LMFDB - Embedded newform 429.2.bq.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(29,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bq (of order $30$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	429.29
Dual form			429.2.bq.a.74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.276807 + 2.63364i) q^{2} +(-1.73182 - 0.0281544i) q^{3} +(-4.90316 - 1.04220i) q^{4} +(-1.71868 - 2.36556i) q^{5} +(0.553529 - 4.55321i) q^{6} +(-0.0575585 + 0.270792i) q^{7} +(2.46537 - 7.58762i) q^{8} +(2.99841 + 0.0975169i) q^{9} +O(q^{10})$	\(q+(-0.276807 + 2.63364i) q^{2} +(-1.73182 - 0.0281544i) q^{3} +(-4.90316 - 1.04220i) q^{4} +(-1.71868 - 2.36556i) q^{5} +(0.553529 - 4.55321i) q^{6} +(-0.0575585 + 0.270792i) q^{7} +(2.46537 - 7.58762i) q^{8} +(2.99841 + 0.0975169i) q^{9} +(6.70579 - 3.87159i) q^{10} +(-2.60140 + 2.05735i) q^{11} +(8.46206 + 1.94295i) q^{12} +(0.759816 + 3.52458i) q^{13} +(-0.697236 - 0.226546i) q^{14} +(2.90985 + 4.14512i) q^{15} +(10.1420 + 4.51550i) q^{16} +(-0.0368807 - 0.350896i) q^{17} +(-1.08681 + 7.86976i) q^{18} +(5.71882 - 5.14925i) q^{19} +(5.96158 + 13.3899i) q^{20} +(0.107305 - 0.467342i) q^{21} +(-4.69824 - 7.42066i) q^{22} +(-1.43809 + 0.830281i) q^{23} +(-4.48320 + 13.0710i) q^{24} +(-1.09693 + 3.37600i) q^{25} +(-9.49282 + 1.02546i) q^{26} +(-5.18997 - 0.253301i) q^{27} +(0.564438 - 1.26775i) q^{28} +(4.98586 - 5.53736i) q^{29} +(-11.7222 + 6.51610i) q^{30} +(6.84271 + 4.97152i) q^{31} +(-6.72151 + 11.6420i) q^{32} +(4.56309 - 3.48973i) q^{33} +0.934345 q^{34} +(0.739499 - 0.329246i) q^{35} +(-14.6001 - 3.60309i) q^{36} +(6.20598 - 6.89244i) q^{37} +(11.9783 + 16.4867i) q^{38} +(-1.21663 - 6.12534i) q^{39} +(-22.1861 + 7.20872i) q^{40} +(-1.57684 + 0.335167i) q^{41} +(1.20111 + 0.411967i) q^{42} +(-3.03684 - 1.75332i) q^{43} +(14.8993 - 7.37635i) q^{44} +(-4.92263 - 7.26053i) q^{45} +(-1.78859 - 4.01724i) q^{46} +(-2.43781 - 0.792093i) q^{47} +(-17.4370 - 8.10559i) q^{48} +(6.32480 + 2.81598i) q^{49} +(-8.58755 - 3.82342i) q^{50} +(0.0539915 + 0.608728i) q^{51} +(-0.0521845 - 18.0735i) q^{52} +(4.57928 - 6.30284i) q^{53} +(2.10373 - 13.5984i) q^{54} +(9.33777 + 2.61785i) q^{55} +(1.91276 + 1.10433i) q^{56} +(-10.0490 + 8.75658i) q^{57} +(13.2033 + 14.6638i) q^{58} +(-0.497786 + 2.34190i) q^{59} +(-9.94742 - 23.3568i) q^{60} +(-2.52127 + 0.264996i) q^{61} +(-14.9873 + 16.6451i) q^{62} +(-0.198991 + 0.806332i) q^{63} +(-10.8373 - 7.87372i) q^{64} +(7.03173 - 7.85502i) q^{65} +(7.92760 + 12.9835i) q^{66} +(-0.190638 - 0.330195i) q^{67} +(-0.184872 + 1.75894i) q^{68} +(2.51389 - 1.39741i) q^{69} +(0.662418 + 2.03871i) q^{70} +(-0.277213 + 0.0291362i) q^{71} +(8.13211 - 22.5104i) q^{72} +(-2.49733 + 0.811431i) q^{73} +(16.4344 + 18.2522i) q^{74} +(1.99474 - 5.81575i) q^{75} +(-33.4069 + 19.2875i) q^{76} +(-0.407380 - 0.822856i) q^{77} +(16.4687 - 1.50864i) q^{78} +(4.27539 - 5.88457i) q^{79} +(-6.74914 - 31.7522i) q^{80} +(8.98098 + 0.584792i) q^{81} +(-0.446231 - 4.24561i) q^{82} +(-10.4557 + 7.59651i) q^{83} +(-1.01320 + 2.17962i) q^{84} +(-0.766680 + 0.690322i) q^{85} +(5.45823 - 7.51261i) q^{86} +(-8.79053 + 9.44935i) q^{87} +(9.19698 + 24.8106i) q^{88} +(8.24438 - 4.75989i) q^{89} +(20.4843 - 10.9547i) q^{90} +(-0.998161 + 0.00288204i) q^{91} +(7.91650 - 2.57223i) q^{92} +(-11.7104 - 8.80244i) q^{93} +(2.76090 - 6.20107i) q^{94} +(-22.0097 - 4.67831i) q^{95} +(11.9682 - 19.9726i) q^{96} +(-4.75182 + 2.11565i) q^{97} +(-9.16705 + 15.8778i) q^{98} +(-8.00072 + 5.91511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	$ 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.276807	+	2.63364i	−0.195732	+	1.86227i	0.251510	+	0.967855i	$0.419073\pi$
$2$	−0.276807	+	2.63364i	−0.195732	+	1.86227i	−0.447242	+	0.894413i	$0.647594\pi$
$3$	−1.73182	−	0.0281544i	−0.999868	−	0.0162550i
$3$	−1.73182	−	0.0281544i	−0.999868	−	0.0162550i
$4$	−4.90316	−	1.04220i	−2.45158	−	0.521100i
$5$	−1.71868	−	2.36556i	−0.768617	−	1.05791i	−0.996448	−	0.0842101i	$-0.973163\pi$
$5$	−1.71868	−	2.36556i	−0.768617	−	1.05791i	0.227831	−	0.973701i	$-0.426837\pi$
$6$	0.553529	−	4.55321i	0.225977	−	1.85884i
$7$	−0.0575585	+	0.270792i	−0.0217551	+	0.102350i	−0.987686	−	0.156452i	$-0.949994\pi$
$7$	−0.0575585	+	0.270792i	−0.0217551	+	0.102350i	0.965930	+	0.258802i	$0.0833276\pi$
$8$	2.46537	−	7.58762i	0.871639	−	2.68263i
$9$	2.99841	+	0.0975169i	0.999472	+	0.0325056i
$10$	6.70579	−	3.87159i	2.12056	−	1.22430i
$11$	−2.60140	+	2.05735i	−0.784353	+	0.620315i
$11$	−2.60140	+	2.05735i	−0.784353	+	0.620315i
$12$	8.46206	+	1.94295i	2.44279	+	0.560881i
$13$	0.759816	+	3.52458i	0.210735	+	0.977543i
$13$	0.759816	+	3.52458i	0.210735	+	0.977543i
$14$	−0.697236	−	0.226546i	−0.186344	−	0.0605469i
$15$	2.90985	+	4.14512i	0.751319	+	1.07026i
$16$	10.1420	+	4.51550i	2.53550	+	1.12888i
$17$	−0.0368807	−	0.350896i	−0.00894488	−	0.0851048i	0.989139	−	0.146985i	$-0.0469570\pi$
$17$	−0.0368807	−	0.350896i	−0.00894488	−	0.0851048i	−0.998084	+	0.0618803i	$0.980290\pi$
$18$	−1.08681	+	7.86976i	−0.256163	+	1.85492i
$19$	5.71882	−	5.14925i	1.31199	−	1.18132i	0.341579	−	0.939853i	$-0.389038\pi$
$19$	5.71882	−	5.14925i	1.31199	−	1.18132i	0.970409	−	0.241466i	$-0.0776283\pi$
$20$	5.96158	+	13.3899i	1.33305	+	2.99408i
$21$	0.107305	−	0.467342i	0.0234159	−	0.101982i
$22$	−4.69824	−	7.42066i	−1.00167	−	1.58209i
$23$	−1.43809	+	0.830281i	−0.299862	+	0.173125i	−0.642381	−	0.766385i	$-0.722053\pi$
$23$	−1.43809	+	0.830281i	−0.299862	+	0.173125i	0.342519	+	0.939511i	$0.388720\pi$
$24$	−4.48320	+	13.0710i	−0.915130	+	2.66811i
$25$	−1.09693	+	3.37600i	−0.219386	+	0.675200i
$26$	−9.49282	+	1.02546i	−1.86169	+	0.201108i
$27$	−5.18997	−	0.253301i	−0.998811	−	0.0487477i
$28$	0.564438	−	1.26775i	0.106669	−	0.239582i
$29$	4.98586	−	5.53736i	0.925851	−	1.02826i	−0.0736687	−	0.997283i	$-0.523471\pi$
$29$	4.98586	−	5.53736i	0.925851	−	1.02826i	0.999520	−	0.0309793i	$-0.00986261\pi$
$30$	−11.7222	+	6.51610i	−2.14018	+	1.18967i
$31$	6.84271	+	4.97152i	1.22899	+	0.892911i	0.996814	−	0.0797637i	$-0.0254166\pi$
$31$	6.84271	+	4.97152i	1.22899	+	0.892911i	0.232173	+	0.972675i	$0.425417\pi$
$32$	−6.72151	+	11.6420i	−1.18821	+	2.05803i
$33$	4.56309	−	3.48973i	0.794332	−	0.607483i
$34$	0.934345			0.160239
$35$	0.739499	−	0.329246i	0.124998	−	0.0556527i
$36$	−14.6001	−	3.60309i	−2.43335	−	0.600515i
$37$	6.20598	−	6.89244i	1.02026	−	1.13311i	0.0292127	−	0.999573i	$-0.490700\pi$
$37$	6.20598	−	6.89244i	1.02026	−	1.13311i	0.991044	−	0.133537i	$-0.0426333\pi$
$38$	11.9783	+	16.4867i	1.94313	+	2.67450i
$39$	−1.21663	−	6.12534i	−0.194817	−	0.980840i
$40$	−22.1861	+	7.20872i	−3.50794	+	1.13980i
$41$	−1.57684	+	0.335167i	−0.246261	+	0.0523443i	−0.329388	−	0.944195i	$-0.606842\pi$
$41$	−1.57684	+	0.335167i	−0.246261	+	0.0523443i	0.0831274	+	0.996539i	$0.473509\pi$
$42$	1.20111	+	0.411967i	0.185335	+	0.0635679i
$43$	−3.03684	−	1.75332i	−0.463113	−	0.267378i	0.250239	−	0.968184i	$-0.419491\pi$
$43$	−3.03684	−	1.75332i	−0.463113	−	0.267378i	−0.713352	+	0.700806i	$0.752824\pi$
$44$	14.8993	−	7.37635i	2.24615	−	1.11203i
$45$	−4.92263	−	7.26053i	−0.733823	−	1.08234i
$46$	−1.78859	−	4.01724i	−0.263713	−	0.592310i
$47$	−2.43781	−	0.792093i	−0.355592	−	0.115539i	0.125773	−	0.992059i	$-0.459859\pi$
$47$	−2.43781	−	0.792093i	−0.355592	−	0.115539i	−0.481365	+	0.876520i	$0.659859\pi$
$48$	−17.4370	−	8.10559i	−2.51681	−	1.16994i
$49$	6.32480	+	2.81598i	0.903543	+	0.402283i
$50$	−8.58755	−	3.82342i	−1.21446	−	0.540714i
$51$	0.0539915	+	0.608728i	0.00756032	+	0.0852390i
$52$	−0.0521845	−	18.0735i	−0.00723669	−	2.50634i
$53$	4.57928	−	6.30284i	0.629013	−	0.865762i	−0.368957	−	0.929446i	$-0.620285\pi$
$53$	4.57928	−	6.30284i	0.629013	−	0.865762i	0.997970	+	0.0636843i	$0.0202851\pi$
$54$	2.10373	−	13.5984i	0.286281	−	1.85051i
$55$	9.33777	+	2.61785i	1.25910	+	0.352991i
$56$	1.91276	+	1.10433i	0.255603	+	0.147573i
$57$	−10.0490	+	8.75658i	−1.33102	+	1.15984i
$58$	13.2033	+	14.6638i	1.73368	+	1.92545i
$59$	−0.497786	+	2.34190i	−0.0648062	+	0.304889i	−0.998598	−	0.0529266i	$-0.983145\pi$
$59$	−0.497786	+	2.34190i	−0.0648062	+	0.304889i	0.933792	+	0.357816i	$0.116478\pi$
$60$	−9.94742	−	23.3568i	−1.28421	−	3.01535i
$61$	−2.52127	+	0.264996i	−0.322815	+	0.0339293i	−0.264550	−	0.964372i	$-0.585224\pi$
$61$	−2.52127	+	0.264996i	−0.322815	+	0.0339293i	−0.0582651	+	0.998301i	$0.518557\pi$
$62$	−14.9873	+	16.6451i	−1.90339	+	2.11393i
$63$	−0.198991	+	0.806332i	−0.0250705	+	0.101588i
$64$	−10.8373	−	7.87372i	−1.35466	−	0.984216i
$65$	7.03173	−	7.85502i	0.872179	−	0.974295i
$66$	7.92760	+	12.9835i	0.975820	+	1.59816i
$67$	−0.190638	−	0.330195i	−0.0232902	−	0.0403398i	0.854145	−	0.520034i	$-0.174081\pi$
$67$	−0.190638	−	0.330195i	−0.0232902	−	0.0403398i	−0.877436	+	0.479694i	$0.840747\pi$
$68$	−0.184872	+	1.75894i	−0.0224190	+	0.213303i
$69$	2.51389	−	1.39741i	0.302637	−	0.168228i
$70$	0.662418	+	2.03871i	0.0791741	+	0.243673i
$71$	−0.277213	+	0.0291362i	−0.0328991	+	0.00345783i	−0.120964	−	0.992657i	$-0.538598\pi$
$71$	−0.277213	+	0.0291362i	−0.0328991	+	0.00345783i	0.0880646	+	0.996115i	$0.471932\pi$
$72$	8.13211	−	22.5104i	0.958379	−	2.65288i
$73$	−2.49733	+	0.811431i	−0.292290	+	0.0949708i	−0.451492	−	0.892275i	$-0.649108\pi$
$73$	−2.49733	+	0.811431i	−0.292290	+	0.0949708i	0.159202	+	0.987246i	$0.449108\pi$
$74$	16.4344	+	18.2522i	1.91046	+	2.12178i
$75$	1.99474	−	5.81575i	0.230332	−	0.671545i
$76$	−33.4069	+	19.2875i	−3.83203	+	2.21242i
$77$	−0.407380	−	0.822856i	−0.0464253	−	0.0937732i
$78$	16.4687	−	1.50864i	1.86472	−	0.170820i
$79$	4.27539	−	5.88457i	0.481019	−	0.662066i	−0.497681	−	0.867360i	$-0.665815\pi$
$79$	4.27539	−	5.88457i	0.481019	−	0.662066i	0.978700	+	0.205294i	$0.0658151\pi$
$80$	−6.74914	−	31.7522i	−0.754576	−	3.55000i
$81$	8.98098	+	0.584792i	0.997887	+	0.0649769i
$82$	−0.446231	−	4.24561i	−0.0492780	−	0.468849i
$83$	−10.4557	+	7.59651i	−1.14766	+	0.833826i	−0.988168	−	0.153373i	$-0.950986\pi$
$83$	−10.4557	+	7.59651i	−1.14766	+	0.833826i	−0.159494	+	0.987199i	$0.550986\pi$
$84$	−1.01320	+	2.17962i	−0.110549	+	0.237816i
$85$	−0.766680	+	0.690322i	−0.0831581	+	0.0748759i
$86$	5.45823	−	7.51261i	0.588576	−	0.810106i
$87$	−8.79053	+	9.44935i	−0.942443	+	1.01308i
$88$	9.19698	+	24.8106i	0.980402	+	2.64482i
$89$	8.24438	−	4.75989i	0.873902	−	0.504548i	0.00525925	−	0.999986i	$-0.498326\pi$
$89$	8.24438	−	4.75989i	0.873902	−	0.504548i	0.868643	+	0.495438i	$0.164993\pi$
$90$	20.4843	−	10.9547i	2.15923	−	1.15473i
$91$	−0.998161	+	0.00288204i	−0.104636	+	0.000302120i
$92$	7.91650	−	2.57223i	0.825352	−	0.268173i
$93$	−11.7104	−	8.80244i	−1.21431	−	0.912770i
$94$	2.76090	−	6.20107i	0.284765	−	0.639592i
$95$	−22.0097	−	4.67831i	−2.25815	−	0.479984i
$96$	11.9682	−	19.9726i	1.22150	−	2.03845i
$97$	−4.75182	+	2.11565i	−0.482474	+	0.214811i	−0.633536	−	0.773713i	$-0.718397\pi$
$97$	−4.75182	+	2.11565i	−0.482474	+	0.214811i	0.151062	+	0.988524i	$0.451731\pi$
$98$	−9.16705	+	15.8778i	−0.926012	+	1.60390i
$99$	−8.00072	+	5.91511i	−0.804102	+	0.594491i
$100$	8.89689	−	15.4099i	0.889689	−	1.54099i
$101$	0.143983	−	1.36991i	0.0143268	−	0.136311i	−0.985020	−	0.172438i	$-0.944836\pi$
$101$	0.143983	−	1.36991i	0.0143268	−	0.136311i	0.999347	+	0.0361274i	$0.0115022\pi$
$102$	−1.61812	−	0.0263059i	−0.160218	−	0.00260468i
$103$	1.95141	+	6.00582i	0.192278	+	0.591771i	0.999998	+	0.00220432i	$0.000701656\pi$
$103$	1.95141	+	6.00582i	0.192278	+	0.591771i	−0.807719	+	0.589567i	$0.799298\pi$
$104$	28.6164	+	2.92419i	2.80607	+	0.286741i
$105$	−1.28995	+	0.549375i	−0.125886	+	0.0536135i
$106$	15.3319	+	13.8049i	1.48916	+	1.34085i
$107$	14.5784	−	3.09873i	1.40934	−	0.299565i	0.560476	−	0.828171i	$-0.310618\pi$
$107$	14.5784	−	3.09873i	1.40934	−	0.299565i	0.848867	+	0.528606i	$0.177285\pi$
$108$	25.1833	+	6.65096i	2.42326	+	0.639989i
$109$		−	12.3824i		−	1.18602i	−0.805197	−	0.593008i	$-0.797940\pi$
$109$		−	12.3824i		−	1.18602i	0.805197	−	0.593008i	$-0.202060\pi$
$110$	−9.47925	+	23.8677i	−0.903811	+	2.27570i
$111$	−10.9417	+	11.7617i	−1.03854	+	1.11638i
$112$	−1.80652	+	2.48646i	−0.170700	+	0.234948i
$113$	12.7029	−	11.4377i	1.19499	−	1.07597i	0.199617	−	0.979874i	$-0.436030\pi$
$113$	12.7029	−	11.4377i	1.19499	−	1.07597i	0.995372	−	0.0960982i	$-0.0306363\pi$
$114$	−20.2801	−	28.8893i	−1.89940	−	2.70573i
$115$	4.43569	+	1.97490i	0.413630	+	0.184160i
$116$	−30.2175	+	21.9543i	−2.80563	+	2.03841i
$117$	1.93454	+	10.6423i	0.178848	+	0.983877i
$118$	−6.02994	−	1.95924i	−0.555101	−	0.180363i
$119$	0.0971425	+	0.0102101i	0.00890504	+	0.000935958i
$120$	38.6254	−	11.8596i	3.52600	−	1.08263i
$121$	2.53461	−	10.7040i	0.230419	−	0.973092i
$122$		−	6.71348i		−	0.607810i
$123$	2.74024	−	0.536055i	0.247079	−	0.0483345i
$124$	−28.3696	−	31.5076i	−2.54767	−	2.82947i
$125$	−4.03301	+	1.31040i	−0.360723	+	0.117206i
$126$	−2.06851	−	0.747270i	−0.184278	−	0.0665721i
$127$	−2.04892	+	4.60196i	−0.181813	+	0.408358i	−0.981342	−	0.192269i	$-0.938415\pi$
$127$	−2.04892	+	4.60196i	−0.181813	+	0.408358i	0.799530	+	0.600627i	$0.205082\pi$
$128$	5.74614	−	6.38173i	0.507892	−	0.564071i
$129$	5.20989	+	3.12193i	0.458706	+	0.274871i
$130$	18.7409	+	20.6934i	1.64369	+	1.81493i
$131$	18.1463			1.58545			0.792724	−	0.609581i	$-0.208662\pi$
$131$	18.1463			1.58545			0.792724	+	0.609581i	$0.208662\pi$
$132$	−26.0106	+	12.3550i	−2.26393	+	1.07537i
$133$	1.06521	+	1.84499i	0.0923652	+	0.159981i
$134$	0.922387	−	0.410673i	0.0796821	−	0.0354768i
$135$	8.32071	+	12.7125i	0.716133	+	1.09412i
$136$	−2.75339	−	0.585251i	−0.236101	−	0.0501849i
$137$	−0.515041	+	0.0541330i	−0.0440029	+	0.00462489i	−0.126504	−	0.991966i	$-0.540376\pi$
$137$	−0.515041	+	0.0541330i	−0.0440029	+	0.00462489i	0.0825014	+	0.996591i	$0.473709\pi$
$138$	2.98442	+	7.00750i	0.254050	+	0.596518i
$139$	3.53809	−	16.6454i	0.300097	−	1.41185i	−0.527037	−	0.849842i	$-0.676697\pi$
$139$	3.53809	−	16.6454i	0.300097	−	1.41185i	0.827134	−	0.562004i	$-0.189970\pi$
$140$	−3.96902	+	0.843642i	−0.335444	+	0.0713007i
$141$	4.19956	+	1.44040i	0.353667	+	0.121304i
$142$		−	0.738144i		−	0.0619437i
$143$	−9.22789	−	7.60565i	−0.771675	−	0.636017i
$144$	29.9695	+	14.5284i	2.49746	+	1.21070i
$145$	−21.6681	−	2.27741i	−1.79943	−	0.189128i
$146$	−1.44574	−	6.80168i	−0.119650	−	0.562911i
$147$	−10.8742	−	5.05485i	−0.896885	−	0.416917i
$148$	−37.6122	+	27.3269i	−3.09171	+	2.24626i
$149$	−1.83942	−	17.5009i	−0.150691	−	1.43373i	−0.764676	−	0.644415i	$-0.777101\pi$
$149$	−1.83942	−	17.5009i	−0.150691	−	1.43373i	0.613984	−	0.789318i	$-0.289566\pi$
$150$	14.7645	+	6.86327i	1.20551	+	0.560383i
$151$	2.37101	+	0.770387i	0.192950	+	0.0626932i	0.403898	−	0.914804i	$-0.367655\pi$
$151$	2.37101	+	0.770387i	0.192950	+	0.0626932i	−0.210948	+	0.977497i	$0.567655\pi$
$152$	−24.9716	−	56.0870i	−2.02546	−	4.54926i
$153$	−0.0763653	−	1.05573i	−0.00617377	−	0.0853506i
$154$	2.27988	−	0.845123i	0.183718	−	0.0681019i
$155$		−	24.7313i		−	1.98646i
$156$	−0.418474	+	31.3015i	−0.0335048	+	2.50613i
$157$	−1.95253	+	6.00926i	−0.155828	+	0.479591i	−0.998244	−	0.0592378i	$-0.981133\pi$
$157$	−1.95253	+	6.00926i	−0.155828	+	0.479591i	0.842415	+	0.538829i	$0.181133\pi$
$158$	14.3144	+	12.8887i	1.13879	+	1.02537i
$159$	−8.10796	+	10.7865i	−0.643003	+	0.855423i
$160$	39.0920	−	4.10873i	3.09049	−	0.324824i
$161$	−0.142059	−	0.437212i	−0.0111958	−	0.0344571i
$162$	−4.02613	+	23.4908i	−0.316323	+	1.84561i
$163$	−11.0558	+	4.92236i	−0.865956	+	0.385549i	−0.791130	−	0.611648i	$-0.790507\pi$
$163$	−11.0558	+	4.92236i	−0.865956	+	0.385549i	−0.0748263	+	0.997197i	$0.523840\pi$
$164$	8.08081			0.631005
$165$	−16.0977	−	4.79655i	−1.25320	−	0.373411i
$166$	−17.1123	−	29.6394i	−1.32817	−	2.30046i
$167$	0.443761	−	4.22210i	0.0343392	−	0.326716i	−0.963844	−	0.266467i	$-0.914144\pi$
$167$	0.443761	−	4.22210i	0.0343392	−	0.326716i	0.998183	−	0.0602493i	$-0.0191896\pi$
$168$	−3.28147	−	1.96636i	−0.253171	−	0.151708i
$169$	−11.8454	+	5.35607i	−0.911181	+	0.412005i
$170$	−1.60584	−	2.21025i	−0.123162	−	0.169518i
$171$	17.6495	−	14.8819i	1.34969	−	1.13805i
$172$	13.0628	+	11.7618i	0.996029	+	0.896828i
$173$	6.76298	+	7.51105i	0.514180	+	0.571054i	0.943194	−	0.332243i	$-0.107806\pi$
$173$	6.76298	+	7.51105i	0.514180	+	0.571054i	−0.429014	+	0.903298i	$0.641139\pi$
$174$	−22.4529	−	25.7668i	−1.70215	−	1.95337i
$175$	−0.851055	−	0.491357i	−0.0643337	−	0.0371431i
$176$	−35.6734	+	9.11898i	−2.68898	+	0.687369i
$177$	0.928011	−	4.04174i	0.0697536	−	0.303795i
$178$	10.2538	+	23.0303i	0.768552	+	1.72620i
$179$	0.0396541	+	0.186558i	0.00296389	+	0.0139440i	0.979605	−	0.200934i	$-0.0643978\pi$
$179$	0.0396541	+	0.186558i	0.00296389	+	0.0139440i	−0.976641	+	0.214878i	$0.931064\pi$
$180$	16.5696	+	40.7299i	1.23502	+	3.03583i
$181$	9.04251	−	6.56977i	0.672124	−	0.488327i	−0.198611	−	0.980078i	$-0.563643\pi$
$181$	9.04251	−	6.56977i	0.672124	−	0.488327i	0.870736	+	0.491751i	$0.163643\pi$
$182$	0.268708	−	2.62960i	0.0199179	−	0.194919i
$183$	4.37385	−	0.387941i	0.323324	−	0.0286774i
$184$	2.75444	+	12.9586i	0.203060	+	0.955321i
$185$	−26.9706	−	2.83472i	−1.98292	−	0.208413i
$186$	26.4240	−	28.4044i	1.93750	−	2.08271i
$187$	0.817859	+	0.836947i	0.0598077	+	0.0612036i
$188$	11.1275	+	6.42445i	0.811555	+	0.468551i
$189$	0.367319	−	1.39082i	0.0267185	−	0.101167i
$190$	18.4134	−	56.6707i	1.33585	−	4.11133i
$191$	−1.70305	+	8.01222i	−0.123228	+	0.579744i	0.872595	+	0.488444i	$0.162435\pi$
$191$	−1.70305	+	8.01222i	−0.123228	+	0.579744i	−0.995823	+	0.0912997i	$0.970898\pi$
$192$	18.5465	+	13.9410i	1.33848	+	1.00611i
$193$	−3.59700	+	8.07900i	−0.258918	+	0.581539i	−0.995495	−	0.0948145i	$-0.969774\pi$
$193$	−3.59700	+	8.07900i	−0.258918	+	0.581539i	0.736577	+	0.676354i	$0.236441\pi$
$194$	−4.25652	−	13.1002i	−0.305600	−	0.940541i
$195$	−12.3989	+	13.4055i	−0.887901	+	0.959989i
$196$	−28.0767	−	20.3989i	−2.00548	−	1.45707i
$197$	4.55646	+	7.89202i	0.324634	+	0.562283i	0.981438	−	0.191778i	$-0.0614255\pi$
$197$	4.55646	+	7.89202i	0.324634	+	0.562283i	−0.656804	+	0.754061i	$0.728092\pi$
$198$	−13.3636	−	22.7084i	−0.949713	−	1.61381i
$199$	−7.02507	+	12.1678i	−0.497994	+	0.862551i	−0.999997	−	0.00231450i	$-0.999263\pi$
$199$	−7.02507	+	12.1678i	−0.497994	+	0.862551i	0.502003	+	0.864866i	$0.332597\pi$
$200$	22.9115	+	16.6462i	1.62009	+	1.17706i
$201$	0.320855	+	0.577207i	0.0226314	+	0.0407130i
$202$	3.56799	+	0.758399i	0.251043	+	0.0533608i
$203$	1.21249	+	1.66885i	0.0851002	+	0.117130i
$204$	0.369687	−	3.04096i	0.0258833	−	0.212910i
$205$	3.50294	+	3.15406i	0.244656	+	0.220289i
$206$	−16.3574	+	3.47687i	−1.13967	+	0.242245i
$207$	−4.39295	+	2.34929i	−0.305331	+	0.163287i
$208$	−8.20922	+	39.1772i	−0.569207	+	2.71645i
$209$	−4.28315	+	25.1609i	−0.296272	+	1.74042i
$210$	−1.08979	−	3.54934i	−0.0752028	−	0.244928i
$211$	−7.73949	−	0.813453i	−0.532808	−	0.0560004i	−0.165696	−	0.986177i	$-0.552987\pi$
$211$	−7.73949	−	0.813453i	−0.532808	−	0.0560004i	−0.367113	+	0.930176i	$0.619654\pi$
$212$	−29.0218	+	26.1313i	−1.99323	+	1.79471i
$213$	0.480903	−	0.0426540i	0.0329509	−	0.00292260i
$214$	4.12555	+	39.2520i	0.282017	+	2.68321i
$215$	1.07177	+	10.1972i	0.0730941	+	0.695444i
$216$	−14.7171	+	38.7551i	−1.00137	+	2.63695i
$217$	−1.74010	+	1.56679i	−0.118126	+	0.106361i
$218$	32.6108	+	3.42753i	2.20868	+	0.232141i
$219$	4.34777	−	1.33494i	0.293795	−	0.0902071i
$220$	−43.0563	−	22.5676i	−2.90286	−	1.52151i
$221$	1.20874	−	0.396606i	0.0813087	−	0.0266786i
$222$	−27.9475	−	32.0723i	−1.87571	−	2.15255i
$223$	8.61585	−	1.83136i	0.576960	−	0.122637i	0.0898162	−	0.995958i	$-0.471372\pi$
$223$	8.61585	−	1.83136i	0.576960	−	0.122637i	0.487144	+	0.873322i	$0.338039\pi$
$224$	−2.76568	−	2.49023i	−0.184789	−	0.166385i
$225$	−3.61827	+	10.0157i	−0.241218	+	0.667712i
$226$	26.6067	+	36.6210i	1.76985	+	2.43599i
$227$	13.7592	+	2.92462i	0.913233	+	0.194114i	0.640484	−	0.767972i	$-0.278734\pi$
$227$	13.7592	+	2.92462i	0.913233	+	0.194114i	0.272749	+	0.962085i	$0.412067\pi$
$228$	58.3978	−	32.4619i	3.86749	−	2.14984i
$229$	−8.18568	−	5.94725i	−0.540925	−	0.393005i	0.283503	−	0.958971i	$-0.408503\pi$
$229$	−8.18568	−	5.94725i	−0.540925	−	0.393005i	−0.824429	+	0.565966i	$0.808503\pi$
$230$	−6.42901	+	11.1354i	−0.423916	+	0.734245i
$231$	0.682343	+	1.43651i	0.0448949	+	0.0945155i
$232$	−29.7234	−	51.4824i	−1.95144	−	3.37999i
$233$	−12.2958	−	8.93342i	−0.805525	−	0.585248i	0.107005	−	0.994258i	$-0.465874\pi$
$233$	−12.2958	−	8.93342i	−0.805525	−	0.585248i	−0.912530	+	0.409011i	$0.865874\pi$
$234$	−28.5634	+	2.14903i	−1.86725	+	0.140487i
$235$	2.31608	+	7.12815i	0.151084	+	0.464989i
$236$	4.88145	−	10.9639i	0.317755	−	0.713690i
$237$	−7.56989	+	10.0707i	−0.491717	+	0.654159i
$238$	−0.0537795	+	0.253013i	−0.00348601	+	0.0164004i
$239$	−4.69754	+	14.4575i	−0.303858	+	0.935180i	0.676242	+	0.736679i	$0.263607\pi$
$239$	−4.69754	+	14.4575i	−0.303858	+	0.935180i	−0.980101	+	0.198501i	$0.936393\pi$
$240$	10.7943	+	55.1792i	0.696772	+	3.56180i
$241$	−5.30431	−	3.06244i	−0.341680	−	0.197269i	0.319334	−	0.947642i	$-0.396541\pi$
$241$	−5.30431	−	3.06244i	−0.341680	−	0.197269i	−0.661015	+	0.750373i	$0.729874\pi$
$242$	27.4889	+	9.63820i	1.76706	+	0.619567i
$243$	−15.5370	−	1.26561i	−0.996699	−	0.0811889i
$244$	12.6384	+	1.32835i	0.809089	+	0.0850387i
$245$	−4.20893	−	19.8015i	−0.268899	−	1.26507i
$246$	0.653261	+	7.36520i	0.0416504	+	0.469588i
$247$	22.4942	+	16.2440i	1.43127	+	1.03358i
$248$	54.5918	−	39.6632i	3.46658	−	2.51862i
$249$	18.3213	−	12.8614i	1.16106	−	0.815060i
$250$	−2.33477	−	10.9842i	−0.147664	−	0.694704i
$251$	8.90002	+	19.9898i	0.561764	+	1.26174i	0.941614	+	0.336695i	$0.109309\pi$
$251$	8.90002	+	19.9898i	0.561764	+	1.26174i	−0.379849	+	0.925048i	$0.624024\pi$
$252$	1.81605	−	3.74619i	0.114400	−	0.235988i
$253$	2.03287	−	5.11855i	0.127805	−	0.321800i
$254$	−11.5528	−	6.66999i	−0.724885	−	0.418513i
$255$	1.34719	−	1.17393i	0.0843643	−	0.0735143i
$256$	−2.71014	−	3.00992i	−0.169384	−	0.188120i
$257$	10.7897	+	9.71511i	0.673044	+	0.606012i	0.933115	−	0.359578i	$-0.117079\pi$
$257$	10.7897	+	9.71511i	0.673044	+	0.606012i	−0.260071	+	0.965589i	$0.583746\pi$
$258$	−9.66420	+	12.8568i	−0.601667	+	0.800432i
$259$	1.50921	+	2.07725i	0.0937776	+	0.129074i
$260$	−42.6642	+	31.1860i	−2.64592	+	1.93407i
$261$	15.4897	−	16.1171i	0.958786	−	0.997623i
$262$	−5.02302	+	47.7908i	−0.310323	+	2.95253i
$263$	5.72512	+	9.91619i	0.353026	+	0.611459i	0.986778	−	0.162077i	$-0.0518194\pi$
$263$	5.72512	+	9.91619i	0.353026	+	0.611459i	−0.633752	+	0.773536i	$0.718486\pi$
$264$	−15.2290	−	43.2265i	−0.937281	−	2.66040i
$265$	−22.7801			−1.39937
$266$	−5.15391	+	2.29467i	−0.316007	+	0.140695i
$267$	−14.4118	+	8.01117i	−0.881988	+	0.490276i
$268$	0.590602	+	1.81769i	0.0360767	+	0.111033i
$269$	−5.82142	+	0.611856i	−0.354938	+	0.0373055i	−0.280320	−	0.959907i	$-0.590441\pi$
$269$	−5.82142	+	0.611856i	−0.354938	+	0.0373055i	−0.0746185	+	0.997212i	$0.523774\pi$
$270$	−35.7835	+	18.3949i	−2.17772	+	1.11948i
$271$	−11.9327	−	10.7443i	−0.724862	−	0.652669i	0.221728	−	0.975109i	$-0.428830\pi$
$271$	−11.9327	−	10.7443i	−0.724862	−	0.652669i	−0.946590	+	0.322440i	$0.895497\pi$
$272$	1.21043	−	3.72532i	0.0733931	−	0.225881i
$273$	1.72872	+	0.0231115i	0.104627	+	0.00139877i
$274$		−	1.37142i		−	0.0828505i
$275$	−4.09207	−	11.0391i	−0.246761	−	0.665684i
$276$	−13.7824	+	4.23175i	−0.829602	+	0.254722i
$277$	−3.77053	−	8.46876i	−0.226549	−	0.508838i	0.764128	−	0.645064i	$-0.223169\pi$
$277$	−3.77053	−	8.46876i	−0.226549	−	0.508838i	−0.990678	+	0.136226i	$0.956503\pi$
$278$	42.8588	+	13.9257i	2.57050	+	0.835205i
$279$	20.0325	+	15.5740i	1.19931	+	0.932388i
$280$	−0.675058	−	6.42274i	−0.0403424	−	0.383832i
$281$	−17.9685	+	13.0549i	−1.07191	+	0.778787i	−0.976254	−	0.216627i	$-0.930494\pi$
$281$	−17.9685	+	13.0549i	−1.07191	+	0.778787i	−0.0956545	+	0.995415i	$0.530494\pi$
$282$	−4.95597	+	10.6614i	−0.295124	+	0.634879i
$283$	−4.52478	−	21.2874i	−0.268970	−	1.26540i	−0.880448	−	0.474143i	$-0.842758\pi$
$283$	−4.52478	−	21.2874i	−0.268970	−	1.26540i	0.611478	−	0.791262i	$-0.290575\pi$
$284$	1.38958	+	0.146051i	0.0824566	+	0.00866654i
$285$	37.9852	+	8.72166i	2.25005	+	0.516627i
$286$	22.5849	−	22.1977i	1.33548	−	1.31258i
$287$		−	0.446286i		−	0.0263434i
$288$	−21.2892	+	34.2521i	−1.25448	+	2.01832i
$289$	16.5067	−	3.50862i	0.970985	−	0.206389i
$290$	11.9958	−	56.4356i	0.704415	−	3.31401i
$291$	8.28887	−	3.53014i	0.485902	−	0.206940i
$292$	13.0905	−	1.37586i	0.766062	−	0.0805164i
$293$	6.24984	+	1.32844i	0.365119	+	0.0776085i	0.386818	−	0.922156i	$-0.373574\pi$
$293$	6.24984	+	1.32844i	0.365119	+	0.0776085i	−0.0216987	+	0.999765i	$0.506907\pi$
$294$	16.3227	−	27.2394i	0.951961	−	1.58864i
$295$	6.39544	−	2.84743i	0.372357	−	0.165784i
$296$	−36.9972	−	64.0810i	−2.15042	−	3.72463i
$297$	14.0224	−	10.0187i	0.813659	−	0.581342i
$298$	46.6004			2.69949
$299$	−4.01907	−	4.43780i	−0.232429	−	0.256645i
$300$	−15.8417	+	26.4367i	−0.914620	+	1.52632i
$301$	0.649579	−	0.721431i	0.0374411	−	0.0415826i
$302$	−2.68524	+	6.03114i	−0.154518	+	0.347053i
$303$	−0.287922	+	2.36838i	−0.0165407	+	0.136060i
$304$	81.2517	−	26.4003i	4.66010	−	1.51416i
$305$	4.96012	+	5.50877i	0.284016	+	0.315431i
$306$	2.80155	+	0.0911144i	0.160154	+	0.00520866i
$307$			24.1056i			1.37578i	0.725816	+	0.687889i	$0.241462\pi$
$307$			24.1056i			1.37578i	−0.725816	+	0.687889i	$0.758538\pi$
$308$	1.13987	+	4.45917i	0.0649503	+	0.254085i
$309$	−3.21041	−	10.4560i	−0.182634	−	0.594819i
$310$	65.1334	+	6.84580i	3.69933	+	0.388815i
$311$	−3.68300	−	1.19668i	−0.208844	−	0.0678575i	0.202727	−	0.979235i	$-0.435020\pi$
$311$	−3.68300	−	1.19668i	−0.208844	−	0.0678575i	−0.411571	+	0.911378i	$0.635020\pi$
$312$	−49.4762	−	5.86986i	−2.80104	−	0.332315i
$313$	26.1555	−	19.0031i	1.47840	−	1.07412i	0.500329	−	0.865835i	$-0.333212\pi$
$313$	26.1555	−	19.0031i	1.47840	−	1.07412i	0.978068	−	0.208284i	$-0.0667878\pi$
$314$	−15.2858	−	6.80566i	−0.862626	−	0.384066i
$315$	2.24943	−	0.915102i	0.126741	−	0.0515602i
$316$	−27.0958	+	24.3972i	−1.52426	+	1.37245i
$317$	6.04951	−	8.32644i	0.339775	−	0.467660i	−0.604601	−	0.796528i	$-0.706667\pi$
$317$	6.04951	−	8.32644i	0.339775	−	0.467660i	0.944376	+	0.328869i	$0.106667\pi$
$318$	−26.1634	−	24.3392i	−1.46717	−	1.36488i
$319$	−1.57795	+	24.6626i	−0.0883480	+	1.38084i
$320$			39.1686i			2.18959i
$321$	−25.3344	+	4.95600i	−1.41403	+	0.276617i
$322$	1.19078	−	0.253109i	0.0663598	−	0.0141052i
$323$	−2.01777	−	1.81681i	−0.112272	−	0.101090i
$324$	−43.4257	−	12.2273i	−2.41254	−	0.679295i
$325$	−12.7325	−	1.30108i	−0.706270	−	0.0721708i
$326$	−9.90341	−	30.4796i	−0.548499	−	1.68811i
$327$	−0.348618	+	21.4441i	−0.0192786	+	1.18586i
$328$	−1.34436	+	12.7908i	−0.0742300	+	0.706251i
$329$	0.354809	−	0.614547i	0.0195613	−	0.0338811i
$330$	17.0884	−	41.0678i	0.940683	−	2.26071i
$331$	15.4907	−	26.8306i	0.851443	−	1.47474i	−0.0284624	−	0.999595i	$-0.509061\pi$
$331$	15.4907	−	26.8306i	0.851443	−	1.47474i	0.879906	−	0.475148i	$-0.157606\pi$
$332$	59.1831	−	26.3500i	3.24810	−	1.44615i
$333$	19.2802	−	20.0612i	1.05655	−	1.09935i
$334$	10.9967	+	2.33742i	0.601711	+	0.127898i
$335$	−0.453451	+	1.01847i	−0.0247747	+	0.0556448i
$336$	3.19857	−	4.25524i	0.174496	−	0.232143i
$337$	9.54908	−	3.10269i	0.520172	−	0.169014i	−0.0371515	−	0.999310i	$-0.511828\pi$
$337$	9.54908	−	3.10269i	0.520172	−	0.169014i	0.557323	+	0.830296i	$0.311828\pi$
$338$	−10.8271	−	32.6791i	−0.588917	−	1.77751i
$339$	−22.3212	+	19.4505i	−1.21232	+	1.05641i
$340$	4.47861	−	2.58573i	0.242887	−	0.140231i
$341$	−28.0288	+	1.14493i	−1.51785	+	0.0620012i
$342$	34.3081	+	50.6020i	1.85517	+	2.73624i
$343$	−2.26565	+	3.11840i	−0.122334	+	0.168378i
$344$	−20.7904	+	18.7198i	−1.12094	+	1.00930i
$345$	−7.62623	−	3.54506i	−0.410582	−	0.190859i
$346$	−21.6535	+	15.7322i	−1.16410	+	0.845766i
$347$	−1.98197	−	18.8572i	−0.106398	−	1.01231i	−0.909284	−	0.416175i	$-0.863370\pi$
$347$	−1.98197	−	18.8572i	−0.106398	−	1.01231i	0.802887	−	0.596132i	$-0.203296\pi$
$348$	52.9495	−	37.1702i	2.83839	−	1.99253i
$349$	−0.759354	−	3.57248i	−0.0406473	−	0.191231i	0.953139	−	0.302531i	$-0.0978317\pi$
$349$	−0.759354	−	3.57248i	−0.0406473	−	0.191231i	−0.993787	+	0.111301i	$0.964498\pi$
$350$	1.52964	−	2.10537i	0.0817626	−	0.112537i
$351$	−3.05065	−	18.4850i	−0.162832	−	0.986654i
$352$	−6.46632	−	44.1141i	−0.344656	−	2.35129i
$353$	−26.8720	+	15.5146i	−1.43025	+	0.825758i	−0.997140	−	0.0755808i	$-0.975919\pi$
$353$	−26.8720	+	15.5146i	−1.43025	+	0.825758i	−0.433115	+	0.901339i	$0.642586\pi$
$354$	10.3876	+	3.56283i	0.552095	+	0.189362i
$355$	0.545363	+	0.605687i	0.0289449	+	0.0321465i
$356$	−45.3843	+	14.7463i	−2.40536	+	0.781550i
$357$	−0.167946	−	0.0204171i	−0.00888865	−	0.00108059i
$358$	−0.502304	+	0.0527942i	−0.0265476	+	0.00279026i
$359$	9.25776	+	28.4925i	0.488606	+	1.50377i	0.826689	+	0.562659i	$0.190221\pi$
$359$	9.25776	+	28.4925i	0.488606	+	1.50377i	−0.338083	+	0.941116i	$0.609779\pi$
$360$	−67.2262	+	19.4512i	−3.54313	+	1.02517i
$361$	4.20411	−	39.9994i	0.221269	−	2.10523i
$362$	14.7994	+	25.6333i	0.777839	+	1.34726i
$363$	−4.69086	+	18.4661i	−0.246206	+	0.969217i
$364$	4.89715	+	1.02615i	0.256680	+	0.0537850i
$365$	6.21159	+	4.51299i	0.325130	+	0.236221i
$366$	−0.189014	+	11.6265i	−0.00987993	+	0.607729i
$367$	−10.4110	+	11.5626i	−0.543452	+	0.603565i	−0.950837	−	0.309692i	$-0.899774\pi$
$367$	−10.4110	+	11.5626i	−0.543452	+	0.603565i	0.407385	+	0.913257i	$0.366441\pi$
$368$	−18.3342	+	1.92700i	−0.955737	+	0.100452i
$369$	−4.76070	+	0.851202i	−0.247832	+	0.0443118i
$370$	14.9313	−	70.2462i	0.776241	−	3.65193i
$371$	1.44318	+	1.60281i	0.0749262	+	0.0832140i
$372$	48.2440	+	55.3643i	2.50134	+	2.87051i
$373$	27.1281	+	15.6624i	1.40464	+	0.810969i	0.994864	−	0.101217i	$-0.0322736\pi$
$373$	27.1281	+	15.6624i	1.40464	+	0.810969i	0.409776	+	0.912186i	$0.365607\pi$
$374$	−2.43061	+	1.92228i	−0.125684	+	0.0993985i
$375$	7.02134	−	2.15584i	0.362581	−	0.111327i
$376$	−12.0202	+	16.5444i	−0.619895	+	0.853212i
$377$	23.3052	+	13.3657i	1.20028	+	0.688369i
$378$	3.56125	+	1.35238i	0.183171	+	0.0695588i
$379$	−9.04897	−	4.02886i	−0.464814	−	0.206949i	0.160947	−	0.986963i	$-0.448545\pi$
$379$	−9.04897	−	4.02886i	−0.464814	−	0.206949i	−0.625762	+	0.780014i	$0.715212\pi$
$380$	103.041	+	45.8770i	5.28591	+	2.35344i
$381$	3.67794	−	7.91209i	0.188426	−	0.405349i
$382$	−20.6299	−	6.70307i	−1.05552	−	0.342959i
$383$	0.487269	+	1.09442i	0.0248983	+	0.0559224i	0.925567	−	0.378585i	$-0.123589\pi$
$383$	0.487269	+	1.09442i	0.0248983	+	0.0559224i	−0.900668	+	0.434507i	$0.856923\pi$
$384$	−10.1310	+	10.8902i	−0.516994	+	0.555741i
$385$	−1.24636	+	2.37791i	−0.0635204	+	0.121190i
$386$	−20.2815	−	11.7095i	−1.03230	−	0.596000i
$387$	−8.93471	−	5.55332i	−0.454177	−	0.282291i
$388$	25.5039	−	5.42101i	1.29476	−	0.275210i
$389$	29.5540	−	9.60266i	1.49844	−	0.486874i	0.558881	−	0.829248i	$-0.311231\pi$
$389$	29.5540	−	9.60266i	1.49844	−	0.486874i	0.939564	+	0.342374i	$0.111231\pi$
$390$	−31.8733	−	36.3649i	−1.61397	−	1.84141i
$391$	0.344380	+	0.473998i	0.0174160	+	0.0239711i
$392$	36.9596	−	41.0478i	1.86674	−	2.07322i
$393$	−31.4261	−	0.510898i	−1.58524	−	0.0257714i
$394$	−22.0460	+	9.81552i	−1.11066	+	0.494499i
$395$	−21.2683			−1.07013
$396$	45.3935	−	20.6644i	2.28111	−	1.03843i
$397$	−16.2125	+	28.0808i	−0.813681	+	1.40934i	0.0965907	+	0.995324i	$0.469206\pi$
$397$	−16.2125	+	28.0808i	−0.813681	+	1.40934i	−0.910271	+	0.414012i	$0.864127\pi$
$398$	−30.1010	−	21.8697i	−1.50883	−	1.09623i
$399$	−1.79280	−	3.22519i	−0.0897525	−	0.161461i
$400$	−26.3694	+	29.2862i	−1.31847	+	1.46431i
$401$	8.31090	−	18.6666i	0.415027	−	0.932165i	−0.578192	−	0.815901i	$-0.696241\pi$
$401$	8.31090	−	18.6666i	0.415027	−	0.932165i	0.993218	−	0.116264i	$-0.0370919\pi$
$402$	−1.60897	+	0.685244i	−0.0802483	+	0.0341768i
$403$	−12.3233	+	27.8951i	−0.613868	+	1.38956i
$404$	−2.13369	+	6.56681i	−0.106155	+	0.326711i
$405$	−14.0521	−	22.2501i	−0.698253	−	1.10562i
$406$	−4.73079	+	2.73132i	−0.234785	+	0.135553i
$407$	−1.96409	+	30.6979i	−0.0973565	+	1.52164i
$408$	4.75191	+	1.09107i	0.235254	+	0.0540161i
$409$	−8.00403	−	17.9774i	−0.395774	−	0.888923i	−0.996022	−	0.0891088i	$-0.971598\pi$
$409$	−8.00403	−	17.9774i	−0.395774	−	0.888923i	0.600248	−	0.799814i	$-0.295069\pi$
$410$	−9.27631	+	8.35243i	−0.458124	+	0.412497i
$411$	0.893484	−	0.0792480i	0.0440723	−	0.00390902i
$412$	−3.30882	−	31.4813i	−0.163014	−	1.55097i
$413$	−0.605514	−	0.269592i	−0.0297954	−	0.0132658i
$414$	−4.97119	−	12.2198i	−0.244321	−	0.600569i
$415$	35.9400	+	11.6776i	1.76423	+	0.573232i
$416$	−46.1403	−	14.8447i	−2.26221	−	0.727823i
$417$	−6.59599	+	28.7273i	−0.323007	+	1.40678i
$418$	−65.0793	−	18.2450i	−3.18313	−	0.892393i
$419$	29.0750	−	16.7865i	1.42041	−	0.820072i	0.424073	−	0.905628i	$-0.360600\pi$
$419$	29.0750	−	16.7865i	1.42041	−	0.820072i	0.996333	+	0.0855563i	$0.0272668\pi$
$420$	6.89739	−	1.34929i	0.336558	−	0.0658387i
$421$	−5.01299	+	15.4284i	−0.244318	+	0.751935i	0.751429	+	0.659814i	$0.229365\pi$
$421$	−5.01299	+	15.4284i	−0.244318	+	0.751935i	−0.995748	+	0.0921212i	$0.970635\pi$
$422$	4.28469	−	20.1579i	0.208576	−	0.981271i
$423$	−7.23233	−	2.61275i	−0.351648	−	0.127036i
$424$	−36.5340	−	50.2847i	−1.77425	−	2.44204i
$425$	1.22508	+	0.260399i	0.0594252	+	0.0126312i
$426$	−0.0207820	+	1.27833i	−0.00100689	+	0.0619355i
$427$	0.0733618	−	0.697991i	0.00355023	−	0.0337782i
$428$	−74.7096			−3.61122
$429$	15.7669	+	13.4314i	0.761235	+	0.648476i
$430$	−27.1525			−1.30941
$431$	−0.130639	+	1.24295i	−0.00629266	+	0.0598707i	−0.997218	−	0.0745458i	$-0.976249\pi$
$431$	−0.130639	+	1.24295i	−0.00629266	+	0.0598707i	0.990925	+	0.134416i	$0.0429160\pi$
$432$	−51.4929	−	26.0043i	−2.47745	−	1.25113i
$433$	0.760060	+	0.161556i	0.0365262	+	0.00776387i	0.226139	−	0.974095i	$-0.427390\pi$
$433$	0.760060	+	0.161556i	0.0365262	+	0.00776387i	−0.189612	+	0.981859i	$0.560723\pi$
$434$	−3.64471	−	5.01651i	−0.174951	−	0.240800i
$435$	37.4611	+	4.55411i	1.79612	+	0.218353i
$436$	−12.9049	+	60.7128i	−0.618033	+	2.90761i
$437$	−3.94885	+	12.1533i	−0.188899	+	0.581371i
$438$	2.31227	+	11.8200i	0.110485	+	0.564781i
$439$	14.5676	−	8.41058i	0.695272	−	0.401415i	−0.110312	−	0.993897i	$-0.535185\pi$
$439$	14.5676	−	8.41058i	0.695272	−	0.401415i	0.805584	+	0.592482i	$0.201852\pi$
$440$	42.8843	−	64.3975i	2.04443	−	3.07003i
$441$	18.6898	+	9.06026i	0.889989	+	0.431441i
$442$	0.709930	+	3.29317i	0.0337679	+	0.156640i
$443$	0.887591	+	0.288396i	0.0421707	+	0.0137021i	0.330026	−	0.943972i	$-0.392942\pi$
$443$	0.887591	+	0.288396i	0.0421707	+	0.0137021i	−0.287856	+	0.957674i	$0.592942\pi$
$444$	65.9070	−	46.2663i	3.12781	−	2.19570i
$445$	−25.4293	−	11.3218i	−1.20546	−	0.536707i
$446$	2.43821	+	23.1980i	0.115453	+	1.09846i
$447$	2.69282	+	30.3603i	0.127366	+	1.43599i
$448$	2.75591	−	2.48144i	0.130205	−	0.117237i
$449$	−13.5135	−	30.3518i	−0.637740	−	1.43239i	−0.885996	−	0.463694i	$-0.846524\pi$
$449$	−13.5135	−	30.3518i	−0.637740	−	1.43239i	0.248255	−	0.968695i	$-0.420143\pi$
$450$	−25.3762	−	12.3016i	−1.19624	−	0.579905i
$451$	3.41244	−	4.11602i	0.160685	−	0.193816i
$452$	−74.2048	+	42.8422i	−3.49030	+	2.01513i
$453$	−4.08447	−	1.40093i	−0.191905	−	0.0658213i
$454$	−11.5111	+	35.4274i	−0.540241	+	1.66269i
$455$	1.72234	+	2.35626i	0.0807444	+	0.110463i
$456$	41.6672	+	97.8358i	1.95125	+	4.58158i
$457$	2.18462	−	4.90674i	0.102192	−	0.229528i	−0.855212	−	0.518278i	$-0.826573\pi$
$457$	2.18462	−	4.90674i	0.102192	−	0.229528i	0.957404	+	0.288751i	$0.0932398\pi$
$458$	17.9288	−	19.9119i	0.837757	−	0.930424i
$459$	0.102528	+	1.83048i	0.00478558	+	0.0854397i
$460$	−19.6907	−	14.3061i	−0.918083	−	0.667026i
$461$	13.5980	−	23.5525i	0.633323	−	1.09695i	−0.353545	−	0.935417i	$-0.615024\pi$
$461$	13.5980	−	23.5525i	0.633323	−	1.09695i	0.986868	−	0.161530i	$-0.0516428\pi$
$462$	−3.97213	+	1.39941i	−0.184800	+	0.0651066i
$463$	12.1152			0.563040			0.281520	−	0.959555i	$-0.409161\pi$
$463$	12.1152			0.563040			0.281520	+	0.959555i	$0.409161\pi$
$464$	75.5705	−	33.6462i	3.50827	−	1.56198i
$465$	−0.696295	+	42.8302i	−0.0322899	+	1.98620i
$466$	26.9310	−	29.9099i	1.24756	−	1.38555i
$467$	−18.4503	−	25.3946i	−0.853776	−	1.17512i	−0.983018	−	0.183509i	$-0.941254\pi$
$467$	−18.4503	−	25.3946i	−0.853776	−	1.17512i	0.129242	−	0.991613i	$-0.458746\pi$
$468$	1.60600	−	54.1969i	0.0742373	−	2.50525i
$469$	0.100387	−	0.0326177i	0.00463544	−	0.00150615i
$470$	−19.4141	+	4.12660i	−0.895506	+	0.190346i
$471$	3.55061	−	10.3520i	0.163604	−	0.476994i
$472$	16.5422	+	9.55065i	0.761417	+	0.439604i
$473$	11.5072	−	1.68675i	0.529103	−	0.0775568i
$474$	−24.4271	−	22.7240i	−1.12197	−	1.04375i
$475$	11.1107	+	24.9551i	0.509796	+	1.14502i
$476$	−0.465665	−	0.151304i	−0.0213437	−	0.00693499i
$477$	14.3452	−	18.4520i	0.656823	−	0.844858i
$478$	−36.7757	−	16.3736i	−1.68208	−	0.748911i
$479$	7.77529	+	3.46178i	0.355262	+	0.158173i	0.576605	−	0.817023i	$-0.304377\pi$
$479$	7.77529	+	3.46178i	0.355262	+	0.158173i	−0.221343	+	0.975196i	$0.571044\pi$
$480$	−67.8160	+	6.01498i	−3.09536	+	0.274545i
$481$	29.0084	+	16.6365i	1.32267	+	0.758559i
$482$	9.53365	−	13.1219i	0.434246	−	0.597688i
$483$	0.233711	+	0.761173i	0.0106342	+	0.0346346i
$484$	−23.5833	+	49.8419i	−1.07197	+	2.26554i
$485$	13.1715	+	7.60459i	0.598089	+	0.345307i
$486$	7.63392	−	40.5686i	0.346282	−	1.84023i
$487$	8.63026	+	9.58487i	0.391074	+	0.434332i	0.906243	−	0.422757i	$-0.138938\pi$
$487$	8.63026	+	9.58487i	0.391074	+	0.434332i	−0.515169	+	0.857089i	$0.672271\pi$
$488$	−4.20516	+	19.7837i	−0.190359	+	0.895568i
$489$	19.2852	−	8.21337i	0.872109	−	0.371422i
$490$	53.3151	−	5.60364i	2.40853	−	0.253147i
$491$	−8.48082	+	9.41890i	−0.382734	+	0.425069i	−0.903472	−	0.428648i	$-0.858990\pi$
$491$	−8.48082	+	9.41890i	−0.382734	+	0.425069i	0.520738	+	0.853717i	$0.325657\pi$
$492$	−13.9945	−	0.227511i	−0.630922	−	0.0102570i
$493$	−2.12692	−	1.54530i	−0.0957917	−	0.0695968i
$494$	−49.0074	+	54.7453i	−2.20495	+	2.46311i
$495$	27.7432	+	8.75999i	1.24697	+	0.393732i
$496$	46.9497	+	81.3193i	2.10811	+	3.65135i
$497$	0.00806610	−	0.0767438i	0.000361814	−	0.00344243i
$498$	28.8010	+	51.8119i	1.29060	+	2.32175i
$499$	−6.44531	−	19.8366i	−0.288532	−	0.888009i	−0.985318	−	0.170730i	$-0.945387\pi$
$499$	−6.44531	−	19.8366i	−0.288532	−	0.888009i	0.696786	−	0.717279i	$-0.254613\pi$
$500$	21.1402	−	2.22192i	0.945418	−	0.0993675i
$501$	−0.887385	+	7.29943i	−0.0396454	+	0.326115i
$502$	−55.1095	+	17.9062i	−2.45966	+	0.799192i
$503$	−3.81077	−	4.23229i	−0.169914	−	0.188708i	0.652174	−	0.758070i	$-0.273857\pi$
$503$	−3.81077	−	4.23229i	−0.169914	−	0.188708i	−0.822087	+	0.569361i	$0.807191\pi$
$504$	5.62756	+	3.49777i	0.250671	+	0.155803i
$505$	−3.48805	+	2.01383i	−0.155216	+	0.0896142i
$506$	12.9177	+	6.77071i	0.574263	+	0.300995i
$507$	20.6648	−	8.94226i	0.917758	−	0.397140i
$508$	14.8424	−	20.4288i	0.658524	−	0.906380i
$509$	1.05142	+	4.94654i	0.0466034	+	0.219252i	0.995287	−	0.0969760i	$-0.0309170\pi$
$509$	1.05142	+	4.94654i	0.0466034	+	0.219252i	−0.948683	+	0.316228i	$0.897584\pi$
$510$	2.71880	+	3.87297i	0.120391	+	0.171498i
$511$	−0.0759861	−	0.722960i	−0.00336143	−	0.0319819i
$512$	22.5721	−	16.3996i	0.997553	−	0.724765i
$513$	−30.9849	+	25.2759i	−1.36801	+	1.11596i
$514$	−28.5728	+	25.7271i	−1.26029	+	1.13477i
$515$	10.8533	−	14.9383i	0.478253	−	0.658259i
$516$	−22.2913	−	20.7371i	−0.981319	−	0.912900i
$517$	7.97135	−	2.95488i	0.350580	−	0.129956i
$518$	−5.88848	+	3.39972i	−0.258725	+	0.149375i
$519$	−11.5008	−	13.1982i	−0.504829	−	0.579337i
$520$	−42.2651	−	72.7196i	−1.85345	−	3.18897i
$521$	−7.43636	+	2.41622i	−0.325793	+	0.105856i	−0.467347	−	0.884074i	$-0.654790\pi$
$521$	−7.43636	+	2.41622i	−0.325793	+	0.105856i	0.141554	+	0.989931i	$0.454790\pi$
$522$	38.1590	+	45.2556i	1.67018	+	1.98078i
$523$	−5.01584	+	11.2658i	−0.219328	+	0.492618i	−0.989378	−	0.145365i	$-0.953564\pi$
$523$	−5.01584	+	11.2658i	−0.219328	+	0.492618i	0.770051	+	0.637983i	$0.220231\pi$
$524$	−88.9741	−	18.9120i	−3.88685	−	0.826176i
$525$	1.46004	+	0.874904i	0.0637215	+	0.0381839i
$526$	−27.7005	+	12.3330i	−1.20780	+	0.537746i
$527$	1.49212	−	2.58443i	0.0649979	−	0.112580i
$528$	62.0367	−	14.7881i	2.69980	−	0.643569i
$529$	−10.1213	+	17.5306i	−0.440055	+	0.762198i
$530$	6.30569	−	59.9946i	0.273902	−	2.60600i
$531$	−1.72094	+	6.97344i	−0.0746826	+	0.302621i
$532$	−3.30003	−	10.1565i	−0.143075	−	0.440338i
$533$	−2.37943	−	5.30303i	−0.103065	−	0.229700i
$534$	−17.1093	−	40.1731i	−0.740391	−	1.73846i
$535$	−32.3858	−	29.1603i	−1.40016	−	1.26071i
$536$	−2.97539	+	0.632439i	−0.128517	+	0.0273172i
$537$	−0.0634214	−	0.324202i	−0.00273684	−	0.0139903i
$538$		−	15.5009i		−	0.668292i
$539$	−22.2468	+	5.68683i	−0.958239	+	0.244949i
$540$	−27.5488	−	71.0035i	−1.18551	−	3.05550i
$541$	−22.7725	+	31.3437i	−0.979068	+	1.34757i	−0.0417377	+	0.999129i	$0.513289\pi$
$541$	−22.7725	+	31.3437i	−0.979068	+	1.34757i	−0.937330	+	0.348443i	$0.886711\pi$
$542$	31.5997	−	28.4525i	1.35732	−	1.22214i
$543$	−15.8450	+	11.1231i	−0.679973	+	0.477337i
$544$	4.33303	+	1.92919i	0.185777	+	0.0827133i
$545$	−29.2912	+	21.2813i	−1.25470	+	0.911592i
$546$	−0.539389	+	4.54643i	−0.0230837	+	0.194569i
$547$	−34.7029	−	11.2757i	−1.48379	−	0.482113i	−0.548548	−	0.836119i	$-0.684819\pi$
$547$	−34.7029	−	11.2757i	−1.48379	−	0.482113i	−0.935243	+	0.354006i	$0.884819\pi$
$548$	2.58175	+	0.271353i	0.110287	+	0.0115916i
$549$	−7.58565	+	0.548702i	−0.323748	+	0.0234180i
$550$	30.2058	−	7.72134i	1.28798	−	0.329239i
$551$		−	57.3406i		−	2.44279i
$552$	−4.40535	−	22.5196i	−0.187504	−	0.958496i
$553$	1.34741	+	1.49645i	0.0572975	+	0.0636354i
$554$	23.3474	−	7.58603i	0.991936	−	0.322300i
$555$	46.6284	+	5.66857i	1.97927	+	0.240618i
$556$	−34.6957	+	77.9279i	−1.47143	+	3.30488i
$557$	−4.21890	+	4.68556i	−0.178760	+	0.198534i	−0.825865	−	0.563867i	$-0.809313\pi$
$557$	−4.21890	+	4.68556i	−0.178760	+	0.198534i	0.647105	+	0.762401i	$0.275980\pi$
$558$	−46.5614	+	48.4474i	−1.97110	+	2.05094i
$559$	3.87228	−	12.0358i	0.163780	−	0.509059i
$560$	8.98670			0.379757
$561$	−1.39282	−	1.47247i	−0.0588050	−	0.0621677i
$562$	−29.4080	−	50.9362i	−1.24050	−	2.14862i
$563$	−0.504007	+	0.224398i	−0.0212414	+	0.00945727i	−0.417330	−	0.908755i	$-0.637034\pi$
$563$	−0.504007	+	0.224398i	−0.0212414	+	0.00945727i	0.396088	+	0.918212i	$0.370367\pi$
$564$	−19.0899	−	11.4393i	−0.803831	−	0.481681i
$565$	−48.8889	−	10.3917i	−2.05677	−	0.437180i
$566$	57.3159	−	6.02415i	2.40917	−	0.253214i
$567$	−0.675289	+	2.39831i	−0.0283595	+	0.100720i
$568$	−0.462356	+	2.17521i	−0.0194000	+	0.0912699i
$569$	−14.3414	+	3.04837i	−0.601225	+	0.127794i	−0.498462	−	0.866912i	$-0.666102\pi$
$569$	−14.3414	+	3.04837i	−0.601225	+	0.127794i	−0.102763	+	0.994706i	$0.532768\pi$
$570$	−33.4843	+	97.6252i	−1.40250	+	4.08907i
$571$		−	22.1995i		−	0.929019i	−0.885568	−	0.464510i	$-0.846231\pi$
$571$		−	22.1995i		−	0.929019i	0.885568	−	0.464510i	$-0.153769\pi$
$572$	37.3193	+	46.9091i	1.56040	+	1.96137i
$573$	3.17496	−	13.8278i	0.132636	−	0.577664i
$574$	1.17536	+	0.123535i	0.0490585	+	0.00515626i
$575$	−1.22555	−	5.76575i	−0.0511089	−	0.240448i
$576$	−31.7268	−	24.6655i	−1.32195	−	1.02773i
$577$	14.1890	−	10.3089i	0.590698	−	0.429167i	−0.251867	−	0.967762i	$-0.581045\pi$
$577$	14.1890	−	10.3089i	0.590698	−	0.429167i	0.842565	+	0.538595i	$0.181045\pi$
$578$	4.67126	+	44.4441i	0.194299	+	1.84863i
$579$	6.45683	−	13.8901i	0.268337	−	0.577254i
$580$	103.869	+	33.7489i	4.31291	+	1.40135i
$581$	−1.45526	−	3.26856i	−0.0603742	−	0.135603i
$582$	7.00271	+	22.8071i	0.290271	+	0.945384i
$583$	1.05460	+	25.8174i	0.0436769	+	1.06925i
$584$			20.9492i			0.866885i
$585$	21.8500	−	22.8669i	0.903388	−	0.945430i
$586$	−5.22865	+	16.0921i	−0.215994	+	0.664760i
$587$	−23.2596	−	20.9430i	−0.960025	−	0.864411i	0.0308047	−	0.999525i	$-0.490193\pi$
$587$	−23.2596	−	20.9430i	−0.960025	−	0.864411i	−0.990830	+	0.135115i	$0.956860\pi$
$588$	48.0496	+	36.1178i	1.98153	+	1.48947i
$589$	64.7318	−	6.80359i	2.66723	−	0.280337i
$590$	5.72882	+	17.6315i	0.235852	+	0.725877i
$591$	−7.66878	−	13.7959i	−0.315451	−	0.567486i
$592$	94.0638	−	41.8799i	3.86600	−	1.72125i
$593$	32.8267			1.34803			0.674015	−	0.738718i	$-0.264568\pi$
$593$	32.8267			1.34803			0.674015	+	0.738718i	$0.264568\pi$
$594$	22.5041	+	39.7031i	0.923355	+	1.62904i
$595$	−0.142804	−	0.247344i	−0.00585441	−	0.0101401i
$596$	−9.22048	+	87.7270i	−0.377686	+	3.59344i
$597$	12.5088	−	20.8746i	0.511949	−	0.854342i
$598$	12.8001	−	9.35640i	0.523435	−	0.382612i
$599$	17.1493	+	23.6040i	0.700703	+	0.964435i	0.999947	+	0.0102587i	$0.00326549\pi$
$599$	17.1493	+	23.6040i	0.700703	+	0.964435i	−0.299244	+	0.954177i	$0.596735\pi$
$600$	−39.2099	−	29.4733i	−1.60074	−	1.20324i
$601$	16.7387	+	15.0716i	0.682787	+	0.614784i	0.935738	−	0.352695i	$-0.114735\pi$
$601$	16.7387	+	15.0716i	0.682787	+	0.614784i	−0.252951	+	0.967479i	$0.581401\pi$
$602$	1.72018	+	1.91046i	0.0701095	+	0.0778645i
$603$	−0.539413	−	1.00865i	−0.0219666	−	0.0410755i
$604$	−10.8225	−	6.24839i	−0.440363	−	0.254244i
$605$	−29.6772	+	12.4010i	−1.20655	+	0.504172i
$606$	−6.15777	−	1.41387i	−0.250142	−	0.0574344i
$607$	−9.46554	−	21.2600i	−0.384194	−	0.862915i	−0.997336	−	0.0729419i	$-0.976761\pi$
$607$	−9.46554	−	21.2600i	−0.384194	−	0.862915i	0.613142	−	0.789973i	$-0.289905\pi$
$608$	21.5084	+	101.189i	0.872283	+	4.10377i
$609$	−2.05283	−	2.92429i	−0.0831850	−	0.118498i
$610$	−15.8811	+	11.5383i	−0.643008	+	0.467173i
$611$	0.939509	−	9.19412i	0.0380085	−	0.371954i
$612$	−0.725849	+	5.25600i	−0.0293407	+	0.212461i
$613$	−3.90897	−	18.3903i	−0.157882	−	0.742776i	−0.983841	−	0.179046i	$-0.942699\pi$
$613$	−3.90897	−	18.3903i	−0.157882	−	0.742776i	0.825959	−	0.563730i	$-0.190634\pi$
$614$	−63.4855	−	6.67260i	−2.56207	−	0.269284i
$615$	−5.97767	−	5.56090i	−0.241043	−	0.224237i
$616$	−7.24786	+	1.06240i	−0.292025	+	0.0428055i
$617$	38.1324	+	22.0158i	1.53515	+	0.886321i	0.999112	+	0.0421291i	$0.0134141\pi$
$617$	38.1324	+	22.0158i	1.53515	+	0.886321i	0.536041	+	0.844192i	$0.319919\pi$
$618$	28.4259	−	5.56078i	1.14346	−	0.223687i
$619$	−3.05870	+	9.41372i	−0.122940	+	0.378369i	−0.993520	−	0.113657i	$-0.963744\pi$
$619$	−3.05870	+	9.41372i	−0.122940	+	0.378369i	0.870580	+	0.492026i	$0.163744\pi$
$620$	−25.7749	+	121.262i	−1.03515	+	4.86998i
$621$	7.67395	−	3.94487i	0.307945	−	0.158302i
$622$	4.17111	−	9.36847i	0.167246	−	0.375641i
$623$	0.814405	+	2.50648i	0.0326284	+	0.100420i
$624$	15.3199	−	67.6168i	0.613288	−	2.70684i
$625$	24.3903	+	17.7206i	0.975611	+	0.708823i
$626$	42.8074	+	74.1445i	1.71093	+	2.96341i
$627$	8.12605	−	43.4536i	0.324523	−	1.73537i
$628$	15.8364	−	27.4294i	0.631941	−	1.09455i
$629$	−2.64741	−	1.92346i	−0.105559	−	0.0766932i
$630$	1.78740	+	6.17751i	0.0712115	+	0.246118i
$631$	14.8387	+	3.15407i	0.590721	+	0.125562i	0.493567	−	0.869708i	$-0.335693\pi$
$631$	14.8387	+	3.15407i	0.590721	+	0.125562i	0.0971538	+	0.995269i	$0.469026\pi$
$632$	−34.1095	−	46.9476i	−1.35680	−	1.86748i
$633$	13.3805	+	1.62666i	0.531828	+	0.0646538i
$634$	20.2543	+	18.2371i	0.804402	+	0.724287i
$635$	14.4077	−	3.06244i	0.571751	−	0.121529i
$636$	50.9963	−	44.4377i	2.02214	−	1.76207i
$637$	−5.11948	+	24.4319i	−0.202841	+	0.968028i
$638$	−64.5157	−	10.9825i	−2.55420	−	0.434802i
$639$	−0.834039	+	0.0603295i	−0.0329941	+	0.00238660i
$640$	−24.9722	−	2.62468i	−0.987111	−	0.103750i
$641$	19.0843	−	17.1836i	0.753784	−	0.678710i	−0.199800	−	0.979837i	$-0.564029\pi$
$641$	19.0843	−	17.1836i	0.753784	−	0.678710i	0.953584	+	0.301126i	$0.0973626\pi$
$642$	−6.03960	−	68.0935i	−0.238364	−	2.68744i
$643$	−0.888382	−	8.45239i	−0.0350343	−	0.333330i	−0.997975	−	0.0636146i	$-0.979737\pi$
$643$	−0.888382	−	8.45239i	−0.0350343	−	0.333330i	0.962940	−	0.269715i	$-0.0869295\pi$
$644$	0.240875	+	2.29177i	0.00949181	+	0.0903086i
$645$	−1.56902	−	17.6899i	−0.0617800	−	0.696540i
$646$	5.34335	−	4.81118i	0.210231	−	0.189293i
$647$	6.03081	+	0.633864i	0.237096	+	0.0249198i	0.222331	−	0.974971i	$-0.428633\pi$
$647$	6.03081	+	0.633864i	0.237096	+	0.0249198i	0.0147646	+	0.999891i	$0.495300\pi$
$648$	26.5786	−	66.7025i	1.04411	−	2.62032i
$649$	−3.52317	−	7.11634i	−0.138296	−	0.279341i
$650$	6.95101	−	33.1726i	0.272641	−	1.30114i
$651$	3.05766	−	2.66442i	0.119839	−	0.104427i
$652$	59.3384	−	12.6128i	2.32387	−	0.493954i
$653$	10.0843	+	9.07997i	0.394630	+	0.355327i	0.842429	−	0.538808i	$-0.181125\pi$
$653$	10.0843	+	9.07997i	0.394630	+	0.355327i	−0.447798	+	0.894135i	$0.647792\pi$
$654$	−56.3795	−	6.85401i	−2.20461	−	0.268013i
$655$	−31.1876	−	42.9261i	−1.21860	−	1.67726i
$656$	−17.5057	−	3.72096i	−0.683484	−	0.145279i
$657$	−7.56715	+	2.18947i	−0.295223	+	0.0854195i
$658$	1.52029	+	1.10455i	0.0592669	+	0.0430599i
$659$	10.8839	−	18.8515i	0.423978	−	0.734351i	−0.572347	−	0.820012i	$-0.693967\pi$
$659$	10.8839	−	18.8515i	0.423978	−	0.734351i	0.996324	+	0.0856609i	$0.0273002\pi$
$660$	73.9305	+	40.2952i	2.87774	+	1.56849i
$661$	19.8817	+	34.4361i	0.773309	+	1.33941i	0.935740	+	0.352690i	$0.114733\pi$
$661$	19.8817	+	34.4361i	0.773309	+	1.33941i	−0.162432	+	0.986720i	$0.551934\pi$
$662$	66.3743	+	48.2238i	2.57971	+	1.87427i
$663$	−2.10449	+	0.652819i	−0.0817316	+	0.0253534i
$664$	31.8623	+	98.0621i	1.23650	+	3.80555i
$665$	2.53369	−	5.69076i	0.0982523	−	0.220678i
$666$	47.4971	+	56.3303i	1.84048	+	2.18276i
$667$	−2.57255	+	12.1029i	−0.0996094	+	0.468625i
$668$	−6.57610	+	20.2392i	−0.254437	+	0.783077i
$669$	−14.9727	+	2.92901i	−0.578877	+	0.113242i
$670$	−2.55676	−	1.47615i	−0.0987763	−	0.0570285i
$671$	6.01365	−	5.87650i	0.232154	−	0.226860i
$672$	4.71955	+	4.39049i	0.182060	+	0.169367i
$673$	−2.99764	−	0.315064i	−0.115550	−	0.0121448i	0.0465767	−	0.998915i	$-0.485169\pi$
$673$	−2.99764	−	0.315064i	−0.115550	−	0.0121448i	−0.162127	+	0.986770i	$0.551835\pi$
$674$	5.52811	+	26.0077i	0.212935	+	1.00178i
$675$	6.54818	−	17.2435i	0.252040	−	0.663703i
$676$	63.6618	−	13.9165i	2.44853	−	0.535248i
$677$	−17.1304	+	12.4460i	−0.658375	+	0.478338i	−0.866114	−	0.499847i	$-0.833390\pi$
$677$	−17.1304	+	12.4460i	−0.658375	+	0.478338i	0.207738	+	0.978184i	$0.433390\pi$
$678$	−45.0470	−	64.1701i	−1.73002	−	2.46444i
$679$	−0.299391	−	1.40853i	−0.0114896	−	0.0540542i
$680$	3.34775	+	7.51917i	0.128380	+	0.288347i
$681$	−23.7462	−	5.45230i	−0.909957	−	0.208933i
$682$	4.74325	−	74.1348i	0.181628	−	2.83877i
$683$	−10.3528	−	5.97718i	−0.396138	−	0.228710i	0.288678	−	0.957426i	$-0.406784\pi$
$683$	−10.3528	−	5.97718i	−0.396138	−	0.228710i	−0.684816	+	0.728716i	$0.740118\pi$
$684$	−102.049	+	54.5741i	−3.90192	+	2.08669i
$685$	1.01325	+	1.12532i	0.0387141	+	0.0429964i
$686$	−7.58562	−	6.83012i	−0.289620	−	0.260775i
$687$	14.0087	+	10.5300i	0.534465	+	0.401746i
$688$	−22.8824	−	31.4950i	−0.872385	−	1.20073i
$689$	25.6943	+	11.3511i	0.978875	+	0.432441i
$690$	11.4474	−	19.1035i	0.435795	−	0.727257i
$691$	−1.48602	+	14.1386i	−0.0565310	+	0.537857i	0.929206	+	0.369563i	$0.120492\pi$
$691$	−1.48602	+	14.1386i	−0.0565310	+	0.537857i	−0.985737	+	0.168294i	$0.946174\pi$
$692$	−25.3320	−	43.8763i	−0.962977	−	1.66793i
$693$	−1.14125	−	2.50699i	−0.0433526	−	0.0952327i
$694$	50.2118			1.90601
$695$	−45.4566	+	20.2386i	−1.72427	+	0.767694i
$696$	50.0262	+	89.9953i	1.89624	+	3.41126i
$697$	0.175764	+	0.540946i	0.00665753	+	0.0204898i
$698$	9.61884	−	1.01098i	0.364078	−	0.0382662i
$699$	21.0426	+	15.8173i	0.795905	+	0.598264i
$700$	3.66077	+	3.29617i	0.138364	+	0.124584i
$701$	−1.99357	+	6.13559i	−0.0752962	+	0.231738i	−0.981620	−	0.190846i	$-0.938877\pi$
$701$	−1.99357	+	6.13559i	−0.0752962	+	0.231738i	0.906324	+	0.422584i	$0.138877\pi$
$702$	49.5272	−	2.91755i	1.86928	−	0.110116i
$703$		−	71.3728i		−	2.69188i
$704$	44.3911	−	1.81330i	1.67305	−	0.0683412i
$705$	−3.81034	−	12.4099i	−0.143506	−	0.467384i
$706$	−33.4215	−	75.0659i	−1.25784	−	2.82514i
$707$	0.362671	+	0.117839i	0.0136397	+	0.00443179i
$708$	−8.76249	+	18.8501i	−0.329314	+	0.708431i
$709$	4.86225	+	46.2612i	0.182606	+	1.73738i	0.575508	+	0.817796i	$0.304804\pi$
$709$	4.86225	+	46.2612i	0.182606	+	1.73738i	−0.392903	+	0.919580i	$0.628529\pi$
$710$	−1.74612	+	1.26863i	−0.0655309	+	0.0476110i
$711$	13.3932	−	17.2275i	0.502285	−	0.646080i
$712$	−15.7908	−	74.2901i	−0.591787	−	2.78414i
$713$	−13.9682	−	1.46811i	−0.523112	−	0.0549813i
$714$	0.100260	−	0.436659i	0.00375213	−	0.0163415i
$715$	−2.13184	+	34.9008i	−0.0797262	+	1.30522i
$716$		−	0.956052i		−	0.0357293i
$717$	8.54234	−	24.9056i	0.319020	−	0.930117i
$718$	−77.6016	+	16.4947i	−2.89607	+	0.615578i
$719$	5.77141	−	27.1524i	0.215237	−	1.01261i	−0.729296	−	0.684198i	$-0.760152\pi$
$719$	5.77141	−	27.1524i	0.215237	−	1.01261i	0.944534	−	0.328414i	$-0.106514\pi$
$720$	−17.1403	−	95.8644i	−0.638783	−	3.57266i
$721$	−1.73865	+	0.182739i	−0.0647506	+	0.00680556i
$722$	104.180	+	22.1442i	3.87720	+	0.824123i
$723$	9.09989	+	5.45294i	0.338429	+	0.202797i
$724$	−51.1839	+	22.7885i	−1.90223	+	0.846930i
$725$	13.2250	+	22.9064i	0.491164	+	0.850721i
$726$	−47.3346	−	17.4656i	−1.75675	−	0.648209i
$727$	−25.0755			−0.929997			−0.464999	−	0.885311i	$-0.653945\pi$
$727$	−25.0755			−0.929997			−0.464999	+	0.885311i	$0.653945\pi$
$728$	−2.43896	+	7.58077i	−0.0903940	+	0.280962i
$729$	26.8717	+	2.62925i	0.995247	+	0.0973795i
$730$	−13.6050	+	15.1099i	−0.503544	+	0.559243i
$731$	−0.503232	+	1.13028i	−0.0186127	+	0.0418048i
$732$	−21.8500	−	2.65629i	−0.807600	−	0.0981792i
$733$	−13.8081	+	4.48653i	−0.510014	+	0.165714i	−0.552709	−	0.833375i	$-0.686406\pi$
$733$	−13.8081	+	4.48653i	−0.510014	+	0.165714i	0.0426946	+	0.999088i	$0.486406\pi$
$734$	−27.5700	−	30.6196i	−1.01763	−	1.13019i
$735$	6.73163	+	34.4111i	0.248300	+	1.26927i
$736$		−	22.3230i		−	0.822835i
$737$	1.17526	+	0.466761i	0.0432911	+	0.0171934i
$738$	−0.923968	−	12.7736i	−0.0340117	−	0.470203i
$739$	−35.3980	−	3.72048i	−1.30214	−	0.136860i	−0.572053	−	0.820217i	$-0.693853\pi$
$739$	−35.3980	−	3.72048i	−1.30214	−	0.136860i	−0.730085	+	0.683356i	$0.760520\pi$
$740$	129.287	+	42.0078i	4.75268	+	1.54424i
$741$	−38.4986	−	28.7650i	−1.41428	−	1.05671i
$742$	−4.62072	+	3.35715i	−0.169632	+	0.123245i
$743$	−9.82212	−	4.37309i	−0.360339	−	0.160433i	0.218579	−	0.975819i	$-0.429858\pi$
$743$	−9.82212	−	4.37309i	−0.360339	−	0.160433i	−0.578917	+	0.815386i	$0.696525\pi$
$744$	−95.6599	+	67.1527i	−3.50706	+	2.46194i
$745$	−38.2382	+	34.4298i	−1.40094	+	1.26141i
$746$	−48.7585	+	67.1103i	−1.78518	+	2.45708i
$747$	−32.0913	+	21.7579i	−1.17416	+	0.796080i
$748$	−3.13783	−	4.95606i	−0.114730	−	0.181211i
$749$			4.12605i			0.150763i
$750$	3.73415	+	19.0885i	0.136352	+	0.697012i
$751$	−22.0674	+	4.69057i	−0.805250	+	0.171161i	−0.592107	−	0.805860i	$-0.701704\pi$
$751$	−22.0674	+	4.69057i	−0.805250	+	0.171161i	−0.213144	+	0.977021i	$0.568370\pi$
$752$	−21.1476	−	19.0414i	−0.771172	−	0.694367i
$753$	−14.8505	−	34.8693i	−0.541181	−	1.27071i
$754$	−41.6516	+	57.6779i	−1.51686	+	2.10051i
$755$	−2.25261	−	6.93281i	−0.0819807	−	0.252311i
$756$	−3.25054	+	6.43661i	−0.118221	+	0.234097i
$757$	3.01868	−	28.7208i	0.109716	−	1.04388i	−0.791697	−	0.610914i	$-0.790802\pi$
$757$	3.01868	−	28.7208i	0.109716	−	1.04388i	0.901412	−	0.432961i	$-0.142531\pi$
$758$	13.1154	−	22.7166i	0.476373	−	0.825102i
$759$	−3.66468	+	8.80718i	−0.133019	+	0.319680i
$760$	−89.7592	+	155.467i	−3.25591	+	5.63940i
$761$	−10.5017	+	4.67565i	−0.380685	+	0.169492i	−0.588153	−	0.808750i	$-0.700145\pi$
$761$	−10.5017	+	4.67565i	−0.380685	+	0.169492i	0.207467	+	0.978242i	$0.433478\pi$
$762$	19.8195	+	11.8765i	0.717987	+	0.430240i
$763$	3.35304	+	0.712711i	0.121388	+	0.0258019i
$764$	16.7007	−	37.5103i	0.604209	−	1.35708i
$765$	−2.36614	+	1.99511i	−0.0855481	+	0.0721333i
$766$	−3.01720	+	0.980348i	−0.109016	+	0.0354214i
$767$	−8.63244	+	0.0249249i	−0.311699	+	0.000899986i
$768$	4.60874	+	5.28894i	0.166304	+	0.190848i
$769$	−2.16354	+	1.24912i	−0.0780194	+	0.0450445i	−0.538502	−	0.842624i	$-0.681010\pi$
$769$	−2.16354	+	1.24912i	−0.0780194	+	0.0450445i	0.460483	+	0.887669i	$0.347676\pi$
$770$	−5.91757	−	3.94069i	−0.213254	−	0.142013i
$771$	−18.4123	−	17.1286i	−0.663104	−	0.616872i
$772$	26.0566	−	35.8639i	0.937798	−	1.29077i
$773$	−5.40612	+	4.86770i	−0.194445	+	0.175079i	−0.760602	−	0.649218i	$-0.775096\pi$
$773$	−5.40612	+	4.86770i	−0.194445	+	0.175079i	0.566157	+	0.824297i	$0.308429\pi$
$774$	17.0987	−	21.9937i	0.614598	−	0.790546i
$775$	−24.2898	+	17.6476i	−0.872516	+	0.633920i
$776$	4.33774	+	41.2708i	0.155716	+	1.48154i
$777$	−2.55519	−	3.63991i	−0.0916671	−	0.130581i
$778$	17.1092	+	80.4927i	0.613396	+	2.88580i
$779$	−7.29180	+	10.0363i	−0.261256	+	0.359588i
$780$	74.7649	−	52.8074i	2.67701	−	1.89081i
$781$	0.661198	−	0.646119i	0.0236595	−	0.0231199i
$782$	−1.34367	+	0.775768i	−0.0480495	+	0.0277414i
$783$	−27.2791	+	27.4758i	−0.974876	+	0.981907i
$784$	51.4305	+	57.1193i	1.83680	+	2.03998i
$785$	17.5710	−	5.70917i	0.627137	−	0.203769i
$786$	10.0445	−	82.6238i	0.358275	−	2.94709i
$787$	−41.2651	+	4.33714i	−1.47094	+	0.154602i	−0.805832	−	0.592144i	$-0.798282\pi$
$787$	−41.2651	+	4.33714i	−1.47094	+	0.154602i	−0.665109	+	0.746746i	$0.731615\pi$
$788$	−14.1160	−	43.4446i	−0.502862	−	1.54765i
$789$	−9.63570	−	17.3343i	−0.343040	−	0.617116i
$790$	5.88723	−	56.0132i	0.209458	−	1.99286i
$791$	2.36608	+	4.09818i	0.0841283	+	0.145714i
$792$	25.1569	+	75.2893i	0.893912	+	2.67529i
$793$	−2.84970	−	8.68507i	−0.101196	−	0.308416i
$794$	−69.4672	−	50.4709i	−2.46530	−	1.79114i
$795$	39.4511	+	0.641360i	1.39918	+	0.0227467i
$796$	47.1263	−	52.3391i	1.67035	−	1.85511i
$797$	−42.2752	+	4.44330i	−1.49746	+	0.157390i	−0.817531	−	0.575884i	$-0.804658\pi$
$797$	−42.2752	+	4.44330i	−1.49746	+	0.157390i	−0.679933	+	0.733274i	$0.737991\pi$
$798$	8.99026	−	3.82885i	0.318252	−	0.135540i
$799$	−0.188034	+	0.884632i	−0.00665218	+	0.0312960i
$800$	−31.9304	−	35.4623i	−1.12891	−	1.25378i
$801$	25.1842	−	13.4682i	0.889841	−	0.475874i
$802$	46.8606	+	27.0550i	1.65471	+	0.955345i
$803$	4.82716	−	7.24874i	0.170347	−	0.255802i
$804$	−0.971641	−	3.16453i	−0.0342671	−	0.111605i
$805$	−0.790098	+	1.08748i	−0.0278473	+	0.0383285i
$806$	−70.0546	−	40.1768i	−2.46757	−	1.41517i
$807$	10.0989	−	0.895727i	0.355498	−	0.0315311i
$808$	−10.0393	−	4.46981i	−0.353183	−	0.157247i
$809$	3.24130	+	1.44312i	0.113958	+	0.0507374i	0.462924	−	0.886398i	$-0.346800\pi$
$809$	3.24130	+	1.44312i	0.113958	+	0.0507374i	−0.348966	+	0.937136i	$0.613467\pi$
$810$	62.4886	−	30.8492i	2.19563	−	1.08393i
$811$	−31.1933	−	10.1353i	−1.09534	−	0.355899i	−0.295035	−	0.955486i	$-0.595331\pi$
$811$	−31.1933	−	10.1353i	−1.09534	−	0.355899i	−0.800309	+	0.599588i	$0.795331\pi$
$812$	−4.20577	−	9.44631i	−0.147594	−	0.331501i
$813$	20.3629	+	18.9431i	0.714157	+	0.664365i
$814$	−80.3037	−	13.6701i	−2.81464	−	0.479137i
$815$	30.6455	+	17.6932i	1.07347	+	0.619765i
$816$	−2.20113	+	6.41751i	−0.0770551	+	0.224658i
$817$	−26.3954	+	5.61052i	−0.923458	+	0.196287i
$818$	49.5615	−	16.1035i	1.73288	−	0.563046i
$819$	−2.99318	−	0.0886960i	−0.104590	−	0.00309929i
$820$	−13.8883	−	19.1156i	−0.485001	−	0.667547i
$821$	−10.7099	+	11.8945i	−0.373777	+	0.415121i	−0.900459	−	0.434941i	$-0.856769\pi$
$821$	−10.7099	+	11.8945i	−0.373777	+	0.415121i	0.526682	+	0.850062i	$0.323436\pi$
$822$	−0.0386115	+	2.37505i	−0.00134673	+	0.0828395i
$823$	−4.73633	+	2.10875i	−0.165098	+	0.0735064i	−0.487622	−	0.873055i	$-0.662135\pi$
$823$	−4.73633	+	2.10875i	−0.165098	+	0.0735064i	0.322524	+	0.946561i	$0.395469\pi$
$824$	50.3808			1.75510
$825$	6.77593	+	19.2330i	0.235908	+	0.669607i
$826$	0.877621	−	1.52008i	0.0305363	−	0.0528905i
$827$	−11.6110	−	8.43586i	−0.403753	−	0.293343i	0.367315	−	0.930097i	$-0.380277\pi$
$827$	−11.6110	−	8.43586i	−0.403753	−	0.293343i	−0.771068	+	0.636753i	$0.780277\pi$
$828$	23.9878	−	6.94061i	0.833633	−	0.241203i
$829$	−8.11705	+	9.01490i	−0.281917	+	0.313100i	−0.867427	−	0.497565i	$-0.834228\pi$
$829$	−8.11705	+	9.01490i	−0.281917	+	0.313100i	0.585510	+	0.810665i	$0.300894\pi$
$830$	−40.7032	+	91.4208i	−1.41283	+	3.17326i
$831$	6.29146	+	14.7725i	0.218248	+	0.512454i
$832$	19.5173	−	44.1794i	0.676640	−	1.53164i
$833$	0.754855	−	2.32321i	0.0261542	−	0.0804943i
$834$	−73.8317	−	25.3234i	−2.55658	−	0.876878i
$835$	−10.7503	+	6.20670i	−0.372030	+	0.214792i
$836$	47.2237	−	118.904i	1.63327	−	4.11239i
$837$	−34.2542	−	27.5353i	−1.18400	−	0.951760i
$838$	36.1614	+	81.2198i	1.24917	+	2.80569i
$839$	−2.87321	+	2.58705i	−0.0991943	+	0.0893149i	−0.717236	−	0.696830i	$-0.754593\pi$
$839$	−2.87321	+	2.58705i	−0.0991943	+	0.0893149i	0.618042	+	0.786145i	$0.287926\pi$
$840$	0.988251	+	11.1421i	0.0340979	+	0.384437i
$841$	−2.77222	−	26.3759i	−0.0955938	−	0.909514i
$842$	−39.2453	−	17.4731i	−1.35248	−	0.602164i
$843$	31.4857	−	22.1028i	1.08443	−	0.761261i
$844$	37.1002	+	12.0546i	1.27704	+	0.414936i
$845$	33.0285	+	18.8155i	1.13621	+	0.647274i
$846$	8.88302	−	18.3242i	0.305405	−	0.629998i
$847$	2.75267	+	1.30246i	0.0945827	+	0.0447530i
$848$	74.9036	−	43.2456i	2.57220	−	1.48506i
$849$	7.23677	+	36.9934i	0.248365	+	1.26961i
$850$	−1.02491	+	3.15435i	−0.0351541	+	0.108193i
$851$	−3.20209	+	15.0646i	−0.109766	+	0.516409i
$852$	−2.40240	−	0.292058i	−0.0823049	−	0.0100057i
$853$	−19.0606	−	26.2347i	−0.652624	−	0.898259i	0.346586	−	0.938018i	$-0.387341\pi$
$853$	−19.0606	−	26.2347i	−0.652624	−	0.898259i	−0.999209	+	0.0397589i	$0.987341\pi$
$854$	1.81795	+	0.386418i	0.0622091	+	0.0132229i
$855$	−65.5380	−	16.1738i	−2.24135	−	0.553133i
$856$	12.4290	−	118.254i	0.424816	−	4.04186i
$857$	−22.0083			−0.751789			−0.375895	−	0.926662i	$-0.622665\pi$
$857$	−22.0083			−0.751789			−0.375895	+	0.926662i	$0.622665\pi$
$858$	−39.7380	+	37.8066i	−1.35663	+	1.29070i
$859$	26.9936			0.921008			0.460504	−	0.887658i	$-0.347669\pi$
$859$	26.9936			0.921008			0.460504	+	0.887658i	$0.347669\pi$
$860$	5.37247	−	51.1156i	0.183200	−	1.74303i
$861$	−0.0125649	+	0.772888i	−0.000428212	+	0.0263400i
$862$	−3.23732	−	0.688114i	−0.110264	−	0.0234372i
$863$	23.5721	+	32.4443i	0.802405	+	1.10442i	0.992451	+	0.122641i	$0.0391363\pi$
$863$	23.5721	+	32.4443i	0.802405	+	1.10442i	−0.190046	+	0.981775i	$0.560864\pi$
$864$	37.8334	−	58.7191i	1.28712	−	1.99767i
$865$	6.14444	−	28.9073i	0.208917	−	0.982878i
$866$	−0.635870	+	1.95701i	−0.0216078	+	0.0665018i
$867$	−28.6855	+	5.61156i	−0.974211	+	0.190579i
$868$	10.1649	−	5.86872i	0.345020	−	0.199197i
$869$	0.984610	+	24.1041i	0.0334006	+	0.817676i
$870$	−22.3634	+	97.3986i	−0.758191	+	3.30212i
$871$	1.01895	−	0.922808i	0.0345258	−	0.0312682i
$872$	−93.9527	−	30.5271i	−3.18164	−	1.03378i
$873$	−14.4542	+	5.88020i	−0.489202	+	0.199015i
$874$	−30.9144	−	13.7640i	−1.04570	−	0.465574i
$875$	−0.122712	−	1.16753i	−0.00414843	−	0.0394697i
$876$	−22.7091	+	2.01420i	−0.767270	+	0.0680534i
$877$	−6.13925	+	5.52781i	−0.207308	+	0.186661i	−0.766244	−	0.642550i	$-0.777876\pi$
$877$	−6.13925	+	5.52781i	−0.207308	+	0.186661i	0.558936	+	0.829211i	$0.311210\pi$
$878$	18.1181	+	40.6939i	0.611456	+	1.37335i
$879$	−10.7862	−	2.47659i	−0.363810	−	0.0835333i
$880$	82.8827	+	68.7149i	2.79397	+	2.31638i
$881$	−7.35993	+	4.24926i	−0.247962	+	0.143161i	−0.618831	−	0.785524i	$-0.712393\pi$
$881$	−7.35993	+	4.24926i	−0.247962	+	0.143161i	0.370868	+	0.928685i	$0.379060\pi$
$882$	−29.0350	+	46.7143i	−0.977658	+	1.57295i
$883$	14.1312	−	43.4914i	0.475553	−	1.46360i	−0.369657	−	0.929168i	$-0.620525\pi$
$883$	14.1312	−	43.4914i	0.475553	−	1.46360i	0.845210	−	0.534434i	$-0.179475\pi$
$884$	−6.33999	+	0.684874i	−0.213237	+	0.0230348i
$885$	−11.1559	+	4.75119i	−0.375002	+	0.159709i
$886$	−1.00522	+	2.25777i	−0.0337712	+	0.0758513i
$887$	−26.0742	+	28.9584i	−0.875487	+	0.972327i	−0.999802	−	0.0199156i	$-0.993660\pi$
$887$	−26.0742	+	28.9584i	−0.875487	+	0.972327i	0.124314	+	0.992243i	$0.460327\pi$
$888$	62.2683	+	112.018i	2.08959	+	3.75909i
$889$	−1.12824	−	0.819714i	−0.0378399	−	0.0274923i
$890$	36.8567	−	63.8377i	1.23544	−	2.13984i
$891$	−24.5663	+	16.9558i	−0.823002	+	0.568039i
$892$	−44.1536			−1.47837
$893$	−18.0201	+	8.02307i	−0.603020	+	0.268482i
$894$	−80.7036	−	1.31201i	−2.69913	−	0.0438801i
$895$	0.373161	−	0.414438i	0.0124734	−	0.0138531i
$896$	1.39738	+	1.92333i	0.0466832	+	0.0642539i
$897$	6.83538	+	7.79863i	0.228227	+	0.260389i
$898$	83.6764	−	27.1881i	2.79232	−	0.907279i
$899$	61.6459	−	13.1032i	2.05601	−	0.437017i
$900$	28.1793	−	45.3376i	0.939310	−	1.51125i
$901$	−2.38053	−	1.37440i	−0.0793070	−	0.0457879i
$902$	9.89554	+	10.1265i	0.329485	+	0.337175i
$903$	−1.14527	+	1.23110i	−0.0381121	+	0.0409685i
$904$	−55.4679	−	124.583i	−1.84484	−	4.14357i
$905$	−31.0824	−	10.0993i	−1.03321	−	0.335711i
$906$	4.82015	−	10.3693i	0.160139	−	0.344496i
$907$	−21.8122	−	9.71140i	−0.724261	−	0.322462i	0.0112854	−	0.999936i	$-0.496408\pi$
$907$	−21.8122	−	9.71140i	−0.724261	−	0.322462i	−0.735546	+	0.677475i	$0.763074\pi$
$908$	−64.4158	−	28.6797i	−2.13771	−	0.951771i
$909$	0.565309	−	4.09350i	0.0187501	−	0.135773i
$910$	−6.68230	+	3.88379i	−0.221516	+	0.128747i
$911$	19.7271	−	27.1520i	0.653587	−	0.899586i	−0.345661	−	0.938360i	$-0.612345\pi$
$911$	19.7271	−	27.1520i	0.653587	−	0.899586i	0.999248	+	0.0387739i	$0.0123452\pi$
$912$	−141.457	+	43.4330i	−4.68410	+	1.43821i
$913$	11.5708	−	41.2727i	0.382938	−	1.36593i
$914$	12.3179	+	7.11174i	0.407440	+	0.235235i
$915$	−8.43495	−	9.67986i	−0.278851	−	0.320006i
$916$	33.9375	+	37.6914i	1.12133	+	1.24536i
$917$	−1.04447	+	4.91386i	−0.0344915	+	0.162270i
$918$	−4.84923	−	0.236670i	−0.160048	−	0.00781128i
$919$	10.1031	−	1.06188i	0.333272	−	0.0350283i	0.0635853	−	0.997976i	$-0.479747\pi$
$919$	10.1031	−	1.06188i	0.333272	−	0.0350283i	0.269687	+	0.962948i	$0.413080\pi$
$920$	25.9204	−	28.7875i	0.854569	−	0.949096i
$921$	0.678679	−	41.7466i	0.0223632	−	1.37560i
$922$	58.2648	+	42.3318i	1.91885	+	1.39412i
$923$	−0.313323	−	0.954920i	−0.0103132	−	0.0314316i
$924$	−1.84851	−	7.75458i	−0.0608115	−	0.255107i
$925$	16.4614	+	28.5119i	0.541246	+	0.937466i
$926$	−3.35357	+	31.9070i	−0.110205	+	1.04853i
$927$	5.26547	+	18.1982i	0.172941	+	0.597709i
$928$	30.9534	+	95.2648i	1.01610	+	3.12722i
$929$	−5.48206	+	0.576188i	−0.179861	+	0.0189041i	−0.194031	−	0.980995i	$-0.562156\pi$
$929$	−5.48206	+	0.576188i	−0.179861	+	0.0189041i	0.0141699	+	0.999900i	$0.495489\pi$
$930$	−112.607	−	13.6895i	−3.69252	−	0.448896i
$931$	50.6706	−	16.4639i	1.66066	−	0.539582i
$932$	50.9779	+	56.6167i	1.66984	+	1.85454i
$933$	6.34461	+	2.17613i	0.207713	+	0.0712433i
$934$	71.9875	−	41.5620i	2.35550	−	1.35995i
$935$	0.574210	−	3.37314i	0.0187787	−	0.110313i
$936$	85.5187	+	11.5585i	2.79527	+	0.377802i
$937$	−32.9697	+	45.3789i	−1.07707	+	1.48246i	−0.214369	+	0.976753i	$0.568770\pi$
$937$	−32.9697	+	45.3789i	−1.07707	+	1.48246i	−0.862703	+	0.505710i	$0.831230\pi$
$938$	0.0581156	+	0.273412i	0.00189754	+	0.00892723i
$939$	−45.8317	+	32.1736i	−1.49566	+	1.04995i
$940$	−3.92715	−	37.3643i	−0.128089	−	1.21869i
$941$	−46.7870	+	33.9927i	−1.52521	+	1.10813i	−0.566384	+	0.824142i	$0.691658\pi$
$941$	−46.7870	+	33.9927i	−1.52521	+	1.10813i	−0.958827	+	0.283989i	$0.908342\pi$
$942$	26.2806	+	12.2166i	0.856269	+	0.398037i
$943$	1.98935	−	1.79122i	0.0647821	−	0.0583301i
$944$	−15.6234	+	21.5037i	−0.508498	+	0.699887i
$945$	−3.92138	+	1.52146i	−0.127562	+	0.0494932i
$946$	1.25702	+	30.7728i	0.0408691	+	1.00051i
$947$	39.8020	−	22.9797i	1.29339	−	0.746740i	0.314137	−	0.949378i	$-0.398285\pi$
$947$	39.8020	−	22.9797i	1.29339	−	0.746740i	0.979254	+	0.202638i	$0.0649514\pi$
$948$	47.6120	−	41.4887i	1.54637	−	1.34749i
$949$	−4.75746	−	8.18549i	−0.154434	−	0.265712i
$950$	−68.7985	+	22.3540i	−2.23212	+	0.725259i
$951$	−10.7111	+	14.2496i	−0.347331	+	0.462075i
$952$	0.316962	−	0.711909i	0.0102728	−	0.0230731i
$953$	0.639499	+	0.135930i	0.0207154	+	0.00440319i	0.218258	−	0.975891i	$-0.429963\pi$
$953$	0.639499	+	0.135930i	0.0207154	+	0.00440319i	−0.197542	+	0.980294i	$0.563296\pi$
$954$	44.6251	+	42.8879i	1.44479	+	1.38855i
$955$	21.8804	−	9.74178i	0.708033	−	0.315237i
$956$	38.1004	−	65.9919i	1.23226	−	2.13433i
$957$	3.42708	−	42.6668i	0.110782	−	1.37922i
$958$	−11.2694	+	19.5191i	−0.364096	+	0.630633i
$959$	0.0149862	−	0.142585i	0.000483931	−	0.00460430i
$960$	1.10277	−	67.8330i	0.0355917	−	2.18930i
$961$	12.5271	+	38.5545i	0.404101	+	1.24369i
$962$	−51.8443	+	71.7926i	−1.67153	+	2.31469i
$963$	44.0141	−	7.86963i	1.41834	−	0.253595i
$964$	22.8162	+	20.5438i	0.734860	+	0.661671i
$965$	25.2935	−	5.37629i	0.814225	−	0.173069i
$966$	−2.06935	+	0.404814i	−0.0665803	+	0.0130247i
$967$			5.04455i			0.162222i	0.996705	+	0.0811109i	$0.0258468\pi$
$967$			5.04455i			0.162222i	−0.996705	+	0.0811109i	$0.974153\pi$
$968$	−74.9692	−	45.6209i	−2.40960	−	1.46631i
$969$	3.44326	+	3.20319i	0.110614	+	0.102901i
$970$	−23.6738	+	32.5841i	−0.760119	+	1.04621i
$971$	−33.6821	+	30.3275i	−1.08091	+	0.973257i	−0.999725	−	0.0234421i	$-0.992537\pi$
$971$	−33.6821	+	30.3275i	−1.08091	+	0.973257i	−0.0811861	+	0.996699i	$0.525871\pi$
$972$	74.8614	+	22.3981i	2.40118	+	0.718421i
$973$	4.30379	+	1.91617i	0.137973	+	0.0614297i
$974$	−27.6321	+	20.0759i	−0.885388	+	0.643272i
$975$	22.0137	+	2.61171i	0.705003	+	0.0836417i
$976$	−26.7673	−	8.69721i	−0.856799	−	0.278391i
$977$	39.4928	+	4.15086i	1.26349	+	0.132798i	0.712474	−	0.701699i	$-0.247575\pi$
$977$	39.4928	+	4.15086i	1.26349	+	0.132798i	0.551013	+	0.834497i	$0.314241\pi$
$978$	16.2928	+	53.0640i	0.520987	+	1.69680i
$979$	−11.6542	+	29.3440i	−0.372469	+	0.937838i
$980$			101.476i			3.24155i
$981$	1.20749	−	37.1275i	0.0385522	−	1.18539i
$982$	−22.4585	−	24.9427i	−0.716679	−	0.795953i
$983$	11.5146	−	3.74132i	0.367258	−	0.119329i	−0.119573	−	0.992825i	$-0.538153\pi$
$983$	11.5146	−	3.74132i	0.367258	−	0.119329i	0.486831	+	0.873496i	$0.338153\pi$
$984$	2.68831	−	22.1135i	0.0857003	−	0.704952i
$985$	10.8380	−	24.3424i	0.345326	−	0.775615i
$986$	4.65851	−	5.17380i	0.148357	−	0.164767i
$987$	−0.631768	+	1.05430i	−0.0201094	+	0.0335587i
$988$	−93.3633	−	103.090i	−2.97028	−	3.27974i
$989$	5.82298			0.185160
$990$	−30.7502	+	70.6410i	−0.977306	+	2.24512i
$991$	−8.74959	−	15.1547i	−0.277940	−	0.481406i	0.692933	−	0.721002i	$-0.256318\pi$
$991$	−8.74959	−	15.1547i	−0.277940	−	0.481406i	−0.970873	+	0.239596i	$0.922985\pi$
$992$	−103.872	+	46.2467i	−3.29793	+	1.46833i
$993$	−27.5825	+	46.0297i	−0.875303	+	1.46071i
$994$	0.199883	+	0.0424865i	0.00633991	+	0.00134759i
$995$	40.8575	−	4.29429i	1.29527	−	0.136138i
$996$	−103.237	+	43.9673i	−3.27117	+	1.39316i
$997$	−0.999910	+	4.70421i	−0.0316675	+	0.148984i	−0.991141	−	0.132816i	$-0.957598\pi$
$997$	−0.999910	+	4.70421i	−0.0316675	+	0.148984i	0.959473	+	0.281800i	$0.0909314\pi$
$998$	54.0267	−	11.4837i	1.71019	−	0.363511i
$999$	−33.9547	+	34.1996i	−1.07428	+	1.08203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bq.a.29.1	✓	416
3.2	odd	2	inner	429.2.bq.a.29.52	yes	416
11.8	odd	10	inner	429.2.bq.a.107.1	yes	416
13.9	even	3	inner	429.2.bq.a.425.52	yes	416
33.8	even	10	inner	429.2.bq.a.107.52	yes	416
39.35	odd	6	inner	429.2.bq.a.425.1	yes	416
143.74	odd	30	inner	429.2.bq.a.74.52	yes	416
429.74	even	30	inner	429.2.bq.a.74.1	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bq.a.29.1	✓	416	1.1	even	1	trivial
429.2.bq.a.29.52	yes	416	3.2	odd	2	inner
429.2.bq.a.74.1	yes	416	429.74	even	30	inner
429.2.bq.a.74.52	yes	416	143.74	odd	30	inner
429.2.bq.a.107.1	yes	416	11.8	odd	10	inner
429.2.bq.a.107.52	yes	416	33.8	even	10	inner
429.2.bq.a.425.1	yes	416	39.35	odd	6	inner
429.2.bq.a.425.52	yes	416	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.276807 + 2.63364i) q^{2} +(-1.73182 - 0.0281544i) q^{3} +(-4.90316 - 1.04220i) q^{4} +(-1.71868 - 2.36556i) q^{5} +(0.553529 - 4.55321i) q^{6} +(-0.0575585 + 0.270792i) q^{7} +(2.46537 - 7.58762i) q^{8} +(2.99841 + 0.0975169i) q^{9} +O(q^{10})\)	\(q+(-0.276807 + 2.63364i) q^{2} +(-1.73182 - 0.0281544i) q^{3} +(-4.90316 - 1.04220i) q^{4} +(-1.71868 - 2.36556i) q^{5} +(0.553529 - 4.55321i) q^{6} +(-0.0575585 + 0.270792i) q^{7} +(2.46537 - 7.58762i) q^{8} +(2.99841 + 0.0975169i) q^{9} +(6.70579 - 3.87159i) q^{10} +(-2.60140 + 2.05735i) q^{11} +(8.46206 + 1.94295i) q^{12} +(0.759816 + 3.52458i) q^{13} +(-0.697236 - 0.226546i) q^{14} +(2.90985 + 4.14512i) q^{15} +(10.1420 + 4.51550i) q^{16} +(-0.0368807 - 0.350896i) q^{17} +(-1.08681 + 7.86976i) q^{18} +(5.71882 - 5.14925i) q^{19} +(5.96158 + 13.3899i) q^{20} +(0.107305 - 0.467342i) q^{21} +(-4.69824 - 7.42066i) q^{22} +(-1.43809 + 0.830281i) q^{23} +(-4.48320 + 13.0710i) q^{24} +(-1.09693 + 3.37600i) q^{25} +(-9.49282 + 1.02546i) q^{26} +(-5.18997 - 0.253301i) q^{27} +(0.564438 - 1.26775i) q^{28} +(4.98586 - 5.53736i) q^{29} +(-11.7222 + 6.51610i) q^{30} +(6.84271 + 4.97152i) q^{31} +(-6.72151 + 11.6420i) q^{32} +(4.56309 - 3.48973i) q^{33} +0.934345 q^{34} +(0.739499 - 0.329246i) q^{35} +(-14.6001 - 3.60309i) q^{36} +(6.20598 - 6.89244i) q^{37} +(11.9783 + 16.4867i) q^{38} +(-1.21663 - 6.12534i) q^{39} +(-22.1861 + 7.20872i) q^{40} +(-1.57684 + 0.335167i) q^{41} +(1.20111 + 0.411967i) q^{42} +(-3.03684 - 1.75332i) q^{43} +(14.8993 - 7.37635i) q^{44} +(-4.92263 - 7.26053i) q^{45} +(-1.78859 - 4.01724i) q^{46} +(-2.43781 - 0.792093i) q^{47} +(-17.4370 - 8.10559i) q^{48} +(6.32480 + 2.81598i) q^{49} +(-8.58755 - 3.82342i) q^{50} +(0.0539915 + 0.608728i) q^{51} +(-0.0521845 - 18.0735i) q^{52} +(4.57928 - 6.30284i) q^{53} +(2.10373 - 13.5984i) q^{54} +(9.33777 + 2.61785i) q^{55} +(1.91276 + 1.10433i) q^{56} +(-10.0490 + 8.75658i) q^{57} +(13.2033 + 14.6638i) q^{58} +(-0.497786 + 2.34190i) q^{59} +(-9.94742 - 23.3568i) q^{60} +(-2.52127 + 0.264996i) q^{61} +(-14.9873 + 16.6451i) q^{62} +(-0.198991 + 0.806332i) q^{63} +(-10.8373 - 7.87372i) q^{64} +(7.03173 - 7.85502i) q^{65} +(7.92760 + 12.9835i) q^{66} +(-0.190638 - 0.330195i) q^{67} +(-0.184872 + 1.75894i) q^{68} +(2.51389 - 1.39741i) q^{69} +(0.662418 + 2.03871i) q^{70} +(-0.277213 + 0.0291362i) q^{71} +(8.13211 - 22.5104i) q^{72} +(-2.49733 + 0.811431i) q^{73} +(16.4344 + 18.2522i) q^{74} +(1.99474 - 5.81575i) q^{75} +(-33.4069 + 19.2875i) q^{76} +(-0.407380 - 0.822856i) q^{77} +(16.4687 - 1.50864i) q^{78} +(4.27539 - 5.88457i) q^{79} +(-6.74914 - 31.7522i) q^{80} +(8.98098 + 0.584792i) q^{81} +(-0.446231 - 4.24561i) q^{82} +(-10.4557 + 7.59651i) q^{83} +(-1.01320 + 2.17962i) q^{84} +(-0.766680 + 0.690322i) q^{85} +(5.45823 - 7.51261i) q^{86} +(-8.79053 + 9.44935i) q^{87} +(9.19698 + 24.8106i) q^{88} +(8.24438 - 4.75989i) q^{89} +(20.4843 - 10.9547i) q^{90} +(-0.998161 + 0.00288204i) q^{91} +(7.91650 - 2.57223i) q^{92} +(-11.7104 - 8.80244i) q^{93} +(2.76090 - 6.20107i) q^{94} +(-22.0097 - 4.67831i) q^{95} +(11.9682 - 19.9726i) q^{96} +(-4.75182 + 2.11565i) q^{97} +(-9.16705 + 15.8778i) q^{98} +(-8.00072 + 5.91511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9}+O(q^{10}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9	\( 416 q - 3 q^{3} + 42 q^{4} - 5 q^{6} - 10 q^{7} + 3 q^{9} - 52 q^{12} - 20 q^{13} - 3 q^{15} + 30 q^{16} - 20 q^{18} - 10 q^{19} + 4 q^{22} + 5 q^{24} + 60 q^{25} - 24 q^{27} - 10 q^{28} - 65 q^{30} - 8 q^{31} + 49 q^{33} - 24 q^{34} + 3 q^{36} - 6 q^{37} - 35 q^{39} - 120 q^{40} - 13 q^{42} - 32 q^{45} - 30 q^{46} - 33 q^{48} - 26 q^{49} - 100 q^{51} - 60 q^{52} - 42 q^{55} - 20 q^{57} - 34 q^{58} + 32 q^{60} - 30 q^{61} - 45 q^{63} + 40 q^{64} + 42 q^{66} + 32 q^{67} - 33 q^{69} - 268 q^{70} + 55 q^{72} - 40 q^{73} + 9 q^{75} - 32 q^{78} - 37 q^{81} + 28 q^{82} - 180 q^{84} - 10 q^{85} - 142 q^{88} - 30 q^{90} + 8 q^{91} - 26 q^{93} - 90 q^{94} + 330 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 416 * q - 3 * q^3 + 42 * q^4 - 5 * q^6 - 10 * q^7 + 3 * q^9 - 52 * q^12 - 20 * q^13 - 3 * q^15 + 30 * q^16 - 20 * q^18 - 10 * q^19 + 4 * q^22 + 5 * q^24 + 60 * q^25 - 24 * q^27 - 10 * q^28 - 65 * q^30 - 8 * q^31 + 49 * q^33 - 24 * q^34 + 3 * q^36 - 6 * q^37 - 35 * q^39 - 120 * q^40 - 13 * q^42 - 32 * q^45 - 30 * q^46 - 33 * q^48 - 26 * q^49 - 100 * q^51 - 60 * q^52 - 42 * q^55 - 20 * q^57 - 34 * q^58 + 32 * q^60 - 30 * q^61 - 45 * q^63 + 40 * q^64 + 42 * q^66 + 32 * q^67 - 33 * q^69 - 268 * q^70 + 55 * q^72 - 40 * q^73 + 9 * q^75 - 32 * q^78 - 37 * q^81 + 28 * q^82 - 180 * q^84 - 10 * q^85 - 142 * q^88 - 30 * q^90 + 8 * q^91 - 26 * q^93 - 90 * q^94 + 330 * q^96 - 14 * q^97 - 4 * q^99

Introduction

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