LMFDB - Embedded newform 10.22.a.d.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10,22,Mod(1,10)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10.1"); S:= CuspForms(chi, 22); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 22, names="a")

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	10.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,2048,30972] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$27.9477344287$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1179649}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 294912 $ x^2 - x - 294912
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-542.558$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1024.00 q^{2} +145820. q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} +1.49320e8 q^{6} -2.36011e8 q^{7} +1.07374e9 q^{8} +1.08031e10 q^{9} -1.00000e10 q^{10} +1.49202e11 q^{11} +1.52903e11 q^{12} +4.89350e11 q^{13} -2.41675e11 q^{14} -1.42402e12 q^{15} +1.09951e12 q^{16} +5.46288e12 q^{17} +1.10624e13 q^{18} -1.12049e13 q^{19} -1.02400e13 q^{20} -3.44151e13 q^{21} +1.52783e14 q^{22} +1.78791e13 q^{23} +1.56573e14 q^{24} +9.53674e13 q^{25} +5.01094e14 q^{26} +4.99812e13 q^{27} -2.47475e14 q^{28} -2.82120e15 q^{29} -1.45820e15 q^{30} +4.24797e15 q^{31} +1.12590e15 q^{32} +2.17567e16 q^{33} +5.59399e15 q^{34} +2.30479e15 q^{35} +1.13279e16 q^{36} +5.74457e16 q^{37} -1.14738e16 q^{38} +7.13570e16 q^{39} -1.04858e16 q^{40} -3.51283e16 q^{41} -3.52410e16 q^{42} -2.62144e17 q^{43} +1.56450e17 q^{44} -1.05499e17 q^{45} +1.83081e16 q^{46} +1.08406e17 q^{47} +1.60331e17 q^{48} -5.02845e17 q^{49} +9.76562e16 q^{50} +7.96597e17 q^{51} +5.13120e17 q^{52} -2.47953e18 q^{53} +5.11807e16 q^{54} -1.45705e18 q^{55} -2.53415e17 q^{56} -1.63389e18 q^{57} -2.88891e18 q^{58} +2.14259e17 q^{59} -1.49320e18 q^{60} +3.64272e18 q^{61} +4.34992e18 q^{62} -2.54965e18 q^{63} +1.15292e18 q^{64} -4.77881e18 q^{65} +2.22788e19 q^{66} -1.13372e19 q^{67} +5.72825e18 q^{68} +2.60712e18 q^{69} +2.36011e18 q^{70} +2.44087e19 q^{71} +1.15998e19 q^{72} -4.12244e19 q^{73} +5.88244e19 q^{74} +1.39065e19 q^{75} -1.17492e19 q^{76} -3.52133e19 q^{77} +7.30695e19 q^{78} +6.83832e19 q^{79} -1.07374e19 q^{80} -1.05716e20 q^{81} -3.59714e19 q^{82} +1.39311e20 q^{83} -3.60868e19 q^{84} -5.33484e19 q^{85} -2.68435e20 q^{86} -4.11387e20 q^{87} +1.60205e20 q^{88} -4.04817e20 q^{89} -1.08031e20 q^{90} -1.15492e20 q^{91} +1.87475e19 q^{92} +6.19438e20 q^{93} +1.11008e20 q^{94} +1.09423e20 q^{95} +1.64179e20 q^{96} -9.18963e20 q^{97} -5.14913e20 q^{98} +1.61185e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2048 q^{2} + 30972 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 31715328 q^{6} - 439959356 q^{7} + 2147483648 q^{8} + 13532817186 q^{9} - 20000000000 q^{10} + 105191777184 q^{11} + 32476495872 q^{12}+ \cdots + 14\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q + 2048 * q^2 + 30972 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 31715328 * q^6 - 439959356 * q^7 + 2147483648 * q^8 + 13532817186 * q^9 - 20000000000 * q^10 + 105191777184 * q^11 + 32476495872 * q^12 + 308456648932 * q^13 - 450518380544 * q^14 - 302460937500 * q^15 + 2199023255552 * q^16 + 18393996100404 * q^17 + 13857604798464 * q^18 + 23821216715800 * q^19 - 20480000000000 * q^20 - 10991999204616 * q^21 + 107716379836416 * q^22 - 82586042978868 * q^23 + 33255931772928 * q^24 + 190734863281250 * q^25 + 315859608506368 * q^26 + 937830505785480 * q^27 - 461330821677056 * q^28 - 167038888446420 * q^29 - 309720000000000 * q^30 + 5373084998145784 * q^31 + 2251799813685248 * q^32 + 26811195444517824 * q^33 + 18835452006813696 * q^34 + 4296478085937500 * q^35 + 14190187313627136 * q^36 + 83725084127912164 * q^37 + 24392925916979200 * q^38 + 92132195361143352 * q^39 - 20971520000000000 * q^40 - 63222375005514036 * q^41 - 11255807185526784 * q^42 - 113835841911164948 * q^43 + 110301572952489984 * q^44 - 132156417832031250 * q^45 - 84568108010360832 * q^46 + 13253549001226164 * q^47 + 34054074135478272 * q^48 - 1019795619700635846 * q^49 + 195312500000000000 * q^50 - 688515197556670056 * q^51 + 323440239110520832 * q^52 - 1445751023743904748 * q^53 + 960338437924331520 * q^54 - 1027263449062500000 * q^55 - 472402761397305344 * q^56 - 5656568844707914800 * q^57 - 171047821769134080 * q^58 - 817060118931432840 * q^59 - 317153280000000000 * q^60 - 4580997169825849436 * q^61 + 5502039038101282816 * q^62 - 3106370208073453308 * q^63 + 2305843009213693952 * q^64 - 3012271962226562500 * q^65 + 27454664135186251776 * q^66 - 28808031668773210556 * q^67 + 19287502854977224704 * q^68 + 14145335707649957352 * q^69 + 4399593560000000000 * q^70 + 51140957732016114984 * q^71 + 14530751809154187264 * q^72 + 14792322512082321412 * q^73 + 85734486146982055936 * q^74 + 2953720092773437500 * q^75 + 24978356138986700800 * q^76 - 26237463329898773952 * q^77 + 94343368049810792448 * q^78 + 25077766877525032720 * q^79 - 21474836480000000000 * q^80 - 236237497961757285078 * q^81 - 64739712005646372864 * q^82 - 120090321897786074868 * q^83 - 11525946557979426816 * q^84 - 179628868168007812500 * q^85 - 116567902117032906752 * q^86 - 716212291756398367320 * q^87 + 112948810703349743616 * q^88 + 104228468137266844980 * q^89 - 135328171860000000000 * q^90 - 78598912899601639096 * q^91 - 86597742602609491968 * q^92 + 490220677944452503824 * q^93 + 13571634177255591936 * q^94 - 232629069490234375000 * q^95 + 34871371914729750528 * q^96 - 260893520515229908796 * q^97 - 1044270714573451106304 * q^98 + 1491713506648872042912 * q^99

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 $

$2$	1024.00	0.707107
$2$	1024.00	0.707107
$3$	145820.	1.42575	0.712876	−	0.701290i	$-0.247392\pi$
$3$	145820.	1.42575	0.712876	+	0.701290i	$0.247392\pi$
$4$	1.04858e6	0.500000
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	1.49320e8	1.00816
$7$	−2.36011e8	−0.315793	−0.157896	−	0.987456i	$-0.550471\pi$
$7$	−2.36011e8	−0.315793	−0.157896	+	0.987456i	$0.550471\pi$
$8$	1.07374e9	0.353553
$9$	1.08031e10	1.03277
$10$	−1.00000e10	−0.316228
$11$	1.49202e11	1.73441	0.867206	−	0.497949i	$-0.165913\pi$
$11$	1.49202e11	1.73441	0.867206	+	0.497949i	$0.165913\pi$
$12$	1.52903e11	0.712876
$13$	4.89350e11	0.984497	0.492248	−	0.870455i	$-0.336175\pi$
$13$	4.89350e11	0.984497	0.492248	+	0.870455i	$0.336175\pi$
$14$	−2.41675e11	−0.223299
$15$	−1.42402e12	−0.637615
$16$	1.09951e12	0.250000
$17$	5.46288e12	0.657216	0.328608	−	0.944466i	$-0.393421\pi$
$17$	5.46288e12	0.657216	0.328608	+	0.944466i	$0.393421\pi$
$18$	1.10624e13	0.730277
$19$	−1.12049e13	−0.419270	−0.209635	−	0.977780i	$-0.567228\pi$
$19$	−1.12049e13	−0.419270	−0.209635	+	0.977780i	$0.567228\pi$
$20$	−1.02400e13	−0.223607
$21$	−3.44151e13	−0.450242
$22$	1.52783e14	1.22641
$23$	1.78791e13	0.0899916	0.0449958	−	0.998987i	$-0.485673\pi$
$23$	1.78791e13	0.0899916	0.0449958	+	0.998987i	$0.485673\pi$
$24$	1.56573e14	0.504079
$25$	9.53674e13	0.200000
$26$	5.01094e14	0.696144
$27$	4.99812e13	0.0467183
$28$	−2.47475e14	−0.157896
$29$	−2.82120e15	−1.24525	−0.622623	−	0.782522i	$-0.713933\pi$
$29$	−2.82120e15	−1.24525	−0.622623	+	0.782522i	$0.713933\pi$
$30$	−1.45820e15	−0.450862
$31$	4.24797e15	0.930858	0.465429	−	0.885085i	$-0.345900\pi$
$31$	4.24797e15	0.930858	0.465429	+	0.885085i	$0.345900\pi$
$32$	1.12590e15	0.176777
$33$	2.17567e16	2.47284
$34$	5.59399e15	0.464722
$35$	2.30479e15	0.141227
$36$	1.13279e16	0.516384
$37$	5.74457e16	1.96399	0.981995	−	0.188909i	$-0.0604951\pi$
$37$	5.74457e16	1.96399	0.981995	+	0.188909i	$0.0604951\pi$
$38$	−1.14738e16	−0.296469
$39$	7.13570e16	1.40365
$40$	−1.04858e16	−0.158114
$41$	−3.51283e16	−0.408721	−0.204361	−	0.978896i	$-0.565512\pi$
$41$	−3.51283e16	−0.408721	−0.204361	+	0.978896i	$0.565512\pi$
$42$	−3.52410e16	−0.318369
$43$	−2.62144e17	−1.84978	−0.924891	−	0.380233i	$-0.875844\pi$
$43$	−2.62144e17	−1.84978	−0.924891	+	0.380233i	$0.875844\pi$
$44$	1.56450e17	0.867206
$45$	−1.05499e17	−0.461868
$46$	1.83081e16	0.0636337
$47$	1.08406e17	0.300626	0.150313	−	0.988638i	$-0.451972\pi$
$47$	1.08406e17	0.300626	0.150313	+	0.988638i	$0.451972\pi$
$48$	1.60331e17	0.356438
$49$	−5.02845e17	−0.900275
$50$	9.76562e16	0.141421
$51$	7.96597e17	0.937027
$52$	5.13120e17	0.492248
$53$	−2.47953e18	−1.94748	−0.973740	−	0.227662i	$-0.926892\pi$
$53$	−2.47953e18	−1.94748	−0.973740	+	0.227662i	$0.926892\pi$
$54$	5.11807e16	0.0330348
$55$	−1.45705e18	−0.775653
$56$	−2.53415e17	−0.111650
$57$	−1.63389e18	−0.597775
$58$	−2.88891e18	−0.880521
$59$	2.14259e17	0.0545748	0.0272874	−	0.999628i	$-0.491313\pi$
$59$	2.14259e17	0.0545748	0.0272874	+	0.999628i	$0.491313\pi$
$60$	−1.49320e18	−0.318808
$61$	3.64272e18	0.653826	0.326913	−	0.945054i	$-0.393992\pi$
$61$	3.64272e18	0.653826	0.326913	+	0.945054i	$0.393992\pi$
$62$	4.34992e18	0.658216
$63$	−2.54965e18	−0.326141
$64$	1.15292e18	0.125000
$65$	−4.77881e18	−0.440280
$66$	2.22788e19	1.74856
$67$	−1.13372e19	−0.759835	−0.379918	−	0.925020i	$-0.624048\pi$
$67$	−1.13372e19	−0.759835	−0.379918	+	0.925020i	$0.624048\pi$
$68$	5.72825e18	0.328608
$69$	2.60712e18	0.128306
$70$	2.36011e18	0.0998625
$71$	2.44087e19	0.889882	0.444941	−	0.895560i	$-0.353225\pi$
$71$	2.44087e19	0.889882	0.444941	+	0.895560i	$0.353225\pi$
$72$	1.15998e19	0.365138
$73$	−4.12244e19	−1.12270	−0.561350	−	0.827578i	$-0.689718\pi$
$73$	−4.12244e19	−1.12270	−0.561350	+	0.827578i	$0.689718\pi$
$74$	5.88244e19	1.38875
$75$	1.39065e19	0.285150
$76$	−1.17492e19	−0.209635
$77$	−3.52133e19	−0.547715
$78$	7.30695e19	0.992529
$79$	6.83832e19	0.812578	0.406289	−	0.913745i	$-0.366823\pi$
$79$	6.83832e19	0.812578	0.406289	+	0.913745i	$0.366823\pi$
$80$	−1.07374e19	−0.111803
$81$	−1.05716e20	−0.966159
$82$	−3.59714e19	−0.289009
$83$	1.39311e20	0.985522	0.492761	−	0.870165i	$-0.335988\pi$
$83$	1.39311e20	0.985522	0.492761	+	0.870165i	$0.335988\pi$
$84$	−3.60868e19	−0.225121
$85$	−5.33484e19	−0.293916
$86$	−2.68435e20	−1.30799
$87$	−4.11387e20	−1.77541
$88$	1.60205e20	0.613207
$89$	−4.04817e20	−1.37614	−0.688072	−	0.725643i	$-0.741542\pi$
$89$	−4.04817e20	−1.37614	−0.688072	+	0.725643i	$0.741542\pi$
$90$	−1.08031e20	−0.326590
$91$	−1.15492e20	−0.310897
$92$	1.87475e19	0.0449958
$93$	6.19438e20	1.32717
$94$	1.11008e20	0.212575
$95$	1.09423e20	0.187503
$96$	1.64179e20	0.252040
$97$	−9.18963e20	−1.26530	−0.632652	−	0.774436i	$-0.718034\pi$
$97$	−9.18963e20	−1.26530	−0.632652	+	0.774436i	$0.718034\pi$
$98$	−5.14913e20	−0.636590
$99$	1.61185e21	1.79124
$100$	1.00000e20	0.100000
$101$	3.74073e20	0.336963	0.168481	−	0.985705i	$-0.446114\pi$
$101$	3.74073e20	0.336963	0.168481	+	0.985705i	$0.446114\pi$
$102$	8.15716e20	0.662578
$103$	1.43042e21	1.04875	0.524375	−	0.851488i	$-0.324299\pi$
$103$	1.43042e21	1.04875	0.524375	+	0.851488i	$0.324299\pi$
$104$	5.25435e20	0.348072
$105$	3.36085e20	0.201354
$106$	−2.53904e21	−1.37708
$107$	−2.52568e20	−0.124122	−0.0620611	−	0.998072i	$-0.519767\pi$
$107$	−2.52568e20	−0.124122	−0.0620611	+	0.998072i	$0.519767\pi$
$108$	5.24090e19	0.0233591
$109$	−1.76002e21	−0.712096	−0.356048	−	0.934468i	$-0.615876\pi$
$109$	−1.76002e21	−0.712096	−0.356048	+	0.934468i	$0.615876\pi$
$110$	−1.49202e21	−0.548469
$111$	8.37672e21	2.80016
$112$	−2.59497e20	−0.0789482
$113$	−4.42156e21	−1.22533	−0.612663	−	0.790344i	$-0.709902\pi$
$113$	−4.42156e21	−1.22533	−0.612663	+	0.790344i	$0.709902\pi$
$114$	−1.67311e21	−0.422691
$115$	−1.74600e20	−0.0402455
$116$	−2.95824e21	−0.622623
$117$	5.28650e21	1.01676
$118$	2.19401e20	0.0385902
$119$	−1.28930e21	−0.207544
$120$	−1.52903e21	−0.225431
$121$	1.48611e22	2.00819
$122$	3.73014e21	0.462325
$123$	−5.12241e21	−0.582735
$124$	4.45432e21	0.465429
$125$	−9.31323e20	−0.0894427
$126$	−2.61084e21	−0.230616
$127$	−1.71933e22	−1.39772	−0.698860	−	0.715259i	$-0.746309\pi$
$127$	−1.71933e22	−1.39772	−0.698860	+	0.715259i	$0.746309\pi$
$128$	1.18059e21	0.0883883
$129$	−3.82258e22	−2.63733
$130$	−4.89350e21	−0.311325
$131$	−3.15817e22	−1.85390	−0.926951	−	0.375182i	$-0.877580\pi$
$131$	−3.15817e22	−1.85390	−0.926951	+	0.375182i	$0.877580\pi$
$132$	2.28135e22	1.23642
$133$	2.64447e21	0.132403
$134$	−1.16093e22	−0.537285
$135$	−4.88097e20	−0.0208930
$136$	5.86572e21	0.232361
$137$	3.69519e22	1.35541	0.677705	−	0.735334i	$-0.262975\pi$
$137$	3.69519e22	1.35541	0.677705	+	0.735334i	$0.262975\pi$
$138$	2.66969e21	0.0907259
$139$	−1.17938e22	−0.371533	−0.185766	−	0.982594i	$-0.559477\pi$
$139$	−1.17938e22	−0.371533	−0.185766	+	0.982594i	$0.559477\pi$
$140$	2.41675e21	0.0706134
$141$	1.58078e22	0.428618
$142$	2.49945e22	0.629242
$143$	7.30121e22	1.70752
$144$	1.18781e22	0.258192
$145$	2.75508e22	0.556891
$146$	−4.22138e22	−0.793869
$147$	−7.33248e22	−1.28357
$148$	6.02361e22	0.981995
$149$	−7.15203e21	−0.108636	−0.0543180	−	0.998524i	$-0.517298\pi$
$149$	−7.15203e21	−0.108636	−0.0543180	+	0.998524i	$0.517298\pi$
$150$	1.42402e22	0.201632
$151$	4.84896e22	0.640311	0.320155	−	0.947365i	$-0.396265\pi$
$151$	4.84896e22	0.640311	0.320155	+	0.947365i	$0.396265\pi$
$152$	−1.20311e22	−0.148234
$153$	5.90161e22	0.678751
$154$	−3.60585e22	−0.387293
$155$	−4.14840e22	−0.416292
$156$	7.48232e22	0.701824
$157$	7.61443e22	0.667869	0.333934	−	0.942596i	$-0.391624\pi$
$157$	7.61443e22	0.667869	0.333934	+	0.942596i	$0.391624\pi$
$158$	7.00244e22	0.574580
$159$	−3.61565e23	−2.77662
$160$	−1.09951e22	−0.0790569
$161$	−4.21965e21	−0.0284187
$162$	−1.08253e23	−0.683177
$163$	2.43191e23	1.43872	0.719362	−	0.694636i	$-0.244434\pi$
$163$	2.43191e23	1.43872	0.719362	+	0.694636i	$0.244434\pi$
$164$	−3.68347e22	−0.204361
$165$	−2.12468e23	−1.10589
$166$	1.42655e23	0.696869
$167$	7.07489e22	0.324487	0.162243	−	0.986751i	$-0.448127\pi$
$167$	7.07489e22	0.324487	0.162243	+	0.986751i	$0.448127\pi$
$168$	−3.69529e22	−0.159185
$169$	−7.60128e21	−0.0307664
$170$	−5.46288e22	−0.207830
$171$	−1.21047e23	−0.433009
$172$	−2.74877e23	−0.924891
$173$	−6.67282e22	−0.211264	−0.105632	−	0.994405i	$-0.533687\pi$
$173$	−6.67282e22	−0.211264	−0.105632	+	0.994405i	$0.533687\pi$
$174$	−4.21261e23	−1.25540
$175$	−2.25077e22	−0.0631586
$176$	1.64050e23	0.433603
$177$	3.12432e22	0.0778102
$178$	−4.14533e23	−0.973080
$179$	3.54801e23	0.785287	0.392643	−	0.919691i	$-0.371561\pi$
$179$	3.54801e23	0.785287	0.392643	+	0.919691i	$0.371561\pi$
$180$	−1.10624e23	−0.230934
$181$	4.64442e23	0.914759	0.457380	−	0.889272i	$-0.348788\pi$
$181$	4.64442e23	0.914759	0.457380	+	0.889272i	$0.348788\pi$
$182$	−1.18264e23	−0.219837
$183$	5.31181e23	0.932193
$184$	1.91975e22	0.0318169
$185$	−5.60993e23	−0.878323
$186$	6.34305e23	0.938452
$187$	8.15074e23	1.13988
$188$	1.13672e23	0.150313
$189$	−1.17961e22	−0.0147533
$190$	1.12049e23	0.132585
$191$	8.73751e23	0.978447	0.489223	−	0.872158i	$-0.337280\pi$
$191$	8.73751e23	0.978447	0.489223	+	0.872158i	$0.337280\pi$
$192$	1.68119e23	0.178219
$193$	1.27124e24	1.27607	0.638036	−	0.770006i	$-0.279747\pi$
$193$	1.27124e24	1.27607	0.638036	+	0.770006i	$0.279747\pi$
$194$	−9.41019e23	−0.894705
$195$	−6.96846e23	−0.627730
$196$	−5.27271e23	−0.450137
$197$	−4.11184e23	−0.332767	−0.166384	−	0.986061i	$-0.553209\pi$
$197$	−4.11184e23	−0.332767	−0.166384	+	0.986061i	$0.553209\pi$
$198$	1.65053e24	1.26660
$199$	−2.46871e24	−1.79686	−0.898428	−	0.439121i	$-0.855290\pi$
$199$	−2.46871e24	−1.79686	−0.898428	+	0.439121i	$0.855290\pi$
$200$	1.02400e23	0.0707107
$201$	−1.65319e24	−1.08334
$202$	3.83051e23	0.238269
$203$	6.65833e23	0.393240
$204$	8.35293e23	0.468513
$205$	3.43050e23	0.182786
$206$	1.46475e24	0.741578
$207$	1.93149e23	0.0929404
$208$	5.38046e23	0.246124
$209$	−1.67179e24	−0.727187
$210$	3.44151e23	0.142379
$211$	−2.00142e24	−0.787723	−0.393861	−	0.919170i	$-0.628861\pi$
$211$	−2.00142e24	−0.787723	−0.393861	+	0.919170i	$0.628861\pi$
$212$	−2.59998e24	−0.973740
$213$	3.55928e24	1.26875
$214$	−2.58630e23	−0.0877676
$215$	2.56000e24	0.827248
$216$	5.36669e22	0.0165174
$217$	−1.00257e24	−0.293958
$218$	−1.80226e24	−0.503528
$219$	−6.01134e24	−1.60069
$220$	−1.52783e24	−0.387826
$221$	2.67326e24	0.647027
$222$	8.57777e24	1.98001
$223$	−5.12870e24	−1.12929	−0.564646	−	0.825333i	$-0.690987\pi$
$223$	−5.12870e24	−1.12929	−0.564646	+	0.825333i	$0.690987\pi$
$224$	−2.65724e23	−0.0558248
$225$	1.03027e24	0.206553
$226$	−4.52768e24	−0.866437
$227$	−6.33336e24	−1.15708	−0.578539	−	0.815654i	$-0.696377\pi$
$227$	−6.33336e24	−1.15708	−0.578539	+	0.815654i	$0.696377\pi$
$228$	−1.71326e24	−0.298888
$229$	−1.10871e24	−0.184734	−0.0923671	−	0.995725i	$-0.529443\pi$
$229$	−1.10871e24	−0.184734	−0.0923671	+	0.995725i	$0.529443\pi$
$230$	−1.78791e23	−0.0284579
$231$	−5.13481e24	−0.780906
$232$	−3.02924e24	−0.440261
$233$	1.82788e24	0.253928	0.126964	−	0.991907i	$-0.459477\pi$
$233$	1.82788e24	0.253928	0.126964	+	0.991907i	$0.459477\pi$
$234$	5.41338e24	0.718955
$235$	−1.05866e24	−0.134444
$236$	2.24667e23	0.0272874
$237$	9.97164e24	1.15853
$238$	−1.32024e24	−0.146756
$239$	1.53311e25	1.63078	0.815392	−	0.578910i	$-0.196522\pi$
$239$	1.53311e25	1.63078	0.815392	+	0.578910i	$0.196522\pi$
$240$	−1.56573e24	−0.159404
$241$	1.14922e25	1.12002	0.560008	−	0.828487i	$-0.310798\pi$
$241$	1.14922e25	1.12002	0.560008	+	0.828487i	$0.310798\pi$
$242$	1.52177e25	1.42000
$243$	−1.59383e25	−1.42422
$244$	3.81966e24	0.326913
$245$	4.91059e24	0.402615
$246$	−5.24535e24	−0.412056
$247$	−5.48310e24	−0.412770
$248$	4.56122e24	0.329108
$249$	2.03144e25	1.40511
$250$	−9.53674e23	−0.0632456
$251$	2.87805e25	1.83031	0.915155	−	0.403102i	$-0.132068\pi$
$251$	2.87805e25	1.83031	0.915155	+	0.403102i	$0.132068\pi$
$252$	−2.67350e24	−0.163070
$253$	2.66760e24	0.156083
$254$	−1.76059e25	−0.988337
$255$	−7.77927e24	−0.419051
$256$	1.20893e24	0.0625000
$257$	1.15320e25	0.572279	0.286140	−	0.958188i	$-0.407628\pi$
$257$	1.15320e25	0.572279	0.286140	+	0.958188i	$0.407628\pi$
$258$	−3.91432e25	−1.86487
$259$	−1.35578e25	−0.620214
$260$	−5.01094e24	−0.220140
$261$	−3.04777e25	−1.28605
$262$	−3.23397e25	−1.31091
$263$	1.45289e24	0.0565844	0.0282922	−	0.999600i	$-0.490993\pi$
$263$	1.45289e24	0.0565844	0.0282922	+	0.999600i	$0.490993\pi$
$264$	2.33611e25	0.874281
$265$	2.42142e25	0.870940
$266$	2.70794e24	0.0936227
$267$	−5.90304e25	−1.96204
$268$	−1.18879e25	−0.379918
$269$	6.13764e25	1.88626	0.943131	−	0.332420i	$-0.107865\pi$
$269$	6.13764e25	1.88626	0.943131	+	0.332420i	$0.107865\pi$
$270$	−4.99812e23	−0.0147736
$271$	−6.52956e25	−1.85655	−0.928274	−	0.371897i	$-0.878707\pi$
$271$	−6.52956e25	−1.85655	−0.928274	+	0.371897i	$0.878707\pi$
$272$	6.00650e24	0.164304
$273$	−1.68410e25	−0.443262
$274$	3.78387e25	0.958420
$275$	1.42290e25	0.346882
$276$	2.73377e24	0.0641529
$277$	−2.58414e25	−0.583820	−0.291910	−	0.956446i	$-0.594291\pi$
$277$	−2.58414e25	−0.583820	−0.291910	+	0.956446i	$0.594291\pi$
$278$	−1.20768e25	−0.262713
$279$	4.58913e25	0.961359
$280$	2.47475e24	0.0499312
$281$	−4.28312e25	−0.832423	−0.416212	−	0.909268i	$-0.636642\pi$
$281$	−4.28312e25	−0.832423	−0.416212	+	0.909268i	$0.636642\pi$
$282$	1.61872e25	0.303079
$283$	2.55709e25	0.461306	0.230653	−	0.973036i	$-0.425914\pi$
$283$	2.55709e25	0.461306	0.230653	+	0.973036i	$0.425914\pi$
$284$	2.55944e25	0.444941
$285$	1.59560e25	0.267333
$286$	7.47644e25	1.20740
$287$	8.29067e24	0.129071
$288$	1.21632e25	0.182569
$289$	−3.92489e25	−0.568067
$290$	2.82120e25	0.393781
$291$	−1.34003e26	−1.80401
$292$	−4.32269e25	−0.561350
$293$	8.04265e25	1.00760	0.503801	−	0.863820i	$-0.331934\pi$
$293$	8.04265e25	1.00760	0.503801	+	0.863820i	$0.331934\pi$
$294$	−7.50846e25	−0.907620
$295$	−2.09237e24	−0.0244066
$296$	6.16818e25	0.694375
$297$	7.45730e24	0.0810287
$298$	−7.32368e24	−0.0768172
$299$	8.74911e24	0.0885965
$300$	1.45820e25	0.142575
$301$	6.18687e25	0.584148
$302$	4.96534e25	0.452768
$303$	5.45473e25	0.480425
$304$	−1.23199e25	−0.104818
$305$	−3.55734e25	−0.292400
$306$	6.04325e25	0.479950
$307$	1.68725e26	1.29487	0.647436	−	0.762120i	$-0.275841\pi$
$307$	1.68725e26	1.29487	0.647436	+	0.762120i	$0.275841\pi$
$308$	−3.69239e25	−0.273858
$309$	2.08583e26	1.49526
$310$	−4.24797e25	−0.294363
$311$	−1.48552e26	−0.995163	−0.497581	−	0.867417i	$-0.665778\pi$
$311$	−1.48552e26	−0.995163	−0.497581	+	0.867417i	$0.665778\pi$
$312$	7.66190e25	0.496264
$313$	−2.05064e26	−1.28432	−0.642162	−	0.766569i	$-0.721962\pi$
$313$	−2.05064e26	−1.28432	−0.642162	+	0.766569i	$0.721962\pi$
$314$	7.79718e25	0.472255
$315$	2.48989e25	0.145855
$316$	7.17050e25	0.406289
$317$	1.29090e26	0.707570	0.353785	−	0.935327i	$-0.384894\pi$
$317$	1.29090e26	0.707570	0.353785	+	0.935327i	$0.384894\pi$
$318$	−3.70243e26	−1.96337
$319$	−4.20929e26	−2.15977
$320$	−1.12590e25	−0.0559017
$321$	−3.68295e25	−0.176967
$322$	−4.32092e24	−0.0200951
$323$	−6.12109e25	−0.275551
$324$	−1.10851e26	−0.483079
$325$	4.66680e25	0.196899
$326$	2.49027e26	1.01733
$327$	−2.56645e26	−1.01527
$328$	−3.77188e25	−0.144505
$329$	−2.55851e25	−0.0949357
$330$	−2.17567e26	−0.781981
$331$	−3.05719e25	−0.106446	−0.0532229	−	0.998583i	$-0.516949\pi$
$331$	−3.05719e25	−0.106446	−0.0532229	+	0.998583i	$0.516949\pi$
$332$	1.46078e26	0.492761
$333$	6.20592e26	2.02834
$334$	7.24469e25	0.229447
$335$	1.10715e26	0.339809
$336$	−3.78398e25	−0.112561
$337$	−1.13350e26	−0.326820	−0.163410	−	0.986558i	$-0.552249\pi$
$337$	−1.13350e26	−0.326820	−0.163410	+	0.986558i	$0.552249\pi$
$338$	−7.78371e24	−0.0217551
$339$	−6.44752e26	−1.74701
$340$	−5.59399e25	−0.146958
$341$	6.33806e26	1.61449
$342$	−1.23953e26	−0.306183
$343$	2.50500e26	0.600093
$344$	−2.81475e26	−0.653997
$345$	−2.54602e25	−0.0573801
$346$	−6.83296e25	−0.149386
$347$	2.45240e25	0.0520153	0.0260077	−	0.999662i	$-0.491721\pi$
$347$	2.45240e25	0.0520153	0.0260077	+	0.999662i	$0.491721\pi$
$348$	−4.31371e26	−0.887705
$349$	−5.35297e25	−0.106888	−0.0534438	−	0.998571i	$-0.517020\pi$
$349$	−5.35297e25	−0.106888	−0.0534438	+	0.998571i	$0.517020\pi$
$350$	−2.30479e25	−0.0446599
$351$	2.44583e25	0.0459940
$352$	1.67987e26	0.306604
$353$	9.40765e26	1.66666	0.833329	−	0.552777i	$-0.186432\pi$
$353$	9.40765e26	1.66666	0.833329	+	0.552777i	$0.186432\pi$
$354$	3.19930e25	0.0550201
$355$	−2.38367e26	−0.397967
$356$	−4.24481e26	−0.688072
$357$	−1.88006e26	−0.295906
$358$	3.63317e26	0.555282
$359$	5.56389e25	0.0825822	0.0412911	−	0.999147i	$-0.486853\pi$
$359$	5.56389e25	0.0825822	0.0412911	+	0.999147i	$0.486853\pi$
$360$	−1.13279e26	−0.163295
$361$	−5.88660e26	−0.824213
$362$	4.75589e26	0.646832
$363$	2.16704e27	2.86317
$364$	−1.21102e26	−0.155449
$365$	4.02582e26	0.502087
$366$	5.43929e26	0.659160
$367$	−6.30707e26	−0.742736	−0.371368	−	0.928486i	$-0.621111\pi$
$367$	−6.30707e26	−0.742736	−0.371368	+	0.928486i	$0.621111\pi$
$368$	1.96582e25	0.0224979
$369$	−3.79495e26	−0.422114
$370$	−5.74457e26	−0.621068
$371$	5.85196e26	0.615001
$372$	6.49528e26	0.663586
$373$	5.07549e26	0.504122	0.252061	−	0.967711i	$-0.418892\pi$
$373$	5.07549e26	0.504122	0.252061	+	0.967711i	$0.418892\pi$
$374$	8.34636e26	0.806019
$375$	−1.35805e26	−0.127523
$376$	1.16400e26	0.106287
$377$	−1.38055e27	−1.22594
$378$	−1.20792e25	−0.0104322
$379$	−9.91065e26	−0.832512	−0.416256	−	0.909248i	$-0.636658\pi$
$379$	−9.91065e26	−0.832512	−0.416256	+	0.909248i	$0.636658\pi$
$380$	1.14738e26	0.0937517
$381$	−2.50713e27	−1.99280
$382$	8.94721e26	0.691866
$383$	6.75228e26	0.507999	0.254000	−	0.967204i	$-0.418254\pi$
$383$	6.75228e26	0.507999	0.254000	+	0.967204i	$0.418254\pi$
$384$	1.72154e26	0.126020
$385$	3.43880e26	0.244946
$386$	1.30175e27	0.902319
$387$	−2.83197e27	−1.91039
$388$	−9.63603e26	−0.632652
$389$	−3.61783e25	−0.0231194	−0.0115597	−	0.999933i	$-0.503680\pi$
$389$	−3.61783e25	−0.0231194	−0.0115597	+	0.999933i	$0.503680\pi$
$390$	−7.13570e26	−0.443872
$391$	9.76711e25	0.0591439
$392$	−5.39925e26	−0.318295
$393$	−4.60524e27	−2.64320
$394$	−4.21052e26	−0.235302
$395$	−6.67805e26	−0.363396
$396$	1.69015e27	0.895622
$397$	1.33109e27	0.686921	0.343460	−	0.939167i	$-0.388401\pi$
$397$	1.33109e27	0.686921	0.343460	+	0.939167i	$0.388401\pi$
$398$	−2.52796e27	−1.27057
$399$	3.85617e26	0.188773
$400$	1.04858e26	0.0500000
$401$	−2.02246e27	−0.939428	−0.469714	−	0.882819i	$-0.655643\pi$
$401$	−2.02246e27	−0.939428	−0.469714	+	0.882819i	$0.655643\pi$
$402$	−1.69286e27	−0.766035
$403$	2.07874e27	0.916426
$404$	3.92244e26	0.168481
$405$	1.03238e27	0.432079
$406$	6.81813e26	0.278062
$407$	8.57102e27	3.40637
$408$	8.55340e26	0.331289
$409$	−8.47227e26	−0.319820	−0.159910	−	0.987132i	$-0.551120\pi$
$409$	−8.47227e26	−0.319820	−0.159910	+	0.987132i	$0.551120\pi$
$410$	3.51283e26	0.129249
$411$	5.38833e27	1.93248
$412$	1.49990e27	0.524375
$413$	−5.05674e25	−0.0172343
$414$	1.97785e26	0.0657188
$415$	−1.36046e27	−0.440739
$416$	5.50959e26	0.174036
$417$	−1.71977e27	−0.529713
$418$	−1.71192e27	−0.514199
$419$	1.21097e26	0.0354720	0.0177360	−	0.999843i	$-0.494354\pi$
$419$	1.21097e26	0.0354720	0.0177360	+	0.999843i	$0.494354\pi$
$420$	3.52410e26	0.100677
$421$	−2.14501e27	−0.597677	−0.298839	−	0.954304i	$-0.596599\pi$
$421$	−2.14501e27	−0.597677	−0.298839	+	0.954304i	$0.596599\pi$
$422$	−2.04946e27	−0.557004
$423$	1.17113e27	0.310477
$424$	−2.66238e27	−0.688538
$425$	5.20981e26	0.131443
$426$	3.64470e27	0.897143
$427$	−8.59720e26	−0.206474
$428$	−2.64837e26	−0.0620611
$429$	1.06466e28	2.43450
$430$	2.62144e27	0.584952
$431$	−6.54117e27	−1.42444	−0.712220	−	0.701956i	$-0.752310\pi$
$431$	−6.54117e27	−1.42444	−0.712220	+	0.701956i	$0.752310\pi$
$432$	5.49549e25	0.0116796
$433$	−5.01504e27	−1.04028	−0.520141	−	0.854080i	$-0.674121\pi$
$433$	−5.01504e27	−1.04028	−0.520141	+	0.854080i	$0.674121\pi$
$434$	−1.02663e27	−0.207860
$435$	4.01745e27	0.793988
$436$	−1.84551e27	−0.356048
$437$	−2.00332e26	−0.0377308
$438$	−6.15561e27	−1.13186
$439$	−1.69183e26	−0.0303725	−0.0151862	−	0.999885i	$-0.504834\pi$
$439$	−1.69183e26	−0.0303725	−0.0151862	+	0.999885i	$0.504834\pi$
$440$	−1.56450e27	−0.274235
$441$	−5.43229e27	−0.929775
$442$	2.73742e27	0.457517
$443$	−9.61737e26	−0.156970	−0.0784851	−	0.996915i	$-0.525008\pi$
$443$	−9.61737e26	−0.156970	−0.0784851	+	0.996915i	$0.525008\pi$
$444$	8.78363e27	1.40008
$445$	3.95329e27	0.615430
$446$	−5.25179e27	−0.798529
$447$	−1.04291e27	−0.154888
$448$	−2.72102e26	−0.0394741
$449$	6.24039e27	0.884353	0.442176	−	0.896928i	$-0.354207\pi$
$449$	6.24039e27	0.884353	0.442176	+	0.896928i	$0.354207\pi$
$450$	1.05499e27	0.146055
$451$	−5.24123e27	−0.708891
$452$	−4.63634e27	−0.612663
$453$	7.07075e27	0.912924
$454$	−6.48537e27	−0.818178
$455$	1.12785e27	0.139037
$456$	−1.75438e27	−0.211345
$457$	3.52032e27	0.414440	0.207220	−	0.978294i	$-0.433558\pi$
$457$	3.52032e27	0.414440	0.207220	+	0.978294i	$0.433558\pi$
$458$	−1.13532e27	−0.130627
$459$	2.73041e26	0.0307040
$460$	−1.83081e26	−0.0201227
$461$	−1.20890e28	−1.29877	−0.649385	−	0.760460i	$-0.724974\pi$
$461$	−1.20890e28	−1.29877	−0.649385	+	0.760460i	$0.724974\pi$
$462$	−5.25804e27	−0.552184
$463$	1.11633e28	1.14602	0.573011	−	0.819548i	$-0.305775\pi$
$463$	1.11633e28	1.14602	0.573011	+	0.819548i	$0.305775\pi$
$464$	−3.10194e27	−0.311311
$465$	−6.04920e27	−0.593529
$466$	1.87175e27	0.179554
$467$	−7.95837e26	−0.0746443	−0.0373222	−	0.999303i	$-0.511883\pi$
$467$	−7.95837e26	−0.0746443	−0.0373222	+	0.999303i	$0.511883\pi$
$468$	5.54330e27	0.508378
$469$	2.67570e27	0.239951
$470$	−1.08406e27	−0.0950664
$471$	1.11034e28	0.952215
$472$	2.30059e26	0.0192951
$473$	−3.91124e28	−3.20828
$474$	1.02110e28	0.819208
$475$	−1.06858e27	−0.0838540
$476$	−1.35193e27	−0.103772
$477$	−2.67867e28	−2.01129
$478$	1.56991e28	1.15314
$479$	−2.17497e28	−1.56290	−0.781448	−	0.623970i	$-0.785519\pi$
$479$	−2.17497e28	−1.56290	−0.781448	+	0.623970i	$0.785519\pi$
$480$	−1.60331e27	−0.112716
$481$	2.81110e28	1.93354
$482$	1.17680e28	0.791971
$483$	−6.15309e26	−0.0405180
$484$	1.55830e28	1.00409
$485$	8.97425e27	0.565861
$486$	−1.63209e28	−1.00708
$487$	5.73428e27	0.346278	0.173139	−	0.984897i	$-0.444609\pi$
$487$	5.73428e27	0.346278	0.173139	+	0.984897i	$0.444609\pi$
$488$	3.91134e27	0.231162
$489$	3.54621e28	2.05126
$490$	5.02845e27	0.284692
$491$	2.57469e28	1.42682	0.713411	−	0.700746i	$-0.247149\pi$
$491$	2.57469e28	1.42682	0.713411	+	0.700746i	$0.247149\pi$
$492$	−5.37124e27	−0.291367
$493$	−1.54119e28	−0.818395
$494$	−5.61470e27	−0.291873
$495$	−1.57407e28	−0.801069
$496$	4.67069e27	0.232714
$497$	−5.76072e27	−0.281019
$498$	2.08019e28	0.993562
$499$	−8.46999e27	−0.396120	−0.198060	−	0.980190i	$-0.563464\pi$
$499$	−8.46999e27	−0.396120	−0.198060	+	0.980190i	$0.563464\pi$
$500$	−9.76563e26	−0.0447214
$501$	1.03166e28	0.462637
$502$	2.94713e28	1.29422
$503$	6.31847e27	0.271737	0.135868	−	0.990727i	$-0.456618\pi$
$503$	6.31847e27	0.271737	0.135868	+	0.990727i	$0.456618\pi$
$504$	−2.73767e27	−0.115308
$505$	−3.65306e27	−0.150694
$506$	2.73162e27	0.110367
$507$	−1.10842e27	−0.0438652
$508$	−1.80285e28	−0.698860
$509$	−2.12183e28	−0.805701	−0.402851	−	0.915266i	$-0.631981\pi$
$509$	−2.12183e28	−0.805701	−0.402851	+	0.915266i	$0.631981\pi$
$510$	−7.96597e27	−0.296314
$511$	9.72940e27	0.354541
$512$	1.23794e27	0.0441942
$513$	−5.60032e26	−0.0195876
$514$	1.18088e28	0.404662
$515$	−1.39689e28	−0.469015
$516$	−4.00826e28	−1.31866
$517$	1.61745e28	0.521410
$518$	−1.38832e28	−0.438557
$519$	−9.73030e27	−0.301210
$520$	−5.13120e27	−0.155663
$521$	2.15042e28	0.639333	0.319666	−	0.947530i	$-0.396429\pi$
$521$	2.15042e28	0.639333	0.319666	+	0.947530i	$0.396429\pi$
$522$	−3.12092e28	−0.909374
$523$	2.33910e28	0.668006	0.334003	−	0.942572i	$-0.391600\pi$
$523$	2.33910e28	0.668006	0.334003	+	0.942572i	$0.391600\pi$
$524$	−3.31158e28	−0.926951
$525$	−3.28208e27	−0.0900484
$526$	1.48776e27	0.0400112
$527$	2.32061e28	0.611774
$528$	2.39217e28	0.618210
$529$	−3.91519e28	−0.991902
$530$	2.47953e28	0.615847
$531$	2.31466e27	0.0563631
$532$	2.77293e27	0.0662013
$533$	−1.71900e28	−0.402385
$534$	−6.04471e28	−1.38737
$535$	2.46649e27	0.0555091
$536$	−1.21732e28	−0.268642
$537$	5.17371e28	1.11962
$538$	6.28494e28	1.33379
$539$	−7.50256e28	−1.56145
$540$	−5.11807e26	−0.0104465
$541$	−8.51648e28	−1.70486	−0.852430	−	0.522841i	$-0.824872\pi$
$541$	−8.51648e28	−1.70486	−0.852430	+	0.522841i	$0.824872\pi$
$542$	−6.68627e28	−1.31278
$543$	6.77250e28	1.30422
$544$	6.15066e27	0.116180
$545$	1.71877e28	0.318459
$546$	−1.72452e28	−0.313434
$547$	−2.74194e28	−0.488868	−0.244434	−	0.969666i	$-0.578602\pi$
$547$	−2.74194e28	−0.488868	−0.244434	+	0.969666i	$0.578602\pi$
$548$	3.87469e28	0.677705
$549$	3.93527e28	0.675250
$550$	1.45705e28	0.245283
$551$	3.16112e28	0.522094
$552$	2.79938e27	0.0453629
$553$	−1.61392e28	−0.256606
$554$	−2.64616e28	−0.412823
$555$	−8.18040e28	−1.25227
$556$	−1.23667e28	−0.185766
$557$	9.36354e28	1.38026	0.690130	−	0.723686i	$-0.257553\pi$
$557$	9.36354e28	1.38026	0.690130	+	0.723686i	$0.257553\pi$
$558$	4.69926e28	0.679784
$559$	−1.28280e29	−1.82110
$560$	2.53415e27	0.0353067
$561$	1.18854e29	1.62519
$562$	−4.38592e28	−0.588612
$563$	1.15762e27	0.0152485	0.00762423	−	0.999971i	$-0.497573\pi$
$563$	1.15762e27	0.0152485	0.00762423	+	0.999971i	$0.497573\pi$
$564$	1.65757e28	0.214309
$565$	4.31793e28	0.547983
$566$	2.61846e28	0.326192
$567$	2.49501e28	0.305106
$568$	2.62087e28	0.314621
$569$	1.15072e29	1.35609	0.678046	−	0.735020i	$-0.262827\pi$
$569$	1.15072e29	1.35609	0.678046	+	0.735020i	$0.262827\pi$
$570$	1.63389e28	0.189033
$571$	2.31271e27	0.0262689	0.0131344	−	0.999914i	$-0.495819\pi$
$571$	2.31271e27	0.0262689	0.0131344	+	0.999914i	$0.495819\pi$
$572$	7.65588e28	0.853761
$573$	1.27410e29	1.39502
$574$	8.48964e27	0.0912671
$575$	1.70508e27	0.0179983
$576$	1.24551e28	0.129096
$577$	1.04522e29	1.06380	0.531900	−	0.846807i	$-0.321478\pi$
$577$	1.04522e29	1.06380	0.531900	+	0.846807i	$0.321478\pi$
$578$	−4.01908e28	−0.401684
$579$	1.85372e29	1.81936
$580$	2.88891e28	0.278445
$581$	−3.28789e28	−0.311221
$582$	−1.37219e29	−1.27563
$583$	−3.69952e29	−3.37773
$584$	−4.42643e28	−0.396935
$585$	−5.16260e28	−0.454707
$586$	8.23568e28	0.712483
$587$	−6.14643e28	−0.522304	−0.261152	−	0.965298i	$-0.584102\pi$
$587$	−6.14643e28	−0.522304	−0.261152	+	0.965298i	$0.584102\pi$
$588$	−7.68866e28	−0.641784
$589$	−4.75979e28	−0.390281
$590$	−2.14259e27	−0.0172581
$591$	−5.99588e28	−0.474443
$592$	6.31622e28	0.490997
$593$	5.04078e28	0.384967	0.192484	−	0.981300i	$-0.438346\pi$
$593$	5.04078e28	0.384967	0.192484	+	0.981300i	$0.438346\pi$
$594$	7.63628e27	0.0572960
$595$	1.25908e28	0.0928166
$596$	−7.49945e27	−0.0543180
$597$	−3.59988e29	−2.56187
$598$	8.95909e27	0.0626472
$599$	−1.05424e29	−0.724369	−0.362184	−	0.932107i	$-0.617969\pi$
$599$	−1.05424e29	−0.724369	−0.362184	+	0.932107i	$0.617969\pi$
$600$	1.49320e28	0.100816
$601$	1.74685e28	0.115897	0.0579486	−	0.998320i	$-0.481544\pi$
$601$	1.74685e28	0.115897	0.0579486	+	0.998320i	$0.481544\pi$
$602$	6.33536e28	0.413055
$603$	−1.22477e29	−0.784733
$604$	5.08450e28	0.320155
$605$	−1.45128e29	−0.898088
$606$	5.58564e28	0.339712
$607$	5.07197e28	0.303177	0.151588	−	0.988444i	$-0.451561\pi$
$607$	5.07197e28	0.303177	0.151588	+	0.988444i	$0.451561\pi$
$608$	−1.26156e28	−0.0741172
$609$	9.70918e28	0.560662
$610$	−3.64272e28	−0.206758
$611$	5.30486e28	0.295966
$612$	6.18829e28	0.339376
$613$	−1.33432e29	−0.719326	−0.359663	−	0.933082i	$-0.617108\pi$
$613$	−1.33432e29	−0.719326	−0.359663	+	0.933082i	$0.617108\pi$
$614$	1.72774e29	0.915612
$615$	5.00236e28	0.260607
$616$	−3.78100e28	−0.193647
$617$	2.59409e29	1.30614	0.653072	−	0.757296i	$-0.273480\pi$
$617$	2.59409e29	1.30614	0.653072	+	0.757296i	$0.273480\pi$
$618$	2.13589e29	1.05731
$619$	4.50651e27	0.0219325	0.0109663	−	0.999940i	$-0.496509\pi$
$619$	4.50651e27	0.0219325	0.0109663	+	0.999940i	$0.496509\pi$
$620$	−4.34992e28	−0.208146
$621$	8.93616e26	0.00420425
$622$	−1.52117e29	−0.703686
$623$	9.55411e28	0.434576
$624$	7.84578e28	0.350912
$625$	9.09495e27	0.0400000
$626$	−2.09986e29	−0.908155
$627$	−2.43781e29	−1.03679
$628$	7.98431e28	0.333934
$629$	3.13819e29	1.29077
$630$	2.54965e28	0.103135
$631$	−2.27120e29	−0.903539	−0.451769	−	0.892135i	$-0.649207\pi$
$631$	−2.27120e29	−0.903539	−0.451769	+	0.892135i	$0.649207\pi$
$632$	7.34260e28	0.287290
$633$	−2.91848e29	−1.12310
$634$	1.32188e29	0.500328
$635$	1.67903e29	0.625079
$636$	−3.79129e29	−1.38831
$637$	−2.46067e29	−0.886318
$638$	−4.31032e29	−1.52719
$639$	2.63690e29	0.919042
$640$	−1.15292e28	−0.0395285
$641$	3.34335e29	1.12765	0.563824	−	0.825895i	$-0.309330\pi$
$641$	3.34335e29	1.12765	0.563824	+	0.825895i	$0.309330\pi$
$642$	−3.77134e28	−0.125135
$643$	2.54505e29	0.830769	0.415385	−	0.909646i	$-0.363647\pi$
$643$	2.54505e29	0.830769	0.415385	+	0.909646i	$0.363647\pi$
$644$	−4.42462e27	−0.0142094
$645$	3.73299e29	1.17945
$646$	−6.26799e28	−0.194844
$647$	3.47025e29	1.06137	0.530683	−	0.847570i	$-0.321935\pi$
$647$	3.47025e29	1.06137	0.530683	+	0.847570i	$0.321935\pi$
$648$	−1.13512e29	−0.341589
$649$	3.19679e28	0.0946553
$650$	4.77881e28	0.139229
$651$	−1.46194e29	−0.419111
$652$	2.55004e29	0.719362
$653$	8.56072e28	0.237641	0.118821	−	0.992916i	$-0.462089\pi$
$653$	8.56072e28	0.237641	0.118821	+	0.992916i	$0.462089\pi$
$654$	−2.62805e29	−0.717905
$655$	3.08415e29	0.829090
$656$	−3.86240e28	−0.102180
$657$	−4.45352e29	−1.15949
$658$	−2.61991e28	−0.0671297
$659$	4.44478e29	1.12086	0.560432	−	0.828200i	$-0.310635\pi$
$659$	4.44478e29	1.12086	0.560432	+	0.828200i	$0.310635\pi$
$660$	−2.22788e29	−0.552944
$661$	−3.57515e29	−0.873330	−0.436665	−	0.899624i	$-0.643841\pi$
$661$	−3.57515e29	−0.873330	−0.436665	+	0.899624i	$0.643841\pi$
$662$	−3.13056e28	−0.0752685
$663$	3.89815e29	0.922500
$664$	1.49584e29	0.348435
$665$	−2.58249e28	−0.0592122
$666$	6.35486e29	1.43426
$667$	−5.04404e28	−0.112062
$668$	7.41856e28	0.162243
$669$	−7.47866e29	−1.61009
$670$	1.13372e29	0.240281
$671$	5.43502e29	1.13400
$672$	−3.87479e28	−0.0795923
$673$	6.36881e29	1.28795	0.643977	−	0.765045i	$-0.277283\pi$
$673$	6.36881e29	1.28795	0.643977	+	0.765045i	$0.277283\pi$
$674$	−1.16071e29	−0.231096
$675$	4.76657e27	0.00934365
$676$	−7.97052e27	−0.0153832
$677$	4.25804e29	0.809149	0.404575	−	0.914505i	$-0.367420\pi$
$677$	4.25804e29	0.809149	0.404575	+	0.914505i	$0.367420\pi$
$678$	−6.60226e29	−1.23532
$679$	2.16885e29	0.399574
$680$	−5.72825e28	−0.103915
$681$	−9.23531e29	−1.64971
$682$	6.49018e29	1.14162
$683$	−4.90070e29	−0.848869	−0.424435	−	0.905459i	$-0.639527\pi$
$683$	−4.90070e29	−0.848869	−0.424435	+	0.905459i	$0.639527\pi$
$684$	−1.26927e29	−0.216504
$685$	−3.60858e29	−0.606158
$686$	2.56512e29	0.424330
$687$	−1.61673e29	−0.263385
$688$	−2.88230e29	−0.462445
$689$	−1.21336e30	−1.91729
$690$	−2.60712e28	−0.0405738
$691$	−9.54239e29	−1.46264	−0.731320	−	0.682034i	$-0.761095\pi$
$691$	−9.54239e29	−1.46264	−0.731320	+	0.682034i	$0.761095\pi$
$692$	−6.99695e28	−0.105632
$693$	−3.80414e29	−0.565662
$694$	2.51126e28	0.0367804
$695$	1.15173e29	0.166154
$696$	−4.41724e29	−0.627702
$697$	−1.91902e29	−0.268618
$698$	−5.48144e28	−0.0755810
$699$	2.66542e29	0.362039
$700$	−2.36011e28	−0.0315793
$701$	1.07881e30	1.42202	0.711009	−	0.703183i	$-0.248238\pi$
$701$	1.07881e30	1.42202	0.711009	+	0.703183i	$0.248238\pi$
$702$	2.50453e28	0.0325227
$703$	−6.43671e29	−0.823442
$704$	1.72019e29	0.216802
$705$	−1.54373e29	−0.191684
$706$	9.63343e29	1.17851
$707$	−8.82852e28	−0.106410
$708$	3.27609e28	0.0389051
$709$	−3.07083e29	−0.359311	−0.179656	−	0.983730i	$-0.557498\pi$
$709$	−3.07083e29	−0.359311	−0.179656	+	0.983730i	$0.557498\pi$
$710$	−2.44087e29	−0.281406
$711$	7.38752e29	0.839205
$712$	−4.34669e29	−0.486540
$713$	7.59496e28	0.0837694
$714$	−1.92518e29	−0.209237
$715$	−7.13009e29	−0.763627
$716$	3.72036e29	0.392643
$717$	2.23559e30	2.32509
$718$	5.69742e28	0.0583945
$719$	4.72676e29	0.477431	0.238715	−	0.971090i	$-0.423274\pi$
$719$	4.72676e29	0.477431	0.238715	+	0.971090i	$0.423274\pi$
$720$	−1.15998e29	−0.115467
$721$	−3.37594e29	−0.331188
$722$	−6.02788e29	−0.582806
$723$	1.67579e30	1.59686
$724$	4.87003e29	0.457380
$725$	−2.69051e29	−0.249049
$726$	2.21905e30	2.02457
$727$	−6.61062e29	−0.594472	−0.297236	−	0.954804i	$-0.596065\pi$
$727$	−6.61062e29	−0.594472	−0.297236	+	0.954804i	$0.596065\pi$
$728$	−1.24008e29	−0.109919
$729$	−1.21830e30	−1.06443
$730$	4.12244e29	0.355029
$731$	−1.43206e30	−1.21571
$732$	5.56983e29	0.466096
$733$	2.18574e30	1.80304	0.901522	−	0.432733i	$-0.142451\pi$
$733$	2.18574e30	1.80304	0.901522	+	0.432733i	$0.142451\pi$
$734$	−6.45844e29	−0.525193
$735$	7.16063e29	0.574029
$736$	2.01300e28	0.0159084
$737$	−1.69153e30	−1.31787
$738$	−3.88603e29	−0.298480
$739$	3.79526e29	0.287392	0.143696	−	0.989622i	$-0.454101\pi$
$739$	3.79526e29	0.287392	0.143696	+	0.989622i	$0.454101\pi$
$740$	−5.88244e29	−0.439161
$741$	−7.99546e29	−0.588508
$742$	5.99241e29	0.434871
$743$	−2.37676e29	−0.170060	−0.0850301	−	0.996378i	$-0.527099\pi$
$743$	−2.37676e29	−0.170060	−0.0850301	+	0.996378i	$0.527099\pi$
$744$	6.65117e29	0.469226
$745$	6.98440e28	0.0485835
$746$	5.19730e29	0.356468
$747$	1.50499e30	1.01781
$748$	8.54667e29	0.569942
$749$	5.96089e28	0.0391969
$750$	−1.39065e29	−0.0901724
$751$	−1.40557e30	−0.898736	−0.449368	−	0.893347i	$-0.648351\pi$
$751$	−1.40557e30	−0.898736	−0.449368	+	0.893347i	$0.648351\pi$
$752$	1.19194e29	0.0751566
$753$	4.19678e30	2.60957
$754$	−1.41369e30	−0.866870
$755$	−4.73531e29	−0.286356
$756$	−1.23691e28	−0.00737665
$757$	−2.92590e30	−1.72089	−0.860445	−	0.509544i	$-0.829814\pi$
$757$	−2.92590e30	−1.72089	−0.860445	+	0.509544i	$0.829814\pi$
$758$	−1.01485e30	−0.588675
$759$	3.88989e29	0.222535
$760$	1.17492e29	0.0662924
$761$	−5.26624e29	−0.293063	−0.146532	−	0.989206i	$-0.546811\pi$
$761$	−5.26624e29	−0.293063	−0.146532	+	0.989206i	$0.546811\pi$
$762$	−2.56730e30	−1.40912
$763$	4.15383e29	0.224875
$764$	9.16194e29	0.489223
$765$	−5.76329e29	−0.303547
$766$	6.91433e29	0.359210
$767$	1.04848e29	0.0537288
$768$	1.76286e29	0.0891095
$769$	−3.65277e30	−1.82136	−0.910680	−	0.413113i	$-0.864441\pi$
$769$	−3.65277e30	−1.82136	−0.910680	+	0.413113i	$0.864441\pi$
$770$	3.52133e29	0.173203
$771$	1.68160e30	0.815928
$772$	1.33299e30	0.638036
$773$	3.30545e29	0.156079	0.0780397	−	0.996950i	$-0.475134\pi$
$773$	3.30545e29	0.156079	0.0780397	+	0.996950i	$0.475134\pi$
$774$	−2.89993e30	−1.35085
$775$	4.05118e29	0.186172
$776$	−9.86729e29	−0.447353
$777$	−1.97700e30	−0.884271
$778$	−3.70466e28	−0.0163479
$779$	3.93608e29	0.171365
$780$	−7.30695e29	−0.313865
$781$	3.64184e30	1.54342
$782$	1.00015e29	0.0418211
$783$	−1.41007e29	−0.0581757
$784$	−5.52884e29	−0.225069
$785$	−7.43597e29	−0.298680
$786$	−4.71577e30	−1.86903
$787$	−1.40282e30	−0.548616	−0.274308	−	0.961642i	$-0.588449\pi$
$787$	−1.40282e30	−0.548616	−0.274308	+	0.961642i	$0.588449\pi$
$788$	−4.31157e29	−0.166384
$789$	2.11860e29	0.0806753
$790$	−6.83832e29	−0.256960
$791$	1.04354e30	0.386949
$792$	1.73071e30	0.633301
$793$	1.78256e30	0.643689
$794$	1.36303e30	0.485726
$795$	3.53091e30	1.24174
$796$	−2.58863e30	−0.898428
$797$	1.75762e30	0.602023	0.301011	−	0.953621i	$-0.402676\pi$
$797$	1.75762e30	0.602023	0.301011	+	0.953621i	$0.402676\pi$
$798$	3.94871e29	0.133483
$799$	5.92211e29	0.197576
$800$	1.07374e29	0.0353553
$801$	−4.37328e30	−1.42124
$802$	−2.07100e30	−0.664276
$803$	−6.15077e30	−1.94723
$804$	−1.73349e30	−0.541668
$805$	4.12075e28	0.0127092
$806$	2.12863e30	0.648011
$807$	8.94990e30	2.68934
$808$	4.01658e29	0.119134
$809$	3.77067e30	1.10397	0.551987	−	0.833853i	$-0.313870\pi$
$809$	3.77067e30	1.10397	0.551987	+	0.833853i	$0.313870\pi$
$810$	1.05716e30	0.305526
$811$	3.20340e30	0.913885	0.456943	−	0.889496i	$-0.348944\pi$
$811$	3.20340e30	0.913885	0.456943	+	0.889496i	$0.348944\pi$
$812$	6.98177e29	0.196620
$813$	−9.52140e30	−2.64698
$814$	8.77673e30	2.40867
$815$	−2.37491e30	−0.643417
$816$	8.75868e29	0.234257
$817$	2.93728e30	0.775558
$818$	−8.67561e29	−0.226147
$819$	−1.24767e30	−0.321084
$820$	3.59714e29	0.0913928
$821$	4.79109e30	1.20180	0.600899	−	0.799325i	$-0.294810\pi$
$821$	4.79109e30	1.20180	0.600899	+	0.799325i	$0.294810\pi$
$822$	5.51765e30	1.36647
$823$	2.15990e30	0.528123	0.264062	−	0.964506i	$-0.414938\pi$
$823$	2.15990e30	0.528123	0.264062	+	0.964506i	$0.414938\pi$
$824$	1.53590e30	0.370789
$825$	2.07488e30	0.494568
$826$	−5.17810e28	−0.0121865
$827$	−7.12411e30	−1.65548	−0.827738	−	0.561115i	$-0.810373\pi$
$827$	−7.12411e30	−1.65548	−0.827738	+	0.561115i	$0.810373\pi$
$828$	2.02532e29	0.0464702
$829$	4.53775e30	1.02806	0.514029	−	0.857773i	$-0.328152\pi$
$829$	4.53775e30	1.02806	0.514029	+	0.857773i	$0.328152\pi$
$830$	−1.39311e30	−0.311649
$831$	−3.76820e30	−0.832382
$832$	5.64182e29	0.123062
$833$	−2.74698e30	−0.591675
$834$	−1.76104e30	−0.374564
$835$	−6.90907e29	−0.145115
$836$	−1.75300e30	−0.363594
$837$	2.12318e29	0.0434881
$838$	1.24003e29	0.0250825
$839$	−7.62675e30	−1.52349	−0.761743	−	0.647879i	$-0.775656\pi$
$839$	−7.62675e30	−1.52349	−0.761743	+	0.647879i	$0.775656\pi$
$840$	3.60868e29	0.0711895
$841$	2.82633e30	0.550635
$842$	−2.19649e30	−0.422622
$843$	−6.24565e30	−1.18683
$844$	−2.09865e30	−0.393861
$845$	7.42312e28	0.0137591
$846$	1.19923e30	0.219540
$847$	−3.50737e30	−0.634171
$848$	−2.72627e30	−0.486870
$849$	3.72875e30	0.657707
$850$	5.33484e29	0.0929444
$851$	1.02707e30	0.176743
$852$	3.73218e30	0.634376
$853$	1.80719e30	0.303416	0.151708	−	0.988425i	$-0.451523\pi$
$853$	1.80719e30	0.303416	0.151708	+	0.988425i	$0.451523\pi$
$854$	−8.80353e29	−0.145999
$855$	1.18210e30	0.193647
$856$	−2.71193e29	−0.0438838
$857$	1.07620e30	0.172026	0.0860132	−	0.996294i	$-0.472587\pi$
$857$	1.07620e30	0.172026	0.0860132	+	0.996294i	$0.472587\pi$
$858$	1.09021e31	1.72145
$859$	−1.30046e29	−0.0202847	−0.0101423	−	0.999949i	$-0.503228\pi$
$859$	−1.30046e29	−0.0202847	−0.0101423	+	0.999949i	$0.503228\pi$
$860$	2.68435e30	0.413624
$861$	1.20894e30	0.184024
$862$	−6.69816e30	−1.00723
$863$	−2.62521e28	−0.00389987	−0.00194993	−	0.999998i	$-0.500621\pi$
$863$	−2.62521e28	−0.00389987	−0.00194993	+	0.999998i	$0.500621\pi$
$864$	5.62738e28	0.00825870
$865$	6.51642e29	0.0944800
$866$	−5.13540e30	−0.735591
$867$	−5.72327e30	−0.809923
$868$	−1.05127e30	−0.146979
$869$	1.02029e31	1.40935
$870$	4.11387e30	0.561434
$871$	−5.54785e30	−0.748055
$872$	−1.88980e30	−0.251764
$873$	−9.92767e30	−1.30677
$874$	−2.05140e29	−0.0266797
$875$	2.19802e29	0.0282454
$876$	−6.30334e30	−0.800346
$877$	6.55749e30	0.822701	0.411350	−	0.911477i	$-0.365057\pi$
$877$	6.55749e30	0.822701	0.411350	+	0.911477i	$0.365057\pi$
$878$	−1.73244e29	−0.0214766
$879$	1.17278e31	1.43659
$880$	−1.60205e30	−0.193913
$881$	−6.61120e29	−0.0790739	−0.0395370	−	0.999218i	$-0.512588\pi$
$881$	−6.61120e29	−0.0790739	−0.0395370	+	0.999218i	$0.512588\pi$
$882$	−5.56266e30	−0.657450
$883$	−6.57705e30	−0.768145	−0.384073	−	0.923303i	$-0.625479\pi$
$883$	−6.57705e30	−0.768145	−0.384073	+	0.923303i	$0.625479\pi$
$884$	2.80312e30	0.323513
$885$	−3.05109e29	−0.0347978
$886$	−9.84819e29	−0.110995
$887$	−1.00815e31	−1.12287	−0.561433	−	0.827522i	$-0.689750\pi$
$887$	−1.00815e31	−1.12287	−0.561433	+	0.827522i	$0.689750\pi$
$888$	8.99444e30	0.990006
$889$	4.05780e30	0.441390
$890$	4.04817e30	0.435175
$891$	−1.57731e31	−1.67572
$892$	−5.37783e30	−0.564646
$893$	−1.21468e30	−0.126044
$894$	−1.06794e30	−0.109522
$895$	−3.46486e30	−0.351191
$896$	−2.78632e29	−0.0279124
$897$	1.27580e30	0.126317
$898$	6.39016e30	0.625332
$899$	−1.19844e31	−1.15915
$900$	1.08031e30	0.103277
$901$	−1.35454e31	−1.27992
$902$	−5.36702e30	−0.501262
$903$	9.02169e30	0.832850
$904$	−4.74761e30	−0.433218
$905$	−4.53557e30	−0.409093
$906$	7.24045e30	0.645535
$907$	1.41780e31	1.24950	0.624751	−	0.780824i	$-0.285200\pi$
$907$	1.41780e31	1.24950	0.624751	+	0.780824i	$0.285200\pi$
$908$	−6.64101e30	−0.578539
$909$	4.04115e30	0.348004
$910$	1.15492e30	0.0983143
$911$	2.18902e31	1.84208	0.921038	−	0.389472i	$-0.127343\pi$
$911$	2.18902e31	1.84208	0.921038	+	0.389472i	$0.127343\pi$
$912$	−1.79649e30	−0.149444
$913$	2.07856e31	1.70930
$914$	3.60481e30	0.293054
$915$	−5.18731e30	−0.416889
$916$	−1.16257e30	−0.0923671
$917$	7.45362e30	0.585449
$918$	2.79594e29	0.0217110
$919$	1.03315e31	0.793144	0.396572	−	0.918004i	$-0.370200\pi$
$919$	1.03315e31	0.793144	0.396572	+	0.918004i	$0.370200\pi$
$920$	−1.87475e29	−0.0142289
$921$	2.46035e31	1.84616
$922$	−1.23792e31	−0.918369
$923$	1.19444e31	0.876086
$924$	−5.38424e30	−0.390453
$925$	5.47844e30	0.392798
$926$	1.14312e31	0.810360
$927$	1.54529e31	1.08311
$928$	−3.17639e30	−0.220130
$929$	1.11191e31	0.761912	0.380956	−	0.924593i	$-0.375595\pi$
$929$	1.11191e31	0.761912	0.380956	+	0.924593i	$0.375595\pi$
$930$	−6.19438e30	−0.419689
$931$	5.63431e30	0.377458
$932$	1.91667e30	0.126964
$933$	−2.16618e31	−1.41885
$934$	−8.14937e29	−0.0527815
$935$	−7.95971e30	−0.509771
$936$	5.67634e30	0.359478
$937$	3.58584e30	0.224556	0.112278	−	0.993677i	$-0.464185\pi$
$937$	3.58584e30	0.224556	0.112278	+	0.993677i	$0.464185\pi$
$938$	2.73991e30	0.169671
$939$	−2.99025e31	−1.83113
$940$	−1.11008e30	−0.0672221
$941$	−3.45702e30	−0.207019	−0.103510	−	0.994628i	$-0.533007\pi$
$941$	−3.45702e30	−0.207019	−0.103510	+	0.994628i	$0.533007\pi$
$942$	1.13698e31	0.673318
$943$	−6.28061e29	−0.0367815
$944$	2.35580e29	0.0136437
$945$	1.15196e29	0.00659788
$946$	−4.00511e31	−2.26860
$947$	2.52124e31	1.41234	0.706170	−	0.708043i	$-0.250422\pi$
$947$	2.52124e31	1.41234	0.706170	+	0.708043i	$0.250422\pi$
$948$	1.04560e31	0.579267
$949$	−2.01731e31	−1.10530
$950$	−1.09423e30	−0.0592938
$951$	1.88239e31	1.00882
$952$	−1.38437e30	−0.0733779
$953$	−1.95398e31	−1.02434	−0.512169	−	0.858884i	$-0.671158\pi$
$953$	−1.95398e31	−1.02434	−0.512169	+	0.858884i	$0.671158\pi$
$954$	−2.74295e31	−1.42220
$955$	−8.53272e30	−0.437575
$956$	1.60759e31	0.815392
$957$	−6.13799e31	−3.07929
$958$	−2.22717e31	−1.10513
$959$	−8.72105e30	−0.428029
$960$	−1.64179e30	−0.0797019
$961$	−2.78029e30	−0.133504
$962$	2.87857e31	1.36722
$963$	−2.72853e30	−0.128189
$964$	1.20504e31	0.560008
$965$	−1.24144e31	−0.570677
$966$	−6.30076e29	−0.0286506
$967$	5.59458e30	0.251646	0.125823	−	0.992053i	$-0.459843\pi$
$967$	5.59458e30	0.251646	0.125823	+	0.992053i	$0.459843\pi$
$968$	1.59570e31	0.710001
$969$	−8.92577e30	−0.392867
$970$	9.18963e30	0.400124
$971$	1.38546e31	0.596749	0.298374	−	0.954449i	$-0.403556\pi$
$971$	1.38546e31	0.596749	0.298374	+	0.954449i	$0.403556\pi$
$972$	−1.67126e31	−0.712110
$973$	2.78345e30	0.117327
$974$	5.87190e30	0.244855
$975$	6.80513e30	0.280730
$976$	4.00521e30	0.163456
$977$	2.01846e31	0.814945	0.407472	−	0.913218i	$-0.366410\pi$
$977$	2.01846e31	0.814945	0.407472	+	0.913218i	$0.366410\pi$
$978$	3.63132e31	1.45046
$979$	−6.03996e31	−2.38680
$980$	5.14913e30	0.201308
$981$	−1.90136e31	−0.735429
$982$	2.63648e31	1.00891
$983$	1.07859e31	0.408361	0.204181	−	0.978933i	$-0.434547\pi$
$983$	1.07859e31	0.408361	0.204181	+	0.978933i	$0.434547\pi$
$984$	−5.50015e30	−0.206028
$985$	4.01547e30	0.148818
$986$	−1.57818e31	−0.578693
$987$	−3.73081e30	−0.135355
$988$	−5.74945e30	−0.206385
$989$	−4.68688e30	−0.166465
$990$	−1.61185e31	−0.566441
$991$	3.01081e31	1.04691	0.523456	−	0.852053i	$-0.324642\pi$
$991$	3.01081e31	1.04691	0.523456	+	0.852053i	$0.324642\pi$
$992$	4.78278e30	0.164554
$993$	−4.45799e30	−0.151765
$994$	−5.89898e30	−0.198710
$995$	2.41085e31	0.803578
$996$	2.13012e31	0.702554
$997$	−4.18588e31	−1.36612	−0.683058	−	0.730364i	$-0.739350\pi$
$997$	−4.18588e31	−1.36612	−0.683058	+	0.730364i	$0.739350\pi$
$998$	−8.67327e30	−0.280099
$999$	2.87120e30	0.0917542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.a.d.1.2	✓	2
4.3	odd	2		80.22.a.c.1.1		2
5.2	odd	4		50.22.b.e.49.3		4
5.3	odd	4		50.22.b.e.49.2		4
5.4	even	2		50.22.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.a.d.1.2	✓	2	1.1	even	1	trivial
50.22.a.d.1.1		2	5.4	even	2
50.22.b.e.49.2		4	5.3	odd	4
50.22.b.e.49.3		4	5.2	odd	4
80.22.a.c.1.1		2	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q+1024.00 q^{2} +145820. q^{3} +1.04858e6 q^{4} -9.76562e6 q^{5} +1.49320e8 q^{6} -2.36011e8 q^{7} +1.07374e9 q^{8} +1.08031e10 q^{9} -1.00000e10 q^{10} +1.49202e11 q^{11} +1.52903e11 q^{12} +4.89350e11 q^{13} -2.41675e11 q^{14} -1.42402e12 q^{15} +1.09951e12 q^{16} +5.46288e12 q^{17} +1.10624e13 q^{18} -1.12049e13 q^{19} -1.02400e13 q^{20} -3.44151e13 q^{21} +1.52783e14 q^{22} +1.78791e13 q^{23} +1.56573e14 q^{24} +9.53674e13 q^{25} +5.01094e14 q^{26} +4.99812e13 q^{27} -2.47475e14 q^{28} -2.82120e15 q^{29} -1.45820e15 q^{30} +4.24797e15 q^{31} +1.12590e15 q^{32} +2.17567e16 q^{33} +5.59399e15 q^{34} +2.30479e15 q^{35} +1.13279e16 q^{36} +5.74457e16 q^{37} -1.14738e16 q^{38} +7.13570e16 q^{39} -1.04858e16 q^{40} -3.51283e16 q^{41} -3.52410e16 q^{42} -2.62144e17 q^{43} +1.56450e17 q^{44} -1.05499e17 q^{45} +1.83081e16 q^{46} +1.08406e17 q^{47} +1.60331e17 q^{48} -5.02845e17 q^{49} +9.76562e16 q^{50} +7.96597e17 q^{51} +5.13120e17 q^{52} -2.47953e18 q^{53} +5.11807e16 q^{54} -1.45705e18 q^{55} -2.53415e17 q^{56} -1.63389e18 q^{57} -2.88891e18 q^{58} +2.14259e17 q^{59} -1.49320e18 q^{60} +3.64272e18 q^{61} +4.34992e18 q^{62} -2.54965e18 q^{63} +1.15292e18 q^{64} -4.77881e18 q^{65} +2.22788e19 q^{66} -1.13372e19 q^{67} +5.72825e18 q^{68} +2.60712e18 q^{69} +2.36011e18 q^{70} +2.44087e19 q^{71} +1.15998e19 q^{72} -4.12244e19 q^{73} +5.88244e19 q^{74} +1.39065e19 q^{75} -1.17492e19 q^{76} -3.52133e19 q^{77} +7.30695e19 q^{78} +6.83832e19 q^{79} -1.07374e19 q^{80} -1.05716e20 q^{81} -3.59714e19 q^{82} +1.39311e20 q^{83} -3.60868e19 q^{84} -5.33484e19 q^{85} -2.68435e20 q^{86} -4.11387e20 q^{87} +1.60205e20 q^{88} -4.04817e20 q^{89} -1.08031e20 q^{90} -1.15492e20 q^{91} +1.87475e19 q^{92} +6.19438e20 q^{93} +1.11008e20 q^{94} +1.09423e20 q^{95} +1.64179e20 q^{96} -9.18963e20 q^{97} -5.14913e20 q^{98} +1.61185e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2048 q^{2} + 30972 q^{3} + 2097152 q^{4} - 19531250 q^{5} + 31715328 q^{6} - 439959356 q^{7} + 2147483648 q^{8} + 13532817186 q^{9} - 20000000000 q^{10} + 105191777184 q^{11} + 32476495872 q^{12}+ \cdots + 14\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q + 2048 * q^2 + 30972 * q^3 + 2097152 * q^4 - 19531250 * q^5 + 31715328 * q^6 - 439959356 * q^7 + 2147483648 * q^8 + 13532817186 * q^9 - 20000000000 * q^10 + 105191777184 * q^11 + 32476495872 * q^12 + 308456648932 * q^13 - 450518380544 * q^14 - 302460937500 * q^15 + 2199023255552 * q^16 + 18393996100404 * q^17 + 13857604798464 * q^18 + 23821216715800 * q^19 - 20480000000000 * q^20 - 10991999204616 * q^21 + 107716379836416 * q^22 - 82586042978868 * q^23 + 33255931772928 * q^24 + 190734863281250 * q^25 + 315859608506368 * q^26 + 937830505785480 * q^27 - 461330821677056 * q^28 - 167038888446420 * q^29 - 309720000000000 * q^30 + 5373084998145784 * q^31 + 2251799813685248 * q^32 + 26811195444517824 * q^33 + 18835452006813696 * q^34 + 4296478085937500 * q^35 + 14190187313627136 * q^36 + 83725084127912164 * q^37 + 24392925916979200 * q^38 + 92132195361143352 * q^39 - 20971520000000000 * q^40 - 63222375005514036 * q^41 - 11255807185526784 * q^42 - 113835841911164948 * q^43 + 110301572952489984 * q^44 - 132156417832031250 * q^45 - 84568108010360832 * q^46 + 13253549001226164 * q^47 + 34054074135478272 * q^48 - 1019795619700635846 * q^49 + 195312500000000000 * q^50 - 688515197556670056 * q^51 + 323440239110520832 * q^52 - 1445751023743904748 * q^53 + 960338437924331520 * q^54 - 1027263449062500000 * q^55 - 472402761397305344 * q^56 - 5656568844707914800 * q^57 - 171047821769134080 * q^58 - 817060118931432840 * q^59 - 317153280000000000 * q^60 - 4580997169825849436 * q^61 + 5502039038101282816 * q^62 - 3106370208073453308 * q^63 + 2305843009213693952 * q^64 - 3012271962226562500 * q^65 + 27454664135186251776 * q^66 - 28808031668773210556 * q^67 + 19287502854977224704 * q^68 + 14145335707649957352 * q^69 + 4399593560000000000 * q^70 + 51140957732016114984 * q^71 + 14530751809154187264 * q^72 + 14792322512082321412 * q^73 + 85734486146982055936 * q^74 + 2953720092773437500 * q^75 + 24978356138986700800 * q^76 - 26237463329898773952 * q^77 + 94343368049810792448 * q^78 + 25077766877525032720 * q^79 - 21474836480000000000 * q^80 - 236237497961757285078 * q^81 - 64739712005646372864 * q^82 - 120090321897786074868 * q^83 - 11525946557979426816 * q^84 - 179628868168007812500 * q^85 - 116567902117032906752 * q^86 - 716212291756398367320 * q^87 + 112948810703349743616 * q^88 + 104228468137266844980 * q^89 - 135328171860000000000 * q^90 - 78598912899601639096 * q^91 - 86597742602609491968 * q^92 + 490220677944452503824 * q^93 + 13571634177255591936 * q^94 - 232629069490234375000 * q^95 + 34871371914729750528 * q^96 - 260893520515229908796 * q^97 - 1044270714573451106304 * q^98 + 1491713506648872042912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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