LMFDB - Embedded newform 25.34.b.d.24.14

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			24.14
Character	$\chi$	$=$	25.24
Dual form			25.34.b.d.24.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+41215.3i q^{2} -1.10688e8i q^{3} +6.89123e9 q^{4} +4.56203e12 q^{6} +7.02715e13i q^{7} +6.38061e14i q^{8} -6.69270e15 q^{9} +O(q^{10})$	\(q+41215.3i q^{2} -1.10688e8i q^{3} +6.89123e9 q^{4} +4.56203e12 q^{6} +7.02715e13i q^{7} +6.38061e14i q^{8} -6.69270e15 q^{9} -5.33049e16 q^{11} -7.62774e17i q^{12} -1.55892e18i q^{13} -2.89626e18 q^{14} +3.28973e19 q^{16} -1.77770e20i q^{17} -2.75842e20i q^{18} +1.06994e20 q^{19} +7.77819e21 q^{21} -2.19698e21i q^{22} +5.14386e22i q^{23} +7.06255e22 q^{24} +6.42516e22 q^{26} +1.25480e23i q^{27} +4.84257e23i q^{28} -8.16333e23 q^{29} -3.64925e24 q^{31} +6.83678e24i q^{32} +5.90020e24i q^{33} +7.32687e24 q^{34} -4.61209e25 q^{36} -9.53287e25i q^{37} +4.40979e24i q^{38} -1.72554e26 q^{39} +2.96590e26 q^{41} +3.20581e26i q^{42} -5.30852e26i q^{43} -3.67337e26 q^{44} -2.12006e27 q^{46} +6.47397e27i q^{47} -3.64133e27i q^{48} +2.79291e27 q^{49} -1.96770e28 q^{51} -1.07429e28i q^{52} -1.72950e28i q^{53} -5.17169e27 q^{54} -4.48376e28 q^{56} -1.18429e28i q^{57} -3.36454e28i q^{58} -3.23790e28 q^{59} -5.51249e29 q^{61} -1.50405e29i q^{62} -4.70306e29i q^{63} +8.05483e26 q^{64} -2.43179e29 q^{66} -2.40123e30i q^{67} -1.22506e30i q^{68} +5.69362e30 q^{69} -6.55819e30 q^{71} -4.27035e30i q^{72} -2.45217e30i q^{73} +3.92900e30 q^{74} +7.37319e29 q^{76} -3.74582e30i q^{77} -7.11185e30i q^{78} -2.98501e31 q^{79} -2.33161e31 q^{81} +1.22240e31i q^{82} +4.29885e31i q^{83} +5.36013e31 q^{84} +2.18793e31 q^{86} +9.03580e31i q^{87} -3.40118e31i q^{88} +3.69934e31 q^{89} +1.09548e32 q^{91} +3.54475e32i q^{92} +4.03927e32i q^{93} -2.66827e32 q^{94} +7.56747e32 q^{96} +6.32291e32i q^{97} +1.15111e32i q^{98} +3.56754e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	41215.3i	0.444697i	0.974967	+	0.222348i	$0.0713722\pi$
$2$	41215.3i	0.444697i	−0.974967	+	0.222348i	$0.928628\pi$
$3$	− 1.10688e8i	− 1.48456i	−0.670088	−	0.742281i	$-0.733744\pi$
$3$	− 1.10688e8i	− 1.48456i	0.670088	−	0.742281i	$-0.266256\pi$
$4$	6.89123e9	0.802245
$5$	0	0
$5$	0	0
$6$	4.56203e12	0.660180
$7$	7.02715e13i	0.799211i	0.916687	+	0.399606i	$0.130853\pi$
$7$	7.02715e13i	0.799211i	−0.916687	+	0.399606i	$0.869147\pi$
$8$	6.38061e14i	0.801452i
$9$	−6.69270e15	−1.20393
$10$	0	0
$11$	−5.33049e16	−0.349774	−0.174887	−	0.984588i	$-0.555956\pi$
$11$	−5.33049e16	−0.349774	−0.174887	+	0.984588i	$0.555956\pi$
$12$	− 7.62774e17i	− 1.19098i
$13$	− 1.55892e18i	− 0.649770i	−0.945754	−	0.324885i	$-0.894674\pi$
$13$	− 1.55892e18i	− 0.649770i	0.945754	−	0.324885i	$-0.105326\pi$
$14$	−2.89626e18	−0.355407
$15$	0	0
$16$	3.28973e19	0.445842
$17$	− 1.77770e20i	− 0.886038i	−0.896512	−	0.443019i	$-0.853907\pi$
$17$	− 1.77770e20i	− 0.886038i	0.896512	−	0.443019i	$-0.146093\pi$
$18$	− 2.75842e20i	− 0.535382i
$19$	1.06994e20	0.0850990	0.0425495	−	0.999094i	$-0.486452\pi$
$19$	1.06994e20	0.0850990	0.0425495	+	0.999094i	$0.486452\pi$
$20$	0	0
$21$	7.77819e21	1.18648
$22$	− 2.19698e21i	− 0.155544i
$23$	5.14386e22i	1.74896i	0.485061	+	0.874480i	$0.338797\pi$
$23$	5.14386e22i	1.74896i	−0.485061	+	0.874480i	$0.661203\pi$
$24$	7.06255e22	1.18981
$25$	0	0
$26$	6.42516e22	0.288950
$27$	1.25480e23i	0.302741i
$28$	4.84257e23i	0.641163i
$29$	−8.16333e23	−0.605760	−0.302880	−	0.953029i	$-0.597948\pi$
$29$	−8.16333e23	−0.605760	−0.302880	+	0.953029i	$0.597948\pi$
$30$	0	0
$31$	−3.64925e24	−0.901022	−0.450511	−	0.892771i	$-0.648758\pi$
$31$	−3.64925e24	−0.901022	−0.450511	+	0.892771i	$0.648758\pi$
$32$	6.83678e24i	0.999717i
$33$	5.90020e24i	0.519262i
$34$	7.32687e24	0.394018
$35$	0	0
$36$	−4.61209e25	−0.965843
$37$	− 9.53287e25i	− 1.27027i	−0.772402	−	0.635134i	$-0.780945\pi$
$37$	− 9.53287e25i	− 1.27027i	0.772402	−	0.635134i	$-0.219055\pi$
$38$	4.40979e24i	0.0378432i
$39$	−1.72554e26	−0.964624
$40$	0	0
$41$	2.96590e26	0.726478	0.363239	−	0.931696i	$-0.381671\pi$
$41$	2.96590e26	0.726478	0.363239	+	0.931696i	$0.381671\pi$
$42$	3.20581e26i	0.527624i
$43$	− 5.30852e26i	− 0.592576i	−0.955099	−	0.296288i	$-0.904251\pi$
$43$	− 5.30852e26i	− 0.592576i	0.955099	−	0.296288i	$-0.0957489\pi$
$44$	−3.67337e26	−0.280605
$45$	0	0
$46$	−2.12006e27	−0.777757
$47$	6.47397e27i	1.66554i	0.553616	+	0.832772i	$0.313247\pi$
$47$	6.47397e27i	1.66554i	−0.553616	+	0.832772i	$0.686753\pi$
$48$	− 3.64133e27i	− 0.661880i
$49$	2.79291e27	0.361261
$50$	0	0
$51$	−1.96770e28	−1.31538
$52$	− 1.07429e28i	− 0.521274i
$53$	− 1.72950e28i	− 0.612870i	−0.951892	−	0.306435i	$-0.900864\pi$
$53$	− 1.72950e28i	− 0.612870i	0.951892	−	0.306435i	$-0.0991362\pi$
$54$	−5.17169e27	−0.134628
$55$	0	0
$56$	−4.48376e28	−0.640530
$57$	− 1.18429e28i	− 0.126335i
$58$	− 3.36454e28i	− 0.269379i
$59$	−3.23790e28	−0.195526	−0.0977631	−	0.995210i	$-0.531169\pi$
$59$	−3.23790e28	−0.195526	−0.0977631	+	0.995210i	$0.531169\pi$
$60$	0	0
$61$	−5.51249e29	−1.92046	−0.960230	−	0.279210i	$-0.909927\pi$
$61$	−5.51249e29	−1.92046	−0.960230	+	0.279210i	$0.909927\pi$
$62$	− 1.50405e29i	− 0.400681i
$63$	− 4.70306e29i	− 0.962192i
$64$	8.05483e26	0.00127083
$65$	0	0
$66$	−2.43179e29	−0.230914
$67$	− 2.40123e30i	− 1.77910i	−0.456840	−	0.889549i	$-0.651019\pi$
$67$	− 2.40123e30i	− 1.77910i	0.456840	−	0.889549i	$-0.348981\pi$
$68$	− 1.22506e30i	− 0.710820i
$69$	5.69362e30	2.59644
$70$	0	0
$71$	−6.55819e30	−1.86647	−0.933235	−	0.359266i	$-0.883027\pi$
$71$	−6.55819e30	−1.86647	−0.933235	+	0.359266i	$0.883027\pi$
$72$	− 4.27035e30i	− 0.964889i
$73$	− 2.45217e30i	− 0.441290i	−0.975354	−	0.220645i	$-0.929184\pi$
$73$	− 2.45217e30i	− 0.441290i	0.975354	−	0.220645i	$-0.0708162\pi$
$74$	3.92900e30	0.564884
$75$	0	0
$76$	7.37319e29	0.0682702
$77$	− 3.74582e30i	− 0.279544i
$78$	− 7.11185e30i	− 0.428965i
$79$	−2.98501e31	−1.45914	−0.729572	−	0.683904i	$-0.760281\pi$
$79$	−2.98501e31	−1.45914	−0.729572	+	0.683904i	$0.760281\pi$
$80$	0	0
$81$	−2.33161e31	−0.754488
$82$	1.22240e31i	0.323062i
$83$	4.29885e31i	0.930174i	0.885265	+	0.465087i	$0.153977\pi$
$83$	4.29885e31i	0.930174i	−0.885265	+	0.465087i	$0.846023\pi$
$84$	5.36013e31	0.951847
$85$	0	0
$86$	2.18793e31	0.263517
$87$	9.03580e31i	0.899288i
$88$	− 3.40118e31i	− 0.280328i
$89$	3.69934e31	0.253040	0.126520	−	0.991964i	$-0.459619\pi$
$89$	3.69934e31	0.253040	0.126520	+	0.991964i	$0.459619\pi$
$90$	0	0
$91$	1.09548e32	0.519303
$92$	3.54475e32i	1.40309i
$93$	4.03927e32i	1.33762i
$94$	−2.66827e32	−0.740662
$95$	0	0
$96$	7.56747e32	1.48414
$97$	6.32291e32i	1.04516i	0.852590	+	0.522581i	$0.175031\pi$
$97$	6.32291e32i	1.04516i	−0.852590	+	0.522581i	$0.824969\pi$
$98$	1.15111e32i	0.160652i
$99$	3.56754e32	0.421103
$100$	0	0
$101$	3.14082e30	0.00266526	0.00133263	−	0.999999i	$-0.499576\pi$
$101$	3.14082e30	0.00266526	0.00133263	+	0.999999i	$0.499576\pi$
$102$	− 8.10994e32i	− 0.584945i
$103$	1.86610e33i	1.14583i	0.819614	+	0.572916i	$0.194188\pi$
$103$	1.86610e33i	1.14583i	−0.819614	+	0.572916i	$0.805812\pi$
$104$	9.94689e32	0.520759
$105$	0	0
$106$	7.12819e32	0.272541
$107$	− 2.91020e33i	− 0.952996i	−0.879176	−	0.476498i	$-0.841906\pi$
$107$	− 2.91020e33i	− 0.952996i	0.879176	−	0.476498i	$-0.158094\pi$
$108$	8.64709e32i	0.242872i
$109$	4.63672e33	1.11860	0.559299	−	0.828966i	$-0.311070\pi$
$109$	4.63672e33	1.11860	0.559299	+	0.828966i	$0.311070\pi$
$110$	0	0
$111$	−1.05517e34	−1.88579
$112$	2.31174e33i	0.356322i
$113$	− 8.12565e33i	− 1.08159i	−0.841153	−	0.540797i	$-0.818123\pi$
$113$	− 8.12565e33i	− 1.08159i	0.841153	−	0.540797i	$-0.181877\pi$
$114$	4.88109e32	0.0561807
$115$	0	0
$116$	−5.62554e33	−0.485968
$117$	1.04334e34i	0.782275i
$118$	− 1.33451e33i	− 0.0869499i
$119$	1.24922e34	0.708132
$120$	0	0
$121$	−2.03837e34	−0.877658
$122$	− 2.27199e34i	− 0.854022i
$123$	− 3.28288e34i	− 1.07850i
$124$	−2.51478e34	−0.722840
$125$	0	0
$126$	1.93838e34	0.427883
$127$	− 2.59944e34i	− 0.503638i	−0.967774	−	0.251819i	$-0.918971\pi$
$127$	− 2.59944e34i	− 0.503638i	0.967774	−	0.251819i	$-0.0810287\pi$
$128$	5.87607e34i	1.00028i
$129$	−5.87588e34	−0.879717
$130$	0	0
$131$	−2.90139e34	−0.336999	−0.168500	−	0.985702i	$-0.553892\pi$
$131$	−2.90139e34	−0.336999	−0.168500	+	0.985702i	$0.553892\pi$
$132$	4.06596e34i	0.416575i
$133$	7.51862e33i	0.0680121i
$134$	9.89676e34	0.791159
$135$	0	0
$136$	1.13428e35	0.710117
$137$	1.48624e35i	0.824515i	0.911067	+	0.412257i	$0.135260\pi$
$137$	1.48624e35i	0.824515i	−0.911067	+	0.412257i	$0.864740\pi$
$138$	2.34664e35i	1.15463i
$139$	−2.66665e35	−1.16472	−0.582360	−	0.812931i	$-0.697871\pi$
$139$	−2.66665e35	−1.16472	−0.582360	+	0.812931i	$0.697871\pi$
$140$	0	0
$141$	7.16589e35	2.47260
$142$	− 2.70298e35i	− 0.830013i
$143$	8.30983e34i	0.227273i
$144$	−2.20172e35	−0.536760
$145$	0	0
$146$	1.01067e35	0.196240
$147$	− 3.09140e35i	− 0.536315i
$148$	− 6.56932e35i	− 1.01907i
$149$	−2.53958e35	−0.352524	−0.176262	−	0.984343i	$-0.556401\pi$
$149$	−2.53958e35	−0.352524	−0.176262	+	0.984343i	$0.556401\pi$
$150$	0	0
$151$	−1.66980e36	−1.86014	−0.930069	−	0.367384i	$-0.880253\pi$
$151$	−1.66980e36	−1.86014	−0.930069	+	0.367384i	$0.880253\pi$
$152$	6.82686e34i	0.0682028i
$153$	1.18976e36i	1.06672i
$154$	1.54385e35	0.124312
$155$	0	0
$156$	−1.18911e36	−0.773864
$157$	4.38081e35i	0.256573i	0.991737	+	0.128286i	$0.0409477\pi$
$157$	4.38081e35i	0.256573i	−0.991737	+	0.128286i	$0.959052\pi$
$158$	− 1.23028e36i	− 0.648877i
$159$	−1.91434e36	−0.909844
$160$	0	0
$161$	−3.61467e36	−1.39779
$162$	− 9.60979e35i	− 0.335518i
$163$	1.18076e36i	0.372449i	0.982507	+	0.186225i	$0.0596252\pi$
$163$	1.18076e36i	0.372449i	−0.982507	+	0.186225i	$0.940375\pi$
$164$	2.04387e36	0.582813
$165$	0	0
$166$	−1.77179e36	−0.413645
$167$	− 4.57158e36i	− 0.966594i	−0.875456	−	0.483297i	$-0.839439\pi$
$167$	− 4.57158e36i	− 0.966594i	0.875456	−	0.483297i	$-0.160561\pi$
$168$	4.96296e36i	0.950907i
$169$	3.32589e36	0.577799
$170$	0	0
$171$	−7.16078e35	−0.102453
$172$	− 3.65823e36i	− 0.475391i
$173$	5.32136e36i	0.628437i	0.949351	+	0.314219i	$0.101742\pi$
$173$	5.32136e36i	0.628437i	−0.949351	+	0.314219i	$0.898258\pi$
$174$	−3.72414e36	−0.399911
$175$	0	0
$176$	−1.75359e36	−0.155944
$177$	3.58395e36i	0.290271i
$178$	1.52470e36i	0.112526i
$179$	−3.41887e36	−0.230042	−0.115021	−	0.993363i	$-0.536694\pi$
$179$	−3.41887e36	−0.230042	−0.115021	+	0.993363i	$0.536694\pi$
$180$	0	0
$181$	8.81890e36	0.493990	0.246995	−	0.969017i	$-0.420557\pi$
$181$	8.81890e36	0.493990	0.246995	+	0.969017i	$0.420557\pi$
$182$	4.51505e36i	0.230933i
$183$	6.10164e37i	2.85104i
$184$	−3.28210e37	−1.40171
$185$	0	0
$186$	−1.66480e37	−0.594837
$187$	9.47604e36i	0.309914i
$188$	4.46136e37i	1.33617i
$189$	−8.81765e36	−0.241954
$190$	0	0
$191$	−7.82915e36	−0.180578	−0.0902888	−	0.995916i	$-0.528779\pi$
$191$	−7.82915e36	−0.180578	−0.0902888	+	0.995916i	$0.528779\pi$
$192$	− 8.91570e34i	− 0.00188662i
$193$	4.62710e37i	0.898696i	0.893357	+	0.449348i	$0.148344\pi$
$193$	4.62710e37i	0.898696i	−0.893357	+	0.449348i	$0.851656\pi$
$194$	−2.60601e37	−0.464780
$195$	0	0
$196$	1.92466e37	0.289820
$197$	− 5.06770e37i	− 0.701646i	−0.936442	−	0.350823i	$-0.885902\pi$
$197$	− 5.06770e37i	− 0.701646i	0.936442	−	0.350823i	$-0.114098\pi$
$198$	1.47037e37i	0.187263i
$199$	−1.14736e38	−1.34470	−0.672351	−	0.740233i	$-0.734715\pi$
$199$	−1.14736e38	−1.34470	−0.672351	+	0.740233i	$0.734715\pi$
$200$	0	0
$201$	−2.65787e38	−2.64118
$202$	1.29450e35i	0.00118523i
$203$	− 5.73650e37i	− 0.484130i
$204$	−1.35599e38	−1.05526
$205$	0	0
$206$	−7.69120e37	−0.509548
$207$	− 3.44263e38i	− 2.10562i
$208$	− 5.12844e37i	− 0.289694i
$209$	−5.70330e36	−0.0297655
$210$	0	0
$211$	−1.96269e38	−0.875367	−0.437684	−	0.899129i	$-0.644201\pi$
$211$	−1.96269e38	−0.875367	−0.437684	+	0.899129i	$0.644201\pi$
$212$	− 1.19184e38i	− 0.491672i
$213$	7.25911e38i	2.77089i
$214$	1.19945e38	0.423794
$215$	0	0
$216$	−8.00638e37	−0.242633
$217$	− 2.56438e38i	− 0.720107i
$218$	1.91104e38i	0.497437i
$219$	−2.71425e38	−0.655122
$220$	0	0
$221$	−2.77131e38	−0.575721
$222$	− 4.34892e38i	− 0.838605i
$223$	4.51819e38i	0.808974i	0.914544	+	0.404487i	$0.132550\pi$
$223$	4.51819e38i	0.808974i	−0.914544	+	0.404487i	$0.867450\pi$
$224$	−4.80431e38	−0.798985
$225$	0	0
$226$	3.34902e38	0.480981
$227$	9.47354e38i	1.26499i	0.774566	+	0.632493i	$0.217968\pi$
$227$	9.47354e38i	1.26499i	−0.774566	+	0.632493i	$0.782032\pi$
$228$	− 8.16121e37i	− 0.101351i
$229$	−1.07617e39	−1.24336	−0.621679	−	0.783272i	$-0.713549\pi$
$229$	−1.07617e39	−1.24336	−0.621679	+	0.783272i	$0.713549\pi$
$230$	0	0
$231$	−4.14616e38	−0.415000
$232$	− 5.20871e38i	− 0.485488i
$233$	1.15508e39i	1.00286i	0.865199	+	0.501429i	$0.167192\pi$
$233$	1.15508e39i	1.00286i	−0.865199	+	0.501429i	$0.832808\pi$
$234$	−4.30016e38	−0.347875
$235$	0	0
$236$	−2.23131e38	−0.156860
$237$	3.30403e39i	2.16619i
$238$	5.14870e38i	0.314904i
$239$	2.69091e39	1.53579	0.767897	−	0.640573i	$-0.221303\pi$
$239$	2.69091e39	1.53579	0.767897	+	0.640573i	$0.221303\pi$
$240$	0	0
$241$	2.30016e39	1.14413	0.572066	−	0.820208i	$-0.306142\pi$
$241$	2.30016e39	1.14413	0.572066	+	0.820208i	$0.306142\pi$
$242$	− 8.40123e38i	− 0.390292i
$243$	3.27835e39i	1.42283i
$244$	−3.79878e39	−1.54068
$245$	0	0
$246$	1.35305e39	0.479606
$247$	− 1.66795e38i	− 0.0552947i
$248$	− 2.32844e39i	− 0.722126i
$249$	4.75830e39	1.38090
$250$	0	0
$251$	−7.74615e39	−1.97002	−0.985008	−	0.172510i	$-0.944812\pi$
$251$	−7.74615e39	−1.97002	−0.985008	+	0.172510i	$0.944812\pi$
$252$	− 3.24099e39i	− 0.771913i
$253$	− 2.74193e39i	− 0.611742i
$254$	1.07137e39	0.223966
$255$	0	0
$256$	−2.41492e39	−0.443551
$257$	− 1.56075e39i	− 0.268805i	−0.990927	−	0.134403i	$-0.957088\pi$
$257$	− 1.56075e39i	− 0.268805i	0.990927	−	0.134403i	$-0.0429116\pi$
$258$	− 2.42176e39i	− 0.391207i
$259$	6.69889e39	1.01521
$260$	0	0
$261$	5.46347e39	0.729290
$262$	− 1.19582e39i	− 0.149863i
$263$	− 9.80391e39i	− 1.15380i	−0.816816	−	0.576899i	$-0.804263\pi$
$263$	− 9.80391e39i	− 1.15380i	0.816816	−	0.576899i	$-0.195737\pi$
$264$	−3.76469e39	−0.416164
$265$	0	0
$266$	−3.09882e38	−0.0302448
$267$	− 4.09471e39i	− 0.375654i
$268$	− 1.65474e40i	− 1.42727i
$269$	1.14488e40	0.928636	0.464318	−	0.885669i	$-0.346299\pi$
$269$	1.14488e40	0.928636	0.464318	+	0.885669i	$0.346299\pi$
$270$	0	0
$271$	6.66438e39	0.478373	0.239186	−	0.970974i	$-0.423119\pi$
$271$	6.66438e39	0.478373	0.239186	+	0.970974i	$0.423119\pi$
$272$	− 5.84817e39i	− 0.395033i
$273$	− 1.21256e40i	− 0.770938i
$274$	−6.12557e39	−0.366659
$275$	0	0
$276$	3.92360e40	2.08298
$277$	3.73373e40i	1.86735i	0.358119	+	0.933676i	$0.383418\pi$
$277$	3.73373e40i	1.86735i	−0.358119	+	0.933676i	$0.616582\pi$
$278$	− 1.09907e40i	− 0.517948i
$279$	2.44233e40	1.08476
$280$	0	0
$281$	−8.40358e39	−0.331749	−0.165875	−	0.986147i	$-0.553045\pi$
$281$	−8.40358e39	−0.331749	−0.165875	+	0.986147i	$0.553045\pi$
$282$	2.95344e40i	1.09956i
$283$	2.30451e40i	0.809287i	0.914474	+	0.404644i	$0.132604\pi$
$283$	2.30451e40i	0.809287i	−0.914474	+	0.404644i	$0.867396\pi$
$284$	−4.51940e40	−1.49737
$285$	0	0
$286$	−3.42493e39	−0.101068
$287$	2.08418e40i	0.580609i
$288$	− 4.57565e40i	− 1.20358i
$289$	8.65216e39	0.214936
$290$	0	0
$291$	6.99868e40	1.55161
$292$	− 1.68985e40i	− 0.354022i
$293$	− 3.75727e40i	− 0.743972i	−0.928238	−	0.371986i	$-0.878677\pi$
$293$	− 3.75727e40i	− 0.743972i	0.928238	−	0.371986i	$-0.121323\pi$
$294$	1.27413e40	0.238497
$295$	0	0
$296$	6.08256e40	1.01806
$297$	− 6.68869e39i	− 0.105891i
$298$	− 1.04670e40i	− 0.156766i
$299$	8.01889e40	1.13642
$300$	0	0
$301$	3.73038e40	0.473594
$302$	− 6.88215e40i	− 0.827198i
$303$	− 3.47650e38i	− 0.00395675i
$304$	3.51981e39	0.0379407
$305$	0	0
$306$	−4.90365e40	−0.474369
$307$	1.05115e41i	0.963569i	0.876290	+	0.481784i	$0.160011\pi$
$307$	1.05115e41i	0.963569i	−0.876290	+	0.481784i	$0.839989\pi$
$308$	− 2.58133e40i	− 0.224263i
$309$	2.06555e41	1.70106
$310$	0	0
$311$	−8.81846e40	−0.652900	−0.326450	−	0.945215i	$-0.605852\pi$
$311$	−8.81846e40	−0.652900	−0.326450	+	0.945215i	$0.605852\pi$
$312$	− 1.10100e41i	− 0.773100i
$313$	− 1.44579e40i	− 0.0962993i	−0.998840	−	0.0481497i	$-0.984668\pi$
$313$	− 1.44579e40i	− 0.0962993i	0.998840	−	0.0481497i	$-0.0153324\pi$
$314$	−1.80557e40	−0.114097
$315$	0	0
$316$	−2.05704e41	−1.17059
$317$	2.06744e41i	1.11675i	0.829589	+	0.558375i	$0.188575\pi$
$317$	2.06744e41i	1.11675i	−0.829589	+	0.558375i	$0.811425\pi$
$318$	− 7.89003e40i	− 0.404605i
$319$	4.35146e40	0.211879
$320$	0	0
$321$	−3.22124e41	−1.41478
$322$	− 1.48980e41i	− 0.621592i
$323$	− 1.90203e40i	− 0.0754009i
$324$	−1.60676e41	−0.605284
$325$	0	0
$326$	−4.86655e40	−0.165627
$327$	− 5.13228e41i	− 1.66063i
$328$	1.89242e41i	0.582237i
$329$	−4.54936e41	−1.33112
$330$	0	0
$331$	2.13786e41	0.566002	0.283001	−	0.959120i	$-0.408670\pi$
$331$	2.13786e41	0.566002	0.283001	+	0.959120i	$0.408670\pi$
$332$	2.96244e41i	0.746227i
$333$	6.38006e41i	1.52931i
$334$	1.88419e41	0.429841
$335$	0	0
$336$	2.55881e41	0.528982
$337$	6.42857e41i	1.26538i	0.774405	+	0.632690i	$0.218049\pi$
$337$	6.42857e41i	1.26538i	−0.774405	+	0.632690i	$0.781951\pi$
$338$	1.37078e41i	0.256945i
$339$	−8.99410e41	−1.60569
$340$	0	0
$341$	1.94523e41	0.315154
$342$	− 2.95134e40i	− 0.0455605i
$343$	7.39531e41i	1.08794i
$344$	3.38716e41	0.474922
$345$	0	0
$346$	−2.19322e41	−0.279464
$347$	− 6.54319e41i	− 0.794975i	−0.917608	−	0.397487i	$-0.869882\pi$
$347$	− 6.54319e41i	− 0.794975i	0.917608	−	0.397487i	$-0.130118\pi$
$348$	6.22678e41i	0.721449i
$349$	−1.14531e42	−1.26562	−0.632808	−	0.774309i	$-0.718098\pi$
$349$	−1.14531e42	−1.26562	−0.632808	+	0.774309i	$0.718098\pi$
$350$	0	0
$351$	1.95613e41	0.196712
$352$	− 3.64434e41i	− 0.349675i
$353$	2.76137e41i	0.252837i	0.991977	+	0.126419i	$0.0403483\pi$
$353$	2.76137e41i	0.252837i	−0.991977	+	0.126419i	$0.959652\pi$
$354$	−1.47714e41	−0.129083
$355$	0	0
$356$	2.54930e41	0.203000
$357$	− 1.38273e42i	− 1.05127i
$358$	− 1.40910e41i	− 0.102299i
$359$	−4.96782e41	−0.344435	−0.172218	−	0.985059i	$-0.555093\pi$
$359$	−4.96782e41	−0.344435	−0.172218	+	0.985059i	$0.555093\pi$
$360$	0	0
$361$	−1.56932e42	−0.992758
$362$	3.63474e41i	0.219676i
$363$	2.25623e42i	1.30294i
$364$	7.54920e41	0.416608
$365$	0	0
$366$	−2.51481e42	−1.26785
$367$	− 3.87241e42i	− 1.86634i	−0.359433	−	0.933171i	$-0.617030\pi$
$367$	− 3.87241e42i	− 1.86634i	0.359433	−	0.933171i	$-0.382970\pi$
$368$	1.69219e42i	0.779759i
$369$	−1.98498e42	−0.874625
$370$	0	0
$371$	1.21535e42	0.489813
$372$	2.78355e42i	1.07310i
$373$	− 4.76216e42i	− 1.75634i	−0.478349	−	0.878170i	$-0.658765\pi$
$373$	− 4.76216e42i	− 1.75634i	0.478349	−	0.878170i	$-0.341235\pi$
$374$	−3.90558e41	−0.137818
$375$	0	0
$376$	−4.13079e42	−1.33485
$377$	1.27260e42i	0.393604i
$378$	− 3.63422e41i	− 0.107596i
$379$	−1.25232e42	−0.354952	−0.177476	−	0.984125i	$-0.556793\pi$
$379$	−1.25232e42	−0.354952	−0.177476	+	0.984125i	$0.556793\pi$
$380$	0	0
$381$	−2.87726e42	−0.747682
$382$	− 3.22681e41i	− 0.0803023i
$383$	− 4.54583e42i	− 1.08351i	−0.840536	−	0.541756i	$-0.817760\pi$
$383$	− 4.54583e42i	− 1.08351i	0.840536	−	0.541756i	$-0.182240\pi$
$384$	6.50408e42	1.48498
$385$	0	0
$386$	−1.90707e42	−0.399647
$387$	3.55284e42i	0.713418i
$388$	4.35726e42i	0.838476i
$389$	4.94431e42	0.911880	0.455940	−	0.890011i	$-0.349303\pi$
$389$	4.94431e42	0.911880	0.455940	+	0.890011i	$0.349303\pi$
$390$	0	0
$391$	9.14427e42	1.54965
$392$	1.78205e42i	0.289534i
$393$	3.21148e42i	0.500297i
$394$	2.08867e42	0.312020
$395$	0	0
$396$	2.45847e42	0.337827
$397$	3.41993e42i	0.450790i	0.974268	+	0.225395i	$0.0723672\pi$
$397$	3.41993e42i	0.450790i	−0.974268	+	0.225395i	$0.927633\pi$
$398$	− 4.72890e42i	− 0.597984i
$399$	8.32219e41	0.100968
$400$	0	0
$401$	1.52388e43	1.70243	0.851214	−	0.524819i	$-0.175867\pi$
$401$	1.52388e43	1.70243	0.851214	+	0.524819i	$0.175867\pi$
$402$	− 1.09545e43i	− 1.17453i
$403$	5.68890e42i	0.585457i
$404$	2.16441e40	0.00213819
$405$	0	0
$406$	2.36432e42	0.215291
$407$	5.08149e42i	0.444307i
$408$	− 1.25551e43i	− 1.05421i
$409$	−1.60341e43	−1.29303	−0.646515	−	0.762901i	$-0.723774\pi$
$409$	−1.60341e43	−1.29303	−0.646515	+	0.762901i	$0.723774\pi$
$410$	0	0
$411$	1.64508e43	1.22404
$412$	1.28597e43i	0.919238i
$413$	− 2.27532e42i	− 0.156267i
$414$	1.41889e43	0.936362
$415$	0	0
$416$	1.06580e43	0.649586
$417$	2.95165e43i	1.72910i
$418$	− 2.35063e41i	− 0.0132366i
$419$	1.34781e43	0.729619	0.364810	−	0.931082i	$-0.381134\pi$
$419$	1.34781e43	0.729619	0.364810	+	0.931082i	$0.381134\pi$
$420$	0	0
$421$	−2.74653e42	−0.137445	−0.0687227	−	0.997636i	$-0.521892\pi$
$421$	−2.74653e42	−0.137445	−0.0687227	+	0.997636i	$0.521892\pi$
$422$	− 8.08928e42i	− 0.389273i
$423$	− 4.33283e43i	− 2.00519i
$424$	1.10353e43	0.491186
$425$	0	0
$426$	−2.99187e43	−1.23221
$427$	− 3.87371e43i	− 1.53485i
$428$	− 2.00549e43i	− 0.764536i
$429$	9.19796e42	0.337401
$430$	0	0
$431$	−1.45031e43	−0.492704	−0.246352	−	0.969180i	$-0.579232\pi$
$431$	−1.45031e43	−0.492704	−0.246352	+	0.969180i	$0.579232\pi$
$432$	4.12794e42i	0.134975i
$433$	− 1.91134e43i	− 0.601571i	−0.953692	−	0.300786i	$-0.902751\pi$
$433$	− 1.91134e43i	− 0.601571i	0.953692	−	0.300786i	$-0.0972489\pi$
$434$	1.05692e43	0.320229
$435$	0	0
$436$	3.19527e43	0.897389
$437$	5.50362e42i	0.148835i
$438$	− 1.11869e43i	− 0.291331i
$439$	−1.38556e43	−0.347504	−0.173752	−	0.984789i	$-0.555589\pi$
$439$	−1.38556e43	−0.347504	−0.173752	+	0.984789i	$0.555589\pi$
$440$	0	0
$441$	−1.86921e43	−0.434932
$442$	− 1.14220e43i	− 0.256021i
$443$	− 5.77425e43i	− 1.24691i	−0.781860	−	0.623454i	$-0.785729\pi$
$443$	− 5.77425e43i	− 1.24691i	0.781860	−	0.623454i	$-0.214271\pi$
$444$	−7.27143e43	−1.51287
$445$	0	0
$446$	−1.86219e43	−0.359748
$447$	2.81100e43i	0.523344i
$448$	5.66025e40i	0.00101566i
$449$	7.38143e43	1.27666	0.638331	−	0.769762i	$-0.279625\pi$
$449$	7.38143e43	1.27666	0.638331	+	0.769762i	$0.279625\pi$
$450$	0	0
$451$	−1.58097e43	−0.254103
$452$	− 5.59958e43i	− 0.867703i
$453$	1.84826e44i	2.76149i
$454$	−3.90455e43	−0.562535
$455$	0	0
$456$	7.55650e42	0.101251
$457$	7.32136e42i	0.0946182i	0.998880	+	0.0473091i	$0.0150646\pi$
$457$	7.32136e42i	0.0946182i	−0.998880	+	0.0473091i	$0.984935\pi$
$458$	− 4.43548e43i	− 0.552917i
$459$	2.23066e43	0.268240
$460$	0	0
$461$	8.00539e43	0.896019	0.448010	−	0.894029i	$-0.352133\pi$
$461$	8.00539e43	0.896019	0.448010	+	0.894029i	$0.352133\pi$
$462$	− 1.70885e43i	− 0.184549i
$463$	1.25843e44i	1.31142i	0.755013	+	0.655710i	$0.227630\pi$
$463$	1.25843e44i	1.31142i	−0.755013	+	0.655710i	$0.772370\pi$
$464$	−2.68552e43	−0.270073
$465$	0	0
$466$	−4.76070e43	−0.445968
$467$	2.38936e43i	0.216049i	0.994148	+	0.108025i	$0.0344525\pi$
$467$	2.38936e43i	0.216049i	−0.994148	+	0.108025i	$0.965547\pi$
$468$	7.18990e43i	0.627576i
$469$	1.68738e44	1.42188
$470$	0	0
$471$	4.84902e43	0.380898
$472$	− 2.06598e43i	− 0.156705i
$473$	2.82971e43i	0.207268i
$474$	−1.36177e44	−0.963298
$475$	0	0
$476$	8.60866e43	0.568095
$477$	1.15750e44i	0.737850i
$478$	1.10907e44i	0.682963i
$479$	−2.83365e44	−1.68582	−0.842909	−	0.538057i	$-0.819159\pi$
$479$	−2.83365e44	−1.68582	−0.842909	+	0.538057i	$0.819159\pi$
$480$	0	0
$481$	−1.48610e44	−0.825381
$482$	9.48017e43i	0.508792i
$483$	4.00099e44i	2.07511i
$484$	−1.40469e44	−0.704096
$485$	0	0
$486$	−1.35118e44	−0.632726
$487$	1.52190e44i	0.688903i	0.938804	+	0.344452i	$0.111935\pi$
$487$	1.52190e44i	0.688903i	−0.938804	+	0.344452i	$0.888065\pi$
$488$	− 3.51731e44i	− 1.53916i
$489$	1.30696e44	0.552924
$490$	0	0
$491$	−3.23940e44	−1.28121	−0.640605	−	0.767870i	$-0.721316\pi$
$491$	−3.23940e44	−1.28121	−0.640605	+	0.767870i	$0.721316\pi$
$492$	− 2.26231e44i	− 0.865222i
$493$	1.45120e44i	0.536726i
$494$	6.87452e42	0.0245894
$495$	0	0
$496$	−1.20050e44	−0.401713
$497$	− 4.60854e44i	− 1.49170i
$498$	1.96115e44i	0.614082i
$499$	−5.09440e44	−1.54324	−0.771621	−	0.636082i	$-0.780554\pi$
$499$	−5.09440e44	−1.54324	−0.771621	+	0.636082i	$0.780554\pi$
$500$	0	0
$501$	−5.06017e44	−1.43497
$502$	− 3.19260e44i	− 0.876059i
$503$	− 1.67732e44i	− 0.445393i	−0.974888	−	0.222696i	$-0.928514\pi$
$503$	− 1.67732e44i	− 0.445393i	0.974888	−	0.222696i	$-0.0714859\pi$
$504$	3.00084e44	0.771151
$505$	0	0
$506$	1.13010e44	0.272040
$507$	− 3.68135e44i	− 0.857779i
$508$	− 1.79133e44i	− 0.404041i
$509$	2.79924e44	0.611219	0.305610	−	0.952157i	$-0.401140\pi$
$509$	2.79924e44	0.611219	0.305610	+	0.952157i	$0.401140\pi$
$510$	0	0
$511$	1.72318e44	0.352684
$512$	4.05219e44i	0.803036i
$513$	1.34256e43i	0.0257630i
$514$	6.43270e43	0.119537
$515$	0	0
$516$	−4.04921e44	−0.705748
$517$	− 3.45095e44i	− 0.582565i
$518$	2.76097e44i	0.451462i
$519$	5.89009e44	0.932954
$520$	0	0
$521$	1.01436e45	1.50788	0.753942	−	0.656941i	$-0.228150\pi$
$521$	1.01436e45	1.50788	0.753942	+	0.656941i	$0.228150\pi$
$522$	2.25179e44i	0.324313i
$523$	− 8.69993e44i	− 1.21405i	−0.794681	−	0.607027i	$-0.792362\pi$
$523$	− 8.69993e44i	− 1.21405i	0.794681	−	0.607027i	$-0.207638\pi$
$524$	−1.99941e44	−0.270356
$525$	0	0
$526$	4.04072e44	0.513090
$527$	6.48728e44i	0.798340i
$528$	1.94101e44i	0.231509i
$529$	−1.78093e45	−2.05886
$530$	0	0
$531$	2.16703e44	0.235399
$532$	5.18125e43i	0.0545623i
$533$	− 4.62360e44i	− 0.472043i
$534$	1.68765e44	0.167052
$535$	0	0
$536$	1.53213e45	1.42586
$537$	3.78426e44i	0.341512i
$538$	4.71864e44i	0.412961i
$539$	−1.48876e44	−0.126360
$540$	0	0
$541$	3.27991e44	0.261883	0.130941	−	0.991390i	$-0.458200\pi$
$541$	3.27991e44	0.261883	0.130941	+	0.991390i	$0.458200\pi$
$542$	2.74675e44i	0.212731i
$543$	− 9.76144e44i	− 0.733359i
$544$	1.21538e45	0.885787
$545$	0	0
$546$	4.99761e44	0.342834
$547$	3.10667e44i	0.206778i	0.994641	+	0.103389i	$0.0329686\pi$
$547$	3.10667e44i	0.206778i	−0.994641	+	0.103389i	$0.967031\pi$
$548$	1.02420e45i	0.661463i
$549$	3.68934e45	2.31209
$550$	0	0
$551$	−8.73426e43	−0.0515495
$552$	3.63288e45i	2.08092i
$553$	− 2.09761e45i	− 1.16616i
$554$	−1.53887e45	−0.830405
$555$	0	0
$556$	−1.83765e45	−0.934391
$557$	2.55556e43i	0.0126146i	0.999980	+	0.00630732i	$0.00200770\pi$
$557$	2.55556e43i	0.0126146i	−0.999980	+	0.00630732i	$0.997992\pi$
$558$	1.00661e45i	0.482391i
$559$	−8.27558e44	−0.385038
$560$	0	0
$561$	1.04888e45	0.460086
$562$	− 3.46357e44i	− 0.147528i
$563$	− 3.81676e45i	− 1.57872i	−0.613928	−	0.789362i	$-0.710412\pi$
$563$	− 3.81676e45i	− 1.57872i	0.613928	−	0.789362i	$-0.289588\pi$
$564$	4.93818e45	1.98363
$565$	0	0
$566$	−9.49812e44	−0.359887
$567$	− 1.63846e45i	− 0.602995i
$568$	− 4.18453e45i	− 1.49589i
$569$	−1.11203e45	−0.386155	−0.193078	−	0.981183i	$-0.561847\pi$
$569$	−1.11203e45	−0.386155	−0.193078	+	0.981183i	$0.561847\pi$
$570$	0	0
$571$	2.78341e45	0.912183	0.456092	−	0.889933i	$-0.349249\pi$
$571$	2.78341e45	0.912183	0.456092	+	0.889933i	$0.349249\pi$
$572$	5.72650e44i	0.182328i
$573$	8.66590e44i	0.268079i
$574$	−8.59002e44	−0.258195
$575$	0	0
$576$	−5.39085e42	−0.00152998
$577$	− 4.82547e45i	− 1.33088i	−0.746452	−	0.665439i	$-0.768244\pi$
$577$	− 4.82547e45i	− 1.33088i	0.746452	−	0.665439i	$-0.231756\pi$
$578$	3.56602e44i	0.0955815i
$579$	5.12162e45	1.33417
$580$	0	0
$581$	−3.02087e45	−0.743406
$582$	2.88453e45i	0.689995i
$583$	9.21908e44i	0.214366i
$584$	1.56464e45	0.353673
$585$	0	0
$586$	1.54857e45	0.330842
$587$	− 9.27014e45i	− 1.92556i	−0.270281	−	0.962781i	$-0.587117\pi$
$587$	− 9.27014e45i	− 1.92556i	0.270281	−	0.962781i	$-0.412883\pi$
$588$	− 2.13036e45i	− 0.430256i
$589$	−3.90447e44	−0.0766760
$590$	0	0
$591$	−5.60932e45	−1.04164
$592$	− 3.13606e45i	− 0.566338i
$593$	− 1.07501e45i	− 0.188804i	−0.995534	−	0.0944018i	$-0.969906\pi$
$593$	− 1.07501e45i	− 0.188804i	0.995534	−	0.0944018i	$-0.0300938\pi$
$594$	2.75676e44	0.0470894
$595$	0	0
$596$	−1.75008e45	−0.282811
$597$	1.26999e46i	1.99629i
$598$	3.30501e45i	0.505363i
$599$	−1.10591e46	−1.64505	−0.822525	−	0.568729i	$-0.807435\pi$
$599$	−1.10591e46	−1.64505	−0.822525	+	0.568729i	$0.807435\pi$
$600$	0	0
$601$	4.33341e45	0.610100	0.305050	−	0.952336i	$-0.401327\pi$
$601$	4.33341e45	0.610100	0.305050	+	0.952336i	$0.401327\pi$
$602$	1.53749e45i	0.210606i
$603$	1.60707e46i	2.14190i
$604$	−1.15070e46	−1.49229
$605$	0	0
$606$	1.43285e43	0.00175955
$607$	6.02981e45i	0.720594i	0.932838	+	0.360297i	$0.117325\pi$
$607$	6.02981e45i	0.720594i	−0.932838	+	0.360297i	$0.882675\pi$
$608$	7.31493e44i	0.0850749i
$609$	−6.34959e45	−0.718722
$610$	0	0
$611$	1.00924e46	1.08222
$612$	8.19894e45i	0.855774i
$613$	− 4.15532e45i	− 0.422189i	−0.977466	−	0.211094i	$-0.932297\pi$
$613$	− 4.15532e45i	− 0.422189i	0.977466	−	0.211094i	$-0.0677028\pi$
$614$	−4.33236e45	−0.428496
$615$	0	0
$616$	2.39006e45	0.224041
$617$	− 1.47278e46i	− 1.34410i	−0.740506	−	0.672049i	$-0.765414\pi$
$617$	− 1.47278e46i	− 1.34410i	0.740506	−	0.672049i	$-0.234586\pi$
$618$	8.51321e45i	0.756456i
$619$	1.07597e46	0.930899	0.465449	−	0.885074i	$-0.345893\pi$
$619$	1.07597e46	0.930899	0.465449	+	0.885074i	$0.345893\pi$
$620$	0	0
$621$	−6.45450e45	−0.529482
$622$	− 3.63456e45i	− 0.290342i
$623$	2.59958e45i	0.202233i
$624$	−5.67655e45	−0.430069
$625$	0	0
$626$	5.95887e44	0.0428240
$627$	6.31285e44i	0.0441887i
$628$	3.01892e45i	0.205834i
$629$	−1.69466e46	−1.12551
$630$	0	0
$631$	−6.39538e45	−0.403072	−0.201536	−	0.979481i	$-0.564593\pi$
$631$	−6.39538e45	−0.403072	−0.201536	+	0.979481i	$0.564593\pi$
$632$	− 1.90462e46i	− 1.16943i
$633$	2.17245e46i	1.29954i
$634$	−8.52104e45	−0.496615
$635$	0	0
$636$	−1.31922e46	−0.729918
$637$	− 4.35393e45i	− 0.234736i
$638$	1.79347e45i	0.0942220i
$639$	4.38920e46	2.24709
$640$	0	0
$641$	−3.35160e46	−1.62965	−0.814826	−	0.579706i	$-0.803167\pi$
$641$	−3.35160e46	−1.62965	−0.814826	+	0.579706i	$0.803167\pi$
$642$	− 1.32764e46i	− 0.629149i
$643$	2.31180e45i	0.106775i	0.998574	+	0.0533875i	$0.0170019\pi$
$643$	2.31180e45i	0.106775i	−0.998574	+	0.0533875i	$0.982998\pi$
$644$	−2.49095e46	−1.12137
$645$	0	0
$646$	7.83930e44	0.0335306
$647$	− 6.62781e45i	− 0.276344i	−0.990408	−	0.138172i	$-0.955877\pi$
$647$	− 6.62781e45i	− 0.276344i	0.990408	−	0.138172i	$-0.0441226\pi$
$648$	− 1.48771e46i	− 0.604686i
$649$	1.72596e45	0.0683901
$650$	0	0
$651$	−2.83845e46	−1.06904
$652$	8.13691e45i	0.298796i
$653$	3.31697e46i	1.18761i	0.804608	+	0.593806i	$0.202375\pi$
$653$	3.31697e46i	1.18761i	−0.804608	+	0.593806i	$0.797625\pi$
$654$	2.11529e46	0.738476
$655$	0	0
$656$	9.75700e45	0.323894
$657$	1.64116e46i	0.531280i
$658$	− 1.87503e46i	− 0.591945i
$659$	2.44156e46	0.751724	0.375862	−	0.926676i	$-0.377347\pi$
$659$	2.44156e46	0.751724	0.375862	+	0.926676i	$0.377347\pi$
$660$	0	0
$661$	8.20573e45	0.240322	0.120161	−	0.992754i	$-0.461659\pi$
$661$	8.20573e45	0.240322	0.120161	+	0.992754i	$0.461659\pi$
$662$	8.81128e45i	0.251699i
$663$	3.06749e46i	0.854694i
$664$	−2.74293e46	−0.745490
$665$	0	0
$666$	−2.62956e46	−0.680078
$667$	− 4.19910e46i	− 1.05945i
$668$	− 3.15038e46i	− 0.775445i
$669$	5.00108e46	1.20097
$670$	0	0
$671$	2.93843e46	0.671728
$672$	5.31778e46i	1.18614i
$673$	− 7.33965e46i	− 1.59745i	−0.601698	−	0.798724i	$-0.705509\pi$
$673$	− 7.33965e46i	− 1.59745i	0.601698	−	0.798724i	$-0.294491\pi$
$674$	−2.64956e46	−0.562710
$675$	0	0
$676$	2.29195e46	0.463536
$677$	− 2.34099e45i	− 0.0462048i	−0.999733	−	0.0231024i	$-0.992646\pi$
$677$	− 2.34099e45i	− 0.0462048i	0.999733	−	0.0231024i	$-0.00735438\pi$
$678$	− 3.70695e46i	− 0.714046i
$679$	−4.44321e46	−0.835305
$680$	0	0
$681$	1.04860e47	1.87795
$682$	8.01733e45i	0.140148i
$683$	4.27807e46i	0.729972i	0.931013	+	0.364986i	$0.118926\pi$
$683$	4.27807e46i	0.729972i	−0.931013	+	0.364986i	$0.881074\pi$
$684$	−4.93466e45	−0.0821923
$685$	0	0
$686$	−3.04800e46	−0.483801
$687$	1.19119e47i	1.84584i
$688$	− 1.74636e46i	− 0.264195i
$689$	−2.69616e46	−0.398224
$690$	0	0
$691$	7.57621e46	1.06675	0.533377	−	0.845878i	$-0.320923\pi$
$691$	7.57621e46	1.06675	0.533377	+	0.845878i	$0.320923\pi$
$692$	3.66707e46i	0.504160i
$693$	2.50696e46i	0.336550i
$694$	2.69680e46	0.353523
$695$	0	0
$696$	−5.76540e46	−0.720737
$697$	− 5.27249e46i	− 0.643687i
$698$	− 4.72041e46i	− 0.562815i
$699$	1.27853e47	1.48881
$700$	0	0
$701$	1.38596e47	1.53958	0.769792	−	0.638294i	$-0.220360\pi$
$701$	1.38596e47	1.53958	0.769792	+	0.638294i	$0.220360\pi$
$702$	8.06227e45i	0.0874772i
$703$	− 1.01996e46i	− 0.108098i
$704$	−4.29362e43	−0.000444503 0
$705$	0	0
$706$	−1.13811e46	−0.112436
$707$	2.20710e44i	0.00213011i
$708$	2.46979e46i	0.232868i
$709$	1.17635e46	0.108361	0.0541804	−	0.998531i	$-0.482745\pi$
$709$	1.17635e46	0.108361	0.0541804	+	0.998531i	$0.482745\pi$
$710$	0	0
$711$	1.99777e47	1.75670
$712$	2.36041e46i	0.202800i
$713$	− 1.87712e47i	− 1.57585i
$714$	5.69898e46	0.467495
$715$	0	0
$716$	−2.35602e46	−0.184550
$717$	− 2.97850e47i	− 2.27998i
$718$	− 2.04750e46i	− 0.153169i
$719$	−1.69294e47	−1.23770	−0.618848	−	0.785510i	$-0.712400\pi$
$719$	−1.69294e47	−1.23770	−0.618848	+	0.785510i	$0.712400\pi$
$720$	0	0
$721$	−1.31134e47	−0.915763
$722$	− 6.46802e46i	− 0.441476i
$723$	− 2.54599e47i	− 1.69854i
$724$	6.07731e46	0.396301
$725$	0	0
$726$	−9.29912e46	−0.579412
$727$	− 9.92859e46i	− 0.604742i	−0.953190	−	0.302371i	$-0.902222\pi$
$727$	− 9.92859e46i	− 0.604742i	0.953190	−	0.302371i	$-0.0977781\pi$
$728$	6.98983e46i	0.416197i
$729$	2.33257e47	1.35779
$730$	0	0
$731$	−9.43699e46	−0.525045
$732$	4.20478e47i	2.28723i
$733$	− 1.92063e47i	− 1.02148i	−0.859736	−	0.510738i	$-0.829372\pi$
$733$	− 1.92063e47i	− 1.02148i	0.859736	−	0.510738i	$-0.170628\pi$
$734$	1.59603e47	0.829956
$735$	0	0
$736$	−3.51674e47	−1.74846
$737$	1.27998e47i	0.622283i
$738$	− 8.18118e46i	− 0.388943i
$739$	−1.43931e47	−0.669148	−0.334574	−	0.942369i	$-0.608592\pi$
$739$	−1.43931e47	−0.669148	−0.334574	+	0.942369i	$0.608592\pi$
$740$	0	0
$741$	−1.84622e46	−0.0820885
$742$	5.00909e46i	0.217818i
$743$	1.55796e47i	0.662585i	0.943528	+	0.331293i	$0.107485\pi$
$743$	1.55796e47i	0.662585i	−0.943528	+	0.331293i	$0.892515\pi$
$744$	−2.57730e47	−1.07204
$745$	0	0
$746$	1.96274e47	0.781038
$747$	− 2.87709e47i	− 1.11986i
$748$	6.53016e46i	0.248627i
$749$	2.04504e47	0.761645
$750$	0	0
$751$	−1.64177e46	−0.0585131	−0.0292566	−	0.999572i	$-0.509314\pi$
$751$	−1.64177e46	−0.0585131	−0.0292566	+	0.999572i	$0.509314\pi$
$752$	2.12976e47i	0.742569i
$753$	8.57403e47i	2.92461i
$754$	−5.24507e46	−0.175035
$755$	0	0
$756$	−6.07645e46	−0.194106
$757$	− 4.39475e46i	− 0.137357i	−0.997639	−	0.0686786i	$-0.978122\pi$
$757$	− 4.39475e46i	− 0.137357i	0.997639	−	0.0686786i	$-0.0218783\pi$
$758$	− 5.16150e46i	− 0.157846i
$759$	−3.03498e47	−0.908169
$760$	0	0
$761$	2.40229e47	0.688301	0.344151	−	0.938914i	$-0.388167\pi$
$761$	2.40229e47	0.688301	0.344151	+	0.938914i	$0.388167\pi$
$762$	− 1.18587e47i	− 0.332492i
$763$	3.25830e47i	0.893996i
$764$	−5.39525e46	−0.144867
$765$	0	0
$766$	1.87358e47	0.481834
$767$	5.04764e46i	0.127047i
$768$	2.67302e47i	0.658480i
$769$	−5.82753e46	−0.140508	−0.0702538	−	0.997529i	$-0.522381\pi$
$769$	−5.82753e46	−0.140508	−0.0702538	+	0.997529i	$0.522381\pi$
$770$	0	0
$771$	−1.72756e47	−0.399058
$772$	3.18864e47i	0.720974i
$773$	2.31995e47i	0.513472i	0.966482	+	0.256736i	$0.0826471\pi$
$773$	2.31995e47i	0.513472i	−0.966482	+	0.256736i	$0.917353\pi$
$774$	−1.46431e47	−0.317255
$775$	0	0
$776$	−4.03441e47	−0.837647
$777$	− 7.41485e47i	− 1.50715i
$778$	2.03782e47i	0.405510i
$779$	3.17333e46	0.0618225
$780$	0	0
$781$	3.49584e47	0.652844
$782$	3.76884e47i	0.689122i
$783$	− 1.02433e47i	− 0.183388i
$784$	9.18791e46	0.161065
$785$	0	0
$786$	−1.32362e47	−0.222480
$787$	− 4.47982e47i	− 0.737356i	−0.929557	−	0.368678i	$-0.879810\pi$
$787$	− 4.47982e47i	− 0.737356i	0.929557	−	0.368678i	$-0.120190\pi$
$788$	− 3.49227e47i	− 0.562892i
$789$	−1.08517e48	−1.71288
$790$	0	0
$791$	5.71002e47	0.864422
$792$	2.27631e47i	0.337494i
$793$	8.59354e47i	1.24786i
$794$	−1.40954e47	−0.200465
$795$	0	0
$796$	−7.90676e47	−1.07878
$797$	− 7.37692e47i	− 0.985854i	−0.870071	−	0.492927i	$-0.835927\pi$
$797$	− 7.37692e47i	− 0.985854i	0.870071	−	0.492927i	$-0.164073\pi$
$798$	3.43002e46i	0.0449002i
$799$	1.15088e48	1.47574
$800$	0	0
$801$	−2.47586e47	−0.304642
$802$	6.28073e47i	0.757064i
$803$	1.30713e47i	0.154352i
$804$	−1.83160e48	−2.11887
$805$	0	0
$806$	−2.34470e47	−0.260351
$807$	− 1.26724e48i	− 1.37862i
$808$	2.00404e45i	0.00213608i
$809$	1.81827e48	1.89892	0.949460	−	0.313888i	$-0.101632\pi$
$809$	1.81827e48	1.89892	0.949460	+	0.313888i	$0.101632\pi$
$810$	0	0
$811$	−1.21694e48	−1.22018	−0.610092	−	0.792331i	$-0.708867\pi$
$811$	−1.21694e48	−1.22018	−0.610092	+	0.792331i	$0.708867\pi$
$812$	− 3.95315e47i	− 0.388391i
$813$	− 7.37665e47i	− 0.710175i
$814$	−2.09435e47	−0.197582
$815$	0	0
$816$	−6.47320e47	−0.586451
$817$	− 5.67979e46i	− 0.0504276i
$818$	− 6.60849e47i	− 0.575007i
$819$	−7.33171e47	−0.625203
$820$	0	0
$821$	−1.74103e48	−1.42608	−0.713039	−	0.701124i	$-0.752682\pi$
$821$	−1.74103e48	−1.42608	−0.713039	+	0.701124i	$0.752682\pi$
$822$	6.78025e47i	0.544328i
$823$	6.11641e46i	0.0481282i	0.999710	+	0.0240641i	$0.00766058\pi$
$823$	6.11641e46i	0.0481282i	−0.999710	+	0.0240641i	$0.992339\pi$
$824$	−1.19069e48	−0.918330
$825$	0	0
$826$	9.37781e46	0.0694913
$827$	1.15003e48i	0.835347i	0.908597	+	0.417673i	$0.137154\pi$
$827$	1.15003e48i	0.835347i	−0.908597	+	0.417673i	$0.862846\pi$
$828$	− 2.37240e48i	− 1.68922i
$829$	1.70589e48	1.19070	0.595348	−	0.803468i	$-0.297014\pi$
$829$	1.70589e48	1.19070	0.595348	+	0.803468i	$0.297014\pi$
$830$	0	0
$831$	4.13277e48	2.77220
$832$	− 1.25569e45i	0 0.000825745i
$833$	− 4.96496e47i	− 0.320091i
$834$	−1.21653e48	−0.768926
$835$	0	0
$836$	−3.93028e46	−0.0238792
$837$	− 4.57906e47i	− 0.272776i
$838$	5.55503e47i	0.324459i
$839$	2.03384e48	1.16478	0.582391	−	0.812909i	$-0.302117\pi$
$839$	2.03384e48	1.16478	0.582391	+	0.812909i	$0.302117\pi$
$840$	0	0
$841$	−1.14968e48	−0.633055
$842$	− 1.13199e47i	− 0.0611215i
$843$	9.30173e47i	0.492503i
$844$	−1.35253e48	−0.702259
$845$	0	0
$846$	1.78579e48	0.891702
$847$	− 1.43240e48i	− 0.701434i
$848$	− 5.68959e47i	− 0.273243i
$849$	2.55081e48	1.20144
$850$	0	0
$851$	4.90358e48	2.22165
$852$	5.00242e48i	2.22293i
$853$	− 1.36680e48i	− 0.595725i	−0.954609	−	0.297862i	$-0.903726\pi$
$853$	− 1.36680e48i	− 0.595725i	0.954609	−	0.297862i	$-0.0962736\pi$
$854$	1.59656e48	0.682544
$855$	0	0
$856$	1.85689e48	0.763781
$857$	1.91121e48i	0.771126i	0.922682	+	0.385563i	$0.125993\pi$
$857$	1.91121e48i	0.771126i	−0.922682	+	0.385563i	$0.874007\pi$
$858$	3.79097e47i	0.150041i
$859$	3.86858e48	1.50198	0.750991	−	0.660312i	$-0.229576\pi$
$859$	3.86858e48	1.50198	0.750991	+	0.660312i	$0.229576\pi$
$860$	0	0
$861$	2.30693e48	0.861951
$862$	− 5.97750e47i	− 0.219104i
$863$	5.14820e48i	1.85130i	0.378379	+	0.925651i	$0.376482\pi$
$863$	5.14820e48i	1.85130i	−0.378379	+	0.925651i	$0.623518\pi$
$864$	−8.57877e47	−0.302655
$865$	0	0
$866$	7.87764e47	0.267517
$867$	− 9.57687e47i	− 0.319087i
$868$	− 1.76717e48i	− 0.577702i
$869$	1.59116e48	0.510371
$870$	0	0
$871$	−3.74334e48	−1.15600
$872$	2.95851e48i	0.896503i
$873$	− 4.23173e48i	− 1.25830i
$874$	−2.26833e47	−0.0661863
$875$	0	0
$876$	−1.87045e48	−0.525568
$877$	− 4.88143e47i	− 0.134603i	−0.997733	−	0.0673014i	$-0.978561\pi$
$877$	− 4.88143e47i	− 0.134603i	0.997733	−	0.0673014i	$-0.0214389\pi$
$878$	− 5.71061e47i	− 0.154534i
$879$	−4.15883e48	−1.10447
$880$	0	0
$881$	−3.52849e48	−0.902581	−0.451291	−	0.892377i	$-0.649036\pi$
$881$	−3.52849e48	−0.902581	−0.451291	+	0.892377i	$0.649036\pi$
$882$	− 7.70400e47i	− 0.193413i
$883$	− 3.98184e48i	− 0.981143i	−0.871401	−	0.490572i	$-0.836788\pi$
$883$	− 3.98184e48i	− 0.981143i	0.871401	−	0.490572i	$-0.163212\pi$
$884$	−1.90977e48	−0.461869
$885$	0	0
$886$	2.37988e48	0.554495
$887$	5.91188e47i	0.135203i	0.997712	+	0.0676014i	$0.0215346\pi$
$887$	5.91188e47i	0.135203i	−0.997712	+	0.0676014i	$0.978465\pi$
$888$	− 6.73264e48i	− 1.51137i
$889$	1.82667e48	0.402513
$890$	0	0
$891$	1.24286e48	0.263901
$892$	3.11359e48i	0.648995i
$893$	6.92675e47i	0.141736i
$894$	−1.15857e48	−0.232729
$895$	0	0
$896$	−4.12920e48	−0.799437
$897$	− 8.87592e48i	− 1.68709i
$898$	3.04228e48i	0.567728i
$899$	2.97900e48	0.545803
$900$	0	0
$901$	−3.07454e48	−0.543026
$902$	− 6.51602e47i	− 0.112999i
$903$	− 4.12907e48i	− 0.703080i
$904$	5.18467e48	0.866846
$905$	0	0
$906$	−7.61769e48	−1.22803
$907$	− 6.17429e47i	− 0.0977387i	−0.998805	−	0.0488693i	$-0.984438\pi$
$907$	− 6.17429e47i	− 0.0977387i	0.998805	−	0.0488693i	$-0.0155618\pi$
$908$	6.52844e48i	1.01483i
$909$	−2.10206e46	−0.00320878
$910$	0	0
$911$	1.02328e49	1.50640	0.753202	−	0.657789i	$-0.228508\pi$
$911$	1.02328e49	1.50640	0.753202	+	0.657789i	$0.228508\pi$
$912$	− 3.89599e47i	− 0.0563253i
$913$	− 2.29150e48i	− 0.325351i
$914$	−3.01752e47	−0.0420764
$915$	0	0
$916$	−7.41615e48	−0.997477
$917$	− 2.03885e48i	− 0.269334i
$918$	9.19373e47i	0.119286i
$919$	−6.01378e48	−0.766375	−0.383188	−	0.923671i	$-0.625174\pi$
$919$	−6.01378e48	−0.766375	−0.383188	+	0.923671i	$0.625174\pi$
$920$	0	0
$921$	1.16350e49	1.43048
$922$	3.29945e48i	0.398457i
$923$	1.02237e49i	1.21278i
$924$	−2.85721e48	−0.332932
$925$	0	0
$926$	−5.18665e48	−0.583184
$927$	− 1.24893e49i	− 1.37950i
$928$	− 5.58109e48i	− 0.605588i
$929$	−1.60989e49	−1.71608	−0.858041	−	0.513582i	$-0.828318\pi$
$929$	−1.60989e49	−1.71608	−0.858041	+	0.513582i	$0.828318\pi$
$930$	0	0
$931$	2.98824e47	0.0307429
$932$	7.95992e48i	0.804538i
$933$	9.76095e48i	0.969270i
$934$	−9.84782e47	−0.0960764
$935$	0	0
$936$	−6.65715e48	−0.626956
$937$	− 1.43294e49i	− 1.32594i	−0.748646	−	0.662970i	$-0.769296\pi$
$937$	− 1.43294e49i	− 1.32594i	0.748646	−	0.662970i	$-0.230704\pi$
$938$	6.95460e48i	0.632303i
$939$	−1.60031e48	−0.142962
$940$	0	0
$941$	−8.95533e48	−0.772419	−0.386209	−	0.922411i	$-0.626216\pi$
$941$	−8.95533e48	−0.772419	−0.386209	+	0.922411i	$0.626216\pi$
$942$	1.99854e48i	0.169384i
$943$	1.52562e49i	1.27058i
$944$	−1.06518e48	−0.0871737
$945$	0	0
$946$	−1.16627e48	−0.0921714
$947$	7.82324e48i	0.607592i	0.952737	+	0.303796i	$0.0982541\pi$
$947$	7.82324e48i	0.607592i	−0.952737	+	0.303796i	$0.901746\pi$
$948$	2.27689e49i	1.73782i
$949$	−3.82275e48	−0.286737
$950$	0	0
$951$	2.28841e49	1.65789
$952$	7.97079e48i	0.567534i
$953$	2.53171e48i	0.177166i	0.996069	+	0.0885831i	$0.0282339\pi$
$953$	2.53171e48i	0.177166i	−0.996069	+	0.0885831i	$0.971766\pi$
$954$	−4.77068e48	−0.328120
$955$	0	0
$956$	1.85437e49	1.23208
$957$	− 4.81653e48i	− 0.314548i
$958$	− 1.16790e49i	− 0.749678i
$959$	−1.04440e49	−0.658961
$960$	0	0
$961$	−3.08647e48	−0.188160
$962$	− 6.12502e48i	− 0.367044i
$963$	1.94771e49i	1.14734i
$964$	1.58509e49	0.917874
$965$	0	0
$966$	−1.64902e49	−0.922793
$967$	2.10473e49i	1.15787i	0.815374	+	0.578935i	$0.196531\pi$
$967$	2.10473e49i	1.15787i	−0.815374	+	0.578935i	$0.803469\pi$
$968$	− 1.30061e49i	− 0.703401i
$969$	−2.10532e48	−0.111937
$970$	0	0
$971$	−1.83573e49	−0.943389	−0.471695	−	0.881762i	$-0.656358\pi$
$971$	−1.83573e49	−0.943389	−0.471695	+	0.881762i	$0.656358\pi$
$972$	2.25919e49i	1.14145i
$973$	− 1.87390e49i	− 0.930858i
$974$	−6.27256e48	−0.306353
$975$	0	0
$976$	−1.81346e49	−0.856221
$977$	− 2.94025e49i	− 1.36497i	−0.730898	−	0.682487i	$-0.760899\pi$
$977$	− 2.94025e49i	− 1.36497i	0.730898	−	0.682487i	$-0.239101\pi$
$978$	5.38667e48i	0.245884i
$979$	−1.97193e48	−0.0885070
$980$	0	0
$981$	−3.10322e49	−1.34671
$982$	− 1.33513e49i	− 0.569750i
$983$	6.14212e48i	0.257742i	0.991661	+	0.128871i	$0.0411353\pi$
$983$	6.14212e48i	0.257742i	−0.991661	+	0.128871i	$0.958865\pi$
$984$	2.09468e49	0.864368
$985$	0	0
$986$	−5.98117e48	−0.238680
$987$	5.03558e49i	1.97613i
$988$	− 1.14942e48i	− 0.0443599i
$989$	2.73063e49	1.03639
$990$	0	0
$991$	−2.23877e49	−0.821855	−0.410927	−	0.911668i	$-0.634795\pi$
$991$	−2.23877e49	−0.821855	−0.410927	+	0.911668i	$0.634795\pi$
$992$	− 2.49491e49i	− 0.900767i
$993$	− 2.36635e49i	− 0.840266i
$994$	1.89942e49	0.663356
$995$	0	0
$996$	3.27905e49	1.10782
$997$	− 5.31982e49i	− 1.76778i	−0.467699	−	0.883888i	$-0.654917\pi$
$997$	− 5.31982e49i	− 1.76778i	0.467699	−	0.883888i	$-0.345083\pi$
$998$	− 2.09968e49i	− 0.686275i
$999$	1.19618e49	0.384562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.34.b.d.24.14		22
5.2	odd	4		25.34.a.e.1.5	yes	11
5.3	odd	4		25.34.a.d.1.7	✓	11
5.4	even	2	inner	25.34.b.d.24.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.34.a.d.1.7	✓	11	5.3	odd	4
25.34.a.e.1.5	yes	11	5.2	odd	4
25.34.b.d.24.9		22	5.4	even	2	inner
25.34.b.d.24.14		22	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+41215.3i q^{2} -1.10688e8i q^{3} +6.89123e9 q^{4} +4.56203e12 q^{6} +7.02715e13i q^{7} +6.38061e14i q^{8} -6.69270e15 q^{9} +O(q^{10})\)	\(q+41215.3i q^{2} -1.10688e8i q^{3} +6.89123e9 q^{4} +4.56203e12 q^{6} +7.02715e13i q^{7} +6.38061e14i q^{8} -6.69270e15 q^{9} -5.33049e16 q^{11} -7.62774e17i q^{12} -1.55892e18i q^{13} -2.89626e18 q^{14} +3.28973e19 q^{16} -1.77770e20i q^{17} -2.75842e20i q^{18} +1.06994e20 q^{19} +7.77819e21 q^{21} -2.19698e21i q^{22} +5.14386e22i q^{23} +7.06255e22 q^{24} +6.42516e22 q^{26} +1.25480e23i q^{27} +4.84257e23i q^{28} -8.16333e23 q^{29} -3.64925e24 q^{31} +6.83678e24i q^{32} +5.90020e24i q^{33} +7.32687e24 q^{34} -4.61209e25 q^{36} -9.53287e25i q^{37} +4.40979e24i q^{38} -1.72554e26 q^{39} +2.96590e26 q^{41} +3.20581e26i q^{42} -5.30852e26i q^{43} -3.67337e26 q^{44} -2.12006e27 q^{46} +6.47397e27i q^{47} -3.64133e27i q^{48} +2.79291e27 q^{49} -1.96770e28 q^{51} -1.07429e28i q^{52} -1.72950e28i q^{53} -5.17169e27 q^{54} -4.48376e28 q^{56} -1.18429e28i q^{57} -3.36454e28i q^{58} -3.23790e28 q^{59} -5.51249e29 q^{61} -1.50405e29i q^{62} -4.70306e29i q^{63} +8.05483e26 q^{64} -2.43179e29 q^{66} -2.40123e30i q^{67} -1.22506e30i q^{68} +5.69362e30 q^{69} -6.55819e30 q^{71} -4.27035e30i q^{72} -2.45217e30i q^{73} +3.92900e30 q^{74} +7.37319e29 q^{76} -3.74582e30i q^{77} -7.11185e30i q^{78} -2.98501e31 q^{79} -2.33161e31 q^{81} +1.22240e31i q^{82} +4.29885e31i q^{83} +5.36013e31 q^{84} +2.18793e31 q^{86} +9.03580e31i q^{87} -3.40118e31i q^{88} +3.69934e31 q^{89} +1.09548e32 q^{91} +3.54475e32i q^{92} +4.03927e32i q^{93} -2.66827e32 q^{94} +7.56747e32 q^{96} +6.32291e32i q^{97} +1.15111e32i q^{98} +3.56754e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 98676413354 q^{4} - 35567955353446 q^{6} - 48\!\cdots\!16 q^{9}+O(q^{10}) \) 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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