LMFDB - Embedded newform 8.15.d.b.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,15,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$9.94631745215$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 4349 x^{10} - 33891 x^{9} + 12151288 x^{8} - 474141530 x^{7} + 82897017850 x^{6} + \cdots + 37\!\cdots\!50 $ x^12 - x^11 + 4349x^10 - 33891x^9 + 12151288x^8 - 474141530x^7 + 82897017850x^6 - 1813403462870x^5 + 371618750972305x^4 - 24344904673267125x^3 + 1896685485375873305x^2 - 84437535339775221175x + 3788457560343891547750
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{66}\cdot 3^{6}\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.12
Root			$50.2622 + 24.1659i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.15.d.b.3.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(118.524 + 48.3317i) q^{2} -1152.97 q^{3} +(11712.1 + 11457.0i) q^{4} -9668.61i q^{5} +(-136655. - 55725.2i) q^{6} +1.34658e6i q^{7} +(834433. + 1.92400e6i) q^{8} -3.45362e6 q^{9} +O(q^{10})$	\(q+(118.524 + 48.3317i) q^{2} -1152.97 q^{3} +(11712.1 + 11457.0i) q^{4} -9668.61i q^{5} +(-136655. - 55725.2i) q^{6} +1.34658e6i q^{7} +(834433. + 1.92400e6i) q^{8} -3.45362e6 q^{9} +(467301. - 1.14597e6i) q^{10} -897115. q^{11} +(-1.35037e7 - 1.32096e7i) q^{12} +5.37757e7i q^{13} +(-6.50826e7 + 1.59603e8i) q^{14} +1.11476e7i q^{15} +(5.91058e6 + 2.68370e8i) q^{16} -1.06550e8 q^{17} +(-4.09339e8 - 1.66920e8i) q^{18} +9.74607e8 q^{19} +(1.10773e8 - 1.13240e8i) q^{20} -1.55257e9i q^{21} +(-1.06330e8 - 4.33591e7i) q^{22} -4.91613e9i q^{23} +(-9.62079e8 - 2.21832e9i) q^{24} +6.01003e9 q^{25} +(-2.59907e9 + 6.37373e9i) q^{26} +9.49657e9 q^{27} +(-1.54277e10 + 1.57713e10i) q^{28} -1.32148e10i q^{29} +(-5.38785e8 + 1.32127e9i) q^{30} -3.03739e8i q^{31} +(-1.22703e10 + 3.20941e10i) q^{32} +1.03435e9 q^{33} +(-1.26288e10 - 5.14974e9i) q^{34} +1.30196e10 q^{35} +(-4.04491e10 - 3.95681e10i) q^{36} +7.87376e10i q^{37} +(1.15515e11 + 4.71044e10i) q^{38} -6.20019e10i q^{39} +(1.86024e10 - 8.06781e9i) q^{40} -2.80442e11 q^{41} +(7.50384e10 - 1.84018e11i) q^{42} +3.24393e11 q^{43} +(-1.05071e10 - 1.02782e10i) q^{44} +3.33917e10i q^{45} +(2.37605e11 - 5.82682e11i) q^{46} +2.85501e10i q^{47} +(-6.81474e9 - 3.09424e11i) q^{48} -1.13506e12 q^{49} +(7.12336e11 + 2.90475e11i) q^{50} +1.22849e11 q^{51} +(-6.16107e11 + 6.29826e11i) q^{52} +2.31690e12i q^{53} +(1.12558e12 + 4.58985e11i) q^{54} +8.67386e9i q^{55} +(-2.59082e12 + 1.12363e12i) q^{56} -1.12370e12 q^{57} +(6.38693e11 - 1.56627e12i) q^{58} +3.41902e12 q^{59} +(-1.27718e11 + 1.30562e11i) q^{60} -5.23972e12i q^{61} +(1.46802e10 - 3.60005e10i) q^{62} -4.65058e12i q^{63} +(-3.00549e12 + 3.21089e12i) q^{64} +5.19936e11 q^{65} +(1.22596e11 + 4.99919e10i) q^{66} +7.72604e12 q^{67} +(-1.24792e12 - 1.22074e12i) q^{68} +5.66817e12i q^{69} +(1.54314e12 + 6.29258e11i) q^{70} -5.57201e12i q^{71} +(-2.88182e12 - 6.64476e12i) q^{72} -4.34932e12 q^{73} +(-3.80552e12 + 9.33232e12i) q^{74} -6.92940e12 q^{75} +(1.14147e13 + 1.11661e13i) q^{76} -1.20804e12i q^{77} +(2.99666e12 - 7.34874e12i) q^{78} +2.63814e13i q^{79} +(2.59477e12 - 5.71471e10i) q^{80} +5.56929e12 q^{81} +(-3.32393e13 - 1.35543e13i) q^{82} -3.06972e13 q^{83} +(1.77878e13 - 1.81838e13i) q^{84} +1.03019e12i q^{85} +(3.84486e13 + 1.56785e13i) q^{86} +1.52363e13i q^{87} +(-7.48583e11 - 1.72605e12i) q^{88} +3.63245e13 q^{89} +(-1.61388e12 + 3.95774e12i) q^{90} -7.24133e13 q^{91} +(5.63241e13 - 5.75782e13i) q^{92} +3.50203e11i q^{93} +(-1.37988e12 + 3.38389e12i) q^{94} -9.42310e12i q^{95} +(1.41473e13 - 3.70036e13i) q^{96} +7.63764e13 q^{97} +(-1.34532e14 - 5.48592e13i) q^{98} +3.09830e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9}+O(q^{10}) $ 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9} - 14533440 q^{10} - 28256720 q^{11} + 34920024 q^{12} + 191568384 q^{14} - 185822448 q^{16} + 270339544 q^{17} + 1420811358 q^{18} - 2481505872 q^{19} - 1679371200 q^{20} + 3042383484 q^{22} + 7581335184 q^{24} - 15857276820 q^{25} - 2773507776 q^{26} - 16574868000 q^{27} + 25329333120 q^{28} + 42207767040 q^{30} + 38309251808 q^{32} - 136227597840 q^{33} + 350437044 q^{34} + 149949623040 q^{35} - 150590403492 q^{36} + 102789916636 q^{38} - 66999085440 q^{40} + 264287409880 q^{41} - 110343609600 q^{42} + 32253127344 q^{43} - 585547356392 q^{44} + 864780977664 q^{46} - 2387663418144 q^{48} - 646589230644 q^{49} - 388785556630 q^{50} + 4755867895776 q^{51} + 798005307840 q^{52} + 1305053764344 q^{54} - 1050155264256 q^{56} - 7479401742480 q^{57} + 389204742720 q^{58} + 1223083947184 q^{59} + 4350689397120 q^{60} + 9957296947200 q^{62} - 16809671099328 q^{64} - 8069319822720 q^{65} - 6067132925784 q^{66} - 9309378171216 q^{67} + 32301846360616 q^{68} + 35197935521280 q^{70} - 43695386222808 q^{72} + 3619334364696 q^{73} - 55499920147776 q^{74} + 9079078926000 q^{75} + 33532610502360 q^{76} + 92515055193600 q^{78} - 86826189154560 q^{80} + 56467107312444 q^{81} - 146233962574956 q^{82} - 18774355695824 q^{83} + 186893160787200 q^{84} + 96253393476220 q^{86} - 166888683024624 q^{88} + 54781416936088 q^{89} - 488020221650880 q^{90} + 36699395136768 q^{91} + 413167093560960 q^{92} + 496016398930944 q^{94} - 616114307580864 q^{96} + 73839238696536 q^{97} - 523654870565638 q^{98} - 223606851712368 q^{99}+O(q^{100}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9 - 14533440 * q^10 - 28256720 * q^11 + 34920024 * q^12 + 191568384 * q^14 - 185822448 * q^16 + 270339544 * q^17 + 1420811358 * q^18 - 2481505872 * q^19 - 1679371200 * q^20 + 3042383484 * q^22 + 7581335184 * q^24 - 15857276820 * q^25 - 2773507776 * q^26 - 16574868000 * q^27 + 25329333120 * q^28 + 42207767040 * q^30 + 38309251808 * q^32 - 136227597840 * q^33 + 350437044 * q^34 + 149949623040 * q^35 - 150590403492 * q^36 + 102789916636 * q^38 - 66999085440 * q^40 + 264287409880 * q^41 - 110343609600 * q^42 + 32253127344 * q^43 - 585547356392 * q^44 + 864780977664 * q^46 - 2387663418144 * q^48 - 646589230644 * q^49 - 388785556630 * q^50 + 4755867895776 * q^51 + 798005307840 * q^52 + 1305053764344 * q^54 - 1050155264256 * q^56 - 7479401742480 * q^57 + 389204742720 * q^58 + 1223083947184 * q^59 + 4350689397120 * q^60 + 9957296947200 * q^62 - 16809671099328 * q^64 - 8069319822720 * q^65 - 6067132925784 * q^66 - 9309378171216 * q^67 + 32301846360616 * q^68 + 35197935521280 * q^70 - 43695386222808 * q^72 + 3619334364696 * q^73 - 55499920147776 * q^74 + 9079078926000 * q^75 + 33532610502360 * q^76 + 92515055193600 * q^78 - 86826189154560 * q^80 + 56467107312444 * q^81 - 146233962574956 * q^82 - 18774355695824 * q^83 + 186893160787200 * q^84 + 96253393476220 * q^86 - 166888683024624 * q^88 + 54781416936088 * q^89 - 488020221650880 * q^90 + 36699395136768 * q^91 + 413167093560960 * q^92 + 496016398930944 * q^94 - 616114307580864 * q^96 + 73839238696536 * q^97 - 523654870565638 * q^98 - 223606851712368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	118.524	+	48.3317i	0.925972	+	0.377592i
$2$	118.524	+	48.3317i	0.925972	+	0.377592i
$3$	−1152.97			−0.527194			−0.263597	−	0.964633i	$-0.584909\pi$
$3$	−1152.97			−0.527194			−0.263597	+	0.964633i	$0.584909\pi$
$4$	11712.1	+	11457.0i	0.714849	+	0.699279i
$5$		−	9668.61i		−	0.123758i	−0.998084	−	0.0618791i	$-0.980291\pi$
$5$		−	9668.61i		−	0.123758i	0.998084	−	0.0618791i	$-0.0197093\pi$
$6$	−136655.	−	55725.2i	−0.488167	−	0.199064i
$7$			1.34658e6i			1.63511i	0.575853	+	0.817553i	$0.304670\pi$
$7$			1.34658e6i			1.63511i	−0.575853	+	0.817553i	$0.695330\pi$
$8$	834433.	+	1.92400e6i	0.397889	+	0.917434i
$9$	−3.45362e6			−0.722067
$10$	467301.	−	1.14597e6i	0.0467301	−	0.114597i
$11$	−897115.			−0.0460362			−0.0230181	−	0.999735i	$-0.507328\pi$
$11$	−897115.			−0.0460362			−0.0230181	+	0.999735i	$0.507328\pi$
$12$	−1.35037e7	−	1.32096e7i	−0.376864	−	0.368655i
$13$			5.37757e7i			0.857003i	0.903541	+	0.428502i	$0.140958\pi$
$13$			5.37757e7i			0.857003i	−0.903541	+	0.428502i	$0.859042\pi$
$14$	−6.50826e7	+	1.59603e8i	−0.617402	+	1.51406i
$15$			1.11476e7i			0.0652446i
$16$	5.91058e6	+	2.68370e8i	0.0220186	+	0.999758i
$17$	−1.06550e8			−0.259663			−0.129832	−	0.991536i	$-0.541444\pi$
$17$	−1.06550e8			−0.259663			−0.129832	+	0.991536i	$0.541444\pi$
$18$	−4.09339e8	−	1.66920e8i	−0.668614	−	0.272646i
$19$	9.74607e8			1.09032			0.545160	−	0.838332i	$-0.316469\pi$
$19$	9.74607e8			1.09032			0.545160	+	0.838332i	$0.316469\pi$
$20$	1.10773e8	−	1.13240e8i	0.0865415	−	0.0884685i
$21$		−	1.55257e9i		−	0.862018i
$22$	−1.06330e8	−	4.33591e7i	−0.0426282	−	0.0173829i
$23$		−	4.91613e9i		−	1.44387i	−0.691960	−	0.721936i	$-0.743252\pi$
$23$		−	4.91613e9i		−	1.44387i	0.691960	−	0.721936i	$-0.256748\pi$
$24$	−9.62079e8	−	2.21832e9i	−0.209764	−	0.483665i
$25$	6.01003e9			0.984684
$26$	−2.59907e9	+	6.37373e9i	−0.323597	+	0.793561i
$27$	9.49657e9			0.907863
$28$	−1.54277e10	+	1.57713e10i	−1.14340	+	1.16885i
$29$		−	1.32148e10i		−	0.766079i	−0.923732	−	0.383040i	$-0.874877\pi$
$29$		−	1.32148e10i		−	0.766079i	0.923732	−	0.383040i	$-0.125123\pi$
$30$	−5.38785e8	+	1.32127e9i	−0.0246358	+	0.0604147i
$31$		−	3.03739e8i		−	0.0110400i	−0.999985	−	0.00552000i	$-0.998243\pi$
$31$		−	3.03739e8i		−	0.0110400i	0.999985	−	0.00552000i	$-0.00175708\pi$
$32$	−1.22703e10	+	3.20941e10i	−0.357111	+	0.934062i
$33$	1.03435e9			0.0242700
$34$	−1.26288e10	−	5.14974e9i	−0.240441	−	0.0980466i
$35$	1.30196e10			0.202358
$36$	−4.04491e10	−	3.95681e10i	−0.516169	−	0.504926i
$37$			7.87376e10i			0.829411i	0.909956	+	0.414706i	$0.136115\pi$
$37$			7.87376e10i			0.829411i	−0.909956	+	0.414706i	$0.863885\pi$
$38$	1.15515e11	+	4.71044e10i	1.00961	+	0.411696i
$39$		−	6.20019e10i		−	0.451807i
$40$	1.86024e10	−	8.06781e9i	0.113540	−	0.0492420i
$41$	−2.80442e11			−1.43998			−0.719991	−	0.693984i	$-0.755854\pi$
$41$	−2.80442e11			−1.43998			−0.719991	+	0.693984i	$0.755854\pi$
$42$	7.50384e10	−	1.84018e11i	0.325491	−	0.798205i
$43$	3.24393e11			1.19342			0.596709	−	0.802457i	$-0.296475\pi$
$43$	3.24393e11			1.19342			0.596709	+	0.802457i	$0.296475\pi$
$44$	−1.05071e10	−	1.02782e10i	−0.0329089	−	0.0321921i
$45$			3.33917e10i			0.0893617i
$46$	2.37605e11	−	5.82682e11i	0.545194	−	1.33699i
$47$			2.85501e10i			0.0563538i	0.999603	+	0.0281769i	$0.00897017\pi$
$47$			2.85501e10i			0.0563538i	−0.999603	+	0.0281769i	$0.991030\pi$
$48$	−6.81474e9	−	3.09424e11i	−0.0116081	−	0.527066i
$49$	−1.13506e12			−1.67357
$50$	7.12336e11	+	2.90475e11i	0.911790	+	0.371808i
$51$	1.22849e11			0.136893
$52$	−6.16107e11	+	6.29826e11i	−0.599284	+	0.612628i
$53$			2.31690e12i			1.97231i	0.165815	+	0.986157i	$0.446974\pi$
$53$			2.31690e12i			1.97231i	−0.165815	+	0.986157i	$0.553026\pi$
$54$	1.12558e12	+	4.58985e11i	0.840656	+	0.342801i
$55$			8.67386e9i			0.00569736i
$56$	−2.59082e12	+	1.12363e12i	−1.50010	+	0.650590i
$57$	−1.12370e12			−0.574810
$58$	6.38693e11	−	1.56627e12i	0.289265	−	0.709368i
$59$	3.41902e12			1.37385			0.686923	−	0.726730i	$-0.258961\pi$
$59$	3.41902e12			1.37385			0.686923	+	0.726730i	$0.258961\pi$
$60$	−1.27718e11	+	1.30562e11i	−0.0456241	+	0.0466400i
$61$		−	5.23972e12i		−	1.66724i	−0.552336	−	0.833622i	$-0.686263\pi$
$61$		−	5.23972e12i		−	1.66724i	0.552336	−	0.833622i	$-0.313737\pi$
$62$	1.46802e10	−	3.60005e10i	0.00416861	−	0.0102227i
$63$		−	4.65058e12i		−	1.18066i
$64$	−3.00549e12	+	3.21089e12i	−0.683369	+	0.730073i
$65$	5.19936e11			0.106061
$66$	1.22596e11	+	4.99919e10i	0.0224733	+	0.00916415i
$67$	7.72604e12			1.27477			0.637387	−	0.770544i	$-0.280015\pi$
$67$	7.72604e12			1.27477			0.637387	+	0.770544i	$0.280015\pi$
$68$	−1.24792e12	−	1.22074e12i	−0.185620	−	0.181577i
$69$			5.66817e12i			0.761200i
$70$	1.54314e12	+	6.29258e11i	0.187378	+	0.0764086i
$71$		−	5.57201e12i		−	0.612637i	−0.951929	−	0.306319i	$-0.900903\pi$
$71$		−	5.57201e12i		−	0.612637i	0.951929	−	0.306319i	$-0.0990973\pi$
$72$	−2.88182e12	−	6.64476e12i	−0.287302	−	0.662448i
$73$	−4.34932e12			−0.393697			−0.196848	−	0.980434i	$-0.563071\pi$
$73$	−4.34932e12			−0.393697			−0.196848	+	0.980434i	$0.563071\pi$
$74$	−3.80552e12	+	9.33232e12i	−0.313179	+	0.768012i
$75$	−6.92940e12			−0.519119
$76$	1.14147e13	+	1.11661e13i	0.779415	+	0.762438i
$77$		−	1.20804e12i		−	0.0752741i
$78$	2.99666e12	−	7.34874e12i	0.170598	−	0.418361i
$79$			2.63814e13i			1.37375i	0.726776	+	0.686875i	$0.241018\pi$
$79$			2.63814e13i			1.37375i	−0.726776	+	0.686875i	$0.758982\pi$
$80$	2.59477e12	−	5.71471e10i	0.123728	−	0.00272499i
$81$	5.56929e12			0.243447
$82$	−3.32393e13	−	1.35543e13i	−1.33338	−	0.543725i
$83$	−3.06972e13			−1.13123			−0.565617	−	0.824668i	$-0.691362\pi$
$83$	−3.06972e13			−1.13123			−0.565617	+	0.824668i	$0.691362\pi$
$84$	1.77878e13	−	1.81838e13i	0.602791	−	0.616213i
$85$			1.03019e12i			0.0321354i
$86$	3.84486e13	+	1.56785e13i	1.10507	+	0.450625i
$87$			1.52363e13i			0.403872i
$88$	−7.48583e11	−	1.72605e12i	−0.0183173	−	0.0422352i
$89$	3.63245e13			0.821239			0.410619	−	0.911807i	$-0.365313\pi$
$89$	3.63245e13			0.821239			0.410619	+	0.911807i	$0.365313\pi$
$90$	−1.61388e12	+	3.95774e12i	−0.0337422	+	0.0827465i
$91$	−7.24133e13			−1.40129
$92$	5.63241e13	−	5.75782e13i	1.00967	−	1.03215i
$93$			3.50203e11i			0.00582021i
$94$	−1.37988e12	+	3.38389e12i	−0.0212787	+	0.0521821i
$95$		−	9.42310e12i		−	0.134936i
$96$	1.41473e13	−	3.70036e13i	0.188267	−	0.492432i
$97$	7.63764e13			0.945272			0.472636	−	0.881258i	$-0.343302\pi$
$97$	7.63764e13			0.945272			0.472636	+	0.881258i	$0.343302\pi$
$98$	−1.34532e14	−	5.48592e13i	−1.54968	−	0.631927i
$99$	3.09830e12			0.0332412
$100$	7.03900e13	+	6.88568e13i	0.703900	+	0.688568i
$101$		−	1.59872e14i		−	1.49116i	−0.666417	−	0.745579i	$-0.732173\pi$
$101$		−	1.59872e14i		−	1.49116i	0.666417	−	0.745579i	$-0.267827\pi$
$102$	1.45606e13	+	5.93751e12i	0.126759	+	0.0516896i
$103$			2.68602e13i			0.218398i	0.994020	+	0.109199i	$0.0348286\pi$
$103$			2.68602e13i			0.218398i	−0.994020	+	0.109199i	$0.965171\pi$
$104$	−1.03464e14	+	4.48722e13i	−0.786244	+	0.340992i
$105$	−1.50112e13			−0.106682
$106$	−1.11980e14	+	2.74609e14i	−0.744729	+	1.82631i
$107$	1.18086e14			0.735383			0.367692	−	0.929948i	$-0.380148\pi$
$107$	1.18086e14			0.735383			0.367692	+	0.929948i	$0.380148\pi$
$108$	1.11225e14	+	1.08802e14i	0.648985	+	0.634849i
$109$			2.30519e14i			1.26102i	0.776183	+	0.630508i	$0.217153\pi$
$109$			2.30519e14i			1.26102i	−0.776183	+	0.630508i	$0.782847\pi$
$110$	−4.19223e11	+	1.02806e12i	−0.00215127	+	0.00527560i
$111$		−	9.07822e13i		−	0.437260i
$112$	−3.61382e14	+	7.95907e12i	−1.63471	+	0.0360028i
$113$	1.10695e14			0.470523			0.235261	−	0.971932i	$-0.424405\pi$
$113$	1.10695e14			0.470523			0.235261	+	0.971932i	$0.424405\pi$
$114$	−1.33185e14	−	5.43101e13i	−0.532258	−	0.217044i
$115$	−4.75322e13			−0.178691
$116$	1.51401e14	−	1.54773e14i	0.535703	−	0.547631i
$117$		−	1.85721e14i		−	0.618814i
$118$	4.05238e14	+	1.65247e14i	1.27214	+	0.518753i
$119$		−	1.43478e14i		−	0.424577i
$120$	−2.14480e13	+	9.30196e12i	−0.0598576	+	0.0259601i
$121$	−3.78945e14			−0.997881
$122$	2.53245e14	−	6.21035e14i	0.629537	−	1.54382i
$123$	3.23343e14			0.759149
$124$	3.47993e12	−	3.55742e12i	0.00772003	−	0.00789193i
$125$		−	1.17121e14i		−	0.245621i
$126$	2.24771e14	−	5.51208e14i	0.445806	−	1.09325i
$127$			1.93111e14i			0.362394i	0.983447	+	0.181197i	$0.0579972\pi$
$127$			1.93111e14i			0.362394i	−0.983447	+	0.181197i	$0.942003\pi$
$128$	−5.11412e14	+	2.35309e14i	−0.908450	+	0.417993i
$129$	−3.74017e14			−0.629163
$130$	6.16252e13	+	2.51294e13i	0.0982097	+	0.0400478i
$131$	1.90547e14			0.287809			0.143904	−	0.989592i	$-0.454034\pi$
$131$	1.90547e14			0.287809			0.143904	+	0.989592i	$0.454034\pi$
$132$	1.21144e13	+	1.18505e13i	0.0173494	+	0.0169715i
$133$			1.31239e15i			1.78279i
$134$	9.15724e14	+	3.73413e14i	1.18041	+	0.481344i
$135$		−	9.18186e13i		−	0.112355i
$136$	−8.89087e13	−	2.05002e14i	−0.103317	−	0.238224i
$137$	−1.05935e15			−1.16949			−0.584744	−	0.811218i	$-0.698805\pi$
$137$	−1.05935e15			−1.16949			−0.584744	+	0.811218i	$0.698805\pi$
$138$	−2.73952e14	+	6.71816e14i	−0.287423	+	0.704851i
$139$	−2.27377e14			−0.226800			−0.113400	−	0.993549i	$-0.536174\pi$
$139$	−2.27377e14			−0.226800			−0.113400	+	0.993549i	$0.536174\pi$
$140$	1.52486e14	+	1.49165e14i	0.144655	+	0.141505i
$141$		−	3.29175e13i		−	0.0297094i
$142$	2.69305e14	−	6.60419e14i	0.231327	−	0.567285i
$143$		−	4.82430e13i		−	0.0394532i
$144$	−2.04129e13	−	9.26850e14i	−0.0158989	−	0.721892i
$145$	−1.27769e14			−0.0948086
$146$	−5.15501e14	−	2.10210e14i	−0.364552	−	0.148657i
$147$	1.30869e15			0.882297
$148$	−9.02095e14	+	9.22181e14i	−0.579990	+	0.592904i
$149$		−	1.33781e14i		−	0.0820520i	−0.999158	−	0.0410260i	$-0.986937\pi$
$149$		−	1.33781e14i		−	0.0820520i	0.999158	−	0.0410260i	$-0.0130626\pi$
$150$	−8.21304e14	−	3.34910e14i	−0.480690	−	0.196015i
$151$			4.96646e14i			0.277465i	0.990330	+	0.138732i	$0.0443028\pi$
$151$			4.96646e14i			0.277465i	−0.990330	+	0.138732i	$0.955697\pi$
$152$	8.13244e14	+	1.87514e15i	0.433826	+	1.00030i
$153$	3.67983e14			0.187494
$154$	5.83866e13	−	1.43182e14i	0.0284229	−	0.0697017i
$155$	−2.93673e12			−0.00136629
$156$	7.10355e14	−	7.26172e14i	0.315939	−	0.322974i
$157$		−	3.46838e15i		−	1.47512i	−0.675279	−	0.737562i	$-0.735977\pi$
$157$		−	3.46838e15i		−	1.47512i	0.675279	−	0.737562i	$-0.264023\pi$
$158$	−1.27506e15	+	3.12684e15i	−0.518716	+	1.27205i
$159$		−	2.67132e15i		−	1.03979i
$160$	3.10306e14	+	1.18636e14i	0.115598	+	0.0441955i
$161$	6.61997e15			2.36089
$162$	6.60097e14	+	2.69173e14i	0.225425	+	0.0919236i
$163$	−2.37354e15			−0.776395			−0.388198	−	0.921576i	$-0.626902\pi$
$163$	−2.37354e15			−0.776395			−0.388198	+	0.921576i	$0.626902\pi$
$164$	−3.28457e15	−	3.21302e15i	−1.02937	−	1.00695i
$165$		−	1.00007e13i		−	0.00300361i
$166$	−3.63837e15	−	1.48365e15i	−1.04749	−	0.427144i
$167$		−	2.99177e14i		−	0.0825872i	−0.999147	−	0.0412936i	$-0.986852\pi$
$167$		−	2.99177e14i		−	0.0825872i	0.999147	−	0.0412936i	$-0.0131479\pi$
$168$	2.98714e15	−	1.29552e15i	0.790844	−	0.342987i
$169$	1.04555e15			0.265545
$170$	−4.97908e13	+	1.22103e14i	−0.0121341	+	0.0297565i
$171$	−3.36593e15			−0.787284
$172$	3.79932e15	+	3.71657e15i	0.853114	+	0.834532i
$173$			5.36115e14i			0.115594i	0.998328	+	0.0577970i	$0.0184076\pi$
$173$			5.36115e14i			0.115594i	−0.998328	+	0.0577970i	$0.981592\pi$
$174$	−7.36396e14	+	1.80587e15i	−0.152499	+	0.373975i
$175$			8.09299e15i			1.61006i
$176$	−5.30247e12	−	2.40759e14i	−0.00101365	−	0.0460250i
$177$	−3.94204e15			−0.724283
$178$	4.30534e15	+	1.75563e15i	0.760444	+	0.310093i
$179$	−4.72352e15			−0.802222			−0.401111	−	0.916029i	$-0.631376\pi$
$179$	−4.72352e15			−0.802222			−0.401111	+	0.916029i	$0.631376\pi$
$180$	−3.82569e14	+	3.91087e14i	−0.0624887	+	0.0638801i
$181$		−	6.84548e14i		−	0.107561i	−0.998553	−	0.0537804i	$-0.982873\pi$
$181$		−	6.84548e14i		−	0.107561i	0.998553	−	0.0537804i	$-0.0171271\pi$
$182$	−8.58275e15	−	3.49986e15i	−1.29756	−	0.529116i
$183$			6.04125e15i			0.878960i
$184$	9.45863e15	−	4.10218e15i	1.32466	−	0.574500i
$185$	7.61283e14			0.102646
$186$	−1.69259e13	+	4.15076e13i	−0.00219766	+	0.00538936i
$187$	9.55875e13			0.0119539
$188$	−3.27098e14	+	3.34382e14i	−0.0394070	+	0.0402845i
$189$			1.27879e16i			1.48445i
$190$	4.55435e14	−	1.11687e15i	0.0509508	−	0.124947i
$191$		−	9.51417e15i		−	1.02598i	−0.858396	−	0.512988i	$-0.828538\pi$
$191$		−	9.51417e15i		−	1.02598i	0.858396	−	0.512988i	$-0.171462\pi$
$192$	3.46525e15	−	3.70207e15i	0.360268	−	0.384890i
$193$	−2.64607e13			−0.00265277			−0.00132638	−	0.999999i	$-0.500422\pi$
$193$	−2.64607e13			−0.00265277			−0.00132638	+	0.999999i	$0.500422\pi$
$194$	9.05247e15	+	3.69140e15i	0.875296	+	0.356927i
$195$	−5.99472e14			−0.0559148
$196$	−1.32939e16	−	1.30043e16i	−1.19635	−	1.17029i
$197$		−	1.52214e16i		−	1.32188i	−0.750440	−	0.660938i	$-0.770158\pi$
$197$		−	1.52214e16i		−	1.32188i	0.750440	−	0.660938i	$-0.229842\pi$
$198$	3.67224e14	+	1.49746e14i	0.0307804	+	0.0125516i
$199$		−	1.33076e16i		−	1.07678i	−0.842695	−	0.538392i	$-0.819032\pi$
$199$		−	1.33076e16i		−	1.07678i	0.842695	−	0.538392i	$-0.180968\pi$
$200$	5.01497e15	+	1.15633e16i	0.391795	+	0.903382i
$201$	−8.90791e15			−0.672053
$202$	7.72690e15	−	1.89488e16i	0.563049	−	1.38077i
$203$	1.77948e16			1.25262
$204$	1.43882e15	+	1.40748e15i	0.0978577	+	0.0957262i
$205$			2.71149e15i			0.178210i
$206$	−1.29820e15	+	3.18359e15i	−0.0824652	+	0.202230i
$207$			1.69785e16i			1.04257i
$208$	−1.44318e16	+	3.17845e14i	−0.856796	+	0.0188700i
$209$	−8.74335e14			−0.0501942
$210$	−1.77919e15	−	7.25517e14i	−0.0987844	−	0.0402822i
$211$	7.12307e15			0.382551			0.191276	−	0.981536i	$-0.438738\pi$
$211$	7.12307e15			0.382551			0.191276	+	0.981536i	$0.438738\pi$
$212$	−2.65447e16	+	2.71357e16i	−1.37920	+	1.40991i
$213$			6.42437e15i			0.322978i
$214$	1.39961e16	+	5.70732e15i	0.680944	+	0.277675i
$215$		−	3.13643e15i		−	0.147695i
$216$	7.92425e15	+	1.82714e16i	0.361228	+	0.832904i
$217$	4.09009e14			0.0180516
$218$	−1.11414e16	+	2.73221e16i	−0.476149	+	1.16767i
$219$	5.01465e15			0.207554
$220$	−9.93763e13	+	1.01589e14i	−0.00398404	+	0.00407275i
$221$		−	5.72979e15i		−	0.222532i
$222$	4.38766e15	−	1.07599e16i	0.165106	−	0.404891i
$223$		−	3.96105e16i		−	1.44436i	−0.691704	−	0.722181i	$-0.743140\pi$
$223$		−	3.96105e16i		−	1.44436i	0.691704	−	0.722181i	$-0.256860\pi$
$224$	−4.32173e16	−	1.65229e16i	−1.52729	−	0.583915i
$225$	−2.07564e16			−0.711008
$226$	1.31201e16	+	5.35010e15i	0.435691	+	0.177665i
$227$	3.32499e16			1.07056			0.535278	−	0.844676i	$-0.320207\pi$
$227$	3.32499e16			1.07056			0.535278	+	0.844676i	$0.320207\pi$
$228$	−1.31608e16	−	1.28742e16i	−0.410903	−	0.401953i
$229$			2.75324e16i			0.833672i	0.908982	+	0.416836i	$0.136861\pi$
$229$			2.75324e16i			0.833672i	−0.908982	+	0.416836i	$0.863139\pi$
$230$	−5.63373e15	−	2.29731e15i	−0.165463	−	0.0674723i
$231$			1.39283e15i			0.0396840i
$232$	2.54252e16	−	1.10268e16i	0.702827	−	0.304814i
$233$	1.51187e16			0.405529			0.202765	−	0.979227i	$-0.435007\pi$
$233$	1.51187e16			0.405529			0.202765	+	0.979227i	$0.435007\pi$
$234$	8.97621e15	−	2.20125e16i	0.233659	−	0.573004i
$235$	2.76040e14			0.00697425
$236$	4.00439e16	+	3.91717e16i	0.982093	+	0.960701i
$237$		−	3.04170e16i		−	0.724232i
$238$	6.93453e15	−	1.70056e16i	0.160317	−	0.393146i
$239$			2.42808e16i			0.545101i	0.962141	+	0.272551i	$0.0878672\pi$
$239$			2.42808e16i			0.545101i	−0.962141	+	0.272551i	$0.912133\pi$
$240$	−2.99170e15	+	6.58890e13i	−0.0652287	+	0.00143660i
$241$	−5.40577e16			−1.14482			−0.572411	−	0.819967i	$-0.693992\pi$
$241$	−5.40577e16			−1.14482			−0.572411	+	0.819967i	$0.693992\pi$
$242$	−4.49142e16	−	1.83151e16i	−0.924010	−	0.376791i
$243$	−5.18430e16			−1.03621
$244$	6.00313e16	−	6.13680e16i	1.16587	−	1.19183i
$245$			1.09744e16i			0.207118i
$246$	3.83240e16	+	1.56277e16i	0.702951	+	0.286648i
$247$			5.24102e16i			0.934409i
$248$	5.84393e14	−	2.53450e14i	0.0101285	−	0.00439269i
$249$	3.53930e16			0.596379
$250$	5.66067e15	−	1.38817e16i	0.0927444	−	0.227438i
$251$	−1.67557e16			−0.266960			−0.133480	−	0.991052i	$-0.542615\pi$
$251$	−1.67557e16			−0.266960			−0.133480	+	0.991052i	$0.542615\pi$
$252$	5.32816e16	−	5.44680e16i	0.825608	−	0.843991i
$253$			4.41034e15i			0.0664704i
$254$	−9.33339e15	+	2.28884e16i	−0.136837	+	0.335567i
$255$		−	1.18778e15i		−	0.0169416i
$256$	−7.19877e16	+	3.17245e15i	−0.999030	+	0.0440266i
$257$	7.49407e16			1.01201			0.506006	−	0.862530i	$-0.331121\pi$
$257$	7.49407e16			1.01201			0.506006	+	0.862530i	$0.331121\pi$
$258$	−4.43301e16	−	1.80769e16i	−0.582587	−	0.237567i
$259$	−1.06026e17			−1.35618
$260$	6.08954e15	+	5.95690e15i	0.0758178	+	0.0741663i
$261$			4.56389e16i			0.553161i
$262$	2.25845e16	+	9.20948e15i	0.266503	+	0.108674i
$263$		−	5.38423e16i		−	0.618634i	−0.950959	−	0.309317i	$-0.899900\pi$
$263$		−	5.38423e16i		−	0.618634i	0.950959	−	0.309317i	$-0.100100\pi$
$264$	8.63095e14	+	1.99009e15i	0.00965676	+	0.0222661i
$265$	2.24012e16			0.244090
$266$	−6.34299e16	+	1.55550e17i	−0.673167	+	1.65081i
$267$	−4.18811e16			−0.432952
$268$	9.04881e16	+	8.85171e16i	0.911271	+	0.891422i
$269$		−	9.47522e16i		−	0.929658i	−0.885400	−	0.464829i	$-0.846116\pi$
$269$		−	9.47522e16i		−	0.929658i	0.885400	−	0.464829i	$-0.153884\pi$
$270$	4.43775e15	−	1.08827e16i	0.0424245	−	0.104038i
$271$			1.74807e17i			1.62845i	0.580552	+	0.814223i	$0.302837\pi$
$271$			1.74807e17i			1.62845i	−0.580552	+	0.814223i	$0.697163\pi$
$272$	−6.29771e14	−	2.85948e16i	−0.00571742	−	0.259600i
$273$	8.34906e16			0.738752
$274$	−1.25559e17	−	5.12003e16i	−1.08291	−	0.441589i
$275$	−5.39169e15			−0.0453311
$276$	−6.49401e16	+	6.63861e16i	−0.532291	+	0.544144i
$277$		−	7.80617e16i		−	0.623849i	−0.950107	−	0.311925i	$-0.899026\pi$
$277$		−	7.80617e16i		−	0.623849i	0.950107	−	0.311925i	$-0.100974\pi$
$278$	−2.69497e16	−	1.09895e16i	−0.210010	−	0.0856376i
$279$			1.04900e15i			0.00797161i
$280$	1.08640e16	+	2.50496e16i	0.0805159	+	0.185650i
$281$	1.10986e17			0.802280			0.401140	−	0.916017i	$-0.368614\pi$
$281$	1.10986e17			0.802280			0.401140	+	0.916017i	$0.368614\pi$
$282$	1.59096e15	−	3.90153e15i	0.0112180	−	0.0275101i
$283$	1.95794e17			1.34677			0.673386	−	0.739291i	$-0.264839\pi$
$283$	1.95794e17			1.34677			0.673386	+	0.739291i	$0.264839\pi$
$284$	6.38384e16	−	6.52598e16i	0.428404	−	0.437943i
$285$			1.08646e16i			0.0711375i
$286$	2.33167e15	−	5.71797e15i	0.0148972	−	0.0365326i
$287$		−	3.77638e17i		−	2.35452i
$288$	4.23768e16	−	1.10841e17i	0.257858	−	0.674455i
$289$	−1.57025e17			−0.932575
$290$	−1.51437e16	−	6.17527e15i	−0.0877902	−	0.0357989i
$291$	−8.80599e16			−0.498342
$292$	−5.09397e16	−	4.98301e16i	−0.281434	−	0.275304i
$293$		−	1.92545e17i		−	1.03863i	−0.854584	−	0.519313i	$-0.826188\pi$
$293$		−	1.92545e17i		−	1.03863i	0.854584	−	0.519313i	$-0.173812\pi$
$294$	1.55112e17	+	6.32512e16i	0.816983	+	0.333148i
$295$		−	3.30572e16i		−	0.170025i
$296$	−1.51491e17	+	6.57012e16i	−0.760930	+	0.330013i
$297$	−8.51952e15			−0.0417946
$298$	6.46585e15	−	1.58563e16i	0.0309821	−	0.0759779i
$299$	2.64368e17			1.23740
$300$	−8.11578e16	−	7.93901e16i	−0.371092	−	0.363009i
$301$			4.36822e17i			1.95137i
$302$	−2.40037e16	+	5.88646e16i	−0.104768	+	0.256925i
$303$			1.84328e17i			0.786129i
$304$	5.76049e15	+	2.61556e17i	0.0240074	+	1.09006i
$305$	−5.06608e16			−0.206335
$306$	4.36150e16	+	1.77852e16i	0.173614	+	0.0707962i
$307$	−6.14199e16			−0.238968			−0.119484	−	0.992836i	$-0.538124\pi$
$307$	−6.14199e16			−0.238968			−0.119484	+	0.992836i	$0.538124\pi$
$308$	1.38405e16	−	1.41486e16i	0.0526376	−	0.0538096i
$309$		−	3.09691e16i		−	0.115138i
$310$	−3.48075e14	−	1.41937e14i	−0.00126515	−	0.000515900i
$311$			2.78857e17i			0.990967i	0.868617	+	0.495483i	$0.165009\pi$
$311$			2.78857e17i			0.990967i	−0.868617	+	0.495483i	$0.834991\pi$
$312$	1.19292e17	−	5.17364e16i	0.414503	−	0.179769i
$313$	−5.39882e17			−1.83438			−0.917188	−	0.398454i	$-0.869547\pi$
$313$	−5.39882e17			−1.83438			−0.917188	+	0.398454i	$0.869547\pi$
$314$	1.67633e17	−	4.11087e17i	0.556995	−	1.36592i
$315$	−4.49647e16			−0.146116
$316$	−3.02251e17	+	3.08981e17i	−0.960634	+	0.982024i
$317$			1.21764e17i			0.378534i	0.981926	+	0.189267i	$0.0606111\pi$
$317$			1.21764e17i			0.378534i	−0.981926	+	0.189267i	$0.939389\pi$
$318$	1.29110e17	−	3.16617e17i	0.392617	−	0.962818i
$319$			1.18552e16i			0.0352674i
$320$	3.10449e16	+	2.90589e16i	0.0903525	+	0.0845726i
$321$	−1.36150e17			−0.387689
$322$	7.84628e17	+	3.19955e17i	2.18611	+	0.891450i
$323$	−1.03844e17			−0.283116
$324$	6.52280e16	+	6.38073e16i	0.174028	+	0.170237i
$325$			3.23194e17i			0.843877i
$326$	−2.81322e17	−	1.14717e17i	−0.718921	−	0.293160i
$327$		−	2.65782e17i		−	0.664800i
$328$	−2.34010e17	−	5.39571e17i	−0.572952	−	1.32109i
$329$	−3.84451e16			−0.0921445
$330$	4.83352e14	−	1.18533e15i	0.00113414	−	0.00278126i
$331$	3.71696e17			0.853871			0.426935	−	0.904282i	$-0.359593\pi$
$331$	3.71696e17			0.853871			0.426935	+	0.904282i	$0.359593\pi$
$332$	−3.59528e17	−	3.51697e17i	−0.808661	−	0.791047i
$333$		−	2.71930e17i		−	0.598890i
$334$	1.44597e16	−	3.54598e16i	0.0311843	−	0.0764735i
$335$		−	7.47001e16i		−	0.157764i
$336$	4.16664e17	−	9.17659e15i	0.861809	−	0.0189804i
$337$	3.91380e17			0.792848			0.396424	−	0.918068i	$-0.370251\pi$
$337$	3.91380e17			0.792848			0.396424	+	0.918068i	$0.370251\pi$
$338$	1.23923e17	+	5.05333e16i	0.245888	+	0.100268i
$339$	−1.27629e17			−0.248057
$340$	−1.18029e16	+	1.20657e16i	−0.0224716	+	0.0229720i
$341$			2.72489e14i			0.000508239i
$342$	−3.98944e17	−	1.62681e17i	−0.729004	−	0.297272i
$343$		−	6.15162e17i		−	1.10136i
$344$	2.70685e17	+	6.24132e17i	0.474848	+	1.09488i
$345$	5.48033e16			0.0942048
$346$	−2.59114e16	+	6.35427e16i	−0.0436473	+	0.107037i
$347$	3.64414e17			0.601573			0.300787	−	0.953691i	$-0.402751\pi$
$347$	3.64414e17			0.601573			0.300787	+	0.953691i	$0.402751\pi$
$348$	−1.74562e17	+	1.78449e17i	−0.282419	+	0.288708i
$349$		−	8.34394e17i		−	1.32310i	−0.749901	−	0.661551i	$-0.769899\pi$
$349$		−	8.34394e17i		−	1.32310i	0.749901	−	0.661551i	$-0.230101\pi$
$350$	−3.91148e17	+	9.59218e17i	−0.607946	+	1.49087i
$351$			5.10684e17i			0.778041i
$352$	1.10078e16	−	2.87921e16i	0.0164401	−	0.0430007i
$353$	2.08881e17			0.305827			0.152914	−	0.988240i	$-0.451134\pi$
$353$	2.08881e17			0.305827			0.152914	+	0.988240i	$0.451134\pi$
$354$	−4.67228e17	−	1.90526e17i	−0.670666	−	0.273483i
$355$	−5.38736e16			−0.0758189
$356$	4.25436e17	+	4.16169e17i	0.587062	+	0.574275i
$357$			1.65426e17i			0.223834i
$358$	−5.59853e17	−	2.28296e17i	−0.742836	−	0.302912i
$359$			7.02144e17i			0.913618i	0.889565	+	0.456809i	$0.151008\pi$
$359$			7.02144e17i			0.913618i	−0.889565	+	0.456809i	$0.848992\pi$
$360$	−6.42456e16	+	2.78632e16i	−0.0819834	+	0.0355560i
$361$	1.50852e17			0.188800
$362$	3.30854e16	−	8.11356e16i	0.0406140	−	0.0995982i
$363$	4.36913e17			0.526076
$364$	−8.48111e17	−	8.29638e17i	−1.00171	−	0.979893i
$365$			4.20519e16i			0.0487232i
$366$	−2.91984e17	+	7.16036e17i	−0.331888	+	0.813893i
$367$		−	1.00579e18i		−	1.12162i	−0.827944	−	0.560811i	$-0.810490\pi$
$367$		−	1.00579e18i		−	1.12162i	0.827944	−	0.560811i	$-0.189510\pi$
$368$	1.31934e18	−	2.90572e16i	1.44352	−	0.0317921i
$369$	9.68543e17			1.03976
$370$	9.02306e16	+	3.67941e16i	0.0950478	+	0.0387584i
$371$	−3.11989e18			−3.22494
$372$	−4.01227e15	+	4.10161e15i	−0.00406995	+	0.00416058i
$373$			2.57669e17i			0.256507i	0.991741	+	0.128254i	$0.0409372\pi$
$373$			2.57669e17i			0.256507i	−0.991741	+	0.128254i	$0.959063\pi$
$374$	1.13295e16	+	4.61991e15i	0.0110690	+	0.00451369i
$375$			1.35038e17i			0.129490i
$376$	−5.49304e16	+	2.38232e16i	−0.0517009	+	0.0224225i
$377$	7.10634e17			0.656533
$378$	−6.18061e17	+	1.51568e18i	−0.560517	+	1.37456i
$379$	1.19914e18			1.06757			0.533783	−	0.845622i	$-0.320770\pi$
$379$	1.19914e18			1.06757			0.533783	+	0.845622i	$0.320770\pi$
$380$	1.07960e17	−	1.10364e17i	0.0943580	−	0.0964590i
$381$		−	2.22652e17i		−	0.191052i
$382$	4.59836e17	−	1.12766e18i	0.387400	−	0.950026i
$383$			1.73787e18i			1.43756i	0.695236	+	0.718781i	$0.255300\pi$
$383$			1.73787e18i			1.43756i	−0.695236	+	0.718781i	$0.744700\pi$
$384$	5.89644e17	−	2.71305e17i	0.478929	−	0.220363i
$385$	−1.16801e16			−0.00931579
$386$	−3.13623e15	−	1.27889e15i	−0.00245639	−	0.00100166i
$387$	−1.12033e18			−0.861728
$388$	8.94527e17	+	8.75043e17i	0.675727	+	0.661009i
$389$		−	1.90052e17i		−	0.141002i	−0.997512	−	0.0705010i	$-0.977540\pi$
$389$		−	1.90052e17i		−	0.141002i	0.997512	−	0.0705010i	$-0.0224598\pi$
$390$	−7.10521e16	−	2.89735e16i	−0.0517756	−	0.0211130i
$391$			5.23813e17i			0.374920i
$392$	−9.47128e17	−	2.18385e18i	−0.665896	−	1.53539i
$393$	−2.19696e17			−0.151731
$394$	7.35677e17	−	1.80411e18i	0.499130	−	1.22402i
$395$	2.55071e17			0.170013
$396$	3.62875e16	+	3.54971e16i	0.0237625	+	0.0232449i
$397$		−	1.09062e18i		−	0.701682i	−0.936435	−	0.350841i	$-0.885896\pi$
$397$		−	1.09062e18i		−	0.701682i	0.936435	−	0.350841i	$-0.114104\pi$
$398$	6.43180e17	−	1.57728e18i	0.406584	−	0.997072i
$399$		−	1.51315e18i		−	0.939876i
$400$	3.55228e16	+	1.61291e18i	0.0216814	+	0.984445i
$401$	−9.97128e17			−0.598054			−0.299027	−	0.954245i	$-0.596662\pi$
$401$	−9.97128e17			−0.598054			−0.299027	+	0.954245i	$0.596662\pi$
$402$	−1.05581e18	−	4.30535e17i	−0.622302	−	0.253762i
$403$	1.63338e16			0.00946131
$404$	1.83165e18	−	1.87244e18i	1.04273	−	1.06595i
$405$		−	5.38473e16i		−	0.0301286i
$406$	2.10911e18	+	8.60051e17i	1.15989	+	0.472979i
$407$		−	7.06367e16i		−	0.0381829i
$408$	1.02509e17	+	2.36361e17i	0.0544681	+	0.125590i
$409$	−1.66884e18			−0.871670			−0.435835	−	0.900027i	$-0.643547\pi$
$409$	−1.66884e18			−0.871670			−0.435835	+	0.900027i	$0.643547\pi$
$410$	−1.31051e17	+	3.21378e17i	−0.0672904	+	0.165017i
$411$	1.22140e18			0.616547
$412$	−3.07737e17	+	3.14589e17i	−0.152721	+	0.156122i
$413$			4.60399e18i			2.24638i
$414$	−8.20599e17	+	2.01236e18i	−0.393667	+	0.965393i
$415$			2.96799e17i			0.139999i
$416$	−1.72588e18	−	6.59841e17i	−0.800494	−	0.306046i
$417$	2.62159e17			0.119567
$418$	−1.03630e17	−	4.22581e16i	−0.0464785	−	0.0189529i
$419$	−1.98698e18			−0.876384			−0.438192	−	0.898881i	$-0.644381\pi$
$419$	−1.98698e18			−0.876384			−0.438192	+	0.898881i	$0.644381\pi$
$420$	−1.75813e17	−	1.71983e17i	−0.0762614	−	0.0746003i
$421$		−	2.83575e16i		−	0.0120974i	−0.999982	−	0.00604872i	$-0.998075\pi$
$421$		−	2.83575e16i		−	0.0120974i	0.999982	−	0.00604872i	$-0.00192538\pi$
$422$	8.44257e17	+	3.44270e17i	0.354232	+	0.144448i
$423$		−	9.86014e16i		−	0.0406912i
$424$	−4.45771e18	+	1.93330e18i	−1.80947	+	0.784761i
$425$	−6.40368e17			−0.255686
$426$	−3.10501e17	+	7.61445e17i	−0.121954	+	0.299069i
$427$	7.05570e18			2.72612
$428$	1.38304e18	+	1.35291e18i	0.525688	+	0.514238i
$429$			5.56229e16i			0.0207995i
$430$	1.51589e17	−	3.71744e17i	0.0557685	−	0.136762i
$431$		−	6.83692e17i		−	0.247468i	−0.992315	−	0.123734i	$-0.960513\pi$
$431$		−	6.83692e17i		−	0.247468i	0.992315	−	0.123734i	$-0.0394870\pi$
$432$	5.61302e16	+	2.54860e18i	0.0199899	+	0.907643i
$433$	−4.04121e18			−1.41611			−0.708054	−	0.706159i	$-0.750427\pi$
$433$	−4.04121e18			−1.41611			−0.708054	+	0.706159i	$0.750427\pi$
$434$	4.84776e16	+	1.97681e16i	0.0167152	+	0.00681612i
$435$	1.47314e17			0.0499825
$436$	−2.64105e18	+	2.69986e18i	−0.881802	+	0.901437i
$437$		−	4.79130e18i		−	1.57428i
$438$	5.94359e17	+	2.42367e17i	0.192190	+	0.0783708i
$439$		−	3.61267e18i		−	1.14968i	−0.818267	−	0.574839i	$-0.805065\pi$
$439$		−	3.61267e18i		−	1.14968i	0.818267	−	0.574839i	$-0.194935\pi$
$440$	−1.66885e16	+	7.23776e15i	−0.00522695	+	0.00226691i
$441$	3.92006e18			1.20843
$442$	2.76931e17	−	6.79120e17i	0.0840263	−	0.206059i
$443$	1.78111e18			0.531943			0.265972	−	0.963981i	$-0.414307\pi$
$443$	1.78111e18			0.531943			0.265972	+	0.963981i	$0.414307\pi$
$444$	1.04009e18	−	1.06325e18i	0.305767	−	0.312575i
$445$		−	3.51207e17i		−	0.101635i
$446$	1.91444e18	−	4.69481e18i	0.545379	−	1.33744i
$447$			1.54245e17i			0.0432573i
$448$	−4.32373e18	−	4.04713e18i	−1.19375	−	1.11738i
$449$	9.58632e17			0.260572			0.130286	−	0.991476i	$-0.458410\pi$
$449$	9.58632e17			0.260572			0.130286	+	0.991476i	$0.458410\pi$
$450$	−2.46014e18	−	1.00319e18i	−0.658373	−	0.268470i
$451$	2.51589e17			0.0662913
$452$	1.29648e18	+	1.26824e18i	0.336353	+	0.329027i
$453$		−	5.72619e17i		−	0.146278i
$454$	3.94092e18	+	1.60702e18i	0.991304	+	0.404233i
$455$			7.00136e17i			0.173421i
$456$	−9.37649e17	−	2.16199e18i	−0.228711	−	0.527350i
$457$	−2.36962e17			−0.0569202			−0.0284601	−	0.999595i	$-0.509060\pi$
$457$	−2.36962e17			−0.0569202			−0.0284601	+	0.999595i	$0.509060\pi$
$458$	−1.33069e18	+	3.26326e18i	−0.314788	+	0.771957i
$459$	−1.01186e18			−0.235738
$460$	−5.56701e17	−	5.44575e17i	−0.127737	−	0.124955i
$461$			9.84218e17i			0.222426i	0.993797	+	0.111213i	$0.0354735\pi$
$461$			9.84218e17i			0.222426i	−0.993797	+	0.111213i	$0.964526\pi$
$462$	−6.73181e16	+	1.65085e17i	−0.0149844	+	0.0367463i
$463$		−	3.18452e18i		−	0.698195i	−0.937086	−	0.349098i	$-0.886488\pi$
$463$		−	3.18452e18i		−	0.698195i	0.937086	−	0.349098i	$-0.113512\pi$
$464$	3.54645e18	−	7.81070e16i	0.765894	−	0.0168680i
$465$	3.38597e15			0.000720299
$466$	1.79193e18	+	7.30712e17i	0.375509	+	0.153125i
$467$	−8.96570e18			−1.85083			−0.925414	−	0.378958i	$-0.876282\pi$
$467$	−8.96570e18			−1.85083			−0.925414	+	0.378958i	$0.876282\pi$
$468$	2.12780e18	−	2.17518e18i	0.432723	−	0.442358i
$469$			1.04037e19i			2.08439i
$470$	3.27175e16	+	1.33415e16i	0.00645796	+	0.00263342i
$471$			3.99894e18i			0.777676i
$472$	2.85295e18	+	6.57820e18i	0.546638	+	1.26041i
$473$	−2.91018e17			−0.0549405
$474$	1.47011e18	−	3.60516e18i	0.273464	−	0.670619i
$475$	5.85742e18			1.07362
$476$	1.64382e18	−	1.68043e18i	0.296898	−	0.303508i
$477$		−	8.00169e18i		−	1.42414i
$478$	−1.17353e18	+	2.87786e18i	−0.205826	+	0.504749i
$479$			7.93615e18i			1.37171i	0.727740	+	0.685853i	$0.240571\pi$
$479$			7.93615e18i			1.37171i	−0.727740	+	0.685853i	$0.759429\pi$
$480$	−3.57774e17	−	1.36784e17i	−0.0609425	−	0.0232996i
$481$	−4.23417e18			−0.710808
$482$	−6.40715e18	−	2.61270e18i	−1.06007	−	0.432275i
$483$	−7.63264e18			−1.24464
$484$	−4.43824e18	−	4.34157e18i	−0.713334	−	0.697797i
$485$		−	7.38454e17i		−	0.116985i
$486$	−6.14467e18	−	2.50566e18i	−0.959499	−	0.391263i
$487$			3.30184e18i			0.508221i	0.967175	+	0.254111i	$0.0817828\pi$
$487$			3.30184e18i			0.508221i	−0.967175	+	0.254111i	$0.918217\pi$
$488$	1.00812e19	−	4.37219e18i	1.52959	−	0.663377i
$489$	2.73662e18			0.409311
$490$	−5.30412e17	+	1.30074e18i	−0.0782062	+	0.191786i
$491$	1.82118e18			0.264718			0.132359	−	0.991202i	$-0.457745\pi$
$491$	1.82118e18			0.264718			0.132359	+	0.991202i	$0.457745\pi$
$492$	3.78702e18	+	3.70453e18i	0.542677	+	0.530857i
$493$			1.40803e18i			0.198923i
$494$	−2.53307e18	+	6.21189e18i	−0.352825	+	0.865237i
$495$		−	2.99562e16i		−	0.00411387i
$496$	8.15146e16	−	1.79527e15i	0.0110373	−	0.000243085i
$497$	7.50316e18			1.00173
$498$	4.19494e18	+	1.71061e18i	0.552230	+	0.225188i
$499$	−1.08282e19			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$499$	−1.08282e19			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$500$	1.34186e18	−	1.37173e18i	0.171758	−	0.175582i
$501$			3.44943e17i			0.0435395i
$502$	−1.98596e18	−	8.09831e17i	−0.247197	−	0.100802i
$503$		−	3.39344e18i		−	0.416547i	−0.978071	−	0.208274i	$-0.933216\pi$
$503$		−	3.39344e18i		−	0.416547i	0.978071	−	0.208274i	$-0.0667845\pi$
$504$	8.94771e18	−	3.88060e18i	1.08317	−	0.469770i
$505$	−1.54574e18			−0.184543
$506$	−2.13159e17	+	5.22733e17i	−0.0250987	+	0.0615497i
$507$	−1.20549e18			−0.139994
$508$	−2.21247e18	+	2.26173e18i	−0.253415	+	0.259057i
$509$		−	2.74342e18i		−	0.309933i	−0.987920	−	0.154966i	$-0.950473\pi$
$509$		−	2.74342e18i		−	0.309933i	0.987920	−	0.154966i	$-0.0495269\pi$
$510$	5.74074e16	−	1.40781e17i	0.00639701	−	0.0156875i
$511$		−	5.85671e18i		−	0.643736i
$512$	−8.68564e18	−	3.10328e18i	−0.941698	−	0.336458i
$513$	9.25542e18			0.989862
$514$	8.88231e18	+	3.62201e18i	0.937096	+	0.382128i
$515$	2.59701e17			0.0270285
$516$	−4.38052e18	−	4.28510e18i	−0.449757	−	0.439960i
$517$		−	2.56128e16i		−	0.00259432i
$518$	−1.25667e19	−	5.12444e18i	−1.25578	−	0.512080i
$519$		−	6.18126e17i		−	0.0609404i
$520$	4.33852e17	+	1.00036e18i	0.0422006	+	0.0973041i
$521$	1.14151e19			1.09551			0.547753	−	0.836640i	$-0.315483\pi$
$521$	1.14151e19			1.09551			0.547753	+	0.836640i	$0.315483\pi$
$522$	−2.20580e18	+	5.40932e18i	−0.208869	+	0.512211i
$523$	1.85196e19			1.73029			0.865147	−	0.501519i	$-0.167225\pi$
$523$	1.85196e19			1.73029			0.865147	+	0.501519i	$0.167225\pi$
$524$	2.23171e18	+	2.18310e18i	0.205740	+	0.201258i
$525$		−	9.33100e18i		−	0.848815i
$526$	2.60229e18	−	6.38163e18i	0.233591	−	0.572838i
$527$			3.23633e16i			0.00286668i
$528$	6.11360e15	+	2.77589e17i	0.000534392	+	0.0242641i
$529$	−1.25755e19			−1.08477
$530$	2.65509e18	+	1.08269e18i	0.226021	+	0.0921663i
$531$	−1.18080e19			−0.992009
$532$	−1.50360e19	+	1.53708e19i	−1.24667	+	1.27443i
$533$		−	1.50810e19i		−	1.23407i
$534$	−4.96394e18	−	2.02419e18i	−0.400901	−	0.163479i
$535$		−	1.14173e18i		−	0.0910097i
$536$	6.44686e18	+	1.48649e19i	0.507218	+	1.16952i
$537$	5.44609e18			0.422927
$538$	4.57954e18	−	1.12304e19i	0.351031	−	0.860837i
$539$	1.01828e18			0.0770450
$540$	1.05196e18	−	1.07539e18i	0.0785678	−	0.0803172i
$541$			5.62589e18i			0.414773i	0.978259	+	0.207386i	$0.0664957\pi$
$541$			5.62589e18i			0.414773i	−0.978259	+	0.207386i	$0.933504\pi$
$542$	−8.44872e18	+	2.07189e19i	−0.614888	+	1.50790i
$543$			7.89265e17i			0.0567053i
$544$	1.30739e18	−	3.41962e18i	0.0927287	−	0.242541i
$545$	2.22880e18			0.156061
$546$	9.89567e18	+	4.03524e18i	0.684064	+	0.278947i
$547$	2.24193e19			1.53007			0.765033	−	0.643991i	$-0.222723\pi$
$547$	2.24193e19			1.53007			0.765033	+	0.643991i	$0.222723\pi$
$548$	−1.24072e19	−	1.21370e19i	−0.836008	−	0.817798i
$549$			1.80960e19i			1.20386i
$550$	−6.39047e17	−	2.60590e17i	−0.0419753	−	0.0171166i
$551$		−	1.28792e19i		−	0.835272i
$552$	−1.09055e19	+	4.72971e18i	−0.698351	+	0.302873i
$553$	−3.55246e19			−2.24623
$554$	3.77286e18	−	9.25222e18i	0.235560	−	0.577667i
$555$	−8.77738e17			−0.0541146
$556$	−2.66306e18	−	2.60505e18i	−0.162128	−	0.158596i
$557$			2.80539e19i			1.68658i	0.537458	+	0.843290i	$0.319385\pi$
$557$			2.80539e19i			1.68658i	−0.537458	+	0.843290i	$0.680615\pi$
$558$	−5.07000e16	+	1.24332e17i	−0.00301001	+	0.00738149i
$559$			1.74445e19i			1.02276i
$560$	7.69531e16	+	3.49407e18i	0.00445564	+	0.202309i
$561$	−1.10210e17			−0.00630202
$562$	1.31546e19	+	5.36417e18i	0.742889	+	0.302934i
$563$	−2.17104e18			−0.121090			−0.0605451	−	0.998165i	$-0.519284\pi$
$563$	−2.17104e18			−0.121090			−0.0605451	+	0.998165i	$0.519284\pi$
$564$	3.77136e17	−	3.85533e17i	0.0207751	−	0.0212377i
$565$		−	1.07027e18i		−	0.0582311i
$566$	2.32064e19	+	9.46306e18i	1.24707	+	0.508530i
$567$			7.49950e18i			0.398062i
$568$	1.07205e19	−	4.64947e18i	0.562054	−	0.243761i
$569$	−2.07628e19			−1.07523			−0.537614	−	0.843191i	$-0.680674\pi$
$569$	−2.07628e19			−1.07523			−0.537614	+	0.843191i	$0.680674\pi$
$570$	−5.25104e17	+	1.28772e18i	−0.0268609	+	0.0658714i
$571$	7.11341e18			0.359439			0.179720	−	0.983718i	$-0.442481\pi$
$571$	7.11341e18			0.359439			0.179720	+	0.983718i	$0.442481\pi$
$572$	5.52719e17	−	5.65026e17i	0.0275888	−	0.0282031i
$573$			1.09696e19i			0.540888i
$574$	1.82519e19	−	4.47594e19i	0.889048	−	2.18022i
$575$		−	2.95461e19i		−	1.42176i
$576$	1.03798e19	−	1.10892e19i	0.493438	−	0.527161i
$577$	−9.42450e18			−0.442616			−0.221308	−	0.975204i	$-0.571033\pi$
$577$	−9.42450e18			−0.442616			−0.221308	+	0.975204i	$0.571033\pi$
$578$	−1.86113e19	−	7.58929e18i	−0.863539	−	0.352133i
$579$	3.05084e16			0.00139852
$580$	−1.49644e18	−	1.46384e18i	−0.0677739	−	0.0662977i
$581$		−	4.13363e19i		−	1.84969i
$582$	−1.04373e19	−	4.25609e18i	−0.461451	−	0.188170i
$583$		−	2.07853e18i		−	0.0907978i
$584$	−3.62922e18	−	8.36809e18i	−0.156647	−	0.361191i
$585$	−1.79566e18			−0.0765833
$586$	9.30604e18	−	2.28213e19i	0.392177	−	0.961739i
$587$	9.63417e18			0.401188			0.200594	−	0.979674i	$-0.435713\pi$
$587$	9.63417e18			0.401188			0.200594	+	0.979674i	$0.435713\pi$
$588$	1.53275e19	+	1.49936e19i	0.630709	+	0.616972i
$589$		−	2.96026e17i		−	0.0120371i
$590$	1.59771e18	−	3.91809e18i	0.0641999	−	0.157438i
$591$			1.75499e19i			0.696885i
$592$	−2.11308e19	+	4.65384e17i	−0.829210	+	0.0182625i
$593$	2.68077e19			1.03963			0.519813	−	0.854280i	$-0.326002\pi$
$593$	2.68077e19			1.03963			0.519813	+	0.854280i	$0.326002\pi$
$594$	−1.00977e18	−	4.11763e17i	−0.0387006	−	0.0157813i
$595$	−1.38723e18			−0.0525449
$596$	1.53272e18	−	1.56685e18i	0.0573772	−	0.0586548i
$597$			1.53433e19i			0.567674i
$598$	3.13341e19	+	1.27774e19i	1.14580	+	0.467233i
$599$			3.28367e19i			1.18678i	0.804914	+	0.593391i	$0.202211\pi$
$599$			3.28367e19i			1.18678i	−0.804914	+	0.593391i	$0.797789\pi$
$600$	−5.78212e18	−	1.33322e19i	−0.206552	−	0.476257i
$601$	9.68831e18			0.342079			0.171040	−	0.985264i	$-0.445287\pi$
$601$	9.68831e18			0.342079			0.171040	+	0.985264i	$0.445287\pi$
$602$	−2.11124e19	+	5.17741e19i	−0.736820	+	1.80691i
$603$	−2.66828e19			−0.920472
$604$	−5.69006e18	+	5.81676e18i	−0.194025	+	0.198345i
$605$			3.66387e18i			0.123496i
$606$	−8.90891e18	+	2.18474e19i	−0.296836	+	0.727934i
$607$		−	4.91663e19i		−	1.61937i	−0.586864	−	0.809686i	$-0.699638\pi$
$607$		−	4.91663e19i		−	1.61937i	0.586864	−	0.809686i	$-0.300362\pi$
$608$	−1.19587e19	+	3.12792e19i	−0.389366	+	1.01843i
$609$	−2.05169e19			−0.660374
$610$	−6.00454e18	−	2.44852e18i	−0.191061	−	0.0779104i
$611$	−1.53530e18			−0.0482954
$612$	4.30985e18	+	4.21597e18i	0.134030	+	0.131111i
$613$			2.87841e19i			0.884972i	0.896776	+	0.442486i	$0.145903\pi$
$613$			2.87841e19i			0.884972i	−0.896776	+	0.442486i	$0.854097\pi$
$614$	−7.27976e18	−	2.96853e18i	−0.221278	−	0.0902324i
$615$		−	3.12627e18i		−	0.0939509i
$616$	2.32426e18	−	1.00803e18i	0.0690590	−	0.0299507i
$617$	5.20211e19			1.52821			0.764105	−	0.645092i	$-0.223181\pi$
$617$	5.20211e19			1.52821			0.764105	+	0.645092i	$0.223181\pi$
$618$	1.49679e18	−	3.67059e18i	0.0434751	−	0.106615i
$619$	−2.13270e19			−0.612485			−0.306242	−	0.951954i	$-0.599072\pi$
$619$	−2.13270e19			−0.612485			−0.306242	+	0.951954i	$0.599072\pi$
$620$	−3.43953e16	−	3.36461e16i	−0.000976691	−	0.000955417i
$621$		−	4.66864e19i		−	1.31084i
$622$	−1.34777e19	+	3.30514e19i	−0.374181	+	0.917608i
$623$			4.89138e19i			1.34281i
$624$	1.66395e19	−	3.66467e17i	0.451697	−	0.00994816i
$625$	3.55499e19			0.954286
$626$	−6.39892e19	−	2.60934e19i	−1.69858	−	0.692645i
$627$	1.00808e18			0.0264621
$628$	3.97371e19	−	4.06219e19i	1.03152	−	1.05449i
$629$		−	8.38947e18i		−	0.215367i
$630$	−5.32941e18	−	2.17322e18i	−0.135299	−	0.0551721i
$631$		−	1.78824e19i		−	0.448973i	−0.974477	−	0.224486i	$-0.927930\pi$
$631$		−	1.78824e19i		−	0.448973i	0.974477	−	0.224486i	$-0.0720704\pi$
$632$	−5.07577e19	+	2.20135e19i	−1.26032	+	0.546599i
$633$	−8.21270e18			−0.201679
$634$	−5.88507e18	+	1.44320e19i	−0.142931	+	0.350512i
$635$	1.86712e18			0.0448493
$636$	3.06053e19	−	3.12867e19i	0.727104	−	0.743294i
$637$		−	6.10384e19i		−	1.43426i
$638$	−5.72981e17	+	1.40513e18i	−0.0133167	+	0.0326566i
$639$			1.92436e19i			0.442365i
$640$	2.27511e18	+	4.94464e18i	0.0517301	+	0.112428i
$641$	1.54885e19			0.348340			0.174170	−	0.984716i	$-0.444276\pi$
$641$	1.54885e19			0.348340			0.174170	+	0.984716i	$0.444276\pi$
$642$	−1.61372e19	−	6.58039e18i	−0.358990	−	0.146388i
$643$	7.62999e18			0.167899			0.0839493	−	0.996470i	$-0.473247\pi$
$643$	7.62999e18			0.167899			0.0839493	+	0.996470i	$0.473247\pi$
$644$	7.75337e19	+	7.58449e19i	1.68768	+	1.65092i
$645$			3.61622e18i			0.0778641i
$646$	−1.23081e19	−	5.01897e18i	−0.262158	−	0.106902i
$647$		−	4.64615e19i		−	0.978956i	−0.872016	−	0.489478i	$-0.837187\pi$
$647$		−	4.64615e19i		−	0.978956i	0.872016	−	0.489478i	$-0.162813\pi$
$648$	4.64720e18	+	1.07153e19i	0.0968649	+	0.223347i
$649$	−3.06726e18			−0.0632467
$650$	−1.56205e19	+	3.83064e19i	−0.318641	+	0.781407i
$651$	−4.71576e17			−0.00951667
$652$	−2.77991e19	−	2.71936e19i	−0.555006	−	0.542917i
$653$			1.12862e18i			0.0222924i	0.999938	+	0.0111462i	$0.00354802\pi$
$653$			1.12862e18i			0.0222924i	−0.999938	+	0.0111462i	$0.996452\pi$
$654$	1.28457e19	−	3.15016e19i	0.251023	−	0.615586i
$655$		−	1.84233e18i		−	0.0356187i
$656$	−1.65758e18	−	7.52625e19i	−0.0317064	−	1.43963i
$657$	1.50209e19			0.284275
$658$	−4.55668e18	−	1.85812e18i	−0.0853232	−	0.0347930i
$659$	−1.47168e19			−0.272655			−0.136328	−	0.990664i	$-0.543530\pi$
$659$	−1.47168e19			−0.272655			−0.136328	+	0.990664i	$0.543530\pi$
$660$	1.14578e17	−	1.17129e17i	0.00210036	−	0.00214713i
$661$			6.12352e19i			1.11068i	0.831622	+	0.555342i	$0.187413\pi$
$661$			6.12352e19i			1.11068i	−0.831622	+	0.555342i	$0.812587\pi$
$662$	4.40551e19	+	1.79647e19i	0.790661	+	0.322415i
$663$			6.60629e18i			0.117318i
$664$	−2.56148e19	−	5.90613e19i	−0.450105	−	1.03783i
$665$	1.26890e19			0.220635
$666$	1.31428e19	−	3.22303e19i	0.226136	−	0.554556i
$667$	−6.49656e19			−1.10612
$668$	3.42767e18	−	3.50399e18i	0.0577515	−	0.0590374i
$669$			4.56698e19i			0.761459i
$670$	3.61038e18	−	8.85378e18i	0.0595703	−	0.146085i
$671$			4.70063e18i			0.0767536i
$672$	4.98284e19	+	1.90504e19i	0.805178	+	0.307836i
$673$	−2.80877e19			−0.449170			−0.224585	−	0.974455i	$-0.572103\pi$
$673$	−2.80877e19			−0.449170			−0.224585	+	0.974455i	$0.572103\pi$
$674$	4.63881e19	+	1.89161e19i	0.734155	+	0.299373i
$675$	5.70747e19			0.893958
$676$	1.22456e19	+	1.19789e19i	0.189825	+	0.185690i
$677$		−	4.56893e19i		−	0.700962i	−0.936570	−	0.350481i	$-0.886018\pi$
$677$		−	4.56893e19i		−	0.700962i	0.936570	−	0.350481i	$-0.113982\pi$
$678$	−1.51271e19	−	6.16852e18i	−0.229694	−	0.0936641i
$679$			1.02847e20i			1.54562i
$680$	−1.98208e18	+	8.59624e17i	−0.0294821	+	0.0127863i
$681$	−3.83362e19			−0.564390
$682$	−1.31699e16	+	3.22966e16i	−0.000191907	+	0.000470615i
$683$	−9.99326e19			−1.44133			−0.720663	−	0.693286i	$-0.756162\pi$
$683$	−9.99326e19			−1.44133			−0.720663	+	0.693286i	$0.756162\pi$
$684$	−3.94220e19	−	3.85633e19i	−0.562790	−	0.550531i
$685$			1.02425e19i			0.144734i
$686$	2.97318e19	−	7.29118e19i	0.415866	−	1.01983i
$687$		−	3.17441e19i		−	0.439507i
$688$	1.91735e18	+	8.70576e19i	0.0262774	+	1.19313i
$689$	−1.24593e20			−1.69028
$690$	6.49553e18	+	2.64874e18i	0.0872310	+	0.0355709i
$691$	5.80040e19			0.771102			0.385551	−	0.922687i	$-0.374011\pi$
$691$	5.80040e19			0.771102			0.385551	+	0.922687i	$0.374011\pi$
$692$	−6.14226e18	+	6.27902e18i	−0.0808324	+	0.0826322i
$693$			4.17211e18i			0.0543529i
$694$	4.31919e19	+	1.76127e19i	0.557040	+	0.227149i
$695$			2.19842e18i			0.0280683i
$696$	−2.93146e19	+	1.27137e19i	−0.370526	+	0.160696i
$697$	2.98811e19			0.373910
$698$	4.03277e19	−	9.88961e19i	0.499592	−	1.22516i
$699$	−1.74314e19			−0.213793
$700$	−9.27213e19	+	9.47859e19i	−1.12588	+	1.15095i
$701$			8.89167e19i			1.06895i	0.845185	+	0.534475i	$0.179490\pi$
$701$			8.89167e19i			1.06895i	−0.845185	+	0.534475i	$0.820510\pi$
$702$	−2.46823e19	+	6.05286e19i	−0.293782	+	0.720445i
$703$			7.67382e19i			0.904324i
$704$	2.69627e18	−	2.88054e18i	0.0314597	−	0.0336098i
$705$	−3.18267e17			−0.00367678
$706$	2.47575e19	+	1.00956e19i	0.283187	+	0.115478i
$707$	2.15281e20			2.43820
$708$	−4.61695e19	−	4.51639e19i	−0.517753	−	0.506476i
$709$			1.21670e19i			0.135101i	0.997716	+	0.0675506i	$0.0215184\pi$
$709$			1.21670e19i			0.135101i	−0.997716	+	0.0675506i	$0.978482\pi$
$710$	−6.38534e18	−	2.60380e18i	−0.0702062	−	0.0286286i
$711$		−	9.11113e19i		−	0.991939i
$712$	3.03104e19	+	6.98882e19i	0.326762	+	0.753432i
$713$	−1.49322e18			−0.0159403
$714$	−7.99533e18	+	1.96070e19i	−0.0845179	+	0.207264i
$715$	−4.66443e17			−0.00488266
$716$	−5.53223e19	−	5.41173e19i	−0.573468	−	0.560977i
$717$		−	2.79951e19i		−	0.287374i
$718$	−3.39358e19	+	8.32212e19i	−0.344975	+	0.845985i
$719$		−	1.86127e20i		−	1.87373i	−0.349696	−	0.936863i	$-0.613715\pi$
$719$		−	1.86127e20i		−	1.87373i	0.349696	−	0.936863i	$-0.386285\pi$
$720$	−8.96135e18	+	1.97364e17i	−0.0893400	+	0.00196762i
$721$	−3.61694e19			−0.357104
$722$	1.78797e19	+	7.29095e18i	0.174823	+	0.0712892i
$723$	6.23270e19			0.603543
$724$	7.84285e18	−	8.01748e18i	0.0752149	−	0.0768897i
$725$		−	7.94212e19i		−	0.754346i
$726$	5.17849e19	+	2.11168e19i	0.487132	+	0.198642i
$727$		−	1.09187e20i		−	1.01726i	−0.860986	−	0.508629i	$-0.830152\pi$
$727$		−	1.09187e20i		−	1.01726i	0.860986	−	0.508629i	$-0.169848\pi$
$728$	−6.04240e19	−	1.39323e20i	−0.557558	−	1.28559i
$729$	3.31358e19			0.302834
$730$	−2.03244e18	+	4.98418e18i	−0.0183975	+	0.0451163i
$731$	−3.45641e19			−0.309887
$732$	−6.92145e19	+	7.07557e19i	−0.614638	+	0.628324i
$733$		−	3.97132e19i		−	0.349307i	−0.984630	−	0.174654i	$-0.944119\pi$
$733$		−	3.97132e19i		−	0.349307i	0.984630	−	0.174654i	$-0.0558806\pi$
$734$	4.86117e19	−	1.19211e20i	0.423515	−	1.03859i
$735$		−	1.26532e19i		−	0.109192i
$736$	1.57779e20	+	6.03222e19i	1.34867	+	0.515623i
$737$	−6.93115e18			−0.0586858
$738$	1.14796e20	+	4.68113e19i	0.962791	+	0.392606i
$739$	7.78406e19			0.646689			0.323344	−	0.946281i	$-0.395193\pi$
$739$	7.78406e19			0.646689			0.323344	+	0.946281i	$0.395193\pi$
$740$	8.91621e18	+	8.72200e18i	0.0733767	+	0.0717785i
$741$		−	6.04275e19i		−	0.492614i
$742$	−3.69783e20	−	1.50790e20i	−2.98621	−	1.21771i
$743$			1.03483e20i			0.827839i	0.910313	+	0.413920i	$0.135841\pi$
$743$			1.03483e20i			0.827839i	−0.910313	+	0.413920i	$0.864159\pi$
$744$	−6.73789e17	+	2.92221e17i	−0.00533966	+	0.00231580i
$745$	−1.29347e18			−0.0101546
$746$	−1.24536e19	+	3.05400e19i	−0.0968550	+	0.237519i
$747$	1.06017e20			0.816826
$748$	1.11953e18	+	1.09514e18i	0.00854524	+	0.00835911i
$749$			1.59013e20i			1.20243i
$750$	−6.52660e18	+	1.60053e19i	−0.0488943	+	0.119904i
$751$			1.09267e20i			0.810978i	0.914100	+	0.405489i	$0.132899\pi$
$751$			1.09267e20i			0.810978i	−0.914100	+	0.405489i	$0.867101\pi$
$752$	−7.66201e18	+	1.68748e17i	−0.0563401	+	0.00124083i
$753$	1.93188e19			0.140740
$754$	8.42275e19	+	3.43462e19i	0.607931	+	0.247901i
$755$	4.80187e18			0.0343386
$756$	−1.46511e20	+	1.49773e20i	−1.03805	+	1.06116i
$757$		−	1.56866e20i		−	1.10118i	−0.834777	−	0.550588i	$-0.814403\pi$
$757$		−	1.56866e20i		−	1.10118i	0.834777	−	0.550588i	$-0.185597\pi$
$758$	1.42127e20	+	5.79564e19i	0.988536	+	0.403104i
$759$		−	5.08500e18i		−	0.0350428i
$760$	1.81300e19	−	7.86294e18i	0.123795	−	0.0536896i
$761$	−1.12594e20			−0.761766			−0.380883	−	0.924623i	$-0.624380\pi$
$761$	−1.12594e20			−0.761766			−0.380883	+	0.924623i	$0.624380\pi$
$762$	1.07611e19	−	2.63897e19i	0.0721396	−	0.176909i
$763$	−3.10412e20			−2.06190
$764$	1.09004e20	−	1.11431e20i	0.717443	−	0.733418i
$765$		−	3.55788e18i		−	0.0232039i
$766$	−8.39944e19	+	2.05980e20i	−0.542811	+	1.33114i
$767$			1.83860e20i			1.17739i
$768$	8.29999e19	−	3.65775e18i	0.526683	−	0.0232105i
$769$	1.82674e20			1.14866			0.574330	−	0.818624i	$-0.305263\pi$
$769$	1.82674e20			1.14866			0.574330	+	0.818624i	$0.305263\pi$
$770$	−1.38437e18	−	5.64517e17i	−0.00862616	−	0.00351756i
$771$	−8.64046e19			−0.533527
$772$	−3.09910e17	−	3.03159e17i	−0.00189633	−	0.00185503i
$773$			2.52736e20i			1.53254i	0.642521	+	0.766268i	$0.277888\pi$
$773$			2.52736e20i			1.53254i	−0.642521	+	0.766268i	$0.722112\pi$
$774$	−1.32787e20	−	5.41476e19i	−0.797936	−	0.325381i
$775$		−	1.82548e18i		−	0.0108709i
$776$	6.37310e19	+	1.46948e20i	0.376113	+	0.867225i
$777$	1.22246e20			0.714967
$778$	9.18555e18	−	2.25258e19i	0.0532412	−	0.130564i
$779$	−2.73321e20			−1.57004
$780$	−7.02107e18	−	6.86814e18i	−0.0399707	−	0.0391000i
$781$			4.99873e18i			0.0282035i
$782$	−2.53168e19	+	6.20847e19i	−0.141567	+	0.347166i
$783$		−	1.25495e20i		−	0.695495i
$784$	−6.70884e18	−	3.04615e20i	−0.0368498	−	1.67317i
$785$	−3.35344e19			−0.182559
$786$	−2.60393e19	−	1.06183e19i	−0.140499	−	0.0572923i
$787$	3.84464e18			0.0205604			0.0102802	−	0.999947i	$-0.496728\pi$
$787$	3.84464e18			0.0205604			0.0102802	+	0.999947i	$0.496728\pi$
$788$	1.74391e20	−	1.78274e20i	0.924360	−	0.944943i
$789$			6.20787e19i			0.326140i
$790$	3.02322e19	+	1.23280e19i	0.157427	+	0.0641954i
$791$			1.49060e20i			0.769355i
$792$	2.58532e18	+	5.96112e18i	0.0132263	+	0.0304966i
$793$	2.81769e20			1.42883
$794$	5.27116e19	−	1.29265e20i	0.264949	−	0.649738i
$795$	−2.58280e19			−0.128683
$796$	1.52465e20	−	1.55860e20i	0.752972	−	0.769738i
$797$		−	3.29134e20i		−	1.61126i	−0.592421	−	0.805629i	$-0.701828\pi$
$797$		−	3.29134e20i		−	1.61126i	0.592421	−	0.805629i	$-0.298172\pi$
$798$	7.31330e19	−	1.79345e20i	0.354889	−	0.870299i
$799$		−	3.04201e18i		−	0.0146330i
$800$	−7.37446e19	+	1.92887e20i	−0.351642	+	0.919756i
$801$	−1.25451e20			−0.592989
$802$	−1.18184e20	−	4.81929e19i	−0.553781	−	0.225820i
$803$	3.90184e18			0.0181243
$804$	−1.04330e20	−	1.02058e20i	−0.480417	−	0.469952i
$805$		−	6.40059e19i		−	0.292179i
$806$	1.93595e18	+	7.89440e17i	0.00876091	+	0.00357251i
$807$			1.09247e20i			0.490110i
$808$	3.07594e20	−	1.33403e20i	1.36804	−	0.593315i
$809$	−3.71764e20			−1.63918			−0.819591	−	0.572948i	$-0.805800\pi$
$809$	−3.71764e20			−1.63918			−0.819591	+	0.572948i	$0.805800\pi$
$810$	2.60253e18	−	6.38222e18i	0.0113763	−	0.0278982i
$811$	−1.66516e20			−0.721623			−0.360812	−	0.932639i	$-0.617500\pi$
$811$	−1.66516e20			−0.721623			−0.360812	+	0.932639i	$0.617500\pi$
$812$	2.08414e20	+	2.03874e20i	0.895435	+	0.875931i
$813$		−	2.01547e20i		−	0.858507i
$814$	3.41399e18	−	8.37217e18i	0.0144176	−	0.0353563i
$815$			2.29488e19i			0.0960853i
$816$	7.26109e17	+	3.29690e19i	0.00301419	+	0.136860i
$817$	3.16156e20			1.30121
$818$	−1.97799e20	−	8.06580e19i	−0.807142	−	0.329135i
$819$	2.50088e20			1.01183
$820$	−3.10655e19	+	3.17572e19i	−0.124618	+	0.127393i
$821$			3.55397e20i			1.41355i	0.707439	+	0.706775i	$0.249851\pi$
$821$			3.55397e20i			1.41355i	−0.707439	+	0.706775i	$0.750149\pi$
$822$	1.44766e20	+	5.90325e19i	0.570905	+	0.232803i
$823$		−	1.76938e20i		−	0.691868i	−0.938259	−	0.345934i	$-0.887562\pi$
$823$		−	1.76938e20i		−	0.691868i	0.938259	−	0.345934i	$-0.112438\pi$
$824$	−5.16789e19	+	2.24130e19i	−0.200366	+	0.0868980i
$825$	6.21648e18			0.0238983
$826$	−2.22519e20	+	5.45685e20i	−0.848216	+	2.08009i
$827$	1.89586e20			0.716585			0.358292	−	0.933609i	$-0.383359\pi$
$827$	1.89586e20			0.716585			0.358292	+	0.933609i	$0.383359\pi$
$828$	−1.94522e20	+	1.98853e20i	−0.729049	+	0.745282i
$829$			1.36473e19i			0.0507182i	0.999678	+	0.0253591i	$0.00807292\pi$
$829$			1.36473e19i			0.0507182i	−0.999678	+	0.0253591i	$0.991927\pi$
$830$	−1.43448e19	+	3.51780e19i	−0.0528626	+	0.129636i
$831$			9.00030e19i			0.328889i
$832$	−1.72668e20	−	1.61622e20i	−0.625675	−	0.585650i
$833$	1.20940e20			0.434565
$834$	3.10723e19	+	1.26706e19i	0.110716	+	0.0451476i
$835$	−2.89263e18			−0.0102209
$836$	−1.02403e19	−	1.00172e19i	−0.0358813	−	0.0350998i
$837$		−	2.88448e18i		−	0.0100228i
$838$	−2.35505e20	−	9.60340e19i	−0.811507	−	0.330915i
$839$		−	1.46870e20i		−	0.501881i	−0.968003	−	0.250940i	$-0.919260\pi$
$839$		−	1.46870e20i		−	0.501881i	0.968003	−	0.250940i	$-0.0807398\pi$
$840$	−1.25258e19	−	2.88815e19i	−0.0424475	−	0.0978735i
$841$	1.22928e20			0.413122
$842$	1.37057e18	−	3.36106e18i	0.00456789	−	0.0112019i
$843$	−1.27964e20			−0.422957
$844$	8.34260e19	+	8.16088e19i	0.273467	+	0.267510i
$845$		−	1.01090e19i		−	0.0328634i
$846$	4.76558e18	−	1.16867e19i	0.0153647	−	0.0376789i
$847$		−	5.10280e20i		−	1.63164i
$848$	−6.21787e20	+	1.36942e19i	−1.97184	+	0.0434276i
$849$	−2.25745e20			−0.710010
$850$	−7.58993e19	−	3.09501e19i	−0.236758	−	0.0965449i
$851$	3.87084e20			1.19756
$852$	−7.36039e19	+	7.52428e19i	−0.225852	+	0.230881i
$853$		−	3.50995e20i		−	1.06821i	−0.845418	−	0.534106i	$-0.820648\pi$
$853$		−	3.50995e20i		−	1.06821i	0.845418	−	0.534106i	$-0.179352\pi$
$854$	8.36273e20	+	3.41014e20i	2.52431	+	1.02936i
$855$			3.25438e19i			0.0974329i
$856$	9.85353e19	+	2.27198e20i	0.292601	+	0.674665i
$857$	−2.55087e20			−0.751316			−0.375658	−	0.926758i	$-0.622583\pi$
$857$	−2.55087e20			−0.751316			−0.375658	+	0.926758i	$0.622583\pi$
$858$	−2.68835e18	+	6.59267e18i	−0.00785371	+	0.0192597i
$859$	7.55650e19			0.218962			0.109481	−	0.993989i	$-0.465081\pi$
$859$	7.55650e19			0.218962			0.109481	+	0.993989i	$0.465081\pi$
$860$	3.59341e19	−	3.67342e19i	0.103280	−	0.105580i
$861$			4.35407e20i			1.24129i
$862$	3.30440e19	−	8.10342e19i	0.0934420	−	0.229149i
$863$			1.41475e20i			0.396828i	0.980118	+	0.198414i	$0.0635791\pi$
$863$			1.41475e20i			0.396828i	−0.980118	+	0.198414i	$0.936421\pi$
$864$	−1.16525e20	+	3.04784e20i	−0.324208	+	0.848000i
$865$	5.18349e18			0.0143057
$866$	−4.78982e20	−	1.95319e20i	−1.31128	−	0.534710i
$867$	1.81045e20			0.491648
$868$	4.79035e18	+	4.68601e18i	0.0129041	+	0.0126231i
$869$		−	2.36671e19i		−	0.0632422i
$870$	1.74603e19	+	7.11992e18i	0.0462824	+	0.0188730i
$871$			4.15473e20i			1.09249i
$872$	−4.43518e20	+	1.92352e20i	−1.15690	+	0.501744i
$873$	−2.63775e20			−0.682550
$874$	2.31572e20	−	5.67886e20i	0.594437	−	1.45774i
$875$	1.57713e20			0.401616
$876$	5.87320e19	+	5.74528e19i	0.148370	+	0.145138i
$877$			5.06062e18i			0.0126826i	0.999980	+	0.00634128i	$0.00201851\pi$
$877$			5.06062e18i			0.0126826i	−0.999980	+	0.00634128i	$0.997981\pi$
$878$	1.74606e20	−	4.28189e20i	0.434109	−	1.06457i
$879$			2.21999e20i			0.547557i
$880$	−2.32781e18	+	5.12675e16i	−0.00569598	+	0.000125448i
$881$	1.14311e20			0.277495			0.138748	−	0.990328i	$-0.455692\pi$
$881$	1.14311e20			0.277495			0.138748	+	0.990328i	$0.455692\pi$
$882$	4.64622e20	+	1.89463e20i	1.11897	+	0.456294i
$883$	−1.53959e20			−0.367858			−0.183929	−	0.982940i	$-0.558882\pi$
$883$	−1.53959e20			−0.367858			−0.183929	+	0.982940i	$0.558882\pi$
$884$	6.56461e19	−	6.71078e19i	0.155612	−	0.159077i
$885$			3.81141e19i			0.0896360i
$886$	2.11105e20	+	8.60842e19i	0.492565	+	0.200857i
$887$		−	5.99847e20i		−	1.38859i	−0.719688	−	0.694297i	$-0.755715\pi$
$887$		−	5.99847e20i		−	1.38859i	0.719688	−	0.694297i	$-0.244285\pi$
$888$	1.74665e20	−	7.57517e19i	0.401157	−	0.173981i
$889$	−2.60040e20			−0.592553
$890$	1.69745e19	−	4.16267e19i	0.0383765	−	0.0941112i
$891$	−4.99630e18			−0.0112074
$892$	4.53817e20	−	4.63922e20i	1.01001	−	1.03250i
$893$			2.78252e19i			0.0614437i
$894$	−7.45494e18	+	1.82818e19i	−0.0163336	+	0.0400551i
$895$			4.56699e19i			0.0992816i
$896$	−3.16863e20	−	6.88657e20i	−0.683463	−	1.48541i
$897$	−3.04810e20			−0.652351
$898$	1.13621e20	+	4.63323e19i	0.241282	+	0.0983898i
$899$	−4.01384e18			−0.00845751
$900$	−2.43101e20	−	2.37806e20i	−0.508263	−	0.497192i
$901$		−	2.46865e20i		−	0.512137i
$902$	2.98195e19	+	1.21597e19i	0.0613839	+	0.0250310i
$903$		−	5.03644e20i		−	1.02875i
$904$	9.23680e19	+	2.12978e20i	0.187216	+	0.431674i
$905$	−6.61863e18			−0.0133115
$906$	2.76757e19	−	6.78693e19i	0.0552332	−	0.135449i
$907$	−4.98635e19			−0.0987488			−0.0493744	−	0.998780i	$-0.515723\pi$
$907$	−4.98635e19			−0.0987488			−0.0493744	+	0.998780i	$0.515723\pi$
$908$	3.89425e20	+	3.80943e20i	0.765285	+	0.748616i
$909$			5.52139e20i			1.07672i
$910$	−3.38388e19	+	8.29832e19i	−0.0654825	+	0.160583i
$911$		−	5.85138e19i		−	0.112365i	−0.998421	−	0.0561823i	$-0.982107\pi$
$911$		−	5.85138e19i		−	0.112365i	0.998421	−	0.0561823i	$-0.0178928\pi$
$912$	−6.64169e18	−	3.01567e20i	−0.0126565	−	0.574671i
$913$	2.75389e19			0.0520777
$914$	−2.80858e19	−	1.14528e19i	−0.0527065	−	0.0214926i
$915$	5.84105e19			0.108779
$916$	−3.15438e20	+	3.22462e20i	−0.582969	+	0.595950i
$917$			2.56587e20i			0.470598i
$918$	−1.19930e20	−	4.89048e19i	−0.218287	−	0.0890129i
$919$			9.47150e20i			1.71084i	0.517932	+	0.855422i	$0.326702\pi$
$919$			9.47150e20i			1.71084i	−0.517932	+	0.855422i	$0.673298\pi$
$920$	−3.96624e19	−	9.14518e19i	−0.0710992	−	0.163937i
$921$	7.08154e19			0.125983
$922$	−4.75689e19	+	1.16654e20i	−0.0839860	+	0.205960i
$923$	2.99639e20			0.525032
$924$	−1.59577e19	+	1.63130e19i	−0.0277502	+	0.0283681i
$925$			4.73215e20i			0.816708i
$926$	1.53913e20	−	3.77443e20i	0.263633	−	0.646510i
$927$		−	9.27649e19i		−	0.157698i
$928$	4.24117e20	+	1.62149e20i	0.715566	+	0.273576i
$929$	−4.81038e20			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$929$	−4.81038e20			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$930$	4.01321e17	+	1.63650e17i	0.000666977	+	0.000271979i
$931$	−1.10623e21			−1.82473
$932$	1.77071e20	+	1.73214e20i	0.289892	+	0.283578i
$933$		−	3.21515e20i		−	0.522432i
$934$	−1.06265e21	−	4.33328e20i	−1.71381	−	0.698857i
$935$		−	9.24198e17i		−	0.00147939i
$936$	3.57327e20	−	1.54972e20i	0.567720	−	0.246219i
$937$	2.60931e20			0.411480			0.205740	−	0.978607i	$-0.434040\pi$
$937$	2.60931e20			0.411480			0.205740	+	0.978607i	$0.434040\pi$
$938$	−5.02830e20	+	1.23310e21i	−0.787049	+	1.93009i
$939$	6.22469e20			0.967072
$940$	3.23301e18	+	3.16259e18i	0.00498553	+	0.00487694i
$941$		−	8.35688e20i		−	1.27914i	−0.768734	−	0.639568i	$-0.779113\pi$
$941$		−	8.35688e20i		−	1.27914i	0.768734	−	0.639568i	$-0.220887\pi$
$942$	−1.93276e20	+	4.73973e20i	−0.293644	+	0.720107i
$943$			1.37869e21i			2.07915i
$944$	2.02084e19	+	9.17565e20i	0.0302502	+	1.37351i
$945$	1.23641e20			0.183713
$946$	−3.44928e19	−	1.40654e19i	−0.0508733	−	0.0207451i
$947$	−7.49531e20			−1.09734			−0.548668	−	0.836040i	$-0.684865\pi$
$947$	−7.49531e20			−1.09734			−0.548668	+	0.836040i	$0.684865\pi$
$948$	3.48487e20	−	3.56246e20i	0.506440	−	0.517717i
$949$		−	2.33888e20i		−	0.337399i
$950$	6.94248e20	+	2.83099e20i	0.994144	+	0.405390i
$951$		−	1.40391e20i		−	0.199561i
$952$	2.76051e20	−	1.19723e20i	0.389521	−	0.168934i
$953$	1.36160e21			1.90721			0.953607	−	0.301055i	$-0.0973386\pi$
$953$	1.36160e21			1.90721			0.953607	+	0.301055i	$0.0973386\pi$
$954$	3.86736e20	−	9.48396e20i	0.537744	−	1.31872i
$955$	−9.19888e19			−0.126973
$956$	−2.78184e20	+	2.84379e20i	−0.381178	+	0.389665i
$957$		−	1.36687e19i		−	0.0185927i
$958$	−3.83568e20	+	9.40627e20i	−0.517945	+	1.27016i
$959$		−	1.42650e21i		−	1.91224i
$960$	−3.57939e19	−	3.35041e19i	−0.0476333	−	0.0445861i
$961$	7.56852e20			0.999878
$962$	−5.01852e20	−	2.04645e20i	−0.658189	−	0.268395i
$963$	−4.07826e20			−0.530996
$964$	−6.33128e20	−	6.19338e20i	−0.818375	−	0.800549i
$965$			2.55838e17i			0.000328302i
$966$	−9.04655e20	−	3.68899e20i	−1.15251	−	0.469967i
$967$		−	4.87174e20i		−	0.616167i	−0.951359	−	0.308084i	$-0.900312\pi$
$967$		−	4.87174e20i		−	0.616167i	0.951359	−	0.308084i	$-0.0996876\pi$
$968$	−3.16204e20	−	7.29089e20i	−0.397045	−	0.915489i
$969$	1.19730e20			0.149257
$970$	3.56907e19	−	8.75248e19i	0.0441726	−	0.108325i
$971$	4.11013e20			0.505034			0.252517	−	0.967592i	$-0.418742\pi$
$971$	4.11013e20			0.505034			0.252517	+	0.967592i	$0.418742\pi$
$972$	−6.07190e20	−	5.93965e20i	−0.740731	−	0.724597i
$973$		−	3.06181e20i		−	0.370842i
$974$	−1.59583e20	+	3.91348e20i	−0.191900	+	0.470599i
$975$		−	3.72634e20i		−	0.444887i
$976$	1.40618e21	−	3.09698e19i	1.66684	−	0.0367104i
$977$	1.05489e21			1.24150			0.620750	−	0.784009i	$-0.286828\pi$
$977$	1.05489e21			1.24150			0.620750	+	0.784009i	$0.286828\pi$
$978$	3.24357e20	+	1.32266e20i	0.379010	+	0.154552i
$979$	−3.25873e19			−0.0378067
$980$	−1.25734e20	+	1.28533e20i	−0.144834	+	0.148058i
$981$		−	7.96125e20i		−	0.910538i
$982$	2.15855e20	+	8.80209e19i	0.245121	+	0.0999552i
$983$			6.46899e20i			0.729393i	0.931126	+	0.364697i	$0.118827\pi$
$983$			6.46899e20i			0.729393i	−0.931126	+	0.364697i	$0.881173\pi$
$984$	2.69808e20	+	6.22110e20i	0.302057	+	0.696469i
$985$	−1.47170e20			−0.163593
$986$	−6.80526e19	+	1.66886e20i	−0.0751115	+	0.184197i
$987$	4.43261e19			0.0485780
$988$	−6.00462e20	+	6.13833e20i	−0.653412	+	0.667961i
$989$		−	1.59476e21i		−	1.72314i
$990$	1.44784e18	−	3.55055e18i	0.00155336	−	0.00380933i
$991$		−	8.45945e20i		−	0.901211i	−0.892723	−	0.450605i	$-0.851208\pi$
$991$		−	8.45945e20i		−	0.901211i	0.892723	−	0.450605i	$-0.148792\pi$
$992$	9.74824e18	+	3.72696e18i	0.0103120	+	0.00394251i
$993$	−4.28556e20			−0.450155
$994$	8.89307e20	+	3.62641e20i	0.927571	+	0.378244i
$995$	−1.28666e20			−0.133261
$996$	4.14526e20	+	4.05497e20i	0.426321	+	0.417035i
$997$			1.67537e21i			1.71098i	0.517822	+	0.855489i	$0.326743\pi$
$997$			1.67537e21i			1.71098i	−0.517822	+	0.855489i	$0.673257\pi$
$998$	−1.28340e21	−	5.23344e20i	−1.30151	−	0.530729i
$999$			7.47736e20i			0.752991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.15.d.b.3.12	yes	12
3.2	odd	2		72.15.b.b.19.1		12
4.3	odd	2		32.15.d.b.15.7		12
8.3	odd	2	inner	8.15.d.b.3.11	✓	12
8.5	even	2		32.15.d.b.15.8		12
24.11	even	2		72.15.b.b.19.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.15.d.b.3.11	✓	12	8.3	odd	2	inner
8.15.d.b.3.12	yes	12	1.1	even	1	trivial
32.15.d.b.15.7		12	4.3	odd	2
32.15.d.b.15.8		12	8.5	even	2
72.15.b.b.19.1		12	3.2	odd	2
72.15.b.b.19.2		12	24.11	even	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(118.524 + 48.3317i) q^{2} -1152.97 q^{3} +(11712.1 + 11457.0i) q^{4} -9668.61i q^{5} +(-136655. - 55725.2i) q^{6} +1.34658e6i q^{7} +(834433. + 1.92400e6i) q^{8} -3.45362e6 q^{9} +O(q^{10})\)	\(q+(118.524 + 48.3317i) q^{2} -1152.97 q^{3} +(11712.1 + 11457.0i) q^{4} -9668.61i q^{5} +(-136655. - 55725.2i) q^{6} +1.34658e6i q^{7} +(834433. + 1.92400e6i) q^{8} -3.45362e6 q^{9} +(467301. - 1.14597e6i) q^{10} -897115. q^{11} +(-1.35037e7 - 1.32096e7i) q^{12} +5.37757e7i q^{13} +(-6.50826e7 + 1.59603e8i) q^{14} +1.11476e7i q^{15} +(5.91058e6 + 2.68370e8i) q^{16} -1.06550e8 q^{17} +(-4.09339e8 - 1.66920e8i) q^{18} +9.74607e8 q^{19} +(1.10773e8 - 1.13240e8i) q^{20} -1.55257e9i q^{21} +(-1.06330e8 - 4.33591e7i) q^{22} -4.91613e9i q^{23} +(-9.62079e8 - 2.21832e9i) q^{24} +6.01003e9 q^{25} +(-2.59907e9 + 6.37373e9i) q^{26} +9.49657e9 q^{27} +(-1.54277e10 + 1.57713e10i) q^{28} -1.32148e10i q^{29} +(-5.38785e8 + 1.32127e9i) q^{30} -3.03739e8i q^{31} +(-1.22703e10 + 3.20941e10i) q^{32} +1.03435e9 q^{33} +(-1.26288e10 - 5.14974e9i) q^{34} +1.30196e10 q^{35} +(-4.04491e10 - 3.95681e10i) q^{36} +7.87376e10i q^{37} +(1.15515e11 + 4.71044e10i) q^{38} -6.20019e10i q^{39} +(1.86024e10 - 8.06781e9i) q^{40} -2.80442e11 q^{41} +(7.50384e10 - 1.84018e11i) q^{42} +3.24393e11 q^{43} +(-1.05071e10 - 1.02782e10i) q^{44} +3.33917e10i q^{45} +(2.37605e11 - 5.82682e11i) q^{46} +2.85501e10i q^{47} +(-6.81474e9 - 3.09424e11i) q^{48} -1.13506e12 q^{49} +(7.12336e11 + 2.90475e11i) q^{50} +1.22849e11 q^{51} +(-6.16107e11 + 6.29826e11i) q^{52} +2.31690e12i q^{53} +(1.12558e12 + 4.58985e11i) q^{54} +8.67386e9i q^{55} +(-2.59082e12 + 1.12363e12i) q^{56} -1.12370e12 q^{57} +(6.38693e11 - 1.56627e12i) q^{58} +3.41902e12 q^{59} +(-1.27718e11 + 1.30562e11i) q^{60} -5.23972e12i q^{61} +(1.46802e10 - 3.60005e10i) q^{62} -4.65058e12i q^{63} +(-3.00549e12 + 3.21089e12i) q^{64} +5.19936e11 q^{65} +(1.22596e11 + 4.99919e10i) q^{66} +7.72604e12 q^{67} +(-1.24792e12 - 1.22074e12i) q^{68} +5.66817e12i q^{69} +(1.54314e12 + 6.29258e11i) q^{70} -5.57201e12i q^{71} +(-2.88182e12 - 6.64476e12i) q^{72} -4.34932e12 q^{73} +(-3.80552e12 + 9.33232e12i) q^{74} -6.92940e12 q^{75} +(1.14147e13 + 1.11661e13i) q^{76} -1.20804e12i q^{77} +(2.99666e12 - 7.34874e12i) q^{78} +2.63814e13i q^{79} +(2.59477e12 - 5.71471e10i) q^{80} +5.56929e12 q^{81} +(-3.32393e13 - 1.35543e13i) q^{82} -3.06972e13 q^{83} +(1.77878e13 - 1.81838e13i) q^{84} +1.03019e12i q^{85} +(3.84486e13 + 1.56785e13i) q^{86} +1.52363e13i q^{87} +(-7.48583e11 - 1.72605e12i) q^{88} +3.63245e13 q^{89} +(-1.61388e12 + 3.95774e12i) q^{90} -7.24133e13 q^{91} +(5.63241e13 - 5.75782e13i) q^{92} +3.50203e11i q^{93} +(-1.37988e12 + 3.38389e12i) q^{94} -9.42310e12i q^{95} +(1.41473e13 - 3.70036e13i) q^{96} +7.63764e13 q^{97} +(-1.34532e14 - 5.48592e13i) q^{98} +3.09830e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9}+O(q^{10}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9	\( 12 q + 218 q^{2} - 3024 q^{3} - 30828 q^{4} + 518556 q^{6} - 1097608 q^{8} + 13188036 q^{9} - 14533440 q^{10} - 28256720 q^{11} + 34920024 q^{12} + 191568384 q^{14} - 185822448 q^{16} + 270339544 q^{17} + 1420811358 q^{18} - 2481505872 q^{19} - 1679371200 q^{20} + 3042383484 q^{22} + 7581335184 q^{24} - 15857276820 q^{25} - 2773507776 q^{26} - 16574868000 q^{27} + 25329333120 q^{28} + 42207767040 q^{30} + 38309251808 q^{32} - 136227597840 q^{33} + 350437044 q^{34} + 149949623040 q^{35} - 150590403492 q^{36} + 102789916636 q^{38} - 66999085440 q^{40} + 264287409880 q^{41} - 110343609600 q^{42} + 32253127344 q^{43} - 585547356392 q^{44} + 864780977664 q^{46} - 2387663418144 q^{48} - 646589230644 q^{49} - 388785556630 q^{50} + 4755867895776 q^{51} + 798005307840 q^{52} + 1305053764344 q^{54} - 1050155264256 q^{56} - 7479401742480 q^{57} + 389204742720 q^{58} + 1223083947184 q^{59} + 4350689397120 q^{60} + 9957296947200 q^{62} - 16809671099328 q^{64} - 8069319822720 q^{65} - 6067132925784 q^{66} - 9309378171216 q^{67} + 32301846360616 q^{68} + 35197935521280 q^{70} - 43695386222808 q^{72} + 3619334364696 q^{73} - 55499920147776 q^{74} + 9079078926000 q^{75} + 33532610502360 q^{76} + 92515055193600 q^{78} - 86826189154560 q^{80} + 56467107312444 q^{81} - 146233962574956 q^{82} - 18774355695824 q^{83} + 186893160787200 q^{84} + 96253393476220 q^{86} - 166888683024624 q^{88} + 54781416936088 q^{89} - 488020221650880 q^{90} + 36699395136768 q^{91} + 413167093560960 q^{92} + 496016398930944 q^{94} - 616114307580864 q^{96} + 73839238696536 q^{97} - 523654870565638 q^{98} - 223606851712368 q^{99}+O(q^{100}) \) 12 * q + 218 * q^2 - 3024 * q^3 - 30828 * q^4 + 518556 * q^6 - 1097608 * q^8 + 13188036 * q^9 - 14533440 * q^10 - 28256720 * q^11 + 34920024 * q^12 + 191568384 * q^14 - 185822448 * q^16 + 270339544 * q^17 + 1420811358 * q^18 - 2481505872 * q^19 - 1679371200 * q^20 + 3042383484 * q^22 + 7581335184 * q^24 - 15857276820 * q^25 - 2773507776 * q^26 - 16574868000 * q^27 + 25329333120 * q^28 + 42207767040 * q^30 + 38309251808 * q^32 - 136227597840 * q^33 + 350437044 * q^34 + 149949623040 * q^35 - 150590403492 * q^36 + 102789916636 * q^38 - 66999085440 * q^40 + 264287409880 * q^41 - 110343609600 * q^42 + 32253127344 * q^43 - 585547356392 * q^44 + 864780977664 * q^46 - 2387663418144 * q^48 - 646589230644 * q^49 - 388785556630 * q^50 + 4755867895776 * q^51 + 798005307840 * q^52 + 1305053764344 * q^54 - 1050155264256 * q^56 - 7479401742480 * q^57 + 389204742720 * q^58 + 1223083947184 * q^59 + 4350689397120 * q^60 + 9957296947200 * q^62 - 16809671099328 * q^64 - 8069319822720 * q^65 - 6067132925784 * q^66 - 9309378171216 * q^67 + 32301846360616 * q^68 + 35197935521280 * q^70 - 43695386222808 * q^72 + 3619334364696 * q^73 - 55499920147776 * q^74 + 9079078926000 * q^75 + 33532610502360 * q^76 + 92515055193600 * q^78 - 86826189154560 * q^80 + 56467107312444 * q^81 - 146233962574956 * q^82 - 18774355695824 * q^83 + 186893160787200 * q^84 + 96253393476220 * q^86 - 166888683024624 * q^88 + 54781416936088 * q^89 - 488020221650880 * q^90 + 36699395136768 * q^91 + 413167093560960 * q^92 + 496016398930944 * q^94 - 616114307580864 * q^96 + 73839238696536 * q^97 - 523654870565638 * q^98 - 223606851712368 * q^99

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