LMFDB - Embedded newform 1.32.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,32,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

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:	yes
Analytic conductor:	$6.08771328190$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4573872 $ x^2 - x - 4573872
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2139.16$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-31347.9 q^{2} -1.34921e7 q^{3} -1.16479e9 q^{4} +6.31161e10 q^{5} +4.22947e11 q^{6} +1.88207e13 q^{7} +1.03833e14 q^{8} -4.35638e14 q^{9} +O(q^{10})$	\(q-31347.9 q^{2} -1.34921e7 q^{3} -1.16479e9 q^{4} +6.31161e10 q^{5} +4.22947e11 q^{6} +1.88207e13 q^{7} +1.03833e14 q^{8} -4.35638e14 q^{9} -1.97855e15 q^{10} -5.37973e15 q^{11} +1.57155e16 q^{12} +2.76595e17 q^{13} -5.89989e17 q^{14} -8.51566e17 q^{15} -7.53562e17 q^{16} +6.29817e18 q^{17} +1.36563e19 q^{18} +1.91455e18 q^{19} -7.35172e19 q^{20} -2.53930e20 q^{21} +1.68643e20 q^{22} +1.90120e21 q^{23} -1.40092e21 q^{24} -6.72976e20 q^{25} -8.67065e21 q^{26} +1.42113e22 q^{27} -2.19223e22 q^{28} +5.22675e22 q^{29} +2.66948e22 q^{30} -6.09679e22 q^{31} -1.99357e23 q^{32} +7.25837e22 q^{33} -1.97434e23 q^{34} +1.18789e24 q^{35} +5.07428e23 q^{36} -2.07091e24 q^{37} -6.00172e22 q^{38} -3.73183e24 q^{39} +6.55352e24 q^{40} -5.09498e24 q^{41} +7.96017e24 q^{42} +8.39002e24 q^{43} +6.26628e24 q^{44} -2.74957e25 q^{45} -5.95984e25 q^{46} +2.13587e25 q^{47} +1.01671e25 q^{48} +1.96444e26 q^{49} +2.10964e25 q^{50} -8.49753e25 q^{51} -3.22176e26 q^{52} +1.59213e26 q^{53} -4.45495e26 q^{54} -3.39547e26 q^{55} +1.95421e27 q^{56} -2.58313e25 q^{57} -1.63847e27 q^{58} +2.16250e27 q^{59} +9.91899e26 q^{60} -6.60780e27 q^{61} +1.91122e27 q^{62} -8.19901e27 q^{63} +7.86767e27 q^{64} +1.74576e28 q^{65} -2.27534e27 q^{66} -2.77322e26 q^{67} -7.33607e27 q^{68} -2.56510e28 q^{69} -3.72378e28 q^{70} +7.68524e28 q^{71} -4.52335e28 q^{72} +2.29610e28 q^{73} +6.49186e28 q^{74} +9.07984e27 q^{75} -2.23006e27 q^{76} -1.01250e29 q^{77} +1.16985e29 q^{78} -2.99014e29 q^{79} -4.75619e28 q^{80} +7.73416e28 q^{81} +1.59717e29 q^{82} +1.89466e29 q^{83} +2.95777e29 q^{84} +3.97516e29 q^{85} -2.63009e29 q^{86} -7.05196e29 q^{87} -5.58593e29 q^{88} -2.41523e30 q^{89} +8.61933e29 q^{90} +5.20571e30 q^{91} -2.21450e30 q^{92} +8.22583e29 q^{93} -6.69551e29 q^{94} +1.20839e29 q^{95} +2.68973e30 q^{96} -3.68010e30 q^{97} -6.15810e30 q^{98} +2.34361e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 39960 q^{2} + 17363160 q^{3} + 1772534336 q^{4} - 19391218020 q^{5} + 2623167496224 q^{6} + 30257527577200 q^{7} + 160155058705920 q^{8} - 101266456303926 q^{9}+O(q^{10}) $ 2 * q + 39960 * q^2 + 17363160 * q^3 + 1772534336 * q^4 - 19391218020 * q^5 + 2623167496224 * q^6 + 30257527577200 * q^7 + 160155058705920 * q^8 - 101266456303926 * q^9	$ 2 q + 39960 q^{2} + 17363160 q^{3} + 1772534336 q^{4} - 19391218020 q^{5} + 2623167496224 q^{6} + 30257527577200 q^{7} + 160155058705920 q^{8} - 101266456303926 q^{9} - 78\!\cdots\!20 q^{10}+ \cdots + 15\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 39960 * q^2 + 17363160 * q^3 + 1772534336 * q^4 - 19391218020 * q^5 + 2623167496224 * q^6 + 30257527577200 * q^7 + 160155058705920 * q^8 - 101266456303926 * q^9 - 7861972212281520 * q^10 - 7782353745118776 * q^11 + 106347410955313920 * q^12 + 74708953050260620 * q^13 + 225544963845241152 * q^14 - 3397345822674581040 * q^15 - 3045212913684901888 * q^16 + 17224607828987089380 * q^17 + 37499616229575978360 * q^18 - 12370563328022164040 * q^19 - 315868245501283090560 * q^20 + 98954957416071161664 * q^21 - 2682713032996690080 * q^22 + 1897344841989911219280 * q^23 + 336914041234261985280 * q^24 + 1477861250884539239150 * q^25 - 23066680666744323279216 * q^26 + 5469986602319662295280 * q^27 + 11671395808124240043520 * q^28 + 128576144217217055807340 * q^29 - 154839394101764341823040 * q^30 + 125733527517961838793664 * q^31 - 483720527174276002775040 * q^32 - 1549761835334435045280 * q^33 + 581706909571293028834992 * q^34 + 244269703121729304206880 * q^35 + 1489586748818199413504832 * q^36 - 833815207054016911025060 * q^37 - 1078658489244045513633120 * q^38 - 9961054164411363568284912 * q^39 + 1906531481497967156966400 * q^40 + 8724924335662925840671284 * q^41 + 33123669600002676603713280 * q^42 - 18397105293779438708372600 * q^43 - 791008370873332311322368 * q^44 - 55083793466681039024257140 * q^45 - 59873011445275600509089856 * q^46 + 95450963964856190793148320 * q^47 - 60542278614741008947691520 * q^48 + 169469294372320202530407186 * q^49 + 174468018688948298981615400 * q^50 + 252162404739970320085380144 * q^51 - 915180155081494236104643200 * q^52 + 194822508473721098983660860 * q^53 - 1068822271687374190070274240 * q^54 - 141313671368671671047892240 * q^55 + 2598355397749815172431728640 * q^56 - 466601717043760934967596640 * q^57 + 3802934506602438134028187920 * q^58 - 198723263547765513990746520 * q^59 - 6485894626584890581155141120 * q^60 - 12056218201113004361157656276 * q^61 + 15224500099333079134598257920 * q^62 - 4374875036601718967620305360 * q^63 - 7488413368264058547677691904 * q^64 + 34114584794425827928886318760 * q^65 - 7561640583442461364265814912 * q^66 - 9688140802872256994032247720 * q^67 + 24758471836626330094958252160 * q^68 - 25769856286394326078494576192 * q^69 - 104525335953756946154610069120 * q^70 + 55784576625034657512878287344 * q^71 - 26400994734811244163462812160 * q^72 + 62234095932086098750552955380 * q^73 + 153133163632488378484794299472 * q^74 + 75444402265645086720647965800 * q^75 - 44190149699939358902474481920 * q^76 - 128728748793695217194494555200 * q^77 - 327207773523327347562124449600 * q^78 - 119164191093299704964212710560 * q^79 + 141515971255973138522638049280 * q^80 - 398906922646891269649062634158 * q^81 + 1145184549692595779551104209520 * q^82 - 264863373681569145625357596360 * q^83 + 1332316649919851794889339185152 * q^84 - 503995105657776450242931421320 * q^85 - 2173142482222838422832927019936 * q^86 + 1649324800814841914442821796240 * q^87 - 693913929707398651948752168960 * q^88 - 2154414614246670291602721895980 * q^89 - 1105313102749861362639913526640 * q^90 + 2896781368068903069956049509024 * q^91 - 2225812737244025604862645470720 * q^92 + 6583298380663842229690665227520 * q^93 + 4613808251402558431525114250112 * q^94 + 1299465173198290044974084355600 * q^95 - 6084370432669606716368714858496 * q^96 - 9060767994874032615529957205180 * q^97 - 8081619677193750912975770689320 * q^98 + 1540246307744094989457731085288 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−31347.9	−0.676462	−0.338231	−	0.941063i	$-0.609828\pi$
$2$	−31347.9	−0.676462	−0.338231	+	0.941063i	$0.609828\pi$
$3$	−1.34921e7	−0.542874	−0.271437	−	0.962456i	$-0.587499\pi$
$3$	−1.34921e7	−0.542874	−0.271437	+	0.962456i	$0.587499\pi$
$4$	−1.16479e9	−0.542400
$5$	6.31161e10	0.924921	0.462461	−	0.886640i	$-0.346967\pi$
$5$	6.31161e10	0.924921	0.462461	+	0.886640i	$0.346967\pi$
$6$	4.22947e11	0.367233
$7$	1.88207e13	1.49836	0.749181	−	0.662366i	$-0.230447\pi$
$7$	1.88207e13	1.49836	0.749181	+	0.662366i	$0.230447\pi$
$8$	1.03833e14	1.04337
$9$	−4.35638e14	−0.705288
$10$	−1.97855e15	−0.625674
$11$	−5.37973e15	−0.388306	−0.194153	−	0.980971i	$-0.562196\pi$
$11$	−5.37973e15	−0.388306	−0.194153	+	0.980971i	$0.562196\pi$
$12$	1.57155e16	0.294455
$13$	2.76595e17	1.49872	0.749362	−	0.662161i	$-0.230360\pi$
$13$	2.76595e17	1.49872	0.749362	+	0.662161i	$0.230360\pi$
$14$	−5.89989e17	−1.01358
$15$	−8.51566e17	−0.502115
$16$	−7.53562e17	−0.163403
$17$	6.29817e18	0.533649	0.266825	−	0.963745i	$-0.414026\pi$
$17$	6.29817e18	0.533649	0.266825	+	0.963745i	$0.414026\pi$
$18$	1.36563e19	0.477100
$19$	1.91455e18	0.0289326	0.0144663	−	0.999895i	$-0.495395\pi$
$19$	1.91455e18	0.0289326	0.0144663	+	0.999895i	$0.495395\pi$
$20$	−7.35172e19	−0.501677
$21$	−2.53930e20	−0.813421
$22$	1.68643e20	0.262674
$23$	1.90120e21	1.48678	0.743388	−	0.668861i	$-0.233218\pi$
$23$	1.90120e21	1.48678	0.743388	+	0.668861i	$0.233218\pi$
$24$	−1.40092e21	−0.566420
$25$	−6.72976e20	−0.144521
$26$	−8.67065e21	−1.01383
$27$	1.42113e22	0.925756
$28$	−2.19223e22	−0.812711
$29$	5.22675e22	1.12477	0.562384	−	0.826877i	$-0.309884\pi$
$29$	5.22675e22	1.12477	0.562384	+	0.826877i	$0.309884\pi$
$30$	2.66948e22	0.339662
$31$	−6.09679e22	−0.466654	−0.233327	−	0.972398i	$-0.574961\pi$
$31$	−6.09679e22	−0.466654	−0.233327	+	0.972398i	$0.574961\pi$
$32$	−1.99357e23	−0.932838
$33$	7.25837e22	0.210801
$34$	−1.97434e23	−0.360993
$35$	1.18789e24	1.38587
$36$	5.07428e23	0.382548
$37$	−2.07091e24	−1.02102	−0.510510	−	0.859872i	$-0.670543\pi$
$37$	−2.07091e24	−1.02102	−0.510510	+	0.859872i	$0.670543\pi$
$38$	−6.00172e22	−0.0195718
$39$	−3.73183e24	−0.813618
$40$	6.55352e24	0.965039
$41$	−5.09498e24	−0.511673	−0.255837	−	0.966720i	$-0.582351\pi$
$41$	−5.09498e24	−0.511673	−0.255837	+	0.966720i	$0.582351\pi$
$42$	7.96017e24	0.550248
$43$	8.39002e24	0.402719	0.201359	−	0.979517i	$-0.435464\pi$
$43$	8.39002e24	0.402719	0.201359	+	0.979517i	$0.435464\pi$
$44$	6.26628e24	0.210617
$45$	−2.74957e25	−0.652336
$46$	−5.95984e25	−1.00575
$47$	2.13587e25	0.258261	0.129130	−	0.991628i	$-0.458781\pi$
$47$	2.13587e25	0.258261	0.129130	+	0.991628i	$0.458781\pi$
$48$	1.01671e25	0.0887071
$49$	1.96444e26	1.24509
$50$	2.10964e25	0.0977626
$51$	−8.49753e25	−0.289704
$52$	−3.22176e26	−0.812907
$53$	1.59213e26	0.299022	0.149511	−	0.988760i	$-0.452230\pi$
$53$	1.59213e26	0.299022	0.149511	+	0.988760i	$0.452230\pi$
$54$	−4.45495e26	−0.626238
$55$	−3.39547e26	−0.359152
$56$	1.95421e27	1.56335
$57$	−2.58313e25	−0.0157067
$58$	−1.63847e27	−0.760862
$59$	2.16250e27	0.770459	0.385229	−	0.922821i	$-0.374122\pi$
$59$	2.16250e27	0.770459	0.385229	+	0.922821i	$0.374122\pi$
$60$	9.91899e26	0.272347
$61$	−6.60780e27	−1.40425	−0.702125	−	0.712053i	$-0.747765\pi$
$61$	−6.60780e27	−1.40425	−0.702125	+	0.712053i	$0.747765\pi$
$62$	1.91122e27	0.315674
$63$	−8.19901e27	−1.05678
$64$	7.86767e27	0.794432
$65$	1.74576e28	1.38620
$66$	−2.27534e27	−0.142599
$67$	−2.77322e26	−0.0137665	−0.00688326	−	0.999976i	$-0.502191\pi$
$67$	−2.77322e26	−0.0137665	−0.00688326	+	0.999976i	$0.502191\pi$
$68$	−7.33607e27	−0.289451
$69$	−2.56510e28	−0.807131
$70$	−3.72378e28	−0.937485
$71$	7.68524e28	1.55293	0.776467	−	0.630158i	$-0.217010\pi$
$71$	7.68524e28	1.55293	0.776467	+	0.630158i	$0.217010\pi$
$72$	−4.52335e28	−0.735879
$73$	2.29610e28	0.301639	0.150819	−	0.988561i	$-0.451809\pi$
$73$	2.29610e28	0.301639	0.150819	+	0.988561i	$0.451809\pi$
$74$	6.49186e28	0.690681
$75$	9.07984e27	0.0784564
$76$	−2.23006e27	−0.0156930
$77$	−1.01250e29	−0.581823
$78$	1.16985e29	0.550381
$79$	−2.99014e29	−1.15471	−0.577353	−	0.816494i	$-0.695914\pi$
$79$	−2.99014e29	−1.15471	−0.577353	+	0.816494i	$0.695914\pi$
$80$	−4.75619e28	−0.151135
$81$	7.73416e28	0.202719
$82$	1.59717e29	0.346127
$83$	1.89466e29	0.340267	0.170134	−	0.985421i	$-0.445580\pi$
$83$	1.89466e29	0.340267	0.170134	+	0.985421i	$0.445580\pi$
$84$	2.95777e29	0.441199
$85$	3.97516e29	0.493584
$86$	−2.63009e29	−0.272424
$87$	−7.05196e29	−0.610606
$88$	−5.58593e29	−0.405148
$89$	−2.41523e30	−1.47032	−0.735162	−	0.677892i	$-0.762894\pi$
$89$	−2.41523e30	−1.47032	−0.735162	+	0.677892i	$0.762894\pi$
$90$	8.61933e29	0.441280
$91$	5.20571e30	2.24563
$92$	−2.21450e30	−0.806426
$93$	8.22583e29	0.253334
$94$	−6.69551e29	−0.174704
$95$	1.20839e29	0.0267603
$96$	2.68973e30	0.506414
$97$	−3.68010e30	−0.590062	−0.295031	−	0.955488i	$-0.595330\pi$
$97$	−3.68010e30	−0.590062	−0.295031	+	0.955488i	$0.595330\pi$
$98$	−6.15810e30	−0.842254
$99$	2.34361e30	0.273868
$100$	7.83879e29	0.0783879
$101$	−4.69650e30	−0.402526	−0.201263	−	0.979537i	$-0.564505\pi$
$101$	−4.69650e30	−0.402526	−0.201263	+	0.979537i	$0.564505\pi$
$102$	2.66379e30	0.195974
$103$	5.49646e30	0.347621	0.173811	−	0.984779i	$-0.444392\pi$
$103$	5.49646e30	0.347621	0.173811	+	0.984779i	$0.444392\pi$
$104$	2.87196e31	1.56373
$105$	−1.60271e31	−0.752351
$106$	−4.99100e30	−0.202277
$107$	5.31108e30	0.186095	0.0930475	−	0.995662i	$-0.470339\pi$
$107$	5.31108e30	0.186095	0.0930475	+	0.995662i	$0.470339\pi$
$108$	−1.65533e31	−0.502130
$109$	−5.09224e31	−1.33906	−0.669528	−	0.742787i	$-0.733503\pi$
$109$	−5.09224e31	−1.33906	−0.669528	+	0.742787i	$0.733503\pi$
$110$	1.06441e31	0.242953
$111$	2.79408e31	0.554285
$112$	−1.41826e31	−0.244836
$113$	5.75758e31	0.866012	0.433006	−	0.901391i	$-0.357453\pi$
$113$	5.75758e31	0.866012	0.433006	+	0.901391i	$0.357453\pi$
$114$	8.09756e29	0.0106250
$115$	1.19996e32	1.37515
$116$	−6.08809e31	−0.610073
$117$	−1.20495e32	−1.05703
$118$	−6.77897e31	−0.521186
$119$	1.18536e32	0.799600
$120$	−8.84205e31	−0.523894
$121$	−1.63002e32	−0.849219
$122$	2.07141e32	0.949922
$123$	6.87418e31	0.277774
$124$	7.10151e31	0.253113
$125$	−3.36383e32	−1.05859
$126$	2.57022e32	0.714869
$127$	3.71246e32	0.913490	0.456745	−	0.889598i	$-0.349015\pi$
$127$	3.71246e32	0.913490	0.456745	+	0.889598i	$0.349015\pi$
$128$	1.81481e32	0.395436
$129$	−1.13199e32	−0.218626
$130$	−5.47257e32	−0.937712
$131$	−6.43836e32	−0.979648	−0.489824	−	0.871821i	$-0.662939\pi$
$131$	−6.43836e32	−0.979648	−0.489824	+	0.871821i	$0.662939\pi$
$132$	−8.45451e31	−0.114338
$133$	3.60333e31	0.0433514
$134$	8.69344e30	0.00931252
$135$	8.96964e32	0.856252
$136$	6.53957e32	0.556796
$137$	−5.70054e32	−0.433259	−0.216629	−	0.976254i	$-0.569506\pi$
$137$	−5.70054e32	−0.433259	−0.216629	+	0.976254i	$0.569506\pi$
$138$	8.04106e32	0.545993
$139$	1.35322e33	0.821557	0.410779	−	0.911735i	$-0.365257\pi$
$139$	1.35322e33	0.821557	0.410779	+	0.911735i	$0.365257\pi$
$140$	−1.38365e33	−0.751694
$141$	−2.88173e32	−0.140203
$142$	−2.40916e33	−1.05050
$143$	−1.48800e33	−0.581963
$144$	3.28280e32	0.115246
$145$	3.29892e33	1.04032
$146$	−7.19780e32	−0.204047
$147$	−2.65044e33	−0.675925
$148$	2.41218e33	0.553801
$149$	5.42559e33	1.12217	0.561086	−	0.827757i	$-0.310384\pi$
$149$	5.42559e33	1.12217	0.561086	+	0.827757i	$0.310384\pi$
$150$	−2.84634e32	−0.0530727
$151$	−2.39015e33	−0.402051	−0.201026	−	0.979586i	$-0.564427\pi$
$151$	−2.39015e33	−0.402051	−0.201026	+	0.979586i	$0.564427\pi$
$152$	1.98794e32	0.0301875
$153$	−2.74372e33	−0.376377
$154$	3.17399e33	0.393581
$155$	−3.84806e33	−0.431619
$156$	4.34682e33	0.441306
$157$	−1.98794e34	−1.82792	−0.913961	−	0.405802i	$-0.866992\pi$
$157$	−1.98794e34	−1.82792	−0.913961	+	0.405802i	$0.866992\pi$
$158$	9.37345e33	0.781115
$159$	−2.14812e33	−0.162331
$160$	−1.25826e34	−0.862802
$161$	3.57819e34	2.22773
$162$	−2.42449e33	−0.137132
$163$	7.84574e33	0.403391	0.201696	−	0.979448i	$-0.435355\pi$
$163$	7.84574e33	0.403391	0.201696	+	0.979448i	$0.435355\pi$
$164$	5.93460e33	0.277531
$165$	4.58119e33	0.194974
$166$	−5.93935e33	−0.230178
$167$	−5.15166e34	−1.81904	−0.909519	−	0.415662i	$-0.863550\pi$
$167$	−5.15166e34	−1.81904	−0.909519	+	0.415662i	$0.863550\pi$
$168$	−2.63663e34	−0.848703
$169$	4.24446e34	1.24617
$170$	−1.24613e34	−0.333890
$171$	−8.34052e32	−0.0204058
$172$	−9.77265e33	−0.218435
$173$	5.04795e34	1.03134	0.515668	−	0.856788i	$-0.327544\pi$
$173$	5.04795e34	1.03134	0.515668	+	0.856788i	$0.327544\pi$
$174$	2.21064e34	0.413052
$175$	−1.26659e34	−0.216544
$176$	4.05396e33	0.0634503
$177$	−2.91765e34	−0.418262
$178$	7.57122e34	0.994617
$179$	−2.60297e34	−0.313507	−0.156754	−	0.987638i	$-0.550103\pi$
$179$	−2.60297e34	−0.313507	−0.156754	+	0.987638i	$0.550103\pi$
$180$	3.20269e34	0.353827
$181$	−1.20765e35	−1.22440	−0.612198	−	0.790705i	$-0.709714\pi$
$181$	−1.20765e35	−1.22440	−0.612198	+	0.790705i	$0.709714\pi$
$182$	−1.63188e35	−1.51908
$183$	8.91529e34	0.762331
$184$	1.97407e35	1.55126
$185$	−1.30708e35	−0.944363
$186$	−2.57862e34	−0.171371
$187$	−3.38825e34	−0.207219
$188$	−2.48785e34	−0.140081
$189$	2.67468e35	1.38712
$190$	−3.78805e33	−0.0181023
$191$	2.27571e35	1.00253	0.501267	−	0.865293i	$-0.332868\pi$
$191$	2.27571e35	1.00253	0.501267	+	0.865293i	$0.332868\pi$
$192$	−1.06151e35	−0.431276
$193$	−1.78027e35	−0.667339	−0.333670	−	0.942690i	$-0.608287\pi$
$193$	−1.78027e35	−0.667339	−0.333670	+	0.942690i	$0.608287\pi$
$194$	1.15363e35	0.399154
$195$	−2.35538e35	−0.752532
$196$	−2.28817e35	−0.675335
$197$	−2.53071e35	−0.690264	−0.345132	−	0.938554i	$-0.612166\pi$
$197$	−2.53071e35	−0.690264	−0.345132	+	0.938554i	$0.612166\pi$
$198$	−7.34673e34	−0.185261
$199$	4.51723e35	1.05354	0.526768	−	0.850009i	$-0.323404\pi$
$199$	4.51723e35	1.05354	0.526768	+	0.850009i	$0.323404\pi$
$200$	−6.98771e34	−0.150789
$201$	3.74164e33	0.00747348
$202$	1.47225e35	0.272293
$203$	9.83712e35	1.68531
$204$	9.89787e34	0.157136
$205$	−3.21575e35	−0.473257
$206$	−1.72302e35	−0.235152
$207$	−8.28232e35	−1.04860
$208$	−2.08431e35	−0.244896
$209$	−1.02998e34	−0.0112347
$210$	5.02415e35	0.508936
$211$	6.25554e34	0.0588690	0.0294345	−	0.999567i	$-0.490629\pi$
$211$	6.25554e34	0.0588690	0.0294345	+	0.999567i	$0.490629\pi$
$212$	−1.85451e35	−0.162190
$213$	−1.03690e36	−0.843047
$214$	−1.66491e35	−0.125886
$215$	5.29545e35	0.372483
$216$	1.47560e36	0.965910
$217$	−1.14746e36	−0.699217
$218$	1.59631e36	0.905819
$219$	−3.09792e35	−0.163752
$220$	3.95503e35	0.194804
$221$	1.74204e36	0.799793
$222$	−8.75886e35	−0.374953
$223$	1.14032e35	0.0455303	0.0227652	−	0.999741i	$-0.492753\pi$
$223$	1.14032e35	0.0455303	0.0227652	+	0.999741i	$0.492753\pi$
$224$	−3.75204e36	−1.39773
$225$	2.93174e35	0.101929
$226$	−1.80488e36	−0.585824
$227$	1.82276e35	0.0552496	0.0276248	−	0.999618i	$-0.491206\pi$
$227$	1.82276e35	0.0552496	0.0276248	+	0.999618i	$0.491206\pi$
$228$	3.00881e34	0.00851932
$229$	2.02123e36	0.534768	0.267384	−	0.963590i	$-0.413841\pi$
$229$	2.02123e36	0.534768	0.267384	+	0.963590i	$0.413841\pi$
$230$	−3.76162e36	−0.930236
$231$	1.36608e36	0.315856
$232$	5.42708e36	1.17355
$233$	3.92949e35	0.0794912	0.0397456	−	0.999210i	$-0.487345\pi$
$233$	3.92949e35	0.0794912	0.0397456	+	0.999210i	$0.487345\pi$
$234$	3.77726e36	0.715042
$235$	1.34808e36	0.238871
$236$	−2.51886e36	−0.417897
$237$	4.03432e36	0.626860
$238$	−3.71585e36	−0.540898
$239$	−1.39161e37	−1.89823	−0.949115	−	0.314931i	$-0.898019\pi$
$239$	−1.39161e37	−1.89823	−0.949115	+	0.314931i	$0.898019\pi$
$240$	6.41708e35	0.0820471
$241$	−1.56350e36	−0.187428	−0.0937140	−	0.995599i	$-0.529874\pi$
$241$	−1.56350e36	−0.187428	−0.0937140	+	0.995599i	$0.529874\pi$
$242$	5.10976e36	0.574464
$243$	−9.82146e36	−1.03581
$244$	7.69673e36	0.761665
$245$	1.23988e37	1.15161
$246$	−2.15491e36	−0.187903
$247$	5.29555e35	0.0433619
$248$	−6.33048e36	−0.486895
$249$	−2.55628e36	−0.184722
$250$	1.05449e37	0.716096
$251$	7.69469e36	0.491189	0.245594	−	0.969373i	$-0.421017\pi$
$251$	7.69469e36	0.491189	0.245594	+	0.969373i	$0.421017\pi$
$252$	9.55017e36	0.573195
$253$	−1.02279e37	−0.577324
$254$	−1.16378e37	−0.617941
$255$	−5.36330e36	−0.267954
$256$	−2.25847e37	−1.06193
$257$	4.19824e37	1.85825	0.929125	−	0.369765i	$-0.120562\pi$
$257$	4.19824e37	1.85825	0.929125	+	0.369765i	$0.120562\pi$
$258$	3.54854e36	0.147892
$259$	−3.89760e37	−1.52986
$260$	−2.03345e37	−0.751875
$261$	−2.27697e37	−0.793285
$262$	2.01829e37	0.662694
$263$	5.61748e37	1.73871	0.869356	−	0.494186i	$-0.164534\pi$
$263$	5.61748e37	1.73871	0.869356	+	0.494186i	$0.164534\pi$
$264$	7.53657e36	0.219944
$265$	1.00489e37	0.276572
$266$	−1.12957e36	−0.0293256
$267$	3.25864e37	0.798200
$268$	3.23023e35	0.00746696
$269$	−3.06746e37	−0.669296	−0.334648	−	0.942343i	$-0.608617\pi$
$269$	−3.06746e37	−0.669296	−0.334648	+	0.942343i	$0.608617\pi$
$270$	−2.81179e37	−0.579221
$271$	−6.26560e35	−0.0121882	−0.00609409	−	0.999981i	$-0.501940\pi$
$271$	−6.26560e35	−0.0121882	−0.00609409	+	0.999981i	$0.501940\pi$
$272$	−4.74606e36	−0.0871998
$273$	−7.02357e37	−1.21909
$274$	1.78700e37	0.293083
$275$	3.62043e36	0.0561182
$276$	2.98782e37	0.437788
$277$	−4.05908e37	−0.562330	−0.281165	−	0.959660i	$-0.590721\pi$
$277$	−4.05908e37	−0.562330	−0.281165	+	0.959660i	$0.590721\pi$
$278$	−4.24205e37	−0.555752
$279$	2.65599e37	0.329126
$280$	1.23342e38	1.44598
$281$	7.11328e37	0.789082	0.394541	−	0.918878i	$-0.370904\pi$
$281$	7.11328e37	0.789082	0.394541	+	0.918878i	$0.370904\pi$
$282$	9.03362e36	0.0948420
$283$	−5.52066e36	−0.0548657	−0.0274329	−	0.999624i	$-0.508733\pi$
$283$	−5.52066e36	−0.0548657	−0.0274329	+	0.999624i	$0.508733\pi$
$284$	−8.95173e37	−0.842311
$285$	−1.63037e36	−0.0145275
$286$	4.66458e37	0.393676
$287$	−9.58912e37	−0.766671
$288$	8.68473e37	0.657920
$289$	−9.96220e37	−0.715218
$290$	−1.03414e38	−0.703737
$291$	4.96521e37	0.320329
$292$	−2.67449e37	−0.163609
$293$	−5.84412e36	−0.0339056	−0.0169528	−	0.999856i	$-0.505396\pi$
$293$	−5.84412e36	−0.0339056	−0.0169528	+	0.999856i	$0.505396\pi$
$294$	8.30855e37	0.457237
$295$	1.36488e38	0.712614
$296$	−2.15028e38	−1.06531
$297$	−7.64532e37	−0.359477
$298$	−1.70081e38	−0.759107
$299$	5.25860e38	2.22827
$300$	−1.05761e37	−0.0425547
$301$	1.57906e38	0.603419
$302$	7.49260e37	0.271972
$303$	6.33655e37	0.218521
$304$	−1.44274e36	−0.00472766
$305$	−4.17058e38	−1.29882
$306$	8.60098e37	0.254604
$307$	−5.70867e38	−1.60653	−0.803267	−	0.595619i	$-0.796907\pi$
$307$	−5.70867e38	−1.60653	−0.803267	+	0.595619i	$0.796907\pi$
$308$	1.17936e38	0.315580
$309$	−7.41586e37	−0.188714
$310$	1.20628e38	0.291973
$311$	−2.73000e38	−0.628604	−0.314302	−	0.949323i	$-0.601770\pi$
$311$	−2.73000e38	−0.628604	−0.314302	+	0.949323i	$0.601770\pi$
$312$	−3.87487e38	−0.848908
$313$	7.96309e38	1.66014	0.830070	−	0.557659i	$-0.188301\pi$
$313$	7.96309e38	1.66014	0.830070	+	0.557659i	$0.188301\pi$
$314$	6.23176e38	1.23652
$315$	−5.17489e38	−0.977435
$316$	3.48290e38	0.626313
$317$	3.34956e38	0.573548	0.286774	−	0.957998i	$-0.407417\pi$
$317$	3.34956e38	0.573548	0.286774	+	0.957998i	$0.407417\pi$
$318$	6.73389e37	0.109811
$319$	−2.81185e38	−0.436754
$320$	4.96577e38	0.734787
$321$	−7.16575e37	−0.101026
$322$	−1.12169e39	−1.50697
$323$	1.20582e37	0.0154398
$324$	−9.00871e37	−0.109955
$325$	−1.86142e38	−0.216596
$326$	−2.45947e38	−0.272879
$327$	6.87049e38	0.726938
$328$	−5.29026e38	−0.533866
$329$	4.01987e38	0.386968
$330$	−1.43611e38	−0.131893
$331$	−8.30533e38	−0.727818	−0.363909	−	0.931435i	$-0.618558\pi$
$331$	−8.30533e38	−0.727818	−0.363909	+	0.931435i	$0.618558\pi$
$332$	−2.20689e38	−0.184561
$333$	9.02166e38	0.720113
$334$	1.61494e39	1.23051
$335$	−1.75034e37	−0.0127330
$336$	1.91352e38	0.132915
$337$	1.14148e39	0.757187	0.378594	−	0.925563i	$-0.376408\pi$
$337$	1.14148e39	0.757187	0.378594	+	0.925563i	$0.376408\pi$
$338$	−1.33055e39	−0.842988
$339$	−7.76816e38	−0.470135
$340$	−4.63024e38	−0.267720
$341$	3.27991e38	0.181205
$342$	2.61457e37	0.0138037
$343$	7.27773e38	0.367229
$344$	8.71160e38	0.420187
$345$	−1.61899e39	−0.746533
$346$	−1.58242e39	−0.697660
$347$	−3.74946e39	−1.58075	−0.790373	−	0.612626i	$-0.790113\pi$
$347$	−3.74946e39	−1.58075	−0.790373	+	0.612626i	$0.790113\pi$
$348$	8.21408e38	0.331193
$349$	7.67977e38	0.296179	0.148089	−	0.988974i	$-0.452688\pi$
$349$	7.67977e38	0.296179	0.148089	+	0.988974i	$0.452688\pi$
$350$	3.97049e38	0.146484
$351$	3.93078e39	1.38745
$352$	1.07249e39	0.362227
$353$	−2.48278e39	−0.802472	−0.401236	−	0.915975i	$-0.631419\pi$
$353$	−2.48278e39	−0.802472	−0.401236	+	0.915975i	$0.631419\pi$
$354$	9.14622e38	0.282938
$355$	4.85062e39	1.43634
$356$	2.81324e39	0.797503
$357$	−1.59930e39	−0.434082
$358$	8.15976e38	0.212076
$359$	−6.14909e39	−1.53055	−0.765274	−	0.643704i	$-0.777397\pi$
$359$	−6.14909e39	−1.53055	−0.765274	+	0.643704i	$0.777397\pi$
$360$	−2.85496e39	−0.680631
$361$	−4.37520e39	−0.999163
$362$	3.78571e39	0.828256
$363$	2.19923e39	0.461018
$364$	−6.06358e39	−1.21803
$365$	1.44921e39	0.278992
$366$	−2.79475e39	−0.515687
$367$	5.66753e39	1.00247	0.501233	−	0.865312i	$-0.332880\pi$
$367$	5.66753e39	1.00247	0.501233	+	0.865312i	$0.332880\pi$
$368$	−1.43267e39	−0.242943
$369$	2.21956e39	0.360877
$370$	4.09741e39	0.638826
$371$	2.99651e39	0.448043
$372$	−9.58140e38	−0.137409
$373$	−8.05893e39	−1.10864	−0.554320	−	0.832303i	$-0.687022\pi$
$373$	−8.05893e39	−1.10864	−0.554320	+	0.832303i	$0.687022\pi$
$374$	1.06214e39	0.140176
$375$	4.53850e39	0.574682
$376$	2.21774e39	0.269463
$377$	1.44569e40	1.68572
$378$	−8.38454e39	−0.938332
$379$	−9.24240e39	−0.992835	−0.496417	−	0.868084i	$-0.665351\pi$
$379$	−9.24240e39	−0.992835	−0.496417	+	0.868084i	$0.665351\pi$
$380$	−1.40753e38	−0.0145148
$381$	−5.00887e39	−0.495910
$382$	−7.13385e39	−0.678175
$383$	9.14893e39	0.835198	0.417599	−	0.908631i	$-0.362872\pi$
$383$	9.14893e39	0.835198	0.417599	+	0.908631i	$0.362872\pi$
$384$	−2.44855e39	−0.214672
$385$	−6.39053e39	−0.538140
$386$	5.58076e39	0.451429
$387$	−3.65501e39	−0.284033
$388$	4.28656e39	0.320049
$389$	−2.19075e40	−1.57172	−0.785858	−	0.618407i	$-0.787778\pi$
$389$	−2.19075e40	−1.57172	−0.785858	+	0.618407i	$0.787778\pi$
$390$	7.38363e39	0.509059
$391$	1.19741e40	0.793417
$392$	2.03974e40	1.29909
$393$	8.68667e39	0.531825
$394$	7.93323e39	0.466937
$395$	−1.88726e40	−1.06801
$396$	−2.72983e39	−0.148546
$397$	2.07807e40	1.08744	0.543722	−	0.839265i	$-0.317015\pi$
$397$	2.07807e40	1.08744	0.543722	+	0.839265i	$0.317015\pi$
$398$	−1.41605e40	−0.712676
$399$	−4.86163e38	−0.0235343
$400$	5.07130e38	0.0236151
$401$	−2.58688e40	−1.15888	−0.579441	−	0.815014i	$-0.696729\pi$
$401$	−2.58688e40	−1.15888	−0.579441	+	0.815014i	$0.696729\pi$
$402$	−1.17292e38	−0.00505552
$403$	−1.68634e40	−0.699386
$404$	5.47046e39	0.218330
$405$	4.88150e39	0.187500
$406$	−3.08373e40	−1.14005
$407$	1.11409e40	0.396468
$408$	−8.82323e39	−0.302270
$409$	4.06410e40	1.34046	0.670229	−	0.742155i	$-0.266196\pi$
$409$	4.06410e40	1.34046	0.670229	+	0.742155i	$0.266196\pi$
$410$	1.00807e40	0.320140
$411$	7.69121e39	0.235205
$412$	−6.40225e39	−0.188550
$413$	4.06997e40	1.15443
$414$	2.59633e40	0.709341
$415$	1.19583e40	0.314721
$416$	−5.51410e40	−1.39807
$417$	−1.82577e40	−0.446002
$418$	3.22876e38	0.00759983
$419$	−6.77858e40	−1.53752	−0.768761	−	0.639536i	$-0.779126\pi$
$419$	−6.77858e40	−1.53752	−0.768761	+	0.639536i	$0.779126\pi$
$420$	1.86683e40	0.408075
$421$	3.82000e40	0.804805	0.402403	−	0.915463i	$-0.368175\pi$
$421$	3.82000e40	0.804805	0.402403	+	0.915463i	$0.368175\pi$
$422$	−1.96098e39	−0.0398226
$423$	−9.30467e39	−0.182148
$424$	1.65316e40	0.311992
$425$	−4.23852e39	−0.0771233
$426$	3.25045e40	0.570289
$427$	−1.24364e41	−2.10407
$428$	−6.18632e39	−0.100938
$429$	2.00762e40	0.315933
$430$	−1.66001e40	−0.251971
$431$	1.21642e41	1.78109	0.890547	−	0.454890i	$-0.150322\pi$
$431$	1.21642e41	1.78109	0.890547	+	0.454890i	$0.150322\pi$
$432$	−1.07091e40	−0.151271
$433$	3.18876e39	0.0434570	0.0217285	−	0.999764i	$-0.493083\pi$
$433$	3.18876e39	0.0434570	0.0217285	+	0.999764i	$0.493083\pi$
$434$	3.59704e40	0.472993
$435$	−4.45092e40	−0.564763
$436$	5.93142e40	0.726303
$437$	3.63994e39	0.0430162
$438$	9.71131e39	0.110772
$439$	7.39242e40	0.813929	0.406965	−	0.913444i	$-0.366587\pi$
$439$	7.39242e40	0.813929	0.406965	+	0.913444i	$0.366587\pi$
$440$	−3.52562e40	−0.374730
$441$	−8.55785e40	−0.878145
$442$	−5.46092e40	−0.541029
$443$	2.28069e40	0.218177	0.109088	−	0.994032i	$-0.465207\pi$
$443$	2.28069e40	0.218177	0.109088	+	0.994032i	$0.465207\pi$
$444$	−3.25453e40	−0.300644
$445$	−1.52440e41	−1.35993
$446$	−3.57466e39	−0.0307995
$447$	−7.32024e40	−0.609198
$448$	1.48075e41	1.19035
$449$	6.27451e40	0.487261	0.243630	−	0.969868i	$-0.421662\pi$
$449$	6.27451e40	0.487261	0.243630	+	0.969868i	$0.421662\pi$
$450$	−9.19038e39	−0.0689508
$451$	2.74096e40	0.198686
$452$	−6.70639e40	−0.469725
$453$	3.22480e40	0.218263
$454$	−5.71397e39	−0.0373742
$455$	3.28564e41	2.07703
$456$	−2.68214e39	−0.0163880
$457$	−2.37596e39	−0.0140326	−0.00701629	−	0.999975i	$-0.502233\pi$
$457$	−2.37596e39	−0.0140326	−0.00701629	+	0.999975i	$0.502233\pi$
$458$	−6.33612e40	−0.361750
$459$	8.95054e40	0.494029
$460$	−1.39771e41	−0.745881
$461$	−6.79165e40	−0.350438	−0.175219	−	0.984529i	$-0.556063\pi$
$461$	−6.79165e40	−0.350438	−0.175219	+	0.984529i	$0.556063\pi$
$462$	−4.28236e40	−0.213665
$463$	−1.40330e41	−0.677090	−0.338545	−	0.940950i	$-0.609935\pi$
$463$	−1.40330e41	−0.677090	−0.338545	+	0.940950i	$0.609935\pi$
$464$	−3.93868e40	−0.183790
$465$	5.19182e40	0.234314
$466$	−1.23181e40	−0.0537727
$467$	−2.95535e41	−1.24795	−0.623976	−	0.781444i	$-0.714484\pi$
$467$	−2.95535e41	−1.24795	−0.623976	+	0.781444i	$0.714484\pi$
$468$	1.40352e41	0.573334
$469$	−5.21939e39	−0.0206272
$470$	−4.22594e40	−0.161587
$471$	2.68214e41	0.992331
$472$	2.24538e41	0.803877
$473$	−4.51361e40	−0.156378
$474$	−1.26467e41	−0.424047
$475$	−1.28845e39	−0.00418135
$476$	−1.38070e41	−0.433703
$477$	−6.93593e40	−0.210897
$478$	4.36239e41	1.28408
$479$	3.59879e41	1.02555	0.512774	−	0.858524i	$-0.328618\pi$
$479$	3.59879e41	1.02555	0.512774	+	0.858524i	$0.328618\pi$
$480$	1.69765e41	0.468393
$481$	−5.72802e41	−1.53023
$482$	4.90125e40	0.126788
$483$	−4.82771e41	−1.20937
$484$	1.89864e41	0.460616
$485$	−2.32273e41	−0.545761
$486$	3.07882e41	0.700684
$487$	8.64633e41	1.90604	0.953022	−	0.302901i	$-0.0979550\pi$
$487$	8.64633e41	1.90604	0.953022	+	0.302901i	$0.0979550\pi$
$488$	−6.86107e41	−1.46516
$489$	−1.05855e41	−0.218990
$490$	−3.88675e41	−0.779018
$491$	−8.25010e41	−1.60212	−0.801062	−	0.598582i	$-0.795731\pi$
$491$	−8.25010e41	−1.60212	−0.801062	+	0.598582i	$0.795731\pi$
$492$	−8.00700e40	−0.150664
$493$	3.29189e41	0.600231
$494$	−1.66004e40	−0.0293327
$495$	1.47920e41	0.253306
$496$	4.59431e40	0.0762526
$497$	1.44642e42	2.32686
$498$	8.01340e40	0.124957
$499$	−4.70553e41	−0.711295	−0.355647	−	0.934620i	$-0.615740\pi$
$499$	−4.70553e41	−0.711295	−0.355647	+	0.934620i	$0.615740\pi$
$500$	3.91817e41	0.574180
$501$	6.95065e41	0.987508
$502$	−2.41212e41	−0.332270
$503$	1.02731e41	0.137214	0.0686068	−	0.997644i	$-0.478145\pi$
$503$	1.02731e41	0.137214	0.0686068	+	0.997644i	$0.478145\pi$
$504$	−8.51327e41	−1.10261
$505$	−2.96425e41	−0.372304
$506$	3.20624e41	0.390537
$507$	−5.72665e41	−0.676515
$508$	−4.32425e41	−0.495477
$509$	−6.79468e41	−0.755168	−0.377584	−	0.925975i	$-0.623245\pi$
$509$	−6.79468e41	−0.755168	−0.377584	+	0.925975i	$0.623245\pi$
$510$	1.68128e41	0.181260
$511$	4.32143e41	0.451964
$512$	3.18257e41	0.322919
$513$	2.72084e40	0.0267845
$514$	−1.31606e42	−1.25704
$515$	3.46915e41	0.321522
$516$	1.31853e41	0.118582
$517$	−1.14904e41	−0.100284
$518$	1.22181e42	1.03489
$519$	−6.81073e41	−0.559886
$520$	1.81267e42	1.44633
$521$	4.70689e41	0.364543	0.182272	−	0.983248i	$-0.441655\pi$
$521$	4.70689e41	0.364543	0.182272	+	0.983248i	$0.441655\pi$
$522$	7.13781e41	0.536627
$523$	−1.48934e42	−1.08697	−0.543485	−	0.839419i	$-0.682895\pi$
$523$	−1.48934e42	−1.08697	−0.543485	+	0.839419i	$0.682895\pi$
$524$	7.49937e41	0.531361
$525$	1.70889e41	0.117556
$526$	−1.76096e42	−1.17617
$527$	−3.83986e41	−0.249030
$528$	−5.46963e40	−0.0344455
$529$	1.97937e42	1.21050
$530$	−3.15012e41	−0.187090
$531$	−9.42065e41	−0.543395
$532$	−4.19714e40	−0.0235138
$533$	−1.40924e42	−0.766857
$534$	−1.02151e42	−0.539951
$535$	3.35215e41	0.172123
$536$	−2.87951e40	−0.0143636
$537$	3.51194e41	0.170195
$538$	9.61583e41	0.452753
$539$	−1.05682e42	−0.483475
$540$	−1.04478e42	−0.464431
$541$	2.37435e42	1.02562	0.512811	−	0.858502i	$-0.328604\pi$
$541$	2.37435e42	1.02562	0.512811	+	0.858502i	$0.328604\pi$
$542$	1.96413e40	0.00824484
$543$	1.62936e42	0.664692
$544$	−1.25558e42	−0.497809
$545$	−3.21402e42	−1.23852
$546$	2.20174e42	0.824670
$547$	3.75591e42	1.36745	0.683725	−	0.729740i	$-0.260359\pi$
$547$	3.75591e42	1.36745	0.683725	+	0.729740i	$0.260359\pi$
$548$	6.63996e41	0.235000
$549$	2.87861e42	0.990401
$550$	−1.13493e41	−0.0379618
$551$	1.00069e41	0.0325424
$552$	−2.66342e42	−0.842140
$553$	−5.62766e42	−1.73017
$554$	1.27243e42	0.380394
$555$	1.76352e42	0.512670
$556$	−1.57622e42	−0.445613
$557$	−5.38624e42	−1.48092	−0.740458	−	0.672103i	$-0.765391\pi$
$557$	−5.38624e42	−1.48092	−0.740458	+	0.672103i	$0.765391\pi$
$558$	−8.32597e41	−0.222641
$559$	2.32063e42	0.603565
$560$	−8.95149e41	−0.226454
$561$	4.57144e41	0.112494
$562$	−2.22986e42	−0.533784
$563$	2.93646e42	0.683823	0.341912	−	0.939732i	$-0.388926\pi$
$563$	2.93646e42	0.683823	0.341912	+	0.939732i	$0.388926\pi$
$564$	3.35663e41	0.0760461
$565$	3.63395e42	0.800993
$566$	1.73061e41	0.0371145
$567$	1.45562e42	0.303747
$568$	7.97981e42	1.62029
$569$	1.22480e42	0.242005	0.121002	−	0.992652i	$-0.461389\pi$
$569$	1.22480e42	0.242005	0.121002	+	0.992652i	$0.461389\pi$
$570$	5.11086e40	0.00982728
$571$	−8.00625e42	−1.49820	−0.749099	−	0.662458i	$-0.769513\pi$
$571$	−8.00625e42	−1.49820	−0.749099	+	0.662458i	$0.769513\pi$
$572$	1.73322e42	0.315657
$573$	−3.07040e42	−0.544249
$574$	3.00598e42	0.518624
$575$	−1.27946e42	−0.214870
$576$	−3.42746e42	−0.560304
$577$	−5.67748e42	−0.903505	−0.451753	−	0.892143i	$-0.649201\pi$
$577$	−5.67748e42	−0.903505	−0.451753	+	0.892143i	$0.649201\pi$
$578$	3.12294e42	0.483818
$579$	2.40195e42	0.362281
$580$	−3.84256e42	−0.564270
$581$	3.56588e42	0.509843
$582$	−1.55649e42	−0.216690
$583$	−8.56525e41	−0.116112
$584$	2.38411e42	0.314722
$585$	−7.60517e42	−0.977672
$586$	1.83201e41	0.0229358
$587$	3.58214e41	0.0436770	0.0218385	−	0.999762i	$-0.493048\pi$
$587$	3.58214e41	0.0436770	0.0218385	+	0.999762i	$0.493048\pi$
$588$	3.08721e42	0.366622
$589$	−1.16726e41	−0.0135015
$590$	−4.27862e42	−0.482056
$591$	3.41445e42	0.374726
$592$	1.56056e42	0.166838
$593$	1.84785e43	1.92450	0.962251	−	0.272164i	$-0.0877395\pi$
$593$	1.84785e43	1.92450	0.962251	+	0.272164i	$0.0877395\pi$
$594$	2.39664e42	0.243172
$595$	7.48153e42	0.739567
$596$	−6.31970e42	−0.608666
$597$	−6.09467e42	−0.571937
$598$	−1.64846e43	−1.50734
$599$	−3.08643e42	−0.275005	−0.137503	−	0.990501i	$-0.543908\pi$
$599$	−3.08643e42	−0.275005	−0.137503	+	0.990501i	$0.543908\pi$
$600$	9.42786e41	0.0818594
$601$	2.05195e43	1.73625	0.868125	−	0.496346i	$-0.165325\pi$
$601$	2.05195e43	1.73625	0.868125	+	0.496346i	$0.165325\pi$
$602$	−4.95003e42	−0.408189
$603$	1.20812e41	0.00970937
$604$	2.78403e42	0.218073
$605$	−1.02880e43	−0.785460
$606$	−1.98637e42	−0.147821
$607$	−2.07151e43	−1.50267	−0.751333	−	0.659923i	$-0.770589\pi$
$607$	−2.07151e43	−1.50267	−0.751333	+	0.659923i	$0.770589\pi$
$608$	−3.81679e41	−0.0269894
$609$	−1.32723e43	−0.914909
$610$	1.30739e43	0.878603
$611$	5.90771e42	0.387062
$612$	3.19587e42	0.204147
$613$	−6.35024e42	−0.395506	−0.197753	−	0.980252i	$-0.563364\pi$
$613$	−6.35024e42	−0.395506	−0.197753	+	0.980252i	$0.563364\pi$
$614$	1.78955e43	1.08676
$615$	4.33871e42	0.256919
$616$	−1.05131e43	−0.607059
$617$	1.92676e43	1.08495	0.542473	−	0.840073i	$-0.317488\pi$
$617$	1.92676e43	1.08495	0.542473	+	0.840073i	$0.317488\pi$
$618$	2.32471e42	0.127658
$619$	7.41921e42	0.397331	0.198666	−	0.980067i	$-0.436339\pi$
$619$	7.41921e42	0.397331	0.198666	+	0.980067i	$0.436339\pi$
$620$	4.48220e42	0.234110
$621$	2.70185e43	1.37639
$622$	8.55798e42	0.425226
$623$	−4.54563e43	−2.20308
$624$	2.81217e42	0.132947
$625$	−1.80974e43	−0.834593
$626$	−2.49626e43	−1.12302
$627$	1.38965e41	0.00609901
$628$	2.31554e43	0.991465
$629$	−1.30429e43	−0.544867
$630$	1.62222e43	0.661197
$631$	−1.64967e43	−0.656058	−0.328029	−	0.944668i	$-0.606384\pi$
$631$	−1.64967e43	−0.656058	−0.328029	+	0.944668i	$0.606384\pi$
$632$	−3.10475e43	−1.20479
$633$	−8.44001e41	−0.0319584
$634$	−1.05002e43	−0.387983
$635$	2.34316e43	0.844906
$636$	2.50211e42	0.0880485
$637$	5.43354e43	1.86604
$638$	8.81455e42	0.295447
$639$	−3.34798e43	−1.09527
$640$	1.14543e43	0.365747
$641$	1.02463e43	0.319349	0.159675	−	0.987170i	$-0.448955\pi$
$641$	1.02463e43	0.319349	0.159675	+	0.987170i	$0.448955\pi$
$642$	2.24631e42	0.0683403
$643$	1.32606e43	0.393817	0.196908	−	0.980422i	$-0.436910\pi$
$643$	1.32606e43	0.393817	0.196908	+	0.980422i	$0.436910\pi$
$644$	−4.16785e43	−1.20832
$645$	−7.14466e42	−0.202211
$646$	−3.77998e41	−0.0104445
$647$	4.58618e43	1.23718	0.618592	−	0.785712i	$-0.287703\pi$
$647$	4.58618e43	1.23718	0.618592	+	0.785712i	$0.287703\pi$
$648$	8.03060e42	0.211512
$649$	−1.16337e43	−0.299174
$650$	5.83514e42	0.146519
$651$	1.54816e43	0.379586
$652$	−9.13868e42	−0.218799
$653$	−1.96584e43	−0.459614	−0.229807	−	0.973236i	$-0.573810\pi$
$653$	−1.96584e43	−0.459614	−0.229807	+	0.973236i	$0.573810\pi$
$654$	−2.15375e43	−0.491746
$655$	−4.06364e43	−0.906097
$656$	3.83938e42	0.0836088
$657$	−1.00027e43	−0.212742
$658$	−1.26014e43	−0.261769
$659$	4.60611e43	0.934568	0.467284	−	0.884107i	$-0.345233\pi$
$659$	4.60611e43	0.934568	0.467284	+	0.884107i	$0.345233\pi$
$660$	−5.33615e42	−0.105754
$661$	−6.03515e43	−1.16833	−0.584165	−	0.811635i	$-0.698578\pi$
$661$	−6.03515e43	−1.16833	−0.584165	+	0.811635i	$0.698578\pi$
$662$	2.60354e43	0.492341
$663$	−2.35037e43	−0.434187
$664$	1.96728e43	0.355026
$665$	2.27428e42	0.0400967
$666$	−2.82810e43	−0.487129
$667$	9.93707e43	1.67228
$668$	6.00063e43	0.986646
$669$	−1.53853e42	−0.0247172
$670$	5.48696e41	0.00861335
$671$	3.55482e43	0.545279
$672$	5.06227e43	0.758790
$673$	−5.70208e43	−0.835218	−0.417609	−	0.908627i	$-0.637132\pi$
$673$	−5.70208e43	−0.835218	−0.417609	+	0.908627i	$0.637132\pi$
$674$	−3.57829e43	−0.512208
$675$	−9.56389e42	−0.133791
$676$	−4.94392e43	−0.675924
$677$	−1.60365e43	−0.214282	−0.107141	−	0.994244i	$-0.534170\pi$
$677$	−1.60365e43	−0.214282	−0.107141	+	0.994244i	$0.534170\pi$
$678$	2.43515e43	0.318028
$679$	−6.92621e43	−0.884126
$680$	4.12752e43	0.514992
$681$	−2.45928e42	−0.0299935
$682$	−1.02818e43	−0.122578
$683$	−6.08600e43	−0.709269	−0.354634	−	0.935005i	$-0.615395\pi$
$683$	−6.08600e43	−0.709269	−0.354634	+	0.935005i	$0.615395\pi$
$684$	9.71499e41	0.0110681
$685$	−3.59796e43	−0.400730
$686$	−2.28141e43	−0.248416
$687$	−2.72705e43	−0.290311
$688$	−6.32240e42	−0.0658054
$689$	4.40375e43	0.448152
$690$	5.07520e43	0.505001
$691$	1.43014e44	1.39146	0.695729	−	0.718304i	$-0.255082\pi$
$691$	1.43014e44	1.39146	0.695729	+	0.718304i	$0.255082\pi$
$692$	−5.87983e43	−0.559397
$693$	4.41085e43	0.410353
$694$	1.17538e44	1.06931
$695$	8.54097e43	0.759876
$696$	−7.32225e43	−0.637091
$697$	−3.20890e43	−0.273054
$698$	−2.40744e43	−0.200354
$699$	−5.30169e42	−0.0431537
$700$	1.47532e43	0.117453
$701$	−5.20421e43	−0.405252	−0.202626	−	0.979256i	$-0.564948\pi$
$701$	−5.20421e43	−0.405252	−0.202626	+	0.979256i	$0.564948\pi$
$702$	−1.23222e44	−0.938559
$703$	−3.96487e42	−0.0295407
$704$	−4.23260e43	−0.308483
$705$	−1.81884e43	−0.129677
$706$	7.78298e43	0.542842
$707$	−8.83916e43	−0.603129
$708$	3.39847e43	0.226865
$709$	2.25028e44	1.46967	0.734836	−	0.678245i	$-0.237259\pi$
$709$	2.25028e44	1.46967	0.734836	+	0.678245i	$0.237259\pi$
$710$	−1.52057e44	−0.971630
$711$	1.30262e44	0.814401
$712$	−2.50780e44	−1.53410
$713$	−1.15912e44	−0.693810
$714$	5.01345e43	0.293640
$715$	−9.39170e43	−0.538270
$716$	3.03193e43	0.170046
$717$	1.87756e44	1.03050
$718$	1.92761e44	1.03536
$719$	−2.22431e44	−1.16922	−0.584611	−	0.811314i	$-0.698753\pi$
$719$	−2.22431e44	−1.16922	−0.584611	+	0.811314i	$0.698753\pi$
$720$	2.07197e43	0.106594
$721$	1.03447e44	0.520862
$722$	1.37153e44	0.675895
$723$	2.10949e43	0.101750
$724$	1.40666e44	0.664112
$725$	−3.51748e43	−0.162552
$726$	−6.89412e43	−0.311861
$727$	−4.26635e44	−1.88918	−0.944591	−	0.328251i	$-0.893541\pi$
$727$	−4.26635e44	−1.88918	−0.944591	+	0.328251i	$0.893541\pi$
$728$	5.40524e44	2.34303
$729$	8.47399e43	0.359593
$730$	−4.54297e43	−0.188727
$731$	5.28418e43	0.214911
$732$	−1.03845e44	−0.413488
$733$	−2.38496e44	−0.929758	−0.464879	−	0.885374i	$-0.653902\pi$
$733$	−2.38496e44	−0.929758	−0.464879	+	0.885374i	$0.653902\pi$
$734$	−1.77665e44	−0.678130
$735$	−1.67285e44	−0.625178
$736$	−3.79016e44	−1.38692
$737$	1.49192e42	0.00534562
$738$	−6.95786e43	−0.244119
$739$	3.50761e44	1.20510	0.602549	−	0.798082i	$-0.294152\pi$
$739$	3.50761e44	1.20510	0.602549	+	0.798082i	$0.294152\pi$
$740$	1.52248e44	0.512223
$741$	−7.14479e42	−0.0235400
$742$	−9.39342e43	−0.303084
$743$	−7.53875e43	−0.238217	−0.119108	−	0.992881i	$-0.538004\pi$
$743$	−7.53875e43	−0.238217	−0.119108	+	0.992881i	$0.538004\pi$
$744$	8.54112e43	0.264323
$745$	3.42442e44	1.03792
$746$	2.52630e44	0.749953
$747$	−8.25384e43	−0.239986
$748$	3.94661e43	0.112396
$749$	9.99584e43	0.278838
$750$	−1.42272e44	−0.388750
$751$	6.25728e44	1.67481	0.837407	−	0.546580i	$-0.184071\pi$
$751$	6.25728e44	1.67481	0.837407	+	0.546580i	$0.184071\pi$
$752$	−1.60951e43	−0.0422006
$753$	−1.03817e44	−0.266654
$754$	−4.53193e44	−1.14032
$755$	−1.50857e44	−0.371866
$756$	−3.11545e44	−0.752372
$757$	−2.09917e43	−0.0496663	−0.0248332	−	0.999692i	$-0.507905\pi$
$757$	−2.09917e43	−0.0496663	−0.0248332	+	0.999692i	$0.507905\pi$
$758$	2.89730e44	0.671615
$759$	1.37996e44	0.313414
$760$	1.25471e43	0.0279210
$761$	−3.45290e43	−0.0752873	−0.0376436	−	0.999291i	$-0.511985\pi$
$761$	−3.45290e43	−0.0752873	−0.0376436	+	0.999291i	$0.511985\pi$
$762$	1.57017e44	0.335464
$763$	−9.58397e44	−2.00639
$764$	−2.65073e44	−0.543774
$765$	−1.73173e44	−0.348119
$766$	−2.86800e44	−0.564979
$767$	5.98135e44	1.15470
$768$	3.04715e44	0.576493
$769$	7.01102e44	1.29994	0.649970	−	0.759960i	$-0.274782\pi$
$769$	7.01102e44	1.29994	0.649970	+	0.759960i	$0.274782\pi$
$770$	2.00329e44	0.364031
$771$	−5.66430e44	−1.00880
$772$	2.07364e44	0.361965
$773$	−2.53762e44	−0.434154	−0.217077	−	0.976154i	$-0.569652\pi$
$773$	−2.53762e44	−0.434154	−0.217077	+	0.976154i	$0.569652\pi$
$774$	1.14577e44	0.192137
$775$	4.10300e43	0.0674411
$776$	−3.82115e44	−0.615655
$777$	5.25867e44	0.830519
$778$	6.86753e44	1.06321
$779$	−9.75461e42	−0.0148040
$780$	2.74354e44	0.408173
$781$	−4.13445e44	−0.603014
$782$	−3.75361e44	−0.536716
$783$	7.42791e44	1.04126
$784$	−1.48033e44	−0.203451
$785$	−1.25471e45	−1.69068
$786$	−2.72309e44	−0.359759
$787$	5.16912e44	0.669589	0.334795	−	0.942291i	$-0.391333\pi$
$787$	5.16912e44	0.669589	0.334795	+	0.942291i	$0.391333\pi$
$788$	2.94775e44	0.374399
$789$	−7.57914e44	−0.943901
$790$	5.91615e44	0.722470
$791$	1.08362e45	1.29760
$792$	2.43344e44	0.285746
$793$	−1.82768e45	−2.10458
$794$	−6.51430e44	−0.735614
$795$	−1.35581e44	−0.150144
$796$	−5.26164e44	−0.571437
$797$	−2.24914e44	−0.239559	−0.119780	−	0.992800i	$-0.538219\pi$
$797$	−2.24914e44	−0.239559	−0.119780	+	0.992800i	$0.538219\pi$
$798$	1.52402e43	0.0159201
$799$	1.34521e44	0.137821
$800$	1.34162e44	0.134814
$801$	1.05216e45	1.03700
$802$	8.10933e44	0.783939
$803$	−1.23524e44	−0.117128
$804$	−4.35824e42	−0.00405362
$805$	2.25841e45	2.06047
$806$	5.28632e44	0.473108
$807$	4.13863e44	0.363343
$808$	−4.87652e44	−0.419985
$809$	−1.09436e45	−0.924612	−0.462306	−	0.886720i	$-0.652978\pi$
$809$	−1.09436e45	−0.924612	−0.462306	+	0.886720i	$0.652978\pi$
$810$	−1.53025e44	−0.126836
$811$	−1.65483e44	−0.134564	−0.0672821	−	0.997734i	$-0.521433\pi$
$811$	−1.65483e44	−0.134564	−0.0672821	+	0.997734i	$0.521433\pi$
$812$	−1.14582e45	−0.914110
$813$	8.45359e42	0.00661664
$814$	−3.49245e44	−0.268196
$815$	4.95192e44	0.373105
$816$	6.40342e43	0.0473385
$817$	1.60632e43	0.0116517
$818$	−1.27401e45	−0.906768
$819$	−2.26780e45	−1.58382
$820$	3.74569e44	0.256695
$821$	1.30182e45	0.875454	0.437727	−	0.899108i	$-0.355784\pi$
$821$	1.30182e45	0.875454	0.437727	+	0.899108i	$0.355784\pi$
$822$	−2.41103e44	−0.159107
$823$	−8.40972e43	−0.0544608	−0.0272304	−	0.999629i	$-0.508669\pi$
$823$	−8.40972e43	−0.0544608	−0.0272304	+	0.999629i	$0.508669\pi$
$824$	5.70713e44	0.362699
$825$	−4.88471e43	−0.0304651
$826$	−1.27585e45	−0.780924
$827$	2.14145e45	1.28639	0.643196	−	0.765702i	$-0.277608\pi$
$827$	2.14145e45	1.28639	0.643196	+	0.765702i	$0.277608\pi$
$828$	9.64721e44	0.568763
$829$	−8.75462e44	−0.506573	−0.253286	−	0.967391i	$-0.581512\pi$
$829$	−8.75462e44	−0.506573	−0.253286	+	0.967391i	$0.581512\pi$
$830$	−3.74868e44	−0.212896
$831$	5.47653e44	0.305274
$832$	2.17616e45	1.19063
$833$	1.23724e45	0.664440
$834$	5.72339e44	0.301703
$835$	−3.25152e45	−1.68247
$836$	1.19971e43	0.00609369
$837$	−8.66436e44	−0.432008
$838$	2.12494e45	1.04007
$839$	8.96946e44	0.430979	0.215489	−	0.976506i	$-0.430865\pi$
$839$	8.96946e44	0.430979	0.215489	+	0.976506i	$0.430865\pi$
$840$	−1.66414e45	−0.784983
$841$	5.72465e44	0.265101
$842$	−1.19749e45	−0.544420
$843$	−9.59728e44	−0.428372
$844$	−7.28641e43	−0.0319305
$845$	2.67894e45	1.15261
$846$	2.91682e44	0.123216
$847$	−3.06781e45	−1.27244
$848$	−1.19977e44	−0.0488611
$849$	7.44850e43	0.0297851
$850$	1.32869e44	0.0521710
$851$	−3.93720e45	−1.51803
$852$	1.20777e45	0.457269
$853$	−3.47906e45	−1.29346	−0.646728	−	0.762721i	$-0.723863\pi$
$853$	−3.47906e45	−1.29346	−0.646728	+	0.762721i	$0.723863\pi$
$854$	3.89853e45	1.42333
$855$	−5.26421e43	−0.0188737
$856$	5.51465e44	0.194167
$857$	7.25970e44	0.251024	0.125512	−	0.992092i	$-0.459943\pi$
$857$	7.25970e44	0.251024	0.125512	+	0.992092i	$0.459943\pi$
$858$	−6.29348e44	−0.213716
$859$	4.44826e45	1.48353	0.741765	−	0.670660i	$-0.233989\pi$
$859$	4.44826e45	1.48353	0.741765	+	0.670660i	$0.233989\pi$
$860$	−6.16811e44	−0.202035
$861$	1.29377e45	0.416206
$862$	−3.81323e45	−1.20484
$863$	2.69165e45	0.835318	0.417659	−	0.908604i	$-0.362851\pi$
$863$	2.69165e45	0.835318	0.417659	+	0.908604i	$0.362851\pi$
$864$	−2.83313e45	−0.863581
$865$	3.18607e45	0.953905
$866$	−9.99609e43	−0.0293970
$867$	1.34411e45	0.388273
$868$	1.33656e45	0.379255
$869$	1.60862e45	0.448379
$870$	1.39527e45	0.382040
$871$	−7.67056e43	−0.0206322
$872$	−5.28742e45	−1.39714
$873$	1.60319e45	0.416164
$874$	−1.14104e44	−0.0290988
$875$	−6.33096e45	−1.58615
$876$	3.60844e44	0.0888189
$877$	−5.87091e44	−0.141975	−0.0709875	−	0.997477i	$-0.522615\pi$
$877$	−5.87091e44	−0.141975	−0.0709875	+	0.997477i	$0.522615\pi$
$878$	−2.31737e45	−0.550592
$879$	7.88492e43	0.0184064
$880$	2.55870e44	0.0586865
$881$	−5.61916e45	−1.26632	−0.633162	−	0.774020i	$-0.718243\pi$
$881$	−5.61916e45	−1.26632	−0.633162	+	0.774020i	$0.718243\pi$
$882$	2.68270e45	0.594031
$883$	3.14941e45	0.685232	0.342616	−	0.939476i	$-0.388687\pi$
$883$	3.14941e45	0.685232	0.342616	+	0.939476i	$0.388687\pi$
$884$	−2.02912e45	−0.433808
$885$	−1.84151e45	−0.386859
$886$	−7.14947e44	−0.147588
$887$	3.05461e45	0.619641	0.309821	−	0.950795i	$-0.399731\pi$
$887$	3.05461e45	0.619641	0.309821	+	0.950795i	$0.399731\pi$
$888$	2.90118e45	0.578327
$889$	6.98711e45	1.36874
$890$	4.77866e45	0.919942
$891$	−4.16077e44	−0.0787171
$892$	−1.32824e44	−0.0246956
$893$	4.08924e43	0.00747215
$894$	2.29474e45	0.412099
$895$	−1.64289e45	−0.289969
$896$	3.41560e45	0.592506
$897$	−7.09494e45	−1.20967
$898$	−1.96692e45	−0.329613
$899$	−3.18664e45	−0.524877
$900$	−3.41487e44	−0.0552861
$901$	1.00275e45	0.159573
$902$	−8.59233e44	−0.134403
$903$	−2.13048e45	−0.327580
$904$	5.97826e45	0.903574
$905$	−7.62218e45	−1.13247
$906$	−1.01091e45	−0.147647
$907$	1.69836e44	0.0243847	0.0121924	−	0.999926i	$-0.496119\pi$
$907$	1.69836e44	0.0243847	0.0121924	+	0.999926i	$0.496119\pi$
$908$	−2.12314e44	−0.0299673
$909$	2.04597e45	0.283896
$910$	−1.02998e46	−1.40503
$911$	1.24574e46	1.67067	0.835336	−	0.549739i	$-0.185273\pi$
$911$	1.24574e46	1.67067	0.835336	+	0.549739i	$0.185273\pi$
$912$	1.94655e43	0.00256652
$913$	−1.01927e45	−0.132128
$914$	7.44812e43	0.00949250
$915$	5.62698e45	0.705096
$916$	−2.35432e45	−0.290058
$917$	−1.21175e46	−1.46787
$918$	−2.80580e45	−0.334192
$919$	−1.08191e46	−1.26707	−0.633535	−	0.773714i	$-0.718397\pi$
$919$	−1.08191e46	−1.26707	−0.633535	+	0.773714i	$0.718397\pi$
$920$	1.24595e46	1.43480
$921$	7.70217e45	0.872145
$922$	2.12904e45	0.237058
$923$	2.12570e46	2.32742
$924$	−1.59120e45	−0.171320
$925$	1.39367e45	0.147558
$926$	4.39906e45	0.458025
$927$	−2.39447e45	−0.245173
$928$	−1.04199e46	−1.04923
$929$	−9.79872e45	−0.970344	−0.485172	−	0.874419i	$-0.661243\pi$
$929$	−9.79872e45	−0.970344	−0.485172	+	0.874419i	$0.661243\pi$
$930$	−1.62753e45	−0.158505
$931$	3.76103e44	0.0360235
$932$	−4.57704e44	−0.0431160
$933$	3.68334e45	0.341253
$934$	9.26440e45	0.844191
$935$	−2.13853e45	−0.191661
$936$	−1.25113e46	−1.10288
$937$	1.01455e46	0.879650	0.439825	−	0.898083i	$-0.355040\pi$
$937$	1.01455e46	0.879650	0.439825	+	0.898083i	$0.355040\pi$
$938$	1.63617e44	0.0139535
$939$	−1.07439e46	−0.901246
$940$	−1.57024e45	−0.129564
$941$	−1.48680e46	−1.20674	−0.603370	−	0.797461i	$-0.706176\pi$
$941$	−1.48680e46	−1.20674	−0.603370	+	0.797461i	$0.706176\pi$
$942$	−8.40792e45	−0.671274
$943$	−9.68655e45	−0.760743
$944$	−1.62958e45	−0.125895
$945$	1.68815e46	1.28297
$946$	1.41492e45	0.105784
$947$	2.27265e46	1.67151	0.835754	−	0.549104i	$-0.185031\pi$
$947$	2.27265e46	1.67151	0.835754	+	0.549104i	$0.185031\pi$
$948$	−4.69915e45	−0.340009
$949$	6.35090e45	0.452073
$950$	4.03901e43	0.00282852
$951$	−4.51925e45	−0.311364
$952$	1.23079e46	0.834282
$953$	−7.58661e45	−0.505950	−0.252975	−	0.967473i	$-0.581409\pi$
$953$	−7.58661e45	−0.505950	−0.252975	+	0.967473i	$0.581409\pi$
$954$	2.17427e45	0.142664
$955$	1.43634e46	0.927265
$956$	1.62093e46	1.02960
$957$	3.79377e45	0.237102
$958$	−1.12814e46	−0.693744
$959$	−1.07288e46	−0.649178
$960$	−6.69984e45	−0.398897
$961$	−1.33521e46	−0.782234
$962$	1.79561e46	1.03514
$963$	−2.31371e45	−0.131251
$964$	1.82116e45	0.101661
$965$	−1.12363e46	−0.617236
$966$	1.51338e46	0.818095
$967$	−3.35350e46	−1.78397	−0.891986	−	0.452064i	$-0.850688\pi$
$967$	−3.35350e46	−1.78397	−0.891986	+	0.452064i	$0.850688\pi$
$968$	−1.69250e46	−0.886053
$969$	−1.62690e44	−0.00838188
$970$	7.28127e45	0.369186
$971$	−2.14498e46	−1.07035	−0.535175	−	0.844741i	$-0.679754\pi$
$971$	−2.14498e46	−1.07035	−0.535175	+	0.844741i	$0.679754\pi$
$972$	1.14400e46	0.561822
$973$	2.54685e46	1.23099
$974$	−2.71044e46	−1.28937
$975$	2.51143e45	0.117584
$976$	4.97939e45	0.229458
$977$	1.98478e46	0.900215	0.450107	−	0.892974i	$-0.351386\pi$
$977$	1.98478e46	0.900215	0.450107	+	0.892974i	$0.351386\pi$
$978$	3.31834e45	0.148139
$979$	1.29933e46	0.570935
$980$	−1.44420e46	−0.624632
$981$	2.21837e46	0.944420
$982$	2.58623e46	1.08377
$983$	−1.53482e46	−0.633107	−0.316554	−	0.948575i	$-0.602526\pi$
$983$	−1.53482e46	−0.633107	−0.316554	+	0.948575i	$0.602526\pi$
$984$	7.13765e45	0.289822
$985$	−1.59728e46	−0.638440
$986$	−1.03194e46	−0.406033
$987$	−5.42363e45	−0.210075
$988$	−6.16823e44	−0.0235195
$989$	1.59511e46	0.598753
$990$	−4.63697e45	−0.171352
$991$	−8.58630e45	−0.312367	−0.156183	−	0.987728i	$-0.549919\pi$
$991$	−8.58630e45	−0.312367	−0.156183	+	0.987728i	$0.549919\pi$
$992$	1.21544e46	0.435313
$993$	1.12056e46	0.395113
$994$	−4.53421e46	−1.57403
$995$	2.85109e46	0.974437
$996$	2.97754e45	0.100193
$997$	3.45614e46	1.14503	0.572514	−	0.819895i	$-0.305968\pi$
$997$	3.45614e46	1.14503	0.572514	+	0.819895i	$0.305968\pi$
$998$	1.47508e46	0.481164
$999$	−2.94304e46	−0.945216

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.32.a.a.1.1	✓	2	1.1	even	1	trivial
9.32.a.a.1.2		2	3.2	odd	2
16.32.a.b.1.2		2	4.3	odd	2
25.32.a.a.1.2		2	5.4	even	2
25.32.b.a.24.2		4	5.2	odd	4
25.32.b.a.24.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-31347.9 q^{2} -1.34921e7 q^{3} -1.16479e9 q^{4} +6.31161e10 q^{5} +4.22947e11 q^{6} +1.88207e13 q^{7} +1.03833e14 q^{8} -4.35638e14 q^{9} +O(q^{10})\)	\(q-31347.9 q^{2} -1.34921e7 q^{3} -1.16479e9 q^{4} +6.31161e10 q^{5} +4.22947e11 q^{6} +1.88207e13 q^{7} +1.03833e14 q^{8} -4.35638e14 q^{9} -1.97855e15 q^{10} -5.37973e15 q^{11} +1.57155e16 q^{12} +2.76595e17 q^{13} -5.89989e17 q^{14} -8.51566e17 q^{15} -7.53562e17 q^{16} +6.29817e18 q^{17} +1.36563e19 q^{18} +1.91455e18 q^{19} -7.35172e19 q^{20} -2.53930e20 q^{21} +1.68643e20 q^{22} +1.90120e21 q^{23} -1.40092e21 q^{24} -6.72976e20 q^{25} -8.67065e21 q^{26} +1.42113e22 q^{27} -2.19223e22 q^{28} +5.22675e22 q^{29} +2.66948e22 q^{30} -6.09679e22 q^{31} -1.99357e23 q^{32} +7.25837e22 q^{33} -1.97434e23 q^{34} +1.18789e24 q^{35} +5.07428e23 q^{36} -2.07091e24 q^{37} -6.00172e22 q^{38} -3.73183e24 q^{39} +6.55352e24 q^{40} -5.09498e24 q^{41} +7.96017e24 q^{42} +8.39002e24 q^{43} +6.26628e24 q^{44} -2.74957e25 q^{45} -5.95984e25 q^{46} +2.13587e25 q^{47} +1.01671e25 q^{48} +1.96444e26 q^{49} +2.10964e25 q^{50} -8.49753e25 q^{51} -3.22176e26 q^{52} +1.59213e26 q^{53} -4.45495e26 q^{54} -3.39547e26 q^{55} +1.95421e27 q^{56} -2.58313e25 q^{57} -1.63847e27 q^{58} +2.16250e27 q^{59} +9.91899e26 q^{60} -6.60780e27 q^{61} +1.91122e27 q^{62} -8.19901e27 q^{63} +7.86767e27 q^{64} +1.74576e28 q^{65} -2.27534e27 q^{66} -2.77322e26 q^{67} -7.33607e27 q^{68} -2.56510e28 q^{69} -3.72378e28 q^{70} +7.68524e28 q^{71} -4.52335e28 q^{72} +2.29610e28 q^{73} +6.49186e28 q^{74} +9.07984e27 q^{75} -2.23006e27 q^{76} -1.01250e29 q^{77} +1.16985e29 q^{78} -2.99014e29 q^{79} -4.75619e28 q^{80} +7.73416e28 q^{81} +1.59717e29 q^{82} +1.89466e29 q^{83} +2.95777e29 q^{84} +3.97516e29 q^{85} -2.63009e29 q^{86} -7.05196e29 q^{87} -5.58593e29 q^{88} -2.41523e30 q^{89} +8.61933e29 q^{90} +5.20571e30 q^{91} -2.21450e30 q^{92} +8.22583e29 q^{93} -6.69551e29 q^{94} +1.20839e29 q^{95} +2.68973e30 q^{96} -3.68010e30 q^{97} -6.15810e30 q^{98} +2.34361e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 39960 q^{2} + 17363160 q^{3} + 1772534336 q^{4} - 19391218020 q^{5} + 2623167496224 q^{6} + 30257527577200 q^{7} + 160155058705920 q^{8} - 101266456303926 q^{9}+O(q^{10}) \) 2 * q + 39960 * q^2 + 17363160 * q^3 + 1772534336 * q^4 - 19391218020 * q^5 + 2623167496224 * q^6 + 30257527577200 * q^7 + 160155058705920 * q^8 - 101266456303926 * q^9	\( 2 q + 39960 q^{2} + 17363160 q^{3} + 1772534336 q^{4} - 19391218020 q^{5} + 2623167496224 q^{6} + 30257527577200 q^{7} + 160155058705920 q^{8} - 101266456303926 q^{9} - 78\!\cdots\!20 q^{10}+ \cdots + 15\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 39960 * q^2 + 17363160 * q^3 + 1772534336 * q^4 - 19391218020 * q^5 + 2623167496224 * q^6 + 30257527577200 * q^7 + 160155058705920 * q^8 - 101266456303926 * q^9 - 7861972212281520 * q^10 - 7782353745118776 * q^11 + 106347410955313920 * q^12 + 74708953050260620 * q^13 + 225544963845241152 * q^14 - 3397345822674581040 * q^15 - 3045212913684901888 * q^16 + 17224607828987089380 * q^17 + 37499616229575978360 * q^18 - 12370563328022164040 * q^19 - 315868245501283090560 * q^20 + 98954957416071161664 * q^21 - 2682713032996690080 * q^22 + 1897344841989911219280 * q^23 + 336914041234261985280 * q^24 + 1477861250884539239150 * q^25 - 23066680666744323279216 * q^26 + 5469986602319662295280 * q^27 + 11671395808124240043520 * q^28 + 128576144217217055807340 * q^29 - 154839394101764341823040 * q^30 + 125733527517961838793664 * q^31 - 483720527174276002775040 * q^32 - 1549761835334435045280 * q^33 + 581706909571293028834992 * q^34 + 244269703121729304206880 * q^35 + 1489586748818199413504832 * q^36 - 833815207054016911025060 * q^37 - 1078658489244045513633120 * q^38 - 9961054164411363568284912 * q^39 + 1906531481497967156966400 * q^40 + 8724924335662925840671284 * q^41 + 33123669600002676603713280 * q^42 - 18397105293779438708372600 * q^43 - 791008370873332311322368 * q^44 - 55083793466681039024257140 * q^45 - 59873011445275600509089856 * q^46 + 95450963964856190793148320 * q^47 - 60542278614741008947691520 * q^48 + 169469294372320202530407186 * q^49 + 174468018688948298981615400 * q^50 + 252162404739970320085380144 * q^51 - 915180155081494236104643200 * q^52 + 194822508473721098983660860 * q^53 - 1068822271687374190070274240 * q^54 - 141313671368671671047892240 * q^55 + 2598355397749815172431728640 * q^56 - 466601717043760934967596640 * q^57 + 3802934506602438134028187920 * q^58 - 198723263547765513990746520 * q^59 - 6485894626584890581155141120 * q^60 - 12056218201113004361157656276 * q^61 + 15224500099333079134598257920 * q^62 - 4374875036601718967620305360 * q^63 - 7488413368264058547677691904 * q^64 + 34114584794425827928886318760 * q^65 - 7561640583442461364265814912 * q^66 - 9688140802872256994032247720 * q^67 + 24758471836626330094958252160 * q^68 - 25769856286394326078494576192 * q^69 - 104525335953756946154610069120 * q^70 + 55784576625034657512878287344 * q^71 - 26400994734811244163462812160 * q^72 + 62234095932086098750552955380 * q^73 + 153133163632488378484794299472 * q^74 + 75444402265645086720647965800 * q^75 - 44190149699939358902474481920 * q^76 - 128728748793695217194494555200 * q^77 - 327207773523327347562124449600 * q^78 - 119164191093299704964212710560 * q^79 + 141515971255973138522638049280 * q^80 - 398906922646891269649062634158 * q^81 + 1145184549692595779551104209520 * q^82 - 264863373681569145625357596360 * q^83 + 1332316649919851794889339185152 * q^84 - 503995105657776450242931421320 * q^85 - 2173142482222838422832927019936 * q^86 + 1649324800814841914442821796240 * q^87 - 693913929707398651948752168960 * q^88 - 2154414614246670291602721895980 * q^89 - 1105313102749861362639913526640 * q^90 + 2896781368068903069956049509024 * q^91 - 2225812737244025604862645470720 * q^92 + 6583298380663842229690665227520 * q^93 + 4613808251402558431525114250112 * q^94 + 1299465173198290044974084355600 * q^95 - 6084370432669606716368714858496 * q^96 - 9060767994874032615529957205180 * q^97 - 8081619677193750912975770689320 * q^98 + 1540246307744094989457731085288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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