LMFDB - Embedded newform 25.24.b.a.24.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,24,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, 24, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 24 $
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:	$83.8010093363$
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} + 72085x^{2} + 1299025764 $ x^4 + 72085*x^2 + 1299025764
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.2
Root			$-189.348i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.24.b.a.24.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4016.35i q^{2} -388445. i q^{3} -7.74247e6 q^{4} -1.56013e9 q^{6} +3.81217e9i q^{7} -2.59512e9i q^{8} -5.67462e10 q^{9} +O(q^{10})$	\(q-4016.35i q^{2} -388445. i q^{3} -7.74247e6 q^{4} -1.56013e9 q^{6} +3.81217e9i q^{7} -2.59512e9i q^{8} -5.67462e10 q^{9} +2.52200e11 q^{11} +3.00752e12i q^{12} +3.59099e12i q^{13} +1.53110e13 q^{14} -7.53715e13 q^{16} +2.34190e14i q^{17} +2.27913e14i q^{18} +6.23086e14 q^{19} +1.48082e15 q^{21} -1.01292e15i q^{22} +3.58786e15i q^{23} -1.00806e15 q^{24} +1.44227e16 q^{26} -1.45267e16i q^{27} -2.95156e16i q^{28} +2.05923e16 q^{29} +1.36357e17 q^{31} +2.80949e17i q^{32} -9.79656e16i q^{33} +9.40588e17 q^{34} +4.39356e17 q^{36} -1.23898e18i q^{37} -2.50253e18i q^{38} +1.39490e18 q^{39} +1.40074e18 q^{41} -5.94748e18i q^{42} -2.18793e17i q^{43} -1.95265e18 q^{44} +1.44101e19 q^{46} -8.67836e18i q^{47} +2.92777e19i q^{48} +1.28361e19 q^{49} +9.09698e19 q^{51} -2.78032e19i q^{52} +7.63436e19i q^{53} -5.83441e19 q^{54} +9.89304e18 q^{56} -2.42034e20i q^{57} -8.27059e19i q^{58} +1.01862e18 q^{59} +2.87337e20 q^{61} -5.47658e20i q^{62} -2.16326e20i q^{63} +4.96127e20 q^{64} -3.93464e20 q^{66} +1.47683e21i q^{67} -1.81321e21i q^{68} +1.39369e21 q^{69} +7.64346e20 q^{71} +1.47263e20i q^{72} +3.49433e21i q^{73} -4.97617e21 q^{74} -4.82422e21 q^{76} +9.61427e20i q^{77} -5.60242e21i q^{78} -1.02350e22 q^{79} -1.09851e22 q^{81} -5.62587e21i q^{82} +7.71597e21i q^{83} -1.14652e22 q^{84} -8.78750e20 q^{86} -7.99897e21i q^{87} -6.54489e20i q^{88} -4.58518e21 q^{89} -1.36895e22 q^{91} -2.77789e22i q^{92} -5.29672e22i q^{93} -3.48553e22 q^{94} +1.09133e23 q^{96} -1.13703e23i q^{97} -5.15544e22i q^{98} -1.43114e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 50653312 q^{4} - 3619346112 q^{6} + 69998788332 q^{9}+O(q^{10}) $ 4 * q - 50653312 * q^4 - 3619346112 * q^6 + 69998788332 * q^9	$ 4 q - 50653312 q^{4} - 3619346112 q^{6} + 69998788332 q^{9} + 1713603936528 q^{11} + 83332069059456 q^{14} + 31913172803584 q^{16} - 8521201959920 q^{19} + 34\!\cdots\!88 q^{21}+ \cdots + 82\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 50653312 * q^4 - 3619346112 * q^6 + 69998788332 * q^9 + 1713603936528 * q^11 + 83332069059456 * q^14 + 31913172803584 * q^16 - 8521201959920 * q^19 + 3468063275445888 * q^21 + 2573244630282240 * q^24 + 110051709317470368 * q^26 - 41636867203246680 * q^29 + 275428034354000768 * q^31 + 1678967311922650656 * q^34 - 2347832600155149696 * q^36 + 3570022947330058464 * q^39 - 4588870954336629912 * q^41 - 25168177680066077184 * q^44 - 17626412036100442752 * q^46 + 26923963408752401628 * q^49 + 179996725690156584288 * q^51 - 209462446834079598720 * q^54 - 464913424108576235520 * q^56 - 561745979942681543760 * q^59 - 360905785033004447272 * q^61 + 1787380508938705829888 * q^64 - 1088676281827303766784 * q^66 + 2341121344344808447104 * q^69 + 6110067020388286657248 * q^71 - 13430688566297615514144 * q^74 + 12414308589026161180160 * q^76 - 12489833629119279961280 * q^79 - 5587057161859667951196 * q^81 - 31835503814380804952064 * q^84 - 21832577625837998486592 * q^86 - 12790186172346140009640 * q^89 - 109780356325409120292032 * q^91 - 318801036013069863654144 * q^94 + 211184243339168788512768 * q^96 + 82316490264624271963824 * 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 $

$2$	− 4016.35i	− 1.38671i	−0.720595	−	0.693357i	$-0.756131\pi$
$2$	− 4016.35i	− 1.38671i	0.720595	−	0.693357i	$-0.243869\pi$
$3$	− 388445.i	− 1.26600i	−0.774150	−	0.633002i	$-0.781823\pi$
$3$	− 388445.i	− 1.26600i	0.774150	−	0.633002i	$-0.218177\pi$
$4$	−7.74247e6	−0.922974
$5$	0	0
$5$	0	0
$6$	−1.56013e9	−1.75558
$7$	3.81217e9i	0.728693i	0.931263	+	0.364346i	$0.118708\pi$
$7$	3.81217e9i	0.728693i	−0.931263	+	0.364346i	$0.881292\pi$
$8$	− 2.59512e9i	− 0.106813i
$9$	−5.67462e10	−0.602765
$10$	0	0
$11$	2.52200e11	0.266519	0.133260	−	0.991081i	$-0.457456\pi$
$11$	2.52200e11	0.266519	0.133260	+	0.991081i	$0.457456\pi$
$12$	3.00752e12i	1.16849i
$13$	3.59099e12i	0.555733i	0.960620	+	0.277867i	$0.0896273\pi$
$13$	3.59099e12i	0.555733i	−0.960620	+	0.277867i	$0.910373\pi$
$14$	1.53110e13	1.01049
$15$	0	0
$16$	−7.53715e13	−1.07109
$17$	2.34190e14i	1.65731i	0.559756	+	0.828657i	$0.310895\pi$
$17$	2.34190e14i	1.65731i	−0.559756	+	0.828657i	$0.689105\pi$
$18$	2.27913e14i	0.835863i
$19$	6.23086e14	1.22710	0.613552	−	0.789654i	$-0.289740\pi$
$19$	6.23086e14	1.22710	0.613552	+	0.789654i	$0.289740\pi$
$20$	0	0
$21$	1.48082e15	0.922528
$22$	− 1.01292e15i	− 0.369586i
$23$	3.58786e15i	0.785173i	0.919715	+	0.392587i	$0.128420\pi$
$23$	3.58786e15i	0.785173i	−0.919715	+	0.392587i	$0.871580\pi$
$24$	−1.00806e15	−0.135225
$25$	0	0
$26$	1.44227e16	0.770642
$27$	− 1.45267e16i	− 0.502901i
$28$	− 2.95156e16i	− 0.672565i
$29$	2.05923e16	0.313421	0.156710	−	0.987645i	$-0.449911\pi$
$29$	2.05923e16	0.313421	0.156710	+	0.987645i	$0.449911\pi$
$30$	0	0
$31$	1.36357e17	0.963870	0.481935	−	0.876207i	$-0.339934\pi$
$31$	1.36357e17	0.963870	0.481935	+	0.876207i	$0.339934\pi$
$32$	2.80949e17i	1.37849i
$33$	− 9.79656e16i	− 0.337414i
$34$	9.40588e17	2.29822
$35$	0	0
$36$	4.39356e17	0.556337
$37$	− 1.23898e18i	− 1.14484i	−0.819961	−	0.572419i	$-0.806005\pi$
$37$	− 1.23898e18i	− 1.14484i	0.819961	−	0.572419i	$-0.193995\pi$
$38$	− 2.50253e18i	− 1.70164i
$39$	1.39490e18	0.703560
$40$	0	0
$41$	1.40074e18	0.397506	0.198753	−	0.980050i	$-0.436311\pi$
$41$	1.40074e18	0.397506	0.198753	+	0.980050i	$0.436311\pi$
$42$	− 5.94748e18i	− 1.27928i
$43$	− 2.18793e17i	− 0.0359043i	−0.999839	−	0.0179522i	$-0.994285\pi$
$43$	− 2.18793e17i	− 0.0359043i	0.999839	−	0.0179522i	$-0.00571465\pi$
$44$	−1.95265e18	−0.245990
$45$	0	0
$46$	1.44101e19	1.08881
$47$	− 8.67836e18i	− 0.512050i	−0.966670	−	0.256025i	$-0.917587\pi$
$47$	− 8.67836e18i	− 0.512050i	0.966670	−	0.256025i	$-0.0824129\pi$
$48$	2.92777e19i	1.35601i
$49$	1.28361e19	0.469007
$50$	0	0
$51$	9.09698e19	2.09817
$52$	− 2.78032e19i	− 0.512927i
$53$	7.63436e19i	1.13136i	0.824626	+	0.565679i	$0.191386\pi$
$53$	7.63436e19i	1.13136i	−0.824626	+	0.565679i	$0.808614\pi$
$54$	−5.83441e19	−0.697379
$55$	0	0
$56$	9.89304e18	0.0778337
$57$	− 2.42034e20i	− 1.55352i
$58$	− 8.27059e19i	− 0.434625i
$59$	1.01862e18	0.00439760	0.00219880	−	0.999998i	$-0.499300\pi$
$59$	1.01862e18	0.00439760	0.00219880	+	0.999998i	$0.499300\pi$
$60$	0	0
$61$	2.87337e20	0.845472	0.422736	−	0.906253i	$-0.361070\pi$
$61$	2.87337e20	0.845472	0.422736	+	0.906253i	$0.361070\pi$
$62$	− 5.47658e20i	− 1.33661i
$63$	− 2.16326e20i	− 0.439231i
$64$	4.96127e20	0.840472
$65$	0	0
$66$	−3.93464e20	−0.467897
$67$	1.47683e21i	1.47730i	0.674088	+	0.738652i	$0.264537\pi$
$67$	1.47683e21i	1.47730i	−0.674088	+	0.738652i	$0.735463\pi$
$68$	− 1.81321e21i	− 1.52966i
$69$	1.39369e21	0.994032
$70$	0	0
$71$	7.64346e20	0.392481	0.196241	−	0.980556i	$-0.437127\pi$
$71$	7.64346e20	0.392481	0.196241	+	0.980556i	$0.437127\pi$
$72$	1.47263e20i	0.0643830i
$73$	3.49433e21i	1.30362i	0.758382	+	0.651810i	$0.225990\pi$
$73$	3.49433e21i	1.30362i	−0.758382	+	0.651810i	$0.774010\pi$
$74$	−4.97617e21	−1.58756
$75$	0	0
$76$	−4.82422e21	−1.13259
$77$	9.61427e20i	0.194211i
$78$	− 5.60242e21i	− 0.975636i
$79$	−1.02350e22	−1.53948	−0.769742	−	0.638356i	$-0.779615\pi$
$79$	−1.02350e22	−1.53948	−0.769742	+	0.638356i	$0.779615\pi$
$80$	0	0
$81$	−1.09851e22	−1.23944
$82$	− 5.62587e21i	− 0.551227i
$83$	7.71597e21i	0.657646i	0.944392	+	0.328823i	$0.106652\pi$
$83$	7.71597e21i	0.657646i	−0.944392	+	0.328823i	$0.893348\pi$
$84$	−1.14652e22	−0.851469
$85$	0	0
$86$	−8.78750e20	−0.0497890
$87$	− 7.99897e21i	− 0.396792i
$88$	− 6.54489e20i	− 0.0284676i
$89$	−4.58518e21	−0.175134	−0.0875672	−	0.996159i	$-0.527909\pi$
$89$	−4.58518e21	−0.175134	−0.0875672	+	0.996159i	$0.527909\pi$
$90$	0	0
$91$	−1.36895e22	−0.404959
$92$	− 2.77789e22i	− 0.724695i
$93$	− 5.29672e22i	− 1.22026i
$94$	−3.48553e22	−0.710067
$95$	0	0
$96$	1.09133e23	1.74517
$97$	− 1.13703e23i	− 1.61398i	−0.590564	−	0.806991i	$-0.701095\pi$
$97$	− 1.13703e23i	− 1.61398i	0.590564	−	0.806991i	$-0.298905\pi$
$98$	− 5.15544e22i	− 0.650378i
$99$	−1.43114e22	−0.160648
$100$	0	0
$101$	1.36243e23	1.21512	0.607558	−	0.794275i	$-0.292149\pi$
$101$	1.36243e23	1.21512	0.607558	+	0.794275i	$0.292149\pi$
$102$	− 3.65366e23i	− 2.90956i
$103$	− 1.41401e22i	− 0.100653i	−0.998733	−	0.0503264i	$-0.983974\pi$
$103$	− 1.41401e22i	− 0.100653i	0.998733	−	0.0503264i	$-0.0160262\pi$
$104$	9.31907e21	0.0593594
$105$	0	0
$106$	3.06623e23	1.56887
$107$	6.02971e22i	0.276938i	0.990367	+	0.138469i	$0.0442182\pi$
$107$	6.02971e22i	0.276938i	−0.990367	+	0.138469i	$0.955782\pi$
$108$	1.12472e23i	0.464164i
$109$	5.58169e22	0.207186	0.103593	−	0.994620i	$-0.466966\pi$
$109$	5.58169e22	0.207186	0.103593	+	0.994620i	$0.466966\pi$
$110$	0	0
$111$	−4.81275e23	−1.44937
$112$	− 2.87329e23i	− 0.780498i
$113$	− 3.51523e23i	− 0.862089i	−0.902331	−	0.431044i	$-0.858145\pi$
$113$	− 3.51523e23i	− 0.862089i	0.902331	−	0.431044i	$-0.141855\pi$
$114$	−9.72095e23	−2.15428
$115$	0	0
$116$	−1.59435e23	−0.289279
$117$	− 2.03775e23i	− 0.334976i
$118$	− 4.09115e21i	− 0.00609821i
$119$	−8.92770e23	−1.20767
$120$	0	0
$121$	−8.31826e23	−0.928968
$122$	− 1.15405e24i	− 1.17243i
$123$	− 5.44111e23i	− 0.503244i
$124$	−1.05574e24	−0.889627
$125$	0	0
$126$	−8.68842e23	−0.609087
$127$	2.32044e24i	1.48535i	0.669653	+	0.742674i	$0.266443\pi$
$127$	2.32044e24i	1.48535i	−0.669653	+	0.742674i	$0.733557\pi$
$128$	3.64148e23i	0.212992i
$129$	−8.49891e22	−0.0454550
$130$	0	0
$131$	8.70825e23	0.390221	0.195111	−	0.980781i	$-0.437493\pi$
$131$	8.70825e23	0.390221	0.195111	+	0.980781i	$0.437493\pi$
$132$	7.58496e23i	0.311425i
$133$	2.37531e24i	0.894182i
$134$	5.93146e24	2.04860
$135$	0	0
$136$	6.07751e23	0.177022
$137$	4.43869e24i	1.18841i	0.804312	+	0.594207i	$0.202534\pi$
$137$	4.43869e24i	1.18841i	−0.804312	+	0.594207i	$0.797466\pi$
$138$	− 5.59753e24i	− 1.37844i
$139$	4.97229e23	0.112690	0.0563452	−	0.998411i	$-0.482055\pi$
$139$	4.97229e23	0.112690	0.0563452	+	0.998411i	$0.482055\pi$
$140$	0	0
$141$	−3.37106e24	−0.648257
$142$	− 3.06988e24i	− 0.544259i
$143$	9.05647e23i	0.148114i
$144$	4.27705e24	0.645617
$145$	0	0
$146$	1.40345e25	1.80775
$147$	− 4.98613e24i	− 0.593764i
$148$	9.59276e24i	1.05666i
$149$	−1.10598e24	−0.112748	−0.0563738	−	0.998410i	$-0.517954\pi$
$149$	−1.10598e24	−0.112748	−0.0563738	+	0.998410i	$0.517954\pi$
$150$	0	0
$151$	3.76304e24	0.329082	0.164541	−	0.986370i	$-0.447386\pi$
$151$	3.76304e24	0.329082	0.164541	+	0.986370i	$0.447386\pi$
$152$	− 1.61698e24i	− 0.131070i
$153$	− 1.32894e25i	− 0.998972i
$154$	3.86143e24	0.269315
$155$	0	0
$156$	−1.08000e25	−0.649368
$157$	1.50090e25i	0.838504i	0.907870	+	0.419252i	$0.137708\pi$
$157$	1.50090e25i	0.838504i	−0.907870	+	0.419252i	$0.862292\pi$
$158$	4.11072e25i	2.13482i
$159$	2.96553e25	1.43230
$160$	0	0
$161$	−1.36775e25	−0.572150
$162$	4.41199e25i	1.71875i
$163$	2.61170e25i	0.947907i	0.880550	+	0.473953i	$0.157173\pi$
$163$	2.61170e25i	0.947907i	−0.880550	+	0.473953i	$0.842827\pi$
$164$	−1.08452e25	−0.366888
$165$	0	0
$166$	3.09900e25	0.911967
$167$	1.77408e25i	0.487230i	0.969872	+	0.243615i	$0.0783334\pi$
$167$	1.77408e25i	0.487230i	−0.969872	+	0.243615i	$0.921667\pi$
$168$	− 3.84290e24i	− 0.0985377i
$169$	2.88587e25	0.691161
$170$	0	0
$171$	−3.53578e25	−0.739656
$172$	1.69400e24i	0.0331387i
$173$	− 1.04109e26i	− 1.90528i	−0.304100	−	0.952640i	$-0.598356\pi$
$173$	− 1.04109e26i	− 1.90528i	0.304100	−	0.952640i	$-0.401644\pi$
$174$	−3.21267e25	−0.550237
$175$	0	0
$176$	−1.90087e25	−0.285467
$177$	− 3.95679e23i	− 0.00556737i
$178$	1.84157e25i	0.242861i
$179$	1.00142e25	0.123824	0.0619122	−	0.998082i	$-0.480280\pi$
$179$	1.00142e25	0.123824	0.0619122	+	0.998082i	$0.480280\pi$
$180$	0	0
$181$	−5.17169e25	−0.562768	−0.281384	−	0.959595i	$-0.590793\pi$
$181$	−5.17169e25	−0.562768	−0.281384	+	0.959595i	$0.590793\pi$
$182$	5.49817e25i	0.561562i
$183$	− 1.11615e26i	− 1.07037i
$184$	9.31094e24	0.0838665
$185$	0	0
$186$	−2.12735e26	−1.69216
$187$	5.90625e25i	0.441706i
$188$	6.71919e25i	0.472609i
$189$	5.53780e25	0.366460
$190$	0	0
$191$	3.10126e26	1.81825	0.909127	−	0.416520i	$-0.136750\pi$
$191$	3.10126e26	1.81825	0.909127	+	0.416520i	$0.136750\pi$
$192$	− 1.92718e26i	− 1.06404i
$193$	1.28183e26i	0.666687i	0.942805	+	0.333344i	$0.108177\pi$
$193$	1.28183e26i	0.666687i	−0.942805	+	0.333344i	$0.891823\pi$
$194$	−4.56673e26	−2.23813
$195$	0	0
$196$	−9.93833e25	−0.432881
$197$	− 3.89967e26i	− 1.60201i	−0.598655	−	0.801007i	$-0.704298\pi$
$197$	− 3.89967e26i	− 1.60201i	0.598655	−	0.801007i	$-0.295702\pi$
$198$	5.74795e25i	0.222773i
$199$	1.25611e26	0.459426	0.229713	−	0.973258i	$-0.426221\pi$
$199$	1.25611e26	0.459426	0.229713	+	0.973258i	$0.426221\pi$
$200$	0	0
$201$	5.73666e26	1.87027
$202$	− 5.47199e26i	− 1.68502i
$203$	7.85013e25i	0.228387i
$204$	−7.04330e26	−1.93655
$205$	0	0
$206$	−5.67918e25	−0.139577
$207$	− 2.03598e26i	− 0.473275i
$208$	− 2.70658e26i	− 0.595242i
$209$	1.57142e26	0.327047
$210$	0	0
$211$	5.88286e26	1.09734	0.548669	−	0.836040i	$-0.315135\pi$
$211$	5.88286e26	1.09734	0.548669	+	0.836040i	$0.315135\pi$
$212$	− 5.91088e26i	− 1.04421i
$213$	− 2.96906e26i	− 0.496883i
$214$	2.42174e26	0.384034
$215$	0	0
$216$	−3.76984e25	−0.0537162
$217$	5.19817e26i	0.702365i
$218$	− 2.24180e26i	− 0.287308i
$219$	1.35735e27	1.65039
$220$	0	0
$221$	−8.40974e26	−0.921025
$222$	1.93297e27i	2.00986i
$223$	− 1.38821e27i	− 1.37072i	−0.728203	−	0.685361i	$-0.759644\pi$
$223$	− 1.38821e27i	− 1.37072i	0.728203	−	0.685361i	$-0.240356\pi$
$224$	−1.07102e27	−1.00449
$225$	0	0
$226$	−1.41184e27	−1.19547
$227$	− 2.14958e27i	− 1.73004i	−0.501734	−	0.865022i	$-0.667304\pi$
$227$	− 2.14958e27i	− 1.73004i	0.501734	−	0.865022i	$-0.332696\pi$
$228$	1.87394e27i	1.43386i
$229$	6.39851e26	0.465554	0.232777	−	0.972530i	$-0.425219\pi$
$229$	6.39851e26	0.465554	0.232777	+	0.972530i	$0.425219\pi$
$230$	0	0
$231$	3.73461e26	0.245871
$232$	− 5.34395e25i	− 0.0334773i
$233$	− 2.19149e27i	− 1.30661i	−0.757094	−	0.653306i	$-0.773381\pi$
$233$	− 2.19149e27i	− 1.30661i	0.757094	−	0.653306i	$-0.226619\pi$
$234$	−8.18434e26	−0.464516
$235$	0	0
$236$	−7.88666e24	−0.00405887
$237$	3.97572e27i	1.94899i
$238$	3.58568e27i	1.67470i
$239$	−1.09944e27	−0.489322	−0.244661	−	0.969609i	$-0.578677\pi$
$239$	−1.09944e27	−0.489322	−0.244661	+	0.969609i	$0.578677\pi$
$240$	0	0
$241$	−1.44651e27	−0.584961	−0.292480	−	0.956272i	$-0.594481\pi$
$241$	−1.44651e27	−0.584961	−0.292480	+	0.956272i	$0.594481\pi$
$242$	3.34090e27i	1.28821i
$243$	2.89951e27i	1.06623i
$244$	−2.22470e27	−0.780349
$245$	0	0
$246$	−2.18534e27	−0.697855
$247$	2.23750e27i	0.681942i
$248$	− 3.53864e26i	− 0.102954i
$249$	2.99723e27	0.832582
$250$	0	0
$251$	2.24453e26	0.0568693	0.0284346	−	0.999596i	$-0.490948\pi$
$251$	2.24453e26	0.0568693	0.0284346	+	0.999596i	$0.490948\pi$
$252$	1.67490e27i	0.405399i
$253$	9.04857e26i	0.209264i
$254$	9.31972e27	2.05975
$255$	0	0
$256$	5.62436e27	1.13583
$257$	− 3.95005e27i	− 0.762732i	−0.924424	−	0.381366i	$-0.875454\pi$
$257$	− 3.95005e27i	− 0.762732i	0.924424	−	0.381366i	$-0.124546\pi$
$258$	3.41346e26i	0.0630330i
$259$	4.72320e27	0.834236
$260$	0	0
$261$	−1.16853e27	−0.188919
$262$	− 3.49754e27i	− 0.541125i
$263$	− 2.01521e27i	− 0.298420i	−0.988805	−	0.149210i	$-0.952327\pi$
$263$	− 2.01521e27i	− 0.298420i	0.988805	−	0.149210i	$-0.0476731\pi$
$264$	−2.54233e26	−0.0360401
$265$	0	0
$266$	9.54007e27	1.23997
$267$	1.78109e27i	0.221721i
$268$	− 1.14343e28i	− 1.36351i
$269$	−5.72063e27	−0.653571	−0.326785	−	0.945099i	$-0.605965\pi$
$269$	−5.72063e27	−0.653571	−0.326785	+	0.945099i	$0.605965\pi$
$270$	0	0
$271$	5.18050e27	0.543531	0.271766	−	0.962363i	$-0.412392\pi$
$271$	5.18050e27	0.543531	0.271766	+	0.962363i	$0.412392\pi$
$272$	− 1.76512e28i	− 1.77514i
$273$	5.31761e27i	0.512679i
$274$	1.78273e28	1.64799
$275$	0	0
$276$	−1.07906e28	−0.917466
$277$	1.29611e28i	1.05712i	0.848896	+	0.528560i	$0.177268\pi$
$277$	1.29611e28i	1.05712i	−0.848896	+	0.528560i	$0.822732\pi$
$278$	− 1.99705e27i	− 0.156269i
$279$	−7.73776e27	−0.580987
$280$	0	0
$281$	1.24154e28	0.858691	0.429346	−	0.903140i	$-0.358744\pi$
$281$	1.24154e28	0.858691	0.429346	+	0.903140i	$0.358744\pi$
$282$	1.35394e28i	0.898947i
$283$	2.15031e28i	1.37074i	0.728193	+	0.685372i	$0.240360\pi$
$283$	2.15031e28i	1.37074i	−0.728193	+	0.685372i	$0.759640\pi$
$284$	−5.91792e27	−0.362250
$285$	0	0
$286$	3.63740e27	0.205391
$287$	5.33986e27i	0.289660i
$288$	− 1.59428e28i	− 0.830903i
$289$	−3.48772e28	−1.74669
$290$	0	0
$291$	−4.41675e28	−2.04331
$292$	− 2.70547e28i	− 1.20321i
$293$	1.20307e28i	0.514416i	0.966356	+	0.257208i	$0.0828026\pi$
$293$	1.20307e28i	0.514416i	−0.966356	+	0.257208i	$0.917197\pi$
$294$	−2.00260e28	−0.823380
$295$	0	0
$296$	−3.21530e27	−0.122283
$297$	− 3.66362e27i	− 0.134033i
$298$	4.44202e27i	0.156349i
$299$	−1.28840e28	−0.436347
$300$	0	0
$301$	8.34076e26	0.0261632
$302$	− 1.51137e28i	− 0.456342i
$303$	− 5.29228e28i	− 1.53834i
$304$	−4.69629e28	−1.31434
$305$	0	0
$306$	−5.33748e28	−1.38529
$307$	− 4.70428e28i	− 1.17598i	−0.808867	−	0.587992i	$-0.799919\pi$
$307$	− 4.70428e28i	− 1.17598i	0.808867	−	0.587992i	$-0.200081\pi$
$308$	− 7.44382e27i	− 0.179251i
$309$	−5.49267e27	−0.127427
$310$	0	0
$311$	−8.99672e26	−0.0193794	−0.00968968	−	0.999953i	$-0.503084\pi$
$311$	−8.99672e26	−0.0193794	−0.00968968	+	0.999953i	$0.503084\pi$
$312$	− 3.61994e27i	− 0.0751492i
$313$	1.13525e28i	0.227159i	0.993529	+	0.113579i	$0.0362317\pi$
$313$	1.13525e28i	0.227159i	−0.993529	+	0.113579i	$0.963768\pi$
$314$	6.02814e28	1.16277
$315$	0	0
$316$	7.92439e28	1.42090
$317$	1.37896e28i	0.238436i	0.992868	+	0.119218i	$0.0380387\pi$
$317$	1.37896e28i	0.238436i	−0.992868	+	0.119218i	$0.961961\pi$
$318$	− 1.19106e29i	− 1.98619i
$319$	5.19337e27	0.0835326
$320$	0	0
$321$	2.34221e28	0.350605
$322$	5.49338e28i	0.793408i
$323$	1.45920e29i	2.03370i
$324$	8.50516e28	1.14397
$325$	0	0
$326$	1.04895e29	1.31448
$327$	− 2.16818e28i	− 0.262298i
$328$	− 3.63510e27i	− 0.0424587i
$329$	3.30834e28	0.373127
$330$	0	0
$331$	1.62668e29	1.71112	0.855559	−	0.517706i	$-0.173214\pi$
$331$	1.62668e29	1.71112	0.855559	+	0.517706i	$0.173214\pi$
$332$	− 5.97406e28i	− 0.606990i
$333$	7.03074e28i	0.690069i
$334$	7.12534e28	0.675649
$335$	0	0
$336$	−1.11611e29	−0.988113
$337$	− 1.64138e29i	− 1.40432i	−0.712019	−	0.702160i	$-0.752219\pi$
$337$	− 1.64138e29i	− 1.40432i	0.712019	−	0.702160i	$-0.247781\pi$
$338$	− 1.15907e29i	− 0.958442i
$339$	−1.36547e29	−1.09141
$340$	0	0
$341$	3.43892e28	0.256890
$342$	1.42009e29i	1.02569i
$343$	1.53268e29i	1.07045i
$344$	−5.67795e26	−0.00383504
$345$	0	0
$346$	−4.18139e29	−2.64208
$347$	1.45586e29i	0.889876i	0.895561	+	0.444938i	$0.146774\pi$
$347$	1.45586e29i	0.889876i	−0.895561	+	0.444938i	$0.853226\pi$
$348$	6.19318e28i	0.366229i
$349$	−2.22110e28	−0.127080	−0.0635398	−	0.997979i	$-0.520239\pi$
$349$	−2.22110e28	−0.127080	−0.0635398	+	0.997979i	$0.520239\pi$
$350$	0	0
$351$	5.21651e28	0.279479
$352$	7.08552e28i	0.367393i
$353$	− 2.57166e28i	− 0.129064i	−0.997916	−	0.0645320i	$-0.979445\pi$
$353$	− 2.57166e28i	− 0.129064i	0.997916	−	0.0645320i	$-0.0205555\pi$
$354$	−1.58919e27	−0.00772035
$355$	0	0
$356$	3.55006e28	0.161644
$357$	3.46792e29i	1.52892i
$358$	− 4.02205e28i	− 0.171709i
$359$	3.34157e29	1.38154	0.690771	−	0.723074i	$-0.257271\pi$
$359$	3.34157e29	1.38154	0.690771	+	0.723074i	$0.257271\pi$
$360$	0	0
$361$	1.30406e29	0.505785
$362$	2.07713e29i	0.780398i
$363$	3.23118e29i	1.17608i
$364$	1.05990e29	0.373766
$365$	0	0
$366$	−4.48284e29	−1.48430
$367$	1.62664e29i	0.521954i	0.965345	+	0.260977i	$0.0840447\pi$
$367$	1.62664e29i	0.521954i	−0.965345	+	0.260977i	$0.915955\pi$
$368$	− 2.70422e29i	− 0.840994i
$369$	−7.94868e28	−0.239603
$370$	0	0
$371$	−2.91034e29	−0.824412
$372$	4.10097e29i	1.12627i
$373$	− 1.03540e29i	− 0.275712i	−0.990452	−	0.137856i	$-0.955979\pi$
$373$	− 1.03540e29i	− 0.275712i	0.990452	−	0.137856i	$-0.0440211\pi$
$374$	2.37216e29	0.612520
$375$	0	0
$376$	−2.25214e28	−0.0546935
$377$	7.39468e28i	0.174178i
$378$	− 2.22418e29i	− 0.508175i
$379$	−6.62210e29	−1.46772	−0.733862	−	0.679298i	$-0.762284\pi$
$379$	−6.62210e29	−1.46772	−0.733862	+	0.679298i	$0.762284\pi$
$380$	0	0
$381$	9.01364e29	1.88046
$382$	− 1.24557e30i	− 2.52140i
$383$	− 2.96585e29i	− 0.582591i	−0.956633	−	0.291295i	$-0.905914\pi$
$383$	− 2.96585e29i	− 0.582591i	0.956633	−	0.291295i	$-0.0940862\pi$
$384$	1.41451e29	0.269648
$385$	0	0
$386$	5.14829e29	0.924504
$387$	1.24157e28i	0.0216419i
$388$	8.80345e29i	1.48966i
$389$	1.06609e30	1.75134	0.875672	−	0.482906i	$-0.160419\pi$
$389$	1.06609e30	1.75134	0.875672	+	0.482906i	$0.160419\pi$
$390$	0	0
$391$	−8.40240e29	−1.30128
$392$	− 3.33113e28i	− 0.0500959i
$393$	− 3.38267e29i	− 0.494021i
$394$	−1.56624e30	−2.22153
$395$	0	0
$396$	1.10805e29	0.148274
$397$	1.67462e28i	0.0217683i	0.999941	+	0.0108842i	$0.00346461\pi$
$397$	1.67462e28i	0.0217683i	−0.999941	+	0.0108842i	$0.996535\pi$
$398$	− 5.04496e29i	− 0.637093i
$399$	9.22676e29	1.13204
$400$	0	0
$401$	3.87121e29	0.448421	0.224211	−	0.974541i	$-0.428020\pi$
$401$	3.87121e29	0.448421	0.224211	+	0.974541i	$0.428020\pi$
$402$	− 2.30404e30i	− 2.59353i
$403$	4.89658e29i	0.535654i
$404$	−1.05486e30	−1.12152
$405$	0	0
$406$	3.15289e29	0.316708
$407$	− 3.12470e29i	− 0.305121i
$408$	− 2.36078e29i	− 0.224111i
$409$	−5.00511e29	−0.461950	−0.230975	−	0.972960i	$-0.574192\pi$
$409$	−5.00511e29	−0.461950	−0.230975	+	0.972960i	$0.574192\pi$
$410$	0	0
$411$	1.72418e30	1.50454
$412$	1.09480e29i	0.0928999i
$413$	3.88316e27i	0.00320450i
$414$	−8.17719e29	−0.656297
$415$	0	0
$416$	−1.00889e30	−0.766070
$417$	− 1.93146e29i	− 0.142666i
$418$	− 6.31137e29i	− 0.453520i
$419$	−1.70760e30	−1.19378	−0.596891	−	0.802322i	$-0.703598\pi$
$419$	−1.70760e30	−1.19378	−0.596891	+	0.802322i	$0.703598\pi$
$420$	0	0
$421$	−5.97218e29	−0.395265	−0.197633	−	0.980276i	$-0.563325\pi$
$421$	−5.97218e29	−0.395265	−0.197633	+	0.980276i	$0.563325\pi$
$422$	− 2.36276e30i	− 1.52169i
$423$	4.92464e29i	0.308646i
$424$	1.98121e29	0.120843
$425$	0	0
$426$	−1.19248e30	−0.689034
$427$	1.09538e30i	0.616089i
$428$	− 4.66848e29i	− 0.255607i
$429$	3.51794e29	0.187512
$430$	0	0
$431$	1.91854e30	0.969353	0.484676	−	0.874694i	$-0.338937\pi$
$431$	1.91854e30	0.969353	0.484676	+	0.874694i	$0.338937\pi$
$432$	1.09490e30i	0.538653i
$433$	2.68456e30i	1.28606i	0.765839	+	0.643032i	$0.222324\pi$
$433$	2.68456e30i	1.28606i	−0.765839	+	0.643032i	$0.777676\pi$
$434$	2.08777e30	0.973980
$435$	0	0
$436$	−4.32160e29	−0.191228
$437$	2.23555e30i	0.963489i
$438$	− 5.45161e30i	− 2.28862i
$439$	−2.11168e29	−0.0863549	−0.0431775	−	0.999067i	$-0.513748\pi$
$439$	−2.11168e29	−0.0863549	−0.0431775	+	0.999067i	$0.513748\pi$
$440$	0	0
$441$	−7.28401e29	−0.282701
$442$	3.37765e30i	1.27720i
$443$	8.12623e29i	0.299396i	0.988732	+	0.149698i	$0.0478302\pi$
$443$	8.12623e29i	0.299396i	−0.988732	+	0.149698i	$0.952170\pi$
$444$	3.72626e30	1.33773
$445$	0	0
$446$	−5.57554e30	−1.90080
$447$	4.29614e29i	0.142739i
$448$	1.89132e30i	0.612446i
$449$	3.76596e30	1.18862	0.594310	−	0.804236i	$-0.297425\pi$
$449$	3.76596e30	1.18862	0.594310	+	0.804236i	$0.297425\pi$
$450$	0	0
$451$	3.53267e29	0.105943
$452$	2.72166e30i	0.795686i
$453$	− 1.46173e30i	− 0.416619i
$454$	−8.63348e30	−2.39907
$455$	0	0
$456$	−6.28109e29	−0.165936
$457$	2.14090e30i	0.551518i	0.961227	+	0.275759i	$0.0889291\pi$
$457$	2.14090e30i	0.551518i	−0.961227	+	0.275759i	$0.911071\pi$
$458$	− 2.56986e30i	− 0.645591i
$459$	3.40199e30	0.833465
$460$	0	0
$461$	4.76379e30	1.11018	0.555088	−	0.831792i	$-0.312685\pi$
$461$	4.76379e30	1.11018	0.555088	+	0.831792i	$0.312685\pi$
$462$	− 1.49995e30i	− 0.340953i
$463$	7.67574e30i	1.70192i	0.525232	+	0.850959i	$0.323979\pi$
$463$	7.67574e30i	1.70192i	−0.525232	+	0.850959i	$0.676021\pi$
$464$	−1.55207e30	−0.335703
$465$	0	0
$466$	−8.80180e30	−1.81190
$467$	− 2.87884e30i	− 0.578194i	−0.957300	−	0.289097i	$-0.906645\pi$
$467$	− 2.87884e30i	− 0.578194i	0.957300	−	0.289097i	$-0.0933551\pi$
$468$	1.57772e30i	0.309175i
$469$	−5.62992e30	−1.07650
$470$	0	0
$471$	5.83016e30	1.06155
$472$	− 2.64345e27i	0 0.000469719i
$473$	− 5.51796e28i	− 0.00956919i
$474$	1.59679e31	2.70269
$475$	0	0
$476$	6.91225e30	1.11465
$477$	− 4.33221e30i	− 0.681943i
$478$	4.41573e30i	0.678549i
$479$	−6.82143e30	−1.02333	−0.511666	−	0.859184i	$-0.670972\pi$
$479$	−6.82143e30	−1.02333	−0.511666	+	0.859184i	$0.670972\pi$
$480$	0	0
$481$	4.44917e30	0.636224
$482$	5.80971e30i	0.811173i
$483$	5.31297e30i	0.724344i
$484$	6.44038e30	0.857413
$485$	0	0
$486$	1.16455e31	1.47856
$487$	8.59361e29i	0.106560i	0.998580	+	0.0532798i	$0.0169675\pi$
$487$	8.59361e29i	0.106560i	−0.998580	+	0.0532798i	$0.983032\pi$
$488$	− 7.45676e29i	− 0.0903071i
$489$	1.01450e31	1.20005
$490$	0	0
$491$	−7.15140e30	−0.807149	−0.403575	−	0.914947i	$-0.632232\pi$
$491$	−7.15140e30	−0.807149	−0.403575	+	0.914947i	$0.632232\pi$
$492$	4.21276e30i	0.464481i
$493$	4.82250e30i	0.519437i
$494$	8.98658e30	0.945659
$495$	0	0
$496$	−1.02774e31	−1.03239
$497$	2.91382e30i	0.285998i
$498$	− 1.20379e31i	− 1.15455i
$499$	−1.77913e31	−1.66744	−0.833722	−	0.552185i	$-0.813794\pi$
$499$	−1.77913e31	−1.66744	−0.833722	+	0.552185i	$0.813794\pi$
$500$	0	0
$501$	6.89133e30	0.616835
$502$	− 9.01483e29i	− 0.0788614i
$503$	− 6.56155e30i	− 0.561015i	−0.959852	−	0.280507i	$-0.909497\pi$
$503$	− 6.56155e30i	− 0.561015i	0.959852	−	0.280507i	$-0.0905027\pi$
$504$	−5.61393e29	−0.0469154
$505$	0	0
$506$	3.63422e30	0.290189
$507$	− 1.12100e31i	− 0.875012i
$508$	− 1.79660e31i	− 1.37094i
$509$	1.19826e31	0.893917	0.446959	−	0.894555i	$-0.352507\pi$
$509$	1.19826e31	0.893917	0.446959	+	0.894555i	$0.352507\pi$
$510$	0	0
$511$	−1.33210e31	−0.949939
$512$	− 1.95347e31i	− 1.36208i
$513$	− 9.05135e30i	− 0.617112i
$514$	−1.58648e31	−1.05769
$515$	0	0
$516$	6.58025e29	0.0419538
$517$	− 2.18868e30i	− 0.136471i
$518$	− 1.89700e31i	− 1.15685i
$519$	−4.04407e31	−2.41209
$520$	0	0
$521$	−2.26240e31	−1.29103	−0.645514	−	0.763749i	$-0.723357\pi$
$521$	−2.26240e31	−1.29103	−0.645514	+	0.763749i	$0.723357\pi$
$522$	4.69325e30i	0.261977i
$523$	3.41914e31i	1.86702i	0.358557	+	0.933508i	$0.383269\pi$
$523$	3.41914e31i	1.86702i	−0.358557	+	0.933508i	$0.616731\pi$
$524$	−6.74233e30	−0.360164
$525$	0	0
$526$	−8.09378e30	−0.413824
$527$	3.19334e31i	1.59744i
$528$	7.38381e30i	0.361402i
$529$	8.00772e30	0.383503
$530$	0	0
$531$	−5.78030e28	−0.00265072
$532$	− 1.83907e31i	− 0.825307i
$533$	5.03006e30i	0.220907i
$534$	7.15348e30	0.307463
$535$	0	0
$536$	3.83255e30	0.157795
$537$	− 3.88996e30i	− 0.156762i
$538$	2.29761e31i	0.906315i
$539$	3.23726e30	0.124999
$540$	0	0
$541$	−2.75024e30	−0.101766	−0.0508829	−	0.998705i	$-0.516204\pi$
$541$	−2.75024e30	−0.101766	−0.0508829	+	0.998705i	$0.516204\pi$
$542$	− 2.08067e31i	− 0.753722i
$543$	2.00892e31i	0.712466i
$544$	−6.57953e31	−2.28459
$545$	0	0
$546$	2.13574e31	0.710939
$547$	− 1.03197e31i	− 0.336367i	−0.985756	−	0.168184i	$-0.946210\pi$
$547$	− 1.03197e31i	− 0.336367i	0.985756	−	0.168184i	$-0.0537901\pi$
$548$	− 3.43664e31i	− 1.09688i
$549$	−1.63053e31	−0.509621
$550$	0	0
$551$	1.28308e31	0.384600
$552$	− 3.61679e30i	− 0.106175i
$553$	− 3.90174e31i	− 1.12181i
$554$	5.20563e31	1.46592
$555$	0	0
$556$	−3.84978e30	−0.104010
$557$	1.36262e31i	0.360613i	0.983610	+	0.180307i	$0.0577090\pi$
$557$	1.36262e31i	0.360613i	−0.983610	+	0.180307i	$0.942291\pi$
$558$	3.10775e31i	0.805663i
$559$	7.85685e29	0.0199532
$560$	0	0
$561$	2.29425e31	0.559202
$562$	− 4.98645e31i	− 1.19076i
$563$	− 3.09091e31i	− 0.723169i	−0.932339	−	0.361585i	$-0.882236\pi$
$563$	− 3.09091e31i	− 0.723169i	0.932339	−	0.361585i	$-0.117764\pi$
$564$	2.61004e31	0.598325
$565$	0	0
$566$	8.63638e31	1.90083
$567$	− 4.18769e31i	− 0.903171i
$568$	− 1.98357e30i	− 0.0419220i
$569$	6.93051e31	1.43540	0.717702	−	0.696350i	$-0.245194\pi$
$569$	6.93051e31	1.43540	0.717702	+	0.696350i	$0.245194\pi$
$570$	0	0
$571$	−6.24961e30	−0.124319	−0.0621595	−	0.998066i	$-0.519799\pi$
$571$	−6.24961e30	−0.124319	−0.0621595	+	0.998066i	$0.519799\pi$
$572$	− 7.01195e30i	− 0.136705i
$573$	− 1.20467e32i	− 2.30192i
$574$	2.14468e31	0.401675
$575$	0	0
$576$	−2.81534e31	−0.506607
$577$	− 1.59740e31i	− 0.281768i	−0.990026	−	0.140884i	$-0.955006\pi$
$577$	− 1.59740e31i	− 0.281768i	0.990026	−	0.140884i	$-0.0449944\pi$
$578$	1.40079e32i	2.42216i
$579$	4.97921e31	0.844029
$580$	0	0
$581$	−2.94146e31	−0.479222
$582$	1.77392e32i	2.83348i
$583$	1.92538e31i	0.301529i
$584$	9.06822e30	0.139243
$585$	0	0
$586$	4.83197e31	0.713348
$587$	8.16635e31i	1.18220i	0.806599	+	0.591099i	$0.201306\pi$
$587$	8.16635e31i	1.18220i	−0.806599	+	0.591099i	$0.798694\pi$
$588$	3.86049e31i	0.548029i
$589$	8.49622e31	1.18277
$590$	0	0
$591$	−1.51481e32	−2.02816
$592$	9.33837e31i	1.22623i
$593$	5.61370e30i	0.0722970i	0.999346	+	0.0361485i	$0.0115089\pi$
$593$	5.61370e30i	0.0722970i	−0.999346	+	0.0361485i	$0.988491\pi$
$594$	−1.47144e31	−0.185865
$595$	0	0
$596$	8.56305e30	0.104063
$597$	− 4.87928e31i	− 0.581635i
$598$	5.17466e31i	0.605088i
$599$	−1.60231e32	−1.83797	−0.918985	−	0.394293i	$-0.870990\pi$
$599$	−1.60231e32	−1.83797	−0.918985	+	0.394293i	$0.870990\pi$
$600$	0	0
$601$	8.47641e31	0.935741	0.467870	−	0.883797i	$-0.345021\pi$
$601$	8.47641e31	0.935741	0.467870	+	0.883797i	$0.345021\pi$
$602$	− 3.34994e30i	− 0.0362809i
$603$	− 8.38044e31i	− 0.890467i
$604$	−2.91352e31	−0.303734
$605$	0	0
$606$	−2.12557e32	−2.13324
$607$	− 1.63793e31i	− 0.161296i	−0.996743	−	0.0806481i	$-0.974301\pi$
$607$	− 1.63793e31i	− 0.161296i	0.996743	−	0.0806481i	$-0.0256990\pi$
$608$	1.75055e32i	1.69155i
$609$	3.04934e31	0.289139
$610$	0	0
$611$	3.11639e31	0.284563
$612$	1.02893e32i	0.922025i
$613$	− 1.93558e31i	− 0.170222i	−0.996371	−	0.0851110i	$-0.972876\pi$
$613$	− 1.93558e31i	− 0.170222i	0.996371	−	0.0851110i	$-0.0271245\pi$
$614$	−1.88940e32	−1.63075
$615$	0	0
$616$	2.49502e30	0.0207442
$617$	5.25618e31i	0.428934i	0.976731	+	0.214467i	$0.0688015\pi$
$617$	5.25618e31i	0.428934i	−0.976731	+	0.214467i	$0.931199\pi$
$618$	2.20605e31i	0.176704i
$619$	9.42009e31	0.740650	0.370325	−	0.928902i	$-0.379246\pi$
$619$	9.42009e31	0.740650	0.370325	+	0.928902i	$0.379246\pi$
$620$	0	0
$621$	5.21196e31	0.394864
$622$	3.61340e30i	0.0268736i
$623$	− 1.74795e31i	− 0.127619i
$624$	−1.05136e32	−0.753578
$625$	0	0
$626$	4.55954e31	0.315004
$627$	− 6.10410e31i	− 0.414042i
$628$	− 1.16207e32i	− 0.773918i
$629$	2.90156e32	1.89736
$630$	0	0
$631$	−2.22784e32	−1.40458	−0.702288	−	0.711892i	$-0.747838\pi$
$631$	−2.22784e32	−1.40458	−0.702288	+	0.711892i	$0.747838\pi$
$632$	2.65610e31i	0.164436i
$633$	− 2.28517e32i	− 1.38923i
$634$	5.53840e31	0.330642
$635$	0	0
$636$	−2.29605e32	−1.32198
$637$	4.60944e31i	0.260642i
$638$	− 2.08584e31i	− 0.115836i
$639$	−4.33738e31	−0.236574
$640$	0	0
$641$	1.38602e32	0.729295	0.364648	−	0.931146i	$-0.381189\pi$
$641$	1.38602e32	0.729295	0.364648	+	0.931146i	$0.381189\pi$
$642$	− 9.40714e31i	− 0.486188i
$643$	− 3.71401e31i	− 0.188546i	−0.995546	−	0.0942729i	$-0.969947\pi$
$643$	− 3.71401e31i	− 0.188546i	0.995546	−	0.0942729i	$-0.0300526\pi$
$644$	1.05898e32	0.528080
$645$	0	0
$646$	5.86067e32	2.82016
$647$	− 3.77554e32i	− 1.78476i	−0.451286	−	0.892379i	$-0.649035\pi$
$647$	− 3.77554e32i	− 1.78476i	0.451286	−	0.892379i	$-0.350965\pi$
$648$	2.85076e31i	0.132388i
$649$	2.56896e29	0.00117204
$650$	0	0
$651$	2.01920e32	0.889197
$652$	− 2.02210e32i	− 0.874893i
$653$	8.58042e31i	0.364760i	0.983228	+	0.182380i	$0.0583801\pi$
$653$	8.58042e31i	0.364760i	−0.983228	+	0.182380i	$0.941620\pi$
$654$	−8.70816e31	−0.363733
$655$	0	0
$656$	−1.05576e32	−0.425766
$657$	− 1.98290e32i	− 0.785777i
$658$	− 1.32874e32i	− 0.517421i
$659$	−1.46687e32	−0.561319	−0.280660	−	0.959807i	$-0.590553\pi$
$659$	−1.46687e32	−0.561319	−0.280660	+	0.959807i	$0.590553\pi$
$660$	0	0
$661$	2.02066e32	0.746752	0.373376	−	0.927680i	$-0.378200\pi$
$661$	2.02066e32	0.746752	0.373376	+	0.927680i	$0.378200\pi$
$662$	− 6.53331e32i	− 2.37283i
$663$	3.26672e32i	1.16602i
$664$	2.00239e31	0.0702450
$665$	0	0
$666$	2.82379e32	0.956927
$667$	7.38823e31i	0.246090i
$668$	− 1.37358e32i	− 0.449701i
$669$	−5.39243e32	−1.73534
$670$	0	0
$671$	7.24664e31	0.225334
$672$	4.16034e32i	1.27169i
$673$	− 5.34692e32i	− 1.60668i	−0.595519	−	0.803341i	$-0.703053\pi$
$673$	− 5.34692e32i	− 1.60668i	0.595519	−	0.803341i	$-0.296947\pi$
$674$	−6.59237e32	−1.94739
$675$	0	0
$676$	−2.23437e32	−0.637924
$677$	1.10049e32i	0.308899i	0.988001	+	0.154449i	$0.0493604\pi$
$677$	1.10049e32i	0.308899i	−0.988001	+	0.154449i	$0.950640\pi$
$678$	5.48422e32i	1.51347i
$679$	4.33457e32	1.17610
$680$	0	0
$681$	−8.34995e32	−2.19024
$682$	− 1.38119e32i	− 0.356233i
$683$	2.97297e32i	0.753967i	0.926220	+	0.376983i	$0.123039\pi$
$683$	2.97297e32i	0.753967i	−0.926220	+	0.376983i	$0.876961\pi$
$684$	2.73756e32	0.682683
$685$	0	0
$686$	6.15577e32	1.48441
$687$	− 2.48547e32i	− 0.589394i
$688$	1.64908e31i	0.0384568i
$689$	−2.74149e32	−0.628733
$690$	0	0
$691$	−7.18838e32	−1.59453	−0.797266	−	0.603628i	$-0.793721\pi$
$691$	−7.18838e32	−1.59453	−0.797266	+	0.603628i	$0.793721\pi$
$692$	8.06062e32i	1.75852i
$693$	− 5.45574e31i	− 0.117063i
$694$	5.84723e32	1.23400
$695$	0	0
$696$	−2.07583e31	−0.0423824
$697$	3.28039e32i	0.658793i
$698$	8.92072e31i	0.176223i
$699$	−8.51274e32	−1.65418
$700$	0	0
$701$	−1.02832e33	−1.93362	−0.966810	−	0.255497i	$-0.917761\pi$
$701$	−1.02832e33	−1.93362	−0.966810	+	0.255497i	$0.917761\pi$
$702$	− 2.09513e32i	− 0.387557i
$703$	− 7.71990e32i	− 1.40484i
$704$	1.25123e32	0.224002
$705$	0	0
$706$	−1.03287e32	−0.178975
$707$	5.19380e32i	0.885446i
$708$	3.06353e30i	0.00513854i
$709$	2.50942e32	0.414134	0.207067	−	0.978327i	$-0.433608\pi$
$709$	2.50942e32	0.414134	0.207067	+	0.978327i	$0.433608\pi$
$710$	0	0
$711$	5.80796e32	0.927947
$712$	1.18991e31i	0.0187066i
$713$	4.89231e32i	0.756805i
$714$	1.39284e33	2.12017
$715$	0	0
$716$	−7.75346e31	−0.114287
$717$	4.27071e32i	0.619483i
$718$	− 1.34209e33i	− 1.91580i
$719$	−7.09247e32	−0.996358	−0.498179	−	0.867074i	$-0.665998\pi$
$719$	−7.09247e32	−0.996358	−0.498179	+	0.867074i	$0.665998\pi$
$720$	0	0
$721$	5.39046e31	0.0733450
$722$	− 5.23757e32i	− 0.701378i
$723$	5.61891e32i	0.740562i
$724$	4.00417e32	0.519420
$725$	0	0
$726$	1.29776e33	1.63088
$727$	4.63712e32i	0.573591i	0.957992	+	0.286795i	$0.0925900\pi$
$727$	4.63712e32i	0.573591i	−0.957992	+	0.286795i	$0.907410\pi$
$728$	3.55259e31i	0.0432547i
$729$	9.21300e31	0.110417
$730$	0	0
$731$	5.12391e31	0.0595047
$732$	8.64174e32i	0.987924i
$733$	1.54780e33i	1.74188i	0.491387	+	0.870941i	$0.336490\pi$
$733$	1.54780e33i	1.74188i	−0.491387	+	0.870941i	$0.663510\pi$
$734$	6.53317e32	0.723801
$735$	0	0
$736$	−1.00801e33	−1.08235
$737$	3.72455e32i	0.393730i
$738$	3.19247e32i	0.332260i
$739$	1.49249e33	1.52932	0.764662	−	0.644431i	$-0.222906\pi$
$739$	1.49249e33	1.52932	0.764662	+	0.644431i	$0.222906\pi$
$740$	0	0
$741$	8.69144e32	0.863341
$742$	1.16890e33i	1.14322i
$743$	− 1.19934e32i	− 0.115497i	−0.998331	−	0.0577487i	$-0.981608\pi$
$743$	− 1.19934e32i	− 0.115497i	0.998331	−	0.0577487i	$-0.0183922\pi$
$744$	−1.37456e32	−0.130340
$745$	0	0
$746$	−4.15852e32	−0.382334
$747$	− 4.37852e32i	− 0.396406i
$748$	− 4.57290e32i	− 0.407683i
$749$	−2.29863e32	−0.201803
$750$	0	0
$751$	1.42812e33	1.21592	0.607959	−	0.793969i	$-0.291989\pi$
$751$	1.42812e33	1.21592	0.607959	+	0.793969i	$0.291989\pi$
$752$	6.54101e32i	0.548453i
$753$	− 8.71877e31i	− 0.0719967i
$754$	2.96996e32	0.241535
$755$	0	0
$756$	−4.28763e32	−0.338233
$757$	− 1.56208e33i	− 1.21367i	−0.794828	−	0.606835i	$-0.792439\pi$
$757$	− 1.56208e33i	− 1.21367i	0.794828	−	0.606835i	$-0.207561\pi$
$758$	2.65967e33i	2.03531i
$759$	3.51487e32	0.264929
$760$	0	0
$761$	1.92115e33	1.40488	0.702439	−	0.711744i	$-0.252094\pi$
$761$	1.92115e33	1.40488	0.702439	+	0.711744i	$0.252094\pi$
$762$	− 3.62020e33i	− 2.60765i
$763$	2.12783e32i	0.150975i
$764$	−2.40114e33	−1.67820
$765$	0	0
$766$	−1.19119e33	−0.807886
$767$	3.65787e30i	0.00244389i
$768$	− 2.18475e33i	− 1.43797i
$769$	−1.22615e33	−0.795044	−0.397522	−	0.917593i	$-0.630130\pi$
$769$	−1.22615e33	−0.795044	−0.397522	+	0.917593i	$0.630130\pi$
$770$	0	0
$771$	−1.53438e33	−0.965621
$772$	− 9.92455e32i	− 0.615335i
$773$	8.43914e32i	0.515507i	0.966211	+	0.257753i	$0.0829822\pi$
$773$	8.43914e32i	0.515507i	−0.966211	+	0.257753i	$0.917018\pi$
$774$	4.98658e31	0.0300111
$775$	0	0
$776$	−2.95074e32	−0.172394
$777$	− 1.83470e33i	− 1.05615i
$778$	− 4.28177e33i	− 2.42861i
$779$	8.72782e32	0.487781
$780$	0	0
$781$	1.92768e32	0.104604
$782$	3.37470e33i	1.80450i
$783$	− 2.99137e32i	− 0.157620i
$784$	−9.67477e32	−0.502350
$785$	0	0
$786$	−1.35860e33	−0.685066
$787$	1.37027e33i	0.680919i	0.940259	+	0.340460i	$0.110583\pi$
$787$	1.37027e33i	0.680919i	−0.940259	+	0.340460i	$0.889417\pi$
$788$	3.01931e33i	1.47862i
$789$	−7.82797e32	−0.377801
$790$	0	0
$791$	1.34007e33	0.628198
$792$	3.71398e31i	0.0171593i
$793$	1.03183e33i	0.469857i
$794$	6.72586e31	0.0301865
$795$	0	0
$796$	−9.72536e32	−0.424039
$797$	1.57462e33i	0.676714i	0.941018	+	0.338357i	$0.109871\pi$
$797$	1.57462e33i	0.676714i	−0.941018	+	0.338357i	$0.890129\pi$
$798$	− 3.70579e33i	− 1.56981i
$799$	2.03238e33	0.848628
$800$	0	0
$801$	2.60192e32	0.105565
$802$	− 1.55481e33i	− 0.621832i
$803$	8.81269e32i	0.347440i
$804$	−4.44159e33	−1.72621
$805$	0	0
$806$	1.96664e33	0.742799
$807$	2.22215e33i	0.827423i
$808$	− 3.53567e32i	− 0.129790i
$809$	2.56942e33	0.929882	0.464941	−	0.885342i	$-0.346076\pi$
$809$	2.56942e33	0.929882	0.464941	+	0.885342i	$0.346076\pi$
$810$	0	0
$811$	1.25770e33	0.442423	0.221212	−	0.975226i	$-0.428999\pi$
$811$	1.25770e33	0.442423	0.221212	+	0.975226i	$0.428999\pi$
$812$	− 6.07794e32i	− 0.210796i
$813$	− 2.01234e33i	− 0.688112i
$814$	−1.25499e33	−0.423116
$815$	0	0
$816$	−6.85652e33	−2.24733
$817$	− 1.36327e32i	− 0.0440583i
$818$	2.01023e33i	0.640593i
$819$	7.76826e32	0.244095
$820$	0	0
$821$	−2.38117e32	−0.0727519	−0.0363759	−	0.999338i	$-0.511581\pi$
$821$	−2.38117e32	−0.0727519	−0.0363759	+	0.999338i	$0.511581\pi$
$822$	− 6.92493e33i	− 2.08636i
$823$	− 5.82453e33i	− 1.73047i	−0.501370	−	0.865233i	$-0.667170\pi$
$823$	− 5.82453e33i	− 1.73047i	0.501370	−	0.865233i	$-0.332830\pi$
$824$	−3.66954e31	−0.0107510
$825$	0	0
$826$	1.55961e31	0.00444372
$827$	− 3.61128e33i	− 1.01472i	−0.861733	−	0.507362i	$-0.830621\pi$
$827$	− 3.61128e33i	− 1.01472i	0.861733	−	0.507362i	$-0.169379\pi$
$828$	1.57635e33i	0.436821i
$829$	−6.27935e33	−1.71608	−0.858040	−	0.513584i	$-0.828318\pi$
$829$	−6.27935e33	−1.71608	−0.858040	+	0.513584i	$0.828318\pi$
$830$	0	0
$831$	5.03467e33	1.33832
$832$	1.78159e33i	0.467078i
$833$	3.00609e33i	0.777292i
$834$	−7.75743e32	−0.197837
$835$	0	0
$836$	−1.21667e33	−0.301856
$837$	− 1.98081e33i	− 0.484731i
$838$	6.85832e33i	1.65543i
$839$	−7.51696e32	−0.178970	−0.0894849	−	0.995988i	$-0.528522\pi$
$839$	−7.51696e32	−0.178970	−0.0894849	+	0.995988i	$0.528522\pi$
$840$	0	0
$841$	−3.89268e33	−0.901767
$842$	2.39864e33i	0.548120i
$843$	− 4.82269e33i	− 1.08711i
$844$	−4.55478e33	−1.01281
$845$	0	0
$846$	1.97791e33	0.428003
$847$	− 3.17106e33i	− 0.676932i
$848$	− 5.75412e33i	− 1.21179i
$849$	8.35275e33	1.73537
$850$	0	0
$851$	4.44528e33	0.898896
$852$	2.29879e33i	0.458610i
$853$	9.11290e33i	1.79367i	0.442364	+	0.896836i	$0.354140\pi$
$853$	9.11290e33i	1.79367i	−0.442364	+	0.896836i	$0.645860\pi$
$854$	4.39943e33	0.854339
$855$	0	0
$856$	1.56478e32	0.0295805
$857$	6.17423e33i	1.15160i	0.817589	+	0.575802i	$0.195310\pi$
$857$	6.17423e33i	1.15160i	−0.817589	+	0.575802i	$0.804690\pi$
$858$	− 1.41293e33i	− 0.260026i
$859$	1.86175e33	0.338065	0.169033	−	0.985610i	$-0.445936\pi$
$859$	1.86175e33	0.338065	0.169033	+	0.985610i	$0.445936\pi$
$860$	0	0
$861$	2.07424e33	0.366710
$862$	− 7.70552e33i	− 1.34421i
$863$	5.22144e33i	0.898806i	0.893329	+	0.449403i	$0.148363\pi$
$863$	5.22144e33i	0.898806i	−0.893329	+	0.449403i	$0.851637\pi$
$864$	4.08125e33	0.693242
$865$	0	0
$866$	1.07821e34	1.78340
$867$	1.35479e34i	2.21132i
$868$	− 4.02466e33i	− 0.648265i
$869$	−2.58126e33	−0.410302
$870$	0	0
$871$	−5.30328e33	−0.820986
$872$	− 1.44852e32i	− 0.0221301i
$873$	6.45224e33i	0.972852i
$874$	8.97874e33	1.33608
$875$	0	0
$876$	−1.05093e34	−1.52327
$877$	− 6.73800e32i	− 0.0963908i	−0.998838	−	0.0481954i	$-0.984653\pi$
$877$	− 6.73800e32i	− 0.0963908i	0.998838	−	0.0481954i	$-0.0153470\pi$
$878$	8.48127e32i	0.119750i
$879$	4.67328e33	0.651253
$880$	0	0
$881$	1.36978e34	1.85963	0.929815	−	0.368028i	$-0.119967\pi$
$881$	1.36978e34	1.85963	0.929815	+	0.368028i	$0.119967\pi$
$882$	2.92552e33i	0.392025i
$883$	− 1.49590e33i	− 0.197859i	−0.995094	−	0.0989294i	$-0.968458\pi$
$883$	− 1.49590e33i	− 0.197859i	0.995094	−	0.0989294i	$-0.0315418\pi$
$884$	6.51121e33	0.850082
$885$	0	0
$886$	3.26378e33	0.415177
$887$	− 6.44904e33i	− 0.809792i	−0.914363	−	0.404896i	$-0.867308\pi$
$887$	− 6.44904e33i	− 0.809792i	0.914363	−	0.404896i	$-0.132692\pi$
$888$	1.24897e33i	0.154811i
$889$	−8.84592e33	−1.08236
$890$	0	0
$891$	−2.77043e33	−0.330334
$892$	1.07482e34i	1.26514i
$893$	− 5.40736e33i	− 0.628339i
$894$	1.72548e33	0.197938
$895$	0	0
$896$	−1.38819e33	−0.155206
$897$	5.00472e33i	0.552417i
$898$	− 1.51254e34i	− 1.64827i
$899$	2.80791e33	0.302097
$900$	0	0
$901$	−1.78789e34	−1.87502
$902$	− 1.41884e33i	− 0.146913i
$903$	− 3.23993e32i	− 0.0331227i
$904$	−9.12246e32	−0.0920820
$905$	0	0
$906$	−5.87083e33	−0.577731
$907$	6.42282e33i	0.624083i	0.950069	+	0.312041i	$0.101013\pi$
$907$	6.42282e33i	0.624083i	−0.950069	+	0.312041i	$0.898987\pi$
$908$	1.66431e34i	1.59679i
$909$	−7.73126e33	−0.732430
$910$	0	0
$911$	−1.48932e34	−1.37571	−0.687855	−	0.725848i	$-0.741447\pi$
$911$	−1.48932e34	−1.37571	−0.687855	+	0.725848i	$0.741447\pi$
$912$	1.82425e34i	1.66396i
$913$	1.94596e33i	0.175275i
$914$	8.59859e33	0.764797
$915$	0	0
$916$	−4.95402e33	−0.429695
$917$	3.31973e33i	0.284351i
$918$	− 1.36636e34i	− 1.15578i
$919$	−3.10701e33	−0.259546	−0.129773	−	0.991544i	$-0.541425\pi$
$919$	−3.10701e33	−0.259546	−0.129773	+	0.991544i	$0.541425\pi$
$920$	0	0
$921$	−1.82735e34	−1.48880
$922$	− 1.91330e34i	− 1.53950i
$923$	2.74476e33i	0.218115i
$924$	−2.89151e33	−0.226933
$925$	0	0
$926$	3.08285e34	2.36007
$927$	8.02400e32i	0.0606700i
$928$	5.78538e33i	0.432046i
$929$	−1.72846e34	−1.27490	−0.637452	−	0.770490i	$-0.720012\pi$
$929$	−1.72846e34	−1.27490	−0.637452	+	0.770490i	$0.720012\pi$
$930$	0	0
$931$	7.99801e33	0.575520
$932$	1.69676e34i	1.20597i
$933$	3.49473e32i	0.0245343i
$934$	−1.15624e34	−0.801790
$935$	0	0
$936$	−5.28822e32	−0.0357797
$937$	− 1.61548e34i	− 1.07969i	−0.841766	−	0.539843i	$-0.818484\pi$
$937$	− 1.61548e34i	− 1.07969i	0.841766	−	0.539843i	$-0.181516\pi$
$938$	2.26117e34i	1.49280i
$939$	4.40980e33	0.287584
$940$	0	0
$941$	7.69275e33	0.489554	0.244777	−	0.969579i	$-0.421285\pi$
$941$	7.69275e33	0.489554	0.244777	+	0.969579i	$0.421285\pi$
$942$	− 2.34160e34i	− 1.47206i
$943$	5.02567e33i	0.312111i
$944$	−7.67751e31	−0.00471023
$945$	0	0
$946$	−2.21620e32	−0.0132697
$947$	− 2.94332e34i	− 1.74106i	−0.492119	−	0.870528i	$-0.663778\pi$
$947$	− 2.94332e34i	− 1.74106i	0.492119	−	0.870528i	$-0.336222\pi$
$948$	− 3.07819e34i	− 1.79887i
$949$	−1.25481e34	−0.724465
$950$	0	0
$951$	5.35651e33	0.301860
$952$	2.31685e33i	0.128995i
$953$	− 1.97292e34i	− 1.08528i	−0.839965	−	0.542641i	$-0.817425\pi$
$953$	− 1.97292e34i	− 1.08528i	0.839965	−	0.542641i	$-0.182575\pi$
$954$	−1.73997e34	−0.945659
$955$	0	0
$956$	8.51236e33	0.451632
$957$	− 2.01734e33i	− 0.105753i
$958$	2.73973e34i	1.41907i
$959$	−1.69210e34	−0.865989
$960$	0	0
$961$	−1.42003e33	−0.0709542
$962$	− 1.78694e34i	− 0.882261i
$963$	− 3.42163e33i	− 0.166929i
$964$	1.11996e34	0.539904
$965$	0	0
$966$	2.13387e34	1.00446
$967$	− 2.03266e34i	− 0.945496i	−0.881198	−	0.472748i	$-0.843262\pi$
$967$	− 2.03266e34i	− 0.945496i	0.881198	−	0.472748i	$-0.156738\pi$
$968$	2.15869e33i	0.0992255i
$969$	5.66820e34	2.57467
$970$	0	0
$971$	3.40470e34	1.51028	0.755141	−	0.655563i	$-0.227569\pi$
$971$	3.40470e34	1.51028	0.755141	+	0.655563i	$0.227569\pi$
$972$	− 2.24494e34i	− 0.984106i
$973$	1.89552e33i	0.0821166i
$974$	3.45150e33	0.147768
$975$	0	0
$976$	−2.16570e34	−0.905579
$977$	− 3.68167e32i	− 0.0152145i	−0.999971	−	0.00760725i	$-0.997579\pi$
$977$	− 3.68167e32i	− 0.0152145i	0.999971	−	0.00760725i	$-0.00242149\pi$
$978$	− 4.07459e34i	− 1.66413i
$979$	−1.15638e33	−0.0466767
$980$	0	0
$981$	−3.16740e33	−0.124885
$982$	2.87225e34i	1.11928i
$983$	8.23724e33i	0.317261i	0.987338	+	0.158630i	$0.0507078\pi$
$983$	8.23724e33i	0.317261i	−0.987338	+	0.158630i	$0.949292\pi$
$984$	−1.41203e33	−0.0537529
$985$	0	0
$986$	1.93689e34	0.720310
$987$	− 1.28511e34i	− 0.472380i
$988$	− 1.73238e34i	− 0.629415i
$989$	7.85000e32	0.0281911
$990$	0	0
$991$	2.70349e33	0.0948590	0.0474295	−	0.998875i	$-0.484897\pi$
$991$	2.70349e33	0.0948590	0.0474295	+	0.998875i	$0.484897\pi$
$992$	3.83094e34i	1.32868i
$993$	− 6.31875e34i	− 2.16628i
$994$	1.17029e34	0.396598
$995$	0	0
$996$	−2.32059e34	−0.768452
$997$	− 4.64692e33i	− 0.152115i	−0.997103	−	0.0760573i	$-0.975767\pi$
$997$	− 4.64692e33i	− 0.152115i	0.997103	−	0.0760573i	$-0.0242332\pi$
$998$	7.14561e34i	2.31227i
$999$	−1.79982e34	−0.575740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.24.b.a.24.2		4
5.2	odd	4		25.24.a.a.1.2		2
5.3	odd	4		1.24.a.a.1.1	✓	2
5.4	even	2	inner	25.24.b.a.24.3		4
15.8	even	4		9.24.a.b.1.2		2
20.3	even	4		16.24.a.b.1.1		2
35.13	even	4		49.24.a.b.1.1		2
40.3	even	4		64.24.a.g.1.2		2
40.13	odd	4		64.24.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.24.a.a.1.1	✓	2	5.3	odd	4
9.24.a.b.1.2		2	15.8	even	4
16.24.a.b.1.1		2	20.3	even	4
25.24.a.a.1.2		2	5.2	odd	4
25.24.b.a.24.2		4	1.1	even	1	trivial
25.24.b.a.24.3		4	5.4	even	2	inner
49.24.a.b.1.1		2	35.13	even	4
64.24.a.d.1.1		2	40.13	odd	4
64.24.a.g.1.2		2	40.3	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:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4016.35i q^{2} -388445. i q^{3} -7.74247e6 q^{4} -1.56013e9 q^{6} +3.81217e9i q^{7} -2.59512e9i q^{8} -5.67462e10 q^{9} +O(q^{10})\)	\(q-4016.35i q^{2} -388445. i q^{3} -7.74247e6 q^{4} -1.56013e9 q^{6} +3.81217e9i q^{7} -2.59512e9i q^{8} -5.67462e10 q^{9} +2.52200e11 q^{11} +3.00752e12i q^{12} +3.59099e12i q^{13} +1.53110e13 q^{14} -7.53715e13 q^{16} +2.34190e14i q^{17} +2.27913e14i q^{18} +6.23086e14 q^{19} +1.48082e15 q^{21} -1.01292e15i q^{22} +3.58786e15i q^{23} -1.00806e15 q^{24} +1.44227e16 q^{26} -1.45267e16i q^{27} -2.95156e16i q^{28} +2.05923e16 q^{29} +1.36357e17 q^{31} +2.80949e17i q^{32} -9.79656e16i q^{33} +9.40588e17 q^{34} +4.39356e17 q^{36} -1.23898e18i q^{37} -2.50253e18i q^{38} +1.39490e18 q^{39} +1.40074e18 q^{41} -5.94748e18i q^{42} -2.18793e17i q^{43} -1.95265e18 q^{44} +1.44101e19 q^{46} -8.67836e18i q^{47} +2.92777e19i q^{48} +1.28361e19 q^{49} +9.09698e19 q^{51} -2.78032e19i q^{52} +7.63436e19i q^{53} -5.83441e19 q^{54} +9.89304e18 q^{56} -2.42034e20i q^{57} -8.27059e19i q^{58} +1.01862e18 q^{59} +2.87337e20 q^{61} -5.47658e20i q^{62} -2.16326e20i q^{63} +4.96127e20 q^{64} -3.93464e20 q^{66} +1.47683e21i q^{67} -1.81321e21i q^{68} +1.39369e21 q^{69} +7.64346e20 q^{71} +1.47263e20i q^{72} +3.49433e21i q^{73} -4.97617e21 q^{74} -4.82422e21 q^{76} +9.61427e20i q^{77} -5.60242e21i q^{78} -1.02350e22 q^{79} -1.09851e22 q^{81} -5.62587e21i q^{82} +7.71597e21i q^{83} -1.14652e22 q^{84} -8.78750e20 q^{86} -7.99897e21i q^{87} -6.54489e20i q^{88} -4.58518e21 q^{89} -1.36895e22 q^{91} -2.77789e22i q^{92} -5.29672e22i q^{93} -3.48553e22 q^{94} +1.09133e23 q^{96} -1.13703e23i q^{97} -5.15544e22i q^{98} -1.43114e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 50653312 q^{4} - 3619346112 q^{6} + 69998788332 q^{9}+O(q^{10}) \) 4 * q - 50653312 * q^4 - 3619346112 * q^6 + 69998788332 * q^9	\( 4 q - 50653312 q^{4} - 3619346112 q^{6} + 69998788332 q^{9} + 1713603936528 q^{11} + 83332069059456 q^{14} + 31913172803584 q^{16} - 8521201959920 q^{19} + 34\!\cdots\!88 q^{21}+ \cdots + 82\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 50653312 * q^4 - 3619346112 * q^6 + 69998788332 * q^9 + 1713603936528 * q^11 + 83332069059456 * q^14 + 31913172803584 * q^16 - 8521201959920 * q^19 + 3468063275445888 * q^21 + 2573244630282240 * q^24 + 110051709317470368 * q^26 - 41636867203246680 * q^29 + 275428034354000768 * q^31 + 1678967311922650656 * q^34 - 2347832600155149696 * q^36 + 3570022947330058464 * q^39 - 4588870954336629912 * q^41 - 25168177680066077184 * q^44 - 17626412036100442752 * q^46 + 26923963408752401628 * q^49 + 179996725690156584288 * q^51 - 209462446834079598720 * q^54 - 464913424108576235520 * q^56 - 561745979942681543760 * q^59 - 360905785033004447272 * q^61 + 1787380508938705829888 * q^64 - 1088676281827303766784 * q^66 + 2341121344344808447104 * q^69 + 6110067020388286657248 * q^71 - 13430688566297615514144 * q^74 + 12414308589026161180160 * q^76 - 12489833629119279961280 * q^79 - 5587057161859667951196 * q^81 - 31835503814380804952064 * q^84 - 21832577625837998486592 * q^86 - 12790186172346140009640 * q^89 - 109780356325409120292032 * q^91 - 318801036013069863654144 * q^94 + 211184243339168788512768 * q^96 + 82316490264624271963824 * q^99

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