LMFDB - Embedded newform 8.17.d.b.3.9

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			3.9
Root			$-30.5698 + 126.646i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.d.b.3.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(37.1396 - 253.292i) q^{2} +11400.0 q^{3} +(-62777.3 - 18814.3i) q^{4} +8041.89i q^{5} +(423391. - 2.88752e6i) q^{6} -7.58607e6i q^{7} +(-7.09702e6 + 1.52022e7i) q^{8} +8.69132e7 q^{9} +O(q^{10})$	\(q+(37.1396 - 253.292i) q^{2} +11400.0 q^{3} +(-62777.3 - 18814.3i) q^{4} +8041.89i q^{5} +(423391. - 2.88752e6i) q^{6} -7.58607e6i q^{7} +(-7.09702e6 + 1.52022e7i) q^{8} +8.69132e7 q^{9} +(2.03694e6 + 298672. i) q^{10} +1.12935e8 q^{11} +(-7.15661e8 - 2.14483e8i) q^{12} -1.21521e9i q^{13} +(-1.92149e9 - 2.81743e8i) q^{14} +9.16775e7i q^{15} +(3.58701e9 + 2.36222e9i) q^{16} -6.69789e9 q^{17} +(3.22792e9 - 2.20144e10i) q^{18} -4.33974e9 q^{19} +(1.51302e8 - 5.04848e8i) q^{20} -8.64811e10i q^{21} +(4.19437e9 - 2.86056e10i) q^{22} +1.36436e11i q^{23} +(-8.09060e10 + 1.73305e11i) q^{24} +1.52523e11 q^{25} +(-3.07802e11 - 4.51323e10i) q^{26} +5.00077e11 q^{27} +(-1.42726e11 + 4.76233e11i) q^{28} -4.52974e10i q^{29} +(2.32212e10 + 3.40486e9i) q^{30} -1.80480e11i q^{31} +(7.31551e11 - 8.20829e11i) q^{32} +1.28746e12 q^{33} +(-2.48757e11 + 1.69652e12i) q^{34} +6.10064e10 q^{35} +(-5.45617e12 - 1.63521e12i) q^{36} +3.25403e12i q^{37} +(-1.61176e11 + 1.09922e12i) q^{38} -1.38534e13i q^{39} +(-1.22255e11 - 5.70735e10i) q^{40} +7.38199e12 q^{41} +(-2.19049e13 - 3.21187e12i) q^{42} +1.28240e13 q^{43} +(-7.08977e12 - 2.12480e12i) q^{44} +6.98946e11i q^{45} +(3.45580e13 + 5.06717e12i) q^{46} +2.62230e13i q^{47} +(4.08919e13 + 2.69293e13i) q^{48} -2.43155e13 q^{49} +(5.66465e12 - 3.86329e13i) q^{50} -7.63560e13 q^{51} +(-2.28633e13 + 7.62875e13i) q^{52} +4.59368e13i q^{53} +(1.85726e13 - 1.26665e14i) q^{54} +9.08213e11i q^{55} +(1.15325e14 + 5.38385e13i) q^{56} -4.94730e13 q^{57} +(-1.14734e13 - 1.68232e12i) q^{58} +7.53538e13 q^{59} +(1.72485e12 - 5.75527e12i) q^{60} +1.29366e14i q^{61} +(-4.57142e13 - 6.70296e12i) q^{62} -6.59329e14i q^{63} +(-1.80740e14 - 2.15781e14i) q^{64} +9.77257e12 q^{65} +(4.78157e13 - 3.26103e14i) q^{66} -6.96261e14 q^{67} +(4.20476e14 + 1.26016e14i) q^{68} +1.55537e15i q^{69} +(2.26575e12 - 1.54524e13i) q^{70} -7.47479e14i q^{71} +(-6.16825e14 + 1.32127e15i) q^{72} +6.29141e14 q^{73} +(8.24217e14 + 1.20853e14i) q^{74} +1.73876e15 q^{75} +(2.72437e14 + 8.16491e13i) q^{76} -8.56734e14i q^{77} +(-3.50894e15 - 5.14508e14i) q^{78} +5.34025e13i q^{79} +(-1.89967e13 + 2.88464e13i) q^{80} +1.95955e15 q^{81} +(2.74164e14 - 1.86980e15i) q^{82} +1.43282e15 q^{83} +(-1.62708e15 + 5.42905e15i) q^{84} -5.38638e13i q^{85} +(4.76277e14 - 3.24821e15i) q^{86} -5.16390e14i q^{87} +(-8.01504e14 + 1.71687e15i) q^{88} -3.88996e15 q^{89} +(1.77037e14 + 2.59586e13i) q^{90} -9.21865e15 q^{91} +(2.56694e15 - 8.56507e15i) q^{92} -2.05748e15i q^{93} +(6.64205e15 + 9.73909e14i) q^{94} -3.48997e13i q^{95} +(8.33967e15 - 9.35744e15i) q^{96} -3.14550e15 q^{97} +(-9.03067e14 + 6.15891e15i) q^{98} +9.81556e15 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 $

$2$	37.1396	−	253.292i	0.145076	−	0.989420i
$2$	37.1396	−	253.292i	0.145076	−	0.989420i
$3$	11400.0			1.73754			0.868770	−	0.495216i	$-0.164911\pi$
$3$	11400.0			1.73754			0.868770	+	0.495216i	$0.164911\pi$
$4$	−62777.3	−	18814.3i	−0.957906	−	0.287083i
$5$			8041.89i			0.0205872i	0.999947	+	0.0102936i	$0.00327662\pi$
$5$			8041.89i			0.0205872i	−0.999947	+	0.0102936i	$0.996723\pi$
$6$	423391.	−	2.88752e6i	0.252076	−	1.71916i
$7$		−	7.58607e6i		−	1.31593i	−0.753049	−	0.657964i	$-0.771418\pi$
$7$		−	7.58607e6i		−	1.31593i	0.753049	−	0.657964i	$-0.228582\pi$
$8$	−7.09702e6	+	1.52022e7i	−0.423016	+	0.906122i
$9$	8.69132e7			2.01904
$10$	2.03694e6	+	298672.i	0.0203694	+	0.00298672i
$11$	1.12935e8			0.526851			0.263426	−	0.964680i	$-0.415148\pi$
$11$	1.12935e8			0.526851			0.263426	+	0.964680i	$0.415148\pi$
$12$	−7.15661e8	−	2.14483e8i	−1.66440	−	0.498818i
$13$		−	1.21521e9i		−	1.48972i	−0.667222	−	0.744859i	$-0.732517\pi$
$13$		−	1.21521e9i		−	1.48972i	0.667222	−	0.744859i	$-0.267483\pi$
$14$	−1.92149e9	−	2.81743e8i	−1.30201	−	0.190910i
$15$			9.16775e7i			0.0357712i
$16$	3.58701e9	+	2.36222e9i	0.835166	+	0.549997i
$17$	−6.69789e9			−0.960167			−0.480084	−	0.877223i	$-0.659394\pi$
$17$	−6.69789e9			−0.960167			−0.480084	+	0.877223i	$0.659394\pi$
$18$	3.22792e9	−	2.20144e10i	0.292915	−	1.99768i
$19$	−4.33974e9			−0.255526			−0.127763	−	0.991805i	$-0.540780\pi$
$19$	−4.33974e9			−0.255526			−0.127763	+	0.991805i	$0.540780\pi$
$20$	1.51302e8	−	5.04848e8i	0.00591025	−	0.0197206i
$21$		−	8.64811e10i		−	2.28648i
$22$	4.19437e9	−	2.86056e10i	0.0764337	−	0.521277i
$23$			1.36436e11i			1.74223i	0.491079	+	0.871115i	$0.336603\pi$
$23$			1.36436e11i			1.74223i	−0.491079	+	0.871115i	$0.663397\pi$
$24$	−8.09060e10	+	1.73305e11i	−0.735006	+	1.57442i
$25$	1.52523e11			0.999576
$26$	−3.07802e11	−	4.51323e10i	−1.47396	−	0.216123i
$27$	5.00077e11			1.77063
$28$	−1.42726e11	+	4.76233e11i	−0.377781	+	1.26054i
$29$		−	4.52974e10i		−	0.0905501i	−0.998975	−	0.0452751i	$-0.985584\pi$
$29$		−	4.52974e10i		−	0.0905501i	0.998975	−	0.0452751i	$-0.0144164\pi$
$30$	2.32212e10	+	3.40486e9i	0.0353927	+	0.00518955i
$31$		−	1.80480e11i		−	0.211610i	−0.994387	−	0.105805i	$-0.966258\pi$
$31$		−	1.80480e11i		−	0.211610i	0.994387	−	0.105805i	$-0.0337419\pi$
$32$	7.31551e11	−	8.20829e11i	0.665341	−	0.746539i
$33$	1.28746e12			0.915425
$34$	−2.48757e11	+	1.69652e12i	−0.139298	+	0.950009i
$35$	6.10064e10			0.0270914
$36$	−5.45617e12	−	1.63521e12i	−1.93405	−	0.579633i
$37$			3.25403e12i			0.926418i	0.886249	+	0.463209i	$0.153302\pi$
$37$			3.25403e12i			0.926418i	−0.886249	+	0.463209i	$0.846698\pi$
$38$	−1.61176e11	+	1.09922e12i	−0.0370708	+	0.252822i
$39$		−	1.38534e13i		−	2.58844i
$40$	−1.22255e11	−	5.70735e10i	−0.0186546	−	0.00870873i
$41$	7.38199e12			0.924491			0.462246	−	0.886752i	$-0.347044\pi$
$41$	7.38199e12			0.924491			0.462246	+	0.886752i	$0.347044\pi$
$42$	−2.19049e13	−	3.21187e12i	−2.26229	−	0.331714i
$43$	1.28240e13			1.09717			0.548587	−	0.836094i	$-0.315166\pi$
$43$	1.28240e13			1.09717			0.548587	+	0.836094i	$0.315166\pi$
$44$	−7.08977e12	−	2.12480e12i	−0.504674	−	0.151250i
$45$			6.98946e11i			0.0415665i
$46$	3.45580e13	+	5.06717e12i	1.72380	+	0.252757i
$47$			2.62230e13i			1.10128i	0.834742	+	0.550641i	$0.185617\pi$
$47$			2.62230e13i			1.10128i	−0.834742	+	0.550641i	$0.814383\pi$
$48$	4.08919e13	+	2.69293e13i	1.45113	+	0.955642i
$49$	−2.43155e13			−0.731669
$50$	5.66465e12	−	3.86329e13i	0.145015	−	0.989001i
$51$	−7.63560e13			−1.66833
$52$	−2.28633e13	+	7.62875e13i	−0.427673	+	1.42701i
$53$			4.59368e13i			0.737825i	0.929464	+	0.368913i	$0.120270\pi$
$53$			4.59368e13i			0.737825i	−0.929464	+	0.368913i	$0.879730\pi$
$54$	1.85726e13	−	1.26665e14i	0.256876	−	1.75189i
$55$			9.08213e11i			0.0108464i
$56$	1.15325e14	+	5.38385e13i	1.19239	+	0.556658i
$57$	−4.94730e13			−0.443986
$58$	−1.14734e13	−	1.68232e12i	−0.0895921	−	0.0131367i
$59$	7.53538e13			0.513203			0.256601	−	0.966517i	$-0.417397\pi$
$59$	7.53538e13			0.513203			0.256601	+	0.966517i	$0.417397\pi$
$60$	1.72485e12	−	5.75527e12i	0.0102693	−	0.0342654i
$61$			1.29366e14i			0.674810i	0.941360	+	0.337405i	$0.109549\pi$
$61$			1.29366e14i			0.674810i	−0.941360	+	0.337405i	$0.890451\pi$
$62$	−4.57142e13	−	6.70296e12i	−0.209371	−	0.0306996i
$63$		−	6.59329e14i		−	2.65692i
$64$	−1.80740e14	−	2.15781e14i	−0.642116	−	0.766608i
$65$	9.77257e12			0.0306692
$66$	4.78157e13	−	3.26103e14i	0.132807	−	0.905740i
$67$	−6.96261e14			−1.71464			−0.857321	−	0.514782i	$-0.827873\pi$
$67$	−6.96261e14			−1.71464			−0.857321	+	0.514782i	$0.827873\pi$
$68$	4.20476e14	+	1.26016e14i	0.919750	+	0.275648i
$69$			1.55537e15i			3.02719i
$70$	2.26575e12	−	1.54524e13i	0.00393032	−	0.0268047i
$71$		−	7.47479e14i		−	1.15753i	−0.815494	−	0.578765i	$-0.803535\pi$
$71$		−	7.47479e14i		−	1.15753i	0.815494	−	0.578765i	$-0.196465\pi$
$72$	−6.16825e14	+	1.32127e15i	−0.854086	+	1.82950i
$73$	6.29141e14			0.780127			0.390063	−	0.920788i	$-0.372453\pi$
$73$	6.29141e14			0.780127			0.390063	+	0.920788i	$0.372453\pi$
$74$	8.24217e14	+	1.20853e14i	0.916617	+	0.134401i
$75$	1.73876e15			1.73680
$76$	2.72437e14	+	8.16491e13i	0.244770	+	0.0733572i
$77$		−	8.56734e14i		−	0.693299i
$78$	−3.50894e15	−	5.14508e14i	−2.56106	−	0.375522i
$79$			5.34025e13i			0.0352002i	0.999845	+	0.0176001i	$0.00560257\pi$
$79$			5.34025e13i			0.0352002i	−0.999845	+	0.0176001i	$0.994397\pi$
$80$	−1.89967e13	+	2.88464e13i	−0.0113229	+	0.0171938i
$81$	1.95955e15			1.05749
$82$	2.74164e14	−	1.86980e15i	0.134122	−	0.914711i
$83$	1.43282e15			0.636160			0.318080	−	0.948064i	$-0.396962\pi$
$83$	1.43282e15			0.636160			0.318080	+	0.948064i	$0.396962\pi$
$84$	−1.62708e15	+	5.42905e15i	−0.656409	+	2.19023i
$85$		−	5.38638e13i		−	0.0197672i
$86$	4.76277e14	−	3.24821e15i	0.159174	−	1.08557i
$87$		−	5.16390e14i		−	0.157334i
$88$	−8.01504e14	+	1.71687e15i	−0.222866	+	0.477392i
$89$	−3.88996e15			−0.988155			−0.494078	−	0.869418i	$-0.664494\pi$
$89$	−3.88996e15			−0.988155			−0.494078	+	0.869418i	$0.664494\pi$
$90$	1.77037e14	+	2.59586e13i	0.0411268	+	0.00603032i
$91$	−9.21865e15			−1.96036
$92$	2.56694e15	−	8.56507e15i	0.500165	−	1.66889i
$93$		−	2.05748e15i		−	0.367681i
$94$	6.64205e15	+	9.73909e14i	1.08963	+	0.159770i
$95$		−	3.48997e13i		−	0.00526057i
$96$	8.33967e15	−	9.35744e15i	1.15606	−	1.29714i
$97$	−3.14550e15			−0.401343			−0.200671	−	0.979659i	$-0.564312\pi$
$97$	−3.14550e15			−0.401343			−0.200671	+	0.979659i	$0.564312\pi$
$98$	−9.03067e14	+	6.15891e15i	−0.106148	+	0.723928i
$99$	9.81556e15			1.06373
$100$	−9.57500e15	−	2.86962e15i	−0.957500	−	0.286962i
$101$			1.22349e16i			1.12987i	0.825136	+	0.564934i	$0.191098\pi$
$101$			1.22349e16i			1.12987i	−0.825136	+	0.564934i	$0.808902\pi$
$102$	−2.83583e15	+	1.93403e16i	−0.242035	+	1.65068i
$103$			1.16911e15i			0.0922910i	0.998935	+	0.0461455i	$0.0146938\pi$
$103$			1.16911e15i			0.0922910i	−0.998935	+	0.0461455i	$0.985306\pi$
$104$	1.84738e16	+	8.62436e15i	1.34987	+	0.630173i
$105$	6.95472e14			0.0470723
$106$	1.16354e16	+	1.70607e15i	0.730019	+	0.107041i
$107$	−1.27286e16			−0.740816			−0.370408	−	0.928869i	$-0.620782\pi$
$107$	−1.27286e16			−0.740816			−0.370408	+	0.928869i	$0.620782\pi$
$108$	−3.13935e16	−	9.40859e15i	−1.69609	−	0.508317i
$109$		−	1.22082e16i		−	0.612687i	−0.951921	−	0.306343i	$-0.900894\pi$
$109$		−	1.22082e16i		−	0.612687i	0.951921	−	0.306343i	$-0.0991056\pi$
$110$	2.30043e14	+	3.37306e13i	0.0107317	+	0.00157356i
$111$			3.70959e16i			1.60969i
$112$	1.79200e16	−	2.72113e16i	0.723757	−	1.09902i
$113$	−1.56253e15			−0.0587763			−0.0293881	−	0.999568i	$-0.509356\pi$
$113$	−1.56253e15			−0.0587763			−0.0293881	+	0.999568i	$0.509356\pi$
$114$	−1.83741e15	+	1.25311e16i	−0.0644119	+	0.439289i
$115$	−1.09720e15			−0.0358677
$116$	−8.52237e14	+	2.84365e15i	−0.0259954	+	0.0867385i
$117$		−	1.05618e17i		−	3.00780i
$118$	2.79861e15	−	1.90865e16i	0.0744536	−	0.507773i
$119$			5.08107e16i			1.26351i
$120$	−1.39370e15	−	6.50638e14i	−0.0324130	−	0.0151318i
$121$	−3.31954e16			−0.722428
$122$	3.27673e16	+	4.80460e15i	0.667671	+	0.0978990i
$123$	8.41547e16			1.60634
$124$	−3.39561e15	+	1.13301e16i	−0.0607497	+	0.202703i
$125$			2.45367e15i			0.0411658i
$126$	−1.67003e17	−	2.44872e16i	−2.62881	−	0.385456i
$127$		−	5.23169e16i		−	0.773059i	−0.922277	−	0.386529i	$-0.873674\pi$
$127$		−	5.23169e16i		−	0.773059i	0.922277	−	0.386529i	$-0.126326\pi$
$128$	−6.13681e16	+	3.77658e16i	−0.851653	+	0.524106i
$129$	1.46193e17			1.90638
$130$	3.62949e14	−	2.47531e15i	0.00444937	−	0.0303447i
$131$	−2.25545e16			−0.260054			−0.130027	−	0.991510i	$-0.541506\pi$
$131$	−2.25545e16			−0.260054			−0.130027	+	0.991510i	$0.541506\pi$
$132$	−8.08233e16	−	2.42227e16i	−0.876890	−	0.262803i
$133$			3.29216e16i			0.336254i
$134$	−2.58588e16	+	1.76357e17i	−0.248754	+	1.69650i
$135$			4.02157e15i			0.0364523i
$136$	4.75351e16	−	1.01823e17i	0.406166	−	0.870029i
$137$	−7.91790e16			−0.638037			−0.319018	−	0.947749i	$-0.603353\pi$
$137$	−7.91790e16			−0.638037			−0.319018	+	0.947749i	$0.603353\pi$
$138$	3.93961e17	+	5.77657e16i	2.99517	+	0.439174i
$139$	−8.16196e15			−0.0585701			−0.0292851	−	0.999571i	$-0.509323\pi$
$139$	−8.16196e15			−0.0585701			−0.0292851	+	0.999571i	$0.509323\pi$
$140$	−3.82981e15	−	1.14779e15i	−0.0259510	−	0.00777747i
$141$			2.98942e17i			1.91352i
$142$	−1.89330e17	−	2.77611e16i	−1.14528	−	0.167930i
$143$		−	1.37240e17i		−	0.784859i
$144$	3.11759e17	+	2.05308e17i	1.68624	+	1.11047i
$145$	3.64277e14			0.00186418
$146$	2.33660e16	−	1.59356e17i	0.113178	−	0.771874i
$147$	−2.77197e17			−1.27130
$148$	6.12222e16	−	2.04279e17i	0.265959	−	0.887421i
$149$			2.17682e17i			0.896051i	0.894021	+	0.448026i	$0.147873\pi$
$149$			2.17682e17i			0.896051i	−0.894021	+	0.448026i	$0.852127\pi$
$150$	6.45769e16	−	4.40414e17i	0.251969	−	1.71843i
$151$		−	4.26162e17i		−	1.57674i	−0.615204	−	0.788368i	$-0.710926\pi$
$151$		−	4.26162e17i		−	1.57674i	0.615204	−	0.788368i	$-0.289074\pi$
$152$	3.07992e16	−	6.59736e16i	0.108091	−	0.231538i
$153$	−5.82135e17			−1.93862
$154$	−2.17004e17	−	3.18187e16i	−0.685964	−	0.100581i
$155$	1.45140e15			0.00435647
$156$	−2.60641e17	+	8.69677e17i	−0.743098	+	2.47948i
$157$		−	4.08567e17i		−	1.10679i	−0.832918	−	0.553396i	$-0.813332\pi$
$157$		−	4.08567e17i		−	1.10679i	0.832918	−	0.553396i	$-0.186668\pi$
$158$	1.35264e16	+	1.98334e15i	0.0348278	+	0.00510671i
$159$			5.23679e17i			1.28200i
$160$	6.60102e15	+	5.88305e15i	0.0153692	+	0.0136976i
$161$	1.03501e18			2.29265
$162$	7.27769e16	−	4.96338e17i	0.153417	−	1.04630i
$163$	1.69114e17			0.339375			0.169687	−	0.985498i	$-0.445724\pi$
$163$	1.69114e17			0.339375			0.169687	+	0.985498i	$0.445724\pi$
$164$	−4.63422e17	−	1.38887e17i	−0.885575	−	0.265406i
$165$			1.03536e16i			0.0188461i
$166$	5.32142e16	−	3.62921e17i	0.0922918	−	0.629430i
$167$		−	1.63194e17i		−	0.269757i	−0.990862	−	0.134878i	$-0.956936\pi$
$167$		−	1.63194e17i		−	0.269757i	0.990862	−	0.134878i	$-0.0430644\pi$
$168$	1.31470e18	+	6.13759e17i	2.07183	+	0.967216i
$169$	−8.11314e17			−1.21926
$170$	−1.36432e16	−	2.00048e15i	−0.0195581	−	0.00286776i
$171$	−3.77180e17			−0.515917
$172$	−8.05055e17	−	2.41274e17i	−1.05099	−	0.314980i
$173$			8.17983e17i			1.01947i	0.860331	+	0.509736i	$0.170257\pi$
$173$			8.17983e17i			1.01947i	−0.860331	+	0.509736i	$0.829743\pi$
$174$	−1.30797e17	−	1.91785e16i	−0.155670	−	0.0228255i
$175$		−	1.15705e18i		−	1.31537i
$176$	4.05100e17	+	2.66778e17i	0.440008	+	0.289767i
$177$	8.59033e17			0.891710
$178$	−1.44471e17	+	9.85295e17i	−0.143358	+	0.977701i
$179$	1.69390e18			1.60718			0.803588	−	0.595186i	$-0.202921\pi$
$179$	1.69390e18			1.60718			0.803588	+	0.595186i	$0.202921\pi$
$180$	1.31502e16	−	4.38780e16i	0.0119331	−	0.0398168i
$181$			1.34685e18i			1.16920i	0.811321	+	0.584601i	$0.198749\pi$
$181$			1.34685e18i			1.16920i	−0.811321	+	0.584601i	$0.801251\pi$
$182$	−3.42377e17	+	2.33501e18i	−0.284402	+	1.93962i
$183$			1.47477e18i			1.17251i
$184$	−2.07413e18	−	9.68288e17i	−1.57867	−	0.736990i
$185$	−2.61685e16			−0.0190724
$186$	−5.21141e17	−	7.64137e16i	−0.363791	−	0.0533418i
$187$	−7.56428e17			−0.505865
$188$	4.93366e17	−	1.64621e18i	0.316160	−	1.05492i
$189$		−	3.79362e18i		−	2.33002i
$190$	−8.83981e15	−	1.29616e15i	−0.00520492	−	0.000763185i
$191$		−	1.70376e18i		−	0.961926i	−0.876741	−	0.480963i	$-0.840287\pi$
$191$		−	1.70376e18i		−	0.961926i	0.876741	−	0.480963i	$-0.159713\pi$
$192$	−2.06043e18	−	2.45990e18i	−1.11570	−	1.33201i
$193$	3.28031e18			1.70395			0.851974	−	0.523585i	$-0.175406\pi$
$193$	3.28031e18			1.70395			0.851974	+	0.523585i	$0.175406\pi$
$194$	−1.16822e17	+	7.96728e17i	−0.0582254	+	0.397097i
$195$	1.11407e17			0.0532889
$196$	1.52646e18	+	4.57479e17i	0.700870	+	0.210050i
$197$		−	1.09897e18i		−	0.484456i	−0.970219	−	0.242228i	$-0.922122\pi$
$197$		−	1.09897e18i		−	0.484456i	0.970219	−	0.242228i	$-0.0778782\pi$
$198$	3.64546e17	−	2.48620e18i	0.154323	−	1.05248i
$199$			1.13921e18i			0.463212i	0.972810	+	0.231606i	$0.0743979\pi$
$199$			1.13921e18i			0.463212i	−0.972810	+	0.231606i	$0.925602\pi$
$200$	−1.08246e18	+	2.31869e18i	−0.422836	+	0.905738i
$201$	−7.93737e18			−2.97926
$202$	3.09899e18	+	4.54397e17i	1.11791	+	0.163917i
$203$	−3.43629e17			−0.119157
$204$	4.79342e18	+	1.43658e18i	1.59810	+	0.478949i
$205$			5.93652e16i			0.0190327i
$206$	2.96127e17	+	4.34204e16i	0.0913146	+	0.0133892i
$207$			1.18581e19i			3.51764i
$208$	2.87059e18	−	4.35897e18i	0.819340	−	1.24416i
$209$	−4.90109e17			−0.134624
$210$	2.58295e16	−	1.76157e17i	0.00682908	−	0.0465743i
$211$	−5.12642e18			−1.30483			−0.652416	−	0.757861i	$-0.726244\pi$
$211$	−5.12642e18			−1.30483			−0.652416	+	0.757861i	$0.726244\pi$
$212$	8.64267e17	−	2.88379e18i	0.211817	−	0.706767i
$213$		−	8.52126e18i		−	2.01125i
$214$	−4.72734e17	+	3.22405e18i	−0.107475	+	0.732978i
$215$			1.03129e17i			0.0225878i
$216$	−3.54906e18	+	7.60228e18i	−0.749002	+	1.60440i
$217$	−1.36914e18			−0.278464
$218$	−3.09223e18	−	4.53406e17i	−0.606205	−	0.0888864i
$219$	7.17221e18			1.35550
$220$	1.70874e16	−	5.70152e16i	0.00311382	−	0.0103898i
$221$			8.13933e18i			1.43038i
$222$	9.39607e18	+	1.37772e18i	1.59266	+	0.233528i
$223$		−	7.50337e18i		−	1.22692i	−0.789725	−	0.613461i	$-0.789777\pi$
$223$		−	7.50337e18i		−	1.22692i	0.789725	−	0.613461i	$-0.210223\pi$
$224$	−6.22686e18	−	5.54959e18i	−0.982392	−	0.875542i
$225$	1.32563e19			2.01819
$226$	−5.80319e16	+	3.95777e17i	−0.00852705	+	0.0581544i
$227$	−2.18857e18			−0.310422			−0.155211	−	0.987881i	$-0.549606\pi$
$227$	−2.18857e18			−0.310422			−0.155211	+	0.987881i	$0.549606\pi$
$228$	3.10578e18	+	9.30799e17i	0.425297	+	0.127461i
$229$			8.69305e18i			1.14944i	0.818348	+	0.574722i	$0.194890\pi$
$229$			8.69305e18i			1.14944i	−0.818348	+	0.574722i	$0.805110\pi$
$230$	−4.07496e16	+	2.77912e17i	−0.00520356	+	0.0354883i
$231$		−	9.76677e18i		−	1.20463i
$232$	6.88620e17	+	3.21476e17i	0.0820495	+	0.0383041i
$233$	−2.41689e18			−0.278234			−0.139117	−	0.990276i	$-0.544426\pi$
$233$	−2.41689e18			−0.278234			−0.139117	+	0.990276i	$0.544426\pi$
$234$	−2.67520e19	−	3.92259e18i	−2.97598	−	0.436361i
$235$	−2.10882e17			−0.0226724
$236$	−4.73051e18	−	1.41773e18i	−0.491600	−	0.147332i
$237$			6.08788e17i			0.0611617i
$238$	1.28699e19	+	1.88709e18i	1.25014	+	0.183306i
$239$		−	1.55291e19i		−	1.45869i	−0.684147	−	0.729344i	$-0.739825\pi$
$239$		−	1.55291e19i		−	1.45869i	0.684147	−	0.729344i	$-0.260175\pi$
$240$	−2.16563e17	+	3.28849e17i	−0.0196740	+	0.0298749i
$241$	−1.42377e19			−1.25113			−0.625567	−	0.780170i	$-0.715132\pi$
$241$	−1.42377e19			−1.25113			−0.625567	+	0.780170i	$0.715132\pi$
$242$	−1.23286e18	+	8.40811e18i	−0.104807	+	0.714785i
$243$	8.12184e17			0.0668043
$244$	2.43393e18	−	8.12125e18i	0.193727	−	0.646404i
$245$		−	1.95543e17i		−	0.0150630i
$246$	3.12547e18	−	2.13157e19i	0.233042	−	1.58935i
$247$			5.27369e18i			0.380661i
$248$	2.74370e18	+	1.28087e18i	0.191745	+	0.0895143i
$249$	1.63341e19			1.10535
$250$	6.21494e17	+	9.11283e16i	0.0407303	+	0.00597218i
$251$	5.11419e17			0.0324629			0.0162314	−	0.999868i	$-0.494833\pi$
$251$	5.11419e17			0.0324629			0.0162314	+	0.999868i	$0.494833\pi$
$252$	−1.24048e19	+	4.13909e19i	−0.762756	+	2.54508i
$253$			1.54084e19i			0.917896i
$254$	−1.32514e19	−	1.94303e18i	−0.764880	−	0.112153i
$255$		−	6.14046e17i		−	0.0343463i
$256$	7.28658e18	+	1.69466e19i	0.395006	+	0.918678i
$257$	2.54196e19			1.33569			0.667843	−	0.744302i	$-0.267218\pi$
$257$	2.54196e19			1.33569			0.667843	+	0.744302i	$0.267218\pi$
$258$	5.42956e18	−	3.70295e19i	0.276571	−	1.88621i
$259$	2.46853e19			1.21910
$260$	−6.13496e17	−	1.83864e17i	−0.0293782	−	0.00880460i
$261$		−	3.93694e18i		−	0.182825i
$262$	−8.37666e17	+	5.71288e18i	−0.0377277	+	0.257303i
$263$			3.16887e18i			0.138439i	0.997601	+	0.0692195i	$0.0220509\pi$
$263$			3.16887e18i			0.138439i	−0.997601	+	0.0692195i	$0.977949\pi$
$264$	−9.13714e18	+	1.95723e19i	−0.387239	+	0.829487i
$265$	−3.69419e17			−0.0151898
$266$	8.33875e18	+	1.22269e18i	0.332696	+	0.0487825i
$267$	−4.43455e19			−1.71696
$268$	4.37094e19	+	1.30997e19i	1.64247	+	0.492245i
$269$		−	2.44066e19i		−	0.890204i	−0.895480	−	0.445102i	$-0.853167\pi$
$269$		−	2.44066e19i		−	0.890204i	0.895480	−	0.445102i	$-0.146833\pi$
$270$	1.01863e18	+	1.49359e17i	0.0360667	+	0.00528837i
$271$			2.84819e19i			0.979074i	0.871983	+	0.489537i	$0.162834\pi$
$271$			2.84819e19i			0.979074i	−0.871983	+	0.489537i	$0.837166\pi$
$272$	−2.40254e19	−	1.58219e19i	−0.801899	−	0.528089i
$273$	−1.05093e20			−3.40621
$274$	−2.94067e18	+	2.00554e19i	−0.0925641	+	0.631286i
$275$	1.72252e19			0.526628
$276$	2.92631e19	−	9.76418e19i	0.869056	−	2.89977i
$277$			4.75469e19i			1.37178i	0.727705	+	0.685890i	$0.240587\pi$
$277$			4.75469e19i			1.37178i	−0.727705	+	0.685890i	$0.759413\pi$
$278$	−3.03132e17	+	2.06736e18i	−0.00849714	+	0.0579505i
$279$		−	1.56861e19i		−	0.427250i
$280$	−4.32963e17	+	9.27432e17i	−0.0114601	+	0.0245481i
$281$	4.87614e19			1.25437			0.627184	−	0.778871i	$-0.284207\pi$
$281$	4.87614e19			1.25437			0.627184	+	0.778871i	$0.284207\pi$
$282$	7.57194e19	+	1.11026e19i	1.89328	+	0.277607i
$283$	−5.32351e19			−1.29392			−0.646958	−	0.762525i	$-0.723959\pi$
$283$	−5.32351e19			−1.29392			−0.646958	+	0.762525i	$0.723959\pi$
$284$	−1.40633e19	+	4.69247e19i	−0.332308	+	1.10881i
$285$		−	3.97857e17i		−	0.00914045i
$286$	−3.47617e19	−	5.09703e18i	−0.776556	−	0.113865i
$287$		−	5.60003e19i		−	1.21656i
$288$	6.35814e19	−	7.13408e19i	1.34335	−	1.50729i
$289$	−3.79941e18			−0.0780789
$290$	1.35291e16	−	9.22682e16i	0.000270448	−	0.00184446i
$291$	−3.58586e19			−0.697349
$292$	−3.94958e19	−	1.18368e19i	−0.747288	−	0.223961i
$293$		−	3.46900e19i		−	0.638650i	−0.947645	−	0.319325i	$-0.896544\pi$
$293$		−	3.46900e19i		−	0.638650i	0.947645	−	0.319325i	$-0.103456\pi$
$294$	−1.02950e19	+	7.02116e19i	−0.184436	+	1.25785i
$295$			6.05987e17i			0.0105654i
$296$	−4.94684e19	−	2.30939e19i	−0.839448	−	0.391889i
$297$	5.64763e19			0.932857
$298$	5.51371e19	+	8.08462e18i	0.886571	+	0.129996i
$299$	1.65798e20			2.59543
$300$	−1.09155e20	−	3.27136e19i	−1.66369	−	0.498607i
$301$		−	9.72836e19i		−	1.44380i
$302$	−1.07943e20	−	1.58275e19i	−1.56005	−	0.228747i
$303$			1.39477e20i			1.96319i
$304$	−1.55667e19	−	1.02514e19i	−0.213407	−	0.140538i
$305$	−1.04035e18			−0.0138925
$306$	−2.16202e19	+	1.47450e20i	−0.281248	+	1.91811i
$307$	4.53779e18			0.0575093			0.0287546	−	0.999587i	$-0.490846\pi$
$307$	4.53779e18			0.0575093			0.0287546	+	0.999587i	$0.490846\pi$
$308$	−1.61188e19	+	5.37835e19i	−0.199034	+	0.664115i
$309$			1.33279e19i			0.160359i
$310$	5.39045e16	−	3.67628e17i	0.000632021	−	0.00431038i
$311$			1.44732e20i			1.65380i	0.562350	+	0.826899i	$0.309897\pi$
$311$			1.44732e20i			1.65380i	−0.562350	+	0.826899i	$0.690103\pi$
$312$	2.10602e20	+	9.83176e19i	2.34545	+	1.09495i
$313$	3.12630e19			0.339372			0.169686	−	0.985498i	$-0.445725\pi$
$313$	3.12630e19			0.339372			0.169686	+	0.985498i	$0.445725\pi$
$314$	−1.03487e20	−	1.51740e19i	−1.09508	−	0.160569i
$315$	5.30226e18			0.0546986
$316$	1.00473e18	−	3.35246e18i	0.0101054	−	0.0337184i
$317$		−	7.83194e19i		−	0.768060i	−0.923321	−	0.384030i	$-0.874536\pi$
$317$		−	7.83194e19i		−	0.768060i	0.923321	−	0.384030i	$-0.125464\pi$
$318$	1.32643e20	+	1.94492e19i	1.26844	+	0.185988i
$319$		−	5.11567e18i		−	0.0477064i
$320$	1.73529e18	−	1.45349e18i	0.0157823	−	0.0132194i
$321$	−1.45106e20			−1.28720
$322$	3.84399e19	−	2.62160e20i	0.332610	−	2.26840i
$323$	2.90671e19			0.245348
$324$	−1.23015e20	−	3.68675e19i	−1.01298	−	0.303588i
$325$		−	1.85347e20i		−	1.48909i
$326$	6.28083e18	−	4.28352e19i	0.0492353	−	0.335784i
$327$		−	1.39173e20i		−	1.06457i
$328$	−5.23902e19	+	1.12223e20i	−0.391074	+	0.837702i
$329$	1.98929e20			1.44921
$330$	2.62249e18	+	3.84529e17i	0.0186467	+	0.00273412i
$331$	−1.31546e20			−0.912965			−0.456482	−	0.889732i	$-0.650891\pi$
$331$	−1.31546e20			−0.912965			−0.456482	+	0.889732i	$0.650891\pi$
$332$	−8.99484e19	−	2.69574e19i	−0.609381	−	0.182631i
$333$			2.82818e20i			1.87048i
$334$	−4.13357e19	−	6.06095e18i	−0.266903	−	0.0391353i
$335$		−	5.59926e18i		−	0.0352998i
$336$	2.04287e20	−	3.10209e20i	1.25756	−	1.90959i
$337$	−1.07266e20			−0.644795			−0.322398	−	0.946604i	$-0.604489\pi$
$337$	−1.07266e20			−0.644795			−0.322398	+	0.946604i	$0.604489\pi$
$338$	−3.01318e19	+	2.05499e20i	−0.176885	+	1.20636i
$339$	−1.78129e19			−0.102126
$340$	−1.01341e18	+	3.38142e18i	−0.00567483	+	0.0189351i
$341$		−	2.03826e19i		−	0.111487i
$342$	−1.40083e19	+	9.55366e19i	−0.0748475	+	0.510459i
$343$		−	6.76482e19i		−	0.353105i
$344$	−9.10121e19	+	1.94953e20i	−0.464121	+	0.994173i
$345$	−1.25081e19			−0.0623216
$346$	2.07188e20	+	3.03796e19i	1.00869	+	0.147901i
$347$	−5.43727e19			−0.258669			−0.129335	−	0.991601i	$-0.541284\pi$
$347$	−5.43727e19			−0.258669			−0.129335	+	0.991601i	$0.541284\pi$
$348$	−9.71550e18	+	3.24176e19i	−0.0451680	+	0.150711i
$349$			3.03512e20i			1.37903i	0.724273	+	0.689513i	$0.242175\pi$
$349$			3.03512e20i			1.37903i	−0.724273	+	0.689513i	$0.757825\pi$
$350$	−2.93071e20	−	4.29724e19i	−1.30146	−	0.190829i
$351$		−	6.07698e20i		−	2.63773i
$352$	8.26178e19	−	9.27005e19i	0.350536	−	0.393315i
$353$	−1.33241e20			−0.552636			−0.276318	−	0.961066i	$-0.589114\pi$
$353$	−1.33241e20			−0.552636			−0.276318	+	0.961066i	$0.589114\pi$
$354$	3.19041e19	−	2.17586e20i	0.129366	−	0.882276i
$355$	6.01115e18			0.0238304
$356$	2.44201e20	+	7.31868e19i	0.946560	+	0.283683i
$357$			5.79241e20i			2.19540i
$358$	6.29107e19	−	4.29051e20i	0.233163	−	1.59017i
$359$			9.11891e19i			0.330512i	0.986251	+	0.165256i	$0.0528450\pi$
$359$			9.11891e19i			0.330512i	−0.986251	+	0.165256i	$0.947155\pi$
$360$	−1.06255e19	−	4.96044e18i	−0.0376644	−	0.0175833i
$361$	−2.69608e20			−0.934707
$362$	3.41145e20	+	5.00213e19i	1.15683	+	0.169624i
$363$	−3.78427e20			−1.25525
$364$	5.78722e20	+	1.73442e20i	1.87784	+	0.562787i
$365$			5.05949e18i			0.0160607i
$366$	3.73547e20	+	5.47724e19i	1.16010	+	0.170103i
$367$			3.81979e20i			1.16068i	0.814376	+	0.580338i	$0.197080\pi$
$367$			3.81979e20i			1.16068i	−0.814376	+	0.580338i	$0.802920\pi$
$368$	−3.22291e20	+	4.89397e20i	−0.958222	+	1.45505i
$369$	6.41592e20			1.86659
$370$	−9.71888e17	+	6.62827e18i	−0.00276696	+	0.0188706i
$371$	3.48479e20			0.970926
$372$	−3.87099e19	+	1.29163e20i	−0.105555	+	0.352204i
$373$		−	4.35744e20i		−	1.16295i	−0.813565	−	0.581474i	$-0.802476\pi$
$373$		−	4.35744e20i		−	1.16295i	0.813565	−	0.581474i	$-0.197524\pi$
$374$	−2.80934e19	+	1.91597e20i	−0.0733891	+	0.500513i
$375$			2.79718e19i			0.0715271i
$376$	−3.98647e20	−	1.86105e20i	−0.997897	−	0.465860i
$377$	−5.50457e19			−0.134894
$378$	−9.60892e20	−	1.40893e20i	−2.30537	−	0.338031i
$379$	−2.50281e20			−0.587915			−0.293957	−	0.955819i	$-0.594972\pi$
$379$	−2.50281e20			−0.587915			−0.293957	+	0.955819i	$0.594972\pi$
$380$	−6.56613e17	+	2.19091e18i	−0.00151022	+	0.00503913i
$381$		−	5.96413e20i		−	1.34322i
$382$	−4.31548e20	−	6.32769e19i	−0.951749	−	0.139553i
$383$			2.60837e20i			0.563350i	0.959510	+	0.281675i	$0.0908901\pi$
$383$			2.60837e20i			0.563350i	−0.959510	+	0.281675i	$0.909110\pi$
$384$	−6.99596e20	+	4.30530e20i	−1.47978	+	0.910654i
$385$	6.88977e18			0.0142731
$386$	1.21829e20	−	8.30875e20i	0.247203	−	1.68592i
$387$	1.11457e21			2.21524
$388$	1.97466e20	+	5.91803e19i	0.384448	+	0.115219i
$389$		−	1.76863e20i		−	0.337318i	−0.985674	−	0.168659i	$-0.946056\pi$
$389$		−	1.76863e20i		−	0.337318i	0.985674	−	0.168659i	$-0.0539437\pi$
$390$	4.13762e18	−	2.82185e19i	0.00773096	−	0.0527251i
$391$		−	9.13832e20i		−	1.67283i
$392$	1.72568e20	−	3.69649e20i	0.309507	−	0.662982i
$393$	−2.57122e20			−0.451854
$394$	−2.78359e20	−	4.08151e19i	−0.479331	−	0.0702832i
$395$	−4.29457e17			−0.000724675
$396$	−6.16194e20	−	1.84673e20i	−1.01896	−	0.305380i
$397$			2.61763e20i			0.424214i	0.977246	+	0.212107i	$0.0680325\pi$
$397$			2.61763e20i			0.424214i	−0.977246	+	0.212107i	$0.931968\pi$
$398$	2.88553e20	+	4.23098e19i	0.458311	+	0.0672011i
$399$			3.75306e20i			0.584254i
$400$	5.47103e20	+	3.60293e20i	0.834813	+	0.549764i
$401$	1.16374e21			1.74061			0.870306	−	0.492512i	$-0.163921\pi$
$401$	1.16374e21			1.74061			0.870306	+	0.492512i	$0.163921\pi$
$402$	−2.94791e20	+	2.01047e21i	−0.432220	+	2.94774i
$403$	−2.19321e20			−0.315239
$404$	2.30190e20	−	7.68071e20i	0.324366	−	1.08231i
$405$			1.57585e19i			0.0217708i
$406$	−1.27622e19	+	8.70383e19i	−0.0172869	+	0.117897i
$407$			3.67494e20i			0.488085i
$408$	5.41900e20	−	1.16078e21i	0.705729	−	1.51171i
$409$	−1.10927e21			−1.41662			−0.708308	−	0.705904i	$-0.750541\pi$
$409$	−1.10927e21			−1.41662			−0.708308	+	0.705904i	$0.750541\pi$
$410$	1.50367e19	+	2.20480e18i	0.0188314	+	0.00276120i
$411$	−9.02640e20			−1.10861
$412$	2.19960e19	−	7.33938e19i	0.0264952	−	0.0884060i
$413$		−	5.71639e20i		−	0.675338i
$414$	3.00355e21	+	4.40403e20i	3.48042	+	0.510326i
$415$			1.15226e19i			0.0130968i
$416$	−9.97477e20	−	8.88986e20i	−1.11213	−	0.991171i
$417$	−9.30463e19			−0.101768
$418$	−1.82025e19	+	1.24141e20i	−0.0195308	+	0.133200i
$419$	−4.23643e20			−0.445952			−0.222976	−	0.974824i	$-0.571577\pi$
$419$	−4.23643e20			−0.445952			−0.222976	+	0.974824i	$0.571577\pi$
$420$	−4.36599e19	−	1.30848e19i	−0.0450908	−	0.0135137i
$421$			1.59237e21i			1.61357i	0.590845	+	0.806785i	$0.298794\pi$
$421$			1.59237e21i			1.61357i	−0.590845	+	0.806785i	$0.701206\pi$
$422$	−1.90393e20	+	1.29848e21i	−0.189300	+	1.29103i
$423$			2.27912e21i			2.22354i
$424$	−6.98341e20	−	3.26014e20i	−0.668560	−	0.312112i
$425$	−1.02158e21			−0.959760
$426$	−2.15836e21	−	3.16476e20i	−1.98998	−	0.291786i
$427$	9.81379e20			0.888002
$428$	7.99067e20	+	2.39479e20i	0.709631	+	0.212676i
$429$		−	1.56453e21i		−	1.36372i
$430$	2.61217e19	+	3.83017e18i	0.0223488	+	0.00327695i
$431$		−	1.53175e21i		−	1.28638i	−0.765706	−	0.643191i	$-0.777610\pi$
$431$		−	1.53175e21i		−	1.28638i	0.765706	−	0.643191i	$-0.222390\pi$
$432$	1.79378e21	+	1.18129e21i	1.47877	+	0.973840i
$433$	1.99504e21			1.61454			0.807269	−	0.590184i	$-0.200945\pi$
$433$	1.99504e21			1.61454			0.807269	+	0.590184i	$0.200945\pi$
$434$	−5.08491e19	+	3.46791e20i	−0.0403985	+	0.275518i
$435$	4.15275e18			0.00323908
$436$	−2.29688e20	+	7.66396e20i	−0.175892	+	0.586896i
$437$		−	5.92096e20i		−	0.445185i
$438$	2.66373e20	−	1.81666e21i	0.196651	−	1.34116i
$439$			1.50927e20i			0.109408i	0.998503	+	0.0547042i	$0.0174216\pi$
$439$			1.50927e20i			0.109408i	−0.998503	+	0.0547042i	$0.982578\pi$
$440$	−1.38068e19	−	6.44561e18i	−0.00982818	−	0.00458820i
$441$	−2.11334e21			−1.47727
$442$	2.06163e21	+	3.02291e20i	1.41524	+	0.207514i
$443$	−3.88698e20			−0.262049			−0.131025	−	0.991379i	$-0.541827\pi$
$443$	−3.88698e20			−0.262049			−0.131025	+	0.991379i	$0.541827\pi$
$444$	6.97932e20	−	2.32878e21i	0.462114	−	1.54193i
$445$		−	3.12827e19i		−	0.0203434i
$446$	−1.90054e21	−	2.78672e20i	−1.21394	−	0.177998i
$447$			2.48158e21i			1.55692i
$448$	−1.63693e21	+	1.37110e21i	−1.00880	+	0.844979i
$449$	−1.74854e21			−1.05854			−0.529268	−	0.848455i	$-0.677533\pi$
$449$	−1.74854e21			−1.05854			−0.529268	+	0.848455i	$0.677533\pi$
$450$	4.92332e20	−	3.35770e21i	0.292791	−	1.99684i
$451$	8.33687e20			0.487069
$452$	9.80917e19	+	2.93980e19i	0.0563021	+	0.0168737i
$453$		−	4.85824e21i		−	2.73964i
$454$	−8.12824e19	+	5.54345e20i	−0.0450349	+	0.307138i
$455$		−	7.41354e19i		−	0.0403585i
$456$	3.51111e20	−	7.52099e20i	0.187813	−	0.402306i
$457$	2.37948e21			1.25070			0.625348	−	0.780346i	$-0.284957\pi$
$457$	2.37948e21			1.25070			0.625348	+	0.780346i	$0.284957\pi$
$458$	2.20188e21	+	3.22856e20i	1.13728	+	0.166757i
$459$	−3.34946e21			−1.70010
$460$	6.88794e19	+	2.06431e19i	0.0343579	+	0.0102970i
$461$			2.89981e21i			1.42155i	0.703419	+	0.710775i	$0.251656\pi$
$461$			2.89981e21i			1.42155i	−0.703419	+	0.710775i	$0.748344\pi$
$462$	−2.47384e21	−	3.62734e20i	−1.19189	−	0.174764i
$463$		−	1.46551e21i		−	0.693968i	−0.937871	−	0.346984i	$-0.887206\pi$
$463$		−	1.46551e21i		−	0.693968i	0.937871	−	0.346984i	$-0.112794\pi$
$464$	1.07002e20	−	1.62482e20i	0.0498023	−	0.0756244i
$465$	1.65460e19			0.00756954
$466$	−8.97624e19	+	6.12179e20i	−0.0403652	+	0.275290i
$467$	1.52883e21			0.675807			0.337904	−	0.941181i	$-0.390282\pi$
$467$	1.52883e21			0.675807			0.337904	+	0.941181i	$0.390282\pi$
$468$	−1.98712e21	+	6.63039e21i	−0.863489	+	2.88119i
$469$			5.28188e21i			2.25635i
$470$	−7.83207e18	+	5.34147e19i	−0.00328923	+	0.0224325i
$471$		−	4.65766e21i		−	1.92309i
$472$	−5.34788e20	+	1.14554e21i	−0.217093	+	0.465025i
$473$	1.44828e21			0.578047
$474$	1.54201e20	+	2.26101e19i	0.0605146	+	0.00887312i
$475$	−6.61911e20			−0.255418
$476$	9.55966e20	−	3.18976e21i	0.362733	−	1.21033i
$477$			3.99251e21i			1.48970i
$478$	−3.93339e21	−	5.76743e20i	−1.44326	−	0.211621i
$479$		−	5.68193e20i		−	0.205027i	−0.994732	−	0.102514i	$-0.967311\pi$
$479$		−	5.68193e20i		−	0.205027i	0.994732	−	0.102514i	$-0.0326885\pi$
$480$	7.52515e19	+	6.70668e19i	0.0267046	+	0.0238000i
$481$	3.95432e21			1.38010
$482$	−5.28782e20	+	3.60629e21i	−0.181510	+	1.23790i
$483$	1.17991e22			3.98357
$484$	2.08392e21	+	6.24547e20i	0.692018	+	0.207397i
$485$		−	2.52957e19i		−	0.00826254i
$486$	3.01642e19	−	2.05720e20i	0.00969173	−	0.0660976i
$487$		−	5.34846e21i		−	1.69043i	−0.534427	−	0.845215i	$-0.679472\pi$
$487$		−	5.34846e21i		−	1.69043i	0.534427	−	0.845215i	$-0.320528\pi$
$488$	−1.96665e21	−	9.18113e20i	−0.611460	−	0.285455i
$489$	1.92790e21			0.589677
$490$	−4.95293e19	−	7.26237e18i	−0.0149037	−	0.00218529i
$491$	−6.54352e21			−1.93713			−0.968567	−	0.248754i	$-0.919979\pi$
$491$	−6.54352e21			−1.93713			−0.968567	+	0.248754i	$0.919979\pi$
$492$	−5.28300e21	−	1.58331e21i	−1.53872	−	0.461153i
$493$			3.03397e20i			0.0869432i
$494$	1.33578e21	+	1.95862e20i	0.376634	+	0.0552250i
$495$			7.89357e19i			0.0218994i
$496$	4.26334e20	−	6.47385e20i	0.116385	−	0.176730i
$497$	−5.67043e21			−1.52323
$498$	6.06642e20	−	4.13729e21i	0.160361	−	1.09366i
$499$	−2.06449e21			−0.537043			−0.268521	−	0.963274i	$-0.586535\pi$
$499$	−2.06449e21			−0.537043			−0.268521	+	0.963274i	$0.586535\pi$
$500$	4.61641e19	−	1.54035e20i	0.0118180	−	0.0394329i
$501$		−	1.86041e21i		−	0.468713i
$502$	1.89939e19	−	1.29538e20i	0.00470960	−	0.0321194i
$503$			5.60405e21i			1.36760i	0.729671	+	0.683799i	$0.239673\pi$
$503$			5.60405e21i			1.36760i	−0.729671	+	0.683799i	$0.760327\pi$
$504$	1.00233e22	+	4.67927e21i	2.40749	+	1.12392i
$505$	−9.83914e19			−0.0232609
$506$	3.90282e21	+	5.72262e20i	0.908185	+	0.133165i
$507$	−9.24897e21			−2.11851
$508$	−9.84306e20	+	3.28432e21i	−0.221932	+	0.740517i
$509$			7.51707e20i			0.166842i	0.996514	+	0.0834212i	$0.0265847\pi$
$509$			7.51707e20i			0.166842i	−0.996514	+	0.0834212i	$0.973415\pi$
$510$	−1.55533e20	−	2.28054e19i	−0.0339829	−	0.00498284i
$511$		−	4.77271e21i		−	1.02659i
$512$	4.56306e21	−	1.21624e21i	0.966265	−	0.257549i
$513$	−2.17020e21			−0.452441
$514$	9.44074e20	−	6.43858e21i	0.193776	−	1.32155i
$515$	−9.40189e18			−0.00190002
$516$	−9.17762e21	−	2.75052e21i	−1.82613	−	0.547290i
$517$			2.96150e21i			0.580212i
$518$	9.16800e20	−	6.25257e21i	0.176863	−	1.20620i
$519$			9.32501e21i			1.77137i
$520$	−6.93562e19	+	1.48565e20i	−0.0129735	+	0.0277900i
$521$	−2.90338e21			−0.534813			−0.267406	−	0.963584i	$-0.586167\pi$
$521$	−2.90338e21			−0.534813			−0.267406	+	0.963584i	$0.586167\pi$
$522$	−9.97193e20	−	1.46216e20i	−0.180890	−	0.0265235i
$523$	3.64624e21			0.651376			0.325688	−	0.945477i	$-0.394404\pi$
$523$	3.64624e21			0.651376			0.325688	+	0.945477i	$0.394404\pi$
$524$	1.41591e21	+	4.24348e20i	0.249107	+	0.0746572i
$525$		−	1.31904e22i		−	2.28551i
$526$	8.02648e20	+	1.17690e20i	0.136974	+	0.0200842i
$527$			1.20884e21i			0.203181i
$528$	4.61814e21	+	3.04127e21i	0.764532	+	0.503481i
$529$	−1.24821e22			−2.03537
$530$	−1.37200e19	+	9.35707e19i	−0.00220368	+	0.0150291i
$531$	6.54924e21			1.03618
$532$	6.19395e20	−	2.06673e21i	0.0965328	−	0.322099i
$533$		−	8.97066e21i		−	1.37723i
$534$	−1.64697e21	+	1.12324e22i	−0.249090	+	1.69879i
$535$		−	1.02362e20i		−	0.0152514i
$536$	4.94138e21	−	1.05847e22i	0.725320	−	1.55368i
$537$	1.93105e22			2.79253
$538$	−6.18199e21	−	9.06451e20i	−0.880786	−	0.129148i
$539$	−2.74608e21			−0.385481
$540$	7.56629e19	−	2.52463e20i	0.0104648	−	0.0349179i
$541$			3.69220e21i			0.503161i	0.967836	+	0.251581i	$0.0809504\pi$
$541$			3.69220e21i			0.503161i	−0.967836	+	0.251581i	$0.919050\pi$
$542$	7.21424e21	+	1.05781e21i	0.968716	+	0.142041i
$543$			1.53540e22i			2.03153i
$544$	−4.89985e21	+	5.49782e21i	−0.638839	+	0.716802i
$545$	9.81768e19			0.0126135
$546$	−3.90309e21	+	2.66191e22i	−0.494160	+	3.37017i
$547$	5.16085e21			0.643906			0.321953	−	0.946756i	$-0.395661\pi$
$547$	5.16085e21			0.643906			0.321953	+	0.946756i	$0.395661\pi$
$548$	4.97065e21	+	1.48970e21i	0.611179	+	0.183170i
$549$			1.12436e22i			1.36247i
$550$	6.39738e20	−	4.36301e21i	0.0764013	−	0.521056i
$551$			1.96579e20i			0.0231379i
$552$	−2.36450e22	−	1.10385e22i	−2.74301	−	1.28055i
$553$	4.05115e20			0.0463209
$554$	1.20432e22	+	1.76587e21i	1.35727	+	0.199013i
$555$	−2.98321e20			−0.0331391
$556$	5.12386e20	+	1.53561e20i	0.0561046	+	0.0168145i
$557$			3.01991e21i			0.325951i	0.986630	+	0.162975i	$0.0521091\pi$
$557$			3.01991e21i			0.325951i	−0.986630	+	0.162975i	$0.947891\pi$
$558$	−3.97316e21	−	5.82576e20i	−0.422730	−	0.0619839i
$559$		−	1.55838e22i		−	1.63448i
$560$	2.18831e20	+	1.44110e20i	0.0226258	+	0.0149002i
$561$	−8.62328e21			−0.878961
$562$	1.81098e21	−	1.23508e22i	0.181979	−	1.24110i
$563$	−9.85764e21			−0.976576			−0.488288	−	0.872683i	$-0.662378\pi$
$563$	−9.85764e21			−0.976576			−0.488288	+	0.872683i	$0.662378\pi$
$564$	5.62437e21	−	1.87667e22i	0.549340	−	1.83297i
$565$		−	1.25657e19i		−	0.00121004i
$566$	−1.97713e21	+	1.34840e22i	−0.187717	+	1.28023i
$567$		−	1.48653e22i		−	1.39158i
$568$	1.13633e22	+	5.30488e21i	1.04886	+	0.489653i
$569$	4.42407e21			0.402647			0.201323	−	0.979525i	$-0.435476\pi$
$569$	4.42407e21			0.402647			0.201323	+	0.979525i	$0.435476\pi$
$570$	−1.00774e20	−	1.47762e19i	−0.00904375	−	0.00132606i
$571$	−1.06170e22			−0.939535			−0.469768	−	0.882790i	$-0.655662\pi$
$571$	−1.06170e22			−0.939535			−0.469768	+	0.882790i	$0.655662\pi$
$572$	−2.58207e21	+	8.61554e21i	−0.225320	+	0.751821i
$573$		−	1.94229e22i		−	1.67138i
$574$	−1.41844e22	−	2.07983e21i	−1.20369	−	0.176495i
$575$			2.08096e22i			1.74149i
$576$	−1.57086e22	−	1.87542e22i	−1.29646	−	1.54781i
$577$	1.07700e22			0.876616			0.438308	−	0.898825i	$-0.355578\pi$
$577$	1.07700e22			0.876616			0.438308	+	0.898825i	$0.355578\pi$
$578$	−1.41109e20	+	9.62360e20i	−0.0113274	+	0.0772529i
$579$	3.73955e22			2.96068
$580$	−2.28683e19	−	6.85360e18i	−0.00178571	−	0.000535174i
$581$		−	1.08695e22i		−	0.837141i
$582$	−1.33177e21	+	9.08269e21i	−0.101169	+	0.689971i
$583$			5.18788e21i			0.388724i
$584$	−4.46503e21	+	9.56434e21i	−0.330006	+	0.706891i
$585$	8.49365e20			0.0619224
$586$	−8.78668e21	−	1.28837e21i	−0.631894	−	0.0926531i
$587$	9.65914e21			0.685226			0.342613	−	0.939477i	$-0.388688\pi$
$587$	9.65914e21			0.685226			0.342613	+	0.939477i	$0.388688\pi$
$588$	1.74017e22	+	5.21525e21i	1.21779	+	0.364970i
$589$			7.83238e20i			0.0540718i
$590$	1.53491e20	+	2.25061e19i	0.0104537	+	0.00153280i
$591$		−	1.25282e22i		−	0.841762i
$592$	−7.68672e21	+	1.16722e22i	−0.509528	+	0.773714i
$593$	−9.15831e21			−0.598933			−0.299466	−	0.954107i	$-0.596809\pi$
$593$	−9.15831e21			−0.598933			−0.299466	+	0.954107i	$0.596809\pi$
$594$	2.09751e21	−	1.43050e22i	0.135336	−	0.922987i
$595$	−4.08614e20			−0.0260122
$596$	4.09554e21	−	1.36655e22i	0.257241	−	0.858333i
$597$			1.29870e22i			0.804848i
$598$	6.15766e21	−	4.19952e22i	0.376536	−	2.56797i
$599$			1.31286e22i			0.792143i	0.918220	+	0.396072i	$0.129627\pi$
$599$			1.31286e22i			0.792143i	−0.918220	+	0.396072i	$0.870373\pi$
$600$	−1.23400e22	+	2.64331e22i	−0.734695	+	1.57376i
$601$	3.82558e21			0.224751			0.112375	−	0.993666i	$-0.464154\pi$
$601$	3.82558e21			0.224751			0.112375	+	0.993666i	$0.464154\pi$
$602$	−2.46411e22	−	3.61307e21i	−1.42853	−	0.209462i
$603$	−6.05142e22			−3.46194
$604$	−8.01793e21	+	2.67533e22i	−0.452654	+	1.51036i
$605$		−	2.66954e20i		−	0.0148728i
$606$	3.53284e22	+	5.18012e21i	1.94242	+	0.284813i
$607$		−	1.40084e22i		−	0.760117i	−0.924962	−	0.380059i	$-0.875904\pi$
$607$		−	1.40084e22i		−	0.760117i	0.924962	−	0.380059i	$-0.124096\pi$
$608$	−3.17474e21	+	3.56218e21i	−0.170012	+	0.190760i
$609$	−3.91737e21			−0.207041
$610$	−3.86381e19	+	2.63511e20i	−0.00201547	+	0.0137455i
$611$	3.18663e22			1.64060
$612$	3.65449e22	+	1.09525e22i	1.85701	+	0.556545i
$613$			1.13416e21i			0.0568842i	0.999595	+	0.0284421i	$0.00905463\pi$
$613$			1.13416e21i			0.0568842i	−0.999595	+	0.0284421i	$0.990945\pi$
$614$	1.68532e20	−	1.14939e21i	0.00834324	−	0.0569008i
$615$			6.76763e20i			0.0330701i
$616$	1.30243e22	+	6.08026e21i	0.628214	+	0.293276i
$617$	−1.76356e22			−0.839669			−0.419834	−	0.907601i	$-0.637912\pi$
$617$	−1.76356e22			−0.839669			−0.419834	+	0.907601i	$0.637912\pi$
$618$	3.37584e21	+	4.94992e20i	0.158663	+	0.0232643i
$619$	−2.69419e22			−1.24998			−0.624990	−	0.780632i	$-0.714897\pi$
$619$	−2.69419e22			−1.24998			−0.624990	+	0.780632i	$0.714897\pi$
$620$	−9.11152e19	−	2.73071e19i	−0.00417309	−	0.00125067i
$621$			6.82284e22i			3.08484i
$622$	3.66595e22	+	5.37530e21i	1.63630	+	0.239927i
$623$			2.95095e22i			1.30034i
$624$	3.27247e22	−	4.96922e22i	1.42364	−	2.16178i
$625$	2.32535e22			0.998729
$626$	1.16109e21	−	7.91865e21i	0.0492348	−	0.335781i
$627$	−5.58724e21			−0.233915
$628$	−7.68689e21	+	2.56487e22i	−0.317741	+	1.06020i
$629$		−	2.17951e22i		−	0.889517i
$630$	1.96923e20	−	1.34302e21i	0.00793548	−	0.0541199i
$631$		−	3.47935e22i		−	1.38440i	−0.721704	−	0.692202i	$-0.756641\pi$
$631$		−	3.47935e22i		−	1.38440i	0.721704	−	0.692202i	$-0.243359\pi$
$632$	−8.11836e20	−	3.78999e20i	−0.0318957	−	0.0148902i
$633$	−5.84411e22			−2.26720
$634$	−1.98377e22	−	2.90875e21i	−0.759935	−	0.111427i
$635$	4.20727e20			0.0159152
$636$	9.85264e21	−	3.28752e22i	0.368041	−	1.22804i
$637$			2.95484e22i			1.08998i
$638$	−1.29576e21	−	1.89994e20i	−0.0472017	−	0.00692108i
$639$		−	6.49658e22i		−	2.33710i
$640$	−3.03709e20	−	4.93516e20i	−0.0107899	−	0.0175332i
$641$	3.79131e22			1.33022			0.665112	−	0.746743i	$-0.268384\pi$
$641$	3.79131e22			1.33022			0.665112	+	0.746743i	$0.268384\pi$
$642$	−5.38917e21	+	3.67541e22i	−0.186742	+	1.27358i
$643$	4.45719e22			1.52536			0.762681	−	0.646775i	$-0.223883\pi$
$643$	4.45719e22			1.52536			0.762681	+	0.646775i	$0.223883\pi$
$644$	−6.49752e22	−	1.94730e22i	−2.19614	−	0.658182i
$645$			1.17567e21i			0.0392471i
$646$	1.07954e21	−	7.36246e21i	0.0355941	−	0.242752i
$647$		−	4.66673e22i		−	1.51977i	−0.650057	−	0.759885i	$-0.725255\pi$
$647$		−	4.66673e22i		−	1.51977i	0.650057	−	0.759885i	$-0.274745\pi$
$648$	−1.39070e22	+	2.97895e22i	−0.447335	+	0.958216i
$649$	8.51010e21			0.270382
$650$	−4.69470e22	−	6.88372e21i	−1.47333	−	0.216031i
$651$	−1.56081e22			−0.483842
$652$	−1.06165e22	−	3.18177e21i	−0.325089	−	0.0974288i
$653$		−	3.34170e22i		−	1.01079i	−0.862887	−	0.505397i	$-0.831346\pi$
$653$		−	3.34170e22i		−	1.01079i	0.862887	−	0.505397i	$-0.168654\pi$
$654$	−3.52514e22	−	5.16883e21i	−1.05330	−	0.154444i
$655$		−	1.81381e20i		−	0.00535380i
$656$	2.64793e22	+	1.74379e22i	0.772104	+	0.508468i
$657$	5.46807e22			1.57511
$658$	7.38814e21	−	5.03871e22i	0.210246	−	1.43388i
$659$	−3.58778e22			−1.00865			−0.504327	−	0.863513i	$-0.668259\pi$
$659$	−3.58778e22			−1.00865			−0.504327	+	0.863513i	$0.668259\pi$
$660$	1.94796e20	−	6.49973e20i	0.00541039	−	0.0180528i
$661$			6.24943e22i			1.71486i	0.514601	+	0.857430i	$0.327940\pi$
$661$			6.24943e22i			1.71486i	−0.514601	+	0.857430i	$0.672060\pi$
$662$	−4.88557e21	+	3.33195e22i	−0.132450	+	0.903306i
$663$			9.27884e22i			2.48534i
$664$	−1.01687e22	+	2.17820e22i	−0.269105	+	0.576439i
$665$	−2.64752e20			−0.00692254
$666$	7.16353e22	+	1.05037e22i	1.85069	+	0.271362i
$667$	6.18018e21			0.157759
$668$	−3.07038e21	+	1.02449e22i	−0.0774426	+	0.258401i
$669$		−	8.55383e22i		−	2.13183i
$670$	−1.41824e21	−	2.07954e20i	−0.0349263	−	0.00512117i
$671$			1.46100e22i			0.355524i
$672$	−7.09862e22	−	6.32653e22i	−1.70695	−	1.52129i
$673$	−3.89635e22			−0.925844			−0.462922	−	0.886399i	$-0.653199\pi$
$673$	−3.89635e22			−0.925844			−0.462922	+	0.886399i	$0.653199\pi$
$674$	−3.98380e21	+	2.71695e22i	−0.0935446	+	0.637973i
$675$	7.62734e22			1.76988
$676$	5.09321e22	+	1.52643e22i	1.16793	+	0.350028i
$677$		−	7.43728e22i		−	1.68541i	−0.538378	−	0.842703i	$-0.680963\pi$
$677$		−	7.43728e22i		−	1.68541i	0.538378	−	0.842703i	$-0.319037\pi$
$678$	−6.61563e20	+	4.51185e21i	−0.0148161	+	0.101046i
$679$			2.38619e22i			0.528138i
$680$	8.18848e20	+	3.82272e20i	0.0179115	+	0.00836183i
$681$	−2.49496e22			−0.539371
$682$	−5.16274e21	−	7.57001e20i	−0.110308	−	0.0161741i
$683$	5.63870e22			1.19073			0.595365	−	0.803455i	$-0.297008\pi$
$683$	5.63870e22			1.19073			0.595365	+	0.803455i	$0.297008\pi$
$684$	2.36784e22	+	7.09638e21i	0.494200	+	0.148111i
$685$		−	6.36749e20i		−	0.0131354i
$686$	−1.71347e22	−	2.51243e21i	−0.349369	−	0.0512272i
$687$			9.91007e22i			1.99721i
$688$	4.59998e22	+	3.02931e22i	0.916322	+	0.603442i
$689$	5.58227e22			1.09915
$690$	−4.64545e20	+	3.16820e21i	−0.00904139	+	0.0616623i
$691$	−7.96104e22			−1.53160			−0.765801	−	0.643078i	$-0.777657\pi$
$691$	−7.96104e22			−1.53160			−0.765801	+	0.643078i	$0.777657\pi$
$692$	1.53898e22	−	5.13508e22i	0.292674	−	0.976559i
$693$		−	7.44615e22i		−	1.39980i
$694$	−2.01938e21	+	1.37722e22i	−0.0375268	+	0.255933i
$695$		−	6.56376e19i		−	0.00120580i
$696$	7.85027e21	+	3.66483e21i	0.142564	+	0.0665549i
$697$	−4.94438e22			−0.887666
$698$	7.68771e22	+	1.12723e22i	1.36444	+	0.200064i
$699$	−2.75526e22			−0.483442
$700$	−2.17691e22	+	7.26366e22i	−0.377621	+	1.26000i
$701$			5.69069e22i			0.975934i	0.872862	+	0.487967i	$0.162261\pi$
$701$			5.69069e22i			0.975934i	−0.872862	+	0.487967i	$0.837739\pi$
$702$	−1.53925e23	−	2.25696e22i	−2.60983	−	0.382673i
$703$		−	1.41216e22i		−	0.236724i
$704$	−2.04119e22	−	2.43693e22i	−0.338299	−	0.403888i
$705$	−2.40406e21			−0.0393941
$706$	−4.94850e21	+	3.37487e22i	−0.0801744	+	0.546789i
$707$	9.28144e22			1.48683
$708$	−5.39278e22	−	1.61621e22i	−0.854174	−	0.255995i
$709$			1.22572e23i			1.91965i	0.280598	+	0.959825i	$0.409467\pi$
$709$			1.22572e23i			1.91965i	−0.280598	+	0.959825i	$0.590533\pi$
$710$	2.23252e20	−	1.52257e21i	0.00345722	−	0.0235783i
$711$			4.64138e21i			0.0710706i
$712$	2.76071e22	−	5.91360e22i	0.418005	−	0.895390i
$713$	2.46240e22			0.368674
$714$	1.46717e23	+	2.15128e22i	2.17217	+	0.318501i
$715$	1.10367e21			0.0161581
$716$	−1.06338e23	−	3.18695e22i	−1.53952	−	0.461393i
$717$		−	1.77031e23i		−	2.53453i
$718$	2.30974e22	+	3.38672e21i	0.327015	+	0.0479495i
$719$			1.27708e22i			0.178808i	0.995995	+	0.0894038i	$0.0284962\pi$
$719$			1.27708e22i			0.178808i	−0.995995	+	0.0894038i	$0.971504\pi$
$720$	−1.65107e21	+	2.50713e21i	−0.0228615	+	0.0347150i
$721$	8.86898e21			0.121448
$722$	−1.00131e22	+	6.82895e22i	−0.135604	+	0.924818i
$723$	−1.62310e23			−2.17389
$724$	2.53399e22	−	8.45514e22i	0.335658	−	1.11998i
$725$		−	6.90890e21i		−	0.0905117i
$726$	−1.40546e22	+	9.58524e22i	−0.182107	+	1.24197i
$727$		−	1.26680e23i		−	1.62343i	−0.584053	−	0.811716i	$-0.698534\pi$
$727$		−	1.26680e23i		−	1.62343i	0.584053	−	0.811716i	$-0.301466\pi$
$728$	6.54250e22	−	1.40144e23i	0.829263	−	1.77633i
$729$	−7.50933e22			−0.941415
$730$	1.28153e21	+	1.87907e20i	0.0158908	+	0.00233002i
$731$	−8.58937e22			−1.05347
$732$	2.77468e22	−	9.25822e22i	0.336607	−	1.12315i
$733$			8.21872e22i			0.986217i	0.869968	+	0.493108i	$0.164139\pi$
$733$			8.21872e22i			0.986217i	−0.869968	+	0.493108i	$0.835861\pi$
$734$	9.67521e22	+	1.41865e22i	1.14840	+	0.168387i
$735$		−	2.22919e21i		−	0.0261726i
$736$	1.11990e23	+	9.98097e22i	1.30064	+	1.15918i
$737$	−7.86324e22			−0.903362
$738$	2.38285e22	−	1.62510e23i	0.270798	−	1.84684i
$739$	1.78827e22			0.201038			0.100519	−	0.994935i	$-0.467950\pi$
$739$	1.78827e22			0.201038			0.100519	+	0.994935i	$0.467950\pi$
$740$	1.64279e21	+	4.92342e20i	0.0182696	+	0.00547537i
$741$			6.01200e22i			0.661414i
$742$	1.29424e22	−	8.82669e22i	0.140858	−	0.960654i
$743$			2.62065e21i			0.0282162i	0.999900	+	0.0141081i	$0.00449090\pi$
$743$			2.62065e21i			0.0282162i	−0.999900	+	0.0141081i	$0.995509\pi$
$744$	3.12782e22	+	1.46019e22i	0.333164	+	0.155535i
$745$	−1.75058e21			−0.0184472
$746$	−1.10370e23	−	1.61833e22i	−1.15065	−	0.168716i
$747$	1.24531e23			1.28443
$748$	4.74865e22	+	1.42317e22i	0.484571	+	0.145225i
$749$			9.65600e22i			0.974861i
$750$	7.08503e21	+	1.03886e21i	0.0707704	+	0.0103769i
$751$		−	5.95428e22i		−	0.588450i	−0.955736	−	0.294225i	$-0.904938\pi$
$751$		−	5.95428e22i		−	0.588450i	0.955736	−	0.294225i	$-0.0950615\pi$
$752$	−6.19444e22	+	9.40621e22i	−0.605702	+	0.919754i
$753$	5.83017e21			0.0564055
$754$	−2.04437e21	+	1.39426e22i	−0.0195699	+	0.133467i
$755$	3.42715e21			0.0324606
$756$	−7.13742e22	+	2.38153e23i	−0.668909	+	2.23194i
$757$			4.91588e22i			0.455863i	0.973677	+	0.227931i	$0.0731962\pi$
$757$			4.91588e22i			0.455863i	−0.973677	+	0.227931i	$0.926804\pi$
$758$	−9.29533e21	+	6.33941e22i	−0.0852926	+	0.581695i
$759$			1.75656e23i			1.59488i
$760$	5.30553e20	+	2.47684e20i	0.00476672	+	0.00222530i
$761$	1.27235e23			1.13117			0.565587	−	0.824689i	$-0.308650\pi$
$761$	1.27235e23			1.13117			0.565587	+	0.824689i	$0.308650\pi$
$762$	−1.51066e23	−	2.21505e22i	−1.32901	−	0.194870i
$763$	−9.26120e22			−0.806252
$764$	−3.20550e22	+	1.06958e23i	−0.276153	+	0.921434i
$765$		−	4.68147e21i		−	0.0399108i
$766$	6.60678e22	+	9.68736e21i	0.557390	+	0.0817289i
$767$		−	9.15705e22i		−	0.764527i
$768$	8.30669e22	+	1.93191e23i	0.686339	+	1.59624i
$769$	−4.12009e22			−0.336896			−0.168448	−	0.985711i	$-0.553875\pi$
$769$	−4.12009e22			−0.336896			−0.168448	+	0.985711i	$0.553875\pi$
$770$	2.55883e20	−	1.74512e21i	0.00207069	−	0.0141221i
$771$	2.89784e23			2.32081
$772$	−2.05929e23	−	6.17166e22i	−1.63222	−	0.489175i
$773$		−	1.72584e23i		−	1.35383i	−0.736060	−	0.676916i	$-0.763316\pi$
$773$		−	1.72584e23i		−	1.35383i	0.736060	−	0.676916i	$-0.236684\pi$
$774$	4.13947e22	−	2.82312e23i	0.321379	−	2.19180i
$775$		−	2.75274e22i		−	0.211520i
$776$	2.23237e22	−	4.78185e22i	0.169774	−	0.363666i
$777$	2.81412e23			2.11824
$778$	−4.47979e22	−	6.56861e21i	−0.333750	−	0.0489369i
$779$	−3.20359e22			−0.236231
$780$	−6.99385e21	−	2.09605e21i	−0.0510457	−	0.0152983i
$781$		−	8.44168e22i		−	0.609846i
$782$	−2.31466e23	−	3.39393e22i	−1.65513	−	0.242689i
$783$		−	2.26522e22i		−	0.160330i
$784$	−8.72200e22	−	5.74386e22i	−0.611065	−	0.402416i
$785$	3.28565e21			0.0227858
$786$	−9.54939e21	+	6.51268e22i	−0.0655534	+	0.447074i
$787$	−8.99010e22			−0.610895			−0.305448	−	0.952209i	$-0.598806\pi$
$787$	−8.99010e22			−0.610895			−0.305448	+	0.952209i	$0.598806\pi$
$788$	−2.06763e22	+	6.89901e22i	−0.139079	+	0.464063i
$789$			3.61251e22i			0.240543i
$790$	−1.59498e19	+	1.08778e20i	−0.000105133	+	0.000717008i
$791$			1.18535e22i			0.0773454i
$792$	−6.96612e22	+	1.49218e23i	−0.449976	+	0.963874i
$793$	1.57207e23			1.00528
$794$	6.63024e22	+	9.72177e21i	0.419726	+	0.0615434i
$795$	−4.21137e21			−0.0263929
$796$	2.14334e22	−	7.15166e22i	0.132980	−	0.443713i
$797$			2.43606e23i			1.49631i	0.663525	+	0.748154i	$0.269059\pi$
$797$			2.43606e23i			1.49631i	−0.663525	+	0.748154i	$0.730941\pi$
$798$	9.50618e22	+	1.39387e22i	0.578073	+	0.0847615i
$799$		−	1.75639e23i		−	1.05742i
$800$	1.11578e23	−	1.25195e23i	0.665059	−	0.746223i
$801$	−3.38089e23			−1.99513
$802$	4.32209e22	−	2.94766e23i	0.252522	−	1.72220i
$803$	7.10522e22			0.411011
$804$	4.98287e23	+	1.49336e23i	2.85385	+	0.855295i
$805$			8.32345e21i			0.0471994i
$806$	−8.14549e21	+	5.55522e22i	−0.0457338	+	0.311904i
$807$		−	2.78235e23i		−	1.54676i
$808$	−1.85997e23	−	8.68310e22i	−1.02380	−	0.477952i
$809$	−2.56684e23			−1.39898			−0.699489	−	0.714643i	$-0.746589\pi$
$809$	−2.56684e23			−1.39898			−0.699489	+	0.714643i	$0.746589\pi$
$810$	3.99150e21	+	5.85264e20i	0.0215405	+	0.00315843i
$811$	1.51026e23			0.807021			0.403510	−	0.914975i	$-0.367790\pi$
$811$	1.51026e23			0.807021			0.403510	+	0.914975i	$0.367790\pi$
$812$	2.15721e22	+	6.46513e21i	0.114142	+	0.0342081i
$813$			3.24694e23i			1.70118i
$814$	9.30832e22	+	1.36486e22i	0.482921	+	0.0708096i
$815$			1.36000e21i			0.00698679i
$816$	−2.73890e23	−	1.80370e23i	−1.39333	−	0.917576i
$817$	−5.56527e22			−0.280356
$818$	−4.11979e22	+	2.80970e23i	−0.205518	+	1.40163i
$819$	−8.01222e23			−3.95805
$820$	1.11691e21	−	3.72679e21i	0.00546398	−	0.0182316i
$821$		−	6.20303e22i		−	0.300510i	−0.988647	−	0.150255i	$-0.951991\pi$
$821$		−	6.20303e22i		−	0.300510i	0.988647	−	0.150255i	$-0.0480094\pi$
$822$	−3.35237e22	+	2.28631e23i	−0.160834	+	1.09688i
$823$		−	2.45805e23i		−	1.16786i	−0.811802	−	0.583932i	$-0.801513\pi$
$823$		−	2.45805e23i		−	1.16786i	0.811802	−	0.583932i	$-0.198487\pi$
$824$	−1.77731e22	−	8.29723e21i	−0.0836269	−	0.0390405i
$825$	1.96368e23			0.915037
$826$	−1.44791e23	−	2.12304e22i	−0.668194	−	0.0979757i
$827$	2.93931e23			1.34339			0.671693	−	0.740829i	$-0.265567\pi$
$827$	2.93931e23			1.34339			0.671693	+	0.740829i	$0.265567\pi$
$828$	2.23101e23	−	7.44417e23i	1.00985	−	3.36956i
$829$		−	2.26218e23i		−	1.01412i	−0.861910	−	0.507061i	$-0.830732\pi$
$829$		−	2.26218e23i		−	1.01412i	0.861910	−	0.507061i	$-0.169268\pi$
$830$	2.91857e21	+	4.27943e20i	0.0129582	+	0.00190003i
$831$			5.42035e23i			2.38352i
$832$	−2.62219e23	+	2.19636e23i	−1.14203	+	0.956571i
$833$	1.62863e23			0.702524
$834$	−3.45570e21	+	2.35678e22i	−0.0147641	+	0.100691i
$835$	1.31239e21			0.00555355
$836$	3.07677e22	+	9.22106e21i	0.128957	+	0.0386483i
$837$		−	9.02541e22i		−	0.374682i
$838$	−1.57339e22	+	1.07305e23i	−0.0646971	+	0.441234i
$839$			2.80264e23i			1.14149i	0.821128	+	0.570744i	$0.193345\pi$
$839$			2.80264e23i			1.14149i	−0.821128	+	0.570744i	$0.806655\pi$
$840$	−4.93578e21	+	1.05727e22i	−0.0199123	+	0.0426533i
$841$	2.48195e23			0.991801
$842$	4.03334e23	+	5.91400e22i	1.59650	+	0.234091i
$843$	5.55879e23			2.17951
$844$	3.21823e23	+	9.64499e22i	1.24991	+	0.374595i
$845$		−	6.52450e21i		−	0.0251011i
$846$	5.77282e23	+	8.46455e22i	2.20001	+	0.322583i
$847$			2.51822e23i			0.950664i
$848$	−1.08513e23	+	1.64776e23i	−0.405802	+	0.616207i
$849$	−6.06879e23			−2.24823
$850$	−3.79412e22	+	2.58759e23i	−0.139239	+	0.949606i
$851$	−4.43965e23			−1.61403
$852$	−1.60321e23	+	5.34942e23i	−0.577397	+	1.92659i
$853$			8.90406e22i			0.317684i	0.987304	+	0.158842i	$0.0507761\pi$
$853$			8.90406e22i			0.317684i	−0.987304	+	0.158842i	$0.949224\pi$
$854$	3.64480e22	−	2.48575e23i	0.128828	−	0.878607i
$855$		−	3.03324e21i		−	0.0106213i
$856$	9.03351e22	−	1.93503e23i	0.313376	−	0.671270i
$857$	1.36979e23			0.470770			0.235385	−	0.971902i	$-0.424365\pi$
$857$	1.36979e23			0.470770			0.235385	+	0.971902i	$0.424365\pi$
$858$	−3.96283e23	−	5.81061e22i	−1.34930	−	0.197844i
$859$	1.02210e22			0.0344783			0.0172392	−	0.999851i	$-0.494512\pi$
$859$	1.02210e22			0.0344783			0.0172392	+	0.999851i	$0.494512\pi$
$860$	1.94030e21	−	6.47417e21i	0.00648457	−	0.0216370i
$861$		−	6.38403e23i		−	2.11383i
$862$	−3.87980e23	−	5.68886e22i	−1.27277	−	0.186624i
$863$		−	1.12197e23i		−	0.364665i	−0.983237	−	0.182332i	$-0.941635\pi$
$863$		−	1.12197e23i		−	0.364665i	0.983237	−	0.182332i	$-0.0583647\pi$
$864$	3.65832e23	−	4.10478e23i	1.17807	−	1.32184i
$865$	−6.57814e21			−0.0209881
$866$	7.40949e22	−	5.05327e23i	0.234231	−	1.59746i
$867$	−4.33133e22			−0.135665
$868$	8.59507e22	+	2.57593e22i	0.266742	+	0.0799423i
$869$			6.03102e21i			0.0185452i
$870$	1.54231e20	−	1.05186e21i	0.000469914	−	0.00320481i
$871$			8.46102e23i			2.55433i
$872$	1.85591e23	+	8.66416e22i	0.555169	+	0.259176i
$873$	−2.73385e23			−0.810328
$874$	−1.49973e23	−	2.19902e22i	−0.440475	−	0.0645858i
$875$	1.86137e22			0.0541712
$876$	−4.50252e23	−	1.34940e23i	−1.29844	−	0.389142i
$877$		−	4.97763e23i		−	1.42241i	−0.702983	−	0.711207i	$-0.748149\pi$
$877$		−	4.97763e23i		−	1.42241i	0.702983	−	0.711207i	$-0.251851\pi$
$878$	3.82285e22	+	5.60536e21i	0.108251	+	0.0158726i
$879$		−	3.95466e23i		−	1.10968i
$880$	−2.14540e21	+	3.25777e21i	−0.00596550	+	0.00905856i
$881$	−3.26122e23			−0.898613			−0.449307	−	0.893378i	$-0.648329\pi$
$881$	−3.26122e23			−0.898613			−0.449307	+	0.893378i	$0.648329\pi$
$882$	−7.84884e22	+	5.35291e23i	−0.214317	+	1.46164i
$883$	4.48800e22			0.121441			0.0607207	−	0.998155i	$-0.480660\pi$
$883$	4.48800e22			0.121441			0.0607207	+	0.998155i	$0.480660\pi$
$884$	1.53136e23	−	5.10965e23i	0.410637	−	1.37017i
$885$			6.90825e21i			0.0183579i
$886$	−1.44361e22	+	9.84541e22i	−0.0380172	+	0.259277i
$887$			4.45254e23i			1.16203i	0.813891	+	0.581017i	$0.197345\pi$
$887$			4.45254e23i			1.16203i	−0.813891	+	0.581017i	$0.802655\pi$
$888$	−5.63939e23	−	2.63270e23i	−1.45857	−	0.680923i
$889$	−3.96880e23			−1.01729
$890$	−7.92364e21	−	1.16182e21i	−0.0201282	−	0.00295135i
$891$	2.21302e23			0.557140
$892$	−1.41170e23	+	4.71041e23i	−0.352229	+	1.17528i
$893$		−	1.13801e23i		−	0.281406i
$894$	6.28563e23	+	9.21647e22i	1.54045	+	0.225873i
$895$			1.36222e22i			0.0330873i
$896$	2.86494e23	+	4.65542e23i	0.689686	+	1.12072i
$897$	1.89009e24			4.50966
$898$	−6.49402e22	+	4.42892e23i	−0.153569	+	1.04734i
$899$	−8.17528e21			−0.0191613
$900$	−8.32193e23	−	2.49407e23i	−1.93323	−	0.579387i
$901$		−	3.07680e23i		−	0.708436i
$902$	3.09628e22	−	2.11166e23i	0.0706623	−	0.481916i
$903$		−	1.10903e24i		−	2.50866i
$904$	1.10893e22	−	2.37540e22i	0.0248633	−	0.0532585i
$905$	−1.08312e22			−0.0240706
$906$	−1.23055e24	−	1.80433e23i	−2.71066	−	0.397457i
$907$	7.50271e23			1.63817			0.819087	−	0.573670i	$-0.194481\pi$
$907$	7.50271e23			1.63817			0.819087	+	0.573670i	$0.194481\pi$
$908$	1.37392e23	+	4.11763e22i	0.297355	+	0.0891170i
$909$			1.06337e24i			2.28125i
$910$	−1.87779e22	−	2.75336e21i	−0.0399315	−	0.00585506i
$911$		−	6.79150e23i		−	1.43159i	−0.698311	−	0.715795i	$-0.746065\pi$
$911$		−	6.79150e23i		−	1.43159i	0.698311	−	0.715795i	$-0.253935\pi$
$912$	−1.77460e23	−	1.16866e23i	−0.370802	−	0.244191i
$913$	1.61816e23			0.335162
$914$	8.83727e22	−	6.02702e23i	0.181447	−	1.23746i
$915$	−1.18600e22			−0.0241387
$916$	1.63553e23	−	5.45726e23i	0.329986	−	1.10106i
$917$			1.71100e23i			0.342213i
$918$	−1.24398e23	+	8.48391e23i	−0.246644	+	1.68211i
$919$		−	2.06494e23i		−	0.405867i	−0.979192	−	0.202934i	$-0.934952\pi$
$919$		−	2.06494e23i		−	0.405867i	0.979192	−	0.202934i	$-0.0650476\pi$
$920$	7.78687e21	−	1.66799e22i	0.0151726	−	0.0325006i
$921$	5.17308e22			0.0999246
$922$	7.34498e23	+	1.07698e23i	1.40651	+	0.206233i
$923$	−9.08343e23			−1.72439
$924$	−1.83755e23	+	6.13131e23i	−0.345830	+	1.15393i
$925$			4.96314e23i			0.926026i
$926$	−3.71200e23	−	5.44283e22i	−0.686626	−	0.100678i
$927$			1.01611e23i			0.186339i
$928$	−3.71814e22	−	3.31373e22i	−0.0675992	−	0.0602467i
$929$	−5.18768e23			−0.935078			−0.467539	−	0.883973i	$-0.654859\pi$
$929$	−5.18768e23			−0.935078			−0.467539	+	0.883973i	$0.654859\pi$
$930$	6.14511e20	−	4.19096e21i	0.00109816	−	0.00748945i
$931$	1.05523e23			0.186960
$932$	1.51726e23	+	4.54721e22i	0.266522	+	0.0798763i
$933$			1.64995e24i			2.87354i
$934$	5.67799e22	−	3.87239e23i	0.0980437	−	0.668658i
$935$		−	6.08312e21i		−	0.0104144i
$936$	1.60562e24	+	7.49570e23i	2.72544	+	1.27235i
$937$	−6.85152e23			−1.15311			−0.576554	−	0.817059i	$-0.695603\pi$
$937$	−6.85152e23			−1.15311			−0.576554	+	0.817059i	$0.695603\pi$
$938$	1.33786e24	+	1.96167e23i	2.23248	+	0.327343i
$939$	3.56398e23			0.589672
$940$	1.32386e22	+	3.96760e21i	0.0217180	+	0.00650886i
$941$		−	6.73594e23i		−	1.09567i	−0.836585	−	0.547837i	$-0.815451\pi$
$941$		−	6.73594e23i		−	1.09567i	0.836585	−	0.547837i	$-0.184549\pi$
$942$	−1.17975e24	−	1.72983e23i	−1.90275	−	0.278996i
$943$			1.00717e24i			1.61068i
$944$	2.70295e23	+	1.78002e23i	0.428610	+	0.282260i
$945$	3.05079e22			0.0479687
$946$	5.37885e22	−	3.66837e23i	0.0838610	−	0.571932i
$947$	−6.42448e23			−0.993203			−0.496601	−	0.867979i	$-0.665419\pi$
$947$	−6.42448e23			−0.993203			−0.496601	+	0.867979i	$0.665419\pi$
$948$	1.14539e22	−	3.82181e22i	0.0175585	−	0.0585871i
$949$		−	7.64537e23i		−	1.16217i
$950$	−2.45831e22	+	1.67656e23i	−0.0370551	+	0.252715i
$951$		−	8.92841e23i		−	1.33453i
$952$	−7.72435e23	−	3.60605e23i	−1.14490	−	0.534485i
$953$	−1.08164e24			−1.58979			−0.794897	−	0.606744i	$-0.792475\pi$
$953$	−1.08164e24			−1.58979			−0.794897	+	0.606744i	$0.792475\pi$
$954$	1.01127e24	+	1.48280e23i	1.47394	+	0.216120i
$955$	1.37015e22			0.0198034
$956$	−2.92168e23	+	9.74874e23i	−0.418765	+	1.39729i
$957$		−	5.83186e22i		−	0.0828918i
$958$	−1.43918e23	−	2.11024e22i	−0.202858	−	0.0297446i
$959$			6.00657e23i			0.839611i
$960$	1.97823e22	−	1.65698e22i	0.0274224	−	0.0229692i
$961$	6.94850e23			0.955221
$962$	1.46862e23	−	1.00160e24i	0.200220	−	1.36550i
$963$	−1.10628e24			−1.49574
$964$	8.93805e23	+	2.67872e23i	1.19847	+	0.359180i
$965$			2.63799e22i			0.0350796i
$966$	4.38214e23	−	2.98862e24i	0.577922	−	3.94143i
$967$			5.45487e23i			0.713465i	0.934207	+	0.356732i	$0.116109\pi$
$967$			5.45487e23i			0.713465i	−0.934207	+	0.356732i	$0.883891\pi$
$968$	2.35588e23	−	5.04643e23i	0.305598	−	0.654608i
$969$	3.31365e23			0.426301
$970$	−6.40720e21	−	9.39473e20i	−0.00817513	−	0.00119870i
$971$	7.23928e22			0.0916097			0.0458049	−	0.998950i	$-0.485415\pi$
$971$	7.23928e22			0.0916097			0.0458049	+	0.998950i	$0.485415\pi$
$972$	−5.09868e22	−	1.52807e22i	−0.0639922	−	0.0191784i
$973$			6.19172e22i			0.0770741i
$974$	−1.35472e24	−	1.98640e23i	−1.67255	−	0.245242i
$975$		−	2.11296e24i		−	2.58734i
$976$	−3.05591e23	+	4.64037e23i	−0.371143	+	0.563578i
$977$	9.20618e23			1.10898			0.554489	−	0.832191i	$-0.312914\pi$
$977$	9.20618e23			1.10898			0.554489	+	0.832191i	$0.312914\pi$
$978$	7.16015e22	−	4.88322e23i	0.0855482	−	0.583439i
$979$	−4.39314e23			−0.520611
$980$	−3.67900e21	+	1.22756e22i	−0.00432435	+	0.0144290i
$981$		−	1.06105e24i		−	1.23704i
$982$	−2.43024e23	+	1.65742e24i	−0.281032	+	1.91664i
$983$		−	4.57246e23i		−	0.524472i	−0.965004	−	0.262236i	$-0.915540\pi$
$983$		−	4.57246e23i		−	0.524472i	0.965004	−	0.262236i	$-0.0844599\pi$
$984$	−5.97248e23	+	1.27934e24i	−0.679507	+	1.45554i
$985$	8.83777e21			0.00997362
$986$	7.68479e22	+	1.12680e22i	0.0860234	+	0.0126134i
$987$	2.26779e24			2.51806
$988$	9.92206e22	−	3.31068e23i	0.109281	−	0.364637i
$989$			1.74965e24i			1.91153i
$990$	1.99937e22	+	2.93164e21i	0.0216677	+	0.00317708i
$991$			8.74434e23i			0.940022i	0.882661	+	0.470011i	$0.155750\pi$
$991$			8.74434e23i			0.940022i	−0.882661	+	0.470011i	$0.844250\pi$
$992$	−1.48143e23	−	1.32031e23i	−0.157975	−	0.140793i
$993$	−1.49962e24			−1.58631
$994$	−2.10597e23	+	1.43627e24i	−0.220984	+	1.50711i
$995$	−9.16141e21			−0.00953625
$996$	−1.02541e24	−	3.07315e23i	−1.05882	−	0.317328i
$997$		−	1.48784e24i		−	1.52404i	−0.647556	−	0.762018i	$-0.724209\pi$
$997$		−	1.48784e24i		−	1.52404i	0.647556	−	0.762018i	$-0.275791\pi$
$998$	−7.66744e22	+	5.22919e23i	−0.0779123	+	0.531361i
$999$			1.62726e24i			1.64034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.9	✓	14
3.2	odd	2		72.17.b.b.19.6		14
4.3	odd	2		32.17.d.b.15.2		14
8.3	odd	2	inner	8.17.d.b.3.10	yes	14
8.5	even	2		32.17.d.b.15.1		14
24.11	even	2		72.17.b.b.19.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.9	✓	14	1.1	even	1	trivial
8.17.d.b.3.10	yes	14	8.3	odd	2	inner
32.17.d.b.15.1		14	8.5	even	2
32.17.d.b.15.2		14	4.3	odd	2
72.17.b.b.19.5		14	24.11	even	2
72.17.b.b.19.6		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)

\(f(q)\)	\(=\)	\(q+(37.1396 - 253.292i) q^{2} +11400.0 q^{3} +(-62777.3 - 18814.3i) q^{4} +8041.89i q^{5} +(423391. - 2.88752e6i) q^{6} -7.58607e6i q^{7} +(-7.09702e6 + 1.52022e7i) q^{8} +8.69132e7 q^{9} +O(q^{10})\)	\(q+(37.1396 - 253.292i) q^{2} +11400.0 q^{3} +(-62777.3 - 18814.3i) q^{4} +8041.89i q^{5} +(423391. - 2.88752e6i) q^{6} -7.58607e6i q^{7} +(-7.09702e6 + 1.52022e7i) q^{8} +8.69132e7 q^{9} +(2.03694e6 + 298672. i) q^{10} +1.12935e8 q^{11} +(-7.15661e8 - 2.14483e8i) q^{12} -1.21521e9i q^{13} +(-1.92149e9 - 2.81743e8i) q^{14} +9.16775e7i q^{15} +(3.58701e9 + 2.36222e9i) q^{16} -6.69789e9 q^{17} +(3.22792e9 - 2.20144e10i) q^{18} -4.33974e9 q^{19} +(1.51302e8 - 5.04848e8i) q^{20} -8.64811e10i q^{21} +(4.19437e9 - 2.86056e10i) q^{22} +1.36436e11i q^{23} +(-8.09060e10 + 1.73305e11i) q^{24} +1.52523e11 q^{25} +(-3.07802e11 - 4.51323e10i) q^{26} +5.00077e11 q^{27} +(-1.42726e11 + 4.76233e11i) q^{28} -4.52974e10i q^{29} +(2.32212e10 + 3.40486e9i) q^{30} -1.80480e11i q^{31} +(7.31551e11 - 8.20829e11i) q^{32} +1.28746e12 q^{33} +(-2.48757e11 + 1.69652e12i) q^{34} +6.10064e10 q^{35} +(-5.45617e12 - 1.63521e12i) q^{36} +3.25403e12i q^{37} +(-1.61176e11 + 1.09922e12i) q^{38} -1.38534e13i q^{39} +(-1.22255e11 - 5.70735e10i) q^{40} +7.38199e12 q^{41} +(-2.19049e13 - 3.21187e12i) q^{42} +1.28240e13 q^{43} +(-7.08977e12 - 2.12480e12i) q^{44} +6.98946e11i q^{45} +(3.45580e13 + 5.06717e12i) q^{46} +2.62230e13i q^{47} +(4.08919e13 + 2.69293e13i) q^{48} -2.43155e13 q^{49} +(5.66465e12 - 3.86329e13i) q^{50} -7.63560e13 q^{51} +(-2.28633e13 + 7.62875e13i) q^{52} +4.59368e13i q^{53} +(1.85726e13 - 1.26665e14i) q^{54} +9.08213e11i q^{55} +(1.15325e14 + 5.38385e13i) q^{56} -4.94730e13 q^{57} +(-1.14734e13 - 1.68232e12i) q^{58} +7.53538e13 q^{59} +(1.72485e12 - 5.75527e12i) q^{60} +1.29366e14i q^{61} +(-4.57142e13 - 6.70296e12i) q^{62} -6.59329e14i q^{63} +(-1.80740e14 - 2.15781e14i) q^{64} +9.77257e12 q^{65} +(4.78157e13 - 3.26103e14i) q^{66} -6.96261e14 q^{67} +(4.20476e14 + 1.26016e14i) q^{68} +1.55537e15i q^{69} +(2.26575e12 - 1.54524e13i) q^{70} -7.47479e14i q^{71} +(-6.16825e14 + 1.32127e15i) q^{72} +6.29141e14 q^{73} +(8.24217e14 + 1.20853e14i) q^{74} +1.73876e15 q^{75} +(2.72437e14 + 8.16491e13i) q^{76} -8.56734e14i q^{77} +(-3.50894e15 - 5.14508e14i) q^{78} +5.34025e13i q^{79} +(-1.89967e13 + 2.88464e13i) q^{80} +1.95955e15 q^{81} +(2.74164e14 - 1.86980e15i) q^{82} +1.43282e15 q^{83} +(-1.62708e15 + 5.42905e15i) q^{84} -5.38638e13i q^{85} +(4.76277e14 - 3.24821e15i) q^{86} -5.16390e14i q^{87} +(-8.01504e14 + 1.71687e15i) q^{88} -3.88996e15 q^{89} +(1.77037e14 + 2.59586e13i) q^{90} -9.21865e15 q^{91} +(2.56694e15 - 8.56507e15i) q^{92} -2.05748e15i q^{93} +(6.64205e15 + 9.73909e14i) q^{94} -3.48997e13i q^{95} +(8.33967e15 - 9.35744e15i) q^{96} -3.14550e15 q^{97} +(-9.03067e14 + 6.15891e15i) q^{98} +9.81556e15 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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