LMFDB - Embedded newform 17.12.b.a.16.12

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			16.12
Root			$586.850i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.12.b.a.16.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+37.8318 q^{2} +586.850i q^{3} -616.752 q^{4} -6253.69i q^{5} +22201.6i q^{6} +63445.7i q^{7} -100812. q^{8} -167246. q^{9} +O(q^{10})$	\(q+37.8318 q^{2} +586.850i q^{3} -616.752 q^{4} -6253.69i q^{5} +22201.6i q^{6} +63445.7i q^{7} -100812. q^{8} -167246. q^{9} -236588. i q^{10} -518365. i q^{11} -361941. i q^{12} -2.42025e6 q^{13} +2.40027e6i q^{14} +3.66998e6 q^{15} -2.55081e6 q^{16} +(-5.85266e6 + 135284. i) q^{17} -6.32722e6 q^{18} +1.20388e7 q^{19} +3.85697e6i q^{20} -3.72331e7 q^{21} -1.96107e7i q^{22} +3.49098e7i q^{23} -5.91618e7i q^{24} +9.71954e6 q^{25} -9.15625e7 q^{26} +5.81044e6i q^{27} -3.91303e7i q^{28} +1.48455e8i q^{29} +1.38842e8 q^{30} +5.98873e7i q^{31} +1.09962e8 q^{32} +3.04202e8 q^{33} +(-2.21417e8 + 5.11806e6i) q^{34} +3.96770e8 q^{35} +1.03149e8 q^{36} -2.67093e8i q^{37} +4.55449e8 q^{38} -1.42032e9i q^{39} +6.30450e8i q^{40} +7.79343e8i q^{41} -1.40860e9 q^{42} +4.04994e8 q^{43} +3.19702e8i q^{44} +1.04590e9i q^{45} +1.32070e9i q^{46} -2.03388e9 q^{47} -1.49694e9i q^{48} -2.04803e9 q^{49} +3.67708e8 q^{50} +(-7.93916e7 - 3.43463e9i) q^{51} +1.49269e9 q^{52} +1.66456e8 q^{53} +2.19820e8i q^{54} -3.24169e9 q^{55} -6.39612e9i q^{56} +7.06496e9i q^{57} +5.61633e9i q^{58} +4.86847e9 q^{59} -2.26346e9 q^{60} -3.94216e9i q^{61} +2.26565e9i q^{62} -1.06110e10i q^{63} +9.38413e9 q^{64} +1.51355e10i q^{65} +1.15085e10 q^{66} -1.51527e10 q^{67} +(3.60964e9 - 8.34369e7i) q^{68} -2.04868e10 q^{69} +1.50105e10 q^{70} +5.71704e9i q^{71} +1.68605e10 q^{72} -1.52855e10i q^{73} -1.01046e10i q^{74} +5.70391e9i q^{75} -7.42494e9 q^{76} +3.28880e10 q^{77} -5.37335e10i q^{78} +2.11716e10i q^{79} +1.59520e10i q^{80} -3.30370e10 q^{81} +2.94840e10i q^{82} +9.52083e9 q^{83} +2.29636e10 q^{84} +(8.46026e8 + 3.66007e10i) q^{85} +1.53217e10 q^{86} -8.71208e10 q^{87} +5.22576e10i q^{88} -2.35158e10 q^{89} +3.95685e10i q^{90} -1.53554e11i q^{91} -2.15307e10i q^{92} -3.51449e10 q^{93} -7.69453e10 q^{94} -7.52868e10i q^{95} +6.45312e10i q^{96} -3.53305e10i q^{97} -7.74808e10 q^{98} +8.66944e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	37.8318			0.835973			0.417987	−	0.908453i	$-0.362736\pi$
$2$	37.8318			0.835973			0.417987	+	0.908453i	$0.362736\pi$
$3$			586.850i			1.39431i	0.716919	+	0.697156i	$0.245552\pi$
$3$			586.850i			1.39431i	−0.716919	+	0.697156i	$0.754448\pi$
$4$	−616.752			−0.301148
$5$		−	6253.69i		−	0.894955i	−0.894295	−	0.447477i	$-0.852323\pi$
$5$		−	6253.69i		−	0.894955i	0.894295	−	0.447477i	$-0.147677\pi$
$6$			22201.6i			1.16561i
$7$			63445.7i			1.42680i	0.700757	+	0.713400i	$0.252846\pi$
$7$			63445.7i			1.42680i	−0.700757	+	0.713400i	$0.747154\pi$
$8$	−100812.			−1.08773
$9$	−167246.			−0.944108
$10$		−	236588.i		−	0.748158i
$11$		−	518365.i		−	0.970455i	−0.874388	−	0.485228i	$-0.838737\pi$
$11$		−	518365.i		−	0.970455i	0.874388	−	0.485228i	$-0.161263\pi$
$12$		−	361941.i		−	0.419895i
$13$	−2.42025e6			−1.80789			−0.903945	−	0.427650i	$-0.859342\pi$
$13$	−2.42025e6			−1.80789			−0.903945	+	0.427650i	$0.859342\pi$
$14$			2.40027e6i			1.19277i
$15$	3.66998e6			1.24785
$16$	−2.55081e6			−0.608161
$17$	−5.85266e6	+	135284.i	−0.999733	+	0.0231089i
$17$	−5.85266e6	+	135284.i	−0.999733	+	0.0231089i
$18$	−6.32722e6			−0.789249
$19$	1.20388e7			1.11542			0.557709	−	0.830036i	$-0.311680\pi$
$19$	1.20388e7			1.11542			0.557709	+	0.830036i	$0.311680\pi$
$20$			3.85697e6i			0.269514i
$21$	−3.72331e7			−1.98941
$22$		−	1.96107e7i		−	0.811275i
$23$			3.49098e7i			1.13095i	0.824765	+	0.565476i	$0.191307\pi$
$23$			3.49098e7i			1.13095i	−0.824765	+	0.565476i	$0.808693\pi$
$24$		−	5.91618e7i		−	1.51663i
$25$	9.71954e6			0.199056
$26$	−9.15625e7			−1.51135
$27$			5.81044e6i			0.0779307i
$28$		−	3.91303e7i		−	0.429678i
$29$			1.48455e8i			1.34402i	0.740542	+	0.672010i	$0.234569\pi$
$29$			1.48455e8i			1.34402i	−0.740542	+	0.672010i	$0.765431\pi$
$30$	1.38842e8			1.04317
$31$			5.98873e7i			0.375704i	0.982197	+	0.187852i	$0.0601525\pi$
$31$			5.98873e7i			0.375704i	−0.982197	+	0.187852i	$0.939847\pi$
$32$	1.09962e8			0.579319
$33$	3.04202e8			1.35312
$34$	−2.21417e8	+	5.11806e6i	−0.835750	+	0.0193184i
$35$	3.96770e8			1.27692
$36$	1.03149e8			0.284317
$37$		−	2.67093e8i		−	0.633217i	−0.948556	−	0.316609i	$-0.897456\pi$
$37$		−	2.67093e8i		−	0.633217i	0.948556	−	0.316609i	$-0.102544\pi$
$38$	4.55449e8			0.932460
$39$		−	1.42032e9i		−	2.52076i
$40$			6.30450e8i			0.973465i
$41$			7.79343e8i			1.05055i	0.850932	+	0.525276i	$0.176038\pi$
$41$			7.79343e8i			1.05055i	−0.850932	+	0.525276i	$0.823962\pi$
$42$	−1.40860e9			−1.66309
$43$	4.04994e8			0.420118			0.210059	−	0.977689i	$-0.432634\pi$
$43$	4.04994e8			0.420118			0.210059	+	0.977689i	$0.432634\pi$
$44$			3.19702e8i			0.292251i
$45$			1.04590e9i			0.844934i
$46$			1.32070e9i			0.945445i
$47$	−2.03388e9			−1.29356			−0.646779	−	0.762677i	$-0.723885\pi$
$47$	−2.03388e9			−1.29356			−0.646779	+	0.762677i	$0.723885\pi$
$48$		−	1.49694e9i		−	0.847967i
$49$	−2.04803e9			−1.03576
$50$	3.67708e8			0.166406
$51$	−7.93916e7	−	3.43463e9i	−0.0322210	−	1.39394i
$52$	1.49269e9			0.544443
$53$	1.66456e8			0.0546740			0.0273370	−	0.999626i	$-0.491297\pi$
$53$	1.66456e8			0.0546740			0.0273370	+	0.999626i	$0.491297\pi$
$54$			2.19820e8i			0.0651480i
$55$	−3.24169e9			−0.868513
$56$		−	6.39612e9i		−	1.55197i
$57$			7.06496e9i			1.55524i
$58$			5.61633e9i			1.12357i
$59$	4.86847e9			0.886557			0.443278	−	0.896384i	$-0.353815\pi$
$59$	4.86847e9			0.886557			0.443278	+	0.896384i	$0.353815\pi$
$60$	−2.26346e9			−0.375787
$61$		−	3.94216e9i		−	0.597613i	−0.954314	−	0.298807i	$-0.903411\pi$
$61$		−	3.94216e9i		−	0.597613i	0.954314	−	0.298807i	$-0.0965886\pi$
$62$			2.26565e9i			0.314078i
$63$		−	1.06110e10i		−	1.34705i
$64$	9.38413e9			1.09246
$65$			1.51355e10i			1.61798i
$66$	1.15085e10			1.13117
$67$	−1.51527e10			−1.37113			−0.685566	−	0.728011i	$-0.740445\pi$
$67$	−1.51527e10			−1.37113			−0.685566	+	0.728011i	$0.740445\pi$
$68$	3.60964e9	−	8.34369e7i	0.301068	−	0.00695920i
$69$	−2.04868e10			−1.57690
$70$	1.50105e10			1.06747
$71$			5.71704e9i			0.376054i	0.982164	+	0.188027i	$0.0602092\pi$
$71$			5.71704e9i			0.376054i	−0.982164	+	0.188027i	$0.939791\pi$
$72$	1.68605e10			1.02693
$73$		−	1.52855e10i		−	0.862987i	−0.902116	−	0.431493i	$-0.857987\pi$
$73$		−	1.52855e10i		−	0.862987i	0.902116	−	0.431493i	$-0.142013\pi$
$74$		−	1.01046e10i		−	0.529353i
$75$			5.70391e9i			0.277546i
$76$	−7.42494e9			−0.335907
$77$	3.28880e10			1.38465
$78$		−	5.37335e10i		−	2.10729i
$79$			2.11716e10i			0.774114i	0.922056	+	0.387057i	$0.126508\pi$
$79$			2.11716e10i			0.774114i	−0.922056	+	0.387057i	$0.873492\pi$
$80$			1.59520e10i			0.544277i
$81$	−3.30370e10			−1.05277
$82$			2.94840e10i			0.878233i
$83$	9.52083e9			0.265305			0.132652	−	0.991163i	$-0.457651\pi$
$83$	9.52083e9			0.265305			0.132652	+	0.991163i	$0.457651\pi$
$84$	2.29636e10			0.599106
$85$	8.46026e8	+	3.66007e10i	0.0206814	+	0.894716i
$86$	1.53217e10			0.351208
$87$	−8.71208e10			−1.87398
$88$			5.22576e10i			1.05559i
$89$	−2.35158e10			−0.446390			−0.223195	−	0.974774i	$-0.571649\pi$
$89$	−2.35158e10			−0.446390			−0.223195	+	0.974774i	$0.571649\pi$
$90$			3.95685e10i			0.706342i
$91$		−	1.53554e11i		−	2.57950i
$92$		−	2.15307e10i		−	0.340584i
$93$	−3.51449e10			−0.523849
$94$	−7.69453e10			−1.08138
$95$		−	7.52868e10i		−	0.998249i
$96$			6.45312e10i			0.807752i
$97$		−	3.53305e10i		−	0.417739i	−0.977943	−	0.208870i	$-0.933022\pi$
$97$		−	3.53305e10i		−	0.417739i	0.977943	−	0.208870i	$-0.0669785\pi$
$98$	−7.74808e10			−0.865866
$99$			8.66944e10i			0.916215i
$100$	−5.99454e9			−0.0599454
$101$	−1.27916e10			−0.121104			−0.0605518	−	0.998165i	$-0.519286\pi$
$101$	−1.27916e10			−0.121104			−0.0605518	+	0.998165i	$0.519286\pi$
$102$	−3.00353e9	−	1.29938e11i	−0.0269359	−	1.16530i
$103$	1.43362e11			1.21851			0.609254	−	0.792975i	$-0.291469\pi$
$103$	1.43362e11			1.21851			0.609254	+	0.792975i	$0.291469\pi$
$104$	2.43991e11			1.96649
$105$			2.32844e11i			1.78043i
$106$	6.29732e9			0.0457060
$107$		−	5.03321e9i		−	0.0346924i	−0.999850	−	0.0173462i	$-0.994478\pi$
$107$		−	5.03321e9i		−	0.0346924i	0.999850	−	0.0173462i	$-0.00552174\pi$
$108$		−	3.58360e9i		−	0.0234687i
$109$		−	1.38902e11i		−	0.864692i	−0.901708	−	0.432346i	$-0.857686\pi$
$109$		−	1.38902e11i		−	0.864692i	0.901708	−	0.432346i	$-0.142314\pi$
$110$	−1.22639e11			−0.726054
$111$	1.56743e11			0.882903
$112$		−	1.61838e11i		−	0.867724i
$113$			3.72392e11i			1.90138i	0.310139	+	0.950691i	$0.399624\pi$
$113$			3.72392e11i			1.90138i	−0.310139	+	0.950691i	$0.600376\pi$
$114$			2.67281e11i			1.30014i
$115$	2.18315e11			1.01215
$116$		−	9.15599e10i		−	0.404750i
$117$	4.04777e11			1.70684
$118$	1.84183e11			0.741138
$119$	−8.58321e9	−	3.71326e11i	−0.0329717	−	1.42642i
$120$	−3.69979e11			−1.35731
$121$	1.66099e10			0.0582167
$122$		−	1.49139e11i		−	0.499589i
$123$	−4.57357e11			−1.46480
$124$		−	3.69356e10i		−	0.113143i
$125$		−	3.66139e11i		−	1.07310i
$126$		−	4.01435e11i		−	1.12610i
$127$	−4.67289e11			−1.25506			−0.627531	−	0.778592i	$-0.715934\pi$
$127$	−4.67289e11			−1.25506			−0.627531	+	0.778592i	$0.715934\pi$
$128$	1.29817e11			0.333946
$129$			2.37670e11i			0.585776i
$130$			5.72603e11i			1.35259i
$131$			3.48665e11i			0.789617i	0.918763	+	0.394809i	$0.129189\pi$
$131$			3.48665e11i			0.789617i	−0.918763	+	0.394809i	$0.870811\pi$
$132$	−1.87617e11			−0.407489
$133$			7.63809e11i			1.59148i
$134$	−5.73255e11			−1.14623
$135$	3.63367e10			0.0697444
$136$	5.90021e11	−	1.36384e10i	1.08744	−	0.0251361i
$137$	−1.84310e11			−0.326277			−0.163139	−	0.986603i	$-0.552162\pi$
$137$	−1.84310e11			−0.326277			−0.163139	+	0.986603i	$0.552162\pi$
$138$	−7.75053e11			−1.31825
$139$		−	5.74130e11i		−	0.938489i	−0.883068	−	0.469244i	$-0.844526\pi$
$139$		−	5.74130e11i		−	0.938489i	0.883068	−	0.469244i	$-0.155474\pi$
$140$	−2.44708e11			−0.384543
$141$		−	1.19358e12i		−	1.80363i
$142$			2.16286e11i			0.314371i
$143$			1.25457e12i			1.75448i
$144$	4.26613e11			0.574170
$145$	9.28391e11			1.20284
$146$		−	5.78279e11i		−	0.721434i
$147$		−	1.20189e12i		−	1.44417i
$148$			1.64730e11i			0.190692i
$149$	−9.75826e11			−1.08855			−0.544274	−	0.838907i	$-0.683195\pi$
$149$	−9.75826e11			−1.08855			−0.544274	+	0.838907i	$0.683195\pi$
$150$			2.15789e11i			0.232021i
$151$	1.36374e12			1.41371			0.706853	−	0.707361i	$-0.250114\pi$
$151$	1.36374e12			1.41371			0.706853	+	0.707361i	$0.250114\pi$
$152$	−1.21366e12			−1.21327
$153$	9.78833e11	−	2.26258e10i	0.943856	−	0.0218173i
$154$	1.24421e12			1.15753
$155$	3.74517e11			0.336238
$156$			8.75987e11i			0.759124i
$157$	2.08101e11			0.174111			0.0870556	−	0.996203i	$-0.472254\pi$
$157$	2.08101e11			0.174111			0.0870556	+	0.996203i	$0.472254\pi$
$158$			8.00961e11i			0.647138i
$159$			9.76844e10i			0.0762327i
$160$		−	6.87668e11i		−	0.518464i
$161$	−2.21488e12			−1.61364
$162$	−1.24985e12			−0.880086
$163$			9.60179e11i			0.653612i	0.945091	+	0.326806i	$0.105972\pi$
$163$			9.60179e11i			0.653612i	−0.945091	+	0.326806i	$0.894028\pi$
$164$		−	4.80661e11i		−	0.316372i
$165$		−	1.90239e12i		−	1.21098i
$166$	3.60190e11			0.221788
$167$			1.33045e11i			0.0792608i	0.999214	+	0.0396304i	$0.0126180\pi$
$167$			1.33045e11i			0.0792608i	−0.999214	+	0.0396304i	$0.987382\pi$
$168$	3.75356e12			2.16393
$169$	4.06545e12			2.26846
$170$	3.20067e10	+	1.38467e12i	0.0172891	+	0.747959i
$171$	−2.01344e12			−1.05308
$172$	−2.49781e11			−0.126518
$173$			7.80003e11i			0.382686i	0.981523	+	0.191343i	$0.0612843\pi$
$173$			7.80003e11i			0.382686i	−0.981523	+	0.191343i	$0.938716\pi$
$174$	−3.29594e12			−1.56660
$175$			6.16663e11i			0.284013i
$176$			1.32225e12i			0.590193i
$177$			2.85706e12i			1.23614i
$178$	−8.89646e11			−0.373170
$179$	1.37405e12			0.558871			0.279435	−	0.960164i	$-0.409853\pi$
$179$	1.37405e12			0.558871			0.279435	+	0.960164i	$0.409853\pi$
$180$		−	6.45063e11i		−	0.254451i
$181$		−	3.51654e12i		−	1.34550i	−0.739871	−	0.672749i	$-0.765113\pi$
$181$		−	3.51654e12i		−	1.34550i	0.739871	−	0.672749i	$-0.234887\pi$
$182$		−	5.80925e12i		−	2.15639i
$183$	2.31346e12			0.833260
$184$		−	3.51934e12i		−	1.23016i
$185$	−1.67031e12			−0.566701
$186$	−1.32960e12			−0.437924
$187$	7.01266e10	+	3.03381e12i	0.0224261	+	0.970196i
$188$	1.25440e12			0.389553
$189$	−3.68648e11			−0.111191
$190$		−	2.84824e12i		−	0.834510i
$191$	−2.34224e12			−0.666727			−0.333364	−	0.942798i	$-0.608184\pi$
$191$	−2.34224e12			−0.666727			−0.333364	+	0.942798i	$0.608184\pi$
$192$			5.50708e12i			1.52323i
$193$			1.99726e12i			0.536871i	0.963298	+	0.268435i	$0.0865066\pi$
$193$			1.99726e12i			0.536871i	−0.963298	+	0.268435i	$0.913493\pi$
$194$		−	1.33662e12i		−	0.349219i
$195$	−8.88226e12			−2.25597
$196$	1.26313e12			0.311917
$197$			3.41732e12i			0.820581i	0.911955	+	0.410291i	$0.134573\pi$
$197$			3.41732e12i			0.820581i	−0.911955	+	0.410291i	$0.865427\pi$
$198$			3.27981e12i			0.765931i
$199$			8.66197e12i			1.96754i	0.179421	+	0.983772i	$0.442578\pi$
$199$			8.66197e12i			1.96754i	−0.179421	+	0.983772i	$0.557422\pi$
$200$	−9.79850e11			−0.216518
$201$		−	8.89237e12i		−	1.91179i
$202$	−4.83929e11			−0.101239
$203$	−9.41883e12			−1.91765
$204$	4.89649e10	+	2.11832e12i	0.00970330	+	0.419783i
$205$	4.87377e12			0.940196
$206$	5.42364e12			1.01864
$207$		−	5.83852e12i		−	1.06774i
$208$	6.17361e12			1.09949
$209$		−	6.24048e12i		−	1.08246i
$210$			8.80893e12i			1.48839i
$211$		−	7.37015e12i		−	1.21317i	−0.795018	−	0.606586i	$-0.792538\pi$
$211$		−	7.37015e12i		−	1.21317i	0.795018	−	0.606586i	$-0.207462\pi$
$212$	−1.02662e11			−0.0164650
$213$	−3.35504e12			−0.524337
$214$		−	1.90416e11i		−	0.0290019i
$215$		−	2.53270e12i		−	0.375987i
$216$		−	5.85765e11i		−	0.0847672i
$217$	−3.79959e12			−0.536054
$218$		−	5.25490e12i		−	0.722859i
$219$	8.97030e12			1.20327
$220$	1.99932e12			0.261551
$221$	1.41649e13	−	3.27422e11i	1.80741	−	0.0417783i
$222$	5.92989e12			0.738083
$223$	−4.27826e12			−0.519506			−0.259753	−	0.965675i	$-0.583641\pi$
$223$	−4.27826e12			−0.519506			−0.259753	+	0.965675i	$0.583641\pi$
$224$			6.97662e12i			0.826572i
$225$	−1.62555e12			−0.187930
$226$			1.40883e13i			1.58951i
$227$		−	7.02870e12i		−	0.773985i	−0.922083	−	0.386993i	$-0.873514\pi$
$227$		−	7.02870e12i		−	0.773985i	0.922083	−	0.386993i	$-0.126486\pi$
$228$		−	4.35733e12i		−	0.468359i
$229$	3.80746e12			0.399521			0.199761	−	0.979845i	$-0.435984\pi$
$229$	3.80746e12			0.399521			0.199761	+	0.979845i	$0.435984\pi$
$230$	8.25925e12			0.846131
$231$			1.93003e13i			1.93063i
$232$		−	1.49661e13i		−	1.46193i
$233$			1.20418e13i			1.14877i	0.818584	+	0.574387i	$0.194760\pi$
$233$			1.20418e13i			1.14877i	−0.818584	+	0.574387i	$0.805240\pi$
$234$	1.53135e13			1.42688
$235$			1.27192e13i			1.15768i
$236$	−3.00264e12			−0.266985
$237$	−1.24246e13			−1.07936
$238$	−3.24719e11	−	1.40479e13i	−0.0275635	−	1.19245i
$239$	−5.97941e12			−0.495986			−0.247993	−	0.968762i	$-0.579771\pi$
$239$	−5.97941e12			−0.495986			−0.247993	+	0.968762i	$0.579771\pi$
$240$	−9.36142e12			−0.758892
$241$		−	1.03726e13i		−	0.821854i	−0.911668	−	0.410927i	$-0.865205\pi$
$241$		−	1.03726e13i		−	0.821854i	0.911668	−	0.410927i	$-0.134795\pi$
$242$	6.28383e11			0.0486676
$243$		−	1.83584e13i		−	1.38996i
$244$			2.43134e12i			0.179970i
$245$			1.28077e13i			0.926956i
$246$	−1.73027e13			−1.22453
$247$	−2.91369e13			−2.01655
$248$		−	6.03739e12i		−	0.408663i
$249$			5.58730e12i			0.369918i
$250$		−	1.38517e13i		−	0.897084i
$251$	2.17735e13			1.37950			0.689750	−	0.724047i	$-0.257720\pi$
$251$	2.17735e13			1.37950			0.689750	+	0.724047i	$0.257720\pi$
$252$			6.54438e12i			0.405663i
$253$	1.80960e13			1.09754
$254$	−1.76784e13			−1.04920
$255$	−2.14791e13	+	4.96490e11i	−1.24751	+	0.0288363i
$256$	−1.43075e13			−0.813287
$257$	−9.86332e12			−0.548771			−0.274385	−	0.961620i	$-0.588474\pi$
$257$	−9.86332e12			−0.548771			−0.274385	+	0.961620i	$0.588474\pi$
$258$			8.99151e12i			0.489694i
$259$	1.69459e13			0.903474
$260$		−	9.33484e12i		−	0.487252i
$261$		−	2.48285e13i		−	1.26890i
$262$			1.31907e13i			0.660099i
$263$	1.50798e13			0.738991			0.369496	−	0.929232i	$-0.379530\pi$
$263$	1.50798e13			0.738991			0.369496	+	0.929232i	$0.379530\pi$
$264$	−3.06674e13			−1.47182
$265$		−	1.04096e12i		−	0.0489308i
$266$			2.88963e13i			1.33043i
$267$		−	1.38002e13i		−	0.622408i
$268$	9.34547e12			0.412914
$269$			2.51532e13i			1.08882i	0.838820	+	0.544409i	$0.183246\pi$
$269$			2.51532e13i			1.08882i	−0.838820	+	0.544409i	$0.816754\pi$
$270$	1.37468e12			0.0583045
$271$	−2.43577e13			−1.01229			−0.506146	−	0.862448i	$-0.668930\pi$
$271$	−2.43577e13			−1.01229			−0.506146	+	0.862448i	$0.668930\pi$
$272$	1.49290e13	−	3.45085e11i	0.607999	−	0.0140539i
$273$	9.01135e13			3.59662
$274$	−6.97280e12			−0.272759
$275$		−	5.03826e12i		−	0.193175i
$276$	1.26353e13			0.474881
$277$			3.41464e13i			1.25807i	0.777376	+	0.629037i	$0.216551\pi$
$277$			3.41464e13i			1.25807i	−0.777376	+	0.629037i	$0.783449\pi$
$278$		−	2.17204e13i		−	0.784552i
$279$		−	1.00159e13i		−	0.354705i
$280$	−3.99993e13			−1.38894
$281$	4.45935e12			0.151840			0.0759202	−	0.997114i	$-0.475811\pi$
$281$	4.45935e12			0.151840			0.0759202	+	0.997114i	$0.475811\pi$
$282$		−	4.51553e13i		−	1.50778i
$283$			1.41412e13i			0.463085i	0.972825	+	0.231543i	$0.0743773\pi$
$283$			1.41412e13i			0.463085i	−0.972825	+	0.231543i	$0.925623\pi$
$284$		−	3.52599e12i		−	0.113248i
$285$	4.41821e13			1.39187
$286$			4.74628e13i			1.46669i
$287$	−4.94460e13			−1.49893
$288$	−1.83907e13			−0.546940
$289$	3.42353e13	−	1.58355e12i	0.998932	−	0.0462054i
$290$	3.51227e13			1.00554
$291$	2.07337e13			0.582460
$292$			9.42736e12i			0.259887i
$293$	−9.78501e12			−0.264722			−0.132361	−	0.991202i	$-0.542256\pi$
$293$	−9.78501e12			−0.264722			−0.132361	+	0.991202i	$0.542256\pi$
$294$		−	4.54696e13i		−	1.20729i
$295$		−	3.04459e13i		−	0.793428i
$296$			2.69263e13i			0.688766i
$297$	3.01193e12			0.0756282
$298$	−3.69173e13			−0.909998
$299$		−	8.44904e13i		−	2.04463i
$300$		−	3.51790e12i		−	0.0835827i
$301$			2.56951e13i			0.599425i
$302$	5.15929e13			1.18182
$303$		−	7.50674e12i		−	0.168856i
$304$	−3.07087e13			−0.678354
$305$	−2.46530e13			−0.534837
$306$	3.70311e13	−	8.55974e11i	0.789039	−	0.0182387i
$307$	−1.32352e13			−0.276994			−0.138497	−	0.990363i	$-0.544227\pi$
$307$	−1.32352e13			−0.276994			−0.138497	+	0.990363i	$0.544227\pi$
$308$	−2.02837e13			−0.416984
$309$			8.41319e13i			1.69898i
$310$	1.41687e13			0.281086
$311$		−	3.19053e12i		−	0.0621844i	−0.999517	−	0.0310922i	$-0.990101\pi$
$311$		−	3.19053e12i		−	0.0621844i	0.999517	−	0.0310922i	$-0.00989855\pi$
$312$			1.43186e14i			2.74190i
$313$		−	6.23501e13i		−	1.17312i	−0.809905	−	0.586561i	$-0.800481\pi$
$313$		−	6.23501e13i		−	1.17312i	0.809905	−	0.586561i	$-0.199519\pi$
$314$	7.87285e12			0.145552
$315$	−6.63581e13			−1.20555
$316$		−	1.30576e13i		−	0.233123i
$317$			7.63440e13i			1.33952i	0.742578	+	0.669760i	$0.233603\pi$
$317$			7.63440e13i			1.33952i	−0.742578	+	0.669760i	$0.766397\pi$
$318$			3.69558e12i			0.0637285i
$319$	7.69538e13			1.30431
$320$		−	5.86854e13i		−	0.977699i
$321$	2.95374e12			0.0483720
$322$	−8.37928e13			−1.34896
$323$	−7.04589e13	+	1.62866e12i	−1.11512	+	0.0257761i
$324$	2.03756e13			0.317039
$325$	−2.35237e13			−0.359871
$326$			3.63253e13i			0.546402i
$327$	8.15144e13			1.20565
$328$		−	7.85675e13i		−	1.14271i
$329$		−	1.29041e14i		−	1.84565i
$330$		−	7.19707e13i		−	1.01235i
$331$	−1.01593e14			−1.40544			−0.702719	−	0.711467i	$-0.748031\pi$
$331$	−1.01593e14			−1.40544			−0.702719	+	0.711467i	$0.748031\pi$
$332$	−5.87199e12			−0.0798961
$333$			4.46702e13i			0.597825i
$334$			5.03334e12i			0.0662599i
$335$			9.47603e13i			1.22710i
$336$	9.49747e13			1.20988
$337$		−	1.46643e14i		−	1.83779i	−0.394500	−	0.918896i	$-0.629082\pi$
$337$		−	1.46643e14i		−	1.83779i	0.394500	−	0.918896i	$-0.370918\pi$
$338$	1.53803e14			1.89638
$339$	−2.18539e14			−2.65112
$340$	−5.21788e11	−	2.25735e13i	−0.00622817	−	0.269442i
$341$	3.10435e13			0.364604
$342$	−7.61721e13			−0.880344
$343$		−	4.48591e12i		−	0.0510191i
$344$	−4.08284e13			−0.456973
$345$			1.28118e14i			1.41125i
$346$			2.95089e13i			0.319915i
$347$			1.13622e14i			1.21241i	0.795308	+	0.606205i	$0.207309\pi$
$347$			1.13622e14i			1.21241i	−0.795308	+	0.606205i	$0.792691\pi$
$348$	5.37319e13			0.564347
$349$	−1.56940e14			−1.62253			−0.811266	−	0.584678i	$-0.801221\pi$
$349$	−1.56940e14			−1.62253			−0.811266	+	0.584678i	$0.801221\pi$
$350$			2.33295e13i			0.237428i
$351$		−	1.40627e13i		−	0.140890i
$352$		−	5.70004e13i		−	0.562203i
$353$	7.63247e13			0.741147			0.370573	−	0.928803i	$-0.379161\pi$
$353$	7.63247e13			0.741147			0.370573	+	0.928803i	$0.379161\pi$
$354$			1.08088e14i			1.03338i
$355$	3.57526e13			0.336551
$356$	1.45034e13			0.134430
$357$	2.17913e14	−	5.03706e12i	1.98887	−	0.0459729i
$358$	5.19829e13			0.467201
$359$	−9.49543e13			−0.840417			−0.420209	−	0.907428i	$-0.638043\pi$
$359$	−9.49543e13			−0.840417			−0.420209	+	0.907428i	$0.638043\pi$
$360$		−	1.05440e14i		−	0.919056i
$361$	2.84421e13			0.244159
$362$		−	1.33037e14i		−	1.12480i
$363$			9.74752e12i			0.0811723i
$364$			9.47050e13i			0.776811i
$365$	−9.55907e13			−0.772334
$366$	8.75224e13			0.696583
$367$			2.41964e14i			1.89709i	0.316642	+	0.948545i	$0.397445\pi$
$367$			2.41964e14i			1.89709i	−0.316642	+	0.948545i	$0.602555\pi$
$368$		−	8.90483e13i		−	0.687801i
$369$		−	1.30342e14i		−	0.991834i
$370$	−6.31911e13			−0.473747
$371$			1.05609e13i			0.0780089i
$372$	2.16757e13			0.157756
$373$	1.92022e14			1.37706			0.688528	−	0.725210i	$-0.258257\pi$
$373$	1.92022e14			1.37706			0.688528	+	0.725210i	$0.258257\pi$
$374$	2.65302e12	+	1.14775e14i	0.0187476	+	0.811058i
$375$	2.14868e14			1.49624
$376$	2.05040e14			1.40704
$377$		−	3.59298e14i		−	2.42984i
$378$	−1.39466e13			−0.0929531
$379$			2.95711e14i			1.94246i	0.238143	+	0.971230i	$0.423461\pi$
$379$			2.95711e14i			1.94246i	−0.238143	+	0.971230i	$0.576539\pi$
$380$			4.64333e13i			0.300621i
$381$		−	2.74228e14i		−	1.74995i
$382$	−8.86113e13			−0.557366
$383$	−1.08616e14			−0.673440			−0.336720	−	0.941605i	$-0.609318\pi$
$383$	−1.08616e14			−0.673440			−0.336720	+	0.941605i	$0.609318\pi$
$384$			7.61830e13i			0.465625i
$385$		−	2.05671e14i		−	1.23919i
$386$			7.55601e13i			0.448810i
$387$	−6.77335e13			−0.396637
$388$			2.17902e13i			0.125802i
$389$	2.12787e14			1.21122			0.605610	−	0.795762i	$-0.292929\pi$
$389$	2.12787e14			1.21122			0.605610	+	0.795762i	$0.292929\pi$
$390$	−3.36032e14			−1.88593
$391$	−4.72275e12	−	2.04315e14i	−0.0261350	−	1.13065i
$392$	2.06467e14			1.12662
$393$	−2.04614e14			−1.10097
$394$			1.29284e14i			0.685984i
$395$	1.32401e14			0.692797
$396$		−	5.34689e13i		−	0.275917i
$397$			2.47588e14i			1.26003i	0.776582	+	0.630016i	$0.216952\pi$
$397$			2.47588e14i			1.26003i	−0.776582	+	0.630016i	$0.783048\pi$
$398$			3.27698e14i			1.64482i
$399$	−4.48242e14			−2.21902
$400$	−2.47927e13			−0.121058
$401$			1.25462e14i			0.604251i	0.953268	+	0.302125i	$0.0976961\pi$
$401$			1.25462e14i			0.604251i	−0.953268	+	0.302125i	$0.902304\pi$
$402$		−	3.36415e14i		−	1.59820i
$403$		−	1.44942e14i		−	0.679231i
$404$	7.88923e12			0.0364701
$405$			2.06603e14i			0.942180i
$406$	−3.56332e14			−1.60310
$407$	−1.38451e14			−0.614509
$408$	8.00367e12	+	3.46254e14i	0.0350476	+	1.51622i
$409$	−3.86683e14			−1.67062			−0.835309	−	0.549781i	$-0.814711\pi$
$409$	−3.86683e14			−1.67062			−0.835309	+	0.549781i	$0.814711\pi$
$410$	1.84384e14			0.785979
$411$		−	1.08163e14i		−	0.454932i
$412$	−8.84186e13			−0.366952
$413$			3.08884e14i			1.26494i
$414$		−	2.20882e14i		−	0.892603i
$415$		−	5.95403e13i		−	0.237436i
$416$	−2.66135e14			−1.04734
$417$	3.36928e14			1.30855
$418$		−	2.36089e14i		−	0.904911i
$419$		−	1.40503e14i		−	0.531508i	−0.964041	−	0.265754i	$-0.914379\pi$
$419$		−	1.40503e14i		−	0.531508i	0.964041	−	0.265754i	$-0.0856209\pi$
$420$		−	1.43607e14i		−	0.536173i
$421$	4.49336e14			1.65585			0.827923	−	0.560842i	$-0.189522\pi$
$421$	4.49336e14			1.65585			0.827923	+	0.560842i	$0.189522\pi$
$422$		−	2.78826e14i		−	1.01418i
$423$	3.40157e14			1.22126
$424$	−1.67808e13			−0.0594703
$425$	−5.68851e13	+	1.31490e12i	−0.199003	+	0.00459996i
$426$	−1.26927e14			−0.438332
$427$	2.50113e14			0.852675
$428$			3.10424e12i			0.0104476i
$429$	−7.36245e14			−2.44629
$430$		−	9.58168e13i		−	0.314315i
$431$		−	2.57736e14i		−	0.834739i	−0.908737	−	0.417369i	$-0.862952\pi$
$431$		−	2.57736e14i		−	0.834739i	0.908737	−	0.417369i	$-0.137048\pi$
$432$		−	1.48213e13i		−	0.0473944i
$433$	1.16383e14			0.367458			0.183729	−	0.982977i	$-0.441183\pi$
$433$	1.16383e14			0.367458			0.183729	+	0.982977i	$0.441183\pi$
$434$	−1.43746e14			−0.448127
$435$			5.44826e14i			1.67713i
$436$			8.56678e13i			0.260401i
$437$			4.20271e14i			1.26148i
$438$	3.39363e14			1.00590
$439$		−	1.50170e14i		−	0.439570i	−0.975548	−	0.219785i	$-0.929464\pi$
$439$		−	1.50170e14i		−	0.439570i	0.975548	−	0.219785i	$-0.0705356\pi$
$440$	3.26803e14			0.944704
$441$	3.42525e14			0.977867
$442$	5.35884e14	−	1.23870e13i	1.51094	−	0.0349255i
$443$	3.94391e14			1.09826			0.549132	−	0.835736i	$-0.314958\pi$
$443$	3.94391e14			1.09826			0.549132	+	0.835736i	$0.314958\pi$
$444$	−9.66718e13			−0.265885
$445$			1.47060e14i			0.399499i
$446$	−1.61854e14			−0.434293
$447$		−	5.72663e14i		−	1.51778i
$448$			5.95383e14i			1.55872i
$449$		−	1.21477e14i		−	0.314153i	−0.987586	−	0.157076i	$-0.949793\pi$
$449$		−	1.21477e14i		−	0.314153i	0.987586	−	0.157076i	$-0.0502069\pi$
$450$	−6.14977e13			−0.157105
$451$	4.03984e14			1.01951
$452$		−	2.29674e14i		−	0.572598i
$453$			8.00312e14i			1.97115i
$454$		−	2.65909e14i		−	0.647031i
$455$	−9.60282e14			−2.30853
$456$		−	7.12236e14i		−	1.69168i
$457$	5.40004e14			1.26724			0.633619	−	0.773645i	$-0.281569\pi$
$457$	5.40004e14			1.26724			0.633619	+	0.773645i	$0.281569\pi$
$458$	1.44043e14			0.333989
$459$	−7.86062e11	−	3.40065e13i	−0.00180089	−	0.0779098i
$460$	−1.34646e14			−0.304807
$461$	−5.02253e14			−1.12349			−0.561743	−	0.827312i	$-0.689869\pi$
$461$	−5.02253e14			−1.12349			−0.561743	+	0.827312i	$0.689869\pi$
$462$			7.30167e14i			1.61395i
$463$	4.95165e14			1.08157			0.540785	−	0.841161i	$-0.318127\pi$
$463$	4.95165e14			1.08157			0.540785	+	0.841161i	$0.318127\pi$
$464$		−	3.78681e14i		−	0.817381i
$465$			2.19785e14i			0.468821i
$466$			4.55564e14i			0.960345i
$467$	3.20932e14			0.668605			0.334302	−	0.942466i	$-0.391499\pi$
$467$	3.20932e14			0.668605			0.334302	+	0.942466i	$0.391499\pi$
$468$	−2.49647e14			−0.514013
$469$		−	9.61375e14i		−	1.95633i
$470$			4.81191e14i			0.967787i
$471$			1.22124e14i			0.242765i
$472$	−4.90802e14			−0.964330
$473$		−	2.09934e14i		−	0.407706i
$474$	−4.70044e14			−0.902313
$475$	1.17011e14			0.222031
$476$	5.29371e12	+	2.29016e14i	0.00992938	+	0.429564i
$477$	−2.78390e13			−0.0516182
$478$	−2.26212e14			−0.414631
$479$			2.42741e13i			0.0439842i	0.999758	+	0.0219921i	$0.00700087\pi$
$479$			2.42741e13i			0.0439842i	−0.999758	+	0.0219921i	$0.992999\pi$
$480$	4.03558e14			0.722901
$481$			6.46431e14i			1.14479i
$482$		−	3.92415e14i		−	0.687048i
$483$		−	1.29980e15i		−	2.24992i
$484$	−1.02442e13			−0.0175319
$485$	−2.20946e14			−0.373858
$486$		−	6.94534e14i		−	1.16197i
$487$		−	2.82695e14i		−	0.467637i	−0.972280	−	0.233818i	$-0.924878\pi$
$487$		−	2.82695e14i		−	0.467637i	0.972280	−	0.233818i	$-0.0751221\pi$
$488$			3.97419e14i			0.650039i
$489$	−5.63481e14			−0.911340
$490$			4.84541e14i			0.774911i
$491$	−4.15858e14			−0.657653			−0.328827	−	0.944390i	$-0.606653\pi$
$491$	−4.15858e14			−0.657653			−0.328827	+	0.944390i	$0.606653\pi$
$492$	2.82076e14			0.441121
$493$	−2.00836e13	−	8.68856e14i	−0.0310588	−	1.34366i
$494$	−1.10230e15			−1.68579
$495$	5.42159e14			0.819971
$496$		−	1.52761e14i		−	0.228489i
$497$	−3.62721e14			−0.536554
$498$			2.11378e14i			0.309242i
$499$		−	3.05542e13i		−	0.0442098i	−0.999756	−	0.0221049i	$-0.992963\pi$
$499$		−	3.05542e13i		−	0.0442098i	0.999756	−	0.0221049i	$-0.00703678\pi$
$500$			2.25817e14i			0.323163i
$501$	−7.80775e13			−0.110514
$502$	8.23730e14			1.15323
$503$			5.64433e14i			0.781608i	0.920474	+	0.390804i	$0.127803\pi$
$503$			5.64433e14i			0.781608i	−0.920474	+	0.390804i	$0.872197\pi$
$504$			1.06972e15i			1.46522i
$505$			7.99946e13i			0.108382i
$506$	6.84605e14			0.917512
$507$			2.38581e15i			3.16295i
$508$	2.88201e14			0.377960
$509$	3.75941e13			0.0487721			0.0243861	−	0.999703i	$-0.492237\pi$
$509$	3.75941e13			0.0487721			0.0243861	+	0.999703i	$0.492237\pi$
$510$	−8.12594e14	+	1.87831e13i	−1.04289	+	0.0241064i
$511$	9.69800e14			1.23131
$512$	−8.07143e14			−1.01383
$513$			6.99507e13i			0.0869253i
$514$	−3.73148e14			−0.458758
$515$		−	8.96539e14i		−	1.09051i
$516$		−	1.46584e14i		−	0.176406i
$517$			1.05429e15i			1.25534i
$518$	6.41094e14			0.755280
$519$	−4.57745e14			−0.533584
$520$		−	1.52585e15i		−	1.75992i
$521$		−	1.02004e15i		−	1.16416i	−0.813132	−	0.582079i	$-0.802240\pi$
$521$		−	1.02004e15i		−	1.16416i	0.813132	−	0.582079i	$-0.197760\pi$
$522$		−	9.39308e14i		−	1.06077i
$523$	3.31531e14			0.370480			0.185240	−	0.982693i	$-0.440694\pi$
$523$	3.31531e14			0.370480			0.185240	+	0.982693i	$0.440694\pi$
$524$		−	2.15040e14i		−	0.237792i
$525$	−3.61889e14			−0.396003
$526$	5.70497e14			0.617777
$527$	−8.10182e12	−	3.50500e14i	−0.00868209	−	0.375604i
$528$	−7.75963e14			−0.822914
$529$	−2.65883e14			−0.279051
$530$		−	3.93815e13i		−	0.0409048i
$531$	−8.14232e14			−0.837005
$532$		−	4.71081e14i		−	0.479271i
$533$		−	1.88620e15i		−	1.89928i
$534$		−	5.22089e14i		−	0.520316i
$535$	−3.14761e13			−0.0310481
$536$	1.52758e15			1.49141
$537$			8.06362e14i			0.779241i
$538$			9.51591e14i			0.910223i
$539$			1.06163e15i			1.00516i
$540$	−2.24107e13			−0.0210034
$541$			9.60735e14i			0.891289i	0.895210	+	0.445645i	$0.147026\pi$
$541$			9.60735e14i			0.891289i	−0.895210	+	0.445645i	$0.852974\pi$
$542$	−9.21498e14			−0.846250
$543$	2.06368e15			1.87605
$544$	−6.43570e14	+	1.48761e13i	−0.579164	+	0.0133874i
$545$	−8.68647e14			−0.773860
$546$	3.40916e15			3.00668
$547$		−	6.04769e14i		−	0.528031i	−0.964518	−	0.264015i	$-0.914953\pi$
$547$		−	6.04769e14i		−	0.528031i	0.964518	−	0.264015i	$-0.0850470\pi$
$548$	1.13674e14			0.0982578
$549$			6.59310e14i			0.564212i
$550$		−	1.90607e14i		−	0.161489i
$551$			1.78722e15i			1.49915i
$552$	2.06533e15			1.71523
$553$	−1.34325e15			−1.10451
$554$			1.29182e15i			1.05172i
$555$		−	9.80224e14i		−	0.790158i
$556$			3.54096e14i			0.282624i
$557$	−1.13402e15			−0.896224			−0.448112	−	0.893978i	$-0.647903\pi$
$557$	−1.13402e15			−0.896224			−0.448112	+	0.893978i	$0.647903\pi$
$558$		−	3.78920e14i		−	0.296524i
$559$	−9.80186e14			−0.759527
$560$	−1.01209e15			−0.776574
$561$	−1.78039e15	+	4.11538e13i	−1.35276	+	0.0312690i
$562$	1.68706e14			0.126935
$563$	1.64146e15			1.22302			0.611511	−	0.791236i	$-0.290562\pi$
$563$	1.64146e15			1.22302			0.611511	+	0.791236i	$0.290562\pi$
$564$			7.36143e14i			0.543159i
$565$	2.32883e15			1.70165
$566$			5.34988e14i			0.387127i
$567$		−	2.09605e15i		−	1.50209i
$568$		−	5.76349e14i		−	0.409043i
$569$	2.14679e15			1.50894			0.754470	−	0.656335i	$-0.227894\pi$
$569$	2.14679e15			1.50894			0.754470	+	0.656335i	$0.227894\pi$
$570$	1.67149e15			1.16357
$571$			9.07633e14i			0.625766i	0.949792	+	0.312883i	$0.101295\pi$
$571$			9.07633e14i			0.625766i	−0.949792	+	0.312883i	$0.898705\pi$
$572$		−	7.73759e14i		−	0.528357i
$573$		−	1.37455e15i		−	0.929627i
$574$	−1.87063e15			−1.25306
$575$			3.39307e14i			0.225123i
$576$	−1.56946e15			−1.03140
$577$	−8.65629e14			−0.563463			−0.281731	−	0.959493i	$-0.590909\pi$
$577$	−8.65629e14			−0.563463			−0.281731	+	0.959493i	$0.590909\pi$
$578$	1.29518e15	−	5.99085e13i	0.835081	−	0.0386265i
$579$	−1.17209e15			−0.748566
$580$	−5.72587e14			−0.362232
$581$			6.04056e14i			0.378537i
$582$	7.84395e14			0.486921
$583$		−	8.62847e13i		−	0.0530587i
$584$			1.54097e15i			0.938693i
$585$		−	2.53135e15i		−	1.52755i
$586$	−3.70185e14			−0.221300
$587$	−6.61689e14			−0.391872			−0.195936	−	0.980617i	$-0.562774\pi$
$587$	−6.61689e14			−0.391872			−0.195936	+	0.980617i	$0.562774\pi$
$588$			7.41266e14i			0.434910i
$589$			7.20971e14i			0.419067i
$590$		−	1.15182e15i		−	0.663285i
$591$	−2.00545e15			−1.14415
$592$			6.81304e14i			0.385098i
$593$	−2.09497e15			−1.17321			−0.586606	−	0.809873i	$-0.699536\pi$
$593$	−2.09497e15			−1.17321			−0.586606	+	0.809873i	$0.699536\pi$
$594$	1.13947e14			0.0632232
$595$	−2.32216e15	+	5.36767e13i	−1.27658	+	0.0295082i
$596$	6.01842e14			0.327815
$597$	−5.08328e15			−2.74337
$598$		−	3.19643e15i		−	1.70926i
$599$	1.81800e15			0.963266			0.481633	−	0.876373i	$-0.340044\pi$
$599$	1.81800e15			0.963266			0.481633	+	0.876373i	$0.340044\pi$
$600$		−	5.75025e14i		−	0.301894i
$601$			3.23713e15i			1.68403i	0.539452	+	0.842017i	$0.318632\pi$
$601$			3.23713e15i			1.68403i	−0.539452	+	0.842017i	$0.681368\pi$
$602$			9.72093e14i			0.501103i
$603$	2.53423e15			1.29450
$604$	−8.41090e14			−0.425735
$605$		−	1.03873e14i		−	0.0521013i
$606$		−	2.83994e14i		−	0.141159i
$607$			1.43281e15i			0.705748i	0.935671	+	0.352874i	$0.114796\pi$
$607$			1.43281e15i			0.705748i	−0.935671	+	0.352874i	$0.885204\pi$
$608$	1.32381e15			0.646183
$609$		−	5.52744e15i		−	2.67380i
$610$	−9.32670e14			−0.447109
$611$	4.92249e15			2.33861
$612$	−6.03697e14	+	1.39545e13i	−0.284241	+	0.00657024i
$613$	−7.90746e14			−0.368981			−0.184491	−	0.982834i	$-0.559064\pi$
$613$	−7.90746e14			−0.368981			−0.184491	+	0.982834i	$0.559064\pi$
$614$	−5.00714e14			−0.231560
$615$			2.86017e15i			1.31093i
$616$	−3.31552e15			−1.50611
$617$			1.24950e15i			0.562561i	0.959626	+	0.281280i	$0.0907591\pi$
$617$			1.24950e15i			0.562561i	−0.959626	+	0.281280i	$0.909241\pi$
$618$			3.18286e15i			1.42030i
$619$		−	1.41749e15i		−	0.626935i	−0.949599	−	0.313467i	$-0.898509\pi$
$619$		−	1.41749e15i		−	0.626935i	0.949599	−	0.313467i	$-0.101491\pi$
$620$	−2.30984e14			−0.101258
$621$	−2.02841e14			−0.0881358
$622$		−	1.20704e14i		−	0.0519845i
$623$		−	1.49198e15i		−	0.636909i
$624$			3.62298e15i			1.53303i
$625$	−1.81513e15			−0.761321
$626$		−	2.35882e15i		−	0.980699i
$627$	3.66223e15			1.50929
$628$	−1.28347e14			−0.0524333
$629$	3.61335e13	+	1.56320e15i	0.0146329	+	0.633048i
$630$	−2.51045e15			−1.00781
$631$	7.87451e14			0.313373			0.156687	−	0.987648i	$-0.449919\pi$
$631$	7.87451e14			0.313373			0.156687	+	0.987648i	$0.449919\pi$
$632$		−	2.13436e15i		−	0.842023i
$633$	4.32517e15			1.69154
$634$			2.88824e15i			1.11980i
$635$			2.92228e15i			1.12322i
$636$		−	6.02471e13i		−	0.0229574i
$637$	4.95675e15			1.87254
$638$	2.91130e15			1.09037
$639$		−	9.56151e14i		−	0.355036i
$640$		−	8.11833e14i		−	0.298866i
$641$		−	1.11021e15i		−	0.405216i	−0.979260	−	0.202608i	$-0.935058\pi$
$641$		−	1.11021e15i		−	0.405216i	0.979260	−	0.202608i	$-0.0649417\pi$
$642$	1.11745e14			0.0404377
$643$		−	4.50108e15i		−	1.61494i	−0.589908	−	0.807470i	$-0.700836\pi$
$643$		−	4.50108e15i		−	1.61494i	0.589908	−	0.807470i	$-0.299164\pi$
$644$	1.36603e15			0.485945
$645$	1.48632e15			0.524243
$646$	−2.66559e15	+	6.16152e13i	−0.932211	+	0.0215481i
$647$	−1.80184e15			−0.624804			−0.312402	−	0.949950i	$-0.601134\pi$
$647$	−1.80184e15			−0.624804			−0.312402	+	0.949950i	$0.601134\pi$
$648$	3.33054e15			1.14512
$649$		−	2.52364e15i		−	0.860363i
$650$	−8.89945e14			−0.300843
$651$		−	2.22979e15i		−	0.747427i
$652$		−	5.92192e14i		−	0.196834i
$653$			5.73199e14i			0.188922i	0.995529	+	0.0944611i	$0.0301128\pi$
$653$			5.73199e14i			0.188922i	−0.995529	+	0.0944611i	$0.969887\pi$
$654$	3.08384e15			1.00789
$655$	2.18044e15			0.706672
$656$		−	1.98796e15i		−	0.638905i
$657$			2.55644e15i			0.814753i
$658$		−	4.88185e15i		−	1.54291i
$659$	2.36503e15			0.741255			0.370627	−	0.928782i	$-0.379143\pi$
$659$	2.36503e15			0.741255			0.370627	+	0.928782i	$0.379143\pi$
$660$			1.17330e15i			0.364684i
$661$	−5.70954e14			−0.175992			−0.0879960	−	0.996121i	$-0.528046\pi$
$661$	−5.70954e14			−0.175992			−0.0879960	+	0.996121i	$0.528046\pi$
$662$	−3.84347e15			−1.17491
$663$	1.92148e14	+	8.31267e15i	0.0582520	+	2.52009i
$664$	−9.59818e14			−0.288579
$665$	4.77662e15			1.42430
$666$			1.68996e15i			0.499766i
$667$	−5.18253e15			−1.52002
$668$		−	8.20558e13i		−	0.0238693i
$669$		−	2.51070e15i		−	0.724353i
$670$			3.58496e15i			1.02582i
$671$	−2.04348e15			−0.579957
$672$	−4.09423e15			−1.15250
$673$			2.96067e15i			0.826621i	0.910590	+	0.413311i	$0.135628\pi$
$673$			2.96067e15i			0.826621i	−0.910590	+	0.413311i	$0.864372\pi$
$674$		−	5.54777e15i		−	1.53635i
$675$			5.64748e13i			0.0155126i
$676$	−2.50737e15			−0.683144
$677$			2.36373e15i			0.638794i	0.947621	+	0.319397i	$0.103480\pi$
$677$			2.36373e15i			0.638794i	−0.947621	+	0.319397i	$0.896520\pi$
$678$	−8.26771e15			−2.21627
$679$	2.24157e15			0.596031
$680$	−8.52900e13	−	3.68980e15i	−0.0224957	−	0.973205i
$681$	4.12479e15			1.07918
$682$	1.17443e15			0.304799
$683$			2.49130e15i			0.641374i	0.947185	+	0.320687i	$0.103914\pi$
$683$			2.49130e15i			0.641374i	−0.947185	+	0.320687i	$0.896086\pi$
$684$	1.24179e15			0.317132
$685$			1.15262e15i			0.292003i
$686$		−	1.69710e14i		−	0.0426506i
$687$			2.23441e15i			0.557058i
$688$	−1.03306e15			−0.255500
$689$	−4.02864e14			−0.0988446
$690$			4.84694e15i			1.17977i
$691$		−	2.66797e14i		−	0.0644245i	−0.999481	−	0.0322123i	$-0.989745\pi$
$691$		−	2.66797e14i		−	0.0644245i	0.999481	−	0.0322123i	$-0.0102553\pi$
$692$		−	4.81068e14i		−	0.115245i
$693$	−5.50039e15			−1.30725
$694$			4.29852e15i			1.01354i
$695$	−3.59043e15			−0.839905
$696$	8.78286e15			2.03838
$697$	−1.05433e14	−	4.56123e15i	−0.0242771	−	1.05027i
$698$	−5.93732e15			−1.35639
$699$	−7.06674e15			−1.60175
$700$		−	3.80328e14i		−	0.0855301i
$701$	2.33460e14			0.0520910			0.0260455	−	0.999661i	$-0.491709\pi$
$701$	2.33460e14			0.0520910			0.0260455	+	0.999661i	$0.491709\pi$
$702$		−	5.32019e14i		−	0.117780i
$703$		−	3.21547e15i		−	0.706302i
$704$		−	4.86440e15i		−	1.06018i
$705$	−7.46427e15			−1.61416
$706$	2.88750e15			0.619579
$707$		−	8.11571e14i		−	0.172791i
$708$		−	1.76210e15i		−	0.372261i
$709$		−	3.00192e15i		−	0.629281i	−0.949211	−	0.314640i	$-0.898116\pi$
$709$		−	3.00192e15i		−	0.629281i	0.949211	−	0.314640i	$-0.101884\pi$
$710$	1.35258e15			0.281348
$711$		−	3.54086e15i		−	0.730847i
$712$	2.37069e15			0.485550
$713$	−2.09065e15			−0.424903
$714$	8.24404e15	−	1.90561e14i	1.66265	−	0.0384321i
$715$	7.84570e15			1.57018
$716$	−8.47449e14			−0.168303
$717$		−	3.50902e15i		−	0.691560i
$718$	−3.59229e15			−0.702566
$719$		−	9.14388e15i		−	1.77469i	−0.461111	−	0.887343i	$-0.652549\pi$
$719$		−	9.14388e15i		−	1.77469i	0.461111	−	0.887343i	$-0.347451\pi$
$720$		−	2.66790e15i		−	0.513856i
$721$			9.09569e15i			1.73857i
$722$	1.07602e15			0.204110
$723$	6.08717e15			1.14592
$724$			2.16883e15i			0.405195i
$725$			1.44291e15i			0.267535i
$726$			3.68767e14i			0.0678579i
$727$	3.71308e15			0.678102			0.339051	−	0.940768i	$-0.389894\pi$
$727$	3.71308e15			0.678102			0.339051	+	0.940768i	$0.389894\pi$
$728$			1.54802e16i			2.80578i
$729$	4.92125e15			0.885267
$730$	−3.61637e15			−0.645651
$731$	−2.37029e15	+	5.47893e13i	−0.420006	+	0.00970846i
$732$	−1.42683e15			−0.250935
$733$	−9.14411e14			−0.159613			−0.0798067	−	0.996810i	$-0.525430\pi$
$733$	−9.14411e14			−0.159613			−0.0798067	+	0.996810i	$0.525430\pi$
$734$			9.15396e15i			1.58592i
$735$	−7.51623e15			−1.29247
$736$			3.83875e15i			0.655181i
$737$			7.85463e15i			1.33062i
$738$		−	4.93108e15i		−	0.829147i
$739$	−7.54834e15			−1.25981			−0.629907	−	0.776670i	$-0.716907\pi$
$739$	−7.54834e15			−1.25981			−0.629907	+	0.776670i	$0.716907\pi$
$740$	1.03017e15			0.170661
$741$		−	1.70990e16i		−	2.81171i
$742$			3.99538e14i			0.0652134i
$743$		−	8.31403e14i		−	0.134702i	−0.997729	−	0.0673508i	$-0.978545\pi$
$743$		−	8.31403e14i		−	0.134702i	0.997729	−	0.0673508i	$-0.0214547\pi$
$744$	3.54304e15			0.569804
$745$			6.10251e15i			0.974202i
$746$	7.26453e15			1.15118
$747$	−1.59232e15			−0.250476
$748$	−4.32507e13	−	1.87111e15i	−0.00675359	−	0.292173i
$749$	3.19336e14			0.0494991
$750$	8.12887e15			1.25082
$751$		−	4.71042e15i		−	0.719516i	−0.933046	−	0.359758i	$-0.882859\pi$
$751$		−	4.71042e15i		−	0.719516i	0.933046	−	0.359758i	$-0.117141\pi$
$752$	5.18804e15			0.786692
$753$			1.27778e16i			1.92346i
$754$		−	1.35929e16i		−	2.03128i
$755$		−	8.52841e15i		−	1.26520i
$756$	2.27364e14			0.0334851
$757$	4.29101e15			0.627382			0.313691	−	0.949525i	$-0.398434\pi$
$757$	4.29101e15			0.627382			0.313691	+	0.949525i	$0.398434\pi$
$758$			1.11873e16i			1.62385i
$759$			1.06196e16i			1.53031i
$760$			7.58985e15i			1.08582i
$761$	−1.19922e16			−1.70326			−0.851632	−	0.524141i	$-0.824387\pi$
$761$	−1.19922e16			−1.70326			−0.851632	+	0.524141i	$0.824387\pi$
$762$		−	1.03746e16i		−	1.46291i
$763$	8.81271e15			1.23374
$764$	1.44458e15			0.200784
$765$	−1.41494e14	−	6.12131e15i	−0.0195255	−	0.844708i
$766$	−4.10913e15			−0.562978
$767$	−1.17829e16			−1.60280
$768$		−	8.39635e15i		−	1.13398i
$769$	9.09187e15			1.21915			0.609577	−	0.792727i	$-0.291339\pi$
$769$	9.09187e15			1.21915			0.609577	+	0.792727i	$0.291339\pi$
$770$		−	7.78092e15i		−	1.03593i
$771$		−	5.78829e15i		−	0.765158i
$772$		−	1.23181e15i		−	0.161678i
$773$	8.34556e14			0.108760			0.0543799	−	0.998520i	$-0.482682\pi$
$773$	8.34556e14			0.108760			0.0543799	+	0.998520i	$0.482682\pi$
$774$	−2.56248e15			−0.331578
$775$			5.82077e14i			0.0747861i
$776$			3.56176e15i			0.454386i
$777$			9.94470e15i			1.25973i
$778$	8.05013e15			1.01255
$779$			9.38234e15i			1.17181i
$780$	5.47815e15			0.679381
$781$	2.96351e15			0.364943
$782$	−1.78670e14	−	7.72961e15i	−0.0218482	−	0.945193i
$783$	−8.62589e14			−0.104740
$784$	5.22415e15			0.629908
$785$		−	1.30140e15i		−	0.155822i
$786$	−7.74094e15			−0.920385
$787$		−	1.03995e16i		−	1.22786i	−0.789359	−	0.613932i	$-0.789587\pi$
$787$		−	1.03995e16i		−	1.22786i	0.789359	−	0.613932i	$-0.210413\pi$
$788$		−	2.10764e15i		−	0.247117i
$789$			8.84959e15i			1.03039i
$790$	5.00896e15			0.579160
$791$	−2.36267e16			−2.71289
$792$		−	8.73987e15i		−	0.996590i
$793$			9.54102e15i			1.08042i
$794$			9.36670e15i			1.05335i
$795$	6.10888e14			0.0682248
$796$		−	5.34228e15i		−	0.592523i
$797$	1.72248e16			1.89729			0.948644	−	0.316346i	$-0.102456\pi$
$797$	1.72248e16			1.89729			0.948644	+	0.316346i	$0.102456\pi$
$798$	−1.69578e16			−1.85504
$799$	1.19036e16	−	2.75152e14i	1.29321	−	0.0298927i
$800$	1.06878e15			0.115317
$801$	3.93292e15			0.421441
$802$			4.74645e15i			0.505138i
$803$	−7.92346e15			−0.837490
$804$			5.48439e15i			0.575731i
$805$			1.38511e16i			1.44414i
$806$		−	5.48343e15i		−	0.567819i
$807$	−1.47611e16			−1.51815
$808$	1.28955e15			0.131727
$809$		−	1.85089e16i		−	1.87787i	−0.344101	−	0.938933i	$-0.611816\pi$
$809$		−	1.85089e16i		−	1.87787i	0.344101	−	0.938933i	$-0.388184\pi$
$810$			7.81617e15i			0.787637i
$811$		−	3.29176e15i		−	0.329469i	−0.986338	−	0.164734i	$-0.947323\pi$
$811$		−	3.29176e15i		−	0.329469i	0.986338	−	0.164734i	$-0.0526767\pi$
$812$	5.80908e15			0.577497
$813$		−	1.42943e16i		−	1.41145i
$814$	−5.23787e15			−0.513713
$815$	6.00465e15			0.584953
$816$	2.02513e14	+	8.76110e15i	0.0195956	+	0.847741i
$817$	4.87563e15			0.468608
$818$	−1.46289e16			−1.39659
$819$			2.56814e16i			2.43532i
$820$	−3.00590e15			−0.283139
$821$		−	4.39702e15i		−	0.411406i	−0.978614	−	0.205703i	$-0.934052\pi$
$821$		−	4.39702e15i		−	0.411406i	0.978614	−	0.205703i	$-0.0659481\pi$
$822$		−	4.09199e15i		−	0.380311i
$823$		−	5.49094e15i		−	0.506930i	−0.967345	−	0.253465i	$-0.918430\pi$
$823$		−	5.49094e15i		−	0.506930i	0.967345	−	0.253465i	$-0.0815702\pi$
$824$	−1.44527e16			−1.32540
$825$	2.95670e15			0.269346
$826$			1.16856e16i			1.05746i
$827$		−	2.44144e15i		−	0.219465i	−0.993961	−	0.109733i	$-0.965001\pi$
$827$		−	2.44144e15i		−	0.219465i	0.993961	−	0.109733i	$-0.0349995\pi$
$828$			3.60092e15i			0.321548i
$829$	1.71931e15			0.152512			0.0762560	−	0.997088i	$-0.475703\pi$
$829$	1.71931e15			0.152512			0.0762560	+	0.997088i	$0.475703\pi$
$830$		−	2.25252e15i		−	0.198490i
$831$	−2.00388e16			−1.75415
$832$	−2.27119e16			−1.97504
$833$	1.19864e16	−	2.77067e14i	1.03548	−	0.0239352i
$834$	1.27466e16			1.09391
$835$	8.32022e14			0.0709348
$836$			3.84883e15i			0.325982i
$837$	−3.47972e14			−0.0292788
$838$		−	5.31550e15i		−	0.444327i
$839$		−	2.71458e15i		−	0.225430i	−0.993627	−	0.112715i	$-0.964045\pi$
$839$		−	2.71458e15i		−	0.225430i	0.993627	−	0.112715i	$-0.0359547\pi$
$840$		−	2.34736e16i		−	1.93662i
$841$	−9.83837e15			−0.806390
$842$	1.69992e16			1.38424
$843$			2.61697e15i			0.211713i
$844$			4.54555e15i			0.365345i
$845$		−	2.54240e16i		−	2.03017i
$846$	1.28688e16			1.02094
$847$			1.05383e15i			0.0830636i
$848$	−4.24597e14			−0.0332506
$849$	−8.29876e15			−0.645686
$850$	−2.15207e15	+	4.97451e13i	−0.166361	+	0.00384545i
$851$	9.32415e15			0.716138
$852$	2.06923e15			0.157903
$853$		−	1.05851e16i		−	0.802553i	−0.915957	−	0.401277i	$-0.868567\pi$
$853$		−	1.05851e16i		−	0.802553i	0.915957	−	0.401277i	$-0.131433\pi$
$854$	9.46224e15			0.712813
$855$			1.25914e16i			0.942455i
$856$			5.07410e14i			0.0377358i
$857$			2.05349e16i			1.51740i	0.651443	+	0.758698i	$0.274164\pi$
$857$			2.05349e16i			1.51740i	−0.651443	+	0.758698i	$0.725836\pi$
$858$	−2.78535e16			−2.04503
$859$	4.20448e15			0.306726			0.153363	−	0.988170i	$-0.450990\pi$
$859$	4.20448e15			0.306726			0.153363	+	0.988170i	$0.450990\pi$
$860$			1.56205e15i			0.113228i
$861$		−	2.90174e16i		−	2.08997i
$862$		−	9.75064e15i		−	0.697820i
$863$	−6.77990e15			−0.482130			−0.241065	−	0.970509i	$-0.577497\pi$
$863$	−6.77990e15			−0.482130			−0.241065	+	0.970509i	$0.577497\pi$
$864$			6.38927e14i			0.0451467i
$865$	4.87789e15			0.342487
$866$	4.40300e15			0.307185
$867$	9.29304e14	+	2.00910e16i	0.0644248	+	1.39282i
$868$	2.34341e15			0.161432
$869$	1.09746e16			0.751243
$870$			2.06118e16i			1.40204i
$871$	3.66734e16			2.47885
$872$			1.40030e16i			0.940547i
$873$			5.90889e15i			0.394391i
$874$			1.58996e16i			1.05457i
$875$	2.32299e16			1.53110
$876$	−5.53245e15			−0.362364
$877$			5.94669e15i			0.387059i	0.981094	+	0.193530i	$0.0619935\pi$
$877$			5.94669e15i			0.387059i	−0.981094	+	0.193530i	$0.938006\pi$
$878$		−	5.68121e15i		−	0.367469i
$879$		−	5.74233e15i		−	0.369105i
$880$	8.26894e15			0.528196
$881$			1.54574e16i			0.981228i	0.871377	+	0.490614i	$0.163227\pi$
$881$			1.54574e16i			0.981228i	−0.871377	+	0.490614i	$0.836773\pi$
$882$	1.29583e16			0.817471
$883$	−1.08853e16			−0.682426			−0.341213	−	0.939986i	$-0.610838\pi$
$883$	−1.08853e16			−0.682426			−0.341213	+	0.939986i	$0.610838\pi$
$884$	−8.73622e15	+	2.01938e14i	−0.544297	+	0.0125815i
$885$	1.78672e16			1.10629
$886$	1.49205e16			0.918120
$887$		−	1.81312e16i		−	1.10878i	−0.832256	−	0.554392i	$-0.812951\pi$
$887$		−	1.81312e16i		−	1.10878i	0.832256	−	0.554392i	$-0.187049\pi$
$888$	−1.58017e16			−0.960356
$889$		−	2.96475e16i		−	1.79072i
$890$			5.56357e15i			0.333971i
$891$			1.71252e16i			1.02166i
$892$	2.63862e15			0.156448
$893$	−2.44854e16			−1.44286
$894$		−	2.16649e16i		−	1.26882i
$895$		−	8.59289e15i		−	0.500164i
$896$			8.23632e15i			0.476474i
$897$	4.95832e16			2.85086
$898$		−	4.59571e15i		−	0.262623i
$899$	−8.89057e15			−0.504954
$900$	1.00256e15			0.0565950
$901$	−9.74207e14	+	2.25188e13i	−0.0546594	+	0.00126345i
$902$	1.52834e16			0.852286
$903$	−1.50792e16			−0.835786
$904$		−	3.75418e16i		−	2.06818i
$905$	−2.19913e16			−1.20416
$906$			3.02773e16i			1.64783i
$907$			1.65075e16i			0.892978i	0.894789	+	0.446489i	$0.147326\pi$
$907$			1.65075e16i			0.892978i	−0.894789	+	0.446489i	$0.852674\pi$
$908$			4.33496e15i			0.233084i
$909$	2.13934e15			0.114335
$910$	−3.63292e16			−1.92987
$911$			2.88205e16i			1.52177i	0.648884	+	0.760887i	$0.275236\pi$
$911$			2.88205e16i			1.52177i	−0.648884	+	0.760887i	$0.724764\pi$
$912$		−	1.80214e16i		−	0.945838i
$913$		−	4.93526e15i		−	0.257466i
$914$	2.04294e16			1.05938
$915$		−	1.44676e16i		−	0.745730i
$916$	−2.34826e15			−0.120315
$917$	−2.21213e16			−1.12663
$918$	−2.97382e13	−	1.28653e15i	−0.00150550	−	0.0651306i
$919$	−4.27361e15			−0.215060			−0.107530	−	0.994202i	$-0.534294\pi$
$919$	−4.27361e15			−0.215060			−0.107530	+	0.994202i	$0.534294\pi$
$920$	−2.20089e16			−1.10094
$921$		−	7.76711e15i		−	0.386217i
$922$	−1.90012e16			−0.939204
$923$		−	1.38367e16i		−	0.679864i
$924$		−	1.19035e16i		−	0.581406i
$925$		−	2.59602e15i		−	0.126046i
$926$	1.87330e16			0.904164
$927$	−2.39767e16			−1.15040
$928$			1.63244e16i			0.778616i
$929$			3.11578e15i			0.147734i	0.997268	+	0.0738669i	$0.0235340\pi$
$929$			3.11578e15i			0.147734i	−0.997268	+	0.0738669i	$0.976466\pi$
$930$			8.31487e15i			0.391922i
$931$	−2.46558e16			−1.15530
$932$		−	7.42682e15i		−	0.345951i
$933$	1.87237e15			0.0867045
$934$	1.21414e16			0.558936
$935$	1.89725e16	−	4.38550e14i	0.868281	−	0.0200704i
$936$	−4.08066e16			−1.85658
$937$	−1.51080e16			−0.683345			−0.341673	−	0.939819i	$-0.610993\pi$
$937$	−1.51080e16			−0.683345			−0.341673	+	0.939819i	$0.610993\pi$
$938$		−	3.63706e16i		−	1.63544i
$939$	3.65902e16			1.63570
$940$		−	7.84460e15i		−	0.348632i
$941$			3.03298e16i			1.34007i	0.742331	+	0.670033i	$0.233720\pi$
$941$			3.03298e16i			1.34007i	−0.742331	+	0.670033i	$0.766280\pi$
$942$			4.62018e15i			0.202945i
$943$	−2.72067e16			−1.18812
$944$	−1.24186e16			−0.539169
$945$			2.30541e15i			0.0995113i
$946$		−	7.94220e15i		−	0.340831i
$947$		−	1.87330e16i		−	0.799248i	−0.916679	−	0.399624i	$-0.869141\pi$
$947$		−	1.87330e16i		−	0.799248i	0.916679	−	0.399624i	$-0.130859\pi$
$948$	7.66287e15			0.325046
$949$			3.69947e16i			1.56018i
$950$	4.42676e15			0.185612
$951$	−4.48025e16			−1.86771
$952$	8.65295e14	+	3.74343e16i	0.0358642	+	1.55155i
$953$	3.15154e16			1.29871			0.649355	−	0.760485i	$-0.275039\pi$
$953$	3.15154e16			1.29871			0.649355	+	0.760485i	$0.275039\pi$
$954$	−1.05320e15			−0.0431514
$955$			1.46476e16i			0.596691i
$956$	3.68781e15			0.149366
$957$			4.51603e16i			1.81862i
$958$			9.18332e14i			0.0367697i
$959$		−	1.16937e16i		−	0.465532i
$960$	3.44395e16			1.36322
$961$	2.18220e16			0.858847
$962$			2.44557e16i			0.957011i
$963$			8.41784e14i			0.0327534i
$964$			6.39733e15i			0.247500i
$965$	1.24902e16			0.480475
$966$		−	4.91738e16i		−	1.88087i
$967$	−1.21277e16			−0.461246			−0.230623	−	0.973043i	$-0.574076\pi$
$967$	−1.21277e16			−0.461246			−0.230623	+	0.973043i	$0.574076\pi$
$968$	−1.67449e15			−0.0633238
$969$	−9.55779e14	−	4.13488e16i	−0.0359399	−	1.55483i
$970$	−8.35879e15			−0.312535
$971$	−1.53806e16			−0.571832			−0.285916	−	0.958255i	$-0.592298\pi$
$971$	−1.53806e16			−0.571832			−0.285916	+	0.958255i	$0.592298\pi$
$972$			1.13226e16i			0.418583i
$973$	3.64261e16			1.33904
$974$		−	1.06949e16i		−	0.390932i
$975$		−	1.38049e16i		−	0.501773i
$976$			1.00557e16i			0.363445i
$977$	−2.63621e16			−0.947459			−0.473730	−	0.880670i	$-0.657093\pi$
$977$	−2.63621e16			−0.947459			−0.473730	+	0.880670i	$0.657093\pi$
$978$	−2.13175e16			−0.761856
$979$			1.21898e16i			0.433202i
$980$		−	7.89920e15i		−	0.279151i
$981$			2.32307e16i			0.816363i
$982$	−1.57327e16			−0.549781
$983$		−	2.24678e16i		−	0.780758i	−0.920654	−	0.390379i	$-0.872344\pi$
$983$		−	2.24678e16i		−	0.780758i	0.920654	−	0.390379i	$-0.127656\pi$
$984$	4.61073e16			1.59330
$985$	2.13708e16			0.734383
$986$	−7.59801e14	−	3.28704e16i	−0.0259643	−	1.12327i
$987$	7.57275e16			2.57341
$988$	1.79702e16			0.607282
$989$			1.41382e16i			0.475133i
$990$	2.05109e16			0.685474
$991$		−	4.43814e16i		−	1.47501i	−0.675340	−	0.737507i	$-0.736003\pi$
$991$		−	4.43814e16i		−	1.47501i	0.675340	−	0.737507i	$-0.263997\pi$
$992$			6.58533e15i			0.217652i
$993$		−	5.96201e16i		−	1.95962i
$994$	−1.37224e16			−0.448545
$995$	5.41692e16			1.76086
$996$		−	3.44598e15i		−	0.111400i
$997$		−	3.83200e16i		−	1.23198i	−0.787756	−	0.615988i	$-0.788757\pi$
$997$		−	3.83200e16i		−	1.23198i	0.787756	−	0.615988i	$-0.211243\pi$
$998$		−	1.15592e15i		−	0.0369582i
$999$	1.55193e15			0.0493470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.b.a.16.12	yes	16
3.2	odd	2		153.12.d.b.118.6		16
4.3	odd	2		272.12.b.c.33.3		16
17.16	even	2	inner	17.12.b.a.16.11	✓	16
51.50	odd	2		153.12.d.b.118.5		16
68.67	odd	2		272.12.b.c.33.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.b.a.16.11	✓	16	17.16	even	2	inner
17.12.b.a.16.12	yes	16	1.1	even	1	trivial
153.12.d.b.118.5		16	51.50	odd	2
153.12.d.b.118.6		16	3.2	odd	2
272.12.b.c.33.3		16	4.3	odd	2
272.12.b.c.33.14		16	68.67	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)

\(f(q)\)	\(=\)	\(q+37.8318 q^{2} +586.850i q^{3} -616.752 q^{4} -6253.69i q^{5} +22201.6i q^{6} +63445.7i q^{7} -100812. q^{8} -167246. q^{9} +O(q^{10})\)	\(q+37.8318 q^{2} +586.850i q^{3} -616.752 q^{4} -6253.69i q^{5} +22201.6i q^{6} +63445.7i q^{7} -100812. q^{8} -167246. q^{9} -236588. i q^{10} -518365. i q^{11} -361941. i q^{12} -2.42025e6 q^{13} +2.40027e6i q^{14} +3.66998e6 q^{15} -2.55081e6 q^{16} +(-5.85266e6 + 135284. i) q^{17} -6.32722e6 q^{18} +1.20388e7 q^{19} +3.85697e6i q^{20} -3.72331e7 q^{21} -1.96107e7i q^{22} +3.49098e7i q^{23} -5.91618e7i q^{24} +9.71954e6 q^{25} -9.15625e7 q^{26} +5.81044e6i q^{27} -3.91303e7i q^{28} +1.48455e8i q^{29} +1.38842e8 q^{30} +5.98873e7i q^{31} +1.09962e8 q^{32} +3.04202e8 q^{33} +(-2.21417e8 + 5.11806e6i) q^{34} +3.96770e8 q^{35} +1.03149e8 q^{36} -2.67093e8i q^{37} +4.55449e8 q^{38} -1.42032e9i q^{39} +6.30450e8i q^{40} +7.79343e8i q^{41} -1.40860e9 q^{42} +4.04994e8 q^{43} +3.19702e8i q^{44} +1.04590e9i q^{45} +1.32070e9i q^{46} -2.03388e9 q^{47} -1.49694e9i q^{48} -2.04803e9 q^{49} +3.67708e8 q^{50} +(-7.93916e7 - 3.43463e9i) q^{51} +1.49269e9 q^{52} +1.66456e8 q^{53} +2.19820e8i q^{54} -3.24169e9 q^{55} -6.39612e9i q^{56} +7.06496e9i q^{57} +5.61633e9i q^{58} +4.86847e9 q^{59} -2.26346e9 q^{60} -3.94216e9i q^{61} +2.26565e9i q^{62} -1.06110e10i q^{63} +9.38413e9 q^{64} +1.51355e10i q^{65} +1.15085e10 q^{66} -1.51527e10 q^{67} +(3.60964e9 - 8.34369e7i) q^{68} -2.04868e10 q^{69} +1.50105e10 q^{70} +5.71704e9i q^{71} +1.68605e10 q^{72} -1.52855e10i q^{73} -1.01046e10i q^{74} +5.70391e9i q^{75} -7.42494e9 q^{76} +3.28880e10 q^{77} -5.37335e10i q^{78} +2.11716e10i q^{79} +1.59520e10i q^{80} -3.30370e10 q^{81} +2.94840e10i q^{82} +9.52083e9 q^{83} +2.29636e10 q^{84} +(8.46026e8 + 3.66007e10i) q^{85} +1.53217e10 q^{86} -8.71208e10 q^{87} +5.22576e10i q^{88} -2.35158e10 q^{89} +3.95685e10i q^{90} -1.53554e11i q^{91} -2.15307e10i q^{92} -3.51449e10 q^{93} -7.69453e10 q^{94} -7.52868e10i q^{95} +6.45312e10i q^{96} -3.53305e10i q^{97} -7.74808e10 q^{98} +8.66944e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more