LMFDB - Embedded newform 8.17.d.b.3.2

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			3.2
Root			$109.380 - 40.6323i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.d.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-242.759 + 81.2647i) q^{2} -7667.81 q^{3} +(52328.1 - 39455.5i) q^{4} +557358. i q^{5} +(1.86143e6 - 623122. i) q^{6} +8.55454e6i q^{7} +(-9.49679e6 + 1.38306e7i) q^{8} +1.57485e7 q^{9} +O(q^{10})$	\(q+(-242.759 + 81.2647i) q^{2} -7667.81 q^{3} +(52328.1 - 39455.5i) q^{4} +557358. i q^{5} +(1.86143e6 - 623122. i) q^{6} +8.55454e6i q^{7} +(-9.49679e6 + 1.38306e7i) q^{8} +1.57485e7 q^{9} +(-4.52935e7 - 1.35304e8i) q^{10} +1.51024e8 q^{11} +(-4.01242e8 + 3.02537e8i) q^{12} +3.64901e8i q^{13} +(-6.95181e8 - 2.07669e9i) q^{14} -4.27371e9i q^{15} +(1.18149e9 - 4.12926e9i) q^{16} -1.29368e10 q^{17} +(-3.82310e9 + 1.27980e9i) q^{18} +2.11348e9 q^{19} +(2.19908e10 + 2.91655e10i) q^{20} -6.55945e10i q^{21} +(-3.66624e10 + 1.22729e10i) q^{22} +7.33433e10i q^{23} +(7.28196e10 - 1.06050e11i) q^{24} -1.58060e11 q^{25} +(-2.96535e10 - 8.85830e10i) q^{26} +2.09317e11 q^{27} +(3.37523e11 + 4.47643e11i) q^{28} +2.80131e11i q^{29} +(3.47302e11 + 1.03748e12i) q^{30} -9.63483e11i q^{31} +(4.87445e10 + 1.09843e12i) q^{32} -1.15802e12 q^{33} +(3.14054e12 - 1.05131e12i) q^{34} -4.76794e12 q^{35} +(8.24090e11 - 6.21366e11i) q^{36} -5.53641e12i q^{37} +(-5.13066e11 + 1.71751e11i) q^{38} -2.79799e12i q^{39} +(-7.70860e12 - 5.29311e12i) q^{40} -1.80493e11 q^{41} +(5.33052e12 + 1.59237e13i) q^{42} +2.29216e12 q^{43} +(7.90278e12 - 5.95871e12i) q^{44} +8.77757e12i q^{45} +(-5.96022e12 - 1.78048e13i) q^{46} +1.12569e13i q^{47} +(-9.05947e12 + 3.16624e13i) q^{48} -3.99471e13 q^{49} +(3.83705e13 - 1.28447e13i) q^{50} +9.91972e13 q^{51} +(1.43973e13 + 1.90946e13i) q^{52} -8.73423e12i q^{53} +(-5.08137e13 + 1.70101e13i) q^{54} +8.41742e13i q^{55} +(-1.18314e14 - 8.12407e13i) q^{56} -1.62057e13 q^{57} +(-2.27647e13 - 6.80043e13i) q^{58} +2.07936e14 q^{59} +(-1.68621e14 - 2.23635e14i) q^{60} +8.30772e12i q^{61} +(7.82971e13 + 2.33894e14i) q^{62} +1.34721e14i q^{63} +(-1.01097e14 - 2.62693e14i) q^{64} -2.03380e14 q^{65} +(2.81120e14 - 9.41061e13i) q^{66} -8.80887e13 q^{67} +(-6.76960e14 + 5.10429e14i) q^{68} -5.62382e14i q^{69} +(1.15746e15 - 3.87465e14i) q^{70} -6.03023e14i q^{71} +(-1.49560e14 + 2.17812e14i) q^{72} -1.18912e15 q^{73} +(4.49915e14 + 1.34401e15i) q^{74} +1.21197e15 q^{75} +(1.10594e14 - 8.33882e13i) q^{76} +1.29194e15i q^{77} +(2.27378e14 + 6.79238e14i) q^{78} +1.98915e15i q^{79} +(2.30148e15 + 6.58515e14i) q^{80} -2.28293e15 q^{81} +(4.38164e13 - 1.46677e13i) q^{82} +1.65008e15 q^{83} +(-2.58806e15 - 3.43244e15i) q^{84} -7.21045e15i q^{85} +(-5.56443e14 + 1.86272e14i) q^{86} -2.14799e15i q^{87} +(-1.43424e15 + 2.08875e15i) q^{88} -2.34380e15 q^{89} +(-7.13306e14 - 2.13084e15i) q^{90} -3.12156e15 q^{91} +(2.89380e15 + 3.83791e15i) q^{92} +7.38780e15i q^{93} +(-9.14792e14 - 2.73273e15i) q^{94} +1.17796e15i q^{95} +(-3.73763e14 - 8.42255e15i) q^{96} +1.05424e16 q^{97} +(9.69754e15 - 3.24629e15i) q^{98} +2.37840e15 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 $

$2$	−242.759	+	81.2647i	−0.948278	+	0.317440i
$2$	−242.759	+	81.2647i	−0.948278	+	0.317440i
$3$	−7667.81			−1.16869			−0.584347	−	0.811504i	$-0.698649\pi$
$3$	−7667.81			−1.16869			−0.584347	+	0.811504i	$0.698649\pi$
$4$	52328.1	−	39455.5i	0.798464	−	0.602043i
$5$			557358.i			1.42684i	0.700739	+	0.713418i	$0.252854\pi$
$5$			557358.i			1.42684i	−0.700739	+	0.713418i	$0.747146\pi$
$6$	1.86143e6	−	623122.i	1.10825	−	0.370991i
$7$			8.55454e6i			1.48393i	0.670441	+	0.741963i	$0.266105\pi$
$7$			8.55454e6i			1.48393i	−0.670441	+	0.741963i	$0.733895\pi$
$8$	−9.49679e6	+	1.38306e7i	−0.566053	+	0.824369i
$9$	1.57485e7			0.365847
$10$	−4.52935e7	−	1.35304e8i	−0.452935	−	1.35304i
$11$	1.51024e8			0.704536			0.352268	−	0.935899i	$-0.385410\pi$
$11$	1.51024e8			0.704536			0.352268	+	0.935899i	$0.385410\pi$
$12$	−4.01242e8	+	3.02537e8i	−0.933160	+	0.703605i
$13$			3.64901e8i			0.447330i	0.974666	+	0.223665i	$0.0718021\pi$
$13$			3.64901e8i			0.447330i	−0.974666	+	0.223665i	$0.928198\pi$
$14$	−6.95181e8	−	2.07669e9i	−0.471057	−	1.40717i
$15$		−	4.27371e9i		−	1.66754i
$16$	1.18149e9	−	4.12926e9i	0.275088	−	0.961419i
$17$	−1.29368e10			−1.85454			−0.927271	−	0.374390i	$-0.877852\pi$
$17$	−1.29368e10			−1.85454			−0.927271	+	0.374390i	$0.877852\pi$
$18$	−3.82310e9	+	1.27980e9i	−0.346925	+	0.116135i
$19$	2.11348e9			0.124442			0.0622212	−	0.998062i	$-0.480182\pi$
$19$	2.11348e9			0.124442			0.0622212	+	0.998062i	$0.480182\pi$
$20$	2.19908e10	+	2.91655e10i	0.859017	+	1.13928i
$21$		−	6.55945e10i		−	1.73426i
$22$	−3.66624e10	+	1.22729e10i	−0.668097	+	0.223648i
$23$			7.33433e10i			0.936564i	0.883579	+	0.468282i	$0.155127\pi$
$23$			7.33433e10i			0.936564i	−0.883579	+	0.468282i	$0.844873\pi$
$24$	7.28196e10	−	1.06050e11i	0.661543	−	0.963435i
$25$	−1.58060e11			−1.03586
$26$	−2.96535e10	−	8.85830e10i	−0.142000	−	0.424193i
$27$	2.09317e11			0.741131
$28$	3.37523e11	+	4.47643e11i	0.893387	+	1.18486i
$29$			2.80131e11i			0.559985i	0.960002	+	0.279993i	$0.0903320\pi$
$29$			2.80131e11i			0.559985i	−0.960002	+	0.279993i	$0.909668\pi$
$30$	3.47302e11	+	1.03748e12i	0.529343	+	1.58129i
$31$		−	9.63483e11i		−	1.12967i	−0.825205	−	0.564834i	$-0.808940\pi$
$31$		−	9.63483e11i		−	1.12967i	0.825205	−	0.564834i	$-0.191060\pi$
$32$	4.87445e10	+	1.09843e12i	0.0443329	+	0.999017i
$33$	−1.15802e12			−0.823388
$34$	3.14054e12	−	1.05131e12i	1.75862	−	0.588706i
$35$	−4.76794e12			−2.11732
$36$	8.24090e11	−	6.21366e11i	0.292116	−	0.220256i
$37$		−	5.53641e12i		−	1.57621i	−0.615540	−	0.788106i	$-0.711062\pi$
$37$		−	5.53641e12i		−	1.57621i	0.615540	−	0.788106i	$-0.288938\pi$
$38$	−5.13066e11	+	1.71751e11i	−0.118006	+	0.0395030i
$39$		−	2.79799e12i		−	0.522792i
$40$	−7.70860e12	−	5.29311e12i	−1.17624	−	0.807665i
$41$	−1.80493e11			−0.0226042			−0.0113021	−	0.999936i	$-0.503598\pi$
$41$	−1.80493e11			−0.0226042			−0.0113021	+	0.999936i	$0.503598\pi$
$42$	5.33052e12	+	1.59237e13i	0.550522	+	1.64456i
$43$	2.29216e12			0.196109			0.0980544	−	0.995181i	$-0.468738\pi$
$43$	2.29216e12			0.196109			0.0980544	+	0.995181i	$0.468738\pi$
$44$	7.90278e12	−	5.95871e12i	0.562547	−	0.424161i
$45$			8.77757e12i			0.522004i
$46$	−5.96022e12	−	1.78048e13i	−0.297303	−	0.888124i
$47$			1.12569e13i			0.472757i	0.971661	+	0.236378i	$0.0759604\pi$
$47$			1.12569e13i			0.472757i	−0.971661	+	0.236378i	$0.924040\pi$
$48$	−9.05947e12	+	3.16624e13i	−0.321494	+	1.12361i
$49$	−3.99471e13			−1.20204
$50$	3.83705e13	−	1.28447e13i	0.982286	−	0.328824i
$51$	9.91972e13			2.16739
$52$	1.43973e13	+	1.90946e13i	0.269312	+	0.357177i
$53$		−	8.73423e12i		−	0.140287i	−0.997537	−	0.0701435i	$-0.977654\pi$
$53$		−	8.73423e12i		−	0.140287i	0.997537	−	0.0701435i	$-0.0223457\pi$
$54$	−5.08137e13	+	1.70101e13i	−0.702798	+	0.235265i
$55$			8.41742e13i			1.00526i
$56$	−1.18314e14	−	8.12407e13i	−1.22330	−	0.839981i
$57$	−1.62057e13			−0.145435
$58$	−2.27647e13	−	6.80043e13i	−0.177762	−	0.531022i
$59$	2.07936e14			1.41616			0.708082	−	0.706131i	$-0.249561\pi$
$59$	2.07936e14			1.41616			0.708082	+	0.706131i	$0.249561\pi$
$60$	−1.68621e14	−	2.23635e14i	−1.00393	−	1.33147i
$61$			8.30772e12i			0.0433354i	0.999765	+	0.0216677i	$0.00689759\pi$
$61$			8.30772e12i			0.0433354i	−0.999765	+	0.0216677i	$0.993102\pi$
$62$	7.82971e13	+	2.33894e14i	0.358602	+	1.07124i
$63$			1.34721e14i			0.542890i
$64$	−1.01097e14	−	2.62693e14i	−0.359168	−	0.933273i
$65$	−2.03380e14			−0.638267
$66$	2.81120e14	−	9.41061e13i	0.780801	−	0.261376i
$67$	−8.80887e13			−0.216931			−0.108466	−	0.994100i	$-0.534594\pi$
$67$	−8.80887e13			−0.216931			−0.108466	+	0.994100i	$0.534594\pi$
$68$	−6.76960e14	+	5.10429e14i	−1.48078	+	1.11651i
$69$		−	5.62382e14i		−	1.09456i
$70$	1.15746e15	−	3.87465e14i	2.00781	−	0.672122i
$71$		−	6.03023e14i		−	0.933829i	−0.884302	−	0.466915i	$-0.845366\pi$
$71$		−	6.03023e14i		−	0.933829i	0.884302	−	0.466915i	$-0.154634\pi$
$72$	−1.49560e14	+	2.17812e14i	−0.207089	+	0.301593i
$73$	−1.18912e15			−1.47449			−0.737244	−	0.675627i	$-0.763873\pi$
$73$	−1.18912e15			−1.47449			−0.737244	+	0.675627i	$0.763873\pi$
$74$	4.49915e14	+	1.34401e15i	0.500353	+	1.49469i
$75$	1.21197e15			1.21061
$76$	1.10594e14	−	8.33882e13i	0.0993627	−	0.0749197i
$77$			1.29194e15i			1.04548i
$78$	2.27378e14	+	6.79238e14i	0.165955	+	0.495752i
$79$			1.98915e15i			1.31115i	0.755132	+	0.655573i	$0.227573\pi$
$79$			1.98915e15i			1.31115i	−0.755132	+	0.655573i	$0.772427\pi$
$80$	2.30148e15	+	6.58515e14i	1.37179	+	0.392506i
$81$	−2.28293e15			−1.23200
$82$	4.38164e13	−	1.46677e13i	0.0214351	−	0.00717549i
$83$	1.65008e15			0.732621			0.366311	−	0.930493i	$-0.380621\pi$
$83$	1.65008e15			0.732621			0.366311	+	0.930493i	$0.380621\pi$
$84$	−2.58806e15	−	3.43244e15i	−1.04410	−	1.38474i
$85$		−	7.21045e15i		−	2.64613i
$86$	−5.56443e14	+	1.86272e14i	−0.185966	+	0.0622528i
$87$		−	2.14799e15i		−	0.654452i
$88$	−1.43424e15	+	2.08875e15i	−0.398805	+	0.580798i
$89$	−2.34380e15			−0.595389			−0.297695	−	0.954661i	$-0.596218\pi$
$89$	−2.34380e15			−0.595389			−0.297695	+	0.954661i	$0.596218\pi$
$90$	−7.13306e14	−	2.13084e15i	−0.165705	−	0.495005i
$91$	−3.12156e15			−0.663804
$92$	2.89380e15	+	3.83791e15i	0.563852	+	0.747812i
$93$			7.38780e15i			1.32024i
$94$	−9.14792e14	−	2.73273e15i	−0.150072	−	0.448305i
$95$			1.17796e15i			0.177559i
$96$	−3.73763e14	−	8.42255e15i	−0.0518116	−	1.16755i
$97$	1.05424e16			1.34513			0.672566	−	0.740038i	$-0.265192\pi$
$97$	1.05424e16			1.34513			0.672566	+	0.740038i	$0.265192\pi$
$98$	9.69754e15	−	3.24629e15i	1.13986	−	0.381574i
$99$	2.37840e15			0.257753
$100$	−8.27098e15	+	6.23634e15i	−0.827098	+	0.623634i
$101$			1.99013e16i			1.83785i	0.394431	+	0.918926i	$0.370942\pi$
$101$			1.99013e16i			1.83785i	−0.394431	+	0.918926i	$0.629058\pi$
$102$	−2.40810e16	+	8.06123e15i	−2.05529	+	0.688018i
$103$		−	6.97952e15i		−	0.550970i	−0.961305	−	0.275485i	$-0.911162\pi$
$103$		−	6.97952e15i		−	0.550970i	0.961305	−	0.275485i	$-0.0888384\pi$
$104$	−5.04680e15	−	3.46539e15i	−0.368765	−	0.253212i
$105$	3.65596e16			2.47450
$106$	7.09784e14	+	2.12031e15i	0.0445327	+	0.133031i
$107$	−1.15042e16			−0.669555			−0.334777	−	0.942297i	$-0.608661\pi$
$107$	−1.15042e16			−0.669555			−0.334777	+	0.942297i	$0.608661\pi$
$108$	1.09532e16	−	8.25872e15i	0.591766	−	0.446193i
$109$		−	2.34185e16i		−	1.17530i	−0.809116	−	0.587648i	$-0.800054\pi$
$109$		−	2.34185e16i		−	1.17530i	0.809116	−	0.587648i	$-0.199946\pi$
$110$	−6.84039e15	−	2.04341e16i	−0.319109	−	0.953265i
$111$			4.24521e16i			1.84211i
$112$	3.53239e16	+	1.01071e16i	1.42667	+	0.408210i
$113$	−1.76133e16			−0.662542			−0.331271	−	0.943536i	$-0.607477\pi$
$113$	−1.76133e16			−0.662542			−0.331271	+	0.943536i	$0.607477\pi$
$114$	3.93409e15	−	1.31695e15i	0.137913	−	0.0461670i
$115$	−4.08785e16			−1.33632
$116$	1.10527e16	+	1.46587e16i	0.337135	+	0.447128i
$117$			5.74665e15i			0.163654i
$118$	−5.04784e16	+	1.68978e16i	−1.34292	+	0.449547i
$119$		−	1.10669e17i		−	2.75200i
$120$	5.91081e16	+	4.05866e16i	1.37466	+	0.943914i
$121$	−2.31416e16			−0.503628
$122$	−6.75124e14	−	2.01678e15i	−0.0137564	−	0.0410940i
$123$	1.38399e15			0.0264174
$124$	−3.80147e16	−	5.04173e16i	−0.680108	−	0.901998i
$125$		−	3.04994e15i		−	0.0511695i
$126$	−1.09481e16	−	3.27048e16i	−0.172335	−	0.514811i
$127$		−	1.43339e15i		−	0.0211805i	−0.999944	−	0.0105902i	$-0.996629\pi$
$127$		−	1.43339e15i		−	0.0211805i	0.999944	−	0.0105902i	$-0.00337104\pi$
$128$	4.58898e16	+	5.55556e16i	0.636849	+	0.770988i
$129$	−1.75758e16			−0.229191
$130$	4.93725e16	−	1.65276e16i	0.605254	−	0.202611i
$131$	−3.24094e16			−0.373681			−0.186840	−	0.982390i	$-0.559825\pi$
$131$	−3.24094e16			−0.373681			−0.186840	+	0.982390i	$0.559825\pi$
$132$	−6.05970e16	+	4.56903e16i	−0.657445	+	0.495715i
$133$			1.80798e16i			0.184663i
$134$	2.13843e16	−	7.15850e15i	0.205711	−	0.0688626i
$135$			1.16665e17i			1.05747i
$136$	1.22859e17	−	1.78924e17i	1.04977	−	1.52883i
$137$	1.75284e17			1.41246			0.706231	−	0.707982i	$-0.250394\pi$
$137$	1.75284e17			1.41246			0.706231	+	0.707982i	$0.250394\pi$
$138$	4.57018e16	+	1.36523e17i	0.347456	+	1.03795i
$139$	−6.24449e16			−0.448104			−0.224052	−	0.974577i	$-0.571928\pi$
$139$	−6.24449e16			−0.448104			−0.224052	+	0.974577i	$0.571928\pi$
$140$	−2.49497e17	+	1.88121e17i	−1.69060	+	1.27472i
$141$		−	8.63160e16i		−	0.552508i
$142$	4.90045e16	+	1.46390e17i	0.296435	+	0.885530i
$143$			5.51086e16i			0.315160i
$144$	1.86068e16	−	6.50298e16i	0.100640	−	0.351733i
$145$	−1.56133e17			−0.799008
$146$	2.88669e17	−	9.66330e16i	1.39822	−	0.468061i
$147$	3.06307e17			1.40481
$148$	−2.18442e17	−	2.89710e17i	−0.948947	−	1.25855i
$149$			1.99108e17i			0.819593i	0.912177	+	0.409796i	$0.134400\pi$
$149$			1.99108e17i			0.819593i	−0.912177	+	0.409796i	$0.865600\pi$
$150$	−2.94218e17	+	9.84906e16i	−1.14799	+	0.384295i
$151$		−	9.45575e16i		−	0.349849i	−0.984582	−	0.174924i	$-0.944032\pi$
$151$		−	9.45575e16i		−	0.349849i	0.984582	−	0.174924i	$-0.0559681\pi$
$152$	−2.00712e16	+	2.92307e16i	−0.0704410	+	0.102586i
$153$	−2.03736e17			−0.678479
$154$	−1.04989e17	−	3.13630e17i	−0.331877	−	0.991406i
$155$	5.37005e17			1.61185
$156$	−1.10396e17	−	1.46413e17i	−0.314743	−	0.417430i
$157$		−	7.05881e16i		−	0.191220i	−0.995419	−	0.0956102i	$-0.969520\pi$
$157$		−	7.05881e16i		−	0.191220i	0.995419	−	0.0956102i	$-0.0304802\pi$
$158$	−1.61648e17	−	4.82885e17i	−0.416211	−	1.24333i
$159$			6.69724e16i			0.163953i
$160$	−6.12219e17	+	2.71681e16i	−1.42543	+	0.0632558i
$161$	−6.27418e17			−1.38979
$162$	5.54202e17	−	1.85521e17i	1.16828	−	0.391087i
$163$	2.34479e17			0.470547			0.235274	−	0.971929i	$-0.424401\pi$
$163$	2.34479e17			0.470547			0.235274	+	0.971929i	$0.424401\pi$
$164$	−9.44486e15	+	7.12144e15i	−0.0180487	+	0.0136087i
$165$		−	6.45432e17i		−	1.17484i
$166$	−4.00571e17	+	1.34093e17i	−0.694729	+	0.232563i
$167$			9.91844e17i			1.63950i	0.572721	+	0.819751i	$0.305888\pi$
$167$			9.91844e17i			1.63950i	−0.572721	+	0.819751i	$0.694112\pi$
$168$	9.07212e17	+	6.22938e17i	1.42967	+	0.981681i
$169$	5.32264e17			0.799896
$170$	5.85955e17	+	1.75040e18i	0.839987	+	2.50927i
$171$	3.32841e16			0.0455269
$172$	1.19944e17	−	9.04383e16i	0.156586	−	0.118066i
$173$			4.60112e17i			0.573449i	0.958013	+	0.286724i	$0.0925664\pi$
$173$			4.60112e17i			0.573449i	−0.958013	+	0.286724i	$0.907434\pi$
$174$	1.74555e17	+	5.21444e17i	0.207749	+	0.620603i
$175$		−	1.35213e18i		−	1.53714i
$176$	1.78434e17	−	6.23616e17i	0.193810	−	0.677355i
$177$	−1.59441e18			−1.65506
$178$	5.68980e17	−	1.90468e17i	0.564595	−	0.189000i
$179$	−1.47277e18			−1.39737			−0.698683	−	0.715431i	$-0.746230\pi$
$179$	−1.47277e18			−1.39737			−0.698683	+	0.715431i	$0.746230\pi$
$180$	3.46323e17	+	4.59313e17i	0.314269	+	0.416801i
$181$		−	6.60815e17i		−	0.573655i	−0.957982	−	0.286828i	$-0.907399\pi$
$181$		−	6.60815e17i		−	0.573655i	0.957982	−	0.286828i	$-0.0926007\pi$
$182$	7.57787e17	−	2.53672e17i	0.629471	−	0.210718i
$183$		−	6.37020e16i		−	0.0506459i
$184$	−1.01438e18	−	6.96526e17i	−0.772074	−	0.530145i
$185$	3.08576e18			2.24900
$186$	−6.00367e17	−	1.79346e18i	−0.419096	−	1.25195i
$187$	−1.95377e18			−1.30659
$188$	4.44148e17	+	5.89054e17i	0.284620	+	0.377479i
$189$			1.79061e18i			1.09978i
$190$	−9.57267e16	−	2.85961e17i	−0.0563643	−	0.168375i
$191$		−	1.53435e18i		−	0.866280i	−0.901327	−	0.433140i	$-0.857406\pi$
$191$		−	1.53435e18i		−	0.866280i	0.901327	−	0.433140i	$-0.142594\pi$
$192$	7.75190e17	+	2.01428e18i	0.419758	+	1.09071i
$193$	7.58207e16			0.0393849			0.0196924	−	0.999806i	$-0.493731\pi$
$193$	7.58207e16			0.0393849			0.0196924	+	0.999806i	$0.493731\pi$
$194$	−2.55926e18	+	8.56723e17i	−1.27556	+	0.426999i
$195$	1.55948e18			0.745939
$196$	−2.09036e18	+	1.57613e18i	−0.959781	+	0.723677i
$197$		−	9.73556e17i		−	0.429172i	−0.976705	−	0.214586i	$-0.931160\pi$
$197$		−	9.73556e17i		−	0.429172i	0.976705	−	0.214586i	$-0.0688402\pi$
$198$	−5.77379e17	+	1.93280e17i	−0.244421	+	0.0818211i
$199$			8.87051e17i			0.360681i	0.983604	+	0.180341i	$0.0577200\pi$
$199$			8.87051e17i			0.360681i	−0.983604	+	0.180341i	$0.942280\pi$
$200$	1.50106e18	−	2.18607e18i	0.586353	−	0.853932i
$201$	6.75447e17			0.253526
$202$	−1.61727e18	−	4.83122e18i	−0.583408	−	1.74279i
$203$	−2.39639e18			−0.830977
$204$	5.19080e18	−	3.91387e18i	1.73059	−	1.30486i
$205$		−	1.00599e17i		−	0.0322525i
$206$	5.67188e17	+	1.69434e18i	0.174900	+	0.522473i
$207$			1.15505e18i			0.342639i
$208$	1.50677e18	+	4.31128e17i	0.430072	+	0.123055i
$209$	3.19185e17			0.0876742
$210$	−8.87519e18	+	2.97101e18i	−2.34651	+	0.785505i
$211$	1.81860e17			0.0462890			0.0231445	−	0.999732i	$-0.492632\pi$
$211$	1.81860e17			0.0462890			0.0231445	+	0.999732i	$0.492632\pi$
$212$	−3.44613e17	−	4.57046e17i	−0.0844588	−	0.112014i
$213$			4.62387e18i			1.09136i
$214$	2.79275e18	−	9.34885e17i	0.634924	−	0.212544i
$215$			1.27755e18i			0.279815i
$216$	−1.98784e18	+	2.89499e18i	−0.419519	+	0.610965i
$217$	8.24215e18			1.67634
$218$	1.90310e18	+	5.68506e18i	0.373086	+	1.11451i
$219$	9.11790e18			1.72323
$220$	3.32114e18	+	4.40468e18i	0.605209	+	0.802662i
$221$		−	4.72066e18i		−	0.829592i
$222$	−3.44986e18	−	1.03056e19i	−0.584760	−	1.74683i
$223$			4.73123e18i			0.773633i	0.922157	+	0.386816i	$0.126425\pi$
$223$			4.73123e18i			0.773633i	−0.922157	+	0.386816i	$0.873575\pi$
$224$	−9.39656e18	+	4.16987e17i	−1.48247	+	0.0657867i
$225$	−2.48921e18			−0.378967
$226$	4.27579e18	−	1.43134e18i	0.628274	−	0.210317i
$227$	−1.01230e19			−1.43583			−0.717913	−	0.696133i	$-0.754902\pi$
$227$	−1.01230e19			−1.43583			−0.717913	+	0.696133i	$0.754902\pi$
$228$	−8.48015e17	+	6.39405e17i	−0.116125	+	0.0875582i
$229$			1.24157e19i			1.64168i	0.571159	+	0.820840i	$0.306494\pi$
$229$			1.24157e19i			1.64168i	−0.571159	+	0.820840i	$0.693506\pi$
$230$	9.92362e18	−	3.32197e18i	1.26721	−	0.424203i
$231$		−	9.90632e18i		−	1.22185i
$232$	−3.87438e18	−	2.66034e18i	−0.461634	−	0.316981i
$233$	−9.63007e18			−1.10862			−0.554309	−	0.832311i	$-0.687018\pi$
$233$	−9.63007e18			−1.10862			−0.554309	+	0.832311i	$0.687018\pi$
$234$	−4.67000e17	−	1.39505e18i	−0.0519505	−	0.155190i
$235$	−6.27415e18			−0.674546
$236$	1.08809e19	−	8.20421e18i	1.13075	−	0.852591i
$237$		−	1.52524e19i		−	1.53233i
$238$	8.99345e18	+	2.68658e19i	0.873596	+	2.60967i
$239$		−	1.17222e19i		−	1.10109i	−0.834804	−	0.550547i	$-0.814419\pi$
$239$		−	1.17222e19i		−	1.10109i	0.834804	−	0.550547i	$-0.185581\pi$
$240$	−1.76473e19	−	5.04937e18i	−1.60320	−	0.458719i
$241$	−8.99136e18			−0.790112			−0.395056	−	0.918657i	$-0.629275\pi$
$241$	−8.99136e18			−0.790112			−0.395056	+	0.918657i	$0.629275\pi$
$242$	5.61783e18	−	1.88059e18i	0.477580	−	0.159872i
$243$	8.49461e18			0.698704
$244$	3.27785e17	+	4.34727e17i	0.0260898	+	0.0346018i
$245$		−	2.22649e19i		−	1.71511i
$246$	−3.35975e17	+	1.12469e17i	−0.0250511	+	0.00838596i
$247$			7.71209e17i			0.0556668i
$248$	1.33256e19	+	9.15000e18i	0.931263	+	0.639452i
$249$	−1.26525e19			−0.856210
$250$	2.47852e17	+	7.40401e17i	0.0162432	+	0.0485229i
$251$	−8.44272e17			−0.0535911			−0.0267955	−	0.999641i	$-0.508530\pi$
$251$	−8.44272e17			−0.0535911			−0.0267955	+	0.999641i	$0.508530\pi$
$252$	5.31550e18	+	7.04971e18i	0.326843	+	0.433478i
$253$			1.10766e19i			0.659844i
$254$	1.16484e17	+	3.47969e17i	0.00672353	+	0.0200850i
$255$			5.52883e19i			3.09252i
$256$	−1.56549e19	−	9.75740e18i	−0.848653	−	0.528950i
$257$	−1.12539e19			−0.591343			−0.295672	−	0.955290i	$-0.595543\pi$
$257$	−1.12539e19			−0.591343			−0.295672	+	0.955290i	$0.595543\pi$
$258$	4.26670e18	−	1.42829e18i	0.217337	−	0.0727546i
$259$	4.73614e19			2.33898
$260$	−1.06425e19	+	8.02447e18i	−0.509633	+	0.384264i
$261$			4.41164e18i			0.204869i
$262$	7.86768e18	−	2.63374e18i	0.354353	−	0.118621i
$263$		−	2.11514e19i		−	0.924046i	−0.886868	−	0.462023i	$-0.847124\pi$
$263$		−	2.11514e19i		−	0.924046i	0.886868	−	0.462023i	$-0.152876\pi$
$264$	1.09975e19	−	1.60161e19i	0.466081	−	0.678775i
$265$	4.86809e18			0.200167
$266$	−1.46925e18	−	4.38904e18i	−0.0586195	−	0.175112i
$267$	1.79718e19			0.695828
$268$	−4.60951e18	+	3.47558e18i	−0.173212	+	0.130602i
$269$			3.46645e19i			1.26435i	0.774826	+	0.632174i	$0.217837\pi$
$269$			3.46645e19i			1.26435i	−0.774826	+	0.632174i	$0.782163\pi$
$270$	−9.48071e18	−	2.83214e19i	−0.335684	−	1.00278i
$271$		−	1.79486e19i		−	0.616986i	−0.951227	−	0.308493i	$-0.900175\pi$
$271$		−	1.79486e19i		−	0.616986i	0.951227	−	0.308493i	$-0.0998246\pi$
$272$	−1.52848e19	+	5.34196e19i	−0.510163	+	1.78299i
$273$	2.39355e19			0.775785
$274$	−4.25517e19	+	1.42444e19i	−1.33941	+	0.448372i
$275$	−2.38708e19			−0.729803
$276$	−2.21891e19	−	2.94284e19i	−0.658971	−	0.873964i
$277$		−	1.89220e19i		−	0.545920i	−0.962025	−	0.272960i	$-0.911997\pi$
$277$		−	1.89220e19i		−	0.545920i	0.962025	−	0.272960i	$-0.0880027\pi$
$278$	1.51591e19	−	5.07456e18i	0.424927	−	0.142246i
$279$		−	1.51734e19i		−	0.413286i
$280$	4.52801e19	−	6.59435e19i	1.19851	−	1.74545i
$281$	−2.99742e19			−0.771077			−0.385538	−	0.922692i	$-0.625984\pi$
$281$	−2.99742e19			−0.771077			−0.385538	+	0.922692i	$0.625984\pi$
$282$	7.01444e18	+	2.09540e19i	0.175388	+	0.523931i
$283$	−2.97748e19			−0.723697			−0.361849	−	0.932237i	$-0.617854\pi$
$283$	−2.97748e19			−0.723697			−0.361849	+	0.932237i	$0.617854\pi$
$284$	−2.37926e19	−	3.15551e19i	−0.562205	−	0.745629i
$285$		−	9.03239e18i		−	0.207512i
$286$	−4.47839e18	−	1.33781e19i	−0.100045	−	0.298860i
$287$		−	1.54403e18i		−	0.0335430i
$288$	7.67654e17	+	1.72987e19i	0.0162191	+	0.365488i
$289$	1.18701e20			2.43933
$290$	3.79027e19	−	1.26881e19i	0.757681	−	0.253637i
$291$	−8.08369e19			−1.57205
$292$	−6.22241e19	+	4.69171e19i	−1.17732	+	0.887705i
$293$		−	3.21807e18i		−	0.0592453i	−0.999561	−	0.0296227i	$-0.990569\pi$
$293$		−	3.21807e18i		−	0.0592453i	0.999561	−	0.0296227i	$-0.00943057\pi$
$294$	−7.43589e19	+	2.48919e19i	−1.33215	+	0.445944i
$295$			1.15895e20i			2.02063i
$296$	7.65720e19	+	5.25782e19i	1.29938	+	0.892219i
$297$	3.16119e19			0.522154
$298$	−1.61804e19	−	4.83353e19i	−0.260172	−	0.777202i
$299$	−2.67630e19			−0.418953
$300$	6.34203e19	−	4.78190e19i	0.966625	−	0.728837i
$301$			1.96084e19i			0.291011i
$302$	7.68418e18	+	2.29547e19i	0.111056	+	0.331754i
$303$		−	1.52599e20i		−	2.14789i
$304$	2.49706e18	−	8.72710e18i	0.0342326	−	0.119641i
$305$	−4.63037e18			−0.0618326
$306$	4.94588e19	−	1.65565e19i	0.643387	−	0.215377i
$307$	5.81978e19			0.737564			0.368782	−	0.929516i	$-0.379775\pi$
$307$	5.81978e19			0.737564			0.368782	+	0.929516i	$0.379775\pi$
$308$	5.09740e19	+	6.76046e19i	0.629424	+	0.834777i
$309$			5.35176e19i			0.643915i
$310$	−1.30363e20	+	4.36395e19i	−1.52848	+	0.511666i
$311$		−	1.04256e20i		−	1.19129i	−0.803248	−	0.595645i	$-0.796896\pi$
$311$		−	1.04256e20i		−	1.19129i	0.803248	−	0.595645i	$-0.203104\pi$
$312$	3.86979e19	+	2.65719e19i	0.430974	+	0.295928i
$313$	−1.60356e20			−1.74073			−0.870365	−	0.492407i	$-0.836117\pi$
$313$	−1.60356e20			−1.74073			−0.870365	+	0.492407i	$0.836117\pi$
$314$	5.73632e18	+	1.71359e19i	0.0607010	+	0.181330i
$315$	−7.50880e19			−0.774615
$316$	7.84830e19	+	1.04089e20i	0.789367	+	1.04690i
$317$		−	1.13662e19i		−	0.111466i	−0.998446	−	0.0557329i	$-0.982250\pi$
$317$		−	1.13662e19i		−	0.111466i	0.998446	−	0.0557329i	$-0.0177495\pi$
$318$	−5.44249e18	−	1.62582e19i	−0.0520452	−	0.155473i
$319$			4.23064e19i			0.394530i
$320$	1.46414e20	−	5.63471e19i	1.33163	−	0.512474i
$321$	8.82120e19			0.782505
$322$	1.52311e20	−	5.09869e19i	1.31791	−	0.441176i
$323$	−2.73417e19			−0.230784
$324$	−1.19461e20	+	9.00740e19i	−0.983710	+	0.741719i
$325$		−	5.76762e19i		−	0.463372i
$326$	−5.69220e19	+	1.90549e19i	−0.446210	+	0.149371i
$327$			1.79569e20i			1.37356i
$328$	1.71411e18	−	2.49633e18i	0.0127952	−	0.0186342i
$329$	−9.62979e19			−0.701535
$330$	5.24508e19	+	1.56685e20i	0.372941	+	1.11408i
$331$	4.34350e18			0.0301450			0.0150725	−	0.999886i	$-0.495202\pi$
$331$	4.34350e18			0.0301450			0.0150725	+	0.999886i	$0.495202\pi$
$332$	8.63454e19	−	6.51046e19i	0.584971	−	0.441070i
$333$		−	8.71903e19i		−	0.576653i
$334$	−8.06019e19	−	2.40779e20i	−0.520443	−	1.55470i
$335$		−	4.90969e19i		−	0.309525i
$336$	−2.70857e20	−	7.74996e19i	−1.66735	−	0.477073i
$337$	5.38785e19			0.323874			0.161937	−	0.986801i	$-0.448226\pi$
$337$	5.38785e19			0.323874			0.161937	+	0.986801i	$0.448226\pi$
$338$	−1.29212e20	+	4.32543e19i	−0.758524	+	0.253919i
$339$	1.35055e20			0.774309
$340$	−2.84492e20	−	3.77309e20i	−1.59308	−	2.11284i
$341$		−	1.45509e20i		−	0.795892i
$342$	−8.08003e18	+	2.70482e18i	−0.0431722	+	0.0144521i
$343$		−	5.74370e19i		−	0.299805i
$344$	−2.17682e19	+	3.17020e19i	−0.111008	+	0.161666i
$345$	3.13448e20			1.56175
$346$	−3.73908e19	−	1.11696e20i	−0.182036	−	0.543789i
$347$	1.01011e18			0.00480544			0.00240272	−	0.999997i	$-0.499235\pi$
$347$	1.01011e18			0.00480544			0.00240272	+	0.999997i	$0.499235\pi$
$348$	−8.47499e19	−	1.12400e20i	−0.394008	−	0.522556i
$349$			1.68723e20i			0.766602i	0.923624	+	0.383301i	$0.125213\pi$
$349$			1.68723e20i			0.766602i	−0.923624	+	0.383301i	$0.874787\pi$
$350$	1.09880e20	+	3.28242e20i	0.487951	+	1.45764i
$351$			7.63800e19i			0.331530i
$352$	7.36157e18	+	1.65889e20i	0.0312341	+	0.703844i
$353$	−2.84133e20			−1.17849			−0.589243	−	0.807956i	$-0.700574\pi$
$353$	−2.84133e20			−1.17849			−0.589243	+	0.807956i	$0.700574\pi$
$354$	3.87058e20	−	1.29569e20i	1.56946	−	0.525383i
$355$	3.36100e20			1.33242
$356$	−1.22647e20	+	9.24759e19i	−0.475397	+	0.358450i
$357$			8.48586e20i			3.21625i
$358$	3.57528e20	−	1.19684e20i	1.32509	−	0.443580i
$359$			2.04614e20i			0.741617i	0.928709	+	0.370809i	$0.120919\pi$
$359$			2.04614e20i			0.741617i	−0.928709	+	0.370809i	$0.879081\pi$
$360$	−1.21399e20	−	8.33587e19i	−0.430324	−	0.295482i
$361$	−2.83975e20			−0.984514
$362$	5.37009e19	+	1.60419e20i	0.182101	+	0.543985i
$363$	1.77445e20			0.588588
$364$	−1.63345e20	+	1.23163e20i	−0.530024	+	0.399639i
$365$		−	6.62763e20i		−	2.10385i
$366$	5.17672e18	+	1.54642e19i	0.0160770	+	0.0480264i
$367$		−	1.00923e20i		−	0.306664i	−0.988175	−	0.153332i	$-0.951000\pi$
$367$		−	1.00923e20i		−	0.306664i	0.988175	−	0.153332i	$-0.0490004\pi$
$368$	3.02854e20	+	8.66547e19i	0.900431	+	0.257638i
$369$	−2.84250e18			−0.00826970
$370$	−7.49097e20	+	2.50763e20i	−2.13267	+	0.713922i
$371$	7.47173e19			0.208176
$372$	2.91489e20	+	3.86590e20i	0.794839	+	1.05416i
$373$		−	6.48351e20i		−	1.73037i	−0.501451	−	0.865186i	$-0.667200\pi$
$373$		−	6.48351e20i		−	1.73037i	0.501451	−	0.865186i	$-0.332800\pi$
$374$	4.74295e20	−	1.58772e20i	1.23901	−	0.414765i
$375$			2.33863e19i			0.0598015i
$376$	−1.55690e20	−	1.06905e20i	−0.389726	−	0.267605i
$377$	−1.02220e20			−0.250498
$378$	−1.45513e20	−	4.34688e20i	−0.349115	−	1.04290i
$379$	4.49795e18			0.0105658			0.00528288	−	0.999986i	$-0.498318\pi$
$379$	4.49795e18			0.0105658			0.00528288	+	0.999986i	$0.498318\pi$
$380$	4.64771e19	+	6.16405e19i	0.106898	+	0.141774i
$381$			1.09910e19i			0.0247535i
$382$	1.24689e20	+	3.72478e20i	0.274992	+	0.821474i
$383$			5.53477e20i			1.19539i	0.801724	+	0.597694i	$0.203916\pi$
$383$			5.53477e20i			1.19539i	−0.801724	+	0.597694i	$0.796084\pi$
$384$	−3.51874e20	−	4.25989e20i	−0.744283	−	0.901050i
$385$	−7.20072e20			−1.49173
$386$	−1.84062e19	+	6.16155e18i	−0.0373478	+	0.0125023i
$387$	3.60981e19			0.0717459
$388$	5.51663e20	−	4.15955e20i	1.07404	−	0.809827i
$389$			1.51215e19i			0.0288402i	0.999896	+	0.0144201i	$0.00459022\pi$
$389$			1.51215e19i			0.0288402i	−0.999896	+	0.0144201i	$0.995410\pi$
$390$	−3.78578e20	+	1.26731e20i	−0.707358	+	0.236791i
$391$		−	9.48830e20i		−	1.73690i
$392$	3.79370e20	−	5.52494e20i	0.680416	−	0.990920i
$393$	2.48509e20			0.436719
$394$	7.91157e19	+	2.36340e20i	0.136236	+	0.406974i
$395$	−1.10867e21			−1.87079
$396$	1.24457e20	−	9.38409e19i	0.205806	−	0.155178i
$397$			6.46671e20i			1.04800i	0.851720	+	0.523998i	$0.175560\pi$
$397$			6.46671e20i			1.04800i	−0.851720	+	0.523998i	$0.824440\pi$
$398$	−7.20859e19	−	2.15340e20i	−0.114495	−	0.342026i
$399$		−	1.38632e20i		−	0.215815i
$400$	−1.86747e20	+	6.52671e20i	−0.284953	+	0.995898i
$401$	2.36360e20			0.353524			0.176762	−	0.984254i	$-0.443438\pi$
$401$	2.36360e20			0.353524			0.176762	+	0.984254i	$0.443438\pi$
$402$	−1.63971e20	+	5.48900e19i	−0.240413	+	0.0804794i
$403$	3.51576e20			0.505334
$404$	7.85216e20	+	1.04140e21i	1.10647	+	1.46746i
$405$		−	1.27241e21i		−	1.75787i
$406$	5.81745e20	−	1.94742e20i	0.787997	−	0.263785i
$407$		−	8.36129e20i		−	1.11050i
$408$	−9.42055e20	+	1.37196e21i	−1.22686	+	1.78673i
$409$	1.09893e21			1.40341			0.701706	−	0.712467i	$-0.252422\pi$
$409$	1.09893e21			1.40341			0.701706	+	0.712467i	$0.252422\pi$
$410$	8.17517e18	+	2.44214e19i	0.0102382	+	0.0305844i
$411$	−1.34404e21			−1.65074
$412$	−2.75380e20	−	3.65225e20i	−0.331708	−	0.439929i
$413$			1.77879e21i			2.10148i
$414$	−9.38646e19	−	2.80399e20i	−0.108767	−	0.324918i
$415$			9.19684e20i			1.04533i
$416$	−4.00818e20	+	1.77869e19i	−0.446890	+	0.0198314i
$417$	4.78815e20			0.523696
$418$	−7.74851e19	+	2.59384e19i	−0.0831395	+	0.0278313i
$419$	−5.87615e19			−0.0618559			−0.0309279	−	0.999522i	$-0.509846\pi$
$419$	−5.87615e19			−0.0618559			−0.0309279	+	0.999522i	$0.509846\pi$
$420$	1.91310e21	−	1.44248e21i	1.97580	−	1.48976i
$421$			8.68806e20i			0.880372i	0.897907	+	0.440186i	$0.145087\pi$
$421$			8.68806e20i			0.880372i	−0.897907	+	0.440186i	$0.854913\pi$
$422$	−4.41483e19	+	1.47788e19i	−0.0438949	+	0.0146940i
$423$			1.77280e20i			0.172957i
$424$	1.20800e20	+	8.29472e19i	0.115648	+	0.0794099i
$425$	2.04480e21			1.92105
$426$	−3.75757e20	−	1.12249e21i	−0.346442	−	1.03491i
$427$	−7.10687e19			−0.0643065
$428$	−6.01993e20	+	4.53904e20i	−0.534615	+	0.403101i
$429$		−	4.22562e20i		−	0.368326i
$430$	−1.03820e20	−	3.10138e20i	−0.0888246	−	0.265343i
$431$		−	1.92605e20i		−	0.161752i	−0.996724	−	0.0808758i	$-0.974228\pi$
$431$		−	1.92605e20i		−	0.161752i	0.996724	−	0.0808758i	$-0.0257717\pi$
$432$	2.47307e20	−	8.64326e20i	0.203876	−	0.712537i
$433$	−2.34786e20			−0.190006			−0.0950032	−	0.995477i	$-0.530286\pi$
$433$	−2.34786e20			−0.190006			−0.0950032	+	0.995477i	$0.530286\pi$
$434$	−2.00086e21	+	6.69796e20i	−1.58964	+	0.532138i
$435$	1.19720e21			0.933796
$436$	−9.23990e20	−	1.22545e21i	−0.707579	−	0.938432i
$437$			1.55009e20i			0.116548i
$438$	−2.21346e21	+	7.40963e20i	−1.63410	+	0.547021i
$439$			2.18515e21i			1.58404i	0.610497	+	0.792018i	$0.290970\pi$
$439$			2.18515e21i			1.58404i	−0.610497	+	0.792018i	$0.709030\pi$
$440$	−1.16418e21	−	7.99385e20i	−0.828704	−	0.569030i
$441$	−6.29109e20			−0.439761
$442$	3.83623e20	+	1.14598e21i	0.263346	+	0.786685i
$443$	1.07184e21			0.722602			0.361301	−	0.932449i	$-0.382333\pi$
$443$	1.07184e21			0.722602			0.361301	+	0.932449i	$0.382333\pi$
$444$	1.67497e21	+	2.22144e21i	1.10903	+	1.47086i
$445$		−	1.30634e21i		−	0.849523i
$446$	−3.84481e20	−	1.14855e21i	−0.245582	−	0.733619i
$447$		−	1.52672e21i		−	0.957854i
$448$	2.24722e21	−	8.64836e20i	1.38491	−	0.532978i
$449$	−1.09657e21			−0.663842			−0.331921	−	0.943307i	$-0.607697\pi$
$449$	−1.09657e21			−0.663842			−0.331921	+	0.943307i	$0.607697\pi$
$450$	6.04279e20	−	2.02285e20i	0.359367	−	0.120299i
$451$	−2.72587e19			−0.0159255
$452$	−9.21671e20	+	6.94942e20i	−0.529016	+	0.398879i
$453$			7.25048e20i			0.408866i
$454$	2.45745e21	−	8.22641e20i	1.36156	−	0.455789i
$455$		−	1.73982e21i		−	0.947140i
$456$	1.53902e20	−	2.24135e20i	0.0823240	−	0.119892i
$457$	−6.92574e20			−0.364030			−0.182015	−	0.983296i	$-0.558262\pi$
$457$	−6.92574e20			−0.364030			−0.182015	+	0.983296i	$0.558262\pi$
$458$	−1.00896e21	−	3.01403e21i	−0.521135	−	1.55677i
$459$	−2.70790e21			−1.37446
$460$	−2.13909e21	+	1.61288e21i	−1.06701	+	0.804525i
$461$		−	1.76325e21i		−	0.864384i	−0.901782	−	0.432192i	$-0.857740\pi$
$461$		−	1.76325e21i		−	0.864384i	0.901782	−	0.432192i	$-0.142260\pi$
$462$	8.05034e20	+	2.40485e21i	0.387863	+	1.15865i
$463$			8.88321e20i			0.420651i	0.977631	+	0.210325i	$0.0674524\pi$
$463$			8.88321e20i			0.420651i	−0.977631	+	0.210325i	$0.932548\pi$
$464$	1.15673e21	+	3.30973e20i	0.538381	+	0.154045i
$465$	−4.11765e21			−1.88376
$466$	2.33779e21	−	7.82585e20i	1.05128	−	0.351920i
$467$	2.42168e21			1.07049			0.535244	−	0.844697i	$-0.320220\pi$
$467$	2.42168e21			1.07049			0.535244	+	0.844697i	$0.320220\pi$
$468$	2.26737e20	+	3.00711e20i	0.0985270	+	0.130672i
$469$		−	7.53558e20i		−	0.321910i
$470$	1.52311e21	−	5.09866e20i	0.639658	−	0.214128i
$471$			5.41256e20i			0.223478i
$472$	−1.97472e21	+	2.87588e21i	−0.801624	+	1.16744i
$473$	3.46170e20			0.138166
$474$	1.23948e21	+	3.70267e21i	0.486423	+	1.45308i
$475$	−3.34056e20			−0.128905
$476$	−4.36649e21	−	5.79108e21i	−1.65682	−	2.19737i
$477$		−	1.37551e20i		−	0.0513236i
$478$	9.52597e20	+	2.84566e21i	0.349531	+	1.04414i
$479$		−	2.90885e21i		−	1.04963i	−0.851215	−	0.524817i	$-0.824134\pi$
$479$		−	2.90885e21i		−	1.04963i	0.851215	−	0.524817i	$-0.175866\pi$
$480$	4.69438e21	−	2.08320e20i	1.66590	−	0.0739267i
$481$	2.02024e21			0.705087
$482$	2.18274e21	−	7.30680e20i	0.749247	−	0.250813i
$483$	4.81092e21			1.62424
$484$	−1.21096e21	+	9.13063e20i	−0.402129	+	0.303206i
$485$			5.87588e21i			1.91928i
$486$	−2.06215e21	+	6.90312e20i	−0.662566	+	0.221797i
$487$			3.94387e21i			1.24650i	0.782024	+	0.623249i	$0.214187\pi$
$487$			3.94387e21i			1.24650i	−0.782024	+	0.623249i	$0.785813\pi$
$488$	−1.14901e20	−	7.88967e19i	−0.0357244	−	0.0245301i
$489$	−1.79794e21			−0.549926
$490$	1.80935e21	+	5.40500e21i	0.544444	+	1.62640i
$491$	−6.54682e21			−1.93811			−0.969056	−	0.246842i	$-0.920607\pi$
$491$	−6.54682e21			−1.93811			−0.969056	+	0.246842i	$0.920607\pi$
$492$	7.24214e19	−	5.46059e19i	0.0210934	−	0.0159044i
$493$		−	3.62401e21i		−	1.03852i
$494$	−6.26720e19	−	1.87218e20i	−0.0176709	−	0.0527876i
$495$			1.32562e21i			0.367771i
$496$	−3.97848e21	−	1.13835e21i	−1.08608	−	0.310758i
$497$	5.15859e21			1.38573
$498$	3.07150e21	−	1.02820e21i	0.811926	−	0.271796i
$499$	5.84564e21			1.52064			0.760322	−	0.649546i	$-0.225041\pi$
$499$	5.84564e21			1.52064			0.760322	+	0.649546i	$0.225041\pi$
$500$	−1.20337e20	−	1.59598e20i	−0.0308062	−	0.0408570i
$501$		−	7.60527e21i		−	1.91608i
$502$	2.04955e20	−	6.86095e19i	0.0508192	−	0.0170120i
$503$			5.16336e21i			1.26005i	0.776574	+	0.630026i	$0.216956\pi$
$503$			5.16336e21i			1.26005i	−0.776574	+	0.630026i	$0.783044\pi$
$504$	−1.86328e21	−	1.27942e21i	−0.447542	−	0.307305i
$505$	−1.10921e22			−2.62231
$506$	−9.00134e20	−	2.68894e21i	−0.209461	−	0.625715i
$507$	−4.08130e21			−0.934834
$508$	−5.65552e19	−	7.50067e19i	−0.0127516	−	0.0169118i
$509$			1.25680e21i			0.278948i	0.990226	+	0.139474i	$0.0445412\pi$
$509$			1.25680e21i			0.278948i	−0.990226	+	0.139474i	$0.955459\pi$
$510$	−4.49299e21	−	1.34218e22i	−0.981689	−	2.93257i
$511$		−	1.01723e22i		−	2.18803i
$512$	4.59330e21	+	1.09651e21i	0.972669	+	0.232195i
$513$	4.42387e20			0.0922281
$514$	2.73200e21	−	9.14548e20i	0.560758	−	0.187716i
$515$	3.89009e21			0.786144
$516$	−9.19710e20	+	6.93463e20i	−0.183001	+	0.137983i
$517$			1.70006e21i			0.333074i
$518$	−1.14974e22	+	3.84881e21i	−2.21800	+	0.742486i
$519$		−	3.52805e21i		−	0.670186i
$520$	1.93146e21	−	2.81288e21i	0.361293	−	0.526167i
$521$	4.04183e21			0.744520			0.372260	−	0.928129i	$-0.378583\pi$
$521$	4.04183e21			0.744520			0.372260	+	0.928129i	$0.378583\pi$
$522$	−3.58511e20	−	1.07097e21i	−0.0650337	−	0.194273i
$523$	5.82231e21			1.04012			0.520058	−	0.854131i	$-0.325910\pi$
$523$	5.82231e21			1.04012			0.520058	+	0.854131i	$0.325910\pi$
$524$	−1.69592e21	+	1.27873e21i	−0.298371	+	0.224972i
$525$			1.03679e22i			1.79645i
$526$	1.71886e21	+	5.13470e21i	0.293329	+	0.876253i
$527$			1.24644e22i			2.09502i
$528$	−1.36819e21	+	4.78177e21i	−0.226504	+	0.791621i
$529$	7.53376e20			0.122848
$530$	−1.18177e21	+	3.95604e20i	−0.189814	+	0.0635409i
$531$	3.27468e21			0.518099
$532$	7.13347e20	+	9.46082e20i	0.111175	+	0.147447i
$533$		−	6.58621e19i		−	0.0101115i
$534$	−4.36283e21	+	1.46047e21i	−0.659839	+	0.220884i
$535$		−	6.41196e21i		−	0.955345i
$536$	8.36560e20	−	1.21832e21i	0.122794	−	0.178831i
$537$	1.12929e22			1.63309
$538$	−2.81700e21	−	8.41513e21i	−0.401355	−	1.19895i
$539$	−6.03296e21			−0.846878
$540$	4.60306e21	+	6.10484e21i	0.636644	+	0.844353i
$541$			3.05007e21i			0.415654i	0.978166	+	0.207827i	$0.0666391\pi$
$541$			3.05007e21i			0.415654i	−0.978166	+	0.207827i	$0.933361\pi$
$542$	1.45858e21	+	4.35718e21i	0.195856	+	0.585074i
$543$			5.06700e21i			0.670428i
$544$	−6.30600e20	−	1.42102e22i	−0.0822172	−	1.85272i
$545$	1.30525e22			1.67696
$546$	−5.81056e21	+	1.94511e21i	−0.735660	+	0.246265i
$547$	−9.94165e21			−1.24039			−0.620197	−	0.784446i	$-0.712947\pi$
$547$	−9.94165e21			−1.24039			−0.620197	+	0.784446i	$0.712947\pi$
$548$	9.17225e21	−	6.91590e21i	1.12780	−	0.850363i
$549$			1.30834e20i			0.0158541i
$550$	5.79486e21	−	1.93985e21i	0.692056	−	0.231669i
$551$			5.92049e20i			0.0696859i
$552$	7.77809e21	+	5.34083e21i	0.902319	+	0.619578i
$553$	−1.70163e22			−1.94564
$554$	1.53769e21	+	4.59350e21i	0.173297	+	0.517685i
$555$	−2.36610e22			−2.62839
$556$	−3.26762e21	+	2.46379e21i	−0.357794	+	0.269778i
$557$		−	1.20851e22i		−	1.30440i	−0.758048	−	0.652199i	$-0.773847\pi$
$557$		−	1.20851e22i		−	1.30440i	0.758048	−	0.652199i	$-0.226153\pi$
$558$	1.23306e21	+	3.68349e21i	0.131193	+	0.391910i
$559$			8.36411e20i			0.0877254i
$560$	−5.63329e21	+	1.96881e22i	−0.582449	+	2.03563i
$561$	1.49811e22			1.52701
$562$	7.27652e21	−	2.43585e21i	0.731195	−	0.244771i
$563$	1.12872e22			1.11820			0.559100	−	0.829100i	$-0.311147\pi$
$563$	1.12872e22			1.11820			0.559100	+	0.829100i	$0.311147\pi$
$564$	−3.40564e21	−	4.51675e21i	−0.332634	−	0.441158i
$565$		−	9.81692e21i		−	0.945339i
$566$	7.22810e21	−	2.41964e21i	0.686266	−	0.229731i
$567$		−	1.95294e22i		−	1.82820i
$568$	8.34018e21	+	5.72679e21i	0.769820	+	0.528597i
$569$	5.86823e21			0.534083			0.267042	−	0.963685i	$-0.413954\pi$
$569$	5.86823e21			0.534083			0.267042	+	0.963685i	$0.413954\pi$
$570$	7.34014e20	+	2.19270e21i	0.0658727	+	0.196779i
$571$	−1.37932e22			−1.22061			−0.610304	−	0.792168i	$-0.708953\pi$
$571$	−1.37932e22			−1.22061			−0.610304	+	0.792168i	$0.708953\pi$
$572$	2.17434e21	+	2.88373e21i	0.189740	+	0.251644i
$573$			1.17651e22i			1.01242i
$574$	1.25475e20	+	3.74829e20i	0.0106479	+	0.0318081i
$575$		−	1.15926e22i		−	0.970151i
$576$	−1.59213e21	−	4.13703e21i	−0.131401	−	0.341435i
$577$	−2.09216e22			−1.70290			−0.851449	−	0.524437i	$-0.824276\pi$
$577$	−2.09216e22			−1.70290			−0.851449	+	0.524437i	$0.824276\pi$
$578$	−2.88157e22	+	9.64617e21i	−2.31316	+	0.774341i
$579$	−5.81379e20			−0.0460289
$580$	−8.17015e21	+	6.16031e21i	−0.637978	+	0.481037i
$581$			1.41156e22i			1.08716i
$582$	1.96239e22	−	6.56918e21i	1.49074	−	0.499031i
$583$		−	1.31907e21i		−	0.0988373i
$584$	1.12928e22	−	1.64462e22i	0.834638	−	1.21552i
$585$	−3.20294e21			−0.233508
$586$	2.61515e20	+	7.81216e20i	0.0188068	+	0.0561811i
$587$	−1.05244e22			−0.746608			−0.373304	−	0.927709i	$-0.621775\pi$
$587$	−1.05244e22			−0.746608			−0.373304	+	0.927709i	$0.621775\pi$
$588$	1.60285e22	−	1.20855e22i	1.12169	−	0.845757i
$589$		−	2.03630e21i		−	0.140579i
$590$	−9.41815e21	−	2.81345e22i	−0.641430	−	1.91612i
$591$			7.46504e21i			0.501571i
$592$	−2.28613e22	−	6.54124e21i	−1.51540	−	0.433597i
$593$	−1.40079e22			−0.916085			−0.458042	−	0.888930i	$-0.651449\pi$
$593$	−1.40079e22			−0.916085			−0.458042	+	0.888930i	$0.651449\pi$
$594$	−7.67407e21	+	2.56893e21i	−0.495147	+	0.165753i
$595$	6.16821e22			3.92666
$596$	7.85590e21	+	1.04189e22i	0.493430	+	0.654415i
$597$		−	6.80173e21i		−	0.421526i
$598$	6.49697e21	−	2.17489e21i	0.397284	−	0.132993i
$599$			1.63288e22i			0.985233i	0.870247	+	0.492616i	$0.163959\pi$
$599$			1.63288e22i			0.985233i	−0.870247	+	0.492616i	$0.836041\pi$
$600$	−1.15099e22	+	1.67623e22i	−0.685268	+	0.997986i
$601$	−9.56729e20			−0.0562074			−0.0281037	−	0.999605i	$-0.508947\pi$
$601$	−9.56729e20			−0.0562074			−0.0281037	+	0.999605i	$0.508947\pi$
$602$	−1.59347e21	−	4.76011e21i	−0.0923786	−	0.275959i
$603$	−1.38727e21			−0.0793636
$604$	−3.73081e21	−	4.94801e21i	−0.210624	−	0.279341i
$605$		−	1.28981e22i		−	0.718595i
$606$	1.24009e22	+	3.70449e22i	0.681825	+	2.03679i
$607$			3.42389e22i			1.85785i	0.370273	+	0.928923i	$0.379264\pi$
$607$			3.42389e22i			1.85785i	−0.370273	+	0.928923i	$0.620736\pi$
$608$	1.03020e20	+	2.32151e21i	0.00551689	+	0.124320i
$609$	1.83750e22			0.971158
$610$	1.12407e21	−	3.76286e20i	0.0586345	−	0.0196281i
$611$	−4.10767e21			−0.211478
$612$	−1.06611e22	+	8.03851e21i	−0.541741	+	0.408474i
$613$		−	3.27644e22i		−	1.64330i	−0.569990	−	0.821652i	$-0.693053\pi$
$613$		−	3.27644e22i		−	1.64330i	0.569990	−	0.821652i	$-0.306947\pi$
$614$	−1.41281e22	+	4.72942e21i	−0.699416	+	0.234132i
$615$			7.71376e20i			0.0376934i
$616$	−1.78683e22	−	1.22693e22i	−0.861861	−	0.591797i
$617$	−2.90372e21			−0.138253			−0.0691264	−	0.997608i	$-0.522021\pi$
$617$	−2.90372e21			−0.138253			−0.0691264	+	0.997608i	$0.522021\pi$
$618$	−4.34909e21	−	1.29919e22i	−0.204405	−	0.610611i
$619$	2.23150e22			1.03531			0.517657	−	0.855588i	$-0.326804\pi$
$619$	2.23150e22			1.03531			0.517657	+	0.855588i	$0.326804\pi$
$620$	2.81005e22	−	2.11878e22i	1.28700	−	0.970404i
$621$			1.53520e22i			0.694117i
$622$	8.47233e21	+	2.53091e22i	0.378163	+	1.12968i
$623$		−	2.00501e22i		−	0.883513i
$624$	−1.15536e22	−	3.30581e21i	−0.502622	−	0.143814i
$625$	−2.24181e22			−0.962852
$626$	3.89280e22	−	1.30313e22i	1.65070	−	0.552578i
$627$	−2.44745e21			−0.102464
$628$	−2.78509e21	−	3.69374e21i	−0.115123	−	0.152683i
$629$			7.16237e22i			2.92315i
$630$	1.82283e22	−	6.10200e21i	0.734551	−	0.245894i
$631$			2.79894e22i			1.11368i	0.830621	+	0.556838i	$0.187986\pi$
$631$			2.79894e22i			1.11368i	−0.830621	+	0.556838i	$0.812014\pi$
$632$	−2.75112e22	−	1.88906e22i	−1.08087	−	0.742179i
$633$	−1.39447e21			−0.0540977
$634$	9.23672e20	+	2.75925e21i	0.0353837	+	0.105701i
$635$	7.98913e20			0.0302211
$636$	2.64243e21	+	3.50454e21i	0.0987066	+	0.130910i
$637$		−	1.45767e22i		−	0.537706i
$638$	−3.43801e21	−	1.02703e22i	−0.125240	−	0.374124i
$639$		−	9.49673e21i		−	0.341639i
$640$	−3.09643e22	+	2.55771e22i	−1.10007	+	0.908680i
$641$	−2.28901e21			−0.0803125			−0.0401563	−	0.999193i	$-0.512786\pi$
$641$	−2.28901e21			−0.0803125			−0.0401563	+	0.999193i	$0.512786\pi$
$642$	−2.14143e22	+	7.16852e21i	−0.742033	+	0.248399i
$643$	3.53144e22			1.20855			0.604274	−	0.796777i	$-0.293463\pi$
$643$	3.53144e22			1.20855			0.604274	+	0.796777i	$0.293463\pi$
$644$	−3.28316e22	+	2.47551e22i	−1.10970	+	0.836714i
$645$		−	9.79603e21i		−	0.327019i
$646$	6.63745e21	−	2.22191e21i	0.218847	−	0.0732600i
$647$		−	5.78292e22i		−	1.88327i	−0.336634	−	0.941636i	$-0.609288\pi$
$647$		−	5.78292e22i		−	1.88327i	0.336634	−	0.941636i	$-0.390712\pi$
$648$	2.16805e22	−	3.15743e22i	0.697379	−	1.01562i
$649$	3.14032e22			0.997739
$650$	4.68704e21	+	1.40014e22i	0.147093	+	0.439406i
$651$	−6.31992e22			−1.95913
$652$	1.22698e22	−	9.25149e21i	0.375715	−	0.283290i
$653$		−	4.75473e22i		−	1.43820i	−0.694904	−	0.719102i	$-0.744553\pi$
$653$		−	4.75473e22i		−	1.43820i	0.694904	−	0.719102i	$-0.255447\pi$
$654$	−1.45926e22	−	4.35920e22i	−0.436024	−	1.30252i
$655$		−	1.80636e22i		−	0.533181i
$656$	−2.13252e20	+	7.45303e20i	−0.00621815	+	0.0217321i
$657$	−1.87268e22			−0.539437
$658$	2.33772e22	−	7.82562e21i	0.665251	−	0.222695i
$659$	1.20594e22			0.339035			0.169517	−	0.985527i	$-0.445779\pi$
$659$	1.20594e22			0.339035			0.169517	+	0.985527i	$0.445779\pi$
$660$	−2.54658e22	−	3.37742e22i	−0.707304	−	0.938067i
$661$			1.63382e22i			0.448326i	0.974552	+	0.224163i	$0.0719648\pi$
$661$			1.63382e22i			0.448326i	−0.974552	+	0.224163i	$0.928035\pi$
$662$	−1.05442e21	+	3.52973e20i	−0.0285859	+	0.00956924i
$663$			3.61971e22i			0.969540i
$664$	−1.56704e22	+	2.28216e22i	−0.414702	+	0.603950i
$665$	−1.00769e22			−0.263484
$666$	7.08549e21	+	2.11663e22i	0.183053	+	0.546827i
$667$	−2.05457e22			−0.524462
$668$	3.91337e22	+	5.19013e22i	0.987050	+	1.30908i
$669$		−	3.62781e22i		−	0.904140i
$670$	3.98985e21	+	1.19187e22i	0.0982557	+	0.293516i
$671$			1.25466e21i			0.0305314i
$672$	7.20510e22	−	3.19737e21i	1.73255	−	0.0768845i
$673$	−6.92380e22			−1.64522			−0.822610	−	0.568607i	$-0.807483\pi$
$673$	−6.92380e22			−1.64522			−0.822610	+	0.568607i	$0.807483\pi$
$674$	−1.30795e22	+	4.37842e21i	−0.307123	+	0.102811i
$675$	−3.30847e22			−0.767710
$676$	2.78524e22	−	2.10007e22i	0.638688	−	0.481572i
$677$		−	5.05127e22i		−	1.14470i	−0.820010	−	0.572350i	$-0.806032\pi$
$677$		−	5.05127e22i		−	1.14470i	0.820010	−	0.572350i	$-0.193968\pi$
$678$	−3.27859e22	+	1.09752e22i	−0.734261	+	0.245797i
$679$			9.01851e22i			1.99607i
$680$	9.97250e22	+	6.84762e22i	2.18139	+	1.49785i
$681$	7.76211e22			1.67804
$682$	1.18247e22	+	3.53236e22i	0.252648	+	0.754727i
$683$	−6.89980e22			−1.45704			−0.728519	−	0.685025i	$-0.759791\pi$
$683$	−6.89980e22			−1.45704			−0.728519	+	0.685025i	$0.759791\pi$
$684$	1.74169e21	−	1.31324e21i	0.0363516	−	0.0274092i
$685$			9.76957e22i			2.01535i
$686$	4.66760e21	+	1.39434e22i	0.0951701	+	0.284299i
$687$		−	9.52014e22i		−	1.91862i
$688$	2.70817e21	−	9.46493e21i	0.0539472	−	0.188543i
$689$	3.18713e21			0.0627546
$690$	−7.60924e22	+	2.54723e22i	−1.48098	+	0.495764i
$691$	1.01417e23			1.95114			0.975569	−	0.219694i	$-0.0705059\pi$
$691$	1.01417e23			1.95114			0.975569	+	0.219694i	$0.0705059\pi$
$692$	1.81539e22	+	2.40768e22i	0.345241	+	0.457878i
$693$			2.03461e22i			0.382486i
$694$	−2.45214e20	+	8.20863e19i	−0.00455690	+	0.00152544i
$695$		−	3.48041e22i		−	0.639370i
$696$	2.97080e22	+	2.03990e22i	0.539510	+	0.370454i
$697$	2.33501e21			0.0419205
$698$	−1.37112e22	−	4.09590e22i	−0.243350	−	0.726952i
$699$	7.38415e22			1.29564
$700$	−5.33490e22	−	7.07544e22i	−0.925426	−	1.22735i
$701$			3.43490e22i			0.589075i	0.955640	+	0.294537i	$0.0951655\pi$
$701$			3.43490e22i			0.589075i	−0.955640	+	0.294537i	$0.904834\pi$
$702$	−6.20700e21	−	1.85420e22i	−0.105241	−	0.314383i
$703$		−	1.17011e22i		−	0.196148i
$704$	−1.52680e22	−	3.96729e22i	−0.253047	−	0.657525i
$705$	4.81089e22			0.788339
$706$	6.89760e22	−	2.30900e22i	1.11753	−	0.374099i
$707$	−1.70246e23			−2.72723
$708$	−8.34326e22	+	6.29083e22i	−1.32151	+	0.996419i
$709$		−	5.45976e22i		−	0.855074i	−0.903998	−	0.427537i	$-0.859381\pi$
$709$		−	5.45976e22i		−	0.855074i	0.903998	−	0.427537i	$-0.140619\pi$
$710$	−8.15914e22	+	2.73130e22i	−1.26351	+	0.422964i
$711$			3.13262e22i			0.479679i
$712$	2.22586e22	−	3.24162e22i	0.337022	−	0.490820i
$713$	7.06650e22			1.05801
$714$	−6.89600e22	−	2.06002e23i	−1.02097	−	3.04990i
$715$	−3.07152e22			−0.449682
$716$	−7.70672e22	+	5.81088e22i	−1.11575	+	0.841275i
$717$			8.98832e22i			1.28684i
$718$	−1.66279e22	−	4.96719e22i	−0.235419	−	0.703260i
$719$			3.00804e22i			0.421165i	0.977576	+	0.210583i	$0.0675361\pi$
$719$			3.00804e22i			0.421165i	−0.977576	+	0.210583i	$0.932464\pi$
$720$	3.62449e22	+	1.03706e22i	0.501865	+	0.143597i
$721$	5.97065e22			0.817598
$722$	6.89375e22	−	2.30771e22i	0.933593	−	0.312524i
$723$	6.89440e22			0.923400
$724$	−2.60728e22	−	3.45792e22i	−0.345365	−	0.458043i
$725$		−	4.42775e22i		−	0.580068i
$726$	−4.30765e22	+	1.44200e22i	−0.558145	+	0.186841i
$727$		−	1.19550e23i		−	1.53206i	−0.642806	−	0.766029i	$-0.722230\pi$
$727$		−	1.19550e23i		−	1.53206i	0.642806	−	0.766029i	$-0.277770\pi$
$728$	2.96448e22	−	4.31730e22i	0.375748	−	0.547220i
$729$	3.31374e22			0.415431
$730$	5.38592e22	+	1.60892e23i	0.667847	+	1.99504i
$731$	−2.96533e22			−0.363692
$732$	−2.51339e21	−	3.33340e21i	−0.0304910	−	0.0404389i
$733$			3.41068e22i			0.409270i	0.978838	+	0.204635i	$0.0656007\pi$
$733$			3.41068e22i			0.409270i	−0.978838	+	0.204635i	$0.934399\pi$
$734$	8.20149e21	+	2.45000e22i	0.0973474	+	0.290803i
$735$			1.70723e23i			2.00444i
$736$	−8.05625e22	+	3.57508e21i	−0.935643	+	0.0415206i
$737$	−1.33035e22			−0.152836
$738$	6.90043e20	−	2.30995e20i	0.00784197	−	0.00262513i
$739$	−4.42548e22			−0.497513			−0.248757	−	0.968566i	$-0.580022\pi$
$739$	−4.42548e22			−0.497513			−0.248757	+	0.968566i	$0.580022\pi$
$740$	1.61472e23	−	1.21750e23i	1.79574	−	1.35399i
$741$		−	5.91348e21i		−	0.0650575i
$742$	−1.81383e22	+	6.07187e21i	−0.197408	+	0.0660833i
$743$		−	6.24045e21i		−	0.0671901i	−0.999436	−	0.0335951i	$-0.989304\pi$
$743$		−	6.24045e21i		−	0.0671901i	0.999436	−	0.0335951i	$-0.0106957\pi$
$744$	−1.02178e23	−	7.01604e22i	−1.08836	−	0.747324i
$745$	−1.10974e23			−1.16942
$746$	5.26880e22	+	1.57393e23i	0.549289	+	1.64087i
$747$	2.59863e22			0.268027
$748$	−1.02237e23	+	7.70869e22i	−1.04327	+	0.786625i
$749$		−	9.84131e22i		−	0.993570i
$750$	−1.90048e21	−	5.67725e21i	−0.0189834	−	0.0567085i
$751$		−	3.46827e22i		−	0.342762i	−0.985205	−	0.171381i	$-0.945177\pi$
$751$		−	3.46827e22i		−	0.342762i	0.985205	−	0.171381i	$-0.0548229\pi$
$752$	4.64829e22	+	1.33000e22i	0.454517	+	0.130050i
$753$	6.47371e21			0.0626316
$754$	2.48148e22	−	8.30687e21i	0.237542	−	0.0795182i
$755$	5.27024e22			0.499177
$756$	7.06495e22	+	9.36993e22i	0.662117	+	0.878137i
$757$			3.91438e22i			0.362991i	0.983392	+	0.181495i	$0.0580938\pi$
$757$			3.91438e22i			0.362991i	−0.983392	+	0.181495i	$0.941906\pi$
$758$	−1.09192e21	+	3.65524e20i	−0.0100193	+	0.00335400i
$759$		−	8.49330e22i		−	0.771156i
$760$	−1.62919e22	−	1.11869e22i	−0.146374	−	0.100508i
$761$	−7.00706e22			−0.622958			−0.311479	−	0.950253i	$-0.600824\pi$
$761$	−7.00706e22			−0.622958			−0.311479	+	0.950253i	$0.600824\pi$
$762$	−8.93178e20	−	2.66816e21i	−0.00785775	−	0.0234732i
$763$	2.00335e23			1.74405
$764$	−6.05386e22	−	8.02898e22i	−0.521538	−	0.691693i
$765$		−	1.13554e23i		−	0.968079i
$766$	−4.49781e22	−	1.34362e23i	−0.379464	−	1.13356i
$767$			7.58760e22i			0.633492i
$768$	1.20039e23	+	7.48179e22i	0.991816	+	0.618181i
$769$	−3.23281e22			−0.264344			−0.132172	−	0.991227i	$-0.542195\pi$
$769$	−3.23281e22			−0.264344			−0.132172	+	0.991227i	$0.542195\pi$
$770$	1.74804e23	−	5.85164e22i	1.41457	−	0.473534i
$771$	8.62930e22			0.691100
$772$	3.96756e21	−	2.99154e21i	0.0314474	−	0.0237114i
$773$			1.25542e23i			0.984809i	0.870366	+	0.492405i	$0.163882\pi$
$773$			1.25542e23i			0.984809i	−0.870366	+	0.492405i	$0.836118\pi$
$774$	−8.76316e21	+	2.93350e21i	−0.0680351	+	0.0227750i
$775$			1.52288e23i			1.17018i
$776$	−1.00119e23	+	1.45808e23i	−0.761416	+	1.10888i
$777$	−3.63158e23			−2.73355
$778$	−1.22884e21	−	3.67088e21i	−0.00915503	−	0.0273485i
$779$	−3.81468e20			−0.00281292
$780$	8.16047e22	−	6.15301e22i	0.595605	−	0.449087i
$781$		−	9.10708e22i		−	0.657917i
$782$	7.71064e22	+	2.30337e23i	0.551361	+	1.64706i
$783$			5.86362e22i			0.415022i
$784$	−4.71973e22	+	1.64952e23i	−0.330666	+	1.15566i
$785$	3.93428e22			0.272840
$786$	−6.03279e22	+	2.01950e22i	−0.414131	+	0.138632i
$787$	1.23669e22			0.0840353			0.0420176	−	0.999117i	$-0.486621\pi$
$787$	1.23669e22			0.0840353			0.0420176	+	0.999117i	$0.486621\pi$
$788$	−3.84121e22	−	5.09443e22i	−0.258380	−	0.342678i
$789$			1.62185e23i			1.07993i
$790$	2.69140e23	−	9.00957e22i	1.77403	−	0.593864i
$791$		−	1.50674e23i		−	0.983163i
$792$	−2.25872e22	+	3.28947e22i	−0.145902	+	0.212483i
$793$	−3.03149e21			−0.0193852
$794$	−5.25515e22	−	1.56985e23i	−0.332676	−	0.993791i
$795$	−3.73276e22			−0.233934
$796$	3.49990e22	+	4.64177e22i	0.217146	+	0.287991i
$797$		−	2.33288e23i		−	1.43294i	−0.697620	−	0.716468i	$-0.745758\pi$
$797$		−	2.33288e23i		−	1.43294i	0.697620	−	0.716468i	$-0.254242\pi$
$798$	1.12659e22	+	3.36543e22i	0.0685083	+	0.204653i
$799$		−	1.45629e23i		−	0.876747i
$800$	−7.70456e21	−	1.73618e23i	−0.0459227	−	1.03484i
$801$	−3.69114e22			−0.217821
$802$	−5.73786e22	+	1.92077e22i	−0.335239	+	0.112223i
$803$	−1.79585e23			−1.03883
$804$	3.53449e22	−	2.66501e22i	0.202431	−	0.152634i
$805$		−	3.49696e23i		−	1.98301i
$806$	−8.53483e22	+	2.85707e22i	−0.479197	+	0.160413i
$807$		−	2.65801e23i		−	1.47764i
$808$	−2.75247e23	−	1.88999e23i	−1.51507	−	1.04032i
$809$	1.68226e22			0.0916865			0.0458433	−	0.998949i	$-0.485403\pi$
$809$	1.68226e22			0.0916865			0.0458433	+	0.998949i	$0.485403\pi$
$810$	1.03402e23	+	3.08889e23i	0.558017	+	1.66695i
$811$	−2.04733e22			−0.109401			−0.0547004	−	0.998503i	$-0.517420\pi$
$811$	−2.04733e22			−0.109401			−0.0547004	+	0.998503i	$0.517420\pi$
$812$	−1.25398e23	+	9.45507e22i	−0.663505	+	0.500284i
$813$			1.37626e23i			0.721068i
$814$	6.79477e22	+	2.02978e23i	0.352517	+	1.05306i
$815$			1.30689e23i			0.671394i
$816$	1.17201e23	−	4.09611e23i	0.596224	−	2.08377i
$817$	4.84442e21			0.0244043
$818$	−2.66776e23	+	8.93045e22i	−1.33082	+	0.445499i
$819$	−4.91599e22			−0.242851
$820$	−3.96919e21	−	5.26417e21i	−0.0194174	−	0.0257525i
$821$			2.90138e23i			1.40559i	0.711392	+	0.702795i	$0.248065\pi$
$821$			2.90138e23i			1.40559i	−0.711392	+	0.702795i	$0.751935\pi$
$822$	3.26278e23	−	1.09223e23i	1.56536	−	0.524010i
$823$			3.39906e23i			1.61495i	0.589900	+	0.807476i	$0.299167\pi$
$823$			3.39906e23i			1.61495i	−0.589900	+	0.807476i	$0.700833\pi$
$824$	9.65310e22	+	6.62831e22i	0.454202	+	0.311878i
$825$	1.83037e23			0.852917
$826$	−1.44553e23	−	4.31819e23i	−0.667094	−	1.99279i
$827$	2.71198e23			1.23949			0.619745	−	0.784803i	$-0.287236\pi$
$827$	2.71198e23			1.23949			0.619745	+	0.784803i	$0.287236\pi$
$828$	4.55730e22	+	6.04415e22i	0.206284	+	0.273585i
$829$			2.18126e23i			0.977848i	0.872326	+	0.488924i	$0.162611\pi$
$829$			2.18126e23i			0.977848i	−0.872326	+	0.488924i	$0.837389\pi$
$830$	−7.47378e22	−	2.23262e23i	−0.331830	−	0.991264i
$831$			1.45090e23i			0.638014i
$832$	9.58569e22	−	3.68903e22i	0.417481	−	0.160667i
$833$	5.16790e23			2.22923
$834$	−1.16237e23	+	3.89108e22i	−0.496610	+	0.166242i
$835$	−5.52812e23			−2.33930
$836$	1.67023e22	−	1.25936e22i	0.0700047	−	0.0527837i
$837$		−	2.01674e23i		−	0.837231i
$838$	1.42649e22	−	4.77524e21i	0.0586566	−	0.0196355i
$839$			9.38513e22i			0.382248i	0.981566	+	0.191124i	$0.0612132\pi$
$839$			9.38513e22i			0.382248i	−0.981566	+	0.191124i	$0.938787\pi$
$840$	−3.47199e23	+	5.05642e23i	−1.40070	+	2.03990i
$841$	1.71773e23			0.686416
$842$	−7.06032e22	−	2.10911e23i	−0.279465	−	0.834837i
$843$	2.29837e23			0.901153
$844$	9.51640e21	−	7.17539e21i	0.0369601	−	0.0278680i
$845$			2.96662e23i			1.14132i
$846$	−1.44066e22	−	4.30364e22i	−0.0549034	−	0.164011i
$847$		−	1.97966e23i		−	0.747347i
$848$	−3.60659e22	−	1.03194e22i	−0.134875	−	0.0385913i
$849$	2.28307e23			0.845781
$850$	−4.96393e23	+	1.66170e23i	−1.82169	+	0.609819i
$851$	4.06058e23			1.47622
$852$	1.82437e23	+	2.41958e23i	0.657047	+	0.871412i
$853$			1.61571e23i			0.576462i	0.957561	+	0.288231i	$0.0930670\pi$
$853$			1.61571e23i			0.576462i	−0.957561	+	0.288231i	$0.906933\pi$
$854$	1.72526e22	−	5.77537e21i	0.0609805	−	0.0204135i
$855$			1.85512e22i			0.0649594i
$856$	1.09253e23	−	1.59110e23i	0.379004	−	0.551960i
$857$	−3.29920e23			−1.13387			−0.566933	−	0.823764i	$-0.691870\pi$
$857$	−3.29920e23			−1.13387			−0.566933	+	0.823764i	$0.691870\pi$
$858$	3.43394e22	+	1.02581e23i	0.116921	+	0.349276i
$859$	3.82694e23			1.29094			0.645470	−	0.763785i	$-0.276661\pi$
$859$	3.82694e23			1.29094			0.645470	+	0.763785i	$0.276661\pi$
$860$	5.04065e22	+	6.68520e22i	0.168461	+	0.223422i
$861$			1.18394e22i			0.0392015i
$862$	1.56519e22	+	4.67565e22i	0.0513464	+	0.153385i
$863$		−	4.07008e23i		−	1.32287i	−0.750003	−	0.661435i	$-0.769948\pi$
$863$		−	4.07008e23i		−	1.32287i	0.750003	−	0.661435i	$-0.230052\pi$
$864$	1.02031e22	+	2.29920e23i	0.0328565	+	0.740402i
$865$	−2.56447e23			−0.818217
$866$	5.69964e22	−	1.90798e22i	0.180179	−	0.0603156i
$867$	−9.10173e23			−2.85083
$868$	4.31296e23	−	3.25198e23i	1.33850	−	1.00923i
$869$			3.00409e23i			0.923751i
$870$	−2.90631e23	+	9.72899e22i	−0.885498	+	0.296424i
$871$		−	3.21436e22i		−	0.0970398i
$872$	3.23893e23	+	2.22401e23i	0.968878	+	0.665280i
$873$	1.66027e23			0.492113
$874$	−1.25968e22	−	3.76299e22i	−0.0369971	−	0.110520i
$875$	2.60908e22			0.0759317
$876$	4.77123e23	−	3.59751e23i	1.37593	−	1.03746i
$877$		−	4.28239e23i		−	1.22374i	−0.790958	−	0.611871i	$-0.790417\pi$
$877$		−	4.28239e23i		−	1.22374i	0.790958	−	0.611871i	$-0.209583\pi$
$878$	−1.77576e23	−	5.30466e23i	−0.502837	−	1.50211i
$879$			2.46755e22i			0.0692397i
$880$	3.47578e23	+	9.94514e22i	0.966474	+	0.276535i
$881$	−3.65451e23			−1.00698			−0.503491	−	0.864000i	$-0.667951\pi$
$881$	−3.65451e23			−1.00698			−0.503491	+	0.864000i	$0.667951\pi$
$882$	1.52722e23	−	5.11243e22i	0.417016	−	0.139598i
$883$	−4.78165e23			−1.29387			−0.646937	−	0.762543i	$-0.723950\pi$
$883$	−4.78165e23			−1.29387			−0.646937	+	0.762543i	$0.723950\pi$
$884$	−1.86256e23	−	2.47023e23i	−0.499450	−	0.662399i
$885$		−	8.88658e23i		−	2.36150i
$886$	−2.60198e23	+	8.71025e22i	−0.685227	+	0.229383i
$887$			4.68950e23i			1.22388i	0.790905	+	0.611939i	$0.209610\pi$
$887$			4.68950e23i			1.22388i	−0.790905	+	0.611939i	$0.790390\pi$
$888$	−5.87139e23	−	4.03159e23i	−1.51858	−	1.04273i
$889$	1.22620e22			0.0314302
$890$	1.06159e23	+	3.17125e23i	0.269673	+	0.805584i
$891$	−3.44776e23			−0.867991
$892$	1.86673e23	+	2.47576e23i	0.465760	+	0.617717i
$893$			2.37913e22i			0.0588310i
$894$	1.24068e23	+	3.70625e23i	0.304061	+	0.908312i
$895$		−	8.20860e23i		−	1.99381i
$896$	−4.75252e23	+	3.92566e23i	−1.14409	+	0.945037i
$897$	2.05214e23			0.489628
$898$	2.66202e23	−	8.91123e22i	0.629507	−	0.210730i
$899$	2.69901e23			0.632597
$900$	−1.30256e23	+	9.82131e22i	−0.302592	+	0.228155i
$901$			1.12993e23i			0.260168i
$902$	6.61731e21	−	2.21517e21i	0.0151018	−	0.00505539i
$903$		−	1.50353e23i		−	0.340103i
$904$	1.67270e23	−	2.43603e23i	0.375034	−	0.546179i
$905$	3.68310e23			0.818513
$906$	−5.89208e22	−	1.76012e23i	−0.129791	−	0.387719i
$907$	−2.76998e22			−0.0604810			−0.0302405	−	0.999543i	$-0.509627\pi$
$907$	−2.76998e22			−0.0604810			−0.0302405	+	0.999543i	$0.509627\pi$
$908$	−5.29717e23	+	3.99407e23i	−1.14645	+	0.864429i
$909$			3.13416e23i			0.672373i
$910$	1.41386e23	+	4.22358e23i	0.300660	+	0.898153i
$911$			6.80989e23i			1.43547i	0.696318	+	0.717734i	$0.254820\pi$
$911$			6.80989e23i			1.43547i	−0.696318	+	0.717734i	$0.745180\pi$
$912$	−1.91470e22	+	6.69177e22i	−0.0400075	+	0.139824i
$913$	2.49201e23			0.516158
$914$	1.68129e23	−	5.62818e22i	0.345201	−	0.115558i
$915$	3.55048e22			0.0722634
$916$	4.89869e23	+	6.49691e23i	0.988362	+	1.31082i
$917$		−	2.77247e23i		−	0.554515i
$918$	6.57369e23	−	2.20057e23i	1.30337	−	0.436308i
$919$			4.10602e23i			0.807043i	0.914970	+	0.403522i	$0.132214\pi$
$919$			4.10602e23i			0.807043i	−0.914970	+	0.403522i	$0.867786\pi$
$920$	3.88214e23	−	5.65374e23i	0.756430	−	1.10162i
$921$	−4.46249e23			−0.861987
$922$	1.43290e23	+	4.28045e23i	0.274390	+	0.819676i
$923$	2.20044e23			0.417730
$924$	−3.90859e23	−	5.18379e23i	−0.735604	−	0.975600i
$925$			8.75085e23i			1.63274i
$926$	−7.21891e22	−	2.15648e23i	−0.133531	−	0.398894i
$927$		−	1.09917e23i		−	0.201571i
$928$	−3.07704e23	+	1.36548e22i	−0.559435	+	0.0248258i
$929$	−5.97517e23			−1.07702			−0.538511	−	0.842618i	$-0.681013\pi$
$929$	−5.97517e23			−1.07702			−0.538511	+	0.842618i	$0.681013\pi$
$930$	9.99598e23	−	3.34619e23i	1.78633	−	0.597981i
$931$	−8.44273e22			−0.149584
$932$	−5.03923e23	+	3.79959e23i	−0.885192	+	0.667436i
$933$			7.99414e23i			1.39226i
$934$	−5.87886e23	+	1.96797e23i	−1.01512	+	0.339816i
$935$		−	1.08895e24i		−	1.86429i
$936$	−7.94797e22	−	5.45747e22i	−0.134912	−	0.0926371i
$937$	7.64808e22			0.128717			0.0643585	−	0.997927i	$-0.479500\pi$
$937$	7.64808e22			0.128717			0.0643585	+	0.997927i	$0.479500\pi$
$938$	6.12376e22	+	1.82933e23i	0.102187	+	0.305260i
$939$	1.22958e24			2.03438
$940$	−3.28314e23	+	2.47550e23i	−0.538601	+	0.406106i
$941$		−	9.30929e23i		−	1.51426i	−0.653266	−	0.757129i	$-0.726601\pi$
$941$		−	9.30929e23i		−	1.51426i	0.653266	−	0.757129i	$-0.273399\pi$
$942$	−4.39850e22	−	1.31395e23i	−0.0709410	−	0.211920i
$943$		−	1.32380e22i		−	0.0211703i
$944$	2.45675e23	−	8.58622e23i	0.389570	−	1.36153i
$945$	−9.98012e23			−1.56921
$946$	−8.40361e22	+	2.81314e22i	−0.131020	+	0.0438594i
$947$	−2.38672e23			−0.368979			−0.184489	−	0.982835i	$-0.559063\pi$
$947$	−2.38672e23			−0.368979			−0.184489	+	0.982835i	$0.559063\pi$
$948$	−6.01792e23	−	7.98131e23i	−0.922529	−	1.22351i
$949$		−	4.33909e23i		−	0.659582i
$950$	8.10952e22	−	2.71469e22i	0.122238	−	0.0409197i
$951$			8.71539e22i			0.130270i
$952$	1.53062e24	+	1.05100e24i	2.26867	+	1.55778i
$953$	8.09862e23			1.19033			0.595166	−	0.803603i	$-0.297086\pi$
$953$	8.09862e23			1.19033			0.595166	+	0.803603i	$0.297086\pi$
$954$	1.11781e22	+	3.33918e22i	0.0162922	+	0.0486691i
$955$	8.55184e23			1.23604
$956$	−4.62504e23	−	6.13398e23i	−0.662906	−	0.879183i
$957$		−	3.24397e23i		−	0.461085i
$958$	2.36387e23	+	7.06151e23i	0.333196	+	0.995344i
$959$			1.49947e24i			2.09599i
$960$	−1.12267e24	+	4.32059e23i	−1.55627	+	0.598925i
$961$	−2.00877e23			−0.276148
$962$	−4.90432e23	+	1.64174e23i	−0.668618	+	0.223823i
$963$	−1.81174e23			−0.244955
$964$	−4.70501e23	+	3.54758e23i	−0.630876	+	0.475682i
$965$			4.22593e22i			0.0561958i
$966$	−1.16789e24	+	3.90957e23i	−1.54023	+	0.515600i
$967$			1.42829e24i			1.86812i	0.357120	+	0.934059i	$0.383759\pi$
$967$			1.42829e24i			1.86812i	−0.357120	+	0.934059i	$0.616241\pi$
$968$	2.19771e23	−	3.20062e23i	0.285080	−	0.415176i
$969$	2.09651e23			0.269716
$970$	−4.77501e23	−	1.42642e24i	−0.609257	−	1.82001i
$971$	1.39310e24			1.76290			0.881451	−	0.472276i	$-0.156568\pi$
$971$	1.39310e24			1.76290			0.881451	+	0.472276i	$0.156568\pi$
$972$	4.44507e23	−	3.35159e23i	0.557890	−	0.420650i
$973$		−	5.34187e23i		−	0.664952i
$974$	−3.20498e23	−	9.57412e23i	−0.395688	−	1.18203i
$975$			4.42250e23i			0.541541i
$976$	3.43048e22	+	9.81552e21i	0.0416635	+	0.0119211i
$977$	−1.28434e24			−1.54712			−0.773561	−	0.633722i	$-0.781526\pi$
$977$	−1.28434e24			−1.54712			−0.773561	+	0.633722i	$0.781526\pi$
$978$	4.36467e23	−	1.46109e23i	0.521483	−	0.174569i
$979$	−3.53970e23			−0.419473
$980$	−8.78471e23	−	1.16508e24i	−1.03257	−	1.36945i
$981$		−	3.68807e23i		−	0.429979i
$982$	1.58930e24	−	5.32025e23i	1.83787	−	0.615234i
$983$		−	6.92489e23i		−	0.794300i	−0.917754	−	0.397150i	$-0.869999\pi$
$983$		−	6.92489e23i		−	0.794300i	0.917754	−	0.397150i	$-0.130001\pi$
$984$	−1.31434e22	+	1.91414e22i	−0.0149537	+	0.0217777i
$985$	5.42619e23			0.612358
$986$	2.94504e23	+	8.79761e23i	0.329667	+	0.984803i
$987$	7.38394e23			0.819881
$988$	3.04284e22	+	4.03559e22i	0.0335138	+	0.0444479i
$989$			1.68114e23i			0.183669i
$990$	−1.07726e23	−	3.21807e23i	−0.116745	−	0.348749i
$991$		−	1.54253e24i		−	1.65823i	−0.559075	−	0.829117i	$-0.688844\pi$
$991$		−	1.54253e24i		−	1.65823i	0.559075	−	0.829117i	$-0.311156\pi$
$992$	1.05832e24	−	4.69645e22i	1.12856	−	0.0500814i
$993$	−3.33051e22			−0.0352303
$994$	−1.25229e24	+	4.19211e23i	−1.31406	+	0.439887i
$995$	−4.94405e23			−0.514633
$996$	−6.62080e23	+	4.99210e23i	−0.683653	+	0.515476i
$997$			1.85521e24i			1.90034i	0.311726	+	0.950172i	$0.399093\pi$
$997$			1.85521e24i			1.90034i	−0.311726	+	0.950172i	$0.600907\pi$
$998$	−1.41908e24	+	4.75044e23i	−1.44199	+	0.482714i
$999$		−	1.15887e24i		−	1.16818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.2	yes	14
3.2	odd	2		72.17.b.b.19.13		14
4.3	odd	2		32.17.d.b.15.12		14
8.3	odd	2	inner	8.17.d.b.3.1	✓	14
8.5	even	2		32.17.d.b.15.11		14
24.11	even	2		72.17.b.b.19.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.1	✓	14	8.3	odd	2	inner
8.17.d.b.3.2	yes	14	1.1	even	1	trivial
32.17.d.b.15.11		14	8.5	even	2
32.17.d.b.15.12		14	4.3	odd	2
72.17.b.b.19.13		14	3.2	odd	2
72.17.b.b.19.14		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)

\(f(q)\)	\(=\)	\(q+(-242.759 + 81.2647i) q^{2} -7667.81 q^{3} +(52328.1 - 39455.5i) q^{4} +557358. i q^{5} +(1.86143e6 - 623122. i) q^{6} +8.55454e6i q^{7} +(-9.49679e6 + 1.38306e7i) q^{8} +1.57485e7 q^{9} +O(q^{10})\)	\(q+(-242.759 + 81.2647i) q^{2} -7667.81 q^{3} +(52328.1 - 39455.5i) q^{4} +557358. i q^{5} +(1.86143e6 - 623122. i) q^{6} +8.55454e6i q^{7} +(-9.49679e6 + 1.38306e7i) q^{8} +1.57485e7 q^{9} +(-4.52935e7 - 1.35304e8i) q^{10} +1.51024e8 q^{11} +(-4.01242e8 + 3.02537e8i) q^{12} +3.64901e8i q^{13} +(-6.95181e8 - 2.07669e9i) q^{14} -4.27371e9i q^{15} +(1.18149e9 - 4.12926e9i) q^{16} -1.29368e10 q^{17} +(-3.82310e9 + 1.27980e9i) q^{18} +2.11348e9 q^{19} +(2.19908e10 + 2.91655e10i) q^{20} -6.55945e10i q^{21} +(-3.66624e10 + 1.22729e10i) q^{22} +7.33433e10i q^{23} +(7.28196e10 - 1.06050e11i) q^{24} -1.58060e11 q^{25} +(-2.96535e10 - 8.85830e10i) q^{26} +2.09317e11 q^{27} +(3.37523e11 + 4.47643e11i) q^{28} +2.80131e11i q^{29} +(3.47302e11 + 1.03748e12i) q^{30} -9.63483e11i q^{31} +(4.87445e10 + 1.09843e12i) q^{32} -1.15802e12 q^{33} +(3.14054e12 - 1.05131e12i) q^{34} -4.76794e12 q^{35} +(8.24090e11 - 6.21366e11i) q^{36} -5.53641e12i q^{37} +(-5.13066e11 + 1.71751e11i) q^{38} -2.79799e12i q^{39} +(-7.70860e12 - 5.29311e12i) q^{40} -1.80493e11 q^{41} +(5.33052e12 + 1.59237e13i) q^{42} +2.29216e12 q^{43} +(7.90278e12 - 5.95871e12i) q^{44} +8.77757e12i q^{45} +(-5.96022e12 - 1.78048e13i) q^{46} +1.12569e13i q^{47} +(-9.05947e12 + 3.16624e13i) q^{48} -3.99471e13 q^{49} +(3.83705e13 - 1.28447e13i) q^{50} +9.91972e13 q^{51} +(1.43973e13 + 1.90946e13i) q^{52} -8.73423e12i q^{53} +(-5.08137e13 + 1.70101e13i) q^{54} +8.41742e13i q^{55} +(-1.18314e14 - 8.12407e13i) q^{56} -1.62057e13 q^{57} +(-2.27647e13 - 6.80043e13i) q^{58} +2.07936e14 q^{59} +(-1.68621e14 - 2.23635e14i) q^{60} +8.30772e12i q^{61} +(7.82971e13 + 2.33894e14i) q^{62} +1.34721e14i q^{63} +(-1.01097e14 - 2.62693e14i) q^{64} -2.03380e14 q^{65} +(2.81120e14 - 9.41061e13i) q^{66} -8.80887e13 q^{67} +(-6.76960e14 + 5.10429e14i) q^{68} -5.62382e14i q^{69} +(1.15746e15 - 3.87465e14i) q^{70} -6.03023e14i q^{71} +(-1.49560e14 + 2.17812e14i) q^{72} -1.18912e15 q^{73} +(4.49915e14 + 1.34401e15i) q^{74} +1.21197e15 q^{75} +(1.10594e14 - 8.33882e13i) q^{76} +1.29194e15i q^{77} +(2.27378e14 + 6.79238e14i) q^{78} +1.98915e15i q^{79} +(2.30148e15 + 6.58515e14i) q^{80} -2.28293e15 q^{81} +(4.38164e13 - 1.46677e13i) q^{82} +1.65008e15 q^{83} +(-2.58806e15 - 3.43244e15i) q^{84} -7.21045e15i q^{85} +(-5.56443e14 + 1.86272e14i) q^{86} -2.14799e15i q^{87} +(-1.43424e15 + 2.08875e15i) q^{88} -2.34380e15 q^{89} +(-7.13306e14 - 2.13084e15i) q^{90} -3.12156e15 q^{91} +(2.89380e15 + 3.83791e15i) q^{92} +7.38780e15i q^{93} +(-9.14792e14 - 2.73273e15i) q^{94} +1.17796e15i q^{95} +(-3.73763e14 - 8.42255e15i) q^{96} +1.05424e16 q^{97} +(9.69754e15 - 3.24629e15i) q^{98} +2.37840e15 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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