LMFDB - Embedded newform 42.9.g.a.19.2

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			19.2
Root			$-3.06219 - 5.30387i$ of defining polynomial
Character	$\chi$	$=$	42.19
Dual form			42.9.g.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.65685 + 9.79796i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-64.0000 - 110.851i) q^{4} +(198.356 + 114.521i) q^{5} +529.090i q^{6} +(-2266.33 - 792.819i) q^{7} +1448.15 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})$	\(q+(-5.65685 + 9.79796i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-64.0000 - 110.851i) q^{4} +(198.356 + 114.521i) q^{5} +529.090i q^{6} +(-2266.33 - 792.819i) q^{7} +1448.15 q^{8} +(1093.50 - 1894.00i) q^{9} +(-2244.14 + 1295.66i) q^{10} +(-2681.51 - 4644.51i) q^{11} +(-5184.00 - 2992.98i) q^{12} +55774.8i q^{13} +(20588.3 - 17720.5i) q^{14} +10711.2 q^{15} +(-8192.00 + 14189.0i) q^{16} +(-85725.7 + 49493.7i) q^{17} +(12371.5 + 21428.1i) q^{18} +(-78930.9 - 45570.8i) q^{19} -29317.4i q^{20} +(-110324. + 20883.6i) q^{21} +60675.6 q^{22} +(26885.7 - 46567.5i) q^{23} +(58650.3 - 33861.7i) q^{24} +(-169082. - 292859. i) q^{25} +(-546479. - 315510. i) q^{26} -102276. i q^{27} +(57159.9 + 301966. i) q^{28} -1.32881e6 q^{29} +(-60591.9 + 104948. i) q^{30} +(-897669. + 518270. i) q^{31} +(-92681.9 - 160530. i) q^{32} +(-217202. - 125402. i) q^{33} -1.11992e6i q^{34} +(-358745. - 416803. i) q^{35} -279936. q^{36} +(-11331.2 + 19626.2i) q^{37} +(893001. - 515575. i) q^{38} +(1.30416e6 + 2.25888e6i) q^{39} +(287250. + 165844. i) q^{40} +2.91739e6i q^{41} +(419473. - 1.19909e6i) q^{42} +4.71324e6 q^{43} +(-343233. + 594497. i) q^{44} +(433805. - 250457. i) q^{45} +(304177. + 526851. i) q^{46} +(-6.68209e6 - 3.85791e6i) q^{47} +766204. i q^{48} +(4.50768e6 + 3.59358e6i) q^{49} +3.82590e6 q^{50} +(-2.31459e6 + 4.00899e6i) q^{51} +(6.18271e6 - 3.56959e6i) q^{52} +(2.74030e6 + 4.74633e6i) q^{53} +(1.00209e6 + 578560. i) q^{54} -1.22836e6i q^{55} +(-3.28199e6 - 1.14813e6i) q^{56} -4.26227e6 q^{57} +(7.51688e6 - 1.30196e7i) q^{58} +(7.35698e6 - 4.24755e6i) q^{59} +(-685519. - 1.18735e6i) q^{60} +(3.06956e6 + 1.77221e6i) q^{61} -1.17271e7i q^{62} +(-3.97983e6 + 3.42547e6i) q^{63} +2.09715e6 q^{64} +(-6.38738e6 + 1.10633e7i) q^{65} +(2.45736e6 - 1.41876e6i) q^{66} +(4.24118e6 + 7.34593e6i) q^{67} +(1.09729e7 + 6.33520e6i) q^{68} -2.51464e6i q^{69} +(6.11319e6 - 1.15718e6i) q^{70} -2.14497e7 q^{71} +(1.58356e6 - 2.74280e6i) q^{72} +(3.42172e7 - 1.97553e7i) q^{73} +(-128198. - 222045. i) q^{74} +(-1.36957e7 - 7.90720e6i) q^{75} +1.16661e7i q^{76} +(2.39492e6 + 1.26519e7i) q^{77} -2.95099e7 q^{78} +(-6.05659e6 + 1.04903e7i) q^{79} +(-3.24987e6 + 1.87631e6i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(-2.85845e7 - 1.65033e7i) q^{82} +5.06437e7i q^{83} +(9.37574e6 + 1.08931e7i) q^{84} -2.26723e7 q^{85} +(-2.66621e7 + 4.61802e7i) q^{86} +(-5.38168e7 + 3.10711e7i) q^{87} +(-3.88324e6 - 6.72597e6i) q^{88} +(-5.21951e7 - 3.01348e7i) q^{89} +5.66720e6i q^{90} +(4.42193e7 - 1.26404e8i) q^{91} -6.88275e6 q^{92} +(-2.42371e7 + 4.19798e7i) q^{93} +(7.55993e7 - 4.36473e7i) q^{94} +(-1.04376e7 - 1.80785e7i) q^{95} +(-7.50723e6 - 4.33430e6i) q^{96} -1.77657e7i q^{97} +(-6.07090e7 + 2.38377e7i) q^{98} -1.17289e7 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 $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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
$5$	198.356	+	114.521i	0.317370	+	0.183234i	0.650220	−	0.759746i	$-0.274677\pi$
$5$	198.356	+	114.521i	0.317370	+	0.183234i	−0.332850	+	0.942980i	$0.608010\pi$
$6$			529.090i			0.408248i
$7$	−2266.33	−	792.819i	−0.943910	−	0.330204i
$7$	−2266.33	−	792.819i	−0.943910	−	0.330204i
$8$	1448.15			0.353553
$9$	1093.50	−	1894.00i	0.166667	−	0.288675i
$10$	−2244.14	+	1295.66i	−0.224414	+	0.129566i
$11$	−2681.51	−	4644.51i	−0.183151	−	0.317226i	0.759801	−	0.650155i	$-0.225296\pi$
$11$	−2681.51	−	4644.51i	−0.183151	−	0.317226i	−0.942952	+	0.332929i	$0.891963\pi$
$12$	−5184.00	−	2992.98i	−0.250000	−	0.144338i
$13$			55774.8i			1.95283i	0.215901	+	0.976415i	$0.430731\pi$
$13$			55774.8i			1.95283i	−0.215901	+	0.976415i	$0.569269\pi$
$14$	20588.3	−	17720.5i	0.535930	−	0.461280i
$15$	10711.2			0.211580
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	−85725.7	+	49493.7i	−1.02640	+	0.592590i	−0.915950	−	0.401292i	$-0.868561\pi$
$17$	−85725.7	+	49493.7i	−1.02640	+	0.592590i	−0.110446	+	0.993882i	$0.535228\pi$
$18$	12371.5	+	21428.1i	0.117851	+	0.204124i
$19$	−78930.9	−	45570.8i	−0.605665	−	0.349681i	0.165602	−	0.986193i	$-0.447043\pi$
$19$	−78930.9	−	45570.8i	−0.605665	−	0.349681i	−0.771267	+	0.636512i	$0.780377\pi$
$20$		−	29317.4i		−	0.183234i
$21$	−110324.	+	20883.6i	−0.567276	+	0.107381i
$22$	60675.6			0.259014
$23$	26885.7	−	46567.5i	0.0960750	−	0.166407i	−0.813982	−	0.580890i	$-0.802704\pi$
$23$	26885.7	−	46567.5i	0.0960750	−	0.166407i	0.910057	+	0.414484i	$0.136038\pi$
$24$	58650.3	−	33861.7i	0.176777	−	0.102062i
$25$	−169082.	−	292859.i	−0.432851	−	0.749720i
$26$	−546479.	−	315510.i	−1.19586	−	0.690430i
$27$		−	102276.i		−	0.192450i
$28$	57159.9	+	301966.i	0.0929949	+	0.491276i
$29$	−1.32881e6			−1.87876			−0.939379	−	0.342880i	$-0.888597\pi$
$29$	−1.32881e6			−1.87876			−0.939379	+	0.342880i	$0.888597\pi$
$30$	−60591.9	+	104948.i	−0.0748048	+	0.129566i
$31$	−897669.	+	518270.i	−0.972007	+	0.561189i	−0.899848	−	0.436204i	$-0.856322\pi$
$31$	−897669.	+	518270.i	−0.972007	+	0.561189i	−0.0721597	+	0.997393i	$0.522989\pi$
$32$	−92681.9	−	160530.i	−0.0883883	−	0.153093i
$33$	−217202.	−	125402.i	−0.183151	−	0.105742i
$34$		−	1.11992e6i		−	0.838049i
$35$	−358745.	−	416803.i	−0.239064	−	0.277753i
$36$	−279936.			−0.166667
$37$	−11331.2	+	19626.2i	−0.00604602	+	0.0104720i	−0.869033	−	0.494755i	$-0.835258\pi$
$37$	−11331.2	+	19626.2i	−0.00604602	+	0.0104720i	0.862987	+	0.505227i	$0.168591\pi$
$38$	893001.	−	515575.i	0.428270	−	0.247262i
$39$	1.30416e6	+	2.25888e6i	0.563734	+	0.976415i
$40$	287250.	+	165844.i	0.112207	+	0.0647828i
$41$			2.91739e6i			1.03243i	0.856460	+	0.516213i	$0.172659\pi$
$41$			2.91739e6i			1.03243i	−0.856460	+	0.516213i	$0.827341\pi$
$42$	419473.	−	1.19909e6i	0.134805	−	0.385349i
$43$	4.71324e6			1.37862			0.689312	−	0.724464i	$-0.257913\pi$
$43$	4.71324e6			1.37862			0.689312	+	0.724464i	$0.257913\pi$
$44$	−343233.	+	594497.i	−0.0915753	+	0.158613i
$45$	433805.	−	250457.i	0.105790	−	0.0610779i
$46$	304177.	+	526851.i	0.0679353	+	0.117667i
$47$	−6.68209e6	−	3.85791e6i	−1.36937	−	0.790607i	−0.378523	−	0.925592i	$-0.623568\pi$
$47$	−6.68209e6	−	3.85791e6i	−1.36937	−	0.790607i	−0.990848	+	0.134985i	$0.956901\pi$
$48$			766204.i			0.144338i
$49$	4.50768e6	+	3.59358e6i	0.781931	+	0.623365i
$50$	3.82590e6			0.612144
$51$	−2.31459e6	+	4.00899e6i	−0.342132	+	0.592590i
$52$	6.18271e6	−	3.56959e6i	0.845600	−	0.488208i
$53$	2.74030e6	+	4.74633e6i	0.347291	+	0.601526i	0.985767	−	0.168116i	$-0.0537682\pi$
$53$	2.74030e6	+	4.74633e6i	0.347291	+	0.601526i	−0.638476	+	0.769642i	$0.720435\pi$
$54$	1.00209e6	+	578560.i	0.117851	+	0.0680414i
$55$		−	1.22836e6i		−	0.134237i
$56$	−3.28199e6	−	1.14813e6i	−0.333722	−	0.116745i
$57$	−4.26227e6			−0.403777
$58$	7.51688e6	−	1.30196e7i	0.664241	−	1.15050i
$59$	7.35698e6	−	4.24755e6i	0.607143	−	0.350534i	−0.164703	−	0.986343i	$-0.552667\pi$
$59$	7.35698e6	−	4.24755e6i	0.607143	−	0.350534i	0.771847	+	0.635809i	$0.219333\pi$
$60$	−685519.	−	1.18735e6i	−0.0528950	−	0.0916168i
$61$	3.06956e6	+	1.77221e6i	0.221696	+	0.127996i	0.606735	−	0.794904i	$-0.292479\pi$
$61$	3.06956e6	+	1.77221e6i	0.221696	+	0.127996i	−0.385040	+	0.922900i	$0.625812\pi$
$62$		−	1.17271e7i		−	0.793641i
$63$	−3.97983e6	+	3.42547e6i	−0.252640	+	0.217449i
$64$	2.09715e6			0.125000
$65$	−6.38738e6	+	1.10633e7i	−0.357824	+	0.619770i
$66$	2.45736e6	−	1.41876e6i	0.129507	−	0.0747709i
$67$	4.24118e6	+	7.34593e6i	0.210469	+	0.364542i	0.951861	−	0.306529i	$-0.0991677\pi$
$67$	4.24118e6	+	7.34593e6i	0.210469	+	0.364542i	−0.741393	+	0.671071i	$0.765834\pi$
$68$	1.09729e7	+	6.33520e6i	0.513198	+	0.296295i
$69$		−	2.51464e6i		−	0.110938i
$70$	6.11319e6	−	1.15718e6i	0.254610	−	0.0481958i
$71$	−2.14497e7			−0.844088			−0.422044	−	0.906575i	$-0.638687\pi$
$71$	−2.14497e7			−0.844088			−0.422044	+	0.906575i	$0.638687\pi$
$72$	1.58356e6	−	2.74280e6i	0.0589256	−	0.102062i
$73$	3.42172e7	−	1.97553e7i	1.20491	−	0.695652i	0.243263	−	0.969960i	$-0.421782\pi$
$73$	3.42172e7	−	1.97553e7i	1.20491	−	0.695652i	0.961642	+	0.274308i	$0.0884488\pi$
$74$	−128198.	−	222045.i	−0.00427518	−	0.00740483i
$75$	−1.36957e7	−	7.90720e6i	−0.432851	−	0.249907i
$76$			1.16661e7i			0.349681i
$77$	2.39492e6	+	1.26519e7i	0.0681283	+	0.359910i
$78$	−2.95099e7			−0.797240
$79$	−6.05659e6	+	1.04903e7i	−0.155496	+	0.269328i	−0.933240	−	0.359254i	$-0.883031\pi$
$79$	−6.05659e6	+	1.04903e7i	−0.155496	+	0.269328i	0.777743	+	0.628582i	$0.216364\pi$
$80$	−3.24987e6	+	1.87631e6i	−0.0793425	+	0.0458084i
$81$	−2.39148e6	−	4.14217e6i	−0.0555556	−	0.0962250i
$82$	−2.85845e7	−	1.65033e7i	−0.632230	−	0.365018i
$83$			5.06437e7i			1.06712i	0.845763	+	0.533559i	$0.179146\pi$
$83$			5.06437e7i			1.06712i	−0.845763	+	0.533559i	$0.820854\pi$
$84$	9.37574e6	+	1.08931e7i	0.188317	+	0.218793i
$85$	−2.26723e7			−0.434330
$86$	−2.66621e7	+	4.61802e7i	−0.487417	+	0.844232i
$87$	−5.38168e7	+	3.10711e7i	−0.939379	+	0.542351i
$88$	−3.88324e6	−	6.72597e6i	−0.0647535	−	0.112156i
$89$	−5.21951e7	−	3.01348e7i	−0.831897	−	0.480296i	0.0226047	−	0.999744i	$-0.492804\pi$
$89$	−5.21951e7	−	3.01348e7i	−0.831897	−	0.480296i	−0.854502	+	0.519448i	$0.826137\pi$
$90$			5.66720e6i			0.0863771i
$91$	4.42193e7	−	1.26404e8i	0.644832	−	1.84330i
$92$	−6.88275e6			−0.0960750
$93$	−2.42371e7	+	4.19798e7i	−0.324002	+	0.561189i
$94$	7.55993e7	−	4.36473e7i	0.968292	−	0.559043i
$95$	−1.04376e7	−	1.80785e7i	−0.128147	−	0.221956i
$96$	−7.50723e6	−	4.33430e6i	−0.0883883	−	0.0510310i
$97$		−	1.77657e7i		−	0.200676i	−0.994953	−	0.100338i	$-0.968008\pi$
$97$		−	1.77657e7i		−	0.200676i	0.994953	−	0.100338i	$-0.0319924\pi$
$98$	−6.07090e7	+	2.38377e7i	−0.658186	+	0.258440i
$99$	−1.17289e7			−0.122100
$100$	−2.16425e7	+	3.74860e7i	−0.216425	+	0.374860i
$101$	5.90802e7	−	3.41100e7i	0.567749	−	0.327790i	−0.188501	−	0.982073i	$-0.560363\pi$
$101$	5.90802e7	−	3.41100e7i	0.567749	−	0.327790i	0.756250	+	0.654283i	$0.227029\pi$
$102$	−2.61866e7	−	4.53566e7i	−0.241924	−	0.419025i
$103$	4.21424e7	+	2.43309e7i	0.374430	+	0.216177i	0.675392	−	0.737459i	$-0.263974\pi$
$103$	4.21424e7	+	2.43309e7i	0.374430	+	0.216177i	−0.300962	+	0.953636i	$0.597308\pi$
$104$			8.07705e7i			0.690430i
$105$	−2.42752e7	−	8.49207e6i	−0.199712	−	0.0698645i
$106$	−6.20058e7			−0.491144
$107$	9.53521e7	−	1.65155e8i	0.727436	−	1.25996i	−0.230527	−	0.973066i	$-0.574045\pi$
$107$	9.53521e7	−	1.65155e8i	0.727436	−	1.25996i	0.957963	−	0.286891i	$-0.0926217\pi$
$108$	−1.13374e7	+	6.54566e6i	−0.0833333	+	0.0481125i
$109$	5.18074e7	+	8.97330e7i	0.367016	+	0.635691i	0.989098	−	0.147262i	$-0.0470459\pi$
$109$	5.18074e7	+	8.97330e7i	0.367016	+	0.635691i	−0.622081	+	0.782953i	$0.713713\pi$
$110$	1.20354e7	+	6.94863e6i	0.0822032	+	0.0474601i
$111$			1.05982e6i			0.00698134i
$112$	2.98150e7	−	2.56620e7i	0.189480	−	0.163087i
$113$	−2.55956e8			−1.56983			−0.784914	−	0.619605i	$-0.787293\pi$
$113$	−2.55956e8			−1.56983			−0.784914	+	0.619605i	$0.787293\pi$
$114$	2.41110e7	−	4.17615e7i	0.142757	−	0.247262i
$115$	1.06659e7	−	6.15796e6i	0.0609826	−	0.0352083i
$116$	8.50438e7	+	1.47300e8i	0.469690	+	0.813526i
$117$	1.05637e8	+	6.09897e7i	0.563734	+	0.325472i
$118$			9.61111e7i			0.495731i
$119$	2.33522e8	−	4.42040e7i	1.16450	−	0.220432i
$120$	1.55115e7			0.0748048
$121$	9.27985e7	−	1.60732e8i	0.432912	−	0.749825i
$122$	−3.47281e7	+	2.00503e7i	−0.156763	+	0.0905069i
$123$	6.82164e7	+	1.18154e8i	0.298036	+	0.516213i
$124$	1.14902e8	+	6.63385e7i	0.486004	+	0.280594i
$125$		−	1.66923e8i		−	0.683718i
$126$	−1.10493e7	−	5.83716e7i	−0.0438382	−	0.231590i
$127$	2.01146e8			0.773207			0.386603	−	0.922246i	$-0.373648\pi$
$127$	2.01146e8			0.773207			0.386603	+	0.922246i	$0.373648\pi$
$128$	−1.18633e7	+	2.05478e7i	−0.0441942	+	0.0765466i
$129$	1.90886e8	−	1.10208e8i	0.689312	−	0.397975i
$130$	−7.22650e7	−	1.25167e8i	−0.253020	−	0.438243i
$131$	−3.01124e7	−	1.73854e7i	−0.102249	−	0.0590337i	0.448003	−	0.894032i	$-0.352135\pi$
$131$	−3.01124e7	−	1.73854e7i	−0.102249	−	0.0590337i	−0.550253	+	0.834998i	$0.685469\pi$
$132$			3.21028e7i			0.105742i
$133$	1.42754e8	+	1.65856e8i	0.456227	+	0.530060i
$134$	−9.59669e7			−0.297647
$135$	1.17127e7	−	2.02870e7i	0.0352633	−	0.0610779i
$136$	−1.24144e8	+	7.16746e7i	−0.362886	+	0.209512i
$137$	−2.67164e7	−	4.62741e7i	−0.0758395	−	0.131358i	0.825612	−	0.564239i	$-0.190830\pi$
$137$	−2.67164e7	−	4.62741e7i	−0.0758395	−	0.131358i	−0.901451	+	0.432881i	$0.857497\pi$
$138$	2.46384e7	+	1.42250e7i	0.0679353	+	0.0392225i
$139$			7.13368e8i			1.91097i	0.295037	+	0.955486i	$0.404668\pi$
$139$			7.13368e8i			1.91097i	−0.295037	+	0.955486i	$0.595332\pi$
$140$	−2.32434e7	+	6.64428e7i	−0.0605044	+	0.172956i
$141$	−3.60833e8			−0.912914
$142$	1.21338e8	−	2.10163e8i	0.298430	−	0.516896i
$143$	2.59046e8	−	1.49561e8i	0.619489	−	0.357662i
$144$	1.79159e7	+	3.10313e7i	0.0416667	+	0.0721688i
$145$	−2.63578e8	−	1.52177e8i	−0.596261	−	0.344252i
$146$			4.47011e8i			0.983801i
$147$	2.66588e8	+	4.01383e7i	0.570915	+	0.0859586i
$148$	2.90079e6			0.00604602
$149$	2.18921e8	−	3.79183e8i	0.444163	−	0.769314i	−0.553830	−	0.832630i	$-0.686834\pi$
$149$	2.18921e8	−	3.79183e8i	0.444163	−	0.769314i	0.997994	+	0.0633161i	$0.0201676\pi$
$150$	1.54949e8	−	8.94598e7i	0.306072	−	0.176711i
$151$	−2.09026e8	−	3.62043e8i	−0.402061	−	0.696390i	0.591913	−	0.806002i	$-0.298373\pi$
$151$	−2.09026e8	−	3.62043e8i	−0.402061	−	0.696390i	−0.993975	+	0.109611i	$0.965039\pi$
$152$	−1.14304e8	−	6.59935e7i	−0.214135	−	0.123631i
$153$			2.16486e8i			0.395060i
$154$	−1.37511e8	−	4.81048e7i	−0.244486	−	0.0855274i
$155$	−2.37411e8			−0.411314
$156$	1.66933e8	−	2.89137e8i	0.281867	−	0.488208i
$157$	−8.79971e8	+	5.08051e8i	−1.44834	+	0.836198i	−0.998383	−	0.0568534i	$-0.981893\pi$
$157$	−8.79971e8	+	5.08051e8i	−1.44834	+	0.836198i	−0.449955	+	0.893051i	$0.648560\pi$
$158$	−6.85225e7	−	1.18685e8i	−0.109952	−	0.190443i
$159$	2.21964e8	+	1.28151e8i	0.347291	+	0.200509i
$160$		−	4.24561e7i		−	0.0647828i
$161$	−9.78515e7	+	8.42216e7i	−0.145634	+	0.125349i
$162$	5.41131e7			0.0785674
$163$	5.58144e7	−	9.66734e7i	0.0790672	−	0.136948i	−0.823781	−	0.566909i	$-0.808139\pi$
$163$	5.58144e7	−	9.66734e7i	0.0790672	−	0.136948i	0.902848	+	0.429960i	$0.141473\pi$
$164$	3.23396e8	−	1.86713e8i	0.447054	−	0.258107i
$165$	−2.87223e7	−	4.97484e7i	−0.0387510	−	0.0671187i
$166$	−4.96205e8	−	2.86484e8i	−0.653474	−	0.377283i
$167$		−	2.99845e8i		−	0.385506i	−0.981247	−	0.192753i	$-0.938258\pi$
$167$		−	2.99845e8i		−	0.385506i	0.981247	−	0.192753i	$-0.0617417\pi$
$168$	−1.59767e8	+	3.02427e7i	−0.200563	+	0.0379650i
$169$	−2.29510e9			−2.81355
$170$	1.28254e8	−	2.22142e8i	0.153559	−	0.265972i
$171$	−1.72622e8	+	9.96633e7i	−0.201888	+	0.116560i
$172$	−3.01648e8	−	5.22469e8i	−0.344656	−	0.596962i
$173$	−5.86489e8	−	3.38610e8i	−0.654750	−	0.378020i	0.135524	−	0.990774i	$-0.456728\pi$
$173$	−5.86489e8	−	3.38610e8i	−0.654750	−	0.378020i	−0.790274	+	0.612754i	$0.790062\pi$
$174$		−	7.03060e8i		−	0.767000i
$175$	1.51011e8	+	7.97767e8i	0.161012	+	0.850597i
$176$	8.78676e7			0.0915753
$177$	1.98638e8	−	3.44052e8i	0.202381	−	0.350534i
$178$	5.90520e8	−	3.40937e8i	0.588240	−	0.339621i
$179$	−1.05589e8	−	1.82886e8i	−0.102851	−	0.178143i	0.810007	−	0.586420i	$-0.199463\pi$
$179$	−1.05589e8	−	1.82886e8i	−0.102851	−	0.178143i	−0.912858	+	0.408277i	$0.866130\pi$
$180$	−5.55270e7	−	3.20585e7i	−0.0528950	−	0.0305389i
$181$			1.76472e9i			1.64423i	0.569323	+	0.822114i	$0.307205\pi$
$181$			1.76472e9i			1.64423i	−0.569323	+	0.822114i	$0.692795\pi$
$182$	9.88358e8	+	1.14831e9i	0.900801	+	1.04658i
$183$	1.65756e8			0.147797
$184$	3.89347e7	−	6.74369e7i	0.0339677	−	0.0588337i
$185$	−4.49523e6	+	2.59532e6i	−0.00383765	+	0.00221567i
$186$	−2.74211e8	−	4.74948e8i	−0.229104	−	0.396820i
$187$	4.59748e8	+	2.65436e8i	0.375970	+	0.217067i
$188$			9.87625e8i			0.790607i
$189$	−8.10863e7	+	2.31791e8i	−0.0635478	+	0.181655i
$190$	2.36176e8			0.181227
$191$	6.96035e7	−	1.20557e8i	0.0522995	−	0.0905854i	−0.838690	−	0.544608i	$-0.816678\pi$
$191$	6.96035e7	−	1.20557e8i	0.0522995	−	0.0905854i	0.890990	+	0.454023i	$0.150012\pi$
$192$	8.49347e7	−	4.90370e7i	0.0625000	−	0.0360844i
$193$	−6.12057e8	−	1.06011e9i	−0.441126	−	0.764052i	0.556647	−	0.830749i	$-0.312087\pi$
$193$	−6.12057e8	−	1.06011e9i	−0.441126	−	0.764052i	−0.997773	+	0.0666965i	$0.978754\pi$
$194$	1.74067e8	+	1.00498e8i	0.122888	+	0.0709495i
$195$			5.97417e8i			0.413180i
$196$	1.09861e8	−	7.29670e8i	0.0744424	−	0.494427i
$197$	1.16668e9			0.774615			0.387307	−	0.921951i	$-0.373405\pi$
$197$	1.16668e9			0.774615			0.387307	+	0.921951i	$0.373405\pi$
$198$	6.63488e7	−	1.14919e8i	0.0431690	−	0.0747709i
$199$	5.25369e7	−	3.03322e7i	0.0335006	−	0.0193416i	−0.483156	−	0.875534i	$-0.660510\pi$
$199$	5.25369e7	−	3.03322e7i	0.0335006	−	0.0193416i	0.516657	+	0.856193i	$0.327176\pi$
$200$	−2.44857e8	−	4.24106e8i	−0.153036	−	0.265066i
$201$	3.43535e8	+	1.98340e8i	0.210469	+	0.121514i
$202$			7.71820e8i			0.463565i
$203$	3.01152e9	+	1.05351e9i	1.77338	+	0.620373i
$204$	5.92536e8			0.342132
$205$	−3.34102e8	+	5.78682e8i	−0.189175	+	0.327661i
$206$	−4.76787e8	+	2.75273e8i	−0.264762	+	0.152860i
$207$	−5.87991e7	−	1.01843e8i	−0.0320250	−	0.0554690i
$208$	−7.91386e8	−	4.56907e8i	−0.422800	−	0.244104i
$209$			4.88794e8i			0.256177i
$210$	2.20526e8	−	1.89809e8i	0.113392	−	0.0975975i
$211$	1.27077e9			0.641118			0.320559	−	0.947229i	$-0.396129\pi$
$211$	1.27077e9			0.641118			0.320559	+	0.947229i	$0.396129\pi$
$212$	3.50758e8	−	6.07530e8i	0.173646	−	0.300763i
$213$	−8.68712e8	+	5.01551e8i	−0.422044	+	0.243667i
$214$	1.07879e9	+	1.86851e9i	0.514375	+	0.890924i
$215$	9.34901e8	+	5.39765e8i	0.437534	+	0.252610i
$216$		−	1.48111e8i		−	0.0680414i
$217$	2.44531e9	−	4.62879e8i	1.10279	−	0.208751i
$218$	−1.17227e9			−0.519040
$219$	9.23864e8	−	1.60018e9i	0.401635	−	0.695652i
$220$	−1.36165e8	+	7.86148e7i	−0.0581265	+	0.0335593i
$221$	−2.76050e9	−	4.78133e9i	−1.15723	−	2.00438i
$222$	−1.03840e7	−	5.99523e6i	−0.00427518	−	0.00246828i
$223$			3.30814e8i			0.133772i	0.997761	+	0.0668858i	$0.0213063\pi$
$223$			3.30814e8i			0.133772i	−0.997761	+	0.0668858i	$0.978694\pi$
$224$	8.27764e7	+	4.37293e8i	0.0328787	+	0.173692i
$225$	−7.39566e8			−0.288567
$226$	1.44791e9	−	2.50785e9i	0.555018	−	0.961319i
$227$	3.24822e9	−	1.87536e9i	1.22332	−	0.706287i	0.257699	−	0.966225i	$-0.417036\pi$
$227$	3.24822e9	−	1.87536e9i	1.22332	−	0.706287i	0.965625	+	0.259938i	$0.0837022\pi$
$228$	2.72785e8	+	4.72478e8i	0.100944	+	0.174841i
$229$	1.60970e8	+	9.29359e7i	0.0585332	+	0.0337942i	0.528981	−	0.848634i	$-0.322574\pi$
$229$	1.60970e8	+	9.29359e7i	0.0585332	+	0.0337942i	−0.470448	+	0.882428i	$0.655908\pi$
$230$			1.39339e8i			0.0497921i
$231$	3.92830e8	+	4.56403e8i	0.137961	+	0.160288i
$232$	−1.92432e9			−0.664241
$233$	−1.24296e9	+	2.15286e9i	−0.421728	+	0.730454i	−0.996109	−	0.0881344i	$-0.971910\pi$
$233$	−1.24296e9	+	2.15286e9i	−0.421728	+	0.730454i	0.574381	+	0.818588i	$0.305243\pi$
$234$	−1.19515e9	+	6.90020e8i	−0.398620	+	0.230143i
$235$	−8.83623e8	−	1.53048e9i	−0.289731	−	0.501829i
$236$	−9.41693e8	−	5.43687e8i	−0.303572	−	0.175267i
$237$			5.66478e8i			0.179552i
$238$	−8.87891e8	+	2.53809e9i	−0.276727	+	0.791043i
$239$	−5.77097e9			−1.76871			−0.884356	−	0.466812i	$-0.845402\pi$
$239$	−5.77097e9			−1.76871			−0.884356	+	0.466812i	$0.845402\pi$
$240$	−8.77464e7	+	1.51981e8i	−0.0264475	+	0.0458084i
$241$	2.95932e9	−	1.70856e9i	0.877250	−	0.506481i	0.00749929	−	0.999972i	$-0.497613\pi$
$241$	2.95932e9	−	1.70856e9i	0.877250	−	0.506481i	0.869751	+	0.493491i	$0.164280\pi$
$242$	1.04989e9	+	1.81847e9i	0.306115	+	0.530206i
$243$	−1.93710e8	−	1.11839e8i	−0.0555556	−	0.0320750i
$244$		−	4.53687e8i		−	0.127996i
$245$	4.82585e8	+	1.22903e9i	0.133940	+	0.341113i
$246$	−1.54356e9			−0.421486
$247$	2.54170e9	−	4.40236e9i	0.682868	−	1.18276i
$248$	−1.29996e9	+	7.50534e8i	−0.343656	+	0.198410i
$249$	1.18418e9	+	2.05107e9i	0.308051	+	0.533559i
$250$	1.63551e9	+	9.44262e8i	0.418690	+	0.241731i
$251$		−	9.64717e8i		−	0.243055i	−0.992588	−	0.121528i	$-0.961221\pi$
$251$		−	9.64717e8i		−	0.243055i	0.992588	−	0.121528i	$-0.0387793\pi$
$252$	6.34427e8	+	2.21939e8i	0.157318	+	0.0550340i
$253$	−2.88377e8			−0.0703848
$254$	−1.13785e9	+	1.97082e9i	−0.273370	+	0.473491i
$255$	−9.18228e8	+	5.30139e8i	−0.217165	+	0.125380i
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	−4.71005e9	−	2.71935e9i	−1.07967	−	0.623350i	−0.148866	−	0.988857i	$-0.547562\pi$
$257$	−4.71005e9	−	2.71935e9i	−1.07967	−	0.623350i	−0.930809	+	0.365507i	$0.880896\pi$
$258$			2.49373e9i			0.562821i
$259$	4.12403e7	−	3.54958e7i	0.00916479	−	0.00788821i
$260$	1.63517e9			0.357824
$261$	−1.45305e9	+	2.51676e9i	−0.313126	+	0.542351i
$262$	3.40683e8	−	1.96694e8i	0.0723013	−	0.0417432i
$263$	1.48892e9	+	2.57888e9i	0.311206	+	0.539025i	0.978624	−	0.205659i	$-0.0659338\pi$
$263$	1.48892e9	+	2.57888e9i	0.311206	+	0.539025i	−0.667418	+	0.744684i	$0.732600\pi$
$264$	−3.14542e8	−	1.81601e8i	−0.0647535	−	0.0373855i
$265$			1.25529e9i			0.254542i
$266$	−2.43259e9	+	4.60472e8i	−0.485895	+	0.0919764i
$267$	−2.81853e9			−0.554598
$268$	5.42871e8	−	9.40279e8i	0.105234	−	0.182271i
$269$	−3.58740e9	+	2.07119e9i	−0.685127	+	0.395558i	−0.801784	−	0.597614i	$-0.796116\pi$
$269$	−3.58740e9	+	2.07119e9i	−0.685127	+	0.395558i	0.116657	+	0.993172i	$0.462782\pi$
$270$	1.32514e8	+	2.29522e8i	0.0249349	+	0.0431886i
$271$	8.82215e9	+	5.09347e9i	1.63568	+	0.944358i	0.982298	+	0.187326i	$0.0599820\pi$
$271$	8.82215e9	+	5.09347e9i	1.63568	+	0.944358i	0.653378	+	0.757032i	$0.273351\pi$
$272$		−	1.62181e9i		−	0.296295i
$273$	−1.16478e9	−	6.15333e9i	−0.209698	−	1.10779i
$274$	6.04523e8			0.107253
$275$	−9.06791e8	+	1.57061e9i	−0.158554	+	0.274623i
$276$	−2.78751e8	+	1.60937e8i	−0.0480375	+	0.0277345i
$277$	−3.26174e9	−	5.64950e9i	−0.554026	−	0.959602i	−0.997979	−	0.0635514i	$-0.979757\pi$
$277$	−3.26174e9	−	5.64950e9i	−0.554026	−	0.959602i	0.443952	−	0.896051i	$-0.353576\pi$
$278$	−6.98955e9	−	4.03542e9i	−1.17023	−	0.675630i
$279$			2.26691e9i			0.374126i
$280$	−5.19519e8	−	6.03595e8i	−0.0845219	−	0.0982004i
$281$	−3.13246e9			−0.502413			−0.251206	−	0.967934i	$-0.580827\pi$
$281$	−3.13246e9			−0.502413			−0.251206	+	0.967934i	$0.580827\pi$
$282$	2.04118e9	−	3.53543e9i	0.322764	−	0.559043i
$283$	−2.21348e9	+	1.27796e9i	−0.345089	+	0.199237i	−0.662520	−	0.749044i	$-0.730513\pi$
$283$	−2.21348e9	+	1.27796e9i	−0.345089	+	0.199237i	0.317431	+	0.948281i	$0.397180\pi$
$284$	1.37278e9	+	2.37772e9i	0.211022	+	0.365501i
$285$	−8.45447e8	−	4.88119e8i	−0.128147	−	0.0739855i
$286$			3.38417e9i			0.505811i
$287$	2.31296e9	−	6.61176e9i	0.340911	−	0.974517i
$288$	−4.05391e8			−0.0589256
$289$	1.41138e9	−	2.44459e9i	0.202327	−	0.350440i
$290$	2.98204e9	−	1.72168e9i	0.421620	−	0.243423i
$291$	−4.15409e8	−	7.19510e8i	−0.0579301	−	0.100338i
$292$	−4.37980e9	−	2.52868e9i	−0.602453	−	0.347826i
$293$			8.29811e9i			1.12592i	0.826483	+	0.562962i	$0.190338\pi$
$293$			8.29811e9i			1.12592i	−0.826483	+	0.562962i	$0.809662\pi$
$294$	−1.90132e9	+	2.38497e9i	−0.254488	+	0.319222i
$295$	1.94574e9			0.256919
$296$	−1.64093e7	+	2.84218e7i	−0.00213759	+	0.00370241i
$297$	−4.75021e8	+	2.74254e8i	−0.0610502	+	0.0352473i
$298$	2.47681e9	+	4.28996e9i	0.314071	+	0.543987i
$299$	2.59729e9	+	1.49955e9i	0.324964	+	0.187618i
$300$			2.02424e9i			0.249907i
$301$	−1.06818e10	−	3.73675e9i	−1.30130	−	0.455227i
$302$	4.72971e9			0.568600
$303$	1.59517e9	−	2.76291e9i	0.189250	−	0.327790i
$304$	1.29320e9	−	7.46632e8i	0.151416	−	0.0874203i
$305$	4.05911e8	+	7.03059e8i	0.0469063	+	0.0812442i
$306$	−2.12112e9	−	1.22463e9i	−0.241924	−	0.139675i
$307$		−	6.23304e9i		−	0.701691i	−0.936433	−	0.350846i	$-0.885894\pi$
$307$		−	6.23304e9i		−	0.701691i	0.936433	−	0.350846i	$-0.114106\pi$
$308$	1.24921e9	−	1.07520e9i	0.138813	−	0.119478i
$309$	2.27569e9			0.249620
$310$	1.34300e9	−	2.32614e9i	0.145422	−	0.251878i
$311$	7.96731e9	−	4.59993e9i	0.851668	−	0.491711i	−0.00954550	−	0.999954i	$-0.503038\pi$
$311$	7.96731e9	−	4.59993e9i	0.851668	−	0.491711i	0.861213	+	0.508244i	$0.169705\pi$
$312$	1.88863e9	+	3.27121e9i	0.199310	+	0.345215i
$313$	6.52348e9	+	3.76633e9i	0.679676	+	0.392411i	0.799733	−	0.600356i	$-0.204974\pi$
$313$	6.52348e9	+	3.76633e9i	0.679676	+	0.392411i	−0.120057	+	0.992767i	$0.538308\pi$
$314$		−	1.14959e10i		−	1.18256i
$315$	−1.18171e9	+	2.23689e8i	−0.120024	+	0.0227197i
$316$	1.55049e9			0.155496
$317$	−7.41798e9	+	1.28483e10i	−0.734596	+	1.27236i	0.220305	+	0.975431i	$0.429295\pi$
$317$	−7.41798e9	+	1.28483e10i	−0.734596	+	1.27236i	−0.954900	+	0.296926i	$0.904038\pi$
$318$	−2.51123e9	+	1.44986e9i	−0.245572	+	0.141781i
$319$	3.56321e9	+	6.17167e9i	0.344096	+	0.595991i
$320$	4.15983e8	+	2.40168e8i	0.0396712	+	0.0229042i
$321$		−	8.91835e9i		−	0.839971i
$322$	−2.71668e8	−	1.43517e9i	−0.0252706	−	0.133500i
$323$	9.02187e9			0.828871
$324$	−3.06110e8	+	5.30198e8i	−0.0277778	+	0.0481125i
$325$	1.63342e10	−	9.43054e9i	1.46408	−	0.845285i
$326$	6.31468e8	+	1.09374e9i	0.0559089	+	0.0968371i
$327$	4.19640e9	+	2.42279e9i	0.367016	+	0.211897i
$328$			4.22483e9i			0.365018i
$329$	1.20852e10	+	1.40410e10i	1.03150	+	1.19843i
$330$	6.49910e8			0.0548022
$331$	−8.27229e9	+	1.43280e10i	−0.689150	+	1.19364i	0.282963	+	0.959131i	$0.408683\pi$
$331$	−8.27229e9	+	1.43280e10i	−0.689150	+	1.19364i	−0.972113	+	0.234513i	$0.924651\pi$
$332$	5.61391e9	−	3.24119e9i	0.462076	−	0.266780i
$333$	2.47813e7	+	4.29226e7i	0.00201534	+	0.00349067i
$334$	2.93787e9	+	1.69618e9i	0.236073	+	0.136297i
$335$			1.94281e9i			0.154260i
$336$	6.07461e8	−	1.73647e9i	0.0476608	−	0.136242i
$337$	−1.41852e10			−1.09980			−0.549902	−	0.835229i	$-0.685335\pi$
$337$	−1.41852e10			−1.09980			−0.549902	+	0.835229i	$0.685335\pi$
$338$	1.29830e10	−	2.24873e10i	0.994739	−	1.72294i
$339$	−1.03662e10	+	5.98495e9i	−0.784914	+	0.453170i
$340$	1.45103e9	+	2.51325e9i	0.108582	+	0.188070i
$341$	4.81421e9	+	2.77949e9i	0.356047	+	0.205564i
$342$		−	2.25512e9i		−	0.164841i
$343$	−7.36681e9	−	1.17180e10i	−0.532234	−	0.846597i
$344$	6.82551e9			0.487417
$345$	2.87979e8	−	4.98795e8i	0.0203275	−	0.0352083i
$346$	6.63537e9	−	3.83093e9i	0.462978	−	0.267301i
$347$	7.42031e9	+	1.28524e10i	0.511805	+	0.886472i	0.999906	+	0.0136849i	$0.00435617\pi$
$347$	7.42031e9	+	1.28524e10i	0.511805	+	0.886472i	−0.488102	+	0.872787i	$0.662310\pi$
$348$	6.88855e9	+	3.97711e9i	0.469690	+	0.271175i
$349$			1.29408e9i			0.0872286i	0.999048	+	0.0436143i	$0.0138873\pi$
$349$			1.29408e9i			0.0872286i	−0.999048	+	0.0436143i	$0.986113\pi$
$350$	−8.67074e9	−	3.03325e9i	−0.577808	−	0.202132i
$351$	5.70442e9			0.375822
$352$	−4.97054e8	+	8.60924e8i	−0.0323768	+	0.0560782i
$353$	−1.62211e10	+	9.36525e9i	−1.04467	+	0.603143i	−0.921154	−	0.389199i	$-0.872752\pi$
$353$	−1.62211e10	+	9.36525e9i	−1.04467	+	0.603143i	−0.123521	+	0.992342i	$0.539419\pi$
$354$	2.24734e9	+	3.89250e9i	0.143105	+	0.247865i
$355$	−4.25468e9	−	2.45644e9i	−0.267888	−	0.154665i
$356$			7.71452e9i			0.480296i
$357$	8.42403e9	−	7.25064e9i	0.518618	−	0.446378i
$358$	2.38921e9			0.145453
$359$	−1.47575e10	+	2.55607e10i	−0.888454	+	1.53885i	−0.0467503	+	0.998907i	$0.514887\pi$
$359$	−1.47575e10	+	2.55607e10i	−0.888454	+	1.53885i	−0.841703	+	0.539940i	$0.818447\pi$
$360$	6.28217e8	−	3.62701e8i	0.0374024	−	0.0215943i
$361$	−4.33839e9	−	7.51431e9i	−0.255446	−	0.442446i
$362$	−1.72907e10	−	9.98277e9i	−1.00688	−	0.581322i
$363$		−	8.67951e9i		−	0.499883i
$364$	−1.68421e10	+	3.18808e9i	−0.959378	+	0.181603i
$365$	9.04959e9			0.509867
$366$	−9.37660e8	+	1.62407e9i	−0.0522542	+	0.0905069i
$367$	−2.18997e10	+	1.26438e10i	−1.20719	+	0.696969i	−0.962143	−	0.272544i	$-0.912135\pi$
$367$	−2.18997e10	+	1.26438e10i	−1.20719	+	0.696969i	−0.245042	+	0.969513i	$0.578802\pi$
$368$	4.40496e8	+	7.62961e8i	0.0240188	+	0.0416017i
$369$	5.52553e9	+	3.19017e9i	0.298036	+	0.172071i
$370$		−	5.87254e7i		−	0.00313342i
$371$	−2.44742e9	−	1.29293e10i	−0.129185	−	0.682463i
$372$	6.20469e9			0.324002
$373$	−1.58564e10	+	2.74641e10i	−0.819160	+	1.41883i	0.0871420	+	0.996196i	$0.472227\pi$
$373$	−1.58564e10	+	2.74641e10i	−0.819160	+	1.41883i	−0.906302	+	0.422631i	$0.861107\pi$
$374$	−5.20146e9	+	3.00306e9i	−0.265851	+	0.153489i
$375$	−3.90312e9	−	6.76040e9i	−0.197373	−	0.341859i
$376$	−9.67671e9	−	5.58685e9i	−0.484146	−	0.279522i
$377$		−	7.41141e10i		−	3.66890i
$378$	−1.81238e9	−	2.10569e9i	−0.0887733	−	0.103140i
$379$	−4.77654e9			−0.231503			−0.115751	−	0.993278i	$-0.536928\pi$
$379$	−4.77654e9			−0.231503			−0.115751	+	0.993278i	$0.536928\pi$
$380$	−1.33602e9	+	2.31405e9i	−0.0640733	+	0.110978i
$381$	8.14640e9	−	4.70332e9i	0.386603	−	0.223206i
$382$	7.87473e8	+	1.36394e9i	0.0369813	+	0.0640535i
$383$	−1.00673e10	−	5.81236e9i	−0.467862	−	0.270120i	0.247482	−	0.968892i	$-0.420397\pi$
$383$	−1.00673e10	−	5.81236e9i	−0.467862	−	0.270120i	−0.715344	+	0.698772i	$0.753730\pi$
$384$			1.10958e9i			0.0510310i
$385$	−9.73864e8	+	2.78386e9i	−0.0443257	+	0.126708i
$386$	1.38493e10			0.623846
$387$	5.15393e9	−	8.92687e9i	0.229771	−	0.397975i
$388$	−1.96935e9	+	1.13700e9i	−0.0868951	+	0.0501689i
$389$	1.60070e9	+	2.77250e9i	0.0699056	+	0.121080i	0.898860	−	0.438237i	$-0.144397\pi$
$389$	1.60070e9	+	2.77250e9i	0.0699056	+	0.121080i	−0.828954	+	0.559317i	$0.811064\pi$
$390$	−5.85347e9	−	3.37950e9i	−0.253020	−	0.146081i
$391$			5.32270e9i			0.227733i
$392$	6.52781e9	+	5.20405e9i	0.276454	+	0.220393i
$393$	−1.62607e9			−0.0681663
$394$	−6.59972e9	+	1.14311e10i	−0.273868	+	0.474353i
$395$	−2.40273e9	+	1.38721e9i	−0.0986997	+	0.0569843i
$396$	7.50651e8	+	1.30016e9i	0.0305251	+	0.0528710i
$397$	2.80910e10	+	1.62184e10i	1.13085	+	0.652897i	0.944149	−	0.329519i	$-0.106887\pi$
$397$	2.80910e10	+	1.62184e10i	1.13085	+	0.652897i	0.186702	+	0.982417i	$0.440220\pi$
$398$			6.86339e8i			0.0273531i
$399$	9.65970e9	+	3.37921e9i	0.381129	+	0.133329i
$400$	5.54049e9			0.216425
$401$	−6.74502e9	+	1.16827e10i	−0.260859	+	0.451821i	−0.966470	−	0.256778i	$-0.917339\pi$
$401$	−6.74502e9	+	1.16827e10i	−0.260859	+	0.451821i	0.705611	+	0.708599i	$0.250672\pi$
$402$	−3.88666e9	+	2.24396e9i	−0.148824	+	0.0859234i
$403$	−2.89064e10	−	5.00673e10i	−1.09591	−	1.89817i
$404$	−7.56226e9	−	4.36608e9i	−0.283875	−	0.163895i
$405$		−	1.09550e9i		−	0.0407186i
$406$	−2.73579e10	+	2.35472e10i	−1.00688	+	0.866633i
$407$	1.21539e8			0.00442932
$408$	−3.35189e9	+	5.80564e9i	−0.120962	+	0.209512i
$409$	−4.16751e9	+	2.40612e9i	−0.148931	+	0.0859851i	−0.572614	−	0.819825i	$-0.694070\pi$
$409$	−4.16751e9	+	2.40612e9i	−0.148931	+	0.0859851i	0.423683	+	0.905811i	$0.360737\pi$
$410$	−3.77994e9	−	6.54704e9i	−0.133767	−	0.231691i
$411$	−2.16403e9	−	1.24940e9i	−0.0758395	−	0.0437860i
$412$		−	6.22872e9i		−	0.216177i
$413$	−2.00409e10	+	3.79359e9i	−0.688836	+	0.130392i
$414$	1.33047e9			0.0452902
$415$	−5.79976e9	+	1.00455e10i	−0.195532	+	0.338671i
$416$	8.95351e9	−	5.16931e9i	0.298965	−	0.172607i
$417$	1.66805e10	+	2.88914e10i	0.551650	+	0.955486i
$418$	−4.78918e9	−	2.76503e9i	−0.156876	−	0.0905723i
$419$		−	2.40256e10i		−	0.779505i	−0.920920	−	0.389752i	$-0.872561\pi$
$419$		−	2.40256e10i		−	0.779505i	0.920920	−	0.389752i	$-0.127439\pi$
$420$	6.12253e8	+	3.23442e9i	0.0196759	+	0.103944i
$421$	5.73168e10			1.82454			0.912270	−	0.409589i	$-0.134328\pi$
$421$	5.73168e10			1.82454			0.912270	+	0.409589i	$0.134328\pi$
$422$	−7.18857e9	+	1.24510e10i	−0.226669	+	0.392603i
$423$	−1.46137e10	+	8.43725e9i	−0.456457	+	0.263536i
$424$	3.96837e9	+	6.87342e9i	0.122786	+	0.212672i
$425$	2.89894e10	+	1.67370e10i	0.888554	+	0.513007i
$426$		−	1.13488e10i		−	0.344597i
$427$	−5.55159e9	−	6.45002e9i	−0.166996	−	0.194021i
$428$	−2.44101e10			−0.727436
$429$	6.99425e9	−	1.21144e10i	0.206496	−	0.357662i
$430$	−1.05772e10	+	6.10675e9i	−0.309383	+	0.178622i
$431$	5.33199e9	+	9.23527e9i	0.154518	+	0.267634i	0.932884	−	0.360178i	$-0.117284\pi$
$431$	5.33199e9	+	9.23527e9i	0.154518	+	0.267634i	−0.778365	+	0.627812i	$0.783951\pi$
$432$	1.45119e9	+	8.37844e8i	0.0416667	+	0.0240563i
$433$		−	1.43357e10i		−	0.407818i	−0.978990	−	0.203909i	$-0.934635\pi$
$433$		−	1.43357e10i		−	0.407818i	0.978990	−	0.203909i	$-0.0653647\pi$
$434$	−9.29747e9	+	2.65774e10i	−0.262063	+	0.749125i
$435$	−1.42332e10			−0.397507
$436$	6.63134e9	−	1.14858e10i	0.183508	−	0.317846i
$437$	−4.24423e9	+	2.45041e9i	−0.116379	+	0.0671912i
$438$	1.04523e10	+	1.81040e10i	0.283999	+	0.491900i
$439$	1.80232e10	+	1.04057e10i	0.485258	+	0.280164i	0.722605	−	0.691261i	$-0.242944\pi$
$439$	1.80232e10	+	1.04057e10i	0.485258	+	0.280164i	−0.237347	+	0.971425i	$0.576278\pi$
$440$		−	1.77885e9i		−	0.0474601i
$441$	1.17354e10	−	4.60795e9i	0.310272	−	0.121830i
$442$	6.24631e10			1.63657
$443$	1.36221e10	−	2.35942e10i	0.353696	−	0.612620i	−0.633198	−	0.773990i	$-0.718258\pi$
$443$	1.36221e10	−	2.35942e10i	0.353696	−	0.612620i	0.986894	+	0.161370i	$0.0515913\pi$
$444$	1.17482e8	−	6.78282e7i	0.00302301	−	0.00174533i
$445$	−6.90214e9	−	1.19549e10i	−0.176013	−	0.304863i
$446$	−3.24130e9	−	1.87136e9i	−0.0819180	−	0.0472954i
$447$		−	2.04759e10i		−	0.512876i
$448$	−4.75283e9	−	1.66266e9i	−0.117989	−	0.0412755i
$449$	6.25513e10			1.53904			0.769522	−	0.638621i	$-0.220495\pi$
$449$	6.25513e10			1.53904			0.769522	+	0.638621i	$0.220495\pi$
$450$	4.18362e9	−	7.24624e9i	0.102024	−	0.176711i
$451$	1.35498e10	−	7.82301e9i	0.327513	−	0.189090i
$452$	1.63812e10	+	2.83731e10i	0.392457	+	0.679755i
$453$	−1.69311e10	−	9.77517e9i	−0.402061	−	0.232130i
$454$			4.24345e10i			0.998840i
$455$	2.32471e10	−	2.00090e10i	0.542404	−	0.466852i
$456$	−6.17242e9			−0.142757
$457$	4.24919e8	−	7.35982e8i	0.00974186	−	0.0168734i	−0.861113	−	0.508413i	$-0.830232\pi$
$457$	4.24919e8	−	7.35982e8i	0.00974186	−	0.0168734i	0.870855	+	0.491540i	$0.163566\pi$
$458$	−1.82116e9	+	1.05145e9i	−0.0413892	+	0.0238961i
$459$	5.06202e9	+	8.76767e9i	0.114044	+	0.197530i
$460$	−1.36524e9	−	7.88219e8i	−0.0304913	−	0.0176042i
$461$			4.68577e10i			1.03747i	0.854934	+	0.518737i	$0.173598\pi$
$461$			4.68577e10i			1.03747i	−0.854934	+	0.518737i	$0.826402\pi$
$462$	−6.69400e9	+	1.26713e9i	−0.146933	+	0.0278133i
$463$	3.76747e10			0.819834			0.409917	−	0.912123i	$-0.365558\pi$
$463$	3.76747e10			0.819834			0.409917	+	0.912123i	$0.365558\pi$
$464$	1.08856e10	−	1.88544e10i	0.234845	−	0.406763i
$465$	−9.61514e9	+	5.55131e9i	−0.205657	+	0.118736i
$466$	−1.40624e10	−	2.43569e10i	−0.298206	−	0.516509i
$467$	1.78136e10	+	1.02847e10i	0.374527	+	0.216233i	0.675435	−	0.737420i	$-0.263956\pi$
$467$	1.78136e10	+	1.02847e10i	0.374527	+	0.216233i	−0.300907	+	0.953653i	$0.597289\pi$
$468$		−	1.56134e10i		−	0.325472i
$469$	−3.78789e9	−	2.00108e10i	−0.0782900	−	0.413592i
$470$	1.99941e10			0.409742
$471$	−2.37592e10	+	4.11522e10i	−0.482779	+	0.836198i
$472$	1.06540e10	−	6.15111e9i	0.214658	−	0.123933i
$473$	−1.26386e10	−	2.18907e10i	−0.252496	−	0.437336i
$474$	−5.55033e9	−	3.20448e9i	−0.109952	−	0.0634811i
$475$			3.08209e10i			0.605439i
$476$	−1.98455e10	−	2.30572e10i	−0.386575	−	0.449136i
$477$	1.19861e10			0.231528
$478$	3.26455e10	−	5.65437e10i	0.625334	−	1.08311i
$479$	−6.05093e10	+	3.49351e10i	−1.14942	+	0.663620i	−0.948747	−	0.316038i	$-0.897647\pi$
$479$	−6.05093e10	+	3.49351e10i	−1.14942	+	0.663620i	−0.200677	+	0.979658i	$0.564314\pi$
$480$	−9.92737e8	−	1.71947e9i	−0.0187012	−	0.0323914i
$481$	−1.09465e9	−	6.31996e8i	−0.0204501	−	0.0118068i
$482$			3.86604e10i			0.716272i
$483$	−1.99366e9	+	5.69900e9i	−0.0366321	+	0.104715i
$484$	−2.37564e10			−0.432912
$485$	2.03454e9	−	3.52393e9i	0.0367705	−	0.0636884i
$486$	2.19158e9	−	1.26531e9i	0.0392837	−	0.0226805i
$487$	−2.69794e10	−	4.67297e10i	−0.479641	−	0.830763i	0.520086	−	0.854114i	$-0.325900\pi$
$487$	−2.69794e10	−	4.67297e10i	−0.479641	−	0.830763i	−0.999727	+	0.0233510i	$0.992566\pi$
$488$	4.44520e9	+	2.56644e9i	0.0783813	+	0.0452534i
$489$		−	5.22037e9i		−	0.0912989i
$490$	−1.47719e10	−	2.22410e9i	−0.256243	−	0.0385807i
$491$	−8.79465e10			−1.51319			−0.756594	−	0.653885i	$-0.773138\pi$
$491$	−8.79465e10			−1.51319			−0.756594	+	0.653885i	$0.773138\pi$
$492$	8.73170e9	−	1.51238e10i	0.149018	−	0.258107i
$493$	1.13913e11	−	6.57678e10i	1.92835	−	1.11333i
$494$	2.87561e10	+	4.98070e10i	0.482860	+	0.836339i
$495$	−2.32650e9	−	1.34321e9i	−0.0387510	−	0.0223729i
$496$		−	1.69827e10i		−	0.280594i
$497$	4.86120e10	+	1.70057e10i	0.796742	+	0.278721i
$498$	−2.67950e10			−0.435649
$499$	−2.65859e10	+	4.60482e10i	−0.428795	+	0.742695i	−0.996766	−	0.0803533i	$-0.974395\pi$
$499$	−2.65859e10	+	4.60482e10i	−0.428795	+	0.742695i	0.567971	+	0.823048i	$0.307728\pi$
$500$	−1.85037e10	+	1.06831e10i	−0.296059	+	0.170930i
$501$	−7.01119e9	−	1.21437e10i	−0.111286	−	0.192753i
$502$	9.45225e9	+	5.45726e9i	0.148840	+	0.0859330i
$503$		−	9.27008e10i		−	1.44814i	−0.689724	−	0.724072i	$-0.742268\pi$
$503$		−	9.27008e10i		−	1.44814i	0.689724	−	0.724072i	$-0.257732\pi$
$504$	−5.76340e9	+	4.96061e9i	−0.0893217	+	0.0768799i
$505$	1.56252e10			0.240249
$506$	1.63131e9	−	2.82551e9i	0.0248848	−	0.0431017i
$507$	−9.29514e10	+	5.36655e10i	−1.40677	+	0.812201i
$508$	−1.28733e10	−	2.22972e10i	−0.193302	−	0.334808i
$509$	−1.00934e10	−	5.82744e9i	−0.150372	−	0.0868174i	0.422926	−	0.906164i	$-0.361003\pi$
$509$	−1.00934e10	−	5.82744e9i	−0.150372	−	0.0868174i	−0.573298	+	0.819347i	$0.694336\pi$
$510$		−	1.19957e10i		−	0.177314i
$511$	−9.32097e10	+	1.76439e10i	−1.36703	+	0.258769i
$512$	3.03700e9			0.0441942
$513$	−4.66079e9	+	8.07273e9i	−0.0672961	+	0.116560i
$514$	5.32881e10	−	3.07659e10i	0.763445	−	0.440775i
$515$	5.57281e9	+	9.65238e9i	0.0792219	+	0.137216i
$516$	−2.44335e10	−	1.41067e10i	−0.344656	−	0.198987i
$517$			4.13800e10i			0.579200i
$518$	1.14497e8	+	6.04865e8i	0.00159028	+	0.00840117i
$519$	−3.16704e10			−0.436500
$520$	−9.24992e9	+	1.60213e10i	−0.126510	+	0.219122i
$521$	−8.67767e10	+	5.01006e10i	−1.17775	+	0.679973i	−0.955492	−	0.295015i	$-0.904675\pi$
$521$	−8.67767e10	+	5.01006e10i	−1.17775	+	0.679973i	−0.222255	+	0.974988i	$0.571342\pi$
$522$	−1.64394e10	−	2.84739e10i	−0.221414	−	0.383500i
$523$	2.72478e10	+	1.57315e10i	0.364187	+	0.210263i	0.670916	−	0.741534i	$-0.265901\pi$
$523$	2.72478e10	+	1.57315e10i	0.364187	+	0.210263i	−0.306729	+	0.951797i	$0.599235\pi$
$524$			4.45067e9i			0.0590337i
$525$	2.47699e10	+	2.87785e10i	0.326052	+	0.378818i
$526$	−3.36904e10			−0.440112
$527$	5.13022e10	−	8.88580e10i	0.665110	−	1.15200i
$528$	3.55864e9	−	2.05458e9i	0.0457876	−	0.0264355i
$529$	3.77098e10	+	6.53153e10i	0.481539	+	0.834050i
$530$	−1.22992e10	−	7.10097e9i	−0.155874	−	0.0899941i
$531$		−	1.85788e10i		−	0.233690i
$532$	9.24913e9	−	2.64392e10i	0.115466	−	0.330067i
$533$	−1.62717e11			−2.01615
$534$	1.59440e10	−	2.76159e10i	0.196080	−	0.339621i
$535$	3.78273e10	−	2.18396e10i	0.461733	−	0.266582i
$536$	6.14188e9	+	1.06380e10i	0.0744119	+	0.128885i
$537$	−8.55273e9	−	4.93792e9i	−0.102851	−	0.0593809i
$538$		−	4.68657e10i		−	0.559404i
$539$	4.60303e9	−	3.05721e10i	0.0545366	−	0.362219i
$540$	−2.99846e9			−0.0352633
$541$	−1.75184e10	+	3.03427e10i	−0.204506	+	0.354214i	−0.949975	−	0.312326i	$-0.898892\pi$
$541$	−1.75184e10	+	3.03427e10i	−0.204506	+	0.354214i	0.745470	+	0.666540i	$0.232225\pi$
$542$	−9.98112e10	+	5.76260e10i	−1.15660	+	0.667762i
$543$	4.12639e10	+	7.14712e10i	0.474648	+	0.822114i
$544$	1.58904e10	+	9.17435e9i	0.181443	+	0.104756i
$545$			2.37321e10i			0.268999i
$546$	6.68790e10	+	2.33960e10i	0.752522	+	0.263252i
$547$	−1.20488e11			−1.34584			−0.672922	−	0.739714i	$-0.734961\pi$
$547$	−1.20488e11			−1.34584			−0.672922	+	0.739714i	$0.734961\pi$
$548$	−3.41970e9	+	5.92309e9i	−0.0379197	+	0.0656789i
$549$	6.71313e9	−	3.87583e9i	0.0738986	−	0.0426654i
$550$	−1.02592e10	−	1.77694e10i	−0.112114	−	0.194188i
$551$	1.04884e11	+	6.05549e10i	1.13790	+	0.656966i
$552$		−	3.64159e9i		−	0.0392225i
$553$	2.20432e10	−	1.89727e10i	0.235707	−	0.202875i
$554$	7.38048e10			0.783512
$555$	−1.21371e8	+	2.10221e8i	−0.00127922	+	0.00221567i
$556$	7.90777e10	−	4.56555e10i	0.827475	−	0.477743i
$557$	−3.56051e10	−	6.16698e10i	−0.369906	−	0.640696i	0.619645	−	0.784883i	$-0.287277\pi$
$557$	−3.56051e10	−	6.16698e10i	−0.369906	−	0.640696i	−0.989551	+	0.144187i	$0.953943\pi$
$558$	−2.22111e10	−	1.28236e10i	−0.229104	−	0.132273i
$559$			2.62880e11i			2.69222i
$560$	8.85284e9	−	1.67578e9i	0.0900182	−	0.0170398i
$561$	2.48264e10			0.250647
$562$	1.77199e10	−	3.06917e10i	0.177630	−	0.307664i
$563$	7.96843e10	−	4.60057e10i	0.793120	−	0.457908i	−0.0479396	−	0.998850i	$-0.515265\pi$
$563$	7.96843e10	−	4.60057e10i	0.793120	−	0.457908i	0.841060	+	0.540942i	$0.181932\pi$
$564$	2.30933e10	+	3.99988e10i	0.228229	+	0.395303i
$565$	−5.07705e10	−	2.93124e10i	−0.498216	−	0.287645i
$566$		−	2.89168e10i		−	0.281764i
$567$	2.13589e9	+	1.12835e10i	0.0206655	+	0.109172i
$568$	−3.10625e10			−0.298430
$569$	−6.30580e10	+	1.09220e11i	−0.601577	+	1.04196i	0.391005	+	0.920388i	$0.372127\pi$
$569$	−6.30580e10	+	1.09220e11i	−0.601577	+	1.04196i	−0.992582	+	0.121574i	$0.961206\pi$
$570$	9.56514e9	−	5.52244e9i	0.0906133	−	0.0523156i
$571$	−8.17585e10	−	1.41610e11i	−0.769110	−	1.33214i	−0.938046	−	0.346510i	$-0.887367\pi$
$571$	−8.17585e10	−	1.41610e11i	−0.769110	−	1.33214i	0.168936	−	0.985627i	$-0.445967\pi$
$572$	−3.31579e10	−	1.91437e10i	−0.309744	−	0.178831i
$573$		−	6.51006e9i		−	0.0603902i
$574$	5.16977e10	+	6.00641e10i	0.476237	+	0.553309i
$575$	−1.81836e10			−0.166345
$576$	2.29324e9	−	3.97200e9i	0.0208333	−	0.0360844i
$577$	9.09364e10	−	5.25022e10i	0.820417	−	0.473668i	−0.0301433	−	0.999546i	$-0.509596\pi$
$577$	9.09364e10	−	5.25022e10i	0.820417	−	0.473668i	0.850560	+	0.525878i	$0.176263\pi$
$578$	1.59680e10	+	2.76573e10i	0.143067	+	0.247799i
$579$	−4.95766e10	−	2.86231e10i	−0.441126	−	0.254684i
$580$			3.89572e10i			0.344252i
$581$	4.01513e10	−	1.14775e11i	0.352367	−	1.00726i
$582$	9.39963e9			0.0819255
$583$	1.46962e10	−	2.54546e10i	0.127213	−	0.220340i
$584$	4.95518e10	−	2.86087e10i	0.425998	−	0.245950i
$585$	1.39692e10	+	2.41954e10i	0.119275	+	0.206590i
$586$	−8.13046e10	−	4.69412e10i	−0.689484	−	0.398074i
$587$			6.19187e10i			0.521519i	0.965404	+	0.260759i	$0.0839729\pi$
$587$			6.19187e10i			0.521519i	−0.965404	+	0.260759i	$0.916027\pi$
$588$	−1.26123e10	−	3.21205e10i	−0.105508	−	0.268703i
$589$	9.44718e10			0.784948
$590$	−1.10067e10	+	1.90642e10i	−0.0908345	+	0.157330i
$591$	4.72504e10	−	2.72801e10i	0.387307	−	0.223612i
$592$	−1.85650e8	−	3.21556e8i	−0.00151150	−	0.00261800i
$593$	−1.37618e11	−	7.94536e10i	−1.11290	−	0.642532i	−0.173320	−	0.984866i	$-0.555449\pi$
$593$	−1.37618e11	−	7.94536e10i	−1.11290	−	0.642532i	−0.939578	+	0.342334i	$0.888783\pi$
$594$		−	6.20565e9i		−	0.0498473i
$595$	5.13828e10	+	1.79750e10i	0.409968	+	0.143417i
$596$	−5.60438e10			−0.444163
$597$	1.41850e9	−	2.45691e9i	0.0111669	−	0.0193416i
$598$	−2.93850e10	+	1.69654e10i	−0.229785	+	0.132666i
$599$	7.03020e10	+	1.21767e11i	0.546085	+	0.945847i	0.998538	+	0.0540584i	$0.0172157\pi$
$599$	7.03020e10	+	1.21767e11i	0.546085	+	0.945847i	−0.452453	+	0.891788i	$0.649451\pi$
$600$	−1.98335e10	−	1.14508e10i	−0.153036	−	0.0883553i
$601$			2.64617e10i			0.202824i	0.994845	+	0.101412i	$0.0323360\pi$
$601$			2.64617e10i			0.202824i	−0.994845	+	0.101412i	$0.967664\pi$
$602$	9.70376e10	−	8.35211e10i	0.738847	−	0.635931i
$603$	1.85509e10			0.140312
$604$	−2.67553e10	+	4.63416e10i	−0.201031	+	0.348195i
$605$	3.68143e10	−	2.12547e10i	0.274786	−	0.158648i
$606$	1.80472e10	+	3.12587e10i	0.133820	+	0.231783i
$607$	1.13356e11	+	6.54461e10i	0.835006	+	0.482091i	0.855564	−	0.517698i	$-0.173211\pi$
$607$	1.13356e11	+	6.54461e10i	0.835006	+	0.482091i	−0.0205577	+	0.999789i	$0.506544\pi$
$608$			1.68943e10i			0.123631i
$609$	1.46600e11	−	2.77504e10i	1.06578	−	0.201744i
$610$	−9.18472e9			−0.0663356
$611$	2.15174e11	−	3.72692e11i	1.54392	−	2.67415i
$612$	2.39977e10	−	1.38551e10i	0.171066	−	0.0987651i
$613$	−1.30407e11	−	2.25872e11i	−0.923550	−	1.59964i	−0.793876	−	0.608079i	$-0.791940\pi$
$613$	−1.30407e11	−	2.25872e11i	−0.923550	−	1.59964i	−0.129674	−	0.991557i	$-0.541393\pi$
$614$	6.10710e10	+	3.52594e10i	0.429697	+	0.248085i
$615$			3.12488e10i			0.218441i
$616$	3.46821e9	+	1.83219e10i	0.0240870	+	0.127247i
$617$	−2.19036e11			−1.51138			−0.755691	−	0.654928i	$-0.772699\pi$
$617$	−2.19036e11			−1.51138			−0.755691	+	0.654928i	$0.772699\pi$
$618$	−1.28733e10	+	2.22971e10i	−0.0882540	+	0.152860i
$619$	1.57334e11	−	9.08365e10i	1.07166	−	0.618726i	0.143028	−	0.989719i	$-0.454316\pi$
$619$	1.57334e11	−	9.08365e10i	1.07166	−	0.618726i	0.928636	+	0.370993i	$0.120983\pi$
$620$	1.51943e10	+	2.63173e10i	0.102829	+	0.178104i
$621$	−4.76273e9	−	2.74976e9i	−0.0320250	−	0.0184897i
$622$			1.04085e11i			0.695384i
$623$	9.43996e10	+	1.09677e11i	0.626640	+	0.728052i
$624$	−4.27349e10			−0.281867
$625$	−4.69316e10	+	8.12879e10i	−0.307571	+	0.532728i
$626$	−7.38047e10	+	4.26112e10i	−0.480603	+	0.277477i
$627$	1.14293e10	+	1.97961e10i	0.0739520	+	0.128089i
$628$	1.12636e11	+	6.50306e10i	0.724169	+	0.418099i
$629$		−	2.24330e9i		−	0.0143312i
$630$	4.49307e9	−	1.28437e10i	0.0285221	−	0.0815322i
$631$	−1.92621e11			−1.21502			−0.607512	−	0.794310i	$-0.707832\pi$
$631$	−1.92621e11			−1.21502			−0.607512	+	0.794310i	$0.707832\pi$
$632$	−8.77089e9	+	1.51916e10i	−0.0549762	+	0.0952217i
$633$	5.14663e10	−	2.97141e10i	0.320559	−	0.185075i
$634$	−8.39248e10	−	1.45362e11i	−0.519438	−	0.899692i
$635$	3.98985e10	+	2.30354e10i	0.245393	+	0.141677i
$636$		−	3.28066e10i		−	0.200509i
$637$	−2.00431e11	+	2.51415e11i	−1.21733	+	1.52698i
$638$	−8.06263e10			−0.486625
$639$	−2.34552e10	+	4.06257e10i	−0.140681	+	0.243667i
$640$	−4.70631e9	+	2.71719e9i	−0.0280518	+	0.0161957i
$641$	1.53678e11	+	2.66179e11i	0.910291	+	1.57667i	0.813653	+	0.581351i	$0.197476\pi$
$641$	1.53678e11	+	2.66179e11i	0.910291	+	1.57667i	0.0966388	+	0.995320i	$0.469191\pi$
$642$	8.73816e10	+	5.04498e10i	0.514375	+	0.296975i
$643$			8.86136e10i			0.518390i	0.965825	+	0.259195i	$0.0834572\pi$
$643$			8.86136e10i			0.518390i	−0.965825	+	0.259195i	$0.916543\pi$
$644$	1.55986e10	+	5.45678e9i	0.0906862	+	0.0317244i
$645$	5.04846e10			0.291689
$646$	−5.10354e10	+	8.83960e10i	−0.293050	+	0.507577i
$647$	1.80088e11	−	1.03974e11i	1.02770	−	0.593343i	0.111375	−	0.993778i	$-0.464474\pi$
$647$	1.80088e11	−	1.03974e11i	1.02770	−	0.593343i	0.916325	+	0.400435i	$0.131141\pi$
$648$	−3.46324e9	−	5.99851e9i	−0.0196419	−	0.0340207i
$649$	−3.94556e10	−	2.27797e10i	−0.222397	−	0.128401i
$650$			2.13389e11i			1.19541i
$651$	8.82116e10	−	7.59244e10i	0.491136	−	0.422725i
$652$	−1.42885e10			−0.0790672
$653$	7.32026e10	−	1.26791e11i	0.402600	−	0.697324i	−0.591439	−	0.806350i	$-0.701440\pi$
$653$	7.32026e10	−	1.26791e11i	0.402600	−	0.697324i	0.994039	+	0.109026i	$0.0347732\pi$
$654$	−4.74768e10	+	2.74108e10i	−0.259520	+	0.149834i
$655$	−3.98199e9	−	6.89701e9i	−0.0216339	−	0.0374711i
$656$	−4.13947e10	−	2.38993e10i	−0.223527	−	0.129053i
$657$		−	8.64097e10i		−	0.463768i
$658$	−2.05937e11	+	3.89824e10i	−1.09858	+	0.207953i
$659$	3.15143e11			1.67096			0.835480	−	0.549521i	$-0.185190\pi$
$659$	3.15143e11			1.67096			0.835480	+	0.549521i	$0.185190\pi$
$660$	−3.67645e9	+	6.36780e9i	−0.0193755	+	0.0335593i
$661$	1.38040e10	−	7.96974e9i	0.0723101	−	0.0417483i	−0.463409	−	0.886145i	$-0.653374\pi$
$661$	1.38040e10	−	7.96974e9i	0.0723101	−	0.0417483i	0.535719	+	0.844396i	$0.320041\pi$
$662$	−9.35903e10	−	1.62103e11i	−0.487303	−	0.844033i
$663$	−2.23601e11	−	1.29096e11i	−1.15723	−	0.668126i
$664$			7.33399e10i			0.377283i
$665$	9.32208e9	+	4.92469e10i	0.0476679	+	0.251821i
$666$	−5.60738e8			−0.00285012
$667$	−3.57260e10	+	6.18793e10i	−0.180502	+	0.312638i
$668$	−3.32382e10	+	1.91901e10i	−0.166929	+	0.0963766i
$669$	7.73531e9	+	1.33980e10i	0.0386165	+	0.0668858i
$670$	−1.90356e10	−	1.09902e10i	−0.0944643	−	0.0545390i
$671$		−	1.90088e10i		−	0.0937702i
$672$	1.35775e10	+	1.57748e10i	0.0665800	+	0.0773549i
$673$	−4.43694e10			−0.216283			−0.108142	−	0.994135i	$-0.534490\pi$
$673$	−4.43694e10			−0.216283			−0.108142	+	0.994135i	$0.534490\pi$
$674$	8.02435e10	−	1.38986e11i	0.388839	−	0.673489i
$675$	−2.99524e10	+	1.72930e10i	−0.144284	+	0.0833022i
$676$	1.46886e11	+	2.54414e11i	0.703387	+	1.21830i
$677$	−6.69597e10	−	3.86592e10i	−0.318757	−	0.184034i	0.332082	−	0.943251i	$-0.392249\pi$
$677$	−6.69597e10	−	3.86592e10i	−0.318757	−	0.184034i	−0.650838	+	0.759216i	$0.725582\pi$
$678$		−	1.35424e11i		−	0.640880i
$679$	−1.40850e10	+	4.02628e10i	−0.0662639	+	0.189420i
$680$	−3.28330e10			−0.153559
$681$	8.77019e10	−	1.51904e11i	0.407775	−	0.706287i
$682$	−5.44666e10	+	3.14463e10i	−0.251764	+	0.145356i
$683$	−1.68358e11	−	2.91605e11i	−0.773664	−	1.34002i	−0.935543	−	0.353214i	$-0.885089\pi$
$683$	−1.68358e11	−	2.91605e11i	−0.773664	−	1.34002i	0.161879	−	0.986811i	$-0.448245\pi$
$684$	2.20956e10	+	1.27569e10i	0.100944	+	0.0582802i
$685$		−	1.22383e10i		−	0.0555854i
$686$	1.56485e11	−	5.89272e9i	0.706606	−	0.0266084i
$687$	8.69237e9			0.0390221
$688$	−3.86109e10	+	6.68760e10i	−0.172328	+	0.298481i
$689$	−2.64726e11	+	1.52839e11i	−1.17468	+	0.678201i
$690$	3.25811e9	+	5.64322e9i	0.0143737	+	0.0248961i
$691$	−3.58845e11	−	2.07179e11i	−1.57397	−	0.908729i	−0.995676	−	0.0928976i	$-0.970387\pi$
$691$	−3.58845e11	−	2.07179e11i	−1.57397	−	0.908729i	−0.578290	−	0.815832i	$-0.696280\pi$
$692$			8.66841e10i			0.378020i
$693$	2.65816e10	+	9.29891e9i	0.115252	+	0.0403180i
$694$	−1.67902e11			−0.723801
$695$	−8.16956e10	+	1.41501e11i	−0.350154	+	0.606485i
$696$	−7.79351e10	+	4.49958e10i	−0.332121	+	0.191750i
$697$	−1.44393e11	−	2.50095e11i	−0.611806	−	1.05968i
$698$	−1.26793e10	−	7.32042e9i	−0.0534164	−	0.0308400i
$699$			1.16255e11i			0.486969i
$700$	7.87687e10	−	6.77969e10i	0.328066	−	0.282369i
$701$	−2.42044e11			−1.00236			−0.501179	−	0.865344i	$-0.667100\pi$
$701$	−2.42044e11			−1.00236			−0.501179	+	0.865344i	$0.667100\pi$
$702$	−3.22690e10	+	5.58916e10i	−0.132873	+	0.230143i
$703$	1.78876e9	−	1.03274e9i	0.00732372	−	0.00422835i
$704$	−5.62353e9	−	9.74024e9i	−0.0228938	−	0.0396533i
$705$	−7.15735e10	−	4.13230e10i	−0.289731	−	0.167276i
$706$		−	2.11911e11i		−	0.852973i
$707$	−1.60938e11	+	3.04644e10i	−0.644141	+	0.121931i
$708$	−5.08514e10			−0.202381
$709$	1.74404e11	−	3.02077e11i	0.690194	−	1.19545i	−0.281580	−	0.959538i	$-0.590858\pi$
$709$	1.74404e11	−	3.02077e11i	0.690194	−	1.19545i	0.971774	−	0.235914i	$-0.0758083\pi$
$710$	4.81362e10	−	2.77914e10i	0.189425	−	0.109365i
$711$	1.32458e10	+	2.29423e10i	0.0518321	+	0.0897758i
$712$	−7.55866e10	−	4.36399e10i	−0.294120	−	0.169810i
$713$			5.57362e10i			0.215665i
$714$	2.33879e10	+	1.23554e11i	0.0899908	+	0.475406i
$715$	6.85113e10			0.262143
$716$	−1.35154e10	+	2.34094e10i	−0.0514254	+	0.0890714i
$717$	−2.33724e11	+	1.34941e11i	−0.884356	+	0.510583i
$718$	−1.66962e11	−	2.89187e11i	−0.628232	−	1.08813i
$719$	1.56999e11	+	9.06435e10i	0.587465	+	0.339173i	0.764094	−	0.645104i	$-0.223186\pi$
$719$	1.56999e11	+	9.06435e10i	0.587465	+	0.339173i	−0.176630	+	0.984277i	$0.556520\pi$
$720$			8.20699e9i			0.0305389i
$721$	−7.62185e10	−	8.85532e10i	−0.282046	−	0.327690i
$722$	9.81665e10			0.361256
$723$	7.99016e10	−	1.38394e11i	0.292417	−	0.506481i
$724$	1.95622e11	−	1.12942e11i	0.711971	−	0.411057i
$725$	2.24678e11	+	3.89154e11i	0.813222	+	1.40854i
$726$	8.50415e10	+	4.90987e10i	0.306115	+	0.176735i
$727$			2.81361e11i			1.00722i	0.863930	+	0.503612i	$0.167996\pi$
$727$			2.81361e11i			1.00722i	−0.863930	+	0.503612i	$0.832004\pi$
$728$	6.40365e10	−	1.83052e11i	0.227983	−	0.651703i
$729$	−1.04604e10			−0.0370370
$730$	−5.11922e10	+	8.86675e10i	−0.180265	+	0.312229i
$731$	−4.04046e11	+	2.33276e11i	−1.41502	+	0.816960i
$732$	−1.06084e10	−	1.83743e10i	−0.0369493	−	0.0639980i
$733$	2.43377e11	+	1.40514e11i	0.843070	+	0.486747i	0.858307	−	0.513137i	$-0.171517\pi$
$733$	2.43377e11	+	1.40514e11i	0.843070	+	0.486747i	−0.0152365	+	0.999884i	$0.504850\pi$
$734$		−	2.86096e11i		−	0.985663i
$735$	4.82828e10	+	3.84916e10i	0.165441	+	0.131892i
$736$	−9.96729e9			−0.0339677
$737$	2.27455e10	−	3.93964e10i	0.0770949	−	0.133532i
$738$	−6.25142e10	+	3.60926e10i	−0.210743	+	0.121673i
$739$	9.46678e10	+	1.63970e11i	0.317413	+	0.549775i	0.979947	−	0.199256i	$-0.0638525\pi$
$739$	9.46678e10	+	1.63970e11i	0.317413	+	0.549775i	−0.662534	+	0.749031i	$0.730519\pi$
$740$	5.75389e8	+	3.32201e8i	0.00191882	+	0.00110783i
$741$		−	2.37727e11i		−	0.788508i
$742$	1.40525e11	+	4.91594e10i	0.463596	+	0.162178i
$743$	4.17979e11			1.37151			0.685755	−	0.727832i	$-0.259472\pi$
$743$	4.17979e11			1.37151			0.685755	+	0.727832i	$0.259472\pi$
$744$	−3.50990e10	+	6.07933e10i	−0.114552	+	0.198410i
$745$	8.68487e10	−	5.01421e10i	0.281928	−	0.162771i
$746$	−1.79394e11	−	3.10720e11i	−0.579234	−	1.00326i
$747$	9.59190e10	+	5.53788e10i	0.308051	+	0.177853i
$748$		−	6.79515e10i		−	0.217067i
$749$	−3.47037e11	+	2.98697e11i	−1.10268	+	0.949083i
$750$	8.83175e10			0.279127
$751$	1.36155e11	−	2.35827e11i	0.428028	−	0.741367i	−0.568670	−	0.822566i	$-0.692542\pi$
$751$	1.36155e11	−	2.35827e11i	0.428028	−	0.741367i	0.996698	+	0.0811992i	$0.0258750\pi$
$752$	1.09479e11	−	6.32080e10i	0.342343	−	0.197652i
$753$	−2.25577e10	−	3.90710e10i	−0.0701640	−	0.121528i
$754$	7.26167e11	+	4.19253e11i	2.24673	+	1.29715i
$755$		−	9.57514e10i		−	0.294684i
$756$	3.08838e10	−	5.84608e9i	0.0945461	−	0.0178969i
$757$	1.46033e11			0.444701			0.222350	−	0.974967i	$-0.428627\pi$
$757$	1.46033e11			0.444701			0.222350	+	0.974967i	$0.428627\pi$
$758$	2.70202e10	−	4.68003e10i	0.0818487	−	0.141766i
$759$	−1.16793e10	+	6.74303e9i	−0.0351924	+	0.0203183i
$760$	−1.51153e10	−	2.61804e10i	−0.0453067	−	0.0784734i
$761$	−2.17647e10	−	1.25659e10i	−0.0648954	−	0.0374674i	0.467201	−	0.884151i	$-0.345262\pi$
$761$	−2.17647e10	−	1.25659e10i	−0.0648954	−	0.0374674i	−0.532097	+	0.846684i	$0.678596\pi$
$762$			1.06424e11i			0.315660i
$763$	−4.62704e10	−	2.44438e11i	−0.136523	−	0.721225i
$764$	−1.78185e10			−0.0522995
$765$	−2.47921e10	+	4.29413e10i	−0.0723883	+	0.125380i
$766$	1.13898e11	−	6.57593e10i	0.330828	−	0.191004i
$767$	2.36906e11	+	4.10334e11i	0.684534	+	1.18565i
$768$	−1.08716e10	−	6.27674e9i	−0.0312500	−	0.0180422i
$769$			2.36713e11i			0.676889i	0.940986	+	0.338445i	$0.109901\pi$
$769$			2.36713e11i			0.676889i	−0.940986	+	0.338445i	$0.890099\pi$
$770$	−2.17671e10	−	2.52897e10i	−0.0619209	−	0.0719418i
$771$	−2.54343e11			−0.719783
$772$	−7.83433e10	+	1.35695e11i	−0.220563	+	0.382026i
$773$	−1.05440e11	+	6.08757e10i	−0.295316	+	0.170501i	−0.640337	−	0.768094i	$-0.721205\pi$
$773$	−1.05440e11	+	6.08757e10i	−0.295316	+	0.170501i	0.345021	+	0.938595i	$0.387872\pi$
$774$	5.83101e10	+	1.00996e11i	0.162472	+	0.281411i
$775$	3.03560e11	+	1.75261e11i	0.841469	+	0.485822i
$776$		−	2.57274e10i		−	0.0709495i
$777$	8.40243e8	−	2.40189e9i	0.00230526	−	0.00658975i
$778$	−3.62197e10			−0.0988614
$779$	1.32948e11	−	2.30272e11i	0.361020	−	0.625305i
$780$	6.62244e10	−	3.82347e10i	0.178912	−	0.103295i
$781$	5.75175e10	+	9.96232e10i	0.154595	+	0.267767i
$782$	−5.21516e10	−	3.01098e10i	−0.139457	−	0.0805156i
$783$			1.35905e11i			0.361567i
$784$	−8.79160e10	+	3.45206e10i	−0.232704	+	0.0913723i
$785$	−2.32730e11			−0.612878
$786$	9.19845e9	−	1.59322e10i	0.0241004	−	0.0417432i
$787$	1.87230e11	−	1.08097e11i	0.488064	−	0.281784i	−0.235707	−	0.971824i	$-0.575741\pi$
$787$	1.87230e11	−	1.08097e11i	0.488064	−	0.281784i	0.723771	+	0.690040i	$0.242407\pi$
$788$	−7.46674e10	−	1.29328e11i	−0.193654	−	0.335418i
$789$	1.20602e11	+	6.96298e10i	0.311206	+	0.179675i
$790$		−	3.13891e10i		−	0.0805880i
$791$	5.80081e11	+	2.02927e11i	1.48178	+	0.518363i
$792$	−1.69853e10			−0.0431690
$793$	−9.88448e10	+	1.71204e11i	−0.249955	+	0.432934i
$794$	−3.17814e11	+	1.83490e11i	−0.799632	+	0.461668i
$795$	2.93519e10	+	5.08390e10i	0.0734799	+	0.127271i
$796$	−6.72472e9	−	3.88252e9i	−0.0167503	−	0.00967078i
$797$		−	4.76628e11i		−	1.18126i	−0.806942	−	0.590631i	$-0.798879\pi$
$797$		−	4.76628e11i		−	1.18126i	0.806942	−	0.590631i	$-0.201121\pi$
$798$	−8.77529e10	+	7.55296e10i	−0.216396	+	0.186254i
$799$	7.63769e11			1.87402
$800$	−3.13418e10	+	5.42855e10i	−0.0765180	+	0.132533i
$801$	−1.14151e11	+	6.59049e10i	−0.277299	+	0.160099i
$802$	−7.63112e10	−	1.32175e11i	−0.184455	−	0.319486i
$803$	−1.83507e11	−	1.05948e11i	−0.441358	−	0.254818i
$804$		−	5.07751e10i		−	0.121514i
$805$	−2.90546e10	+	5.49982e9i	−0.0691880	+	0.0130968i
$806$	6.54077e11			1.54985
$807$	−9.68599e10	+	1.67766e11i	−0.228376	+	0.395558i
$808$	8.55573e10	−	4.93965e10i	0.200730	−	0.115891i
$809$	−8.27214e10	−	1.43278e11i	−0.193118	−	0.334491i	0.753164	−	0.657833i	$-0.228527\pi$
$809$	−8.27214e10	−	1.43278e11i	−0.193118	−	0.334491i	−0.946282	+	0.323342i	$0.895193\pi$
$810$	1.07337e10	+	6.19709e9i	0.0249349	+	0.0143962i
$811$		−	4.95222e11i		−	1.14476i	−0.819987	−	0.572382i	$-0.806019\pi$
$811$		−	4.95222e11i		−	1.14476i	0.819987	−	0.572382i	$-0.193981\pi$
$812$	−7.59546e10	−	4.01255e11i	−0.174715	−	0.922988i
$813$	4.76396e11			1.09045
$814$	−6.87528e8	+	1.19083e9i	−0.00156600	+	0.00271240i
$815$	2.21423e10	−	1.27838e10i	0.0501871	−	0.0289755i
$816$	−3.79223e10	−	6.56833e10i	−0.0855331	−	0.148148i
$817$	−3.72021e11	−	2.14786e11i	−0.834985	−	0.482079i
$818$		−	5.44442e10i		−	0.121601i
$819$	−1.91055e11	−	2.21974e11i	−0.424642	−	0.493363i
$820$	8.55302e10			0.189175
$821$	−4.33283e11	+	7.50469e11i	−0.953673	+	1.65181i	−0.216295	+	0.976328i	$0.569397\pi$
$821$	−4.33283e11	+	7.50469e11i	−0.953673	+	1.65181i	−0.737377	+	0.675481i	$0.763936\pi$
$822$	2.44832e10	−	1.41354e10i	0.0536266	−	0.0309613i
$823$	−2.48620e10	−	4.30622e10i	−0.0541921	−	0.0938635i	0.837657	−	0.546197i	$-0.183925\pi$
$823$	−2.48620e10	−	4.30622e10i	−0.0541921	−	0.0938635i	−0.891849	+	0.452333i	$0.850592\pi$
$824$	6.10288e10	+	3.52350e10i	0.132381	+	0.0764302i
$825$			8.48129e10i			0.183082i
$826$	7.61988e10	−	2.17819e11i	0.163692	−	0.467925i
$827$	−5.85387e11			−1.25147			−0.625736	−	0.780035i	$-0.715201\pi$
$827$	−5.85387e11			−1.25147			−0.625736	+	0.780035i	$0.715201\pi$
$828$	−7.52629e9	+	1.30359e10i	−0.0160125	+	0.0277345i
$829$	−3.13411e11	+	1.80948e11i	−0.663584	+	0.383120i	−0.793641	−	0.608386i	$-0.791817\pi$
$829$	−3.13411e11	+	1.80948e11i	−0.663584	+	0.383120i	0.130057	+	0.991506i	$0.458484\pi$
$830$	−6.56168e10	−	1.13652e11i	−0.138262	−	0.239477i
$831$	−2.64201e11	−	1.52537e11i	−0.554026	−	0.319867i
$832$			1.16968e11i			0.244104i
$833$	−5.64283e11	−	8.49600e10i	−1.17197	−	0.176455i
$834$	−3.77436e11			−0.780151
$835$	3.43386e10	−	5.94762e10i	0.0706377	−	0.122348i
$836$	5.41834e10	−	3.12828e10i	0.110928	−	0.0640443i
$837$	5.30065e10	+	9.18099e10i	0.108001	+	0.187063i
$838$	2.35402e11	+	1.35909e11i	0.477347	+	0.275596i
$839$			2.17678e11i			0.439305i	0.975578	+	0.219652i	$0.0704923\pi$
$839$			2.17678e11i			0.439305i	−0.975578	+	0.219652i	$0.929508\pi$
$840$	−3.51542e10	−	1.22978e10i	−0.0706090	−	0.0247008i
$841$	1.26549e12			2.52973
$842$	−3.24233e11	+	5.61588e11i	−0.645073	+	1.11730i
$843$	−1.26865e11	+	7.32454e10i	−0.251206	+	0.145034i
$844$	−8.13294e10	−	1.40867e11i	−0.160279	−	0.277612i
$845$	−4.55247e11	−	2.62837e11i	−0.892935	−	0.515536i
$846$		−	1.90913e11i		−	0.372696i
$847$	−3.37743e11	+	2.90698e11i	−0.656225	+	0.564818i
$848$	−8.97940e10			−0.173646
$849$	−5.97641e10	+	1.03514e11i	−0.115030	+	0.199237i
$850$	−3.27978e11	+	1.89358e11i	−0.628302	+	0.362750i
$851$	6.09296e8	+	1.05533e9i	0.00116174	+	0.00201220i
$852$	1.11195e11	+	6.41986e10i	0.211022	+	0.121834i
$853$		−	2.59248e11i		−	0.489688i	−0.969562	−	0.244844i	$-0.921263\pi$
$853$		−	2.59248e11i		−	0.489688i	0.969562	−	0.244844i	$-0.0787368\pi$
$854$	9.46016e10	−	1.79074e10i	0.177855	−	0.0336667i
$855$	−4.56542e10			−0.0854311
$856$	1.38085e11	−	2.39169e11i	0.257188	−	0.445462i
$857$	4.58730e11	−	2.64848e11i	0.850422	−	0.490991i	−0.0103715	−	0.999946i	$-0.503301\pi$
$857$	4.58730e11	−	2.64848e11i	0.850422	−	0.490991i	0.860793	+	0.508955i	$0.169968\pi$
$858$	7.91310e10	+	1.37059e11i	0.146015	+	0.252905i
$859$	−2.79468e11	−	1.61351e11i	−0.513286	−	0.296346i	0.220898	−	0.975297i	$-0.429101\pi$
$859$	−2.79468e11	−	1.61351e11i	−0.513286	−	0.296346i	−0.734183	+	0.678951i	$0.762435\pi$
$860$		−	1.38180e11i		−	0.252610i
$861$	−6.09257e10	−	3.21860e11i	−0.110863	−	0.585671i
$862$	−1.20649e11			−0.218522
$863$	7.95930e10	−	1.37859e11i	0.143493	−	0.248538i	−0.785317	−	0.619094i	$-0.787500\pi$
$863$	7.95930e10	−	1.37859e11i	0.143493	−	0.248538i	0.928810	+	0.370557i	$0.120833\pi$
$864$	−1.64183e10	+	9.47912e9i	−0.0294628	+	0.0170103i
$865$	−7.75558e10	−	1.34331e11i	−0.138532	−	0.239944i
$866$	1.40460e11	+	8.10948e10i	0.249737	+	0.144185i
$867$		−	1.32008e11i		−	0.233627i
$868$	−2.07810e11	−	2.41441e11i	−0.366090	−	0.425336i
$869$	6.49632e10			0.113917
$870$	8.05151e10	−	1.39456e11i	0.140540	−	0.243423i
$871$	−4.09718e11	+	2.36551e11i	−0.711889	+	0.411009i
$872$	7.50251e10	+	1.29947e11i	0.129760	+	0.224751i
$873$	−3.36481e10	−	1.94268e10i	−0.0579301	−	0.0334459i
$874$		−	5.54464e10i		−	0.0950228i
$875$	−1.32340e11	+	3.78303e11i	−0.225766	+	0.645368i
$876$	−2.36509e11			−0.401635
$877$	1.99603e11	−	3.45723e11i	0.337419	−	0.584426i	−0.646528	−	0.762891i	$-0.723780\pi$
$877$	1.99603e11	−	3.45723e11i	0.337419	−	0.584426i	0.983946	+	0.178464i	$0.0571129\pi$
$878$	−2.03909e11	+	1.17727e11i	−0.343129	+	0.198106i
$879$	1.94032e11	+	3.36074e11i	0.325026	+	0.562962i
$880$	1.74291e10	+	1.00627e10i	0.0290632	+	0.0167797i
$881$		−	7.07257e11i		−	1.17402i	−0.809581	−	0.587008i	$-0.800306\pi$
$881$		−	7.07257e11i		−	1.17402i	0.809581	−	0.587008i	$-0.199694\pi$
$882$	−2.12368e10	+	1.41049e11i	−0.0350925	+	0.233075i
$883$	−5.52083e11			−0.908158			−0.454079	−	0.890961i	$-0.650032\pi$
$883$	−5.52083e11			−0.908158			−0.454079	+	0.890961i	$0.650032\pi$
$884$	−3.53344e11	+	6.12011e11i	−0.578614	+	1.00219i
$885$	7.88023e10	−	4.54965e10i	0.128459	−	0.0741660i
$886$	1.54117e11	+	2.66938e11i	0.250101	+	0.433188i
$887$	3.72379e11	+	2.14993e11i	0.601576	+	0.347320i	0.769661	−	0.638452i	$-0.220425\pi$
$887$	3.72379e11	+	2.14993e11i	0.601576	+	0.347320i	−0.168085	+	0.985772i	$0.553758\pi$
$888$			1.53478e9i			0.00246828i
$889$	−4.55862e11	−	1.59472e11i	−0.729837	−	0.255316i
$890$	1.56178e11			0.248920
$891$	−1.28256e10	+	2.22145e10i	−0.0203501	+	0.0352473i
$892$	3.66711e10	−	2.11721e10i	0.0579248	−	0.0334429i
$893$	3.51616e11	+	6.09016e11i	0.552920	+	0.957686i
$894$	2.00622e11	+	1.15829e11i	0.314071	+	0.181329i
$895$		−	4.83687e10i		−	0.0753829i
$896$	4.31768e10	−	3.71626e10i	0.0669913	−	0.0576599i
$897$	1.40254e11			0.216643
$898$	−3.53843e11	+	6.12875e11i	−0.544134	+	0.942468i
$899$	1.19283e12	−	6.88682e11i	1.82617	−	1.05434i
$900$	4.73322e10	+	8.19819e10i	0.0721418	+	0.124953i
$901$	−4.69827e11	−	2.71255e11i	−0.712917	−	0.411603i
$902$			1.77014e11i			0.267413i
$903$	−5.19986e11	+	9.84296e10i	−0.782061	+	0.148039i
$904$	−3.70664e11			−0.555018
$905$	−2.02098e11	+	3.50043e11i	−0.301278	+	0.521828i
$906$	1.91553e11	−	1.10593e11i	0.284300	−	0.164141i
$907$	−2.59290e10	−	4.49104e10i	−0.0383140	−	0.0663617i	0.846233	−	0.532814i	$-0.178865\pi$
$907$	−2.59290e10	−	4.49104e10i	−0.0383140	−	0.0663617i	−0.884547	+	0.466452i	$0.845532\pi$
$908$	−4.15772e11	−	2.40046e11i	−0.611662	−	0.353143i
$909$		−	1.49197e11i		−	0.218527i
$910$	6.45416e10	+	3.40962e11i	0.0941183	+	0.497210i
$911$	−4.06380e11			−0.590009			−0.295004	−	0.955496i	$-0.595321\pi$
$911$	−4.06380e11			−0.590009			−0.295004	+	0.955496i	$0.595321\pi$
$912$	3.49165e10	−	6.04772e10i	0.0504721	−	0.0874203i
$913$	2.35215e11	−	1.35801e11i	0.338518	−	0.195443i
$914$	4.80741e9	+	8.32669e9i	0.00688853	+	0.0119313i
$915$	3.28788e10	+	1.89826e10i	0.0469063	+	0.0270814i
$916$		−	2.37916e10i		−	0.0337942i
$917$	5.44611e10	+	6.32748e10i	0.0770210	+	0.0894857i
$918$	−1.14540e11			−0.161283
$919$	−5.61460e11	+	9.72477e11i	−0.787148	+	1.36338i	0.140559	+	0.990072i	$0.455110\pi$
$919$	−5.61460e11	+	9.72477e11i	−0.787148	+	1.36338i	−0.927707	+	0.373308i	$0.878223\pi$
$920$	1.54459e10	−	8.91768e9i	0.0215606	−	0.0124480i
$921$	−1.45745e11	−	2.52438e11i	−0.202561	−	0.350846i
$922$	−4.59110e11	−	2.65067e11i	−0.635320	−	0.366802i
$923$		−	1.19635e12i		−	1.64836i
$924$	2.54518e10	−	7.27555e10i	0.0349164	−	0.0998109i
$925$	7.66363e9			0.0104681
$926$	−2.13120e11	+	3.69135e11i	−0.289855	+	0.502044i
$927$	9.21655e10	−	5.32118e10i	0.124810	−	0.0720591i
$928$	1.23157e11	+	2.13314e11i	0.166060	+	0.287625i
$929$	8.87235e11	+	5.12245e11i	1.19118	+	0.687726i	0.958573	−	0.284846i	$-0.0919425\pi$
$929$	8.87235e11	+	5.12245e11i	1.19118	+	0.687726i	0.232603	+	0.972572i	$0.425276\pi$
$930$		−	1.25612e11i		−	0.167918i
$931$	−1.92033e11	−	4.89063e11i	−0.255609	−	0.650977i
$932$	3.18197e11			0.421728
$933$	2.15117e11	−	3.72594e11i	0.283889	−	0.491711i
$934$	−2.01538e11	+	1.16358e11i	−0.264831	+	0.152900i
$935$	6.07959e10	+	1.05302e11i	0.0795478	+	0.137781i
$936$	1.52979e11	+	8.83226e10i	0.199310	+	0.115072i
$937$			2.25714e11i			0.292819i	0.989224	+	0.146410i	$0.0467718\pi$
$937$			2.25714e11i			0.292819i	−0.989224	+	0.146410i	$0.953228\pi$
$938$	2.17492e11	+	7.60844e10i	0.280952	+	0.0982843i
$939$	3.52268e11			0.453117
$940$	−1.13104e11	+	1.95901e11i	−0.144866	+	0.250915i
$941$	3.00991e10	−	1.73777e10i	0.0383879	−	0.0221633i	−0.480683	−	0.876894i	$-0.659611\pi$
$941$	3.00991e10	−	1.73777e10i	0.0383879	−	0.0221633i	0.519071	+	0.854731i	$0.326278\pi$
$942$	−2.68805e11	−	4.65584e11i	−0.341376	−	0.591281i
$943$	1.35855e11	+	7.84362e10i	0.171803	+	0.0991904i
$944$			1.39184e11i			0.175267i
$945$	−4.26288e10	+	3.66910e10i	−0.0534535	+	0.0460079i
$946$	2.85979e11			0.357083
$947$	3.45508e11	−	5.98437e11i	0.429594	−	0.744078i	−0.567243	−	0.823550i	$-0.691990\pi$
$947$	3.45508e11	−	5.98437e11i	0.429594	−	0.744078i	0.996837	+	0.0794721i	$0.0253235\pi$
$948$	6.27948e10	−	3.62546e10i	0.0777482	−	0.0448879i
$949$	1.10185e12	+	1.90846e12i	1.35849	+	2.35298i
$950$	−3.01982e11	−	1.74349e11i	−0.370754	−	0.214055i
$951$			6.93809e11i			0.848238i
$952$	3.38176e11	−	6.40143e10i	0.411713	−	0.0779344i
$953$	1.59108e12			1.92895			0.964474	−	0.264177i	$-0.0851002\pi$
$953$	1.59108e12			1.92895			0.964474	+	0.264177i	$0.0851002\pi$
$954$	−6.78033e10	+	1.17439e11i	−0.0818573	+	0.141781i
$955$	2.76126e10	−	1.59421e10i	0.0331966	−	0.0191660i
$956$	3.69342e11	+	6.39719e11i	0.442178	+	0.765875i
$957$	2.88620e11	+	1.66635e11i	0.344096	+	0.198664i
$958$		−	7.90490e11i		−	0.938500i
$959$	2.38610e10	+	1.26054e11i	0.0282108	+	0.149032i
$960$	2.24631e10			0.0264475
$961$	1.10761e11	−	1.91844e11i	0.129866	−	0.224934i
$962$	1.23845e10	−	7.15021e9i	0.0144604	−	0.00834870i
$963$	−2.08535e11	−	3.61193e11i	−0.242479	−	0.419986i
$964$	−3.78793e11	−	2.18696e11i	−0.438625	−	0.253240i
$965$		−	2.80373e11i		−	0.323316i
$966$	−4.45608e10	−	5.17722e10i	−0.0511734	−	0.0594550i
$967$	−6.93305e11			−0.792899			−0.396450	−	0.918056i	$-0.629758\pi$
$967$	−6.93305e11			−0.792899			−0.396450	+	0.918056i	$0.629758\pi$
$968$	1.34387e11	−	2.32764e11i	0.153057	−	0.265103i
$969$	3.65386e11	−	2.10956e11i	0.414435	−	0.239274i
$970$	2.30182e10	+	3.98687e10i	0.0260007	+	0.0450345i
$971$	−1.38136e12	−	7.97528e11i	−1.55392	−	0.897159i	−0.997816	−	0.0660486i	$-0.978961\pi$
$971$	−1.38136e12	−	7.97528e11i	−1.55392	−	0.897159i	−0.556108	−	0.831110i	$-0.687706\pi$
$972$			2.86307e10i			0.0320750i
$973$	5.65572e11	−	1.61672e12i	0.631010	−	1.80378i
$974$	6.10474e11			0.678315
$975$	4.41023e11	−	7.63873e11i	0.488025	−	0.845285i
$976$	−5.02917e10	+	2.90359e10i	−0.0554239	+	0.0319990i
$977$	−3.10683e11	−	5.38119e11i	−0.340988	−	0.590609i	0.643628	−	0.765338i	$-0.277428\pi$
$977$	−3.10683e11	−	5.38119e11i	−0.340988	−	0.590609i	−0.984616	+	0.174730i	$0.944095\pi$
$978$	5.11489e10	+	2.95308e10i	0.0559089	+	0.0322790i
$979$			3.23227e11i			0.351866i
$980$	1.05354e11	−	1.32153e11i	0.114221	−	0.143276i
$981$	2.26605e11			0.244678
$982$	4.97501e11	−	8.61696e11i	0.534993	−	0.926634i
$983$	4.23650e11	−	2.44594e11i	0.453725	−	0.261958i	−0.255677	−	0.966762i	$-0.582298\pi$
$983$	4.23650e11	−	2.44594e11i	0.453725	−	0.261958i	0.709402	+	0.704804i	$0.248965\pi$
$984$	9.87879e10	+	1.71106e11i	0.105372	+	0.182509i
$985$	2.31418e11	+	1.33609e11i	0.245839	+	0.141935i
$986$			1.48815e12i			1.57449i
$987$	8.17766e11	+	2.86075e11i	0.861708	+	0.301448i
$988$	−6.50675e11			−0.682868
$989$	1.26719e11	−	2.19484e11i	0.132451	−	0.229413i
$990$	2.63214e10	−	1.51967e10i	0.0274011	−	0.0158200i
$991$	2.37498e11	+	4.11359e11i	0.246244	+	0.426507i	0.962481	−	0.271350i	$-0.0874702\pi$
$991$	2.37498e11	+	4.11359e11i	0.246244	+	0.426507i	−0.716237	+	0.697857i	$0.754137\pi$
$992$	1.66395e11	+	9.60684e10i	0.171828	+	0.0992051i
$993$			7.73714e11i			0.795762i
$994$	−4.41612e11	+	3.80099e11i	−0.452372	+	0.389360i
$995$	1.38947e10			0.0141761
$996$	1.51576e11	−	2.62537e11i	0.154025	−	0.266780i
$997$	−9.69150e11	+	5.59539e11i	−0.980867	+	0.566304i	−0.902532	−	0.430623i	$-0.858294\pi$
$997$	−9.69150e11	+	5.59539e11i	−0.980867	+	0.566304i	−0.0783354	+	0.996927i	$0.524961\pi$
$998$	−3.00786e11	−	5.20976e11i	−0.303204	−	0.525165i
$999$	2.00729e9	+	1.15891e9i	0.00201534	+	0.00116356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.9.g.a.19.2	✓	8
3.2	odd	2		126.9.n.a.19.3		8
7.2	even	3		294.9.c.a.97.7		8
7.3	odd	6	inner	42.9.g.a.31.2	yes	8
7.5	odd	6		294.9.c.a.97.6		8
21.17	even	6		126.9.n.a.73.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.9.g.a.19.2	✓	8	1.1	even	1	trivial
42.9.g.a.31.2	yes	8	7.3	odd	6	inner
126.9.n.a.19.3		8	3.2	odd	2
126.9.n.a.73.3		8	21.17	even	6
294.9.c.a.97.6		8	7.5	odd	6
294.9.c.a.97.7		8	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-5.65685 + 9.79796i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-64.0000 - 110.851i) q^{4} +(198.356 + 114.521i) q^{5} +529.090i q^{6} +(-2266.33 - 792.819i) q^{7} +1448.15 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\)	\(q+(-5.65685 + 9.79796i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-64.0000 - 110.851i) q^{4} +(198.356 + 114.521i) q^{5} +529.090i q^{6} +(-2266.33 - 792.819i) q^{7} +1448.15 q^{8} +(1093.50 - 1894.00i) q^{9} +(-2244.14 + 1295.66i) q^{10} +(-2681.51 - 4644.51i) q^{11} +(-5184.00 - 2992.98i) q^{12} +55774.8i q^{13} +(20588.3 - 17720.5i) q^{14} +10711.2 q^{15} +(-8192.00 + 14189.0i) q^{16} +(-85725.7 + 49493.7i) q^{17} +(12371.5 + 21428.1i) q^{18} +(-78930.9 - 45570.8i) q^{19} -29317.4i q^{20} +(-110324. + 20883.6i) q^{21} +60675.6 q^{22} +(26885.7 - 46567.5i) q^{23} +(58650.3 - 33861.7i) q^{24} +(-169082. - 292859. i) q^{25} +(-546479. - 315510. i) q^{26} -102276. i q^{27} +(57159.9 + 301966. i) q^{28} -1.32881e6 q^{29} +(-60591.9 + 104948. i) q^{30} +(-897669. + 518270. i) q^{31} +(-92681.9 - 160530. i) q^{32} +(-217202. - 125402. i) q^{33} -1.11992e6i q^{34} +(-358745. - 416803. i) q^{35} -279936. q^{36} +(-11331.2 + 19626.2i) q^{37} +(893001. - 515575. i) q^{38} +(1.30416e6 + 2.25888e6i) q^{39} +(287250. + 165844. i) q^{40} +2.91739e6i q^{41} +(419473. - 1.19909e6i) q^{42} +4.71324e6 q^{43} +(-343233. + 594497. i) q^{44} +(433805. - 250457. i) q^{45} +(304177. + 526851. i) q^{46} +(-6.68209e6 - 3.85791e6i) q^{47} +766204. i q^{48} +(4.50768e6 + 3.59358e6i) q^{49} +3.82590e6 q^{50} +(-2.31459e6 + 4.00899e6i) q^{51} +(6.18271e6 - 3.56959e6i) q^{52} +(2.74030e6 + 4.74633e6i) q^{53} +(1.00209e6 + 578560. i) q^{54} -1.22836e6i q^{55} +(-3.28199e6 - 1.14813e6i) q^{56} -4.26227e6 q^{57} +(7.51688e6 - 1.30196e7i) q^{58} +(7.35698e6 - 4.24755e6i) q^{59} +(-685519. - 1.18735e6i) q^{60} +(3.06956e6 + 1.77221e6i) q^{61} -1.17271e7i q^{62} +(-3.97983e6 + 3.42547e6i) q^{63} +2.09715e6 q^{64} +(-6.38738e6 + 1.10633e7i) q^{65} +(2.45736e6 - 1.41876e6i) q^{66} +(4.24118e6 + 7.34593e6i) q^{67} +(1.09729e7 + 6.33520e6i) q^{68} -2.51464e6i q^{69} +(6.11319e6 - 1.15718e6i) q^{70} -2.14497e7 q^{71} +(1.58356e6 - 2.74280e6i) q^{72} +(3.42172e7 - 1.97553e7i) q^{73} +(-128198. - 222045. i) q^{74} +(-1.36957e7 - 7.90720e6i) q^{75} +1.16661e7i q^{76} +(2.39492e6 + 1.26519e7i) q^{77} -2.95099e7 q^{78} +(-6.05659e6 + 1.04903e7i) q^{79} +(-3.24987e6 + 1.87631e6i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(-2.85845e7 - 1.65033e7i) q^{82} +5.06437e7i q^{83} +(9.37574e6 + 1.08931e7i) q^{84} -2.26723e7 q^{85} +(-2.66621e7 + 4.61802e7i) q^{86} +(-5.38168e7 + 3.10711e7i) q^{87} +(-3.88324e6 - 6.72597e6i) q^{88} +(-5.21951e7 - 3.01348e7i) q^{89} +5.66720e6i q^{90} +(4.42193e7 - 1.26404e8i) q^{91} -6.88275e6 q^{92} +(-2.42371e7 + 4.19798e7i) q^{93} +(7.55993e7 - 4.36473e7i) q^{94} +(-1.04376e7 - 1.80785e7i) q^{95} +(-7.50723e6 - 4.33430e6i) q^{96} -1.77657e7i q^{97} +(-6.07090e7 + 2.38377e7i) q^{98} -1.17289e7 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

Modular forms

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