LMFDB - Embedded newform 380.2.bj.a.23.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(23,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 27, 4]))

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

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

chi := DirichletCharacter("380.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bj (of order $36$, degree $12$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$56$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			23.20
Character	$\chi$	$=$	380.23
Dual form			380.2.bj.a.347.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.631329 - 1.26547i) q^{2} +(-2.52409 - 1.76739i) q^{3} +(-1.20285 + 1.59786i) q^{4} +(-2.23416 + 0.0923380i) q^{5} +(-0.643051 + 4.30997i) q^{6} +(1.52327 - 0.408158i) q^{7} +(2.78144 + 0.513399i) q^{8} +(2.22131 + 6.10300i) q^{9} +O(q^{10})$	\(q+(-0.631329 - 1.26547i) q^{2} +(-2.52409 - 1.76739i) q^{3} +(-1.20285 + 1.59786i) q^{4} +(-2.23416 + 0.0923380i) q^{5} +(-0.643051 + 4.30997i) q^{6} +(1.52327 - 0.408158i) q^{7} +(2.78144 + 0.513399i) q^{8} +(2.22131 + 6.10300i) q^{9} +(1.52734 + 2.76898i) q^{10} +(-4.28352 + 2.47309i) q^{11} +(5.86013 - 1.90724i) q^{12} +(-0.673330 + 0.471470i) q^{13} +(-1.47819 - 1.66997i) q^{14} +(5.80242 + 3.71555i) q^{15} +(-1.10631 - 3.84397i) q^{16} +(1.87271 - 0.873258i) q^{17} +(6.32081 - 6.66400i) q^{18} +(0.360371 - 4.34398i) q^{19} +(2.53981 - 3.68094i) q^{20} +(-4.56623 - 1.66197i) q^{21} +(5.83394 + 3.85935i) q^{22} +(-0.881292 + 0.0771030i) q^{23} +(-6.11323 - 6.21174i) q^{24} +(4.98295 - 0.412596i) q^{25} +(1.02173 + 0.554428i) q^{26} +(2.78704 - 10.4014i) q^{27} +(-1.18008 + 2.92492i) q^{28} +(1.43637 + 3.94638i) q^{29} +(1.03871 - 9.68854i) q^{30} +(3.62274 + 2.09159i) q^{31} +(-4.16599 + 3.82681i) q^{32} +(15.1829 + 1.32833i) q^{33} +(-2.28738 - 1.81855i) q^{34} +(-3.36553 + 1.05255i) q^{35} +(-12.4236 - 3.79164i) q^{36} +(6.99664 - 6.99664i) q^{37} +(-5.72470 + 2.28644i) q^{38} +2.53281 q^{39} +(-6.26160 - 0.890182i) q^{40} +(0.908048 + 5.14979i) q^{41} +(0.779610 + 6.82770i) q^{42} +(-0.980528 + 11.2075i) q^{43} +(1.20077 - 9.81921i) q^{44} +(-5.52630 - 13.4300i) q^{45} +(0.653957 + 1.06657i) q^{46} +(-7.36699 - 3.43528i) q^{47} +(-4.00134 + 11.6578i) q^{48} +(-3.90843 + 2.25653i) q^{49} +(-3.66801 - 6.04531i) q^{50} +(-6.27027 - 1.10562i) q^{51} +(0.0565697 - 1.64299i) q^{52} +(0.531062 + 6.07007i) q^{53} +(-14.9222 + 3.03976i) q^{54} +(9.34170 - 5.92081i) q^{55} +(4.44643 - 0.353225i) q^{56} +(-8.58709 + 10.3277i) q^{57} +(4.08722 - 4.30915i) q^{58} +(12.7934 + 4.65642i) q^{59} +(-12.9164 + 4.80220i) q^{60} +(2.16836 + 1.81947i) q^{61} +(0.359713 - 5.90497i) q^{62} +(5.87463 + 8.38984i) q^{63} +(7.47284 + 2.85598i) q^{64} +(1.46079 - 1.11551i) q^{65} +(-7.90442 - 20.0521i) q^{66} +(3.70483 + 1.72759i) q^{67} +(-0.857240 + 4.04272i) q^{68} +(2.36073 + 1.36297i) q^{69} +(3.45673 + 3.59449i) q^{70} +(2.94490 + 3.50959i) q^{71} +(3.04517 + 18.1155i) q^{72} +(3.58119 - 5.11447i) q^{73} +(-13.2713 - 4.43689i) q^{74} +(-13.3066 - 7.76536i) q^{75} +(6.50759 + 5.80097i) q^{76} +(-5.51552 + 5.51552i) q^{77} +(-1.59904 - 3.20521i) q^{78} +(2.01022 + 11.4005i) q^{79} +(2.82662 + 8.48588i) q^{80} +(-10.4923 + 8.80411i) q^{81} +(5.94365 - 4.40032i) q^{82} +(1.16760 + 4.35755i) q^{83} +(8.14808 - 5.29710i) q^{84} +(-4.10330 + 2.12392i) q^{85} +(14.8018 - 5.83477i) q^{86} +(3.34926 - 12.4996i) q^{87} +(-13.1840 + 4.67960i) q^{88} +(-7.20130 - 1.26978i) q^{89} +(-13.5064 + 15.4721i) q^{90} +(-0.833226 + 0.993000i) q^{91} +(0.936860 - 1.50092i) q^{92} +(-5.44747 - 11.6821i) q^{93} +(0.303730 + 11.4915i) q^{94} +(-0.404013 + 9.73842i) q^{95} +(17.2788 - 2.29630i) q^{96} +(12.8539 - 5.99386i) q^{97} +(5.32309 + 3.52140i) q^{98} +(-24.6083 - 20.6488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	$ 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) $ 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.631329	−	1.26547i	−0.446417	−	0.894825i
$2$	−0.631329	−	1.26547i	−0.446417	−	0.894825i
$3$	−2.52409	−	1.76739i	−1.45728	−	1.02040i	−0.990721	−	0.135912i	$-0.956604\pi$
$3$	−2.52409	−	1.76739i	−1.45728	−	1.02040i	−0.466562	−	0.884488i	$-0.654508\pi$
$4$	−1.20285	+	1.59786i	−0.601424	+	0.798930i
$5$	−2.23416	+	0.0923380i	−0.999147	+	0.0412948i
$5$	−2.23416	+	0.0923380i	−0.999147	+	0.0412948i
$6$	−0.643051	+	4.30997i	−0.262525	+	1.75954i
$7$	1.52327	−	0.408158i	0.575741	−	0.154269i	0.0408125	−	0.999167i	$-0.487005\pi$
$7$	1.52327	−	0.408158i	0.575741	−	0.154269i	0.534928	+	0.844898i	$0.320339\pi$
$8$	2.78144	+	0.513399i	0.983388	+	0.181514i
$9$	2.22131	+	6.10300i	0.740436	+	2.03433i
$10$	1.52734	+	2.76898i	0.482988	+	0.875627i
$11$	−4.28352	+	2.47309i	−1.29153	+	0.745664i	−0.978925	−	0.204219i	$-0.934534\pi$
$11$	−4.28352	+	2.47309i	−1.29153	+	0.745664i	−0.312603	+	0.949884i	$0.601201\pi$
$12$	5.86013	−	1.90724i	1.69167	−	0.550573i
$13$	−0.673330	+	0.471470i	−0.186748	+	0.130762i	−0.663212	−	0.748432i	$-0.730807\pi$
$13$	−0.673330	+	0.471470i	−0.186748	+	0.130762i	0.476464	+	0.879194i	$0.341918\pi$
$14$	−1.47819	−	1.66997i	−0.395064	−	0.446319i
$15$	5.80242	+	3.71555i	1.49818	+	0.959352i
$16$	−1.10631	−	3.84397i	−0.276578	−	0.960991i
$17$	1.87271	−	0.873258i	0.454199	−	0.211796i	−0.182036	−	0.983292i	$-0.558269\pi$
$17$	1.87271	−	0.873258i	0.454199	−	0.211796i	0.636235	+	0.771496i	$0.280491\pi$
$18$	6.32081	−	6.66400i	1.48983	−	1.57072i
$19$	0.360371	−	4.34398i	0.0826748	−	0.996577i
$19$	0.360371	−	4.34398i	0.0826748	−	0.996577i
$20$	2.53981	−	3.68094i	0.567920	−	0.823084i
$21$	−4.56623	−	1.66197i	−0.996433	−	0.362672i
$22$	5.83394	+	3.85935i	1.24380	+	0.822815i
$23$	−0.881292	+	0.0771030i	−0.183762	+	0.0160771i	−0.178665	−	0.983910i	$-0.557178\pi$
$23$	−0.881292	+	0.0771030i	−0.183762	+	0.0160771i	−0.00509676	+	0.999987i	$0.501622\pi$
$24$	−6.11323	−	6.21174i	−1.24786	−	1.26797i
$25$	4.98295	−	0.412596i	0.996589	−	0.0825191i
$26$	1.02173	+	0.554428i	0.200377	+	0.108732i
$27$	2.78704	−	10.4014i	0.536366	−	2.00174i
$28$	−1.18008	+	2.92492i	−0.223014	+	0.552758i
$29$	1.43637	+	3.94638i	0.266726	+	0.732824i	0.998675	+	0.0514646i	$0.0163889\pi$
$29$	1.43637	+	3.94638i	0.266726	+	0.732824i	−0.731949	+	0.681360i	$0.761389\pi$
$30$	1.03871	−	9.68854i	0.189641	−	1.76888i
$31$	3.62274	+	2.09159i	0.650664	+	0.375661i	0.788711	−	0.614765i	$-0.210749\pi$
$31$	3.62274	+	2.09159i	0.650664	+	0.375661i	−0.138047	+	0.990426i	$0.544082\pi$
$32$	−4.16599	+	3.82681i	−0.736450	+	0.676492i
$33$	15.1829	+	1.32833i	2.64300	+	0.231232i
$34$	−2.28738	−	1.81855i	−0.392282	−	0.311879i
$35$	−3.36553	+	1.05255i	−0.568879	+	0.177913i
$36$	−12.4236	−	3.79164i	−2.07061	−	0.631940i
$37$	6.99664	−	6.99664i	1.15024	−	1.15024i	0.163737	−	0.986504i	$-0.447645\pi$
$37$	6.99664	−	6.99664i	1.15024	−	1.15024i	0.986504	−	0.163737i	$-0.0523550\pi$
$38$	−5.72470	+	2.28644i	−0.928669	+	0.370909i
$39$	2.53281			0.405575
$40$	−6.26160	−	0.890182i	−0.990045	−	0.140750i
$41$	0.908048	+	5.14979i	0.141813	+	0.804263i	0.969871	+	0.243620i	$0.0783349\pi$
$41$	0.908048	+	5.14979i	0.141813	+	0.804263i	−0.828058	+	0.560643i	$0.810554\pi$
$42$	0.779610	+	6.82770i	0.120296	+	1.05354i
$43$	−0.980528	+	11.2075i	−0.149529	+	1.70913i	0.437218	+	0.899355i	$0.355964\pi$
$43$	−0.980528	+	11.2075i	−0.149529	+	1.70913i	−0.586747	+	0.809770i	$0.699592\pi$
$44$	1.20077	−	9.81921i	0.181023	−	1.48030i
$45$	−5.52630	−	13.4300i	−0.823812	−	2.00202i
$46$	0.653957	+	1.06657i	0.0964206	+	0.157258i
$47$	−7.36699	−	3.43528i	−1.07459	−	0.501088i	−0.196949	−	0.980414i	$-0.563103\pi$
$47$	−7.36699	−	3.43528i	−1.07459	−	0.501088i	−0.877637	+	0.479326i	$0.840881\pi$
$48$	−4.00134	+	11.6578i	−0.577544	+	1.68266i
$49$	−3.90843	+	2.25653i	−0.558347	+	0.322362i
$50$	−3.66801	−	6.04531i	−0.518734	−	0.854935i
$51$	−6.27027	−	1.10562i	−0.878013	−	0.154817i
$52$	0.0565697	−	1.64299i	0.00784480	−	0.227842i
$53$	0.531062	+	6.07007i	0.0729470	+	0.833788i	0.941240	+	0.337737i	$0.109662\pi$
$53$	0.531062	+	6.07007i	0.0729470	+	0.833788i	−0.868293	+	0.496051i	$0.834783\pi$
$54$	−14.9222	+	3.03976i	−2.03065	+	0.413658i
$55$	9.34170	−	5.92081i	1.25963	−	0.798362i
$56$	4.44643	−	0.353225i	0.594179	−	0.0472017i
$57$	−8.58709	+	10.3277i	−1.13739	+	1.36793i
$58$	4.08722	−	4.30915i	0.536679	−	0.565819i
$59$	12.7934	+	4.65642i	1.66556	+	0.606214i	0.991222	−	0.132208i	$-0.0422067\pi$
$59$	12.7934	+	4.65642i	1.66556	+	0.606214i	0.674338	+	0.738422i	$0.264429\pi$
$60$	−12.9164	+	4.80220i	−1.66749	+	0.619961i
$61$	2.16836	+	1.81947i	0.277630	+	0.232959i	0.770961	−	0.636882i	$-0.219776\pi$
$61$	2.16836	+	1.81947i	0.277630	+	0.232959i	−0.493331	+	0.869842i	$0.664221\pi$
$62$	0.359713	−	5.90497i	0.0456836	−	0.749932i
$63$	5.87463	+	8.38984i	0.740134	+	1.05702i
$64$	7.47284	+	2.85598i	0.934105	+	0.356997i
$65$	1.46079	−	1.11551i	0.181189	−	0.138363i
$66$	−7.90442	−	20.0521i	−0.972966	−	2.46825i
$67$	3.70483	+	1.72759i	0.452617	+	0.211059i	0.635539	−	0.772069i	$-0.280778\pi$
$67$	3.70483	+	1.72759i	0.452617	+	0.211059i	−0.182922	+	0.983127i	$0.558556\pi$
$68$	−0.857240	+	4.04272i	−0.103956	+	0.490252i
$69$	2.36073	+	1.36297i	0.284198	+	0.164082i
$70$	3.45673	+	3.59449i	0.413158	+	0.429624i
$71$	2.94490	+	3.50959i	0.349495	+	0.416512i	0.911941	−	0.410322i	$-0.134584\pi$
$71$	2.94490	+	3.50959i	0.349495	+	0.416512i	−0.562445	+	0.826834i	$0.690139\pi$
$72$	3.04517	+	18.1155i	0.358877	+	2.13494i
$73$	3.58119	−	5.11447i	0.419147	−	0.598604i	−0.552941	−	0.833220i	$-0.686495\pi$
$73$	3.58119	−	5.11447i	0.419147	−	0.598604i	0.972088	+	0.234617i	$0.0753835\pi$
$74$	−13.2713	−	4.43689i	−1.54275	−	0.515778i
$75$	−13.3066	−	7.76536i	−1.53652	−	0.896667i
$76$	6.50759	+	5.80097i	0.746472	+	0.665417i
$77$	−5.51552	+	5.51552i	−0.628552	+	0.628552i
$78$	−1.59904	−	3.20521i	−0.181055	−	0.362918i
$79$	2.01022	+	11.4005i	0.226167	+	1.28266i	0.860441	+	0.509550i	$0.170188\pi$
$79$	2.01022	+	11.4005i	0.226167	+	1.28266i	−0.634274	+	0.773108i	$0.718701\pi$
$80$	2.82662	+	8.48588i	0.316026	+	0.948751i
$81$	−10.4923	+	8.80411i	−1.16581	+	0.978234i
$82$	5.94365	−	4.40032i	0.656367	−	0.485934i
$83$	1.16760	+	4.35755i	0.128161	+	0.478303i	0.999933	−	0.0116092i	$-0.00369540\pi$
$83$	1.16760	+	4.35755i	0.128161	+	0.478303i	−0.871772	+	0.489912i	$0.837029\pi$
$84$	8.14808	−	5.29710i	0.889029	−	0.577961i
$85$	−4.10330	+	2.12392i	−0.445065	+	0.230372i
$86$	14.8018	−	5.83477i	1.59612	−	0.629180i
$87$	3.34926	−	12.4996i	0.359079	−	1.34010i
$88$	−13.1840	+	4.67960i	−1.40542	+	0.498847i
$89$	−7.20130	−	1.26978i	−0.763336	−	0.134597i	−0.221591	−	0.975140i	$-0.571125\pi$
$89$	−7.20130	−	1.26978i	−0.763336	−	0.134597i	−0.541745	+	0.840543i	$0.682236\pi$
$90$	−13.5064	+	15.4721i	−1.42369	+	1.63090i
$91$	−0.833226	+	0.993000i	−0.0873458	+	0.104095i
$92$	0.936860	−	1.50092i	0.0976744	−	0.156482i
$93$	−5.44747	−	11.6821i	−0.564877	−	1.21138i
$94$	0.303730	+	11.4915i	0.0313273	+	1.18526i
$95$	−0.404013	+	9.73842i	−0.0414508	+	0.999141i
$96$	17.2788	−	2.29630i	1.76351	−	0.234365i
$97$	12.8539	−	5.99386i	1.30511	−	0.608585i	0.359278	−	0.933231i	$-0.383023\pi$
$97$	12.8539	−	5.99386i	1.30511	−	0.608585i	0.945836	+	0.324646i	$0.105245\pi$
$98$	5.32309	+	3.52140i	0.537713	+	0.355715i
$99$	−24.6083	−	20.6488i	−2.47322	−	2.07528i
$100$	−5.33446	+	8.45834i	−0.533446	+	0.845834i
$101$	−2.47216	+	14.0203i	−0.245989	+	1.39507i	0.572195	+	0.820117i	$0.306092\pi$
$101$	−2.47216	+	14.0203i	−0.245989	+	1.39507i	−0.818184	+	0.574956i	$0.805019\pi$
$102$	2.55947	+	8.63287i	0.253425	+	0.854781i
$103$	−3.81892	−	1.02328i	−0.376289	−	0.100826i	0.0657173	−	0.997838i	$-0.479066\pi$
$103$	−3.81892	−	1.02328i	−0.376289	−	0.100826i	−0.442006	+	0.897012i	$0.645733\pi$
$104$	−2.11488	+	0.965681i	−0.207381	+	0.0946929i
$105$	10.3552	+	3.29148i	1.01056	+	0.321215i
$106$	7.34624	−	4.50425i	0.713530	−	0.437492i
$107$	−2.39309	+	0.641227i	−0.231349	+	0.0619897i	−0.372631	−	0.927980i	$-0.621544\pi$
$107$	−2.39309	+	0.641227i	−0.231349	+	0.0619897i	0.141282	+	0.989969i	$0.454878\pi$
$108$	13.2675	+	16.9646i	1.27667	+	1.63242i
$109$	−4.84538	−	5.77450i	−0.464103	−	0.553097i	0.482333	−	0.875988i	$-0.339790\pi$
$109$	−4.84538	−	5.77450i	−0.464103	−	0.553097i	−0.946436	+	0.322891i	$0.895345\pi$
$110$	−13.3903	−	8.08370i	−1.27672	−	0.770751i
$111$	−30.0259	+	5.29438i	−2.84993	+	0.502520i
$112$	−3.25415	−	5.40383i	−0.307489	−	0.510614i
$113$	−5.31933	−	5.31933i	−0.500400	−	0.500400i	0.411162	−	0.911562i	$-0.365123\pi$
$113$	−5.31933	−	5.31933i	−0.500400	−	0.500400i	−0.911562	+	0.411162i	$0.865123\pi$
$114$	18.4907	+	4.34659i	1.73181	+	0.407095i
$115$	1.96183	−	0.253637i	0.182941	−	0.0236518i
$116$	−8.03349	−	2.45179i	−0.745891	−	0.227643i
$117$	−4.37306	−	3.06205i	−0.404289	−	0.283086i
$118$	−2.18427	−	19.1295i	−0.201078	−	1.76101i
$119$	2.49621	−	2.09457i	0.228827	−	0.192009i
$120$	14.2315	+	13.3136i	1.29915	+	1.21536i
$121$	6.73234	−	11.6607i	0.612031	−	1.06007i
$122$	0.933545	−	3.89269i	0.0845192	−	0.352427i
$123$	6.80968	−	14.6034i	0.614008	−	1.31674i
$124$	−7.69968	+	3.27277i	−0.691452	+	0.293903i
$125$	−11.0946	+	1.38192i	−0.992332	+	0.123603i
$126$	6.90830	−	12.7309i	0.615441	−	1.13416i
$127$	−8.54365	+	5.98233i	−0.758127	+	0.530846i	−0.887532	−	0.460746i	$-0.847582\pi$
$127$	−8.54365	+	5.98233i	−0.758127	+	0.530846i	0.129405	+	0.991592i	$0.458693\pi$
$128$	−1.10366	−	11.2597i	−0.0975504	−	0.995231i
$129$	22.2829	−	26.5557i	1.96190	−	2.33810i
$130$	−2.33389	−	1.14434i	−0.204696	−	0.100365i
$131$	4.39982	−	12.0884i	0.384414	−	1.05617i	−0.585063	−	0.810988i	$-0.698930\pi$
$131$	4.39982	−	12.0884i	0.384414	−	1.05617i	0.969477	−	0.245182i	$-0.0788476\pi$
$132$	−20.3852	+	22.6623i	−1.77430	+	1.97250i
$133$	−1.22409	−	6.76412i	−0.106142	−	0.586524i
$134$	−0.152744	−	5.77904i	−0.0131951	−	0.499233i
$135$	−5.26625	+	23.4957i	−0.453246	+	2.02219i
$136$	5.65716	−	1.46747i	0.485098	−	0.125835i
$137$	−5.00702	+	0.438058i	−0.427779	+	0.0374258i	−0.299013	−	0.954249i	$-0.596657\pi$
$137$	−5.00702	+	0.438058i	−0.427779	+	0.0374258i	−0.128766	+	0.991675i	$0.541102\pi$
$138$	0.234404	−	3.84792i	0.0199538	−	0.327557i
$139$	−2.67951	+	15.1963i	−0.227273	+	1.28893i	0.631019	+	0.775767i	$0.282637\pi$
$139$	−2.67951	+	15.1963i	−0.227273	+	1.28893i	−0.858292	+	0.513162i	$0.828474\pi$
$140$	2.36641	−	6.64370i	0.199998	−	0.561495i
$141$	12.5235	+	21.6913i	1.05467	+	1.82674i
$142$	2.58210	−	5.94240i	0.216685	−	0.498675i
$143$	1.71823	−	3.68475i	0.143686	−	0.308135i
$144$	21.0022	−	15.2905i	1.75019	−	1.27420i
$145$	−3.57347	−	8.68422i	−0.296761	−	0.721185i
$146$	−8.73314	−	1.30299i	−0.722760	−	0.107836i
$147$	13.8534	+	1.21201i	1.14261	+	0.0999653i
$148$	2.76376	+	19.5956i	0.227179	+	1.61075i
$149$	11.8967	−	2.09771i	0.974617	−	0.171851i	0.336410	−	0.941716i	$-0.390787\pi$
$149$	11.8967	−	2.09771i	0.974617	−	0.171851i	0.638207	+	0.769864i	$0.279676\pi$
$150$	−1.42602	+	21.7417i	−0.116434	+	1.77520i
$151$			15.8424i			1.28924i	0.764505	+	0.644618i	$0.222983\pi$
$151$			15.8424i			1.28924i	−0.764505	+	0.644618i	$0.777017\pi$
$152$	3.23254	−	11.8975i	0.262194	−	0.965015i
$153$	9.48936	+	9.48936i	0.767169	+	0.767169i
$154$	10.4619	+	3.49764i	0.843041	+	0.281848i
$155$	−8.28692	−	4.33844i	−0.665622	−	0.348472i
$156$	−3.04659	+	4.04708i	−0.243922	+	0.324026i
$157$	−0.641728	+	7.33498i	−0.0512155	+	0.585395i	0.926617	+	0.376007i	$0.122703\pi$
$157$	−0.641728	+	7.33498i	−0.0512155	+	0.585395i	−0.977832	+	0.209389i	$0.932853\pi$
$158$	13.1579	−	9.74135i	1.04679	−	0.774980i
$159$	9.38771	−	16.2600i	0.744493	−	1.28950i
$160$	8.95414	−	8.93440i	0.707887	−	0.706326i
$161$	−1.31097	+	0.477155i	−0.103319	+	0.0376051i
$162$	17.7655	+	7.71948i	1.39579	+	0.606500i
$163$	1.89945	+	0.508956i	0.148776	+	0.0398645i	0.332439	−	0.943125i	$-0.392129\pi$
$163$	1.89945	+	0.508956i	0.148776	+	0.0398645i	−0.183662	+	0.982989i	$0.558795\pi$
$164$	−9.32089	−	4.74349i	−0.727840	−	0.370404i
$165$	−34.0436	−	1.56575i	−2.65029	−	0.121893i
$166$	4.77723	−	4.22862i	0.370785	−	0.328204i
$167$	0.314006	+	3.58911i	0.0242985	+	0.277734i	0.998618	+	0.0525620i	$0.0167387\pi$
$167$	0.314006	+	3.58911i	0.0242985	+	0.277734i	−0.974319	+	0.225172i	$0.927706\pi$
$168$	−11.8475	−	6.96698i	−0.914051	−	0.537514i
$169$	−4.21517	+	11.5811i	−0.324244	+	0.890853i
$170$	5.27830	+	3.85172i	0.404827	+	0.295414i
$171$	27.3118	−	7.44997i	2.08858	−	0.569714i
$172$	−16.7286	−	15.0477i	−1.27554	−	1.14737i
$173$	−3.25997	−	6.99103i	−0.247851	−	0.531518i	0.742542	−	0.669799i	$-0.233620\pi$
$173$	−3.25997	−	6.99103i	−0.247851	−	0.531518i	−0.990393	+	0.138281i	$0.955842\pi$
$174$	−17.9324	+	3.65296i	−1.35945	+	0.276930i
$175$	7.42195	−	2.66232i	0.561047	−	0.201253i
$176$	14.2454	+	13.7297i	1.07379	+	1.03491i
$177$	−24.0620	−	34.3641i	−1.80861	−	2.58296i
$178$	2.93951	+	9.91470i	0.220325	+	0.743138i
$179$	−7.40696	−	12.8292i	−0.553622	−	0.958901i	−0.998009	−	0.0630666i	$-0.979912\pi$
$179$	−7.40696	−	12.8292i	−0.553622	−	0.958901i	0.444387	−	0.895835i	$-0.353421\pi$
$180$	28.1065	+	7.32396i	2.09493	+	0.545896i
$181$	−9.14218	+	3.32748i	−0.679533	+	0.247330i	−0.658647	−	0.752452i	$-0.728871\pi$
$181$	−9.14218	+	3.32748i	−0.679533	+	0.247330i	−0.0208860	+	0.999782i	$0.506649\pi$
$182$	1.78265	+	0.427516i	0.132139	+	0.0316896i
$183$	−2.25743	−	8.42484i	−0.166874	−	0.622782i
$184$	−2.49085	−	0.237996i	−0.183628	−	0.0175453i
$185$	−14.9856	+	16.2777i	−1.10176	+	1.19676i
$186$	−11.3443	+	14.2689i	−0.831805	+	1.04625i
$187$	−5.86213	+	8.37199i	−0.428681	+	0.612221i
$188$	14.3505	−	7.63929i	1.04662	−	0.557153i
$189$		−	16.9816i		−	1.23523i
$190$	12.5788	−	5.63687i	0.912560	−	0.408942i
$191$			2.08894i			0.151151i	0.997140	+	0.0755753i	$0.0240793\pi$
$191$			2.08894i			0.151151i	−0.997140	+	0.0755753i	$0.975921\pi$
$192$	−13.8145	−	20.4161i	−0.996976	−	1.47341i
$193$	−9.39274	+	13.4142i	−0.676104	+	0.965577i	0.323707	+	0.946157i	$0.395071\pi$
$193$	−9.39274	+	13.4142i	−0.676104	+	0.965577i	−0.999811	+	0.0194194i	$0.993818\pi$
$194$	−15.7001	−	12.4822i	−1.12720	−	0.896166i
$195$	−5.65871	+	0.233875i	−0.405229	+	0.0167481i
$196$	1.09563	−	8.95939i	0.0782589	−	0.639957i
$197$	0.476532	+	1.77844i	0.0339515	+	0.126709i	0.980822	−	0.194907i	$-0.0624406\pi$
$197$	0.476532	+	1.77844i	0.0339515	+	0.126709i	−0.946870	+	0.321616i	$0.895774\pi$
$198$	−10.5946	+	44.1773i	−0.752925	+	3.13954i
$199$	15.5789	−	5.67026i	1.10436	−	0.401954i	0.275438	−	0.961319i	$-0.411177\pi$
$199$	15.5789	−	5.67026i	1.10436	−	0.401954i	0.828922	+	0.559365i	$0.188955\pi$
$200$	14.0716	+	1.41063i	0.995013	+	0.0997464i
$201$	−6.29799	−	10.9084i	−0.444226	−	0.769422i
$202$	19.3031	−	5.72297i	1.35816	−	0.402667i
$203$	3.79871	+	5.42512i	0.266617	+	0.380769i
$204$	9.30880	−	8.68912i	0.651746	−	0.608360i
$205$	−2.50425	−	11.4216i	−0.174904	−	0.797721i
$206$	1.11606	+	5.47876i	0.0777598	+	0.381723i
$207$	−2.42818	−	5.20725i	−0.168770	−	0.361929i
$208$	2.55723	+	2.06666i	0.177312	+	0.143297i
$209$	9.19939	+	19.4987i	0.636335	+	1.34875i
$210$	−2.37223	−	15.1822i	−0.163699	−	1.04767i
$211$	5.55503	−	15.2623i	0.382424	−	1.05070i	−0.587909	−	0.808927i	$-0.700049\pi$
$211$	5.55503	−	15.2623i	0.382424	−	1.05070i	0.970333	−	0.241774i	$-0.0777291\pi$
$212$	−10.3379	−	6.45281i	−0.710010	−	0.443181i
$213$	−1.23038	−	14.0633i	−0.0843042	−	0.963601i
$214$	2.32228	+	2.62357i	0.158748	+	0.179343i
$215$	1.15578	−	25.1299i	0.0788236	−	1.71384i
$216$	13.0920	−	27.4999i	0.890800	−	1.87113i
$217$	6.37210	+	1.70740i	0.432567	+	0.115906i
$218$	−4.24845	+	9.77731i	−0.287742	+	0.662203i
$219$	−18.0785	+	6.58003i	−1.22163	+	0.444637i
$220$	−1.77603	+	22.0486i	−0.119740	+	1.48651i
$221$	−0.849235	+	1.47092i	−0.0571257	+	0.0989446i
$222$	25.6561	+	34.6545i	1.72193	+	2.32586i
$223$	−1.30824	+	14.9533i	−0.0876065	+	1.00135i	0.817434	+	0.576022i	$0.195396\pi$
$223$	−1.30824	+	14.9533i	−0.0876065	+	1.00135i	−0.905041	+	0.425325i	$0.860160\pi$
$224$	−4.78397	+	7.52964i	−0.319642	+	0.503095i
$225$	13.5867	+	29.4944i	0.905782	+	1.96629i
$226$	−3.37323	+	10.0897i	−0.224384	+	0.671158i
$227$	6.95531	+	6.95531i	0.461640	+	0.461640i	0.899193	−	0.437553i	$-0.144155\pi$
$227$	6.95531	+	6.95531i	0.461640	+	0.461640i	−0.437553	+	0.899193i	$0.644155\pi$
$228$	−6.17320	−	26.1436i	−0.408830	−	1.73140i
$229$			25.6925i			1.69781i	0.528548	+	0.848903i	$0.322737\pi$
$229$			25.6925i			1.69781i	−0.528548	+	0.848903i	$0.677263\pi$
$230$	−1.55953	−	2.32251i	−0.102832	−	0.153142i
$231$	23.6697	−	4.17361i	1.55735	−	0.274603i
$232$	1.96910	+	11.7141i	0.129278	+	0.769066i
$233$	−8.75189	−	0.765691i	−0.573355	−	0.0501621i	−0.203209	−	0.979135i	$-0.565137\pi$
$233$	−8.75189	−	0.765691i	−0.573355	−	0.0501621i	−0.370146	+	0.928973i	$0.620693\pi$
$234$	−1.11410	+	7.46714i	−0.0728313	+	0.488143i
$235$	16.7762	+	6.99472i	1.09436	+	0.456286i
$236$	−22.8288	+	14.8411i	−1.48603	+	0.966074i
$237$	15.0751	−	32.3287i	0.979235	−	2.09998i
$238$	−4.22655	−	1.83652i	−0.273966	−	0.119044i
$239$	8.85663	+	15.3401i	0.572888	+	0.992271i	0.996268	+	0.0863187i	$0.0275103\pi$
$239$	8.85663	+	15.3401i	0.572888	+	0.992271i	−0.423380	+	0.905952i	$0.639156\pi$
$240$	7.86318	−	26.4148i	0.507566	−	1.70507i
$241$	3.81379	−	21.6291i	0.245668	−	1.39325i	−0.573269	−	0.819367i	$-0.694325\pi$
$241$	3.81379	−	21.6291i	0.245668	−	1.39325i	0.818937	−	0.573884i	$-0.194564\pi$
$242$	−19.0067	−	1.15783i	−1.22180	−	0.0744282i
$243$	9.86188	−	0.862803i	0.632640	−	0.0553488i
$244$	−5.51547	+	1.27619i	−0.353092	+	0.0816996i
$245$	8.52370	−	5.40235i	0.544559	−	0.345144i
$246$	−22.7794	+	0.602076i	−1.45236	+	0.0383870i
$247$	1.80541	+	3.09483i	0.114875	+	0.196919i
$248$	9.00263	+	7.67755i	0.571668	+	0.487525i
$249$	4.75434	−	13.0624i	0.301294	−	0.827799i
$250$	8.75313	+	13.1675i	0.553596	+	0.832785i
$251$	11.5846	−	13.8060i	0.731216	−	0.871430i	−0.264453	−	0.964399i	$-0.585191\pi$
$251$	11.5846	−	13.8060i	0.731216	−	0.871430i	0.995669	+	0.0929690i	$0.0296358\pi$
$252$	−20.4721	−	0.704871i	−1.28962	−	0.0444027i
$253$	3.58434	−	2.50978i	0.225346	−	0.157789i
$254$	12.9643	+	7.03496i	0.813455	+	0.441412i
$255$	14.1109	+	1.89114i	0.883657	+	0.118428i
$256$	−13.5521	+	8.50525i	−0.847009	+	0.531578i
$257$	2.54340	−	5.45433i	0.158653	−	0.340232i	−0.810873	−	0.585223i	$-0.801007\pi$
$257$	2.54340	−	5.45433i	0.158653	−	0.340232i	0.969525	+	0.244991i	$0.0787849\pi$
$258$	−47.6734	−	11.4330i	−2.96802	−	0.711789i
$259$	7.80202	−	13.5135i	0.484794	−	0.839687i
$260$	0.0253249	+	3.67594i	0.00157059	+	0.227972i
$261$	−20.8941	+	17.5323i	−1.29331	+	1.08522i
$262$	−18.0753	+	2.06390i	−1.11670	+	0.127508i
$263$	0.176381	+	0.123504i	0.0108761	+	0.00761556i	0.579002	−	0.815326i	$-0.303442\pi$
$263$	0.176381	+	0.123504i	0.0108761	+	0.00761556i	−0.568126	+	0.822942i	$0.692331\pi$
$264$	41.5483	+	11.4895i	2.55712	+	0.707132i
$265$	−1.74698	−	13.5125i	−0.107316	−	0.830065i
$266$	−7.78702	+	5.81943i	−0.477453	+	0.356812i
$267$	15.9325	+	15.9325i	0.975054	+	0.975054i
$268$	−7.21679	+	3.84177i	−0.440836	+	0.234673i
$269$	30.4270	−	5.36510i	1.85517	−	0.327116i	0.869254	−	0.494366i	$-0.164600\pi$
$269$	30.4270	−	5.36510i	1.85517	−	0.327116i	0.985914	+	0.167250i	$0.0534888\pi$
$270$	33.0579	−	8.16919i	2.01184	−	0.497161i
$271$	8.86433	+	10.5641i	0.538470	+	0.641724i	0.964844	−	0.262823i	$-0.0846537\pi$
$271$	8.86433	+	10.5641i	0.538470	+	0.641724i	−0.426374	+	0.904547i	$0.640209\pi$
$272$	−5.42858	−	6.23253i	−0.329156	−	0.377903i
$273$	3.85815	−	1.03379i	0.233506	−	0.0625677i
$274$	3.71543	+	6.05970i	0.224457	+	0.366080i
$275$	−20.3241	+	14.0906i	−1.22559	+	0.849697i
$276$	−5.01743	+	2.13267i	−0.302014	+	0.128372i
$277$	−27.4856	−	7.36476i	−1.65145	−	0.442505i	−0.691433	−	0.722440i	$-0.743020\pi$
$277$	−27.4856	−	7.36476i	−1.65145	−	0.442505i	−0.960019	+	0.279935i	$0.909687\pi$
$278$	20.9221	−	6.20298i	1.25482	−	0.372030i
$279$	−4.71775	+	26.7557i	−0.282444	+	1.60182i
$280$	−9.90141	+	1.19974i	−0.591723	+	0.0716979i
$281$	−4.16801	−	3.49737i	−0.248642	−	0.208636i	0.509945	−	0.860207i	$-0.329666\pi$
$281$	−4.16801	−	3.49737i	−0.248642	−	0.208636i	−0.758587	+	0.651571i	$0.774110\pi$
$282$	19.5433	−	29.5424i	1.16379	−	1.75923i
$283$	−12.7381	+	5.93986i	−0.757199	+	0.353088i	−0.762577	−	0.646898i	$-0.776066\pi$
$283$	−12.7381	+	5.93986i	−0.757199	+	0.353088i	0.00537759	+	0.999986i	$0.498288\pi$
$284$	−9.15011	+	0.484026i	−0.542959	+	0.0287217i
$285$	18.2313	−	23.8666i	1.07993	−	1.41373i
$286$	−5.74773	+	0.151917i	−0.339870	+	0.00898303i
$287$	3.48513	+	7.47388i	0.205721	+	0.441169i
$288$	−32.6090	−	16.9245i	−1.92150	−	0.997286i
$289$	−8.18293	+	9.75204i	−0.481349	+	0.573649i
$290$	−8.73362	+	10.0047i	−0.512856	+	0.587498i
$291$	−43.0378	−	7.58872i	−2.52292	−	0.444859i
$292$	3.86458	+	11.8742i	0.226157	+	0.694883i
$293$	−2.46225	+	9.18922i	−0.143846	+	0.536840i	0.855958	+	0.517045i	$0.172968\pi$
$293$	−2.46225	+	9.18922i	−0.143846	+	0.536840i	−0.999804	+	0.0197951i	$0.993699\pi$
$294$	−7.21227	−	18.2963i	−0.420628	−	1.06706i
$295$	−29.0125	−	9.22188i	−1.68917	−	0.536918i
$296$	23.0528	−	15.8687i	1.33992	−	0.922349i
$297$	13.7852	+	51.4470i	0.799897	+	2.98526i
$298$	−10.1653	−	13.7306i	−0.588862	−	0.795395i
$299$	0.557048	−	0.467419i	0.0322149	−	0.0270315i
$300$	28.4138	−	11.9216i	1.64047	−	0.688291i
$301$	3.08082	+	17.4722i	0.177575	+	1.00708i
$302$	20.0481	−	10.0018i	1.15364	−	0.575536i
$303$	31.0193	−	31.0193i	1.78201	−	1.78201i
$304$	−17.0968	+	3.42054i	−0.980568	+	0.196181i
$305$	−5.01247	−	3.86477i	−0.287013	−	0.221296i
$306$	6.01763	−	17.9994i	0.344005	−	1.02896i
$307$	6.16452	−	8.80385i	0.351828	−	0.502462i	−0.603761	−	0.797165i	$-0.706332\pi$
$307$	6.16452	−	8.80385i	0.351828	−	0.502462i	0.955589	+	0.294703i	$0.0952208\pi$
$308$	−2.17870	−	15.4474i	−0.124143	−	0.880196i
$309$	7.83076	+	9.33233i	0.445476	+	0.530898i
$310$	−0.258404	+	13.2259i	−0.0146764	+	0.751179i
$311$	−24.7676	−	14.2996i	−1.40444	−	0.810856i	−0.409599	−	0.912266i	$-0.634331\pi$
$311$	−24.7676	−	14.2996i	−1.40444	−	0.810856i	−0.994845	+	0.101410i	$0.967665\pi$
$312$	7.04487	+	1.30034i	0.398837	+	0.0736174i
$313$	7.48052	+	3.48822i	0.422824	+	0.197166i	0.622371	−	0.782722i	$-0.286169\pi$
$313$	7.48052	+	3.48822i	0.422824	+	0.197166i	−0.199547	+	0.979888i	$0.563947\pi$
$314$	9.68737	−	3.81870i	0.546690	−	0.215501i
$315$	−13.8996	−	18.2018i	−0.783152	−	1.02556i
$316$	−20.6344	−	10.5010i	−1.16078	−	0.590730i
$317$	7.73699	+	11.0496i	0.434553	+	0.620605i	0.975381	−	0.220528i	$-0.0707780\pi$
$317$	7.73699	+	11.0496i	0.434553	+	0.620605i	−0.540828	+	0.841133i	$0.681889\pi$
$318$	−26.5033	−	1.61450i	−1.48623	−	0.0905369i
$319$	−15.9124	−	13.3521i	−0.890926	−	0.747575i
$320$	−16.9592	−	5.69068i	−0.948051	−	0.318119i
$321$	7.17367	+	2.61100i	0.400395	+	0.145732i
$322$	1.43148	+	1.35776i	0.0797733	+	0.0756649i
$323$	−3.11854	−	8.44970i	−0.173520	−	0.470154i
$324$	−1.44705	−	27.3553i	−0.0803918	−	1.51974i
$325$	−3.16064	+	2.62713i	−0.175321	+	0.145727i
$326$	−0.555106	−	2.72502i	−0.0307445	−	0.150925i
$327$	2.02440	+	23.1390i	0.111950	+	1.27959i
$328$	−0.118214	+	14.7900i	−0.00652730	+	0.816644i
$329$	−12.6240	−	2.22596i	−0.695985	−	0.122721i
$330$	19.5113	+	44.0698i	1.07406	+	2.42596i
$331$	6.89094	−	3.97849i	0.378760	−	0.218677i	−0.298518	−	0.954404i	$-0.596492\pi$
$331$	6.89094	−	3.97849i	0.378760	−	0.218677i	0.677279	+	0.735726i	$0.263159\pi$
$332$	−8.36720	−	3.37581i	−0.459210	−	0.185272i
$333$	58.2422	+	27.1588i	3.19165	+	1.48829i
$334$	4.34368	−	2.66327i	0.237676	−	0.145728i
$335$	−8.43670	−	3.51762i	−0.460946	−	0.192188i
$336$	−1.33689	+	19.3911i	−0.0729333	+	1.05787i
$337$	−0.419422	+	4.79401i	−0.0228474	+	0.261146i	0.976177	+	0.216977i	$0.0696197\pi$
$337$	−0.419422	+	4.79401i	−0.0228474	+	0.261146i	−0.999024	+	0.0441694i	$0.985936\pi$
$338$	17.3167	−	1.97728i	0.941906	−	0.107550i
$339$	4.02515	+	22.8278i	0.218616	+	1.23983i
$340$	1.54192	−	9.11125i	0.0836221	−	0.494127i
$341$	−20.6908			−1.12047
$342$	−26.6704	−	29.8589i	−1.44217	−	1.61459i
$343$	−12.8383	+	12.8383i	−0.693204	+	0.693204i
$344$	−8.48119	+	30.6696i	−0.457275	+	1.65359i
$345$	−5.40010	−	2.82710i	−0.290732	−	0.152206i
$346$	−6.78885	+	8.53904i	−0.364971	+	0.459062i
$347$	−4.95789	−	0.433759i	−0.266154	−	0.0232854i	−0.0467022	−	0.998909i	$-0.514871\pi$
$347$	−4.95789	−	0.433759i	−0.266154	−	0.0232854i	−0.219451	+	0.975623i	$0.570427\pi$
$348$	15.9440	+	20.3868i	0.854688	+	1.09285i
$349$	−4.19713	−	2.42322i	−0.224667	−	0.129712i	0.383442	−	0.923565i	$-0.374739\pi$
$349$	−4.19713	−	2.42322i	−0.224667	−	0.129712i	−0.608110	+	0.793853i	$0.708072\pi$
$350$	−8.05479	−	7.71149i	−0.430547	−	0.412196i
$351$	3.02734	+	8.31755i	0.161588	+	0.443958i
$352$	8.38104	−	26.6951i	0.446711	−	1.42285i
$353$	2.02379	−	7.55289i	0.107716	−	0.402000i	−0.890924	−	0.454153i	$-0.849942\pi$
$353$	2.02379	−	7.55289i	0.107716	−	0.402000i	0.998639	+	0.0521534i	$0.0166085\pi$
$354$	−28.2958	+	52.1449i	−1.50391	+	2.77147i
$355$	−6.90345	−	7.56907i	−0.366397	−	0.401725i
$356$	10.6910	−	9.97930i	0.566622	−	0.528902i
$357$	−10.0026	+	0.875110i	−0.529391	+	0.0463157i
$358$	−11.5588	+	17.4728i	−0.610903	+	0.923465i
$359$	−14.1744	−	5.15908i	−0.748099	−	0.272286i	−0.0602933	−	0.998181i	$-0.519204\pi$
$359$	−14.1744	−	5.15908i	−0.748099	−	0.272286i	−0.687806	+	0.725895i	$0.741426\pi$
$360$	−8.47616	−	40.1919i	−0.446733	−	2.11830i
$361$	−18.7403	−	3.13089i	−0.986330	−	0.164783i
$362$	9.98256	+	9.46846i	0.524672	+	0.497651i
$363$	−37.6021	+	17.5341i	−1.97360	+	0.920303i
$364$	−0.584430	−	2.52581i	−0.0306325	−	0.132388i
$365$	−7.52870	+	11.7572i	−0.394070	+	0.615402i
$366$	−9.23623	+	8.17556i	−0.482785	+	0.427343i
$367$	19.3416	−	13.5431i	1.00962	−	0.706945i	0.0530953	−	0.998589i	$-0.483091\pi$
$367$	19.3416	−	13.5431i	1.00962	−	0.706945i	0.956527	+	0.291644i	$0.0942024\pi$
$368$	1.27136	+	3.30235i	0.0662745	+	0.172147i
$369$	−29.4121	+	16.9811i	−1.53113	+	0.884001i
$370$	30.0598	+	8.68728i	1.56273	+	0.451630i
$371$	3.28650	+	9.02957i	0.170626	+	0.468792i
$372$	25.2189	+	5.34755i	1.30754	+	0.277258i
$373$	15.1813	−	4.06780i	0.786055	−	0.210623i	0.156603	−	0.987662i	$-0.449946\pi$
$373$	15.1813	−	4.06780i	0.786055	−	0.210623i	0.629453	+	0.777039i	$0.283279\pi$
$374$	14.2955	+	2.13290i	0.739201	+	0.110289i
$375$	30.4462	+	16.1204i	1.57223	+	0.832452i
$376$	−18.7272	−	13.3372i	−0.965781	−	0.687816i
$377$	−2.82775	−	1.98001i	−0.145636	−	0.101976i
$378$	−21.4898	+	10.7210i	−1.10531	+	0.551427i
$379$	16.8880			0.867478			0.433739	−	0.901038i	$-0.357194\pi$
$379$	16.8880			0.867478			0.433739	+	0.901038i	$0.357194\pi$
$380$	−15.0747	−	12.3594i	−0.773314	−	0.634024i
$381$	32.1380			1.64648
$382$	2.64350	−	1.31881i	0.135253	−	0.0674762i
$383$	11.1799	+	7.82823i	0.571265	+	0.400004i	0.823210	−	0.567738i	$-0.192181\pi$
$383$	11.1799	+	7.82823i	0.571265	+	0.400004i	−0.251945	+	0.967742i	$0.581070\pi$
$384$	−17.1146	+	30.3712i	−0.873375	+	1.54987i
$385$	11.8133	−	12.8319i	0.602060	−	0.653972i
$386$	22.9052	+	3.41748i	1.16585	+	0.173945i
$387$	−70.5773	+	18.9111i	−3.58765	+	0.961307i
$388$	−5.88392	+	27.7484i	−0.298711	+	1.40871i
$389$	9.05922	+	24.8900i	0.459321	+	1.26197i	0.925992	+	0.377542i	$0.123231\pi$
$389$	9.05922	+	24.8900i	0.459321	+	1.26197i	−0.466672	+	0.884431i	$0.654547\pi$
$390$	3.86847	+	7.01330i	0.195888	+	0.355132i
$391$	−1.58307	+	0.913987i	−0.0800594	+	0.0462223i
$392$	−12.0296	+	4.26984i	−0.607585	+	0.215659i
$393$	−32.4704	+	22.7360i	−1.63792	+	1.14688i
$394$	1.94972	−	1.72582i	0.0982256	−	0.0869455i
$395$	−5.54385	−	25.2850i	−0.278941	−	1.27222i
$396$	62.5939	−	14.4832i	3.14546	−	0.727808i
$397$	5.48737	−	2.55880i	0.275403	−	0.128423i	−0.280010	−	0.959997i	$-0.590338\pi$
$397$	5.48737	−	2.55880i	0.275403	−	0.128423i	0.555413	+	0.831574i	$0.312560\pi$
$398$	−17.0110	−	16.1349i	−0.852683	−	0.808770i
$399$	−8.86511	+	19.2367i	−0.443810	+	0.963038i
$400$	−7.09870	−	18.6978i	−0.354935	−	0.934891i
$401$	7.32048	+	2.66444i	0.365567	+	0.133056i	0.518271	−	0.855216i	$-0.326576\pi$
$401$	7.32048	+	2.66444i	0.365567	+	0.133056i	−0.152704	+	0.988272i	$0.548798\pi$
$402$	−9.82825	+	14.8568i	−0.490188	+	0.740988i
$403$	−3.42542	+	0.299686i	−0.170633	+	0.0149284i
$404$	−19.4289	−	20.8145i	−0.966622	−	1.03556i
$405$	22.6286	−	20.6386i	1.12442	−	1.02554i
$406$	4.46712	−	8.23221i	0.221699	−	0.408558i
$407$	−12.6669	+	47.2736i	−0.627876	+	2.34326i
$408$	−16.8728	−	6.29436i	−0.835326	−	0.311617i
$409$	−13.0562	−	35.8715i	−0.645585	−	1.77373i	−0.633424	−	0.773805i	$-0.718351\pi$
$409$	−13.0562	−	35.8715i	−0.645585	−	1.77373i	−0.0121619	−	0.999926i	$-0.503871\pi$
$410$	−12.8728	+	10.3799i	−0.635740	+	0.512625i
$411$	13.4124	+	7.74364i	0.661584	+	0.381966i
$412$	6.22863	−	4.87125i	0.306862	−	0.239989i
$413$	21.3883	+	1.87124i	1.05245	+	0.0920775i
$414$	−5.05666	+	6.36029i	−0.248521	+	0.312591i
$415$	−3.01098	−	9.62765i	−0.147803	−	0.472603i
$416$	1.00086	−	4.54085i	0.0490710	−	0.222633i
$417$	33.6210	−	33.6210i	1.64643	−	1.64643i
$418$	18.8673	−	23.9517i	0.922829	−	1.17152i
$419$	−7.66463			−0.374442			−0.187221	−	0.982318i	$-0.559948\pi$
$419$	−7.66463			−0.374442			−0.187221	+	0.982318i	$0.559948\pi$
$420$	−17.7150	+	12.5869i	−0.864403	+	0.614180i
$421$	1.94008	+	11.0027i	0.0945536	+	0.536240i	0.994883	+	0.101031i	$0.0322143\pi$
$421$	1.94008	+	11.0027i	0.0945536	+	0.536240i	−0.900330	+	0.435209i	$0.856675\pi$
$422$	−22.8211	+	2.60579i	−1.11091	+	0.126848i
$423$	4.60116	−	52.5916i	0.223716	−	2.55709i
$424$	−1.63925	+	17.1562i	−0.0796088	+	0.833179i
$425$	8.97131	−	5.12407i	0.435172	−	0.248554i
$426$	−17.0200	+	10.4356i	−0.824620	+	0.505605i
$427$	4.04562	+	1.88650i	0.195781	+	0.0912944i
$428$	1.85393	−	4.59512i	0.0896133	−	0.222114i
$429$	−10.8493	+	6.26387i	−0.523811	+	0.302423i
$430$	−32.5309	+	14.4026i	−1.56878	+	0.694555i
$431$	22.1193	+	3.90023i	1.06545	+	0.187867i	0.678773	−	0.734348i	$-0.262512\pi$
$431$	22.1193	+	3.90023i	1.06545	+	0.187867i	0.386676	+	0.922216i	$0.373623\pi$
$432$	−43.0658	+	0.793877i	−2.07201	+	0.0381954i
$433$	2.21816	+	25.3537i	0.106598	+	1.21842i	0.841503	+	0.540253i	$0.181671\pi$
$433$	2.21816	+	25.3537i	0.106598	+	1.21842i	−0.734905	+	0.678170i	$0.762773\pi$
$434$	−1.86222	−	9.14166i	−0.0893895	−	0.438814i
$435$	−6.32860	+	28.2354i	−0.303433	+	1.35379i
$436$	15.0551	−	0.796392i	0.721009	−	0.0381403i
$437$	0.0173418	+	3.85610i	0.000829573	+	0.184462i
$438$	19.7403	+	18.7237i	0.943229	+	0.894652i
$439$	9.57869	+	3.48636i	0.457166	+	0.166395i	0.560330	−	0.828270i	$-0.310674\pi$
$439$	9.57869	+	3.48636i	0.457166	+	0.166395i	−0.103164	+	0.994664i	$0.532897\pi$
$440$	29.0231	−	11.6724i	1.38362	−	0.556459i
$441$	−22.4534	−	18.8407i	−1.06921	−	0.897175i
$442$	2.39755	+	0.146052i	0.114040	+	0.00694698i
$443$	−7.14528	−	10.2045i	−0.339483	−	0.484832i	0.612719	−	0.790301i	$-0.290076\pi$
$443$	−7.14528	−	10.2045i	−0.339483	−	0.484832i	−0.952202	+	0.305469i	$0.901187\pi$
$444$	27.6569	−	54.3455i	1.31254	−	2.57913i
$445$	16.2061	+	2.17195i	0.768243	+	0.102960i
$446$	19.7489	−	7.78489i	0.935139	−	0.368625i
$447$	−33.7358	−	15.7313i	−1.59565	−	0.744064i
$448$	12.5488	+	1.30031i	0.592876	+	0.0614340i
$449$	10.9496	+	6.32177i	0.516745	+	0.298343i	0.735602	−	0.677414i	$-0.236900\pi$
$449$	10.9496	+	6.32177i	0.516745	+	0.298343i	−0.218857	+	0.975757i	$0.570233\pi$
$450$	28.7467	−	35.8143i	1.35513	−	1.68830i
$451$	−16.6255	−	19.8135i	−0.782866	−	0.932983i
$452$	14.8979	−	2.10120i	0.700738	−	0.0988320i
$453$	27.9996	−	39.9876i	1.31554	−	1.87878i
$454$	4.41068	−	13.1929i	0.207003	−	0.619171i
$455$	1.76987	−	2.29546i	0.0829727	−	0.107613i
$456$	−29.1867	+	24.3172i	−1.36679	+	1.13876i
$457$	−8.61320	+	8.61320i	−0.402909	+	0.402909i	−0.879257	−	0.476348i	$-0.841960\pi$
$457$	−8.61320	+	8.61320i	−0.402909	+	0.402909i	0.476348	+	0.879257i	$0.341960\pi$
$458$	32.5132	−	16.2204i	1.51924	−	0.757929i
$459$	−3.86377	−	21.9125i	−0.180345	−	1.02279i
$460$	−1.95450	+	3.43981i	−0.0911292	+	0.160382i
$461$	7.60729	−	6.38327i	0.354307	−	0.297299i	−0.448210	−	0.893928i	$-0.647938\pi$
$461$	7.60729	−	6.38327i	0.354307	−	0.297299i	0.802517	+	0.596630i	$0.203494\pi$
$462$	−20.2250	−	27.3185i	−0.940951	−	1.27097i
$463$	−1.98287	−	7.40016i	−0.0921516	−	0.343915i	0.904421	−	0.426642i	$-0.140304\pi$
$463$	−1.98287	−	7.40016i	−0.0921516	−	0.343915i	−0.996572	+	0.0827275i	$0.973637\pi$
$464$	13.5807	−	9.88727i	0.630467	−	0.459005i
$465$	13.2492	+	25.5968i	0.614419	+	1.18702i
$466$	4.55635	+	11.5587i	0.211069	+	0.535446i
$467$	4.46619	−	16.6680i	0.206671	−	0.771305i	−0.782263	−	0.622948i	$-0.785935\pi$
$467$	4.46619	−	16.6680i	0.206671	−	0.771305i	0.988934	−	0.148357i	$-0.0473985\pi$
$468$	10.1528	−	3.30435i	0.469315	−	0.152744i
$469$	6.34857	+	1.11942i	0.293150	+	0.0516902i
$470$	−1.73969	−	25.6459i	−0.0802457	−	1.18296i
$471$	14.5835	−	17.3800i	0.671973	−	0.800827i
$472$	33.1935	+	19.5197i	1.52786	+	0.898466i
$473$	−23.5170	−	50.4324i	−1.08131	−	2.31888i
$474$	−50.4285	+	1.33286i	−2.31626	+	0.0612205i
$475$	0.00340349	−	21.7945i	0.000156163	−	1.00000i
$476$	0.344265	+	6.50803i	0.0157794	+	0.298295i
$477$	−35.8660	+	16.7246i	−1.64219	+	0.765766i
$478$	13.8211	−	20.8925i	0.632162	−	0.955601i
$479$	−12.1608	−	10.2041i	−0.555641	−	0.466238i	0.321205	−	0.947010i	$-0.395912\pi$
$479$	−12.1608	−	10.2041i	−0.555641	−	0.466238i	−0.876846	+	0.480771i	$0.840357\pi$
$480$	−38.3916	+	6.72580i	−1.75233	+	0.306989i
$481$	−1.41234	+	8.00976i	−0.0643970	+	0.365214i
$482$	−29.7788	+	8.82881i	−1.35639	+	0.402141i
$483$	4.15232	+	1.11261i	0.188937	+	0.0506256i
$484$	10.5343	+	24.7834i	0.478830	+	1.12652i
$485$	−28.1642	+	14.5782i	−1.27887	+	0.661960i
$486$	−7.31794	−	11.9352i	−0.331949	−	0.541394i
$487$	6.51306	−	1.74517i	0.295135	−	0.0790812i	−0.108213	−	0.994128i	$-0.534513\pi$
$487$	6.51306	−	1.74517i	0.295135	−	0.0790812i	0.403348	+	0.915047i	$0.367846\pi$
$488$	5.09706	+	6.17399i	0.230733	+	0.279483i
$489$	−3.89485	−	4.64171i	−0.176131	−	0.209905i
$490$	−12.2178	−	7.37586i	−0.551944	−	0.333207i
$491$	20.6093	−	3.63397i	0.930084	−	0.163999i	0.311974	−	0.950091i	$-0.399010\pi$
$491$	20.6093	−	3.63397i	0.930084	−	0.163999i	0.618110	+	0.786092i	$0.287899\pi$
$492$	15.1432	+	28.4466i	0.682707	+	1.28247i
$493$	6.13610	+	6.13610i	0.276356	+	0.276356i
$494$	2.77662	−	4.23855i	0.124926	−	0.190702i
$495$	56.8855	+	43.8604i	2.55681	+	1.97138i
$496$	4.03212	−	16.2397i	0.181048	−	0.729182i
$497$	5.91833	+	4.14406i	0.265474	+	0.185887i
$498$	−19.5317	+	2.23020i	−0.875238	+	0.0999377i
$499$	−19.0699	+	16.0015i	−0.853685	+	0.716327i	−0.960598	−	0.277942i	$-0.910348\pi$
$499$	−19.0699	+	16.0015i	−0.853685	+	0.716327i	0.106913	+	0.994268i	$0.465903\pi$
$500$	11.1370	−	19.3899i	0.498062	−	0.867141i
$501$	5.55076	−	9.61420i	0.247990	−	0.429531i
$502$	−24.7849	−	5.94392i	−1.10620	−	0.265290i
$503$	−7.35057	+	15.7634i	−0.327746	+	0.702853i	−0.999273	−	0.0381269i	$-0.987861\pi$
$503$	−7.35057	+	15.7634i	−0.327746	+	0.702853i	0.671527	+	0.740980i	$0.265639\pi$
$504$	12.0326	+	26.3519i	0.535975	+	1.17381i
$505$	4.22859	−	31.5519i	0.188170	−	1.40404i
$506$	−5.43897	−	2.95139i	−0.241792	−	0.131205i
$507$	31.1077	−	21.7819i	1.38154	−	0.967367i
$508$	0.717794	−	20.8474i	0.0318470	−	0.924954i
$509$	−5.38835	+	6.42159i	−0.238835	+	0.284632i	−0.872126	−	0.489282i	$-0.837259\pi$
$509$	−5.38835	+	6.42159i	−0.238835	+	0.284632i	0.633291	+	0.773913i	$0.281703\pi$
$510$	−6.51541	−	19.0509i	−0.288507	−	0.843587i
$511$	3.36760	−	9.25239i	0.148974	−	0.409302i
$512$	19.3190	+	11.7803i	0.853789	+	0.520620i
$513$	−44.1789	−	15.8552i	−1.95055	−	0.700023i
$514$	−8.50804	+	0.224874i	−0.375273	+	0.00991876i
$515$	8.62656	+	1.93353i	0.380132	+	0.0852015i
$516$	15.6294	+	67.5474i	0.688045	+	2.97361i
$517$	40.0524	−	3.50413i	1.76150	−	0.154111i
$518$	−22.0266	−	1.34180i	−0.967793	−	0.0589551i
$519$	−4.12739	+	23.4076i	−0.181172	+	1.02748i
$520$	4.63581	−	2.35277i	0.203294	−	0.103176i
$521$	12.2659	+	21.2452i	0.537380	+	0.930770i	0.999044	+	0.0437146i	$0.0139192\pi$
$521$	12.2659	+	21.2452i	0.537380	+	0.930770i	−0.461664	+	0.887055i	$0.652747\pi$
$522$	35.3777	+	15.3724i	1.54844	+	0.672830i
$523$	8.76486	−	18.7963i	0.383261	−	0.821905i	−0.616152	−	0.787628i	$-0.711309\pi$
$523$	8.76486	−	18.7963i	0.383261	−	0.821905i	0.999412	−	0.0342777i	$-0.0109131\pi$
$524$	14.0233	+	21.5708i	0.612609	+	0.942326i
$525$	−23.4390	−	6.39751i	−1.02296	−	0.279210i
$526$	0.0449359	−	0.301177i	0.00195930	−	0.0131320i
$527$	8.61084	+	0.753351i	0.375094	+	0.0328165i
$528$	−11.6909	−	59.8320i	−0.508783	−	2.60385i
$529$	−21.8798	+	3.85801i	−0.951298	+	0.167739i
$530$	−15.9968	+	10.7416i	−0.694855	+	0.466584i
$531$			88.4215i			3.83717i
$532$	12.2805	+	6.18029i	0.532428	+	0.267950i
$533$	−3.03939	−	3.03939i	−0.131651	−	0.131651i
$534$	10.1035	−	30.2208i	0.437222	−	1.30778i
$535$	5.28734	−	1.65358i	0.228592	−	0.0714903i
$536$	9.41782	+	6.70724i	0.406788	+	0.289709i
$537$	−3.97838	+	45.4730i	−0.171680	+	1.96231i
$538$	−25.9988	−	35.1175i	−1.12089	−	1.51402i
$539$	11.1612	−	19.3318i	0.480748	−	0.832679i
$540$	−31.2083	−	36.6765i	−1.34299	−	1.57830i
$541$	7.04742	−	2.56505i	0.302992	−	0.110280i	−0.186050	−	0.982540i	$-0.559569\pi$
$541$	7.04742	−	2.56505i	0.302992	−	0.110280i	0.489042	+	0.872260i	$0.337346\pi$
$542$	7.77229	−	17.8870i	0.333848	−	0.768313i
$543$	28.9566	+	7.75890i	1.24265	+	0.332966i
$544$	−4.45989	+	10.8045i	−0.191216	+	0.463239i
$545$	11.3586	+	12.4538i	0.486548	+	0.533460i
$546$	−3.74399	−	4.22973i	−0.160228	−	0.181016i
$547$	−1.75257	−	20.0320i	−0.0749346	−	0.856506i	−0.936913	−	0.349562i	$-0.886330\pi$
$547$	−1.75257	−	20.0320i	−0.0749346	−	0.856506i	0.861979	−	0.506945i	$-0.169225\pi$
$548$	5.32273	−	8.52744i	0.227376	−	0.364274i
$549$	−6.28762	+	17.2751i	−0.268349	+	0.737284i
$550$	30.6625	+	16.8239i	1.30746	+	0.717372i
$551$	17.6606	−	4.81738i	0.752367	−	0.205227i
$552$	5.86649	+	5.00301i	0.249694	+	0.212942i
$553$	7.71531	+	16.5455i	0.328088	+	0.703588i
$554$	8.03257	+	39.4319i	0.341271	+	1.67530i
$555$	66.5939	−	14.6010i	2.82675	−	0.619779i
$556$	−21.0584	−	22.5603i	−0.893077	−	0.956768i
$557$	15.8476	+	22.6327i	0.671483	+	0.958977i	0.999896	+	0.0144424i	$0.00459733\pi$
$557$	15.8476	+	22.6327i	0.671483	+	0.958977i	−0.328413	+	0.944534i	$0.606514\pi$
$558$	36.8370	−	10.9214i	1.55944	−	0.462341i
$559$	−4.62378	−	8.00862i	−0.195565	−	0.338729i
$560$	7.76928	+	11.7726i	0.328312	+	0.497481i
$561$	29.5931	−	10.7710i	1.24942	−	0.454752i
$562$	−1.79445	+	7.48250i	−0.0756944	+	0.315630i
$563$	3.66023	+	13.6602i	0.154260	+	0.575707i	0.999168	+	0.0407944i	$0.0129889\pi$
$563$	3.66023	+	13.6602i	0.154260	+	0.575707i	−0.844907	+	0.534913i	$0.820344\pi$
$564$	−49.7234	−	6.08058i	−2.09373	−	0.256038i
$565$	12.3754	+	11.3931i	0.520638	+	0.479310i
$566$	15.5586	+	12.3697i	0.653978	+	0.519937i
$567$	−12.3891	+	17.6935i	−0.520295	+	0.743058i
$568$	6.38925	+	11.2736i	0.268087	+	0.473031i
$569$		−	15.0486i		−	0.630868i	−0.948947	−	0.315434i	$-0.897850\pi$
$569$		−	15.0486i		−	0.630868i	0.948947	−	0.315434i	$-0.102150\pi$
$570$	−41.7125	−	8.00358i	−1.74714	−	0.335233i
$571$		−	12.7481i		−	0.533489i	−0.963767	−	0.266745i	$-0.914052\pi$
$571$		−	12.7481i		−	0.533489i	0.963767	−	0.266745i	$-0.0859481\pi$
$572$	3.82095	+	7.17769i	0.159762	+	0.300114i
$573$	3.69197	−	5.27268i	0.154234	−	0.220269i
$574$	7.25774	−	9.12881i	0.302932	−	0.381029i
$575$	−4.35962	+	0.747817i	−0.181809	+	0.0311861i
$576$	−0.830520	+	51.9507i	−0.0346050	+	2.16461i
$577$	−3.57681	−	13.3488i	−0.148904	−	0.555719i	−0.999550	−	0.0299801i	$-0.990456\pi$
$577$	−3.57681	−	13.3488i	−0.148904	−	0.555719i	0.850646	−	0.525739i	$-0.176211\pi$
$578$	17.5071	+	4.19855i	0.728198	+	0.174636i
$579$	47.4162	−	17.2581i	1.97055	−	0.717221i
$580$	18.1745	+	4.73589i	0.754655	+	0.196647i
$581$	3.55714	+	6.16114i	0.147575	+	0.255607i
$582$	17.5677	+	59.2542i	0.728203	+	2.45616i
$583$	−17.2866	−	24.6879i	−0.715939	−	1.02247i
$584$	12.5866	−	12.3870i	0.520839	−	0.512579i
$585$	10.0529	+	6.43730i	0.415634	+	0.266150i
$586$	13.1832	−	2.68551i	0.544593	−	0.110938i
$587$	−7.28108	−	15.6143i	−0.300522	−	0.644472i	0.696827	−	0.717240i	$-0.254595\pi$
$587$	−7.28108	−	15.6143i	−0.300522	−	0.644472i	−0.997349	+	0.0727674i	$0.976817\pi$
$588$	−18.6002	+	20.6779i	−0.767057	+	0.852742i
$589$	10.3914	−	14.9834i	0.428168	−	0.617379i
$590$	6.64638	+	42.5366i	0.273627	+	1.75120i
$591$	1.94038	−	5.33116i	0.0798167	−	0.219294i
$592$	−34.6353	−	19.1544i	−1.42350	−	0.787241i
$593$	3.95841	+	45.2448i	0.162552	+	1.85798i	0.440969	+	0.897522i	$0.354635\pi$
$593$	3.95841	+	45.2448i	0.162552	+	1.85798i	−0.278416	+	0.960460i	$0.589810\pi$
$594$	56.4019	−	49.9248i	2.31420	−	2.04844i
$595$	−5.38352	+	4.91009i	−0.220703	+	0.201294i
$596$	−10.9581	+	21.5325i	−0.448861	+	0.882006i
$597$	−49.3441	−	13.2217i	−2.01952	−	0.541128i
$598$	−0.943186	−	0.409835i	−0.0385698	−	0.0167594i
$599$	−0.924099	+	0.336345i	−0.0377577	+	0.0137427i	−0.360830	−	0.932632i	$-0.617507\pi$
$599$	−0.924099	+	0.336345i	−0.0377577	+	0.0137427i	0.323072	+	0.946374i	$0.395284\pi$
$600$	−33.0249	−	28.4305i	−1.34823	−	1.16067i
$601$	12.3304	−	21.3568i	0.502967	−	0.871164i	−0.497028	−	0.867735i	$-0.665575\pi$
$601$	12.3304	−	21.3568i	0.502967	−	0.871164i	0.999994	−	0.00342888i	$-0.00109145\pi$
$602$	20.1656	−	14.9294i	0.821888	−	0.608477i
$603$	−2.31390	+	26.4481i	−0.0942295	+	1.07705i
$604$	−25.3139	−	19.0560i	−1.03001	−	0.775377i
$605$	−13.9644	+	26.6736i	−0.567733	+	1.08444i
$606$	−58.8374	−	19.6707i	−2.39011	−	0.799068i
$607$	0.423728	+	0.423728i	0.0171986	+	0.0171986i	0.715654	−	0.698455i	$-0.246129\pi$
$607$	0.423728	+	0.423728i	0.0171986	+	0.0171986i	−0.698455	+	0.715654i	$0.746129\pi$
$608$	15.1223	+	19.4760i	0.613290	+	0.789858i
$609$		−	20.4073i		−	0.826945i
$610$	−1.72625	+	8.78309i	−0.0698936	+	0.355617i
$611$	6.58005	−	1.16024i	0.266200	−	0.0469383i
$612$	−26.5769	+	3.74841i	−1.07431	+	0.151520i
$613$	−35.8224	−	3.13405i	−1.44685	−	0.126583i	−0.663507	−	0.748170i	$-0.730933\pi$
$613$	−35.8224	−	3.13405i	−1.44685	−	0.126583i	−0.783345	+	0.621587i	$0.786488\pi$
$614$	−15.0329	−	2.24292i	−0.606677	−	0.0905168i
$615$	−13.8655	+	33.2551i	−0.559110	+	1.34098i
$616$	−18.1728	+	12.5094i	−0.732202	+	0.504020i
$617$	4.07808	−	8.74546i	0.164177	−	0.352079i	−0.806958	−	0.590609i	$-0.798888\pi$
$617$	4.07808	−	8.74546i	0.164177	−	0.352079i	0.971135	+	0.238530i	$0.0766655\pi$
$618$	6.86604	−	15.8014i	0.276193	−	0.635625i
$619$	17.0888	+	29.5986i	0.686856	+	1.18967i	0.972850	+	0.231438i	$0.0743429\pi$
$619$	17.0888	+	29.5986i	0.686856	+	1.18967i	−0.285994	+	0.958231i	$0.592324\pi$
$620$	16.9001	−	8.02286i	0.678725	−	0.322206i
$621$	−1.65422	+	9.38152i	−0.0663814	+	0.376468i
$622$	−2.45925	+	40.3705i	−0.0986071	+	1.61871i
$623$	−11.4878	+	1.00505i	−0.460247	+	0.0402664i
$624$	−2.80208	−	9.73605i	−0.112173	−	0.389754i
$625$	24.6595	−	4.11189i	0.986381	−	0.164475i
$626$	−0.308410	−	11.6686i	−0.0123266	−	0.466372i
$627$	11.2417	−	65.4754i	0.448950	−	2.61483i
$628$	−10.9484	−	9.84826i	−0.436888	−	0.392989i
$629$	6.99280	−	19.2126i	0.278821	−	0.766055i
$630$	−14.2587	+	29.0809i	−0.568081	+	1.15861i
$631$	−24.1243	+	28.7503i	−0.960375	+	1.14453i	0.0290635	+	0.999578i	$0.490748\pi$
$631$	−24.1243	+	28.7503i	−0.960375	+	1.14453i	−0.989439	+	0.144953i	$0.953697\pi$
$632$	−0.261701	+	32.7419i	−0.0104099	+	1.30240i
$633$	−40.9958	+	28.7055i	−1.62944	+	1.14094i
$634$	9.09835	−	16.7669i	0.361342	−	0.665897i
$635$	18.5355	−	14.1544i	0.735559	−	0.561700i
$636$	14.6892	+	34.5585i	0.582464	+	1.37033i
$637$	1.56777	−	3.36210i	0.0621174	−	0.133211i
$638$	−6.85078	+	28.5664i	−0.271225	+	1.13095i
$639$	−14.8775	+	25.7686i	−0.588545	+	1.01939i
$640$	3.50545	+	25.0542i	0.138565	+	0.990353i
$641$	28.8740	−	24.2281i	1.14045	−	0.956954i	0.141000	−	0.990010i	$-0.454968\pi$
$641$	28.8740	−	24.2281i	1.14045	−	0.956954i	0.999454	+	0.0330559i	$0.0105239\pi$
$642$	−1.22479	−	10.7265i	−0.0483385	−	0.423341i
$643$	−32.1457	−	22.5086i	−1.26770	−	0.887654i	−0.270522	−	0.962714i	$-0.587196\pi$
$643$	−32.1457	−	22.5086i	−1.26770	−	0.887654i	−0.997179	+	0.0750598i	$0.976085\pi$
$644$	0.814474	−	2.66869i	0.0320948	−	0.105161i
$645$	−47.3314	+	61.3873i	−1.86367	+	2.41712i
$646$	−8.72405	+	9.28097i	−0.343243	+	0.365155i
$647$	24.9968	+	24.9968i	0.982726	+	0.982726i	0.999853	−	0.0171276i	$-0.00545216\pi$
$647$	24.9968	+	24.9968i	0.982726	+	0.982726i	−0.0171276	+	0.999853i	$0.505452\pi$
$648$	−33.7038	+	19.1014i	−1.32401	+	0.750373i
$649$	−66.3165	+	11.6934i	−2.60315	+	0.459006i
$650$	5.31996	+	2.34113i	0.208666	+	0.0918265i
$651$	−13.0661	−	15.5716i	−0.512101	−	0.610299i
$652$	−3.09799	+	2.42286i	−0.121327	+	0.0948863i
$653$	−4.40968	+	1.18157i	−0.172564	+	0.0462384i	−0.344066	−	0.938945i	$-0.611805\pi$
$653$	−4.40968	+	1.18157i	−0.172564	+	0.0462384i	0.171502	+	0.985184i	$0.445138\pi$
$654$	28.0038	−	17.1701i	1.09503	−	0.671406i
$655$	−8.71369	+	27.4137i	−0.340472	+	1.07114i
$656$	18.7911	−	9.18778i	0.733667	−	0.358723i
$657$	39.1685	+	10.4952i	1.52811	+	0.409456i
$658$	5.15302	+	17.3807i	0.200886	+	0.677570i
$659$	1.46781	−	8.32438i	0.0571779	−	0.324272i	−0.942780	−	0.333415i	$-0.891799\pi$
$659$	1.46781	−	8.32438i	0.0571779	−	0.324272i	0.999958	+	0.00914270i	$0.00291025\pi$
$660$	43.4512	−	52.5136i	1.69133	−	2.04409i
$661$	11.7363	+	9.84792i	0.456489	+	0.383040i	0.841837	−	0.539732i	$-0.181474\pi$
$661$	11.7363	+	9.84792i	0.456489	+	0.383040i	−0.385348	+	0.922771i	$0.625919\pi$
$662$	−9.38512	−	6.20857i	−0.364763	−	0.241303i
$663$	4.74322	−	2.21180i	0.184211	−	0.0858992i
$664$	1.01046	+	12.7197i	0.0392134	+	0.493621i
$665$	3.35939	+	14.9991i	0.130272	+	0.581640i
$666$	−2.40124	−	90.8501i	−0.0930460	−	3.52037i
$667$	−1.57013	−	3.36716i	−0.0607958	−	0.130377i
$668$	−6.11259	−	3.81542i	−0.236503	−	0.147623i
$669$	29.7304	−	35.4313i	1.14944	−	1.36985i
$670$	0.874880	+	12.8972i	0.0337996	+	0.498262i
$671$	−13.7879	−	2.43118i	−0.532277	−	0.0938548i
$672$	25.3829	−	10.5504i	0.979168	−	0.406989i
$673$	12.2404	−	45.6819i	0.471834	−	1.76091i	−0.161341	−	0.986899i	$-0.551582\pi$
$673$	12.2404	−	45.6819i	0.471834	−	1.76091i	0.633175	−	0.774009i	$-0.281751\pi$
$674$	6.33149	−	2.49583i	0.243880	−	0.0961358i
$675$	9.59610	−	52.9794i	0.369354	−	2.03918i
$676$	−13.4348	−	20.6656i	−0.516721	−	0.794829i
$677$	−8.72865	−	32.5758i	−0.335469	−	1.25199i	−0.903360	−	0.428884i	$-0.858907\pi$
$677$	−8.72865	−	32.5758i	−0.335469	−	1.25199i	0.567891	−	0.823104i	$-0.307760\pi$
$678$	26.3467	−	19.5055i	1.01184	−	0.749106i
$679$	17.1334	−	14.3767i	0.657521	−	0.551726i
$680$	−12.5035	+	3.80094i	−0.479487	+	0.145759i
$681$	−5.26310	−	29.8485i	−0.201683	−	1.14380i
$682$	13.0627	+	26.1836i	0.500196	+	1.00262i
$683$	−22.4750	+	22.4750i	−0.859982	+	0.859982i	−0.991336	−	0.131354i	$-0.958068\pi$
$683$	−22.4750	+	22.4750i	−0.859982	+	0.859982i	0.131354	+	0.991336i	$0.458068\pi$
$684$	−20.9479	+	52.6016i	−0.800963	+	2.01127i
$685$	11.1460	−	1.44103i	0.425868	−	0.0550589i
$686$	24.3518	+	8.14136i	0.929754	+	0.310838i
$687$	45.4085	−	64.8501i	1.73244	−	2.47418i
$688$	44.1660	−	8.62986i	1.68381	−	0.329010i
$689$	−3.21944	−	3.83678i	−0.122651	−	0.146170i
$690$	−0.168387	+	8.61852i	−0.00641038	+	0.328101i
$691$	−24.2372	−	13.9933i	−0.922026	−	0.532332i	−0.0377451	−	0.999287i	$-0.512017\pi$
$691$	−24.2372	−	13.9933i	−0.922026	−	0.532332i	−0.884281	+	0.466956i	$0.845351\pi$
$692$	15.0919	+	3.20017i	0.573709	+	0.121652i
$693$	−45.9129	−	21.4095i	−1.74409	−	0.813281i
$694$	2.58115	+	6.54793i	0.0979790	+	0.248556i
$695$	4.58326	−	34.1983i	0.173853	−	1.29722i
$696$	15.7331	−	33.0475i	0.596361	−	1.25266i
$697$	6.19761	+	8.85111i	0.234751	+	0.335260i
$698$	−0.416746	+	6.84121i	−0.0157741	+	0.258943i
$699$	20.7373	+	17.4006i	0.784355	+	0.658152i
$700$	−4.67346	+	15.0616i	−0.176640	+	0.569275i
$701$	6.22614	+	2.26613i	0.235158	+	0.0855905i	0.456911	−	0.889512i	$-0.348956\pi$
$701$	6.22614	+	2.26613i	0.235158	+	0.0855905i	−0.221753	+	0.975103i	$0.571178\pi$
$702$	8.61440	−	9.08213i	0.325129	−	0.342783i
$703$	−27.8719	−	32.9146i	−1.05121	−	1.24140i
$704$	−39.0731	+	6.24739i	−1.47262	+	0.235457i
$705$	−29.9824	−	47.3054i	−1.12920	−	1.78162i
$706$	−10.8357	+	2.20730i	−0.407806	+	0.0830729i
$707$	1.95675	+	22.3657i	0.0735910	+	0.841149i
$708$	83.8520	+	2.88710i	3.15135	+	0.108504i
$709$	29.1973	+	5.14826i	1.09653	+	0.193347i	0.692512	−	0.721406i	$-0.256504\pi$
$709$	29.1973	+	5.14826i	1.09653	+	0.193347i	0.404013	+	0.914753i	$0.367615\pi$
$710$	−5.22012	+	13.5147i	−0.195908	+	0.507198i
$711$	−65.1120	+	37.5924i	−2.44189	+	1.40983i
$712$	−19.3781	−	7.22896i	−0.726224	−	0.270917i
$713$	−3.35396	−	1.56398i	−0.125607	−	0.0585714i
$714$	7.42233	+	12.1055i	0.277774	+	0.453036i
$715$	−3.49856	+	8.39099i	−0.130839	+	0.313805i
$716$	29.4088	+	3.59633i	1.09906	+	0.134401i
$717$	4.75702	−	54.3729i	0.177654	−	2.03059i
$718$	2.42006	+	21.1945i	0.0903157	+	0.790970i
$719$	−2.02064	−	11.4596i	−0.0753571	−	0.427371i	−0.999024	−	0.0441746i	$-0.985934\pi$
$719$	−2.02064	−	11.4596i	−0.0753571	−	0.427371i	0.923667	−	0.383197i	$-0.125177\pi$
$720$	−45.5105	+	36.1006i	−1.69608	+	1.34539i
$721$	−6.23488			−0.232199
$722$	7.86921	+	25.6919i	0.292862	+	0.956155i
$723$	−47.8533	+	47.8533i	−1.77968	+	1.77968i
$724$	5.67981	−	18.6104i	0.211088	−	0.691649i
$725$	8.78559	+	19.0720i	0.326289	+	0.708315i
$726$	45.9282	+	36.5146i	1.70456	+	1.35518i
$727$	−17.7430	−	1.55231i	−0.658052	−	0.0575721i	−0.246761	−	0.969076i	$-0.579366\pi$
$727$	−17.7430	−	1.55231i	−0.658052	−	0.0575721i	−0.411291	+	0.911504i	$0.634922\pi$
$728$	−2.82737	+	2.33419i	−0.104789	+	0.0865110i
$729$	9.16806	+	5.29318i	0.339558	+	0.196044i
$730$	19.6315	+	2.10469i	0.726596	+	0.0778982i
$731$	7.95079	+	21.8446i	0.294070	+	0.807952i
$732$	16.1770	+	6.52675i	0.597921	+	0.241235i
$733$	4.86724	−	18.1648i	0.179776	−	0.670932i	−0.815913	−	0.578175i	$-0.803765\pi$
$733$	4.86724	−	18.1648i	0.179776	−	0.670932i	0.995689	−	0.0927574i	$-0.0295681\pi$
$734$	−29.3494	−	15.9261i	−1.08330	−	0.587843i
$735$	−31.0626	−	1.42864i	−1.14576	−	0.0526962i
$736$	3.37640	−	3.69375i	0.124456	−	0.136153i
$737$	−20.1422	+	1.76221i	−0.741946	+	0.0649119i
$738$	40.0579	+	26.4996i	1.47455	+	0.975465i
$739$	28.7128	+	10.4506i	1.05622	+	0.384431i	0.811005	−	0.585039i	$-0.198921\pi$
$739$	28.7128	+	10.4506i	1.05622	+	0.384431i	0.245210	+	0.969470i	$0.421143\pi$
$740$	−7.98409	−	43.5244i	−0.293501	−	1.59999i
$741$	0.912752	−	11.0025i	0.0335308	−	0.404186i
$742$	9.35183	−	9.85960i	0.343317	−	0.361957i
$743$	−7.78004	+	3.62789i	−0.285422	+	0.133094i	−0.560057	−	0.828454i	$-0.689221\pi$
$743$	−7.78004	+	3.62789i	−0.285422	+	0.133094i	0.274635	+	0.961549i	$0.411443\pi$
$744$	−9.15424	−	35.2899i	−0.335611	−	1.29379i
$745$	−26.3855	+	5.78515i	−0.966689	+	0.211951i
$746$	−14.7321	−	16.6434i	−0.539379	−	0.609357i
$747$	−24.0005	+	16.8053i	−0.878133	+	0.614875i
$748$	−6.32601	−	19.4371i	−0.231302	−	0.710691i
$749$	−3.38359	+	1.95352i	−0.123634	+	0.0713800i
$750$	1.17837	−	48.7061i	0.0430279	−	1.77849i
$751$	−7.71588	−	21.1992i	−0.281557	−	0.773570i	−0.997177	−	0.0750813i	$-0.976078\pi$
$751$	−7.71588	−	21.1992i	−0.281557	−	0.773570i	0.715621	−	0.698489i	$-0.246144\pi$
$752$	−5.05493	+	32.1190i	−0.184334	+	1.17126i
$753$	−53.6413	+	14.3731i	−1.95480	+	0.523786i
$754$	−0.720413	+	4.82848i	−0.0262359	+	0.175843i
$755$	−1.46285	−	35.3944i	−0.0532387	−	1.28814i
$756$	27.1342	+	20.4263i	0.986862	+	0.742897i
$757$	15.4831	+	10.8414i	0.562744	+	0.394037i	0.820049	−	0.572293i	$-0.193946\pi$
$757$	15.4831	+	10.8414i	0.562744	+	0.394037i	−0.257306	+	0.966330i	$0.582835\pi$
$758$	−10.6619	−	21.3713i	−0.387257	−	0.776242i
$759$	−13.4830			−0.489400
$760$	−6.12343	+	26.8794i	−0.222120	+	0.975019i
$761$	−21.8436			−0.791829			−0.395914	−	0.918287i	$-0.629572\pi$
$761$	−21.8436			−0.791829			−0.395914	+	0.918287i	$0.629572\pi$
$762$	−20.2897	−	40.6698i	−0.735017	−	1.47331i
$763$	−9.73772	−	6.81842i	−0.352529	−	0.246843i
$764$	−3.33784	−	2.51268i	−0.120759	−	0.0909056i
$765$	−22.0770	−	20.3245i	−0.798195	−	0.734835i
$766$	2.84825	−	19.0900i	0.102911	−	0.689751i
$767$	−10.8095	+	2.89641i	−0.390310	+	0.104583i
$768$	49.2389	+	2.48387i	1.77675	+	0.0896289i
$769$	−2.81005	−	7.72056i	−0.101333	−	0.278411i	0.878658	−	0.477452i	$-0.158439\pi$
$769$	−2.81005	−	7.72056i	−0.101333	−	0.278411i	−0.979991	+	0.199041i	$0.936217\pi$
$770$	−23.6964	−	6.84827i	−0.853960	−	0.246795i
$771$	−16.0597	+	9.27206i	−0.578375	+	0.333925i
$772$	−10.1360	−	31.1435i	−0.364803	−	1.12088i
$773$	−2.72857	+	1.91057i	−0.0981400	+	0.0687184i	−0.621616	−	0.783322i	$-0.713524\pi$
$773$	−2.72857	+	1.91057i	−0.0981400	+	0.0687184i	0.523476	+	0.852040i	$0.324635\pi$
$774$	68.4890	+	77.3746i	2.46179	+	2.78117i
$775$	18.9149	+	8.92756i	0.679444	+	0.320688i
$776$	38.8296	−	10.0724i	1.39390	−	0.361579i
$777$	−43.5765	+	20.3201i	−1.56330	+	0.728978i
$778$	25.7783	−	27.1780i	0.924197	−	0.974378i
$779$	22.6978	−	2.08870i	0.813234	−	0.0748355i
$780$	6.43287	−	9.32314i	0.230334	−	0.333822i
$781$	−21.2941	−	7.75040i	−0.761961	−	0.277331i
$782$	2.15606	+	1.42631i	0.0771007	+	0.0510047i
$783$	45.0509	−	3.94145i	1.60999	−	0.140856i
$784$	12.9980	+	12.5274i	0.464214	+	0.447409i
$785$	0.756426	−	16.4468i	0.0269980	−	0.587011i
$786$	49.2714	+	26.7366i	1.75745	+	0.953662i
$787$	−3.42262	+	12.7734i	−0.122003	+	0.455322i	−0.999715	−	0.0238665i	$-0.992402\pi$
$787$	−3.42262	+	12.7734i	−0.122003	+	0.455322i	0.877712	+	0.479189i	$0.159069\pi$
$788$	−3.41489	−	1.37776i	−0.121651	−	0.0490808i
$789$	−0.226924	−	0.623468i	−0.00807870	−	0.0221960i
$790$	−28.4975	+	22.9787i	−1.01389	+	0.817546i
$791$	−10.2739	−	5.93163i	−0.365297	−	0.210904i
$792$	−57.8454	−	70.0673i	−2.05545	−	2.48973i
$793$	−2.31785	−	0.202785i	−0.0823092	−	0.00720112i
$794$	−6.70243	−	5.32868i	−0.237860	−	0.189108i
$795$	−19.4722	+	37.1943i	−0.690609	+	1.31914i
$796$	−9.67879	+	31.7134i	−0.343055	+	1.12405i
$797$	−29.1171	+	29.1171i	−1.03138	+	1.03138i	−0.0318885	+	0.999491i	$0.510152\pi$
$797$	−29.1171	+	29.1171i	−1.03138	+	1.03138i	−0.999491	+	0.0318885i	$0.989848\pi$
$798$	29.9403	−	0.926104i	1.05988	−	0.0327837i
$799$	−16.7961			−0.594204
$800$	−19.1800	+	20.7877i	−0.678115	+	0.734956i
$801$	−8.24682	−	46.7701i	−0.291387	−	1.65254i
$802$	−1.24985	−	10.9460i	−0.0441338	−	0.386517i
$803$	−2.69155	+	30.7645i	−0.0949826	+	1.08566i
$804$	25.0057	+	3.05789i	0.881883	+	0.107844i
$805$	2.88486	−	1.18709i	0.101678	−	0.0418395i
$806$	2.54181	+	4.14558i	0.0895315	+	0.146022i
$807$	−86.2827	−	40.2343i	−3.03729	−	1.41631i
$808$	−14.0742	+	37.7275i	−0.495128	+	1.32725i
$809$	19.2650	−	11.1226i	0.677321	−	0.391051i	−0.121524	−	0.992589i	$-0.538778\pi$
$809$	19.2650	−	11.1226i	0.677321	−	0.391051i	0.798845	+	0.601537i	$0.205445\pi$
$810$	−40.4037	−	15.6061i	−1.41964	−	0.548344i
$811$	−25.3042	−	4.46182i	−0.888552	−	0.156676i	−0.289302	−	0.957238i	$-0.593423\pi$
$811$	−25.3042	−	4.46182i	−0.888552	−	0.156676i	−0.599250	+	0.800562i	$0.704534\pi$
$812$	−13.2379	−	0.455791i	−0.464558	−	0.0159951i
$813$	−3.70352	−	42.3314i	−0.129888	−	1.48463i
$814$	67.8204	−	13.8155i	2.37711	−	0.484233i
$815$	−4.29067	−	0.961697i	−0.150296	−	0.0336868i
$816$	2.68692	+	25.3258i	0.0940608	+	0.886582i
$817$	48.3317	+	8.29824i	1.69091	+	0.290319i
$818$	−37.1517	+	39.1689i	−1.29898	+	1.36951i
$819$	−7.91113	−	2.87941i	−0.276437	−	0.100615i
$820$	21.2624	+	9.73704i	0.742514	+	0.340032i
$821$	−0.130008	−	0.109090i	−0.00453732	−	0.00380726i	0.640516	−	0.767945i	$-0.278720\pi$
$821$	−0.130008	−	0.109090i	−0.00453732	−	0.00380726i	−0.645053	+	0.764137i	$0.723165\pi$
$822$	1.33176	−	21.8618i	0.0464503	−	0.762518i
$823$	29.2989	+	41.8431i	1.02129	+	1.45856i	0.883690	+	0.468072i	$0.155051\pi$
$823$	29.2989	+	41.8431i	1.02129	+	1.45856i	0.137604	+	0.990487i	$0.456060\pi$
$824$	−10.0967	−	4.80681i	−0.351737	−	0.167453i
$825$	76.2035	+	0.354607i	2.65307	+	0.0123458i
$826$	−11.1351	−	28.2477i	−0.387438	−	0.982864i
$827$	8.89100	+	4.14594i	0.309170	+	0.144169i	0.571011	−	0.820943i	$-0.306552\pi$
$827$	8.89100	+	4.14594i	0.309170	+	0.144169i	−0.261840	+	0.965111i	$0.584329\pi$
$828$	11.2412	+	2.38364i	0.390658	+	0.0828372i
$829$	−41.3530	−	23.8752i	−1.43625	−	0.829219i	−0.438663	−	0.898652i	$-0.644548\pi$
$829$	−41.3530	−	23.8752i	−1.43625	−	0.829219i	−0.997587	+	0.0694328i	$0.977881\pi$
$830$	−10.2826	+	9.88853i	−0.356915	+	0.343236i
$831$	56.3598	+	67.1670i	1.95510	+	2.33000i
$832$	−6.37820	+	1.60021i	−0.221124	+	0.0554773i
$833$	−5.34882	+	7.63890i	−0.185325	+	0.264672i
$834$	−63.7723	−	21.3206i	−2.20825	−	0.738271i
$835$	−1.03295	−	7.98965i	−0.0357468	−	0.276493i
$836$	−42.2217	−	8.75467i	−1.46027	−	0.302787i
$837$	31.8521	−	31.8521i	1.10097	−	1.10097i
$838$	4.83890	+	9.69939i	0.167157	+	0.335060i
$839$	1.22790	+	6.96379i	0.0423920	+	0.240417i	0.998640	−	0.0521413i	$-0.0166046\pi$
$839$	1.22790	+	6.96379i	0.0423920	+	0.240417i	−0.956248	+	0.292558i	$0.905494\pi$
$840$	27.1124	+	14.4714i	0.935468	+	0.499310i
$841$	8.70451	−	7.30395i	0.300156	−	0.251860i
$842$	12.6988	−	9.40145i	0.437631	−	0.323996i
$843$	4.33921	+	16.1942i	0.149450	+	0.557756i
$844$	17.7052	+	27.2344i	0.609437	+	0.937447i
$845$	8.34800	−	26.2632i	0.287180	−	0.903483i
$846$	−69.4581	+	27.3799i	−2.38802	+	0.941340i
$847$	5.49571	−	20.5103i	0.188835	−	0.704742i
$848$	22.7456	−	8.75678i	0.781088	−	0.300709i
$849$	42.6500	+	7.52035i	1.46374	+	0.258098i
$850$	−12.1482	−	8.11798i	−0.416681	−	0.278444i
$851$	−5.62662	+	6.70555i	−0.192878	+	0.229863i
$852$	23.9511	+	14.9500i	0.820552	+	0.512180i
$853$	2.01358	+	4.31813i	0.0689436	+	0.147850i	0.937760	−	0.347285i	$-0.112896\pi$
$853$	2.01358	+	4.31813i	0.0689436	+	0.147850i	−0.868816	+	0.495135i	$0.835119\pi$
$854$	−0.166795	−	6.31063i	−0.00570760	−	0.215945i
$855$	−60.3310	+	19.1663i	−2.06328	+	0.655475i
$856$	−6.98545	+	0.554926i	−0.238758	+	0.0189670i
$857$	−19.2586	+	8.98044i	−0.657862	+	0.306766i	−0.722733	−	0.691128i	$-0.757114\pi$
$857$	−19.2586	+	8.98044i	−0.657862	+	0.306766i	0.0648710	+	0.997894i	$0.479336\pi$
$858$	14.7763	+	9.77500i	0.504453	+	0.333713i
$859$	−33.4873	−	28.0992i	−1.14257	−	0.958732i	−0.143052	−	0.989715i	$-0.545692\pi$
$859$	−33.4873	−	28.0992i	−1.14257	−	0.958732i	−0.999520	+	0.0309832i	$0.990136\pi$
$860$	38.7638	+	32.0742i	1.32183	+	1.09372i
$861$	4.41246	−	25.0243i	0.150376	−	0.852826i
$862$	−9.02891	−	30.4537i	−0.307526	−	1.03726i
$863$	54.1178	+	14.5008i	1.84219	+	0.493613i	0.999029	−	0.0440486i	$-0.0140256\pi$
$863$	54.1178	+	14.5008i	1.84219	+	0.493613i	0.843161	+	0.537662i	$0.180692\pi$
$864$	28.1933	+	53.9975i	0.959156	+	1.83703i
$865$	7.92883	+	15.3181i	0.269588	+	0.520830i
$866$	30.6841	−	18.8136i	1.04269	−	0.639311i
$867$	37.8901	−	10.1526i	1.28681	−	0.344801i
$868$	−10.3929	+	8.12798i	−0.352757	+	0.275882i
$869$	−36.8053	−	43.8628i	−1.24853	−	1.48794i
$870$	39.7266	−	9.81715i	1.34686	−	0.332833i
$871$	−3.30908	+	0.583479i	−0.112124	+	0.0197704i
$872$	−10.5125	−	18.5491i	−0.355999	−	0.628150i
$873$	65.1330	+	65.1330i	2.20442	+	2.20442i
$874$	4.86884	−	2.45641i	0.164691	−	0.0830893i
$875$	−16.3360	+	6.63338i	−0.552258	+	0.224249i
$876$	11.2317	−	36.8017i	0.379484	−	1.24341i
$877$	5.94667	+	4.16390i	0.200805	+	0.140605i	0.669654	−	0.742673i	$-0.266442\pi$
$877$	5.94667	+	4.16390i	0.200805	+	0.140605i	−0.468849	+	0.883278i	$0.655331\pi$
$878$	−1.63541	−	14.3226i	−0.0551923	−	0.483365i
$879$	22.4558	−	18.8427i	0.757416	−	0.635548i
$880$	−33.0942	−	29.3589i	−1.11561	−	0.989689i
$881$	0.912655	−	1.58076i	0.0307481	−	0.0532573i	−0.850242	−	0.526392i	$-0.823544\pi$
$881$	0.912655	−	1.58076i	0.0307481	−	0.0532573i	0.880990	+	0.473135i	$0.156878\pi$
$882$	−9.66688	+	40.3089i	−0.325501	+	1.35727i
$883$	−8.00389	+	17.1644i	−0.269352	+	0.577628i	−0.993734	−	0.111771i	$-0.964348\pi$
$883$	−8.00389	+	17.1644i	−0.269352	+	0.577628i	0.724382	+	0.689399i	$0.242125\pi$
$884$	−1.32882	−	3.12625i	−0.0446930	−	0.105147i
$885$	56.9315	+	74.5531i	1.91373	+	2.50608i
$886$	−8.40254	+	15.4846i	−0.282289	+	0.520215i
$887$	−5.10059	+	3.57147i	−0.171261	+	0.119918i	−0.656064	−	0.754705i	$-0.727780\pi$
$887$	−5.10059	+	3.57147i	−0.171261	+	0.119918i	0.484803	+	0.874623i	$0.338891\pi$
$888$	−86.2335	−	0.689250i	−2.89381	−	0.0231297i
$889$	−10.5725	+	12.5998i	−0.354591	+	0.422585i
$890$	−7.48283	−	21.8796i	−0.250825	−	0.733406i
$891$	23.1707	−	63.6610i	0.776248	−	2.13272i
$892$	−22.3196	−	20.0769i	−0.747317	−	0.672226i
$893$	−17.5776	+	30.7641i	−0.588213	+	1.02948i
$894$	1.39088	+	52.6234i	0.0465179	+	1.75999i
$895$	17.7330	+	27.9786i	0.592747	+	0.935222i
$896$	−6.27692	−	16.7011i	−0.209697	−	0.557946i
$897$	−2.23215	+	0.195288i	−0.0745292	+	0.00652046i
$898$	1.08722	−	17.8476i	0.0362811	−	0.595581i
$899$	−3.05064	+	17.3010i	−0.101744	+	0.577021i
$900$	−63.4707	−	13.7676i	−2.11569	−	0.458920i
$901$	6.29526	+	10.9037i	0.209726	+	0.363255i
$902$	−14.5773	+	33.5480i	−0.485372	+	1.11703i
$903$	23.1038	−	49.5464i	0.768848	−	1.64880i
$904$	−12.0645	−	17.5263i	−0.401258	−	0.582918i
$905$	20.1178	−	8.27830i	0.668740	−	0.275180i
$906$	−68.2802	−	10.1875i	−2.26846	−	0.338456i
$907$	25.8179	+	2.25877i	0.857269	+	0.0750013i	0.507310	−	0.861764i	$-0.330640\pi$
$907$	25.8179	+	2.25877i	0.857269	+	0.0750013i	0.349959	+	0.936765i	$0.386195\pi$
$908$	−19.4798	+	2.74743i	−0.646460	+	0.0911766i
$909$	−91.0574	+	16.0559i	−3.02018	+	0.532540i
$910$	−4.02221	−	0.790533i	−0.133335	−	0.0262059i
$911$		−	40.0967i		−	1.32846i	−0.747527	−	0.664232i	$-0.768759\pi$
$911$		−	40.0967i		−	1.32846i	0.747527	−	0.664232i	$-0.231241\pi$
$912$	49.1992	+	21.5829i	1.62915	+	0.714680i
$913$	−15.7780	−	15.7780i	−0.522177	−	0.522177i
$914$	16.3375	+	5.46202i	0.540398	+	0.180668i
$915$	5.82139	+	18.6140i	0.192449	+	0.615359i
$916$	−41.0530	−	30.9042i	−1.35643	−	1.02110i
$917$	1.76812	−	20.2097i	0.0583884	−	0.667383i
$918$	−25.2904	+	18.7235i	−0.834708	+	0.617968i
$919$	−24.0727	+	41.6951i	−0.794085	+	1.37539i	0.129334	+	0.991601i	$0.458716\pi$
$919$	−24.0727	+	41.6951i	−0.794085	+	1.37539i	−0.923419	+	0.383794i	$0.874617\pi$
$920$	5.58693	+	0.301722i	0.184196	+	0.00994748i
$921$	−31.1196	+	11.3266i	−1.02542	+	0.373224i
$922$	−12.8806	−	5.59688i	−0.424199	−	0.184323i
$923$	−3.63756	−	0.974680i	−0.119732	−	0.0320820i
$924$	−21.8022	+	42.8411i	−0.717241	+	1.40937i
$925$	31.9771	−	37.7507i	1.05140	−	1.24124i
$926$	−8.11287	+	7.18120i	−0.266605	+	0.235989i
$927$	−2.23795	−	25.5798i	−0.0735038	−	0.840152i
$928$	−21.0860	−	10.9439i	−0.692180	−	0.359251i
$929$	−15.3505	+	42.1753i	−0.503635	+	1.38373i	0.384066	+	0.923306i	$0.374523\pi$
$929$	−15.3505	+	42.1753i	−0.503635	+	1.38373i	−0.887701	+	0.460420i	$0.847699\pi$
$930$	24.0274	−	32.9265i	0.787891	−	1.07970i
$931$	8.39384	+	17.7913i	0.275097	+	0.583087i
$932$	11.7507	−	13.0633i	0.384906	−	0.427902i
$933$	37.2428	+	79.8674i	1.21927	+	2.61474i
$934$	−23.9126	+	4.87117i	−0.782444	+	0.159389i
$935$	12.3239	−	19.2457i	0.403034	−	0.629401i
$936$	−10.5914	−	10.7620i	−0.346189	−	0.351768i
$937$	19.7629	+	28.2243i	0.645625	+	0.922048i	0.999914	−	0.0130882i	$-0.00416622\pi$
$937$	19.7629	+	28.2243i	0.645625	+	0.922048i	−0.354290	+	0.935136i	$0.615277\pi$
$938$	−2.59143	−	8.74067i	−0.0846132	−	0.285393i
$939$	−12.7165	−	22.0256i	−0.414986	−	0.718777i
$940$	−31.3559	+	18.3925i	−1.02272	+	0.599897i
$941$	−36.9496	+	13.4486i	−1.20452	+	0.438411i	−0.864801	−	0.502115i	$-0.832555\pi$
$941$	−36.9496	+	13.4486i	−1.20452	+	0.438411i	−0.339723	+	0.940526i	$0.610333\pi$
$942$	−31.2009	−	7.48260i	−1.01658	−	0.243796i
$943$	−1.19732	−	4.46846i	−0.0389901	−	0.145513i
$944$	3.74562	−	54.3289i	0.121910	−	1.76825i
$945$	1.56805	+	37.9396i	0.0510086	+	1.23418i
$946$	−48.9739	+	61.5995i	−1.59228	+	2.00277i
$947$	−16.3884	+	23.4050i	−0.532550	+	0.760560i	−0.991807	−	0.127743i	$-0.959227\pi$
$947$	−16.3884	+	23.4050i	−0.532550	+	0.760560i	0.459257	+	0.888303i	$0.348116\pi$
$948$	33.5237	+	62.9745i	1.08880	+	2.04532i
$949$			5.13215i			0.166597i
$950$	−27.5825	+	13.7552i	−0.894895	+	0.446277i
$951$		−	41.5643i		−	1.34782i
$952$	8.01840	−	4.54437i	0.259878	−	0.147284i
$953$	8.46693	−	12.0920i	0.274271	−	0.391699i	−0.658259	−	0.752791i	$-0.728707\pi$
$953$	8.46693	−	12.0920i	0.274271	−	0.391699i	0.932530	+	0.361092i	$0.117596\pi$
$954$	43.8077	+	34.8287i	1.41833	+	1.12762i
$955$	−0.192889	−	4.66703i	−0.00624173	−	0.151022i
$956$	−35.1646	−	4.30020i	−1.13730	−	0.139078i
$957$	16.5661	+	61.8254i	0.535505	+	1.99853i
$958$	−5.23559	+	21.8313i	−0.169154	+	0.705338i
$959$	−7.44823	+	2.71093i	−0.240516	+	0.0875406i
$960$	32.7490	+	44.3373i	1.05697	+	1.43098i
$961$	−6.75049	−	11.6922i	−0.217758	−	0.377167i
$962$	11.0278	−	3.26951i	0.355550	−	0.105413i
$963$	−9.22920	−	13.1807i	−0.297407	−	0.424741i
$964$	29.9728	+	32.1104i	0.965360	+	1.03421i
$965$	19.7462	−	30.8368i	0.635654	−	0.992673i
$966$	−1.21350	−	5.95708i	−0.0390437	−	0.191666i
$967$	13.1303	+	28.1580i	0.422242	+	0.905502i	0.996239	+	0.0866442i	$0.0276143\pi$
$967$	13.1303	+	28.1580i	0.422242	+	0.905502i	−0.573997	+	0.818857i	$0.694608\pi$
$968$	24.7122	−	28.9773i	0.794281	−	0.931367i
$969$	−7.06240	+	26.8395i	−0.226877	+	0.862208i
$970$	36.2291	+	26.4374i	1.16325	+	0.848854i
$971$	−7.61328	+	20.9173i	−0.244322	+	0.671268i	0.755548	+	0.655094i	$0.227371\pi$
$971$	−7.61328	+	20.9173i	−0.244322	+	0.671268i	−0.999869	+	0.0161744i	$0.994851\pi$
$972$	−10.4837	+	16.7957i	−0.336265	+	0.538723i
$973$	2.12087	+	24.2416i	0.0679918	+	0.777150i
$974$	−6.32035	−	7.14033i	−0.202517	−	0.228791i
$975$	12.6209	−	1.04503i	0.404191	−	0.0334677i
$976$	4.59510	−	10.3480i	0.147086	−	0.331232i
$977$	−35.3320	−	9.46717i	−1.13037	−	0.302882i	−0.355297	−	0.934754i	$-0.615620\pi$
$977$	−35.3320	−	9.46717i	−1.13037	−	0.302882i	−0.775073	+	0.631872i	$0.782287\pi$
$978$	−3.41502	+	7.85928i	−0.109200	+	0.251312i
$979$	33.9871	−	12.3703i	1.08623	−	0.395357i
$980$	−1.62051	+	20.1179i	−0.0517653	+	0.642642i
$981$	24.4787	−	42.3983i	0.781544	−	1.35367i
$982$	−17.6099	−	23.7863i	−0.561955	−	0.759051i
$983$	3.61862	−	41.3610i	0.115416	−	1.31921i	−0.688834	−	0.724919i	$-0.741877\pi$
$983$	3.61862	−	41.3610i	0.115416	−	1.31921i	0.804250	−	0.594291i	$-0.202567\pi$
$984$	26.4381	−	37.1225i	0.842816	−	1.18342i
$985$	−1.22887	−	3.92932i	−0.0391549	−	0.125199i
$986$	3.89118	−	11.6390i	0.123920	−	0.370661i
$987$	27.9300	+	27.9300i	0.889023	+	0.889023i
$988$	−7.11674	−	0.837825i	−0.226414	−	0.0266547i
$989$		−	9.95266i		−	0.316476i
$990$	19.5908	−	99.6774i	0.622636	−	3.16796i
$991$	42.7855	−	7.54423i	1.35913	−	0.239650i	0.553882	−	0.832595i	$-0.313146\pi$
$991$	42.7855	−	7.54423i	1.35913	−	0.239650i	0.805243	+	0.592945i	$0.202035\pi$
$992$	−23.0965	+	5.15001i	−0.733313	+	0.163513i
$993$	−24.4249	−	2.13690i	−0.775099	−	0.0678124i
$994$	1.50779	−	10.1058i	0.0478241	−	0.320535i
$995$	−34.2822	+	14.1068i	−1.08682	+	0.447216i
$996$	15.1532	+	23.3089i	0.480148	+	0.738571i
$997$	−16.3069	+	34.9703i	−0.516445	+	1.10752i	0.459234	+	0.888315i	$0.348124\pi$
$997$	−16.3069	+	34.9703i	−0.516445	+	1.10752i	−0.975679	+	0.219204i	$0.929654\pi$
$998$	32.2889	+	14.0302i	1.02209	+	0.444119i
$999$	−53.2747	−	92.2746i	−1.68554	−	2.91944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bj.a.23.20	✓	672
4.3	odd	2	inner	380.2.bj.a.23.35	yes	672
5.2	odd	4	inner	380.2.bj.a.327.47	yes	672
19.5	even	9	inner	380.2.bj.a.43.8	yes	672
20.7	even	4	inner	380.2.bj.a.327.8	yes	672
76.43	odd	18	inner	380.2.bj.a.43.47	yes	672
95.62	odd	36	inner	380.2.bj.a.347.35	yes	672
380.347	even	36	inner	380.2.bj.a.347.20	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bj.a.23.20	✓	672	1.1	even	1	trivial
380.2.bj.a.23.35	yes	672	4.3	odd	2	inner
380.2.bj.a.43.8	yes	672	19.5	even	9	inner
380.2.bj.a.43.47	yes	672	76.43	odd	18	inner
380.2.bj.a.327.8	yes	672	20.7	even	4	inner
380.2.bj.a.327.47	yes	672	5.2	odd	4	inner
380.2.bj.a.347.20	yes	672	380.347	even	36	inner
380.2.bj.a.347.35	yes	672	95.62	odd	36	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bj (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631329 - 1.26547i) q^{2} +(-2.52409 - 1.76739i) q^{3} +(-1.20285 + 1.59786i) q^{4} +(-2.23416 + 0.0923380i) q^{5} +(-0.643051 + 4.30997i) q^{6} +(1.52327 - 0.408158i) q^{7} +(2.78144 + 0.513399i) q^{8} +(2.22131 + 6.10300i) q^{9} +O(q^{10})\)	\(q+(-0.631329 - 1.26547i) q^{2} +(-2.52409 - 1.76739i) q^{3} +(-1.20285 + 1.59786i) q^{4} +(-2.23416 + 0.0923380i) q^{5} +(-0.643051 + 4.30997i) q^{6} +(1.52327 - 0.408158i) q^{7} +(2.78144 + 0.513399i) q^{8} +(2.22131 + 6.10300i) q^{9} +(1.52734 + 2.76898i) q^{10} +(-4.28352 + 2.47309i) q^{11} +(5.86013 - 1.90724i) q^{12} +(-0.673330 + 0.471470i) q^{13} +(-1.47819 - 1.66997i) q^{14} +(5.80242 + 3.71555i) q^{15} +(-1.10631 - 3.84397i) q^{16} +(1.87271 - 0.873258i) q^{17} +(6.32081 - 6.66400i) q^{18} +(0.360371 - 4.34398i) q^{19} +(2.53981 - 3.68094i) q^{20} +(-4.56623 - 1.66197i) q^{21} +(5.83394 + 3.85935i) q^{22} +(-0.881292 + 0.0771030i) q^{23} +(-6.11323 - 6.21174i) q^{24} +(4.98295 - 0.412596i) q^{25} +(1.02173 + 0.554428i) q^{26} +(2.78704 - 10.4014i) q^{27} +(-1.18008 + 2.92492i) q^{28} +(1.43637 + 3.94638i) q^{29} +(1.03871 - 9.68854i) q^{30} +(3.62274 + 2.09159i) q^{31} +(-4.16599 + 3.82681i) q^{32} +(15.1829 + 1.32833i) q^{33} +(-2.28738 - 1.81855i) q^{34} +(-3.36553 + 1.05255i) q^{35} +(-12.4236 - 3.79164i) q^{36} +(6.99664 - 6.99664i) q^{37} +(-5.72470 + 2.28644i) q^{38} +2.53281 q^{39} +(-6.26160 - 0.890182i) q^{40} +(0.908048 + 5.14979i) q^{41} +(0.779610 + 6.82770i) q^{42} +(-0.980528 + 11.2075i) q^{43} +(1.20077 - 9.81921i) q^{44} +(-5.52630 - 13.4300i) q^{45} +(0.653957 + 1.06657i) q^{46} +(-7.36699 - 3.43528i) q^{47} +(-4.00134 + 11.6578i) q^{48} +(-3.90843 + 2.25653i) q^{49} +(-3.66801 - 6.04531i) q^{50} +(-6.27027 - 1.10562i) q^{51} +(0.0565697 - 1.64299i) q^{52} +(0.531062 + 6.07007i) q^{53} +(-14.9222 + 3.03976i) q^{54} +(9.34170 - 5.92081i) q^{55} +(4.44643 - 0.353225i) q^{56} +(-8.58709 + 10.3277i) q^{57} +(4.08722 - 4.30915i) q^{58} +(12.7934 + 4.65642i) q^{59} +(-12.9164 + 4.80220i) q^{60} +(2.16836 + 1.81947i) q^{61} +(0.359713 - 5.90497i) q^{62} +(5.87463 + 8.38984i) q^{63} +(7.47284 + 2.85598i) q^{64} +(1.46079 - 1.11551i) q^{65} +(-7.90442 - 20.0521i) q^{66} +(3.70483 + 1.72759i) q^{67} +(-0.857240 + 4.04272i) q^{68} +(2.36073 + 1.36297i) q^{69} +(3.45673 + 3.59449i) q^{70} +(2.94490 + 3.50959i) q^{71} +(3.04517 + 18.1155i) q^{72} +(3.58119 - 5.11447i) q^{73} +(-13.2713 - 4.43689i) q^{74} +(-13.3066 - 7.76536i) q^{75} +(6.50759 + 5.80097i) q^{76} +(-5.51552 + 5.51552i) q^{77} +(-1.59904 - 3.20521i) q^{78} +(2.01022 + 11.4005i) q^{79} +(2.82662 + 8.48588i) q^{80} +(-10.4923 + 8.80411i) q^{81} +(5.94365 - 4.40032i) q^{82} +(1.16760 + 4.35755i) q^{83} +(8.14808 - 5.29710i) q^{84} +(-4.10330 + 2.12392i) q^{85} +(14.8018 - 5.83477i) q^{86} +(3.34926 - 12.4996i) q^{87} +(-13.1840 + 4.67960i) q^{88} +(-7.20130 - 1.26978i) q^{89} +(-13.5064 + 15.4721i) q^{90} +(-0.833226 + 0.993000i) q^{91} +(0.936860 - 1.50092i) q^{92} +(-5.44747 - 11.6821i) q^{93} +(0.303730 + 11.4915i) q^{94} +(-0.404013 + 9.73842i) q^{95} +(17.2788 - 2.29630i) q^{96} +(12.8539 - 5.99386i) q^{97} +(5.32309 + 3.52140i) q^{98} +(-24.6083 - 20.6488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8}+O(q^{10}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8	\( 672 q - 12 q^{2} - 24 q^{5} - 36 q^{6} - 6 q^{8} - 12 q^{10} - 6 q^{12} - 24 q^{13} - 36 q^{16} - 24 q^{17} - 24 q^{18} + 36 q^{20} - 48 q^{21} - 24 q^{22} - 24 q^{25} - 60 q^{26} - 24 q^{28} - 6 q^{30} + 18 q^{32} - 60 q^{33} + 24 q^{36} - 48 q^{37} - 114 q^{38} - 42 q^{40} - 24 q^{41} - 48 q^{42} - 12 q^{45} - 12 q^{46} - 96 q^{48} - 6 q^{50} - 12 q^{52} - 24 q^{53} - 48 q^{56} - 24 q^{57} + 120 q^{58} - 12 q^{60} - 48 q^{61} + 36 q^{62} - 12 q^{65} - 96 q^{66} - 6 q^{68} - 12 q^{70} + 120 q^{72} - 24 q^{73} - 96 q^{76} - 360 q^{77} - 126 q^{78} + 48 q^{80} - 48 q^{81} + 228 q^{82} - 24 q^{85} - 132 q^{86} - 102 q^{88} + 78 q^{90} + 108 q^{92} - 60 q^{93} - 144 q^{96} - 24 q^{97} + 18 q^{98}+O(q^{100}) \) 672 * q - 12 * q^2 - 24 * q^5 - 36 * q^6 - 6 * q^8 - 12 * q^10 - 6 * q^12 - 24 * q^13 - 36 * q^16 - 24 * q^17 - 24 * q^18 + 36 * q^20 - 48 * q^21 - 24 * q^22 - 24 * q^25 - 60 * q^26 - 24 * q^28 - 6 * q^30 + 18 * q^32 - 60 * q^33 + 24 * q^36 - 48 * q^37 - 114 * q^38 - 42 * q^40 - 24 * q^41 - 48 * q^42 - 12 * q^45 - 12 * q^46 - 96 * q^48 - 6 * q^50 - 12 * q^52 - 24 * q^53 - 48 * q^56 - 24 * q^57 + 120 * q^58 - 12 * q^60 - 48 * q^61 + 36 * q^62 - 12 * q^65 - 96 * q^66 - 6 * q^68 - 12 * q^70 + 120 * q^72 - 24 * q^73 - 96 * q^76 - 360 * q^77 - 126 * q^78 + 48 * q^80 - 48 * q^81 + 228 * q^82 - 24 * q^85 - 132 * q^86 - 102 * q^88 + 78 * q^90 + 108 * q^92 - 60 * q^93 - 144 * q^96 - 24 * q^97 + 18 * q^98

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