LMFDB - Embedded newform 5.18.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,18,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	5.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:	$9.16110436723$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 50686x + 2014936 $ x^3 - x^2 - 50686*x + 2014936
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-242.397$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+524.793 q^{2} +8850.68 q^{3} +144336. q^{4} +390625. q^{5} +4.64478e6 q^{6} +1.13170e7 q^{7} +6.96092e6 q^{8} -5.08056e7 q^{9} +O(q^{10})$	\(q+524.793 q^{2} +8850.68 q^{3} +144336. q^{4} +390625. q^{5} +4.64478e6 q^{6} +1.13170e7 q^{7} +6.96092e6 q^{8} -5.08056e7 q^{9} +2.04997e8 q^{10} +3.42656e7 q^{11} +1.27747e9 q^{12} +4.29572e9 q^{13} +5.93907e9 q^{14} +3.45730e9 q^{15} -1.52654e10 q^{16} -4.75231e10 q^{17} -2.66624e10 q^{18} -7.29121e9 q^{19} +5.63813e10 q^{20} +1.00163e11 q^{21} +1.79824e10 q^{22} -5.76644e11 q^{23} +6.16089e10 q^{24} +1.52588e11 q^{25} +2.25437e12 q^{26} -1.59264e12 q^{27} +1.63345e12 q^{28} -1.27199e12 q^{29} +1.81437e12 q^{30} +6.09351e12 q^{31} -8.92355e12 q^{32} +3.03274e11 q^{33} -2.49398e13 q^{34} +4.42069e12 q^{35} -7.33308e12 q^{36} +9.62495e12 q^{37} -3.82638e12 q^{38} +3.80201e13 q^{39} +2.71911e12 q^{40} +6.45036e13 q^{41} +5.25648e13 q^{42} -5.47296e13 q^{43} +4.94577e12 q^{44} -1.98459e13 q^{45} -3.02619e14 q^{46} +2.90697e14 q^{47} -1.35109e14 q^{48} -1.04557e14 q^{49} +8.00771e13 q^{50} -4.20612e14 q^{51} +6.20028e14 q^{52} +4.38751e14 q^{53} -8.35808e14 q^{54} +1.33850e13 q^{55} +7.87764e13 q^{56} -6.45322e13 q^{57} -6.67530e14 q^{58} -3.50833e14 q^{59} +4.99013e14 q^{60} +2.64349e15 q^{61} +3.19783e15 q^{62} -5.74965e14 q^{63} -2.68216e15 q^{64} +1.67802e15 q^{65} +1.59156e14 q^{66} -2.24704e15 q^{67} -6.85930e15 q^{68} -5.10369e15 q^{69} +2.31995e15 q^{70} -1.01099e15 q^{71} -3.53653e14 q^{72} +2.73949e15 q^{73} +5.05111e15 q^{74} +1.35051e15 q^{75} -1.05238e15 q^{76} +3.87783e14 q^{77} +1.99527e16 q^{78} +9.55239e14 q^{79} -5.96304e15 q^{80} -7.53494e15 q^{81} +3.38511e16 q^{82} -2.07999e16 q^{83} +1.44571e16 q^{84} -1.85637e16 q^{85} -2.87218e16 q^{86} -1.12579e16 q^{87} +2.38520e14 q^{88} -3.36906e16 q^{89} -1.04150e16 q^{90} +4.86145e16 q^{91} -8.32305e16 q^{92} +5.39317e16 q^{93} +1.52556e17 q^{94} -2.84813e15 q^{95} -7.89795e16 q^{96} -4.29630e16 q^{97} -5.48707e16 q^{98} -1.74088e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9}+O(q^{10}) $ 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9	\( 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9} + 46093750 q^{10} + 1789747516 q^{11} + 3112179088 q^{12} + 5414696794 q^{13} + 10507173312 q^{14} + 6228125000 q^{15} - 16203699952 q^{16} - 27402303962 q^{17} - 142746901186 q^{18} - 29956565300 q^{19} + 6607812500 q^{20} - 224495442624 q^{21} - 294714945304 q^{22} + 16254077844 q^{23} + 897428301600 q^{24} + 457763671875 q^{25} + 2017382699956 q^{26} + 3131715461840 q^{27} + 1119244517216 q^{28} - 2528278831750 q^{29} - 944946875000 q^{30} - 521256054664 q^{31} - 10880399775712 q^{32} + 1732417161568 q^{33} - 32147385667828 q^{34} + 835667187500 q^{35} - 14985377520892 q^{36} + 31762746900498 q^{37} - 40258035935240 q^{38} + 43003853320688 q^{39} + 25410328125000 q^{40} + 86833482954446 q^{41} + 153974403759936 q^{42} + 89258046385744 q^{43} - 124942202946448 q^{44} + 126520483984375 q^{45} - 323339762673024 q^{46} + 348182738140228 q^{47} - 729510516165056 q^{48} - 387320833396229 q^{49} + 18005371093750 q^{50} - 12409602773744 q^{51} + 552556858385688 q^{52} + 44014499212594 q^{53} - 22\!\cdots\!00 q^{54}+ \cdots + 29\!\cdots\!08 q^{99}+O(q^{100}) \) 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9 + 46093750 * q^10 + 1789747516 * q^11 + 3112179088 * q^12 + 5414696794 * q^13 + 10507173312 * q^14 + 6228125000 * q^15 - 16203699952 * q^16 - 27402303962 * q^17 - 142746901186 * q^18 - 29956565300 * q^19 + 6607812500 * q^20 - 224495442624 * q^21 - 294714945304 * q^22 + 16254077844 * q^23 + 897428301600 * q^24 + 457763671875 * q^25 + 2017382699956 * q^26 + 3131715461840 * q^27 + 1119244517216 * q^28 - 2528278831750 * q^29 - 944946875000 * q^30 - 521256054664 * q^31 - 10880399775712 * q^32 + 1732417161568 * q^33 - 32147385667828 * q^34 + 835667187500 * q^35 - 14985377520892 * q^36 + 31762746900498 * q^37 - 40258035935240 * q^38 + 43003853320688 * q^39 + 25410328125000 * q^40 + 86833482954446 * q^41 + 153974403759936 * q^42 + 89258046385744 * q^43 - 124942202946448 * q^44 + 126520483984375 * q^45 - 323339762673024 * q^46 + 348182738140228 * q^47 - 729510516165056 * q^48 - 387320833396229 * q^49 + 18005371093750 * q^50 - 12409602773744 * q^51 + 552556858385688 * q^52 + 44014499212594 * q^53 - 2265337034433200 * q^54 + 699120123437500 * q^55 - 490455582129600 * q^56 + 4293013923032480 * q^57 + 597742677475540 * q^58 - 2133293278957100 * q^59 + 1215694956250000 * q^60 + 2822990449991866 * q^61 + 5338539124096416 * q^62 - 4366406213760516 * q^63 - 2533946722090944 * q^64 + 2115115935156250 * q^65 - 4908048881135008 * q^66 + 374173462156688 * q^67 - 6873999340144024 * q^68 - 13800336843711552 * q^69 + 4104364575000000 * q^70 - 9029705707562224 * q^71 + 14996701114647720 * q^72 - 5906564941861106 * q^73 + 2774091820866692 * q^74 + 2432861328125000 * q^75 + 17087125269517200 * q^76 - 5362490012556624 * q^77 + 15760779344737648 * q^78 + 9183397142621600 * q^79 - 6329570293750000 * q^80 + 11504008140536443 * q^81 + 34156701290034076 * q^82 + 15992201117651544 * q^83 + 20750744922079872 * q^84 - 10704024985156250 * q^85 - 41302213526621384 * q^86 - 124899722203208080 * q^87 + 46255695387619680 * q^88 - 31272661736951250 * q^89 - 55760508275781250 * q^90 + 42991889981897896 * q^91 - 161631619485465312 * q^92 - 55524596752956672 * q^93 + 206283262927378352 * q^94 - 11701783320312500 * q^95 - 45608798390141824 * q^96 + 28207632381796278 * q^97 - 22149964169860474 * q^98 + 293120596614370508 * 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 $

$2$	524.793	1.44955	0.724775	−	0.688985i	$-0.241944\pi$
$2$	524.793	1.44955	0.724775	+	0.688985i	$0.241944\pi$
$3$	8850.68	0.778836	0.389418	−	0.921061i	$-0.372676\pi$
$3$	8850.68	0.778836	0.389418	+	0.921061i	$0.372676\pi$
$4$	144336.	1.10120
$5$	390625.	0.447214
$5$	390625.	0.447214
$6$	4.64478e6	1.12896
$7$	1.13170e7	0.741988	0.370994	−	0.928635i	$-0.379017\pi$
$7$	1.13170e7	0.741988	0.370994	+	0.928635i	$0.379017\pi$
$8$	6.96092e6	0.146690
$9$	−5.08056e7	−0.393414
$10$	2.04997e8	0.648259
$11$	3.42656e7	0.0481971	0.0240985	−	0.999710i	$-0.492328\pi$
$11$	3.42656e7	0.0481971	0.0240985	+	0.999710i	$0.492328\pi$
$12$	1.27747e9	0.857652
$13$	4.29572e9	1.46055	0.730277	−	0.683151i	$-0.239391\pi$
$13$	4.29572e9	1.46055	0.730277	+	0.683151i	$0.239391\pi$
$14$	5.93907e9	1.07555
$15$	3.45730e9	0.348306
$16$	−1.52654e10	−0.888562
$17$	−4.75231e10	−1.65230	−0.826150	−	0.563450i	$-0.809474\pi$
$17$	−4.75231e10	−1.65230	−0.826150	+	0.563450i	$0.809474\pi$
$18$	−2.66624e10	−0.570274
$19$	−7.29121e9	−0.0984904	−0.0492452	−	0.998787i	$-0.515682\pi$
$19$	−7.29121e9	−0.0984904	−0.0492452	+	0.998787i	$0.515682\pi$
$20$	5.63813e10	0.492470
$21$	1.00163e11	0.577887
$22$	1.79824e10	0.0698641
$23$	−5.76644e11	−1.53540	−0.767699	−	0.640810i	$-0.778598\pi$
$23$	−5.76644e11	−1.53540	−0.767699	+	0.640810i	$0.778598\pi$
$24$	6.16089e10	0.114248
$25$	1.52588e11	0.200000
$26$	2.25437e12	2.11715
$27$	−1.59264e12	−1.08524
$28$	1.63345e12	0.817075
$29$	−1.27199e12	−0.472171	−0.236085	−	0.971732i	$-0.575865\pi$
$29$	−1.27199e12	−0.472171	−0.236085	+	0.971732i	$0.575865\pi$
$30$	1.81437e12	0.504887
$31$	6.09351e12	1.28320	0.641598	−	0.767041i	$-0.278272\pi$
$31$	6.09351e12	1.28320	0.641598	+	0.767041i	$0.278272\pi$
$32$	−8.92355e12	−1.43471
$33$	3.03274e11	0.0375377
$34$	−2.49398e13	−2.39509
$35$	4.42069e12	0.331827
$36$	−7.33308e12	−0.433226
$37$	9.62495e12	0.450489	0.225244	−	0.974302i	$-0.427682\pi$
$37$	9.62495e12	0.450489	0.225244	+	0.974302i	$0.427682\pi$
$38$	−3.82638e12	−0.142767
$39$	3.80201e13	1.13753
$40$	2.71911e12	0.0656019
$41$	6.45036e13	1.26160	0.630800	−	0.775946i	$-0.282727\pi$
$41$	6.45036e13	1.26160	0.630800	+	0.775946i	$0.282727\pi$
$42$	5.25648e13	0.837676
$43$	−5.47296e13	−0.714070	−0.357035	−	0.934091i	$-0.616212\pi$
$43$	−5.47296e13	−0.714070	−0.357035	+	0.934091i	$0.616212\pi$
$44$	4.94577e12	0.0530745
$45$	−1.98459e13	−0.175940
$46$	−3.02619e14	−2.22564
$47$	2.90697e14	1.78078	0.890388	−	0.455202i	$-0.150433\pi$
$47$	2.90697e14	1.78078	0.890388	+	0.455202i	$0.150433\pi$
$48$	−1.35109e14	−0.692044
$49$	−1.04557e14	−0.449454
$50$	8.00771e13	0.289910
$51$	−4.20612e14	−1.28687
$52$	6.20028e14	1.60836
$53$	4.38751e14	0.967996	0.483998	−	0.875069i	$-0.339184\pi$
$53$	4.38751e14	0.967996	0.483998	+	0.875069i	$0.339184\pi$
$54$	−8.35808e14	−1.57311
$55$	1.33850e13	0.0215544
$56$	7.87764e13	0.108842
$57$	−6.45322e13	−0.0767079
$58$	−6.67530e14	−0.684436
$59$	−3.50833e14	−0.311071	−0.155535	−	0.987830i	$-0.549710\pi$
$59$	−3.50833e14	−0.311071	−0.155535	+	0.987830i	$0.549710\pi$
$60$	4.99013e14	0.383554
$61$	2.64349e15	1.76553	0.882764	−	0.469817i	$-0.155680\pi$
$61$	2.64349e15	1.76553	0.882764	+	0.469817i	$0.155680\pi$
$62$	3.19783e15	1.86006
$63$	−5.74965e14	−0.291908
$64$	−2.68216e15	−1.19112
$65$	1.67802e15	0.653180
$66$	1.59156e14	0.0544127
$67$	−2.24704e15	−0.676044	−0.338022	−	0.941138i	$-0.609758\pi$
$67$	−2.24704e15	−0.676044	−0.338022	+	0.941138i	$0.609758\pi$
$68$	−6.85930e15	−1.81951
$69$	−5.10369e15	−1.19582
$70$	2.31995e15	0.481000
$71$	−1.01099e15	−0.185803	−0.0929015	−	0.995675i	$-0.529614\pi$
$71$	−1.01099e15	−0.185803	−0.0929015	+	0.995675i	$0.529614\pi$
$72$	−3.53653e14	−0.0577100
$73$	2.73949e15	0.397581	0.198790	−	0.980042i	$-0.436299\pi$
$73$	2.73949e15	0.397581	0.198790	+	0.980042i	$0.436299\pi$
$74$	5.05111e15	0.653006
$75$	1.35051e15	0.155767
$76$	−1.05238e15	−0.108457
$77$	3.87783e14	0.0357617
$78$	1.99527e16	1.64891
$79$	9.55239e14	0.0708405	0.0354203	−	0.999373i	$-0.488723\pi$
$79$	9.55239e14	0.0708405	0.0354203	+	0.999373i	$0.488723\pi$
$80$	−5.96304e15	−0.397377
$81$	−7.53494e15	−0.451811
$82$	3.38511e16	1.82875
$83$	−2.07999e16	−1.01367	−0.506837	−	0.862042i	$-0.669185\pi$
$83$	−2.07999e16	−1.01367	−0.506837	+	0.862042i	$0.669185\pi$
$84$	1.44571e16	0.636367
$85$	−1.85637e16	−0.738931
$86$	−2.87218e16	−1.03508
$87$	−1.12579e16	−0.367744
$88$	2.38520e14	0.00707005
$89$	−3.36906e16	−0.907182	−0.453591	−	0.891210i	$-0.649857\pi$
$89$	−3.36906e16	−0.907182	−0.453591	+	0.891210i	$0.649857\pi$
$90$	−1.04150e16	−0.255034
$91$	4.86145e16	1.08371
$92$	−8.32305e16	−1.69078
$93$	5.39317e16	0.999400
$94$	1.52556e17	2.58133
$95$	−2.84813e15	−0.0440463
$96$	−7.89795e16	−1.11740
$97$	−4.29630e16	−0.556589	−0.278295	−	0.960496i	$-0.589769\pi$
$97$	−4.29630e16	−0.556589	−0.278295	+	0.960496i	$0.589769\pi$
$98$	−5.48707e16	−0.651507
$99$	−1.74088e15	−0.0189614
$100$	2.20239e16	0.220239
$101$	1.06174e17	0.975635	0.487818	−	0.872946i	$-0.337793\pi$
$101$	1.06174e17	0.975635	0.487818	+	0.872946i	$0.337793\pi$
$102$	−2.20734e17	−1.86538
$103$	2.00378e17	1.55860	0.779298	−	0.626654i	$-0.215576\pi$
$103$	2.00378e17	1.55860	0.779298	+	0.626654i	$0.215576\pi$
$104$	2.99022e16	0.214249
$105$	3.91261e16	0.258439
$106$	2.30254e17	1.40316
$107$	9.71152e16	0.546418	0.273209	−	0.961955i	$-0.411915\pi$
$107$	9.71152e16	0.546418	0.273209	+	0.961955i	$0.411915\pi$
$108$	−2.29876e17	−1.19506
$109$	−8.25421e16	−0.396781	−0.198390	−	0.980123i	$-0.563571\pi$
$109$	−8.25421e16	−0.396781	−0.198390	+	0.980123i	$0.563571\pi$
$110$	7.02437e15	0.0312442
$111$	8.51874e16	0.350857
$112$	−1.72758e17	−0.659302
$113$	3.40019e16	0.120320	0.0601598	−	0.998189i	$-0.480839\pi$
$113$	3.40019e16	0.120320	0.0601598	+	0.998189i	$0.480839\pi$
$114$	−3.38661e16	−0.111192
$115$	−2.25252e17	−0.686651
$116$	−1.83593e17	−0.519953
$117$	−2.18247e17	−0.574603
$118$	−1.84115e17	−0.450913
$119$	−5.37817e17	−1.22599
$120$	2.40660e16	0.0510931
$121$	−5.04273e17	−0.997677
$122$	1.38729e18	2.55922
$123$	5.70901e17	0.982579
$124$	8.79513e17	1.41305
$125$	5.96046e16	0.0894427
$126$	−3.01738e17	−0.423136
$127$	1.21062e18	1.58736	0.793682	−	0.608333i	$-0.208162\pi$
$127$	1.21062e18	1.58736	0.793682	+	0.608333i	$0.208162\pi$
$128$	−2.37951e17	−0.291878
$129$	−4.84395e17	−0.556144
$130$	8.80612e17	0.946817
$131$	−1.01480e18	−1.02229	−0.511146	−	0.859494i	$-0.670779\pi$
$131$	−1.01480e18	−1.02229	−0.511146	+	0.859494i	$0.670779\pi$
$132$	4.37734e16	0.0413364
$133$	−8.25144e16	−0.0730787
$134$	−1.17923e18	−0.979960
$135$	−6.22126e17	−0.485335
$136$	−3.30804e17	−0.242376
$137$	2.16928e17	0.149345	0.0746724	−	0.997208i	$-0.476209\pi$
$137$	2.16928e17	0.149345	0.0746724	+	0.997208i	$0.476209\pi$
$138$	−2.67838e18	−1.73341
$139$	−1.02691e17	−0.0625041	−0.0312520	−	0.999512i	$-0.509949\pi$
$139$	−1.02691e17	−0.0625041	−0.0312520	+	0.999512i	$0.509949\pi$
$140$	6.38065e17	0.365407
$141$	2.57287e18	1.38693
$142$	−5.30563e17	−0.269331
$143$	1.47196e17	0.0703945
$144$	7.75566e17	0.349573
$145$	−4.96869e17	−0.211161
$146$	1.43767e18	0.576313
$147$	−9.25399e17	−0.350051
$148$	1.38923e18	0.496077
$149$	−5.07005e18	−1.70973	−0.854867	−	0.518847i	$-0.826362\pi$
$149$	−5.07005e18	−1.70973	−0.854867	+	0.518847i	$0.826362\pi$
$150$	7.08737e17	0.225793
$151$	1.31132e18	0.394826	0.197413	−	0.980320i	$-0.436746\pi$
$151$	1.31132e18	0.394826	0.197413	+	0.980320i	$0.436746\pi$
$152$	−5.07535e16	−0.0144476
$153$	2.41444e18	0.650038
$154$	2.03506e17	0.0518383
$155$	2.38028e18	0.573863
$156$	5.48767e18	1.25265
$157$	−4.59295e18	−0.992989	−0.496495	−	0.868040i	$-0.665380\pi$
$157$	−4.59295e18	−0.992989	−0.496495	+	0.868040i	$0.665380\pi$
$158$	5.01303e17	0.102687
$159$	3.88325e18	0.753910
$160$	−3.48576e18	−0.641620
$161$	−6.52586e18	−1.13925
$162$	−3.95429e18	−0.654923
$163$	3.53678e18	0.555922	0.277961	−	0.960592i	$-0.410341\pi$
$163$	3.53678e18	0.555922	0.277961	+	0.960592i	$0.410341\pi$
$164$	9.31020e18	1.38927
$165$	1.18467e17	0.0167873
$166$	−1.09157e19	−1.46937
$167$	3.24042e18	0.414487	0.207244	−	0.978289i	$-0.433551\pi$
$167$	3.24042e18	0.414487	0.207244	+	0.978289i	$0.433551\pi$
$168$	6.97225e17	0.0847704
$169$	9.80281e18	1.13322
$170$	−9.74211e18	−1.07112
$171$	3.70434e17	0.0387475
$172$	−7.89946e18	−0.786332
$173$	−5.74444e18	−0.544322	−0.272161	−	0.962252i	$-0.587738\pi$
$173$	−5.74444e18	−0.544322	−0.272161	+	0.962252i	$0.587738\pi$
$174$	−5.90809e18	−0.533063
$175$	1.72683e18	0.148398
$176$	−5.23078e17	−0.0428261
$177$	−3.10512e18	−0.242273
$178$	−1.76806e19	−1.31501
$179$	1.82373e19	1.29333	0.646665	−	0.762774i	$-0.276163\pi$
$179$	1.82373e19	1.29333	0.646665	+	0.762774i	$0.276163\pi$
$180$	−2.86448e18	−0.193745
$181$	−8.40143e18	−0.542107	−0.271054	−	0.962564i	$-0.587372\pi$
$181$	−8.40143e18	−0.542107	−0.271054	+	0.962564i	$0.587372\pi$
$182$	2.55126e19	1.57090
$183$	2.33967e19	1.37506
$184$	−4.01397e18	−0.225228
$185$	3.75975e18	0.201465
$186$	2.83030e19	1.44868
$187$	−1.62841e18	−0.0796361
$188$	4.19581e19	1.96099
$189$	−1.80239e19	−0.805236
$190$	−1.49468e18	−0.0638473
$191$	5.49941e18	0.224663	0.112332	−	0.993671i	$-0.464168\pi$
$191$	5.49941e18	0.224663	0.112332	+	0.993671i	$0.464168\pi$
$192$	−2.37389e19	−0.927685
$193$	−3.82521e19	−1.43027	−0.715134	−	0.698987i	$-0.753634\pi$
$193$	−3.82521e19	−1.43027	−0.715134	+	0.698987i	$0.753634\pi$
$194$	−2.25467e19	−0.806804
$195$	1.48516e19	0.508720
$196$	−1.50913e19	−0.494938
$197$	−5.45369e19	−1.71288	−0.856442	−	0.516244i	$-0.827330\pi$
$197$	−5.45369e19	−1.71288	−0.856442	+	0.516244i	$0.827330\pi$
$198$	−9.13605e17	−0.0274855
$199$	−6.32273e18	−0.182244	−0.0911220	−	0.995840i	$-0.529045\pi$
$199$	−6.32273e18	−0.182244	−0.0911220	+	0.995840i	$0.529045\pi$
$200$	1.06215e18	0.0293381
$201$	−1.98878e19	−0.526528
$202$	5.57196e19	1.41423
$203$	−1.43950e19	−0.350345
$204$	−6.07095e19	−1.41710
$205$	2.51967e19	0.564204
$206$	1.05157e20	2.25926
$207$	2.92967e19	0.604047
$208$	−6.55758e19	−1.29779
$209$	−2.49838e17	−0.00474695
$210$	2.05331e19	0.374620
$211$	−1.71215e19	−0.300014	−0.150007	−	0.988685i	$-0.547930\pi$
$211$	−1.71215e19	−0.300014	−0.150007	+	0.988685i	$0.547930\pi$
$212$	6.33277e19	1.06595
$213$	−8.94799e18	−0.144710
$214$	5.09654e19	0.792061
$215$	−2.13788e19	−0.319342
$216$	−1.10863e19	−0.159194
$217$	6.89600e19	0.952115
$218$	−4.33176e19	−0.575154
$219$	2.42464e19	0.309650
$220$	1.93194e18	0.0237356
$221$	−2.04146e20	−2.41327
$222$	4.47058e19	0.508585
$223$	1.32004e20	1.44543	0.722713	−	0.691148i	$-0.242895\pi$
$223$	1.32004e20	1.44543	0.722713	+	0.691148i	$0.242895\pi$
$224$	−1.00988e20	−1.06453
$225$	−7.75231e18	−0.0786828
$226$	1.78440e19	0.174409
$227$	−4.22527e19	−0.397772	−0.198886	−	0.980023i	$-0.563732\pi$
$227$	−4.22527e19	−0.397772	−0.198886	+	0.980023i	$0.563732\pi$
$228$	−9.31433e18	−0.0844705
$229$	1.81555e20	1.58638	0.793189	−	0.608975i	$-0.208419\pi$
$229$	1.81555e20	1.58638	0.793189	+	0.608975i	$0.208419\pi$
$230$	−1.18211e20	−0.995335
$231$	3.43214e18	0.0278525
$232$	−8.85418e18	−0.0692629
$233$	2.06715e20	1.55900	0.779501	−	0.626401i	$-0.215473\pi$
$233$	2.06715e20	1.55900	0.779501	+	0.626401i	$0.215473\pi$
$234$	−1.14534e20	−0.832915
$235$	1.13554e20	0.796388
$236$	−5.06379e19	−0.342550
$237$	8.45452e18	0.0551732
$238$	−2.82243e20	−1.77713
$239$	−2.14126e20	−1.30103	−0.650515	−	0.759494i	$-0.725447\pi$
$239$	−2.14126e20	−1.30103	−0.650515	+	0.759494i	$0.725447\pi$
$240$	−5.27770e19	−0.309492
$241$	−7.68495e19	−0.435007	−0.217504	−	0.976060i	$-0.569791\pi$
$241$	−7.68495e19	−0.435007	−0.217504	+	0.976060i	$0.569791\pi$
$242$	−2.64639e20	−1.44618
$243$	1.38985e20	0.733354
$244$	3.81551e20	1.94419
$245$	−4.08425e19	−0.201002
$246$	2.99605e20	1.42430
$247$	−3.13210e19	−0.143851
$248$	4.24164e19	0.188232
$249$	−1.84094e20	−0.789486
$250$	3.12801e19	0.129652
$251$	2.94340e20	1.17930	0.589648	−	0.807660i	$-0.299266\pi$
$251$	2.94340e20	1.17930	0.589648	+	0.807660i	$0.299266\pi$
$252$	−8.29882e19	−0.321449
$253$	−1.97591e19	−0.0740018
$254$	6.35326e20	2.30096
$255$	−1.64302e20	−0.575506
$256$	2.26681e20	0.768024
$257$	−3.24303e20	−1.06296	−0.531482	−	0.847069i	$-0.678365\pi$
$257$	−3.24303e20	−1.06296	−0.531482	+	0.847069i	$0.678365\pi$
$258$	−2.54207e20	−0.806158
$259$	1.08925e20	0.334257
$260$	2.42198e20	0.719280
$261$	6.46239e19	0.185759
$262$	−5.32561e20	−1.48187
$263$	3.90895e20	1.05302	0.526509	−	0.850169i	$-0.323501\pi$
$263$	3.90895e20	1.05302	0.526509	+	0.850169i	$0.323501\pi$
$264$	2.11107e18	0.00550641
$265$	1.71387e20	0.432901
$266$	−4.33030e19	−0.105931
$267$	−2.98185e20	−0.706546
$268$	−3.24329e20	−0.744458
$269$	−7.80535e20	−1.73579	−0.867897	−	0.496744i	$-0.834529\pi$
$269$	−7.80535e20	−1.73579	−0.867897	+	0.496744i	$0.834529\pi$
$270$	−3.26488e20	−0.703517
$271$	−7.30723e20	−1.52586	−0.762928	−	0.646483i	$-0.776239\pi$
$271$	−7.30723e20	−1.52586	−0.762928	+	0.646483i	$0.776239\pi$
$272$	7.25458e20	1.46817
$273$	4.30272e20	0.844035
$274$	1.13842e20	0.216483
$275$	5.22852e18	0.00963942
$276$	−7.36647e20	−1.31684
$277$	7.84861e19	0.136055	0.0680275	−	0.997683i	$-0.478329\pi$
$277$	7.84861e19	0.136055	0.0680275	+	0.997683i	$0.478329\pi$
$278$	−5.38918e19	−0.0906028
$279$	−3.09584e20	−0.504827
$280$	3.07720e19	0.0486758
$281$	5.82064e20	0.893238	0.446619	−	0.894724i	$-0.352628\pi$
$281$	5.82064e20	0.893238	0.446619	+	0.894724i	$0.352628\pi$
$282$	1.35023e21	2.01043
$283$	−5.44303e19	−0.0786423	−0.0393212	−	0.999227i	$-0.512520\pi$
$283$	−5.44303e19	−0.0786423	−0.0393212	+	0.999227i	$0.512520\pi$
$284$	−1.45923e20	−0.204606
$285$	−2.52079e19	−0.0343048
$286$	7.72473e19	0.102040
$287$	7.29985e20	0.936091
$288$	4.53366e20	0.564433
$289$	1.43120e21	1.73009
$290$	−2.60754e20	−0.306089
$291$	−3.80252e20	−0.433492
$292$	3.95407e20	0.437815
$293$	2.57250e19	0.0276682	0.0138341	−	0.999904i	$-0.495596\pi$
$293$	2.57250e19	0.0276682	0.0138341	+	0.999904i	$0.495596\pi$
$294$	−4.85643e20	−0.507417
$295$	−1.37044e20	−0.139115
$296$	6.69985e19	0.0660823
$297$	−5.45729e19	−0.0523055
$298$	−2.66073e21	−2.47835
$299$	−2.47710e21	−2.24253
$300$	1.94927e20	0.171530
$301$	−6.19373e20	−0.529831
$302$	6.88173e20	0.572320
$303$	9.39715e20	0.759860
$304$	1.11303e20	0.0875148
$305$	1.03261e21	0.789568
$306$	1.26708e21	0.942263
$307$	−1.08504e21	−0.784818	−0.392409	−	0.919791i	$-0.628358\pi$
$307$	−1.08504e21	−0.784818	−0.392409	+	0.919791i	$0.628358\pi$
$308$	5.59711e19	0.0393806
$309$	1.77348e21	1.21389
$310$	1.24915e21	0.831843
$311$	−8.51293e20	−0.551589	−0.275795	−	0.961217i	$-0.588941\pi$
$311$	−8.51293e20	−0.551589	−0.275795	+	0.961217i	$0.588941\pi$
$312$	2.64655e20	0.166865
$313$	−1.57118e21	−0.964050	−0.482025	−	0.876157i	$-0.660099\pi$
$313$	−1.57118e21	−0.964050	−0.482025	+	0.876157i	$0.660099\pi$
$314$	−2.41035e21	−1.43939
$315$	−2.24596e20	−0.130545
$316$	1.37875e20	0.0780094
$317$	3.96975e20	0.218655	0.109328	−	0.994006i	$-0.465130\pi$
$317$	3.96975e20	0.218655	0.109328	+	0.994006i	$0.465130\pi$
$318$	2.03790e21	1.09283
$319$	−4.35854e19	−0.0227573
$320$	−1.04772e21	−0.532684
$321$	8.59536e20	0.425570
$322$	−3.42473e21	−1.65140
$323$	3.46501e20	0.162736
$324$	−1.08756e21	−0.497533
$325$	6.55475e20	0.292111
$326$	1.85608e21	0.805837
$327$	−7.30554e20	−0.309027
$328$	4.49004e20	0.185064
$329$	3.28981e21	1.32131
$330$	6.21704e19	0.0243341
$331$	3.38133e21	1.28988	0.644941	−	0.764232i	$-0.276882\pi$
$331$	3.38133e21	1.28988	0.644941	+	0.764232i	$0.276882\pi$
$332$	−3.00218e21	−1.11626
$333$	−4.89001e20	−0.177229
$334$	1.70055e21	0.600821
$335$	−8.77750e20	−0.302336
$336$	−1.52902e21	−0.513488
$337$	4.08000e21	1.33600	0.668000	−	0.744161i	$-0.267151\pi$
$337$	4.08000e21	1.33600	0.668000	+	0.744161i	$0.267151\pi$
$338$	5.14445e21	1.64266
$339$	3.00940e20	0.0937093
$340$	−2.67941e21	−0.813709
$341$	2.08798e20	0.0618463
$342$	1.94401e20	0.0561665
$343$	−3.81594e21	−1.07548
$344$	−3.80968e20	−0.104747
$345$	−1.99363e21	−0.534789
$346$	−3.01464e21	−0.789022
$347$	7.66737e20	0.195815	0.0979075	−	0.995196i	$-0.468785\pi$
$347$	7.66737e20	0.195815	0.0979075	+	0.995196i	$0.468785\pi$
$348$	−1.62493e21	−0.404958
$349$	2.53612e21	0.616814	0.308407	−	0.951254i	$-0.400204\pi$
$349$	2.53612e21	0.616814	0.308407	+	0.951254i	$0.400204\pi$
$350$	9.06230e20	0.215110
$351$	−6.84155e21	−1.58505
$352$	−3.05771e20	−0.0691487
$353$	−3.09253e21	−0.682699	−0.341349	−	0.939937i	$-0.610884\pi$
$353$	−3.09253e21	−0.682699	−0.341349	+	0.939937i	$0.610884\pi$
$354$	−1.62954e21	−0.351187
$355$	−3.94920e20	−0.0830937
$356$	−4.86278e21	−0.998986
$357$	−4.76005e21	−0.954842
$358$	9.57081e21	1.87475
$359$	7.26601e21	1.38993	0.694965	−	0.719043i	$-0.255420\pi$
$359$	7.26601e21	1.38993	0.694965	+	0.719043i	$0.255420\pi$
$360$	−1.38146e20	−0.0258087
$361$	−5.42723e21	−0.990300
$362$	−4.40901e21	−0.785812
$363$	−4.46316e21	−0.777027
$364$	7.01683e21	1.19338
$365$	1.07011e21	0.177804
$366$	1.22784e22	1.99321
$367$	1.79841e21	0.285251	0.142626	−	0.989777i	$-0.454446\pi$
$367$	1.79841e21	0.285251	0.142626	+	0.989777i	$0.454446\pi$
$368$	8.80269e21	1.36430
$369$	−3.27714e21	−0.496331
$370$	1.97309e21	0.292033
$371$	4.96533e21	0.718241
$372$	7.78429e21	1.10054
$373$	−1.32890e21	−0.183640	−0.0918200	−	0.995776i	$-0.529268\pi$
$373$	−1.32890e21	−0.183640	−0.0918200	+	0.995776i	$0.529268\pi$
$374$	−8.54578e20	−0.115436
$375$	5.27542e20	0.0696612
$376$	2.02352e21	0.261223
$377$	−5.46410e21	−0.689631
$378$	−9.45881e21	−1.16723
$379$	−1.26304e22	−1.52400	−0.762001	−	0.647576i	$-0.775783\pi$
$379$	−1.26304e22	−1.52400	−0.762001	+	0.647576i	$0.775783\pi$
$380$	−4.11088e20	−0.0485036
$381$	1.07148e22	1.23630
$382$	2.88605e21	0.325661
$383$	−1.18651e21	−0.130943	−0.0654715	−	0.997854i	$-0.520855\pi$
$383$	−1.18651e21	−0.130943	−0.0654715	+	0.997854i	$0.520855\pi$
$384$	−2.10603e21	−0.227326
$385$	1.51478e20	0.0159931
$386$	−2.00744e22	−2.07325
$387$	2.78057e21	0.280925
$388$	−6.20111e21	−0.612915
$389$	−6.09749e21	−0.589630	−0.294815	−	0.955554i	$-0.595258\pi$
$389$	−6.09749e21	−0.589630	−0.294815	+	0.955554i	$0.595258\pi$
$390$	7.79402e21	0.737415
$391$	2.74039e22	2.53694
$392$	−7.27811e20	−0.0659306
$393$	−8.98169e21	−0.796199
$394$	−2.86206e22	−2.48291
$395$	3.73140e20	0.0316808
$396$	−2.51272e20	−0.0208803
$397$	1.21993e22	0.992237	0.496118	−	0.868255i	$-0.334758\pi$
$397$	1.21993e22	0.992237	0.496118	+	0.868255i	$0.334758\pi$
$398$	−3.31813e21	−0.264172
$399$	−7.30309e20	−0.0569163
$400$	−2.32931e21	−0.177712
$401$	−7.23480e21	−0.540380	−0.270190	−	0.962807i	$-0.587087\pi$
$401$	−7.23480e21	−0.540380	−0.270190	+	0.962807i	$0.587087\pi$
$402$	−1.04370e22	−0.763229
$403$	2.61760e22	1.87418
$404$	1.53248e22	1.07437
$405$	−2.94334e21	−0.202056
$406$	−7.55441e21	−0.507843
$407$	3.29805e20	0.0217123
$408$	−2.92784e21	−0.188772
$409$	5.52627e21	0.348967	0.174483	−	0.984660i	$-0.444174\pi$
$409$	5.52627e21	0.348967	0.174483	+	0.984660i	$0.444174\pi$
$410$	1.32231e22	0.817843
$411$	1.91996e21	0.116315
$412$	2.89218e22	1.71632
$413$	−3.97037e21	−0.230811
$414$	1.53747e22	0.875597
$415$	−8.12498e21	−0.453329
$416$	−3.83331e22	−2.09547
$417$	−9.08889e20	−0.0486804
$418$	−1.31113e20	−0.00688095
$419$	−5.01859e21	−0.258085	−0.129043	−	0.991639i	$-0.541190\pi$
$419$	−5.01859e21	−0.258085	−0.129043	+	0.991639i	$0.541190\pi$
$420$	5.64731e21	0.284592
$421$	−1.52175e20	−0.00751527	−0.00375763	−	0.999993i	$-0.501196\pi$
$421$	−1.52175e20	−0.00751527	−0.00375763	+	0.999993i	$0.501196\pi$
$422$	−8.98527e21	−0.434886
$423$	−1.47690e22	−0.700583
$424$	3.05411e21	0.141996
$425$	−7.25145e21	−0.330460
$426$	−4.69585e21	−0.209765
$427$	2.99163e22	1.31000
$428$	1.40172e22	0.601714
$429$	1.30278e21	0.0548258
$430$	−1.12194e22	−0.462902
$431$	3.82430e21	0.154702	0.0773509	−	0.997004i	$-0.475354\pi$
$431$	3.82430e21	0.154702	0.0773509	+	0.997004i	$0.475354\pi$
$432$	2.43123e22	0.964304
$433$	−8.67729e21	−0.337471	−0.168736	−	0.985661i	$-0.553968\pi$
$433$	−8.67729e21	−0.337471	−0.168736	+	0.985661i	$0.553968\pi$
$434$	3.61898e22	1.38014
$435$	−4.39763e21	−0.164460
$436$	−1.19138e22	−0.436934
$437$	4.20443e21	0.151222
$438$	1.27243e22	0.448854
$439$	−1.94972e22	−0.674566	−0.337283	−	0.941403i	$-0.609508\pi$
$439$	−1.94972e22	−0.674566	−0.337283	+	0.941403i	$0.609508\pi$
$440$	9.31719e19	0.00316182
$441$	5.31207e21	0.176822
$442$	−1.07134e23	−3.49816
$443$	−1.02685e22	−0.328909	−0.164455	−	0.986385i	$-0.552586\pi$
$443$	−1.02685e22	−0.328909	−0.164455	+	0.986385i	$0.552586\pi$
$444$	1.22956e22	0.386363
$445$	−1.31604e22	−0.405704
$446$	6.92749e22	2.09522
$447$	−4.48734e22	−1.33160
$448$	−3.03539e22	−0.883794
$449$	−3.10415e22	−0.886847	−0.443424	−	0.896312i	$-0.646236\pi$
$449$	−3.10415e22	−0.886847	−0.443424	+	0.896312i	$0.646236\pi$
$450$	−4.06836e21	−0.114055
$451$	2.21026e21	0.0608054
$452$	4.90770e21	0.132496
$453$	1.16061e22	0.307505
$454$	−2.21739e22	−0.576591
$455$	1.89901e22	0.484651
$456$	−4.49203e20	−0.0112523
$457$	−3.81576e22	−0.938196	−0.469098	−	0.883146i	$-0.655421\pi$
$457$	−3.81576e22	−0.938196	−0.469098	+	0.883146i	$0.655421\pi$
$458$	9.52789e22	2.29954
$459$	7.56873e22	1.79314
$460$	−3.25119e22	−0.756138
$461$	−2.24516e22	−0.512613	−0.256307	−	0.966596i	$-0.582506\pi$
$461$	−2.24516e22	−0.512613	−0.256307	+	0.966596i	$0.582506\pi$
$462$	1.80117e21	0.0403736
$463$	5.59192e22	1.23062	0.615308	−	0.788287i	$-0.289032\pi$
$463$	5.59192e22	1.23062	0.615308	+	0.788287i	$0.289032\pi$
$464$	1.94173e22	0.419553
$465$	2.10671e22	0.446945
$466$	1.08483e23	2.25985
$467$	2.11695e22	0.433029	0.216515	−	0.976279i	$-0.430531\pi$
$467$	2.11695e22	0.433029	0.216515	+	0.976279i	$0.430531\pi$
$468$	−3.15009e22	−0.632751
$469$	−2.54297e22	−0.501616
$470$	5.95922e22	1.15440
$471$	−4.06507e22	−0.773376
$472$	−2.44212e21	−0.0456310
$473$	−1.87535e21	−0.0344161
$474$	4.43688e21	0.0799763
$475$	−1.11255e21	−0.0196981
$476$	−7.76264e22	−1.35005
$477$	−2.22910e22	−0.380823
$478$	−1.12372e23	−1.88591
$479$	1.08389e22	0.178703	0.0893516	−	0.996000i	$-0.471521\pi$
$479$	1.08389e22	0.178703	0.0893516	+	0.996000i	$0.471521\pi$
$480$	−3.08514e22	−0.499717
$481$	4.13461e22	0.657963
$482$	−4.03301e22	−0.630565
$483$	−5.77583e22	−0.887287
$484$	−7.27848e22	−1.09864
$485$	−1.67824e22	−0.248914
$486$	7.29383e22	1.06303
$487$	5.96186e22	0.853857	0.426929	−	0.904285i	$-0.359596\pi$
$487$	5.96186e22	0.853857	0.426929	+	0.904285i	$0.359596\pi$
$488$	1.84011e22	0.258986
$489$	3.13030e22	0.432972
$490$	−2.14339e22	−0.291363
$491$	−1.45796e23	−1.94784	−0.973920	−	0.226894i	$-0.927143\pi$
$491$	−1.45796e23	−1.94784	−0.973920	+	0.226894i	$0.927143\pi$
$492$	8.24017e22	1.08201
$493$	6.04487e22	0.780168
$494$	−1.64371e22	−0.208519
$495$	−6.80033e20	−0.00847980
$496$	−9.30197e22	−1.14020
$497$	−1.14414e22	−0.137864
$498$	−9.66112e22	−1.14440
$499$	8.79023e22	1.02364	0.511818	−	0.859094i	$-0.328972\pi$
$499$	8.79023e22	1.02364	0.511818	+	0.859094i	$0.328972\pi$
$500$	8.60310e21	0.0984941
$501$	2.86799e22	0.322818
$502$	1.54468e23	1.70945
$503$	−4.89762e22	−0.532914	−0.266457	−	0.963847i	$-0.585853\pi$
$503$	−4.89762e22	−0.532914	−0.266457	+	0.963847i	$0.585853\pi$
$504$	−4.00228e21	−0.0428201
$505$	4.14743e22	0.436317
$506$	−1.03694e22	−0.107269
$507$	8.67616e22	0.882592
$508$	1.74736e23	1.74800
$509$	−6.60271e22	−0.649563	−0.324781	−	0.945789i	$-0.605291\pi$
$509$	−6.60271e22	−0.649563	−0.324781	+	0.945789i	$0.605291\pi$
$510$	−8.62243e22	−0.834225
$511$	3.10027e22	0.295000
$512$	1.50149e23	1.40517
$513$	1.16123e22	0.106886
$514$	−1.70192e23	−1.54082
$515$	7.82726e22	0.697025
$516$	−6.99157e22	−0.612424
$517$	9.96093e21	0.0858283
$518$	5.71633e22	0.484523
$519$	−5.08422e22	−0.423938
$520$	1.16805e22	0.0958151
$521$	−8.78437e22	−0.708908	−0.354454	−	0.935073i	$-0.615333\pi$
$521$	−8.78437e22	−0.708908	−0.354454	+	0.935073i	$0.615333\pi$
$522$	3.39142e22	0.269267
$523$	−1.21083e23	−0.945845	−0.472922	−	0.881104i	$-0.656801\pi$
$523$	−1.21083e23	−0.945845	−0.472922	+	0.881104i	$0.656801\pi$
$524$	−1.46473e23	−1.12575
$525$	1.52836e22	0.115577
$526$	2.05139e23	1.52640
$527$	−2.89582e23	−2.12022
$528$	−4.62960e21	−0.0333545
$529$	1.91468e23	1.35745
$530$	8.99429e22	0.627512
$531$	1.78243e22	0.122380
$532$	−1.19098e22	−0.0804740
$533$	2.77090e23	1.84263
$534$	−1.56486e23	−1.02417
$535$	3.79356e22	0.244366
$536$	−1.56415e22	−0.0991691
$537$	1.61412e23	1.00729
$538$	−4.09620e23	−2.51612
$539$	−3.58270e21	−0.0216624
$540$	−8.97953e22	−0.534449
$541$	8.15663e22	0.477897	0.238948	−	0.971032i	$-0.423197\pi$
$541$	8.15663e22	0.477897	0.238948	+	0.971032i	$0.423197\pi$
$542$	−3.83478e23	−2.21181
$543$	−7.43584e22	−0.422213
$544$	4.24075e23	2.37056
$545$	−3.22430e22	−0.177446
$546$	2.25804e23	1.22347
$547$	−1.79789e23	−0.959114	−0.479557	−	0.877511i	$-0.659203\pi$
$547$	−1.79789e23	−0.959114	−0.479557	+	0.877511i	$0.659203\pi$
$548$	3.13105e22	0.164458
$549$	−1.34304e23	−0.694583
$550$	2.74389e21	0.0139728
$551$	9.27431e21	0.0465043
$552$	−3.55264e22	−0.175416
$553$	1.08104e22	0.0525628
$554$	4.11890e22	0.197219
$555$	3.32763e22	0.156908
$556$	−1.48221e22	−0.0688293
$557$	−5.19905e22	−0.237769	−0.118884	−	0.992908i	$-0.537932\pi$
$557$	−5.19905e22	−0.237769	−0.118884	+	0.992908i	$0.537932\pi$
$558$	−1.62468e23	−0.731773
$559$	−2.35103e23	−1.04294
$560$	−6.74835e22	−0.294849
$561$	−1.44125e22	−0.0620234
$562$	3.05463e23	1.29479
$563$	2.85062e23	1.19019	0.595097	−	0.803654i	$-0.297114\pi$
$563$	2.85062e23	1.19019	0.595097	+	0.803654i	$0.297114\pi$
$564$	3.71358e23	1.52729
$565$	1.32820e22	0.0538086
$566$	−2.85647e22	−0.113996
$567$	−8.52727e22	−0.335238
$568$	−7.03745e21	−0.0272555
$569$	1.64302e23	0.626885	0.313443	−	0.949607i	$-0.398518\pi$
$569$	1.64302e23	0.626885	0.313443	+	0.949607i	$0.398518\pi$
$570$	−1.32289e22	−0.0497266
$571$	−1.77423e23	−0.657057	−0.328529	−	0.944494i	$-0.606553\pi$
$571$	−1.77423e23	−0.657057	−0.328529	+	0.944494i	$0.606553\pi$
$572$	2.12456e22	0.0775182
$573$	4.86735e22	0.174976
$574$	3.83091e23	1.35691
$575$	−8.79889e22	−0.307080
$576$	1.36268e23	0.468602
$577$	−1.86761e23	−0.632837	−0.316419	−	0.948620i	$-0.602480\pi$
$577$	−1.86761e23	−0.632837	−0.316419	+	0.948620i	$0.602480\pi$
$578$	7.51086e23	2.50786
$579$	−3.38557e23	−1.11395
$580$	−7.17162e22	−0.232530
$581$	−2.35392e23	−0.752134
$582$	−1.99554e23	−0.628369
$583$	1.50341e22	0.0466546
$584$	1.90694e22	0.0583212
$585$	−8.52525e22	−0.256970
$586$	1.35003e22	0.0401065
$587$	2.99557e23	0.877112	0.438556	−	0.898704i	$-0.355490\pi$
$587$	2.99557e23	0.877112	0.438556	+	0.898704i	$0.355490\pi$
$588$	−1.33569e23	−0.385476
$589$	−4.44290e22	−0.126382
$590$	−7.19200e22	−0.201654
$591$	−4.82689e23	−1.33406
$592$	−1.46929e23	−0.400287
$593$	4.98123e23	1.33774	0.668870	−	0.743380i	$-0.266778\pi$
$593$	4.98123e23	1.33774	0.668870	+	0.743380i	$0.266778\pi$
$594$	−2.86395e22	−0.0758195
$595$	−2.10085e23	−0.548278
$596$	−7.31791e23	−1.88275
$597$	−5.59605e22	−0.141938
$598$	−1.29997e24	−3.25066
$599$	1.47366e23	0.363304	0.181652	−	0.983363i	$-0.441856\pi$
$599$	1.47366e23	0.363304	0.181652	+	0.983363i	$0.441856\pi$
$600$	9.40077e21	0.0228496
$601$	1.47101e22	0.0352519	0.0176260	−	0.999845i	$-0.494389\pi$
$601$	1.47101e22	0.0352519	0.0176260	+	0.999845i	$0.494389\pi$
$602$	−3.25043e23	−0.768017
$603$	1.14162e23	0.265965
$604$	1.89271e23	0.434781
$605$	−1.96982e23	−0.446175
$606$	4.93156e23	1.10146
$607$	7.96986e23	1.75528	0.877641	−	0.479319i	$-0.159116\pi$
$607$	7.96986e23	1.75528	0.877641	+	0.479319i	$0.159116\pi$
$608$	6.50635e22	0.141305
$609$	−1.27406e23	−0.272861
$610$	5.41909e23	1.14452
$611$	1.24876e24	2.60092
$612$	3.48490e23	0.715820
$613$	−6.05621e23	−1.22684	−0.613418	−	0.789758i	$-0.710206\pi$
$613$	−6.05621e23	−1.22684	−0.613418	+	0.789758i	$0.710206\pi$
$614$	−5.69421e23	−1.13763
$615$	2.23008e23	0.439423
$616$	2.69932e21	0.00524589
$617$	3.03134e23	0.581046	0.290523	−	0.956868i	$-0.406171\pi$
$617$	3.03134e23	0.581046	0.290523	+	0.956868i	$0.406171\pi$
$618$	9.30711e23	1.75960
$619$	4.52968e23	0.844689	0.422344	−	0.906435i	$-0.361207\pi$
$619$	4.52968e23	0.844689	0.422344	+	0.906435i	$0.361207\pi$
$620$	3.43560e23	0.631936
$621$	9.18388e23	1.66628
$622$	−4.46753e23	−0.799557
$623$	−3.81276e23	−0.673118
$624$	−5.80391e23	−1.01077
$625$	2.32831e22	0.0400000
$626$	−8.24546e23	−1.39744
$627$	−2.21124e21	−0.00369710
$628$	−6.62928e23	−1.09348
$629$	−4.57407e23	−0.744342
$630$	−1.17866e23	−0.189232
$631$	−6.45639e23	−1.02268	−0.511340	−	0.859378i	$-0.670851\pi$
$631$	−6.45639e23	−1.02268	−0.511340	+	0.859378i	$0.670851\pi$
$632$	6.64934e21	0.0103916
$633$	−1.51537e23	−0.233662
$634$	2.08330e23	0.316952
$635$	4.72899e23	0.709891
$636$	5.60493e23	0.830204
$637$	−4.49147e23	−0.656452
$638$	−2.28733e22	−0.0329878
$639$	5.13641e22	0.0730975
$640$	−9.29494e22	−0.130532
$641$	−2.44330e23	−0.338597	−0.169298	−	0.985565i	$-0.554150\pi$
$641$	−2.44330e23	−0.338597	−0.169298	+	0.985565i	$0.554150\pi$
$642$	4.51079e23	0.616886
$643$	6.40456e23	0.864363	0.432181	−	0.901787i	$-0.357744\pi$
$643$	6.40456e23	0.864363	0.432181	+	0.901787i	$0.357744\pi$
$644$	−9.41917e23	−1.25454
$645$	−1.89217e23	−0.248715
$646$	1.81841e23	0.235894
$647$	−5.78975e23	−0.741265	−0.370632	−	0.928780i	$-0.620859\pi$
$647$	−5.78975e23	−0.741265	−0.370632	+	0.928780i	$0.620859\pi$
$648$	−5.24501e22	−0.0662764
$649$	−1.20215e22	−0.0149927
$650$	3.43989e23	0.423429
$651$	6.10343e23	0.741542
$652$	5.10486e23	0.612180
$653$	1.11309e23	0.131755	0.0658777	−	0.997828i	$-0.479015\pi$
$653$	1.11309e23	0.131755	0.0658777	+	0.997828i	$0.479015\pi$
$654$	−3.83390e23	−0.447951
$655$	−3.96407e23	−0.457183
$656$	−9.84672e23	−1.12101
$657$	−1.39181e23	−0.156414
$658$	1.72647e24	1.91531
$659$	−9.34482e23	−1.02340	−0.511700	−	0.859164i	$-0.670984\pi$
$659$	−9.34482e23	−1.02340	−0.511700	+	0.859164i	$0.670984\pi$
$660$	1.70990e22	0.0184862
$661$	−8.08010e23	−0.862392	−0.431196	−	0.902258i	$-0.641908\pi$
$661$	−8.08010e23	−0.862392	−0.431196	+	0.902258i	$0.641908\pi$
$662$	1.77450e24	1.86975
$663$	−1.80683e24	−1.87954
$664$	−1.44787e23	−0.148696
$665$	−3.22322e22	−0.0326818
$666$	−2.56625e23	−0.256902
$667$	7.33483e23	0.724970
$668$	4.67710e23	0.456432
$669$	1.16833e24	1.12575
$670$	−4.60637e23	−0.438252
$671$	9.05809e22	0.0850933
$672$	−8.93809e23	−0.829098
$673$	−1.88528e24	−1.72682	−0.863412	−	0.504499i	$-0.831677\pi$
$673$	−1.88528e24	−1.72682	−0.863412	+	0.504499i	$0.831677\pi$
$674$	2.14116e24	1.93660
$675$	−2.43018e23	−0.217048
$676$	1.41490e24	1.24790
$677$	1.78460e22	0.0155431	0.00777156	−	0.999970i	$-0.497526\pi$
$677$	1.78460e22	0.0155431	0.00777156	+	0.999970i	$0.497526\pi$
$678$	1.57931e23	0.135836
$679$	−4.86211e23	−0.412982
$680$	−1.29220e23	−0.108394
$681$	−3.73965e23	−0.309800
$682$	1.09576e23	0.0896494
$683$	1.18259e24	0.955562	0.477781	−	0.878479i	$-0.341441\pi$
$683$	1.18259e24	0.955562	0.477781	+	0.878479i	$0.341441\pi$
$684$	5.34670e22	0.0426686
$685$	8.47374e22	0.0667890
$686$	−2.00258e24	−1.55896
$687$	1.60689e24	1.23553
$688$	8.35469e23	0.634495
$689$	1.88475e24	1.41381
$690$	−1.04624e24	−0.775203
$691$	6.08137e23	0.445080	0.222540	−	0.974924i	$-0.428565\pi$
$691$	6.08137e23	0.445080	0.222540	+	0.974924i	$0.428565\pi$
$692$	−8.29130e23	−0.599406
$693$	−1.97015e22	−0.0140691
$694$	4.02379e23	0.283844
$695$	−4.01138e22	−0.0279527
$696$	−7.83656e22	−0.0539445
$697$	−3.06541e24	−2.08454
$698$	1.33094e24	0.894104
$699$	1.82957e24	1.21421
$700$	2.49244e23	0.163415
$701$	4.94208e23	0.320116	0.160058	−	0.987108i	$-0.448832\pi$
$701$	4.94208e23	0.320116	0.160058	+	0.987108i	$0.448832\pi$
$702$	−3.59040e24	−2.29762
$703$	−7.01775e22	−0.0443688
$704$	−9.19058e22	−0.0574084
$705$	1.00503e24	0.620256
$706$	−1.62294e24	−0.989606
$707$	1.20157e24	0.723909
$708$	−4.48180e23	−0.266790
$709$	7.05062e23	0.414700	0.207350	−	0.978267i	$-0.433516\pi$
$709$	7.05062e23	0.414700	0.207350	+	0.978267i	$0.433516\pi$
$710$	−2.07251e23	−0.120448
$711$	−4.85314e22	−0.0278697
$712$	−2.34518e23	−0.133075
$713$	−3.51378e24	−1.97022
$714$	−2.49804e24	−1.38409
$715$	5.74983e22	0.0314814
$716$	2.63230e24	1.42421
$717$	−1.89516e24	−1.01329
$718$	3.81315e24	2.01477
$719$	−3.34634e24	−1.74733	−0.873664	−	0.486530i	$-0.838262\pi$
$719$	−3.34634e24	−1.74733	−0.873664	+	0.486530i	$0.838262\pi$
$720$	3.02955e23	0.156334
$721$	2.26767e24	1.15646
$722$	−2.84817e24	−1.43549
$723$	−6.80171e23	−0.338799
$724$	−1.21263e24	−0.596967
$725$	−1.94090e23	−0.0944342
$726$	−2.34224e24	−1.12634
$727$	6.84098e23	0.325144	0.162572	−	0.986697i	$-0.448021\pi$
$727$	6.84098e23	0.325144	0.162572	+	0.986697i	$0.448021\pi$
$728$	3.38402e23	0.158970
$729$	2.20317e24	1.02297
$730$	5.61588e23	0.257735
$731$	2.60092e24	1.17986
$732$	3.37699e24	1.51421
$733$	1.70794e24	0.756987	0.378493	−	0.925604i	$-0.376442\pi$
$733$	1.70794e24	0.756987	0.378493	+	0.925604i	$0.376442\pi$
$734$	9.43794e23	0.413486
$735$	−3.61484e23	−0.156548
$736$	5.14571e24	2.20285
$737$	−7.69963e22	−0.0325834
$738$	−1.71982e24	−0.719457
$739$	9.67570e22	0.0400133	0.0200067	−	0.999800i	$-0.493631\pi$
$739$	9.67570e22	0.0400133	0.0200067	+	0.999800i	$0.493631\pi$
$740$	5.42667e23	0.221852
$741$	−2.77212e23	−0.112036
$742$	2.60577e24	1.04113
$743$	2.97215e22	0.0117399	0.00586997	−	0.999983i	$-0.498132\pi$
$743$	2.97215e22	0.0117399	0.00586997	+	0.999983i	$0.498132\pi$
$744$	3.75414e23	0.146602
$745$	−1.98049e24	−0.764617
$746$	−6.97398e23	−0.266195
$747$	1.05675e24	0.398794
$748$	−2.35038e23	−0.0876950
$749$	1.09905e24	0.405435
$750$	2.76850e23	0.100977
$751$	−2.81672e24	−1.01579	−0.507896	−	0.861419i	$-0.669576\pi$
$751$	−2.81672e24	−1.01579	−0.507896	+	0.861419i	$0.669576\pi$
$752$	−4.43761e24	−1.58233
$753$	2.60511e24	0.918479
$754$	−2.86752e24	−0.999655
$755$	5.12235e23	0.176571
$756$	−2.60150e24	−0.886723
$757$	5.02489e24	1.69360	0.846802	−	0.531908i	$-0.178525\pi$
$757$	5.02489e24	1.69360	0.846802	+	0.531908i	$0.178525\pi$
$758$	−6.62837e24	−2.20912
$759$	−1.74881e23	−0.0576352
$760$	−1.98256e22	−0.00646116
$761$	−4.00608e24	−1.29107	−0.645535	−	0.763731i	$-0.723365\pi$
$761$	−4.00608e24	−1.29107	−0.645535	+	0.763731i	$0.723365\pi$
$762$	5.62307e24	1.79207
$763$	−9.34127e23	−0.294406
$764$	7.93763e23	0.247399
$765$	9.43139e23	0.290706
$766$	−6.22673e23	−0.189808
$767$	−1.50708e24	−0.454335
$768$	2.00628e24	0.598165
$769$	−6.03695e24	−1.78010	−0.890048	−	0.455866i	$-0.849330\pi$
$769$	−6.03695e24	−1.78010	−0.890048	+	0.455866i	$0.849330\pi$
$770$	7.94945e22	0.0231828
$771$	−2.87030e24	−0.827875
$772$	−5.52115e24	−1.57501
$773$	1.30380e24	0.367862	0.183931	−	0.982939i	$-0.441118\pi$
$773$	1.30380e24	0.367862	0.183931	+	0.982939i	$0.441118\pi$
$774$	1.45922e24	0.407215
$775$	9.29795e23	0.256639
$776$	−2.99062e23	−0.0816463
$777$	9.64063e23	0.260332
$778$	−3.19992e24	−0.854698
$779$	−4.70309e23	−0.124255
$780$	2.14362e24	0.560201
$781$	−3.46424e22	−0.00895517
$782$	1.43814e25	3.67742
$783$	2.02582e24	0.512419
$784$	1.59610e24	0.399368
$785$	−1.79412e24	−0.444078
$786$	−4.71353e24	−1.15413
$787$	5.61762e24	1.36072	0.680358	−	0.732880i	$-0.261824\pi$
$787$	5.61762e24	1.36072	0.680358	+	0.732880i	$0.261824\pi$
$788$	−7.87165e24	−1.88622
$789$	3.45969e24	0.820129
$790$	1.95822e23	0.0459230
$791$	3.84798e23	0.0892757
$792$	−1.21181e22	−0.00278146
$793$	1.13557e25	2.57865
$794$	6.40211e24	1.43830
$795$	1.51689e24	0.337159
$796$	−9.12598e23	−0.200687
$797$	−7.18870e24	−1.56406	−0.782032	−	0.623238i	$-0.785817\pi$
$797$	−7.18870e24	−1.56406	−0.782032	+	0.623238i	$0.785817\pi$
$798$	−3.83261e23	−0.0825031
$799$	−1.38148e25	−2.94238
$800$	−1.36163e24	−0.286941
$801$	1.71167e24	0.356898
$802$	−3.79678e24	−0.783308
$803$	9.38703e22	0.0191622
$804$	−2.87053e24	−0.579811
$805$	−2.54916e24	−0.509487
$806$	1.37370e25	2.71671
$807$	−6.90827e24	−1.35190
$808$	7.39070e23	0.143116
$809$	6.58695e24	1.26218	0.631091	−	0.775709i	$-0.282607\pi$
$809$	6.58695e24	1.26218	0.631091	+	0.775709i	$0.282607\pi$
$810$	−1.54464e24	−0.292891
$811$	−2.21064e23	−0.0414802	−0.0207401	−	0.999785i	$-0.506602\pi$
$811$	−2.21064e23	−0.0414802	−0.0207401	+	0.999785i	$0.506602\pi$
$812$	−2.07772e24	−0.385799
$813$	−6.46740e24	−1.18839
$814$	1.73080e23	0.0314730
$815$	1.38156e24	0.248616
$816$	6.42080e24	1.14346
$817$	3.99045e23	0.0703290
$818$	2.90015e24	0.505845
$819$	−2.46989e24	−0.426348
$820$	3.63680e24	0.621300
$821$	5.30318e24	0.896643	0.448321	−	0.893872i	$-0.352022\pi$
$821$	5.30318e24	0.896643	0.448321	+	0.893872i	$0.352022\pi$
$822$	1.00758e24	0.168605
$823$	−5.54095e24	−0.917669	−0.458834	−	0.888522i	$-0.651733\pi$
$823$	−5.54095e24	−0.917669	−0.458834	+	0.888522i	$0.651733\pi$
$824$	1.39481e24	0.228631
$825$	4.62760e22	0.00750753
$826$	−2.08362e24	−0.334572
$827$	1.98642e24	0.315700	0.157850	−	0.987463i	$-0.449544\pi$
$827$	1.98642e24	0.315700	0.157850	+	0.987463i	$0.449544\pi$
$828$	4.22857e24	0.665175
$829$	4.32599e24	0.673554	0.336777	−	0.941584i	$-0.390663\pi$
$829$	4.32599e24	0.673554	0.336777	+	0.941584i	$0.390663\pi$
$830$	−4.26394e24	−0.657123
$831$	6.94655e23	0.105965
$832$	−1.15218e25	−1.73969
$833$	4.96886e24	0.742633
$834$	−4.76979e23	−0.0705648
$835$	1.26579e24	0.185364
$836$	−3.60606e22	−0.00522733
$837$	−9.70478e24	−1.39258
$838$	−2.63373e24	−0.374107
$839$	−6.94249e24	−0.976199	−0.488100	−	0.872788i	$-0.662310\pi$
$839$	−6.94249e24	−0.976199	−0.488100	+	0.872788i	$0.662310\pi$
$840$	2.72354e23	0.0379105
$841$	−5.63920e24	−0.777055
$842$	−7.98602e22	−0.0108938
$843$	5.15166e24	0.695686
$844$	−2.47126e24	−0.330375
$845$	3.82922e24	0.506791
$846$	−7.75070e24	−1.01553
$847$	−5.70684e24	−0.740264
$848$	−6.69771e24	−0.860124
$849$	−4.81746e23	−0.0612495
$850$	−3.80551e24	−0.479018
$851$	−5.55017e24	−0.691680
$852$	−1.29152e24	−0.159354
$853$	1.08193e25	1.32170	0.660850	−	0.750518i	$-0.270196\pi$
$853$	1.08193e25	1.32170	0.660850	+	0.750518i	$0.270196\pi$
$854$	1.56999e25	1.89891
$855$	1.44701e23	0.0173284
$856$	6.76011e23	0.0801542
$857$	5.95426e24	0.699022	0.349511	−	0.936932i	$-0.386348\pi$
$857$	5.95426e24	0.699022	0.349511	+	0.936932i	$0.386348\pi$
$858$	6.83691e23	0.0794727
$859$	1.48205e25	1.70578	0.852888	−	0.522094i	$-0.174849\pi$
$859$	1.48205e25	1.70578	0.852888	+	0.522094i	$0.174849\pi$
$860$	−3.08573e24	−0.351658
$861$	6.46087e24	0.729062
$862$	2.00697e24	0.224248
$863$	−7.80490e24	−0.863527	−0.431763	−	0.901987i	$-0.642108\pi$
$863$	−7.80490e24	−0.863527	−0.431763	+	0.901987i	$0.642108\pi$
$864$	1.42120e25	1.55700
$865$	−2.24392e24	−0.243428
$866$	−4.55378e24	−0.489182
$867$	1.26671e25	1.34746
$868$	9.95342e24	1.04847
$869$	3.27319e22	0.00341431
$870$	−2.30785e24	−0.238393
$871$	−9.65266e24	−0.987399
$872$	−5.74569e23	−0.0582039
$873$	2.18276e24	0.218970
$874$	2.20646e24	0.219204
$875$	6.74544e23	0.0663654
$876$	3.49962e24	0.340986
$877$	−1.08922e25	−1.05104	−0.525522	−	0.850780i	$-0.676130\pi$
$877$	−1.08922e25	−1.05104	−0.525522	+	0.850780i	$0.676130\pi$
$878$	−1.02320e25	−0.977818
$879$	2.27684e23	0.0215490
$880$	−2.04327e23	−0.0191524
$881$	1.08635e25	1.00850	0.504248	−	0.863559i	$-0.331770\pi$
$881$	1.08635e25	1.00850	0.504248	+	0.863559i	$0.331770\pi$
$882$	2.78774e24	0.256312
$883$	4.33461e24	0.394715	0.197357	−	0.980332i	$-0.436764\pi$
$883$	4.33461e24	0.394715	0.197357	+	0.980332i	$0.436764\pi$
$884$	−2.94656e25	−2.65749
$885$	−1.21294e24	−0.108348
$886$	−5.38885e24	−0.476771
$887$	1.91922e25	1.68180	0.840901	−	0.541188i	$-0.182025\pi$
$887$	1.91922e25	1.68180	0.840901	+	0.541188i	$0.182025\pi$
$888$	5.92982e23	0.0514673
$889$	1.37006e25	1.17780
$890$	−6.90650e24	−0.588089
$891$	−2.58189e23	−0.0217760
$892$	1.90530e25	1.59170
$893$	−2.11954e24	−0.175389
$894$	−2.35493e25	−1.93023
$895$	7.12394e24	0.578395
$896$	−2.69288e24	−0.216570
$897$	−2.19240e25	−1.74657
$898$	−1.62904e25	−1.28553
$899$	−7.75085e24	−0.605888
$900$	−1.11894e24	−0.0866453
$901$	−2.08508e25	−1.59942
$902$	1.15993e24	0.0881405
$903$	−5.48188e24	−0.412652
$904$	2.36684e23	0.0176497
$905$	−3.28181e24	−0.242438
$906$	6.09081e24	0.445744
$907$	1.99582e25	1.44697	0.723485	−	0.690341i	$-0.242539\pi$
$907$	1.99582e25	1.44697	0.723485	+	0.690341i	$0.242539\pi$
$908$	−6.09859e24	−0.438026
$909$	−5.39424e24	−0.383829
$910$	9.96586e24	0.702527
$911$	−1.73050e24	−0.120855	−0.0604276	−	0.998173i	$-0.519246\pi$
$911$	−1.73050e24	−0.120855	−0.0604276	+	0.998173i	$0.519246\pi$
$912$	9.85108e23	0.0681597
$913$	−7.12723e23	−0.0488562
$914$	−2.00249e25	−1.35996
$915$	9.13934e24	0.614944
$916$	2.62050e25	1.74692
$917$	−1.14845e25	−0.758529
$918$	3.97202e25	2.59925
$919$	1.90398e25	1.23447	0.617234	−	0.786780i	$-0.288253\pi$
$919$	1.90398e25	1.23447	0.617234	+	0.786780i	$0.288253\pi$
$920$	−1.56796e24	−0.100725
$921$	−9.60334e24	−0.611245
$922$	−1.17825e25	−0.743059
$923$	−4.34295e24	−0.271375
$924$	4.95382e23	0.0306711
$925$	1.46865e24	0.0900977
$926$	2.93460e25	1.78384
$927$	−1.01803e25	−0.613173
$928$	1.13506e25	0.677426
$929$	−1.36892e25	−0.809552	−0.404776	−	0.914416i	$-0.632650\pi$
$929$	−1.36892e25	−0.809552	−0.404776	+	0.914416i	$0.632650\pi$
$930$	1.10559e25	0.647869
$931$	7.62346e23	0.0442669
$932$	2.98364e25	1.71677
$933$	−7.53453e24	−0.429598
$934$	1.11096e25	0.627698
$935$	−6.36097e23	−0.0356143
$936$	−1.51920e24	−0.0842886
$937$	−2.61150e24	−0.143583	−0.0717915	−	0.997420i	$-0.522872\pi$
$937$	−2.61150e24	−0.143583	−0.0717915	+	0.997420i	$0.522872\pi$
$938$	−1.33453e25	−0.727118
$939$	−1.39060e25	−0.750837
$940$	1.63899e25	0.876980
$941$	6.02471e24	0.319466	0.159733	−	0.987160i	$-0.448937\pi$
$941$	6.02471e24	0.319466	0.159733	+	0.987160i	$0.448937\pi$
$942$	−2.13332e25	−1.12105
$943$	−3.71956e25	−1.93706
$944$	5.35561e24	0.276405
$945$	−7.04058e24	−0.360112
$946$	−9.84169e23	−0.0498879
$947$	4.07517e24	0.204725	0.102363	−	0.994747i	$-0.467360\pi$
$947$	4.07517e24	0.204725	0.102363	+	0.994747i	$0.467360\pi$
$948$	1.22029e24	0.0607565
$949$	1.17681e25	0.580688
$950$	−5.83859e23	−0.0285534
$951$	3.51350e24	0.170297
$952$	−3.74370e24	−0.179840
$953$	2.17779e23	0.0103687	0.00518437	−	0.999987i	$-0.498350\pi$
$953$	2.17779e23	0.0103687	0.00518437	+	0.999987i	$0.498350\pi$
$954$	−1.16982e25	−0.552023
$955$	2.14821e24	0.100473
$956$	−3.09061e25	−1.43269
$957$	−3.85761e23	−0.0177242
$958$	5.68817e24	0.259039
$959$	2.45496e24	0.110812
$960$	−9.27302e24	−0.414873
$961$	1.45807e25	0.646592
$962$	2.16982e25	0.953751
$963$	−4.93399e24	−0.214969
$964$	−1.10922e25	−0.479029
$965$	−1.49422e25	−0.639636
$966$	−3.03112e25	−1.28617
$967$	3.80614e25	1.60089	0.800443	−	0.599409i	$-0.204598\pi$
$967$	3.80614e25	1.60089	0.800443	+	0.599409i	$0.204598\pi$
$968$	−3.51020e24	−0.146350
$969$	3.06677e24	0.126744
$970$	−8.80730e24	−0.360814
$971$	2.89853e25	1.17710	0.588551	−	0.808460i	$-0.299699\pi$
$971$	2.89853e25	1.17710	0.588551	+	0.808460i	$0.299699\pi$
$972$	2.00605e25	0.807568
$973$	−1.16216e24	−0.0463772
$974$	3.12874e25	1.23771
$975$	5.80140e24	0.227507
$976$	−4.03539e25	−1.56878
$977$	−1.73436e25	−0.668397	−0.334199	−	0.942503i	$-0.608466\pi$
$977$	−1.73436e25	−0.668397	−0.334199	+	0.942503i	$0.608466\pi$
$978$	1.64276e25	0.627615
$979$	−1.15443e24	−0.0437235
$980$	−5.89505e24	−0.221343
$981$	4.19360e24	0.156099
$982$	−7.65128e25	−2.82349
$983$	9.52964e24	0.348636	0.174318	−	0.984689i	$-0.444228\pi$
$983$	9.52964e24	0.348636	0.174318	+	0.984689i	$0.444228\pi$
$984$	3.97400e24	0.144135
$985$	−2.13035e25	−0.766025
$986$	3.17231e25	1.13089
$987$	2.91171e25	1.02909
$988$	−4.52075e24	−0.158408
$989$	3.15595e25	1.09638
$990$	−3.56877e23	−0.0122919
$991$	−3.45153e25	−1.17865	−0.589325	−	0.807896i	$-0.700606\pi$
$991$	−3.45153e25	−1.17865	−0.589325	+	0.807896i	$0.700606\pi$
$992$	−5.43757e25	−1.84101
$993$	2.99271e25	1.00461
$994$	−6.00437e24	−0.199840
$995$	−2.46982e24	−0.0815020
$996$	−2.65714e25	−0.869380
$997$	7.09635e24	0.230211	0.115106	−	0.993353i	$-0.463279\pi$
$997$	7.09635e24	0.230211	0.115106	+	0.993353i	$0.463279\pi$
$998$	4.61306e25	1.48381
$999$	−1.53291e25	−0.488889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.18.a.b.1.3	✓	3
3.2	odd	2		45.18.a.c.1.1		3
4.3	odd	2		80.18.a.g.1.2		3
5.2	odd	4		25.18.b.c.24.6		6
5.3	odd	4		25.18.b.c.24.1		6
5.4	even	2		25.18.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.18.a.b.1.3	✓	3	1.1	even	1	trivial
25.18.a.c.1.1		3	5.4	even	2
25.18.b.c.24.1		6	5.3	odd	4
25.18.b.c.24.6		6	5.2	odd	4
45.18.a.c.1.1		3	3.2	odd	2
80.18.a.g.1.2		3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+524.793 q^{2} +8850.68 q^{3} +144336. q^{4} +390625. q^{5} +4.64478e6 q^{6} +1.13170e7 q^{7} +6.96092e6 q^{8} -5.08056e7 q^{9} +O(q^{10})\)	\(q+524.793 q^{2} +8850.68 q^{3} +144336. q^{4} +390625. q^{5} +4.64478e6 q^{6} +1.13170e7 q^{7} +6.96092e6 q^{8} -5.08056e7 q^{9} +2.04997e8 q^{10} +3.42656e7 q^{11} +1.27747e9 q^{12} +4.29572e9 q^{13} +5.93907e9 q^{14} +3.45730e9 q^{15} -1.52654e10 q^{16} -4.75231e10 q^{17} -2.66624e10 q^{18} -7.29121e9 q^{19} +5.63813e10 q^{20} +1.00163e11 q^{21} +1.79824e10 q^{22} -5.76644e11 q^{23} +6.16089e10 q^{24} +1.52588e11 q^{25} +2.25437e12 q^{26} -1.59264e12 q^{27} +1.63345e12 q^{28} -1.27199e12 q^{29} +1.81437e12 q^{30} +6.09351e12 q^{31} -8.92355e12 q^{32} +3.03274e11 q^{33} -2.49398e13 q^{34} +4.42069e12 q^{35} -7.33308e12 q^{36} +9.62495e12 q^{37} -3.82638e12 q^{38} +3.80201e13 q^{39} +2.71911e12 q^{40} +6.45036e13 q^{41} +5.25648e13 q^{42} -5.47296e13 q^{43} +4.94577e12 q^{44} -1.98459e13 q^{45} -3.02619e14 q^{46} +2.90697e14 q^{47} -1.35109e14 q^{48} -1.04557e14 q^{49} +8.00771e13 q^{50} -4.20612e14 q^{51} +6.20028e14 q^{52} +4.38751e14 q^{53} -8.35808e14 q^{54} +1.33850e13 q^{55} +7.87764e13 q^{56} -6.45322e13 q^{57} -6.67530e14 q^{58} -3.50833e14 q^{59} +4.99013e14 q^{60} +2.64349e15 q^{61} +3.19783e15 q^{62} -5.74965e14 q^{63} -2.68216e15 q^{64} +1.67802e15 q^{65} +1.59156e14 q^{66} -2.24704e15 q^{67} -6.85930e15 q^{68} -5.10369e15 q^{69} +2.31995e15 q^{70} -1.01099e15 q^{71} -3.53653e14 q^{72} +2.73949e15 q^{73} +5.05111e15 q^{74} +1.35051e15 q^{75} -1.05238e15 q^{76} +3.87783e14 q^{77} +1.99527e16 q^{78} +9.55239e14 q^{79} -5.96304e15 q^{80} -7.53494e15 q^{81} +3.38511e16 q^{82} -2.07999e16 q^{83} +1.44571e16 q^{84} -1.85637e16 q^{85} -2.87218e16 q^{86} -1.12579e16 q^{87} +2.38520e14 q^{88} -3.36906e16 q^{89} -1.04150e16 q^{90} +4.86145e16 q^{91} -8.32305e16 q^{92} +5.39317e16 q^{93} +1.52556e17 q^{94} -2.84813e15 q^{95} -7.89795e16 q^{96} -4.29630e16 q^{97} -5.48707e16 q^{98} -1.74088e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9}+O(q^{10}) \) 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9	\( 3 q + 118 q^{2} + 15944 q^{3} + 16916 q^{4} + 1171875 q^{5} - 2419064 q^{6} + 2139308 q^{7} + 65050440 q^{8} + 323892439 q^{9} + 46093750 q^{10} + 1789747516 q^{11} + 3112179088 q^{12} + 5414696794 q^{13} + 10507173312 q^{14} + 6228125000 q^{15} - 16203699952 q^{16} - 27402303962 q^{17} - 142746901186 q^{18} - 29956565300 q^{19} + 6607812500 q^{20} - 224495442624 q^{21} - 294714945304 q^{22} + 16254077844 q^{23} + 897428301600 q^{24} + 457763671875 q^{25} + 2017382699956 q^{26} + 3131715461840 q^{27} + 1119244517216 q^{28} - 2528278831750 q^{29} - 944946875000 q^{30} - 521256054664 q^{31} - 10880399775712 q^{32} + 1732417161568 q^{33} - 32147385667828 q^{34} + 835667187500 q^{35} - 14985377520892 q^{36} + 31762746900498 q^{37} - 40258035935240 q^{38} + 43003853320688 q^{39} + 25410328125000 q^{40} + 86833482954446 q^{41} + 153974403759936 q^{42} + 89258046385744 q^{43} - 124942202946448 q^{44} + 126520483984375 q^{45} - 323339762673024 q^{46} + 348182738140228 q^{47} - 729510516165056 q^{48} - 387320833396229 q^{49} + 18005371093750 q^{50} - 12409602773744 q^{51} + 552556858385688 q^{52} + 44014499212594 q^{53} - 22\!\cdots\!00 q^{54}+ \cdots + 29\!\cdots\!08 q^{99}+O(q^{100}) \) 3 * q + 118 * q^2 + 15944 * q^3 + 16916 * q^4 + 1171875 * q^5 - 2419064 * q^6 + 2139308 * q^7 + 65050440 * q^8 + 323892439 * q^9 + 46093750 * q^10 + 1789747516 * q^11 + 3112179088 * q^12 + 5414696794 * q^13 + 10507173312 * q^14 + 6228125000 * q^15 - 16203699952 * q^16 - 27402303962 * q^17 - 142746901186 * q^18 - 29956565300 * q^19 + 6607812500 * q^20 - 224495442624 * q^21 - 294714945304 * q^22 + 16254077844 * q^23 + 897428301600 * q^24 + 457763671875 * q^25 + 2017382699956 * q^26 + 3131715461840 * q^27 + 1119244517216 * q^28 - 2528278831750 * q^29 - 944946875000 * q^30 - 521256054664 * q^31 - 10880399775712 * q^32 + 1732417161568 * q^33 - 32147385667828 * q^34 + 835667187500 * q^35 - 14985377520892 * q^36 + 31762746900498 * q^37 - 40258035935240 * q^38 + 43003853320688 * q^39 + 25410328125000 * q^40 + 86833482954446 * q^41 + 153974403759936 * q^42 + 89258046385744 * q^43 - 124942202946448 * q^44 + 126520483984375 * q^45 - 323339762673024 * q^46 + 348182738140228 * q^47 - 729510516165056 * q^48 - 387320833396229 * q^49 + 18005371093750 * q^50 - 12409602773744 * q^51 + 552556858385688 * q^52 + 44014499212594 * q^53 - 2265337034433200 * q^54 + 699120123437500 * q^55 - 490455582129600 * q^56 + 4293013923032480 * q^57 + 597742677475540 * q^58 - 2133293278957100 * q^59 + 1215694956250000 * q^60 + 2822990449991866 * q^61 + 5338539124096416 * q^62 - 4366406213760516 * q^63 - 2533946722090944 * q^64 + 2115115935156250 * q^65 - 4908048881135008 * q^66 + 374173462156688 * q^67 - 6873999340144024 * q^68 - 13800336843711552 * q^69 + 4104364575000000 * q^70 - 9029705707562224 * q^71 + 14996701114647720 * q^72 - 5906564941861106 * q^73 + 2774091820866692 * q^74 + 2432861328125000 * q^75 + 17087125269517200 * q^76 - 5362490012556624 * q^77 + 15760779344737648 * q^78 + 9183397142621600 * q^79 - 6329570293750000 * q^80 + 11504008140536443 * q^81 + 34156701290034076 * q^82 + 15992201117651544 * q^83 + 20750744922079872 * q^84 - 10704024985156250 * q^85 - 41302213526621384 * q^86 - 124899722203208080 * q^87 + 46255695387619680 * q^88 - 31272661736951250 * q^89 - 55760508275781250 * q^90 + 42991889981897896 * q^91 - 161631619485465312 * q^92 - 55524596752956672 * q^93 + 206283262927378352 * q^94 - 11701783320312500 * q^95 - 45608798390141824 * q^96 + 28207632381796278 * q^97 - 22149964169860474 * q^98 + 293120596614370508 * q^99

Introduction

L-functions

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