LMFDB - Embedded newform 17.12.b.a.16.16

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			16.16
Root			$710.682i$ of defining polynomial
Character	$\chi$	$=$	17.16
Dual form			17.12.b.a.16.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+87.4420 q^{2} +710.682i q^{3} +5598.10 q^{4} +776.017i q^{5} +62143.4i q^{6} -46177.6i q^{7} +310427. q^{8} -327922. q^{9} +O(q^{10})$	\(q+87.4420 q^{2} +710.682i q^{3} +5598.10 q^{4} +776.017i q^{5} +62143.4i q^{6} -46177.6i q^{7} +310427. q^{8} -327922. q^{9} +67856.4i q^{10} +473622. i q^{11} +3.97847e6i q^{12} -1.12485e6 q^{13} -4.03786e6i q^{14} -551501. q^{15} +1.56795e7 q^{16} +(1.74214e6 - 5.58899e6i) q^{17} -2.86741e7 q^{18} -270211. q^{19} +4.34422e6i q^{20} +3.28176e7 q^{21} +4.14144e7i q^{22} -5.01946e7i q^{23} +2.20615e8i q^{24} +4.82259e7 q^{25} -9.83592e7 q^{26} -1.07153e8i q^{27} -2.58506e8i q^{28} +1.13464e8i q^{29} -4.82244e7 q^{30} -8.48204e6i q^{31} +7.35289e8 q^{32} -3.36595e8 q^{33} +(1.52336e8 - 4.88712e8i) q^{34} +3.58346e7 q^{35} -1.83574e9 q^{36} -3.20768e8i q^{37} -2.36278e7 q^{38} -7.99412e8i q^{39} +2.40897e8i q^{40} +2.66859e8i q^{41} +2.86963e9 q^{42} -9.77253e7 q^{43} +2.65138e9i q^{44} -2.54473e8i q^{45} -4.38912e9i q^{46} -1.55133e9 q^{47} +1.11431e10i q^{48} -1.55041e8 q^{49} +4.21697e9 q^{50} +(3.97200e9 + 1.23811e9i) q^{51} -6.29703e9 q^{52} -2.97819e9 q^{53} -9.36968e9i q^{54} -3.67539e8 q^{55} -1.43348e10i q^{56} -1.92034e8i q^{57} +9.92154e9i q^{58} -4.41582e9 q^{59} -3.08736e9 q^{60} +4.37822e9i q^{61} -7.41686e8i q^{62} +1.51426e10i q^{63} +3.21836e10 q^{64} -8.72904e8i q^{65} -2.94325e10 q^{66} +9.47419e9 q^{67} +(9.75268e9 - 3.12877e10i) q^{68} +3.56724e10 q^{69} +3.13345e9 q^{70} +9.53366e9i q^{71} -1.01796e11 q^{72} +1.49814e10i q^{73} -2.80486e10i q^{74} +3.42733e10i q^{75} -1.51267e9 q^{76} +2.18707e10 q^{77} -6.99021e10i q^{78} -1.78480e10i q^{79} +1.21675e10i q^{80} +1.80614e10 q^{81} +2.33347e10i q^{82} -6.44756e10 q^{83} +1.83716e11 q^{84} +(4.33715e9 + 1.35193e9i) q^{85} -8.54529e9 q^{86} -8.06370e10 q^{87} +1.47025e11i q^{88} +1.27278e10 q^{89} -2.22516e10i q^{90} +5.19429e10i q^{91} -2.80994e11i q^{92} +6.02803e9 q^{93} -1.35651e11 q^{94} -2.09688e8i q^{95} +5.22557e11i q^{96} +1.84889e10i q^{97} -1.35571e10 q^{98} -1.55311e11i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	87.4420			1.93221			0.966106	−	0.258144i	$-0.0831111\pi$
$2$	87.4420			1.93221			0.966106	+	0.258144i	$0.0831111\pi$
$3$			710.682i			1.68853i	0.535927	+	0.844264i	$0.319962\pi$
$3$			710.682i			1.68853i	−0.535927	+	0.844264i	$0.680038\pi$
$4$	5598.10			2.73345
$5$			776.017i			0.111054i	0.998457	+	0.0555272i	$0.0176840\pi$
$5$			776.017i			0.111054i	−0.998457	+	0.0555272i	$0.982316\pi$
$6$			62143.4i			3.26260i
$7$		−	46177.6i		−	1.03846i	−0.854633	−	0.519232i	$-0.826218\pi$
$7$		−	46177.6i		−	1.03846i	0.854633	−	0.519232i	$-0.173782\pi$
$8$	310427.			3.34939
$9$	−327922.			−1.85113
$10$			67856.4i			0.214581i
$11$			473622.i			0.886691i	0.896351	+	0.443345i	$0.146208\pi$
$11$			473622.i			0.886691i	−0.896351	+	0.443345i	$0.853792\pi$
$12$			3.97847e6i			4.61550i
$13$	−1.12485e6			−0.840247			−0.420123	−	0.907467i	$-0.638013\pi$
$13$	−1.12485e6			−0.840247			−0.420123	+	0.907467i	$0.638013\pi$
$14$		−	4.03786e6i		−	2.00654i
$15$	−551501.			−0.187519
$16$	1.56795e7			3.73828
$17$	1.74214e6	−	5.58899e6i	0.297587	−	0.954695i
$17$	1.74214e6	−	5.58899e6i	0.297587	−	0.954695i
$18$	−2.86741e7			−3.57678
$19$	−270211.			−0.0250356			−0.0125178	−	0.999922i	$-0.503985\pi$
$19$	−270211.			−0.0250356			−0.0125178	+	0.999922i	$0.503985\pi$
$20$			4.34422e6i			0.303561i
$21$	3.28176e7			1.75348
$22$			4.14144e7i			1.71328i
$23$		−	5.01946e7i		−	1.62613i	−0.582176	−	0.813063i	$-0.697798\pi$
$23$		−	5.01946e7i		−	1.62613i	0.582176	−	0.813063i	$-0.302202\pi$
$24$			2.20615e8i			5.65553i
$25$	4.82259e7			0.987667
$26$	−9.83592e7			−1.62354
$27$		−	1.07153e8i		−	1.43716i
$28$		−	2.58506e8i		−	2.83859i
$29$			1.13464e8i			1.02724i	0.858019	+	0.513618i	$0.171695\pi$
$29$			1.13464e8i			1.02724i	−0.858019	+	0.513618i	$0.828305\pi$
$30$	−4.82244e7			−0.362326
$31$		−	8.48204e6i		−	0.0532122i	−0.999646	−	0.0266061i	$-0.991530\pi$
$31$		−	8.48204e6i		−	0.0532122i	0.999646	−	0.0266061i	$-0.00846998\pi$
$32$	7.35289e8			3.87377
$33$	−3.36595e8			−1.49720
$34$	1.52336e8	−	4.88712e8i	0.575002	−	1.84467i
$35$	3.58346e7			0.115326
$36$	−1.83574e9			−5.05996
$37$		−	3.20768e8i		−	0.760470i	−0.924890	−	0.380235i	$-0.875843\pi$
$37$		−	3.20768e8i		−	0.760470i	0.924890	−	0.380235i	$-0.124157\pi$
$38$	−2.36278e7			−0.0483741
$39$		−	7.99412e8i		−	1.41878i
$40$			2.40897e8i			0.371964i
$41$			2.66859e8i			0.359726i	0.983692	+	0.179863i	$0.0575654\pi$
$41$			2.66859e8i			0.359726i	−0.983692	+	0.179863i	$0.942435\pi$
$42$	2.86963e9			3.38809
$43$	−9.77253e7			−0.101375			−0.0506874	−	0.998715i	$-0.516141\pi$
$43$	−9.77253e7			−0.101375			−0.0506874	+	0.998715i	$0.516141\pi$
$44$			2.65138e9i			2.42372i
$45$		−	2.54473e8i		−	0.205576i
$46$		−	4.38912e9i		−	3.14202i
$47$	−1.55133e9			−0.986654			−0.493327	−	0.869844i	$-0.664219\pi$
$47$	−1.55133e9			−0.986654			−0.493327	+	0.869844i	$0.664219\pi$
$48$			1.11431e10i			6.31219i
$49$	−1.55041e8			−0.0784094
$50$	4.21697e9			1.90838
$51$	3.97200e9	+	1.23811e9i	1.61203	+	0.502485i
$52$	−6.29703e9			−2.29677
$53$	−2.97819e9			−0.978216			−0.489108	−	0.872223i	$-0.662678\pi$
$53$	−2.97819e9			−0.978216			−0.489108	+	0.872223i	$0.662678\pi$
$54$		−	9.36968e9i		−	2.77689i
$55$	−3.67539e8			−0.0984710
$56$		−	1.43348e10i		−	3.47822i
$57$		−	1.92034e8i		−	0.0422733i
$58$			9.92154e9i			1.98484i
$59$	−4.41582e9			−0.804127			−0.402064	−	0.915612i	$-0.631707\pi$
$59$	−4.41582e9			−0.804127			−0.402064	+	0.915612i	$0.631707\pi$
$60$	−3.08736e9			−0.512572
$61$			4.37822e9i			0.663718i	0.943329	+	0.331859i	$0.107676\pi$
$61$			4.37822e9i			0.663718i	−0.943329	+	0.331859i	$0.892324\pi$
$62$		−	7.41686e8i		−	0.102817i
$63$			1.51426e10i			1.92233i
$64$	3.21836e10			3.74666
$65$		−	8.72904e8i		−	0.0933132i
$66$	−2.94325e10			−2.89291
$67$	9.47419e9			0.857296			0.428648	−	0.903472i	$-0.358990\pi$
$67$	9.47419e9			0.857296			0.428648	+	0.903472i	$0.358990\pi$
$68$	9.75268e9	−	3.12877e10i	0.813439	−	2.60961i
$69$	3.56724e10			2.74576
$70$	3.13345e9			0.222835
$71$			9.53366e9i			0.627102i	0.949571	+	0.313551i	$0.101519\pi$
$71$			9.53366e9i			0.627102i	−0.949571	+	0.313551i	$0.898481\pi$
$72$	−1.01796e11			−6.20015
$73$			1.49814e10i			0.845820i	0.906172	+	0.422910i	$0.138991\pi$
$73$			1.49814e10i			0.845820i	−0.906172	+	0.422910i	$0.861009\pi$
$74$		−	2.80486e10i		−	1.46939i
$75$			3.42733e10i			1.66770i
$76$	−1.51267e9			−0.0684335
$77$	2.18707e10			0.920797
$78$		−	6.99021e10i		−	2.74139i
$79$		−	1.78480e10i		−	0.652591i	−0.945268	−	0.326295i	$-0.894200\pi$
$79$		−	1.78480e10i		−	0.652591i	0.945268	−	0.326295i	$-0.105800\pi$
$80$			1.21675e10i			0.415153i
$81$	1.80614e10			0.575550
$82$			2.33347e10i			0.695066i
$83$	−6.44756e10			−1.79666			−0.898330	−	0.439322i	$-0.855219\pi$
$83$	−6.44756e10			−1.79666			−0.898330	+	0.439322i	$0.855219\pi$
$84$	1.83716e11			4.79304
$85$	4.33715e9	+	1.35193e9i	0.106023	+	0.0330484i
$86$	−8.54529e9			−0.195878
$87$	−8.06370e10			−1.73452
$88$			1.47025e11i			2.96987i
$89$	1.27278e10			0.241605			0.120803	−	0.992677i	$-0.461453\pi$
$89$	1.27278e10			0.241605			0.120803	+	0.992677i	$0.461453\pi$
$90$		−	2.22516e10i		−	0.397217i
$91$			5.19429e10i			0.872567i
$92$		−	2.80994e11i		−	4.44493i
$93$	6.02803e9			0.0898503
$94$	−1.35651e11			−1.90643
$95$		−	2.09688e8i		−	0.00278032i
$96$			5.22557e11i			6.54096i
$97$			1.84889e10i			0.218608i	0.994008	+	0.109304i	$0.0348622\pi$
$97$			1.84889e10i			0.218608i	−0.994008	+	0.109304i	$0.965138\pi$
$98$	−1.35571e10			−0.151504
$99$		−	1.55311e11i		−	1.64138i
$100$	2.69973e11			2.69973
$101$	2.50776e10			0.237420			0.118710	−	0.992929i	$-0.462124\pi$
$101$	2.50776e10			0.237420			0.118710	+	0.992929i	$0.462124\pi$
$102$	3.47319e11	+	1.08263e11i	3.11478	+	0.970908i
$103$	−1.25782e11			−1.06909			−0.534543	−	0.845142i	$-0.679516\pi$
$103$	−1.25782e11			−1.06909			−0.534543	+	0.845142i	$0.679516\pi$
$104$	−3.49185e11			−2.81431
$105$			2.54670e10i			0.194732i
$106$	−2.60418e11			−1.89012
$107$			9.14996e10i			0.630679i	0.948979	+	0.315339i	$0.102118\pi$
$107$			9.14996e10i			0.630679i	−0.948979	+	0.315339i	$0.897882\pi$
$108$		−	5.99853e11i		−	3.92839i
$109$		−	1.47997e11i		−	0.921314i	−0.887578	−	0.460657i	$-0.847614\pi$
$109$		−	1.47997e11i		−	0.921314i	0.887578	−	0.460657i	$-0.152386\pi$
$110$	−3.21383e10			−0.190267
$111$	2.27964e11			1.28408
$112$		−	7.24040e11i		−	3.88207i
$113$		−	2.54426e11i		−	1.29906i	−0.760336	−	0.649530i	$-0.774966\pi$
$113$		−	2.54426e11i		−	1.29906i	0.760336	−	0.649530i	$-0.225034\pi$
$114$		−	1.67918e10i		−	0.0816811i
$115$	3.89519e10			0.180589
$116$			6.35184e11i			2.80789i
$117$	3.68864e11			1.55540
$118$	−3.86128e11			−1.55375
$119$	−2.58086e11	−	8.04479e10i	−0.991417	−	0.309034i
$120$	−1.71201e11			−0.628072
$121$	6.09938e10			0.213779
$122$			3.82840e11i			1.28244i
$123$	−1.89652e11			−0.607407
$124$		−	4.74833e10i		−	0.145453i
$125$			7.53156e10i			0.220739i
$126$			1.32410e12i			3.71436i
$127$	−8.46258e10			−0.227291			−0.113645	−	0.993521i	$-0.536253\pi$
$127$	−8.46258e10			−0.227291			−0.113645	+	0.993521i	$0.536253\pi$
$128$	1.30832e12			3.36558
$129$		−	6.94516e10i		−	0.171174i
$130$		−	7.63284e10i		−	0.180301i
$131$			7.05350e11i			1.59739i	0.601733	+	0.798697i	$0.294477\pi$
$131$			7.05350e11i			1.59739i	−0.601733	+	0.798697i	$0.705523\pi$
$132$	−1.88429e12			−4.09252
$133$			1.24777e10i			0.0259986i
$134$	8.28442e11			1.65648
$135$	8.31526e10			0.159603
$136$	5.40809e11	−	1.73498e12i	0.996735	−	3.19764i
$137$	−5.48455e11			−0.970908			−0.485454	−	0.874262i	$-0.661346\pi$
$137$	−5.48455e11			−0.970908			−0.485454	+	0.874262i	$0.661346\pi$
$138$	3.11927e12			5.30539
$139$			3.87308e11i			0.633104i	0.948575	+	0.316552i	$0.102525\pi$
$139$			3.87308e11i			0.633104i	−0.948575	+	0.316552i	$0.897475\pi$
$140$	2.00605e11			0.315238
$141$		−	1.10250e12i		−	1.66599i
$142$			8.33642e11i			1.21170i
$143$		−	5.32755e11i		−	0.745039i
$144$	−5.14165e12			−6.92004
$145$	−8.80502e10			−0.114079
$146$			1.31001e12i			1.63430i
$147$		−	1.10185e11i		−	0.132397i
$148$		−	1.79569e12i		−	2.07870i
$149$	1.14266e12			1.27465			0.637325	−	0.770595i	$-0.280041\pi$
$149$	1.14266e12			1.27465			0.637325	+	0.770595i	$0.280041\pi$
$150$			2.99692e12i			3.22236i
$151$	4.21268e9			0.00436702			0.00218351	−	0.999998i	$-0.499305\pi$
$151$	4.21268e9			0.00436702			0.00218351	+	0.999998i	$0.499305\pi$
$152$	−8.38809e10			−0.0838539
$153$	−5.71287e11	+	1.83275e12i	−0.550873	+	1.76726i
$154$	1.91242e12			1.77918
$155$	6.58221e9			0.00590945
$156$		−	4.47518e12i		−	3.87816i
$157$	5.31667e11			0.444828			0.222414	−	0.974952i	$-0.428606\pi$
$157$	5.31667e11			0.444828			0.222414	+	0.974952i	$0.428606\pi$
$158$		−	1.56067e12i		−	1.26094i
$159$		−	2.11654e12i		−	1.65175i
$160$			5.70597e11i			0.430199i
$161$	−2.31787e12			−1.68867
$162$	1.57932e12			1.11209
$163$			2.31185e12i			1.57372i	0.617129	+	0.786862i	$0.288296\pi$
$163$			2.31185e12i			1.57372i	−0.617129	+	0.786862i	$0.711704\pi$
$164$			1.49391e12i			0.983291i
$165$		−	2.61203e11i		−	0.166271i
$166$	−5.63787e12			−3.47153
$167$		−	1.44156e12i		−	0.858800i	−0.903114	−	0.429400i	$-0.858725\pi$
$167$		−	1.44156e12i		−	0.858800i	0.903114	−	0.429400i	$-0.141275\pi$
$168$	1.01875e13			5.87307
$169$	−5.26870e11			−0.293986
$170$	3.79249e11	+	1.18216e11i	0.204859	+	0.0638566i
$171$	8.86081e10			0.0463441
$172$	−5.47075e11			−0.277103
$173$			2.51650e12i			1.23465i	0.786708	+	0.617325i	$0.211784\pi$
$173$			2.51650e12i			1.23465i	−0.786708	+	0.617325i	$0.788216\pi$
$174$	−7.05106e12			−3.35146
$175$		−	2.22696e12i		−	1.02566i
$176$			7.42615e12i			3.31470i
$177$		−	3.13824e12i		−	1.35779i
$178$	1.11294e12			0.466833
$179$	4.08550e12			1.66171			0.830853	−	0.556493i	$-0.187853\pi$
$179$	4.08550e12			1.66171			0.830853	+	0.556493i	$0.187853\pi$
$180$		−	1.42456e12i		−	0.561931i
$181$		−	1.84764e12i		−	0.706945i	−0.935445	−	0.353473i	$-0.885001\pi$
$181$		−	1.84764e12i		−	0.706945i	0.935445	−	0.353473i	$-0.114999\pi$
$182$			4.54199e12i			1.68598i
$183$	−3.11152e12			−1.12071
$184$		−	1.55818e13i		−	5.44652i
$185$	2.48922e11			0.0844536
$186$	5.27103e11			0.173610
$187$	2.64707e12	+	8.25117e11i	0.846519	+	0.263868i
$188$	−8.68448e12			−2.69697
$189$	−4.94807e12			−1.49244
$190$		−	1.83355e10i		−	0.00537216i
$191$	5.72263e12			1.62897			0.814484	−	0.580187i	$-0.197020\pi$
$191$	5.72263e12			1.62897			0.814484	+	0.580187i	$0.197020\pi$
$192$			2.28723e13i			6.32634i
$193$		−	4.40121e12i		−	1.18306i	−0.806283	−	0.591530i	$-0.798524\pi$
$193$		−	4.40121e12i		−	1.18306i	0.806283	−	0.591530i	$-0.201476\pi$
$194$			1.61671e12i			0.422397i
$195$	6.20357e11			0.157562
$196$	−8.67935e11			−0.214328
$197$		−	3.95909e12i		−	0.950673i	−0.879804	−	0.475337i	$-0.842326\pi$
$197$		−	3.95909e12i		−	0.950673i	0.879804	−	0.475337i	$-0.157674\pi$
$198$		−	1.35807e13i		−	3.17149i
$199$			5.44580e12i			1.23700i	0.785785	+	0.618500i	$0.212259\pi$
$199$			5.44580e12i			1.23700i	−0.785785	+	0.618500i	$0.787741\pi$
$200$	1.49706e13			3.30808
$201$			6.73314e12i			1.44757i
$202$	2.19283e12			0.458746
$203$	5.23950e12			1.06675
$204$	2.22356e13	+	6.93105e12i	4.40639	+	1.37352i
$205$	−2.07087e11			−0.0399491
$206$	−1.09986e13			−2.06570
$207$			1.64599e13i			3.01017i
$208$	−1.76371e13			−3.14108
$209$		−	1.27978e11i		−	0.0221988i
$210$			2.22688e12i			0.376263i
$211$		−	3.99311e12i		−	0.657290i	−0.944453	−	0.328645i	$-0.893408\pi$
$211$		−	3.99311e12i		−	0.657290i	0.944453	−	0.328645i	$-0.106592\pi$
$212$	−1.66722e13			−2.67390
$213$	−6.77540e12			−1.05888
$214$			8.00090e12i			1.21861i
$215$		−	7.58364e10i		−	0.0112581i
$216$		−	3.32633e13i		−	4.81359i
$217$	−3.91680e11			−0.0552590
$218$		−	1.29412e13i		−	1.78017i
$219$	−1.06470e13			−1.42819
$220$	−2.05752e12			−0.269165
$221$	−1.95965e12	+	6.28679e12i	−0.250047	+	0.802179i
$222$	1.99337e13			2.48111
$223$	6.66835e12			0.809732			0.404866	−	0.914376i	$-0.367318\pi$
$223$	6.66835e12			0.809732			0.404866	+	0.914376i	$0.367318\pi$
$224$		−	3.39539e13i		−	4.02277i
$225$	−1.58143e13			−1.82830
$226$		−	2.22475e13i		−	2.51006i
$227$		−	3.90758e12i		−	0.430294i	−0.976582	−	0.215147i	$-0.930977\pi$
$227$		−	3.90758e12i		−	0.430294i	0.976582	−	0.215147i	$-0.0690230\pi$
$228$		−	1.07503e12i		−	0.115552i
$229$	1.42848e13			1.49892			0.749460	−	0.662049i	$-0.230313\pi$
$229$	1.42848e13			1.49892			0.749460	+	0.662049i	$0.230313\pi$
$230$	3.40603e12			0.348936
$231$			1.55431e13i			1.55479i
$232$			3.52224e13i			3.44061i
$233$			1.72881e13i			1.64927i	0.565669	+	0.824633i	$0.308618\pi$
$233$			1.72881e13i			1.64927i	−0.565669	+	0.824633i	$0.691382\pi$
$234$	3.22542e13			3.00537
$235$		−	1.20386e12i		−	0.109572i
$236$	−2.47202e13			−2.19804
$237$	1.26843e13			1.10192
$238$	−2.25676e13	−	7.03452e12i	−1.91563	−	0.597120i
$239$	7.67752e12			0.636843			0.318422	−	0.947949i	$-0.396847\pi$
$239$	7.67752e12			0.636843			0.318422	+	0.947949i	$0.396847\pi$
$240$	−8.64725e12			−0.700997
$241$			2.68821e11i			0.0212995i	0.999943	+	0.0106498i	$0.00338998\pi$
$241$			2.68821e11i			0.0212995i	−0.999943	+	0.0106498i	$0.996610\pi$
$242$	5.33342e12			0.413067
$243$		−	6.14595e12i		−	0.465323i
$244$			2.45097e13i			1.81424i
$245$		−	1.20314e11i		−	0.00870772i
$246$	−1.65836e13			−1.17364
$247$	3.03947e11			0.0210361
$248$		−	2.63306e12i		−	0.178228i
$249$		−	4.58216e13i		−	3.03371i
$250$			6.58574e12i			0.426515i
$251$	−1.08453e13			−0.687127			−0.343564	−	0.939129i	$-0.611634\pi$
$251$	−1.08453e13			−0.687127			−0.343564	+	0.939129i	$0.611634\pi$
$252$			8.47700e13i			5.25459i
$253$	2.37733e13			1.44187
$254$	−7.39984e12			−0.439174
$255$	−9.60794e11	+	3.08234e12i	−0.0558032	+	0.179023i
$256$	4.84902e13			2.75635
$257$	2.39809e13			1.33424			0.667119	−	0.744952i	$-0.267527\pi$
$257$	2.39809e13			1.33424			0.667119	+	0.744952i	$0.267527\pi$
$258$		−	6.07298e12i		−	0.330745i
$259$	−1.48123e13			−0.789722
$260$		−	4.88660e12i		−	0.255066i
$261$		−	3.72074e13i		−	1.90155i
$262$			6.16772e13i			3.08651i
$263$	−3.30607e12			−0.162015			−0.0810076	−	0.996713i	$-0.525814\pi$
$263$	−3.30607e12			−0.162015			−0.0810076	+	0.996713i	$0.525814\pi$
$264$	−1.04488e14			−5.01471
$265$		−	2.31112e12i		−	0.108635i
$266$			1.09107e12i			0.0502348i
$267$			9.04538e12i			0.407958i
$268$	5.30374e13			2.34337
$269$		−	2.12362e13i		−	0.919262i	−0.888110	−	0.459631i	$-0.847982\pi$
$269$		−	2.12362e13i		−	0.919262i	0.888110	−	0.459631i	$-0.152018\pi$
$270$	7.27103e12			0.308386
$271$	−3.67319e13			−1.52655			−0.763277	−	0.646072i	$-0.776411\pi$
$271$	−3.67319e13			−1.52655			−0.763277	+	0.646072i	$0.776411\pi$
$272$	2.73159e13	−	8.76325e13i	1.11246	−	3.56892i
$273$	−3.69149e13			−1.47335
$274$	−4.79580e13			−1.87600
$275$			2.28409e13i			0.875755i
$276$	1.99698e14			7.50539
$277$		−	3.60387e13i		−	1.32779i	−0.747825	−	0.663896i	$-0.768902\pi$
$277$		−	3.60387e13i		−	1.32779i	0.747825	−	0.663896i	$-0.231098\pi$
$278$			3.38670e13i			1.22329i
$279$			2.78145e12i			0.0985026i
$280$	1.11240e13			0.386272
$281$	−2.28769e13			−0.778954			−0.389477	−	0.921036i	$-0.627344\pi$
$281$	−2.28769e13			−0.778954			−0.389477	+	0.921036i	$0.627344\pi$
$282$		−	9.64048e13i		−	3.21906i
$283$		−	1.00818e13i		−	0.330152i	−0.986281	−	0.165076i	$-0.947213\pi$
$283$		−	1.00818e13i		−	0.330152i	0.986281	−	0.165076i	$-0.0527869\pi$
$284$			5.33703e13i			1.71415i
$285$	1.49022e11			0.00469464
$286$		−	4.65851e13i		−	1.43957i
$287$	1.23229e13			0.373562
$288$	−2.41118e14			−7.17084
$289$	−2.82018e13	−	1.94736e13i	−0.822884	−	0.568210i
$290$	−7.69928e12			−0.220425
$291$	−1.31397e13			−0.369126
$292$			8.38676e13i			2.31200i
$293$	2.33329e13			0.631243			0.315622	−	0.948885i	$-0.397787\pi$
$293$	2.33329e13			0.631243			0.315622	+	0.948885i	$0.397787\pi$
$294$		−	9.63478e12i		−	0.255818i
$295$		−	3.42675e12i		−	0.0893020i
$296$		−	9.95753e13i		−	2.54711i
$297$	5.07501e13			1.27431
$298$	9.99160e13			2.46289
$299$			5.64615e13i			1.36635i
$300$			1.91865e14i			4.55858i
$301$			4.51271e12i			0.105274i
$302$	3.68365e11			0.00843801
$303$			1.78222e13i			0.400891i
$304$	−4.23677e12			−0.0935901
$305$	−3.39757e12			−0.0737089
$306$	−4.99544e13	+	1.60260e14i	−1.06440	+	3.41473i
$307$	6.20111e13			1.29780			0.648901	−	0.760873i	$-0.275229\pi$
$307$	6.20111e13			1.29780			0.648901	+	0.760873i	$0.275229\pi$
$308$	1.22434e14			2.51695
$309$		−	8.93907e13i		−	1.80518i
$310$	5.75561e11			0.0114183
$311$			8.01732e13i			1.56260i	0.624157	+	0.781299i	$0.285442\pi$
$311$			8.01732e13i			1.56260i	−0.624157	+	0.781299i	$0.714558\pi$
$312$		−	2.48159e14i		−	4.75204i
$313$		−	7.76361e13i		−	1.46073i	−0.683057	−	0.730365i	$-0.739350\pi$
$313$		−	7.76361e13i		−	1.46073i	0.683057	−	0.730365i	$-0.260650\pi$
$314$	4.64900e13			0.859502
$315$	−1.17509e13			−0.213484
$316$		−	9.99149e13i		−	1.78382i
$317$			6.05076e13i			1.06166i	0.847480	+	0.530828i	$0.178119\pi$
$317$			6.05076e13i			1.06166i	−0.847480	+	0.530828i	$0.821881\pi$
$318$		−	1.85075e14i		−	3.19152i
$319$	−5.37392e13			−0.910841
$320$			2.49750e13i			0.416083i
$321$	−6.50271e13			−1.06492
$322$	−2.02679e14			−3.26288
$323$	−4.70746e11	+	1.51021e12i	−0.00745028	+	0.0239014i
$324$	1.01109e14			1.57324
$325$	−5.42470e13			−0.829884
$326$			2.02153e14i			3.04077i
$327$	1.05179e14			1.55567
$328$			8.28405e13i			1.20486i
$329$			7.16365e13i			1.02461i
$330$		−	2.28401e13i		−	0.321271i
$331$	−3.60613e13			−0.498870			−0.249435	−	0.968392i	$-0.580245\pi$
$331$	−3.60613e13			−0.498870			−0.249435	+	0.968392i	$0.580245\pi$
$332$	−3.60941e14			−4.91107
$333$			1.05187e14i			1.40773i
$334$		−	1.26053e14i		−	1.65938i
$335$			7.35213e12i			0.0952066i
$336$	5.14562e14			6.55499
$337$			6.26381e13i			0.785008i	0.919750	+	0.392504i	$0.128391\pi$
$337$			6.26381e13i			0.785008i	−0.919750	+	0.392504i	$0.871609\pi$
$338$	−4.60705e13			−0.568043
$339$	1.80816e14			2.19350
$340$	2.42798e13	+	7.56824e12i	0.289808	+	0.0903360i
$341$	4.01728e12			0.0471827
$342$	7.74807e12			0.0895467
$343$		−	8.41487e13i		−	0.957040i
$344$	−3.03366e13			−0.339544
$345$			2.76824e13i			0.304929i
$346$			2.20048e14i			2.38561i
$347$			3.06548e13i			0.327104i	0.986535	+	0.163552i	$0.0522952\pi$
$347$			3.06548e13i			0.327104i	−0.986535	+	0.163552i	$0.947705\pi$
$348$	−4.51414e14			−4.74121
$349$	8.68435e13			0.897837			0.448919	−	0.893573i	$-0.351809\pi$
$349$	8.68435e13			0.897837			0.448919	+	0.893573i	$0.351809\pi$
$350$		−	1.94729e14i		−	1.98179i
$351$			1.20531e14i			1.20757i
$352$			3.48249e14i			3.43483i
$353$	−8.33877e13			−0.809732			−0.404866	−	0.914376i	$-0.632682\pi$
$353$	−8.33877e13			−0.809732			−0.404866	+	0.914376i	$0.632682\pi$
$354$		−	2.74414e14i		−	2.62354i
$355$	−7.39828e12			−0.0696425
$356$	7.12512e13			0.660415
$357$	5.71729e13	−	1.83417e14i	0.521813	−	1.67404i
$358$	3.57244e14			3.21077
$359$	1.06917e14			0.946299			0.473150	−	0.880982i	$-0.343117\pi$
$359$	1.06917e14			0.946299			0.473150	+	0.880982i	$0.343117\pi$
$360$		−	7.89954e13i		−	0.688554i
$361$	−1.16417e14			−0.999373
$362$		−	1.61561e14i		−	1.36597i
$363$			4.33472e13i			0.360973i
$364$			2.90781e14i			2.38511i
$365$	−1.16259e13			−0.0939321
$366$	−2.72078e14			−2.16544
$367$		−	1.44123e14i		−	1.12998i	−0.825099	−	0.564988i	$-0.808881\pi$
$367$		−	1.44123e14i		−	1.12998i	0.825099	−	0.564988i	$-0.191119\pi$
$368$		−	7.87026e14i		−	6.07891i
$369$		−	8.75091e13i		−	0.665899i
$370$	2.17662e13			0.163182
$371$			1.37525e14i			1.01584i
$372$	3.37455e13			0.245601
$373$	8.38393e13			0.601242			0.300621	−	0.953744i	$-0.402806\pi$
$373$	8.38393e13			0.601242			0.300621	+	0.953744i	$0.402806\pi$
$374$	2.31465e14	+	7.21498e13i	1.63565	+	0.509849i
$375$	−5.35254e13			−0.372725
$376$	−4.81574e14			−3.30469
$377$		−	1.27630e14i		−	0.863131i
$378$	−4.32669e14			−2.88370
$379$			3.02187e14i			1.98500i	0.122244	+	0.992500i	$0.460991\pi$
$379$			3.02187e14i			1.98500i	−0.122244	+	0.992500i	$0.539009\pi$
$380$		−	1.17385e12i		−	0.00759984i
$381$		−	6.01420e13i		−	0.383787i
$382$	5.00398e14			3.14751
$383$	3.98382e13			0.247006			0.123503	−	0.992344i	$-0.460587\pi$
$383$	3.98382e13			0.247006			0.123503	+	0.992344i	$0.460587\pi$
$384$			9.29800e14i			5.68287i
$385$			1.69720e13i			0.102259i
$386$		−	3.84850e14i		−	2.28592i
$387$	3.20463e13			0.187658
$388$			1.03503e14i			0.597554i
$389$	2.59309e13			0.147603			0.0738013	−	0.997273i	$-0.476487\pi$
$389$	2.59309e13			0.147603			0.0738013	+	0.997273i	$0.476487\pi$
$390$	5.42452e13			0.304443
$391$	−2.80537e14	−	8.74462e13i	−1.55245	−	0.483915i
$392$	−4.81290e13			−0.262623
$393$	−5.01279e14			−2.69725
$394$		−	3.46191e14i		−	1.83690i
$395$	1.38504e13			0.0724731
$396$		−	8.69447e14i		−	4.48662i
$397$		−	3.21362e14i		−	1.63548i	−0.575584	−	0.817742i	$-0.695225\pi$
$397$		−	3.21362e14i		−	1.63548i	0.575584	−	0.817742i	$-0.304775\pi$
$398$			4.76191e14i			2.39015i
$399$	−8.86767e12			−0.0438994
$400$	7.56158e14			3.69218
$401$			2.85382e14i			1.37446i	0.726439	+	0.687231i	$0.241174\pi$
$401$			2.85382e14i			1.37446i	−0.726439	+	0.687231i	$0.758826\pi$
$402$			5.88759e14i			2.79701i
$403$			9.54103e12i			0.0447113i
$404$	1.40387e14			0.648975
$405$			1.40159e13i			0.0639174i
$406$	4.58153e14			2.06118
$407$	1.51923e14			0.674302
$408$	1.23302e15	+	3.84343e14i	5.39931	+	1.68302i
$409$	−2.43294e14			−1.05112			−0.525561	−	0.850756i	$-0.676145\pi$
$409$	−2.43294e14			−1.05112			−0.525561	+	0.850756i	$0.676145\pi$
$410$	−1.81081e13			−0.0771903
$411$		−	3.89777e14i		−	1.63941i
$412$	−7.04137e14			−2.92229
$413$			2.03912e14i			0.835058i
$414$			1.43929e15i			5.81629i
$415$		−	5.00341e13i		−	0.199527i
$416$	−8.27091e14			−3.25492
$417$	−2.75253e14			−1.06901
$418$		−	1.11906e13i		−	0.0428929i
$419$			1.85135e14i			0.700344i	0.936685	+	0.350172i	$0.113877\pi$
$419$			1.85135e14i			0.700344i	−0.936685	+	0.350172i	$0.886123\pi$
$420$			1.42567e14i			0.532288i
$421$	3.51846e14			1.29659			0.648293	−	0.761391i	$-0.275483\pi$
$421$	3.51846e14			1.29659			0.648293	+	0.761391i	$0.275483\pi$
$422$		−	3.49165e14i		−	1.27002i
$423$	5.08714e14			1.82642
$424$	−9.24511e14			−3.27642
$425$	8.40164e13	−	2.69534e14i	0.293917	−	0.942920i
$426$	−5.92454e14			−2.04598
$427$	2.02176e14			0.689248
$428$			5.12224e14i			1.72393i
$429$	3.78619e14			1.25802
$430$		−	6.63129e12i		−	0.0217531i
$431$		−	2.66064e14i		−	0.861709i	−0.902421	−	0.430855i	$-0.858212\pi$
$431$		−	2.66064e14i		−	0.861709i	0.902421	−	0.430855i	$-0.141788\pi$
$432$		−	1.68010e15i		−	5.37249i
$433$	8.93073e13			0.281970			0.140985	−	0.990012i	$-0.454973\pi$
$433$	8.93073e13			0.281970			0.140985	+	0.990012i	$0.454973\pi$
$434$	−3.42493e13			−0.106772
$435$		−	6.25757e13i		−	0.192626i
$436$		−	8.28503e14i		−	2.51836i
$437$			1.35631e13i			0.0407110i
$438$	−9.30998e14			−2.75957
$439$		−	2.16899e14i		−	0.634895i	−0.948276	−	0.317448i	$-0.897174\pi$
$439$		−	2.16899e14i		−	0.634895i	0.948276	−	0.317448i	$-0.102826\pi$
$440$	−1.14094e14			−0.329817
$441$	5.08414e13			0.145146
$442$	−1.71356e14	+	5.49729e14i	−0.483144	+	1.54998i
$443$	1.90577e14			0.530701			0.265351	−	0.964152i	$-0.414512\pi$
$443$	1.90577e14			0.530701			0.265351	+	0.964152i	$0.414512\pi$
$444$	1.27617e15			3.50995
$445$			9.87695e12i			0.0268314i
$446$	5.83093e14			1.56457
$447$			8.12065e14i			2.15228i
$448$		−	1.48616e15i		−	3.89077i
$449$			5.72125e14i			1.47957i	0.672843	+	0.739786i	$0.265073\pi$
$449$			5.72125e14i			1.47957i	−0.672843	+	0.739786i	$0.734927\pi$
$450$	−1.38284e15			−3.53266
$451$	−1.26391e14			−0.318965
$452$		−	1.42430e15i		−	3.55091i
$453$			2.99388e12i			0.00737384i
$454$		−	3.41686e14i		−	0.831419i
$455$	−4.03086e13			−0.0969024
$456$		−	5.96126e13i		−	0.141590i
$457$	3.94282e14			0.925269			0.462634	−	0.886549i	$-0.346904\pi$
$457$	3.94282e14			0.925269			0.462634	+	0.886549i	$0.346904\pi$
$458$	1.24909e15			2.89623
$459$	−5.98878e14	−	1.86676e14i	−1.37205	−	0.427680i
$460$	2.18056e14			0.493629
$461$	−1.44827e14			−0.323962			−0.161981	−	0.986794i	$-0.551788\pi$
$461$	−1.44827e14			−0.323962			−0.161981	+	0.986794i	$0.551788\pi$
$462$			1.35912e15i			3.00419i
$463$	−7.67918e14			−1.67733			−0.838667	−	0.544644i	$-0.816665\pi$
$463$	−7.67918e14			−1.67733			−0.838667	+	0.544644i	$0.816665\pi$
$464$			1.77906e15i			3.84009i
$465$			4.67786e12i			0.00997828i
$466$			1.51171e15i			3.18673i
$467$	−8.33842e14			−1.73716			−0.868582	−	0.495545i	$-0.834968\pi$
$467$	−8.33842e14			−1.73716			−0.868582	+	0.495545i	$0.834968\pi$
$468$	2.06493e15			4.25162
$469$		−	4.37495e14i		−	0.890272i
$470$		−	1.05267e14i		−	0.211717i
$471$			3.77846e14i			0.751105i
$472$	−1.37079e15			−2.69333
$473$		−	4.62848e13i		−	0.0898882i
$474$	1.10914e15			2.12914
$475$	−1.30312e13			−0.0247268
$476$	−1.44479e15	−	4.50355e14i	−2.70998	−	0.844728i
$477$	9.76613e14			1.81080
$478$	6.71338e14			1.23052
$479$		−	1.58143e14i		−	0.286553i	−0.989683	−	0.143277i	$-0.954236\pi$
$479$		−	1.58143e14i		−	0.286553i	0.989683	−	0.143277i	$-0.0457639\pi$
$480$	−4.05513e14			−0.726404
$481$			3.60817e14i			0.638982i
$482$			2.35062e13i			0.0411552i
$483$		−	1.64727e15i		−	2.85138i
$484$	3.41449e14			0.584355
$485$	−1.43477e13			−0.0242774
$486$		−	5.37414e14i		−	0.899103i
$487$		−	1.45195e13i		−	0.0240184i	−0.999928	−	0.0120092i	$-0.996177\pi$
$487$		−	1.45195e13i		−	0.0240184i	0.999928	−	0.0120092i	$-0.00382274\pi$
$488$			1.35912e15i			2.22305i
$489$	−1.64299e15			−2.65728
$490$		−	1.05205e13i		−	0.0168252i
$491$	−4.43633e14			−0.701578			−0.350789	−	0.936454i	$-0.614087\pi$
$491$	−4.43633e14			−0.701578			−0.350789	+	0.936454i	$0.614087\pi$
$492$	−1.06169e15			−1.66031
$493$	6.34151e14	+	1.97671e14i	0.980696	+	0.305692i
$494$	2.65777e13			0.0406462
$495$	1.20524e14			0.182283
$496$		−	1.32994e14i		−	0.198922i
$497$	4.40241e14			0.651224
$498$		−	4.00673e15i		−	5.86177i
$499$		−	3.98564e14i		−	0.576694i	−0.957526	−	0.288347i	$-0.906894\pi$
$499$		−	3.98564e14i		−	0.576694i	0.957526	−	0.288347i	$-0.0931056\pi$
$500$			4.21624e14i			0.603379i
$501$	1.02449e15			1.45011
$502$	−9.48337e14			−1.32768
$503$			9.95328e14i			1.37830i	0.724621	+	0.689148i	$0.242015\pi$
$503$			9.95328e14i			1.37830i	−0.724621	+	0.689148i	$0.757985\pi$
$504$			4.70069e15i			6.43863i
$505$			1.94606e13i			0.0263666i
$506$	2.07878e15			2.78600
$507$		−	3.74437e14i		−	0.496403i
$508$	−4.73743e14			−0.621287
$509$	1.65499e14			0.214707			0.107354	−	0.994221i	$-0.465762\pi$
$509$	1.65499e14			0.214707			0.107354	+	0.994221i	$0.465762\pi$
$510$	−8.40137e13	+	2.69526e14i	−0.107824	+	0.345911i
$511$	6.91807e14			0.878354
$512$	1.56064e15			1.96028
$513$			2.89539e13i			0.0359801i
$514$	2.09694e15			2.57803
$515$		−	9.76086e13i		−	0.118727i
$516$		−	3.88797e14i		−	0.467896i
$517$		−	7.34743e14i		−	0.874857i
$518$	−1.29522e15			−1.52591
$519$	−1.78843e15			−2.08474
$520$		−	2.70973e14i		−	0.312542i
$521$		−	1.14257e15i		−	1.30399i	−0.758223	−	0.651996i	$-0.773932\pi$
$521$		−	1.14257e15i		−	1.30399i	0.758223	−	0.651996i	$-0.226068\pi$
$522$		−	3.25349e15i		−	3.67419i
$523$	−8.34324e14			−0.932343			−0.466171	−	0.884694i	$-0.654367\pi$
$523$	−8.34324e14			−0.932343			−0.466171	+	0.884694i	$0.654367\pi$
$524$			3.94862e15i			4.36639i
$525$	1.58266e15			1.73185
$526$	−2.89089e14			−0.313048
$527$	−4.74061e13	−	1.47769e13i	−0.0508014	−	0.0158353i
$528$	−5.27763e15			−5.59696
$529$	−1.56669e15			−1.64429
$530$		−	2.02089e14i		−	0.209906i
$531$	1.44804e15			1.48854
$532$			6.98513e13i			0.0710658i
$533$		−	3.00177e14i		−	0.302258i
$534$			7.90946e14i			0.788261i
$535$	−7.10052e13			−0.0700397
$536$	2.94105e15			2.87142
$537$			2.90349e15i			2.80584i
$538$		−	1.85694e15i		−	1.77621i
$539$		−	7.34309e13i		−	0.0695249i
$540$	4.65496e14			0.436265
$541$			1.32863e15i			1.23260i	0.787513	+	0.616298i	$0.211368\pi$
$541$			1.32863e15i			1.23260i	−0.787513	+	0.616298i	$0.788632\pi$
$542$	−3.21191e15			−2.94963
$543$	1.31309e15			1.19370
$544$	1.28098e15	−	4.10953e15i	1.15278	−	3.69826i
$545$	1.14848e14			0.102316
$546$	−3.22791e15			−2.84683
$547$			9.15007e14i			0.798903i	0.916754	+	0.399452i	$0.130799\pi$
$547$			9.15007e14i			0.798903i	−0.916754	+	0.399452i	$0.869201\pi$
$548$	−3.07031e15			−2.65392
$549$		−	1.43572e15i		−	1.22863i
$550$			1.99725e15i			1.69215i
$551$		−	3.06593e13i		−	0.0257175i
$552$	1.10737e16			9.19661
$553$	−8.24178e14			−0.677693
$554$		−	3.15129e15i		−	2.56558i
$555$			1.76904e14i			0.142602i
$556$			2.16819e15i			1.73056i
$557$	−3.48741e14			−0.275613			−0.137806	−	0.990459i	$-0.544005\pi$
$557$	−3.48741e14			−0.275613			−0.137806	+	0.990459i	$0.544005\pi$
$558$			2.43215e14i			0.190328i
$559$	1.09926e14			0.0851799
$560$	5.61868e14			0.431122
$561$	−5.86396e14	+	1.88123e15i	−0.445549	+	1.42937i
$562$	−2.00040e15			−1.50510
$563$	6.93853e14			0.516977			0.258489	−	0.966014i	$-0.416776\pi$
$563$	6.93853e14			0.516977			0.258489	+	0.966014i	$0.416776\pi$
$564$		−	6.17190e15i		−	4.55390i
$565$	1.97439e14			0.144267
$566$		−	8.81575e14i		−	0.637924i
$567$		−	8.34030e14i		−	0.597689i
$568$			2.95951e15i			2.10041i
$569$	6.94040e14			0.487828			0.243914	−	0.969797i	$-0.421568\pi$
$569$	6.94040e14			0.487828			0.243914	+	0.969797i	$0.421568\pi$
$570$	1.30307e13			0.00907105
$571$		−	4.38968e14i		−	0.302646i	−0.988484	−	0.151323i	$-0.951647\pi$
$571$		−	4.38968e14i		−	0.302646i	0.988484	−	0.151323i	$-0.0483533\pi$
$572$		−	2.98241e15i		−	2.03652i
$573$			4.06697e15i			2.75056i
$574$	1.07754e15			0.721802
$575$		−	2.42068e15i		−	1.60607i
$576$	−1.05537e16			−6.93555
$577$	9.20213e14			0.598992			0.299496	−	0.954098i	$-0.403181\pi$
$577$	9.20213e14			0.598992			0.299496	+	0.954098i	$0.403181\pi$
$578$	−2.46602e15	−	1.70281e15i	−1.58999	−	1.09790i
$579$	3.12786e15			1.99763
$580$	−4.92913e14			−0.311829
$581$			2.97733e15i			1.86577i
$582$	−1.14896e15			−0.713230
$583$		−	1.41053e15i		−	0.867375i
$584$			4.65065e15i			2.83298i
$585$			2.86244e14i			0.172735i
$586$	2.04027e15			1.21970
$587$	−1.32763e15			−0.786261			−0.393131	−	0.919483i	$-0.628608\pi$
$587$	−1.32763e15			−0.786261			−0.393131	+	0.919483i	$0.628608\pi$
$588$		−	6.16826e14i		−	0.361899i
$589$			2.29194e12i			0.00133220i
$590$		−	2.99642e14i		−	0.172550i
$591$	2.81365e15			1.60524
$592$		−	5.02948e15i		−	2.84285i
$593$	2.49333e15			1.39630			0.698149	−	0.715952i	$-0.254007\pi$
$593$	2.49333e15			1.39630			0.698149	+	0.715952i	$0.254007\pi$
$594$	4.43769e15			2.46224
$595$	6.24289e13	−	2.00279e14i	0.0343196	−	0.110101i
$596$	6.39670e15			3.48419
$597$	−3.87023e15			−2.08871
$598$			4.93710e15i			2.64007i
$599$	−2.96255e15			−1.56971			−0.784854	−	0.619681i	$-0.787262\pi$
$599$	−2.96255e15			−1.56971			−0.784854	+	0.619681i	$0.787262\pi$
$600$			1.06394e16i			5.58578i
$601$		−	2.63903e15i		−	1.37289i	−0.727183	−	0.686444i	$-0.759171\pi$
$601$		−	2.63903e15i		−	1.37289i	0.727183	−	0.686444i	$-0.240829\pi$
$602$			3.94601e14i			0.203412i
$603$	−3.10680e15			−1.58697
$604$	2.35830e13			0.0119370
$605$			4.73322e13i			0.0237412i
$606$			1.55841e15i			0.774606i
$607$		−	2.69291e14i		−	0.132643i	−0.997798	−	0.0663215i	$-0.978874\pi$
$607$		−	2.69291e14i		−	0.132643i	0.997798	−	0.0663215i	$-0.0211263\pi$
$608$	−1.98683e14			−0.0969821
$609$			3.72362e15i			1.80124i
$610$	−2.97091e14			−0.142421
$611$	1.74501e15			0.829033
$612$	−3.19812e15	+	1.02599e16i	−1.50578	+	4.83072i
$613$	−3.63016e15			−1.69392			−0.846962	−	0.531654i	$-0.821571\pi$
$613$	−3.63016e15			−1.69392			−0.846962	+	0.531654i	$0.821571\pi$
$614$	5.42237e15			2.50763
$615$		−	1.47173e14i		−	0.0674553i
$616$	6.78927e15			3.08411
$617$		−	2.57720e15i		−	1.16033i	−0.814500	−	0.580163i	$-0.802989\pi$
$617$		−	2.57720e15i		−	1.16033i	0.814500	−	0.580163i	$-0.197011\pi$
$618$		−	7.81650e15i		−	3.48799i
$619$			3.82516e14i			0.169181i	0.996416	+	0.0845905i	$0.0269582\pi$
$619$			3.82516e14i			0.169181i	−0.996416	+	0.0845905i	$0.973042\pi$
$620$	3.68478e13			0.0161532
$621$	−5.37851e15			−2.33700
$622$			7.01050e15i			3.01927i
$623$		−	5.87737e14i		−	0.250899i
$624$		−	1.25344e16i		−	5.30380i
$625$	2.29634e15			0.963153
$626$		−	6.78865e15i		−	2.82244i
$627$	9.09516e13			0.0374834
$628$	2.97633e15			1.21591
$629$	−1.79277e15	−	5.58824e14i	−0.726017	−	0.226306i
$630$	−1.02753e15			−0.412496
$631$	1.24426e14			0.0495165			0.0247583	−	0.999693i	$-0.492118\pi$
$631$	1.24426e14			0.0495165			0.0247583	+	0.999693i	$0.492118\pi$
$632$		−	5.54051e15i		−	2.18578i
$633$	2.83783e15			1.10985
$634$			5.29090e15i			2.05134i
$635$		−	6.56710e13i		−	0.0252417i
$636$		−	1.18486e16i		−	4.51496i
$637$	1.74398e14			0.0658832
$638$	−4.69906e15			−1.75994
$639$		−	3.12630e15i		−	1.16085i
$640$			1.01528e15i			0.373762i
$641$			1.02867e15i			0.375454i	0.982221	+	0.187727i	$0.0601120\pi$
$641$			1.02867e15i			0.375454i	−0.982221	+	0.187727i	$0.939888\pi$
$642$	−5.68610e15			−2.05765
$643$			1.58681e14i			0.0569331i	0.999595	+	0.0284665i	$0.00906241\pi$
$643$			1.58681e14i			0.0569331i	−0.999595	+	0.0284665i	$0.990938\pi$
$644$	−1.29756e16			−4.61590
$645$	5.38956e13			0.0190097
$646$	−4.11629e13	+	1.32055e14i	−0.0143955	+	0.0461825i
$647$	5.69761e15			1.97569			0.987846	−	0.155435i	$-0.0496779\pi$
$647$	5.69761e15			1.97569			0.987846	+	0.155435i	$0.0496779\pi$
$648$	5.60675e15			1.92774
$649$		−	2.09143e15i		−	0.713012i
$650$	−4.74346e15			−1.60351
$651$		−	2.78360e14i		−	0.0933064i
$652$			1.29420e16i			4.30169i
$653$		−	4.07315e15i		−	1.34248i	−0.741241	−	0.671239i	$-0.765762\pi$
$653$		−	4.07315e15i		−	1.34248i	0.741241	−	0.671239i	$-0.234238\pi$
$654$	9.19705e15			3.00588
$655$	−5.47363e14			−0.177398
$656$			4.18422e15i			1.34476i
$657$		−	4.91274e15i		−	1.56572i
$658$			6.26404e15i			1.97976i
$659$	−3.28592e15			−1.02988			−0.514941	−	0.857226i	$-0.672186\pi$
$659$	−3.28592e15			−1.02988			−0.514941	+	0.857226i	$0.672186\pi$
$660$		−	1.46224e15i		−	0.454493i
$661$	6.10929e15			1.88314			0.941570	−	0.336818i	$-0.109351\pi$
$661$	6.10929e15			1.88314			0.941570	+	0.336818i	$0.109351\pi$
$662$	−3.15327e15			−0.963923
$663$	−4.46791e15	−	1.39269e15i	−1.35450	−	0.422211i
$664$	−2.00150e16			−6.01771
$665$	−9.68289e12			−0.00288726
$666$			9.19776e15i			2.72003i
$667$	5.69530e15			1.67041
$668$		−	8.06999e15i		−	2.34748i
$669$			4.73907e15i			1.36726i
$670$			6.42885e14i			0.183959i
$671$	−2.07362e15			−0.588513
$672$	2.41304e16			6.79256
$673$		−	2.62428e15i		−	0.732701i	−0.930477	−	0.366351i	$-0.880607\pi$
$673$		−	2.62428e15i		−	0.732701i	0.930477	−	0.366351i	$-0.119393\pi$
$674$			5.47720e15i			1.51680i
$675$		−	5.16756e15i		−	1.41943i
$676$	−2.94947e15			−0.803594
$677$		−	4.23839e15i		−	1.14542i	−0.819759	−	0.572709i	$-0.805893\pi$
$677$		−	4.23839e15i		−	1.14542i	0.819759	−	0.572709i	$-0.194107\pi$
$678$	1.58109e16			4.23831
$679$	8.53772e14			0.227017
$680$	1.34637e15	+	4.19677e14i	0.355112	+	0.110692i
$681$	2.77704e15			0.726564
$682$	3.51279e14			0.0911671
$683$		−	3.41052e14i		−	0.0878024i	−0.999036	−	0.0439012i	$-0.986021\pi$
$683$		−	3.41052e14i		−	0.0878024i	0.999036	−	0.0439012i	$-0.0139787\pi$
$684$	4.96037e14			0.126679
$685$		−	4.25611e14i		−	0.107824i
$686$		−	7.35813e15i		−	1.84920i
$687$			1.01519e16i			2.53097i
$688$	−1.53228e15			−0.378968
$689$	3.35002e15			0.821942
$690$			2.42060e15i			0.589188i
$691$		−	2.32757e15i		−	0.562048i	−0.959701	−	0.281024i	$-0.909326\pi$
$691$		−	2.32757e15i		−	0.562048i	0.959701	−	0.281024i	$-0.0906741\pi$
$692$			1.40876e16i			3.37485i
$693$	−7.17189e15			−1.70451
$694$			2.68051e15i			0.632035i
$695$	−3.00558e14			−0.0703091
$696$	−2.50319e16			−5.80957
$697$	1.49148e15	+	4.64907e14i	0.343428	+	0.107050i
$698$	7.59377e15			1.73481
$699$	−1.22864e16			−2.78483
$700$		−	1.24667e16i		−	2.80358i
$701$	1.12025e15			0.249957			0.124979	−	0.992159i	$-0.460114\pi$
$701$	1.12025e15			0.249957			0.124979	+	0.992159i	$0.460114\pi$
$702$			1.05395e16i			2.33327i
$703$			8.66751e13i			0.0190388i
$704$			1.52428e16i			3.32213i
$705$	8.55559e14			0.185016
$706$	−7.29158e15			−1.56457
$707$		−	1.15802e15i		−	0.246553i
$708$		−	1.75682e16i		−	3.71145i
$709$		−	3.02338e15i		−	0.633781i	−0.948462	−	0.316890i	$-0.897361\pi$
$709$		−	3.02338e15i		−	0.633781i	0.948462	−	0.316890i	$-0.102639\pi$
$710$	−6.46920e14			−0.134564
$711$			5.85276e15i			1.20803i
$712$	3.95104e15			0.809230
$713$	−4.25753e14			−0.0865297
$714$	4.99931e15	−	1.60384e16i	1.00825	−	3.23459i
$715$	4.13426e14			0.0827399
$716$	2.28710e16			4.54218
$717$			5.45628e15i			1.07533i
$718$	9.34906e15			1.82845
$719$			5.64267e15i			1.09516i	0.836755	+	0.547578i	$0.184450\pi$
$719$			5.64267e15i			1.09516i	−0.836755	+	0.547578i	$0.815550\pi$
$720$		−	3.99000e15i		−	0.768501i
$721$			5.80829e15i			1.11021i
$722$	−1.01798e16			−1.93100
$723$	−1.91046e14			−0.0359648
$724$		−	1.03433e16i		−	1.93240i
$725$			5.47192e15i			1.01457i
$726$			3.79036e15i			0.697476i
$727$	−7.89635e15			−1.44207			−0.721036	−	0.692897i	$-0.756334\pi$
$727$	−7.89635e15			−1.44207			−0.721036	+	0.692897i	$0.756334\pi$
$728$			1.61245e16i			2.92256i
$729$	7.56734e15			1.36126
$730$	−1.01659e15			−0.181497
$731$	−1.70251e14	+	5.46186e14i	−0.0301679	+	0.0967820i
$732$	−1.74186e16			−3.06339
$733$	−5.03959e15			−0.879678			−0.439839	−	0.898077i	$-0.644964\pi$
$733$	−5.03959e15			−0.879678			−0.439839	+	0.898077i	$0.644964\pi$
$734$		−	1.26024e16i		−	2.18335i
$735$	8.55053e13			0.0147032
$736$		−	3.69076e16i		−	6.29923i
$737$			4.48719e15i			0.760156i
$738$		−	7.65197e15i		−	1.28666i
$739$	−4.89231e15			−0.816525			−0.408262	−	0.912865i	$-0.633865\pi$
$739$	−4.89231e15			−0.816525			−0.408262	+	0.912865i	$0.633865\pi$
$740$	1.39349e15			0.230849
$741$			2.16010e14i			0.0355200i
$742$			1.20255e16i			1.96282i
$743$		−	1.77416e15i		−	0.287444i	−0.989618	−	0.143722i	$-0.954093\pi$
$743$		−	1.77416e15i		−	0.287444i	0.989618	−	0.143722i	$-0.0459072\pi$
$744$	1.87127e15			0.300943
$745$			8.86720e14i			0.141556i
$746$	7.33108e15			1.16173
$747$	2.11430e16			3.32585
$748$	1.48186e16	+	4.61908e15i	2.31391	+	0.721269i
$749$	4.22523e15			0.654938
$750$	−4.68037e15			−0.720183
$751$		−	8.85651e15i		−	1.35283i	−0.736521	−	0.676415i	$-0.763533\pi$
$751$		−	8.85651e15i		−	1.35283i	0.736521	−	0.676415i	$-0.236467\pi$
$752$	−2.43240e16			−3.68839
$753$		−	7.70758e15i		−	1.16023i
$754$		−	1.11603e16i		−	1.66775i
$755$			3.26911e12i			0.000484977i
$756$	−2.76998e16			−4.07949
$757$	2.96452e15			0.433438			0.216719	−	0.976234i	$-0.430464\pi$
$757$	2.96452e15			0.433438			0.216719	+	0.976234i	$0.430464\pi$
$758$			2.64239e16i			3.83544i
$759$			1.68952e16i			2.43464i
$760$		−	6.50930e13i		−	0.00931235i
$761$	3.71686e15			0.527911			0.263956	−	0.964535i	$-0.414973\pi$
$761$	3.71686e15			0.527911			0.263956	+	0.964535i	$0.414973\pi$
$762$		−	5.25893e15i		−	0.741559i
$763$	−6.83415e15			−0.956752
$764$	3.20358e16			4.45269
$765$	−1.42225e15	−	4.43328e14i	−0.196262	−	0.0611769i
$766$	3.48353e15			0.477268
$767$	4.96714e15			0.675665
$768$			3.44611e16i			4.65418i
$769$	5.69248e15			0.763320			0.381660	−	0.924303i	$-0.375353\pi$
$769$	5.69248e15			0.763320			0.381660	+	0.924303i	$0.375353\pi$
$770$			1.48407e15i			0.197585i
$771$			1.70428e16i			2.25290i
$772$		−	2.46384e16i		−	3.23383i
$773$	−2.65143e15			−0.345536			−0.172768	−	0.984963i	$-0.555271\pi$
$773$	−2.65143e15			−0.345536			−0.172768	+	0.984963i	$0.555271\pi$
$774$	2.80219e15			0.362595
$775$		−	4.09054e14i		−	0.0525559i
$776$			5.73946e15i			0.732203i
$777$		−	1.05268e16i		−	1.33347i
$778$	2.26744e15			0.285200
$779$		−	7.21083e13i		−	0.00900595i
$780$	3.47282e15			0.430687
$781$	−4.51535e15			−0.556046
$782$	−2.45307e16	−	7.64647e15i	−2.99967	−	0.935026i
$783$	1.21580e16			1.47630
$784$	−2.43096e15			−0.293116
$785$			4.12583e14i			0.0494001i
$786$	−4.38328e16			−5.21165
$787$			5.54898e15i			0.655168i	0.944822	+	0.327584i	$0.106234\pi$
$787$			5.54898e15i			0.655168i	−0.944822	+	0.327584i	$0.893766\pi$
$788$		−	2.21634e16i		−	2.59861i
$789$		−	2.34957e15i		−	0.273567i
$790$	1.21110e15			0.140034
$791$	−1.17488e16			−1.34903
$792$		−	4.82128e16i		−	5.49761i
$793$		−	4.92485e15i		−	0.557687i
$794$		−	2.81005e16i		−	3.16010i
$795$	1.64247e15			0.183434
$796$			3.04861e16i			3.38127i
$797$	−6.88125e15			−0.757961			−0.378980	−	0.925405i	$-0.623725\pi$
$797$	−6.88125e15			−0.757961			−0.378980	+	0.925405i	$0.623725\pi$
$798$	−7.75406e14			−0.0848229
$799$	−2.70263e15	+	8.67035e15i	−0.293616	+	0.941954i
$800$	3.54600e16			3.82599
$801$	−4.17371e15			−0.447243
$802$			2.49544e16i			2.65575i
$803$	−7.09554e15			−0.749981
$804$			3.76928e16i			3.95685i
$805$		−	1.79870e15i		−	0.187535i
$806$			8.34287e14i			0.0863918i
$807$	1.50922e16			1.55220
$808$	7.78476e15			0.795212
$809$		−	1.06801e16i		−	1.08357i	−0.840516	−	0.541787i	$-0.817748\pi$
$809$		−	1.06801e16i		−	1.08357i	0.840516	−	0.541787i	$-0.182252\pi$
$810$			1.22558e15i			0.123502i
$811$		−	1.34966e16i		−	1.35086i	−0.737425	−	0.675429i	$-0.763958\pi$
$811$		−	1.34966e16i		−	1.35086i	0.737425	−	0.675429i	$-0.236042\pi$
$812$	2.93313e16			2.91590
$813$		−	2.61047e16i		−	2.57763i
$814$	1.32844e16			1.30289
$815$	−1.79404e15			−0.174769
$816$	6.22789e16	+	1.94129e16i	6.02622	+	1.87843i
$817$	2.64064e13			0.00253798
$818$	−2.12741e16			−2.03099
$819$		−	1.70332e16i		−	1.61523i
$820$	−1.15930e15			−0.109199
$821$			5.23105e15i			0.489442i	0.969594	+	0.244721i	$0.0786964\pi$
$821$			5.23105e15i			0.489442i	−0.969594	+	0.244721i	$0.921304\pi$
$822$		−	3.40829e16i		−	3.16768i
$823$			3.90932e15i			0.360913i	0.983583	+	0.180456i	$0.0577575\pi$
$823$			3.90932e15i			0.360913i	−0.983583	+	0.180456i	$0.942243\pi$
$824$	−3.90460e16			−3.58078
$825$	−1.62326e16			−1.47874
$826$			1.78304e16i			1.61351i
$827$			1.11877e16i			1.00568i	0.864380	+	0.502839i	$0.167711\pi$
$827$			1.11877e16i			1.00568i	−0.864380	+	0.502839i	$0.832289\pi$
$828$			9.21442e16i			8.22813i
$829$	−1.20287e16			−1.06701			−0.533507	−	0.845795i	$-0.679126\pi$
$829$	−1.20287e16			−1.06701			−0.533507	+	0.845795i	$0.679126\pi$
$830$		−	4.37508e15i		−	0.385529i
$831$	2.56120e16			2.24202
$832$	−3.62017e16			−3.14812
$833$	−2.70104e14	+	8.66523e14i	−0.0233337	+	0.0748570i
$834$	−2.40687e16			−2.06556
$835$	1.11867e15			0.0953736
$836$		−	7.16432e14i		−	0.0606793i
$837$	−9.08877e14			−0.0764742
$838$			1.61886e16i			1.35321i
$839$			2.17271e16i			1.80431i	0.431415	+	0.902154i	$0.358015\pi$
$839$			2.17271e16i			1.80431i	−0.431415	+	0.902154i	$0.641985\pi$
$840$			7.90565e15i			0.652231i
$841$	−6.73632e14			−0.0552134
$842$	3.07661e16			2.50528
$843$		−	1.62582e16i		−	1.31529i
$844$		−	2.23538e16i		−	1.79667i
$845$		−	4.08860e14i		−	0.0326484i
$846$	4.44830e16			3.52904
$847$		−	2.81654e15i		−	0.222003i
$848$	−4.66964e16			−3.65684
$849$	7.16497e15			0.557471
$850$	7.34656e15	−	2.35686e16i	0.567911	−	1.82192i
$851$	−1.61009e16			−1.23662
$852$	−3.79293e16			−2.89439
$853$			4.57654e15i			0.346991i	0.984835	+	0.173495i	$0.0555062\pi$
$853$			4.57654e15i			0.346991i	−0.984835	+	0.173495i	$0.944494\pi$
$854$	1.76786e16			1.33177
$855$			6.87614e13i			0.00514672i
$856$			2.84040e16i			2.11239i
$857$		−	6.83638e14i		−	0.0505163i	−0.999681	−	0.0252582i	$-0.991959\pi$
$857$		−	6.83638e14i		−	0.0505163i	0.999681	−	0.0252582i	$-0.00804078\pi$
$858$	3.31072e16			2.43076
$859$	−7.45499e15			−0.543857			−0.271928	−	0.962317i	$-0.587661\pi$
$859$	−7.45499e15			−0.543857			−0.271928	+	0.962317i	$0.587661\pi$
$860$		−	4.24540e14i		−	0.0307735i
$861$			8.75768e15i			0.630771i
$862$		−	2.32651e16i		−	1.66501i
$863$	1.57976e15			0.112339			0.0561695	−	0.998421i	$-0.482111\pi$
$863$	1.57976e15			0.112339			0.0561695	+	0.998421i	$0.482111\pi$
$864$		−	7.87885e16i		−	5.56721i
$865$	−1.95285e15			−0.137113
$866$	7.80921e15			0.544827
$867$	1.38396e16	−	2.00425e16i	0.959439	−	1.38946i
$868$	−2.19266e15			−0.151047
$869$	8.45322e15			0.578646
$870$		−	5.47174e15i		−	0.372194i
$871$	−1.06571e16			−0.720340
$872$		−	4.59424e16i		−	3.08584i
$873$		−	6.06291e15i		−	0.404672i
$874$			1.18599e15i			0.0786624i
$875$	3.47789e15			0.229230
$876$	−5.96032e16			−3.90388
$877$		−	1.11556e16i		−	0.726098i	−0.931770	−	0.363049i	$-0.881736\pi$
$877$		−	1.11556e16i		−	0.726098i	0.931770	−	0.363049i	$-0.118264\pi$
$878$		−	1.89660e16i		−	1.22675i
$879$			1.65823e16i			1.06587i
$880$	−5.76282e15			−0.368112
$881$			1.88073e16i			1.19388i	0.802287	+	0.596939i	$0.203617\pi$
$881$			1.88073e16i			1.19388i	−0.802287	+	0.596939i	$0.796383\pi$
$882$	4.44567e15			0.280453
$883$	−1.99716e15			−0.125207			−0.0626036	−	0.998038i	$-0.519940\pi$
$883$	−1.99716e15			−0.125207			−0.0626036	+	0.998038i	$0.519940\pi$
$884$	−1.09703e16	+	3.51940e16i	−0.683489	+	2.19271i
$885$	2.43533e15			0.150789
$886$	1.66644e16			1.02543
$887$			4.16074e15i			0.254443i	0.991874	+	0.127221i	$0.0406059\pi$
$887$			4.16074e15i			0.254443i	−0.991874	+	0.127221i	$0.959394\pi$
$888$	7.07664e16			4.30086
$889$			3.90781e15i			0.236034i
$890$			8.63660e14i			0.0518439i
$891$			8.55427e15i			0.510335i
$892$	3.73301e16			2.21336
$893$	4.19185e14			0.0247015
$894$			7.10085e16i			4.15867i
$895$			3.17042e15i			0.184540i
$896$		−	6.04151e16i		−	3.49503i
$897$	−4.01262e16			−2.30712
$898$			5.00277e16i			2.85885i
$899$	9.62408e14			0.0546614
$900$	−8.85302e16			−4.99756
$901$	−5.18842e15	+	1.66451e16i	−0.291105	+	0.933897i
$902$	−1.10518e16			−0.616309
$903$	−3.20711e15			−0.177759
$904$		−	7.89807e16i		−	4.35106i
$905$	1.43380e15			0.0785094
$906$			2.61790e14i			0.0142478i
$907$		−	1.41265e16i		−	0.764179i	−0.924125	−	0.382089i	$-0.875205\pi$
$907$		−	1.41265e16i		−	0.764179i	0.924125	−	0.382089i	$-0.124795\pi$
$908$		−	2.18750e16i		−	1.17618i
$909$	−8.22348e15			−0.439496
$910$	−3.52466e15			−0.187236
$911$			1.02000e15i			0.0538580i	0.999637	+	0.0269290i	$0.00857281\pi$
$911$			1.02000e15i			0.0538580i	−0.999637	+	0.0269290i	$0.991427\pi$
$912$		−	3.01099e15i		−	0.158030i
$913$		−	3.05371e16i		−	1.59308i
$914$	3.44768e16			1.78782
$915$		−	2.41459e15i		−	0.124460i
$916$	7.99676e16			4.09722
$917$	3.25713e16			1.65884
$918$	−5.23670e16	−	1.63233e16i	−2.65108	−	0.826368i
$919$	1.55500e16			0.782517			0.391259	−	0.920281i	$-0.372040\pi$
$919$	1.55500e16			0.782517			0.391259	+	0.920281i	$0.372040\pi$
$920$	1.20917e16			0.604861
$921$			4.40702e16i			2.19138i
$922$	−1.26639e16			−0.625963
$923$		−	1.07239e16i		−	0.526921i
$924$			8.70119e16i			4.24994i
$925$		−	1.54694e16i		−	0.751091i
$926$	−6.71483e16			−3.24097
$927$	4.12465e16			1.97901
$928$			8.34291e16i			3.97927i
$929$		−	2.75600e16i		−	1.30675i	−0.757035	−	0.653375i	$-0.773353\pi$
$929$		−	2.75600e16i		−	1.30675i	0.757035	−	0.653375i	$-0.226647\pi$
$930$			4.09041e14i			0.0192802i
$931$	4.18938e13			0.00196303
$932$			9.67807e16i			4.50818i
$933$	−5.69777e16			−2.63849
$934$	−7.29128e16			−3.35657
$935$	−6.40305e14	+	2.05417e15i	−0.0293037	+	0.0940097i
$936$	1.14505e17			5.20965
$937$	−6.15835e15			−0.278546			−0.139273	−	0.990254i	$-0.544477\pi$
$937$	−6.15835e15			−0.278546			−0.139273	+	0.990254i	$0.544477\pi$
$938$		−	3.82554e16i		−	1.72019i
$939$	5.51746e16			2.46648
$940$		−	6.73930e15i		−	0.299510i
$941$			1.33247e16i			0.588726i	0.955694	+	0.294363i	$0.0951074\pi$
$941$			1.33247e16i			0.588726i	−0.955694	+	0.294363i	$0.904893\pi$
$942$			3.30396e16i			1.45129i
$943$	1.33949e16			0.584959
$944$	−6.92377e16			−3.00605
$945$		−	3.83978e15i		−	0.165742i
$946$		−	4.04724e15i		−	0.173683i
$947$			3.47558e16i			1.48287i	0.671025	+	0.741435i	$0.265854\pi$
$947$			3.47558e16i			1.48287i	−0.671025	+	0.741435i	$0.734146\pi$
$948$	7.10077e16			3.01203
$949$		−	1.68519e16i		−	0.710697i
$950$	−1.13947e15			−0.0477775
$951$	−4.30016e16			−1.79264
$952$	−8.01170e16	−	2.49732e16i	−3.32064	−	1.03507i
$953$	4.19978e16			1.73067			0.865337	−	0.501190i	$-0.167104\pi$
$953$	4.19978e16			1.73067			0.865337	+	0.501190i	$0.167104\pi$
$954$	8.53969e16			3.49886
$955$			4.44086e15i			0.180904i
$956$	4.29795e16			1.74078
$957$		−	3.81915e16i		−	1.53798i
$958$		−	1.38284e16i		−	0.553682i
$959$			2.53263e16i			1.00825i
$960$	−1.77493e16			−0.702569
$961$	2.53365e16			0.997168
$962$			3.15505e16i			1.23465i
$963$		−	3.00047e16i		−	1.16747i
$964$			1.50489e15i			0.0582210i
$965$	3.41541e15			0.131384
$966$		−	1.44040e17i		−	5.50946i
$967$	−2.58759e16			−0.984124			−0.492062	−	0.870560i	$-0.663757\pi$
$967$	−2.58759e16			−0.984124			−0.492062	+	0.870560i	$0.663757\pi$
$968$	1.89341e16			0.716030
$969$	−1.07328e15	−	3.34551e14i	−0.0403581	−	0.0125800i
$970$	−1.25459e15			−0.0469091
$971$	−5.07676e15			−0.188747			−0.0943736	−	0.995537i	$-0.530085\pi$
$971$	−5.07676e15			−0.188747			−0.0943736	+	0.995537i	$0.530085\pi$
$972$		−	3.44056e16i		−	1.27194i
$973$	1.78849e16			0.657456
$974$		−	1.26962e15i		−	0.0464086i
$975$		−	3.85524e16i		−	1.40128i
$976$			6.86482e16i			2.48116i
$977$	−2.41379e15			−0.0867518			−0.0433759	−	0.999059i	$-0.513811\pi$
$977$	−2.41379e15			−0.0867518			−0.0433759	+	0.999059i	$0.513811\pi$
$978$	−1.43667e17			−5.13443
$979$			6.02814e15i			0.214229i
$980$		−	6.73532e14i		−	0.0238021i
$981$			4.85315e16i			1.70547i
$982$	−3.87922e16			−1.35560
$983$		−	6.20708e15i		−	0.215696i	−0.994167	−	0.107848i	$-0.965604\pi$
$983$		−	6.20708e15i		−	0.215696i	0.994167	−	0.107848i	$-0.0343960\pi$
$984$	−5.88733e16			−2.03444
$985$	3.07232e15			0.105577
$986$	5.54514e16	+	1.72847e16i	1.89491	+	0.590663i
$987$	−5.09108e16			−1.73008
$988$	1.70153e15			0.0575010
$989$			4.90528e15i			0.164848i
$990$	1.05389e16			0.352209
$991$		−	4.22406e15i		−	0.140386i	−0.997533	−	0.0701931i	$-0.977638\pi$
$991$		−	4.22406e15i		−	0.140386i	0.997533	−	0.0701931i	$-0.0223616\pi$
$992$		−	6.23675e15i		−	0.206131i
$993$		−	2.56281e16i		−	0.842356i
$994$	3.84955e16			1.25830
$995$	−4.22603e15			−0.137374
$996$		−	2.56514e17i		−	8.29248i
$997$		−	2.05807e16i		−	0.661663i	−0.943690	−	0.330831i	$-0.892671\pi$
$997$		−	2.05807e16i		−	0.661663i	0.943690	−	0.330831i	$-0.107329\pi$
$998$		−	3.48512e16i		−	1.11430i
$999$	−3.43713e16			−1.09291

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	17.12.b.a.16.16	yes	16
3.2	odd	2		153.12.d.b.118.1		16
4.3	odd	2		272.12.b.c.33.2		16
17.16	even	2	inner	17.12.b.a.16.15	✓	16
51.50	odd	2		153.12.d.b.118.2		16
68.67	odd	2		272.12.b.c.33.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.12.b.a.16.15	✓	16	17.16	even	2	inner
17.12.b.a.16.16	yes	16	1.1	even	1	trivial
153.12.d.b.118.1		16	3.2	odd	2
153.12.d.b.118.2		16	51.50	odd	2
272.12.b.c.33.2		16	4.3	odd	2
272.12.b.c.33.15		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)

\(f(q)\)	\(=\)	\(q+87.4420 q^{2} +710.682i q^{3} +5598.10 q^{4} +776.017i q^{5} +62143.4i q^{6} -46177.6i q^{7} +310427. q^{8} -327922. q^{9} +O(q^{10})\)	\(q+87.4420 q^{2} +710.682i q^{3} +5598.10 q^{4} +776.017i q^{5} +62143.4i q^{6} -46177.6i q^{7} +310427. q^{8} -327922. q^{9} +67856.4i q^{10} +473622. i q^{11} +3.97847e6i q^{12} -1.12485e6 q^{13} -4.03786e6i q^{14} -551501. q^{15} +1.56795e7 q^{16} +(1.74214e6 - 5.58899e6i) q^{17} -2.86741e7 q^{18} -270211. q^{19} +4.34422e6i q^{20} +3.28176e7 q^{21} +4.14144e7i q^{22} -5.01946e7i q^{23} +2.20615e8i q^{24} +4.82259e7 q^{25} -9.83592e7 q^{26} -1.07153e8i q^{27} -2.58506e8i q^{28} +1.13464e8i q^{29} -4.82244e7 q^{30} -8.48204e6i q^{31} +7.35289e8 q^{32} -3.36595e8 q^{33} +(1.52336e8 - 4.88712e8i) q^{34} +3.58346e7 q^{35} -1.83574e9 q^{36} -3.20768e8i q^{37} -2.36278e7 q^{38} -7.99412e8i q^{39} +2.40897e8i q^{40} +2.66859e8i q^{41} +2.86963e9 q^{42} -9.77253e7 q^{43} +2.65138e9i q^{44} -2.54473e8i q^{45} -4.38912e9i q^{46} -1.55133e9 q^{47} +1.11431e10i q^{48} -1.55041e8 q^{49} +4.21697e9 q^{50} +(3.97200e9 + 1.23811e9i) q^{51} -6.29703e9 q^{52} -2.97819e9 q^{53} -9.36968e9i q^{54} -3.67539e8 q^{55} -1.43348e10i q^{56} -1.92034e8i q^{57} +9.92154e9i q^{58} -4.41582e9 q^{59} -3.08736e9 q^{60} +4.37822e9i q^{61} -7.41686e8i q^{62} +1.51426e10i q^{63} +3.21836e10 q^{64} -8.72904e8i q^{65} -2.94325e10 q^{66} +9.47419e9 q^{67} +(9.75268e9 - 3.12877e10i) q^{68} +3.56724e10 q^{69} +3.13345e9 q^{70} +9.53366e9i q^{71} -1.01796e11 q^{72} +1.49814e10i q^{73} -2.80486e10i q^{74} +3.42733e10i q^{75} -1.51267e9 q^{76} +2.18707e10 q^{77} -6.99021e10i q^{78} -1.78480e10i q^{79} +1.21675e10i q^{80} +1.80614e10 q^{81} +2.33347e10i q^{82} -6.44756e10 q^{83} +1.83716e11 q^{84} +(4.33715e9 + 1.35193e9i) q^{85} -8.54529e9 q^{86} -8.06370e10 q^{87} +1.47025e11i q^{88} +1.27278e10 q^{89} -2.22516e10i q^{90} +5.19429e10i q^{91} -2.80994e11i q^{92} +6.02803e9 q^{93} -1.35651e11 q^{94} -2.09688e8i q^{95} +5.22557e11i q^{96} +1.84889e10i q^{97} -1.35571e10 q^{98} -1.55311e11i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 20338 q^{4} - 4098 q^{8} - 1191496 q^{9}+O(q^{10}) \) 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

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