LMFDB - Embedded newform 25.38.b.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,38,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, 38, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 38);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 38 $
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:	$216.785095312$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 31868761x^{2} + 253904465984400 $ x^4 + 31868761*x^2 + 253904465984400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-3992.29i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.38.b.a.24.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-480412. i q^{2} -3.45869e7i q^{3} -9.33565e10 q^{4} -1.66160e13 q^{6} -5.42222e15i q^{7} -2.11777e16i q^{8} +4.49088e17 q^{9} +O(q^{10})$	\(q-480412. i q^{2} -3.45869e7i q^{3} -9.33565e10 q^{4} -1.66160e13 q^{6} -5.42222e15i q^{7} -2.11777e16i q^{8} +4.49088e17 q^{9} -1.03285e18 q^{11} +3.22892e18i q^{12} +1.23244e19i q^{13} -2.60490e21 q^{14} -2.30048e22 q^{16} -5.41594e22i q^{17} -2.15747e23i q^{18} +3.08845e23 q^{19} -1.87538e23 q^{21} +4.96192e23i q^{22} +2.61592e25i q^{23} -7.32473e23 q^{24} +5.92077e24 q^{26} -3.11065e25i q^{27} +5.06199e26i q^{28} -2.49238e26 q^{29} -2.34643e27 q^{31} +8.14116e27i q^{32} +3.57230e25i q^{33} -2.60188e28 q^{34} -4.19253e28 q^{36} +6.21792e28i q^{37} -1.48373e29i q^{38} +4.26262e26 q^{39} -8.53404e29 q^{41} +9.00954e28i q^{42} -3.53994e29i q^{43} +9.64230e28 q^{44} +1.25672e31 q^{46} +6.68978e29i q^{47} +7.95667e29i q^{48} -1.08383e31 q^{49} -1.87321e30 q^{51} -1.15056e30i q^{52} -1.24128e32i q^{53} -1.49439e31 q^{54} -1.14830e32 q^{56} -1.06820e31i q^{57} +1.19737e32i q^{58} -6.57033e31 q^{59} -1.06034e33 q^{61} +1.12725e33i q^{62} -2.43505e33i q^{63} +7.49344e32 q^{64} +1.71618e31 q^{66} -8.44869e33i q^{67} +5.05613e33i q^{68} +9.04768e32 q^{69} -7.04837e33 q^{71} -9.51066e33i q^{72} -9.36735e33i q^{73} +2.98716e34 q^{74} -2.88327e34 q^{76} +5.60032e33i q^{77} -2.04781e32i q^{78} -1.51854e35 q^{79} +2.01141e35 q^{81} +4.09985e35i q^{82} +1.43761e35i q^{83} +1.75079e34 q^{84} -1.70063e35 q^{86} +8.62039e33i q^{87} +2.18734e34i q^{88} -2.28283e35 q^{89} +6.68253e34 q^{91} -2.44213e36i q^{92} +8.11557e34i q^{93} +3.21385e35 q^{94} +2.81578e35 q^{96} +7.07361e36i q^{97} +5.20686e36i q^{98} -4.63839e35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 75440539648 q^{4} - 45013087694592 q^{6} + 17\!\cdots\!28 q^{9}+O(q^{10}) $ 4 * q - 75440539648 * q^4 - 45013087694592 * q^6 + 1797894756803538828 * q^9	$ 4 q - 75440539648 q^{4} - 45013087694592 q^{6} + 17\!\cdots\!28 q^{9}+ \cdots - 24\!\cdots\!84 q^{99}+O(q^{100}) $ 4 * q - 75440539648 * q^4 - 45013087694592 * q^6 + 1797894756803538828 * q^9 - 53468072709697076112 * q^11 - 6338838239168130372096 * q^14 - 62304680212386352726016 * q^16 - 746552933145027427412240 * q^19 - 456377731622756562390912 * q^21 - 3739591058186201911787520 * q^24 + 322396580542781534089442688 * q^26 + 2541347654251764835903258440 * q^29 + 522841639582837790963090048 * q^31 - 31856790960783222718230988416 * q^34 - 33793503315298662900199643136 * q^36 + 23215418940485201693602693536 * q^39 - 2520966590932746267949369683672 * q^41 - 2666988540110127096326793977856 * q^44 + 25087518794220441775096515245568 * q^46 + 7656027316299536676614307676572 * q^49 - 2293205978177429604169034585952 * q^51 - 40492586655842738676101442685440 * q^54 - 447650982444052146061518514421760 * q^56 + 475924919212180257517798739401680 * q^59 + 203597682746077400400212510399288 * q^61 - 3749345404038864334832998367100928 * q^64 + 337112749155120186234694899096576 * q^66 + 1806159650811062164844443598560896 * q^69 - 1492266179587664985379924317736032 * q^71 + 134223318190050404586810430559958144 * q^74 - 133566840432061294264268018268037120 * q^76 - 544803276068191678071295890289348160 * q^79 + 806647675100076682006471654701238884 * q^81 + 30492439951528129009923673520799744 * q^84 - 2012857661573965282511992269432943872 * q^86 + 2665737843422476235828687957589885720 * q^89 + 2276797572623063452955712766020415168 * q^91 - 1406921774426085174217572329151998976 * q^94 + 346517251436435219180772622942076928 * q^96 - 24051537836769278923892831683960619184 * 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 $

$2$	− 480412.i	− 1.29586i	−0.761699	−	0.647931i	$-0.775635\pi$
$2$	− 480412.i	− 1.29586i	0.761699	−	0.647931i	$-0.224365\pi$
$3$	− 3.45869e7i	− 0.0515429i	−0.999668	−	0.0257715i	$-0.991796\pi$
$3$	− 3.45869e7i	− 0.0515429i	0.999668	−	0.0257715i	$-0.00820422\pi$
$4$	−9.33565e10	−0.679258
$5$	0	0
$5$	0	0
$6$	−1.66160e13	−0.0667925
$7$	− 5.42222e15i	− 1.25853i	−0.777191	−	0.629264i	$-0.783356\pi$
$7$	− 5.42222e15i	− 1.25853i	0.777191	−	0.629264i	$-0.216644\pi$
$8$	− 2.11777e16i	− 0.415637i
$9$	4.49088e17	0.997343
$10$	0	0
$11$	−1.03285e18	−0.0560108	−0.0280054	−	0.999608i	$-0.508916\pi$
$11$	−1.03285e18	−0.0560108	−0.0280054	+	0.999608i	$0.508916\pi$
$12$	3.22892e18i	0.0350109i
$13$	1.23244e19i	0.0303957i	0.999885	+	0.0151979i	$0.00483781\pi$
$13$	1.23244e19i	0.0303957i	−0.999885	+	0.0151979i	$0.995162\pi$
$14$	−2.60490e21	−1.63088
$15$	0	0
$16$	−2.30048e22	−1.21787
$17$	− 5.41594e22i	− 0.934047i	−0.884245	−	0.467023i	$-0.845326\pi$
$17$	− 5.41594e22i	− 0.934047i	0.884245	−	0.467023i	$-0.154674\pi$
$18$	− 2.15747e23i	− 1.29242i
$19$	3.08845e23	0.680455	0.340228	−	0.940343i	$-0.389496\pi$
$19$	3.08845e23	0.680455	0.340228	+	0.940343i	$0.389496\pi$
$20$	0	0
$21$	−1.87538e23	−0.0648682
$22$	4.96192e23i	0.0725822i
$23$	2.61592e25i	1.68136i	0.541535	+	0.840678i	$0.317844\pi$
$23$	2.61592e25i	1.68136i	−0.541535	+	0.840678i	$0.682156\pi$
$24$	−7.32473e23	−0.0214232
$25$	0	0
$26$	5.92077e24	0.0393886
$27$	− 3.11065e25i	− 0.102949i
$28$	5.06199e26i	0.854866i
$29$	−2.49238e26	−0.219913	−0.109957	−	0.993936i	$-0.535071\pi$
$29$	−2.49238e26	−0.219913	−0.109957	+	0.993936i	$0.535071\pi$
$30$	0	0
$31$	−2.34643e27	−0.602859	−0.301429	−	0.953489i	$-0.597464\pi$
$31$	−2.34643e27	−0.602859	−0.301429	+	0.953489i	$0.597464\pi$
$32$	8.14116e27i	1.16255i
$33$	3.57230e25i	0.00288696i
$34$	−2.60188e28	−1.21040
$35$	0	0
$36$	−4.19253e28	−0.677453
$37$	6.21792e28i	0.605220i	0.953114	+	0.302610i	$0.0978580\pi$
$37$	6.21792e28i	0.605220i	−0.953114	+	0.302610i	$0.902142\pi$
$38$	− 1.48373e29i	− 0.881776i
$39$	4.26262e26	0.00156668
$40$	0	0
$41$	−8.53404e29	−1.24352	−0.621761	−	0.783207i	$-0.713582\pi$
$41$	−8.53404e29	−1.24352	−0.621761	+	0.783207i	$0.713582\pi$
$42$	9.00954e28i	0.0840603i
$43$	− 3.53994e29i	− 0.213713i	−0.994274	−	0.106856i	$-0.965922\pi$
$43$	− 3.53994e29i	− 0.213713i	0.994274	−	0.106856i	$-0.0340785\pi$
$44$	9.64230e28	0.0380457
$45$	0	0
$46$	1.25672e31	2.17881
$47$	6.68978e29i	0.0779115i	0.999241	+	0.0389557i	$0.0124031\pi$
$47$	6.68978e29i	0.0779115i	−0.999241	+	0.0389557i	$0.987597\pi$
$48$	7.95667e29i	0.0627724i
$49$	−1.08383e31	−0.583895
$50$	0	0
$51$	−1.87321e30	−0.0481435
$52$	− 1.15056e30i	− 0.0206465i
$53$	− 1.24128e32i	− 1.56591i	−0.622077	−	0.782956i	$-0.713711\pi$
$53$	− 1.24128e32i	− 1.56591i	0.622077	−	0.782956i	$-0.286289\pi$
$54$	−1.49439e31	−0.133408
$55$	0	0
$56$	−1.14830e32	−0.523092
$57$	− 1.06820e31i	− 0.0350726i
$58$	1.19737e32i	0.284977i
$59$	−6.57033e31	−0.113979	−0.0569895	−	0.998375i	$-0.518150\pi$
$59$	−6.57033e31	−0.113979	−0.0569895	+	0.998375i	$0.518150\pi$
$60$	0	0
$61$	−1.06034e33	−0.992758	−0.496379	−	0.868106i	$-0.665337\pi$
$61$	−1.06034e33	−0.992758	−0.496379	+	0.868106i	$0.665337\pi$
$62$	1.12725e33i	0.781222i
$63$	− 2.43505e33i	− 1.25519i
$64$	7.49344e32	0.288637
$65$	0	0
$66$	1.71618e31	0.00374110
$67$	− 8.44869e33i	− 1.39446i	−0.716849	−	0.697229i	$-0.754416\pi$
$67$	− 8.44869e33i	− 1.39446i	0.716849	−	0.697229i	$-0.245584\pi$
$68$	5.05613e33i	0.634459i
$69$	9.04768e32	0.0866620
$70$	0	0
$71$	−7.04837e33	−0.397932	−0.198966	−	0.980006i	$-0.563758\pi$
$71$	−7.04837e33	−0.397932	−0.198966	+	0.980006i	$0.563758\pi$
$72$	− 9.51066e33i	− 0.414533i
$73$	− 9.36735e33i	− 0.316333i	−0.987412	−	0.158166i	$-0.949442\pi$
$73$	− 9.36735e33i	− 0.316333i	0.987412	−	0.158166i	$-0.0505582\pi$
$74$	2.98716e34	0.784282
$75$	0	0
$76$	−2.88327e34	−0.462205
$77$	5.60032e33i	0.0704911i
$78$	− 2.04781e32i	− 0.00203021i
$79$	−1.51854e35	−1.18940	−0.594698	−	0.803949i	$-0.702728\pi$
$79$	−1.51854e35	−1.18940	−0.594698	+	0.803949i	$0.702728\pi$
$80$	0	0
$81$	2.01141e35	0.992037
$82$	4.09985e35i	1.61143i
$83$	1.43761e35i	0.451541i	0.974180	+	0.225771i	$0.0724900\pi$
$83$	1.43761e35i	0.451541i	−0.974180	+	0.225771i	$0.927510\pi$
$84$	1.75079e34	0.0440623
$85$	0	0
$86$	−1.70063e35	−0.276942
$87$	8.62039e33i	0.0113350i
$88$	2.18734e34i	0.0232802i
$89$	−2.28283e35	−0.197133	−0.0985664	−	0.995130i	$-0.531426\pi$
$89$	−2.28283e35	−0.197133	−0.0985664	+	0.995130i	$0.531426\pi$
$90$	0	0
$91$	6.68253e34	0.0382539
$92$	− 2.44213e36i	− 1.14208i
$93$	8.11557e34i	0.0310731i
$94$	3.21385e35	0.100962
$95$	0	0
$96$	2.81578e35	0.0599212
$97$	7.07361e36i	1.24269i	0.783535	+	0.621347i	$0.213414\pi$
$97$	7.07361e36i	1.24269i	−0.783535	+	0.621347i	$0.786586\pi$
$98$	5.20686e36i	0.756647i
$99$	−4.63839e35	−0.0558620
$100$	0	0
$101$	−1.31355e37	−1.09270	−0.546350	−	0.837557i	$-0.683983\pi$
$101$	−1.31355e37	−1.09270	−0.546350	+	0.837557i	$0.683983\pi$
$102$	8.99911e35i	0.0623873i
$103$	− 2.33181e37i	− 1.34960i	−0.738000	−	0.674800i	$-0.764230\pi$
$103$	− 2.33181e37i	− 1.34960i	0.738000	−	0.674800i	$-0.235770\pi$
$104$	2.61002e35	0.0126336
$105$	0	0
$106$	−5.96327e37	−2.02920
$107$	3.01693e36i	0.0862909i	0.999069	+	0.0431454i	$0.0137379\pi$
$107$	3.01693e36i	0.0862909i	−0.999069	+	0.0431454i	$0.986262\pi$
$108$	2.90400e36i	0.0699289i
$109$	−3.05531e37	−0.620391	−0.310195	−	0.950673i	$-0.600394\pi$
$109$	−3.05531e37	−0.620391	−0.310195	+	0.950673i	$0.600394\pi$
$110$	0	0
$111$	2.15059e36	0.0311948
$112$	1.24737e38i	1.53272i
$113$	− 4.21983e37i	− 0.439890i	−0.975512	−	0.219945i	$-0.929412\pi$
$113$	− 4.21983e37i	− 0.439890i	0.975512	−	0.219945i	$-0.0705878\pi$
$114$	−5.13177e36	−0.0454493
$115$	0	0
$116$	2.32680e37	0.149378
$117$	5.53472e36i	0.0303150i
$118$	3.15646e37i	0.147701i
$119$	−2.93664e38	−1.17552
$120$	0	0
$121$	−3.38973e38	−0.996863
$122$	5.09400e38i	1.28648i
$123$	2.95166e37i	0.0640947i
$124$	2.19054e38	0.409497
$125$	0	0
$126$	−1.16983e39	−1.62655
$127$	1.09656e39i	1.31724i	0.752476	+	0.658619i	$0.228859\pi$
$127$	1.09656e39i	1.31724i	−0.752476	+	0.658619i	$0.771141\pi$
$128$	7.58918e38i	0.788516i
$129$	−1.22436e37	−0.0110154
$130$	0	0
$131$	−2.36928e39	−1.60360	−0.801802	−	0.597590i	$-0.796125\pi$
$131$	−2.36928e39	−1.60360	−0.801802	+	0.597590i	$0.796125\pi$
$132$	− 3.33498e36i	− 0.00196099i
$133$	− 1.67463e39i	− 0.856373i
$134$	−4.05885e39	−1.80702
$135$	0	0
$136$	−1.14697e39	−0.388225
$137$	2.55274e39i	0.754529i	0.926105	+	0.377265i	$0.123135\pi$
$137$	2.55274e39i	0.754529i	−0.926105	+	0.377265i	$0.876865\pi$
$138$	− 4.34661e38i	− 0.112302i
$139$	6.38958e39	1.44444	0.722219	−	0.691665i	$-0.243122\pi$
$139$	6.38958e39	1.44444	0.722219	+	0.691665i	$0.243122\pi$
$140$	0	0
$141$	2.31379e37	0.00401578
$142$	3.38612e39i	0.515665i
$143$	− 1.27292e37i	− 0.00170249i
$144$	−1.03312e40	−1.21463
$145$	0	0
$146$	−4.50019e39	−0.409923
$147$	3.74864e38i	0.0300956i
$148$	− 5.80483e39i	− 0.411100i
$149$	3.49035e39	0.218234	0.109117	−	0.994029i	$-0.465198\pi$
$149$	3.49035e39	0.218234	0.109117	+	0.994029i	$0.465198\pi$
$150$	0	0
$151$	−1.43880e40	−0.702953	−0.351476	−	0.936197i	$-0.614320\pi$
$151$	−1.43880e40	−0.702953	−0.351476	+	0.936197i	$0.614320\pi$
$152$	− 6.54064e39i	− 0.282823i
$153$	− 2.43223e40i	− 0.931565i
$154$	2.69046e39	0.0913468
$155$	0	0
$156$	−3.97943e37	−0.00106418
$157$	3.81842e40i	0.907277i	0.891186	+	0.453639i	$0.149874\pi$
$157$	3.81842e40i	0.907277i	−0.891186	+	0.453639i	$0.850126\pi$
$158$	7.29527e40i	1.54129i
$159$	−4.29322e39	−0.0807116
$160$	0	0
$161$	1.41841e41	2.11604
$162$	− 9.66305e40i	− 1.28554i
$163$	7.49639e40i	0.889982i	0.895535	+	0.444991i	$0.146793\pi$
$163$	7.49639e40i	0.889982i	−0.895535	+	0.444991i	$0.853207\pi$
$164$	7.96708e40	0.844672
$165$	0	0
$166$	6.90646e40	0.585135
$167$	− 1.87857e41i	− 1.42421i	−0.702074	−	0.712104i	$-0.747743\pi$
$167$	− 1.87857e41i	− 1.42421i	0.702074	−	0.712104i	$-0.252257\pi$
$168$	3.97163e39i	0.0269617i
$169$	1.64249e41	0.999076
$170$	0	0
$171$	1.38699e41	0.678648
$172$	3.30477e40i	0.145166i
$173$	− 2.98432e41i	− 1.17759i	−0.808284	−	0.588793i	$-0.799603\pi$
$173$	− 2.98432e41i	− 1.17759i	0.808284	−	0.588793i	$-0.200397\pi$
$174$	4.14134e39	0.0146886
$175$	0	0
$176$	2.37605e40	0.0682136
$177$	2.27248e39i	0.00587481i
$178$	1.09670e41i	0.255457i
$179$	−3.46258e41	−0.727141	−0.363570	−	0.931567i	$-0.618442\pi$
$179$	−3.46258e41	−0.727141	−0.363570	+	0.931567i	$0.618442\pi$
$180$	0	0
$181$	4.05668e41	0.693613	0.346806	−	0.937937i	$-0.387266\pi$
$181$	4.05668e41	0.693613	0.346806	+	0.937937i	$0.387266\pi$
$182$	− 3.21037e40i	− 0.0495717i
$183$	3.66740e40i	0.0511697i
$184$	5.53993e41	0.698835
$185$	0	0
$186$	3.89882e40	0.0402664
$187$	5.59384e40i	0.0523167i
$188$	− 6.24534e40i	− 0.0529220i
$189$	−1.68666e41	−0.129564
$190$	0	0
$191$	−1.41675e42	−0.895726	−0.447863	−	0.894102i	$-0.647815\pi$
$191$	−1.41675e42	−0.895726	−0.447863	+	0.894102i	$0.647815\pi$
$192$	− 2.59175e40i	− 0.0148772i
$193$	1.28639e42i	0.670751i	0.942085	+	0.335375i	$0.108863\pi$
$193$	1.28639e42i	0.670751i	−0.942085	+	0.335375i	$0.891137\pi$
$194$	3.39825e42	1.61036
$195$	0	0
$196$	1.01183e42	0.396615
$197$	3.68135e41i	0.131336i	0.997842	+	0.0656678i	$0.0209178\pi$
$197$	3.68135e41i	0.131336i	−0.997842	+	0.0656678i	$0.979082\pi$
$198$	2.22834e41i	0.0723894i
$199$	−3.12066e42	−0.923557	−0.461779	−	0.886995i	$-0.652789\pi$
$199$	−3.12066e42	−0.923557	−0.461779	+	0.886995i	$0.652789\pi$
$200$	0	0
$201$	−2.92214e41	−0.0718744
$202$	6.31044e42i	1.41599i
$203$	1.35142e42i	0.276767i
$204$	1.74876e41	0.0327019
$205$	0	0
$206$	−1.12023e43	−1.74890
$207$	1.17478e43i	1.67689i
$208$	− 2.83520e41i	− 0.0370179i
$209$	−3.18990e41	−0.0381128
$210$	0	0
$211$	−7.58037e42	−0.759391	−0.379695	−	0.925112i	$-0.623971\pi$
$211$	−7.58037e42	−0.759391	−0.379695	+	0.925112i	$0.623971\pi$
$212$	1.15882e43i	1.06366i
$213$	2.43782e41i	0.0205106i
$214$	1.44937e42	0.111821
$215$	0	0
$216$	−6.58765e41	−0.0427894
$217$	1.27228e43i	0.758715i
$218$	1.46781e43i	0.803941i
$219$	−3.23988e41	−0.0163047
$220$	0	0
$221$	6.67479e41	0.0283910
$222$	− 1.03317e42i	− 0.0404242i
$223$	− 4.00362e43i	− 1.44149i	−0.693198	−	0.720747i	$-0.743799\pi$
$223$	− 4.00362e43i	− 1.44149i	0.693198	−	0.720747i	$-0.256201\pi$
$224$	4.41431e43	1.46310
$225$	0	0
$226$	−2.02726e43	−0.570037
$227$	3.89322e43i	1.00886i	0.863453	+	0.504430i	$0.168297\pi$
$227$	3.89322e43i	1.00886i	−0.863453	+	0.504430i	$0.831703\pi$
$228$	9.97236e41i	0.0238234i
$229$	3.32118e43	0.731704	0.365852	−	0.930673i	$-0.380778\pi$
$229$	3.32118e43	0.731704	0.365852	+	0.930673i	$0.380778\pi$
$230$	0	0
$231$	1.93698e41	0.00363332
$232$	5.27830e42i	0.0914043i
$233$	7.95672e43i	1.27248i	0.771493	+	0.636238i	$0.219510\pi$
$233$	7.95672e43i	1.27248i	−0.771493	+	0.636238i	$0.780490\pi$
$234$	2.65894e42	0.0392840
$235$	0	0
$236$	6.13383e42	0.0774211
$237$	5.25218e42i	0.0613049i
$238$	1.41080e44i	1.52332i
$239$	1.42241e44	1.42123	0.710615	−	0.703581i	$-0.248417\pi$
$239$	1.42241e44	1.42123	0.710615	+	0.703581i	$0.248417\pi$
$240$	0	0
$241$	1.48641e44	1.27299	0.636494	−	0.771282i	$-0.280384\pi$
$241$	1.48641e44	1.27299	0.636494	+	0.771282i	$0.280384\pi$
$242$	1.62846e44i	1.29180i
$243$	− 2.09636e43i	− 0.154081i
$244$	9.89897e43	0.674339
$245$	0	0
$246$	1.41801e43	0.0830579
$247$	3.80632e42i	0.0206829i
$248$	4.96920e43i	0.250571i
$249$	4.97227e42	0.0232738
$250$	0	0
$251$	1.84398e44	0.744377	0.372189	−	0.928157i	$-0.378607\pi$
$251$	1.84398e44	0.744377	0.372189	+	0.928157i	$0.378607\pi$
$252$	2.27328e44i	0.852595i
$253$	− 2.70185e43i	− 0.0941741i
$254$	5.26801e44	1.70696
$255$	0	0
$256$	4.67582e44	1.31044
$257$	− 2.92391e44i	− 0.762433i	−0.924486	−	0.381216i	$-0.875505\pi$
$257$	− 2.92391e44i	− 0.762433i	0.924486	−	0.381216i	$-0.124495\pi$
$258$	5.88196e42i	0.0142744i
$259$	3.37149e44	0.761687
$260$	0	0
$261$	−1.11930e44	−0.219329
$262$	1.13823e45i	2.07805i
$263$	4.07317e44i	0.693029i	0.938045	+	0.346514i	$0.112635\pi$
$263$	4.07317e44i	0.693029i	−0.938045	+	0.346514i	$0.887365\pi$
$264$	7.56533e41	0.00119993
$265$	0	0
$266$	−8.04510e44	−1.10974
$267$	7.89562e42i	0.0101608i
$268$	7.88740e44i	0.947196i
$269$	6.06370e44	0.679705	0.339853	−	0.940479i	$-0.389623\pi$
$269$	6.06370e44	0.679705	0.339853	+	0.940479i	$0.389623\pi$
$270$	0	0
$271$	−1.82672e45	−1.78542	−0.892711	−	0.450630i	$-0.851200\pi$
$271$	−1.82672e45	−1.78542	−0.892711	+	0.450630i	$0.851200\pi$
$272$	1.24593e45i	1.13754i
$273$	− 2.31128e42i	− 0.00197172i
$274$	1.22637e45	0.977766
$275$	0	0
$276$	−8.44659e43	−0.0588659
$277$	2.33400e45i	1.52134i	0.649141	+	0.760668i	$0.275128\pi$
$277$	2.33400e45i	1.52134i	−0.649141	+	0.760668i	$0.724872\pi$
$278$	− 3.06963e45i	− 1.87179i
$279$	−1.05375e45	−0.601257
$280$	0	0
$281$	−1.00137e45	−0.500643	−0.250322	−	0.968163i	$-0.580536\pi$
$281$	−1.00137e45	−0.500643	−0.250322	+	0.968163i	$0.580536\pi$
$282$	− 1.11157e43i	− 0.00520390i
$283$	2.73703e45i	1.20014i	0.799948	+	0.600069i	$0.204860\pi$
$283$	2.73703e45i	1.20014i	−0.799948	+	0.600069i	$0.795140\pi$
$284$	6.58011e44	0.270299
$285$	0	0
$286$	−6.11525e42	−0.00220619
$287$	4.62734e45i	1.56501i
$288$	3.65609e45i	1.15946i
$289$	4.28857e44	0.127557
$290$	0	0
$291$	2.44655e44	0.0640521
$292$	8.74503e44i	0.214871i
$293$	− 1.07452e45i	− 0.247836i	−0.992292	−	0.123918i	$-0.960454\pi$
$293$	− 1.07452e45i	− 0.247836i	0.992292	−	0.123918i	$-0.0395459\pi$
$294$	1.80089e44	0.0389998
$295$	0	0
$296$	1.31681e45	0.251552
$297$	3.21283e43i	0.00576625i
$298$	− 1.67680e45i	− 0.282801i
$299$	−3.22396e44	−0.0511060
$300$	0	0
$301$	−1.91943e45	−0.268963
$302$	6.91215e45i	0.910930i
$303$	4.54316e44i	0.0563209i
$304$	−7.10494e45	−0.828704
$305$	0	0
$306$	−1.16847e46	−1.20718
$307$	− 1.41267e46i	− 1.37398i	−0.726668	−	0.686989i	$-0.758932\pi$
$307$	− 1.41267e46i	− 1.37398i	0.726668	−	0.686989i	$-0.241068\pi$
$308$	− 5.22826e44i	− 0.0478817i
$309$	−8.06503e44	−0.0695624
$310$	0	0
$311$	1.21153e46	0.927399	0.463700	−	0.885992i	$-0.346522\pi$
$311$	1.21153e46	0.927399	0.463700	+	0.885992i	$0.346522\pi$
$312$	− 9.02726e42i	0 0.000651172i
$313$	− 8.67864e45i	− 0.590040i	−0.955491	−	0.295020i	$-0.904674\pi$
$313$	− 8.67864e45i	− 0.590040i	0.955491	−	0.295020i	$-0.0953263\pi$
$314$	1.83441e46	1.17571
$315$	0	0
$316$	1.41766e46	0.807906
$317$	− 2.34417e46i	− 1.26006i	−0.776570	−	0.630031i	$-0.783042\pi$
$317$	− 2.34417e46i	− 1.26006i	0.776570	−	0.630031i	$-0.216958\pi$
$318$	2.06251e45i	0.104591i
$319$	2.57425e44	0.0123175
$320$	0	0
$321$	1.04346e44	0.00444768
$322$	− 6.81421e46i	− 2.74209i
$323$	− 1.67269e46i	− 0.635577i
$324$	−1.87778e46	−0.673849
$325$	0	0
$326$	3.60135e46	1.15329
$327$	1.05674e45i	0.0319768i
$328$	1.80732e46i	0.516854i
$329$	3.62734e45	0.0980538
$330$	0	0
$331$	5.11187e46	1.23527	0.617635	−	0.786465i	$-0.288091\pi$
$331$	5.11187e46	1.23527	0.617635	+	0.786465i	$0.288091\pi$
$332$	− 1.34211e46i	− 0.306713i
$333$	2.79239e46i	0.603612i
$334$	−9.02488e46	−1.84558
$335$	0	0
$336$	4.31428e45	0.0790009
$337$	2.29819e46i	0.398320i	0.979967	+	0.199160i	$0.0638214\pi$
$337$	2.29819e46i	0.398320i	−0.979967	+	0.199160i	$0.936179\pi$
$338$	− 7.89071e46i	− 1.29466i
$339$	−1.45951e45	−0.0226732
$340$	0	0
$341$	2.42350e45	0.0337666
$342$	− 6.66325e46i	− 0.879433i
$343$	− 4.18801e46i	− 0.523680i
$344$	−7.49680e45	−0.0888269
$345$	0	0
$346$	−1.43370e47	−1.52599
$347$	− 8.38076e46i	− 0.845645i	−0.906213	−	0.422822i	$-0.861039\pi$
$347$	− 8.38076e46i	− 0.845645i	0.906213	−	0.422822i	$-0.138961\pi$
$348$	− 8.04770e44i	− 0.00769938i
$349$	−1.33845e47	−1.21432	−0.607158	−	0.794581i	$-0.707690\pi$
$349$	−1.33845e47	−1.21432	−0.607158	+	0.794581i	$0.707690\pi$
$350$	0	0
$351$	3.83368e44	0.00312920
$352$	− 8.40857e45i	− 0.0651153i
$353$	− 1.44127e46i	− 0.105904i	−0.998597	−	0.0529520i	$-0.983137\pi$
$353$	− 1.44127e46i	− 0.105904i	0.998597	−	0.0529520i	$-0.0168630\pi$
$354$	1.09172e45	0.00761294
$355$	0	0
$356$	2.13117e46	0.133904
$357$	1.01569e46i	0.0605900i
$358$	1.66346e47i	0.942274i
$359$	−6.57303e46	−0.353605	−0.176802	−	0.984246i	$-0.556575\pi$
$359$	−6.57303e46	−0.353605	−0.176802	+	0.984246i	$0.556575\pi$
$360$	0	0
$361$	−1.10622e47	−0.536981
$362$	− 1.94888e47i	− 0.898826i
$363$	1.17240e46i	0.0513812i
$364$	−6.23858e45	−0.0259842
$365$	0	0
$366$	1.76186e46	0.0663088
$367$	2.16797e47i	0.775768i	0.921708	+	0.387884i	$0.126794\pi$
$367$	2.16797e47i	0.775768i	−0.921708	+	0.387884i	$0.873206\pi$
$368$	− 6.01789e47i	− 2.04767i
$369$	−3.83253e47	−1.24022
$370$	0	0
$371$	−6.73051e47	−1.97074
$372$	− 7.57641e45i	− 0.0211066i
$373$	− 2.47528e47i	− 0.656163i	−0.944649	−	0.328081i	$-0.893598\pi$
$373$	− 2.47528e47i	− 0.656163i	0.944649	−	0.328081i	$-0.106402\pi$
$374$	2.68734e46	0.0677952
$375$	0	0
$376$	1.41674e46	0.0323829
$377$	− 3.07170e45i	− 0.00668442i
$378$	8.10293e46i	0.167897i
$379$	−1.02737e47	−0.202722	−0.101361	−	0.994850i	$-0.532320\pi$
$379$	−1.02737e47	−0.202722	−0.101361	+	0.994850i	$0.532320\pi$
$380$	0	0
$381$	3.79267e46	0.0678943
$382$	6.80622e47i	1.16074i
$383$	1.22188e48i	1.98541i	0.120559	+	0.992706i	$0.461531\pi$
$383$	1.22188e48i	1.98541i	−0.120559	+	0.992706i	$0.538469\pi$
$384$	2.62487e46	0.0406424
$385$	0	0
$386$	6.17995e47	0.869200
$387$	− 1.58975e47i	− 0.213145i
$388$	− 6.60368e47i	− 0.844110i
$389$	1.16416e48	1.41888	0.709440	−	0.704766i	$-0.248948\pi$
$389$	1.16416e48	1.41888	0.709440	+	0.704766i	$0.248948\pi$
$390$	0	0
$391$	1.41677e48	1.57047
$392$	2.29531e47i	0.242688i
$393$	8.19461e46i	0.0826544i
$394$	1.76857e47	0.170193
$395$	0	0
$396$	4.33024e46	0.0379447
$397$	− 1.33628e48i	− 1.11756i	−0.829315	−	0.558781i	$-0.811269\pi$
$397$	− 1.33628e48i	− 1.11756i	0.829315	−	0.558781i	$-0.188731\pi$
$398$	1.49920e48i	1.19680i
$399$	−5.79202e46	−0.0441399
$400$	0	0
$401$	2.54007e47	0.176472	0.0882358	−	0.996100i	$-0.471877\pi$
$401$	2.54007e47	0.176472	0.0882358	+	0.996100i	$0.471877\pi$
$402$	1.40383e47i	0.0931393i
$403$	− 2.89182e46i	− 0.0183243i
$404$	1.22628e48	0.742225
$405$	0	0
$406$	6.49240e47	0.358652
$407$	− 6.42216e46i	− 0.0338988i
$408$	3.96703e46i	0.0200102i
$409$	1.33788e48	0.644967	0.322484	−	0.946575i	$-0.395482\pi$
$409$	1.33788e48	0.644967	0.322484	+	0.946575i	$0.395482\pi$
$410$	0	0
$411$	8.82915e46	0.0388906
$412$	2.17690e48i	0.916727i
$413$	3.56257e47i	0.143446i
$414$	5.64377e48	2.17302
$415$	0	0
$416$	−1.00334e47	−0.0353365
$417$	− 2.20996e47i	− 0.0744505i
$418$	1.53247e47i	0.0493889i
$419$	−2.08239e48	−0.642101	−0.321050	−	0.947062i	$-0.604036\pi$
$419$	−2.08239e48	−0.642101	−0.321050	+	0.947062i	$0.604036\pi$
$420$	0	0
$421$	−4.42178e48	−1.24847	−0.624236	−	0.781236i	$-0.714590\pi$
$421$	−4.42178e48	−1.24847	−0.624236	+	0.781236i	$0.714590\pi$
$422$	3.64170e48i	0.984065i
$423$	3.00430e47i	0.0777045i
$424$	−2.62876e48	−0.650851
$425$	0	0
$426$	1.17116e47	0.0265789
$427$	5.74940e48i	1.24941i
$428$	− 2.81650e47i	− 0.0586138i
$429$	−4.40263e44	−8.77511e−5 0
$430$	0	0
$431$	3.37175e48	0.616631	0.308315	−	0.951284i	$-0.400235\pi$
$431$	3.37175e48	0.616631	0.308315	+	0.951284i	$0.400235\pi$
$432$	7.15601e47i	0.125378i
$433$	− 2.37577e48i	− 0.398822i	−0.979916	−	0.199411i	$-0.936097\pi$
$433$	− 2.37577e48i	− 0.398822i	0.979916	−	0.199411i	$-0.0639028\pi$
$434$	6.11220e48	0.983190
$435$	0	0
$436$	2.85233e48	0.421405
$437$	8.07916e48i	1.14409i
$438$	1.55648e47i	0.0211286i
$439$	2.31976e48	0.301890	0.150945	−	0.988542i	$-0.451768\pi$
$439$	2.31976e48	0.301890	0.150945	+	0.988542i	$0.451768\pi$
$440$	0	0
$441$	−4.86736e48	−0.582344
$442$	− 3.20665e47i	− 0.0367908i
$443$	1.52174e49i	1.67444i	0.546864	+	0.837222i	$0.315822\pi$
$443$	1.52174e49i	1.67444i	−0.546864	+	0.837222i	$0.684178\pi$
$444$	−2.00771e47	−0.0211893
$445$	0	0
$446$	−1.92339e49	−1.86798
$447$	− 1.20720e47i	− 0.0112484i
$448$	− 4.06311e48i	− 0.363258i
$449$	−1.92781e49	−1.65390	−0.826948	−	0.562279i	$-0.809925\pi$
$449$	−1.92781e49	−1.65390	−0.826948	+	0.562279i	$0.809925\pi$
$450$	0	0
$451$	8.81436e47	0.0696506
$452$	3.93949e48i	0.298799i
$453$	4.97636e47i	0.0362322i
$454$	1.87035e49	1.30734
$455$	0	0
$456$	−2.26221e47	−0.0145775
$457$	1.19646e49i	0.740367i	0.928959	+	0.370183i	$0.120705\pi$
$457$	1.19646e49i	0.740367i	−0.928959	+	0.370183i	$0.879295\pi$
$458$	− 1.59553e49i	− 0.948187i
$459$	−1.68471e48	−0.0961591
$460$	0	0
$461$	−2.78549e49	−1.46702	−0.733508	−	0.679680i	$-0.762119\pi$
$461$	−2.78549e49	−1.46702	−0.733508	+	0.679680i	$0.762119\pi$
$462$	− 9.30548e46i	− 0.00470828i
$463$	1.11920e49i	0.544075i	0.962287	+	0.272038i	$0.0876975\pi$
$463$	1.11920e49i	0.544075i	−0.962287	+	0.272038i	$0.912303\pi$
$464$	5.73369e48	0.267825
$465$	0	0
$466$	3.82250e49	1.64895
$467$	− 1.63248e49i	− 0.676840i	−0.940995	−	0.338420i	$-0.890108\pi$
$467$	− 1.63248e49i	− 0.676840i	0.940995	−	0.338420i	$-0.109892\pi$
$468$	− 5.16702e47i	− 0.0205917i
$469$	−4.58106e49	−1.75497
$470$	0	0
$471$	1.32067e48	0.0467637
$472$	1.39145e48i	0.0473739i
$473$	3.65622e47i	0.0119702i
$474$	2.52321e48	0.0794427
$475$	0	0
$476$	2.74154e49	0.798485
$477$	− 5.57445e49i	− 1.56175i
$478$	− 6.83344e49i	− 1.84172i
$479$	−2.63654e49	−0.683639	−0.341820	−	0.939766i	$-0.611043\pi$
$479$	−2.63654e49	−0.683639	−0.341820	+	0.939766i	$0.611043\pi$
$480$	0	0
$481$	−7.66319e47	−0.0183961
$482$	− 7.14090e49i	− 1.64962i
$483$	− 4.90585e48i	− 0.109067i
$484$	3.16453e49	0.677127
$485$	0	0
$486$	−1.00712e49	−0.199668
$487$	− 7.78447e49i	− 1.48574i	−0.669435	−	0.742871i	$-0.733464\pi$
$487$	− 7.78447e49i	− 1.48574i	0.669435	−	0.742871i	$-0.266536\pi$
$488$	2.24556e49i	0.412628i
$489$	2.59277e48	0.0458723
$490$	0	0
$491$	9.85282e49	1.61642	0.808208	−	0.588897i	$-0.200438\pi$
$491$	9.85282e49	1.61642	0.808208	+	0.588897i	$0.200438\pi$
$492$	− 2.75557e48i	− 0.0435368i
$493$	1.34986e49i	0.205409i
$494$	1.82860e48	0.0268022
$495$	0	0
$496$	5.39792e49	0.734201
$497$	3.82178e49i	0.500809i
$498$	− 2.38874e48i	− 0.0301596i
$499$	−1.25338e50	−1.52483	−0.762415	−	0.647088i	$-0.775987\pi$
$499$	−1.25338e50	−1.52483	−0.762415	+	0.647088i	$0.775987\pi$
$500$	0	0
$501$	−6.49741e48	−0.0734078
$502$	− 8.85871e49i	− 0.964610i
$503$	1.11020e50i	1.16518i	0.812767	+	0.582589i	$0.197960\pi$
$503$	1.11020e50i	1.16518i	−0.812767	+	0.582589i	$0.802040\pi$
$504$	−5.15688e49	−0.521702
$505$	0	0
$506$	−1.29800e49	−0.122037
$507$	− 5.68087e48i	− 0.0514953i
$508$	− 1.02371e50i	− 0.894745i
$509$	1.38813e50	1.16991	0.584955	−	0.811066i	$-0.301112\pi$
$509$	1.38813e50	1.16991	0.584955	+	0.811066i	$0.301112\pi$
$510$	0	0
$511$	−5.07918e49	−0.398114
$512$	− 1.20327e50i	− 0.909639i
$513$	− 9.60711e48i	− 0.0700521i
$514$	−1.40468e50	−0.988007
$515$	0	0
$516$	1.14302e48	0.00748228
$517$	− 6.90952e47i	− 0.00436388i
$518$	− 1.61970e50i	− 0.987041i
$519$	−1.03219e49	−0.0606962
$520$	0	0
$521$	−2.33871e50	−1.28079	−0.640396	−	0.768045i	$-0.721230\pi$
$521$	−2.33871e50	−1.28079	−0.640396	+	0.768045i	$0.721230\pi$
$522$	5.37724e49i	0.284220i
$523$	1.30285e50i	0.664679i	0.943160	+	0.332340i	$0.107838\pi$
$523$	1.30285e50i	0.664679i	−0.943160	+	0.332340i	$0.892162\pi$
$524$	2.21188e50	1.08926
$525$	0	0
$526$	1.95680e50	0.898070
$527$	1.27081e50i	0.563098i
$528$	− 8.21803e47i	− 0.00351593i
$529$	−4.42241e50	−1.82696
$530$	0	0
$531$	−2.95065e49	−0.113676
$532$	1.56337e50i	0.581698i
$533$	− 1.05177e49i	− 0.0377977i
$534$	3.79315e48	0.0131670
$535$	0	0
$536$	−1.78924e50	−0.579589
$537$	1.19760e49i	0.0374789i
$538$	− 2.91307e50i	− 0.880804i
$539$	1.11943e49	0.0327044
$540$	0	0
$541$	−5.31273e50	−1.44933	−0.724667	−	0.689099i	$-0.758007\pi$
$541$	−5.31273e50	−1.44933	−0.724667	+	0.689099i	$0.758007\pi$
$542$	8.77579e50i	2.31366i
$543$	− 1.40308e49i	− 0.0357508i
$544$	4.40920e50	1.08588
$545$	0	0
$546$	−1.11037e48	−0.00255507
$547$	− 7.47732e49i	− 0.166334i	−0.996536	−	0.0831669i	$-0.973497\pi$
$547$	− 7.47732e49i	− 0.166334i	0.996536	−	0.0831669i	$-0.0265035\pi$
$548$	− 2.38315e50i	− 0.512520i
$549$	−4.76186e50	−0.990121
$550$	0	0
$551$	−7.69761e49	−0.149641
$552$	− 1.91609e49i	− 0.0360200i
$553$	8.23388e50i	1.49689i
$554$	1.12128e51	1.97144
$555$	0	0
$556$	−5.96509e50	−0.981146
$557$	3.60496e50i	0.573560i	0.957996	+	0.286780i	$0.0925849\pi$
$557$	3.60496e50i	0.573560i	−0.957996	+	0.286780i	$0.907415\pi$
$558$	5.06234e50i	0.779146i
$559$	4.36275e48	0.00649594
$560$	0	0
$561$	1.93474e48	0.00269655
$562$	4.81071e50i	0.648764i
$563$	3.94055e50i	0.514223i	0.966382	+	0.257112i	$0.0827708\pi$
$563$	3.94055e50i	0.514223i	−0.966382	+	0.257112i	$0.917229\pi$
$564$	−2.16007e48	−0.00272775
$565$	0	0
$566$	1.31490e51	1.55521
$567$	− 1.09063e51i	− 1.24851i
$568$	1.49268e50i	0.165396i
$569$	1.14686e50	0.123008	0.0615040	−	0.998107i	$-0.480410\pi$
$569$	1.14686e50	0.123008	0.0615040	+	0.998107i	$0.480410\pi$
$570$	0	0
$571$	1.48184e51	1.48948	0.744739	−	0.667356i	$-0.232574\pi$
$571$	1.48184e51	1.48948	0.744739	+	0.667356i	$0.232574\pi$
$572$	1.18835e48i	0.00115643i
$573$	4.90010e49i	0.0461683i
$574$	2.22303e51	2.02803
$575$	0	0
$576$	3.36521e50	0.287870
$577$	1.51306e51i	1.25344i	0.779243	+	0.626722i	$0.215604\pi$
$577$	1.51306e51i	1.25344i	−0.779243	+	0.626722i	$0.784396\pi$
$578$	− 2.06028e50i	− 0.165296i
$579$	4.44922e49	0.0345725
$580$	0	0
$581$	7.79505e50	0.568278
$582$	− 1.17535e50i	− 0.0830027i
$583$	1.28206e50i	0.0877079i
$584$	−1.98379e50	−0.131480
$585$	0	0
$586$	−5.16213e50	−0.321161
$587$	8.72797e50i	0.526148i	0.964776	+	0.263074i	$0.0847364\pi$
$587$	8.72797e50i	0.526148i	−0.964776	+	0.263074i	$0.915264\pi$
$588$	− 3.49960e49i	− 0.0204427i
$589$	−7.24683e50	−0.410218
$590$	0	0
$591$	1.27327e49	0.00676942
$592$	− 1.43042e51i	− 0.737077i
$593$	− 4.58679e49i	− 0.0229085i	−0.999934	−	0.0114543i	$-0.996354\pi$
$593$	− 4.58679e49i	− 0.0229085i	0.999934	−	0.0114543i	$-0.00364608\pi$
$594$	1.54348e49	0.00747226
$595$	0	0
$596$	−3.25846e50	−0.148237
$597$	1.07934e50i	0.0476028i
$598$	1.54883e50i	0.0662263i
$599$	2.10919e51	0.874420	0.437210	−	0.899360i	$-0.355967\pi$
$599$	2.10919e51	0.874420	0.437210	+	0.899360i	$0.355967\pi$
$600$	0	0
$601$	−2.46594e51	−0.961179	−0.480589	−	0.876946i	$-0.659577\pi$
$601$	−2.46594e51	−0.961179	−0.480589	+	0.876946i	$0.659577\pi$
$602$	9.22119e50i	0.348539i
$603$	− 3.79420e51i	− 1.39075i
$604$	1.34321e51	0.477486
$605$	0	0
$606$	2.18259e50	0.0729841
$607$	− 4.33541e51i	− 1.40618i	−0.711103	−	0.703088i	$-0.751804\pi$
$607$	− 4.33541e51i	− 1.40618i	0.711103	−	0.703088i	$-0.248196\pi$
$608$	2.51436e51i	0.791063i
$609$	4.67416e49	0.0142654
$610$	0	0
$611$	−8.24472e48	−0.00236817
$612$	2.27065e51i	0.632773i
$613$	1.36136e51i	0.368091i	0.982918	+	0.184046i	$0.0589194\pi$
$613$	1.36136e51i	0.368091i	−0.982918	+	0.184046i	$0.941081\pi$
$614$	−6.78662e51	−1.78049
$615$	0	0
$616$	1.18602e50	0.0292988
$617$	3.77980e51i	0.906136i	0.891476	+	0.453068i	$0.149671\pi$
$617$	3.77980e51i	0.906136i	−0.891476	+	0.453068i	$0.850329\pi$
$618$	3.87454e50i	0.0901432i
$619$	−6.56261e50	−0.148183	−0.0740917	−	0.997251i	$-0.523606\pi$
$619$	−6.56261e50	−0.148183	−0.0740917	+	0.997251i	$0.523606\pi$
$620$	0	0
$621$	8.13722e50	0.173094
$622$	− 5.82033e51i	− 1.20178i
$623$	1.23780e51i	0.248097i
$624$	−9.80609e48	−0.00190801
$625$	0	0
$626$	−4.16932e51	−0.764610
$627$	1.10329e49i	0.00196445i
$628$	− 3.56474e51i	− 0.616275i
$629$	3.36759e51	0.565304
$630$	0	0
$631$	3.19436e51	0.505640	0.252820	−	0.967513i	$-0.418642\pi$
$631$	3.19436e51	0.505640	0.252820	+	0.967513i	$0.418642\pi$
$632$	3.21593e51i	0.494357i
$633$	2.62182e50i	0.0391412i
$634$	−1.12617e52	−1.63287
$635$	0	0
$636$	4.00800e50	0.0548240
$637$	− 1.33575e50i	− 0.0177479i
$638$	− 1.23670e50i	− 0.0159618i
$639$	−3.16534e51	−0.396875
$640$	0	0
$641$	−1.48064e52	−1.75217	−0.876085	−	0.482157i	$-0.839853\pi$
$641$	−1.48064e52	−1.75217	−0.876085	+	0.482157i	$0.839853\pi$
$642$	− 5.01292e49i	− 0.00576358i
$643$	− 6.82003e51i	− 0.761874i	−0.924601	−	0.380937i	$-0.875601\pi$
$643$	− 6.82003e51i	− 0.761874i	0.924601	−	0.380937i	$-0.124399\pi$
$644$	−1.32418e52	−1.43733
$645$	0	0
$646$	−8.03579e51	−0.823620
$647$	− 2.43296e51i	− 0.242329i	−0.992632	−	0.121165i	$-0.961337\pi$
$647$	− 2.43296e51i	− 0.242329i	0.992632	−	0.121165i	$-0.0386629\pi$
$648$	− 4.25971e51i	− 0.412328i
$649$	6.78614e49	0.00638405
$650$	0	0
$651$	4.40044e50	0.0391064
$652$	− 6.99837e51i	− 0.604528i
$653$	− 5.92349e51i	− 0.497375i	−0.968584	−	0.248687i	$-0.920001\pi$
$653$	− 5.92349e51i	− 0.497375i	0.968584	−	0.248687i	$-0.0799991\pi$
$654$	5.07670e50	0.0414375
$655$	0	0
$656$	1.96324e52	1.51444
$657$	− 4.20676e51i	− 0.315492i
$658$	− 1.74262e51i	− 0.127064i
$659$	−2.77432e51	−0.196687	−0.0983437	−	0.995153i	$-0.531354\pi$
$659$	−2.77432e51	−0.196687	−0.0983437	+	0.995153i	$0.531354\pi$
$660$	0	0
$661$	1.53847e52	1.03124	0.515622	−	0.856816i	$-0.327561\pi$
$661$	1.53847e52	1.03124	0.515622	+	0.856816i	$0.327561\pi$
$662$	− 2.45580e52i	− 1.60074i
$663$	− 2.30861e49i	− 0.00146336i
$664$	3.04454e51	0.187677
$665$	0	0
$666$	1.34150e52	0.782198
$667$	− 6.51988e51i	− 0.369753i
$668$	1.75377e52i	0.967404i
$669$	−1.38473e51	−0.0742988
$670$	0	0
$671$	1.09517e51	0.0556051
$672$	− 1.52678e51i	− 0.0754125i
$673$	8.54768e50i	0.0410742i	0.999789	+	0.0205371i	$0.00653763\pi$
$673$	8.54768e50i	0.0410742i	−0.999789	+	0.0205371i	$0.993462\pi$
$674$	1.10408e52	0.516168
$675$	0	0
$676$	−1.53337e52	−0.678630
$677$	− 3.33629e52i	− 1.43673i	−0.695669	−	0.718363i	$-0.744892\pi$
$677$	− 3.33629e52i	− 1.43673i	0.695669	−	0.718363i	$-0.255108\pi$
$678$	7.01167e50i	0.0293814i
$679$	3.83547e52	1.56397
$680$	0	0
$681$	1.34655e51	0.0519996
$682$	− 1.16428e51i	− 0.0437568i
$683$	− 3.41377e52i	− 1.24868i	−0.781153	−	0.624340i	$-0.785368\pi$
$683$	− 3.41377e52i	− 1.24868i	0.781153	−	0.624340i	$-0.214632\pi$
$684$	−1.29484e52	−0.460977
$685$	0	0
$686$	−2.01197e52	−0.678618
$687$	− 1.14869e51i	− 0.0377142i
$688$	8.14359e51i	0.260273i
$689$	1.52980e51	0.0475970
$690$	0	0
$691$	5.92716e52	1.74784	0.873922	−	0.486066i	$-0.161569\pi$
$691$	5.92716e52	1.74784	0.873922	+	0.486066i	$0.161569\pi$
$692$	2.78606e52i	0.799884i
$693$	2.51504e51i	0.0703039i
$694$	−4.02621e52	−1.09584
$695$	0	0
$696$	1.82560e50	0.00471124
$697$	4.62198e52i	1.16151i
$698$	6.43007e52i	1.57359i
$699$	2.75199e51	0.0655871
$700$	0	0
$701$	4.09077e52	0.924744	0.462372	−	0.886686i	$-0.346998\pi$
$701$	4.09077e52	0.924744	0.462372	+	0.886686i	$0.346998\pi$
$702$	− 1.84174e50i	− 0.00405502i
$703$	1.92038e52i	0.411825i
$704$	−7.73958e50	−0.0161668
$705$	0	0
$706$	−6.92401e51	−0.137237
$707$	7.12235e52i	1.37519i
$708$	− 2.12150e50i	− 0.00399051i
$709$	8.44115e52	1.54684	0.773422	−	0.633891i	$-0.218543\pi$
$709$	8.44115e52	1.54684	0.773422	+	0.633891i	$0.218543\pi$
$710$	0	0
$711$	−6.81960e52	−1.18624
$712$	4.83452e51i	0.0819357i
$713$	− 6.13807e52i	− 1.01362i
$714$	4.87951e51	0.0785162
$715$	0	0
$716$	3.23254e52	0.493916
$717$	− 4.91969e51i	− 0.0732544i
$718$	3.15776e52i	0.458223i
$719$	2.81946e52	0.398733	0.199367	−	0.979925i	$-0.436112\pi$
$719$	2.81946e52	0.398733	0.199367	+	0.979925i	$0.436112\pi$
$720$	0	0
$721$	−1.26436e53	−1.69851
$722$	5.31442e52i	0.695853i
$723$	− 5.14105e51i	− 0.0656135i
$724$	−3.78717e52	−0.471142
$725$	0	0
$726$	5.63236e51	0.0665830
$727$	6.98427e52i	0.804886i	0.915445	+	0.402443i	$0.131839\pi$
$727$	6.98427e52i	0.804886i	−0.915445	+	0.402443i	$0.868161\pi$
$728$	− 1.41521e51i	− 0.0158997i
$729$	8.98455e52	0.984095
$730$	0	0
$731$	−1.91721e52	−0.199618
$732$	− 3.42375e51i	− 0.0347574i
$733$	− 3.54513e52i	− 0.350921i	−0.984487	−	0.175460i	$-0.943859\pi$
$733$	− 3.54513e52i	− 0.350921i	0.984487	−	0.175460i	$-0.0561414\pi$
$734$	1.04152e53	1.00529
$735$	0	0
$736$	−2.12966e53	−1.95466
$737$	8.72620e51i	0.0781046i
$738$	1.84119e53i	1.60715i
$739$	−1.51689e53	−1.29131	−0.645655	−	0.763629i	$-0.723416\pi$
$739$	−1.51689e53	−1.29131	−0.645655	+	0.763629i	$0.723416\pi$
$740$	0	0
$741$	1.31649e50	0.00106606
$742$	3.23341e53i	2.55381i
$743$	− 1.52901e53i	− 1.17793i	−0.808159	−	0.588964i	$-0.799536\pi$
$743$	− 1.52901e53i	− 1.17793i	0.808159	−	0.588964i	$-0.200464\pi$
$744$	1.71869e51	0.0129151
$745$	0	0
$746$	−1.18916e53	−0.850296
$747$	6.45615e52i	0.450342i
$748$	− 5.22221e51i	− 0.0355365i
$749$	1.63584e52	0.108600
$750$	0	0
$751$	1.42568e53	0.900916	0.450458	−	0.892798i	$-0.351261\pi$
$751$	1.42568e53	0.900916	0.450458	+	0.892798i	$0.351261\pi$
$752$	− 1.53897e52i	− 0.0948858i
$753$	− 6.37778e51i	− 0.0383674i
$754$	−1.47568e51	−0.00866209
$755$	0	0
$756$	1.57461e52	0.0880075
$757$	− 2.82784e53i	− 1.54234i	−0.636628	−	0.771171i	$-0.719671\pi$
$757$	− 2.82784e53i	− 1.54234i	0.636628	−	0.771171i	$-0.280329\pi$
$758$	4.93559e52i	0.262699i
$759$	−9.34487e50	−0.00485401
$760$	0	0
$761$	3.71288e52	0.183694	0.0918470	−	0.995773i	$-0.470723\pi$
$761$	3.71288e52	0.183694	0.0918470	+	0.995773i	$0.470723\pi$
$762$	− 1.82204e52i	− 0.0879817i
$763$	1.65666e53i	0.780780i
$764$	1.32263e53	0.608429
$765$	0	0
$766$	5.87005e53	2.57282
$767$	− 8.09750e50i	− 0.00346447i
$768$	− 1.61722e52i	− 0.0675441i
$769$	6.15158e52	0.250813	0.125406	−	0.992105i	$-0.459977\pi$
$769$	6.15158e52	0.250813	0.125406	+	0.992105i	$0.459977\pi$
$770$	0	0
$771$	−1.01129e52	−0.0392980
$772$	− 1.20093e53i	− 0.455613i
$773$	2.28656e53i	0.846960i	0.905905	+	0.423480i	$0.139192\pi$
$773$	2.28656e53i	0.846960i	−0.905905	+	0.423480i	$0.860808\pi$
$774$	−7.63732e52	−0.276206
$775$	0	0
$776$	1.49803e53	0.516510
$777$	− 1.16610e52i	− 0.0392596i
$778$	− 5.59277e53i	− 1.83867i
$779$	−2.63570e53	−0.846161
$780$	0	0
$781$	7.27989e51	0.0222885
$782$	− 6.80632e53i	− 2.03511i
$783$	7.75294e51i	0.0226399i
$784$	2.49334e53	0.711106
$785$	0	0
$786$	3.93679e52	0.107109
$787$	7.05791e52i	0.187561i	0.995593	+	0.0937807i	$0.0298953\pi$
$787$	7.05791e52i	0.187561i	−0.995593	+	0.0937807i	$0.970105\pi$
$788$	− 3.43678e52i	− 0.0892108i
$789$	1.40879e52	0.0357207
$790$	0	0
$791$	−2.28809e53	−0.553614
$792$	9.82306e51i	0.0232183i
$793$	− 1.30680e52i	− 0.0301756i
$794$	−6.41963e53	−1.44821
$795$	0	0
$796$	2.91333e53	0.627334
$797$	− 8.88567e53i	− 1.86944i	−0.355387	−	0.934719i	$-0.615651\pi$
$797$	− 8.88567e53i	− 1.86944i	0.355387	−	0.934719i	$-0.384349\pi$
$798$	2.78256e52i	0.0571993i
$799$	3.62314e52	0.0727729
$800$	0	0
$801$	−1.02519e53	−0.196609
$802$	− 1.22028e53i	− 0.228683i
$803$	9.67504e51i	0.0177180i
$804$	2.72801e52	0.0488213
$805$	0	0
$806$	−1.38926e52	−0.0237458
$807$	− 2.09725e52i	− 0.0350340i
$808$	2.78180e53i	0.454167i
$809$	−3.72232e53	−0.593972	−0.296986	−	0.954882i	$-0.595981\pi$
$809$	−3.72232e53	−0.593972	−0.296986	+	0.954882i	$0.595981\pi$
$810$	0	0
$811$	−5.96718e53	−0.909668	−0.454834	−	0.890576i	$-0.650301\pi$
$811$	−5.96718e53	−0.909668	−0.454834	+	0.890576i	$0.650301\pi$
$812$	− 1.26164e53i	− 0.187996i
$813$	6.31808e52i	0.0920259i
$814$	−3.08528e52	−0.0439282
$815$	0	0
$816$	4.30929e52	0.0586324
$817$	− 1.09330e53i	− 0.145422i
$818$	− 6.42736e53i	− 0.835788i
$819$	3.00104e52	0.0381522
$820$	0	0
$821$	8.74697e52	0.106294	0.0531471	−	0.998587i	$-0.483075\pi$
$821$	8.74697e52	0.106294	0.0531471	+	0.998587i	$0.483075\pi$
$822$	− 4.24163e52i	− 0.0503969i
$823$	− 1.05135e54i	− 1.22138i	−0.791869	−	0.610692i	$-0.790892\pi$
$823$	− 1.05135e54i	− 1.22138i	0.791869	−	0.610692i	$-0.209108\pi$
$824$	−4.93825e53	−0.560945
$825$	0	0
$826$	1.71150e53	0.185886
$827$	− 1.54483e53i	− 0.164069i	−0.996629	−	0.0820347i	$-0.973858\pi$
$827$	− 1.54483e53i	− 0.164069i	0.996629	−	0.0820347i	$-0.0261418\pi$
$828$	− 1.09673e54i	− 1.13904i
$829$	−2.69934e53	−0.274156	−0.137078	−	0.990560i	$-0.543771\pi$
$829$	−2.69934e53	−0.274156	−0.137078	+	0.990560i	$0.543771\pi$
$830$	0	0
$831$	8.07259e52	0.0784141
$832$	9.23518e51i	0.00877332i
$833$	5.86997e53i	0.545385i
$834$	−1.06169e53	−0.0964776
$835$	0	0
$836$	2.97798e52	0.0258884
$837$	7.29891e52i	0.0620636i
$838$	1.00041e54i	0.832074i
$839$	−2.43290e54	−1.97937	−0.989686	−	0.143252i	$-0.954244\pi$
$839$	−2.43290e54	−1.97937	−0.989686	+	0.143252i	$0.954244\pi$
$840$	0	0
$841$	−1.22236e54	−0.951638
$842$	2.12428e54i	1.61785i
$843$	3.46344e52i	0.0258046i
$844$	7.07677e53	0.515822
$845$	0	0
$846$	1.44330e53	0.100694
$847$	1.83798e54i	1.25458i
$848$	2.85555e54i	1.90707i
$849$	9.46656e52	0.0618586
$850$	0	0
$851$	−1.62656e54	−1.01759
$852$	− 2.27586e52i	− 0.0139320i
$853$	− 9.59321e53i	− 0.574654i	−0.957832	−	0.287327i	$-0.907233\pi$
$853$	− 9.59321e53i	− 0.574654i	0.957832	−	0.287327i	$-0.0927667\pi$
$854$	2.76208e54	1.61907
$855$	0	0
$856$	6.38917e52	0.0358657
$857$	3.59352e52i	0.0197413i	0.999951	+	0.00987063i	$0.00314197\pi$
$857$	3.59352e52i	0.0197413i	−0.999951	+	0.00987063i	$0.996858\pi$
$858$	2.11508e50i	0 0.000113713i
$859$	−8.55580e53	−0.450181	−0.225091	−	0.974338i	$-0.572268\pi$
$859$	−8.55580e53	−0.450181	−0.225091	+	0.974338i	$0.572268\pi$
$860$	0	0
$861$	1.60046e53	0.0806651
$862$	− 1.61983e54i	− 0.799068i
$863$	− 1.56057e54i	− 0.753502i	−0.926315	−	0.376751i	$-0.877041\pi$
$863$	− 1.56057e54i	− 0.753502i	0.926315	−	0.376751i	$-0.122959\pi$
$864$	2.53243e53	0.119683
$865$	0	0
$866$	−1.14135e54	−0.516818
$867$	− 1.48329e52i	− 0.00657464i
$868$	− 1.18776e54i	− 0.515363i
$869$	1.56842e53	0.0666190
$870$	0	0
$871$	1.04125e53	0.0423855
$872$	6.47046e53i	0.257858i
$873$	3.17667e54i	1.23939i
$874$	3.88132e54	1.48258
$875$	0	0
$876$	3.02464e52	0.0110751
$877$	− 3.37270e54i	− 1.20916i	−0.796544	−	0.604581i	$-0.793341\pi$
$877$	− 3.37270e54i	− 1.20916i	0.796544	−	0.604581i	$-0.206659\pi$
$878$	− 1.11444e54i	− 0.391208i
$879$	−3.71644e52	−0.0127742
$880$	0	0
$881$	1.67513e54	0.552069	0.276034	−	0.961148i	$-0.410980\pi$
$881$	1.67513e54	0.552069	0.276034	+	0.961148i	$0.410980\pi$
$882$	2.33834e54i	0.754637i
$883$	− 1.42002e54i	− 0.448767i	−0.974501	−	0.224383i	$-0.927963\pi$
$883$	− 1.42002e54i	− 0.448767i	0.974501	−	0.224383i	$-0.0720368\pi$
$884$	−6.23135e52	−0.0192848
$885$	0	0
$886$	7.31060e54	2.16985
$887$	1.98874e54i	0.578085i	0.957316	+	0.289042i	$0.0933369\pi$
$887$	1.98874e54i	0.578085i	−0.957316	+	0.289042i	$0.906663\pi$
$888$	− 4.55446e52i	− 0.0129657i
$889$	5.94580e54	1.65778
$890$	0	0
$891$	−2.07748e53	−0.0555647
$892$	3.73764e54i	0.979147i
$893$	2.06611e53i	0.0530153i
$894$	−5.79955e52	−0.0145764
$895$	0	0
$896$	4.11502e54	0.992370
$897$	1.11507e52i	0.00263415i
$898$	9.26145e54i	2.14322i
$899$	5.84819e53	0.132577
$900$	0	0
$901$	−6.72271e54	−1.46263
$902$	− 4.23452e53i	− 0.0902575i
$903$	6.63874e52i	0.0138632i
$904$	−8.93665e53	−0.182835
$905$	0	0
$906$	2.39070e53	0.0469520
$907$	− 6.36503e54i	− 1.22480i	−0.790547	−	0.612401i	$-0.790204\pi$
$907$	− 6.36503e54i	− 1.22480i	0.790547	−	0.612401i	$-0.209796\pi$
$908$	− 3.63458e54i	− 0.685276i
$909$	−5.89899e54	−1.08980
$910$	0	0
$911$	2.93922e54	0.521365	0.260683	−	0.965425i	$-0.416052\pi$
$911$	2.93922e54	0.521365	0.260683	+	0.965425i	$0.416052\pi$
$912$	2.45738e53i	0.0427138i
$913$	− 1.48484e53i	− 0.0252912i
$914$	5.74791e54	0.959413
$915$	0	0
$916$	−3.10053e54	−0.497016
$917$	1.28467e55i	2.01818i
$918$	8.09354e53i	0.124609i
$919$	7.57823e54	1.14349	0.571743	−	0.820433i	$-0.306267\pi$
$919$	7.57823e54	1.14349	0.571743	+	0.820433i	$0.306267\pi$
$920$	0	0
$921$	−4.88598e53	−0.0708189
$922$	1.33818e55i	1.90105i
$923$	− 8.68666e52i	− 0.0120954i
$924$	−1.80830e52	−0.00246796
$925$	0	0
$926$	5.37676e54	0.705046
$927$	− 1.04719e55i	− 1.34602i
$928$	− 2.02909e54i	− 0.255660i
$929$	−6.55047e53	−0.0809062	−0.0404531	−	0.999181i	$-0.512880\pi$
$929$	−6.55047e53	−0.0809062	−0.0404531	+	0.999181i	$0.512880\pi$
$930$	0	0
$931$	−3.34737e54	−0.397314
$932$	− 7.42812e54i	− 0.864340i
$933$	− 4.19031e53i	− 0.0478009i
$934$	−7.84263e54	−0.877091
$935$	0	0
$936$	1.17213e53	0.0126000
$937$	− 3.87596e54i	− 0.408505i	−0.978918	−	0.204253i	$-0.934524\pi$
$937$	− 3.87596e54i	− 0.408505i	0.978918	−	0.204253i	$-0.0654764\pi$
$938$	2.20080e55i	2.27419i
$939$	−3.00168e53	−0.0304124
$940$	0	0
$941$	−1.38620e55	−1.35027	−0.675133	−	0.737696i	$-0.735914\pi$
$941$	−1.38620e55	−1.35027	−0.675133	+	0.737696i	$0.735914\pi$
$942$	− 6.34468e53i	− 0.0605993i
$943$	− 2.23244e55i	− 2.09080i
$944$	1.51149e54	0.138811
$945$	0	0
$946$	1.75649e53	0.0155117
$947$	− 8.86598e53i	− 0.0767807i	−0.999263	−	0.0383903i	$-0.987777\pi$
$947$	− 8.86598e53i	− 0.0767807i	0.999263	−	0.0383903i	$-0.0122230\pi$
$948$	− 4.90325e53i	− 0.0416419i
$949$	1.15447e53	0.00961515
$950$	0	0
$951$	−8.10776e53	−0.0649473
$952$	6.21913e54i	0.488592i
$953$	− 1.94425e55i	− 1.49807i	−0.662530	−	0.749036i	$-0.730517\pi$
$953$	− 1.94425e55i	− 1.49807i	0.662530	−	0.749036i	$-0.269483\pi$
$954$	−2.67803e55	−2.02381
$955$	0	0
$956$	−1.32791e55	−0.965382
$957$	− 8.90355e51i	0 0.000634881i
$958$	1.26662e55i	0.885902i
$959$	1.38415e55	0.949597
$960$	0	0
$961$	−9.64324e54	−0.636561
$962$	3.68148e53i	0.0238388i
$963$	1.35486e54i	0.0860616i
$964$	−1.38766e55	−0.864687
$965$	0	0
$966$	−2.35683e54	−0.141335
$967$	6.67380e54i	0.392630i	0.980541	+	0.196315i	$0.0628975\pi$
$967$	6.67380e54i	0.392630i	−0.980541	+	0.196315i	$0.937103\pi$
$968$	7.17867e54i	0.414333i
$969$	−5.78532e53	−0.0327595
$970$	0	0
$971$	−3.90466e52	−0.00212827	−0.00106414	−	0.999999i	$-0.500339\pi$
$971$	−3.90466e52	−0.00212827	−0.00106414	+	0.999999i	$0.500339\pi$
$972$	1.95709e54i	0.104661i
$973$	− 3.46457e55i	− 1.81787i
$974$	−3.73975e55	−1.92532
$975$	0	0
$976$	2.43930e55	1.20905
$977$	− 6.49911e54i	− 0.316085i	−0.987432	−	0.158043i	$-0.949482\pi$
$977$	− 6.49911e54i	− 0.316085i	0.987432	−	0.158043i	$-0.0505184\pi$
$978$	− 1.24560e54i	− 0.0594441i
$979$	2.35782e53	0.0110416
$980$	0	0
$981$	−1.37210e55	−0.618743
$982$	− 4.73341e55i	− 2.09465i
$983$	− 1.39076e55i	− 0.603967i	−0.953313	−	0.301984i	$-0.902351\pi$
$983$	− 1.39076e55i	− 0.603967i	0.953313	−	0.301984i	$-0.0976488\pi$
$984$	6.25095e53	0.0266402
$985$	0	0
$986$	6.48488e54	0.266182
$987$	− 1.25459e53i	− 0.00505398i
$988$	− 3.55345e53i	− 0.0140490i
$989$	9.26022e54	0.359327
$990$	0	0
$991$	4.28319e55	1.60105	0.800525	−	0.599300i	$-0.204554\pi$
$991$	4.28319e55	1.60105	0.800525	+	0.599300i	$0.204554\pi$
$992$	− 1.91026e55i	− 0.700853i
$993$	− 1.76804e54i	− 0.0636695i
$994$	1.83603e55	0.648980
$995$	0	0
$996$	−4.64193e53	−0.0158089
$997$	− 3.24811e55i	− 1.08585i	−0.839781	−	0.542925i	$-0.817317\pi$
$997$	− 3.24811e55i	− 1.08585i	0.839781	−	0.542925i	$-0.182683\pi$
$998$	6.02137e55i	1.97597i
$999$	1.93418e54	0.0623067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.38.b.a.24.1		4
5.2	odd	4		25.38.a.a.1.2		2
5.3	odd	4		1.38.a.a.1.1	✓	2
5.4	even	2	inner	25.38.b.a.24.4		4
15.8	even	4		9.38.a.a.1.2		2
20.3	even	4		16.38.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.38.a.a.1.1	✓	2	5.3	odd	4
9.38.a.a.1.2		2	15.8	even	4
16.38.a.b.1.1		2	20.3	even	4
25.38.a.a.1.2		2	5.2	odd	4
25.38.b.a.24.1		4	1.1	even	1	trivial
25.38.b.a.24.4		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-480412. i q^{2} -3.45869e7i q^{3} -9.33565e10 q^{4} -1.66160e13 q^{6} -5.42222e15i q^{7} -2.11777e16i q^{8} +4.49088e17 q^{9} +O(q^{10})\)	\(q-480412. i q^{2} -3.45869e7i q^{3} -9.33565e10 q^{4} -1.66160e13 q^{6} -5.42222e15i q^{7} -2.11777e16i q^{8} +4.49088e17 q^{9} -1.03285e18 q^{11} +3.22892e18i q^{12} +1.23244e19i q^{13} -2.60490e21 q^{14} -2.30048e22 q^{16} -5.41594e22i q^{17} -2.15747e23i q^{18} +3.08845e23 q^{19} -1.87538e23 q^{21} +4.96192e23i q^{22} +2.61592e25i q^{23} -7.32473e23 q^{24} +5.92077e24 q^{26} -3.11065e25i q^{27} +5.06199e26i q^{28} -2.49238e26 q^{29} -2.34643e27 q^{31} +8.14116e27i q^{32} +3.57230e25i q^{33} -2.60188e28 q^{34} -4.19253e28 q^{36} +6.21792e28i q^{37} -1.48373e29i q^{38} +4.26262e26 q^{39} -8.53404e29 q^{41} +9.00954e28i q^{42} -3.53994e29i q^{43} +9.64230e28 q^{44} +1.25672e31 q^{46} +6.68978e29i q^{47} +7.95667e29i q^{48} -1.08383e31 q^{49} -1.87321e30 q^{51} -1.15056e30i q^{52} -1.24128e32i q^{53} -1.49439e31 q^{54} -1.14830e32 q^{56} -1.06820e31i q^{57} +1.19737e32i q^{58} -6.57033e31 q^{59} -1.06034e33 q^{61} +1.12725e33i q^{62} -2.43505e33i q^{63} +7.49344e32 q^{64} +1.71618e31 q^{66} -8.44869e33i q^{67} +5.05613e33i q^{68} +9.04768e32 q^{69} -7.04837e33 q^{71} -9.51066e33i q^{72} -9.36735e33i q^{73} +2.98716e34 q^{74} -2.88327e34 q^{76} +5.60032e33i q^{77} -2.04781e32i q^{78} -1.51854e35 q^{79} +2.01141e35 q^{81} +4.09985e35i q^{82} +1.43761e35i q^{83} +1.75079e34 q^{84} -1.70063e35 q^{86} +8.62039e33i q^{87} +2.18734e34i q^{88} -2.28283e35 q^{89} +6.68253e34 q^{91} -2.44213e36i q^{92} +8.11557e34i q^{93} +3.21385e35 q^{94} +2.81578e35 q^{96} +7.07361e36i q^{97} +5.20686e36i q^{98} -4.63839e35 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 75440539648 q^{4} - 45013087694592 q^{6} + 17\!\cdots\!28 q^{9}+O(q^{10}) \) 4 * q - 75440539648 * q^4 - 45013087694592 * q^6 + 1797894756803538828 * q^9	\( 4 q - 75440539648 q^{4} - 45013087694592 q^{6} + 17\!\cdots\!28 q^{9}+ \cdots - 24\!\cdots\!84 q^{99}+O(q^{100}) \) 4 * q - 75440539648 * q^4 - 45013087694592 * q^6 + 1797894756803538828 * q^9 - 53468072709697076112 * q^11 - 6338838239168130372096 * q^14 - 62304680212386352726016 * q^16 - 746552933145027427412240 * q^19 - 456377731622756562390912 * q^21 - 3739591058186201911787520 * q^24 + 322396580542781534089442688 * q^26 + 2541347654251764835903258440 * q^29 + 522841639582837790963090048 * q^31 - 31856790960783222718230988416 * q^34 - 33793503315298662900199643136 * q^36 + 23215418940485201693602693536 * q^39 - 2520966590932746267949369683672 * q^41 - 2666988540110127096326793977856 * q^44 + 25087518794220441775096515245568 * q^46 + 7656027316299536676614307676572 * q^49 - 2293205978177429604169034585952 * q^51 - 40492586655842738676101442685440 * q^54 - 447650982444052146061518514421760 * q^56 + 475924919212180257517798739401680 * q^59 + 203597682746077400400212510399288 * q^61 - 3749345404038864334832998367100928 * q^64 + 337112749155120186234694899096576 * q^66 + 1806159650811062164844443598560896 * q^69 - 1492266179587664985379924317736032 * q^71 + 134223318190050404586810430559958144 * q^74 - 133566840432061294264268018268037120 * q^76 - 544803276068191678071295890289348160 * q^79 + 806647675100076682006471654701238884 * q^81 + 30492439951528129009923673520799744 * q^84 - 2012857661573965282511992269432943872 * q^86 + 2665737843422476235828687957589885720 * q^89 + 2276797572623063452955712766020415168 * q^91 - 1406921774426085174217572329151998976 * q^94 + 346517251436435219180772622942076928 * q^96 - 24051537836769278923892831683960619184 * q^99

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