LMFDB - Embedded newform 25.32.b.a.24.4

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			24.4
Root			$2139.16i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.32.b.a.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+71307.9i q^{2} -3.08552e7i q^{3} -2.93733e9 q^{4} +2.20022e12 q^{6} +1.14368e13i q^{7} -5.63222e13i q^{8} -3.34371e14 q^{9} +O(q^{10})$	\(q+71307.9i q^{2} -3.08552e7i q^{3} -2.93733e9 q^{4} +2.20022e12 q^{6} +1.14368e13i q^{7} -5.63222e13i q^{8} -3.34371e14 q^{9} -2.40262e15 q^{11} +9.06319e16i q^{12} +2.01886e17i q^{13} -8.15534e17 q^{14} -2.29165e18 q^{16} +1.09264e19i q^{17} -2.38433e19i q^{18} +1.42851e19 q^{19} +3.52885e20 q^{21} -1.71326e20i q^{22} +3.85062e18i q^{23} -1.73783e21 q^{24} -1.43960e22 q^{26} -8.74135e21i q^{27} -3.35937e22i q^{28} -7.63087e22 q^{29} +1.86701e23 q^{31} -2.84364e23i q^{32} +7.41334e22i q^{33} -7.79141e23 q^{34} +9.82158e23 q^{36} +1.23709e24i q^{37} +1.01864e24i q^{38} +6.22922e24 q^{39} +1.38199e25 q^{41} +2.51635e25i q^{42} +2.67871e25i q^{43} +7.05729e24 q^{44} -2.74580e23 q^{46} +7.40922e25i q^{47} +7.07094e25i q^{48} +2.69748e25 q^{49} +3.37138e26 q^{51} -5.93004e26i q^{52} -3.56092e25i q^{53} +6.23327e26 q^{54} +6.44146e26 q^{56} -4.40770e26i q^{57} -5.44141e27i q^{58} +2.36122e27 q^{59} -5.44842e27 q^{61} +1.33133e28i q^{62} -3.82414e27i q^{63} +1.53561e28 q^{64} -5.28630e27 q^{66} -9.41082e27i q^{67} -3.20945e28i q^{68} +1.18812e26 q^{69} -2.10678e28 q^{71} +1.88325e28i q^{72} -3.92731e28i q^{73} -8.82146e28 q^{74} -4.19601e28 q^{76} -2.74783e28i q^{77} +4.44193e29i q^{78} -1.79850e29 q^{79} -4.76249e29 q^{81} +9.85468e29i q^{82} +4.54329e29i q^{83} -1.03654e30 q^{84} -1.91013e30 q^{86} +2.35452e30i q^{87} +1.35321e29i q^{88} -2.60812e29 q^{89} -2.30893e30 q^{91} -1.13106e28i q^{92} -5.76072e30i q^{93} -5.28336e30 q^{94} -8.77410e30 q^{96} -5.38067e30i q^{97} +1.92352e30i q^{98} +8.03368e29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	71307.9i	1.53877i	0.638788	+	0.769383i	$0.279436\pi$
$2$	71307.9i	1.53877i	−0.638788	+	0.769383i	$0.720564\pi$
$3$	− 3.08552e7i	− 1.24151i	−0.784006	−	0.620754i	$-0.786827\pi$
$3$	− 3.08552e7i	− 1.24151i	0.784006	−	0.620754i	$-0.213173\pi$
$4$	−2.93733e9	−1.36780
$5$	0	0
$5$	0	0
$6$	2.20022e12	1.91039
$7$	1.14368e13i	0.910511i	0.890361	+	0.455256i	$0.150452\pi$
$7$	1.14368e13i	0.910511i	−0.890361	+	0.455256i	$0.849548\pi$
$8$	− 5.63222e13i	− 0.565959i
$9$	−3.34371e14	−0.541340
$10$	0	0
$11$	−2.40262e15	−0.173420	−0.0867099	−	0.996234i	$-0.527635\pi$
$11$	−2.40262e15	−0.173420	−0.0867099	+	0.996234i	$0.527635\pi$
$12$	9.06319e16i	1.69813i
$13$	2.01886e17i	1.09391i	0.837161	+	0.546957i	$0.184214\pi$
$13$	2.01886e17i	1.09391i	−0.837161	+	0.546957i	$0.815786\pi$
$14$	−8.15534e17	−1.40106
$15$	0	0
$16$	−2.29165e18	−0.496923
$17$	1.09264e19i	0.925807i	0.886409	+	0.462903i	$0.153192\pi$
$17$	1.09264e19i	0.925807i	−0.886409	+	0.462903i	$0.846808\pi$
$18$	− 2.38433e19i	− 0.832995i
$19$	1.42851e19	0.215875	0.107938	−	0.994158i	$-0.465575\pi$
$19$	1.42851e19	0.215875	0.107938	+	0.994158i	$0.465575\pi$
$20$	0	0
$21$	3.52885e20	1.13041
$22$	− 1.71326e20i	− 0.266853i
$23$	3.85062e18i	0.00301127i	0.999999	+	0.00150564i	$0.000479259\pi$
$23$	3.85062e18i	0.00301127i	−0.999999	+	0.00150564i	$0.999521\pi$
$24$	−1.73783e21	−0.702642
$25$	0	0
$26$	−1.43960e22	−1.68328
$27$	− 8.74135e21i	− 0.569430i
$28$	− 3.35937e22i	− 1.24540i
$29$	−7.63087e22	−1.64212	−0.821060	−	0.570842i	$-0.806617\pi$
$29$	−7.63087e22	−1.64212	−0.821060	+	0.570842i	$0.806617\pi$
$30$	0	0
$31$	1.86701e23	1.42903	0.714515	−	0.699620i	$-0.246647\pi$
$31$	1.86701e23	1.42903	0.714515	+	0.699620i	$0.246647\pi$
$32$	− 2.84364e23i	− 1.33061i
$33$	7.41334e22i	0.215302i
$34$	−7.79141e23	−1.42460
$35$	0	0
$36$	9.82158e23	0.740445
$37$	1.23709e24i	0.609924i	0.952364	+	0.304962i	$0.0986438\pi$
$37$	1.23709e24i	0.609924i	−0.952364	+	0.304962i	$0.901356\pi$
$38$	1.01864e24i	0.332182i
$39$	6.22922e24	1.35810
$40$	0	0
$41$	1.38199e25	1.38789	0.693945	−	0.720028i	$-0.255871\pi$
$41$	1.38199e25	1.38789	0.693945	+	0.720028i	$0.255871\pi$
$42$	2.51635e25i	1.73943i
$43$	2.67871e25i	1.28578i	0.765960	+	0.642888i	$0.222264\pi$
$43$	2.67871e25i	1.28578i	−0.765960	+	0.642888i	$0.777736\pi$
$44$	7.05729e24	0.237204
$45$	0	0
$46$	−2.74580e23	−0.00463364
$47$	7.40922e25i	0.895892i	0.894061	+	0.447946i	$0.147844\pi$
$47$	7.40922e25i	0.895892i	−0.894061	+	0.447946i	$0.852156\pi$
$48$	7.07094e25i	0.616933i
$49$	2.69748e25	0.170970
$50$	0	0
$51$	3.37138e26	1.14940
$52$	− 5.93004e26i	− 1.49626i
$53$	− 3.56092e25i	− 0.0668784i	−0.999441	−	0.0334392i	$-0.989354\pi$
$53$	− 3.56092e25i	− 0.0668784i	0.999441	−	0.0334392i	$-0.0106460\pi$
$54$	6.23327e26	0.876219
$55$	0	0
$56$	6.44146e26	0.515312
$57$	− 4.40770e26i	− 0.268011i
$58$	− 5.44141e27i	− 2.52684i
$59$	2.36122e27	0.841260	0.420630	−	0.907232i	$-0.361809\pi$
$59$	2.36122e27	0.841260	0.420630	+	0.907232i	$0.361809\pi$
$60$	0	0
$61$	−5.44842e27	−1.15786	−0.578932	−	0.815376i	$-0.696530\pi$
$61$	−5.44842e27	−1.15786	−0.578932	+	0.815376i	$0.696530\pi$
$62$	1.33133e28i	2.19894i
$63$	− 3.82414e27i	− 0.492896i
$64$	1.53561e28	1.55057
$65$	0	0
$66$	−5.28630e27	−0.331299
$67$	− 9.41082e27i	− 0.467163i	−0.972337	−	0.233581i	$-0.924956\pi$
$67$	− 9.41082e27i	− 0.467163i	0.972337	−	0.233581i	$-0.0750445\pi$
$68$	− 3.20945e28i	− 1.26632i
$69$	1.18812e26	0.00373851
$70$	0	0
$71$	−2.10678e28	−0.425712	−0.212856	−	0.977084i	$-0.568276\pi$
$71$	−2.10678e28	−0.425712	−0.212856	+	0.977084i	$0.568276\pi$
$72$	1.88325e28i	0.306376i
$73$	− 3.92731e28i	− 0.515929i	−0.966154	−	0.257965i	$-0.916948\pi$
$73$	− 3.92731e28i	− 0.515929i	0.966154	−	0.257965i	$-0.0830518\pi$
$74$	−8.82146e28	−0.938531
$75$	0	0
$76$	−4.19601e28	−0.295274
$77$	− 2.74783e28i	− 0.157901i
$78$	4.44193e29i	2.08980i
$79$	−1.79850e29	−0.694529	−0.347264	−	0.937767i	$-0.612889\pi$
$79$	−1.79850e29	−0.694529	−0.347264	+	0.937767i	$0.612889\pi$
$80$	0	0
$81$	−4.76249e29	−1.24829
$82$	9.85468e29i	2.13564i
$83$	4.54329e29i	0.815944i	0.912995	+	0.407972i	$0.133764\pi$
$83$	4.54329e29i	0.815944i	−0.912995	+	0.407972i	$0.866236\pi$
$84$	−1.03654e30	−1.54617
$85$	0	0
$86$	−1.91013e30	−1.97851
$87$	2.35452e30i	2.03870i
$88$	1.35321e29i	0.0981485i
$89$	−2.60812e29	−0.158775	−0.0793875	−	0.996844i	$-0.525296\pi$
$89$	−2.60812e29	−0.158775	−0.0793875	+	0.996844i	$0.525296\pi$
$90$	0	0
$91$	−2.30893e30	−0.996021
$92$	− 1.13106e28i	− 0.00411882i
$93$	− 5.76072e30i	− 1.77415i
$94$	−5.28336e30	−1.37857
$95$	0	0
$96$	−8.77410e30	−1.65196
$97$	− 5.38067e30i	− 0.862729i	−0.902178	−	0.431365i	$-0.858032\pi$
$97$	− 5.38067e30i	− 0.862729i	0.902178	−	0.431365i	$-0.141968\pi$
$98$	1.92352e30i	0.263082i
$99$	8.03368e29	0.0938791
$100$	0	0
$101$	−1.28863e31	−1.10445	−0.552225	−	0.833695i	$-0.686221\pi$
$101$	−1.28863e31	−1.10445	−0.552225	+	0.833695i	$0.686221\pi$
$102$	2.40406e31i	1.76865i
$103$	− 1.91208e31i	− 1.20928i	−0.796497	−	0.604642i	$-0.793316\pi$
$103$	− 1.91208e31i	− 1.20928i	0.796497	−	0.604642i	$-0.206684\pi$
$104$	1.13706e31	0.619110
$105$	0	0
$106$	2.53922e30	0.102910
$107$	3.15334e31i	1.10490i	0.833547	+	0.552449i	$0.186307\pi$
$107$	3.15334e31i	1.10490i	−0.833547	+	0.552449i	$0.813693\pi$
$108$	2.56762e31i	0.778866i
$109$	3.61029e31	0.949360	0.474680	−	0.880158i	$-0.342564\pi$
$109$	3.61029e31	0.949360	0.474680	+	0.880158i	$0.342564\pi$
$110$	0	0
$111$	3.81708e31	0.757226
$112$	− 2.62092e31i	− 0.452453i
$113$	− 1.52549e31i	− 0.229454i	−0.993397	−	0.114727i	$-0.963401\pi$
$113$	− 1.52549e31i	− 0.229454i	0.993397	−	0.114727i	$-0.0365992\pi$
$114$	3.14304e31	0.412406
$115$	0	0
$116$	2.24144e32	2.24609
$117$	− 6.75047e31i	− 0.592179i
$118$	1.68374e32i	1.29450i
$119$	−1.24964e32	−0.842957
$120$	0	0
$121$	−1.86171e32	−0.969926
$122$	− 3.88515e32i	− 1.78168i
$123$	− 4.26416e32i	− 1.72308i
$124$	−5.48404e32	−1.95463
$125$	0	0
$126$	2.72691e32	0.758451
$127$	− 5.69060e32i	− 1.40023i	−0.714029	−	0.700116i	$-0.753131\pi$
$127$	− 5.69060e32i	− 1.40023i	0.714029	−	0.700116i	$-0.246869\pi$
$128$	4.84344e32i	1.05536i
$129$	8.26523e32	1.59630
$130$	0	0
$131$	1.80373e31	0.0274452	0.0137226	−	0.999906i	$-0.495632\pi$
$131$	1.80373e31	0.0274452	0.0137226	+	0.999906i	$0.495632\pi$
$132$	− 2.17754e32i	− 0.294490i
$133$	1.63376e32i	0.196557i
$134$	6.71065e32	0.718854
$135$	0	0
$136$	6.15401e32	0.523968
$137$	− 1.53340e32i	− 0.116543i	−0.998301	−	0.0582716i	$-0.981441\pi$
$137$	− 1.53340e32i	− 0.116543i	0.998301	−	0.0582716i	$-0.0185589\pi$
$138$	8.47222e30i	0.00575270i
$139$	−1.88034e33	−1.14158	−0.570791	−	0.821095i	$-0.693364\pi$
$139$	−1.88034e33	−1.14158	−0.570791	+	0.821095i	$0.693364\pi$
$140$	0	0
$141$	2.28613e33	1.11226
$142$	− 1.50230e33i	− 0.655070i
$143$	− 4.85055e32i	− 0.189706i
$144$	7.66262e32	0.269004
$145$	0	0
$146$	2.80048e33	0.793895
$147$	− 8.32313e32i	− 0.212260i
$148$	− 3.63375e33i	− 0.834255i
$149$	−6.64703e33	−1.37480	−0.687401	−	0.726278i	$-0.741249\pi$
$149$	−6.64703e33	−1.37480	−0.687401	+	0.726278i	$0.741249\pi$
$150$	0	0
$151$	−6.58887e33	−1.10833	−0.554164	−	0.832408i	$-0.686962\pi$
$151$	−6.58887e33	−1.10833	−0.554164	+	0.832408i	$0.686962\pi$
$152$	− 8.04569e32i	− 0.122177i
$153$	− 3.65349e33i	− 0.501176i
$154$	1.95942e33	0.242972
$155$	0	0
$156$	−1.82973e34	−1.85761
$157$	1.60319e34i	1.47414i	0.675814	+	0.737072i	$0.263792\pi$
$157$	1.60319e34i	1.47414i	−0.675814	+	0.737072i	$0.736208\pi$
$158$	− 1.28247e34i	− 1.06872i
$159$	−1.09873e33	−0.0830300
$160$	0	0
$161$	−4.40389e31	−0.00274179
$162$	− 3.39603e34i	− 1.92083i
$163$	1.63484e34i	0.840555i	0.907396	+	0.420277i	$0.138067\pi$
$163$	1.63484e34i	0.840555i	−0.907396	+	0.420277i	$0.861933\pi$
$164$	−4.05936e34	−1.89836
$165$	0	0
$166$	−3.23972e34	−1.25555
$167$	1.68065e34i	0.593433i	0.954966	+	0.296717i	$0.0958917\pi$
$167$	1.68065e34i	0.593433i	−0.954966	+	0.296717i	$0.904108\pi$
$168$	− 1.98753e34i	− 0.639763i
$169$	−6.69784e33	−0.196649
$170$	0	0
$171$	−4.77653e33	−0.116862
$172$	− 7.86826e34i	− 1.75868i
$173$	− 1.67734e34i	− 0.342695i	−0.985211	−	0.171347i	$-0.945188\pi$
$173$	− 1.67734e34i	− 0.342695i	0.985211	−	0.171347i	$-0.0548120\pi$
$174$	−1.67896e35	−3.13709
$175$	0	0
$176$	5.50597e33	0.0861762
$177$	− 7.28560e34i	− 1.04443i
$178$	− 1.85979e34i	− 0.244318i
$179$	−5.67856e33	−0.0683937	−0.0341968	−	0.999415i	$-0.510887\pi$
$179$	−5.67856e33	−0.0683937	−0.0341968	+	0.999415i	$0.510887\pi$
$180$	0	0
$181$	1.47595e35	1.49642	0.748210	−	0.663462i	$-0.230914\pi$
$181$	1.47595e35	1.49642	0.748210	+	0.663462i	$0.230914\pi$
$182$	− 1.64645e35i	− 1.53264i
$183$	1.68112e35i	1.43750i
$184$	2.16876e32	0.00170425
$185$	0	0
$186$	4.10784e35	2.73000
$187$	− 2.62521e34i	− 0.160553i
$188$	− 2.17633e35i	− 1.22540i
$189$	9.99731e34	0.518472
$190$	0	0
$191$	−4.38203e34	−0.193045	−0.0965224	−	0.995331i	$-0.530772\pi$
$191$	−4.38203e34	−0.193045	−0.0965224	+	0.995331i	$0.530772\pi$
$192$	− 4.73815e35i	− 1.92504i
$193$	− 2.63656e35i	− 0.988323i	−0.869370	−	0.494161i	$-0.835475\pi$
$193$	− 2.63656e35i	− 0.988323i	0.869370	−	0.494161i	$-0.164525\pi$
$194$	3.83684e35	1.32754
$195$	0	0
$196$	−7.92339e34	−0.233852
$197$	− 2.72680e35i	− 0.743749i	−0.928283	−	0.371875i	$-0.878715\pi$
$197$	− 2.72680e35i	− 0.743749i	0.928283	−	0.371875i	$-0.121285\pi$
$198$	5.72864e34i	0.144458i
$199$	−3.17714e35	−0.740991	−0.370496	−	0.928834i	$-0.620812\pi$
$199$	−3.17714e35	−0.740991	−0.370496	+	0.928834i	$0.620812\pi$
$200$	0	0
$201$	−2.90373e35	−0.579986
$202$	− 9.18893e35i	− 1.69949i
$203$	− 8.72728e35i	− 1.49517i
$204$	−9.90284e35	−1.57214
$205$	0	0
$206$	1.36346e36	1.86081
$207$	− 1.28754e33i	− 0.00163012i
$208$	− 4.62651e35i	− 0.543591i
$209$	−3.43217e34	−0.0374371
$210$	0	0
$211$	−2.10102e36	−1.97721	−0.988604	−	0.150541i	$-0.951898\pi$
$211$	−2.10102e36	−1.97721	−0.988604	+	0.150541i	$0.951898\pi$
$212$	1.04596e35i	0.0914763i
$213$	6.50053e35i	0.528524i
$214$	−2.24858e36	−1.70018
$215$	0	0
$216$	−4.92332e35	−0.322274
$217$	2.13527e36i	1.30115i
$218$	2.57442e36i	1.46084i
$219$	−1.21178e36	−0.640530
$220$	0	0
$221$	−2.20589e36	−1.01275
$222$	2.72188e36i	1.16519i
$223$	2.62490e36i	1.04806i	0.851699	+	0.524032i	$0.175573\pi$
$223$	2.62490e36i	1.04806i	−0.851699	+	0.524032i	$0.824427\pi$
$224$	3.25221e36	1.21153
$225$	0	0
$226$	1.08780e36	0.353075
$227$	1.16088e35i	0.0351874i	0.999845	+	0.0175937i	$0.00560054\pi$
$227$	1.16088e35i	0.0351874i	−0.999845	+	0.0175937i	$0.994399\pi$
$228$	1.29469e36i	0.366585i
$229$	−1.39980e36	−0.370353	−0.185177	−	0.982705i	$-0.559286\pi$
$229$	−1.39980e36	−0.370353	−0.185177	+	0.982705i	$0.559286\pi$
$230$	0	0
$231$	−8.47850e35	−0.196035
$232$	4.29787e36i	0.929372i
$233$	− 7.15120e36i	− 1.44665i	−0.690510	−	0.723323i	$-0.742614\pi$
$233$	− 7.15120e36i	− 1.44665i	0.690510	−	0.723323i	$-0.257386\pi$
$234$	4.81362e36	0.911226
$235$	0	0
$236$	−6.93568e36	−1.15068
$237$	5.54931e36i	0.862262i
$238$	− 8.91089e36i	− 1.29711i
$239$	−2.96558e36	−0.404522	−0.202261	−	0.979332i	$-0.564829\pi$
$239$	−2.96558e36	−0.404522	−0.202261	+	0.979332i	$0.564829\pi$
$240$	0	0
$241$	−7.20536e36	−0.863757	−0.431879	−	0.901932i	$-0.642149\pi$
$241$	−7.20536e36	−0.863757	−0.431879	+	0.901932i	$0.642149\pi$
$242$	− 1.32754e37i	− 1.49249i
$243$	9.29545e36i	0.980332i
$244$	1.60038e37	1.58373
$245$	0	0
$246$	3.04068e37	2.65141
$247$	2.88396e36i	0.236149i
$248$	− 1.05154e37i	− 0.808772i
$249$	1.40184e37	1.01300
$250$	0	0
$251$	9.47842e36	0.605053	0.302526	−	0.953141i	$-0.402170\pi$
$251$	9.47842e36	0.605053	0.302526	+	0.953141i	$0.402170\pi$
$252$	1.12328e37i	0.674183i
$253$	− 9.25159e33i	0 0.000522214i
$254$	4.05784e37	2.15463
$255$	0	0
$256$	−1.56056e36	−0.0733772
$257$	3.15504e37i	1.39650i	0.715852	+	0.698252i	$0.246038\pi$
$257$	3.15504e37i	1.39650i	−0.715852	+	0.698252i	$0.753962\pi$
$258$	5.89376e37i	2.45633i
$259$	−1.41484e37	−0.555343
$260$	0	0
$261$	2.55154e37	0.888945
$262$	1.28620e36i	0.0422318i
$263$	1.25731e37i	0.389159i	0.980887	+	0.194580i	$0.0623343\pi$
$263$	1.25731e37i	0.389159i	−0.980887	+	0.194580i	$0.937666\pi$
$264$	4.17536e36	0.121852
$265$	0	0
$266$	−1.16500e37	−0.302455
$267$	8.04741e36i	0.197120i
$268$	2.76427e37i	0.638985i
$269$	−3.34018e37	−0.728801	−0.364401	−	0.931242i	$-0.618726\pi$
$269$	−3.34018e37	−0.728801	−0.364401	+	0.931242i	$0.618726\pi$
$270$	0	0
$271$	−4.00526e36	−0.0779125	−0.0389562	−	0.999241i	$-0.512403\pi$
$271$	−4.00526e36	−0.0779125	−0.0389562	+	0.999241i	$0.512403\pi$
$272$	− 2.50396e37i	− 0.460054i
$273$	7.12424e37i	1.23657i
$274$	1.09344e37	0.179333
$275$	0	0
$276$	−3.48990e35	−0.00511354
$277$	− 7.94796e37i	− 1.10108i	−0.834808	−	0.550541i	$-0.814422\pi$
$277$	− 7.94796e37i	− 1.10108i	0.834808	−	0.550541i	$-0.185578\pi$
$278$	− 1.34083e38i	− 1.75663i
$279$	−6.24276e37	−0.773591
$280$	0	0
$281$	−1.69314e38	−1.87822	−0.939108	−	0.343621i	$-0.888346\pi$
$281$	−1.69314e38	−1.87822	−0.939108	+	0.343621i	$0.888346\pi$
$282$	1.63019e38i	1.71150i
$283$	− 1.18735e38i	− 1.18002i	−0.807397	−	0.590008i	$-0.799125\pi$
$283$	− 1.18735e38i	− 1.18002i	0.807397	−	0.590008i	$-0.200875\pi$
$284$	6.18832e37	0.582288
$285$	0	0
$286$	3.45882e37	0.291914
$287$	1.58056e38i	1.26369i
$288$	9.50830e37i	0.720310i
$289$	1.99019e37	0.142882
$290$	0	0
$291$	−1.66022e38	−1.07108
$292$	1.15358e38i	0.705689i
$293$	− 9.32191e37i	− 0.540825i	−0.962745	−	0.270413i	$-0.912840\pi$
$293$	− 9.32191e37i	− 0.540825i	0.962745	−	0.270413i	$-0.0871601\pi$
$294$	5.93505e37	0.326618
$295$	0	0
$296$	6.96759e37	0.345192
$297$	2.10022e37i	0.0987504i
$298$	− 4.73985e38i	− 2.11550i
$299$	−7.77386e35	−0.00329407
$300$	0	0
$301$	−3.06359e38	−1.17071
$302$	− 4.69838e38i	− 1.70546i
$303$	3.97609e38i	1.37118i
$304$	−3.27365e37	−0.107273
$305$	0	0
$306$	2.60522e38	0.771193
$307$	− 2.10829e38i	− 0.593314i	−0.954984	−	0.296657i	$-0.904128\pi$
$307$	− 2.10829e38i	− 0.593314i	0.954984	−	0.296657i	$-0.0958719\pi$
$308$	8.07129e37i	0.215977i
$309$	−5.89976e38	−1.50134
$310$	0	0
$311$	4.24765e38	0.978053	0.489027	−	0.872269i	$-0.337352\pi$
$311$	4.24765e38	0.978053	0.489027	+	0.872269i	$0.337352\pi$
$312$	− 3.50844e38i	− 0.768630i
$313$	3.07637e38i	0.641360i	0.947188	+	0.320680i	$0.103911\pi$
$313$	3.07637e38i	0.641360i	−0.947188	+	0.320680i	$0.896089\pi$
$314$	−1.14320e39	−2.26836
$315$	0	0
$316$	5.28278e38	0.949976
$317$	− 9.76522e38i	− 1.67210i	−0.548650	−	0.836052i	$-0.684858\pi$
$317$	− 9.76522e38i	− 1.67210i	0.548650	−	0.836052i	$-0.315142\pi$
$318$	− 7.83480e37i	− 0.127764i
$319$	1.83341e38	0.284776
$320$	0	0
$321$	9.72970e38	1.37174
$322$	− 3.14032e36i	− 0.00421898i
$323$	1.56085e38i	0.199859i
$324$	1.39890e39	1.70741
$325$	0	0
$326$	−1.16577e39	−1.29342
$327$	− 1.11396e39i	− 1.17864i
$328$	− 7.78367e38i	− 0.785489i
$329$	−8.47379e38	−0.815720
$330$	0	0
$331$	8.30576e38	0.727856	0.363928	−	0.931427i	$-0.381435\pi$
$331$	8.30576e38	0.727856	0.363928	+	0.931427i	$0.381435\pi$
$332$	− 1.33451e39i	− 1.11605i
$333$	− 4.13649e38i	− 0.330176i
$334$	−1.19844e39	−0.913155
$335$	0	0
$336$	−8.08690e38	−0.561724
$337$	1.84495e39i	1.22383i	0.790923	+	0.611916i	$0.209601\pi$
$337$	1.84495e39i	1.22383i	−0.790923	+	0.611916i	$0.790399\pi$
$338$	− 4.77609e38i	− 0.302596i
$339$	−4.70695e38	−0.284868
$340$	0	0
$341$	−4.48573e38	−0.247822
$342$	− 3.40604e38i	− 0.179823i
$343$	2.11295e39i	1.06618i
$344$	1.50871e39	0.727696
$345$	0	0
$346$	1.19608e39	0.527327
$347$	− 3.59852e39i	− 1.51711i	−0.651609	−	0.758555i	$-0.725906\pi$
$347$	− 3.59852e39i	− 1.51711i	0.651609	−	0.758555i	$-0.274094\pi$
$348$	− 6.91600e39i	− 2.78854i
$349$	−4.09325e38	−0.157861	−0.0789303	−	0.996880i	$-0.525150\pi$
$349$	−4.09325e38	−0.157861	−0.0789303	+	0.996880i	$0.525150\pi$
$350$	0	0
$351$	1.76475e39	0.622907
$352$	6.83218e38i	0.230754i
$353$	5.32510e39i	1.72116i	0.509319	+	0.860578i	$0.329897\pi$
$353$	5.32510e39i	1.72116i	−0.509319	+	0.860578i	$0.670103\pi$
$354$	5.19520e39	1.60713
$355$	0	0
$356$	7.66090e38	0.217173
$357$	3.85578e39i	1.04654i
$358$	− 4.04926e38i	− 0.105242i
$359$	−4.10824e39	−1.02257	−0.511283	−	0.859412i	$-0.670830\pi$
$359$	−4.10824e39	−1.02257	−0.511283	+	0.859412i	$0.670830\pi$
$360$	0	0
$361$	−4.17480e39	−0.953398
$362$	1.05247e40i	2.30264i
$363$	5.74434e39i	1.20417i
$364$	6.78208e39	1.36236
$365$	0	0
$366$	−1.19877e40	−2.21197
$367$	9.50139e39i	1.68060i	0.542125	+	0.840298i	$0.317620\pi$
$367$	9.50139e39i	1.68060i	−0.542125	+	0.840298i	$0.682380\pi$
$368$	− 8.82429e36i	− 0.00149637i
$369$	−4.62098e39	−0.751320
$370$	0	0
$371$	4.07255e38	0.0608935
$372$	1.69211e40i	2.42669i
$373$	− 5.31105e39i	− 0.730624i	−0.930885	−	0.365312i	$-0.880962\pi$
$373$	− 5.31105e39i	− 0.730624i	0.930885	−	0.365312i	$-0.119038\pi$
$374$	1.87198e39	0.247054
$375$	0	0
$376$	4.17304e39	0.507038
$377$	− 1.54056e40i	− 1.79634i
$378$	7.12887e39i	0.797807i
$379$	−6.56433e39	−0.705152	−0.352576	−	0.935783i	$-0.614694\pi$
$379$	−6.56433e39	−0.705152	−0.352576	+	0.935783i	$0.614694\pi$
$380$	0	0
$381$	−1.75585e40	−1.73840
$382$	− 3.12473e39i	− 0.297051i
$383$	− 4.90622e39i	− 0.447884i	−0.974602	−	0.223942i	$-0.928107\pi$
$383$	− 4.90622e39i	− 0.447884i	0.974602	−	0.223942i	$-0.0718926\pi$
$384$	1.49445e40	1.31023
$385$	0	0
$386$	1.88007e40	1.52080
$387$	− 8.95685e39i	− 0.696041i
$388$	1.58048e40i	1.18004i
$389$	−1.47786e40	−1.06026	−0.530132	−	0.847915i	$-0.677858\pi$
$389$	−1.47786e40	−1.06026	−0.530132	+	0.847915i	$0.677858\pi$
$390$	0	0
$391$	−4.20736e37	−0.00278785
$392$	− 1.51928e39i	− 0.0967617i
$393$	− 5.56545e38i	− 0.0340734i
$394$	1.94442e40	1.14446
$395$	0	0
$396$	−2.35976e39	−0.128408
$397$	9.79733e39i	0.512690i	0.966585	+	0.256345i	$0.0825184\pi$
$397$	9.79733e39i	0.512690i	−0.966585	+	0.256345i	$0.917482\pi$
$398$	− 2.26555e40i	− 1.14021i
$399$	5.04101e39	0.244027
$400$	0	0
$401$	1.11974e40	0.501624	0.250812	−	0.968036i	$-0.419302\pi$
$401$	1.11974e40	0.501624	0.250812	+	0.968036i	$0.419302\pi$
$402$	− 2.07059e40i	− 0.892462i
$403$	3.76923e40i	1.56324i
$404$	3.78513e40	1.51067
$405$	0	0
$406$	6.22323e40	2.30071
$407$	− 2.97227e39i	− 0.105773i
$408$	− 1.89883e40i	− 0.650510i
$409$	2.34914e40	0.774815	0.387408	−	0.921909i	$-0.373371\pi$
$409$	2.34914e40	0.774815	0.387408	+	0.921909i	$0.373371\pi$
$410$	0	0
$411$	−4.73134e39	−0.144689
$412$	5.61640e40i	1.65406i
$413$	2.70048e40i	0.765977i
$414$	9.18116e37	0.00250837
$415$	0	0
$416$	5.74089e40	1.45557
$417$	5.80184e40i	1.41728i
$418$	− 2.44741e39i	− 0.0576069i
$419$	−4.42578e40	−1.00386	−0.501929	−	0.864909i	$-0.667376\pi$
$419$	−4.42578e40	−1.00386	−0.501929	+	0.864909i	$0.667376\pi$
$420$	0	0
$421$	−4.58467e40	−0.965907	−0.482954	−	0.875646i	$-0.660436\pi$
$421$	−4.58467e40	−0.965907	−0.482954	+	0.875646i	$0.660436\pi$
$422$	− 1.49819e41i	− 3.04246i
$423$	− 2.47743e40i	− 0.484982i
$424$	−2.00559e39	−0.0378504
$425$	0	0
$426$	−4.63539e40	−0.813275
$427$	− 6.23125e40i	− 1.05425i
$428$	− 9.26239e40i	− 1.51128i
$429$	−1.49665e40	−0.235522
$430$	0	0
$431$	−1.63894e40	−0.239975	−0.119987	−	0.992775i	$-0.538285\pi$
$431$	−1.63894e40	−0.239975	−0.119987	+	0.992775i	$0.538285\pi$
$432$	2.00321e40i	0.282962i
$433$	− 7.21840e39i	− 0.0983737i	−0.998790	−	0.0491868i	$-0.984337\pi$
$433$	− 7.21840e39i	− 0.0983737i	0.998790	−	0.0491868i	$-0.0156630\pi$
$434$	−1.52261e41	−2.00216
$435$	0	0
$436$	−1.06046e41	−1.29854
$437$	5.50066e37i	0 0.000650059i
$438$	− 8.64094e40i	− 0.985626i
$439$	−1.72040e40	−0.189422	−0.0947109	−	0.995505i	$-0.530193\pi$
$439$	−1.72040e40	−0.189422	−0.0947109	+	0.995505i	$0.530193\pi$
$440$	0	0
$441$	−9.01960e39	−0.0925527
$442$	− 1.57297e41i	− 1.55839i
$443$	9.22567e39i	0.0882552i	0.999026	+	0.0441276i	$0.0140508\pi$
$443$	9.22567e39i	0.0882552i	−0.999026	+	0.0441276i	$0.985949\pi$
$444$	−1.12120e41	−1.03573
$445$	0	0
$446$	−1.87176e41	−1.61272
$447$	2.05095e41i	1.70683i
$448$	1.75625e41i	1.41181i
$449$	−1.80147e41	−1.39897	−0.699484	−	0.714648i	$-0.746587\pi$
$449$	−1.80147e41	−1.39897	−0.699484	+	0.714648i	$0.746587\pi$
$450$	0	0
$451$	−3.32040e40	−0.240688
$452$	4.48088e40i	0.313847i
$453$	2.03301e41i	1.37600i
$454$	−8.27801e39	−0.0541452
$455$	0	0
$456$	−2.48252e40	−0.151683
$457$	7.03528e40i	0.415509i	0.978181	+	0.207754i	$0.0666154\pi$
$457$	7.03528e40i	0.415509i	−0.978181	+	0.207754i	$0.933385\pi$
$458$	− 9.98168e40i	− 0.569887i
$459$	9.55118e40	0.527182
$460$	0	0
$461$	−2.15013e40	−0.110943	−0.0554717	−	0.998460i	$-0.517666\pi$
$461$	−2.15013e40	−0.110943	−0.0554717	+	0.998460i	$0.517666\pi$
$462$	− 6.04584e40i	− 0.301652i
$463$	− 3.68798e41i	− 1.77944i	−0.456506	−	0.889720i	$-0.650899\pi$
$463$	− 3.68798e41i	− 1.77944i	0.456506	−	0.889720i	$-0.349101\pi$
$464$	1.74873e41	0.816006
$465$	0	0
$466$	5.09937e41	2.22605
$467$	− 3.35225e41i	− 1.41555i	−0.706438	−	0.707775i	$-0.749699\pi$
$467$	− 3.35225e41i	− 1.41555i	0.706438	−	0.707775i	$-0.250301\pi$
$468$	1.98284e41i	0.809983i
$469$	1.07630e41	0.425357
$470$	0	0
$471$	4.94668e41	1.83016
$472$	− 1.32989e41i	− 0.476118i
$473$	− 6.43593e40i	− 0.222979i
$474$	−3.95709e41	−1.32682
$475$	0	0
$476$	3.67059e41	1.15300
$477$	1.19067e40i	0.0362040i
$478$	− 2.11469e41i	− 0.622464i
$479$	1.78256e41	0.507976	0.253988	−	0.967207i	$-0.418258\pi$
$479$	1.78256e41	0.507976	0.253988	+	0.967207i	$0.418258\pi$
$480$	0	0
$481$	−2.49751e41	−0.667205
$482$	− 5.13799e41i	− 1.32912i
$483$	1.35883e39i	0.00340396i
$484$	5.46845e41	1.32666
$485$	0	0
$486$	−6.62839e41	−1.50850
$487$	− 2.96115e41i	− 0.652772i	−0.945237	−	0.326386i	$-0.894169\pi$
$487$	− 2.96115e41i	− 0.652772i	0.945237	−	0.326386i	$-0.105831\pi$
$488$	3.06867e41i	0.655304i
$489$	5.04432e41	1.04355
$490$	0	0
$491$	2.87172e41	0.557671	0.278836	−	0.960339i	$-0.410052\pi$
$491$	2.87172e41	0.557671	0.278836	+	0.960339i	$0.410052\pi$
$492$	1.25252e42i	2.35682i
$493$	− 8.33782e41i	− 1.52029i
$494$	−2.05649e41	−0.363378
$495$	0	0
$496$	−4.27855e41	−0.710117
$497$	− 2.40949e41i	− 0.387615i
$498$	9.99624e41i	1.55877i
$499$	1.19160e42	1.80125	0.900623	−	0.434601i	$-0.143111\pi$
$499$	1.19160e42	1.80125	0.900623	+	0.434601i	$0.143111\pi$
$500$	0	0
$501$	5.18568e41	0.736752
$502$	6.75886e41i	0.931035i
$503$	− 1.92359e41i	− 0.256926i	−0.991714	−	0.128463i	$-0.958996\pi$
$503$	− 1.92359e41i	− 0.256926i	0.991714	−	0.128463i	$-0.0410044\pi$
$504$	−2.15384e41	−0.278959
$505$	0	0
$506$	6.59712e38	0.000803565 0
$507$	2.06663e41i	0.244141i
$508$	1.67152e42i	1.91524i
$509$	4.08219e41	0.453699	0.226849	−	0.973930i	$-0.427157\pi$
$509$	4.08219e41	0.453699	0.226849	+	0.973930i	$0.427157\pi$
$510$	0	0
$511$	4.49158e41	0.469759
$512$	9.28840e41i	0.942446i
$513$	− 1.24871e41i	− 0.122926i
$514$	−2.24980e42	−2.14889
$515$	0	0
$516$	−2.42777e42	−2.18342
$517$	− 1.78016e41i	− 0.155366i
$518$	− 1.00889e42i	− 0.854543i
$519$	−5.17548e41	−0.425458
$520$	0	0
$521$	8.76030e41	0.678476	0.339238	−	0.940701i	$-0.389831\pi$
$521$	8.76030e41	0.678476	0.339238	+	0.940701i	$0.389831\pi$
$522$	1.81945e42i	1.36788i
$523$	1.52051e42i	1.10972i	0.831944	+	0.554859i	$0.187228\pi$
$523$	1.52051e42i	1.10972i	−0.831944	+	0.554859i	$0.812772\pi$
$524$	−5.29815e40	−0.0375396
$525$	0	0
$526$	−8.96559e41	−0.598825
$527$	2.03998e42i	1.32301i
$528$	− 1.69888e41i	− 0.106988i
$529$	1.63516e42	0.999991
$530$	0	0
$531$	−7.89524e41	−0.455408
$532$	− 4.79889e41i	− 0.268851i
$533$	2.79004e42i	1.51823i
$534$	−5.73844e41	−0.303322
$535$	0	0
$536$	−5.30038e41	−0.264395
$537$	1.75213e41i	0.0849113i
$538$	− 2.38181e42i	− 1.12145i
$539$	−6.48102e40	−0.0296495
$540$	0	0
$541$	2.17683e42	0.940301	0.470150	−	0.882586i	$-0.344200\pi$
$541$	2.17683e42	0.940301	0.470150	+	0.882586i	$0.344200\pi$
$542$	− 2.85607e41i	− 0.119889i
$543$	− 4.55407e42i	− 1.85782i
$544$	3.10708e42	1.23188
$545$	0	0
$546$	−5.08015e42	−1.90279
$547$	2.57006e42i	0.935707i	0.883806	+	0.467854i	$0.154973\pi$
$547$	2.57006e42i	0.935707i	−0.883806	+	0.467854i	$0.845027\pi$
$548$	4.50410e41i	0.159408i
$549$	1.82179e42	0.626798
$550$	0	0
$551$	−1.09008e42	−0.354493
$552$	− 6.69174e39i	− 0.00211584i
$553$	− 2.05691e42i	− 0.632376i
$554$	5.66752e42	1.69431
$555$	0	0
$556$	5.52318e42	1.56146
$557$	− 2.88974e42i	− 0.794517i	−0.917707	−	0.397258i	$-0.869962\pi$
$557$	− 2.88974e42i	− 0.794517i	0.917707	−	0.397258i	$-0.130038\pi$
$558$	− 4.45158e42i	− 1.19038i
$559$	−5.40793e42	−1.40653
$560$	0	0
$561$	−8.10014e41	−0.199328
$562$	− 1.20734e43i	− 2.89014i
$563$	5.57652e42i	1.29862i	0.760522	+	0.649312i	$0.224943\pi$
$563$	5.57652e42i	1.29862i	−0.760522	+	0.649312i	$0.775057\pi$
$564$	−6.71512e42	−1.52135
$565$	0	0
$566$	8.46672e42	1.81577
$567$	− 5.44676e42i	− 1.13658i
$568$	1.18659e42i	0.240935i
$569$	3.00301e42	0.593357	0.296679	−	0.954977i	$-0.404121\pi$
$569$	3.00301e42	0.593357	0.296679	+	0.954977i	$0.404121\pi$
$570$	0	0
$571$	1.00812e43	1.88649	0.943245	−	0.332099i	$-0.107757\pi$
$571$	1.00812e43	1.88649	0.943245	+	0.332099i	$0.107757\pi$
$572$	1.42477e42i	0.259481i
$573$	1.35208e42i	0.239666i
$574$	−1.12706e43	−1.94452
$575$	0	0
$576$	−5.13463e42	−0.839385
$577$	− 7.02075e42i	− 1.11727i	−0.829413	−	0.558635i	$-0.811325\pi$
$577$	− 7.02075e42i	− 1.11727i	0.829413	−	0.558635i	$-0.188675\pi$
$578$	1.41916e42i	0.219862i
$579$	−8.13515e42	−1.22701
$580$	0	0
$581$	−5.19607e42	−0.742926
$582$	− 1.18387e43i	− 1.64815i
$583$	8.55554e40i	0.0115980i
$584$	−2.21194e42	−0.291995
$585$	0	0
$586$	6.64726e42	0.832203
$587$	1.56627e43i	1.90974i	0.297018	+	0.954872i	$0.404008\pi$
$587$	1.56627e43i	1.90974i	−0.297018	+	0.954872i	$0.595992\pi$
$588$	2.44478e42i	0.290329i
$589$	2.66705e42	0.308492
$590$	0	0
$591$	−8.41360e42	−0.923370
$592$	− 2.83499e42i	− 0.303085i
$593$	1.51645e42i	0.157936i	0.996877	+	0.0789678i	$0.0251624\pi$
$593$	1.51645e42i	0.157936i	−0.996877	+	0.0789678i	$0.974838\pi$
$594$	−1.49762e42	−0.151954
$595$	0	0
$596$	1.95245e43	1.88046
$597$	9.80312e42i	0.919946i
$598$	− 5.54337e40i	− 0.00506880i
$599$	8.56958e42	0.763561	0.381781	−	0.924253i	$-0.375311\pi$
$599$	8.56958e42	0.763561	0.381781	+	0.924253i	$0.375311\pi$
$600$	0	0
$601$	−2.71633e42	−0.229841	−0.114921	−	0.993375i	$-0.536661\pi$
$601$	−2.71633e42	−0.229841	−0.114921	+	0.993375i	$0.536661\pi$
$602$	− 2.18458e43i	− 1.80145i
$603$	3.14671e42i	0.252894i
$604$	1.93537e43	1.51597
$605$	0	0
$606$	−2.83527e43	−2.10993
$607$	5.39744e42i	0.391528i	0.980651	+	0.195764i	$0.0627187\pi$
$607$	5.39744e42i	0.391528i	−0.980651	+	0.195764i	$0.937281\pi$
$608$	− 4.06217e42i	− 0.287245i
$609$	−2.69282e43	−1.85626
$610$	0	0
$611$	−1.49582e43	−0.980030
$612$	1.07315e43i	0.685509i
$613$	− 6.77481e42i	− 0.421949i	−0.977492	−	0.210975i	$-0.932336\pi$
$613$	− 6.77481e42i	− 0.421949i	0.977492	−	0.210975i	$-0.0676637\pi$
$614$	1.50337e43	0.912972
$615$	0	0
$616$	−1.54764e42	−0.0893653
$617$	− 8.39156e41i	− 0.0472523i	−0.999721	−	0.0236261i	$-0.992479\pi$
$617$	− 8.39156e41i	− 0.0472523i	0.999721	−	0.0236261i	$-0.00752113\pi$
$618$	− 4.20699e43i	− 2.31020i
$619$	−1.34876e43	−0.722318	−0.361159	−	0.932504i	$-0.617619\pi$
$619$	−1.34876e43	−0.722318	−0.361159	+	0.932504i	$0.617619\pi$
$620$	0	0
$621$	3.36597e40	0.00171471
$622$	3.02891e43i	1.50499i
$623$	− 2.98286e42i	− 0.144566i
$624$	−1.42752e43	−0.674872
$625$	0	0
$626$	−2.19370e43	−0.986902
$627$	1.05900e42i	0.0464784i
$628$	− 4.70909e43i	− 2.01634i
$629$	−1.35170e43	−0.564672
$630$	0	0
$631$	−4.65263e42	−0.185031	−0.0925153	−	0.995711i	$-0.529491\pi$
$631$	−4.65263e42	−0.185031	−0.0925153	+	0.995711i	$0.529491\pi$
$632$	1.01295e43i	0.393074i
$633$	6.48274e43i	2.45472i
$634$	6.96337e43	2.57298
$635$	0	0
$636$	3.22733e42	0.113569
$637$	5.44582e42i	0.187026i
$638$	1.30736e43i	0.438204i
$639$	7.04448e42	0.230455
$640$	0	0
$641$	4.24972e43	1.32453	0.662263	−	0.749271i	$-0.269596\pi$
$641$	4.24972e43	1.32453	0.662263	+	0.749271i	$0.269596\pi$
$642$	6.93804e43i	2.11078i
$643$	5.33186e43i	1.58347i	0.610868	+	0.791733i	$0.290821\pi$
$643$	5.33186e43i	1.58347i	−0.610868	+	0.791733i	$0.709179\pi$
$644$	1.29357e41	0.00375023
$645$	0	0
$646$	−1.11301e43	−0.307536
$647$	− 1.00492e43i	− 0.271092i	−0.990771	−	0.135546i	$-0.956721\pi$
$647$	− 1.00492e43i	− 0.271092i	0.990771	−	0.135546i	$-0.0432788\pi$
$648$	2.68234e43i	0.706481i
$649$	−5.67312e42	−0.145891
$650$	0	0
$651$	6.58842e43	1.61538
$652$	− 4.80205e43i	− 1.14971i
$653$	7.98263e43i	1.86634i	0.359430	+	0.933172i	$0.382971\pi$
$653$	7.98263e43i	1.86634i	−0.359430	+	0.933172i	$0.617029\pi$
$654$	7.94343e43	1.81365
$655$	0	0
$656$	−3.16704e43	−0.689674
$657$	1.31318e43i	0.279293i
$658$	− 6.04248e43i	− 1.25520i
$659$	−7.54017e43	−1.52988	−0.764940	−	0.644102i	$-0.777231\pi$
$659$	−7.54017e43	−1.52988	−0.764940	+	0.644102i	$0.777231\pi$
$660$	0	0
$661$	−3.00409e42	−0.0581555	−0.0290777	−	0.999577i	$-0.509257\pi$
$661$	−3.00409e42	−0.0581555	−0.0290777	+	0.999577i	$0.509257\pi$
$662$	5.92266e43i	1.12000i
$663$	6.80632e43i	1.25734i
$664$	2.55888e43	0.461790
$665$	0	0
$666$	2.94964e43	0.508064
$667$	− 2.93836e41i	− 0.00494487i
$668$	− 4.93662e43i	− 0.811698i
$669$	8.09919e43	1.30118
$670$	0	0
$671$	1.30905e43	0.200797
$672$	− 1.00348e44i	− 1.50412i
$673$	− 2.05730e43i	− 0.301346i	−0.988584	−	0.150673i	$-0.951856\pi$
$673$	− 2.05730e43i	− 0.301346i	0.988584	−	0.150673i	$-0.0481440\pi$
$674$	−1.31560e44	−1.88319
$675$	0	0
$676$	1.96738e43	0.268976
$677$	− 1.03692e44i	− 1.38554i	−0.721157	−	0.692772i	$-0.756389\pi$
$677$	− 1.03692e44i	− 1.38554i	0.721157	−	0.692772i	$-0.243611\pi$
$678$	− 3.35642e43i	− 0.438345i
$679$	6.15377e43	0.785524
$680$	0	0
$681$	3.58193e42	0.0436855
$682$	− 3.19868e43i	− 0.381340i
$683$	− 1.01818e44i	− 1.18660i	−0.804980	−	0.593302i	$-0.797824\pi$
$683$	− 1.01818e44i	− 1.18660i	0.804980	−	0.593302i	$-0.202176\pi$
$684$	1.40302e43	0.159844
$685$	0	0
$686$	−1.50670e44	−1.64060
$687$	4.31911e43i	0.459796i
$688$	− 6.13867e43i	− 0.638931i
$689$	7.18898e42	0.0731593
$690$	0	0
$691$	1.12626e44	1.09579	0.547895	−	0.836547i	$-0.315429\pi$
$691$	1.12626e44	1.09579	0.547895	+	0.836547i	$0.315429\pi$
$692$	4.92691e43i	0.468738i
$693$	9.18796e42i	0.0854779i
$694$	2.56603e44	2.33448
$695$	0	0
$696$	1.32612e44	1.15382
$697$	1.51002e44i	1.28492i
$698$	− 2.91881e43i	− 0.242911i
$699$	−2.20652e44	−1.79602
$700$	0	0
$701$	3.06210e43	0.238446	0.119223	−	0.992867i	$-0.461960\pi$
$701$	3.06210e43	0.238446	0.119223	+	0.992867i	$0.461960\pi$
$702$	1.25841e44i	0.958509i
$703$	1.76720e43i	0.131668i
$704$	−3.68949e43	−0.268899
$705$	0	0
$706$	−3.79722e44	−2.64846
$707$	− 1.47378e44i	− 1.00561i
$708$	2.14002e44i	1.42857i
$709$	9.24433e43	0.603752	0.301876	−	0.953347i	$-0.402387\pi$
$709$	9.24433e43	0.603752	0.301876	+	0.953347i	$0.402387\pi$
$710$	0	0
$711$	6.01366e43	0.375976
$712$	1.46895e43i	0.0898601i
$713$	7.18917e41i	0.00430320i
$714$	−2.74947e44	−1.61038
$715$	0	0
$716$	1.66798e43	0.0935489
$717$	9.15036e43i	0.502217i
$718$	− 2.92950e44i	− 1.57349i
$719$	9.29670e43	0.488687	0.244344	−	0.969689i	$-0.421428\pi$
$719$	9.29670e43	0.488687	0.244344	+	0.969689i	$0.421428\pi$
$720$	0	0
$721$	2.18681e44	1.10107
$722$	− 2.97696e44i	− 1.46706i
$723$	2.22323e44i	1.07236i
$724$	−4.33535e44	−2.04680
$725$	0	0
$726$	−4.09617e44	−1.85293
$727$	1.34756e44i	0.596710i	0.954455	+	0.298355i	$0.0964379\pi$
$727$	1.34756e44i	0.596710i	−0.954455	+	0.298355i	$0.903562\pi$
$728$	1.30044e44i	0.563707i
$729$	−7.35277e42	−0.0312014
$730$	0	0
$731$	−2.92688e44	−1.19038
$732$	− 4.93800e44i	− 1.96621i
$733$	− 1.96770e44i	− 0.767093i	−0.923522	−	0.383546i	$-0.874703\pi$
$733$	− 1.96770e44i	− 0.767093i	0.923522	−	0.383546i	$-0.125297\pi$
$734$	−6.77524e44	−2.58604
$735$	0	0
$736$	1.09498e42	0.00400681
$737$	2.26106e43i	0.0810153i
$738$	− 3.29512e44i	− 1.15611i
$739$	3.41064e44	1.17178	0.585891	−	0.810390i	$-0.300745\pi$
$739$	3.41064e44	1.17178	0.585891	+	0.810390i	$0.300745\pi$
$740$	0	0
$741$	8.89852e43	0.293181
$742$	2.90405e43i	0.0937009i
$743$	2.64820e44i	0.836805i	0.908262	+	0.418403i	$0.137410\pi$
$743$	2.64820e44i	0.836805i	−0.908262	+	0.418403i	$0.862590\pi$
$744$	−3.24456e44	−1.00410
$745$	0	0
$746$	3.78720e44	1.12426
$747$	− 1.51915e44i	− 0.441703i
$748$	7.71111e43i	0.219605i
$749$	−3.60641e44	−1.00602
$750$	0	0
$751$	3.88190e44	1.03902	0.519511	−	0.854464i	$-0.326114\pi$
$751$	3.88190e44	1.03902	0.519511	+	0.854464i	$0.326114\pi$
$752$	− 1.69794e44i	− 0.445189i
$753$	− 2.92459e44i	− 0.751177i
$754$	1.09854e45	2.76414
$755$	0	0
$756$	−2.93654e44	−0.709166
$757$	2.10907e44i	0.499004i	0.968374	+	0.249502i	$0.0802670\pi$
$757$	2.10907e44i	0.499004i	−0.968374	+	0.249502i	$0.919733\pi$
$758$	− 4.68088e44i	− 1.08506i
$759$	−2.85460e41	−0.000648332 0
$760$	0	0
$761$	3.24151e43	0.0706782	0.0353391	−	0.999375i	$-0.488749\pi$
$761$	3.24151e43	0.0706782	0.0353391	+	0.999375i	$0.488749\pi$
$762$	− 1.25206e45i	− 2.67499i
$763$	4.12902e44i	0.864403i
$764$	1.28715e44	0.264047
$765$	0	0
$766$	3.49852e44	0.689189
$767$	4.76696e44i	0.920266i
$768$	4.81514e43i	0.0910983i
$769$	6.38736e44	1.18430	0.592152	−	0.805827i	$-0.298279\pi$
$769$	6.38736e44	1.18430	0.592152	+	0.805827i	$0.298279\pi$
$770$	0	0
$771$	9.73496e44	1.73377
$772$	7.74443e44i	1.35183i
$773$	8.28645e44i	1.41771i	0.705356	+	0.708853i	$0.250787\pi$
$773$	8.28645e44i	1.41771i	−0.705356	+	0.708853i	$0.749213\pi$
$774$	6.38694e44	1.07104
$775$	0	0
$776$	−3.03051e44	−0.488269
$777$	4.36552e44i	0.689462i
$778$	− 1.05383e45i	− 1.63150i
$779$	1.97419e44	0.299611
$780$	0	0
$781$	5.06180e43	0.0738268
$782$	− 3.00018e42i	− 0.00428985i
$783$	6.67041e44i	0.935072i
$784$	−6.18168e43	−0.0849587
$785$	0	0
$786$	3.96860e43	0.0524310
$787$	− 8.07362e44i	− 1.04583i	−0.852386	−	0.522913i	$-0.824845\pi$
$787$	− 8.07362e44i	− 1.04583i	0.852386	−	0.522913i	$-0.175155\pi$
$788$	8.00950e44i	1.01730i
$789$	3.87945e44	0.483144
$790$	0	0
$791$	1.74468e44	0.208920
$792$	− 4.52474e43i	− 0.0531317i
$793$	− 1.09996e45i	− 1.26660i
$794$	−6.98627e44	−0.788910
$795$	0	0
$796$	9.33229e44	1.01353
$797$	8.20375e44i	0.873792i	0.899512	+	0.436896i	$0.143922\pi$
$797$	8.20375e44i	0.873792i	−0.899512	+	0.436896i	$0.856078\pi$
$798$	3.59463e44i	0.375500i
$799$	−8.09564e44	−0.829423
$800$	0	0
$801$	8.72080e43	0.0859513
$802$	7.98461e44i	0.771882i
$803$	9.43583e43i	0.0894724i
$804$	8.52921e44	0.793304
$805$	0	0
$806$	−2.68776e45	−2.40546
$807$	1.03062e45i	0.904812i
$808$	7.25784e44i	0.625073i
$809$	2.25872e44	0.190836	0.0954182	−	0.995437i	$-0.469581\pi$
$809$	2.25872e44	0.190836	0.0954182	+	0.995437i	$0.469581\pi$
$810$	0	0
$811$	−1.42546e45	−1.15913	−0.579565	−	0.814926i	$-0.696778\pi$
$811$	−1.42546e45	−1.15913	−0.579565	+	0.814926i	$0.696778\pi$
$812$	2.56349e45i	2.04509i
$813$	1.23583e44i	0.0967289i
$814$	2.11946e44	0.162760
$815$	0	0
$816$	−7.72602e44	−0.571161
$817$	3.82657e44i	0.277567i
$818$	1.67512e45i	1.19226i
$819$	7.72039e44	0.539186
$820$	0	0
$821$	−2.34861e44	−0.157940	−0.0789699	−	0.996877i	$-0.525163\pi$
$821$	−2.34861e44	−0.157940	−0.0789699	+	0.996877i	$0.525163\pi$
$822$	− 3.37382e44i	− 0.222643i
$823$	− 2.26372e45i	− 1.46597i	−0.680246	−	0.732984i	$-0.738127\pi$
$823$	− 2.26372e45i	− 1.46597i	0.680246	−	0.732984i	$-0.261873\pi$
$824$	−1.07692e45	−0.684405
$825$	0	0
$826$	−1.92566e45	−1.17866
$827$	1.11856e45i	0.671929i	0.941875	+	0.335965i	$0.109062\pi$
$827$	1.11856e45i	0.671929i	−0.941875	+	0.335965i	$0.890938\pi$
$828$	3.78192e42i	0.00222968i
$829$	2.19670e45	1.27109	0.635544	−	0.772064i	$-0.280776\pi$
$829$	2.19670e45	1.27109	0.635544	+	0.772064i	$0.280776\pi$
$830$	0	0
$831$	−2.45236e45	−1.36700
$832$	3.10017e45i	1.69619i
$833$	2.94738e44i	0.158285i
$834$	−4.13717e45	−2.18087
$835$	0	0
$836$	1.00814e44	0.0512064
$837$	− 1.63202e45i	− 0.813733i
$838$	− 3.15593e45i	− 1.54470i
$839$	−3.71878e45	−1.78686	−0.893429	−	0.449204i	$-0.851707\pi$
$839$	−3.71878e45	−1.78686	−0.893429	+	0.449204i	$0.851707\pi$
$840$	0	0
$841$	3.66359e45	1.69656
$842$	− 3.26923e45i	− 1.48631i
$843$	5.22423e45i	2.33182i
$844$	6.17139e45	2.70442
$845$	0	0
$846$	1.76660e45	0.746274
$847$	− 2.12920e45i	− 0.883128i
$848$	8.16038e43i	0.0332334i
$849$	−3.66359e45	−1.46500
$850$	0	0
$851$	−4.76359e42	−0.00183665
$852$	− 1.90942e45i	− 0.722915i
$853$	− 2.48938e45i	− 0.925509i	−0.886487	−	0.462754i	$-0.846861\pi$
$853$	− 2.48938e45i	− 0.925509i	0.886487	−	0.462754i	$-0.153139\pi$
$854$	4.44337e45	1.62224
$855$	0	0
$856$	1.77603e45	0.625326
$857$	− 8.68133e44i	− 0.300181i	−0.988672	−	0.150091i	$-0.952043\pi$
$857$	− 8.68133e44i	− 0.300181i	0.988672	−	0.150091i	$-0.0479565\pi$
$858$	− 1.06723e45i	− 0.362413i
$859$	1.43587e45	0.478875	0.239437	−	0.970912i	$-0.423037\pi$
$859$	1.43587e45	0.478875	0.239437	+	0.970912i	$0.423037\pi$
$860$	0	0
$861$	4.87684e45	1.56888
$862$	− 1.16869e45i	− 0.369265i
$863$	3.91776e45i	1.21582i	0.794005	+	0.607911i	$0.207992\pi$
$863$	3.91776e45i	1.21582i	−0.794005	+	0.607911i	$0.792008\pi$
$864$	−2.48572e45	−0.757687
$865$	0	0
$866$	5.14729e44	0.151374
$867$	− 6.14076e44i	− 0.177389i
$868$	− 6.27199e45i	− 1.77971i
$869$	4.32111e44	0.120445
$870$	0	0
$871$	1.89991e45	0.511036
$872$	− 2.03339e45i	− 0.537299i
$873$	1.79914e45i	0.467030i
$874$	−3.92241e42	−0.00100029
$875$	0	0
$876$	3.55939e45	0.876117
$877$	− 2.59910e45i	− 0.628535i	−0.949335	−	0.314267i	$-0.898241\pi$
$877$	− 2.59910e45i	− 0.628535i	0.949335	−	0.314267i	$-0.101759\pi$
$878$	− 1.22678e45i	− 0.291476i
$879$	−2.87630e45	−0.671438
$880$	0	0
$881$	1.04135e45	0.234676	0.117338	−	0.993092i	$-0.462564\pi$
$881$	1.04135e45	0.234676	0.117338	+	0.993092i	$0.462564\pi$
$882$	− 6.43168e44i	− 0.142417i
$883$	9.31982e44i	0.202776i	0.994847	+	0.101388i	$0.0323284\pi$
$883$	9.31982e44i	0.202776i	−0.994847	+	0.101388i	$0.967672\pi$
$884$	6.47943e45	1.38524
$885$	0	0
$886$	−6.57863e44	−0.135804
$887$	1.93996e45i	0.393529i	0.980451	+	0.196764i	$0.0630434\pi$
$887$	1.93996e45i	0.393529i	−0.980451	+	0.196764i	$0.936957\pi$
$888$	− 2.14986e45i	− 0.428558i
$889$	6.50823e45	1.27493
$890$	0	0
$891$	1.14425e45	0.216478
$892$	− 7.71020e45i	− 1.43354i
$893$	1.05842e45i	0.193401i
$894$	−1.46249e46	−2.62641
$895$	0	0
$896$	−5.53934e45	−0.960913
$897$	2.39864e43i	0.00408961i
$898$	− 1.28459e46i	− 2.15269i
$899$	−1.42469e46	−2.34664
$900$	0	0
$901$	3.89082e44	0.0619165
$902$	− 2.36771e45i	− 0.370362i
$903$	9.45278e45i	1.45345i
$904$	−8.59192e44	−0.129861
$905$	0	0
$906$	−1.44970e46	−2.11734
$907$	− 8.10222e45i	− 1.16330i	−0.813440	−	0.581649i	$-0.802408\pi$
$907$	− 8.10222e45i	− 1.16330i	0.813440	−	0.581649i	$-0.197592\pi$
$908$	− 3.40990e44i	− 0.0481294i
$909$	4.30880e45	0.597883
$910$	0	0
$911$	−1.13425e46	−1.52115	−0.760575	−	0.649250i	$-0.775083\pi$
$911$	−1.13425e46	−1.52115	−0.760575	+	0.649250i	$0.775083\pi$
$912$	1.01009e45i	0.133181i
$913$	− 1.09158e45i	− 0.141501i
$914$	−5.01671e45	−0.639370
$915$	0	0
$916$	4.11167e45	0.506569
$917$	2.06289e44i	0.0249892i
$918$	6.81075e45i	0.811210i
$919$	−1.39631e46	−1.63527	−0.817637	−	0.575734i	$-0.804717\pi$
$919$	−1.39631e46	−1.63527	−0.817637	+	0.575734i	$0.804717\pi$
$920$	0	0
$921$	−6.50516e45	−0.736604
$922$	− 1.53322e45i	− 0.170716i
$923$	− 4.25329e45i	− 0.465692i
$924$	2.49041e45	0.268137
$925$	0	0
$926$	2.62982e46	2.73814
$927$	6.39344e45i	0.654634i
$928$	2.16994e46i	2.18501i
$929$	3.21761e45	0.318632	0.159316	−	0.987228i	$-0.449071\pi$
$929$	3.21761e45	0.318632	0.159316	+	0.987228i	$0.449071\pi$
$930$	0	0
$931$	3.85338e44	0.0369081
$932$	2.10054e46i	1.97872i
$933$	− 1.31062e46i	− 1.21426i
$934$	2.39042e46	2.17820
$935$	0	0
$936$	−3.80201e45	−0.335149
$937$	1.44001e46i	1.24853i	0.781211	+	0.624267i	$0.214602\pi$
$937$	1.44001e46i	1.24853i	−0.781211	+	0.624267i	$0.785398\pi$
$938$	7.67485e45i	0.654524i
$939$	9.49221e45	0.796252
$940$	0	0
$941$	−1.38781e46	−1.12640	−0.563198	−	0.826322i	$-0.690429\pi$
$941$	−1.38781e46	−1.12640	−0.563198	+	0.826322i	$0.690429\pi$
$942$	3.52737e46i	2.81619i
$943$	5.32153e43i	0.00417931i
$944$	−5.41109e45	−0.418041
$945$	0	0
$946$	4.58933e45	0.343112
$947$	− 3.58686e45i	− 0.263809i	−0.991262	−	0.131905i	$-0.957891\pi$
$947$	− 3.58686e45i	− 0.263809i	0.991262	−	0.131905i	$-0.0421093\pi$
$948$	− 1.63001e46i	− 1.17940i
$949$	7.92866e45	0.564383
$950$	0	0
$951$	−3.01308e46	−2.07593
$952$	7.03822e45i	0.477079i
$953$	− 8.63539e45i	− 0.575893i	−0.957646	−	0.287947i	$-0.907027\pi$
$953$	− 8.63539e45i	− 0.575893i	0.957646	−	0.287947i	$-0.0929725\pi$
$954$	−8.49040e44	−0.0557094
$955$	0	0
$956$	8.71088e45	0.553305
$957$	− 5.65702e45i	− 0.353552i
$958$	1.27110e46i	0.781656i
$959$	1.75372e45	0.106114
$960$	0	0
$961$	1.77883e46	1.04213
$962$	− 1.78092e46i	− 1.02667i
$963$	− 1.05439e46i	− 0.598125i
$964$	2.11645e46	1.18145
$965$	0	0
$966$	−9.68952e43	−0.00523789
$967$	− 1.07239e46i	− 0.570481i	−0.958456	−	0.285241i	$-0.907927\pi$
$967$	− 1.07239e46i	− 0.570481i	0.958456	−	0.285241i	$-0.0920735\pi$
$968$	1.04855e46i	0.548938i
$969$	4.81605e45	0.248126
$970$	0	0
$971$	1.69197e46	0.844295	0.422148	−	0.906527i	$-0.361276\pi$
$971$	1.69197e46	0.844295	0.422148	+	0.906527i	$0.361276\pi$
$972$	− 2.73038e46i	− 1.34090i
$973$	− 2.15051e46i	− 1.03942i
$974$	2.11153e46	1.00446
$975$	0	0
$976$	1.24859e46	0.575369
$977$	− 1.63831e46i	− 0.743069i	−0.928419	−	0.371534i	$-0.878832\pi$
$977$	− 1.63831e46i	− 0.743069i	0.928419	−	0.371534i	$-0.121168\pi$
$978$	3.59700e46i	1.60579i
$979$	6.26632e44	0.0275347
$980$	0	0
$981$	−1.20718e46	−0.513927
$982$	2.04776e46i	0.858126i
$983$	− 1.26750e46i	− 0.522839i	−0.965225	−	0.261419i	$-0.915809\pi$
$983$	− 1.26750e46i	− 0.522839i	0.965225	−	0.261419i	$-0.0841906\pi$
$984$	−2.40167e46	−0.975190
$985$	0	0
$986$	5.94552e46	2.33936
$987$	2.61461e46i	1.01272i
$988$	− 8.47114e45i	− 0.323005i
$989$	−1.03147e44	−0.00387182
$990$	0	0
$991$	−3.41939e46	−1.24396	−0.621980	−	0.783033i	$-0.713672\pi$
$991$	−3.41939e46	−1.24396	−0.621980	+	0.783033i	$0.713672\pi$
$992$	− 5.30911e46i	− 1.90148i
$993$	− 2.56276e46i	− 0.903638i
$994$	1.71815e46	0.596449
$995$	0	0
$996$	−4.11767e46	−1.38558
$997$	3.16608e46i	1.04893i	0.851432	+	0.524466i	$0.175735\pi$
$997$	3.16608e46i	1.04893i	−0.851432	+	0.524466i	$0.824265\pi$
$998$	8.49707e46i	2.77170i
$999$	1.08139e46	0.347309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.32.b.a.24.4		4
5.2	odd	4		25.32.a.a.1.1		2
5.3	odd	4		1.32.a.a.1.2	✓	2
5.4	even	2	inner	25.32.b.a.24.1		4
15.8	even	4		9.32.a.a.1.1		2
20.3	even	4		16.32.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.2	✓	2	5.3	odd	4
9.32.a.a.1.1		2	15.8	even	4
16.32.a.b.1.1		2	20.3	even	4
25.32.a.a.1.1		2	5.2	odd	4
25.32.b.a.24.1		4	5.4	even	2	inner
25.32.b.a.24.4		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)

\(f(q)\)	\(=\)	\(q+71307.9i q^{2} -3.08552e7i q^{3} -2.93733e9 q^{4} +2.20022e12 q^{6} +1.14368e13i q^{7} -5.63222e13i q^{8} -3.34371e14 q^{9} +O(q^{10})\)	\(q+71307.9i q^{2} -3.08552e7i q^{3} -2.93733e9 q^{4} +2.20022e12 q^{6} +1.14368e13i q^{7} -5.63222e13i q^{8} -3.34371e14 q^{9} -2.40262e15 q^{11} +9.06319e16i q^{12} +2.01886e17i q^{13} -8.15534e17 q^{14} -2.29165e18 q^{16} +1.09264e19i q^{17} -2.38433e19i q^{18} +1.42851e19 q^{19} +3.52885e20 q^{21} -1.71326e20i q^{22} +3.85062e18i q^{23} -1.73783e21 q^{24} -1.43960e22 q^{26} -8.74135e21i q^{27} -3.35937e22i q^{28} -7.63087e22 q^{29} +1.86701e23 q^{31} -2.84364e23i q^{32} +7.41334e22i q^{33} -7.79141e23 q^{34} +9.82158e23 q^{36} +1.23709e24i q^{37} +1.01864e24i q^{38} +6.22922e24 q^{39} +1.38199e25 q^{41} +2.51635e25i q^{42} +2.67871e25i q^{43} +7.05729e24 q^{44} -2.74580e23 q^{46} +7.40922e25i q^{47} +7.07094e25i q^{48} +2.69748e25 q^{49} +3.37138e26 q^{51} -5.93004e26i q^{52} -3.56092e25i q^{53} +6.23327e26 q^{54} +6.44146e26 q^{56} -4.40770e26i q^{57} -5.44141e27i q^{58} +2.36122e27 q^{59} -5.44842e27 q^{61} +1.33133e28i q^{62} -3.82414e27i q^{63} +1.53561e28 q^{64} -5.28630e27 q^{66} -9.41082e27i q^{67} -3.20945e28i q^{68} +1.18812e26 q^{69} -2.10678e28 q^{71} +1.88325e28i q^{72} -3.92731e28i q^{73} -8.82146e28 q^{74} -4.19601e28 q^{76} -2.74783e28i q^{77} +4.44193e29i q^{78} -1.79850e29 q^{79} -4.76249e29 q^{81} +9.85468e29i q^{82} +4.54329e29i q^{83} -1.03654e30 q^{84} -1.91013e30 q^{86} +2.35452e30i q^{87} +1.35321e29i q^{88} -2.60812e29 q^{89} -2.30893e30 q^{91} -1.13106e28i q^{92} -5.76072e30i q^{93} -5.28336e30 q^{94} -8.77410e30 q^{96} -5.38067e30i q^{97} +1.92352e30i q^{98} +8.03368e29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3545068672 q^{4} + 5246334992448 q^{6} + 202532912607852 q^{9}+O(q^{10}) \) 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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