LMFDB - Embedded newform 8.17.d.b.3.4

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			3.4
Root			$101.867 - 58.4667i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.17.d.b.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-227.734 + 116.933i) q^{2} +6146.29 q^{3} +(38189.2 - 53259.3i) q^{4} -351107. i q^{5} +(-1.39972e6 + 718707. i) q^{6} +1.24931e6i q^{7} +(-2.46917e6 + 1.65945e7i) q^{8} -5.26981e6 q^{9} +O(q^{10})$	\(q+(-227.734 + 116.933i) q^{2} +6146.29 q^{3} +(38189.2 - 53259.3i) q^{4} -351107. i q^{5} +(-1.39972e6 + 718707. i) q^{6} +1.24931e6i q^{7} +(-2.46917e6 + 1.65945e7i) q^{8} -5.26981e6 q^{9} +(4.10562e7 + 7.99589e7i) q^{10} -2.06484e8 q^{11} +(2.34722e8 - 3.27347e8i) q^{12} -1.33000e9i q^{13} +(-1.46086e8 - 2.84510e8i) q^{14} -2.15801e9i q^{15} +(-1.37814e9 - 4.06786e9i) q^{16} +4.19741e9 q^{17} +(1.20011e9 - 6.16216e8i) q^{18} -1.43002e10 q^{19} +(-1.86997e10 - 1.34085e10i) q^{20} +7.67862e9i q^{21} +(4.70234e10 - 2.41449e10i) q^{22} -1.00379e11i q^{23} +(-1.51762e10 + 1.01995e11i) q^{24} +2.93115e10 q^{25} +(1.55522e11 + 3.02887e11i) q^{26} -2.96968e11 q^{27} +(6.65374e10 + 4.77101e10i) q^{28} -1.67262e11i q^{29} +(2.52343e11 + 4.91451e11i) q^{30} +1.59955e11i q^{31} +(7.89517e11 + 7.65238e11i) q^{32} -1.26911e12 q^{33} +(-9.55890e11 + 4.90817e11i) q^{34} +4.38642e11 q^{35} +(-2.01250e11 + 2.80666e11i) q^{36} -6.26866e12i q^{37} +(3.25663e12 - 1.67217e12i) q^{38} -8.17460e12i q^{39} +(5.82646e12 + 8.66944e11i) q^{40} -1.26072e13 q^{41} +(-8.97887e11 - 1.74868e12i) q^{42} +2.52302e12 q^{43} +(-7.88546e12 + 1.09972e13i) q^{44} +1.85027e12i q^{45} +(1.17376e13 + 2.28596e13i) q^{46} +3.05775e13i q^{47} +(-8.47045e12 - 2.50022e13i) q^{48} +3.16722e13 q^{49} +(-6.67521e12 + 3.42749e12i) q^{50} +2.57985e13 q^{51} +(-7.08351e13 - 5.07918e13i) q^{52} +4.55717e13i q^{53} +(6.76295e13 - 3.47254e13i) q^{54} +7.24981e13i q^{55} +(-2.07317e13 - 3.08476e12i) q^{56} -8.78931e13 q^{57} +(1.95586e13 + 3.80913e13i) q^{58} +1.99749e14 q^{59} +(-1.14934e14 - 8.24126e13i) q^{60} -1.04180e14i q^{61} +(-1.87041e13 - 3.64271e13i) q^{62} -6.58362e12i q^{63} +(-2.69281e14 - 8.19494e13i) q^{64} -4.66974e14 q^{65} +(2.89019e14 - 1.48401e14i) q^{66} +6.31598e14 q^{67} +(1.60295e14 - 2.23551e14i) q^{68} -6.16958e14i q^{69} +(-9.98935e13 + 5.12919e13i) q^{70} +9.94832e14i q^{71} +(1.30121e13 - 8.74500e13i) q^{72} -8.30960e14 q^{73} +(7.33015e14 + 1.42758e15i) q^{74} +1.80157e14 q^{75} +(-5.46112e14 + 7.61618e14i) q^{76} -2.57963e14i q^{77} +(9.55883e14 + 1.86163e15i) q^{78} -1.59174e15i q^{79} +(-1.42826e15 + 4.83875e14i) q^{80} -1.59840e15 q^{81} +(2.87108e15 - 1.47420e15i) q^{82} -5.20043e14 q^{83} +(4.08958e14 + 2.93240e14i) q^{84} -1.47374e15i q^{85} +(-5.74576e14 + 2.95025e14i) q^{86} -1.02804e15i q^{87} +(5.09844e14 - 3.42650e15i) q^{88} +1.46614e15 q^{89} +(-2.16358e14 - 4.21368e14i) q^{90} +1.66159e15 q^{91} +(-5.34611e15 - 3.83338e15i) q^{92} +9.83131e14i q^{93} +(-3.57552e15 - 6.96351e15i) q^{94} +5.02090e15i q^{95} +(4.85260e15 + 4.70337e15i) q^{96} +4.30286e15 q^{97} +(-7.21281e15 + 3.70353e15i) q^{98} +1.08813e15 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 $

$2$	−227.734	+	116.933i	−0.889584	+	0.456771i
$2$	−227.734	+	116.933i	−0.889584	+	0.456771i
$3$	6146.29			0.936792			0.468396	−	0.883519i	$-0.344832\pi$
$3$	6146.29			0.936792			0.468396	+	0.883519i	$0.344832\pi$
$4$	38189.2	−	53259.3i	0.582721	−	0.812673i
$5$		−	351107.i		−	0.898835i	−0.893322	−	0.449417i	$-0.851632\pi$
$5$		−	351107.i		−	0.898835i	0.893322	−	0.449417i	$-0.148368\pi$
$6$	−1.39972e6	+	718707.i	−0.833356	+	0.427899i
$7$			1.24931e6i			0.216713i	0.994112	+	0.108357i	$0.0345589\pi$
$7$			1.24931e6i			0.216713i	−0.994112	+	0.108357i	$0.965441\pi$
$8$	−2.46917e6	+	1.65945e7i	−0.147174	+	0.989111i
$9$	−5.26981e6			−0.122421
$10$	4.10562e7	+	7.99589e7i	0.410562	+	0.799589i
$11$	−2.06484e8			−0.963263			−0.481632	−	0.876374i	$-0.659956\pi$
$11$	−2.06484e8			−0.963263			−0.481632	+	0.876374i	$0.659956\pi$
$12$	2.34722e8	−	3.27347e8i	0.545888	−	0.761305i
$13$		−	1.33000e9i		−	1.63045i	−0.579147	−	0.815223i	$-0.696614\pi$
$13$		−	1.33000e9i		−	1.63045i	0.579147	−	0.815223i	$-0.303386\pi$
$14$	−1.46086e8	−	2.84510e8i	−0.0989884	−	0.192785i
$15$		−	2.15801e9i		−	0.842021i
$16$	−1.37814e9	−	4.06786e9i	−0.320873	−	0.947122i
$17$	4.19741e9			0.601713			0.300857	−	0.953669i	$-0.402727\pi$
$17$	4.19741e9			0.601713			0.300857	+	0.953669i	$0.402727\pi$
$18$	1.20011e9	−	6.16216e8i	0.108904	−	0.0559182i
$19$	−1.43002e10			−0.842001			−0.421001	−	0.907060i	$-0.638321\pi$
$19$	−1.43002e10			−0.842001			−0.421001	+	0.907060i	$0.638321\pi$
$20$	−1.86997e10	−	1.34085e10i	−0.730458	−	0.523770i
$21$			7.67862e9i			0.203015i
$22$	4.70234e10	−	2.41449e10i	0.856904	−	0.439991i
$23$		−	1.00379e11i		−	1.28180i	−0.767625	−	0.640899i	$-0.778562\pi$
$23$		−	1.00379e11i		−	1.28180i	0.767625	−	0.640899i	$-0.221438\pi$
$24$	−1.51762e10	+	1.01995e11i	−0.137871	+	0.926591i
$25$	2.93115e10			0.192096
$26$	1.55522e11	+	3.02887e11i	0.744740	+	1.45042i
$27$	−2.96968e11			−1.05147
$28$	6.65374e10	+	4.77101e10i	0.176117	+	0.126283i
$29$		−	1.67262e11i		−	0.334360i	−0.985926	−	0.167180i	$-0.946534\pi$
$29$		−	1.67262e11i		−	0.334360i	0.985926	−	0.167180i	$-0.0534661\pi$
$30$	2.52343e11	+	4.91451e11i	0.384611	+	0.749049i
$31$			1.59955e11i			0.187545i	0.995594	+	0.0937723i	$0.0298926\pi$
$31$			1.59955e11i			0.187545i	−0.995594	+	0.0937723i	$0.970107\pi$
$32$	7.89517e11	+	7.65238e11i	0.718062	+	0.695980i
$33$	−1.26911e12			−0.902378
$34$	−9.55890e11	+	4.90817e11i	−0.535275	+	0.274845i
$35$	4.38642e11			0.194790
$36$	−2.01250e11	+	2.80666e11i	−0.0713371	+	0.0994879i
$37$		−	6.26866e12i		−	1.78468i	−0.451362	−	0.892341i	$-0.649062\pi$
$37$		−	6.26866e12i		−	1.78468i	0.451362	−	0.892341i	$-0.350938\pi$
$38$	3.25663e12	−	1.67217e12i	0.749031	−	0.384602i
$39$		−	8.17460e12i		−	1.52739i
$40$	5.82646e12	+	8.66944e11i	0.889047	+	0.132285i
$41$	−1.26072e13			−1.57888			−0.789438	−	0.613830i	$-0.789628\pi$
$41$	−1.26072e13			−1.57888			−0.789438	+	0.613830i	$0.789628\pi$
$42$	−8.97887e11	−	1.74868e12i	−0.0927315	−	0.180599i
$43$	2.52302e12			0.215860			0.107930	−	0.994158i	$-0.465578\pi$
$43$	2.52302e12			0.215860			0.107930	+	0.994158i	$0.465578\pi$
$44$	−7.88546e12	+	1.09972e13i	−0.561314	+	0.782818i
$45$			1.85027e12i			0.110036i
$46$	1.17376e13	+	2.28596e13i	0.585488	+	1.14027i
$47$			3.05775e13i			1.28416i	0.766639	+	0.642079i	$0.221928\pi$
$47$			3.05775e13i			1.28416i	−0.766639	+	0.642079i	$0.778072\pi$
$48$	−8.47045e12	−	2.50022e13i	−0.300591	−	0.887257i
$49$	3.16722e13			0.953035
$50$	−6.67521e12	+	3.42749e12i	−0.170885	+	0.0877438i
$51$	2.57985e13			0.563680
$52$	−7.08351e13	−	5.07918e13i	−1.32502	−	0.950094i
$53$			4.55717e13i			0.731961i	0.930622	+	0.365981i	$0.119266\pi$
$53$			4.55717e13i			0.731961i	−0.930622	+	0.365981i	$0.880734\pi$
$54$	6.76295e13	−	3.47254e13i	0.935376	−	0.480283i
$55$			7.24981e13i			0.865815i
$56$	−2.07317e13	−	3.08476e12i	−0.214354	−	0.0318946i
$57$	−8.78931e13			−0.788780
$58$	1.95586e13	+	3.80913e13i	0.152726	+	0.297441i
$59$	1.99749e14			1.36041			0.680204	−	0.733023i	$-0.261891\pi$
$59$	1.99749e14			1.36041			0.680204	+	0.733023i	$0.261891\pi$
$60$	−1.14934e14	−	8.24126e13i	−0.684288	−	0.490663i
$61$		−	1.04180e14i		−	0.543431i	−0.962378	−	0.271715i	$-0.912409\pi$
$61$		−	1.04180e14i		−	0.543431i	0.962378	−	0.271715i	$-0.0875910\pi$
$62$	−1.87041e13	−	3.64271e13i	−0.0856649	−	0.166837i
$63$		−	6.58362e12i		−	0.0265302i
$64$	−2.69281e14	−	8.19494e13i	−0.956680	−	0.291143i
$65$	−4.66974e14			−1.46550
$66$	2.89019e14	−	1.48401e14i	0.802741	−	0.412180i
$67$	6.31598e14			1.55540			0.777700	−	0.628635i	$-0.216386\pi$
$67$	6.31598e14			1.55540			0.777700	+	0.628635i	$0.216386\pi$
$68$	1.60295e14	−	2.23551e14i	0.350631	−	0.488996i
$69$		−	6.16958e14i		−	1.20078i
$70$	−9.98935e13	+	5.12919e13i	−0.173282	+	0.0889742i
$71$			9.94832e14i			1.54058i	0.637697	+	0.770288i	$0.279887\pi$
$71$			9.94832e14i			1.54058i	−0.637697	+	0.770288i	$0.720113\pi$
$72$	1.30121e13	−	8.74500e13i	0.0180171	−	0.121088i
$73$	−8.30960e14			−1.03038			−0.515190	−	0.857076i	$-0.672279\pi$
$73$	−8.30960e14			−1.03038			−0.515190	+	0.857076i	$0.672279\pi$
$74$	7.33015e14	+	1.42758e15i	0.815191	+	1.58763i
$75$	1.80157e14			0.179954
$76$	−5.46112e14	+	7.61618e14i	−0.490652	+	0.684271i
$77$		−	2.57963e14i		−	0.208752i
$78$	9.55883e14	+	1.86163e15i	0.697667	+	1.35874i
$79$		−	1.59174e15i		−	1.04919i	−0.851351	−	0.524597i	$-0.824216\pi$
$79$		−	1.59174e15i		−	1.04919i	0.851351	−	0.524597i	$-0.175784\pi$
$80$	−1.42826e15	+	4.83875e14i	−0.851306	+	0.288412i
$81$	−1.59840e15			−0.862593
$82$	2.87108e15	−	1.47420e15i	1.40454	−	0.721185i
$83$	−5.20043e14			−0.230895			−0.115448	−	0.993314i	$-0.536830\pi$
$83$	−5.20043e14			−0.230895			−0.115448	+	0.993314i	$0.536830\pi$
$84$	4.08958e14	+	2.93240e14i	0.164985	+	0.118301i
$85$		−	1.47374e15i		−	0.540841i
$86$	−5.74576e14	+	2.95025e14i	−0.192026	+	0.0985986i
$87$		−	1.02804e15i		−	0.313226i
$88$	5.09844e14	−	3.42650e15i	0.141767	−	0.952774i
$89$	1.46614e15			0.372439			0.186219	−	0.982508i	$-0.440376\pi$
$89$	1.46614e15			0.372439			0.186219	+	0.982508i	$0.440376\pi$
$90$	−2.16358e14	−	4.21368e14i	−0.0502612	−	0.0978863i
$91$	1.66159e15			0.353339
$92$	−5.34611e15	−	3.83338e15i	−1.04168	−	0.746930i
$93$			9.83131e14i			0.175690i
$94$	−3.57552e15	−	6.96351e15i	−0.586566	−	1.14237i
$95$			5.02090e15i			0.756820i
$96$	4.85260e15	+	4.70337e15i	0.672674	+	0.651988i
$97$	4.30286e15			0.549014			0.274507	−	0.961585i	$-0.411485\pi$
$97$	4.30286e15			0.549014			0.274507	+	0.961585i	$0.411485\pi$
$98$	−7.21281e15	+	3.70353e15i	−0.847805	+	0.435319i
$99$	1.08813e15			0.117923
$100$	1.11938e15	−	1.56111e15i	0.111938	−	0.156111i
$101$			9.16479e15i			0.846353i	0.906047	+	0.423176i	$0.139085\pi$
$101$			9.16479e15i			0.846353i	−0.906047	+	0.423176i	$0.860915\pi$
$102$	−5.87518e15	+	3.01670e15i	−0.501441	+	0.257473i
$103$			1.13403e16i			0.895211i	0.894231	+	0.447606i	$0.147723\pi$
$103$			1.13403e16i			0.895211i	−0.894231	+	0.447606i	$0.852277\pi$
$104$	2.20708e16	+	3.28401e15i	1.61269	+	0.239959i
$105$	2.69602e15			0.182477
$106$	−5.32885e15	−	1.03782e16i	−0.334339	−	0.651141i
$107$	−5.95530e15			−0.346604			−0.173302	−	0.984869i	$-0.555444\pi$
$107$	−5.95530e15			−0.346604			−0.173302	+	0.984869i	$0.555444\pi$
$108$	−1.13409e16	+	1.58163e16i	−0.612716	+	0.854505i
$109$			1.47401e16i			0.739756i	0.929080	+	0.369878i	$0.120600\pi$
$109$			1.47401e16i			0.739756i	−0.929080	+	0.369878i	$0.879400\pi$
$110$	−8.47744e15	−	1.65102e16i	−0.395479	−	0.770215i
$111$		−	3.85290e16i		−	1.67188i
$112$	5.08202e15	−	1.72172e15i	0.205254	−	0.0695375i
$113$	4.25399e16			1.60018			0.800090	−	0.599881i	$-0.204785\pi$
$113$	4.25399e16			1.60018			0.800090	+	0.599881i	$0.204785\pi$
$114$	2.00162e16	−	1.02776e16i	0.701687	−	0.360292i
$115$	−3.52437e16			−1.15212
$116$	−8.90828e15	−	6.38761e15i	−0.271725	−	0.194839i
$117$			7.00887e15i			0.199600i
$118$	−4.54896e16	+	2.33573e16i	−1.21020	+	0.621394i
$119$			5.24386e15i			0.130399i
$120$	3.58111e16	+	5.32849e15i	0.832852	+	0.123924i
$121$	−3.31405e15			−0.0721235
$122$	1.21821e16	+	2.37252e16i	0.248223	+	0.483428i
$123$	−7.74876e16			−1.47908
$124$	8.51910e15	+	6.10855e15i	0.152412	+	0.109286i
$125$		−	6.38662e16i		−	1.07150i
$126$	7.69845e14	+	1.49931e15i	0.0121182	+	0.0236009i
$127$		−	1.15489e17i		−	1.70652i	−0.521489	−	0.853258i	$-0.674623\pi$
$127$		−	1.15489e17i		−	1.70652i	0.521489	−	0.853258i	$-0.325377\pi$
$128$	7.09070e16	−	1.28253e16i	0.984033	−	0.177987i
$129$	1.55072e16			0.202216
$130$	1.06346e17	−	5.46049e16i	1.30369	−	0.669398i
$131$	8.84758e15			0.102013			0.0510064	−	0.998698i	$-0.483757\pi$
$131$	8.84758e15			0.102013			0.0510064	+	0.998698i	$0.483757\pi$
$132$	−4.84663e16	+	6.75920e16i	−0.525834	+	0.733337i
$133$		−	1.78654e16i		−	0.182473i
$134$	−1.43836e17	+	7.38549e16i	−1.38366	+	0.710462i
$135$			1.04267e17i			0.945102i
$136$	−1.03641e16	+	6.96539e16i	−0.0885566	+	0.595161i
$137$	−1.24391e17			−1.00236			−0.501181	−	0.865342i	$-0.667101\pi$
$137$	−1.24391e17			−1.00236			−0.501181	+	0.865342i	$0.667101\pi$
$138$	7.21429e16	+	1.40502e17i	0.548480	+	1.06819i
$139$	1.98945e17			1.42763			0.713813	−	0.700337i	$-0.246967\pi$
$139$	1.98945e17			1.42763			0.713813	+	0.700337i	$0.246967\pi$
$140$	1.67514e16	−	2.33618e16i	0.113508	−	0.158300i
$141$			1.87938e17i			1.20299i
$142$	−1.16329e17	−	2.26557e17i	−0.703690	−	1.37047i
$143$			2.74625e17i			1.57055i
$144$	7.26253e15	+	2.14368e16i	0.0392815	+	0.115947i
$145$	−5.87271e16			−0.300534
$146$	1.89238e17	−	9.71669e16i	0.916610	−	0.470647i
$147$	1.94666e17			0.892796
$148$	−3.33864e17	−	2.39395e17i	−1.45036	−	1.03997i
$149$		−	9.34460e16i		−	0.384654i	−0.981331	−	0.192327i	$-0.938397\pi$
$149$		−	9.34460e16i		−	0.384654i	0.981331	−	0.192327i	$-0.0616035\pi$
$150$	−4.10278e16	+	2.10664e16i	−0.160084	+	0.0821977i
$151$		−	1.66223e17i		−	0.615000i	−0.951548	−	0.307500i	$-0.900508\pi$
$151$		−	1.66223e17i		−	0.615000i	0.951548	−	0.307500i	$-0.0994924\pi$
$152$	3.53096e16	−	2.37305e17i	0.123921	−	0.832832i
$153$	−2.21195e16			−0.0736621
$154$	3.01644e16	+	5.87468e16i	0.0953519	+	0.185703i
$155$	5.61614e16			0.168572
$156$	−4.35373e17	−	3.12181e17i	−1.24127	−	0.890041i
$157$		−	5.16693e17i		−	1.39970i	−0.714289	−	0.699851i	$-0.753250\pi$
$157$		−	5.16693e17i		−	1.39970i	0.714289	−	0.699851i	$-0.246750\pi$
$158$	1.86128e17	+	3.62493e17i	0.479241	+	0.933347i
$159$			2.80097e17i			0.685695i
$160$	2.68681e17	−	2.77205e17i	0.625571	−	0.645419i
$161$	1.25404e17			0.277783
$162$	3.64010e17	−	1.86906e17i	0.767349	−	0.394007i
$163$	6.79422e16			0.136345			0.0681725	−	0.997674i	$-0.478283\pi$
$163$	6.79422e16			0.136345			0.0681725	+	0.997674i	$0.478283\pi$
$164$	−4.81459e17	+	6.71451e17i	−0.920044	+	1.28311i
$165$			4.45594e17i			0.811088i
$166$	1.18431e17	−	6.08104e16i	0.205401	−	0.105466i
$167$		−	1.09077e17i		−	0.180303i	−0.995928	−	0.0901513i	$-0.971265\pi$
$167$		−	1.09077e17i		−	0.180303i	0.995928	−	0.0901513i	$-0.0287351\pi$
$168$	−1.27423e17	−	1.89598e16i	−0.200805	−	0.0298786i
$169$	−1.10350e18			−1.65835
$170$	1.72329e17	+	3.35620e17i	0.247040	+	0.481124i
$171$	7.53592e16			0.103078
$172$	9.63520e16	−	1.34374e17i	0.125786	−	0.175424i
$173$			4.58352e17i			0.571256i	0.958341	+	0.285628i	$0.0922021\pi$
$173$			4.58352e17i			0.571256i	−0.958341	+	0.285628i	$0.907798\pi$
$174$	1.20213e17	+	2.34120e17i	0.143072	+	0.278641i
$175$			3.66191e16i			0.0416298i
$176$	2.84564e17	+	8.39948e17i	0.309085	+	0.912328i
$177$	1.22772e18			1.27442
$178$	−3.33889e17	+	1.71441e17i	−0.331316	+	0.170119i
$179$	2.02397e17			0.192035			0.0960173	−	0.995380i	$-0.469390\pi$
$179$	2.02397e17			0.192035			0.0960173	+	0.995380i	$0.469390\pi$
$180$	9.85440e16	+	7.06602e16i	0.0894232	+	0.0641202i
$181$		−	1.57735e18i		−	1.36931i	−0.728869	−	0.684654i	$-0.759954\pi$
$181$		−	1.57735e18i		−	1.36931i	0.728869	−	0.684654i	$-0.240046\pi$
$182$	−3.78399e17	+	1.94295e17i	−0.314325	+	0.161395i
$183$		−	6.40319e17i		−	0.509082i
$184$	1.66574e18	+	2.47852e17i	1.26784	+	0.188647i
$185$	−2.20097e18			−1.60413
$186$	−1.14961e17	−	2.23892e17i	−0.0802502	−	0.156291i
$187$	−8.66697e17			−0.579608
$188$	1.62853e18	+	1.16773e18i	1.04360	+	0.748305i
$189$		−	3.71004e17i		−	0.227869i
$190$	−5.87111e17	−	1.14343e18i	−0.345693	−	0.673255i
$191$		−	6.99925e17i		−	0.395171i	−0.980286	−	0.197585i	$-0.936690\pi$
$191$		−	6.99925e17i		−	0.395171i	0.980286	−	0.197585i	$-0.0633099\pi$
$192$	−1.65508e18	−	5.03685e17i	−0.896210	−	0.272740i
$193$	2.38156e18			1.23710			0.618548	−	0.785747i	$-0.287721\pi$
$193$	2.38156e18			1.23710			0.618548	+	0.785747i	$0.287721\pi$
$194$	−9.79906e17	+	5.03148e17i	−0.488394	+	0.250774i
$195$	−2.87016e18			−1.37287
$196$	1.20953e18	−	1.68684e18i	0.555353	−	0.774506i
$197$			9.20680e17i			0.405862i	0.979193	+	0.202931i	$0.0650468\pi$
$197$			9.20680e17i			0.405862i	−0.979193	+	0.202931i	$0.934953\pi$
$198$	−2.47804e17	+	1.27239e17i	−0.104903	+	0.0538640i
$199$		−	5.74716e17i		−	0.233684i	−0.993151	−	0.116842i	$-0.962723\pi$
$199$		−	5.74716e17i		−	0.233684i	0.993151	−	0.116842i	$-0.0372771\pi$
$200$	−7.23751e16	+	4.86410e17i	−0.0282715	+	0.190004i
$201$	3.88199e18			1.45709
$202$	−1.07167e18	−	2.08713e18i	−0.386589	−	0.752902i
$203$	2.08963e17			0.0724603
$204$	9.85223e17	−	1.37401e18i	0.328468	−	0.458087i
$205$			4.42648e18i			1.41915i
$206$	−1.32606e18	−	2.58256e18i	−0.408906	−	0.796366i
$207$			5.28977e17i			0.156918i
$208$	−5.41027e18	+	1.83293e18i	−1.54423	+	0.523166i
$209$	2.95276e18			0.811069
$210$	−6.13975e17	+	3.15255e17i	−0.162329	+	0.0833503i
$211$	1.62835e18			0.414464			0.207232	−	0.978292i	$-0.433554\pi$
$211$	1.62835e18			0.414464			0.207232	+	0.978292i	$0.433554\pi$
$212$	2.42712e18	+	1.74035e18i	0.594845	+	0.426529i
$213$			6.11453e18i			1.44320i
$214$	1.35622e18	−	6.96373e17i	0.308333	−	0.158319i
$215$		−	8.85850e17i		−	0.194023i
$216$	7.33264e17	−	4.92803e18i	0.154750	−	1.04002i
$217$	−1.99833e17			−0.0406434
$218$	−1.72361e18	−	3.35682e18i	−0.337899	−	0.658075i
$219$	−5.10732e18			−0.965251
$220$	3.86120e18	+	2.76864e18i	0.703624	+	0.504528i
$221$		−	5.58257e18i		−	0.981061i
$222$	4.50533e18	+	8.77435e18i	0.763664	+	1.48727i
$223$			7.06603e18i			1.15541i	0.816245	+	0.577706i	$0.196052\pi$
$223$			7.06603e18i			1.15541i	−0.816245	+	0.577706i	$0.803948\pi$
$224$	−9.56019e17	+	9.86352e17i	−0.150828	+	0.155614i
$225$	−1.54466e17			−0.0235165
$226$	−9.68776e18	+	4.97433e18i	−1.42349	+	0.730915i
$227$	2.38938e18			0.338905			0.169452	−	0.985538i	$-0.445800\pi$
$227$	2.38938e18			0.338905			0.169452	+	0.985538i	$0.445800\pi$
$228$	−3.35657e18	+	4.68113e18i	−0.459639	+	0.641020i
$229$		−	5.49161e18i		−	0.726133i	−0.931763	−	0.363067i	$-0.881730\pi$
$229$		−	5.49161e18i		−	0.726133i	0.931763	−	0.363067i	$-0.118270\pi$
$230$	8.02618e18	−	4.12117e18i	1.02491	−	0.526257i
$231$		−	1.58551e18i		−	0.195557i
$232$	2.77564e18	+	4.12999e17i	0.330719	+	0.0492091i
$233$	−1.33345e19			−1.53507			−0.767537	−	0.641005i	$-0.778518\pi$
$233$	−1.33345e19			−1.53507			−0.767537	+	0.641005i	$0.778518\pi$
$234$	−8.19571e17	−	1.59616e18i	−0.0911716	−	0.177561i
$235$	1.07360e19			1.15425
$236$	7.62826e18	−	1.06385e19i	0.792737	−	1.10557i
$237$		−	9.78331e18i		−	0.982877i
$238$	−6.13182e17	−	1.19420e18i	−0.0595626	−	0.116001i
$239$		−	1.76364e19i		−	1.65663i	−0.560261	−	0.828316i	$-0.689299\pi$
$239$		−	1.76364e19i		−	1.65663i	0.560261	−	0.828316i	$-0.310701\pi$
$240$	−8.77847e18	+	2.97404e18i	−0.797497	+	0.270182i
$241$	−8.95188e18			−0.786644			−0.393322	−	0.919401i	$-0.628674\pi$
$241$	−8.95188e18			−0.786644			−0.393322	+	0.919401i	$0.628674\pi$
$242$	7.54721e17	−	3.87523e17i	0.0641599	−	0.0329439i
$243$	2.95924e18			0.243405
$244$	−5.54854e18	−	3.97854e18i	−0.441631	−	0.316668i
$245$		−	1.11203e19i		−	0.856621i
$246$	1.76465e19	−	9.06088e18i	1.31577	−	0.675600i
$247$			1.90193e19i			1.37284i
$248$	−2.65438e18	−	3.94956e17i	−0.185502	−	0.0276017i
$249$	−3.19634e18			−0.216301
$250$	7.46809e18	+	1.45445e19i	0.489429	+	0.953187i
$251$	−4.29164e18			−0.272417			−0.136208	−	0.990680i	$-0.543492\pi$
$251$	−4.29164e18			−0.272417			−0.136208	+	0.990680i	$0.543492\pi$
$252$	−3.50639e17	−	2.51423e17i	−0.0215604	−	0.0154597i
$253$			2.07266e19i			1.23471i
$254$	1.35045e19	+	2.63007e19i	0.779487	+	1.51809i
$255$		−	9.05804e18i		−	0.506655i
$256$	−1.46482e19	+	1.12122e19i	−0.794081	+	0.607812i
$257$	−8.15512e18			−0.428514			−0.214257	−	0.976777i	$-0.568733\pi$
$257$	−8.15512e18			−0.428514			−0.214257	+	0.976777i	$0.568733\pi$
$258$	−3.53151e18	+	1.81331e18i	−0.179888	+	0.0923664i
$259$	7.83150e18			0.386765
$260$	−1.78334e19	+	2.48707e19i	−0.853978	+	1.19097i
$261$			8.81441e17i			0.0409326i
$262$	−2.01489e18	+	1.03458e18i	−0.0907489	+	0.0465964i
$263$			1.89202e19i			0.826569i	0.910602	+	0.413284i	$0.135618\pi$
$263$			1.89202e19i			0.826569i	−0.910602	+	0.413284i	$0.864382\pi$
$264$	3.13365e18	−	2.10603e19i	0.132807	−	0.892551i
$265$	1.60006e19			0.657912
$266$	2.08906e18	+	4.06854e18i	0.0833484	+	0.162325i
$267$	9.01132e18			0.348898
$268$	2.41202e19	−	3.36385e19i	0.906364	−	1.26403i
$269$		−	2.36137e19i		−	0.861284i	−0.902523	−	0.430642i	$-0.858287\pi$
$269$		−	2.36137e19i		−	0.861284i	0.902523	−	0.430642i	$-0.141713\pi$
$270$	−1.21923e19	−	2.37452e19i	−0.431695	−	0.840748i
$271$			1.84749e19i			0.635079i	0.948245	+	0.317540i	$0.102857\pi$
$271$			1.84749e19i			0.635079i	−0.948245	+	0.317540i	$0.897143\pi$
$272$	−5.78461e18	−	1.70745e19i	−0.193074	−	0.569896i
$273$	1.02126e19			0.331006
$274$	2.83280e19	−	1.45455e19i	0.891686	−	0.457850i
$275$	−6.05236e18			−0.185039
$276$	−3.28587e19	−	2.35611e19i	−0.975839	−	0.699718i
$277$			3.75389e19i			1.08304i	0.840689	+	0.541519i	$0.182151\pi$
$277$			3.75389e19i			1.08304i	−0.840689	+	0.541519i	$0.817849\pi$
$278$	−4.53064e19	+	2.32633e19i	−1.26999	+	0.652098i
$279$		−	8.42933e17i		−	0.0229593i
$280$	−1.08308e18	+	7.27905e18i	−0.0286680	+	0.192668i
$281$	1.38818e19			0.357105			0.178552	−	0.983930i	$-0.442859\pi$
$281$	1.38818e19			0.357105			0.178552	+	0.983930i	$0.442859\pi$
$282$	−2.19762e19	−	4.27998e19i	−0.549490	−	1.07016i
$283$	1.68512e19			0.409580			0.204790	−	0.978806i	$-0.434349\pi$
$283$	1.68512e19			0.409580			0.204790	+	0.978806i	$0.434349\pi$
$284$	5.29841e19	+	3.79918e19i	1.25198	+	0.897725i
$285$			3.08599e19i			0.708983i
$286$	−3.21128e19	−	6.25413e19i	−0.717381	−	1.39714i
$287$		−	1.57503e19i		−	0.342164i
$288$	−4.16060e18	−	4.03266e18i	−0.0879056	−	0.0852023i
$289$	−3.10430e19			−0.637941
$290$	1.33741e19	−	6.86715e18i	0.267351	−	0.137275i
$291$	2.64466e19			0.514312
$292$	−3.17337e19	+	4.42564e19i	−0.600423	+	0.837361i
$293$		−	5.59155e19i		−	1.02942i	−0.857366	−	0.514708i	$-0.827900\pi$
$293$		−	5.59155e19i		−	1.02942i	0.857366	−	0.514708i	$-0.172100\pi$
$294$	−4.43321e19	+	2.27630e19i	−0.794217	+	0.407803i
$295$		−	7.01334e19i		−	1.22278i
$296$	1.04025e20	+	1.54784e19i	1.76525	+	0.262659i
$297$	6.13191e19			1.01285
$298$	1.09270e19	+	2.12808e19i	0.175699	+	0.342183i
$299$	−1.33504e20			−2.08990
$300$	6.88005e18	−	9.59504e18i	0.104863	−	0.146244i
$301$			3.15203e18i			0.0467798i
$302$	1.94370e19	+	3.78545e19i	0.280914	+	0.547095i
$303$			5.63295e19i			0.792857i
$304$	1.97077e19	+	5.81711e19i	0.270176	+	0.797478i
$305$	−3.65783e19			−0.488455
$306$	5.03736e18	−	2.58651e18i	0.0655287	−	0.0336467i
$307$	−6.75951e19			−0.856659			−0.428330	−	0.903623i	$-0.640898\pi$
$307$	−6.75951e19			−0.856659			−0.428330	+	0.903623i	$0.640898\pi$
$308$	−1.37389e19	−	9.85138e18i	−0.169647	−	0.121644i
$309$			6.97006e19i			0.838627i
$310$	−1.27898e19	+	6.56714e18i	−0.149959	+	0.0769986i
$311$		−	1.25476e20i		−	1.43377i	−0.697192	−	0.716884i	$-0.745567\pi$
$311$		−	1.25476e20i		−	1.43377i	0.697192	−	0.716884i	$-0.254433\pi$
$312$	1.35654e20	+	2.01845e19i	1.51076	+	0.224792i
$313$	1.62679e20			1.76594			0.882971	−	0.469427i	$-0.155540\pi$
$313$	1.62679e20			1.76594			0.882971	+	0.469427i	$0.155540\pi$
$314$	6.04187e19	+	1.17668e20i	0.639343	+	1.24515i
$315$	−2.31156e18			−0.0238463
$316$	−8.47751e19	−	6.07873e19i	−0.852651	−	0.611387i
$317$		−	1.81279e19i		−	0.177776i	−0.996042	−	0.0888881i	$-0.971669\pi$
$317$		−	1.81279e19i		−	0.177776i	0.996042	−	0.0888881i	$-0.0283313\pi$
$318$	−3.27527e19	−	6.37875e19i	−0.313206	−	0.609984i
$319$			3.45370e19i			0.322077i
$320$	−2.87730e19	+	9.45467e19i	−0.261689	+	0.859897i
$321$	−3.66030e19			−0.324696
$322$	−2.85588e19	+	1.46639e19i	−0.247111	+	0.126883i
$323$	−6.00237e19			−0.506643
$324$	−6.10416e19	+	8.51297e19i	−0.502650	+	0.701005i
$325$		−	3.89844e19i		−	0.313202i
$326$	−1.54727e19	+	7.94471e18i	−0.121290	+	0.0622784i
$327$			9.05970e19i			0.692997i
$328$	3.11294e19	−	2.09211e20i	0.232370	−	1.56168i
$329$	−3.82007e19			−0.278294
$330$	−5.21049e19	−	1.01477e20i	−0.370482	−	0.721532i
$331$	6.03102e18			0.0418569			0.0209285	−	0.999781i	$-0.493338\pi$
$331$	6.03102e18			0.0418569			0.0209285	+	0.999781i	$0.493338\pi$
$332$	−1.98600e19	+	2.76971e19i	−0.134547	+	0.187642i
$333$			3.30346e19i			0.218482i
$334$	1.27548e19	+	2.48405e19i	0.0823570	+	0.160394i
$335$		−	2.21759e20i		−	1.39805i
$336$	3.12356e19	−	1.05822e19i	0.192280	−	0.0651422i
$337$	−7.23763e19			−0.435068			−0.217534	−	0.976053i	$-0.569801\pi$
$337$	−7.23763e19			−0.435068			−0.217534	+	0.976053i	$0.569801\pi$
$338$	2.51303e20	−	1.29035e20i	1.47524	−	0.757487i
$339$	2.61462e20			1.49904
$340$	−7.84904e19	−	5.62809e19i	−0.439526	−	0.315159i
$341$		−	3.30282e19i		−	0.180655i
$342$	−1.71618e19	+	8.81201e18i	−0.0916969	+	0.0470832i
$343$			8.10866e19i			0.423249i
$344$	−6.22976e18	+	4.18683e19i	−0.0317690	+	0.213510i
$345$	−2.16618e20			−1.07930
$346$	−5.35967e19	−	1.04382e20i	−0.260933	−	0.508180i
$347$	1.11127e20			0.528670			0.264335	−	0.964431i	$-0.414848\pi$
$347$	1.11127e20			0.528670			0.264335	+	0.964431i	$0.414848\pi$
$348$	−5.47529e19	−	3.92602e19i	−0.254550	−	0.182523i
$349$		−	1.41872e20i		−	0.644605i	−0.946637	−	0.322302i	$-0.895543\pi$
$349$		−	1.41872e20i		−	0.644605i	0.946637	−	0.322302i	$-0.104457\pi$
$350$	−4.28200e18	−	8.33941e18i	−0.0190153	−	0.0370332i
$351$			3.94968e20i			1.71437i
$352$	−1.63023e20	−	1.58009e20i	−0.691683	−	0.670412i
$353$	5.76243e19			0.239005			0.119503	−	0.992834i	$-0.461870\pi$
$353$	5.76243e19			0.239005			0.119503	+	0.992834i	$0.461870\pi$
$354$	−2.79592e20	+	1.43561e20i	−1.13370	+	0.582117i
$355$	3.49293e20			1.38472
$356$	5.59906e19	−	7.80855e19i	0.217028	−	0.302671i
$357$			3.22303e19i			0.122157i
$358$	−4.60926e19	+	2.36670e19i	−0.170831	+	0.0877159i
$359$			2.86545e20i			1.03857i	0.854600	+	0.519287i	$0.173802\pi$
$359$			2.86545e20i			1.03857i	−0.854600	+	0.519287i	$0.826198\pi$
$360$	−3.07043e19	−	4.56863e18i	−0.108838	−	0.0161944i
$361$	−8.39462e19			−0.291034
$362$	1.84445e20	+	3.59217e20i	0.625460	+	1.21811i
$363$	−2.03691e19			−0.0675647
$364$	6.34547e19	−	8.84950e19i	0.205898	−	0.287149i
$365$			2.91756e20i			0.926141i
$366$	7.48746e19	+	1.45822e20i	0.232534	+	0.452871i
$367$			2.23404e20i			0.678833i	0.940636	+	0.339417i	$0.110230\pi$
$367$			2.23404e20i			0.678833i	−0.940636	+	0.339417i	$0.889770\pi$
$368$	−4.08327e20	+	1.38336e20i	−1.21402	+	0.411294i
$369$	6.64376e19			0.193287
$370$	5.01235e20	−	2.57367e20i	1.42701	−	0.732722i
$371$	−5.69331e19			−0.158626
$372$	5.23609e19	+	3.75450e19i	0.142779	+	0.102378i
$373$			9.37028e19i			0.250082i	0.992152	+	0.125041i	$0.0399062\pi$
$373$			9.37028e19i			0.250082i	−0.992152	+	0.125041i	$0.960094\pi$
$374$	1.97376e20	−	1.01346e20i	0.515611	−	0.264748i
$375$		−	3.92540e20i		−	1.00377i
$376$	−5.07418e20	−	7.55010e19i	−1.27017	−	0.188995i
$377$	−2.22460e20			−0.545156
$378$	4.33828e19	+	8.44902e19i	0.104084	+	0.202708i
$379$	−2.81031e20			−0.660148			−0.330074	−	0.943955i	$-0.607074\pi$
$379$	−2.81031e20			−0.660148			−0.330074	+	0.943955i	$0.607074\pi$
$380$	2.67410e20	+	1.91744e20i	0.615047	+	0.441015i
$381$		−	7.09828e20i		−	1.59865i
$382$	8.18446e19	+	1.59396e20i	0.180502	+	0.351538i
$383$		−	8.11531e20i		−	1.75273i	−0.481648	−	0.876365i	$-0.659962\pi$
$383$		−	8.11531e20i		−	1.75273i	0.481648	−	0.876365i	$-0.340038\pi$
$384$	4.35815e20	−	7.88283e19i	0.921834	−	0.166737i
$385$	−9.05726e19			−0.187634
$386$	−5.42362e20	+	2.78484e20i	−1.10050	+	0.565069i
$387$	−1.32958e19			−0.0264257
$388$	1.64323e20	−	2.29167e20i	0.319922	−	0.446168i
$389$		−	4.38343e20i		−	0.836021i	−0.908442	−	0.418011i	$-0.862727\pi$
$389$		−	4.38343e20i		−	0.836021i	0.908442	−	0.418011i	$-0.137273\pi$
$390$	6.53632e20	−	3.35618e20i	1.22128	−	0.627087i
$391$		−	4.21331e20i		−	0.771274i
$392$	−7.82040e19	+	5.25584e20i	−0.140262	+	0.942657i
$393$	5.43798e19			0.0955647
$394$	−1.07658e20	−	2.09670e20i	−0.185386	−	0.361049i
$395$	−5.58872e20			−0.943052
$396$	4.15549e19	−	5.79531e19i	0.0687164	−	0.0958331i
$397$			3.64149e20i			0.590140i	0.955476	+	0.295070i	$0.0953429\pi$
$397$			3.64149e20i			0.590140i	−0.955476	+	0.295070i	$0.904657\pi$
$398$	6.72034e19	+	1.30882e20i	0.106740	+	0.207881i
$399$		−	1.09806e20i		−	0.170939i
$400$	−4.03954e19	−	1.19235e20i	−0.0616384	−	0.181938i
$401$	2.15346e20			0.322094			0.161047	−	0.986947i	$-0.448513\pi$
$401$	2.15346e20			0.322094			0.161047	+	0.986947i	$0.448513\pi$
$402$	−8.84059e20	+	4.53934e20i	−1.29620	+	0.665555i
$403$	2.12741e20			0.305781
$404$	4.88110e20	+	3.49996e20i	0.687808	+	0.493187i
$405$			5.61210e20i			0.775328i
$406$	−4.75878e19	+	2.44347e19i	−0.0644596	+	0.0330978i
$407$			1.29438e21i			1.71912i
$408$	−6.37009e19	+	4.28113e20i	−0.0829591	+	0.557542i
$409$	7.48017e18			0.00955267			0.00477633	−	0.999989i	$-0.498480\pi$
$409$	7.48017e18			0.00955267			0.00477633	+	0.999989i	$0.498480\pi$
$410$	−5.17604e20	−	1.00806e21i	−0.648226	−	1.26245i
$411$	−7.64544e20			−0.939005
$412$	6.03975e20	+	4.33075e20i	0.727513	+	0.521658i
$413$			2.49549e20i			0.294819i
$414$	−6.18551e19	−	1.20466e20i	−0.0716758	−	0.139592i
$415$			1.82591e20i			0.207537i
$416$	1.01777e21	−	1.05006e21i	1.13476	−	1.17076i
$417$	1.22277e21			1.33739
$418$	−6.72443e20	+	3.45276e20i	−0.721514	+	0.370473i
$419$	7.29288e20			0.767692			0.383846	−	0.923397i	$-0.374599\pi$
$419$	7.29288e20			0.767692			0.383846	+	0.923397i	$0.374599\pi$
$420$	1.02959e20	−	1.43588e20i	0.106333	−	0.148294i
$421$		−	6.57781e20i		−	0.666537i	−0.942832	−	0.333269i	$-0.891848\pi$
$421$		−	6.57781e20i		−	0.666537i	0.942832	−	0.333269i	$-0.108152\pi$
$422$	−3.70829e20	+	1.90408e20i	−0.368701	+	0.189315i
$423$		−	1.61137e20i		−	0.157207i
$424$	−7.56240e20	−	1.12524e20i	−0.723991	−	0.107726i
$425$	1.23032e20			0.115587
$426$	−7.14992e20	−	1.39248e21i	−0.659211	−	1.28385i
$427$	1.30153e20			0.117769
$428$	−2.27428e20	+	3.17175e20i	−0.201973	+	0.281675i
$429$			1.68792e21i			1.47128i
$430$	1.03585e20	+	2.01738e20i	0.0886239	+	0.172600i
$431$		−	1.05438e21i		−	0.885479i	−0.896650	−	0.442740i	$-0.854007\pi$
$431$		−	1.05438e21i		−	0.885479i	0.896650	−	0.442740i	$-0.145993\pi$
$432$	4.09263e20	+	1.20802e21i	0.337390	+	0.995875i
$433$	5.56564e20			0.450414			0.225207	−	0.974311i	$-0.427694\pi$
$433$	5.56564e20			0.450414			0.225207	+	0.974311i	$0.427694\pi$
$434$	4.55088e19	−	2.33672e19i	0.0361558	−	0.0185647i
$435$	−3.60954e20			−0.281538
$436$	7.85047e20	+	5.62912e20i	0.601179	+	0.431071i
$437$			1.43544e21i			1.07928i
$438$	1.16311e21	−	5.97216e20i	0.858673	−	0.440899i
$439$			5.29504e20i			0.383842i	0.981410	+	0.191921i	$0.0614718\pi$
$439$			5.29504e20i			0.383842i	−0.981410	+	0.191921i	$0.938528\pi$
$440$	−1.20307e21	−	1.79010e20i	−0.856387	−	0.127425i
$441$	−1.66906e20			−0.116671
$442$	6.52788e20	+	1.27134e21i	0.448120	+	0.872736i
$443$	−2.55534e21			−1.72274			−0.861368	−	0.507982i	$-0.830392\pi$
$443$	−2.55534e21			−1.72274			−0.861368	+	0.507982i	$0.830392\pi$
$444$	−2.05203e21	−	1.47139e21i	−1.35869	−	0.974237i
$445$		−	5.14772e20i		−	0.334761i
$446$	−8.26255e20	−	1.60917e21i	−0.527758	−	1.02784i
$447$		−	5.74347e20i		−	0.360341i
$448$	1.02380e20	−	3.36416e20i	0.0630946	−	0.207325i
$449$	1.76856e21			1.07065			0.535326	−	0.844645i	$-0.320189\pi$
$449$	1.76856e21			1.07065			0.535326	+	0.844645i	$0.320189\pi$
$450$	3.51771e19	−	1.80622e19i	0.0209199	−	0.0107417i
$451$	2.60319e21			1.52087
$452$	1.62456e21	−	2.26564e21i	0.932457	−	1.30042i
$453$		−	1.02165e21i		−	0.576127i
$454$	−5.44141e20	+	2.79398e20i	−0.301484	+	0.154802i
$455$		−	5.83396e20i		−	0.317594i
$456$	2.17023e20	−	1.45854e21i	0.116088	−	0.780191i
$457$	−2.60728e21			−1.37043			−0.685216	−	0.728340i	$-0.740292\pi$
$457$	−2.60728e21			−1.37043			−0.685216	+	0.728340i	$0.740292\pi$
$458$	6.42153e20	+	1.25063e21i	0.331676	+	0.645957i
$459$	−1.24649e21			−0.632686
$460$	−1.34593e21	+	1.87706e21i	−0.671367	+	0.936300i
$461$		−	3.31279e21i		−	1.62400i	−0.583657	−	0.812001i	$-0.698379\pi$
$461$		−	3.31279e21i		−	1.62400i	0.583657	−	0.812001i	$-0.301621\pi$
$462$	1.85399e20	+	3.61075e20i	0.0893249	+	0.173965i
$463$			2.53975e21i			1.20266i	0.799001	+	0.601330i	$0.205362\pi$
$463$			2.53975e21i			1.20266i	−0.799001	+	0.601330i	$0.794638\pi$
$464$	−6.80400e20	+	2.30511e20i	−0.316680	+	0.107287i
$465$	3.45184e20			0.157917
$466$	3.03671e21	−	1.55925e21i	1.36558	−	0.701177i
$467$	2.59760e21			1.14825			0.574125	−	0.818767i	$-0.305342\pi$
$467$	2.59760e21			1.14825			0.574125	+	0.818767i	$0.305342\pi$
$468$	3.73288e20	+	2.67663e20i	0.162210	+	0.116311i
$469$			7.89062e20i			0.337076i
$470$	−2.44494e21	+	1.25539e21i	−1.02680	+	0.527226i
$471$		−	3.17575e21i		−	1.31123i
$472$	−4.93215e20	+	3.31474e21i	−0.200217	+	1.34559i
$473$	−5.20963e20			−0.207930
$474$	1.14400e21	+	2.22799e21i	0.448949	+	0.874352i
$475$	−4.19160e20			−0.161745
$476$	2.79284e20	+	2.00259e20i	0.105972	+	0.0759864i
$477$		−	2.40154e20i		−	0.0896072i
$478$	2.06228e21	+	4.01640e21i	0.756702	+	1.47371i
$479$			3.81083e21i			1.37510i	0.726135	+	0.687552i	$0.241315\pi$
$479$			3.81083e21i			1.37510i	−0.726135	+	0.687552i	$0.758685\pi$
$480$	1.65139e21	−	1.70378e21i	0.586030	−	0.604623i
$481$	−8.33735e21			−2.90983
$482$	2.03864e21	−	1.04677e21i	0.699786	−	0.359316i
$483$	7.70771e20			0.260225
$484$	−1.26561e20	+	1.76504e20i	−0.0420278	+	0.0586128i
$485$		−	1.51077e21i		−	0.493473i
$486$	−6.73917e20	+	3.46033e20i	−0.216529	+	0.111180i
$487$		−	2.90389e20i		−	0.0917800i	−0.998946	−	0.0458900i	$-0.985388\pi$
$487$		−	2.90389e20i		−	0.0917800i	0.998946	−	0.0458900i	$-0.0146124\pi$
$488$	1.72881e21	+	2.57237e20i	0.537513	+	0.0799789i
$489$	4.17593e20			0.127727
$490$	1.30034e21	+	2.53247e21i	0.391280	+	0.762037i
$491$	2.22031e21			0.657296			0.328648	−	0.944452i	$-0.393407\pi$
$491$	2.22031e21			0.657296			0.328648	+	0.944452i	$0.393407\pi$
$492$	−2.95919e21	+	4.12693e21i	−0.861890	+	1.20201i
$493$		−	7.02068e20i		−	0.201189i
$494$	−2.22399e21	−	4.33134e21i	−0.627072	−	1.22125i
$495$		−	3.82051e20i		−	0.105994i
$496$	6.50675e20	−	2.20440e20i	0.177628	−	0.0601780i
$497$	−1.24285e21			−0.333863
$498$	7.27913e20	−	3.73758e20i	0.192418	−	0.0987999i
$499$	6.02483e21			1.56726			0.783629	−	0.621229i	$-0.213366\pi$
$499$	6.02483e21			1.56726			0.783629	+	0.621229i	$0.213366\pi$
$500$	−3.40147e21	−	2.43900e21i	−0.870776	−	0.624384i
$501$		−	6.70420e20i		−	0.168906i
$502$	9.77351e20	−	5.01836e20i	0.242338	−	0.124432i
$503$			1.72593e20i			0.0421190i	0.999778	+	0.0210595i	$0.00670395\pi$
$503$			1.72593e20i			0.0421190i	−0.999778	+	0.0210595i	$0.993296\pi$
$504$	1.09252e20	+	1.62561e19i	0.0262413	+	0.00390456i
$505$	3.21782e21			0.760731
$506$	−2.42363e21	−	4.72015e21i	−0.563979	−	1.09838i
$507$	−6.78241e21			−1.55353
$508$	−6.15086e21	−	4.41043e21i	−1.38684	−	0.994422i
$509$			6.16966e21i			1.36936i	0.728842	+	0.684682i	$0.240059\pi$
$509$			6.16966e21i			1.36936i	−0.728842	+	0.684682i	$0.759941\pi$
$510$	1.05919e21	+	2.06282e21i	0.231425	+	0.450713i
$511$		−	1.03813e21i		−	0.223297i
$512$	2.02481e21	−	4.26625e21i	0.428771	−	0.903413i
$513$	4.24669e21			0.885343
$514$	1.85719e21	−	9.53606e20i	0.381200	−	0.195733i
$515$	3.98165e21			0.804647
$516$	5.92207e20	−	8.25903e20i	0.117835	−	0.164335i
$517$		−	6.31376e21i		−	1.23698i
$518$	−1.78350e21	+	9.15763e20i	−0.344060	+	0.176663i
$519$			2.81717e21i			0.535148i
$520$	1.15304e21	−	7.74922e21i	0.215684	−	1.44954i
$521$	7.51952e21			1.38512			0.692561	−	0.721359i	$-0.256482\pi$
$521$	7.51952e21			1.38512			0.692561	+	0.721359i	$0.256482\pi$
$522$	−1.03070e20	−	2.00734e20i	−0.0186968	−	0.0364130i
$523$	−7.56950e21			−1.35224			−0.676120	−	0.736791i	$-0.736340\pi$
$523$	−7.56950e21			−1.35224			−0.676120	+	0.736791i	$0.736340\pi$
$524$	3.37882e20	−	4.71216e20i	0.0594449	−	0.0829029i
$525$			2.25072e20i			0.0389984i
$526$	−2.21240e21	−	4.30876e21i	−0.377553	−	0.735303i
$527$			6.71396e20i			0.112848i
$528$	1.74901e21	+	5.16257e21i	0.289549	+	0.854662i
$529$	−3.94330e21			−0.643004
$530$	−3.64386e21	+	1.87100e21i	−0.585268	+	0.300515i
$531$	−1.05264e21			−0.166542
$532$	−9.51497e20	−	6.82264e20i	−0.148291	−	0.106331i
$533$			1.67676e22i			2.57427i
$534$	−2.05218e21	+	1.05372e21i	−0.310374	+	0.159366i
$535$			2.09095e21i			0.311540i
$536$	−1.55952e21	+	1.04811e22i	−0.228915	+	1.53846i
$537$	1.24399e21			0.179897
$538$	2.76123e21	+	5.37764e21i	0.393410	+	0.766185i
$539$	−6.53980e21			−0.918024
$540$	5.55321e21	+	3.98189e21i	0.768059	+	0.550731i
$541$		−	5.81897e21i		−	0.792991i	−0.918037	−	0.396495i	$-0.870226\pi$
$541$		−	5.81897e21i		−	0.792991i	0.918037	−	0.396495i	$-0.129774\pi$
$542$	−2.16033e21	−	4.20736e21i	−0.290086	−	0.564956i
$543$		−	9.69489e21i		−	1.28276i
$544$	3.31392e21	+	3.21201e21i	0.432067	+	0.418780i
$545$	5.17536e21			0.664918
$546$	−2.32575e21	+	1.19419e21i	−0.294457	+	0.151194i
$547$	1.49752e22			1.86841			0.934207	−	0.356731i	$-0.116109\pi$
$547$	1.49752e22			1.86841			0.934207	+	0.356731i	$0.116109\pi$
$548$	−4.75039e21	+	6.62498e21i	−0.584097	+	0.814592i
$549$			5.49007e20i			0.0665272i
$550$	1.37833e21	−	7.07723e20i	0.164608	−	0.0845204i
$551$			2.39188e21i			0.281532i
$552$	1.02381e22	+	1.52337e21i	1.18770	+	0.176723i
$553$	1.98858e21			0.227374
$554$	−4.38955e21	−	8.54887e21i	−0.494700	−	0.963454i
$555$	−1.35278e22			−1.50274
$556$	7.59754e21	−	1.05957e22i	0.831907	−	1.16019i
$557$			6.42638e21i			0.693625i	0.937934	+	0.346813i	$0.112736\pi$
$557$			6.42638e21i			0.693625i	−0.937934	+	0.346813i	$0.887264\pi$
$558$	9.85669e19	+	1.91964e20i	0.0104872	+	0.0204243i
$559$		−	3.35562e21i		−	0.351948i
$560$	−6.04510e20	−	1.78433e21i	−0.0625028	−	0.184490i
$561$	−5.32698e21			−0.542973
$562$	−3.16135e21	+	1.62325e21i	−0.317675	+	0.163115i
$563$	−7.69156e21			−0.761986			−0.380993	−	0.924578i	$-0.624418\pi$
$563$	−7.69156e21			−0.761986			−0.380993	+	0.924578i	$0.624418\pi$
$564$	1.00094e22	+	7.17720e21i	0.977636	+	0.701006i
$565$		−	1.49361e22i		−	1.43830i
$566$	−3.83758e21	+	1.97046e21i	−0.364356	+	0.187084i
$567$		−	1.99690e21i		−	0.186935i
$568$	−1.65088e22	−	2.45641e21i	−1.52380	−	0.226733i
$569$	3.65030e21			0.332223			0.166112	−	0.986107i	$-0.446879\pi$
$569$	3.65030e21			0.332223			0.166112	+	0.986107i	$0.446879\pi$
$570$	−3.60855e21	−	7.02784e21i	−0.323843	−	0.630700i
$571$	−2.61778e21			−0.231656			−0.115828	−	0.993269i	$-0.536952\pi$
$571$	−2.61778e21			−0.231656			−0.115828	+	0.993269i	$0.536952\pi$
$572$	1.46263e22	+	1.04877e22i	1.27634	+	0.915191i
$573$		−	4.30194e21i		−	0.370193i
$574$	1.84174e21	+	3.58687e21i	0.156290	+	0.304383i
$575$		−	2.94225e21i		−	0.246228i
$576$	1.41906e21	+	4.31858e20i	0.117117	+	0.0356419i
$577$	−1.24124e22			−1.01029			−0.505147	−	0.863033i	$-0.668562\pi$
$577$	−1.24124e22			−1.01029			−0.505147	+	0.863033i	$0.668562\pi$
$578$	7.06953e21	−	3.62996e21i	0.567503	−	0.291393i
$579$	1.46378e22			1.15890
$580$	−2.24274e21	+	3.12776e21i	−0.175128	+	0.244236i
$581$		−	6.49695e20i		−	0.0500381i
$582$	−6.02279e21	+	3.09249e21i	−0.457524	+	0.234923i
$583$		−	9.40983e21i		−	0.705071i
$584$	2.05178e21	−	1.37894e22i	0.151645	−	1.01916i
$585$	2.46087e21			0.179408
$586$	6.53838e21	+	1.27338e22i	0.470207	+	0.915752i
$587$	−2.08530e22			−1.47933			−0.739664	−	0.672977i	$-0.765015\pi$
$587$	−2.08530e22			−1.47933			−0.739664	+	0.672977i	$0.765015\pi$
$588$	7.43415e21	−	1.03678e22i	0.520251	−	0.725551i
$589$		−	2.28739e21i		−	0.157913i
$590$	8.20093e21	+	1.59717e22i	0.558531	+	1.08777i
$591$			5.65877e21i			0.380209i
$592$	−2.55000e22	+	8.63909e21i	−1.69031	+	0.572657i
$593$	2.01094e22			1.31511			0.657556	−	0.753406i	$-0.271591\pi$
$593$	2.01094e22			1.31511			0.657556	+	0.753406i	$0.271591\pi$
$594$	−1.39644e22	+	7.17024e21i	−0.901013	+	0.462639i
$595$	1.84116e21			0.117207
$596$	−4.97687e21	−	3.56863e21i	−0.312598	−	0.224146i
$597$		−	3.53237e21i		−	0.218913i
$598$	3.04034e22	−	1.56111e22i	1.85914	−	0.954606i
$599$		−	4.00111e21i		−	0.241416i	−0.992688	−	0.120708i	$-0.961484\pi$
$599$		−	4.00111e21i		−	0.241416i	0.992688	−	0.120708i	$-0.0385165\pi$
$600$	−4.44839e20	+	2.98962e21i	−0.0264845	+	0.177994i
$601$	−1.72555e22			−1.01375			−0.506877	−	0.862018i	$-0.669200\pi$
$601$	−1.72555e22			−1.01375			−0.506877	+	0.862018i	$0.669200\pi$
$602$	−3.68577e20	−	7.17823e20i	−0.0213677	−	0.0416146i
$603$	−3.32840e21			−0.190413
$604$	−8.85292e21	−	6.34792e21i	−0.499794	−	0.358373i
$605$			1.16359e21i			0.0648271i
$606$	−6.58679e21	−	1.28281e22i	−0.362154	−	0.705313i
$607$			1.06494e22i			0.577850i	0.957352	+	0.288925i	$0.0932977\pi$
$607$			1.06494e22i			0.577850i	−0.957352	+	0.288925i	$0.906702\pi$
$608$	−1.12902e22	−	1.09430e22i	−0.604609	−	0.586016i
$609$	1.28435e21			0.0678802
$610$	8.33010e21	−	4.27722e21i	0.434522	−	0.223112i
$611$	4.06682e22			2.09375
$612$	−8.44727e20	+	1.17807e21i	−0.0429245	+	0.0598632i
$613$			2.97501e22i			1.49212i	0.665878	+	0.746061i	$0.268057\pi$
$613$			2.97501e22i			1.49212i	−0.665878	+	0.746061i	$0.731943\pi$
$614$	1.53937e22	−	7.90412e21i	0.762071	−	0.391297i
$615$			2.72065e22i			1.32945i
$616$	4.28077e21	+	6.36954e20i	0.206479	+	0.0307229i
$617$	−6.30890e21			−0.300381			−0.150190	−	0.988657i	$-0.547989\pi$
$617$	−6.30890e21			−0.300381			−0.150190	+	0.988657i	$0.547989\pi$
$618$	−8.15032e21	−	1.58732e22i	−0.383060	−	0.746029i
$619$	2.47725e22			1.14933			0.574665	−	0.818388i	$-0.305132\pi$
$619$	2.47725e22			1.14933			0.574665	+	0.818388i	$0.305132\pi$
$620$	2.14476e21	−	2.99112e21i	0.0982301	−	0.136993i
$621$			2.98092e22i			1.34778i
$622$	1.46724e22	+	2.85752e22i	0.654904	+	1.27546i
$623$			1.83166e21i			0.0807125i
$624$	−3.32531e22	+	1.12657e22i	−1.44662	+	0.490098i
$625$	−1.79513e22			−0.771003
$626$	−3.70474e22	+	1.90226e22i	−1.57095	+	0.806631i
$627$	1.81485e22			0.759803
$628$	−2.75187e22	−	1.97321e22i	−1.13750	−	0.815635i
$629$		−	2.63121e22i		−	1.07387i
$630$	5.26420e20	−	2.70298e20i	0.0212133	−	0.0108923i
$631$			4.47176e22i			1.77928i	0.456664	+	0.889639i	$0.349044\pi$
$631$			4.47176e22i			1.77928i	−0.456664	+	0.889639i	$0.650956\pi$
$632$	2.64142e22	+	3.93028e21i	1.03777	+	0.154414i
$633$	1.00083e22			0.388267
$634$	2.11976e21	+	4.12833e21i	0.0812030	+	0.158147i
$635$	−4.05490e22			−1.53388
$636$	1.49178e22	+	1.06967e22i	0.557246	+	0.399569i
$637$		−	4.21241e22i		−	1.55387i
$638$	−4.03853e21	−	7.86524e21i	−0.147115	−	0.286515i
$639$		−	5.24257e21i		−	0.188598i
$640$	−4.50307e21	−	2.48960e22i	−0.159981	−	0.884483i
$641$	−9.68837e21			−0.339928			−0.169964	−	0.985450i	$-0.554365\pi$
$641$	−9.68837e21			−0.339928			−0.169964	+	0.985450i	$0.554365\pi$
$642$	8.33574e21	−	4.28011e21i	0.288844	−	0.148312i
$643$	4.66137e22			1.59524			0.797620	−	0.603160i	$-0.206092\pi$
$643$	4.66137e22			1.59524			0.797620	+	0.603160i	$0.206092\pi$
$644$	4.78909e21	−	6.67894e21i	0.161870	−	0.225746i
$645$		−	5.44469e21i		−	0.181759i
$646$	1.36694e22	−	7.01877e21i	0.450702	−	0.231420i
$647$		−	5.48740e22i		−	1.78703i	−0.449031	−	0.893516i	$-0.648231\pi$
$647$		−	5.48740e22i		−	1.78703i	0.449031	−	0.893516i	$-0.351769\pi$
$648$	3.94673e21	−	2.65247e22i	0.126951	−	0.853199i
$649$	−4.12450e22			−1.31043
$650$	4.55858e21	+	8.87807e21i	0.143061	+	0.278619i
$651$	−1.22823e21			−0.0380744
$652$	2.59466e21	−	3.61856e21i	0.0794510	−	0.110804i
$653$		−	4.41151e22i		−	1.33439i	−0.744884	−	0.667194i	$-0.767495\pi$
$653$		−	4.41151e22i		−	1.33439i	0.744884	−	0.667194i	$-0.232505\pi$
$654$	−1.05938e22	−	2.06320e22i	−0.316541	−	0.616480i
$655$		−	3.10645e21i		−	0.0916926i
$656$	1.73745e22	+	5.12843e22i	0.506619	+	1.49539i
$657$	4.37900e21			0.126140
$658$	8.69959e21	−	4.46694e21i	0.247566	−	0.127117i
$659$	−4.33423e22			−1.21851			−0.609255	−	0.792975i	$-0.708531\pi$
$659$	−4.33423e22			−1.21851			−0.609255	+	0.792975i	$0.708531\pi$
$660$	2.37321e22	+	1.70169e22i	0.659149	+	0.472638i
$661$			3.24070e21i			0.0889257i	0.999011	+	0.0444628i	$0.0141576\pi$
$661$			3.24070e21i			0.0889257i	−0.999011	+	0.0444628i	$0.985842\pi$
$662$	−1.37347e21	+	7.05228e20i	−0.0372352	+	0.0191190i
$663$		−	3.43121e22i		−	0.919050i
$664$	1.28408e21	−	8.62987e21i	0.0339818	−	0.228381i
$665$	−6.27266e21			−0.164013
$666$	−3.86285e21	−	7.52310e21i	−0.0997962	−	0.194358i
$667$	−1.67896e22			−0.428582
$668$	−5.80937e21	−	4.16557e21i	−0.146527	−	0.105066i
$669$			4.34299e22i			1.08238i
$670$	2.59310e22	+	5.05019e22i	0.638588	+	1.24368i
$671$			2.15114e22i			0.523467i
$672$	−5.87597e21	+	6.06240e21i	−0.141295	+	0.145778i
$673$	5.90544e22			1.40324			0.701620	−	0.712552i	$-0.252461\pi$
$673$	5.90544e22			1.40324			0.701620	+	0.712552i	$0.252461\pi$
$674$	1.64825e22	−	8.46320e21i	0.387030	−	0.198726i
$675$	−8.70456e21			−0.201984
$676$	−4.21416e22	+	5.87714e22i	−0.966357	+	1.34770i
$677$			1.87182e22i			0.424185i	0.977250	+	0.212092i	$0.0680278\pi$
$677$			1.87182e22i			0.424185i	−0.977250	+	0.212092i	$0.931972\pi$
$678$	−5.95438e22	+	3.05737e22i	−1.33352	+	0.684716i
$679$			5.37561e21i			0.118979i
$680$	2.44560e22	+	3.63892e21i	0.534951	+	0.0795977i
$681$	1.46858e22			0.317483
$682$	3.86210e21	+	7.52163e21i	0.0825179	+	0.160708i
$683$	−5.13569e22			−1.08451			−0.542255	−	0.840214i	$-0.682429\pi$
$683$	−5.13569e22			−1.08451			−0.542255	+	0.840214i	$0.682429\pi$
$684$	2.87791e21	−	4.01358e21i	0.0600659	−	0.0837690i
$685$			4.36746e22i			0.900958i
$686$	−9.48172e21	−	1.84661e22i	−0.193328	−	0.376516i
$687$		−	3.37531e22i		−	0.680236i
$688$	−3.47707e21	−	1.02633e22i	−0.0692637	−	0.204446i
$689$	6.06105e22			1.19342
$690$	4.93313e22	−	2.53299e22i	0.960129	−	0.492993i
$691$	1.82383e22			0.350880			0.175440	−	0.984490i	$-0.443865\pi$
$691$	1.82383e22			0.350880			0.175440	+	0.984490i	$0.443865\pi$
$692$	2.44115e22	+	1.75041e22i	0.464244	+	0.332883i
$693$			1.35941e21i			0.0255556i
$694$	−2.53074e22	+	1.29945e22i	−0.470296	+	0.241481i
$695$		−	6.98510e22i		−	1.28320i
$696$	1.70599e22	+	2.53842e21i	0.309815	+	0.0460987i
$697$	−5.29176e22			−0.950031
$698$	1.65896e22	+	3.23090e22i	0.294437	+	0.573430i
$699$	−8.19577e22			−1.43804
$700$	1.95031e21	+	1.39846e21i	0.0338314	+	0.0242585i
$701$			3.19182e22i			0.547386i	0.961817	+	0.273693i	$0.0882453\pi$
$701$			3.19182e22i			0.547386i	−0.961817	+	0.273693i	$0.911755\pi$
$702$	−4.61850e22	−	8.99475e22i	−0.783075	−	1.52508i
$703$			8.96430e22i			1.50270i
$704$	5.56023e22	+	1.69213e22i	0.921535	+	0.280447i
$705$	6.59864e22			1.08129
$706$	−1.31230e22	+	6.73820e21i	−0.212616	+	0.109171i
$707$	−1.14497e22			−0.183416
$708$	4.68855e22	−	6.53873e22i	0.742630	−	1.03568i
$709$		−	1.40972e22i		−	0.220782i	−0.993888	−	0.110391i	$-0.964790\pi$
$709$		−	1.40972e22i		−	0.220782i	0.993888	−	0.110391i	$-0.0352102\pi$
$710$	−7.95457e22	+	4.08440e22i	−1.23183	+	0.632501i
$711$			8.38817e21i			0.128443i
$712$	−3.62015e21	+	2.43299e22i	−0.0548133	+	0.368383i
$713$	1.60561e22			0.240394
$714$	−3.76880e21	−	7.33992e21i	−0.0557978	−	0.108669i
$715$	9.64228e22			1.41166
$716$	7.72937e21	−	1.07795e22i	0.111903	−	0.156061i
$717$		−	1.08398e23i		−	1.55192i
$718$	−3.35067e22	−	6.52559e22i	−0.474390	−	0.923899i
$719$		−	3.68096e21i		−	0.0515383i	−0.999668	−	0.0257692i	$-0.991797\pi$
$719$		−	3.68096e21i		−	0.0515383i	0.999668	−	0.0257692i	$-0.00820349\pi$
$720$	7.52663e21	−	2.54993e21i	0.104218	−	0.0353076i
$721$	−1.41675e22			−0.194004
$722$	1.91174e22	−	9.81611e21i	0.258899	−	0.132936i
$723$	−5.50209e22			−0.736922
$724$	−8.40088e22	−	6.02379e22i	−1.11280	−	0.797924i
$725$		−	4.90271e21i		−	0.0642292i
$726$	4.63874e21	−	2.38183e21i	0.0601045	−	0.0308616i
$727$			1.19286e22i			0.152867i	0.997075	+	0.0764333i	$0.0243532\pi$
$727$			1.19286e22i			0.152867i	−0.997075	+	0.0764333i	$0.975647\pi$
$728$	−4.10274e21	+	2.75733e22i	−0.0520024	+	0.349492i
$729$	8.69943e22			1.09061
$730$	−3.41160e22	−	6.64427e22i	−0.423034	−	0.823881i
$731$	1.05901e22			0.129886
$732$	−3.41029e22	−	2.44533e22i	−0.413717	−	0.296652i
$733$			1.19156e23i			1.42983i	0.699210	+	0.714917i	$0.253535\pi$
$733$			1.19156e23i			1.42983i	−0.699210	+	0.714917i	$0.746465\pi$
$734$	−2.61234e22	−	5.08767e22i	−0.310071	−	0.603879i
$735$		−	6.83488e22i		−	0.802476i
$736$	7.68136e22	−	7.92508e22i	0.892105	−	0.920410i
$737$	−1.30415e23			−1.49826
$738$	−1.51301e22	+	7.76877e21i	−0.171945	+	0.0882879i
$739$	1.70930e23			1.92160			0.960801	−	0.277239i	$-0.0894195\pi$
$739$	1.70930e23			1.92160			0.960801	+	0.277239i	$0.0894195\pi$
$740$	−8.40533e22	+	1.17222e23i	−0.934762	+	1.30364i
$741$			1.16898e23i			1.28606i
$742$	1.29656e22	−	6.65738e21i	0.141111	−	0.0724557i
$743$			9.75747e22i			1.05057i	0.850925	+	0.525287i	$0.176042\pi$
$743$			9.75747e22i			1.05057i	−0.850925	+	0.525287i	$0.823958\pi$
$744$	−1.63146e22	−	2.42752e21i	−0.173777	−	0.0258570i
$745$	−3.28096e22			−0.345741
$746$	−1.09570e22	−	2.13393e22i	−0.114230	−	0.222469i
$747$	2.74053e21			0.0282663
$748$	−3.30985e22	+	4.61597e22i	−0.337750	+	0.471032i
$749$		−	7.44002e21i		−	0.0751137i
$750$	4.59011e22	+	8.93947e22i	0.458493	+	0.892938i
$751$			3.66593e22i			0.362297i	0.983456	+	0.181148i	$0.0579814\pi$
$751$			3.66593e22i			0.362297i	−0.983456	+	0.181148i	$0.942019\pi$
$752$	1.24385e23	−	4.21400e22i	1.21625	−	0.412052i
$753$	−2.63777e22			−0.255198
$754$	5.06616e22	−	2.60130e22i	0.484962	−	0.249011i
$755$	−5.83621e22			−0.552784
$756$	−1.97594e22	−	1.41684e22i	−0.185183	−	0.132784i
$757$		−	1.87857e23i		−	1.74205i	−0.491242	−	0.871023i	$-0.663457\pi$
$757$		−	1.87857e23i		−	1.74205i	0.491242	−	0.871023i	$-0.336543\pi$
$758$	6.40003e22	−	3.28619e22i	0.587257	−	0.301536i
$759$			1.27392e23i			1.15667i
$760$	−8.33194e22	−	1.23975e22i	−0.748579	−	0.111384i
$761$	4.65702e22			0.414029			0.207015	−	0.978338i	$-0.433625\pi$
$761$	4.65702e22			0.414029			0.207015	+	0.978338i	$0.433625\pi$
$762$	8.30026e22	+	1.61652e23i	0.730217	+	1.42213i
$763$	−1.84150e22			−0.160315
$764$	−3.72775e22	−	2.67296e22i	−0.321144	−	0.230274i
$765$			7.76633e21i			0.0662101i
$766$	9.48951e22	+	1.84813e23i	0.800596	+	1.55920i
$767$		−	2.65667e23i		−	2.21807i
$768$	−9.00322e22	+	6.89132e22i	−0.743889	+	0.569394i
$769$	−7.52802e22			−0.615560			−0.307780	−	0.951458i	$-0.599586\pi$
$769$	−7.52802e22			−0.615560			−0.307780	+	0.951458i	$0.599586\pi$
$770$	2.06264e22	−	1.05910e22i	0.166916	−	0.0857056i
$771$	−5.01238e22			−0.401429
$772$	9.09499e22	−	1.26840e23i	0.720881	−	1.00535i
$773$		−	1.37402e22i		−	0.107785i	−0.998547	−	0.0538924i	$-0.982837\pi$
$773$		−	1.37402e22i		−	0.107785i	0.998547	−	0.0538924i	$-0.0171628\pi$
$774$	3.02790e21	−	1.55472e21i	0.0235079	−	0.0120705i
$775$			4.68852e21i			0.0360265i
$776$	−1.06245e22	+	7.14039e22i	−0.0808006	+	0.543035i
$777$	4.81347e22			0.362318
$778$	5.12569e22	+	9.98255e22i	0.381870	+	0.743712i
$779$	1.80285e23			1.32942
$780$	−1.09609e23	+	1.52863e23i	−0.800000	+	1.11569i
$781$		−	2.05417e23i		−	1.48398i
$782$	4.92676e22	+	9.59511e22i	0.352296	+	0.686114i
$783$			4.96715e22i			0.351571i
$784$	−4.36487e22	−	1.28838e23i	−0.305803	−	0.902641i
$785$	−1.81415e23			−1.25810
$786$	−1.23841e22	+	6.35882e21i	−0.0850129	+	0.0436512i
$787$	−2.58316e23			−1.75531			−0.877655	−	0.479293i	$-0.840893\pi$
$787$	−2.58316e23			−1.75531			−0.877655	+	0.479293i	$0.840893\pi$
$788$	4.90348e22	+	3.51600e22i	0.329833	+	0.236504i
$789$			1.16289e23i			0.774323i
$790$	1.27274e23	−	6.53508e22i	0.838925	−	0.430759i
$791$			5.31455e22i			0.346780i
$792$	−2.68678e21	+	1.80570e22i	−0.0173553	+	0.116639i
$793$	−1.38559e23			−0.886035
$794$	−4.25811e22	−	8.29289e22i	−0.269559	−	0.524979i
$795$	9.83441e22			0.616327
$796$	−3.06090e22	−	2.19479e22i	−0.189908	−	0.136172i
$797$		−	1.34029e23i		−	0.823252i	−0.911353	−	0.411626i	$-0.864961\pi$
$797$		−	1.34029e23i		−	0.823252i	0.911353	−	0.411626i	$-0.135039\pi$
$798$	1.28400e22	+	2.50065e22i	0.0780801	+	0.152065i
$799$			1.28346e23i			0.772695i
$800$	2.31419e22	+	2.24303e22i	0.137937	+	0.133695i
$801$	−7.72627e21			−0.0455942
$802$	−4.90416e22	+	2.51812e22i	−0.286530	+	0.147123i
$803$	1.71580e23			0.992527
$804$	1.48250e23	−	2.06752e23i	0.849075	−	1.18413i
$805$		−	4.40304e22i		−	0.249681i
$806$	−4.84483e22	+	2.48765e22i	−0.272018	+	0.139672i
$807$		−	1.45137e23i		−	0.806844i
$808$	−1.52085e23	−	2.26294e22i	−0.837137	−	0.124561i
$809$	9.67336e22			0.527217			0.263608	−	0.964630i	$-0.415087\pi$
$809$	9.67336e22			0.527217			0.263608	+	0.964630i	$0.415087\pi$
$810$	−6.56242e22	−	1.27806e23i	−0.354147	−	0.689720i
$811$	1.68080e23			0.898153			0.449076	−	0.893493i	$-0.351753\pi$
$811$	1.68080e23			0.898153			0.449076	+	0.893493i	$0.351753\pi$
$812$	7.98011e21	−	1.11292e22i	0.0422241	−	0.0588865i
$813$			1.13552e23i			0.594937i
$814$	−1.51356e23	−	2.94773e23i	−0.785244	−	1.52930i
$815$		−	2.38550e22i		−	0.122552i
$816$	−3.55539e22	−	1.04945e23i	−0.180870	−	0.533874i
$817$	−3.60796e22			−0.181755
$818$	−1.70349e21	+	8.74681e20i	−0.00849791	+	0.00436338i
$819$	−8.75625e21			−0.0432561
$820$	2.35751e23	+	1.69044e23i	1.15330	+	0.826967i
$821$			1.40786e22i			0.0682045i	0.999418	+	0.0341022i	$0.0108572\pi$
$821$			1.40786e22i			0.0682045i	−0.999418	+	0.0341022i	$0.989143\pi$
$822$	1.74112e23	−	8.94007e22i	0.835324	−	0.428910i
$823$		−	2.86333e23i		−	1.36042i	−0.733017	−	0.680210i	$-0.761889\pi$
$823$		−	2.86333e23i		−	1.36042i	0.733017	−	0.680210i	$-0.238111\pi$
$824$	−1.88186e23	−	2.80011e22i	−0.885463	−	0.131752i
$825$	−3.71996e22			−0.173343
$826$	−2.91806e22	−	5.68306e22i	−0.134665	−	0.262266i
$827$	−4.74803e22			−0.217005			−0.108502	−	0.994096i	$-0.534606\pi$
$827$	−4.74803e22			−0.217005			−0.108502	+	0.994096i	$0.534606\pi$
$828$	2.81730e22	+	2.02012e22i	0.127523	+	0.0914397i
$829$			1.32164e23i			0.592485i	0.955113	+	0.296242i	$0.0957336\pi$
$829$			1.32164e23i			0.592485i	−0.955113	+	0.296242i	$0.904266\pi$
$830$	−2.13510e22	−	4.15821e22i	−0.0947967	−	0.184621i
$831$			2.30725e23i			1.01458i
$832$	−1.08993e23	+	3.58145e23i	−0.474693	+	1.55981i
$833$	1.32941e23			0.573454
$834$	−2.78467e23	+	1.42983e23i	−1.18972	+	0.610880i
$835$	−3.82978e22			−0.162062
$836$	1.12764e23	−	1.57262e23i	0.472627	−	0.659134i
$837$		−	4.75015e22i		−	0.197198i
$838$	−1.66083e23	+	8.52781e22i	−0.682926	+	0.350659i
$839$			4.80138e23i			1.95556i	0.209641	+	0.977778i	$0.432771\pi$
$839$			4.80138e23i			1.95556i	−0.209641	+	0.977778i	$0.567229\pi$
$840$	−6.65694e21	+	4.47392e22i	−0.0268559	+	0.180490i
$841$	2.22270e23			0.888203
$842$	7.69165e22	+	1.49799e23i	0.304455	+	0.592941i
$843$	8.53216e22			0.334533
$844$	6.21852e22	−	8.67246e22i	0.241517	−	0.336824i
$845$			3.87445e23i			1.49059i
$846$	1.88423e22	+	3.66964e22i	0.0718078	+	0.139849i
$847$		−	4.14028e21i		−	0.0156301i
$848$	1.85379e23	−	6.28041e22i	0.693257	−	0.234867i
$849$	1.03572e23			0.383691
$850$	−2.80186e22	+	1.43866e22i	−0.102824	+	0.0527966i
$851$	−6.29241e23			−2.28760
$852$	3.25655e23	+	2.33509e23i	1.17285	+	0.840982i
$853$			6.99794e22i			0.249677i	0.992177	+	0.124838i	$0.0398412\pi$
$853$			6.99794e22i			0.249677i	−0.992177	+	0.124838i	$0.960159\pi$
$854$	−2.96401e22	+	1.52192e22i	−0.104765	+	0.0537934i
$855$		−	2.64592e22i		−	0.0926504i
$856$	1.47047e22	−	9.88254e22i	0.0510111	−	0.342830i
$857$	3.39918e23			1.16823			0.584115	−	0.811671i	$-0.301442\pi$
$857$	3.39918e23			1.16823			0.584115	+	0.811671i	$0.301442\pi$
$858$	−1.97375e23	−	3.84397e23i	−0.672037	−	1.30883i
$859$	6.53135e22			0.220322			0.110161	−	0.993914i	$-0.464863\pi$
$859$	6.53135e22			0.220322			0.110161	+	0.993914i	$0.464863\pi$
$860$	−4.71797e22	−	3.38299e22i	−0.157677	−	0.113061i
$861$		−	9.68060e22i		−	0.320536i
$862$	1.23292e23	+	2.40117e23i	0.404461	+	0.787708i
$863$			7.96035e22i			0.258729i	0.991597	+	0.129365i	$0.0412938\pi$
$863$			7.96035e22i			0.258729i	−0.991597	+	0.129365i	$0.958706\pi$
$864$	−2.34461e23	−	2.27251e23i	−0.755024	−	0.731805i
$865$	1.60931e23			0.513465
$866$	−1.26748e23	+	6.50809e22i	−0.400681	+	0.205736i
$867$	−1.90799e23			−0.597618
$868$	−7.63148e21	+	1.06430e22i	−0.0236838	+	0.0330298i
$869$			3.28669e23i			1.01065i
$870$	8.22013e22	−	4.22075e22i	0.250452	−	0.128599i
$871$		−	8.40028e23i		−	2.53600i
$872$	−2.44605e23	−	3.63958e22i	−0.731700	−	0.108873i
$873$	−2.26752e22			−0.0672107
$874$	−1.67850e23	−	3.26897e23i	−0.492981	−	0.960106i
$875$	7.97887e22			0.232208
$876$	−1.95044e23	+	2.72012e23i	−0.562472	+	0.784433i
$877$		−	2.03187e22i		−	0.0580629i	−0.999578	−	0.0290314i	$-0.990758\pi$
$877$		−	2.03187e22i		−	0.0580629i	0.999578	−	0.0290314i	$-0.00924229\pi$
$878$	−6.19166e22	−	1.20586e23i	−0.175328	−	0.341460i
$879$		−	3.43673e23i		−	0.964349i
$880$	2.94912e23	−	9.99125e22i	0.820032	−	0.277817i
$881$	2.10400e23			0.579748			0.289874	−	0.957065i	$-0.406387\pi$
$881$	2.10400e23			0.579748			0.289874	+	0.957065i	$0.406387\pi$
$882$	3.80101e22	−	1.95169e22i	0.103789	−	0.0532920i
$883$	−4.59241e23			−1.24267			−0.621334	−	0.783546i	$-0.713409\pi$
$883$	−4.59241e23			−1.24267			−0.621334	+	0.783546i	$0.713409\pi$
$884$	−2.97324e23	−	2.13194e23i	−0.797281	−	0.571684i
$885$		−	4.31060e23i		−	1.14549i
$886$	5.81936e23	−	2.98804e23i	1.53252	−	0.786895i
$887$			1.22969e23i			0.320926i	0.987042	+	0.160463i	$0.0512988\pi$
$887$			1.22969e23i			0.320926i	−0.987042	+	0.160463i	$0.948701\pi$
$888$	6.39371e23	+	9.51347e22i	1.65367	+	0.246057i
$889$	1.44281e23			0.369825
$890$	6.01940e22	+	1.17231e23i	0.152909	+	0.297798i
$891$	3.30044e23			0.830904
$892$	3.76332e23	+	2.69846e23i	0.938971	+	0.673282i
$893$		−	4.37263e23i		−	1.08126i
$894$	6.71603e22	+	1.30798e23i	0.164593	+	0.320554i
$895$		−	7.10631e22i		−	0.172607i
$896$	1.60228e22	+	8.85849e22i	0.0385722	+	0.213253i
$897$	−8.20556e23			−1.95780
$898$	−4.02760e23	+	2.06803e23i	−0.952436	+	0.489043i
$899$	2.67545e22			0.0627074
$900$	−5.89893e21	+	8.22675e21i	−0.0137036	+	0.0191112i
$901$			1.91283e23i			0.440431i
$902$	−5.92833e23	+	3.04399e23i	−1.35295	+	0.694691i
$903$			1.93733e22i			0.0438229i
$904$	−1.05038e23	+	7.05929e23i	−0.235505	+	1.58275i
$905$	−5.53821e23			−1.23078
$906$	1.19465e23	+	2.32665e23i	0.263158	+	0.512514i
$907$	−3.08303e23			−0.673162			−0.336581	−	0.941655i	$-0.609271\pi$
$907$	−3.08303e23			−0.673162			−0.336581	+	0.941655i	$0.609271\pi$
$908$	9.12483e22	−	1.27257e23i	0.197487	−	0.275419i
$909$		−	4.82967e22i		−	0.103611i
$910$	6.82184e22	+	1.32859e23i	0.145068	+	0.282527i
$911$			1.35597e22i			0.0285826i	0.999898	+	0.0142913i	$0.00454922\pi$
$911$			1.35597e22i			0.0285826i	−0.999898	+	0.0142913i	$0.995451\pi$
$912$	1.21129e23	+	3.57537e23i	0.253098	+	0.747071i
$913$	1.07381e23			0.222413
$914$	5.93765e23	−	3.04878e23i	1.21912	−	0.625974i
$915$	−2.24821e23			−0.457580
$916$	−2.92480e23	−	2.09720e23i	−0.590108	−	0.423133i
$917$			1.10534e22i			0.0221075i
$918$	2.83868e23	−	1.45757e23i	0.562828	−	0.288993i
$919$			4.62319e23i			0.908694i	0.890825	+	0.454347i	$0.150127\pi$
$919$			4.62319e23i			0.908694i	−0.890825	+	0.454347i	$0.849873\pi$
$920$	8.70228e22	−	5.84853e23i	0.169563	−	1.13958i
$921$	−4.15459e23			−0.802512
$922$	3.87376e23	+	7.54433e23i	0.741797	+	1.44469i
$923$	1.32313e24			2.51182
$924$	−8.44434e22	−	6.05495e22i	−0.158924	−	0.113955i
$925$		−	1.83744e23i		−	0.342830i
$926$	−2.96981e23	−	5.78386e23i	−0.549340	−	1.06987i
$927$		−	5.97610e22i		−	0.109592i
$928$	1.27995e23	−	1.32057e23i	0.232708	−	0.240091i
$929$	6.23774e23			1.12435			0.562175	−	0.827018i	$-0.309965\pi$
$929$	6.23774e23			1.12435			0.562175	+	0.827018i	$0.309965\pi$
$930$	−7.86101e22	+	4.03636e22i	−0.140480	+	0.0721317i
$931$	−4.52918e23			−0.802457
$932$	−5.09233e23	+	7.10186e23i	−0.894519	+	1.24751i
$933$		−	7.71215e23i		−	1.34314i
$934$	−5.91560e23	+	3.03746e23i	−1.02147	+	0.524488i
$935$			3.04304e23i			0.520972i
$936$	−1.16309e23	−	1.73061e22i	−0.197427	−	0.0293760i
$937$	−2.64667e22			−0.0445433			−0.0222716	−	0.999752i	$-0.507090\pi$
$937$	−2.64667e22			−0.0445433			−0.0222716	+	0.999752i	$0.507090\pi$
$938$	−9.22676e22	−	1.79696e23i	−0.153967	−	0.299858i
$939$	9.99872e23			1.65432
$940$	4.09998e23	−	5.71790e23i	0.672603	−	0.938024i
$941$			5.00138e23i			0.813528i	0.913533	+	0.406764i	$0.133343\pi$
$941$			5.00138e23i			0.813528i	−0.913533	+	0.406764i	$0.866657\pi$
$942$	3.71351e23	+	7.23224e23i	0.598931	+	1.16645i
$943$			1.26550e24i			2.02380i
$944$	−2.75282e23	−	8.12551e23i	−0.436518	−	1.28847i
$945$	−1.30262e23			−0.204816
$946$	1.18641e23	−	6.09179e22i	0.184971	−	0.0949765i
$947$	3.08810e23			0.477410			0.238705	−	0.971092i	$-0.423277\pi$
$947$	3.08810e23			0.477410			0.238705	+	0.971092i	$0.423277\pi$
$948$	−5.21052e23	−	3.73617e23i	−0.798757	−	0.572743i
$949$			1.10518e24i			1.67998i
$950$	9.54568e22	−	4.90138e22i	0.143886	−	0.0738804i
$951$		−	1.11419e23i		−	0.166539i
$952$	−8.70194e22	−	1.29480e22i	−0.128979	−	0.0191914i
$953$	−8.16640e23			−1.20029			−0.600147	−	0.799890i	$-0.704891\pi$
$953$	−8.16640e23			−1.20029			−0.600147	+	0.799890i	$0.704891\pi$
$954$	2.80820e22	+	5.46911e22i	0.0409300	+	0.0797132i
$955$	−2.45749e23			−0.355193
$956$	−9.39301e23	−	6.73519e23i	−1.34630	−	0.965354i
$957$			2.12275e23i			0.301719i
$958$	−4.45613e23	−	8.67855e23i	−0.628108	−	1.22327i
$959$		−	1.55403e23i		−	0.217225i
$960$	−1.76848e23	+	5.81112e23i	−0.245148	+	0.805545i
$961$	7.01837e23			0.964827
$962$	1.89869e24	−	9.74914e23i	2.58854	−	1.32912i
$963$	3.13833e22			0.0424315
$964$	−3.41865e23	+	4.76771e23i	−0.458394	+	0.639284i
$965$		−	8.36184e23i		−	1.11194i
$966$	−1.75530e23	+	9.01289e22i	−0.231492	+	0.118863i
$967$		−	6.99104e23i		−	0.914387i	−0.889367	−	0.457193i	$-0.848855\pi$
$967$		−	6.99104e23i		−	0.914387i	0.889367	−	0.457193i	$-0.151145\pi$
$968$	8.18297e21	−	5.49951e22i	0.0106147	−	0.0713381i
$969$	−3.68923e23			−0.474619
$970$	1.76659e23	+	3.44052e23i	0.225404	+	0.438986i
$971$	2.49451e23			0.315668			0.157834	−	0.987466i	$-0.449549\pi$
$971$	2.49451e23			0.315668			0.157834	+	0.987466i	$0.449549\pi$
$972$	1.13011e23	−	1.57607e23i	0.141837	−	0.197809i
$973$			2.48544e23i			0.309386i
$974$	3.39561e22	+	6.61313e22i	0.0419225	+	0.0816461i
$975$		−	2.39610e23i		−	0.293405i
$976$	−4.23788e23	+	1.43574e23i	−0.514695	+	0.174372i
$977$	1.35612e23			0.163358			0.0816792	−	0.996659i	$-0.473972\pi$
$977$	1.35612e23			0.163358			0.0816792	+	0.996659i	$0.473972\pi$
$978$	−9.50999e22	+	4.88305e22i	−0.113624	+	0.0583419i
$979$	−3.02734e23			−0.358757
$980$	−5.92261e23	−	4.24676e23i	−0.696153	−	0.499171i
$981$		−	7.76775e22i		−	0.0905614i
$982$	−5.05638e23	+	2.59628e23i	−0.584720	+	0.300234i
$983$		−	3.03248e22i		−	0.0347832i	−0.999849	−	0.0173916i	$-0.994464\pi$
$983$		−	3.03248e22i		−	0.0347832i	0.999849	−	0.0173916i	$-0.00553619\pi$
$984$	1.91330e23	−	1.28587e24i	0.217682	−	1.46297i
$985$	3.23258e23			0.364803
$986$	8.20952e22	+	1.59885e23i	0.0918972	+	0.178974i
$987$	−2.34793e23			−0.260704
$988$	1.01296e24	+	7.26332e23i	1.11567	+	0.799981i
$989$		−	2.53257e23i		−	0.276689i
$990$	4.46745e22	+	8.70059e22i	0.0484148	+	0.0942903i
$991$		−	7.02317e23i		−	0.754995i	−0.926011	−	0.377498i	$-0.876785\pi$
$991$		−	7.02317e23i		−	0.754995i	0.926011	−	0.377498i	$-0.123215\pi$
$992$	−1.22404e23	+	1.26287e23i	−0.130527	+	0.134669i
$993$	3.70684e22			0.0392112
$994$	2.83039e23	−	1.45331e23i	0.297000	−	0.152499i
$995$	−2.01787e23			−0.210043
$996$	−1.22066e23	+	1.70235e23i	−0.126043	+	0.175782i
$997$		−	3.30021e23i		−	0.338050i	−0.985612	−	0.169025i	$-0.945938\pi$
$997$		−	3.30021e23i		−	0.338050i	0.985612	−	0.169025i	$-0.0540618\pi$
$998$	−1.37206e24	+	7.04504e23i	−1.39421	+	0.715878i
$999$			1.86159e24i			1.87655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.17.d.b.3.4	yes	14
3.2	odd	2		72.17.b.b.19.11		14
4.3	odd	2		32.17.d.b.15.5		14
8.3	odd	2	inner	8.17.d.b.3.3	✓	14
8.5	even	2		32.17.d.b.15.6		14
24.11	even	2		72.17.b.b.19.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.17.d.b.3.3	✓	14	8.3	odd	2	inner
8.17.d.b.3.4	yes	14	1.1	even	1	trivial
32.17.d.b.15.5		14	4.3	odd	2
32.17.d.b.15.6		14	8.5	even	2
72.17.b.b.19.11		14	3.2	odd	2
72.17.b.b.19.12		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)

\(f(q)\)	\(=\)	\(q+(-227.734 + 116.933i) q^{2} +6146.29 q^{3} +(38189.2 - 53259.3i) q^{4} -351107. i q^{5} +(-1.39972e6 + 718707. i) q^{6} +1.24931e6i q^{7} +(-2.46917e6 + 1.65945e7i) q^{8} -5.26981e6 q^{9} +O(q^{10})\)	\(q+(-227.734 + 116.933i) q^{2} +6146.29 q^{3} +(38189.2 - 53259.3i) q^{4} -351107. i q^{5} +(-1.39972e6 + 718707. i) q^{6} +1.24931e6i q^{7} +(-2.46917e6 + 1.65945e7i) q^{8} -5.26981e6 q^{9} +(4.10562e7 + 7.99589e7i) q^{10} -2.06484e8 q^{11} +(2.34722e8 - 3.27347e8i) q^{12} -1.33000e9i q^{13} +(-1.46086e8 - 2.84510e8i) q^{14} -2.15801e9i q^{15} +(-1.37814e9 - 4.06786e9i) q^{16} +4.19741e9 q^{17} +(1.20011e9 - 6.16216e8i) q^{18} -1.43002e10 q^{19} +(-1.86997e10 - 1.34085e10i) q^{20} +7.67862e9i q^{21} +(4.70234e10 - 2.41449e10i) q^{22} -1.00379e11i q^{23} +(-1.51762e10 + 1.01995e11i) q^{24} +2.93115e10 q^{25} +(1.55522e11 + 3.02887e11i) q^{26} -2.96968e11 q^{27} +(6.65374e10 + 4.77101e10i) q^{28} -1.67262e11i q^{29} +(2.52343e11 + 4.91451e11i) q^{30} +1.59955e11i q^{31} +(7.89517e11 + 7.65238e11i) q^{32} -1.26911e12 q^{33} +(-9.55890e11 + 4.90817e11i) q^{34} +4.38642e11 q^{35} +(-2.01250e11 + 2.80666e11i) q^{36} -6.26866e12i q^{37} +(3.25663e12 - 1.67217e12i) q^{38} -8.17460e12i q^{39} +(5.82646e12 + 8.66944e11i) q^{40} -1.26072e13 q^{41} +(-8.97887e11 - 1.74868e12i) q^{42} +2.52302e12 q^{43} +(-7.88546e12 + 1.09972e13i) q^{44} +1.85027e12i q^{45} +(1.17376e13 + 2.28596e13i) q^{46} +3.05775e13i q^{47} +(-8.47045e12 - 2.50022e13i) q^{48} +3.16722e13 q^{49} +(-6.67521e12 + 3.42749e12i) q^{50} +2.57985e13 q^{51} +(-7.08351e13 - 5.07918e13i) q^{52} +4.55717e13i q^{53} +(6.76295e13 - 3.47254e13i) q^{54} +7.24981e13i q^{55} +(-2.07317e13 - 3.08476e12i) q^{56} -8.78931e13 q^{57} +(1.95586e13 + 3.80913e13i) q^{58} +1.99749e14 q^{59} +(-1.14934e14 - 8.24126e13i) q^{60} -1.04180e14i q^{61} +(-1.87041e13 - 3.64271e13i) q^{62} -6.58362e12i q^{63} +(-2.69281e14 - 8.19494e13i) q^{64} -4.66974e14 q^{65} +(2.89019e14 - 1.48401e14i) q^{66} +6.31598e14 q^{67} +(1.60295e14 - 2.23551e14i) q^{68} -6.16958e14i q^{69} +(-9.98935e13 + 5.12919e13i) q^{70} +9.94832e14i q^{71} +(1.30121e13 - 8.74500e13i) q^{72} -8.30960e14 q^{73} +(7.33015e14 + 1.42758e15i) q^{74} +1.80157e14 q^{75} +(-5.46112e14 + 7.61618e14i) q^{76} -2.57963e14i q^{77} +(9.55883e14 + 1.86163e15i) q^{78} -1.59174e15i q^{79} +(-1.42826e15 + 4.83875e14i) q^{80} -1.59840e15 q^{81} +(2.87108e15 - 1.47420e15i) q^{82} -5.20043e14 q^{83} +(4.08958e14 + 2.93240e14i) q^{84} -1.47374e15i q^{85} +(-5.74576e14 + 2.95025e14i) q^{86} -1.02804e15i q^{87} +(5.09844e14 - 3.42650e15i) q^{88} +1.46614e15 q^{89} +(-2.16358e14 - 4.21368e14i) q^{90} +1.66159e15 q^{91} +(-5.34611e15 - 3.83338e15i) q^{92} +9.83131e14i q^{93} +(-3.57552e15 - 6.96351e15i) q^{94} +5.02090e15i q^{95} +(4.85260e15 + 4.70337e15i) q^{96} +4.30286e15 q^{97} +(-7.21281e15 + 3.70353e15i) q^{98} +1.08813e15 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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