LMFDB - Embedded newform 17.12.b.a.16.5

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			16.5
Root			$-260.983i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.12.b.a.16.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-49.4086 q^{2} -260.983i q^{3} +393.209 q^{4} -5284.72i q^{5} +12894.8i q^{6} -52066.0i q^{7} +81760.9 q^{8} +109035. q^{9} +O(q^{10})$	\(q-49.4086 q^{2} -260.983i q^{3} +393.209 q^{4} -5284.72i q^{5} +12894.8i q^{6} -52066.0i q^{7} +81760.9 q^{8} +109035. q^{9} +261110. i q^{10} -421531. i q^{11} -102621. i q^{12} -641960. q^{13} +2.57251e6i q^{14} -1.37922e6 q^{15} -4.84498e6 q^{16} +(-5.63169e6 - 1.59874e6i) q^{17} -5.38725e6 q^{18} -7.30873e6 q^{19} -2.07800e6i q^{20} -1.35883e7 q^{21} +2.08272e7i q^{22} +3.67081e7i q^{23} -2.13382e7i q^{24} +2.08999e7 q^{25} +3.17183e7 q^{26} -7.46886e7i q^{27} -2.04728e7i q^{28} -9.51230e7i q^{29} +6.81454e7 q^{30} +1.93501e8i q^{31} +7.19375e7 q^{32} -1.10012e8 q^{33} +(2.78254e8 + 7.89914e7i) q^{34} -2.75154e8 q^{35} +4.28734e7 q^{36} -5.49363e8i q^{37} +3.61114e8 q^{38} +1.67541e8i q^{39} -4.32083e8i q^{40} +1.27787e9i q^{41} +6.71381e8 q^{42} +1.18585e8 q^{43} -1.65750e8i q^{44} -5.76218e8i q^{45} -1.81370e9i q^{46} -8.61987e8 q^{47} +1.26446e9i q^{48} -7.33537e8 q^{49} -1.03263e9 q^{50} +(-4.17244e8 + 1.46978e9i) q^{51} -2.52424e8 q^{52} -3.20786e9 q^{53} +3.69026e9i q^{54} -2.22767e9 q^{55} -4.25696e9i q^{56} +1.90746e9i q^{57} +4.69989e9i q^{58} -8.21106e8 q^{59} -5.42323e8 q^{60} +8.35550e8i q^{61} -9.56061e9i q^{62} -5.67700e9i q^{63} +6.36820e9 q^{64} +3.39257e9i q^{65} +5.43556e9 q^{66} +1.08918e10 q^{67} +(-2.21443e9 - 6.28638e8i) q^{68} +9.58021e9 q^{69} +1.35950e10 q^{70} -8.90138e9i q^{71} +8.91478e9 q^{72} -1.10163e10i q^{73} +2.71432e10i q^{74} -5.45453e9i q^{75} -2.87386e9 q^{76} -2.19474e10 q^{77} -8.27795e9i q^{78} +2.45877e10i q^{79} +2.56044e10i q^{80} -1.77310e8 q^{81} -6.31379e10i q^{82} -5.46453e10 q^{83} -5.34306e9 q^{84} +(-8.44888e9 + 2.97619e10i) q^{85} -5.85910e9 q^{86} -2.48255e10 q^{87} -3.44647e10i q^{88} -3.36499e10 q^{89} +2.84701e10i q^{90} +3.34242e10i q^{91} +1.44340e10i q^{92} +5.05005e10 q^{93} +4.25896e10 q^{94} +3.86245e10i q^{95} -1.87745e10i q^{96} -1.79012e10i q^{97} +3.62430e10 q^{98} -4.59615e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−49.4086			−1.09179			−0.545893	−	0.837855i	$-0.683809\pi$
$2$	−49.4086			−1.09179			−0.545893	+	0.837855i	$0.683809\pi$
$3$		−	260.983i		−	0.620077i	−0.950724	−	0.310039i	$-0.899658\pi$
$3$		−	260.983i		−	0.620077i	0.950724	−	0.310039i	$-0.100342\pi$
$4$	393.209			0.191997
$5$		−	5284.72i		−	0.756287i	−0.925747	−	0.378143i	$-0.876563\pi$
$5$		−	5284.72i		−	0.756287i	0.925747	−	0.378143i	$-0.123437\pi$
$6$			12894.8i			0.676992i
$7$		−	52066.0i		−	1.17089i	−0.810714	−	0.585443i	$-0.800921\pi$
$7$		−	52066.0i		−	1.17089i	0.810714	−	0.585443i	$-0.199079\pi$
$8$	81760.9			0.882167
$9$	109035.			0.615504
$10$			261110.i			0.825703i
$11$		−	421531.i		−	0.789168i	−0.918860	−	0.394584i	$-0.870889\pi$
$11$		−	421531.i		−	0.789168i	0.918860	−	0.394584i	$-0.129111\pi$
$12$		−	102621.i		−	0.119053i
$13$	−641960.			−0.479534			−0.239767	−	0.970830i	$-0.577071\pi$
$13$	−641960.			−0.479534			−0.239767	+	0.970830i	$0.577071\pi$
$14$			2.57251e6i			1.27836i
$15$	−1.37922e6			−0.468956
$16$	−4.84498e6			−1.15513
$17$	−5.63169e6	−	1.59874e6i	−0.961988	−	0.273092i
$17$	−5.63169e6	−	1.59874e6i	−0.961988	−	0.273092i
$18$	−5.38725e6			−0.671999
$19$	−7.30873e6			−0.677169			−0.338584	−	0.940936i	$-0.609948\pi$
$19$	−7.30873e6			−0.677169			−0.338584	+	0.940936i	$0.609948\pi$
$20$		−	2.07800e6i		−	0.145205i
$21$	−1.35883e7			−0.726040
$22$			2.08272e7i			0.861603i
$23$			3.67081e7i			1.18921i	0.804017	+	0.594606i	$0.202692\pi$
$23$			3.67081e7i			1.18921i	−0.804017	+	0.594606i	$0.797308\pi$
$24$		−	2.13382e7i		−	0.547012i
$25$	2.08999e7			0.428030
$26$	3.17183e7			0.523548
$27$		−	7.46886e7i		−	1.00174i
$28$		−	2.04728e7i		−	0.224806i
$29$		−	9.51230e7i		−	0.861185i	−0.902546	−	0.430593i	$-0.858305\pi$
$29$		−	9.51230e7i		−	0.861185i	0.902546	−	0.430593i	$-0.141695\pi$
$30$	6.81454e7			0.512000
$31$			1.93501e8i			1.21393i	0.794728	+	0.606965i	$0.207613\pi$
$31$			1.93501e8i			1.21393i	−0.794728	+	0.606965i	$0.792387\pi$
$32$	7.19375e7			0.378992
$33$	−1.10012e8			−0.489345
$34$	2.78254e8	+	7.89914e7i	1.05029	+	0.298158i
$35$	−2.75154e8			−0.885526
$36$	4.28734e7			0.118175
$37$		−	5.49363e8i		−	1.30242i	−0.758899	−	0.651208i	$-0.774263\pi$
$37$		−	5.49363e8i		−	1.30242i	0.758899	−	0.651208i	$-0.225737\pi$
$38$	3.61114e8			0.739323
$39$			1.67541e8i			0.297348i
$40$		−	4.32083e8i		−	0.667171i
$41$			1.27787e9i			1.72257i	0.508124	+	0.861284i	$0.330339\pi$
$41$			1.27787e9i			1.72257i	−0.508124	+	0.861284i	$0.669661\pi$
$42$	6.71381e8			0.792680
$43$	1.18585e8			0.123013			0.0615066	−	0.998107i	$-0.480409\pi$
$43$	1.18585e8			0.123013			0.0615066	+	0.998107i	$0.480409\pi$
$44$		−	1.65750e8i		−	0.151518i
$45$		−	5.76218e8i		−	0.465498i
$46$		−	1.81370e9i		−	1.29836i
$47$	−8.61987e8			−0.548230			−0.274115	−	0.961697i	$-0.588385\pi$
$47$	−8.61987e8			−0.548230			−0.274115	+	0.961697i	$0.588385\pi$
$48$			1.26446e9i			0.716272i
$49$	−7.33537e8			−0.370974
$50$	−1.03263e9			−0.467317
$51$	−4.17244e8	+	1.46978e9i	−0.169338	+	0.596507i
$52$	−2.52424e8			−0.0920689
$53$	−3.20786e9			−1.05365			−0.526827	−	0.849973i	$-0.676618\pi$
$53$	−3.20786e9			−1.05365			−0.526827	+	0.849973i	$0.676618\pi$
$54$			3.69026e9i			1.09368i
$55$	−2.22767e9			−0.596838
$56$		−	4.25696e9i		−	1.03292i
$57$			1.90746e9i			0.419897i
$58$			4.69989e9i			0.940230i
$59$	−8.21106e8			−0.149525			−0.0747624	−	0.997201i	$-0.523820\pi$
$59$	−8.21106e8			−0.149525			−0.0747624	+	0.997201i	$0.523820\pi$
$60$	−5.42323e8			−0.0900380
$61$			8.35550e8i			0.126666i	0.997992	+	0.0633328i	$0.0201729\pi$
$61$			8.35550e8i			0.126666i	−0.997992	+	0.0633328i	$0.979827\pi$
$62$		−	9.56061e9i		−	1.32535i
$63$		−	5.67700e9i		−	0.720685i
$64$	6.36820e9			0.741356
$65$			3.39257e9i			0.362665i
$66$	5.43556e9			0.534260
$67$	1.08918e10			0.985574			0.492787	−	0.870150i	$-0.335978\pi$
$67$	1.08918e10			0.985574			0.492787	+	0.870150i	$0.335978\pi$
$68$	−2.21443e9	−	6.28638e8i	−0.184698	−	0.0524327i
$69$	9.58021e9			0.737403
$70$	1.35950e10			0.966805
$71$		−	8.90138e9i		−	0.585513i	−0.956187	−	0.292757i	$-0.905427\pi$
$71$		−	8.90138e9i		−	0.585513i	0.956187	−	0.292757i	$-0.0945726\pi$
$72$	8.91478e9			0.542977
$73$		−	1.10163e10i		−	0.621957i	−0.950417	−	0.310978i	$-0.899343\pi$
$73$		−	1.10163e10i		−	0.621957i	0.950417	−	0.310978i	$-0.100657\pi$
$74$			2.71432e10i			1.42196i
$75$		−	5.45453e9i		−	0.265412i
$76$	−2.87386e9			−0.130014
$77$	−2.19474e10			−0.924026
$78$		−	8.27795e9i		−	0.324640i
$79$			2.45877e10i			0.899021i	0.893275	+	0.449510i	$0.148401\pi$
$79$			2.45877e10i			0.899021i	−0.893275	+	0.449510i	$0.851599\pi$
$80$			2.56044e10i			0.873613i
$81$	−1.77310e8			−0.00565021
$82$		−	6.31379e10i		−	1.88068i
$83$	−5.46453e10			−1.52273			−0.761366	−	0.648323i	$-0.775471\pi$
$83$	−5.46453e10			−1.52273			−0.761366	+	0.648323i	$0.775471\pi$
$84$	−5.34306e9			−0.139397
$85$	−8.44888e9	+	2.97619e10i	−0.206536	+	0.727539i
$86$	−5.85910e9			−0.134304
$87$	−2.48255e10			−0.534001
$88$		−	3.44647e10i		−	0.696178i
$89$	−3.36499e10			−0.638762			−0.319381	−	0.947626i	$-0.603475\pi$
$89$	−3.36499e10			−0.638762			−0.319381	+	0.947626i	$0.603475\pi$
$90$			2.84701e10i			0.508224i
$91$			3.34242e10i			0.561480i
$92$			1.44340e10i			0.228325i
$93$	5.05005e10			0.752731
$94$	4.25896e10			0.598550
$95$			3.86245e10i			0.512134i
$96$		−	1.87745e10i		−	0.235004i
$97$		−	1.79012e10i		−	0.211660i	−0.994384	−	0.105830i	$-0.966250\pi$
$97$		−	1.79012e10i		−	0.211660i	0.994384	−	0.105830i	$-0.0337499\pi$
$98$	3.62430e10			0.405024
$99$		−	4.59615e10i		−	0.485736i
$100$	8.21803e9			0.0821803
$101$	−1.04132e11			−0.985867			−0.492933	−	0.870067i	$-0.664075\pi$
$101$	−1.04132e11			−0.985867			−0.492933	+	0.870067i	$0.664075\pi$
$102$	2.06154e10	−	7.26196e10i	0.184881	−	0.651258i
$103$	2.20583e10			0.187486			0.0937429	−	0.995596i	$-0.470117\pi$
$103$	2.20583e10			0.187486			0.0937429	+	0.995596i	$0.470117\pi$
$104$	−5.24872e10			−0.423029
$105$			7.18105e10i			0.549094i
$106$	1.58496e11			1.15036
$107$			1.56670e11i			1.07988i	0.841704	+	0.539939i	$0.181553\pi$
$107$			1.56670e11i			1.07988i	−0.841704	+	0.539939i	$0.818447\pi$
$108$		−	2.93682e10i		−	0.192330i
$109$		−	2.03893e11i		−	1.26928i	−0.772810	−	0.634638i	$-0.781149\pi$
$109$		−	2.03893e11i		−	1.26928i	0.772810	−	0.634638i	$-0.218851\pi$
$110$	1.10066e11			0.651619
$111$	−1.43374e11			−0.807598
$112$			2.52259e11i			1.35253i
$113$		−	2.77420e11i		−	1.41647i	−0.705978	−	0.708233i	$-0.749492\pi$
$113$		−	2.77420e11i		−	1.41647i	0.705978	−	0.708233i	$-0.250508\pi$
$114$		−	9.42447e10i		−	0.458438i
$115$	1.93992e11			0.899385
$116$		−	3.74032e10i		−	0.165345i
$117$	−6.99959e10			−0.295155
$118$	4.05697e10			0.163249
$119$	−8.32398e10	+	2.93219e11i	−0.319759	+	1.12638i
$120$	−1.12766e11			−0.413698
$121$	1.07623e11			0.377214
$122$		−	4.12834e10i		−	0.138292i
$123$	3.33503e11			1.06812
$124$			7.60863e10i			0.233071i
$125$		−	3.68493e11i		−	1.08000i
$126$			2.80492e11i			0.786834i
$127$	5.13152e11			1.37824			0.689121	−	0.724647i	$-0.257997\pi$
$127$	5.13152e11			1.37824			0.689121	+	0.724647i	$0.257997\pi$
$128$	−4.61972e11			−1.18839
$129$		−	3.09486e10i		−	0.0762777i
$130$		−	1.67622e11i		−	0.395953i
$131$			9.21624e10i			0.208719i	0.994540	+	0.104359i	$0.0332792\pi$
$131$			9.21624e10i			0.208719i	−0.994540	+	0.104359i	$0.966721\pi$
$132$	−4.32579e10			−0.0939526
$133$			3.80536e11i			0.792887i
$134$	−5.38150e11			−1.07604
$135$	−3.94708e11			−0.757601
$136$	−4.60452e11	−	1.30714e11i	−0.848634	−	0.240912i
$137$	6.26767e11			1.10954			0.554770	−	0.832003i	$-0.312806\pi$
$137$	6.26767e11			1.10954			0.554770	+	0.832003i	$0.312806\pi$
$138$	−4.73345e11			−0.805086
$139$		−	9.04008e11i		−	1.47772i	−0.673861	−	0.738858i	$-0.735366\pi$
$139$		−	9.04008e11i		−	1.47772i	0.673861	−	0.738858i	$-0.264634\pi$
$140$	−1.08193e11			−0.170018
$141$			2.24964e11i			0.339945i
$142$			4.39805e11i			0.639255i
$143$			2.70606e11i			0.378433i
$144$	−5.28271e11			−0.710990
$145$	−5.02698e11			−0.651303
$146$			5.44300e11i			0.679044i
$147$			1.91441e11i			0.230032i
$148$		−	2.16014e11i		−	0.250059i
$149$	7.03236e11			0.784471			0.392235	−	0.919865i	$-0.371702\pi$
$149$	7.03236e11			0.784471			0.392235	+	0.919865i	$0.371702\pi$
$150$			2.69500e11i			0.289773i
$151$	−8.37771e11			−0.868465			−0.434232	−	0.900801i	$-0.642980\pi$
$151$	−8.37771e11			−0.868465			−0.434232	+	0.900801i	$0.642980\pi$
$152$	−5.97568e11			−0.597376
$153$	−6.14050e11	−	1.74318e11i	−0.592108	−	0.168089i
$154$	1.08439e12			1.00884
$155$	1.02260e12			0.918080
$156$			6.58785e10i			0.0570898i
$157$	2.22295e12			1.85987			0.929933	−	0.367729i	$-0.119865\pi$
$157$	2.22295e12			1.85987			0.929933	+	0.367729i	$0.119865\pi$
$158$		−	1.21485e12i		−	0.981538i
$159$			8.37198e11i			0.653347i
$160$		−	3.80169e11i		−	0.286627i
$161$	1.91124e12			1.39243
$162$	8.76062e9			0.00616882
$163$		−	1.66941e12i		−	1.13640i	−0.822890	−	0.568201i	$-0.807640\pi$
$163$		−	1.66941e12i		−	1.13640i	0.822890	−	0.568201i	$-0.192360\pi$
$164$			5.02471e11i			0.330727i
$165$			5.81385e11i			0.370085i
$166$	2.69995e12			1.66250
$167$		−	2.48200e12i		−	1.47863i	−0.673358	−	0.739316i	$-0.735149\pi$
$167$		−	2.48200e12i		−	1.47863i	0.673358	−	0.739316i	$-0.264851\pi$
$168$	−1.11099e12			−0.640488
$169$	−1.38005e12			−0.770047
$170$	4.17447e11	−	1.47049e12i	0.225493	−	0.794317i
$171$	−7.96905e11			−0.416800
$172$	4.66285e10			0.0236181
$173$			3.66476e12i			1.79801i	0.437941	+	0.899004i	$0.355708\pi$
$173$			3.66476e12i			1.79801i	−0.437941	+	0.899004i	$0.644292\pi$
$174$	1.22659e12			0.583015
$175$		−	1.08817e12i		−	0.501174i
$176$			2.04231e12i			0.911595i
$177$			2.14295e11i			0.0927170i
$178$	1.66260e12			0.697391
$179$	−4.69810e12			−1.91087			−0.955435	−	0.295203i	$-0.904613\pi$
$179$	−4.69810e12			−1.91087			−0.955435	+	0.295203i	$0.904613\pi$
$180$		−	2.26574e11i		−	0.0893740i
$181$			1.54380e12i			0.590689i	0.955391	+	0.295344i	$0.0954344\pi$
$181$			1.54380e12i			0.590689i	−0.955391	+	0.295344i	$0.904566\pi$
$182$		−	1.65144e12i		−	0.613015i
$183$	2.18065e11			0.0785424
$184$			3.00129e12i			1.04908i
$185$	−2.90323e12			−0.985000
$186$	−2.49516e12			−0.821821
$187$	−6.73918e11	+	2.37393e12i	−0.215515	+	0.759170i
$188$	−3.38941e11			−0.105258
$189$	−3.88874e12			−1.17292
$190$		−	1.90838e12i		−	0.559141i
$191$	3.04300e11			0.0866199			0.0433100	−	0.999062i	$-0.486210\pi$
$191$	3.04300e11			0.0866199			0.0433100	+	0.999062i	$0.486210\pi$
$192$		−	1.66199e12i		−	0.459698i
$193$		−	6.02039e12i		−	1.61830i	−0.587600	−	0.809151i	$-0.699927\pi$
$193$		−	6.02039e12i		−	1.61830i	0.587600	−	0.809151i	$-0.300073\pi$
$194$			8.84474e11i			0.231087i
$195$	8.85405e11			0.224880
$196$	−2.88433e11			−0.0712257
$197$		−	1.42133e12i		−	0.341296i	−0.985332	−	0.170648i	$-0.945414\pi$
$197$		−	1.42133e12i		−	0.341296i	0.985332	−	0.170648i	$-0.0545861\pi$
$198$			2.27089e12i			0.530320i
$199$			6.36042e12i			1.44475i	0.691499	+	0.722377i	$0.256950\pi$
$199$			6.36042e12i			1.44475i	−0.691499	+	0.722377i	$0.743050\pi$
$200$	1.70879e12			0.377594
$201$		−	2.84258e12i		−	0.611132i
$202$	5.14503e12			1.07636
$203$	−4.95267e12			−1.00835
$204$	−1.64064e11	+	5.77929e11i	−0.0325123	+	0.114527i
$205$	6.75319e12			1.30276
$206$	−1.08987e12			−0.204694
$207$			4.00246e12i			0.731965i
$208$	3.11028e12			0.553926
$209$			3.08085e12i			0.534400i
$210$		−	3.54806e12i		−	0.599493i
$211$		−	4.25508e12i		−	0.700413i	−0.936673	−	0.350206i	$-0.886111\pi$
$211$		−	4.25508e12i		−	0.700413i	0.936673	−	0.350206i	$-0.113889\pi$
$212$	−1.26136e12			−0.202298
$213$	−2.32311e12			−0.363063
$214$		−	7.74083e12i		−	1.17899i
$215$		−	6.26686e11i		−	0.0930333i
$216$		−	6.10661e12i		−	0.883699i
$217$	1.00748e13			1.42137
$218$			1.00741e13i			1.38578i
$219$	−2.87507e12			−0.385661
$220$	−8.75940e11			−0.114591
$221$	3.61532e12	+	1.02633e12i	0.461306	+	0.130957i
$222$	7.08393e12			0.881724
$223$	−2.60764e12			−0.316643			−0.158322	−	0.987388i	$-0.550608\pi$
$223$	−2.60764e12			−0.316643			−0.158322	+	0.987388i	$0.550608\pi$
$224$		−	3.74549e12i		−	0.443757i
$225$	2.27882e12			0.263454
$226$			1.37069e13i			1.54648i
$227$			1.29059e12i			0.142117i	0.997472	+	0.0710584i	$0.0226377\pi$
$227$			1.29059e12i			0.142117i	−0.997472	+	0.0710584i	$0.977362\pi$
$228$			7.50029e11i			0.0806188i
$229$	−8.55818e12			−0.898020			−0.449010	−	0.893527i	$-0.648223\pi$
$229$	−8.55818e12			−0.898020			−0.449010	+	0.893527i	$0.648223\pi$
$230$	−9.58488e12			−0.981936
$231$			5.72791e12i			0.572967i
$232$		−	7.77734e12i		−	0.759709i
$233$		−	1.03162e13i		−	0.984153i	−0.870552	−	0.492077i	$-0.836238\pi$
$233$		−	1.03162e13i		−	0.984153i	0.870552	−	0.492077i	$-0.163762\pi$
$234$	3.45840e12			0.322246
$235$			4.55536e12i			0.414619i
$236$	−3.22866e11			−0.0287083
$237$	6.41699e12			0.557462
$238$	4.11276e12	−	1.44876e13i	0.349109	−	1.22976i
$239$	−2.05778e12			−0.170691			−0.0853455	−	0.996351i	$-0.527199\pi$
$239$	−2.05778e12			−0.170691			−0.0853455	+	0.996351i	$0.527199\pi$
$240$	6.68231e12			0.541707
$241$		−	5.37241e12i		−	0.425672i	−0.977088	−	0.212836i	$-0.931730\pi$
$241$		−	5.37241e12i		−	0.425672i	0.977088	−	0.212836i	$-0.0682700\pi$
$242$	−5.31752e12			−0.411836
$243$		−	1.31846e13i		−	0.998234i
$244$			3.28546e11i			0.0243194i
$245$			3.87653e12i			0.280563i
$246$	−1.64779e13			−1.16616
$247$	4.69191e12			0.324725
$248$			1.58208e13i			1.07089i
$249$			1.42615e13i			0.944211i
$250$			1.82067e13i			1.17913i
$251$	7.92474e12			0.502088			0.251044	−	0.967976i	$-0.419226\pi$
$251$	7.92474e12			0.502088			0.251044	+	0.967976i	$0.419226\pi$
$252$		−	2.23225e12i		−	0.138369i
$253$	1.54736e13			0.938488
$254$	−2.53541e13			−1.50474
$255$	7.76735e12	+	2.20502e12i	0.451130	+	0.128068i
$256$	9.78330e12			0.556116
$257$	6.75303e12			0.375722			0.187861	−	0.982196i	$-0.439845\pi$
$257$	6.75303e12			0.375722			0.187861	+	0.982196i	$0.439845\pi$
$258$			1.52913e12i			0.0832789i
$259$	−2.86031e13			−1.52498
$260$			1.33399e12i			0.0696305i
$261$		−	1.03717e13i		−	0.530063i
$262$		−	4.55361e12i		−	0.227876i
$263$	−3.53042e13			−1.73009			−0.865047	−	0.501691i	$-0.832711\pi$
$263$	−3.53042e13			−1.73009			−0.865047	+	0.501691i	$0.832711\pi$
$264$	−8.99472e12			−0.431684
$265$			1.69526e13i			0.796865i
$266$		−	1.88017e13i		−	0.865663i
$267$			8.78207e12i			0.396082i
$268$	4.28276e12			0.189227
$269$		−	3.17055e13i		−	1.37245i	−0.727389	−	0.686225i	$-0.759267\pi$
$269$		−	3.17055e13i		−	1.37245i	0.727389	−	0.686225i	$-0.240733\pi$
$270$	1.95020e13			0.827138
$271$	−3.82354e13			−1.58904			−0.794519	−	0.607240i	$-0.792277\pi$
$271$	−3.82354e13			−1.58904			−0.794519	+	0.607240i	$0.792277\pi$
$272$	2.72854e13	+	7.74586e12i	1.11122	+	0.315457i
$273$	8.72317e12			0.348161
$274$	−3.09677e13			−1.21138
$275$		−	8.80995e12i		−	0.337788i
$276$	3.76702e12			0.141579
$277$		−	2.34562e13i		−	0.864209i	−0.901823	−	0.432105i	$-0.857771\pi$
$277$		−	2.34562e13i		−	0.864209i	0.901823	−	0.432105i	$-0.142229\pi$
$278$			4.46658e13i			1.61335i
$279$			2.10983e13i			0.747179i
$280$	−2.24968e13			−0.781181
$281$	3.57426e13			1.21703			0.608515	−	0.793543i	$-0.291766\pi$
$281$	3.57426e13			1.21703			0.608515	+	0.793543i	$0.291766\pi$
$282$		−	1.11152e13i		−	0.371147i
$283$			2.68278e12i			0.0878535i	0.999035	+	0.0439268i	$0.0139868\pi$
$283$			2.68278e12i			0.0878535i	−0.999035	+	0.0439268i	$0.986013\pi$
$284$		−	3.50010e12i		−	0.112417i
$285$	1.00804e13			0.317563
$286$		−	1.33703e13i		−	0.413168i
$287$	6.65336e13			2.01693
$288$	7.84368e12			0.233271
$289$	2.91600e13	+	1.80072e13i	0.850842	+	0.525422i
$290$	2.48376e13			0.711084
$291$	−4.67192e12			−0.131245
$292$		−	4.33171e12i		−	0.119414i
$293$	3.11947e13			0.843935			0.421967	−	0.906611i	$-0.361340\pi$
$293$	3.11947e13			0.843935			0.421967	+	0.906611i	$0.361340\pi$
$294$		−	9.45882e12i		−	0.251146i
$295$			4.33931e12i			0.113084i
$296$		−	4.49164e13i		−	1.14895i
$297$	−3.14836e13			−0.790539
$298$	−3.47459e13			−0.856474
$299$		−	2.35651e13i		−	0.570267i
$300$		−	2.14477e12i		−	0.0509581i
$301$		−	6.17422e12i		−	0.144034i
$302$	4.13931e13			0.948178
$303$			2.71768e13i			0.611314i
$304$	3.54107e13			0.782221
$305$	4.41565e12			0.0957955
$306$	3.03393e13	+	8.61281e12i	0.646455	+	0.183517i
$307$	1.14677e13			0.240001			0.120001	−	0.992774i	$-0.461710\pi$
$307$	1.14677e13			0.240001			0.120001	+	0.992774i	$0.461710\pi$
$308$	−8.62992e12			−0.177410
$309$		−	5.75686e12i		−	0.116256i
$310$	−5.05251e13			−1.00235
$311$			3.89031e13i			0.758231i	0.925349	+	0.379116i	$0.123772\pi$
$311$			3.89031e13i			0.758231i	−0.925349	+	0.379116i	$0.876228\pi$
$312$			1.36983e13i			0.262311i
$313$			4.46402e13i			0.839910i	0.907545	+	0.419955i	$0.137954\pi$
$313$			4.46402e13i			0.839910i	−0.907545	+	0.419955i	$0.862046\pi$
$314$	−1.09833e14			−2.03058
$315$	−3.00013e13			−0.545045
$316$			9.66812e12i			0.172609i
$317$		−	9.07410e13i		−	1.59213i	−0.605213	−	0.796063i	$-0.706912\pi$
$317$		−	9.07410e13i		−	1.59213i	0.605213	−	0.796063i	$-0.293088\pi$
$318$		−	4.13648e13i		−	0.713315i
$319$	−4.00973e13			−0.679620
$320$		−	3.36541e13i		−	0.560678i
$321$	4.08882e13			0.669607
$322$	−9.44319e13			−1.52024
$323$	4.11605e13	+	1.16847e13i	0.651428	+	0.184929i
$324$	−6.97198e10			−0.00108482
$325$	−1.34169e13			−0.205255
$326$			8.24833e13i			1.24071i
$327$	−5.32126e13			−0.787049
$328$			1.04480e14i			1.51959i
$329$			4.48802e13i			0.641914i
$330$		−	2.87254e13i		−	0.404054i
$331$	−1.20718e14			−1.67001			−0.835006	−	0.550241i	$-0.814536\pi$
$331$	−1.20718e14			−1.67001			−0.835006	+	0.550241i	$0.814536\pi$
$332$	−2.14870e13			−0.292359
$333$		−	5.98996e13i		−	0.801642i
$334$			1.22632e14i			1.61435i
$335$		−	5.75602e13i		−	0.745377i
$336$	6.58353e13			0.838673
$337$			5.11117e12i			0.0640554i	0.999487	+	0.0320277i	$0.0101965\pi$
$337$			5.11117e12i			0.0640554i	−0.999487	+	0.0320277i	$0.989804\pi$
$338$	6.81862e13			0.840727
$339$	−7.24020e13			−0.878319
$340$	−3.32218e12	+	1.17026e13i	−0.0396541	+	0.139685i
$341$	8.15666e13			0.957995
$342$	3.93740e13			0.455057
$343$		−	6.47591e13i		−	0.736518i
$344$	9.69558e12			0.108518
$345$		−	5.06287e13i		−	0.557688i
$346$		−	1.81070e14i		−	1.96304i
$347$			8.14275e13i			0.868879i	0.900701	+	0.434439i	$0.143053\pi$
$347$			8.14275e13i			0.868879i	−0.900701	+	0.434439i	$0.856947\pi$
$348$	−9.76162e12			−0.102526
$349$	1.93593e12			0.0200147			0.0100073	−	0.999950i	$-0.496815\pi$
$349$	1.93593e12			0.0200147			0.0100073	+	0.999950i	$0.496815\pi$
$350$			5.37651e13i			0.547175i
$351$			4.79471e13i			0.480367i
$352$		−	3.03239e13i		−	0.299089i
$353$	1.80364e14			1.75142			0.875708	−	0.482842i	$-0.160395\pi$
$353$	1.80364e14			1.75142			0.875708	+	0.482842i	$0.160395\pi$
$354$		−	1.05880e13i		−	0.101227i
$355$	−4.70413e13			−0.442816
$356$	−1.32315e13			−0.122640
$357$	7.65253e13	+	2.17242e13i	0.698441	+	0.198275i
$358$	2.32127e14			2.08626
$359$	−2.57874e13			−0.228238			−0.114119	−	0.993467i	$-0.536404\pi$
$359$	−2.57874e13			−0.228238			−0.114119	+	0.993467i	$0.536404\pi$
$360$		−	4.71121e13i		−	0.410647i
$361$	−6.30728e13			−0.541443
$362$		−	7.62769e13i		−	0.644905i
$363$		−	2.80879e13i		−	0.233901i
$364$			1.31427e13i			0.107802i
$365$	−5.82180e13			−0.470378
$366$	−1.07743e13			−0.0857515
$367$			2.81088e13i			0.220384i	0.993910	+	0.110192i	$0.0351465\pi$
$367$			2.81088e13i			0.220384i	−0.993910	+	0.110192i	$0.964853\pi$
$368$		−	1.77850e14i		−	1.37370i
$369$			1.39332e14i			1.06025i
$370$	1.43444e14			1.07541
$371$			1.67020e14i			1.23371i
$372$	1.98573e13			0.144522
$373$	−1.26844e14			−0.909643			−0.454822	−	0.890583i	$-0.650297\pi$
$373$	−1.26844e14			−0.909643			−0.454822	+	0.890583i	$0.650297\pi$
$374$	3.32973e13	−	1.17293e14i	0.235297	−	0.828852i
$375$	−9.61705e13			−0.669684
$376$	−7.04768e13			−0.483630
$377$			6.10651e13i			0.412968i
$378$	1.92137e14			1.28058
$379$		−	8.55456e13i		−	0.561930i	−0.959718	−	0.280965i	$-0.909346\pi$
$379$		−	8.55456e13i		−	0.561930i	0.959718	−	0.280965i	$-0.0906544\pi$
$380$			1.51875e13i			0.0983280i
$381$		−	1.33924e14i		−	0.854616i
$382$	−1.50350e13			−0.0945704
$383$	−1.88435e14			−1.16834			−0.584168	−	0.811633i	$-0.698579\pi$
$383$	−1.88435e14			−1.16834			−0.584168	+	0.811633i	$0.698579\pi$
$384$			1.20567e14i			0.736896i
$385$			1.15986e14i			0.698829i
$386$			2.97459e14i			1.76684i
$387$	1.29298e13			0.0757152
$388$		−	7.03892e12i		−	0.0406379i
$389$	−1.92546e14			−1.09600			−0.548000	−	0.836478i	$-0.684611\pi$
$389$	−1.92546e14			−1.09600			−0.548000	+	0.836478i	$0.684611\pi$
$390$	−4.37466e13			−0.245521
$391$	5.86867e13	−	2.06729e14i	0.324764	−	1.14401i
$392$	−5.99746e13			−0.327261
$393$	2.40528e13			0.129422
$394$			7.02260e13i			0.372622i
$395$	1.29939e14			0.679918
$396$		−	1.80725e13i		−	0.0932597i
$397$			1.74764e14i			0.889414i	0.895676	+	0.444707i	$0.146692\pi$
$397$			1.74764e14i			0.889414i	−0.895676	+	0.444707i	$0.853308\pi$
$398$		−	3.14259e14i		−	1.57736i
$399$	9.93135e13			0.491651
$400$	−1.01260e14			−0.494432
$401$		−	1.57298e14i		−	0.757580i	−0.925483	−	0.378790i	$-0.876340\pi$
$401$		−	1.57298e14i		−	0.757580i	0.925483	−	0.378790i	$-0.123660\pi$
$402$			1.40448e14i			0.667225i
$403$		−	1.24220e14i		−	0.582121i
$404$	−4.09458e13			−0.189283
$405$			9.37031e11i			0.00427318i
$406$	2.44704e14			1.10090
$407$	−2.31573e14			−1.02783
$408$	−3.41142e13	+	1.20170e14i	−0.149384	+	0.526219i
$409$	1.89817e14			0.820082			0.410041	−	0.912067i	$-0.365514\pi$
$409$	1.89817e14			0.820082			0.410041	+	0.912067i	$0.365514\pi$
$410$	−3.33666e14			−1.42233
$411$		−	1.63576e14i		−	0.688001i
$412$	8.67354e12			0.0359966
$413$			4.27517e13i			0.175077i
$414$		−	1.97756e14i		−	0.799149i
$415$			2.88785e14i			1.15162i
$416$	−4.61810e13			−0.181740
$417$	−2.35931e14			−0.916298
$418$		−	1.52221e14i		−	0.583450i
$419$			8.54010e13i			0.323062i	0.986868	+	0.161531i	$0.0516431\pi$
$419$			8.54010e13i			0.323062i	−0.986868	+	0.161531i	$0.948357\pi$
$420$			2.82365e13i			0.105424i
$421$	3.85506e14			1.42063			0.710313	−	0.703886i	$-0.248553\pi$
$421$	3.85506e14			1.42063			0.710313	+	0.703886i	$0.248553\pi$
$422$			2.10237e14i			0.764701i
$423$	−9.39865e13			−0.337438
$424$	−2.62277e14			−0.929499
$425$	−1.17702e14	−	3.34135e13i	−0.411760	−	0.116891i
$426$	1.14782e14			0.396387
$427$	4.35037e13			0.148311
$428$			6.16040e13i			0.207333i
$429$	7.06236e13			0.234658
$430$			3.09637e13i			0.101572i
$431$			2.53267e14i			0.820265i	0.912026	+	0.410132i	$0.134518\pi$
$431$			2.53267e14i			0.820265i	−0.912026	+	0.410132i	$0.865482\pi$
$432$			3.61865e14i			1.15714i
$433$	5.73737e14			1.81146			0.905731	−	0.423853i	$-0.139323\pi$
$433$	5.73737e14			1.81146			0.905731	+	0.423853i	$0.139323\pi$
$434$	−4.97782e14			−1.55184
$435$			1.31196e14i			0.403858i
$436$		−	8.01724e13i		−	0.243697i
$437$		−	2.68290e14i		−	0.805297i
$438$	1.42053e14			0.421059
$439$		−	4.96647e14i		−	1.45376i	−0.686764	−	0.726880i	$-0.740970\pi$
$439$		−	4.96647e14i		−	1.45376i	0.686764	−	0.726880i	$-0.259030\pi$
$440$	−1.82136e14			−0.526510
$441$	−7.99810e13			−0.228336
$442$	−1.78628e14	−	5.07093e13i	−0.503647	−	0.142977i
$443$	2.27553e14			0.633670			0.316835	−	0.948481i	$-0.397380\pi$
$443$	2.27553e14			0.633670			0.316835	+	0.948481i	$0.397380\pi$
$444$	−5.63761e13			−0.155056
$445$			1.77830e14i			0.483087i
$446$	1.28840e14			0.345707
$447$		−	1.83533e14i		−	0.486433i
$448$		−	3.31566e14i		−	0.868043i
$449$		−	3.52049e14i		−	0.910434i	−0.890381	−	0.455217i	$-0.849562\pi$
$449$		−	3.52049e14i		−	0.910434i	0.890381	−	0.455217i	$-0.150438\pi$
$450$	−1.12593e14			−0.287636
$451$	5.38663e14			1.35940
$452$		−	1.09084e14i		−	0.271957i
$453$			2.18644e14i			0.538515i
$454$		−	6.37661e13i		−	0.155161i
$455$	1.76638e14			0.424640
$456$			1.55955e14i			0.370419i
$457$	−4.41710e14			−1.03657			−0.518284	−	0.855208i	$-0.673429\pi$
$457$	−4.41710e14			−1.03657			−0.518284	+	0.855208i	$0.673429\pi$
$458$	4.22848e14			0.980446
$459$	−1.19408e14	+	4.20623e14i	−0.273566	+	0.963659i
$460$	7.62794e13			0.172679
$461$	5.66692e14			1.26763			0.633814	−	0.773486i	$-0.281489\pi$
$461$	5.66692e14			1.26763			0.633814	+	0.773486i	$0.281489\pi$
$462$		−	2.83008e14i		−	0.625558i
$463$	6.96702e14			1.52178			0.760890	−	0.648881i	$-0.224763\pi$
$463$	6.96702e14			1.52178			0.760890	+	0.648881i	$0.224763\pi$
$464$			4.60869e14i			0.994784i
$465$		−	2.66881e14i		−	0.569280i
$466$			5.09710e14i			1.07448i
$467$	1.90096e14			0.396033			0.198016	−	0.980199i	$-0.436550\pi$
$467$	1.90096e14			0.396033			0.198016	+	0.980199i	$0.436550\pi$
$468$	−2.75230e13			−0.0566688
$469$		−	5.67093e14i		−	1.15399i
$470$		−	2.25074e14i		−	0.452675i
$471$		−	5.80153e14i		−	1.15326i
$472$	−6.71344e13			−0.131906
$473$		−	4.99871e13i		−	0.0970781i
$474$	−3.17054e14			−0.608629
$475$	−1.52752e14			−0.289849
$476$	−3.27307e13	+	1.15296e14i	−0.0613927	+	0.216261i
$477$	−3.49768e14			−0.648529
$478$	1.01672e14			0.186358
$479$			1.00529e15i			1.82157i	0.412883	+	0.910784i	$0.364522\pi$
$479$			1.00529e15i			1.82157i	−0.412883	+	0.910784i	$0.635478\pi$
$480$	−9.92178e13			−0.177731
$481$			3.52669e14i			0.624553i
$482$			2.65443e14i			0.464743i
$483$		−	4.98803e14i		−	0.863415i
$484$	4.23185e13			0.0724237
$485$	−9.46029e13			−0.160075
$486$			6.51432e14i			1.08986i
$487$		−	4.84667e14i		−	0.801740i	−0.916135	−	0.400870i	$-0.868708\pi$
$487$		−	4.84667e14i		−	0.801740i	0.916135	−	0.400870i	$-0.131292\pi$
$488$			6.83153e13i			0.111740i
$489$	−4.35689e14			−0.704656
$490$		−	1.91534e14i		−	0.306314i
$491$	−3.22437e14			−0.509914			−0.254957	−	0.966952i	$-0.582061\pi$
$491$	−3.22437e14			−0.509914			−0.254957	+	0.966952i	$0.582061\pi$
$492$	1.31137e14			0.205076
$493$	−1.52077e14	+	5.35703e14i	−0.235183	+	0.828450i
$494$	−2.31821e14			−0.354531
$495$	−2.42893e14			−0.367356
$496$		−	9.37509e14i		−	1.40225i
$497$	−4.63459e14			−0.685569
$498$		−	7.04641e14i		−	1.03088i
$499$			1.15064e15i			1.66490i	0.554104	+	0.832448i	$0.313061\pi$
$499$			1.15064e15i			1.66490i	−0.554104	+	0.832448i	$0.686939\pi$
$500$		−	1.44895e14i		−	0.207356i
$501$	−6.47759e14			−0.916866
$502$	−3.91550e14			−0.548172
$503$		−	1.49386e14i		−	0.206865i	−0.994636	−	0.103432i	$-0.967017\pi$
$503$		−	1.49386e14i		−	0.206865i	0.994636	−	0.103432i	$-0.0329825\pi$
$504$		−	4.64156e14i		−	0.635765i
$505$			5.50310e14i			0.745598i
$506$	−7.64529e14			−1.02463
$507$			3.60169e14i			0.477489i
$508$	2.01776e14			0.264618
$509$	−4.38029e14			−0.568270			−0.284135	−	0.958784i	$-0.591706\pi$
$509$	−4.38029e14			−0.568270			−0.284135	+	0.958784i	$0.591706\pi$
$510$	−3.83774e14	−	1.08947e14i	−0.492538	−	0.139823i
$511$	−5.73574e14			−0.728240
$512$	4.62739e14			0.581234
$513$			5.45879e14i			0.678345i
$514$	−3.33658e14			−0.410208
$515$		−	1.16572e14i		−	0.141793i
$516$		−	1.21693e13i		−	0.0146451i
$517$			3.63354e14i			0.432645i
$518$	1.41324e15			1.66495
$519$	9.56440e14			1.11490
$520$			2.77380e14i			0.319931i
$521$		−	8.19780e14i		−	0.935599i	−0.883835	−	0.467799i	$-0.845047\pi$
$521$		−	8.19780e14i		−	0.935599i	0.883835	−	0.467799i	$-0.154953\pi$
$522$			5.12452e14i			0.578716i
$523$	−4.83134e13			−0.0539894			−0.0269947	−	0.999636i	$-0.508594\pi$
$523$	−4.83134e13			−0.0539894			−0.0269947	+	0.999636i	$0.508594\pi$
$524$			3.62391e13i			0.0400733i
$525$	−2.83995e14			−0.310767
$526$	1.74433e15			1.88889
$527$	3.09357e14	−	1.08974e15i	0.331514	−	1.16779i
$528$	5.33009e14			0.565259
$529$	−3.94678e14			−0.414225
$530$		−	8.37605e14i		−	0.870006i
$531$	−8.95291e13			−0.0920332
$532$			1.49630e14i			0.152232i
$533$		−	8.20343e14i		−	0.826030i
$534$		−	4.33909e14i		−	0.432436i
$535$	8.27955e14			0.816697
$536$	8.90525e14			0.869441
$537$			1.22613e15i			1.18489i
$538$			1.56652e15i			1.49842i
$539$			3.09208e14i			0.292761i
$540$	−1.55203e14			−0.145457
$541$		−	1.09019e15i		−	1.01139i	−0.862713	−	0.505693i	$-0.831237\pi$
$541$		−	1.09019e15i		−	1.01139i	0.862713	−	0.505693i	$-0.168763\pi$
$542$	1.88916e15			1.73489
$543$	4.02906e14			0.366273
$544$	−4.05130e14	−	1.15009e14i	−0.364586	−	0.103500i
$545$	−1.07751e15			−0.959937
$546$	−4.30999e14			−0.380117
$547$		−	2.18294e15i		−	1.90595i	−0.303049	−	0.952975i	$-0.598005\pi$
$547$		−	2.18294e15i		−	1.90595i	0.303049	−	0.952975i	$-0.401995\pi$
$548$	2.46451e14			0.213028
$549$			9.11040e13i			0.0779632i
$550$			4.35287e14i			0.368792i
$551$			6.95228e14i			0.583168i
$552$	7.83287e14			0.650513
$553$	1.28018e15			1.05265
$554$			1.15894e15i			0.943532i
$555$			7.57693e14i			0.610776i
$556$		−	3.55464e14i		−	0.283716i
$557$	−1.63217e15			−1.28992			−0.644958	−	0.764218i	$-0.723125\pi$
$557$	−1.63217e15			−1.28992			−0.644958	+	0.764218i	$0.723125\pi$
$558$		−	1.04244e15i		−	0.815760i
$559$	−7.61265e13			−0.0589890
$560$	1.33312e15			1.02290
$561$	6.19556e14	+	1.75881e14i	0.470744	+	0.133636i
$562$	−1.76599e15			−1.32874
$563$	7.12025e14			0.530517			0.265258	−	0.964177i	$-0.414543\pi$
$563$	7.12025e14			0.530517			0.265258	+	0.964177i	$0.414543\pi$
$564$			8.84580e13i			0.0652682i
$565$	−1.46609e15			−1.07126
$566$		−	1.32552e14i		−	0.0959173i
$567$			9.23180e12i			0.00661576i
$568$		−	7.27785e14i		−	0.516520i
$569$	−1.50018e15			−1.05445			−0.527223	−	0.849727i	$-0.676767\pi$
$569$	−1.50018e15			−1.05445			−0.527223	+	0.849727i	$0.676767\pi$
$570$	−4.98056e14			−0.346710
$571$		−	1.32789e15i		−	0.915509i	−0.889079	−	0.457755i	$-0.848654\pi$
$571$		−	1.32789e15i		−	0.915509i	0.889079	−	0.457755i	$-0.151346\pi$
$572$			1.06405e14i			0.0726578i
$573$		−	7.94171e13i		−	0.0537110i
$574$	−3.28733e15			−2.20206
$575$			7.67197e14i			0.509018i
$576$	6.94355e14			0.456308
$577$	2.32701e15			1.51471			0.757357	−	0.653001i	$-0.226490\pi$
$577$	2.32701e15			1.51471			0.757357	+	0.653001i	$0.226490\pi$
$578$	−1.44075e15	−	8.89710e14i	−0.928937	−	0.573648i
$579$	−1.57122e15			−1.00347
$580$	−1.97665e14			−0.125048
$581$			2.84516e15i			1.78294i
$582$	2.30833e14			0.143292
$583$			1.35221e15i			0.831510i
$584$		−	9.00703e14i		−	0.548670i
$585$			3.69908e14i			0.223222i
$586$	−1.54129e15			−0.921396
$587$	2.85903e15			1.69320			0.846601	−	0.532229i	$-0.178645\pi$
$587$	2.85903e15			1.69320			0.846601	+	0.532229i	$0.178645\pi$
$588$			7.52762e13i			0.0441654i
$589$		−	1.41425e15i		−	0.822036i
$590$		−	2.14399e14i		−	0.123463i
$591$	−3.70944e14			−0.211630
$592$			2.66165e15i			1.50446i
$593$	−2.48337e15			−1.39072			−0.695362	−	0.718659i	$-0.744756\pi$
$593$	−2.48337e15			−1.39072			−0.695362	+	0.718659i	$0.744756\pi$
$594$	1.55556e15			0.863100
$595$	1.54958e15	+	4.39899e14i	0.851865	+	0.241830i
$596$	2.76519e14			0.150616
$597$	1.65996e15			0.895859
$598$			1.16432e15i			0.622610i
$599$	−2.47574e15			−1.31177			−0.655886	−	0.754860i	$-0.727705\pi$
$599$	−2.47574e15			−1.31177			−0.655886	+	0.754860i	$0.727705\pi$
$600$		−	4.45967e14i		−	0.234137i
$601$		−	7.19440e13i		−	0.0374270i	−0.999825	−	0.0187135i	$-0.994043\pi$
$601$		−	7.19440e13i		−	0.0374270i	0.999825	−	0.0187135i	$-0.00595704\pi$
$602$			3.05060e14i			0.157255i
$603$	1.18759e15			0.606625
$604$	−3.29419e14			−0.166742
$605$		−	5.68759e14i		−	0.285282i
$606$		−	1.34277e15i		−	0.667424i
$607$		−	7.00081e14i		−	0.344835i	−0.985024	−	0.172417i	$-0.944842\pi$
$607$		−	7.00081e14i		−	0.344835i	0.985024	−	0.172417i	$-0.0551577\pi$
$608$	−5.25771e14			−0.256642
$609$			1.29256e15i			0.625255i
$610$	−2.18171e14			−0.104588
$611$	5.53361e14			0.262895
$612$	−2.41450e14	−	6.85434e13i	−0.113683	−	0.0322725i
$613$	−1.13421e15			−0.529249			−0.264625	−	0.964351i	$-0.585248\pi$
$613$	−1.13421e15			−0.529249			−0.264625	+	0.964351i	$0.585248\pi$
$614$	−5.66601e14			−0.262030
$615$		−	1.76247e15i		−	0.807809i
$616$	−1.79444e15			−0.815145
$617$		−	2.49245e15i		−	1.12217i	−0.827759	−	0.561083i	$-0.810385\pi$
$617$		−	2.49245e15i		−	1.12217i	0.827759	−	0.561083i	$-0.189615\pi$
$618$			2.84438e14i			0.126926i
$619$		−	1.90954e15i		−	0.844558i	−0.906466	−	0.422279i	$-0.861230\pi$
$619$		−	1.90954e15i		−	0.844558i	0.906466	−	0.422279i	$-0.138770\pi$
$620$	4.02095e14			0.176268
$621$	2.74168e15			1.19128
$622$		−	1.92215e15i		−	0.827826i
$623$			1.75201e15i			0.747917i
$624$		−	8.11732e14i		−	0.343477i
$625$	−9.26877e14			−0.388760
$626$		−	2.20561e15i		−	0.917002i
$627$	8.04051e14			0.331369
$628$	8.74084e14			0.357088
$629$	−8.78287e14	+	3.09384e15i	−0.355679	+	1.25291i
$630$	1.48232e15			0.595072
$631$	2.73679e15			1.08913			0.544565	−	0.838719i	$-0.316695\pi$
$631$	2.73679e15			1.08913			0.544565	+	0.838719i	$0.316695\pi$
$632$			2.01032e15i			0.793086i
$633$	−1.11050e15			−0.434310
$634$			4.48339e15i			1.73826i
$635$		−	2.71186e15i		−	1.04235i
$636$			3.29194e14i			0.125440i
$637$	4.70901e14			0.177895
$638$	1.98115e15			0.742000
$639$		−	9.70560e14i		−	0.360386i
$640$			2.44139e15i			0.898767i
$641$			3.19575e15i			1.16641i	0.812323	+	0.583207i	$0.198203\pi$
$641$			3.19575e15i			1.16641i	−0.812323	+	0.583207i	$0.801797\pi$
$642$	−2.02023e15			−0.731068
$643$			1.34086e15i			0.481087i	0.970638	+	0.240543i	$0.0773256\pi$
$643$			1.34086e15i			0.481087i	−0.970638	+	0.240543i	$0.922674\pi$
$644$	7.51518e14			0.267342
$645$	−1.63555e14			−0.0576878
$646$	−2.03368e15	−	5.77327e14i	−0.711220	−	0.201903i
$647$	−1.60554e15			−0.556735			−0.278367	−	0.960475i	$-0.589793\pi$
$647$	−1.60554e15			−0.556735			−0.278367	+	0.960475i	$0.589793\pi$
$648$	−1.44970e13			−0.00498443
$649$			3.46122e14i			0.118000i
$650$	6.62910e14			0.224094
$651$		−	2.62936e15i		−	0.881362i
$652$		−	6.56428e14i		−	0.218185i
$653$			4.37708e14i			0.144265i	0.997395	+	0.0721326i	$0.0229805\pi$
$653$			4.37708e14i			0.144265i	−0.997395	+	0.0721326i	$0.977020\pi$
$654$	2.62916e15			0.859289
$655$	4.87052e14			0.157851
$656$		−	6.19127e15i		−	1.98980i
$657$		−	1.20116e15i		−	0.382817i
$658$		−	2.21747e15i		−	0.700833i
$659$	−8.25001e14			−0.258574			−0.129287	−	0.991607i	$-0.541269\pi$
$659$	−8.25001e14			−0.258574			−0.129287	+	0.991607i	$0.541269\pi$
$660$			2.28606e14i			0.0710551i
$661$	−6.24739e14			−0.192571			−0.0962854	−	0.995354i	$-0.530696\pi$
$661$	−6.24739e14			−0.192571			−0.0962854	+	0.995354i	$0.530696\pi$
$662$	5.96453e15			1.82330
$663$	2.67854e14	−	9.43537e14i	0.0812033	−	0.286045i
$664$	−4.46785e15			−1.34330
$665$	2.01102e15			0.599650
$666$			2.95956e15i			0.875222i
$667$	3.49179e15			1.02413
$668$		−	9.75943e14i		−	0.283892i
$669$			6.80550e14i			0.196343i
$670$			2.84397e15i			0.813792i
$671$	3.52210e14			0.0999604
$672$	−9.77511e14			−0.275163
$673$			2.85949e15i			0.798372i	0.916870	+	0.399186i	$0.130707\pi$
$673$			2.85949e15i			0.798372i	−0.916870	+	0.399186i	$0.869293\pi$
$674$		−	2.52536e14i		−	0.0699348i
$675$		−	1.56099e15i		−	0.428774i
$676$	−5.42647e14			−0.147846
$677$		−	1.51820e15i		−	0.410289i	−0.978732	−	0.205145i	$-0.934233\pi$
$677$		−	1.51820e15i		−	0.410289i	0.978732	−	0.205145i	$-0.0657665\pi$
$678$	3.57728e15			0.958936
$679$	−9.32044e14			−0.247829
$680$	−6.90788e14	+	2.43336e15i	−0.182199	+	0.641811i
$681$	3.36822e14			0.0881234
$682$	−4.03009e15			−1.04593
$683$		−	4.95061e15i		−	1.27452i	−0.770651	−	0.637258i	$-0.780069\pi$
$683$		−	4.95061e15i		−	1.27452i	0.770651	−	0.637258i	$-0.219931\pi$
$684$	−3.13350e14			−0.0800242
$685$		−	3.31229e15i		−	0.839131i
$686$			3.19966e15i			0.804120i
$687$			2.23354e15i			0.556842i
$688$	−5.74540e14			−0.142097
$689$	2.05932e15			0.505263
$690$			2.50149e15i			0.608876i
$691$			5.48439e15i			1.32434i	0.749354	+	0.662170i	$0.230364\pi$
$691$			5.48439e15i			1.32434i	−0.749354	+	0.662170i	$0.769636\pi$
$692$			1.44102e15i			0.345211i
$693$	−2.39303e15			−0.568742
$694$		−	4.02322e15i		−	0.948630i
$695$	−4.77743e15			−1.11758
$696$	−2.02976e15			−0.471078
$697$	2.04298e15	−	7.19658e15i	0.470419	−	1.65709i
$698$	−9.56514e13			−0.0218518
$699$	−2.69236e15			−0.610251
$700$		−	4.27880e14i		−	0.0962238i
$701$	2.78603e15			0.621637			0.310819	−	0.950469i	$-0.399397\pi$
$701$	2.78603e15			0.621637			0.310819	+	0.950469i	$0.399397\pi$
$702$		−	2.36900e15i		−	0.524458i
$703$			4.01514e15i			0.881955i
$704$		−	2.68439e15i		−	0.585054i
$705$	1.18887e15			0.257096
$706$	−8.91154e15			−1.91217
$707$			5.42175e15i			1.15434i
$708$			8.42627e13i			0.0178013i
$709$			1.21468e15i			0.254629i	0.991862	+	0.127315i	$0.0406358\pi$
$709$			1.21468e15i			0.254629i	−0.991862	+	0.127315i	$0.959364\pi$
$710$	2.32424e15			0.483460
$711$			2.68092e15i			0.553351i
$712$	−2.75125e15			−0.563494
$713$	−7.10306e15			−1.44362
$714$	−3.78101e15	−	1.07336e15i	−0.762549	−	0.216474i
$715$	1.43007e15			0.286204
$716$	−1.84734e15			−0.366880
$717$			5.37046e14i			0.105842i
$718$	1.27412e15			0.249187
$719$			5.74415e15i			1.11485i	0.830227	+	0.557426i	$0.188211\pi$
$719$			5.74415e15i			1.11485i	−0.830227	+	0.557426i	$0.811789\pi$
$720$			2.79176e15i			0.537712i
$721$		−	1.14849e15i		−	0.219524i
$722$	3.11634e15			0.591139
$723$	−1.40211e15			−0.263950
$724$			6.07036e14i			0.113410i
$725$		−	1.98806e15i		−	0.368613i
$726$			1.38778e15i			0.255370i
$727$	1.17491e15			0.214568			0.107284	−	0.994228i	$-0.465785\pi$
$727$	1.17491e15			0.214568			0.107284	+	0.994228i	$0.465785\pi$
$728$			2.73280e15i			0.495319i
$729$	−3.47237e15			−0.624632
$730$	2.87647e15			0.513552
$731$	−6.67832e14	−	1.89586e14i	−0.118337	−	0.0335939i
$732$	8.57450e13			0.0150799
$733$	1.69827e15			0.296438			0.148219	−	0.988955i	$-0.452646\pi$
$733$	1.69827e15			0.296438			0.148219	+	0.988955i	$0.452646\pi$
$734$		−	1.38882e15i		−	0.240612i
$735$	1.01171e15			0.173971
$736$			2.64069e15i			0.450702i
$737$		−	4.59124e15i		−	0.777784i
$738$		−	6.88422e15i		−	1.15756i
$739$	9.30618e15			1.55320			0.776599	−	0.629995i	$-0.216943\pi$
$739$	9.30618e15			1.55320			0.776599	+	0.629995i	$0.216943\pi$
$740$	−1.14157e15			−0.189117
$741$		−	1.22451e15i		−	0.201355i
$742$		−	8.25223e15i		−	1.34695i
$743$		−	2.23903e15i		−	0.362761i	−0.983413	−	0.181381i	$-0.941943\pi$
$743$		−	2.23903e15i		−	0.362761i	0.983413	−	0.181381i	$-0.0580566\pi$
$744$	4.12897e15			0.664034
$745$		−	3.71640e15i		−	0.593285i
$746$	6.26718e15			0.993136
$747$	−5.95824e15			−0.937248
$748$	−2.64990e14	+	9.33451e14i	−0.0413782	+	0.145758i
$749$	8.15716e15			1.26441
$750$	4.75165e15			0.731151
$751$			7.94182e14i			0.121311i	0.998159	+	0.0606556i	$0.0193191\pi$
$751$			7.94182e14i			0.121311i	−0.998159	+	0.0606556i	$0.980681\pi$
$752$	4.17631e15			0.633279
$753$		−	2.06822e15i		−	0.311333i
$754$		−	3.01714e15i		−	0.450872i
$755$			4.42738e15i			0.656809i
$756$	−1.52909e15			−0.225197
$757$	3.92161e15			0.573373			0.286687	−	0.958024i	$-0.407446\pi$
$757$	3.92161e15			0.573373			0.286687	+	0.958024i	$0.407446\pi$
$758$			4.22669e15i			0.613507i
$759$		−	4.03835e15i		−	0.581935i
$760$			3.15798e15i			0.451787i
$761$	7.75629e15			1.10164			0.550819	−	0.834625i	$-0.314316\pi$
$761$	7.75629e15			1.10164			0.550819	+	0.834625i	$0.314316\pi$
$762$			6.61700e15i			0.933058i
$763$	−1.06159e16			−1.48618
$764$	1.19653e14			0.0166307
$765$	−9.21221e14	+	3.24508e15i	−0.127124	+	0.447803i
$766$	9.31030e15			1.27557
$767$	5.27117e14			0.0717022
$768$		−	2.55328e15i		−	0.344835i
$769$	4.51047e15			0.604821			0.302410	−	0.953178i	$-0.402209\pi$
$769$	4.51047e15			0.604821			0.302410	+	0.953178i	$0.402209\pi$
$770$		−	5.73069e15i		−	0.762971i
$771$		−	1.76243e15i		−	0.232977i
$772$		−	2.36727e15i		−	0.310709i
$773$	−2.50674e15			−0.326680			−0.163340	−	0.986570i	$-0.552227\pi$
$773$	−2.50674e15			−0.326680			−0.163340	+	0.986570i	$0.552227\pi$
$774$	−6.38845e14			−0.0826647
$775$			4.04415e15i			0.519599i
$776$		−	1.46362e15i		−	0.186719i
$777$			7.46493e15i			0.945605i
$778$	9.51341e15			1.19660
$779$		−	9.33962e15i		−	1.16647i
$780$	3.48149e14			0.0431763
$781$	−3.75221e15			−0.462068
$782$	−2.89963e15	+	1.02142e16i	−0.354573	+	1.24901i
$783$	−7.10461e15			−0.862682
$784$	3.55397e15			0.428524
$785$		−	1.17477e16i		−	1.40659i
$786$	−1.18842e15			−0.141301
$787$			1.32407e16i			1.56333i	0.623699	+	0.781665i	$0.285629\pi$
$787$			1.32407e16i			1.56333i	−0.623699	+	0.781665i	$0.714371\pi$
$788$		−	5.58880e14i		−	0.0655276i
$789$			9.21380e15i			1.07279i
$790$	−6.42011e15			−0.742324
$791$	−1.44441e16			−1.65852
$792$		−	3.75785e15i		−	0.428501i
$793$		−	5.36390e14i		−	0.0607404i
$794$		−	8.63484e15i		−	0.971050i
$795$	4.42435e15			0.494118
$796$			2.50097e15i			0.277388i
$797$	−1.31202e16			−1.44517			−0.722585	−	0.691282i	$-0.757046\pi$
$797$	−1.31202e16			−1.44517			−0.722585	+	0.691282i	$0.757046\pi$
$798$	−4.90694e15			−0.536778
$799$	4.85444e15	+	1.37809e15i	0.527390	+	0.149717i
$800$	1.50349e15			0.162220
$801$	−3.66901e15			−0.393161
$802$			7.77186e15i			0.827115i
$803$	−4.64371e15			−0.490829
$804$		−	1.11773e15i		−	0.117335i
$805$		−	1.01004e16i		−	1.05308i
$806$			6.13753e15i			0.635551i
$807$	−8.27459e15			−0.851025
$808$	−8.51396e15			−0.869699
$809$			3.28366e15i			0.333151i	0.986029	+	0.166575i	$0.0532709\pi$
$809$			3.28366e15i			0.333151i	−0.986029	+	0.166575i	$0.946729\pi$
$810$		−	4.62974e13i		−	0.00466540i
$811$		−	1.25997e16i		−	1.26109i	−0.776153	−	0.630544i	$-0.782832\pi$
$811$		−	1.25997e16i		−	1.26109i	0.776153	−	0.630544i	$-0.217168\pi$
$812$	−1.94743e15			−0.193600
$813$			9.97879e15i			0.985326i
$814$	1.14417e16			1.12217
$815$	−8.82237e15			−0.859445
$816$	2.02154e15	−	7.12104e15i	0.195608	−	0.689045i
$817$	−8.66702e14			−0.0833007
$818$	−9.37859e15			−0.895353
$819$			3.64440e15i			0.345593i
$820$	2.65542e15			0.250125
$821$			1.25891e16i			1.17789i	0.808172	+	0.588947i	$0.200457\pi$
$821$			1.25891e16i			1.17789i	−0.808172	+	0.588947i	$0.799543\pi$
$822$			8.08205e15i			0.751150i
$823$		−	2.04250e16i		−	1.88566i	−0.333279	−	0.942828i	$-0.608155\pi$
$823$		−	2.04250e16i		−	1.88566i	0.333279	−	0.942828i	$-0.391845\pi$
$824$	1.80351e15			0.165394
$825$	−2.29925e15			−0.209454
$826$		−	2.11230e15i		−	0.191146i
$827$			1.06581e16i			0.958075i	0.877794	+	0.479038i	$0.159014\pi$
$827$			1.06581e16i			0.958075i	−0.877794	+	0.479038i	$0.840986\pi$
$828$			1.57380e15i			0.140535i
$829$	1.70062e16			1.50854			0.754272	−	0.656562i	$-0.227990\pi$
$829$	1.70062e16			1.50854			0.754272	+	0.656562i	$0.227990\pi$
$830$		−	1.42685e16i		−	1.25732i
$831$	−6.12168e15			−0.535877
$832$	−4.08813e15			−0.355505
$833$	4.13105e15	+	1.17273e15i	0.356872	+	0.101310i
$834$	1.16570e16			1.00040
$835$	−1.31166e16			−1.11827
$836$			1.21142e15i			0.102603i
$837$	1.44523e16			1.21604
$838$		−	4.21954e15i		−	0.352714i
$839$			7.71216e15i			0.640450i	0.947341	+	0.320225i	$0.103759\pi$
$839$			7.71216e15i			0.640450i	−0.947341	+	0.320225i	$0.896241\pi$
$840$			5.87129e15i			0.484393i
$841$	3.15212e15			0.258360
$842$	−1.90473e16			−1.55102
$843$		−	9.32821e15i		−	0.754652i
$844$		−	1.67313e15i		−	0.134477i
$845$			7.29316e15i			0.582377i
$846$	4.64374e15			0.368410
$847$		−	5.60352e15i		−	0.441674i
$848$	1.55420e16			1.21711
$849$	7.00160e14			0.0544760
$850$	5.81548e15	+	1.65091e15i	0.449554	+	0.127620i
$851$	2.01661e16			1.54885
$852$	−9.13469e14			−0.0697069
$853$			1.92566e16i			1.46003i	0.683433	+	0.730013i	$0.260486\pi$
$853$			1.92566e16i			1.46003i	−0.683433	+	0.730013i	$0.739514\pi$
$854$	−2.14946e15			−0.161924
$855$			4.21142e15i			0.315221i
$856$			1.28095e16i			0.952632i
$857$		−	3.68907e15i		−	0.272598i	−0.990668	−	0.136299i	$-0.956479\pi$
$857$		−	3.68907e15i		−	0.272598i	0.990668	−	0.136299i	$-0.0435207\pi$
$858$	−3.48941e15			−0.256196
$859$	1.91408e16			1.39636			0.698181	−	0.715921i	$-0.253993\pi$
$859$	1.91408e16			1.39636			0.698181	+	0.715921i	$0.253993\pi$
$860$		−	2.46419e14i		−	0.0178621i
$861$		−	1.73642e16i		−	1.25065i
$862$		−	1.25136e16i		−	0.895554i
$863$	−1.09926e16			−0.781700			−0.390850	−	0.920454i	$-0.627819\pi$
$863$	−1.09926e16			−0.781700			−0.390850	+	0.920454i	$0.627819\pi$
$864$		−	5.37291e15i		−	0.379651i
$865$	1.93672e16			1.35981
$866$	−2.83475e16			−1.97773
$867$	4.69958e15	−	7.61026e15i	0.325802	−	0.527588i
$868$	3.96151e15			0.272899
$869$	1.03645e16			0.709478
$870$		−	6.48220e15i		−	0.440927i
$871$	−6.99211e15			−0.472616
$872$		−	1.66704e16i		−	1.11971i
$873$		−	1.95185e15i		−	0.130277i
$874$			1.32558e16i			0.879212i
$875$	−1.91859e16			−1.26456
$876$	−1.13050e15			−0.0740456
$877$		−	1.39005e16i		−	0.904758i	−0.891826	−	0.452379i	$-0.850576\pi$
$877$		−	1.39005e16i		−	0.904758i	0.891826	−	0.452379i	$-0.149424\pi$
$878$			2.45386e16i			1.58720i
$879$		−	8.14130e15i		−	0.523305i
$880$	1.07930e16			0.689427
$881$			3.85468e15i			0.244693i	0.992487	+	0.122346i	$0.0390418\pi$
$881$			3.85468e15i			0.244693i	−0.992487	+	0.122346i	$0.960958\pi$
$882$	3.95175e15			0.249294
$883$	4.81323e15			0.301754			0.150877	−	0.988553i	$-0.451790\pi$
$883$	4.81323e15			0.301754			0.150877	+	0.988553i	$0.451790\pi$
$884$	1.42158e15	+	4.03561e14i	0.0885692	+	0.0251432i
$885$	1.13249e15			0.0701206
$886$	−1.12431e16			−0.691832
$887$		−	6.36888e14i		−	0.0389478i	−0.999810	−	0.0194739i	$-0.993801\pi$
$887$		−	6.36888e14i		−	0.0389478i	0.999810	−	0.0194739i	$-0.00619913\pi$
$888$	−1.17224e16			−0.712436
$889$		−	2.67177e16i		−	1.61376i
$890$		−	8.78634e15i		−	0.527428i
$891$			7.47415e13i			0.00445897i
$892$	−1.02535e15			−0.0607945
$893$	6.30003e15			0.371244
$894$			9.06810e15i			0.531080i
$895$			2.48281e16i			1.44517i
$896$			2.40530e16i			1.39147i
$897$	−6.15011e15			−0.353610
$898$			1.73943e16i			0.993999i
$899$	1.84064e16			1.04542
$900$	8.96051e14			0.0505823
$901$	1.80657e16	+	5.12853e15i	1.01360	+	0.287744i
$902$	−2.66146e16			−1.48417
$903$	−1.61137e15			−0.0893125
$904$		−	2.26821e16i		−	1.24956i
$905$	8.15854e15			0.446730
$906$		−	1.08029e16i		−	0.587943i
$907$			1.48394e16i			0.802744i	0.915915	+	0.401372i	$0.131467\pi$
$907$			1.48394e16i			0.802744i	−0.915915	+	0.401372i	$0.868533\pi$
$908$			5.07471e14i			0.0272859i
$909$	−1.13540e16			−0.606805
$910$	−8.72742e15			−0.463616
$911$		−	4.59808e15i		−	0.242787i	−0.992604	−	0.121393i	$-0.961264\pi$
$911$		−	4.59808e15i		−	0.242787i	0.992604	−	0.121393i	$-0.0387363\pi$
$912$		−	9.24159e15i		−	0.485037i
$913$			2.30347e16i			1.20169i
$914$	2.18243e16			1.13171
$915$		−	1.15241e15i		−	0.0594006i
$916$	−3.36515e15			−0.172417
$917$	4.79852e15			0.244386
$918$	5.89976e15	−	2.07824e16i	0.298676	−	1.05211i
$919$	1.54342e16			0.776692			0.388346	−	0.921514i	$-0.373047\pi$
$919$	1.54342e16			0.776692			0.388346	+	0.921514i	$0.373047\pi$
$920$	1.58610e16			0.793408
$921$		−	2.99287e15i		−	0.148819i
$922$	−2.79994e16			−1.38398
$923$			5.71433e15i			0.280773i
$924$			2.25226e15i			0.110008i
$925$		−	1.14816e16i		−	0.557473i
$926$	−3.44231e16			−1.66146
$927$	2.40513e15			0.115398
$928$		−	6.84291e15i		−	0.326383i
$929$		−	2.47095e16i		−	1.17159i	−0.810458	−	0.585797i	$-0.800782\pi$
$929$		−	2.47095e16i		−	1.17159i	0.810458	−	0.585797i	$-0.199218\pi$
$930$			1.31862e16i			0.621532i
$931$	5.36122e15			0.251212
$932$		−	4.05643e15i		−	0.188954i
$933$	1.01530e16			0.470162
$934$	−9.39240e15			−0.432383
$935$	1.25456e16	+	3.56146e15i	0.574151	+	0.162991i
$936$	−5.72293e15			−0.260376
$937$	−1.83949e16			−0.832014			−0.416007	−	0.909361i	$-0.636571\pi$
$937$	−1.83949e16			−0.832014			−0.416007	+	0.909361i	$0.636571\pi$
$938$			2.80193e16i			1.25992i
$939$	1.16504e16			0.520809
$940$			1.79121e15i			0.0796054i
$941$		−	2.09349e16i		−	0.924968i	−0.886628	−	0.462484i	$-0.846958\pi$
$941$		−	2.09349e16i		−	0.924968i	0.886628	−	0.462484i	$-0.153042\pi$
$942$			2.86645e16i			1.25911i
$943$	−4.69083e16			−2.04850
$944$	3.97825e15			0.172721
$945$			2.05509e16i			0.887064i
$946$			2.46979e15i			0.105989i
$947$		−	1.35875e16i		−	0.579714i	−0.957070	−	0.289857i	$-0.906392\pi$
$947$		−	1.35875e16i		−	0.579714i	0.957070	−	0.289857i	$-0.0936077\pi$
$948$	2.52322e15			0.107031
$949$			7.07202e15i			0.298249i
$950$	7.54725e15			0.316453
$951$	−2.36819e16			−0.987241
$952$	−6.80576e15	+	2.39739e16i	−0.282081	+	0.993653i
$953$	1.63484e16			0.673697			0.336848	−	0.941559i	$-0.390639\pi$
$953$	1.63484e16			0.673697			0.336848	+	0.941559i	$0.390639\pi$
$954$	1.72815e16			0.708054
$955$		−	1.60814e15i		−	0.0655095i
$956$	−8.09138e14			−0.0327721
$957$			1.04647e16i			0.421417i
$958$		−	4.96699e16i		−	1.98876i
$959$		−	3.26332e16i		−	1.29915i
$960$	−8.78316e15			−0.347663
$961$	−1.20341e16			−0.473627
$962$		−	1.74249e16i		−	0.681878i
$963$			1.70824e16i			0.664669i
$964$		−	2.11248e15i		−	0.0817276i
$965$	−3.18161e16			−1.22390
$966$			2.46451e16i			0.942664i
$967$	−1.49779e16			−0.569648			−0.284824	−	0.958580i	$-0.591935\pi$
$967$	−1.49779e16			−0.569648			−0.284824	+	0.958580i	$0.591935\pi$
$968$	8.79939e15			0.332765
$969$	3.04952e15	−	1.07422e16i	0.114670	−	0.403936i
$970$	4.67419e15			0.174768
$971$	1.67078e16			0.621174			0.310587	−	0.950545i	$-0.399474\pi$
$971$	1.67078e16			0.621174			0.310587	+	0.950545i	$0.399474\pi$
$972$		−	5.18430e15i		−	0.191657i
$973$	−4.70680e16			−1.73024
$974$			2.39467e16i			0.875329i
$975$			3.50159e15i			0.127274i
$976$		−	4.04823e15i		−	0.146316i
$977$	−5.40503e15			−0.194258			−0.0971288	−	0.995272i	$-0.530966\pi$
$977$	−5.40503e15			−0.194258			−0.0971288	+	0.995272i	$0.530966\pi$
$978$	2.15268e16			0.769334
$979$			1.41845e16i			0.504091i
$980$			1.52429e15i			0.0538671i
$981$		−	2.22314e16i		−	0.781245i
$982$	1.59312e16			0.556717
$983$			4.43476e16i			1.54108i	0.637391	+	0.770541i	$0.280014\pi$
$983$			4.43476e16i			1.54108i	−0.637391	+	0.770541i	$0.719986\pi$
$984$	2.72675e16			0.942264
$985$	−7.51133e15			−0.258118
$986$	7.51390e15	−	2.64683e16i	0.256769	−	0.904490i
$987$	1.17130e16			0.398037
$988$	1.84490e15			0.0623462
$989$			4.35302e15i			0.146289i
$990$	1.20010e16			0.401074
$991$		−	1.21814e16i		−	0.404848i	−0.979298	−	0.202424i	$-0.935118\pi$
$991$		−	1.21814e16i		−	0.404848i	0.979298	−	0.202424i	$-0.0648819\pi$
$992$			1.39200e16i			0.460070i
$993$			3.15055e16i			1.03554i
$994$	2.28989e16			0.748495
$995$	3.36130e16			1.09265
$996$			5.60775e15i			0.181285i
$997$		−	1.32238e16i		−	0.425141i	−0.977146	−	0.212570i	$-0.931817\pi$
$997$		−	1.32238e16i		−	0.425141i	0.977146	−	0.212570i	$-0.0681834\pi$
$998$		−	5.68516e16i		−	1.81771i
$999$	−4.10312e16			−1.30468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.b.a.16.5	✓	16
3.2	odd	2		153.12.d.b.118.12		16
4.3	odd	2		272.12.b.c.33.11		16
17.16	even	2	inner	17.12.b.a.16.6	yes	16
51.50	odd	2		153.12.d.b.118.11		16
68.67	odd	2		272.12.b.c.33.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.b.a.16.5	✓	16	1.1	even	1	trivial
17.12.b.a.16.6	yes	16	17.16	even	2	inner
153.12.d.b.118.11		16	51.50	odd	2
153.12.d.b.118.12		16	3.2	odd	2
272.12.b.c.33.6		16	68.67	odd	2
272.12.b.c.33.11		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)

\(f(q)\)	\(=\)	\(q-49.4086 q^{2} -260.983i q^{3} +393.209 q^{4} -5284.72i q^{5} +12894.8i q^{6} -52066.0i q^{7} +81760.9 q^{8} +109035. q^{9} +O(q^{10})\)	\(q-49.4086 q^{2} -260.983i q^{3} +393.209 q^{4} -5284.72i q^{5} +12894.8i q^{6} -52066.0i q^{7} +81760.9 q^{8} +109035. q^{9} +261110. i q^{10} -421531. i q^{11} -102621. i q^{12} -641960. q^{13} +2.57251e6i q^{14} -1.37922e6 q^{15} -4.84498e6 q^{16} +(-5.63169e6 - 1.59874e6i) q^{17} -5.38725e6 q^{18} -7.30873e6 q^{19} -2.07800e6i q^{20} -1.35883e7 q^{21} +2.08272e7i q^{22} +3.67081e7i q^{23} -2.13382e7i q^{24} +2.08999e7 q^{25} +3.17183e7 q^{26} -7.46886e7i q^{27} -2.04728e7i q^{28} -9.51230e7i q^{29} +6.81454e7 q^{30} +1.93501e8i q^{31} +7.19375e7 q^{32} -1.10012e8 q^{33} +(2.78254e8 + 7.89914e7i) q^{34} -2.75154e8 q^{35} +4.28734e7 q^{36} -5.49363e8i q^{37} +3.61114e8 q^{38} +1.67541e8i q^{39} -4.32083e8i q^{40} +1.27787e9i q^{41} +6.71381e8 q^{42} +1.18585e8 q^{43} -1.65750e8i q^{44} -5.76218e8i q^{45} -1.81370e9i q^{46} -8.61987e8 q^{47} +1.26446e9i q^{48} -7.33537e8 q^{49} -1.03263e9 q^{50} +(-4.17244e8 + 1.46978e9i) q^{51} -2.52424e8 q^{52} -3.20786e9 q^{53} +3.69026e9i q^{54} -2.22767e9 q^{55} -4.25696e9i q^{56} +1.90746e9i q^{57} +4.69989e9i q^{58} -8.21106e8 q^{59} -5.42323e8 q^{60} +8.35550e8i q^{61} -9.56061e9i q^{62} -5.67700e9i q^{63} +6.36820e9 q^{64} +3.39257e9i q^{65} +5.43556e9 q^{66} +1.08918e10 q^{67} +(-2.21443e9 - 6.28638e8i) q^{68} +9.58021e9 q^{69} +1.35950e10 q^{70} -8.90138e9i q^{71} +8.91478e9 q^{72} -1.10163e10i q^{73} +2.71432e10i q^{74} -5.45453e9i q^{75} -2.87386e9 q^{76} -2.19474e10 q^{77} -8.27795e9i q^{78} +2.45877e10i q^{79} +2.56044e10i q^{80} -1.77310e8 q^{81} -6.31379e10i q^{82} -5.46453e10 q^{83} -5.34306e9 q^{84} +(-8.44888e9 + 2.97619e10i) q^{85} -5.85910e9 q^{86} -2.48255e10 q^{87} -3.44647e10i q^{88} -3.36499e10 q^{89} +2.84701e10i q^{90} +3.34242e10i q^{91} +1.44340e10i q^{92} +5.05005e10 q^{93} +4.25896e10 q^{94} +3.86245e10i q^{95} -1.87745e10i q^{96} -1.79012e10i q^{97} +3.62430e10 q^{98} -4.59615e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9}+O(q^{10}) \) 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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