LMFDB - Embedded newform 25.38.b.a.24.3

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			24.3
Root			$3991.29i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.38.b.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+286012. i q^{2} +2.05955e7i q^{3} +5.56362e10 q^{4} -5.89057e12 q^{6} +1.97377e15i q^{7} +5.52218e16i q^{8} +4.49860e17 q^{9} +O(q^{10})$	\(q+286012. i q^{2} +2.05955e7i q^{3} +5.56362e10 q^{4} -5.89057e12 q^{6} +1.97377e15i q^{7} +5.52218e16i q^{8} +4.49860e17 q^{9} -2.57012e19 q^{11} +1.14586e18i q^{12} -5.42906e20i q^{13} -5.64522e20 q^{14} -8.14749e21 q^{16} -3.52797e22i q^{17} +1.28665e23i q^{18} -6.82122e23 q^{19} -4.06509e22 q^{21} -7.35084e24i q^{22} +8.19547e22i q^{23} -1.13732e24 q^{24} +1.55278e26 q^{26} +1.85389e25i q^{27} +1.09813e26i q^{28} +1.51991e27 q^{29} +2.60785e27 q^{31} +5.25934e27i q^{32} -5.29330e26i q^{33} +1.00904e28 q^{34} +2.50285e28 q^{36} -1.30205e29i q^{37} -1.95095e29i q^{38} +1.11814e28 q^{39} -4.07079e29 q^{41} -1.16266e28i q^{42} +2.92424e30i q^{43} -1.42992e30 q^{44} -2.34400e28 q^{46} +3.58323e30i q^{47} -1.67802e29i q^{48} +1.46663e31 q^{49} +7.26605e29 q^{51} -3.02052e31i q^{52} -3.56714e31i q^{53} -5.30236e30 q^{54} -1.08995e32 q^{56} -1.40487e31i q^{57} +4.34713e32i q^{58} +3.03666e32 q^{59} +1.16214e33 q^{61} +7.45875e32i q^{62} +8.87921e32i q^{63} -2.62402e33 q^{64} +1.51395e32 q^{66} -2.44324e33i q^{67} -1.96283e33i q^{68} -1.68790e30 q^{69} +6.30224e33 q^{71} +2.48421e34i q^{72} -1.02725e34i q^{73} +3.72400e34 q^{74} -3.79507e34 q^{76} -5.07283e34i q^{77} +3.19803e33i q^{78} -1.20547e35 q^{79} +2.02183e35 q^{81} -1.16430e35i q^{82} +3.26699e35i q^{83} -2.26166e33 q^{84} -8.36366e35 q^{86} +3.13034e34i q^{87} -1.41927e36i q^{88} +1.56115e36 q^{89} +1.07157e36 q^{91} +4.55965e33i q^{92} +5.37100e34i q^{93} -1.02485e36 q^{94} -1.08319e35 q^{96} -1.07155e36i q^{97} +4.19474e36i q^{98} -1.15619e37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	286012.i	0.771488i	0.922606	+	0.385744i	$0.126055\pi$
$2$	286012.i	0.771488i	−0.922606	+	0.385744i	$0.873945\pi$
$3$	2.05955e7i	0.0306923i	0.999882	+	0.0153462i	$0.00488503\pi$
$3$	2.05955e7i	0.0306923i	−0.999882	+	0.0153462i	$0.995115\pi$
$4$	5.56362e10	0.404807
$5$	0	0
$5$	0	0
$6$	−5.89057e12	−0.0236788
$7$	1.97377e15i	0.458124i	0.973412	+	0.229062i	$0.0735659\pi$
$7$	1.97377e15i	0.458124i	−0.973412	+	0.229062i	$0.926434\pi$
$8$	5.52218e16i	1.08379i
$9$	4.49860e17	0.999058
$10$	0	0
$11$	−2.57012e19	−1.39376	−0.696881	−	0.717187i	$-0.745429\pi$
$11$	−2.57012e19	−1.39376	−0.696881	+	0.717187i	$0.745429\pi$
$12$	1.14586e18i	0.0124245i
$13$	− 5.42906e20i	− 1.33898i	−0.742823	−	0.669488i	$-0.766514\pi$
$13$	− 5.42906e20i	− 1.33898i	0.742823	−	0.669488i	$-0.233486\pi$
$14$	−5.64522e20	−0.353437
$15$	0	0
$16$	−8.14749e21	−0.431325
$17$	− 3.52797e22i	− 0.608443i	−0.952601	−	0.304221i	$-0.901604\pi$
$17$	− 3.52797e22i	− 0.608443i	0.952601	−	0.304221i	$-0.0983963\pi$
$18$	1.28665e23i	0.770761i
$19$	−6.82122e23	−1.50287	−0.751433	−	0.659809i	$-0.770637\pi$
$19$	−6.82122e23	−1.50287	−0.751433	+	0.659809i	$0.770637\pi$
$20$	0	0
$21$	−4.06509e22	−0.0140609
$22$	− 7.35084e24i	− 1.07527i
$23$	8.19547e22i	0.00526755i	0.999997	+	0.00263378i	$0.000838358\pi$
$23$	8.19547e22i	0.00526755i	−0.999997	+	0.00263378i	$0.999162\pi$
$24$	−1.13732e24	−0.0332641
$25$	0	0
$26$	1.55278e26	1.03300
$27$	1.85389e25i	0.0613558i
$28$	1.09813e26i	0.185452i
$29$	1.51991e27	1.34108	0.670541	−	0.741872i	$-0.266062\pi$
$29$	1.51991e27	1.34108	0.670541	+	0.741872i	$0.266062\pi$
$30$	0	0
$31$	2.60785e27	0.670025	0.335012	−	0.942214i	$-0.391260\pi$
$31$	2.60785e27	0.670025	0.335012	+	0.942214i	$0.391260\pi$
$32$	5.25934e27i	0.751030i
$33$	− 5.29330e26i	− 0.0427778i
$34$	1.00904e28	0.469406
$35$	0	0
$36$	2.50285e28	0.404426
$37$	− 1.30205e29i	− 1.26734i	−0.773602	−	0.633672i	$-0.781547\pi$
$37$	− 1.30205e29i	− 1.26734i	0.773602	−	0.633672i	$-0.218453\pi$
$38$	− 1.95095e29i	− 1.15944i
$39$	1.11814e28	0.0410963
$40$	0	0
$41$	−4.07079e29	−0.593168	−0.296584	−	0.955007i	$-0.595847\pi$
$41$	−4.07079e29	−0.593168	−0.296584	+	0.955007i	$0.595847\pi$
$42$	− 1.16266e28i	− 0.0108478i
$43$	2.92424e30i	1.76541i	0.469926	+	0.882706i	$0.344281\pi$
$43$	2.92424e30i	1.76541i	−0.469926	+	0.882706i	$0.655719\pi$
$44$	−1.42992e30	−0.564204
$45$	0	0
$46$	−2.34400e28	−0.00406385
$47$	3.58323e30i	0.417315i	0.977989	+	0.208658i	$0.0669094\pi$
$47$	3.58323e30i	0.417315i	−0.977989	+	0.208658i	$0.933091\pi$
$48$	− 1.67802e29i	− 0.0132384i
$49$	1.46663e31	0.790122
$50$	0	0
$51$	7.26605e29	0.0186745
$52$	− 3.02052e31i	− 0.542027i
$53$	− 3.56714e31i	− 0.450005i	−0.974358	−	0.225002i	$-0.927761\pi$
$53$	− 3.56714e31i	− 0.450005i	0.974358	−	0.225002i	$-0.0722390\pi$
$54$	−5.30236e30	−0.0473352
$55$	0	0
$56$	−1.08995e32	−0.496511
$57$	− 1.40487e31i	− 0.0461265i
$58$	4.34713e32i	1.03463i
$59$	3.03666e32	0.526785	0.263393	−	0.964689i	$-0.415159\pi$
$59$	3.03666e32	0.526785	0.263393	+	0.964689i	$0.415159\pi$
$60$	0	0
$61$	1.16214e33	1.08807	0.544034	−	0.839063i	$-0.316896\pi$
$61$	1.16214e33	1.08807	0.544034	+	0.839063i	$0.316896\pi$
$62$	7.45875e32i	0.516916i
$63$	8.87921e32i	0.457693i
$64$	−2.62402e33	−1.01073
$65$	0	0
$66$	1.51395e32	0.0330026
$67$	− 2.44324e33i	− 0.403257i	−0.979462	−	0.201628i	$-0.935377\pi$
$67$	− 2.44324e33i	− 0.403257i	0.979462	−	0.201628i	$-0.0646234\pi$
$68$	− 1.96283e33i	− 0.246302i
$69$	−1.68790e30	−0.000161673 0
$70$	0	0
$71$	6.30224e33	0.355808	0.177904	−	0.984048i	$-0.443068\pi$
$71$	6.30224e33	0.355808	0.177904	+	0.984048i	$0.443068\pi$
$72$	2.48421e34i	1.08277i
$73$	− 1.02725e34i	− 0.346899i	−0.984843	−	0.173450i	$-0.944509\pi$
$73$	− 1.02725e34i	− 0.346899i	0.984843	−	0.173450i	$-0.0554914\pi$
$74$	3.72400e34	0.977740
$75$	0	0
$76$	−3.79507e34	−0.608371
$77$	− 5.07283e34i	− 0.638516i
$78$	3.19803e33i	0.0317053i
$79$	−1.20547e35	−0.944182	−0.472091	−	0.881550i	$-0.656501\pi$
$79$	−1.20547e35	−0.944182	−0.472091	+	0.881550i	$0.656501\pi$
$80$	0	0
$81$	2.02183e35	0.997175
$82$	− 1.16430e35i	− 0.457622i
$83$	3.26699e35i	1.02613i	0.858349	+	0.513066i	$0.171490\pi$
$83$	3.26699e35i	1.02613i	−0.858349	+	0.513066i	$0.828510\pi$
$84$	−2.26166e33	−0.00569195
$85$	0	0
$86$	−8.36366e35	−1.36199
$87$	3.13034e34i	0.0411610i
$88$	− 1.41927e36i	− 1.51055i
$89$	1.56115e36	1.34812	0.674062	−	0.738674i	$-0.264548\pi$
$89$	1.56115e36	1.34812	0.674062	+	0.738674i	$0.264548\pi$
$90$	0	0
$91$	1.07157e36	0.613418
$92$	4.55965e33i	0.00213234i
$93$	5.37100e34i	0.0205646i
$94$	−1.02485e36	−0.321954
$95$	0	0
$96$	−1.08319e35	−0.0230509
$97$	− 1.07155e36i	− 0.188251i	−0.995560	−	0.0941254i	$-0.969995\pi$
$97$	− 1.07155e36i	− 0.188251i	0.995560	−	0.0941254i	$-0.0300054\pi$
$98$	4.19474e36i	0.609569i
$99$	−1.15619e37	−1.39245
$100$	0	0
$101$	1.29521e37	1.07744	0.538721	−	0.842484i	$-0.318908\pi$
$101$	1.29521e37	1.07744	0.538721	+	0.842484i	$0.318908\pi$
$102$	2.07817e35i	0.0144072i
$103$	3.39568e36i	0.196534i	0.995160	+	0.0982672i	$0.0313300\pi$
$103$	3.39568e36i	0.196534i	−0.995160	+	0.0982672i	$0.968670\pi$
$104$	2.99802e37	1.45117
$105$	0	0
$106$	1.02025e37	0.347173
$107$	− 1.58608e37i	− 0.453653i	−0.973935	−	0.226827i	$-0.927165\pi$
$107$	− 1.58608e37i	− 0.453653i	0.973935	−	0.226827i	$-0.0728351\pi$
$108$	1.03144e36i	0.0248372i
$109$	1.06858e36	0.0216978	0.0108489	−	0.999941i	$-0.496547\pi$
$109$	1.06858e36	0.0216978	0.0108489	+	0.999941i	$0.496547\pi$
$110$	0	0
$111$	2.68163e36	0.0388977
$112$	− 1.60813e37i	− 0.197600i
$113$	− 1.64170e37i	− 0.171136i	−0.996332	−	0.0855682i	$-0.972729\pi$
$113$	− 1.64170e37i	− 0.171136i	0.996332	−	0.0855682i	$-0.0272706\pi$
$114$	4.01809e36	0.0355860
$115$	0	0
$116$	8.45622e37	0.542879
$117$	− 2.44232e38i	− 1.33771i
$118$	8.68520e37i	0.406408i
$119$	6.96341e37	0.278743
$120$	0	0
$121$	3.20512e38	0.942572
$122$	3.32386e38i	0.839432i
$123$	− 8.38402e36i	− 0.0182057i
$124$	1.45091e38	0.271231
$125$	0	0
$126$	−2.53956e38	−0.353104
$127$	− 1.42456e39i	− 1.71124i	−0.517606	−	0.855619i	$-0.673177\pi$
$127$	− 1.42456e39i	− 1.71124i	0.517606	−	0.855619i	$-0.326823\pi$
$128$	− 2.76609e37i	− 0.0287397i
$129$	−6.02262e37	−0.0541846
$130$	0	0
$131$	2.12044e39	1.43518	0.717590	−	0.696466i	$-0.245245\pi$
$131$	2.12044e39	1.43518	0.717590	+	0.696466i	$0.245245\pi$
$132$	− 2.94499e37i	− 0.0173168i
$133$	− 1.34635e39i	− 0.688500i
$134$	6.98795e38	0.311108
$135$	0	0
$136$	1.94821e39	0.659425
$137$	− 1.25855e39i	− 0.371999i	−0.982550	−	0.185999i	$-0.940448\pi$
$137$	− 1.25855e39i	− 0.371999i	0.982550	−	0.185999i	$-0.0595522\pi$
$138$	− 4.82760e35i	0 0.000124729i
$139$	3.12966e39	0.707494	0.353747	−	0.935341i	$-0.384907\pi$
$139$	3.12966e39	0.707494	0.353747	+	0.935341i	$0.384907\pi$
$140$	0	0
$141$	−7.37986e37	−0.0128084
$142$	1.80251e39i	0.274501i
$143$	1.39533e40i	1.86621i
$144$	−3.66523e39	−0.430918
$145$	0	0
$146$	2.93806e39	0.267628
$147$	3.02061e38i	0.0242507i
$148$	− 7.24409e39i	− 0.513029i
$149$	−2.99066e39	−0.186991	−0.0934956	−	0.995620i	$-0.529804\pi$
$149$	−2.99066e39	−0.186991	−0.0934956	+	0.995620i	$0.529804\pi$
$150$	0	0
$151$	−7.06984e39	−0.345411	−0.172706	−	0.984973i	$-0.555251\pi$
$151$	−7.06984e39	−0.345411	−0.172706	+	0.984973i	$0.555251\pi$
$152$	− 3.76680e40i	− 1.62879i
$153$	− 1.58709e40i	− 0.607870i
$154$	1.45089e40	0.492607
$155$	0	0
$156$	6.22094e38	0.0166361
$157$	7.04676e40i	1.67435i	0.546937	+	0.837174i	$0.315794\pi$
$157$	7.04676e40i	1.67435i	−0.546937	+	0.837174i	$0.684206\pi$
$158$	− 3.44779e40i	− 0.728425i
$159$	7.34673e38	0.0138117
$160$	0	0
$161$	−1.61760e38	−0.00241319
$162$	5.78267e40i	0.769308i
$163$	8.16698e40i	0.969596i	0.874626	+	0.484798i	$0.161107\pi$
$163$	8.16698e40i	0.969596i	−0.874626	+	0.484798i	$0.838893\pi$
$164$	−2.26484e40	−0.240119
$165$	0	0
$166$	−9.34397e40	−0.791648
$167$	− 3.94031e40i	− 0.298728i	−0.988782	−	0.149364i	$-0.952277\pi$
$167$	− 3.94031e40i	− 0.298728i	0.988782	−	0.149364i	$-0.0477226\pi$
$168$	− 2.24482e39i	− 0.0152391i
$169$	−1.30346e41	−0.792856
$170$	0	0
$171$	−3.06859e41	−1.50145
$172$	1.62693e41i	0.714651i
$173$	− 2.61566e41i	− 1.03212i	−0.856554	−	0.516058i	$-0.827399\pi$
$173$	− 2.61566e41i	− 1.03212i	0.856554	−	0.516058i	$-0.172601\pi$
$174$	−8.95315e39	−0.0317552
$175$	0	0
$176$	2.09400e41	0.601164
$177$	6.25416e39i	0.0161683i
$178$	4.46508e41i	1.04006i
$179$	4.21879e41	0.885946	0.442973	−	0.896535i	$-0.353924\pi$
$179$	4.21879e41	0.885946	0.442973	+	0.896535i	$0.353924\pi$
$180$	0	0
$181$	−9.51260e40	−0.162647	−0.0813234	−	0.996688i	$-0.525915\pi$
$181$	−9.51260e40	−0.162647	−0.0813234	+	0.996688i	$0.525915\pi$
$182$	3.06483e41i	0.473244i
$183$	2.39349e40i	0.0333954i
$184$	−4.52568e39	−0.00570892
$185$	0	0
$186$	−1.53617e40	−0.0158654
$187$	9.06730e41i	0.848024i
$188$	1.99357e41i	0.168932i
$189$	−3.65917e40	−0.0281086
$190$	0	0
$191$	−2.61439e41	−0.165292	−0.0826462	−	0.996579i	$-0.526337\pi$
$191$	−2.61439e41	−0.165292	−0.0826462	+	0.996579i	$0.526337\pi$
$192$	− 5.40431e40i	− 0.0310218i
$193$	6.27072e41i	0.326969i	0.986546	+	0.163485i	$0.0522734\pi$
$193$	6.27072e41i	0.326969i	−0.986546	+	0.163485i	$0.947727\pi$
$194$	3.06477e41	0.145233
$195$	0	0
$196$	8.15980e41	0.319847
$197$	− 1.81081e42i	− 0.646021i	−0.946395	−	0.323010i	$-0.895305\pi$
$197$	− 1.81081e42i	− 0.646021i	0.946395	−	0.323010i	$-0.104695\pi$
$198$	− 3.30685e42i	− 1.07426i
$199$	3.78123e41	0.111906	0.0559528	−	0.998433i	$-0.482180\pi$
$199$	3.78123e41	0.111906	0.0559528	+	0.998433i	$0.482180\pi$
$200$	0	0
$201$	5.03198e40	0.0123769
$202$	3.70445e42i	0.831233i
$203$	2.99996e42i	0.614383i
$204$	4.04255e40	0.00755958
$205$	0	0
$206$	−9.71205e41	−0.151624
$207$	3.68681e40i	0.00526259i
$208$	4.42332e42i	0.577533i
$209$	1.75313e43	2.09464
$210$	0	0
$211$	1.66783e43	1.67081	0.835404	−	0.549637i	$-0.185234\pi$
$211$	1.66783e43	1.67081	0.835404	+	0.549637i	$0.185234\pi$
$212$	− 1.98462e42i	− 0.182165i
$213$	1.29798e41i	0.0109206i
$214$	4.53636e42	0.349988
$215$	0	0
$216$	−1.02375e42	−0.0664968
$217$	5.14730e42i	0.306955i
$218$	3.05626e41i	0.0167396i
$219$	2.11568e41	0.0106472
$220$	0	0
$221$	−1.91536e43	−0.814690
$222$	7.66979e41i	0.0300091i
$223$	3.60083e43i	1.29647i	0.761439	+	0.648236i	$0.224493\pi$
$223$	3.60083e43i	1.29647i	−0.761439	+	0.648236i	$0.775507\pi$
$224$	−1.03808e43	−0.344065
$225$	0	0
$226$	4.69546e42	0.132030
$227$	6.76307e43i	1.75253i	0.481830	+	0.876265i	$0.339972\pi$
$227$	6.76307e43i	1.75253i	−0.481830	+	0.876265i	$0.660028\pi$
$228$	− 7.81615e41i	− 0.0186723i
$229$	5.09302e43	1.12207	0.561033	−	0.827793i	$-0.310404\pi$
$229$	5.09302e43	1.12207	0.561033	+	0.827793i	$0.310404\pi$
$230$	0	0
$231$	1.04478e42	0.0195976
$232$	8.39322e43i	1.45345i
$233$	− 1.79375e43i	− 0.286865i	−0.989660	−	0.143432i	$-0.954186\pi$
$233$	− 1.79375e43i	− 0.286865i	0.989660	−	0.143432i	$-0.0458140\pi$
$234$	6.98531e43	1.03203
$235$	0	0
$236$	1.68948e43	0.213246
$237$	− 2.48273e42i	− 0.0289792i
$238$	1.99162e43i	0.215046i
$239$	2.86950e43	0.286711	0.143356	−	0.989671i	$-0.454211\pi$
$239$	2.86950e43	0.286711	0.143356	+	0.989671i	$0.454211\pi$
$240$	0	0
$241$	−1.12255e44	−0.961372	−0.480686	−	0.876893i	$-0.659612\pi$
$241$	−1.12255e44	−0.961372	−0.480686	+	0.876893i	$0.659612\pi$
$242$	9.16701e43i	0.727182i
$243$	1.25119e43i	0.0919614i
$244$	6.46571e43	0.440458
$245$	0	0
$246$	2.39793e42	0.0140455
$247$	3.70328e44i	2.01230i
$248$	1.44010e44i	0.726167i
$249$	−6.72854e42	−0.0314944
$250$	0	0
$251$	−4.02278e44	−1.62391	−0.811955	−	0.583720i	$-0.801597\pi$
$251$	−4.02278e44	−1.62391	−0.811955	+	0.583720i	$0.801597\pi$
$252$	4.94006e43i	0.185277i
$253$	− 2.10633e42i	− 0.00734171i
$254$	4.07440e44	1.32020
$255$	0	0
$256$	−3.52731e44	−0.988562
$257$	5.42969e44i	1.41583i	0.706296	+	0.707917i	$0.250365\pi$
$257$	5.42969e44i	1.41583i	−0.706296	+	0.707917i	$0.749635\pi$
$258$	− 1.72254e43i	− 0.0418028i
$259$	2.56994e44	0.580601
$260$	0	0
$261$	6.83747e44	1.33982
$262$	6.06470e44i	1.10722i
$263$	7.98181e44i	1.35806i	0.734109	+	0.679031i	$0.237600\pi$
$263$	7.98181e44i	1.35806i	−0.734109	+	0.679031i	$0.762400\pi$
$264$	2.92305e43	0.0463622
$265$	0	0
$266$	3.85073e44	0.531169
$267$	3.21528e43i	0.0413771i
$268$	− 1.35933e44i	− 0.163241i
$269$	1.02189e45	1.14548	0.572739	−	0.819738i	$-0.305881\pi$
$269$	1.02189e45	1.14548	0.572739	+	0.819738i	$0.305881\pi$
$270$	0	0
$271$	−2.63101e44	−0.257152	−0.128576	−	0.991700i	$-0.541041\pi$
$271$	−2.63101e44	−0.257152	−0.128576	+	0.991700i	$0.541041\pi$
$272$	2.87441e44i	0.262436i
$273$	2.20696e43i	0.0188272i
$274$	3.59961e44	0.286992
$275$	0	0
$276$	−9.39085e40	−6.54465e−5 0
$277$	1.60882e45i	1.04865i	0.851517	+	0.524327i	$0.175683\pi$
$277$	1.60882e45i	1.04865i	−0.851517	+	0.524327i	$0.824317\pi$
$278$	8.95119e44i	0.545823i
$279$	1.17317e45	0.669393
$280$	0	0
$281$	2.86236e45	1.43106	0.715529	−	0.698583i	$-0.246186\pi$
$281$	2.86236e45	1.43106	0.715529	+	0.698583i	$0.246186\pi$
$282$	− 2.11073e43i	− 0.00988151i
$283$	− 7.97480e44i	− 0.349680i	−0.984597	−	0.174840i	$-0.944059\pi$
$283$	− 7.97480e44i	− 0.349680i	0.984597	−	0.174840i	$-0.0559408\pi$
$284$	3.50633e44	0.144033
$285$	0	0
$286$	−3.99082e45	−1.43976
$287$	− 8.03482e44i	− 0.271745i
$288$	2.36597e45i	0.750322i
$289$	2.11744e45	0.629797
$290$	0	0
$291$	2.20692e43	0.00577786
$292$	− 5.71523e44i	− 0.140427i
$293$	− 5.17198e44i	− 0.119290i	−0.998220	−	0.0596452i	$-0.981003\pi$
$293$	− 5.17198e44i	− 0.119290i	0.998220	−	0.0596452i	$-0.0189969\pi$
$294$	−8.63931e43	−0.0187091
$295$	0	0
$296$	7.19013e45	1.37354
$297$	− 4.76473e44i	− 0.0855153i
$298$	− 8.55364e44i	− 0.144261i
$299$	4.44937e43	0.00705312
$300$	0	0
$301$	−5.77178e45	−0.808778
$302$	− 2.02206e45i	− 0.266480i
$303$	2.66755e44i	0.0330692i
$304$	5.55758e45	0.648223
$305$	0	0
$306$	4.53927e45	0.468964
$307$	9.59117e45i	0.932850i	0.884561	+	0.466425i	$0.154458\pi$
$307$	9.59117e45i	0.932850i	−0.884561	+	0.466425i	$0.845542\pi$
$308$	− 2.82233e45i	− 0.258476i
$309$	−6.99360e43	−0.00603210
$310$	0	0
$311$	−5.05857e45	−0.387222	−0.193611	−	0.981078i	$-0.562020\pi$
$311$	−5.05857e45	−0.387222	−0.193611	+	0.981078i	$0.562020\pi$
$312$	6.17459e44i	0.0445398i
$313$	− 5.12462e45i	− 0.348410i	−0.984709	−	0.174205i	$-0.944264\pi$
$313$	− 5.12462e45i	− 0.348410i	0.984709	−	0.174205i	$-0.0557356\pi$
$314$	−2.01546e46	−1.29174
$315$	0	0
$316$	−6.70679e45	−0.382211
$317$	− 2.14514e46i	− 1.15308i	−0.817068	−	0.576541i	$-0.804402\pi$
$317$	− 2.14514e46i	− 1.15308i	0.817068	−	0.576541i	$-0.195598\pi$
$318$	2.10125e44i	0.0106556i
$319$	−3.90635e46	−1.86915
$320$	0	0
$321$	3.26661e44	0.0139237
$322$	− 4.62652e43i	− 0.00186175i
$323$	2.40651e46i	0.914408i
$324$	1.12487e46	0.403663
$325$	0	0
$326$	−2.33585e46	−0.748032
$327$	2.20080e43i	0 0.000665958i
$328$	− 2.24796e46i	− 0.642870i
$329$	−7.07248e45	−0.191182
$330$	0	0
$331$	1.85276e46	0.447714	0.223857	−	0.974622i	$-0.428135\pi$
$331$	1.85276e46	0.447714	0.223857	+	0.974622i	$0.428135\pi$
$332$	1.81763e46i	0.415385i
$333$	− 5.85738e46i	− 1.26615i
$334$	1.12698e46	0.230465
$335$	0	0
$336$	3.31203e44	0.00606482
$337$	− 9.22947e46i	− 1.59965i	−0.600236	−	0.799823i	$-0.704927\pi$
$337$	− 9.22947e46i	− 1.59965i	0.600236	−	0.799823i	$-0.295073\pi$
$338$	− 3.72805e46i	− 0.611679i
$339$	3.38117e44	0.00525258
$340$	0	0
$341$	−6.70248e46	−0.933855
$342$	− 8.77653e46i	− 1.15835i
$343$	6.55854e46i	0.820099i
$344$	−1.61481e47	−1.91334
$345$	0	0
$346$	7.48110e46	0.796265
$347$	− 5.27249e46i	− 0.532011i	−0.963972	−	0.266005i	$-0.914296\pi$
$347$	− 5.27249e46i	− 0.532011i	0.963972	−	0.266005i	$-0.0857039\pi$
$348$	1.74160e45i	0.0166622i
$349$	−9.71277e46	−0.881196	−0.440598	−	0.897704i	$-0.645234\pi$
$349$	−9.71277e46	−0.881196	−0.440598	+	0.897704i	$0.645234\pi$
$350$	0	0
$351$	1.00649e46	0.0821539
$352$	− 1.35171e47i	− 1.04676i
$353$	− 1.73375e47i	− 1.27396i	−0.770881	−	0.636979i	$-0.780184\pi$
$353$	− 1.73375e47i	− 1.27396i	0.770881	−	0.636979i	$-0.219816\pi$
$354$	−1.78876e45	−0.0124736
$355$	0	0
$356$	8.68566e46	0.545730
$357$	1.43415e45i	0.00855526i
$358$	1.20662e47i	0.683497i
$359$	1.13075e47	0.608301	0.304150	−	0.952624i	$-0.401627\pi$
$359$	1.13075e47	0.608301	0.304150	+	0.952624i	$0.401627\pi$
$360$	0	0
$361$	2.59283e47	1.25861
$362$	− 2.72072e46i	− 0.125480i
$363$	6.60111e45i	0.0289297i
$364$	5.96183e46	0.248316
$365$	0	0
$366$	−6.84566e45	−0.0257641
$367$	− 8.74068e46i	− 0.312768i	−0.987696	−	0.156384i	$-0.950016\pi$
$367$	− 8.74068e46i	− 0.312768i	0.987696	−	0.156384i	$-0.0499838\pi$
$368$	− 6.67725e44i	− 0.00227202i
$369$	−1.83129e47	−0.592609
$370$	0	0
$371$	7.04073e46	0.206158
$372$	2.98822e45i	0.00832470i
$373$	− 2.70122e47i	− 0.716056i	−0.933711	−	0.358028i	$-0.883449\pi$
$373$	− 2.70122e47i	− 0.716056i	0.933711	−	0.358028i	$-0.116551\pi$
$374$	−2.59335e47	−0.654240
$375$	0	0
$376$	−1.97872e47	−0.452283
$377$	− 8.25170e47i	− 1.79568i
$378$	− 1.04657e46i	− 0.0216854i
$379$	4.13508e47	0.815940	0.407970	−	0.912995i	$-0.366237\pi$
$379$	4.13508e47	0.815940	0.407970	+	0.912995i	$0.366237\pi$
$380$	0	0
$381$	2.93395e46	0.0525219
$382$	− 7.47746e46i	− 0.127521i
$383$	6.64131e47i	1.07914i	0.841942	+	0.539569i	$0.181413\pi$
$383$	6.64131e47i	1.07914i	−0.841942	+	0.539569i	$0.818587\pi$
$384$	5.69691e44	0.000882088 0
$385$	0	0
$386$	−1.79350e47	−0.252253
$387$	1.31550e48i	1.76375i
$388$	− 5.96172e46i	− 0.0762052i
$389$	−4.74132e46	−0.0577872	−0.0288936	−	0.999582i	$-0.509198\pi$
$389$	−4.74132e46	−0.0577872	−0.0288936	+	0.999582i	$0.509198\pi$
$390$	0	0
$391$	2.89134e45	0.00320500
$392$	8.09901e47i	0.856327i
$393$	4.36716e46i	0.0440491i
$394$	5.17912e47	0.498397
$395$	0	0
$396$	−6.43262e47	−0.563673
$397$	6.00594e47i	0.502292i	0.967949	+	0.251146i	$0.0808075\pi$
$397$	6.00594e47i	0.502292i	−0.967949	+	0.251146i	$0.919193\pi$
$398$	1.08148e47i	0.0863337i
$399$	2.77289e46	0.0211317
$400$	0	0
$401$	−9.30169e47	−0.646235	−0.323118	−	0.946359i	$-0.604731\pi$
$401$	−9.30169e47	−0.646235	−0.323118	+	0.946359i	$0.604731\pi$
$402$	1.43921e46i	0.00954863i
$403$	− 1.41582e48i	− 0.897147i
$404$	7.20605e47	0.436156
$405$	0	0
$406$	−8.58024e47	−0.473989
$407$	3.34641e48i	1.76637i
$408$	4.01244e46i	0.0202393i
$409$	2.60436e47	0.125551	0.0627755	−	0.998028i	$-0.480005\pi$
$409$	2.60436e47	0.125551	0.0627755	+	0.998028i	$0.480005\pi$
$410$	0	0
$411$	2.59206e46	0.0114175
$412$	1.88923e47i	0.0795585i
$413$	5.99367e47i	0.241333i
$414$	−1.05447e46	−0.00406002
$415$	0	0
$416$	2.85533e48	1.00561
$417$	6.44570e46i	0.0217147i
$418$	5.01417e48i	1.61599i
$419$	3.92255e48	1.20951	0.604755	−	0.796412i	$-0.293271\pi$
$419$	3.92255e48	1.20951	0.604755	+	0.796412i	$0.293271\pi$
$420$	0	0
$421$	−3.86983e48	−1.09263	−0.546315	−	0.837580i	$-0.683970\pi$
$421$	−3.86983e48	−1.09263	−0.546315	+	0.837580i	$0.683970\pi$
$422$	4.77019e48i	1.28901i
$423$	1.61195e48i	0.416922i
$424$	1.96984e48	0.487711
$425$	0	0
$426$	−3.71238e46	−0.00842509
$427$	2.29380e48i	0.498471i
$428$	− 8.82433e47i	− 0.183642i
$429$	−2.87377e47	−0.0572785
$430$	0	0
$431$	2.97992e48	0.544973	0.272487	−	0.962160i	$-0.412154\pi$
$431$	2.97992e48	0.544973	0.272487	+	0.962160i	$0.412154\pi$
$432$	− 1.51046e47i	− 0.0264643i
$433$	2.20884e48i	0.370798i	0.982663	+	0.185399i	$0.0593578\pi$
$433$	2.20884e48i	0.370798i	−0.982663	+	0.185399i	$0.940642\pi$
$434$	−1.47219e48	−0.236812
$435$	0	0
$436$	5.94517e46	0.00878344
$437$	− 5.59031e46i	− 0.00791643i
$438$	6.05109e46i	0.00821414i
$439$	1.14225e49	1.48650	0.743252	−	0.669011i	$-0.233282\pi$
$439$	1.14225e49	1.48650	0.743252	+	0.669011i	$0.233282\pi$
$440$	0	0
$441$	6.59779e48	0.789378
$442$	− 5.47814e48i	− 0.628523i
$443$	− 8.78568e48i	− 0.966733i	−0.875418	−	0.483366i	$-0.839414\pi$
$443$	− 8.78568e48i	− 0.966733i	0.875418	−	0.483366i	$-0.160586\pi$
$444$	1.49196e47	0.0157461
$445$	0	0
$446$	−1.02988e49	−1.00021
$447$	− 6.15943e46i	− 0.00573920i
$448$	− 5.17921e48i	− 0.463042i
$449$	8.94932e48	0.767773	0.383886	−	0.923380i	$-0.374585\pi$
$449$	8.94932e48	0.767773	0.383886	+	0.923380i	$0.374585\pi$
$450$	0	0
$451$	1.04624e49	0.826735
$452$	− 9.13380e47i	− 0.0692772i
$453$	− 1.45607e47i	− 0.0106015i
$454$	−1.93432e49	−1.35205
$455$	0	0
$456$	7.75793e47	0.0499915
$457$	3.77717e48i	0.233731i	0.993148	+	0.116866i	$0.0372847\pi$
$457$	3.77717e48i	0.233731i	−0.993148	+	0.116866i	$0.962715\pi$
$458$	1.45666e49i	0.865661i
$459$	6.54048e47	0.0373315
$460$	0	0
$461$	8.89831e48	0.468641	0.234320	−	0.972159i	$-0.424714\pi$
$461$	8.89831e48	0.468641	0.234320	+	0.972159i	$0.424714\pi$
$462$	2.98819e47i	0.0151193i
$463$	3.35423e49i	1.63059i	0.579047	+	0.815294i	$0.303425\pi$
$463$	3.35423e49i	1.63059i	−0.579047	+	0.815294i	$0.696575\pi$
$464$	−1.23835e49	−0.578442
$465$	0	0
$466$	5.13034e48	0.221313
$467$	− 3.67520e49i	− 1.52377i	−0.647714	−	0.761884i	$-0.724275\pi$
$467$	− 3.67520e49i	− 1.52377i	0.647714	−	0.761884i	$-0.275725\pi$
$468$	− 1.35881e49i	− 0.541516i
$469$	4.82240e48	0.184742
$470$	0	0
$471$	−1.45132e48	−0.0513897
$472$	1.67690e49i	0.570925i
$473$	− 7.51563e49i	− 2.46056i
$474$	7.10091e47	0.0223571
$475$	0	0
$476$	3.87418e48	0.112837
$477$	− 1.60471e49i	− 0.449581i
$478$	8.20711e48i	0.221194i
$479$	−4.73384e49	−1.22746	−0.613730	−	0.789516i	$-0.710331\pi$
$479$	−4.73384e49	−1.22746	−0.613730	+	0.789516i	$0.710331\pi$
$480$	0	0
$481$	−7.06889e49	−1.69694
$482$	− 3.21063e49i	− 0.741686i
$483$	− 3.33153e45i	0 7.40666e-5i
$484$	1.78321e49	0.381560
$485$	0	0
$486$	−3.57854e48	−0.0709471
$487$	7.97298e48i	0.152172i	0.997101	+	0.0760860i	$0.0242424\pi$
$487$	7.97298e48i	0.152172i	−0.997101	+	0.0760860i	$0.975758\pi$
$488$	6.41754e49i	1.17924i
$489$	−1.68203e48	−0.0297592
$490$	0	0
$491$	3.59851e49	0.590358	0.295179	−	0.955442i	$-0.404621\pi$
$491$	3.59851e49	0.590358	0.295179	+	0.955442i	$0.404621\pi$
$492$	− 4.66455e47i	− 0.00736980i
$493$	− 5.36220e49i	− 0.815972i
$494$	−1.05918e50	−1.55247
$495$	0	0
$496$	−2.12474e49	−0.288998
$497$	1.24392e49i	0.163004i
$498$	− 1.92444e48i	− 0.0242975i
$499$	−7.98372e49	−0.971282	−0.485641	−	0.874158i	$-0.661414\pi$
$499$	−7.98372e49	−0.971282	−0.485641	+	0.874158i	$0.661414\pi$
$500$	0	0
$501$	8.11529e47	0.00916866
$502$	− 1.15056e50i	− 1.25283i
$503$	− 6.32137e49i	− 0.663443i	−0.943377	−	0.331721i	$-0.892371\pi$
$503$	− 6.32137e49i	− 0.663443i	0.943377	−	0.331721i	$-0.107629\pi$
$504$	−4.90326e49	−0.496043
$505$	0	0
$506$	6.02436e47	0.00566404
$507$	− 2.68455e48i	− 0.0243346i
$508$	− 7.92569e49i	− 0.692721i
$509$	1.42477e50	1.20078	0.600392	−	0.799706i	$-0.295011\pi$
$509$	1.42477e50	1.20078	0.600392	+	0.799706i	$0.295011\pi$
$510$	0	0
$511$	2.02756e49	0.158923
$512$	− 1.04687e50i	− 0.791403i
$513$	− 1.26458e49i	− 0.0922095i
$514$	−1.55295e50	−1.09230
$515$	0	0
$516$	−3.35076e48	−0.0219343
$517$	− 9.20932e49i	− 0.581638i
$518$	7.35034e49i	0.447927i
$519$	5.38710e48	0.0316781
$520$	0	0
$521$	1.18735e50	0.650251	0.325125	−	0.945671i	$-0.394593\pi$
$521$	1.18735e50	0.650251	0.325125	+	0.945671i	$0.394593\pi$
$522$	1.95560e50i	1.03365i
$523$	− 6.66586e49i	− 0.340075i	−0.985438	−	0.170038i	$-0.945611\pi$
$523$	− 6.66586e49i	− 0.340075i	0.985438	−	0.170038i	$-0.0543889\pi$
$524$	1.17973e50	0.580971
$525$	0	0
$526$	−2.28289e50	−1.04773
$527$	− 9.20040e49i	− 0.407672i
$528$	4.31271e48i	0.0184511i
$529$	2.42057e50	0.999972
$530$	0	0
$531$	1.36607e50	0.526289
$532$	− 7.49061e49i	− 0.278709i
$533$	2.21006e50i	0.794238i
$534$	−9.19607e48	−0.0319219
$535$	0	0
$536$	1.34920e50	0.437046
$537$	8.68884e48i	0.0271918i
$538$	2.92272e50i	0.883722i
$539$	−3.76942e50	−1.10124
$540$	0	0
$541$	7.31652e50	1.99597	0.997987	−	0.0634127i	$-0.0201984\pi$
$541$	7.31652e50	1.99597	0.997987	+	0.0634127i	$0.0201984\pi$
$542$	− 7.52499e49i	− 0.198390i
$543$	− 1.95917e48i	− 0.00499201i
$544$	1.85548e50	0.456959
$545$	0	0
$546$	−6.31218e48	−0.0145250
$547$	1.90668e50i	0.424143i	0.977254	+	0.212072i	$0.0680210\pi$
$547$	1.90668e50i	0.424143i	−0.977254	+	0.212072i	$0.931979\pi$
$548$	− 7.00212e49i	− 0.150588i
$549$	5.22800e50	1.08704
$550$	0	0
$551$	−1.03677e51	−2.01547
$552$	− 9.32089e46i	0 0.000175220i
$553$	− 2.37933e50i	− 0.432553i
$554$	−4.60142e50	−0.809024
$555$	0	0
$556$	1.74122e50	0.286399
$557$	6.78617e50i	1.07970i	0.841761	+	0.539851i	$0.181519\pi$
$557$	6.78617e50i	1.07970i	−0.841761	+	0.539851i	$0.818481\pi$
$558$	3.35539e50i	0.516429i
$559$	1.58759e51	2.36384
$560$	0	0
$561$	−1.86746e49	−0.0260279
$562$	8.18669e50i	1.10404i
$563$	− 6.45010e50i	− 0.841708i	−0.907128	−	0.420854i	$-0.861730\pi$
$563$	− 6.45010e50i	− 0.841708i	0.907128	−	0.420854i	$-0.138270\pi$
$564$	−4.10587e48	−0.00518492
$565$	0	0
$566$	2.28089e50	0.269774
$567$	3.99063e50i	0.456830i
$568$	3.48021e50i	0.385621i
$569$	−2.68168e50	−0.287627	−0.143814	−	0.989605i	$-0.545937\pi$
$569$	−2.68168e50	−0.287627	−0.143814	+	0.989605i	$0.545937\pi$
$570$	0	0
$571$	−3.44946e50	−0.346724	−0.173362	−	0.984858i	$-0.555463\pi$
$571$	−3.44946e50	−0.346724	−0.173362	+	0.984858i	$0.555463\pi$
$572$	7.76311e50i	0.755456i
$573$	− 5.38448e48i	− 0.00507321i
$574$	2.29805e50	0.209648
$575$	0	0
$576$	−1.18044e51	−1.00978
$577$	2.52648e50i	0.209297i	0.994509	+	0.104648i	$0.0333717\pi$
$577$	2.52648e50i	0.209297i	−0.994509	+	0.104648i	$0.966628\pi$
$578$	6.05612e50i	0.485881i
$579$	−1.29149e49	−0.0100355
$580$	0	0
$581$	−6.44830e50	−0.470096
$582$	6.31206e48i	0.00445754i
$583$	9.16799e50i	0.627199i
$584$	5.67266e50	0.375966
$585$	0	0
$586$	1.47925e50	0.0920311
$587$	1.13653e51i	0.685134i	0.939493	+	0.342567i	$0.111296\pi$
$587$	1.13653e51i	0.685134i	−0.939493	+	0.342567i	$0.888704\pi$
$588$	1.68055e49i	0.00981685i
$589$	−1.77887e51	−1.00696
$590$	0	0
$591$	3.72945e49	0.0198279
$592$	1.06084e51i	0.546636i
$593$	1.23614e51i	0.617383i	0.951162	+	0.308692i	$0.0998911\pi$
$593$	1.23614e51i	0.617383i	−0.951162	+	0.308692i	$0.900109\pi$
$594$	1.36277e50	0.0659740
$595$	0	0
$596$	−1.66389e50	−0.0756954
$597$	7.78766e48i	0.00343464i
$598$	1.27257e49i	0.00544140i
$599$	4.59427e51	1.90467	0.952336	−	0.305052i	$-0.0986737\pi$
$599$	4.59427e51	1.90467	0.952336	+	0.305052i	$0.0986737\pi$
$600$	0	0
$601$	−1.48401e49	−0.00578442	−0.00289221	−	0.999996i	$-0.500921\pi$
$601$	−1.48401e49	−0.00578442	−0.00289221	+	0.999996i	$0.500921\pi$
$602$	− 1.65080e51i	− 0.623962i
$603$	− 1.09911e51i	− 0.402877i
$604$	−3.93340e50	−0.139825
$605$	0	0
$606$	−7.62951e49	−0.0255125
$607$	2.59968e51i	0.843198i	0.906782	+	0.421599i	$0.138531\pi$
$607$	2.59968e51i	0.843198i	−0.906782	+	0.421599i	$0.861469\pi$
$608$	− 3.58751e51i	− 1.12870i
$609$	−6.17859e49	−0.0188568
$610$	0	0
$611$	1.94536e51	0.558775
$612$	− 8.82998e50i	− 0.246070i
$613$	− 1.49376e50i	− 0.0403890i	−0.999796	−	0.0201945i	$-0.993571\pi$
$613$	− 1.49376e50i	− 0.0403890i	0.999796	−	0.0201945i	$-0.00642854\pi$
$614$	−2.74319e51	−0.719682
$615$	0	0
$616$	2.80131e51	0.692018
$617$	− 6.30081e51i	− 1.51050i	−0.655437	−	0.755250i	$-0.727516\pi$
$617$	− 6.30081e51i	− 1.51050i	0.655437	−	0.755250i	$-0.272484\pi$
$618$	− 2.00025e49i	− 0.00465369i
$619$	−5.97852e51	−1.34995	−0.674974	−	0.737842i	$-0.735845\pi$
$619$	−5.97852e51	−1.34995	−0.674974	+	0.737842i	$0.735845\pi$
$620$	0	0
$621$	−1.51935e48	−0.000323195 0
$622$	− 1.44681e51i	− 0.298737i
$623$	3.08136e51i	0.617609i
$624$	−9.11007e49	−0.0177258
$625$	0	0
$626$	1.46570e51	0.268794
$627$	3.61068e50i	0.0642893i
$628$	3.92055e51i	0.677787i
$629$	−4.59358e51	−0.771106
$630$	0	0
$631$	−3.17011e51	−0.501800	−0.250900	−	0.968013i	$-0.580727\pi$
$631$	−3.17011e51	−0.501800	−0.250900	+	0.968013i	$0.580727\pi$
$632$	− 6.65683e51i	− 1.02330i
$633$	3.43499e50i	0.0512810i
$634$	6.13536e51	0.889588
$635$	0	0
$636$	4.08744e49	0.00559107
$637$	− 7.96244e51i	− 1.05795i
$638$	− 1.11726e52i	− 1.44203i
$639$	2.83512e51	0.355473
$640$	0	0
$641$	1.15243e52	1.36377	0.681885	−	0.731459i	$-0.261160\pi$
$641$	1.15243e52	1.36377	0.681885	+	0.731459i	$0.261160\pi$
$642$	9.34289e49i	0.0107420i
$643$	− 1.66832e52i	− 1.86370i	−0.362842	−	0.931851i	$-0.618193\pi$
$643$	− 1.66832e52i	− 1.86370i	0.362842	−	0.931851i	$-0.381807\pi$
$644$	−8.99971e48	−0.000976877 0
$645$	0	0
$646$	−6.88289e51	−0.705455
$647$	− 1.67531e52i	− 1.66865i	−0.551270	−	0.834327i	$-0.685856\pi$
$647$	− 1.67531e52i	− 1.66865i	0.551270	−	0.834327i	$-0.314144\pi$
$648$	1.11649e52i	1.08073i
$649$	−7.80457e51	−0.734213
$650$	0	0
$651$	−1.06011e50	−0.00942116
$652$	4.54380e51i	0.392499i
$653$	9.01096e51i	0.756619i	0.925679	+	0.378309i	$0.123494\pi$
$653$	9.01096e51i	0.756619i	−0.925679	+	0.378309i	$0.876506\pi$
$654$	−6.29454e48	−0.000513778 0
$655$	0	0
$656$	3.31668e51	0.255848
$657$	− 4.62118e51i	− 0.346572i
$658$	− 2.02281e51i	− 0.147495i
$659$	−1.92183e52	−1.36249	−0.681247	−	0.732054i	$-0.738562\pi$
$659$	−1.92183e52	−1.36249	−0.681247	+	0.732054i	$0.738562\pi$
$660$	0	0
$661$	−1.12368e51	−0.0753213	−0.0376606	−	0.999291i	$-0.511991\pi$
$661$	−1.12368e51	−0.0753213	−0.0376606	+	0.999291i	$0.511991\pi$
$662$	5.29910e51i	0.345405i
$663$	− 3.94478e50i	− 0.0250048i
$664$	−1.80409e52	−1.11211
$665$	0	0
$666$	1.67528e52	0.976819
$667$	1.24564e50i	0.00706422i
$668$	− 2.19224e51i	− 0.120927i
$669$	−7.41611e50	−0.0397918
$670$	0	0
$671$	−2.98684e52	−1.51651
$672$	− 2.13797e50i	− 0.0105602i
$673$	− 6.07438e51i	− 0.291893i	−0.989292	−	0.145946i	$-0.953377\pi$
$673$	− 6.07438e51i	− 0.291893i	0.989292	−	0.145946i	$-0.0466227\pi$
$674$	2.63974e52	1.23411
$675$	0	0
$676$	−7.25197e51	−0.320954
$677$	3.94010e52i	1.69675i	0.529398	+	0.848373i	$0.322418\pi$
$677$	3.94010e52i	1.69675i	−0.529398	+	0.848373i	$0.677582\pi$
$678$	9.67055e49i	0.00405230i
$679$	2.11500e51	0.0862423
$680$	0	0
$681$	−1.39289e51	−0.0537892
$682$	− 1.91699e52i	− 0.720457i
$683$	2.05041e52i	0.749993i	0.927026	+	0.374996i	$0.122356\pi$
$683$	2.05041e52i	0.749993i	−0.927026	+	0.374996i	$0.877644\pi$
$684$	−1.70725e52	−0.607798
$685$	0	0
$686$	−1.87582e52	−0.632696
$687$	1.04893e51i	0.0344389i
$688$	− 2.38252e52i	− 0.761465i
$689$	−1.93662e52	−0.602545
$690$	0	0
$691$	4.63109e51	0.136565	0.0682825	−	0.997666i	$-0.478248\pi$
$691$	4.63109e51	0.136565	0.0682825	+	0.997666i	$0.478248\pi$
$692$	− 1.45525e52i	− 0.417808i
$693$	− 2.28206e52i	− 0.637915i
$694$	1.50799e52	0.410440
$695$	0	0
$696$	−1.72863e51	−0.0446099
$697$	1.43616e52i	0.360909i
$698$	− 2.77797e52i	− 0.679832i
$699$	3.69433e50	0.00880456
$700$	0	0
$701$	−6.34322e51	−0.143392	−0.0716962	−	0.997427i	$-0.522841\pi$
$701$	−6.34322e51	−0.143392	−0.0716962	+	0.997427i	$0.522841\pi$
$702$	2.87868e51i	0.0633807i
$703$	8.88154e52i	1.90465i
$704$	6.74404e52	1.40872
$705$	0	0
$706$	4.95873e52	0.982842
$707$	2.55645e52i	0.493602i
$708$	3.47958e50i	0.00654503i
$709$	7.70939e52	1.41275	0.706374	−	0.707839i	$-0.250330\pi$
$709$	7.70939e52	1.41275	0.706374	+	0.707839i	$0.250330\pi$
$710$	0	0
$711$	−5.42293e52	−0.943293
$712$	8.62096e52i	1.46109i
$713$	2.13725e50i	0.00352939i
$714$	−4.10184e50	−0.00660028
$715$	0	0
$716$	2.34718e52	0.358637
$717$	5.90989e50i	0.00879985i
$718$	3.23407e52i	0.469296i
$719$	−5.22428e52	−0.738826	−0.369413	−	0.929265i	$-0.620441\pi$
$719$	−5.22428e52	−0.738826	−0.369413	+	0.929265i	$0.620441\pi$
$720$	0	0
$721$	−6.70231e51	−0.0900372
$722$	7.41579e52i	0.971000i
$723$	− 2.31196e51i	− 0.0295068i
$724$	−5.29245e51	−0.0658406
$725$	0	0
$726$	−1.88800e51	−0.0223189
$727$	− 1.24495e53i	− 1.43471i	−0.696708	−	0.717354i	$-0.745353\pi$
$727$	− 1.24495e53i	− 1.43471i	0.696708	−	0.717354i	$-0.254647\pi$
$728$	5.91742e52i	0.664816i
$729$	9.07820e52	0.994352
$730$	0	0
$731$	1.03166e53	1.07415
$732$	1.33165e51i	0.0135187i
$733$	1.12627e52i	0.111485i	0.998445	+	0.0557427i	$0.0177526\pi$
$733$	1.12627e52i	0.111485i	−0.998445	+	0.0557427i	$0.982247\pi$
$734$	2.49994e52	0.241297
$735$	0	0
$736$	−4.31028e50	−0.00395609
$737$	6.27941e52i	0.562044i
$738$	− 5.23769e52i	− 0.457191i
$739$	2.92067e52	0.248634	0.124317	−	0.992243i	$-0.460326\pi$
$739$	2.92067e52	0.248634	0.124317	+	0.992243i	$0.460326\pi$
$740$	0	0
$741$	−7.62711e51	−0.0617623
$742$	2.01373e52i	0.159048i
$743$	− 3.47917e52i	− 0.268029i	−0.990979	−	0.134015i	$-0.957213\pi$
$743$	− 3.47917e52i	− 0.268029i	0.990979	−	0.134015i	$-0.0427869\pi$
$744$	−2.96596e51	−0.0222878
$745$	0	0
$746$	7.72582e52	0.552429
$747$	1.46969e53i	1.02516i
$748$	5.04470e52i	0.343286i
$749$	3.13055e52	0.207830
$750$	0	0
$751$	1.55213e53	0.980818	0.490409	−	0.871492i	$-0.336847\pi$
$751$	1.55213e53	0.980818	0.490409	+	0.871492i	$0.336847\pi$
$752$	− 2.91943e52i	− 0.179998i
$753$	− 8.28513e51i	− 0.0498416i
$754$	2.36008e53	1.38534
$755$	0	0
$756$	−2.03582e51	−0.0113785
$757$	− 1.00018e51i	− 0.00545510i	−0.999996	−	0.00272755i	$-0.999132\pi$
$757$	− 1.00018e51i	− 0.00545510i	0.999996	−	0.00272755i	$-0.000868207\pi$
$758$	1.18268e53i	0.629488i
$759$	4.33811e49	0.000225334 0
$760$	0	0
$761$	−3.93324e53	−1.94596	−0.972981	−	0.230886i	$-0.925838\pi$
$761$	−3.93324e53	−1.94596	−0.972981	+	0.230886i	$0.925838\pi$
$762$	8.39144e51i	0.0405200i
$763$	2.10913e51i	0.00994031i
$764$	−1.45455e52	−0.0669115
$765$	0	0
$766$	−1.89949e53	−0.832541
$767$	− 1.64862e53i	− 0.705353i
$768$	− 7.26468e51i	− 0.0303413i
$769$	−4.31322e53	−1.75859	−0.879295	−	0.476278i	$-0.841985\pi$
$769$	−4.31322e53	−1.75859	−0.879295	+	0.476278i	$0.841985\pi$
$770$	0	0
$771$	−1.11827e52	−0.0434552
$772$	3.48879e52i	0.132359i
$773$	− 1.93734e53i	− 0.717604i	−0.933414	−	0.358802i	$-0.883185\pi$
$773$	− 1.93734e53i	− 0.717604i	0.933414	−	0.358802i	$-0.116815\pi$
$774$	−3.76247e53	−1.36071
$775$	0	0
$776$	5.91731e52	0.204024
$777$	5.29294e51i	0.0178200i
$778$	− 1.35607e52i	− 0.0445821i
$779$	2.77678e53	0.891452
$780$	0	0
$781$	−1.61975e53	−0.495911
$782$	8.26956e50i	0.00247262i
$783$	2.81776e52i	0.0822832i
$784$	−1.19494e53	−0.340799
$785$	0	0
$786$	−1.24906e52	−0.0339833
$787$	− 1.53439e52i	− 0.0407759i	−0.999792	−	0.0203880i	$-0.993510\pi$
$787$	− 1.53439e52i	− 0.0407759i	0.999792	−	0.0203880i	$-0.00649014\pi$
$788$	− 1.00746e53i	− 0.261514i
$789$	−1.64390e52	−0.0416821
$790$	0	0
$791$	3.24034e52	0.0784018
$792$	− 6.38470e53i	− 1.50912i
$793$	− 6.30933e53i	− 1.45690i
$794$	−1.71777e53	−0.387512
$795$	0	0
$796$	2.10374e52	0.0453001
$797$	5.82231e53i	1.22494i	0.790493	+	0.612472i	$0.209825\pi$
$797$	5.82231e53i	1.22494i	−0.790493	+	0.612472i	$0.790175\pi$
$798$	7.93079e51i	0.0163028i
$799$	1.26415e53	0.253912
$800$	0	0
$801$	7.02299e53	1.34685
$802$	− 2.66039e53i	− 0.498563i
$803$	2.64015e53i	0.483495i
$804$	2.79960e51	0.00501025
$805$	0	0
$806$	4.04940e53	0.692137
$807$	2.10464e52i	0.0351574i
$808$	7.15236e53i	1.16772i
$809$	−7.29683e53	−1.16436	−0.582179	−	0.813061i	$-0.697800\pi$
$809$	−7.29683e53	−1.16436	−0.582179	+	0.813061i	$0.697800\pi$
$810$	0	0
$811$	−8.04109e53	−1.22583	−0.612914	−	0.790150i	$-0.710003\pi$
$811$	−8.04109e53	−1.22583	−0.612914	+	0.790150i	$0.710003\pi$
$812$	1.66907e53i	0.248706i
$813$	− 5.41870e51i	− 0.00789261i
$814$	−9.57113e53	−1.36274
$815$	0	0
$816$	−5.92000e51	−0.00805479
$817$	− 1.99469e54i	− 2.65318i
$818$	7.44878e52i	0.0968611i
$819$	4.82058e53	0.612840
$820$	0	0
$821$	−1.06873e52	−0.0129873	−0.00649364	−	0.999979i	$-0.502067\pi$
$821$	−1.06873e52	−0.0129873	−0.00649364	+	0.999979i	$0.502067\pi$
$822$	7.41360e51i	0.00880847i
$823$	− 1.55439e54i	− 1.80578i	−0.429874	−	0.902889i	$-0.641442\pi$
$823$	− 1.55439e54i	− 1.80578i	0.429874	−	0.902889i	$-0.358558\pi$
$824$	−1.87516e53	−0.213002
$825$	0	0
$826$	−1.71426e53	−0.186186
$827$	− 1.52865e54i	− 1.62352i	−0.583992	−	0.811759i	$-0.698510\pi$
$827$	− 1.52865e54i	− 1.62352i	0.583992	−	0.811759i	$-0.301490\pi$
$828$	2.05120e51i	0.00213033i
$829$	−4.48559e53	−0.455576	−0.227788	−	0.973711i	$-0.573149\pi$
$829$	−4.48559e53	−0.455576	−0.227788	+	0.973711i	$0.573149\pi$
$830$	0	0
$831$	−3.31346e52	−0.0321857
$832$	1.42459e54i	1.35335i
$833$	− 5.17424e53i	− 0.480744i
$834$	−1.84355e52	−0.0167526
$835$	0	0
$836$	9.75378e53	0.847924
$837$	4.83467e52i	0.0411099i
$838$	1.12190e54i	0.933122i
$839$	1.70786e54	1.38949	0.694747	−	0.719254i	$-0.255516\pi$
$839$	1.70786e54	1.38949	0.694747	+	0.719254i	$0.255516\pi$
$840$	0	0
$841$	1.02566e54	0.798502
$842$	− 1.10682e54i	− 0.842950i
$843$	5.89519e52i	0.0439226i
$844$	9.27918e53	0.676354
$845$	0	0
$846$	−4.61037e53	−0.321650
$847$	6.32617e53i	0.431815i
$848$	2.90633e53i	0.194098i
$849$	1.64245e52	0.0107325
$850$	0	0
$851$	1.06709e52	0.00667580
$852$	7.22147e51i	0.00442072i
$853$	1.02278e54i	0.612667i	0.951924	+	0.306334i	$0.0991023\pi$
$853$	1.02278e54i	0.612667i	−0.951924	+	0.306334i	$0.900898\pi$
$854$	−6.56054e53	−0.384564
$855$	0	0
$856$	8.75859e53	0.491666
$857$	7.33586e52i	0.0403001i	0.999797	+	0.0201500i	$0.00641439\pi$
$857$	7.33586e52i	0.0403001i	−0.999797	+	0.0201500i	$0.993586\pi$
$858$	− 8.21931e52i	− 0.0441896i
$859$	−1.46329e54	−0.769938	−0.384969	−	0.922929i	$-0.625788\pi$
$859$	−1.46329e54	−0.769938	−0.384969	+	0.922929i	$0.625788\pi$
$860$	0	0
$861$	1.65482e52	0.00834049
$862$	8.52292e53i	0.420440i
$863$	− 2.49462e54i	− 1.20449i	−0.798310	−	0.602247i	$-0.794272\pi$
$863$	− 2.49462e54i	− 1.20449i	0.798310	−	0.602247i	$-0.205728\pi$
$864$	−9.75027e52	−0.0460800
$865$	0	0
$866$	−6.31753e53	−0.286066
$867$	4.36098e52i	0.0193300i
$868$	2.86376e53i	0.124257i
$869$	3.09821e54	1.31597
$870$	0	0
$871$	−1.32645e54	−0.539951
$872$	5.90088e52i	0.0235159i
$873$	− 4.82049e53i	− 0.188073i
$874$	1.59889e52	0.00610742
$875$	0	0
$876$	1.17708e52	0.00431004
$877$	4.03070e54i	1.44507i	0.691335	+	0.722534i	$0.257023\pi$
$877$	4.03070e54i	1.44507i	−0.691335	+	0.722534i	$0.742977\pi$
$878$	3.26696e54i	1.14682i
$879$	1.06520e52	0.00366130
$880$	0	0
$881$	−2.32935e54	−0.767679	−0.383840	−	0.923400i	$-0.625398\pi$
$881$	−2.32935e54	−0.767679	−0.383840	+	0.923400i	$0.625398\pi$
$882$	1.88705e54i	0.608995i
$883$	2.99176e54i	0.945482i	0.881202	+	0.472741i	$0.156735\pi$
$883$	2.99176e54i	0.945482i	−0.881202	+	0.472741i	$0.843265\pi$
$884$	−1.06563e54	−0.329792
$885$	0	0
$886$	2.51281e54	0.745822
$887$	5.34771e54i	1.55447i	0.629213	+	0.777233i	$0.283377\pi$
$887$	5.34771e54i	1.55447i	−0.629213	+	0.777233i	$0.716623\pi$
$888$	1.48085e53i	0.0421570i
$889$	2.81175e54	0.783960
$890$	0	0
$891$	−5.19634e54	−1.38982
$892$	2.00337e54i	0.524821i
$893$	− 2.44420e54i	− 0.627169i
$894$	1.76167e52	0.00442772
$895$	0	0
$896$	5.45963e52	0.0131663
$897$	9.16372e50i	0 0.000216477i
$898$	2.55961e54i	0.592327i
$899$	3.96370e54	0.898558
$900$	0	0
$901$	−1.25848e54	−0.273802
$902$	2.99238e54i	0.637816i
$903$	− 1.18873e53i	− 0.0248233i
$904$	9.06576e53	0.185476
$905$	0	0
$906$	4.16454e52	0.00817891
$907$	− 6.45044e54i	− 1.24124i	−0.784113	−	0.620618i	$-0.786882\pi$
$907$	− 6.45044e54i	− 1.24124i	0.784113	−	0.620618i	$-0.213118\pi$
$908$	3.76271e54i	0.709436i
$909$	5.82662e54	1.07643
$910$	0	0
$911$	2.81261e54	0.498907	0.249453	−	0.968387i	$-0.419749\pi$
$911$	2.81261e54	0.498907	0.249453	+	0.968387i	$0.419749\pi$
$912$	1.14461e53i	0.0198955i
$913$	− 8.39655e54i	− 1.43018i
$914$	−1.08031e54	−0.180321
$915$	0	0
$916$	2.83356e54	0.454220
$917$	4.18526e54i	0.657491i
$918$	1.87066e53i	0.0288008i
$919$	−5.50843e54	−0.831171	−0.415586	−	0.909554i	$-0.636423\pi$
$919$	−5.50843e54	−0.831171	−0.415586	+	0.909554i	$0.636423\pi$
$920$	0	0
$921$	−1.97535e53	−0.0286314
$922$	2.54502e54i	0.361551i
$923$	− 3.42152e54i	− 0.476418i
$924$	5.81275e52	0.00793323
$925$	0	0
$926$	−9.59349e54	−1.25798
$927$	1.52758e54i	0.196349i
$928$	7.99374e54i	1.00719i
$929$	−9.70568e54	−1.19877	−0.599384	−	0.800461i	$-0.704588\pi$
$929$	−9.70568e54	−1.19877	−0.599384	+	0.800461i	$0.704588\pi$
$930$	0	0
$931$	−1.00042e55	−1.18745
$932$	− 9.97975e53i	− 0.116125i
$933$	− 1.04184e53i	− 0.0118848i
$934$	1.05115e55	1.17557
$935$	0	0
$936$	1.34869e55	1.44980
$937$	− 4.05525e54i	− 0.427401i	−0.976899	−	0.213701i	$-0.931448\pi$
$937$	− 4.05525e54i	− 0.427401i	0.976899	−	0.213701i	$-0.0685517\pi$
$938$	1.37926e54i	0.142526i
$939$	1.05544e53	0.0106935
$940$	0	0
$941$	4.56539e54	0.444703	0.222351	−	0.974967i	$-0.428627\pi$
$941$	4.56539e54	0.444703	0.222351	+	0.974967i	$0.428627\pi$
$942$	− 4.15094e53i	− 0.0396465i
$943$	− 3.33621e52i	− 0.00312454i
$944$	−2.47411e54	−0.227215
$945$	0	0
$946$	2.14956e55	1.89829
$947$	− 1.72468e55i	− 1.49360i	−0.665051	−	0.746798i	$-0.731590\pi$
$947$	− 1.72468e55i	− 1.49360i	0.665051	−	0.746798i	$-0.268410\pi$
$948$	− 1.38130e53i	− 0.0117310i
$949$	−5.57700e54	−0.464490
$950$	0	0
$951$	4.41804e53	0.0353908
$952$	3.84532e54i	0.302099i
$953$	− 6.30605e52i	− 0.00485891i	−0.999997	−	0.00242945i	$-0.999227\pi$
$953$	− 6.30605e52i	− 0.00485891i	0.999997	−	0.00242945i	$-0.000773320\pi$
$954$	4.58967e54	0.346846
$955$	0	0
$956$	1.59648e54	0.116063
$957$	− 8.04535e53i	− 0.0573686i
$958$	− 1.35394e55i	− 0.946969i
$959$	2.48410e54	0.170422
$960$	0	0
$961$	−8.34809e54	−0.551067
$962$	− 2.02178e55i	− 1.30917i
$963$	− 7.13512e54i	− 0.453226i
$964$	−6.24546e54	−0.389170
$965$	0	0
$966$	9.52858e50	5.71415e−5 0
$967$	− 1.73337e55i	− 1.01977i	−0.860244	−	0.509883i	$-0.829689\pi$
$967$	− 1.73337e55i	− 1.01977i	0.860244	−	0.509883i	$-0.170311\pi$
$968$	1.76992e55i	1.02155i
$969$	−4.95633e53	−0.0280653
$970$	0	0
$971$	1.04588e55	0.570067	0.285033	−	0.958518i	$-0.407995\pi$
$971$	1.04588e55	0.570067	0.285033	+	0.958518i	$0.407995\pi$
$972$	6.96112e53i	0.0372266i
$973$	6.17723e54i	0.324121i
$974$	−2.28037e54	−0.117399
$975$	0	0
$976$	−9.46852e54	−0.469311
$977$	− 1.65065e55i	− 0.802798i	−0.915903	−	0.401399i	$-0.868524\pi$
$977$	− 1.65065e55i	− 0.802798i	0.915903	−	0.401399i	$-0.131476\pi$
$978$	− 4.81082e53i	− 0.0229588i
$979$	−4.01235e55	−1.87896
$980$	0	0
$981$	4.80711e53	0.0216774
$982$	1.02922e55i	0.455454i
$983$	− 3.82232e55i	− 1.65992i	−0.557823	−	0.829960i	$-0.688363\pi$
$983$	− 3.82232e55i	− 1.65992i	0.557823	−	0.829960i	$-0.311637\pi$
$984$	4.62981e53	0.0197312
$985$	0	0
$986$	1.53365e55	0.629512
$987$	− 1.45662e53i	− 0.00586783i
$988$	2.06037e55i	0.814593i
$989$	−2.39655e53	−0.00929939
$990$	0	0
$991$	−4.27417e55	−1.59768	−0.798838	−	0.601546i	$-0.794552\pi$
$991$	−4.27417e55	−1.59768	−0.798838	+	0.601546i	$0.794552\pi$
$992$	1.37156e55i	0.503208i
$993$	3.81585e53i	0.0137414i
$994$	−3.55775e54	−0.125756
$995$	0	0
$996$	−3.74351e53	−0.0127491
$997$	− 3.39750e55i	− 1.13579i	−0.823100	−	0.567896i	$-0.807757\pi$
$997$	− 3.39750e55i	− 1.13579i	0.823100	−	0.567896i	$-0.192243\pi$
$998$	− 2.28344e55i	− 0.749332i
$999$	2.41386e54	0.0777588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.38.b.a.24.3		4
5.2	odd	4		25.38.a.a.1.1		2
5.3	odd	4		1.38.a.a.1.2	✓	2
5.4	even	2	inner	25.38.b.a.24.2		4
15.8	even	4		9.38.a.a.1.1		2
20.3	even	4		16.38.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.38.a.a.1.2	✓	2	5.3	odd	4
9.38.a.a.1.1		2	15.8	even	4
16.38.a.b.1.2		2	20.3	even	4
25.38.a.a.1.1		2	5.2	odd	4
25.38.b.a.24.2		4	5.4	even	2	inner
25.38.b.a.24.3		4	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:	\( k \)	\(=\)	\( 38 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+286012. i q^{2} +2.05955e7i q^{3} +5.56362e10 q^{4} -5.89057e12 q^{6} +1.97377e15i q^{7} +5.52218e16i q^{8} +4.49860e17 q^{9} +O(q^{10})\)	\(q+286012. i q^{2} +2.05955e7i q^{3} +5.56362e10 q^{4} -5.89057e12 q^{6} +1.97377e15i q^{7} +5.52218e16i q^{8} +4.49860e17 q^{9} -2.57012e19 q^{11} +1.14586e18i q^{12} -5.42906e20i q^{13} -5.64522e20 q^{14} -8.14749e21 q^{16} -3.52797e22i q^{17} +1.28665e23i q^{18} -6.82122e23 q^{19} -4.06509e22 q^{21} -7.35084e24i q^{22} +8.19547e22i q^{23} -1.13732e24 q^{24} +1.55278e26 q^{26} +1.85389e25i q^{27} +1.09813e26i q^{28} +1.51991e27 q^{29} +2.60785e27 q^{31} +5.25934e27i q^{32} -5.29330e26i q^{33} +1.00904e28 q^{34} +2.50285e28 q^{36} -1.30205e29i q^{37} -1.95095e29i q^{38} +1.11814e28 q^{39} -4.07079e29 q^{41} -1.16266e28i q^{42} +2.92424e30i q^{43} -1.42992e30 q^{44} -2.34400e28 q^{46} +3.58323e30i q^{47} -1.67802e29i q^{48} +1.46663e31 q^{49} +7.26605e29 q^{51} -3.02052e31i q^{52} -3.56714e31i q^{53} -5.30236e30 q^{54} -1.08995e32 q^{56} -1.40487e31i q^{57} +4.34713e32i q^{58} +3.03666e32 q^{59} +1.16214e33 q^{61} +7.45875e32i q^{62} +8.87921e32i q^{63} -2.62402e33 q^{64} +1.51395e32 q^{66} -2.44324e33i q^{67} -1.96283e33i q^{68} -1.68790e30 q^{69} +6.30224e33 q^{71} +2.48421e34i q^{72} -1.02725e34i q^{73} +3.72400e34 q^{74} -3.79507e34 q^{76} -5.07283e34i q^{77} +3.19803e33i q^{78} -1.20547e35 q^{79} +2.02183e35 q^{81} -1.16430e35i q^{82} +3.26699e35i q^{83} -2.26166e33 q^{84} -8.36366e35 q^{86} +3.13034e34i q^{87} -1.41927e36i q^{88} +1.56115e36 q^{89} +1.07157e36 q^{91} +4.55965e33i q^{92} +5.37100e34i q^{93} -1.02485e36 q^{94} -1.08319e35 q^{96} -1.07155e36i q^{97} +4.19474e36i q^{98} -1.15619e37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 75440539648 q^{4} - 45013087694592 q^{6} + 17\!\cdots\!28 q^{9}+O(q^{10}) \) 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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