LMFDB - Embedded newform 38.10.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(1,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 8016x^{2} - 155839x + 2105804 $ x^4 - 2x^3 - 8016x^2 - 155839*x + 2105804
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-73.1023$ of defining polynomial
Character	$\chi$	$=$	38.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} -206.847 q^{3} +256.000 q^{4} -845.315 q^{5} -3309.55 q^{6} -6607.98 q^{7} +4096.00 q^{8} +23102.6 q^{9} +O(q^{10})$	\(q+16.0000 q^{2} -206.847 q^{3} +256.000 q^{4} -845.315 q^{5} -3309.55 q^{6} -6607.98 q^{7} +4096.00 q^{8} +23102.6 q^{9} -13525.0 q^{10} +56450.6 q^{11} -52952.8 q^{12} -101405. q^{13} -105728. q^{14} +174851. q^{15} +65536.0 q^{16} +624347. q^{17} +369641. q^{18} -130321. q^{19} -216401. q^{20} +1.36684e6 q^{21} +903210. q^{22} +2.61755e6 q^{23} -847244. q^{24} -1.23857e6 q^{25} -1.62248e6 q^{26} -707323. q^{27} -1.69164e6 q^{28} +2.86799e6 q^{29} +2.79761e6 q^{30} -2.44968e6 q^{31} +1.04858e6 q^{32} -1.16766e7 q^{33} +9.98955e6 q^{34} +5.58583e6 q^{35} +5.91425e6 q^{36} -6.66624e6 q^{37} -2.08514e6 q^{38} +2.09753e7 q^{39} -3.46241e6 q^{40} +3.70089e6 q^{41} +2.18694e7 q^{42} +2.02637e7 q^{43} +1.44514e7 q^{44} -1.95289e7 q^{45} +4.18808e7 q^{46} +9.25239e6 q^{47} -1.35559e7 q^{48} +3.31184e6 q^{49} -1.98171e7 q^{50} -1.29144e8 q^{51} -2.59597e7 q^{52} -3.19002e7 q^{53} -1.13172e7 q^{54} -4.77185e7 q^{55} -2.70663e7 q^{56} +2.69565e7 q^{57} +4.58878e7 q^{58} -1.34485e8 q^{59} +4.47617e7 q^{60} -4.24287e7 q^{61} -3.91949e7 q^{62} -1.52661e8 q^{63} +1.67772e7 q^{64} +8.57193e7 q^{65} -1.86826e8 q^{66} +2.70669e8 q^{67} +1.59833e8 q^{68} -5.41432e8 q^{69} +8.93732e7 q^{70} +2.67893e8 q^{71} +9.46281e7 q^{72} +2.72432e8 q^{73} -1.06660e8 q^{74} +2.56194e8 q^{75} -3.33622e7 q^{76} -3.73025e8 q^{77} +3.35605e8 q^{78} -9.46452e7 q^{79} -5.53985e7 q^{80} -3.08420e8 q^{81} +5.92142e7 q^{82} +6.12610e8 q^{83} +3.49911e8 q^{84} -5.27769e8 q^{85} +3.24220e8 q^{86} -5.93234e8 q^{87} +2.31222e8 q^{88} +2.50492e7 q^{89} -3.12463e8 q^{90} +6.70084e8 q^{91} +6.70093e8 q^{92} +5.06709e8 q^{93} +1.48038e8 q^{94} +1.10162e8 q^{95} -2.16894e8 q^{96} +8.03901e7 q^{97} +5.29895e7 q^{98} +1.30415e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9}+O(q^{10}) $ 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9	\( 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9} + 13856 q^{10} + 119234 q^{11} + 57856 q^{12} - 6748 q^{13} + 42720 q^{14} + 355904 q^{15} + 262144 q^{16} + 678624 q^{17} + 809696 q^{18} - 521284 q^{19} + 221696 q^{20} + 1586736 q^{21} + 1907744 q^{22} + 2911868 q^{23} + 925696 q^{24} + 268766 q^{25} - 107968 q^{26} + 2802058 q^{27} + 683520 q^{28} + 8291104 q^{29} + 5694464 q^{30} + 3445468 q^{31} + 4194304 q^{32} - 5321788 q^{33} + 10857984 q^{34} + 7715058 q^{35} + 12955136 q^{36} - 1005524 q^{37} - 8340544 q^{38} + 34055900 q^{39} + 3547136 q^{40} + 8514124 q^{41} + 25387776 q^{42} + 13900726 q^{43} + 30523904 q^{44} - 8962202 q^{45} + 46589888 q^{46} - 36334954 q^{47} + 14811136 q^{48} - 30891808 q^{49} + 4300256 q^{50} - 203869074 q^{51} - 1727488 q^{52} - 113969356 q^{53} + 44832928 q^{54} - 178140098 q^{55} + 10936320 q^{56} - 29452546 q^{57} + 132657664 q^{58} - 396773766 q^{59} + 91111424 q^{60} - 298192066 q^{61} + 55127488 q^{62} - 458723694 q^{63} + 67108864 q^{64} - 291187676 q^{65} - 85148608 q^{66} - 113551722 q^{67} + 173727744 q^{68} - 671519716 q^{69} + 123440928 q^{70} + 4659620 q^{71} + 207282176 q^{72} + 136198452 q^{73} - 16088384 q^{74} + 29308274 q^{75} - 133448704 q^{76} + 120551886 q^{77} + 544894400 q^{78} + 67255424 q^{79} + 56754176 q^{80} + 982241180 q^{81} + 136225984 q^{82} + 1376505216 q^{83} + 406204416 q^{84} + 638402178 q^{85} + 222411616 q^{86} + 630635524 q^{87} + 488382464 q^{88} + 1557211260 q^{89} - 143395232 q^{90} + 1422773730 q^{91} + 745438208 q^{92} + 2036686084 q^{93} - 581359264 q^{94} - 112857986 q^{95} + 236978176 q^{96} + 975818188 q^{97} - 494268928 q^{98} + 502820650 q^{99}+O(q^{100}) \) 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9 + 13856 * q^10 + 119234 * q^11 + 57856 * q^12 - 6748 * q^13 + 42720 * q^14 + 355904 * q^15 + 262144 * q^16 + 678624 * q^17 + 809696 * q^18 - 521284 * q^19 + 221696 * q^20 + 1586736 * q^21 + 1907744 * q^22 + 2911868 * q^23 + 925696 * q^24 + 268766 * q^25 - 107968 * q^26 + 2802058 * q^27 + 683520 * q^28 + 8291104 * q^29 + 5694464 * q^30 + 3445468 * q^31 + 4194304 * q^32 - 5321788 * q^33 + 10857984 * q^34 + 7715058 * q^35 + 12955136 * q^36 - 1005524 * q^37 - 8340544 * q^38 + 34055900 * q^39 + 3547136 * q^40 + 8514124 * q^41 + 25387776 * q^42 + 13900726 * q^43 + 30523904 * q^44 - 8962202 * q^45 + 46589888 * q^46 - 36334954 * q^47 + 14811136 * q^48 - 30891808 * q^49 + 4300256 * q^50 - 203869074 * q^51 - 1727488 * q^52 - 113969356 * q^53 + 44832928 * q^54 - 178140098 * q^55 + 10936320 * q^56 - 29452546 * q^57 + 132657664 * q^58 - 396773766 * q^59 + 91111424 * q^60 - 298192066 * q^61 + 55127488 * q^62 - 458723694 * q^63 + 67108864 * q^64 - 291187676 * q^65 - 85148608 * q^66 - 113551722 * q^67 + 173727744 * q^68 - 671519716 * q^69 + 123440928 * q^70 + 4659620 * q^71 + 207282176 * q^72 + 136198452 * q^73 - 16088384 * q^74 + 29308274 * q^75 - 133448704 * q^76 + 120551886 * q^77 + 544894400 * q^78 + 67255424 * q^79 + 56754176 * q^80 + 982241180 * q^81 + 136225984 * q^82 + 1376505216 * q^83 + 406204416 * q^84 + 638402178 * q^85 + 222411616 * q^86 + 630635524 * q^87 + 488382464 * q^88 + 1557211260 * q^89 - 143395232 * q^90 + 1422773730 * q^91 + 745438208 * q^92 + 2036686084 * q^93 - 581359264 * q^94 - 112857986 * q^95 + 236978176 * q^96 + 975818188 * q^97 - 494268928 * q^98 + 502820650 * 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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−206.847	−1.47436	−0.737179	−	0.675698i	$-0.763843\pi$
$3$	−206.847	−1.47436	−0.737179	+	0.675698i	$0.763843\pi$
$4$	256.000	0.500000
$5$	−845.315	−0.604858	−0.302429	−	0.953172i	$-0.597798\pi$
$5$	−845.315	−0.604858	−0.302429	+	0.953172i	$0.597798\pi$
$6$	−3309.55	−1.04253
$7$	−6607.98	−1.04023	−0.520113	−	0.854097i	$-0.674110\pi$
$7$	−6607.98	−1.04023	−0.520113	+	0.854097i	$0.674110\pi$
$8$	4096.00	0.353553
$9$	23102.6	1.17373
$10$	−13525.0	−0.427699
$11$	56450.6	1.16252	0.581262	−	0.813717i	$-0.302559\pi$
$11$	56450.6	1.16252	0.581262	+	0.813717i	$0.302559\pi$
$12$	−52952.8	−0.737179
$13$	−101405.	−0.984726	−0.492363	−	0.870390i	$-0.663867\pi$
$13$	−101405.	−0.984726	−0.492363	+	0.870390i	$0.663867\pi$
$14$	−105728.	−0.735551
$15$	174851.	0.891777
$16$	65536.0	0.250000
$17$	624347.	1.81303	0.906516	−	0.422171i	$-0.138732\pi$
$17$	624347.	1.81303	0.906516	+	0.422171i	$0.138732\pi$
$18$	369641.	0.829953
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	−216401.	−0.302429
$21$	1.36684e6	1.53367
$22$	903210.	0.822028
$23$	2.61755e6	1.95038	0.975192	−	0.221361i	$-0.0710499\pi$
$23$	2.61755e6	1.95038	0.975192	+	0.221361i	$0.0710499\pi$
$24$	−847244.	−0.521264
$25$	−1.23857e6	−0.634147
$26$	−1.62248e6	−0.696306
$27$	−707323.	−0.256142
$28$	−1.69164e6	−0.520113
$29$	2.86799e6	0.752986	0.376493	−	0.926420i	$-0.377130\pi$
$29$	2.86799e6	0.752986	0.376493	+	0.926420i	$0.377130\pi$
$30$	2.79761e6	0.630582
$31$	−2.44968e6	−0.476412	−0.238206	−	0.971215i	$-0.576559\pi$
$31$	−2.44968e6	−0.476412	−0.238206	+	0.971215i	$0.576559\pi$
$32$	1.04858e6	0.176777
$33$	−1.16766e7	−1.71398
$34$	9.98955e6	1.28201
$35$	5.58583e6	0.629189
$36$	5.91425e6	0.586866
$37$	−6.66624e6	−0.584754	−0.292377	−	0.956303i	$-0.594446\pi$
$37$	−6.66624e6	−0.584754	−0.292377	+	0.956303i	$0.594446\pi$
$38$	−2.08514e6	−0.162221
$39$	2.09753e7	1.45184
$40$	−3.46241e6	−0.213850
$41$	3.70089e6	0.204540	0.102270	−	0.994757i	$-0.467389\pi$
$41$	3.70089e6	0.204540	0.102270	+	0.994757i	$0.467389\pi$
$42$	2.18694e7	1.08447
$43$	2.02637e7	0.903881	0.451941	−	0.892048i	$-0.350732\pi$
$43$	2.02637e7	0.903881	0.451941	+	0.892048i	$0.350732\pi$
$44$	1.44514e7	0.581262
$45$	−1.95289e7	−0.709941
$46$	4.18808e7	1.37913
$47$	9.25239e6	0.276575	0.138288	−	0.990392i	$-0.455840\pi$
$47$	9.25239e6	0.276575	0.138288	+	0.990392i	$0.455840\pi$
$48$	−1.35559e7	−0.368589
$49$	3.31184e6	0.0820706
$50$	−1.98171e7	−0.448410
$51$	−1.29144e8	−2.67306
$52$	−2.59597e7	−0.492363
$53$	−3.19002e7	−0.555331	−0.277666	−	0.960678i	$-0.589561\pi$
$53$	−3.19002e7	−0.555331	−0.277666	+	0.960678i	$0.589561\pi$
$54$	−1.13172e7	−0.181120
$55$	−4.77185e7	−0.703161
$56$	−2.70663e7	−0.367776
$57$	2.69565e7	0.338241
$58$	4.58878e7	0.532441
$59$	−1.34485e8	−1.44491	−0.722455	−	0.691417i	$-0.756987\pi$
$59$	−1.34485e8	−1.44491	−0.722455	+	0.691417i	$0.756987\pi$
$60$	4.47617e7	0.445889
$61$	−4.24287e7	−0.392351	−0.196176	−	0.980569i	$-0.562852\pi$
$61$	−4.24287e7	−0.392351	−0.196176	+	0.980569i	$0.562852\pi$
$62$	−3.91949e7	−0.336874
$63$	−1.52661e8	−1.22095
$64$	1.67772e7	0.125000
$65$	8.57193e7	0.595619
$66$	−1.86826e8	−1.21196
$67$	2.70669e8	1.64097	0.820486	−	0.571666i	$-0.193703\pi$
$67$	2.70669e8	1.64097	0.820486	+	0.571666i	$0.193703\pi$
$68$	1.59833e8	0.906516
$69$	−5.41432e8	−2.87556
$70$	8.93732e7	0.444904
$71$	2.67893e8	1.25112	0.625560	−	0.780176i	$-0.284870\pi$
$71$	2.67893e8	1.25112	0.625560	+	0.780176i	$0.284870\pi$
$72$	9.46281e7	0.414977
$73$	2.72432e8	1.12281	0.561404	−	0.827542i	$-0.310261\pi$
$73$	2.72432e8	1.12281	0.561404	+	0.827542i	$0.310261\pi$
$74$	−1.06660e8	−0.413484
$75$	2.56194e8	0.934959
$76$	−3.33622e7	−0.114708
$77$	−3.73025e8	−1.20929
$78$	3.35605e8	1.02660
$79$	−9.46452e7	−0.273386	−0.136693	−	0.990613i	$-0.543647\pi$
$79$	−9.46452e7	−0.273386	−0.136693	+	0.990613i	$0.543647\pi$
$80$	−5.53985e7	−0.151214
$81$	−3.08420e8	−0.796086
$82$	5.92142e7	0.144632
$83$	6.12610e8	1.41688	0.708439	−	0.705772i	$-0.249400\pi$
$83$	6.12610e8	1.41688	0.708439	+	0.705772i	$0.249400\pi$
$84$	3.49911e8	0.766833
$85$	−5.27769e8	−1.09663
$86$	3.24220e8	0.639141
$87$	−5.93234e8	−1.11017
$88$	2.31222e8	0.411014
$89$	2.50492e7	0.0423194	0.0211597	−	0.999776i	$-0.493264\pi$
$89$	2.50492e7	0.0423194	0.0211597	+	0.999776i	$0.493264\pi$
$90$	−3.12463e8	−0.502004
$91$	6.70084e8	1.02434
$92$	6.70093e8	0.975192
$93$	5.06709e8	0.702401
$94$	1.48038e8	0.195568
$95$	1.10162e8	0.138764
$96$	−2.16894e8	−0.260632
$97$	8.03901e7	0.0921998	0.0460999	−	0.998937i	$-0.485321\pi$
$97$	8.03901e7	0.0921998	0.0460999	+	0.998937i	$0.485321\pi$
$98$	5.29895e7	0.0580327
$99$	1.30415e9	1.36449
$100$	−3.17073e8	−0.317073
$101$	−5.53223e7	−0.0528998	−0.0264499	−	0.999650i	$-0.508420\pi$
$101$	−5.53223e7	−0.0528998	−0.0264499	+	0.999650i	$0.508420\pi$
$102$	−2.06630e9	−1.89014
$103$	1.38567e9	1.21309	0.606544	−	0.795050i	$-0.292555\pi$
$103$	1.38567e9	1.21309	0.606544	+	0.795050i	$0.292555\pi$
$104$	−4.15356e8	−0.348153
$105$	−1.15541e9	−0.927650
$106$	−5.10404e8	−0.392679
$107$	1.59612e9	1.17717	0.588583	−	0.808437i	$-0.299686\pi$
$107$	1.59612e9	1.17717	0.588583	+	0.808437i	$0.299686\pi$
$108$	−1.81075e8	−0.128071
$109$	−1.19649e8	−0.0811876	−0.0405938	−	0.999176i	$-0.512925\pi$
$109$	−1.19649e8	−0.0811876	−0.0405938	+	0.999176i	$0.512925\pi$
$110$	−7.63497e8	−0.497210
$111$	1.37889e9	0.862137
$112$	−4.33061e8	−0.260057
$113$	2.30409e9	1.32937	0.664687	−	0.747122i	$-0.268565\pi$
$113$	2.30409e9	1.32937	0.664687	+	0.747122i	$0.268565\pi$
$114$	4.31303e8	0.239172
$115$	−2.21266e9	−1.17971
$116$	7.34205e8	0.376493
$117$	−2.34272e9	−1.15580
$118$	−2.15177e9	−1.02171
$119$	−4.12567e9	−1.88596
$120$	7.16188e8	0.315291
$121$	8.28724e8	0.351460
$122$	−6.78859e8	−0.277434
$123$	−7.65516e8	−0.301565
$124$	−6.27119e8	−0.238206
$125$	2.69799e9	0.988427
$126$	−2.44258e9	−0.863339
$127$	−7.12901e8	−0.243171	−0.121586	−	0.992581i	$-0.538798\pi$
$127$	−7.12901e8	−0.243171	−0.121586	+	0.992581i	$0.538798\pi$
$128$	2.68435e8	0.0883883
$129$	−4.19149e9	−1.33264
$130$	1.37151e9	0.421166
$131$	4.90435e9	1.45499	0.727496	−	0.686111i	$-0.240684\pi$
$131$	4.90435e9	1.45499	0.727496	+	0.686111i	$0.240684\pi$
$132$	−2.98922e9	−0.856988
$133$	8.61159e8	0.238644
$134$	4.33070e9	1.16034
$135$	5.97911e8	0.154930
$136$	2.55732e9	0.641004
$137$	3.64681e9	0.884444	0.442222	−	0.896906i	$-0.354190\pi$
$137$	3.64681e9	0.884444	0.442222	+	0.896906i	$0.354190\pi$
$138$	−8.66291e9	−2.03333
$139$	−5.71759e9	−1.29911	−0.649555	−	0.760314i	$-0.725045\pi$
$139$	−5.71759e9	−1.29911	−0.649555	+	0.760314i	$0.725045\pi$
$140$	1.42997e9	0.314595
$141$	−1.91383e9	−0.407771
$142$	4.28629e9	0.884676
$143$	−5.72439e9	−1.14477
$144$	1.51405e9	0.293433
$145$	−2.42435e9	−0.455449
$146$	4.35891e9	0.793945
$147$	−6.85044e8	−0.121001
$148$	−1.70656e9	−0.292377
$149$	−1.20353e9	−0.200040	−0.100020	−	0.994985i	$-0.531891\pi$
$149$	−1.20353e9	−0.200040	−0.100020	+	0.994985i	$0.531891\pi$
$150$	4.09910e9	0.661116
$151$	7.99457e9	1.25141	0.625704	−	0.780061i	$-0.284812\pi$
$151$	7.99457e9	1.25141	0.625704	+	0.780061i	$0.284812\pi$
$152$	−5.33795e8	−0.0811107
$153$	1.44240e10	2.12801
$154$	−5.96840e9	−0.855095
$155$	2.07075e9	0.288161
$156$	5.36969e9	0.725919
$157$	4.88685e9	0.641920	0.320960	−	0.947093i	$-0.395995\pi$
$157$	4.88685e9	0.641920	0.320960	+	0.947093i	$0.395995\pi$
$158$	−1.51432e9	−0.193313
$159$	6.59845e9	0.818757
$160$	−8.86377e8	−0.106925
$161$	−1.72967e10	−2.02884
$162$	−4.93472e9	−0.562918
$163$	−5.04358e9	−0.559622	−0.279811	−	0.960055i	$-0.590272\pi$
$163$	−5.04358e9	−0.559622	−0.279811	+	0.960055i	$0.590272\pi$
$164$	9.47427e8	0.102270
$165$	9.87042e9	1.03671
$166$	9.80176e9	1.00188
$167$	−1.80629e10	−1.79707	−0.898533	−	0.438907i	$-0.855366\pi$
$167$	−1.80629e10	−1.79707	−0.898533	+	0.438907i	$0.855366\pi$
$168$	5.59857e9	0.542233
$169$	−3.21480e8	−0.0303155
$170$	−8.44431e9	−0.775433
$171$	−3.01075e9	−0.269272
$172$	5.18752e9	0.451941
$173$	−1.62799e10	−1.38180	−0.690899	−	0.722952i	$-0.742785\pi$
$173$	−1.62799e10	−1.38180	−0.690899	+	0.722952i	$0.742785\pi$
$174$	−9.49175e9	−0.785009
$175$	8.18444e9	0.659656
$176$	3.69955e9	0.290631
$177$	2.78179e10	2.13032
$178$	4.00787e8	0.0299243
$179$	1.29852e9	0.0945385	0.0472693	−	0.998882i	$-0.484948\pi$
$179$	1.29852e9	0.0945385	0.0472693	+	0.998882i	$0.484948\pi$
$180$	−4.99941e9	−0.354970
$181$	−2.61567e10	−1.81146	−0.905730	−	0.423855i	$-0.860676\pi$
$181$	−2.61567e10	−1.81146	−0.905730	+	0.423855i	$0.860676\pi$
$182$	1.07213e10	0.724316
$183$	8.77623e9	0.578466
$184$	1.07215e10	0.689565
$185$	5.63507e9	0.353693
$186$	8.10734e9	0.496673
$187$	3.52448e10	2.10769
$188$	2.36861e9	0.138288
$189$	4.67398e9	0.266446
$190$	1.76260e9	0.0981209
$191$	2.34031e10	1.27240	0.636199	−	0.771525i	$-0.280506\pi$
$191$	2.34031e10	1.27240	0.636199	+	0.771525i	$0.280506\pi$
$192$	−3.47031e9	−0.184295
$193$	−5.69597e9	−0.295501	−0.147751	−	0.989025i	$-0.547203\pi$
$193$	−5.69597e9	−0.295501	−0.147751	+	0.989025i	$0.547203\pi$
$194$	1.28624e9	0.0651951
$195$	−1.77308e10	−0.878156
$196$	8.47832e8	0.0410353
$197$	3.89538e9	0.184269	0.0921343	−	0.995747i	$-0.470631\pi$
$197$	3.89538e9	0.184269	0.0921343	+	0.995747i	$0.470631\pi$
$198$	2.08665e10	0.964840
$199$	−3.42553e10	−1.54842	−0.774210	−	0.632929i	$-0.781853\pi$
$199$	−3.42553e10	−1.54842	−0.774210	+	0.632929i	$0.781853\pi$
$200$	−5.07317e9	−0.224205
$201$	−5.59869e10	−2.41938
$202$	−8.85157e8	−0.0374058
$203$	−1.89516e10	−0.783275
$204$	−3.30609e10	−1.33653
$205$	−3.12841e9	−0.123718
$206$	2.21707e10	0.857783
$207$	6.04721e10	2.28923
$208$	−6.64569e9	−0.246181
$209$	−7.35670e9	−0.266701
$210$	−1.84866e10	−0.655948
$211$	−2.23159e10	−0.775075	−0.387538	−	0.921854i	$-0.626674\pi$
$211$	−2.23159e10	−0.775075	−0.387538	+	0.921854i	$0.626674\pi$
$212$	−8.16646e9	−0.277666
$213$	−5.54128e10	−1.84460
$214$	2.55379e10	0.832382
$215$	−1.71292e10	−0.546720
$216$	−2.89719e9	−0.0905599
$217$	1.61875e10	0.495576
$218$	−1.91438e9	−0.0574083
$219$	−5.63517e10	−1.65542
$220$	−1.22159e10	−0.351581
$221$	−6.33120e10	−1.78534
$222$	2.20622e10	0.609623
$223$	5.10965e10	1.38363	0.691814	−	0.722075i	$-0.256812\pi$
$223$	5.10965e10	1.38363	0.691814	+	0.722075i	$0.256812\pi$
$224$	−6.92897e9	−0.183888
$225$	−2.86141e10	−0.744318
$226$	3.68655e10	0.940010
$227$	2.02005e10	0.504946	0.252473	−	0.967604i	$-0.418756\pi$
$227$	2.02005e10	0.504946	0.252473	+	0.967604i	$0.418756\pi$
$228$	6.90086e9	0.169120
$229$	5.41812e9	0.130193	0.0650967	−	0.997879i	$-0.479264\pi$
$229$	5.41812e9	0.130193	0.0650967	+	0.997879i	$0.479264\pi$
$230$	−3.54025e10	−0.834178
$231$	7.71589e10	1.78292
$232$	1.17473e10	0.266221
$233$	−8.78210e10	−1.95208	−0.976038	−	0.217598i	$-0.930178\pi$
$233$	−8.78210e10	−1.95208	−0.976038	+	0.217598i	$0.930178\pi$
$234$	−3.74835e10	−0.817276
$235$	−7.82118e9	−0.167289
$236$	−3.44283e10	−0.722455
$237$	1.95770e10	0.403069
$238$	−6.60108e10	−1.33358
$239$	8.01415e10	1.58879	0.794395	−	0.607401i	$-0.207788\pi$
$239$	8.01415e10	1.58879	0.794395	+	0.607401i	$0.207788\pi$
$240$	1.14590e10	0.222944
$241$	8.20990e10	1.56769	0.783846	−	0.620955i	$-0.213255\pi$
$241$	8.20990e10	1.56769	0.783846	+	0.620955i	$0.213255\pi$
$242$	1.32596e10	0.248520
$243$	7.77179e10	1.42986
$244$	−1.08617e10	−0.196176
$245$	−2.79955e9	−0.0496410
$246$	−1.22483e10	−0.213239
$247$	1.32152e10	0.225912
$248$	−1.00339e10	−0.168437
$249$	−1.26716e11	−2.08899
$250$	4.31678e10	0.698923
$251$	1.05193e11	1.67284	0.836421	−	0.548087i	$-0.184644\pi$
$251$	1.05193e11	1.67284	0.836421	+	0.548087i	$0.184644\pi$
$252$	−3.90813e10	−0.610473
$253$	1.47762e11	2.26737
$254$	−1.14064e10	−0.171948
$255$	1.09167e11	1.61682
$256$	4.29497e9	0.0625000
$257$	1.05293e11	1.50557	0.752785	−	0.658266i	$-0.228710\pi$
$257$	1.05293e11	1.50557	0.752785	+	0.658266i	$0.228710\pi$
$258$	−6.70638e10	−0.942322
$259$	4.40504e10	0.608277
$260$	2.19441e10	0.297810
$261$	6.62579e10	0.883803
$262$	7.84696e10	1.02884
$263$	−3.06635e10	−0.395204	−0.197602	−	0.980282i	$-0.563315\pi$
$263$	−3.06635e10	−0.395204	−0.197602	+	0.980282i	$0.563315\pi$
$264$	−4.78274e10	−0.605982
$265$	2.69657e10	0.335897
$266$	1.37785e10	0.168747
$267$	−5.18135e9	−0.0623939
$268$	6.92912e10	0.820486
$269$	−1.04539e11	−1.21728	−0.608641	−	0.793446i	$-0.708285\pi$
$269$	−1.04539e11	−1.21728	−0.608641	+	0.793446i	$0.708285\pi$
$270$	9.56657e9	0.109552
$271$	−2.13535e10	−0.240496	−0.120248	−	0.992744i	$-0.538369\pi$
$271$	−2.13535e10	−0.240496	−0.120248	+	0.992744i	$0.538369\pi$
$272$	4.09172e10	0.453258
$273$	−1.38605e11	−1.51024
$274$	5.83490e10	0.625397
$275$	−6.99179e10	−0.737210
$276$	−1.38607e11	−1.43778
$277$	5.19260e9	0.0529940	0.0264970	−	0.999649i	$-0.491565\pi$
$277$	5.19260e9	0.0529940	0.0264970	+	0.999649i	$0.491565\pi$
$278$	−9.14814e10	−0.918610
$279$	−5.65939e10	−0.559179
$280$	2.28795e10	0.222452
$281$	−8.01407e10	−0.766787	−0.383394	−	0.923585i	$-0.625245\pi$
$281$	−8.01407e10	−0.766787	−0.383394	+	0.923585i	$0.625245\pi$
$282$	−3.06212e10	−0.288338
$283$	−7.99995e10	−0.741393	−0.370696	−	0.928754i	$-0.620881\pi$
$283$	−7.99995e10	−0.741393	−0.370696	+	0.928754i	$0.620881\pi$
$284$	6.85807e10	0.625560
$285$	−2.27867e10	−0.204588
$286$	−9.15902e10	−0.809472
$287$	−2.44554e10	−0.212768
$288$	2.42248e10	0.207488
$289$	2.71221e11	2.28709
$290$	−3.87897e10	−0.322051
$291$	−1.66284e10	−0.135935
$292$	6.97426e10	0.561404
$293$	−1.16971e11	−0.927203	−0.463602	−	0.886044i	$-0.653443\pi$
$293$	−1.16971e11	−0.927203	−0.463602	+	0.886044i	$0.653443\pi$
$294$	−1.09607e10	−0.0855609
$295$	1.13682e11	0.873966
$296$	−2.73049e10	−0.206742
$297$	−3.99288e10	−0.297771
$298$	−1.92564e10	−0.141450
$299$	−2.65433e11	−1.92059
$300$	6.55856e10	0.467480
$301$	−1.33902e11	−0.940241
$302$	1.27913e11	0.884879
$303$	1.14432e10	0.0779932
$304$	−8.54072e9	−0.0573539
$305$	3.58656e10	0.237317
$306$	2.30784e11	1.50473
$307$	7.32180e10	0.470430	0.235215	−	0.971943i	$-0.424421\pi$
$307$	7.32180e10	0.470430	0.235215	+	0.971943i	$0.424421\pi$
$308$	−9.54943e10	−0.604644
$309$	−2.86621e11	−1.78853
$310$	3.31320e10	0.203761
$311$	3.05081e11	1.84924	0.924619	−	0.380893i	$-0.124383\pi$
$311$	3.05081e11	1.84924	0.924619	+	0.380893i	$0.124383\pi$
$312$	8.59150e10	0.513302
$313$	3.41729e10	0.201248	0.100624	−	0.994925i	$-0.467916\pi$
$313$	3.41729e10	0.201248	0.100624	+	0.994925i	$0.467916\pi$
$314$	7.81897e10	0.453906
$315$	1.29047e11	0.738499
$316$	−2.42292e10	−0.136693
$317$	−1.49061e11	−0.829083	−0.414541	−	0.910030i	$-0.636058\pi$
$317$	−1.49061e11	−0.829083	−0.414541	+	0.910030i	$0.636058\pi$
$318$	1.05575e11	0.578949
$319$	1.61900e11	0.875363
$320$	−1.41820e10	−0.0756072
$321$	−3.30152e11	−1.73556
$322$	−2.76748e11	−1.43461
$323$	−8.13655e10	−0.415938
$324$	−7.89555e10	−0.398043
$325$	1.25597e11	0.624461
$326$	−8.06972e10	−0.395712
$327$	2.47490e10	0.119700
$328$	1.51588e10	0.0723159
$329$	−6.11396e10	−0.287701
$330$	1.57927e11	0.733066
$331$	−2.80683e11	−1.28526	−0.642630	−	0.766177i	$-0.722157\pi$
$331$	−2.80683e11	−1.28526	−0.642630	+	0.766177i	$0.722157\pi$
$332$	1.56828e11	0.708439
$333$	−1.54007e11	−0.686344
$334$	−2.89007e11	−1.27072
$335$	−2.28800e11	−0.992555
$336$	8.95772e10	0.383416
$337$	2.81220e11	1.18771	0.593856	−	0.804572i	$-0.297605\pi$
$337$	2.81220e11	1.18771	0.593856	+	0.804572i	$0.297605\pi$
$338$	−5.14369e9	−0.0214363
$339$	−4.76594e11	−1.95997
$340$	−1.35109e11	−0.548314
$341$	−1.38286e11	−0.553839
$342$	−4.81720e10	−0.190404
$343$	2.44771e11	0.954854
$344$	8.30003e10	0.319570
$345$	4.57680e11	1.73931
$346$	−2.60478e11	−0.977078
$347$	−1.32820e11	−0.491792	−0.245896	−	0.969296i	$-0.579082\pi$
$347$	−1.32820e11	−0.491792	−0.245896	+	0.969296i	$0.579082\pi$
$348$	−1.51868e11	−0.555085
$349$	3.22183e11	1.16249	0.581243	−	0.813730i	$-0.302567\pi$
$349$	3.22183e11	1.16249	0.581243	+	0.813730i	$0.302567\pi$
$350$	1.30951e11	0.466447
$351$	7.17262e10	0.252230
$352$	5.91928e10	0.205507
$353$	−1.54437e11	−0.529378	−0.264689	−	0.964334i	$-0.585269\pi$
$353$	−1.54437e11	−0.529378	−0.264689	+	0.964334i	$0.585269\pi$
$354$	4.45086e11	1.50636
$355$	−2.26454e11	−0.756750
$356$	6.41260e9	0.0211597
$357$	8.53382e11	2.78059
$358$	2.07763e10	0.0668488
$359$	4.71815e11	1.49916	0.749578	−	0.661916i	$-0.230256\pi$
$359$	4.71815e11	1.49916	0.749578	+	0.661916i	$0.230256\pi$
$360$	−7.99905e10	−0.251002
$361$	1.69836e10	0.0526316
$362$	−4.18507e11	−1.28090
$363$	−1.71419e11	−0.518178
$364$	1.71542e11	0.512169
$365$	−2.30291e11	−0.679139
$366$	1.40420e11	0.409038
$367$	−2.36396e11	−0.680210	−0.340105	−	0.940388i	$-0.610463\pi$
$367$	−2.36396e11	−0.680210	−0.340105	+	0.940388i	$0.610463\pi$
$368$	1.71544e11	0.487596
$369$	8.54999e10	0.240075
$370$	9.01612e10	0.250099
$371$	2.10796e11	0.577670
$372$	1.29717e11	0.351201
$373$	2.37957e10	0.0636515	0.0318258	−	0.999493i	$-0.489868\pi$
$373$	2.37957e10	0.0636515	0.0318258	+	0.999493i	$0.489868\pi$
$374$	5.63916e11	1.49036
$375$	−5.58069e11	−1.45729
$376$	3.78978e10	0.0977842
$377$	−2.90829e11	−0.741484
$378$	7.47837e10	0.188406
$379$	−5.99221e11	−1.49180	−0.745900	−	0.666058i	$-0.767980\pi$
$379$	−5.99221e11	−1.49180	−0.745900	+	0.666058i	$0.767980\pi$
$380$	2.82015e10	0.0693820
$381$	1.47461e11	0.358522
$382$	3.74450e11	0.899722
$383$	−2.76508e11	−0.656619	−0.328310	−	0.944570i	$-0.606479\pi$
$383$	−2.76508e11	−0.656619	−0.328310	+	0.944570i	$0.606479\pi$
$384$	−5.55250e10	−0.130316
$385$	3.15323e11	0.731447
$386$	−9.11355e10	−0.208951
$387$	4.68144e11	1.06091
$388$	2.05799e10	0.0460999
$389$	5.87952e11	1.30187	0.650936	−	0.759132i	$-0.274377\pi$
$389$	5.87952e11	1.30187	0.650936	+	0.759132i	$0.274377\pi$
$390$	−2.83692e11	−0.620950
$391$	1.63426e12	3.53611
$392$	1.35653e10	0.0290163
$393$	−1.01445e12	−2.14518
$394$	6.23260e10	0.130298
$395$	8.00049e10	0.165360
$396$	3.33863e11	0.682245
$397$	−7.56517e11	−1.52849	−0.764243	−	0.644929i	$-0.776887\pi$
$397$	−7.56517e11	−1.52849	−0.764243	+	0.644929i	$0.776887\pi$
$398$	−5.48085e11	−1.09490
$399$	−1.78128e11	−0.351847
$400$	−8.11708e10	−0.158537
$401$	8.23616e11	1.59065	0.795326	−	0.606183i	$-0.207300\pi$
$401$	8.23616e11	1.59065	0.795326	+	0.606183i	$0.207300\pi$
$402$	−8.95790e11	−1.71076
$403$	2.48411e11	0.469135
$404$	−1.41625e10	−0.0264499
$405$	2.60712e11	0.481519
$406$	−3.03226e11	−0.553859
$407$	−3.76314e11	−0.679790
$408$	−5.28974e11	−0.945069
$409$	−6.88609e11	−1.21680	−0.608398	−	0.793632i	$-0.708188\pi$
$409$	−6.88609e11	−1.21680	−0.608398	+	0.793632i	$0.708188\pi$
$410$	−5.00546e10	−0.0874816
$411$	−7.54331e11	−1.30399
$412$	3.54732e11	0.606544
$413$	8.88677e11	1.50303
$414$	9.67554e11	1.61873
$415$	−5.17848e11	−0.857010
$416$	−1.06331e11	−0.174077
$417$	1.18266e12	1.91535
$418$	−1.17707e11	−0.188586
$419$	−3.80083e11	−0.602443	−0.301221	−	0.953554i	$-0.597394\pi$
$419$	−3.80083e11	−0.602443	−0.301221	+	0.953554i	$0.597394\pi$
$420$	−2.95785e11	−0.463825
$421$	−4.07825e11	−0.632709	−0.316355	−	0.948641i	$-0.602459\pi$
$421$	−4.07825e11	−0.632709	−0.316355	+	0.948641i	$0.602459\pi$
$422$	−3.57055e11	−0.548061
$423$	2.13754e11	0.324625
$424$	−1.30663e11	−0.196339
$425$	−7.73296e11	−1.14973
$426$	−8.86605e11	−1.30433
$427$	2.80368e11	0.408134
$428$	4.08606e11	0.588583
$429$	1.18407e12	1.68780
$430$	−2.74068e11	−0.386589
$431$	1.31622e11	0.183730	0.0918652	−	0.995771i	$-0.470717\pi$
$431$	1.31622e11	0.183730	0.0918652	+	0.995771i	$0.470717\pi$
$432$	−4.63551e10	−0.0640355
$433$	−4.03435e11	−0.551542	−0.275771	−	0.961223i	$-0.588933\pi$
$433$	−4.03435e11	−0.551542	−0.275771	+	0.961223i	$0.588933\pi$
$434$	2.58999e11	0.350425
$435$	5.01470e11	0.671495
$436$	−3.06301e10	−0.0405938
$437$	−3.41122e11	−0.447449
$438$	−9.01627e11	−1.17056
$439$	3.67019e11	0.471627	0.235813	−	0.971798i	$-0.424225\pi$
$439$	3.67019e11	0.471627	0.235813	+	0.971798i	$0.424225\pi$
$440$	−1.95455e11	−0.248605
$441$	7.65120e10	0.0963288
$442$	−1.01299e12	−1.26243
$443$	1.13716e12	1.40283	0.701413	−	0.712755i	$-0.252553\pi$
$443$	1.13716e12	1.40283	0.701413	+	0.712755i	$0.252553\pi$
$444$	3.52996e11	0.431069
$445$	−2.11745e10	−0.0255972
$446$	8.17545e11	0.978373
$447$	2.48946e11	0.294931
$448$	−1.10864e11	−0.130028
$449$	−2.91536e11	−0.338520	−0.169260	−	0.985571i	$-0.554138\pi$
$449$	−2.91536e11	−0.338520	−0.169260	+	0.985571i	$0.554138\pi$
$450$	−4.57825e11	−0.526312
$451$	2.08917e11	0.237783
$452$	5.89848e11	0.664687
$453$	−1.65365e12	−1.84502
$454$	3.23207e11	0.357051
$455$	−5.66432e11	−0.619579
$456$	1.10414e11	0.119586
$457$	6.40979e11	0.687418	0.343709	−	0.939076i	$-0.388317\pi$
$457$	6.40979e11	0.687418	0.343709	+	0.939076i	$0.388317\pi$
$458$	8.66899e10	0.0920606
$459$	−4.41615e11	−0.464394
$460$	−5.66440e11	−0.589853
$461$	2.34006e11	0.241309	0.120654	−	0.992695i	$-0.461501\pi$
$461$	2.34006e11	0.241309	0.120654	+	0.992695i	$0.461501\pi$
$462$	1.23454e12	1.26072
$463$	−1.40386e12	−1.41974	−0.709869	−	0.704334i	$-0.751246\pi$
$463$	−1.40386e12	−1.41974	−0.709869	+	0.704334i	$0.751246\pi$
$464$	1.87957e11	0.188246
$465$	−4.28328e11	−0.424853
$466$	−1.40514e12	−1.38033
$467$	−2.52215e11	−0.245383	−0.122691	−	0.992445i	$-0.539153\pi$
$467$	−2.52215e11	−0.245383	−0.122691	+	0.992445i	$0.539153\pi$
$468$	−5.99736e11	−0.577902
$469$	−1.78857e12	−1.70698
$470$	−1.25139e11	−0.118291
$471$	−1.01083e12	−0.946420
$472$	−5.50852e11	−0.510853
$473$	1.14390e12	1.05078
$474$	3.13233e11	0.285013
$475$	1.61411e11	0.145483
$476$	−1.05617e12	−0.942982
$477$	−7.36976e11	−0.651810
$478$	1.28226e12	1.12344
$479$	1.11246e11	0.0965550	0.0482775	−	0.998834i	$-0.484627\pi$
$479$	1.11246e11	0.0965550	0.0482775	+	0.998834i	$0.484627\pi$
$480$	1.83344e11	0.157645
$481$	6.75992e11	0.575822
$482$	1.31358e12	1.10853
$483$	3.57777e12	2.99124
$484$	2.12153e11	0.175730
$485$	−6.79549e10	−0.0557678
$486$	1.24349e12	1.01106
$487$	−7.14621e11	−0.575699	−0.287850	−	0.957676i	$-0.592940\pi$
$487$	−7.14621e11	−0.575699	−0.287850	+	0.957676i	$0.592940\pi$
$488$	−1.73788e11	−0.138717
$489$	1.04325e12	0.825083
$490$	−4.47928e10	−0.0351015
$491$	−7.32610e11	−0.568861	−0.284431	−	0.958697i	$-0.591805\pi$
$491$	−7.32610e11	−0.568861	−0.284431	+	0.958697i	$0.591805\pi$
$492$	−1.95972e11	−0.150783
$493$	1.79062e12	1.36519
$494$	2.11444e11	0.159744
$495$	−1.10242e12	−0.825322
$496$	−1.60542e11	−0.119103
$497$	−1.77023e12	−1.30145
$498$	−2.02746e12	−1.47714
$499$	−1.78905e12	−1.29172	−0.645862	−	0.763454i	$-0.723502\pi$
$499$	−1.78905e12	−1.29172	−0.645862	+	0.763454i	$0.723502\pi$
$500$	6.90684e11	0.494213
$501$	3.73626e12	2.64952
$502$	1.68309e12	1.18288
$503$	−6.21430e11	−0.432849	−0.216424	−	0.976299i	$-0.569439\pi$
$503$	−6.21430e11	−0.432849	−0.216424	+	0.976299i	$0.569439\pi$
$504$	−6.25301e11	−0.431670
$505$	4.67647e10	0.0319969
$506$	2.36420e12	1.60327
$507$	6.64972e10	0.0446959
$508$	−1.82503e11	−0.121586
$509$	−3.21924e11	−0.212580	−0.106290	−	0.994335i	$-0.533897\pi$
$509$	−3.21924e11	−0.212580	−0.106290	+	0.994335i	$0.533897\pi$
$510$	1.74668e12	1.14327
$511$	−1.80023e12	−1.16797
$512$	6.87195e10	0.0441942
$513$	9.21790e10	0.0587630
$514$	1.68469e12	1.06460
$515$	−1.17133e12	−0.733746
$516$	−1.07302e12	−0.666322
$517$	5.22303e11	0.321525
$518$	7.04807e11	0.430117
$519$	3.36744e12	2.03726
$520$	3.51106e11	0.210583
$521$	2.47818e12	1.47354	0.736772	−	0.676141i	$-0.236349\pi$
$521$	2.47818e12	1.47354	0.736772	+	0.676141i	$0.236349\pi$
$522$	1.06013e12	0.624943
$523$	−1.02959e12	−0.601737	−0.300868	−	0.953666i	$-0.597276\pi$
$523$	−1.02959e12	−0.601737	−0.300868	+	0.953666i	$0.597276\pi$
$524$	1.25551e12	0.727496
$525$	−1.69292e12	−0.972569
$526$	−4.90617e11	−0.279451
$527$	−1.52945e12	−0.863750
$528$	−7.65239e11	−0.428494
$529$	5.05043e12	2.80400
$530$	4.31452e11	0.237515
$531$	−3.10696e12	−1.69594
$532$	2.20457e11	0.119322
$533$	−3.75289e11	−0.201416
$534$	−8.29015e10	−0.0441191
$535$	−1.34922e12	−0.712018
$536$	1.10866e12	0.580171
$537$	−2.68594e11	−0.139384
$538$	−1.67262e12	−0.860748
$539$	1.86956e11	0.0954089
$540$	1.53065e11	0.0774648
$541$	−1.59499e11	−0.0800518	−0.0400259	−	0.999199i	$-0.512744\pi$
$541$	−1.59499e11	−0.0800518	−0.0400259	+	0.999199i	$0.512744\pi$
$542$	−3.41656e11	−0.170056
$543$	5.41042e12	2.67074
$544$	6.54675e11	0.320502
$545$	1.01141e11	0.0491070
$546$	−2.21767e12	−1.06790
$547$	−2.01115e12	−0.960507	−0.480253	−	0.877130i	$-0.659455\pi$
$547$	−2.01115e12	−0.960507	−0.480253	+	0.877130i	$0.659455\pi$
$548$	9.33583e11	0.442222
$549$	−9.80211e11	−0.460515
$550$	−1.11869e12	−0.521286
$551$	−3.73759e11	−0.172747
$552$	−2.21771e12	−1.01667
$553$	6.25414e11	0.284383
$554$	8.30817e10	0.0374724
$555$	−1.16560e12	−0.521470
$556$	−1.46370e12	−0.649555
$557$	2.36839e12	1.04257	0.521285	−	0.853383i	$-0.325453\pi$
$557$	2.36839e12	1.04257	0.521285	+	0.853383i	$0.325453\pi$
$558$	−9.05503e11	−0.395399
$559$	−2.05485e12	−0.890075
$560$	3.66073e11	0.157297
$561$	−7.29026e12	−3.10749
$562$	−1.28225e12	−0.542200
$563$	2.58137e12	1.08284	0.541418	−	0.840753i	$-0.317888\pi$
$563$	2.58137e12	1.08284	0.541418	+	0.840753i	$0.317888\pi$
$564$	−4.89939e11	−0.203886
$565$	−1.94769e12	−0.804083
$566$	−1.27999e12	−0.524244
$567$	2.03804e12	0.828110
$568$	1.09729e12	0.442338
$569$	−1.17458e12	−0.469760	−0.234880	−	0.972024i	$-0.575470\pi$
$569$	−1.17458e12	−0.469760	−0.234880	+	0.972024i	$0.575470\pi$
$570$	−3.64587e11	−0.144665
$571$	2.83392e11	0.111564	0.0557822	−	0.998443i	$-0.482235\pi$
$571$	2.83392e11	0.111564	0.0557822	+	0.998443i	$0.482235\pi$
$572$	−1.46544e12	−0.572383
$573$	−4.84085e12	−1.87597
$574$	−3.91286e11	−0.150450
$575$	−3.24202e12	−1.23683
$576$	3.87597e11	0.146716
$577$	5.05702e12	1.89934	0.949671	−	0.313248i	$-0.101417\pi$
$577$	5.05702e12	1.89934	0.949671	+	0.313248i	$0.101417\pi$
$578$	4.33953e12	1.61721
$579$	1.17819e12	0.435675
$580$	−6.20635e11	−0.227725
$581$	−4.04812e12	−1.47387
$582$	−2.66055e11	−0.0961209
$583$	−1.80079e12	−0.645586
$584$	1.11588e12	0.396972
$585$	1.98034e12	0.699097
$586$	−1.87154e12	−0.655632
$587$	−5.33268e12	−1.85385	−0.926923	−	0.375251i	$-0.877556\pi$
$587$	−5.33268e12	−1.85385	−0.926923	+	0.375251i	$0.877556\pi$
$588$	−1.75371e11	−0.0605007
$589$	3.19245e11	0.109296
$590$	1.81892e12	0.617987
$591$	−8.05746e11	−0.271678
$592$	−4.36879e11	−0.146189
$593$	7.44755e11	0.247325	0.123662	−	0.992324i	$-0.460536\pi$
$593$	7.44755e11	0.247325	0.123662	+	0.992324i	$0.460536\pi$
$594$	−6.38861e11	−0.210556
$595$	3.48749e12	1.14074
$596$	−3.08103e11	−0.100020
$597$	7.08559e12	2.28293
$598$	−4.24694e12	−1.35806
$599$	−4.03747e12	−1.28141	−0.640706	−	0.767786i	$-0.721358\pi$
$599$	−4.03747e12	−1.28141	−0.640706	+	0.767786i	$0.721358\pi$
$600$	1.04937e12	0.330558
$601$	−1.69994e12	−0.531493	−0.265747	−	0.964043i	$-0.585618\pi$
$601$	−1.69994e12	−0.531493	−0.265747	+	0.964043i	$0.585618\pi$
$602$	−2.14244e12	−0.664851
$603$	6.25313e12	1.92606
$604$	2.04661e12	0.625704
$605$	−7.00533e11	−0.212583
$606$	1.83092e11	0.0551495
$607$	−1.78826e12	−0.534665	−0.267332	−	0.963604i	$-0.586142\pi$
$607$	−1.78826e12	−0.534665	−0.267332	+	0.963604i	$0.586142\pi$
$608$	−1.36651e11	−0.0405554
$609$	3.92008e12	1.15483
$610$	5.73849e11	0.167808
$611$	−9.38241e11	−0.272351
$612$	3.69254e12	1.06401
$613$	1.12945e12	0.323070	0.161535	−	0.986867i	$-0.448356\pi$
$613$	1.12945e12	0.323070	0.161535	+	0.986867i	$0.448356\pi$
$614$	1.17149e12	0.332644
$615$	6.47102e11	0.182404
$616$	−1.52791e12	−0.427548
$617$	3.04020e12	0.844537	0.422269	−	0.906471i	$-0.361234\pi$
$617$	3.04020e12	0.844537	0.422269	+	0.906471i	$0.361234\pi$
$618$	−4.58594e12	−1.26468
$619$	3.80882e12	1.04276	0.521378	−	0.853326i	$-0.325418\pi$
$619$	3.80882e12	1.04276	0.521378	+	0.853326i	$0.325418\pi$
$620$	5.30113e11	0.144081
$621$	−1.85145e12	−0.499575
$622$	4.88129e12	1.30761
$623$	−1.65525e11	−0.0440217
$624$	1.37464e12	0.362959
$625$	1.38432e11	0.0362891
$626$	5.46766e11	0.142304
$627$	1.52171e12	0.393213
$628$	1.25103e12	0.320960
$629$	−4.16205e12	−1.06018
$630$	2.06475e12	0.522198
$631$	−4.63806e12	−1.16467	−0.582336	−	0.812948i	$-0.697861\pi$
$631$	−4.63806e12	−1.16467	−0.582336	+	0.812948i	$0.697861\pi$
$632$	−3.87667e11	−0.0966566
$633$	4.61598e12	1.14274
$634$	−2.38498e12	−0.586250
$635$	6.02626e11	0.147084
$636$	1.68920e12	0.409379
$637$	−3.35838e11	−0.0808170
$638$	2.59040e12	0.618975
$639$	6.18902e12	1.46848
$640$	−2.26912e11	−0.0534624
$641$	2.15146e12	0.503352	0.251676	−	0.967812i	$-0.419018\pi$
$641$	2.15146e12	0.503352	0.251676	+	0.967812i	$0.419018\pi$
$642$	−5.28243e12	−1.22723
$643$	−1.29916e12	−0.299718	−0.149859	−	0.988707i	$-0.547882\pi$
$643$	−1.29916e12	−0.299718	−0.149859	+	0.988707i	$0.547882\pi$
$644$	−4.42797e12	−1.01442
$645$	3.54313e12	0.806061
$646$	−1.30185e12	−0.294113
$647$	4.92268e12	1.10442	0.552208	−	0.833706i	$-0.313785\pi$
$647$	4.92268e12	1.10442	0.552208	+	0.833706i	$0.313785\pi$
$648$	−1.26329e12	−0.281459
$649$	−7.59178e12	−1.67974
$650$	2.00956e12	0.441560
$651$	−3.34832e12	−0.730656
$652$	−1.29116e12	−0.279811
$653$	−1.85912e12	−0.400126	−0.200063	−	0.979783i	$-0.564115\pi$
$653$	−1.85912e12	−0.400126	−0.200063	+	0.979783i	$0.564115\pi$
$654$	3.95984e11	0.0846404
$655$	−4.14572e12	−0.880064
$656$	2.42541e11	0.0511350
$657$	6.29388e12	1.31787
$658$	−9.78234e11	−0.203435
$659$	−2.37300e12	−0.490131	−0.245066	−	0.969506i	$-0.578810\pi$
$659$	−2.37300e12	−0.490131	−0.245066	+	0.969506i	$0.578810\pi$
$660$	2.52683e12	0.518356
$661$	−3.80465e12	−0.775190	−0.387595	−	0.921830i	$-0.626694\pi$
$661$	−3.80465e12	−0.775190	−0.387595	+	0.921830i	$0.626694\pi$
$662$	−4.49094e12	−0.908816
$663$	1.30959e13	2.63223
$664$	2.50925e12	0.500942
$665$	−7.27950e11	−0.144346
$666$	−2.46412e12	−0.485319
$667$	7.50711e12	1.46861
$668$	−4.62411e12	−0.898533
$669$	−1.05692e13	−2.03996
$670$	−3.66080e12	−0.701842
$671$	−2.39513e12	−0.456118
$672$	1.43324e12	0.271116
$673$	6.08819e12	1.14399	0.571993	−	0.820259i	$-0.306171\pi$
$673$	6.08819e12	1.14399	0.571993	+	0.820259i	$0.306171\pi$
$674$	4.49951e12	0.839839
$675$	8.76068e11	0.162432
$676$	−8.22990e10	−0.0151577
$677$	1.19617e12	0.218849	0.109425	−	0.993995i	$-0.465099\pi$
$677$	1.19617e12	0.218849	0.109425	+	0.993995i	$0.465099\pi$
$678$	−7.62551e12	−1.38591
$679$	−5.31217e11	−0.0959086
$680$	−2.16174e12	−0.387716
$681$	−4.17840e12	−0.744471
$682$	−2.21258e12	−0.391624
$683$	8.85156e11	0.155642	0.0778210	−	0.996967i	$-0.475204\pi$
$683$	8.85156e11	0.155642	0.0778210	+	0.996967i	$0.475204\pi$
$684$	−7.70751e11	−0.134636
$685$	−3.08270e12	−0.534963
$686$	3.91634e12	0.675184
$687$	−1.12072e12	−0.191952
$688$	1.32800e12	0.225970
$689$	3.23485e12	0.546849
$690$	7.32289e12	1.22988
$691$	1.12523e13	1.87755	0.938774	−	0.344533i	$-0.111963\pi$
$691$	1.12523e13	1.87755	0.938774	+	0.344533i	$0.111963\pi$
$692$	−4.16765e12	−0.690899
$693$	−8.61782e12	−1.41938
$694$	−2.12512e12	−0.347750
$695$	4.83316e12	0.785777
$696$	−2.42989e12	−0.392504
$697$	2.31064e12	0.370838
$698$	5.15492e12	0.822002
$699$	1.81655e13	2.87806
$700$	2.09522e12	0.329828
$701$	6.34827e12	0.992943	0.496472	−	0.868053i	$-0.334629\pi$
$701$	6.34827e12	0.992943	0.496472	+	0.868053i	$0.334629\pi$
$702$	1.14762e12	0.178353
$703$	8.68751e11	0.134152
$704$	9.47084e11	0.145315
$705$	1.61779e12	0.246644
$706$	−2.47100e12	−0.374327
$707$	3.65569e11	0.0550278
$708$	7.12137e12	1.06516
$709$	−4.39087e12	−0.652593	−0.326297	−	0.945267i	$-0.605801\pi$
$709$	−4.39087e12	−0.652593	−0.326297	+	0.945267i	$0.605801\pi$
$710$	−3.62326e12	−0.535103
$711$	−2.18654e12	−0.320882
$712$	1.02602e11	0.0149622
$713$	−6.41217e12	−0.929185
$714$	1.36541e13	1.96617
$715$	4.83891e12	0.692421
$716$	3.32420e11	0.0472693
$717$	−1.65770e13	−2.34245
$718$	7.54905e12	1.06006
$719$	−1.25472e13	−1.75093	−0.875463	−	0.483286i	$-0.839443\pi$
$719$	−1.25472e13	−1.75093	−0.875463	+	0.483286i	$0.839443\pi$
$720$	−1.27985e12	−0.177485
$721$	−9.15649e12	−1.26189
$722$	2.71737e11	0.0372161
$723$	−1.69819e13	−2.31134
$724$	−6.69610e12	−0.905730
$725$	−3.55220e12	−0.477503
$726$	−2.74270e12	−0.366407
$727$	−2.66870e12	−0.354320	−0.177160	−	0.984182i	$-0.556691\pi$
$727$	−2.66870e12	−0.354320	−0.177160	+	0.984182i	$0.556691\pi$
$728$	2.74466e12	0.362158
$729$	−1.00051e13	−1.31204
$730$	−3.68465e12	−0.480224
$731$	1.26516e13	1.63877
$732$	2.24672e12	0.289233
$733$	−4.69949e12	−0.601288	−0.300644	−	0.953736i	$-0.597202\pi$
$733$	−4.69949e12	−0.601288	−0.300644	+	0.953736i	$0.597202\pi$
$734$	−3.78234e12	−0.480981
$735$	5.79078e11	0.0731887
$736$	2.74470e12	0.344782
$737$	1.52794e13	1.90767
$738$	1.36800e12	0.169759
$739$	2.64399e12	0.326107	0.163053	−	0.986617i	$-0.447866\pi$
$739$	2.64399e12	0.326107	0.163053	+	0.986617i	$0.447866\pi$
$740$	1.44258e12	0.176847
$741$	−2.73353e12	−0.333074
$742$	3.37274e12	0.408475
$743$	−2.42749e12	−0.292219	−0.146109	−	0.989268i	$-0.546675\pi$
$743$	−2.42749e12	−0.292219	−0.146109	+	0.989268i	$0.546675\pi$
$744$	2.07548e12	0.248336
$745$	1.01736e12	0.120996
$746$	3.80731e11	0.0450084
$747$	1.41528e13	1.66303
$748$	9.02266e12	1.05385
$749$	−1.05471e13	−1.22452
$750$	−8.92911e12	−1.03046
$751$	7.04687e12	0.808382	0.404191	−	0.914675i	$-0.367553\pi$
$751$	7.04687e12	0.808382	0.404191	+	0.914675i	$0.367553\pi$
$752$	6.06365e11	0.0691438
$753$	−2.17588e13	−2.46637
$754$	−4.65327e12	−0.524308
$755$	−6.75793e12	−0.756924
$756$	1.19654e12	0.133223
$757$	8.95156e12	0.990758	0.495379	−	0.868677i	$-0.335029\pi$
$757$	8.95156e12	0.990758	0.495379	+	0.868677i	$0.335029\pi$
$758$	−9.58754e12	−1.05486
$759$	−3.05642e13	−3.34291
$760$	4.51225e11	0.0490605
$761$	−1.16001e13	−1.25381	−0.626905	−	0.779096i	$-0.715678\pi$
$761$	−1.16001e13	−1.25381	−0.626905	+	0.779096i	$0.715678\pi$
$762$	2.35938e12	0.253513
$763$	7.90638e11	0.0844535
$764$	5.99119e12	0.636199
$765$	−1.21928e13	−1.28715
$766$	−4.42413e12	−0.464300
$767$	1.36375e13	1.42284
$768$	−8.88400e11	−0.0921474
$769$	3.31475e12	0.341808	0.170904	−	0.985288i	$-0.445331\pi$
$769$	3.31475e12	0.341808	0.170904	+	0.985288i	$0.445331\pi$
$770$	5.04517e12	0.517211
$771$	−2.17795e13	−2.21975
$772$	−1.45817e12	−0.147751
$773$	1.50546e13	1.51656	0.758282	−	0.651927i	$-0.226039\pi$
$773$	1.50546e13	1.51656	0.758282	+	0.651927i	$0.226039\pi$
$774$	7.49030e12	0.750179
$775$	3.03410e12	0.302115
$776$	3.29278e11	0.0325975
$777$	−9.11168e12	−0.896818
$778$	9.40723e12	0.920563
$779$	−4.82303e11	−0.0469247
$780$	−4.53907e12	−0.439078
$781$	1.51227e13	1.45446
$782$	2.61482e13	2.50041
$783$	−2.02860e12	−0.192871
$784$	2.17045e11	0.0205176
$785$	−4.13093e12	−0.388270
$786$	−1.62312e13	−1.51687
$787$	9.73805e12	0.904869	0.452434	−	0.891798i	$-0.350556\pi$
$787$	9.73805e12	0.904869	0.452434	+	0.891798i	$0.350556\pi$
$788$	9.97217e11	0.0921343
$789$	6.34265e12	0.582672
$790$	1.28008e12	0.116927
$791$	−1.52254e13	−1.38285
$792$	5.34181e12	0.482420
$793$	4.30249e12	0.386359
$794$	−1.21043e13	−1.08080
$795$	−5.57777e12	−0.495232
$796$	−8.76935e12	−0.774210
$797$	6.67166e12	0.585695	0.292847	−	0.956159i	$-0.405397\pi$
$797$	6.67166e12	0.585695	0.292847	+	0.956159i	$0.405397\pi$
$798$	−2.85005e12	−0.248793
$799$	5.77670e12	0.501440
$800$	−1.29873e12	−0.112102
$801$	5.78701e11	0.0496715
$802$	1.31779e13	1.12476
$803$	1.53790e13	1.30529
$804$	−1.43326e13	−1.20969
$805$	1.46212e13	1.22716
$806$	3.97457e12	0.331728
$807$	2.16234e13	1.79471
$808$	−2.26600e11	−0.0187029
$809$	1.67936e13	1.37840	0.689200	−	0.724572i	$-0.257962\pi$
$809$	1.67936e13	1.37840	0.689200	+	0.724572i	$0.257962\pi$
$810$	4.17139e12	0.340485
$811$	−1.81147e13	−1.47041	−0.735205	−	0.677845i	$-0.762914\pi$
$811$	−1.81147e13	−1.47041	−0.735205	+	0.677845i	$0.762914\pi$
$812$	−4.85162e12	−0.391638
$813$	4.41690e12	0.354577
$814$	−6.02102e12	−0.480684
$815$	4.26341e12	0.338492
$816$	−8.46358e12	−0.668265
$817$	−2.64079e12	−0.207365
$818$	−1.10177e13	−0.860405
$819$	1.54807e13	1.20230
$820$	−8.00874e11	−0.0618589
$821$	−2.26176e13	−1.73741	−0.868704	−	0.495331i	$-0.835047\pi$
$821$	−2.26176e13	−1.73741	−0.868704	+	0.495331i	$0.835047\pi$
$822$	−1.20693e13	−0.922059
$823$	−3.91065e12	−0.297132	−0.148566	−	0.988902i	$-0.547466\pi$
$823$	−3.91065e12	−0.297132	−0.148566	+	0.988902i	$0.547466\pi$
$824$	5.67571e12	0.428892
$825$	1.44623e13	1.08691
$826$	1.42188e13	1.06281
$827$	−5.82888e11	−0.0433322	−0.0216661	−	0.999765i	$-0.506897\pi$
$827$	−5.82888e11	−0.0433322	−0.0216661	+	0.999765i	$0.506897\pi$
$828$	1.54809e13	1.14461
$829$	2.07138e13	1.52323	0.761613	−	0.648032i	$-0.224408\pi$
$829$	2.07138e13	1.52323	0.761613	+	0.648032i	$0.224408\pi$
$830$	−8.28557e12	−0.605998
$831$	−1.07407e12	−0.0781321
$832$	−1.70130e12	−0.123091
$833$	2.06774e12	0.148797
$834$	1.89226e13	1.35436
$835$	1.52689e13	1.08697
$836$	−1.88332e12	−0.133351
$837$	1.73272e12	0.122029
$838$	−6.08133e12	−0.425991
$839$	9.57474e12	0.667111	0.333555	−	0.942730i	$-0.391752\pi$
$839$	9.57474e12	0.667111	0.333555	+	0.942730i	$0.391752\pi$
$840$	−4.73256e12	−0.327974
$841$	−6.28178e12	−0.433013
$842$	−6.52520e12	−0.447393
$843$	1.65768e13	1.13052
$844$	−5.71288e12	−0.387538
$845$	2.71752e11	0.0183366
$846$	3.42006e12	0.229545
$847$	−5.47620e12	−0.365598
$848$	−2.09061e12	−0.138833
$849$	1.65476e13	1.09308
$850$	−1.23727e13	−0.812981
$851$	−1.74492e13	−1.14050
$852$	−1.41857e13	−0.922300
$853$	−9.22119e12	−0.596371	−0.298186	−	0.954508i	$-0.596381\pi$
$853$	−9.22119e12	−0.596371	−0.298186	+	0.954508i	$0.596381\pi$
$854$	4.48589e12	0.288595
$855$	2.54503e12	0.162872
$856$	6.53770e12	0.416191
$857$	2.38518e13	1.51045	0.755227	−	0.655464i	$-0.227527\pi$
$857$	2.38518e13	1.51045	0.755227	+	0.655464i	$0.227527\pi$
$858$	1.89451e13	1.19345
$859$	1.01547e13	0.636352	0.318176	−	0.948032i	$-0.396930\pi$
$859$	1.01547e13	0.636352	0.318176	+	0.948032i	$0.396930\pi$
$860$	−4.38508e12	−0.273360
$861$	5.05852e12	0.313696
$862$	2.10595e12	0.129917
$863$	−2.32087e13	−1.42430	−0.712150	−	0.702027i	$-0.752278\pi$
$863$	−2.32087e13	−1.42430	−0.712150	+	0.702027i	$0.752278\pi$
$864$	−7.41682e11	−0.0452799
$865$	1.37616e13	0.835791
$866$	−6.45496e12	−0.389999
$867$	−5.61011e13	−3.37199
$868$	4.14399e12	0.247788
$869$	−5.34278e12	−0.317818
$870$	8.02351e12	0.474819
$871$	−2.74472e13	−1.61591
$872$	−4.90082e11	−0.0287042
$873$	1.85722e12	0.108218
$874$	−5.45795e12	−0.316394
$875$	−1.78282e13	−1.02819
$876$	−1.44260e13	−0.827710
$877$	−1.03798e11	−0.00592501	−0.00296251	−	0.999996i	$-0.500943\pi$
$877$	−1.03798e11	−0.00592501	−0.00296251	+	0.999996i	$0.500943\pi$
$878$	5.87231e12	0.333491
$879$	2.41951e13	1.36703
$880$	−3.12728e12	−0.175790
$881$	−1.16399e13	−0.650966	−0.325483	−	0.945548i	$-0.605527\pi$
$881$	−1.16399e13	−0.650966	−0.325483	+	0.945548i	$0.605527\pi$
$882$	1.22419e12	0.0681147
$883$	−1.20009e13	−0.664342	−0.332171	−	0.943219i	$-0.607781\pi$
$883$	−1.20009e13	−0.664342	−0.332171	+	0.943219i	$0.607781\pi$
$884$	−1.62079e13	−0.892670
$885$	−2.35148e13	−1.28854
$886$	1.81945e13	0.991948
$887$	3.10614e13	1.68486	0.842431	−	0.538804i	$-0.181124\pi$
$887$	3.10614e13	1.68486	0.842431	+	0.538804i	$0.181124\pi$
$888$	5.64793e12	0.304811
$889$	4.71084e12	0.252953
$890$	−3.38791e11	−0.0181000
$891$	−1.74105e13	−0.925469
$892$	1.30807e13	0.691814
$893$	−1.20578e12	−0.0634507
$894$	3.98313e12	0.208548
$895$	−1.09766e12	−0.0571824
$896$	−1.77382e12	−0.0919439
$897$	5.49040e13	2.83164
$898$	−4.66458e12	−0.239370
$899$	−7.02567e12	−0.358731
$900$	−7.32521e12	−0.372159
$901$	−1.99168e13	−1.00683
$902$	3.34268e12	0.168138
$903$	2.76973e13	1.38625
$904$	9.43757e12	0.470005
$905$	2.21106e13	1.09568
$906$	−2.64584e13	−1.30463
$907$	2.74070e12	0.134471	0.0672355	−	0.997737i	$-0.478582\pi$
$907$	2.74070e12	0.134471	0.0672355	+	0.997737i	$0.478582\pi$
$908$	5.17132e12	0.252473
$909$	−1.27809e12	−0.0620901
$910$	−9.06291e12	−0.438108
$911$	1.98126e13	0.953037	0.476518	−	0.879164i	$-0.341899\pi$
$911$	1.98126e13	0.953037	0.476518	+	0.879164i	$0.341899\pi$
$912$	1.76662e12	0.0845602
$913$	3.45822e13	1.64715
$914$	1.02557e13	0.486078
$915$	−7.41868e12	−0.349890
$916$	1.38704e12	0.0650967
$917$	−3.24079e13	−1.51352
$918$	−7.06584e12	−0.328376
$919$	1.57861e12	0.0730053	0.0365026	−	0.999334i	$-0.488378\pi$
$919$	1.57861e12	0.0730053	0.0365026	+	0.999334i	$0.488378\pi$
$920$	−9.06304e12	−0.417089
$921$	−1.51449e13	−0.693582
$922$	3.74410e12	0.170631
$923$	−2.71658e13	−1.23201
$924$	1.97527e13	0.891461
$925$	8.25660e12	0.370820
$926$	−2.24617e13	−1.00391
$927$	3.20125e13	1.42384
$928$	3.00731e12	0.133110
$929$	6.37690e12	0.280892	0.140446	−	0.990088i	$-0.455146\pi$
$929$	6.37690e12	0.280892	0.140446	+	0.990088i	$0.455146\pi$
$930$	−6.85325e12	−0.300416
$931$	−4.31603e11	−0.0188283
$932$	−2.24822e13	−0.976038
$933$	−6.31049e13	−2.72644
$934$	−4.03543e12	−0.173512
$935$	−2.97929e13	−1.27485
$936$	−9.59578e12	−0.408638
$937$	4.32674e12	0.183372	0.0916859	−	0.995788i	$-0.470774\pi$
$937$	4.32674e12	0.183372	0.0916859	+	0.995788i	$0.470774\pi$
$938$	−2.86172e13	−1.20702
$939$	−7.06854e12	−0.296712
$940$	−2.00222e12	−0.0836444
$941$	−3.31544e13	−1.37844	−0.689221	−	0.724551i	$-0.742047\pi$
$941$	−3.31544e13	−1.37844	−0.689221	+	0.724551i	$0.742047\pi$
$942$	−1.61733e13	−0.669220
$943$	9.68727e12	0.398932
$944$	−8.81364e12	−0.361228
$945$	−3.95098e12	−0.161162
$946$	1.83024e13	0.743016
$947$	−1.96120e13	−0.792406	−0.396203	−	0.918163i	$-0.629672\pi$
$947$	−1.96120e13	−0.792406	−0.396203	+	0.918163i	$0.629672\pi$
$948$	5.01172e12	0.201534
$949$	−2.76260e13	−1.10566
$950$	2.58258e12	0.102872
$951$	3.08328e13	1.22236
$952$	−1.68988e13	−0.666789
$953$	−2.71573e13	−1.06652	−0.533260	−	0.845951i	$-0.679033\pi$
$953$	−2.71573e13	−1.06652	−0.533260	+	0.845951i	$0.679033\pi$
$954$	−1.17916e13	−0.460899
$955$	−1.97830e13	−0.769621
$956$	2.05162e13	0.794395
$957$	−3.34884e13	−1.29060
$958$	1.77994e12	0.0682747
$959$	−2.40981e13	−0.920022
$960$	2.93351e12	0.111472
$961$	−2.04387e13	−0.773032
$962$	1.08159e13	0.407168
$963$	3.68744e13	1.38168
$964$	2.10173e13	0.783846
$965$	4.81489e12	0.178736
$966$	5.72444e13	2.11512
$967$	2.39547e13	0.880992	0.440496	−	0.897755i	$-0.354803\pi$
$967$	2.39547e13	0.880992	0.440496	+	0.897755i	$0.354803\pi$
$968$	3.39446e12	0.124260
$969$	1.68302e13	0.613242
$970$	−1.08728e12	−0.0394338
$971$	3.77872e13	1.36414	0.682068	−	0.731289i	$-0.261081\pi$
$971$	3.77872e13	1.36414	0.682068	+	0.731289i	$0.261081\pi$
$972$	1.98958e13	0.714929
$973$	3.77817e13	1.35137
$974$	−1.14339e13	−0.407081
$975$	−2.59794e13	−0.920679
$976$	−2.78061e12	−0.0980879
$977$	−6.72456e11	−0.0236123	−0.0118061	−	0.999930i	$-0.503758\pi$
$977$	−6.72456e11	−0.0236123	−0.0118061	+	0.999930i	$0.503758\pi$
$978$	1.66920e13	0.583421
$979$	1.41404e12	0.0491972
$980$	−7.16685e11	−0.0248205
$981$	−2.76420e12	−0.0952924
$982$	−1.17218e13	−0.402245
$983$	1.15186e13	0.393466	0.196733	−	0.980457i	$-0.436967\pi$
$983$	1.15186e13	0.393466	0.196733	+	0.980457i	$0.436967\pi$
$984$	−3.13555e12	−0.106619
$985$	−3.29282e12	−0.111456
$986$	2.86499e13	0.965333
$987$	1.26465e13	0.424174
$988$	3.38310e12	0.112956
$989$	5.30414e13	1.76292
$990$	−1.76387e13	−0.583591
$991$	2.90337e13	0.956250	0.478125	−	0.878292i	$-0.341317\pi$
$991$	2.90337e13	0.956250	0.478125	+	0.878292i	$0.341317\pi$
$992$	−2.56868e12	−0.0842185
$993$	5.80584e13	1.89493
$994$	−2.83237e13	−0.920263
$995$	2.89565e13	0.936574
$996$	−3.24394e13	−1.04449
$997$	−3.50537e13	−1.12358	−0.561792	−	0.827279i	$-0.689888\pi$
$997$	−3.50537e13	−1.12358	−0.561792	+	0.827279i	$0.689888\pi$
$998$	−2.86248e13	−0.913387
$999$	4.71519e12	0.149780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.a.e.1.1	✓	4
3.2	odd	2		342.10.a.i.1.3		4
4.3	odd	2		304.10.a.d.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.a.e.1.1	✓	4	1.1	even	1	trivial
304.10.a.d.1.4		4	4.3	odd	2
342.10.a.i.1.3		4	3.2	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -206.847 q^{3} +256.000 q^{4} -845.315 q^{5} -3309.55 q^{6} -6607.98 q^{7} +4096.00 q^{8} +23102.6 q^{9} +O(q^{10})\)	\(q+16.0000 q^{2} -206.847 q^{3} +256.000 q^{4} -845.315 q^{5} -3309.55 q^{6} -6607.98 q^{7} +4096.00 q^{8} +23102.6 q^{9} -13525.0 q^{10} +56450.6 q^{11} -52952.8 q^{12} -101405. q^{13} -105728. q^{14} +174851. q^{15} +65536.0 q^{16} +624347. q^{17} +369641. q^{18} -130321. q^{19} -216401. q^{20} +1.36684e6 q^{21} +903210. q^{22} +2.61755e6 q^{23} -847244. q^{24} -1.23857e6 q^{25} -1.62248e6 q^{26} -707323. q^{27} -1.69164e6 q^{28} +2.86799e6 q^{29} +2.79761e6 q^{30} -2.44968e6 q^{31} +1.04858e6 q^{32} -1.16766e7 q^{33} +9.98955e6 q^{34} +5.58583e6 q^{35} +5.91425e6 q^{36} -6.66624e6 q^{37} -2.08514e6 q^{38} +2.09753e7 q^{39} -3.46241e6 q^{40} +3.70089e6 q^{41} +2.18694e7 q^{42} +2.02637e7 q^{43} +1.44514e7 q^{44} -1.95289e7 q^{45} +4.18808e7 q^{46} +9.25239e6 q^{47} -1.35559e7 q^{48} +3.31184e6 q^{49} -1.98171e7 q^{50} -1.29144e8 q^{51} -2.59597e7 q^{52} -3.19002e7 q^{53} -1.13172e7 q^{54} -4.77185e7 q^{55} -2.70663e7 q^{56} +2.69565e7 q^{57} +4.58878e7 q^{58} -1.34485e8 q^{59} +4.47617e7 q^{60} -4.24287e7 q^{61} -3.91949e7 q^{62} -1.52661e8 q^{63} +1.67772e7 q^{64} +8.57193e7 q^{65} -1.86826e8 q^{66} +2.70669e8 q^{67} +1.59833e8 q^{68} -5.41432e8 q^{69} +8.93732e7 q^{70} +2.67893e8 q^{71} +9.46281e7 q^{72} +2.72432e8 q^{73} -1.06660e8 q^{74} +2.56194e8 q^{75} -3.33622e7 q^{76} -3.73025e8 q^{77} +3.35605e8 q^{78} -9.46452e7 q^{79} -5.53985e7 q^{80} -3.08420e8 q^{81} +5.92142e7 q^{82} +6.12610e8 q^{83} +3.49911e8 q^{84} -5.27769e8 q^{85} +3.24220e8 q^{86} -5.93234e8 q^{87} +2.31222e8 q^{88} +2.50492e7 q^{89} -3.12463e8 q^{90} +6.70084e8 q^{91} +6.70093e8 q^{92} +5.06709e8 q^{93} +1.48038e8 q^{94} +1.10162e8 q^{95} -2.16894e8 q^{96} +8.03901e7 q^{97} +5.29895e7 q^{98} +1.30415e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9}+O(q^{10}) \) 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9	\( 4 q + 64 q^{2} + 226 q^{3} + 1024 q^{4} + 866 q^{5} + 3616 q^{6} + 2670 q^{7} + 16384 q^{8} + 50606 q^{9} + 13856 q^{10} + 119234 q^{11} + 57856 q^{12} - 6748 q^{13} + 42720 q^{14} + 355904 q^{15} + 262144 q^{16} + 678624 q^{17} + 809696 q^{18} - 521284 q^{19} + 221696 q^{20} + 1586736 q^{21} + 1907744 q^{22} + 2911868 q^{23} + 925696 q^{24} + 268766 q^{25} - 107968 q^{26} + 2802058 q^{27} + 683520 q^{28} + 8291104 q^{29} + 5694464 q^{30} + 3445468 q^{31} + 4194304 q^{32} - 5321788 q^{33} + 10857984 q^{34} + 7715058 q^{35} + 12955136 q^{36} - 1005524 q^{37} - 8340544 q^{38} + 34055900 q^{39} + 3547136 q^{40} + 8514124 q^{41} + 25387776 q^{42} + 13900726 q^{43} + 30523904 q^{44} - 8962202 q^{45} + 46589888 q^{46} - 36334954 q^{47} + 14811136 q^{48} - 30891808 q^{49} + 4300256 q^{50} - 203869074 q^{51} - 1727488 q^{52} - 113969356 q^{53} + 44832928 q^{54} - 178140098 q^{55} + 10936320 q^{56} - 29452546 q^{57} + 132657664 q^{58} - 396773766 q^{59} + 91111424 q^{60} - 298192066 q^{61} + 55127488 q^{62} - 458723694 q^{63} + 67108864 q^{64} - 291187676 q^{65} - 85148608 q^{66} - 113551722 q^{67} + 173727744 q^{68} - 671519716 q^{69} + 123440928 q^{70} + 4659620 q^{71} + 207282176 q^{72} + 136198452 q^{73} - 16088384 q^{74} + 29308274 q^{75} - 133448704 q^{76} + 120551886 q^{77} + 544894400 q^{78} + 67255424 q^{79} + 56754176 q^{80} + 982241180 q^{81} + 136225984 q^{82} + 1376505216 q^{83} + 406204416 q^{84} + 638402178 q^{85} + 222411616 q^{86} + 630635524 q^{87} + 488382464 q^{88} + 1557211260 q^{89} - 143395232 q^{90} + 1422773730 q^{91} + 745438208 q^{92} + 2036686084 q^{93} - 581359264 q^{94} - 112857986 q^{95} + 236978176 q^{96} + 975818188 q^{97} - 494268928 q^{98} + 502820650 q^{99}+O(q^{100}) \) 4 * q + 64 * q^2 + 226 * q^3 + 1024 * q^4 + 866 * q^5 + 3616 * q^6 + 2670 * q^7 + 16384 * q^8 + 50606 * q^9 + 13856 * q^10 + 119234 * q^11 + 57856 * q^12 - 6748 * q^13 + 42720 * q^14 + 355904 * q^15 + 262144 * q^16 + 678624 * q^17 + 809696 * q^18 - 521284 * q^19 + 221696 * q^20 + 1586736 * q^21 + 1907744 * q^22 + 2911868 * q^23 + 925696 * q^24 + 268766 * q^25 - 107968 * q^26 + 2802058 * q^27 + 683520 * q^28 + 8291104 * q^29 + 5694464 * q^30 + 3445468 * q^31 + 4194304 * q^32 - 5321788 * q^33 + 10857984 * q^34 + 7715058 * q^35 + 12955136 * q^36 - 1005524 * q^37 - 8340544 * q^38 + 34055900 * q^39 + 3547136 * q^40 + 8514124 * q^41 + 25387776 * q^42 + 13900726 * q^43 + 30523904 * q^44 - 8962202 * q^45 + 46589888 * q^46 - 36334954 * q^47 + 14811136 * q^48 - 30891808 * q^49 + 4300256 * q^50 - 203869074 * q^51 - 1727488 * q^52 - 113969356 * q^53 + 44832928 * q^54 - 178140098 * q^55 + 10936320 * q^56 - 29452546 * q^57 + 132657664 * q^58 - 396773766 * q^59 + 91111424 * q^60 - 298192066 * q^61 + 55127488 * q^62 - 458723694 * q^63 + 67108864 * q^64 - 291187676 * q^65 - 85148608 * q^66 - 113551722 * q^67 + 173727744 * q^68 - 671519716 * q^69 + 123440928 * q^70 + 4659620 * q^71 + 207282176 * q^72 + 136198452 * q^73 - 16088384 * q^74 + 29308274 * q^75 - 133448704 * q^76 + 120551886 * q^77 + 544894400 * q^78 + 67255424 * q^79 + 56754176 * q^80 + 982241180 * q^81 + 136225984 * q^82 + 1376505216 * q^83 + 406204416 * q^84 + 638402178 * q^85 + 222411616 * q^86 + 630635524 * q^87 + 488382464 * q^88 + 1557211260 * q^89 - 143395232 * q^90 + 1422773730 * q^91 + 745438208 * q^92 + 2036686084 * q^93 - 581359264 * q^94 - 112857986 * q^95 + 236978176 * q^96 + 975818188 * q^97 - 494268928 * q^98 + 502820650 * q^99

Introduction

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