LMFDB - Embedded newform 42.9.g.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,9,Mod(19,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("42.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	42.g (of order $6$, 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:	$17.1099016226$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 243x^{6} - 2x^{5} + 49033x^{4} - 23088x^{3} + 2105352x^{2} + 2056320x + 73410624 $ x^8 - 2x^7 + 243x^6 - 2x^5 + 49033x^4 - 23088x^3 + 2105352x^2 + 2056320*x + 73410624
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{2}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.1
Root			$3.56219 - 6.16990i$ of defining polynomial
Character	$\chi$	$=$	42.31
Dual form			42.9.g.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 - 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-271.195 + 156.575i) q^{5} -529.090i q^{6} +(746.403 - 2282.04i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})$	\(q+(-5.65685 - 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-271.195 + 156.575i) q^{5} -529.090i q^{6} +(746.403 - 2282.04i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(3068.22 + 1771.44i) q^{10} +(-5337.31 + 9244.49i) q^{11} +(-5184.00 + 2992.98i) q^{12} +20875.6i q^{13} +(-26581.6 + 5595.92i) q^{14} -14644.5 q^{15} +(-8192.00 - 14189.0i) q^{16} +(54768.8 + 31620.8i) q^{17} +(12371.5 - 21428.1i) q^{18} +(-79634.8 + 45977.2i) q^{19} -40083.1i q^{20} +(83589.4 - 74969.5i) q^{21} +120769. q^{22} +(245015. + 424379. i) q^{23} +(58650.3 + 33861.7i) q^{24} +(-146281. + 253367. i) q^{25} +(204538. - 118090. i) q^{26} +102276. i q^{27} +(205197. + 228790. i) q^{28} +1.10983e6 q^{29} +(82842.0 + 143487. i) q^{30} +(952777. + 550086. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(-432322. + 249601. i) q^{33} -715497. i q^{34} +(154888. + 735744. i) q^{35} -279936. q^{36} +(-538894. - 933391. i) q^{37} +(900965. + 520172. i) q^{38} +(-488127. + 845460. i) q^{39} +(-392732. + 226744. i) q^{40} +798155. i q^{41} +(-1.20740e6 - 394914. i) q^{42} -2.93656e6 q^{43} +(-683175. - 1.18329e6i) q^{44} +(-593104. - 342429. i) q^{45} +(2.77203e6 - 4.80130e6i) q^{46} +(-3.93113e6 + 2.26964e6i) q^{47} -766204. i q^{48} +(-4.65057e6 - 3.40663e6i) q^{49} +3.30997e6 q^{50} +(1.47876e6 + 2.56128e6i) q^{51} +(-2.31408e6 - 1.33604e6i) q^{52} +(-1.45492e6 + 2.51999e6i) q^{53} +(1.00209e6 - 578560. i) q^{54} -3.34275e6i q^{55} +(1.08091e6 - 3.30474e6i) q^{56} -4.30028e6 q^{57} +(-6.27817e6 - 1.08741e7i) q^{58} +(1.25697e7 + 7.25714e6i) q^{59} +(937250. - 1.62337e6i) q^{60} +(-8.82748e6 + 5.09655e6i) q^{61} -1.24470e7i q^{62} +(5.13836e6 - 1.08172e6i) q^{63} +2.09715e6 q^{64} +(-3.26858e6 - 5.66135e6i) q^{65} +(4.89116e6 + 2.82391e6i) q^{66} +(1.40362e7 - 2.43114e7i) q^{67} +(-7.01041e6 + 4.04746e6i) q^{68} +2.29165e7i q^{69} +(6.33262e6 - 5.67958e6i) q^{70} -2.65070e7 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(-4.39640e6 - 2.53826e6i) q^{73} +(-6.09689e6 + 1.05601e7i) q^{74} +(-1.18488e7 + 6.84090e6i) q^{75} -1.17702e7i q^{76} +(1.71125e7 + 1.90800e7i) q^{77} +1.10450e7 q^{78} +(-6.92960e6 - 1.20024e7i) q^{79} +(4.44326e6 + 2.56532e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(7.82029e6 - 4.51505e6i) q^{82} +4.69473e7i q^{83} +(2.96074e6 + 1.40640e7i) q^{84} -1.98040e7 q^{85} +(1.66117e7 + 2.87723e7i) q^{86} +(4.49483e7 + 2.59509e7i) q^{87} +(-7.72925e6 + 1.33874e7i) q^{88} +(1.96492e7 - 1.13445e7i) q^{89} +7.74827e6i q^{90} +(4.76388e7 + 1.55816e7i) q^{91} -6.27239e7 q^{92} +(2.57250e7 + 4.45570e7i) q^{93} +(4.44756e7 + 2.56780e7i) q^{94} +(1.43977e7 - 2.49376e7i) q^{95} +(-7.50723e6 + 4.33430e6i) q^{96} -1.32519e8i q^{97} +(-7.07049e6 + 6.48369e7i) q^{98} -2.33454e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9}+O(q^{10}) $ 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9	\( 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9} - 21888 q^{10} - 7434 q^{11} - 41472 q^{12} + 32256 q^{14} - 120204 q^{15} - 65536 q^{16} + 7932 q^{17} - 773082 q^{19} + 130410 q^{21} + 557568 q^{22} + 391200 q^{23} - 138886 q^{25} - 805632 q^{26} + 654080 q^{28} - 2318196 q^{29} - 590976 q^{30} - 3212544 q^{31} - 602154 q^{33} + 3340932 q^{35} - 2239488 q^{36} + 544802 q^{37} - 1570560 q^{38} + 1341522 q^{39} + 2801664 q^{40} - 72576 q^{42} + 552284 q^{43} - 951552 q^{44} - 4868262 q^{45} + 7878912 q^{46} - 15735252 q^{47} - 588196 q^{49} + 25400832 q^{50} + 214164 q^{51} + 6359808 q^{52} + 10935222 q^{53} - 8601600 q^{56} - 41746428 q^{57} - 8158848 q^{58} + 63840318 q^{59} + 7693056 q^{60} + 43108176 q^{61} + 10869390 q^{63} + 16777216 q^{64} - 9118644 q^{65} + 22581504 q^{66} + 48827290 q^{67} - 1015296 q^{68} + 11053056 q^{70} - 164526744 q^{71} + 150530022 q^{73} - 31064064 q^{74} - 11249766 q^{75} - 137090394 q^{77} - 43504128 q^{78} - 18689696 q^{79} + 36470784 q^{80} - 19131876 q^{81} - 33914880 q^{82} + 18144000 q^{84} - 190617576 q^{85} - 37077504 q^{86} - 93886938 q^{87} - 35684352 q^{88} - 191605284 q^{89} + 110138574 q^{91} - 100147200 q^{92} - 86738688 q^{93} + 302275584 q^{94} + 260649552 q^{95} - 282428160 q^{98} - 32516316 q^{99}+O(q^{100}) \) 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9 - 21888 * q^10 - 7434 * q^11 - 41472 * q^12 + 32256 * q^14 - 120204 * q^15 - 65536 * q^16 + 7932 * q^17 - 773082 * q^19 + 130410 * q^21 + 557568 * q^22 + 391200 * q^23 - 138886 * q^25 - 805632 * q^26 + 654080 * q^28 - 2318196 * q^29 - 590976 * q^30 - 3212544 * q^31 - 602154 * q^33 + 3340932 * q^35 - 2239488 * q^36 + 544802 * q^37 - 1570560 * q^38 + 1341522 * q^39 + 2801664 * q^40 - 72576 * q^42 + 552284 * q^43 - 951552 * q^44 - 4868262 * q^45 + 7878912 * q^46 - 15735252 * q^47 - 588196 * q^49 + 25400832 * q^50 + 214164 * q^51 + 6359808 * q^52 + 10935222 * q^53 - 8601600 * q^56 - 41746428 * q^57 - 8158848 * q^58 + 63840318 * q^59 + 7693056 * q^60 + 43108176 * q^61 + 10869390 * q^63 + 16777216 * q^64 - 9118644 * q^65 + 22581504 * q^66 + 48827290 * q^67 - 1015296 * q^68 + 11053056 * q^70 - 164526744 * q^71 + 150530022 * q^73 - 31064064 * q^74 - 11249766 * q^75 - 137090394 * q^77 - 43504128 * q^78 - 18689696 * q^79 + 36470784 * q^80 - 19131876 * q^81 - 33914880 * q^82 + 18144000 * q^84 - 190617576 * q^85 - 37077504 * q^86 - 93886938 * q^87 - 35684352 * q^88 - 191605284 * q^89 + 110138574 * q^91 - 100147200 * q^92 - 86738688 * q^93 + 302275584 * q^94 + 260649552 * q^95 - 282428160 * q^98 - 32516316 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$2$	−5.65685	−	9.79796i	−0.353553	−	0.612372i
$3$	40.5000	+	23.3827i	0.500000	+	0.288675i
$3$	40.5000	+	23.3827i	0.500000	+	0.288675i
$4$	−64.0000	+	110.851i	−0.250000	+	0.433013i
$5$	−271.195	+	156.575i	−0.433912	+	0.250519i	−0.701012	−	0.713150i	$-0.747268\pi$
$5$	−271.195	+	156.575i	−0.433912	+	0.250519i	0.267100	+	0.963669i	$0.413935\pi$
$6$		−	529.090i		−	0.408248i
$7$	746.403	−	2282.04i	0.310872	−	0.950452i
$7$	746.403	−	2282.04i	0.310872	−	0.950452i
$8$	1448.15			0.353553
$9$	1093.50	+	1894.00i	0.166667	+	0.288675i
$10$	3068.22	+	1771.44i	0.306822	+	0.177144i
$11$	−5337.31	+	9244.49i	−0.364545	+	0.631411i	−0.988703	−	0.149887i	$-0.952109\pi$
$11$	−5337.31	+	9244.49i	−0.364545	+	0.631411i	0.624158	+	0.781298i	$0.285442\pi$
$12$	−5184.00	+	2992.98i	−0.250000	+	0.144338i
$13$			20875.6i			0.730912i	0.930829	+	0.365456i	$0.119087\pi$
$13$			20875.6i			0.730912i	−0.930829	+	0.365456i	$0.880913\pi$
$14$	−26581.6	+	5595.92i	−0.691940	+	0.145666i
$15$	−14644.5			−0.289275
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$	54768.8	+	31620.8i	0.655749	+	0.378597i	0.790655	−	0.612261i	$-0.209740\pi$
$17$	54768.8	+	31620.8i	0.655749	+	0.378597i	−0.134906	+	0.990858i	$0.543073\pi$
$18$	12371.5	−	21428.1i	0.117851	−	0.204124i
$19$	−79634.8	+	45977.2i	−0.611066	+	0.352799i	−0.773383	−	0.633939i	$-0.781437\pi$
$19$	−79634.8	+	45977.2i	−0.611066	+	0.352799i	0.162316	+	0.986739i	$0.448104\pi$
$20$		−	40083.1i		−	0.250519i
$21$	83589.4	−	74969.5i	0.429808	−	0.385485i
$22$	120769.			0.515545
$23$	245015.	+	424379.i	0.875552	+	1.51650i	0.856174	+	0.516688i	$0.172835\pi$
$23$	245015.	+	424379.i	0.875552	+	1.51650i	0.0193778	+	0.999812i	$0.493831\pi$
$24$	58650.3	+	33861.7i	0.176777	+	0.102062i
$25$	−146281.	+	253367.i	−0.374480	+	0.648619i
$26$	204538.	−	118090.i	0.447590	−	0.258416i
$27$			102276.i			0.192450i
$28$	205197.	+	228790.i	0.333840	+	0.372224i
$29$	1.10983e6			1.56916			0.784578	−	0.620030i	$-0.212880\pi$
$29$	1.10983e6			1.56916			0.784578	+	0.620030i	$0.212880\pi$
$30$	82842.0	+	143487.i	0.102274	+	0.177144i
$31$	952777.	+	550086.i	1.03168	+	0.595640i	0.917465	−	0.397816i	$-0.130232\pi$
$31$	952777.	+	550086.i	1.03168	+	0.595640i	0.114214	+	0.993456i	$0.463565\pi$
$32$	−92681.9	+	160530.i	−0.0883883	+	0.153093i
$33$	−432322.	+	249601.i	−0.364545	+	0.210470i
$34$		−	715497.i		−	0.535417i
$35$	154888.	+	735744.i	0.103216	+	0.490292i
$36$	−279936.			−0.166667
$37$	−538894.	−	933391.i	−0.287539	−	0.498031i	0.685683	−	0.727900i	$-0.259504\pi$
$37$	−538894.	−	933391.i	−0.287539	−	0.498031i	−0.973222	+	0.229869i	$0.926170\pi$
$38$	900965.	+	520172.i	0.432089	+	0.249467i
$39$	−488127.	+	845460.i	−0.210996	+	0.365456i
$40$	−392732.	+	226744.i	−0.153411	+	0.0885720i
$41$			798155.i			0.282457i	0.989977	+	0.141228i	$0.0451052\pi$
$41$			798155.i			0.282457i	−0.989977	+	0.141228i	$0.954895\pi$
$42$	−1.20740e6	−	394914.i	−0.388020	−	0.126913i
$43$	−2.93656e6			−0.858945			−0.429473	−	0.903080i	$-0.641301\pi$
$43$	−2.93656e6			−0.858945			−0.429473	+	0.903080i	$0.641301\pi$
$44$	−683175.	−	1.18329e6i	−0.182273	−	0.315705i
$45$	−593104.	−	342429.i	−0.144637	−	0.0835064i
$46$	2.77203e6	−	4.80130e6i	0.619109	−	1.07233i
$47$	−3.93113e6	+	2.26964e6i	−0.805612	+	0.465120i	−0.845430	−	0.534087i	$-0.820656\pi$
$47$	−3.93113e6	+	2.26964e6i	−0.805612	+	0.465120i	0.0398178	+	0.999207i	$0.487322\pi$
$48$		−	766204.i		−	0.144338i
$49$	−4.65057e6	−	3.40663e6i	−0.806718	−	0.590937i
$50$	3.30997e6			0.529595
$51$	1.47876e6	+	2.56128e6i	0.218583	+	0.378597i
$52$	−2.31408e6	−	1.33604e6i	−0.316494	−	0.182728i
$53$	−1.45492e6	+	2.51999e6i	−0.184389	+	0.319371i	−0.943371	−	0.331741i	$-0.892364\pi$
$53$	−1.45492e6	+	2.51999e6i	−0.184389	+	0.319371i	0.758981	+	0.651112i	$0.225697\pi$
$54$	1.00209e6	−	578560.i	0.117851	−	0.0680414i
$55$		−	3.34275e6i		−	0.365302i
$56$	1.08091e6	−	3.30474e6i	0.109910	−	0.336035i
$57$	−4.30028e6			−0.407378
$58$	−6.27817e6	−	1.08741e7i	−0.554781	−	0.960908i
$59$	1.25697e7	+	7.25714e6i	1.03733	+	0.598904i	0.919077	−	0.394079i	$-0.128936\pi$
$59$	1.25697e7	+	7.25714e6i	1.03733	+	0.598904i	0.118256	+	0.992983i	$0.462270\pi$
$60$	937250.	−	1.62337e6i	0.0723187	−	0.125260i
$61$	−8.82748e6	+	5.09655e6i	−0.637555	+	0.368092i	−0.783672	−	0.621175i	$-0.786656\pi$
$61$	−8.82748e6	+	5.09655e6i	−0.637555	+	0.368092i	0.146117	+	0.989267i	$0.453322\pi$
$62$		−	1.24470e7i		−	0.842362i
$63$	5.13836e6	−	1.08172e6i	0.326184	−	0.0686677i
$64$	2.09715e6			0.125000
$65$	−3.26858e6	−	5.66135e6i	−0.183107	−	0.317151i
$66$	4.89116e6	+	2.82391e6i	0.257772	+	0.148825i
$67$	1.40362e7	−	2.43114e7i	0.696547	−	1.20645i	−0.273109	−	0.961983i	$-0.588052\pi$
$67$	1.40362e7	−	2.43114e7i	0.696547	−	1.20645i	0.969656	−	0.244472i	$-0.0786146\pi$
$68$	−7.01041e6	+	4.04746e6i	−0.327875	+	0.189298i
$69$			2.29165e7i			1.01100i
$70$	6.33262e6	−	5.67958e6i	0.263749	−	0.236551i
$71$	−2.65070e7			−1.04310			−0.521552	−	0.853220i	$-0.674647\pi$
$71$	−2.65070e7			−1.04310			−0.521552	+	0.853220i	$0.674647\pi$
$72$	1.58356e6	+	2.74280e6i	0.0589256	+	0.102062i
$73$	−4.39640e6	−	2.53826e6i	−0.154813	−	0.0893810i	0.420592	−	0.907250i	$-0.361822\pi$
$73$	−4.39640e6	−	2.53826e6i	−0.154813	−	0.0893810i	−0.575405	+	0.817869i	$0.695156\pi$
$74$	−6.09689e6	+	1.05601e7i	−0.203320	+	0.352161i
$75$	−1.18488e7	+	6.84090e6i	−0.374480	+	0.216206i
$76$		−	1.17702e7i		−	0.352799i
$77$	1.71125e7	+	1.90800e7i	0.486799	+	0.542770i
$78$	1.10450e7			0.298393
$79$	−6.92960e6	−	1.20024e7i	−0.177910	−	0.308149i	0.763255	−	0.646098i	$-0.223600\pi$
$79$	−6.92960e6	−	1.20024e7i	−0.177910	−	0.308149i	−0.941164	+	0.337949i	$0.890267\pi$
$80$	4.44326e6	+	2.56532e6i	0.108478	+	0.0626298i
$81$	−2.39148e6	+	4.14217e6i	−0.0555556	+	0.0962250i
$82$	7.82029e6	−	4.51505e6i	0.172969	−	0.0998635i
$83$			4.69473e7i			0.989232i	0.869112	+	0.494616i	$0.164691\pi$
$83$			4.69473e7i			0.989232i	−0.869112	+	0.494616i	$0.835309\pi$
$84$	2.96074e6	+	1.40640e7i	0.0594680	+	0.282483i
$85$	−1.98040e7			−0.379383
$86$	1.66117e7	+	2.87723e7i	0.303683	+	0.525994i
$87$	4.49483e7	+	2.59509e7i	0.784578	+	0.452976i
$88$	−7.72925e6	+	1.33874e7i	−0.128886	+	0.223237i
$89$	1.96492e7	−	1.13445e7i	0.313173	−	0.180811i	−0.335172	−	0.942157i	$-0.608795\pi$
$89$	1.96492e7	−	1.13445e7i	0.313173	−	0.180811i	0.648346	+	0.761346i	$0.275461\pi$
$90$			7.74827e6i			0.118096i
$91$	4.76388e7	+	1.55816e7i	0.694696	+	0.227220i
$92$	−6.27239e7			−0.875552
$93$	2.57250e7	+	4.45570e7i	0.343893	+	0.595640i
$94$	4.44756e7	+	2.56780e7i	0.569654	+	0.328890i
$95$	1.43977e7	−	2.49376e7i	0.176766	−	0.306168i
$96$	−7.50723e6	+	4.33430e6i	−0.0883883	+	0.0510310i
$97$		−	1.32519e8i		−	1.49690i	−0.663194	−	0.748448i	$-0.730800\pi$
$97$		−	1.32519e8i		−	1.49690i	0.663194	−	0.748448i	$-0.269200\pi$
$98$	−7.07049e6	+	6.48369e7i	−0.0766558	+	0.702939i
$99$	−2.33454e7			−0.243030
$100$	−1.87240e7	−	3.24309e7i	−0.187240	−	0.324309i
$101$	9.02526e7	+	5.21074e7i	0.867310	+	0.500742i	0.866453	−	0.499258i	$-0.166394\pi$
$101$	9.02526e7	+	5.21074e7i	0.867310	+	0.500742i	0.000856524		1.00000i	$0.499727\pi$
$102$	1.67302e7	−	2.89776e7i	0.154562	−	0.267708i
$103$	6.00402e6	−	3.46642e6i	0.0533450	−	0.0307987i	−0.473090	−	0.881014i	$-0.656862\pi$
$103$	6.00402e6	−	3.46642e6i	0.0533450	−	0.0307987i	0.526435	+	0.850215i	$0.323528\pi$
$104$			3.02310e7i			0.258416i
$105$	−1.09307e7	+	3.34193e7i	−0.0899273	+	0.274942i
$106$	3.29211e7			0.260766
$107$	−5.85728e7	−	1.01451e8i	−0.446849	−	0.773965i	0.551330	−	0.834287i	$-0.314121\pi$
$107$	−5.85728e7	−	1.01451e8i	−0.446849	−	0.773965i	−0.998179	+	0.0603223i	$0.980787\pi$
$108$	−1.13374e7	−	6.54566e6i	−0.0833333	−	0.0481125i
$109$	5.34519e7	−	9.25815e7i	0.378667	−	0.655870i	−0.612202	−	0.790702i	$-0.709716\pi$
$109$	5.34519e7	−	9.25815e7i	0.378667	−	0.655870i	0.990869	+	0.134831i	$0.0430493\pi$
$110$	−3.27521e7	+	1.89094e7i	−0.223701	+	0.129154i
$111$		−	5.04031e7i		−	0.332021i
$112$	−3.84942e7	+	8.10375e6i	−0.244638	+	0.0515008i
$113$	−3.93200e7			−0.241157			−0.120578	−	0.992704i	$-0.538475\pi$
$113$	−3.93200e7			−0.241157			−0.120578	+	0.992704i	$0.538475\pi$
$114$	2.43260e7	+	4.21340e7i	0.144030	+	0.249467i
$115$	−1.32894e8	−	7.67263e7i	−0.759825	−	0.438685i
$116$	−7.10294e7	+	1.23027e8i	−0.392289	+	0.679465i
$117$	−3.95383e7	+	2.28274e7i	−0.210996	+	0.121819i
$118$		−	1.64210e8i		−	0.846979i
$119$	1.13039e8	−	1.01383e8i	0.563692	−	0.505563i
$120$	−2.12076e7			−0.102274
$121$	5.02058e7	+	8.69589e7i	0.234214	+	0.405670i
$122$	9.98716e7	+	5.76609e7i	0.450819	+	0.260281i
$123$	−1.86630e7	+	3.23253e7i	−0.0815382	+	0.141228i
$124$	−1.21955e8	+	7.04110e7i	−0.515839	+	0.297820i
$125$		−	2.13940e8i		−	0.876297i
$126$	−3.96656e7	−	4.42263e7i	−0.157374	−	0.175468i
$127$	−4.14788e8			−1.59445			−0.797225	−	0.603682i	$-0.793700\pi$
$127$	−4.14788e8			−1.59445			−0.797225	+	0.603682i	$0.793700\pi$
$128$	−1.18633e7	−	2.05478e7i	−0.0441942	−	0.0765466i
$129$	−1.18931e8	−	6.86647e7i	−0.429473	−	0.247956i
$130$	−3.69798e7	+	6.40509e7i	−0.129477	+	0.224260i
$131$	3.05356e8	−	1.76298e8i	1.03686	−	0.598634i	0.117921	−	0.993023i	$-0.462377\pi$
$131$	3.05356e8	−	1.76298e8i	1.03686	−	0.598634i	0.918943	+	0.394389i	$0.129044\pi$
$132$		−	6.38979e7i		−	0.210470i
$133$	4.54819e7	+	2.16047e8i	0.145356	+	0.690465i
$134$	−3.17603e8			−0.985066
$135$	−1.60138e7	−	2.77367e7i	−0.0482125	−	0.0835064i
$136$	7.93137e7	+	4.57918e7i	0.231842	+	0.133854i
$137$	1.16143e8	−	2.01166e8i	0.329694	−	0.571047i	−0.652757	−	0.757567i	$-0.726388\pi$
$137$	1.16143e8	−	2.01166e8i	0.329694	−	0.571047i	0.982451	+	0.186521i	$0.0597211\pi$
$138$	2.24535e8	−	1.29635e8i	0.619109	−	0.357442i
$139$		−	4.08503e8i		−	1.09430i	−0.837035	−	0.547149i	$-0.815713\pi$
$139$		−	4.08503e8i		−	1.09430i	0.837035	−	0.547149i	$-0.184287\pi$
$140$	−9.14710e7	−	2.99181e7i	−0.238107	−	0.0778794i
$141$	−2.12281e8			−0.537075
$142$	1.49946e8	+	2.59715e8i	0.368793	+	0.638768i
$143$	−1.92984e8	−	1.11419e8i	−0.461505	−	0.266450i
$144$	1.79159e7	−	3.10313e7i	0.0416667	−	0.0721688i
$145$	−3.00982e8	+	1.73772e8i	−0.680876	+	0.393104i
$146$			5.74344e7i			0.126404i
$147$	−1.08692e8	−	2.46711e8i	−0.232770	−	0.528348i
$148$	1.37957e8			0.287539
$149$	3.71818e8	+	6.44008e8i	0.754372	+	1.30661i	0.945686	+	0.325081i	$0.105392\pi$
$149$	3.71818e8	+	6.44008e8i	0.754372	+	1.30661i	−0.191314	+	0.981529i	$0.561275\pi$
$150$	1.34054e8	+	7.73959e7i	0.264797	+	0.152881i
$151$	−2.98222e8	+	5.16535e8i	−0.573629	+	0.993555i	0.422560	+	0.906335i	$0.361132\pi$
$151$	−2.98222e8	+	5.16535e8i	−0.573629	+	0.993555i	−0.996189	+	0.0872200i	$0.972202\pi$
$152$	−1.15323e8	+	6.65821e7i	−0.216045	+	0.124733i
$153$			1.38309e8i			0.252398i
$154$	9.01427e7	−	2.75600e8i	0.160268	−	0.490001i
$155$	−3.44518e8			−0.596877
$156$	−6.24802e7	−	1.08219e8i	−0.105498	−	0.182728i
$157$	7.75761e8	+	4.47886e8i	1.27682	+	0.737172i	0.976262	−	0.216592i	$-0.0694940\pi$
$157$	7.75761e8	+	4.47886e8i	1.27682	+	0.737172i	0.300557	+	0.953764i	$0.402827\pi$
$158$	−7.83995e7	+	1.35792e8i	−0.125801	+	0.217894i
$159$	−1.17848e8	+	6.80398e7i	−0.184389	+	0.106457i
$160$		−	5.80465e7i		−	0.0885720i
$161$	1.15133e9	−	2.42376e8i	1.71354	−	0.360733i
$162$	5.41131e7			0.0785674
$163$	6.28399e8	+	1.08842e9i	0.890195	+	1.54186i	0.839642	+	0.543141i	$0.182765\pi$
$163$	6.28399e8	+	1.08842e9i	0.890195	+	1.54186i	0.0505529	+	0.998721i	$0.483902\pi$
$164$	−8.84765e7	−	5.10819e7i	−0.122307	−	0.0706141i
$165$	7.81624e7	−	1.35381e8i	0.105454	−	0.182651i
$166$	4.59988e8	−	2.65574e8i	0.605779	−	0.349746i
$167$		−	7.96368e8i		−	1.02388i	−0.859022	−	0.511939i	$-0.828927\pi$
$167$		−	7.96368e8i		−	1.02388i	0.859022	−	0.511939i	$-0.171073\pi$
$168$	1.21050e8	−	1.08567e8i	0.151960	−	0.136290i
$169$	3.79941e8			0.465768
$170$	1.12029e8	+	1.94039e8i	0.134132	+	0.232324i
$171$	−1.74161e8	−	1.00552e8i	−0.203689	−	0.117600i
$172$	1.87940e8	−	3.25522e8i	0.214736	−	0.371934i
$173$	−7.51267e8	+	4.33744e8i	−0.838707	+	0.484228i	−0.856824	−	0.515608i	$-0.827566\pi$
$173$	−7.51267e8	+	4.33744e8i	−0.838707	+	0.484228i	0.0181177	+	0.999836i	$0.494233\pi$
$174$		−	5.87202e8i		−	0.640605i
$175$	4.69007e8	+	5.22933e8i	0.500066	+	0.557563i
$176$	1.74893e8			0.182273
$177$	3.39383e8	+	5.87828e8i	0.345778	+	0.598904i
$178$	−2.22305e8	−	1.28348e8i	−0.221447	−	0.127852i
$179$	−3.03044e8	+	5.24887e8i	−0.295184	+	0.511274i	−0.975028	−	0.222083i	$-0.928714\pi$
$179$	−3.03044e8	+	5.24887e8i	−0.295184	+	0.511274i	0.679844	+	0.733357i	$0.262048\pi$
$180$	7.59173e7	−	4.38309e7i	0.0723187	−	0.0417532i
$181$			9.88091e8i			0.920624i	0.887757	+	0.460312i	$0.152263\pi$
$181$			9.88091e8i			0.920624i	−0.887757	+	0.460312i	$0.847737\pi$
$182$	−1.16818e8	−	5.54905e8i	−0.106469	−	0.505747i
$183$	−4.76684e8			−0.425036
$184$	3.54820e8	+	6.14566e8i	0.309554	+	0.536164i
$185$	2.92291e8	+	1.68754e8i	0.249533	+	0.144068i
$186$	2.91045e8	−	5.04105e8i	0.243169	−	0.421181i
$187$	−5.84636e8	+	3.37540e8i	−0.478100	+	0.276031i
$188$		−	5.81027e8i		−	0.465120i
$189$	2.33397e8	+	7.63390e7i	0.182915	+	0.0598273i
$190$	−3.25783e8			−0.249985
$191$	−8.69255e8	−	1.50559e9i	−0.653151	−	1.13129i	−0.982354	−	0.187032i	$-0.940113\pi$
$191$	−8.69255e8	−	1.50559e9i	−0.653151	−	1.13129i	0.329203	−	0.944259i	$-0.393220\pi$
$192$	8.49347e7	+	4.90370e7i	0.0625000	+	0.0360844i
$193$	−1.34689e9	+	2.33289e9i	−0.970741	+	1.68137i	−0.277414	+	0.960751i	$0.589477\pi$
$193$	−1.34689e9	+	2.33289e9i	−0.970741	+	1.68137i	−0.693328	+	0.720623i	$0.743856\pi$
$194$	−1.29842e9	+	7.49641e8i	−0.916657	+	0.529232i
$195$		−	3.05713e8i		−	0.211434i
$196$	6.75266e8	−	2.97497e8i	0.457563	−	0.201585i
$197$	−4.94896e8			−0.328586			−0.164293	−	0.986412i	$-0.552534\pi$
$197$	−4.94896e8			−0.328586			−0.164293	+	0.986412i	$0.552534\pi$
$198$	1.32061e8	+	2.28737e8i	0.0859241	+	0.148825i
$199$	−1.54061e9	−	8.89472e8i	−0.982382	−	0.567179i	−0.0793936	−	0.996843i	$-0.525298\pi$
$199$	−1.54061e9	−	8.89472e8i	−0.982382	−	0.567179i	−0.902988	+	0.429665i	$0.858632\pi$
$200$	−2.11838e8	+	3.66914e8i	−0.132399	+	0.229321i
$201$	1.13693e9	−	6.56408e8i	0.696547	−	0.402152i
$202$		−	1.17906e9i		−	0.708156i
$203$	8.28384e8	−	2.53268e9i	0.487806	−	1.49141i
$204$	−3.78562e8			−0.218583
$205$	−1.24971e8	−	2.16456e8i	−0.0707608	−	0.122561i
$206$	−6.79278e7	−	3.92181e7i	−0.0377206	−	0.0217780i
$207$	−5.35848e8	+	9.28117e8i	−0.291851	+	0.505500i
$208$	2.96203e8	−	1.71013e8i	0.158247	−	0.0913639i
$209$		−	9.81577e8i		−	0.514445i
$210$	3.89275e8	−	8.19496e7i	0.200161	−	0.0421376i
$211$	−2.03106e9			−1.02469			−0.512346	−	0.858779i	$-0.671223\pi$
$211$	−2.03106e9			−1.02469			−0.512346	+	0.858779i	$0.671223\pi$
$212$	−1.86230e8	−	3.22559e8i	−0.0921946	−	0.159686i
$213$	−1.07353e9	−	6.19805e8i	−0.521552	−	0.301118i
$214$	−6.62675e8	+	1.14779e9i	−0.315970	+	0.547276i
$215$	7.96382e8	−	4.59791e8i	0.372707	−	0.215182i
$216$			1.48111e8i			0.0680414i
$217$	1.96647e9	−	1.76368e9i	0.886847	−	0.795393i
$218$	−1.20948e9			−0.535516
$219$	−1.18703e8	−	2.05599e8i	−0.0516042	−	0.0893810i
$220$	3.70548e8	+	2.13936e8i	0.158181	+	0.0913256i
$221$	−6.60102e8	+	1.14333e9i	−0.276721	+	0.479295i
$222$	−4.93848e8	+	2.85123e8i	−0.203320	+	0.117387i
$223$		−	4.75239e9i		−	1.92173i	−0.277014	−	0.960866i	$-0.589345\pi$
$223$		−	4.75239e9i		−	1.92173i	0.277014	−	0.960866i	$-0.410655\pi$
$224$	2.97157e8	+	3.31323e8i	0.118030	+	0.131601i
$225$	−6.39834e8			−0.249653
$226$	2.22427e8	+	3.85255e8i	0.0852618	+	0.147678i
$227$	1.75696e9	+	1.01438e9i	0.661697	+	0.382031i	0.792923	−	0.609321i	$-0.208558\pi$
$227$	1.75696e9	+	1.01438e9i	0.661697	+	0.382031i	−0.131226	+	0.991352i	$0.541891\pi$
$228$	2.75218e8	−	4.76691e8i	0.101844	−	0.176400i
$229$	1.78737e9	−	1.03194e9i	0.649939	−	0.375243i	−0.138494	−	0.990363i	$-0.544226\pi$
$229$	1.78737e9	−	1.03194e9i	0.649939	−	0.375243i	0.788433	+	0.615121i	$0.210893\pi$
$230$			1.73612e9i			0.620395i
$231$	2.46912e8	+	1.17288e9i	0.0867151	+	0.411912i
$232$	1.60721e9			0.554781
$233$	1.34446e9	+	2.32868e9i	0.456168	+	0.790107i	0.998755	−	0.0498932i	$-0.0158881\pi$
$233$	1.34446e9	+	2.32868e9i	0.456168	+	0.790107i	−0.542586	+	0.840000i	$0.682555\pi$
$234$	4.47324e8	+	2.58263e8i	0.149197	+	0.0861388i
$235$	7.10735e8	−	1.23103e9i	0.233043	−	0.403643i
$236$	−1.60893e9	+	9.28914e8i	−0.518666	+	0.299452i
$237$		−	6.48130e8i		−	0.205432i
$238$	−1.63279e9	−	5.34049e8i	−0.508888	−	0.166446i
$239$	−3.30381e8			−0.101257			−0.0506283	−	0.998718i	$-0.516122\pi$
$239$	−3.30381e8			−0.101257			−0.0506283	+	0.998718i	$0.516122\pi$
$240$	1.19968e8	+	2.07791e8i	0.0361593	+	0.0626298i
$241$	2.36127e9	+	1.36328e9i	0.699966	+	0.404126i	0.807335	−	0.590094i	$-0.200909\pi$
$241$	2.36127e9	+	1.36328e9i	0.699966	+	0.404126i	−0.107369	+	0.994219i	$0.534243\pi$
$242$	5.68013e8	−	9.83828e8i	0.165614	−	0.286852i
$243$	−1.93710e8	+	1.11839e8i	−0.0555556	+	0.0320750i
$244$		−	1.30472e9i		−	0.368092i
$245$	1.79460e9	+	1.95702e8i	0.498086	+	0.0543164i
$246$	4.22296e8			0.115312
$247$	−9.59799e8	−	1.66242e9i	−0.257865	−	0.446636i
$248$	1.37977e9	+	7.96610e8i	0.364754	+	0.210591i
$249$	−1.09775e9	+	1.90137e9i	−0.285567	+	0.494616i
$250$	−2.09617e9	+	1.21023e9i	−0.536620	+	0.309818i
$251$		−	5.27962e8i		−	0.133017i	−0.997786	−	0.0665087i	$-0.978814\pi$
$251$		−	5.27962e8i		−	0.133017i	0.997786	−	0.0665087i	$-0.0211860\pi$
$252$	−2.08945e8	+	6.38824e8i	−0.0518119	+	0.158409i
$253$	−5.23089e9			−1.27671
$254$	2.34639e9	+	4.06407e9i	0.563723	+	0.976398i
$255$	−8.02064e8	−	4.63072e8i	−0.189692	−	0.109519i
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	1.72030e7	−	9.93215e6i	0.00394340	−	0.00227673i	−0.498027	−	0.867162i	$-0.665942\pi$
$257$	1.72030e7	−	9.93215e6i	0.00394340	−	0.00227673i	0.501970	+	0.864885i	$0.332609\pi$
$258$			1.55371e9i			0.350663i
$259$	−2.53226e9	+	5.33088e8i	−0.562743	+	0.118468i
$260$	8.36757e8			0.183107
$261$	1.21360e9	+	2.10202e9i	0.261526	+	0.452976i
$262$	−3.45471e9	−	1.99458e9i	−0.733174	−	0.423298i
$263$	−1.91915e9	+	3.32406e9i	−0.401130	+	0.694778i	−0.993863	−	0.110621i	$-0.964716\pi$
$263$	−1.91915e9	+	3.32406e9i	−0.401130	+	0.694778i	0.592732	+	0.805400i	$0.298049\pi$
$264$	−6.26069e8	+	3.61461e8i	−0.128886	+	0.0744125i
$265$		−	9.11213e8i		−	0.184772i
$266$	1.85953e9	−	1.66778e9i	0.371431	−	0.333128i
$267$	1.06106e9			0.208782
$268$	1.79663e9	+	3.11186e9i	0.348274	+	0.603227i
$269$	4.56937e9	+	2.63813e9i	0.872665	+	0.503833i	0.868233	−	0.496157i	$-0.165256\pi$
$269$	4.56937e9	+	2.63813e9i	0.872665	+	0.503833i	0.00443216	+	0.999990i	$0.498589\pi$
$270$	−1.81175e8	+	3.13805e8i	−0.0340914	+	0.0590480i
$271$	6.94720e9	−	4.01097e9i	1.28805	−	0.743655i	0.309743	−	0.950820i	$-0.399757\pi$
$271$	6.94720e9	−	4.01097e9i	1.28805	−	0.743655i	0.978306	+	0.207165i	$0.0664237\pi$
$272$		−	1.03615e9i		−	0.189298i
$273$	1.56503e9	+	1.74498e9i	0.281755	+	0.314151i
$274$	−2.62802e9			−0.466258
$275$	−1.56150e9	−	2.70459e9i	−0.273030	−	0.472902i
$276$	−2.54032e9	−	1.46665e9i	−0.437776	−	0.252750i
$277$	1.87568e9	−	3.24877e9i	0.318595	−	0.551823i	−0.661600	−	0.749857i	$-0.730122\pi$
$277$	1.87568e9	−	3.24877e9i	0.318595	−	0.551823i	0.980195	+	0.198034i	$0.0634556\pi$
$278$	−4.00249e9	+	2.31084e9i	−0.670118	+	0.386893i
$279$			2.40608e9i			0.397093i
$280$	2.24302e8	+	1.06547e9i	0.0364922	+	0.173344i
$281$	1.60467e9			0.257371			0.128685	−	0.991685i	$-0.458924\pi$
$281$	1.60467e9			0.257371			0.128685	+	0.991685i	$0.458924\pi$
$282$	1.20084e9	+	2.07992e9i	0.189885	+	0.328890i
$283$	3.94475e9	+	2.27750e9i	0.614998	+	0.355069i	0.774919	−	0.632061i	$-0.217791\pi$
$283$	3.94475e9	+	2.27750e9i	0.614998	+	0.355069i	−0.159921	+	0.987130i	$0.551124\pi$
$284$	1.69645e9	−	2.93834e9i	0.260776	−	0.451677i
$285$	1.16621e9	−	6.73314e8i	0.176766	−	0.102056i
$286$			2.52113e9i			0.376818i
$287$	1.82142e9	+	5.95745e8i	0.268461	+	0.0878077i
$288$	−4.05391e8			−0.0589256
$289$	−1.48813e9	−	2.57752e9i	−0.213329	−	0.369496i
$290$	3.40522e9	+	1.96600e9i	0.481452	+	0.277966i
$291$	3.09865e9	−	5.36702e9i	0.432116	−	0.748448i
$292$	5.62740e8	−	3.24898e8i	0.0774063	−	0.0446905i
$293$			9.82843e9i			1.33356i	0.745253	+	0.666782i	$0.232329\pi$
$293$			9.82843e9i			1.33356i	−0.745253	+	0.666782i	$0.767671\pi$
$294$	−1.80242e9	+	2.46057e9i	−0.241249	+	0.329341i
$295$	−4.54513e9			−0.600148
$296$	−7.80401e8	−	1.35169e9i	−0.101660	−	0.176081i
$297$	−9.45488e8	−	5.45878e8i	−0.121515	−	0.0701568i
$298$	4.20664e9	−	7.28612e9i	0.533421	−	0.923913i
$299$	−8.85915e9	+	5.11483e9i	−1.10843	+	0.639951i
$300$		−	1.75127e9i		−	0.216206i
$301$	−2.19186e9	+	6.70134e9i	−0.267022	+	0.816386i
$302$	6.74798e9			0.811234
$303$	2.43682e9	+	4.22070e9i	0.289103	+	0.500742i
$304$	1.30474e9	+	7.53290e8i	0.152767	+	0.0881998i
$305$	1.59598e9	−	2.76432e9i	0.184429	−	0.319440i
$306$	1.35515e9	−	7.82396e8i	0.154562	−	0.0892361i
$307$		−	1.19446e10i		−	1.34468i	−0.740245	−	0.672338i	$-0.765290\pi$
$307$		−	1.19446e10i		−	1.34468i	0.740245	−	0.672338i	$-0.234710\pi$
$308$	−3.21024e9	+	6.75816e8i	−0.356726	+	0.0750975i
$309$	3.24217e8			0.0355633
$310$	1.94889e9	+	3.37557e9i	0.211028	+	0.365511i
$311$	−1.18412e10	−	6.83652e9i	−1.26577	−	0.730791i	−0.291583	−	0.956545i	$-0.594182\pi$
$311$	−1.18412e10	−	6.83652e9i	−1.26577	−	0.730791i	−0.974184	+	0.225754i	$0.927515\pi$
$312$	−7.06883e8	+	1.22436e9i	−0.0745983	+	0.129208i
$313$	8.49373e9	−	4.90386e9i	0.884954	−	0.510929i	0.0126657	−	0.999920i	$-0.495968\pi$
$313$	8.49373e9	−	4.90386e9i	0.884954	−	0.510929i	0.872289	+	0.488991i	$0.162635\pi$
$314$		−	1.01345e10i		−	1.04252i
$315$	−1.22413e9	+	1.09789e9i	−0.124333	+	0.111511i
$316$	1.77398e9			0.177910
$317$	−7.71024e9	−	1.33545e10i	−0.763538	−	1.32249i	−0.941016	−	0.338362i	$-0.890127\pi$
$317$	−7.71024e9	−	1.33545e10i	−0.763538	−	1.32249i	0.177477	−	0.984125i	$-0.443206\pi$
$318$	1.33330e9	+	7.69783e8i	0.130383	+	0.0752765i
$319$	−5.92353e9	+	1.02598e10i	−0.572028	+	0.990782i
$320$	−5.68737e8	+	3.28361e8i	−0.0542390	+	0.0313149i
$321$		−	5.47835e9i		−	0.515977i
$322$	−8.88768e9	−	9.90958e9i	−0.826732	−	0.921789i
$323$	−5.81534e9			−0.534275
$324$	−3.06110e8	−	5.30198e8i	−0.0277778	−	0.0481125i
$325$	−5.28917e9	−	3.05370e9i	−0.474083	−	0.273712i
$326$	7.10952e9	−	1.23141e10i	0.629463	−	1.09026i
$327$	4.32961e9	−	2.49970e9i	0.378667	−	0.218623i
$328$			1.15585e9i			0.0998635i
$329$	2.24519e9	+	1.06650e10i	0.191633	+	0.910288i
$330$	−1.76861e9			−0.149134
$331$	−1.12822e9	−	1.95413e9i	−0.0939896	−	0.162795i	0.815197	−	0.579184i	$-0.196629\pi$
$331$	−1.12822e9	−	1.95413e9i	−0.0939896	−	0.162795i	−0.909186	+	0.416389i	$0.863295\pi$
$332$	−5.20417e9	−	3.00463e9i	−0.428350	−	0.247308i
$333$	1.17856e9	−	2.04133e9i	0.0958462	−	0.166010i
$334$	−7.80278e9	+	4.50494e9i	−0.626994	+	0.361995i
$335$			8.79085e9i			0.697994i
$336$	−1.74850e9	−	5.71897e8i	−0.137186	−	0.0448705i
$337$	9.39663e9			0.728539			0.364269	−	0.931294i	$-0.381319\pi$
$337$	9.39663e9			0.728539			0.364269	+	0.931294i	$0.381319\pi$
$338$	−2.14927e9	−	3.72265e9i	−0.164674	−	0.285224i
$339$	−1.59246e9	−	9.19406e8i	−0.120578	−	0.0696159i
$340$	1.26746e9	−	2.19530e9i	0.0948458	−	0.164278i
$341$	−1.01705e10	+	5.87196e9i	−0.752187	+	0.434275i
$342$			2.27523e9i			0.166311i
$343$	−1.12453e10	+	8.07003e9i	−0.812443	+	0.583041i
$344$	−4.25260e9			−0.303683
$345$	−3.58813e9	−	6.21483e9i	−0.253275	−	0.438685i
$346$	8.49962e9	+	4.90726e9i	0.593055	+	0.342401i
$347$	−1.60828e9	+	2.78563e9i	−0.110929	+	0.192135i	−0.916145	−	0.400847i	$-0.868716\pi$
$347$	−1.60828e9	+	2.78563e9i	−0.110929	+	0.192135i	0.805216	+	0.592981i	$0.202049\pi$
$348$	−5.75338e9	+	3.32172e9i	−0.392289	+	0.226488i
$349$			2.49150e10i			1.67942i	0.543033	+	0.839711i	$0.317276\pi$
$349$			2.49150e10i			1.67942i	−0.543033	+	0.839711i	$0.682724\pi$
$350$	2.47057e9	−	7.55346e9i	0.164636	−	0.503354i
$351$	−2.13507e9			−0.140664
$352$	−9.89343e8	−	1.71359e9i	−0.0644431	−	0.111619i
$353$	3.66422e9	+	2.11554e9i	0.235984	+	0.136246i	0.613330	−	0.789827i	$-0.289830\pi$
$353$	3.66422e9	+	2.11554e9i	0.235984	+	0.136246i	−0.377345	+	0.926073i	$0.623163\pi$
$354$	3.83968e9	−	6.65052e9i	0.244502	−	0.423489i
$355$	7.18857e9	−	4.15033e9i	0.452615	−	0.261318i
$356$			2.90418e9i			0.180811i
$357$	6.94869e9	−	1.46283e9i	0.427789	−	0.0900576i
$358$	6.85709e9			0.417453
$359$	−1.00950e10	−	1.74850e10i	−0.607753	−	1.05266i	−0.991610	−	0.129267i	$-0.958738\pi$
$359$	−1.00950e10	−	1.74850e10i	−0.607753	−	1.05266i	0.383857	−	0.923393i	$-0.374596\pi$
$360$	−8.58906e8	−	4.95890e8i	−0.0511370	−	0.0295240i
$361$	−4.26398e9	+	7.38543e9i	−0.251065	+	0.434858i
$362$	9.68127e9	−	5.58948e9i	0.563765	−	0.325490i
$363$			4.69578e9i			0.270447i
$364$	−4.77612e9	+	4.28360e9i	−0.272063	+	0.244007i
$365$	1.58971e9			0.0895667
$366$	2.69653e9	+	4.67053e9i	0.150273	+	0.260281i
$367$	2.33465e10	+	1.34791e10i	1.28694	+	0.743015i	0.978107	−	0.208102i	$-0.0667285\pi$
$367$	2.33465e10	+	1.34791e10i	1.28694	+	0.743015i	0.308832	+	0.951117i	$0.400062\pi$
$368$	4.01433e9	−	6.95302e9i	0.218888	−	0.379125i
$369$	−1.51170e9	+	8.72782e8i	−0.0815382	+	0.0470761i
$370$		−	3.81847e9i		−	0.203743i
$371$	4.66476e9	+	5.20111e9i	0.246226	+	0.274536i
$372$	−6.58559e9			−0.343893
$373$	−4.14336e9	−	7.17652e9i	−0.214051	−	0.370748i	0.738927	−	0.673785i	$-0.235333\pi$
$373$	−4.14336e9	−	7.17652e9i	−0.214051	−	0.370748i	−0.952979	+	0.303037i	$0.901999\pi$
$374$	6.61440e9	+	3.81883e9i	0.338068	+	0.195184i
$375$	5.00248e9	−	8.66455e9i	0.252965	−	0.438148i
$376$	−5.69288e9	+	3.28679e9i	−0.284827	+	0.164445i
$377$			2.31684e10i			1.14691i
$378$	−5.72327e8	−	2.71865e9i	−0.0280335	−	0.133164i
$379$	2.50361e10			1.21341			0.606707	−	0.794925i	$-0.292490\pi$
$379$	2.50361e10			1.21341			0.606707	+	0.794925i	$0.292490\pi$
$380$	1.84291e9	+	3.19201e9i	0.0883831	+	0.153084i
$381$	−1.67989e10	−	9.69885e9i	−0.797225	−	0.460278i
$382$	−9.83450e9	+	1.70338e10i	−0.461848	+	0.799943i
$383$	3.17591e10	−	1.83361e10i	1.47596	−	0.852144i	0.476324	−	0.879270i	$-0.341969\pi$
$383$	3.17591e10	−	1.83361e10i	1.47596	−	0.852144i	0.999632	+	0.0271262i	$0.00863559\pi$
$384$		−	1.10958e9i		−	0.0510310i
$385$	−7.62826e9	−	2.49503e9i	−0.347202	−	0.113562i
$386$	3.04767e10			1.37284
$387$	−3.21113e9	−	5.56184e9i	−0.143158	−	0.247956i
$388$	1.46899e10	+	8.48122e9i	0.648175	+	0.374224i
$389$	−8.22463e9	+	1.42455e10i	−0.359185	+	0.622126i	−0.987825	−	0.155570i	$-0.950279\pi$
$389$	−8.22463e9	+	1.42455e10i	−0.359185	+	0.622126i	0.628640	+	0.777696i	$0.283612\pi$
$390$	−2.99536e9	+	1.72937e9i	−0.129477	+	0.0747533i
$391$			3.09903e10i			1.32592i
$392$	−6.73474e9	−	4.93333e9i	−0.285218	−	0.208928i
$393$	1.64892e10			0.691243
$394$	2.79955e9	+	4.84897e9i	0.116173	+	0.201217i
$395$	3.75855e9	+	2.17000e9i	0.154394	+	0.0891396i
$396$	1.49410e9	−	2.58786e9i	0.0607575	−	0.105235i
$397$	2.00693e10	−	1.15870e10i	0.807923	−	0.466454i	−0.0383113	−	0.999266i	$-0.512198\pi$
$397$	2.00693e10	−	1.15870e10i	0.807923	−	0.466454i	0.846234	+	0.532812i	$0.178865\pi$
$398$			2.01264e10i			0.802112i
$399$	−3.20974e9	+	9.81339e9i	−0.126642	+	0.387193i
$400$	4.79335e9			0.187240
$401$	−1.85283e10	−	3.20919e10i	−0.716568	−	1.24113i	−0.962352	−	0.271807i	$-0.912379\pi$
$401$	−1.85283e10	−	3.20919e10i	−0.716568	−	1.24113i	0.245784	−	0.969325i	$-0.420955\pi$
$402$	−1.28629e10	−	7.42641e9i	−0.492533	−	0.284364i
$403$	−1.14834e10	+	1.98898e10i	−0.435360	+	0.754066i
$404$	−1.15523e10	+	6.66974e9i	−0.433655	+	0.250371i
$405$		−	1.49778e9i		−	0.0556710i
$406$	−2.95012e10	+	6.21054e9i	−1.08576	+	0.228573i
$407$	1.15050e10			0.419283
$408$	2.14147e9	+	3.70914e9i	0.0772808	+	0.133854i
$409$	−2.36712e10	−	1.36666e10i	−0.845915	−	0.488389i	0.0133555	−	0.999911i	$-0.495749\pi$
$409$	−2.36712e10	−	1.36666e10i	−0.845915	−	0.488389i	−0.859270	+	0.511522i	$0.829082\pi$
$410$	−1.41388e9	+	2.44892e9i	−0.0500355	+	0.0866640i
$411$	9.40758e9	−	5.43147e9i	0.329694	−	0.190349i
$412$			8.87405e8i			0.0307987i
$413$	2.59431e10	−	2.32678e10i	0.891707	−	0.799752i
$414$	1.21249e10			0.412739
$415$	−7.35076e9	−	1.27319e10i	−0.247822	−	0.429240i
$416$	−3.35115e9	−	1.93479e9i	−0.111898	−	0.0646041i
$417$	9.55189e9	−	1.65444e10i	0.315897	−	0.547149i
$418$	−9.61745e9	+	5.55264e9i	−0.315032	+	0.181884i
$419$			2.67578e10i			0.868150i	0.900877	+	0.434075i	$0.142925\pi$
$419$			2.67578e10i			0.868150i	−0.900877	+	0.434075i	$0.857075\pi$
$420$	−3.00501e9	−	3.35052e9i	−0.0965714	−	0.107675i
$421$	1.39300e10			0.443427			0.221714	−	0.975112i	$-0.428835\pi$
$421$	1.39300e10			0.443427			0.221714	+	0.975112i	$0.428835\pi$
$422$	1.14894e10	+	1.99003e10i	0.362283	+	0.627493i
$423$	−8.59738e9	−	4.96370e9i	−0.268537	−	0.155040i
$424$	−2.10695e9	+	3.64934e9i	−0.0651914	+	0.112915i
$425$	−1.60233e10	+	9.25106e9i	−0.491130	+	0.283554i
$426$			1.40246e10i			0.425845i
$427$	5.04165e9	+	2.39487e10i	0.151656	+	0.720395i
$428$	1.49946e10			0.446849
$429$	−5.21056e9	−	9.02496e9i	−0.153835	−	0.266450i
$430$	−9.01003e9	−	5.20194e9i	−0.263544	−	0.152157i
$431$	1.89667e10	−	3.28513e10i	0.549646	−	0.952014i	−0.448653	−	0.893706i	$-0.648096\pi$
$431$	1.89667e10	−	3.28513e10i	0.549646	−	0.952014i	0.998299	−	0.0583083i	$-0.0185706\pi$
$432$	1.45119e9	−	8.37844e8i	0.0416667	−	0.0240563i
$433$		−	6.34652e10i		−	1.80544i	−0.430225	−	0.902721i	$-0.641566\pi$
$433$		−	6.34652e10i		−	1.80544i	0.430225	−	0.902721i	$-0.358434\pi$
$434$	−2.84046e10	−	9.29050e9i	−0.800625	−	0.261867i
$435$	−1.62530e10			−0.453917
$436$	6.84185e9	+	1.18504e10i	0.189333	+	0.327935i
$437$	−3.90235e10	−	2.25302e10i	−1.07004	−	0.617788i
$438$	−1.34297e9	+	2.32609e9i	−0.0364897	+	0.0632019i
$439$	−1.16119e10	+	6.70416e9i	−0.312642	+	0.180504i	−0.648108	−	0.761548i	$-0.724439\pi$
$439$	−1.16119e10	+	6.70416e9i	−0.312642	+	0.180504i	0.335466	+	0.942052i	$0.391106\pi$
$440$		−	4.84081e9i		−	0.129154i
$441$	1.36676e9	−	1.25333e10i	0.0361359	−	0.331369i
$442$	1.49364e10			0.391342
$443$	1.04656e10	+	1.81270e10i	0.271738	+	0.470665i	0.969307	−	0.245853i	$-0.0790681\pi$
$443$	1.04656e10	+	1.81270e10i	0.271738	+	0.470665i	−0.697569	+	0.716518i	$0.745735\pi$
$444$	5.58725e9	+	3.22580e9i	0.143769	+	0.0830052i
$445$	−3.55251e9	+	6.15313e9i	−0.0905931	+	0.156912i
$446$	−4.65637e10	+	2.68836e10i	−1.17682	+	0.679435i
$447$			3.47764e10i			0.871074i
$448$	1.56532e9	−	4.78577e9i	0.0388590	−	0.118806i
$449$	−1.59276e10			−0.391891			−0.195945	−	0.980615i	$-0.562778\pi$
$449$	−1.59276e10			−0.391891			−0.195945	+	0.980615i	$0.562778\pi$
$450$	3.61945e9	+	6.26907e9i	0.0882658	+	0.152881i
$451$	−7.37853e9	−	4.26000e9i	−0.178346	−	0.102968i
$452$	2.51648e9	−	4.35867e9i	0.0602892	−	0.104424i
$453$	−2.41560e10	+	1.39464e10i	−0.573629	+	0.331185i
$454$		−	2.29529e10i		−	0.540274i
$455$	−1.53591e10	+	3.23337e9i	−0.358360	+	0.0754415i
$456$	−6.22747e9			−0.144030
$457$	−4.01471e10	−	6.95369e10i	−0.920428	−	1.59423i	−0.798754	−	0.601657i	$-0.794507\pi$
$457$	−4.01471e10	−	6.95369e10i	−0.920428	−	1.59423i	−0.121673	−	0.992570i	$-0.538826\pi$
$458$	−2.02218e10	−	1.16751e10i	−0.459576	−	0.265337i
$459$	−3.23404e9	+	5.60153e9i	−0.0728610	+	0.126199i
$460$	1.70104e10	−	9.82097e9i	0.379913	−	0.219343i
$461$			4.04801e10i			0.896269i	0.893966	+	0.448134i	$0.147911\pi$
$461$			4.04801e10i			0.896269i	−0.893966	+	0.448134i	$0.852089\pi$
$462$	1.00950e10	−	9.05403e9i	0.221585	−	0.198735i
$463$	4.08946e10			0.889902			0.444951	−	0.895555i	$-0.353221\pi$
$463$	4.08946e10			0.889902			0.444951	+	0.895555i	$0.353221\pi$
$464$	−9.09176e9	−	1.57474e10i	−0.196145	−	0.339732i
$465$	−1.39530e10	−	8.05576e9i	−0.298439	−	0.172304i
$466$	1.52109e10	−	2.63460e10i	0.322560	−	0.558690i
$467$	7.76552e10	−	4.48342e10i	1.63269	−	0.942632i	0.649427	−	0.760424i	$-0.275009\pi$
$467$	7.76552e10	−	4.48342e10i	1.63269	−	0.942632i	0.983260	−	0.182208i	$-0.0583245\pi$
$468$		−	5.84382e9i		−	0.121819i
$469$	−4.50028e10	−	5.01772e10i	−0.930141	−	1.03709i
$470$	−1.60821e10			−0.329573
$471$	2.09456e10	+	3.62788e10i	0.425606	+	0.737172i
$472$	1.82029e10	+	1.05095e10i	0.366752	+	0.211745i
$473$	1.56733e10	−	2.71470e10i	0.313124	−	0.542347i
$474$	−6.35036e9	+	3.66638e9i	−0.125801	+	0.0726313i
$475$		−	2.69024e10i		−	0.528465i
$476$	4.00386e9	+	1.90190e10i	0.0779922	+	0.370476i
$477$	−6.36381e9			−0.122926
$478$	1.86892e9	+	3.23706e9i	0.0357996	+	0.0620068i
$479$	−7.72751e10	−	4.46148e10i	−1.46790	−	0.847495i	−0.468550	−	0.883437i	$-0.655224\pi$
$479$	−7.72751e10	−	4.46148e10i	−1.46790	−	0.847495i	−0.999354	+	0.0359419i	$0.988557\pi$
$480$	1.35728e9	−	2.35088e9i	0.0255685	−	0.0442860i
$481$	1.94851e10	−	1.12497e10i	0.364017	−	0.210165i
$482$		−	3.08475e10i		−	0.571520i
$483$	5.22962e10	+	1.71049e10i	0.960907	+	0.314291i
$484$	−1.28527e10			−0.234214
$485$	2.07491e10	+	3.59385e10i	0.375001	+	0.649521i
$486$	2.19158e9	+	1.26531e9i	0.0392837	+	0.0226805i
$487$	−4.27471e10	+	7.40401e10i	−0.759959	+	1.31629i	0.182911	+	0.983129i	$0.441448\pi$
$487$	−4.27471e10	+	7.40401e10i	−0.759959	+	1.31629i	−0.942871	+	0.333159i	$0.891885\pi$
$488$	−1.27836e10	+	7.38059e9i	−0.225410	+	0.130140i
$489$			5.87746e10i			1.02791i
$490$	−8.23433e9	−	1.86905e10i	−0.142838	−	0.324218i
$491$	9.48434e9			0.163185			0.0815927	−	0.996666i	$-0.473999\pi$
$491$	9.48434e9			0.163185			0.0815927	+	0.996666i	$0.473999\pi$
$492$	−2.38886e9	−	4.13763e9i	−0.0407691	−	0.0706141i
$493$	6.07843e10	+	3.50938e10i	1.02897	+	0.594078i
$494$	−1.08589e10	+	1.88081e10i	−0.182338	+	0.315819i
$495$	6.33115e9	−	3.65529e9i	0.105454	−	0.0608837i
$496$		−	1.80252e10i		−	0.297820i
$497$	−1.97849e10	+	6.04899e10i	−0.324271	+	0.991420i
$498$	2.48393e10			0.403852
$499$	9.19732e9	+	1.59302e10i	0.148340	+	0.256933i	0.930614	−	0.366002i	$-0.119274\pi$
$499$	9.19732e9	+	1.59302e10i	0.148340	+	0.256933i	−0.782274	+	0.622935i	$0.785940\pi$
$500$	2.37155e10	+	1.36921e10i	0.379448	+	0.219074i
$501$	1.86212e10	−	3.22529e10i	0.295568	−	0.511939i
$502$	−5.17295e9	+	2.98661e9i	−0.0814561	+	0.0470287i
$503$		−	2.57417e10i		−	0.402128i	−0.979578	−	0.201064i	$-0.935560\pi$
$503$		−	2.57417e10i		−	0.402128i	0.979578	−	0.201064i	$-0.0644400\pi$
$504$	7.44114e9	−	1.56650e9i	0.115323	−	0.0242777i
$505$	−3.26348e10			−0.501782
$506$	2.95904e10	+	5.12520e10i	0.451386	+	0.781824i
$507$	1.53876e10	+	8.88405e9i	0.232884	+	0.134456i
$508$	2.65464e10	−	4.59797e10i	0.398613	−	0.690417i
$509$	1.30008e9	−	7.50604e8i	0.0193687	−	0.0111825i	−0.490284	−	0.871563i	$-0.663107\pi$
$509$	1.30008e9	−	7.50604e8i	0.0193687	−	0.0111825i	0.509653	+	0.860380i	$0.329774\pi$
$510$			1.04781e10i			0.154883i
$511$	−9.07390e9	+	8.13818e9i	−0.133079	+	0.119356i
$512$	3.03700e9			0.0441942
$513$	−4.70235e9	−	8.14472e9i	−0.0678963	−	0.117600i
$514$	−1.94630e8	−	1.12369e8i	−0.00278841	−	0.00160989i
$515$	−1.08551e9	+	1.88016e9i	−0.0154314	+	0.0267279i
$516$	1.52231e10	−	8.78908e9i	0.214736	−	0.123978i
$517$		−	4.84550e10i		−	0.678229i
$518$	1.95478e10	+	2.17954e10i	0.271506	+	0.302723i
$519$	−4.05684e10			−0.559138
$520$	−4.73341e9	−	8.19851e9i	−0.0647383	−	0.112130i
$521$	7.29061e10	+	4.20923e10i	0.989493	+	0.571284i	0.905123	−	0.425150i	$-0.139779\pi$
$521$	7.29061e10	+	4.20923e10i	0.989493	+	0.571284i	0.0843704	+	0.996434i	$0.473112\pi$
$522$	1.37304e10	−	2.37817e10i	0.184927	−	0.320303i
$523$	6.98087e10	−	4.03041e10i	0.933045	−	0.538694i	0.0452718	−	0.998975i	$-0.485585\pi$
$523$	6.98087e10	−	4.03041e10i	0.933045	−	0.538694i	0.887773	+	0.460281i	$0.152251\pi$
$524$			4.51322e10i			0.598634i
$525$	6.76721e9	+	3.21454e10i	0.0890784	+	0.423138i
$526$	4.34254e10			0.567284
$527$	3.47883e10	+	6.02551e10i	0.451015	+	0.781181i
$528$	7.08316e9	+	4.08946e9i	0.0911363	+	0.0526176i
$529$	−8.09095e10	+	1.40139e11i	−1.03318	+	1.78952i
$530$	−8.92803e9	+	5.15460e9i	−0.113149	+	0.0653268i
$531$			3.17427e10i			0.399270i
$532$	−2.68599e10	−	8.78528e9i	−0.335319	−	0.109675i
$533$	−1.66619e10			−0.206451
$534$	−6.00224e9	−	1.03962e10i	−0.0738156	−	0.127852i
$535$	3.17693e10	+	1.83420e10i	0.387786	+	0.223889i
$536$	2.03266e10	−	3.52067e10i	0.246267	−	0.426546i
$537$	−2.45465e10	+	1.41719e10i	−0.295184	+	0.170425i
$538$		−	5.96941e10i		−	0.712528i
$539$	5.63141e10	−	2.48098e10i	0.667209	−	0.293947i
$540$	4.09953e9			0.0482125
$541$	−2.92250e10	−	5.06192e10i	−0.341166	−	0.590917i	0.643484	−	0.765460i	$-0.277488\pi$
$541$	−2.92250e10	−	5.06192e10i	−0.341166	−	0.590917i	−0.984650	+	0.174543i	$0.944155\pi$
$542$	−7.85986e10	−	4.53789e10i	−0.910788	−	0.525844i
$543$	−2.31042e10	+	4.00177e10i	−0.265761	+	0.460312i
$544$	−1.01522e10	+	5.86135e9i	−0.115921	+	0.0669271i
$545$			3.34769e10i			0.379454i
$546$	8.24406e9	−	2.52052e10i	0.0927620	−	0.283609i
$547$	−2.79718e10			−0.312444			−0.156222	−	0.987722i	$-0.549931\pi$
$547$	−2.79718e10			−0.312444			−0.156222	+	0.987722i	$0.549931\pi$
$548$	1.48663e10	+	2.57492e10i	0.164847	+	0.285523i
$549$	−1.93057e10	−	1.11462e10i	−0.212518	−	0.122697i
$550$	−1.76663e10	+	3.05990e10i	−0.193061	+	0.334392i
$551$	−8.83814e10	+	5.10270e10i	−0.958859	+	0.553597i
$552$			3.31866e10i			0.357442i
$553$	−3.25622e10	+	6.85495e9i	−0.348188	+	0.0733000i
$554$	−4.24418e10			−0.450562
$555$	7.89185e9	+	1.36691e10i	0.0831777	+	0.144068i
$556$	4.52830e10	+	2.61442e10i	0.473845	+	0.273575i
$557$	4.08184e10	−	7.06996e10i	0.424068	−	0.734507i	−0.572265	−	0.820069i	$-0.693935\pi$
$557$	4.08184e10	−	7.06996e10i	0.424068	−	0.734507i	0.996333	+	0.0855617i	$0.0272685\pi$
$558$	2.35746e10	−	1.36108e10i	0.243169	−	0.140394i
$559$		−	6.13024e10i		−	0.627813i
$560$	9.17061e9	−	8.22492e9i	0.0932494	−	0.0836333i
$561$	−3.15703e10			−0.318734
$562$	−9.07736e9	−	1.57225e10i	−0.0909944	−	0.157607i
$563$	3.62218e10	+	2.09126e10i	0.360525	+	0.208149i	0.669311	−	0.742982i	$-0.266589\pi$
$563$	3.62218e10	+	2.09126e10i	0.360525	+	0.208149i	−0.308786	+	0.951132i	$0.599923\pi$
$564$	1.35860e10	−	2.35316e10i	0.134269	−	0.232560i
$565$	1.06634e10	−	6.15651e9i	0.104641	−	0.0604144i
$566$		−	5.15340e10i		−	0.502144i
$567$	7.66757e9	+	8.54918e9i	0.0741866	+	0.0827165i
$568$	−3.83863e10			−0.368793
$569$	4.62699e10	+	8.01418e10i	0.441417	+	0.764558i	0.997795	−	0.0663722i	$-0.0211425\pi$
$569$	4.62699e10	+	8.01418e10i	0.441417	+	0.764558i	−0.556377	+	0.830930i	$0.687809\pi$
$570$	−1.31942e10	−	7.61768e9i	−0.124993	−	0.0721645i
$571$	−1.87831e10	+	3.25333e10i	−0.176695	+	0.306044i	−0.940746	−	0.339111i	$-0.889874\pi$
$571$	−1.87831e10	+	3.25333e10i	−0.176695	+	0.306044i	0.764052	+	0.645155i	$0.223207\pi$
$572$	2.47019e10	−	1.42617e10i	0.230753	−	0.133225i
$573$		−	8.13021e10i		−	0.754194i
$574$	−4.46641e9	−	2.12162e10i	−0.0411444	−	0.195443i
$575$	−1.43365e11			−1.31151
$576$	2.29324e9	+	3.97200e9i	0.0208333	+	0.0360844i
$577$	1.42827e11	+	8.24610e10i	1.28856	+	0.743952i	0.978398	−	0.206730i	$-0.0662822\pi$
$577$	1.42827e11	+	8.24610e10i	1.28856	+	0.743952i	0.310165	+	0.950683i	$0.399616\pi$
$578$	−1.68363e10	+	2.91613e10i	−0.150846	+	0.261273i
$579$	−1.09098e11	+	6.29879e10i	−0.970741	+	0.560458i
$580$		−	4.44856e10i		−	0.393104i
$581$	1.07135e11	+	3.50416e10i	0.940218	+	0.307524i
$582$	−7.01145e10			−0.611105
$583$	−1.55307e10	−	2.69000e10i	−0.134436	−	0.232851i
$584$	−6.36667e9	−	3.67580e9i	−0.0547345	−	0.0316010i
$585$	7.14839e9	−	1.23814e10i	0.0610358	−	0.105717i
$586$	9.62986e10	−	5.55980e10i	0.816638	−	0.471486i
$587$		−	1.39888e11i		−	1.17823i	−0.808051	−	0.589113i	$-0.799477\pi$
$587$		−	1.39888e11i		−	1.17823i	0.808051	−	0.589113i	$-0.200523\pi$
$588$	3.43045e10	+	3.74092e9i	0.286974	+	0.0312946i
$589$	−1.01166e11			−0.840566
$590$	2.57112e10	+	4.45330e10i	0.212184	+	0.367514i
$591$	−2.00433e10	−	1.15720e10i	−0.164293	−	0.0948545i
$592$	−8.82923e9	+	1.52927e10i	−0.0718846	+	0.124508i
$593$	1.27088e11	−	7.33743e10i	1.02775	−	0.593369i	0.111408	−	0.993775i	$-0.464464\pi$
$593$	1.27088e11	−	7.33743e10i	1.02775	−	0.593369i	0.916338	+	0.400405i	$0.131131\pi$
$594$			1.23518e10i			0.0992166i
$595$	−1.47818e10	+	4.51935e10i	−0.117940	+	0.360586i
$596$	−9.51854e10			−0.754372
$597$	−4.15965e10	−	7.20472e10i	−0.327461	−	0.567179i
$598$	1.00230e11	+	5.78677e10i	0.783777	+	0.452514i
$599$	9.17780e10	−	1.58964e11i	0.712905	−	1.23479i	−0.250857	−	0.968024i	$-0.580713\pi$
$599$	9.17780e10	−	1.58964e11i	0.712905	−	1.23479i	0.963762	−	0.266763i	$-0.0859542\pi$
$600$	−1.71589e10	+	9.90668e9i	−0.132399	+	0.0764404i
$601$		−	1.07731e11i		−	0.825740i	−0.910790	−	0.412870i	$-0.864526\pi$
$601$		−	1.07731e11i		−	0.825740i	0.910790	−	0.412870i	$-0.135474\pi$
$602$	7.80585e10	−	1.64328e10i	0.594339	−	0.125119i
$603$	6.13944e10			0.464365
$604$	−3.81724e10	−	6.61165e10i	−0.286815	−	0.496778i
$605$	−2.72311e10	−	1.57219e10i	−0.203256	−	0.117350i
$606$	2.75695e10	−	4.77517e10i	0.204427	−	0.354078i
$607$	−1.56874e11	+	9.05712e10i	−1.15557	+	0.667168i	−0.950238	−	0.311524i	$-0.899161\pi$
$607$	−1.56874e11	+	9.05712e10i	−1.15557	+	0.667168i	−0.205331	+	0.978693i	$0.565827\pi$
$608$		−	1.70450e10i		−	0.124733i
$609$	9.27704e10	−	8.32038e10i	0.674435	−	0.604886i
$610$	−3.61129e10			−0.260821
$611$	−4.73800e10	−	8.20645e10i	−0.339962	−	0.588831i
$612$	−1.53318e10	−	8.85180e9i	−0.109292	−	0.0630995i
$613$	−3.20819e10	+	5.55675e10i	−0.227205	+	0.393531i	−0.956979	−	0.290158i	$-0.906292\pi$
$613$	−3.20819e10	+	5.55675e10i	−0.227205	+	0.393531i	0.729774	+	0.683689i	$0.239625\pi$
$614$	−1.17032e11	+	6.75687e10i	−0.823442	+	0.475414i
$615$		−	1.16886e10i		−	0.0817076i
$616$	2.47815e10	+	2.76308e10i	0.172109	+	0.191898i
$617$	−2.71684e10			−0.187466			−0.0937331	−	0.995597i	$-0.529880\pi$
$617$	−2.71684e10			−0.187466			−0.0937331	+	0.995597i	$0.529880\pi$
$618$	−1.83405e9	−	3.17667e9i	−0.0125735	−	0.0217780i
$619$	1.21053e11	+	6.98899e10i	0.824542	+	0.476049i	0.851980	−	0.523574i	$-0.175402\pi$
$619$	1.21053e11	+	6.98899e10i	0.824542	+	0.476049i	−0.0274385	+	0.999623i	$0.508735\pi$
$620$	2.20491e10	−	3.81902e10i	0.149219	−	0.258455i
$621$	−4.34037e10	+	2.50591e10i	−0.291851	+	0.168500i
$622$			1.54693e11i			1.03349i
$623$	−1.12223e10	−	5.33077e10i	−0.0744951	−	0.353865i
$624$	1.59949e10			0.105498
$625$	−2.36436e10	−	4.09520e10i	−0.154951	−	0.268383i
$626$	−9.60955e10	−	5.54808e10i	−0.625757	−	0.361281i
$627$	2.29519e10	−	3.97539e10i	0.148508	−	0.257223i
$628$	−9.92974e10	+	5.73294e10i	−0.638410	+	0.368586i
$629$		−	6.81610e10i		−	0.435445i
$630$	1.76818e10	+	5.78333e9i	0.112245	+	0.0367127i
$631$	−2.76921e10			−0.174678			−0.0873391	−	0.996179i	$-0.527836\pi$
$631$	−2.76921e10			−0.174678			−0.0873391	+	0.996179i	$0.527836\pi$
$632$	−1.00351e10	−	1.73814e10i	−0.0629006	−	0.108947i
$633$	−8.22580e10	−	4.74917e10i	−0.512346	−	0.295803i
$634$	−8.72314e10	+	1.51089e11i	−0.539903	+	0.935140i
$635$	1.12488e11	−	6.49452e10i	0.691852	−	0.399441i
$636$		−	1.74182e10i		−	0.106457i
$637$	7.11154e10	−	9.70832e10i	0.431923	−	0.589639i
$638$	1.34034e11			0.808970
$639$	−2.89854e10	−	5.02042e10i	−0.173851	−	0.301118i
$640$	6.43453e9	+	3.71498e9i	0.0383528	+	0.0221430i
$641$	−9.69671e10	+	1.67952e11i	−0.574371	+	0.994840i	0.421739	+	0.906717i	$0.361420\pi$
$641$	−9.69671e10	+	1.67952e11i	−0.574371	+	0.994840i	−0.996110	+	0.0881223i	$0.971913\pi$
$642$	−5.36767e10	+	3.09903e10i	−0.315970	+	0.182425i
$643$		−	2.81542e11i		−	1.64702i	−0.567302	−	0.823510i	$-0.692013\pi$
$643$		−	2.81542e11i		−	1.64702i	0.567302	−	0.823510i	$-0.307987\pi$
$644$	−4.68173e10	+	1.43138e11i	−0.272184	+	0.832170i
$645$	4.30046e10			0.248471
$646$	3.28965e10	+	5.69784e10i	0.188895	+	0.327175i
$647$	−1.81931e11	−	1.05038e11i	−1.03822	−	0.599417i	−0.118891	−	0.992907i	$-0.537934\pi$
$647$	−1.81931e11	−	1.05038e11i	−1.03822	−	0.599417i	−0.919329	+	0.393491i	$0.871267\pi$
$648$	−3.46324e9	+	5.99851e9i	−0.0196419	+	0.0340207i
$649$	−1.34177e11	+	7.74672e10i	−0.756309	+	0.436655i
$650$			6.90975e10i			0.387087i
$651$	1.20882e11	−	2.54479e10i	0.673034	−	0.141686i
$652$	−1.60870e11			−0.890195
$653$	9.58283e10	+	1.65979e11i	0.527037	+	0.912855i	0.999504	+	0.0315062i	$0.0100304\pi$
$653$	9.58283e10	+	1.65979e11i	0.527037	+	0.912855i	−0.472467	+	0.881349i	$0.656636\pi$
$654$	−4.89839e10	−	2.82809e10i	−0.267758	−	0.154590i
$655$	−5.52074e10	+	9.56221e10i	−0.299939	+	0.519509i
$656$	1.13250e10	−	6.53848e9i	0.0611536	−	0.0353071i
$657$		−	1.11024e10i		−	0.0595874i
$658$	9.17949e10	−	8.23288e10i	0.489683	−	0.439186i
$659$	−3.45275e11			−1.83073			−0.915363	−	0.402629i	$-0.868096\pi$
$659$	−3.45275e11			−1.83073			−0.915363	+	0.402629i	$0.868096\pi$
$660$	1.00048e10	+	1.73288e10i	0.0527269	+	0.0913256i
$661$	3.00609e11	+	1.73557e11i	1.57469	+	0.909150i	0.995581	+	0.0939015i	$0.0299339\pi$
$661$	3.00609e11	+	1.73557e11i	1.57469	+	0.909150i	0.579112	+	0.815248i	$0.303399\pi$
$662$	−1.27643e10	+	2.21084e10i	−0.0664607	+	0.115113i
$663$	−5.34683e10	+	3.08699e10i	−0.276721	+	0.159765i
$664$			6.79870e10i			0.349746i
$665$	−4.61619e10	−	5.14696e10i	−0.236046	−	0.263187i
$666$	−2.66678e10			−0.135547
$667$	2.71926e11	+	4.70990e11i	1.37388	+	2.37963i
$668$	8.82784e10	+	5.09676e10i	0.443352	+	0.255969i
$669$	1.11124e11	−	1.92472e11i	0.554756	−	0.960866i
$670$	8.61324e10	−	4.97286e10i	0.427432	−	0.246778i
$671$		−	1.08807e11i		−	0.536745i
$672$	4.28761e9	+	2.03669e10i	0.0210251	+	0.0998730i
$673$	1.96199e11			0.956391			0.478195	−	0.878253i	$-0.341291\pi$
$673$	1.96199e11			0.956391			0.478195	+	0.878253i	$0.341291\pi$
$674$	−5.31554e10	−	9.20678e10i	−0.257577	−	0.446137i
$675$	−2.59133e10	−	1.49610e10i	−0.124827	−	0.0720687i
$676$	−2.43163e10	+	4.21170e10i	−0.116442	+	0.201684i
$677$	−2.37133e11	+	1.36909e11i	−1.12885	+	0.651743i	−0.943646	−	0.330957i	$-0.892629\pi$
$677$	−2.37133e11	+	1.36909e11i	−1.12885	+	0.651743i	−0.185206	+	0.982700i	$0.559295\pi$
$678$			2.08038e10i			0.0984518i
$679$	−3.02413e11	−	9.89126e10i	−1.42273	−	0.465342i
$680$	−2.86793e10			−0.134132
$681$	4.74380e10	+	8.21651e10i	0.220566	+	0.382031i
$682$	1.15066e11	+	6.64336e10i	0.531877	+	0.307079i
$683$	1.70877e11	−	2.95968e11i	0.785238	−	1.36007i	−0.143619	−	0.989633i	$-0.545874\pi$
$683$	1.70877e11	−	2.95968e11i	0.785238	−	1.36007i	0.928857	−	0.370439i	$-0.120793\pi$
$684$	2.22926e10	−	1.28707e10i	0.101844	−	0.0587999i
$685$			7.27402e10i			0.330379i
$686$	1.42683e11	+	6.45295e10i	0.644280	+	0.291382i
$687$	9.65180e10			0.433293
$688$	2.40563e10	+	4.16668e10i	0.107368	+	0.185967i
$689$	−5.26063e10	−	3.03723e10i	−0.233432	−	0.134772i
$690$	−4.05951e10	+	7.03128e10i	−0.179092	+	0.310197i
$691$	2.54200e11	−	1.46762e11i	1.11497	−	0.643728i	0.174858	−	0.984594i	$-0.444053\pi$
$691$	2.54200e11	−	1.46762e11i	1.11497	−	0.643728i	0.940112	+	0.340865i	$0.110720\pi$
$692$		−	1.11039e11i		−	0.484228i
$693$	−1.74251e10	+	5.32750e10i	−0.0755512	+	0.230988i
$694$	3.63913e10			0.156877
$695$	6.39611e10	+	1.10784e11i	0.274143	+	0.474829i
$696$	6.50921e10	+	3.75809e10i	0.277390	+	0.160151i
$697$	−2.52383e10	+	4.37140e10i	−0.106937	+	0.185221i
$698$	2.44117e11	−	1.40941e11i	1.02843	−	0.593765i
$699$			1.25749e11i			0.526738i
$700$	−8.79842e10	+	1.85223e10i	−0.366448	+	0.0771441i
$701$	3.50386e11			1.45103			0.725513	−	0.688209i	$-0.241603\pi$
$701$	3.50386e11			1.45103			0.725513	+	0.688209i	$0.241603\pi$
$702$	1.20778e10	+	2.09193e10i	0.0497322	+	0.0861388i
$703$	8.58294e10	+	4.95536e10i	0.351410	+	0.202887i
$704$	−1.11931e10	+	1.93871e10i	−0.0455682	+	0.0789264i
$705$	5.75696e10	−	3.32378e10i	0.233043	−	0.134548i
$706$		−	4.78692e10i		−	0.192680i
$707$	1.86276e11	−	1.67067e11i	0.745553	−	0.668670i
$708$	−8.68820e10			−0.345778
$709$	−3.26898e10	−	5.66205e10i	−0.129368	−	0.224072i	0.794064	−	0.607835i	$-0.207962\pi$
$709$	−3.26898e10	−	5.66205e10i	−0.129368	−	0.224072i	−0.923432	+	0.383762i	$0.874628\pi$
$710$	−8.13294e10	−	4.69556e10i	−0.320047	−	0.184779i
$711$	1.51550e10	−	2.62493e10i	0.0593032	−	0.102716i
$712$	2.84551e10	−	1.64285e10i	0.110723	−	0.0639262i
$713$			5.39118e11i			2.08605i
$714$	−5.36405e10	−	5.98080e10i	−0.206395	−	0.230126i
$715$	6.97817e10			0.267004
$716$	−3.87896e10	−	6.71855e10i	−0.147592	−	0.255637i
$717$	−1.33804e10	−	7.72519e9i	−0.0506283	−	0.0292303i
$718$	−1.14212e11	+	1.97820e11i	−0.429746	+	0.744342i
$719$	−4.67029e10	+	2.69639e10i	−0.174754	+	0.100894i	−0.584826	−	0.811159i	$-0.698837\pi$
$719$	−4.67029e10	+	2.69639e10i	−0.174754	+	0.100894i	0.410071	+	0.912053i	$0.365504\pi$
$720$			1.12207e10i			0.0417532i
$721$	−3.42908e9	−	1.62887e10i	−0.0126893	−	0.0602763i
$722$	9.64829e10			0.355060
$723$	6.37542e10	+	1.10426e11i	0.233322	+	0.404126i
$724$	−1.09531e11	−	6.32378e10i	−0.398642	−	0.230156i
$725$	−1.62348e11	+	2.81195e11i	−0.587618	+	1.01778i
$726$	4.60091e10	−	2.65634e10i	0.165614	−	0.0956173i
$727$			2.16859e9i			0.00776319i	0.999992	+	0.00388160i	$0.00123555\pi$
$727$			2.16859e9i			0.00776319i	−0.999992	+	0.00388160i	$0.998764\pi$
$728$	6.89883e10	+	2.25645e10i	0.245612	+	0.0803343i
$729$	−1.04604e10			−0.0370370
$730$	−8.99276e9	−	1.55759e10i	−0.0316666	−	0.0548482i
$731$	−1.60832e11	−	9.28564e10i	−0.563253	−	0.325194i
$732$	3.05078e10	−	5.28410e10i	0.106259	−	0.184046i
$733$	1.06323e11	−	6.13854e10i	0.368307	−	0.212642i	−0.304412	−	0.952541i	$-0.598460\pi$
$733$	1.06323e11	−	6.13854e10i	0.368307	−	0.212642i	0.672718	+	0.739899i	$0.265127\pi$
$734$		−	3.04998e11i		−	1.05078i
$735$	6.81054e10	+	4.98886e10i	0.233363	+	0.170943i
$736$	−9.08339e10			−0.309554
$737$	1.49831e11	+	2.59515e11i	0.507846	+	0.879615i
$738$	1.71030e10	+	9.87440e9i	0.0576562	+	0.0332878i
$739$	−2.53851e10	+	4.39682e10i	−0.0851139	+	0.147422i	−0.905440	−	0.424475i	$-0.860459\pi$
$739$	−2.53851e10	+	4.39682e10i	−0.0851139	+	0.147422i	0.820326	+	0.571896i	$0.193792\pi$
$740$	−3.74132e10	+	2.16005e10i	−0.124766	+	0.0720340i
$741$		−	8.97707e10i		−	0.297757i
$742$	2.45724e10	−	7.51270e10i	0.0810646	−	0.247845i
$743$	−2.75538e11			−0.904122			−0.452061	−	0.891987i	$-0.649311\pi$
$743$	−2.75538e11			−0.904122			−0.452061	+	0.891987i	$0.649311\pi$
$744$	3.72537e10	+	6.45254e10i	0.121585	+	0.210591i
$745$	−2.01670e11	−	1.16435e11i	−0.654662	−	0.377969i
$746$	−4.68768e10	+	8.11930e10i	−0.151357	+	0.262158i
$747$	−8.89181e10	+	5.13369e10i	−0.285567	+	0.164872i
$748$		−	8.64102e10i		−	0.276031i
$749$	−2.75234e11	+	5.79418e10i	−0.874529	+	0.184105i
$750$	−1.13193e11			−0.357747
$751$	−1.90358e11	−	3.29709e11i	−0.598426	−	1.03650i	−0.993054	−	0.117663i	$-0.962460\pi$
$751$	−1.90358e11	−	3.29709e11i	−0.598426	−	1.03650i	0.394627	−	0.918841i	$-0.370874\pi$
$752$	6.44076e10	+	3.71858e10i	0.201403	+	0.116280i
$753$	1.23452e10	−	2.13825e10i	0.0383988	−	0.0665087i
$754$	2.27003e11	−	1.31060e11i	0.702339	−	0.405496i
$755$		−	1.86776e11i		−	0.574821i
$756$	−2.33997e10	+	2.09867e10i	−0.0716346	+	0.0642475i
$757$	1.59448e11			0.485552			0.242776	−	0.970082i	$-0.421942\pi$
$757$	1.59448e11			0.485552			0.242776	+	0.970082i	$0.421942\pi$
$758$	−1.41625e11	−	2.45302e11i	−0.429007	−	0.743062i
$759$	−2.11851e11	−	1.22312e11i	−0.638356	−	0.368555i
$760$	2.08501e10	−	3.61135e10i	0.0624963	−	0.108247i
$761$	−9.43701e10	+	5.44846e10i	−0.281382	+	0.162456i	−0.634049	−	0.773293i	$-0.718608\pi$
$761$	−9.43701e10	+	5.44846e10i	−0.281382	+	0.162456i	0.352667	+	0.935749i	$0.385275\pi$
$762$			2.19460e11i			0.650932i
$763$	−1.71377e11	−	1.91082e11i	−0.505656	−	0.563796i
$764$	2.22529e11			0.653151
$765$	−2.16557e10	−	3.75088e10i	−0.0632306	−	0.109519i
$766$	−3.59313e11	−	2.07450e11i	−1.04366	−	0.602557i
$767$	−1.51497e11	+	2.62400e11i	−0.437746	+	0.758198i
$768$	−1.08716e10	+	6.27674e9i	−0.0312500	+	0.0180422i
$769$		−	4.45208e11i		−	1.27309i	−0.771241	−	0.636543i	$-0.780364\pi$
$769$		−	4.45208e11i		−	1.27309i	0.771241	−	0.636543i	$-0.219636\pi$
$770$	1.87057e10	+	8.88555e10i	0.0532123	+	0.252767i
$771$	9.28961e8			0.00262894
$772$	−1.72402e11	−	2.98609e11i	−0.485371	−	0.840687i
$773$	2.58785e11	+	1.49409e11i	0.724804	+	0.418466i	0.816518	−	0.577320i	$-0.195901\pi$
$773$	2.58785e11	+	1.49409e11i	0.724804	+	0.418466i	−0.0917145	+	0.995785i	$0.529235\pi$
$774$	−3.63298e10	+	6.29251e10i	−0.101228	+	0.175331i
$775$	−2.78747e11	+	1.60935e11i	−0.772686	+	0.446111i
$776$		−	1.91908e11i		−	0.529232i
$777$	−1.15022e11	−	3.76210e10i	−0.315570	−	0.103216i
$778$	1.86102e11			0.507964
$779$	−3.66969e10	−	6.35609e10i	−0.0996505	−	0.172600i
$780$	3.38887e10	+	1.95656e10i	0.0915537	+	0.0528586i
$781$	1.41476e11	−	2.45044e11i	0.380258	−	0.658627i
$782$	3.03642e11	−	1.75308e11i	0.811960	−	0.468785i
$783$			1.13509e11i			0.301984i
$784$	−1.02392e10	+	9.38939e10i	−0.0271019	+	0.248527i
$785$	−2.80510e11			−0.738703
$786$	−9.32773e10	−	1.61561e11i	−0.244391	−	0.423298i
$787$	−1.30973e11	−	7.56172e10i	−0.341415	−	0.197116i	0.319483	−	0.947592i	$-0.396491\pi$
$787$	−1.30973e11	−	7.56172e10i	−0.341415	−	0.197116i	−0.660897	+	0.750476i	$0.729824\pi$
$788$	3.16733e10	−	5.48598e10i	0.0821464	−	0.142282i
$789$	−1.55451e11	+	8.97497e10i	−0.401130	+	0.231593i
$790$		−	4.91014e10i		−	0.126062i
$791$	−2.93485e10	+	8.97295e10i	−0.0749688	+	0.229208i
$792$	−3.38077e10			−0.0859241
$793$	−1.06393e11	−	1.84279e11i	−0.269043	−	0.465996i
$794$	−2.27058e11	−	1.31092e11i	−0.571288	−	0.329833i
$795$	2.13066e10	−	3.69041e10i	0.0533391	−	0.0923861i
$796$	1.97198e11	−	1.13852e11i	0.491191	−	0.283589i
$797$			6.06360e11i			1.50279i	0.659855	+	0.751393i	$0.270618\pi$
$797$			6.06360e11i			1.50279i	−0.659855	+	0.751393i	$0.729382\pi$
$798$	1.14308e11	−	2.40640e10i	0.281881	−	0.0593412i
$799$	−2.87071e11			−0.704372
$800$	−2.71153e10	−	4.69650e10i	−0.0661994	−	0.114661i
$801$	4.29728e10	+	2.48103e10i	0.104391	+	0.0602702i
$802$	−2.09623e11	+	3.63078e11i	−0.506690	+	0.877613i
$803$	4.69299e10	−	2.70950e10i	0.112872	−	0.0651669i
$804$			1.68041e11i			0.402152i
$805$	−2.74285e11	+	2.46000e11i	−0.653157	+	0.585802i
$806$	2.59839e11			0.615692
$807$	1.23373e11	+	2.13688e11i	0.290888	+	0.503833i
$808$	1.30700e11	+	7.54595e10i	0.306640	+	0.177039i
$809$	2.91061e11	−	5.04133e11i	0.679501	−	1.17693i	−0.295630	−	0.955302i	$-0.595530\pi$
$809$	2.91061e11	−	5.04133e11i	0.679501	−	1.17693i	0.975131	−	0.221628i	$-0.0711370\pi$
$810$	−1.46752e10	+	8.47274e9i	−0.0340914	+	0.0196827i
$811$			5.74358e10i			0.132770i	0.997794	+	0.0663849i	$0.0211465\pi$
$811$			5.74358e10i			0.132770i	−0.997794	+	0.0663849i	$0.978853\pi$
$812$	2.27734e11	+	2.53919e11i	0.523847	+	0.584078i
$813$	3.75149e11			0.858699
$814$	−6.50819e10	−	1.12725e11i	−0.148239	−	0.256758i
$815$	−3.40837e11	−	1.96783e11i	−0.772533	−	0.446022i
$816$	2.42280e10	−	4.19641e10i	0.0546458	−	0.0946492i
$817$	2.33853e11	−	1.35015e11i	0.524873	−	0.303035i
$818$			3.09239e11i			0.690687i
$819$	2.25815e10	+	1.07266e11i	0.0501900	+	0.238411i
$820$	3.19925e10			0.0707608
$821$	2.45137e11	+	4.24590e11i	0.539556	+	0.934539i	0.998928	+	0.0462948i	$0.0147414\pi$
$821$	2.45137e11	+	4.24590e11i	0.539556	+	0.934539i	−0.459371	+	0.888244i	$0.651925\pi$
$822$	−1.06435e11	−	6.14501e10i	−0.233129	−	0.134597i
$823$	1.09655e11	−	1.89929e11i	0.239018	−	0.413992i	−0.721415	−	0.692503i	$-0.756508\pi$
$823$	1.09655e11	−	1.89929e11i	0.239018	−	0.413992i	0.960433	+	0.278512i	$0.0898411\pi$
$824$	8.69476e9	−	5.01992e9i	0.0188603	−	0.0108890i
$825$		−	1.46048e11i		−	0.315268i
$826$	−3.74734e11	−	1.22567e11i	−0.805012	−	0.263302i
$827$	7.82313e11			1.67247			0.836236	−	0.548370i	$-0.184751\pi$
$827$	7.82313e11			1.67247			0.836236	+	0.548370i	$0.184751\pi$
$828$	−6.85886e10	−	1.18799e11i	−0.145925	−	0.252750i
$829$	−4.69138e11	−	2.70857e11i	−0.993306	−	0.573485i	−0.0870448	−	0.996204i	$-0.527742\pi$
$829$	−4.69138e11	−	2.70857e11i	−0.993306	−	0.573485i	−0.906261	+	0.422719i	$0.861076\pi$
$830$	−8.31643e10	+	1.44045e11i	−0.175236	+	0.303519i
$831$	1.51930e11	−	8.77168e10i	0.318595	−	0.183941i
$832$			4.37792e10i			0.0913639i
$833$	−1.46986e11	−	3.33632e11i	−0.305277	−	0.692927i
$834$	−2.16135e11			−0.446745
$835$	1.24691e11	+	2.15971e11i	0.256501	+	0.444273i
$836$	1.08809e11	+	6.28209e10i	0.222761	+	0.128611i
$837$	−5.62605e10	+	9.74461e10i	−0.114631	+	0.198547i
$838$	2.62172e11	−	1.51365e11i	0.531631	−	0.306937i
$839$			8.56628e11i			1.72880i	0.502806	+	0.864399i	$0.332301\pi$
$839$			8.56628e11i			1.72880i	−0.502806	+	0.864399i	$0.667699\pi$
$840$	−1.58294e10	+	4.83964e10i	−0.0317941	+	0.0972066i
$841$	7.31486e11			1.46225
$842$	−7.88000e10	−	1.36486e11i	−0.156775	−	0.271543i
$843$	6.49890e10	+	3.75214e10i	0.128685	+	0.0742966i
$844$	1.29988e11	−	2.25146e11i	0.256173	−	0.443705i
$845$	−1.03038e11	+	5.94892e10i	−0.202103	+	0.116684i
$846$			1.12316e11i			0.219260i
$847$	2.35917e11	−	4.96649e10i	0.458380	−	0.0964975i
$848$	4.76748e10			0.0921946
$849$	1.06508e11	+	1.84478e11i	0.204999	+	0.355069i
$850$	1.81283e11	+	1.04664e11i	0.347281	+	0.200503i
$851$	2.64074e11	−	4.57390e11i	0.503510	−	0.872105i
$852$	1.37412e11	−	7.93351e10i	0.260776	−	0.150559i
$853$			1.34602e11i			0.254246i	0.991887	+	0.127123i	$0.0405743\pi$
$853$			1.34602e11i			0.254246i	−0.991887	+	0.127123i	$0.959426\pi$
$854$	2.06129e11	−	1.84872e11i	0.387531	−	0.347568i
$855$	6.29756e10			0.117844
$856$	−8.48224e10	−	1.46917e11i	−0.157985	−	0.273638i
$857$	1.87689e11	+	1.08362e11i	0.347949	+	0.200888i	0.663781	−	0.747927i	$-0.268950\pi$
$857$	1.87689e11	+	1.08362e11i	0.347949	+	0.200888i	−0.315833	+	0.948815i	$0.602284\pi$
$858$	−5.89508e10	+	1.02106e11i	−0.108778	+	0.188409i
$859$	−5.81757e11	+	3.35878e11i	−1.06849	+	0.616891i	−0.927768	−	0.373158i	$-0.878275\pi$
$859$	−5.81757e11	+	3.35878e11i	−1.06849	+	0.616891i	−0.140719	+	0.990050i	$0.544942\pi$
$860$			1.17707e11i			0.215182i
$861$	5.98373e10	+	6.67173e10i	0.108883	+	0.121402i
$862$	−4.29168e11			−0.777316
$863$	−4.55310e11	−	7.88620e11i	−0.820851	−	1.42176i	−0.905049	−	0.425306i	$-0.860166\pi$
$863$	−4.55310e11	−	7.88620e11i	−0.820851	−	1.42176i	0.0841987	−	0.996449i	$-0.473167\pi$
$864$	−1.64183e10	−	9.47912e9i	−0.0294628	−	0.0170103i
$865$	1.35827e11	−	2.35259e11i	0.242617	−	0.420224i
$866$	−6.21829e11	+	3.59013e11i	−1.10560	+	0.638320i
$867$		−	1.39186e11i		−	0.246331i
$868$	6.96525e10	+	3.30862e11i	0.122704	+	0.582864i
$869$	1.47942e11			0.259425
$870$	9.19409e10	+	1.59246e11i	0.160484	+	0.277966i
$871$	5.07515e11	+	2.93014e11i	0.881812	+	0.509114i
$872$	7.74067e10	−	1.34072e11i	0.133879	−	0.231885i
$873$	2.50991e11	−	1.44910e11i	0.432116	−	0.249483i
$874$			5.09801e11i			0.873684i
$875$	−4.88218e11	−	1.59685e11i	−0.832878	−	0.272416i
$876$	3.03879e10			0.0516042
$877$	−2.54114e11	−	4.40139e11i	−0.429567	−	0.744031i	0.567268	−	0.823533i	$-0.308000\pi$
$877$	−2.54114e11	−	4.40139e11i	−0.429567	−	0.744031i	−0.996835	+	0.0795018i	$0.974667\pi$
$878$	1.31374e11	+	7.58489e10i	0.221071	+	0.127635i
$879$	−2.29815e11	+	3.98052e11i	−0.384967	+	0.666782i
$880$	−4.74301e10	+	2.73838e10i	−0.0790903	+	0.0456628i
$881$			7.70244e11i			1.27857i	0.768970	+	0.639285i	$0.220770\pi$
$881$			7.70244e11i			1.27857i	−0.768970	+	0.639285i	$0.779230\pi$
$882$	−1.30533e11	+	5.75077e10i	−0.215697	+	0.0950279i
$883$	1.13977e12			1.87488			0.937440	−	0.348147i	$-0.113189\pi$
$883$	1.13977e12			1.87488			0.937440	+	0.348147i	$0.113189\pi$
$884$	−8.44930e10	−	1.46346e11i	−0.138360	−	0.239647i
$885$	−1.84078e11	−	1.06277e11i	−0.300074	−	0.173248i
$886$	1.18405e11	−	2.05084e11i	0.192148	−	0.332810i
$887$	−2.67833e11	+	1.54633e11i	−0.432682	+	0.249809i	−0.700489	−	0.713664i	$-0.747035\pi$
$887$	−2.67833e11	+	1.54633e11i	−0.432682	+	0.249809i	0.267807	+	0.963473i	$0.413701\pi$
$888$		−	7.29915e10i		−	0.117387i
$889$	−3.09599e11	+	9.46560e11i	−0.495670	+	1.51545i
$890$	8.03841e10			0.128118
$891$	−2.55282e10	−	4.42161e10i	−0.0405050	−	0.0701568i
$892$	5.26809e11	+	3.04153e11i	0.832134	+	0.480433i
$893$	2.08703e11	−	3.61484e11i	0.328188	−	0.568439i
$894$	3.40738e11	−	1.96725e11i	0.533421	−	0.307971i
$895$		−	1.89796e11i		−	0.295797i
$896$	−5.57456e10	+	1.17355e10i	−0.0864925	+	0.0182083i
$897$	−4.78394e11			−0.738952
$898$	9.01001e10	+	1.56058e11i	0.138554	+	0.239983i
$899$	1.05742e12	+	6.10504e11i	1.61887	+	0.934652i
$900$	4.09494e10	−	7.09264e10i	0.0624134	−	0.108103i
$901$	−1.59368e11	+	9.20114e10i	−0.241826	+	0.139618i
$902$			9.63927e10i			0.145619i
$903$	−2.45466e11	+	2.20153e11i	−0.369181	+	0.331111i
$904$	−5.69414e10			−0.0852618
$905$	−1.54710e11	−	2.67965e11i	−0.230634	−	0.399470i
$906$	2.73293e11	+	1.57786e11i	0.405617	+	0.234183i
$907$	1.18964e11	−	2.06052e11i	0.175787	−	0.304472i	−0.764646	−	0.644450i	$-0.777086\pi$
$907$	1.18964e11	−	2.06052e11i	0.175787	−	0.304472i	0.940433	+	0.339978i	$0.110420\pi$
$908$	−2.24891e11	+	1.29841e11i	−0.330849	+	0.191016i
$909$			2.27918e11i			0.333828i
$910$	1.18565e11	+	1.32197e11i	0.172898	+	0.192777i
$911$	−6.96249e11			−1.01086			−0.505430	−	0.862868i	$-0.668666\pi$
$911$	−6.96249e11			−1.01086			−0.505430	+	0.862868i	$0.668666\pi$
$912$	3.52279e10	+	6.10165e10i	0.0509222	+	0.0881998i
$913$	−4.34004e11	−	2.50572e11i	−0.624612	−	0.360620i
$914$	−4.54213e11	+	7.86720e11i	−0.650841	+	1.12729i
$915$	1.29274e11	−	7.46366e10i	0.184429	−	0.106480i
$916$			2.64176e11i			0.375243i
$917$	−1.74398e11	−	8.28423e11i	−0.246641	−	1.17159i
$918$	7.31781e10			0.103041
$919$	9.88101e10	+	1.71144e11i	0.138529	+	0.239939i	0.926940	−	0.375210i	$-0.122429\pi$
$919$	9.88101e10	+	1.71144e11i	0.138529	+	0.239939i	−0.788411	+	0.615148i	$0.789096\pi$
$920$	−1.92451e11	−	1.11112e11i	−0.268639	−	0.155099i
$921$	2.79296e11	−	4.83755e11i	0.388174	−	0.672338i
$922$	3.96623e11	−	2.28990e11i	0.548850	−	0.316879i
$923$		−	5.53349e11i		−	0.762417i
$924$	−1.45817e11	−	4.76936e10i	−0.200042	−	0.0654292i
$925$	3.15320e11			0.430710
$926$	−2.31335e11	−	4.00684e11i	−0.314628	−	0.544952i
$927$	1.31308e10	+	7.58107e9i	0.0177817	+	0.0102662i
$928$	−1.02862e11	+	1.78161e11i	−0.138695	+	0.240227i
$929$	1.31963e10	−	7.61890e9i	0.0177170	−	0.0102289i	−0.491115	−	0.871095i	$-0.663411\pi$
$929$	1.31963e10	−	7.61890e9i	0.0177170	−	0.0102289i	0.508832	+	0.860866i	$0.330077\pi$
$930$			1.82281e11i			0.243674i
$931$	5.26974e11	+	5.74668e10i	0.701440	+	0.0764923i
$932$	−3.44183e11			−0.456168
$933$	−3.19712e11	−	5.53758e11i	−0.421922	−	0.730791i
$934$	−8.78568e11	−	5.07242e11i	−1.15448	−	0.666542i
$935$	1.05700e11	−	1.83078e11i	0.138302	−	0.239547i
$936$	−5.72575e10	+	3.30577e10i	−0.0745983	+	0.0430694i
$937$			1.39294e11i			0.180706i	0.995910	+	0.0903532i	$0.0287996\pi$
$937$			1.39294e11i			0.180706i	−0.995910	+	0.0903532i	$0.971200\pi$
$938$	−2.37060e11	+	7.24781e11i	−0.306229	+	0.936258i
$939$	4.58661e11			0.589970
$940$	9.09741e10	+	1.57572e11i	0.116522	+	0.201821i
$941$	−1.20831e10	−	6.97619e9i	−0.0154106	−	0.00889733i	0.492275	−	0.870440i	$-0.336165\pi$
$941$	−1.20831e10	−	6.97619e9i	−0.0154106	−	0.00889733i	−0.507686	+	0.861542i	$0.669499\pi$
$942$	2.36972e11	−	4.10447e11i	0.300949	−	0.521259i
$943$	−3.38720e11	+	1.95560e11i	−0.428345	+	0.247305i
$944$		−	2.37802e11i		−	0.299452i
$945$	−7.52489e10	+	1.58413e10i	−0.0943567	+	0.0198638i
$946$	−3.54647e11			−0.442825
$947$	−2.49846e11	−	4.32746e11i	−0.310651	−	0.538063i	0.667853	−	0.744293i	$-0.267214\pi$
$947$	−2.49846e11	−	4.32746e11i	−0.310651	−	0.538063i	−0.978503	+	0.206231i	$0.933880\pi$
$948$	7.18461e10	+	4.14804e10i	0.0889549	+	0.0513581i
$949$	5.29877e10	−	9.17774e10i	0.0653296	−	0.113154i
$950$	−2.63589e11	+	1.52183e11i	−0.323618	+	0.186841i
$951$		−	7.21145e11i		−	0.881658i
$952$	1.63698e11	−	1.46818e11i	0.199295	−	0.178743i
$953$	2.03306e11			0.246478			0.123239	−	0.992377i	$-0.460672\pi$
$953$	2.03306e11			0.246478			0.123239	+	0.992377i	$0.460672\pi$
$954$	3.59992e10	+	6.23524e10i	0.0434609	+	0.0752765i
$955$	4.71475e11	+	2.72206e11i	0.566820	+	0.327254i
$956$	2.11444e10	−	3.66231e10i	0.0253142	−	0.0438454i
$957$	−4.79806e11	+	2.77016e11i	−0.572028	+	0.330261i
$958$			1.00952e12i			1.19854i
$959$	−3.72378e11	−	4.15193e11i	−0.440260	−	0.490880i
$960$	−3.07118e10			−0.0361593
$961$	1.78744e11	+	3.09593e11i	0.209574	+	0.362993i
$962$	−2.20448e11	−	1.27276e11i	−0.257399	−	0.148609i
$963$	1.28099e11	−	2.21873e11i	0.148950	−	0.257988i
$964$	−3.02242e11	+	1.74500e11i	−0.349983	+	0.202063i
$965$		−	8.43556e11i		−	0.972758i
$966$	−1.28239e11	−	6.09156e11i	−0.147269	−	0.699552i
$967$	−1.41239e12			−1.61529			−0.807643	−	0.589672i	$-0.799257\pi$
$967$	−1.41239e12			−1.61529			−0.807643	+	0.589672i	$0.799257\pi$
$968$	7.27057e10	+	1.25930e11i	0.0828070	+	0.143426i
$969$	−2.35521e11	−	1.35978e11i	−0.267137	−	0.154232i
$970$	2.34749e11	−	4.06598e11i	0.265166	−	0.459281i
$971$	3.17901e11	−	1.83540e11i	0.357614	−	0.206469i	−0.310420	−	0.950600i	$-0.600470\pi$
$971$	3.17901e11	−	1.83540e11i	0.357614	−	0.206469i	0.668034	+	0.744131i	$0.267136\pi$
$972$		−	2.86307e10i		−	0.0320750i
$973$	−9.32217e11	−	3.04908e11i	−1.04008	−	0.340186i
$974$	9.67256e11			1.07474
$975$	−1.42808e11	−	2.47350e11i	−0.158028	−	0.273712i
$976$	1.44629e11	+	8.35019e10i	0.159389	+	0.0920231i
$977$	6.46452e11	−	1.11969e12i	0.709509	−	1.22891i	−0.255530	−	0.966801i	$-0.582250\pi$
$977$	6.46452e11	−	1.11969e12i	0.709509	−	1.22891i	0.965039	−	0.262105i	$-0.0844166\pi$
$978$	5.75871e11	−	3.32479e11i	0.629463	−	0.363420i
$979$			2.42196e11i			0.263655i
$980$	−1.36548e11	+	1.86409e11i	−0.148041	+	0.202098i
$981$	2.33799e11			0.252445
$982$	−5.36516e10	−	9.29272e10i	−0.0576948	−	0.0999303i
$983$	8.15971e11	+	4.71101e11i	0.873898	+	0.504545i	0.868641	−	0.495441i	$-0.164994\pi$
$983$	8.15971e11	+	4.71101e11i	0.873898	+	0.504545i	0.00525608	+	0.999986i	$0.498327\pi$
$984$	−2.70269e10	+	4.68120e10i	−0.0288281	+	0.0499317i
$985$	1.34213e11	−	7.74881e10i	0.142577	−	0.0823171i
$986$		−	7.94083e11i		−	0.840153i
$987$	−1.58447e11	+	4.84433e11i	−0.166961	+	0.510464i
$988$	2.45709e11			0.257865
$989$	−7.19503e11	−	1.24622e12i	−0.752051	−	1.30259i
$990$	−7.16288e10	−	4.13549e10i	−0.0745671	−	0.0430513i
$991$	−4.69078e11	+	8.12467e11i	−0.486352	+	0.842386i	−0.999877	−	0.0156884i	$-0.995006\pi$
$991$	−4.69078e11	+	8.12467e11i	−0.486352	+	0.842386i	0.513525	+	0.858075i	$0.328339\pi$
$992$	−1.76610e11	+	1.01966e11i	−0.182377	+	0.105295i
$993$		−	1.05523e11i		−	0.108530i
$994$	7.04598e11	−	1.48331e11i	0.721765	−	0.151945i
$995$	5.57075e11			0.568357
$996$	−1.40513e11	−	2.43375e11i	−0.142783	−	0.247308i
$997$	−5.89544e11	−	3.40373e11i	−0.596672	−	0.344489i	0.171059	−	0.985261i	$-0.445281\pi$
$997$	−5.89544e11	−	3.40373e11i	−0.596672	−	0.344489i	−0.767731	+	0.640772i	$0.778614\pi$
$998$	1.04056e11	−	1.80230e11i	0.104892	−	0.181679i
$999$	9.54634e10	−	5.51158e10i	0.0958462	−	0.0553368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.a.31.1	yes	8
3.2	odd	2		126.9.n.a.73.4		8
7.3	odd	6		294.9.c.a.97.8		8
7.4	even	3		294.9.c.a.97.5		8
7.5	odd	6	inner	42.9.g.a.19.1	✓	8
21.5	even	6		126.9.n.a.19.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.a.19.1	✓	8	7.5	odd	6	inner
42.9.g.a.31.1	yes	8	1.1	even	1	trivial
126.9.n.a.19.4		8	21.5	even	6
126.9.n.a.73.4		8	3.2	odd	2
294.9.c.a.97.5		8	7.4	even	3
294.9.c.a.97.8		8	7.3	odd	6

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:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	42.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65685 - 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-271.195 + 156.575i) q^{5} -529.090i q^{6} +(746.403 - 2282.04i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +O(q^{10})\)	\(q+(-5.65685 - 9.79796i) q^{2} +(40.5000 + 23.3827i) q^{3} +(-64.0000 + 110.851i) q^{4} +(-271.195 + 156.575i) q^{5} -529.090i q^{6} +(746.403 - 2282.04i) q^{7} +1448.15 q^{8} +(1093.50 + 1894.00i) q^{9} +(3068.22 + 1771.44i) q^{10} +(-5337.31 + 9244.49i) q^{11} +(-5184.00 + 2992.98i) q^{12} +20875.6i q^{13} +(-26581.6 + 5595.92i) q^{14} -14644.5 q^{15} +(-8192.00 - 14189.0i) q^{16} +(54768.8 + 31620.8i) q^{17} +(12371.5 - 21428.1i) q^{18} +(-79634.8 + 45977.2i) q^{19} -40083.1i q^{20} +(83589.4 - 74969.5i) q^{21} +120769. q^{22} +(245015. + 424379. i) q^{23} +(58650.3 + 33861.7i) q^{24} +(-146281. + 253367. i) q^{25} +(204538. - 118090. i) q^{26} +102276. i q^{27} +(205197. + 228790. i) q^{28} +1.10983e6 q^{29} +(82842.0 + 143487. i) q^{30} +(952777. + 550086. i) q^{31} +(-92681.9 + 160530. i) q^{32} +(-432322. + 249601. i) q^{33} -715497. i q^{34} +(154888. + 735744. i) q^{35} -279936. q^{36} +(-538894. - 933391. i) q^{37} +(900965. + 520172. i) q^{38} +(-488127. + 845460. i) q^{39} +(-392732. + 226744. i) q^{40} +798155. i q^{41} +(-1.20740e6 - 394914. i) q^{42} -2.93656e6 q^{43} +(-683175. - 1.18329e6i) q^{44} +(-593104. - 342429. i) q^{45} +(2.77203e6 - 4.80130e6i) q^{46} +(-3.93113e6 + 2.26964e6i) q^{47} -766204. i q^{48} +(-4.65057e6 - 3.40663e6i) q^{49} +3.30997e6 q^{50} +(1.47876e6 + 2.56128e6i) q^{51} +(-2.31408e6 - 1.33604e6i) q^{52} +(-1.45492e6 + 2.51999e6i) q^{53} +(1.00209e6 - 578560. i) q^{54} -3.34275e6i q^{55} +(1.08091e6 - 3.30474e6i) q^{56} -4.30028e6 q^{57} +(-6.27817e6 - 1.08741e7i) q^{58} +(1.25697e7 + 7.25714e6i) q^{59} +(937250. - 1.62337e6i) q^{60} +(-8.82748e6 + 5.09655e6i) q^{61} -1.24470e7i q^{62} +(5.13836e6 - 1.08172e6i) q^{63} +2.09715e6 q^{64} +(-3.26858e6 - 5.66135e6i) q^{65} +(4.89116e6 + 2.82391e6i) q^{66} +(1.40362e7 - 2.43114e7i) q^{67} +(-7.01041e6 + 4.04746e6i) q^{68} +2.29165e7i q^{69} +(6.33262e6 - 5.67958e6i) q^{70} -2.65070e7 q^{71} +(1.58356e6 + 2.74280e6i) q^{72} +(-4.39640e6 - 2.53826e6i) q^{73} +(-6.09689e6 + 1.05601e7i) q^{74} +(-1.18488e7 + 6.84090e6i) q^{75} -1.17702e7i q^{76} +(1.71125e7 + 1.90800e7i) q^{77} +1.10450e7 q^{78} +(-6.92960e6 - 1.20024e7i) q^{79} +(4.44326e6 + 2.56532e6i) q^{80} +(-2.39148e6 + 4.14217e6i) q^{81} +(7.82029e6 - 4.51505e6i) q^{82} +4.69473e7i q^{83} +(2.96074e6 + 1.40640e7i) q^{84} -1.98040e7 q^{85} +(1.66117e7 + 2.87723e7i) q^{86} +(4.49483e7 + 2.59509e7i) q^{87} +(-7.72925e6 + 1.33874e7i) q^{88} +(1.96492e7 - 1.13445e7i) q^{89} +7.74827e6i q^{90} +(4.76388e7 + 1.55816e7i) q^{91} -6.27239e7 q^{92} +(2.57250e7 + 4.45570e7i) q^{93} +(4.44756e7 + 2.56780e7i) q^{94} +(1.43977e7 - 2.49376e7i) q^{95} +(-7.50723e6 + 4.33430e6i) q^{96} -1.32519e8i q^{97} +(-7.07049e6 + 6.48369e7i) q^{98} -2.33454e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9}+O(q^{10}) \) 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9	\( 8 q + 324 q^{3} - 512 q^{4} - 2226 q^{5} - 140 q^{7} + 8748 q^{9} - 21888 q^{10} - 7434 q^{11} - 41472 q^{12} + 32256 q^{14} - 120204 q^{15} - 65536 q^{16} + 7932 q^{17} - 773082 q^{19} + 130410 q^{21} + 557568 q^{22} + 391200 q^{23} - 138886 q^{25} - 805632 q^{26} + 654080 q^{28} - 2318196 q^{29} - 590976 q^{30} - 3212544 q^{31} - 602154 q^{33} + 3340932 q^{35} - 2239488 q^{36} + 544802 q^{37} - 1570560 q^{38} + 1341522 q^{39} + 2801664 q^{40} - 72576 q^{42} + 552284 q^{43} - 951552 q^{44} - 4868262 q^{45} + 7878912 q^{46} - 15735252 q^{47} - 588196 q^{49} + 25400832 q^{50} + 214164 q^{51} + 6359808 q^{52} + 10935222 q^{53} - 8601600 q^{56} - 41746428 q^{57} - 8158848 q^{58} + 63840318 q^{59} + 7693056 q^{60} + 43108176 q^{61} + 10869390 q^{63} + 16777216 q^{64} - 9118644 q^{65} + 22581504 q^{66} + 48827290 q^{67} - 1015296 q^{68} + 11053056 q^{70} - 164526744 q^{71} + 150530022 q^{73} - 31064064 q^{74} - 11249766 q^{75} - 137090394 q^{77} - 43504128 q^{78} - 18689696 q^{79} + 36470784 q^{80} - 19131876 q^{81} - 33914880 q^{82} + 18144000 q^{84} - 190617576 q^{85} - 37077504 q^{86} - 93886938 q^{87} - 35684352 q^{88} - 191605284 q^{89} + 110138574 q^{91} - 100147200 q^{92} - 86738688 q^{93} + 302275584 q^{94} + 260649552 q^{95} - 282428160 q^{98} - 32516316 q^{99}+O(q^{100}) \) 8 * q + 324 * q^3 - 512 * q^4 - 2226 * q^5 - 140 * q^7 + 8748 * q^9 - 21888 * q^10 - 7434 * q^11 - 41472 * q^12 + 32256 * q^14 - 120204 * q^15 - 65536 * q^16 + 7932 * q^17 - 773082 * q^19 + 130410 * q^21 + 557568 * q^22 + 391200 * q^23 - 138886 * q^25 - 805632 * q^26 + 654080 * q^28 - 2318196 * q^29 - 590976 * q^30 - 3212544 * q^31 - 602154 * q^33 + 3340932 * q^35 - 2239488 * q^36 + 544802 * q^37 - 1570560 * q^38 + 1341522 * q^39 + 2801664 * q^40 - 72576 * q^42 + 552284 * q^43 - 951552 * q^44 - 4868262 * q^45 + 7878912 * q^46 - 15735252 * q^47 - 588196 * q^49 + 25400832 * q^50 + 214164 * q^51 + 6359808 * q^52 + 10935222 * q^53 - 8601600 * q^56 - 41746428 * q^57 - 8158848 * q^58 + 63840318 * q^59 + 7693056 * q^60 + 43108176 * q^61 + 10869390 * q^63 + 16777216 * q^64 - 9118644 * q^65 + 22581504 * q^66 + 48827290 * q^67 - 1015296 * q^68 + 11053056 * q^70 - 164526744 * q^71 + 150530022 * q^73 - 31064064 * q^74 - 11249766 * q^75 - 137090394 * q^77 - 43504128 * q^78 - 18689696 * q^79 + 36470784 * q^80 - 19131876 * q^81 - 33914880 * q^82 + 18144000 * q^84 - 190617576 * q^85 - 37077504 * q^86 - 93886938 * q^87 - 35684352 * q^88 - 191605284 * q^89 + 110138574 * q^91 - 100147200 * q^92 - 86738688 * q^93 + 302275584 * q^94 + 260649552 * q^95 - 282428160 * q^98 - 32516316 * q^99

Introduction

L-functions

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