LMFDB - Embedded newform 50.24.b.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,24,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, 24, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 24 $
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:	$167.602018673$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.24.b.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2048.00i q^{2} -505908. i q^{3} -4.19430e6 q^{4} +1.03610e9 q^{6} -6.87226e9i q^{7} -8.58993e9i q^{8} -1.61800e11 q^{9} +O(q^{10})$	\(q+2048.00i q^{2} -505908. i q^{3} -4.19430e6 q^{4} +1.03610e9 q^{6} -6.87226e9i q^{7} -8.58993e9i q^{8} -1.61800e11 q^{9} -9.65329e11 q^{11} +2.12193e12i q^{12} +5.42360e11i q^{13} +1.40744e13 q^{14} +1.75922e13 q^{16} -8.20835e13i q^{17} -3.31366e14i q^{18} -5.55749e14 q^{19} -3.47673e15 q^{21} -1.97699e15i q^{22} +6.50864e15i q^{23} -4.34572e15 q^{24} -1.11075e15 q^{26} +3.42280e16i q^{27} +2.88243e16i q^{28} +1.22020e16 q^{29} +1.19978e17 q^{31} +3.60288e16i q^{32} +4.88368e17i q^{33} +1.68107e17 q^{34} +6.78637e17 q^{36} +6.19511e17i q^{37} -1.13817e18i q^{38} +2.74384e17 q^{39} -1.58774e18 q^{41} -7.12034e18i q^{42} +8.37772e18i q^{43} +4.04888e18 q^{44} -1.33297e19 q^{46} -1.31005e19i q^{47} -8.90003e18i q^{48} -1.98591e19 q^{49} -4.15267e19 q^{51} -2.27482e18i q^{52} +4.17960e19i q^{53} -7.00989e19 q^{54} -5.90322e19 q^{56} +2.81158e20i q^{57} +2.49898e19i q^{58} +7.43839e19 q^{59} -2.71922e20 q^{61} +2.45715e20i q^{62} +1.11193e21i q^{63} -7.37870e19 q^{64} -1.00018e21 q^{66} -1.74814e21i q^{67} +3.44283e20i q^{68} +3.29277e21 q^{69} -2.71799e21 q^{71} +1.38985e21i q^{72} +4.31278e21i q^{73} -1.26876e21 q^{74} +2.33098e21 q^{76} +6.63399e21i q^{77} +5.61939e20i q^{78} -3.59856e21 q^{79} +2.08387e21 q^{81} -3.25168e21i q^{82} -2.25004e20i q^{83} +1.45825e22 q^{84} -1.71576e22 q^{86} -6.17311e21i q^{87} +8.29211e21i q^{88} -3.38924e22 q^{89} +3.72724e21 q^{91} -2.72992e22i q^{92} -6.06978e22i q^{93} +2.68297e22 q^{94} +1.82273e22 q^{96} -9.21216e22i q^{97} -4.06715e22i q^{98} +1.56190e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8388608 q^{4} + 2072199168 q^{6} - 323599451274 q^{9}+O(q^{10}) $ 2 * q - 8388608 * q^4 + 2072199168 * q^6 - 323599451274 * q^9	$ 2 q - 8388608 q^{4} + 2072199168 q^{6} - 323599451274 q^{9} - 1930657597176 q^{11} + 28148756873216 q^{14} + 35184372088832 q^{16} - 11\!\cdots\!00 q^{19}+ \cdots + 31\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 8388608 * q^4 + 2072199168 * q^6 - 323599451274 * q^9 - 1930657597176 * q^11 + 28148756873216 * q^14 + 35184372088832 * q^16 - 1111497103233400 * q^19 - 6953457662214336 * q^21 - 8691433259139072 * q^24 - 2221506556485632 * q^26 + 24404075831200980 * q^29 + 239956022085498304 * q^31 + 336214168638529536 * q^34 + 1357274472876343296 * q^36 + 548768524891861872 * q^39 - 3175471107543872076 * q^41 + 8097764882465685504 * q^44 - 26659382029373571072 * q^46 - 39718285528834105746 * q^49 - 83053436341592383056 * q^51 - 140197840009435054080 * q^54 - 118064443548357361664 * q^56 + 148767730562810108760 * q^59 - 543844073173894354196 * q^61 - 147573952589676412928 * q^64 - 2000353533280493174784 * q^66 + 6585544259627111618112 * q^69 - 5435973316463881934736 * q^71 - 2537516975175357374464 * q^74 + 4661956746080262553600 * q^76 - 7197125568823552221280 * q^79 + 4167745183504692944082 * q^81 + 29164915286456238342144 * q^84 - 34315129413789729308672 * q^86 - 67784845741841350657620 * q^89 + 7454472535940330255264 * q^91 + 53659471956973412745216 * q^94 + 36454513284540046245888 * q^96 + 312379869522066466001112 * 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 $

$2$	2048.00i	0.707107i
$2$	2048.00i	0.707107i
$3$	− 505908.i	− 1.64883i	−0.565982	−	0.824417i	$-0.691503\pi$
$3$	− 505908.i	− 1.64883i	0.565982	−	0.824417i	$-0.308497\pi$
$4$	−4.19430e6	−0.500000
$5$	0	0
$5$	0	0
$6$	1.03610e9	1.16590
$7$	− 6.87226e9i	− 1.31363i	−0.754053	−	0.656813i	$-0.771904\pi$
$7$	− 6.87226e9i	− 1.31363i	0.754053	−	0.656813i	$-0.228096\pi$
$8$	− 8.58993e9i	− 0.353553i
$9$	−1.61800e11	−1.71866
$10$	0	0
$11$	−9.65329e11	−1.02014	−0.510070	−	0.860133i	$-0.670380\pi$
$11$	−9.65329e11	−1.02014	−0.510070	+	0.860133i	$0.670380\pi$
$12$	2.12193e12i	0.824417i
$13$	5.42360e11i	0.0839342i	0.999119	+	0.0419671i	$0.0133625\pi$
$13$	5.42360e11i	0.0839342i	−0.999119	+	0.0419671i	$0.986638\pi$
$14$	1.40744e13	0.928874
$15$	0	0
$16$	1.75922e13	0.250000
$17$	− 8.20835e13i	− 0.580889i	−0.956892	−	0.290445i	$-0.906197\pi$
$17$	− 8.20835e13i	− 0.580889i	0.956892	−	0.290445i	$-0.0938032\pi$
$18$	− 3.31366e14i	− 1.21527i
$19$	−5.55749e14	−1.09449	−0.547245	−	0.836972i	$-0.684323\pi$
$19$	−5.55749e14	−1.09449	−0.547245	+	0.836972i	$0.684323\pi$
$20$	0	0
$21$	−3.47673e15	−2.16595
$22$	− 1.97699e15i	− 0.721347i
$23$	6.50864e15i	1.42436i	0.701996	+	0.712180i	$0.252292\pi$
$23$	6.50864e15i	1.42436i	−0.701996	+	0.712180i	$0.747708\pi$
$24$	−4.34572e15	−0.582951
$25$	0	0
$26$	−1.11075e15	−0.0593505
$27$	3.42280e16i	1.18494i
$28$	2.88243e16i	0.656813i
$29$	1.22020e16	0.185719	0.0928593	−	0.995679i	$-0.470399\pi$
$29$	1.22020e16	0.185719	0.0928593	+	0.995679i	$0.470399\pi$
$30$	0	0
$31$	1.19978e17	0.848090	0.424045	−	0.905641i	$-0.360610\pi$
$31$	1.19978e17	0.848090	0.424045	+	0.905641i	$0.360610\pi$
$32$	3.60288e16i	0.176777i
$33$	4.88368e17i	1.68204i
$34$	1.68107e17	0.410751
$35$	0	0
$36$	6.78637e17	0.859328
$37$	6.19511e17i	0.572439i	0.958164	+	0.286219i	$0.0923986\pi$
$37$	6.19511e17i	0.572439i	−0.958164	+	0.286219i	$0.907601\pi$
$38$	− 1.13817e18i	− 0.773922i
$39$	2.74384e17	0.138394
$40$	0	0
$41$	−1.58774e18	−0.450572	−0.225286	−	0.974293i	$-0.572332\pi$
$41$	−1.58774e18	−0.450572	−0.225286	+	0.974293i	$0.572332\pi$
$42$	− 7.12034e18i	− 1.53156i
$43$	8.37772e18i	1.37480i	0.726281	+	0.687398i	$0.241247\pi$
$43$	8.37772e18i	1.37480i	−0.726281	+	0.687398i	$0.758753\pi$
$44$	4.04888e18	0.510070
$45$	0	0
$46$	−1.33297e19	−1.00718
$47$	− 1.31005e19i	− 0.772967i	−0.922296	−	0.386484i	$-0.873690\pi$
$47$	− 1.31005e19i	− 0.772967i	0.922296	−	0.386484i	$-0.126310\pi$
$48$	− 8.90003e18i	− 0.412209i
$49$	−1.98591e19	−0.725614
$50$	0	0
$51$	−4.15267e19	−0.957791
$52$	− 2.27482e18i	− 0.0419671i
$53$	4.17960e19i	0.619387i	0.950836	+	0.309693i	$0.100226\pi$
$53$	4.17960e19i	0.619387i	−0.950836	+	0.309693i	$0.899774\pi$
$54$	−7.00989e19	−0.837882
$55$	0	0
$56$	−5.90322e19	−0.464437
$57$	2.81158e20i	1.80463i
$58$	2.49898e19i	0.131323i
$59$	7.43839e19	0.321130	0.160565	−	0.987025i	$-0.448668\pi$
$59$	7.43839e19	0.321130	0.160565	+	0.987025i	$0.448668\pi$
$60$	0	0
$61$	−2.71922e20	−0.800113	−0.400056	−	0.916490i	$-0.631009\pi$
$61$	−2.71922e20	−0.800113	−0.400056	+	0.916490i	$0.631009\pi$
$62$	2.45715e20i	0.599691i
$63$	1.11193e21i	2.25767i
$64$	−7.37870e19	−0.125000
$65$	0	0
$66$	−1.00018e21	−1.18938
$67$	− 1.74814e21i	− 1.74870i	−0.485296	−	0.874350i	$-0.661288\pi$
$67$	− 1.74814e21i	− 1.74870i	0.485296	−	0.874350i	$-0.338712\pi$
$68$	3.44283e20i	0.290445i
$69$	3.29277e21	2.34854
$70$	0	0
$71$	−2.71799e21	−1.39565	−0.697825	−	0.716269i	$-0.745849\pi$
$71$	−2.71799e21	−1.39565	−0.697825	+	0.716269i	$0.745849\pi$
$72$	1.38985e21i	0.607637i
$73$	4.31278e21i	1.60896i	0.593982	+	0.804479i	$0.297555\pi$
$73$	4.31278e21i	1.60896i	−0.593982	+	0.804479i	$0.702445\pi$
$74$	−1.26876e21	−0.404775
$75$	0	0
$76$	2.33098e21	0.547245
$77$	6.63399e21i	1.34008i
$78$	5.61939e20i	0.0978591i
$79$	−3.59856e21	−0.541274	−0.270637	−	0.962681i	$-0.587234\pi$
$79$	−3.59856e21	−0.541274	−0.270637	+	0.962681i	$0.587234\pi$
$80$	0	0
$81$	2.08387e21	0.235122
$82$	− 3.25168e21i	− 0.318602i
$83$	− 2.25004e20i	− 0.0191775i	−0.999954	−	0.00958876i	$-0.996948\pi$
$83$	− 2.25004e20i	− 0.0191775i	0.999954	−	0.00958876i	$-0.00305224\pi$
$84$	1.45825e22	1.08298
$85$	0	0
$86$	−1.71576e22	−0.972128
$87$	− 6.17311e21i	− 0.306219i
$88$	8.29211e21i	0.360674i
$89$	−3.38924e22	−1.29455	−0.647273	−	0.762258i	$-0.724091\pi$
$89$	−3.38924e22	−1.29455	−0.647273	+	0.762258i	$0.724091\pi$
$90$	0	0
$91$	3.72724e21	0.110258
$92$	− 2.72992e22i	− 0.712180i
$93$	− 6.06978e22i	− 1.39836i
$94$	2.68297e22	0.546570
$95$	0	0
$96$	1.82273e22	0.291476
$97$	− 9.21216e22i	− 1.30763i	−0.756652	−	0.653817i	$-0.773166\pi$
$97$	− 9.21216e22i	− 1.30763i	0.756652	−	0.653817i	$-0.226834\pi$
$98$	− 4.06715e22i	− 0.513086i
$99$	1.56190e23	1.75327
$100$	0	0
$101$	1.42425e23	1.27026	0.635129	−	0.772406i	$-0.280947\pi$
$101$	1.42425e23	1.27026	0.635129	+	0.772406i	$0.280947\pi$
$102$	− 8.50467e22i	− 0.677260i
$103$	− 1.07041e23i	− 0.761946i	−0.924586	−	0.380973i	$-0.875589\pi$
$103$	− 1.07041e23i	− 0.761946i	0.924586	−	0.380973i	$-0.124411\pi$
$104$	4.65884e21	0.0296752
$105$	0	0
$106$	−8.55982e22	−0.437973
$107$	− 1.90048e23i	− 0.872872i	−0.899735	−	0.436436i	$-0.856240\pi$
$107$	− 1.90048e23i	− 0.872872i	0.899735	−	0.436436i	$-0.143760\pi$
$108$	− 1.43563e23i	− 0.592472i
$109$	4.03432e23	1.49750	0.748749	−	0.662854i	$-0.230655\pi$
$109$	4.03432e23	1.49750	0.748749	+	0.662854i	$0.230655\pi$
$110$	0	0
$111$	3.13416e23	0.943857
$112$	− 1.20898e23i	− 0.328407i
$113$	− 4.80831e23i	− 1.17921i	−0.807693	−	0.589604i	$-0.799284\pi$
$113$	− 4.80831e23i	− 1.17921i	0.807693	−	0.589604i	$-0.200716\pi$
$114$	−5.75811e23	−1.27607
$115$	0	0
$116$	−5.11791e22	−0.0928593
$117$	− 8.77537e22i	− 0.144254i
$118$	1.52338e23i	0.227073i
$119$	−5.64099e23	−0.763072
$120$	0	0
$121$	3.64294e22	0.0406837
$122$	− 5.56896e23i	− 0.565765i
$123$	8.03248e23i	0.742918i
$124$	−5.03224e23	−0.424045
$125$	0	0
$126$	−2.27723e24	−1.59641
$127$	2.24142e24i	1.43476i	0.696681	+	0.717381i	$0.254659\pi$
$127$	2.24142e24i	1.43476i	−0.696681	+	0.717381i	$0.745341\pi$
$128$	− 1.51116e23i	− 0.0883883i
$129$	4.23835e24	2.26681
$130$	0	0
$131$	3.40494e24	1.52577	0.762887	−	0.646532i	$-0.223781\pi$
$131$	3.40494e24	1.52577	0.762887	+	0.646532i	$0.223781\pi$
$132$	− 2.04836e24i	− 0.841020i
$133$	3.81925e24i	1.43775i
$134$	3.58018e24	1.23652
$135$	0	0
$136$	−7.05092e23	−0.205375
$137$	4.70653e24i	1.26013i	0.776544	+	0.630063i	$0.216971\pi$
$137$	4.70653e24i	1.26013i	−0.776544	+	0.630063i	$0.783029\pi$
$138$	6.74360e24i	1.66067i
$139$	−5.18506e23	−0.117512	−0.0587562	−	0.998272i	$-0.518713\pi$
$139$	−5.18506e23	−0.117512	−0.0587562	+	0.998272i	$0.518713\pi$
$140$	0	0
$141$	−6.62763e24	−1.27450
$142$	− 5.56644e24i	− 0.986873i
$143$	− 5.23556e23i	− 0.0856246i
$144$	−2.84641e24	−0.429664
$145$	0	0
$146$	−8.83258e24	−1.13770
$147$	1.00469e25i	1.19642i
$148$	− 2.59842e24i	− 0.286219i
$149$	−1.00676e25	−1.02632	−0.513160	−	0.858293i	$-0.671525\pi$
$149$	−1.00676e25	−1.02632	−0.513160	+	0.858293i	$0.671525\pi$
$150$	0	0
$151$	1.12958e25	0.987832	0.493916	−	0.869509i	$-0.335565\pi$
$151$	1.12958e25	0.987832	0.493916	+	0.869509i	$0.335565\pi$
$152$	4.77384e24i	0.386961i
$153$	1.32811e25i	0.998349i
$154$	−1.35864e25	−0.947581
$155$	0	0
$156$	−1.15085e24	−0.0691968
$157$	− 4.49140e24i	− 0.250920i	−0.992099	−	0.125460i	$-0.959959\pi$
$157$	− 4.49140e24i	− 0.250920i	0.992099	−	0.125460i	$-0.0400407\pi$
$158$	− 7.36986e24i	− 0.382739i
$159$	2.11449e25	1.02127
$160$	0	0
$161$	4.47290e25	1.87108
$162$	4.26777e24i	0.166256i
$163$	− 3.38828e25i	− 1.22977i	−0.788619	−	0.614883i	$-0.789203\pi$
$163$	− 3.38828e25i	− 1.22977i	0.788619	−	0.614883i	$-0.210797\pi$
$164$	6.65945e24	0.225286
$165$	0	0
$166$	4.60809e23	0.0135606
$167$	2.60376e24i	0.0715092i	0.999361	+	0.0357546i	$0.0113835\pi$
$167$	2.60376e24i	0.0715092i	−0.999361	+	0.0357546i	$0.988617\pi$
$168$	2.98649e25i	0.765780i
$169$	4.14598e25	0.992955
$170$	0	0
$171$	8.99200e25	1.88105
$172$	− 3.51387e25i	− 0.687398i
$173$	3.96085e25i	0.724866i	0.932010	+	0.362433i	$0.118054\pi$
$173$	3.96085e25i	0.724866i	−0.932010	+	0.362433i	$0.881946\pi$
$174$	1.26425e25	0.216530
$175$	0	0
$176$	−1.69822e25	−0.255035
$177$	− 3.76314e25i	− 0.529490i
$178$	− 6.94117e25i	− 0.915382i
$179$	4.42305e25	0.546905	0.273453	−	0.961885i	$-0.411834\pi$
$179$	4.42305e25	0.546905	0.273453	+	0.961885i	$0.411834\pi$
$180$	0	0
$181$	−8.22310e25	−0.894813	−0.447406	−	0.894331i	$-0.647652\pi$
$181$	−8.22310e25	−0.894813	−0.447406	+	0.894331i	$0.647652\pi$
$182$	7.63338e24i	0.0779643i
$183$	1.37568e26i	1.31925i
$184$	5.59088e25	0.503588
$185$	0	0
$186$	1.24309e26	0.988791
$187$	7.92376e25i	0.592588i
$188$	5.49473e25i	0.386484i
$189$	2.35223e26	1.55657
$190$	0	0
$191$	5.22803e25	0.306517	0.153258	−	0.988186i	$-0.451023\pi$
$191$	5.22803e25	0.306517	0.153258	+	0.988186i	$0.451023\pi$
$192$	3.73294e25i	0.206104i
$193$	2.67638e26i	1.39200i	0.718043	+	0.695999i	$0.245038\pi$
$193$	2.67638e26i	1.39200i	−0.718043	+	0.695999i	$0.754962\pi$
$194$	1.88665e26	0.924637
$195$	0	0
$196$	8.32953e25	0.362807
$197$	− 8.45015e25i	− 0.347139i	−0.984822	−	0.173569i	$-0.944470\pi$
$197$	− 8.45015e25i	− 0.347139i	0.984822	−	0.173569i	$-0.0555301\pi$
$198$	3.19877e26i	1.23975i
$199$	1.66457e25	0.0608823	0.0304411	−	0.999537i	$-0.490309\pi$
$199$	1.66457e25	0.0608823	0.0304411	+	0.999537i	$0.490309\pi$
$200$	0	0
$201$	−8.84397e26	−2.88332
$202$	2.91687e26i	0.898208i
$203$	− 8.38555e25i	− 0.243965i
$204$	1.74176e26	0.478895
$205$	0	0
$206$	2.19221e26	0.538777
$207$	− 1.05310e27i	− 2.44799i
$208$	9.54130e24i	0.0209836i
$209$	5.36480e26	1.11653
$210$	0	0
$211$	2.79674e26	0.521680	0.260840	−	0.965382i	$-0.416001\pi$
$211$	2.79674e26	0.521680	0.260840	+	0.965382i	$0.416001\pi$
$212$	− 1.75305e26i	− 0.309693i
$213$	1.37505e27i	2.30120i
$214$	3.89219e26	0.617214
$215$	0	0
$216$	2.94016e26	0.418941
$217$	− 8.24519e26i	− 1.11407i
$218$	8.26230e26i	1.05889i
$219$	2.18187e27	2.65290
$220$	0	0
$221$	4.45188e25	0.0487565
$222$	6.41875e26i	0.667408i
$223$	− 5.45249e26i	− 0.538380i	−0.963087	−	0.269190i	$-0.913244\pi$
$223$	− 5.45249e26i	− 0.538380i	0.963087	−	0.269190i	$-0.0867560\pi$
$224$	2.47599e26	0.232219
$225$	0	0
$226$	9.84742e26	0.833826
$227$	1.15345e27i	0.928326i	0.885750	+	0.464163i	$0.153645\pi$
$227$	1.15345e27i	0.928326i	−0.885750	+	0.464163i	$0.846355\pi$
$228$	− 1.17926e27i	− 0.902317i
$229$	−1.17499e27	−0.854922	−0.427461	−	0.904034i	$-0.640592\pi$
$229$	−1.17499e27	−0.854922	−0.427461	+	0.904034i	$0.640592\pi$
$230$	0	0
$231$	3.35619e27	2.20957
$232$	− 1.04815e26i	− 0.0656614i
$233$	5.77127e26i	0.344095i	0.985089	+	0.172048i	$0.0550383\pi$
$233$	5.77127e26i	0.344095i	−0.985089	+	0.172048i	$0.944962\pi$
$234$	1.79720e26	0.102003
$235$	0	0
$236$	−3.11989e26	−0.160565
$237$	1.82054e27i	0.892472i
$238$	− 1.15527e27i	− 0.539573i
$239$	3.06102e26	0.136236	0.0681178	−	0.997677i	$-0.478301\pi$
$239$	3.06102e26	0.136236	0.0681178	+	0.997677i	$0.478301\pi$
$240$	0	0
$241$	1.82530e27	0.738139	0.369070	−	0.929402i	$-0.379676\pi$
$241$	1.82530e27	0.738139	0.369070	+	0.929402i	$0.379676\pi$
$242$	7.46075e25i	0.0287677i
$243$	2.16808e27i	0.797267i
$244$	1.14052e27	0.400056
$245$	0	0
$246$	−1.64505e27	−0.525322
$247$	− 3.01416e26i	− 0.0918652i
$248$	− 1.03060e27i	− 0.299845i
$249$	−1.13831e26	−0.0316206
$250$	0	0
$251$	−1.72473e27	−0.436991	−0.218495	−	0.975838i	$-0.570115\pi$
$251$	−1.72473e27	−0.436991	−0.218495	+	0.975838i	$0.570115\pi$
$252$	− 4.66377e27i	− 1.12884i
$253$	− 6.28298e27i	− 1.45305i
$254$	−4.59042e27	−1.01453
$255$	0	0
$256$	3.09485e26	0.0625000
$257$	− 5.49958e27i	− 1.06194i	−0.847392	−	0.530968i	$-0.821828\pi$
$257$	− 5.49958e27i	− 1.06194i	0.847392	−	0.530968i	$-0.178172\pi$
$258$	8.68015e27i	1.60288i
$259$	4.25744e27	0.751971
$260$	0	0
$261$	−1.97429e27	−0.319186
$262$	6.97332e27i	1.07888i
$263$	1.10256e28i	1.63272i	0.577543	+	0.816360i	$0.304012\pi$
$263$	1.10256e28i	1.63272i	−0.577543	+	0.816360i	$0.695988\pi$
$264$	4.19505e27	0.594691
$265$	0	0
$266$	−7.82182e27	−1.01664
$267$	1.71464e28i	2.13449i
$268$	7.33222e27i	0.874350i
$269$	−5.47893e26	−0.0625957	−0.0312978	−	0.999510i	$-0.509964\pi$
$269$	−5.47893e26	−0.0625957	−0.0312978	+	0.999510i	$0.509964\pi$
$270$	0	0
$271$	1.43098e28	1.50137	0.750683	−	0.660663i	$-0.229725\pi$
$271$	1.43098e28	1.50137	0.750683	+	0.660663i	$0.229725\pi$
$272$	− 1.44403e27i	− 0.145222i
$273$	− 1.88564e27i	− 0.181798i
$274$	−9.63897e27	−0.891044
$275$	0	0
$276$	−1.38109e28	−1.17427
$277$	4.09302e27i	0.333831i	0.985971	+	0.166915i	$0.0533807\pi$
$277$	4.09302e27i	0.333831i	−0.985971	+	0.166915i	$0.946619\pi$
$278$	− 1.06190e27i	− 0.0830938i
$279$	−1.94124e28	−1.45758
$280$	0	0
$281$	−6.59576e27	−0.456186	−0.228093	−	0.973639i	$-0.573249\pi$
$281$	−6.59576e27	−0.456186	−0.228093	+	0.973639i	$0.573249\pi$
$282$	− 1.35734e28i	− 0.901204i
$283$	− 4.65761e27i	− 0.296906i	−0.988919	−	0.148453i	$-0.952571\pi$
$283$	− 4.65761e27i	− 0.296906i	0.988919	−	0.148453i	$-0.0474294\pi$
$284$	1.14001e28	0.697825
$285$	0	0
$286$	1.07224e27	0.0605457
$287$	1.09113e28i	0.591883i
$288$	− 5.82945e27i	− 0.303818i
$289$	1.32299e28	0.662567
$290$	0	0
$291$	−4.66050e28	−2.15607
$292$	− 1.80891e28i	− 0.804479i
$293$	− 2.37368e28i	− 1.01495i	−0.861666	−	0.507476i	$-0.830579\pi$
$293$	− 2.37368e28i	− 1.01495i	0.861666	−	0.507476i	$-0.169421\pi$
$294$	−2.05760e28	−0.845995
$295$	0	0
$296$	5.32156e27	0.202388
$297$	− 3.30413e28i	− 1.20881i
$298$	− 2.06184e28i	− 0.725718i
$299$	−3.53003e27	−0.119553
$300$	0	0
$301$	5.75738e28	1.80597
$302$	2.31339e28i	0.698503i
$303$	− 7.20542e28i	− 2.09445i
$304$	−9.77683e27	−0.273623
$305$	0	0
$306$	−2.71997e28	−0.705939
$307$	− 3.33435e28i	− 0.833527i	−0.909015	−	0.416763i	$-0.863164\pi$
$307$	− 3.33435e28i	− 0.833527i	0.909015	−	0.416763i	$-0.136836\pi$
$308$	− 2.78250e28i	− 0.670041i
$309$	−5.41531e28	−1.25632
$310$	0	0
$311$	8.79341e28	1.89414	0.947072	−	0.321021i	$-0.104026\pi$
$311$	8.79341e28	1.89414	0.947072	+	0.321021i	$0.104026\pi$
$312$	− 2.35694e27i	− 0.0489296i
$313$	− 9.00131e28i	− 1.80113i	−0.434718	−	0.900567i	$-0.643152\pi$
$313$	− 9.00131e28i	− 1.80113i	0.434718	−	0.900567i	$-0.356848\pi$
$314$	9.19839e27	0.177427
$315$	0	0
$316$	1.50935e28	0.270637
$317$	3.39800e28i	0.587545i	0.955875	+	0.293773i	$0.0949108\pi$
$317$	3.39800e28i	0.587545i	−0.955875	+	0.293773i	$0.905089\pi$
$318$	4.33048e28i	0.722145i
$319$	−1.17790e28	−0.189459
$320$	0	0
$321$	−9.61470e28	−1.43922
$322$	9.16050e28i	1.32305i
$323$	4.56178e28i	0.635778i
$324$	−8.74040e27	−0.117561
$325$	0	0
$326$	6.93920e28	0.869575
$327$	− 2.04100e29i	− 2.46913i
$328$	1.36385e28i	0.159301i
$329$	−9.00297e28	−1.01539
$330$	0	0
$331$	−1.07942e29	−1.13545	−0.567727	−	0.823217i	$-0.692177\pi$
$331$	−1.07942e29	−1.13545	−0.567727	+	0.823217i	$0.692177\pi$
$332$	9.43736e26i	0.00958876i
$333$	− 1.00237e29i	− 0.983826i
$334$	−5.33251e27	−0.0505646
$335$	0	0
$336$	−6.11633e28	−0.541488
$337$	2.54917e28i	0.218100i	0.994036	+	0.109050i	$0.0347808\pi$
$337$	2.54917e28i	0.218100i	−0.994036	+	0.109050i	$0.965219\pi$
$338$	8.49096e28i	0.702125i
$339$	−2.43256e29	−1.94432
$340$	0	0
$341$	−1.15818e29	−0.865170
$342$	1.84156e29i	1.33010i
$343$	− 5.16079e28i	− 0.360441i
$344$	7.19640e28	0.486064
$345$	0	0
$346$	−8.11182e28	−0.512558
$347$	1.17389e29i	0.717525i	0.933429	+	0.358763i	$0.116801\pi$
$347$	1.17389e29i	0.717525i	−0.933429	+	0.358763i	$0.883199\pi$
$348$	2.58919e28i	0.153110i
$349$	2.03481e28	0.116421	0.0582104	−	0.998304i	$-0.481461\pi$
$349$	2.03481e28	0.116421	0.0582104	+	0.998304i	$0.481461\pi$
$350$	0	0
$351$	−1.85639e28	−0.0994574
$352$	− 3.47796e28i	− 0.180337i
$353$	7.43192e28i	0.372985i	0.982456	+	0.186493i	$0.0597121\pi$
$353$	7.43192e28i	0.372985i	−0.982456	+	0.186493i	$0.940288\pi$
$354$	7.70691e28	0.374406
$355$	0	0
$356$	1.42155e29	0.647273
$357$	2.85382e29i	1.25818i
$358$	9.05841e28i	0.386721i
$359$	−6.09639e28	−0.252050	−0.126025	−	0.992027i	$-0.540222\pi$
$359$	−6.09639e28	−0.252050	−0.126025	+	0.992027i	$0.540222\pi$
$360$	0	0
$361$	5.10268e28	0.197909
$362$	− 1.68409e29i	− 0.632728i
$363$	− 1.84299e28i	− 0.0670808i
$364$	−1.56332e28	−0.0551291
$365$	0	0
$366$	−2.81738e29	−0.932853
$367$	1.13728e29i	0.364928i	0.983213	+	0.182464i	$0.0584072\pi$
$367$	1.13728e29i	0.364928i	−0.983213	+	0.182464i	$0.941593\pi$
$368$	1.14501e29i	0.356090i
$369$	2.56895e29	0.774378
$370$	0	0
$371$	2.87233e29	0.813643
$372$	2.54585e29i	0.699180i
$373$	7.16967e29i	1.90918i	0.297920	+	0.954591i	$0.403707\pi$
$373$	7.16967e29i	1.90918i	−0.297920	+	0.954591i	$0.596293\pi$
$374$	−1.62279e29	−0.419023
$375$	0	0
$376$	−1.12532e29	−0.273285
$377$	6.61790e27i	0.0155881i
$378$	4.81738e29i	1.10066i
$379$	6.32589e29	1.40207	0.701036	−	0.713126i	$-0.252721\pi$
$379$	6.32589e29	1.40207	0.701036	+	0.713126i	$0.252721\pi$
$380$	0	0
$381$	1.13395e30	2.36569
$382$	1.07070e29i	0.216740i
$383$	− 6.48766e29i	− 1.27439i	−0.770703	−	0.637195i	$-0.780095\pi$
$383$	− 6.48766e29i	− 1.27439i	0.770703	−	0.637195i	$-0.219905\pi$
$384$	−7.64507e28	−0.145738
$385$	0	0
$386$	−5.48122e29	−0.984291
$387$	− 1.35551e30i	− 2.36280i
$388$	3.86386e29i	0.653817i
$389$	−1.78533e29	−0.293291	−0.146645	−	0.989189i	$-0.546848\pi$
$389$	−1.78533e29	−0.293291	−0.146645	+	0.989189i	$0.546848\pi$
$390$	0	0
$391$	5.34252e29	0.827396
$392$	1.70589e29i	0.256543i
$393$	− 1.72259e30i	− 2.51575i
$394$	1.73059e29	0.245464
$395$	0	0
$396$	−6.55108e29	−0.876634
$397$	9.56321e28i	0.124312i	0.998066	+	0.0621560i	$0.0197976\pi$
$397$	9.56321e28i	0.124312i	−0.998066	+	0.0621560i	$0.980202\pi$
$398$	3.40903e28i	0.0430503i
$399$	1.93219e30	2.37061
$400$	0	0
$401$	6.48450e29	0.751132	0.375566	−	0.926796i	$-0.377448\pi$
$401$	6.48450e29	0.751132	0.375566	+	0.926796i	$0.377448\pi$
$402$	− 1.81124e30i	− 2.03881i
$403$	6.50713e28i	0.0711838i
$404$	−5.97376e29	−0.635129
$405$	0	0
$406$	1.71736e29	0.172509
$407$	− 5.98032e29i	− 0.583967i
$408$	3.56712e29i	0.338630i
$409$	6.20946e29	0.573107	0.286554	−	0.958064i	$-0.407490\pi$
$409$	6.20946e29	0.573107	0.286554	+	0.958064i	$0.407490\pi$
$410$	0	0
$411$	2.38107e30	2.07774
$412$	4.48965e29i	0.380973i
$413$	− 5.11185e29i	− 0.421845i
$414$	2.15674e30	1.73099
$415$	0	0
$416$	−1.95406e28	−0.0148376
$417$	2.62316e29i	0.193758i
$418$	1.09871e30i	0.789508i
$419$	−9.40356e29	−0.657402	−0.328701	−	0.944434i	$-0.606611\pi$
$419$	−9.40356e29	−0.657402	−0.328701	+	0.944434i	$0.606611\pi$
$420$	0	0
$421$	−1.63695e30	−1.08340	−0.541702	−	0.840571i	$-0.682220\pi$
$421$	−1.63695e30	−1.08340	−0.541702	+	0.840571i	$0.682220\pi$
$422$	5.72773e29i	0.368883i
$423$	2.11965e30i	1.32846i
$424$	3.59025e29	0.218986
$425$	0	0
$426$	−2.81610e30	−1.62719
$427$	1.86872e30i	1.05105i
$428$	7.97121e29i	0.436436i
$429$	−2.64871e29	−0.141181
$430$	0	0
$431$	−5.36984e29	−0.271315	−0.135657	−	0.990756i	$-0.543315\pi$
$431$	−5.36984e29	−0.271315	−0.135657	+	0.990756i	$0.543315\pi$
$432$	6.02145e29i	0.296236i
$433$	− 7.10121e29i	− 0.340190i	−0.985428	−	0.170095i	$-0.945593\pi$
$433$	− 7.10121e29i	− 0.340190i	0.985428	−	0.170095i	$-0.0544075\pi$
$434$	1.68862e30	0.787769
$435$	0	0
$436$	−1.69212e30	−0.748749
$437$	− 3.61717e30i	− 1.55895i
$438$	4.46847e30i	1.87589i
$439$	1.78862e30	0.731437	0.365719	−	0.930725i	$-0.380823\pi$
$439$	1.78862e30	0.731437	0.365719	+	0.930725i	$0.380823\pi$
$440$	0	0
$441$	3.21320e30	1.24708
$442$	9.11746e28i	0.0344761i
$443$	3.61961e30i	1.33358i	0.745246	+	0.666790i	$0.232332\pi$
$443$	3.61961e30i	1.33358i	−0.745246	+	0.666790i	$0.767668\pi$
$444$	−1.31456e30	−0.471929
$445$	0	0
$446$	1.11667e30	0.380692
$447$	5.09327e30i	1.69223i
$448$	5.07083e29i	0.164203i
$449$	1.09219e29	0.0344720	0.0172360	−	0.999851i	$-0.494513\pi$
$449$	1.09219e29	0.0344720	0.0172360	+	0.999851i	$0.494513\pi$
$450$	0	0
$451$	1.53269e30	0.459646
$452$	2.01675e30i	0.589604i
$453$	− 5.71465e30i	− 1.62877i
$454$	−2.36226e30	−0.656426
$455$	0	0
$456$	2.41513e30	0.638034
$457$	− 4.42972e30i	− 1.14114i	−0.821248	−	0.570571i	$-0.806722\pi$
$457$	− 4.42972e30i	− 1.14114i	0.821248	−	0.570571i	$-0.193278\pi$
$458$	− 2.40638e30i	− 0.604521i
$459$	2.80955e30	0.688322
$460$	0	0
$461$	−5.24784e30	−1.22298	−0.611491	−	0.791251i	$-0.709430\pi$
$461$	−5.24784e30	−1.22298	−0.611491	+	0.791251i	$0.709430\pi$
$462$	6.87347e30i	1.56240i
$463$	3.94748e30i	0.875263i	0.899154	+	0.437631i	$0.144183\pi$
$463$	3.94748e30i	0.875263i	−0.899154	+	0.437631i	$0.855817\pi$
$464$	2.14661e29	0.0464296
$465$	0	0
$466$	−1.18196e30	−0.243312
$467$	− 2.80285e30i	− 0.562931i	−0.959571	−	0.281466i	$-0.909179\pi$
$467$	− 2.80285e30i	− 0.562931i	0.959571	−	0.281466i	$-0.0908205\pi$
$468$	3.68066e29i	0.0721270i
$469$	−1.20136e31	−2.29714
$470$	0	0
$471$	−2.27224e30	−0.413726
$472$	− 6.38953e29i	− 0.113537i
$473$	− 8.08725e30i	− 1.40248i
$474$	−3.72847e30	−0.631073
$475$	0	0
$476$	2.36600e30	0.381536
$477$	− 6.76258e30i	− 1.06451i
$478$	6.26897e29i	0.0963331i
$479$	−5.55199e30	−0.832895	−0.416447	−	0.909160i	$-0.636725\pi$
$479$	−5.55199e30	−0.832895	−0.416447	+	0.909160i	$0.636725\pi$
$480$	0	0
$481$	−3.35998e29	−0.0480472
$482$	3.73821e30i	0.521943i
$483$	− 2.26288e31i	− 3.08510i
$484$	−1.52796e29	−0.0203419
$485$	0	0
$486$	−4.44024e30	−0.563753
$487$	1.47354e30i	0.182716i	0.995818	+	0.0913582i	$0.0291208\pi$
$487$	1.47354e30i	0.182716i	−0.995818	+	0.0913582i	$0.970879\pi$
$488$	2.33579e30i	0.282883i
$489$	−1.71416e31	−2.02768
$490$	0	0
$491$	−1.67709e29	−0.0189287	−0.00946433	−	0.999955i	$-0.503013\pi$
$491$	−1.67709e29	−0.0189287	−0.00946433	+	0.999955i	$0.503013\pi$
$492$	− 3.36907e30i	− 0.371459i
$493$	− 1.00159e30i	− 0.107882i
$494$	6.17300e29	0.0649585
$495$	0	0
$496$	2.11068e30	0.212023
$497$	1.86787e31i	1.83336i
$498$	− 2.33127e29i	− 0.0223591i
$499$	1.27784e31	1.19762	0.598810	−	0.800891i	$-0.295640\pi$
$499$	1.27784e31	1.19762	0.598810	+	0.800891i	$0.295640\pi$
$500$	0	0
$501$	1.31726e30	0.117907
$502$	− 3.53224e30i	− 0.308999i
$503$	6.62625e30i	0.566547i	0.959039	+	0.283273i	$0.0914204\pi$
$503$	6.62625e30i	0.566547i	−0.959039	+	0.283273i	$0.908580\pi$
$504$	9.55140e30	0.798207
$505$	0	0
$506$	1.28675e31	1.02746
$507$	− 2.09748e31i	− 1.63722i
$508$	− 9.40119e30i	− 0.717381i
$509$	−2.12937e31	−1.58853	−0.794266	−	0.607570i	$-0.792144\pi$
$509$	−2.12937e31	−1.58853	−0.794266	+	0.607570i	$0.792144\pi$
$510$	0	0
$511$	2.96385e31	2.11357
$512$	6.33825e29i	0.0441942i
$513$	− 1.90222e31i	− 1.29691i
$514$	1.12631e31	0.750903
$515$	0	0
$516$	−1.77769e31	−1.13341
$517$	1.26462e31i	0.788534i
$518$	8.71923e30i	0.531724i
$519$	2.00382e31	1.19519
$520$	0	0
$521$	−3.13459e31	−1.78874	−0.894368	−	0.447332i	$-0.852374\pi$
$521$	−3.13459e31	−1.78874	−0.894368	+	0.447332i	$0.852374\pi$
$522$	− 4.04334e30i	− 0.225699i
$523$	− 5.60340e30i	− 0.305972i	−0.988228	−	0.152986i	$-0.951111\pi$
$523$	− 5.60340e30i	− 0.305972i	0.988228	−	0.152986i	$-0.0488890\pi$
$524$	−1.42814e31	−0.762887
$525$	0	0
$526$	−2.25805e31	−1.15451
$527$	− 9.84822e30i	− 0.492647i
$528$	8.59145e30i	0.420510i
$529$	−2.14819e31	−1.02880
$530$	0	0
$531$	−1.20353e31	−0.551912
$532$	− 1.60191e31i	− 0.718876i
$533$	− 8.61124e29i	− 0.0378184i
$534$	−3.51159e31	−1.50931
$535$	0	0
$536$	−1.50164e31	−0.618259
$537$	− 2.23766e31i	− 0.901757i
$538$	− 1.12208e30i	− 0.0442618i
$539$	1.91706e31	0.740227
$540$	0	0
$541$	−2.41300e30	−0.0892873	−0.0446436	−	0.999003i	$-0.514215\pi$
$541$	−2.41300e30	−0.0892873	−0.0446436	+	0.999003i	$0.514215\pi$
$542$	2.93065e31i	1.06163i
$543$	4.16013e31i	1.47540i
$544$	2.95737e30	0.102688
$545$	0	0
$546$	3.86179e30	0.128550
$547$	4.73888e31i	1.54462i	0.635246	+	0.772310i	$0.280899\pi$
$547$	4.73888e31i	1.54462i	−0.635246	+	0.772310i	$0.719101\pi$
$548$	− 1.97406e31i	− 0.630063i
$549$	4.39969e31	1.37512
$550$	0	0
$551$	−6.78126e30	−0.203267
$552$	− 2.82847e31i	− 0.830333i
$553$	2.47302e31i	0.711032i
$554$	−8.38251e30	−0.236054
$555$	0	0
$556$	2.17477e30	0.0587562
$557$	4.15359e31i	1.09923i	0.835417	+	0.549616i	$0.185226\pi$
$557$	4.15359e31i	1.09923i	−0.835417	+	0.549616i	$0.814774\pi$
$558$	− 3.97566e31i	− 1.03066i
$559$	−4.54374e30	−0.115392
$560$	0	0
$561$	4.00869e31	0.977080
$562$	− 1.35081e31i	− 0.322572i
$563$	6.08993e31i	1.42484i	0.701754	+	0.712419i	$0.252401\pi$
$563$	6.08993e31i	1.42484i	−0.701754	+	0.712419i	$0.747599\pi$
$564$	2.77983e31	0.637248
$565$	0	0
$566$	9.53878e30	0.209944
$567$	− 1.43209e31i	− 0.308863i
$568$	2.33473e31i	0.493437i
$569$	−1.66042e31	−0.343897	−0.171948	−	0.985106i	$-0.555006\pi$
$569$	−1.66042e31	−0.343897	−0.171948	+	0.985106i	$0.555006\pi$
$570$	0	0
$571$	3.60619e31	0.717354	0.358677	−	0.933462i	$-0.383228\pi$
$571$	3.60619e31	0.717354	0.358677	+	0.933462i	$0.383228\pi$
$572$	2.19595e30i	0.0428123i
$573$	− 2.64490e31i	− 0.505395i
$574$	−2.23464e31	−0.418524
$575$	0	0
$576$	1.19387e31	0.214832
$577$	1.20260e31i	0.212129i	0.994359	+	0.106064i	$0.0338249\pi$
$577$	1.20260e31i	0.212129i	−0.994359	+	0.106064i	$0.966175\pi$
$578$	2.70948e31i	0.468506i
$579$	1.35400e32	2.29517
$580$	0	0
$581$	−1.54629e30	−0.0251921
$582$	− 9.54471e31i	− 1.52457i
$583$	− 4.03469e31i	− 0.631861i
$584$	3.70465e31	0.568852
$585$	0	0
$586$	4.86130e31	0.717679
$587$	− 5.93652e31i	− 0.859397i	−0.902973	−	0.429698i	$-0.858620\pi$
$587$	− 5.93652e31i	− 0.859397i	0.902973	−	0.429698i	$-0.141380\pi$
$588$	− 4.21397e31i	− 0.598209i
$589$	−6.66776e31	−0.928227
$590$	0	0
$591$	−4.27500e31	−0.572374
$592$	1.08986e31i	0.143110i
$593$	− 1.10327e32i	− 1.42087i	−0.703765	−	0.710433i	$-0.748499\pi$
$593$	− 1.10327e32i	− 1.42087i	0.703765	−	0.710433i	$-0.251501\pi$
$594$	6.76685e31	0.854757
$595$	0	0
$596$	4.22265e31	0.513160
$597$	− 8.42118e30i	− 0.100385i
$598$	− 7.22949e30i	− 0.0845365i
$599$	−9.24234e31	−1.06017	−0.530083	−	0.847946i	$-0.677839\pi$
$599$	−9.24234e31	−1.06017	−0.530083	+	0.847946i	$0.677839\pi$
$600$	0	0
$601$	1.84593e31	0.203778	0.101889	−	0.994796i	$-0.467511\pi$
$601$	1.84593e31	0.203778	0.101889	+	0.994796i	$0.467511\pi$
$602$	1.17911e32i	1.27701i
$603$	2.82848e32i	3.00541i
$604$	−4.73781e31	−0.493916
$605$	0	0
$606$	1.47567e32	1.48100
$607$	1.01802e32i	1.00250i	0.865301	+	0.501252i	$0.167127\pi$
$607$	1.01802e32i	1.00250i	−0.865301	+	0.501252i	$0.832873\pi$
$608$	− 2.00230e31i	− 0.193480i
$609$	−4.24232e31	−0.402258
$610$	0	0
$611$	7.10516e30	0.0648784
$612$	− 5.57049e31i	− 0.499175i
$613$	1.20531e32i	1.06000i	0.847998	+	0.529999i	$0.177808\pi$
$613$	1.20531e32i	1.06000i	−0.847998	+	0.529999i	$0.822192\pi$
$614$	6.82874e31	0.589392
$615$	0	0
$616$	5.69855e31	0.473790
$617$	1.30052e32i	1.06130i	0.847592	+	0.530649i	$0.178052\pi$
$617$	1.30052e32i	1.06130i	−0.847592	+	0.530649i	$0.821948\pi$
$618$	− 1.10906e32i	− 0.888354i
$619$	1.66234e32	1.30701	0.653503	−	0.756924i	$-0.273299\pi$
$619$	1.66234e32	1.30701	0.653503	+	0.756924i	$0.273299\pi$
$620$	0	0
$621$	−2.22778e32	−1.68779
$622$	1.80089e32i	1.33936i
$623$	2.32917e32i	1.70055i
$624$	4.82702e30	0.0345984
$625$	0	0
$626$	1.84347e32	1.27359
$627$	− 2.71410e32i	− 1.84098i
$628$	1.88383e31i	0.125460i
$629$	5.08517e31	0.332524
$630$	0	0
$631$	−3.08263e31	−0.194350	−0.0971749	−	0.995267i	$-0.530981\pi$
$631$	−3.08263e31	−0.194350	−0.0971749	+	0.995267i	$0.530981\pi$
$632$	3.09114e31i	0.191369i
$633$	− 1.41489e32i	− 0.860164i
$634$	−6.95909e31	−0.415457
$635$	0	0
$636$	−8.86882e31	−0.510633
$637$	− 1.07708e31i	− 0.0609038i
$638$	− 2.41233e31i	− 0.133968i
$639$	4.39769e32	2.39864
$640$	0	0
$641$	−8.22287e31	−0.432669	−0.216335	−	0.976319i	$-0.569410\pi$
$641$	−8.22287e31	−0.432669	−0.216335	+	0.976319i	$0.569410\pi$
$642$	− 1.96909e32i	− 1.01768i
$643$	3.16365e32i	1.60606i	0.595936	+	0.803032i	$0.296781\pi$
$643$	3.16365e32i	1.60606i	−0.595936	+	0.803032i	$0.703219\pi$
$644$	−1.87607e32	−0.935539
$645$	0	0
$646$	−9.34253e31	−0.449563
$647$	2.07765e32i	0.982141i	0.871120	+	0.491070i	$0.163394\pi$
$647$	2.07765e32i	0.982141i	−0.871120	+	0.491070i	$0.836606\pi$
$648$	− 1.79003e31i	− 0.0831282i
$649$	−7.18049e31	−0.327597
$650$	0	0
$651$	−4.17131e32	−1.83692
$652$	1.42115e32i	0.614883i
$653$	2.36683e32i	1.00616i	0.864241	+	0.503078i	$0.167799\pi$
$653$	2.36683e32i	1.00616i	−0.864241	+	0.503078i	$0.832201\pi$
$654$	4.17996e32	1.74594
$655$	0	0
$656$	−2.79317e31	−0.112643
$657$	− 6.97807e32i	− 2.76524i
$658$	− 1.84381e32i	− 0.717989i
$659$	−7.16883e31	−0.274325	−0.137163	−	0.990549i	$-0.543798\pi$
$659$	−7.16883e31	−0.274325	−0.137163	+	0.990549i	$0.543798\pi$
$660$	0	0
$661$	−2.52957e32	−0.934824	−0.467412	−	0.884039i	$-0.654814\pi$
$661$	−2.52957e32	−0.934824	−0.467412	+	0.884039i	$0.654814\pi$
$662$	− 2.21066e32i	− 0.802888i
$663$	− 2.25224e31i	− 0.0803914i
$664$	−1.93277e30	−0.00678028
$665$	0	0
$666$	2.05285e32	0.695670
$667$	7.94186e31i	0.264530i
$668$	− 1.09210e31i	− 0.0357546i
$669$	−2.75846e32	−0.887700
$670$	0	0
$671$	2.62494e32	0.816226
$672$	− 1.25262e32i	− 0.382890i
$673$	− 1.17871e32i	− 0.354188i	−0.984194	−	0.177094i	$-0.943330\pi$
$673$	− 1.17871e32i	− 0.354188i	0.984194	−	0.177094i	$-0.0566696\pi$
$674$	−5.22070e31	−0.154220
$675$	0	0
$676$	−1.73895e32	−0.496478
$677$	6.75616e32i	1.89640i	0.317674	+	0.948200i	$0.397098\pi$
$677$	6.75616e32i	1.89640i	−0.317674	+	0.948200i	$0.602902\pi$
$678$	− 4.98189e32i	− 1.37484i
$679$	−6.33083e32	−1.71774
$680$	0	0
$681$	5.83539e32	1.53066
$682$	− 2.37196e32i	− 0.611768i
$683$	− 6.83468e32i	− 1.73333i	−0.498894	−	0.866663i	$-0.666260\pi$
$683$	− 6.83468e32i	− 1.73333i	0.498894	−	0.866663i	$-0.333740\pi$
$684$	−3.77152e32	−0.940526
$685$	0	0
$686$	1.05693e32	0.254870
$687$	5.94438e32i	1.40963i
$688$	1.47382e32i	0.343699i
$689$	−2.26685e31	−0.0519878
$690$	0	0
$691$	6.05837e32	1.34387	0.671936	−	0.740609i	$-0.265463\pi$
$691$	6.05837e32	1.34387	0.671936	+	0.740609i	$0.265463\pi$
$692$	− 1.66130e32i	− 0.362433i
$693$	− 1.07338e33i	− 2.30314i
$694$	−2.40412e32	−0.507367
$695$	0	0
$696$	−5.30266e31	−0.108265
$697$	1.30327e32i	0.261732i
$698$	4.16728e31i	0.0823220i
$699$	2.91973e32	0.567356
$700$	0	0
$701$	−7.67265e32	−1.44274	−0.721370	−	0.692550i	$-0.756487\pi$
$701$	−7.67265e32	−1.44274	−0.721370	+	0.692550i	$0.756487\pi$
$702$	− 3.80189e31i	− 0.0703270i
$703$	− 3.44292e32i	− 0.626529i
$704$	7.12287e31	0.127517
$705$	0	0
$706$	−1.52206e32	−0.263740
$707$	− 9.78784e32i	− 1.66864i
$708$	1.57838e32i	0.264745i
$709$	−9.17188e32	−1.51365	−0.756827	−	0.653615i	$-0.773252\pi$
$709$	−9.17188e32	−1.51365	−0.756827	+	0.653615i	$0.773252\pi$
$710$	0	0
$711$	5.82246e32	0.930265
$712$	2.91134e32i	0.457691i
$713$	7.80893e32i	1.20799i
$714$	−5.84463e32	−0.889667
$715$	0	0
$716$	−1.85516e32	−0.273453
$717$	− 1.54860e32i	− 0.224630i
$718$	− 1.24854e32i	− 0.178226i
$719$	−2.80152e32	−0.393561	−0.196780	−	0.980448i	$-0.563049\pi$
$719$	−2.80152e32	−0.393561	−0.196780	+	0.980448i	$0.563049\pi$
$720$	0	0
$721$	−7.35616e32	−1.00091
$722$	1.04503e32i	0.139943i
$723$	− 9.23434e32i	− 1.21707i
$724$	3.44902e32	0.447406
$725$	0	0
$726$	3.77445e31	0.0474333
$727$	8.07964e32i	0.999416i	0.866194	+	0.499708i	$0.166559\pi$
$727$	8.07964e32i	0.999416i	−0.866194	+	0.499708i	$0.833441\pi$
$728$	− 3.20167e31i	− 0.0389822i
$729$	1.29303e33	1.54968
$730$	0	0
$731$	6.87673e32	0.798605
$732$	− 5.77000e32i	− 0.659627i
$733$	1.23627e32i	0.139129i	0.997577	+	0.0695645i	$0.0221610\pi$
$733$	1.23627e32i	0.139129i	−0.997577	+	0.0695645i	$0.977839\pi$
$734$	−2.32914e32	−0.258043
$735$	0	0
$736$	−2.34498e32	−0.251794
$737$	1.68753e33i	1.78392i
$738$	5.26121e32i	0.547568i
$739$	1.50297e32	0.154007	0.0770034	−	0.997031i	$-0.475465\pi$
$739$	1.50297e32	0.154007	0.0770034	+	0.997031i	$0.475465\pi$
$740$	0	0
$741$	−1.52489e32	−0.151471
$742$	5.88252e32i	0.575332i
$743$	1.35193e33i	1.30192i	0.759114	+	0.650958i	$0.225633\pi$
$743$	1.35193e33i	1.30192i	−0.759114	+	0.650958i	$0.774367\pi$
$744$	−5.21390e32	−0.494395
$745$	0	0
$746$	−1.46835e33	−1.35000
$747$	3.64056e31i	0.0329596i
$748$	− 3.32347e32i	− 0.296294i
$749$	−1.30606e33	−1.14663
$750$	0	0
$751$	−5.66394e32	−0.482236	−0.241118	−	0.970496i	$-0.577514\pi$
$751$	−5.66394e32	−0.482236	−0.241118	+	0.970496i	$0.577514\pi$
$752$	− 2.30466e32i	− 0.193242i
$753$	8.72552e32i	0.720525i
$754$	−1.35535e31	−0.0110225
$755$	0	0
$756$	−9.86599e32	−0.778287
$757$	− 7.79753e32i	− 0.605835i	−0.953017	−	0.302917i	$-0.902039\pi$
$757$	− 7.79753e32i	− 0.605835i	0.953017	−	0.302917i	$-0.0979607\pi$
$758$	1.29554e33i	0.991415i
$759$	−3.17861e33	−2.39583
$760$	0	0
$761$	5.97338e32	0.436814	0.218407	−	0.975858i	$-0.429914\pi$
$761$	5.97338e32	0.436814	0.218407	+	0.975858i	$0.429914\pi$
$762$	2.32233e33i	1.67279i
$763$	− 2.77249e33i	− 1.96715i
$764$	−2.19279e32	−0.153258
$765$	0	0
$766$	1.32867e33	0.901130
$767$	4.03428e31i	0.0269538i
$768$	− 1.56571e32i	− 0.103052i
$769$	7.32351e32	0.474861	0.237431	−	0.971405i	$-0.423695\pi$
$769$	7.32351e32	0.474861	0.237431	+	0.971405i	$0.423695\pi$
$770$	0	0
$771$	−2.78228e33	−1.75096
$772$	− 1.12255e33i	− 0.695999i
$773$	3.08883e33i	1.88682i	0.331633	+	0.943409i	$0.392401\pi$
$773$	3.08883e33i	1.88682i	−0.331633	+	0.943409i	$0.607599\pi$
$774$	2.77609e33	1.67075
$775$	0	0
$776$	−7.91318e32	−0.462319
$777$	− 2.15387e33i	− 1.23988i
$778$	− 3.65636e32i	− 0.207388i
$779$	8.82382e32	0.493146
$780$	0	0
$781$	2.62375e33	1.42376
$782$	1.09415e33i	0.585057i
$783$	4.17651e32i	0.220066i
$784$	−3.49366e32	−0.181403
$785$	0	0
$786$	3.52786e33	1.77890
$787$	− 1.63692e33i	− 0.813427i	−0.913556	−	0.406714i	$-0.866675\pi$
$787$	− 1.63692e33i	− 0.813427i	0.913556	−	0.406714i	$-0.133325\pi$
$788$	3.54425e32i	0.173569i
$789$	5.57795e33	2.69209
$790$	0	0
$791$	−3.30439e33	−1.54904
$792$	− 1.34166e33i	− 0.619874i
$793$	− 1.47480e32i	− 0.0671569i
$794$	−1.95855e32	−0.0879018
$795$	0	0
$796$	−6.98170e31	−0.0304411
$797$	− 3.06247e33i	− 1.31614i	−0.752957	−	0.658069i	$-0.771373\pi$
$797$	− 3.06247e33i	− 1.31614i	0.752957	−	0.658069i	$-0.228627\pi$
$798$	3.95712e33i	1.67628i
$799$	−1.07533e33	−0.449008
$800$	0	0
$801$	5.48378e33	2.22488
$802$	1.32803e33i	0.531131i
$803$	− 4.16325e33i	− 1.64136i
$804$	3.70943e33	1.44166
$805$	0	0
$806$	−1.33266e32	−0.0503346
$807$	2.77183e32i	0.103210i
$808$	− 1.22343e33i	− 0.449104i
$809$	4.44022e33	1.60693	0.803464	−	0.595353i	$-0.202988\pi$
$809$	4.44022e33	1.60693	0.803464	+	0.595353i	$0.202988\pi$
$810$	0	0
$811$	3.17750e33	1.11775	0.558876	−	0.829251i	$-0.311233\pi$
$811$	3.17750e33	1.11775	0.558876	+	0.829251i	$0.311233\pi$
$812$	3.51716e32i	0.121982i
$813$	− 7.23944e33i	− 2.47550i
$814$	1.22477e33	0.412927
$815$	0	0
$816$	−7.30546e32	−0.239448
$817$	− 4.65590e33i	− 1.50470i
$818$	1.27170e33i	0.405248i
$819$	−6.03066e32	−0.189496
$820$	0	0
$821$	3.15264e33	0.963224	0.481612	−	0.876384i	$-0.340051\pi$
$821$	3.15264e33	0.963224	0.481612	+	0.876384i	$0.340051\pi$
$822$	4.87643e33i	1.46918i
$823$	2.38843e33i	0.709600i	0.934942	+	0.354800i	$0.115451\pi$
$823$	2.38843e33i	0.709600i	−0.934942	+	0.354800i	$0.884549\pi$
$824$	−9.19479e32	−0.269389
$825$	0	0
$826$	1.04691e33	0.298289
$827$	− 8.06573e32i	− 0.226637i	−0.993559	−	0.113318i	$-0.963852\pi$
$827$	− 8.06573e32i	− 0.226637i	0.993559	−	0.113318i	$-0.0361480\pi$
$828$	4.41700e33i	1.22399i
$829$	−5.77436e32	−0.157807	−0.0789036	−	0.996882i	$-0.525142\pi$
$829$	−5.77436e32	−0.157807	−0.0789036	+	0.996882i	$0.525142\pi$
$830$	0	0
$831$	2.07069e33	0.550432
$832$	− 4.00191e31i	− 0.0104918i
$833$	1.63011e33i	0.421501i
$834$	−5.37224e32	−0.137008
$835$	0	0
$836$	−2.25016e33	−0.558266
$837$	4.10661e33i	1.00494i
$838$	− 1.92585e33i	− 0.464853i
$839$	1.64111e33	0.390729	0.195364	−	0.980731i	$-0.437411\pi$
$839$	1.64111e33	0.390729	0.195364	+	0.980731i	$0.437411\pi$
$840$	0	0
$841$	−4.16783e33	−0.965509
$842$	− 3.35246e33i	− 0.766082i
$843$	3.33685e33i	0.752175i
$844$	−1.17304e33	−0.260840
$845$	0	0
$846$	−4.34104e33	−0.939366
$847$	− 2.50352e32i	− 0.0534432i
$848$	7.35283e32i	0.154847i
$849$	−2.35632e33	−0.489549
$850$	0	0
$851$	−4.03217e33	−0.815360
$852$	− 5.76738e33i	− 1.15060i
$853$	1.64258e33i	0.323306i	0.986848	+	0.161653i	$0.0516825\pi$
$853$	1.64258e33i	0.323306i	−0.986848	+	0.161653i	$0.948318\pi$
$854$	−3.82713e33	−0.743204
$855$	0	0
$856$	−1.63250e33	−0.308607
$857$	1.00984e34i	1.88353i	0.336277	+	0.941763i	$0.390832\pi$
$857$	1.00984e34i	1.88353i	−0.336277	+	0.941763i	$0.609168\pi$
$858$	− 5.42456e32i	− 0.0998299i
$859$	1.81863e33	0.330235	0.165118	−	0.986274i	$-0.447200\pi$
$859$	1.81863e33	0.330235	0.165118	+	0.986274i	$0.447200\pi$
$860$	0	0
$861$	5.52013e33	0.975917
$862$	− 1.09974e33i	− 0.191848i
$863$	− 3.75334e33i	− 0.646092i	−0.946383	−	0.323046i	$-0.895293\pi$
$863$	− 3.75334e33i	− 0.646092i	0.946383	−	0.323046i	$-0.104707\pi$
$864$	−1.23319e33	−0.209471
$865$	0	0
$866$	1.45433e33	0.240551
$867$	− 6.69309e33i	− 1.09246i
$868$	3.45829e33i	0.557037i
$869$	3.47380e33	0.552175
$870$	0	0
$871$	9.48120e32	0.146776
$872$	− 3.46546e33i	− 0.529445i
$873$	1.49052e34i	2.24737i
$874$	7.40796e33	1.10234
$875$	0	0
$876$	−9.15143e33	−1.32645
$877$	3.70897e33i	0.530589i	0.964167	+	0.265295i	$0.0854692\pi$
$877$	3.70897e33i	0.530589i	−0.964167	+	0.265295i	$0.914531\pi$
$878$	3.66310e33i	0.517204i
$879$	−1.20087e34	−1.67349
$880$	0	0
$881$	4.79707e33	0.651259	0.325629	−	0.945498i	$-0.394424\pi$
$881$	4.79707e33	0.651259	0.325629	+	0.945498i	$0.394424\pi$
$882$	6.58064e33i	0.881819i
$883$	1.57928e33i	0.208886i	0.994531	+	0.104443i	$0.0333060\pi$
$883$	1.57928e33i	0.208886i	−0.994531	+	0.104443i	$0.966694\pi$
$884$	−1.86725e32	−0.0243783
$885$	0	0
$886$	−7.41296e33	−0.942984
$887$	1.49477e34i	1.87695i	0.345348	+	0.938475i	$0.387761\pi$
$887$	1.49477e34i	1.87695i	−0.345348	+	0.938475i	$0.612239\pi$
$888$	− 2.69222e33i	− 0.333704i
$889$	1.54036e34	1.88474
$890$	0	0
$891$	−2.01162e33	−0.239857
$892$	2.28694e33i	0.269190i
$893$	7.28056e33i	0.846005i
$894$	−1.04310e34	−1.19659
$895$	0	0
$896$	−1.03851e33	−0.116109
$897$	1.78587e33i	0.197123i
$898$	2.23681e32i	0.0243754i
$899$	1.46398e33	0.157506
$900$	0	0
$901$	3.43076e33	0.359795
$902$	3.13894e33i	0.325019i
$903$	− 2.91271e34i	− 2.97774i
$904$	−4.13031e33	−0.416913
$905$	0	0
$906$	1.17036e34	1.15172
$907$	− 2.13809e32i	− 0.0207751i	−0.999946	−	0.0103875i	$-0.996693\pi$
$907$	− 2.13809e32i	− 0.0207751i	0.999946	−	0.0103875i	$-0.00330652\pi$
$908$	− 4.83791e33i	− 0.464163i
$909$	−2.30444e34	−2.18314
$910$	0	0
$911$	2.47006e33	0.228164	0.114082	−	0.993471i	$-0.463607\pi$
$911$	2.47006e33	0.228164	0.114082	+	0.993471i	$0.463607\pi$
$912$	4.94618e33i	0.451158i
$913$	2.17203e32i	0.0195637i
$914$	9.07206e33	0.806909
$915$	0	0
$916$	4.92827e33	0.427461
$917$	− 2.33996e34i	− 2.00430i
$918$	5.75397e33i	0.486717i
$919$	−8.02451e33	−0.670333	−0.335166	−	0.942159i	$-0.608792\pi$
$919$	−8.02451e33	−0.670333	−0.335166	+	0.942159i	$0.608792\pi$
$920$	0	0
$921$	−1.68687e34	−1.37435
$922$	− 1.07476e34i	− 0.864779i
$923$	− 1.47413e33i	− 0.117143i
$924$	−1.40769e34	−1.10479
$925$	0	0
$926$	−8.08444e33	−0.618904
$927$	1.73193e34i	1.30952i
$928$	4.39625e32i	0.0328307i
$929$	3.89736e33	0.287468	0.143734	−	0.989616i	$-0.454089\pi$
$929$	3.89736e33	0.287468	0.143734	+	0.989616i	$0.454089\pi$
$930$	0	0
$931$	1.10367e34	0.794177
$932$	− 2.42065e33i	− 0.172048i
$933$	− 4.44866e34i	− 3.12313i
$934$	5.74023e33	0.398052
$935$	0	0
$936$	−7.53799e32	−0.0510015
$937$	− 5.87024e33i	− 0.392329i	−0.980571	−	0.196165i	$-0.937151\pi$
$937$	− 5.87024e33i	− 0.392329i	0.980571	−	0.196165i	$-0.0628487\pi$
$938$	− 2.46039e34i	− 1.62432i
$939$	−4.55384e34	−2.96977
$940$	0	0
$941$	−2.06023e34	−1.31110	−0.655549	−	0.755153i	$-0.727563\pi$
$941$	−2.06023e34	−1.31110	−0.655549	+	0.755153i	$0.727563\pi$
$942$	− 4.65354e33i	− 0.292549i
$943$	− 1.03340e34i	− 0.641777i
$944$	1.30857e33	0.0802824
$945$	0	0
$946$	1.65627e34	0.991706
$947$	− 4.59154e33i	− 0.271602i	−0.990736	−	0.135801i	$-0.956639\pi$
$947$	− 4.59154e33i	− 0.271602i	0.990736	−	0.135801i	$-0.0433608\pi$
$948$	− 7.63591e33i	− 0.446236i
$949$	−2.33908e33	−0.135047
$950$	0	0
$951$	1.71907e34	0.968765
$952$	4.84557e33i	0.269787i
$953$	1.49358e34i	0.821599i	0.911726	+	0.410799i	$0.134750\pi$
$953$	1.49358e34i	0.821599i	−0.911726	+	0.410799i	$0.865250\pi$
$954$	1.38498e34	0.752724
$955$	0	0
$956$	−1.28389e33	−0.0681178
$957$	5.95908e33i	0.312386i
$958$	− 1.13705e34i	− 0.588946i
$959$	3.23445e34	1.65534
$960$	0	0
$961$	−5.61859e33	−0.280743
$962$	− 6.88124e32i	− 0.0339745i
$963$	3.07498e34i	1.50017i
$964$	−7.65586e33	−0.369070
$965$	0	0
$966$	4.63437e34	2.18149
$967$	− 3.92857e34i	− 1.82738i	−0.406407	−	0.913692i	$-0.633219\pi$
$967$	− 3.92857e34i	− 1.82738i	0.406407	−	0.913692i	$-0.366781\pi$
$968$	− 3.12927e32i	− 0.0143839i
$969$	2.30784e34	1.04829
$970$	0	0
$971$	−2.25313e34	−0.999461	−0.499730	−	0.866181i	$-0.666568\pi$
$971$	−2.25313e34	−0.999461	−0.499730	+	0.866181i	$0.666568\pi$
$972$	− 9.09360e33i	− 0.398634i
$973$	3.56330e33i	0.154367i
$974$	−3.01780e33	−0.129200
$975$	0	0
$976$	−4.78370e33	−0.200028
$977$	− 2.96994e34i	− 1.22732i	−0.789569	−	0.613662i	$-0.789696\pi$
$977$	− 2.96994e34i	− 1.22732i	0.789569	−	0.613662i	$-0.210304\pi$
$978$	− 3.51060e34i	− 1.43379i
$979$	3.27173e34	1.32062
$980$	0	0
$981$	−6.52753e34	−2.57368
$982$	− 3.43469e32i	− 0.0133846i
$983$	3.01623e34i	1.16171i	0.814006	+	0.580857i	$0.197282\pi$
$983$	3.01623e34i	1.16171i	−0.814006	+	0.580857i	$0.802718\pi$
$984$	6.89985e33	0.262661
$985$	0	0
$986$	2.05125e33	0.0762841
$987$	4.55467e34i	1.67421i
$988$	1.26423e33i	0.0459326i
$989$	−5.45275e34	−1.95821
$990$	0	0
$991$	−2.58031e34	−0.905368	−0.452684	−	0.891671i	$-0.649533\pi$
$991$	−2.58031e34	−0.905368	−0.452684	+	0.891671i	$0.649533\pi$
$992$	4.32266e33i	0.149923i
$993$	5.46089e34i	1.87218i
$994$	−3.82540e34	−1.29638
$995$	0	0
$996$	4.77444e32	0.0158103
$997$	1.42567e34i	0.466685i	0.972395	+	0.233342i	$0.0749663\pi$
$997$	1.42567e34i	0.466685i	−0.972395	+	0.233342i	$0.925034\pi$
$998$	2.61701e34i	0.846846i
$999$	−2.12046e34	−0.678309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.24.b.a.49.2		2
5.2	odd	4		2.24.a.a.1.1	✓	1
5.3	odd	4		50.24.a.a.1.1		1
5.4	even	2	inner	50.24.b.a.49.1		2
15.2	even	4		18.24.a.d.1.1		1
20.7	even	4		16.24.a.a.1.1		1
40.27	even	4		64.24.a.a.1.1		1
40.37	odd	4		64.24.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.24.a.a.1.1	✓	1	5.2	odd	4
16.24.a.a.1.1		1	20.7	even	4
18.24.a.d.1.1		1	15.2	even	4
50.24.a.a.1.1		1	5.3	odd	4
50.24.b.a.49.1		2	5.4	even	2	inner
50.24.b.a.49.2		2	1.1	even	1	trivial
64.24.a.a.1.1		1	40.27	even	4
64.24.a.c.1.1		1	40.37	odd	4

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:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2048.00i q^{2} -505908. i q^{3} -4.19430e6 q^{4} +1.03610e9 q^{6} -6.87226e9i q^{7} -8.58993e9i q^{8} -1.61800e11 q^{9} +O(q^{10})\)	\(q+2048.00i q^{2} -505908. i q^{3} -4.19430e6 q^{4} +1.03610e9 q^{6} -6.87226e9i q^{7} -8.58993e9i q^{8} -1.61800e11 q^{9} -9.65329e11 q^{11} +2.12193e12i q^{12} +5.42360e11i q^{13} +1.40744e13 q^{14} +1.75922e13 q^{16} -8.20835e13i q^{17} -3.31366e14i q^{18} -5.55749e14 q^{19} -3.47673e15 q^{21} -1.97699e15i q^{22} +6.50864e15i q^{23} -4.34572e15 q^{24} -1.11075e15 q^{26} +3.42280e16i q^{27} +2.88243e16i q^{28} +1.22020e16 q^{29} +1.19978e17 q^{31} +3.60288e16i q^{32} +4.88368e17i q^{33} +1.68107e17 q^{34} +6.78637e17 q^{36} +6.19511e17i q^{37} -1.13817e18i q^{38} +2.74384e17 q^{39} -1.58774e18 q^{41} -7.12034e18i q^{42} +8.37772e18i q^{43} +4.04888e18 q^{44} -1.33297e19 q^{46} -1.31005e19i q^{47} -8.90003e18i q^{48} -1.98591e19 q^{49} -4.15267e19 q^{51} -2.27482e18i q^{52} +4.17960e19i q^{53} -7.00989e19 q^{54} -5.90322e19 q^{56} +2.81158e20i q^{57} +2.49898e19i q^{58} +7.43839e19 q^{59} -2.71922e20 q^{61} +2.45715e20i q^{62} +1.11193e21i q^{63} -7.37870e19 q^{64} -1.00018e21 q^{66} -1.74814e21i q^{67} +3.44283e20i q^{68} +3.29277e21 q^{69} -2.71799e21 q^{71} +1.38985e21i q^{72} +4.31278e21i q^{73} -1.26876e21 q^{74} +2.33098e21 q^{76} +6.63399e21i q^{77} +5.61939e20i q^{78} -3.59856e21 q^{79} +2.08387e21 q^{81} -3.25168e21i q^{82} -2.25004e20i q^{83} +1.45825e22 q^{84} -1.71576e22 q^{86} -6.17311e21i q^{87} +8.29211e21i q^{88} -3.38924e22 q^{89} +3.72724e21 q^{91} -2.72992e22i q^{92} -6.06978e22i q^{93} +2.68297e22 q^{94} +1.82273e22 q^{96} -9.21216e22i q^{97} -4.06715e22i q^{98} +1.56190e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8388608 q^{4} + 2072199168 q^{6} - 323599451274 q^{9}+O(q^{10}) \) 2 * q - 8388608 * q^4 + 2072199168 * q^6 - 323599451274 * q^9	\( 2 q - 8388608 q^{4} + 2072199168 q^{6} - 323599451274 q^{9} - 1930657597176 q^{11} + 28148756873216 q^{14} + 35184372088832 q^{16} - 11\!\cdots\!00 q^{19}+ \cdots + 31\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 8388608 * q^4 + 2072199168 * q^6 - 323599451274 * q^9 - 1930657597176 * q^11 + 28148756873216 * q^14 + 35184372088832 * q^16 - 1111497103233400 * q^19 - 6953457662214336 * q^21 - 8691433259139072 * q^24 - 2221506556485632 * q^26 + 24404075831200980 * q^29 + 239956022085498304 * q^31 + 336214168638529536 * q^34 + 1357274472876343296 * q^36 + 548768524891861872 * q^39 - 3175471107543872076 * q^41 + 8097764882465685504 * q^44 - 26659382029373571072 * q^46 - 39718285528834105746 * q^49 - 83053436341592383056 * q^51 - 140197840009435054080 * q^54 - 118064443548357361664 * q^56 + 148767730562810108760 * q^59 - 543844073173894354196 * q^61 - 147573952589676412928 * q^64 - 2000353533280493174784 * q^66 + 6585544259627111618112 * q^69 - 5435973316463881934736 * q^71 - 2537516975175357374464 * q^74 + 4661956746080262553600 * q^76 - 7197125568823552221280 * q^79 + 4167745183504692944082 * q^81 + 29164915286456238342144 * q^84 - 34315129413789729308672 * q^86 - 67784845741841350657620 * q^89 + 7454472535940330255264 * q^91 + 53659471956973412745216 * q^94 + 36454513284540046245888 * q^96 + 312379869522066466001112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more