LMFDB - Embedded newform 285.10.a.h.1.14

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			1.14
Root			$-43.1627$ 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)

$f(q)$	$=$	$q+42.1627 q^{2} -81.0000 q^{3} +1265.69 q^{4} +625.000 q^{5} -3415.18 q^{6} +4307.69 q^{7} +31777.6 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+42.1627 q^{2} -81.0000 q^{3} +1265.69 q^{4} +625.000 q^{5} -3415.18 q^{6} +4307.69 q^{7} +31777.6 q^{8} +6561.00 q^{9} +26351.7 q^{10} +74234.4 q^{11} -102521. q^{12} +162840. q^{13} +181624. q^{14} -50625.0 q^{15} +691797. q^{16} +354849. q^{17} +276629. q^{18} -130321. q^{19} +791057. q^{20} -348922. q^{21} +3.12992e6 q^{22} -2.24746e6 q^{23} -2.57399e6 q^{24} +390625. q^{25} +6.86576e6 q^{26} -531441. q^{27} +5.45220e6 q^{28} -6.17653e6 q^{29} -2.13449e6 q^{30} -7.22564e6 q^{31} +1.28978e7 q^{32} -6.01298e6 q^{33} +1.49614e7 q^{34} +2.69230e6 q^{35} +8.30420e6 q^{36} +1.44539e7 q^{37} -5.49468e6 q^{38} -1.31900e7 q^{39} +1.98610e7 q^{40} -2.14921e7 q^{41} -1.47115e7 q^{42} +3.51253e7 q^{43} +9.39578e7 q^{44} +4.10062e6 q^{45} -9.47587e7 q^{46} -3.01514e6 q^{47} -5.60355e7 q^{48} -2.17975e7 q^{49} +1.64698e7 q^{50} -2.87428e7 q^{51} +2.06105e8 q^{52} -5.03255e6 q^{53} -2.24070e7 q^{54} +4.63965e7 q^{55} +1.36888e8 q^{56} +1.05560e7 q^{57} -2.60419e8 q^{58} +3.96681e7 q^{59} -6.40756e7 q^{60} +4.80705e7 q^{61} -3.04652e8 q^{62} +2.82627e7 q^{63} +1.89608e8 q^{64} +1.01775e8 q^{65} -2.53523e8 q^{66} +6.24392e7 q^{67} +4.49130e8 q^{68} +1.82044e8 q^{69} +1.13515e8 q^{70} +1.78442e8 q^{71} +2.08493e8 q^{72} +3.85248e8 q^{73} +6.09417e8 q^{74} -3.16406e7 q^{75} -1.64946e8 q^{76} +3.19778e8 q^{77} -5.56126e8 q^{78} -2.10411e8 q^{79} +4.32373e8 q^{80} +4.30467e7 q^{81} -9.06164e8 q^{82} +4.38569e8 q^{83} -4.41628e8 q^{84} +2.21781e8 q^{85} +1.48098e9 q^{86} +5.00299e8 q^{87} +2.35899e9 q^{88} -5.81991e8 q^{89} +1.72893e8 q^{90} +7.01462e8 q^{91} -2.84459e9 q^{92} +5.85277e8 q^{93} -1.27127e8 q^{94} -8.14506e7 q^{95} -1.04473e9 q^{96} -1.26012e9 q^{97} -9.19039e8 q^{98} +4.87052e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	42.1627	1.86334	0.931672	−	0.363300i	$-0.118350\pi$
$2$	42.1627	1.86334	0.931672	+	0.363300i	$0.118350\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	1265.69	2.47205
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−3415.18	−1.07580
$7$	4307.69	0.678114	0.339057	−	0.940766i	$-0.389892\pi$
$7$	4307.69	0.678114	0.339057	+	0.940766i	$0.389892\pi$
$8$	31777.6	2.74294
$9$	6561.00	0.333333
$10$	26351.7	0.833313
$11$	74234.4	1.52876	0.764378	−	0.644769i	$-0.223046\pi$
$11$	74234.4	1.52876	0.764378	+	0.644769i	$0.223046\pi$
$12$	−102521.	−1.42724
$13$	162840.	1.58130	0.790652	−	0.612266i	$-0.209742\pi$
$13$	162840.	1.58130	0.790652	+	0.612266i	$0.209742\pi$
$14$	181624.	1.26356
$15$	−50625.0	−0.258199
$16$	691797.	2.63899
$17$	354849.	1.03044	0.515221	−	0.857057i	$-0.327710\pi$
$17$	354849.	1.03044	0.515221	+	0.857057i	$0.327710\pi$
$18$	276629.	0.621115
$19$	−130321.	−0.229416
$19$	−130321.	−0.229416
$20$	791057.	1.10554
$21$	−348922.	−0.391509
$22$	3.12992e6	2.84860
$23$	−2.24746e6	−1.67462	−0.837309	−	0.546730i	$-0.815873\pi$
$23$	−2.24746e6	−1.67462	−0.837309	+	0.546730i	$0.815873\pi$
$24$	−2.57399e6	−1.58364
$25$	390625.	0.200000
$26$	6.86576e6	2.94651
$27$	−531441.	−0.192450
$28$	5.45220e6	1.67633
$29$	−6.17653e6	−1.62164	−0.810818	−	0.585298i	$-0.800978\pi$
$29$	−6.17653e6	−1.62164	−0.810818	+	0.585298i	$0.800978\pi$
$30$	−2.13449e6	−0.481114
$31$	−7.22564e6	−1.40523	−0.702617	−	0.711568i	$-0.747985\pi$
$31$	−7.22564e6	−1.40523	−0.702617	+	0.711568i	$0.747985\pi$
$32$	1.28978e7	2.17441
$33$	−6.01298e6	−0.882627
$34$	1.49614e7	1.92007
$35$	2.69230e6	0.303262
$36$	8.30420e6	0.824018
$37$	1.44539e7	1.26788	0.633940	−	0.773382i	$-0.281437\pi$
$37$	1.44539e7	1.26788	0.633940	+	0.773382i	$0.281437\pi$
$38$	−5.49468e6	−0.427481
$39$	−1.31900e7	−0.912966
$40$	1.98610e7	1.22668
$41$	−2.14921e7	−1.18782	−0.593911	−	0.804531i	$-0.702417\pi$
$41$	−2.14921e7	−1.18782	−0.593911	+	0.804531i	$0.702417\pi$
$42$	−1.47115e7	−0.729517
$43$	3.51253e7	1.56679	0.783396	−	0.621522i	$-0.213486\pi$
$43$	3.51253e7	1.56679	0.783396	+	0.621522i	$0.213486\pi$
$44$	9.39578e7	3.77916
$45$	4.10062e6	0.149071
$46$	−9.47587e7	−3.12039
$47$	−3.01514e6	−0.0901297	−0.0450648	−	0.998984i	$-0.514349\pi$
$47$	−3.01514e6	−0.0901297	−0.0450648	+	0.998984i	$0.514349\pi$
$48$	−5.60355e7	−1.52362
$49$	−2.17975e7	−0.540161
$50$	1.64698e7	0.372669
$51$	−2.87428e7	−0.594926
$52$	2.06105e8	3.90907
$53$	−5.03255e6	−0.0876087	−0.0438043	−	0.999040i	$-0.513948\pi$
$53$	−5.03255e6	−0.0876087	−0.0438043	+	0.999040i	$0.513948\pi$
$54$	−2.24070e7	−0.358601
$55$	4.63965e7	0.683680
$56$	1.36888e8	1.86003
$57$	1.05560e7	0.132453
$58$	−2.60419e8	−3.02167
$59$	3.96681e7	0.426194	0.213097	−	0.977031i	$-0.431645\pi$
$59$	3.96681e7	0.426194	0.213097	+	0.977031i	$0.431645\pi$
$60$	−6.40756e7	−0.638281
$61$	4.80705e7	0.444524	0.222262	−	0.974987i	$-0.428656\pi$
$61$	4.80705e7	0.444524	0.222262	+	0.974987i	$0.428656\pi$
$62$	−3.04652e8	−2.61844
$63$	2.82627e7	0.226038
$64$	1.89608e8	1.41269
$65$	1.01775e8	0.707180
$66$	−2.53523e8	−1.64464
$67$	6.24392e7	0.378548	0.189274	−	0.981924i	$-0.439387\pi$
$67$	6.24392e7	0.378548	0.189274	+	0.981924i	$0.439387\pi$
$68$	4.49130e8	2.54731
$69$	1.82044e8	0.966841
$70$	1.13515e8	0.565081
$71$	1.78442e8	0.833363	0.416682	−	0.909053i	$-0.363193\pi$
$71$	1.78442e8	0.833363	0.416682	+	0.909053i	$0.363193\pi$
$72$	2.08493e8	0.914314
$73$	3.85248e8	1.58777	0.793886	−	0.608067i	$-0.208055\pi$
$73$	3.85248e8	1.58777	0.793886	+	0.608067i	$0.208055\pi$
$74$	6.09417e8	2.36250
$75$	−3.16406e7	−0.115470
$76$	−1.64946e8	−0.567128
$77$	3.19778e8	1.03667
$78$	−5.56126e8	−1.70117
$79$	−2.10411e8	−0.607781	−0.303890	−	0.952707i	$-0.598286\pi$
$79$	−2.10411e8	−0.607781	−0.303890	+	0.952707i	$0.598286\pi$
$80$	4.32373e8	1.18019
$81$	4.30467e7	0.111111
$82$	−9.06164e8	−2.21332
$83$	4.38569e8	1.01435	0.507173	−	0.861844i	$-0.330690\pi$
$83$	4.38569e8	1.01435	0.507173	+	0.861844i	$0.330690\pi$
$84$	−4.41628e8	−0.967832
$85$	2.21781e8	0.460828
$86$	1.48098e9	2.91948
$87$	5.00299e8	0.936252
$88$	2.35899e9	4.19329
$89$	−5.81991e8	−0.983244	−0.491622	−	0.870809i	$-0.663596\pi$
$89$	−5.81991e8	−0.983244	−0.491622	+	0.870809i	$0.663596\pi$
$90$	1.72893e8	0.277771
$91$	7.01462e8	1.07230
$92$	−2.84459e9	−4.13975
$93$	5.85277e8	0.811312
$94$	−1.27127e8	−0.167943
$95$	−8.14506e7	−0.102598
$96$	−1.04473e9	−1.25540
$97$	−1.26012e9	−1.44524	−0.722619	−	0.691247i	$-0.757062\pi$
$97$	−1.26012e9	−1.44524	−0.722619	+	0.691247i	$0.757062\pi$
$98$	−9.19039e8	−1.00651
$99$	4.87052e8	0.509585
$100$	4.94411e8	0.494411
$101$	−9.27516e8	−0.886901	−0.443451	−	0.896299i	$-0.646246\pi$
$101$	−9.27516e8	−0.886901	−0.443451	+	0.896299i	$0.646246\pi$
$102$	−1.21187e9	−1.10855
$103$	−9.83942e8	−0.861395	−0.430697	−	0.902496i	$-0.641732\pi$
$103$	−9.83942e8	−0.861395	−0.430697	+	0.902496i	$0.641732\pi$
$104$	5.17466e9	4.33742
$105$	−2.18077e8	−0.175088
$106$	−2.12186e8	−0.163245
$107$	−1.36616e9	−1.00757	−0.503786	−	0.863829i	$-0.668060\pi$
$107$	−1.36616e9	−1.00757	−0.503786	+	0.863829i	$0.668060\pi$
$108$	−6.72640e8	−0.475747
$109$	−5.74535e8	−0.389850	−0.194925	−	0.980818i	$-0.562446\pi$
$109$	−5.74535e8	−0.389850	−0.194925	+	0.980818i	$0.562446\pi$
$110$	1.95620e9	1.27393
$111$	−1.17077e9	−0.732011
$112$	2.98004e9	1.78954
$113$	1.54217e9	0.889772	0.444886	−	0.895587i	$-0.353244\pi$
$113$	1.54217e9	0.889772	0.444886	+	0.895587i	$0.353244\pi$
$114$	4.45069e8	0.246806
$115$	−1.40466e9	−0.748912
$116$	−7.81758e9	−4.00877
$117$	1.06839e9	0.527101
$118$	1.67251e9	0.794147
$119$	1.52858e9	0.698758
$120$	−1.60874e9	−0.708225
$121$	3.15279e9	1.33709
$122$	2.02678e9	0.828301
$123$	1.74086e9	0.685790
$124$	−9.14543e9	−3.47381
$125$	2.44141e8	0.0894427
$126$	1.19163e9	0.421187
$127$	1.34581e9	0.459057	0.229529	−	0.973302i	$-0.426282\pi$
$127$	1.34581e9	0.459057	0.229529	+	0.973302i	$0.426282\pi$
$128$	1.39067e9	0.457911
$129$	−2.84515e9	−0.904588
$130$	4.29110e9	1.31772
$131$	−3.79431e9	−1.12567	−0.562836	−	0.826569i	$-0.690290\pi$
$131$	−3.79431e9	−1.12567	−0.562836	+	0.826569i	$0.690290\pi$
$132$	−7.61058e9	−2.18190
$133$	−5.61382e8	−0.155570
$134$	2.63260e9	0.705365
$135$	−3.32151e8	−0.0860663
$136$	1.12763e10	2.82645
$137$	1.43829e9	0.348822	0.174411	−	0.984673i	$-0.444198\pi$
$137$	1.43829e9	0.348822	0.174411	+	0.984673i	$0.444198\pi$
$138$	7.67546e9	1.80156
$139$	3.76934e9	0.856444	0.428222	−	0.903674i	$-0.359140\pi$
$139$	3.76934e9	0.856444	0.428222	+	0.903674i	$0.359140\pi$
$140$	3.40762e9	0.749679
$141$	2.44227e8	0.0520364
$142$	7.52359e9	1.55284
$143$	1.20883e10	2.41743
$144$	4.53888e9	0.879665
$145$	−3.86033e9	−0.725218
$146$	1.62431e10	2.95856
$147$	1.76559e9	0.311862
$148$	1.82942e10	3.13427
$149$	−1.08886e10	−1.80982	−0.904911	−	0.425601i	$-0.860063\pi$
$149$	−1.08886e10	−1.80982	−0.904911	+	0.425601i	$0.860063\pi$
$150$	−1.33405e9	−0.215161
$151$	−1.00665e9	−0.157574	−0.0787868	−	0.996891i	$-0.525105\pi$
$151$	−1.00665e9	−0.157574	−0.0787868	+	0.996891i	$0.525105\pi$
$152$	−4.14129e9	−0.629274
$153$	2.32817e9	0.343481
$154$	1.34827e10	1.93167
$155$	−4.51603e9	−0.628440
$156$	−1.66945e10	−2.25690
$157$	−7.01052e7	−0.00920877	−0.00460438	−	0.999989i	$-0.501466\pi$
$157$	−7.01052e7	−0.00920877	−0.00460438	+	0.999989i	$0.501466\pi$
$158$	−8.87150e9	−1.13250
$159$	4.07637e8	0.0505809
$160$	8.06115e9	0.972428
$161$	−9.68133e9	−1.13558
$162$	1.81497e9	0.207038
$163$	1.67556e10	1.85916	0.929580	−	0.368621i	$-0.120170\pi$
$163$	1.67556e10	1.85916	0.929580	+	0.368621i	$0.120170\pi$
$164$	−2.72024e10	−2.93636
$165$	−3.75811e9	−0.394723
$166$	1.84912e10	1.89008
$167$	1.31550e10	1.30878	0.654388	−	0.756159i	$-0.272926\pi$
$167$	1.31550e10	1.30878	0.654388	+	0.756159i	$0.272926\pi$
$168$	−1.10879e10	−1.07389
$169$	1.59123e10	1.50052
$170$	9.35087e9	0.858681
$171$	−8.55036e8	−0.0764719
$172$	4.44577e10	3.87320
$173$	1.68351e9	0.142892	0.0714460	−	0.997444i	$-0.477239\pi$
$173$	1.68351e9	0.142892	0.0714460	+	0.997444i	$0.477239\pi$
$174$	2.10939e10	1.74456
$175$	1.68269e9	0.135623
$176$	5.13551e10	4.03438
$177$	−3.21312e9	−0.246063
$178$	−2.45383e10	−1.83212
$179$	−8.08125e9	−0.588355	−0.294178	−	0.955751i	$-0.595046\pi$
$179$	−8.08125e9	−0.588355	−0.294178	+	0.955751i	$0.595046\pi$
$180$	5.19013e9	0.368512
$181$	−4.38315e9	−0.303552	−0.151776	−	0.988415i	$-0.548499\pi$
$181$	−4.38315e9	−0.303552	−0.151776	+	0.988415i	$0.548499\pi$
$182$	2.95755e10	1.99807
$183$	−3.89371e9	−0.256646
$184$	−7.14188e10	−4.59338
$185$	9.03371e9	0.567013
$186$	2.46768e10	1.51175
$187$	2.63420e10	1.57529
$188$	−3.81624e9	−0.222805
$189$	−2.28928e9	−0.130503
$190$	−3.43418e9	−0.191175
$191$	2.98562e10	1.62325	0.811623	−	0.584182i	$-0.198585\pi$
$191$	2.98562e10	1.62325	0.811623	+	0.584182i	$0.198585\pi$
$192$	−1.53582e10	−0.815616
$193$	4.60083e9	0.238687	0.119343	−	0.992853i	$-0.461921\pi$
$193$	4.60083e9	0.238687	0.119343	+	0.992853i	$0.461921\pi$
$194$	−5.31301e10	−2.69298
$195$	−8.24376e9	−0.408291
$196$	−2.75889e10	−1.33531
$197$	−3.86777e10	−1.82963	−0.914814	−	0.403875i	$-0.867663\pi$
$197$	−3.86777e10	−1.82963	−0.914814	+	0.403875i	$0.867663\pi$
$198$	2.05354e10	0.949533
$199$	6.60169e8	0.0298412	0.0149206	−	0.999889i	$-0.495250\pi$
$199$	6.60169e8	0.0298412	0.0149206	+	0.999889i	$0.495250\pi$
$200$	1.24131e10	0.548589
$201$	−5.05757e9	−0.218555
$202$	−3.91066e10	−1.65260
$203$	−2.66065e10	−1.09965
$204$	−3.63795e10	−1.47069
$205$	−1.34326e10	−0.531210
$206$	−4.14856e10	−1.60508
$207$	−1.47456e10	−0.558206
$208$	1.12652e11	4.17305
$209$	−9.67430e9	−0.350720
$210$	−9.19469e9	−0.326250
$211$	−4.36337e10	−1.51548	−0.757741	−	0.652556i	$-0.773697\pi$
$211$	−4.36337e10	−1.51548	−0.757741	+	0.652556i	$0.773697\pi$
$212$	−6.36966e9	−0.216573
$213$	−1.44538e10	−0.481142
$214$	−5.76011e10	−1.87745
$215$	2.19533e10	0.700691
$216$	−1.68879e10	−0.527880
$217$	−3.11258e10	−0.952909
$218$	−2.42240e10	−0.726425
$219$	−3.12051e10	−0.916700
$220$	5.87236e10	1.69009
$221$	5.77836e10	1.62944
$222$	−4.93627e10	−1.36399
$223$	−3.72619e10	−1.00900	−0.504502	−	0.863411i	$-0.668324\pi$
$223$	−3.72619e10	−1.00900	−0.504502	+	0.863411i	$0.668324\pi$
$224$	5.55599e10	1.47450
$225$	2.56289e9	0.0666667
$226$	6.50220e10	1.65795
$227$	−6.86748e10	−1.71665	−0.858324	−	0.513109i	$-0.828494\pi$
$227$	−6.86748e10	−1.71665	−0.858324	+	0.513109i	$0.828494\pi$
$228$	1.33606e10	0.327431
$229$	5.06079e10	1.21607	0.608035	−	0.793910i	$-0.291958\pi$
$229$	5.06079e10	1.21607	0.608035	+	0.793910i	$0.291958\pi$
$230$	−5.92242e10	−1.39548
$231$	−2.59020e10	−0.598522
$232$	−1.96276e11	−4.44806
$233$	−3.12776e10	−0.695235	−0.347617	−	0.937636i	$-0.613009\pi$
$233$	−3.12776e10	−0.695235	−0.347617	+	0.937636i	$0.613009\pi$
$234$	4.50462e10	0.982171
$235$	−1.88447e9	−0.0403072
$236$	5.02076e10	1.05357
$237$	1.70433e10	0.350902
$238$	6.44490e10	1.30203
$239$	4.23045e10	0.838680	0.419340	−	0.907829i	$-0.362262\pi$
$239$	4.23045e10	0.838680	0.419340	+	0.907829i	$0.362262\pi$
$240$	−3.50222e10	−0.681386
$241$	3.36067e10	0.641725	0.320863	−	0.947126i	$-0.396027\pi$
$241$	3.36067e10	0.641725	0.320863	+	0.947126i	$0.396027\pi$
$242$	1.32930e11	2.49146
$243$	−3.48678e9	−0.0641500
$244$	6.08425e10	1.09889
$245$	−1.36234e10	−0.241567
$246$	7.33993e10	1.27786
$247$	−2.12214e10	−0.362776
$248$	−2.29614e11	−3.85448
$249$	−3.55241e10	−0.585633
$250$	1.02936e10	0.166663
$251$	1.16669e11	1.85534	0.927670	−	0.373401i	$-0.121808\pi$
$251$	1.16669e11	1.85534	0.927670	+	0.373401i	$0.121808\pi$
$252$	3.57719e10	0.558778
$253$	−1.66838e11	−2.56008
$254$	5.67429e10	0.855382
$255$	−1.79642e10	−0.266059
$256$	−3.84446e10	−0.559443
$257$	1.03923e11	1.48598	0.742989	−	0.669304i	$-0.233407\pi$
$257$	1.03923e11	1.48598	0.742989	+	0.669304i	$0.233407\pi$
$258$	−1.19959e11	−1.68556
$259$	6.22630e10	0.859768
$260$	1.28815e11	1.74819
$261$	−4.05242e10	−0.540545
$262$	−1.59978e11	−2.09751
$263$	6.23590e10	0.803708	0.401854	−	0.915704i	$-0.368366\pi$
$263$	6.23590e10	0.803708	0.401854	+	0.915704i	$0.368366\pi$
$264$	−1.91078e11	−2.42100
$265$	−3.14535e9	−0.0391798
$266$	−2.36694e10	−0.289881
$267$	4.71413e10	0.567676
$268$	7.90287e10	0.935790
$269$	−1.59953e11	−1.86255	−0.931275	−	0.364316i	$-0.881303\pi$
$269$	−1.59953e11	−1.86255	−0.931275	+	0.364316i	$0.881303\pi$
$270$	−1.40044e10	−0.160371
$271$	−2.72801e9	−0.0307245	−0.0153622	−	0.999882i	$-0.504890\pi$
$271$	−2.72801e9	−0.0307245	−0.0153622	+	0.999882i	$0.504890\pi$
$272$	2.45484e11	2.71933
$273$	−5.68184e10	−0.619095
$274$	6.06421e10	0.649975
$275$	2.89978e10	0.305751
$276$	2.30411e11	2.39008
$277$	−1.10528e11	−1.12801	−0.564005	−	0.825771i	$-0.690740\pi$
$277$	−1.10528e11	−1.12801	−0.564005	+	0.825771i	$0.690740\pi$
$278$	1.58926e11	1.59585
$279$	−4.74074e10	−0.468411
$280$	8.55551e10	0.831830
$281$	−7.67249e10	−0.734105	−0.367052	−	0.930200i	$-0.619633\pi$
$281$	−7.67249e10	−0.734105	−0.367052	+	0.930200i	$0.619633\pi$
$282$	1.02973e10	0.0969617
$283$	−6.48484e10	−0.600980	−0.300490	−	0.953785i	$-0.597150\pi$
$283$	−6.48484e10	−0.600980	−0.300490	+	0.953785i	$0.597150\pi$
$284$	2.25852e11	2.06012
$285$	6.59750e9	0.0592349
$286$	5.09675e11	4.50450
$287$	−9.25812e10	−0.805479
$288$	8.46228e10	0.724805
$289$	7.33019e9	0.0618123
$290$	−1.62762e11	−1.35133
$291$	1.02070e11	0.834409
$292$	4.87605e11	3.92505
$293$	7.83259e10	0.620871	0.310435	−	0.950595i	$-0.399525\pi$
$293$	7.83259e10	0.620871	0.310435	+	0.950595i	$0.399525\pi$
$294$	7.44422e10	0.581107
$295$	2.47926e10	0.190600
$296$	4.59312e11	3.47772
$297$	−3.94512e10	−0.294209
$298$	−4.59095e11	−3.37232
$299$	−3.65975e11	−2.64808
$300$	−4.00473e10	−0.285448
$301$	1.51309e11	1.06246
$302$	−4.24432e10	−0.293614
$303$	7.51288e10	0.512053
$304$	−9.01556e10	−0.605427
$305$	3.00441e10	0.198797
$306$	9.81617e10	0.640023
$307$	−1.79134e11	−1.15095	−0.575474	−	0.817820i	$-0.695182\pi$
$307$	−1.79134e11	−1.15095	−0.575474	+	0.817820i	$0.695182\pi$
$308$	4.04741e11	2.56270
$309$	7.96993e10	0.497326
$310$	−1.90408e11	−1.17100
$311$	2.08018e11	1.26090	0.630448	−	0.776232i	$-0.282871\pi$
$311$	2.08018e11	1.26090	0.630448	+	0.776232i	$0.282871\pi$
$312$	−4.19148e11	−2.50421
$313$	−1.16413e11	−0.685572	−0.342786	−	0.939414i	$-0.611371\pi$
$313$	−1.16413e11	−0.685572	−0.342786	+	0.939414i	$0.611371\pi$
$314$	−2.95582e9	−0.0171591
$315$	1.76642e10	0.101087
$316$	−2.66316e11	−1.50247
$317$	−7.33380e10	−0.407908	−0.203954	−	0.978980i	$-0.565379\pi$
$317$	−7.33380e10	−0.407908	−0.203954	+	0.978980i	$0.565379\pi$
$318$	1.71871e10	0.0942496
$319$	−4.58511e11	−2.47908
$320$	1.18505e11	0.631773
$321$	1.10659e11	0.581722
$322$	−4.08191e11	−2.11598
$323$	−4.62443e10	−0.236400
$324$	5.44839e10	0.274673
$325$	6.36092e10	0.316261
$326$	7.06462e11	3.46426
$327$	4.65374e10	0.225080
$328$	−6.82968e11	−3.25813
$329$	−1.29883e10	−0.0611182
$330$	−1.58452e11	−0.735505
$331$	2.18137e11	0.998857	0.499429	−	0.866355i	$-0.333543\pi$
$331$	2.18137e11	0.998857	0.499429	+	0.866355i	$0.333543\pi$
$332$	5.55093e11	2.50752
$333$	9.48323e10	0.422627
$334$	5.54649e11	2.43870
$335$	3.90245e10	0.169292
$336$	−2.41383e11	−1.03319
$337$	1.77079e11	0.747880	0.373940	−	0.927453i	$-0.378007\pi$
$337$	1.77079e11	0.747880	0.373940	+	0.927453i	$0.378007\pi$
$338$	6.70904e11	2.79599
$339$	−1.24916e11	−0.513710
$340$	2.80706e11	1.13919
$341$	−5.36391e11	−2.14826
$342$	−3.60506e10	−0.142494
$343$	−2.67727e11	−1.04441
$344$	1.11620e12	4.29762
$345$	1.13777e11	0.432385
$346$	7.09812e10	0.266257
$347$	−3.26382e11	−1.20849	−0.604246	−	0.796798i	$-0.706525\pi$
$347$	−3.26382e11	−1.20849	−0.604246	+	0.796798i	$0.706525\pi$
$348$	6.33224e11	2.31447
$349$	−4.15204e11	−1.49812	−0.749060	−	0.662502i	$-0.769495\pi$
$349$	−4.15204e11	−1.49812	−0.749060	+	0.662502i	$0.769495\pi$
$350$	7.09467e10	0.252712
$351$	−8.65397e10	−0.304322
$352$	9.57463e11	3.32415
$353$	4.97111e11	1.70399	0.851995	−	0.523550i	$-0.175393\pi$
$353$	4.97111e11	1.70399	0.851995	+	0.523550i	$0.175393\pi$
$354$	−1.35474e11	−0.458501
$355$	1.11526e11	0.372691
$356$	−7.36621e11	−2.43063
$357$	−1.23815e11	−0.403428
$358$	−3.40727e11	−1.09631
$359$	1.57480e11	0.500381	0.250190	−	0.968197i	$-0.419507\pi$
$359$	1.57480e11	0.500381	0.250190	+	0.968197i	$0.419507\pi$
$360$	1.30308e11	0.408894
$361$	1.69836e10	0.0526316
$362$	−1.84805e11	−0.565621
$363$	−2.55376e11	−0.771970
$364$	8.87834e11	2.65079
$365$	2.40780e11	0.710073
$366$	−1.64169e11	−0.478220
$367$	2.64406e10	0.0760806	0.0380403	−	0.999276i	$-0.487888\pi$
$367$	2.64406e10	0.0760806	0.0380403	+	0.999276i	$0.487888\pi$
$368$	−1.55478e12	−4.41931
$369$	−1.41010e11	−0.395941
$370$	3.80885e11	1.05654
$371$	−2.16787e10	−0.0594087
$372$	7.40780e11	2.00561
$373$	5.71401e11	1.52845	0.764226	−	0.644949i	$-0.223121\pi$
$373$	5.71401e11	1.52845	0.764226	+	0.644949i	$0.223121\pi$
$374$	1.11065e12	2.93532
$375$	−1.97754e10	−0.0516398
$376$	−9.58142e10	−0.247221
$377$	−1.00578e12	−2.56430
$378$	−9.65222e10	−0.243172
$379$	−8.32513e10	−0.207260	−0.103630	−	0.994616i	$-0.533046\pi$
$379$	−8.32513e10	−0.207260	−0.103630	+	0.994616i	$0.533046\pi$
$380$	−1.03091e11	−0.253627
$381$	−1.09011e11	−0.265037
$382$	1.25882e12	3.02467
$383$	−5.99445e10	−0.142349	−0.0711746	−	0.997464i	$-0.522675\pi$
$383$	−5.99445e10	−0.142349	−0.0711746	+	0.997464i	$0.522675\pi$
$384$	−1.12645e11	−0.264375
$385$	1.99861e11	0.463613
$386$	1.93983e11	0.444756
$387$	2.30457e11	0.522264
$388$	−1.59492e12	−3.57271
$389$	−2.47682e11	−0.548430	−0.274215	−	0.961668i	$-0.588418\pi$
$389$	−2.47682e11	−0.548430	−0.274215	+	0.961668i	$0.588418\pi$
$390$	−3.47579e11	−0.760786
$391$	−7.97508e11	−1.72560
$392$	−6.92672e11	−1.48163
$393$	3.07339e11	0.649907
$394$	−1.63076e12	−3.40923
$395$	−1.31507e11	−0.271808
$396$	6.16457e11	1.25972
$397$	−3.00342e11	−0.606818	−0.303409	−	0.952860i	$-0.598125\pi$
$397$	−3.00342e11	−0.606818	−0.303409	+	0.952860i	$0.598125\pi$
$398$	2.78345e10	0.0556045
$399$	4.54719e10	0.0898184
$400$	2.70233e11	0.527799
$401$	9.30124e11	1.79635	0.898175	−	0.439637i	$-0.144893\pi$
$401$	9.30124e11	1.79635	0.898175	+	0.439637i	$0.144893\pi$
$402$	−2.13241e11	−0.407243
$403$	−1.17662e12	−2.22210
$404$	−1.17395e12	−2.19247
$405$	2.69042e10	0.0496904
$406$	−1.12180e12	−2.04904
$407$	1.07298e12	1.93828
$408$	−9.13378e11	−1.63185
$409$	1.16060e11	0.205082	0.102541	−	0.994729i	$-0.467303\pi$
$409$	1.16060e11	0.205082	0.102541	+	0.994729i	$0.467303\pi$
$410$	−5.66353e11	−0.989828
$411$	−1.16501e11	−0.201392
$412$	−1.24537e12	−2.12941
$413$	1.70878e11	0.289008
$414$	−6.21712e11	−1.04013
$415$	2.74105e11	0.453629
$416$	2.10028e12	3.43841
$417$	−3.05317e11	−0.494468
$418$	−4.07894e11	−0.653513
$419$	−4.76693e10	−0.0755572	−0.0377786	−	0.999286i	$-0.512028\pi$
$419$	−4.76693e10	−0.0755572	−0.0377786	+	0.999286i	$0.512028\pi$
$420$	−2.76018e11	−0.432828
$421$	−2.00569e11	−0.311168	−0.155584	−	0.987823i	$-0.549726\pi$
$421$	−2.00569e11	−0.311168	−0.155584	+	0.987823i	$0.549726\pi$
$422$	−1.83971e12	−2.82386
$423$	−1.97824e10	−0.0300432
$424$	−1.59923e11	−0.240306
$425$	1.38613e11	0.206089
$426$	−6.09411e11	−0.896534
$427$	2.07073e11	0.301438
$428$	−1.72914e12	−2.49077
$429$	−9.79152e11	−1.39570
$430$	9.25610e11	1.30563
$431$	−2.20817e11	−0.308238	−0.154119	−	0.988052i	$-0.549254\pi$
$431$	−2.20817e11	−0.308238	−0.154119	+	0.988052i	$0.549254\pi$
$432$	−3.67649e11	−0.507875
$433$	5.38843e11	0.736659	0.368329	−	0.929695i	$-0.379930\pi$
$433$	5.38843e11	0.736659	0.368329	+	0.929695i	$0.379930\pi$
$434$	−1.31235e12	−1.77560
$435$	3.12687e11	0.418705
$436$	−7.27185e11	−0.963730
$437$	2.92891e11	0.384184
$438$	−1.31569e12	−1.70813
$439$	−1.32718e11	−0.170545	−0.0852726	−	0.996358i	$-0.527176\pi$
$439$	−1.32718e11	−0.170545	−0.0852726	+	0.996358i	$0.527176\pi$
$440$	1.47437e12	1.87530
$441$	−1.43013e11	−0.180054
$442$	2.43631e12	3.03621
$443$	1.38941e12	1.71401	0.857004	−	0.515310i	$-0.172323\pi$
$443$	1.38941e12	1.71401	0.857004	+	0.515310i	$0.172323\pi$
$444$	−1.48183e12	−1.80957
$445$	−3.63744e11	−0.439720
$446$	−1.57106e12	−1.88012
$447$	8.81980e11	1.04490
$448$	8.16771e11	0.957964
$449$	7.72066e11	0.896491	0.448246	−	0.893910i	$-0.352049\pi$
$449$	7.72066e11	0.896491	0.448246	+	0.893910i	$0.352049\pi$
$450$	1.08058e11	0.124223
$451$	−1.59545e12	−1.81589
$452$	1.95191e12	2.19957
$453$	8.15388e10	0.0909751
$454$	−2.89551e12	−3.19871
$455$	4.38414e11	0.479549
$456$	3.35445e11	0.363312
$457$	1.91930e11	0.205835	0.102918	−	0.994690i	$-0.467182\pi$
$457$	1.91930e11	0.205835	0.102918	+	0.994690i	$0.467182\pi$
$458$	2.13376e12	2.26596
$459$	−1.88582e11	−0.198309
$460$	−1.77787e12	−1.85135
$461$	−6.29659e11	−0.649309	−0.324654	−	0.945833i	$-0.605248\pi$
$461$	−6.29659e11	−0.649309	−0.324654	+	0.945833i	$0.605248\pi$
$462$	−1.09210e12	−1.11525
$463$	−1.37998e12	−1.39560	−0.697798	−	0.716295i	$-0.745837\pi$
$463$	−1.37998e12	−1.39560	−0.697798	+	0.716295i	$0.745837\pi$
$464$	−4.27290e12	−4.27949
$465$	3.65798e11	0.362830
$466$	−1.31875e12	−1.29546
$467$	−2.93064e10	−0.0285126	−0.0142563	−	0.999898i	$-0.504538\pi$
$467$	−2.93064e10	−0.0285126	−0.0142563	+	0.999898i	$0.504538\pi$
$468$	1.35225e12	1.30302
$469$	2.68968e11	0.256699
$470$	−7.94541e10	−0.0751062
$471$	5.67852e9	0.00531669
$472$	1.26056e12	1.16903
$473$	2.60750e12	2.39524
$474$	7.18591e11	0.653852
$475$	−5.09066e10	−0.0458831
$476$	1.93471e12	1.72737
$477$	−3.30186e10	−0.0292029
$478$	1.78367e12	1.56275
$479$	−1.81052e12	−1.57143	−0.785713	−	0.618591i	$-0.787704\pi$
$479$	−1.81052e12	−1.57143	−0.785713	+	0.618591i	$0.787704\pi$
$480$	−6.52953e11	−0.561431
$481$	2.35367e12	2.00490
$482$	1.41695e12	1.19576
$483$	7.84188e11	0.655629
$484$	3.99046e12	3.30536
$485$	−7.87575e11	−0.646330
$486$	−1.47012e11	−0.119534
$487$	6.42786e10	0.0517828	0.0258914	−	0.999665i	$-0.491758\pi$
$487$	6.42786e10	0.0517828	0.0258914	+	0.999665i	$0.491758\pi$
$488$	1.52757e12	1.21930
$489$	−1.35721e12	−1.07339
$490$	−5.74399e11	−0.450123
$491$	−4.82952e11	−0.375005	−0.187503	−	0.982264i	$-0.560039\pi$
$491$	−4.82952e11	−0.375005	−0.187503	+	0.982264i	$0.560039\pi$
$492$	2.20339e12	1.69531
$493$	−2.19174e12	−1.67100
$494$	−8.94752e11	−0.675976
$495$	3.04407e11	0.227893
$496$	−4.99867e12	−3.70841
$497$	7.68671e11	0.565115
$498$	−1.49779e12	−1.09124
$499$	6.03897e11	0.436024	0.218012	−	0.975946i	$-0.430043\pi$
$499$	6.03897e11	0.436024	0.218012	+	0.975946i	$0.430043\pi$
$500$	3.09007e11	0.221107
$501$	−1.06555e12	−0.755623
$502$	4.91908e12	3.45714
$503$	−1.68239e12	−1.17185	−0.585924	−	0.810366i	$-0.699268\pi$
$503$	−1.68239e12	−1.17185	−0.585924	+	0.810366i	$0.699268\pi$
$504$	8.98123e11	0.620009
$505$	−5.79697e11	−0.396634
$506$	−7.03436e12	−4.77031
$507$	−1.28889e12	−0.866326
$508$	1.70338e12	1.13481
$509$	−8.98608e11	−0.593390	−0.296695	−	0.954972i	$-0.595885\pi$
$509$	−8.98608e11	−0.593390	−0.296695	+	0.954972i	$0.595885\pi$
$510$	−7.57421e11	−0.495760
$511$	1.65953e12	1.07669
$512$	−2.33295e12	−1.50035
$513$	6.92579e10	0.0441511
$514$	4.38167e12	2.76889
$515$	−6.14964e11	−0.385227
$516$	−3.60108e12	−2.23619
$517$	−2.23827e11	−0.137786
$518$	2.62517e12	1.60204
$519$	−1.36364e11	−0.0824987
$520$	3.23416e12	1.93976
$521$	−7.14639e11	−0.424930	−0.212465	−	0.977169i	$-0.568149\pi$
$521$	−7.14639e11	−0.424930	−0.212465	+	0.977169i	$0.568149\pi$
$522$	−1.70861e12	−1.00722
$523$	8.33054e11	0.486873	0.243437	−	0.969917i	$-0.421725\pi$
$523$	8.33054e11	0.486873	0.243437	+	0.969917i	$0.421725\pi$
$524$	−4.80242e12	−2.78272
$525$	−1.36298e11	−0.0783019
$526$	2.62922e12	1.49759
$527$	−2.56401e12	−1.44801
$528$	−4.15976e12	−2.32925
$529$	3.24990e12	1.80435
$530$	−1.32616e11	−0.0730055
$531$	2.60263e11	0.142065
$532$	−7.10536e11	−0.384577
$533$	−3.49977e12	−1.87831
$534$	1.98760e12	1.05778
$535$	−8.53853e11	−0.450600
$536$	1.98417e12	1.03833
$537$	6.54581e11	0.339687
$538$	−6.74406e12	−3.47057
$539$	−1.61812e12	−0.825774
$540$	−4.20400e11	−0.212760
$541$	1.76040e12	0.883534	0.441767	−	0.897130i	$-0.354352\pi$
$541$	1.76040e12	0.883534	0.441767	+	0.897130i	$0.354352\pi$
$542$	−1.15020e11	−0.0572503
$543$	3.55035e11	0.175256
$544$	4.57679e12	2.24061
$545$	−3.59085e11	−0.174346
$546$	−2.39562e12	−1.15359
$547$	2.32762e12	1.11165	0.555826	−	0.831298i	$-0.312402\pi$
$547$	2.32762e12	1.11165	0.555826	+	0.831298i	$0.312402\pi$
$548$	1.82043e12	0.862306
$549$	3.15391e11	0.148175
$550$	1.22262e12	0.569720
$551$	8.04931e11	0.372029
$552$	5.78493e12	2.65199
$553$	−9.06385e11	−0.412145
$554$	−4.66015e12	−2.10187
$555$	−7.31730e11	−0.327365
$556$	4.77082e12	2.11718
$557$	1.10535e10	0.00486576	0.00243288	−	0.999997i	$-0.499226\pi$
$557$	1.10535e10	0.00486576	0.00243288	+	0.999997i	$0.499226\pi$
$558$	−1.99882e12	−0.872812
$559$	5.71979e12	2.47757
$560$	1.86253e12	0.800306
$561$	−2.13370e12	−0.909497
$562$	−3.23493e12	−1.36789
$563$	−3.95297e10	−0.0165820	−0.00829098	−	0.999966i	$-0.502639\pi$
$563$	−3.95297e10	−0.0165820	−0.00829098	+	0.999966i	$0.502639\pi$
$564$	3.09116e11	0.128637
$565$	9.63856e11	0.397918
$566$	−2.73418e12	−1.11983
$567$	1.85432e11	0.0753460
$568$	5.67046e12	2.28587
$569$	−2.70995e12	−1.08382	−0.541909	−	0.840437i	$-0.682298\pi$
$569$	−2.70995e12	−1.08382	−0.541909	+	0.840437i	$0.682298\pi$
$570$	2.78168e11	0.110375
$571$	−2.00739e12	−0.790260	−0.395130	−	0.918625i	$-0.629301\pi$
$571$	−2.00739e12	−0.790260	−0.395130	+	0.918625i	$0.629301\pi$
$572$	1.53001e13	5.97600
$573$	−2.41835e12	−0.937181
$574$	−3.90347e12	−1.50089
$575$	−8.77912e11	−0.334924
$576$	1.24402e12	0.470896
$577$	−3.29242e12	−1.23658	−0.618292	−	0.785949i	$-0.712175\pi$
$577$	−3.29242e12	−1.23658	−0.618292	+	0.785949i	$0.712175\pi$
$578$	3.09061e11	0.115178
$579$	−3.72668e11	−0.137806
$580$	−4.88599e12	−1.79278
$581$	1.88922e12	0.687843
$582$	4.30354e12	1.55479
$583$	−3.73588e11	−0.133932
$584$	1.22423e13	4.35517
$585$	6.67744e11	0.235727
$586$	3.30243e12	1.15690
$587$	8.93550e11	0.310633	0.155316	−	0.987865i	$-0.450360\pi$
$587$	8.93550e11	0.310633	0.155316	+	0.987865i	$0.450360\pi$
$588$	2.23470e12	0.770940
$589$	9.41653e11	0.322383
$590$	1.04532e12	0.355153
$591$	3.13290e12	1.05634
$592$	9.99918e12	3.34593
$593$	−4.89417e12	−1.62530	−0.812648	−	0.582754i	$-0.801975\pi$
$593$	−4.89417e12	−1.62530	−0.812648	+	0.582754i	$0.801975\pi$
$594$	−1.66337e12	−0.548213
$595$	9.55362e11	0.312494
$596$	−1.37817e13	−4.47398
$597$	−5.34737e10	−0.0172288
$598$	−1.54305e13	−4.93428
$599$	−5.85373e12	−1.85785	−0.928927	−	0.370262i	$-0.879268\pi$
$599$	−5.85373e12	−1.85785	−0.928927	+	0.370262i	$0.879268\pi$
$600$	−1.00546e12	−0.316728
$601$	−3.52256e8	−0.000110134 0	−5.50672e−5	−	1.00000i	$-0.500018\pi$
$601$	−3.52256e8	−0.000110134 0	−5.50672e−5		1.00000i	$0.500018\pi$
$602$	6.37958e12	1.97974
$603$	4.09663e11	0.126183
$604$	−1.27411e12	−0.389530
$605$	1.97050e12	0.597966
$606$	3.16763e12	0.954130
$607$	1.43160e12	0.428029	0.214015	−	0.976830i	$-0.431346\pi$
$607$	1.43160e12	0.428029	0.214015	+	0.976830i	$0.431346\pi$
$608$	−1.68086e12	−0.498845
$609$	2.15513e12	0.634886
$610$	1.26674e12	0.370427
$611$	−4.90985e11	−0.142522
$612$	2.94674e12	0.849103
$613$	−2.44906e12	−0.700530	−0.350265	−	0.936651i	$-0.613908\pi$
$613$	−2.44906e12	−0.700530	−0.350265	+	0.936651i	$0.613908\pi$
$614$	−7.55278e12	−2.14461
$615$	1.08804e12	0.306694
$616$	1.01618e13	2.84353
$617$	1.27744e12	0.354859	0.177430	−	0.984134i	$-0.443222\pi$
$617$	1.27744e12	0.354859	0.177430	+	0.984134i	$0.443222\pi$
$618$	3.36034e12	0.926691
$619$	3.08748e12	0.845272	0.422636	−	0.906300i	$-0.361105\pi$
$619$	3.08748e12	0.845272	0.422636	+	0.906300i	$0.361105\pi$
$620$	−5.71589e12	−1.55354
$621$	1.19439e12	0.322280
$622$	8.77060e12	2.34948
$623$	−2.50703e12	−0.666752
$624$	−9.12481e12	−2.40931
$625$	1.52588e11	0.0400000
$626$	−4.90829e12	−1.27746
$627$	7.83618e11	0.202489
$628$	−8.87315e10	−0.0227646
$629$	5.12897e12	1.30648
$630$	7.44770e11	0.188360
$631$	−4.36233e12	−1.09543	−0.547717	−	0.836663i	$-0.684503\pi$
$631$	−4.36233e12	−1.09543	−0.547717	+	0.836663i	$0.684503\pi$
$632$	−6.68637e12	−1.66711
$633$	3.53433e12	0.874963
$634$	−3.09212e12	−0.760073
$635$	8.41131e11	0.205297
$636$	5.15943e11	0.125039
$637$	−3.54949e12	−0.854159
$638$	−1.93320e13	−4.61939
$639$	1.17076e12	0.277788
$640$	8.69172e11	0.204784
$641$	−1.54180e12	−0.360717	−0.180359	−	0.983601i	$-0.557726\pi$
$641$	−1.54180e12	−0.360717	−0.180359	+	0.983601i	$0.557726\pi$
$642$	4.66569e12	1.08395
$643$	4.74956e12	1.09573	0.547866	−	0.836566i	$-0.315440\pi$
$643$	4.74956e12	1.09573	0.547866	+	0.836566i	$0.315440\pi$
$644$	−1.22536e13	−2.80722
$645$	−1.77822e12	−0.404544
$646$	−1.94978e12	−0.440494
$647$	1.49108e12	0.334526	0.167263	−	0.985912i	$-0.446507\pi$
$647$	1.49108e12	0.334526	0.167263	+	0.985912i	$0.446507\pi$
$648$	1.36792e12	0.304771
$649$	2.94474e12	0.651547
$650$	2.68194e12	0.589303
$651$	2.52119e12	0.550162
$652$	2.12075e13	4.59594
$653$	1.87208e12	0.402916	0.201458	−	0.979497i	$-0.435432\pi$
$653$	1.87208e12	0.402916	0.201458	+	0.979497i	$0.435432\pi$
$654$	1.96214e12	0.419402
$655$	−2.37144e12	−0.503415
$656$	−1.48682e13	−3.13466
$657$	2.52761e12	0.529257
$658$	−5.47621e11	−0.113884
$659$	3.73969e12	0.772417	0.386208	−	0.922412i	$-0.373785\pi$
$659$	3.73969e12	0.772417	0.386208	+	0.922412i	$0.373785\pi$
$660$	−4.75661e12	−0.975776
$661$	3.42693e11	0.0698229	0.0349115	−	0.999390i	$-0.488885\pi$
$661$	3.42693e11	0.0698229	0.0349115	+	0.999390i	$0.488885\pi$
$662$	9.19724e12	1.86122
$663$	−4.68047e12	−0.940759
$664$	1.39367e13	2.78229
$665$	−3.50864e11	−0.0695730
$666$	3.99838e12	0.787499
$667$	1.38815e13	2.71562
$668$	1.66501e13	3.23537
$669$	3.01821e12	0.582549
$670$	1.64538e12	0.315449
$671$	3.56849e12	0.679568
$672$	−4.50035e12	−0.851303
$673$	−3.70572e11	−0.0696314	−0.0348157	−	0.999394i	$-0.511084\pi$
$673$	−3.70572e11	−0.0696314	−0.0348157	+	0.999394i	$0.511084\pi$
$674$	7.46612e12	1.39356
$675$	−2.07594e11	−0.0384900
$676$	2.01400e13	3.70937
$677$	3.80524e11	0.0696199	0.0348099	−	0.999394i	$-0.488917\pi$
$677$	3.80524e11	0.0696199	0.0348099	+	0.999394i	$0.488917\pi$
$678$	−5.26678e12	−0.957220
$679$	−5.42820e12	−0.980036
$680$	7.04767e12	1.26403
$681$	5.56266e12	0.991107
$682$	−2.26157e13	−4.00295
$683$	8.53340e12	1.50047	0.750237	−	0.661169i	$-0.229939\pi$
$683$	8.53340e12	1.50047	0.750237	+	0.661169i	$0.229939\pi$
$684$	−1.08221e12	−0.189043
$685$	8.98930e11	0.155998
$686$	−1.12881e13	−1.94609
$687$	−4.09924e12	−0.702099
$688$	2.42995e13	4.13476
$689$	−8.19500e11	−0.138536
$690$	4.79716e12	0.805682
$691$	−6.78420e12	−1.13200	−0.566001	−	0.824404i	$-0.691510\pi$
$691$	−6.78420e12	−1.13200	−0.566001	+	0.824404i	$0.691510\pi$
$692$	2.13080e12	0.353237
$693$	2.09807e12	0.345557
$694$	−1.37611e13	−2.25184
$695$	2.35584e12	0.383013
$696$	1.58983e13	2.56809
$697$	−7.62646e12	−1.22398
$698$	−1.75061e13	−2.79152
$699$	2.53348e12	0.401394
$700$	2.12977e12	0.335267
$701$	7.95433e11	0.124415	0.0622074	−	0.998063i	$-0.480186\pi$
$701$	7.95433e11	0.124415	0.0622074	+	0.998063i	$0.480186\pi$
$702$	−3.64874e12	−0.567057
$703$	−1.88365e12	−0.290872
$704$	1.40754e13	2.15965
$705$	1.52642e11	0.0232714
$706$	2.09595e13	3.17512
$707$	−3.99545e12	−0.601420
$708$	−4.06682e12	−0.608282
$709$	−4.69255e12	−0.697430	−0.348715	−	0.937229i	$-0.613382\pi$
$709$	−4.69255e12	−0.697430	−0.348715	+	0.937229i	$0.613382\pi$
$710$	4.70224e12	0.694452
$711$	−1.38051e12	−0.202594
$712$	−1.84943e13	−2.69698
$713$	1.62393e13	2.35323
$714$	−5.22037e12	−0.751725
$715$	7.55519e12	1.08111
$716$	−1.02284e13	−1.45445
$717$	−3.42666e12	−0.484212
$718$	6.63978e12	0.932382
$719$	−1.20325e13	−1.67910	−0.839548	−	0.543285i	$-0.817180\pi$
$719$	−1.20325e13	−1.67910	−0.839548	+	0.543285i	$0.817180\pi$
$720$	2.83680e12	0.393398
$721$	−4.23851e12	−0.584124
$722$	7.16072e11	0.0980708
$723$	−2.72214e12	−0.370500
$724$	−5.54771e12	−0.750396
$725$	−2.41271e12	−0.324327
$726$	−1.07673e13	−1.43845
$727$	−1.16580e13	−1.54781	−0.773907	−	0.633300i	$-0.781700\pi$
$727$	−1.16580e13	−1.54781	−0.773907	+	0.633300i	$0.781700\pi$
$728$	2.22908e13	2.94127
$729$	2.82430e11	0.0370370
$730$	1.01519e13	1.32311
$731$	1.24642e13	1.61449
$732$	−4.92824e12	−0.634442
$733$	−5.51320e12	−0.705400	−0.352700	−	0.935736i	$-0.614736\pi$
$733$	−5.51320e12	−0.705400	−0.352700	+	0.935736i	$0.614736\pi$
$734$	1.11481e12	0.141764
$735$	1.10350e12	0.139469
$736$	−2.89873e13	−3.64131
$737$	4.63513e12	0.578707
$738$	−5.94534e12	−0.737774
$739$	1.00015e13	1.23357	0.616785	−	0.787132i	$-0.288435\pi$
$739$	1.00015e13	1.23357	0.616785	+	0.787132i	$0.288435\pi$
$740$	1.14339e13	1.40169
$741$	1.71894e12	0.209449
$742$	−9.14030e11	−0.110699
$743$	1.17956e13	1.41994	0.709971	−	0.704231i	$-0.248708\pi$
$743$	1.17956e13	1.41994	0.709971	+	0.704231i	$0.248708\pi$
$744$	1.85987e13	2.22538
$745$	−6.80540e12	−0.809377
$746$	2.40918e13	2.84803
$747$	2.87745e12	0.338115
$748$	3.33409e13	3.89421
$749$	−5.88500e12	−0.683248
$750$	−8.33783e11	−0.0962227
$751$	−7.19306e12	−0.825152	−0.412576	−	0.910923i	$-0.635371\pi$
$751$	−7.19306e12	−0.825152	−0.412576	+	0.910923i	$0.635371\pi$
$752$	−2.08587e12	−0.237852
$753$	−9.45018e12	−1.07118
$754$	−4.24065e13	−4.77817
$755$	−6.29158e11	−0.0704690
$756$	−2.89752e12	−0.322611
$757$	1.10668e13	1.22488	0.612438	−	0.790518i	$-0.290189\pi$
$757$	1.10668e13	1.22488	0.612438	+	0.790518i	$0.290189\pi$
$758$	−3.51010e12	−0.386196
$759$	1.35139e13	1.47806
$760$	−2.58831e12	−0.281420
$761$	6.81864e12	0.736998	0.368499	−	0.929628i	$-0.379872\pi$
$761$	6.81864e12	0.736998	0.368499	+	0.929628i	$0.379872\pi$
$762$	−4.59618e12	−0.493855
$763$	−2.47492e12	−0.264363
$764$	3.77887e13	4.01275
$765$	1.45510e12	0.153609
$766$	−2.52742e12	−0.265245
$767$	6.45954e12	0.673942
$768$	3.11401e12	0.322994
$769$	−2.25133e12	−0.232151	−0.116076	−	0.993240i	$-0.537031\pi$
$769$	−2.25133e12	−0.232151	−0.116076	+	0.993240i	$0.537031\pi$
$770$	8.42669e12	0.863871
$771$	−8.41776e12	−0.857930
$772$	5.82324e12	0.590047
$773$	−4.47111e12	−0.450409	−0.225205	−	0.974311i	$-0.572305\pi$
$773$	−4.47111e12	−0.450409	−0.225205	+	0.974311i	$0.572305\pi$
$774$	9.71668e12	0.973158
$775$	−2.82252e12	−0.281047
$776$	−4.00437e13	−3.96421
$777$	−5.04330e12	−0.496387
$778$	−1.04429e13	−1.02191
$779$	2.80087e12	0.272505
$780$	−1.04341e13	−1.00932
$781$	1.32465e13	1.27401
$782$	−3.36251e13	−3.21538
$783$	3.28246e12	0.312084
$784$	−1.50794e13	−1.42548
$785$	−4.38157e10	−0.00411829
$786$	1.29582e13	1.21100
$787$	−1.74254e13	−1.61918	−0.809590	−	0.586995i	$-0.800311\pi$
$787$	−1.74254e13	−1.61918	−0.809590	+	0.586995i	$0.800311\pi$
$788$	−4.89541e13	−4.52294
$789$	−5.05108e12	−0.464021
$790$	−5.54469e12	−0.506472
$791$	6.64318e12	0.603367
$792$	1.54774e13	1.39776
$793$	7.82779e12	0.702926
$794$	−1.26632e13	−1.13071
$795$	2.54773e11	0.0226205
$796$	8.35570e11	0.0737691
$797$	−1.51639e13	−1.33122	−0.665609	−	0.746301i	$-0.731828\pi$
$797$	−1.51639e13	−1.33122	−0.665609	+	0.746301i	$0.731828\pi$
$798$	1.91722e12	0.167363
$799$	−1.06992e12	−0.0928735
$800$	5.03822e12	0.434883
$801$	−3.81844e12	−0.327748
$802$	3.92165e13	3.34722
$803$	2.85987e13	2.42731
$804$	−6.40133e12	−0.540279
$805$	−6.05083e12	−0.507848
$806$	−4.96095e13	−4.14054
$807$	1.29562e13	1.07534
$808$	−2.94743e13	−2.43272
$809$	−8.53556e12	−0.700590	−0.350295	−	0.936639i	$-0.613919\pi$
$809$	−8.53556e12	−0.700590	−0.350295	+	0.936639i	$0.613919\pi$
$810$	1.13435e12	0.0925903
$811$	3.02349e12	0.245423	0.122711	−	0.992442i	$-0.460841\pi$
$811$	3.02349e12	0.245423	0.122711	+	0.992442i	$0.460841\pi$
$812$	−3.36757e13	−2.71840
$813$	2.20969e11	0.0177388
$814$	4.52397e13	3.61168
$815$	1.04723e13	0.831441
$816$	−1.98842e13	−1.57001
$817$	−4.57756e12	−0.359447
$818$	4.89341e12	0.382139
$819$	4.60229e12	0.357435
$820$	−1.70015e13	−1.31318
$821$	1.44269e13	1.10822	0.554112	−	0.832442i	$-0.313058\pi$
$821$	1.44269e13	1.10822	0.554112	+	0.832442i	$0.313058\pi$
$822$	−4.91201e12	−0.375263
$823$	1.81599e13	1.37979	0.689895	−	0.723909i	$-0.257657\pi$
$823$	1.81599e13	1.37979	0.689895	+	0.723909i	$0.257657\pi$
$824$	−3.12674e13	−2.36276
$825$	−2.34882e12	−0.176525
$826$	7.20466e12	0.538522
$827$	−1.95479e13	−1.45320	−0.726598	−	0.687063i	$-0.758900\pi$
$827$	−1.95479e13	−1.45320	−0.726598	+	0.687063i	$0.758900\pi$
$828$	−1.86633e13	−1.37992
$829$	1.13483e13	0.834515	0.417257	−	0.908788i	$-0.362991\pi$
$829$	1.13483e13	0.834515	0.417257	+	0.908788i	$0.362991\pi$
$830$	1.15570e13	0.845268
$831$	8.95276e12	0.651257
$832$	3.08757e13	2.23389
$833$	−7.73481e12	−0.556605
$834$	−1.28730e13	−0.921365
$835$	8.22185e12	0.585303
$836$	−1.22447e13	−0.867000
$837$	3.84000e12	0.270437
$838$	−2.00987e12	−0.140789
$839$	−3.54258e12	−0.246826	−0.123413	−	0.992355i	$-0.539384\pi$
$839$	−3.54258e12	−0.246826	−0.123413	+	0.992355i	$0.539384\pi$
$840$	−6.92996e12	−0.480257
$841$	2.36424e13	1.62970
$842$	−8.45654e12	−0.579814
$843$	6.21472e12	0.423836
$844$	−5.52267e13	−3.74635
$845$	9.94516e12	0.671053
$846$	−8.34077e11	−0.0559809
$847$	1.35812e13	0.906701
$848$	−3.48150e12	−0.231199
$849$	5.25272e12	0.346976
$850$	5.84430e12	0.384014
$851$	−3.24846e13	−2.12322
$852$	−1.82940e13	−1.18941
$853$	−2.35196e13	−1.52111	−0.760554	−	0.649274i	$-0.775073\pi$
$853$	−2.35196e13	−1.52111	−0.760554	+	0.649274i	$0.775073\pi$
$854$	8.73074e12	0.561682
$855$	−5.34398e11	−0.0341993
$856$	−4.34135e13	−2.76371
$857$	−2.87466e13	−1.82042	−0.910211	−	0.414144i	$-0.864081\pi$
$857$	−2.87466e13	−1.82042	−0.910211	+	0.414144i	$0.864081\pi$
$858$	−4.12837e13	−2.60067
$859$	−8.92058e12	−0.559015	−0.279508	−	0.960143i	$-0.590171\pi$
$859$	−8.92058e12	−0.559015	−0.279508	+	0.960143i	$0.590171\pi$
$860$	2.77861e13	1.73215
$861$	7.49908e12	0.465044
$862$	−9.31025e12	−0.574353
$863$	2.81109e13	1.72514	0.862572	−	0.505934i	$-0.168852\pi$
$863$	2.81109e13	1.72514	0.862572	+	0.505934i	$0.168852\pi$
$864$	−6.85444e12	−0.418466
$865$	1.05219e12	0.0639032
$866$	2.27191e13	1.37265
$867$	−5.93746e11	−0.0356874
$868$	−3.93956e13	−2.35564
$869$	−1.56197e13	−0.929148
$870$	1.31837e13	0.780191
$871$	1.01676e13	0.598599
$872$	−1.82574e13	−1.06934
$873$	−8.26765e12	−0.481746
$874$	1.23491e13	0.715867
$875$	1.05168e12	0.0606524
$876$	−3.94960e13	−2.26613
$877$	2.44924e12	0.139808	0.0699042	−	0.997554i	$-0.477731\pi$
$877$	2.44924e12	0.139808	0.0699042	+	0.997554i	$0.477731\pi$
$878$	−5.59575e12	−0.317785
$879$	−6.34440e12	−0.358460
$880$	3.20969e13	1.80423
$881$	−2.82122e13	−1.57777	−0.788887	−	0.614538i	$-0.789342\pi$
$881$	−2.82122e13	−1.57777	−0.788887	+	0.614538i	$0.789342\pi$
$882$	−6.02982e12	−0.335502
$883$	5.81063e12	0.321662	0.160831	−	0.986982i	$-0.448583\pi$
$883$	5.81063e12	0.321662	0.160831	+	0.986982i	$0.448583\pi$
$884$	7.31361e13	4.02807
$885$	−2.00820e12	−0.110043
$886$	5.85811e13	3.19379
$887$	7.85261e12	0.425949	0.212975	−	0.977058i	$-0.431685\pi$
$887$	7.85261e12	0.425949	0.212975	+	0.977058i	$0.431685\pi$
$888$	−3.72043e13	−2.00786
$889$	5.79732e12	0.311293
$890$	−1.53364e13	−0.819350
$891$	3.19555e12	0.169862
$892$	−4.71620e13	−2.49431
$893$	3.92937e11	0.0206772
$894$	3.71867e13	1.94701
$895$	−5.05078e12	−0.263121
$896$	5.99059e12	0.310516
$897$	2.96440e13	1.52887
$898$	3.25524e13	1.67047
$899$	4.46294e13	2.27878
$900$	3.24383e12	0.164804
$901$	−1.78580e12	−0.0902757
$902$	−6.72685e13	−3.38363
$903$	−1.22560e13	−0.613414
$904$	4.90065e13	2.44060
$905$	−2.73947e12	−0.135752
$906$	3.43790e12	0.169518
$907$	5.00320e12	0.245479	0.122740	−	0.992439i	$-0.460832\pi$
$907$	5.00320e12	0.245479	0.122740	+	0.992439i	$0.460832\pi$
$908$	−8.69211e13	−4.24364
$909$	−6.08543e12	−0.295634
$910$	1.84847e13	0.893565
$911$	8.14427e12	0.391760	0.195880	−	0.980628i	$-0.437244\pi$
$911$	8.14427e12	0.391760	0.195880	+	0.980628i	$0.437244\pi$
$912$	7.30261e12	0.349543
$913$	3.25569e13	1.55069
$914$	8.09228e12	0.383542
$915$	−2.43357e12	−0.114775
$916$	6.40540e13	3.00619
$917$	−1.63447e13	−0.763333
$918$	−7.95110e12	−0.369518
$919$	−4.01615e13	−1.85733	−0.928667	−	0.370915i	$-0.879044\pi$
$919$	−4.01615e13	−1.85733	−0.928667	+	0.370915i	$0.879044\pi$
$920$	−4.46368e13	−2.05422
$921$	1.45099e13	0.664500
$922$	−2.65481e13	−1.20989
$923$	2.90574e13	1.31780
$924$	−3.27840e13	−1.47958
$925$	5.64607e12	0.253576
$926$	−5.81838e13	−2.60048
$927$	−6.45565e12	−0.287132
$928$	−7.96639e13	−3.52611
$929$	2.84210e13	1.25190	0.625948	−	0.779865i	$-0.284712\pi$
$929$	2.84210e13	1.25190	0.625948	+	0.779865i	$0.284712\pi$
$930$	1.54230e13	0.676077
$931$	2.84067e12	0.123921
$932$	−3.95878e13	−1.71866
$933$	−1.68495e13	−0.727979
$934$	−1.23564e12	−0.0531287
$935$	1.64638e13	0.704493
$936$	3.39510e13	1.44581
$937$	−2.34042e11	−0.00991896	−0.00495948	−	0.999988i	$-0.501579\pi$
$937$	−2.34042e11	−0.00991896	−0.00495948	+	0.999988i	$0.501579\pi$
$938$	1.13404e13	0.478318
$939$	9.42947e12	0.395815
$940$	−2.38515e12	−0.0996416
$941$	−1.24609e13	−0.518079	−0.259039	−	0.965867i	$-0.583406\pi$
$941$	−1.24609e13	−0.518079	−0.259039	+	0.965867i	$0.583406\pi$
$942$	2.39422e11	0.00990682
$943$	4.83025e13	1.98915
$944$	2.74423e13	1.12472
$945$	−1.43080e12	−0.0583628
$946$	1.09939e14	4.46316
$947$	3.79693e13	1.53412	0.767058	−	0.641578i	$-0.221720\pi$
$947$	3.79693e13	1.53412	0.767058	+	0.641578i	$0.221720\pi$
$948$	2.15716e13	0.867449
$949$	6.27337e13	2.51075
$950$	−2.14636e12	−0.0854961
$951$	5.94037e12	0.235506
$952$	4.85747e13	1.91665
$953$	−5.77774e12	−0.226903	−0.113451	−	0.993544i	$-0.536191\pi$
$953$	−5.77774e12	−0.226903	−0.113451	+	0.993544i	$0.536191\pi$
$954$	−1.39215e12	−0.0544151
$955$	1.86601e13	0.725937
$956$	5.35444e13	2.07326
$957$	3.71394e13	1.43130
$958$	−7.63364e13	−2.92811
$959$	6.19569e12	0.236541
$960$	−9.59889e12	−0.364754
$961$	2.57703e13	0.974684
$962$	9.92372e13	3.73583
$963$	−8.96340e12	−0.335857
$964$	4.25357e13	1.58638
$965$	2.87552e12	0.106744
$966$	3.30635e13	1.22166
$967$	3.46199e13	1.27323	0.636615	−	0.771182i	$-0.280334\pi$
$967$	3.46199e13	1.27323	0.636615	+	0.771182i	$0.280334\pi$
$968$	1.00188e14	3.66757
$969$	3.74579e12	0.136485
$970$	−3.32063e13	−1.20434
$971$	−9.50632e12	−0.343183	−0.171592	−	0.985168i	$-0.554891\pi$
$971$	−9.50632e12	−0.343183	−0.171592	+	0.985168i	$0.554891\pi$
$972$	−4.41319e12	−0.158582
$973$	1.62371e13	0.580767
$974$	2.71016e12	0.0964893
$975$	−5.15235e12	−0.182593
$976$	3.32550e13	1.17310
$977$	4.65814e13	1.63564	0.817818	−	0.575477i	$-0.195183\pi$
$977$	4.65814e13	1.63564	0.817818	+	0.575477i	$0.195183\pi$
$978$	−5.72235e13	−2.00009
$979$	−4.32037e13	−1.50314
$980$	−1.72430e13	−0.597168
$981$	−3.76953e12	−0.129950
$982$	−2.03626e13	−0.698764
$983$	−3.08095e13	−1.05243	−0.526215	−	0.850351i	$-0.676389\pi$
$983$	−3.08095e13	−1.05243	−0.526215	+	0.850351i	$0.676389\pi$
$984$	5.53204e13	1.88108
$985$	−2.41736e13	−0.818235
$986$	−9.24095e13	−3.11366
$987$	1.05205e12	0.0352866
$988$	−2.68598e13	−0.896801
$989$	−7.89425e13	−2.62378
$990$	1.28346e13	0.424644
$991$	1.90167e13	0.626331	0.313166	−	0.949699i	$-0.398611\pi$
$991$	1.90167e13	0.626331	0.313166	+	0.949699i	$0.398611\pi$
$992$	−9.31952e13	−3.05556
$993$	−1.76691e13	−0.576691
$994$	3.24092e13	1.05300
$995$	4.12606e11	0.0133454
$996$	−4.49625e13	−1.44772
$997$	5.10662e13	1.63684	0.818419	−	0.574622i	$-0.194851\pi$
$997$	5.10662e13	1.63684	0.818419	+	0.574622i	$0.194851\pi$
$998$	2.54619e13	0.812462
$999$	−7.68141e12	−0.244004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.h.1.14	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.h.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+42.1627 q^{2} -81.0000 q^{3} +1265.69 q^{4} +625.000 q^{5} -3415.18 q^{6} +4307.69 q^{7} +31777.6 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+42.1627 q^{2} -81.0000 q^{3} +1265.69 q^{4} +625.000 q^{5} -3415.18 q^{6} +4307.69 q^{7} +31777.6 q^{8} +6561.00 q^{9} +26351.7 q^{10} +74234.4 q^{11} -102521. q^{12} +162840. q^{13} +181624. q^{14} -50625.0 q^{15} +691797. q^{16} +354849. q^{17} +276629. q^{18} -130321. q^{19} +791057. q^{20} -348922. q^{21} +3.12992e6 q^{22} -2.24746e6 q^{23} -2.57399e6 q^{24} +390625. q^{25} +6.86576e6 q^{26} -531441. q^{27} +5.45220e6 q^{28} -6.17653e6 q^{29} -2.13449e6 q^{30} -7.22564e6 q^{31} +1.28978e7 q^{32} -6.01298e6 q^{33} +1.49614e7 q^{34} +2.69230e6 q^{35} +8.30420e6 q^{36} +1.44539e7 q^{37} -5.49468e6 q^{38} -1.31900e7 q^{39} +1.98610e7 q^{40} -2.14921e7 q^{41} -1.47115e7 q^{42} +3.51253e7 q^{43} +9.39578e7 q^{44} +4.10062e6 q^{45} -9.47587e7 q^{46} -3.01514e6 q^{47} -5.60355e7 q^{48} -2.17975e7 q^{49} +1.64698e7 q^{50} -2.87428e7 q^{51} +2.06105e8 q^{52} -5.03255e6 q^{53} -2.24070e7 q^{54} +4.63965e7 q^{55} +1.36888e8 q^{56} +1.05560e7 q^{57} -2.60419e8 q^{58} +3.96681e7 q^{59} -6.40756e7 q^{60} +4.80705e7 q^{61} -3.04652e8 q^{62} +2.82627e7 q^{63} +1.89608e8 q^{64} +1.01775e8 q^{65} -2.53523e8 q^{66} +6.24392e7 q^{67} +4.49130e8 q^{68} +1.82044e8 q^{69} +1.13515e8 q^{70} +1.78442e8 q^{71} +2.08493e8 q^{72} +3.85248e8 q^{73} +6.09417e8 q^{74} -3.16406e7 q^{75} -1.64946e8 q^{76} +3.19778e8 q^{77} -5.56126e8 q^{78} -2.10411e8 q^{79} +4.32373e8 q^{80} +4.30467e7 q^{81} -9.06164e8 q^{82} +4.38569e8 q^{83} -4.41628e8 q^{84} +2.21781e8 q^{85} +1.48098e9 q^{86} +5.00299e8 q^{87} +2.35899e9 q^{88} -5.81991e8 q^{89} +1.72893e8 q^{90} +7.01462e8 q^{91} -2.84459e9 q^{92} +5.85277e8 q^{93} -1.27127e8 q^{94} -8.14506e7 q^{95} -1.04473e9 q^{96} -1.26012e9 q^{97} -9.19039e8 q^{98} +4.87052e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 17 q^{2} - 1215 q^{3} + 5055 q^{4} + 9375 q^{5} + 1377 q^{6} + 1352 q^{7} - 3597 q^{8} + 98415 q^{9}+O(q^{10}) \) 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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