LMFDB - Embedded newform 25.18.b.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,18,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	25.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:	$45.8055218361$
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 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.18.b.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-528.000i q^{2} +4284.00i q^{3} -147712. q^{4} +2.26195e6 q^{6} +3.22599e6i q^{7} +8.78592e6i q^{8} +1.10788e8 q^{9} +O(q^{10})$	\(q-528.000i q^{2} +4284.00i q^{3} -147712. q^{4} +2.26195e6 q^{6} +3.22599e6i q^{7} +8.78592e6i q^{8} +1.10788e8 q^{9} -7.53618e8 q^{11} -6.32798e8i q^{12} -2.54106e9i q^{13} +1.70332e9 q^{14} -1.47219e10 q^{16} -5.42974e9i q^{17} -5.84958e10i q^{18} -1.48750e9 q^{19} -1.38201e10 q^{21} +3.97910e11i q^{22} +3.17092e11i q^{23} -3.76389e10 q^{24} -1.34168e12 q^{26} +1.02785e12i q^{27} -4.76518e11i q^{28} -2.43341e12 q^{29} -8.84972e12 q^{31} +8.92477e12i q^{32} -3.22850e12i q^{33} -2.86690e12 q^{34} -1.63646e13 q^{36} +1.26917e13i q^{37} +7.85400e11i q^{38} +1.08859e13 q^{39} +4.88642e13 q^{41} +7.29704e12i q^{42} +9.10200e13i q^{43} +1.11318e14 q^{44} +1.67424e14 q^{46} -4.93050e13i q^{47} -6.30688e13i q^{48} +2.22223e14 q^{49} +2.32610e13 q^{51} +3.75346e14i q^{52} -2.29405e13i q^{53} +5.42705e14 q^{54} -2.83433e13 q^{56} -6.37245e12i q^{57} +1.28484e15i q^{58} -3.26951e13 q^{59} -1.30829e15 q^{61} +4.67265e15i q^{62} +3.57400e14i q^{63} +2.78265e15 q^{64} -1.70465e15 q^{66} +5.19614e15i q^{67} +8.02038e14i q^{68} -1.35842e15 q^{69} -3.70949e15 q^{71} +9.73370e14i q^{72} -3.40237e15i q^{73} +6.70119e15 q^{74} +2.19722e14 q^{76} -2.43117e15i q^{77} -5.74777e15i q^{78} -2.36653e15 q^{79} +9.90381e15 q^{81} -2.58003e16i q^{82} +2.97668e16i q^{83} +2.04140e15 q^{84} +4.80585e16 q^{86} -1.04247e16i q^{87} -6.62123e15i q^{88} -2.91672e16 q^{89} +8.19745e15 q^{91} -4.68383e16i q^{92} -3.79122e16i q^{93} -2.60330e16 q^{94} -3.82337e16 q^{96} -6.37699e16i q^{97} -1.17334e17i q^{98} -8.34915e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 295424 q^{4} + 4523904 q^{6} + 221575014 q^{9}+O(q^{10}) $ 2 * q - 295424 * q^4 + 4523904 * q^6 + 221575014 * q^9	$ 2 q - 295424 q^{4} + 4523904 q^{6} + 221575014 q^{9} - 1507236456 q^{11} + 3406647552 q^{14} - 29443883008 q^{16} - 2974999720 q^{19} - 27640299456 q^{21} - 75277762560 q^{24} - 2683364139456 q^{26} - 4866821205180 q^{29} - 17699444106176 q^{31} - 5733807887808 q^{34} - 32729288467968 q^{36} + 21771840858768 q^{39} + 97728302004564 q^{41} + 222636911388672 q^{44} + 334848965577984 q^{46} + 444446979206286 q^{49} + 46522032180624 q^{51} + 10\!\cdots\!80 q^{54}+ \cdots - 16\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q - 295424 * q^4 + 4523904 * q^6 + 221575014 * q^9 - 1507236456 * q^11 + 3406647552 * q^14 - 29443883008 * q^16 - 2974999720 * q^19 - 27640299456 * q^21 - 75277762560 * q^24 - 2683364139456 * q^26 - 4866821205180 * q^29 - 17699444106176 * q^31 - 5733807887808 * q^34 - 32729288467968 * q^36 + 21771840858768 * q^39 + 97728302004564 * q^41 + 222636911388672 * q^44 + 334848965577984 * q^46 + 444446979206286 * q^49 + 46522032180624 * q^51 + 1085409746023680 * q^54 - 56686615265280 * q^56 - 65390181459960 * q^59 - 2616571709738756 * q^61 + 5565291887067136 * q^64 - 3409296516122112 * q^66 - 2716842743439552 * q^69 - 7418979754824816 * q^71 + 13402385511675072 * q^74 + 439443158640640 * q^76 - 4733067882616480 * q^79 + 19807613439904242 * q^81 + 4082803913244672 * q^84 + 96117092879643264 * q^86 - 58334368201148340 * q^89 + 16394907664719584 * q^91 - 52066073955506688 * q^94 - 76467456951975936 * q^96 - 166982969419755192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 528.000i	− 1.45841i	−0.684297	−	0.729204i	$-0.739891\pi$
$2$	− 528.000i	− 1.45841i	0.684297	−	0.729204i	$-0.260109\pi$
$3$	4284.00i	0.376980i	0.982075	+	0.188490i	$0.0603594\pi$
$3$	4284.00i	0.376980i	−0.982075	+	0.188490i	$0.939641\pi$
$4$	−147712.	−1.12695
$5$	0	0
$5$	0	0
$6$	2.26195e6	0.549791
$7$	3.22599e6i	0.211510i	0.994392	+	0.105755i	$0.0337259\pi$
$7$	3.22599e6i	0.211510i	−0.994392	+	0.105755i	$0.966274\pi$
$8$	8.78592e6i	0.185149i
$9$	1.10788e8	0.857886
$10$	0	0
$11$	−7.53618e8	−1.06002	−0.530009	−	0.847992i	$-0.677812\pi$
$11$	−7.53618e8	−1.06002	−0.530009	+	0.847992i	$0.677812\pi$
$12$	− 6.32798e8i	− 0.424839i
$13$	− 2.54106e9i	− 0.863967i	−0.901881	−	0.431984i	$-0.857814\pi$
$13$	− 2.54106e9i	− 0.863967i	0.901881	−	0.431984i	$-0.142186\pi$
$14$	1.70332e9	0.308467
$15$	0	0
$16$	−1.47219e10	−0.856930
$17$	− 5.42974e9i	− 0.188783i	−0.995535	−	0.0943916i	$-0.969909\pi$
$17$	− 5.42974e9i	− 0.188783i	0.995535	−	0.0943916i	$-0.0300906\pi$
$18$	− 5.84958e10i	− 1.25115i
$19$	−1.48750e9	−0.0200933	−0.0100467	−	0.999950i	$-0.503198\pi$
$19$	−1.48750e9	−0.0200933	−0.0100467	+	0.999950i	$0.503198\pi$
$20$	0	0
$21$	−1.38201e10	−0.0797350
$22$	3.97910e11i	1.54594i
$23$	3.17092e11i	0.844303i	0.906525	+	0.422152i	$0.138725\pi$
$23$	3.17092e11i	0.844303i	−0.906525	+	0.422152i	$0.861275\pi$
$24$	−3.76389e10	−0.0697977
$25$	0	0
$26$	−1.34168e12	−1.26002
$27$	1.02785e12i	0.700387i
$28$	− 4.76518e11i	− 0.238361i
$29$	−2.43341e12	−0.903301	−0.451650	−	0.892195i	$-0.649165\pi$
$29$	−2.43341e12	−0.903301	−0.451650	+	0.892195i	$0.649165\pi$
$30$	0	0
$31$	−8.84972e12	−1.86361	−0.931805	−	0.362958i	$-0.881767\pi$
$31$	−8.84972e12	−1.86361	−0.931805	+	0.362958i	$0.881767\pi$
$32$	8.92477e12i	1.43490i
$33$	− 3.22850e12i	− 0.399606i
$34$	−2.86690e12	−0.275323
$35$	0	0
$36$	−1.63646e13	−0.966797
$37$	1.26917e13i	0.594023i	0.954874	+	0.297012i	$0.0959900\pi$
$37$	1.26917e13i	0.594023i	−0.954874	+	0.297012i	$0.904010\pi$
$38$	7.85400e11i	0.0293042i
$39$	1.08859e13	0.325699
$40$	0	0
$41$	4.88642e13	0.955713	0.477857	−	0.878438i	$-0.341414\pi$
$41$	4.88642e13	0.955713	0.477857	+	0.878438i	$0.341414\pi$
$42$	7.29704e12i	0.116286i
$43$	9.10200e13i	1.18756i	0.804628	+	0.593779i	$0.202365\pi$
$43$	9.10200e13i	1.18756i	−0.804628	+	0.593779i	$0.797635\pi$
$44$	1.11318e14	1.19459
$45$	0	0
$46$	1.67424e14	1.23134
$47$	− 4.93050e13i	− 0.302036i	−0.988531	−	0.151018i	$-0.951745\pi$
$47$	− 4.93050e13i	− 0.302036i	0.988531	−	0.151018i	$-0.0482552\pi$
$48$	− 6.30688e13i	− 0.323046i
$49$	2.22223e14	0.955264
$50$	0	0
$51$	2.32610e13	0.0711676
$52$	3.75346e14i	0.973650i
$53$	− 2.29405e13i	− 0.0506124i	−0.999680	−	0.0253062i	$-0.991944\pi$
$53$	− 2.29405e13i	− 0.0506124i	0.999680	−	0.0253062i	$-0.00805608\pi$
$54$	5.42705e14	1.02145
$55$	0	0
$56$	−2.83433e13	−0.0391609
$57$	− 6.37245e12i	− 0.00757478i
$58$	1.28484e15i	1.31738i
$59$	−3.26951e13	−0.0289895	−0.0144947	−	0.999895i	$-0.504614\pi$
$59$	−3.26951e13	−0.0289895	−0.0144947	+	0.999895i	$0.504614\pi$
$60$	0	0
$61$	−1.30829e15	−0.873774	−0.436887	−	0.899516i	$-0.643919\pi$
$61$	−1.30829e15	−0.873774	−0.436887	+	0.899516i	$0.643919\pi$
$62$	4.67265e15i	2.71790i
$63$	3.57400e14i	0.181451i
$64$	2.78265e15	1.23574
$65$	0	0
$66$	−1.70465e15	−0.582789
$67$	5.19614e15i	1.56331i	0.623711	+	0.781655i	$0.285624\pi$
$67$	5.19614e15i	1.56331i	−0.623711	+	0.781655i	$0.714376\pi$
$68$	8.02038e14i	0.212750i
$69$	−1.35842e15	−0.318286
$70$	0	0
$71$	−3.70949e15	−0.681739	−0.340870	−	0.940111i	$-0.610721\pi$
$71$	−3.70949e15	−0.681739	−0.340870	+	0.940111i	$0.610721\pi$
$72$	9.73370e14i	0.158837i
$73$	− 3.40237e15i	− 0.493785i	−0.969043	−	0.246892i	$-0.920591\pi$
$73$	− 3.40237e15i	− 0.493785i	0.969043	−	0.246892i	$-0.0794094\pi$
$74$	6.70119e15	0.866328
$75$	0	0
$76$	2.19722e14	0.0226442
$77$	− 2.43117e15i	− 0.224204i
$78$	− 5.74777e15i	− 0.475001i
$79$	−2.36653e15	−0.175502	−0.0877511	−	0.996142i	$-0.527968\pi$
$79$	−2.36653e15	−0.175502	−0.0877511	+	0.996142i	$0.527968\pi$
$80$	0	0
$81$	9.90381e15	0.593854
$82$	− 2.58003e16i	− 1.39382i
$83$	2.97668e16i	1.45067i	0.688398	+	0.725333i	$0.258314\pi$
$83$	2.97668e16i	1.45067i	−0.688398	+	0.725333i	$0.741686\pi$
$84$	2.04140e15	0.0898576
$85$	0	0
$86$	4.80585e16	1.73194
$87$	− 1.04247e16i	− 0.340527i
$88$	− 6.62123e15i	− 0.196262i
$89$	−2.91672e16	−0.785379	−0.392690	−	0.919671i	$-0.628455\pi$
$89$	−2.91672e16	−0.785379	−0.392690	+	0.919671i	$0.628455\pi$
$90$	0	0
$91$	8.19745e15	0.182737
$92$	− 4.68383e16i	− 0.951490i
$93$	− 3.79122e16i	− 0.702545i
$94$	−2.60330e16	−0.440492
$95$	0	0
$96$	−3.82337e16	−0.540930
$97$	− 6.37699e16i	− 0.826144i	−0.910698	−	0.413072i	$-0.864456\pi$
$97$	− 6.37699e16i	− 0.826144i	0.910698	−	0.413072i	$-0.135544\pi$
$98$	− 1.17334e17i	− 1.39316i
$99$	−8.34915e16	−0.909375
$100$	0	0
$101$	−1.60611e17	−1.47586	−0.737929	−	0.674878i	$-0.764196\pi$
$101$	−1.60611e17	−1.47586	−0.737929	+	0.674878i	$0.764196\pi$
$102$	− 1.22818e16i	− 0.103791i
$103$	9.07136e16i	0.705596i	0.935700	+	0.352798i	$0.114770\pi$
$103$	9.07136e16i	0.705596i	−0.935700	+	0.352798i	$0.885230\pi$
$104$	2.23256e16	0.159963
$105$	0	0
$106$	−1.21126e16	−0.0738135
$107$	1.95549e17i	1.10026i	0.835080	+	0.550129i	$0.185421\pi$
$107$	1.95549e17i	1.10026i	−0.835080	+	0.550129i	$0.814579\pi$
$108$	− 1.51826e17i	− 0.789303i
$109$	−2.13756e17	−1.02753	−0.513763	−	0.857932i	$-0.671749\pi$
$109$	−2.13756e17	−1.02753	−0.513763	+	0.857932i	$0.671749\pi$
$110$	0	0
$111$	−5.43710e16	−0.223935
$112$	− 4.74929e16i	− 0.181249i
$113$	2.81383e17i	0.995706i	0.867262	+	0.497853i	$0.165878\pi$
$113$	2.81383e17i	0.995706i	−0.867262	+	0.497853i	$0.834122\pi$
$114$	−3.36465e15	−0.0110471
$115$	0	0
$116$	3.59444e17	1.01798
$117$	− 2.81518e17i	− 0.741185i
$118$	1.72630e16i	0.0422785i
$119$	1.75163e16	0.0399295
$120$	0	0
$121$	6.24934e16	0.123640
$122$	6.90775e17i	1.27432i
$123$	2.09334e17i	0.360285i
$124$	1.30721e18	2.10020
$125$	0	0
$126$	1.88707e17	0.264630
$127$	− 8.70305e17i	− 1.14114i	−0.821248	−	0.570571i	$-0.806722\pi$
$127$	− 8.70305e17i	− 1.14114i	0.821248	−	0.570571i	$-0.193278\pi$
$128$	− 2.99449e17i	− 0.367315i
$129$	−3.89930e17	−0.447686
$130$	0	0
$131$	1.31783e17	0.132756	0.0663781	−	0.997795i	$-0.478856\pi$
$131$	1.31783e17	0.132756	0.0663781	+	0.997795i	$0.478856\pi$
$132$	4.76888e17i	0.450338i
$133$	− 4.79866e15i	− 0.00424993i
$134$	2.74356e18	2.27994
$135$	0	0
$136$	4.77053e16	0.0349531
$137$	1.87128e18i	1.28829i	0.764902	+	0.644147i	$0.222787\pi$
$137$	1.87128e18i	1.28829i	−0.764902	+	0.644147i	$0.777213\pi$
$138$	7.17246e17i	0.464190i
$139$	−1.58706e18	−0.965980	−0.482990	−	0.875626i	$-0.660449\pi$
$139$	−1.58706e18	−0.965980	−0.482990	+	0.875626i	$0.660449\pi$
$140$	0	0
$141$	2.11223e17	0.113862
$142$	1.95861e18i	0.994254i
$143$	1.91499e18i	0.915821i
$144$	−1.63101e18	−0.735148
$145$	0	0
$146$	−1.79645e18	−0.720139
$147$	9.52005e17i	0.360116i
$148$	− 1.87471e18i	− 0.669436i
$149$	4.77240e17	0.160936	0.0804680	−	0.996757i	$-0.474359\pi$
$149$	4.77240e17	0.160936	0.0804680	+	0.996757i	$0.474359\pi$
$150$	0	0
$151$	−3.92964e18	−1.18317	−0.591587	−	0.806241i	$-0.701499\pi$
$151$	−3.92964e18	−1.18317	−0.591587	+	0.806241i	$0.701499\pi$
$152$	− 1.30691e16i	− 0.00372026i
$153$	− 6.01548e17i	− 0.161954i
$154$	−1.28366e18	−0.326981
$155$	0	0
$156$	−1.60798e18	−0.367047
$157$	− 2.29453e18i	− 0.496075i	−0.968750	−	0.248038i	$-0.920214\pi$
$157$	− 2.29453e18i	− 0.496075i	0.968750	−	0.248038i	$-0.0797856\pi$
$158$	1.24953e18i	0.255954i
$159$	9.82769e16	0.0190799
$160$	0	0
$161$	−1.02294e18	−0.178578
$162$	− 5.22921e18i	− 0.866081i
$163$	− 8.01044e18i	− 1.25910i	−0.776958	−	0.629552i	$-0.783238\pi$
$163$	− 8.01044e18i	− 1.25910i	0.776958	−	0.629552i	$-0.216762\pi$
$164$	−7.21782e18	−1.07704
$165$	0	0
$166$	1.57168e19	2.11566
$167$	− 8.61477e18i	− 1.10193i	−0.834528	−	0.550965i	$-0.814260\pi$
$167$	− 8.61477e18i	− 1.10193i	0.834528	−	0.550965i	$-0.185740\pi$
$168$	− 1.21423e17i	− 0.0147629i
$169$	2.19341e18	0.253561
$170$	0	0
$171$	−1.64796e17	−0.0172378
$172$	− 1.34447e19i	− 1.33832i
$173$	− 2.31430e18i	− 0.219294i	−0.993971	−	0.109647i	$-0.965028\pi$
$173$	− 2.31430e18i	− 0.219294i	0.993971	−	0.109647i	$-0.0349721\pi$
$174$	−5.50426e18	−0.496627
$175$	0	0
$176$	1.10947e19	0.908362
$177$	− 1.40066e17i	− 0.0109285i
$178$	1.54003e19i	1.14540i
$179$	7.90307e18	0.560461	0.280230	−	0.959933i	$-0.409589\pi$
$179$	7.90307e18	0.560461	0.280230	+	0.959933i	$0.409589\pi$
$180$	0	0
$181$	1.40729e19	0.908060	0.454030	−	0.890986i	$-0.349986\pi$
$181$	1.40729e19	0.908060	0.454030	+	0.890986i	$0.349986\pi$
$182$	− 4.32826e18i	− 0.266505i
$183$	− 5.60470e18i	− 0.329396i
$184$	−2.78594e18	−0.156322
$185$	0	0
$186$	−2.00176e19	−1.02460
$187$	4.09195e18i	0.200114i
$188$	7.28294e18i	0.340381i
$189$	−3.31584e18	−0.148138
$190$	0	0
$191$	−2.82501e19	−1.15408	−0.577040	−	0.816716i	$-0.695792\pi$
$191$	−2.82501e19	−1.15408	−0.577040	+	0.816716i	$0.695792\pi$
$192$	1.19209e19i	0.465851i
$193$	− 4.91755e19i	− 1.83870i	−0.393437	−	0.919351i	$-0.628714\pi$
$193$	− 4.91755e19i	− 1.83870i	0.393437	−	0.919351i	$-0.371286\pi$
$194$	−3.36705e19	−1.20486
$195$	0	0
$196$	−3.28251e19	−1.07654
$197$	1.29458e19i	0.406598i	0.979117	+	0.203299i	$0.0651663\pi$
$197$	1.29458e19i	0.406598i	−0.979117	+	0.203299i	$0.934834\pi$
$198$	4.40835e19i	1.32624i
$199$	5.51755e19	1.59036	0.795179	−	0.606375i	$-0.207377\pi$
$199$	5.51755e19	1.59036	0.795179	+	0.606375i	$0.207377\pi$
$200$	0	0
$201$	−2.22603e19	−0.589338
$202$	8.48028e19i	2.15240i
$203$	− 7.85016e18i	− 0.191057i
$204$	−3.43593e18	−0.0802025
$205$	0	0
$206$	4.78968e19	1.02905
$207$	3.51298e19i	0.724316i
$208$	3.74094e19i	0.740359i
$209$	1.12101e18	0.0212993
$210$	0	0
$211$	1.73510e19	0.304035	0.152017	−	0.988378i	$-0.451423\pi$
$211$	1.73510e19	0.304035	0.152017	+	0.988378i	$0.451423\pi$
$212$	3.38858e18i	0.0570378i
$213$	− 1.58915e19i	− 0.257002i
$214$	1.03250e20	1.60462
$215$	0	0
$216$	−9.03061e18	−0.129676
$217$	− 2.85491e19i	− 0.394171i
$218$	1.12863e20i	1.49855i
$219$	1.45758e19	0.186147
$220$	0	0
$221$	−1.37973e19	−0.163102
$222$	2.87079e19i	0.326589i
$223$	− 9.48415e19i	− 1.03850i	−0.854622	−	0.519251i	$-0.826211\pi$
$223$	− 9.48415e19i	− 1.03850i	0.854622	−	0.519251i	$-0.173789\pi$
$224$	−2.87912e19	−0.303496
$225$	0	0
$226$	1.48570e20	1.45214
$227$	− 1.83782e20i	− 1.73015i	−0.501647	−	0.865073i	$-0.667272\pi$
$227$	− 1.83782e20i	− 1.73015i	0.501647	−	0.865073i	$-0.332728\pi$
$228$	9.41287e17i	0.00853642i
$229$	9.14908e19	0.799422	0.399711	−	0.916641i	$-0.369111\pi$
$229$	9.14908e19	0.799422	0.399711	+	0.916641i	$0.369111\pi$
$230$	0	0
$231$	1.04151e19	0.0845205
$232$	− 2.13798e19i	− 0.167246i
$233$	− 9.87497e19i	− 0.744750i	−0.928082	−	0.372375i	$-0.878544\pi$
$233$	− 9.87497e19i	− 0.744750i	0.928082	−	0.372375i	$-0.121456\pi$
$234$	−1.48642e20	−1.08095
$235$	0	0
$236$	4.82946e18	0.0326698
$237$	− 1.01382e19i	− 0.0661609i
$238$	− 9.24861e18i	− 0.0582334i
$239$	−1.89337e20	−1.15041	−0.575206	−	0.818009i	$-0.695078\pi$
$239$	−1.89337e20	−1.15041	−0.575206	+	0.818009i	$0.695078\pi$
$240$	0	0
$241$	−1.38762e20	−0.785463	−0.392731	−	0.919653i	$-0.628470\pi$
$241$	−1.38762e20	−0.785463	−0.392731	+	0.919653i	$0.628470\pi$
$242$	− 3.29965e19i	− 0.180317i
$243$	1.75165e20i	0.924258i
$244$	1.93250e20	0.984702
$245$	0	0
$246$	1.10528e20	0.525443
$247$	3.77983e18i	0.0173600i
$248$	− 7.77529e19i	− 0.345046i
$249$	−1.27521e20	−0.546873
$250$	0	0
$251$	−3.34508e20	−1.34023	−0.670115	−	0.742257i	$-0.733755\pi$
$251$	−3.34508e20	−1.34023	−0.670115	+	0.742257i	$0.733755\pi$
$252$	− 5.27922e19i	− 0.204487i
$253$	− 2.38966e20i	− 0.894977i
$254$	−4.59521e20	−1.66425
$255$	0	0
$256$	2.06618e20	0.700048
$257$	4.91382e19i	0.161060i	0.996752	+	0.0805300i	$0.0256613\pi$
$257$	4.91382e19i	0.161060i	−0.996752	+	0.0805300i	$0.974339\pi$
$258$	2.05883e20i	0.652909i
$259$	−4.09432e19	−0.125642
$260$	0	0
$261$	−2.69591e20	−0.774929
$262$	− 6.95816e19i	− 0.193613i
$263$	− 1.78845e19i	− 0.0481784i	−0.999710	−	0.0240892i	$-0.992331\pi$
$263$	− 1.78845e19i	− 0.0481784i	0.999710	−	0.0240892i	$-0.00766857\pi$
$264$	2.83653e19	0.0739869
$265$	0	0
$266$	−2.53369e18	−0.00619812
$267$	− 1.24952e20i	− 0.296073i
$268$	− 7.67533e20i	− 1.76178i
$269$	−1.15237e20	−0.256270	−0.128135	−	0.991757i	$-0.540899\pi$
$269$	−1.15237e20	−0.256270	−0.128135	+	0.991757i	$0.540899\pi$
$270$	0	0
$271$	−1.47067e20	−0.307098	−0.153549	−	0.988141i	$-0.549070\pi$
$271$	−1.47067e20	−0.307098	−0.153549	+	0.988141i	$0.549070\pi$
$272$	7.99363e19i	0.161774i
$273$	3.51179e19i	0.0688884i
$274$	9.88038e20	1.87886
$275$	0	0
$276$	2.00655e20	0.358693
$277$	− 1.78744e20i	− 0.309852i	−0.987926	−	0.154926i	$-0.950486\pi$
$277$	− 1.78744e20i	− 0.309852i	0.987926	−	0.154926i	$-0.0495139\pi$
$278$	8.37969e20i	1.40879i
$279$	−9.80439e20	−1.59877
$280$	0	0
$281$	2.80546e20	0.430527	0.215263	−	0.976556i	$-0.430939\pi$
$281$	2.80546e20	0.430527	0.215263	+	0.976556i	$0.430939\pi$
$282$	− 1.11526e20i	− 0.166057i
$283$	− 3.39877e20i	− 0.491062i	−0.969389	−	0.245531i	$-0.921038\pi$
$283$	− 3.39877e20i	− 0.491062i	0.969389	−	0.245531i	$-0.0789624\pi$
$284$	5.47936e20	0.768288
$285$	0	0
$286$	1.01112e21	1.33564
$287$	1.57635e20i	0.202142i
$288$	9.88753e20i	1.23098i
$289$	7.97758e20	0.964361
$290$	0	0
$291$	2.73190e20	0.311440
$292$	5.02571e20i	0.556472i
$293$	7.64887e20i	0.822664i	0.911486	+	0.411332i	$0.134936\pi$
$293$	7.64887e20i	0.822664i	−0.911486	+	0.411332i	$0.865064\pi$
$294$	5.02659e20	0.525196
$295$	0	0
$296$	−1.11508e20	−0.109983
$297$	− 7.74607e20i	− 0.742423i
$298$	− 2.51983e20i	− 0.234710i
$299$	8.05751e20	0.729450
$300$	0	0
$301$	−2.93630e20	−0.251180
$302$	2.07485e21i	1.72555i
$303$	− 6.88059e20i	− 0.556370i
$304$	2.18989e19	0.0172185
$305$	0	0
$306$	−3.17617e20	−0.236196
$307$	1.38472e21i	1.00158i	0.865569	+	0.500789i	$0.166957\pi$
$307$	1.38472e21i	1.00158i	−0.865569	+	0.500789i	$0.833043\pi$
$308$	3.59112e20i	0.252667i
$309$	−3.88617e20	−0.265996
$310$	0	0
$311$	−2.34733e21	−1.52094	−0.760469	−	0.649374i	$-0.775031\pi$
$311$	−2.34733e21	−1.52094	−0.760469	+	0.649374i	$0.775031\pi$
$312$	9.56428e19i	0.0603029i
$313$	− 1.58424e21i	− 0.972065i	−0.873941	−	0.486033i	$-0.838444\pi$
$313$	− 1.58424e21i	− 0.972065i	0.873941	−	0.486033i	$-0.161556\pi$
$314$	−1.21151e21	−0.723480
$315$	0	0
$316$	3.49565e20	0.197783
$317$	8.98378e20i	0.494829i	0.968910	+	0.247415i	$0.0795810\pi$
$317$	8.98378e20i	0.494829i	−0.968910	+	0.247415i	$0.920419\pi$
$318$	− 5.18902e19i	− 0.0278263i
$319$	1.83386e21	0.957516
$320$	0	0
$321$	−8.37734e20	−0.414776
$322$	5.40110e20i	0.260440i
$323$	8.07674e18i	0.00379328i
$324$	−1.46291e21	−0.669245
$325$	0	0
$326$	−4.22951e21	−1.83629
$327$	− 9.15730e20i	− 0.387357i
$328$	4.29317e20i	0.176950i
$329$	1.59058e20	0.0638836
$330$	0	0
$331$	4.00469e21	1.52767	0.763837	−	0.645409i	$-0.223313\pi$
$331$	4.00469e21	1.52767	0.763837	+	0.645409i	$0.223313\pi$
$332$	− 4.39691e21i	− 1.63483i
$333$	1.40608e21i	0.509604i
$334$	−4.54860e21	−1.60706
$335$	0	0
$336$	2.03459e20	0.0683273
$337$	− 1.06753e21i	− 0.349564i	−0.984607	−	0.174782i	$-0.944078\pi$
$337$	− 1.06753e21i	− 0.349564i	0.984607	−	0.174782i	$-0.0559221\pi$
$338$	− 1.15812e21i	− 0.369795i
$339$	−1.20544e21	−0.375362
$340$	0	0
$341$	6.66931e21	1.97546
$342$	8.70125e19i	0.0251397i
$343$	1.46736e21i	0.413557i
$344$	−7.99694e20	−0.219876
$345$	0	0
$346$	−1.22195e21	−0.319821
$347$	− 1.61841e21i	− 0.413321i	−0.978413	−	0.206660i	$-0.933740\pi$
$347$	− 1.61841e21i	− 0.413321i	0.978413	−	0.206660i	$-0.0662595\pi$
$348$	1.53986e21i	0.383758i
$349$	5.60078e21	1.36217	0.681086	−	0.732203i	$-0.261508\pi$
$349$	5.60078e21	1.36217	0.681086	+	0.732203i	$0.261508\pi$
$350$	0	0
$351$	2.61183e21	0.605111
$352$	− 6.72587e21i	− 1.52102i
$353$	− 5.10774e21i	− 1.12757i	−0.825921	−	0.563785i	$-0.809344\pi$
$353$	− 5.10774e21i	− 1.12757i	0.825921	−	0.563785i	$-0.190656\pi$
$354$	−7.39547e19	−0.0159382
$355$	0	0
$356$	4.30834e21	0.885086
$357$	7.50399e19i	0.0150526i
$358$	− 4.17282e21i	− 0.817380i
$359$	−5.84965e21	−1.11899	−0.559496	−	0.828833i	$-0.689005\pi$
$359$	−5.84965e21	−1.11899	−0.559496	+	0.828833i	$0.689005\pi$
$360$	0	0
$361$	−5.47817e21	−0.999596
$362$	− 7.43047e21i	− 1.32432i
$363$	2.67722e20i	0.0466098i
$364$	−1.21086e21	−0.205936
$365$	0	0
$366$	−2.95928e21	−0.480393
$367$	4.29535e20i	0.0681297i	0.999420	+	0.0340649i	$0.0108453\pi$
$367$	4.29535e20i	0.0681297i	−0.999420	+	0.0340649i	$0.989155\pi$
$368$	− 4.66821e21i	− 0.723509i
$369$	5.41354e21	0.819893
$370$	0	0
$371$	7.40057e19	0.0107050
$372$	5.60009e21i	0.791735i
$373$	6.54734e21i	0.904774i	0.891822	+	0.452387i	$0.149427\pi$
$373$	6.54734e21i	0.904774i	−0.891822	+	0.452387i	$0.850573\pi$
$374$	2.16055e21	0.291847
$375$	0	0
$376$	4.33190e20	0.0559218
$377$	6.18345e21i	0.780422i
$378$	1.75076e21i	0.216046i
$379$	−1.51850e21	−0.183223	−0.0916117	−	0.995795i	$-0.529202\pi$
$379$	−1.51850e21	−0.183223	−0.0916117	+	0.995795i	$0.529202\pi$
$380$	0	0
$381$	3.72839e21	0.430188
$382$	1.49160e22i	1.68312i
$383$	8.04597e21i	0.887951i	0.896039	+	0.443975i	$0.146432\pi$
$383$	8.04597e21i	0.887951i	−0.896039	+	0.443975i	$0.853568\pi$
$384$	1.28284e21	0.138470
$385$	0	0
$386$	−2.59647e22	−2.68158
$387$	1.00839e22i	1.01879i
$388$	9.41958e21i	0.931026i
$389$	−6.84040e21	−0.661470	−0.330735	−	0.943724i	$-0.607297\pi$
$389$	−6.84040e21	−0.661470	−0.330735	+	0.943724i	$0.607297\pi$
$390$	0	0
$391$	1.72173e21	0.159390
$392$	1.95244e21i	0.176867i
$393$	5.64560e20i	0.0500465i
$394$	6.83536e21	0.592985
$395$	0	0
$396$	1.23327e22	1.02482
$397$	6.23458e21i	0.507093i	0.967323	+	0.253547i	$0.0815971\pi$
$397$	6.23458e21i	0.507093i	−0.967323	+	0.253547i	$0.918403\pi$
$398$	− 2.91327e22i	− 2.31939i
$399$	2.05575e19	0.00160214
$400$	0	0
$401$	−2.32048e21	−0.173320	−0.0866602	−	0.996238i	$-0.527619\pi$
$401$	−2.32048e21	−0.173320	−0.0866602	+	0.996238i	$0.527619\pi$
$402$	1.17534e22i	0.859494i
$403$	2.24877e22i	1.61010i
$404$	2.37242e22	1.66322
$405$	0	0
$406$	−4.14489e21	−0.278639
$407$	− 9.56466e21i	− 0.629676i
$408$	2.04369e20i	0.0131766i
$409$	−2.38590e22	−1.50662	−0.753312	−	0.657663i	$-0.771545\pi$
$409$	−2.38590e22	−1.50662	−0.753312	+	0.657663i	$0.771545\pi$
$410$	0	0
$411$	−8.01658e21	−0.485661
$412$	− 1.33995e22i	− 0.795173i
$413$	− 1.05474e20i	− 0.00613155i
$414$	1.85485e22	1.05635
$415$	0	0
$416$	2.26784e22	1.23971
$417$	− 6.79898e21i	− 0.364156i
$418$	− 5.91892e20i	− 0.0310630i
$419$	2.61839e22	1.34653	0.673263	−	0.739403i	$-0.264892\pi$
$419$	2.61839e22	1.34653	0.673263	+	0.739403i	$0.264892\pi$
$420$	0	0
$421$	1.11903e22	0.552642	0.276321	−	0.961065i	$-0.410885\pi$
$421$	1.11903e22	0.552642	0.276321	+	0.961065i	$0.410885\pi$
$422$	− 9.16132e21i	− 0.443407i
$423$	− 5.46238e21i	− 0.259113i
$424$	2.01553e20	0.00937086
$425$	0	0
$426$	−8.39069e21	−0.374814
$427$	− 4.22052e21i	− 0.184812i
$428$	− 2.88850e22i	− 1.23994i
$429$	−8.20383e21	−0.345247
$430$	0	0
$431$	1.74296e22	0.705068	0.352534	−	0.935799i	$-0.385320\pi$
$431$	1.74296e22	0.705068	0.352534	+	0.935799i	$0.385320\pi$
$432$	− 1.51319e22i	− 0.600182i
$433$	4.51413e22i	1.75560i	0.479024	+	0.877802i	$0.340991\pi$
$433$	4.51413e22i	1.75560i	−0.479024	+	0.877802i	$0.659009\pi$
$434$	−1.50739e22	−0.574863
$435$	0	0
$436$	3.15743e22	1.15797
$437$	− 4.71674e20i	− 0.0169648i
$438$	− 7.69600e21i	− 0.271478i
$439$	−3.85266e22	−1.33294	−0.666472	−	0.745530i	$-0.732196\pi$
$439$	−3.85266e22	−1.33294	−0.666472	+	0.745530i	$0.732196\pi$
$440$	0	0
$441$	2.46196e22	0.819507
$442$	7.28499e21i	0.237870i
$443$	3.84966e21i	0.123308i	0.998098	+	0.0616539i	$0.0196375\pi$
$443$	3.84966e21i	0.123308i	−0.998098	+	0.0616539i	$0.980363\pi$
$444$	8.03126e21	0.252364
$445$	0	0
$446$	−5.00763e22	−1.51456
$447$	2.04449e21i	0.0606697i
$448$	8.97679e21i	0.261371i
$449$	2.77614e21	0.0793136	0.0396568	−	0.999213i	$-0.487374\pi$
$449$	2.77614e21	0.0793136	0.0396568	+	0.999213i	$0.487374\pi$
$450$	0	0
$451$	−3.68249e22	−1.01307
$452$	− 4.15636e22i	− 1.12211i
$453$	− 1.68346e22i	− 0.446034i
$454$	−9.70368e22	−2.52326
$455$	0	0
$456$	5.59878e19	0.00140247
$457$	− 1.34139e22i	− 0.329814i	−0.986309	−	0.164907i	$-0.947268\pi$
$457$	− 1.34139e22i	− 0.329814i	0.986309	−	0.164907i	$-0.0527323\pi$
$458$	− 4.83071e22i	− 1.16588i
$459$	5.58096e21	0.132221
$460$	0	0
$461$	−4.32728e22	−0.988000	−0.494000	−	0.869462i	$-0.664466\pi$
$461$	−4.32728e22	−0.988000	−0.494000	+	0.869462i	$0.664466\pi$
$462$	− 5.49918e21i	− 0.123265i
$463$	− 3.85721e22i	− 0.848859i	−0.905461	−	0.424429i	$-0.860475\pi$
$463$	− 3.85721e22i	− 0.848859i	0.905461	−	0.424429i	$-0.139525\pi$
$464$	3.58245e22	0.774065
$465$	0	0
$466$	−5.21398e22	−1.08615
$467$	4.96724e22i	1.01607i	0.861338	+	0.508033i	$0.169627\pi$
$467$	4.96724e22i	1.01607i	−0.861338	+	0.508033i	$0.830373\pi$
$468$	4.15836e22i	0.835281i
$469$	−1.67627e22	−0.330655
$470$	0	0
$471$	9.82978e21	0.187011
$472$	− 2.87256e20i	− 0.00536739i
$473$	− 6.85943e22i	− 1.25883i
$474$	−5.35299e21	−0.0964895
$475$	0	0
$476$	−2.58737e21	−0.0449986
$477$	− 2.54152e21i	− 0.0434197i
$478$	9.99699e22i	1.67777i
$479$	4.26513e22	0.703202	0.351601	−	0.936150i	$-0.385637\pi$
$479$	4.26513e22	0.703202	0.351601	+	0.936150i	$0.385637\pi$
$480$	0	0
$481$	3.22503e22	0.513217
$482$	7.32663e22i	1.14553i
$483$	− 4.38226e21i	− 0.0673205i
$484$	−9.23103e21	−0.139336
$485$	0	0
$486$	9.24869e22	1.34794
$487$	− 9.28126e22i	− 1.32926i	−0.747172	−	0.664631i	$-0.768589\pi$
$487$	− 9.28126e22i	− 1.32926i	0.747172	−	0.664631i	$-0.231411\pi$
$488$	− 1.14945e22i	− 0.161779i
$489$	3.43167e22	0.474658
$490$	0	0
$491$	1.29877e21	0.0173516	0.00867579	−	0.999962i	$-0.497238\pi$
$491$	1.29877e21	0.0173516	0.00867579	+	0.999962i	$0.497238\pi$
$492$	− 3.09211e22i	− 0.406024i
$493$	1.32128e22i	0.170528i
$494$	1.99575e21	0.0253179
$495$	0	0
$496$	1.30285e23	1.59698
$497$	− 1.19668e22i	− 0.144194i
$498$	6.73310e22i	0.797564i
$499$	7.66788e22	0.892937	0.446468	−	0.894799i	$-0.352682\pi$
$499$	7.66788e22	0.892937	0.446468	+	0.894799i	$0.352682\pi$
$500$	0	0
$501$	3.69057e22	0.415406
$502$	1.76620e23i	1.95460i
$503$	− 6.67712e22i	− 0.726543i	−0.931683	−	0.363272i	$-0.881660\pi$
$503$	− 6.67712e22i	− 0.726543i	0.931683	−	0.363272i	$-0.118340\pi$
$504$	−3.14008e21	−0.0335956
$505$	0	0
$506$	−1.26174e23	−1.30524
$507$	9.39656e21i	0.0955875i
$508$	1.28555e23i	1.28601i
$509$	1.15659e23	1.13783	0.568916	−	0.822395i	$-0.307363\pi$
$509$	1.15659e23	1.13783	0.568916	+	0.822395i	$0.307363\pi$
$510$	0	0
$511$	1.09760e22	0.104440
$512$	− 1.48344e23i	− 1.38827i
$513$	− 1.52893e21i	− 0.0140731i
$514$	2.59450e22	0.234891
$515$	0	0
$516$	5.75973e22	0.504521
$517$	3.71571e22i	0.320164i
$518$	2.16180e22i	0.183237i
$519$	9.91446e21	0.0826697
$520$	0	0
$521$	−1.79855e23	−1.45145	−0.725725	−	0.687985i	$-0.758496\pi$
$521$	−1.79855e23	−1.45145	−0.725725	+	0.687985i	$0.758496\pi$
$522$	1.42344e23i	1.13016i
$523$	− 9.37211e22i	− 0.732104i	−0.930594	−	0.366052i	$-0.880709\pi$
$523$	− 9.37211e22i	− 0.732104i	0.930594	−	0.366052i	$-0.119291\pi$
$524$	−1.94660e22	−0.149610
$525$	0	0
$526$	−9.44299e21	−0.0702637
$527$	4.80517e22i	0.351818i
$528$	4.75298e22i	0.342435i
$529$	4.05028e22	0.287152
$530$	0	0
$531$	−3.62221e21	−0.0248697
$532$	7.08820e20i	0.00478947i
$533$	− 1.24167e23i	− 0.825705i
$534$	−6.59748e22	−0.431795
$535$	0	0
$536$	−4.56529e22	−0.289446
$537$	3.38568e22i	0.211283i
$538$	6.08452e22i	0.373746i
$539$	−1.67472e23	−1.01260
$540$	0	0
$541$	−1.52396e23	−0.892889	−0.446444	−	0.894811i	$-0.647310\pi$
$541$	−1.52396e23	−0.892889	−0.446444	+	0.894811i	$0.647310\pi$
$542$	7.76514e22i	0.447874i
$543$	6.02881e22i	0.342321i
$544$	4.84592e22	0.270886
$545$	0	0
$546$	1.85422e22	0.100467
$547$	2.04979e23i	1.09349i	0.837298	+	0.546747i	$0.184134\pi$
$547$	2.04979e23i	1.09349i	−0.837298	+	0.546747i	$0.815866\pi$
$548$	− 2.76411e23i	− 1.45185i
$549$	−1.44942e23	−0.749598
$550$	0	0
$551$	3.61970e21	0.0181503
$552$	− 1.19350e22i	− 0.0589304i
$553$	− 7.63442e21i	− 0.0371204i
$554$	−9.43770e22	−0.451890
$555$	0	0
$556$	2.34428e23	1.08861
$557$	− 4.07359e23i	− 1.86298i	−0.363767	−	0.931490i	$-0.618509\pi$
$557$	− 4.07359e23i	− 1.86298i	0.363767	−	0.931490i	$-0.381491\pi$
$558$	5.17672e23i	2.33165i
$559$	2.31288e23	1.02601
$560$	0	0
$561$	−1.75299e22	−0.0754390
$562$	− 1.48128e23i	− 0.627884i
$563$	− 2.21297e23i	− 0.923962i	−0.886890	−	0.461981i	$-0.847139\pi$
$563$	− 2.21297e23i	− 0.923962i	0.886890	−	0.461981i	$-0.152861\pi$
$564$	−3.12001e22	−0.128317
$565$	0	0
$566$	−1.79455e23	−0.716169
$567$	3.19496e22i	0.125606i
$568$	− 3.25913e22i	− 0.126224i
$569$	−4.88686e23	−1.86456	−0.932278	−	0.361743i	$-0.882182\pi$
$569$	−4.88686e23	−1.86456	−0.932278	+	0.361743i	$0.882182\pi$
$570$	0	0
$571$	3.42218e20	0.00126735	0.000633673	−	1.00000i	$-0.499798\pi$
$571$	3.42218e20	0.00126735	0.000633673		1.00000i	$0.499798\pi$
$572$	− 2.82867e23i	− 1.03209i
$573$	− 1.21023e23i	− 0.435065i
$574$	8.32315e22	0.294806
$575$	0	0
$576$	3.08282e23	1.06013
$577$	− 1.95911e23i	− 0.663840i	−0.943308	−	0.331920i	$-0.892304\pi$
$577$	− 1.95911e23i	− 0.663840i	0.943308	−	0.331920i	$-0.107696\pi$
$578$	− 4.21216e23i	− 1.40643i
$579$	2.10668e23	0.693155
$580$	0	0
$581$	−9.60273e22	−0.306830
$582$	− 1.44244e23i	− 0.454207i
$583$	1.72883e22i	0.0536501i
$584$	2.98930e22	0.0914239
$585$	0	0
$586$	4.03860e23	1.19978
$587$	− 4.80676e23i	− 1.40744i	−0.710479	−	0.703719i	$-0.751522\pi$
$587$	− 4.80676e23i	− 1.40744i	0.710479	−	0.703719i	$-0.248478\pi$
$588$	− 1.40623e23i	− 0.405834i
$589$	1.31640e22	0.0374461
$590$	0	0
$591$	−5.54596e22	−0.153279
$592$	− 1.86846e23i	− 0.509036i
$593$	6.40804e23i	1.72092i	0.509519	+	0.860459i	$0.329823\pi$
$593$	6.40804e23i	1.72092i	−0.509519	+	0.860459i	$0.670177\pi$
$594$	−4.08992e23	−1.08276
$595$	0	0
$596$	−7.04940e22	−0.181367
$597$	2.36372e23i	0.599534i
$598$	− 4.25436e23i	− 1.06384i
$599$	−3.60950e23	−0.889854	−0.444927	−	0.895567i	$-0.646770\pi$
$599$	−3.60950e23	−0.889854	−0.444927	+	0.895567i	$0.646770\pi$
$600$	0	0
$601$	6.53955e23	1.56717	0.783583	−	0.621287i	$-0.213390\pi$
$601$	6.53955e23	1.56717	0.783583	+	0.621287i	$0.213390\pi$
$602$	1.55036e23i	0.366323i
$603$	5.75668e23i	1.34114i
$604$	5.80455e23	1.33338
$605$	0	0
$606$	−3.63295e23	−0.811414
$607$	4.08715e23i	0.900154i	0.892990	+	0.450077i	$0.148603\pi$
$607$	4.08715e23i	0.900154i	−0.892990	+	0.450077i	$0.851397\pi$
$608$	− 1.32756e22i	− 0.0288319i
$609$	3.36301e22	0.0720247
$610$	0	0
$611$	−1.25287e23	−0.260949
$612$	8.88558e22i	0.182515i
$613$	− 1.80349e23i	− 0.365343i	−0.983174	−	0.182671i	$-0.941526\pi$
$613$	− 1.80349e23i	− 0.365343i	0.983174	−	0.182671i	$-0.0584744\pi$
$614$	7.31131e23	1.46071
$615$	0	0
$616$	2.13600e22	0.0415113
$617$	4.42851e23i	0.848856i	0.905462	+	0.424428i	$0.139525\pi$
$617$	4.42851e23i	0.848856i	−0.905462	+	0.424428i	$0.860475\pi$
$618$	2.05190e23i	0.387930i
$619$	−1.71098e22	−0.0319062	−0.0159531	−	0.999873i	$-0.505078\pi$
$619$	−1.71098e22	−0.0319062	−0.0159531	+	0.999873i	$0.505078\pi$
$620$	0	0
$621$	−3.25923e23	−0.591339
$622$	1.23939e24i	2.21815i
$623$	− 9.40931e22i	− 0.166115i
$624$	−1.60262e23	−0.279101
$625$	0	0
$626$	−8.36481e23	−1.41767
$627$	4.80239e21i	0.00802941i
$628$	3.38930e23i	0.559053i
$629$	6.89124e22	0.112142
$630$	0	0
$631$	−2.82293e23	−0.447147	−0.223574	−	0.974687i	$-0.571772\pi$
$631$	−2.82293e23	−0.447147	−0.223574	+	0.974687i	$0.571772\pi$
$632$	− 2.07922e22i	− 0.0324941i
$633$	7.43316e22i	0.114615i
$634$	4.74344e23	0.721663
$635$	0	0
$636$	−1.45167e22	−0.0215021
$637$	− 5.64684e23i	− 0.825316i
$638$	− 9.68279e23i	− 1.39645i
$639$	−4.10965e23	−0.584854
$640$	0	0
$641$	−3.77613e23	−0.523304	−0.261652	−	0.965162i	$-0.584267\pi$
$641$	−3.77613e23	−0.523304	−0.261652	+	0.965162i	$0.584267\pi$
$642$	4.42323e23i	0.604912i
$643$	4.65536e23i	0.628289i	0.949375	+	0.314145i	$0.101718\pi$
$643$	4.65536e23i	0.628289i	−0.949375	+	0.314145i	$0.898282\pi$
$644$	1.51100e23	0.201249
$645$	0	0
$646$	4.26452e21	0.00553215
$647$	1.00412e24i	1.28558i	0.766045	+	0.642788i	$0.222222\pi$
$647$	1.00412e24i	1.28558i	−0.766045	+	0.642788i	$0.777778\pi$
$648$	8.70141e22i	0.109952i
$649$	2.46396e22	0.0307294
$650$	0	0
$651$	1.22304e23	0.148595
$652$	1.18324e24i	1.41895i
$653$	− 1.26098e23i	− 0.149261i	−0.997211	−	0.0746304i	$-0.976222\pi$
$653$	− 1.26098e23i	− 0.149261i	0.997211	−	0.0746304i	$-0.0237777\pi$
$654$	−4.83505e23	−0.564924
$655$	0	0
$656$	−7.19375e23	−0.818979
$657$	− 3.76940e23i	− 0.423611i
$658$	− 8.39824e22i	− 0.0931683i
$659$	1.06105e24	1.16201	0.581005	−	0.813900i	$-0.302660\pi$
$659$	1.06105e24	1.16201	0.581005	+	0.813900i	$0.302660\pi$
$660$	0	0
$661$	1.57511e24	1.68112	0.840560	−	0.541719i	$-0.182226\pi$
$661$	1.57511e24	1.68112	0.840560	+	0.541719i	$0.182226\pi$
$662$	− 2.11448e24i	− 2.22797i
$663$	− 5.91077e22i	− 0.0614864i
$664$	−2.61528e23	−0.268590
$665$	0	0
$666$	7.42408e23	0.743211
$667$	− 7.71615e23i	− 0.762660i
$668$	1.27251e24i	1.24182i
$669$	4.06301e23	0.391495
$670$	0	0
$671$	9.85948e23	0.926217
$672$	− 1.23342e23i	− 0.114412i
$673$	− 2.91330e23i	− 0.266844i	−0.991059	−	0.133422i	$-0.957403\pi$
$673$	− 2.91330e23i	− 0.266844i	0.991059	−	0.133422i	$-0.0425966\pi$
$674$	−5.63657e23	−0.509807
$675$	0	0
$676$	−3.23993e23	−0.285751
$677$	1.33861e24i	1.16587i	0.812517	+	0.582937i	$0.198097\pi$
$677$	1.33861e24i	1.16587i	−0.812517	+	0.582937i	$0.801903\pi$
$678$	6.36475e23i	0.547430i
$679$	2.05721e23	0.174737
$680$	0	0
$681$	7.87321e23	0.652231
$682$	− 3.52140e24i	− 2.88103i
$683$	1.05295e24i	0.850812i	0.905003	+	0.425406i	$0.139869\pi$
$683$	1.05295e24i	0.850812i	−0.905003	+	0.425406i	$0.860131\pi$
$684$	2.43424e22	0.0194261
$685$	0	0
$686$	7.74764e23	0.603135
$687$	3.91947e23i	0.301366i
$688$	− 1.33999e24i	− 1.01765i
$689$	−5.82932e22	−0.0437275
$690$	0	0
$691$	−5.71311e22	−0.0418128	−0.0209064	−	0.999781i	$-0.506655\pi$
$691$	−5.71311e22	−0.0418128	−0.0209064	+	0.999781i	$0.506655\pi$
$692$	3.41850e23i	0.247134i
$693$	− 2.69343e23i	− 0.192341i
$694$	−8.54519e23	−0.602790
$695$	0	0
$696$	9.15909e22	0.0630483
$697$	− 2.65320e23i	− 0.180423i
$698$	− 2.95721e24i	− 1.98660i
$699$	4.23044e23	0.280756
$700$	0	0
$701$	−3.18403e23	−0.206241	−0.103120	−	0.994669i	$-0.532883\pi$
$701$	−3.18403e23	−0.206241	−0.103120	+	0.994669i	$0.532883\pi$
$702$	− 1.37905e24i	− 0.882498i
$703$	− 1.88788e22i	− 0.0119359i
$704$	−2.09705e24	−1.30991
$705$	0	0
$706$	−2.69689e24	−1.64446
$707$	− 5.18131e23i	− 0.312158i
$708$	2.06894e22i	0.0123159i
$709$	−2.12997e24	−1.25279	−0.626397	−	0.779504i	$-0.715471\pi$
$709$	−2.12997e24	−1.25279	−0.626397	+	0.779504i	$0.715471\pi$
$710$	0	0
$711$	−2.62182e23	−0.150561
$712$	− 2.56261e23i	− 0.145413i
$713$	− 2.80617e24i	− 1.57345i
$714$	3.96210e22	0.0219529
$715$	0	0
$716$	−1.16738e24	−0.631613
$717$	− 8.11119e23i	− 0.433683i
$718$	3.08861e24i	1.63195i
$719$	2.34234e24	1.22308	0.611540	−	0.791213i	$-0.290550\pi$
$719$	2.34234e24	1.22308	0.611540	+	0.791213i	$0.290550\pi$
$720$	0	0
$721$	−2.92641e23	−0.149240
$722$	2.89248e24i	1.45782i
$723$	− 5.94456e23i	− 0.296104i
$724$	−2.07873e24	−1.02334
$725$	0	0
$726$	1.41357e23	0.0679761
$727$	3.58185e24i	1.70241i	0.524830	+	0.851207i	$0.324129\pi$
$727$	3.58185e24i	1.70241i	−0.524830	+	0.851207i	$0.675871\pi$
$728$	7.20222e22i	0.0338337i
$729$	5.28574e23	0.245427
$730$	0	0
$731$	4.94215e23	0.224191
$732$	8.27881e23i	0.371213i
$733$	3.29013e24i	1.45824i	0.684387	+	0.729119i	$0.260070\pi$
$733$	3.29013e24i	1.45824i	−0.684387	+	0.729119i	$0.739930\pi$
$734$	2.26794e23	0.0993609
$735$	0	0
$736$	−2.82997e24	−1.21149
$737$	− 3.91591e24i	− 1.65714i
$738$	− 2.85835e24i	− 1.19574i
$739$	−1.74130e24	−0.720103	−0.360052	−	0.932932i	$-0.617241\pi$
$739$	−1.74130e24	−0.720103	−0.360052	+	0.932932i	$0.617241\pi$
$740$	0	0
$741$	−1.61928e22	−0.00654436
$742$	− 3.90750e22i	− 0.0156123i
$743$	4.61544e24i	1.82309i	0.411199	+	0.911545i	$0.365110\pi$
$743$	4.61544e24i	1.82309i	−0.411199	+	0.911545i	$0.634890\pi$
$744$	3.33094e23	0.130076
$745$	0	0
$746$	3.45700e24	1.31953
$747$	3.29778e24i	1.24451i
$748$	− 6.04431e23i	− 0.225519i
$749$	−6.30841e23	−0.232715
$750$	0	0
$751$	−8.19607e22	−0.0295574	−0.0147787	−	0.999891i	$-0.504704\pi$
$751$	−8.19607e22	−0.0295574	−0.0147787	+	0.999891i	$0.504704\pi$
$752$	7.25865e23i	0.258824i
$753$	− 1.43303e24i	− 0.505241i
$754$	3.26486e24	1.13817
$755$	0	0
$756$	4.89789e23	0.166945
$757$	− 2.51608e24i	− 0.848025i	−0.905656	−	0.424013i	$-0.860621\pi$
$757$	− 2.51608e24i	− 0.848025i	0.905656	−	0.424013i	$-0.139379\pi$
$758$	8.01767e23i	0.267215i
$759$	1.02373e24	0.337389
$760$	0	0
$761$	−5.27745e23	−0.170081	−0.0850403	−	0.996378i	$-0.527102\pi$
$761$	−5.27745e23	−0.170081	−0.0850403	+	0.996378i	$0.527102\pi$
$762$	− 1.96859e24i	− 0.627390i
$763$	− 6.89574e23i	− 0.217331i
$764$	4.17287e24	1.30059
$765$	0	0
$766$	4.24827e24	1.29499
$767$	8.30803e22i	0.0250460i
$768$	8.85151e23i	0.263905i
$769$	7.51719e23	0.221657	0.110828	−	0.993840i	$-0.464650\pi$
$769$	7.51719e23	0.221657	0.110828	+	0.993840i	$0.464650\pi$
$770$	0	0
$771$	−2.10508e23	−0.0607165
$772$	7.26381e24i	2.07213i
$773$	− 2.81914e24i	− 0.795409i	−0.917514	−	0.397704i	$-0.869807\pi$
$773$	− 2.81914e24i	− 0.795409i	0.917514	−	0.397704i	$-0.130193\pi$
$774$	5.32429e24	1.48581
$775$	0	0
$776$	5.60277e23	0.152960
$777$	− 1.75401e23i	− 0.0473644i
$778$	3.61173e24i	0.964693i
$779$	−7.26854e22	−0.0192034
$780$	0	0
$781$	2.79554e24	0.722656
$782$	− 9.09072e23i	− 0.232456i
$783$	− 2.50118e24i	− 0.632660i
$784$	−3.27156e24	−0.818594
$785$	0	0
$786$	2.98088e23	0.0729882
$787$	− 3.20732e24i	− 0.776887i	−0.921473	−	0.388443i	$-0.873013\pi$
$787$	− 3.20732e24i	− 0.776887i	0.921473	−	0.388443i	$-0.126987\pi$
$788$	− 1.91224e24i	− 0.458216i
$789$	7.66170e22	0.0181623
$790$	0	0
$791$	−9.07739e23	−0.210601
$792$	− 7.33550e23i	− 0.168370i
$793$	3.32444e24i	0.754912i
$794$	3.29186e24	0.739549
$795$	0	0
$796$	−8.15008e24	−1.79226
$797$	2.36328e24i	0.514186i	0.966387	+	0.257093i	$0.0827646\pi$
$797$	2.36328e24i	0.514186i	−0.966387	+	0.257093i	$0.917235\pi$
$798$	− 1.08543e22i	− 0.00233657i
$799$	−2.67713e23	−0.0570194
$800$	0	0
$801$	−3.23136e24	−0.673766
$802$	1.22521e24i	0.252772i
$803$	2.56409e24i	0.523421i
$804$	3.28811e24	0.664156
$805$	0	0
$806$	1.18735e25	2.34818
$807$	− 4.93676e23i	− 0.0966088i
$808$	− 1.41112e24i	− 0.273254i
$809$	−9.60721e24	−1.84092	−0.920460	−	0.390836i	$-0.872186\pi$
$809$	−9.60721e24	−1.84092	−0.920460	+	0.390836i	$0.872186\pi$
$810$	0	0
$811$	−6.64616e24	−1.24708	−0.623539	−	0.781792i	$-0.714306\pi$
$811$	−6.64616e24	−1.24708	−0.623539	+	0.781792i	$0.714306\pi$
$812$	1.15956e24i	0.215312i
$813$	− 6.30035e23i	− 0.115770i
$814$	−5.05014e24	−0.918324
$815$	0	0
$816$	−3.42447e23	−0.0609856
$817$	− 1.35392e23i	− 0.0238620i
$818$	1.25976e25i	2.19727i
$819$	9.08175e23	0.156768
$820$	0	0
$821$	−5.09458e24	−0.861373	−0.430687	−	0.902502i	$-0.641729\pi$
$821$	−5.09458e24	−0.861373	−0.430687	+	0.902502i	$0.641729\pi$
$822$	4.23275e24i	0.708292i
$823$	− 5.78198e24i	− 0.957586i	−0.877928	−	0.478793i	$-0.841074\pi$
$823$	− 5.78198e24i	− 0.957586i	0.877928	−	0.478793i	$-0.158926\pi$
$824$	−7.97002e23	−0.130641
$825$	0	0
$826$	−5.56903e22	−0.00894230
$827$	8.38907e24i	1.33327i	0.745386	+	0.666633i	$0.232265\pi$
$827$	8.38907e24i	1.33327i	−0.745386	+	0.666633i	$0.767735\pi$
$828$	− 5.18909e24i	− 0.816270i
$829$	−5.02769e24	−0.782808	−0.391404	−	0.920219i	$-0.628011\pi$
$829$	−5.02769e24	−0.782808	−0.391404	+	0.920219i	$0.628011\pi$
$830$	0	0
$831$	7.65741e23	0.116808
$832$	− 7.07088e24i	− 1.06764i
$833$	− 1.20662e24i	− 0.180338i
$834$	−3.58986e24	−0.531087
$835$	0	0
$836$	−1.65586e23	−0.0240033
$837$	− 9.09619e24i	− 1.30525i
$838$	− 1.38251e25i	− 1.96378i
$839$	−9.38328e23	−0.131940	−0.0659702	−	0.997822i	$-0.521014\pi$
$839$	−9.38328e23	−0.131940	−0.0659702	+	0.997822i	$0.521014\pi$
$840$	0	0
$841$	−1.33566e24	−0.184048
$842$	− 5.90847e24i	− 0.805977i
$843$	1.20186e24i	0.162300i
$844$	−2.56295e24	−0.342633
$845$	0	0
$846$	−2.88414e24	−0.377892
$847$	2.01603e23i	0.0261510i
$848$	3.37728e23i	0.0433713i
$849$	1.45603e24	0.185121
$850$	0	0
$851$	−4.02442e24	−0.501536
$852$	2.34736e24i	0.289630i
$853$	− 2.33188e24i	− 0.284865i	−0.989805	−	0.142433i	$-0.954508\pi$
$853$	− 2.33188e24i	− 0.284865i	0.989805	−	0.142433i	$-0.0454924\pi$
$854$	−2.22843e24	−0.269531
$855$	0	0
$856$	−1.71808e24	−0.203712
$857$	− 1.09008e25i	− 1.27974i	−0.768482	−	0.639872i	$-0.778988\pi$
$857$	− 1.09008e25i	− 1.27974i	0.768482	−	0.639872i	$-0.221012\pi$
$858$	4.33162e24i	0.503510i
$859$	1.47838e25	1.70155	0.850773	−	0.525533i	$-0.176134\pi$
$859$	1.47838e25	1.70155	0.850773	+	0.525533i	$0.176134\pi$
$860$	0	0
$861$	−6.75310e23	−0.0762037
$862$	− 9.20284e24i	− 1.02828i
$863$	− 5.86087e24i	− 0.648441i	−0.945982	−	0.324220i	$-0.894898\pi$
$863$	− 5.86087e24i	− 0.648441i	0.945982	−	0.324220i	$-0.105102\pi$
$864$	−9.17333e24	−1.00499
$865$	0	0
$866$	2.38346e25	2.56039
$867$	3.41760e24i	0.363545i
$868$	4.21705e24i	0.444213i
$869$	1.78346e24	0.186036
$870$	0	0
$871$	1.32037e25	1.35065
$872$	− 1.87804e24i	− 0.190246i
$873$	− 7.06491e24i	− 0.708737i
$874$	−2.49044e23	−0.0247417
$875$	0	0
$876$	−2.15302e24	−0.209779
$877$	− 1.08364e25i	− 1.04565i	−0.852439	−	0.522827i	$-0.824878\pi$
$877$	− 1.08364e25i	− 1.04565i	0.852439	−	0.522827i	$-0.175122\pi$
$878$	2.03420e25i	1.94398i
$879$	−3.27678e24	−0.310128
$880$	0	0
$881$	5.00054e24	0.464217	0.232109	−	0.972690i	$-0.425437\pi$
$881$	5.00054e24	0.464217	0.232109	+	0.972690i	$0.425437\pi$
$882$	− 1.29991e25i	− 1.19518i
$883$	1.04108e24i	0.0948025i	0.998876	+	0.0474012i	$0.0150939\pi$
$883$	1.04108e24i	0.0948025i	−0.998876	+	0.0474012i	$0.984906\pi$
$884$	2.03803e24	0.183809
$885$	0	0
$886$	2.03262e24	0.179833
$887$	1.47651e25i	1.29386i	0.762550	+	0.646929i	$0.223947\pi$
$887$	1.47651e25i	1.29386i	−0.762550	+	0.646929i	$0.776053\pi$
$888$	− 4.77700e23i	− 0.0414615i
$889$	2.80760e24	0.241363
$890$	0	0
$891$	−7.46369e24	−0.629496
$892$	1.40092e25i	1.17034i
$893$	7.33412e22i	0.00606891i
$894$	1.07949e24	0.0884812
$895$	0	0
$896$	9.66021e23	0.0776906
$897$	3.45184e24i	0.274988i
$898$	− 1.46580e24i	− 0.115672i
$899$	2.15350e25	1.68340
$900$	0	0
$901$	−1.24561e23	−0.00955478
$902$	1.94436e25i	1.47747i
$903$	− 1.25791e24i	− 0.0946899i
$904$	−2.47221e24	−0.184354
$905$	0	0
$906$	−8.88866e24	−0.650499
$907$	− 2.99747e23i	− 0.0217317i	−0.999941	−	0.0108658i	$-0.996541\pi$
$907$	− 2.99747e23i	− 0.0217317i	0.999941	−	0.0108658i	$-0.00345877\pi$
$908$	2.71468e25i	1.94979i
$909$	−1.77937e25	−1.26612
$910$	0	0
$911$	−1.71431e24	−0.119724	−0.0598621	−	0.998207i	$-0.519066\pi$
$911$	−1.71431e24	−0.119724	−0.0598621	+	0.998207i	$0.519066\pi$
$912$	9.38148e22i	0.00649106i
$913$	− 2.24328e25i	− 1.53773i
$914$	−7.08256e24	−0.481003
$915$	0	0
$916$	−1.35143e25	−0.900911
$917$	4.25132e23i	0.0280792i
$918$	− 2.94675e24i	− 0.192832i
$919$	2.42539e25	1.57253	0.786265	−	0.617889i	$-0.212012\pi$
$919$	2.42539e25	1.57253	0.786265	+	0.617889i	$0.212012\pi$
$920$	0	0
$921$	−5.93213e24	−0.377575
$922$	2.28480e25i	1.44091i
$923$	9.42605e24i	0.589000i
$924$	−1.53844e24	−0.0952507
$925$	0	0
$926$	−2.03661e25	−1.23798
$927$	1.00499e25i	0.605320i
$928$	− 2.17176e25i	− 1.29615i
$929$	−1.40138e25	−0.828745	−0.414373	−	0.910107i	$-0.635999\pi$
$929$	−1.40138e25	−0.828745	−0.414373	+	0.910107i	$0.635999\pi$
$930$	0	0
$931$	−3.30557e23	−0.0191944
$932$	1.45865e25i	0.839298i
$933$	− 1.00560e25i	− 0.573364i
$934$	2.62270e25	1.48184
$935$	0	0
$936$	2.47340e24	0.137230
$937$	− 2.43217e25i	− 1.33724i	−0.743606	−	0.668618i	$-0.766886\pi$
$937$	− 2.43217e25i	− 1.33724i	0.743606	−	0.668618i	$-0.233114\pi$
$938$	8.85072e24i	0.482230i
$939$	6.78690e24	0.366449
$940$	0	0
$941$	5.98394e23	0.0317304	0.0158652	−	0.999874i	$-0.494950\pi$
$941$	5.98394e23	0.0317304	0.0158652	+	0.999874i	$0.494950\pi$
$942$	− 5.19012e24i	− 0.272738i
$943$	1.54944e25i	0.806912i
$944$	4.81335e23	0.0248419
$945$	0	0
$946$	−3.62178e25	−1.83589
$947$	3.62477e25i	1.82098i	0.413530	+	0.910491i	$0.364296\pi$
$947$	3.62477e25i	1.82098i	−0.413530	+	0.910491i	$0.635704\pi$
$948$	1.49754e24i	0.0745602i
$949$	−8.64565e24	−0.426614
$950$	0	0
$951$	−3.84865e24	−0.186541
$952$	1.53897e23i	0.00739291i
$953$	1.88157e25i	0.895839i	0.894074	+	0.447919i	$0.147835\pi$
$953$	1.88157e25i	0.895839i	−0.894074	+	0.447919i	$0.852165\pi$
$954$	−1.34192e24	−0.0633236
$955$	0	0
$956$	2.79673e25	1.29646
$957$	7.85627e24i	0.360965i
$958$	− 2.25199e25i	− 1.02556i
$959$	−6.03674e24	−0.272486
$960$	0	0
$961$	5.57675e25	2.47305
$962$	− 1.70282e25i	− 0.748479i
$963$	2.16644e25i	0.943896i
$964$	2.04968e25	0.885180
$965$	0	0
$966$	−2.31383e24	−0.0981807
$967$	− 1.81212e24i	− 0.0762186i	−0.999274	−	0.0381093i	$-0.987866\pi$
$967$	− 1.81212e24i	− 0.0762186i	0.999274	−	0.0381093i	$-0.0121335\pi$
$968$	5.49062e23i	0.0228919i
$969$	−3.46008e22	−0.00142999
$970$	0	0
$971$	2.03685e25	0.827170	0.413585	−	0.910465i	$-0.364276\pi$
$971$	2.03685e25	0.827170	0.413585	+	0.910465i	$0.364276\pi$
$972$	− 2.58739e25i	− 1.04160i
$973$	− 5.11985e24i	− 0.204314i
$974$	−4.90050e25	−1.93861
$975$	0	0
$976$	1.92605e25	0.748763
$977$	− 2.52590e25i	− 0.973449i	−0.873556	−	0.486724i	$-0.838192\pi$
$977$	− 2.52590e25i	− 0.973449i	0.873556	−	0.486724i	$-0.161808\pi$
$978$	− 1.81192e25i	− 0.692244i
$979$	2.19809e25	0.832517
$980$	0	0
$981$	−2.36815e25	−0.881499
$982$	− 6.85750e23i	− 0.0253057i
$983$	1.51840e24i	0.0555495i	0.999614	+	0.0277747i	$0.00884211\pi$
$983$	1.51840e24i	0.0555495i	−0.999614	+	0.0277747i	$0.991158\pi$
$984$	−1.83919e24	−0.0667066
$985$	0	0
$986$	6.97635e24	0.248699
$987$	6.81402e23i	0.0240828i
$988$	− 5.58327e23i	− 0.0195639i
$989$	−2.88617e25	−1.00266
$990$	0	0
$991$	−6.69650e24	−0.228677	−0.114338	−	0.993442i	$-0.536475\pi$
$991$	−6.69650e24	−0.228677	−0.114338	+	0.993442i	$0.536475\pi$
$992$	− 7.89818e25i	− 2.67410i
$993$	1.71561e25i	0.575903i
$994$	−6.31846e24	−0.210294
$995$	0	0
$996$	1.88363e25	0.616300
$997$	− 3.45326e25i	− 1.12026i	−0.828404	−	0.560132i	$-0.810751\pi$
$997$	− 3.45326e25i	− 1.12026i	0.828404	−	0.560132i	$-0.189249\pi$
$998$	− 4.04864e25i	− 1.30227i
$999$	−1.30451e25	−0.416046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.18.b.a.24.1		2
5.2	odd	4		25.18.a.a.1.1		1
5.3	odd	4		1.18.a.a.1.1	✓	1
5.4	even	2	inner	25.18.b.a.24.2		2
15.8	even	4		9.18.a.b.1.1		1
20.3	even	4		16.18.a.b.1.1		1
35.13	even	4		49.18.a.a.1.1		1
40.3	even	4		64.18.a.b.1.1		1
40.13	odd	4		64.18.a.d.1.1		1
55.43	even	4		121.18.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.18.a.a.1.1	✓	1	5.3	odd	4
9.18.a.b.1.1		1	15.8	even	4
16.18.a.b.1.1		1	20.3	even	4
25.18.a.a.1.1		1	5.2	odd	4
25.18.b.a.24.1		2	1.1	even	1	trivial
25.18.b.a.24.2		2	5.4	even	2	inner
49.18.a.a.1.1		1	35.13	even	4
64.18.a.b.1.1		1	40.3	even	4
64.18.a.d.1.1		1	40.13	odd	4
121.18.a.b.1.1		1	55.43	even	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-528.000i q^{2} +4284.00i q^{3} -147712. q^{4} +2.26195e6 q^{6} +3.22599e6i q^{7} +8.78592e6i q^{8} +1.10788e8 q^{9} +O(q^{10})\)	\(q-528.000i q^{2} +4284.00i q^{3} -147712. q^{4} +2.26195e6 q^{6} +3.22599e6i q^{7} +8.78592e6i q^{8} +1.10788e8 q^{9} -7.53618e8 q^{11} -6.32798e8i q^{12} -2.54106e9i q^{13} +1.70332e9 q^{14} -1.47219e10 q^{16} -5.42974e9i q^{17} -5.84958e10i q^{18} -1.48750e9 q^{19} -1.38201e10 q^{21} +3.97910e11i q^{22} +3.17092e11i q^{23} -3.76389e10 q^{24} -1.34168e12 q^{26} +1.02785e12i q^{27} -4.76518e11i q^{28} -2.43341e12 q^{29} -8.84972e12 q^{31} +8.92477e12i q^{32} -3.22850e12i q^{33} -2.86690e12 q^{34} -1.63646e13 q^{36} +1.26917e13i q^{37} +7.85400e11i q^{38} +1.08859e13 q^{39} +4.88642e13 q^{41} +7.29704e12i q^{42} +9.10200e13i q^{43} +1.11318e14 q^{44} +1.67424e14 q^{46} -4.93050e13i q^{47} -6.30688e13i q^{48} +2.22223e14 q^{49} +2.32610e13 q^{51} +3.75346e14i q^{52} -2.29405e13i q^{53} +5.42705e14 q^{54} -2.83433e13 q^{56} -6.37245e12i q^{57} +1.28484e15i q^{58} -3.26951e13 q^{59} -1.30829e15 q^{61} +4.67265e15i q^{62} +3.57400e14i q^{63} +2.78265e15 q^{64} -1.70465e15 q^{66} +5.19614e15i q^{67} +8.02038e14i q^{68} -1.35842e15 q^{69} -3.70949e15 q^{71} +9.73370e14i q^{72} -3.40237e15i q^{73} +6.70119e15 q^{74} +2.19722e14 q^{76} -2.43117e15i q^{77} -5.74777e15i q^{78} -2.36653e15 q^{79} +9.90381e15 q^{81} -2.58003e16i q^{82} +2.97668e16i q^{83} +2.04140e15 q^{84} +4.80585e16 q^{86} -1.04247e16i q^{87} -6.62123e15i q^{88} -2.91672e16 q^{89} +8.19745e15 q^{91} -4.68383e16i q^{92} -3.79122e16i q^{93} -2.60330e16 q^{94} -3.82337e16 q^{96} -6.37699e16i q^{97} -1.17334e17i q^{98} -8.34915e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 295424 q^{4} + 4523904 q^{6} + 221575014 q^{9}+O(q^{10}) \) 2 * q - 295424 * q^4 + 4523904 * q^6 + 221575014 * q^9	\( 2 q - 295424 q^{4} + 4523904 q^{6} + 221575014 q^{9} - 1507236456 q^{11} + 3406647552 q^{14} - 29443883008 q^{16} - 2974999720 q^{19} - 27640299456 q^{21} - 75277762560 q^{24} - 2683364139456 q^{26} - 4866821205180 q^{29} - 17699444106176 q^{31} - 5733807887808 q^{34} - 32729288467968 q^{36} + 21771840858768 q^{39} + 97728302004564 q^{41} + 222636911388672 q^{44} + 334848965577984 q^{46} + 444446979206286 q^{49} + 46522032180624 q^{51} + 10\!\cdots\!80 q^{54}+ \cdots - 16\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q - 295424 * q^4 + 4523904 * q^6 + 221575014 * q^9 - 1507236456 * q^11 + 3406647552 * q^14 - 29443883008 * q^16 - 2974999720 * q^19 - 27640299456 * q^21 - 75277762560 * q^24 - 2683364139456 * q^26 - 4866821205180 * q^29 - 17699444106176 * q^31 - 5733807887808 * q^34 - 32729288467968 * q^36 + 21771840858768 * q^39 + 97728302004564 * q^41 + 222636911388672 * q^44 + 334848965577984 * q^46 + 444446979206286 * q^49 + 46522032180624 * q^51 + 1085409746023680 * q^54 - 56686615265280 * q^56 - 65390181459960 * q^59 - 2616571709738756 * q^61 + 5565291887067136 * q^64 - 3409296516122112 * q^66 - 2716842743439552 * q^69 - 7418979754824816 * q^71 + 13402385511675072 * q^74 + 439443158640640 * q^76 - 4733067882616480 * q^79 + 19807613439904242 * q^81 + 4082803913244672 * q^84 + 96117092879643264 * q^86 - 58334368201148340 * q^89 + 16394907664719584 * q^91 - 52066073955506688 * q^94 - 76467456951975936 * q^96 - 166982969419755192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more