LMFDB - Embedded newform 8.15.d.b.3.4

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			3.4
Root			$-37.2836 + 57.4111i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.15.d.b.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-56.5672 + 114.822i) q^{2} +1525.47 q^{3} +(-9984.31 - 12990.3i) q^{4} +71626.9i q^{5} +(-86291.8 + 175158. i) q^{6} +647418. i q^{7} +(2.05637e6 - 411594. i) q^{8} -2.45590e6 q^{9} +O(q^{10})$	\(q+(-56.5672 + 114.822i) q^{2} +1525.47 q^{3} +(-9984.31 - 12990.3i) q^{4} +71626.9i q^{5} +(-86291.8 + 175158. i) q^{6} +647418. i q^{7} +(2.05637e6 - 411594. i) q^{8} -2.45590e6 q^{9} +(-8.22436e6 - 4.05173e6i) q^{10} -2.62332e7 q^{11} +(-1.52308e7 - 1.98164e7i) q^{12} -4.43764e7i q^{13} +(-7.43380e7 - 3.66226e7i) q^{14} +1.09265e8i q^{15} +(-6.90627e7 + 2.59399e8i) q^{16} -4.73327e8 q^{17} +(1.38923e8 - 2.81992e8i) q^{18} +2.43904e8 q^{19} +(9.30458e8 - 7.15145e8i) q^{20} +9.87620e8i q^{21} +(1.48394e9 - 3.01215e9i) q^{22} +4.19839e9i q^{23} +(3.13693e9 - 6.27875e8i) q^{24} +9.73104e8 q^{25} +(5.09540e9 + 2.51025e9i) q^{26} -1.10427e10 q^{27} +(8.41019e9 - 6.46402e9i) q^{28} +2.44852e10i q^{29} +(-1.25461e10 - 6.18081e9i) q^{30} -1.22090e10i q^{31} +(-2.58781e10 - 2.26034e10i) q^{32} -4.00180e10 q^{33} +(2.67748e10 - 5.43485e10i) q^{34} -4.63726e10 q^{35} +(2.45204e10 + 3.19030e10i) q^{36} +6.12461e10i q^{37} +(-1.37969e10 + 2.80056e10i) q^{38} -6.76950e10i q^{39} +(2.94812e10 + 1.47291e11i) q^{40} +3.09998e11 q^{41} +(-1.13401e11 - 5.58669e10i) q^{42} +2.18162e11 q^{43} +(2.61920e11 + 3.40778e11i) q^{44} -1.75908e11i q^{45} +(-4.82069e11 - 2.37491e11i) q^{46} -8.36231e11i q^{47} +(-1.05353e11 + 3.95707e11i) q^{48} +2.59073e11 q^{49} +(-5.50458e10 + 1.11734e11i) q^{50} -7.22049e11 q^{51} +(-5.76464e11 + 4.43067e11i) q^{52} +2.10869e12i q^{53} +(6.24655e11 - 1.26795e12i) q^{54} -1.87900e12i q^{55} +(2.66473e11 + 1.33133e12i) q^{56} +3.72068e11 q^{57} +(-2.81145e12 - 1.38506e12i) q^{58} -2.27551e12 q^{59} +(1.41939e12 - 1.09093e12i) q^{60} +2.99592e12i q^{61} +(1.40186e12 + 6.90627e11i) q^{62} -1.58999e12i q^{63} +(4.05923e12 - 1.69277e12i) q^{64} +3.17854e12 q^{65} +(2.26371e12 - 4.59496e12i) q^{66} -8.46958e11 q^{67} +(4.72585e12 + 6.14869e12i) q^{68} +6.40454e12i q^{69} +(2.62316e12 - 5.32460e12i) q^{70} +1.11187e13i q^{71} +(-5.05022e12 + 1.01083e12i) q^{72} -9.55414e12 q^{73} +(-7.03241e12 - 3.46452e12i) q^{74} +1.48444e12 q^{75} +(-2.43521e12 - 3.16839e12i) q^{76} -1.69838e13i q^{77} +(7.77289e12 + 3.82932e12i) q^{78} -2.17735e13i q^{79} +(-1.85800e13 - 4.94674e12i) q^{80} -5.09887e12 q^{81} +(-1.75357e13 + 3.55947e13i) q^{82} +1.17387e13 q^{83} +(1.28295e13 - 9.86070e12i) q^{84} -3.39030e13i q^{85} +(-1.23408e13 + 2.50498e13i) q^{86} +3.73516e13i q^{87} +(-5.39450e13 + 1.07974e13i) q^{88} +5.85944e13 q^{89} +(2.01982e13 + 9.95064e12i) q^{90} +2.87301e13 q^{91} +(5.45386e13 - 4.19180e13i) q^{92} -1.86245e13i q^{93} +(9.60180e13 + 4.73033e13i) q^{94} +1.74701e13i q^{95} +(-3.94764e13 - 3.44809e13i) q^{96} -1.22880e14 q^{97} +(-1.46550e13 + 2.97473e13i) q^{98} +6.44260e13 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 $

$2$	−56.5672	+	114.822i	−0.441931	+	0.897049i
$2$	−56.5672	+	114.822i	−0.441931	+	0.897049i
$3$	1525.47			0.697519			0.348759	−	0.937212i	$-0.386603\pi$
$3$	1525.47			0.697519			0.348759	+	0.937212i	$0.386603\pi$
$4$	−9984.31	−	12990.3i	−0.609394	−	0.792868i
$5$			71626.9i			0.916824i	0.888740	+	0.458412i	$0.151582\pi$
$5$			71626.9i			0.916824i	−0.888740	+	0.458412i	$0.848418\pi$
$6$	−86291.8	+	175158.i	−0.308255	+	0.625709i
$7$			647418.i			0.786138i	0.919509	+	0.393069i	$0.128587\pi$
$7$			647418.i			0.786138i	−0.919509	+	0.393069i	$0.871413\pi$
$8$	2.05637e6	−	411594.i	0.980551	−	0.196263i
$9$	−2.45590e6			−0.513467
$10$	−8.22436e6	−	4.05173e6i	−0.822436	−	0.405173i
$11$	−2.62332e7			−1.34618			−0.673089	−	0.739562i	$-0.735033\pi$
$11$	−2.62332e7			−1.34618			−0.673089	+	0.739562i	$0.735033\pi$
$12$	−1.52308e7	−	1.98164e7i	−0.425064	−	0.553040i
$13$		−	4.43764e7i		−	0.707210i	−0.935395	−	0.353605i	$-0.884956\pi$
$13$		−	4.43764e7i		−	0.707210i	0.935395	−	0.353605i	$-0.115044\pi$
$14$	−7.43380e7	−	3.66226e7i	−0.705204	−	0.347419i
$15$			1.09265e8i			0.639502i
$16$	−6.90627e7	+	2.59399e8i	−0.257278	+	0.966337i
$17$	−4.73327e8			−1.15350			−0.576752	−	0.816919i	$-0.695680\pi$
$17$	−4.73327e8			−1.15350			−0.576752	+	0.816919i	$0.695680\pi$
$18$	1.38923e8	−	2.81992e8i	0.226917	−	0.460605i
$19$	2.43904e8			0.272862			0.136431	−	0.990650i	$-0.456437\pi$
$19$	2.43904e8			0.272862			0.136431	+	0.990650i	$0.456437\pi$
$20$	9.30458e8	−	7.15145e8i	0.726920	−	0.558707i
$21$			9.87620e8i			0.548346i
$22$	1.48394e9	−	3.01215e9i	0.594918	−	1.20759i
$23$			4.19839e9i			1.23307i	0.787327	+	0.616535i	$0.211464\pi$
$23$			4.19839e9i			1.23307i	−0.787327	+	0.616535i	$0.788536\pi$
$24$	3.13693e9	−	6.27875e8i	0.683953	−	0.136897i
$25$	9.73104e8			0.159433
$26$	5.09540e9	+	2.51025e9i	0.634402	+	0.312538i
$27$	−1.10427e10			−1.05567
$28$	8.41019e9	−	6.46402e9i	0.623303	−	0.479067i
$29$			2.44852e10i			1.41944i	0.704482	+	0.709722i	$0.251179\pi$
$29$			2.44852e10i			1.41944i	−0.704482	+	0.709722i	$0.748821\pi$
$30$	−1.25461e10	−	6.18081e9i	−0.573665	−	0.282616i
$31$		−	1.22090e10i		−	0.443759i	−0.975074	−	0.221880i	$-0.928781\pi$
$31$		−	1.22090e10i		−	0.443759i	0.975074	−	0.221880i	$-0.0712192\pi$
$32$	−2.58781e10	−	2.26034e10i	−0.753153	−	0.657846i
$33$	−4.00180e10			−0.938984
$34$	2.67748e10	−	5.43485e10i	0.509769	−	1.03475i
$35$	−4.63726e10			−0.720750
$36$	2.45204e10	+	3.19030e10i	0.312904	+	0.407112i
$37$			6.12461e10i			0.645158i	0.946543	+	0.322579i	$0.104550\pi$
$37$			6.12461e10i			0.645158i	−0.946543	+	0.322579i	$0.895450\pi$
$38$	−1.37969e10	+	2.80056e10i	−0.120586	+	0.244770i
$39$		−	6.76950e10i		−	0.493292i
$40$	2.94812e10	+	1.47291e11i	0.179939	+	0.898993i
$41$	3.09998e11			1.59174			0.795871	−	0.605467i	$-0.207013\pi$
$41$	3.09998e11			1.59174			0.795871	+	0.605467i	$0.207013\pi$
$42$	−1.13401e11	−	5.58669e10i	−0.491893	−	0.242331i
$43$	2.18162e11			0.802601			0.401300	−	0.915947i	$-0.368558\pi$
$43$	2.18162e11			0.802601			0.401300	+	0.915947i	$0.368558\pi$
$44$	2.61920e11	+	3.40778e11i	0.820352	+	1.06734i
$45$		−	1.75908e11i		−	0.470759i
$46$	−4.82069e11	−	2.37491e11i	−1.10613	−	0.544932i
$47$		−	8.36231e11i		−	1.65060i	−0.564695	−	0.825299i	$-0.691006\pi$
$47$		−	8.36231e11i		−	1.65060i	0.564695	−	0.825299i	$-0.308994\pi$
$48$	−1.05353e11	+	3.95707e11i	−0.179457	+	0.674039i
$49$	2.59073e11			0.381987
$50$	−5.50458e10	+	1.11734e11i	−0.0704586	+	0.143020i
$51$	−7.22049e11			−0.804591
$52$	−5.76464e11	+	4.43067e11i	−0.560724	+	0.430969i
$53$			2.10869e12i			1.79507i	0.440944	+	0.897534i	$0.354644\pi$
$53$			2.10869e12i			1.79507i	−0.440944	+	0.897534i	$0.645356\pi$
$54$	6.24655e11	−	1.26795e12i	0.466534	−	0.946990i
$55$		−	1.87900e12i		−	1.23421i
$56$	2.66473e11	+	1.33133e12i	0.154290	+	0.770848i
$57$	3.72068e11			0.190326
$58$	−2.81145e12	−	1.38506e12i	−1.27331	−	0.627296i
$59$	−2.27551e12			−0.914353			−0.457177	−	0.889376i	$-0.651139\pi$
$59$	−2.27551e12			−0.914353			−0.457177	+	0.889376i	$0.651139\pi$
$60$	1.41939e12	−	1.09093e12i	0.507041	−	0.389709i
$61$			2.99592e12i			0.953281i	0.879098	+	0.476641i	$0.158146\pi$
$61$			2.99592e12i			0.953281i	−0.879098	+	0.476641i	$0.841854\pi$
$62$	1.40186e12	+	6.90627e11i	0.398074	+	0.196111i
$63$		−	1.58999e12i		−	0.403656i
$64$	4.05923e12	−	1.69277e12i	0.922962	−	0.384892i
$65$	3.17854e12			0.648387
$66$	2.26371e12	−	4.59496e12i	0.414966	−	0.842315i
$67$	−8.46958e11			−0.139746			−0.0698729	−	0.997556i	$-0.522259\pi$
$67$	−8.46958e11			−0.139746			−0.0698729	+	0.997556i	$0.522259\pi$
$68$	4.72585e12	+	6.14869e12i	0.702938	+	0.914576i
$69$			6.40454e12i			0.860090i
$70$	2.62316e12	−	5.32460e12i	0.318522	−	0.646548i
$71$			1.11187e13i			1.22249i	0.791441	+	0.611245i	$0.209331\pi$
$71$			1.11187e13i			1.22249i	−0.791441	+	0.611245i	$0.790669\pi$
$72$	−5.05022e12	+	1.01083e12i	−0.503481	+	0.100775i
$73$	−9.55414e12			−0.864832			−0.432416	−	0.901674i	$-0.642339\pi$
$73$	−9.55414e12			−0.864832			−0.432416	+	0.901674i	$0.642339\pi$
$74$	−7.03241e12	−	3.46452e12i	−0.578738	−	0.285115i
$75$	1.48444e12			0.111208
$76$	−2.43521e12	−	3.16839e12i	−0.166280	−	0.216343i
$77$		−	1.69838e13i		−	1.05828i
$78$	7.77289e12	+	3.82932e12i	0.442507	+	0.218001i
$79$		−	2.17735e13i		−	1.13380i	−0.823785	−	0.566902i	$-0.808142\pi$
$79$		−	2.17735e13i		−	1.13380i	0.823785	−	0.566902i	$-0.191858\pi$
$80$	−1.85800e13	−	4.94674e12i	−0.885961	−	0.235879i
$81$	−5.09887e12			−0.222884
$82$	−1.75357e13	+	3.55947e13i	−0.703440	+	1.42787i
$83$	1.17387e13			0.432586			0.216293	−	0.976328i	$-0.430603\pi$
$83$	1.17387e13			0.432586			0.216293	+	0.976328i	$0.430603\pi$
$84$	1.28295e13	−	9.86070e12i	0.434766	−	0.334159i
$85$		−	3.39030e13i		−	1.05756i
$86$	−1.23408e13	+	2.50498e13i	−0.354694	+	0.719972i
$87$			3.73516e13i			0.990089i
$88$	−5.39450e13	+	1.07974e13i	−1.32000	+	0.264205i
$89$	5.85944e13			1.32473			0.662363	−	0.749183i	$-0.269554\pi$
$89$	5.85944e13			1.32473			0.662363	+	0.749183i	$0.269554\pi$
$90$	2.01982e13	+	9.95064e12i	0.422294	+	0.208043i
$91$	2.87301e13			0.555964
$92$	5.45386e13	−	4.19180e13i	0.977662	−	0.751426i
$93$		−	1.86245e13i		−	0.309530i
$94$	9.60180e13	+	4.73033e13i	1.48067	+	0.729451i
$95$			1.74701e13i			0.250166i
$96$	−3.94764e13	−	3.44809e13i	−0.525338	−	0.458860i
$97$	−1.22880e14			−1.52083			−0.760413	−	0.649440i	$-0.775003\pi$
$97$	−1.22880e14			−1.52083			−0.760413	+	0.649440i	$0.775003\pi$
$98$	−1.46550e13	+	2.97473e13i	−0.168812	+	0.342661i
$99$	6.44260e13			0.691218
$100$	−9.71577e12	−	1.26410e13i	−0.0971577	−	0.126410i
$101$		−	7.56889e13i		−	0.705964i	−0.935630	−	0.352982i	$-0.885168\pi$
$101$		−	7.56889e13i		−	0.705964i	0.935630	−	0.352982i	$-0.114832\pi$
$102$	4.08443e13	−	8.29073e13i	0.355574	−	0.721758i
$103$			1.41406e14i			1.14976i	0.818237	+	0.574881i	$0.194952\pi$
$103$			1.41406e14i			1.14976i	−0.818237	+	0.574881i	$0.805048\pi$
$104$	−1.82650e13	−	9.12540e13i	−0.138799	−	0.693455i
$105$	−7.07401e13			−0.502737
$106$	−2.42124e14	−	1.19283e14i	−1.61026	−	0.793297i
$107$	−1.12012e14			−0.697553			−0.348776	−	0.937206i	$-0.613403\pi$
$107$	−1.12012e14			−0.697553			−0.348776	+	0.937206i	$0.613403\pi$
$108$	1.10254e14	+	1.43449e14i	0.643320	+	0.837008i
$109$			9.21974e13i			0.504351i	0.967682	+	0.252176i	$0.0811460\pi$
$109$			9.21974e13i			0.504351i	−0.967682	+	0.252176i	$0.918854\pi$
$110$	2.15751e14	+	1.06290e14i	1.10715	+	0.545435i
$111$			9.34293e13i			0.450010i
$112$	−1.67940e14	−	4.47124e13i	−0.759674	−	0.202256i
$113$	5.97879e12			0.0254135			0.0127067	−	0.999919i	$-0.495955\pi$
$113$	5.97879e12			0.0254135			0.0127067	+	0.999919i	$0.495955\pi$
$114$	−2.10469e13	+	4.27217e13i	−0.0841111	+	0.170732i
$115$	−3.00718e14			−1.13051
$116$	3.18072e14	−	2.44468e14i	1.12543	−	0.865000i
$117$			1.08984e14i			0.363129i
$118$	1.28719e14	−	2.61279e14i	0.404081	−	0.820220i
$119$		−	3.06441e14i		−	0.906813i
$120$	4.49728e13	+	2.24689e14i	0.125511	+	0.627065i
$121$	3.08430e14			0.812194
$122$	−3.43998e14	−	1.69471e14i	−0.855140	−	0.421285i
$123$	4.72895e14			1.11027
$124$	−1.58599e14	+	1.21898e14i	−0.351842	+	0.270424i
$125$			5.06876e14i			1.06300i
$126$	1.82567e14	+	8.99414e13i	0.362099	+	0.178388i
$127$		−	8.30324e14i		−	1.55819i	−0.626904	−	0.779097i	$-0.715678\pi$
$127$		−	8.30324e14i		−	1.55819i	0.626904	−	0.779097i	$-0.284322\pi$
$128$	−3.52510e13	+	5.61845e14i	−0.0626184	+	0.998038i
$129$	3.32800e14			0.559829
$130$	−1.79801e14	+	3.64967e14i	−0.286542	+	0.581635i
$131$	8.02517e13			0.121215			0.0606073	−	0.998162i	$-0.480696\pi$
$131$	8.02517e13			0.121215			0.0606073	+	0.998162i	$0.480696\pi$
$132$	3.99553e14	+	5.19848e14i	0.572211	+	0.744490i
$133$			1.57908e14i			0.214507i
$134$	4.79101e13	−	9.72497e13i	0.0617580	−	0.125359i
$135$		−	7.90955e14i		−	0.967866i
$136$	−9.73334e14	+	1.94819e14i	−1.13107	+	0.226390i
$137$	7.15609e14			0.790009			0.395005	−	0.918679i	$-0.370743\pi$
$137$	7.15609e14			0.790009			0.395005	+	0.918679i	$0.370743\pi$
$138$	−7.35383e14	−	3.62287e14i	−0.771543	−	0.380101i
$139$	−1.26116e15			−1.25796			−0.628981	−	0.777421i	$-0.716527\pi$
$139$	−1.26116e15			−1.25796			−0.628981	+	0.777421i	$0.716527\pi$
$140$	4.62998e14	+	6.02395e14i	0.439221	+	0.571459i
$141$		−	1.27565e15i		−	1.15132i
$142$	−1.27667e15	−	6.28954e14i	−1.09663	−	0.540257i
$143$			1.16413e15i			0.952030i
$144$	1.69611e14	−	6.37058e14i	0.132104	−	0.496183i
$145$	−1.75380e15			−1.30138
$146$	5.40451e14	−	1.09703e15i	0.382196	−	0.775796i
$147$	3.95209e14			0.266444
$148$	7.95607e14	−	6.11499e14i	0.511525	−	0.393155i
$149$			1.93700e15i			1.18802i	0.804457	+	0.594011i	$0.202457\pi$
$149$			1.93700e15i			1.18802i	−0.804457	+	0.594011i	$0.797543\pi$
$150$	−8.39709e13	+	1.70447e14i	−0.0491462	+	0.0997588i
$151$		−	3.59580e14i		−	0.200890i	−0.994943	−	0.100445i	$-0.967973\pi$
$151$		−	3.59580e14i		−	0.200890i	0.994943	−	0.100445i	$-0.0320266\pi$
$152$	5.01555e14	−	1.00389e14i	0.267555	−	0.0535527i
$153$	1.16244e15			0.592287
$154$	1.95012e15	+	9.60728e14i	0.949330	+	0.467687i
$155$	8.74491e14			0.406849
$156$	−8.79381e14	+	6.75888e14i	−0.391116	+	0.300609i
$157$			3.09607e14i			0.131678i	0.997830	+	0.0658389i	$0.0209724\pi$
$157$			3.09607e14i			0.131678i	−0.997830	+	0.0658389i	$0.979028\pi$
$158$	2.50008e15	+	1.23166e15i	1.01708	+	0.501063i
$159$			3.21675e15i			1.25209i
$160$	1.61901e15	−	1.85357e15i	0.603129	−	0.690508i
$161$	−2.71812e15			−0.969364
$162$	2.88429e14	−	5.85464e14i	0.0984994	−	0.199938i
$163$	5.35319e14			0.175105			0.0875527	−	0.996160i	$-0.472095\pi$
$163$	5.35319e14			0.175105			0.0875527	+	0.996160i	$0.472095\pi$
$164$	−3.09512e15	−	4.02699e15i	−0.969997	−	1.26204i
$165$		−	2.86637e15i		−	0.860884i
$166$	−6.64025e14	+	1.34786e15i	−0.191173	+	0.388051i
$167$			8.36851e14i			0.231011i	0.993307	+	0.115505i	$0.0368488\pi$
$167$			8.36851e14i			0.231011i	−0.993307	+	0.115505i	$0.963151\pi$
$168$	4.06498e14	+	2.03091e15i	0.107620	+	0.537681i
$169$	1.96811e15			0.499854
$170$	3.89282e15	+	1.91780e15i	0.948684	+	0.467369i
$171$	−5.99002e14			−0.140106
$172$	−2.17819e15	−	2.83400e15i	−0.489100	−	0.636356i
$173$		−	5.97565e14i		−	0.128844i	−0.997923	−	0.0644218i	$-0.979480\pi$
$173$		−	5.97565e14i		−	0.128844i	0.997923	−	0.0644218i	$-0.0205203\pi$
$174$	−4.28879e15	−	2.11287e15i	−0.888158	−	0.437551i
$175$			6.30005e14i			0.125337i
$176$	1.81173e15	−	6.80487e15i	0.346343	−	1.30086i
$177$	−3.47123e15			−0.637779
$178$	−3.31452e15	+	6.72795e15i	−0.585438	+	1.18834i
$179$	−2.30776e15			−0.391940			−0.195970	−	0.980610i	$-0.562785\pi$
$179$	−2.30776e15			−0.391940			−0.195970	+	0.980610i	$0.562785\pi$
$180$	−2.28511e15	+	1.75632e15i	−0.373250	+	0.286878i
$181$		−	7.48986e15i		−	1.17686i	−0.808549	−	0.588429i	$-0.799747\pi$
$181$		−	7.48986e15i		−	1.17686i	0.808549	−	0.588429i	$-0.200253\pi$
$182$	−1.62518e15	+	3.29885e15i	−0.245698	+	0.498727i
$183$			4.57019e15i			0.664932i
$184$	1.72803e15	+	8.63343e15i	0.242006	+	1.20909i
$185$	−4.38686e15			−0.591496
$186$	2.13850e15	+	1.05353e15i	0.277664	+	0.136791i
$187$	1.24169e16			1.55282
$188$	−1.08629e16	+	8.34919e15i	−1.30871	+	1.00586i
$189$		−	7.14925e15i		−	0.829904i
$190$	−2.00595e15	−	9.88232e14i	−0.224411	−	0.110556i
$191$		−	7.20198e15i		−	0.776637i	−0.921525	−	0.388319i	$-0.873056\pi$
$191$		−	7.20198e15i		−	0.776637i	0.921525	−	0.388319i	$-0.126944\pi$
$192$	6.19225e15	−	2.58228e15i	0.643783	−	0.268470i
$193$	1.51552e16			1.51935			0.759677	−	0.650300i	$-0.225357\pi$
$193$	1.51552e16			1.51935			0.759677	+	0.650300i	$0.225357\pi$
$194$	6.95098e15	−	1.41094e16i	0.672100	−	1.36425i
$195$	4.84878e15			0.452262
$196$	−2.58666e15	−	3.36544e15i	−0.232781	−	0.302866i
$197$			5.93113e15i			0.515079i	0.966268	+	0.257540i	$0.0829118\pi$
$197$			5.93113e15i			0.515079i	−0.966268	+	0.257540i	$0.917088\pi$
$198$	−3.64440e15	+	7.39754e15i	−0.305471	+	0.620056i
$199$		−	3.39907e15i		−	0.275035i	−0.990499	−	0.137518i	$-0.956088\pi$
$199$		−	3.39907e15i		−	0.275035i	0.990499	−	0.137518i	$-0.0439124\pi$
$200$	2.00106e15	−	4.00523e14i	0.156333	−	0.0312909i
$201$	−1.29201e15			−0.0974753
$202$	8.69077e15	+	4.28151e15i	0.633284	+	0.311987i
$203$	−1.58522e16			−1.11588
$204$	7.20915e15	+	9.37966e15i	0.490313	+	0.637934i
$205$			2.22042e16i			1.45935i
$206$	−1.62366e16	−	7.99896e15i	−1.03139	−	0.508116i
$207$		−	1.03108e16i		−	0.633142i
$208$	1.15112e16	+	3.06475e15i	0.683403	+	0.181950i
$209$	−6.39837e15			−0.367321
$210$	4.00157e15	−	8.12254e15i	0.222175	−	0.450980i
$211$	−1.58626e16			−0.851916			−0.425958	−	0.904743i	$-0.640063\pi$
$211$	−1.58626e16			−0.851916			−0.425958	+	0.904743i	$0.640063\pi$
$212$	2.73926e16	−	2.10538e16i	1.42325	−	1.09390i
$213$			1.69613e16i			0.852710i
$214$	6.33619e15	−	1.28614e16i	0.308270	−	0.625739i
$215$			1.56263e16i			0.735844i
$216$	−2.27078e16	+	4.54511e15i	−1.03514	+	0.207190i
$217$	7.90431e15			0.348856
$218$	−1.05863e16	−	5.21534e15i	−0.452428	−	0.222888i
$219$	−1.45746e16			−0.603237
$220$	−2.44089e16	+	1.87605e16i	−0.978564	+	0.752119i
$221$			2.10045e16i			0.815769i
$222$	−1.07278e16	−	5.28503e15i	−0.403681	−	0.198873i
$223$		−	3.39801e16i		−	1.23906i	−0.784975	−	0.619528i	$-0.787324\pi$
$223$		−	3.39801e16i		−	1.23906i	0.784975	−	0.619528i	$-0.212676\pi$
$224$	1.46339e16	−	1.67540e16i	0.517158	−	0.592082i
$225$	−2.38984e15			−0.0818638
$226$	−3.38203e14	+	6.86498e14i	−0.0112310	+	0.0227971i
$227$	−1.95996e16			−0.631055			−0.315527	−	0.948917i	$-0.602181\pi$
$227$	−1.95996e16			−0.631055			−0.315527	+	0.948917i	$0.602181\pi$
$228$	−3.71485e15	−	4.83330e15i	−0.115984	−	0.150904i
$229$		−	9.76842e15i		−	0.295785i	−0.989003	−	0.147892i	$-0.952751\pi$
$229$		−	9.76842e15i		−	0.295785i	0.989003	−	0.147892i	$-0.0472489\pi$
$230$	1.70108e16	−	3.45291e16i	0.499607	−	1.01412i
$231$		−	2.59084e16i		−	0.738171i
$232$	1.00780e16	+	5.03506e16i	0.278585	+	1.39184i
$233$	−1.90039e16			−0.509743			−0.254872	−	0.966975i	$-0.582033\pi$
$233$	−1.90039e16			−0.509743			−0.254872	+	0.966975i	$0.582033\pi$
$234$	−1.25138e16	−	6.16491e15i	−0.325745	−	0.160478i
$235$	5.98967e16			1.51331
$236$	2.27194e16	+	2.95596e16i	0.557201	+	0.724961i
$237$		−	3.32149e16i		−	0.790850i
$238$	3.51862e16	+	1.73345e16i	0.813456	+	0.400749i
$239$			7.69874e16i			1.72836i	0.503182	+	0.864180i	$0.332162\pi$
$239$			7.69874e16i			1.72836i	−0.503182	+	0.864180i	$0.667838\pi$
$240$	−2.83432e16	−	7.54613e15i	−0.617975	−	0.164530i
$241$	4.00462e16			0.848091			0.424045	−	0.905641i	$-0.360610\pi$
$241$	4.00462e16			0.848091			0.424045	+	0.905641i	$0.360610\pi$
$242$	−1.74470e16	+	3.54147e16i	−0.358934	+	0.728578i
$243$	4.50387e16			0.900206
$244$	3.89180e16	−	2.99122e16i	0.755826	−	0.580924i
$245$			1.85566e16i			0.350215i
$246$	−2.67503e16	+	5.42988e16i	−0.490663	+	0.995967i
$247$		−	1.08236e16i		−	0.192971i
$248$	−5.02514e15	−	2.51061e16i	−0.0870936	−	0.435129i
$249$	1.79071e16			0.301737
$250$	−5.82007e16	−	2.86726e16i	−0.953560	−	0.469771i
$251$	−3.36178e16			−0.535615			−0.267808	−	0.963472i	$-0.586299\pi$
$251$	−3.36178e16			−0.535615			−0.267808	+	0.963472i	$0.586299\pi$
$252$	−2.06546e16	+	1.58750e16i	−0.320046	+	0.245985i
$253$		−	1.10137e17i		−	1.65993i
$254$	9.53396e16	+	4.69691e16i	1.39778	+	0.688614i
$255$		−	5.17181e16i		−	0.737669i
$256$	−6.25183e16	−	3.58296e16i	−0.867616	−	0.497236i
$257$	6.36190e15			0.0859122			0.0429561	−	0.999077i	$-0.486322\pi$
$257$	6.36190e15			0.0859122			0.0429561	+	0.999077i	$0.486322\pi$
$258$	−1.88256e16	+	3.82129e16i	−0.247406	+	0.502194i
$259$	−3.96518e16			−0.507183
$260$	−3.17355e16	−	4.12903e16i	−0.395123	−	0.514085i
$261$		−	6.01332e16i		−	0.728838i
$262$	−4.53961e15	+	9.21468e15i	−0.0535685	+	0.108735i
$263$			5.16278e16i			0.593189i	0.955003	+	0.296595i	$0.0958510\pi$
$263$			5.16278e16i			0.593189i	−0.955003	+	0.296595i	$0.904149\pi$
$264$	−8.22917e16	+	1.64712e16i	−0.920722	+	0.184288i
$265$	−1.51039e17			−1.64576
$266$	−1.81313e16	−	8.93239e15i	−0.192423	−	0.0947973i
$267$	8.93843e16			0.924022
$268$	8.45629e15	+	1.10023e16i	0.0851602	+	0.110800i
$269$			6.56049e16i			0.643681i	0.946794	+	0.321840i	$0.104301\pi$
$269$			6.56049e16i			0.643681i	−0.946794	+	0.321840i	$0.895699\pi$
$270$	9.08192e16	+	4.47421e16i	0.868223	+	0.427730i
$271$			9.82232e16i			0.915017i	0.889205	+	0.457508i	$0.151258\pi$
$271$			9.82232e16i			0.915017i	−0.889205	+	0.457508i	$0.848742\pi$
$272$	3.26893e16	−	1.22781e17i	0.296772	−	1.11467i
$273$	4.38270e16			0.387796
$274$	−4.04800e16	+	8.21679e16i	−0.349130	+	0.708677i
$275$	−2.55276e16			−0.214626
$276$	8.31971e16	−	6.39449e16i	0.681938	−	0.524134i
$277$			6.64910e16i			0.531379i	0.964059	+	0.265690i	$0.0855996\pi$
$277$			6.64910e16i			0.531379i	−0.964059	+	0.265690i	$0.914400\pi$
$278$	7.13404e16	−	1.44809e17i	0.555932	−	1.12845i
$279$			2.99840e16i			0.227856i
$280$	−9.53589e16	+	1.90866e16i	−0.706732	+	0.141457i
$281$	−1.22914e17			−0.888502			−0.444251	−	0.895902i	$-0.646530\pi$
$281$	−1.22914e17			−0.888502			−0.444251	+	0.895902i	$0.646530\pi$
$282$	1.46473e17	+	7.21599e16i	1.03279	+	0.508806i
$283$	3.73195e16			0.256703			0.128351	−	0.991729i	$-0.459031\pi$
$283$	3.73195e16			0.256703			0.128351	+	0.991729i	$0.459031\pi$
$284$	1.44436e17	−	1.11013e17i	0.969273	−	0.744978i
$285$			2.66501e16i			0.174496i
$286$	−1.33668e17	−	6.58518e16i	−0.854017	−	0.420732i
$287$			2.00699e17i			1.25133i
$288$	6.35540e16	+	5.55117e16i	0.386719	+	0.337782i
$289$	5.56610e16			0.330572
$290$	9.92076e16	−	2.01375e17i	0.575121	−	1.16740i
$291$	−1.87450e17			−1.06080
$292$	9.53915e16	+	1.24112e17i	0.527023	+	0.685697i
$293$		−	1.95251e17i		−	1.05322i	−0.850106	−	0.526612i	$-0.823462\pi$
$293$		−	1.95251e17i		−	1.05322i	0.850106	−	0.526612i	$-0.176538\pi$
$294$	−2.23558e16	+	4.53788e16i	−0.117750	+	0.239013i
$295$		−	1.62987e17i		−	0.838301i
$296$	2.52085e16	+	1.25944e17i	0.126621	+	0.632611i
$297$	2.89685e17			1.42112
$298$	−2.22410e17	−	1.09570e17i	−1.06571	−	0.525024i
$299$	1.86309e17			0.872040
$300$	−1.48212e16	−	1.92835e16i	−0.0677693	−	0.0881731i
$301$			1.41242e17i			0.630955i
$302$	4.12878e16	+	2.03405e16i	0.180208	+	0.0887794i
$303$		−	1.15461e17i		−	0.492423i
$304$	−1.68446e16	+	6.32684e16i	−0.0702015	+	0.263677i
$305$	−2.14588e17			−0.873991
$306$	−6.57562e16	+	1.33474e17i	−0.261750	+	0.531310i
$307$	−1.97920e17			−0.770054			−0.385027	−	0.922905i	$-0.625808\pi$
$307$	−1.97920e17			−0.770054			−0.385027	+	0.922905i	$0.625808\pi$
$308$	−2.20626e17	+	1.69572e17i	−0.839077	+	0.644910i
$309$			2.15712e17i			0.801981i
$310$	−4.94675e16	+	1.00411e17i	−0.179799	+	0.364964i
$311$		−	2.81869e17i		−	1.00167i	−0.865543	−	0.500834i	$-0.833027\pi$
$311$		−	2.81869e17i		−	1.00167i	0.865543	−	0.500834i	$-0.166973\pi$
$312$	−2.78628e16	−	1.39206e17i	−0.0968151	−	0.483698i
$313$	1.54447e17			0.524770			0.262385	−	0.964963i	$-0.415491\pi$
$313$	1.54447e17			0.524770			0.262385	+	0.964963i	$0.415491\pi$
$314$	−3.55497e16	−	1.75136e16i	−0.118122	−	0.0581926i
$315$	1.13886e17			0.370082
$316$	−2.82845e17	+	2.17393e17i	−0.898957	+	0.690933i
$317$			1.86896e17i			0.581014i	0.956873	+	0.290507i	$0.0938239\pi$
$317$			1.86896e17i			0.581014i	−0.956873	+	0.290507i	$0.906176\pi$
$318$	−3.69354e17	−	1.81962e17i	−1.12319	−	0.553340i
$319$		−	6.42326e17i		−	1.91082i
$320$	1.21248e17	+	2.90750e17i	0.352878	+	0.846194i
$321$	−1.70871e17			−0.486556
$322$	1.53756e17	−	3.12100e17i	0.428392	−	0.869567i
$323$	−1.15446e17			−0.314747
$324$	5.09087e16	+	6.62361e16i	0.135824	+	0.176718i
$325$		−	4.31828e16i		−	0.112753i
$326$	−3.02815e16	+	6.14666e16i	−0.0773846	+	0.157078i
$327$			1.40645e17i			0.351794i
$328$	6.37470e17	−	1.27593e17i	1.56078	−	0.312400i
$329$	5.41391e17			1.29760
$330$	3.29123e17	+	1.62142e17i	0.772255	+	0.380451i
$331$	−1.92070e17			−0.441230			−0.220615	−	0.975361i	$-0.570806\pi$
$331$	−1.92070e17			−0.441230			−0.220615	+	0.975361i	$0.570806\pi$
$332$	−1.17203e17	−	1.52490e17i	−0.263615	−	0.342984i
$333$		−	1.50414e17i		−	0.331268i
$334$	−9.60891e16	−	4.73383e16i	−0.207228	−	0.102091i
$335$		−	6.06650e16i		−	0.128122i
$336$	−2.56188e17	−	6.82077e16i	−0.529887	−	0.141078i
$337$	4.94908e17			1.00257			0.501285	−	0.865282i	$-0.332861\pi$
$337$	4.94908e17			1.00257			0.501285	+	0.865282i	$0.332861\pi$
$338$	−1.11331e17	+	2.25983e17i	−0.220901	+	0.448394i
$339$	9.12048e15			0.0177264
$340$	−4.40411e17	+	3.38498e17i	−0.838506	+	0.644471i
$341$			3.20280e17i			0.597379i
$342$	3.38839e16	−	6.87788e16i	0.0619170	−	0.125682i
$343$			6.06822e17i			1.08643i
$344$	4.48620e17	−	8.97940e16i	0.786991	−	0.157521i
$345$	−4.58737e17			−0.788552
$346$	6.86138e16	+	3.38026e16i	0.115579	+	0.0569400i
$347$	8.25374e17			1.36253			0.681263	−	0.732039i	$-0.261431\pi$
$347$	8.25374e17			1.36253			0.681263	+	0.732039i	$0.261431\pi$
$348$	4.85210e17	−	3.72930e17i	0.785010	−	0.603354i
$349$		−	8.15432e16i		−	0.129303i	−0.997908	−	0.0646517i	$-0.979406\pi$
$349$		−	8.15432e16i		−	0.129303i	0.997908	−	0.0646517i	$-0.0205936\pi$
$350$	−7.23386e16	−	3.56376e16i	−0.112433	−	0.0553901i
$351$			4.90035e17i			0.746582i
$352$	6.78866e17	+	5.92960e17i	1.01388	+	0.885577i
$353$	−8.56577e17			−1.25413			−0.627066	−	0.778966i	$-0.715744\pi$
$353$	−8.56577e17			−1.25413			−0.627066	+	0.778966i	$0.715744\pi$
$354$	1.96357e17	−	3.98574e17i	0.281854	−	0.572119i
$355$	−7.96398e17			−1.12081
$356$	−5.85025e17	−	7.61162e17i	−0.807280	−	1.05033i
$357$		−	4.67467e17i		−	0.632519i
$358$	1.30543e17	−	2.64982e17i	0.173210	−	0.351589i
$359$			5.84544e17i			0.760600i	0.924863	+	0.380300i	$0.124179\pi$
$359$			5.84544e17i			0.760600i	−0.924863	+	0.380300i	$0.875821\pi$
$360$	−7.24027e16	−	3.61732e17i	−0.0923927	−	0.461604i
$361$	−7.39518e17			−0.925546
$362$	8.60003e17	+	4.23680e17i	1.05570	+	0.520090i
$363$	4.70503e17			0.566521
$364$	−2.86850e17	−	3.73214e17i	−0.338801	−	0.440806i
$365$		−	6.84333e17i		−	0.792899i
$366$	−5.24760e17	−	2.58523e17i	−0.596476	−	0.293854i
$367$		−	1.84196e17i		−	0.205408i	−0.994712	−	0.102704i	$-0.967251\pi$
$367$		−	1.84196e17i		−	0.205408i	0.994712	−	0.102704i	$-0.0327494\pi$
$368$	−1.08906e18	−	2.89952e17i	−1.19156	−	0.317243i
$369$	−7.61325e17			−0.817307
$370$	2.48153e17	−	5.03710e17i	0.261401	−	0.530601i
$371$	−1.36520e18			−1.41117
$372$	−2.41938e17	+	1.85952e17i	−0.245417	+	0.188626i
$373$			1.18928e18i			1.18392i	0.805969	+	0.591958i	$0.201645\pi$
$373$			1.18928e18i			1.18392i	−0.805969	+	0.591958i	$0.798355\pi$
$374$	−7.02388e17	+	1.42574e18i	−0.686240	+	1.39296i
$375$			7.73227e17i			0.741460i
$376$	−3.44188e17	−	1.71960e18i	−0.323952	−	1.61850i
$377$	1.08657e18			1.00384
$378$	8.20893e17	+	4.04413e17i	0.744464	+	0.366760i
$379$	2.03665e18			1.81319			0.906594	−	0.422004i	$-0.138673\pi$
$379$	2.03665e18			1.81319			0.906594	+	0.422004i	$0.138673\pi$
$380$	2.26942e17	−	1.74426e17i	0.198349	−	0.152450i
$381$		−	1.26664e18i		−	1.08687i
$382$	8.26947e17	+	4.07396e17i	0.696682	+	0.343220i
$383$			5.64970e17i			0.467341i	0.972316	+	0.233671i	$0.0750737\pi$
$383$			5.64970e17i			0.467341i	−0.972316	+	0.233671i	$0.924926\pi$
$384$	−5.37745e16	+	8.57080e17i	−0.0436775	+	0.696150i
$385$	1.21650e18			0.970258
$386$	−8.57285e17	+	1.74015e18i	−0.671450	+	1.36294i
$387$	−5.35783e17			−0.412109
$388$	1.22687e18	+	1.59625e18i	0.926782	+	1.20581i
$389$		−	2.56036e18i		−	1.89956i	−0.312911	−	0.949782i	$-0.601304\pi$
$389$		−	2.56036e18i		−	1.89956i	0.312911	−	0.949782i	$-0.398696\pi$
$390$	−2.74282e17	+	5.56748e17i	−0.199869	+	0.405701i
$391$		−	1.98721e18i		−	1.42235i
$392$	5.32748e17	−	1.06633e17i	0.374558	−	0.0749701i
$393$	1.22422e17			0.0845495
$394$	−6.81026e17	−	3.35508e17i	−0.462051	−	0.227630i
$395$	1.55957e18			1.03950
$396$	−6.43249e17	−	8.36917e17i	−0.421224	−	0.548045i
$397$			2.63183e18i			1.69327i	0.532178	+	0.846633i	$0.321374\pi$
$397$			2.63183e18i			1.69327i	−0.532178	+	0.846633i	$0.678626\pi$
$398$	3.90289e17	+	1.92276e17i	0.246720	+	0.121547i
$399$			2.40884e17i			0.149623i
$400$	−6.72052e16	+	2.52422e17i	−0.0410188	+	0.154066i
$401$	−2.68947e16			−0.0161308			−0.00806542	−	0.999967i	$-0.502567\pi$
$401$	−2.68947e16			−0.0161308			−0.00806542	+	0.999967i	$0.502567\pi$
$402$	7.30855e16	−	1.48352e17i	0.0430774	−	0.0874401i
$403$	−5.41790e17			−0.313831
$404$	−9.83225e17	+	7.55701e17i	−0.559736	+	0.430210i
$405$		−	3.65216e17i		−	0.204346i
$406$	8.96714e17	−	1.82018e18i	0.493141	−	1.00100i
$407$		−	1.60668e18i		−	0.868497i
$408$	−1.48480e18	+	2.97191e17i	−0.788943	+	0.157912i
$409$	4.68170e17			0.244535			0.122267	−	0.992497i	$-0.460983\pi$
$409$	4.68170e17			0.244535			0.122267	+	0.992497i	$0.460983\pi$
$410$	−2.54954e18	−	1.25603e18i	−1.30911	−	0.644931i
$411$	1.09164e18			0.551046
$412$	1.83692e18	−	1.41184e18i	0.911610	−	0.700658i
$413$		−	1.47320e18i		−	0.718808i
$414$	1.18391e18	+	5.83254e17i	0.567959	+	0.279805i
$415$			8.40806e17i			0.396606i
$416$	−1.00306e18	+	1.14838e18i	−0.465235	+	0.532637i
$417$	−1.92387e18			−0.877452
$418$	3.61938e17	−	7.34675e17i	0.162330	−	0.329504i
$419$	−2.67204e18			−1.17854			−0.589270	−	0.807936i	$-0.700585\pi$
$419$	−2.67204e18			−1.17854			−0.589270	+	0.807936i	$0.700585\pi$
$420$	7.06291e17	+	9.18939e17i	0.306365	+	0.398604i
$421$			3.04901e18i			1.30072i	0.759625	+	0.650361i	$0.225382\pi$
$421$			3.04901e18i			1.30072i	−0.759625	+	0.650361i	$0.774618\pi$
$422$	8.97302e17	−	1.82138e18i	0.376488	−	0.764210i
$423$			2.05370e18i			0.847528i
$424$	8.67922e17	+	4.33623e18i	0.352306	+	1.76016i
$425$	−4.60597e17			−0.183907
$426$	−1.94753e18	−	9.59452e17i	−0.764923	−	0.376839i
$427$	−1.93961e18			−0.749410
$428$	1.11836e18	+	1.45507e18i	0.425084	+	0.553067i
$429$			1.77586e18i			0.664059i
$430$	−1.79424e18	−	8.83933e17i	−0.660088	−	0.325192i
$431$		−	2.52594e18i		−	0.914287i	−0.889393	−	0.457144i	$-0.848873\pi$
$431$		−	2.52594e18i		−	0.914287i	0.889393	−	0.457144i	$-0.151127\pi$
$432$	7.62639e17	−	2.86447e18i	0.271602	−	1.02014i
$433$	1.70185e18			0.596358			0.298179	−	0.954510i	$-0.403621\pi$
$433$	1.70185e18			0.596358			0.298179	+	0.954510i	$0.403621\pi$
$434$	−4.47125e17	+	9.07591e17i	−0.154170	+	0.312941i
$435$	−2.67538e18			−0.907738
$436$	1.19768e18	−	9.20527e17i	0.399884	−	0.307348i
$437$			1.02400e18i			0.336458i
$438$	8.24444e17	−	1.67349e18i	0.266589	−	0.541133i
$439$		−	4.64881e18i		−	1.47942i	−0.672928	−	0.739708i	$-0.734963\pi$
$439$		−	4.64881e18i		−	1.47942i	0.672928	−	0.739708i	$-0.265037\pi$
$440$	−7.73385e17	−	3.86391e18i	−0.242230	−	1.21020i
$441$	−6.36256e17			−0.196138
$442$	−2.41179e18	−	1.18817e18i	−0.731785	−	0.360514i
$443$	5.37897e18			1.60647			0.803237	−	0.595660i	$-0.203110\pi$
$443$	5.37897e18			1.60647			0.803237	+	0.595660i	$0.203110\pi$
$444$	1.21368e18	−	9.32827e17i	0.356798	−	0.274233i
$445$			4.19694e18i			1.21454i
$446$	3.90167e18	+	1.92216e18i	1.11149	+	0.547577i
$447$			2.95484e18i			0.828668i
$448$	1.09593e18	+	2.62802e18i	0.302578	+	0.725575i
$449$	5.15587e18			1.40145			0.700725	−	0.713431i	$-0.252860\pi$
$449$	5.15587e18			1.40145			0.700725	+	0.713431i	$0.252860\pi$
$450$	1.35187e17	−	2.74407e17i	0.0361782	−	0.0734359i
$451$	−8.13225e18			−2.14277
$452$	−5.96940e16	−	7.76665e16i	−0.0154868	−	0.0201495i
$453$		−	5.48531e17i		−	0.140124i
$454$	1.10870e18	−	2.25047e18i	0.278883	−	0.566087i
$455$			2.05785e18i			0.509722i
$456$	7.65109e17	−	1.53141e17i	0.186625	−	0.0373540i
$457$	−2.95354e18			−0.709462			−0.354731	−	0.934968i	$-0.615428\pi$
$457$	−2.95354e18			−0.709462			−0.354731	+	0.934968i	$0.615428\pi$
$458$	1.12163e18	+	5.52572e17i	0.265333	+	0.130716i
$459$	5.22681e18			1.21772
$460$	3.00246e18	+	3.90643e18i	0.688925	+	0.896344i
$461$		−	5.96403e17i		−	0.134782i	−0.997727	−	0.0673912i	$-0.978532\pi$
$461$		−	5.96403e17i		−	0.134782i	0.997727	−	0.0673912i	$-0.0214675\pi$
$462$	2.97486e18	+	1.46557e18i	0.662176	+	0.326221i
$463$		−	2.71037e18i		−	0.594239i	−0.954840	−	0.297119i	$-0.903974\pi$
$463$		−	2.71037e18i		−	0.594239i	0.954840	−	0.297119i	$-0.0960259\pi$
$464$	−6.35145e18	−	1.69102e18i	−1.37166	−	0.365192i
$465$	1.33401e18			0.283785
$466$	1.07500e18	−	2.18207e18i	0.225271	−	0.457265i
$467$	4.05140e18			0.836348			0.418174	−	0.908367i	$-0.362670\pi$
$467$	4.05140e18			0.836348			0.418174	+	0.908367i	$0.362670\pi$
$468$	1.41574e18	−	1.08813e18i	0.287913	−	0.221289i
$469$		−	5.48336e17i		−	0.109859i
$470$	−3.38819e18	+	6.87747e18i	−0.668778	+	1.35751i
$471$			4.72297e17i			0.0918478i
$472$	−4.67927e18	+	9.36584e17i	−0.896570	+	0.179454i
$473$	−5.72308e18			−1.08044
$474$	3.81381e18	+	1.87887e18i	0.709431	+	0.349501i
$475$	2.37344e17			0.0435033
$476$	−3.98077e18	+	3.05960e18i	−0.718983	+	0.552606i
$477$		−	5.17872e18i		−	0.921709i
$478$	−8.83987e18	−	4.35496e18i	−1.55042	−	0.763816i
$479$		−	1.39642e17i		−	0.0241361i	−0.999927	−	0.0120681i	$-0.996159\pi$
$479$		−	1.39642e17i		−	0.0241361i	0.999927	−	0.0120681i	$-0.00384148\pi$
$480$	2.46976e18	−	2.82757e18i	0.420694	−	0.481643i
$481$	2.71788e18			0.456262
$482$	−2.26530e18	+	4.59820e18i	−0.374798	+	0.760779i
$483$	−4.14641e18			−0.676150
$484$	−3.07946e18	−	4.00662e18i	−0.494946	−	0.643962i
$485$		−	8.80152e18i		−	1.39433i
$486$	−2.54771e18	+	5.17145e18i	−0.397829	+	0.807529i
$487$			5.02238e17i			0.0773048i	0.999253	+	0.0386524i	$0.0123065\pi$
$487$			5.02238e17i			0.0773048i	−0.999253	+	0.0386524i	$0.987693\pi$
$488$	1.23310e18	+	6.16070e18i	0.187094	+	0.934741i
$489$	8.16616e17			0.122139
$490$	−2.13071e18	−	1.04969e18i	−0.314160	−	0.154771i
$491$	1.15407e19			1.67750			0.838751	−	0.544516i	$-0.183287\pi$
$491$	1.15407e19			1.67750			0.838751	+	0.544516i	$0.183287\pi$
$492$	−4.72153e18	−	6.14306e18i	−0.676592	−	0.880297i
$493$		−	1.15895e19i		−	1.63733i
$494$	1.24278e18	+	6.12258e17i	0.173104	+	0.0852797i
$495$			4.61464e18i			0.633725i
$496$	3.16700e18	+	8.43184e17i	0.428821	+	0.114170i
$497$	−7.19845e18			−0.961046
$498$	−1.01295e18	+	2.05613e18i	−0.133347	+	0.270673i
$499$	−4.13260e18			−0.536439			−0.268219	−	0.963358i	$-0.586435\pi$
$499$	−4.13260e18			−0.536439			−0.268219	+	0.963358i	$0.586435\pi$
$500$	6.58450e18	−	5.06081e18i	0.842816	−	0.647783i
$501$			1.27659e18i			0.161135i
$502$	1.90166e18	−	3.86007e18i	0.236705	−	0.480473i
$503$			1.49181e19i			1.83121i	0.402083	+	0.915603i	$0.368286\pi$
$503$			1.49181e19i			1.83121i	−0.402083	+	0.915603i	$0.631714\pi$
$504$	−6.54431e17	−	3.26961e18i	−0.0792228	−	0.395805i
$505$	5.42136e18			0.647245
$506$	1.26462e19	+	6.23015e18i	1.48904	+	0.733576i
$507$	3.00231e18			0.348658
$508$	−1.07862e19	+	8.29021e18i	−1.23544	+	0.949553i
$509$			1.74031e18i			0.196609i	0.995156	+	0.0983043i	$0.0313419\pi$
$509$			1.74031e18i			0.196609i	−0.995156	+	0.0983043i	$0.968658\pi$
$510$	5.93839e18	+	2.92555e18i	0.661725	+	0.325999i
$511$		−	6.18553e18i		−	0.679877i
$512$	7.65052e18	−	5.15171e18i	0.829471	−	0.558550i
$513$	−2.69335e18			−0.288053
$514$	−3.59875e17	+	7.30488e17i	−0.0379673	+	0.0770675i
$515$	−1.01285e19			−1.05413
$516$	−3.32278e18	−	4.32319e18i	−0.341156	−	0.443871i
$517$			2.19370e19i			2.22200i
$518$	2.24299e18	−	4.55291e18i	0.224140	−	0.454968i
$519$		−	9.11571e17i		−	0.0898708i
$520$	6.53624e18	−	1.30827e18i	0.635777	−	0.127254i
$521$	2.81970e18			0.270607			0.135303	−	0.990804i	$-0.456799\pi$
$521$	2.81970e18			0.270607			0.135303	+	0.990804i	$0.456799\pi$
$522$	6.90463e18	+	3.40157e18i	0.653803	+	0.322096i
$523$	8.71465e18			0.814213			0.407106	−	0.913381i	$-0.366538\pi$
$523$	8.71465e18			0.814213			0.407106	+	0.913381i	$0.366538\pi$
$524$	−8.01257e17	−	1.04250e18i	−0.0738674	−	0.0961072i
$525$			9.61057e17i			0.0874246i
$526$	−5.92802e18	−	2.92044e18i	−0.532120	−	0.262149i
$527$			5.77884e18i			0.511878i
$528$	2.76375e18	−	1.03806e19i	0.241580	−	0.907376i
$529$	−6.03365e18			−0.520464
$530$	8.54384e18	−	1.73426e19i	0.727314	−	1.47633i
$531$	5.58841e18			0.469490
$532$	2.05127e18	−	1.57660e18i	0.170076	−	0.130719i
$533$		−	1.37566e19i		−	1.12570i
$534$	−5.05622e18	+	1.02633e19i	−0.408354	+	0.828893i
$535$		−	8.02305e18i		−	0.639533i
$536$	−1.74166e18	+	3.48603e17i	−0.137028	+	0.0274269i
$537$	−3.52042e18			−0.273385
$538$	−7.53291e18	−	3.71109e18i	−0.577413	−	0.284463i
$539$	−6.79630e18			−0.514223
$540$	−1.02748e19	+	7.89713e18i	−0.767390	+	0.589811i
$541$			1.70119e19i			1.25422i	0.778931	+	0.627109i	$0.215762\pi$
$541$			1.70119e19i			1.25422i	−0.778931	+	0.627109i	$0.784238\pi$
$542$	−1.12782e19	−	5.55621e18i	−0.820815	−	0.404374i
$543$		−	1.14256e19i		−	0.820880i
$544$	1.22488e19	+	1.06988e19i	0.868765	+	0.758828i
$545$	−6.60381e18			−0.462401
$546$	−2.47917e18	+	5.03231e18i	−0.171379	+	0.347872i
$547$	−2.75587e19			−1.88082			−0.940411	−	0.340040i	$-0.889560\pi$
$547$	−2.75587e19			−1.88082			−0.940411	+	0.340040i	$0.889560\pi$
$548$	−7.14486e18	−	9.29601e18i	−0.481427	−	0.626373i
$549$		−	7.35767e18i		−	0.489479i
$550$	1.44403e18	−	2.93114e18i	0.0948497	−	0.192530i
$551$			5.97203e18i			0.387312i
$552$	2.63607e18	+	1.31701e19i	0.168804	+	0.843363i
$553$	1.40965e19			0.891326
$554$	−7.63465e18	−	3.76121e18i	−0.476673	−	0.234833i
$555$	−6.69205e18			−0.412580
$556$	1.25918e19	+	1.63829e19i	0.766594	+	0.997397i
$557$			1.38148e19i			0.830535i	0.909699	+	0.415268i	$0.136312\pi$
$557$			1.38148e19i			0.830535i	−0.909699	+	0.415268i	$0.863688\pi$
$558$	−3.44283e18	−	1.69611e18i	−0.204398	−	0.100697i
$559$		−	9.68123e18i		−	0.567607i
$560$	3.20261e18	−	1.20290e19i	0.185433	−	0.696488i
$561$	1.89416e19			1.08312
$562$	6.95292e18	−	1.41133e19i	0.392657	−	0.797030i
$563$	4.00685e18			0.223483			0.111741	−	0.993737i	$-0.464357\pi$
$563$	4.00685e18			0.223483			0.111741	+	0.993737i	$0.464357\pi$
$564$	−1.65711e19	+	1.27365e19i	−0.912848	+	0.701610i
$565$			4.28242e17i			0.0232997i
$566$	−2.11106e18	+	4.28511e18i	−0.113445	+	0.230275i
$567$		−	3.30110e18i		−	0.175218i
$568$	4.57639e18	+	2.28641e19i	0.239930	+	1.19871i
$569$	1.45707e18			0.0754562			0.0377281	−	0.999288i	$-0.487988\pi$
$569$	1.45707e18			0.0754562			0.0377281	+	0.999288i	$0.487988\pi$
$570$	−3.06003e18	−	1.50752e18i	−0.156531	−	0.0771151i
$571$	3.18854e19			1.61116			0.805582	−	0.592484i	$-0.201853\pi$
$571$	3.18854e19			1.61116			0.805582	+	0.592484i	$0.201853\pi$
$572$	1.51225e19	−	1.16231e19i	0.754834	−	0.580161i
$573$		−	1.09864e19i		−	0.541719i
$574$	−2.30447e19	−	1.13530e19i	−1.12250	−	0.553001i
$575$			4.08547e18i			0.196593i
$576$	−9.96905e18	+	4.15728e18i	−0.473911	+	0.197629i
$577$	−5.64678e17			−0.0265198			−0.0132599	−	0.999912i	$-0.504221\pi$
$577$	−5.64678e17			−0.0265198			−0.0132599	+	0.999912i	$0.504221\pi$
$578$	−3.14858e18	+	6.39112e18i	−0.146090	+	0.296539i
$579$	2.31188e19			1.05978
$580$	1.75105e19	+	2.27825e19i	0.793053	+	1.03182i
$581$			7.59984e18i			0.340073i
$582$	1.06035e19	−	2.15235e19i	0.468803	−	0.951594i
$583$		−	5.53176e19i		−	2.41648i
$584$	−1.96468e19	+	3.93242e18i	−0.848012	+	0.169735i
$585$	−7.80617e18			−0.332926
$586$	2.24192e19	+	1.10448e19i	0.944793	+	0.465452i
$587$	−3.74873e19			−1.56105			−0.780527	−	0.625122i	$-0.785049\pi$
$587$	−3.74873e19			−1.56105			−0.780527	+	0.625122i	$0.785049\pi$
$588$	−3.94589e18	−	5.13390e18i	−0.162369	−	0.211254i
$589$		−	2.97781e18i		−	0.121085i
$590$	1.87146e19	+	9.21974e18i	0.751997	+	0.370471i
$591$			9.04779e18i			0.359278i
$592$	−1.58872e19	−	4.22982e18i	−0.623440	−	0.165985i
$593$	2.92956e18			0.113611			0.0568054	−	0.998385i	$-0.481909\pi$
$593$	2.92956e18			0.113611			0.0568054	+	0.998385i	$0.481909\pi$
$594$	−1.63867e19	+	3.32623e19i	−0.628038	+	1.27482i
$595$	2.19494e19			0.831388
$596$	2.51622e19	−	1.93396e19i	0.941945	−	0.723974i
$597$		−	5.18519e18i		−	0.191842i
$598$	−1.05390e19	+	2.13925e19i	−0.385382	+	0.782263i
$599$		−	8.67604e17i		−	0.0313570i	−0.999877	−	0.0156785i	$-0.995009\pi$
$599$		−	8.67604e17i		−	0.0313570i	0.999877	−	0.0156785i	$-0.00499082\pi$
$600$	3.05256e18	−	6.10988e17i	0.109045	−	0.0218260i
$601$	4.45332e19			1.57240			0.786199	−	0.617974i	$-0.212046\pi$
$601$	4.45332e19			1.57240			0.786199	+	0.617974i	$0.212046\pi$
$602$	−1.62177e19	−	7.98966e18i	−0.565997	−	0.278839i
$603$	2.08004e18			0.0717548
$604$	−4.67107e18	+	3.59016e18i	−0.159279	+	0.122421i
$605$			2.20919e19i			0.744639i
$606$	1.32575e19	+	6.53133e18i	0.441728	+	0.217617i
$607$			3.02568e19i			0.996557i	0.867017	+	0.498278i	$0.166034\pi$
$607$			3.02568e19i			0.996557i	−0.867017	+	0.498278i	$0.833966\pi$
$608$	−6.31177e18	−	5.51305e18i	−0.205507	−	0.179501i
$609$	−2.41821e19			−0.778346
$610$	1.21387e19	−	2.46395e19i	0.386244	−	0.784013i
$611$	−3.71089e19			−1.16732
$612$	−1.16062e19	−	1.51005e19i	−0.360936	−	0.469605i
$613$			1.90118e19i			0.584521i	0.956339	+	0.292261i	$0.0944074\pi$
$613$			1.90118e19i			0.584521i	−0.956339	+	0.292261i	$0.905593\pi$
$614$	1.11958e19	−	2.27256e19i	0.340311	−	0.690776i
$615$			3.38720e19i			1.01792i
$616$	−6.99044e18	−	3.49250e19i	−0.207702	−	1.03770i
$617$	−4.15565e19			−1.22079			−0.610397	−	0.792096i	$-0.708990\pi$
$617$	−4.15565e19			−1.22079			−0.610397	+	0.792096i	$0.708990\pi$
$618$	−2.47685e19	−	1.22022e19i	−0.719417	−	0.354421i
$619$	−3.03636e19			−0.872004			−0.436002	−	0.899946i	$-0.643606\pi$
$619$	−3.03636e19			−0.872004			−0.436002	+	0.899946i	$0.643606\pi$
$620$	−8.73119e18	−	1.13599e19i	−0.247931	−	0.322578i
$621$		−	4.63616e19i		−	1.30172i
$622$	3.23648e19	+	1.59445e19i	0.898546	+	0.442669i
$623$			3.79351e19i			1.04142i
$624$	1.75600e19	+	4.67520e18i	0.476687	+	0.126913i
$625$	−3.03666e19			−0.815148
$626$	−8.73662e18	+	1.77339e19i	−0.231912	+	0.470744i
$627$	−9.76054e18			−0.256213
$628$	4.02190e18	−	3.09121e18i	0.104403	−	0.0802437i
$629$		−	2.89894e19i		−	0.744192i
$630$	−6.44223e18	+	1.30767e19i	−0.163551	+	0.331981i
$631$			1.12286e19i			0.281916i	0.990016	+	0.140958i	$0.0450182\pi$
$631$			1.12286e19i			0.281916i	−0.990016	+	0.140958i	$0.954982\pi$
$632$	−8.96182e18	−	4.47742e19i	−0.222524	−	1.11175i
$633$	−2.41980e19			−0.594228
$634$	−2.14599e19	−	1.05722e19i	−0.521198	−	0.256768i
$635$	5.94735e19			1.42859
$636$	4.17867e19	−	3.21170e19i	0.992745	−	0.763019i
$637$		−	1.14967e19i		−	0.270145i
$638$	7.37533e19	+	3.63346e19i	1.71410	+	0.844452i
$639$		−	2.73064e19i		−	0.627709i
$640$	−4.02432e19	−	2.52492e18i	−0.915025	−	0.0574100i
$641$	−2.89341e19			−0.650735			−0.325368	−	0.945588i	$-0.605488\pi$
$641$	−2.89341e19			−0.650735			−0.325368	+	0.945588i	$0.605488\pi$
$642$	9.66569e18	−	1.96198e19i	0.215024	−	0.436465i
$643$	3.51335e19			0.773117			0.386558	−	0.922265i	$-0.373664\pi$
$643$	3.51335e19			0.773117			0.386558	+	0.922265i	$0.373664\pi$
$644$	2.71385e19	+	3.53093e19i	0.590724	+	0.768577i
$645$			2.38374e19i			0.513265i
$646$	6.53047e18	−	1.32558e19i	0.139097	−	0.282344i
$647$			5.98461e19i			1.26097i	0.776200	+	0.630487i	$0.217145\pi$
$647$			5.98461e19i			1.26097i	−0.776200	+	0.630487i	$0.782855\pi$
$648$	−1.04851e19	+	2.09866e18i	−0.218549	+	0.0437439i
$649$	5.96938e19			1.23088
$650$	4.95835e18	+	2.44273e18i	0.101145	+	0.0498290i
$651$	1.20578e19			0.243334
$652$	−5.34479e18	−	6.95398e18i	−0.106708	−	0.138835i
$653$		−	5.01530e18i		−	0.0990614i	−0.998773	−	0.0495307i	$-0.984227\pi$
$653$		−	5.01530e18i		−	0.0990614i	0.998773	−	0.0495307i	$-0.0157726\pi$
$654$	−1.61491e19	−	7.95587e18i	−0.315577	−	0.155469i
$655$			5.74818e18i			0.111133i
$656$	−2.14093e19	+	8.04134e19i	−0.409521	+	1.53816i
$657$	2.34640e19			0.444063
$658$	−3.06250e19	+	6.21638e19i	−0.573449	+	1.16401i
$659$	9.67252e19			1.79202			0.896008	−	0.444038i	$-0.146455\pi$
$659$	9.67252e19			1.79202			0.896008	+	0.444038i	$0.146455\pi$
$660$	−3.72351e19	+	2.86187e19i	−0.682567	+	0.524617i
$661$		−	5.31203e19i		−	0.963497i	−0.876309	−	0.481749i	$-0.840002\pi$
$661$		−	5.31203e19i		−	0.963497i	0.876309	−	0.481749i	$-0.159998\pi$
$662$	1.08649e19	−	2.20540e19i	0.194993	−	0.395805i
$663$			3.20419e19i			0.569015i
$664$	2.41390e19	−	4.83157e18i	0.424173	−	0.0849008i
$665$	−1.13104e19			−0.196665
$666$	1.72709e19	+	8.50850e18i	0.297163	+	0.146397i
$667$	−1.02799e20			−1.75028
$668$	1.08710e19	−	8.35537e18i	0.183161	−	0.140777i
$669$		−	5.18358e19i		−	0.864265i
$670$	6.96569e18	+	3.43165e18i	0.114932	+	0.0566212i
$671$		−	7.85925e19i		−	1.28329i
$672$	2.23236e19	−	2.55577e19i	0.360727	−	0.412988i
$673$	4.86355e19			0.777765			0.388882	−	0.921287i	$-0.372861\pi$
$673$	4.86355e19			0.777765			0.388882	+	0.921287i	$0.372861\pi$
$674$	−2.79955e19	+	5.68265e19i	−0.443067	+	0.899355i
$675$	−1.07457e19			−0.168309
$676$	−1.96503e19	−	2.55665e19i	−0.304608	−	0.396318i
$677$			3.28367e19i			0.503778i	0.967756	+	0.251889i	$0.0810517\pi$
$677$			3.28367e19i			0.503778i	−0.967756	+	0.251889i	$0.918948\pi$
$678$	−5.15920e17	+	1.04723e18i	−0.00783384	+	0.0159014i
$679$		−	7.95548e19i		−	1.19558i
$680$	−1.39542e19	−	6.97169e19i	−0.207560	−	1.03699i
$681$	−2.98987e19			−0.440172
$682$	−3.67753e19	−	1.81174e19i	−0.535878	−	0.264000i
$683$	−8.94919e19			−1.29074			−0.645370	−	0.763870i	$-0.723297\pi$
$683$	−8.94919e19			−1.29074			−0.645370	+	0.763870i	$0.723297\pi$
$684$	5.98062e18	+	7.78125e18i	0.0853795	+	0.111085i
$685$			5.12569e19i			0.724299i
$686$	−6.96767e19	−	3.43262e19i	−0.974583	−	0.480128i
$687$		−	1.49015e19i		−	0.206315i
$688$	−1.50668e19	+	5.65910e19i	−0.206492	+	0.775583i
$689$	9.35759e19			1.26949
$690$	2.59495e19	−	5.26732e19i	0.348486	−	0.707370i
$691$	6.18838e19			0.822680			0.411340	−	0.911482i	$-0.365061\pi$
$691$	6.18838e19			0.822680			0.411340	+	0.911482i	$0.365061\pi$
$692$	−7.76258e18	+	5.96628e18i	−0.102156	+	0.0785165i
$693$			4.17106e19i			0.543393i
$694$	−4.66891e19	+	9.47713e19i	−0.602142	+	1.22225i
$695$		−	9.03331e19i		−	1.15333i
$696$	1.53737e19	+	7.68085e19i	0.194318	+	0.970833i
$697$	−1.46731e20			−1.83608
$698$	9.36298e18	+	4.61267e18i	0.115991	+	0.0571432i
$699$	−2.89900e19			−0.355556
$700$	8.18399e18	−	6.29017e18i	0.0993753	−	0.0763793i
$701$			5.08553e19i			0.611379i	0.952131	+	0.305689i	$0.0988869\pi$
$701$			5.08553e19i			0.611379i	−0.952131	+	0.305689i	$0.901113\pi$
$702$	−5.62669e19	−	2.77199e19i	−0.669720	−	0.329938i
$703$			1.49381e19i			0.176039i
$704$	−1.06486e20	+	4.44068e19i	−1.24247	+	0.518133i
$705$	9.13708e19			1.05556
$706$	4.84541e19	−	9.83541e19i	0.554240	−	1.12502i
$707$	4.90024e19			0.554985
$708$	3.46578e19	+	4.50924e19i	0.388658	+	0.505674i
$709$		−	1.45637e19i		−	0.161714i	−0.996726	−	0.0808572i	$-0.974234\pi$
$709$		−	1.45637e19i		−	0.161714i	0.996726	−	0.0808572i	$-0.0257658\pi$
$710$	4.50500e19	−	9.14442e19i	0.495320	−	1.00542i
$711$			5.34734e19i			0.582171i
$712$	1.20492e20	−	2.41171e19i	1.29896	−	0.259995i
$713$	5.12581e19			0.547187
$714$	5.36757e19	+	2.64433e19i	0.567401	+	0.279530i
$715$	−8.33833e19			−0.872844
$716$	2.30414e19	+	2.99786e19i	0.238845	+	0.310756i
$717$			1.17442e20i			1.20556i
$718$	−6.71187e19	−	3.30660e19i	−0.682295	−	0.336133i
$719$		−	1.21808e20i		−	1.22623i	−0.789993	−	0.613116i	$-0.789916\pi$
$719$		−	1.21808e20i		−	1.22623i	0.789993	−	0.613116i	$-0.210084\pi$
$720$	4.56305e19	+	1.21487e19i	0.454912	+	0.121116i
$721$	−9.15490e19			−0.903872
$722$	4.18324e19	−	8.49131e19i	0.409028	−	0.830260i
$723$	6.10895e19			0.591559
$724$	−9.72959e19	+	7.47811e19i	−0.933092	+	0.717170i
$725$			2.38267e19i			0.226307i
$726$	−2.66150e19	+	5.40242e19i	−0.250363	+	0.508197i
$727$			1.24129e20i			1.15647i	0.815871	+	0.578234i	$0.196258\pi$
$727$			1.24129e20i			1.15647i	−0.815871	+	0.578234i	$0.803742\pi$
$728$	5.90795e19	−	1.18251e19i	0.545152	−	0.109115i
$729$	9.30931e19			0.850795
$730$	7.85767e19	+	3.87108e19i	0.711269	+	0.350407i
$731$	−1.03262e20			−0.925803
$732$	5.93684e19	−	4.56302e19i	0.527203	−	0.405205i
$733$			3.33950e18i			0.0293733i	0.999892	+	0.0146867i	$0.00467508\pi$
$733$			3.33950e18i			0.0293733i	−0.999892	+	0.0146867i	$0.995325\pi$
$734$	2.11498e19	+	1.04194e19i	0.184261	+	0.0907761i
$735$			2.83076e19i			0.244282i
$736$	9.48980e19	−	1.08646e20i	0.811171	−	0.928691i
$737$	2.22184e19			0.188123
$738$	4.30660e19	−	8.74170e19i	0.361193	−	0.733165i
$739$	2.95840e19			0.245780			0.122890	−	0.992420i	$-0.460784\pi$
$739$	2.95840e19			0.245780			0.122890	+	0.992420i	$0.460784\pi$
$740$	4.37998e19	+	5.69869e19i	0.360454	+	0.468978i
$741$		−	1.65110e19i		−	0.134601i
$742$	7.72257e19	−	1.56756e20i	0.623641	−	1.26589i
$743$			8.69608e18i			0.0695668i	0.999395	+	0.0347834i	$0.0110741\pi$
$743$			8.69608e18i			0.0695668i	−0.999395	+	0.0347834i	$0.988926\pi$
$744$	−7.66571e18	−	3.82987e19i	−0.0607494	−	0.303510i
$745$	−1.38741e20			−1.08921
$746$	−1.36555e20	−	6.72740e19i	−1.06203	−	0.523209i
$747$	−2.88290e19			−0.222119
$748$	−1.23974e20	−	1.61300e20i	−0.946280	−	1.23118i
$749$		−	7.25184e19i		−	0.548373i
$750$	−8.87836e19	−	4.37392e19i	−0.665126	−	0.327674i
$751$			1.45806e20i			1.08217i	0.840967	+	0.541087i	$0.181987\pi$
$751$			1.45806e20i			1.08217i	−0.840967	+	0.541087i	$0.818013\pi$
$752$	2.16918e20	+	5.77524e19i	1.59504	+	0.424664i
$753$	−5.12831e19			−0.373602
$754$	−6.14640e19	+	1.24762e20i	−0.443630	+	0.900498i
$755$	2.57556e19			0.184180
$756$	−9.28712e19	+	7.13803e19i	−0.658004	+	0.505738i
$757$			7.53414e19i			0.528887i	0.964401	+	0.264443i	$0.0851882\pi$
$757$			7.53414e19i			0.528887i	−0.964401	+	0.264443i	$0.914812\pi$
$758$	−1.15208e20	+	2.33853e20i	−0.801304	+	1.62652i
$759$		−	1.68011e20i		−	1.15783i
$760$	7.19056e18	+	3.59248e19i	0.0490984	+	0.245301i
$761$	1.06768e20			0.722349			0.361175	−	0.932498i	$-0.382376\pi$
$761$	1.06768e20			0.722349			0.361175	+	0.932498i	$0.382376\pi$
$762$	1.45438e20	+	7.16501e19i	0.974975	+	0.480321i
$763$	−5.96902e19			−0.396489
$764$	−9.35562e19	+	7.19068e19i	−0.615771	+	0.473278i
$765$			8.32622e19i			0.543023i
$766$	−6.48712e19	−	3.19588e19i	−0.419228	−	0.206533i
$767$			1.00979e20i			0.646640i
$768$	−9.53700e19	−	5.46571e19i	−0.605178	−	0.346831i
$769$	−2.91687e19			−0.183414			−0.0917071	−	0.995786i	$-0.529232\pi$
$769$	−2.91687e19			−0.183414			−0.0917071	+	0.995786i	$0.529232\pi$
$770$	−6.88140e19	+	1.39681e20i	−0.428787	+	0.870369i
$771$	9.70491e18			0.0599254
$772$	−1.51314e20	−	1.96871e20i	−0.925885	−	1.20465i
$773$		−	2.51756e20i		−	1.52659i	−0.646047	−	0.763297i	$-0.723579\pi$
$773$		−	2.51756e20i		−	1.52659i	0.646047	−	0.763297i	$-0.276421\pi$
$774$	3.03077e19	−	6.15198e19i	0.182124	−	0.369682i
$775$		−	1.18806e19i		−	0.0707500i
$776$	−2.52686e20	+	5.05767e19i	−1.49125	+	0.298482i
$777$	−6.04878e19			−0.353770
$778$	2.93987e20	+	1.44832e20i	1.70400	+	0.839477i
$779$	7.56097e19			0.434326
$780$	−4.84117e19	−	6.29874e19i	−0.275606	−	0.358584i
$781$		−	2.91679e20i		−	1.64569i
$782$	2.28176e20	+	1.12411e20i	1.27592	+	0.628582i
$783$		−	2.70383e20i		−	1.49847i
$784$	−1.78923e19	+	6.72033e19i	−0.0982772	+	0.369129i
$785$	−2.21762e19			−0.120725
$786$	−6.92506e18	+	1.40568e19i	−0.0373651	+	0.0758450i
$787$	3.55019e20			1.89858			0.949288	−	0.314408i	$-0.101806\pi$
$787$	3.55019e20			1.89858			0.949288	+	0.314408i	$0.101806\pi$
$788$	7.70475e19	−	5.92183e19i	0.408390	−	0.313886i
$789$			7.87569e19i			0.413761i
$790$	−8.82203e19	+	1.79073e20i	−0.459387	+	0.932482i
$791$			3.87077e18i			0.0199785i
$792$	1.32483e20	−	2.65173e19i	0.677775	−	0.135661i
$793$	1.32948e20			0.674170
$794$	−3.02193e20	−	1.48875e20i	−1.51894	−	0.748307i
$795$	−2.30406e20			−1.14795
$796$	−4.41551e19	+	3.39374e19i	−0.218067	+	0.167605i
$797$		−	8.08415e19i		−	0.395755i	−0.980227	−	0.197877i	$-0.936595\pi$
$797$		−	8.08415e19i		−	0.395755i	0.980227	−	0.197877i	$-0.0634048\pi$
$798$	−2.76588e19	−	1.36261e19i	−0.134219	−	0.0661229i
$799$			3.95811e20i			1.90397i
$800$	−2.51821e19	−	2.19955e19i	−0.120078	−	0.104883i
$801$	−1.43902e20			−0.680204
$802$	1.52136e18	−	3.08812e18i	0.00712872	−	0.0144701i
$803$	2.50636e20			1.16422
$804$	1.28999e19	+	1.67837e19i	0.0594008	+	0.0772850i
$805$		−	1.94690e20i		−	0.888736i
$806$	3.06475e19	−	6.22096e19i	0.138692	−	0.281522i
$807$			1.00079e20i			0.448980i
$808$	−3.11531e19	−	1.55644e20i	−0.138555	−	0.692234i
$809$	1.23351e20			0.543880			0.271940	−	0.962314i	$-0.412335\pi$
$809$	1.23351e20			0.543880			0.271940	+	0.962314i	$0.412335\pi$
$810$	4.19350e19	+	2.06593e19i	0.183308	+	0.0903066i
$811$	8.12669e19			0.352183			0.176091	−	0.984374i	$-0.443655\pi$
$811$	8.12669e19			0.352183			0.176091	+	0.984374i	$0.443655\pi$
$812$	1.58273e20	+	2.05925e20i	0.680009	+	0.884744i
$813$			1.49837e20i			0.638241i
$814$	1.84483e20	+	9.08853e19i	0.779085	+	0.383816i
$815$			3.83433e19i			0.160541i
$816$	4.98666e19	−	1.87299e20i	0.207004	−	0.777506i
$817$	5.32104e19			0.218999
$818$	−2.64830e19	+	5.37563e19i	−0.108067	+	0.219359i
$819$	−7.05581e19			−0.285469
$820$	2.88441e20	−	2.21694e20i	1.15707	−	0.889317i
$821$			1.79955e20i			0.715753i	0.933769	+	0.357876i	$0.116499\pi$
$821$			1.79955e20i			0.715753i	−0.933769	+	0.357876i	$0.883501\pi$
$822$	−6.17512e19	+	1.25345e20i	−0.243525	+	0.494316i
$823$			9.11251e19i			0.356319i	0.984002	+	0.178160i	$0.0570143\pi$
$823$			9.11251e19i			0.356319i	−0.984002	+	0.178160i	$0.942986\pi$
$824$	5.82019e19	+	2.90783e20i	0.225656	+	1.12740i
$825$	−3.89417e19			−0.149705
$826$	1.69157e20	+	8.33350e19i	0.644806	+	0.317663i
$827$	−1.81674e20			−0.686681			−0.343340	−	0.939211i	$-0.611558\pi$
$827$	−1.81674e20			−0.686681			−0.343340	+	0.939211i	$0.611558\pi$
$828$	−1.33941e20	+	1.02946e20i	−0.501998	+	0.385833i
$829$		−	3.04508e20i		−	1.13166i	−0.824521	−	0.565831i	$-0.808555\pi$
$829$		−	3.04508e20i		−	1.13166i	0.824521	−	0.565831i	$-0.191445\pi$
$830$	−9.65432e19	−	4.75620e19i	−0.355775	−	0.175272i
$831$			1.01430e20i			0.370647i
$832$	−7.51191e19	−	1.80134e20i	−0.272199	−	0.652727i
$833$	−1.22626e20			−0.440624
$834$	1.08828e20	−	2.20903e20i	0.387773	−	0.787117i
$835$	−5.99410e19			−0.211796
$836$	6.38833e19	+	8.31170e19i	0.223843	+	0.291237i
$837$			1.34820e20i			0.468464i
$838$	1.51150e20	−	3.06809e20i	0.520833	−	1.05721i
$839$		−	3.02591e20i		−	1.03400i	−0.855984	−	0.517002i	$-0.827048\pi$
$839$		−	3.02591e20i		−	1.03400i	0.855984	−	0.517002i	$-0.172952\pi$
$840$	−1.45468e20	+	2.91162e19i	−0.492959	+	0.0986687i
$841$	−3.01968e20			−1.01482
$842$	−3.50095e20	−	1.72474e20i	−1.16681	−	0.574830i
$843$	−1.87503e20			−0.619747
$844$	1.58377e20	+	2.06060e20i	0.519152	+	0.675457i
$845$			1.40970e20i			0.458278i
$846$	−2.35810e20	−	1.16172e20i	−0.760275	−	0.374549i
$847$			1.99683e20i			0.638496i
$848$	−5.46992e20	−	1.45632e20i	−1.73464	−	0.461833i
$849$	5.69299e19			0.179055
$850$	2.60547e19	−	5.28868e19i	0.0812743	−	0.164974i
$851$	−2.57135e20			−0.795526
$852$	2.20333e20	−	1.69347e20i	0.676087	−	0.519636i
$853$			1.49071e20i			0.453680i	0.973932	+	0.226840i	$0.0728394\pi$
$853$			1.49071e20i			0.453680i	−0.973932	+	0.226840i	$0.927161\pi$
$854$	1.09718e20	−	2.22711e20i	0.331188	−	0.672258i
$855$		−	4.29047e19i		−	0.128452i
$856$	−2.30337e20	+	4.61033e19i	−0.683986	+	0.136904i
$857$	7.57613e18			0.0223142			0.0111571	−	0.999938i	$-0.496449\pi$
$857$	7.57613e18			0.0223142			0.0111571	+	0.999938i	$0.496449\pi$
$858$	−2.03908e20	−	1.00455e20i	−0.595693	−	0.293468i
$859$	1.23630e20			0.358237			0.179118	−	0.983828i	$-0.442675\pi$
$859$	1.23630e20			0.358237			0.179118	+	0.983828i	$0.442675\pi$
$860$	2.02990e20	−	1.56017e20i	0.583427	−	0.448419i
$861$			3.06161e20i			0.872825i
$862$	2.90034e20	+	1.42885e20i	0.820160	+	0.404052i
$863$		−	7.06982e20i		−	1.98304i	−0.129936	−	0.991522i	$-0.541477\pi$
$863$		−	7.06982e20i		−	1.98304i	0.129936	−	0.991522i	$-0.458523\pi$
$864$	2.85764e20	+	2.49603e20i	0.795082	+	0.694470i
$865$	4.28018e19			0.118127
$866$	−9.62691e19	+	1.95411e20i	−0.263549	+	0.534962i
$867$	8.49093e19			0.230580
$868$	−7.89191e19	−	1.02680e20i	−0.212591	−	0.276597i
$869$			5.71188e20i			1.52630i
$870$	1.51339e20	−	3.07193e20i	0.401158	−	0.814285i
$871$			3.75849e19i			0.0988295i
$872$	3.79478e19	+	1.89591e20i	0.0989855	+	0.494542i
$873$	3.01781e20			0.780894
$874$	−1.17578e20	−	5.79249e19i	−0.301819	−	0.148691i
$875$	−3.28161e20			−0.835662
$876$	1.45517e20	+	1.89329e20i	0.367609	+	0.478287i
$877$			3.96418e20i			0.993474i	0.867901	+	0.496737i	$0.165469\pi$
$877$			3.96418e20i			0.993474i	−0.867901	+	0.496737i	$0.834531\pi$
$878$	5.33787e20	+	2.62970e20i	1.32711	+	0.653800i
$879$		−	2.97851e20i		−	0.734643i
$880$	4.87412e20	+	1.29769e20i	1.19266	+	0.317535i
$881$	−7.74161e19			−0.187932			−0.0939658	−	0.995575i	$-0.529954\pi$
$881$	−7.74161e19			−0.187932			−0.0939658	+	0.995575i	$0.529954\pi$
$882$	3.59912e19	−	7.30564e19i	0.0866795	−	0.175945i
$883$	9.65286e18			0.0230638			0.0115319	−	0.999934i	$-0.496329\pi$
$883$	9.65286e18			0.0230638			0.0115319	+	0.999934i	$0.496329\pi$
$884$	2.72856e20	−	2.09716e20i	0.646797	−	0.497125i
$885$		−	2.48633e20i		−	0.584731i
$886$	−3.04273e20	+	6.17626e20i	−0.709950	+	1.44108i
$887$			1.26704e20i			0.293308i	0.989188	+	0.146654i	$0.0468504\pi$
$887$			1.26704e20i			0.293308i	−0.989188	+	0.146654i	$0.953150\pi$
$888$	3.84549e19	+	1.92125e20i	0.0883204	+	0.441258i
$889$	5.37567e20			1.22495
$890$	−4.81902e20	−	2.37409e20i	−1.08950	−	0.536744i
$891$	1.33760e20			0.300042
$892$	−4.41414e20	+	3.39268e20i	−0.982407	+	0.755073i
$893$		−	2.03960e20i		−	0.450385i
$894$	−3.39281e20	−	1.67147e20i	−0.743356	−	0.366214i
$895$		−	1.65298e20i		−	0.359340i
$896$	−3.63749e20	−	2.28221e19i	−0.784595	−	0.0492267i
$897$	2.84210e20			0.608264
$898$	−2.91653e20	+	5.92009e20i	−0.619344	+	1.25717i
$899$	2.98940e20			0.629891
$900$	2.38609e19	+	3.10449e19i	0.0498873	+	0.0649072i
$901$		−	9.98099e20i		−	2.07062i
$902$	4.60018e20	−	9.33763e20i	0.946955	−	1.92217i
$903$			2.15461e20i			0.440103i
$904$	1.22946e19	−	2.46083e18i	0.0249192	−	0.00498773i
$905$	5.36476e20			1.07897
$906$	6.29835e19	+	3.10288e19i	0.125698	+	0.0619253i
$907$	1.52949e20			0.302898			0.151449	−	0.988465i	$-0.451606\pi$
$907$	1.52949e20			0.302898			0.151449	+	0.988465i	$0.451606\pi$
$908$	1.95689e20	+	2.54606e20i	0.384561	+	0.500343i
$909$			1.85884e20i			0.362489i
$910$	−2.36286e20	−	1.16407e20i	−0.457245	−	0.225262i
$911$		−	2.85399e20i		−	0.548054i	−0.961722	−	0.274027i	$-0.911644\pi$
$911$		−	2.85399e20i		−	0.548054i	0.961722	−	0.274027i	$-0.0883558\pi$
$912$	−2.56960e19	+	9.65143e19i	−0.0489669	+	0.183919i
$913$	−3.07943e20			−0.582338
$914$	1.67073e20	−	3.39132e20i	0.313533	−	0.636422i
$915$	−3.27349e20			−0.609625
$916$	−1.26895e20	+	9.75309e19i	−0.234518	+	0.180249i
$917$			5.19564e19i			0.0952914i
$918$	−2.95666e20	+	6.00155e20i	−0.538149	+	1.09236i
$919$		−	3.97735e20i		−	0.718432i	−0.933255	−	0.359216i	$-0.883044\pi$
$919$		−	3.97735e20i		−	0.718432i	0.933255	−	0.359216i	$-0.116956\pi$
$920$	−6.18385e20	+	1.23773e20i	−1.10852	+	0.221877i
$921$	−3.01922e20			−0.537127
$922$	6.84803e19	+	3.37368e19i	0.120906	+	0.0595645i
$923$	4.93407e20			0.864557
$924$	−3.36559e20	+	2.58678e20i	−0.585272	+	0.449837i
$925$			5.95988e19i			0.102860i
$926$	3.11210e20	+	1.53318e20i	0.533061	+	0.262613i
$927$		−	3.47280e20i		−	0.590366i
$928$	5.53450e20	−	6.33632e20i	0.933775	−	1.06906i
$929$	−8.72913e20			−1.46171			−0.730854	−	0.682533i	$-0.760878\pi$
$929$	−8.72913e20			−1.46171			−0.730854	+	0.682533i	$0.760878\pi$
$930$	−7.54614e19	+	1.53174e20i	−0.125413	+	0.254569i
$931$	6.31888e19			0.104230
$932$	1.89741e20	+	2.46867e20i	0.310634	+	0.404159i
$933$		−	4.29983e20i		−	0.698683i
$934$	−2.29176e20	+	4.65191e20i	−0.369608	+	0.750245i
$935$			8.89383e20i			1.42366i
$936$	4.48570e19	+	2.24111e20i	0.0712688	+	0.356067i
$937$	−8.31435e20			−1.31115			−0.655573	−	0.755132i	$-0.727573\pi$
$937$	−8.31435e20			−1.31115			−0.655573	+	0.755132i	$0.727573\pi$
$938$	6.29612e19	+	3.10178e19i	0.0985492	+	0.0485503i
$939$	2.35605e20			0.366037
$940$	−5.98027e20	−	7.78078e20i	−0.922201	−	1.19985i
$941$		−	4.35673e17i		−	0.000666857i	−1.00000		0.000333429i	$-0.999894\pi$
$941$		−	4.35673e17i		−	0.000666857i	1.00000		0.000333429i	$-0.000106134\pi$
$942$	−5.42302e19	−	2.67165e19i	−0.0823920	−	0.0405904i
$943$			1.30149e21i			1.96273i
$944$	1.57153e20	−	5.90265e20i	0.235243	−	0.883574i
$945$	5.12078e20			0.760876
$946$	3.23739e20	−	6.57137e20i	0.477481	−	0.969210i
$947$	−1.14167e21			−1.67145			−0.835723	−	0.549150i	$-0.814951\pi$
$947$	−1.14167e21			−1.67145			−0.835723	+	0.549150i	$0.814951\pi$
$948$	−4.31473e20	+	3.31627e20i	−0.627040	+	0.481939i
$949$			4.23978e20i			0.611618i
$950$	−1.34259e19	+	2.72523e19i	−0.0192255	+	0.0390246i
$951$			2.85106e20i			0.405268i
$952$	−1.26129e20	−	6.30154e20i	−0.177974	−	0.889177i
$953$	−5.14432e20			−0.720573			−0.360286	−	0.932842i	$-0.617321\pi$
$953$	−5.14432e20			−0.720573			−0.360286	+	0.932842i	$0.617321\pi$
$954$	5.94633e20	+	2.92946e20i	0.826818	+	0.407332i
$955$	5.15855e20			0.712040
$956$	1.00009e21	−	7.68666e20i	1.37036	−	1.05325i
$957$		−	9.79851e20i		−	1.33284i
$958$	1.60340e19	+	7.89915e18i	0.0216513	+	0.0106665i
$959$			4.63299e20i			0.621056i
$960$	1.84961e20	+	4.43531e20i	0.246139	+	0.590236i
$961$	6.07885e20			0.803078
$962$	−1.53743e20	+	3.12073e20i	−0.201636	+	0.409289i
$963$	2.75089e20			0.358171
$964$	−3.99834e20	−	5.20214e20i	−0.516821	−	0.672424i
$965$			1.08552e21i			1.39298i
$966$	2.34551e20	−	4.76101e20i	0.298812	−	0.606539i
$967$		−	7.55480e20i		−	0.955516i	−0.878492	−	0.477758i	$-0.841450\pi$
$967$		−	7.55480e20i		−	0.955516i	0.878492	−	0.477758i	$-0.158550\pi$
$968$	6.34246e20	−	1.26948e20i	0.796398	−	0.159404i
$969$	−1.76110e20			−0.219542
$970$	1.01061e21	+	4.97877e20i	1.25078	+	0.616198i
$971$	3.42491e20			0.420837			0.210419	−	0.977611i	$-0.432517\pi$
$971$	3.42491e20			0.420837			0.210419	+	0.977611i	$0.432517\pi$
$972$	−4.49680e20	−	5.85068e20i	−0.548580	−	0.713745i
$973$		−	8.16499e20i		−	0.988931i
$974$	−5.76681e19	−	2.84102e19i	−0.0693462	−	0.0341634i
$975$		−	6.58743e19i		−	0.0786472i
$976$	−7.77139e20	−	2.06906e20i	−0.921191	−	0.245259i
$977$	1.09856e21			1.29290			0.646448	−	0.762958i	$-0.276254\pi$
$977$	1.09856e21			1.29290			0.646448	+	0.762958i	$0.276254\pi$
$978$	−4.61936e19	+	9.37657e19i	−0.0539772	+	0.109565i
$979$	−1.53712e21			−1.78332
$980$	2.41056e20	−	1.85275e20i	0.277674	−	0.213419i
$981$		−	2.26427e20i		−	0.258968i
$982$	−6.52827e20	+	1.32513e21i	−0.741340	+	1.50480i
$983$			9.94775e20i			1.12163i	0.827941	+	0.560816i	$0.189512\pi$
$983$			9.94775e20i			1.12163i	−0.827941	+	0.560816i	$0.810488\pi$
$984$	9.72444e20	−	1.94640e20i	1.08868	−	0.217905i
$985$	−4.24829e20			−0.472237
$986$	1.33074e21	+	6.55587e20i	1.46877	+	0.723589i
$987$	8.25879e20			0.905099
$988$	−1.40602e20	+	1.08066e20i	−0.153000	+	0.117595i
$989$			9.15929e20i			0.989664i
$990$	−5.29863e20	−	2.61037e20i	−0.568483	−	0.280063i
$991$			2.50994e20i			0.267392i	0.991022	+	0.133696i	$0.0426846\pi$
$991$			2.50994e20i			0.267392i	−0.991022	+	0.133696i	$0.957315\pi$
$992$	−2.75965e20	+	3.15945e20i	−0.291925	+	0.334218i
$993$	−2.92999e20			−0.307766
$994$	4.07196e20	−	8.26542e20i	0.424716	−	0.862105i
$995$	2.43465e20			0.252159
$996$	−1.78790e20	−	2.32619e20i	−0.183877	−	0.239238i
$997$		−	5.74805e20i		−	0.587022i	−0.955956	−	0.293511i	$-0.905176\pi$
$997$		−	5.74805e20i		−	0.587022i	0.955956	−	0.293511i	$-0.0948237\pi$
$998$	2.33770e20	−	4.74515e20i	0.237069	−	0.481212i
$999$		−	6.76322e20i		−	0.681075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.15.d.b.3.4	yes	12
3.2	odd	2		72.15.b.b.19.9		12
4.3	odd	2		32.15.d.b.15.4		12
8.3	odd	2	inner	8.15.d.b.3.3	✓	12
8.5	even	2		32.15.d.b.15.3		12
24.11	even	2		72.15.b.b.19.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.15.d.b.3.3	✓	12	8.3	odd	2	inner
8.15.d.b.3.4	yes	12	1.1	even	1	trivial
32.15.d.b.15.3		12	8.5	even	2
32.15.d.b.15.4		12	4.3	odd	2
72.15.b.b.19.9		12	3.2	odd	2
72.15.b.b.19.10		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)

\(f(q)\)	\(=\)	\(q+(-56.5672 + 114.822i) q^{2} +1525.47 q^{3} +(-9984.31 - 12990.3i) q^{4} +71626.9i q^{5} +(-86291.8 + 175158. i) q^{6} +647418. i q^{7} +(2.05637e6 - 411594. i) q^{8} -2.45590e6 q^{9} +O(q^{10})\)	\(q+(-56.5672 + 114.822i) q^{2} +1525.47 q^{3} +(-9984.31 - 12990.3i) q^{4} +71626.9i q^{5} +(-86291.8 + 175158. i) q^{6} +647418. i q^{7} +(2.05637e6 - 411594. i) q^{8} -2.45590e6 q^{9} +(-8.22436e6 - 4.05173e6i) q^{10} -2.62332e7 q^{11} +(-1.52308e7 - 1.98164e7i) q^{12} -4.43764e7i q^{13} +(-7.43380e7 - 3.66226e7i) q^{14} +1.09265e8i q^{15} +(-6.90627e7 + 2.59399e8i) q^{16} -4.73327e8 q^{17} +(1.38923e8 - 2.81992e8i) q^{18} +2.43904e8 q^{19} +(9.30458e8 - 7.15145e8i) q^{20} +9.87620e8i q^{21} +(1.48394e9 - 3.01215e9i) q^{22} +4.19839e9i q^{23} +(3.13693e9 - 6.27875e8i) q^{24} +9.73104e8 q^{25} +(5.09540e9 + 2.51025e9i) q^{26} -1.10427e10 q^{27} +(8.41019e9 - 6.46402e9i) q^{28} +2.44852e10i q^{29} +(-1.25461e10 - 6.18081e9i) q^{30} -1.22090e10i q^{31} +(-2.58781e10 - 2.26034e10i) q^{32} -4.00180e10 q^{33} +(2.67748e10 - 5.43485e10i) q^{34} -4.63726e10 q^{35} +(2.45204e10 + 3.19030e10i) q^{36} +6.12461e10i q^{37} +(-1.37969e10 + 2.80056e10i) q^{38} -6.76950e10i q^{39} +(2.94812e10 + 1.47291e11i) q^{40} +3.09998e11 q^{41} +(-1.13401e11 - 5.58669e10i) q^{42} +2.18162e11 q^{43} +(2.61920e11 + 3.40778e11i) q^{44} -1.75908e11i q^{45} +(-4.82069e11 - 2.37491e11i) q^{46} -8.36231e11i q^{47} +(-1.05353e11 + 3.95707e11i) q^{48} +2.59073e11 q^{49} +(-5.50458e10 + 1.11734e11i) q^{50} -7.22049e11 q^{51} +(-5.76464e11 + 4.43067e11i) q^{52} +2.10869e12i q^{53} +(6.24655e11 - 1.26795e12i) q^{54} -1.87900e12i q^{55} +(2.66473e11 + 1.33133e12i) q^{56} +3.72068e11 q^{57} +(-2.81145e12 - 1.38506e12i) q^{58} -2.27551e12 q^{59} +(1.41939e12 - 1.09093e12i) q^{60} +2.99592e12i q^{61} +(1.40186e12 + 6.90627e11i) q^{62} -1.58999e12i q^{63} +(4.05923e12 - 1.69277e12i) q^{64} +3.17854e12 q^{65} +(2.26371e12 - 4.59496e12i) q^{66} -8.46958e11 q^{67} +(4.72585e12 + 6.14869e12i) q^{68} +6.40454e12i q^{69} +(2.62316e12 - 5.32460e12i) q^{70} +1.11187e13i q^{71} +(-5.05022e12 + 1.01083e12i) q^{72} -9.55414e12 q^{73} +(-7.03241e12 - 3.46452e12i) q^{74} +1.48444e12 q^{75} +(-2.43521e12 - 3.16839e12i) q^{76} -1.69838e13i q^{77} +(7.77289e12 + 3.82932e12i) q^{78} -2.17735e13i q^{79} +(-1.85800e13 - 4.94674e12i) q^{80} -5.09887e12 q^{81} +(-1.75357e13 + 3.55947e13i) q^{82} +1.17387e13 q^{83} +(1.28295e13 - 9.86070e12i) q^{84} -3.39030e13i q^{85} +(-1.23408e13 + 2.50498e13i) q^{86} +3.73516e13i q^{87} +(-5.39450e13 + 1.07974e13i) q^{88} +5.85944e13 q^{89} +(2.01982e13 + 9.95064e12i) q^{90} +2.87301e13 q^{91} +(5.45386e13 - 4.19180e13i) q^{92} -1.86245e13i q^{93} +(9.60180e13 + 4.73033e13i) q^{94} +1.74701e13i q^{95} +(-3.94764e13 - 3.44809e13i) q^{96} -1.22880e14 q^{97} +(-1.46550e13 + 2.97473e13i) q^{98} +6.44260e13 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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