LMFDB - Embedded newform 17.12.b.a.16.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [17,12,Mod(16,17)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(17, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("17.16");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 17 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	17.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$13.0618340695$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2012924 x^{14} + 1580196076372 x^{12} + \cdots + 11\!\cdots\!16 $ x^16 + 2012924x^14 + 1580196076372x^12 + 612185482864471968x^10 + 122089588908147616630464x^8 + 12002063596127081323758696960x^6 + 538160293280924897115168650612736x^4 + 8663850655413946592880080714919542784*x^2 + 11159369979872736421907749802317490159616
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{29}\cdot 3^{4}\cdot 17^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			16.13
Root			$-37.5132i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.12.b.a.16.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+61.5054 q^{2} -37.5132i q^{3} +1734.91 q^{4} -7015.33i q^{5} -2307.27i q^{6} -40939.8i q^{7} -19256.6 q^{8} +175740. q^{9} +O(q^{10})$	\(q+61.5054 q^{2} -37.5132i q^{3} +1734.91 q^{4} -7015.33i q^{5} -2307.27i q^{6} -40939.8i q^{7} -19256.6 q^{8} +175740. q^{9} -431481. i q^{10} -436092. i q^{11} -65082.1i q^{12} +954432. q^{13} -2.51802e6i q^{14} -263168. q^{15} -4.73748e6 q^{16} +(1.84007e6 + 5.55752e6i) q^{17} +1.08089e7 q^{18} -2.78988e6 q^{19} -1.21710e7i q^{20} -1.53578e6 q^{21} -2.68220e7i q^{22} -4.14357e7i q^{23} +722376. i q^{24} -386743. q^{25} +5.87027e7 q^{26} -1.32379e7i q^{27} -7.10269e7i q^{28} +1.18734e8i q^{29} -1.61862e7 q^{30} +1.77240e8i q^{31} -2.51943e8 q^{32} -1.63592e7 q^{33} +(1.13174e8 + 3.41817e8i) q^{34} -2.87206e8 q^{35} +3.04893e8 q^{36} +5.80565e8i q^{37} -1.71593e8 q^{38} -3.58038e7i q^{39} +1.35091e8i q^{40} +1.07835e8i q^{41} -9.44590e7 q^{42} -1.42735e7 q^{43} -7.56581e8i q^{44} -1.23287e9i q^{45} -2.54852e9i q^{46} +1.65181e9 q^{47} +1.77718e8i q^{48} +3.01260e8 q^{49} -2.37868e7 q^{50} +(2.08480e8 - 6.90271e7i) q^{51} +1.65586e9 q^{52} -1.69980e9 q^{53} -8.14203e8i q^{54} -3.05933e9 q^{55} +7.88360e8i q^{56} +1.04658e8i q^{57} +7.30279e9i q^{58} +1.97623e9 q^{59} -4.56573e8 q^{60} -7.84931e9i q^{61} +1.09012e10i q^{62} -7.19475e9i q^{63} -5.79350e9 q^{64} -6.69565e9i q^{65} -1.00618e9 q^{66} +1.92771e10 q^{67} +(3.19237e9 + 9.64181e9i) q^{68} -1.55439e9 q^{69} -1.76647e10 q^{70} +4.81174e9i q^{71} -3.38415e9 q^{72} -1.24976e10i q^{73} +3.57079e10i q^{74} +1.45080e7i q^{75} -4.84020e9 q^{76} -1.78535e10 q^{77} -2.20213e9i q^{78} -2.94120e10i q^{79} +3.32350e10i q^{80} +3.06352e10 q^{81} +6.63241e9i q^{82} +2.55654e9 q^{83} -2.66445e9 q^{84} +(3.89878e10 - 1.29087e10i) q^{85} -8.77895e8 q^{86} +4.45410e9 q^{87} +8.39764e9i q^{88} -9.01332e10 q^{89} -7.58283e10i q^{90} -3.90742e10i q^{91} -7.18873e10i q^{92} +6.64885e9 q^{93} +1.01595e11 q^{94} +1.95720e10i q^{95} +9.45120e9i q^{96} -1.01766e10i q^{97} +1.85291e10 q^{98} -7.66387e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 20338 * q^4 - 4098 * q^8 - 1191496 * q^9	$ 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9} - 1045192 q^{13} - 928176 q^{15} + 34826050 q^{16} + 3554632 q^{17} - 35173654 q^{18} + 4588736 q^{19} + 66662344 q^{21} - 58748400 q^{25} - 317977540 q^{26} - 131021808 q^{30} + 1067460734 q^{32} + 724766552 q^{33} - 775893498 q^{34} + 1999765296 q^{35} - 2520870986 q^{36} - 1607971816 q^{38} + 1845301744 q^{42} - 2666979472 q^{43} + 1869667792 q^{47} - 5944064168 q^{49} + 15444320726 q^{50} + 8437689968 q^{51} - 7784119948 q^{52} - 5942183760 q^{53} - 11128140752 q^{55} + 7494118800 q^{59} - 2434494672 q^{60} + 80595388930 q^{64} - 86599472704 q^{66} + 17007290816 q^{67} + 73491523226 q^{68} + 13676754040 q^{69} - 91280536608 q^{70} - 229207542918 q^{72} + 149151579272 q^{76} + 32130668824 q^{77} + 145538020840 q^{81} - 112706231184 q^{83} + 424712287520 q^{84} + 77452876928 q^{85} + 64143446456 q^{86} - 368269123632 q^{87} - 89466414808 q^{89} - 57312497768 q^{93} - 672691463040 q^{94} + 274175066082 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 20338 * q^4 - 4098 * q^8 - 1191496 * q^9 - 1045192 * q^13 - 928176 * q^15 + 34826050 * q^16 + 3554632 * q^17 - 35173654 * q^18 + 4588736 * q^19 + 66662344 * q^21 - 58748400 * q^25 - 317977540 * q^26 - 131021808 * q^30 + 1067460734 * q^32 + 724766552 * q^33 - 775893498 * q^34 + 1999765296 * q^35 - 2520870986 * q^36 - 1607971816 * q^38 + 1845301744 * q^42 - 2666979472 * q^43 + 1869667792 * q^47 - 5944064168 * q^49 + 15444320726 * q^50 + 8437689968 * q^51 - 7784119948 * q^52 - 5942183760 * q^53 - 11128140752 * q^55 + 7494118800 * q^59 - 2434494672 * q^60 + 80595388930 * q^64 - 86599472704 * q^66 + 17007290816 * q^67 + 73491523226 * q^68 + 13676754040 * q^69 - 91280536608 * q^70 - 229207542918 * q^72 + 149151579272 * q^76 + 32130668824 * q^77 + 145538020840 * q^81 - 112706231184 * q^83 + 424712287520 * q^84 + 77452876928 * q^85 + 64143446456 * q^86 - 368269123632 * q^87 - 89466414808 * q^89 - 57312497768 * q^93 - 672691463040 * q^94 + 274175066082 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/17\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	61.5054			1.35909			0.679545	−	0.733634i	$-0.262177\pi$
$2$	61.5054			1.35909			0.679545	+	0.733634i	$0.262177\pi$
$3$		−	37.5132i		−	0.0891287i	−0.999007	−	0.0445643i	$-0.985810\pi$
$3$		−	37.5132i		−	0.0891287i	0.999007	−	0.0445643i	$-0.0141900\pi$
$4$	1734.91			0.847125
$5$		−	7015.33i		−	1.00395i	−0.864881	−	0.501976i	$-0.832606\pi$
$5$		−	7015.33i		−	1.00395i	0.864881	−	0.501976i	$-0.167394\pi$
$6$		−	2307.27i		−	0.121134i
$7$		−	40939.8i		−	0.920675i	−0.887744	−	0.460338i	$-0.847728\pi$
$7$		−	40939.8i		−	0.920675i	0.887744	−	0.460338i	$-0.152272\pi$
$8$	−19256.6			−0.207771
$9$	175740.			0.992056
$10$		−	431481.i		−	1.36446i
$11$		−	436092.i		−	0.816429i	−0.912886	−	0.408214i	$-0.866152\pi$
$11$		−	436092.i		−	0.816429i	0.912886	−	0.408214i	$-0.133848\pi$
$12$		−	65082.1i		−	0.0755031i
$13$	954432.			0.712946			0.356473	−	0.934306i	$-0.383979\pi$
$13$	954432.			0.712946			0.356473	+	0.934306i	$0.383979\pi$
$14$		−	2.51802e6i		−	1.25128i
$15$	−263168.			−0.0894810
$16$	−4.73748e6			−1.12950
$17$	1.84007e6	+	5.55752e6i	0.314316	+	0.949319i
$17$	1.84007e6	+	5.55752e6i	0.314316	+	0.949319i
$18$	1.08089e7			1.34829
$19$	−2.78988e6			−0.258489			−0.129244	−	0.991613i	$-0.541255\pi$
$19$	−2.78988e6			−0.258489			−0.129244	+	0.991613i	$0.541255\pi$
$20$		−	1.21710e7i		−	0.850473i
$21$	−1.53578e6			−0.0820586
$22$		−	2.68220e7i		−	1.10960i
$23$		−	4.14357e7i		−	1.34237i	−0.741291	−	0.671184i	$-0.765786\pi$
$23$		−	4.14357e7i		−	1.34237i	0.741291	−	0.671184i	$-0.234214\pi$
$24$			722376.i			0.0185183i
$25$	−386743.			−0.00792050
$26$	5.87027e7			0.968957
$27$		−	1.32379e7i		−	0.177549i
$28$		−	7.10269e7i		−	0.779927i
$29$			1.18734e8i			1.07495i	0.843281	+	0.537473i	$0.180621\pi$
$29$			1.18734e8i			1.07495i	−0.843281	+	0.537473i	$0.819379\pi$
$30$	−1.61862e7			−0.121613
$31$			1.77240e8i			1.11192i	0.831210	+	0.555959i	$0.187649\pi$
$31$			1.77240e8i			1.11192i	−0.831210	+	0.555959i	$0.812351\pi$
$32$	−2.51943e8			−1.32733
$33$	−1.63592e7			−0.0727672
$34$	1.13174e8	+	3.41817e8i	0.427183	+	1.29021i
$35$	−2.87206e8			−0.924314
$36$	3.04893e8			0.840396
$37$			5.80565e8i			1.37639i	0.725526	+	0.688195i	$0.241596\pi$
$37$			5.80565e8i			1.37639i	−0.725526	+	0.688195i	$0.758404\pi$
$38$	−1.71593e8			−0.351309
$39$		−	3.58038e7i		−	0.0635439i
$40$			1.35091e8i			0.208592i
$41$			1.07835e8i			0.145361i	0.997355	+	0.0726804i	$0.0231553\pi$
$41$			1.07835e8i			0.145361i	−0.997355	+	0.0726804i	$0.976845\pi$
$42$	−9.44590e7			−0.111525
$43$	−1.42735e7			−0.0148065			−0.00740326	−	0.999973i	$-0.502357\pi$
$43$	−1.42735e7			−0.0148065			−0.00740326	+	0.999973i	$0.502357\pi$
$44$		−	7.56581e8i		−	0.691617i
$45$		−	1.23287e9i		−	0.995977i
$46$		−	2.54852e9i		−	1.82440i
$47$	1.65181e9			1.05056			0.525281	−	0.850929i	$-0.323960\pi$
$47$	1.65181e9			1.05056			0.525281	+	0.850929i	$0.323960\pi$
$48$			1.77718e8i			0.100671i
$49$	3.01260e8			0.152357
$50$	−2.37868e7			−0.0107647
$51$	2.08480e8	−	6.90271e7i	0.0846115	−	0.0280145i
$52$	1.65586e9			0.603954
$53$	−1.69980e9			−0.558318			−0.279159	−	0.960245i	$-0.590056\pi$
$53$	−1.69980e9			−0.558318			−0.279159	+	0.960245i	$0.590056\pi$
$54$		−	8.14203e8i		−	0.241305i
$55$	−3.05933e9			−0.819656
$56$			7.88360e8i			0.191289i
$57$			1.04658e8i			0.0230387i
$58$			7.30279e9i			1.46095i
$59$	1.97623e9			0.359876			0.179938	−	0.983678i	$-0.442410\pi$
$59$	1.97623e9			0.359876			0.179938	+	0.983678i	$0.442410\pi$
$60$	−4.56573e8			−0.0758016
$61$		−	7.84931e9i		−	1.18992i	−0.803756	−	0.594960i	$-0.797168\pi$
$61$		−	7.84931e9i		−	1.18992i	0.803756	−	0.594960i	$-0.202832\pi$
$62$			1.09012e10i			1.51120i
$63$		−	7.19475e9i		−	0.913361i
$64$	−5.79350e9			−0.674452
$65$		−	6.69565e9i		−	0.715763i
$66$	−1.00618e9			−0.0988972
$67$	1.92771e10			1.74434			0.872169	−	0.489205i	$-0.162713\pi$
$67$	1.92771e10			1.74434			0.872169	+	0.489205i	$0.162713\pi$
$68$	3.19237e9	+	9.64181e9i	0.266265	+	0.804192i
$69$	−1.55439e9			−0.119643
$70$	−1.76647e10			−1.25623
$71$			4.81174e9i			0.316505i	0.987399	+	0.158253i	$0.0505860\pi$
$71$			4.81174e9i			0.316505i	−0.987399	+	0.158253i	$0.949414\pi$
$72$	−3.38415e9			−0.206120
$73$		−	1.24976e10i		−	0.705586i	−0.935701	−	0.352793i	$-0.885232\pi$
$73$		−	1.24976e10i		−	0.705586i	0.935701	−	0.352793i	$-0.114768\pi$
$74$			3.57079e10i			1.87064i
$75$			1.45080e7i			0.000705944i
$76$	−4.84020e9			−0.218972
$77$	−1.78535e10			−0.751666
$78$		−	2.20213e9i		−	0.0863619i
$79$		−	2.94120e10i		−	1.07541i	−0.843132	−	0.537706i	$-0.819291\pi$
$79$		−	2.94120e10i		−	1.07541i	0.843132	−	0.537706i	$-0.180709\pi$
$80$			3.32350e10i			1.13397i
$81$	3.06352e10			0.976231
$82$			6.63241e9i			0.197558i
$83$	2.55654e9			0.0712399			0.0356199	−	0.999365i	$-0.488659\pi$
$83$	2.55654e9			0.0712399			0.0356199	+	0.999365i	$0.488659\pi$
$84$	−2.66445e9			−0.0695139
$85$	3.89878e10	−	1.29087e10i	0.953071	−	0.315558i
$86$	−8.77895e8			−0.0201234
$87$	4.45410e9			0.0958085
$88$			8.39764e9i			0.169630i
$89$	−9.01332e10			−1.71096			−0.855480	−	0.517837i	$-0.826738\pi$
$89$	−9.01332e10			−1.71096			−0.855480	+	0.517837i	$0.826738\pi$
$90$		−	7.58283e10i		−	1.35362i
$91$		−	3.90742e10i		−	0.656391i
$92$		−	7.18873e10i		−	1.13715i
$93$	6.64885e9			0.0991038
$94$	1.01595e11			1.42781
$95$			1.95720e10i			0.259510i
$96$			9.45120e9i			0.118303i
$97$		−	1.01766e10i		−	0.120325i	−0.998189	−	0.0601626i	$-0.980838\pi$
$97$		−	1.01766e10i		−	0.120325i	0.998189	−	0.0601626i	$-0.0191619\pi$
$98$	1.85291e10			0.207067
$99$		−	7.66387e10i		−	0.809943i
$100$	−6.70965e8			−0.00670965
$101$	6.71725e10			0.635951			0.317976	−	0.948099i	$-0.396997\pi$
$101$	6.71725e10			0.635951			0.317976	+	0.948099i	$0.396997\pi$
$102$	1.28227e10	−	4.24554e9i	0.114995	−	0.0380743i
$103$	−5.26906e10			−0.447846			−0.223923	−	0.974607i	$-0.571886\pi$
$103$	−5.26906e10			−0.447846			−0.223923	+	0.974607i	$0.571886\pi$
$104$	−1.83791e10			−0.148129
$105$			1.07740e10i			0.0823829i
$106$	−1.04547e11			−0.758804
$107$			2.30745e11i			1.59046i	0.606309	+	0.795229i	$0.292650\pi$
$107$			2.30745e11i			1.59046i	−0.606309	+	0.795229i	$0.707350\pi$
$108$		−	2.29666e10i		−	0.150406i
$109$			2.37657e11i			1.47946i	0.672901	+	0.739732i	$0.265048\pi$
$109$			2.37657e11i			1.47946i	−0.672901	+	0.739732i	$0.734952\pi$
$110$	−1.88165e11			−1.11399
$111$	2.17789e10			0.122676
$112$			1.93952e11i			1.03991i
$113$			1.18308e11i			0.604062i	0.953298	+	0.302031i	$0.0976646\pi$
$113$			1.18308e11i			0.604062i	−0.953298	+	0.302031i	$0.902335\pi$
$114$			6.43700e9i			0.0313117i
$115$	−2.90685e11			−1.34767
$116$			2.05993e11i			0.910614i
$117$	1.67732e11			0.707282
$118$	1.21549e11			0.489103
$119$	2.27524e11	−	7.53322e10i	0.874014	−	0.289383i
$120$	5.06771e9			0.0185915
$121$	9.51354e10			0.333444
$122$		−	4.82775e11i		−	1.61721i
$123$	4.04523e9			0.0129558
$124$			3.07496e11i			0.941934i
$125$		−	3.39832e11i		−	0.996001i
$126$		−	4.42516e11i		−	1.24134i
$127$	−5.94266e11			−1.59610			−0.798050	−	0.602591i	$-0.794135\pi$
$127$	−5.94266e11			−1.59610			−0.798050	+	0.602591i	$0.794135\pi$
$128$	1.59648e11			0.410686
$129$			5.35444e8i			0.00131969i
$130$		−	4.11819e11i		−	0.972787i
$131$		−	3.66561e11i		−	0.830145i	−0.909788	−	0.415073i	$-0.863756\pi$
$131$		−	3.66561e11i		−	0.830145i	0.909788	−	0.415073i	$-0.136244\pi$
$132$	−2.83818e10			−0.0616429
$133$			1.14217e11i			0.237984i
$134$	1.18565e12			2.37071
$135$	−9.28684e10			−0.178251
$136$	−3.54335e10	−	1.07019e11i	−0.0653056	−	0.197241i
$137$	1.59466e11			0.282297			0.141148	−	0.989988i	$-0.454921\pi$
$137$	1.59466e11			0.282297			0.141148	+	0.989988i	$0.454921\pi$
$138$	−9.56031e10			−0.162606
$139$			7.52929e11i			1.23076i	0.788231	+	0.615379i	$0.210997\pi$
$139$			7.52929e11i			1.23076i	−0.788231	+	0.615379i	$0.789003\pi$
$140$	−4.98278e11			−0.783010
$141$		−	6.19647e10i		−	0.0936352i
$142$			2.95948e11i			0.430159i
$143$		−	4.16220e11i		−	0.582069i
$144$	−8.32564e11			−1.12053
$145$	8.32959e11			1.07919
$146$		−	7.68669e11i		−	0.958955i
$147$		−	1.13012e10i		−	0.0135794i
$148$			1.00723e12i			1.16597i
$149$	−1.63907e12			−1.82840			−0.914202	−	0.405259i	$-0.867181\pi$
$149$	−1.63907e12			−1.82840			−0.914202	+	0.405259i	$0.867181\pi$
$150$			8.92319e8i			0.000959441i
$151$	1.57160e12			1.62917			0.814587	−	0.580041i	$-0.196963\pi$
$151$	1.57160e12			1.62917			0.814587	+	0.580041i	$0.196963\pi$
$152$	5.37236e10			0.0537063
$153$	3.23374e11	+	9.76677e11i	0.311819	+	0.941777i
$154$	−1.09809e12			−1.02158
$155$	1.24340e12			1.11631
$156$		−	6.21165e10i		−	0.0538296i
$157$	−1.24309e12			−1.04005			−0.520027	−	0.854150i	$-0.674078\pi$
$157$	−1.24309e12			−1.04005			−0.520027	+	0.854150i	$0.674078\pi$
$158$		−	1.80899e12i		−	1.46158i
$159$			6.37651e10i			0.0497621i
$160$			1.76747e12i			1.33257i
$161$	−1.69637e12			−1.23588
$162$	1.88423e12			1.32679
$163$			1.76482e12i			1.20135i	0.799494	+	0.600675i	$0.205101\pi$
$163$			1.76482e12i			1.20135i	−0.799494	+	0.600675i	$0.794899\pi$
$164$			1.87084e11i			0.123139i
$165$			1.14765e11i			0.0730548i
$166$	1.57241e11			0.0968214
$167$		−	2.00184e12i		−	1.19258i	−0.802768	−	0.596292i	$-0.796640\pi$
$167$		−	2.00184e12i		−	1.19258i	0.802768	−	0.596292i	$-0.203360\pi$
$168$	2.95739e10			0.0170494
$169$	−8.81221e11			−0.491709
$170$	2.39796e12	−	7.93956e11i	1.29531	−	0.428872i
$171$	−4.90293e11			−0.256435
$172$	−2.47632e10			−0.0125430
$173$			3.54453e11i			0.173902i	0.996213	+	0.0869511i	$0.0277124\pi$
$173$			3.54453e11i			0.173902i	−0.996213	+	0.0869511i	$0.972288\pi$
$174$	2.73951e11			0.130212
$175$			1.58332e10i			0.00729221i
$176$			2.06598e12i			0.922160i
$177$		−	7.41349e10i		−	0.0320752i
$178$	−5.54368e12			−2.32535
$179$	3.84094e11			0.156223			0.0781116	−	0.996945i	$-0.475111\pi$
$179$	3.84094e11			0.156223			0.0781116	+	0.996945i	$0.475111\pi$
$180$		−	2.13893e12i		−	0.843717i
$181$			3.59801e12i			1.37667i	0.725392	+	0.688336i	$0.241659\pi$
$181$			3.59801e12i			1.37667i	−0.725392	+	0.688336i	$0.758341\pi$
$182$		−	2.40328e12i		−	0.892095i
$183$	−2.94453e11			−0.106056
$184$			7.97910e11i			0.278905i
$185$	4.07285e12			1.38183
$186$	4.08940e11			0.134691
$187$	2.42359e12	−	8.02441e11i	0.775051	−	0.256616i
$188$	2.86574e12			0.889957
$189$	−5.41958e11			−0.163465
$190$			1.20378e12i			0.352698i
$191$	−5.54417e12			−1.57817			−0.789084	−	0.614285i	$-0.789444\pi$
$191$	−5.54417e12			−1.57817			−0.789084	+	0.614285i	$0.789444\pi$
$192$			2.17333e11i			0.0601130i
$193$			6.31838e11i			0.169840i	0.996388	+	0.0849202i	$0.0270635\pi$
$193$			6.31838e11i			0.169840i	−0.996388	+	0.0849202i	$0.972936\pi$
$194$		−	6.25914e11i		−	0.163533i
$195$	−2.51176e11			−0.0637951
$196$	5.22660e11			0.129066
$197$		−	7.74159e12i		−	1.85894i	−0.368895	−	0.929471i	$-0.620264\pi$
$197$		−	7.74159e12i		−	1.85894i	0.368895	−	0.929471i	$-0.379736\pi$
$198$		−	4.71369e12i		−	1.10079i
$199$		−	1.47357e12i		−	0.334718i	−0.985896	−	0.167359i	$-0.946476\pi$
$199$		−	1.47357e12i		−	0.334718i	0.985896	−	0.167359i	$-0.0535239\pi$
$200$	7.44735e9			0.00164565
$201$		−	7.23147e11i		−	0.155471i
$202$	4.13147e12			0.864315
$203$	4.86095e12			0.989676
$204$	3.61695e11	−	1.19756e11i	0.0716765	−	0.0237318i
$205$	7.56496e11			0.145935
$206$	−3.24076e12			−0.608663
$207$		−	7.28190e12i		−	1.33170i
$208$	−4.52160e12			−0.805275
$209$			1.21665e12i			0.211038i
$210$			6.62661e11i			0.111966i
$211$		−	1.93592e11i		−	0.0318664i	−0.999873	−	0.0159332i	$-0.994928\pi$
$211$		−	1.93592e11i		−	0.0318664i	0.999873	−	0.0159332i	$-0.00507191\pi$
$212$	−2.94901e12			−0.472965
$213$	1.80504e11			0.0282097
$214$			1.41921e13i			2.16158i
$215$			1.00133e11i			0.0148650i
$216$			2.54917e11i			0.0368895i
$217$	7.25617e12			1.02372
$218$			1.46172e13i			2.01072i
$219$	−4.68825e11			−0.0628880
$220$	−5.30767e12			−0.694351
$221$	1.75622e12	+	5.30427e12i	0.224090	+	0.676812i
$222$	1.33952e12			0.166727
$223$	−8.10132e12			−0.983737			−0.491869	−	0.870669i	$-0.663686\pi$
$223$	−8.10132e12			−0.983737			−0.491869	+	0.870669i	$0.663686\pi$
$224$			1.03145e13i			1.22204i
$225$	−6.79661e10			−0.00785758
$226$			7.27656e12i			0.820975i
$227$		−	1.47294e13i		−	1.62197i	−0.585065	−	0.810987i	$-0.698931\pi$
$227$		−	1.47294e13i		−	1.62197i	0.585065	−	0.810987i	$-0.301069\pi$
$228$			1.81572e11i			0.0195167i
$229$	−6.60411e12			−0.692977			−0.346489	−	0.938054i	$-0.612626\pi$
$229$	−6.60411e12			−0.692977			−0.346489	+	0.938054i	$0.612626\pi$
$230$	−1.78787e13			−1.83161
$231$			6.69743e11i			0.0669950i
$232$		−	2.28641e12i		−	0.223342i
$233$			1.89377e13i			1.80663i	0.428979	+	0.903314i	$0.358873\pi$
$233$			1.89377e13i			1.80663i	−0.428979	+	0.903314i	$0.641127\pi$
$234$	1.03164e13			0.961260
$235$		−	1.15880e13i		−	1.05471i
$236$	3.42859e12			0.304860
$237$	−1.10334e12			−0.0958501
$238$	1.39939e13	−	4.63334e12i	1.18786	−	0.393297i
$239$	8.13918e12			0.675138			0.337569	−	0.941301i	$-0.390395\pi$
$239$	8.13918e12			0.675138			0.337569	+	0.941301i	$0.390395\pi$
$240$	1.24675e12			0.101069
$241$		−	5.41957e12i		−	0.429409i	−0.976679	−	0.214704i	$-0.931121\pi$
$241$		−	5.41957e12i		−	0.429409i	0.976679	−	0.214704i	$-0.0688788\pi$
$242$	5.85134e12			0.453180
$243$		−	3.49428e12i		−	0.264560i
$244$		−	1.36179e13i		−	1.00801i
$245$		−	2.11344e12i		−	0.152960i
$246$	2.48803e11			0.0176081
$247$	−2.66275e12			−0.184288
$248$		−	3.41304e12i		−	0.231024i
$249$		−	9.59041e10i		−	0.00634952i
$250$		−	2.09015e13i		−	1.35365i
$251$	1.61292e13			1.02190			0.510950	−	0.859610i	$-0.329294\pi$
$251$	1.61292e13			1.02190			0.510950	+	0.859610i	$0.329294\pi$
$252$		−	1.24823e13i		−	0.773731i
$253$	−1.80698e13			−1.09595
$254$	−3.65505e13			−2.16924
$255$	−4.84248e11	−	1.46256e12i	−0.0281253	−	0.0849459i
$256$	2.16843e13			1.23261
$257$	−5.15196e12			−0.286642			−0.143321	−	0.989676i	$-0.545778\pi$
$257$	−5.15196e12			−0.286642			−0.143321	+	0.989676i	$0.545778\pi$
$258$			3.29327e10i			0.00179357i
$259$	2.37682e13			1.26721
$260$		−	1.16164e13i		−	0.606341i
$261$			2.08663e13i			1.06641i
$262$		−	2.25455e13i		−	1.12824i
$263$	1.77857e12			0.0871592			0.0435796	−	0.999050i	$-0.486124\pi$
$263$	1.77857e12			0.0871592			0.0435796	+	0.999050i	$0.486124\pi$
$264$	3.15023e11			0.0151189
$265$			1.19247e13i			0.560525i
$266$			7.02498e12i			0.323442i
$267$			3.38119e12i			0.152496i
$268$	3.34441e13			1.47767
$269$			1.78034e13i			0.770663i	0.922778	+	0.385331i	$0.125913\pi$
$269$			1.78034e13i			0.770663i	−0.922778	+	0.385331i	$0.874087\pi$
$270$	−5.71191e12			−0.242259
$271$	−3.26277e13			−1.35599			−0.677993	−	0.735069i	$-0.737150\pi$
$271$	−3.26277e13			−1.35599			−0.677993	+	0.735069i	$0.737150\pi$
$272$	−8.71732e12	−	2.63287e13i	−0.355021	−	1.07226i
$273$	−1.46580e12			−0.0585033
$274$	9.80804e12			0.383667
$275$			1.68656e11i			0.00646652i
$276$	−2.69672e12			−0.101353
$277$			2.71764e13i			1.00128i	0.865657	+	0.500638i	$0.166901\pi$
$277$			2.71764e13i			1.00128i	−0.865657	+	0.500638i	$0.833099\pi$
$278$			4.63092e13i			1.67271i
$279$			3.11481e13i			1.10309i
$280$	5.53061e12			0.192045
$281$	−3.57016e13			−1.21563			−0.607817	−	0.794077i	$-0.707954\pi$
$281$	−3.57016e13			−1.21563			−0.607817	+	0.794077i	$0.707954\pi$
$282$		−	3.81116e12i		−	0.127259i
$283$			1.04843e13i			0.343333i	0.985155	+	0.171666i	$0.0549151\pi$
$283$			1.04843e13i			0.343333i	−0.985155	+	0.171666i	$0.945085\pi$
$284$			8.34794e12i			0.268120i
$285$	7.34207e11			0.0231298
$286$		−	2.55998e13i		−	0.791085i
$287$	4.41473e12			0.133830
$288$	−4.42765e13			−1.31678
$289$	−2.75002e13	+	2.04525e13i	−0.802411	+	0.596771i
$290$	5.12315e13			1.46672
$291$	−3.81756e11			−0.0107244
$292$		−	2.16822e13i		−	0.597720i
$293$	7.03512e13			1.90327			0.951633	−	0.307238i	$-0.0994047\pi$
$293$	7.03512e13			1.90327			0.951633	+	0.307238i	$0.0994047\pi$
$294$		−	6.95087e11i		−	0.0184556i
$295$		−	1.38639e13i		−	0.361298i
$296$		−	1.11797e13i		−	0.285973i
$297$	−5.77295e12			−0.144956
$298$	−1.00811e14			−2.48497
$299$		−	3.95475e13i		−	0.957035i
$300$			2.51701e10i			0.000598023i
$301$			5.84353e11i			0.0136320i
$302$	9.66616e13			2.21419
$303$		−	2.51986e12i		−	0.0566815i
$304$	1.32170e13			0.291964
$305$	−5.50655e13			−1.19462
$306$	1.98892e13	+	6.00709e13i	0.423790	+	1.27996i
$307$	3.93815e13			0.824197			0.412099	−	0.911139i	$-0.364796\pi$
$307$	3.93815e13			0.824197			0.412099	+	0.911139i	$0.364796\pi$
$308$	−3.09743e13			−0.636755
$309$			1.97659e12i			0.0399159i
$310$	7.64757e13			1.51717
$311$		−	8.38957e13i		−	1.63515i	−0.575823	−	0.817575i	$-0.695318\pi$
$311$		−	8.38957e13i		−	1.63515i	0.575823	−	0.817575i	$-0.304682\pi$
$312$			6.89459e11i			0.0132026i
$313$			5.07613e13i			0.955078i	0.878610	+	0.477539i	$0.158471\pi$
$313$			5.07613e13i			0.955078i	−0.878610	+	0.477539i	$0.841529\pi$
$314$	−7.64570e13			−1.41353
$315$	−5.04735e13			−0.916971
$316$		−	5.10272e13i		−	0.911009i
$317$			7.52575e12i			0.132046i	0.997818	+	0.0660228i	$0.0210310\pi$
$317$			7.52575e12i			0.132046i	−0.997818	+	0.0660228i	$0.978969\pi$
$318$			3.92190e12i			0.0676312i
$319$	5.17790e13			0.877617
$320$			4.06433e13i			0.677118i
$321$	8.65600e12			0.141755
$322$	−1.04336e14			−1.67968
$323$	−5.13359e12	−	1.55048e13i	−0.0812470	−	0.245388i
$324$	5.31493e13			0.826990
$325$	−3.69120e11			−0.00564689
$326$			1.08546e14i			1.63274i
$327$	8.91527e12			0.131863
$328$		−	2.07653e12i		−	0.0302017i
$329$		−	6.76247e13i		−	0.967226i
$330$			7.05868e12i			0.0992881i
$331$	4.92457e13			0.681262			0.340631	−	0.940197i	$-0.389359\pi$
$331$	4.92457e13			0.681262			0.340631	+	0.940197i	$0.389359\pi$
$332$	4.43537e12			0.0603491
$333$			1.02028e14i			1.36546i
$334$		−	1.23124e14i		−	1.62083i
$335$		−	1.35235e14i		−	1.75123i
$336$	7.27575e12			0.0926855
$337$		−	1.20199e13i		−	0.150638i	−0.997159	−	0.0753190i	$-0.976002\pi$
$337$		−	1.20199e13i		−	0.150638i	0.997159	−	0.0753190i	$-0.0239975\pi$
$338$	−5.41998e13			−0.668276
$339$	4.43810e12			0.0538393
$340$	6.76405e13	−	2.23955e13i	0.807370	−	0.267317i
$341$	7.72930e13			0.907802
$342$	−3.01557e13			−0.348518
$343$		−	9.32849e13i		−	1.06095i
$344$	2.74858e11			0.00307636
$345$			1.09045e13i			0.120116i
$346$			2.18008e13i			0.236349i
$347$		−	3.76384e13i		−	0.401624i	−0.979630	−	0.200812i	$-0.935642\pi$
$347$		−	3.76384e13i		−	0.401624i	0.979630	−	0.200812i	$-0.0643580\pi$
$348$	7.72747e12			0.0811618
$349$	−4.41594e13			−0.456545			−0.228273	−	0.973597i	$-0.573308\pi$
$349$	−4.41594e13			−0.456545			−0.228273	+	0.973597i	$0.573308\pi$
$350$			9.73826e11i			0.00991076i
$351$		−	1.26347e13i		−	0.126583i
$352$			1.09870e14i			1.08367i
$353$	1.03528e14			1.00530			0.502652	−	0.864489i	$-0.332358\pi$
$353$	1.03528e14			1.00530			0.502652	+	0.864489i	$0.332358\pi$
$354$		−	4.55970e12i		−	0.0435931i
$355$	3.37559e13			0.317756
$356$	−1.56373e14			−1.44940
$357$	−2.82595e12	−	8.53515e12i	−0.0257923	−	0.0778997i
$358$	2.36238e13			0.212321
$359$	−7.07192e13			−0.625918			−0.312959	−	0.949767i	$-0.601320\pi$
$359$	−7.07192e13			−0.625918			−0.312959	+	0.949767i	$0.601320\pi$
$360$			2.37409e13i			0.206935i
$361$	−1.08707e14			−0.933184
$362$			2.21297e14i			1.87102i
$363$		−	3.56884e12i		−	0.0297194i
$364$		−	6.77904e13i		−	0.556046i
$365$	−8.76747e13			−0.708375
$366$	−1.81104e13			−0.144140
$367$			1.59083e13i			0.124727i	0.998053	+	0.0623636i	$0.0198639\pi$
$367$			1.59083e13i			0.124727i	−0.998053	+	0.0623636i	$0.980136\pi$
$368$			1.96301e14i			1.51621i
$369$			1.89508e13i			0.144206i
$370$	2.50502e14			1.87803
$371$			6.95896e13i			0.514029i
$372$	1.15352e13			0.0839533
$373$	−1.58474e13			−0.113647			−0.0568237	−	0.998384i	$-0.518097\pi$
$373$	−1.58474e13			−0.113647			−0.0568237	+	0.998384i	$0.518097\pi$
$374$	1.49064e14	−	4.93545e13i	1.05336	−	0.348765i
$375$	−1.27482e13			−0.0887722
$376$	−3.18082e13			−0.218276
$377$			1.13324e14i			0.766378i
$378$	−3.33333e13			−0.222164
$379$		−	6.78416e12i		−	0.0445636i	−0.999752	−	0.0222818i	$-0.992907\pi$
$379$		−	6.78416e12i		−	0.0445636i	0.999752	−	0.0222818i	$-0.00709311\pi$
$380$			3.39556e13i			0.219838i
$381$			2.22928e13i			0.142258i
$382$	−3.40996e14			−2.14487
$383$	−8.16812e13			−0.506441			−0.253221	−	0.967409i	$-0.581490\pi$
$383$	−8.16812e13			−0.506441			−0.253221	+	0.967409i	$0.581490\pi$
$384$		−	5.98892e12i		−	0.0366039i
$385$			1.25248e14i			0.754637i
$386$			3.88615e13i			0.230828i
$387$	−2.50842e12			−0.0146889
$388$		−	1.76555e13i		−	0.101931i
$389$	1.02293e14			0.582270			0.291135	−	0.956682i	$-0.405967\pi$
$389$	1.02293e14			0.582270			0.291135	+	0.956682i	$0.405967\pi$
$390$	−1.54486e13			−0.0867032
$391$	2.30280e14	−	7.62447e13i	1.27433	−	0.421927i
$392$	−5.80124e12			−0.0316554
$393$	−1.37509e13			−0.0739897
$394$		−	4.76149e14i		−	2.52647i
$395$	−2.06335e14			−1.07966
$396$		−	1.32961e14i		−	0.686123i
$397$			4.33650e13i			0.220694i	0.993893	+	0.110347i	$0.0351963\pi$
$397$			4.33650e13i			0.220694i	−0.993893	+	0.110347i	$0.964804\pi$
$398$		−	9.06325e13i		−	0.454911i
$399$	4.28466e12			0.0212112
$400$	1.83219e12			0.00894624
$401$		−	1.20106e13i		−	0.0578459i	−0.999582	−	0.0289229i	$-0.990792\pi$
$401$		−	1.20106e13i		−	0.0578459i	0.999582	−	0.0289229i	$-0.00920774\pi$
$402$		−	4.44774e13i		−	0.211298i
$403$			1.69164e14i			0.792737i
$404$	1.16538e14			0.538730
$405$		−	2.14916e14i		−	0.980090i
$406$	2.98975e14			1.34506
$407$	2.53180e14			1.12372
$408$	−4.01462e12	+	1.32923e12i	−0.0175798	+	0.00582060i
$409$	2.37591e14			1.02648			0.513242	−	0.858244i	$-0.328444\pi$
$409$	2.37591e14			1.02648			0.513242	+	0.858244i	$0.328444\pi$
$410$	4.65286e13			0.198339
$411$		−	5.98209e12i		−	0.0251607i
$412$	−9.14136e13			−0.379381
$413$		−	8.09066e13i		−	0.331328i
$414$		−	4.47876e14i		−	1.80991i
$415$		−	1.79350e13i		−	0.0715215i
$416$	−2.40463e14			−0.946312
$417$	2.82448e13			0.109696
$418$			7.48303e13i			0.286819i
$419$		−	4.63527e14i		−	1.75347i	−0.480974	−	0.876735i	$-0.659717\pi$
$419$		−	4.63527e14i		−	1.75347i	0.480974	−	0.876735i	$-0.340283\pi$
$420$			1.86920e13i			0.0697886i
$421$	−5.04223e14			−1.85811			−0.929055	−	0.369942i	$-0.879378\pi$
$421$	−5.04223e14			−1.85811			−0.929055	+	0.369942i	$0.879378\pi$
$422$		−	1.19069e13i		−	0.0433093i
$423$	2.90288e14			1.04222
$424$	3.27324e13			0.116002
$425$	−7.11636e11	−	2.14933e12i	−0.00248954	−	0.00751908i
$426$	1.11020e13			0.0383395
$427$	−3.21349e14			−1.09553
$428$			4.00323e14i			1.34732i
$429$	−1.56138e13			−0.0518791
$430$			6.15872e12i			0.0202029i
$431$			3.94622e14i			1.27807i	0.769176	+	0.639037i	$0.220667\pi$
$431$			3.94622e14i			1.27807i	−0.769176	+	0.639037i	$0.779333\pi$
$432$			6.27144e13i			0.200543i
$433$	−4.14797e14			−1.30964			−0.654820	−	0.755785i	$-0.727256\pi$
$433$	−4.14797e14			−1.30964			−0.654820	+	0.755785i	$0.727256\pi$
$434$	4.46294e14			1.39132
$435$		−	3.12470e13i		−	0.0961872i
$436$			4.12314e14i			1.25329i
$437$			1.15601e14i			0.346987i
$438$	−2.88352e13			−0.0854704
$439$			3.31859e14i			0.971402i	0.874125	+	0.485701i	$0.161436\pi$
$439$			3.31859e14i			0.971402i	−0.874125	+	0.485701i	$0.838564\pi$
$440$	5.89122e13			0.170300
$441$	5.29434e13			0.151147
$442$	1.08017e14	+	3.26241e14i	0.304558	+	0.919849i
$443$	3.44788e13			0.0960135			0.0480067	−	0.998847i	$-0.484713\pi$
$443$	3.44788e13			0.0960135			0.0480067	+	0.998847i	$0.484713\pi$
$444$	3.77844e13			0.103922
$445$			6.32314e14i			1.71772i
$446$	−4.98275e14			−1.33699
$447$			6.14867e13i			0.162963i
$448$			2.37185e14i			0.620951i
$449$		−	2.93233e14i		−	0.758329i	−0.925329	−	0.379164i	$-0.876211\pi$
$449$		−	2.93233e14i		−	0.758329i	0.925329	−	0.379164i	$-0.123789\pi$
$450$	−4.18028e12			−0.0106792
$451$	4.70258e13			0.118677
$452$			2.05254e14i			0.511716i
$453$		−	5.89556e13i		−	0.145206i
$454$		−	9.05939e14i		−	2.20441i
$455$	−2.74119e14			−0.658986
$456$		−	2.01535e12i		−	0.00478678i
$457$	4.64192e14			1.08933			0.544664	−	0.838654i	$-0.316657\pi$
$457$	4.64192e14			1.08933			0.544664	+	0.838654i	$0.316657\pi$
$458$	−4.06188e14			−0.941818
$459$	7.35700e13	−	2.43587e13i	0.168551	−	0.0558065i
$460$	−5.04313e14			−1.14165
$461$	6.23883e14			1.39556			0.697779	−	0.716313i	$-0.254172\pi$
$461$	6.23883e14			1.39556			0.697779	+	0.716313i	$0.254172\pi$
$462$			4.11928e13i			0.0910522i
$463$	2.75054e14			0.600790			0.300395	−	0.953815i	$-0.402881\pi$
$463$	2.75054e14			0.600790			0.300395	+	0.953815i	$0.402881\pi$
$464$		−	5.62501e14i		−	1.21416i
$465$		−	4.66439e13i		−	0.0994955i
$466$			1.16477e15i			2.45537i
$467$	−5.49799e14			−1.14541			−0.572705	−	0.819761i	$-0.694106\pi$
$467$	−5.49799e14			−1.14541			−0.572705	+	0.819761i	$0.694106\pi$
$468$	2.91000e14			0.599156
$469$		−	7.89201e14i		−	1.60597i
$470$		−	7.12724e14i		−	1.43345i
$471$			4.66325e13i			0.0926987i
$472$	−3.80555e13			−0.0747716
$473$			6.22454e12i			0.0120885i
$474$	−6.78612e13			−0.130269
$475$	1.07897e12			0.00204736
$476$	3.94734e14	−	1.30695e14i	0.740399	−	0.245143i
$477$	−2.98723e14			−0.553883
$478$	5.00603e14			0.917573
$479$		−	8.02043e14i		−	1.45329i	−0.687013	−	0.726645i	$-0.741078\pi$
$479$		−	8.02043e14i		−	1.45329i	0.687013	−	0.726645i	$-0.258922\pi$
$480$	6.63033e13			0.118770
$481$			5.54109e14i			0.981291i
$482$		−	3.33333e14i		−	0.583605i
$483$			6.36362e13i			0.110153i
$484$	1.65052e14			0.282469
$485$	−7.13920e13			−0.120801
$486$		−	2.14917e14i		−	0.359560i
$487$			1.07735e15i			1.78216i	0.453843	+	0.891082i	$0.350053\pi$
$487$			1.07735e15i			1.78216i	−0.453843	+	0.891082i	$0.649947\pi$
$488$			1.51151e14i			0.247230i
$489$	6.62042e13			0.107075
$490$		−	1.29988e14i		−	0.207886i
$491$	5.30247e14			0.838552			0.419276	−	0.907859i	$-0.362284\pi$
$491$	5.30247e14			0.838552			0.419276	+	0.907859i	$0.362284\pi$
$492$	7.01811e12			0.0109752
$493$	−6.59867e14	+	2.18480e14i	−1.02047	+	0.337872i
$494$	−1.63774e14			−0.250464
$495$	−5.37646e14			−0.813144
$496$		−	8.39672e14i		−	1.25592i
$497$	1.96991e14			0.291398
$498$		−	5.89862e12i		−	0.00862956i
$499$			4.36944e14i			0.632227i	0.948721	+	0.316113i	$0.102378\pi$
$499$			4.36944e14i			0.632227i	−0.948721	+	0.316113i	$0.897622\pi$
$500$		−	5.89579e14i		−	0.843737i
$501$	−7.50955e13			−0.106293
$502$	9.92035e14			1.38885
$503$			4.09919e14i			0.567642i	0.958877	+	0.283821i	$0.0916022\pi$
$503$			4.09919e14i			0.567642i	−0.958877	+	0.283821i	$0.908398\pi$
$504$			1.38546e14i			0.189770i
$505$		−	4.71237e14i		−	0.638465i
$506$	−1.11139e15			−1.48949
$507$			3.30574e13i			0.0438253i
$508$	−1.03100e15			−1.35210
$509$	1.07378e15			1.39305			0.696524	−	0.717533i	$-0.254729\pi$
$509$	1.07378e15			1.39305			0.696524	+	0.717533i	$0.254729\pi$
$510$	−2.97838e13	−	8.99553e13i	−0.0382248	−	0.115449i
$511$	−5.11648e14			−0.649616
$512$	1.00674e15			1.26454
$513$			3.69323e13i			0.0458945i
$514$	−3.16873e14			−0.389573
$515$			3.69642e14i			0.449616i
$516$			9.28948e11i			0.00111794i
$517$		−	7.20341e14i		−	0.857709i
$518$	1.46187e15			1.72225
$519$	1.32967e13			0.0154997
$520$			1.28935e14i			0.148715i
$521$		−	1.25271e15i		−	1.42970i	−0.699278	−	0.714849i	$-0.746495\pi$
$521$		−	1.25271e15i		−	1.42970i	0.699278	−	0.714849i	$-0.253505\pi$
$522$			1.28339e15i			1.44934i
$523$	−4.63073e14			−0.517476			−0.258738	−	0.965948i	$-0.583307\pi$
$523$	−4.63073e14			−0.517476			−0.258738	+	0.965948i	$0.583307\pi$
$524$		−	6.35951e14i		−	0.703237i
$525$	5.93954e11			0.000649945
$526$	1.09391e14			0.118457
$527$	−9.85016e14	+	3.26135e14i	−1.05556	+	0.349493i
$528$	7.75015e13			0.0821909
$529$	−7.64106e14			−0.801951
$530$			7.33433e14i			0.761803i
$531$	3.47303e14			0.357017
$532$			1.98157e14i			0.201602i
$533$			1.02921e14i			0.103634i
$534$			2.07961e14i			0.207255i
$535$	1.61876e15			1.59674
$536$	−3.71211e14			−0.362422
$537$		−	1.44086e13i		−	0.0139240i
$538$			1.09500e15i			1.04740i
$539$		−	1.31377e14i		−	0.124389i
$540$	−1.61118e14			−0.151001
$541$		−	3.93255e14i		−	0.364829i	−0.983222	−	0.182415i	$-0.941609\pi$
$541$		−	3.93255e14i		−	0.364829i	0.983222	−	0.182415i	$-0.0583913\pi$
$542$	−2.00678e15			−1.84291
$543$	1.34973e14			0.122701
$544$	−4.63594e14	−	1.40018e15i	−0.417200	−	1.26006i
$545$	1.66724e15			1.48531
$546$	−9.01546e13			−0.0795112
$547$			1.15470e15i			1.00818i	0.863652	+	0.504089i	$0.168172\pi$
$547$			1.15470e15i			1.00818i	−0.863652	+	0.504089i	$0.831828\pi$
$548$	2.76660e14			0.239141
$549$		−	1.37944e15i		−	1.18047i
$550$			1.03732e13i			0.00878859i
$551$		−	3.31254e14i		−	0.277861i
$552$	2.99322e13			0.0248584
$553$	−1.20412e15			−0.990105
$554$			1.67150e15i			1.36082i
$555$		−	1.52786e14i		−	0.123161i
$556$			1.30627e15i			1.04261i
$557$	6.77959e14			0.535796			0.267898	−	0.963447i	$-0.413671\pi$
$557$	6.77959e14			0.535796			0.267898	+	0.963447i	$0.413671\pi$
$558$			1.91578e15i			1.49919i
$559$	−1.36230e13			−0.0105562
$560$	1.36063e15			1.04402
$561$	−3.01022e13	−	9.09167e13i	−0.0228719	−	0.0690793i
$562$	−2.19584e15			−1.65215
$563$	−1.64475e15			−1.22547			−0.612735	−	0.790289i	$-0.709931\pi$
$563$	−1.64475e15			−1.22547			−0.612735	+	0.790289i	$0.709931\pi$
$564$		−	1.07503e14i		−	0.0793207i
$565$	8.29968e14			0.606450
$566$			6.44843e14i			0.466620i
$567$		−	1.25420e15i		−	0.898792i
$568$		−	9.26576e13i		−	0.0657605i
$569$	6.00657e14			0.422191			0.211096	−	0.977465i	$-0.432297\pi$
$569$	6.00657e14			0.422191			0.211096	+	0.977465i	$0.432297\pi$
$570$	4.51577e13			0.0314355
$571$			6.83687e14i			0.471367i	0.971830	+	0.235683i	$0.0757328\pi$
$571$			6.83687e14i			0.471367i	−0.971830	+	0.235683i	$0.924267\pi$
$572$		−	7.22105e14i		−	0.493086i
$573$			2.07980e14i			0.140660i
$574$	2.71530e14			0.181887
$575$			1.60250e13i			0.0106322i
$576$	−1.01815e15			−0.669095
$577$	2.27361e15			1.47995			0.739977	−	0.672632i	$-0.234836\pi$
$577$	2.27361e15			1.47995			0.739977	+	0.672632i	$0.234836\pi$
$578$	−1.69141e15	+	1.25794e15i	−1.09055	+	0.811066i
$579$	2.37023e13			0.0151376
$580$	1.44511e15			0.914213
$581$		−	1.04664e14i		−	0.0655888i
$582$	−2.34800e13			−0.0145755
$583$			7.41271e14i			0.455827i
$584$			2.40661e14i			0.146600i
$585$		−	1.17669e15i		−	0.710078i
$586$	4.32698e15			2.58671
$587$	−1.59694e15			−0.945755			−0.472877	−	0.881128i	$-0.656785\pi$
$587$	−1.59694e15			−0.945755			−0.472877	+	0.881128i	$0.656785\pi$
$588$		−	1.96067e13i		−	0.0115035i
$589$		−	4.94479e14i		−	0.287418i
$590$		−	8.52707e14i		−	0.491036i
$591$	−2.90412e14			−0.165685
$592$		−	2.75042e15i		−	1.55464i
$593$	−2.87894e15			−1.61225			−0.806123	−	0.591748i	$-0.798438\pi$
$593$	−2.87894e15			−1.61225			−0.806123	+	0.591748i	$0.798438\pi$
$594$	−3.55068e14			−0.197009
$595$	−5.28480e14	−	1.59615e15i	−0.290526	−	0.877468i
$596$	−2.84364e15			−1.54889
$597$	−5.52783e13			−0.0298330
$598$		−	2.43239e15i		−	1.30070i
$599$	4.13434e14			0.219058			0.109529	−	0.993984i	$-0.465066\pi$
$599$	4.13434e14			0.219058			0.109529	+	0.993984i	$0.465066\pi$
$600$		−	2.79374e11i		−	0.000146674i
$601$		−	2.17849e15i		−	1.13330i	−0.823958	−	0.566652i	$-0.808239\pi$
$601$		−	2.17849e15i		−	1.13330i	0.823958	−	0.566652i	$-0.191761\pi$
$602$			3.59408e13i			0.0185271i
$603$	3.38776e15			1.73048
$604$	2.72658e15			1.38011
$605$		−	6.67407e14i		−	0.334762i
$606$		−	1.54985e14i		−	0.0770352i
$607$		−	3.25356e15i		−	1.60258i	−0.598273	−	0.801292i	$-0.704146\pi$
$607$		−	3.25356e15i		−	1.60258i	0.598273	−	0.801292i	$-0.295854\pi$
$608$	7.02892e14			0.343099
$609$		−	1.82350e14i		−	0.0882085i
$610$	−3.38683e15			−1.62360
$611$	1.57654e15			0.748993
$612$	5.61026e14	+	1.69445e15i	0.264150	+	0.797803i
$613$	1.72107e15			0.803095			0.401547	−	0.915838i	$-0.368472\pi$
$613$	1.72107e15			0.803095			0.401547	+	0.915838i	$0.368472\pi$
$614$	2.42217e15			1.12016
$615$		−	2.83786e13i		−	0.0130070i
$616$	3.43798e14			0.156174
$617$			4.72457e14i			0.212713i	0.994328	+	0.106357i	$0.0339185\pi$
$617$			4.72457e14i			0.212713i	−0.994328	+	0.106357i	$0.966082\pi$
$618$			1.21571e14i			0.0542493i
$619$			3.90001e15i			1.72491i	0.506131	+	0.862456i	$0.331075\pi$
$619$			3.90001e15i			1.72491i	−0.506131	+	0.862456i	$0.668925\pi$
$620$	2.15719e15			0.945657
$621$	−5.48522e14			−0.238336
$622$		−	5.16003e15i		−	2.22231i
$623$			3.69003e15i			1.57524i
$624$			1.69620e14i			0.0717731i
$625$	−2.40292e15			−1.00786
$626$			3.12209e15i			1.29804i
$627$	4.56403e13			0.0188095
$628$	−2.15666e15			−0.881056
$629$	−3.22650e15	+	1.06828e15i	−1.30663	+	0.432621i
$630$	−3.10439e15			−1.24625
$631$	−2.31182e15			−0.920011			−0.460006	−	0.887916i	$-0.652153\pi$
$631$	−2.31182e15			−0.920011			−0.460006	+	0.887916i	$0.652153\pi$
$632$			5.66374e14i			0.223439i
$633$	−7.26225e12			−0.00284021
$634$			4.62874e14i			0.179462i
$635$			4.16897e15i			1.60241i
$636$			1.10627e14i			0.0421548i
$637$	2.87532e14			0.108622
$638$	3.18469e15			1.19276
$639$			8.45613e14i			0.313991i
$640$		−	1.11999e15i		−	0.412309i
$641$			3.34975e15i			1.22263i	0.791389	+	0.611313i	$0.209358\pi$
$641$			3.34975e15i			1.22263i	−0.791389	+	0.611313i	$0.790642\pi$
$642$	5.32391e14			0.192658
$643$			3.23818e15i			1.16182i	0.813966	+	0.580912i	$0.197304\pi$
$643$			3.23818e15i			1.16182i	−0.813966	+	0.580912i	$0.802696\pi$
$644$	−2.94305e15			−1.04695
$645$	3.75631e12			0.00132490
$646$	−3.15743e14	−	9.53631e14i	−0.110422	−	0.333504i
$647$	1.93334e15			0.670401			0.335201	−	0.942147i	$-0.391196\pi$
$647$	1.93334e15			0.670401			0.335201	+	0.942147i	$0.391196\pi$
$648$	−5.89929e14			−0.202832
$649$		−	8.61820e14i		−	0.293813i
$650$	−2.27029e13			−0.00767462
$651$		−	2.72202e14i		−	0.0912424i
$652$			3.06181e15i			1.01769i
$653$			3.67243e15i			1.21041i	0.796071	+	0.605203i	$0.206908\pi$
$653$			3.67243e15i			1.21041i	−0.796071	+	0.605203i	$0.793092\pi$
$654$	5.48337e14			0.179213
$655$	−2.57155e15			−0.833426
$656$		−	5.10865e14i		−	0.164186i
$657$		−	2.19632e15i		−	0.699981i
$658$		−	4.15928e15i		−	1.31455i
$659$	−3.41018e15			−1.06883			−0.534414	−	0.845223i	$-0.679468\pi$
$659$	−3.41018e15			−1.06883			−0.534414	+	0.845223i	$0.679468\pi$
$660$			1.99108e14i			0.0618866i
$661$	3.62601e15			1.11769			0.558845	−	0.829272i	$-0.311245\pi$
$661$	3.62601e15			1.11769			0.558845	+	0.829272i	$0.311245\pi$
$662$	3.02888e15			0.925897
$663$	1.98980e14	−	6.58816e13i	0.0603234	−	0.0199728i
$664$	−4.92302e13			−0.0148016
$665$	8.01272e14			0.238925
$666$			6.27529e15i			1.85578i
$667$	4.91983e15			1.44297
$668$		−	3.47302e15i		−	1.01027i
$669$			3.03907e14i			0.0876792i
$670$		−	8.31770e15i		−	2.38008i
$671$	−3.42302e15			−0.971484
$672$	3.86930e14			0.108919
$673$			2.54005e15i			0.709184i	0.935021	+	0.354592i	$0.115380\pi$
$673$			2.54005e15i			0.709184i	−0.935021	+	0.354592i	$0.884620\pi$
$674$		−	7.39286e14i		−	0.204731i
$675$			5.11967e12i			0.00140628i
$676$	−1.52884e15			−0.416539
$677$		−	5.36364e15i		−	1.44951i	−0.689005	−	0.724757i	$-0.741952\pi$
$677$		−	5.36364e15i		−	1.44951i	0.689005	−	0.724757i	$-0.258048\pi$
$678$	2.72967e14			0.0731724
$679$	−4.16627e14			−0.110780
$680$	−7.50773e14	+	2.48578e14i	−0.198020	+	0.0655637i
$681$	−5.52548e14			−0.144564
$682$	4.75394e15			1.23378
$683$		−	1.42743e15i		−	0.367486i	−0.982974	−	0.183743i	$-0.941179\pi$
$683$		−	1.42743e15i		−	0.367486i	0.982974	−	0.183743i	$-0.0588214\pi$
$684$	−8.50616e14			−0.217233
$685$		−	1.11871e15i		−	0.283412i
$686$		−	5.73752e15i		−	1.44192i
$687$			2.47741e14i			0.0617641i
$688$	6.76203e13			0.0167240
$689$	−1.62235e15			−0.398050
$690$			6.70687e14i			0.163249i
$691$			1.20192e15i			0.290233i	0.989415	+	0.145117i	$0.0463558\pi$
$691$			1.20192e15i			0.290233i	−0.989415	+	0.145117i	$0.953644\pi$
$692$			6.14945e14i			0.147317i
$693$	−3.13757e15			−0.745695
$694$		−	2.31497e15i		−	0.545843i
$695$	5.28205e15			1.23562
$696$	−8.57707e13			−0.0199062
$697$	−5.99293e14	+	1.98424e14i	−0.137994	+	0.0456892i
$698$	−2.71604e15			−0.620486
$699$	7.10413e14			0.161022
$700$			2.74692e13i			0.00617741i
$701$	−1.33740e15			−0.298409			−0.149205	−	0.988806i	$-0.547671\pi$
$701$	−1.33740e15			−0.298409			−0.149205	+	0.988806i	$0.547671\pi$
$702$		−	7.77101e14i		−	0.172038i
$703$		−	1.61971e15i		−	0.355781i
$704$			2.52650e15i			0.550642i
$705$	−4.34703e14			−0.0940053
$706$	6.36753e15			1.36630
$707$		−	2.75003e15i		−	0.585504i
$708$		−	1.28618e14i		−	0.0271717i
$709$			6.70214e15i			1.40494i	0.711711	+	0.702472i	$0.247921\pi$
$709$			6.70214e15i			1.40494i	−0.711711	+	0.702472i	$0.752079\pi$
$710$	2.07617e15			0.431859
$711$		−	5.16885e15i		−	1.06687i
$712$	1.73566e15			0.355487
$713$	7.34407e15			1.49260
$714$	−1.73811e14	−	5.24957e14i	−0.0350540	−	0.105873i
$715$	−2.91992e15			−0.584370
$716$	6.66369e14			0.132341
$717$		−	3.05327e14i		−	0.0601741i
$718$	−4.34961e15			−0.850679
$719$		−	5.55050e15i		−	1.07727i	−0.842540	−	0.538633i	$-0.818941\pi$
$719$		−	5.55050e15i		−	1.07727i	0.842540	−	0.538633i	$-0.181059\pi$
$720$			5.84071e15i			1.12496i
$721$			2.15714e15i			0.412320i
$722$	−6.68605e15			−1.26828
$723$	−2.03306e14			−0.0382726
$724$			6.24224e15i			1.16621i
$725$		−	4.59196e13i		−	0.00851411i
$726$		−	2.19503e14i		−	0.0403914i
$727$	−7.21071e15			−1.31686			−0.658428	−	0.752643i	$-0.728778\pi$
$727$	−7.21071e15			−1.31686			−0.658428	+	0.752643i	$0.728778\pi$
$728$			7.52436e14i			0.136379i
$729$	5.29585e15			0.952652
$730$	−5.39246e15			−0.962746
$731$	−2.62642e13	−	7.93251e13i	−0.00465392	−	0.0140561i
$732$	−5.10850e14			−0.0898426
$733$	−1.98314e15			−0.346163			−0.173082	−	0.984907i	$-0.555372\pi$
$733$	−1.98314e15			−0.346163			−0.173082	+	0.984907i	$0.555372\pi$
$734$			9.78448e14i			0.169516i
$735$	−7.92820e13			−0.0136331
$736$			1.04394e16i			1.78176i
$737$		−	8.40660e15i		−	1.42413i
$738$			1.16558e15i			0.195989i
$739$	−2.59631e15			−0.433323			−0.216662	−	0.976247i	$-0.569517\pi$
$739$	−2.59631e15			−0.433323			−0.216662	+	0.976247i	$0.569517\pi$
$740$	7.06605e15			1.17058
$741$			9.98885e13i			0.0164254i
$742$			4.28014e15i			0.698612i
$743$		−	1.13755e15i		−	0.184304i	−0.995745	−	0.0921518i	$-0.970625\pi$
$743$		−	1.13755e15i		−	0.184304i	0.995745	−	0.0921518i	$-0.0293745\pi$
$744$	−1.28034e14			−0.0205909
$745$			1.14986e16i			1.83563i
$746$	−9.74700e14			−0.154457
$747$	4.49286e14			0.0706740
$748$	4.20472e15	−	1.39217e15i	0.656565	−	0.217386i
$749$	9.44667e15			1.46430
$750$	−7.84083e14			−0.120649
$751$		−	1.21818e16i		−	1.86077i	−0.366586	−	0.930384i	$-0.619473\pi$
$751$		−	1.21818e16i		−	1.86077i	0.366586	−	0.930384i	$-0.380527\pi$
$752$	−7.82542e15			−1.18661
$753$		−	6.05060e14i		−	0.0910806i
$754$			6.97001e15i			1.04158i
$755$		−	1.10253e16i		−	1.63561i
$756$	−9.40249e14			−0.138476
$757$	−1.32645e15			−0.193938			−0.0969689	−	0.995287i	$-0.530915\pi$
$757$	−1.32645e15			−0.193938			−0.0969689	+	0.995287i	$0.530915\pi$
$758$		−	4.17263e14i		−	0.0605660i
$759$			6.77855e14i			0.0976804i
$760$		−	3.76889e14i		−	0.0539186i
$761$	3.04705e15			0.432777			0.216389	−	0.976307i	$-0.430572\pi$
$761$	3.04705e15			0.432777			0.216389	+	0.976307i	$0.430572\pi$
$762$			1.37113e15i			0.193342i
$763$	9.72962e15			1.36211
$764$	−9.61865e15			−1.33691
$765$	6.85171e15	−	2.26858e15i	0.945500	−	0.313051i
$766$	−5.02383e15			−0.688299
$767$	1.88618e15			0.256572
$768$		−	8.13449e14i		−	0.109861i
$769$	−5.94860e15			−0.797664			−0.398832	−	0.917024i	$-0.630584\pi$
$769$	−5.94860e15			−0.797664			−0.398832	+	0.917024i	$0.630584\pi$
$770$			7.70345e15i			1.02562i
$771$			1.93267e14i			0.0255481i
$772$			1.09618e15i			0.143876i
$773$	−1.28250e16			−1.67136			−0.835679	−	0.549218i	$-0.814926\pi$
$773$	−1.28250e16			−1.67136			−0.835679	+	0.549218i	$0.814926\pi$
$774$	−1.54281e14			−0.0199635
$775$		−	6.85464e13i		−	0.00880695i
$776$			1.95966e14i			0.0250001i
$777$		−	8.91622e14i		−	0.112945i
$778$	6.29159e15			0.791357
$779$		−	3.00846e14i		−	0.0375741i
$780$	−4.35768e14			−0.0540424
$781$	2.09836e15			0.258404
$782$	1.41634e16	−	4.68946e15i	1.73193	−	0.573437i
$783$	1.57179e15			0.190856
$784$	−1.42722e15			−0.172088
$785$			8.72072e15i			1.04417i
$786$	−8.45753e14			−0.100559
$787$			1.44859e16i			1.71035i	0.518337	+	0.855177i	$0.326551\pi$
$787$			1.44859e16i			1.71035i	−0.518337	+	0.855177i	$0.673449\pi$
$788$		−	1.34310e16i		−	1.57476i
$789$		−	6.67197e13i		−	0.00776839i
$790$	−1.26907e16			−1.46736
$791$	4.84349e15			0.556145
$792$			1.47580e15i			0.168282i
$793$		−	7.49163e15i		−	0.848348i
$794$			2.66718e15i			0.299944i
$795$	4.47333e14			0.0499588
$796$		−	2.55651e15i		−	0.283548i
$797$	−7.71817e15			−0.850146			−0.425073	−	0.905159i	$-0.639752\pi$
$797$	−7.71817e15			−0.850146			−0.425073	+	0.905159i	$0.639752\pi$
$798$	2.63529e14			0.0288279
$799$	3.03945e15	+	9.17996e15i	0.330208	+	0.997318i
$800$	9.74373e13			0.0105131
$801$	−1.58400e16			−1.69737
$802$		−	7.38719e14i		−	0.0786177i
$803$	−5.45010e15			−0.576061
$804$		−	1.25460e15i		−	0.131703i
$805$			1.19006e16i			1.24077i
$806$			1.04045e16i			1.07740i
$807$	6.67861e14			0.0686882
$808$	−1.29351e15			−0.132132
$809$		−	1.64116e15i		−	0.166508i	−0.996528	−	0.0832540i	$-0.973469\pi$
$809$		−	1.64116e15i		−	0.166508i	0.996528	−	0.0832540i	$-0.0265313\pi$
$810$		−	1.32185e16i		−	1.33203i
$811$		−	9.52939e15i		−	0.953784i	−0.878962	−	0.476892i	$-0.841763\pi$
$811$		−	9.52939e15i		−	0.953784i	0.878962	−	0.476892i	$-0.158237\pi$
$812$	8.43332e15			0.838379
$813$			1.22397e15i			0.120857i
$814$	1.55719e16			1.52724
$815$	1.23808e16			1.20610
$816$	−9.87673e14	+	3.27015e14i	−0.0955690	+	0.0316425i
$817$	3.98213e13			0.00382731
$818$	1.46131e16			1.39508
$819$		−	6.86690e15i		−	0.651177i
$820$	1.31245e15			0.123625
$821$		−	1.50797e16i		−	1.41093i	−0.708746	−	0.705464i	$-0.750739\pi$
$821$		−	1.50797e16i		−	1.41093i	0.708746	−	0.705464i	$-0.249261\pi$
$822$		−	3.67931e14i		−	0.0341957i
$823$		−	1.05599e16i		−	0.974902i	−0.873150	−	0.487451i	$-0.837927\pi$
$823$		−	1.05599e16i		−	0.974902i	0.873150	−	0.487451i	$-0.162073\pi$
$824$	1.01464e15			0.0930492
$825$	6.32681e12			0.000576353
$826$		−	4.97619e15i		−	0.450305i
$827$			1.10007e16i			0.988871i	0.869214	+	0.494435i	$0.164625\pi$
$827$			1.10007e16i			0.988871i	−0.869214	+	0.494435i	$0.835375\pi$
$828$		−	1.26335e16i		−	1.12812i
$829$	−3.29931e15			−0.292667			−0.146334	−	0.989235i	$-0.546747\pi$
$829$	−3.29931e15			−0.292667			−0.146334	+	0.989235i	$0.546747\pi$
$830$		−	1.10310e15i		−	0.0972041i
$831$	1.01948e15			0.0892424
$832$	−5.52950e15			−0.480848
$833$	5.54341e14	+	1.67426e15i	0.0478883	+	0.144636i
$834$	1.73721e15			0.149086
$835$	−1.40436e16			−1.19730
$836$			2.11077e15i			0.178775i
$837$	2.34629e15			0.197420
$838$		−	2.85094e16i		−	2.38312i
$839$		−	7.12405e15i		−	0.591611i	−0.955248	−	0.295806i	$-0.904412\pi$
$839$		−	7.12405e15i		−	0.591611i	0.955248	−	0.295806i	$-0.0955881\pi$
$840$		−	2.07471e14i		−	0.0171167i
$841$	−1.89729e15			−0.155509
$842$	−3.10125e16			−2.52534
$843$			1.33928e15i			0.108348i
$844$		−	3.35865e14i		−	0.0269949i
$845$			6.18205e15i			0.493652i
$846$	1.78543e16			1.41647
$847$		−	3.89482e15i		−	0.306993i
$848$	8.05279e15			0.630622
$849$	3.93301e14			0.0306008
$850$	−4.37694e13	−	1.32196e14i	−0.00338351	−	0.0102191i
$851$	2.40561e16			1.84762
$852$	3.13158e14			0.0238971
$853$			2.31162e16i			1.75266i	0.481713	+	0.876329i	$0.340015\pi$
$853$			2.31162e16i			1.75266i	−0.481713	+	0.876329i	$0.659985\pi$
$854$	−1.97647e16			−1.48892
$855$			3.43957e15i			0.257449i
$856$		−	4.44337e15i		−	0.330451i
$857$			2.55454e16i			1.88764i	0.330466	+	0.943818i	$0.392794\pi$
$857$			2.55454e16i			1.88764i	−0.330466	+	0.943818i	$0.607206\pi$
$858$	−9.60330e14			−0.0705083
$859$	−8.70194e14			−0.0634825			−0.0317412	−	0.999496i	$-0.510105\pi$
$859$	−8.70194e14			−0.0634825			−0.0317412	+	0.999496i	$0.510105\pi$
$860$			1.73722e14i			0.0125925i
$861$		−	1.65611e14i		−	0.0119281i
$862$			2.42714e16i			1.73702i
$863$	7.24118e15			0.514932			0.257466	−	0.966287i	$-0.417112\pi$
$863$	7.24118e15			0.514932			0.257466	+	0.966287i	$0.417112\pi$
$864$			3.33520e15i			0.235666i
$865$	2.48661e15			0.174590
$866$	−2.55122e16			−1.77992
$867$	7.67239e14	+	1.03162e15i	0.0531894	+	0.0715179i
$868$	1.25888e16			0.867215
$869$	−1.28263e16			−0.877998
$870$		−	1.92186e15i		−	0.130727i
$871$	1.83987e16			1.24362
$872$		−	4.57646e15i		−	0.307389i
$873$		−	1.78843e15i		−	0.119369i
$874$			7.11007e15i			0.471586i
$875$	−1.39127e16			−0.916993
$876$	−8.13369e14			−0.0532740
$877$			4.70621e15i			0.306319i	0.988202	+	0.153159i	$0.0489448\pi$
$877$			4.70621e15i			0.306319i	−0.988202	+	0.153159i	$0.951055\pi$
$878$			2.04111e16i			1.32022i
$879$		−	2.63910e15i		−	0.169636i
$880$	1.44935e16			0.925805
$881$		−	6.34030e15i		−	0.402478i	−0.979542	−	0.201239i	$-0.935503\pi$
$881$		−	6.34030e15i		−	0.402478i	0.979542	−	0.201239i	$-0.0644968\pi$
$882$	3.25630e15			0.205422
$883$	−2.54085e16			−1.59292			−0.796461	−	0.604690i	$-0.793297\pi$
$883$	−2.54085e16			−1.59292			−0.796461	+	0.604690i	$0.793297\pi$
$884$	3.04690e15	+	9.20245e15i	0.189832	+	0.573345i
$885$	−5.20081e14			−0.0322020
$886$	2.12063e15			0.130491
$887$		−	4.30148e15i		−	0.263050i	−0.991313	−	0.131525i	$-0.958013\pi$
$887$		−	4.30148e15i		−	0.263050i	0.991313	−	0.131525i	$-0.0419874\pi$
$888$	−4.19386e14			−0.0254884
$889$			2.43291e16i			1.46949i
$890$			3.88907e16i			2.33454i
$891$		−	1.33598e16i		−	0.797023i
$892$	−1.40551e16			−0.833348
$893$	−4.60835e15			−0.271558
$894$			3.78176e15i			0.221482i
$895$		−	2.69455e15i		−	0.156841i
$896$		−	6.53597e15i		−	0.378108i
$897$	−1.48356e15			−0.0852993
$898$		−	1.80354e16i		−	1.03064i
$899$	−2.10445e16			−1.19525
$900$	−1.17915e14			−0.00665635
$901$	−3.12776e15	−	9.44669e15i	−0.175488	−	0.530022i
$902$	2.89234e15			0.161292
$903$	2.19209e13			0.00121500
$904$		−	2.27820e15i		−	0.125506i
$905$	2.52413e16			1.38211
$906$		−	3.62609e15i		−	0.197348i
$907$			8.06988e15i			0.436543i	0.975888	+	0.218272i	$0.0700419\pi$
$907$			8.06988e15i			0.436543i	−0.975888	+	0.218272i	$0.929958\pi$
$908$		−	2.55543e16i		−	1.37401i
$909$	1.18049e16			0.630899
$910$	−1.68598e16			−0.895621
$911$		−	2.04923e16i		−	1.08203i	−0.841013	−	0.541016i	$-0.818040\pi$
$911$		−	2.04923e16i		−	1.08203i	0.841013	−	0.541016i	$-0.181960\pi$
$912$		−	4.95813e14i		−	0.0260224i
$913$		−	1.11489e15i		−	0.0581623i
$914$	2.85503e16			1.48049
$915$			2.06568e15i			0.106475i
$916$	−1.14575e16			−0.587038
$917$	−1.50069e16			−0.764294
$918$	4.52495e15	−	1.49819e15i	0.229076	−	0.0758461i
$919$	1.55836e16			0.784210			0.392105	−	0.919921i	$-0.371747\pi$
$919$	1.55836e16			0.784210			0.392105	+	0.919921i	$0.371747\pi$
$920$	5.59760e15			0.280007
$921$		−	1.47733e15i		−	0.0734596i
$922$	3.83721e16			1.89669
$923$			4.59247e15i			0.225651i
$924$			1.16195e15i			0.0567531i
$925$		−	2.24529e14i		−	0.0109017i
$926$	1.69173e16			0.816528
$927$	−9.25984e15			−0.444288
$928$		−	2.99143e16i		−	1.42680i
$929$		−	2.26357e16i		−	1.07327i	−0.843816	−	0.536633i	$-0.819696\pi$
$929$		−	2.26357e16i		−	1.07327i	0.843816	−	0.536633i	$-0.180304\pi$
$930$		−	2.86885e15i		−	0.135223i
$931$	−8.40481e14			−0.0393826
$932$			3.28552e16i			1.53044i
$933$	−3.14720e15			−0.145739
$934$	−3.38156e16			−1.55672
$935$	−5.62939e15	−	1.70023e16i	−0.257631	−	0.778114i
$936$	−3.22994e15			−0.146952
$937$	2.85278e16			1.29033			0.645164	−	0.764044i	$-0.276789\pi$
$937$	2.85278e16			1.29033			0.645164	+	0.764044i	$0.276789\pi$
$938$		−	4.85401e16i		−	2.18266i
$939$	1.90422e15			0.0851249
$940$		−	2.01041e16i		−	0.893475i
$941$			1.88306e15i			0.0831995i	0.999134	+	0.0415997i	$0.0132454\pi$
$941$			1.88306e15i			0.0831995i	−0.999134	+	0.0415997i	$0.986755\pi$
$942$			2.86815e15i			0.125986i
$943$	4.46820e15			0.195128
$944$	−9.36238e15			−0.406481
$945$			3.80201e15i			0.164111i
$946$			3.82843e14i			0.0164293i
$947$		−	1.78705e16i		−	0.762451i	−0.924482	−	0.381226i	$-0.875502\pi$
$947$		−	1.78705e16i		−	0.762451i	0.924482	−	0.381226i	$-0.124498\pi$
$948$	−1.91419e15			−0.0811970
$949$		−	1.19281e16i		−	0.503045i
$950$	6.63624e13			0.00278254
$951$	2.82315e14			0.0117691
$952$	−4.38133e15	+	1.45064e15i	−0.181594	+	0.0601252i
$953$	1.70042e15			0.0700721			0.0350361	−	0.999386i	$-0.488845\pi$
$953$	1.70042e15			0.0700721			0.0350361	+	0.999386i	$0.488845\pi$
$954$	−1.83731e16			−0.752776
$955$			3.88942e16i			1.58441i
$956$	1.41208e16			0.571926
$957$		−	1.94240e15i		−	0.0782208i
$958$		−	4.93300e16i		−	1.97515i
$959$		−	6.52852e15i		−	0.259904i
$960$	1.52466e15			0.0603506
$961$	−6.00559e15			−0.236362
$962$			3.40807e16i			1.33366i
$963$			4.05511e16i			1.57782i
$964$		−	9.40248e15i		−	0.363763i
$965$	4.43256e15			0.170512
$966$			3.91397e15i			0.149707i
$967$	−2.07223e16			−0.788121			−0.394060	−	0.919085i	$-0.628930\pi$
$967$	−2.07223e16			−0.788121			−0.394060	+	0.919085i	$0.628930\pi$
$968$	−1.83198e15			−0.0692799
$969$	−5.81636e14	+	1.92578e14i	−0.0218711	+	0.00724144i
$970$	−4.39099e15			−0.164179
$971$	7.81060e15			0.290388			0.145194	−	0.989403i	$-0.453619\pi$
$971$	7.81060e15			0.290388			0.145194	+	0.989403i	$0.453619\pi$
$972$		−	6.06227e15i		−	0.224115i
$973$	3.08248e16			1.13313
$974$			6.62628e16i			2.42212i
$975$			1.38469e13i			0.000503299i
$976$			3.71860e16i			1.34402i
$977$	1.83369e16			0.659031			0.329516	−	0.944150i	$-0.393115\pi$
$977$	1.83369e16			0.659031			0.329516	+	0.944150i	$0.393115\pi$
$978$	4.07191e15			0.145524
$979$			3.93064e16i			1.39688i
$980$		−	3.66663e15i		−	0.129576i
$981$			4.17657e16i			1.46771i
$982$	3.26131e16			1.13967
$983$			2.01380e15i			0.0699797i	0.999388	+	0.0349898i	$0.0111399\pi$
$983$			2.01380e15i			0.0699797i	−0.999388	+	0.0349898i	$0.988860\pi$
$984$	−7.78972e13			−0.00269184
$985$	−5.43098e16			−1.86629
$986$	−4.05854e16	+	1.34377e16i	−1.38691	+	0.459199i
$987$	−2.53682e15			−0.0862076
$988$	−4.61964e15			−0.156115
$989$			5.91431e14i			0.0198758i
$990$	−3.30681e16			−1.10514
$991$		−	3.19132e16i		−	1.06063i	−0.847800	−	0.530317i	$-0.822073\pi$
$991$		−	3.19132e16i		−	1.06063i	0.847800	−	0.530317i	$-0.177927\pi$
$992$		−	4.46545e16i		−	1.47588i
$993$		−	1.84736e15i		−	0.0607200i
$994$	1.21160e16			0.396037
$995$	−1.03376e16			−0.336041
$996$		−	1.66385e14i		−	0.00537884i
$997$		−	4.30322e16i		−	1.38347i	−0.722150	−	0.691736i	$-0.756846\pi$
$997$		−	4.30322e16i		−	1.38347i	0.722150	−	0.691736i	$-0.243154\pi$
$998$			2.68744e16i			0.859253i
$999$	7.68547e15			0.244377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.b.a.16.13	✓	16
3.2	odd	2		153.12.d.b.118.4		16
4.3	odd	2		272.12.b.c.33.9		16
17.16	even	2	inner	17.12.b.a.16.14	yes	16
51.50	odd	2		153.12.d.b.118.3		16
68.67	odd	2		272.12.b.c.33.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.b.a.16.13	✓	16	1.1	even	1	trivial
17.12.b.a.16.14	yes	16	17.16	even	2	inner
153.12.d.b.118.3		16	51.50	odd	2
153.12.d.b.118.4		16	3.2	odd	2
272.12.b.c.33.8		16	68.67	odd	2
272.12.b.c.33.9		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+61.5054 q^{2} -37.5132i q^{3} +1734.91 q^{4} -7015.33i q^{5} -2307.27i q^{6} -40939.8i q^{7} -19256.6 q^{8} +175740. q^{9} +O(q^{10})\)	\(q+61.5054 q^{2} -37.5132i q^{3} +1734.91 q^{4} -7015.33i q^{5} -2307.27i q^{6} -40939.8i q^{7} -19256.6 q^{8} +175740. q^{9} -431481. i q^{10} -436092. i q^{11} -65082.1i q^{12} +954432. q^{13} -2.51802e6i q^{14} -263168. q^{15} -4.73748e6 q^{16} +(1.84007e6 + 5.55752e6i) q^{17} +1.08089e7 q^{18} -2.78988e6 q^{19} -1.21710e7i q^{20} -1.53578e6 q^{21} -2.68220e7i q^{22} -4.14357e7i q^{23} +722376. i q^{24} -386743. q^{25} +5.87027e7 q^{26} -1.32379e7i q^{27} -7.10269e7i q^{28} +1.18734e8i q^{29} -1.61862e7 q^{30} +1.77240e8i q^{31} -2.51943e8 q^{32} -1.63592e7 q^{33} +(1.13174e8 + 3.41817e8i) q^{34} -2.87206e8 q^{35} +3.04893e8 q^{36} +5.80565e8i q^{37} -1.71593e8 q^{38} -3.58038e7i q^{39} +1.35091e8i q^{40} +1.07835e8i q^{41} -9.44590e7 q^{42} -1.42735e7 q^{43} -7.56581e8i q^{44} -1.23287e9i q^{45} -2.54852e9i q^{46} +1.65181e9 q^{47} +1.77718e8i q^{48} +3.01260e8 q^{49} -2.37868e7 q^{50} +(2.08480e8 - 6.90271e7i) q^{51} +1.65586e9 q^{52} -1.69980e9 q^{53} -8.14203e8i q^{54} -3.05933e9 q^{55} +7.88360e8i q^{56} +1.04658e8i q^{57} +7.30279e9i q^{58} +1.97623e9 q^{59} -4.56573e8 q^{60} -7.84931e9i q^{61} +1.09012e10i q^{62} -7.19475e9i q^{63} -5.79350e9 q^{64} -6.69565e9i q^{65} -1.00618e9 q^{66} +1.92771e10 q^{67} +(3.19237e9 + 9.64181e9i) q^{68} -1.55439e9 q^{69} -1.76647e10 q^{70} +4.81174e9i q^{71} -3.38415e9 q^{72} -1.24976e10i q^{73} +3.57079e10i q^{74} +1.45080e7i q^{75} -4.84020e9 q^{76} -1.78535e10 q^{77} -2.20213e9i q^{78} -2.94120e10i q^{79} +3.32350e10i q^{80} +3.06352e10 q^{81} +6.63241e9i q^{82} +2.55654e9 q^{83} -2.66445e9 q^{84} +(3.89878e10 - 1.29087e10i) q^{85} -8.77895e8 q^{86} +4.45410e9 q^{87} +8.39764e9i q^{88} -9.01332e10 q^{89} -7.58283e10i q^{90} -3.90742e10i q^{91} -7.18873e10i q^{92} +6.64885e9 q^{93} +1.01595e11 q^{94} +1.95720e10i q^{95} +9.45120e9i q^{96} -1.01766e10i q^{97} +1.85291e10 q^{98} -7.66387e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 20338 * q^4 - 4098 * q^8 - 1191496 * q^9	\( 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9} - 1045192 q^{13} - 928176 q^{15} + 34826050 q^{16} + 3554632 q^{17} - 35173654 q^{18} + 4588736 q^{19} + 66662344 q^{21} - 58748400 q^{25} - 317977540 q^{26} - 131021808 q^{30} + 1067460734 q^{32} + 724766552 q^{33} - 775893498 q^{34} + 1999765296 q^{35} - 2520870986 q^{36} - 1607971816 q^{38} + 1845301744 q^{42} - 2666979472 q^{43} + 1869667792 q^{47} - 5944064168 q^{49} + 15444320726 q^{50} + 8437689968 q^{51} - 7784119948 q^{52} - 5942183760 q^{53} - 11128140752 q^{55} + 7494118800 q^{59} - 2434494672 q^{60} + 80595388930 q^{64} - 86599472704 q^{66} + 17007290816 q^{67} + 73491523226 q^{68} + 13676754040 q^{69} - 91280536608 q^{70} - 229207542918 q^{72} + 149151579272 q^{76} + 32130668824 q^{77} + 145538020840 q^{81} - 112706231184 q^{83} + 424712287520 q^{84} + 77452876928 q^{85} + 64143446456 q^{86} - 368269123632 q^{87} - 89466414808 q^{89} - 57312497768 q^{93} - 672691463040 q^{94} + 274175066082 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 20338 * q^4 - 4098 * q^8 - 1191496 * q^9 - 1045192 * q^13 - 928176 * q^15 + 34826050 * q^16 + 3554632 * q^17 - 35173654 * q^18 + 4588736 * q^19 + 66662344 * q^21 - 58748400 * q^25 - 317977540 * q^26 - 131021808 * q^30 + 1067460734 * q^32 + 724766552 * q^33 - 775893498 * q^34 + 1999765296 * q^35 - 2520870986 * q^36 - 1607971816 * q^38 + 1845301744 * q^42 - 2666979472 * q^43 + 1869667792 * q^47 - 5944064168 * q^49 + 15444320726 * q^50 + 8437689968 * q^51 - 7784119948 * q^52 - 5942183760 * q^53 - 11128140752 * q^55 + 7494118800 * q^59 - 2434494672 * q^60 + 80595388930 * q^64 - 86599472704 * q^66 + 17007290816 * q^67 + 73491523226 * q^68 + 13676754040 * q^69 - 91280536608 * q^70 - 229207542918 * q^72 + 149151579272 * q^76 + 32130668824 * q^77 + 145538020840 * q^81 - 112706231184 * q^83 + 424712287520 * q^84 + 77452876928 * q^85 + 64143446456 * q^86 - 368269123632 * q^87 - 89466414808 * q^89 - 57312497768 * q^93 - 672691463040 * q^94 + 274175066082 * q^98

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