LMFDB - Embedded newform 8.17.d.b.3.13

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			3.13
Root			$-137.581 + 24.7690i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.d.b.3.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(251.161 - 49.5380i) q^{2} +6181.49 q^{3} +(60628.0 - 24884.1i) q^{4} +699404. i q^{5} +(1.55255e6 - 306219. i) q^{6} +4.65744e6i q^{7} +(1.39947e7 - 9.25331e6i) q^{8} -4.83590e6 q^{9} +O(q^{10})$	\(q+(251.161 - 49.5380i) q^{2} +6181.49 q^{3} +(60628.0 - 24884.1i) q^{4} +699404. i q^{5} +(1.55255e6 - 306219. i) q^{6} +4.65744e6i q^{7} +(1.39947e7 - 9.25331e6i) q^{8} -4.83590e6 q^{9} +(3.46471e7 + 1.75663e8i) q^{10} -2.50802e7 q^{11} +(3.74771e8 - 1.53821e8i) q^{12} -9.99771e8i q^{13} +(2.30721e8 + 1.16977e9i) q^{14} +4.32336e9i q^{15} +(3.05653e9 - 3.01734e9i) q^{16} +1.78097e9 q^{17} +(-1.21459e9 + 2.39561e8i) q^{18} +2.70321e10 q^{19} +(1.74040e10 + 4.24035e10i) q^{20} +2.87899e10i q^{21} +(-6.29917e9 + 1.24242e9i) q^{22} -7.64077e10i q^{23} +(8.65080e10 - 5.71992e10i) q^{24} -3.36579e11 q^{25} +(-4.95267e10 - 2.51104e11i) q^{26} -2.95986e11 q^{27} +(1.15896e11 + 2.82371e11i) q^{28} -7.60372e11i q^{29} +(2.14171e11 + 1.08586e12i) q^{30} +2.35983e11i q^{31} +(6.18210e11 - 9.09254e11i) q^{32} -1.55033e11 q^{33} +(4.47310e11 - 8.82257e10i) q^{34} -3.25744e12 q^{35} +(-2.93191e11 + 1.20337e11i) q^{36} +2.42830e12i q^{37} +(6.78943e12 - 1.33912e12i) q^{38} -6.18007e12i q^{39} +(6.47180e12 + 9.78795e12i) q^{40} +1.88090e12 q^{41} +(1.42620e12 + 7.23092e12i) q^{42} -9.47032e12 q^{43} +(-1.52056e12 + 6.24097e11i) q^{44} -3.38225e12i q^{45} +(-3.78509e12 - 1.91907e13i) q^{46} +1.60529e13i q^{47} +(1.88939e13 - 1.86517e13i) q^{48} +1.15412e13 q^{49} +(-8.45355e13 + 1.66734e13i) q^{50} +1.10090e13 q^{51} +(-2.48784e13 - 6.06141e13i) q^{52} -1.92778e13i q^{53} +(-7.43402e13 + 1.46626e13i) q^{54} -1.75412e13i q^{55} +(4.30967e13 + 6.51795e13i) q^{56} +1.67099e14 q^{57} +(-3.76673e13 - 1.90976e14i) q^{58} -3.49569e13 q^{59} +(1.07583e14 + 2.62117e14i) q^{60} +3.45553e14i q^{61} +(1.16901e13 + 5.92698e13i) q^{62} -2.25229e13i q^{63} +(1.10228e14 - 2.58994e14i) q^{64} +6.99244e14 q^{65} +(-3.89382e13 + 7.68002e12i) q^{66} -6.70291e14 q^{67} +(1.07977e14 - 4.43178e13i) q^{68} -4.72314e14i q^{69} +(-8.18142e14 + 1.61367e14i) q^{70} -2.20461e14i q^{71} +(-6.76769e13 + 4.47481e13i) q^{72} +1.81005e14 q^{73} +(1.20293e14 + 6.09895e14i) q^{74} -2.08056e15 q^{75} +(1.63890e15 - 6.72670e14i) q^{76} -1.16809e14i q^{77} +(-3.06149e14 - 1.55220e15i) q^{78} -1.45789e14i q^{79} +(2.11034e15 + 2.13775e15i) q^{80} -1.62146e15 q^{81} +(4.72409e14 - 9.31760e13i) q^{82} -3.18974e14 q^{83} +(7.16411e14 + 1.74548e15i) q^{84} +1.24562e15i q^{85} +(-2.37858e15 + 4.69141e14i) q^{86} -4.70023e15i q^{87} +(-3.50989e14 + 2.32075e14i) q^{88} +2.96458e15 q^{89} +(-1.67550e14 - 8.49491e14i) q^{90} +4.65638e15 q^{91} +(-1.90134e15 - 4.63244e15i) q^{92} +1.45873e15i q^{93} +(7.95231e14 + 4.03188e15i) q^{94} +1.89064e16i q^{95} +(3.82146e15 - 5.62054e15i) q^{96} +7.93720e15 q^{97} +(2.89869e15 - 5.71726e14i) q^{98} +1.21285e14 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 $

$2$	251.161	−	49.5380i	0.981099	−	0.193508i
$2$	251.161	−	49.5380i	0.981099	−	0.193508i
$3$	6181.49			0.942157			0.471078	−	0.882091i	$-0.343865\pi$
$3$	6181.49			0.942157			0.471078	+	0.882091i	$0.343865\pi$
$4$	60628.0	−	24884.1i	0.925109	−	0.379701i
$5$			699404.i			1.79048i	0.445589	+	0.895238i	$0.352994\pi$
$5$			699404.i			1.79048i	−0.445589	+	0.895238i	$0.647006\pi$
$6$	1.55255e6	−	306219.i	0.924349	−	0.182315i
$7$			4.65744e6i			0.807911i	0.914779	+	0.403955i	$0.132365\pi$
$7$			4.65744e6i			0.807911i	−0.914779	+	0.403955i	$0.867635\pi$
$8$	1.39947e7	−	9.25331e6i	0.834148	−	0.551540i
$9$	−4.83590e6			−0.112341
$10$	3.46471e7	+	1.75663e8i	0.346471	+	1.75663i
$11$	−2.50802e7			−0.117001			−0.0585004	−	0.998287i	$-0.518632\pi$
$11$	−2.50802e7			−0.117001			−0.0585004	+	0.998287i	$0.518632\pi$
$12$	3.74771e8	−	1.53821e8i	0.871598	−	0.357738i
$13$		−	9.99771e8i		−	1.22561i	−0.790233	−	0.612807i	$-0.790040\pi$
$13$		−	9.99771e8i		−	1.22561i	0.790233	−	0.612807i	$-0.209960\pi$
$14$	2.30721e8	+	1.16977e9i	0.156337	+	0.792640i
$15$			4.32336e9i			1.68691i
$16$	3.05653e9	−	3.01734e9i	0.711655	−	0.702530i
$17$	1.78097e9			0.255308			0.127654	−	0.991819i	$-0.459255\pi$
$17$	1.78097e9			0.255308			0.127654	+	0.991819i	$0.459255\pi$
$18$	−1.21459e9	+	2.39561e8i	−0.110217	+	0.0217388i
$19$	2.70321e10			1.59166			0.795832	−	0.605517i	$-0.207034\pi$
$19$	2.70321e10			1.59166			0.795832	+	0.605517i	$0.207034\pi$
$20$	1.74040e10	+	4.24035e10i	0.679845	+	1.65639i
$21$			2.87899e10i			0.761178i
$22$	−6.29917e9	+	1.24242e9i	−0.114789	+	0.0226406i
$23$		−	7.64077e10i		−	0.975696i	−0.872929	−	0.487848i	$-0.837782\pi$
$23$		−	7.64077e10i		−	0.975696i	0.872929	−	0.487848i	$-0.162218\pi$
$24$	8.65080e10	−	5.71992e10i	0.785899	−	0.519637i
$25$	−3.36579e11			−2.20580
$26$	−4.95267e10	−	2.51104e11i	−0.237166	−	1.20245i
$27$	−2.95986e11			−1.04800
$28$	1.15896e11	+	2.82371e11i	0.306764	+	0.747406i
$29$		−	7.60372e11i		−	1.51999i	−0.649926	−	0.759997i	$-0.725200\pi$
$29$		−	7.60372e11i		−	1.51999i	0.649926	−	0.759997i	$-0.274800\pi$
$30$	2.14171e11	+	1.08586e12i	0.326430	+	1.65502i
$31$			2.35983e11i			0.276686i	0.990384	+	0.138343i	$0.0441777\pi$
$31$			2.35983e11i			0.276686i	−0.990384	+	0.138343i	$0.955822\pi$
$32$	6.18210e11	−	9.09254e11i	0.562258	−	0.826962i
$33$	−1.55033e11			−0.110233
$34$	4.47310e11	−	8.82257e10i	0.250483	−	0.0494042i
$35$	−3.25744e12			−1.44654
$36$	−2.93191e11	+	1.20337e11i	−0.103928	+	0.0426559i
$37$			2.42830e12i			0.691336i	0.938357	+	0.345668i	$0.112348\pi$
$37$			2.42830e12i			0.691336i	−0.938357	+	0.345668i	$0.887652\pi$
$38$	6.78943e12	−	1.33912e12i	1.56158	−	0.308000i
$39$		−	6.18007e12i		−	1.15472i
$40$	6.47180e12	+	9.78795e12i	0.987519	+	1.49352i
$41$	1.88090e12			0.235556			0.117778	−	0.993040i	$-0.462423\pi$
$41$	1.88090e12			0.235556			0.117778	+	0.993040i	$0.462423\pi$
$42$	1.42620e12	+	7.23092e12i	0.147294	+	0.746791i
$43$	−9.47032e12			−0.810246			−0.405123	−	0.914262i	$-0.632771\pi$
$43$	−9.47032e12			−0.810246			−0.405123	+	0.914262i	$0.632771\pi$
$44$	−1.52056e12	+	6.24097e11i	−0.108239	+	0.0444253i
$45$		−	3.38225e12i		−	0.201143i
$46$	−3.78509e12	−	1.91907e13i	−0.188805	−	0.957254i
$47$			1.60529e13i			0.674174i	0.941474	+	0.337087i	$0.109442\pi$
$47$			1.60529e13i			0.674174i	−0.941474	+	0.337087i	$0.890558\pi$
$48$	1.88939e13	−	1.86517e13i	0.670490	−	0.661893i
$49$	1.15412e13			0.347281
$50$	−8.45355e13	+	1.66734e13i	−2.16411	+	0.426840i
$51$	1.10090e13			0.240540
$52$	−2.48784e13	−	6.06141e13i	−0.465367	−	1.13383i
$53$		−	1.92778e13i		−	0.309635i	−0.987943	−	0.154817i	$-0.950521\pi$
$53$		−	1.92778e13i		−	0.309635i	0.987943	−	0.154817i	$-0.0494789\pi$
$54$	−7.43402e13	+	1.46626e13i	−1.02819	+	0.202796i
$55$		−	1.75412e13i		−	0.209487i
$56$	4.30967e13	+	6.51795e13i	0.445595	+	0.673917i
$57$	1.67099e14			1.49960
$58$	−3.76673e13	−	1.90976e14i	−0.294131	−	1.49126i
$59$	−3.49569e13			−0.238076			−0.119038	−	0.992890i	$-0.537981\pi$
$59$	−3.49569e13			−0.238076			−0.119038	+	0.992890i	$0.537981\pi$
$60$	1.07583e14	+	2.62117e14i	0.640521	+	1.56057i
$61$			3.45553e14i			1.80250i	0.433297	+	0.901251i	$0.357350\pi$
$61$			3.45553e14i			1.80250i	−0.433297	+	0.901251i	$0.642650\pi$
$62$	1.16901e13	+	5.92698e13i	0.0535410	+	0.271456i
$63$		−	2.25229e13i		−	0.0907613i
$64$	1.10228e14	−	2.58994e14i	0.391607	−	0.920132i
$65$	6.99244e14			2.19443
$66$	−3.89382e13	+	7.68002e12i	−0.108150	+	0.0213310i
$67$	−6.70291e14			−1.65069			−0.825344	−	0.564630i	$-0.809019\pi$
$67$	−6.70291e14			−1.65069			−0.825344	+	0.564630i	$0.809019\pi$
$68$	1.07977e14	−	4.43178e13i	0.236188	−	0.0969408i
$69$		−	4.72314e14i		−	0.919259i
$70$	−8.18142e14	+	1.61367e14i	−1.41920	+	0.279918i
$71$		−	2.20461e14i		−	0.341401i	−0.985323	−	0.170700i	$-0.945397\pi$
$71$		−	2.20461e14i		−	0.341401i	0.985323	−	0.170700i	$-0.0546030\pi$
$72$	−6.76769e13	+	4.47481e13i	−0.0937089	+	0.0619604i
$73$	1.81005e14			0.224444			0.112222	−	0.993683i	$-0.464203\pi$
$73$	1.81005e14			0.224444			0.112222	+	0.993683i	$0.464203\pi$
$74$	1.20293e14	+	6.09895e14i	0.133779	+	0.678268i
$75$	−2.08056e15			−2.07821
$76$	1.63890e15	−	6.72670e14i	1.47246	−	0.604356i
$77$		−	1.16809e14i		−	0.0945262i
$78$	−3.06149e14	−	1.55220e15i	−0.223448	−	1.13289i
$79$		−	1.45789e14i		−	0.0960965i	−0.998845	−	0.0480482i	$-0.984700\pi$
$79$		−	1.45789e14i		−	0.0960965i	0.998845	−	0.0480482i	$-0.0153001\pi$
$80$	2.11034e15	+	2.13775e15i	1.25786	+	1.27420i
$81$	−1.62146e15			−0.875039
$82$	4.72409e14	−	9.31760e13i	0.231104	−	0.0455820i
$83$	−3.18974e14			−0.141622			−0.0708110	−	0.997490i	$-0.522559\pi$
$83$	−3.18974e14			−0.141622			−0.0708110	+	0.997490i	$0.522559\pi$
$84$	7.16411e14	+	1.74548e15i	0.289020	+	0.704173i
$85$			1.24562e15i			0.457123i
$86$	−2.37858e15	+	4.69141e14i	−0.794932	+	0.156789i
$87$		−	4.70023e15i		−	1.43207i
$88$	−3.50989e14	+	2.32075e14i	−0.0975961	+	0.0645307i
$89$	2.96458e15			0.753083			0.376541	−	0.926400i	$-0.377113\pi$
$89$	2.96458e15			0.753083			0.376541	+	0.926400i	$0.377113\pi$
$90$	−1.67550e14	−	8.49491e14i	−0.0389229	−	0.197342i
$91$	4.65638e15			0.990186
$92$	−1.90134e15	−	4.63244e15i	−0.370473	−	0.902625i
$93$			1.45873e15i			0.260682i
$94$	7.95231e14	+	4.03188e15i	0.130458	+	0.661431i
$95$			1.89064e16i			2.84984i
$96$	3.82146e15	−	5.62054e15i	0.529735	−	0.779127i
$97$	7.93720e15			1.01273			0.506365	−	0.862319i	$-0.330989\pi$
$97$	7.93720e15			1.01273			0.506365	+	0.862319i	$0.330989\pi$
$98$	2.89869e15	−	5.71726e14i	0.340717	−	0.0672016i
$99$	1.21285e14			0.0131440
$100$	−2.04061e16	+	8.37545e15i	−2.04061	+	0.837545i
$101$		−	1.00307e16i		−	0.926321i	−0.886274	−	0.463160i	$-0.846715\pi$
$101$		−	1.00307e16i		−	0.926321i	0.886274	−	0.463160i	$-0.153285\pi$
$102$	2.76504e15	−	5.45366e14i	0.235994	−	0.0465465i
$103$		−	2.46355e16i		−	1.94475i	−0.233429	−	0.972374i	$-0.574995\pi$
$103$		−	2.46355e16i		−	1.94475i	0.233429	−	0.972374i	$-0.425005\pi$
$104$	−9.25119e15	−	1.39915e16i	−0.675975	−	1.02234i
$105$	−2.01358e16			−1.36287
$106$	−9.54983e14	−	4.84183e15i	−0.0599168	−	0.303782i
$107$	1.00547e16			0.585194			0.292597	−	0.956236i	$-0.405481\pi$
$107$	1.00547e16			0.585194			0.292597	+	0.956236i	$0.405481\pi$
$108$	−1.79450e16	+	7.36534e15i	−0.969514	+	0.397926i
$109$			1.73713e16i			0.871806i	0.899994	+	0.435903i	$0.143571\pi$
$109$			1.73713e16i			0.871806i	−0.899994	+	0.435903i	$0.856429\pi$
$110$	−8.68956e14	−	4.40567e15i	−0.0405374	−	0.205528i
$111$			1.50105e16i			0.651346i
$112$	1.40531e16	+	1.42356e16i	0.567581	+	0.574953i
$113$	−2.11437e16			−0.795342			−0.397671	−	0.917528i	$-0.630181\pi$
$113$	−2.11437e16			−0.795342			−0.397671	+	0.917528i	$0.630181\pi$
$114$	4.19688e16	−	8.27775e15i	1.47125	−	0.290184i
$115$	5.34399e16			1.74696
$116$	−1.89211e16	−	4.60998e16i	−0.577143	−	1.40616i
$117$			4.83479e15i			0.137686i
$118$	−8.77981e15	+	1.73169e15i	−0.233576	+	0.0460697i
$119$			8.29476e15i			0.206266i
$120$	4.00054e16	+	6.05041e16i	0.930397	+	1.40713i
$121$	−4.53207e16			−0.986311
$122$	1.71180e16	+	8.67895e16i	0.348798	+	1.76843i
$123$	1.16267e16			0.221931
$124$	5.87222e15	+	1.43072e16i	0.105058	+	0.255965i
$125$		−	1.28684e17i		−	2.15896i
$126$	−1.11574e15	−	5.65689e15i	−0.0175630	−	0.0890458i
$127$			6.32709e16i			0.934920i	0.884014	+	0.467460i	$0.154831\pi$
$127$			6.32709e16i			0.934920i	−0.884014	+	0.467460i	$0.845169\pi$
$128$	1.48548e16	−	7.05098e16i	0.206152	−	0.978520i
$129$	−5.85407e16			−0.763379
$130$	1.75623e17	−	3.46392e16i	2.15295	−	0.424640i
$131$	−1.18988e17			−1.37194			−0.685968	−	0.727632i	$-0.740621\pi$
$131$	−1.18988e17			−1.37194			−0.685968	+	0.727632i	$0.740621\pi$
$132$	−9.39933e15	+	3.85785e15i	−0.101978	+	0.0418556i
$133$			1.25901e17i			1.28592i
$134$	−1.68351e17	+	3.32049e16i	−1.61949	+	0.319421i
$135$		−	2.07014e17i		−	1.87642i
$136$	2.49241e16	−	1.64799e16i	0.212965	−	0.140813i
$137$	1.01693e16			0.0819460			0.0409730	−	0.999160i	$-0.486954\pi$
$137$	1.01693e16			0.0819460			0.0409730	+	0.999160i	$0.486954\pi$
$138$	−2.33975e16	−	1.18627e17i	−0.177884	−	0.901883i
$139$	−4.95907e16			−0.355862			−0.177931	−	0.984043i	$-0.556940\pi$
$139$	−4.95907e16			−0.355862			−0.177931	+	0.984043i	$0.556940\pi$
$140$	−1.97492e17	+	8.10583e16i	−1.33821	+	0.549254i
$141$			9.92311e16i			0.635177i
$142$	−1.09212e16	−	5.53712e16i	−0.0660637	−	0.334948i
$143$			2.50744e16i			0.143398i
$144$	−1.47811e16	+	1.45916e16i	−0.0799478	+	0.0789227i
$145$	5.31807e17			2.72151
$146$	4.54615e16	−	8.96665e15i	0.220202	−	0.0434317i
$147$	7.13415e16			0.327193
$148$	6.04260e16	+	1.47223e17i	0.262501	+	0.639561i
$149$		−	1.18135e17i		−	0.486284i	−0.969991	−	0.243142i	$-0.921822\pi$
$149$		−	1.18135e17i		−	0.486284i	0.969991	−	0.243142i	$-0.0781781\pi$
$150$	−5.22556e17	+	1.03067e17i	−2.03893	+	0.402150i
$151$			3.38113e17i			1.25097i	0.780237	+	0.625484i	$0.215098\pi$
$151$			3.38113e17i			1.25097i	−0.780237	+	0.625484i	$0.784902\pi$
$152$	3.78306e17	−	2.50137e17i	1.32768	−	0.877867i
$153$	−8.61259e15			−0.0286815
$154$	−5.78651e15	−	2.93380e16i	−0.0182916	−	0.0927396i
$155$	−1.65048e17			−0.495400
$156$	−1.53785e17	−	3.74685e17i	−0.438448	−	1.06824i
$157$			1.51106e17i			0.409341i	0.978831	+	0.204670i	$0.0656122\pi$
$157$			1.51106e17i			0.409341i	−0.978831	+	0.204670i	$0.934388\pi$
$158$	−7.22209e15	−	3.66165e16i	−0.0185954	−	0.0942801i
$159$		−	1.19165e17i		−	0.291725i
$160$	6.35936e17	+	4.32378e17i	1.48065	+	1.00671i
$161$	3.55865e17			0.788275
$162$	−4.07249e17	+	8.03242e16i	−0.858499	+	0.169327i
$163$	−1.53662e16			−0.0308365			−0.0154183	−	0.999881i	$-0.504908\pi$
$163$	−1.53662e16			−0.0308365			−0.0154183	+	0.999881i	$0.504908\pi$
$164$	1.14035e17	−	4.68044e16i	0.217915	−	0.0894408i
$165$		−	1.08431e17i		−	0.197370i
$166$	−8.01140e16	+	1.58014e16i	−0.138945	+	0.0274050i
$167$		−	4.82750e16i		−	0.0797976i	−0.999204	−	0.0398988i	$-0.987296\pi$
$167$		−	4.82750e16i		−	0.0797976i	0.999204	−	0.0398988i	$-0.0127036\pi$
$168$	2.66402e17	+	4.02906e17i	0.419820	+	0.634936i
$169$	−3.34125e17			−0.502130
$170$	6.17055e16	+	3.12851e17i	0.0884570	+	0.448483i
$171$	−1.30725e17			−0.178809
$172$	−5.74166e17	+	2.35660e17i	−0.749567	+	0.307651i
$173$			5.34968e17i			0.666744i	0.942795	+	0.333372i	$0.108186\pi$
$173$			5.34968e17i			0.666744i	−0.942795	+	0.333372i	$0.891814\pi$
$174$	−2.32840e17	−	1.18052e18i	−0.277117	−	1.40500i
$175$		−	1.56760e18i		−	1.78209i
$176$	−7.66584e16	+	7.56755e16i	−0.0832642	+	0.0821966i
$177$	−2.16086e17			−0.224305
$178$	7.44587e17	−	1.46859e17i	0.738849	−	0.145728i
$179$	−1.66428e18			−1.57907			−0.789536	−	0.613704i	$-0.789679\pi$
$179$	−1.66428e18			−1.57907			−0.789536	+	0.613704i	$0.789679\pi$
$180$	−8.41642e16	−	2.05059e17i	−0.0763743	−	0.186080i
$181$		−	8.37583e17i		−	0.727108i	−0.931573	−	0.363554i	$-0.881563\pi$
$181$		−	8.37583e17i		−	0.727108i	0.931573	−	0.363554i	$-0.118437\pi$
$182$	1.16950e18	−	2.30668e17i	0.971471	−	0.191609i
$183$			2.13603e18i			1.69824i
$184$	−7.07024e17	−	1.06930e18i	−0.538135	−	0.813875i
$185$	−1.69837e18			−1.23782
$186$	7.22625e16	+	3.66376e17i	0.0504440	+	0.255754i
$187$	−4.46670e16			−0.0298713
$188$	3.99463e17	+	9.73257e17i	0.255984	+	0.623684i
$189$		−	1.37854e18i		−	0.846690i
$190$	9.36586e17	+	4.74856e18i	0.551466	+	2.79597i
$191$		−	1.41104e18i		−	0.796659i	−0.917242	−	0.398329i	$-0.869590\pi$
$191$		−	1.41104e18i		−	0.796659i	0.917242	−	0.398329i	$-0.130410\pi$
$192$	6.81371e17	−	1.60097e18i	0.368955	−	0.866909i
$193$	2.23870e18			1.16289			0.581444	−	0.813586i	$-0.302488\pi$
$193$	2.23870e18			1.16289			0.581444	+	0.813586i	$0.302488\pi$
$194$	1.99352e18	−	3.93193e17i	0.993588	−	0.195971i
$195$	4.32237e18			2.06750
$196$	6.99717e17	−	2.87191e17i	0.321273	−	0.131863i
$197$			1.68645e18i			0.743436i	0.928346	+	0.371718i	$0.121231\pi$
$197$			1.68645e18i			0.743436i	−0.928346	+	0.371718i	$0.878769\pi$
$198$	3.04622e16	−	6.00824e15i	0.0128955	−	0.00254346i
$199$			2.99452e18i			1.21759i	0.793326	+	0.608797i	$0.208348\pi$
$199$			2.99452e18i			1.21759i	−0.793326	+	0.608797i	$0.791652\pi$
$200$	−4.71031e18	+	3.11447e18i	−1.83997	+	1.21659i
$201$	−4.14340e18			−1.55521
$202$	−4.96903e17	−	2.51933e18i	−0.179250	−	0.908812i
$203$	3.54139e18			1.22802
$204$	6.67456e17	−	2.73950e17i	0.222526	−	0.0913334i
$205$			1.31551e18i			0.421757i
$206$	−1.22039e18	−	6.18748e18i	−0.376324	−	1.90799i
$207$			3.69500e17i			0.109610i
$208$	−3.01665e18	−	3.05583e18i	−0.861030	−	0.872214i
$209$	−6.77971e17			−0.186226
$210$	−5.05734e18	+	9.97489e17i	−1.33711	+	0.263726i
$211$	2.76684e18			0.704246			0.352123	−	0.935954i	$-0.385460\pi$
$211$	2.76684e18			0.704246			0.352123	+	0.935954i	$0.385460\pi$
$212$	−4.79709e17	−	1.16877e18i	−0.117569	−	0.286446i
$213$		−	1.36278e18i		−	0.321653i
$214$	2.52536e18	−	4.98091e17i	0.574133	−	0.113240i
$215$		−	6.62359e18i		−	1.45073i
$216$	−4.14223e18	+	2.73885e18i	−0.874187	+	0.578014i
$217$	−1.09908e18			−0.223538
$218$	8.60539e17	+	4.36299e18i	0.168701	+	0.855327i
$219$	1.11888e18			0.211462
$220$	−4.36496e17	−	1.06349e18i	−0.0795425	−	0.193799i
$221$		−	1.78056e18i		−	0.312909i
$222$	7.43592e17	+	3.77006e18i	0.126041	+	0.639035i
$223$			8.31324e18i			1.35935i	0.733513	+	0.679675i	$0.237879\pi$
$223$			8.31324e18i			1.35935i	−0.733513	+	0.679675i	$0.762121\pi$
$224$	4.23480e18	+	2.87928e18i	0.668111	+	0.454254i
$225$	1.62766e18			0.247802
$226$	−5.31048e18	+	1.04742e18i	−0.780309	+	0.153905i
$227$	−9.98439e18			−1.41617			−0.708083	−	0.706129i	$-0.750440\pi$
$227$	−9.98439e18			−1.41617			−0.708083	+	0.706129i	$0.750440\pi$
$228$	1.01309e19	−	4.15810e18i	1.38729	−	0.569398i
$229$			5.03614e16i			0.00665907i	0.999994	+	0.00332954i	$0.00105983\pi$
$229$			5.03614e16i			0.00665907i	−0.999994	+	0.00332954i	$0.998940\pi$
$230$	1.34220e19	−	2.64731e18i	1.71394	−	0.338051i
$231$		−	7.22057e17i		−	0.0890585i
$232$	−7.03595e18	−	1.06412e19i	−0.838338	−	1.26790i
$233$	6.71996e18			0.773605			0.386803	−	0.922162i	$-0.373579\pi$
$233$	6.71996e18			0.773605			0.386803	+	0.922162i	$0.373579\pi$
$234$	2.39506e17	+	1.21431e18i	0.0266434	+	0.135084i
$235$	−1.12275e19			−1.20709
$236$	−2.11936e18	+	8.69869e17i	−0.220247	+	0.0903978i
$237$		−	9.01192e17i		−	0.0905379i
$238$	4.10906e17	+	2.08332e18i	0.0399142	+	0.202368i
$239$			1.61742e18i			0.151929i	0.997111	+	0.0759643i	$0.0242035\pi$
$239$			1.61742e18i			0.151929i	−0.997111	+	0.0759643i	$0.975796\pi$
$240$	1.30451e19	+	1.32145e19i	1.18510	+	1.20050i
$241$	9.87362e18			0.867641			0.433821	−	0.900999i	$-0.357165\pi$
$241$	9.87362e18			0.867641			0.433821	+	0.900999i	$0.357165\pi$
$242$	−1.13828e19	+	2.24510e18i	−0.967668	+	0.190859i
$243$	2.71816e18			0.223576
$244$	8.59876e18	+	2.09502e19i	0.684411	+	1.66751i
$245$			8.07193e18i			0.621797i
$246$	2.92019e18	−	5.75966e17i	0.217736	−	0.0429454i
$247$		−	2.70259e19i		−	1.95077i
$248$	2.18362e18	+	3.30251e18i	0.152603	+	0.230797i
$249$	−1.97174e18			−0.133430
$250$	−6.37475e18	−	3.23204e19i	−0.417776	−	2.11815i
$251$	−1.58923e19			−1.00878			−0.504390	−	0.863476i	$-0.668283\pi$
$251$	−1.58923e19			−1.00878			−0.504390	+	0.863476i	$0.668283\pi$
$252$	−5.60463e17	−	1.36552e18i	−0.0344621	−	0.0839641i
$253$			1.91632e18i			0.114157i
$254$	3.13432e18	+	1.58912e19i	0.180914	+	0.917248i
$255$			7.69977e18i			0.430682i
$256$	2.38044e17	−	1.84452e19i	0.0129044	−	0.999917i
$257$	−1.59897e19			−0.840187			−0.420093	−	0.907481i	$-0.638003\pi$
$257$	−1.59897e19			−0.840187			−0.420093	+	0.907481i	$0.638003\pi$
$258$	−1.47032e19	+	2.89999e18i	−0.748950	+	0.147720i
$259$	−1.13097e19			−0.558537
$260$	4.23938e19	−	1.74000e19i	2.03009	−	0.833228i
$261$			3.67708e18i			0.170757i
$262$	−2.98853e19	+	5.89445e18i	−1.34600	+	0.265481i
$263$			1.53959e19i			0.672602i	0.941755	+	0.336301i	$0.109176\pi$
$263$			1.53959e19i			0.672602i	−0.941755	+	0.336301i	$0.890824\pi$
$264$	−2.16964e18	+	1.43457e18i	−0.0919508	+	0.0607980i
$265$	1.34830e19			0.554394
$266$	6.23687e18	+	3.16214e19i	0.248836	+	1.26162i
$267$	1.83255e19			0.709522
$268$	−4.06384e19	+	1.66796e19i	−1.52707	+	0.626768i
$269$		−	3.47917e19i		−	1.26899i	−0.772927	−	0.634494i	$-0.781208\pi$
$269$		−	3.47917e19i		−	1.26899i	0.772927	−	0.634494i	$-0.218792\pi$
$270$	−1.02551e19	−	5.19939e19i	−0.363102	−	1.84095i
$271$			1.10793e19i			0.380854i	0.981701	+	0.190427i	$0.0609873\pi$
$271$			1.10793e19i			0.380854i	−0.981701	+	0.190427i	$0.939013\pi$
$272$	5.44359e18	−	5.37379e18i	0.181691	−	0.179362i
$273$	2.87833e19			0.932911
$274$	2.55414e18	−	5.03769e17i	0.0803971	−	0.0158572i
$275$	8.44145e18			0.258081
$276$	−1.17531e19	−	2.86354e19i	−0.349043	−	0.850415i
$277$		−	1.03237e19i		−	0.297850i	−0.988848	−	0.148925i	$-0.952419\pi$
$277$		−	1.03237e19i		−	0.297850i	0.988848	−	0.148925i	$-0.0475813\pi$
$278$	−1.24553e19	+	2.45663e18i	−0.349136	+	0.0688622i
$279$		−	1.14119e18i		−	0.0310831i
$280$	−4.55868e19	+	3.01421e19i	−1.20663	+	0.797827i
$281$	3.43188e19			0.882840			0.441420	−	0.897301i	$-0.354475\pi$
$281$	3.43188e19			0.882840			0.441420	+	0.897301i	$0.354475\pi$
$282$	4.91571e18	+	2.49230e19i	0.122912	+	0.623172i
$283$	3.83778e19			0.932800			0.466400	−	0.884574i	$-0.345551\pi$
$283$	3.83778e19			0.932800			0.466400	+	0.884574i	$0.345551\pi$
$284$	−5.48596e18	−	1.33661e19i	−0.129630	−	0.315833i
$285$			1.16870e20i			2.68499i
$286$	1.24214e18	+	6.29773e18i	0.0277486	+	0.140687i
$287$			8.76017e18i			0.190308i
$288$	−2.98960e18	+	4.39706e18i	−0.0631645	+	0.0929015i
$289$	−4.54893e19			−0.934818
$290$	1.33569e20	−	2.63447e19i	2.67007	−	0.526634i
$291$	4.90637e19			0.954150
$292$	1.09740e19	−	4.50415e18i	0.207635	−	0.0852217i
$293$		−	2.69218e19i		−	0.495636i	−0.968807	−	0.247818i	$-0.920286\pi$
$293$		−	2.69218e19i		−	0.495636i	0.968807	−	0.247818i	$-0.0797136\pi$
$294$	1.79182e19	−	3.53412e18i	0.321008	−	0.0633144i
$295$		−	2.44490e19i		−	0.426270i
$296$	2.24698e19	+	3.39833e19i	0.381299	+	0.576676i
$297$	7.42338e18			0.122617
$298$	−5.85219e18	−	2.96710e19i	−0.0940998	−	0.477092i
$299$	−7.63902e19			−1.19583
$300$	−1.26140e20	+	5.17728e19i	−1.92257	+	0.789099i
$301$		−	4.41075e19i		−	0.654607i
$302$	1.67494e19	+	8.49208e19i	0.242072	+	1.22732i
$303$		−	6.20048e19i		−	0.872739i
$304$	8.26246e19	−	8.15652e19i	1.13272	−	1.11819i
$305$	−2.41681e20			−3.22734
$306$	−2.16315e18	+	4.26651e17i	−0.0281394	+	0.00555011i
$307$	3.17040e19			0.401797			0.200899	−	0.979612i	$-0.435614\pi$
$307$	3.17040e19			0.401797			0.200899	+	0.979612i	$0.435614\pi$
$308$	−2.90670e18	−	7.08192e18i	−0.0358917	−	0.0874471i
$309$		−	1.52284e20i		−	1.83226i
$310$	−4.14536e19	+	8.17614e18i	−0.486036	+	0.0958638i
$311$			1.11218e20i			1.27084i	0.772165	+	0.635422i	$0.219174\pi$
$311$			1.11218e20i			1.27084i	−0.772165	+	0.635422i	$0.780826\pi$
$312$	−5.71861e19	−	8.64882e19i	−0.636875	−	0.963208i
$313$	−2.59112e19			−0.281277			−0.140638	−	0.990061i	$-0.544915\pi$
$313$	−2.59112e19			−0.281277			−0.140638	+	0.990061i	$0.544915\pi$
$314$	7.48550e18	+	3.79520e19i	0.0792107	+	0.401603i
$315$	1.57526e19			0.162506
$316$	−3.62782e18	−	8.83888e18i	−0.0364879	−	0.0888997i
$317$		−	9.95998e19i		−	0.976752i	−0.872633	−	0.488376i	$-0.837589\pi$
$317$		−	9.95998e19i		−	0.976752i	0.872633	−	0.488376i	$-0.162411\pi$
$318$	−5.90322e18	−	2.99297e19i	−0.0564510	−	0.286211i
$319$			1.90703e19i			0.177841i
$320$	1.81142e20	+	7.70937e19i	1.64747	+	0.701163i
$321$	6.21532e19			0.551345
$322$	8.93794e19	−	1.76288e19i	0.773376	−	0.152538i
$323$	4.81434e19			0.406365
$324$	−9.83061e19	+	4.03486e19i	−0.809507	+	0.332253i
$325$			3.36502e20i			2.70346i
$326$	−3.85939e18	+	7.61211e17i	−0.0302537	+	0.00596711i
$327$			1.07380e20i			0.821377i
$328$	2.63226e19	−	1.74045e19i	0.196489	−	0.129919i
$329$	−7.47657e19			−0.544672
$330$	−5.37144e18	−	2.72336e19i	−0.0381926	−	0.193639i
$331$	1.21654e20			0.844311			0.422155	−	0.906524i	$-0.361274\pi$
$331$	1.21654e20			0.844311			0.422155	+	0.906524i	$0.361274\pi$
$332$	−1.93388e19	+	7.93738e18i	−0.131016	+	0.0537740i
$333$		−	1.17430e19i		−	0.0776652i
$334$	−2.39145e18	−	1.21248e19i	−0.0154415	−	0.0782894i
$335$		−	4.68805e20i		−	2.95552i
$336$	8.68691e19	+	8.79974e19i	0.534750	+	0.541696i
$337$	2.30463e20			1.38536			0.692680	−	0.721245i	$-0.256430\pi$
$337$	2.30463e20			1.38536			0.692680	+	0.721245i	$0.256430\pi$
$338$	−8.39194e19	+	1.65519e19i	−0.492639	+	0.0971661i
$339$	−1.30700e20			−0.749337
$340$	3.09960e19	+	7.55193e19i	0.173570	+	0.422889i
$341$		−	5.91850e18i		−	0.0323725i
$342$	−3.28330e19	+	6.47585e18i	−0.175429	+	0.0346009i
$343$			2.08533e20i			1.08848i
$344$	−1.32534e20	+	8.76318e19i	−0.675866	+	0.446883i
$345$	3.30338e20			1.64591
$346$	2.65013e19	+	1.34363e20i	0.129020	+	0.654142i
$347$	−3.36488e20			−1.60079			−0.800393	−	0.599476i	$-0.795376\pi$
$347$	−3.36488e20			−1.60079			−0.800393	+	0.599476i	$0.795376\pi$
$348$	−1.16961e20	−	2.84965e20i	−0.543759	−	1.32482i
$349$		−	5.21190e19i		−	0.236806i	−0.992966	−	0.118403i	$-0.962223\pi$
$349$		−	5.21190e19i		−	0.236806i	0.992966	−	0.118403i	$-0.0377775\pi$
$350$	−7.76556e19	−	3.93719e20i	−0.344849	−	1.74841i
$351$			2.95918e20i			1.28444i
$352$	−1.55048e19	+	2.28042e19i	−0.0657847	+	0.0967552i
$353$	−7.64010e18			−0.0316885			−0.0158442	−	0.999874i	$-0.505044\pi$
$353$	−7.64010e18			−0.0316885			−0.0158442	+	0.999874i	$0.505044\pi$
$354$	−5.42723e19	+	1.07045e19i	−0.220066	+	0.0434049i
$355$	1.54191e20			0.611269
$356$	1.79736e20	−	7.37708e19i	0.696684	−	0.285946i
$357$			5.12740e19i			0.194335i
$358$	−4.18003e20	+	8.24452e19i	−1.54923	+	0.305563i
$359$		−	1.32120e20i		−	0.478865i	−0.970913	−	0.239432i	$-0.923039\pi$
$359$		−	1.32120e20i		−	0.478865i	0.970913	−	0.239432i	$-0.0769613\pi$
$360$	−3.12970e19	−	4.73336e19i	−0.110939	−	0.167783i
$361$	4.42295e20			1.53340
$362$	−4.14922e19	−	2.10368e20i	−0.140701	−	0.713365i
$363$	−2.80150e20			−0.929259
$364$	2.82307e20	−	1.15870e20i	0.916031	−	0.375975i
$365$			1.26596e20i			0.401862i
$366$	1.05815e20	+	5.36488e20i	0.328623	+	1.66614i
$367$			2.21954e20i			0.674425i	0.941429	+	0.337213i	$0.109484\pi$
$367$			2.21954e20i			0.674425i	−0.941429	+	0.337213i	$0.890516\pi$
$368$	−2.30548e20	−	2.33543e20i	−0.685455	−	0.694359i
$369$	−9.09584e18			−0.0264625
$370$	−4.26564e20	+	8.41337e19i	−1.21442	+	0.239528i
$371$	8.97851e19			0.250157
$372$	3.62991e19	+	8.84397e19i	0.0989811	+	0.241159i
$373$		−	5.49011e20i		−	1.46525i	−0.680635	−	0.732623i	$-0.738296\pi$
$373$		−	5.49011e20i		−	1.46525i	0.680635	−	0.732623i	$-0.261704\pi$
$374$	−1.12186e19	+	2.21272e18i	−0.0293067	+	0.00578033i
$375$		−	7.95459e20i		−	2.03408i
$376$	1.48543e20	+	2.24656e20i	0.371834	+	0.562361i
$377$	−7.60198e20			−1.86293
$378$	−6.82901e19	−	3.46235e20i	−0.163841	−	0.830686i
$379$	−1.81621e20			−0.426631			−0.213316	−	0.976983i	$-0.568426\pi$
$379$	−1.81621e20			−0.426631			−0.213316	+	0.976983i	$0.568426\pi$
$380$	4.70468e20	+	1.14626e21i	1.08209	+	2.63641i
$381$			3.91108e20i			0.880841i
$382$	−6.99002e19	−	3.54399e20i	−0.154160	−	0.781601i
$383$			1.94155e20i			0.419333i	0.977773	+	0.209666i	$0.0672378\pi$
$383$			1.94155e20i			0.419333i	−0.977773	+	0.209666i	$0.932762\pi$
$384$	9.18251e19	−	4.35856e20i	0.194228	−	0.921919i
$385$	8.16971e19			0.169247
$386$	5.62275e20	−	1.10901e20i	1.14091	−	0.225028i
$387$	4.57976e19			0.0910237
$388$	4.81216e20	−	1.97510e20i	0.936886	−	0.384534i
$389$			6.76602e20i			1.29044i	0.763998	+	0.645218i	$0.223234\pi$
$389$			6.76602e20i			1.29044i	−0.763998	+	0.645218i	$0.776766\pi$
$390$	1.08561e21	−	2.14122e20i	2.02842	−	0.400077i
$391$		−	1.36080e20i		−	0.249103i
$392$	1.61515e20	−	1.06794e20i	0.289684	−	0.191539i
$393$	−7.35525e20			−1.29258
$394$	8.35435e19	+	4.23571e20i	0.143861	+	0.729384i
$395$	1.01965e20			0.172058
$396$	7.35328e18	−	3.01807e18i	0.0121596	−	0.00499078i
$397$		−	5.08193e20i		−	0.823578i	−0.911279	−	0.411789i	$-0.864904\pi$
$397$		−	5.08193e20i		−	0.823578i	0.911279	−	0.411789i	$-0.135096\pi$
$398$	1.48343e20	+	7.52108e20i	0.235614	+	1.19458i
$399$			7.78254e20i			1.21154i
$400$	−1.02876e21	+	1.01557e21i	−1.56977	+	1.54964i
$401$	6.93111e20			1.03669			0.518344	−	0.855172i	$-0.326549\pi$
$401$	6.93111e20			1.03669			0.518344	+	0.855172i	$0.326549\pi$
$402$	−1.04066e21	+	2.05256e20i	−1.52581	+	0.300945i
$403$	2.35929e20			0.339110
$404$	−2.49605e20	−	6.08143e20i	−0.351725	−	0.856948i
$405$		−	1.13406e21i		−	1.56674i
$406$	8.89460e20	−	1.75433e20i	1.20481	−	0.237632i
$407$		−	6.09022e19i		−	0.0808869i
$408$	1.54068e20	−	1.01870e20i	0.200646	−	0.132668i
$409$	−1.79393e20			−0.229097			−0.114548	−	0.993418i	$-0.536542\pi$
$409$	−1.79393e20			−0.229097			−0.114548	+	0.993418i	$0.536542\pi$
$410$	6.51677e19	+	3.30405e20i	0.0816134	+	0.413786i
$411$	6.28616e19			0.0772060
$412$	−6.13031e20	−	1.49360e21i	−0.738422	−	1.79910i
$413$		−	1.62810e20i		−	0.192344i
$414$	1.83043e19	+	9.28042e19i	0.0212105	+	0.107539i
$415$		−	2.23092e20i		−	0.253571i
$416$	−9.09046e20	−	6.18068e20i	−1.01354	−	0.689112i
$417$	−3.06545e20			−0.335278
$418$	−1.70280e20	+	3.35853e19i	−0.182706	+	0.0360362i
$419$	1.13823e21			1.19817			0.599086	−	0.800685i	$-0.295531\pi$
$419$	1.13823e21			1.19817			0.599086	+	0.800685i	$0.295531\pi$
$420$	−1.22079e21	+	5.01061e20i	−1.26080	+	0.517483i
$421$			1.54426e21i			1.56482i	0.622765	+	0.782409i	$0.286009\pi$
$421$			1.54426e21i			1.56482i	−0.622765	+	0.782409i	$0.713991\pi$
$422$	6.94923e20	−	1.37064e20i	0.690935	−	0.136277i
$423$		−	7.76305e19i		−	0.0757372i
$424$	−1.78383e20	−	2.69786e20i	−0.170776	−	0.258281i
$425$	−5.99436e20			−0.563160
$426$	−6.75092e19	−	3.42276e20i	−0.0622424	−	0.315573i
$427$	−1.60939e21			−1.45626
$428$	6.09598e20	−	2.50203e20i	0.541369	−	0.222199i
$429$			1.54997e20i			0.135103i
$430$	−3.28119e20	−	1.66359e21i	−0.280727	−	1.42331i
$431$			7.13757e20i			0.599421i	0.954030	+	0.299710i	$0.0968901\pi$
$431$			7.13757e20i			0.599421i	−0.954030	+	0.299710i	$0.903110\pi$
$432$	−9.04691e20	+	8.93091e20i	−0.745813	+	0.736251i
$433$	−5.31329e20			−0.429992			−0.214996	−	0.976615i	$-0.568974\pi$
$433$	−5.31329e20			−0.429992			−0.214996	+	0.976615i	$0.568974\pi$
$434$	−2.76046e20	+	5.44462e19i	−0.219312	+	0.0432563i
$435$	3.28736e21			2.56409
$436$	4.32268e20	+	1.05318e21i	0.331025	+	0.806515i
$437$		−	2.06546e21i		−	1.55298i
$438$	2.81020e20	−	5.54272e19i	0.207465	−	0.0409195i
$439$		−	6.79982e20i		−	0.492926i	−0.969152	−	0.246463i	$-0.920732\pi$
$439$		−	6.79982e20i		−	0.492926i	0.969152	−	0.246463i	$-0.0792683\pi$
$440$	−1.62314e20	−	2.45483e20i	−0.115541	−	0.174743i
$441$	−5.58119e19			−0.0390138
$442$	−8.82055e19	−	4.47208e20i	−0.0605505	−	0.306995i
$443$	9.44712e20			0.636898			0.318449	−	0.947940i	$-0.396838\pi$
$443$	9.44712e20			0.636898			0.318449	+	0.947940i	$0.396838\pi$
$444$	3.73523e20	+	9.10057e20i	0.247317	+	0.602567i
$445$			2.07344e21i			1.34838i
$446$	4.11821e20	+	2.08796e21i	0.263045	+	1.33366i
$447$		−	7.30253e20i		−	0.458155i
$448$	1.20625e21	+	5.13379e20i	0.743385	+	0.316384i
$449$	1.93362e21			1.17058			0.585288	−	0.810825i	$-0.300981\pi$
$449$	1.93362e21			1.17058			0.585288	+	0.810825i	$0.300981\pi$
$450$	4.08806e20	−	8.06312e19i	0.243118	−	0.0479516i
$451$	−4.71732e19			−0.0275603
$452$	−1.28190e21	+	5.26142e20i	−0.735778	+	0.301992i
$453$			2.09004e21i			1.17861i
$454$	−2.50769e21	+	4.94607e20i	−1.38940	+	0.274040i
$455$			3.25669e21i			1.77290i
$456$	2.33850e21	−	1.54622e21i	1.25089	−	0.827088i
$457$	−7.52884e19			−0.0395729			−0.0197865	−	0.999804i	$-0.506299\pi$
$457$	−7.52884e19			−0.0395729			−0.0197865	+	0.999804i	$0.506299\pi$
$458$	2.49480e18	+	1.26488e19i	0.00128858	+	0.00653321i
$459$	−5.27142e20			−0.267563
$460$	3.23995e21	−	1.32980e21i	1.61613	−	0.663322i
$461$		−	2.80291e21i		−	1.37405i	−0.726636	−	0.687023i	$-0.758917\pi$
$461$		−	2.80291e21i		−	1.37405i	0.726636	−	0.687023i	$-0.241083\pi$
$462$	−3.57693e19	−	1.81353e20i	−0.0172335	−	0.0873752i
$463$		−	1.79913e21i		−	0.851950i	−0.904735	−	0.425975i	$-0.859931\pi$
$463$		−	1.79913e21i		−	0.851950i	0.904735	−	0.425975i	$-0.140069\pi$
$464$	−2.29430e21	−	2.32410e21i	−1.06784	−	1.08171i
$465$	−1.02024e21			−0.466744
$466$	1.68779e21	−	3.32894e20i	0.758983	−	0.149699i
$467$	−2.66105e21			−1.17630			−0.588150	−	0.808752i	$-0.700143\pi$
$467$	−2.66105e21			−1.17630			−0.588150	+	0.808752i	$0.700143\pi$
$468$	1.20309e20	+	2.93124e20i	0.0522797	+	0.127375i
$469$		−	3.12184e21i		−	1.33361i
$470$	−2.81991e21	+	5.56188e20i	−1.18428	+	0.233582i
$471$			9.34061e20i			0.385663i
$472$	−4.89210e20	+	3.23467e20i	−0.198591	+	0.131309i
$473$	2.37517e20			0.0947995
$474$	−4.46433e19	−	2.26344e20i	−0.0175198	−	0.0888266i
$475$	−9.09844e21			−3.51090
$476$	2.06407e20	+	5.02895e20i	0.0783195	+	0.190819i
$477$			9.32254e19i			0.0347846i
$478$	8.01238e19	+	4.06233e20i	0.0293994	+	0.149057i
$479$		−	3.29728e21i		−	1.18979i	−0.803802	−	0.594897i	$-0.797193\pi$
$479$		−	3.29728e21i		−	1.18979i	0.803802	−	0.594897i	$-0.202807\pi$
$480$	3.93103e21	+	2.67274e21i	1.39501	+	0.948478i
$481$	2.42775e21			0.847310
$482$	2.47987e21	−	4.89120e20i	0.851242	−	0.167896i
$483$	2.19977e21			0.742679
$484$	−2.74770e21	+	1.12776e21i	−0.912445	+	0.374503i
$485$			5.55131e21i			1.81327i
$486$	6.82696e20	−	1.34652e20i	0.219350	−	0.0432637i
$487$		−	3.78361e21i		−	1.19585i	−0.801554	−	0.597923i	$-0.795993\pi$
$487$		−	3.78361e21i		−	1.19585i	0.801554	−	0.597923i	$-0.204007\pi$
$488$	3.19751e21	+	4.83590e21i	0.994152	+	1.50355i
$489$	−9.49859e19			−0.0290528
$490$	3.99868e20	+	2.02736e21i	0.120323	+	0.610045i
$491$	−1.52093e21			−0.450254			−0.225127	−	0.974329i	$-0.572280\pi$
$491$	−1.52093e21			−0.450254			−0.225127	+	0.974329i	$0.572280\pi$
$492$	7.04906e20	−	2.89321e20i	0.205310	−	0.0842673i
$493$		−	1.35420e21i		−	0.388067i
$494$	−1.33881e21	−	6.78787e21i	−0.377489	−	1.91389i
$495$			8.48275e19i			0.0235340i
$496$	7.12042e20	+	7.21290e20i	0.194380	+	0.196905i
$497$	1.02678e21			0.275821
$498$	−4.95224e20	+	9.76759e19i	−0.130908	+	0.0258198i
$499$	−2.42572e20			−0.0631010			−0.0315505	−	0.999502i	$-0.510044\pi$
$499$	−2.42572e20			−0.0631010			−0.0315505	+	0.999502i	$0.510044\pi$
$500$	−3.20218e21	−	7.80185e21i	−0.819759	−	1.99727i
$501$		−	2.98411e20i		−	0.0751819i
$502$	−3.99152e21	+	7.87272e20i	−0.989712	+	0.195207i
$503$			4.58027e21i			1.11776i	0.829250	+	0.558878i	$0.188768\pi$
$503$			4.58027e21i			1.11776i	−0.829250	+	0.558878i	$0.811232\pi$
$504$	−2.08412e20	−	3.15202e20i	−0.0500585	−	0.0757084i
$505$	7.01554e21			1.65855
$506$	9.49307e19	+	4.81305e20i	0.0220903	+	0.112000i
$507$	−2.06539e21			−0.473085
$508$	1.57444e21	+	3.83599e21i	0.354990	+	0.864903i
$509$			4.31209e21i			0.957074i	0.878067	+	0.478537i	$0.158833\pi$
$509$			4.31209e21i			0.957074i	−0.878067	+	0.478537i	$0.841167\pi$
$510$	3.81432e20	+	1.93388e21i	0.0833403	+	0.422541i
$511$			8.43022e20i			0.181331i
$512$	−8.53952e20	−	4.64451e21i	−0.180831	−	0.983514i
$513$	−8.00113e21			−1.66806
$514$	−4.01600e21	+	7.92099e20i	−0.824306	+	0.162583i
$515$	1.72302e22			3.48202
$516$	−3.54920e21	+	1.45673e21i	−0.706209	+	0.289856i
$517$		−	4.02611e20i		−	0.0788789i
$518$	−2.84055e21	+	5.60259e20i	−0.547980	+	0.108081i
$519$			3.30690e21i			0.628177i
$520$	9.78571e21	−	6.47032e21i	1.83048	−	1.21032i
$521$	6.59580e21			1.21497			0.607485	−	0.794331i	$-0.292178\pi$
$521$	6.59580e21			1.21497			0.607485	+	0.794331i	$0.292178\pi$
$522$	1.82155e20	+	9.23541e20i	0.0330429	+	0.167530i
$523$	−1.51693e20			−0.0270990			−0.0135495	−	0.999908i	$-0.504313\pi$
$523$	−1.51693e20			−0.0270990			−0.0135495	+	0.999908i	$0.504313\pi$
$524$	−7.21402e21	+	2.96091e21i	−1.26919	+	0.520925i
$525$		−	9.69008e21i		−	1.67901i
$526$	7.62681e20	+	3.86684e21i	0.130154	+	0.659889i
$527$			4.20279e20i			0.0706403i
$528$	−4.73863e20	+	4.67787e20i	−0.0784479	+	0.0774420i
$529$	2.94471e20			0.0480173
$530$	3.38640e21	−	6.67919e20i	0.543915	−	0.107280i
$531$	1.69048e20			0.0267457
$532$	3.13292e21	+	7.63310e21i	0.488266	+	1.18962i
$533$		−	1.88047e21i		−	0.288701i
$534$	4.60266e21	−	9.07810e20i	0.696111	−	0.137298i
$535$			7.03232e21i			1.04778i
$536$	−9.38052e21	+	6.20241e21i	−1.37692	+	0.910421i
$537$	−1.02877e22			−1.48773
$538$	−1.72351e21	−	8.73834e21i	−0.245559	−	1.24500i
$539$	−2.89454e20			−0.0406321
$540$	−5.15135e21	−	1.25508e22i	−0.712477	−	1.73589i
$541$			9.66048e21i			1.31650i	0.752800	+	0.658250i	$0.228703\pi$
$541$			9.66048e21i			1.31650i	−0.752800	+	0.658250i	$0.771297\pi$
$542$	5.48848e20	+	2.78270e21i	0.0736983	+	0.373655i
$543$		−	5.17751e21i		−	0.685050i
$544$	1.10101e21	−	1.61935e21i	0.143549	−	0.211130i
$545$	−1.21495e22			−1.56095
$546$	7.22926e21	−	1.42587e21i	0.915278	−	0.180526i
$547$	1.48555e21			0.185348			0.0926740	−	0.995697i	$-0.470459\pi$
$547$	1.48555e21			0.185348			0.0926740	+	0.995697i	$0.470459\pi$
$548$	6.16546e20	−	2.53054e20i	0.0758090	−	0.0311150i
$549$		−	1.67106e21i		−	0.202494i
$550$	2.12017e21	−	4.18173e20i	0.253203	−	0.0499407i
$551$		−	2.05545e22i		−	2.41932i
$552$	−4.37046e21	−	6.60988e21i	−0.507008	−	0.766798i
$553$	6.79003e20			0.0776373
$554$	−5.11417e20	−	2.59292e21i	−0.0576364	−	0.292220i
$555$	−1.04984e22			−1.16622
$556$	−3.00659e21	+	1.23402e21i	−0.329212	+	0.135121i
$557$			9.75638e21i			1.05305i	0.850161	+	0.526523i	$0.176505\pi$
$557$			9.75638e21i			1.05305i	−0.850161	+	0.526523i	$0.823495\pi$
$558$	−5.65324e19	−	2.86623e20i	−0.00601483	−	0.0304956i
$559$			9.46815e21i			0.993049i
$560$	−9.95646e21	+	9.82880e21i	−1.02944	+	1.01624i
$561$	−2.76109e20			−0.0281434
$562$	8.61956e21	−	1.70009e21i	0.866153	−	0.170837i
$563$	1.86765e22			1.85025			0.925123	−	0.379668i	$-0.123962\pi$
$563$	1.86765e22			1.85025			0.925123	+	0.379668i	$0.123962\pi$
$564$	2.46927e21	+	6.01618e21i	0.241177	+	0.587608i
$565$		−	1.47880e22i		−	1.42404i
$566$	9.63901e21	−	1.90116e21i	0.915168	−	0.180504i
$567$		−	7.55188e21i		−	0.706953i
$568$	−2.03999e21	−	3.08528e21i	−0.188296	−	0.284779i
$569$	−1.04130e21			−0.0947711			−0.0473856	−	0.998877i	$-0.515089\pi$
$569$	−1.04130e21			−0.0947711			−0.0473856	+	0.998877i	$0.515089\pi$
$570$	5.78950e21	+	2.93531e22i	0.519567	+	2.63424i
$571$	−1.77834e22			−1.57371			−0.786856	−	0.617137i	$-0.788293\pi$
$571$	−1.77834e22			−1.57371			−0.786856	+	0.617137i	$0.788293\pi$
$572$	6.23954e20	+	1.52021e21i	0.0544483	+	0.132659i
$573$		−	8.72233e21i		−	0.750577i
$574$	4.33962e20	+	2.20022e21i	0.0368262	+	0.186711i
$575$			2.57172e22i			2.15219i
$576$	−5.33050e20	+	1.25247e21i	−0.0439935	+	0.103368i
$577$	8.34008e21			0.678834			0.339417	−	0.940636i	$-0.389770\pi$
$577$	8.34008e21			0.678834			0.339417	+	0.940636i	$0.389770\pi$
$578$	−1.14252e22	+	2.25345e21i	−0.917148	+	0.180895i
$579$	1.38385e22			1.09562
$580$	3.22424e22	−	1.32335e22i	2.51770	−	1.03336i
$581$		−	1.48560e21i		−	0.114418i
$582$	1.23229e22	−	2.43052e21i	0.936115	−	0.184636i
$583$			4.83490e20i			0.0362275i
$584$	2.53311e21	−	1.67490e21i	0.187220	−	0.123790i
$585$	−3.38148e21			−0.246524
$586$	−1.33365e21	−	6.76171e21i	−0.0959096	−	0.486268i
$587$	−9.67063e21			−0.686041			−0.343020	−	0.939328i	$-0.611450\pi$
$587$	−9.67063e21			−0.686041			−0.343020	+	0.939328i	$0.611450\pi$
$588$	4.32529e21	−	1.77527e21i	0.302689	−	0.124235i
$589$			6.37913e21i			0.440392i
$590$	−1.21115e21	−	6.14064e21i	−0.0824866	−	0.418213i
$591$			1.04248e22i			0.700434i
$592$	7.32702e21	+	7.42218e21i	0.485684	+	0.491992i
$593$	−2.33346e22			−1.52603			−0.763016	−	0.646379i	$-0.776282\pi$
$593$	−2.33346e22			−1.52603			−0.763016	+	0.646379i	$0.776282\pi$
$594$	1.86447e21	−	3.67740e20i	0.120299	−	0.0237273i
$595$	−5.80139e21			−0.369315
$596$	−2.93969e21	−	7.16231e21i	−0.184642	−	0.449866i
$597$			1.85106e22i			1.14716i
$598$	−1.91863e22	+	3.78422e21i	−1.17322	+	0.231402i
$599$		−	2.00138e22i		−	1.20758i	−0.797144	−	0.603789i	$-0.793657\pi$
$599$		−	2.00138e22i		−	1.20758i	0.797144	−	0.603789i	$-0.206343\pi$
$600$	−2.91168e22	+	1.92520e22i	−1.73354	+	1.14622i
$601$	1.72003e22			1.01051			0.505255	−	0.862970i	$-0.331398\pi$
$601$	1.72003e22			1.01051			0.505255	+	0.862970i	$0.331398\pi$
$602$	−2.18500e21	−	1.10781e22i	−0.126672	−	0.642234i
$603$	3.24146e21			0.185440
$604$	8.41362e21	+	2.04991e22i	0.474993	+	1.15728i
$605$		−	3.16975e22i		−	1.76597i
$606$	−3.07160e21	−	1.55732e22i	−0.168882	−	0.856243i
$607$		−	3.46685e22i		−	1.88116i	−0.339570	−	0.940581i	$-0.610282\pi$
$607$		−	3.46685e22i		−	1.88116i	0.339570	−	0.940581i	$-0.389718\pi$
$608$	1.67115e22	−	2.45791e22i	0.894927	−	1.31625i
$609$	2.18911e22			1.15699
$610$	−6.07009e22	+	1.19724e22i	−3.16633	+	0.624515i
$611$	1.60493e22			0.826277
$612$	−5.22164e20	+	2.14316e20i	−0.0265336	+	0.0108904i
$613$			2.69106e22i			1.34971i	0.737952	+	0.674853i	$0.235793\pi$
$613$			2.69106e22i			1.34971i	−0.737952	+	0.674853i	$0.764207\pi$
$614$	7.96282e21	−	1.57055e21i	0.394203	−	0.0777510i
$615$			8.13180e21i			0.397361i
$616$	−1.08087e21	−	1.63471e21i	−0.0521350	−	0.0788489i
$617$	−1.76570e21			−0.0840689			−0.0420345	−	0.999116i	$-0.513384\pi$
$617$	−1.76570e21			−0.0840689			−0.0420345	+	0.999116i	$0.513384\pi$
$618$	−7.54385e21	−	3.82478e22i	−0.354556	−	1.79763i
$619$	−1.74733e22			−0.810682			−0.405341	−	0.914166i	$-0.632847\pi$
$619$	−1.74733e22			−0.810682			−0.405341	+	0.914166i	$0.632847\pi$
$620$	−1.00065e22	+	4.10706e21i	−0.458299	+	0.188104i
$621$			2.26156e22i			1.02253i
$622$	5.50953e21	+	2.79337e22i	0.245918	+	1.24682i
$623$			1.38074e22i			0.608424i
$624$	−1.86474e22	−	1.88896e22i	−0.811225	−	0.821762i
$625$	3.86443e22			1.65976
$626$	−6.50790e21	+	1.28359e21i	−0.275960	+	0.0544293i
$627$	−4.19087e21			−0.175454
$628$	3.76014e21	+	9.16125e21i	0.155427	+	0.378685i
$629$			4.32473e21i			0.176504i
$630$	3.95645e21	−	7.80355e20i	0.159434	−	0.0314462i
$631$			1.69094e22i			0.672810i	0.941717	+	0.336405i	$0.109211\pi$
$631$			1.69094e22i			0.672810i	−0.941717	+	0.336405i	$0.890789\pi$
$632$	−1.34903e21	−	2.04027e21i	−0.0530010	−	0.0801587i
$633$	1.71032e22			0.663510
$634$	−4.93398e21	−	2.50156e22i	−0.189009	−	0.958290i
$635$	−4.42520e22			−1.67395
$636$	−2.96532e21	−	7.22475e21i	−0.110768	−	0.269877i
$637$		−	1.15385e22i		−	0.425632i
$638$	9.44703e20	+	4.78971e21i	0.0344136	+	0.174479i
$639$			1.06613e21i			0.0383532i
$640$	4.93149e22	+	1.03895e22i	1.75202	+	0.369111i
$641$	1.67907e22			0.589119			0.294560	−	0.955633i	$-0.404827\pi$
$641$	1.67907e22			0.589119			0.294560	+	0.955633i	$0.404827\pi$
$642$	1.56105e22	−	3.07895e21i	0.540924	−	0.106690i
$643$	1.76394e22			0.603665			0.301833	−	0.953361i	$-0.402402\pi$
$643$	1.76394e22			0.603665			0.301833	+	0.953361i	$0.402402\pi$
$644$	2.15753e22	−	8.85536e21i	0.729241	−	0.299309i
$645$		−	4.09436e22i		−	1.36681i
$646$	1.20918e22	−	2.38493e21i	0.398684	−	0.0786349i
$647$			5.24930e22i			1.70949i	0.519046	+	0.854747i	$0.326287\pi$
$647$			5.24930e22i			1.70949i	−0.519046	+	0.854747i	$0.673713\pi$
$648$	−2.26919e22	+	1.50039e22i	−0.729912	+	0.482619i
$649$	8.76724e20			0.0278551
$650$	1.66696e22	+	8.45162e22i	0.523141	+	2.65236i
$651$	−6.79394e21			−0.210607
$652$	−9.31620e20	+	3.82373e20i	−0.0285271	+	0.0117086i
$653$		−	1.05339e22i		−	0.318628i	−0.987228	−	0.159314i	$-0.949072\pi$
$653$		−	1.05339e22i		−	0.318628i	0.987228	−	0.159314i	$-0.0509283\pi$
$654$	5.31941e21	+	2.69698e22i	0.158943	+	0.805852i
$655$		−	8.32209e22i		−	2.45642i
$656$	5.74902e21	−	5.67531e21i	0.167635	−	0.165485i
$657$	−8.75324e20			−0.0252142
$658$	−1.87782e22	+	3.70374e21i	−0.534377	+	0.105398i
$659$	−2.04422e21			−0.0574704			−0.0287352	−	0.999587i	$-0.509148\pi$
$659$	−2.04422e21			−0.0574704			−0.0287352	+	0.999587i	$0.509148\pi$
$660$	−2.69820e21	−	6.57393e21i	−0.0749415	−	0.182589i
$661$			2.82087e22i			0.774055i	0.922068	+	0.387028i	$0.126498\pi$
$661$			2.82087e22i			0.774055i	−0.922068	+	0.387028i	$0.873502\pi$
$662$	3.05548e22	−	6.02650e21i	0.828352	−	0.163381i
$663$		−	1.10065e22i		−	0.294810i
$664$	−4.46395e21	+	2.95157e21i	−0.118134	+	0.0781102i
$665$	−8.80555e22			−2.30241
$666$	−5.81727e20	−	2.94939e21i	−0.0150288	−	0.0761972i
$667$	−5.80983e22			−1.48305
$668$	−1.20128e21	−	2.92681e21i	−0.0302992	−	0.0738215i
$669$			5.13882e22i			1.28072i
$670$	−2.32237e22	−	1.17746e23i	−0.571916	−	2.89965i
$671$		−	8.66653e21i		−	0.210894i
$672$	2.61774e22	+	1.77982e22i	0.629465	+	0.427979i
$673$	−4.51475e21			−0.107279			−0.0536393	−	0.998560i	$-0.517082\pi$
$673$	−4.51475e21			−0.107279			−0.0536393	+	0.998560i	$0.517082\pi$
$674$	5.78835e22	−	1.14167e22i	1.35917	−	0.268078i
$675$	9.96226e22			2.31168
$676$	−2.02573e22	+	8.31440e21i	−0.464525	+	0.190659i
$677$		−	4.53332e22i		−	1.02732i	−0.857993	−	0.513662i	$-0.828289\pi$
$677$		−	4.53332e22i		−	1.02732i	0.857993	−	0.513662i	$-0.171711\pi$
$678$	−3.28267e22	+	6.47461e21i	−0.735173	+	0.145003i
$679$			3.69671e22i			0.818195i
$680$	1.15261e22	+	1.74320e22i	0.252122	+	0.381309i
$681$	−6.17184e22			−1.33425
$682$	−2.93191e20	−	1.48650e21i	−0.00626434	−	0.0317606i
$683$	7.32299e22			1.54640			0.773202	−	0.634160i	$-0.218654\pi$
$683$	7.32299e22			1.54640			0.773202	+	0.634160i	$0.218654\pi$
$684$	−7.92558e21	+	3.25297e21i	−0.165418	+	0.0678939i
$685$			7.11248e21i			0.146722i
$686$	1.03303e22	+	5.23754e22i	0.210630	+	1.06791i
$687$			3.11308e20i			0.00627389i
$688$	−2.89464e22	+	2.85752e22i	−0.576616	+	0.569222i
$689$	−1.92734e22			−0.379493
$690$	8.29682e22	−	1.63643e22i	1.61480	−	0.318497i
$691$	−8.01612e22			−1.54220			−0.771099	−	0.636715i	$-0.780293\pi$
$691$	−8.01612e22			−1.54220			−0.771099	+	0.636715i	$0.780293\pi$
$692$	1.33122e22	+	3.24340e22i	0.253163	+	0.616811i
$693$			5.64879e20i			0.0106192i
$694$	−8.45127e22	+	1.66689e22i	−1.57053	+	0.309765i
$695$		−	3.46840e22i		−	0.637163i
$696$	−4.34927e22	−	6.57783e22i	−0.789845	−	1.19456i
$697$	3.34982e21			0.0601394
$698$	−2.58187e21	−	1.30903e22i	−0.0458239	−	0.232330i
$699$	4.15394e22			0.728857
$700$	−3.90082e22	−	9.50402e22i	−0.676661	−	1.64863i
$701$		−	8.15142e22i		−	1.39794i	−0.715150	−	0.698971i	$-0.753642\pi$
$701$		−	8.15142e22i		−	1.39794i	0.715150	−	0.698971i	$-0.246358\pi$
$702$	1.46592e22	+	7.43232e22i	0.248550	+	1.26016i
$703$			6.56422e22i			1.10037i
$704$	−2.76453e21	+	6.49562e21i	−0.0458184	+	0.107656i
$705$	−6.94027e22			−1.13727
$706$	−1.91890e21	+	3.78476e20i	−0.0310895	+	0.00613198i
$707$	4.67175e22			0.748384
$708$	−1.31008e22	+	5.37709e21i	−0.207507	+	0.0851689i
$709$		−	7.65528e22i		−	1.19892i	−0.800403	−	0.599462i	$-0.795381\pi$
$709$		−	7.65528e22i		−	1.19892i	0.800403	−	0.599462i	$-0.204619\pi$
$710$	3.87269e22	−	7.63833e21i	0.599716	−	0.118286i
$711$			7.05020e20i			0.0107956i
$712$	4.14883e22	−	2.74321e22i	0.628183	−	0.415355i
$713$	1.80309e22			0.269962
$714$	2.54001e21	+	1.28780e22i	0.0376054	+	0.190662i
$715$	−1.75372e22			−0.256750
$716$	−1.00902e23	+	4.14141e22i	−1.46081	+	0.599575i
$717$			9.99807e21i			0.143141i
$718$	−6.54496e21	−	3.31834e22i	−0.0926641	−	0.469813i
$719$		−	1.14958e21i		−	0.0160956i	−0.999968	−	0.00804779i	$-0.997438\pi$
$719$		−	1.14958e21i		−	0.0160956i	0.999968	−	0.00804779i	$-0.00256172\pi$
$720$	−1.02054e22	−	1.03380e22i	−0.141309	−	0.143145i
$721$	1.14738e23			1.57118
$722$	1.11087e23	−	2.19104e22i	1.50441	−	0.296725i
$723$	6.10337e22			0.817454
$724$	−2.08425e22	−	5.07809e22i	−0.276084	−	0.672655i
$725$			2.55925e23i			3.35281i
$726$	−7.03627e22	+	1.38781e22i	−0.911695	+	0.179819i
$727$			6.79227e22i			0.870442i	0.900324	+	0.435221i	$0.143330\pi$
$727$			6.79227e22i			0.870442i	−0.900324	+	0.435221i	$0.856670\pi$
$728$	6.51645e22	−	4.30869e22i	0.825962	−	0.546127i
$729$	8.66010e22			1.08568
$730$	6.27131e21	+	3.17960e22i	0.0777635	+	0.394266i
$731$	−1.68663e22			−0.206863
$732$	5.31532e22	+	1.29503e23i	0.644823	+	1.57106i
$733$			5.54834e22i			0.665781i	0.942966	+	0.332890i	$0.108024\pi$
$733$			5.54834e22i			0.665781i	−0.942966	+	0.332890i	$0.891976\pi$
$734$	1.09952e22	+	5.57462e22i	0.130507	+	0.661678i
$735$			4.98966e22i			0.585831i
$736$	−6.94740e22	−	4.72360e22i	−0.806863	−	0.548593i
$737$	1.68110e22			0.193132
$738$	−2.28452e21	+	4.50590e20i	−0.0259624	+	0.00512071i
$739$	1.07018e23			1.20310			0.601548	−	0.798836i	$-0.294551\pi$
$739$	1.07018e23			1.20310			0.601548	+	0.798836i	$0.294551\pi$
$740$	−1.02968e23	+	4.22622e22i	−1.14512	+	0.470001i
$741$		−	1.67061e23i		−	1.83793i
$742$	2.25505e22	−	4.44778e21i	0.245429	−	0.0484074i
$743$		−	1.43921e23i		−	1.54958i	−0.632217	−	0.774791i	$-0.717855\pi$
$743$		−	1.43921e23i		−	1.54958i	0.632217	−	0.774791i	$-0.282145\pi$
$744$	1.34981e22	+	2.04144e22i	0.143776	+	0.217447i
$745$	8.26244e22			0.870679
$746$	−2.71969e22	−	1.37890e23i	−0.283537	−	1.43755i
$747$	1.54253e21			0.0159099
$748$	−2.70807e21	+	1.11150e21i	−0.0276342	+	0.0113422i
$749$			4.68293e22i			0.472785i
$750$	−3.94055e22	−	1.99788e23i	−0.393610	−	1.99563i
$751$		−	8.40625e22i		−	0.830774i	−0.909645	−	0.415387i	$-0.863646\pi$
$751$		−	8.40625e22i		−	0.830774i	0.909645	−	0.415387i	$-0.136354\pi$
$752$	4.84372e22	+	4.90663e22i	0.473627	+	0.479779i
$753$	−9.82379e22			−0.950428
$754$	−1.90932e23	+	3.76587e22i	−1.82771	+	0.360491i
$755$	−2.36478e23			−2.23983
$756$	−3.43036e22	−	8.35779e22i	−0.321489	−	0.783281i
$757$		−	3.71747e22i		−	0.344731i	−0.985033	−	0.172366i	$-0.944859\pi$
$757$		−	3.71747e22i		−	0.344731i	0.985033	−	0.172366i	$-0.0551410\pi$
$758$	−4.56162e22	+	8.99715e21i	−0.418567	+	0.0825565i
$759$			1.18457e22i			0.107554i
$760$	1.74947e23	+	2.64589e23i	1.57180	+	2.37719i
$761$	−1.53461e23			−1.36434			−0.682168	−	0.731195i	$-0.738963\pi$
$761$	−1.53461e23			−1.36434			−0.682168	+	0.731195i	$0.738963\pi$
$762$	1.93747e22	+	9.82313e22i	0.170450	+	0.864192i
$763$	−8.09057e22			−0.704341
$764$	−3.51124e22	−	8.55485e22i	−0.302492	−	0.736997i
$765$		−	6.02369e21i		−	0.0513536i
$766$	9.61807e21	+	4.87643e22i	0.0811442	+	0.411407i
$767$			3.49489e22i			0.291790i
$768$	1.47147e21	−	1.14019e23i	0.0121580	−	0.942078i
$769$	9.31513e22			0.761690			0.380845	−	0.924639i	$-0.375633\pi$
$769$	9.31513e22			0.761690			0.380845	+	0.924639i	$0.375633\pi$
$770$	2.05191e22	−	4.04711e21i	0.166048	−	0.0327506i
$771$	−9.88403e22			−0.791587
$772$	1.35728e23	−	5.57080e22i	1.07580	−	0.441550i
$773$		−	1.15903e23i		−	0.909196i	−0.890697	−	0.454598i	$-0.849783\pi$
$773$		−	1.15903e23i		−	0.909196i	0.890697	−	0.454598i	$-0.150217\pi$
$774$	1.15026e22	−	2.26872e21i	0.0893033	−	0.0176138i
$775$		−	7.94269e22i		−	0.610315i
$776$	1.11079e23	−	7.34454e22i	0.844767	−	0.558561i
$777$	−6.99107e22			−0.526230
$778$	3.35175e22	+	1.69936e23i	0.249710	+	1.26605i
$779$	5.08447e22			0.374926
$780$	2.62057e23	−	1.07558e23i	1.91266	−	0.785031i
$781$			5.52919e21i			0.0399442i
$782$	−6.74112e21	−	3.41780e22i	−0.0482035	−	0.244395i
$783$			2.25059e23i			1.59295i
$784$	3.52759e22	−	3.48236e22i	0.247144	−	0.243975i
$785$	−1.05684e23			−0.732914
$786$	−1.84735e23	+	3.64365e22i	−1.26815	+	0.250124i
$787$	−2.21417e23			−1.50457			−0.752285	−	0.658838i	$-0.771048\pi$
$787$	−2.21417e23			−1.50457			−0.752285	+	0.658838i	$0.771048\pi$
$788$	4.19658e22	+	1.02246e23i	0.282283	+	0.687760i
$789$			9.51694e22i			0.633696i
$790$	2.56097e22	−	5.05116e21i	0.168806	−	0.0332947i
$791$		−	9.84757e22i		−	0.642565i
$792$	1.69735e21	−	1.12229e21i	0.0109640	−	0.00724943i
$793$	3.45474e23			2.20917
$794$	−2.51749e22	−	1.27638e23i	−0.159369	−	0.808011i
$795$	8.33448e22			0.522326
$796$	7.45159e22	+	1.81552e23i	0.462322	+	1.12641i
$797$		−	1.86468e23i		−	1.14535i	−0.819783	−	0.572674i	$-0.805906\pi$
$797$		−	1.86468e23i		−	1.14535i	0.819783	−	0.572674i	$-0.194094\pi$
$798$	3.85532e22	+	1.95467e23i	0.234443	+	1.18864i
$799$			2.85898e22i			0.172122i
$800$	−2.08076e23	+	3.06036e23i	−1.24023	+	1.82411i
$801$	−1.43364e22			−0.0846019
$802$	1.74083e23	−	3.43354e22i	1.01709	−	0.200607i
$803$	−4.53964e21			−0.0262602
$804$	−2.51206e23	+	1.03105e23i	−1.43874	+	0.590514i
$805$			2.48893e23i			1.41139i
$806$	5.92562e22	−	1.16875e22i	0.332701	−	0.0656206i
$807$		−	2.15065e23i		−	1.19559i
$808$	−9.28174e22	−	1.40377e23i	−0.510903	−	0.772689i
$809$	3.28894e23			1.79254			0.896268	−	0.443514i	$-0.146268\pi$
$809$	3.28894e23			1.79254			0.896268	+	0.443514i	$0.146268\pi$
$810$	−5.61791e22	−	2.84832e23i	−0.303176	−	1.53712i
$811$	1.57001e23			0.838951			0.419476	−	0.907767i	$-0.362214\pi$
$811$	1.57001e23			0.838951			0.419476	+	0.907767i	$0.362214\pi$
$812$	2.14707e23	−	8.81242e22i	1.13605	−	0.466280i
$813$			6.84867e22i			0.358824i
$814$	−3.01698e21	−	1.52963e22i	−0.0156523	−	0.0793580i
$815$		−	1.07472e22i		−	0.0552120i
$816$	3.36495e22	−	3.32180e22i	0.171182	−	0.168987i
$817$	−2.56003e23			−1.28964
$818$	−4.50566e22	+	8.88678e21i	−0.224767	+	0.0443320i
$819$	−2.25178e22			−0.111238
$820$	3.27352e22	+	7.97566e22i	0.160142	+	0.390172i
$821$			1.32878e23i			0.643735i	0.946785	+	0.321868i	$0.104311\pi$
$821$			1.32878e23i			0.643735i	−0.946785	+	0.321868i	$0.895689\pi$
$822$	1.57884e22	−	3.11404e21i	0.0757467	−	0.0149400i
$823$			1.08398e23i			0.515018i	0.966276	+	0.257509i	$0.0829017\pi$
$823$			1.08398e23i			0.515018i	−0.966276	+	0.257509i	$0.917098\pi$
$824$	−2.27960e23	−	3.44766e23i	−1.07261	−	1.62221i
$825$	5.21808e22			0.243153
$826$	−8.06527e21	−	4.08915e22i	−0.0372202	−	0.188709i
$827$	−9.67193e22			−0.442048			−0.221024	−	0.975268i	$-0.570940\pi$
$827$	−9.67193e22			−0.442048			−0.221024	+	0.975268i	$0.570940\pi$
$828$	9.19467e21	+	2.24020e22i	0.0416192	+	0.101402i
$829$			1.48169e22i			0.0664234i	0.999448	+	0.0332117i	$0.0105736\pi$
$829$			1.48169e22i			0.0664234i	−0.999448	+	0.0332117i	$0.989426\pi$
$830$	−1.10515e22	−	5.60321e22i	−0.0490680	−	0.248778i
$831$		−	6.38160e22i		−	0.280622i
$832$	−2.58935e23	−	1.10202e23i	−1.12773	−	0.479959i
$833$	2.05544e22			0.0886636
$834$	−7.69921e22	+	1.51856e22i	−0.328941	+	0.0648790i
$835$	3.37637e22			0.142876
$836$	−4.11040e22	+	1.68707e22i	−0.172280	+	0.0707102i
$837$		−	6.98477e22i		−	0.289967i
$838$	2.85880e23	−	5.63858e22i	1.17552	−	0.231856i
$839$			3.62220e23i			1.47529i	0.675191	+	0.737643i	$0.264061\pi$
$839$			3.62220e23i			1.47529i	−0.675191	+	0.737643i	$0.735939\pi$
$840$	−2.81794e23	+	1.86323e23i	−1.13684	+	0.751678i
$841$	−3.27919e23			−1.31038
$842$	7.64997e22	+	3.87859e23i	0.302805	+	1.53524i
$843$	2.12142e23			0.831774
$844$	1.67748e23	−	6.88503e22i	0.651505	−	0.267403i
$845$		−	2.33689e23i		−	0.899051i
$846$	−3.84566e21	−	1.94978e22i	−0.0146558	−	0.0743057i
$847$		−	2.11079e23i		−	0.796851i
$848$	−5.81676e22	−	5.89231e22i	−0.217528	−	0.220353i
$849$	2.37232e23			0.878843
$850$	−1.50555e23	+	2.96949e22i	−0.552515	+	0.108976i
$851$	1.85541e23			0.674533
$852$	−3.39114e22	−	8.26223e22i	−0.122132	−	0.297564i
$853$		−	3.18100e23i		−	1.13494i	−0.823395	−	0.567469i	$-0.807923\pi$
$853$		−	3.18100e23i		−	1.13494i	0.823395	−	0.567469i	$-0.192077\pi$
$854$	−4.04217e23	+	7.97262e22i	−1.42874	+	0.281798i
$855$		−	9.14295e22i		−	0.320153i
$856$	1.40713e23	−	9.30395e22i	0.488139	−	0.322758i
$857$	−3.38794e23			−1.16436			−0.582182	−	0.813059i	$-0.697801\pi$
$857$	−3.38794e23			−1.16436			−0.582182	+	0.813059i	$0.697801\pi$
$858$	7.67826e21	+	3.89293e22i	0.0261436	+	0.132550i
$859$	5.84793e23			1.97268			0.986341	−	0.164717i	$-0.0526711\pi$
$859$	5.84793e23			1.97268			0.986341	+	0.164717i	$0.0526711\pi$
$860$	−1.64822e23	−	4.01575e23i	−0.550842	−	1.34208i
$861$			5.41509e22i			0.179300i
$862$	3.53581e22	+	1.79268e23i	0.115993	+	0.588091i
$863$			1.38504e23i			0.450170i	0.974339	+	0.225085i	$0.0722659\pi$
$863$			1.38504e23i			0.450170i	−0.974339	+	0.225085i	$0.927734\pi$
$864$	−1.82981e23	+	2.69126e23i	−0.589246	+	0.866655i
$865$	−3.74159e23			−1.19379
$866$	−1.33449e23	+	2.63210e22i	−0.421864	+	0.0832068i
$867$	−2.81192e23			−0.880745
$868$	−6.66349e22	+	2.73495e22i	−0.206797	+	0.0848774i
$869$			3.65641e21i			0.0112434i
$870$	8.25658e23	−	1.62849e23i	2.51563	−	0.496172i
$871$			6.70138e23i			2.02311i
$872$	1.60742e23	+	2.43106e23i	0.480836	+	0.727215i
$873$	−3.83835e22			−0.113771
$874$	−1.02319e23	−	5.18765e23i	−0.300514	−	1.52363i
$875$	5.99338e23			1.74425
$876$	6.78356e22	−	2.78424e22i	0.195625	−	0.0802922i
$877$			3.04222e23i			0.869348i	0.900588	+	0.434674i	$0.143136\pi$
$877$			3.04222e23i			0.869348i	−0.900588	+	0.434674i	$0.856864\pi$
$878$	−3.36850e22	−	1.70785e23i	−0.0953851	−	0.483609i
$879$		−	1.66417e23i		−	0.466967i
$880$	−5.29277e22	−	5.36152e22i	−0.147171	−	0.149083i
$881$	1.55764e23			0.429201			0.214601	−	0.976702i	$-0.431155\pi$
$881$	1.55764e23			0.429201			0.214601	+	0.976702i	$0.431155\pi$
$882$	−1.40178e22	+	2.76481e21i	−0.0382764	+	0.00754948i
$883$	−5.02093e23			−1.35862			−0.679310	−	0.733851i	$-0.737721\pi$
$883$	−5.02093e23			−1.35862			−0.679310	+	0.733851i	$0.737721\pi$
$884$	−4.43076e22	−	1.07952e23i	−0.118812	−	0.289475i
$885$		−	1.51131e23i		−	0.401613i
$886$	2.37275e23	−	4.67992e22i	0.624860	−	0.123245i
$887$		−	6.65140e22i		−	0.173590i	−0.996226	−	0.0867948i	$-0.972338\pi$
$887$		−	6.65140e22i		−	0.173590i	0.996226	−	0.0867948i	$-0.0276625\pi$
$888$	1.38897e23	+	2.10068e23i	0.359244	+	0.543320i
$889$	−2.94681e23			−0.755331
$890$	1.02714e23	+	5.20767e23i	0.260922	+	1.32289i
$891$	4.06666e22			0.102380
$892$	2.06867e23	+	5.04015e23i	0.516146	+	1.25755i
$893$			4.33945e23i			1.07306i
$894$	−3.61753e22	−	1.83411e23i	−0.0886567	−	0.449496i
$895$		−	1.16400e24i		−	2.82729i
$896$	3.28395e23	+	6.91856e22i	0.790557	+	0.166553i
$897$	−4.72205e23			−1.12666
$898$	4.85650e23	−	9.57876e22i	1.14845	−	0.226516i
$899$	1.79435e23			0.420561
$900$	9.86818e22	−	4.05029e22i	0.229244	−	0.0940905i
$901$		−	3.43331e22i		−	0.0790523i
$902$	−1.18481e22	+	2.33687e21i	−0.0270393	+	0.00533313i
$903$		−	2.72650e23i		−	0.616742i
$904$	−2.95900e23	+	1.95649e23i	−0.663433	+	0.438663i
$905$	5.85809e23			1.30187
$906$	1.03537e23	+	5.24937e23i	0.228070	+	1.15633i
$907$	−1.68108e23			−0.367054			−0.183527	−	0.983015i	$-0.558751\pi$
$907$	−1.68108e23			−0.367054			−0.183527	+	0.983015i	$0.558751\pi$
$908$	−6.05333e23	+	2.48452e23i	−1.31011	+	0.537720i
$909$			4.85076e22i			0.104064i
$910$	1.61330e23	+	8.17955e23i	0.343071	+	1.73939i
$911$			5.30378e23i			1.11799i	0.829171	+	0.558996i	$0.188813\pi$
$911$			5.30378e23i			1.11799i	−0.829171	+	0.558996i	$0.811187\pi$
$912$	5.10743e23	−	5.04194e23i	1.06720	−	1.05351i
$913$	7.99993e21			0.0165699
$914$	−1.89095e22	+	3.72964e21i	−0.0388250	+	0.00765768i
$915$	−1.49395e24			−3.04066
$916$	1.25320e21	+	3.05331e21i	0.00252846	+	0.00616037i
$917$		−	5.54181e23i		−	1.10840i
$918$	−1.32398e23	+	2.61136e22i	−0.262506	+	0.0517756i
$919$			6.79014e23i			1.33461i	0.744784	+	0.667305i	$0.232552\pi$
$919$			6.79014e23i			1.33461i	−0.744784	+	0.667305i	$0.767448\pi$
$920$	7.47875e23	−	4.94496e23i	1.45722	−	0.963518i
$921$	1.95978e23			0.378556
$922$	−1.38851e23	−	7.03982e23i	−0.265889	−	1.34807i
$923$	−2.20410e23			−0.418425
$924$	−1.79677e22	−	4.37768e22i	−0.0338156	−	0.0823889i
$925$		−	8.17315e23i		−	1.52495i
$926$	−8.91253e22	−	4.51871e23i	−0.164859	−	0.835847i
$927$			1.19135e23i			0.218474i
$928$	−6.91371e23	−	4.70069e23i	−1.25698	−	0.854629i
$929$	9.06740e23			1.63440			0.817198	−	0.576357i	$-0.195526\pi$
$929$	9.06740e23			1.63440			0.817198	+	0.576357i	$0.195526\pi$
$930$	−2.56245e23	+	5.05407e22i	−0.457922	+	0.0903187i
$931$	3.11982e23			0.552754
$932$	4.07418e23	−	1.67220e23i	0.715670	−	0.293739i
$933$			6.87494e23i			1.19733i
$934$	−6.68352e23	+	1.31823e23i	−1.15407	+	0.227623i
$935$		−	3.12403e22i		−	0.0534838i
$936$	4.47378e22	+	6.76614e22i	0.0759396	+	0.114851i
$937$	−9.57272e23			−1.61108			−0.805542	−	0.592538i	$-0.798126\pi$
$937$	−9.57272e23			−1.61108			−0.805542	+	0.592538i	$0.798126\pi$
$938$	−1.54650e23	−	7.84086e23i	−0.258064	−	1.30840i
$939$	−1.60170e23			−0.265007
$940$	−6.80700e23	+	2.79386e23i	−1.11669	+	0.458334i
$941$			2.45725e23i			0.399698i	0.979827	+	0.199849i	$0.0640451\pi$
$941$			2.45725e23i			0.399698i	−0.979827	+	0.199849i	$0.935955\pi$
$942$	4.62715e22	+	2.34600e23i	0.0746288	+	0.378373i
$943$		−	1.43715e23i		−	0.229831i
$944$	−1.06847e23	+	1.05477e23i	−0.169428	+	0.167256i
$945$	9.64155e23			1.51598
$946$	5.96552e22	−	1.17661e22i	0.0930077	−	0.0183445i
$947$	−4.17834e23			−0.645958			−0.322979	−	0.946406i	$-0.604684\pi$
$947$	−4.17834e23			−0.645958			−0.322979	+	0.946406i	$0.604684\pi$
$948$	−2.24253e22	−	5.46374e22i	−0.0343773	−	0.0837575i
$949$		−	1.80964e23i		−	0.275082i
$950$	−2.28518e24	+	4.50719e23i	−3.44454	+	0.679387i
$951$		−	6.15675e23i		−	0.920253i
$952$	7.67540e22	+	1.16083e23i	0.113764	+	0.172057i
$953$	5.39088e23			0.792348			0.396174	−	0.918175i	$-0.370338\pi$
$953$	5.39088e23			0.792348			0.396174	+	0.918175i	$0.370338\pi$
$954$	4.61820e21	+	2.34146e22i	0.00673110	+	0.0341271i
$955$	9.86888e23			1.42640
$956$	4.02480e22	+	9.80609e22i	0.0576874	+	0.140551i
$957$			1.17883e23i			0.167554i
$958$	−1.63341e23	−	8.28149e23i	−0.230235	−	1.16730i
$959$			4.73631e22i			0.0662051i
$960$	1.11973e24	+	4.76554e23i	1.55218	+	0.660605i
$961$	6.71735e23			0.923445
$962$	6.09756e23	−	1.20266e23i	0.831295	−	0.163961i
$963$	−4.86237e22			−0.0657412
$964$	5.98618e23	−	2.45696e23i	0.802663	−	0.329444i
$965$			1.56576e24i			2.08212i
$966$	5.52498e23	−	1.08972e23i	0.728641	−	0.143714i
$967$		−	7.48210e23i		−	0.978614i	−0.872111	−	0.489307i	$-0.837250\pi$
$967$		−	7.48210e23i		−	0.978614i	0.872111	−	0.489307i	$-0.162750\pi$
$968$	−6.34249e23	+	4.19366e23i	−0.822730	+	0.543990i
$969$	2.97598e23			0.382860
$970$	2.75001e23	+	1.39428e24i	0.350882	+	1.77899i
$971$	1.41552e24			1.79128			0.895640	−	0.444781i	$-0.146718\pi$
$971$	1.41552e24			1.79128			0.895640	+	0.444781i	$0.146718\pi$
$972$	1.64796e23	−	6.76389e22i	0.206832	−	0.0848919i
$973$		−	2.30966e23i		−	0.287505i
$974$	−1.87433e23	−	9.50297e23i	−0.231406	−	1.17324i
$975$			2.08008e24i			2.54708i
$976$	1.04265e24	+	1.05619e24i	1.26631	+	1.28276i
$977$	−3.64742e23			−0.439369			−0.219685	−	0.975571i	$-0.570503\pi$
$977$	−3.64742e23			−0.439369			−0.219685	+	0.975571i	$0.570503\pi$
$978$	−2.38568e22	+	4.70542e21i	−0.0285037	+	0.00562195i
$979$	−7.43521e22			−0.0881113
$980$	2.00863e23	+	4.89385e23i	0.236097	+	0.575231i
$981$		−	8.40058e22i		−	0.0979393i
$982$	−3.81999e23	+	7.53439e22i	−0.441743	+	0.0871277i
$983$		−	1.32002e24i		−	1.51410i	−0.653359	−	0.757049i	$-0.726641\pi$
$983$		−	1.32002e24i		−	1.51410i	0.653359	−	0.757049i	$-0.273359\pi$
$984$	1.62713e23	−	1.07586e23i	0.185123	−	0.122404i
$985$	−1.17951e24			−1.33110
$986$	−6.70843e22	−	3.40122e23i	−0.0750941	−	0.380732i
$987$	−4.62163e23			−0.513166
$988$	−6.72516e23	−	1.63853e24i	−0.740708	−	1.80467i
$989$			7.23606e23i			0.790554i
$990$	4.20219e21	+	2.13054e22i	0.00455401	+	0.0230891i
$991$			7.48922e23i			0.805095i	0.915399	+	0.402548i	$0.131875\pi$
$991$			7.48922e23i			0.805095i	−0.915399	+	0.402548i	$0.868125\pi$
$992$	2.14569e23	+	1.45887e23i	0.228809	+	0.155569i
$993$	7.52003e23			0.795473
$994$	2.57888e23	−	5.08648e22i	0.270608	−	0.0533736i
$995$	−2.09438e24			−2.18007
$996$	−1.19542e23	+	4.90648e22i	−0.123437	+	0.0506635i
$997$		−	4.07882e23i		−	0.417805i	−0.977937	−	0.208902i	$-0.933011\pi$
$997$		−	4.07882e23i		−	0.417805i	0.977937	−	0.208902i	$-0.0669891\pi$
$998$	−6.09247e22	+	1.20165e22i	−0.0619083	+	0.0122105i
$999$		−	7.18743e23i		−	0.724519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.13	✓	14
3.2	odd	2		72.17.b.b.19.2		14
4.3	odd	2		32.17.d.b.15.4		14
8.3	odd	2	inner	8.17.d.b.3.14	yes	14
8.5	even	2		32.17.d.b.15.3		14
24.11	even	2		72.17.b.b.19.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.13	✓	14	1.1	even	1	trivial
8.17.d.b.3.14	yes	14	8.3	odd	2	inner
32.17.d.b.15.3		14	8.5	even	2
32.17.d.b.15.4		14	4.3	odd	2
72.17.b.b.19.1		14	24.11	even	2
72.17.b.b.19.2		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(251.161 - 49.5380i) q^{2} +6181.49 q^{3} +(60628.0 - 24884.1i) q^{4} +699404. i q^{5} +(1.55255e6 - 306219. i) q^{6} +4.65744e6i q^{7} +(1.39947e7 - 9.25331e6i) q^{8} -4.83590e6 q^{9} +O(q^{10})\)	\(q+(251.161 - 49.5380i) q^{2} +6181.49 q^{3} +(60628.0 - 24884.1i) q^{4} +699404. i q^{5} +(1.55255e6 - 306219. i) q^{6} +4.65744e6i q^{7} +(1.39947e7 - 9.25331e6i) q^{8} -4.83590e6 q^{9} +(3.46471e7 + 1.75663e8i) q^{10} -2.50802e7 q^{11} +(3.74771e8 - 1.53821e8i) q^{12} -9.99771e8i q^{13} +(2.30721e8 + 1.16977e9i) q^{14} +4.32336e9i q^{15} +(3.05653e9 - 3.01734e9i) q^{16} +1.78097e9 q^{17} +(-1.21459e9 + 2.39561e8i) q^{18} +2.70321e10 q^{19} +(1.74040e10 + 4.24035e10i) q^{20} +2.87899e10i q^{21} +(-6.29917e9 + 1.24242e9i) q^{22} -7.64077e10i q^{23} +(8.65080e10 - 5.71992e10i) q^{24} -3.36579e11 q^{25} +(-4.95267e10 - 2.51104e11i) q^{26} -2.95986e11 q^{27} +(1.15896e11 + 2.82371e11i) q^{28} -7.60372e11i q^{29} +(2.14171e11 + 1.08586e12i) q^{30} +2.35983e11i q^{31} +(6.18210e11 - 9.09254e11i) q^{32} -1.55033e11 q^{33} +(4.47310e11 - 8.82257e10i) q^{34} -3.25744e12 q^{35} +(-2.93191e11 + 1.20337e11i) q^{36} +2.42830e12i q^{37} +(6.78943e12 - 1.33912e12i) q^{38} -6.18007e12i q^{39} +(6.47180e12 + 9.78795e12i) q^{40} +1.88090e12 q^{41} +(1.42620e12 + 7.23092e12i) q^{42} -9.47032e12 q^{43} +(-1.52056e12 + 6.24097e11i) q^{44} -3.38225e12i q^{45} +(-3.78509e12 - 1.91907e13i) q^{46} +1.60529e13i q^{47} +(1.88939e13 - 1.86517e13i) q^{48} +1.15412e13 q^{49} +(-8.45355e13 + 1.66734e13i) q^{50} +1.10090e13 q^{51} +(-2.48784e13 - 6.06141e13i) q^{52} -1.92778e13i q^{53} +(-7.43402e13 + 1.46626e13i) q^{54} -1.75412e13i q^{55} +(4.30967e13 + 6.51795e13i) q^{56} +1.67099e14 q^{57} +(-3.76673e13 - 1.90976e14i) q^{58} -3.49569e13 q^{59} +(1.07583e14 + 2.62117e14i) q^{60} +3.45553e14i q^{61} +(1.16901e13 + 5.92698e13i) q^{62} -2.25229e13i q^{63} +(1.10228e14 - 2.58994e14i) q^{64} +6.99244e14 q^{65} +(-3.89382e13 + 7.68002e12i) q^{66} -6.70291e14 q^{67} +(1.07977e14 - 4.43178e13i) q^{68} -4.72314e14i q^{69} +(-8.18142e14 + 1.61367e14i) q^{70} -2.20461e14i q^{71} +(-6.76769e13 + 4.47481e13i) q^{72} +1.81005e14 q^{73} +(1.20293e14 + 6.09895e14i) q^{74} -2.08056e15 q^{75} +(1.63890e15 - 6.72670e14i) q^{76} -1.16809e14i q^{77} +(-3.06149e14 - 1.55220e15i) q^{78} -1.45789e14i q^{79} +(2.11034e15 + 2.13775e15i) q^{80} -1.62146e15 q^{81} +(4.72409e14 - 9.31760e13i) q^{82} -3.18974e14 q^{83} +(7.16411e14 + 1.74548e15i) q^{84} +1.24562e15i q^{85} +(-2.37858e15 + 4.69141e14i) q^{86} -4.70023e15i q^{87} +(-3.50989e14 + 2.32075e14i) q^{88} +2.96458e15 q^{89} +(-1.67550e14 - 8.49491e14i) q^{90} +4.65638e15 q^{91} +(-1.90134e15 - 4.63244e15i) q^{92} +1.45873e15i q^{93} +(7.95231e14 + 4.03188e15i) q^{94} +1.89064e16i q^{95} +(3.82146e15 - 5.62054e15i) q^{96} +7.93720e15 q^{97} +(2.89869e15 - 5.71726e14i) q^{98} +1.21285e14 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

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