LMFDB - Embedded newform 50.26.b.e.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 26);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$197.998389976$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 53353x^{2} + 711608976 $ x^4 + 53353*x^2 + 711608976
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 2)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$-162.829i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.26.b.e.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00i q^{2} +1.75788e6i q^{3} -1.67772e7 q^{4} +7.20027e9 q^{6} +3.04153e10i q^{7} +6.87195e10i q^{8} -2.24285e12 q^{9} +2.58704e12 q^{11} -2.94923e13i q^{12} -9.57327e13i q^{13} +1.24581e14 q^{14} +2.81475e14 q^{16} +1.64685e15i q^{17} +9.18671e15i q^{18} -4.95030e15 q^{19} -5.34664e16 q^{21} -1.05965e16i q^{22} -1.07650e16i q^{23} -1.20801e17 q^{24} -3.92121e17 q^{26} -2.45323e18i q^{27} -5.10284e17i q^{28} +1.36741e18 q^{29} -4.42000e18 q^{31} -1.15292e18i q^{32} +4.54771e18i q^{33} +6.74549e18 q^{34} +3.76288e19 q^{36} -1.01944e19i q^{37} +2.02764e19i q^{38} +1.68287e20 q^{39} +1.58687e20 q^{41} +2.18999e20i q^{42} +1.83575e20i q^{43} -4.34034e19 q^{44} -4.40934e19 q^{46} -1.40203e21i q^{47} +4.94799e20i q^{48} +4.15978e20 q^{49} -2.89496e21 q^{51} +1.60613e21i q^{52} -1.99903e21i q^{53} -1.00484e22 q^{54} -2.09012e21 q^{56} -8.70202e21i q^{57} -5.60091e21i q^{58} +4.16691e21 q^{59} +3.42128e22 q^{61} +1.81043e22i q^{62} -6.82170e22i q^{63} -4.72237e21 q^{64} +1.86274e22 q^{66} -8.67051e22i q^{67} -2.76295e22i q^{68} +1.89236e22 q^{69} -5.13159e22 q^{71} -1.54128e23i q^{72} +3.49147e22i q^{73} -4.17563e22 q^{74} +8.30522e22 q^{76} +7.86857e22i q^{77} -6.89302e23i q^{78} -2.91588e23 q^{79} +2.41214e24 q^{81} -6.49981e23i q^{82} -1.64916e24i q^{83} +8.97018e23 q^{84} +7.51925e23 q^{86} +2.40374e24i q^{87} +1.77780e23i q^{88} -8.74435e23 q^{89} +2.91174e24 q^{91} +1.80607e23i q^{92} -7.76982e24i q^{93} -5.74273e24 q^{94} +2.02670e24 q^{96} -1.00608e25i q^{97} -1.70384e24i q^{98} -5.80235e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 67108864 q^{4} + 3111714816 q^{6} - 6589062865332 q^{9} + 16646069220528 q^{11} + 3084590645248 q^{14} + 11\!\cdots\!24 q^{16} + 954158485898800 q^{19} - 18\!\cdots\!12 q^{21} - 52\!\cdots\!56 q^{24}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 67108864 * q^4 + 3111714816 * q^6 - 6589062865332 * q^9 + 16646069220528 * q^11 + 3084590645248 * q^14 + 1125899906842624 * q^16 + 954158485898800 * q^19 - 189721583323504512 * q^21 - 52205911598432256 * q^24 - 872178099423576064 * q^26 - 3448825290412871160 * q^29 - 17376164576702253952 * q^31 - 10877984113573527552 * q^34 + 110546130929253875712 * q^36 + 306988747670662211616 * q^39 + 166028648711906937768 * q^41 - 279274698863749890048 * q^44 - 944578771201833959424 * q^46 + 1709437286023947544092 * q^49 - 13988451985175107641312 * q^51 - 17789497812624611082240 * q^54 - 51750843526905069568 * q^56 + 34827350861264098907280 * q^59 + 67951719906180425620088 * q^61 - 18889465931478580854784 * q^64 - 27497776775209124364288 * q^66 - 250271736165096773468544 * q^69 - 556696016291201627231712 * q^71 + 285969318295553396604928 * q^74 - 16008123016157121740800 * q^76 - 1857092364577563295634240 * q^79 + 3818391604963344095456484 * q^81 + 3182999983280433074798592 * q^84 + 364868473515801819938816 * q^86 + 4693808359348401402489240 * q^89 + 5178590528892421167475648 * q^91 - 15313803116991894321364992 * q^94 + 875869855363803220279296 * q^96 - 23669571375888625607683824 * q^99

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 4096.00i	− 0.707107i
$2$	− 4096.00i	− 0.707107i
$3$	1.75788e6i	1.90974i	0.297031	+	0.954868i	$0.404004\pi$
$3$	1.75788e6i	1.90974i	−0.297031	+	0.954868i	$0.595996\pi$
$4$	−1.67772e7	−0.500000
$5$	0	0
$5$	0	0
$6$	7.20027e9	1.35039
$7$	3.04153e10i	0.830552i	0.909696	+	0.415276i	$0.136315\pi$
$7$	3.04153e10i	0.830552i	−0.909696	+	0.415276i	$0.863685\pi$
$8$	6.87195e10i	0.353553i
$9$	−2.24285e12	−2.64709
$10$	0	0
$11$	2.58704e12	0.248539	0.124270	−	0.992248i	$-0.460341\pi$
$11$	2.58704e12	0.248539	0.124270	+	0.992248i	$0.460341\pi$
$12$	− 2.94923e13i	− 0.954868i
$13$	− 9.57327e13i	− 1.13964i	−0.821769	−	0.569821i	$-0.807012\pi$
$13$	− 9.57327e13i	− 1.13964i	0.821769	−	0.569821i	$-0.192988\pi$
$14$	1.24581e14	0.587289
$15$	0	0
$16$	2.81475e14	0.250000
$17$	1.64685e15i	0.685555i	0.939417	+	0.342777i	$0.111368\pi$
$17$	1.64685e15i	0.685555i	−0.939417	+	0.342777i	$0.888632\pi$
$18$	9.18671e15i	1.87178i
$19$	−4.95030e15	−0.513111	−0.256555	−	0.966530i	$-0.582588\pi$
$19$	−4.95030e15	−0.513111	−0.256555	+	0.966530i	$0.582588\pi$
$20$	0	0
$21$	−5.34664e16	−1.58613
$22$	− 1.05965e16i	− 0.175744i
$23$	− 1.07650e16i	− 0.102427i	−0.998688	−	0.0512136i	$-0.983691\pi$
$23$	− 1.07650e16i	− 0.102427i	0.998688	−	0.0512136i	$-0.0163089\pi$
$24$	−1.20801e17	−0.675194
$25$	0	0
$26$	−3.92121e17	−0.805849
$27$	− 2.45323e18i	− 3.14551i
$28$	− 5.10284e17i	− 0.415276i
$29$	1.36741e18	0.717668	0.358834	−	0.933401i	$-0.383174\pi$
$29$	1.36741e18	0.717668	0.358834	+	0.933401i	$0.383174\pi$
$30$	0	0
$31$	−4.42000e18	−1.00786	−0.503931	−	0.863744i	$-0.668113\pi$
$31$	−4.42000e18	−1.00786	−0.503931	+	0.863744i	$0.668113\pi$
$32$	− 1.15292e18i	− 0.176777i
$33$	4.54771e18i	0.474645i
$34$	6.74549e18	0.484760
$35$	0	0
$36$	3.76288e19	1.32355
$37$	− 1.01944e19i	− 0.254590i	−0.991865	−	0.127295i	$-0.959371\pi$
$37$	− 1.01944e19i	− 0.254590i	0.991865	−	0.127295i	$-0.0406294\pi$
$38$	2.02764e19i	0.362824i
$39$	1.68287e20	2.17642
$40$	0	0
$41$	1.58687e20	1.09835	0.549177	−	0.835706i	$-0.314941\pi$
$41$	1.58687e20	1.09835	0.549177	+	0.835706i	$0.314941\pi$
$42$	2.18999e20i	1.12157i
$43$	1.83575e20i	0.700582i	0.936641	+	0.350291i	$0.113917\pi$
$43$	1.83575e20i	0.700582i	−0.936641	+	0.350291i	$0.886083\pi$
$44$	−4.34034e19	−0.124270
$45$	0	0
$46$	−4.40934e19	−0.0724270
$47$	− 1.40203e21i	− 1.76009i	−0.474890	−	0.880045i	$-0.657512\pi$
$47$	− 1.40203e21i	− 1.76009i	0.474890	−	0.880045i	$-0.342488\pi$
$48$	4.94799e20i	0.477434i
$49$	4.15978e20	0.310184
$50$	0	0
$51$	−2.89496e21	−1.30923
$52$	1.60613e21i	0.569821i
$53$	− 1.99903e21i	− 0.558946i	−0.960154	−	0.279473i	$-0.909840\pi$
$53$	− 1.99903e21i	− 0.558946i	0.960154	−	0.279473i	$-0.0901598\pi$
$54$	−1.00484e22	−2.22421
$55$	0	0
$56$	−2.09012e21	−0.293644
$57$	− 8.70202e21i	− 0.979906i
$58$	− 5.60091e21i	− 0.507468i
$59$	4.16691e21	0.304905	0.152452	−	0.988311i	$-0.451283\pi$
$59$	4.16691e21	0.304905	0.152452	+	0.988311i	$0.451283\pi$
$60$	0	0
$61$	3.42128e22	1.65031	0.825156	−	0.564904i	$-0.191087\pi$
$61$	3.42128e22	1.65031	0.825156	+	0.564904i	$0.191087\pi$
$62$	1.81043e22i	0.712666i
$63$	− 6.82170e22i	− 2.19855i
$64$	−4.72237e21	−0.125000
$65$	0	0
$66$	1.86274e22	0.335624
$67$	− 8.67051e22i	− 1.29452i	−0.762268	−	0.647261i	$-0.775914\pi$
$67$	− 8.67051e22i	− 1.29452i	0.762268	−	0.647261i	$-0.224086\pi$
$68$	− 2.76295e22i	− 0.342777i
$69$	1.89236e22	0.195609
$70$	0	0
$71$	−5.13159e22	−0.371127	−0.185564	−	0.982632i	$-0.559411\pi$
$71$	−5.13159e22	−0.371127	−0.185564	+	0.982632i	$0.559411\pi$
$72$	− 1.54128e23i	− 0.935888i
$73$	3.49147e22i	0.178432i	0.996012	+	0.0892159i	$0.0284361\pi$
$73$	3.49147e22i	0.178432i	−0.996012	+	0.0892159i	$0.971564\pi$
$74$	−4.17563e22	−0.180022
$75$	0	0
$76$	8.30522e22	0.256555
$77$	7.86857e22i	0.206425i
$78$	− 6.89302e23i	− 1.53896i
$79$	−2.91588e23	−0.555176	−0.277588	−	0.960700i	$-0.589535\pi$
$79$	−2.91588e23	−0.555176	−0.277588	+	0.960700i	$0.589535\pi$
$80$	0	0
$81$	2.41214e24	3.36000
$82$	− 6.49981e23i	− 0.776654i
$83$	− 1.64916e24i	− 1.69351i	−0.531986	−	0.846753i	$-0.678554\pi$
$83$	− 1.64916e24i	− 1.69351i	0.531986	−	0.846753i	$-0.321446\pi$
$84$	8.97018e23	0.793067
$85$	0	0
$86$	7.51925e23	0.495386
$87$	2.40374e24i	1.37056i
$88$	1.77780e23i	0.0878720i
$89$	−8.74435e23	−0.375277	−0.187639	−	0.982238i	$-0.560083\pi$
$89$	−8.74435e23	−0.375277	−0.187639	+	0.982238i	$0.560083\pi$
$90$	0	0
$91$	2.91174e24	0.946532
$92$	1.80607e23i	0.0512136i
$93$	− 7.76982e24i	− 1.92475i
$94$	−5.74273e24	−1.24457
$95$	0	0
$96$	2.02670e24	0.337597
$97$	− 1.00608e25i	− 1.47227i	−0.676835	−	0.736134i	$-0.736649\pi$
$97$	− 1.00608e25i	− 1.47227i	0.676835	−	0.736134i	$-0.263351\pi$
$98$	− 1.70384e24i	− 0.219333i
$99$	−5.80235e24	−0.657907
$100$	0	0
$101$	−1.42151e25	−1.25526	−0.627628	−	0.778513i	$-0.715974\pi$
$101$	−1.42151e25	−1.25526	−0.627628	+	0.778513i	$0.715974\pi$
$102$	1.18578e25i	0.925764i
$103$	1.03211e25i	0.713283i	0.934241	+	0.356642i	$0.116078\pi$
$103$	1.03211e25i	0.713283i	−0.934241	+	0.356642i	$0.883922\pi$
$104$	6.57870e24	0.402924
$105$	0	0
$106$	−8.18801e24	−0.395235
$107$	1.74396e25i	0.748582i	0.927311	+	0.374291i	$0.122114\pi$
$107$	1.74396e25i	0.748582i	−0.927311	+	0.374291i	$0.877886\pi$
$108$	4.11583e25i	1.57275i
$109$	1.65117e25	0.562292	0.281146	−	0.959665i	$-0.409286\pi$
$109$	1.65117e25	0.562292	0.281146	+	0.959665i	$0.409286\pi$
$110$	0	0
$111$	1.79205e25	0.486199
$112$	8.56115e24i	0.207638i
$113$	6.96039e25i	1.51061i	0.655372	+	0.755306i	$0.272512\pi$
$113$	6.96039e25i	1.51061i	−0.655372	+	0.755306i	$0.727488\pi$
$114$	−3.56435e25	−0.692898
$115$	0	0
$116$	−2.29413e25	−0.358834
$117$	2.14714e26i	3.01674i
$118$	− 1.70677e25i	− 0.215600i
$119$	−5.00894e25	−0.569389
$120$	0	0
$121$	−1.01654e26	−0.938228
$122$	− 1.40136e26i	− 1.16695i
$123$	2.78952e26i	2.09757i
$124$	7.41552e25	0.503931
$125$	0	0
$126$	−2.79417e26	−1.55461
$127$	6.18922e25i	0.311953i	0.987761	+	0.155977i	$0.0498524\pi$
$127$	6.18922e25i	0.311953i	−0.987761	+	0.155977i	$0.950148\pi$
$128$	1.93428e25i	0.0883883i
$129$	−3.22703e26	−1.33793
$130$	0	0
$131$	−1.39682e26	−0.477805	−0.238902	−	0.971044i	$-0.576788\pi$
$131$	−1.39682e26	−0.477805	−0.238902	+	0.971044i	$0.576788\pi$
$132$	− 7.62979e25i	− 0.237322i
$133$	− 1.50565e26i	− 0.426165i
$134$	−3.55144e26	−0.915366
$135$	0	0
$136$	−1.13171e26	−0.242380
$137$	6.92418e26i	1.35320i	0.736352	+	0.676599i	$0.236547\pi$
$137$	6.92418e26i	1.35320i	−0.736352	+	0.676599i	$0.763453\pi$
$138$	− 7.75109e25i	− 0.138317i
$139$	8.06682e26	1.31528	0.657639	−	0.753333i	$-0.271555\pi$
$139$	8.06682e26	1.31528	0.657639	+	0.753333i	$0.271555\pi$
$140$	0	0
$141$	2.46460e27	3.36131
$142$	2.10190e26i	0.262427i
$143$	− 2.47665e26i	− 0.283246i
$144$	−6.31306e26	−0.661773
$145$	0	0
$146$	1.43010e26	0.126170
$147$	7.31239e26i	0.592369i
$148$	1.71034e26i	0.127295i
$149$	4.24039e26	0.290120	0.145060	−	0.989423i	$-0.453663\pi$
$149$	4.24039e26	0.290120	0.145060	+	0.989423i	$0.453663\pi$
$150$	0	0
$151$	2.51382e27	1.45587	0.727934	−	0.685647i	$-0.240481\pi$
$151$	2.51382e27	1.45587	0.727934	+	0.685647i	$0.240481\pi$
$152$	− 3.40182e26i	− 0.181412i
$153$	− 3.69363e27i	− 1.81473i
$154$	3.22297e26	0.145964
$155$	0	0
$156$	−2.82338e27	−1.08821
$157$	− 4.75882e27i	− 1.69338i	−0.532088	−	0.846689i	$-0.678593\pi$
$157$	− 4.75882e27i	− 1.69338i	0.532088	−	0.846689i	$-0.321407\pi$
$158$	1.19434e27i	0.392569i
$159$	3.51404e27	1.06744
$160$	0	0
$161$	3.27420e26	0.0850712
$162$	− 9.88012e27i	− 2.37588i
$163$	7.59899e26i	0.169204i	0.996415	+	0.0846020i	$0.0269619\pi$
$163$	7.59899e26i	0.169204i	−0.996415	+	0.0846020i	$0.973038\pi$
$164$	−2.66232e27	−0.549177
$165$	0	0
$166$	−6.75496e27	−1.19749
$167$	1.00207e28i	1.64794i	0.566634	+	0.823970i	$0.308245\pi$
$167$	1.00207e28i	1.64794i	−0.566634	+	0.823970i	$0.691755\pi$
$168$	− 3.67419e27i	− 0.560783i
$169$	−2.10835e27	−0.298785
$170$	0	0
$171$	1.11028e28	1.35825
$172$	− 3.07989e27i	− 0.350291i
$173$	− 7.89989e27i	− 0.835689i	−0.908518	−	0.417845i	$-0.862786\pi$
$173$	− 7.89989e27i	− 0.835689i	0.908518	−	0.417845i	$-0.137214\pi$
$174$	9.84571e27	0.969129
$175$	0	0
$176$	7.28188e26	0.0621349
$177$	7.32493e27i	0.582288i
$178$	3.58168e27i	0.265361i
$179$	8.08087e27	0.558207	0.279103	−	0.960261i	$-0.409963\pi$
$179$	8.08087e27	0.558207	0.279103	+	0.960261i	$0.409963\pi$
$180$	0	0
$181$	1.80674e27	0.108621	0.0543104	−	0.998524i	$-0.482704\pi$
$181$	1.80674e27	0.108621	0.0543104	+	0.998524i	$0.482704\pi$
$182$	− 1.19265e28i	− 0.669299i
$183$	6.01420e28i	3.15166i
$184$	7.39765e26	0.0362135
$185$	0	0
$186$	−3.18252e28	−1.36100
$187$	4.26047e27i	0.170387i
$188$	2.35222e28i	0.880045i
$189$	7.46157e28	2.61251
$190$	0	0
$191$	−4.93091e28	−1.51360	−0.756798	−	0.653649i	$-0.773237\pi$
$191$	−4.93091e28	−1.51360	−0.756798	+	0.653649i	$0.773237\pi$
$192$	− 8.30135e27i	− 0.238717i
$193$	1.42443e28i	0.383861i	0.981408	+	0.191931i	$0.0614749\pi$
$193$	1.42443e28i	0.383861i	−0.981408	+	0.191931i	$0.938525\pi$
$194$	−4.12092e28	−1.04105
$195$	0	0
$196$	−6.97895e27	−0.155092
$197$	− 3.59073e28i	− 0.748781i	−0.927271	−	0.374390i	$-0.877852\pi$
$197$	− 3.59073e28i	− 0.748781i	0.927271	−	0.374390i	$-0.122148\pi$
$198$	2.37664e28i	0.465210i
$199$	8.11996e28	1.49242	0.746209	−	0.665712i	$-0.231872\pi$
$199$	8.11996e28	1.49242	0.746209	+	0.665712i	$0.231872\pi$
$200$	0	0
$201$	1.52417e29	2.47220
$202$	5.82250e28i	0.887601i
$203$	4.15902e28i	0.596060i
$204$	4.85694e28	0.654614
$205$	0	0
$206$	4.22753e28	0.504367
$207$	2.41443e28i	0.271134i
$208$	− 2.69464e28i	− 0.284911i
$209$	−1.28066e28	−0.127528
$210$	0	0
$211$	−1.03285e29	−0.913075	−0.456537	−	0.889704i	$-0.650911\pi$
$211$	−1.03285e29	−0.913075	−0.456537	+	0.889704i	$0.650911\pi$
$212$	3.35381e28i	0.279473i
$213$	− 9.02072e28i	− 0.708755i
$214$	7.14326e28	0.529327
$215$	0	0
$216$	1.68585e29	1.11211
$217$	− 1.34436e29i	− 0.837081i
$218$	− 6.76321e28i	− 0.397600i
$219$	−6.13758e28	−0.340757
$220$	0	0
$221$	1.57657e29	0.781287
$222$	− 7.34025e28i	− 0.343795i
$223$	1.15542e29i	0.511597i	0.966730	+	0.255799i	$0.0823384\pi$
$223$	1.15542e29i	0.511597i	−0.966730	+	0.255799i	$0.917662\pi$
$224$	3.50665e28	0.146822
$225$	0	0
$226$	2.85098e29	1.06816
$227$	9.01151e28i	0.319502i	0.987157	+	0.159751i	$0.0510692\pi$
$227$	9.01151e28i	0.319502i	−0.987157	+	0.159751i	$0.948931\pi$
$228$	1.45996e29i	0.489953i
$229$	−3.69415e29	−1.17374	−0.586869	−	0.809682i	$-0.699640\pi$
$229$	−3.69415e29	−1.17374	−0.586869	+	0.809682i	$0.699640\pi$
$230$	0	0
$231$	−1.38320e29	−0.394217
$232$	9.39676e28i	0.253734i
$233$	4.10753e28i	0.105107i	0.998618	+	0.0525536i	$0.0167360\pi$
$233$	4.10753e28i	0.105107i	−0.998618	+	0.0525536i	$0.983264\pi$
$234$	8.79469e29	2.13316
$235$	0	0
$236$	−6.99092e28	−0.152452
$237$	− 5.12576e29i	− 1.06024i
$238$	2.05166e29i	0.402618i
$239$	6.49097e29	1.20875	0.604374	−	0.796701i	$-0.293423\pi$
$239$	6.49097e29	1.20875	0.604374	+	0.796701i	$0.293423\pi$
$240$	0	0
$241$	1.68781e29	0.283212	0.141606	−	0.989923i	$-0.454773\pi$
$241$	1.68781e29	0.283212	0.141606	+	0.989923i	$0.454773\pi$
$242$	4.16376e29i	0.663427i
$243$	2.16165e30i	3.27121i
$244$	−5.73996e29	−0.825156
$245$	0	0
$246$	1.14259e30	1.48320
$247$	4.73905e29i	0.584763i
$248$	− 3.03740e29i	− 0.356333i
$249$	2.89903e30	3.23415
$250$	0	0
$251$	2.65029e29	0.267530	0.133765	−	0.991013i	$-0.457293\pi$
$251$	2.65029e29	0.267530	0.133765	+	0.991013i	$0.457293\pi$
$252$	1.14449e30i	1.09927i
$253$	− 2.78495e28i	− 0.0254572i
$254$	2.53510e29	0.220584
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	− 1.11592e30i	− 0.838433i	−0.907886	−	0.419217i	$-0.862305\pi$
$257$	− 1.11592e30i	− 0.838433i	0.907886	−	0.419217i	$-0.137695\pi$
$258$	1.32179e30i	0.946057i
$259$	3.10066e29	0.211450
$260$	0	0
$261$	−3.06689e30	−1.89973
$262$	5.72139e29i	0.337859i
$263$	1.53721e30i	0.865541i	0.901504	+	0.432770i	$0.142464\pi$
$263$	1.53721e30i	0.865541i	−0.901504	+	0.432770i	$0.857536\pi$
$264$	−3.12516e29	−0.167812
$265$	0	0
$266$	−6.16713e29	−0.301344
$267$	− 1.53715e30i	− 0.716681i
$268$	1.45467e30i	0.647261i
$269$	−2.34612e30	−0.996431	−0.498216	−	0.867053i	$-0.666011\pi$
$269$	−2.34612e30	−0.996431	−0.498216	+	0.867053i	$0.666011\pi$
$270$	0	0
$271$	−1.54578e30	−0.598454	−0.299227	−	0.954182i	$-0.596729\pi$
$271$	−1.54578e30	−0.598454	−0.299227	+	0.954182i	$0.596729\pi$
$272$	4.63547e29i	0.171389i
$273$	5.11849e30i	1.80763i
$274$	2.83614e30	0.956855
$275$	0	0
$276$	−3.17485e29	−0.0978045
$277$	1.21614e30i	0.358085i	0.983841	+	0.179042i	$0.0572999\pi$
$277$	1.21614e30i	0.358085i	−0.983841	+	0.179042i	$0.942700\pi$
$278$	− 3.30417e30i	− 0.930042i
$279$	9.91339e30	2.66790
$280$	0	0
$281$	5.09885e30	1.25500	0.627499	−	0.778617i	$-0.284079\pi$
$281$	5.09885e30	1.25500	0.627499	+	0.778617i	$0.284079\pi$
$282$	− 1.00950e31i	− 2.37680i
$283$	− 1.56288e30i	− 0.352042i	−0.984386	−	0.176021i	$-0.943677\pi$
$283$	− 1.56288e30i	− 0.352042i	0.984386	−	0.176021i	$-0.0563227\pi$
$284$	8.60939e29	0.185564
$285$	0	0
$286$	−1.01444e30	−0.200285
$287$	4.82651e30i	0.912240i
$288$	2.58583e30i	0.467944i
$289$	3.05852e30	0.530015
$290$	0	0
$291$	1.76857e31	2.81164
$292$	− 5.85771e29i	− 0.0892159i
$293$	− 4.17112e30i	− 0.608706i	−0.952559	−	0.304353i	$-0.901560\pi$
$293$	− 4.17112e30i	− 0.608706i	0.952559	−	0.304353i	$-0.0984403\pi$
$294$	2.99515e30	0.418868
$295$	0	0
$296$	7.00555e29	0.0900110
$297$	− 6.34661e30i	− 0.781783i
$298$	− 1.73686e30i	− 0.205146i
$299$	−1.03056e30	−0.116730
$300$	0	0
$301$	−5.58350e30	−0.581870
$302$	− 1.02966e31i	− 1.02945i
$303$	− 2.49884e31i	− 2.39721i
$304$	−1.39338e30	−0.128278
$305$	0	0
$306$	−1.51291e31	−1.28320
$307$	− 7.69994e30i	− 0.626986i	−0.949591	−	0.313493i	$-0.898501\pi$
$307$	− 7.69994e30i	− 0.626986i	0.949591	−	0.313493i	$-0.101499\pi$
$308$	− 1.32013e30i	− 0.103212i
$309$	−1.81433e31	−1.36218
$310$	0	0
$311$	1.54260e31	1.06843	0.534217	−	0.845347i	$-0.320606\pi$
$311$	1.54260e31	1.06843	0.534217	+	0.845347i	$0.320606\pi$
$312$	1.15646e31i	0.769479i
$313$	1.62517e31i	1.03895i	0.854485	+	0.519476i	$0.173873\pi$
$313$	1.62517e31i	1.03895i	−0.854485	+	0.519476i	$0.826127\pi$
$314$	−1.94921e31	−1.19740
$315$	0	0
$316$	4.89203e30	0.277588
$317$	2.29098e31i	1.24963i	0.780773	+	0.624814i	$0.214825\pi$
$317$	2.29098e31i	1.24963i	−0.780773	+	0.624814i	$0.785175\pi$
$318$	− 1.43935e31i	− 0.754794i
$319$	3.53755e30	0.178369
$320$	0	0
$321$	−3.06567e31	−1.42959
$322$	− 1.34111e30i	− 0.0601544i
$323$	− 8.15239e30i	− 0.351765i
$324$	−4.04690e31	−1.68000
$325$	0	0
$326$	3.11255e30	0.119645
$327$	2.90256e31i	1.07383i
$328$	1.09049e31i	0.388327i
$329$	4.26433e31	1.46185
$330$	0	0
$331$	3.45199e31	1.09703	0.548517	−	0.836140i	$-0.315193\pi$
$331$	3.45199e31	1.09703	0.548517	+	0.836140i	$0.315193\pi$
$332$	2.76683e31i	0.846753i
$333$	2.28645e31i	0.673922i
$334$	4.10447e31	1.16527
$335$	0	0
$336$	−1.50495e31	−0.396534
$337$	5.27735e31i	1.33981i	0.742448	+	0.669904i	$0.233665\pi$
$337$	5.27735e31i	1.33981i	−0.742448	+	0.669904i	$0.766335\pi$
$338$	8.63579e30i	0.211273i
$339$	−1.22355e32	−2.88487
$340$	0	0
$341$	−1.14347e31	−0.250493
$342$	− 4.54770e31i	− 0.960429i
$343$	5.34411e31i	1.08818i
$344$	−1.26152e31	−0.247693
$345$	0	0
$346$	−3.23580e31	−0.590922
$347$	− 4.40093e30i	− 0.0775222i	−0.999249	−	0.0387611i	$-0.987659\pi$
$347$	− 4.40093e30i	− 0.0775222i	0.999249	−	0.0387611i	$-0.0123411\pi$
$348$	− 4.03280e31i	− 0.685278i
$349$	−2.98069e31	−0.488651	−0.244326	−	0.969693i	$-0.578567\pi$
$349$	−2.98069e31	−0.488651	−0.244326	+	0.969693i	$0.578567\pi$
$350$	0	0
$351$	−2.34854e32	−3.58476
$352$	− 2.98266e30i	− 0.0439360i
$353$	4.46084e31i	0.634209i	0.948391	+	0.317105i	$0.102711\pi$
$353$	4.46084e31i	0.634209i	−0.948391	+	0.317105i	$0.897289\pi$
$354$	3.00029e31	0.411740
$355$	0	0
$356$	1.46706e31	0.187639
$357$	− 8.80511e31i	− 1.08738i
$358$	− 3.30992e31i	− 0.394712i
$359$	−4.38054e31	−0.504483	−0.252242	−	0.967664i	$-0.581168\pi$
$359$	−4.38054e31	−0.504483	−0.252242	+	0.967664i	$0.581168\pi$
$360$	0	0
$361$	−6.85711e31	−0.736717
$362$	− 7.40039e30i	− 0.0768065i
$363$	− 1.78696e32i	− 1.79177i
$364$	−4.88509e31	−0.473266
$365$	0	0
$366$	2.46342e32	2.22856
$367$	7.76735e31i	0.679121i	0.940584	+	0.339560i	$0.110278\pi$
$367$	7.76735e31i	0.679121i	−0.940584	+	0.339560i	$0.889722\pi$
$368$	− 3.03008e30i	− 0.0256068i
$369$	−3.55911e32	−2.90744
$370$	0	0
$371$	6.08010e31	0.464234
$372$	1.30356e32i	0.962374i
$373$	− 2.37205e32i	− 1.69342i	−0.532058	−	0.846708i	$-0.678581\pi$
$373$	− 2.37205e32i	− 1.69342i	0.532058	−	0.846708i	$-0.321419\pi$
$374$	1.74509e31	0.120482
$375$	0	0
$376$	9.63470e31	0.622286
$377$	− 1.30906e32i	− 0.817884i
$378$	− 3.05626e32i	− 1.84732i
$379$	1.38944e32	0.812551	0.406276	−	0.913751i	$-0.366827\pi$
$379$	1.38944e32	0.812551	0.406276	+	0.913751i	$0.366827\pi$
$380$	0	0
$381$	−1.08799e32	−0.595748
$382$	2.01970e32i	1.07027i
$383$	− 3.79085e31i	− 0.194425i	−0.995264	−	0.0972125i	$-0.969007\pi$
$383$	− 3.79085e31i	− 0.194425i	0.995264	−	0.0972125i	$-0.0309926\pi$
$384$	−3.40023e31	−0.168798
$385$	0	0
$386$	5.83446e31	0.271431
$387$	− 4.11732e32i	− 1.85450i
$388$	1.68793e32i	0.736134i
$389$	2.20209e32	0.929963	0.464982	−	0.885320i	$-0.346061\pi$
$389$	2.20209e32	0.929963	0.464982	+	0.885320i	$0.346061\pi$
$390$	0	0
$391$	1.77283e31	0.0702195
$392$	2.85858e31i	0.109667i
$393$	− 2.45545e32i	− 0.912481i
$394$	−1.47076e32	−0.529468
$395$	0	0
$396$	9.73473e31	0.328953
$397$	− 2.18941e32i	− 0.716877i	−0.933553	−	0.358439i	$-0.883309\pi$
$397$	− 2.18941e32i	− 0.716877i	0.933553	−	0.358439i	$-0.116691\pi$
$398$	− 3.32594e32i	− 1.05530i
$399$	2.64675e32	0.813863
$400$	0	0
$401$	2.99036e32	0.863810	0.431905	−	0.901919i	$-0.357842\pi$
$401$	2.99036e32	0.863810	0.431905	+	0.901919i	$0.357842\pi$
$402$	− 6.24300e32i	− 1.74811i
$403$	4.23138e32i	1.14860i
$404$	2.38490e32	0.627628
$405$	0	0
$406$	1.70353e32	0.421478
$407$	− 2.63734e31i	− 0.0632755i
$408$	− 1.98940e32i	− 0.462882i
$409$	−7.12330e31	−0.160746	−0.0803730	−	0.996765i	$-0.525611\pi$
$409$	−7.12330e31	−0.160746	−0.0803730	+	0.996765i	$0.525611\pi$
$410$	0	0
$411$	−1.21719e33	−2.58425
$412$	− 1.73160e32i	− 0.356642i
$413$	1.26738e32i	0.253239i
$414$	9.88949e31	0.191721
$415$	0	0
$416$	−1.10372e32	−0.201462
$417$	1.41805e33i	2.51183i
$418$	5.24560e31i	0.0901761i
$419$	−2.94461e32	−0.491307	−0.245654	−	0.969358i	$-0.579003\pi$
$419$	−2.94461e32	−0.491307	−0.245654	+	0.969358i	$0.579003\pi$
$420$	0	0
$421$	1.01892e33	1.60182	0.800908	−	0.598787i	$-0.204350\pi$
$421$	1.01892e33	1.60182	0.800908	+	0.598787i	$0.204350\pi$
$422$	4.23055e32i	0.645641i
$423$	3.14455e33i	4.65912i
$424$	1.37372e32	0.197617
$425$	0	0
$426$	−3.69489e32	−0.501166
$427$	1.04059e33i	1.37067i
$428$	− 2.92588e32i	− 0.374291i
$429$	4.35365e32	0.540925
$430$	0	0
$431$	−6.79497e32	−0.796565	−0.398283	−	0.917263i	$-0.630394\pi$
$431$	−6.79497e32	−0.796565	−0.398283	+	0.917263i	$0.630394\pi$
$432$	− 6.90523e32i	− 0.786377i
$433$	− 7.24164e32i	− 0.801195i	−0.916254	−	0.400597i	$-0.868803\pi$
$433$	− 7.24164e32i	− 0.801195i	0.916254	−	0.400597i	$-0.131197\pi$
$434$	−5.50648e32	−0.591906
$435$	0	0
$436$	−2.77021e32	−0.281146
$437$	5.32899e31i	0.0525566i
$438$	2.51395e32i	0.240952i
$439$	9.13459e32	0.850908	0.425454	−	0.904980i	$-0.360114\pi$
$439$	9.13459e32	0.850908	0.425454	+	0.904980i	$0.360114\pi$
$440$	0	0
$441$	−9.32976e32	−0.821085
$442$	− 6.45764e32i	− 0.552453i
$443$	− 3.52555e32i	− 0.293211i	−0.989195	−	0.146605i	$-0.953165\pi$
$443$	− 3.52555e32i	− 0.293211i	0.989195	−	0.146605i	$-0.0468347\pi$
$444$	−3.00657e32	−0.243099
$445$	0	0
$446$	4.73259e32	0.361754
$447$	7.45409e32i	0.554052i
$448$	− 1.43632e32i	− 0.103819i
$449$	−3.70918e32	−0.260735	−0.130367	−	0.991466i	$-0.541616\pi$
$449$	−3.70918e32	−0.260735	−0.130367	+	0.991466i	$0.541616\pi$
$450$	0	0
$451$	4.10530e32	0.272984
$452$	− 1.16776e33i	− 0.755306i
$453$	4.41899e33i	2.78032i
$454$	3.69111e32	0.225922
$455$	0	0
$456$	5.97998e32	0.346449
$457$	− 1.76958e33i	− 0.997512i	−0.866742	−	0.498756i	$-0.833790\pi$
$457$	− 1.76958e33i	− 0.997512i	0.866742	−	0.498756i	$-0.166210\pi$
$458$	1.51313e33i	0.829959i
$459$	4.04009e33	2.15642
$460$	0	0
$461$	7.01018e32	0.354379	0.177189	−	0.984177i	$-0.443299\pi$
$461$	7.01018e32	0.354379	0.177189	+	0.984177i	$0.443299\pi$
$462$	5.66559e32i	0.278753i
$463$	− 9.20521e32i	− 0.440830i	−0.975406	−	0.220415i	$-0.929259\pi$
$463$	− 9.20521e32i	− 0.440830i	0.975406	−	0.220415i	$-0.0707412\pi$
$464$	3.84891e32	0.179417
$465$	0	0
$466$	1.68245e32	0.0743219
$467$	1.84600e33i	0.793908i	0.917838	+	0.396954i	$0.129933\pi$
$467$	1.84600e33i	0.793908i	−0.917838	+	0.396954i	$0.870067\pi$
$468$	− 3.60231e33i	− 1.50837i
$469$	2.63716e33	1.07517
$470$	0	0
$471$	8.36543e33	3.23390
$472$	2.86348e32i	0.107800i
$473$	4.74918e32i	0.174122i
$474$	−2.09951e33	−0.749703
$475$	0	0
$476$	8.40360e32	0.284694
$477$	4.48351e33i	1.47958i
$478$	− 2.65870e33i	− 0.854714i
$479$	3.88481e32	0.121668	0.0608339	−	0.998148i	$-0.480624\pi$
$479$	3.88481e32	0.121668	0.0608339	+	0.998148i	$0.480624\pi$
$480$	0	0
$481$	−9.75939e32	−0.290141
$482$	− 6.91328e32i	− 0.200261i
$483$	5.75566e32i	0.162463i
$484$	1.70548e33	0.469114
$485$	0	0
$486$	8.85414e33	2.31309
$487$	− 4.26102e33i	− 1.08493i	−0.840078	−	0.542465i	$-0.817491\pi$
$487$	− 4.26102e33i	− 1.08493i	0.840078	−	0.542465i	$-0.182509\pi$
$488$	2.35109e33i	0.583474i
$489$	−1.33581e33	−0.323135
$490$	0	0
$491$	−4.52548e33	−1.04027	−0.520134	−	0.854084i	$-0.674118\pi$
$491$	−4.52548e33	−1.04027	−0.520134	+	0.854084i	$0.674118\pi$
$492$	− 4.68004e33i	− 1.04878i
$493$	2.25191e33i	0.492000i
$494$	1.94112e33	0.413490
$495$	0	0
$496$	−1.24412e33	−0.251965
$497$	− 1.56079e33i	− 0.308241i
$498$	− 1.18744e34i	− 2.28689i
$499$	−4.45020e33	−0.835840	−0.417920	−	0.908484i	$-0.637241\pi$
$499$	−4.45020e33	−0.835840	−0.417920	+	0.908484i	$0.637241\pi$
$500$	0	0
$501$	−1.76151e34	−3.14713
$502$	− 1.08556e33i	− 0.189172i
$503$	2.29032e33i	0.389311i	0.980872	+	0.194656i	$0.0623590\pi$
$503$	2.29032e33i	0.389311i	−0.980872	+	0.194656i	$0.937641\pi$
$504$	4.68784e33	0.777304
$505$	0	0
$506$	−1.14072e32	−0.0180010
$507$	− 3.70622e33i	− 0.570600i
$508$	− 1.03838e33i	− 0.155977i
$509$	−5.35889e33	−0.785421	−0.392711	−	0.919662i	$-0.628463\pi$
$509$	−5.35889e33	−0.785421	−0.392711	+	0.919662i	$0.628463\pi$
$510$	0	0
$511$	−1.06194e33	−0.148197
$512$	− 3.24519e32i	− 0.0441942i
$513$	1.21442e34i	1.61400i
$514$	−4.57080e33	−0.592862
$515$	0	0
$516$	5.41407e33	0.668963
$517$	− 3.62712e33i	− 0.437452i
$518$	− 1.27003e33i	− 0.149518i
$519$	1.38871e34	1.59595
$520$	0	0
$521$	−1.14090e34	−1.24961	−0.624807	−	0.780779i	$-0.714822\pi$
$521$	−1.14090e34	−1.24961	−0.624807	+	0.780779i	$0.714822\pi$
$522$	1.25620e34i	1.34331i
$523$	1.37717e34i	1.43786i	0.695085	+	0.718928i	$0.255367\pi$
$523$	1.37717e34i	1.43786i	−0.695085	+	0.718928i	$0.744633\pi$
$524$	2.34348e33	0.238902
$525$	0	0
$526$	6.29643e33	0.612030
$527$	− 7.27906e33i	− 0.690944i
$528$	1.28007e33i	0.118661i
$529$	1.09299e34	0.989509
$530$	0	0
$531$	−9.34576e33	−0.807111
$532$	2.52606e33i	0.213083i
$533$	− 1.51915e34i	− 1.25173i
$534$	−6.29617e33	−0.506770
$535$	0	0
$536$	5.95833e33	0.457683
$537$	1.42052e34i	1.06603i
$538$	9.60972e33i	0.704583i
$539$	1.07615e33	0.0770929
$540$	0	0
$541$	−1.58682e34	−1.08533	−0.542667	−	0.839948i	$-0.682585\pi$
$541$	−1.58682e34	−1.08533	−0.542667	+	0.839948i	$0.682585\pi$
$542$	6.33151e33i	0.423171i
$543$	3.17603e33i	0.207437i
$544$	1.89869e33	0.121190
$545$	0	0
$546$	2.09653e34	1.27818
$547$	8.29322e33i	0.494176i	0.968993	+	0.247088i	$0.0794737\pi$
$547$	8.29322e33i	0.494176i	−0.968993	+	0.247088i	$0.920526\pi$
$548$	− 1.16168e34i	− 0.676599i
$549$	−7.67343e34	−4.36853
$550$	0	0
$551$	−6.76908e33	−0.368243
$552$	1.30042e33i	0.0691583i
$553$	− 8.86874e33i	− 0.461103i
$554$	4.98130e33	0.253204
$555$	0	0
$556$	−1.35339e34	−0.657639
$557$	− 3.56496e34i	− 1.69381i	−0.531744	−	0.846905i	$-0.678463\pi$
$557$	− 3.56496e34i	− 1.69381i	0.531744	−	0.846905i	$-0.321537\pi$
$558$	− 4.06052e34i	− 1.88649i
$559$	1.75742e34	0.798413
$560$	0	0
$561$	−7.48939e33	−0.325395
$562$	− 2.08849e34i	− 0.887417i
$563$	1.62059e34i	0.673471i	0.941599	+	0.336735i	$0.109323\pi$
$563$	1.62059e34i	0.673471i	−0.941599	+	0.336735i	$0.890677\pi$
$564$	−4.13492e34	−1.68065
$565$	0	0
$566$	−6.40155e33	−0.248931
$567$	7.33659e34i	2.79065i
$568$	− 3.52641e33i	− 0.131213i
$569$	−4.19926e34	−1.52851	−0.764257	−	0.644912i	$-0.776894\pi$
$569$	−4.19926e34	−1.52851	−0.764257	+	0.644912i	$0.776894\pi$
$570$	0	0
$571$	2.27922e34	0.794026	0.397013	−	0.917813i	$-0.370047\pi$
$571$	2.27922e34	0.794026	0.397013	+	0.917813i	$0.370047\pi$
$572$	4.15513e33i	0.141623i
$573$	− 8.66794e34i	− 2.89057i
$574$	1.97694e34	0.645051
$575$	0	0
$576$	1.05916e34	0.330886
$577$	1.30064e34i	0.397613i	0.980039	+	0.198807i	$0.0637066\pi$
$577$	1.30064e34i	0.397613i	−0.980039	+	0.198807i	$0.936293\pi$
$578$	− 1.25277e34i	− 0.374777i
$579$	−2.50397e34	−0.733074
$580$	0	0
$581$	5.01597e34	1.40655
$582$	− 7.24407e34i	− 1.98813i
$583$	− 5.17157e33i	− 0.138920i
$584$	−2.39932e33	−0.0630851
$585$	0	0
$586$	−1.70849e34	−0.430420
$587$	− 3.13619e34i	− 0.773440i	−0.922197	−	0.386720i	$-0.873608\pi$
$587$	− 3.13619e34i	− 0.773440i	0.922197	−	0.386720i	$-0.126392\pi$
$588$	− 1.22681e34i	− 0.296185i
$589$	2.18803e34	0.517145
$590$	0	0
$591$	6.31206e34	1.42997
$592$	− 2.86947e33i	− 0.0636474i
$593$	− 6.43753e34i	− 1.39809i	−0.715077	−	0.699046i	$-0.753608\pi$
$593$	− 6.43753e34i	− 1.39809i	0.715077	−	0.699046i	$-0.246392\pi$
$594$	−2.59957e34	−0.552804
$595$	0	0
$596$	−7.11419e33	−0.145060
$597$	1.42739e35i	2.85012i
$598$	4.22118e33i	0.0825409i
$599$	9.82124e34	1.88075	0.940375	−	0.340140i	$-0.110474\pi$
$599$	9.82124e34	1.88075	0.940375	+	0.340140i	$0.110474\pi$
$600$	0	0
$601$	1.10144e34	0.202316	0.101158	−	0.994870i	$-0.467745\pi$
$601$	1.10144e34	0.202316	0.101158	+	0.994870i	$0.467745\pi$
$602$	2.28700e34i	0.411444i
$603$	1.94467e35i	3.42672i
$604$	−4.21749e34	−0.727934
$605$	0	0
$606$	−1.02353e35	−1.69508
$607$	− 9.06735e34i	− 1.47103i	−0.677508	−	0.735516i	$-0.736940\pi$
$607$	− 9.06735e34i	− 1.47103i	0.677508	−	0.735516i	$-0.263060\pi$
$608$	5.70730e33i	0.0907060i
$609$	−7.31105e34	−1.13832
$610$	0	0
$611$	−1.34220e35	−2.00587
$612$	6.19689e34i	0.907363i
$613$	2.62922e34i	0.377199i	0.982054	+	0.188599i	$0.0603948\pi$
$613$	2.62922e34i	0.377199i	−0.982054	+	0.188599i	$0.939605\pi$
$614$	−3.15390e34	−0.443346
$615$	0	0
$616$	−5.40724e33	−0.0729822
$617$	− 6.11422e34i	− 0.808679i	−0.914609	−	0.404340i	$-0.867501\pi$
$617$	− 6.11422e34i	− 0.808679i	0.914609	−	0.404340i	$-0.132499\pi$
$618$	7.43150e34i	0.963208i
$619$	4.66687e34	0.592779	0.296389	−	0.955067i	$-0.404217\pi$
$619$	4.66687e34	0.592779	0.296389	+	0.955067i	$0.404217\pi$
$620$	0	0
$621$	−2.64090e34	−0.322186
$622$	− 6.31848e34i	− 0.755497i
$623$	− 2.65962e34i	− 0.311687i
$624$	4.73685e34	0.544104
$625$	0	0
$626$	6.65672e34	0.734651
$627$	− 2.25125e34i	− 0.243545i
$628$	7.98398e34i	0.846689i
$629$	1.67886e34	0.174535
$630$	0	0
$631$	−7.88083e33	−0.0787417	−0.0393709	−	0.999225i	$-0.512535\pi$
$631$	−7.88083e33	−0.0787417	−0.0393709	+	0.999225i	$0.512535\pi$
$632$	− 2.00378e34i	− 0.196284i
$633$	− 1.81562e35i	− 1.74373i
$634$	9.38386e34	0.883621
$635$	0	0
$636$	−5.89559e34	−0.533720
$637$	− 3.98227e34i	− 0.353499i
$638$	− 1.44898e34i	− 0.126126i
$639$	1.15094e35	0.982408
$640$	0	0
$641$	3.14908e34	0.258499	0.129250	−	0.991612i	$-0.458743\pi$
$641$	3.14908e34	0.258499	0.129250	+	0.991612i	$0.458743\pi$
$642$	1.25570e35i	1.01088i
$643$	8.32480e34i	0.657259i	0.944459	+	0.328630i	$0.106587\pi$
$643$	8.32480e34i	0.657259i	−0.944459	+	0.328630i	$0.893413\pi$
$644$	−5.49320e33	−0.0425356
$645$	0	0
$646$	−3.33922e34	−0.248736
$647$	1.33124e35i	0.972641i	0.873780	+	0.486321i	$0.161661\pi$
$647$	1.33124e35i	0.972641i	−0.873780	+	0.486321i	$0.838339\pi$
$648$	1.65761e35i	1.18794i
$649$	1.07800e34	0.0757809
$650$	0	0
$651$	2.36321e35	1.59860
$652$	− 1.27490e34i	− 0.0846020i
$653$	2.06756e35i	1.34599i	0.739645	+	0.672997i	$0.234993\pi$
$653$	2.06756e35i	1.34599i	−0.739645	+	0.672997i	$0.765007\pi$
$654$	1.18889e35	0.759311
$655$	0	0
$656$	4.46664e34	0.274589
$657$	− 7.83084e34i	− 0.472325i
$658$	− 1.74667e35i	− 1.03368i
$659$	2.57849e35	1.49726	0.748632	−	0.662986i	$-0.230711\pi$
$659$	2.57849e35	1.49726	0.748632	+	0.662986i	$0.230711\pi$
$660$	0	0
$661$	−3.31671e34	−0.185434	−0.0927170	−	0.995692i	$-0.529555\pi$
$661$	−3.31671e34	−0.185434	−0.0927170	+	0.995692i	$0.529555\pi$
$662$	− 1.41394e35i	− 0.775720i
$663$	2.77142e35i	1.49205i
$664$	1.13329e35	0.598745
$665$	0	0
$666$	9.36532e34	0.476535
$667$	− 1.47201e34i	− 0.0735087i
$668$	− 1.68119e35i	− 0.823970i
$669$	−2.03109e35	−0.977016
$670$	0	0
$671$	8.85101e34	0.410168
$672$	6.16426e34i	0.280392i
$673$	− 2.87165e35i	− 1.28216i	−0.767472	−	0.641082i	$-0.778486\pi$
$673$	− 2.87165e35i	− 1.28216i	0.767472	−	0.641082i	$-0.221514\pi$
$674$	2.16160e35	0.947387
$675$	0	0
$676$	3.53722e34	0.149392
$677$	− 3.20244e35i	− 1.32777i	−0.747835	−	0.663885i	$-0.768907\pi$
$677$	− 3.20244e35i	− 1.32777i	0.747835	−	0.663885i	$-0.231093\pi$
$678$	5.01167e35i	2.03991i
$679$	3.06003e35	1.22280
$680$	0	0
$681$	−1.58411e35	−0.610165
$682$	4.68366e34i	0.177125i
$683$	− 4.34050e35i	− 1.61169i	−0.592129	−	0.805843i	$-0.701712\pi$
$683$	− 4.34050e35i	− 1.61169i	0.592129	−	0.805843i	$-0.298288\pi$
$684$	−1.86274e35	−0.679126
$685$	0	0
$686$	2.18895e35	0.769456
$687$	− 6.49388e35i	− 2.24153i
$688$	5.16719e34i	0.175145i
$689$	−1.91372e35	−0.636999
$690$	0	0
$691$	3.59659e35	1.15456	0.577279	−	0.816547i	$-0.304114\pi$
$691$	3.59659e35	1.15456	0.577279	+	0.816547i	$0.304114\pi$
$692$	1.32538e35i	0.417845i
$693$	− 1.76480e35i	− 0.546425i
$694$	−1.80262e34	−0.0548165
$695$	0	0
$696$	−1.65184e35	−0.484565
$697$	2.61333e35i	0.752982i
$698$	1.22089e35i	0.345529i
$699$	−7.22055e34	−0.200727
$700$	0	0
$701$	−4.01671e34	−0.107745	−0.0538723	−	0.998548i	$-0.517156\pi$
$701$	−4.01671e34	−0.107745	−0.0538723	+	0.998548i	$0.517156\pi$
$702$	9.61963e35i	2.53481i
$703$	5.04654e34i	0.130633i
$704$	−1.22170e34	−0.0310674
$705$	0	0
$706$	1.82716e35	0.448454
$707$	− 4.32357e35i	− 1.04256i
$708$	− 1.22892e35i	− 0.291144i
$709$	2.37128e34	0.0551957	0.0275979	−	0.999619i	$-0.491214\pi$
$709$	2.37128e34	0.0551957	0.0275979	+	0.999619i	$0.491214\pi$
$710$	0	0
$711$	6.53988e35	1.46960
$712$	− 6.00907e34i	− 0.132681i
$713$	4.75812e34i	0.103232i
$714$	−3.60657e35	−0.768895
$715$	0	0
$716$	−1.35574e35	−0.279103
$717$	1.14103e36i	2.30839i
$718$	1.79427e35i	0.356724i
$719$	8.41947e35	1.64503	0.822514	−	0.568744i	$-0.192571\pi$
$719$	8.41947e35	1.64503	0.822514	+	0.568744i	$0.192571\pi$
$720$	0	0
$721$	−3.13920e35	−0.592419
$722$	2.80867e35i	0.520938i
$723$	2.96697e35i	0.540859i
$724$	−3.03120e34	−0.0543104
$725$	0	0
$726$	−7.31938e35	−1.26697
$727$	− 8.07486e35i	− 1.37390i	−0.726705	−	0.686950i	$-0.758949\pi$
$727$	− 8.07486e35i	− 1.37390i	0.726705	−	0.686950i	$-0.241051\pi$
$728$	2.00093e35i	0.334650i
$729$	−1.75615e36	−2.88714
$730$	0	0
$731$	−3.02321e35	−0.480287
$732$	− 1.00902e36i	− 1.57583i
$733$	− 9.32041e35i	− 1.43099i	−0.698620	−	0.715493i	$-0.746202\pi$
$733$	− 9.32041e35i	− 1.43099i	0.698620	−	0.715493i	$-0.253798\pi$
$734$	3.18151e35	0.480211
$735$	0	0
$736$	−1.24112e34	−0.0181068
$737$	− 2.24310e35i	− 0.321740i
$738$	1.45781e36i	2.05587i
$739$	9.24490e34	0.128188	0.0640939	−	0.997944i	$-0.479584\pi$
$739$	9.24490e34	0.128188	0.0640939	+	0.997944i	$0.479584\pi$
$740$	0	0
$741$	−8.33068e35	−1.11674
$742$	− 2.49041e35i	− 0.328263i
$743$	3.86129e35i	0.500463i	0.968186	+	0.250232i	$0.0805068\pi$
$743$	3.86129e35i	0.500463i	−0.968186	+	0.250232i	$0.919493\pi$
$744$	5.33938e35	0.680501
$745$	0	0
$746$	−9.71592e35	−1.19743
$747$	3.69882e36i	4.48287i
$748$	− 7.14788e34i	− 0.0851937i
$749$	−5.30431e35	−0.621736
$750$	0	0
$751$	5.31819e35	0.602927	0.301463	−	0.953478i	$-0.402525\pi$
$751$	5.31819e35	0.602927	0.301463	+	0.953478i	$0.402525\pi$
$752$	− 3.94637e35i	− 0.440023i
$753$	4.65889e35i	0.510911i
$754$	−5.36190e35	−0.578332
$755$	0	0
$756$	−1.25184e36	−1.30625
$757$	− 1.46803e36i	− 1.50674i	−0.657599	−	0.753368i	$-0.728428\pi$
$757$	− 1.46803e36i	− 1.50674i	0.657599	−	0.753368i	$-0.271572\pi$
$758$	− 5.69116e35i	− 0.574560i
$759$	4.89561e34	0.0486166
$760$	0	0
$761$	1.26153e36	1.21225	0.606123	−	0.795371i	$-0.292724\pi$
$761$	1.26153e36	1.21225	0.606123	+	0.795371i	$0.292724\pi$
$762$	4.45641e35i	0.421257i
$763$	5.02210e35i	0.467012i
$764$	8.27269e35	0.756798
$765$	0	0
$766$	−1.55273e35	−0.137479
$767$	− 3.98910e35i	− 0.347482i
$768$	1.39274e35i	0.119358i
$769$	9.78483e35	0.825039	0.412519	−	0.910949i	$-0.364649\pi$
$769$	9.78483e35	0.825039	0.412519	+	0.910949i	$0.364649\pi$
$770$	0	0
$771$	1.96165e36	1.60119
$772$	− 2.38980e35i	− 0.191931i
$773$	− 1.97217e36i	− 1.55848i	−0.626728	−	0.779238i	$-0.715606\pi$
$773$	− 1.97217e36i	− 1.55848i	0.626728	−	0.779238i	$-0.284394\pi$
$774$	−1.68646e36	−1.31133
$775$	0	0
$776$	6.91375e35	0.520526
$777$	5.45059e35i	0.403813i
$778$	− 9.01978e35i	− 0.657583i
$779$	−7.85547e35	−0.563578
$780$	0	0
$781$	−1.32757e35	−0.0922398
$782$	− 7.26151e34i	− 0.0496527i
$783$	− 3.35457e36i	− 2.25743i
$784$	1.17087e35	0.0775459
$785$	0	0
$786$	−1.00575e36	−0.645222
$787$	2.25189e35i	0.142188i	0.997470	+	0.0710940i	$0.0226490\pi$
$787$	2.25189e35i	0.142188i	−0.997470	+	0.0710940i	$0.977351\pi$
$788$	6.02424e35i	0.374390i
$789$	−2.70224e36	−1.65295
$790$	0	0
$791$	−2.11702e36	−1.25464
$792$	− 3.98735e35i	− 0.232605i
$793$	− 3.27529e36i	− 1.88077i
$794$	−8.96781e35	−0.506909
$795$	0	0
$796$	−1.36230e36	−0.746209
$797$	− 3.69113e36i	− 1.99035i	−0.0980978	−	0.995177i	$-0.531276\pi$
$797$	− 3.69113e36i	− 1.99035i	0.0980978	−	0.995177i	$-0.468724\pi$
$798$	− 1.08411e36i	− 0.575488i
$799$	2.30893e36	1.20664
$800$	0	0
$801$	1.96123e36	0.993393
$802$	− 1.22485e36i	− 0.610806i
$803$	9.03258e34i	0.0443473i
$804$	−2.55713e36	−1.23610
$805$	0	0
$806$	1.73317e36	0.812184
$807$	− 4.12420e36i	− 1.90292i
$808$	− 9.76854e35i	− 0.443800i
$809$	2.93815e36	1.31437	0.657185	−	0.753730i	$-0.271747\pi$
$809$	2.93815e36	1.31437	0.657185	+	0.753730i	$0.271747\pi$
$810$	0	0
$811$	−2.44583e36	−1.06088	−0.530439	−	0.847723i	$-0.677973\pi$
$811$	−2.44583e36	−1.06088	−0.530439	+	0.847723i	$0.677973\pi$
$812$	− 6.97767e35i	− 0.298030i
$813$	− 2.71729e36i	− 1.14289i
$814$	−1.08025e35	−0.0447426
$815$	0	0
$816$	−8.14859e35	−0.327307
$817$	− 9.08753e35i	− 0.359476i
$818$	2.91771e35i	0.113665i
$819$	−6.53060e36	−2.50556
$820$	0	0
$821$	3.33815e36	1.24227	0.621136	−	0.783703i	$-0.286672\pi$
$821$	3.33815e36	1.24227	0.621136	+	0.783703i	$0.286672\pi$
$822$	4.98560e36i	1.82734i
$823$	2.54036e36i	0.917058i	0.888679	+	0.458529i	$0.151623\pi$
$823$	2.54036e36i	0.917058i	−0.888679	+	0.458529i	$0.848377\pi$
$824$	−7.09263e35	−0.252184
$825$	0	0
$826$	5.19119e35	0.179067
$827$	3.63276e36i	1.23429i	0.786849	+	0.617146i	$0.211711\pi$
$827$	3.63276e36i	1.23429i	−0.786849	+	0.617146i	$0.788289\pi$
$828$	− 4.05074e35i	− 0.135567i
$829$	−1.07727e36	−0.355135	−0.177567	−	0.984109i	$-0.556823\pi$
$829$	−1.07727e36	−0.355135	−0.177567	+	0.984109i	$0.556823\pi$
$830$	0	0
$831$	−2.13782e36	−0.683847
$832$	4.52085e35i	0.142455i
$833$	6.85052e35i	0.212648i
$834$	5.80833e36	1.77613
$835$	0	0
$836$	2.14860e35	0.0637641
$837$	1.08433e37i	3.17024i
$838$	1.20611e36i	0.347407i
$839$	2.96808e36	0.842269	0.421134	−	0.906998i	$-0.361632\pi$
$839$	2.96808e36	0.842269	0.421134	+	0.906998i	$0.361632\pi$
$840$	0	0
$841$	−1.76056e36	−0.484953
$842$	− 4.17349e36i	− 1.13266i
$843$	8.96316e36i	2.39671i
$844$	1.73283e36	0.456537
$845$	0	0
$846$	1.28801e37	3.29450
$847$	− 3.09185e36i	− 0.779247i
$848$	− 5.62676e35i	− 0.139737i
$849$	2.74735e36	0.672308
$850$	0	0
$851$	−1.09743e35	−0.0260769
$852$	1.51343e36i	0.354378i
$853$	6.13786e36i	1.41630i	0.706064	+	0.708148i	$0.250469\pi$
$853$	6.13786e36i	1.41630i	−0.706064	+	0.708148i	$0.749531\pi$
$854$	4.26227e36	0.969210
$855$	0	0
$856$	−1.19844e36	−0.264664
$857$	− 3.16481e36i	− 0.688791i	−0.938825	−	0.344395i	$-0.888084\pi$
$857$	− 3.16481e36i	− 0.688791i	0.938825	−	0.344395i	$-0.111916\pi$
$858$	− 1.78325e36i	− 0.382492i
$859$	−5.65370e36	−1.19514	−0.597569	−	0.801818i	$-0.703866\pi$
$859$	−5.65370e36	−1.19514	−0.597569	+	0.801818i	$0.703866\pi$
$860$	0	0
$861$	−8.48442e36	−1.74214
$862$	2.78322e36i	0.563257i
$863$	− 8.00828e36i	− 1.59736i	−0.601753	−	0.798682i	$-0.705531\pi$
$863$	− 8.00828e36i	− 1.59736i	0.601753	−	0.798682i	$-0.294469\pi$
$864$	−2.82838e36	−0.556053
$865$	0	0
$866$	−2.96617e36	−0.566530
$867$	5.37651e36i	1.01219i
$868$	2.25545e36i	0.418540i
$869$	−7.54351e35	−0.137983
$870$	0	0
$871$	−8.30052e36	−1.47529
$872$	1.13468e36i	0.198800i
$873$	2.25649e37i	3.89723i
$874$	2.18275e35	0.0371631
$875$	0	0
$876$	1.02971e36	0.170379
$877$	− 3.29560e36i	− 0.537575i	−0.963199	−	0.268788i	$-0.913377\pi$
$877$	− 3.29560e36i	− 0.537575i	0.963199	−	0.268788i	$-0.0866230\pi$
$878$	− 3.74153e36i	− 0.601683i
$879$	7.33233e36	1.16247
$880$	0	0
$881$	−8.05386e36	−1.24109	−0.620547	−	0.784169i	$-0.713090\pi$
$881$	−8.05386e36	−1.24109	−0.620547	+	0.784169i	$0.713090\pi$
$882$	3.82147e36i	0.580595i
$883$	− 4.91849e35i	− 0.0736754i	−0.999321	−	0.0368377i	$-0.988272\pi$
$883$	− 4.91849e35i	− 0.0736754i	0.999321	−	0.0368377i	$-0.0117285\pi$
$884$	−2.64505e36	−0.390644
$885$	0	0
$886$	−1.44406e36	−0.207331
$887$	− 7.79484e36i	− 1.10347i	−0.834018	−	0.551737i	$-0.813965\pi$
$887$	− 7.79484e36i	− 1.10347i	0.834018	−	0.551737i	$-0.186035\pi$
$888$	1.23149e36i	0.171897i
$889$	−1.88247e36	−0.259093
$890$	0	0
$891$	6.24031e36	0.835093
$892$	− 1.93847e36i	− 0.255799i
$893$	6.94048e36i	0.903121i
$894$	3.05319e36	0.391774
$895$	0	0
$896$	−5.88318e35	−0.0734111
$897$	− 1.81160e36i	− 0.222924i
$898$	1.51928e36i	0.184367i
$899$	−6.04394e36	−0.723309
$900$	0	0
$901$	3.29209e36	0.383188
$902$	− 1.68153e36i	− 0.193029i
$903$	− 9.81513e36i	− 1.11122i
$904$	−4.78314e36	−0.534082
$905$	0	0
$906$	1.81002e37	1.96599
$907$	1.31417e37i	1.40786i	0.710268	+	0.703932i	$0.248574\pi$
$907$	1.31417e37i	1.40786i	−0.710268	+	0.703932i	$0.751426\pi$
$908$	− 1.51188e36i	− 0.159751i
$909$	3.18823e37	3.32278
$910$	0	0
$911$	1.44767e37	1.46788	0.733940	−	0.679214i	$-0.237679\pi$
$911$	1.44767e37	1.46788	0.733940	+	0.679214i	$0.237679\pi$
$912$	− 2.44940e36i	− 0.244977i
$913$	− 4.26645e36i	− 0.420903i
$914$	−7.24821e36	−0.705347
$915$	0	0
$916$	6.19776e36	0.586869
$917$	− 4.24848e36i	− 0.396842i
$918$	− 1.65482e37i	− 1.52482i
$919$	1.03191e37	0.937990	0.468995	−	0.883201i	$-0.344616\pi$
$919$	1.03191e37	0.937990	0.468995	+	0.883201i	$0.344616\pi$
$920$	0	0
$921$	1.35356e37	1.19738
$922$	− 2.87137e36i	− 0.250584i
$923$	4.91262e36i	0.422953i
$924$	2.32062e36	0.197108
$925$	0	0
$926$	−3.77045e36	−0.311714
$927$	− 2.31487e37i	− 1.88813i
$928$	− 1.57651e36i	− 0.126867i
$929$	2.17912e37	1.73015	0.865075	−	0.501642i	$-0.167271\pi$
$929$	2.17912e37	1.73015	0.865075	+	0.501642i	$0.167271\pi$
$930$	0	0
$931$	−2.05921e36	−0.159159
$932$	− 6.89130e35i	− 0.0525536i
$933$	2.71170e37i	2.04043i
$934$	7.56121e36	0.561378
$935$	0	0
$936$	−1.47550e37	−1.06658
$937$	2.08020e37i	1.48375i	0.670540	+	0.741873i	$0.266062\pi$
$937$	2.08020e37i	1.48375i	−0.670540	+	0.741873i	$0.733938\pi$
$938$	− 1.08018e37i	− 0.760258i
$939$	−2.85686e37	−1.98413
$940$	0	0
$941$	2.39454e37	1.61939	0.809695	−	0.586851i	$-0.199632\pi$
$941$	2.39454e37	1.61939	0.809695	+	0.586851i	$0.199632\pi$
$942$	− 3.42648e37i	− 2.28672i
$943$	− 1.70826e36i	− 0.112501i
$944$	1.17288e36	0.0762262
$945$	0	0
$946$	1.94526e36	0.123123
$947$	8.06134e36i	0.503539i	0.967787	+	0.251769i	$0.0810124\pi$
$947$	8.06134e36i	0.503539i	−0.967787	+	0.251769i	$0.918988\pi$
$948$	8.59960e36i	0.530120i
$949$	3.34248e36	0.203348
$950$	0	0
$951$	−4.02727e37	−2.38646
$952$	− 3.44212e36i	− 0.201309i
$953$	− 1.92589e37i	− 1.11166i	−0.831297	−	0.555829i	$-0.812401\pi$
$953$	− 1.92589e37i	− 1.11166i	0.831297	−	0.555829i	$-0.187599\pi$
$954$	1.83645e37	1.04622
$955$	0	0
$956$	−1.08900e37	−0.604374
$957$	6.21858e36i	0.340637i
$958$	− 1.59122e36i	− 0.0860321i
$959$	−2.10601e37	−1.12390
$960$	0	0
$961$	3.03575e35	0.0157842
$962$	3.99745e36i	0.205161i
$963$	− 3.91144e37i	− 1.98157i
$964$	−2.83168e36	−0.141606
$965$	0	0
$966$	2.35752e36	0.114879
$967$	− 2.29324e37i	− 1.10311i	−0.834139	−	0.551554i	$-0.814035\pi$
$967$	− 2.29324e37i	− 1.10311i	0.834139	−	0.551554i	$-0.185965\pi$
$968$	− 6.98563e36i	− 0.331714i
$969$	1.43309e37	0.671779
$970$	0	0
$971$	2.10199e37	0.960265	0.480132	−	0.877196i	$-0.340589\pi$
$971$	2.10199e37	0.960265	0.480132	+	0.877196i	$0.340589\pi$
$972$	− 3.62665e37i	− 1.63560i
$973$	2.45355e37i	1.09241i
$974$	−1.74531e37	−0.767161
$975$	0	0
$976$	9.63006e36	0.412578
$977$	3.52592e37i	1.49139i	0.666289	+	0.745694i	$0.267882\pi$
$977$	3.52592e37i	1.49139i	−0.666289	+	0.745694i	$0.732118\pi$
$978$	5.47148e36i	0.228491i
$979$	−2.26220e36	−0.0932712
$980$	0	0
$981$	−3.70334e37	−1.48844
$982$	1.85363e37i	0.735581i
$983$	7.31962e36i	0.286794i	0.989665	+	0.143397i	$0.0458025\pi$
$983$	7.31962e36i	0.286794i	−0.989665	+	0.143397i	$0.954197\pi$
$984$	−1.91694e37	−0.741602
$985$	0	0
$986$	9.22384e36	0.347897
$987$	7.49617e37i	2.79174i
$988$	− 7.95081e36i	− 0.292381i
$989$	1.97619e36	0.0717587
$990$	0	0
$991$	1.16985e37	0.414200	0.207100	−	0.978320i	$-0.433597\pi$
$991$	1.16985e37	0.414200	0.207100	+	0.978320i	$0.433597\pi$
$992$	5.09591e36i	0.178166i
$993$	6.06819e37i	2.09504i
$994$	−6.39300e36	−0.217959
$995$	0	0
$996$	−4.86376e37	−1.61708
$997$	− 2.33411e37i	− 0.766358i	−0.923674	−	0.383179i	$-0.874829\pi$
$997$	− 2.33411e37i	− 0.766358i	0.923674	−	0.383179i	$-0.125171\pi$
$998$	1.82280e37i	0.591028i
$999$	−2.50092e37	−0.800814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.b.e.49.2		4
5.2	odd	4		2.26.a.b.1.2	✓	2
5.3	odd	4		50.26.a.c.1.1		2
5.4	even	2	inner	50.26.b.e.49.3		4
15.2	even	4		18.26.a.e.1.2		2
20.7	even	4		16.26.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.26.a.b.1.2	✓	2	5.2	odd	4
16.26.a.c.1.1		2	20.7	even	4
18.26.a.e.1.2		2	15.2	even	4
50.26.a.c.1.1		2	5.3	odd	4
50.26.b.e.49.2		4	1.1	even	1	trivial
50.26.b.e.49.3		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-4096.00i q^{2} +1.75788e6i q^{3} -1.67772e7 q^{4} +7.20027e9 q^{6} +3.04153e10i q^{7} +6.87195e10i q^{8} -2.24285e12 q^{9} +2.58704e12 q^{11} -2.94923e13i q^{12} -9.57327e13i q^{13} +1.24581e14 q^{14} +2.81475e14 q^{16} +1.64685e15i q^{17} +9.18671e15i q^{18} -4.95030e15 q^{19} -5.34664e16 q^{21} -1.05965e16i q^{22} -1.07650e16i q^{23} -1.20801e17 q^{24} -3.92121e17 q^{26} -2.45323e18i q^{27} -5.10284e17i q^{28} +1.36741e18 q^{29} -4.42000e18 q^{31} -1.15292e18i q^{32} +4.54771e18i q^{33} +6.74549e18 q^{34} +3.76288e19 q^{36} -1.01944e19i q^{37} +2.02764e19i q^{38} +1.68287e20 q^{39} +1.58687e20 q^{41} +2.18999e20i q^{42} +1.83575e20i q^{43} -4.34034e19 q^{44} -4.40934e19 q^{46} -1.40203e21i q^{47} +4.94799e20i q^{48} +4.15978e20 q^{49} -2.89496e21 q^{51} +1.60613e21i q^{52} -1.99903e21i q^{53} -1.00484e22 q^{54} -2.09012e21 q^{56} -8.70202e21i q^{57} -5.60091e21i q^{58} +4.16691e21 q^{59} +3.42128e22 q^{61} +1.81043e22i q^{62} -6.82170e22i q^{63} -4.72237e21 q^{64} +1.86274e22 q^{66} -8.67051e22i q^{67} -2.76295e22i q^{68} +1.89236e22 q^{69} -5.13159e22 q^{71} -1.54128e23i q^{72} +3.49147e22i q^{73} -4.17563e22 q^{74} +8.30522e22 q^{76} +7.86857e22i q^{77} -6.89302e23i q^{78} -2.91588e23 q^{79} +2.41214e24 q^{81} -6.49981e23i q^{82} -1.64916e24i q^{83} +8.97018e23 q^{84} +7.51925e23 q^{86} +2.40374e24i q^{87} +1.77780e23i q^{88} -8.74435e23 q^{89} +2.91174e24 q^{91} +1.80607e23i q^{92} -7.76982e24i q^{93} -5.74273e24 q^{94} +2.02670e24 q^{96} -1.00608e25i q^{97} -1.70384e24i q^{98} -5.80235e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 67108864 q^{4} + 3111714816 q^{6} - 6589062865332 q^{9} + 16646069220528 q^{11} + 3084590645248 q^{14} + 11\!\cdots\!24 q^{16} + 954158485898800 q^{19} - 18\!\cdots\!12 q^{21} - 52\!\cdots\!56 q^{24}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 67108864 * q^4 + 3111714816 * q^6 - 6589062865332 * q^9 + 16646069220528 * q^11 + 3084590645248 * q^14 + 1125899906842624 * q^16 + 954158485898800 * q^19 - 189721583323504512 * q^21 - 52205911598432256 * q^24 - 872178099423576064 * q^26 - 3448825290412871160 * q^29 - 17376164576702253952 * q^31 - 10877984113573527552 * q^34 + 110546130929253875712 * q^36 + 306988747670662211616 * q^39 + 166028648711906937768 * q^41 - 279274698863749890048 * q^44 - 944578771201833959424 * q^46 + 1709437286023947544092 * q^49 - 13988451985175107641312 * q^51 - 17789497812624611082240 * q^54 - 51750843526905069568 * q^56 + 34827350861264098907280 * q^59 + 67951719906180425620088 * q^61 - 18889465931478580854784 * q^64 - 27497776775209124364288 * q^66 - 250271736165096773468544 * q^69 - 556696016291201627231712 * q^71 + 285969318295553396604928 * q^74 - 16008123016157121740800 * q^76 - 1857092364577563295634240 * q^79 + 3818391604963344095456484 * q^81 + 3182999983280433074798592 * q^84 + 364868473515801819938816 * q^86 + 4693808359348401402489240 * q^89 + 5178590528892421167475648 * q^91 - 15313803116991894321364992 * q^94 + 875869855363803220279296 * q^96 - 23669571375888625607683824 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more