LMFDB - Embedded newform 25.32.b.a.24.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,32,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, 32, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 32 $
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:	$152.192832048$
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} + 9147745x^{2} + 20920305072384 $ x^4 + 9147745*x^2 + 20920305072384
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.3
Root			$2138.16i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.32.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)

$f(q)$	$=$	$q+31347.9i q^{2} -1.34921e7i q^{3} +1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13i q^{7} +1.03833e14i q^{8} +4.35638e14 q^{9} +O(q^{10})$	\(q+31347.9i q^{2} -1.34921e7i q^{3} +1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13i q^{7} +1.03833e14i q^{8} +4.35638e14 q^{9} -5.37973e15 q^{11} -1.57155e16i q^{12} +2.76595e17i q^{13} +5.89989e17 q^{14} -7.53562e17 q^{16} -6.29817e18i q^{17} +1.36563e19i q^{18} -1.91455e18 q^{19} -2.53930e20 q^{21} -1.68643e20i q^{22} +1.90120e21i q^{23} +1.40092e21 q^{24} -8.67065e21 q^{26} -1.42113e22i q^{27} -2.19223e22i q^{28} -5.22675e22 q^{29} -6.09679e22 q^{31} +1.99357e23i q^{32} +7.25837e22i q^{33} +1.97434e23 q^{34} +5.07428e23 q^{36} +2.07091e24i q^{37} -6.00172e22i q^{38} +3.73183e24 q^{39} -5.09498e24 q^{41} -7.96017e24i q^{42} +8.39002e24i q^{43} -6.26628e24 q^{44} -5.95984e25 q^{46} -2.13587e25i q^{47} +1.01671e25i q^{48} -1.96444e26 q^{49} -8.49753e25 q^{51} +3.22176e26i q^{52} +1.59213e26i q^{53} +4.45495e26 q^{54} +1.95421e27 q^{56} +2.58313e25i q^{57} -1.63847e27i q^{58} -2.16250e27 q^{59} -6.60780e27 q^{61} -1.91122e27i q^{62} -8.19901e27i q^{63} -7.86767e27 q^{64} -2.27534e27 q^{66} +2.77322e26i q^{67} -7.33607e27i q^{68} +2.56510e28 q^{69} +7.68524e28 q^{71} +4.52335e28i q^{72} +2.29610e28i q^{73} -6.49186e28 q^{74} -2.23006e27 q^{76} +1.01250e29i q^{77} +1.16985e29i q^{78} +2.99014e29 q^{79} +7.73416e28 q^{81} -1.59717e29i q^{82} +1.89466e29i q^{83} -2.95777e29 q^{84} -2.63009e29 q^{86} +7.05196e29i q^{87} -5.58593e29i q^{88} +2.41523e30 q^{89} +5.20571e30 q^{91} +2.21450e30i q^{92} +8.22583e29i q^{93} +6.69551e29 q^{94} +2.68973e30 q^{96} +3.68010e30i q^{97} -6.15810e30i q^{98} -2.34361e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3545068672 q^{4} + 5246334992448 q^{6} + 202532912607852 q^{9}+O(q^{10}) $ 4 * q - 3545068672 * q^4 + 5246334992448 * q^6 + 202532912607852 * q^9	$ 4 q - 3545068672 q^{4} + 5246334992448 q^{6} + 202532912607852 q^{9} - 15\!\cdots\!52 q^{11}+ \cdots - 30\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 3545068672 * q^4 + 5246334992448 * q^6 + 202532912607852 * q^9 - 15564707490237552 * q^11 - 451089927690482304 * q^14 - 6090425827369803776 * q^16 + 24741126656044328080 * q^19 + 197909914832142323328 * q^21 - 673828082468523970560 * q^24 - 46133361333488646558432 * q^26 - 257152288434434111614680 * q^29 + 251467055035923677587328 * q^31 - 1163413819142586057669984 * q^34 + 2979173497636398827009664 * q^36 + 19922108328822727136569824 * q^39 + 17449848671325851681342568 * q^41 + 1582016741746664622644736 * q^44 - 119746022890551201018179712 * q^46 - 338938588744640405060814372 * q^49 + 504324809479940640170760288 * q^51 + 2137644543374748380140548480 * q^54 + 5196710795499630344863457280 * q^56 + 397446527095531027981493040 * q^59 - 24112436402226008722315312552 * q^61 + 14976826736528117095355383808 * q^64 - 15123281166884922728531629824 * q^66 + 51539712572788652156989152384 * q^69 + 111569153250069315025756574688 * q^71 - 306266327264976756969588598944 * q^74 - 88380299399878717804948963840 * q^76 + 238328382186599409928425421120 * q^79 - 797813845293782539298125268316 * q^81 - 2664633299839703589778678370304 * q^84 - 4346284964445676845665854039872 * q^86 + 4308829228493340583205443791960 * q^89 + 5793562736137806139912099018048 * q^91 - 9227616502805116863050228500224 * q^94 - 12168740865339213432737429716992 * q^96 - 3080492615488189978915462170576 * 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 $

$2$	31347.9i	0.676462i	0.941063	+	0.338231i	$0.109828\pi$
$2$	31347.9i	0.676462i	−0.941063	+	0.338231i	$0.890172\pi$
$3$	− 1.34921e7i	− 0.542874i	−0.962456	−	0.271437i	$-0.912501\pi$
$3$	− 1.34921e7i	− 0.542874i	0.962456	−	0.271437i	$-0.0874988\pi$
$4$	1.16479e9	0.542400
$5$	0	0
$5$	0	0
$6$	4.22947e11	0.367233
$7$	− 1.88207e13i	− 1.49836i	−0.662366	−	0.749181i	$-0.730447\pi$
$7$	− 1.88207e13i	− 1.49836i	0.662366	−	0.749181i	$-0.269553\pi$
$8$	1.03833e14i	1.04337i
$9$	4.35638e14	0.705288
$10$	0	0
$11$	−5.37973e15	−0.388306	−0.194153	−	0.980971i	$-0.562196\pi$
$11$	−5.37973e15	−0.388306	−0.194153	+	0.980971i	$0.562196\pi$
$12$	− 1.57155e16i	− 0.294455i
$13$	2.76595e17i	1.49872i	0.662161	+	0.749362i	$0.269640\pi$
$13$	2.76595e17i	1.49872i	−0.662161	+	0.749362i	$0.730360\pi$
$14$	5.89989e17	1.01358
$15$	0	0
$16$	−7.53562e17	−0.163403
$17$	− 6.29817e18i	− 0.533649i	−0.963745	−	0.266825i	$-0.914026\pi$
$17$	− 6.29817e18i	− 0.533649i	0.963745	−	0.266825i	$-0.0859745\pi$
$18$	1.36563e19i	0.477100i
$19$	−1.91455e18	−0.0289326	−0.0144663	−	0.999895i	$-0.504605\pi$
$19$	−1.91455e18	−0.0289326	−0.0144663	+	0.999895i	$0.504605\pi$
$20$	0	0
$21$	−2.53930e20	−0.813421
$22$	− 1.68643e20i	− 0.262674i
$23$	1.90120e21i	1.48678i	0.668861	+	0.743388i	$0.266782\pi$
$23$	1.90120e21i	1.48678i	−0.668861	+	0.743388i	$0.733218\pi$
$24$	1.40092e21	0.566420
$25$	0	0
$26$	−8.67065e21	−1.01383
$27$	− 1.42113e22i	− 0.925756i
$28$	− 2.19223e22i	− 0.812711i
$29$	−5.22675e22	−1.12477	−0.562384	−	0.826877i	$-0.690116\pi$
$29$	−5.22675e22	−1.12477	−0.562384	+	0.826877i	$0.690116\pi$
$30$	0	0
$31$	−6.09679e22	−0.466654	−0.233327	−	0.972398i	$-0.574961\pi$
$31$	−6.09679e22	−0.466654	−0.233327	+	0.972398i	$0.574961\pi$
$32$	1.99357e23i	0.932838i
$33$	7.25837e22i	0.210801i
$34$	1.97434e23	0.360993
$35$	0	0
$36$	5.07428e23	0.382548
$37$	2.07091e24i	1.02102i	0.859872	+	0.510510i	$0.170543\pi$
$37$	2.07091e24i	1.02102i	−0.859872	+	0.510510i	$0.829457\pi$
$38$	− 6.00172e22i	− 0.0195718i
$39$	3.73183e24	0.813618
$40$	0	0
$41$	−5.09498e24	−0.511673	−0.255837	−	0.966720i	$-0.582351\pi$
$41$	−5.09498e24	−0.511673	−0.255837	+	0.966720i	$0.582351\pi$
$42$	− 7.96017e24i	− 0.550248i
$43$	8.39002e24i	0.402719i	0.979517	+	0.201359i	$0.0645359\pi$
$43$	8.39002e24i	0.402719i	−0.979517	+	0.201359i	$0.935464\pi$
$44$	−6.26628e24	−0.210617
$45$	0	0
$46$	−5.95984e25	−1.00575
$47$	− 2.13587e25i	− 0.258261i	−0.991628	−	0.129130i	$-0.958781\pi$
$47$	− 2.13587e25i	− 0.258261i	0.991628	−	0.129130i	$-0.0412186\pi$
$48$	1.01671e25i	0.0887071i
$49$	−1.96444e26	−1.24509
$50$	0	0
$51$	−8.49753e25	−0.289704
$52$	3.22176e26i	0.812907i
$53$	1.59213e26i	0.299022i	0.988760	+	0.149511i	$0.0477700\pi$
$53$	1.59213e26i	0.299022i	−0.988760	+	0.149511i	$0.952230\pi$
$54$	4.45495e26	0.626238
$55$	0	0
$56$	1.95421e27	1.56335
$57$	2.58313e25i	0.0157067i
$58$	− 1.63847e27i	− 0.760862i
$59$	−2.16250e27	−0.770459	−0.385229	−	0.922821i	$-0.625878\pi$
$59$	−2.16250e27	−0.770459	−0.385229	+	0.922821i	$0.625878\pi$
$60$	0	0
$61$	−6.60780e27	−1.40425	−0.702125	−	0.712053i	$-0.747765\pi$
$61$	−6.60780e27	−1.40425	−0.702125	+	0.712053i	$0.747765\pi$
$62$	− 1.91122e27i	− 0.315674i
$63$	− 8.19901e27i	− 1.05678i
$64$	−7.86767e27	−0.794432
$65$	0	0
$66$	−2.27534e27	−0.142599
$67$	2.77322e26i	0.0137665i	0.999976	+	0.00688326i	$0.00219103\pi$
$67$	2.77322e26i	0.0137665i	−0.999976	+	0.00688326i	$0.997809\pi$
$68$	− 7.33607e27i	− 0.289451i
$69$	2.56510e28	0.807131
$70$	0	0
$71$	7.68524e28	1.55293	0.776467	−	0.630158i	$-0.217010\pi$
$71$	7.68524e28	1.55293	0.776467	+	0.630158i	$0.217010\pi$
$72$	4.52335e28i	0.735879i
$73$	2.29610e28i	0.301639i	0.988561	+	0.150819i	$0.0481912\pi$
$73$	2.29610e28i	0.301639i	−0.988561	+	0.150819i	$0.951809\pi$
$74$	−6.49186e28	−0.690681
$75$	0	0
$76$	−2.23006e27	−0.0156930
$77$	1.01250e29i	0.581823i
$78$	1.16985e29i	0.550381i
$79$	2.99014e29	1.15471	0.577353	−	0.816494i	$-0.304086\pi$
$79$	2.99014e29	1.15471	0.577353	+	0.816494i	$0.304086\pi$
$80$	0	0
$81$	7.73416e28	0.202719
$82$	− 1.59717e29i	− 0.346127i
$83$	1.89466e29i	0.340267i	0.985421	+	0.170134i	$0.0544199\pi$
$83$	1.89466e29i	0.340267i	−0.985421	+	0.170134i	$0.945580\pi$
$84$	−2.95777e29	−0.441199
$85$	0	0
$86$	−2.63009e29	−0.272424
$87$	7.05196e29i	0.610606i
$88$	− 5.58593e29i	− 0.405148i
$89$	2.41523e30	1.47032	0.735162	−	0.677892i	$-0.237106\pi$
$89$	2.41523e30	1.47032	0.735162	+	0.677892i	$0.237106\pi$
$90$	0	0
$91$	5.20571e30	2.24563
$92$	2.21450e30i	0.806426i
$93$	8.22583e29i	0.253334i
$94$	6.69551e29	0.174704
$95$	0	0
$96$	2.68973e30	0.506414
$97$	3.68010e30i	0.590062i	0.955488	+	0.295031i	$0.0953299\pi$
$97$	3.68010e30i	0.590062i	−0.955488	+	0.295031i	$0.904670\pi$
$98$	− 6.15810e30i	− 0.842254i
$99$	−2.34361e30	−0.273868
$100$	0	0
$101$	−4.69650e30	−0.402526	−0.201263	−	0.979537i	$-0.564505\pi$
$101$	−4.69650e30	−0.402526	−0.201263	+	0.979537i	$0.564505\pi$
$102$	− 2.66379e30i	− 0.195974i
$103$	5.49646e30i	0.347621i	0.984779	+	0.173811i	$0.0556080\pi$
$103$	5.49646e30i	0.347621i	−0.984779	+	0.173811i	$0.944392\pi$
$104$	−2.87196e31	−1.56373
$105$	0	0
$106$	−4.99100e30	−0.202277
$107$	− 5.31108e30i	− 0.186095i	−0.995662	−	0.0930475i	$-0.970339\pi$
$107$	− 5.31108e30i	− 0.186095i	0.995662	−	0.0930475i	$-0.0296608\pi$
$108$	− 1.65533e31i	− 0.502130i
$109$	5.09224e31	1.33906	0.669528	−	0.742787i	$-0.266497\pi$
$109$	5.09224e31	1.33906	0.669528	+	0.742787i	$0.266497\pi$
$110$	0	0
$111$	2.79408e31	0.554285
$112$	1.41826e31i	0.244836i
$113$	5.75758e31i	0.866012i	0.901391	+	0.433006i	$0.142547\pi$
$113$	5.75758e31i	0.866012i	−0.901391	+	0.433006i	$0.857453\pi$
$114$	−8.09756e29	−0.0106250
$115$	0	0
$116$	−6.08809e31	−0.610073
$117$	1.20495e32i	1.05703i
$118$	− 6.77897e31i	− 0.521186i
$119$	−1.18536e32	−0.799600
$120$	0	0
$121$	−1.63002e32	−0.849219
$122$	− 2.07141e32i	− 0.949922i
$123$	6.87418e31i	0.277774i
$124$	−7.10151e31	−0.253113
$125$	0	0
$126$	2.57022e32	0.714869
$127$	− 3.71246e32i	− 0.913490i	−0.889598	−	0.456745i	$-0.849015\pi$
$127$	− 3.71246e32i	− 0.913490i	0.889598	−	0.456745i	$-0.150985\pi$
$128$	1.81481e32i	0.395436i
$129$	1.13199e32	0.218626
$130$	0	0
$131$	−6.43836e32	−0.979648	−0.489824	−	0.871821i	$-0.662939\pi$
$131$	−6.43836e32	−0.979648	−0.489824	+	0.871821i	$0.662939\pi$
$132$	8.45451e31i	0.114338i
$133$	3.60333e31i	0.0433514i
$134$	−8.69344e30	−0.00931252
$135$	0	0
$136$	6.53957e32	0.556796
$137$	5.70054e32i	0.433259i	0.976254	+	0.216629i	$0.0695063\pi$
$137$	5.70054e32i	0.433259i	−0.976254	+	0.216629i	$0.930494\pi$
$138$	8.04106e32i	0.545993i
$139$	−1.35322e33	−0.821557	−0.410779	−	0.911735i	$-0.634743\pi$
$139$	−1.35322e33	−0.821557	−0.410779	+	0.911735i	$0.634743\pi$
$140$	0	0
$141$	−2.88173e32	−0.140203
$142$	2.40916e33i	1.05050i
$143$	− 1.48800e33i	− 0.581963i
$144$	−3.28280e32	−0.115246
$145$	0	0
$146$	−7.19780e32	−0.204047
$147$	2.65044e33i	0.675925i
$148$	2.41218e33i	0.553801i
$149$	−5.42559e33	−1.12217	−0.561086	−	0.827757i	$-0.689616\pi$
$149$	−5.42559e33	−1.12217	−0.561086	+	0.827757i	$0.689616\pi$
$150$	0	0
$151$	−2.39015e33	−0.402051	−0.201026	−	0.979586i	$-0.564427\pi$
$151$	−2.39015e33	−0.402051	−0.201026	+	0.979586i	$0.564427\pi$
$152$	− 1.98794e32i	− 0.0301875i
$153$	− 2.74372e33i	− 0.376377i
$154$	−3.17399e33	−0.393581
$155$	0	0
$156$	4.34682e33	0.441306
$157$	1.98794e34i	1.82792i	0.405802	+	0.913961i	$0.366992\pi$
$157$	1.98794e34i	1.82792i	−0.405802	+	0.913961i	$0.633008\pi$
$158$	9.37345e33i	0.781115i
$159$	2.14812e33	0.162331
$160$	0	0
$161$	3.57819e34	2.22773
$162$	2.42449e33i	0.137132i
$163$	7.84574e33i	0.403391i	0.979448	+	0.201696i	$0.0646451\pi$
$163$	7.84574e33i	0.403391i	−0.979448	+	0.201696i	$0.935355\pi$
$164$	−5.93460e33	−0.277531
$165$	0	0
$166$	−5.93935e33	−0.230178
$167$	5.15166e34i	1.81904i	0.415662	+	0.909519i	$0.363550\pi$
$167$	5.15166e34i	1.81904i	−0.415662	+	0.909519i	$0.636450\pi$
$168$	− 2.63663e34i	− 0.848703i
$169$	−4.24446e34	−1.24617
$170$	0	0
$171$	−8.34052e32	−0.0204058
$172$	9.77265e33i	0.218435i
$173$	5.04795e34i	1.03134i	0.856788	+	0.515668i	$0.172456\pi$
$173$	5.04795e34i	1.03134i	−0.856788	+	0.515668i	$0.827544\pi$
$174$	−2.21064e34	−0.413052
$175$	0	0
$176$	4.05396e33	0.0634503
$177$	2.91765e34i	0.418262i
$178$	7.57122e34i	0.994617i
$179$	2.60297e34	0.313507	0.156754	−	0.987638i	$-0.449897\pi$
$179$	2.60297e34	0.313507	0.156754	+	0.987638i	$0.449897\pi$
$180$	0	0
$181$	−1.20765e35	−1.22440	−0.612198	−	0.790705i	$-0.709714\pi$
$181$	−1.20765e35	−1.22440	−0.612198	+	0.790705i	$0.709714\pi$
$182$	1.63188e35i	1.51908i
$183$	8.91529e34i	0.762331i
$184$	−1.97407e35	−1.55126
$185$	0	0
$186$	−2.57862e34	−0.171371
$187$	3.38825e34i	0.207219i
$188$	− 2.48785e34i	− 0.140081i
$189$	−2.67468e35	−1.38712
$190$	0	0
$191$	2.27571e35	1.00253	0.501267	−	0.865293i	$-0.332868\pi$
$191$	2.27571e35	1.00253	0.501267	+	0.865293i	$0.332868\pi$
$192$	1.06151e35i	0.431276i
$193$	− 1.78027e35i	− 0.667339i	−0.942690	−	0.333670i	$-0.891713\pi$
$193$	− 1.78027e35i	− 0.667339i	0.942690	−	0.333670i	$-0.108287\pi$
$194$	−1.15363e35	−0.399154
$195$	0	0
$196$	−2.28817e35	−0.675335
$197$	2.53071e35i	0.690264i	0.938554	+	0.345132i	$0.112166\pi$
$197$	2.53071e35i	0.690264i	−0.938554	+	0.345132i	$0.887834\pi$
$198$	− 7.34673e34i	− 0.185261i
$199$	−4.51723e35	−1.05354	−0.526768	−	0.850009i	$-0.676596\pi$
$199$	−4.51723e35	−1.05354	−0.526768	+	0.850009i	$0.676596\pi$
$200$	0	0
$201$	3.74164e33	0.00747348
$202$	− 1.47225e35i	− 0.272293i
$203$	9.83712e35i	1.68531i
$204$	−9.89787e34	−0.157136
$205$	0	0
$206$	−1.72302e35	−0.235152
$207$	8.28232e35i	1.04860i
$208$	− 2.08431e35i	− 0.244896i
$209$	1.02998e34	0.0112347
$210$	0	0
$211$	6.25554e34	0.0588690	0.0294345	−	0.999567i	$-0.490629\pi$
$211$	6.25554e34	0.0588690	0.0294345	+	0.999567i	$0.490629\pi$
$212$	1.85451e35i	0.162190i
$213$	− 1.03690e36i	− 0.843047i
$214$	1.66491e35	0.125886
$215$	0	0
$216$	1.47560e36	0.965910
$217$	1.14746e36i	0.699217i
$218$	1.59631e36i	0.905819i
$219$	3.09792e35	0.163752
$220$	0	0
$221$	1.74204e36	0.799793
$222$	8.75886e35i	0.374953i
$223$	1.14032e35i	0.0455303i	0.999741	+	0.0227652i	$0.00724701\pi$
$223$	1.14032e35i	0.0455303i	−0.999741	+	0.0227652i	$0.992753\pi$
$224$	3.75204e36	1.39773
$225$	0	0
$226$	−1.80488e36	−0.585824
$227$	− 1.82276e35i	− 0.0552496i	−0.999618	−	0.0276248i	$-0.991206\pi$
$227$	− 1.82276e35i	− 0.0552496i	0.999618	−	0.0276248i	$-0.00879436\pi$
$228$	3.00881e34i	0.00851932i
$229$	−2.02123e36	−0.534768	−0.267384	−	0.963590i	$-0.586159\pi$
$229$	−2.02123e36	−0.534768	−0.267384	+	0.963590i	$0.586159\pi$
$230$	0	0
$231$	1.36608e36	0.315856
$232$	− 5.42708e36i	− 1.17355i
$233$	3.92949e35i	0.0794912i	0.999210	+	0.0397456i	$0.0126547\pi$
$233$	3.92949e35i	0.0794912i	−0.999210	+	0.0397456i	$0.987345\pi$
$234$	−3.77726e36	−0.715042
$235$	0	0
$236$	−2.51886e36	−0.417897
$237$	− 4.03432e36i	− 0.626860i
$238$	− 3.71585e36i	− 0.540898i
$239$	1.39161e37	1.89823	0.949115	−	0.314931i	$-0.101981\pi$
$239$	1.39161e37	1.89823	0.949115	+	0.314931i	$0.101981\pi$
$240$	0	0
$241$	−1.56350e36	−0.187428	−0.0937140	−	0.995599i	$-0.529874\pi$
$241$	−1.56350e36	−0.187428	−0.0937140	+	0.995599i	$0.529874\pi$
$242$	− 5.10976e36i	− 0.574464i
$243$	− 9.82146e36i	− 1.03581i
$244$	−7.69673e36	−0.761665
$245$	0	0
$246$	−2.15491e36	−0.187903
$247$	− 5.29555e35i	− 0.0433619i
$248$	− 6.33048e36i	− 0.486895i
$249$	2.55628e36	0.184722
$250$	0	0
$251$	7.69469e36	0.491189	0.245594	−	0.969373i	$-0.421017\pi$
$251$	7.69469e36	0.491189	0.245594	+	0.969373i	$0.421017\pi$
$252$	− 9.55017e36i	− 0.573195i
$253$	− 1.02279e37i	− 0.577324i
$254$	1.16378e37	0.617941
$255$	0	0
$256$	−2.25847e37	−1.06193
$257$	− 4.19824e37i	− 1.85825i	−0.369765	−	0.929125i	$-0.620562\pi$
$257$	− 4.19824e37i	− 1.85825i	0.369765	−	0.929125i	$-0.379438\pi$
$258$	3.54854e36i	0.147892i
$259$	3.89760e37	1.52986
$260$	0	0
$261$	−2.27697e37	−0.793285
$262$	− 2.01829e37i	− 0.662694i
$263$	5.61748e37i	1.73871i	0.494186	+	0.869356i	$0.335466\pi$
$263$	5.61748e37i	1.73871i	−0.494186	+	0.869356i	$0.664534\pi$
$264$	−7.53657e36	−0.219944
$265$	0	0
$266$	−1.12957e36	−0.0293256
$267$	− 3.25864e37i	− 0.798200i
$268$	3.23023e35i	0.00746696i
$269$	3.06746e37	0.669296	0.334648	−	0.942343i	$-0.391383\pi$
$269$	3.06746e37	0.669296	0.334648	+	0.942343i	$0.391383\pi$
$270$	0	0
$271$	−6.26560e35	−0.0121882	−0.00609409	−	0.999981i	$-0.501940\pi$
$271$	−6.26560e35	−0.0121882	−0.00609409	+	0.999981i	$0.501940\pi$
$272$	4.74606e36i	0.0871998i
$273$	− 7.02357e37i	− 1.21909i
$274$	−1.78700e37	−0.293083
$275$	0	0
$276$	2.98782e37	0.437788
$277$	4.05908e37i	0.562330i	0.959660	+	0.281165i	$0.0907207\pi$
$277$	4.05908e37i	0.562330i	−0.959660	+	0.281165i	$0.909279\pi$
$278$	− 4.24205e37i	− 0.555752i
$279$	−2.65599e37	−0.329126
$280$	0	0
$281$	7.11328e37	0.789082	0.394541	−	0.918878i	$-0.370904\pi$
$281$	7.11328e37	0.789082	0.394541	+	0.918878i	$0.370904\pi$
$282$	− 9.03362e36i	− 0.0948420i
$283$	− 5.52066e36i	− 0.0548657i	−0.999624	−	0.0274329i	$-0.991267\pi$
$283$	− 5.52066e36i	− 0.0548657i	0.999624	−	0.0274329i	$-0.00873324\pi$
$284$	8.95173e37	0.842311
$285$	0	0
$286$	4.66458e37	0.393676
$287$	9.58912e37i	0.766671i
$288$	8.68473e37i	0.657920i
$289$	9.96220e37	0.715218
$290$	0	0
$291$	4.96521e37	0.320329
$292$	2.67449e37i	0.163609i
$293$	− 5.84412e36i	− 0.0339056i	−0.999856	−	0.0169528i	$-0.994604\pi$
$293$	− 5.84412e36i	− 0.0339056i	0.999856	−	0.0169528i	$-0.00539650\pi$
$294$	−8.30855e37	−0.457237
$295$	0	0
$296$	−2.15028e38	−1.06531
$297$	7.64532e37i	0.359477i
$298$	− 1.70081e38i	− 0.759107i
$299$	−5.25860e38	−2.22827
$300$	0	0
$301$	1.57906e38	0.603419
$302$	− 7.49260e37i	− 0.271972i
$303$	6.33655e37i	0.218521i
$304$	1.44274e36	0.00472766
$305$	0	0
$306$	8.60098e37	0.254604
$307$	5.70867e38i	1.60653i	0.595619	+	0.803267i	$0.296907\pi$
$307$	5.70867e38i	1.60653i	−0.595619	+	0.803267i	$0.703093\pi$
$308$	1.17936e38i	0.315580i
$309$	7.41586e37	0.188714
$310$	0	0
$311$	−2.73000e38	−0.628604	−0.314302	−	0.949323i	$-0.601770\pi$
$311$	−2.73000e38	−0.628604	−0.314302	+	0.949323i	$0.601770\pi$
$312$	3.87487e38i	0.848908i
$313$	7.96309e38i	1.66014i	0.557659	+	0.830070i	$0.311699\pi$
$313$	7.96309e38i	1.66014i	−0.557659	+	0.830070i	$0.688301\pi$
$314$	−6.23176e38	−1.23652
$315$	0	0
$316$	3.48290e38	0.626313
$317$	− 3.34956e38i	− 0.573548i	−0.957998	−	0.286774i	$-0.907417\pi$
$317$	− 3.34956e38i	− 0.573548i	0.957998	−	0.286774i	$-0.0925828\pi$
$318$	6.73389e37i	0.109811i
$319$	2.81185e38	0.436754
$320$	0	0
$321$	−7.16575e37	−0.101026
$322$	1.12169e39i	1.50697i
$323$	1.20582e37i	0.0154398i
$324$	9.00871e37	0.109955
$325$	0	0
$326$	−2.45947e38	−0.272879
$327$	− 6.87049e38i	− 0.726938i
$328$	− 5.29026e38i	− 0.533866i
$329$	−4.01987e38	−0.386968
$330$	0	0
$331$	−8.30533e38	−0.727818	−0.363909	−	0.931435i	$-0.618558\pi$
$331$	−8.30533e38	−0.727818	−0.363909	+	0.931435i	$0.618558\pi$
$332$	2.20689e38i	0.184561i
$333$	9.02166e38i	0.720113i
$334$	−1.61494e39	−1.23051
$335$	0	0
$336$	1.91352e38	0.132915
$337$	− 1.14148e39i	− 0.757187i	−0.925563	−	0.378594i	$-0.876408\pi$
$337$	− 1.14148e39i	− 0.757187i	0.925563	−	0.378594i	$-0.123592\pi$
$338$	− 1.33055e39i	− 0.842988i
$339$	7.76816e38	0.470135
$340$	0	0
$341$	3.27991e38	0.181205
$342$	− 2.61457e37i	− 0.0138037i
$343$	7.27773e38i	0.367229i
$344$	−8.71160e38	−0.420187
$345$	0	0
$346$	−1.58242e39	−0.697660
$347$	3.74946e39i	1.58075i	0.612626	+	0.790373i	$0.290113\pi$
$347$	3.74946e39i	1.58075i	−0.612626	+	0.790373i	$0.709887\pi$
$348$	8.21408e38i	0.331193i
$349$	−7.67977e38	−0.296179	−0.148089	−	0.988974i	$-0.547312\pi$
$349$	−7.67977e38	−0.296179	−0.148089	+	0.988974i	$0.547312\pi$
$350$	0	0
$351$	3.93078e39	1.38745
$352$	− 1.07249e39i	− 0.362227i
$353$	− 2.48278e39i	− 0.802472i	−0.915975	−	0.401236i	$-0.868581\pi$
$353$	− 2.48278e39i	− 0.802472i	0.915975	−	0.401236i	$-0.131419\pi$
$354$	−9.14622e38	−0.282938
$355$	0	0
$356$	2.81324e39	0.797503
$357$	1.59930e39i	0.434082i
$358$	8.15976e38i	0.212076i
$359$	6.14909e39	1.53055	0.765274	−	0.643704i	$-0.222603\pi$
$359$	6.14909e39	1.53055	0.765274	+	0.643704i	$0.222603\pi$
$360$	0	0
$361$	−4.37520e39	−0.999163
$362$	− 3.78571e39i	− 0.828256i
$363$	2.19923e39i	0.461018i
$364$	6.06358e39	1.21803
$365$	0	0
$366$	−2.79475e39	−0.515687
$367$	− 5.66753e39i	− 1.00247i	−0.865312	−	0.501233i	$-0.832880\pi$
$367$	− 5.66753e39i	− 1.00247i	0.865312	−	0.501233i	$-0.167120\pi$
$368$	− 1.43267e39i	− 0.242943i
$369$	−2.21956e39	−0.360877
$370$	0	0
$371$	2.99651e39	0.448043
$372$	9.58140e38i	0.137409i
$373$	− 8.05893e39i	− 1.10864i	−0.832303	−	0.554320i	$-0.812978\pi$
$373$	− 8.05893e39i	− 1.10864i	0.832303	−	0.554320i	$-0.187022\pi$
$374$	−1.06214e39	−0.140176
$375$	0	0
$376$	2.21774e39	0.269463
$377$	− 1.44569e40i	− 1.68572i
$378$	− 8.38454e39i	− 0.938332i
$379$	9.24240e39	0.992835	0.496417	−	0.868084i	$-0.334649\pi$
$379$	9.24240e39	0.992835	0.496417	+	0.868084i	$0.334649\pi$
$380$	0	0
$381$	−5.00887e39	−0.495910
$382$	7.13385e39i	0.678175i
$383$	9.14893e39i	0.835198i	0.908631	+	0.417599i	$0.137128\pi$
$383$	9.14893e39i	0.835198i	−0.908631	+	0.417599i	$0.862872\pi$
$384$	2.44855e39	0.214672
$385$	0	0
$386$	5.58076e39	0.451429
$387$	3.65501e39i	0.284033i
$388$	4.28656e39i	0.320049i
$389$	2.19075e40	1.57172	0.785858	−	0.618407i	$-0.212222\pi$
$389$	2.19075e40	1.57172	0.785858	+	0.618407i	$0.212222\pi$
$390$	0	0
$391$	1.19741e40	0.793417
$392$	− 2.03974e40i	− 1.29909i
$393$	8.68667e39i	0.531825i
$394$	−7.93323e39	−0.466937
$395$	0	0
$396$	−2.72983e39	−0.148546
$397$	− 2.07807e40i	− 1.08744i	−0.839265	−	0.543722i	$-0.817015\pi$
$397$	− 2.07807e40i	− 1.08744i	0.839265	−	0.543722i	$-0.182985\pi$
$398$	− 1.41605e40i	− 0.712676i
$399$	4.86163e38	0.0235343
$400$	0	0
$401$	−2.58688e40	−1.15888	−0.579441	−	0.815014i	$-0.696729\pi$
$401$	−2.58688e40	−1.15888	−0.579441	+	0.815014i	$0.696729\pi$
$402$	1.17292e38i	0.00505552i
$403$	− 1.68634e40i	− 0.699386i
$404$	−5.47046e39	−0.218330
$405$	0	0
$406$	−3.08373e40	−1.14005
$407$	− 1.11409e40i	− 0.396468i
$408$	− 8.82323e39i	− 0.302270i
$409$	−4.06410e40	−1.34046	−0.670229	−	0.742155i	$-0.733804\pi$
$409$	−4.06410e40	−1.34046	−0.670229	+	0.742155i	$0.733804\pi$
$410$	0	0
$411$	7.69121e39	0.235205
$412$	6.40225e39i	0.188550i
$413$	4.06997e40i	1.15443i
$414$	−2.59633e40	−0.709341
$415$	0	0
$416$	−5.51410e40	−1.39807
$417$	1.82577e40i	0.446002i
$418$	3.22876e38i	0.00759983i
$419$	6.77858e40	1.53752	0.768761	−	0.639536i	$-0.220874\pi$
$419$	6.77858e40	1.53752	0.768761	+	0.639536i	$0.220874\pi$
$420$	0	0
$421$	3.82000e40	0.804805	0.402403	−	0.915463i	$-0.368175\pi$
$421$	3.82000e40	0.804805	0.402403	+	0.915463i	$0.368175\pi$
$422$	1.96098e39i	0.0398226i
$423$	− 9.30467e39i	− 0.182148i
$424$	−1.65316e40	−0.311992
$425$	0	0
$426$	3.25045e40	0.570289
$427$	1.24364e41i	2.10407i
$428$	− 6.18632e39i	− 0.100938i
$429$	−2.00762e40	−0.315933
$430$	0	0
$431$	1.21642e41	1.78109	0.890547	−	0.454890i	$-0.150322\pi$
$431$	1.21642e41	1.78109	0.890547	+	0.454890i	$0.150322\pi$
$432$	1.07091e40i	0.151271i
$433$	3.18876e39i	0.0434570i	0.999764	+	0.0217285i	$0.00691694\pi$
$433$	3.18876e39i	0.0434570i	−0.999764	+	0.0217285i	$0.993083\pi$
$434$	−3.59704e40	−0.472993
$435$	0	0
$436$	5.93142e40	0.726303
$437$	− 3.63994e39i	− 0.0430162i
$438$	9.71131e39i	0.110772i
$439$	−7.39242e40	−0.813929	−0.406965	−	0.913444i	$-0.633413\pi$
$439$	−7.39242e40	−0.813929	−0.406965	+	0.913444i	$0.633413\pi$
$440$	0	0
$441$	−8.55785e40	−0.878145
$442$	5.46092e40i	0.541029i
$443$	2.28069e40i	0.218177i	0.994032	+	0.109088i	$0.0347931\pi$
$443$	2.28069e40i	0.218177i	−0.994032	+	0.109088i	$0.965207\pi$
$444$	3.25453e40	0.300644
$445$	0	0
$446$	−3.57466e39	−0.0307995
$447$	7.32024e40i	0.609198i
$448$	1.48075e41i	1.19035i
$449$	−6.27451e40	−0.487261	−0.243630	−	0.969868i	$-0.578338\pi$
$449$	−6.27451e40	−0.487261	−0.243630	+	0.969868i	$0.578338\pi$
$450$	0	0
$451$	2.74096e40	0.198686
$452$	6.70639e40i	0.469725i
$453$	3.22480e40i	0.218263i
$454$	5.71397e39	0.0373742
$455$	0	0
$456$	−2.68214e39	−0.0163880
$457$	2.37596e39i	0.0140326i	0.999975	+	0.00701629i	$0.00223337\pi$
$457$	2.37596e39i	0.0140326i	−0.999975	+	0.00701629i	$0.997767\pi$
$458$	− 6.33612e40i	− 0.361750i
$459$	−8.95054e40	−0.494029
$460$	0	0
$461$	−6.79165e40	−0.350438	−0.175219	−	0.984529i	$-0.556063\pi$
$461$	−6.79165e40	−0.350438	−0.175219	+	0.984529i	$0.556063\pi$
$462$	4.28236e40i	0.213665i
$463$	− 1.40330e41i	− 0.677090i	−0.940950	−	0.338545i	$-0.890065\pi$
$463$	− 1.40330e41i	− 0.677090i	0.940950	−	0.338545i	$-0.109935\pi$
$464$	3.93868e40	0.183790
$465$	0	0
$466$	−1.23181e40	−0.0537727
$467$	2.95535e41i	1.24795i	0.781444	+	0.623976i	$0.214484\pi$
$467$	2.95535e41i	1.24795i	−0.781444	+	0.623976i	$0.785516\pi$
$468$	1.40352e41i	0.573334i
$469$	5.21939e39	0.0206272
$470$	0	0
$471$	2.68214e41	0.992331
$472$	− 2.24538e41i	− 0.803877i
$473$	− 4.51361e40i	− 0.156378i
$474$	1.26467e41	0.424047
$475$	0	0
$476$	−1.38070e41	−0.433703
$477$	6.93593e40i	0.210897i
$478$	4.36239e41i	1.28408i
$479$	−3.59879e41	−1.02555	−0.512774	−	0.858524i	$-0.671382\pi$
$479$	−3.59879e41	−1.02555	−0.512774	+	0.858524i	$0.671382\pi$
$480$	0	0
$481$	−5.72802e41	−1.53023
$482$	− 4.90125e40i	− 0.126788i
$483$	− 4.82771e41i	− 1.20937i
$484$	−1.89864e41	−0.460616
$485$	0	0
$486$	3.07882e41	0.700684
$487$	− 8.64633e41i	− 1.90604i	−0.302901	−	0.953022i	$-0.597955\pi$
$487$	− 8.64633e41i	− 1.90604i	0.302901	−	0.953022i	$-0.402045\pi$
$488$	− 6.86107e41i	− 1.46516i
$489$	1.05855e41	0.218990
$490$	0	0
$491$	−8.25010e41	−1.60212	−0.801062	−	0.598582i	$-0.795731\pi$
$491$	−8.25010e41	−1.60212	−0.801062	+	0.598582i	$0.795731\pi$
$492$	8.00700e40i	0.150664i
$493$	3.29189e41i	0.600231i
$494$	1.66004e40	0.0293327
$495$	0	0
$496$	4.59431e40	0.0762526
$497$	− 1.44642e42i	− 2.32686i
$498$	8.01340e40i	0.124957i
$499$	4.70553e41	0.711295	0.355647	−	0.934620i	$-0.384260\pi$
$499$	4.70553e41	0.711295	0.355647	+	0.934620i	$0.384260\pi$
$500$	0	0
$501$	6.95065e41	0.987508
$502$	2.41212e41i	0.332270i
$503$	1.02731e41i	0.137214i	0.997644	+	0.0686068i	$0.0218554\pi$
$503$	1.02731e41i	0.137214i	−0.997644	+	0.0686068i	$0.978145\pi$
$504$	8.51327e41	1.10261
$505$	0	0
$506$	3.20624e41	0.390537
$507$	5.72665e41i	0.676515i
$508$	− 4.32425e41i	− 0.495477i
$509$	6.79468e41	0.755168	0.377584	−	0.925975i	$-0.376755\pi$
$509$	6.79468e41	0.755168	0.377584	+	0.925975i	$0.376755\pi$
$510$	0	0
$511$	4.32143e41	0.451964
$512$	− 3.18257e41i	− 0.322919i
$513$	2.72084e40i	0.0267845i
$514$	1.31606e42	1.25704
$515$	0	0
$516$	1.31853e41	0.118582
$517$	1.14904e41i	0.100284i
$518$	1.22181e42i	1.03489i
$519$	6.81073e41	0.559886
$520$	0	0
$521$	4.70689e41	0.364543	0.182272	−	0.983248i	$-0.441655\pi$
$521$	4.70689e41	0.364543	0.182272	+	0.983248i	$0.441655\pi$
$522$	− 7.13781e41i	− 0.536627i
$523$	− 1.48934e42i	− 1.08697i	−0.839419	−	0.543485i	$-0.817105\pi$
$523$	− 1.48934e42i	− 1.08697i	0.839419	−	0.543485i	$-0.182895\pi$
$524$	−7.49937e41	−0.531361
$525$	0	0
$526$	−1.76096e42	−1.17617
$527$	3.83986e41i	0.249030i
$528$	− 5.46963e40i	− 0.0344455i
$529$	−1.97937e42	−1.21050
$530$	0	0
$531$	−9.42065e41	−0.543395
$532$	4.19714e40i	0.0235138i
$533$	− 1.40924e42i	− 0.766857i
$534$	1.02151e42	0.539951
$535$	0	0
$536$	−2.87951e40	−0.0143636
$537$	− 3.51194e41i	− 0.170195i
$538$	9.61583e41i	0.452753i
$539$	1.05682e42	0.483475
$540$	0	0
$541$	2.37435e42	1.02562	0.512811	−	0.858502i	$-0.328604\pi$
$541$	2.37435e42	1.02562	0.512811	+	0.858502i	$0.328604\pi$
$542$	− 1.96413e40i	− 0.00824484i
$543$	1.62936e42i	0.664692i
$544$	1.25558e42	0.497809
$545$	0	0
$546$	2.20174e42	0.824670
$547$	− 3.75591e42i	− 1.36745i	−0.729740	−	0.683725i	$-0.760359\pi$
$547$	− 3.75591e42i	− 1.36745i	0.729740	−	0.683725i	$-0.239641\pi$
$548$	6.63996e41i	0.235000i
$549$	−2.87861e42	−0.990401
$550$	0	0
$551$	1.00069e41	0.0325424
$552$	2.66342e42i	0.842140i
$553$	− 5.62766e42i	− 1.73017i
$554$	−1.27243e42	−0.380394
$555$	0	0
$556$	−1.57622e42	−0.445613
$557$	5.38624e42i	1.48092i	0.672103	+	0.740458i	$0.265391\pi$
$557$	5.38624e42i	1.48092i	−0.672103	+	0.740458i	$0.734609\pi$
$558$	− 8.32597e41i	− 0.222641i
$559$	−2.32063e42	−0.603565
$560$	0	0
$561$	4.57144e41	0.112494
$562$	2.22986e42i	0.533784i
$563$	2.93646e42i	0.683823i	0.939732	+	0.341912i	$0.111074\pi$
$563$	2.93646e42i	0.683823i	−0.939732	+	0.341912i	$0.888926\pi$
$564$	−3.35663e41	−0.0760461
$565$	0	0
$566$	1.73061e41	0.0371145
$567$	− 1.45562e42i	− 0.303747i
$568$	7.97981e42i	1.62029i
$569$	−1.22480e42	−0.242005	−0.121002	−	0.992652i	$-0.538611\pi$
$569$	−1.22480e42	−0.242005	−0.121002	+	0.992652i	$0.538611\pi$
$570$	0	0
$571$	−8.00625e42	−1.49820	−0.749099	−	0.662458i	$-0.769513\pi$
$571$	−8.00625e42	−1.49820	−0.749099	+	0.662458i	$0.769513\pi$
$572$	− 1.73322e42i	− 0.315657i
$573$	− 3.07040e42i	− 0.544249i
$574$	−3.00598e42	−0.518624
$575$	0	0
$576$	−3.42746e42	−0.560304
$577$	5.67748e42i	0.903505i	0.892143	+	0.451753i	$0.149201\pi$
$577$	5.67748e42i	0.903505i	−0.892143	+	0.451753i	$0.850799\pi$
$578$	3.12294e42i	0.483818i
$579$	−2.40195e42	−0.362281
$580$	0	0
$581$	3.56588e42	0.509843
$582$	1.55649e42i	0.216690i
$583$	− 8.56525e41i	− 0.116112i
$584$	−2.38411e42	−0.314722
$585$	0	0
$586$	1.83201e41	0.0229358
$587$	− 3.58214e41i	− 0.0436770i	−0.999762	−	0.0218385i	$-0.993048\pi$
$587$	− 3.58214e41i	− 0.0436770i	0.999762	−	0.0218385i	$-0.00695196\pi$
$588$	3.08721e42i	0.366622i
$589$	1.16726e41	0.0135015
$590$	0	0
$591$	3.41445e42	0.374726
$592$	− 1.56056e42i	− 0.166838i
$593$	1.84785e43i	1.92450i	0.272164	+	0.962251i	$0.412261\pi$
$593$	1.84785e43i	1.92450i	−0.272164	+	0.962251i	$0.587739\pi$
$594$	−2.39664e42	−0.243172
$595$	0	0
$596$	−6.31970e42	−0.608666
$597$	6.09467e42i	0.571937i
$598$	− 1.64846e43i	− 1.50734i
$599$	3.08643e42	0.275005	0.137503	−	0.990501i	$-0.456092\pi$
$599$	3.08643e42	0.275005	0.137503	+	0.990501i	$0.456092\pi$
$600$	0	0
$601$	2.05195e43	1.73625	0.868125	−	0.496346i	$-0.165325\pi$
$601$	2.05195e43	1.73625	0.868125	+	0.496346i	$0.165325\pi$
$602$	4.95003e42i	0.408189i
$603$	1.20812e41i	0.00970937i
$604$	−2.78403e42	−0.218073
$605$	0	0
$606$	−1.98637e42	−0.147821
$607$	2.07151e43i	1.50267i	0.659923	+	0.751333i	$0.270589\pi$
$607$	2.07151e43i	1.50267i	−0.659923	+	0.751333i	$0.729411\pi$
$608$	− 3.81679e41i	− 0.0269894i
$609$	1.32723e43	0.914909
$610$	0	0
$611$	5.90771e42	0.387062
$612$	− 3.19587e42i	− 0.204147i
$613$	− 6.35024e42i	− 0.395506i	−0.980252	−	0.197753i	$-0.936636\pi$
$613$	− 6.35024e42i	− 0.395506i	0.980252	−	0.197753i	$-0.0633643\pi$
$614$	−1.78955e43	−1.08676
$615$	0	0
$616$	−1.05131e43	−0.607059
$617$	− 1.92676e43i	− 1.08495i	−0.840073	−	0.542473i	$-0.817488\pi$
$617$	− 1.92676e43i	− 1.08495i	0.840073	−	0.542473i	$-0.182512\pi$
$618$	2.32471e42i	0.127658i
$619$	−7.41921e42	−0.397331	−0.198666	−	0.980067i	$-0.563661\pi$
$619$	−7.41921e42	−0.397331	−0.198666	+	0.980067i	$0.563661\pi$
$620$	0	0
$621$	2.70185e43	1.37639
$622$	− 8.55798e42i	− 0.425226i
$623$	− 4.54563e43i	− 2.20308i
$624$	−2.81217e42	−0.132947
$625$	0	0
$626$	−2.49626e43	−1.12302
$627$	− 1.38965e41i	− 0.00609901i
$628$	2.31554e43i	0.991465i
$629$	1.30429e43	0.544867
$630$	0	0
$631$	−1.64967e43	−0.656058	−0.328029	−	0.944668i	$-0.606384\pi$
$631$	−1.64967e43	−0.656058	−0.328029	+	0.944668i	$0.606384\pi$
$632$	3.10475e43i	1.20479i
$633$	− 8.44001e41i	− 0.0319584i
$634$	1.05002e43	0.387983
$635$	0	0
$636$	2.50211e42	0.0880485
$637$	− 5.43354e43i	− 1.86604i
$638$	8.81455e42i	0.295447i
$639$	3.34798e43	1.09527
$640$	0	0
$641$	1.02463e43	0.319349	0.159675	−	0.987170i	$-0.448955\pi$
$641$	1.02463e43	0.319349	0.159675	+	0.987170i	$0.448955\pi$
$642$	− 2.24631e42i	− 0.0683403i
$643$	1.32606e43i	0.393817i	0.980422	+	0.196908i	$0.0630901\pi$
$643$	1.32606e43i	0.393817i	−0.980422	+	0.196908i	$0.936910\pi$
$644$	4.16785e43	1.20832
$645$	0	0
$646$	−3.77998e41	−0.0104445
$647$	− 4.58618e43i	− 1.23718i	−0.785712	−	0.618592i	$-0.787703\pi$
$647$	− 4.58618e43i	− 1.23718i	0.785712	−	0.618592i	$-0.212297\pi$
$648$	8.03060e42i	0.211512i
$649$	1.16337e43	0.299174
$650$	0	0
$651$	1.54816e43	0.379586
$652$	9.13868e42i	0.218799i
$653$	− 1.96584e43i	− 0.459614i	−0.973236	−	0.229807i	$-0.926190\pi$
$653$	− 1.96584e43i	− 0.459614i	0.973236	−	0.229807i	$-0.0738095\pi$
$654$	2.15375e43	0.491746
$655$	0	0
$656$	3.83938e42	0.0836088
$657$	1.00027e43i	0.212742i
$658$	− 1.26014e43i	− 0.261769i
$659$	−4.60611e43	−0.934568	−0.467284	−	0.884107i	$-0.654767\pi$
$659$	−4.60611e43	−0.934568	−0.467284	+	0.884107i	$0.654767\pi$
$660$	0	0
$661$	−6.03515e43	−1.16833	−0.584165	−	0.811635i	$-0.698578\pi$
$661$	−6.03515e43	−1.16833	−0.584165	+	0.811635i	$0.698578\pi$
$662$	− 2.60354e43i	− 0.492341i
$663$	− 2.35037e43i	− 0.434187i
$664$	−1.96728e43	−0.355026
$665$	0	0
$666$	−2.82810e43	−0.487129
$667$	− 9.93707e43i	− 1.67228i
$668$	6.00063e43i	0.986646i
$669$	1.53853e42	0.0247172
$670$	0	0
$671$	3.55482e43	0.545279
$672$	− 5.06227e43i	− 0.758790i
$673$	− 5.70208e43i	− 0.835218i	−0.908627	−	0.417609i	$-0.862868\pi$
$673$	− 5.70208e43i	− 0.835218i	0.908627	−	0.417609i	$-0.137132\pi$
$674$	3.57829e43	0.512208
$675$	0	0
$676$	−4.94392e43	−0.675924
$677$	1.60365e43i	0.214282i	0.994244	+	0.107141i	$0.0341696\pi$
$677$	1.60365e43i	0.214282i	−0.994244	+	0.107141i	$0.965830\pi$
$678$	2.43515e43i	0.318028i
$679$	6.92621e43	0.884126
$680$	0	0
$681$	−2.45928e42	−0.0299935
$682$	1.02818e43i	0.122578i
$683$	− 6.08600e43i	− 0.709269i	−0.935005	−	0.354634i	$-0.884605\pi$
$683$	− 6.08600e43i	− 0.709269i	0.935005	−	0.354634i	$-0.115395\pi$
$684$	−9.71499e41	−0.0110681
$685$	0	0
$686$	−2.28141e43	−0.248416
$687$	2.72705e43i	0.290311i
$688$	− 6.32240e42i	− 0.0658054i
$689$	−4.40375e43	−0.448152
$690$	0	0
$691$	1.43014e44	1.39146	0.695729	−	0.718304i	$-0.255082\pi$
$691$	1.43014e44	1.39146	0.695729	+	0.718304i	$0.255082\pi$
$692$	5.87983e43i	0.559397i
$693$	4.41085e43i	0.410353i
$694$	−1.17538e44	−1.06931
$695$	0	0
$696$	−7.32225e43	−0.637091
$697$	3.20890e43i	0.273054i
$698$	− 2.40744e43i	− 0.200354i
$699$	5.30169e42	0.0431537
$700$	0	0
$701$	−5.20421e43	−0.405252	−0.202626	−	0.979256i	$-0.564948\pi$
$701$	−5.20421e43	−0.405252	−0.202626	+	0.979256i	$0.564948\pi$
$702$	1.23222e44i	0.938559i
$703$	− 3.96487e42i	− 0.0295407i
$704$	4.23260e43	0.308483
$705$	0	0
$706$	7.78298e43	0.542842
$707$	8.83916e43i	0.603129i
$708$	3.39847e43i	0.226865i
$709$	−2.25028e44	−1.46967	−0.734836	−	0.678245i	$-0.762741\pi$
$709$	−2.25028e44	−1.46967	−0.734836	+	0.678245i	$0.762741\pi$
$710$	0	0
$711$	1.30262e44	0.814401
$712$	2.50780e44i	1.53410i
$713$	− 1.15912e44i	− 0.693810i
$714$	−5.01345e43	−0.293640
$715$	0	0
$716$	3.03193e43	0.170046
$717$	− 1.87756e44i	− 1.03050i
$718$	1.92761e44i	1.03536i
$719$	2.22431e44	1.16922	0.584611	−	0.811314i	$-0.301247\pi$
$719$	2.22431e44	1.16922	0.584611	+	0.811314i	$0.301247\pi$
$720$	0	0
$721$	1.03447e44	0.520862
$722$	− 1.37153e44i	− 0.675895i
$723$	2.10949e43i	0.101750i
$724$	−1.40666e44	−0.664112
$725$	0	0
$726$	−6.89412e43	−0.311861
$727$	4.26635e44i	1.88918i	0.328251	+	0.944591i	$0.393541\pi$
$727$	4.26635e44i	1.88918i	−0.328251	+	0.944591i	$0.606459\pi$
$728$	5.40524e44i	2.34303i
$729$	−8.47399e43	−0.359593
$730$	0	0
$731$	5.28418e43	0.214911
$732$	1.03845e44i	0.413488i
$733$	− 2.38496e44i	− 0.929758i	−0.885374	−	0.464879i	$-0.846098\pi$
$733$	− 2.38496e44i	− 0.929758i	0.885374	−	0.464879i	$-0.153902\pi$
$734$	1.77665e44	0.678130
$735$	0	0
$736$	−3.79016e44	−1.38692
$737$	− 1.49192e42i	− 0.00534562i
$738$	− 6.95786e43i	− 0.244119i
$739$	−3.50761e44	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$739$	−3.50761e44	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$740$	0	0
$741$	−7.14479e42	−0.0235400
$742$	9.39342e43i	0.303084i
$743$	− 7.53875e43i	− 0.238217i	−0.992881	−	0.119108i	$-0.961996\pi$
$743$	− 7.53875e43i	− 0.238217i	0.992881	−	0.119108i	$-0.0380036\pi$
$744$	−8.54112e43	−0.264323
$745$	0	0
$746$	2.52630e44	0.749953
$747$	8.25384e43i	0.239986i
$748$	3.94661e43i	0.112396i
$749$	−9.99584e43	−0.278838
$750$	0	0
$751$	6.25728e44	1.67481	0.837407	−	0.546580i	$-0.184071\pi$
$751$	6.25728e44	1.67481	0.837407	+	0.546580i	$0.184071\pi$
$752$	1.60951e43i	0.0422006i
$753$	− 1.03817e44i	− 0.266654i
$754$	4.53193e44	1.14032
$755$	0	0
$756$	−3.11545e44	−0.752372
$757$	2.09917e43i	0.0496663i	0.999692	+	0.0248332i	$0.00790545\pi$
$757$	2.09917e43i	0.0496663i	−0.999692	+	0.0248332i	$0.992095\pi$
$758$	2.89730e44i	0.671615i
$759$	−1.37996e44	−0.313414
$760$	0	0
$761$	−3.45290e43	−0.0752873	−0.0376436	−	0.999291i	$-0.511985\pi$
$761$	−3.45290e43	−0.0752873	−0.0376436	+	0.999291i	$0.511985\pi$
$762$	− 1.57017e44i	− 0.335464i
$763$	− 9.58397e44i	− 2.00639i
$764$	2.65073e44	0.543774
$765$	0	0
$766$	−2.86800e44	−0.564979
$767$	− 5.98135e44i	− 1.15470i
$768$	3.04715e44i	0.576493i
$769$	−7.01102e44	−1.29994	−0.649970	−	0.759960i	$-0.725218\pi$
$769$	−7.01102e44	−1.29994	−0.649970	+	0.759960i	$0.725218\pi$
$770$	0	0
$771$	−5.66430e44	−1.00880
$772$	− 2.07364e44i	− 0.361965i
$773$	− 2.53762e44i	− 0.434154i	−0.976154	−	0.217077i	$-0.930348\pi$
$773$	− 2.53762e44i	− 0.434154i	0.976154	−	0.217077i	$-0.0696523\pi$
$774$	−1.14577e44	−0.192137
$775$	0	0
$776$	−3.82115e44	−0.615655
$777$	− 5.25867e44i	− 0.830519i
$778$	6.86753e44i	1.06321i
$779$	9.75461e42	0.0148040
$780$	0	0
$781$	−4.13445e44	−0.603014
$782$	3.75361e44i	0.536716i
$783$	7.42791e44i	1.04126i
$784$	1.48033e44	0.203451
$785$	0	0
$786$	−2.72309e44	−0.359759
$787$	− 5.16912e44i	− 0.669589i	−0.942291	−	0.334795i	$-0.891333\pi$
$787$	− 5.16912e44i	− 0.669589i	0.942291	−	0.334795i	$-0.108667\pi$
$788$	2.94775e44i	0.374399i
$789$	7.57914e44	0.943901
$790$	0	0
$791$	1.08362e45	1.29760
$792$	− 2.43344e44i	− 0.285746i
$793$	− 1.82768e45i	− 2.10458i
$794$	6.51430e44	0.735614
$795$	0	0
$796$	−5.26164e44	−0.571437
$797$	2.24914e44i	0.239559i	0.992800	+	0.119780i	$0.0382188\pi$
$797$	2.24914e44i	0.239559i	−0.992800	+	0.119780i	$0.961781\pi$
$798$	1.52402e43i	0.0159201i
$799$	−1.34521e44	−0.137821
$800$	0	0
$801$	1.05216e45	1.03700
$802$	− 8.10933e44i	− 0.783939i
$803$	− 1.23524e44i	− 0.117128i
$804$	4.35824e42	0.00405362
$805$	0	0
$806$	5.28632e44	0.473108
$807$	− 4.13863e44i	− 0.363343i
$808$	− 4.87652e44i	− 0.419985i
$809$	1.09436e45	0.924612	0.462306	−	0.886720i	$-0.347022\pi$
$809$	1.09436e45	0.924612	0.462306	+	0.886720i	$0.347022\pi$
$810$	0	0
$811$	−1.65483e44	−0.134564	−0.0672821	−	0.997734i	$-0.521433\pi$
$811$	−1.65483e44	−0.134564	−0.0672821	+	0.997734i	$0.521433\pi$
$812$	1.14582e45i	0.914110i
$813$	8.45359e42i	0.00661664i
$814$	3.49245e44	0.268196
$815$	0	0
$816$	6.40342e43	0.0473385
$817$	− 1.60632e43i	− 0.0116517i
$818$	− 1.27401e45i	− 0.906768i
$819$	2.26780e45	1.58382
$820$	0	0
$821$	1.30182e45	0.875454	0.437727	−	0.899108i	$-0.355784\pi$
$821$	1.30182e45	0.875454	0.437727	+	0.899108i	$0.355784\pi$
$822$	2.41103e44i	0.159107i
$823$	− 8.40972e43i	− 0.0544608i	−0.999629	−	0.0272304i	$-0.991331\pi$
$823$	− 8.40972e43i	− 0.0544608i	0.999629	−	0.0272304i	$-0.00866878\pi$
$824$	−5.70713e44	−0.362699
$825$	0	0
$826$	−1.27585e45	−0.780924
$827$	− 2.14145e45i	− 1.28639i	−0.765702	−	0.643196i	$-0.777608\pi$
$827$	− 2.14145e45i	− 1.28639i	0.765702	−	0.643196i	$-0.222392\pi$
$828$	9.64721e44i	0.568763i
$829$	8.75462e44	0.506573	0.253286	−	0.967391i	$-0.418488\pi$
$829$	8.75462e44	0.506573	0.253286	+	0.967391i	$0.418488\pi$
$830$	0	0
$831$	5.47653e44	0.305274
$832$	− 2.17616e45i	− 1.19063i
$833$	1.23724e45i	0.664440i
$834$	−5.72339e44	−0.301703
$835$	0	0
$836$	1.19971e43	0.00609369
$837$	8.66436e44i	0.432008i
$838$	2.12494e45i	1.04007i
$839$	−8.96946e44	−0.430979	−0.215489	−	0.976506i	$-0.569135\pi$
$839$	−8.96946e44	−0.430979	−0.215489	+	0.976506i	$0.569135\pi$
$840$	0	0
$841$	5.72465e44	0.265101
$842$	1.19749e45i	0.544420i
$843$	− 9.59728e44i	− 0.428372i
$844$	7.28641e43	0.0319305
$845$	0	0
$846$	2.91682e44	0.123216
$847$	3.06781e45i	1.27244i
$848$	− 1.19977e44i	− 0.0488611i
$849$	−7.44850e43	−0.0297851
$850$	0	0
$851$	−3.93720e45	−1.51803
$852$	− 1.20777e45i	− 0.457269i
$853$	− 3.47906e45i	− 1.29346i	−0.762721	−	0.646728i	$-0.776137\pi$
$853$	− 3.47906e45i	− 1.29346i	0.762721	−	0.646728i	$-0.223863\pi$
$854$	−3.89853e45	−1.42333
$855$	0	0
$856$	5.51465e44	0.194167
$857$	− 7.25970e44i	− 0.251024i	−0.992092	−	0.125512i	$-0.959943\pi$
$857$	− 7.25970e44i	− 0.251024i	0.992092	−	0.125512i	$-0.0400574\pi$
$858$	− 6.29348e44i	− 0.213716i
$859$	−4.44826e45	−1.48353	−0.741765	−	0.670660i	$-0.766011\pi$
$859$	−4.44826e45	−1.48353	−0.741765	+	0.670660i	$0.766011\pi$
$860$	0	0
$861$	1.29377e45	0.416206
$862$	3.81323e45i	1.20484i
$863$	2.69165e45i	0.835318i	0.908604	+	0.417659i	$0.137149\pi$
$863$	2.69165e45i	0.835318i	−0.908604	+	0.417659i	$0.862851\pi$
$864$	2.83313e45	0.863581
$865$	0	0
$866$	−9.99609e43	−0.0293970
$867$	− 1.34411e45i	− 0.388273i
$868$	1.33656e45i	0.379255i
$869$	−1.60862e45	−0.448379
$870$	0	0
$871$	−7.67056e43	−0.0206322
$872$	5.28742e45i	1.39714i
$873$	1.60319e45i	0.416164i
$874$	1.14104e44	0.0290988
$875$	0	0
$876$	3.60844e44	0.0888189
$877$	5.87091e44i	0.141975i	0.997477	+	0.0709875i	$0.0226151\pi$
$877$	5.87091e44i	0.141975i	−0.997477	+	0.0709875i	$0.977385\pi$
$878$	− 2.31737e45i	− 0.550592i
$879$	−7.88492e43	−0.0184064
$880$	0	0
$881$	−5.61916e45	−1.26632	−0.633162	−	0.774020i	$-0.718243\pi$
$881$	−5.61916e45	−1.26632	−0.633162	+	0.774020i	$0.718243\pi$
$882$	− 2.68270e45i	− 0.594031i
$883$	3.14941e45i	0.685232i	0.939476	+	0.342616i	$0.111313\pi$
$883$	3.14941e45i	0.685232i	−0.939476	+	0.342616i	$0.888687\pi$
$884$	2.02912e45	0.433808
$885$	0	0
$886$	−7.14947e44	−0.147588
$887$	− 3.05461e45i	− 0.619641i	−0.950795	−	0.309821i	$-0.899731\pi$
$887$	− 3.05461e45i	− 0.619641i	0.950795	−	0.309821i	$-0.100269\pi$
$888$	2.90118e45i	0.578327i
$889$	−6.98711e45	−1.36874
$890$	0	0
$891$	−4.16077e44	−0.0787171
$892$	1.32824e44i	0.0246956i
$893$	4.08924e43i	0.00747215i
$894$	−2.29474e45	−0.412099
$895$	0	0
$896$	3.41560e45	0.592506
$897$	7.09494e45i	1.20967i
$898$	− 1.96692e45i	− 0.329613i
$899$	3.18664e45	0.524877
$900$	0	0
$901$	1.00275e45	0.159573
$902$	8.59233e44i	0.134403i
$903$	− 2.13048e45i	− 0.327580i
$904$	−5.97826e45	−0.903574
$905$	0	0
$906$	−1.01091e45	−0.147647
$907$	− 1.69836e44i	− 0.0243847i	−0.999926	−	0.0121924i	$-0.996119\pi$
$907$	− 1.69836e44i	− 0.0243847i	0.999926	−	0.0121924i	$-0.00388104\pi$
$908$	− 2.12314e44i	− 0.0299673i
$909$	−2.04597e45	−0.283896
$910$	0	0
$911$	1.24574e46	1.67067	0.835336	−	0.549739i	$-0.185273\pi$
$911$	1.24574e46	1.67067	0.835336	+	0.549739i	$0.185273\pi$
$912$	− 1.94655e43i	− 0.00256652i
$913$	− 1.01927e45i	− 0.132128i
$914$	−7.44812e43	−0.00949250
$915$	0	0
$916$	−2.35432e45	−0.290058
$917$	1.21175e46i	1.46787i
$918$	− 2.80580e45i	− 0.334192i
$919$	1.08191e46	1.26707	0.633535	−	0.773714i	$-0.281603\pi$
$919$	1.08191e46	1.26707	0.633535	+	0.773714i	$0.281603\pi$
$920$	0	0
$921$	7.70217e45	0.872145
$922$	− 2.12904e45i	− 0.237058i
$923$	2.12570e46i	2.32742i
$924$	1.59120e45	0.171320
$925$	0	0
$926$	4.39906e45	0.458025
$927$	2.39447e45i	0.245173i
$928$	− 1.04199e46i	− 1.04923i
$929$	9.79872e45	0.970344	0.485172	−	0.874419i	$-0.338757\pi$
$929$	9.79872e45	0.970344	0.485172	+	0.874419i	$0.338757\pi$
$930$	0	0
$931$	3.76103e44	0.0360235
$932$	4.57704e44i	0.0431160i
$933$	3.68334e45i	0.341253i
$934$	−9.26440e45	−0.844191
$935$	0	0
$936$	−1.25113e46	−1.10288
$937$	− 1.01455e46i	− 0.879650i	−0.898083	−	0.439825i	$-0.855040\pi$
$937$	− 1.01455e46i	− 0.879650i	0.898083	−	0.439825i	$-0.144960\pi$
$938$	1.63617e44i	0.0139535i
$939$	1.07439e46	0.901246
$940$	0	0
$941$	−1.48680e46	−1.20674	−0.603370	−	0.797461i	$-0.706176\pi$
$941$	−1.48680e46	−1.20674	−0.603370	+	0.797461i	$0.706176\pi$
$942$	8.40792e45i	0.671274i
$943$	− 9.68655e45i	− 0.760743i
$944$	1.62958e45	0.125895
$945$	0	0
$946$	1.41492e45	0.105784
$947$	− 2.27265e46i	− 1.67151i	−0.549104	−	0.835754i	$-0.685031\pi$
$947$	− 2.27265e46i	− 1.67151i	0.549104	−	0.835754i	$-0.314969\pi$
$948$	− 4.69915e45i	− 0.340009i
$949$	−6.35090e45	−0.452073
$950$	0	0
$951$	−4.51925e45	−0.311364
$952$	− 1.23079e46i	− 0.834282i
$953$	− 7.58661e45i	− 0.505950i	−0.967473	−	0.252975i	$-0.918591\pi$
$953$	− 7.58661e45i	− 0.505950i	0.967473	−	0.252975i	$-0.0814091\pi$
$954$	−2.17427e45	−0.142664
$955$	0	0
$956$	1.62093e46	1.02960
$957$	− 3.79377e45i	− 0.237102i
$958$	− 1.12814e46i	− 0.693744i
$959$	1.07288e46	0.649178
$960$	0	0
$961$	−1.33521e46	−0.782234
$962$	− 1.79561e46i	− 1.03514i
$963$	− 2.31371e45i	− 0.131251i
$964$	−1.82116e45	−0.101661
$965$	0	0
$966$	1.51338e46	0.818095
$967$	3.35350e46i	1.78397i	0.452064	+	0.891986i	$0.350688\pi$
$967$	3.35350e46i	1.78397i	−0.452064	+	0.891986i	$0.649312\pi$
$968$	− 1.69250e46i	− 0.886053i
$969$	1.62690e44	0.00838188
$970$	0	0
$971$	−2.14498e46	−1.07035	−0.535175	−	0.844741i	$-0.679754\pi$
$971$	−2.14498e46	−1.07035	−0.535175	+	0.844741i	$0.679754\pi$
$972$	− 1.14400e46i	− 0.561822i
$973$	2.54685e46i	1.23099i
$974$	2.71044e46	1.28937
$975$	0	0
$976$	4.97939e45	0.229458
$977$	− 1.98478e46i	− 0.900215i	−0.892974	−	0.450107i	$-0.851386\pi$
$977$	− 1.98478e46i	− 0.900215i	0.892974	−	0.450107i	$-0.148614\pi$
$978$	3.31834e45i	0.148139i
$979$	−1.29933e46	−0.570935
$980$	0	0
$981$	2.21837e46	0.944420
$982$	− 2.58623e46i	− 1.08377i
$983$	− 1.53482e46i	− 0.633107i	−0.948575	−	0.316554i	$-0.897474\pi$
$983$	− 1.53482e46i	− 0.633107i	0.948575	−	0.316554i	$-0.102526\pi$
$984$	−7.13765e45	−0.289822
$985$	0	0
$986$	−1.03194e46	−0.406033
$987$	5.42363e45i	0.210075i
$988$	− 6.16823e44i	− 0.0235195i
$989$	−1.59511e46	−0.598753
$990$	0	0
$991$	−8.58630e45	−0.312367	−0.156183	−	0.987728i	$-0.549919\pi$
$991$	−8.58630e45	−0.312367	−0.156183	+	0.987728i	$0.549919\pi$
$992$	− 1.21544e46i	− 0.435313i
$993$	1.12056e46i	0.395113i
$994$	4.53421e46	1.57403
$995$	0	0
$996$	2.97754e45	0.100193
$997$	− 3.45614e46i	− 1.14503i	−0.819895	−	0.572514i	$-0.805968\pi$
$997$	− 3.45614e46i	− 1.14503i	0.819895	−	0.572514i	$-0.194032\pi$
$998$	1.47508e46i	0.481164i
$999$	2.94304e46	0.945216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.32.b.a.24.3		4
5.2	odd	4		1.32.a.a.1.1	✓	2
5.3	odd	4		25.32.a.a.1.2		2
5.4	even	2	inner	25.32.b.a.24.2		4
15.2	even	4		9.32.a.a.1.2		2
20.7	even	4		16.32.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.1	✓	2	5.2	odd	4
9.32.a.a.1.2		2	15.2	even	4
16.32.a.b.1.2		2	20.7	even	4
25.32.a.a.1.2		2	5.3	odd	4
25.32.b.a.24.2		4	5.4	even	2	inner
25.32.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:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+31347.9i q^{2} -1.34921e7i q^{3} +1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13i q^{7} +1.03833e14i q^{8} +4.35638e14 q^{9} +O(q^{10})\)	\(q+31347.9i q^{2} -1.34921e7i q^{3} +1.16479e9 q^{4} +4.22947e11 q^{6} -1.88207e13i q^{7} +1.03833e14i q^{8} +4.35638e14 q^{9} -5.37973e15 q^{11} -1.57155e16i q^{12} +2.76595e17i q^{13} +5.89989e17 q^{14} -7.53562e17 q^{16} -6.29817e18i q^{17} +1.36563e19i q^{18} -1.91455e18 q^{19} -2.53930e20 q^{21} -1.68643e20i q^{22} +1.90120e21i q^{23} +1.40092e21 q^{24} -8.67065e21 q^{26} -1.42113e22i q^{27} -2.19223e22i q^{28} -5.22675e22 q^{29} -6.09679e22 q^{31} +1.99357e23i q^{32} +7.25837e22i q^{33} +1.97434e23 q^{34} +5.07428e23 q^{36} +2.07091e24i q^{37} -6.00172e22i q^{38} +3.73183e24 q^{39} -5.09498e24 q^{41} -7.96017e24i q^{42} +8.39002e24i q^{43} -6.26628e24 q^{44} -5.95984e25 q^{46} -2.13587e25i q^{47} +1.01671e25i q^{48} -1.96444e26 q^{49} -8.49753e25 q^{51} +3.22176e26i q^{52} +1.59213e26i q^{53} +4.45495e26 q^{54} +1.95421e27 q^{56} +2.58313e25i q^{57} -1.63847e27i q^{58} -2.16250e27 q^{59} -6.60780e27 q^{61} -1.91122e27i q^{62} -8.19901e27i q^{63} -7.86767e27 q^{64} -2.27534e27 q^{66} +2.77322e26i q^{67} -7.33607e27i q^{68} +2.56510e28 q^{69} +7.68524e28 q^{71} +4.52335e28i q^{72} +2.29610e28i q^{73} -6.49186e28 q^{74} -2.23006e27 q^{76} +1.01250e29i q^{77} +1.16985e29i q^{78} +2.99014e29 q^{79} +7.73416e28 q^{81} -1.59717e29i q^{82} +1.89466e29i q^{83} -2.95777e29 q^{84} -2.63009e29 q^{86} +7.05196e29i q^{87} -5.58593e29i q^{88} +2.41523e30 q^{89} +5.20571e30 q^{91} +2.21450e30i q^{92} +8.22583e29i q^{93} +6.69551e29 q^{94} +2.68973e30 q^{96} +3.68010e30i q^{97} -6.15810e30i q^{98} -2.34361e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3545068672 q^{4} + 5246334992448 q^{6} + 202532912607852 q^{9}+O(q^{10}) \) 4 * q - 3545068672 * q^4 + 5246334992448 * q^6 + 202532912607852 * q^9	\( 4 q - 3545068672 q^{4} + 5246334992448 q^{6} + 202532912607852 q^{9} - 15\!\cdots\!52 q^{11}+ \cdots - 30\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 3545068672 * q^4 + 5246334992448 * q^6 + 202532912607852 * q^9 - 15564707490237552 * q^11 - 451089927690482304 * q^14 - 6090425827369803776 * q^16 + 24741126656044328080 * q^19 + 197909914832142323328 * q^21 - 673828082468523970560 * q^24 - 46133361333488646558432 * q^26 - 257152288434434111614680 * q^29 + 251467055035923677587328 * q^31 - 1163413819142586057669984 * q^34 + 2979173497636398827009664 * q^36 + 19922108328822727136569824 * q^39 + 17449848671325851681342568 * q^41 + 1582016741746664622644736 * q^44 - 119746022890551201018179712 * q^46 - 338938588744640405060814372 * q^49 + 504324809479940640170760288 * q^51 + 2137644543374748380140548480 * q^54 + 5196710795499630344863457280 * q^56 + 397446527095531027981493040 * q^59 - 24112436402226008722315312552 * q^61 + 14976826736528117095355383808 * q^64 - 15123281166884922728531629824 * q^66 + 51539712572788652156989152384 * q^69 + 111569153250069315025756574688 * q^71 - 306266327264976756969588598944 * q^74 - 88380299399878717804948963840 * q^76 + 238328382186599409928425421120 * q^79 - 797813845293782539298125268316 * q^81 - 2664633299839703589778678370304 * q^84 - 4346284964445676845665854039872 * q^86 + 4308829228493340583205443791960 * q^89 + 5793562736137806139912099018048 * q^91 - 9227616502805116863050228500224 * q^94 - 12168740865339213432737429716992 * q^96 - 3080492615488189978915462170576 * q^99

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