LMFDB - Embedded newform 126.9.s.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,9,Mod(53,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("126.53");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	126.s (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:	$51.3297048677$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 5826111 x^{18} - 52434714 x^{17} + 14609902138197 x^{16} - 116878028586684 x^{15} + \cdots + 46\!\cdots\!67 $ x^20 - 10x^19 + 5826111x^18 - 52434714x^17 + 14609902138197x^16 - 116878028586684x^15 + 20570415019216091666x^14 - 143990859773172188876x^13 + 17778850839861393261577389x^12 - 106671233163309243180965870x^11 + 9680290789684647638481756224861x^10 - 48400476132217676087684309052126x^9 + 3275735646651808421941058995933509711x^8 - 13102652184923818063474053937427650164x^7 + 653502209053902071586784989674537854288110x^6 - 1960460768082339807775059434296031383524340x^5 + 68850375563113059318225998877994832003827914811x^4 - 137697483706898978818817917958243091010522758690x^3 + 3066443413106133675142280126674379287603657139937675x^2 - 3066374564691021503239083252322344289284140820347058*x + 46867859601845955405133191126273914741044351570054374867
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{16}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Root			$0.500000 - 196.888i$ of defining polynomial
Character	$\chi$	$=$	126.107
Dual form			126.9.s.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(-171.260 - 98.8770i) q^{5} +(-1595.48 + 1794.23i) q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(-171.260 - 98.8770i) q^{5} +(-1595.48 + 1794.23i) q^{7} -1448.15i q^{8} +(1118.67 + 1937.59i) q^{10} +(-1666.85 + 962.354i) q^{11} -31981.6 q^{13} +(25782.1 - 8554.37i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(-27578.5 + 15922.5i) q^{17} +(-734.759 + 1272.64i) q^{19} -25312.5i q^{20} +21775.6 q^{22} +(118751. + 68560.7i) q^{23} +(-175759. - 304424. i) q^{25} +(313354. + 180915. i) q^{26} +(-301003. - 62030.3i) q^{28} +150554. i q^{29} +(120377. + 208498. i) q^{31} +(160530. - 92681.9i) q^{32} +360284. q^{34} +(450650. - 149523. i) q^{35} +(-899006. + 1.55712e6i) q^{37} +(14398.3 - 8312.85i) q^{38} +(-143189. + 248011. i) q^{40} +2.54545e6i q^{41} -320439. q^{43} +(-213356. - 123181. i) q^{44} +(-775675. - 1.34351e6i) q^{46} +(5.31136e6 + 3.06651e6i) q^{47} +(-673698. - 5.72530e6i) q^{49} +3.97698e6i q^{50} +(-2.04682e6 - 3.54520e6i) q^{52} +(7.42970e6 - 4.28954e6i) q^{53} +380619. q^{55} +(2.59832e6 + 2.31050e6i) q^{56} +(851660. - 1.47512e6i) q^{58} +(6.20225e6 - 3.58087e6i) q^{59} +(2.97248e6 - 5.14848e6i) q^{61} -2.72381e6i q^{62} -2.09715e6 q^{64} +(5.47717e6 + 3.16224e6i) q^{65} +(-1.20290e7 - 2.08348e7i) q^{67} +(-3.53005e6 - 2.03807e6i) q^{68} +(-5.26128e6 - 1.08424e6i) q^{70} -2.30321e7i q^{71} +(-1.63452e7 - 2.83108e7i) q^{73} +(1.76169e7 - 1.01711e7i) q^{74} -188098. q^{76} +(932736. - 4.52612e6i) q^{77} +(3.31671e7 - 5.74472e7i) q^{79} +(2.80592e6 - 1.62000e6i) q^{80} +(1.43992e7 - 2.49402e7i) q^{82} -4.15284e7i q^{83} +6.29746e6 q^{85} +(3.13965e6 + 1.81268e6i) q^{86} +(1.39364e6 + 2.41385e6i) q^{88} +(4.09096e7 + 2.36192e7i) q^{89} +(5.10259e7 - 5.73822e7i) q^{91} +1.75515e7i q^{92} +(-3.46936e7 - 6.00911e7i) q^{94} +(251670. - 145302. i) q^{95} +1.26007e7 q^{97} +(-2.57863e7 + 5.99073e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) $ 20 * q + 1280 * q^4 - 3710 * q^7	$ 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) $ 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$2$	−9.79796	−	5.65685i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	−171.260	−	98.8770i	−0.274016	−	0.158203i	0.356695	−	0.934221i	$-0.383903\pi$
$5$	−171.260	−	98.8770i	−0.274016	−	0.158203i	−0.630711	+	0.776018i	$0.717237\pi$
$6$		0			0
$7$	−1595.48	+	1794.23i	−0.664506	+	0.747283i
$7$	−1595.48	+	1794.23i	−0.664506	+	0.747283i
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	1118.67	+	1937.59i	0.111867	+	0.193759i
$11$	−1666.85	+	962.354i	−0.113848	+	0.0657301i	−0.555843	−	0.831288i	$-0.687604\pi$
$11$	−1666.85	+	962.354i	−0.113848	+	0.0657301i	0.441995	+	0.897018i	$0.354271\pi$
$12$		0			0
$13$	−31981.6			−1.11976			−0.559882	−	0.828572i	$-0.689154\pi$
$13$	−31981.6			−1.11976			−0.559882	+	0.828572i	$0.689154\pi$
$14$	25782.1	−	8554.37i	0.671130	−	0.222677i
$15$		0			0
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$	−27578.5	+	15922.5i	−0.330198	+	0.190640i	−0.655929	−	0.754822i	$-0.727723\pi$
$17$	−27578.5	+	15922.5i	−0.330198	+	0.190640i	0.325731	+	0.945463i	$0.394390\pi$
$18$		0			0
$19$	−734.759	+	1272.64i	−0.00563807	+	0.00976542i	−0.868831	−	0.495109i	$-0.835128\pi$
$19$	−734.759	+	1272.64i	−0.00563807	+	0.00976542i	0.863193	+	0.504875i	$0.168461\pi$
$20$		−	25312.5i		−	0.158203i
$21$		0			0
$22$	21775.6			0.0929564
$23$	118751.	+	68560.7i	0.424350	+	0.244999i	0.696937	−	0.717133i	$-0.254546\pi$
$23$	118751.	+	68560.7i	0.424350	+	0.244999i	−0.272587	+	0.962131i	$0.587879\pi$
$24$		0			0
$25$	−175759.	−	304424.i	−0.449943	−	0.779325i
$26$	313354.	+	180915.i	0.685713	+	0.395896i
$27$		0			0
$28$	−301003.	−	62030.3i	−0.489710	−	0.100919i
$29$			150554.i			0.212862i	0.994320	+	0.106431i	$0.0339424\pi$
$29$			150554.i			0.212862i	−0.994320	+	0.106431i	$0.966058\pi$
$30$		0			0
$31$	120377.	+	208498.i	0.130345	+	0.225765i	0.923810	−	0.382852i	$-0.125058\pi$
$31$	120377.	+	208498.i	0.130345	+	0.225765i	−0.793464	+	0.608617i	$0.791725\pi$
$32$	160530.	−	92681.9i	0.153093	−	0.0883883i
$33$		0			0
$34$	360284.			0.269606
$35$	450650.	−	149523.i	0.300308	−	0.0996406i
$36$		0			0
$37$	−899006.	+	1.55712e6i	−0.479685	+	0.830838i	−0.999728	−	0.0233014i	$-0.992582\pi$
$37$	−899006.	+	1.55712e6i	−0.479685	+	0.830838i	0.520044	+	0.854140i	$0.325916\pi$
$38$	14398.3	−	8312.85i	0.00690520	−	0.00398672i
$39$		0			0
$40$	−143189.	+	248011.i	−0.0559333	+	0.0968793i
$41$			2.54545e6i			0.900800i	0.892827	+	0.450400i	$0.148719\pi$
$41$			2.54545e6i			0.900800i	−0.892827	+	0.450400i	$0.851281\pi$
$42$		0			0
$43$	−320439.			−0.0937286			−0.0468643	−	0.998901i	$-0.514923\pi$
$43$	−320439.			−0.0937286			−0.0468643	+	0.998901i	$0.514923\pi$
$44$	−213356.	−	123181.i	−0.0569239	−	0.0328650i
$45$		0			0
$46$	−775675.	−	1.34351e6i	−0.173240	−	0.300061i
$47$	5.31136e6	+	3.06651e6i	1.08846	+	0.628425i	0.933167	−	0.359443i	$-0.117033\pi$
$47$	5.31136e6	+	3.06651e6i	1.08846	+	0.628425i	0.155297	+	0.987868i	$0.450367\pi$
$48$		0			0
$49$	−673698.	−	5.72530e6i	−0.116864	−	0.993148i
$50$			3.97698e6i			0.636316i
$51$		0			0
$52$	−2.04682e6	−	3.54520e6i	−0.279941	−	0.484872i
$53$	7.42970e6	−	4.28954e6i	0.941603	−	0.543635i	0.0511409	−	0.998691i	$-0.483714\pi$
$53$	7.42970e6	−	4.28954e6i	0.941603	−	0.543635i	0.890463	+	0.455056i	$0.150381\pi$
$54$		0			0
$55$	380619.			0.0415949
$56$	2.59832e6	+	2.31050e6i	0.264204	+	0.234938i
$57$		0			0
$58$	851660.	−	1.47512e6i	0.0752583	−	0.130351i
$59$	6.20225e6	−	3.58087e6i	0.511848	−	0.295516i	−0.221745	−	0.975105i	$-0.571175\pi$
$59$	6.20225e6	−	3.58087e6i	0.511848	−	0.295516i	0.733593	+	0.679589i	$0.237842\pi$
$60$		0			0
$61$	2.97248e6	−	5.14848e6i	0.214684	−	0.371843i	−0.738491	−	0.674263i	$-0.764461\pi$
$61$	2.97248e6	−	5.14848e6i	0.214684	−	0.371843i	0.953175	+	0.302420i	$0.0977946\pi$
$62$		−	2.72381e6i		−	0.184336i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	5.47717e6	+	3.16224e6i	0.306833	+	0.177150i
$66$		0			0
$67$	−1.20290e7	−	2.08348e7i	−0.596938	−	1.03393i	−0.993270	−	0.115820i	$-0.963051\pi$
$67$	−1.20290e7	−	2.08348e7i	−0.596938	−	1.03393i	0.396332	−	0.918107i	$-0.370283\pi$
$68$	−3.53005e6	−	2.03807e6i	−0.165099	−	0.0953201i
$69$		0			0
$70$	−5.26128e6	−	1.08424e6i	−0.219129	−	0.0451577i
$71$		−	2.30321e7i		−	0.906359i	−0.891419	−	0.453180i	$-0.850290\pi$
$71$		−	2.30321e7i		−	0.906359i	0.891419	−	0.453180i	$-0.149710\pi$
$72$		0			0
$73$	−1.63452e7	−	2.83108e7i	−0.575573	−	0.996921i	−0.995979	−	0.0895851i	$-0.971446\pi$
$73$	−1.63452e7	−	2.83108e7i	−0.575573	−	0.996921i	0.420407	−	0.907336i	$-0.361887\pi$
$74$	1.76169e7	−	1.01711e7i	0.587491	−	0.339188i
$75$		0			0
$76$	−188098.			−0.00563807
$77$	932736.	−	4.52612e6i	0.0265336	−	0.128755i
$78$		0			0
$79$	3.31671e7	−	5.74472e7i	0.851529	−	1.47489i	−0.0282989	−	0.999600i	$-0.509009\pi$
$79$	3.31671e7	−	5.74472e7i	0.851529	−	1.47489i	0.879828	−	0.475292i	$-0.157658\pi$
$80$	2.80592e6	−	1.62000e6i	0.0685040	−	0.0395508i
$81$		0			0
$82$	1.43992e7	−	2.49402e7i	0.318481	−	0.551625i
$83$		−	4.15284e7i		−	0.875050i	−0.899206	−	0.437525i	$-0.855855\pi$
$83$		−	4.15284e7i		−	0.875050i	0.899206	−	0.437525i	$-0.144145\pi$
$84$		0			0
$85$	6.29746e6			0.120640
$86$	3.13965e6	+	1.81268e6i	0.0573968	+	0.0331381i
$87$		0			0
$88$	1.39364e6	+	2.41385e6i	0.0232391	+	0.0402513i
$89$	4.09096e7	+	2.36192e7i	0.652026	+	0.376448i	0.789232	−	0.614095i	$-0.210479\pi$
$89$	4.09096e7	+	2.36192e7i	0.652026	+	0.376448i	−0.137206	+	0.990543i	$0.543812\pi$
$90$		0			0
$91$	5.10259e7	−	5.73822e7i	0.744090	−	0.836781i
$92$			1.75515e7i			0.244999i
$93$		0			0
$94$	−3.46936e7	−	6.00911e7i	−0.444363	−	0.769660i
$95$	251670.	−	145302.i	0.00308984	−	0.00178392i
$96$		0			0
$97$	1.26007e7			0.142333			0.0711667	−	0.997464i	$-0.477328\pi$
$97$	1.26007e7			0.142333			0.0711667	+	0.997464i	$0.477328\pi$
$98$	−2.57863e7	+	5.99073e7i	−0.279566	+	0.649494i
$99$		0			0
$100$	2.24972e7	−	3.89662e7i	0.224972	−	0.389662i
$101$	1.67188e8	−	9.65259e7i	1.60664	−	0.927594i	0.616526	−	0.787335i	$-0.288540\pi$
$101$	1.67188e8	−	9.65259e7i	1.60664	−	0.927594i	0.990115	−	0.140260i	$-0.0447938\pi$
$102$		0			0
$103$	9.91508e6	−	1.71734e7i	0.0880942	−	0.152584i	−0.818611	−	0.574348i	$-0.805256\pi$
$103$	9.91508e6	−	1.71734e7i	0.0880942	−	0.152584i	0.906706	+	0.421764i	$0.138589\pi$
$104$			4.63143e7i			0.395896i
$105$		0			0
$106$	−9.70612e7			−0.768816
$107$	−4.19826e6	−	2.42387e6i	−0.0320284	−	0.0184916i	0.483900	−	0.875123i	$-0.339220\pi$
$107$	−4.19826e6	−	2.42387e6i	−0.0320284	−	0.0184916i	−0.515929	+	0.856632i	$0.672553\pi$
$108$		0			0
$109$	7.19688e6	+	1.24654e7i	0.0509845	+	0.0883078i	0.890391	−	0.455196i	$-0.150431\pi$
$109$	7.19688e6	+	1.24654e7i	0.0509845	+	0.0883078i	−0.839407	+	0.543504i	$0.817097\pi$
$110$	−3.72929e6	−	2.15311e6i	−0.0254715	−	0.0147060i
$111$		0			0
$112$	−1.23881e7	−	3.73365e7i	−0.0787283	−	0.237280i
$113$		−	7.43251e7i		−	0.455850i	−0.973679	−	0.227925i	$-0.926806\pi$
$113$		−	7.43251e7i		−	0.455850i	0.973679	−	0.227925i	$-0.0731941\pi$
$114$		0			0
$115$	−1.35581e7	−	2.34834e7i	−0.0775192	−	0.134267i
$116$	−1.66891e7	+	9.63543e6i	−0.0921722	+	0.0532156i
$117$		0			0
$118$	−8.10258e7			−0.417922
$119$	1.54324e7	−	7.48860e7i	0.0769566	−	0.373433i
$120$		0			0
$121$	−1.05327e8	+	1.82432e8i	−0.491359	+	0.851059i
$122$	−5.82484e7	+	3.36298e7i	−0.262933	+	0.151804i
$123$		0			0
$124$	−1.54082e7	+	2.66878e7i	−0.0651726	+	0.112882i
$125$			1.46762e8i			0.601137i
$126$		0			0
$127$	−9.93092e6			−0.0381746			−0.0190873	−	0.999818i	$-0.506076\pi$
$127$	−9.93092e6			−0.0381746			−0.0190873	+	0.999818i	$0.506076\pi$
$128$	2.05478e7	+	1.18633e7i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.57767e7	−	6.19671e7i	−0.125264	−	0.216964i
$131$	6.70794e6	+	3.87283e6i	0.0227774	+	0.0131505i	0.511345	−	0.859375i	$-0.329147\pi$
$131$	6.70794e6	+	3.87283e6i	0.0227774	+	0.0131505i	−0.488568	+	0.872526i	$0.662481\pi$
$132$		0			0
$133$	−1.11111e6	−	3.34879e6i	−0.00355100	−	0.0107024i
$134$			2.72184e8i			0.844198i
$135$		0			0
$136$	2.30582e7	+	3.99379e7i	0.0674015	+	0.116743i
$137$	2.16227e8	−	1.24839e8i	0.613800	−	0.354378i	−0.160651	−	0.987011i	$-0.551359\pi$
$137$	2.16227e8	−	1.24839e8i	0.613800	−	0.354378i	0.774451	+	0.632633i	$0.218026\pi$
$138$		0			0
$139$	2.72630e8			0.730323			0.365161	−	0.930944i	$-0.381014\pi$
$139$	2.72630e8			0.730323			0.365161	+	0.930944i	$0.381014\pi$
$140$	4.54164e7	+	4.03856e7i	0.118223	+	0.105127i
$141$		0			0
$142$	−1.30289e8	+	2.25668e8i	−0.320446	+	0.555030i
$143$	5.33084e7	−	3.07776e7i	0.127483	−	0.0736022i
$144$		0			0
$145$	1.48863e7	−	2.57838e7i	0.0336755	−	0.0583277i
$146$			3.69851e8i			0.813982i
$147$		0			0
$148$	−2.30146e8			−0.479685
$149$	−3.89447e8	−	2.24848e8i	−0.790140	−	0.456187i	0.0498721	−	0.998756i	$-0.484119\pi$
$149$	−3.89447e8	−	2.24848e8i	−0.790140	−	0.456187i	−0.840012	+	0.542568i	$0.817452\pi$
$150$		0			0
$151$	3.53682e8	+	6.12595e8i	0.680307	+	1.17833i	0.974887	+	0.222700i	$0.0714869\pi$
$151$	3.53682e8	+	6.12595e8i	0.680307	+	1.17833i	−0.294580	+	0.955627i	$0.595180\pi$
$152$	1.84298e6	+	1.06404e6i	0.00345260	+	0.00199336i
$153$		0			0
$154$	−3.47425e7	+	3.90703e7i	−0.0617701	+	0.0694647i
$155$		−	4.76099e7i		−	0.0824842i
$156$		0			0
$157$	3.73780e8	+	6.47406e8i	0.615201	+	1.06556i	0.990349	+	0.138595i	$0.0442586\pi$
$157$	3.73780e8	+	6.47406e8i	0.615201	+	1.06556i	−0.375148	+	0.926965i	$0.622408\pi$
$158$	−6.49940e8	+	3.75243e8i	−1.04291	+	0.602122i
$159$		0			0
$160$	−3.66564e7			−0.0559333
$161$	−3.12477e8	+	1.03678e8i	−0.465066	+	0.154307i
$162$		0			0
$163$	−4.75843e8	+	8.24185e8i	−0.674083	+	1.16755i	0.302653	+	0.953101i	$0.402128\pi$
$163$	−4.75843e8	+	8.24185e8i	−0.674083	+	1.16755i	−0.976736	+	0.214445i	$0.931206\pi$
$164$	−2.82166e8	+	1.62909e8i	−0.390058	+	0.225200i
$165$		0			0
$166$	−2.34920e8	+	4.06893e8i	−0.309377	+	0.535856i
$167$		−	2.18457e8i		−	0.280867i	−0.990090	−	0.140433i	$-0.955150\pi$
$167$		−	2.18457e8i		−	0.280867i	0.990090	−	0.140433i	$-0.0448496\pi$
$168$		0			0
$169$	2.07091e8			0.253872
$170$	−6.17023e7	−	3.56238e7i	−0.0738763	−	0.0426525i
$171$		0			0
$172$	−2.05081e7	−	3.55211e7i	−0.0234321	−	0.0405857i
$173$	−1.34855e9	−	7.78588e8i	−1.50551	−	0.869207i	−0.999980	−	0.00639918i	$-0.997963\pi$
$173$	−1.34855e9	−	7.78588e8i	−1.50551	−	0.869207i	−0.505532	−	0.862808i	$-0.668704\pi$
$174$		0			0
$175$	8.26625e8	+	1.70350e8i	0.881366	+	0.181631i
$176$		−	3.15344e7i		−	0.0328650i
$177$		0			0
$178$	−2.67220e8	−	4.62839e8i	−0.266189	−	0.461052i
$179$	6.65302e8	−	3.84112e8i	0.648047	−	0.374150i	−0.139660	−	0.990199i	$-0.544601\pi$
$179$	6.65302e8	−	3.84112e8i	0.648047	−	0.374150i	0.787708	+	0.616049i	$0.211268\pi$
$180$		0			0
$181$	6.74800e8			0.628725			0.314362	−	0.949303i	$-0.398209\pi$
$181$	6.74800e8			0.628725			0.314362	+	0.949303i	$0.398209\pi$
$182$	−8.24553e8	+	2.73582e8i	−0.751507	+	0.249346i
$183$		0			0
$184$	9.92864e7	−	1.71969e8i	0.0866201	−	0.150030i
$185$	3.07928e8	−	1.77782e8i	0.262883	−	0.151775i
$186$		0			0
$187$	3.06461e7	−	5.30806e7i	0.0250616	−	0.0434079i
$188$			7.85027e8i			0.628425i
$189$		0			0
$190$	−3.28780e6			−0.00252285
$191$	−4.94315e8	−	2.85393e8i	−0.371425	−	0.214442i	0.302656	−	0.953100i	$-0.402127\pi$
$191$	−4.94315e8	−	2.85393e8i	−0.371425	−	0.214442i	−0.674081	+	0.738658i	$0.735460\pi$
$192$		0			0
$193$	6.94859e8	+	1.20353e9i	0.500804	+	0.867417i	1.00000		0.000928232i	$0.000295466\pi$
$193$	6.94859e8	+	1.20353e9i	0.500804	+	0.867417i	−0.499196	+	0.866489i	$0.666371\pi$
$194$	−1.23461e8	−	7.12801e7i	−0.0871610	−	0.0503224i
$195$		0			0
$196$	5.91540e8	−	4.41099e8i	0.400830	−	0.298891i
$197$		−	1.90181e9i		−	1.26270i	−0.775497	−	0.631352i	$-0.782500\pi$
$197$		−	1.90181e9i		−	1.26270i	0.775497	−	0.631352i	$-0.217500\pi$
$198$		0			0
$199$	1.05430e8	+	1.82610e8i	0.0672282	+	0.116443i	0.897680	−	0.440647i	$-0.145251\pi$
$199$	1.05430e8	+	1.82610e8i	0.0672282	+	0.116443i	−0.830452	+	0.557090i	$0.811918\pi$
$200$	−4.40853e8	+	2.54526e8i	−0.275533	+	0.159079i
$201$		0			0
$202$	−2.18413e9			−1.31182
$203$	−2.70127e8	−	2.40205e8i	−0.159069	−	0.141448i
$204$		0			0
$205$	2.51686e8	−	4.35933e8i	0.142510	−	0.246834i
$206$	−1.94295e8	+	1.12176e8i	−0.107893	+	0.0622920i
$207$		0			0
$208$	2.61993e8	−	4.53785e8i	0.139971	−	0.242436i
$209$		−	2.82839e6i		−	0.00148236i
$210$		0			0
$211$	8.26709e8			0.417083			0.208542	−	0.978013i	$-0.433128\pi$
$211$	8.26709e8			0.417083			0.208542	+	0.978013i	$0.433128\pi$
$212$	9.51002e8	+	5.49061e8i	0.470802	+	0.271818i
$213$		0			0
$214$	2.74229e7	+	4.74979e7i	0.0130755	+	0.0226475i
$215$	5.48785e7	+	3.16841e7i	0.0256831	+	0.0148282i
$216$		0			0
$217$	−5.66152e8	−	1.16672e8i	−0.255325	−	0.0526171i
$218$		−	1.62847e8i		−	0.0721030i
$219$		0			0
$220$	2.43596e7	+	4.21921e7i	0.0103987	+	0.0180111i
$221$	8.82004e8	−	5.09225e8i	0.369744	−	0.213472i
$222$		0			0
$223$	−2.28784e9			−0.925138			−0.462569	−	0.886583i	$-0.653072\pi$
$223$	−2.28784e9			−0.925138			−0.462569	+	0.886583i	$0.653072\pi$
$224$	−8.98294e7	+	4.35899e8i	−0.0356801	+	0.173138i
$225$		0			0
$226$	−4.20446e8	+	7.28235e8i	−0.161167	+	0.279150i
$227$	−9.79197e8	+	5.65339e8i	−0.368779	+	0.212915i	−0.672925	−	0.739711i	$-0.734962\pi$
$227$	−9.79197e8	+	5.65339e8i	−0.368779	+	0.212915i	0.304146	+	0.952626i	$0.401629\pi$
$228$		0			0
$229$	9.62109e8	−	1.66642e9i	0.349850	−	0.605959i	−0.636372	−	0.771382i	$-0.719566\pi$
$229$	9.62109e8	−	1.66642e9i	0.349850	−	0.605959i	0.986223	+	0.165423i	$0.0528991\pi$
$230$			3.06786e8i			0.109629i
$231$		0			0
$232$	2.18025e8			0.0752583
$233$	3.07839e9	+	1.77731e9i	1.04448	+	0.603031i	0.921099	−	0.389328i	$-0.127293\pi$
$233$	3.07839e9	+	1.77731e9i	1.04448	+	0.603031i	0.123382	+	0.992359i	$0.460626\pi$
$234$		0			0
$235$	−6.06415e8	−	1.05034e9i	−0.198838	−	0.344397i
$236$	7.93888e8	+	4.58351e8i	0.255924	+	0.147758i
$237$		0			0
$238$	−5.74825e8	+	6.46431e8i	−0.179155	+	0.201472i
$239$		−	1.25038e9i		−	0.383223i	−0.981471	−	0.191611i	$-0.938629\pi$
$239$		−	1.25038e9i		−	0.383223i	0.981471	−	0.191611i	$-0.0613713\pi$
$240$		0			0
$241$	−3.50034e8	−	6.06277e8i	−0.103763	−	0.179723i	0.809469	−	0.587162i	$-0.199755\pi$
$241$	−3.50034e8	−	6.06277e8i	−0.103763	−	0.179723i	−0.913232	+	0.407440i	$0.866422\pi$
$242$	2.06398e9	−	1.19164e9i	0.601790	−	0.347443i
$243$		0			0
$244$	7.60954e8			0.214684
$245$	−4.50723e8	+	1.04713e9i	−0.125097	+	0.290627i
$246$		0			0
$247$	2.34988e7	−	4.07010e7i	0.00631331	−	0.0109350i
$248$	3.01938e8	−	1.74324e8i	0.0798199	−	0.0460840i
$249$		0			0
$250$	8.30210e8	−	1.43797e9i	0.212534	−	0.368119i
$251$			5.90578e9i			1.48793i	0.668219	+	0.743965i	$0.267057\pi$
$251$			5.90578e9i			1.48793i	−0.668219	+	0.743965i	$0.732943\pi$
$252$		0			0
$253$	−2.63919e8			−0.0644151
$254$	9.73027e7	+	5.61778e7i	0.0233771	+	0.0134968i
$255$		0			0
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	4.27845e9	+	2.47016e9i	0.980740	+	0.566230i	0.902493	−	0.430704i	$-0.141735\pi$
$257$	4.27845e9	+	2.47016e9i	0.980740	+	0.566230i	0.0782463	+	0.996934i	$0.475068\pi$
$258$		0			0
$259$	−1.35949e9	−	4.09738e9i	−0.302118	−	0.910557i
$260$			8.09535e8i			0.177150i
$261$		0			0
$262$	−4.38161e7	−	7.58916e7i	−0.00929882	−	0.0161060i
$263$	7.12835e9	−	4.11555e9i	1.48993	−	0.860212i	0.489997	−	0.871724i	$-0.336998\pi$
$263$	7.12835e9	−	4.11555e9i	1.48993	−	0.860212i	0.999934	+	0.0115124i	$0.00366460\pi$
$264$		0			0
$265$	−1.69655e9			−0.344019
$266$	−8.05700e6	+	3.90967e7i	−0.00160934	+	0.00780933i
$267$		0			0
$268$	1.53971e9	−	2.66685e9i	0.298469	−	0.516963i
$269$	3.11461e9	−	1.79822e9i	0.594833	−	0.343427i	−0.172173	−	0.985067i	$-0.555079\pi$
$269$	3.11461e9	−	1.79822e9i	0.594833	−	0.343427i	0.767006	+	0.641640i	$0.221746\pi$
$270$		0			0
$271$	3.73069e9	−	6.46174e9i	0.691691	−	1.19804i	−0.279593	−	0.960119i	$-0.590200\pi$
$271$	3.73069e9	−	6.46174e9i	0.691691	−	1.19804i	0.971284	−	0.237925i	$-0.0764671\pi$
$272$		−	5.21747e8i		−	0.0953201i
$273$		0			0
$274$	−2.82477e9			−0.501166
$275$	5.85927e8	+	3.38285e8i	0.102450	+	0.0591496i
$276$		0			0
$277$	−3.71421e9	−	6.43321e9i	−0.630882	−	1.09272i	−0.987372	−	0.158420i	$-0.949360\pi$
$277$	−3.71421e9	−	6.43321e9i	−0.630882	−	1.09272i	0.356490	−	0.934299i	$-0.383973\pi$
$278$	−2.67122e9	−	1.54223e9i	−0.447230	−	0.258208i
$279$		0			0
$280$	−2.16533e8	−	6.52610e8i	−0.0352283	−	0.106175i
$281$		−	2.04779e9i		−	0.328442i	−0.986424	−	0.164221i	$-0.947489\pi$
$281$		−	2.04779e9i		−	0.328442i	0.986424	−	0.164221i	$-0.0525111\pi$
$282$		0			0
$283$	9.59007e8	+	1.66105e9i	0.149512	+	0.258962i	0.931047	−	0.364899i	$-0.118896\pi$
$283$	9.59007e8	+	1.66105e9i	0.149512	+	0.258962i	−0.781535	+	0.623861i	$0.785563\pi$
$284$	2.55314e9	−	1.47406e9i	0.392465	−	0.226590i
$285$		0			0
$286$	−6.96418e8			−0.104089
$287$	−4.56711e9	−	4.06121e9i	−0.673153	−	0.598587i
$288$		0			0
$289$	−2.98083e9	+	5.16295e9i	−0.427313	+	0.740127i
$290$	−2.91711e8	+	1.68419e8i	−0.0412439	+	0.0238122i
$291$		0			0
$292$	2.09219e9	−	3.62378e9i	0.287786	−	0.498460i
$293$			5.84219e9i			0.792693i	0.918101	+	0.396346i	$0.129722\pi$
$293$			5.84219e9i			0.792693i	−0.918101	+	0.396346i	$0.870278\pi$
$294$		0			0
$295$	−1.41626e9			−0.187006
$296$	2.25496e9	+	1.30190e9i	0.293746	+	0.169594i
$297$		0			0
$298$	2.54386e9	+	4.40610e9i	0.322573	+	0.558713i
$299$	−3.79783e9	−	2.19268e9i	−0.475172	−	0.274341i
$300$		0			0
$301$	5.11254e8	−	5.74941e8i	0.0622832	−	0.0700418i
$302$		−	8.00291e9i		−	0.962099i
$303$		0			0
$304$	−1.20383e7	−	2.08509e7i	−0.00140952	−	0.00244136i
$305$	−1.01813e9	+	5.87820e8i	−0.117654	+	0.0679274i
$306$		0			0
$307$	−1.35970e10			−1.53070			−0.765349	−	0.643615i	$-0.777434\pi$
$307$	−1.35970e10			−1.53070			−0.765349	+	0.643615i	$0.777434\pi$
$308$	5.61421e8	−	1.86276e8i	0.0623858	−	0.0206993i
$309$		0			0
$310$	−2.69322e8	+	4.66480e8i	−0.0291626	+	0.0505111i
$311$	−9.38392e9	+	5.41781e9i	−1.00310	+	0.579138i	−0.909163	−	0.416440i	$-0.863278\pi$
$311$	−9.38392e9	+	5.41781e9i	−1.00310	+	0.579138i	−0.0939339	+	0.995578i	$0.529944\pi$
$312$		0			0
$313$	5.41454e9	−	9.37825e9i	0.564136	−	0.977113i	−0.432993	−	0.901397i	$-0.642543\pi$
$313$	5.41454e9	−	9.37825e9i	0.564136	−	0.977113i	0.997129	−	0.0757154i	$-0.0241240\pi$
$314$		−	8.45767e9i		−	0.870026i
$315$		0			0
$316$	8.49078e9			0.851529
$317$	6.54201e9	+	3.77703e9i	0.647850	+	0.374036i	0.787632	−	0.616146i	$-0.211307\pi$
$317$	6.54201e9	+	3.77703e9i	0.647850	+	0.374036i	−0.139782	+	0.990182i	$0.544640\pi$
$318$		0			0
$319$	−1.44886e8	−	2.50950e8i	−0.0139915	−	0.0242339i
$320$	3.59158e8	+	2.07360e8i	0.0342520	+	0.0197754i
$321$		0			0
$322$	3.64813e9	+	7.51802e8i	0.339349	+	0.0699327i
$323$		−	4.67967e7i		−	0.00429937i
$324$		0			0
$325$	5.62106e9	+	9.73596e9i	0.503831	+	0.872660i
$326$	9.32458e9	−	5.38355e9i	0.825580	−	0.476649i
$327$		0			0
$328$	3.68620e9			0.318481
$329$	−1.39762e10	+	4.63722e9i	−1.19290	+	0.395799i
$330$		0			0
$331$	6.13250e9	−	1.06218e10i	0.510887	−	0.884883i	−0.489033	−	0.872265i	$-0.662650\pi$
$331$	6.13250e9	−	1.06218e10i	0.510887	−	0.884883i	0.999920	−	0.0126177i	$-0.00401645\pi$
$332$	4.60347e9	−	2.65782e9i	0.378908	−	0.218762i
$333$		0			0
$334$	−1.23578e9	+	2.14043e9i	−0.0993014	+	0.171995i
$335$			4.75755e9i			0.377750i
$336$		0			0
$337$	−5.45247e9			−0.422740			−0.211370	−	0.977406i	$-0.567793\pi$
$337$	−5.45247e9			−0.422740			−0.211370	+	0.977406i	$0.567793\pi$
$338$	−2.02907e9	−	1.17149e9i	−0.155464	−	0.0897574i
$339$		0			0
$340$	4.03038e8	+	6.98081e8i	0.0301599	+	0.0522385i
$341$	−4.01299e8	−	2.31690e8i	−0.0296791	−	0.0171352i
$342$		0			0
$343$	1.13474e10	+	7.92583e9i	0.819819	+	0.572622i
$344$			4.64046e8i			0.0331381i
$345$		0			0
$346$	8.80872e9	+	1.52571e10i	0.614622	+	1.06456i
$347$	−1.04361e10	+	6.02531e9i	−0.719817	+	0.415587i	−0.814685	−	0.579903i	$-0.803090\pi$
$347$	−1.04361e10	+	6.02531e9i	−0.719817	+	0.415587i	0.0948682	+	0.995490i	$0.469757\pi$
$348$		0			0
$349$	−8.92075e9			−0.601312			−0.300656	−	0.953733i	$-0.597206\pi$
$349$	−8.92075e9			−0.601312			−0.300656	+	0.953733i	$0.597206\pi$
$350$	−7.13560e9	−	6.34518e9i	−0.475508	−	0.422836i
$351$		0			0
$352$	−1.78386e8	+	3.08973e8i	−0.0116195	+	0.0201256i
$353$	−5.31646e9	+	3.06946e9i	−0.342392	+	0.197680i	−0.661329	−	0.750096i	$-0.730007\pi$
$353$	−5.31646e9	+	3.06946e9i	−0.342392	+	0.197680i	0.318937	+	0.947776i	$0.396674\pi$
$354$		0			0
$355$	−2.27735e9	+	3.94448e9i	−0.143389	+	0.248357i
$356$			6.04651e9i			0.376448i
$357$		0			0
$358$	−8.69147e9			−0.529128
$359$	−1.82700e10	−	1.05482e10i	−1.09992	−	0.635039i	−0.163720	−	0.986507i	$-0.552349\pi$
$359$	−1.82700e10	−	1.05482e10i	−1.09992	−	0.635039i	−0.936200	+	0.351468i	$0.885683\pi$
$360$		0			0
$361$	8.49070e9	+	1.47063e10i	0.499936	+	0.865915i
$362$	−6.61166e9	−	3.81724e9i	−0.385014	−	0.222288i
$363$		0			0
$364$	9.62655e9	+	1.98383e9i	0.548359	+	0.113005i
$365$			6.46468e9i			0.364230i
$366$		0			0
$367$	4.45366e9	+	7.71397e9i	0.245501	+	0.425220i	0.962272	−	0.272088i	$-0.0877143\pi$
$367$	4.45366e9	+	7.71397e9i	0.245501	+	0.425220i	−0.716772	+	0.697308i	$0.754381\pi$
$368$	−1.94561e9	+	1.12330e9i	−0.106088	+	0.0612497i
$369$		0			0
$370$	−4.02275e9			−0.214643
$371$	−4.15752e9	+	2.01744e10i	−0.219452	+	1.06489i
$372$		0			0
$373$	−1.76581e10	+	3.05847e10i	−0.912239	+	1.58004i	−0.101345	+	0.994851i	$0.532315\pi$
$373$	−1.76581e10	+	3.05847e10i	−0.912239	+	1.58004i	−0.810894	+	0.585193i	$0.801019\pi$
$374$	−6.00538e8	+	3.46721e8i	−0.0306940	+	0.0177212i
$375$		0			0
$376$	4.44078e9	−	7.69166e9i	0.222182	−	0.384830i
$377$		−	4.81494e9i		−	0.238356i
$378$		0			0
$379$	−2.49049e10			−1.20706			−0.603528	−	0.797342i	$-0.706239\pi$
$379$	−2.49049e10			−1.20706			−0.603528	+	0.797342i	$0.706239\pi$
$380$	3.22137e7	+	1.85986e7i	0.00154492	+	0.000891961i
$381$		0			0
$382$	3.22885e9	+	5.59254e9i	0.151633	+	0.262637i
$383$	4.39469e9	+	2.53727e9i	0.204236	+	0.117916i	0.598630	−	0.801026i	$-0.295712\pi$
$383$	4.39469e9	+	2.53727e9i	0.204236	+	0.117916i	−0.394394	+	0.918942i	$0.629045\pi$
$384$		0			0
$385$	−6.07269e8	+	6.82917e8i	−0.0276400	+	0.0310831i
$386$		−	1.57229e10i		−	0.708243i
$387$		0			0
$388$	8.06443e8	+	1.39680e9i	0.0355833	+	0.0616321i
$389$	1.94521e10	−	1.12307e10i	0.849509	−	0.490464i	−0.0109764	−	0.999940i	$-0.503494\pi$
$389$	1.94521e10	−	1.12307e10i	0.849509	−	0.490464i	0.860485	+	0.509476i	$0.170161\pi$
$390$		0			0
$391$	−4.36662e9			−0.186826
$392$	−8.29112e9	+	9.75619e8i	−0.351131	+	0.0413177i
$393$		0			0
$394$	−1.07582e10	+	1.86338e10i	−0.446433	+	0.773245i
$395$	−1.13604e10	+	6.55893e9i	−0.466665	+	0.269429i
$396$		0			0
$397$	3.39312e9	−	5.87706e9i	0.136596	−	0.236591i	−0.789610	−	0.613609i	$-0.789717\pi$
$397$	3.39312e9	−	5.87706e9i	0.136596	−	0.236591i	0.926206	+	0.377018i	$0.123051\pi$
$398$		−	2.38561e9i		−	0.0950750i
$399$		0			0
$400$	5.75928e9			0.224972
$401$	9.30454e9	+	5.37198e9i	0.359846	+	0.207757i	0.669013	−	0.743250i	$-0.266717\pi$
$401$	9.30454e9	+	5.37198e9i	0.359846	+	0.207757i	−0.309167	+	0.951008i	$0.600050\pi$
$402$		0			0
$403$	−3.84984e9	−	6.66811e9i	−0.145956	−	0.252803i
$404$	2.14000e10	+	1.23553e10i	0.803320	+	0.463797i
$405$		0			0
$406$	1.28789e9	+	3.88159e9i	0.0473996	+	0.142858i
$407$		−	3.46065e9i		−	0.126119i
$408$		0			0
$409$	1.40465e10	+	2.43292e10i	0.501966	+	0.869431i	0.999997	+	0.00227173i	$0.000723115\pi$
$409$	1.40465e10	+	2.43292e10i	0.501966	+	0.869431i	−0.498031	+	0.867159i	$0.665944\pi$
$410$	−4.93202e9	+	2.84750e9i	−0.174538	+	0.100769i
$411$		0			0
$412$	2.53826e9			0.0880942
$413$	−3.47066e9	+	1.68414e10i	−0.119292	+	0.578867i
$414$		0			0
$415$	−4.10620e9	+	7.11215e9i	−0.138436	+	0.239778i
$416$	−5.13400e9	+	2.96411e9i	−0.171428	+	0.0989741i
$417$		0			0
$418$	−1.59998e7	+	2.77125e7i	−0.000524094	+	0.000907758i
$419$			4.54744e10i			1.47540i	0.675126	+	0.737702i	$0.264089\pi$
$419$			4.54744e10i			1.47540i	−0.675126	+	0.737702i	$0.735911\pi$
$420$		0			0
$421$	−2.36007e10			−0.751272			−0.375636	−	0.926767i	$-0.622576\pi$
$421$	−2.36007e10			−0.751272			−0.375636	+	0.926767i	$0.622576\pi$
$422$	−8.10006e9	−	4.67657e9i	−0.255410	−	0.147461i
$423$		0			0
$424$	−6.21192e9	−	1.07594e10i	−0.192204	−	0.332907i
$425$	9.69435e9	+	5.59704e9i	0.297141	+	0.171555i
$426$		0			0
$427$	4.49502e9	+	1.35476e10i	0.135214	+	0.407522i
$428$		−	6.20510e8i		−	0.0184916i
$429$		0			0
$430$	−3.58465e8	−	6.20879e8i	−0.0104851	−	0.0181607i
$431$	1.52928e10	−	8.82930e9i	0.443178	−	0.255869i	−0.261767	−	0.965131i	$-0.584305\pi$
$431$	1.52928e10	−	8.82930e9i	0.443178	−	0.255869i	0.704945	+	0.709262i	$0.250972\pi$
$432$		0			0
$433$	1.78840e10			0.508761			0.254381	−	0.967104i	$-0.418128\pi$
$433$	1.78840e10			0.508761			0.254381	+	0.967104i	$0.418128\pi$
$434$	4.88714e9	+	4.34578e9i	0.137751	+	0.122492i
$435$		0			0
$436$	−9.21201e8	+	1.59557e9i	−0.0254923	+	0.0441539i
$437$	−1.74506e8	+	1.00751e8i	−0.00478503	+	0.00276264i
$438$		0			0
$439$	3.02983e10	−	5.24782e10i	0.815756	−	1.41293i	−0.0930271	−	0.995664i	$-0.529654\pi$
$439$	3.02983e10	−	5.24782e10i	0.815756	−	1.41293i	0.908783	−	0.417268i	$-0.137012\pi$
$440$		−	5.51195e8i		−	0.0147060i
$441$		0			0
$442$	−1.15225e10			−0.301895
$443$	−3.75551e10	−	2.16825e10i	−0.975112	−	0.562981i	−0.0743210	−	0.997234i	$-0.523679\pi$
$443$	−3.75551e10	−	2.16825e10i	−0.975112	−	0.562981i	−0.900791	+	0.434253i	$0.857012\pi$
$444$		0			0
$445$	−4.67079e9	−	8.09004e9i	−0.119110	−	0.206305i
$446$	2.24162e10	+	1.29420e10i	0.566529	+	0.327086i
$447$		0			0
$448$	3.34596e9	−	3.76277e9i	0.0830632	−	0.0934104i
$449$		−	6.31578e10i		−	1.55397i	−0.629522	−	0.776983i	$-0.716749\pi$
$449$		−	6.31578e10i		−	1.55397i	0.629522	−	0.776983i	$-0.283251\pi$
$450$		0			0
$451$	−2.44962e9	−	4.24287e9i	−0.0592097	−	0.102554i
$452$	8.23903e9	−	4.75681e9i	0.197389	−	0.113962i
$453$		0			0
$454$	1.27922e10			0.301107
$455$	−1.44125e10	+	4.78199e9i	−0.336274	+	0.111574i
$456$		0			0
$457$	1.62105e9	−	2.80774e9i	0.0371648	−	0.0643712i	−0.846845	−	0.531840i	$-0.821501\pi$
$457$	1.62105e9	−	2.80774e9i	0.0371648	−	0.0643712i	0.884009	+	0.467469i	$0.154834\pi$
$458$	−1.88534e10	+	1.08850e10i	−0.428477	+	0.247382i
$459$		0			0
$460$	1.73544e9	−	3.00588e9i	0.0387596	−	0.0671336i
$461$		−	5.71588e10i		−	1.26555i	−0.774335	−	0.632775i	$-0.781916\pi$
$461$		−	5.71588e10i		−	1.26555i	0.774335	−	0.632775i	$-0.218084\pi$
$462$		0			0
$463$	−2.13128e10			−0.463786			−0.231893	−	0.972741i	$-0.574492\pi$
$463$	−2.13128e10			−0.463786			−0.231893	+	0.972741i	$0.574492\pi$
$464$	−2.13620e9	−	1.23333e9i	−0.0460861	−	0.0266078i
$465$		0			0
$466$	−2.01080e10	−	3.48280e10i	−0.426407	−	0.738559i
$467$	3.74128e10	+	2.16003e10i	0.786597	+	0.454142i	0.838763	−	0.544496i	$-0.183279\pi$
$467$	3.74128e10	+	2.16003e10i	0.786597	+	0.454142i	−0.0521659	+	0.998638i	$0.516612\pi$
$468$		0			0
$469$	5.65743e10	+	1.16588e10i	1.16930	+	0.240969i
$470$			1.37216e10i			0.281199i
$471$		0			0
$472$	−5.18565e9	−	8.98181e9i	−0.104481	−	0.180966i
$473$	5.34123e8	−	3.08376e8i	0.0106708	−	0.00616079i
$474$		0			0
$475$	5.16562e8			0.0101472
$476$	9.28888e9	−	3.08200e9i	0.180940	−	0.0600351i
$477$		0			0
$478$	−7.07323e9	+	1.22512e10i	−0.135490	+	0.234675i
$479$	−8.04998e8	+	4.64766e8i	−0.0152916	+	0.00882861i	−0.507626	−	0.861577i	$-0.669477\pi$
$479$	−8.04998e8	+	4.64766e8i	−0.0152916	+	0.00882861i	0.492335	+	0.870406i	$0.336144\pi$
$480$		0			0
$481$	2.87516e10	−	4.97993e10i	0.537134	−	0.930343i
$482$			7.92036e9i			0.146743i
$483$		0			0
$484$	−2.69638e10			−0.491359
$485$	−2.15799e9	−	1.24592e9i	−0.0390016	−	0.0225176i
$486$		0			0
$487$	−3.21775e10	−	5.57331e10i	−0.572053	−	0.990825i	−0.996355	−	0.0853044i	$-0.972814\pi$
$487$	−3.21775e10	−	5.57331e10i	−0.572053	−	0.990825i	0.424302	−	0.905521i	$-0.360520\pi$
$488$	−7.45580e9	−	4.30461e9i	−0.131466	−	0.0759022i
$489$		0			0
$490$	1.03396e10	−	7.71005e9i	0.179358	−	0.133743i
$491$		−	6.74776e10i		−	1.16100i	−0.814259	−	0.580502i	$-0.802856\pi$
$491$		−	6.74776e10i		−	1.16100i	0.814259	−	0.580502i	$-0.197144\pi$
$492$		0			0
$493$	−2.39718e9	−	4.15204e9i	−0.0405801	−	0.0702869i
$494$	−4.60480e8	+	2.65858e8i	−0.00773219	+	0.00446418i
$495$		0			0
$496$	−3.94450e9			−0.0651726
$497$	4.13248e10	+	3.67472e10i	0.677307	+	0.602281i
$498$		0			0
$499$	2.50293e10	−	4.33519e10i	0.403688	−	0.699208i	−0.590480	−	0.807052i	$-0.701061\pi$
$499$	2.50293e10	−	4.33519e10i	0.403688	−	0.699208i	0.994168	+	0.107844i	$0.0343948\pi$
$500$	−1.62687e10	+	9.39276e9i	−0.260300	+	0.150284i
$501$		0			0
$502$	3.34081e10	−	5.78646e10i	0.526063	−	0.911167i
$503$		−	9.49666e10i		−	1.48354i	−0.670655	−	0.741769i	$-0.733987\pi$
$503$		−	9.49666e10i		−	1.48354i	0.670655	−	0.741769i	$-0.266013\pi$
$504$		0			0
$505$	−3.81768e10			−0.586994
$506$	2.58586e9	+	1.49295e9i	0.0394460	+	0.0227742i
$507$		0			0
$508$	−6.35579e8	−	1.10085e9i	−0.00954365	−	0.0165301i
$509$	1.04921e11	+	6.05761e10i	1.56311	+	0.902464i	0.996939	+	0.0781783i	$0.0249103\pi$
$509$	1.04921e11	+	6.05761e10i	1.56311	+	0.902464i	0.566174	+	0.824286i	$0.308423\pi$
$510$		0			0
$511$	7.68745e10	+	1.58422e10i	1.12745	+	0.232344i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	−2.79467e10	−	4.84051e10i	−0.400385	−	0.693488i
$515$	−3.39611e9	+	1.96075e9i	−0.0482784	+	0.0278736i
$516$		0			0
$517$	−1.18043e10			−0.165226
$518$	−9.85806e9	+	4.78364e10i	−0.136922	+	0.664415i
$519$		0			0
$520$	4.57942e9	−	7.93179e9i	0.0626321	−	0.108482i
$521$	1.05280e11	−	6.07835e10i	1.42888	−	0.824964i	0.431846	−	0.901947i	$-0.357862\pi$
$521$	1.05280e11	−	6.07835e10i	1.42888	−	0.824964i	0.997032	+	0.0769837i	$0.0245289\pi$
$522$		0			0
$523$	4.42108e10	−	7.65753e10i	0.590910	−	1.02349i	−0.403200	−	0.915112i	$-0.632102\pi$
$523$	4.42108e10	−	7.65753e10i	0.590910	−	1.02349i	0.994110	−	0.108374i	$-0.0345645\pi$
$524$			9.91444e8i			0.0131505i
$525$		0			0
$526$	−9.31244e10			−1.21652
$527$	−6.63961e9	−	3.83338e9i	−0.0860796	−	0.0496981i
$528$		0			0
$529$	−2.97544e10	−	5.15361e10i	−0.379951	−	0.658095i
$530$	1.66227e10	+	9.59713e9i	0.210668	+	0.121629i
$531$		0			0
$532$	3.00107e8	−	3.37491e8i	0.00374653	−	0.00421323i
$533$		−	8.14074e10i		−	1.00868i
$534$		0			0
$535$	4.79330e8	+	8.30224e8i	0.00585086	+	0.0101340i
$536$	−3.01720e10	+	1.74198e10i	−0.365548	+	0.211049i
$537$		0			0
$538$	−4.06891e10			−0.485679
$539$	6.63272e9	+	8.89486e9i	0.0785844	+	0.105386i
$540$		0			0
$541$	−1.76404e10	+	3.05541e10i	−0.205930	+	0.356681i	−0.950429	−	0.310943i	$-0.899355\pi$
$541$	−1.76404e10	+	3.05541e10i	−0.205930	+	0.356681i	0.744499	+	0.667624i	$0.232689\pi$
$542$	−7.31063e10	+	4.22079e10i	−0.847144	+	0.489099i
$543$		0			0
$544$	−2.95145e9	+	5.11206e9i	−0.0337007	+	0.0583714i
$545$		−	2.84643e9i		−	0.0322637i
$546$		0			0
$547$	−6.12483e10			−0.684140			−0.342070	−	0.939674i	$-0.611128\pi$
$547$	−6.12483e10			−0.684140			−0.342070	+	0.939674i	$0.611128\pi$
$548$	2.76770e10	+	1.59793e10i	0.306900	+	0.177189i
$549$		0			0
$550$	−3.82726e9	−	6.62901e9i	−0.0418251	−	0.0724432i
$551$	−1.91600e8	−	1.10621e8i	−0.00207869	−	0.00120013i
$552$		0			0
$553$	5.01558e10	+	1.51165e11i	0.536316	+	1.61641i
$554$			8.40431e10i			0.892202i
$555$		0			0
$556$	1.74483e10	+	3.02214e10i	0.182581	+	0.316239i
$557$	7.54559e10	−	4.35645e10i	0.783922	−	0.452597i	−0.0538966	−	0.998547i	$-0.517164\pi$
$557$	7.54559e10	−	4.35645e10i	0.783922	−	0.452597i	0.837818	+	0.545949i	$0.183831\pi$
$558$		0			0
$559$	1.02482e10			0.104954
$560$	−1.57014e9	+	7.61914e9i	−0.0159657	+	0.0774736i
$561$		0			0
$562$	−1.15840e10	+	2.00641e10i	−0.116122	+	0.201129i
$563$	−1.64086e11	+	9.47353e10i	−1.63320	+	0.942927i	−0.650100	+	0.759849i	$0.725273\pi$
$563$	−1.64086e11	+	9.47353e10i	−1.63320	+	0.942927i	−0.983098	+	0.183079i	$0.941394\pi$
$564$		0			0
$565$	−7.34905e9	+	1.27289e10i	−0.0721169	+	0.124910i
$566$		−	2.16999e10i		−	0.211442i
$567$		0			0
$568$	−3.33541e10			−0.320446
$569$	−1.56963e9	−	9.06225e8i	−0.0149743	−	0.00864544i	0.492494	−	0.870316i	$-0.336085\pi$
$569$	−1.56963e9	−	9.06225e8i	−0.0149743	−	0.00864544i	−0.507468	+	0.861670i	$0.669419\pi$
$570$		0			0
$571$	−5.71165e10	−	9.89287e10i	−0.537300	−	0.930632i	−0.999048	−	0.0436203i	$-0.986111\pi$
$571$	−5.71165e10	−	9.89287e10i	−0.537300	−	0.930632i	0.461748	−	0.887011i	$-0.347223\pi$
$572$	6.82347e9	+	3.93953e9i	0.0637414	+	0.0368011i
$573$		0			0
$574$	2.17747e10	+	6.56270e10i	0.200588	+	0.604554i
$575$		−	4.82007e10i		−	0.440942i
$576$		0			0
$577$	1.09856e11	+	1.90276e11i	0.991106	+	1.71665i	0.610798	+	0.791786i	$0.290849\pi$
$577$	1.09856e11	+	1.90276e11i	0.991106	+	1.71665i	0.380308	+	0.924860i	$0.375818\pi$
$578$	5.84121e10	−	3.37242e10i	0.523349	−	0.302156i
$579$		0			0
$580$	3.81089e9			0.0336755
$581$	7.45113e10	+	6.62576e10i	0.653910	+	0.581476i
$582$		0			0
$583$	−8.25612e9	+	1.43000e10i	−0.0714663	+	0.123783i
$584$	−4.09984e10	+	2.36704e10i	−0.352465	+	0.203496i
$585$		0			0
$586$	3.30484e10	−	5.72415e10i	0.280259	−	0.485423i
$587$		−	5.60721e10i		−	0.472274i	−0.971720	−	0.236137i	$-0.924119\pi$
$587$		−	5.60721e10i		−	0.472274i	0.971720	−	0.236137i	$-0.0758815\pi$
$588$		0			0
$589$	−3.53791e8			−0.00293958
$590$	1.38765e10	+	8.01159e9i	0.114517	+	0.0661166i
$591$		0			0
$592$	−1.47293e10	−	2.55119e10i	−0.119921	−	0.207710i
$593$	1.49592e11	+	8.63670e10i	1.20973	+	0.698440i	0.962701	−	0.270568i	$-0.0872114\pi$
$593$	1.49592e11	+	8.63670e10i	1.20973	+	0.698440i	0.247032	+	0.969007i	$0.420545\pi$
$594$		0			0
$595$	−1.00475e10	+	1.12991e10i	−0.0801657	+	0.0901519i
$596$		−	5.75610e10i		−	0.456187i
$597$		0			0
$598$	2.48073e10	+	4.29676e10i	0.193988	+	0.335997i
$599$	−2.14744e11	+	1.23982e11i	−1.66807	+	0.963059i	−0.699389	+	0.714741i	$0.746545\pi$
$599$	−2.14744e11	+	1.23982e11i	−1.66807	+	0.963059i	−0.968678	+	0.248319i	$0.920122\pi$
$600$		0			0
$601$	3.32972e9			0.0255217			0.0127609	−	0.999919i	$-0.495938\pi$
$601$	3.32972e9			0.0255217			0.0127609	+	0.999919i	$0.495938\pi$
$602$	−8.26160e9	+	2.74116e9i	−0.0629040	+	0.0208712i
$603$		0			0
$604$	−4.52713e10	+	7.84121e10i	−0.340154	+	0.589163i
$605$	3.60767e10	−	2.08289e10i	0.269281	−	0.155469i
$606$		0			0
$607$	7.89183e10	−	1.36691e11i	0.581330	−	1.00689i	−0.413992	−	0.910281i	$-0.635866\pi$
$607$	7.89183e10	−	1.36691e11i	0.581330	−	1.00689i	0.995322	−	0.0966130i	$-0.0308009\pi$
$608$			2.72395e8i			0.00199336i
$609$		0			0
$610$	1.33008e10			0.0960638
$611$	−1.69866e11	−	9.80720e10i	−1.21882	−	0.703688i
$612$		0			0
$613$	5.50852e9	+	9.54104e9i	0.0390115	+	0.0675700i	0.884872	−	0.465834i	$-0.154246\pi$
$613$	5.50852e9	+	9.54104e9i	0.0390115	+	0.0675700i	−0.845860	+	0.533404i	$0.820912\pi$
$614$	1.33223e11	+	7.69163e10i	0.937358	+	0.541184i
$615$		0			0
$616$	−6.55452e9	−	1.35075e9i	−0.0455216	−	0.00938104i
$617$			1.38018e11i			0.952344i	0.879352	+	0.476172i	$0.157976\pi$
$617$			1.38018e11i			0.952344i	−0.879352	+	0.476172i	$0.842024\pi$
$618$		0			0
$619$	1.13462e11	+	1.96522e11i	0.772837	+	1.33859i	0.936002	+	0.351994i	$0.114496\pi$
$619$	1.13462e11	+	1.96522e11i	0.772837	+	1.33859i	−0.163165	+	0.986599i	$0.552170\pi$
$620$	5.27762e9	−	3.04704e9i	0.0357167	−	0.0206210i
$621$		0			0
$622$	1.22591e11			0.819025
$623$	−1.07649e11	+	3.57172e10i	−0.714588	+	0.237097i
$624$		0			0
$625$	−5.41445e10	+	9.37811e10i	−0.354842	+	0.614604i
$626$	−1.06103e11	+	6.12585e10i	−0.690923	+	0.398905i
$627$		0			0
$628$	−4.78438e10	+	8.28679e10i	−0.307601	+	0.532780i
$629$		−	5.72575e10i		−	0.365789i
$630$		0			0
$631$	−2.39586e11			−1.51127			−0.755637	−	0.654991i	$-0.772673\pi$
$631$	−2.39586e11			−1.51127			−0.755637	+	0.654991i	$0.772673\pi$
$632$	−8.31924e10	−	4.80311e10i	−0.521453	−	0.301061i
$633$		0			0
$634$	−4.27322e10	−	7.40144e10i	−0.264484	−	0.458099i
$635$	1.70077e9	+	9.81940e8i	0.0104605	+	0.00603935i
$636$		0			0
$637$	2.15459e10	+	1.83104e11i	0.130860	+	1.11209i
$638$			3.27839e9i			0.0197869i
$639$		0			0
$640$	−2.34601e9	−	4.06341e9i	−0.0139833	−	0.0242198i
$641$	1.25526e11	−	7.24724e10i	0.743534	−	0.429280i	−0.0798186	−	0.996809i	$-0.525434\pi$
$641$	1.25526e11	−	7.24724e10i	0.743534	−	0.429280i	0.823353	+	0.567530i	$0.192101\pi$
$642$		0			0
$643$	3.60021e10			0.210612			0.105306	−	0.994440i	$-0.466418\pi$
$643$	3.60021e10			0.210612			0.105306	+	0.994440i	$0.466418\pi$
$644$	−3.14914e10	−	2.80031e10i	−0.183083	−	0.162803i
$645$		0			0
$646$	−2.64722e8	+	4.58512e8i	−0.00152006	+	0.00263282i
$647$	−1.29700e11	+	7.48823e10i	−0.740155	+	0.427329i	−0.822126	−	0.569306i	$-0.807212\pi$
$647$	−1.29700e11	+	7.48823e10i	−0.740155	+	0.427329i	0.0819708	+	0.996635i	$0.473879\pi$
$648$		0			0
$649$	−6.89213e9	+	1.19375e10i	−0.0388485	+	0.0672876i
$650$		−	1.27190e11i		−	0.712524i
$651$		0			0
$652$	−1.21816e11			−0.674083
$653$	−1.98018e11	−	1.14326e11i	−1.08906	−	0.628769i	−0.155734	−	0.987799i	$-0.549774\pi$
$653$	−1.98018e11	−	1.14326e11i	−1.08906	−	0.628769i	−0.933326	+	0.359030i	$0.883108\pi$
$654$		0			0
$655$	−7.65868e8	−	1.32652e9i	−0.00416091	−	0.00720691i
$656$	−3.61172e10	−	2.08523e10i	−0.195029	−	0.112600i
$657$		0			0
$658$	1.63170e11	+	3.36259e10i	0.870436	+	0.179378i
$659$		−	2.21982e11i		−	1.17700i	−0.808497	−	0.588501i	$-0.799718\pi$
$659$		−	2.21982e11i		−	1.17700i	0.808497	−	0.588501i	$-0.200282\pi$
$660$		0			0
$661$	1.14572e11	+	1.98445e11i	0.600169	+	1.03952i	0.992795	+	0.119824i	$0.0382331\pi$
$661$	1.14572e11	+	1.98445e11i	0.600169	+	1.03952i	−0.392627	+	0.919698i	$0.628434\pi$
$662$	−1.20172e11	+	6.93813e10i	−0.625707	+	0.361252i
$663$		0			0
$664$	−6.01395e10			−0.309377
$665$	−1.40830e8	+	6.83378e8i	−0.000720124	+	0.00349441i
$666$		0			0
$667$	−1.03221e10	+	1.78783e10i	−0.0521510	+	0.0903282i
$668$	2.42162e10	−	1.39813e10i	0.121619	−	0.0702167i
$669$		0			0
$670$	2.69128e10	−	4.66143e10i	0.133555	−	0.231324i
$671$			1.14423e10i			0.0564447i
$672$		0			0
$673$	−3.92559e10			−0.191357			−0.0956785	−	0.995412i	$-0.530502\pi$
$673$	−3.92559e10			−0.191357			−0.0956785	+	0.995412i	$0.530502\pi$
$674$	5.34231e10	+	3.08438e10i	0.258875	+	0.149461i
$675$		0			0
$676$	1.32538e10	+	2.29563e10i	0.0634680	+	0.109930i
$677$	1.42190e11	+	8.20935e10i	0.676885	+	0.390800i	0.798680	−	0.601756i	$-0.205532\pi$
$677$	1.42190e11	+	8.20935e10i	0.676885	+	0.390800i	−0.121795	+	0.992555i	$0.538865\pi$
$678$		0			0
$679$	−2.01041e10	+	2.26085e10i	−0.0945813	+	0.106363i
$680$		−	9.11970e9i		−	0.0426525i
$681$		0			0
$682$	2.62127e9	+	4.54018e9i	0.0121164	+	0.0209863i
$683$	−3.56551e10	+	2.05855e10i	−0.163847	+	0.0945972i	−0.579681	−	0.814843i	$-0.696823\pi$
$683$	−3.56551e10	+	2.05855e10i	−0.163847	+	0.0945972i	0.415834	+	0.909440i	$0.363490\pi$
$684$		0			0
$685$	−4.93747e10			−0.224255
$686$	−6.63457e10	−	1.41847e11i	−0.299582	−	0.640508i
$687$		0			0
$688$	2.62504e9	−	4.54670e9i	0.0117161	−	0.0202928i
$689$	−2.37614e11	+	1.37186e11i	−1.05437	+	0.608743i
$690$		0			0
$691$	9.40673e10	−	1.62929e11i	0.412598	−	0.714640i	−0.582575	−	0.812777i	$-0.697955\pi$
$691$	9.40673e10	−	1.62929e11i	0.412598	−	0.714640i	0.995173	+	0.0981367i	$0.0312883\pi$
$692$		−	1.99319e11i		−	0.869207i
$693$		0			0
$694$	1.36337e11			0.587728
$695$	−4.66907e10	−	2.69569e10i	−0.200120	−	0.115539i
$696$		0			0
$697$	−4.05298e10	−	7.01996e10i	−0.171729	−	0.297443i
$698$	8.74052e10	+	5.04634e10i	0.368227	+	0.212596i
$699$		0			0
$700$	3.40205e10	+	1.02535e11i	0.141693	+	0.427051i
$701$		−	2.36106e11i		−	0.977768i	−0.872349	−	0.488884i	$-0.837404\pi$
$701$		−	2.36106e11i		−	0.977768i	0.872349	−	0.488884i	$-0.162596\pi$
$702$		0			0
$703$	−1.32111e9	−	2.28822e9i	−0.00540899	−	0.00936865i
$704$	3.49563e9	−	2.01820e9i	0.0142310	−	0.00821626i
$705$		0			0
$706$	6.94540e10			0.279562
$707$	−9.35551e10	+	4.53978e11i	−0.374446	+	1.81701i
$708$		0			0
$709$	8.89130e10	−	1.54002e11i	0.351868	−	0.609454i	−0.634709	−	0.772752i	$-0.718880\pi$
$709$	8.89130e10	−	1.54002e11i	0.351868	−	0.609454i	0.986577	+	0.163298i	$0.0522132\pi$
$710$	4.46267e10	−	2.57652e10i	0.175615	−	0.101391i
$711$		0			0
$712$	3.42042e10	−	5.92434e10i	0.133094	−	0.230526i
$713$			3.30124e10i			0.127738i
$714$		0			0
$715$	−1.21728e10			−0.0465764
$716$	8.51587e10	+	4.91664e10i	0.324024	+	0.187075i
$717$		0			0
$718$	1.19339e11	+	2.06702e11i	0.449041	+	0.777761i
$719$	−2.57443e10	−	1.48635e10i	−0.0963310	−	0.0556167i	0.451061	−	0.892493i	$-0.351046\pi$
$719$	−2.57443e10	−	1.48635e10i	−0.0963310	−	0.0556167i	−0.547392	+	0.836877i	$0.684379\pi$
$720$		0			0
$721$	1.49937e10	+	4.51897e10i	0.0554841	+	0.167224i
$722$		−	1.92123e11i		−	0.707017i
$723$		0			0
$724$	4.31872e10	+	7.48024e10i	0.157181	+	0.272246i
$725$	4.58321e10	−	2.64612e10i	0.165889	−	0.0957761i
$726$		0			0
$727$	−1.92981e11			−0.690838			−0.345419	−	0.938449i	$-0.612263\pi$
$727$	−1.92981e11			−0.690838			−0.345419	+	0.938449i	$0.612263\pi$
$728$	−8.30983e10	−	7.38934e10i	−0.295847	−	0.263076i
$729$		0			0
$730$	3.65697e10	−	6.33407e10i	0.128775	−	0.223044i
$731$	8.83724e9	−	5.10218e9i	0.0309490	−	0.0178684i
$732$		0			0
$733$	1.64779e11	−	2.85406e11i	0.570803	−	0.988659i	−0.425681	−	0.904873i	$-0.639965\pi$
$733$	1.64779e11	−	2.85406e11i	0.570803	−	0.988659i	0.996484	−	0.0837859i	$-0.0267012\pi$
$734$		−	1.00775e11i		−	0.347191i
$735$		0			0
$736$	2.54173e10			0.0866201
$737$	4.01009e10	+	2.31523e10i	0.135920	+	0.0784735i
$738$		0			0
$739$	−1.86924e11	−	3.23763e11i	−0.626741	−	1.08555i	−0.988201	−	0.153160i	$-0.951055\pi$
$739$	−1.86924e11	−	3.23763e11i	−0.626741	−	1.08555i	0.361460	−	0.932388i	$-0.382278\pi$
$740$	3.94147e10	+	2.27561e10i	0.131441	+	0.0758877i
$741$		0			0
$742$	1.54859e11	−	1.74150e11i	0.510883	−	0.574523i
$743$			5.74032e11i			1.88357i	0.336221	+	0.941783i	$0.390851\pi$
$743$			5.74032e11i			1.88357i	−0.336221	+	0.941783i	$0.609149\pi$
$744$		0			0
$745$	4.44645e10	+	7.70148e10i	0.144341	+	0.250005i
$746$	3.46027e11	−	1.99779e11i	1.11726	−	0.645050i
$747$		0			0
$748$	7.84540e9			0.0250616
$749$	1.10472e10	−	3.66541e9i	0.0351015	−	0.0116465i
$750$		0			0
$751$	1.07558e11	−	1.86296e11i	0.338130	−	0.585659i	−0.645951	−	0.763379i	$-0.723539\pi$
$751$	1.07558e11	−	1.86296e11i	0.338130	−	0.585659i	0.984081	+	0.177720i	$0.0568723\pi$
$752$	−8.70213e10	+	5.02417e10i	−0.272116	+	0.157106i
$753$		0			0
$754$	−2.72374e10	+	4.71766e10i	−0.0842715	+	0.145963i
$755$		−	1.39884e11i		−	0.430507i
$756$		0			0
$757$	−4.36464e11			−1.32912			−0.664561	−	0.747234i	$-0.731382\pi$
$757$	−4.36464e11			−1.32912			−0.664561	+	0.747234i	$0.731382\pi$
$758$	2.44017e11	+	1.40883e11i	0.739167	+	0.426758i
$759$		0			0
$760$	−2.10419e8	−	3.64457e8i	−0.000630712	−	0.00109242i
$761$	2.96924e11	+	1.71429e11i	0.885333	+	0.511147i	0.872413	−	0.488769i	$-0.162554\pi$
$761$	2.96924e11	+	1.71429e11i	0.885333	+	0.511147i	0.0129199	+	0.999917i	$0.495887\pi$
$762$		0			0
$763$	−3.38482e10	−	6.97539e9i	−0.0998705	−	0.0205812i
$764$		−	7.30606e10i		−	0.214442i
$765$		0			0
$766$	−2.87060e10	−	4.97202e10i	−0.0833791	−	0.144417i
$767$	−1.98358e11	+	1.14522e11i	−0.573149	+	0.330908i
$768$		0			0
$769$	−3.38850e11			−0.968953			−0.484477	−	0.874804i	$-0.660990\pi$
$769$	−3.38850e11			−0.968953			−0.484477	+	0.874804i	$0.660990\pi$
$770$	9.81316e9	−	3.25596e9i	0.0279155	−	0.00926223i
$771$		0			0
$772$	−8.89420e10	+	1.54052e11i	−0.250402	+	0.433709i
$773$	4.39630e11	−	2.53821e11i	1.23132	−	0.710901i	0.264012	−	0.964519i	$-0.414954\pi$
$773$	4.39630e11	−	2.53821e11i	1.23132	−	0.710901i	0.967304	+	0.253619i	$0.0816209\pi$
$774$		0			0
$775$	4.23146e10	−	7.32910e10i	0.117296	−	0.203163i
$776$		−	1.82477e10i		−	0.0503224i
$777$		0			0
$778$	−2.54121e11			−0.693621
$779$	−3.23944e9	−	1.87029e9i	−0.00879670	−	0.00507877i
$780$		0			0
$781$	2.21651e10	+	3.83910e10i	0.0595751	+	0.103187i
$782$	4.27839e10	+	2.47013e10i	0.114407	+	0.0660531i
$783$		0			0
$784$	8.67550e10	+	3.73426e10i	0.229631	+	0.0988417i
$785$		−	1.47833e11i		−	0.389307i
$786$		0			0
$787$	−1.58814e11	−	2.75074e11i	−0.413991	−	0.717053i	0.581331	−	0.813667i	$-0.302532\pi$
$787$	−1.58814e11	−	2.75074e11i	−0.413991	−	0.717053i	−0.995322	+	0.0966140i	$0.969199\pi$
$788$	2.10818e11	−	1.21716e11i	0.546767	−	0.315676i
$789$		0			0
$790$	1.48412e11			0.381031
$791$	1.33356e11	+	1.18584e11i	0.340649	+	0.302915i
$792$		0			0
$793$	−9.50646e10	+	1.64657e11i	−0.240395	+	0.416377i
$794$	−6.64913e10	+	3.83888e10i	−0.167295	+	0.0965878i
$795$		0			0
$796$	−1.34950e10	+	2.33741e10i	−0.0336141	+	0.0582213i
$797$			7.56297e11i			1.87439i	0.348810	+	0.937193i	$0.386586\pi$
$797$			7.56297e11i			1.87439i	−0.348810	+	0.937193i	$0.613414\pi$
$798$		0			0
$799$	−1.95306e11			−0.479212
$800$	−5.64292e10	−	3.25794e10i	−0.137766	−	0.0795395i
$801$		0			0
$802$	−6.07770e10	−	1.05269e11i	−0.146907	−	0.254450i
$803$	5.44900e10	+	3.14598e10i	0.131055	+	0.0756649i
$804$		0			0
$805$	6.37663e10	+	1.31409e10i	0.151847	+	0.0312925i
$806$			8.71118e10i			0.206413i
$807$		0			0
$808$	−1.39784e11	−	2.42114e11i	−0.327954	−	0.568033i
$809$	4.60309e11	−	2.65760e11i	1.07462	−	0.620433i	0.145181	−	0.989405i	$-0.453624\pi$
$809$	4.60309e11	−	2.65760e11i	1.07462	−	0.620433i	0.929440	+	0.368972i	$0.120290\pi$
$810$		0			0
$811$	4.13088e10			0.0954904			0.0477452	−	0.998860i	$-0.484796\pi$
$811$	4.13088e10			0.0954904			0.0477452	+	0.998860i	$0.484796\pi$
$812$	9.33888e9	−	4.53171e10i	0.0214818	−	0.104241i
$813$		0			0
$814$	−1.95764e10	+	3.39073e10i	−0.0445897	+	0.0772317i
$815$	1.62986e11	−	9.40999e10i	0.369419	−	0.213284i
$816$		0			0
$817$	2.35446e8	−	4.07804e8i	0.000528448	−	0.000915299i
$818$		−	3.17836e11i		−	0.709887i
$819$		0			0
$820$	6.44317e10			0.142510
$821$	9.03196e10	+	5.21460e10i	0.198797	+	0.114775i	0.596094	−	0.802915i	$-0.296719\pi$
$821$	9.03196e10	+	5.21460e10i	0.198797	+	0.114775i	−0.397297	+	0.917690i	$0.630052\pi$
$822$		0			0
$823$	−3.83355e11	−	6.63991e11i	−0.835607	−	1.44731i	−0.893535	−	0.448993i	$-0.851783\pi$
$823$	−3.83355e11	−	6.63991e11i	−0.835607	−	1.44731i	0.0579279	−	0.998321i	$-0.481551\pi$
$824$	−2.48698e10	−	1.43586e10i	−0.0539465	−	0.0311460i
$825$		0			0
$826$	1.29275e11	−	1.45379e11i	0.277712	−	0.312306i
$827$		−	6.72849e11i		−	1.43845i	−0.694776	−	0.719227i	$-0.744496\pi$
$827$		−	6.72849e11i		−	1.43845i	0.694776	−	0.719227i	$-0.255504\pi$
$828$		0			0
$829$	−7.10353e10	−	1.23037e11i	−0.150403	−	0.260505i	0.780973	−	0.624565i	$-0.214724\pi$
$829$	−7.10353e10	−	1.23037e11i	−0.150403	−	0.260505i	−0.931376	+	0.364060i	$0.881390\pi$
$830$	8.04648e10	−	4.64564e10i	0.169548	−	0.0978888i
$831$		0			0
$832$	6.70703e10			0.139971
$833$	1.09740e11	+	1.47168e11i	0.227922	+	0.305657i
$834$		0			0
$835$	−2.16004e10	+	3.74130e10i	−0.0444340	+	0.0769620i
$836$	3.13531e8	−	1.81017e8i	0.000641882	−	0.000370591i
$837$		0			0
$838$	2.57242e11	−	4.45556e11i	0.521634	−	0.903497i
$839$			8.30737e11i			1.67655i	0.545249	+	0.838274i	$0.316435\pi$
$839$			8.30737e11i			1.67655i	−0.545249	+	0.838274i	$0.683565\pi$
$840$		0			0
$841$	4.77580e11			0.954690
$842$	2.31239e11	+	1.33506e11i	0.460058	+	0.265615i
$843$		0			0
$844$	5.29094e10	+	9.16417e10i	0.104271	+	0.180602i
$845$	−3.54665e10	−	2.04766e10i	−0.0695651	−	0.0401634i
$846$		0			0
$847$	−1.59277e11	−	4.80047e11i	−0.309471	−	0.932718i
$848$			1.40560e11i			0.271818i
$849$		0			0
$850$	−6.33232e10	−	1.09679e11i	−0.121307	−	0.210111i
$851$	−2.13515e11	+	1.23273e11i	−0.407108	+	0.235044i
$852$		0			0
$853$	−9.79209e10			−0.184961			−0.0924803	−	0.995715i	$-0.529480\pi$
$853$	−9.79209e10			−0.184961			−0.0924803	+	0.995715i	$0.529480\pi$
$854$	3.25947e10	−	1.58166e11i	0.0612796	−	0.297360i
$855$		0			0
$856$	−3.51014e9	+	6.07974e9i	−0.00653776	+	0.0113237i
$857$	5.12045e11	−	2.95630e11i	0.949260	−	0.548055i	0.0564090	−	0.998408i	$-0.482035\pi$
$857$	5.12045e11	−	2.95630e11i	0.949260	−	0.548055i	0.892851	+	0.450352i	$0.148702\pi$
$858$		0			0
$859$	2.60577e11	−	4.51332e11i	0.478589	−	0.828941i	−0.521109	−	0.853490i	$-0.674482\pi$
$859$	2.60577e11	−	4.51332e11i	0.478589	−	0.828941i	0.999699	+	0.0245491i	$0.00781502\pi$
$860$			8.11113e9i			0.0148282i
$861$		0			0
$862$	−1.99784e11			−0.361853
$863$	−4.20566e11	−	2.42814e11i	−0.758213	−	0.437755i	0.0704407	−	0.997516i	$-0.477559\pi$
$863$	−4.20566e11	−	2.42814e11i	−0.758213	−	0.437755i	−0.828654	+	0.559761i	$0.810893\pi$
$864$		0			0
$865$	1.53969e11	+	2.66682e11i	0.275023	+	0.476354i
$866$	−1.75227e11	−	1.01167e11i	−0.311551	−	0.179874i
$867$		0			0
$868$	−2.33005e10	−	7.02256e10i	−0.0410475	−	0.123713i
$869$			1.27674e11i			0.223884i
$870$		0			0
$871$	3.84705e11	+	6.66329e11i	0.668430	+	1.15775i
$872$	1.80518e10	−	1.04222e10i	0.0312215	−	0.0180258i
$873$		0			0
$874$	2.27974e9			0.00390696
$875$	−2.63324e11	−	2.34155e11i	−0.449219	−	0.399459i
$876$		0			0
$877$	−2.67750e11	+	4.63757e11i	−0.452618	+	0.783957i	−0.998548	−	0.0538741i	$-0.982843\pi$
$877$	−2.67750e11	+	4.63757e11i	−0.452618	+	0.783957i	0.545930	+	0.837831i	$0.316176\pi$
$878$	−5.93723e11	+	3.42786e11i	−0.999093	+	0.576827i
$879$		0			0
$880$	−3.11803e9	+	5.40059e9i	−0.00519936	+	0.00900555i
$881$		−	1.22613e11i		−	0.203532i	−0.994808	−	0.101766i	$-0.967551\pi$
$881$		−	1.22613e11i		−	0.203532i	0.994808	−	0.101766i	$-0.0324494\pi$
$882$		0			0
$883$	6.63409e11			1.09129			0.545643	−	0.838018i	$-0.316285\pi$
$883$	6.63409e11			1.09129			0.545643	+	0.838018i	$0.316285\pi$
$884$	1.12897e11	+	6.51809e10i	0.184872	+	0.106736i
$885$		0			0
$886$	2.45309e11	+	4.24888e11i	0.398088	+	0.689508i
$887$	−8.01600e11	−	4.62804e11i	−1.29498	−	0.747657i	−0.315447	−	0.948943i	$-0.602155\pi$
$887$	−8.01600e11	−	4.62804e11i	−1.29498	−	0.747657i	−0.979532	+	0.201286i	$0.935488\pi$
$888$		0			0
$889$	1.58446e10	−	1.78183e10i	0.0253672	−	0.0285272i
$890$			1.05688e11i			0.168448i
$891$		0			0
$892$	−1.46422e11	−	2.53610e11i	−0.231284	−	0.400596i
$893$	−7.80513e9	+	4.50629e9i	−0.0122737	+	0.00708620i
$894$		0			0
$895$	−1.51920e11			−0.236767
$896$	−5.40690e10	+	1.79398e10i	−0.0838912	+	0.0278347i
$897$		0			0
$898$	−3.57274e11	+	6.18817e11i	−0.549410	+	0.951606i
$899$	−3.13902e10	+	1.81231e10i	−0.0480568	+	0.0277456i
$900$		0			0
$901$	−1.36600e11	+	2.36598e11i	−0.207277	+	0.359015i
$902$			5.54286e10i			0.0837351i
$903$		0			0
$904$	−1.07634e11			−0.161167
$905$	−1.15566e11	−	6.67222e10i	−0.172281	−	0.0994663i
$906$		0			0
$907$	2.58067e11	+	4.46986e11i	0.381333	+	0.660488i	0.991253	−	0.131975i	$-0.0421319\pi$
$907$	2.58067e11	+	4.46986e11i	0.381333	+	0.660488i	−0.609920	+	0.792463i	$0.708799\pi$
$908$	−1.25337e11	−	7.23634e10i	−0.184390	−	0.106457i
$909$		0			0
$910$	1.68264e11	+	3.46756e10i	0.245372	+	0.0505660i
$911$		−	1.01888e12i		−	1.47928i	−0.673002	−	0.739641i	$-0.734995\pi$
$911$		−	1.01888e12i		−	1.47928i	0.673002	−	0.739641i	$-0.265005\pi$
$912$		0			0
$913$	3.99650e10	+	6.92214e10i	0.0575171	+	0.0996225i
$914$	−3.17659e10	+	1.83401e10i	−0.0455173	+	0.0262795i
$915$		0			0
$916$	2.46300e11			0.349850
$917$	−1.76511e10	+	5.85654e9i	−0.0249629	+	0.00828255i
$918$		0			0
$919$	2.21434e11	−	3.83535e11i	0.310444	−	0.537704i	−0.668015	−	0.744148i	$-0.732856\pi$
$919$	2.21434e11	−	3.83535e11i	0.310444	−	0.537704i	0.978458	+	0.206444i	$0.0661890\pi$
$920$	−3.40076e10	+	1.96343e10i	−0.0474706	+	0.0274072i
$921$		0			0
$922$	−3.23339e11	+	5.60040e11i	−0.447440	+	0.774988i
$923$			7.36604e11i			1.01491i
$924$		0			0
$925$	6.32034e11			0.863324
$926$	2.08822e11	+	1.20564e11i	0.284010	+	0.163973i
$927$		0			0
$928$	1.39536e10	+	2.41683e10i	0.0188146	+	0.0325878i
$929$	−5.15528e11	−	2.97640e11i	−0.692132	−	0.399603i	0.112278	−	0.993677i	$-0.464185\pi$
$929$	−5.15528e11	−	2.97640e11i	−0.692132	−	0.399603i	−0.804410	+	0.594074i	$0.797519\pi$
$930$		0			0
$931$	7.78125e9	+	3.34934e9i	0.0103574	+	0.00445821i
$932$			4.54992e11i			0.603031i
$933$		0			0
$934$	−2.44379e11	−	4.23277e11i	−0.321127	−	0.556208i
$935$	−1.04969e10	+	6.06039e9i	−0.0137346	+	0.00792965i
$936$		0			0
$937$	−4.82929e11			−0.626506			−0.313253	−	0.949670i	$-0.601419\pi$
$937$	−4.82929e11			−0.626506			−0.313253	+	0.949670i	$0.601419\pi$
$938$	−4.88361e11	−	4.34264e11i	−0.630855	−	0.560974i
$939$		0			0
$940$	7.76212e10	−	1.34444e11i	0.0994189	−	0.172199i
$941$	2.83502e11	−	1.63680e11i	0.361575	−	0.208755i	−0.308197	−	0.951323i	$-0.599725\pi$
$941$	2.83502e11	−	1.63680e11i	0.361575	−	0.208755i	0.669771	+	0.742567i	$0.266392\pi$
$942$		0			0
$943$	−1.74518e11	+	3.02273e11i	−0.220695	+	0.382255i
$944$			1.17338e11i			0.147758i
$945$		0			0
$946$	−6.97775e9			−0.00871267
$947$	−1.54364e11	−	8.91219e10i	−0.191931	−	0.110811i	0.400955	−	0.916098i	$-0.368678\pi$
$947$	−1.54364e11	−	8.91219e10i	−0.191931	−	0.110811i	−0.592886	+	0.805286i	$0.702012\pi$
$948$		0			0
$949$	5.22747e11	+	9.05424e11i	0.644506	+	1.11632i
$950$	−5.06126e9	−	2.92212e9i	−0.00621390	−	0.00358759i
$951$		0			0
$952$	−1.08447e11	−	2.23485e10i	−0.132029	−	0.0272083i
$953$		−	1.17372e11i		−	0.142296i	−0.997466	−	0.0711482i	$-0.977334\pi$
$953$		−	1.17372e11i		−	0.142296i	0.997466	−	0.0711482i	$-0.0226663\pi$
$954$		0			0
$955$	5.64376e10	+	9.77529e10i	0.0678509	+	0.117521i
$956$	1.38606e11	−	8.00245e10i	0.165940	−	0.0958057i
$957$		0			0
$958$	1.05164e10			0.0124855
$959$	−1.20996e11	+	5.87137e11i	−0.143053	+	0.694169i
$960$		0			0
$961$	3.97464e11	−	6.88429e11i	0.466020	−	0.807171i
$962$	−5.63415e11	+	3.25288e11i	−0.657852	+	0.379811i
$963$		0			0
$964$	4.48043e10	−	7.76034e10i	0.0518814	−	0.0898613i
$965$		−	2.74822e11i		−	0.316915i
$966$		0			0
$967$	−2.35101e11			−0.268874			−0.134437	−	0.990922i	$-0.542923\pi$
$967$	−2.35101e11			−0.268874			−0.134437	+	0.990922i	$0.542923\pi$
$968$	2.64190e11	+	1.52530e11i	0.300895	+	0.173722i
$969$		0			0
$970$	1.40959e10	+	2.44149e10i	0.0159223	+	0.0275783i
$971$	−8.30114e11	−	4.79266e11i	−0.933814	−	0.539138i	−0.0457985	−	0.998951i	$-0.514583\pi$
$971$	−8.30114e11	−	4.79266e11i	−0.933814	−	0.539138i	−0.888016	+	0.459813i	$0.847917\pi$
$972$		0			0
$973$	−4.34976e11	+	4.89161e11i	−0.485304	+	0.545758i
$974$			7.28094e11i			0.809005i
$975$		0			0
$976$	4.87011e10	+	8.43527e10i	0.0536710	+	0.0929608i
$977$	−7.32139e11	+	4.22701e11i	−0.803554	+	0.463932i	−0.844712	−	0.535220i	$-0.820229\pi$
$977$	−7.32139e11	+	4.22701e11i	−0.803554	+	0.463932i	0.0411582	+	0.999153i	$0.486895\pi$
$978$		0			0
$979$	−9.09200e10			−0.0989757
$980$	−1.44922e11	+	1.70530e10i	−0.157119	+	0.0184883i
$981$		0			0
$982$	−3.81711e11	+	6.61143e11i	−0.410477	+	0.710967i
$983$	1.15979e12	−	6.69605e11i	1.24212	−	0.717141i	0.272598	−	0.962128i	$-0.412117\pi$
$983$	1.15979e12	−	6.69605e11i	1.24212	−	0.717141i	0.969526	+	0.244987i	$0.0787838\pi$
$984$		0			0
$985$	−1.88045e11	+	3.25703e11i	−0.199764	+	0.346001i
$986$			5.42421e10i			0.0573890i
$987$		0			0
$988$	6.01568e9			0.00631331
$989$	−3.80523e10	−	2.19695e10i	−0.0397737	−	0.0229634i
$990$		0			0
$991$	8.96509e11	+	1.55280e12i	0.929523	+	1.60998i	0.784121	+	0.620607i	$0.213114\pi$
$991$	8.96509e11	+	1.55280e12i	0.929523	+	1.60998i	0.145401	+	0.989373i	$0.453553\pi$
$992$	3.86481e10	+	2.23135e10i	0.0399099	+	0.0230420i
$993$		0			0
$994$	−1.97025e11	−	5.93817e11i	−0.201826	−	0.608285i
$995$		−	4.16984e10i		−	0.0425429i
$996$		0			0
$997$	9.15620e10	+	1.58590e11i	0.0926690	+	0.160507i	0.908633	−	0.417595i	$-0.137127\pi$
$997$	9.15620e10	+	1.58590e11i	0.0926690	+	0.160507i	−0.815964	+	0.578102i	$0.803793\pi$
$998$	−4.90471e11	+	2.83174e11i	−0.494415	+	0.285450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.9.s.a.107.3	yes	20
3.2	odd	2	inner	126.9.s.a.107.8	yes	20
7.4	even	3	inner	126.9.s.a.53.8	yes	20
21.11	odd	6	inner	126.9.s.a.53.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.9.s.a.53.3	✓	20	21.11	odd	6	inner
126.9.s.a.53.8	yes	20	7.4	even	3	inner
126.9.s.a.107.3	yes	20	1.1	even	1	trivial
126.9.s.a.107.8	yes	20	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	126.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(-171.260 - 98.8770i) q^{5} +(-1595.48 + 1794.23i) q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+(-9.79796 - 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(-171.260 - 98.8770i) q^{5} +(-1595.48 + 1794.23i) q^{7} -1448.15i q^{8} +(1118.67 + 1937.59i) q^{10} +(-1666.85 + 962.354i) q^{11} -31981.6 q^{13} +(25782.1 - 8554.37i) q^{14} +(-8192.00 + 14189.0i) q^{16} +(-27578.5 + 15922.5i) q^{17} +(-734.759 + 1272.64i) q^{19} -25312.5i q^{20} +21775.6 q^{22} +(118751. + 68560.7i) q^{23} +(-175759. - 304424. i) q^{25} +(313354. + 180915. i) q^{26} +(-301003. - 62030.3i) q^{28} +150554. i q^{29} +(120377. + 208498. i) q^{31} +(160530. - 92681.9i) q^{32} +360284. q^{34} +(450650. - 149523. i) q^{35} +(-899006. + 1.55712e6i) q^{37} +(14398.3 - 8312.85i) q^{38} +(-143189. + 248011. i) q^{40} +2.54545e6i q^{41} -320439. q^{43} +(-213356. - 123181. i) q^{44} +(-775675. - 1.34351e6i) q^{46} +(5.31136e6 + 3.06651e6i) q^{47} +(-673698. - 5.72530e6i) q^{49} +3.97698e6i q^{50} +(-2.04682e6 - 3.54520e6i) q^{52} +(7.42970e6 - 4.28954e6i) q^{53} +380619. q^{55} +(2.59832e6 + 2.31050e6i) q^{56} +(851660. - 1.47512e6i) q^{58} +(6.20225e6 - 3.58087e6i) q^{59} +(2.97248e6 - 5.14848e6i) q^{61} -2.72381e6i q^{62} -2.09715e6 q^{64} +(5.47717e6 + 3.16224e6i) q^{65} +(-1.20290e7 - 2.08348e7i) q^{67} +(-3.53005e6 - 2.03807e6i) q^{68} +(-5.26128e6 - 1.08424e6i) q^{70} -2.30321e7i q^{71} +(-1.63452e7 - 2.83108e7i) q^{73} +(1.76169e7 - 1.01711e7i) q^{74} -188098. q^{76} +(932736. - 4.52612e6i) q^{77} +(3.31671e7 - 5.74472e7i) q^{79} +(2.80592e6 - 1.62000e6i) q^{80} +(1.43992e7 - 2.49402e7i) q^{82} -4.15284e7i q^{83} +6.29746e6 q^{85} +(3.13965e6 + 1.81268e6i) q^{86} +(1.39364e6 + 2.41385e6i) q^{88} +(4.09096e7 + 2.36192e7i) q^{89} +(5.10259e7 - 5.73822e7i) q^{91} +1.75515e7i q^{92} +(-3.46936e7 - 6.00911e7i) q^{94} +(251670. - 145302. i) q^{95} +1.26007e7 q^{97} +(-2.57863e7 + 5.99073e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 1280 q^{4} - 3710 q^{7}+O(q^{10}) \) 20 * q + 1280 * q^4 - 3710 * q^7	\( 20 q + 1280 q^{4} - 3710 q^{7} - 3040 q^{10} + 133668 q^{13} - 163840 q^{16} + 180526 q^{19} - 371648 q^{22} + 1919806 q^{25} + 136192 q^{28} - 2496630 q^{31} - 7741568 q^{34} + 2579434 q^{37} + 389120 q^{40} + 9786628 q^{43} + 6602944 q^{46} - 16557394 q^{49} + 8554752 q^{52} - 48224 q^{55} + 11294336 q^{58} - 45256440 q^{61} - 41943040 q^{64} - 5459674 q^{67} + 36416128 q^{70} - 154260166 q^{73} + 46214656 q^{76} - 147636618 q^{79} - 123306336 q^{82} - 6742976 q^{85} - 23785472 q^{88} - 32944086 q^{91} - 95141856 q^{94} + 268865432 q^{97}+O(q^{100}) \) 20 * q + 1280 * q^4 - 3710 * q^7 - 3040 * q^10 + 133668 * q^13 - 163840 * q^16 + 180526 * q^19 - 371648 * q^22 + 1919806 * q^25 + 136192 * q^28 - 2496630 * q^31 - 7741568 * q^34 + 2579434 * q^37 + 389120 * q^40 + 9786628 * q^43 + 6602944 * q^46 - 16557394 * q^49 + 8554752 * q^52 - 48224 * q^55 + 11294336 * q^58 - 45256440 * q^61 - 41943040 * q^64 - 5459674 * q^67 + 36416128 * q^70 - 154260166 * q^73 + 46214656 * q^76 - 147636618 * q^79 - 123306336 * q^82 - 6742976 * q^85 - 23785472 * q^88 - 32944086 * q^91 - 95141856 * q^94 + 268865432 * q^97

Introduction

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