LMFDB - Embedded newform 8.17.d.b.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,17,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, 17, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 17 $
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:	$12.9859635085$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} + 7894 x^{12} + 219192 x^{11} - 135772320 x^{10} + 11331786624 x^{9} + \cdots + 27\!\cdots\!20 $ x^14 - 7x^13 + 7894x^12 + 219192x^11 - 135772320x^10 + 11331786624x^9 - 652293490688x^8 + 465478371454976x^7 - 697940891942912x^6 + 5355071973862932480x^5 + 64434406660761845760x^4 - 122098039773726666915840x^3 + 21723325027733376807731200x^2 - 2811006993630615015868334080*x + 279841437428593117864520581120
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{91}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.12
Root			$-93.5934 - 98.6231i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.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)

$f(q)$	$=$	$q+(163.187 + 197.246i) q^{2} -2122.49 q^{3} +(-12276.1 + 64376.0i) q^{4} +155753. i q^{5} +(-346362. - 418652. i) q^{6} -829393. i q^{7} +(-1.47012e7 + 8.08389e6i) q^{8} -3.85418e7 q^{9} +O(q^{10})$	\(q+(163.187 + 197.246i) q^{2} -2122.49 q^{3} +(-12276.1 + 64376.0i) q^{4} +155753. i q^{5} +(-346362. - 418652. i) q^{6} -829393. i q^{7} +(-1.47012e7 + 8.08389e6i) q^{8} -3.85418e7 q^{9} +(-3.07217e7 + 2.54169e7i) q^{10} -7.43384e7 q^{11} +(2.60559e7 - 1.36637e8i) q^{12} -6.40971e8i q^{13} +(1.63595e8 - 1.35346e8i) q^{14} -3.30584e8i q^{15} +(-3.99356e9 - 1.58057e9i) q^{16} -4.86041e9 q^{17} +(-6.28951e9 - 7.60222e9i) q^{18} -1.49278e10 q^{19} +(-1.00268e10 - 1.91205e9i) q^{20} +1.76038e9i q^{21} +(-1.21311e10 - 1.46630e10i) q^{22} +5.37845e10i q^{23} +(3.12031e10 - 1.71579e10i) q^{24} +1.28329e11 q^{25} +(1.26429e11 - 1.04598e11i) q^{26} +1.73170e11 q^{27} +(5.33930e10 + 1.01817e10i) q^{28} +5.66928e11i q^{29} +(6.52065e10 - 5.39470e10i) q^{30} +1.31363e12i q^{31} +(-3.39934e11 - 1.04564e12i) q^{32} +1.57782e11 q^{33} +(-7.93154e11 - 9.58697e11i) q^{34} +1.29181e11 q^{35} +(4.73144e11 - 2.48116e12i) q^{36} +2.80322e12i q^{37} +(-2.43602e12 - 2.94445e12i) q^{38} +1.36045e12i q^{39} +(-1.25909e12 - 2.28976e12i) q^{40} -9.61440e11 q^{41} +(-3.47227e11 + 2.87270e11i) q^{42} -6.98588e12 q^{43} +(9.12588e11 - 4.78561e12i) q^{44} -6.00301e12i q^{45} +(-1.06088e13 + 8.77692e12i) q^{46} +1.89348e13i q^{47} +(8.47628e12 + 3.35475e12i) q^{48} +3.25450e13 q^{49} +(2.09416e13 + 2.53124e13i) q^{50} +1.03161e13 q^{51} +(4.12631e13 + 7.86863e12i) q^{52} -8.89397e13i q^{53} +(2.82591e13 + 3.41572e13i) q^{54} -1.15785e13i q^{55} +(6.70472e12 + 1.21931e13i) q^{56} +3.16840e13 q^{57} +(-1.11824e14 + 9.25152e13i) q^{58} -2.65601e14 q^{59} +(2.12817e13 + 4.05829e12i) q^{60} -2.98587e14i q^{61} +(-2.59108e14 + 2.14367e14i) q^{62} +3.19663e13i q^{63} +(1.50776e14 - 2.37686e14i) q^{64} +9.98333e13 q^{65} +(2.57480e13 + 3.11220e13i) q^{66} -5.63647e13 q^{67} +(5.96669e13 - 3.12893e14i) q^{68} -1.14157e14i q^{69} +(2.10806e13 + 2.54804e13i) q^{70} +1.07888e15i q^{71} +(5.66611e14 - 3.11567e14i) q^{72} +9.51683e14 q^{73} +(-5.52925e14 + 4.57449e14i) q^{74} -2.72376e14 q^{75} +(1.83255e14 - 9.60990e14i) q^{76} +6.16558e13i q^{77} +(-2.68344e14 + 2.22008e14i) q^{78} +2.31187e15i q^{79} +(2.46180e14 - 6.22010e14i) q^{80} +1.29154e15 q^{81} +(-1.56894e14 - 1.89640e14i) q^{82} -1.49381e15 q^{83} +(-1.13326e14 - 2.16106e13i) q^{84} -7.57024e14i q^{85} +(-1.14000e15 - 1.37794e15i) q^{86} -1.20330e15i q^{87} +(1.09287e15 - 6.00944e14i) q^{88} -1.19755e15 q^{89} +(1.18407e15 - 9.79612e14i) q^{90} -5.31617e14 q^{91} +(-3.46243e15 - 6.60265e14i) q^{92} -2.78815e15i q^{93} +(-3.73481e15 + 3.08990e15i) q^{94} -2.32505e15i q^{95} +(7.21506e14 + 2.21936e15i) q^{96} -5.34164e15 q^{97} +(5.31092e15 + 6.41938e15i) q^{98} +2.86513e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) $ 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9 + 87155280 * q^10 - 49140292 * q^11 + 31616184 * q^12 - 2675193504 * q^14 + 9716374544 * q^16 - 9985136356 * q^17 - 7692086106 * q^18 + 62922133180 * q^19 + 31953450720 * q^20 - 51493048676 * q^22 + 54962419344 * q^24 - 429906632050 * q^25 - 518273679696 * q^26 + 655936606584 * q^27 + 102542376000 * q^28 - 364331826720 * q^30 + 95751080800 * q^32 + 4034287537464 * q^33 + 1015818512644 * q^34 - 3057653406720 * q^35 - 9569289445092 * q^36 + 9010383442844 * q^38 - 4027933291200 * q^40 + 8719629072668 * q^41 - 6653698130880 * q^42 + 16716309178300 * q^43 - 4351929975880 * q^44 + 21043605267744 * q^46 + 46562301973344 * q^48 - 104740771400434 * q^49 - 54483696687710 * q^50 + 40911296041848 * q^51 - 73249356722400 * q^52 - 18031398151752 * q^54 + 110873799752064 * q^56 - 310730528383176 * q^57 + 256627273576560 * q^58 + 347007330293180 * q^59 - 83822619107520 * q^60 + 346701622780800 * q^62 - 332173589517760 * q^64 + 220877370432000 * q^65 + 875905832132808 * q^66 - 614258765968196 * q^67 - 1235787871965976 * q^68 - 442172390987520 * q^70 - 1312232111609976 * q^72 - 542888518370276 * q^73 + 2394643836493776 * q^74 + 2861985572983740 * q^75 - 614792000883272 * q^76 - 4928152344599520 * q^78 + 6402194304908160 * q^80 - 5344304371237818 * q^81 + 4810720063300804 * q^82 + 7362421930746044 * q^83 - 9316784627856000 * q^84 - 8963192329247716 * q^86 + 3396904358318224 * q^88 - 408131327364580 * q^89 + 14680290550241520 * q^90 - 7162887702930432 * q^91 - 9213856910218560 * q^92 - 15838781433150144 * q^94 + 48917704300183104 * q^96 + 18372136634257180 * q^97 + 34005570793293730 * q^98 - 18934692015468492 * 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 $

$2$	163.187	+	197.246i	0.637449	+	0.770493i
$2$	163.187	+	197.246i	0.637449	+	0.770493i
$3$	−2122.49			−0.323500			−0.161750	−	0.986832i	$-0.551714\pi$
$3$	−2122.49			−0.323500			−0.161750	+	0.986832i	$0.551714\pi$
$4$	−12276.1	+	64376.0i	−0.187319	+	0.982299i
$5$			155753.i			0.398728i	0.979925	+	0.199364i	$0.0638877\pi$
$5$			155753.i			0.398728i	−0.979925	+	0.199364i	$0.936112\pi$
$6$	−346362.	−	418652.i	−0.206215	−	0.249255i
$7$		−	829393.i		−	0.143872i	−0.997409	−	0.0719360i	$-0.977082\pi$
$7$		−	829393.i		−	0.143872i	0.997409	−	0.0719360i	$-0.0229177\pi$
$8$	−1.47012e7	+	8.08389e6i	−0.876261	+	0.481837i
$9$	−3.85418e7			−0.895347
$10$	−3.07217e7	+	2.54169e7i	−0.307217	+	0.254169i
$11$	−7.43384e7			−0.346794			−0.173397	−	0.984852i	$-0.555474\pi$
$11$	−7.43384e7			−0.346794			−0.173397	+	0.984852i	$0.555474\pi$
$12$	2.60559e7	−	1.36637e8i	0.0605977	−	0.317774i
$13$		−	6.40971e8i		−	0.785763i	−0.919589	−	0.392881i	$-0.871478\pi$
$13$		−	6.40971e8i		−	0.785763i	0.919589	−	0.392881i	$-0.128522\pi$
$14$	1.63595e8	−	1.35346e8i	0.110852	−	0.0917110i
$15$		−	3.30584e8i		−	0.128989i
$16$	−3.99356e9	−	1.58057e9i	−0.929823	−	0.368006i
$17$	−4.86041e9			−0.696757			−0.348378	−	0.937354i	$-0.613268\pi$
$17$	−4.86041e9			−0.696757			−0.348378	+	0.937354i	$0.613268\pi$
$18$	−6.28951e9	−	7.60222e9i	−0.570738	−	0.689859i
$19$	−1.49278e10			−0.878955			−0.439477	−	0.898254i	$-0.644836\pi$
$19$	−1.49278e10			−0.878955			−0.439477	+	0.898254i	$0.644836\pi$
$20$	−1.00268e10	−	1.91205e9i	−0.391671	−	0.0746893i
$21$			1.76038e9i			0.0465426i
$22$	−1.21311e10	−	1.46630e10i	−0.221063	−	0.267202i
$23$			5.37845e10i			0.686806i	0.939188	+	0.343403i	$0.111580\pi$
$23$			5.37845e10i			0.686806i	−0.939188	+	0.343403i	$0.888420\pi$
$24$	3.12031e10	−	1.71579e10i	0.283471	−	0.155875i
$25$	1.28329e11			0.841016
$26$	1.26429e11	−	1.04598e11i	0.605424	−	0.500883i
$27$	1.73170e11			0.613146
$28$	5.33930e10	+	1.01817e10i	0.141325	+	0.0269499i
$29$			5.66928e11i			1.13330i	0.823959	+	0.566649i	$0.191760\pi$
$29$			5.66928e11i			1.13330i	−0.823959	+	0.566649i	$0.808240\pi$
$30$	6.52065e10	−	5.39470e10i	0.0993850	−	0.0822237i
$31$			1.31363e12i			1.54020i	0.637920	+	0.770102i	$0.279795\pi$
$31$			1.31363e12i			1.54020i	−0.637920	+	0.770102i	$0.720205\pi$
$32$	−3.39934e11	−	1.04564e12i	−0.309168	−	0.951007i
$33$	1.57782e11			0.112188
$34$	−7.93154e11	−	9.58697e11i	−0.444147	−	0.536846i
$35$	1.29181e11			0.0573658
$36$	4.73144e11	−	2.48116e12i	0.167715	−	0.879499i
$37$			2.80322e12i			0.798074i	0.916935	+	0.399037i	$0.130656\pi$
$37$			2.80322e12i			0.798074i	−0.916935	+	0.399037i	$0.869344\pi$
$38$	−2.43602e12	−	2.94445e12i	−0.560288	−	0.677229i
$39$			1.36045e12i			0.254195i
$40$	−1.25909e12	−	2.28976e12i	−0.192122	−	0.349390i
$41$	−9.61440e11			−0.120407			−0.0602035	−	0.998186i	$-0.519175\pi$
$41$	−9.61440e11			−0.120407			−0.0602035	+	0.998186i	$0.519175\pi$
$42$	−3.47227e11	+	2.87270e11i	−0.0358608	+	0.0296685i
$43$	−6.98588e12			−0.597687			−0.298843	−	0.954302i	$-0.596601\pi$
$43$	−6.98588e12			−0.597687			−0.298843	+	0.954302i	$0.596601\pi$
$44$	9.12588e11	−	4.78561e12i	0.0649611	−	0.340656i
$45$		−	6.00301e12i		−	0.357000i
$46$	−1.06088e13	+	8.77692e12i	−0.529179	+	0.437804i
$47$			1.89348e13i			0.795201i	0.917559	+	0.397600i	$0.130157\pi$
$47$			1.89348e13i			0.795201i	−0.917559	+	0.397600i	$0.869843\pi$
$48$	8.47628e12	+	3.35475e12i	0.300798	+	0.119050i
$49$	3.25450e13			0.979301
$50$	2.09416e13	+	2.53124e13i	0.536104	+	0.647997i
$51$	1.03161e13			0.225401
$52$	4.12631e13	+	7.86863e12i	0.771854	+	0.147188i
$53$		−	8.89397e13i		−	1.42853i	−0.699876	−	0.714264i	$-0.746762\pi$
$53$		−	8.89397e13i		−	1.42853i	0.699876	−	0.714264i	$-0.253238\pi$
$54$	2.82591e13	+	3.41572e13i	0.390849	+	0.472424i
$55$		−	1.15785e13i		−	0.138277i
$56$	6.70472e12	+	1.21931e13i	0.0693229	+	0.126069i
$57$	3.16840e13			0.284342
$58$	−1.11824e14	+	9.25152e13i	−0.873198	+	0.722419i
$59$	−2.65601e14			−1.80890			−0.904449	−	0.426582i	$-0.859718\pi$
$59$	−2.65601e14			−1.80890			−0.904449	+	0.426582i	$0.859718\pi$
$60$	2.12817e13	+	4.05829e12i	0.126706	+	0.0241620i
$61$		−	2.98587e14i		−	1.55752i	−0.627324	−	0.778758i	$-0.715850\pi$
$61$		−	2.98587e14i		−	1.55752i	0.627324	−	0.778758i	$-0.284150\pi$
$62$	−2.59108e14	+	2.14367e14i	−1.18672	+	0.981801i
$63$			3.19663e13i			0.128815i
$64$	1.50776e14	−	2.37686e14i	0.535666	−	0.844430i
$65$	9.98333e13			0.313306
$66$	2.57480e13	+	3.11220e13i	0.0715141	+	0.0864401i
$67$	−5.63647e13			−0.138806			−0.0694031	−	0.997589i	$-0.522109\pi$
$67$	−5.63647e13			−0.138806			−0.0694031	+	0.997589i	$0.522109\pi$
$68$	5.96669e13	−	3.12893e14i	0.130516	−	0.684424i
$69$		−	1.14157e14i		−	0.222182i
$70$	2.10806e13	+	2.54804e13i	0.0365678	+	0.0442000i
$71$			1.07888e15i			1.67073i	0.549698	+	0.835364i	$0.314743\pi$
$71$			1.07888e15i			1.67073i	−0.549698	+	0.835364i	$0.685257\pi$
$72$	5.66611e14	−	3.11567e14i	0.784558	−	0.431412i
$73$	9.51683e14			1.18007			0.590037	−	0.807376i	$-0.299113\pi$
$73$	9.51683e14			1.18007			0.590037	+	0.807376i	$0.299113\pi$
$74$	−5.52925e14	+	4.57449e14i	−0.614911	+	0.508731i
$75$	−2.72376e14			−0.272069
$76$	1.83255e14	−	9.60990e14i	0.164645	−	0.863397i
$77$			6.16558e13i			0.0498940i
$78$	−2.68344e14	+	2.22008e14i	−0.195855	+	0.162036i
$79$			2.31187e15i			1.52387i	0.647655	+	0.761933i	$0.275750\pi$
$79$			2.31187e15i			1.52387i	−0.647655	+	0.761933i	$0.724250\pi$
$80$	2.46180e14	−	6.22010e14i	0.146735	−	0.370747i
$81$	1.29154e15			0.696995
$82$	−1.56894e14	−	1.89640e14i	−0.0767532	−	0.0927727i
$83$	−1.49381e15			−0.663240			−0.331620	−	0.943413i	$-0.607595\pi$
$83$	−1.49381e15			−0.663240			−0.331620	+	0.943413i	$0.607595\pi$
$84$	−1.13326e14	−	2.16106e13i	−0.0457188	−	0.00871831i
$85$		−	7.57024e14i		−	0.277817i
$86$	−1.14000e15	−	1.37794e15i	−0.380995	−	0.460514i
$87$		−	1.20330e15i		−	0.366622i
$88$	1.09287e15	−	6.00944e14i	0.303882	−	0.167098i
$89$	−1.19755e15			−0.304209			−0.152105	−	0.988364i	$-0.548605\pi$
$89$	−1.19755e15			−0.304209			−0.152105	+	0.988364i	$0.548605\pi$
$90$	1.18407e15	−	9.79612e14i	0.275066	−	0.227569i
$91$	−5.31617e14			−0.113049
$92$	−3.46243e15	−	6.60265e14i	−0.674649	−	0.128652i
$93$		−	2.78815e15i		−	0.498257i
$94$	−3.73481e15	+	3.08990e15i	−0.612697	+	0.506900i
$95$		−	2.32505e15i		−	0.350464i
$96$	7.21506e14	+	2.21936e15i	0.100016	+	0.307651i
$97$	−5.34164e15			−0.681555			−0.340777	−	0.940144i	$-0.610690\pi$
$97$	−5.34164e15			−0.681555			−0.340777	+	0.940144i	$0.610690\pi$
$98$	5.31092e15	+	6.41938e15i	0.624254	+	0.754544i
$99$	2.86513e15			0.310501
$100$	−1.57538e15	+	8.26129e15i	−0.157538	+	0.826129i
$101$			2.66542e15i			0.246147i	0.992398	+	0.123074i	$0.0392751\pi$
$101$			2.66542e15i			0.246147i	−0.992398	+	0.123074i	$0.960725\pi$
$102$	1.68346e15	+	2.03482e15i	0.143682	+	0.173670i
$103$		−	2.02700e16i		−	1.60013i	−0.599911	−	0.800066i	$-0.704797\pi$
$103$		−	2.02700e16i		−	1.60013i	0.599911	−	0.800066i	$-0.295203\pi$
$104$	5.18154e15	+	9.42305e15i	0.378610	+	0.688533i
$105$	−2.74184e14			−0.0185579
$106$	1.75430e16	−	1.45138e16i	1.10067	−	0.910613i
$107$	2.16884e16			1.26229			0.631143	−	0.775667i	$-0.282586\pi$
$107$	2.16884e16			1.26229			0.631143	+	0.775667i	$0.282586\pi$
$108$	−2.12586e15	+	1.11480e16i	−0.114854	+	0.602293i
$109$			1.36907e16i			0.687088i	0.939137	+	0.343544i	$0.111627\pi$
$109$			1.36907e16i			0.687088i	−0.939137	+	0.343544i	$0.888373\pi$
$110$	2.28381e15	−	1.88945e15i	0.106541	−	0.0881443i
$111$		−	5.94980e15i		−	0.258177i
$112$	−1.31092e15	+	3.31223e15i	−0.0529458	+	0.133776i
$113$	−1.22049e16			−0.459099			−0.229549	−	0.973297i	$-0.573725\pi$
$113$	−1.22049e16			−0.459099			−0.229549	+	0.973297i	$0.573725\pi$
$114$	5.17041e15	+	6.24955e15i	0.181254	+	0.219084i
$115$	−8.37711e15			−0.273849
$116$	−3.64965e16	−	6.95968e15i	−1.11324	−	0.212288i
$117$			2.47041e16i			0.703530i
$118$	−4.33426e16	−	5.23888e16i	−1.15308	−	1.39374i
$119$			4.03119e15i			0.100244i
$120$	2.67241e15	+	4.85999e15i	0.0621516	+	0.113028i
$121$	−4.04235e16			−0.879734
$122$	5.88952e16	−	4.87255e16i	1.20006	−	0.992837i
$123$	2.04064e15			0.0389517
$124$	−8.45660e16	−	1.61262e16i	−1.51294	−	0.288509i
$125$			4.37537e16i			0.734065i
$126$	−6.30523e15	+	5.21648e15i	−0.0992513	+	0.0821132i
$127$			8.56558e15i			0.126569i	0.997996	+	0.0632845i	$0.0201575\pi$
$127$			8.56558e15i			0.126569i	−0.997996	+	0.0632845i	$0.979842\pi$
$128$	7.14874e16	−	9.04714e15i	0.992087	−	0.125554i
$129$	1.48274e16			0.193352
$130$	1.62915e16	+	1.96917e16i	0.199716	+	0.241400i
$131$	9.39220e16			1.08292			0.541460	−	0.840726i	$-0.317872\pi$
$131$	9.39220e16			1.08292			0.541460	+	0.840726i	$0.317872\pi$
$132$	−1.93695e15	+	1.01574e16i	−0.0210149	+	0.110202i
$133$			1.23810e16i			0.126457i
$134$	−9.19797e15	−	1.11177e16i	−0.0884818	−	0.106949i
$135$			2.69719e16i			0.244479i
$136$	7.14539e16	−	3.92910e16i	0.610541	−	0.335723i
$137$	1.14525e17			0.922862			0.461431	−	0.887176i	$-0.347336\pi$
$137$	1.14525e17			0.922862			0.461431	+	0.887176i	$0.347336\pi$
$138$	2.25170e16	−	1.86289e16i	0.171190	−	0.141630i
$139$	−1.18099e17			−0.847475			−0.423737	−	0.905785i	$-0.639282\pi$
$139$	−1.18099e17			−0.847475			−0.423737	+	0.905785i	$0.639282\pi$
$140$	−1.58584e15	+	8.31613e15i	−0.0107457	+	0.0563504i
$141$		−	4.01888e16i		−	0.257248i
$142$	−2.12805e17	+	1.76059e17i	−1.28728	+	1.06500i
$143$			4.76487e16i			0.272498i
$144$	1.53919e17	+	6.09181e16i	0.832515	+	0.329493i
$145$	−8.83009e16			−0.451878
$146$	1.55302e17	+	1.87716e17i	0.752237	+	0.909239i
$147$	−6.90764e16			−0.316804
$148$	−1.80460e17	−	3.44127e16i	−0.783948	−	0.149494i
$149$		−	2.97816e17i		−	1.22591i	−0.790118	−	0.612955i	$-0.789981\pi$
$149$		−	2.97816e17i		−	1.22591i	0.790118	−	0.612955i	$-0.210019\pi$
$150$	−4.44482e16	−	5.37252e16i	−0.173430	−	0.209627i
$151$		−	1.41121e17i		−	0.522125i	−0.965322	−	0.261063i	$-0.915927\pi$
$151$		−	1.41121e17i		−	0.522125i	0.965322	−	0.261063i	$-0.0840729\pi$
$152$	2.19457e17	−	1.20675e17i	0.770194	−	0.423513i
$153$	1.87329e17			0.623839
$154$	−1.21614e16	+	1.00614e16i	−0.0384429	+	0.0318048i
$155$	−2.04602e17			−0.614123
$156$	−8.75804e16	−	1.67011e16i	−0.249695	−	0.0476154i
$157$		−	6.22474e17i		−	1.68626i	−0.537711	−	0.843129i	$-0.680711\pi$
$157$		−	6.22474e17i		−	1.68626i	0.537711	−	0.843129i	$-0.319289\pi$
$158$	−4.56008e17	+	3.77267e17i	−1.17413	+	0.971387i
$159$			1.88773e17i			0.462130i
$160$	1.62862e17	−	5.29459e16i	0.379194	−	0.123274i
$161$	4.46085e16			0.0988122
$162$	2.10763e17	+	2.54752e17i	0.444298	+	0.537029i
$163$	−5.38042e17			−1.07973			−0.539865	−	0.841751i	$-0.681525\pi$
$163$	−5.38042e17			−1.07973			−0.539865	+	0.841751i	$0.681525\pi$
$164$	1.18028e16	−	6.18936e16i	0.0225545	−	0.118276i
$165$			2.45751e16i			0.0447326i
$166$	−2.43770e17	−	2.94649e17i	−0.422782	−	0.511022i
$167$			6.89737e17i			1.14012i	0.821602	+	0.570061i	$0.193081\pi$
$167$			6.89737e17i			1.14012i	−0.821602	+	0.570061i	$0.806919\pi$
$168$	−1.42307e16	−	2.58797e16i	−0.0224260	−	0.0407835i
$169$	2.54573e17			0.382577
$170$	1.49320e17	−	1.23536e17i	0.214056	−	0.177094i
$171$	5.75343e17			0.786970
$172$	8.57596e16	−	4.49723e17i	0.111958	−	0.587107i
$173$			1.05838e18i			1.31908i	0.751667	+	0.659542i	$0.229250\pi$
$173$			1.05838e18i			1.31908i	−0.751667	+	0.659542i	$0.770750\pi$
$174$	2.37346e17	−	1.96362e17i	0.282480	−	0.233703i
$175$		−	1.06435e17i		−	0.120999i
$176$	2.96875e17	+	1.17497e17i	0.322457	+	0.127622i
$177$	5.63735e17			0.585179
$178$	−1.95424e17	−	2.36212e17i	−0.193918	−	0.234391i
$179$	5.20539e17			0.493889			0.246944	−	0.969030i	$-0.420574\pi$
$179$	5.20539e17			0.493889			0.246944	+	0.969030i	$0.420574\pi$
$180$	3.86449e17	+	7.36937e16i	0.350681	+	0.0668729i
$181$			6.39138e17i			0.554837i	0.960749	+	0.277419i	$0.0894789\pi$
$181$			6.39138e17i			0.554837i	−0.960749	+	0.277419i	$0.910521\pi$
$182$	−8.67528e16	−	1.04859e17i	−0.0720630	−	0.0871036i
$183$			6.33748e17i			0.503857i
$184$	−4.34788e17	−	7.90697e17i	−0.330929	−	0.601821i
$185$	−4.36611e17			−0.318215
$186$	5.49953e17	−	4.54990e17i	0.383903	−	0.317613i
$187$	3.61315e17			0.241631
$188$	−1.21894e18	−	2.32445e17i	−0.781125	−	0.148956i
$189$		−	1.43626e17i		−	0.0882145i
$190$	4.58608e17	−	3.79418e17i	0.270030	−	0.223403i
$191$		−	1.53627e18i		−	0.867364i	−0.901066	−	0.433682i	$-0.857214\pi$
$191$		−	1.53627e18i		−	0.867364i	0.901066	−	0.433682i	$-0.142786\pi$
$192$	−3.20021e17	+	5.04485e17i	−0.173288	+	0.273174i
$193$	−3.34859e18			−1.73942			−0.869708	−	0.493567i	$-0.835693\pi$
$193$	−3.34859e18			−1.73942			−0.869708	+	0.493567i	$0.835693\pi$
$194$	−8.71685e17	−	1.05362e18i	−0.434456	−	0.525133i
$195$	−2.11895e17			−0.101355
$196$	−3.99527e17	+	2.09512e18i	−0.183441	+	0.961966i
$197$			1.29451e18i			0.570658i	0.958430	+	0.285329i	$0.0921028\pi$
$197$			1.29451e18i			0.570658i	−0.958430	+	0.285329i	$0.907897\pi$
$198$	4.67552e17	+	5.65137e17i	0.197929	+	0.239239i
$199$		−	2.68662e18i		−	1.09240i	−0.837655	−	0.546199i	$-0.816074\pi$
$199$		−	2.68662e18i		−	1.09240i	0.837655	−	0.546199i	$-0.183926\pi$
$200$	−1.88659e18	+	1.03740e18i	−0.736949	+	0.405233i
$201$	1.19633e17			0.0449038
$202$	−5.25744e17	+	4.34961e17i	−0.189655	+	0.156906i
$203$	4.70206e17			0.163050
$204$	−1.26642e17	+	6.64112e17i	−0.0422219	+	0.221411i
$205$		−	1.49747e17i		−	0.0480096i
$206$	3.99818e18	−	3.30780e18i	1.23289	−	1.02000i
$207$		−	2.07295e18i		−	0.614930i
$208$	−1.01310e18	+	2.55976e18i	−0.289165	+	0.730620i
$209$	1.10971e18			0.304816
$210$	−4.47433e16	−	5.40818e16i	−0.0118297	−	0.0142987i
$211$	3.40294e18			0.866153			0.433076	−	0.901357i	$-0.357428\pi$
$211$	3.40294e18			0.866153			0.433076	+	0.901357i	$0.357428\pi$
$212$	5.72558e18	+	1.09184e18i	1.40324	+	0.267590i
$213$		−	2.28990e18i		−	0.540481i
$214$	3.53926e18	+	4.27796e18i	0.804642	+	0.972582i
$215$		−	1.08807e18i		−	0.238315i
$216$	−2.54582e18	+	1.39989e18i	−0.537276	+	0.295437i
$217$	1.08951e18			0.221592
$218$	−2.70043e18	+	2.23413e18i	−0.529396	+	0.437983i
$219$	−2.01993e18			−0.381755
$220$	7.45374e17	+	1.42139e17i	0.135829	+	0.0259018i
$221$			3.11538e18i			0.547485i
$222$	1.17357e18	−	9.70928e17i	0.198924	−	0.164575i
$223$			1.73332e18i			0.283427i	0.989908	+	0.141713i	$0.0452611\pi$
$223$			1.73332e18i			0.283427i	−0.989908	+	0.141713i	$0.954739\pi$
$224$	−8.67250e17	+	2.81939e17i	−0.136823	+	0.0444807i
$225$	−4.94602e18			−0.753001
$226$	−1.99168e18	−	2.40737e18i	−0.292652	−	0.353732i
$227$	1.32844e18			0.188424			0.0942118	−	0.995552i	$-0.469967\pi$
$227$	1.32844e18			0.188424			0.0942118	+	0.995552i	$0.469967\pi$
$228$	−3.88957e17	+	2.03969e18i	−0.0532627	+	0.279309i
$229$		−	1.86035e17i		−	0.0245986i	−0.999924	−	0.0122993i	$-0.996085\pi$
$229$		−	1.86035e17i		−	0.0245986i	0.999924	−	0.0122993i	$-0.00391510\pi$
$230$	−1.36703e18	−	1.65235e18i	−0.174565	−	0.210999i
$231$		−	1.30864e17i		−	0.0161407i
$232$	−4.58298e18	−	8.33453e18i	−0.546065	−	0.993064i
$233$	9.97551e17			0.114839			0.0574193	−	0.998350i	$-0.481713\pi$
$233$	9.97551e17			0.114839			0.0574193	+	0.998350i	$0.481713\pi$
$234$	−4.87280e18	+	4.03139e18i	−0.542065	+	0.448464i
$235$	−2.94915e18			−0.317069
$236$	3.26055e18	−	1.70983e19i	0.338841	−	1.77688i
$237$		−	4.90692e18i		−	0.492972i
$238$	−7.95136e17	+	6.57837e17i	−0.0772371	+	0.0639002i
$239$			1.47084e19i			1.38160i	0.723044	+	0.690802i	$0.242742\pi$
$239$			1.47084e19i			1.38160i	−0.723044	+	0.690802i	$0.757258\pi$
$240$	−5.22513e17	+	1.32021e18i	−0.0474687	+	0.119937i
$241$	1.20869e19			1.06213			0.531064	−	0.847332i	$-0.321792\pi$
$241$	1.20869e19			1.06213			0.531064	+	0.847332i	$0.321792\pi$
$242$	−6.59659e18	−	7.97339e18i	−0.560785	−	0.677829i
$243$	−1.01957e19			−0.838624
$244$	1.92218e19	+	3.66550e18i	1.52995	+	0.291752i
$245$			5.06900e18i			0.390475i
$246$	3.33006e17	+	4.02509e17i	0.0248297	+	0.0300120i
$247$			9.56827e18i			0.690650i
$248$	−1.06192e19	−	1.93119e19i	−0.742128	−	1.34962i
$249$	3.17059e18			0.214559
$250$	−8.63025e18	+	7.14003e18i	−0.565592	+	0.467929i
$251$	−4.08290e18			−0.259167			−0.129583	−	0.991569i	$-0.541364\pi$
$251$	−4.08290e18			−0.259167			−0.129583	+	0.991569i	$0.541364\pi$
$252$	−2.05786e18	−	3.92422e17i	−0.126535	−	0.0241295i
$253$		−	3.99825e18i		−	0.238180i
$254$	−1.68953e18	+	1.39779e18i	−0.0975205	+	0.0806812i
$255$			1.60677e18i			0.0898738i
$256$	1.34503e19	+	1.26242e19i	0.729143	+	0.684361i
$257$	4.85369e18			0.255039			0.127520	−	0.991836i	$-0.459298\pi$
$257$	4.85369e18			0.255039			0.127520	+	0.991836i	$0.459298\pi$
$258$	2.41964e18	+	2.92466e18i	0.123252	+	0.148976i
$259$	2.32497e18			0.114821
$260$	−1.22557e18	+	6.42686e18i	−0.0586881	+	0.307760i
$261$		−	2.18504e19i		−	1.01469i
$262$	1.53268e19	+	1.85257e19i	0.690306	+	0.834383i
$263$			1.57338e19i			0.687367i	0.939086	+	0.343684i	$0.111675\pi$
$263$			1.57338e19i			0.687367i	−0.939086	+	0.343684i	$0.888325\pi$
$264$	−2.31959e18	+	1.27549e18i	−0.0983060	+	0.0540564i
$265$	1.38527e19			0.569595
$266$	−2.44211e18	+	2.02042e18i	−0.0974342	+	0.0806098i
$267$	2.54178e18			0.0984119
$268$	6.91940e17	−	3.62853e18i	0.0260010	−	0.136349i
$269$		−	6.65389e18i		−	0.242693i	−0.992610	−	0.121347i	$-0.961279\pi$
$269$		−	6.65389e18i		−	0.242693i	0.992610	−	0.121347i	$-0.0387212\pi$
$270$	−5.32010e18	+	4.40145e18i	−0.188369	+	0.155843i
$271$		−	1.90144e19i		−	0.653624i	−0.945089	−	0.326812i	$-0.894026\pi$
$271$		−	1.90144e19i		−	0.653624i	0.945089	−	0.326812i	$-0.105974\pi$
$272$	1.94103e19	+	7.68223e18i	0.647861	+	0.256411i
$273$	1.12835e18			0.0365715
$274$	1.86890e19	+	2.25897e19i	0.588277	+	0.711058i
$275$	−9.53976e18			−0.291659
$276$	7.34896e18	+	1.40140e18i	0.218249	+	0.0416189i
$277$		−	1.51676e19i		−	0.437601i	−0.975770	−	0.218800i	$-0.929786\pi$
$277$		−	1.51676e19i		−	0.437601i	0.975770	−	0.218800i	$-0.0702143\pi$
$278$	−1.92722e19	−	2.32945e19i	−0.540222	−	0.652973i
$279$		−	5.06295e19i		−	1.37902i
$280$	−1.89911e18	+	1.04428e18i	−0.0502674	+	0.0276410i
$281$	−4.91877e19			−1.26534			−0.632668	−	0.774423i	$-0.718040\pi$
$281$	−4.91877e19			−1.26534			−0.632668	+	0.774423i	$0.718040\pi$
$282$	7.92708e18	−	6.55828e18i	0.198208	−	0.163982i
$283$	−4.56385e17			−0.0110928			−0.00554639	−	0.999985i	$-0.501765\pi$
$283$	−4.56385e17			−0.0110928			−0.00554639	+	0.999985i	$0.501765\pi$
$284$	−6.94538e19	−	1.32444e19i	−1.64115	−	0.312959i
$285$			4.93489e18i			0.113375i
$286$	−9.39853e18	+	7.77565e18i	−0.209958	+	0.173703i
$287$			7.97412e17i			0.0173232i
$288$	1.31017e19	+	4.03010e19i	0.276813	+	0.851482i
$289$	−2.50376e19			−0.514530
$290$	−1.44095e19	−	1.74170e19i	−0.288049	−	0.348169i
$291$	1.13376e19			0.220483
$292$	−1.16830e19	+	6.12655e19i	−0.221050	+	1.15919i
$293$			8.30507e19i			1.52898i	0.644635	+	0.764491i	$0.277010\pi$
$293$			8.30507e19i			1.52898i	−0.644635	+	0.764491i	$0.722990\pi$
$294$	−1.12724e19	−	1.36251e19i	−0.201946	−	0.244095i
$295$		−	4.13683e19i		−	0.721259i
$296$	−2.26609e19	−	4.12107e19i	−0.384542	−	0.699321i
$297$	−1.28732e19			−0.212635
$298$	5.87432e19	−	4.85997e19i	0.944555	−	0.781455i
$299$	3.44743e19			0.539667
$300$	3.34372e18	−	1.75345e19i	0.0509636	−	0.267253i
$301$			5.79404e18i			0.0859904i
$302$	2.78355e19	−	2.30290e19i	0.402294	−	0.332828i
$303$		−	5.65732e18i		−	0.0796287i
$304$	5.96150e19	+	2.35945e19i	0.817273	+	0.323461i
$305$	4.65060e19			0.621026
$306$	3.05696e19	+	3.69499e19i	0.397665	+	0.480664i
$307$	8.66152e19			1.09771			0.548854	−	0.835918i	$-0.315064\pi$
$307$	8.66152e19			1.09771			0.548854	+	0.835918i	$0.315064\pi$
$308$	−3.96915e18	−	7.56894e17i	−0.0490108	−	0.00934608i
$309$			4.30228e19i			0.517644i
$310$	−3.33883e19	−	4.03569e19i	−0.391472	−	0.473178i
$311$			1.24327e20i			1.42064i	0.703879	+	0.710320i	$0.251450\pi$
$311$			1.24327e20i			1.42064i	−0.703879	+	0.710320i	$0.748550\pi$
$312$	−1.09977e19	−	2.00003e19i	−0.122480	−	0.222741i
$313$	−1.34204e19			−0.145683			−0.0728416	−	0.997344i	$-0.523207\pi$
$313$	−1.34204e19			−0.145683			−0.0728416	+	0.997344i	$0.523207\pi$
$314$	1.22781e20	−	1.01580e20i	1.29925	−	1.07490i
$315$	−4.97885e18			−0.0513624
$316$	−1.48829e20	−	2.83808e19i	−1.49689	−	0.285449i
$317$			1.50020e20i			1.47121i	0.677408	+	0.735607i	$0.263103\pi$
$317$			1.50020e20i			1.47121i	−0.677408	+	0.735607i	$0.736897\pi$
$318$	−3.72348e19	+	3.08053e19i	−0.356068	+	0.294584i
$319$		−	4.21445e19i		−	0.393021i
$320$	3.70204e19	+	2.34839e19i	0.336698	+	0.213585i
$321$	−4.60334e19			−0.408350
$322$	7.27952e18	+	8.79885e18i	0.0629877	+	0.0761341i
$323$	7.25551e19			0.612418
$324$	−1.58552e19	+	8.31444e19i	−0.130560	+	0.684657i
$325$		−	8.22550e19i		−	0.660839i
$326$	−8.78014e19	−	1.06127e20i	−0.688273	−	0.831925i
$327$		−	2.90582e19i		−	0.222273i
$328$	1.41343e19	−	7.77218e18i	0.105508	−	0.0580165i
$329$	1.57044e19			0.114407
$330$	−4.84735e18	+	4.01033e18i	−0.0344661	+	0.0285147i
$331$	−2.70629e20			−1.87823			−0.939117	−	0.343597i	$-0.888355\pi$
$331$	−2.70629e20			−1.87823			−0.939117	+	0.343597i	$0.888355\pi$
$332$	1.83382e19	−	9.61655e19i	0.124237	−	0.651500i
$333$		−	1.08041e20i		−	0.714554i
$334$	−1.36048e20	+	1.12556e20i	−0.878456	+	0.726769i
$335$		−	8.77898e18i		−	0.0553459i
$336$	2.78241e18	−	7.03017e18i	0.0171280	−	0.0432764i
$337$	−2.88550e19			−0.173453			−0.0867264	−	0.996232i	$-0.527641\pi$
$337$	−2.88550e19			−0.173453			−0.0867264	+	0.996232i	$0.527641\pi$
$338$	4.15430e19	+	5.02136e19i	0.243873	+	0.294773i
$339$	2.59047e19			0.148519
$340$	4.87342e19	+	9.29332e18i	0.272899	+	0.0520403i
$341$		−	9.76529e19i		−	0.534134i
$342$	9.38884e19	+	1.13484e20i	0.501653	+	0.606355i
$343$		−	5.45558e19i		−	0.284766i
$344$	1.02701e20	−	5.64731e19i	0.523729	−	0.287988i
$345$	1.77803e19			0.0885903
$346$	−2.08761e20	+	1.72714e20i	−1.01635	+	0.840849i
$347$	3.65838e19			0.174042			0.0870208	−	0.996206i	$-0.472265\pi$
$347$	3.65838e19			0.174042			0.0870208	+	0.996206i	$0.472265\pi$
$348$	7.74634e19	+	1.47718e19i	0.360133	+	0.0686752i
$349$		−	2.97879e20i		−	1.35343i	−0.736244	−	0.676717i	$-0.763402\pi$
$349$		−	2.97879e20i		−	1.35343i	0.736244	−	0.676717i	$-0.236598\pi$
$350$	2.09939e19	−	1.73688e19i	0.0932285	−	0.0771304i
$351$		−	1.10997e20i		−	0.481787i
$352$	2.52702e19	+	7.77315e19i	0.107218	+	0.329804i
$353$	2.74176e20			1.13719			0.568594	−	0.822619i	$-0.307488\pi$
$353$	2.74176e20			1.13719			0.568594	+	0.822619i	$0.307488\pi$
$354$	9.19941e19	+	1.11195e20i	0.373022	+	0.450877i
$355$	−1.68039e20			−0.666166
$356$	1.47012e19	−	7.70933e19i	0.0569841	−	0.298825i
$357$		−	8.55614e18i		−	0.0324289i
$358$	8.49451e19	+	1.02674e20i	0.314828	+	0.380538i
$359$			2.86460e20i			1.03827i	0.854694	+	0.519133i	$0.173745\pi$
$359$			2.86460e20i			1.03827i	−0.854694	+	0.519133i	$0.826255\pi$
$360$	4.85276e19	+	8.82515e19i	0.172016	+	0.312825i
$361$	−6.56026e19			−0.227438
$362$	−1.26067e20	+	1.04299e20i	−0.427498	+	0.353680i
$363$	8.57984e19			0.284594
$364$	6.52619e18	−	3.42233e19i	0.0211762	−	0.111048i
$365$			1.48228e20i			0.470529i
$366$	−1.25004e20	+	1.03419e20i	−0.388219	+	0.321183i
$367$			3.47851e20i			1.05697i	0.848941	+	0.528487i	$0.177240\pi$
$367$			3.47851e20i			1.05697i	−0.848941	+	0.528487i	$0.822760\pi$
$368$	8.50104e19	−	2.14792e20i	0.252749	−	0.638609i
$369$	3.70556e19			0.107806
$370$	−7.12491e19	−	8.61198e19i	−0.202846	−	0.245182i
$371$	−7.37660e19			−0.205525
$372$	1.79490e20	+	3.42277e19i	0.489437	+	0.0933329i
$373$		−	3.27053e20i		−	0.872867i	−0.899737	−	0.436433i	$-0.856241\pi$
$373$		−	3.27053e20i		−	0.872867i	0.899737	−	0.436433i	$-0.143759\pi$
$374$	5.89618e19	+	7.12680e19i	0.154027	+	0.186175i
$375$		−	9.28666e19i		−	0.237470i
$376$	−1.53066e20	−	2.78364e20i	−0.383157	−	0.696803i
$377$	3.63384e20			0.890503
$378$	2.83298e19	−	2.34379e19i	0.0679686	−	0.0562322i
$379$	−2.83688e20			−0.666389			−0.333195	−	0.942858i	$-0.608127\pi$
$379$	−2.83688e20			−0.666389			−0.333195	+	0.942858i	$0.608127\pi$
$380$	1.49677e20	+	2.85426e19i	0.344261	+	0.0656485i
$381$		−	1.81803e19i		−	0.0409451i
$382$	3.03024e20	−	2.50700e20i	0.668298	−	0.552900i
$383$			2.89174e20i			0.624552i	0.949991	+	0.312276i	$0.101091\pi$
$383$			2.89174e20i			0.624552i	−0.949991	+	0.312276i	$0.898909\pi$
$384$	−1.51731e20	+	1.92024e19i	−0.320941	+	0.0406169i
$385$	−9.60309e18			−0.0198941
$386$	−5.46446e20	−	6.60496e20i	−1.10879	−	1.34021i
$387$	2.69248e20			0.535137
$388$	6.55747e19	−	3.43873e20i	0.127668	−	0.669491i
$389$			6.10890e20i			1.16511i	0.812792	+	0.582554i	$0.197947\pi$
$389$			6.10890e20i			1.16511i	−0.812792	+	0.582554i	$0.802053\pi$
$390$	−3.45784e19	−	4.17954e19i	−0.0646083	−	0.0780930i
$391$		−	2.61414e20i		−	0.478537i
$392$	−4.78452e20	+	2.63090e20i	−0.858123	+	0.471864i
$393$	−1.99348e20			−0.350325
$394$	−2.55337e20	+	2.11247e20i	−0.439688	+	0.363765i
$395$	−3.60082e20			−0.607609
$396$	−3.51727e19	+	1.84446e20i	−0.0581627	+	0.305005i
$397$			3.16280e20i			0.512564i	0.966602	+	0.256282i	$0.0824975\pi$
$397$			3.16280e20i			0.512564i	−0.966602	+	0.256282i	$0.917503\pi$
$398$	5.29925e20	−	4.38421e20i	0.841686	−	0.696348i
$399$		−	2.62785e19i		−	0.0409089i
$400$	−5.12489e20	−	2.02833e20i	−0.781996	−	0.309499i
$401$	−1.16782e21			−1.74671			−0.873353	−	0.487088i	$-0.838059\pi$
$401$	−1.16782e21			−1.74671			−0.873353	+	0.487088i	$0.838059\pi$
$402$	1.95226e19	+	2.35972e19i	0.0286239	+	0.0345981i
$403$	8.41996e20			1.21023
$404$	−1.71589e20	−	3.27210e19i	−0.241790	−	0.0461080i
$405$			2.01162e20i			0.277912i
$406$	7.67315e19	+	9.27464e19i	0.103936	+	0.125629i
$407$		−	2.08387e20i		−	0.276768i
$408$	−1.51660e20	+	8.33946e19i	−0.197510	+	0.108607i
$409$	5.03253e20			0.642688			0.321344	−	0.946963i	$-0.395865\pi$
$409$	5.03253e20			0.642688			0.321344	+	0.946963i	$0.395865\pi$
$410$	2.95371e19	−	2.44368e19i	0.0369911	−	0.0306037i
$411$	−2.43078e20			−0.298546
$412$	1.30490e21	+	2.48837e20i	1.57181	+	0.299735i
$413$			2.20288e20i			0.260250i
$414$	4.08881e20	−	3.38278e20i	0.473800	−	0.391986i
$415$		−	2.32666e20i		−	0.264453i
$416$	−6.70227e20	+	2.17888e20i	−0.747266	+	0.242933i
$417$	2.50663e20			0.274159
$418$	1.81090e20	+	2.18886e20i	0.194305	+	0.234859i
$419$	1.62983e21			1.71566			0.857830	−	0.513934i	$-0.171812\pi$
$419$	1.62983e21			1.71566			0.857830	+	0.513934i	$0.171812\pi$
$420$	3.36592e18	−	1.76509e19i	0.00347624	−	0.0182294i
$421$			2.56154e20i			0.259564i	0.991543	+	0.129782i	$0.0414278\pi$
$421$			2.56154e20i			0.259564i	−0.991543	+	0.129782i	$0.958572\pi$
$422$	5.55315e20	+	6.71217e20i	0.552128	+	0.667364i
$423$		−	7.29779e20i		−	0.711981i
$424$	7.18979e20	+	1.30752e21i	0.688318	+	1.25176i
$425$	−6.23730e20			−0.585983
$426$	4.51675e20	−	3.73682e20i	0.416437	−	0.344529i
$427$	−2.47646e20			−0.224083
$428$	−2.66250e20	+	1.39621e21i	−0.236450	+	1.23994i
$429$		−	1.01134e20i		−	0.0881532i
$430$	2.14619e20	−	1.77559e20i	0.183620	−	0.151913i
$431$		−	2.14260e21i		−	1.79938i	−0.436531	−	0.899689i	$-0.643793\pi$
$431$		−	2.14260e21i		−	1.79938i	0.436531	−	0.899689i	$-0.356207\pi$
$432$	−6.91567e20	−	2.73709e20i	−0.570117	−	0.225641i
$433$	1.52365e20			0.123305			0.0616527	−	0.998098i	$-0.480363\pi$
$433$	1.52365e20			0.123305			0.0616527	+	0.998098i	$0.480363\pi$
$434$	1.77794e20	+	2.14902e20i	0.141254	+	0.170735i
$435$	1.87417e20			0.146183
$436$	−8.81349e20	−	1.68068e20i	−0.674926	−	0.128704i
$437$		−	8.02883e20i		−	0.603672i
$438$	−3.29627e20	−	3.98424e20i	−0.243349	−	0.294139i
$439$			4.68251e20i			0.339440i	0.985492	+	0.169720i	$0.0542863\pi$
$439$			4.68251e20i			0.339440i	−0.985492	+	0.169720i	$0.945714\pi$
$440$	9.35989e19	+	1.70217e20i	0.0666269	+	0.121166i
$441$	−1.25434e21			−0.876815
$442$	−6.14496e20	+	5.08389e20i	−0.421834	+	0.348994i
$443$	−2.15205e21			−1.45085			−0.725427	−	0.688299i	$-0.758358\pi$
$443$	−2.15205e21			−1.45085			−0.725427	+	0.688299i	$0.758358\pi$
$444$	3.83024e20	+	7.30404e19i	0.253607	+	0.0483615i
$445$		−	1.86522e20i		−	0.121297i
$446$	−3.41891e20	+	2.82855e20i	−0.218378	+	0.180670i
$447$			6.32111e20i			0.396582i
$448$	−1.97135e20	−	1.25053e20i	−0.121490	−	0.0770672i
$449$	−4.38633e20			−0.265540			−0.132770	−	0.991147i	$-0.542387\pi$
$449$	−4.38633e20			−0.265540			−0.132770	+	0.991147i	$0.542387\pi$
$450$	−8.07125e20	−	9.75584e20i	−0.480000	−	0.580182i
$451$	7.14719e19			0.0417564
$452$	1.49829e20	−	7.85701e20i	0.0859978	−	0.450972i
$453$			2.99527e20i			0.168908i
$454$	2.16784e20	+	2.62030e20i	0.120110	+	0.145179i
$455$		−	8.28010e19i		−	0.0450759i
$456$	−4.65794e20	+	2.56130e20i	−0.249158	+	0.137007i
$457$	2.15371e21			1.13203			0.566013	−	0.824396i	$-0.308485\pi$
$457$	2.15371e21			1.13203			0.566013	+	0.824396i	$0.308485\pi$
$458$	3.66947e19	−	3.03585e19i	0.0189531	−	0.0156804i
$459$	−8.41679e20			−0.427213
$460$	1.02838e20	−	5.39284e20i	0.0512971	−	0.269002i
$461$		−	1.47139e21i		−	0.721308i	−0.932700	−	0.360654i	$-0.882554\pi$
$461$		−	1.47139e21i		−	0.721308i	0.932700	−	0.360654i	$-0.117446\pi$
$462$	2.58123e19	−	2.13552e19i	0.0124363	−	0.0102889i
$463$			3.24714e21i			1.53763i	0.639469	+	0.768817i	$0.279154\pi$
$463$			3.24714e21i			1.53763i	−0.639469	+	0.768817i	$0.720846\pi$
$464$	8.96072e20	−	2.26406e21i	0.417060	−	1.05377i
$465$	4.34264e20			0.198669
$466$	1.62787e20	+	1.96763e20i	0.0732036	+	0.0884823i
$467$	3.16701e21			1.39995			0.699977	−	0.714165i	$-0.253193\pi$
$467$	3.16701e21			1.39995			0.699977	+	0.714165i	$0.253193\pi$
$468$	−1.59035e21	−	3.03271e20i	−0.691077	−	0.131784i
$469$			4.67485e19i			0.0199703i
$470$	−4.81262e20	−	5.81709e20i	−0.202115	−	0.244300i
$471$			1.32119e21i			0.545505i
$472$	3.90466e21	−	2.14709e21i	1.58507	−	0.871595i
$473$	5.19320e20			0.207274
$474$	9.67871e20	−	8.00744e20i	0.379831	−	0.314244i
$475$	−1.91566e21			−0.739215
$476$	−2.59512e20	−	4.94874e19i	−0.0984694	−	0.0187775i
$477$			3.42789e21i			1.27903i
$478$	−2.90119e21	+	2.40023e21i	−1.06452	+	0.880702i
$479$		−	5.70051e20i		−	0.205698i	−0.994697	−	0.102849i	$-0.967204\pi$
$479$		−	5.70051e20i		−	0.205698i	0.994697	−	0.102849i	$-0.0327958\pi$
$480$	−3.45673e20	+	1.12377e20i	−0.122669	+	0.0398793i
$481$	1.79678e21			0.627097
$482$	1.97242e21	+	2.38409e21i	0.677052	+	0.818363i
$483$	−9.46809e19			−0.0319658
$484$	4.96244e20	−	2.60230e21i	0.164791	−	0.864162i
$485$		−	8.31978e20i		−	0.271755i
$486$	−1.66381e21	−	2.01106e21i	−0.534579	−	0.646154i
$487$			4.66825e21i			1.47544i	0.675105	+	0.737721i	$0.264098\pi$
$487$			4.66825e21i			1.47544i	−0.675105	+	0.737721i	$0.735902\pi$
$488$	2.41375e21	+	4.38960e21i	0.750470	+	1.36479i
$489$	1.14199e21			0.349293
$490$	−9.99840e20	+	8.27193e20i	−0.300858	+	0.248908i
$491$	−3.71283e21			−1.09914			−0.549571	−	0.835447i	$-0.685209\pi$
$491$	−3.71283e21			−1.09914			−0.549571	+	0.835447i	$0.685209\pi$
$492$	−2.50512e19	+	1.31368e20i	−0.00729638	+	0.0382622i
$493$		−	2.75550e21i		−	0.789633i
$494$	−1.88731e21	+	1.56142e21i	−0.532141	+	0.440254i
$495$			4.46254e20i			0.123806i
$496$	2.07628e21	−	5.24605e21i	0.566805	−	1.43212i
$497$	8.94814e20			0.240371
$498$	5.17399e20	+	6.25387e20i	0.136770	+	0.165316i
$499$	9.76924e20			0.254130			0.127065	−	0.991894i	$-0.459444\pi$
$499$	9.76924e20			0.254130			0.127065	+	0.991894i	$0.459444\pi$
$500$	−2.81669e21	−	5.37126e20i	−0.721072	−	0.137504i
$501$		−	1.46396e21i		−	0.368830i
$502$	−6.66276e20	−	8.05337e20i	−0.165205	−	0.199686i
$503$		−	3.93473e21i		−	0.960220i	−0.877208	−	0.480110i	$-0.840597\pi$
$503$		−	3.93473e21i		−	0.960220i	0.877208	−	0.480110i	$-0.159403\pi$
$504$	−2.58412e20	−	4.69943e20i	−0.0620681	−	0.112876i
$505$	−4.15148e20			−0.0981458
$506$	7.88640e20	−	6.52462e20i	0.183516	−	0.151828i
$507$	−5.40328e20			−0.123764
$508$	−5.51418e20	−	1.05152e20i	−0.124329	−	0.0237087i
$509$		−	2.62826e21i		−	0.583345i	−0.956518	−	0.291672i	$-0.905788\pi$
$509$		−	2.62826e21i		−	0.583345i	0.956518	−	0.291672i	$-0.0942117\pi$
$510$	−3.16930e20	+	2.62204e20i	−0.0692471	+	0.0572899i
$511$		−	7.89320e20i		−	0.169780i
$512$	−2.95170e20	+	4.71313e21i	−0.0625046	+	0.998045i
$513$	−2.58505e21			−0.538927
$514$	7.92059e20	+	9.57373e20i	0.162575	+	0.196506i
$515$	3.15712e21			0.638018
$516$	−1.82024e20	+	9.54531e20i	−0.0362185	+	0.189929i
$517$		−	1.40758e21i		−	0.275771i
$518$	3.79405e20	+	4.58592e20i	0.0731922	+	0.0884684i
$519$		−	2.24640e21i		−	0.426724i
$520$	−1.46767e21	+	8.07041e20i	−0.274538	+	0.150962i
$521$	−5.24072e21			−0.965360			−0.482680	−	0.875797i	$-0.660337\pi$
$521$	−5.24072e21			−0.965360			−0.482680	+	0.875797i	$0.660337\pi$
$522$	4.30991e21	−	3.56570e21i	0.781815	−	0.646816i
$523$	−9.57500e21			−1.71051			−0.855254	−	0.518209i	$-0.826599\pi$
$523$	−9.57500e21			−1.71051			−0.855254	+	0.518209i	$0.826599\pi$
$524$	−1.15300e21	+	6.04632e21i	−0.202851	+	1.06375i
$525$			2.25907e20i			0.0391431i
$526$	−3.10344e21	+	2.56756e21i	−0.529612	+	0.438161i
$527$		−	6.38476e21i		−	1.07315i
$528$	−6.30113e20	−	2.49387e20i	−0.104315	−	0.0412859i
$529$	3.23984e21			0.528297
$530$	2.26057e21	+	2.73238e21i	0.363087	+	0.438869i
$531$	1.02367e22			1.61959
$532$	−7.97039e20	−	1.51991e20i	−0.124219	−	0.0236878i
$533$			6.16255e20i			0.0946112i
$534$	4.14785e20	+	5.01356e20i	0.0627325	+	0.0758257i
$535$			3.37804e21i			0.503309i
$536$	8.28629e20	−	4.55646e20i	0.121630	−	0.0668820i
$537$	−1.10484e21			−0.159773
$538$	1.31245e21	−	1.08583e21i	0.186993	−	0.154704i
$539$	−2.41935e21			−0.339616
$540$	−1.73634e21	−	3.31110e20i	−0.240151	−	0.0457954i
$541$			1.03824e21i			0.141488i	0.997495	+	0.0707440i	$0.0225374\pi$
$541$			1.03824e21i			0.141488i	−0.997495	+	0.0707440i	$0.977463\pi$
$542$	3.75052e21	−	3.10290e21i	0.503613	−	0.416652i
$543$		−	1.35656e21i		−	0.179490i
$544$	1.65222e21	+	5.08225e21i	0.215415	+	0.662621i
$545$	−2.13236e21			−0.273961
$546$	1.84132e20	+	2.22563e20i	0.0233124	+	0.0281781i
$547$	1.01712e22			1.26904			0.634520	−	0.772906i	$-0.281198\pi$
$547$	1.01712e22			1.26904			0.634520	+	0.772906i	$0.281198\pi$
$548$	−1.40593e21	+	7.37267e21i	−0.172869	+	0.906526i
$549$			1.15081e22i			1.39452i
$550$	−1.55676e21	−	1.88168e21i	−0.185918	−	0.224721i
$551$		−	8.46298e21i		−	0.996117i
$552$	9.22831e20	+	1.67824e21i	0.107056	+	0.194690i
$553$	1.91745e21			0.219242
$554$	2.99175e21	−	2.47515e21i	0.337168	−	0.278948i
$555$	9.26700e20			0.102943
$556$	1.44979e21	−	7.60272e21i	0.158748	−	0.832474i
$557$			1.33679e22i			1.44285i	0.692494	+	0.721423i	$0.256512\pi$
$557$			1.33679e22i			1.44285i	−0.692494	+	0.721423i	$0.743488\pi$
$558$	9.98648e21	−	8.26207e21i	1.06252	−	0.879053i
$559$			4.47775e21i			0.469640i
$560$	−5.15891e20	−	2.04180e20i	−0.0533401	−	0.0211110i
$561$	−7.66886e20			−0.0781678
$562$	−8.02678e21	−	9.70209e21i	−0.806587	−	0.974933i
$563$	1.54188e22			1.52751			0.763755	−	0.645507i	$-0.223354\pi$
$563$	1.54188e22			1.52751			0.763755	+	0.645507i	$0.223354\pi$
$564$	2.58719e21	+	4.93362e20i	0.252694	+	0.0481873i
$565$		−	1.90095e21i		−	0.183056i
$566$	−7.44760e19	−	9.00202e19i	−0.00707107	−	0.00854690i
$567$		−	1.07120e21i		−	0.100278i
$568$	−8.72153e21	−	1.58608e22i	−0.805019	−	1.46399i
$569$	−8.53566e21			−0.776854			−0.388427	−	0.921480i	$-0.626981\pi$
$569$	−8.53566e21			−0.776854			−0.388427	+	0.921480i	$0.626981\pi$
$570$	−9.73388e20	+	8.05309e20i	−0.0873549	+	0.0722709i
$571$	−2.12394e22			−1.87955			−0.939776	−	0.341792i	$-0.888966\pi$
$571$	−2.12394e22			−1.87955			−0.939776	+	0.341792i	$0.888966\pi$
$572$	−3.06743e21	−	5.84942e20i	−0.267674	−	0.0510440i
$573$			3.26072e21i			0.280593i
$574$	−1.57286e20	+	1.30127e20i	−0.0133474	+	0.0110426i
$575$			6.90210e21i			0.577615i
$576$	−5.81119e21	+	9.16084e21i	−0.479607	+	0.756058i
$577$	−4.58869e21			−0.373493			−0.186747	−	0.982408i	$-0.559794\pi$
$577$	−4.58869e21			−0.373493			−0.186747	+	0.982408i	$0.559794\pi$
$578$	−4.08581e21	−	4.93858e21i	−0.327986	−	0.396442i
$579$	7.10733e21			0.562702
$580$	1.08399e21	−	5.68445e21i	0.0846452	−	0.443879i
$581$			1.23896e21i			0.0954217i
$582$	1.85014e21	+	2.23629e21i	0.140547	+	0.169881i
$583$			6.61164e21i			0.495405i
$584$	−1.39909e22	+	7.69330e21i	−1.03405	+	0.568604i
$585$	−3.84775e21			−0.280518
$586$	−1.63814e22	+	1.35528e22i	−1.17807	+	0.974647i
$587$	−1.15351e22			−0.818311			−0.409156	−	0.912465i	$-0.634177\pi$
$587$	−1.15351e22			−0.818311			−0.409156	+	0.912465i	$0.634177\pi$
$588$	8.47990e20	−	4.44686e21i	0.0593434	−	0.311197i
$589$		−	1.96095e22i		−	1.35377i
$590$	8.15973e21	−	6.75076e21i	0.555725	−	0.459765i
$591$		−	2.74758e21i		−	0.184608i
$592$	4.43070e21	−	1.11948e22i	0.293696	−	0.742068i
$593$	1.18941e22			0.777849			0.388924	−	0.921270i	$-0.372847\pi$
$593$	1.18941e22			0.777849			0.388924	+	0.921270i	$0.372847\pi$
$594$	−2.10074e21	−	2.53919e21i	−0.135544	−	0.163834i
$595$	−6.27871e20			−0.0399700
$596$	1.91722e22	+	3.65603e21i	1.20421	+	0.229636i
$597$			5.70231e21i			0.353392i
$598$	5.62575e21	+	6.79992e21i	0.344010	+	0.415809i
$599$		−	1.16597e22i		−	0.703513i	−0.936092	−	0.351757i	$-0.885585\pi$
$599$		−	1.16597e22i		−	0.703513i	0.936092	−	0.351757i	$-0.114415\pi$
$600$	4.00426e21	−	2.20186e21i	0.238403	−	0.131093i
$601$	1.73486e22			1.01922			0.509610	−	0.860405i	$-0.329790\pi$
$601$	1.73486e22			1.01922			0.509610	+	0.860405i	$0.329790\pi$
$602$	−1.14285e21	+	9.45512e20i	−0.0662550	+	0.0548144i
$603$	2.17239e21			0.124280
$604$	9.08477e21	+	1.73241e21i	0.512883	+	0.0978039i
$605$		−	6.29610e21i		−	0.350775i
$606$	1.11588e21	−	9.23200e20i	0.0613533	−	0.0507592i
$607$			1.62508e22i			0.881790i	0.897559	+	0.440895i	$0.145339\pi$
$607$			1.62508e22i			0.881790i	−0.897559	+	0.440895i	$0.854661\pi$
$608$	5.07446e21	+	1.56091e22i	0.271745	+	0.835892i
$609$	−9.98006e20			−0.0527467
$610$	7.58916e21	+	9.17312e21i	0.395872	+	0.478496i
$611$	1.21366e22			0.624839
$612$	−2.29967e21	+	1.20595e22i	−0.116857	+	0.612797i
$613$		−	3.18950e22i		−	1.59970i	−0.600201	−	0.799849i	$-0.704913\pi$
$613$		−	3.18950e22i		−	1.59970i	0.600201	−	0.799849i	$-0.295087\pi$
$614$	1.41345e22	+	1.70845e22i	0.699733	+	0.845777i
$615$			3.17837e20i			0.0155311i
$616$	−4.98418e20	−	9.06415e20i	−0.0240408	−	0.0437201i
$617$	8.89989e21			0.423744			0.211872	−	0.977297i	$-0.432044\pi$
$617$	8.89989e21			0.423744			0.211872	+	0.977297i	$0.432044\pi$
$618$	−8.48609e21	+	7.02076e21i	−0.398841	+	0.329971i
$619$	−3.37488e22			−1.56579			−0.782893	−	0.622156i	$-0.786257\pi$
$619$	−3.37488e22			−1.56579			−0.782893	+	0.622156i	$0.786257\pi$
$620$	2.51172e21	−	1.31714e22i	0.115037	−	0.603253i
$621$			9.31388e21i			0.421112i
$622$	−2.45231e22	+	2.02886e22i	−1.09459	+	0.905585i
$623$			9.93238e20i			0.0437672i
$624$	2.15029e21	−	5.43305e21i	0.0935452	−	0.236356i
$625$	1.27666e22			0.548323
$626$	−2.19003e21	−	2.64712e21i	−0.0928656	−	0.112248i
$627$	−2.35534e21			−0.0986083
$628$	4.00724e22	+	7.64157e21i	1.65641	+	0.315868i
$629$		−	1.36248e22i		−	0.556064i
$630$	−8.12483e20	−	9.82060e20i	−0.0327409	−	0.0395743i
$631$			2.52421e22i			1.00436i	0.864762	+	0.502181i	$0.167469\pi$
$631$			2.52421e22i			1.00436i	−0.864762	+	0.502181i	$0.832531\pi$
$632$	−1.86889e22	−	3.39873e22i	−0.734256	−	1.33530i
$633$	−7.22269e21			−0.280201
$634$	−2.95909e22	+	2.44813e22i	−1.13356	+	0.937824i
$635$	−1.33412e21			−0.0504666
$636$	−1.21525e22	−	2.31741e21i	−0.453949	−	0.0865655i
$637$		−	2.08604e22i		−	0.769498i
$638$	8.31285e21	−	6.87743e21i	0.302820	−	0.250531i
$639$		−	4.15819e22i		−	1.49588i
$640$	1.40912e21	+	1.11344e22i	0.0500621	+	0.395573i
$641$	−1.79523e22			−0.629877			−0.314938	−	0.949112i	$-0.601984\pi$
$641$	−1.79523e22			−0.629877			−0.314938	+	0.949112i	$0.601984\pi$
$642$	−7.51204e21	−	9.07991e21i	−0.260302	−	0.314631i
$643$	−7.84394e21			−0.268440			−0.134220	−	0.990952i	$-0.542853\pi$
$643$	−7.84394e21			−0.268440			−0.134220	+	0.990952i	$0.542853\pi$
$644$	−5.47619e20	+	2.87171e21i	−0.0185094	+	0.0970631i
$645$			2.30942e21i			0.0770949i
$646$	1.18400e22	+	1.43112e22i	0.390385	+	0.471864i
$647$			1.66207e22i			0.541272i	0.962682	+	0.270636i	$0.0872340\pi$
$647$			1.66207e22i			0.541272i	−0.962682	+	0.270636i	$0.912766\pi$
$648$	−1.89873e22	+	1.04407e22i	−0.610749	+	0.335838i
$649$	1.97444e22			0.627315
$650$	1.62245e22	−	1.34229e22i	0.509171	−	0.421251i
$651$	−2.31248e21			−0.0716852
$652$	6.60507e21	−	3.46370e22i	0.202254	−	1.06062i
$653$			1.87172e22i			0.566154i	0.959097	+	0.283077i	$0.0913552\pi$
$653$			1.87172e22i			0.566154i	−0.959097	+	0.283077i	$0.908645\pi$
$654$	5.73163e21	−	4.74192e21i	0.171260	−	0.141688i
$655$			1.46287e22i			0.431791i
$656$	3.83957e21	+	1.51963e21i	0.111957	+	0.0443105i
$657$	−3.66796e22			−1.05658
$658$	2.56274e21	+	3.09762e21i	0.0729286	+	0.0881499i
$659$	3.74922e22			1.05404			0.527020	−	0.849853i	$-0.323309\pi$
$659$	3.74922e22			1.05404			0.527020	+	0.849853i	$0.323309\pi$
$660$	−1.58205e21	−	3.01687e20i	−0.0439408	−	0.00837925i
$661$			1.50320e22i			0.412482i	0.978501	+	0.206241i	$0.0661231\pi$
$661$			1.50320e22i			0.412482i	−0.978501	+	0.206241i	$0.933877\pi$
$662$	−4.41630e22	−	5.33805e22i	−1.19728	−	1.44717i
$663$		−	6.61235e21i		−	0.177112i
$664$	2.19608e22	−	1.20758e22i	0.581171	−	0.319574i
$665$	−1.92838e21			−0.0504220
$666$	2.13107e22	−	1.76309e22i	0.550559	−	0.455491i
$667$	−3.04919e22			−0.778356
$668$	−4.44025e22	−	8.46729e21i	−1.11994	−	0.213566i
$669$		−	3.67895e21i		−	0.0916886i
$670$	1.73162e21	−	1.43261e21i	0.0426437	−	0.0352802i
$671$			2.21965e22i			0.540138i
$672$	1.84073e21	−	5.98412e20i	0.0442624	−	0.0143895i
$673$	5.54399e22			1.31735			0.658676	−	0.752426i	$-0.271117\pi$
$673$	5.54399e22			1.31735			0.658676	+	0.752426i	$0.271117\pi$
$674$	−4.70875e21	−	5.69153e21i	−0.110567	−	0.133644i
$675$	2.22228e22			0.515665
$676$	−3.12517e21	+	1.63884e22i	−0.0716639	+	0.375805i
$677$			7.84790e22i			1.77846i	0.457461	+	0.889230i	$0.348759\pi$
$677$			7.84790e22i			1.77846i	−0.457461	+	0.889230i	$0.651241\pi$
$678$	4.22731e21	+	5.10960e21i	0.0946730	+	0.114433i
$679$			4.43032e21i			0.0980566i
$680$	6.11970e21	+	1.11292e22i	0.133862	+	0.243440i
$681$	−2.81960e21			−0.0609551
$682$	1.92617e22	−	1.59357e22i	0.411546	−	0.340483i
$683$	−2.01336e22			−0.425163			−0.212582	−	0.977143i	$-0.568187\pi$
$683$	−2.01336e22			−0.425163			−0.212582	+	0.977143i	$0.568187\pi$
$684$	−7.06299e21	+	3.70383e22i	−0.147414	+	0.773040i
$685$			1.78377e22i			0.367971i
$686$	1.07609e22	−	8.90279e21i	0.219410	−	0.181524i
$687$			3.94857e20i			0.00795767i
$688$	2.78986e22	+	1.10417e22i	0.555743	+	0.219952i
$689$	−5.70077e22			−1.12248
$690$	2.90151e21	+	3.50710e21i	0.0564718	+	0.0682582i
$691$	1.00138e23			1.92652			0.963261	−	0.268568i	$-0.0865506\pi$
$691$	1.00138e23			1.92652			0.963261	+	0.268568i	$0.0865506\pi$
$692$	−6.81342e22	−	1.29928e22i	−1.29574	−	0.247089i
$693$		−	2.37632e21i		−	0.0446724i
$694$	5.97000e21	+	7.21602e21i	0.110943	+	0.134098i
$695$		−	1.83943e22i		−	0.337912i
$696$	9.72732e21	+	1.76899e22i	0.176652	+	0.321257i
$697$	4.67299e21			0.0838943
$698$	5.87556e22	−	4.86100e22i	1.04281	−	0.862744i
$699$	−2.11729e21			−0.0371503
$700$	6.85186e21	+	1.30661e21i	0.118857	+	0.0226653i
$701$			6.01878e22i			1.03220i	0.856528	+	0.516101i	$0.172617\pi$
$701$			6.01878e22i			1.03220i	−0.856528	+	0.516101i	$0.827383\pi$
$702$	2.18938e22	−	1.81133e22i	0.371213	−	0.307114i
$703$		−	4.18459e22i		−	0.701471i
$704$	−1.12085e22	+	1.76692e22i	−0.185766	+	0.292844i
$705$	6.25953e21			0.102572
$706$	4.47419e22	+	5.40802e22i	0.724898	+	0.876195i
$707$	2.21068e21			0.0354137
$708$	−6.92048e21	+	3.62910e22i	−0.109615	+	0.574821i
$709$		−	1.09074e23i		−	1.70825i	−0.520067	−	0.854126i	$-0.674093\pi$
$709$		−	1.09074e23i		−	1.70825i	0.520067	−	0.854126i	$-0.325907\pi$
$710$	−2.74217e22	−	3.31450e22i	−0.424647	−	0.513277i
$711$		−	8.91036e22i		−	1.36439i
$712$	1.76054e22	−	9.68084e21i	0.266567	−	0.146579i
$713$	−7.06527e22			−1.05782
$714$	1.68767e21	−	1.39625e21i	0.0249862	−	0.0206718i
$715$	−7.42145e21			−0.108653
$716$	−6.39020e21	+	3.35102e22i	−0.0925146	+	0.485146i
$717$		−	3.12185e22i		−	0.446950i
$718$	−5.65031e22	+	4.67465e22i	−0.799976	+	0.661841i
$719$		−	5.43927e22i		−	0.761570i	−0.924664	−	0.380785i	$-0.875654\pi$
$719$		−	5.43927e22i		−	0.761570i	0.924664	−	0.380785i	$-0.124346\pi$
$720$	−9.48820e21	+	2.39734e22i	−0.131378	+	0.331947i
$721$	−1.68118e22			−0.230214
$722$	−1.07055e22	−	1.29399e22i	−0.144980	−	0.175240i
$723$	−2.56542e22			−0.343599
$724$	−4.11451e22	−	7.84613e21i	−0.545016	−	0.103931i
$725$			7.27532e22i			0.953121i
$726$	1.40012e22	+	1.69234e22i	0.181414	+	0.219278i
$727$			2.85836e22i			0.366304i	0.983085	+	0.183152i	$0.0586301\pi$
$727$			2.85836e22i			0.366304i	−0.983085	+	0.183152i	$0.941370\pi$
$728$	7.81541e21	−	4.29753e21i	0.0990606	−	0.0544713i
$729$	−3.39565e22			−0.425699
$730$	−2.92374e22	+	2.41888e22i	−0.362540	+	0.299938i
$731$	3.39542e22			0.416442
$732$	−4.07981e22	−	7.77996e21i	−0.494939	−	0.0943819i
$733$		−	6.26149e22i		−	0.751356i	−0.926750	−	0.375678i	$-0.877410\pi$
$733$		−	6.26149e22i		−	0.751356i	0.926750	−	0.375678i	$-0.122590\pi$
$734$	−6.86122e22	+	5.67646e22i	−0.814391	+	0.673766i
$735$		−	1.07589e22i		−	0.126319i
$736$	5.62394e22	−	1.82832e22i	0.653158	−	0.212339i
$737$	4.19006e21			0.0481372
$738$	6.04699e21	+	7.30908e21i	0.0687208	+	0.0830638i
$739$	−1.42143e23			−1.59797			−0.798987	−	0.601349i	$-0.794630\pi$
$739$	−1.42143e23			−1.59797			−0.798987	+	0.601349i	$0.794630\pi$
$740$	5.35989e21	−	2.81072e22i	0.0596076	−	0.312582i
$741$		−	2.03085e22i		−	0.223426i
$742$	−1.20376e22	−	1.45501e22i	−0.131012	−	0.158356i
$743$			5.61709e21i			0.0604784i	0.999543	+	0.0302392i	$0.00962691\pi$
$743$			5.61709e21i			0.0604784i	−0.999543	+	0.0302392i	$0.990373\pi$
$744$	2.25391e22	+	4.09893e22i	0.240079	+	0.436603i
$745$	4.63859e22			0.488805
$746$	6.45100e22	−	5.33708e22i	0.672538	−	0.556408i
$747$	5.75741e22			0.593830
$748$	−4.43555e21	+	2.32600e22i	−0.0452621	+	0.237354i
$749$		−	1.79882e22i		−	0.181607i
$750$	1.83176e22	−	1.51546e22i	0.182969	−	0.151375i
$751$			4.24239e22i			0.419268i	0.977780	+	0.209634i	$0.0672272\pi$
$751$			4.24239e22i			0.419268i	−0.977780	+	0.209634i	$0.932773\pi$
$752$	2.99278e22	−	7.56171e22i	0.292639	−	0.739396i
$753$	8.66591e21			0.0838406
$754$	5.92995e22	+	7.16761e22i	0.567650	+	0.686126i
$755$	2.19800e22			0.208186
$756$	9.24609e21	+	1.76318e21i	0.0866530	+	0.0165242i
$757$			4.23765e22i			0.392969i	0.980507	+	0.196484i	$0.0629525\pi$
$757$			4.23765e22i			0.392969i	−0.980507	+	0.196484i	$0.937048\pi$
$758$	−4.62942e22	−	5.59565e22i	−0.424789	−	0.513448i
$759$			8.48624e21i			0.0770515i
$760$	1.87955e22	+	3.41811e22i	0.168867	+	0.307098i
$761$	1.93452e23			1.71987			0.859937	−	0.510401i	$-0.170503\pi$
$761$	1.93452e23			1.71987			0.859937	+	0.510401i	$0.170503\pi$
$762$	3.58600e21	−	2.96679e21i	0.0315479	−	0.0261004i
$763$	1.13549e22			0.0988527
$764$	9.88991e22	+	1.88595e22i	0.852011	+	0.162474i
$765$			2.91771e22i			0.248742i
$766$	−5.70384e22	+	4.71893e22i	−0.481213	+	0.398120i
$767$			1.70243e23i			1.42136i
$768$	−2.85481e22	−	2.67948e22i	−0.235878	−	0.221391i
$769$	3.13181e22			0.256085			0.128043	−	0.991769i	$-0.459131\pi$
$769$	3.13181e22			0.256085			0.128043	+	0.991769i	$0.459131\pi$
$770$	−1.56710e21	−	1.89417e21i	−0.0126815	−	0.0153283i
$771$	−1.03019e22			−0.0825054
$772$	4.11077e22	−	2.15569e23i	0.325825	−	1.70863i
$773$		−	8.03867e22i		−	0.630592i	−0.948993	−	0.315296i	$-0.897896\pi$
$773$		−	8.03867e22i		−	0.630592i	0.948993	−	0.315296i	$-0.102104\pi$
$774$	4.39378e22	+	5.31082e22i	0.341123	+	0.412320i
$775$			1.68576e23i			1.29534i
$776$	7.85286e22	−	4.31812e22i	0.597220	−	0.328399i
$777$	−4.93472e21			−0.0371445
$778$	−1.20496e23	+	9.96893e22i	−0.897708	+	0.742697i
$779$	1.43522e22			0.105832
$780$	2.60125e21	−	1.36409e22i	0.0189856	−	0.0995605i
$781$		−	8.02021e22i		−	0.579399i
$782$	5.15630e22	−	4.26594e22i	0.368709	−	0.305043i
$783$			9.81752e22i			0.694877i
$784$	−1.29971e23	−	5.14399e22i	−0.910577	−	0.360389i
$785$	9.69524e22			0.672359
$786$	−3.25310e22	−	3.93206e22i	−0.223314	−	0.269923i
$787$	−1.84830e23			−1.25596			−0.627980	−	0.778230i	$-0.716118\pi$
$787$	−1.84830e23			−1.25596			−0.627980	+	0.778230i	$0.716118\pi$
$788$	−8.33353e22	−	1.58916e22i	−0.560556	−	0.106895i
$789$		−	3.33949e22i		−	0.222364i
$790$	−5.87606e22	−	7.10247e22i	−0.387319	−	0.468158i
$791$			1.01226e22i			0.0660514i
$792$	−4.21210e22	+	2.31614e22i	−0.272080	+	0.149611i
$793$	−1.91386e23			−1.22384
$794$	−6.23850e22	+	5.16127e22i	−0.394927	+	0.326733i
$795$	−2.94021e22			−0.184264
$796$	1.72954e23	+	3.29813e22i	1.07306	+	0.204627i
$797$			1.22724e23i			0.753812i	0.926252	+	0.376906i	$0.123012\pi$
$797$			1.22724e23i			0.753812i	−0.926252	+	0.376906i	$0.876988\pi$
$798$	5.18334e21	−	4.28831e21i	0.0315200	−	0.0260773i
$799$		−	9.20306e22i		−	0.554062i
$800$	−4.36234e22	−	1.34186e23i	−0.260015	−	0.799812i
$801$	4.61556e22			0.272373
$802$	−1.90572e23	−	2.30347e23i	−1.11344	−	1.34582i
$803$	−7.07466e22			−0.409243
$804$	−1.46863e21	+	7.70151e21i	−0.00841133	+	0.0441090i
$805$			6.94792e21i			0.0393992i
$806$	1.37403e23	+	1.66081e23i	0.771462	+	0.932478i
$807$			1.41228e22i			0.0785113i
$808$	−2.15470e22	−	3.91849e22i	−0.118603	−	0.215689i
$809$	−5.33214e22			−0.290612			−0.145306	−	0.989387i	$-0.546417\pi$
$809$	−5.33214e22			−0.290612			−0.145306	+	0.989387i	$0.546417\pi$
$810$	−3.96785e22	+	3.28270e22i	−0.214129	+	0.177154i
$811$	3.93928e22			0.210499			0.105250	−	0.994446i	$-0.466436\pi$
$811$	3.93928e22			0.210499			0.105250	+	0.994446i	$0.466436\pi$
$812$	−5.77231e21	+	3.02700e22i	−0.0305423	+	0.160164i
$813$			4.03578e22i			0.211448i
$814$	4.11035e22	−	3.40060e22i	0.213247	−	0.176425i
$815$		−	8.38018e22i		−	0.430519i
$816$	−4.11982e22	−	1.63054e22i	−0.209583	−	0.0829490i
$817$	1.04284e23			0.525340
$818$	8.21243e22	+	9.92647e22i	0.409680	+	0.495186i
$819$	2.04894e22			0.101218
$820$	9.64014e21	+	1.83832e21i	0.0471598	+	0.00899311i
$821$		−	1.52052e23i		−	0.736626i	−0.929702	−	0.368313i	$-0.879935\pi$
$821$		−	1.52052e23i		−	0.736626i	0.929702	−	0.368313i	$-0.120065\pi$
$822$	−3.96672e22	−	4.79463e22i	−0.190308	−	0.230028i
$823$		−	2.45587e23i		−	1.16683i	−0.812175	−	0.583413i	$-0.801717\pi$
$823$		−	2.45587e23i		−	1.16683i	0.812175	−	0.583413i	$-0.198283\pi$
$824$	1.63860e23	+	2.97994e23i	0.771004	+	1.40213i
$825$	2.02480e22			0.0943519
$826$	−4.34509e22	+	3.59481e22i	−0.200521	+	0.165896i
$827$	2.67245e23			1.22142			0.610711	−	0.791854i	$-0.290884\pi$
$827$	2.67245e23			1.22142			0.610711	+	0.791854i	$0.290884\pi$
$828$	1.33448e23	+	2.54478e22i	0.604046	+	0.115188i
$829$		−	2.05884e23i		−	0.922967i	−0.887149	−	0.461483i	$-0.847317\pi$
$829$		−	2.05884e23i		−	0.922967i	0.887149	−	0.461483i	$-0.152683\pi$
$830$	4.58925e22	−	3.79680e22i	0.203759	−	0.168575i
$831$			3.21930e22i			0.141564i
$832$	−1.52350e23	−	9.66433e22i	−0.663522	−	0.420906i
$833$	−1.58182e23			−0.682334
$834$	4.09049e22	+	4.94423e22i	0.174762	+	0.211237i
$835$	−1.07429e23			−0.454599
$836$	−1.36229e22	+	7.14385e22i	−0.0570978	+	0.299421i
$837$			2.27481e23i			0.944370i
$838$	2.65967e23	+	3.21479e23i	1.09364	+	1.32190i
$839$		−	2.39362e23i		−	0.974898i	−0.873151	−	0.487449i	$-0.837927\pi$
$839$		−	2.39362e23i		−	0.974898i	0.873151	−	0.487449i	$-0.162073\pi$
$840$	4.03084e21	−	2.21648e21i	0.0162615	−	0.00894188i
$841$	−7.11609e22			−0.284363
$842$	−5.05254e22	+	4.18010e22i	−0.199992	+	0.165459i
$843$	1.04400e23			0.409337
$844$	−4.17749e22	+	2.19067e23i	−0.162247	+	0.850821i
$845$			3.96506e22i			0.152544i
$846$	1.43946e23	−	1.19090e23i	0.548576	−	0.453851i
$847$			3.35270e22i			0.126569i
$848$	−1.40576e23	+	3.55186e23i	−0.525707	+	1.32828i
$849$	9.68671e20			0.00358852
$850$	−1.01785e23	−	1.23028e23i	−0.373534	−	0.451496i
$851$	−1.50770e23			−0.548123
$852$	1.47415e23	+	2.81111e22i	0.530914	+	0.101242i
$853$			1.44641e23i			0.516060i	0.966137	+	0.258030i	$0.0830733\pi$
$853$			1.44641e23i			0.516060i	−0.966137	+	0.258030i	$0.916927\pi$
$854$	−4.04126e22	−	4.88473e22i	−0.142841	−	0.172654i
$855$			8.96116e22i			0.313787i
$856$	−3.18846e23	+	1.75327e23i	−1.10609	+	0.608216i
$857$	−1.51502e23			−0.520681			−0.260341	−	0.965517i	$-0.583835\pi$
$857$	−1.51502e23			−0.520681			−0.260341	+	0.965517i	$0.583835\pi$
$858$	1.99483e22	−	1.65037e22i	0.0679214	−	0.0561931i
$859$	4.09005e23			1.37969			0.689847	−	0.723955i	$-0.257678\pi$
$859$	4.09005e23			1.37969			0.689847	+	0.723955i	$0.257678\pi$
$860$	7.00458e22	+	1.33573e22i	0.234096	+	0.0446408i
$861$		−	1.69250e21i		−	0.00560406i
$862$	4.22619e23	−	3.49644e23i	1.38641	−	1.14701i
$863$		−	3.89747e23i		−	1.26677i	−0.773839	−	0.633383i	$-0.781666\pi$
$863$		−	3.89747e23i		−	1.26677i	0.773839	−	0.633383i	$-0.218334\pi$
$864$	−5.88666e22	−	1.81075e23i	−0.189565	−	0.583106i
$865$	−1.64846e23			−0.525956
$866$	2.48640e22	+	3.00534e22i	0.0786009	+	0.0950059i
$867$	5.31421e22			0.166451
$868$	−1.33750e22	+	7.01384e22i	−0.0415084	+	0.217670i
$869$		−	1.71861e23i		−	0.528468i
$870$	3.05841e22	+	3.69674e22i	0.0931839	+	0.112633i
$871$			3.61281e22i			0.109069i
$872$	−1.10674e23	−	2.01269e23i	−0.331065	−	0.602068i
$873$	2.05876e23			0.610228
$874$	1.58366e23	−	1.31020e23i	0.465125	−	0.384810i
$875$	3.62890e22			0.105611
$876$	2.47970e22	−	1.30035e23i	0.0715098	−	0.374997i
$877$			5.89955e23i			1.68586i	0.538020	+	0.842932i	$0.319172\pi$
$877$			5.89955e23i			1.68586i	−0.538020	+	0.842932i	$0.680828\pi$
$878$	−9.23607e22	+	7.64124e22i	−0.261536	+	0.216375i
$879$		−	1.76274e23i		−	0.494626i
$880$	−1.83006e22	+	4.62393e22i	−0.0508867	+	0.128573i
$881$	−1.17568e23			−0.323953			−0.161976	−	0.986795i	$-0.551787\pi$
$881$	−1.17568e23			−0.323953			−0.161976	+	0.986795i	$0.551787\pi$
$882$	−2.04692e23	−	2.47414e23i	−0.558924	−	0.675579i
$883$	−3.48160e22			−0.0942091			−0.0471045	−	0.998890i	$-0.514999\pi$
$883$	−3.48160e22			−0.0942091			−0.0471045	+	0.998890i	$0.514999\pi$
$884$	−2.00555e23	−	3.82448e22i	−0.537794	−	0.102554i
$885$			8.78036e22i			0.233328i
$886$	−3.51187e23	−	4.24485e23i	−0.924844	−	1.11787i
$887$			4.69958e23i			1.22651i	0.789886	+	0.613254i	$0.210140\pi$
$887$			4.69958e23i			1.22651i	−0.789886	+	0.613254i	$0.789860\pi$
$888$	4.80975e22	+	8.74692e22i	0.124400	+	0.226231i
$889$	7.10424e21			0.0182097
$890$	3.67907e22	−	3.04379e22i	0.0934584	−	0.0773206i
$891$	−9.60114e22			−0.241714
$892$	−1.11584e23	−	2.12785e22i	−0.278410	−	0.0530911i
$893$		−	2.82654e23i		−	0.698946i
$894$	−1.24682e23	+	1.03152e23i	−0.305564	+	0.252801i
$895$			8.10756e22i			0.196927i
$896$	−7.50364e21	−	5.92911e22i	−0.0180637	−	0.142733i
$897$	−7.31712e22			−0.174582
$898$	−7.15791e22	−	8.65187e22i	−0.169268	−	0.204597i
$899$	−7.44732e23			−1.74551
$900$	6.07179e22	−	3.18405e23i	0.141051	−	0.739673i
$901$			4.32283e23i			0.995337i
$902$	1.16633e22	+	1.40976e22i	0.0266176	+	0.0321730i
$903$		−	1.22978e22i		−	0.0278179i
$904$	1.79427e23	−	9.86629e22i	0.402290	−	0.221211i
$905$	−9.95478e22			−0.221229
$906$	−5.90805e22	+	4.88788e22i	−0.130142	+	0.107670i
$907$	6.93053e23			1.51324			0.756620	−	0.653855i	$-0.226849\pi$
$907$	6.93053e23			1.51324			0.756620	+	0.653855i	$0.226849\pi$
$908$	−1.63081e22	+	8.55197e22i	−0.0352953	+	0.185088i
$909$		−	1.02730e23i		−	0.220387i
$910$	1.63322e22	−	1.35120e22i	0.0347307	−	0.0287336i
$911$		−	4.79128e22i		−	0.100996i	−0.998724	−	0.0504980i	$-0.983919\pi$
$911$		−	4.79128e22i		−	0.100996i	0.998724	−	0.0504980i	$-0.0160809\pi$
$912$	−1.26532e23	−	5.00790e22i	−0.264388	−	0.104640i
$913$	1.11048e23			0.230008
$914$	3.51456e23	+	4.24810e23i	0.721609	+	0.872219i
$915$	−9.87083e22			−0.200902
$916$	1.19762e22	+	2.28379e21i	0.0241632	+	0.00460779i
$917$		−	7.78982e22i		−	0.155802i
$918$	−1.37351e23	−	1.66018e23i	−0.272327	−	0.329165i
$919$			2.31913e22i			0.0455828i	0.999740	+	0.0227914i	$0.00725535\pi$
$919$			2.31913e22i			0.0455828i	−0.999740	+	0.0227914i	$0.992745\pi$
$920$	1.23154e23	−	6.77196e22i	0.239963	−	0.131951i
$921$	−1.83840e23			−0.355109
$922$	2.90226e23	−	2.40112e23i	0.555762	−	0.459796i
$923$	6.91529e23			1.31280
$924$	8.42447e21	+	1.60650e21i	0.0158550	+	0.00302346i
$925$			3.59734e23i			0.671193i
$926$	−6.40486e23	+	5.29890e23i	−1.18474	+	0.980162i
$927$			7.81242e23i			1.43268i
$928$	5.92805e23	−	1.92718e23i	1.07777	−	0.350380i
$929$	5.47436e23			0.986750			0.493375	−	0.869817i	$-0.335763\pi$
$929$	5.47436e23			0.986750			0.493375	+	0.869817i	$0.335763\pi$
$930$	7.08662e22	+	8.56570e22i	0.126641	+	0.153073i
$931$	−4.85825e23			−0.860761
$932$	−1.22461e22	+	6.42183e22i	−0.0215114	+	0.112806i
$933$		−	2.63883e23i		−	0.459578i
$934$	5.16814e23	+	6.24680e23i	0.892399	+	1.07866i
$935$			5.62760e22i			0.0963452i
$936$	−1.99706e23	−	3.63181e23i	−0.338987	−	0.616476i
$937$	8.64799e23			1.45545			0.727727	−	0.685867i	$-0.240577\pi$
$937$	8.64799e23			1.45545			0.727727	+	0.685867i	$0.240577\pi$
$938$	−9.22096e21	+	7.62874e21i	−0.0153870	+	0.0127300i
$939$	2.84845e22			0.0471286
$940$	3.62041e22	−	1.89854e23i	0.0593930	−	0.311457i
$941$		−	1.11394e24i		−	1.81195i	−0.423336	−	0.905973i	$-0.639141\pi$
$941$		−	1.11394e24i		−	1.81195i	0.423336	−	0.905973i	$-0.360859\pi$
$942$	−2.60600e23	+	2.15601e23i	−0.420308	+	0.347732i
$943$		−	5.17106e22i		−	0.0826962i
$944$	1.06069e24	+	4.19803e23i	1.68196	+	0.665686i
$945$	2.23703e22			0.0351736
$946$	8.47461e22	+	1.02434e23i	0.132127	+	0.159703i
$947$	−8.81367e23			−1.36256			−0.681282	−	0.732021i	$-0.738577\pi$
$947$	−8.81367e23			−1.36256			−0.681282	+	0.732021i	$0.738577\pi$
$948$	3.15887e23	+	6.02379e22i	0.484246	+	0.0923428i
$949$		−	6.10001e23i		−	0.927259i
$950$	−3.12611e23	−	3.77858e23i	−0.471211	−	0.569560i
$951$		−	3.18416e23i		−	0.475939i
$952$	−3.25877e22	−	5.92634e22i	−0.0483012	−	0.0878397i
$953$	2.68365e23			0.394441			0.197220	−	0.980359i	$-0.436809\pi$
$953$	2.68365e23			0.394441			0.197220	+	0.980359i	$0.436809\pi$
$954$	−6.76139e23	+	5.59387e23i	−0.985483	+	0.815315i
$955$	2.39280e23			0.345843
$956$	−9.46871e23	−	1.80563e23i	−1.35715	−	0.258800i
$957$			8.94512e22i			0.127142i
$958$	1.12440e23	−	9.30248e22i	0.158489	−	0.131122i
$959$		−	9.49864e22i		−	0.132774i
$960$	−7.85752e22	−	4.98443e22i	−0.108922	−	0.0690949i
$961$	−9.98192e23			−1.37223
$962$	2.93211e23	+	3.54408e23i	0.399742	+	0.483174i
$963$	−8.35910e23			−1.13018
$964$	−1.48380e23	+	7.78103e23i	−0.198957	+	1.04333i
$965$		−	5.21554e23i		−	0.693554i
$966$	−1.54507e22	−	1.86754e22i	−0.0203765	−	0.0246294i
$967$			2.89285e23i			0.378368i	0.981942	+	0.189184i	$0.0605842\pi$
$967$			2.89285e23i			0.378368i	−0.981942	+	0.189184i	$0.939416\pi$
$968$	5.94275e23	−	3.26779e23i	0.770876	−	0.423889i
$969$	−1.53997e23			−0.198117
$970$	1.64105e23	−	1.35768e23i	0.209386	−	0.173230i
$971$	−5.10302e23			−0.645764			−0.322882	−	0.946439i	$-0.604652\pi$
$971$	−5.10302e23			−0.645764			−0.322882	+	0.946439i	$0.604652\pi$
$972$	1.25164e23	−	6.56358e23i	0.157090	−	0.823779i
$973$			9.79503e22i			0.121928i
$974$	−9.20794e23	+	7.61797e23i	−1.13682	+	0.940519i
$975$			1.74585e23i			0.213782i
$976$	−4.71940e23	+	1.19243e24i	−0.573176	+	1.44822i
$977$	3.54353e23			0.426854			0.213427	−	0.976959i	$-0.431537\pi$
$977$	3.54353e23			0.426854			0.213427	+	0.976959i	$0.431537\pi$
$978$	1.86357e23	+	2.25253e23i	0.222656	+	0.269128i
$979$	8.90238e22			0.105498
$980$	−3.26321e23	−	6.22276e22i	−0.383563	−	0.0731433i
$981$		−	5.27662e23i		−	0.615182i
$982$	−6.05886e23	−	7.32342e23i	−0.700646	−	0.846881i
$983$		−	8.54925e23i		−	0.980618i	−0.871549	−	0.490309i	$-0.836884\pi$
$983$		−	8.54925e23i		−	0.980618i	0.871549	−	0.490309i	$-0.163116\pi$
$984$	−2.99999e22	+	1.64963e22i	−0.0341318	+	0.0187684i
$985$	−2.01624e23			−0.227537
$986$	5.43512e23	−	4.49661e23i	0.608406	−	0.503350i
$987$	−3.33323e22			−0.0370107
$988$	−6.15967e23	−	1.17461e23i	−0.678425	−	0.129372i
$989$		−	3.75732e23i		−	0.410495i
$990$	−8.80219e22	+	7.28228e22i	−0.0953914	+	0.0789198i
$991$		−	5.21592e23i		−	0.560714i	−0.959896	−	0.280357i	$-0.909547\pi$
$991$		−	5.21592e23i		−	0.560714i	0.959896	−	0.280357i	$-0.0904529\pi$
$992$	1.37359e24	−	4.46547e23i	1.46475	−	0.476182i
$993$	5.74406e23			0.607610
$994$	1.46022e23	+	1.76499e23i	0.153224	+	0.185204i
$995$	4.18449e23			0.435570
$996$	−3.89226e22	+	2.04110e23i	−0.0401908	+	0.210761i
$997$			1.14311e24i			1.17091i	0.810703	+	0.585457i	$0.199085\pi$
$997$			1.14311e24i			1.17091i	−0.810703	+	0.585457i	$0.800915\pi$
$998$	1.59421e23	+	1.92695e23i	0.161995	+	0.195806i
$999$			4.85435e23i			0.489336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.12	yes	14
3.2	odd	2		72.17.b.b.19.3		14
4.3	odd	2		32.17.d.b.15.10		14
8.3	odd	2	inner	8.17.d.b.3.11	✓	14
8.5	even	2		32.17.d.b.15.9		14
24.11	even	2		72.17.b.b.19.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.11	✓	14	8.3	odd	2	inner
8.17.d.b.3.12	yes	14	1.1	even	1	trivial
32.17.d.b.15.9		14	8.5	even	2
32.17.d.b.15.10		14	4.3	odd	2
72.17.b.b.19.3		14	3.2	odd	2
72.17.b.b.19.4		14	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:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(163.187 + 197.246i) q^{2} -2122.49 q^{3} +(-12276.1 + 64376.0i) q^{4} +155753. i q^{5} +(-346362. - 418652. i) q^{6} -829393. i q^{7} +(-1.47012e7 + 8.08389e6i) q^{8} -3.85418e7 q^{9} +O(q^{10})\)	\(q+(163.187 + 197.246i) q^{2} -2122.49 q^{3} +(-12276.1 + 64376.0i) q^{4} +155753. i q^{5} +(-346362. - 418652. i) q^{6} -829393. i q^{7} +(-1.47012e7 + 8.08389e6i) q^{8} -3.85418e7 q^{9} +(-3.07217e7 + 2.54169e7i) q^{10} -7.43384e7 q^{11} +(2.60559e7 - 1.36637e8i) q^{12} -6.40971e8i q^{13} +(1.63595e8 - 1.35346e8i) q^{14} -3.30584e8i q^{15} +(-3.99356e9 - 1.58057e9i) q^{16} -4.86041e9 q^{17} +(-6.28951e9 - 7.60222e9i) q^{18} -1.49278e10 q^{19} +(-1.00268e10 - 1.91205e9i) q^{20} +1.76038e9i q^{21} +(-1.21311e10 - 1.46630e10i) q^{22} +5.37845e10i q^{23} +(3.12031e10 - 1.71579e10i) q^{24} +1.28329e11 q^{25} +(1.26429e11 - 1.04598e11i) q^{26} +1.73170e11 q^{27} +(5.33930e10 + 1.01817e10i) q^{28} +5.66928e11i q^{29} +(6.52065e10 - 5.39470e10i) q^{30} +1.31363e12i q^{31} +(-3.39934e11 - 1.04564e12i) q^{32} +1.57782e11 q^{33} +(-7.93154e11 - 9.58697e11i) q^{34} +1.29181e11 q^{35} +(4.73144e11 - 2.48116e12i) q^{36} +2.80322e12i q^{37} +(-2.43602e12 - 2.94445e12i) q^{38} +1.36045e12i q^{39} +(-1.25909e12 - 2.28976e12i) q^{40} -9.61440e11 q^{41} +(-3.47227e11 + 2.87270e11i) q^{42} -6.98588e12 q^{43} +(9.12588e11 - 4.78561e12i) q^{44} -6.00301e12i q^{45} +(-1.06088e13 + 8.77692e12i) q^{46} +1.89348e13i q^{47} +(8.47628e12 + 3.35475e12i) q^{48} +3.25450e13 q^{49} +(2.09416e13 + 2.53124e13i) q^{50} +1.03161e13 q^{51} +(4.12631e13 + 7.86863e12i) q^{52} -8.89397e13i q^{53} +(2.82591e13 + 3.41572e13i) q^{54} -1.15785e13i q^{55} +(6.70472e12 + 1.21931e13i) q^{56} +3.16840e13 q^{57} +(-1.11824e14 + 9.25152e13i) q^{58} -2.65601e14 q^{59} +(2.12817e13 + 4.05829e12i) q^{60} -2.98587e14i q^{61} +(-2.59108e14 + 2.14367e14i) q^{62} +3.19663e13i q^{63} +(1.50776e14 - 2.37686e14i) q^{64} +9.98333e13 q^{65} +(2.57480e13 + 3.11220e13i) q^{66} -5.63647e13 q^{67} +(5.96669e13 - 3.12893e14i) q^{68} -1.14157e14i q^{69} +(2.10806e13 + 2.54804e13i) q^{70} +1.07888e15i q^{71} +(5.66611e14 - 3.11567e14i) q^{72} +9.51683e14 q^{73} +(-5.52925e14 + 4.57449e14i) q^{74} -2.72376e14 q^{75} +(1.83255e14 - 9.60990e14i) q^{76} +6.16558e13i q^{77} +(-2.68344e14 + 2.22008e14i) q^{78} +2.31187e15i q^{79} +(2.46180e14 - 6.22010e14i) q^{80} +1.29154e15 q^{81} +(-1.56894e14 - 1.89640e14i) q^{82} -1.49381e15 q^{83} +(-1.13326e14 - 2.16106e13i) q^{84} -7.57024e14i q^{85} +(-1.14000e15 - 1.37794e15i) q^{86} -1.20330e15i q^{87} +(1.09287e15 - 6.00944e14i) q^{88} -1.19755e15 q^{89} +(1.18407e15 - 9.79612e14i) q^{90} -5.31617e14 q^{91} +(-3.46243e15 - 6.60265e14i) q^{92} -2.78815e15i q^{93} +(-3.73481e15 + 3.08990e15i) q^{94} -2.32505e15i q^{95} +(7.21506e14 + 2.21936e15i) q^{96} -5.34164e15 q^{97} +(5.31092e15 + 6.41938e15i) q^{98} +2.86513e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9}+O(q^{10}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9	\( 14 q - 350 q^{2} + 11964 q^{3} - 54220 q^{4} + 4868124 q^{6} + 10899160 q^{8} + 86397354 q^{9} + 87155280 q^{10} - 49140292 q^{11} + 31616184 q^{12} - 2675193504 q^{14} + 9716374544 q^{16} - 9985136356 q^{17} - 7692086106 q^{18} + 62922133180 q^{19} + 31953450720 q^{20} - 51493048676 q^{22} + 54962419344 q^{24} - 429906632050 q^{25} - 518273679696 q^{26} + 655936606584 q^{27} + 102542376000 q^{28} - 364331826720 q^{30} + 95751080800 q^{32} + 4034287537464 q^{33} + 1015818512644 q^{34} - 3057653406720 q^{35} - 9569289445092 q^{36} + 9010383442844 q^{38} - 4027933291200 q^{40} + 8719629072668 q^{41} - 6653698130880 q^{42} + 16716309178300 q^{43} - 4351929975880 q^{44} + 21043605267744 q^{46} + 46562301973344 q^{48} - 104740771400434 q^{49} - 54483696687710 q^{50} + 40911296041848 q^{51} - 73249356722400 q^{52} - 18031398151752 q^{54} + 110873799752064 q^{56} - 310730528383176 q^{57} + 256627273576560 q^{58} + 347007330293180 q^{59} - 83822619107520 q^{60} + 346701622780800 q^{62} - 332173589517760 q^{64} + 220877370432000 q^{65} + 875905832132808 q^{66} - 614258765968196 q^{67} - 12\!\cdots\!76 q^{68}+ \cdots - 18\!\cdots\!92 q^{99}+O(q^{100}) \) 14 * q - 350 * q^2 + 11964 * q^3 - 54220 * q^4 + 4868124 * q^6 + 10899160 * q^8 + 86397354 * q^9 + 87155280 * q^10 - 49140292 * q^11 + 31616184 * q^12 - 2675193504 * q^14 + 9716374544 * q^16 - 9985136356 * q^17 - 7692086106 * q^18 + 62922133180 * q^19 + 31953450720 * q^20 - 51493048676 * q^22 + 54962419344 * q^24 - 429906632050 * q^25 - 518273679696 * q^26 + 655936606584 * q^27 + 102542376000 * q^28 - 364331826720 * q^30 + 95751080800 * q^32 + 4034287537464 * q^33 + 1015818512644 * q^34 - 3057653406720 * q^35 - 9569289445092 * q^36 + 9010383442844 * q^38 - 4027933291200 * q^40 + 8719629072668 * q^41 - 6653698130880 * q^42 + 16716309178300 * q^43 - 4351929975880 * q^44 + 21043605267744 * q^46 + 46562301973344 * q^48 - 104740771400434 * q^49 - 54483696687710 * q^50 + 40911296041848 * q^51 - 73249356722400 * q^52 - 18031398151752 * q^54 + 110873799752064 * q^56 - 310730528383176 * q^57 + 256627273576560 * q^58 + 347007330293180 * q^59 - 83822619107520 * q^60 + 346701622780800 * q^62 - 332173589517760 * q^64 + 220877370432000 * q^65 + 875905832132808 * q^66 - 614258765968196 * q^67 - 1235787871965976 * q^68 - 442172390987520 * q^70 - 1312232111609976 * q^72 - 542888518370276 * q^73 + 2394643836493776 * q^74 + 2861985572983740 * q^75 - 614792000883272 * q^76 - 4928152344599520 * q^78 + 6402194304908160 * q^80 - 5344304371237818 * q^81 + 4810720063300804 * q^82 + 7362421930746044 * q^83 - 9316784627856000 * q^84 - 8963192329247716 * q^86 + 3396904358318224 * q^88 - 408131327364580 * q^89 + 14680290550241520 * q^90 - 7162887702930432 * q^91 - 9213856910218560 * q^92 - 15838781433150144 * q^94 + 48917704300183104 * q^96 + 18372136634257180 * q^97 + 34005570793293730 * q^98 - 18934692015468492 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more