LMFDB - Embedded newform 285.10.a.h.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 6356 x^{13} + 18436 x^{12} + 15858707 x^{11} - 49616078 x^{10} + \cdots + 15\!\cdots\!00 $ x^15 - 2x^14 - 6356x^13 + 18436x^12 + 15858707x^11 - 49616078x^10 - 19804799606x^9 + 51117957936x^8 + 13077899446663x^7 - 17762605232062x^6 - 4369460380063800x^5 - 1105301955330540x^4 + 617735239298795077x^3 + 844341253042208334x^2 - 21881601450607548510x + 15712212684310961400
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{6}\cdot 5^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-30.5956$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+29.5956 q^{2} -81.0000 q^{3} +363.897 q^{4} +625.000 q^{5} -2397.24 q^{6} +5260.19 q^{7} -4383.19 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+29.5956 q^{2} -81.0000 q^{3} +363.897 q^{4} +625.000 q^{5} -2397.24 q^{6} +5260.19 q^{7} -4383.19 q^{8} +6561.00 q^{9} +18497.2 q^{10} -16671.4 q^{11} -29475.7 q^{12} +87976.8 q^{13} +155678. q^{14} -50625.0 q^{15} -316038. q^{16} -38968.0 q^{17} +194176. q^{18} -130321. q^{19} +227436. q^{20} -426075. q^{21} -493398. q^{22} +1.43783e6 q^{23} +355038. q^{24} +390625. q^{25} +2.60372e6 q^{26} -531441. q^{27} +1.91417e6 q^{28} +5.99644e6 q^{29} -1.49828e6 q^{30} -6.55958e6 q^{31} -7.10913e6 q^{32} +1.35038e6 q^{33} -1.15328e6 q^{34} +3.28762e6 q^{35} +2.38753e6 q^{36} -720606. q^{37} -3.85692e6 q^{38} -7.12612e6 q^{39} -2.73949e6 q^{40} +1.52841e7 q^{41} -1.26099e7 q^{42} +5.25803e6 q^{43} -6.06666e6 q^{44} +4.10062e6 q^{45} +4.25535e7 q^{46} -2.40643e7 q^{47} +2.55991e7 q^{48} -1.26840e7 q^{49} +1.15608e7 q^{50} +3.15641e6 q^{51} +3.20145e7 q^{52} +5.99941e7 q^{53} -1.57283e7 q^{54} -1.04196e7 q^{55} -2.30564e7 q^{56} +1.05560e7 q^{57} +1.77468e8 q^{58} -2.20079e7 q^{59} -1.84223e7 q^{60} -1.56098e8 q^{61} -1.94134e8 q^{62} +3.45121e7 q^{63} -4.85872e7 q^{64} +5.49855e7 q^{65} +3.99653e7 q^{66} +2.29519e8 q^{67} -1.41803e7 q^{68} -1.16465e8 q^{69} +9.72988e7 q^{70} +2.87813e8 q^{71} -2.87581e7 q^{72} +1.04710e8 q^{73} -2.13268e7 q^{74} -3.16406e7 q^{75} -4.74234e7 q^{76} -8.76945e7 q^{77} -2.10901e8 q^{78} +4.55596e8 q^{79} -1.97524e8 q^{80} +4.30467e7 q^{81} +4.52341e8 q^{82} -4.84057e7 q^{83} -1.55047e8 q^{84} -2.43550e7 q^{85} +1.55614e8 q^{86} -4.85712e8 q^{87} +7.30738e7 q^{88} +7.55034e7 q^{89} +1.21360e8 q^{90} +4.62774e8 q^{91} +5.23224e8 q^{92} +5.31326e8 q^{93} -7.12197e8 q^{94} -8.14506e7 q^{95} +5.75840e8 q^{96} -2.70214e8 q^{97} -3.75391e8 q^{98} -1.09381e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) $ 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * 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 $

$2$	29.5956	1.30795	0.653976	−	0.756516i	$-0.273100\pi$
$2$	29.5956	1.30795	0.653976	+	0.756516i	$0.273100\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	363.897	0.710736
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−2397.24	−0.755146
$7$	5260.19	0.828056	0.414028	−	0.910264i	$-0.364121\pi$
$7$	5260.19	0.828056	0.414028	+	0.910264i	$0.364121\pi$
$8$	−4383.19	−0.378343
$9$	6561.00	0.333333
$10$	18497.2	0.584934
$11$	−16671.4	−0.343324	−0.171662	−	0.985156i	$-0.554914\pi$
$11$	−16671.4	−0.343324	−0.171662	+	0.985156i	$0.554914\pi$
$12$	−29475.7	−0.410344
$13$	87976.8	0.854325	0.427162	−	0.904175i	$-0.359513\pi$
$13$	87976.8	0.854325	0.427162	+	0.904175i	$0.359513\pi$
$14$	155678.	1.08306
$15$	−50625.0	−0.258199
$16$	−316038.	−1.20559
$17$	−38968.0	−0.113159	−0.0565793	−	0.998398i	$-0.518019\pi$
$17$	−38968.0	−0.113159	−0.0565793	+	0.998398i	$0.518019\pi$
$18$	194176.	0.435984
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	227436.	0.317851
$21$	−426075.	−0.478079
$22$	−493398.	−0.449051
$23$	1.43783e6	1.07136	0.535678	−	0.844422i	$-0.320056\pi$
$23$	1.43783e6	1.07136	0.535678	+	0.844422i	$0.320056\pi$
$24$	355038.	0.218436
$25$	390625.	0.200000
$26$	2.60372e6	1.11742
$27$	−531441.	−0.192450
$28$	1.91417e6	0.588530
$29$	5.99644e6	1.57436	0.787178	−	0.616726i	$-0.211541\pi$
$29$	5.99644e6	1.57436	0.787178	+	0.616726i	$0.211541\pi$
$30$	−1.49828e6	−0.337712
$31$	−6.55958e6	−1.27570	−0.637850	−	0.770161i	$-0.720176\pi$
$31$	−6.55958e6	−1.27570	−0.637850	+	0.770161i	$0.720176\pi$
$32$	−7.10913e6	−1.19851
$33$	1.35038e6	0.198218
$34$	−1.15328e6	−0.148006
$35$	3.28762e6	0.370318
$36$	2.38753e6	0.236912
$37$	−720606.	−0.0632107	−0.0316053	−	0.999500i	$-0.510062\pi$
$37$	−720606.	−0.0632107	−0.0316053	+	0.999500i	$0.510062\pi$
$38$	−3.85692e6	−0.300065
$39$	−7.12612e6	−0.493245
$40$	−2.73949e6	−0.169200
$41$	1.52841e7	0.844719	0.422360	−	0.906428i	$-0.361202\pi$
$41$	1.52841e7	0.844719	0.422360	+	0.906428i	$0.361202\pi$
$42$	−1.26099e7	−0.625304
$43$	5.25803e6	0.234539	0.117269	−	0.993100i	$-0.462586\pi$
$43$	5.25803e6	0.234539	0.117269	+	0.993100i	$0.462586\pi$
$44$	−6.06666e6	−0.244013
$45$	4.10062e6	0.149071
$46$	4.25535e7	1.40128
$47$	−2.40643e7	−0.719339	−0.359669	−	0.933080i	$-0.617111\pi$
$47$	−2.40643e7	−0.719339	−0.359669	+	0.933080i	$0.617111\pi$
$48$	2.55991e7	0.696048
$49$	−1.26840e7	−0.314322
$50$	1.15608e7	0.261590
$51$	3.15641e6	0.0653322
$52$	3.20145e7	0.607200
$53$	5.99941e7	1.04440	0.522201	−	0.852823i	$-0.325111\pi$
$53$	5.99941e7	1.04440	0.522201	+	0.852823i	$0.325111\pi$
$54$	−1.57283e7	−0.251715
$55$	−1.04196e7	−0.153539
$56$	−2.30564e7	−0.313289
$57$	1.05560e7	0.132453
$58$	1.77468e8	2.05918
$59$	−2.20079e7	−0.236453	−0.118226	−	0.992987i	$-0.537721\pi$
$59$	−2.20079e7	−0.236453	−0.118226	+	0.992987i	$0.537721\pi$
$60$	−1.84223e7	−0.183511
$61$	−1.56098e8	−1.44349	−0.721743	−	0.692161i	$-0.756659\pi$
$61$	−1.56098e8	−1.44349	−0.721743	+	0.692161i	$0.756659\pi$
$62$	−1.94134e8	−1.66855
$63$	3.45121e7	0.276019
$64$	−4.85872e7	−0.362003
$65$	5.49855e7	0.382066
$66$	3.99653e7	0.259260
$67$	2.29519e8	1.39150	0.695748	−	0.718286i	$-0.255073\pi$
$67$	2.29519e8	1.39150	0.695748	+	0.718286i	$0.255073\pi$
$68$	−1.41803e7	−0.0804260
$69$	−1.16465e8	−0.618547
$70$	9.72988e7	0.484358
$71$	2.87813e8	1.34415	0.672074	−	0.740484i	$-0.265404\pi$
$71$	2.87813e8	1.34415	0.672074	+	0.740484i	$0.265404\pi$
$72$	−2.87581e7	−0.126114
$73$	1.04710e8	0.431554	0.215777	−	0.976443i	$-0.430772\pi$
$73$	1.04710e8	0.431554	0.215777	+	0.976443i	$0.430772\pi$
$74$	−2.13268e7	−0.0826765
$75$	−3.16406e7	−0.115470
$76$	−4.74234e7	−0.163054
$77$	−8.76945e7	−0.284292
$78$	−2.10901e8	−0.645140
$79$	4.55596e8	1.31601	0.658003	−	0.753016i	$-0.271402\pi$
$79$	4.55596e8	1.31601	0.658003	+	0.753016i	$0.271402\pi$
$80$	−1.97524e8	−0.539156
$81$	4.30467e7	0.111111
$82$	4.52341e8	1.10485
$83$	−4.84057e7	−0.111955	−0.0559777	−	0.998432i	$-0.517828\pi$
$83$	−4.84057e7	−0.111955	−0.0559777	+	0.998432i	$0.517828\pi$
$84$	−1.55047e8	−0.339788
$85$	−2.43550e7	−0.0506061
$86$	1.55614e8	0.306765
$87$	−4.85712e8	−0.908955
$88$	7.30738e7	0.129894
$89$	7.55034e7	0.127559	0.0637795	−	0.997964i	$-0.479685\pi$
$89$	7.55034e7	0.127559	0.0637795	+	0.997964i	$0.479685\pi$
$90$	1.21360e8	0.194978
$91$	4.62774e8	0.707429
$92$	5.23224e8	0.761451
$93$	5.31326e8	0.736525
$94$	−7.12197e8	−0.940860
$95$	−8.14506e7	−0.102598
$96$	5.75840e8	0.691960
$97$	−2.70214e8	−0.309909	−0.154955	−	0.987922i	$-0.549523\pi$
$97$	−2.70214e8	−0.309909	−0.154955	+	0.987922i	$0.549523\pi$
$98$	−3.75391e8	−0.411118
$99$	−1.09381e8	−0.114441
$100$	1.42147e8	0.142147
$101$	−4.02870e8	−0.385229	−0.192614	−	0.981275i	$-0.561697\pi$
$101$	−4.02870e8	−0.385229	−0.192614	+	0.981275i	$0.561697\pi$
$102$	9.34156e7	0.0854513
$103$	2.05018e9	1.79483	0.897417	−	0.441184i	$-0.145441\pi$
$103$	2.05018e9	1.79483	0.897417	+	0.441184i	$0.145441\pi$
$104$	−3.85619e8	−0.323228
$105$	−2.66297e8	−0.213803
$106$	1.77556e9	1.36603
$107$	1.17752e9	0.868446	0.434223	−	0.900805i	$-0.357023\pi$
$107$	1.17752e9	0.868446	0.434223	+	0.900805i	$0.357023\pi$
$108$	−1.93390e8	−0.136781
$109$	−8.09835e8	−0.549512	−0.274756	−	0.961514i	$-0.588597\pi$
$109$	−8.09835e8	−0.549512	−0.274756	+	0.961514i	$0.588597\pi$
$110$	−3.08374e8	−0.200822
$111$	5.83691e7	0.0364947
$112$	−1.66242e9	−0.998297
$113$	8.11057e8	0.467949	0.233975	−	0.972243i	$-0.424827\pi$
$113$	8.11057e8	0.467949	0.233975	+	0.972243i	$0.424827\pi$
$114$	3.12411e8	0.173242
$115$	8.98647e8	0.479125
$116$	2.18209e9	1.11895
$117$	5.77216e8	0.284775
$118$	−6.51336e8	−0.309269
$119$	−2.04979e8	−0.0937017
$120$	2.21899e8	0.0976877
$121$	−2.08001e9	−0.882129
$122$	−4.61980e9	−1.88801
$123$	−1.23801e9	−0.487699
$124$	−2.38701e9	−0.906686
$125$	2.44141e8	0.0894427
$126$	1.02140e9	0.361019
$127$	4.58160e9	1.56279	0.781394	−	0.624037i	$-0.214509\pi$
$127$	4.58160e9	1.56279	0.781394	+	0.624037i	$0.214509\pi$
$128$	2.20191e9	0.725028
$129$	−4.25900e8	−0.135411
$130$	1.62733e9	0.499723
$131$	3.93266e9	1.16672	0.583358	−	0.812215i	$-0.301738\pi$
$131$	3.93266e9	1.16672	0.583358	+	0.812215i	$0.301738\pi$
$132$	4.91400e8	0.140881
$133$	−6.85513e8	−0.189969
$134$	6.79274e9	1.82001
$135$	−3.32151e8	−0.0860663
$136$	1.70804e8	0.0428127
$137$	3.90112e9	0.946121	0.473060	−	0.881030i	$-0.343149\pi$
$137$	3.90112e9	0.946121	0.473060	+	0.881030i	$0.343149\pi$
$138$	−3.44683e9	−0.809030
$139$	6.90330e9	1.56852	0.784260	−	0.620432i	$-0.213043\pi$
$139$	6.90330e9	1.56852	0.784260	+	0.620432i	$0.213043\pi$
$140$	1.19635e9	0.263199
$141$	1.94921e9	0.415310
$142$	8.51797e9	1.75808
$143$	−1.46669e9	−0.293310
$144$	−2.07353e9	−0.401863
$145$	3.74778e9	0.704073
$146$	3.09895e9	0.564451
$147$	1.02741e9	0.181474
$148$	−2.62227e8	−0.0449261
$149$	8.37260e9	1.39163	0.695813	−	0.718223i	$-0.255044\pi$
$149$	8.37260e9	1.39163	0.695813	+	0.718223i	$0.255044\pi$
$150$	−9.36422e8	−0.151029
$151$	−3.18560e9	−0.498649	−0.249324	−	0.968420i	$-0.580209\pi$
$151$	−3.18560e9	−0.498649	−0.249324	+	0.968420i	$0.580209\pi$
$152$	5.71222e8	0.0867978
$153$	−2.55669e8	−0.0377195
$154$	−2.59537e9	−0.371840
$155$	−4.09974e9	−0.570510
$156$	−2.59317e9	−0.350567
$157$	8.30989e9	1.09156	0.545779	−	0.837929i	$-0.316234\pi$
$157$	8.30989e9	1.09156	0.545779	+	0.837929i	$0.316234\pi$
$158$	1.34836e10	1.72127
$159$	−4.85952e9	−0.602985
$160$	−4.44321e9	−0.535990
$161$	7.56328e9	0.887143
$162$	1.27399e9	0.145328
$163$	6.52494e9	0.723990	0.361995	−	0.932180i	$-0.382096\pi$
$163$	6.52494e9	0.723990	0.361995	+	0.932180i	$0.382096\pi$
$164$	5.56184e9	0.600373
$165$	8.43988e8	0.0886459
$166$	−1.43259e9	−0.146432
$167$	7.21410e9	0.717725	0.358863	−	0.933390i	$-0.383165\pi$
$167$	7.21410e9	0.717725	0.358863	+	0.933390i	$0.383165\pi$
$168$	1.86757e9	0.180878
$169$	−2.86458e9	−0.270129
$170$	−7.20799e8	−0.0661903
$171$	−8.55036e8	−0.0764719
$172$	1.91338e9	0.166695
$173$	−2.18345e10	−1.85325	−0.926627	−	0.375981i	$-0.877306\pi$
$173$	−2.18345e10	−1.85325	−0.926627	+	0.375981i	$0.877306\pi$
$174$	−1.43749e10	−1.18887
$175$	2.05476e9	0.165611
$176$	5.26879e9	0.413908
$177$	1.78264e9	0.136516
$178$	2.23456e9	0.166841
$179$	−1.28038e10	−0.932178	−0.466089	−	0.884738i	$-0.654337\pi$
$179$	−1.28038e10	−0.932178	−0.466089	+	0.884738i	$0.654337\pi$
$180$	1.49221e9	0.105950
$181$	2.29543e10	1.58968	0.794842	−	0.606816i	$-0.207554\pi$
$181$	2.29543e10	1.58968	0.794842	+	0.606816i	$0.207554\pi$
$182$	1.36961e10	0.925283
$183$	1.26439e10	0.833397
$184$	−6.30230e9	−0.405340
$185$	−4.50379e8	−0.0282687
$186$	1.57249e10	0.963339
$187$	6.49649e8	0.0388501
$188$	−8.75694e9	−0.511260
$189$	−2.79548e9	−0.159360
$190$	−2.41058e9	−0.134193
$191$	−2.87136e10	−1.56112	−0.780561	−	0.625080i	$-0.785066\pi$
$191$	−2.87136e10	−1.56112	−0.780561	+	0.625080i	$0.785066\pi$
$192$	3.93556e9	0.209003
$193$	1.82235e10	0.945419	0.472710	−	0.881218i	$-0.343276\pi$
$193$	1.82235e10	0.945419	0.472710	+	0.881218i	$0.343276\pi$
$194$	−7.99712e9	−0.405346
$195$	−4.45382e9	−0.220586
$196$	−4.61569e9	−0.223400
$197$	5.85082e9	0.276770	0.138385	−	0.990379i	$-0.455809\pi$
$197$	5.85082e9	0.276770	0.138385	+	0.990379i	$0.455809\pi$
$198$	−3.23719e9	−0.149684
$199$	−1.64666e10	−0.744330	−0.372165	−	0.928167i	$-0.621385\pi$
$199$	−1.64666e10	−0.744330	−0.372165	+	0.928167i	$0.621385\pi$
$200$	−1.71218e9	−0.0756685
$201$	−1.85910e10	−0.803380
$202$	−1.19232e10	−0.503860
$203$	3.15424e10	1.30366
$204$	1.14861e9	0.0464339
$205$	9.55256e9	0.377770
$206$	6.06762e10	2.34755
$207$	9.43363e9	0.357119
$208$	−2.78040e10	−1.02997
$209$	2.17263e9	0.0787639
$210$	−7.88121e9	−0.279644
$211$	2.37649e10	0.825400	0.412700	−	0.910867i	$-0.364586\pi$
$211$	2.37649e10	0.825400	0.412700	+	0.910867i	$0.364586\pi$
$212$	2.18317e10	0.742294
$213$	−2.33128e10	−0.776044
$214$	3.48495e10	1.13588
$215$	3.28627e9	0.104889
$216$	2.32941e9	0.0728121
$217$	−3.45046e10	−1.05635
$218$	−2.39675e10	−0.718735
$219$	−8.48150e9	−0.249158
$220$	−3.79166e9	−0.109126
$221$	−3.42828e9	−0.0966742
$222$	1.72747e9	0.0477333
$223$	1.07774e10	0.291837	0.145919	−	0.989297i	$-0.453386\pi$
$223$	1.07774e10	0.291837	0.145919	+	0.989297i	$0.453386\pi$
$224$	−3.73954e10	−0.992434
$225$	2.56289e9	0.0666667
$226$	2.40037e10	0.612055
$227$	−3.35431e10	−0.838468	−0.419234	−	0.907878i	$-0.637701\pi$
$227$	−3.35431e10	−0.838468	−0.419234	+	0.907878i	$0.637701\pi$
$228$	3.84130e9	0.0941393
$229$	−5.58240e10	−1.34141	−0.670704	−	0.741725i	$-0.734008\pi$
$229$	−5.58240e10	−1.34141	−0.670704	+	0.741725i	$0.734008\pi$
$230$	2.65959e10	0.626672
$231$	7.10326e9	0.164136
$232$	−2.62836e10	−0.595646
$233$	−1.09578e10	−0.243569	−0.121784	−	0.992557i	$-0.538862\pi$
$233$	−1.09578e10	−0.243569	−0.121784	+	0.992557i	$0.538862\pi$
$234$	1.70830e10	0.372472
$235$	−1.50402e10	−0.321698
$236$	−8.00861e9	−0.168056
$237$	−3.69032e10	−0.759796
$238$	−6.06646e9	−0.122557
$239$	−7.42341e10	−1.47168	−0.735839	−	0.677157i	$-0.763212\pi$
$239$	−7.42341e10	−1.47168	−0.735839	+	0.677157i	$0.763212\pi$
$240$	1.59994e10	0.311282
$241$	−7.94561e10	−1.51723	−0.758613	−	0.651541i	$-0.774123\pi$
$241$	−7.94561e10	−1.51723	−0.758613	+	0.651541i	$0.774123\pi$
$242$	−6.15591e10	−1.15378
$243$	−3.48678e9	−0.0641500
$244$	−5.68035e10	−1.02594
$245$	−7.92753e9	−0.140569
$246$	−3.66396e10	−0.637886
$247$	−1.14652e10	−0.195996
$248$	2.87519e10	0.482652
$249$	3.92086e9	0.0646375
$250$	7.22548e9	0.116987
$251$	2.75852e10	0.438676	0.219338	−	0.975649i	$-0.429610\pi$
$251$	2.75852e10	0.438676	0.219338	+	0.975649i	$0.429610\pi$
$252$	1.25588e10	0.196177
$253$	−2.39707e10	−0.367822
$254$	1.35595e11	2.04405
$255$	1.97275e9	0.0292174
$256$	9.00434e10	1.31030
$257$	6.17608e10	0.883108	0.441554	−	0.897235i	$-0.354427\pi$
$257$	6.17608e10	0.883108	0.441554	+	0.897235i	$0.354427\pi$
$258$	−1.26048e10	−0.177111
$259$	−3.79052e9	−0.0523420
$260$	2.00091e10	0.271548
$261$	3.93427e10	0.524785
$262$	1.16389e11	1.52601
$263$	−4.24114e10	−0.546615	−0.273308	−	0.961927i	$-0.588118\pi$
$263$	−4.24114e10	−0.546615	−0.273308	+	0.961927i	$0.588118\pi$
$264$	−5.91898e9	−0.0749944
$265$	3.74963e10	0.467070
$266$	−2.02881e10	−0.248470
$267$	−6.11577e9	−0.0736463
$268$	8.35212e10	0.988986
$269$	7.71799e10	0.898709	0.449355	−	0.893353i	$-0.351654\pi$
$269$	7.71799e10	0.898709	0.449355	+	0.893353i	$0.351654\pi$
$270$	−9.83018e9	−0.112571
$271$	1.30709e10	0.147213	0.0736064	−	0.997287i	$-0.476549\pi$
$271$	1.30709e10	0.147213	0.0736064	+	0.997287i	$0.476549\pi$
$272$	1.23154e10	0.136423
$273$	−3.74847e10	−0.408434
$274$	1.15456e11	1.23748
$275$	−6.51225e9	−0.0686648
$276$	−4.23811e10	−0.439624
$277$	−3.09264e10	−0.315624	−0.157812	−	0.987469i	$-0.550444\pi$
$277$	−3.09264e10	−0.315624	−0.157812	+	0.987469i	$0.550444\pi$
$278$	2.04307e11	2.05155
$279$	−4.30374e10	−0.425233
$280$	−1.44102e10	−0.140107
$281$	1.97645e11	1.89107	0.945533	−	0.325527i	$-0.105542\pi$
$281$	1.97645e11	1.89107	0.945533	+	0.325527i	$0.105542\pi$
$282$	5.76880e10	0.543206
$283$	2.35003e9	0.0217788	0.0108894	−	0.999941i	$-0.496534\pi$
$283$	2.35003e9	0.0217788	0.0108894	+	0.999941i	$0.496534\pi$
$284$	1.04734e11	0.955335
$285$	6.59750e9	0.0592349
$286$	−4.34076e10	−0.383635
$287$	8.03972e10	0.699475
$288$	−4.66430e10	−0.399503
$289$	−1.17069e11	−0.987195
$290$	1.10918e11	0.920893
$291$	2.18873e10	0.178926
$292$	3.81036e10	0.306721
$293$	−1.89958e11	−1.50575	−0.752875	−	0.658164i	$-0.771333\pi$
$293$	−1.89958e11	−1.50575	−0.752875	+	0.658164i	$0.771333\pi$
$294$	3.04067e10	0.237359
$295$	−1.37549e10	−0.105745
$296$	3.15856e9	0.0239153
$297$	8.85985e9	0.0660727
$298$	2.47792e11	1.82018
$299$	1.26496e11	0.915286
$300$	−1.15139e10	−0.0820688
$301$	2.76582e10	0.194211
$302$	−9.42796e10	−0.652209
$303$	3.26325e10	0.222412
$304$	4.11864e10	0.276581
$305$	−9.75612e10	−0.645547
$306$	−7.56666e9	−0.0493353
$307$	−1.83901e11	−1.18158	−0.590788	−	0.806827i	$-0.701183\pi$
$307$	−1.83901e11	−1.18158	−0.590788	+	0.806827i	$0.701183\pi$
$308$	−3.19118e10	−0.202056
$309$	−1.66064e11	−1.03625
$310$	−1.21334e11	−0.746199
$311$	1.47297e11	0.892835	0.446418	−	0.894825i	$-0.352700\pi$
$311$	1.47297e11	0.892835	0.446418	+	0.894825i	$0.352700\pi$
$312$	3.12351e10	0.186616
$313$	2.99716e11	1.76506	0.882532	−	0.470253i	$-0.155837\pi$
$313$	2.99716e11	1.76506	0.882532	+	0.470253i	$0.155837\pi$
$314$	2.45936e11	1.42770
$315$	2.15701e10	0.123439
$316$	1.65790e11	0.935333
$317$	−1.65038e11	−0.917946	−0.458973	−	0.888450i	$-0.651782\pi$
$317$	−1.65038e11	−0.917946	−0.458973	+	0.888450i	$0.651782\pi$
$318$	−1.43820e11	−0.788675
$319$	−9.99689e10	−0.540514
$320$	−3.03670e10	−0.161893
$321$	−9.53795e10	−0.501398
$322$	2.23839e11	1.16034
$323$	5.07835e9	0.0259604
$324$	1.56646e10	0.0789707
$325$	3.43659e10	0.170865
$326$	1.93109e11	0.946943
$327$	6.55966e10	0.317261
$328$	−6.69931e10	−0.319593
$329$	−1.26583e11	−0.595653
$330$	2.49783e10	0.115944
$331$	1.12912e11	0.517028	0.258514	−	0.966007i	$-0.416767\pi$
$331$	1.12912e11	0.517028	0.258514	+	0.966007i	$0.416767\pi$
$332$	−1.76147e10	−0.0795707
$333$	−4.72790e9	−0.0210702
$334$	2.13505e11	0.938749
$335$	1.43449e11	0.622296
$336$	1.34656e11	0.576367
$337$	−1.08997e11	−0.460342	−0.230171	−	0.973150i	$-0.573929\pi$
$337$	−1.08997e11	−0.460342	−0.230171	+	0.973150i	$0.573929\pi$
$338$	−8.47790e10	−0.353316
$339$	−6.56956e10	−0.270171
$340$	−8.86271e9	−0.0359676
$341$	1.09357e11	0.437978
$342$	−2.53053e10	−0.100022
$343$	−2.78988e11	−1.08833
$344$	−2.30469e10	−0.0887360
$345$	−7.27904e10	−0.276623
$346$	−6.46203e11	−2.42397
$347$	−9.48580e10	−0.351230	−0.175615	−	0.984459i	$-0.556191\pi$
$347$	−9.48580e10	−0.351230	−0.175615	+	0.984459i	$0.556191\pi$
$348$	−1.76749e11	−0.646027
$349$	−1.91771e11	−0.691941	−0.345970	−	0.938245i	$-0.612450\pi$
$349$	−1.91771e11	−0.691941	−0.345970	+	0.938245i	$0.612450\pi$
$350$	6.08118e10	0.216611
$351$	−4.67545e10	−0.164415
$352$	1.18519e11	0.411477
$353$	7.46866e10	0.256010	0.128005	−	0.991774i	$-0.459143\pi$
$353$	7.46866e10	0.256010	0.128005	+	0.991774i	$0.459143\pi$
$354$	5.27582e10	0.178556
$355$	1.79883e11	0.601121
$356$	2.74755e10	0.0906609
$357$	1.66033e10	0.0540987
$358$	−3.78935e11	−1.21924
$359$	2.57741e11	0.818951	0.409475	−	0.912321i	$-0.365712\pi$
$359$	2.57741e11	0.818951	0.409475	+	0.912321i	$0.365712\pi$
$360$	−1.79738e10	−0.0564000
$361$	1.69836e10	0.0526316
$362$	6.79346e11	2.07923
$363$	1.68481e11	0.509297
$364$	1.68402e11	0.502796
$365$	6.54437e10	0.192997
$366$	3.74204e11	1.09004
$367$	6.10014e11	1.75526	0.877632	−	0.479336i	$-0.159122\pi$
$367$	6.10014e11	1.75526	0.877632	+	0.479336i	$0.159122\pi$
$368$	−4.54411e11	−1.29162
$369$	1.00279e11	0.281573
$370$	−1.33292e10	−0.0369740
$371$	3.15580e11	0.864823
$372$	1.93348e11	0.523475
$373$	−4.42938e11	−1.18482	−0.592411	−	0.805636i	$-0.701824\pi$
$373$	−4.42938e11	−1.18482	−0.592411	+	0.805636i	$0.701824\pi$
$374$	1.92267e10	0.0508140
$375$	−1.97754e10	−0.0516398
$376$	1.05479e11	0.272157
$377$	5.27548e11	1.34501
$378$	−8.27338e10	−0.208435
$379$	−4.25185e11	−1.05853	−0.529263	−	0.848458i	$-0.677532\pi$
$379$	−4.25185e11	−1.05853	−0.529263	+	0.848458i	$0.677532\pi$
$380$	−2.96396e10	−0.0729200
$381$	−3.71109e11	−0.902277
$382$	−8.49794e11	−2.04187
$383$	3.55576e11	0.844380	0.422190	−	0.906507i	$-0.361261\pi$
$383$	3.55576e11	0.844380	0.422190	+	0.906507i	$0.361261\pi$
$384$	−1.78355e11	−0.418595
$385$	−5.48091e10	−0.127139
$386$	5.39335e11	1.23656
$387$	3.44979e10	0.0781796
$388$	−9.83299e10	−0.220264
$389$	−3.81169e11	−0.844003	−0.422001	−	0.906595i	$-0.638672\pi$
$389$	−3.81169e11	−0.844003	−0.422001	+	0.906595i	$0.638672\pi$
$390$	−1.31813e11	−0.288515
$391$	−5.60295e10	−0.121233
$392$	5.55966e10	0.118922
$393$	−3.18545e11	−0.673604
$394$	1.73158e11	0.362001
$395$	2.84747e11	0.588535
$396$	−3.98034e10	−0.0813376
$397$	−1.30221e11	−0.263103	−0.131551	−	0.991309i	$-0.541996\pi$
$397$	−1.30221e11	−0.263103	−0.131551	+	0.991309i	$0.541996\pi$
$398$	−4.87339e11	−0.973548
$399$	5.55265e10	0.109679
$400$	−1.23452e11	−0.241118
$401$	−4.01929e11	−0.776247	−0.388124	−	0.921607i	$-0.626877\pi$
$401$	−4.01929e11	−0.776247	−0.388124	+	0.921607i	$0.626877\pi$
$402$	−5.50212e11	−1.05078
$403$	−5.77091e11	−1.08986
$404$	−1.46603e11	−0.273796
$405$	2.69042e10	0.0496904
$406$	9.33515e11	1.70512
$407$	1.20135e10	0.0217017
$408$	−1.38351e10	−0.0247179
$409$	1.82150e10	0.0321865	0.0160933	−	0.999870i	$-0.494877\pi$
$409$	1.82150e10	0.0321865	0.0160933	+	0.999870i	$0.494877\pi$
$410$	2.82713e11	0.494105
$411$	−3.15991e11	−0.546243
$412$	7.46054e11	1.27565
$413$	−1.15766e11	−0.195796
$414$	2.79194e11	0.467094
$415$	−3.02535e10	−0.0500680
$416$	−6.25439e11	−1.02392
$417$	−5.59167e11	−0.905585
$418$	6.43002e10	0.103019
$419$	−1.41367e11	−0.224071	−0.112036	−	0.993704i	$-0.535737\pi$
$419$	−1.41367e11	−0.224071	−0.112036	+	0.993704i	$0.535737\pi$
$420$	−9.69047e10	−0.151958
$421$	−1.78853e11	−0.277477	−0.138738	−	0.990329i	$-0.544305\pi$
$421$	−1.78853e11	−0.277477	−0.138738	+	0.990329i	$0.544305\pi$
$422$	7.03334e11	1.07958
$423$	−1.57886e11	−0.239780
$424$	−2.62966e11	−0.395142
$425$	−1.52219e10	−0.0226317
$426$	−6.89956e11	−1.01503
$427$	−8.21104e11	−1.19529
$428$	4.28498e11	0.617236
$429$	1.18802e11	0.169343
$430$	9.72589e10	0.137190
$431$	−6.15558e10	−0.0859253	−0.0429626	−	0.999077i	$-0.513680\pi$
$431$	−6.15558e10	−0.0859253	−0.0429626	+	0.999077i	$0.513680\pi$
$432$	1.67956e11	0.232016
$433$	−3.99697e11	−0.546431	−0.273216	−	0.961953i	$-0.588087\pi$
$433$	−3.99697e11	−0.546431	−0.273216	+	0.961953i	$0.588087\pi$
$434$	−1.02118e12	−1.38166
$435$	−3.03570e11	−0.406497
$436$	−2.94696e11	−0.390558
$437$	−1.87380e11	−0.245786
$438$	−2.51015e11	−0.325886
$439$	−9.24508e11	−1.18801	−0.594006	−	0.804461i	$-0.702454\pi$
$439$	−9.24508e11	−1.18801	−0.594006	+	0.804461i	$0.702454\pi$
$440$	4.56711e10	0.0580904
$441$	−8.32200e10	−0.104774
$442$	−1.01462e11	−0.126445
$443$	−3.47428e11	−0.428596	−0.214298	−	0.976768i	$-0.568746\pi$
$443$	−3.47428e11	−0.428596	−0.214298	+	0.976768i	$0.568746\pi$
$444$	2.12404e10	0.0259381
$445$	4.71896e10	0.0570462
$446$	3.18962e11	0.381709
$447$	−6.78181e11	−0.803455
$448$	−2.55578e11	−0.299759
$449$	−4.16089e11	−0.483145	−0.241573	−	0.970383i	$-0.577663\pi$
$449$	−4.16089e11	−0.483145	−0.241573	+	0.970383i	$0.577663\pi$
$450$	7.58502e10	0.0871967
$451$	−2.54807e11	−0.290012
$452$	2.95141e11	0.332588
$453$	2.58034e11	0.287895
$454$	−9.92726e11	−1.09668
$455$	2.89234e11	0.316372
$456$	−4.62690e10	−0.0501127
$457$	1.83365e12	1.96650	0.983248	−	0.182272i	$-0.0583452\pi$
$457$	1.83365e12	1.96650	0.983248	+	0.182272i	$0.0583452\pi$
$458$	−1.65214e12	−1.75450
$459$	2.07092e10	0.0217774
$460$	3.27015e11	0.340531
$461$	2.92228e11	0.301347	0.150674	−	0.988584i	$-0.451856\pi$
$461$	2.92228e11	0.301347	0.150674	+	0.988584i	$0.451856\pi$
$462$	2.10225e11	0.214682
$463$	−7.89652e11	−0.798585	−0.399292	−	0.916824i	$-0.630744\pi$
$463$	−7.89652e11	−0.798585	−0.399292	+	0.916824i	$0.630744\pi$
$464$	−1.89511e12	−1.89803
$465$	3.32079e11	0.329384
$466$	−3.24302e11	−0.318576
$467$	−4.14792e11	−0.403557	−0.201778	−	0.979431i	$-0.564672\pi$
$467$	−4.14792e11	−0.403557	−0.201778	+	0.979431i	$0.564672\pi$
$468$	2.10047e11	0.202400
$469$	1.20731e12	1.15224
$470$	−4.45123e11	−0.420765
$471$	−6.73101e11	−0.630211
$472$	9.64648e10	0.0894602
$473$	−8.76585e10	−0.0805228
$474$	−1.09217e12	−0.993776
$475$	−5.09066e10	−0.0458831
$476$	−7.45912e10	−0.0665972
$477$	3.93621e11	0.348134
$478$	−2.19700e12	−1.92488
$479$	−1.02167e12	−0.886753	−0.443377	−	0.896335i	$-0.646220\pi$
$479$	−1.02167e12	−0.886753	−0.443377	+	0.896335i	$0.646220\pi$
$480$	3.59900e11	0.309454
$481$	−6.33966e10	−0.0540024
$482$	−2.35155e12	−1.98446
$483$	−6.12625e11	−0.512192
$484$	−7.56911e11	−0.626961
$485$	−1.68883e11	−0.138596
$486$	−1.03193e11	−0.0839051
$487$	1.46586e12	1.18090	0.590450	−	0.807074i	$-0.298950\pi$
$487$	1.46586e12	1.18090	0.590450	+	0.807074i	$0.298950\pi$
$488$	6.84207e11	0.546133
$489$	−5.28520e11	−0.417996
$490$	−2.34620e11	−0.183858
$491$	−1.46210e12	−1.13530	−0.567648	−	0.823271i	$-0.692146\pi$
$491$	−1.46210e12	−1.13530	−0.567648	+	0.823271i	$0.692146\pi$
$492$	−4.50509e11	−0.346625
$493$	−2.33669e11	−0.178152
$494$	−3.39320e11	−0.256353
$495$	−6.83630e10	−0.0511797
$496$	2.07308e12	1.53797
$497$	1.51395e12	1.11303
$498$	1.16040e11	0.0845426
$499$	−6.11177e10	−0.0441281	−0.0220640	−	0.999757i	$-0.507024\pi$
$499$	−6.11177e10	−0.0441281	−0.0220640	+	0.999757i	$0.507024\pi$
$500$	8.88420e10	0.0635702
$501$	−5.84342e11	−0.414379
$502$	8.16399e11	0.573767
$503$	−1.16995e12	−0.814911	−0.407455	−	0.913225i	$-0.633584\pi$
$503$	−1.16995e12	−0.814911	−0.407455	+	0.913225i	$0.633584\pi$
$504$	−1.51273e11	−0.104430
$505$	−2.51794e11	−0.172279
$506$	−7.09425e11	−0.481093
$507$	2.32031e11	0.155959
$508$	1.66723e12	1.11073
$509$	−1.28470e12	−0.848345	−0.424172	−	0.905582i	$-0.639435\pi$
$509$	−1.28470e12	−0.848345	−0.424172	+	0.905582i	$0.639435\pi$
$510$	5.83847e10	0.0382150
$511$	5.50793e11	0.357351
$512$	1.53751e12	0.988786
$513$	6.92579e10	0.0441511
$514$	1.82785e12	1.15506
$515$	1.28136e12	0.802674
$516$	−1.54984e11	−0.0962415
$517$	4.01185e11	0.246966
$518$	−1.12183e11	−0.0684608
$519$	1.76859e12	1.06998
$520$	−2.41012e11	−0.144552
$521$	−3.01378e12	−1.79202	−0.896008	−	0.444037i	$-0.853546\pi$
$521$	−3.01378e12	−1.79202	−0.896008	+	0.444037i	$0.853546\pi$
$522$	1.16437e12	0.686393
$523$	−2.73739e12	−1.59985	−0.799923	−	0.600102i	$-0.795127\pi$
$523$	−2.73739e12	−1.59985	−0.799923	+	0.600102i	$0.795127\pi$
$524$	1.43108e12	0.829228
$525$	−1.66436e11	−0.0956157
$526$	−1.25519e12	−0.714946
$527$	2.55613e11	0.144356
$528$	−4.26772e11	−0.238970
$529$	2.66215e11	0.147803
$530$	1.10972e12	0.610905
$531$	−1.44394e11	−0.0788176
$532$	−2.49456e11	−0.135018
$533$	1.34465e12	0.721665
$534$	−1.81000e11	−0.0963257
$535$	7.35953e11	0.388381
$536$	−1.00602e12	−0.526462
$537$	1.03710e12	0.538193
$538$	2.28418e12	1.17547
$539$	2.11460e11	0.107914
$540$	−1.20869e11	−0.0611704
$541$	5.49896e9	0.00275990	0.00137995	−	0.999999i	$-0.499561\pi$
$541$	5.49896e9	0.00275990	0.00137995	+	0.999999i	$0.499561\pi$
$542$	3.86842e11	0.192547
$543$	−1.85930e12	−0.917805
$544$	2.77029e11	0.135622
$545$	−5.06147e11	−0.245749
$546$	−1.10938e12	−0.534212
$547$	2.60625e12	1.24473	0.622363	−	0.782729i	$-0.286173\pi$
$547$	2.60625e12	1.24473	0.622363	+	0.782729i	$0.286173\pi$
$548$	1.41961e12	0.672442
$549$	−1.02416e12	−0.481162
$550$	−1.92734e11	−0.0898102
$551$	−7.81463e11	−0.361182
$552$	5.10486e11	0.234023
$553$	2.39652e12	1.08973
$554$	−9.15284e11	−0.412821
$555$	3.64807e10	0.0163209
$556$	2.51209e12	1.11480
$557$	1.20429e12	0.530132	0.265066	−	0.964230i	$-0.414606\pi$
$557$	1.20429e12	0.530132	0.265066	+	0.964230i	$0.414606\pi$
$558$	−1.27372e12	−0.556184
$559$	4.62584e11	0.200372
$560$	−1.03901e12	−0.446452
$561$	−5.26216e10	−0.0224301
$562$	5.84940e12	2.47342
$563$	−1.72761e12	−0.724700	−0.362350	−	0.932042i	$-0.618025\pi$
$563$	−1.72761e12	−0.724700	−0.362350	+	0.932042i	$0.618025\pi$
$564$	7.09312e11	0.295176
$565$	5.06911e11	0.209273
$566$	6.95503e10	0.0284856
$567$	2.26434e11	0.0920063
$568$	−1.26154e12	−0.508549
$569$	−1.64332e12	−0.657229	−0.328615	−	0.944464i	$-0.606582\pi$
$569$	−1.64332e12	−0.657229	−0.328615	+	0.944464i	$0.606582\pi$
$570$	1.95257e11	0.0774763
$571$	1.14332e12	0.450097	0.225048	−	0.974348i	$-0.427746\pi$
$571$	1.14332e12	0.450097	0.225048	+	0.974348i	$0.427746\pi$
$572$	−5.33725e11	−0.208466
$573$	2.32580e12	0.901314
$574$	2.37940e12	0.914879
$575$	5.61654e11	0.214271
$576$	−3.18781e11	−0.120668
$577$	4.41190e12	1.65704	0.828522	−	0.559956i	$-0.189182\pi$
$577$	4.41190e12	1.65704	0.828522	+	0.559956i	$0.189182\pi$
$578$	−3.46473e12	−1.29120
$579$	−1.47611e12	−0.545838
$580$	1.36381e12	0.500410
$581$	−2.54623e11	−0.0927054
$582$	6.47767e11	0.234027
$583$	−1.00018e12	−0.358568
$584$	−4.58963e11	−0.163275
$585$	3.60760e11	0.127355
$586$	−5.62190e12	−1.96945
$587$	−1.28967e12	−0.448338	−0.224169	−	0.974550i	$-0.571967\pi$
$587$	−1.28967e12	−0.448338	−0.224169	+	0.974550i	$0.571967\pi$
$588$	3.73871e11	0.128980
$589$	8.54851e11	0.292665
$590$	−4.07085e11	−0.138309
$591$	−4.73916e11	−0.159793
$592$	2.27739e11	0.0762062
$593$	3.18276e12	1.05696	0.528479	−	0.848946i	$-0.322762\pi$
$593$	3.18276e12	1.05696	0.528479	+	0.848946i	$0.322762\pi$
$594$	2.62212e11	0.0864199
$595$	−1.28112e11	−0.0419047
$596$	3.04677e12	0.989079
$597$	1.33380e12	0.429739
$598$	3.74372e12	1.19715
$599$	−2.55801e12	−0.811860	−0.405930	−	0.913904i	$-0.633052\pi$
$599$	−2.55801e12	−0.811860	−0.405930	+	0.913904i	$0.633052\pi$
$600$	1.38687e11	0.0436873
$601$	−1.36893e12	−0.428003	−0.214001	−	0.976833i	$-0.568650\pi$
$601$	−1.36893e12	−0.428003	−0.214001	+	0.976833i	$0.568650\pi$
$602$	8.18560e11	0.254019
$603$	1.50587e12	0.463832
$604$	−1.15923e12	−0.354408
$605$	−1.30001e12	−0.394500
$606$	9.65776e11	0.290904
$607$	−8.14502e11	−0.243525	−0.121762	−	0.992559i	$-0.538855\pi$
$607$	−8.14502e11	−0.243525	−0.121762	+	0.992559i	$0.538855\pi$
$608$	9.26469e11	0.274957
$609$	−2.55494e12	−0.752666
$610$	−2.88738e12	−0.844344
$611$	−2.11710e12	−0.614549
$612$	−9.30371e10	−0.0268087
$613$	5.83933e12	1.67029	0.835143	−	0.550033i	$-0.185385\pi$
$613$	5.83933e12	1.67029	0.835143	+	0.550033i	$0.185385\pi$
$614$	−5.44266e12	−1.54544
$615$	−7.73757e11	−0.218106
$616$	3.84382e11	0.107560
$617$	−3.61192e12	−1.00335	−0.501677	−	0.865055i	$-0.667283\pi$
$617$	−3.61192e12	−1.00335	−0.501677	+	0.865055i	$0.667283\pi$
$618$	−4.91477e12	−1.35536
$619$	5.35038e11	0.146479	0.0732397	−	0.997314i	$-0.476666\pi$
$619$	5.35038e11	0.146479	0.0732397	+	0.997314i	$0.476666\pi$
$620$	−1.49188e12	−0.405482
$621$	−7.64124e11	−0.206182
$622$	4.35933e12	1.16778
$623$	3.97162e11	0.105626
$624$	2.25213e12	0.594651
$625$	1.52588e11	0.0400000
$626$	8.87026e12	2.30862
$627$	−1.75983e11	−0.0454744
$628$	3.02394e12	0.775810
$629$	2.80806e10	0.00715283
$630$	6.38378e11	0.161453
$631$	5.79758e12	1.45584	0.727922	−	0.685660i	$-0.240486\pi$
$631$	5.79758e12	1.45584	0.727922	+	0.685660i	$0.240486\pi$
$632$	−1.99696e12	−0.497901
$633$	−1.92495e12	−0.476545
$634$	−4.88439e12	−1.20063
$635$	2.86350e12	0.698900
$636$	−1.76837e12	−0.428564
$637$	−1.11590e12	−0.268533
$638$	−2.95864e12	−0.706966
$639$	1.88834e12	0.448049
$640$	1.37619e12	0.324242
$641$	−2.92898e12	−0.685259	−0.342630	−	0.939471i	$-0.611318\pi$
$641$	−2.92898e12	−0.685259	−0.342630	+	0.939471i	$0.611318\pi$
$642$	−2.82281e12	−0.655803
$643$	6.45660e12	1.48955	0.744774	−	0.667317i	$-0.232557\pi$
$643$	6.45660e12	1.48955	0.744774	+	0.667317i	$0.232557\pi$
$644$	2.75225e12	0.630525
$645$	−2.66188e11	−0.0605577
$646$	1.50296e11	0.0339549
$647$	−3.54280e11	−0.0794835	−0.0397417	−	0.999210i	$-0.512654\pi$
$647$	−3.54280e11	−0.0794835	−0.0397417	+	0.999210i	$0.512654\pi$
$648$	−1.88682e11	−0.0420381
$649$	3.66902e11	0.0811799
$650$	1.01708e12	0.223483
$651$	2.79487e12	0.609885
$652$	2.37441e12	0.514566
$653$	3.28963e12	0.708007	0.354003	−	0.935244i	$-0.384820\pi$
$653$	3.28963e12	0.708007	0.354003	+	0.935244i	$0.384820\pi$
$654$	1.94137e12	0.414962
$655$	2.45791e12	0.521772
$656$	−4.83036e12	−1.01839
$657$	6.87001e11	0.143851
$658$	−3.74629e12	−0.779085
$659$	3.73744e12	0.771951	0.385976	−	0.922509i	$-0.373865\pi$
$659$	3.73744e12	0.771951	0.385976	+	0.922509i	$0.373865\pi$
$660$	3.07125e11	0.0630039
$661$	−6.49443e11	−0.132323	−0.0661613	−	0.997809i	$-0.521075\pi$
$661$	−6.49443e11	−0.132323	−0.0661613	+	0.997809i	$0.521075\pi$
$662$	3.34170e12	0.676248
$663$	2.77690e11	0.0558149
$664$	2.12171e11	0.0423575
$665$	−4.28445e11	−0.0849568
$666$	−1.39925e11	−0.0275588
$667$	8.62189e12	1.68669
$668$	2.62519e12	0.510113
$669$	−8.72967e11	−0.168492
$670$	4.24546e12	0.813932
$671$	2.60236e12	0.495584
$672$	3.02903e12	0.572982
$673$	−5.14852e12	−0.967419	−0.483709	−	0.875229i	$-0.660711\pi$
$673$	−5.14852e12	−0.967419	−0.483709	+	0.875229i	$0.660711\pi$
$674$	−3.22583e12	−0.602105
$675$	−2.07594e11	−0.0384900
$676$	−1.04241e12	−0.191991
$677$	8.32214e11	0.152260	0.0761300	−	0.997098i	$-0.475744\pi$
$677$	8.32214e11	0.152260	0.0761300	+	0.997098i	$0.475744\pi$
$678$	−1.94430e12	−0.353370
$679$	−1.42137e12	−0.256622
$680$	1.06753e11	0.0191464
$681$	2.71699e12	0.484090
$682$	3.23649e12	0.572854
$683$	−4.67046e12	−0.821233	−0.410616	−	0.911808i	$-0.634686\pi$
$683$	−4.67046e12	−0.821233	−0.410616	+	0.911808i	$0.634686\pi$
$684$	−3.11145e11	−0.0543514
$685$	2.43820e12	0.423118
$686$	−8.25680e12	−1.42349
$687$	4.52174e12	0.774463
$688$	−1.66174e12	−0.282758
$689$	5.27809e12	0.892258
$690$	−2.15427e12	−0.361809
$691$	3.89265e12	0.649523	0.324761	−	0.945796i	$-0.394716\pi$
$691$	3.89265e12	0.649523	0.324761	+	0.945796i	$0.394716\pi$
$692$	−7.94550e12	−1.31718
$693$	−5.75364e11	−0.0947639
$694$	−2.80738e12	−0.459392
$695$	4.31456e12	0.701463
$696$	2.12897e12	0.343896
$697$	−5.95590e11	−0.0955873
$698$	−5.67557e12	−0.905024
$699$	8.87581e11	0.140624
$700$	7.47721e11	0.117706
$701$	3.75867e12	0.587900	0.293950	−	0.955821i	$-0.405030\pi$
$701$	3.75867e12	0.587900	0.293950	+	0.955821i	$0.405030\pi$
$702$	−1.38372e12	−0.215047
$703$	9.39102e10	0.0145015
$704$	8.10015e11	0.124284
$705$	1.21826e12	0.185732
$706$	2.21039e12	0.334848
$707$	−2.11917e12	−0.318991
$708$	6.48697e11	0.0970270
$709$	6.21551e12	0.923780	0.461890	−	0.886937i	$-0.347171\pi$
$709$	6.21551e12	0.923780	0.461890	+	0.886937i	$0.347171\pi$
$710$	5.32373e12	0.786237
$711$	2.98916e12	0.438668
$712$	−3.30946e11	−0.0482611
$713$	−9.43159e12	−1.36673
$714$	4.91383e11	0.0707585
$715$	−9.16683e11	−0.131172
$716$	−4.65925e12	−0.662533
$717$	6.01296e12	0.849673
$718$	7.62798e12	1.07115
$719$	5.09419e12	0.710878	0.355439	−	0.934699i	$-0.384331\pi$
$719$	5.09419e12	0.710878	0.355439	+	0.934699i	$0.384331\pi$
$720$	−1.29595e12	−0.179719
$721$	1.07843e13	1.48622
$722$	5.02638e11	0.0688395
$723$	6.43594e12	0.875971
$724$	8.35301e12	1.12985
$725$	2.34236e12	0.314871
$726$	4.98629e12	0.666136
$727$	−9.82717e12	−1.30474	−0.652370	−	0.757901i	$-0.726225\pi$
$727$	−9.82717e12	−1.30474	−0.652370	+	0.757901i	$0.726225\pi$
$728$	−2.02843e12	−0.267651
$729$	2.82430e11	0.0370370
$730$	1.93684e12	0.252430
$731$	−2.04895e11	−0.0265401
$732$	4.60109e12	0.592326
$733$	−2.57361e12	−0.329287	−0.164644	−	0.986353i	$-0.552647\pi$
$733$	−2.57361e12	−0.329287	−0.164644	+	0.986353i	$0.552647\pi$
$734$	1.80537e13	2.29580
$735$	6.42130e11	0.0811577
$736$	−1.02218e13	−1.28403
$737$	−3.82639e12	−0.477734
$738$	2.96781e12	0.368284
$739$	2.03828e12	0.251400	0.125700	−	0.992068i	$-0.459882\pi$
$739$	2.03828e12	0.251400	0.125700	+	0.992068i	$0.459882\pi$
$740$	−1.63892e11	−0.0200916
$741$	9.28683e11	0.113158
$742$	9.33978e12	1.13115
$743$	1.31950e13	1.58840	0.794202	−	0.607654i	$-0.207889\pi$
$743$	1.31950e13	1.58840	0.794202	+	0.607654i	$0.207889\pi$
$744$	−2.32890e12	−0.278659
$745$	5.23288e12	0.622354
$746$	−1.31090e13	−1.54969
$747$	−3.17590e11	−0.0373185
$748$	2.36406e11	0.0276122
$749$	6.19400e12	0.719122
$750$	−5.85264e11	−0.0675423
$751$	−2.43761e12	−0.279631	−0.139815	−	0.990178i	$-0.544651\pi$
$751$	−2.43761e12	−0.279631	−0.139815	+	0.990178i	$0.544651\pi$
$752$	7.60525e12	0.867228
$753$	−2.23440e12	−0.253270
$754$	1.56131e13	1.75921
$755$	−1.99100e12	−0.223003
$756$	−1.01727e12	−0.113263
$757$	−8.60187e12	−0.952054	−0.476027	−	0.879431i	$-0.657924\pi$
$757$	−8.60187e12	−0.952054	−0.476027	+	0.879431i	$0.657924\pi$
$758$	−1.25836e13	−1.38450
$759$	1.94162e12	0.212362
$760$	3.57014e11	0.0388171
$761$	−1.60647e13	−1.73636	−0.868182	−	0.496245i	$-0.834712\pi$
$761$	−1.60647e13	−1.73636	−0.868182	+	0.496245i	$0.834712\pi$
$762$	−1.09832e13	−1.18013
$763$	−4.25988e12	−0.455027
$764$	−1.04488e13	−1.10955
$765$	−1.59793e11	−0.0168687
$766$	1.05235e13	1.10441
$767$	−1.93618e12	−0.202008
$768$	−7.29352e12	−0.756505
$769$	−1.72667e13	−1.78050	−0.890250	−	0.455473i	$-0.849470\pi$
$769$	−1.72667e13	−1.78050	−0.890250	+	0.455473i	$0.849470\pi$
$770$	−1.62211e12	−0.166292
$771$	−5.00262e12	−0.509863
$772$	6.63149e12	0.671944
$773$	6.52549e12	0.657364	0.328682	−	0.944441i	$-0.393396\pi$
$773$	6.52549e12	0.657364	0.328682	+	0.944441i	$0.393396\pi$
$774$	1.02098e12	0.102255
$775$	−2.56234e12	−0.255140
$776$	1.18440e12	0.117252
$777$	3.07032e11	0.0302197
$778$	−1.12809e13	−1.10391
$779$	−1.99184e12	−0.193792
$780$	−1.62073e12	−0.156778
$781$	−4.79823e12	−0.461478
$782$	−1.65822e12	−0.158567
$783$	−3.18676e12	−0.302985
$784$	4.00864e12	0.378944
$785$	5.19368e12	0.488159
$786$	−9.42753e12	−0.881041
$787$	−2.21013e12	−0.205367	−0.102684	−	0.994714i	$-0.532743\pi$
$787$	−2.21013e12	−0.205367	−0.102684	+	0.994714i	$0.532743\pi$
$788$	2.12909e12	0.196710
$789$	3.43532e12	0.315588
$790$	8.42725e12	0.769776
$791$	4.26631e12	0.387488
$792$	4.79437e11	0.0432981
$793$	−1.37330e13	−1.23321
$794$	−3.85398e12	−0.344125
$795$	−3.03720e12	−0.269663
$796$	−5.99216e12	−0.529023
$797$	−7.85507e12	−0.689585	−0.344792	−	0.938679i	$-0.612051\pi$
$797$	−7.85507e12	−0.689585	−0.344792	+	0.938679i	$0.612051\pi$
$798$	1.64334e12	0.143454
$799$	9.37738e11	0.0813994
$800$	−2.77701e12	−0.239702
$801$	4.95378e11	0.0425197
$802$	−1.18953e13	−1.01529
$803$	−1.74566e12	−0.148163
$804$	−6.76522e12	−0.570992
$805$	4.72705e12	0.396742
$806$	−1.70793e13	−1.42549
$807$	−6.25157e12	−0.518870
$808$	1.76586e12	0.145748
$809$	−2.06218e12	−0.169261	−0.0846306	−	0.996412i	$-0.526971\pi$
$809$	−2.06218e12	−0.169261	−0.0846306	+	0.996412i	$0.526971\pi$
$810$	7.96245e11	0.0649926
$811$	1.38445e13	1.12379	0.561894	−	0.827209i	$-0.310073\pi$
$811$	1.38445e13	1.12379	0.561894	+	0.827209i	$0.310073\pi$
$812$	1.14782e13	0.926555
$813$	−1.05875e12	−0.0849933
$814$	3.55546e11	0.0283848
$815$	4.07809e12	0.323778
$816$	−9.97545e11	−0.0787638
$817$	−6.85231e11	−0.0538069
$818$	5.39083e11	0.0420984
$819$	3.03626e12	0.235810
$820$	3.47615e12	0.268495
$821$	−1.45310e13	−1.11622	−0.558110	−	0.829767i	$-0.688473\pi$
$821$	−1.45310e13	−1.11622	−0.558110	+	0.829767i	$0.688473\pi$
$822$	−9.35192e12	−0.714459
$823$	2.32460e12	0.176623	0.0883117	−	0.996093i	$-0.471853\pi$
$823$	2.32460e12	0.176623	0.0883117	+	0.996093i	$0.471853\pi$
$824$	−8.98632e12	−0.679062
$825$	5.27493e11	0.0396436
$826$	−3.42615e12	−0.256092
$827$	−2.05883e12	−0.153054	−0.0765272	−	0.997067i	$-0.524383\pi$
$827$	−2.05883e12	−0.153054	−0.0765272	+	0.997067i	$0.524383\pi$
$828$	3.43287e12	0.253817
$829$	1.36524e13	1.00395	0.501976	−	0.864881i	$-0.332607\pi$
$829$	1.36524e13	1.00395	0.501976	+	0.864881i	$0.332607\pi$
$830$	−8.95371e11	−0.0654864
$831$	2.50504e12	0.182226
$832$	−4.27455e12	−0.309268
$833$	4.94272e11	0.0355683
$834$	−1.65489e13	−1.18446
$835$	4.50881e12	0.320976
$836$	7.90613e11	0.0559804
$837$	3.48603e12	0.245508
$838$	−4.18384e12	−0.293074
$839$	−4.85609e11	−0.0338344	−0.0169172	−	0.999857i	$-0.505385\pi$
$839$	−4.85609e11	−0.0338344	−0.0169172	+	0.999857i	$0.505385\pi$
$840$	1.16723e12	0.0808909
$841$	2.14502e13	1.47860
$842$	−5.29325e12	−0.362926
$843$	−1.60092e13	−1.09181
$844$	8.64796e12	0.586642
$845$	−1.79037e12	−0.120805
$846$	−4.67273e12	−0.313620
$847$	−1.09413e13	−0.730452
$848$	−1.89604e13	−1.25912
$849$	−1.90352e11	−0.0125740
$850$	−4.50500e11	−0.0296012
$851$	−1.03611e12	−0.0677211
$852$	−8.48346e12	−0.551563
$853$	1.53349e13	0.991769	0.495885	−	0.868388i	$-0.334844\pi$
$853$	1.53349e13	0.991769	0.495885	+	0.868388i	$0.334844\pi$
$854$	−2.43010e13	−1.56338
$855$	−5.34398e11	−0.0341993
$856$	−5.16131e12	−0.328570
$857$	1.97939e13	1.25348	0.626741	−	0.779227i	$-0.284388\pi$
$857$	1.97939e13	1.25348	0.626741	+	0.779227i	$0.284388\pi$
$858$	3.51602e12	0.221492
$859$	2.23583e13	1.40110	0.700552	−	0.713601i	$-0.252937\pi$
$859$	2.23583e13	1.40110	0.700552	+	0.713601i	$0.252937\pi$
$860$	1.19586e12	0.0745484
$861$	−6.51217e12	−0.403842
$862$	−1.82178e12	−0.112386
$863$	1.95758e13	1.20135	0.600677	−	0.799491i	$-0.294898\pi$
$863$	1.95758e13	1.20135	0.600677	+	0.799491i	$0.294898\pi$
$864$	3.77809e12	0.230653
$865$	−1.36465e13	−0.828801
$866$	−1.18293e13	−0.714705
$867$	9.48262e12	0.569957
$868$	−1.25561e13	−0.750787
$869$	−7.59540e12	−0.451816
$870$	−8.98432e12	−0.531678
$871$	2.01923e13	1.18879
$872$	3.54966e12	0.207904
$873$	−1.77287e12	−0.103303
$874$	−5.54562e12	−0.321476
$875$	1.28423e12	0.0740636
$876$	−3.08639e12	−0.177085
$877$	−1.67759e13	−0.957610	−0.478805	−	0.877921i	$-0.658930\pi$
$877$	−1.67759e13	−0.957610	−0.478805	+	0.877921i	$0.658930\pi$
$878$	−2.73613e13	−1.55386
$879$	1.53866e13	0.869345
$880$	3.29299e12	0.185105
$881$	−3.98822e12	−0.223043	−0.111521	−	0.993762i	$-0.535572\pi$
$881$	−3.98822e12	−0.223043	−0.111521	+	0.993762i	$0.535572\pi$
$882$	−2.46294e12	−0.137039
$883$	3.81379e12	0.211122	0.105561	−	0.994413i	$-0.466336\pi$
$883$	3.81379e12	0.211122	0.105561	+	0.994413i	$0.466336\pi$
$884$	−1.24754e12	−0.0687099
$885$	1.11415e12	0.0610519
$886$	−1.02823e13	−0.560583
$887$	−1.33479e13	−0.724030	−0.362015	−	0.932172i	$-0.617911\pi$
$887$	−1.33479e13	−0.724030	−0.362015	+	0.932172i	$0.617911\pi$
$888$	−2.55843e11	−0.0138075
$889$	2.41001e13	1.29408
$890$	1.39660e12	0.0746136
$891$	−7.17648e11	−0.0381471
$892$	3.92185e12	0.207419
$893$	3.13609e12	0.165028
$894$	−2.00711e13	−1.05088
$895$	−8.00235e12	−0.416883
$896$	1.15825e13	0.600364
$897$	−1.02462e13	−0.528440
$898$	−1.23144e13	−0.631931
$899$	−3.93341e13	−2.00840
$900$	9.32628e11	0.0473824
$901$	−2.33785e12	−0.118183
$902$	−7.54115e12	−0.379322
$903$	−2.24031e12	−0.112128
$904$	−3.55502e12	−0.177045
$905$	1.43465e13	0.710928
$906$	7.63665e12	0.376553
$907$	−3.70231e12	−0.181652	−0.0908259	−	0.995867i	$-0.528951\pi$
$907$	−3.70231e12	−0.181652	−0.0908259	+	0.995867i	$0.528951\pi$
$908$	−1.22062e13	−0.595930
$909$	−2.64323e12	−0.128410
$910$	8.56004e12	0.413799
$911$	1.63023e13	0.784180	0.392090	−	0.919927i	$-0.371752\pi$
$911$	1.63023e13	0.784180	0.392090	+	0.919927i	$0.371752\pi$
$912$	−3.33610e12	−0.159684
$913$	8.06989e11	0.0384370
$914$	5.42678e13	2.57208
$915$	7.90245e12	0.372707
$916$	−2.03142e13	−0.953388
$917$	2.06865e13	0.966107
$918$	6.12900e11	0.0284838
$919$	2.82000e13	1.30416	0.652078	−	0.758152i	$-0.273897\pi$
$919$	2.82000e13	1.30416	0.652078	+	0.758152i	$0.273897\pi$
$920$	−3.93894e12	−0.181273
$921$	1.48960e13	0.682184
$922$	8.64864e12	0.394147
$923$	2.53208e13	1.14834
$924$	2.58485e12	0.116657
$925$	−2.81487e11	−0.0126421
$926$	−2.33702e13	−1.04451
$927$	1.34512e13	0.598278
$928$	−4.26295e13	−1.88688
$929$	2.39572e13	1.05527	0.527637	−	0.849470i	$-0.323078\pi$
$929$	2.39572e13	1.05527	0.527637	+	0.849470i	$0.323078\pi$
$930$	9.82805e12	0.430818
$931$	1.65300e12	0.0721105
$932$	−3.98751e12	−0.173113
$933$	−1.19310e13	−0.515479
$934$	−1.22760e13	−0.527832
$935$	4.06031e11	0.0173743
$936$	−2.53005e12	−0.107743
$937$	3.25022e13	1.37748	0.688739	−	0.725009i	$-0.258165\pi$
$937$	3.25022e13	1.37748	0.688739	+	0.725009i	$0.258165\pi$
$938$	3.57311e13	1.50707
$939$	−2.42770e13	−1.01906
$940$	−5.47309e12	−0.228643
$941$	1.61244e12	0.0670394	0.0335197	−	0.999438i	$-0.489328\pi$
$941$	1.61244e12	0.0670394	0.0335197	+	0.999438i	$0.489328\pi$
$942$	−1.99208e13	−0.824285
$943$	2.19760e13	0.904995
$944$	6.95534e12	0.285065
$945$	−1.74717e12	−0.0712678
$946$	−2.59430e12	−0.105320
$947$	1.29935e13	0.524989	0.262494	−	0.964933i	$-0.415455\pi$
$947$	1.29935e13	0.524989	0.262494	+	0.964933i	$0.415455\pi$
$948$	−1.34290e13	−0.540015
$949$	9.21204e12	0.368687
$950$	−1.50661e12	−0.0600129
$951$	1.33681e13	0.529976
$952$	8.98461e11	0.0354514
$953$	−3.92521e13	−1.54150	−0.770752	−	0.637135i	$-0.780119\pi$
$953$	−3.92521e13	−1.54150	−0.770752	+	0.637135i	$0.780119\pi$
$954$	1.16494e13	0.455342
$955$	−1.79460e13	−0.698155
$956$	−2.70136e13	−1.04597
$957$	8.09748e12	0.312066
$958$	−3.02370e13	−1.15983
$959$	2.05206e13	0.783441
$960$	2.45973e12	0.0934688
$961$	1.65884e13	0.627409
$962$	−1.87626e12	−0.0706326
$963$	7.72574e12	0.289482
$964$	−2.89138e13	−1.07835
$965$	1.13897e13	0.422804
$966$	−1.81310e13	−0.669922
$967$	−2.88812e13	−1.06218	−0.531088	−	0.847317i	$-0.678217\pi$
$967$	−2.88812e13	−1.06218	−0.531088	+	0.847317i	$0.678217\pi$
$968$	9.11709e12	0.333747
$969$	−4.11346e11	−0.0149882
$970$	−4.99820e12	−0.181276
$971$	5.10843e12	0.184417	0.0922084	−	0.995740i	$-0.470607\pi$
$971$	5.10843e12	0.184417	0.0922084	+	0.995740i	$0.470607\pi$
$972$	−1.26883e12	−0.0455938
$973$	3.63126e13	1.29882
$974$	4.33831e13	1.54456
$975$	−2.78364e12	−0.0986489
$976$	4.93329e13	1.74025
$977$	−5.21936e13	−1.83270	−0.916351	−	0.400377i	$-0.868879\pi$
$977$	−5.21936e13	−1.83270	−0.916351	+	0.400377i	$0.868879\pi$
$978$	−1.56419e13	−0.546718
$979$	−1.25874e12	−0.0437941
$980$	−2.88480e12	−0.0999077
$981$	−5.31333e12	−0.183171
$982$	−4.32715e13	−1.48491
$983$	−4.44000e13	−1.51667	−0.758337	−	0.651862i	$-0.773988\pi$
$983$	−4.44000e13	−1.51667	−0.758337	+	0.651862i	$0.773988\pi$
$984$	5.42644e12	0.184517
$985$	3.65676e12	0.123775
$986$	−6.91557e12	−0.233014
$987$	1.02532e13	0.343901
$988$	−4.17216e12	−0.139301
$989$	7.56017e12	0.251274
$990$	−2.02324e12	−0.0669406
$991$	3.75510e13	1.23677	0.618387	−	0.785874i	$-0.287786\pi$
$991$	3.75510e13	1.23677	0.618387	+	0.785874i	$0.287786\pi$
$992$	4.66329e13	1.52894
$993$	−9.14588e12	−0.298506
$994$	4.48061e13	1.45579
$995$	−1.02916e13	−0.332875
$996$	1.42679e12	0.0459402
$997$	−4.47382e13	−1.43400	−0.717002	−	0.697072i	$-0.754486\pi$
$997$	−4.47382e13	−1.43400	−0.717002	+	0.697072i	$0.754486\pi$
$998$	−1.80881e12	−0.0577173
$999$	3.82960e11	0.0121649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.13	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.13	✓	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	285.a (trivial)

\(f(q)\)	\(=\)	\(q+29.5956 q^{2} -81.0000 q^{3} +363.897 q^{4} +625.000 q^{5} -2397.24 q^{6} +5260.19 q^{7} -4383.19 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+29.5956 q^{2} -81.0000 q^{3} +363.897 q^{4} +625.000 q^{5} -2397.24 q^{6} +5260.19 q^{7} -4383.19 q^{8} +6561.00 q^{9} +18497.2 q^{10} -16671.4 q^{11} -29475.7 q^{12} +87976.8 q^{13} +155678. q^{14} -50625.0 q^{15} -316038. q^{16} -38968.0 q^{17} +194176. q^{18} -130321. q^{19} +227436. q^{20} -426075. q^{21} -493398. q^{22} +1.43783e6 q^{23} +355038. q^{24} +390625. q^{25} +2.60372e6 q^{26} -531441. q^{27} +1.91417e6 q^{28} +5.99644e6 q^{29} -1.49828e6 q^{30} -6.55958e6 q^{31} -7.10913e6 q^{32} +1.35038e6 q^{33} -1.15328e6 q^{34} +3.28762e6 q^{35} +2.38753e6 q^{36} -720606. q^{37} -3.85692e6 q^{38} -7.12612e6 q^{39} -2.73949e6 q^{40} +1.52841e7 q^{41} -1.26099e7 q^{42} +5.25803e6 q^{43} -6.06666e6 q^{44} +4.10062e6 q^{45} +4.25535e7 q^{46} -2.40643e7 q^{47} +2.55991e7 q^{48} -1.26840e7 q^{49} +1.15608e7 q^{50} +3.15641e6 q^{51} +3.20145e7 q^{52} +5.99941e7 q^{53} -1.57283e7 q^{54} -1.04196e7 q^{55} -2.30564e7 q^{56} +1.05560e7 q^{57} +1.77468e8 q^{58} -2.20079e7 q^{59} -1.84223e7 q^{60} -1.56098e8 q^{61} -1.94134e8 q^{62} +3.45121e7 q^{63} -4.85872e7 q^{64} +5.49855e7 q^{65} +3.99653e7 q^{66} +2.29519e8 q^{67} -1.41803e7 q^{68} -1.16465e8 q^{69} +9.72988e7 q^{70} +2.87813e8 q^{71} -2.87581e7 q^{72} +1.04710e8 q^{73} -2.13268e7 q^{74} -3.16406e7 q^{75} -4.74234e7 q^{76} -8.76945e7 q^{77} -2.10901e8 q^{78} +4.55596e8 q^{79} -1.97524e8 q^{80} +4.30467e7 q^{81} +4.52341e8 q^{82} -4.84057e7 q^{83} -1.55047e8 q^{84} -2.43550e7 q^{85} +1.55614e8 q^{86} -4.85712e8 q^{87} +7.30738e7 q^{88} +7.55034e7 q^{89} +1.21360e8 q^{90} +4.62774e8 q^{91} +5.23224e8 q^{92} +5.31326e8 q^{93} -7.12197e8 q^{94} -8.14506e7 q^{95} +5.75840e8 q^{96} -2.70214e8 q^{97} -3.75391e8 q^{98} -1.09381e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9} - 10625 q^{10} + 138230 q^{11} - 409455 q^{12} - 176712 q^{13} - 555994 q^{14} - 759375 q^{15} + 1695731 q^{16} - 274992 q^{17} - 111537 q^{18} - 1954815 q^{19} + 3159375 q^{20} - 109512 q^{21} - 1031106 q^{22} + 1714212 q^{23} + 291357 q^{24} + 5859375 q^{25} + 9500004 q^{26} - 7971615 q^{27} + 14545598 q^{28} + 1754340 q^{29} + 860625 q^{30} + 8442914 q^{31} + 35638859 q^{32} - 11196630 q^{33} + 47218266 q^{34} + 845000 q^{35} + 33165855 q^{36} + 2956096 q^{37} + 2215457 q^{38} + 14313672 q^{39} - 2248125 q^{40} - 38550502 q^{41} + 45035514 q^{42} + 50753570 q^{43} + 212125630 q^{44} + 61509375 q^{45} - 117130008 q^{46} - 40252876 q^{47} - 137354211 q^{48} + 110123035 q^{49} - 6640625 q^{50} + 22274352 q^{51} - 87136648 q^{52} + 65532542 q^{53} + 9034497 q^{54} + 86393750 q^{55} - 377288898 q^{56} + 158340015 q^{57} + 211630876 q^{58} + 175407418 q^{59} - 255909375 q^{60} + 151231854 q^{61} - 30983940 q^{62} + 8870472 q^{63} + 836879575 q^{64} - 110445000 q^{65} + 83519586 q^{66} + 40009476 q^{67} - 124850430 q^{68} - 138851172 q^{69} - 347496250 q^{70} + 87578500 q^{71} - 23599917 q^{72} - 360657638 q^{73} + 1373397084 q^{74} - 474609375 q^{75} - 658772655 q^{76} - 304618172 q^{77} - 769500324 q^{78} + 205798286 q^{79} + 1059831875 q^{80} + 645700815 q^{81} - 2327138772 q^{82} - 63321462 q^{83} - 1178193438 q^{84} - 171870000 q^{85} - 848405762 q^{86} - 142101540 q^{87} - 3211126502 q^{88} - 381069174 q^{89} - 69710625 q^{90} + 1476892872 q^{91} - 2382818588 q^{92} - 683876034 q^{93} - 5137318040 q^{94} - 1221759375 q^{95} - 2886747579 q^{96} - 3915268828 q^{97} - 8273557437 q^{98} + 906927030 q^{99}+O(q^{100}) \) 15 * q - 17 * q^2 - 1215 * q^3 + 5055 * q^4 + 9375 * q^5 + 1377 * q^6 + 1352 * q^7 - 3597 * q^8 + 98415 * q^9 - 10625 * q^10 + 138230 * q^11 - 409455 * q^12 - 176712 * q^13 - 555994 * q^14 - 759375 * q^15 + 1695731 * q^16 - 274992 * q^17 - 111537 * q^18 - 1954815 * q^19 + 3159375 * q^20 - 109512 * q^21 - 1031106 * q^22 + 1714212 * q^23 + 291357 * q^24 + 5859375 * q^25 + 9500004 * q^26 - 7971615 * q^27 + 14545598 * q^28 + 1754340 * q^29 + 860625 * q^30 + 8442914 * q^31 + 35638859 * q^32 - 11196630 * q^33 + 47218266 * q^34 + 845000 * q^35 + 33165855 * q^36 + 2956096 * q^37 + 2215457 * q^38 + 14313672 * q^39 - 2248125 * q^40 - 38550502 * q^41 + 45035514 * q^42 + 50753570 * q^43 + 212125630 * q^44 + 61509375 * q^45 - 117130008 * q^46 - 40252876 * q^47 - 137354211 * q^48 + 110123035 * q^49 - 6640625 * q^50 + 22274352 * q^51 - 87136648 * q^52 + 65532542 * q^53 + 9034497 * q^54 + 86393750 * q^55 - 377288898 * q^56 + 158340015 * q^57 + 211630876 * q^58 + 175407418 * q^59 - 255909375 * q^60 + 151231854 * q^61 - 30983940 * q^62 + 8870472 * q^63 + 836879575 * q^64 - 110445000 * q^65 + 83519586 * q^66 + 40009476 * q^67 - 124850430 * q^68 - 138851172 * q^69 - 347496250 * q^70 + 87578500 * q^71 - 23599917 * q^72 - 360657638 * q^73 + 1373397084 * q^74 - 474609375 * q^75 - 658772655 * q^76 - 304618172 * q^77 - 769500324 * q^78 + 205798286 * q^79 + 1059831875 * q^80 + 645700815 * q^81 - 2327138772 * q^82 - 63321462 * q^83 - 1178193438 * q^84 - 171870000 * q^85 - 848405762 * q^86 - 142101540 * q^87 - 3211126502 * q^88 - 381069174 * q^89 - 69710625 * q^90 + 1476892872 * q^91 - 2382818588 * q^92 - 683876034 * q^93 - 5137318040 * q^94 - 1221759375 * q^95 - 2886747579 * q^96 - 3915268828 * q^97 - 8273557437 * q^98 + 906927030 * q^99

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