
$580$	0	0
$581$	1.50944e34	0.423268
$582$	1.15157e34i	0.316049i
$583$	7.12795e33i	0.191473i
$584$	−2.23511e34	−0.587677
$585$	0	0
$586$	−1.77194e34	−0.446404
$587$	3.71765e33i	0.0916837i	0.998949	+	0.0458418i	$0.0145970\pi$
$587$	3.71765e33i	0.0916837i	−0.998949	+	0.0458418i	$0.985403\pi$
$588$	2.49765e34i	0.602996i
$589$	3.99691e33	0.0944677
$590$	0	0
$591$	−3.63198e34	−0.822810
$592$	− 1.48930e34i	− 0.330339i
$593$	− 4.27000e34i	− 0.927351i	−0.886005	−	0.463676i	$-0.846530\pi$
$593$	− 4.27000e34i	− 0.927351i	0.886005	−	0.463676i	$-0.153470\pi$
$594$	−2.74797e34	−0.584361
$595$	0	0
$596$	1.22036e34	0.248835
$597$	− 4.20733e34i	− 0.840093i
$598$	− 1.31767e34i	− 0.257656i
$599$	3.95633e34	0.757631	0.378816	−	0.925472i	$-0.376331\pi$
$599$	3.95633e34	0.757631	0.378816	+	0.925472i	$0.376331\pi$
$600$	0	0
$601$	−5.03622e33	−0.0925069	−0.0462535	−	0.998930i	$-0.514728\pi$
$601$	−5.03622e33	−0.0925069	−0.0462535	+	0.998930i	$0.514728\pi$
$602$	1.65761e33i	0.0298212i
$603$	− 2.75787e34i	− 0.485969i
$604$	−1.66569e33	−0.0287496
$605$	0	0
$606$	9.00400e34	1.49117
$607$	1.09922e35i	1.78331i	0.452716	+	0.891655i	$0.350455\pi$
$607$	1.09922e35i	1.78331i	−0.452716	+	0.891655i	$0.649545\pi$
$608$	6.48780e33i	0.103110i
$609$	6.34040e34	0.987190
$610$	0	0
$611$	−1.38130e35	−2.06430
$612$	1.42399e35i	2.08504i
$613$	− 7.49713e34i	− 1.07557i	−0.843082	−	0.537786i	$-0.819261\pi$
$613$	− 7.49713e34i	− 1.07557i	0.843082	−	0.537786i	$-0.180739\pi$
$614$	5.77463e34	0.811745
$615$	0	0
$616$	5.92268e33	0.0799391
$617$	− 9.19873e34i	− 1.21664i	−0.793691	−	0.608321i	$-0.791843\pi$
$617$	− 9.19873e34i	− 1.21664i	0.793691	−	0.608321i	$-0.208157\pi$
$618$	1.39546e35i	1.80868i
$619$	−1.17365e35	−1.49075	−0.745375	−	0.666646i	$-0.767729\pi$
$619$	−1.17365e35	−1.49075	−0.745375	+	0.666646i	$0.767729\pi$
$620$	0	0
$621$	3.97505e34	0.484950
$622$	− 1.76515e34i	− 0.211058i
$623$	− 3.97422e34i	− 0.465748i
$624$	−6.03718e34	−0.693468
$625$	0	0
$626$	9.21430e33	0.101691
$627$	− 3.82125e34i	− 0.413391i
$628$	− 3.81125e33i	− 0.0404177i
$629$	2.44699e35	2.54389
$630$	0	0
$631$	−5.93583e34	−0.593082	−0.296541	−	0.955020i	$-0.595833\pi$
$631$	−5.93583e34	−0.593082	−0.296541	+	0.955020i	$0.595833\pi$
$632$	4.17113e34i	0.408592i
$633$	2.78024e35i	2.67015i
$634$	3.06024e34	0.288164
$635$	0	0
$636$	−4.72415e34	−0.427671
$637$	− 1.19030e35i	− 1.05661i
$638$	3.16252e34i	0.275280i
$639$	−4.10083e35	−3.50035
$640$	0	0
$641$	−6.98225e34	−0.573152	−0.286576	−	0.958058i	$-0.592517\pi$
$641$	−6.98225e34	−0.573152	−0.286576	+	0.958058i	$0.592517\pi$
$642$	− 2.00554e35i	− 1.61452i
$643$	4.37990e34i	0.345802i	0.984939	+	0.172901i	$0.0553141\pi$
$643$	4.37990e34i	0.345802i	−0.984939	+	0.172901i	$0.944686\pi$
$644$	−8.56739e33	−0.0663400
$645$	0	0
$646$	−1.06598e35	−0.794038
$647$	− 2.19963e35i	− 1.60711i	−0.595231	−	0.803555i	$-0.702939\pi$
$647$	− 2.19963e35i	− 1.60711i	0.595231	−	0.803555i	$-0.297061\pi$
$648$	− 7.52673e34i	− 0.539410i
$649$	9.52052e34	0.669271
$650$	0	0
$651$	2.41827e34	0.163585
$652$	− 8.68480e34i	− 0.576322i
$653$	− 5.77474e34i	− 0.375939i	−0.982175	−	0.187970i	$-0.939809\pi$
$653$	− 5.77474e34i	− 0.375939i	0.982175	−	0.187970i	$-0.0601907\pi$
$654$	−4.02352e34	−0.256971
$655$	0	0
$656$	−7.25404e34	−0.445946
$657$	5.96921e35i	3.60039i
$658$	8.98113e34i	0.531505i
$659$	2.55494e34	0.148359	0.0741793	−	0.997245i	$-0.476366\pi$
$659$	2.55494e34	0.148359	0.0741793	+	0.997245i	$0.476366\pi$
$660$	0	0
$661$	1.14583e35	0.640623	0.320312	−	0.947312i	$-0.396212\pi$
$661$	1.14583e35	0.640623	0.320312	+	0.947312i	$0.396212\pi$
$662$	− 4.15385e34i	− 0.227890i
$663$	− 9.91938e35i	− 5.34030i
$664$	−4.98991e34	−0.263628
$665$	0	0
$666$	−3.97740e35	−2.02382
$667$	− 4.57471e34i	− 0.228450i
$668$	1.72747e34i	0.0846652i
$669$	−2.69730e35	−1.29749
$670$	0	0
$671$	−3.73230e33	−0.0172960
$672$	3.92534e34i	0.178551i
$673$	1.32743e34i	0.0592683i	0.999561	+	0.0296342i	$0.00943423\pi$
$673$	1.32743e34i	0.0592683i	−0.999561	+	0.0296342i	$0.990566\pi$
$674$	−1.74921e35	−0.766644
$675$	0	0
$676$	1.69327e35	0.715143
$677$	1.09080e35i	0.452257i	0.974098	+	0.226128i	$0.0726069\pi$
$677$	1.09080e35i	0.452257i	−0.974098	+	0.226128i	$0.927393\pi$
$678$	− 2.15784e35i	− 0.878310i
$679$	−3.56831e34	−0.142590
$680$	0	0
$681$	8.36830e35	3.22328
$682$	1.20621e34i	0.0456159i
$683$	− 2.56303e35i	− 0.951690i	−0.879529	−	0.475845i	$-0.842142\pi$
$683$	− 2.56303e35i	− 0.951690i	0.879529	−	0.475845i	$-0.157858\pi$
$684$	1.73267e35	0.631704
$685$	0	0
$686$	−1.91580e35	−0.673438
$687$	2.04769e35i	0.706814i
$688$	− 5.47971e33i	− 0.0185739i
$689$	2.25139e35	0.749395
$690$	0	0
$691$	1.27544e35	0.409436	0.204718	−	0.978821i	$-0.434372\pi$
$691$	1.27544e35	0.409436	0.204718	+	0.978821i	$0.434372\pi$
$692$	− 2.08957e35i	− 0.658766i
$693$	− 1.58174e35i	− 0.489745i
$694$	5.85696e33	0.0178106
$695$	0	0
$696$	−2.09601e35	−0.614861
$697$	− 1.19187e36i	− 3.43416i
$698$	− 1.45642e34i	− 0.0412187i
$699$	−9.34471e35	−2.59777
$700$	0	0
$701$	−3.29520e35	−0.883907	−0.441953	−	0.897038i	$-0.645714\pi$
$701$	−3.29520e35	−0.883907	−0.441953	+	0.897038i	$0.645714\pi$
$702$	8.67957e35i	2.28709i
$703$	− 2.97742e35i	− 0.770722i
$704$	−1.95792e34	−0.0497893
$705$	0	0
$706$	−2.71963e35	−0.667500
$707$	2.79001e35i	0.672764i
$708$	6.30987e35i	1.49487i
$709$	3.54372e35	0.824863	0.412432	−	0.910989i	$-0.364680\pi$
$709$	3.54372e35	0.824863	0.412432	+	0.910989i	$0.364680\pi$
$710$	0	0
$711$	1.11396e36	2.50323
$712$	1.31379e35i	0.290086i
$713$	− 1.74482e34i	− 0.0378558i
$714$	−6.44953e35	−1.37499
$715$	0	0
$716$	7.69429e34	0.158400
$717$	9.91715e35i	2.00631i
$718$	7.63230e34i	0.151740i
$719$	−8.25549e34	−0.161299	−0.0806495	−	0.996743i	$-0.525699\pi$
$719$	−8.25549e34	−0.161299	−0.0806495	+	0.996743i	$0.525699\pi$
$720$	0	0
$721$	−4.32403e35	−0.816014
$722$	− 2.51537e35i	− 0.466538i
$723$	8.37424e35i	1.52657i
$724$	2.09302e35	0.375010
$725$	0	0
$726$	−6.11541e35	−1.05857
$727$	− 8.59682e35i	− 1.46271i	−0.681998	−	0.731354i	$-0.738889\pi$
$727$	− 8.59682e35i	− 1.46271i	0.681998	−	0.731354i	$-0.261111\pi$
$728$	− 1.87070e35i	− 0.312869i
$729$	2.35421e35	0.387036
$730$	0	0
$731$	9.00343e34	0.143035
$732$	− 2.47364e34i	− 0.0386320i
$733$	1.11362e36i	1.70977i	0.518821	+	0.854883i	$0.326371\pi$
$733$	1.11362e36i	1.70977i	−0.518821	+	0.854883i	$0.673629\pi$
$734$	3.54825e35	0.535567
$735$	0	0
$736$	2.83220e34	0.0413192
$737$	6.23034e34i	0.0893651i
$738$	1.93730e36i	2.73208i
$739$	−8.39662e34	−0.116426	−0.0582129	−	0.998304i	$-0.518540\pi$
$739$	−8.39662e34	−0.116426	−0.0582129	+	0.998304i	$0.518540\pi$
$740$	0	0
$741$	−1.20696e36	−1.61795
$742$	− 1.46384e35i	− 0.192950i
$743$	− 8.61824e35i	− 1.11701i	−0.829500	−	0.558506i	$-0.811375\pi$
$743$	− 8.61824e35i	− 1.11701i	0.829500	−	0.558506i	$-0.188625\pi$
$744$	−7.99430e34	−0.101887
$745$	0	0
$746$	1.03582e36	1.27658
$747$	1.33263e36i	1.61511i
$748$	− 3.21695e35i	− 0.383420i
$749$	6.21444e35	0.728415
$750$	0	0
$751$	−8.00202e35	−0.907195	−0.453597	−	0.891207i	$-0.649860\pi$
$751$	−8.00202e35	−0.907195	−0.453597	+	0.891207i	$0.649860\pi$
$752$	− 2.96898e35i	− 0.331043i
$753$	− 4.12356e35i	− 0.452204i
$754$	9.98894e35	1.07740
$755$	0	0
$756$	5.64341e35	0.588869
$757$	7.91448e35i	0.812314i	0.913803	+	0.406157i	$0.133131\pi$
$757$	7.91448e35i	0.812314i	−0.913803	+	0.406157i	$0.866869\pi$
$758$	3.23577e35i	0.326673i
$759$	−1.66814e35	−0.165657
$760$	0	0
$761$	2.09934e34	0.0201732	0.0100866	−	0.999949i	$-0.496789\pi$
$761$	2.09934e34	0.0201732	0.0100866	+	0.999949i	$0.496789\pi$
$762$	7.54452e35i	0.713173i
$763$	− 1.24674e35i	− 0.115936i
$764$	9.77792e35	0.894498
$765$	0	0
$766$	−8.60607e35	−0.761983
$767$	− 3.00709e36i	− 2.61942i
$768$	− 1.29764e35i	− 0.111209i
$769$	7.23123e35	0.609723	0.304862	−	0.952397i	$-0.401390\pi$
$769$	7.23123e35	0.609723	0.304862	+	0.952397i	$0.401390\pi$
$770$	0	0
$771$	−7.08396e35	−0.578225
$772$	3.47664e35i	0.279218i
$773$	− 1.19333e36i	− 0.943014i	−0.881862	−	0.471507i	$-0.843710\pi$
$773$	− 1.19333e36i	− 0.943014i	0.881862	−	0.471507i	$-0.156290\pi$
$774$	−1.46344e35	−0.113792
$775$	0	0
$776$	1.17961e35	0.0888110
$777$	− 1.80144e36i	− 1.33462i
$778$	− 5.71531e35i	− 0.416672i
$779$	−1.45023e36	−1.04045
$780$	0	0
$781$	9.26423e35	0.643682
$782$	4.65345e35i	0.318193i
$783$	3.01340e36i	2.02784i
$784$	2.55845e35	0.169444
$785$	0	0
$786$	1.52118e36	0.975883
$787$	− 4.78974e35i	− 0.302432i	−0.988501	−	0.151216i	$-0.951681\pi$
$787$	− 4.78974e35i	− 0.302432i	0.988501	−	0.151216i	$-0.0483189\pi$
$788$	3.72040e35i	0.231213i
$789$	4.92912e36	3.01514
$790$	0	0
$791$	6.68636e35	0.396263
$792$	5.22891e35i	0.305033i
$793$	1.17886e35i	0.0676937i
$794$	−6.51114e35	−0.368045
$795$	0	0
$796$	−4.30975e35	−0.236069
$797$	− 2.29881e36i	− 1.23958i	−0.784769	−	0.619788i	$-0.787218\pi$
$797$	− 2.29881e36i	− 1.23958i	0.784769	−	0.619788i	$-0.212782\pi$
$798$	7.84757e35i	0.416581i
$799$	4.87818e36	2.54931
$800$	0	0
$801$	3.50869e36	1.77721
$802$	1.81604e36i	0.905621i
$803$	− 1.34851e36i	− 0.662078i
$804$	−4.12925e35	−0.199604
$805$	0	0
$806$	3.80985e35	0.178533
$807$	8.34476e35i	0.385030i
$808$	− 9.22320e35i	− 0.419025i
$809$	−1.08839e36	−0.486885	−0.243442	−	0.969915i	$-0.578277\pi$
$809$	−1.08839e36	−0.486885	−0.243442	+	0.969915i	$0.578277\pi$
$810$	0	0
$811$	4.47699e36	1.94189	0.970946	−	0.239299i	$-0.0769178\pi$
$811$	4.47699e36	1.94189	0.970946	+	0.239299i	$0.0769178\pi$
$812$	− 6.49476e35i	− 0.277404i
$813$	− 1.73509e36i	− 0.729776i
$814$	8.98537e35	0.372161
$815$	0	0
$816$	2.13208e36	0.856400
$817$	− 1.09551e35i	− 0.0433351i
$818$	5.79056e35i	0.225582i
$819$	−4.99599e36	−1.91678
$820$	0	0
$821$	3.35501e36	1.24855	0.624274	−	0.781206i	$-0.285395\pi$
$821$	3.35501e36	1.24855	0.624274	+	0.781206i	$0.285395\pi$
$822$	− 4.57141e36i	− 1.67553i
$823$	− 1.04609e36i	− 0.377636i	−0.982012	−	0.188818i	$-0.939534\pi$
$823$	− 1.04609e36i	− 0.377636i	0.982012	−	0.188818i	$-0.0604655\pi$
$824$	1.42944e36	0.508246
$825$	0	0
$826$	−1.95520e36	−0.674435
$827$	1.70274e36i	0.578535i	0.957248	+	0.289267i	$0.0934117\pi$
$827$	1.70274e36i	0.578535i	−0.957248	+	0.289267i	$0.906588\pi$
$828$	− 7.56383e35i	− 0.253141i
$829$	−3.63214e36	−1.19738	−0.598688	−	0.800983i	$-0.704311\pi$
$829$	−3.63214e36	−1.19738	−0.598688	+	0.800983i	$0.704311\pi$
$830$	0	0
$831$	−9.29763e36	−2.97413
$832$	6.18415e35i	0.194867i
$833$	4.20366e36i	1.30486i
$834$	−3.37505e36	−1.03206
$835$	0	0
$836$	−3.91428e35	−0.116164
$837$	1.14933e36i	0.336029i
$838$	− 2.31708e36i	− 0.667407i
$839$	4.10710e36	1.16550	0.582748	−	0.812653i	$-0.301977\pi$
$839$	4.10710e36	1.16550	0.582748	+	0.812653i	$0.301977\pi$
$840$	0	0
$841$	−1.62368e35	−0.0447251
$842$	− 3.80476e36i	− 1.03258i
$843$	2.46372e36i	0.658790i
$844$	2.84793e36	0.750323
$845$	0	0
$846$	−7.92911e36	−2.02813
$847$	− 1.89494e36i	− 0.477588i
$848$	4.83916e35i	0.120177i
$849$	−7.32074e36	−1.79147
$850$	0	0
$851$	−1.29977e36	−0.308850
$852$	6.14000e36i	1.43772i
$853$	2.01380e36i	0.464680i	0.972635	+	0.232340i	$0.0746383\pi$
$853$	2.01380e36i	0.464680i	−0.972635	+	0.232340i	$0.925362\pi$
$854$	7.66490e34	0.0174294
$855$	0	0
$856$	−2.05437e36	−0.453686
$857$	3.20819e36i	0.698232i	0.937080	+	0.349116i	$0.113518\pi$
$857$	3.20819e36i	0.698232i	−0.937080	+	0.349116i	$0.886482\pi$
$858$	− 3.64241e36i	− 0.781263i
$859$	1.62270e36	0.343024	0.171512	−	0.985182i	$-0.445135\pi$
$859$	1.62270e36	0.343024	0.171512	+	0.985182i	$0.445135\pi$
$860$	0	0
$861$	−8.77441e36	−1.80168
$862$	− 4.10739e36i	− 0.831237i
$863$	2.34665e36i	0.468074i	0.972228	+	0.234037i	$0.0751936\pi$
$863$	2.34665e36i	0.468074i	−0.972228	+	0.234037i	$0.924806\pi$
$864$	−1.86559e36	−0.366771
$865$	0	0
$866$	2.17991e35	0.0416356
$867$	2.55797e37i	4.81567i
$868$	− 2.47714e35i	− 0.0459679i
$869$	−2.51656e36	−0.460321
$870$	0	0
$871$	1.96788e36	0.349761
$872$	4.12147e35i	0.0722098i
$873$	− 3.15033e36i	− 0.544099i
$874$	5.66216e35	0.0964027
$875$	0	0
$876$	8.93744e36	1.47881
$877$	1.82745e36i	0.298092i	0.988830	+	0.149046i	$0.0476202\pi$
$877$	1.82745e36i	0.298092i	−0.988830	+	0.149046i	$0.952380\pi$
$878$	2.02894e36i	0.326278i
$879$	7.08537e36	1.12331
$880$	0	0
$881$	1.92548e36	0.296715	0.148358	−	0.988934i	$-0.452601\pi$
$881$	1.92548e36	0.296715	0.148358	+	0.988934i	$0.452601\pi$
$882$	− 6.83274e36i	− 1.03810i
$883$	5.88853e36i	0.882060i	0.897492	+	0.441030i	$0.145387\pi$
$883$	5.88853e36i	0.882060i	−0.897492	+	0.441030i	$0.854613\pi$
$884$	−1.01609e37	−1.50064
$885$	0	0
$886$	2.45842e36	0.352967
$887$	− 1.17351e37i	− 1.66128i	−0.556809	−	0.830640i	$-0.687975\pi$
$887$	− 1.17351e37i	− 1.66128i	0.556809	−	0.830640i	$-0.312025\pi$
$888$	5.95519e36i	0.831253i
$889$	−2.33777e36	−0.321759
$890$	0	0
$891$	4.54110e36	0.607700
$892$	2.76296e36i	0.364598i
$893$	− 5.93560e36i	− 0.772363i
$894$	−4.87981e36	−0.626158
$895$	0	0
$896$	4.02090e35	0.0501734
$897$	5.26889e36i	0.648356i
$898$	− 1.00164e35i	− 0.0121551i
$899$	1.32271e36	0.158296
$900$	0	0
$901$	−7.95098e36	−0.925467
$902$	− 4.37658e36i	− 0.502404i
$903$	− 6.62820e35i	− 0.0750410i
$904$	−2.21037e36	−0.246808
$905$	0	0
$906$	6.66051e35	0.0723444
$907$	− 9.60913e36i	− 1.02942i	−0.857364	−	0.514711i	$-0.827899\pi$
$907$	− 9.60913e36i	− 1.02942i	0.857364	−	0.514711i	$-0.172101\pi$
$908$	− 8.57203e36i	− 0.905754i
$909$	−2.46320e37	−2.56715
$910$	0	0
$911$	3.31132e36	0.335754	0.167877	−	0.985808i	$-0.446309\pi$
$911$	3.31132e36	0.335754	0.167877	+	0.985808i	$0.446309\pi$
$912$	− 2.59424e36i	− 0.259463i
$913$	− 3.01056e36i	− 0.297004i
$914$	−6.76849e36	−0.658665
$915$	0	0
$916$	2.09754e36	0.198617
$917$	4.71357e36i	0.440284i
$918$	− 3.06526e37i	− 2.82445i
$919$	6.37787e36	0.579738	0.289869	−	0.957066i	$-0.406388\pi$
$919$	6.37787e36	0.579738	0.289869	+	0.957066i	$0.406388\pi$
$920$	0	0
$921$	−2.30908e37	−2.04264
$922$	4.78281e36i	0.417394i
$923$	− 2.92614e37i	− 2.51927i
$924$	−2.36827e36	−0.201156
$925$	0	0
$926$	9.79880e36	0.810094
$927$	− 3.81753e37i	− 3.11376i
$928$	2.14703e36i	0.172778i
$929$	1.01760e37	0.807940	0.403970	−	0.914772i	$-0.367630\pi$
$929$	1.01760e37	0.807940	0.403970	+	0.914772i	$0.367630\pi$
$930$	0	0
$931$	5.11488e36	0.395334
$932$	9.57221e36i	0.729984i
$933$	7.05824e36i	0.531099i
$934$	1.83239e37	1.36045
$935$	0	0
$936$	1.65157e37	1.19385
$937$	− 5.01714e36i	− 0.357859i	−0.983862	−	0.178929i	$-0.942737\pi$
$937$	− 5.01714e36i	− 0.357859i	0.983862	−	0.178929i	$-0.0572633\pi$
$938$	− 1.27950e36i	− 0.0900546i
$939$	−3.68448e36	−0.255892
$940$	0	0
$941$	1.04889e37	0.709348	0.354674	−	0.934990i	$-0.384592\pi$
$941$	1.04889e37	0.709348	0.354674	+	0.934990i	$0.384592\pi$
$942$	1.52399e36i	0.101706i
$943$	6.33089e36i	0.416936i
$944$	6.46348e36	0.420065
$945$	0	0
$946$	3.30607e35	0.0209254
$947$	3.09440e37i	1.93286i	0.256923	+	0.966432i	$0.417291\pi$
$947$	3.09440e37i	1.93286i	−0.256923	+	0.966432i	$0.582709\pi$
$948$	− 1.66789e37i	− 1.02817i
$949$	−4.25932e37	−2.59127
$950$	0	0
$951$	−1.22368e37	−0.725125
$952$	6.60654e36i	0.386378i
$953$	− 2.63074e34i	− 0.00151851i	−1.00000		0.000759254i	$-0.999758\pi$
$953$	− 2.63074e34i	− 0.00151851i	1.00000		0.000759254i	$-0.000241678\pi$
$954$	1.29237e37	0.736263
$955$	0	0
$956$	1.01586e37	0.563780
$957$	− 1.26458e37i	− 0.692704i
$958$	− 9.57503e36i	− 0.517692i
$959$	1.41651e37	0.755941
$960$	0	0
$961$	−1.87283e37	−0.973769
$962$	− 2.83807e37i	− 1.45658i
$963$	5.48650e37i	2.77950i
$964$	8.57811e36	0.428972
$965$	0	0
$966$	3.42580e36	0.166935
$967$	1.63641e37i	0.787158i	0.919291	+	0.393579i	$0.128763\pi$
$967$	1.63641e37i	0.787158i	−0.919291	+	0.393579i	$0.871237\pi$
$968$	6.26429e36i	0.297461i
$969$	4.26247e37	1.99809
$970$	0	0
$971$	−3.01907e37	−1.37922	−0.689610	−	0.724181i	$-0.742218\pi$
$971$	−3.01907e37	−1.37922	−0.689610	+	0.724181i	$0.742218\pi$
$972$	7.09461e36i	0.319963i
$973$	− 1.04581e37i	− 0.465629i
$974$	−5.23376e36	−0.230053
$975$	0	0
$976$	−2.53386e35	−0.0108557
$977$	3.79611e36i	0.160567i	0.996772	+	0.0802837i	$0.0255826\pi$
$977$	3.79611e36i	0.160567i	−0.996772	+	0.0802837i	$0.974417\pi$
$978$	3.47275e37i	1.45023i
$979$	−7.92650e36	−0.326812
$980$	0	0
$981$	1.10070e37	0.442392
$982$	2.24509e37i	0.890923i
$983$	− 6.46957e36i	− 0.253487i	−0.991936	−	0.126744i	$-0.959547\pi$
$983$	− 6.46957e36i	− 0.253487i	0.991936	−	0.126744i	$-0.0404526\pi$
$984$	2.90064e37	1.12216
$985$	0	0
$986$	−3.52768e37	−1.33054
$987$	− 3.59124e37i	− 1.33746i
$988$	1.23634e37i	0.454649i
$989$	−4.78236e35	−0.0173656
$990$	0	0
$991$	−3.19318e37	−1.13058	−0.565291	−	0.824891i	$-0.691236\pi$
$991$	−3.19318e37	−1.13058	−0.565291	+	0.824891i	$0.691236\pi$
$992$	8.18892e35i	0.0286306i
$993$	1.66098e37i	0.573455i
$994$	−1.90256e37	−0.648648
$995$	0	0
$996$	1.99529e37	0.663384
$997$	− 3.10721e37i	− 1.02019i	−0.860118	−	0.510095i	$-0.829610\pi$
$997$	− 3.10721e37i	− 1.02019i	0.860118	−	0.510095i	$-0.170390\pi$
$998$	− 1.32686e37i	− 0.430224i
$999$	8.56169e37	2.74152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.b.f.49.3		4
5.2	odd	4		10.26.a.b.1.1	✓	2
5.3	odd	4		50.26.a.f.1.2		2
5.4	even	2	inner	50.26.b.f.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.b.1.1	✓	2	5.2	odd	4
50.26.a.f.1.2		2	5.3	odd	4
50.26.b.f.49.2		4	5.4	even	2	inner
50.26.b.f.49.3		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4096.00i q^{2} -1.63785e6i q^{3} -1.67772e7 q^{4} +6.70863e9 q^{6} +2.07876e10i q^{7} -6.87195e10i q^{8} -1.83526e12 q^{9} +4.14605e12 q^{11} +2.74785e13i q^{12} -1.30955e14i q^{13} -8.51459e13 q^{14} +2.81475e14 q^{16} +4.62477e15i q^{17} -7.51722e15i q^{18} +5.62727e15 q^{19} +3.40469e16 q^{21} +1.69822e16i q^{22} -2.45654e16i q^{23} -1.12552e17 q^{24} +5.36390e17 q^{26} +1.61815e18i q^{27} -3.48758e17i q^{28} +1.86225e18 q^{29} +7.10276e17 q^{31} +1.15292e18i q^{32} -6.79060e18i q^{33} -1.89431e19 q^{34} +3.07905e19 q^{36} -5.29105e19i q^{37} +2.30493e19i q^{38} -2.14484e20 q^{39} -2.57715e20 q^{41} +1.39456e20i q^{42} -1.94678e19i q^{43} -6.95591e19 q^{44} +1.00620e20 q^{46} -1.05479e21i q^{47} -4.61013e20i q^{48} +9.08945e20 q^{49} +7.57467e21 q^{51} +2.19705e21i q^{52} +1.71922e21i q^{53} -6.62792e21 q^{54} +1.42851e21 q^{56} -9.21661e21i q^{57} +7.62780e21i q^{58} +2.29629e22 q^{59} -9.00207e20 q^{61} +2.90929e21i q^{62} -3.81506e22i q^{63} -4.72237e21 q^{64} +2.78143e22 q^{66} +1.50272e22i q^{67} -7.75908e22i q^{68} -4.02345e22 q^{69} +2.23447e23 q^{71} +1.26118e23i q^{72} -3.25252e23i q^{73} +2.16721e23 q^{74} -9.44099e22 q^{76} +8.61863e22i q^{77} -8.78525e23i q^{78} -6.06979e23 q^{79} +1.09528e24 q^{81} -1.05560e24i q^{82} -7.26128e23i q^{83} -5.71212e23 q^{84} +7.97403e22 q^{86} -3.05009e24i q^{87} -2.84914e23i q^{88} -1.91182e24 q^{89} +2.72223e24 q^{91} +4.12140e23i q^{92} -1.16332e24i q^{93} +4.32043e24 q^{94} +1.88831e24 q^{96} +1.71656e24i q^{97} +3.72304e24i q^{98} -7.60907e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 67108864 q^{4} + 3592912896 q^{6} - 4852391719572 q^{9} + 38689365583968 q^{11} - 278598423642112 q^{14} + 11\!\cdots\!24 q^{16} - 27069564790640 q^{19} + 36\!\cdots\!68 q^{21} - 60\!\cdots\!36 q^{24}+ \cdots - 33\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 67108864 * q^4 + 3592912896 * q^6 - 4852391719572 * q^9 + 38689365583968 * q^11 - 278598423642112 * q^14 + 1125899906842624 * q^16 - 27069564790640 * q^19 + 36382943373231168 * q^21 - 60279075725377536 * q^24 + 1046905225491152896 * q^26 + 3352194974618066760 * q^29 + 14251730312692753328 * q^31 - 24566644208258875392 * q^34 + 81409623995870871552 * q^36 - 436543015316491576944 * q^39 - 557953890277086019512 * q^41 - 649099843305197273088 * q^44 + 1448349866251256365056 * q^46 + 4150436861800468606332 * q^49 + 19049132675049275084688 * q^51 - 15774334415689015296000 * q^54 + 4674105930703219720192 * q^56 + 7531122243979537536720 * q^59 + 2177681218008805632248 * q^61 - 18889465931478580854784 * q^64 - 93688004873690155450368 * q^66 + 284670059282373004612416 * q^69 + 242975004103174569736848 * q^71 + 688208474290658872229888 * q^74 + 454151935518562058240 * q^76 - 1642777411067289683461280 * q^79 + 451795166977848570924804 * q^81 - 610404499688467923468288 * q^84 - 3493737291012689868652544 * q^86 - 10118439858808991441985960 * q^89 + 5360939619520672539104368 * q^91 + 9073628451972583753678848 * q^94 + 1011315073725015603019776 * q^96 - 33181012666288372472905824 * q^99

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