LMFDB - Embedded newform 50.10.b.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,10,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, 10, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$25.7517918082$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.10.b.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000i q^{2} +174.000i q^{3} -256.000 q^{4} +2784.00 q^{6} -4658.00i q^{7} +4096.00i q^{8} -10593.0 q^{9} +O(q^{10})$	\(q-16.0000i q^{2} +174.000i q^{3} -256.000 q^{4} +2784.00 q^{6} -4658.00i q^{7} +4096.00i q^{8} -10593.0 q^{9} +28992.0 q^{11} -44544.0i q^{12} -164446. i q^{13} -74528.0 q^{14} +65536.0 q^{16} +594822. i q^{17} +169488. i q^{18} +295780. q^{19} +810492. q^{21} -463872. i q^{22} +2.54453e6i q^{23} -712704. q^{24} -2.63114e6 q^{26} +1.58166e6i q^{27} +1.19245e6i q^{28} +3.72297e6 q^{29} +2.33577e6 q^{31} -1.04858e6i q^{32} +5.04461e6i q^{33} +9.51715e6 q^{34} +2.71181e6 q^{36} -1.08404e7i q^{37} -4.73248e6i q^{38} +2.86136e7 q^{39} +2.15939e7 q^{41} -1.29679e7i q^{42} +1.08323e7i q^{43} -7.42195e6 q^{44} +4.07125e7 q^{46} -5.17214e6i q^{47} +1.14033e7i q^{48} +1.86566e7 q^{49} -1.03499e8 q^{51} +4.20982e7i q^{52} +9.81797e7i q^{53} +2.53066e7 q^{54} +1.90792e7 q^{56} +5.14657e7i q^{57} -5.95675e7i q^{58} -1.61629e7 q^{59} -4.39282e7 q^{61} -3.73724e7i q^{62} +4.93422e7i q^{63} -1.67772e7 q^{64} +8.07137e7 q^{66} +8.15574e7i q^{67} -1.52274e8i q^{68} -4.42749e8 q^{69} +1.61308e8 q^{71} -4.33889e7i q^{72} -2.47148e8i q^{73} -1.73447e8 q^{74} -7.57197e7 q^{76} -1.35045e8i q^{77} -4.57818e8i q^{78} +5.83346e8 q^{79} -4.83711e8 q^{81} -3.45502e8i q^{82} -1.45718e7i q^{83} -2.07486e8 q^{84} +1.73317e8 q^{86} +6.47797e8i q^{87} +1.18751e8i q^{88} -4.70134e8 q^{89} -7.65989e8 q^{91} -6.51401e8i q^{92} +4.06424e8i q^{93} -8.27542e7 q^{94} +1.82452e8 q^{96} +1.17838e8i q^{97} -2.98506e8i q^{98} -3.07112e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 512 q^{4} + 5568 q^{6} - 21186 q^{9}+O(q^{10}) $ 2 * q - 512 * q^4 + 5568 * q^6 - 21186 * q^9	$ 2 q - 512 q^{4} + 5568 q^{6} - 21186 q^{9} + 57984 q^{11} - 149056 q^{14} + 131072 q^{16} + 591560 q^{19} + 1620984 q^{21} - 1425408 q^{24} - 5262272 q^{26} + 7445940 q^{29} + 4671544 q^{31} + 19034304 q^{34} + 5423616 q^{36} + 57227208 q^{39} + 43187724 q^{41} - 14843904 q^{44} + 81425088 q^{46} + 37313286 q^{49} - 206998056 q^{51} + 50613120 q^{54} + 38158336 q^{56} - 32325720 q^{59} - 87856316 q^{61} - 33554432 q^{64} + 161427456 q^{66} - 885497832 q^{69} + 322615464 q^{71} - 346893376 q^{74} - 151439360 q^{76} + 1166691440 q^{79} - 967421718 q^{81} - 414971904 q^{84} + 346633408 q^{86} - 940267380 q^{89} - 1531978936 q^{91} - 165508416 q^{94} + 364904448 q^{96} - 614224512 q^{99}+O(q^{100}) $ 2 * q - 512 * q^4 + 5568 * q^6 - 21186 * q^9 + 57984 * q^11 - 149056 * q^14 + 131072 * q^16 + 591560 * q^19 + 1620984 * q^21 - 1425408 * q^24 - 5262272 * q^26 + 7445940 * q^29 + 4671544 * q^31 + 19034304 * q^34 + 5423616 * q^36 + 57227208 * q^39 + 43187724 * q^41 - 14843904 * q^44 + 81425088 * q^46 + 37313286 * q^49 - 206998056 * q^51 + 50613120 * q^54 + 38158336 * q^56 - 32325720 * q^59 - 87856316 * q^61 - 33554432 * q^64 + 161427456 * q^66 - 885497832 * q^69 + 322615464 * q^71 - 346893376 * q^74 - 151439360 * q^76 + 1166691440 * q^79 - 967421718 * q^81 - 414971904 * q^84 + 346633408 * q^86 - 940267380 * q^89 - 1531978936 * q^91 - 165508416 * q^94 + 364904448 * q^96 - 614224512 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	− 16.0000i	− 0.707107i
$2$	− 16.0000i	− 0.707107i
$3$	174.000i	1.24023i	0.784509	+	0.620117i	$0.212915\pi$
$3$	174.000i	1.24023i	−0.784509	+	0.620117i	$0.787085\pi$
$4$	−256.000	−0.500000
$5$	0	0
$5$	0	0
$6$	2784.00	0.876978
$7$	− 4658.00i	− 0.733261i	−0.930367	−	0.366630i	$-0.880511\pi$
$7$	− 4658.00i	− 0.733261i	0.930367	−	0.366630i	$-0.119489\pi$
$8$	4096.00i	0.353553i
$9$	−10593.0	−0.538180
$10$	0	0
$11$	28992.0	0.597051	0.298525	−	0.954402i	$-0.403505\pi$
$11$	28992.0	0.597051	0.298525	+	0.954402i	$0.403505\pi$
$12$	− 44544.0i	− 0.620117i
$13$	− 164446.i	− 1.59690i	−0.602060	−	0.798451i	$-0.705653\pi$
$13$	− 164446.i	− 1.59690i	0.602060	−	0.798451i	$-0.294347\pi$
$14$	−74528.0	−0.518493
$15$	0	0
$16$	65536.0	0.250000
$17$	594822.i	1.72730i	0.504095	+	0.863648i	$0.331826\pi$
$17$	594822.i	1.72730i	−0.504095	+	0.863648i	$0.668174\pi$
$18$	169488.i	0.380551i
$19$	295780.	0.520688	0.260344	−	0.965516i	$-0.416164\pi$
$19$	295780.	0.520688	0.260344	+	0.965516i	$0.416164\pi$
$20$	0	0
$21$	810492.	0.909415
$22$	− 463872.i	− 0.422178i
$23$	2.54453e6i	1.89598i	0.318305	+	0.947988i	$0.396886\pi$
$23$	2.54453e6i	1.89598i	−0.318305	+	0.947988i	$0.603114\pi$
$24$	−712704.	−0.438489
$25$	0	0
$26$	−2.63114e6	−1.12918
$27$	1.58166e6i	0.572765i
$28$	1.19245e6i	0.366630i
$29$	3.72297e6	0.977459	0.488729	−	0.872435i	$-0.337461\pi$
$29$	3.72297e6	0.977459	0.488729	+	0.872435i	$0.337461\pi$
$30$	0	0
$31$	2.33577e6	0.454258	0.227129	−	0.973865i	$-0.427066\pi$
$31$	2.33577e6	0.454258	0.227129	+	0.973865i	$0.427066\pi$
$32$	− 1.04858e6i	− 0.176777i
$33$	5.04461e6i	0.740482i
$34$	9.51715e6	1.22138
$35$	0	0
$36$	2.71181e6	0.269090
$37$	− 1.08404e7i	− 0.950907i	−0.879741	−	0.475454i	$-0.842284\pi$
$37$	− 1.08404e7i	− 0.950907i	0.879741	−	0.475454i	$-0.157716\pi$
$38$	− 4.73248e6i	− 0.368182i
$39$	2.86136e7	1.98053
$40$	0	0
$41$	2.15939e7	1.19345	0.596723	−	0.802447i	$-0.296469\pi$
$41$	2.15939e7	1.19345	0.596723	+	0.802447i	$0.296469\pi$
$42$	− 1.29679e7i	− 0.643053i
$43$	1.08323e7i	0.483184i	0.970378	+	0.241592i	$0.0776695\pi$
$43$	1.08323e7i	0.483184i	−0.970378	+	0.241592i	$0.922330\pi$
$44$	−7.42195e6	−0.298525
$45$	0	0
$46$	4.07125e7	1.34066
$47$	− 5.17214e6i	− 0.154607i	−0.997008	−	0.0773036i	$-0.975369\pi$
$47$	− 5.17214e6i	− 0.154607i	0.997008	−	0.0773036i	$-0.0246311\pi$
$48$	1.14033e7i	0.310058i
$49$	1.86566e7	0.462329
$50$	0	0
$51$	−1.03499e8	−2.14225
$52$	4.20982e7i	0.798451i
$53$	9.81797e7i	1.70915i	0.519328	+	0.854575i	$0.326182\pi$
$53$	9.81797e7i	1.70915i	−0.519328	+	0.854575i	$0.673818\pi$
$54$	2.53066e7	0.405006
$55$	0	0
$56$	1.90792e7	0.259247
$57$	5.14657e7i	0.645775i
$58$	− 5.95675e7i	− 0.691168i
$59$	−1.61629e7	−0.173654	−0.0868269	−	0.996223i	$-0.527673\pi$
$59$	−1.61629e7	−0.173654	−0.0868269	+	0.996223i	$0.527673\pi$
$60$	0	0
$61$	−4.39282e7	−0.406218	−0.203109	−	0.979156i	$-0.565105\pi$
$61$	−4.39282e7	−0.406218	−0.203109	+	0.979156i	$0.565105\pi$
$62$	− 3.73724e7i	− 0.321209i
$63$	4.93422e7i	0.394626i
$64$	−1.67772e7	−0.125000
$65$	0	0
$66$	8.07137e7	0.523600
$67$	8.15574e7i	0.494455i	0.968957	+	0.247228i	$0.0795195\pi$
$67$	8.15574e7i	0.494455i	−0.968957	+	0.247228i	$0.920480\pi$
$68$	− 1.52274e8i	− 0.863648i
$69$	−4.42749e8	−2.35145
$70$	0	0
$71$	1.61308e8	0.753343	0.376671	−	0.926347i	$-0.377069\pi$
$71$	1.61308e8	0.753343	0.376671	+	0.926347i	$0.377069\pi$
$72$	− 4.33889e7i	− 0.190275i
$73$	− 2.47148e8i	− 1.01860i	−0.860589	−	0.509301i	$-0.829904\pi$
$73$	− 2.47148e8i	− 1.01860i	0.860589	−	0.509301i	$-0.170096\pi$
$74$	−1.73447e8	−0.672393
$75$	0	0
$76$	−7.57197e7	−0.260344
$77$	− 1.35045e8i	− 0.437794i
$78$	− 4.57818e8i	− 1.40045i
$79$	5.83346e8	1.68502	0.842508	−	0.538684i	$-0.181078\pi$
$79$	5.83346e8	1.68502	0.842508	+	0.538684i	$0.181078\pi$
$80$	0	0
$81$	−4.83711e8	−1.24854
$82$	− 3.45502e8i	− 0.843894i
$83$	− 1.45718e7i	− 0.0337024i	−0.999858	−	0.0168512i	$-0.994636\pi$
$83$	− 1.45718e7i	− 0.0337024i	0.999858	−	0.0168512i	$-0.00536416\pi$
$84$	−2.07486e8	−0.454707
$85$	0	0
$86$	1.73317e8	0.341663
$87$	6.47797e8i	1.21228i
$88$	1.18751e8i	0.211089i
$89$	−4.70134e8	−0.794267	−0.397133	−	0.917761i	$-0.629995\pi$
$89$	−4.70134e8	−0.794267	−0.397133	+	0.917761i	$0.629995\pi$
$90$	0	0
$91$	−7.65989e8	−1.17095
$92$	− 6.51401e8i	− 0.947988i
$93$	4.06424e8i	0.563386i
$94$	−8.27542e7	−0.109324
$95$	0	0
$96$	1.82452e8	0.219244
$97$	1.17838e8i	0.135149i	0.997714	+	0.0675747i	$0.0215261\pi$
$97$	1.17838e8i	0.135149i	−0.997714	+	0.0675747i	$0.978474\pi$
$98$	− 2.98506e8i	− 0.326916i
$99$	−3.07112e8	−0.321321
$100$	0	0
$101$	−8.60927e7	−0.0823228	−0.0411614	−	0.999153i	$-0.513106\pi$
$101$	−8.60927e7	−0.0823228	−0.0411614	+	0.999153i	$0.513106\pi$
$102$	1.65598e9i	1.51480i
$103$	1.92872e9i	1.68850i	0.535947	+	0.844252i	$0.319955\pi$
$103$	1.92872e9i	1.68850i	−0.535947	+	0.844252i	$0.680045\pi$
$104$	6.73571e8	0.564590
$105$	0	0
$106$	1.57087e9	1.20855
$107$	− 1.39685e9i	− 1.03020i	−0.857130	−	0.515100i	$-0.827755\pi$
$107$	− 1.39685e9i	− 1.03020i	0.857130	−	0.515100i	$-0.172245\pi$
$108$	− 4.04905e8i	− 0.286382i
$109$	6.04327e8	0.410065	0.205033	−	0.978755i	$-0.434270\pi$
$109$	6.04327e8	0.410065	0.205033	+	0.978755i	$0.434270\pi$
$110$	0	0
$111$	1.88623e9	1.17935
$112$	− 3.05267e8i	− 0.183315i
$113$	− 1.68580e9i	− 0.972643i	−0.873780	−	0.486322i	$-0.838338\pi$
$113$	− 1.68580e9i	− 0.972643i	0.873780	−	0.486322i	$-0.161662\pi$
$114$	8.23452e8	0.456632
$115$	0	0
$116$	−9.53080e8	−0.488729
$117$	1.74198e9i	0.859421i
$118$	2.58606e8i	0.122792i
$119$	2.77068e9	1.26656
$120$	0	0
$121$	−1.51741e9	−0.643531
$122$	7.02851e8i	0.287239i
$123$	3.75733e9i	1.48015i
$124$	−5.97958e8	−0.227129
$125$	0	0
$126$	7.89475e8	0.279043
$127$	− 3.70716e9i	− 1.26452i	−0.774758	−	0.632258i	$-0.782128\pi$
$127$	− 3.70716e9i	− 1.26452i	0.774758	−	0.632258i	$-0.217872\pi$
$128$	2.68435e8i	0.0883883i
$129$	−1.88482e9	−0.599261
$130$	0	0
$131$	2.54080e9	0.753789	0.376895	−	0.926256i	$-0.376992\pi$
$131$	2.54080e9	0.753789	0.376895	+	0.926256i	$0.376992\pi$
$132$	− 1.29142e9i	− 0.370241i
$133$	− 1.37774e9i	− 0.381800i
$134$	1.30492e9	0.349633
$135$	0	0
$136$	−2.43639e9	−0.610692
$137$	1.15390e9i	0.279849i	0.990162	+	0.139925i	$0.0446860\pi$
$137$	1.15390e9i	0.279849i	−0.990162	+	0.139925i	$0.955314\pi$
$138$	7.08398e9i	1.66273i
$139$	5.62721e9	1.27858	0.639288	−	0.768968i	$-0.279229\pi$
$139$	5.62721e9	1.27858	0.639288	+	0.768968i	$0.279229\pi$
$140$	0	0
$141$	8.99952e8	0.191749
$142$	− 2.58092e9i	− 0.532694i
$143$	− 4.76762e9i	− 0.953431i
$144$	−6.94223e8	−0.134545
$145$	0	0
$146$	−3.95437e9	−0.720260
$147$	3.24626e9i	0.573396i
$148$	2.77515e9i	0.475454i
$149$	2.13688e9	0.355174	0.177587	−	0.984105i	$-0.443171\pi$
$149$	2.13688e9	0.355174	0.177587	+	0.984105i	$0.443171\pi$
$150$	0	0
$151$	−9.67515e6	−0.00151447	−0.000757236	−	1.00000i	$-0.500241\pi$
$151$	−9.67515e6	−0.00151447	−0.000757236		1.00000i	$0.500241\pi$
$152$	1.21151e9i	0.184091i
$153$	− 6.30095e9i	− 0.929597i
$154$	−2.16072e9	−0.309567
$155$	0	0
$156$	−7.32508e9	−0.990266
$157$	6.88488e8i	0.0904373i	0.998977	+	0.0452187i	$0.0143985\pi$
$157$	6.88488e8i	0.0904373i	−0.998977	+	0.0452187i	$0.985602\pi$
$158$	− 9.33353e9i	− 1.19149i
$159$	−1.70833e10	−2.11975
$160$	0	0
$161$	1.18524e10	1.39024
$162$	7.73937e9i	0.882853i
$163$	− 1.43082e10i	− 1.58759i	−0.608182	−	0.793797i	$-0.708101\pi$
$163$	− 1.43082e10i	− 1.58759i	0.608182	−	0.793797i	$-0.291899\pi$
$164$	−5.52803e9	−0.596723
$165$	0	0
$166$	−2.33149e8	−0.0238312
$167$	− 9.98735e9i	− 0.993633i	−0.867856	−	0.496817i	$-0.834502\pi$
$167$	− 9.98735e9i	− 0.993633i	0.867856	−	0.496817i	$-0.165498\pi$
$168$	3.31978e9i	0.321527i
$169$	−1.64380e10	−1.55010
$170$	0	0
$171$	−3.13320e9	−0.280224
$172$	− 2.77307e9i	− 0.241592i
$173$	3.51396e9i	0.298256i	0.988818	+	0.149128i	$0.0476466\pi$
$173$	3.51396e9i	0.298256i	−0.988818	+	0.149128i	$0.952353\pi$
$174$	1.03647e10	0.857210
$175$	0	0
$176$	1.90002e9	0.149263
$177$	− 2.81234e9i	− 0.215371i
$178$	7.52214e9i	0.561631i
$179$	−1.19502e9	−0.0870038	−0.0435019	−	0.999053i	$-0.513851\pi$
$179$	−1.19502e9	−0.0870038	−0.0435019	+	0.999053i	$0.513851\pi$
$180$	0	0
$181$	−9.12053e9	−0.631635	−0.315818	−	0.948820i	$-0.602279\pi$
$181$	−9.12053e9	−0.631635	−0.315818	+	0.948820i	$0.602279\pi$
$182$	1.22558e10i	0.827983i
$183$	− 7.64350e9i	− 0.503805i
$184$	−1.04224e10	−0.670329
$185$	0	0
$186$	6.50279e9	0.398374
$187$	1.72451e10i	1.03128i
$188$	1.32407e9i	0.0773036i
$189$	7.36737e9	0.419986
$190$	0	0
$191$	−9.37431e9	−0.509670	−0.254835	−	0.966985i	$-0.582021\pi$
$191$	−9.37431e9	−0.509670	−0.254835	+	0.966985i	$0.582021\pi$
$192$	− 2.91924e9i	− 0.155029i
$193$	2.40000e10i	1.24510i	0.782580	+	0.622550i	$0.213903\pi$
$193$	2.40000e10i	1.24510i	−0.782580	+	0.622550i	$0.786097\pi$
$194$	1.88542e9	0.0955651
$195$	0	0
$196$	−4.77610e9	−0.231165
$197$	5.56124e8i	0.0263071i	0.999913	+	0.0131536i	$0.00418703\pi$
$197$	5.56124e8i	0.0263071i	−0.999913	+	0.0131536i	$0.995813\pi$
$198$	4.91380e9i	0.227208i
$199$	2.51255e10	1.13573	0.567866	−	0.823121i	$-0.307769\pi$
$199$	2.51255e10	1.13573	0.567866	+	0.823121i	$0.307769\pi$
$200$	0	0
$201$	−1.41910e10	−0.613240
$202$	1.37748e9i	0.0582110i
$203$	− 1.73416e10i	− 0.716732i
$204$	2.64958e10	1.07113
$205$	0	0
$206$	3.08595e10	1.19395
$207$	− 2.69542e10i	− 1.02038i
$208$	− 1.07771e10i	− 0.399225i
$209$	8.57525e9	0.310877
$210$	0	0
$211$	−1.63915e10	−0.569309	−0.284654	−	0.958630i	$-0.591879\pi$
$211$	−1.63915e10	−0.569309	−0.284654	+	0.958630i	$0.591879\pi$
$212$	− 2.51340e10i	− 0.854575i
$213$	2.80675e10i	0.934321i
$214$	−2.23495e10	−0.728461
$215$	0	0
$216$	−6.47848e9	−0.202503
$217$	− 1.08800e10i	− 0.333090i
$218$	− 9.66924e9i	− 0.289960i
$219$	4.30037e10	1.26330
$220$	0	0
$221$	9.78161e10	2.75832
$222$	− 3.01797e10i	− 0.833925i
$223$	4.65257e10i	1.25986i	0.776654	+	0.629928i	$0.216916\pi$
$223$	4.65257e10i	1.25986i	−0.776654	+	0.629928i	$0.783084\pi$
$224$	−4.88427e9	−0.129623
$225$	0	0
$226$	−2.69728e10	−0.687763
$227$	1.91415e9i	0.0478475i	0.999714	+	0.0239237i	$0.00761589\pi$
$227$	1.91415e9i	0.0478475i	−0.999714	+	0.0239237i	$0.992384\pi$
$228$	− 1.31752e10i	− 0.322887i
$229$	1.45825e10	0.350406	0.175203	−	0.984532i	$-0.443942\pi$
$229$	1.45825e10	0.350406	0.175203	+	0.984532i	$0.443942\pi$
$230$	0	0
$231$	2.34978e10	0.542966
$232$	1.52493e10i	0.345584i
$233$	4.12790e10i	0.917545i	0.888554	+	0.458773i	$0.151711\pi$
$233$	4.12790e10i	0.917545i	−0.888554	+	0.458773i	$0.848289\pi$
$234$	2.78716e10	0.607702
$235$	0	0
$236$	4.13769e9	0.0868269
$237$	1.01502e11i	2.08981i
$238$	− 4.43309e10i	− 0.895592i
$239$	−3.65502e10	−0.724602	−0.362301	−	0.932061i	$-0.618009\pi$
$239$	−3.65502e10	−0.724602	−0.362301	+	0.932061i	$0.618009\pi$
$240$	0	0
$241$	−8.66070e10	−1.65377	−0.826887	−	0.562368i	$-0.809890\pi$
$241$	−8.66070e10	−1.65377	−0.826887	+	0.562368i	$0.809890\pi$
$242$	2.42786e10i	0.455045i
$243$	− 5.30339e10i	− 0.975720i
$244$	1.12456e10	0.203109
$245$	0	0
$246$	6.01173e10	1.04663
$247$	− 4.86398e10i	− 0.831488i
$248$	9.56732e9i	0.160605i
$249$	2.53549e9	0.0417989
$250$	0	0
$251$	−7.20769e10	−1.14621	−0.573105	−	0.819482i	$-0.694261\pi$
$251$	−7.20769e10	−1.14621	−0.573105	+	0.819482i	$0.694261\pi$
$252$	− 1.26316e10i	− 0.197313i
$253$	7.37711e10i	1.13199i
$254$	−5.93145e10	−0.894148
$255$	0	0
$256$	4.29497e9	0.0625000
$257$	1.12729e11i	1.61190i	0.591986	+	0.805948i	$0.298344\pi$
$257$	1.12729e11i	1.61190i	−0.591986	+	0.805948i	$0.701656\pi$
$258$	3.01571e10i	0.423741i
$259$	−5.04947e10	−0.697263
$260$	0	0
$261$	−3.94374e10	−0.526049
$262$	− 4.06528e10i	− 0.533009i
$263$	5.55225e10i	0.715596i	0.933799	+	0.357798i	$0.116472\pi$
$263$	5.55225e10i	0.715596i	−0.933799	+	0.357798i	$0.883528\pi$
$264$	−2.06627e10	−0.261800
$265$	0	0
$266$	−2.20439e10	−0.269973
$267$	− 8.18033e10i	− 0.985076i
$268$	− 2.08787e10i	− 0.247228i
$269$	−2.79726e10	−0.325722	−0.162861	−	0.986649i	$-0.552072\pi$
$269$	−2.79726e10	−0.325722	−0.162861	+	0.986649i	$0.552072\pi$
$270$	0	0
$271$	3.32884e10	0.374914	0.187457	−	0.982273i	$-0.439975\pi$
$271$	3.32884e10	0.374914	0.187457	+	0.982273i	$0.439975\pi$
$272$	3.89823e10i	0.431824i
$273$	− 1.33282e11i	− 1.45225i
$274$	1.84623e10	0.197883
$275$	0	0
$276$	1.13344e11	1.17573
$277$	− 5.46240e10i	− 0.557474i	−0.960367	−	0.278737i	$-0.910084\pi$
$277$	− 5.46240e10i	− 0.557474i	0.960367	−	0.278737i	$-0.0899158\pi$
$278$	− 9.00353e10i	− 0.904090i
$279$	−2.47428e10	−0.244473
$280$	0	0
$281$	−8.37818e10	−0.801625	−0.400813	−	0.916160i	$-0.631272\pi$
$281$	−8.37818e10	−0.801625	−0.400813	+	0.916160i	$0.631272\pi$
$282$	− 1.43992e10i	− 0.135587i
$283$	− 8.36086e10i	− 0.774840i	−0.921903	−	0.387420i	$-0.873366\pi$
$283$	− 8.36086e10i	− 0.774840i	0.921903	−	0.387420i	$-0.126634\pi$
$284$	−4.12948e10	−0.376671
$285$	0	0
$286$	−7.62819e10	−0.674178
$287$	− 1.00584e11i	− 0.875107i
$288$	1.11076e10i	0.0951377i
$289$	−2.35225e11	−1.98355
$290$	0	0
$291$	−2.05039e10	−0.167617
$292$	6.32699e10i	0.509301i
$293$	− 2.28547e11i	− 1.81164i	−0.423666	−	0.905819i	$-0.639257\pi$
$293$	− 2.28547e11i	− 1.81164i	0.423666	−	0.905819i	$-0.360743\pi$
$294$	5.19401e10	0.405452
$295$	0	0
$296$	4.44024e10	0.336197
$297$	4.58555e10i	0.341969i
$298$	− 3.41900e10i	− 0.251146i
$299$	4.18438e11	3.02769
$300$	0	0
$301$	5.04568e10	0.354300
$302$	1.54802e8i	0.00107089i
$303$	− 1.49801e10i	− 0.102100i
$304$	1.93842e10	0.130172
$305$	0	0
$306$	−1.00815e11	−0.657324
$307$	− 1.95064e11i	− 1.25330i	−0.779302	−	0.626648i	$-0.784426\pi$
$307$	− 1.95064e11i	− 1.25330i	0.779302	−	0.626648i	$-0.215574\pi$
$308$	3.45715e10i	0.218897i
$309$	−3.35598e11	−2.09414
$310$	0	0
$311$	2.15637e11	1.30708	0.653540	−	0.756892i	$-0.273283\pi$
$311$	2.15637e11	1.30708	0.653540	+	0.756892i	$0.273283\pi$
$312$	1.17201e11i	0.700224i
$313$	1.91755e11i	1.12927i	0.825341	+	0.564635i	$0.190983\pi$
$313$	1.91755e11i	1.12927i	−0.825341	+	0.564635i	$0.809017\pi$
$314$	1.10158e10	0.0639488
$315$	0	0
$316$	−1.49337e11	−0.842508
$317$	3.38886e11i	1.88489i	0.334358	+	0.942446i	$0.391481\pi$
$317$	3.38886e11i	1.88489i	−0.334358	+	0.942446i	$0.608519\pi$
$318$	2.73332e11i	1.49889i
$319$	1.07936e11	0.583592
$320$	0	0
$321$	2.43051e11	1.27769
$322$	− 1.89639e11i	− 0.983052i
$323$	1.75936e11i	0.899383i
$324$	1.23830e11	0.624271
$325$	0	0
$326$	−2.28931e11	−1.12260
$327$	1.05153e11i	0.508577i
$328$	8.84485e10i	0.421947i
$329$	−2.40918e10	−0.113367
$330$	0	0
$331$	−1.78427e11	−0.817022	−0.408511	−	0.912753i	$-0.633952\pi$
$331$	−1.78427e11	−0.817022	−0.408511	+	0.912753i	$0.633952\pi$
$332$	3.73038e9i	0.0168512i
$333$	1.14833e11i	0.511760i
$334$	−1.59798e11	−0.702605
$335$	0	0
$336$	5.31164e10	0.227354
$337$	− 2.64693e11i	− 1.11791i	−0.829196	−	0.558957i	$-0.811202\pi$
$337$	− 2.64693e11i	− 1.11791i	0.829196	−	0.558957i	$-0.188798\pi$
$338$	2.63008e11i	1.09608i
$339$	2.93330e11	1.20631
$340$	0	0
$341$	6.77187e10	0.271215
$342$	5.01312e10i	0.198148i
$343$	− 2.74870e11i	− 1.07227i
$344$	−4.43691e10	−0.170831
$345$	0	0
$346$	5.62233e10	0.210899
$347$	8.11912e10i	0.300626i	0.988638	+	0.150313i	$0.0480281\pi$
$347$	8.11912e10i	0.300626i	−0.988638	+	0.150313i	$0.951972\pi$
$348$	− 1.65836e11i	− 0.606139i
$349$	2.26688e11	0.817926	0.408963	−	0.912551i	$-0.365890\pi$
$349$	2.26688e11	0.817926	0.408963	+	0.912551i	$0.365890\pi$
$350$	0	0
$351$	2.60098e11	0.914649
$352$	− 3.04003e10i	− 0.105545i
$353$	3.28733e10i	0.112683i	0.998412	+	0.0563413i	$0.0179435\pi$
$353$	3.28733e10i	0.112683i	−0.998412	+	0.0563413i	$0.982056\pi$
$354$	−4.49974e10	−0.152290
$355$	0	0
$356$	1.20354e11	0.397133
$357$	4.82098e11i	1.57083i
$358$	1.91204e10i	0.0615210i
$359$	3.12096e11	0.991661	0.495831	−	0.868419i	$-0.334864\pi$
$359$	3.12096e11	0.991661	0.495831	+	0.868419i	$0.334864\pi$
$360$	0	0
$361$	−2.35202e11	−0.728884
$362$	1.45928e11i	0.446634i
$363$	− 2.64030e11i	− 0.798129i
$364$	1.96093e11	0.585473
$365$	0	0
$366$	−1.22296e11	−0.356244
$367$	− 6.28209e11i	− 1.80762i	−0.427934	−	0.903810i	$-0.640759\pi$
$367$	− 6.28209e11i	− 1.80762i	0.427934	−	0.903810i	$-0.359241\pi$
$368$	1.66759e11i	0.473994i
$369$	−2.28744e11	−0.642289
$370$	0	0
$371$	4.57321e11	1.25325
$372$	− 1.04045e11i	− 0.281693i
$373$	− 9.84770e10i	− 0.263418i	−0.991288	−	0.131709i	$-0.957954\pi$
$373$	− 9.84770e10i	− 0.263418i	0.991288	−	0.131709i	$-0.0420464\pi$
$374$	2.75921e11	0.729227
$375$	0	0
$376$	2.11851e10	0.0546619
$377$	− 6.12228e11i	− 1.56091i
$378$	− 1.17878e11i	− 0.296975i
$379$	−2.89024e11	−0.719544	−0.359772	−	0.933040i	$-0.617145\pi$
$379$	−2.89024e11	−0.719544	−0.359772	+	0.933040i	$0.617145\pi$
$380$	0	0
$381$	6.45046e11	1.56830
$382$	1.49989e11i	0.360391i
$383$	2.01350e11i	0.478141i	0.971002	+	0.239071i	$0.0768427\pi$
$383$	2.01350e11i	0.478141i	−0.971002	+	0.239071i	$0.923157\pi$
$384$	−4.67078e10	−0.109622
$385$	0	0
$386$	3.84001e11	0.880418
$387$	− 1.14746e11i	− 0.260040i
$388$	− 3.01666e10i	− 0.0675747i
$389$	−3.93769e11	−0.871904	−0.435952	−	0.899970i	$-0.643588\pi$
$389$	−3.93769e11	−0.871904	−0.435952	+	0.899970i	$0.643588\pi$
$390$	0	0
$391$	−1.51354e12	−3.27491
$392$	7.64176e10i	0.163458i
$393$	4.42099e11i	0.934875i
$394$	8.89798e9	0.0186019
$395$	0	0
$396$	7.86207e10	0.160660
$397$	5.15625e11i	1.04178i	0.853623	+	0.520891i	$0.174400\pi$
$397$	5.15625e11i	1.04178i	−0.853623	+	0.520891i	$0.825600\pi$
$398$	− 4.02008e11i	− 0.803084i
$399$	2.39727e11	0.473521
$400$	0	0
$401$	−8.43309e11	−1.62869	−0.814343	−	0.580384i	$-0.802902\pi$
$401$	−8.43309e11	−1.62869	−0.814343	+	0.580384i	$0.802902\pi$
$402$	2.27056e11i	0.433626i
$403$	− 3.84108e11i	− 0.725406i
$404$	2.20397e10	0.0411614
$405$	0	0
$406$	−2.77466e11	−0.506806
$407$	− 3.14285e11i	− 0.567740i
$408$	− 4.23932e11i	− 0.757400i
$409$	−5.64549e11	−0.997577	−0.498789	−	0.866724i	$-0.666222\pi$
$409$	−5.64549e11	−0.997577	−0.498789	+	0.866724i	$0.666222\pi$
$410$	0	0
$411$	−2.00778e11	−0.347078
$412$	− 4.93753e11i	− 0.844252i
$413$	7.52866e10i	0.127333i
$414$	−4.31268e11	−0.721516
$415$	0	0
$416$	−1.72434e11	−0.282295
$417$	9.79134e11i	1.58573i
$418$	− 1.37204e11i	− 0.219823i
$419$	−6.92475e11	−1.09759	−0.548796	−	0.835956i	$-0.684914\pi$
$419$	−6.92475e11	−1.09759	−0.548796	+	0.835956i	$0.684914\pi$
$420$	0	0
$421$	4.08125e11	0.633176	0.316588	−	0.948563i	$-0.397463\pi$
$421$	4.08125e11	0.633176	0.316588	+	0.948563i	$0.397463\pi$
$422$	2.62264e11i	0.402562i
$423$	5.47885e10i	0.0832065i
$424$	−4.02144e11	−0.604276
$425$	0	0
$426$	4.49081e11	0.660665
$427$	2.04617e11i	0.297863i
$428$	3.57592e11i	0.515100i
$429$	8.29566e11	1.18248
$430$	0	0
$431$	4.41055e11	0.615665	0.307833	−	0.951441i	$-0.400396\pi$
$431$	4.41055e11	0.615665	0.307833	+	0.951441i	$0.400396\pi$
$432$	1.03656e11i	0.143191i
$433$	− 7.15390e10i	− 0.0978019i	−0.998804	−	0.0489009i	$-0.984428\pi$
$433$	− 7.15390e10i	− 0.0978019i	0.998804	−	0.0489009i	$-0.0155719\pi$
$434$	−1.74080e11	−0.235530
$435$	0	0
$436$	−1.54708e11	−0.205033
$437$	7.52622e11i	0.987212i
$438$	− 6.88060e11i	− 0.893291i
$439$	−4.74967e11	−0.610342	−0.305171	−	0.952298i	$-0.598714\pi$
$439$	−4.74967e11	−0.610342	−0.305171	+	0.952298i	$0.598714\pi$
$440$	0	0
$441$	−1.97630e11	−0.248816
$442$	− 1.56506e12i	− 1.95043i
$443$	− 1.97072e11i	− 0.243113i	−0.992585	−	0.121556i	$-0.961211\pi$
$443$	− 1.97072e11i	− 0.243113i	0.992585	−	0.121556i	$-0.0387885\pi$
$444$	−4.82876e11	−0.589674
$445$	0	0
$446$	7.44411e11	0.890853
$447$	3.71817e11i	0.440499i
$448$	7.81483e10i	0.0916576i
$449$	6.20156e11	0.720100	0.360050	−	0.932933i	$-0.382760\pi$
$449$	6.20156e11	0.720100	0.360050	+	0.932933i	$0.382760\pi$
$450$	0	0
$451$	6.26049e11	0.712548
$452$	4.31565e11i	0.486322i
$453$	− 1.68348e9i	− 0.00187830i
$454$	3.06264e10	0.0338333
$455$	0	0
$456$	−2.10804e11	−0.228316
$457$	− 7.88006e11i	− 0.845097i	−0.906340	−	0.422549i	$-0.861136\pi$
$457$	− 7.88006e11i	− 0.845097i	0.906340	−	0.422549i	$-0.138864\pi$
$458$	− 2.33319e11i	− 0.247774i
$459$	−9.40806e11	−0.989334
$460$	0	0
$461$	1.53496e10	0.0158286	0.00791429	−	0.999969i	$-0.497481\pi$
$461$	1.53496e10	0.0158286	0.00791429	+	0.999969i	$0.497481\pi$
$462$	− 3.75965e11i	− 0.383935i
$463$	1.94494e11i	0.196694i	0.995152	+	0.0983471i	$0.0313555\pi$
$463$	1.94494e11i	0.196694i	−0.995152	+	0.0983471i	$0.968644\pi$
$464$	2.43989e11	0.244365
$465$	0	0
$466$	6.60464e11	0.648802
$467$	− 1.06503e11i	− 0.103618i	−0.998657	−	0.0518089i	$-0.983501\pi$
$467$	− 1.06503e11i	− 0.103618i	0.998657	−	0.0518089i	$-0.0164987\pi$
$468$	− 4.45946e11i	− 0.429710i
$469$	3.79894e11	0.362564
$470$	0	0
$471$	−1.19797e11	−0.112163
$472$	− 6.62031e10i	− 0.0613959i
$473$	3.14050e11i	0.288485i
$474$	1.62403e12	1.47772
$475$	0	0
$476$	−7.09294e11	−0.633279
$477$	− 1.04002e12i	− 0.919831i
$478$	5.84803e11i	0.512371i
$479$	8.31146e11	0.721386	0.360693	−	0.932685i	$-0.382540\pi$
$479$	8.31146e11	0.721386	0.360693	+	0.932685i	$0.382540\pi$
$480$	0	0
$481$	−1.78266e12	−1.51851
$482$	1.38571e12i	1.16939i
$483$	2.06232e12i	1.72423i
$484$	3.88457e11	0.321765
$485$	0	0
$486$	−8.48542e11	−0.689938
$487$	1.38566e12i	1.11629i	0.829743	+	0.558146i	$0.188487\pi$
$487$	1.38566e12i	1.11629i	−0.829743	+	0.558146i	$0.811513\pi$
$488$	− 1.79930e11i	− 0.143620i
$489$	2.48962e12	1.96899
$490$	0	0
$491$	3.92804e11	0.305007	0.152503	−	0.988303i	$-0.451266\pi$
$491$	3.92804e11	0.305007	0.152503	+	0.988303i	$0.451266\pi$
$492$	− 9.61877e11i	− 0.740076i
$493$	2.21450e12i	1.68836i
$494$	−7.78237e11	−0.587951
$495$	0	0
$496$	1.53077e11	0.113565
$497$	− 7.51371e11i	− 0.552397i
$498$	− 4.05679e10i	− 0.0295563i
$499$	7.52029e11	0.542978	0.271489	−	0.962442i	$-0.412484\pi$
$499$	7.52029e11	0.542978	0.271489	+	0.962442i	$0.412484\pi$
$500$	0	0
$501$	1.73780e12	1.23234
$502$	1.15323e12i	0.810493i
$503$	− 1.83429e12i	− 1.27765i	−0.769351	−	0.638826i	$-0.779420\pi$
$503$	− 1.83429e12i	− 1.27765i	0.769351	−	0.638826i	$-0.220580\pi$
$504$	−2.02106e11	−0.139521
$505$	0	0
$506$	1.18034e12	0.800441
$507$	− 2.86021e12i	− 1.92248i
$508$	9.49033e11i	0.632258i
$509$	6.19864e11	0.409323	0.204662	−	0.978833i	$-0.434391\pi$
$509$	6.19864e11	0.409323	0.204662	+	0.978833i	$0.434391\pi$
$510$	0	0
$511$	−1.15122e12	−0.746900
$512$	− 6.87195e10i	− 0.0441942i
$513$	4.67823e11i	0.298232i
$514$	1.80367e12	1.13978
$515$	0	0
$516$	4.82514e11	0.299630
$517$	− 1.49951e11i	− 0.0923083i
$518$	8.07915e11i	0.493039i
$519$	−6.11428e11	−0.369907
$520$	0	0
$521$	5.25683e11	0.312575	0.156287	−	0.987712i	$-0.450047\pi$
$521$	5.25683e11	0.312575	0.156287	+	0.987712i	$0.450047\pi$
$522$	6.30999e11i	0.371973i
$523$	1.68426e11i	0.0984353i	0.998788	+	0.0492177i	$0.0156728\pi$
$523$	1.68426e11i	0.0984353i	−0.998788	+	0.0492177i	$0.984327\pi$
$524$	−6.50445e11	−0.376895
$525$	0	0
$526$	8.88360e11	0.506003
$527$	1.38937e12i	0.784639i
$528$	3.30603e11i	0.185121i
$529$	−4.67350e12	−2.59473
$530$	0	0
$531$	1.71213e11	0.0934570
$532$	3.52702e11i	0.190900i
$533$	− 3.55102e12i	− 1.90582i
$534$	−1.30885e12	−0.696554
$535$	0	0
$536$	−3.34059e11	−0.174816
$537$	− 2.07934e11i	− 0.107905i
$538$	4.47561e11i	0.230320i
$539$	5.40893e11	0.276034
$540$	0	0
$541$	2.20612e12	1.10724	0.553620	−	0.832769i	$-0.313246\pi$
$541$	2.20612e12	1.10724	0.553620	+	0.832769i	$0.313246\pi$
$542$	− 5.32615e11i	− 0.265104i
$543$	− 1.58697e12i	− 0.783375i
$544$	6.23716e11	0.305346
$545$	0	0
$546$	−2.13251e12	−1.02689
$547$	3.51639e12i	1.67940i	0.543049	+	0.839701i	$0.317270\pi$
$547$	3.51639e12i	1.67940i	−0.543049	+	0.839701i	$0.682730\pi$
$548$	− 2.95397e11i	− 0.139925i
$549$	4.65331e11	0.218618
$550$	0	0
$551$	1.10118e12	0.508951
$552$	− 1.81350e12i	− 0.831365i
$553$	− 2.71722e12i	− 1.23556i
$554$	−8.73985e11	−0.394194
$555$	0	0
$556$	−1.44057e12	−0.639288
$557$	− 6.29996e11i	− 0.277325i	−0.990340	−	0.138663i	$-0.955720\pi$
$557$	− 6.29996e11i	− 0.277325i	0.990340	−	0.138663i	$-0.0442803\pi$
$558$	3.95885e11i	0.172868i
$559$	1.78133e12	0.771597
$560$	0	0
$561$	−3.00064e12	−1.27903
$562$	1.34051e12i	0.566835i
$563$	4.02619e11i	0.168891i	0.996428	+	0.0844455i	$0.0269119\pi$
$563$	4.02619e11i	0.168891i	−0.996428	+	0.0844455i	$0.973088\pi$
$564$	−2.30388e11	−0.0958746
$565$	0	0
$566$	−1.33774e12	−0.547894
$567$	2.25313e12i	0.915507i
$568$	6.60716e11i	0.266347i
$569$	−2.55482e12	−1.02177	−0.510887	−	0.859648i	$-0.670683\pi$
$569$	−2.55482e12	−1.02177	−0.510887	+	0.859648i	$0.670683\pi$
$570$	0	0
$571$	1.16243e12	0.457620	0.228810	−	0.973471i	$-0.426516\pi$
$571$	1.16243e12	0.457620	0.228810	+	0.973471i	$0.426516\pi$
$572$	1.22051e12i	0.476716i
$573$	− 1.63113e12i	− 0.632110i
$574$	−1.60935e12	−0.618794
$575$	0	0
$576$	1.77721e11	0.0672725
$577$	− 4.66332e12i	− 1.75148i	−0.482787	−	0.875738i	$-0.660375\pi$
$577$	− 4.66332e12i	− 1.75148i	0.482787	−	0.875738i	$-0.339625\pi$
$578$	3.76361e12i	1.40258i
$579$	−4.17601e12	−1.54421
$580$	0	0
$581$	−6.78754e10	−0.0247127
$582$	3.28062e11i	0.118523i
$583$	2.84643e12i	1.02045i
$584$	1.01232e12	0.360130
$585$	0	0
$586$	−3.65675e12	−1.28102
$587$	− 3.88422e12i	− 1.35030i	−0.737678	−	0.675152i	$-0.764078\pi$
$587$	− 3.88422e12i	− 1.35030i	0.737678	−	0.675152i	$-0.235922\pi$
$588$	− 8.31042e11i	− 0.286698i
$589$	6.90875e11	0.236527
$590$	0	0
$591$	−9.67655e10	−0.0326270
$592$	− 7.10438e11i	− 0.237727i
$593$	− 2.01341e12i	− 0.668631i	−0.942461	−	0.334315i	$-0.891495\pi$
$593$	− 2.01341e12i	− 0.668631i	0.942461	−	0.334315i	$-0.108505\pi$
$594$	7.33688e11	0.241809
$595$	0	0
$596$	−5.47041e11	−0.177587
$597$	4.37184e12i	1.40857i
$598$	− 6.69502e12i	− 2.14090i
$599$	−2.10578e12	−0.668333	−0.334166	−	0.942514i	$-0.608455\pi$
$599$	−2.10578e12	−0.668333	−0.334166	+	0.942514i	$0.608455\pi$
$600$	0	0
$601$	4.74058e12	1.48216	0.741082	−	0.671415i	$-0.234313\pi$
$601$	4.74058e12	1.48216	0.741082	+	0.671415i	$0.234313\pi$
$602$	− 8.07309e11i	− 0.250528i
$603$	− 8.63938e11i	− 0.266106i
$604$	2.47684e9	0.000757236 0
$605$	0	0
$606$	−2.39682e11	−0.0721953
$607$	4.01476e12i	1.20036i	0.799866	+	0.600179i	$0.204904\pi$
$607$	4.01476e12i	1.20036i	−0.799866	+	0.600179i	$0.795096\pi$
$608$	− 3.10148e11i	− 0.0920455i
$609$	3.01744e12	0.888915
$610$	0	0
$611$	−8.50537e11	−0.246893
$612$	1.61304e12i	0.464798i
$613$	1.30399e12i	0.372993i	0.982456	+	0.186496i	$0.0597133\pi$
$613$	1.30399e12i	0.372993i	−0.982456	+	0.186496i	$0.940287\pi$
$614$	−3.12102e12	−0.886214
$615$	0	0
$616$	5.53143e11	0.154783
$617$	− 5.10164e12i	− 1.41719i	−0.705618	−	0.708593i	$-0.749330\pi$
$617$	− 5.10164e12i	− 1.41719i	0.705618	−	0.708593i	$-0.250670\pi$
$618$	5.36956e12i	1.48078i
$619$	4.50630e11	0.123371	0.0616854	−	0.998096i	$-0.480352\pi$
$619$	4.50630e11	0.123371	0.0616854	+	0.998096i	$0.480352\pi$
$620$	0	0
$621$	−4.02459e12	−1.08595
$622$	− 3.45020e12i	− 0.924246i
$623$	2.18988e12i	0.582404i
$624$	1.87522e12	0.495133
$625$	0	0
$626$	3.06808e12	0.798514
$627$	1.49209e12i	0.385560i
$628$	− 1.76253e11i	− 0.0452187i
$629$	6.44812e12	1.64250
$630$	0	0
$631$	7.97105e10	0.0200163	0.0100081	−	0.999950i	$-0.496814\pi$
$631$	7.97105e10	0.0200163	0.0100081	+	0.999950i	$0.496814\pi$
$632$	2.38938e12i	0.595743i
$633$	− 2.85212e12i	− 0.706076i
$634$	5.42217e12	1.33282
$635$	0	0
$636$	4.37332e12	1.05987
$637$	− 3.06801e12i	− 0.738294i
$638$	− 1.72698e12i	− 0.412662i
$639$	−1.70873e12	−0.405434
$640$	0	0
$641$	−3.12648e12	−0.731468	−0.365734	−	0.930719i	$-0.619182\pi$
$641$	−3.12648e12	−0.731468	−0.365734	+	0.930719i	$0.619182\pi$
$642$	− 3.88882e12i	− 0.903462i
$643$	− 5.94982e12i	− 1.37263i	−0.727303	−	0.686316i	$-0.759227\pi$
$643$	− 5.94982e12i	− 1.37263i	0.727303	−	0.686316i	$-0.240773\pi$
$644$	−3.03422e12	−0.695122
$645$	0	0
$646$	2.81498e12	0.635960
$647$	− 3.56187e12i	− 0.799115i	−0.916708	−	0.399557i	$-0.869164\pi$
$647$	− 3.56187e12i	− 0.799115i	0.916708	−	0.399557i	$-0.130836\pi$
$648$	− 1.98128e12i	− 0.441426i
$649$	−4.68594e11	−0.103680
$650$	0	0
$651$	1.89312e12	0.413109
$652$	3.66289e12i	0.793797i
$653$	− 1.37883e11i	− 0.0296757i	−0.999890	−	0.0148379i	$-0.995277\pi$
$653$	− 1.37883e11i	− 0.0296757i	0.999890	−	0.0148379i	$-0.00472321\pi$
$654$	1.68245e12	0.359618
$655$	0	0
$656$	1.41518e12	0.298362
$657$	2.61804e12i	0.548191i
$658$	3.85469e11i	0.0801628i
$659$	4.16654e12	0.860581	0.430290	−	0.902691i	$-0.358411\pi$
$659$	4.16654e12	0.860581	0.430290	+	0.902691i	$0.358411\pi$
$660$	0	0
$661$	−3.29083e12	−0.670500	−0.335250	−	0.942129i	$-0.608821\pi$
$661$	−3.29083e12	−0.670500	−0.335250	+	0.942129i	$0.608821\pi$
$662$	2.85483e12i	0.577722i
$663$	1.70200e13i	3.42097i
$664$	5.96860e10	0.0119156
$665$	0	0
$666$	1.83732e12	0.361869
$667$	9.47322e12i	1.85324i
$668$	2.55676e12i	0.496817i
$669$	−8.09547e12	−1.56252
$670$	0	0
$671$	−1.27357e12	−0.242532
$672$	− 8.49862e11i	− 0.160763i
$673$	5.74732e12i	1.07993i	0.841686	+	0.539967i	$0.181563\pi$
$673$	5.74732e12i	1.07993i	−0.841686	+	0.539967i	$0.818437\pi$
$674$	−4.23510e12	−0.790485
$675$	0	0
$676$	4.20812e12	0.775048
$677$	− 9.31245e12i	− 1.70379i	−0.523716	−	0.851893i	$-0.675455\pi$
$677$	− 9.31245e12i	− 1.70379i	0.523716	−	0.851893i	$-0.324545\pi$
$678$	− 4.69327e12i	− 0.852987i
$679$	5.48892e11	0.0990998
$680$	0	0
$681$	−3.33062e11	−0.0593421
$682$	− 1.08350e12i	− 0.191778i
$683$	9.19967e12i	1.61763i	0.588063	+	0.808815i	$0.299891\pi$
$683$	9.19967e12i	1.61763i	−0.588063	+	0.808815i	$0.700109\pi$
$684$	8.02099e11	0.140112
$685$	0	0
$686$	−4.39792e12	−0.758208
$687$	2.53735e12i	0.434585i
$688$	7.09905e11i	0.120796i
$689$	1.61453e13	2.72934
$690$	0	0
$691$	1.03125e13	1.72074	0.860369	−	0.509672i	$-0.170233\pi$
$691$	1.03125e13	1.72074	0.860369	+	0.509672i	$0.170233\pi$
$692$	− 8.99573e11i	− 0.149128i
$693$	1.43053e12i	0.235612i
$694$	1.29906e12	0.212574
$695$	0	0
$696$	−2.65338e12	−0.428605
$697$	1.28445e13i	2.06144i
$698$	− 3.62701e12i	− 0.578361i
$699$	−7.18255e12	−1.13797
$700$	0	0
$701$	−9.52566e12	−1.48992	−0.744961	−	0.667108i	$-0.767532\pi$
$701$	−9.52566e12	−1.48992	−0.744961	+	0.667108i	$0.767532\pi$
$702$	− 4.16156e12i	− 0.646754i
$703$	− 3.20638e12i	− 0.495126i
$704$	−4.86405e11	−0.0746313
$705$	0	0
$706$	5.25973e11	0.0796787
$707$	4.01020e11i	0.0603641i
$708$	7.19958e11i	0.107686i
$709$	8.38537e12	1.24628	0.623138	−	0.782112i	$-0.285858\pi$
$709$	8.38537e12	1.24628	0.623138	+	0.782112i	$0.285858\pi$
$710$	0	0
$711$	−6.17938e12	−0.906842
$712$	− 1.92567e12i	− 0.280816i
$713$	5.94345e12i	0.861263i
$714$	7.71358e12	1.11074
$715$	0	0
$716$	3.05926e11	0.0435019
$717$	− 6.35974e12i	− 0.898676i
$718$	− 4.99354e12i	− 0.701211i
$719$	−6.94013e12	−0.968473	−0.484236	−	0.874937i	$-0.660903\pi$
$719$	−6.94013e12	−0.968473	−0.484236	+	0.874937i	$0.660903\pi$
$720$	0	0
$721$	8.98398e12	1.23811
$722$	3.76323e12i	0.515399i
$723$	− 1.50696e13i	− 2.05107i
$724$	2.33485e12	0.315818
$725$	0	0
$726$	−4.22447e12	−0.564362
$727$	− 7.74984e12i	− 1.02893i	−0.857510	−	0.514467i	$-0.827990\pi$
$727$	− 7.74984e12i	− 1.02893i	0.857510	−	0.514467i	$-0.172010\pi$
$728$	− 3.13749e12i	− 0.413992i
$729$	−2.92986e11	−0.0384214
$730$	0	0
$731$	−6.44329e12	−0.834602
$732$	1.95674e12i	0.251902i
$733$	4.12555e12i	0.527854i	0.964543	+	0.263927i	$0.0850178\pi$
$733$	4.12555e12i	0.527854i	−0.964543	+	0.263927i	$0.914982\pi$
$734$	−1.00513e13	−1.27818
$735$	0	0
$736$	2.66814e12	0.335164
$737$	2.36451e12i	0.295215i
$738$	3.65990e12i	0.454167i
$739$	−3.33931e12	−0.411867	−0.205933	−	0.978566i	$-0.566023\pi$
$739$	−3.33931e12	−0.411867	−0.205933	+	0.978566i	$0.566023\pi$
$740$	0	0
$741$	8.46333e12	1.03124
$742$	− 7.31713e12i	− 0.886183i
$743$	− 1.26471e13i	− 1.52245i	−0.648489	−	0.761224i	$-0.724599\pi$
$743$	− 1.26471e13i	− 1.52245i	0.648489	−	0.761224i	$-0.275401\pi$
$744$	−1.66471e12	−0.199187
$745$	0	0
$746$	−1.57563e12	−0.186265
$747$	1.54359e11i	0.0181380i
$748$	− 4.41474e12i	− 0.515642i
$749$	−6.50651e12	−0.755405
$750$	0	0
$751$	1.56552e12	0.179588	0.0897941	−	0.995960i	$-0.471379\pi$
$751$	1.56552e12	0.179588	0.0897941	+	0.995960i	$0.471379\pi$
$752$	− 3.38961e11i	− 0.0386518i
$753$	− 1.25414e13i	− 1.42157i
$754$	−9.79564e12	−1.10373
$755$	0	0
$756$	−1.88605e12	−0.209993
$757$	− 9.54781e11i	− 0.105675i	−0.998603	−	0.0528375i	$-0.983173\pi$
$757$	− 9.54781e11i	− 0.105675i	0.998603	−	0.0528375i	$-0.0168265\pi$
$758$	4.62438e12i	0.508794i
$759$	−1.28362e13	−1.40394
$760$	0	0
$761$	5.27330e12	0.569969	0.284985	−	0.958532i	$-0.408012\pi$
$761$	5.27330e12	0.569969	0.284985	+	0.958532i	$0.408012\pi$
$762$	− 1.03207e13i	− 1.10895i
$763$	− 2.81496e12i	− 0.300685i
$764$	2.39982e12	0.254835
$765$	0	0
$766$	3.22159e12	0.338097
$767$	2.65792e12i	0.277308i
$768$	7.47324e11i	0.0775146i
$769$	6.96923e12	0.718648	0.359324	−	0.933213i	$-0.383007\pi$
$769$	6.96923e12	0.718648	0.359324	+	0.933213i	$0.383007\pi$
$770$	0	0
$771$	−1.96149e13	−1.99913
$772$	− 6.14401e12i	− 0.622550i
$773$	− 3.79383e12i	− 0.382182i	−0.981572	−	0.191091i	$-0.938797\pi$
$773$	− 3.79383e12i	− 0.382182i	0.981572	−	0.191091i	$-0.0612025\pi$
$774$	−1.83594e12	−0.183876
$775$	0	0
$776$	−4.82666e11	−0.0477825
$777$	− 8.78607e12i	− 0.864769i
$778$	6.30031e12i	0.616530i
$779$	6.38703e12	0.621413
$780$	0	0
$781$	4.67663e12	0.449784
$782$	2.42167e13i	2.31571i
$783$	5.88847e12i	0.559854i
$784$	1.22268e12	0.115582
$785$	0	0
$786$	7.07359e12	0.661056
$787$	2.05939e13i	1.91361i	0.290736	+	0.956803i	$0.406100\pi$
$787$	2.05939e13i	1.91361i	−0.290736	+	0.956803i	$0.593900\pi$
$788$	− 1.42368e11i	− 0.0131536i
$789$	−9.66092e12	−0.887507
$790$	0	0
$791$	−7.85247e12	−0.713201
$792$	− 1.25793e12i	− 0.113604i
$793$	7.22381e12i	0.648690i
$794$	8.25000e12	0.736651
$795$	0	0
$796$	−6.43213e12	−0.567866
$797$	− 1.45507e12i	− 0.127738i	−0.997958	−	0.0638690i	$-0.979656\pi$
$797$	− 1.45507e12i	− 0.127738i	0.997958	−	0.0638690i	$-0.0203440\pi$
$798$	− 3.83564e12i	− 0.334830i
$799$	3.07650e12	0.267052
$800$	0	0
$801$	4.98013e12	0.427459
$802$	1.34929e13i	1.15165i
$803$	− 7.16531e12i	− 0.608156i
$804$	3.63289e12	0.306620
$805$	0	0
$806$	−6.14573e12	−0.512939
$807$	− 4.86722e12i	− 0.403971i
$808$	− 3.52636e11i	− 0.0291055i
$809$	−1.31749e13	−1.08138	−0.540690	−	0.841222i	$-0.681837\pi$
$809$	−1.31749e13	−1.08138	−0.540690	+	0.841222i	$0.681837\pi$
$810$	0	0
$811$	9.97833e12	0.809961	0.404980	−	0.914325i	$-0.367278\pi$
$811$	9.97833e12	0.809961	0.404980	+	0.914325i	$0.367278\pi$
$812$	4.43945e12i	0.358366i
$813$	5.79219e12i	0.464981i
$814$	−5.02857e12	−0.401453
$815$	0	0
$816$	−6.78291e12	−0.535563
$817$	3.20398e12i	0.251588i
$818$	9.03278e12i	0.705394i
$819$	8.11413e12	0.630179
$820$	0	0
$821$	−1.80913e13	−1.38972	−0.694859	−	0.719146i	$-0.744533\pi$
$821$	−1.80913e13	−1.38972	−0.694859	+	0.719146i	$0.744533\pi$
$822$	3.21245e12i	0.245422i
$823$	1.39801e12i	0.106221i	0.998589	+	0.0531107i	$0.0169136\pi$
$823$	1.39801e12i	0.106221i	−0.998589	+	0.0531107i	$0.983086\pi$
$824$	−7.90004e12	−0.596976
$825$	0	0
$826$	1.20459e12	0.0900383
$827$	− 2.26201e13i	− 1.68159i	−0.541354	−	0.840794i	$-0.682088\pi$
$827$	− 2.26201e13i	− 1.68159i	0.541354	−	0.840794i	$-0.317912\pi$
$828$	6.90029e12i	0.510189i
$829$	−1.72646e13	−1.26959	−0.634793	−	0.772682i	$-0.718915\pi$
$829$	−1.72646e13	−1.26959	−0.634793	+	0.772682i	$0.718915\pi$
$830$	0	0
$831$	9.50458e12	0.691398
$832$	2.75895e12i	0.199613i
$833$	1.10974e13i	0.798579i
$834$	1.56662e13	1.12128
$835$	0	0
$836$	−2.19526e12	−0.155439
$837$	3.69440e12i	0.260183i
$838$	1.10796e13i	0.776115i
$839$	1.76607e12	0.123049	0.0615245	−	0.998106i	$-0.480404\pi$
$839$	1.76607e12	0.123049	0.0615245	+	0.998106i	$0.480404\pi$
$840$	0	0
$841$	−6.46640e11	−0.0445739
$842$	− 6.53001e12i	− 0.447723i
$843$	− 1.45780e13i	− 0.994203i
$844$	4.19622e12	0.284654
$845$	0	0
$846$	8.76615e11	0.0588359
$847$	7.06810e12i	0.471876i
$848$	6.43430e12i	0.427287i
$849$	1.45479e13	0.960983
$850$	0	0
$851$	2.75838e13	1.80290
$852$	− 7.18529e12i	− 0.467161i
$853$	− 2.37844e13i	− 1.53823i	−0.639109	−	0.769116i	$-0.720697\pi$
$853$	− 2.37844e13i	− 1.53823i	0.639109	−	0.769116i	$-0.279303\pi$
$854$	3.27388e12	0.210621
$855$	0	0
$856$	5.72148e12	0.364230
$857$	− 7.61941e12i	− 0.482511i	−0.970462	−	0.241256i	$-0.922441\pi$
$857$	− 7.61941e12i	− 0.482511i	0.970462	−	0.241256i	$-0.0775593\pi$
$858$	− 1.32730e13i	− 0.836138i
$859$	1.27695e13	0.800212	0.400106	−	0.916469i	$-0.368973\pi$
$859$	1.27695e13	0.800212	0.400106	+	0.916469i	$0.368973\pi$
$860$	0	0
$861$	1.75017e13	1.08534
$862$	− 7.05687e12i	− 0.435341i
$863$	2.63038e13i	1.61425i	0.590382	+	0.807124i	$0.298977\pi$
$863$	2.63038e13i	1.61425i	−0.590382	+	0.807124i	$0.701023\pi$
$864$	1.65849e12	0.101251
$865$	0	0
$866$	−1.14462e12	−0.0691564
$867$	− 4.09292e13i	− 2.46007i
$868$	2.78529e12i	0.166545i
$869$	1.69124e13	1.00604
$870$	0	0
$871$	1.34118e13	0.789596
$872$	2.47532e12i	0.144980i
$873$	− 1.24826e12i	− 0.0727347i
$874$	1.20420e13	0.698065
$875$	0	0
$876$	−1.10090e13	−0.631652
$877$	− 4.76832e11i	− 0.0272187i	−0.999907	−	0.0136093i	$-0.995668\pi$
$877$	− 4.76832e11i	− 0.0272187i	0.999907	−	0.0136093i	$-0.00433212\pi$
$878$	7.59947e12i	0.431577i
$879$	3.97672e13	2.24685
$880$	0	0
$881$	1.74839e13	0.977791	0.488896	−	0.872342i	$-0.337400\pi$
$881$	1.74839e13	0.977791	0.488896	+	0.872342i	$0.337400\pi$
$882$	3.16208e12i	0.175940i
$883$	− 6.48321e12i	− 0.358894i	−0.983768	−	0.179447i	$-0.942569\pi$
$883$	− 6.48321e12i	− 0.358894i	0.983768	−	0.179447i	$-0.0574309\pi$
$884$	−2.50409e13	−1.37916
$885$	0	0
$886$	−3.15315e12	−0.171907
$887$	9.92450e12i	0.538335i	0.963093	+	0.269167i	$0.0867485\pi$
$887$	9.92450e12i	0.538335i	−0.963093	+	0.269167i	$0.913252\pi$
$888$	7.72601e12i	0.416962i
$889$	−1.72679e13	−0.927220
$890$	0	0
$891$	−1.40237e13	−0.745443
$892$	− 1.19106e13i	− 0.629928i
$893$	− 1.52981e12i	− 0.0805021i
$894$	5.94907e12	0.311480
$895$	0	0
$896$	1.25037e12	0.0648117
$897$	7.28083e13i	3.75504i
$898$	− 9.92250e12i	− 0.509187i
$899$	8.69601e12	0.444019
$900$	0	0
$901$	−5.83994e13	−2.95221
$902$	− 1.00168e13i	− 0.503847i
$903$	8.77949e12i	0.439414i
$904$	6.90505e12	0.343881
$905$	0	0
$906$	−2.69356e10	−0.00132816
$907$	− 1.40768e12i	− 0.0690671i	−0.999404	−	0.0345335i	$-0.989005\pi$
$907$	− 1.40768e12i	− 0.0690671i	0.999404	−	0.0345335i	$-0.0109946\pi$
$908$	− 4.90022e11i	− 0.0239237i
$909$	9.11980e11	0.0443045
$910$	0	0
$911$	6.91343e12	0.332553	0.166277	−	0.986079i	$-0.446826\pi$
$911$	6.91343e12	0.332553	0.166277	+	0.986079i	$0.446826\pi$
$912$	3.37286e12i	0.161444i
$913$	− 4.22465e11i	− 0.0201221i
$914$	−1.26081e13	−0.597574
$915$	0	0
$916$	−3.73311e12	−0.175203
$917$	− 1.18351e13i	− 0.552724i
$918$	1.50529e13i	0.699565i
$919$	8.50189e12	0.393184	0.196592	−	0.980485i	$-0.437013\pi$
$919$	8.50189e12	0.393184	0.196592	+	0.980485i	$0.437013\pi$
$920$	0	0
$921$	3.39411e13	1.55438
$922$	− 2.45593e11i	− 0.0111925i
$923$	− 2.65264e13i	− 1.20301i
$924$	−6.01543e12	−0.271483
$925$	0	0
$926$	3.11190e12	0.139084
$927$	− 2.04309e13i	− 0.908719i
$928$	− 3.90382e12i	− 0.172792i
$929$	−8.90639e12	−0.392311	−0.196156	−	0.980573i	$-0.562846\pi$
$929$	−8.90639e12	−0.392311	−0.196156	+	0.980573i	$0.562846\pi$
$930$	0	0
$931$	5.51826e12	0.240729
$932$	− 1.05674e13i	− 0.458773i
$933$	3.75209e13i	1.62109i
$934$	−1.70404e12	−0.0732689
$935$	0	0
$936$	−7.13514e12	−0.303851
$937$	− 7.40064e12i	− 0.313647i	−0.987627	−	0.156824i	$-0.949875\pi$
$937$	− 7.40064e12i	− 0.313647i	0.987627	−	0.156824i	$-0.0501254\pi$
$938$	− 6.07831e12i	− 0.256372i
$939$	−3.33654e13	−1.40056
$940$	0	0
$941$	−8.13867e12	−0.338377	−0.169188	−	0.985584i	$-0.554115\pi$
$941$	−8.13867e12	−0.338377	−0.169188	+	0.985584i	$0.554115\pi$
$942$	1.91675e12i	0.0793115i
$943$	5.49463e13i	2.26275i
$944$	−1.05925e12	−0.0434134
$945$	0	0
$946$	5.02480e12	0.203990
$947$	1.16975e13i	0.472627i	0.971677	+	0.236313i	$0.0759392\pi$
$947$	1.16975e13i	0.472627i	−0.971677	+	0.236313i	$0.924061\pi$
$948$	− 2.59846e13i	− 1.04491i
$949$	−4.06425e13	−1.62661
$950$	0	0
$951$	−5.89661e13	−2.33771
$952$	1.13487e13i	0.447796i
$953$	− 2.50410e13i	− 0.983406i	−0.870763	−	0.491703i	$-0.836375\pi$
$953$	− 2.50410e13i	− 0.983406i	0.870763	−	0.491703i	$-0.163625\pi$
$954$	−1.66403e13	−0.650418
$955$	0	0
$956$	9.35686e12	0.362301
$957$	1.87809e13i	0.723791i
$958$	− 1.32983e13i	− 0.510097i
$959$	5.37485e12	0.205202
$960$	0	0
$961$	−2.09838e13	−0.793649
$962$	2.85226e13i	1.07375i
$963$	1.47968e13i	0.554433i
$964$	2.21714e13	0.826887
$965$	0	0
$966$	3.29972e13	1.21921
$967$	− 2.68904e13i	− 0.988960i	−0.869189	−	0.494480i	$-0.835359\pi$
$967$	− 2.68904e13i	− 0.988960i	0.869189	−	0.494480i	$-0.164641\pi$
$968$	− 6.21532e12i	− 0.227522i
$969$	−3.06129e13	−1.11544
$970$	0	0
$971$	3.28780e13	1.18691	0.593456	−	0.804866i	$-0.297763\pi$
$971$	3.28780e13	1.18691	0.593456	+	0.804866i	$0.297763\pi$
$972$	1.35767e13i	0.487860i
$973$	− 2.62115e13i	− 0.937529i
$974$	2.21706e13	0.789338
$975$	0	0
$976$	−2.87888e12	−0.101554
$977$	8.13505e11i	0.0285650i	0.999898	+	0.0142825i	$0.00454642\pi$
$977$	8.13505e11i	0.0285650i	−0.999898	+	0.0142825i	$0.995454\pi$
$978$	− 3.98339e13i	− 1.39229i
$979$	−1.36301e13	−0.474217
$980$	0	0
$981$	−6.40164e12	−0.220689
$982$	− 6.28487e12i	− 0.215672i
$983$	− 4.13240e13i	− 1.41160i	−0.708412	−	0.705800i	$-0.750588\pi$
$983$	− 4.13240e13i	− 1.41160i	0.708412	−	0.705800i	$-0.249412\pi$
$984$	−1.53900e13	−0.523313
$985$	0	0
$986$	3.54321e13	1.19385
$987$	− 4.19198e12i	− 0.140602i
$988$	1.24518e13i	0.415744i
$989$	−2.75631e13	−0.916105
$990$	0	0
$991$	−3.61227e13	−1.18973	−0.594866	−	0.803825i	$-0.702795\pi$
$991$	−3.61227e13	−1.18973	−0.594866	+	0.803825i	$0.702795\pi$
$992$	− 2.44923e12i	− 0.0803023i
$993$	− 3.10462e13i	− 1.01330i
$994$	−1.20219e13	−0.390603
$995$	0	0
$996$	−6.49086e11	−0.0208995
$997$	3.07166e13i	0.984565i	0.870435	+	0.492283i	$0.163837\pi$
$997$	3.07166e13i	0.984565i	−0.870435	+	0.492283i	$0.836163\pi$
$998$	− 1.20325e13i	− 0.383944i
$999$	1.71459e13	0.544646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.10.b.d.49.1		2
4.3	odd	2		400.10.c.c.49.1		2
5.2	odd	4		10.10.a.c.1.1	✓	1
5.3	odd	4		50.10.a.a.1.1		1
5.4	even	2	inner	50.10.b.d.49.2		2
15.2	even	4		90.10.a.e.1.1		1
20.3	even	4		400.10.a.j.1.1		1
20.7	even	4		80.10.a.a.1.1		1
20.19	odd	2		400.10.c.c.49.2		2
40.27	even	4		320.10.a.i.1.1		1
40.37	odd	4		320.10.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.10.a.c.1.1	✓	1	5.2	odd	4
50.10.a.a.1.1		1	5.3	odd	4
50.10.b.d.49.1		2	1.1	even	1	trivial
50.10.b.d.49.2		2	5.4	even	2	inner
80.10.a.a.1.1		1	20.7	even	4
90.10.a.e.1.1		1	15.2	even	4
320.10.a.b.1.1		1	40.37	odd	4
320.10.a.i.1.1		1	40.27	even	4
400.10.a.j.1.1		1	20.3	even	4
400.10.c.c.49.1		2	4.3	odd	2
400.10.c.c.49.2		2	20.19	odd	2

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-16.0000i q^{2} +174.000i q^{3} -256.000 q^{4} +2784.00 q^{6} -4658.00i q^{7} +4096.00i q^{8} -10593.0 q^{9} +O(q^{10})\)	\(q-16.0000i q^{2} +174.000i q^{3} -256.000 q^{4} +2784.00 q^{6} -4658.00i q^{7} +4096.00i q^{8} -10593.0 q^{9} +28992.0 q^{11} -44544.0i q^{12} -164446. i q^{13} -74528.0 q^{14} +65536.0 q^{16} +594822. i q^{17} +169488. i q^{18} +295780. q^{19} +810492. q^{21} -463872. i q^{22} +2.54453e6i q^{23} -712704. q^{24} -2.63114e6 q^{26} +1.58166e6i q^{27} +1.19245e6i q^{28} +3.72297e6 q^{29} +2.33577e6 q^{31} -1.04858e6i q^{32} +5.04461e6i q^{33} +9.51715e6 q^{34} +2.71181e6 q^{36} -1.08404e7i q^{37} -4.73248e6i q^{38} +2.86136e7 q^{39} +2.15939e7 q^{41} -1.29679e7i q^{42} +1.08323e7i q^{43} -7.42195e6 q^{44} +4.07125e7 q^{46} -5.17214e6i q^{47} +1.14033e7i q^{48} +1.86566e7 q^{49} -1.03499e8 q^{51} +4.20982e7i q^{52} +9.81797e7i q^{53} +2.53066e7 q^{54} +1.90792e7 q^{56} +5.14657e7i q^{57} -5.95675e7i q^{58} -1.61629e7 q^{59} -4.39282e7 q^{61} -3.73724e7i q^{62} +4.93422e7i q^{63} -1.67772e7 q^{64} +8.07137e7 q^{66} +8.15574e7i q^{67} -1.52274e8i q^{68} -4.42749e8 q^{69} +1.61308e8 q^{71} -4.33889e7i q^{72} -2.47148e8i q^{73} -1.73447e8 q^{74} -7.57197e7 q^{76} -1.35045e8i q^{77} -4.57818e8i q^{78} +5.83346e8 q^{79} -4.83711e8 q^{81} -3.45502e8i q^{82} -1.45718e7i q^{83} -2.07486e8 q^{84} +1.73317e8 q^{86} +6.47797e8i q^{87} +1.18751e8i q^{88} -4.70134e8 q^{89} -7.65989e8 q^{91} -6.51401e8i q^{92} +4.06424e8i q^{93} -8.27542e7 q^{94} +1.82452e8 q^{96} +1.17838e8i q^{97} -2.98506e8i q^{98} -3.07112e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 512 q^{4} + 5568 q^{6} - 21186 q^{9}+O(q^{10}) \) 2 * q - 512 * q^4 + 5568 * q^6 - 21186 * q^9	\( 2 q - 512 q^{4} + 5568 q^{6} - 21186 q^{9} + 57984 q^{11} - 149056 q^{14} + 131072 q^{16} + 591560 q^{19} + 1620984 q^{21} - 1425408 q^{24} - 5262272 q^{26} + 7445940 q^{29} + 4671544 q^{31} + 19034304 q^{34} + 5423616 q^{36} + 57227208 q^{39} + 43187724 q^{41} - 14843904 q^{44} + 81425088 q^{46} + 37313286 q^{49} - 206998056 q^{51} + 50613120 q^{54} + 38158336 q^{56} - 32325720 q^{59} - 87856316 q^{61} - 33554432 q^{64} + 161427456 q^{66} - 885497832 q^{69} + 322615464 q^{71} - 346893376 q^{74} - 151439360 q^{76} + 1166691440 q^{79} - 967421718 q^{81} - 414971904 q^{84} + 346633408 q^{86} - 940267380 q^{89} - 1531978936 q^{91} - 165508416 q^{94} + 364904448 q^{96} - 614224512 q^{99}+O(q^{100}) \) 2 * q - 512 * q^4 + 5568 * q^6 - 21186 * q^9 + 57984 * q^11 - 149056 * q^14 + 131072 * q^16 + 591560 * q^19 + 1620984 * q^21 - 1425408 * q^24 - 5262272 * q^26 + 7445940 * q^29 + 4671544 * q^31 + 19034304 * q^34 + 5423616 * q^36 + 57227208 * q^39 + 43187724 * q^41 - 14843904 * q^44 + 81425088 * q^46 + 37313286 * q^49 - 206998056 * q^51 + 50613120 * q^54 + 38158336 * q^56 - 32325720 * q^59 - 87856316 * q^61 - 33554432 * q^64 + 161427456 * q^66 - 885497832 * q^69 + 322615464 * q^71 - 346893376 * q^74 - 151439360 * q^76 + 1166691440 * q^79 - 967421718 * q^81 - 414971904 * q^84 + 346633408 * q^86 - 940267380 * q^89 - 1531978936 * q^91 - 165508416 * q^94 + 364904448 * q^96 - 614224512 * q^99

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