LMFDB - Embedded newform 25.34.b.d.24.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,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, 34, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
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:	$172.457072203$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.7
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-100295. i q^{2} +1.18201e8i q^{3} -1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13i q^{7} -7.14175e14i q^{8} -8.41244e15 q^{9} +O(q^{10})$	\(q-100295. i q^{2} +1.18201e8i q^{3} -1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13i q^{7} -7.14175e14i q^{8} -8.41244e15 q^{9} +2.38218e17 q^{11} -1.73662e17i q^{12} -1.09650e18i q^{13} -1.07734e18 q^{14} -8.42488e19 q^{16} -2.82710e20i q^{17} +8.43728e20i q^{18} -4.67870e20 q^{19} +1.26968e21 q^{21} -2.38922e22i q^{22} -1.10068e21i q^{23} +8.44163e22 q^{24} -1.09973e23 q^{26} -3.37272e23i q^{27} +1.57817e22i q^{28} -1.88825e24 q^{29} -7.01821e24 q^{31} +2.31504e24i q^{32} +2.81577e25i q^{33} -2.83544e25 q^{34} +1.23596e25 q^{36} -6.16972e25i q^{37} +4.69252e25i q^{38} +1.29607e26 q^{39} +2.46253e25 q^{41} -1.27343e26i q^{42} +2.92621e25i q^{43} -3.49992e26 q^{44} -1.10393e26 q^{46} +4.02156e27i q^{47} -9.95830e27i q^{48} +7.61561e27 q^{49} +3.34166e28 q^{51} +1.61098e27i q^{52} +4.79966e28i q^{53} -3.38268e28 q^{54} -7.67144e27 q^{56} -5.53028e28i q^{57} +1.89382e29i q^{58} -1.22509e29 q^{59} +7.09485e28 q^{61} +7.03894e29i q^{62} +9.03637e28i q^{63} -4.91504e29 q^{64} +2.82408e30 q^{66} +4.28703e29i q^{67} +4.15359e29i q^{68} +1.30102e29 q^{69} +6.98564e30 q^{71} +6.00795e30i q^{72} +5.69333e30i q^{73} -6.18794e30 q^{74} +6.87398e29 q^{76} -2.55887e30i q^{77} -1.29990e31i q^{78} -2.53634e31 q^{79} -6.89932e30 q^{81} -2.46981e30i q^{82} +6.16471e31i q^{83} -1.86542e30 q^{84} +2.93485e30 q^{86} -2.23193e32i q^{87} -1.70130e32i q^{88} -1.29871e32 q^{89} -1.17782e31 q^{91} +1.61713e30i q^{92} -8.29560e32i q^{93} +4.03344e32 q^{94} -2.73640e32 q^{96} -4.34255e32i q^{97} -7.63810e32i q^{98} -2.00400e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	$ 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) $ 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * 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 $

$2$	− 100295.i	− 1.08215i	−0.840976	−	0.541073i	$-0.818018\pi$
$2$	− 100295.i	− 1.08215i	0.840976	−	0.541073i	$-0.181982\pi$
$3$	1.18201e8i	1.58533i	0.609655	+	0.792667i	$0.291308\pi$
$3$	1.18201e8i	1.58533i	−0.609655	+	0.792667i	$0.708692\pi$
$4$	−1.46921e9	−0.171038
$5$	0	0
$5$	0	0
$6$	1.18550e13	1.71556
$7$	− 1.07417e13i	− 0.122167i	−0.998133	−	0.0610836i	$-0.980544\pi$
$7$	− 1.07417e13i	− 0.122167i	0.998133	−	0.0610836i	$-0.0194556\pi$
$8$	− 7.14175e14i	− 0.897057i
$9$	−8.41244e15	−1.51328
$10$	0	0
$11$	2.38218e17	1.56313	0.781567	−	0.623822i	$-0.214421\pi$
$11$	2.38218e17	1.56313	0.781567	+	0.623822i	$0.214421\pi$
$12$	− 1.73662e17i	− 0.271153i
$13$	− 1.09650e18i	− 0.457027i	−0.973541	−	0.228514i	$-0.926613\pi$
$13$	− 1.09650e18i	− 0.457027i	0.973541	−	0.228514i	$-0.0733865\pi$
$14$	−1.07734e18	−0.132203
$15$	0	0
$16$	−8.42488e19	−1.14178
$17$	− 2.82710e20i	− 1.40907i	−0.709668	−	0.704536i	$-0.751155\pi$
$17$	− 2.82710e20i	− 1.40907i	0.709668	−	0.704536i	$-0.248845\pi$
$18$	8.43728e20i	1.63759i
$19$	−4.67870e20	−0.372127	−0.186063	−	0.982538i	$-0.559573\pi$
$19$	−4.67870e20	−0.372127	−0.186063	+	0.982538i	$0.559573\pi$
$20$	0	0
$21$	1.26968e21	0.193676
$22$	− 2.38922e22i	− 1.69154i
$23$	− 1.10068e21i	− 0.0374241i	−0.999825	−	0.0187121i	$-0.994043\pi$
$23$	− 1.10068e21i	− 0.0374241i	0.999825	−	0.0187121i	$-0.00595658\pi$
$24$	8.44163e22	1.42214
$25$	0	0
$26$	−1.09973e23	−0.494570
$27$	− 3.37272e23i	− 0.813726i
$28$	1.57817e22i	0.0208952i
$29$	−1.88825e24	−1.40117	−0.700587	−	0.713567i	$-0.747078\pi$
$29$	−1.88825e24	−1.40117	−0.700587	+	0.713567i	$0.747078\pi$
$30$	0	0
$31$	−7.01821e24	−1.73284	−0.866420	−	0.499315i	$-0.833585\pi$
$31$	−7.01821e24	−1.73284	−0.866420	+	0.499315i	$0.833585\pi$
$32$	2.31504e24i	0.338519i
$33$	2.81577e25i	2.47809i
$34$	−2.83544e25	−1.52482
$35$	0	0
$36$	1.23596e25	0.258829
$37$	− 6.16972e25i	− 0.822124i	−0.911607	−	0.411062i	$-0.865158\pi$
$37$	− 6.16972e25i	− 0.822124i	0.911607	−	0.411062i	$-0.134842\pi$
$38$	4.69252e25i	0.402695i
$39$	1.29607e26	0.724540
$40$	0	0
$41$	2.46253e25	0.0603182	0.0301591	−	0.999545i	$-0.490399\pi$
$41$	2.46253e25	0.0603182	0.0301591	+	0.999545i	$0.490399\pi$
$42$	− 1.27343e26i	− 0.209585i
$43$	2.92621e25i	0.0326645i	0.999867	+	0.0163322i	$0.00519894\pi$
$43$	2.92621e25i	0.0326645i	−0.999867	+	0.0163322i	$0.994801\pi$
$44$	−3.49992e26	−0.267355
$45$	0	0
$46$	−1.10393e26	−0.0404983
$47$	4.02156e27i	1.03462i	0.855799	+	0.517309i	$0.173066\pi$
$47$	4.02156e27i	1.03462i	−0.855799	+	0.517309i	$0.826934\pi$
$48$	− 9.95830e27i	− 1.81011i
$49$	7.61561e27	0.985075
$50$	0	0
$51$	3.34166e28	2.23385
$52$	1.61098e27i	0.0781691i
$53$	4.79966e28i	1.70082i	0.526121	+	0.850410i	$0.323646\pi$
$53$	4.79966e28i	1.70082i	−0.526121	+	0.850410i	$0.676354\pi$
$54$	−3.38268e28	−0.880570
$55$	0	0
$56$	−7.67144e27	−0.109591
$57$	− 5.53028e28i	− 0.589946i
$58$	1.89382e29i	1.51627i
$59$	−1.22509e29	−0.739790	−0.369895	−	0.929074i	$-0.620606\pi$
$59$	−1.22509e29	−0.739790	−0.369895	+	0.929074i	$0.620606\pi$
$60$	0	0
$61$	7.09485e28	0.247173	0.123586	−	0.992334i	$-0.460560\pi$
$61$	7.09485e28	0.247173	0.123586	+	0.992334i	$0.460560\pi$
$62$	7.03894e29i	1.87518i
$63$	9.03637e28i	0.184874i
$64$	−4.91504e29	−0.775457
$65$	0	0
$66$	2.82408e30	2.68165
$67$	4.28703e29i	0.317630i	0.987308	+	0.158815i	$0.0507674\pi$
$67$	4.28703e29i	0.317630i	−0.987308	+	0.158815i	$0.949233\pi$
$68$	4.15359e29i	0.241005i
$69$	1.30102e29	0.0593298
$70$	0	0
$71$	6.98564e30	1.98812	0.994061	−	0.108822i	$-0.0347078\pi$
$71$	6.98564e30	1.98812	0.994061	+	0.108822i	$0.0347078\pi$
$72$	6.00795e30i	1.35750i
$73$	5.69333e30i	1.02456i	0.858817	+	0.512282i	$0.171200\pi$
$73$	5.69333e30i	1.02456i	−0.858817	+	0.512282i	$0.828800\pi$
$74$	−6.18794e30	−0.889657
$75$	0	0
$76$	6.87398e29	0.0636479
$77$	− 2.55887e30i	− 0.190964i
$78$	− 1.29990e31i	− 0.784058i
$79$	−2.53634e31	−1.23983	−0.619913	−	0.784671i	$-0.712832\pi$
$79$	−2.53634e31	−1.23983	−0.619913	+	0.784671i	$0.712832\pi$
$80$	0	0
$81$	−6.89932e30	−0.223256
$82$	− 2.46981e30i	− 0.0652731i
$83$	6.16471e31i	1.33390i	0.745102	+	0.666951i	$0.232401\pi$
$83$	6.16471e31i	1.33390i	−0.745102	+	0.666951i	$0.767599\pi$
$84$	−1.86542e30	−0.0331259
$85$	0	0
$86$	2.93485e30	0.0353477
$87$	− 2.23193e32i	− 2.22133i
$88$	− 1.70130e32i	− 1.40222i
$89$	−1.29871e32	−0.888337	−0.444168	−	0.895943i	$-0.646501\pi$
$89$	−1.29871e32	−0.888337	−0.444168	+	0.895943i	$0.646501\pi$
$90$	0	0
$91$	−1.17782e31	−0.0558337
$92$	1.61713e30i	0.00640095i
$93$	− 8.29560e32i	− 2.74713i
$94$	4.03344e32	1.11961
$95$	0	0
$96$	−2.73640e32	−0.536666
$97$	− 4.34255e32i	− 0.717812i	−0.933374	−	0.358906i	$-0.883150\pi$
$97$	− 4.34255e32i	− 0.717812i	0.933374	−	0.358906i	$-0.116850\pi$
$98$	− 7.63810e32i	− 1.06599i
$99$	−2.00400e33	−2.36546
$100$	0	0
$101$	−2.04084e33	−1.73183	−0.865917	−	0.500187i	$-0.833264\pi$
$101$	−2.04084e33	−1.73183	−0.865917	+	0.500187i	$0.833264\pi$
$102$	− 3.35153e33i	− 2.41735i
$103$	1.31588e33i	0.807982i	0.914763	+	0.403991i	$0.132377\pi$
$103$	1.31588e33i	0.807982i	−0.914763	+	0.403991i	$0.867623\pi$
$104$	−7.83091e32	−0.409979
$105$	0	0
$106$	4.81383e33	1.84053
$107$	1.85120e33i	0.606207i	0.952958	+	0.303104i	$0.0980229\pi$
$107$	1.85120e33i	0.606207i	−0.952958	+	0.303104i	$0.901977\pi$
$108$	4.95522e32i	0.139178i
$109$	−6.95162e33	−1.67706	−0.838531	−	0.544855i	$-0.816585\pi$
$109$	−6.95162e33	−1.67706	−0.838531	+	0.544855i	$0.816585\pi$
$110$	0	0
$111$	7.29268e33	1.30334
$112$	9.04974e32i	0.139489i
$113$	− 1.10974e34i	− 1.47716i	−0.674164	−	0.738581i	$-0.735496\pi$
$113$	− 1.10974e34i	− 1.47716i	0.674164	−	0.738581i	$-0.264504\pi$
$114$	−5.54661e33	−0.638407
$115$	0	0
$116$	2.77422e33	0.239654
$117$	9.22421e33i	0.691612i
$118$	1.22870e34i	0.800560i
$119$	−3.03678e33	−0.172142
$120$	0	0
$121$	3.35229e34	1.44339
$122$	− 7.11579e33i	− 0.267477i
$123$	2.91074e33i	0.0956245i
$124$	1.03112e34	0.296382
$125$	0	0
$126$	9.06305e33	0.200060
$127$	− 9.12271e32i	− 0.0176751i	−0.999961	−	0.00883757i	$-0.997187\pi$
$127$	− 9.12271e32i	− 0.0176751i	0.999961	−	0.00883757i	$-0.00281312\pi$
$128$	6.91816e34i	1.17768i
$129$	−3.45881e33	−0.0517841
$130$	0	0
$131$	−1.56684e35	−1.81990	−0.909950	−	0.414718i	$-0.863880\pi$
$131$	−1.56684e35	−1.81990	−0.909950	+	0.414718i	$0.863880\pi$
$132$	− 4.13694e34i	− 0.423848i
$133$	5.02571e33i	0.0454617i
$134$	4.29969e34	0.343722
$135$	0	0
$136$	−2.01904e35	−1.26402
$137$	2.80790e35i	1.55773i	0.627191	+	0.778865i	$0.284204\pi$
$137$	2.80790e35i	1.55773i	−0.627191	+	0.778865i	$0.715796\pi$
$138$	− 1.30486e34i	− 0.0642034i
$139$	3.00000e35	1.31032	0.655160	−	0.755490i	$-0.272601\pi$
$139$	3.00000e35	1.31032	0.655160	+	0.755490i	$0.272601\pi$
$140$	0	0
$141$	−4.75353e35	−1.64022
$142$	− 7.00626e35i	− 2.15144i
$143$	− 2.61206e35i	− 0.714394i
$144$	7.08738e35	1.72784
$145$	0	0
$146$	5.71015e35	1.10873
$147$	9.00173e35i	1.56167i
$148$	9.06460e34i	0.140615i
$149$	−9.25696e33	−0.0128498	−0.00642488	−	0.999979i	$-0.502045\pi$
$149$	−9.25696e33	−0.0128498	−0.00642488	+	0.999979i	$0.502045\pi$
$150$	0	0
$151$	−4.37112e35	−0.486938	−0.243469	−	0.969909i	$-0.578285\pi$
$151$	−4.37112e35	−0.486938	−0.243469	+	0.969909i	$0.578285\pi$
$152$	3.34141e35i	0.333819i
$153$	2.37828e36i	2.13233i
$154$	−2.56642e35	−0.206650
$155$	0	0
$156$	−1.90420e35	−0.123924
$157$	− 5.98664e35i	− 0.350622i	−0.984513	−	0.175311i	$-0.943907\pi$
$157$	− 5.98664e35i	− 0.350622i	0.984513	−	0.175311i	$-0.0560930\pi$
$158$	2.54383e36i	1.34167i
$159$	−5.67325e36	−2.69637
$160$	0	0
$161$	−1.18232e34	−0.00457200
$162$	6.91969e35i	0.241596i
$163$	7.06844e35i	0.222961i	0.993767	+	0.111480i	$0.0355592\pi$
$163$	7.06844e35i	0.222961i	−0.993767	+	0.111480i	$0.964441\pi$
$164$	−3.61797e34	−0.0103167
$165$	0	0
$166$	6.18291e36	1.44348
$167$	− 3.67014e36i	− 0.775999i	−0.921660	−	0.387999i	$-0.873166\pi$
$167$	− 3.67014e36i	− 0.775999i	0.921660	−	0.387999i	$-0.126834\pi$
$168$	− 9.06773e35i	− 0.173738i
$169$	4.55383e36	0.791126
$170$	0	0
$171$	3.93593e36	0.563134
$172$	− 4.29920e34i	− 0.00558687i
$173$	− 6.08763e36i	− 0.718931i	−0.933158	−	0.359466i	$-0.882959\pi$
$173$	− 6.08763e36i	− 0.718931i	0.933158	−	0.359466i	$-0.117041\pi$
$174$	−2.23852e37	−2.40380
$175$	0	0
$176$	−2.00696e37	−1.78476
$177$	− 1.44806e37i	− 1.17281i
$178$	1.30255e37i	0.961309i
$179$	−1.93784e37	−1.30390	−0.651948	−	0.758264i	$-0.726048\pi$
$179$	−1.93784e37	−1.30390	−0.651948	+	0.758264i	$0.726048\pi$
$180$	0	0
$181$	−1.38808e36	−0.0777529	−0.0388765	−	0.999244i	$-0.512378\pi$
$181$	−1.38808e36	−0.0777529	−0.0388765	+	0.999244i	$0.512378\pi$
$182$	1.18130e36i	0.0604202i
$183$	8.38618e36i	0.391851i
$184$	−7.86078e35	−0.0335716
$185$	0	0
$186$	−8.32010e37	−2.97279
$187$	− 6.73466e37i	− 2.20257i
$188$	− 5.90851e36i	− 0.176959i
$189$	−3.62287e36	−0.0994106
$190$	0	0
$191$	−5.84448e36	−0.134802	−0.0674008	−	0.997726i	$-0.521471\pi$
$191$	−5.84448e36	−0.134802	−0.0674008	+	0.997726i	$0.521471\pi$
$192$	− 5.80964e37i	− 1.22936i
$193$	6.95190e37i	1.35023i	0.737712	+	0.675115i	$0.235906\pi$
$193$	6.95190e37i	1.35023i	−0.737712	+	0.675115i	$0.764094\pi$
$194$	−4.35537e37	−0.776777
$195$	0	0
$196$	−1.11889e37	−0.168485
$197$	4.77416e37i	0.661004i	0.943805	+	0.330502i	$0.107218\pi$
$197$	4.77416e37i	0.661004i	−0.943805	+	0.330502i	$0.892782\pi$
$198$	2.00991e38i	2.55978i
$199$	4.17107e37	0.488846	0.244423	−	0.969669i	$-0.421401\pi$
$199$	4.17107e37	0.488846	0.244423	+	0.969669i	$0.421401\pi$
$200$	0	0
$201$	−5.06731e37	−0.503550
$202$	2.04687e38i	1.87410i
$203$	2.02829e37i	0.171177i
$204$	−4.90959e37	−0.382074
$205$	0	0
$206$	1.31976e38	0.874354
$207$	9.25940e36i	0.0566333i
$208$	9.23785e37i	0.521826i
$209$	−1.11455e38	−0.581684
$210$	0	0
$211$	−1.72498e38	−0.769348	−0.384674	−	0.923052i	$-0.625686\pi$
$211$	−1.72498e38	−0.769348	−0.384674	+	0.923052i	$0.625686\pi$
$212$	− 7.05169e37i	− 0.290905i
$213$	8.25710e38i	3.15184i
$214$	1.85667e38	0.656004
$215$	0	0
$216$	−2.40871e38	−0.729959
$217$	7.53874e37i	0.211696i
$218$	6.97215e38i	1.81482i
$219$	−6.72958e38	−1.62428
$220$	0	0
$221$	−3.09990e38	−0.643984
$222$	− 7.31421e38i	− 1.41040i
$223$	− 5.99984e37i	− 0.107426i	−0.998556	−	0.0537130i	$-0.982894\pi$
$223$	− 5.99984e37i	− 0.107426i	0.998556	−	0.0537130i	$-0.0171056\pi$
$224$	2.48674e37	0.0413559
$225$	0	0
$226$	−1.11302e39	−1.59850
$227$	− 3.73826e38i	− 0.499164i	−0.968354	−	0.249582i	$-0.919707\pi$
$227$	− 3.73826e38i	− 0.499164i	0.968354	−	0.249582i	$-0.0802932\pi$
$228$	8.12512e37i	0.100903i
$229$	−8.71546e38	−1.00694	−0.503472	−	0.864012i	$-0.667944\pi$
$229$	−8.71546e38	−1.00694	−0.503472	+	0.864012i	$0.667944\pi$
$230$	0	0
$231$	3.02461e38	0.302741
$232$	1.34854e39i	1.25693i
$233$	− 2.14446e39i	− 1.86185i	−0.365210	−	0.930925i	$-0.619003\pi$
$233$	− 2.14446e39i	− 1.86185i	0.365210	−	0.930925i	$-0.380997\pi$
$234$	9.25144e38	0.748424
$235$	0	0
$236$	1.79990e38	0.126532
$237$	− 2.99798e39i	− 1.96554i
$238$	3.04574e38i	0.186283i
$239$	−7.11923e38	−0.406320	−0.203160	−	0.979146i	$-0.565121\pi$
$239$	−7.11923e38	−0.406320	−0.203160	+	0.979146i	$0.565121\pi$
$240$	0	0
$241$	−1.59013e39	−0.790957	−0.395478	−	0.918475i	$-0.629421\pi$
$241$	−1.59013e39	−0.790957	−0.395478	+	0.918475i	$0.629421\pi$
$242$	− 3.36218e39i	− 1.56195i
$243$	− 2.69042e39i	− 1.16766i
$244$	−1.04238e38	−0.0422760
$245$	0	0
$246$	2.91934e38	0.103480
$247$	5.13018e38i	0.170072i
$248$	5.01223e39i	1.55446i
$249$	−7.28675e39	−2.11468
$250$	0	0
$251$	1.75524e39	0.446395	0.223198	−	0.974773i	$-0.428351\pi$
$251$	1.75524e39	0.446395	0.223198	+	0.974773i	$0.428351\pi$
$252$	− 1.32763e38i	− 0.0316204i
$253$	− 2.62202e38i	− 0.0584989i
$254$	−9.14965e37	−0.0191271
$255$	0	0
$256$	2.71659e39	0.498960
$257$	9.54443e39i	1.64382i	0.569619	+	0.821909i	$0.307091\pi$
$257$	9.54443e39i	1.64382i	−0.569619	+	0.821909i	$0.692909\pi$
$258$	3.46902e38i	0.0560379i
$259$	−6.62732e38	−0.100437
$260$	0	0
$261$	1.58848e40	2.12037
$262$	1.57146e40i	1.96940i
$263$	− 9.19136e39i	− 1.08171i	−0.841117	−	0.540854i	$-0.818101\pi$
$263$	− 9.19136e39i	− 1.08171i	0.841117	−	0.540854i	$-0.181899\pi$
$264$	2.01095e40	2.22299
$265$	0	0
$266$	5.04055e38	0.0491962
$267$	− 1.53509e40i	− 1.40831i
$268$	− 6.29853e38i	− 0.0543269i
$269$	−7.25506e39	−0.588475	−0.294238	−	0.955732i	$-0.595066\pi$
$269$	−7.25506e39	−0.588475	−0.294238	+	0.955732i	$0.595066\pi$
$270$	0	0
$271$	7.67052e39	0.550594	0.275297	−	0.961359i	$-0.411224\pi$
$271$	7.67052e39	0.550594	0.275297	+	0.961359i	$0.411224\pi$
$272$	2.38179e40i	1.60886i
$273$	− 1.39220e39i	− 0.0885151i
$274$	2.81619e40	1.68569
$275$	0	0
$276$	−1.91146e38	−0.0101477
$277$	− 2.75284e40i	− 1.37678i	−0.725341	−	0.688389i	$-0.758318\pi$
$277$	− 2.75284e40i	− 1.37678i	0.725341	−	0.688389i	$-0.241682\pi$
$278$	− 3.00886e40i	− 1.41796i
$279$	5.90403e40	2.62228
$280$	0	0
$281$	−2.80354e40	−1.10676	−0.553379	−	0.832930i	$-0.686662\pi$
$281$	−2.80354e40	−1.10676	−0.553379	+	0.832930i	$0.686662\pi$
$282$	4.76757e40i	1.77495i
$283$	− 2.01665e40i	− 0.708196i	−0.935208	−	0.354098i	$-0.884788\pi$
$283$	− 2.01665e40i	− 0.708196i	0.935208	−	0.354098i	$-0.115212\pi$
$284$	−1.02633e40	−0.340045
$285$	0	0
$286$	−2.61977e40	−0.773078
$287$	− 2.64517e38i	− 0.00736891i
$288$	− 1.94751e40i	− 0.512275i
$289$	−3.96703e40	−0.985486
$290$	0	0
$291$	5.13294e40	1.13797
$292$	− 8.36468e39i	− 0.175240i
$293$	1.20254e40i	0.238113i	0.992887	+	0.119057i	$0.0379870\pi$
$293$	1.20254e40i	0.238113i	−0.992887	+	0.119057i	$0.962013\pi$
$294$	9.02831e40	1.68996
$295$	0	0
$296$	−4.40626e40	−0.737492
$297$	− 8.03444e40i	− 1.27196i
$298$	9.28430e38i	0.0139053i
$299$	−1.20689e39	−0.0171038
$300$	0	0
$301$	3.14324e38	0.00399053
$302$	4.38403e40i	0.526937i
$303$	− 2.41230e41i	− 2.74554i
$304$	3.94175e40	0.424889
$305$	0	0
$306$	2.38530e41	2.30749
$307$	1.15318e41i	1.05709i	0.848904	+	0.528547i	$0.177263\pi$
$307$	1.15318e41i	1.05709i	−0.848904	+	0.528547i	$0.822737\pi$
$308$	3.75950e39i	0.0326621i
$309$	−1.55538e41	−1.28092
$310$	0	0
$311$	1.68995e41	1.25120	0.625600	−	0.780144i	$-0.284854\pi$
$311$	1.68995e41	1.25120	0.625600	+	0.780144i	$0.284854\pi$
$312$	− 9.25622e40i	− 0.649954i
$313$	− 1.81722e41i	− 1.21039i	−0.796076	−	0.605197i	$-0.793094\pi$
$313$	− 1.81722e41i	− 1.21039i	0.796076	−	0.605197i	$-0.206906\pi$
$314$	−6.00431e40	−0.379424
$315$	0	0
$316$	3.72641e40	0.212058
$317$	2.26568e41i	1.22383i	0.790923	+	0.611916i	$0.209601\pi$
$317$	2.26568e41i	1.22383i	−0.790923	+	0.611916i	$0.790399\pi$
$318$	5.69000e41i	2.91786i
$319$	−4.49815e41	−2.19022
$320$	0	0
$321$	−2.18814e41	−0.961041
$322$	1.18581e39i	0.00494757i
$323$	1.32271e41i	0.524354i
$324$	1.01365e40	0.0381853
$325$	0	0
$326$	7.08931e40	0.241276
$327$	− 8.21689e41i	− 2.65870i
$328$	− 1.75868e40i	− 0.0541089i
$329$	4.31983e40	0.126396
$330$	0	0
$331$	−1.08689e41	−0.287755	−0.143877	−	0.989596i	$-0.545957\pi$
$331$	−1.08689e41	−0.287755	−0.143877	+	0.989596i	$0.545957\pi$
$332$	− 9.05723e40i	− 0.228148i
$333$	5.19024e41i	1.24411i
$334$	−3.68098e41	−0.839743
$335$	0	0
$336$	−1.06969e41	−0.221136
$337$	5.97224e41i	1.17556i	0.809022	+	0.587779i	$0.199997\pi$
$337$	5.97224e41i	1.17556i	−0.809022	+	0.587779i	$0.800003\pi$
$338$	− 4.56727e41i	− 0.856114i
$339$	1.31173e42	2.34180
$340$	0	0
$341$	−1.67187e42	−2.70866
$342$	− 3.94755e41i	− 0.609392i
$343$	− 1.64848e41i	− 0.242511i
$344$	2.08983e40	0.0293019
$345$	0	0
$346$	−6.10560e41	−0.777988
$347$	− 2.05995e41i	− 0.250277i	−0.992139	−	0.125138i	$-0.960062\pi$
$347$	− 2.05995e41i	− 0.250277i	0.992139	−	0.125138i	$-0.0399375\pi$
$348$	3.27916e41i	0.379932i
$349$	−1.68049e41	−0.185702	−0.0928510	−	0.995680i	$-0.529598\pi$
$349$	−1.68049e41	−0.185702	−0.0928510	+	0.995680i	$0.529598\pi$
$350$	0	0
$351$	−3.69818e41	−0.371895
$352$	5.51484e41i	0.529150i
$353$	1.30886e42i	1.19842i	0.800591	+	0.599211i	$0.204519\pi$
$353$	1.30886e42i	1.19842i	−0.800591	+	0.599211i	$0.795481\pi$
$354$	−1.45234e42	−1.26915
$355$	0	0
$356$	1.90808e41	0.151939
$357$	− 3.58950e41i	− 0.272903i
$358$	1.94356e42i	1.41100i
$359$	1.19927e42	0.831494	0.415747	−	0.909480i	$-0.363520\pi$
$359$	1.19927e42	0.831494	0.415747	+	0.909480i	$0.363520\pi$
$360$	0	0
$361$	−1.36187e42	−0.861522
$362$	1.39217e41i	0.0841400i
$363$	3.96244e42i	2.28825i
$364$	1.73046e40	0.00954969
$365$	0	0
$366$	8.41095e41	0.424040
$367$	− 1.58763e42i	− 0.765172i	−0.923920	−	0.382586i	$-0.875034\pi$
$367$	− 1.58763e42i	− 0.765172i	0.923920	−	0.382586i	$-0.124966\pi$
$368$	9.27310e40i	0.0427303i
$369$	−2.07159e41	−0.0912786
$370$	0	0
$371$	5.15564e41	0.207784
$372$	1.21880e42i	0.469864i
$373$	− 2.64106e42i	− 0.974052i	−0.873387	−	0.487026i	$-0.838082\pi$
$373$	− 2.64106e42i	− 0.974052i	0.873387	−	0.487026i	$-0.161918\pi$
$374$	−6.75455e42	−2.38350
$375$	0	0
$376$	2.87210e42	0.928112
$377$	2.07046e42i	0.640374i
$378$	3.63357e41i	0.107577i
$379$	4.63222e42	1.31293	0.656466	−	0.754355i	$-0.272050\pi$
$379$	4.63222e42	1.31293	0.656466	+	0.754355i	$0.272050\pi$
$380$	0	0
$381$	1.07831e41	0.0280210
$382$	5.86174e41i	0.145875i
$383$	− 6.48790e41i	− 0.154641i	−0.997006	−	0.0773205i	$-0.975364\pi$
$383$	− 6.48790e41i	− 0.154641i	0.997006	−	0.0773205i	$-0.0246365\pi$
$384$	−8.17734e42	−1.86701
$385$	0	0
$386$	6.97243e42	1.46115
$387$	− 2.46165e41i	− 0.0494306i
$388$	6.38010e41i	0.122773i
$389$	3.80740e42	0.702199	0.351100	−	0.936338i	$-0.385808\pi$
$389$	3.80740e42	0.702199	0.351100	+	0.936338i	$0.385808\pi$
$390$	0	0
$391$	−3.11173e41	−0.0527333
$392$	− 5.43888e42i	− 0.883669i
$393$	− 1.85202e43i	− 2.88515i
$394$	4.78826e42	0.715302
$395$	0	0
$396$	2.94429e42	0.404585
$397$	− 4.78435e42i	− 0.630638i	−0.948986	−	0.315319i	$-0.897889\pi$
$397$	− 4.78435e42i	− 0.630638i	0.948986	−	0.315319i	$-0.102111\pi$
$398$	− 4.18339e42i	− 0.529002i
$399$	−5.94045e41	−0.0720720
$400$	0	0
$401$	−7.89830e42	−0.882372	−0.441186	−	0.897416i	$-0.645442\pi$
$401$	−7.89830e42	−0.882372	−0.441186	+	0.897416i	$0.645442\pi$
$402$	5.08228e42i	0.544914i
$403$	7.69544e42i	0.791955i
$404$	2.99842e42	0.296210
$405$	0	0
$406$	2.03428e42	0.185239
$407$	− 1.46974e43i	− 1.28509i
$408$	− 2.38653e43i	− 2.00389i
$409$	−3.31586e41	−0.0267400	−0.0133700	−	0.999911i	$-0.504256\pi$
$409$	−3.31586e41	−0.0267400	−0.0133700	+	0.999911i	$0.504256\pi$
$410$	0	0
$411$	−3.31897e43	−2.46952
$412$	− 1.93330e42i	− 0.138196i
$413$	1.31595e42i	0.0903780i
$414$	9.28674e41	0.0612855
$415$	0	0
$416$	2.53843e42	0.154712
$417$	3.54604e43i	2.07730i
$418$	1.11784e43i	0.629467i
$419$	2.00047e43	1.08293	0.541466	−	0.840723i	$-0.317869\pi$
$419$	2.00047e43	1.08293	0.541466	+	0.840723i	$0.317869\pi$
$420$	0	0
$421$	2.36083e43	1.18144	0.590719	−	0.806878i	$-0.298844\pi$
$421$	2.36083e43	1.18144	0.590719	+	0.806878i	$0.298844\pi$
$422$	1.73007e43i	0.832547i
$423$	− 3.38311e43i	− 1.56567i
$424$	3.42780e43	1.52573
$425$	0	0
$426$	8.28148e43	3.41075
$427$	− 7.62106e41i	− 0.0301964i
$428$	− 2.71980e42i	− 0.103685i
$429$	3.08748e43	1.13255
$430$	0	0
$431$	9.17533e42	0.311707	0.155854	−	0.987780i	$-0.450187\pi$
$431$	9.17533e42	0.311707	0.155854	+	0.987780i	$0.450187\pi$
$432$	2.84148e43i	0.929100i
$433$	− 1.77198e43i	− 0.557711i	−0.960333	−	0.278856i	$-0.910045\pi$
$433$	− 1.77198e43i	− 0.557711i	0.960333	−	0.278856i	$-0.0899551\pi$
$434$	7.56100e42	0.229086
$435$	0	0
$436$	1.02134e43	0.286841
$437$	5.14976e41i	0.0139265i
$438$	6.74945e43i	1.75770i
$439$	−1.15735e43	−0.290270	−0.145135	−	0.989412i	$-0.546362\pi$
$439$	−1.15735e43	−0.290270	−0.145135	+	0.989412i	$0.546362\pi$
$440$	0	0
$441$	−6.40658e43	−1.49070
$442$	3.10905e43i	0.696885i
$443$	4.45699e43i	0.962454i	0.876596	+	0.481227i	$0.159809\pi$
$443$	4.45699e43i	0.962454i	−0.876596	+	0.481227i	$0.840191\pi$
$444$	−1.07145e43	−0.222921
$445$	0	0
$446$	−6.01755e42	−0.116250
$447$	− 1.09418e42i	− 0.0203712i
$448$	5.27958e42i	0.0947354i
$449$	−4.27285e43	−0.739015	−0.369508	−	0.929228i	$-0.620474\pi$
$449$	−4.27285e43	−0.739015	−0.369508	+	0.929228i	$0.620474\pi$
$450$	0	0
$451$	5.86621e42	0.0942854
$452$	1.63044e43i	0.252651i
$453$	− 5.16671e43i	− 0.771959i
$454$	−3.74930e43	−0.540168
$455$	0	0
$456$	−3.94959e43	−0.529215
$457$	− 1.01564e44i	− 1.31257i	−0.754514	−	0.656284i	$-0.772127\pi$
$457$	− 1.01564e44i	− 1.31257i	0.754514	−	0.656284i	$-0.227873\pi$
$458$	8.74120e43i	1.08966i
$459$	−9.53501e43	−1.14660
$460$	0	0
$461$	6.03006e43	0.674926	0.337463	−	0.941339i	$-0.390431\pi$
$461$	6.03006e43	0.674926	0.337463	+	0.941339i	$0.390431\pi$
$462$	− 3.03354e43i	− 0.327610i
$463$	− 1.59773e44i	− 1.66501i	−0.554019	−	0.832504i	$-0.686906\pi$
$463$	− 1.59773e44i	− 1.66501i	0.554019	−	0.832504i	$-0.313094\pi$
$464$	1.59083e44	1.59984
$465$	0	0
$466$	−2.15079e44	−2.01479
$467$	− 1.57317e44i	− 1.42248i	−0.702949	−	0.711240i	$-0.748134\pi$
$467$	− 1.57317e44i	− 1.42248i	0.702949	−	0.711240i	$-0.251866\pi$
$468$	− 1.35523e43i	− 0.118292i
$469$	4.60499e42	0.0388040
$470$	0	0
$471$	7.07627e43	0.555852
$472$	8.74926e43i	0.663634i
$473$	6.97077e42i	0.0510589i
$474$	−3.00684e44	−2.12700
$475$	0	0
$476$	4.46165e42	0.0294429
$477$	− 4.03768e44i	− 2.57382i
$478$	7.14025e43i	0.439697i
$479$	−9.07529e43	−0.539914	−0.269957	−	0.962872i	$-0.587010\pi$
$479$	−9.07529e43	−0.539914	−0.269957	+	0.962872i	$0.587010\pi$
$480$	0	0
$481$	−6.76508e43	−0.375733
$482$	1.59483e44i	0.855930i
$483$	− 1.39751e42i	− 0.00724815i
$484$	−4.92520e43	−0.246874
$485$	0	0
$486$	−2.69837e44	−1.26358
$487$	8.20051e43i	0.371204i	0.982625	+	0.185602i	$0.0594236\pi$
$487$	8.20051e43i	0.371204i	−0.982625	+	0.185602i	$0.940576\pi$
$488$	− 5.06696e43i	− 0.221728i
$489$	−8.35498e43	−0.353467
$490$	0	0
$491$	−4.35053e44	−1.72067	−0.860334	−	0.509731i	$-0.829745\pi$
$491$	−4.35053e44	−1.72067	−0.860334	+	0.509731i	$0.829745\pi$
$492$	− 4.27648e42i	− 0.0163554i
$493$	5.33826e44i	1.97435i
$494$	5.14533e43	0.184043
$495$	0	0
$496$	5.91276e44	1.97853
$497$	− 7.50375e43i	− 0.242883i
$498$	7.30827e44i	2.28839i
$499$	−3.20750e44	−0.971645	−0.485822	−	0.874058i	$-0.661480\pi$
$499$	−3.20750e44	−0.971645	−0.485822	+	0.874058i	$0.661480\pi$
$500$	0	0
$501$	4.33815e44	1.23022
$502$	− 1.76042e44i	− 0.483064i
$503$	1.94904e44i	0.517547i	0.965938	+	0.258773i	$0.0833183\pi$
$503$	1.94904e44i	0.517547i	−0.965938	+	0.258773i	$0.916682\pi$
$504$	6.45355e43	0.165842
$505$	0	0
$506$	−2.62976e43	−0.0633043
$507$	5.38267e44i	1.25420i
$508$	1.34031e42i	0.00302312i
$509$	−3.82784e44	−0.835814	−0.417907	−	0.908490i	$-0.637236\pi$
$509$	−3.82784e44	−0.835814	−0.417907	+	0.908490i	$0.637236\pi$
$510$	0	0
$511$	6.11560e43	0.125168
$512$	3.21804e44i	0.637730i
$513$	1.57800e44i	0.302809i
$514$	9.57261e44	1.77885
$515$	0	0
$516$	5.08171e42	0.00885706
$517$	9.58010e44i	1.61725i
$518$	6.64689e43i	0.108687i
$519$	7.19564e44	1.13975
$520$	0	0
$521$	−6.73383e44	−1.00101	−0.500507	−	0.865733i	$-0.666853\pi$
$521$	−6.73383e44	−1.00101	−0.500507	+	0.865733i	$0.666853\pi$
$522$	− 1.59317e45i	− 2.29455i
$523$	− 4.48155e44i	− 0.625389i	−0.949854	−	0.312694i	$-0.898768\pi$
$523$	− 4.48155e44i	− 0.625389i	0.949854	−	0.312694i	$-0.101232\pi$
$524$	2.30201e44	0.311272
$525$	0	0
$526$	−9.21850e44	−1.17056
$527$	1.98412e45i	2.44170i
$528$	− 2.37225e45i	− 2.82944i
$529$	8.63793e44	0.998599
$530$	0	0
$531$	1.03060e45	1.11951
$532$	− 7.38381e42i	− 0.00777568i
$533$	− 2.70016e43i	− 0.0275671i
$534$	−1.53962e45	−1.52400
$535$	0	0
$536$	3.06169e44	0.284933
$537$	− 2.29055e45i	− 2.06711i
$538$	7.27648e44i	0.636816i
$539$	1.81418e45	1.53980
$540$	0	0
$541$	−1.24268e45	−0.992214	−0.496107	−	0.868261i	$-0.665238\pi$
$541$	−1.24268e45	−0.992214	−0.496107	+	0.868261i	$0.665238\pi$
$542$	− 7.69317e44i	− 0.595823i
$543$	− 1.64072e44i	− 0.123264i
$544$	6.54483e44	0.476998
$545$	0	0
$546$	−1.39631e44	−0.0957861
$547$	− 2.79714e44i	− 0.186176i	−0.995658	−	0.0930878i	$-0.970326\pi$
$547$	− 2.79714e44i	− 0.186176i	0.995658	−	0.0930878i	$-0.0296737\pi$
$548$	− 4.12539e44i	− 0.266431i
$549$	−5.96849e44	−0.374043
$550$	0	0
$551$	8.83455e44	0.521414
$552$	− 9.29153e43i	− 0.0532222i
$553$	2.72446e44i	0.151466i
$554$	−2.76096e45	−1.48987
$555$	0	0
$556$	−4.40762e44	−0.224115
$557$	7.31187e44i	0.360926i	0.983582	+	0.180463i	$0.0577595\pi$
$557$	7.31187e44i	0.360926i	−0.983582	+	0.180463i	$0.942240\pi$
$558$	− 5.92146e45i	− 2.83769i
$559$	3.20858e43	0.0149285
$560$	0	0
$561$	7.96045e45	3.49181
$562$	2.81182e45i	1.19767i
$563$	− 1.17142e45i	− 0.484535i	−0.970209	−	0.242268i	$-0.922109\pi$
$563$	− 1.17142e45i	− 0.484535i	0.970209	−	0.242268i	$-0.0778912\pi$
$564$	6.98392e44	0.280539
$565$	0	0
$566$	−2.02260e45	−0.766371
$567$	7.41103e43i	0.0272746i
$568$	− 4.98897e45i	− 1.78346i
$569$	3.31218e45	1.15017	0.575085	−	0.818094i	$-0.304969\pi$
$569$	3.31218e45	1.15017	0.575085	+	0.818094i	$0.304969\pi$
$570$	0	0
$571$	2.01622e45	0.660756	0.330378	−	0.943849i	$-0.392824\pi$
$571$	2.01622e45	0.660756	0.330378	+	0.943849i	$0.392824\pi$
$572$	3.83765e44i	0.122189i
$573$	− 6.90824e44i	− 0.213706i
$574$	−2.65299e43	−0.00797423
$575$	0	0
$576$	4.13475e45	1.17349
$577$	5.76715e45i	1.59060i	0.606217	+	0.795299i	$0.292686\pi$
$577$	5.76715e45i	1.59060i	−0.606217	+	0.795299i	$0.707314\pi$
$578$	3.97874e45i	1.06644i
$579$	−8.21722e45	−2.14057
$580$	0	0
$581$	6.62193e44	0.162959
$582$	− 5.14809e45i	− 1.23145i
$583$	1.14337e46i	2.65861i
$584$	4.06604e45	0.919093
$585$	0	0
$586$	1.20609e45	0.257673
$587$	− 5.34761e45i	− 1.11079i	−0.831588	−	0.555394i	$-0.812568\pi$
$587$	− 5.34761e45i	− 1.11079i	0.831588	−	0.555394i	$-0.187432\pi$
$588$	− 1.32254e45i	− 0.267106i
$589$	3.28361e45	0.644837
$590$	0	0
$591$	−5.64311e45	−1.04791
$592$	5.19792e45i	0.938688i
$593$	2.76974e45i	0.486449i	0.969970	+	0.243224i	$0.0782051\pi$
$593$	2.76974e45i	0.486449i	−0.969970	+	0.243224i	$0.921795\pi$
$594$	−8.05816e45	−1.37645
$595$	0	0
$596$	1.36004e43	0.00219780
$597$	4.93025e45i	0.774984i
$598$	1.21046e44i	0.0185088i
$599$	1.07144e46	1.59376	0.796882	−	0.604135i	$-0.206481\pi$
$599$	1.07144e46	1.59376	0.796882	+	0.604135i	$0.206481\pi$
$600$	0	0
$601$	−7.75480e45	−1.09180	−0.545898	−	0.837851i	$-0.683812\pi$
$601$	−7.75480e45	−1.09180	−0.545898	+	0.837851i	$0.683812\pi$
$602$	− 3.15252e43i	− 0.00431833i
$603$	− 3.60643e45i	− 0.480665i
$604$	6.42208e44	0.0832849
$605$	0	0
$606$	−2.41942e46	−2.97107
$607$	− 9.69667e45i	− 1.15880i	−0.815043	−	0.579401i	$-0.803287\pi$
$607$	− 9.69667e45i	− 1.15880i	0.815043	−	0.579401i	$-0.196713\pi$
$608$	− 1.08314e45i	− 0.125972i
$609$	−2.39747e45	−0.271373
$610$	0	0
$611$	4.40963e45	0.472849
$612$	− 3.49418e45i	− 0.364709i
$613$	4.57708e45i	0.465040i	0.972592	+	0.232520i	$0.0746971\pi$
$613$	4.57708e45i	0.465040i	−0.972592	+	0.232520i	$0.925303\pi$
$614$	1.15658e46	1.14393
$615$	0	0
$616$	−1.82748e45	−0.171305
$617$	9.88010e45i	0.901688i	0.892603	+	0.450844i	$0.148877\pi$
$617$	9.88010e45i	0.901688i	−0.892603	+	0.450844i	$0.851123\pi$
$618$	1.55998e46i	1.38614i
$619$	1.00856e46	0.872584	0.436292	−	0.899805i	$-0.356291\pi$
$619$	1.00856e46	0.872584	0.436292	+	0.899805i	$0.356291\pi$
$620$	0	0
$621$	−3.71229e44	−0.0304530
$622$	− 1.69494e46i	− 1.35398i
$623$	1.39503e45i	0.108526i
$624$	−1.09192e46	−0.827269
$625$	0	0
$626$	−1.82259e46	−1.30982
$627$	− 1.31741e46i	− 0.922164i
$628$	8.79561e44i	0.0599697i
$629$	−1.74424e46	−1.15843
$630$	0	0
$631$	1.57860e46	0.994918	0.497459	−	0.867487i	$-0.334266\pi$
$631$	1.57860e46	0.994918	0.497459	+	0.867487i	$0.334266\pi$
$632$	1.81139e46i	1.11219i
$633$	− 2.03894e46i	− 1.21967i
$634$	2.27237e46	1.32436
$635$	0	0
$636$	8.33517e45	0.461182
$637$	− 8.35049e45i	− 0.450206i
$638$	4.51143e46i	2.37014i
$639$	−5.87662e46	−3.00859
$640$	0	0
$641$	−1.18505e45	−0.0576206	−0.0288103	−	0.999585i	$-0.509172\pi$
$641$	−1.18505e45	−0.0576206	−0.0288103	+	0.999585i	$0.509172\pi$
$642$	2.19460e46i	1.03999i
$643$	3.16044e46i	1.45971i	0.683602	+	0.729855i	$0.260413\pi$
$643$	3.16044e46i	1.45971i	−0.683602	+	0.729855i	$0.739587\pi$
$644$	1.73706e43	0.000781986 0
$645$	0	0
$646$	1.32662e46	0.567427
$647$	− 4.20047e45i	− 0.175137i	−0.996159	−	0.0875683i	$-0.972090\pi$
$647$	− 4.20047e45i	− 0.175137i	0.996159	−	0.0875683i	$-0.0279096\pi$
$648$	4.92732e45i	0.200273i
$649$	−2.91838e46	−1.15639
$650$	0	0
$651$	−8.91087e45	−0.335609
$652$	− 1.03850e45i	− 0.0381348i
$653$	− 1.95321e46i	− 0.699327i	−0.936875	−	0.349664i	$-0.886296\pi$
$653$	− 1.95321e46i	− 0.699327i	0.936875	−	0.349664i	$-0.113704\pi$
$654$	−8.24115e46	−2.87710
$655$	0	0
$656$	−2.07466e45	−0.0688704
$657$	− 4.78948e46i	− 1.55046i
$658$	− 4.33259e45i	− 0.136779i
$659$	4.47813e46	1.37876	0.689378	−	0.724402i	$-0.257884\pi$
$659$	4.47813e46	1.37876	0.689378	+	0.724402i	$0.257884\pi$
$660$	0	0
$661$	3.41637e45	0.100056	0.0500278	−	0.998748i	$-0.484069\pi$
$661$	3.41637e45	0.100056	0.0500278	+	0.998748i	$0.484069\pi$
$662$	1.09010e46i	0.311392i
$663$	− 3.66412e46i	− 1.02093i
$664$	4.40268e46	1.19659
$665$	0	0
$666$	5.20557e46	1.34630
$667$	2.07836e45i	0.0524377i
$668$	5.39220e45i	0.132725i
$669$	7.09187e45	0.170306
$670$	0	0
$671$	1.69012e46	0.386364
$672$	2.93935e45i	0.0655629i
$673$	2.58526e46i	0.562674i	0.959609	+	0.281337i	$0.0907778\pi$
$673$	2.58526e46i	0.562674i	−0.959609	+	0.281337i	$0.909222\pi$
$674$	5.98987e46	1.27212
$675$	0	0
$676$	−6.69051e45	−0.135313
$677$	− 5.00348e46i	− 0.987550i	−0.869590	−	0.493775i	$-0.835617\pi$
$677$	− 5.00348e46i	− 0.987550i	0.869590	−	0.493775i	$-0.164383\pi$
$678$	− 1.31560e47i	− 2.53416i
$679$	−4.66463e45	−0.0876931
$680$	0	0
$681$	4.41867e46	0.791341
$682$	1.67680e47i	2.93116i
$683$	− 7.27991e46i	− 1.24218i	−0.783739	−	0.621090i	$-0.786690\pi$
$683$	− 7.27991e46i	− 1.24218i	0.783739	−	0.621090i	$-0.213310\pi$
$684$	−5.78269e45	−0.0963173
$685$	0	0
$686$	−1.65335e46	−0.262432
$687$	− 1.03018e47i	− 1.59634i
$688$	− 2.46529e45i	− 0.0372958i
$689$	5.26281e46	0.777321
$690$	0	0
$691$	−1.10753e47	−1.55944	−0.779720	−	0.626129i	$-0.784638\pi$
$691$	−1.10753e47	−1.55944	−0.779720	+	0.626129i	$0.784638\pi$
$692$	8.94398e45i	0.122965i
$693$	2.15263e46i	0.288982i
$694$	−2.06603e46	−0.270836
$695$	0	0
$696$	−1.59399e47	−1.99266
$697$	− 6.96182e45i	− 0.0849928i
$698$	1.68545e46i	0.200957i
$699$	2.53477e47	2.95165
$700$	0	0
$701$	−6.39910e46	−0.710839	−0.355420	−	0.934707i	$-0.615662\pi$
$701$	−6.39910e46	−0.710839	−0.355420	+	0.934707i	$0.615662\pi$
$702$	3.70910e46i	0.402444i
$703$	2.88663e46i	0.305934i
$704$	−1.17085e47	−1.21214
$705$	0	0
$706$	1.31272e47	1.29687
$707$	2.19221e46i	0.211573i
$708$	2.12751e46i	0.200596i
$709$	1.32785e47	1.22317	0.611585	−	0.791179i	$-0.290532\pi$
$709$	1.32785e47	1.22317	0.611585	+	0.791179i	$0.290532\pi$
$710$	0	0
$711$	2.13368e47	1.87621
$712$	9.27508e46i	0.796889i
$713$	7.72481e45i	0.0648501i
$714$	−3.60010e46	−0.295321
$715$	0	0
$716$	2.84709e46	0.223016
$717$	− 8.41501e46i	− 0.644152i
$718$	− 1.20281e47i	− 0.899797i
$719$	4.87360e46	0.356306	0.178153	−	0.984003i	$-0.442988\pi$
$719$	4.87360e46	0.356306	0.178153	+	0.984003i	$0.442988\pi$
$720$	0	0
$721$	1.41348e46	0.0987089
$722$	1.36589e47i	0.932291i
$723$	− 1.87956e47i	− 1.25393i
$724$	2.03937e45	0.0132987
$725$	0	0
$726$	3.97414e47	2.47622
$727$	3.19850e47i	1.94818i	0.226159	+	0.974090i	$0.427383\pi$
$727$	3.19850e47i	1.94818i	−0.226159	+	0.974090i	$0.572617\pi$
$728$	8.41171e45i	0.0500860i
$729$	2.79657e47	1.62788
$730$	0	0
$731$	8.27267e45	0.0460266
$732$	− 1.23210e46i	− 0.0670215i
$733$	2.08452e47i	1.10864i	0.832304	+	0.554319i	$0.187021\pi$
$733$	2.08452e47i	1.10864i	−0.832304	+	0.554319i	$0.812979\pi$
$734$	−1.59232e47	−0.828027
$735$	0	0
$736$	2.54811e45	0.0126688
$737$	1.02125e47i	0.496499i
$738$	2.07771e46i	0.0987767i
$739$	−3.11658e47	−1.44892	−0.724461	−	0.689316i	$-0.757911\pi$
$739$	−3.11658e47	−1.44892	−0.724461	+	0.689316i	$0.757911\pi$
$740$	0	0
$741$	−6.06393e46	−0.269621
$742$	− 5.17086e46i	− 0.224853i
$743$	− 1.10806e46i	− 0.0471246i	−0.999722	−	0.0235623i	$-0.992499\pi$
$743$	− 1.10806e46i	− 0.0471246i	0.999722	−	0.0235623i	$-0.00750080\pi$
$744$	−5.92452e47	−2.46433
$745$	0	0
$746$	−2.64886e47	−1.05407
$747$	− 5.18602e47i	− 2.01857i
$748$	9.89461e46i	0.376723i
$749$	1.98850e46	0.0740586
$750$	0	0
$751$	−3.90356e46	−0.139124	−0.0695620	−	0.997578i	$-0.522160\pi$
$751$	−3.90356e46	−0.139124	−0.0695620	+	0.997578i	$0.522160\pi$
$752$	− 3.38812e47i	− 1.18131i
$753$	2.07471e47i	0.707685i
$754$	2.07657e47	0.692978
$755$	0	0
$756$	5.32274e45	0.0170030
$757$	− 4.61535e47i	− 1.44252i	−0.692663	−	0.721261i	$-0.743563\pi$
$757$	− 4.61535e47i	− 1.44252i	0.692663	−	0.721261i	$-0.256437\pi$
$758$	− 4.64590e47i	− 1.42078i
$759$	3.09926e46	0.0927403
$760$	0	0
$761$	−1.37335e47	−0.393490	−0.196745	−	0.980455i	$-0.563037\pi$
$761$	−1.37335e47	−0.393490	−0.196745	+	0.980455i	$0.563037\pi$
$762$	− 1.08150e46i	− 0.0303228i
$763$	7.46721e46i	0.204882i
$764$	8.58675e45	0.0230562
$765$	0	0
$766$	−6.50706e46	−0.167344
$767$	1.34330e47i	0.338104i
$768$	3.21104e47i	0.791018i
$769$	−6.07971e47	−1.46588	−0.732939	−	0.680294i	$-0.761852\pi$
$769$	−6.07971e47	−1.46588	−0.732939	+	0.680294i	$0.761852\pi$
$770$	0	0
$771$	−1.12816e48	−2.60600
$772$	− 1.02138e47i	− 0.230941i
$773$	2.01842e47i	0.446736i	0.974734	+	0.223368i	$0.0717051\pi$
$773$	2.01842e47i	0.446736i	−0.974734	+	0.223368i	$0.928295\pi$
$774$	−2.46892e46	−0.0534911
$775$	0	0
$776$	−3.10134e47	−0.643919
$777$	− 7.83356e46i	− 0.159225i
$778$	− 3.81864e47i	− 0.759881i
$779$	−1.15215e46	−0.0224460
$780$	0	0
$781$	1.66411e48	3.10770
$782$	3.12092e46i	0.0570651i
$783$	6.36853e47i	1.14017i
$784$	−6.41606e47	−1.12474
$785$	0	0
$786$	−1.85749e48	−3.12215
$787$	− 3.53259e47i	− 0.581447i	−0.956807	−	0.290723i	$-0.906104\pi$
$787$	− 3.53259e47i	− 0.581447i	0.956807	−	0.290723i	$-0.0938959\pi$
$788$	− 7.01423e46i	− 0.113057i
$789$	1.08643e48	1.71487
$790$	0	0
$791$	−1.19205e47	−0.180461
$792$	1.43121e48i	2.12196i
$793$	− 7.77947e46i	− 0.112965i
$794$	−4.79848e47	−0.682441
$795$	0	0
$796$	−6.12817e46	−0.0836113
$797$	− 7.65249e47i	− 1.02268i	−0.859378	−	0.511341i	$-0.829149\pi$
$797$	− 7.65249e47i	− 1.02268i	0.859378	−	0.511341i	$-0.170851\pi$
$798$	5.95799e46i	0.0779923i
$799$	1.13693e48	1.45785
$800$	0	0
$801$	1.09253e48	1.34431
$802$	7.92162e47i	0.954854i
$803$	1.35626e48i	1.60153i
$804$	7.44493e46	0.0861263
$805$	0	0
$806$	7.71817e47	0.857010
$807$	− 8.57556e47i	− 0.932930i
$808$	1.45752e48i	1.55355i
$809$	1.19928e47	0.125248	0.0626238	−	0.998037i	$-0.480053\pi$
$809$	1.19928e47	0.125248	0.0626238	+	0.998037i	$0.480053\pi$
$810$	0	0
$811$	1.18185e48	1.18500	0.592502	−	0.805569i	$-0.298140\pi$
$811$	1.18185e48	1.18500	0.592502	+	0.805569i	$0.298140\pi$
$812$	− 2.97998e46i	− 0.0292779i
$813$	9.06664e47i	0.872876i
$814$	−1.47408e48	−1.39065
$815$	0	0
$816$	−2.81531e48	−2.55058
$817$	− 1.36909e46i	− 0.0121553i
$818$	3.32565e46i	0.0289366i
$819$	9.90834e46	0.0844922
$820$	0	0
$821$	−3.09842e47	−0.253792	−0.126896	−	0.991916i	$-0.540501\pi$
$821$	−3.09842e47	−0.253792	−0.126896	+	0.991916i	$0.540501\pi$
$822$	3.32877e48i	2.67238i
$823$	9.72259e47i	0.765041i	0.923947	+	0.382521i	$0.124944\pi$
$823$	9.72259e47i	0.765041i	−0.923947	+	0.382521i	$0.875056\pi$
$824$	9.39769e47	0.724806
$825$	0	0
$826$	1.31983e47	0.0978021
$827$	− 1.72721e48i	− 1.25460i	−0.778779	−	0.627298i	$-0.784161\pi$
$827$	− 1.72721e48i	− 1.25460i	0.778779	−	0.627298i	$-0.215839\pi$
$828$	− 1.36040e46i	− 0.00968646i
$829$	−2.30502e48	−1.60889	−0.804444	−	0.594029i	$-0.797536\pi$
$829$	−2.30502e48	−1.60889	−0.804444	+	0.594029i	$0.797536\pi$
$830$	0	0
$831$	3.25388e48	2.18265
$832$	5.38933e47i	0.354405i
$833$	− 2.15301e48i	− 1.38804i
$834$	3.55651e48	2.24794
$835$	0	0
$836$	1.63751e47	0.0994902
$837$	2.36705e48i	1.41006i
$838$	− 2.00638e48i	− 1.17189i
$839$	−4.09990e47	−0.234801	−0.117401	−	0.993085i	$-0.537456\pi$
$839$	−4.09990e47	−0.234801	−0.117401	+	0.993085i	$0.537456\pi$
$840$	0	0
$841$	1.74940e48	0.963286
$842$	− 2.36780e48i	− 1.27849i
$843$	− 3.31381e48i	− 1.75458i
$844$	2.53435e47	0.131588
$845$	0	0
$846$	−3.39310e48	−1.69428
$847$	− 3.60092e47i	− 0.176334i
$848$	− 4.04365e48i	− 1.94197i
$849$	2.38370e48	1.12273
$850$	0	0
$851$	−6.79089e46	−0.0307673
$852$	− 1.21314e48i	− 0.539085i
$853$	− 7.10700e47i	− 0.309761i	−0.987933	−	0.154881i	$-0.950501\pi$
$853$	− 7.10700e47i	− 0.309761i	0.987933	−	0.154881i	$-0.0494993\pi$
$854$	−7.64356e46	−0.0326769
$855$	0	0
$856$	1.32208e48	0.543803
$857$	− 2.71615e48i	− 1.09590i	−0.836511	−	0.547949i	$-0.815409\pi$
$857$	− 2.71615e48i	− 1.09590i	0.836511	−	0.547949i	$-0.184591\pi$
$858$	− 3.09660e48i	− 1.22559i
$859$	4.17849e47	0.162230	0.0811152	−	0.996705i	$-0.474152\pi$
$859$	4.17849e47	0.162230	0.0811152	+	0.996705i	$0.474152\pi$
$860$	0	0
$861$	3.12663e46	0.0116822
$862$	− 9.20242e47i	− 0.337312i
$863$	− 1.36178e48i	− 0.489697i	−0.969561	−	0.244849i	$-0.921262\pi$
$863$	− 1.36178e48i	− 0.489697i	0.969561	−	0.244849i	$-0.0787383\pi$
$864$	7.80797e47	0.275462
$865$	0	0
$866$	−1.77722e48	−0.603524
$867$	− 4.68907e48i	− 1.56233i
$868$	− 1.10760e47i	− 0.0362081i
$869$	−6.04203e48	−1.93801
$870$	0	0
$871$	4.70071e47	0.145166
$872$	4.96468e48i	1.50442i
$873$	3.65314e48i	1.08625i
$874$	5.16496e46	0.0150705
$875$	0	0
$876$	9.88715e47	0.277813
$877$	4.09886e48i	1.13024i	0.825009	+	0.565119i	$0.191170\pi$
$877$	4.09886e48i	1.13024i	−0.825009	+	0.565119i	$0.808830\pi$
$878$	1.16077e48i	0.314114i
$879$	−1.42141e48	−0.377489
$880$	0	0
$881$	2.24659e48	0.574674	0.287337	−	0.957830i	$-0.407230\pi$
$881$	2.24659e48	0.574674	0.287337	+	0.957830i	$0.407230\pi$
$882$	6.42550e48i	1.61315i
$883$	1.41582e48i	0.348863i	0.984669	+	0.174432i	$0.0558088\pi$
$883$	1.41582e48i	0.348863i	−0.984669	+	0.174432i	$0.944191\pi$
$884$	4.55439e47	0.110146
$885$	0	0
$886$	4.47015e48	1.04152
$887$	− 5.80717e48i	− 1.32808i	−0.747696	−	0.664041i	$-0.768840\pi$
$887$	− 5.80717e48i	− 1.32808i	0.747696	−	0.664041i	$-0.231160\pi$
$888$	− 5.20825e48i	− 1.16917i
$889$	−9.79933e45	−0.00215932
$890$	0	0
$891$	−1.64354e48	−0.348979
$892$	8.81500e46i	0.0183739i
$893$	− 1.88157e48i	− 0.385009i
$894$	−1.09741e47	−0.0220446
$895$	0	0
$896$	7.43126e47	0.143873
$897$	− 1.42656e47i	− 0.0271153i
$898$	4.28547e48i	0.799722i
$899$	1.32521e49	2.42801
$900$	0	0
$901$	1.35691e49	2.39658
$902$	− 5.88353e47i	− 0.102031i
$903$	3.71534e46i	0.00632632i
$904$	−7.92551e48	−1.32510
$905$	0	0
$906$	−5.18197e48	−0.835371
$907$	9.51843e48i	1.50676i	0.657583	+	0.753382i	$0.271579\pi$
$907$	9.51843e48i	1.50676i	−0.657583	+	0.753382i	$0.728421\pi$
$908$	5.49228e47i	0.0853760i
$909$	1.71684e49	2.62076
$910$	0	0
$911$	2.66104e47	0.0391740	0.0195870	−	0.999808i	$-0.493765\pi$
$911$	2.66104e47	0.0391740	0.0195870	+	0.999808i	$0.493765\pi$
$912$	4.65919e48i	0.673590i
$913$	1.46855e49i	2.08507i
$914$	−1.01864e49	−1.42039
$915$	0	0
$916$	1.28048e48	0.172226
$917$	1.68305e48i	0.222332i
$918$	9.56316e48i	1.24079i
$919$	−1.65505e48	−0.210914	−0.105457	−	0.994424i	$-0.533631\pi$
$919$	−1.65505e48	−0.210914	−0.105457	+	0.994424i	$0.533631\pi$
$920$	0	0
$921$	−1.36307e49	−1.67585
$922$	− 6.04787e48i	− 0.730368i
$923$	− 7.65972e48i	− 0.908626i
$924$	−4.44377e47	−0.0517803
$925$	0	0
$926$	−1.60245e49	−1.80178
$927$	− 1.10698e49i	− 1.22271i
$928$	− 4.37136e48i	− 0.474324i
$929$	−1.12664e49	−1.20095	−0.600477	−	0.799642i	$-0.705022\pi$
$929$	−1.12664e49	−1.20095	−0.600477	+	0.799642i	$0.705022\pi$
$930$	0	0
$931$	−3.56312e48	−0.366573
$932$	3.15065e48i	0.318447i
$933$	1.99754e49i	1.98357i
$934$	−1.57781e49	−1.53933
$935$	0	0
$936$	6.58770e48	0.620415
$937$	9.05198e48i	0.837607i	0.908077	+	0.418804i	$0.137550\pi$
$937$	9.05198e48i	0.837607i	−0.908077	+	0.418804i	$0.862450\pi$
$938$	− 4.61858e47i	− 0.0419916i
$939$	2.14798e49	1.91888
$940$	0	0
$941$	−2.06615e49	−1.78211	−0.891054	−	0.453898i	$-0.850033\pi$
$941$	−2.06615e49	−1.78211	−0.891054	+	0.453898i	$0.850033\pi$
$942$	− 7.09717e48i	− 0.601513i
$943$	− 2.71046e46i	− 0.00225736i
$944$	1.03212e49	0.844680
$945$	0	0
$946$	6.99135e47	0.0552532
$947$	− 1.01046e49i	− 0.784774i	−0.919800	−	0.392387i	$-0.871649\pi$
$947$	− 1.01046e49i	− 0.784774i	0.919800	−	0.392387i	$-0.128351\pi$
$948$	4.40466e48i	0.336182i
$949$	6.24272e48	0.468254
$950$	0	0
$951$	−2.67806e49	−1.94018
$952$	2.16879e48i	0.154422i
$953$	3.11277e48i	0.217828i	0.994051	+	0.108914i	$0.0347373\pi$
$953$	3.11277e48i	0.217828i	−0.994051	+	0.108914i	$0.965263\pi$
$954$	−4.04960e49	−2.78525
$955$	0	0
$956$	1.04596e48	0.0694962
$957$	− 5.31686e49i	− 3.47223i
$958$	9.10209e48i	0.584266i
$959$	3.01616e48	0.190304
$960$	0	0
$961$	3.28518e49	2.00274
$962$	6.78506e48i	0.406597i
$963$	− 1.55731e49i	− 0.917364i
$964$	2.33624e48	0.135284
$965$	0	0
$966$	−1.40164e47	−0.00784355
$967$	− 6.39561e48i	− 0.351840i	−0.984404	−	0.175920i	$-0.943710\pi$
$967$	− 6.39561e48i	− 0.351840i	0.984404	−	0.175920i	$-0.0562900\pi$
$968$	− 2.39412e49i	− 1.29480i
$969$	−1.56346e49	−0.831276
$970$	0	0
$971$	−2.23630e49	−1.14924	−0.574622	−	0.818419i	$-0.694851\pi$
$971$	−2.23630e49	−1.14924	−0.574622	+	0.818419i	$0.694851\pi$
$972$	3.95279e48i	0.199715i
$973$	− 3.22251e48i	− 0.160078i
$974$	8.22473e48	0.401697
$975$	0	0
$976$	−5.97732e48	−0.282218
$977$	2.33703e49i	1.08493i	0.840077	+	0.542467i	$0.182510\pi$
$977$	2.33703e49i	1.08493i	−0.840077	+	0.542467i	$0.817490\pi$
$978$	8.37965e48i	0.382503i
$979$	−3.09377e49	−1.38859
$980$	0	0
$981$	5.84801e49	2.53787
$982$	4.36337e49i	1.86201i
$983$	6.12527e48i	0.257035i	0.991707	+	0.128518i	$0.0410219\pi$
$983$	6.12527e48i	0.257035i	−0.991707	+	0.128518i	$0.958978\pi$
$984$	2.07878e48	0.0857807
$985$	0	0
$986$	5.35402e49	2.13654
$987$	5.10609e48i	0.200381i
$988$	− 7.53730e47i	− 0.0290888i
$989$	3.22082e46	0.00122244
$990$	0	0
$991$	−2.52500e49	−0.926929	−0.463465	−	0.886115i	$-0.653394\pi$
$991$	−2.52500e49	−0.926929	−0.463465	+	0.886115i	$0.653394\pi$
$992$	− 1.62474e49i	− 0.586600i
$993$	− 1.28471e49i	− 0.456187i
$994$	−7.52590e48	−0.262835
$995$	0	0
$996$	1.07057e49	0.361691
$997$	1.64715e49i	0.547349i	0.961822	+	0.273674i	$0.0882391\pi$
$997$	1.64715e49i	0.547349i	−0.961822	+	0.273674i	$0.911761\pi$
$998$	3.21697e49i	1.05146i
$999$	−2.08088e49	−0.668984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.7		22
5.2	odd	4		25.34.a.e.1.8	yes	11
5.3	odd	4		25.34.a.d.1.4	✓	11
5.4	even	2	inner	25.34.b.d.24.16		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.4	✓	11	5.3	odd	4
25.34.a.e.1.8	yes	11	5.2	odd	4
25.34.b.d.24.7		22	1.1	even	1	trivial
25.34.b.d.24.16		22	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-100295. i q^{2} +1.18201e8i q^{3} -1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13i q^{7} -7.14175e14i q^{8} -8.41244e15 q^{9} +O(q^{10})\)	\(q-100295. i q^{2} +1.18201e8i q^{3} -1.46921e9 q^{4} +1.18550e13 q^{6} -1.07417e13i q^{7} -7.14175e14i q^{8} -8.41244e15 q^{9} +2.38218e17 q^{11} -1.73662e17i q^{12} -1.09650e18i q^{13} -1.07734e18 q^{14} -8.42488e19 q^{16} -2.82710e20i q^{17} +8.43728e20i q^{18} -4.67870e20 q^{19} +1.26968e21 q^{21} -2.38922e22i q^{22} -1.10068e21i q^{23} +8.44163e22 q^{24} -1.09973e23 q^{26} -3.37272e23i q^{27} +1.57817e22i q^{28} -1.88825e24 q^{29} -7.01821e24 q^{31} +2.31504e24i q^{32} +2.81577e25i q^{33} -2.83544e25 q^{34} +1.23596e25 q^{36} -6.16972e25i q^{37} +4.69252e25i q^{38} +1.29607e26 q^{39} +2.46253e25 q^{41} -1.27343e26i q^{42} +2.92621e25i q^{43} -3.49992e26 q^{44} -1.10393e26 q^{46} +4.02156e27i q^{47} -9.95830e27i q^{48} +7.61561e27 q^{49} +3.34166e28 q^{51} +1.61098e27i q^{52} +4.79966e28i q^{53} -3.38268e28 q^{54} -7.67144e27 q^{56} -5.53028e28i q^{57} +1.89382e29i q^{58} -1.22509e29 q^{59} +7.09485e28 q^{61} +7.03894e29i q^{62} +9.03637e28i q^{63} -4.91504e29 q^{64} +2.82408e30 q^{66} +4.28703e29i q^{67} +4.15359e29i q^{68} +1.30102e29 q^{69} +6.98564e30 q^{71} +6.00795e30i q^{72} +5.69333e30i q^{73} -6.18794e30 q^{74} +6.87398e29 q^{76} -2.55887e30i q^{77} -1.29990e31i q^{78} -2.53634e31 q^{79} -6.89932e30 q^{81} -2.46981e30i q^{82} +6.16471e31i q^{83} -1.86542e30 q^{84} +2.93485e30 q^{86} -2.23193e32i q^{87} -1.70130e32i q^{88} -1.29871e32 q^{89} -1.17782e31 q^{91} +1.61713e30i q^{92} -8.29560e32i q^{93} +4.03344e32 q^{94} -2.73640e32 q^{96} -4.34255e32i q^{97} -7.63810e32i q^{98} -2.00400e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+ \cdots - 26\!\cdots\!12 q^{99}+O(q^{100}) \) 22 * q - 98676413354 * q^4 - 35567955353446 * q^6 - 48599275949251316 * q^9 - 388975069134227046 * q^11 - 19390008595334902068 * q^14 + 575591759119330759202 * q^16 + 4608842794243084808630 * q^19 + 7903359076848510896124 * q^21 + 404192556148581428871090 * q^24 + 464682665356996878920184 * q^26 - 3351264573191459117593680 * q^29 - 3759368993361156279858876 * q^31 + 89746721762579763434900102 * q^34 + 387355373506331566119004012 * q^36 + 718345493252093200854565688 * q^39 + 1099039609507795057059146334 * q^41 + 5953087248173453754548821422 * q^44 + 3376724462669734942026715164 * q^46 + 5003317848948805057160966146 * q^49 + 132635930632492996145333201114 * q^51 + 426786304479392249563776060130 * q^54 + 679074245273936256251630129820 * q^56 + 135413981096960311593168243840 * q^59 - 689538516943594572498942901796 * q^61 - 2840052535921821128029255801474 * q^64 - 320033315173213395102299074022 * q^66 - 14437009323987384127917423522852 * q^69 - 11051811216899923387221184379736 * q^71 - 16966204054892971302102433594308 * q^74 - 7588775596602318790343300932510 * q^76 - 56833627147150708379517479188380 * q^79 - 9022895406968638344517956762058 * q^81 + 599893154314490734522302146543532 * q^84 + 911820864247632195182318378176824 * q^86 + 48061740522903759998741201101110 * q^89 - 693375717774307216790074646600496 * q^91 - 465076424153121919006535311120888 * q^94 - 3684220565182840604743827051904706 * q^96 - 2601899095573470033938075107273612 * q^99

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