LMFDB - Embedded newform 38.10.c.b.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(7,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.c (of order $3$, degree $2$, 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:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 104960 x^{14} - 3899480 x^{13} + 8040649724 x^{12} - 270026959304 x^{11} + \cdots + 13\!\cdots\!00 $ x^16 - 2x^15 + 104960x^14 - 3899480x^13 + 8040649724x^12 - 270026959304x^11 + 275078771318560x^10 - 7559006944968384x^9 + 6786319237849450512x^8 - 132172428275143142112x^7 + 58413131602192832245632x^6 + 306187936352529387788160x^5 + 338231098965100183334201088x^4 + 833605976716998105836915712x^3 + 801869139824974932731497058304x^2 + 7085244797393532409215050711040*x + 1344731733940407880332419688038400
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			7.6
Root			$-34.9668 - 60.5642i$ of defining polynomial
Character	$\chi$	$=$	38.7
Dual form			38.10.c.b.11.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.00000 - 13.8564i) q^{2} +(39.4668 + 68.3585i) q^{3} +(-128.000 + 221.703i) q^{4} +(-134.126 - 232.313i) q^{5} +(631.468 - 1093.74i) q^{6} -5487.23 q^{7} +4096.00 q^{8} +(6726.25 - 11650.2i) q^{9} +O(q^{10})$	\(q+(-8.00000 - 13.8564i) q^{2} +(39.4668 + 68.3585i) q^{3} +(-128.000 + 221.703i) q^{4} +(-134.126 - 232.313i) q^{5} +(631.468 - 1093.74i) q^{6} -5487.23 q^{7} +4096.00 q^{8} +(6726.25 - 11650.2i) q^{9} +(-2146.01 + 3717.01i) q^{10} +10698.5 q^{11} -20207.0 q^{12} +(-18947.9 + 32818.8i) q^{13} +(43897.8 + 76033.2i) q^{14} +(10587.0 - 18337.3i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(289210. + 500927. i) q^{17} -215240. q^{18} +(567636. + 21854.0i) q^{19} +68672.5 q^{20} +(-216563. - 375098. i) q^{21} +(-85587.8 - 148242. i) q^{22} +(2170.26 - 3759.00i) q^{23} +(161656. + 279996. i) q^{24} +(940583. - 1.62914e6i) q^{25} +606334. q^{26} +2.61550e6 q^{27} +(702365. - 1.21653e6i) q^{28} +(2.09782e6 - 3.63353e6i) q^{29} -338785. q^{30} +8.61790e6 q^{31} +(-524288. + 908093. i) q^{32} +(422234. + 731331. i) q^{33} +(4.62736e6 - 8.01483e6i) q^{34} +(735979. + 1.27475e6i) q^{35} +(1.72192e6 + 2.98245e6i) q^{36} -3.67927e6 q^{37} +(-4.23827e6 - 8.04022e6i) q^{38} -2.99126e6 q^{39} +(-549380. - 951554. i) q^{40} +(1.09981e7 + 1.90493e7i) q^{41} +(-3.46501e6 + 6.00157e6i) q^{42} +(6.66965e6 + 1.15522e7i) q^{43} +(-1.36940e6 + 2.37188e6i) q^{44} -3.60866e6 q^{45} -69448.3 q^{46} +(5.23969e6 - 9.07541e6i) q^{47} +(2.58649e6 - 4.47994e6i) q^{48} -1.02439e7 q^{49} -3.00987e7 q^{50} +(-2.28284e7 + 3.95399e7i) q^{51} +(-4.85067e6 - 8.40161e6i) q^{52} +(-1.47068e7 + 2.54729e7i) q^{53} +(-2.09240e7 - 3.62415e7i) q^{54} +(-1.43494e6 - 2.48539e6i) q^{55} -2.24757e7 q^{56} +(2.09088e7 + 3.96652e7i) q^{57} -6.71302e7 q^{58} +(3.67872e6 + 6.37173e6i) q^{59} +(2.71028e6 + 4.69434e6i) q^{60} +(8.61354e7 - 1.49191e8i) q^{61} +(-6.89432e7 - 1.19413e8i) q^{62} +(-3.69084e7 + 6.39273e7i) q^{63} +1.67772e7 q^{64} +1.01656e7 q^{65} +(6.75575e6 - 1.17013e7i) q^{66} +(-1.22829e8 + 2.12747e8i) q^{67} -1.48076e8 q^{68} +342612. q^{69} +(1.17757e7 - 2.03961e7i) q^{70} +(-1.00693e8 - 1.74405e8i) q^{71} +(2.75507e7 - 4.77192e7i) q^{72} +(8.49285e7 + 1.47100e8i) q^{73} +(2.94342e7 + 5.09815e7i) q^{74} +1.48487e8 q^{75} +(-7.75024e7 + 1.23049e8i) q^{76} -5.87049e7 q^{77} +(2.39301e7 + 4.14481e7i) q^{78} +(2.02761e8 + 3.51192e8i) q^{79} +(-8.79008e6 + 1.52249e7i) q^{80} +(-2.91673e7 - 5.05192e7i) q^{81} +(1.75970e8 - 3.04789e8i) q^{82} +1.99408e8 q^{83} +1.10880e8 q^{84} +(7.75812e7 - 1.34375e8i) q^{85} +(1.06714e8 - 1.84835e8i) q^{86} +3.31177e8 q^{87} +4.38209e7 q^{88} +(1.82842e7 - 3.16692e7i) q^{89} +(2.88692e7 + 5.00030e7i) q^{90} +(1.03972e8 - 1.80084e8i) q^{91} +(555586. + 962303. i) q^{92} +(3.40121e8 + 5.89106e8i) q^{93} -1.67670e8 q^{94} +(-7.10577e7 - 1.34800e8i) q^{95} -8.27678e7 q^{96} +(-6.21337e8 - 1.07619e9i) q^{97} +(8.19516e7 + 1.41944e8i) q^{98} +(7.19606e7 - 1.24639e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) $ 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9 - 5456 * q^10 + 106682 * q^11 - 35840 * q^12 - 683 * q^13 - 29632 * q^14 + 2299 * q^15 - 524288 * q^16 - 611267 * q^17 + 1698048 * q^18 - 1609677 * q^19 + 174592 * q^20 - 941048 * q^21 - 853456 * q^22 - 416119 * q^23 + 286720 * q^24 - 3309027 * q^25 + 21856 * q^26 - 16903604 * q^27 - 474112 * q^28 - 5079157 * q^29 - 73568 * q^30 + 8618324 * q^31 - 8388608 * q^32 - 7592195 * q^33 - 9780272 * q^34 - 2035632 * q^35 - 13584384 * q^36 - 33091520 * q^37 + 18612624 * q^38 + 37931126 * q^39 - 1396736 * q^40 - 7394646 * q^41 - 15056768 * q^42 - 98675599 * q^43 - 13655296 * q^44 + 89231852 * q^45 + 13315808 * q^46 + 34129475 * q^47 + 4587520 * q^48 + 65004400 * q^49 + 105888864 * q^50 + 16027749 * q^51 - 174848 * q^52 - 110053995 * q^53 + 135228832 * q^54 + 135992300 * q^55 + 15171584 * q^56 + 14986101 * q^57 + 162533024 * q^58 - 2017760 * q^59 + 588544 * q^60 - 221861413 * q^61 - 68946592 * q^62 + 56812456 * q^63 + 268435456 * q^64 + 262635974 * q^65 - 121475120 * q^66 + 237580440 * q^67 + 312968704 * q^68 - 135348410 * q^69 - 32570112 * q^70 - 431190909 * q^71 - 217350144 * q^72 + 199873544 * q^73 + 264732160 * q^74 - 1822944486 * q^75 + 114275328 * q^76 + 2014342624 * q^77 - 303449008 * q^78 - 296762835 * q^79 - 22347776 * q^80 - 1069077456 * q^81 - 118314336 * q^82 + 1592138306 * q^83 + 481816576 * q^84 - 293558115 * q^85 - 1578809584 * q^86 - 1647860854 * q^87 + 436969472 * q^88 - 444394631 * q^89 - 713854816 * q^90 - 284099544 * q^91 - 106526464 * q^92 + 1322110374 * q^93 - 1092143200 * q^94 + 8705459 * q^95 - 146800640 * q^96 - 611719542 * q^97 - 520035200 * q^98 + 1201848626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$2$	−8.00000	−	13.8564i	−0.353553	−	0.612372i
$3$	39.4668	+	68.3585i	0.281311	+	0.487244i	0.971708	−	0.236186i	$-0.0758976\pi$
$3$	39.4668	+	68.3585i	0.281311	+	0.487244i	−0.690397	+	0.723430i	$0.742564\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	−134.126	−	232.313i	−0.0959727	−	0.166230i	0.814041	−	0.580807i	$-0.197263\pi$
$5$	−134.126	−	232.313i	−0.0959727	−	0.166230i	−0.910014	+	0.414577i	$0.863929\pi$
$6$	631.468	−	1093.74i	0.198917	−	0.344534i
$7$	−5487.23			−0.863797			−0.431899	−	0.901922i	$-0.642156\pi$
$7$	−5487.23			−0.863797			−0.431899	+	0.901922i	$0.642156\pi$
$8$	4096.00			0.353553
$9$	6726.25	−	11650.2i	0.341729	−	0.591892i
$10$	−2146.01	+	3717.01i	−0.0678629	+	0.117542i
$11$	10698.5			0.220320			0.110160	−	0.993914i	$-0.464864\pi$
$11$	10698.5			0.220320			0.110160	+	0.993914i	$0.464864\pi$
$12$	−20207.0			−0.281311
$13$	−18947.9	+	32818.8i	−0.184000	+	0.318697i	−0.943239	−	0.332115i	$-0.892238\pi$
$13$	−18947.9	+	32818.8i	−0.184000	+	0.318697i	0.759239	+	0.650812i	$0.225571\pi$
$14$	43897.8	+	76033.2i	0.305398	+	0.528966i
$15$	10587.0	−	18337.3i	0.0539963	−	0.0935243i
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	289210.	+	500927.i	0.839834	+	1.45464i	0.890033	+	0.455896i	$0.150681\pi$
$17$	289210.	+	500927.i	0.839834	+	1.45464i	−0.0501985	+	0.998739i	$0.515985\pi$
$18$	−215240.			−0.483277
$19$	567636.	+	21854.0i	0.999260	+	0.0384715i
$19$	567636.	+	21854.0i	0.999260	+	0.0384715i
$20$	68672.5			0.0959727
$21$	−216563.	−	375098.i	−0.242995	−	0.420880i
$22$	−85587.8	−	148242.i	−0.0778950	−	0.134918i
$23$	2170.26	−	3759.00i	0.00161710	−	0.00280090i	−0.865216	−	0.501400i	$-0.832819\pi$
$23$	2170.26	−	3759.00i	0.00161710	−	0.00280090i	0.866833	+	0.498599i	$0.166152\pi$
$24$	161656.	+	279996.i	0.0994583	+	0.172267i
$25$	940583.	−	1.62914e6i	0.481578	−	0.834118i
$26$	606334.			0.260215
$27$	2.61550e6			0.947149
$28$	702365.	−	1.21653e6i	0.215949	−	0.374035i
$29$	2.09782e6	−	3.63353e6i	0.550779	−	0.953977i	−0.447440	−	0.894314i	$-0.647664\pi$
$29$	2.09782e6	−	3.63353e6i	0.550779	−	0.953977i	0.998219	−	0.0596627i	$-0.0190025\pi$
$30$	−338785.			−0.0763622
$31$	8.61790e6			1.67600			0.837999	−	0.545671i	$-0.183725\pi$
$31$	8.61790e6			1.67600			0.837999	+	0.545671i	$0.183725\pi$
$32$	−524288.	+	908093.i	−0.0883883	+	0.153093i
$33$	422234.	+	731331.i	0.0619784	+	0.107350i
$34$	4.62736e6	−	8.01483e6i	0.593853	−	1.02858i
$35$	735979.	+	1.27475e6i	0.0829009	+	0.143589i
$36$	1.72192e6	+	2.98245e6i	0.170864	+	0.295946i
$37$	−3.67927e6			−0.322741			−0.161370	−	0.986894i	$-0.551591\pi$
$37$	−3.67927e6			−0.322741			−0.161370	+	0.986894i	$0.551591\pi$
$38$	−4.23827e6	−	8.04022e6i	−0.329733	−	0.625521i
$39$	−2.99126e6			−0.207044
$40$	−549380.	−	951554.i	−0.0339315	−	0.0587710i
$41$	1.09981e7	+	1.90493e7i	0.607843	+	1.05282i	0.991595	+	0.129379i	$0.0412984\pi$
$41$	1.09981e7	+	1.90493e7i	0.607843	+	1.05282i	−0.383752	+	0.923436i	$0.625368\pi$
$42$	−3.46501e6	+	6.00157e6i	−0.171824	+	0.297607i
$43$	6.66965e6	+	1.15522e7i	0.297505	+	0.515294i	0.975565	−	0.219713i	$-0.0705120\pi$
$43$	6.66965e6	+	1.15522e7i	0.297505	+	0.515294i	−0.678059	+	0.735007i	$0.737179\pi$
$44$	−1.36940e6	+	2.37188e6i	−0.0550801	+	0.0954015i
$45$	−3.60866e6			−0.131186
$46$	−69448.3			−0.00228692
$47$	5.23969e6	−	9.07541e6i	0.156627	−	0.271285i	−0.777024	−	0.629472i	$-0.783271\pi$
$47$	5.23969e6	−	9.07541e6i	0.156627	−	0.271285i	0.933650	+	0.358186i	$0.116605\pi$
$48$	2.58649e6	−	4.47994e6i	0.0703276	−	0.121811i
$49$	−1.02439e7			−0.253855
$50$	−3.00987e7			−0.681055
$51$	−2.28284e7	+	3.95399e7i	−0.472509	+	0.818409i
$52$	−4.85067e6	−	8.40161e6i	−0.0919998	−	0.159348i
$53$	−1.47068e7	+	2.54729e7i	−0.256022	+	0.443443i	−0.965173	−	0.261614i	$-0.915745\pi$
$53$	−1.47068e7	+	2.54729e7i	−0.256022	+	0.443443i	0.709151	+	0.705057i	$0.249079\pi$
$54$	−2.09240e7	−	3.62415e7i	−0.334868	−	0.580008i
$55$	−1.43494e6	−	2.48539e6i	−0.0211447	−	0.0366238i
$56$	−2.24757e7			−0.305398
$57$	2.09088e7	+	3.96652e7i	0.262357	+	0.497706i
$58$	−6.71302e7			−0.778919
$59$	3.67872e6	+	6.37173e6i	0.0395242	+	0.0684579i	0.885111	−	0.465380i	$-0.154082\pi$
$59$	3.67872e6	+	6.37173e6i	0.0395242	+	0.0684579i	−0.845587	+	0.533838i	$0.820749\pi$
$60$	2.71028e6	+	4.69434e6i	0.0269981	+	0.0467621i
$61$	8.61354e7	−	1.49191e8i	0.796522	−	1.37962i	−0.125347	−	0.992113i	$-0.540004\pi$
$61$	8.61354e7	−	1.49191e8i	0.796522	−	1.37962i	0.921868	−	0.387503i	$-0.126662\pi$
$62$	−6.89432e7	−	1.19413e8i	−0.592555	−	1.02634i
$63$	−3.69084e7	+	6.39273e7i	−0.295184	+	0.511274i
$64$	1.67772e7			0.125000
$65$	1.01656e7			0.0706358
$66$	6.75575e6	−	1.17013e7i	0.0438254	−	0.0759078i
$67$	−1.22829e8	+	2.12747e8i	−0.744672	+	1.28981i	0.205675	+	0.978620i	$0.434061\pi$
$67$	−1.22829e8	+	2.12747e8i	−0.744672	+	1.28981i	−0.950348	+	0.311190i	$0.899272\pi$
$68$	−1.48076e8			−0.839834
$69$	342612.			0.00181963
$70$	1.17757e7	−	2.03961e7i	0.0586198	−	0.101532i
$71$	−1.00693e8	−	1.74405e8i	−0.470256	−	0.814508i	0.529165	−	0.848519i	$-0.322505\pi$
$71$	−1.00693e8	−	1.74405e8i	−0.470256	−	0.814508i	−0.999421	+	0.0340111i	$0.989172\pi$
$72$	2.75507e7	−	4.77192e7i	0.120819	−	0.209265i
$73$	8.49285e7	+	1.47100e8i	0.350026	+	0.606263i	0.986254	−	0.165238i	$-0.0528394\pi$
$73$	8.49285e7	+	1.47100e8i	0.350026	+	0.606263i	−0.636228	+	0.771501i	$0.719506\pi$
$74$	2.94342e7	+	5.09815e7i	0.114106	+	0.197638i
$75$	1.48487e8			0.541892
$76$	−7.75024e7	+	1.23049e8i	−0.266474	+	0.423074i
$77$	−5.87049e7			−0.190312
$78$	2.39301e7	+	4.14481e7i	0.0732012	+	0.126788i
$79$	2.02761e8	+	3.51192e8i	0.585683	+	1.01443i	0.994790	+	0.101946i	$0.0325068\pi$
$79$	2.02761e8	+	3.51192e8i	0.585683	+	1.01443i	−0.409107	+	0.912486i	$0.634160\pi$
$80$	−8.79008e6	+	1.52249e7i	−0.0239932	+	0.0415574i
$81$	−2.91673e7	−	5.05192e7i	−0.0752858	−	0.130399i
$82$	1.75970e8	−	3.04789e8i	0.429810	−	0.744453i
$83$	1.99408e8			0.461202			0.230601	−	0.973048i	$-0.425931\pi$
$83$	1.99408e8			0.461202			0.230601	+	0.973048i	$0.425931\pi$
$84$	1.10880e8			0.242995
$85$	7.75812e7	−	1.34375e8i	0.161202	−	0.279211i
$86$	1.06714e8	−	1.84835e8i	0.210368	−	0.364368i
$87$	3.31177e8			0.619759
$88$	4.38209e7			0.0778950
$89$	1.82842e7	−	3.16692e7i	0.0308902	−	0.0535034i	−0.850167	−	0.526513i	$-0.823499\pi$
$89$	1.82842e7	−	3.16692e7i	0.0308902	−	0.0535034i	0.881057	+	0.473010i	$0.156832\pi$
$90$	2.88692e7	+	5.00030e7i	0.0463814	+	0.0803350i
$91$	1.03972e8	−	1.80084e8i	0.158938	−	0.275289i
$92$	555586.	+	962303.i	0.000808549	+	0.00140045i
$93$	3.40121e8	+	5.89106e8i	0.471476	+	0.816621i
$94$	−1.67670e8			−0.221503
$95$	−7.10577e7	−	1.34800e8i	−0.0895065	−	0.169799i
$96$	−8.27678e7			−0.0994583
$97$	−6.21337e8	−	1.07619e9i	−0.712614	−	1.23428i	−0.963873	−	0.266364i	$-0.914178\pi$
$97$	−6.21337e8	−	1.07619e9i	−0.712614	−	1.23428i	0.251259	−	0.967920i	$-0.419156\pi$
$98$	8.19516e7	+	1.41944e8i	0.0897511	+	0.155454i
$99$	7.19606e7	−	1.24639e8i	0.0752898	−	0.130406i
$100$	2.40789e8	+	4.17059e8i	0.240789	+	0.417059i
$101$	5.06601e8	−	8.77458e8i	0.484417	−	0.839036i	−0.515422	−	0.856936i	$-0.672365\pi$
$101$	5.06601e8	−	8.77458e8i	0.484417	−	0.839036i	0.999840	+	0.0179007i	$0.00569828\pi$
$102$	7.30509e8			0.668228
$103$	3.02119e8			0.264491			0.132245	−	0.991217i	$-0.457781\pi$
$103$	3.02119e8			0.264491			0.132245	+	0.991217i	$0.457781\pi$
$104$	−7.76108e7	+	1.34426e8i	−0.0650537	+	0.112676i
$105$	−5.80935e7	+	1.00621e8i	−0.0466418	+	0.0807860i
$106$	4.70618e8			0.362070
$107$	−3.38764e8			−0.249845			−0.124923	−	0.992166i	$-0.539868\pi$
$107$	−3.38764e8			−0.249845			−0.124923	+	0.992166i	$0.539868\pi$
$108$	−3.34784e8	+	5.79863e8i	−0.236787	+	0.410127i
$109$	3.34181e8	+	5.78819e8i	0.226758	+	0.392757i	0.956845	−	0.290597i	$-0.0938540\pi$
$109$	3.34181e8	+	5.78819e8i	0.226758	+	0.392757i	−0.730087	+	0.683354i	$0.760521\pi$
$110$	−2.29591e7	+	3.97663e7i	−0.0149516	+	0.0258969i
$111$	−1.45209e8	−	2.51509e8i	−0.0907904	−	0.157254i
$112$	1.79805e8	+	3.11432e8i	0.107975	+	0.187018i
$113$	−1.57897e9			−0.911007			−0.455503	−	0.890234i	$-0.650541\pi$
$113$	−1.57897e9			−0.911007			−0.455503	+	0.890234i	$0.650541\pi$
$114$	3.82346e8	−	6.07043e8i	0.212024	−	0.336626i
$115$	−1.16435e6			−0.000620789
$116$	5.37042e8	+	9.30184e8i	0.275389	+	0.476988i
$117$	2.54897e8	+	4.41495e8i	0.125756	+	0.217816i
$118$	5.88595e7	−	1.01948e8i	0.0279478	−	0.0484070i
$119$	−1.58696e9	−	2.74870e9i	−0.725446	−	1.25651i
$120$	4.33645e7	−	7.51095e7i	0.0190906	−	0.0330658i
$121$	−2.24349e9			−0.951459
$122$	−2.75633e9			−1.12645
$123$	−8.68121e8	+	1.50363e9i	−0.341985	+	0.592336i
$124$	−1.10309e9	+	1.91061e9i	−0.419000	+	0.725729i
$125$	−1.02856e9			−0.376819
$126$	1.18107e9			0.417454
$127$	9.43687e8	−	1.63451e9i	0.321893	−	0.557535i	−0.658986	−	0.752155i	$-0.729014\pi$
$127$	9.43687e8	−	1.63451e9i	0.321893	−	0.557535i	0.980879	+	0.194621i	$0.0623476\pi$
$128$	−1.34218e8	−	2.32472e8i	−0.0441942	−	0.0765466i
$129$	−5.26459e8	+	9.11854e8i	−0.167383	+	0.289916i
$130$	−8.13251e7	−	1.40859e8i	−0.0249735	−	0.0432554i
$131$	1.35079e8	+	2.33964e8i	0.0400745	+	0.0694110i	0.885367	−	0.464893i	$-0.153907\pi$
$131$	1.35079e8	+	2.33964e8i	0.0400745	+	0.0694110i	−0.845292	+	0.534304i	$0.820574\pi$
$132$	−2.16184e8			−0.0619784
$133$	−3.11475e9	−	1.19918e8i	−0.863158	−	0.0332316i
$134$	3.93054e9			1.05313
$135$	−3.50807e8	−	6.07615e8i	−0.0909004	−	0.157444i
$136$	1.18461e9	+	2.05180e9i	0.296926	+	0.514291i
$137$	−8.32667e8	+	1.44222e9i	−0.201943	+	0.349776i	−0.949154	−	0.314811i	$-0.898059\pi$
$137$	−8.32667e8	+	1.44222e9i	−0.201943	+	0.349776i	0.747211	+	0.664586i	$0.231392\pi$
$138$	−2.74090e6	−	4.74738e6i	−0.000643335	−	0.00111429i
$139$	−2.81111e9	+	4.86898e9i	−0.638720	+	1.10630i	0.346994	+	0.937868i	$0.387203\pi$
$139$	−2.81111e9	+	4.86898e9i	−0.638720	+	1.10630i	−0.985714	+	0.168429i	$0.946131\pi$
$140$	−3.76821e8			−0.0829009
$141$	8.27175e8			0.176243
$142$	−1.61108e9	+	2.79047e9i	−0.332521	+	0.575944i
$143$	−2.02714e8	+	3.51111e8i	−0.0405389	+	0.0702154i
$144$	−8.81623e8			−0.170864
$145$	−1.12549e9			−0.211439
$146$	1.35886e9	−	2.35361e9i	0.247506	−	0.428693i
$147$	−4.04296e8	−	7.00260e8i	−0.0714120	−	0.123689i
$148$	4.70947e8	−	8.15703e8i	0.0806852	−	0.139751i
$149$	−2.78278e9	−	4.81992e9i	−0.462531	−	0.801127i	0.536555	−	0.843865i	$-0.319725\pi$
$149$	−2.78278e9	−	4.81992e9i	−0.462531	−	0.801127i	−0.999086	+	0.0427378i	$0.986392\pi$
$150$	−1.18790e9	−	2.05750e9i	−0.191588	−	0.331840i
$151$	7.05639e9			1.10455			0.552277	−	0.833661i	$-0.313759\pi$
$151$	7.05639e9			1.10455			0.552277	+	0.833661i	$0.313759\pi$
$152$	2.32504e9	+	8.95139e7i	0.353292	+	0.0136017i
$153$	7.78120e9			1.14798
$154$	4.69640e8	+	8.13439e8i	0.0672855	+	0.116542i
$155$	−1.15588e9	−	2.00205e9i	−0.160850	−	0.278601i
$156$	3.82881e8	−	6.63169e8i	0.0517610	−	0.0896528i
$157$	3.31888e8	+	5.74846e8i	0.0435956	+	0.0755098i	0.887000	−	0.461770i	$-0.152785\pi$
$157$	3.31888e8	+	5.74846e8i	0.0435956	+	0.0755098i	−0.843404	+	0.537280i	$0.819452\pi$
$158$	3.24417e9	−	5.61907e9i	0.414140	−	0.717312i
$159$	−2.32172e9			−0.288087
$160$	2.81282e8			0.0339315
$161$	−1.19087e7	+	2.06265e7i	−0.00139684	+	0.00241941i
$162$	−4.66676e8	+	8.08307e8i	−0.0532351	+	0.0922059i
$163$	1.69143e10			1.87676			0.938381	−	0.345603i	$-0.112325\pi$
$163$	1.69143e10			1.87676			0.938381	+	0.345603i	$0.112325\pi$
$164$	−5.63104e9			−0.607843
$165$	1.13265e8	−	1.96181e8i	0.0118965	−	0.0206053i
$166$	−1.59526e9	−	2.76308e9i	−0.163060	−	0.282427i
$167$	8.30465e9	−	1.43841e10i	0.826223	−	1.43106i	−0.0747579	−	0.997202i	$-0.523818\pi$
$167$	8.30465e9	−	1.43841e10i	0.826223	−	1.43106i	0.900981	−	0.433859i	$-0.142848\pi$
$168$	−8.87043e8	−	1.53640e9i	−0.0859118	−	0.148804i
$169$	4.58420e9	+	7.94007e9i	0.432288	+	0.748745i
$170$	−2.48260e9			−0.227974
$171$	4.07266e9	−	6.46607e9i	0.364247	−	0.578307i
$172$	−3.41486e9			−0.297505
$173$	1.49430e9	+	2.58821e9i	0.126833	+	0.219681i	0.922448	−	0.386122i	$-0.126186\pi$
$173$	1.49430e9	+	2.58821e9i	0.126833	+	0.219681i	−0.795615	+	0.605802i	$0.792852\pi$
$174$	−2.64941e9	−	4.58892e9i	−0.219118	−	0.379524i
$175$	−5.16119e9	+	8.93945e9i	−0.415986	+	0.720509i
$176$	−3.50567e8	−	6.07201e8i	−0.0275400	−	0.0477008i
$177$	−2.90374e8	+	5.02943e8i	−0.0222371	+	0.0385158i
$178$	−5.85094e8			−0.0436854
$179$	1.21599e10			0.885302			0.442651	−	0.896694i	$-0.354038\pi$
$179$	1.21599e10			0.885302			0.442651	+	0.896694i	$0.354038\pi$
$180$	4.61908e8	−	8.00048e8i	0.0327966	−	0.0568054i
$181$	−9.63746e9	+	1.66926e10i	−0.667435	+	1.15603i	0.311184	+	0.950350i	$0.399274\pi$
$181$	−9.63746e9	+	1.66926e10i	−0.667435	+	1.15603i	−0.978619	+	0.205681i	$0.934059\pi$
$182$	−3.32709e9			−0.224773
$183$	1.35980e10			0.896280
$184$	8.88938e6	−	1.53969e7i	0.000571730	−	0.000990266i
$185$	4.93485e8	+	8.54742e8i	0.0309743	+	0.0536491i
$186$	5.44193e9	−	9.42570e9i	0.333384	−	0.577438i
$187$	3.09411e9	+	5.35915e9i	0.185033	+	0.320486i
$188$	1.34136e9	+	2.32331e9i	0.0783133	+	0.135643i
$189$	−1.43519e10			−0.818144
$190$	−1.29939e9	+	2.06301e9i	−0.0723347	+	0.114844i
$191$	2.89450e9			0.157370			0.0786852	−	0.996900i	$-0.474928\pi$
$191$	2.89450e9			0.157370			0.0786852	+	0.996900i	$0.474928\pi$
$192$	6.62143e8	+	1.14686e9i	0.0351638	+	0.0609055i
$193$	9.18917e9	+	1.59161e10i	0.476725	+	0.825713i	0.999644	−	0.0266698i	$-0.00849026\pi$
$193$	9.18917e9	+	1.59161e10i	0.476725	+	0.825713i	−0.522919	+	0.852382i	$0.675157\pi$
$194$	−9.94139e9	+	1.72190e10i	−0.503894	+	0.872770i
$195$	4.01205e8	+	6.94908e8i	0.0198706	+	0.0344169i
$196$	1.31123e9	−	2.27111e9i	0.0634636	−	0.109922i
$197$	−2.59097e10			−1.22564			−0.612822	−	0.790221i	$-0.709966\pi$
$197$	−2.59097e10			−1.22564			−0.612822	+	0.790221i	$0.709966\pi$
$198$	−2.30274e9			−0.106476
$199$	1.24842e9	−	2.16232e9i	0.0564313	−	0.0977419i	−0.836430	−	0.548074i	$-0.815361\pi$
$199$	1.24842e9	−	2.16232e9i	0.0564313	−	0.0977419i	0.892861	+	0.450332i	$0.148694\pi$
$200$	3.85263e9	−	6.67295e9i	0.170264	−	0.294905i
$201$	−1.93907e10			−0.837937
$202$	−1.62112e10			−0.685070
$203$	−1.15112e10	+	1.99380e10i	−0.475761	+	0.824042i
$204$	−5.84407e9	−	1.01222e10i	−0.236254	−	0.409204i
$205$	2.95027e9	−	5.11001e9i	0.116673	−	0.202083i
$206$	−2.41695e9	−	4.18628e9i	−0.0935115	−	0.161967i
$207$	−2.91954e7	−	5.05679e7i	−0.00110522	−	0.00191429i
$208$	2.48355e9			0.0919998
$209$	6.07283e9	+	2.33804e8i	0.220157	+	0.00847606i
$210$	1.85899e9			0.0659615
$211$	−9.90675e9	−	1.71590e10i	−0.344080	−	0.595965i	0.641106	−	0.767453i	$-0.278476\pi$
$211$	−9.90675e9	−	1.71590e10i	−0.344080	−	0.595965i	−0.985186	+	0.171488i	$0.945143\pi$
$212$	−3.76494e9	−	6.52107e9i	−0.128011	−	0.221721i
$213$	7.94802e9	−	1.37664e10i	0.264576	−	0.458259i
$214$	2.71012e9	+	4.69406e9i	0.0883336	+	0.152998i
$215$	1.78914e9	−	3.09889e9i	0.0571048	−	0.0989084i
$216$	1.07131e10			0.334868
$217$	−4.72884e10			−1.44772
$218$	5.34690e9	−	9.26110e9i	0.160342	−	0.277721i
$219$	−6.70371e9	+	1.16112e10i	−0.196932	+	0.341096i
$220$	7.34690e8			0.0211447
$221$	−2.19198e10			−0.618117
$222$	−2.32334e9	+	4.02415e9i	−0.0641985	+	0.111195i
$223$	−6.75196e9	−	1.16947e10i	−0.182834	−	0.316679i	0.760010	−	0.649911i	$-0.225194\pi$
$223$	−6.75196e9	−	1.16947e10i	−0.182834	−	0.316679i	−0.942845	+	0.333233i	$0.891861\pi$
$224$	2.87689e9	−	4.98292e9i	0.0763496	−	0.132241i
$225$	−1.26532e10	−	2.19160e10i	−0.329138	−	0.570084i
$226$	1.26318e10	+	2.18789e10i	0.322090	+	0.557875i
$227$	7.10534e10			1.77611			0.888053	−	0.459742i	$-0.152058\pi$
$227$	7.10534e10			1.77611			0.888053	+	0.459742i	$0.152058\pi$
$228$	−1.14702e10	−	4.41603e8i	−0.281102	−	0.0108224i
$229$	3.60039e10			0.865147			0.432574	−	0.901599i	$-0.357606\pi$
$229$	3.60039e10			0.865147			0.432574	+	0.901599i	$0.357606\pi$
$230$	9.31481e6	+	1.61337e7i	0.000219482	+	0.000380154i
$231$	−2.31689e9	−	4.01298e9i	−0.0535368	−	0.0927285i
$232$	8.59267e9	−	1.48829e10i	0.194730	−	0.337282i
$233$	−2.95656e10	−	5.12091e10i	−0.657181	−	1.13827i	−0.981342	−	0.192268i	$-0.938416\pi$
$233$	−2.95656e10	−	5.12091e10i	−0.657181	−	1.13827i	0.324162	−	0.946002i	$-0.394918\pi$
$234$	4.07835e9	−	7.06392e9i	0.0889229	−	0.154019i
$235$	−2.81111e9			−0.0601275
$236$	−1.88350e9			−0.0395242
$237$	−1.60046e10	+	2.77208e10i	−0.329517	+	0.570741i
$238$	−2.53914e10	+	4.39792e10i	−0.512968	+	0.888487i
$239$	−3.60871e9			−0.0715421			−0.0357711	−	0.999360i	$-0.511389\pi$
$239$	−3.60871e9			−0.0715421			−0.0357711	+	0.999360i	$0.511389\pi$
$240$	−1.38766e9			−0.0269981
$241$	−4.43442e10	+	7.68064e10i	−0.846759	+	1.46663i	0.0373251	+	0.999303i	$0.488116\pi$
$241$	−4.43442e10	+	7.68064e10i	−0.846759	+	1.46663i	−0.884084	+	0.467327i	$0.845217\pi$
$242$	1.79479e10	+	3.10867e10i	0.336392	+	0.582647i
$243$	2.80427e10	−	4.85715e10i	0.515932	−	0.893620i
$244$	2.20507e10	+	3.81929e10i	0.398261	+	0.689808i
$245$	1.37398e9	+	2.37980e9i	0.0243631	+	0.0421981i
$246$	2.77799e10			0.483640
$247$	−1.14727e10	+	1.82150e10i	−0.196124	+	0.311382i
$248$	3.52989e10			0.592555
$249$	7.86999e9	+	1.36312e10i	0.129741	+	0.224718i
$250$	8.22844e9	+	1.42521e10i	0.133226	+	0.230754i
$251$	7.83137e9	−	1.35643e10i	0.124539	−	0.215708i	−0.797014	−	0.603961i	$-0.793588\pi$
$251$	7.83137e9	−	1.35643e10i	0.124539	−	0.215708i	0.921553	+	0.388253i	$0.126921\pi$
$252$	−9.44856e9	−	1.63654e10i	−0.147592	−	0.255637i
$253$	2.32184e7	−	4.02155e7i	0.000356279	−	0.000617094i
$254$	−3.01980e10			−0.455225
$255$	1.22475e10			0.181392
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	6.48473e10	−	1.12319e11i	0.927242	−	1.60603i	0.139326	−	0.990247i	$-0.455506\pi$
$257$	6.48473e10	−	1.12319e11i	0.927242	−	1.60603i	0.787915	−	0.615783i	$-0.211160\pi$
$258$	1.68467e10			0.236715
$259$	2.01890e10			0.278783
$260$	−1.30120e9	+	2.25375e9i	−0.0176589	+	0.0305862i
$261$	−2.82209e10	−	4.88800e10i	−0.376434	−	0.652002i
$262$	2.16127e9	−	3.74342e9i	0.0283369	−	0.0490810i
$263$	5.57985e10	+	9.66459e10i	0.719154	+	1.24561i	0.961335	+	0.275381i	$0.0888038\pi$
$263$	5.57985e10	+	9.66459e10i	0.719154	+	1.24561i	−0.242181	+	0.970231i	$0.577863\pi$
$264$	1.72947e9	+	2.99553e9i	0.0219127	+	0.0379539i
$265$	7.89026e9			0.0982844
$266$	2.32563e10	+	4.41185e10i	0.284822	+	0.540323i
$267$	2.88647e9			0.0347590
$268$	−3.14443e10	−	5.44631e10i	−0.372336	−	0.644905i
$269$	4.31489e9	+	7.47362e9i	0.0502441	+	0.0870253i	0.890054	−	0.455856i	$-0.150667\pi$
$269$	4.31489e9	+	7.47362e9i	0.0502441	+	0.0870253i	−0.839810	+	0.542881i	$0.817333\pi$
$270$	−5.61291e9	+	9.72184e9i	−0.0642763	+	0.111330i
$271$	−1.26602e10	−	2.19281e10i	−0.142586	−	0.246967i	0.785884	−	0.618375i	$-0.212209\pi$
$271$	−1.26602e10	−	2.19281e10i	−0.142586	−	0.246967i	−0.928470	+	0.371408i	$0.878875\pi$
$272$	1.89537e10	−	3.28287e10i	0.209959	−	0.363659i
$273$	1.64137e10			0.178844
$274$	2.66453e10			0.285591
$275$	1.00628e10	−	1.74293e10i	0.106102	−	0.183773i
$276$	−4.38544e7	+	7.59580e7i	−0.000454907	+	0.000787921i
$277$	−1.02977e11			−1.05095			−0.525475	−	0.850809i	$-0.676113\pi$
$277$	−1.02977e11			−1.05095			−0.525475	+	0.850809i	$0.676113\pi$
$278$	8.99554e10			0.903287
$279$	5.79661e10	−	1.00400e11i	0.572737	−	0.992009i
$280$	3.01457e9	+	5.22139e9i	0.0293099	+	0.0507662i
$281$	3.50963e10	−	6.07886e10i	0.335802	−	0.581626i	−0.647837	−	0.761779i	$-0.724326\pi$
$281$	3.50963e10	−	6.07886e10i	0.335802	−	0.581626i	0.983638	+	0.180154i	$0.0576595\pi$
$282$	−6.61740e9	−	1.14617e10i	−0.0623112	−	0.107926i
$283$	5.84956e10	+	1.01317e11i	0.542106	+	0.938955i	0.998783	+	0.0493225i	$0.0157062\pi$
$283$	5.84956e10	+	1.01317e11i	0.542106	+	0.938955i	−0.456677	+	0.889633i	$0.650960\pi$
$284$	5.15546e10			0.470256
$285$	6.41032e9	−	1.01775e10i	0.0575543	−	0.0913777i
$286$	6.48685e9			0.0573306
$287$	−6.03492e10	−	1.04528e11i	−0.525053	−	0.909419i
$288$	7.05298e9	+	1.22161e10i	0.0604097	+	0.104633i
$289$	−1.07991e11	+	1.87046e11i	−0.910643	+	1.57728i
$290$	9.00390e9	+	1.55952e10i	0.0747549	+	0.129479i
$291$	4.90443e10	−	8.49473e10i	0.400932	−	0.694434i
$292$	−4.34834e10			−0.350026
$293$	−9.43337e10			−0.747760			−0.373880	−	0.927477i	$-0.621973\pi$
$293$	−9.43337e10			−0.747760			−0.373880	+	0.927477i	$0.621973\pi$
$294$	−6.46873e9	+	1.12042e10i	−0.0504959	+	0.0874614i
$295$	9.86823e8	−	1.70923e9i	0.00758648	−	0.0131402i
$296$	−1.50703e10			−0.114106
$297$	2.79819e10			0.208676
$298$	−4.45245e10	+	7.71187e10i	−0.327059	+	0.566483i
$299$	8.22439e7	+	1.42451e8i	0.000595091	+	0.00103073i
$300$	−1.90064e10	+	3.29200e10i	−0.135473	+	0.234646i
$301$	−3.65979e10	−	6.33894e10i	−0.256984	−	0.445110i
$302$	−5.64512e10	−	9.77763e10i	−0.390518	−	0.676398i
$303$	7.99756e10			0.545087
$304$	−1.73599e10	−	3.29327e10i	−0.116578	−	0.221155i
$305$	−4.62120e10			−0.305777
$306$	−6.22496e10	−	1.07819e11i	−0.405873	−	0.702993i
$307$	−1.20124e10	−	2.08060e10i	−0.0771803	−	0.133680i	0.824852	−	0.565349i	$-0.191258\pi$
$307$	−1.20124e10	−	2.08060e10i	−0.0771803	−	0.133680i	−0.902032	+	0.431669i	$0.857925\pi$
$308$	7.51423e9	−	1.30150e10i	0.0475780	−	0.0824076i
$309$	1.19237e10	+	2.06524e10i	0.0744040	+	0.128871i
$310$	−1.84941e10	+	3.20328e10i	−0.113738	+	0.197000i
$311$	−1.51188e11			−0.916420			−0.458210	−	0.888844i	$-0.651509\pi$
$311$	−1.51188e11			−0.916420			−0.458210	+	0.888844i	$0.651509\pi$
$312$	−1.22522e10			−0.0732012
$313$	−1.59056e11	+	2.75492e11i	−0.936698	+	1.62241i	−0.165119	+	0.986274i	$0.552801\pi$
$313$	−1.59056e11	+	2.75492e11i	−0.936698	+	1.62241i	−0.771579	+	0.636134i	$0.780533\pi$
$314$	5.31020e9	−	9.19754e9i	0.0308267	−	0.0533935i
$315$	1.98015e10			0.113319
$316$	−1.03814e11			−0.585683
$317$	−7.32693e10	+	1.26906e11i	−0.407526	+	0.705856i	−0.994612	−	0.103669i	$-0.966942\pi$
$317$	−7.32693e10	+	1.26906e11i	−0.407526	+	0.705856i	0.587086	+	0.809525i	$0.300275\pi$
$318$	1.85738e10	+	3.21707e10i	0.101854	+	0.176416i
$319$	2.24435e10	−	3.88732e10i	0.121348	−	0.210180i
$320$	−2.25026e9	−	3.89756e9i	−0.0119966	−	0.0207787i
$321$	−1.33699e10	−	2.31574e10i	−0.0702841	−	0.121736i
$322$	3.81078e8			0.00197544
$323$	1.53219e11	+	2.90664e11i	0.783251	+	1.48587i
$324$	1.49336e10			0.0752858
$325$	3.56442e10	+	6.17376e10i	0.177221	+	0.306955i
$326$	−1.35314e11	−	2.34371e11i	−0.663536	−	1.14928i
$327$	−2.63781e10	+	4.56882e10i	−0.127579	+	0.220973i
$328$	4.50483e10	+	7.80260e10i	0.214905	+	0.372226i
$329$	−2.87514e10	+	4.97989e10i	−0.135294	+	0.234335i
$330$	−3.62448e9			−0.0168242
$331$	7.52939e10			0.344773			0.172387	−	0.985029i	$-0.444852\pi$
$331$	7.52939e10			0.344773			0.172387	+	0.985029i	$0.444852\pi$
$332$	−2.55242e10	+	4.42093e10i	−0.115300	+	0.199706i
$333$	−2.47477e10	+	4.28642e10i	−0.110290	+	0.191028i
$334$	−2.65749e11			−1.16846
$335$	6.58984e10			0.285873
$336$	−1.41927e10	+	2.45825e10i	−0.0607488	+	0.105220i
$337$	−9.38075e10	−	1.62479e11i	−0.396189	−	0.686220i	0.597063	−	0.802195i	$-0.296334\pi$
$337$	−9.38075e10	−	1.62479e11i	−0.396189	−	0.686220i	−0.993252	+	0.115974i	$0.963001\pi$
$338$	7.33472e10	−	1.27041e11i	0.305674	−	0.529443i
$339$	−6.23170e10	−	1.07936e11i	−0.256276	−	0.443883i
$340$	1.98608e10	+	3.43999e10i	0.0806012	+	0.139605i
$341$	9.21983e10			0.369257
$342$	−1.22178e11	−	4.70385e9i	−0.482920	−	0.0185924i
$343$	2.77640e11			1.08308
$344$	2.73189e10	+	4.73177e10i	0.105184	+	0.182184i
$345$	−4.59532e7	−	7.95933e7i	−0.000174634	−	0.000302476i
$346$	2.39088e10	−	4.14113e10i	0.0896842	−	0.155338i
$347$	1.92966e10	+	3.34227e10i	0.0714494	+	0.123754i	0.899537	−	0.436845i	$-0.143904\pi$
$347$	1.92966e10	+	3.34227e10i	0.0714494	+	0.123754i	−0.828087	+	0.560599i	$0.810571\pi$
$348$	−4.23906e10	+	7.34227e10i	−0.154940	+	0.268364i
$349$	3.51951e11			1.26990			0.634948	−	0.772555i	$-0.281021\pi$
$349$	3.51951e11			1.26990			0.634948	+	0.772555i	$0.281021\pi$
$350$	1.65158e11			0.588293
$351$	−4.95584e10	+	8.58377e10i	−0.174275	+	0.301853i
$352$	−5.60908e9	+	9.71521e9i	−0.0194738	+	0.0337295i
$353$	−1.80679e11			−0.619329			−0.309664	−	0.950846i	$-0.600217\pi$
$353$	−1.80679e11			−0.619329			−0.309664	+	0.950846i	$0.600217\pi$
$354$	9.29198e9			0.0314481
$355$	−2.70109e10	+	4.67843e10i	−0.0902635	+	0.156341i
$356$	4.68075e9	+	8.10730e9i	0.0154451	+	0.0267517i
$357$	1.25265e11	−	2.16965e11i	0.408152	−	0.706939i
$358$	−9.72792e10	−	1.68492e11i	−0.313001	−	0.542134i
$359$	−1.87296e11	−	3.24406e11i	−0.595118	−	1.03077i	−0.993530	−	0.113568i	$-0.963772\pi$
$359$	−1.87296e11	−	3.24406e11i	−0.595118	−	1.03077i	0.398412	−	0.917206i	$-0.369561\pi$
$360$	−1.47811e10			−0.0463814
$361$	3.21733e11	+	2.48102e10i	0.997040	+	0.0768861i
$362$	3.08399e11			0.943895
$363$	−8.85433e10	−	1.53362e11i	−0.267655	−	0.463593i
$364$	2.66167e10	+	4.61016e10i	0.0794692	+	0.137645i
$365$	2.27822e10	−	3.94600e10i	0.0671859	−	0.116369i
$366$	−1.08784e11	−	1.88419e11i	−0.316883	−	0.548857i
$367$	−2.14992e11	+	3.72376e11i	−0.618620	+	1.07148i	0.371118	+	0.928586i	$0.378975\pi$
$367$	−2.14992e11	+	3.72376e11i	−0.618620	+	1.07148i	−0.989738	+	0.142896i	$0.954359\pi$
$368$	−2.84460e8			−0.000808549
$369$	2.95905e11			0.830870
$370$	7.89577e9	−	1.36759e10i	0.0219021	−	0.0379356i
$371$	8.06996e10	−	1.39776e11i	0.221151	−	0.383045i
$372$	−1.74142e11			−0.471476
$373$	1.32783e11			0.355183			0.177591	−	0.984104i	$-0.443169\pi$
$373$	1.32783e11			0.355183			0.177591	+	0.984104i	$0.443169\pi$
$374$	4.95057e10	−	8.57464e10i	0.130838	−	0.226618i
$375$	−4.05938e10	−	7.03105e10i	−0.106003	−	0.183603i
$376$	2.14618e10	−	3.71729e10i	0.0553759	−	0.0959138i
$377$	7.94987e10	+	1.37696e11i	0.202686	+	0.351063i
$378$	1.14815e11	+	1.98865e11i	0.289258	+	0.501009i
$379$	3.14507e11			0.782985			0.391493	−	0.920181i	$-0.371959\pi$
$379$	3.14507e11			0.782985			0.391493	+	0.920181i	$0.371959\pi$
$380$	3.89809e10	+	1.50077e9i	0.0959016	+	0.00369221i
$381$	1.48977e11			0.362207
$382$	−2.31560e10	−	4.01073e10i	−0.0556388	−	0.0963693i
$383$	−8.01083e10	−	1.38752e11i	−0.190232	−	0.329491i	0.755095	−	0.655615i	$-0.227591\pi$
$383$	−8.01083e10	−	1.38752e11i	−0.190232	−	0.329491i	−0.945327	+	0.326124i	$0.894257\pi$
$384$	1.05943e10	−	1.83498e10i	0.0248646	−	0.0430667i
$385$	7.87385e9	+	1.36379e10i	0.0182648	+	0.0316355i
$386$	1.47027e11	−	2.54658e11i	0.337096	−	0.583867i
$387$	1.79447e11			0.406665
$388$	3.18124e11			0.712614
$389$	−1.50789e11	+	2.61174e11i	−0.333884	+	0.578305i	−0.983270	−	0.182155i	$-0.941693\pi$
$389$	−1.50789e11	+	2.61174e11i	−0.333884	+	0.578305i	0.649385	+	0.760459i	$0.275026\pi$
$390$	6.41928e9	−	1.11185e10i	0.0140506	−	0.0243364i
$391$	2.51064e9			0.00543238
$392$	−4.19592e10			−0.0897511
$393$	−1.06623e10	+	1.84676e10i	−0.0225467	+	0.0390521i
$394$	2.07277e11	+	3.59015e11i	0.433330	+	0.750550i
$395$	5.43910e10	−	9.42079e10i	0.112419	−	0.194716i
$396$	1.84219e10	+	3.19077e10i	0.0376449	+	0.0652029i
$397$	1.87971e10	+	3.25575e10i	0.0379781	+	0.0657800i	0.884390	−	0.466749i	$-0.154575\pi$
$397$	1.87971e10	+	3.25575e10i	0.0379781	+	0.0657800i	−0.846412	+	0.532529i	$0.821242\pi$
$398$	−3.99493e10			−0.0798059
$399$	−1.14732e11	−	2.17652e11i	−0.226623	−	0.429917i
$400$	−1.23284e11			−0.240789
$401$	−4.08500e11	−	7.07542e11i	−0.788936	−	1.36648i	−0.926619	−	0.376001i	$-0.877299\pi$
$401$	−4.08500e11	−	7.07542e11i	−0.788936	−	1.36648i	0.137683	−	0.990476i	$-0.456035\pi$
$402$	1.55126e11	+	2.68685e11i	0.296255	+	0.513129i
$403$	−1.63291e11	+	2.82829e11i	−0.308383	+	0.534135i
$404$	1.29690e11	+	2.24629e11i	0.242209	+	0.419518i
$405$	−7.82417e9	+	1.35519e10i	−0.0144508	+	0.0250294i
$406$	3.68359e11			0.672828
$407$	−3.93626e10			−0.0711064
$408$	−9.35051e10	+	1.61956e11i	−0.167057	+	0.289351i
$409$	−1.06939e11	+	1.85225e11i	−0.188966	+	0.327298i	−0.944906	−	0.327343i	$-0.893847\pi$
$409$	−1.06939e11	+	1.85225e11i	−0.188966	+	0.327298i	0.755940	+	0.654641i	$0.227180\pi$
$410$	−9.44086e10			−0.165000
$411$	−1.31451e11			−0.227235
$412$	−3.86712e10	+	6.69805e10i	−0.0661226	+	0.114528i
$413$	−2.01860e10	−	3.49631e10i	−0.0341409	−	0.0591337i
$414$	−4.67126e8	+	8.09086e8i	−0.000781507	+	0.00135361i
$415$	−2.67458e10	−	4.63250e10i	−0.0442628	−	0.0766654i
$416$	−1.98684e10	−	3.44130e10i	−0.0325269	−	0.0563382i
$417$	−4.43781e11			−0.718715
$418$	−4.53430e10	−	8.60181e10i	−0.0726468	−	0.137815i
$419$	−1.00246e12			−1.58892			−0.794462	−	0.607314i	$-0.792247\pi$
$419$	−1.00246e12			−1.58892			−0.794462	+	0.607314i	$0.792247\pi$
$420$	−1.48719e10	−	2.57589e10i	−0.0233209	−	0.0403930i
$421$	−2.68738e11	−	4.65468e11i	−0.416927	−	0.722138i	0.578702	−	0.815539i	$-0.303559\pi$
$421$	−2.68738e11	−	4.65468e11i	−0.416927	−	0.722138i	−0.995629	+	0.0934011i	$0.970226\pi$
$422$	−1.58508e11	+	2.74544e11i	−0.243302	+	0.421411i
$423$	−7.04869e10	−	1.22087e11i	−0.107048	−	0.185412i
$424$	−6.02391e10	+	1.04337e11i	−0.0905174	+	0.156781i
$425$	1.08811e12			1.61778
$426$	−2.54337e11			−0.374167
$427$	−4.72645e11	+	8.18645e11i	−0.688033	+	1.19171i
$428$	4.33619e10	−	7.51049e10i	0.0624613	−	0.108186i
$429$	−3.20019e10			−0.0456161
$430$	−5.72526e10			−0.0807584
$431$	−3.40568e11	+	5.89882e11i	−0.475397	+	0.823412i	−0.999603	−	0.0281797i	$-0.991029\pi$
$431$	−3.40568e11	+	5.89882e11i	−0.475397	+	0.823412i	0.524206	+	0.851592i	$0.324362\pi$
$432$	−8.57048e10	−	1.48445e11i	−0.118394	−	0.205064i
$433$	3.31659e11	−	5.74450e11i	0.453415	−	0.785338i	−0.545180	−	0.838319i	$-0.683539\pi$
$433$	3.31659e11	−	5.74450e11i	0.453415	−	0.785338i	0.998596	+	0.0529805i	$0.0168721\pi$
$434$	3.78307e11	+	6.55247e11i	0.511847	+	0.886546i
$435$	−4.44194e10	−	7.69366e10i	−0.0594800	−	0.103022i
$436$	−1.71101e11			−0.226758
$437$	1.31406e9	−	2.08631e9i	0.00172366	−	0.00273661i
$438$	2.14519e11			0.278504
$439$	−6.76097e11	−	1.17103e12i	−0.868797	−	1.50480i	−0.863227	−	0.504816i	$-0.831560\pi$
$439$	−6.76097e11	−	1.17103e12i	−0.868797	−	1.50480i	−0.00557033	−	0.999984i	$-0.501773\pi$
$440$	−5.87752e9	−	1.01802e10i	−0.00747579	−	0.0129485i
$441$	−6.89033e10	+	1.19344e11i	−0.0867494	+	0.150254i
$442$	1.75358e11	+	3.03729e11i	0.218537	+	0.378518i
$443$	−5.68261e11	+	9.84257e11i	−0.701021	+	1.21420i	0.267087	+	0.963672i	$0.413939\pi$
$443$	−5.68261e11	+	9.84257e11i	−0.701021	+	1.21420i	−0.968108	+	0.250532i	$0.919395\pi$
$444$	7.43470e10			0.0907904
$445$	−9.80954e9			−0.0118585
$446$	−1.08031e11	+	1.87116e11i	−0.129284	+	0.223926i
$447$	2.19655e11	−	3.80453e11i	0.260230	−	0.450731i
$448$	−9.20604e10			−0.107975
$449$	−4.90231e11			−0.569236			−0.284618	−	0.958641i	$-0.591867\pi$
$449$	−4.90231e11			−0.569236			−0.284618	+	0.958641i	$0.591867\pi$
$450$	−2.02451e11	+	3.50655e11i	−0.232736	+	0.403111i
$451$	1.17663e11	+	2.03799e11i	0.133920	+	0.231957i
$452$	2.02108e11	−	3.50062e11i	0.227752	−	0.394477i
$453$	2.78493e11	+	4.82364e11i	0.310722	+	0.538187i
$454$	−5.68427e11	−	9.84545e11i	−0.627948	−	1.08764i
$455$	−5.57812e10			−0.0610150
$456$	8.56426e10	+	1.62469e11i	0.0927573	+	0.175966i
$457$	4.95917e10			0.0531846			0.0265923	−	0.999646i	$-0.491534\pi$
$457$	4.95917e10			0.0531846			0.0265923	+	0.999646i	$0.491534\pi$
$458$	−2.88031e11	−	4.98885e11i	−0.305876	−	0.529792i
$459$	7.56430e11	+	1.31018e12i	0.795448	+	1.37776i
$460$	1.49037e8	−	2.58140e8i	0.000155197	−	0.000268809i
$461$	−8.08211e11	−	1.39986e12i	−0.833433	−	1.44355i	−0.895300	−	0.445464i	$-0.853039\pi$
$461$	−8.08211e11	−	1.39986e12i	−0.833433	−	1.44355i	0.0618667	−	0.998084i	$-0.480295\pi$
$462$	−3.70703e10	+	6.42077e10i	−0.0378562	+	0.0655689i
$463$	4.15062e11			0.419758			0.209879	−	0.977727i	$-0.432693\pi$
$463$	4.15062e11			0.419758			0.209879	+	0.977727i	$0.432693\pi$
$464$	−2.74965e11			−0.275389
$465$	9.12380e10	−	1.58029e11i	0.0904977	−	0.156747i
$466$	−4.73049e11	+	8.19345e11i	−0.464697	+	0.804879i
$467$	−8.73127e11			−0.849477			−0.424738	−	0.905316i	$-0.639634\pi$
$467$	−8.73127e11			−0.849477			−0.424738	+	0.905316i	$0.639634\pi$
$468$	−1.30507e11			−0.125756
$469$	6.73992e11	−	1.16739e12i	0.643246	−	1.11413i
$470$	2.24889e10	+	3.89519e10i	0.0212583	+	0.0368204i
$471$	−2.61971e10	+	4.53746e10i	−0.0245278	+	0.0424834i
$472$	1.50680e10	+	2.60986e10i	0.0139739	+	0.0242035i
$473$	7.13550e10	+	1.23591e11i	0.0655465	+	0.113530i
$474$	5.12148e11			0.466008
$475$	5.69511e11	−	9.04201e11i	0.513312	−	0.814974i
$476$	8.12525e11			0.725446
$477$	1.97843e11	+	3.42675e11i	0.174980	+	0.303074i
$478$	2.88697e10	+	5.00038e10i	0.0252940	+	0.0438104i
$479$	1.65771e11	−	2.87124e11i	0.143880	−	0.249207i	−0.785075	−	0.619401i	$-0.787375\pi$
$479$	1.65771e11	−	2.87124e11i	0.143880	−	0.249207i	0.928954	+	0.370194i	$0.120709\pi$
$480$	1.11013e10	+	1.92280e10i	0.00954528	+	0.0165329i
$481$	6.97146e10	−	1.20749e11i	0.0593842	−	0.102856i
$482$	1.41901e12			1.19750
$483$	−1.87999e9			−0.00157179
$484$	2.87167e11	−	4.97387e11i	0.237865	−	0.411994i
$485$	−1.66675e11	+	2.88689e11i	−0.136783	+	0.236915i
$486$	−8.97368e11			−0.729638
$487$	−6.08813e11			−0.490460			−0.245230	−	0.969465i	$-0.578863\pi$
$487$	−6.08813e11			−0.490460			−0.245230	+	0.969465i	$0.578863\pi$
$488$	3.52811e11	−	6.11086e11i	0.281613	−	0.487768i
$489$	6.67552e11	+	1.15623e12i	0.527953	+	0.914441i
$490$	2.19837e10	−	3.80768e10i	0.0172273	−	0.0298386i
$491$	−6.94140e11	−	1.20229e12i	−0.538989	−	0.933557i	−0.998959	−	0.0456223i	$-0.985473\pi$
$491$	−6.94140e11	−	1.20229e12i	−0.538989	−	0.933557i	0.459969	−	0.887935i	$-0.347860\pi$
$492$	−2.22239e11	−	3.84929e11i	−0.170993	−	0.296168i
$493$	2.42684e12			1.85025
$494$	3.44177e11	+	1.32508e10i	0.260022	+	0.0100109i
$495$	−3.86071e10			−0.0289031
$496$	−2.82391e11	−	4.89116e11i	−0.209500	−	0.362864i
$497$	5.52523e11	+	9.56997e11i	0.406206	+	0.703569i
$498$	1.25920e11	−	2.18100e11i	0.0917407	−	0.158900i
$499$	−2.92298e11	−	5.06274e11i	−0.211044	−	0.365539i	0.740998	−	0.671508i	$-0.234353\pi$
$499$	−2.92298e11	−	5.06274e11i	−0.211044	−	0.365539i	−0.952042	+	0.305969i	$0.901020\pi$
$500$	1.31655e11	−	2.28033e11i	0.0942047	−	0.163167i
$501$	1.31103e12			0.929701
$502$	−2.50604e11			−0.176125
$503$	−1.34277e12	+	2.32574e12i	−0.935288	+	1.61997i	−0.161169	+	0.986927i	$0.551526\pi$
$503$	−1.34277e12	+	2.32574e12i	−0.935288	+	1.61997i	−0.774119	+	0.633040i	$0.781807\pi$
$504$	−1.51177e11	+	2.61846e11i	−0.104363	+	0.180763i
$505$	−2.71793e11			−0.185963
$506$	−7.42990e8			−0.000503855
$507$	−3.61847e11	+	6.26738e11i	−0.243215	+	0.421260i
$508$	2.41584e11	+	4.18435e11i	0.160946	+	0.278767i
$509$	6.50448e10	−	1.12661e11i	0.0429519	−	0.0743950i	−0.843750	−	0.536736i	$-0.819657\pi$
$509$	6.50448e10	−	1.12661e11i	0.0429519	−	0.0743950i	0.886702	+	0.462341i	$0.152990\pi$
$510$	−9.79801e10	−	1.69707e11i	−0.0641316	−	0.111079i
$511$	−4.66022e11	−	8.07174e11i	−0.302352	−	0.523688i
$512$	6.87195e10			0.0441942
$513$	1.48465e12	+	5.71591e10i	0.946448	+	0.0364382i
$514$	−2.07511e12			−1.31132
$515$	−4.05219e10	−	7.01861e10i	−0.0253839	−	0.0439661i
$516$	−1.34774e11	−	2.33435e11i	−0.0836914	−	0.144958i
$517$	5.60567e10	−	9.70930e10i	0.0345080	−	0.0597696i
$518$	−1.61512e11	−	2.79747e11i	−0.0985645	−	0.170719i
$519$	−1.17951e11	+	2.04296e11i	−0.0713587	+	0.123597i
$520$	4.16385e10			0.0249735
$521$	2.41493e12			1.43594			0.717969	−	0.696075i	$-0.245072\pi$
$521$	2.41493e12			1.43594			0.717969	+	0.696075i	$0.245072\pi$
$522$	−4.51534e11	+	7.82081e11i	−0.266179	+	0.461035i
$523$	4.12637e11	−	7.14708e11i	0.241163	−	0.417706i	−0.719883	−	0.694095i	$-0.755805\pi$
$523$	4.12637e11	−	7.14708e11i	0.241163	−	0.417706i	0.961046	+	0.276389i	$0.0891379\pi$
$524$	−6.91605e10			−0.0400745
$525$	−8.14783e11			−0.468085
$526$	8.92777e11	−	1.54633e12i	0.508519	−	0.880780i
$527$	2.49238e12	+	4.31694e12i	1.40756	+	2.43797i
$528$	2.76715e10	−	4.79285e10i	0.0154946	−	0.0268375i
$529$	9.00567e11	+	1.55983e12i	0.499995	+	0.866016i
$530$	−6.31220e10	−	1.09331e11i	−0.0347488	−	0.0601867i
$531$	9.89759e10			0.0540262
$532$	4.25273e11	−	6.75197e11i	0.230179	−	0.365450i
$533$	−8.33568e11			−0.447372
$534$	−2.30918e10	−	3.99962e10i	−0.0122892	−	0.0212854i
$535$	4.54371e10	+	7.86994e10i	0.0239783	+	0.0415316i
$536$	−5.03109e11	+	8.71410e11i	−0.263281	+	0.456017i
$537$	4.79912e11	+	8.31232e11i	0.249045	+	0.431358i
$538$	6.90383e10	−	1.19578e11i	0.0355279	−	0.0615362i
$539$	−1.09595e11			−0.0559293
$540$	1.79613e11			0.0909004
$541$	5.87302e11	−	1.01724e12i	0.294764	−	0.510546i	−0.680166	−	0.733058i	$-0.738092\pi$
$541$	5.87302e11	−	1.01724e12i	0.294764	−	0.510546i	0.974930	+	0.222512i	$0.0714257\pi$
$542$	−2.02563e11	+	3.50849e11i	−0.100824	+	0.174632i
$543$	−1.52144e12			−0.751026
$544$	−6.06518e11			−0.296926
$545$	8.96447e10	−	1.55269e11i	0.0435252	−	0.0753878i
$546$	−1.31310e11	−	2.27435e11i	−0.0632310	−	0.109519i
$547$	1.90629e12	−	3.30179e12i	0.910429	−	1.57691i	0.0969700	−	0.995287i	$-0.469085\pi$
$547$	1.90629e12	−	3.30179e12i	0.910429	−	1.57691i	0.813459	−	0.581622i	$-0.197582\pi$
$548$	−2.13163e11	−	3.69209e11i	−0.100972	−	0.174888i
$549$	−1.15874e12	−	2.00699e12i	−0.544389	−	0.942909i
$550$	−3.22010e11			−0.150050
$551$	1.27020e12	−	2.01668e12i	0.587072	−	0.932081i
$552$	1.40334e9			0.000643335
$553$	−1.11260e12	−	1.92707e12i	−0.505911	−	0.876263i
$554$	8.23818e11	+	1.42689e12i	0.371567	+	0.643573i
$555$	−3.89526e10	+	6.74678e10i	−0.0174268	+	0.0301841i
$556$	−7.19643e11	−	1.24646e12i	−0.319360	−	0.553148i
$557$	−1.37140e12	+	2.37534e12i	−0.603694	+	1.04563i	0.388563	+	0.921422i	$0.372972\pi$
$557$	−1.37140e12	+	2.37534e12i	−0.603694	+	1.04563i	−0.992256	+	0.124206i	$0.960362\pi$
$558$	−1.85492e12			−0.809972
$559$	−5.05504e11			−0.218964
$560$	4.82331e10	−	8.35422e10i	0.0207252	−	0.0358972i
$561$	−2.44229e11	+	4.23017e11i	−0.104103	+	0.180312i
$562$	−1.12308e12			−0.474895
$563$	−4.15893e11			−0.174459			−0.0872296	−	0.996188i	$-0.527801\pi$
$563$	−4.15893e11			−0.174459			−0.0872296	+	0.996188i	$0.527801\pi$
$564$	−1.05878e11	+	1.83387e11i	−0.0440607	+	0.0763154i
$565$	2.11781e11	+	3.66816e11i	0.0874318	+	0.151436i
$566$	9.35929e11	−	1.62108e12i	0.383327	−	0.663941i
$567$	1.60047e11	+	2.77210e11i	0.0650316	+	0.112638i
$568$	−4.12437e11	−	7.14361e11i	−0.166261	−	0.287972i
$569$	−4.18459e12			−1.67358			−0.836792	−	0.547521i	$-0.815572\pi$
$569$	−4.18459e12			−1.67358			−0.836792	+	0.547521i	$0.815572\pi$
$570$	−1.92306e11	−	7.40380e9i	−0.0763057	−	0.00293777i
$571$	−7.79401e11			−0.306830			−0.153415	−	0.988162i	$-0.549027\pi$
$571$	−7.79401e11			−0.306830			−0.153415	+	0.988162i	$0.549027\pi$
$572$	−5.18948e10	−	8.98844e10i	−0.0202694	−	0.0351077i
$573$	1.14237e11	+	1.97863e11i	0.0442700	+	0.0766778i
$574$	−9.65588e11	+	1.67245e12i	−0.371269	+	0.643056i
$575$	−4.08262e9	−	7.07130e9i	−0.00155752	−	0.00269770i
$576$	1.12848e11	−	1.95458e11i	0.0427161	−	0.0739864i
$577$	−4.85565e11			−0.182371			−0.0911857	−	0.995834i	$-0.529066\pi$
$577$	−4.85565e11			−0.182371			−0.0911857	+	0.995834i	$0.529066\pi$
$578$	3.45572e12			1.28784
$579$	−7.25334e11	+	1.25631e12i	−0.268216	+	0.464563i
$580$	1.44062e11	−	2.49523e11i	0.0528597	−	0.0915557i
$581$	−1.09420e12			−0.398385
$582$	−1.56942e12			−0.567003
$583$	−1.57340e11	+	2.72522e11i	−0.0564068	+	0.0976995i
$584$	3.47867e11	+	6.02523e11i	0.123753	+	0.214346i
$585$	6.83766e10	−	1.18432e11i	0.0241383	−	0.0418087i
$586$	7.54669e11	+	1.30713e12i	0.264373	+	0.457908i
$587$	−2.18445e12	−	3.78358e12i	−0.759400	−	1.31532i	−0.943157	−	0.332348i	$-0.892159\pi$
$587$	−2.18445e12	−	3.78358e12i	−0.759400	−	1.31532i	0.183757	−	0.982972i	$-0.441174\pi$
$588$	2.06999e11			0.0714120
$589$	4.89182e12	+	1.88335e11i	1.67476	+	0.0644782i
$590$	−3.15783e10			−0.0107289
$591$	−1.02257e12	−	1.77115e12i	−0.344786	−	0.597187i
$592$	1.20562e11	+	2.08820e11i	0.0403426	+	0.0698754i
$593$	−2.06785e12	+	3.58163e12i	−0.686711	+	1.18942i	0.286185	+	0.958174i	$0.407613\pi$
$593$	−2.06785e12	+	3.58163e12i	−0.686711	+	1.18942i	−0.972896	+	0.231244i	$0.925721\pi$
$594$	−2.23855e11	−	3.87728e11i	−0.0737782	−	0.127788i
$595$	−4.25706e11	+	7.37344e11i	−0.139246	+	0.241181i
$596$	1.42478e12			0.462531
$597$	1.97084e11			0.0634989
$598$	1.31590e9	−	2.27921e9i	0.000420793	−	0.000728834i
$599$	−1.56987e12	+	2.71910e12i	−0.498246	+	0.862987i	−0.999998	−	0.00202420i	$-0.999356\pi$
$599$	−1.56987e12	+	2.71910e12i	−0.498246	+	0.862987i	0.501752	+	0.865012i	$0.332689\pi$
$600$	6.08203e11			0.191588
$601$	−1.07175e12			−0.335086			−0.167543	−	0.985865i	$-0.553583\pi$
$601$	−1.07175e12			−0.335086			−0.167543	+	0.985865i	$0.553583\pi$
$602$	−5.85566e11	+	1.01423e12i	−0.181715	+	0.314740i
$603$	1.65236e12	+	2.86197e12i	0.508952	+	0.881531i
$604$	−9.03219e11	+	1.56442e12i	−0.276138	+	0.478286i
$605$	3.00910e11	+	5.21192e11i	0.0913141	+	0.158161i
$606$	−6.39805e11	−	1.10817e12i	−0.192717	−	0.333796i
$607$	3.26921e12			0.977448			0.488724	−	0.872438i	$-0.337462\pi$
$607$	3.26921e12			0.977448			0.488724	+	0.872438i	$0.337462\pi$
$608$	−3.17450e11	+	5.04008e11i	−0.0942126	+	0.149579i
$609$	−1.81724e12			−0.535346
$610$	3.69696e11	+	6.40332e11i	0.108109	+	0.187250i
$611$	1.98563e11	+	3.43921e11i	0.0576385	+	0.0998328i
$612$	−9.95993e11	+	1.72511e12i	−0.286996	+	0.497091i
$613$	−2.59664e12	−	4.49751e12i	−0.742744	−	1.28647i	−0.951241	−	0.308448i	$-0.900191\pi$
$613$	−2.59664e12	−	4.49751e12i	−0.742744	−	1.28647i	0.208497	−	0.978023i	$-0.433143\pi$
$614$	−1.92198e11	+	3.32897e11i	−0.0545747	+	0.0945261i
$615$	4.65750e11			0.131285
$616$	−2.40455e11			−0.0672855
$617$	−2.10857e12	+	3.65214e12i	−0.585739	+	1.01453i	0.409044	+	0.912515i	$0.365862\pi$
$617$	−2.10857e12	+	3.65214e12i	−0.585739	+	1.01453i	−0.994783	+	0.102014i	$0.967471\pi$
$618$	1.90778e11	−	3.30438e11i	0.0526116	−	0.0911259i
$619$	−2.36183e12			−0.646607			−0.323304	−	0.946295i	$-0.604793\pi$
$619$	−2.36183e12			−0.646607			−0.323304	+	0.946295i	$0.604793\pi$
$620$	5.91812e11			0.160850
$621$	5.67632e9	−	9.83167e9i	0.00153163	−	0.00265286i
$622$	1.20950e12	+	2.09492e12i	0.324003	+	0.561190i
$623$	−1.00330e11	+	1.73776e11i	−0.0266829	+	0.0462161i
$624$	9.80175e10	+	1.69771e11i	0.0258805	+	0.0448264i
$625$	−1.69912e12	−	2.94296e12i	−0.445414	−	0.771480i
$626$	5.08978e12			1.32469
$627$	2.23693e11	+	4.24357e11i	0.0578027	+	0.109655i
$628$	−1.69926e11			−0.0435956
$629$	−1.06408e12	−	1.84305e12i	−0.271049	−	0.469470i
$630$	−1.58412e11	−	2.74378e11i	−0.0400641	−	0.0693931i
$631$	1.53833e12	−	2.66446e12i	0.386293	−	0.669079i	−0.605655	−	0.795727i	$-0.707089\pi$
$631$	1.53833e12	−	2.66446e12i	0.386293	−	0.669079i	0.991948	+	0.126649i	$0.0404221\pi$
$632$	8.30509e11	+	1.43848e12i	0.207070	+	0.358656i
$633$	7.81975e11	−	1.35442e12i	0.193587	−	0.335302i
$634$	2.34462e12			0.576329
$635$	−5.06291e11			−0.123572
$636$	2.97180e11	−	5.14731e11i	0.0720217	−	0.124745i
$637$	1.94102e11	−	3.36194e11i	0.0467091	−	0.0809026i
$638$	−7.18191e11			−0.171612
$639$	−2.70913e12			−0.642800
$640$	−3.60041e10	+	6.23610e10i	−0.00848287	+	0.0146928i
$641$	4.04925e11	+	7.01351e11i	0.0947358	+	0.164087i	0.909498	−	0.415708i	$-0.136466\pi$
$641$	4.04925e11	+	7.01351e11i	0.0947358	+	0.164087i	−0.814763	+	0.579795i	$0.803133\pi$
$642$	−2.13919e11	+	3.70519e11i	−0.0496983	+	0.0860801i
$643$	1.10382e12	+	1.91187e12i	0.254652	+	0.441071i	0.964801	−	0.262981i	$-0.0847057\pi$
$643$	1.10382e12	+	1.91187e12i	0.254652	+	0.441071i	−0.710149	+	0.704052i	$0.751372\pi$
$644$	−3.04863e9	−	5.28038e9i	−0.000698422	−	0.00120970i
$645$	2.82447e11			0.0642567
$646$	2.80181e12	−	4.44838e12i	0.632984	−	1.00497i
$647$	3.74294e12			0.839739			0.419869	−	0.907585i	$-0.362076\pi$
$647$	3.74294e12			0.839739			0.419869	+	0.907585i	$0.362076\pi$
$648$	−1.19469e11	−	2.06927e11i	−0.0266175	−	0.0461029i
$649$	3.93567e10	+	6.81678e10i	0.00870798	+	0.0150827i
$650$	5.70308e11	−	9.87802e11i	0.125314	−	0.217050i
$651$	−1.86632e12	−	3.23256e12i	−0.407260	−	0.705395i
$652$	−2.16503e12	+	3.74994e12i	−0.469190	+	0.812662i
$653$	7.85133e12			1.68979			0.844897	−	0.534929i	$-0.179662\pi$
$653$	7.85133e12			1.68979			0.844897	+	0.534929i	$0.179662\pi$
$654$	8.44100e11			0.180424
$655$	3.62352e10	−	6.27613e10i	0.00769211	−	0.0133231i
$656$	7.20773e11	−	1.24842e12i	0.151961	−	0.263204i
$657$	2.28500e12			0.478456
$658$	9.20044e11			0.191334
$659$	3.55129e12	−	6.15101e12i	0.733502	−	1.27046i	−0.221876	−	0.975075i	$-0.571218\pi$
$659$	3.55129e12	−	6.15101e12i	0.733502	−	1.27046i	0.955377	−	0.295388i	$-0.0954488\pi$
$660$	2.89959e10	+	5.02223e10i	0.00594824	+	0.0103026i
$661$	3.88118e12	−	6.72241e12i	0.790784	−	1.36968i	−0.134699	−	0.990887i	$-0.543007\pi$
$661$	3.88118e12	−	6.72241e12i	0.790784	−	1.36968i	0.925482	−	0.378791i	$-0.123660\pi$
$662$	−6.02351e11	−	1.04330e12i	−0.121896	−	0.211130i
$663$	−8.65102e11	−	1.49840e12i	−0.173883	−	0.301174i
$664$	8.16775e11			0.163060
$665$	3.89910e11	+	7.39679e11i	0.0773155	+	0.146672i
$666$	7.91926e11			0.155973
$667$	−9.10562e9	−	1.57714e10i	−0.00178133	−	0.00308535i
$668$	2.12599e12	+	3.68232e12i	0.413112	+	0.715530i
$669$	5.32956e11	−	9.23108e11i	0.102867	−	0.178170i
$670$	−5.27187e11	−	9.13114e11i	−0.101071	−	0.175061i
$671$	9.21517e11	−	1.59611e12i	0.175490	−	0.303957i
$672$	4.54166e11			0.0859118
$673$	−1.35794e12			−0.255159			−0.127580	−	0.991828i	$-0.540721\pi$
$673$	−1.35794e12			−0.255159			−0.127580	+	0.991828i	$0.540721\pi$
$674$	−1.50092e12	+	2.59967e12i	−0.280148	+	0.485231i
$675$	2.46010e12	−	4.26101e12i	0.456126	−	0.790034i
$676$	−2.34711e12			−0.432288
$677$	−9.00440e12			−1.64743			−0.823713	−	0.567007i	$-0.808101\pi$
$677$	−9.00440e12			−1.64743			−0.823713	+	0.567007i	$0.808101\pi$
$678$	−9.97071e11	+	1.72698e12i	−0.181214	+	0.313872i
$679$	3.40942e12	+	5.90528e12i	0.615554	+	1.06617i
$680$	3.17773e11	−	5.50398e11i	0.0569936	−	0.0987158i
$681$	2.80425e12	+	4.85710e12i	0.499637	+	0.865397i
$682$	−7.37586e11	−	1.27754e12i	−0.130552	−	0.226123i
$683$	−9.18916e10			−0.0161578			−0.00807891	−	0.999967i	$-0.502572\pi$
$683$	−9.18916e10			−0.0161578			−0.00807891	+	0.999967i	$0.502572\pi$
$684$	9.12244e11	+	1.73058e12i	0.159352	+	0.302300i
$685$	4.46729e11			0.0775241
$686$	−2.22112e12	−	3.84710e12i	−0.382925	−	0.663246i
$687$	1.42096e12	+	2.46117e12i	0.243375	+	0.421538i
$688$	4.37102e11	−	7.57083e11i	0.0743763	−	0.128824i
$689$	−5.57328e11	−	9.65320e11i	−0.0942159	−	0.163187i
$690$	−7.35251e8	+	1.27349e9i	−0.000123485	+	0.000213883i
$691$	4.36930e12			0.729055			0.364528	−	0.931193i	$-0.381230\pi$
$691$	4.36930e12			0.729055			0.364528	+	0.931193i	$0.381230\pi$
$692$	−7.65083e11			−0.126833
$693$	−3.94864e11	+	6.83924e11i	−0.0650351	+	0.112644i
$694$	3.08746e11	−	5.34763e11i	0.0505223	−	0.0875073i
$695$	1.50817e12			0.245199
$696$	1.35650e12			0.219118
$697$	−6.36154e12	+	1.10185e13i	−1.02097	+	1.76838i
$698$	−2.81561e12	−	4.87678e12i	−0.448976	−	0.777649i
$699$	2.33372e12	−	4.04211e12i	0.369744	−	0.640415i
$700$	−1.32127e12	−	2.28850e12i	−0.207993	−	0.360255i
$701$	−2.41555e12	−	4.18386e12i	−0.377820	−	0.654404i	0.612924	−	0.790142i	$-0.289993\pi$
$701$	−2.41555e12	−	4.18386e12i	−0.377820	−	0.654404i	−0.990745	+	0.135737i	$0.956660\pi$
$702$	1.58587e12			0.246462
$703$	−2.08848e12	−	8.04067e10i	−0.322502	−	0.0124163i
$704$	1.79491e11			0.0275400
$705$	−1.10946e11	−	1.92163e11i	−0.0169145	−	0.0292968i
$706$	1.44543e12	+	2.50356e12i	0.218966	+	0.379260i
$707$	−2.77983e12	+	4.81481e12i	−0.418438	+	0.724757i
$708$	−7.43359e10	−	1.28753e11i	−0.0111186	−	0.0192579i
$709$	−1.90000e12	+	3.29090e12i	−0.282388	+	0.489110i	−0.971972	−	0.235095i	$-0.924460\pi$
$709$	−1.90000e12	+	3.29090e12i	−0.282388	+	0.489110i	0.689584	+	0.724205i	$0.257793\pi$
$710$	8.64350e11			0.127652
$711$	5.45528e12			0.800578
$712$	7.48921e10	−	1.29717e11i	0.0109213	−	0.0189163i
$713$	1.87031e10	−	3.23947e10i	0.00271025	−	0.00469430i
$714$	−4.00847e12			−0.577213
$715$	1.08757e11			0.0155625
$716$	−1.55647e12	+	2.69588e12i	−0.221325	+	0.383347i
$717$	−1.42424e11	−	2.46686e11i	−0.0201256	−	0.0348585i
$718$	−2.99673e12	+	5.19049e12i	−0.420812	+	0.728868i
$719$	1.11435e12	+	1.93012e12i	0.155504	+	0.269341i	0.933243	−	0.359247i	$-0.116966\pi$
$719$	1.11435e12	+	1.93012e12i	0.155504	+	0.269341i	−0.777738	+	0.628588i	$0.783633\pi$
$720$	1.18248e11	+	2.04812e11i	0.0163983	+	0.0284027i
$721$	−1.65779e12			−0.228466
$722$	−2.23008e12	−	4.65654e12i	−0.305424	−	0.637743i
$723$	−7.00049e12			−0.952809
$724$	−2.46719e12	−	4.27330e12i	−0.333717	−	0.578016i
$725$	−3.94635e12	−	6.83527e12i	−0.530486	−	0.918829i
$726$	−1.41669e12	+	2.45379e12i	−0.189261	+	0.327810i
$727$	5.64222e12	+	9.77262e12i	0.749110	+	1.29750i	0.948250	+	0.317525i	$0.102852\pi$
$727$	5.64222e12	+	9.77262e12i	0.749110	+	1.29750i	−0.199140	+	0.979971i	$0.563815\pi$
$728$	4.25868e11	−	7.37625e11i	0.0561932	−	0.0973295i
$729$	3.27883e12			0.429977
$730$	−7.29031e11			−0.0950152
$731$	−3.85786e12	+	6.68201e12i	−0.499710	+	0.865524i
$732$	−1.74054e12	+	3.01470e12i	−0.224070	+	0.388101i
$733$	−1.38668e13			−1.77422			−0.887112	−	0.461555i	$-0.847292\pi$
$733$	−1.38668e13			−1.77422			−0.887112	+	0.461555i	$0.847292\pi$
$734$	6.87973e12			0.874861
$735$	−1.08453e11	+	1.87846e11i	−0.0137072	+	0.0237416i
$736$	2.27568e9	+	3.94160e9i	0.000285865	+	0.000495133i
$737$	−1.31409e12	+	2.27606e12i	−0.164066	+	0.284172i
$738$	−2.36724e12	−	4.10017e12i	−0.293757	−	0.508802i
$739$	7.70103e12	+	1.33386e13i	0.949837	+	1.64517i	0.745764	+	0.666210i	$0.232084\pi$
$739$	7.70103e12	+	1.33386e13i	0.949837	+	1.64517i	0.204072	+	0.978956i	$0.434582\pi$
$740$	−2.52665e11			−0.0309743
$741$	−1.69794e12	−	6.53709e10i	−0.206891	−	0.00796530i
$742$	−2.58239e12			−0.312755
$743$	−7.74382e12	−	1.34127e13i	−0.932192	−	1.61460i	−0.779566	−	0.626320i	$-0.784560\pi$
$743$	−7.74382e12	−	1.34127e13i	−0.932192	−	1.61460i	−0.152626	−	0.988284i	$-0.548773\pi$
$744$	1.39313e12	+	2.41298e12i	0.166692	+	0.288719i
$745$	−7.46486e11	+	1.29295e12i	−0.0887807	+	0.153773i
$746$	−1.06226e12	−	1.83989e12i	−0.125576	−	0.217504i
$747$	1.34127e12	−	2.32314e12i	0.157606	−	0.272982i
$748$	−1.58418e12			−0.185033
$749$	1.85888e12			0.215816
$750$	−6.49500e11	+	1.12497e12i	−0.0749555	+	0.129827i
$751$	−1.50932e12	+	2.61421e12i	−0.173141	+	0.299889i	−0.939516	−	0.342504i	$-0.888725\pi$
$751$	−1.50932e12	+	2.61421e12i	−0.173141	+	0.299889i	0.766375	+	0.642393i	$0.222058\pi$
$752$	−6.86777e11			−0.0783133
$753$	1.23632e12			0.140137
$754$	1.27198e12	−	2.20313e12i	0.143321	−	0.248239i
$755$	−9.46445e11	−	1.63929e12i	−0.106007	−	0.183609i
$756$	1.83704e12	−	3.18184e12i	0.204536	−	0.354267i
$757$	4.73679e11	+	8.20436e11i	0.0524267	+	0.0908057i	0.891048	−	0.453910i	$-0.149971\pi$
$757$	4.73679e11	+	8.20436e11i	0.0524267	+	0.0908057i	−0.838621	+	0.544715i	$0.816638\pi$
$758$	−2.51605e12	−	4.35793e12i	−0.276827	−	0.479479i
$759$	3.66543e9			0.000400901
$760$	−2.91052e11	−	5.52142e11i	−0.0316453	−	0.0600329i
$761$	1.88869e12			0.204141			0.102070	−	0.994777i	$-0.467453\pi$
$761$	1.88869e12			0.204141			0.102070	+	0.994777i	$0.467453\pi$
$762$	−1.19182e12	−	2.06429e12i	−0.128060	−	0.221806i
$763$	−1.83373e12	−	3.17611e12i	−0.195873	−	0.339262i
$764$	−3.70496e11	+	6.41717e11i	−0.0393426	+	0.0681434i
$765$	−1.04366e12	−	1.80767e12i	−0.110175	−	0.190829i
$766$	−1.28173e12	+	2.22003e12i	−0.134514	+	0.232985i
$767$	−2.78817e11			−0.0290897
$768$	−3.39017e11			−0.0351638
$769$	−6.80698e12	+	1.17900e13i	−0.701917	+	1.21576i	0.265876	+	0.964007i	$0.414339\pi$
$769$	−6.80698e12	+	1.17900e13i	−0.701917	+	1.21576i	−0.967793	+	0.251749i	$0.918994\pi$
$770$	1.25982e11	−	2.18207e11i	0.0129151	−	0.0223697i
$771$	1.02373e13			1.04337
$772$	−4.70485e12			−0.476725
$773$	6.95995e11	−	1.20550e12i	0.0701130	−	0.121439i	−0.828838	−	0.559489i	$-0.810997\pi$
$773$	6.95995e11	−	1.20550e12i	0.0701130	−	0.121439i	0.898951	+	0.438050i	$0.144331\pi$
$774$	−1.43557e12	−	2.48649e12i	−0.143778	−	0.249030i
$775$	8.10585e12	−	1.40397e13i	0.807125	−	1.39798i
$776$	−2.54500e12	−	4.40806e12i	−0.251947	−	0.436385i
$777$	7.96794e11	+	1.38009e12i	0.0784245	+	0.135835i
$778$	4.82525e12			0.472184
$779$	5.82663e12	+	1.10534e13i	0.566890	+	1.07542i
$780$	−2.05417e11			−0.0198706
$781$	−1.07726e12	−	1.86586e12i	−0.103607	−	0.179453i
$782$	−2.00852e10	−	3.47885e10i	−0.00192063	−	0.00332664i
$783$	5.48685e12	−	9.50351e12i	0.521669	−	0.903558i
$784$	3.35674e11	+	5.81404e11i	0.0317318	+	0.0549611i
$785$	8.90294e10	−	1.54203e11i	0.00836797	−	0.0144937i
$786$	3.41193e11			0.0318859
$787$	−6.04877e12			−0.562058			−0.281029	−	0.959699i	$-0.590676\pi$
$787$	−6.04877e12			−0.562058			−0.281029	+	0.959699i	$0.590676\pi$
$788$	3.31644e12	−	5.74424e12i	0.306411	−	0.530719i
$789$	−4.40438e12	+	7.62861e12i	−0.404611	+	0.700807i
$790$	−1.74051e12			−0.158985
$791$	8.66418e12			0.786925
$792$	2.94750e11	−	5.10523e11i	0.0266190	−	0.0461054i
$793$	3.26418e12	+	5.65372e12i	0.293119	+	0.507698i
$794$	3.00754e11	−	5.20920e11i	0.0268546	−	0.0465135i
$795$	3.11403e11	+	5.39366e11i	0.0276484	+	0.0478885i
$796$	3.19594e11	+	5.53553e11i	0.0282157	+	0.0488710i
$797$	−6.70563e11			−0.0588677			−0.0294339	−	0.999567i	$-0.509370\pi$
$797$	−6.70563e11			−0.0588677			−0.0294339	+	0.999567i	$0.509370\pi$
$798$	−2.09802e12	+	3.33098e12i	−0.183146	+	0.290777i
$799$	6.06149e12			0.526161
$800$	9.86273e11	+	1.70827e12i	0.0851319	+	0.147453i
$801$	−2.45968e11	−	4.26029e11i	−0.0211121	−	0.0365673i
$802$	−6.53599e12	+	1.13207e13i	−0.557862	+	0.966246i
$803$	9.08605e11	+	1.57375e12i	0.0771179	+	0.133572i
$804$	2.48201e12	−	4.29897e12i	0.209484	−	0.362837i
$805$	6.38906e9			0.000536236
$806$	5.22533e12			0.436120
$807$	−3.40590e11	+	5.89919e11i	−0.0282684	+	0.0489623i
$808$	2.07504e12	−	3.59407e12i	0.171267	−	0.296644i
$809$	−1.54881e13			−1.27124			−0.635622	−	0.772000i	$-0.719256\pi$
$809$	−1.54881e13			−1.27124			−0.635622	+	0.772000i	$0.719256\pi$
$810$	2.50373e11			0.0204365
$811$	8.55127e12	−	1.48112e13i	0.694124	−	1.20226i	−0.276351	−	0.961057i	$-0.589125\pi$
$811$	8.55127e12	−	1.48112e13i	0.694124	−	1.20226i	0.970475	−	0.241201i	$-0.0775413\pi$
$812$	−2.94687e12	−	5.10413e12i	−0.237881	−	0.412021i
$813$	9.99312e11	−	1.73086e12i	0.0802221	−	0.138949i
$814$	3.14900e11	+	5.45424e11i	0.0251399	+	0.0435436i
$815$	−2.26864e12	−	3.92940e12i	−0.180118	−	0.311973i
$816$	2.99216e12			0.236254
$817$	3.53347e12	+	6.70318e12i	0.277461	+	0.526358i
$818$	3.42206e12			0.267238
$819$	−1.39868e12	−	2.42258e12i	−0.108628	−	0.188149i
$820$	7.55269e11	+	1.30816e12i	0.0583363	+	0.101041i
$821$	1.27995e13	−	2.21694e13i	0.983218	−	1.70298i	0.333617	−	0.942709i	$-0.391731\pi$
$821$	1.27995e13	−	2.21694e13i	0.983218	−	1.70298i	0.649601	−	0.760275i	$-0.274936\pi$
$822$	1.05161e12	+	1.82144e12i	0.0803396	+	0.139152i
$823$	−1.12607e13	+	1.95041e13i	−0.855589	+	1.48192i	0.0205092	+	0.999790i	$0.493471\pi$
$823$	−1.12607e13	+	1.95041e13i	−0.855589	+	1.48192i	−0.876098	+	0.482133i	$0.839862\pi$
$824$	1.23748e12			0.0935115
$825$	1.58859e12			0.119390
$826$	−3.22976e11	+	5.59410e11i	−0.0241412	+	0.0418138i
$827$	2.02112e12	−	3.50069e12i	0.150251	−	0.260243i	−0.781069	−	0.624445i	$-0.785325\pi$
$827$	2.02112e12	−	3.50069e12i	0.150251	−	0.260243i	0.931320	+	0.364203i	$0.118658\pi$
$828$	1.49480e10			0.00110522
$829$	1.36268e13			1.00207			0.501037	−	0.865426i	$-0.332952\pi$
$829$	1.36268e13			1.00207			0.501037	+	0.865426i	$0.332952\pi$
$830$	−4.27932e11	+	7.41201e11i	−0.0312985	+	0.0542106i
$831$	−4.06418e12	−	7.03937e12i	−0.295644	−	0.512070i
$832$	−3.17894e11	+	5.50608e11i	−0.0230000	+	0.0398371i
$833$	−2.96265e12	−	5.13147e12i	−0.213196	−	0.369266i
$834$	3.55025e12	+	6.14921e12i	0.254104	+	0.440121i
$835$	−4.45548e12			−0.317179
$836$	−8.29157e11	+	1.31644e12i	−0.0587096	+	0.0932119i
$837$	2.25401e13			1.58742
$838$	8.01967e12	+	1.38905e13i	0.561770	+	0.973013i
$839$	−5.82459e12	−	1.00885e13i	−0.405823	−	0.702906i	0.588594	−	0.808429i	$-0.299682\pi$
$839$	−5.82459e12	−	1.00885e13i	−0.405823	−	0.702906i	−0.994417	+	0.105523i	$0.966348\pi$
$840$	−2.37951e11	+	4.12143e11i	−0.0164904	+	0.0285622i
$841$	−1.54812e12	−	2.68142e12i	−0.106714	−	0.184835i
$842$	−4.29981e12	+	7.44748e12i	−0.294812	+	0.510629i
$843$	5.54055e12			0.377858
$844$	5.07225e12			0.344080
$845$	1.22972e12	−	2.12994e12i	0.0829757	−	0.143718i
$846$	−1.12779e12	+	1.95339e12i	−0.0756941	+	0.131106i
$847$	1.23105e13			0.821868
$848$	1.92765e12			0.128011
$849$	−4.61727e12	+	7.99734e12i	−0.305000	+	0.528276i
$850$	−8.70484e12	−	1.50772e13i	−0.571973	−	0.990687i
$851$	−7.98497e9	+	1.38304e10i	−0.000521903	+	0.000903963i
$852$	2.03469e12	+	3.52419e12i	0.132288	+	0.229130i
$853$	6.59749e12	+	1.14272e13i	0.426686	+	0.739042i	0.996576	−	0.0826790i	$-0.0263476\pi$
$853$	6.59749e12	+	1.14272e13i	0.426686	+	0.739042i	−0.569890	+	0.821721i	$0.693014\pi$
$854$	1.51246e13			0.973026
$855$	−2.04840e12	−	7.88635e10i	−0.131089	−	0.00504694i
$856$	−1.38758e12			−0.0883336
$857$	4.45587e12	+	7.71779e12i	0.282175	+	0.488741i	0.971920	−	0.235311i	$-0.0756108\pi$
$857$	4.45587e12	+	7.71779e12i	0.282175	+	0.488741i	−0.689745	+	0.724052i	$0.742277\pi$
$858$	2.56015e11	+	4.43431e11i	0.0161277	+	0.0279340i
$859$	−6.94035e12	+	1.20210e13i	−0.434923	+	0.753308i	−0.997289	−	0.0735800i	$-0.976558\pi$
$859$	−6.94035e12	+	1.20210e13i	−0.434923	+	0.753308i	0.562367	+	0.826888i	$0.309891\pi$
$860$	4.58021e11	+	7.93316e11i	0.0285524	+	0.0494542i
$861$	4.76358e12	−	8.25076e12i	0.295406	−	0.511658i
$862$	1.08982e13			0.672313
$863$	4.82148e12			0.295891			0.147946	−	0.988995i	$-0.452734\pi$
$863$	4.82148e12			0.295891			0.147946	+	0.988995i	$0.452734\pi$
$864$	−1.37128e12	+	2.37512e12i	−0.0837169	+	0.145002i
$865$	4.00849e11	−	6.94291e11i	0.0243449	−	0.0421667i
$866$	−1.06131e13			−0.641226
$867$	−1.70483e13			−1.02469
$868$	6.05291e12	−	1.04839e13i	0.361931	−	0.626882i
$869$	2.16923e12	+	3.75722e12i	0.129038	+	0.223500i
$870$	−7.10710e11	+	1.23099e12i	−0.0420587	+	0.0728478i
$871$	−4.65472e12	−	8.06222e12i	−0.274039	−	0.474649i
$872$	1.36881e12	+	2.37084e12i	0.0801711	+	0.138860i
$873$	−1.67171e13			−0.974083
$874$	−3.94213e10	−	1.51772e9i	−0.00228523	−	8.79813e-5i
$875$	5.64392e12			0.325495
$876$	−1.71615e12	−	2.97246e12i	−0.0984661	−	0.170548i
$877$	−1.31043e13	−	2.26973e13i	−0.748023	−	1.29561i	−0.948769	−	0.315970i	$-0.897670\pi$
$877$	−1.31043e13	−	2.26973e13i	−0.748023	−	1.29561i	0.200746	−	0.979643i	$-0.435663\pi$
$878$	−1.08175e13	+	1.87365e13i	−0.614332	+	1.06405i
$879$	−3.72305e12	−	6.44851e12i	−0.210353	−	0.364342i
$880$	−9.40404e10	+	1.62883e11i	−0.00528618	+	0.00915594i
$881$	−2.09627e13			−1.17234			−0.586171	−	0.810187i	$-0.699365\pi$
$881$	−2.09627e13			−1.17234			−0.586171	+	0.810187i	$0.699365\pi$
$882$	2.20491e12			0.122682
$883$	−6.63076e12	+	1.14848e13i	−0.367063	+	0.635771i	−0.989105	−	0.147212i	$-0.952970\pi$
$883$	−6.63076e12	+	1.14848e13i	−0.367063	+	0.635771i	0.622042	+	0.782984i	$0.286303\pi$
$884$	2.80573e12	−	4.85967e12i	0.154529	−	0.267652i
$885$	1.55787e11			0.00853663
$886$	1.81843e13			0.991393
$887$	−1.69857e13	+	2.94202e13i	−0.921358	+	1.59584i	−0.124041	+	0.992277i	$0.539585\pi$
$887$	−1.69857e13	+	2.94202e13i	−0.921358	+	1.59584i	−0.797317	+	0.603561i	$0.793748\pi$
$888$	−5.94776e11	−	1.03018e12i	−0.0320993	−	0.0555975i
$889$	−5.17822e12	+	8.96895e12i	−0.278050	+	0.481597i
$890$	7.84763e10	+	1.35925e11i	0.00419260	+	0.00726180i
$891$	−3.12045e11	−	5.40478e11i	−0.0165870	−	0.0287295i
$892$	3.45700e12			0.182834
$893$	3.17257e12	−	5.03702e12i	0.166947	−	0.265059i
$894$	−7.02896e12			−0.368020
$895$	−1.63096e12	−	2.82490e12i	−0.0849648	−	0.147163i
$896$	7.36483e11	+	1.27563e12i	0.0381748	+	0.0661207i
$897$	−6.49180e9	+	1.12441e10i	−0.000334811	+	0.000579909i
$898$	3.92185e12	+	6.79284e12i	0.201255	+	0.348584i
$899$	1.80788e13	−	3.13134e13i	0.923104	−	1.59886i
$900$	6.47843e12			0.329138
$901$	−1.70134e13			−0.860064
$902$	1.88261e12	−	3.26078e12i	0.0946959	−	0.164018i
$903$	2.88880e12	−	5.00355e12i	0.144585	−	0.250428i
$904$	−6.46747e12			−0.322090
$905$	5.17053e12			0.256222
$906$	4.45589e12	−	7.71783e12i	0.219714	−	0.380556i
$907$	−4.30162e12	−	7.45062e12i	−0.211057	−	0.365561i	0.740989	−	0.671517i	$-0.234357\pi$
$907$	−4.30162e12	−	7.45062e12i	−0.211057	−	0.365561i	−0.952045	+	0.305957i	$0.901024\pi$
$908$	−9.09484e12	+	1.57527e13i	−0.444026	+	0.769076i
$909$	−6.81504e12	−	1.18040e13i	−0.331079	−	0.573445i
$910$	4.46249e11	+	7.72927e11i	0.0215721	+	0.0373639i
$911$	−3.48472e12			−0.167624			−0.0838119	−	0.996482i	$-0.526709\pi$
$911$	−3.48472e12			−0.167624			−0.0838119	+	0.996482i	$0.526709\pi$
$912$	1.56609e12	−	2.48645e12i	0.0749618	−	0.119015i
$913$	2.13336e12			0.101612
$914$	−3.96734e11	−	6.87163e11i	−0.0188036	−	0.0325688i
$915$	−1.82384e12	−	3.15898e12i	−0.0860184	−	0.148988i
$916$	−4.60850e12	+	7.98216e12i	−0.216287	+	0.374620i
$917$	−7.41210e11	−	1.28381e12i	−0.0346162	−	0.0599570i
$918$	1.21029e13	−	2.09628e13i	0.562467	−	0.974221i
$919$	−3.97375e13			−1.83773			−0.918864	−	0.394575i	$-0.870892\pi$
$919$	−3.97375e13			−1.83773			−0.918864	+	0.394575i	$0.870892\pi$
$920$	−4.76918e9			−0.000219482
$921$	9.48180e11	−	1.64230e12i	0.0434233	−	0.0752113i
$922$	−1.29314e13	+	2.23978e13i	−0.589326	+	1.02074i
$923$	7.63166e12			0.346108
$924$	1.18625e12			0.0535368
$925$	−3.46066e12	+	5.99404e12i	−0.155425	+	0.269204i
$926$	−3.32050e12	−	5.75127e12i	−0.148407	−	0.257048i
$927$	2.03212e12	−	3.51974e12i	0.0903840	−	0.156550i
$928$	2.19972e12	+	3.81003e12i	0.0973648	+	0.168641i
$929$	1.75407e13	+	3.03814e13i	0.772638	+	1.33825i	0.936112	+	0.351701i	$0.114397\pi$
$929$	1.75407e13	+	3.03814e13i	0.772638	+	1.33825i	−0.163474	+	0.986548i	$0.552270\pi$
$930$	−2.91962e12			−0.127983
$931$	−5.81483e12	−	2.23871e11i	−0.253667	−	0.00976617i
$932$	1.51376e13			0.657181
$933$	−5.96689e12	−	1.03350e13i	−0.257799	−	0.446520i
$934$	6.98502e12	+	1.20984e13i	0.300335	+	0.520196i
$935$	8.30000e11	−	1.43760e12i	0.0355161	−	0.0615158i
$936$	1.04406e12	+	1.80836e12i	0.0444614	+	0.0770095i
$937$	−1.50831e13	+	2.61247e13i	−0.639237	+	1.10719i	0.346363	+	0.938100i	$0.387416\pi$
$937$	−1.50831e13	+	2.61247e13i	−0.639237	+	1.10719i	−0.985600	+	0.169091i	$0.945917\pi$
$938$	−2.15677e13			−0.909687
$939$	−2.51096e13			−1.05401
$940$	3.59823e11	−	6.23231e11i	0.0150319	−	0.0260360i
$941$	2.15172e13	−	3.72689e13i	0.894608	−	1.54951i	0.0603197	−	0.998179i	$-0.480788\pi$
$941$	2.15172e13	−	3.72689e13i	0.894608	−	1.54951i	0.834289	−	0.551328i	$-0.185879\pi$
$942$	8.38306e11			0.0346875
$943$	9.54751e10			0.00393177
$944$	2.41089e11	−	4.17578e11i	0.00988104	−	0.0171145i
$945$	1.92496e12	+	3.33412e12i	0.0785195	+	0.136000i
$946$	1.14168e12	−	1.97745e12i	0.0463484	−	0.0802777i
$947$	1.24221e13	+	2.15157e13i	0.501902	+	0.869321i	0.999998	+	0.00219814i	$0.000699691\pi$
$947$	1.24221e13	+	2.15157e13i	0.501902	+	0.869321i	−0.498095	+	0.867122i	$0.665967\pi$
$948$	−4.09719e12	−	7.09654e12i	−0.164759	−	0.285370i
$949$	−6.43688e12			−0.257619
$950$	−1.70851e13	−	6.57775e11i	−0.680551	−	0.0262012i
$951$	−1.15668e13			−0.458566
$952$	−6.50020e12	−	1.12587e13i	−0.256484	−	0.444243i
$953$	−3.47342e12	−	6.01614e12i	−0.136408	−	0.236265i	0.789727	−	0.613459i	$-0.210222\pi$
$953$	−3.47342e12	−	6.01614e12i	−0.136408	−	0.236265i	−0.926134	+	0.377194i	$0.876889\pi$
$954$	3.16549e12	−	5.48279e12i	0.123730	−	0.214306i
$955$	−3.88227e11	−	6.72429e11i	−0.0151033	−	0.0261596i
$956$	4.61915e11	−	8.00061e11i	0.0178855	−	0.0309787i
$957$	3.54308e12			0.136546
$958$	−5.30469e12			−0.203477
$959$	4.56903e12	−	7.91380e12i	0.174438	−	0.302135i
$960$	1.77621e11	−	3.07649e11i	0.00674953	−	0.0116905i
$961$	4.78285e13			1.80897
$962$	−2.23087e12			−0.0839819
$963$	−2.27861e12	+	3.94667e12i	−0.0853793	+	0.147881i
$964$	−1.13521e13	−	1.96624e13i	−0.423380	−	0.733315i
$965$	2.46501e12	−	4.26952e12i	0.0915052	−	0.158492i
$966$	1.50399e10	+	2.60499e10i	0.000555711	+	0.000962520i
$967$	5.34253e12	+	9.25354e12i	0.196484	+	0.340321i	0.947386	−	0.320093i	$-0.103714\pi$
$967$	5.34253e12	+	9.25354e12i	0.196484	+	0.340321i	−0.750902	+	0.660414i	$0.770381\pi$
$968$	−9.18934e12			−0.336392
$969$	−1.38223e13	+	2.19454e13i	−0.503644	+	0.799625i
$970$	5.33359e12			0.193440
$971$	1.76786e13	+	3.06202e13i	0.638206	+	1.10541i	0.985826	+	0.167770i	$0.0536567\pi$
$971$	1.76786e13	+	3.06202e13i	0.638206	+	1.10541i	−0.347620	+	0.937636i	$0.613010\pi$
$972$	7.17894e12	+	1.24343e13i	0.257966	+	0.446810i
$973$	1.54252e13	−	2.67172e13i	0.551725	−	0.955615i
$974$	4.87050e12	+	8.43596e12i	0.173404	+	0.300344i
$975$	−2.81353e12	+	4.87317e12i	−0.0997080	+	0.172699i
$976$	−1.12899e13			−0.398261
$977$	6.76845e12			0.237664			0.118832	−	0.992914i	$-0.462085\pi$
$977$	6.76845e12			0.237664			0.118832	+	0.992914i	$0.462085\pi$
$978$	1.06808e13	−	1.84997e13i	0.373319	−	0.646608i
$979$	1.95613e11	−	3.38812e11i	0.00680574	−	0.0117879i
$980$	−7.03477e11			−0.0243631
$981$	8.99114e12			0.309959
$982$	−1.11062e13	+	1.92366e13i	−0.381123	+	0.660125i
$983$	1.84832e13	+	3.20138e13i	0.631372	+	1.09357i	0.987271	+	0.159044i	$0.0508413\pi$
$983$	1.84832e13	+	3.20138e13i	0.631372	+	1.09357i	−0.355899	+	0.934524i	$0.615825\pi$
$984$	−3.55583e12	+	6.15887e12i	−0.120910	+	0.209422i
$985$	3.47516e12	+	6.01915e12i	0.117628	+	0.203738i
$986$	−1.94148e13	−	3.36273e13i	−0.654163	−	1.13304i
$987$	−4.53890e12			−0.152238
$988$	−2.56981e12	−	4.87506e12i	−0.0858014	−	0.162770i
$989$	5.78994e10			0.00192438
$990$	3.08857e11	+	5.34956e11i	0.0102188	+	0.0176994i
$991$	−3.14909e12	−	5.45438e12i	−0.103718	−	0.179645i	0.809496	−	0.587126i	$-0.199741\pi$
$991$	−3.14909e12	−	5.45438e12i	−0.103718	−	0.179645i	−0.913214	+	0.407481i	$0.866407\pi$
$992$	−4.51826e12	+	7.82586e12i	−0.148139	+	0.256584i
$993$	2.97161e12	+	5.14697e12i	0.0969884	+	0.167989i
$994$	8.84036e12	−	1.53120e13i	0.287231	−	0.497499i
$995$	−6.69779e11			−0.0216635
$996$	−4.02944e12			−0.129741
$997$	2.40845e13	−	4.17155e13i	0.771985	−	1.33712i	−0.164489	−	0.986379i	$-0.552598\pi$
$997$	2.40845e13	−	4.17155e13i	0.771985	−	1.33712i	0.936474	−	0.350738i	$-0.114069\pi$
$998$	−4.67676e12	+	8.10039e12i	−0.149231	+	0.258475i
$999$	−9.62314e12			−0.305684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.c.b.7.6	✓	16
19.11	even	3	inner	38.10.c.b.11.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.c.b.7.6	✓	16	1.1	even	1	trivial
38.10.c.b.11.6	yes	16	19.11	even	3	inner

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 - 13.8564i) q^{2} +(39.4668 + 68.3585i) q^{3} +(-128.000 + 221.703i) q^{4} +(-134.126 - 232.313i) q^{5} +(631.468 - 1093.74i) q^{6} -5487.23 q^{7} +4096.00 q^{8} +(6726.25 - 11650.2i) q^{9} +O(q^{10})\)	\(q+(-8.00000 - 13.8564i) q^{2} +(39.4668 + 68.3585i) q^{3} +(-128.000 + 221.703i) q^{4} +(-134.126 - 232.313i) q^{5} +(631.468 - 1093.74i) q^{6} -5487.23 q^{7} +4096.00 q^{8} +(6726.25 - 11650.2i) q^{9} +(-2146.01 + 3717.01i) q^{10} +10698.5 q^{11} -20207.0 q^{12} +(-18947.9 + 32818.8i) q^{13} +(43897.8 + 76033.2i) q^{14} +(10587.0 - 18337.3i) q^{15} +(-32768.0 - 56755.8i) q^{16} +(289210. + 500927. i) q^{17} -215240. q^{18} +(567636. + 21854.0i) q^{19} +68672.5 q^{20} +(-216563. - 375098. i) q^{21} +(-85587.8 - 148242. i) q^{22} +(2170.26 - 3759.00i) q^{23} +(161656. + 279996. i) q^{24} +(940583. - 1.62914e6i) q^{25} +606334. q^{26} +2.61550e6 q^{27} +(702365. - 1.21653e6i) q^{28} +(2.09782e6 - 3.63353e6i) q^{29} -338785. q^{30} +8.61790e6 q^{31} +(-524288. + 908093. i) q^{32} +(422234. + 731331. i) q^{33} +(4.62736e6 - 8.01483e6i) q^{34} +(735979. + 1.27475e6i) q^{35} +(1.72192e6 + 2.98245e6i) q^{36} -3.67927e6 q^{37} +(-4.23827e6 - 8.04022e6i) q^{38} -2.99126e6 q^{39} +(-549380. - 951554. i) q^{40} +(1.09981e7 + 1.90493e7i) q^{41} +(-3.46501e6 + 6.00157e6i) q^{42} +(6.66965e6 + 1.15522e7i) q^{43} +(-1.36940e6 + 2.37188e6i) q^{44} -3.60866e6 q^{45} -69448.3 q^{46} +(5.23969e6 - 9.07541e6i) q^{47} +(2.58649e6 - 4.47994e6i) q^{48} -1.02439e7 q^{49} -3.00987e7 q^{50} +(-2.28284e7 + 3.95399e7i) q^{51} +(-4.85067e6 - 8.40161e6i) q^{52} +(-1.47068e7 + 2.54729e7i) q^{53} +(-2.09240e7 - 3.62415e7i) q^{54} +(-1.43494e6 - 2.48539e6i) q^{55} -2.24757e7 q^{56} +(2.09088e7 + 3.96652e7i) q^{57} -6.71302e7 q^{58} +(3.67872e6 + 6.37173e6i) q^{59} +(2.71028e6 + 4.69434e6i) q^{60} +(8.61354e7 - 1.49191e8i) q^{61} +(-6.89432e7 - 1.19413e8i) q^{62} +(-3.69084e7 + 6.39273e7i) q^{63} +1.67772e7 q^{64} +1.01656e7 q^{65} +(6.75575e6 - 1.17013e7i) q^{66} +(-1.22829e8 + 2.12747e8i) q^{67} -1.48076e8 q^{68} +342612. q^{69} +(1.17757e7 - 2.03961e7i) q^{70} +(-1.00693e8 - 1.74405e8i) q^{71} +(2.75507e7 - 4.77192e7i) q^{72} +(8.49285e7 + 1.47100e8i) q^{73} +(2.94342e7 + 5.09815e7i) q^{74} +1.48487e8 q^{75} +(-7.75024e7 + 1.23049e8i) q^{76} -5.87049e7 q^{77} +(2.39301e7 + 4.14481e7i) q^{78} +(2.02761e8 + 3.51192e8i) q^{79} +(-8.79008e6 + 1.52249e7i) q^{80} +(-2.91673e7 - 5.05192e7i) q^{81} +(1.75970e8 - 3.04789e8i) q^{82} +1.99408e8 q^{83} +1.10880e8 q^{84} +(7.75812e7 - 1.34375e8i) q^{85} +(1.06714e8 - 1.84835e8i) q^{86} +3.31177e8 q^{87} +4.38209e7 q^{88} +(1.82842e7 - 3.16692e7i) q^{89} +(2.88692e7 + 5.00030e7i) q^{90} +(1.03972e8 - 1.80084e8i) q^{91} +(555586. + 962303. i) q^{92} +(3.40121e8 + 5.89106e8i) q^{93} -1.67670e8 q^{94} +(-7.10577e7 - 1.34800e8i) q^{95} -8.27678e7 q^{96} +(-6.21337e8 - 1.07619e9i) q^{97} +(8.19516e7 + 1.41944e8i) q^{98} +(7.19606e7 - 1.24639e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9}+O(q^{10}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9	\( 16 q - 128 q^{2} + 70 q^{3} - 2048 q^{4} - 341 q^{5} + 1120 q^{6} + 3704 q^{7} + 65536 q^{8} - 53064 q^{9} - 5456 q^{10} + 106682 q^{11} - 35840 q^{12} - 683 q^{13} - 29632 q^{14} + 2299 q^{15} - 524288 q^{16} - 611267 q^{17} + 1698048 q^{18} - 1609677 q^{19} + 174592 q^{20} - 941048 q^{21} - 853456 q^{22} - 416119 q^{23} + 286720 q^{24} - 3309027 q^{25} + 21856 q^{26} - 16903604 q^{27} - 474112 q^{28} - 5079157 q^{29} - 73568 q^{30} + 8618324 q^{31} - 8388608 q^{32} - 7592195 q^{33} - 9780272 q^{34} - 2035632 q^{35} - 13584384 q^{36} - 33091520 q^{37} + 18612624 q^{38} + 37931126 q^{39} - 1396736 q^{40} - 7394646 q^{41} - 15056768 q^{42} - 98675599 q^{43} - 13655296 q^{44} + 89231852 q^{45} + 13315808 q^{46} + 34129475 q^{47} + 4587520 q^{48} + 65004400 q^{49} + 105888864 q^{50} + 16027749 q^{51} - 174848 q^{52} - 110053995 q^{53} + 135228832 q^{54} + 135992300 q^{55} + 15171584 q^{56} + 14986101 q^{57} + 162533024 q^{58} - 2017760 q^{59} + 588544 q^{60} - 221861413 q^{61} - 68946592 q^{62} + 56812456 q^{63} + 268435456 q^{64} + 262635974 q^{65} - 121475120 q^{66} + 237580440 q^{67} + 312968704 q^{68} - 135348410 q^{69} - 32570112 q^{70} - 431190909 q^{71} - 217350144 q^{72} + 199873544 q^{73} + 264732160 q^{74} - 1822944486 q^{75} + 114275328 q^{76} + 2014342624 q^{77} - 303449008 q^{78} - 296762835 q^{79} - 22347776 q^{80} - 1069077456 q^{81} - 118314336 q^{82} + 1592138306 q^{83} + 481816576 q^{84} - 293558115 q^{85} - 1578809584 q^{86} - 1647860854 q^{87} + 436969472 q^{88} - 444394631 q^{89} - 713854816 q^{90} - 284099544 q^{91} - 106526464 q^{92} + 1322110374 q^{93} - 1092143200 q^{94} + 8705459 q^{95} - 146800640 q^{96} - 611719542 q^{97} - 520035200 q^{98} + 1201848626 q^{99}+O(q^{100}) \) 16 * q - 128 * q^2 + 70 * q^3 - 2048 * q^4 - 341 * q^5 + 1120 * q^6 + 3704 * q^7 + 65536 * q^8 - 53064 * q^9 - 5456 * q^10 + 106682 * q^11 - 35840 * q^12 - 683 * q^13 - 29632 * q^14 + 2299 * q^15 - 524288 * q^16 - 611267 * q^17 + 1698048 * q^18 - 1609677 * q^19 + 174592 * q^20 - 941048 * q^21 - 853456 * q^22 - 416119 * q^23 + 286720 * q^24 - 3309027 * q^25 + 21856 * q^26 - 16903604 * q^27 - 474112 * q^28 - 5079157 * q^29 - 73568 * q^30 + 8618324 * q^31 - 8388608 * q^32 - 7592195 * q^33 - 9780272 * q^34 - 2035632 * q^35 - 13584384 * q^36 - 33091520 * q^37 + 18612624 * q^38 + 37931126 * q^39 - 1396736 * q^40 - 7394646 * q^41 - 15056768 * q^42 - 98675599 * q^43 - 13655296 * q^44 + 89231852 * q^45 + 13315808 * q^46 + 34129475 * q^47 + 4587520 * q^48 + 65004400 * q^49 + 105888864 * q^50 + 16027749 * q^51 - 174848 * q^52 - 110053995 * q^53 + 135228832 * q^54 + 135992300 * q^55 + 15171584 * q^56 + 14986101 * q^57 + 162533024 * q^58 - 2017760 * q^59 + 588544 * q^60 - 221861413 * q^61 - 68946592 * q^62 + 56812456 * q^63 + 268435456 * q^64 + 262635974 * q^65 - 121475120 * q^66 + 237580440 * q^67 + 312968704 * q^68 - 135348410 * q^69 - 32570112 * q^70 - 431190909 * q^71 - 217350144 * q^72 + 199873544 * q^73 + 264732160 * q^74 - 1822944486 * q^75 + 114275328 * q^76 + 2014342624 * q^77 - 303449008 * q^78 - 296762835 * q^79 - 22347776 * q^80 - 1069077456 * q^81 - 118314336 * q^82 + 1592138306 * q^83 + 481816576 * q^84 - 293558115 * q^85 - 1578809584 * q^86 - 1647860854 * q^87 + 436969472 * q^88 - 444394631 * q^89 - 713854816 * q^90 - 284099544 * q^91 - 106526464 * q^92 + 1322110374 * q^93 - 1092143200 * q^94 + 8705459 * q^95 - 146800640 * q^96 - 611719542 * q^97 - 520035200 * q^98 + 1201848626 * q^99

Introduction

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