LMFDB - Embedded newform 471.2.q.b.19.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(19,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 62]))

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

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

chi := DirichletCharacter("471.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.q (of order $39$, degree $24$, 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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			19.13
Character	$\chi$	$=$	471.19
Dual form			471.2.q.b.124.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10415 + 0.518627i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.38758 + 1.25310i) q^{4} +(-0.272381 + 0.204681i) q^{5} +(-1.50122 - 1.56294i) q^{6} +(2.92878 - 1.53714i) q^{7} +(1.12970 + 1.00083i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(2.10415 + 0.518627i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.38758 + 1.25310i) q^{4} +(-0.272381 + 0.204681i) q^{5} +(-1.50122 - 1.56294i) q^{6} +(2.92878 - 1.53714i) q^{7} +(1.12970 + 1.00083i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.679283 + 0.289416i) q^{10} +(2.38186 + 2.47977i) q^{11} +(-1.34822 - 2.33518i) q^{12} +(2.48774 - 4.30889i) q^{13} +(6.95981 - 1.71544i) q^{14} +(0.339608 - 0.0274160i) q^{15} +(-1.20549 - 1.74646i) q^{16} +(-2.43066 + 1.82653i) q^{17} +(0.433481 + 2.12333i) q^{18} +(-0.449057 + 2.19963i) q^{19} +(-0.906814 + 0.147372i) q^{20} +(-3.29693 - 0.266156i) q^{21} +(3.72571 + 6.45312i) q^{22} +(4.02650 + 5.83339i) q^{23} +(-0.419904 - 1.44968i) q^{24} +(-1.35879 + 4.69109i) q^{25} +(7.46929 - 7.77636i) q^{26} +(0.120537 - 0.992709i) q^{27} +8.91888 q^{28} +(0.0334233 - 0.275266i) q^{29} +(0.728806 + 0.118443i) q^{30} +(-6.52433 - 7.99085i) q^{31} +(-2.70117 - 7.12239i) q^{32} +(-0.687766 - 3.36890i) q^{33} +(-6.06178 + 2.58268i) q^{34} +(-0.483120 + 1.01815i) q^{35} +(-0.108575 + 2.69425i) q^{36} +(-2.17614 - 1.63526i) q^{37} +(-2.08567 + 4.39546i) q^{38} +(-4.40557 + 2.31222i) q^{39} +(-0.512559 - 0.0413780i) q^{40} +(2.10221 - 3.04558i) q^{41} +(-6.79921 - 2.26991i) q^{42} +(-0.763589 + 0.482864i) q^{43} +(2.57946 + 8.90534i) q^{44} +(-0.301686 - 0.158337i) q^{45} +(5.44702 + 14.3626i) q^{46} +(-5.99054 - 2.55233i) q^{47} +(0.0854485 + 2.12038i) q^{48} +(2.23851 - 3.24304i) q^{49} +(-5.29203 + 9.16606i) q^{50} +(3.03059 - 0.244654i) q^{51} +(11.3391 - 7.17042i) q^{52} +(-7.51281 + 2.50814i) q^{53} +(0.768474 - 2.02630i) q^{54} +(-1.15633 - 0.187922i) q^{55} +(4.84707 + 1.19469i) q^{56} +(1.55516 - 1.61910i) q^{57} +(0.213088 - 0.561868i) q^{58} +(-0.929649 + 0.823597i) q^{59} +(0.845195 + 0.360104i) q^{60} +(-2.63996 + 12.9314i) q^{61} +(-9.58392 - 20.1977i) q^{62} +(2.64428 + 1.98705i) q^{63} +(-1.47822 - 12.1742i) q^{64} +(0.204335 + 1.68285i) q^{65} +(0.300038 - 7.44538i) q^{66} +(-4.30980 - 3.81815i) q^{67} +(-8.09221 + 1.31511i) q^{68} +(-0.285409 - 7.08235i) q^{69} +(-1.54460 + 1.89179i) q^{70} +(-10.0339 + 3.34982i) q^{71} +(-0.419904 + 1.44968i) q^{72} +(-5.24729 - 3.31819i) q^{73} +(-3.73084 - 4.56945i) q^{74} +(3.65566 - 3.23863i) q^{75} +(-3.82850 + 4.68907i) q^{76} +(10.7877 + 3.60147i) q^{77} +(-10.4692 + 2.58042i) q^{78} +(-2.08490 + 0.513881i) q^{79} +(0.685819 + 0.228960i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(6.00290 - 5.31811i) q^{82} +(3.79458 + 4.64751i) q^{83} +(-7.53815 - 4.76684i) q^{84} +(0.288211 - 0.995020i) q^{85} +(-1.85713 + 0.620003i) q^{86} +(-0.175369 + 0.214788i) q^{87} +(0.208958 + 5.18523i) q^{88} +(16.5488 - 2.68944i) q^{89} +(-0.552676 - 0.489629i) q^{90} +(0.662663 - 16.4438i) q^{91} +(2.30377 + 18.9733i) q^{92} +(1.24346 + 10.2408i) q^{93} +(-11.2813 - 8.47736i) q^{94} +(-0.327907 - 0.691049i) q^{95} +(-1.52368 + 7.46346i) q^{96} +(17.4334 + 7.42767i) q^{97} +(6.39209 - 5.66289i) q^{98} +(-1.21927 + 3.21495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) $ 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{31}{39}\right)$

Coefficient data

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

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

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

$2$	2.10415	+	0.518627i	1.48786	+	0.366725i	0.897717	−	0.440573i	$-0.145225\pi$
$2$	2.10415	+	0.518627i	1.48786	+	0.366725i	0.590144	+	0.807298i	$0.299071\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	2.38758	+	1.25310i	1.19379	+	0.626548i
$5$	−0.272381	+	0.204681i	−0.121812	+	0.0915360i	−0.659902	−	0.751351i	$-0.729402\pi$
$5$	−0.272381	+	0.204681i	−0.121812	+	0.0915360i	0.538090	+	0.842887i	$0.319146\pi$
$6$	−1.50122	−	1.56294i	−0.612871	−	0.638066i
$7$	2.92878	−	1.53714i	1.10698	−	0.580986i	0.190746	−	0.981639i	$-0.438909\pi$
$7$	2.92878	−	1.53714i	1.10698	−	0.580986i	0.916230	+	0.400654i	$0.131217\pi$
$8$	1.12970	+	1.00083i	0.399410	+	0.353846i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−0.679283	+	0.289416i	−0.214808	+	0.0915212i
$11$	2.38186	+	2.47977i	0.718156	+	0.747680i	0.975825	−	0.218553i	$-0.0701338\pi$
$11$	2.38186	+	2.47977i	0.718156	+	0.747680i	−0.257669	+	0.966233i	$0.582954\pi$
$12$	−1.34822	−	2.33518i	−0.389197	−	0.674109i
$13$	2.48774	−	4.30889i	0.689974	−	1.19507i	−0.281871	−	0.959452i	$-0.590955\pi$
$13$	2.48774	−	4.30889i	0.689974	−	1.19507i	0.971846	−	0.235619i	$-0.0757116\pi$
$14$	6.95981	−	1.71544i	1.86009	−	0.458471i
$15$	0.339608	−	0.0274160i	0.0876864	−	0.00707878i
$16$	−1.20549	−	1.74646i	−0.301373	−	0.436614i
$17$	−2.43066	+	1.82653i	−0.589523	+	0.442998i	−0.853178	−	0.521619i	$-0.825328\pi$
$17$	−2.43066	+	1.82653i	−0.589523	+	0.442998i	0.263656	+	0.964617i	$0.415072\pi$
$18$	0.433481	+	2.12333i	0.102172	+	0.500474i
$19$	−0.449057	+	2.19963i	−0.103021	+	0.504629i	0.895235	+	0.445594i	$0.147008\pi$
$19$	−0.449057	+	2.19963i	−0.103021	+	0.504629i	−0.998256	+	0.0590351i	$0.981198\pi$
$20$	−0.906814	+	0.147372i	−0.202770	+	0.0329533i
$21$	−3.29693	−	0.266156i	−0.719449	−	0.0580799i
$22$	3.72571	+	6.45312i	0.794324	+	1.37581i
$23$	4.02650	+	5.83339i	0.839583	+	1.21635i	0.974253	+	0.225456i	$0.0723871\pi$
$23$	4.02650	+	5.83339i	0.839583	+	1.21635i	−0.134670	+	0.990890i	$0.542998\pi$
$24$	−0.419904	−	1.44968i	−0.0857126	−	0.295914i
$25$	−1.35879	+	4.69109i	−0.271758	+	0.938218i
$26$	7.46929	−	7.77636i	1.46485	−	1.52507i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	8.91888			1.68551
$29$	0.0334233	−	0.275266i	0.00620656	−	0.0511156i	−0.989277	−	0.146055i	$-0.953343\pi$
$29$	0.0334233	−	0.275266i	0.00620656	−	0.0511156i	0.995483	+	0.0949389i	$0.0302656\pi$
$30$	0.728806	+	0.118443i	0.133061	+	0.0216246i
$31$	−6.52433	−	7.99085i	−1.17180	−	1.43520i	−0.877558	−	0.479470i	$-0.840829\pi$
$31$	−6.52433	−	7.99085i	−1.17180	−	1.43520i	−0.294246	−	0.955730i	$-0.595068\pi$
$32$	−2.70117	−	7.12239i	−0.477503	−	1.25907i
$33$	−0.687766	−	3.36890i	−0.119725	−	0.586450i
$34$	−6.06178	+	2.58268i	−1.03959	+	0.442926i
$35$	−0.483120	+	1.01815i	−0.0816621	+	0.172099i
$36$	−0.108575	+	2.69425i	−0.0180958	+	0.449042i
$37$	−2.17614	−	1.63526i	−0.357755	−	0.268835i	0.406634	−	0.913591i	$-0.366703\pi$
$37$	−2.17614	−	1.63526i	−0.357755	−	0.268835i	−0.764389	+	0.644756i	$0.776959\pi$
$38$	−2.08567	+	4.39546i	−0.338341	+	0.713038i
$39$	−4.40557	+	2.31222i	−0.705455	+	0.370251i
$40$	−0.512559	−	0.0413780i	−0.0810427	−	0.00654244i
$41$	2.10221	−	3.04558i	0.328311	−	0.475640i	−0.623718	−	0.781650i	$-0.714379\pi$
$41$	2.10221	−	3.04558i	0.328311	−	0.475640i	0.952028	+	0.306009i	$0.0989939\pi$
$42$	−6.79921	−	2.26991i	−1.04914	−	0.350255i
$43$	−0.763589	+	0.482864i	−0.116446	+	0.0736361i	−0.591419	−	0.806364i	$-0.701432\pi$
$43$	−0.763589	+	0.482864i	−0.116446	+	0.0736361i	0.474973	+	0.880000i	$0.342458\pi$
$44$	2.57946	+	8.90534i	0.388869	+	1.34253i
$45$	−0.301686	−	0.158337i	−0.0449727	−	0.0236035i
$46$	5.44702	+	14.3626i	0.803119	+	2.11765i
$47$	−5.99054	−	2.55233i	−0.873811	−	0.372296i	−0.0919607	−	0.995763i	$-0.529313\pi$
$47$	−5.99054	−	2.55233i	−0.873811	−	0.372296i	−0.781850	+	0.623467i	$0.785724\pi$
$48$	0.0854485	+	2.12038i	0.0123334	+	0.306051i
$49$	2.23851	−	3.24304i	0.319787	−	0.463291i
$50$	−5.29203	+	9.16606i	−0.748406	+	1.29628i
$51$	3.03059	−	0.244654i	0.424367	−	0.0342585i
$52$	11.3391	−	7.17042i	1.57245	−	0.994359i
$53$	−7.51281	+	2.50814i	−1.03196	+	0.344520i	−0.781698	−	0.623657i	$-0.785646\pi$
$53$	−7.51281	+	2.50814i	−1.03196	+	0.344520i	−0.250265	+	0.968177i	$0.580518\pi$
$54$	0.768474	−	2.02630i	0.104576	−	0.275744i
$55$	−1.15633	−	0.187922i	−0.155920	−	0.0253394i
$56$	4.84707	+	1.19469i	0.647717	+	0.159648i
$57$	1.55516	−	1.61910i	0.205987	−	0.214455i
$58$	0.213088	−	0.561868i	0.0279799	−	0.0737768i
$59$	−0.929649	+	0.823597i	−0.121030	+	0.107223i	−0.721467	−	0.692449i	$-0.756532\pi$
$59$	−0.929649	+	0.823597i	−0.121030	+	0.107223i	0.600437	+	0.799672i	$0.294993\pi$
$60$	0.845195	+	0.360104i	0.109114	+	0.0464892i
$61$	−2.63996	+	12.9314i	−0.338012	+	1.65569i	0.355074	+	0.934838i	$0.384456\pi$
$61$	−2.63996	+	12.9314i	−0.338012	+	1.65569i	−0.693086	+	0.720855i	$0.743749\pi$
$62$	−9.58392	−	20.1977i	−1.21716	−	2.56511i
$63$	2.64428	+	1.98705i	0.333148	+	0.250345i
$64$	−1.47822	−	12.1742i	−0.184778	−	1.52178i
$65$	0.204335	+	1.68285i	0.0253446	+	0.208732i
$66$	0.300038	−	7.44538i	0.0369322	−	0.916463i
$67$	−4.30980	−	3.81815i	−0.526526	−	0.466461i	0.357491	−	0.933917i	$-0.383632\pi$
$67$	−4.30980	−	3.81815i	−0.526526	−	0.466461i	−0.884017	+	0.467456i	$0.845171\pi$
$68$	−8.09221	+	1.31511i	−0.981324	+	0.159481i
$69$	−0.285409	−	7.08235i	−0.0343592	−	0.852615i
$70$	−1.54460	+	1.89179i	−0.184615	+	0.226112i
$71$	−10.0339	+	3.34982i	−1.19081	+	0.397550i	−0.841914	−	0.539612i	$-0.818571\pi$
$71$	−10.0339	+	3.34982i	−1.19081	+	0.397550i	−0.348894	+	0.937162i	$0.613443\pi$
$72$	−0.419904	+	1.44968i	−0.0494862	+	0.170846i
$73$	−5.24729	−	3.31819i	−0.614149	−	0.388364i	0.190868	−	0.981616i	$-0.438870\pi$
$73$	−5.24729	−	3.31819i	−0.614149	−	0.388364i	−0.805017	+	0.593251i	$0.797844\pi$
$74$	−3.73084	−	4.56945i	−0.433701	−	0.531187i
$75$	3.65566	−	3.23863i	0.422120	−	0.373965i
$76$	−3.82850	+	4.68907i	−0.439159	+	0.537873i
$77$	10.7877	+	3.60147i	1.22937	+	0.410425i
$78$	−10.4692	+	2.58042i	−1.18540	+	0.292175i
$79$	−2.08490	+	0.513881i	−0.234569	+	0.0578161i	−0.354848	−	0.934924i	$-0.615467\pi$
$79$	−2.08490	+	0.513881i	−0.234569	+	0.0578161i	0.120279	+	0.992740i	$0.461621\pi$
$80$	0.685819	+	0.228960i	0.0766768	+	0.0255985i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	6.00290	−	5.31811i	0.662910	−	0.587287i
$83$	3.79458	+	4.64751i	0.416509	+	0.510131i	0.939660	−	0.342109i	$-0.111141\pi$
$83$	3.79458	+	4.64751i	0.416509	+	0.510131i	−0.523151	+	0.852240i	$0.675244\pi$
$84$	−7.53815	−	4.76684i	−0.822480	−	0.520105i
$85$	0.288211	−	0.995020i	0.0312609	−	0.107925i
$86$	−1.85713	+	0.620003i	−0.200260	+	0.0668566i
$87$	−0.175369	+	0.214788i	−0.0188016	+	0.0230277i
$88$	0.208958	+	5.18523i	0.0222750	+	0.552748i
$89$	16.5488	−	2.68944i	1.75417	−	0.285080i	0.803505	−	0.595298i	$-0.202966\pi$
$89$	16.5488	−	2.68944i	1.75417	−	0.285080i	0.950666	+	0.310218i	$0.100402\pi$
$90$	−0.552676	−	0.489629i	−0.0582572	−	0.0516114i
$91$	0.662663	−	16.4438i	0.0694660	−	1.72378i
$92$	2.30377	+	18.9733i	0.240185	+	1.97810i
$93$	1.24346	+	10.2408i	0.128941	+	1.06192i
$94$	−11.2813	−	8.47736i	−1.16358	−	0.874373i
$95$	−0.327907	−	0.691049i	−0.0336425	−	0.0709001i
$96$	−1.52368	+	7.46346i	−0.155509	+	0.761736i
$97$	17.4334	+	7.42767i	1.77009	+	0.754166i	0.992034	+	0.125974i	$0.0402054\pi$
$97$	17.4334	+	7.42767i	1.77009	+	0.754166i	0.778058	+	0.628192i	$0.216205\pi$
$98$	6.39209	−	5.66289i	0.645698	−	0.572039i
$99$	−1.21927	+	3.21495i	−0.122541	+	0.323115i
$100$	−9.12260	+	9.49763i	−0.912260	+	0.949763i
$101$	−11.7853	−	2.90483i	−1.17269	−	0.289041i	−0.395592	−	0.918426i	$-0.629461\pi$
$101$	−11.7853	−	2.90483i	−1.17269	−	0.289041i	−0.777093	+	0.629385i	$0.783307\pi$
$102$	6.50371	+	1.05696i	0.643963	+	0.104654i
$103$	−3.36376	+	8.86950i	−0.331441	+	0.873937i	0.660908	+	0.750467i	$0.270172\pi$
$103$	−3.36376	+	8.86950i	−0.331441	+	0.873937i	−0.992348	+	0.123470i	$0.960598\pi$
$104$	7.12286	−	2.37796i	0.698454	−	0.233178i
$105$	0.952496	−	0.602322i	0.0929541	−	0.0587806i
$106$	−17.1089	+	1.38117i	−1.66176	+	0.134151i
$107$	5.35603	−	9.27691i	0.517786	−	0.896833i	−0.482000	−	0.876171i	$-0.660089\pi$
$107$	5.35603	−	9.27691i	0.517786	−	0.896833i	0.999787	−	0.0206613i	$-0.00657717\pi$
$108$	1.53175	−	2.21912i	0.147393	−	0.213535i
$109$	−0.136825	−	3.39529i	−0.0131055	−	0.325209i	−0.992422	−	0.122876i	$-0.960788\pi$
$109$	−0.136825	−	3.39529i	−0.0131055	−	0.325209i	0.979317	−	0.202334i	$-0.0648526\pi$
$110$	−2.33564	−	0.995123i	−0.222695	−	0.0948813i
$111$	0.965259	+	2.54518i	0.0916183	+	0.241578i
$112$	−6.21518	−	3.26198i	−0.587279	−	0.308228i
$113$	5.40024	+	18.6438i	0.508012	+	1.75386i	0.645909	+	0.763414i	$0.276478\pi$
$113$	5.40024	+	18.6438i	0.508012	+	1.75386i	−0.137897	+	0.990447i	$0.544034\pi$
$114$	4.11201	−	2.60028i	0.385125	−	0.243538i
$115$	−2.29072	−	0.764755i	−0.213611	−	0.0713138i
$116$	0.424736	−	0.615336i	0.0394357	−	0.0571325i
$117$	4.95934	+	0.400360i	0.458491	+	0.0370132i
$118$	−2.38326	+	1.25083i	−0.219397	+	0.115149i
$119$	−4.31126	+	9.08578i	−0.395212	+	0.832892i
$120$	0.411095	+	0.308918i	0.0375276	+	0.0282002i
$121$	−0.0331193	+	0.821846i	−0.00301084	+	0.0747133i
$122$	−12.2614	+	25.8405i	−1.11010	+	2.33948i
$123$	−3.40453	+	1.45054i	−0.306976	+	0.130790i
$124$	−5.56402	−	27.2544i	−0.499664	−	2.44752i
$125$	−1.19416	−	3.14874i	−0.106809	−	0.281632i
$126$	4.53344	+	5.55245i	0.403871	+	0.494652i
$127$	0.551546	+	0.0896350i	0.0489418	+	0.00795382i	0.184833	−	0.982770i	$-0.440826\pi$
$127$	0.551546	+	0.0896350i	0.0489418	+	0.00795382i	−0.135891	+	0.990724i	$0.543390\pi$
$128$	1.36714	−	11.2594i	0.120839	−	0.995200i
$129$	0.903452			0.0795445
$130$	−0.442820	+	3.64695i	−0.0388378	+	0.319858i
$131$	−1.63868	+	1.70605i	−0.143172	+	0.149058i	−0.788927	−	0.614486i	$-0.789363\pi$
$131$	−1.63868	+	1.70605i	−0.143172	+	0.149058i	0.645755	+	0.763545i	$0.276543\pi$
$132$	2.57946	−	8.90534i	0.224514	−	0.775111i
$133$	2.06595	+	7.13250i	0.179141	+	0.618466i
$134$	−7.08828	−	10.2691i	−0.612334	−	0.887119i
$135$	0.170356	+	0.295066i	0.0146620	+	0.0253952i
$136$	−4.57396	−	0.369249i	−0.392214	−	0.0316628i
$137$	21.9663	−	3.56987i	1.87671	−	0.304995i	0.888591	−	0.458701i	$-0.151685\pi$
$137$	21.9663	−	3.56987i	1.87671	−	0.304995i	0.988117	+	0.153706i	$0.0491210\pi$
$138$	3.07256	−	15.0504i	0.261553	−	1.28117i
$139$	−3.92833	−	19.2423i	−0.333197	−	1.63211i	−0.708859	−	0.705350i	$-0.750790\pi$
$139$	−3.92833	−	19.2423i	−0.333197	−	1.63211i	0.375662	−	0.926757i	$-0.377415\pi$
$140$	−2.42933	+	1.82552i	−0.205316	+	0.154285i
$141$	3.69901	+	5.35895i	0.311513	+	0.451305i
$142$	−22.8502	+	1.84466i	−1.91755	+	0.154801i
$143$	16.6105	−	4.09412i	1.38904	−	0.342368i
$144$	1.06105	−	1.83780i	0.0884210	−	0.153150i
$145$	0.0472378	+	0.0818182i	0.00392288	+	0.00679463i
$146$	−9.32021	−	9.70336i	−0.771346	−	0.803056i
$147$	−3.62525	+	1.54458i	−0.299006	+	0.127395i
$148$	−3.14656	−	6.63122i	−0.258645	−	0.545083i
$149$	5.51917	+	4.88956i	0.452148	+	0.400568i	0.858227	−	0.513269i	$-0.171566\pi$
$149$	5.51917	+	4.88956i	0.452148	+	0.400568i	−0.406079	+	0.913838i	$0.633104\pi$
$150$	9.37172	−	4.91866i	0.765198	−	0.401607i
$151$	−5.48624	−	5.71179i	−0.446464	−	0.464819i	0.459497	−	0.888179i	$-0.348030\pi$
$151$	−5.48624	−	5.71179i	−0.446464	−	0.464819i	−0.905961	+	0.423361i	$0.860850\pi$
$152$	−2.70875	+	2.03549i	−0.219709	+	0.165100i
$153$	−2.69218	−	1.41297i	−0.217650	−	0.114232i
$154$	20.8312	+	13.1728i	1.67862	+	1.06150i
$155$	3.41267	+	0.841149i	0.274113	+	0.0675627i
$156$	−13.4161			−1.07414
$157$	−0.0118910	−	12.5300i	−0.000949005	−	1.00000i
$157$	−0.0118910	−	12.5300i	−0.000949005	−	1.00000i
$158$	−4.65345			−0.370209
$159$	7.69027	+	1.89548i	0.609878	+	0.150321i
$160$	2.19356	+	1.38712i	0.173416	+	0.109662i
$161$	20.7595	+	10.8954i	1.63608	+	0.858680i
$162$	−1.73249	+	1.30188i	−0.136118	+	0.102286i
$163$	6.62518	+	6.89755i	0.518924	+	0.540257i	0.928165	−	0.372169i	$-0.121386\pi$
$163$	6.62518	+	6.89755i	0.518924	+	0.540257i	−0.409241	+	0.912427i	$0.634206\pi$
$164$	8.83561	−	4.63728i	0.689945	−	0.362111i
$165$	0.876883	+	0.776850i	0.0682652	+	0.0604777i
$166$	5.57405	+	11.7471i	0.432630	+	0.911748i
$167$	6.91299	−	2.94535i	0.534944	−	0.227918i	−0.107563	−	0.994198i	$-0.534305\pi$
$167$	6.91299	−	2.94535i	0.534944	−	0.227918i	0.642507	+	0.766280i	$0.277895\pi$
$168$	−3.45817	−	3.60034i	−0.266804	−	0.277772i
$169$	−5.87768	−	10.1804i	−0.452129	−	0.783111i
$170$	1.12248	−	1.94420i	0.0860907	−	0.149113i
$171$	−2.17976	+	0.537263i	−0.166691	+	0.0410855i
$172$	−2.42820	+	0.196025i	−0.185149	+	0.0149467i
$173$	4.27746	+	6.19697i	0.325209	+	0.471147i	0.951152	−	0.308722i	$-0.0999013\pi$
$173$	4.27746	+	6.19697i	0.325209	+	0.471147i	−0.625943	+	0.779869i	$0.715286\pi$
$174$	−0.480399	+	0.360997i	−0.0364190	+	0.0273671i
$175$	3.23128	+	15.8278i	0.244262	+	1.19647i
$176$	1.45951	−	7.14916i	0.110015	−	0.538888i
$177$	1.22591	−	0.199231i	0.0921454	−	0.0149751i
$178$	36.2161	+	2.92366i	2.71451	+	0.219138i
$179$	1.06547	+	1.84545i	0.0796370	+	0.137935i	0.903093	−	0.429444i	$-0.141291\pi$
$179$	1.06547	+	1.84545i	0.0796370	+	0.137935i	−0.823456	+	0.567380i	$0.807957\pi$
$180$	−0.521887	−	0.756084i	−0.0388992	−	0.0563552i
$181$	−1.00783	−	3.47943i	−0.0749114	−	0.258624i	0.914318	−	0.404997i	$-0.132727\pi$
$181$	−1.00783	−	3.47943i	−0.0749114	−	0.258624i	−0.989230	+	0.146373i	$0.953240\pi$
$182$	9.92255	−	34.2566i	0.735509	−	2.53927i
$183$	9.14265	−	9.51851i	0.675844	−	0.703628i
$184$	−1.28948	+	10.6198i	−0.0950617	+	0.782904i
$185$	0.927444			0.0681871
$186$	−2.69474	+	22.1932i	−0.197588	+	1.62728i
$187$	−10.3189	−	1.67698i	−0.754590	−	0.122633i
$188$	−11.1046	−	13.6006i	−0.809883	−	0.991927i
$189$	−1.17291	−	3.09271i	−0.0853167	−	0.224962i
$190$	−0.331569	−	1.62413i	−0.0240546	−	0.117827i
$191$	−8.50779	+	3.62483i	−0.615602	+	0.262283i	−0.677178	−	0.735819i	$-0.736797\pi$
$191$	−8.50779	+	3.62483i	−0.615602	+	0.262283i	0.0615764	+	0.998102i	$0.480387\pi$
$192$	−5.25734	+	11.0796i	−0.379416	+	0.799602i
$193$	−0.516470	+	12.8161i	−0.0371763	+	0.922521i	0.867763	+	0.496979i	$0.165557\pi$
$193$	−0.516470	+	12.8161i	−0.0371763	+	0.922521i	−0.904939	+	0.425542i	$0.860084\pi$
$194$	32.8303	+	24.6704i	2.35708	+	1.77123i
$195$	0.726724	−	1.53154i	0.0520418	−	0.109676i
$196$	9.40844	−	4.93793i	0.672031	−	0.352709i
$197$	−4.86881	−	0.393051i	−0.346888	−	0.0280037i	−0.0942050	−	0.995553i	$-0.530031\pi$
$197$	−4.86881	−	0.393051i	−0.346888	−	0.0280037i	−0.252683	+	0.967549i	$0.581313\pi$
$198$	−4.23289	+	6.13240i	−0.300818	+	0.435811i
$199$	−12.1061	−	4.04161i	−0.858179	−	0.286502i	−0.146676	−	0.989185i	$-0.546857\pi$
$199$	−12.1061	−	4.04161i	−0.858179	−	0.286502i	−0.711504	+	0.702682i	$0.751986\pi$
$200$	−6.23000	+	3.93961i	−0.440528	+	0.278573i
$201$	1.60193	+	5.53050i	0.112991	+	0.390091i
$202$	−23.2916	−	12.2244i	−1.63879	−	0.860106i
$203$	−0.325234	−	0.857571i	−0.0228269	−	0.0601897i
$204$	7.54234	+	3.21349i	0.528069	+	0.224989i
$205$	0.0507698	+	1.25984i	0.00354592	+	0.0879911i
$206$	−11.6778	+	16.9182i	−0.813632	+	1.17875i
$207$	−3.54405	+	6.13847i	−0.246328	+	0.426653i
$208$	−10.5242	+	0.849604i	−0.729725	+	0.0589095i
$209$	−6.52417	+	4.12563i	−0.451286	+	0.285376i
$210$	2.31658	−	0.773388i	0.159859	−	0.0533688i
$211$	3.83344	−	10.1079i	0.263905	−	0.695860i	−0.735919	−	0.677070i	$-0.763249\pi$
$211$	3.83344	−	10.1079i	0.263905	−	0.695860i	0.999823	−	0.0187898i	$-0.00598133\pi$
$212$	−21.0803	−	3.42589i	−1.44780	−	0.235291i
$213$	10.2709	+	2.53156i	0.703753	+	0.173460i
$214$	16.0812	−	16.7423i	1.09929	−	1.14448i
$215$	0.109154	−	0.287815i	0.00744422	−	0.0196288i
$216$	1.12970	−	1.00083i	0.0768665	−	0.0680977i
$217$	−31.3914	−	13.3746i	−2.13099	−	0.907930i
$218$	1.47299	−	7.21516i	0.0997632	−	0.488673i
$219$	2.66150	+	5.60900i	0.179848	+	0.379021i
$220$	−2.52535	−	1.89768i	−0.170259	−	0.127941i
$221$	1.82344	+	15.0174i	0.122658	+	1.01018i
$222$	0.711054	+	5.85606i	0.0477228	+	0.393033i
$223$	0.411817	−	10.2191i	0.0275773	−	0.684324i	−0.924989	−	0.379994i	$-0.875926\pi$
$223$	0.411817	−	10.2191i	0.0275773	−	0.684324i	0.952566	−	0.304331i	$-0.0984328\pi$
$224$	−18.8593	−	16.7079i	−1.26009	−	1.11634i
$225$	−4.82067	+	0.783435i	−0.321378	+	0.0522290i
$226$	1.69376	+	42.0301i	0.112667	+	2.79580i
$227$	15.9101	−	19.4863i	1.05599	−	1.29335i	0.101585	−	0.994827i	$-0.467609\pi$
$227$	15.9101	−	19.4863i	1.05599	−	1.29335i	0.954403	−	0.298523i	$-0.0964938\pi$
$228$	5.74196	−	1.91695i	0.380270	−	0.126953i
$229$	4.36737	−	15.0779i	0.288604	−	0.996375i	−0.676919	−	0.736057i	$-0.736685\pi$
$229$	4.36737	−	15.0779i	0.288604	−	0.996375i	0.965523	−	0.260318i	$-0.0838274\pi$
$230$	−4.42341	−	2.79719i	−0.291671	−	0.184442i
$231$	−7.19280	−	8.80958i	−0.473252	−	0.579628i
$232$	0.313252	−	0.277517i	0.0205660	−	0.0182199i
$233$	1.34029	−	1.64156i	0.0878055	−	0.107542i	−0.728834	−	0.684691i	$-0.759937\pi$
$233$	1.34029	−	1.64156i	0.0878055	−	0.107542i	0.816639	+	0.577149i	$0.195835\pi$
$234$	10.2276	+	3.41447i	0.668598	+	0.223211i
$235$	2.15412	−	0.530943i	0.140519	−	0.0346349i
$236$	−3.25165	+	0.801461i	−0.211665	+	0.0521707i
$237$	2.03679	+	0.679979i	0.132303	+	0.0441694i
$238$	−13.7837	+	16.8819i	−0.893463	+	1.09429i
$239$	−1.45599	+	1.28990i	−0.0941803	+	0.0834364i	−0.708899	−	0.705310i	$-0.750808\pi$
$239$	−1.45599	+	1.28990i	−0.0941803	+	0.0834364i	0.614719	+	0.788746i	$0.289269\pi$
$240$	−0.457276	−	0.560061i	−0.0295170	−	0.0361518i
$241$	15.4972	+	9.79981i	0.998260	+	0.631261i	0.930443	−	0.366437i	$-0.119422\pi$
$241$	15.4972	+	9.79981i	0.998260	+	0.631261i	0.0678168	+	0.997698i	$0.478397\pi$
$242$	−0.495920	+	1.71211i	−0.0318789	+	0.110059i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−22.5074	+	27.5665i	−1.44089	+	1.76477i
$245$	0.0540614	+	1.34152i	0.00345385	+	0.0857065i
$246$	−7.91594	+	1.28647i	−0.504702	+	0.0820221i
$247$	8.36081	+	7.40703i	0.531986	+	0.471298i
$248$	0.626926	−	15.5570i	0.0398099	−	0.987871i
$249$	−0.723202	−	5.95610i	−0.0458311	−	0.377453i
$250$	−0.879673	−	7.24476i	−0.0556354	−	0.458199i
$251$	6.31673	+	4.74672i	0.398709	+	0.299610i	0.781119	−	0.624383i	$-0.214649\pi$
$251$	6.31673	+	4.74672i	0.398709	+	0.299610i	−0.382410	+	0.923993i	$0.624906\pi$
$252$	3.82346	+	8.05777i	0.240855	+	0.507592i
$253$	−4.87495	+	23.8791i	−0.306486	+	1.50127i
$254$	1.11405	+	0.474653i	0.0699018	+	0.0297824i
$255$	−0.775397	+	0.686942i	−0.0485573	+	0.0430180i
$256$	0.0185961	−	0.0490340i	0.00116226	−	0.00306462i
$257$	−17.0896	+	17.7922i	−1.06602	+	1.10985i	−0.0723676	+	0.997378i	$0.523055\pi$
$257$	−17.0896	+	17.7922i	−1.06602	+	1.10985i	−0.993655	+	0.112469i	$0.964124\pi$
$258$	1.90100	+	0.468555i	0.118351	+	0.0291710i
$259$	−8.88707	−	1.44429i	−0.552216	−	0.0897438i
$260$	−1.62091	+	4.27398i	−0.100524	+	0.265061i
$261$	0.263018	−	0.0878082i	0.0162804	−	0.00543519i
$262$	−4.33284	+	2.73992i	−0.267684	+	0.169273i
$263$	−29.0689	+	2.34669i	−1.79247	+	0.144703i	−0.931450	−	0.363871i	$-0.881455\pi$
$263$	−29.0689	+	2.34669i	−1.79247	+	0.144703i	−0.861019	+	0.508574i	$0.830173\pi$
$264$	2.59472	−	4.49419i	0.159694	−	0.276598i
$265$	1.53297	−	2.22090i	0.0941698	−	0.136429i
$266$	0.647975	+	16.0793i	0.0397299	+	0.985887i
$267$	−15.4243	−	6.57168i	−0.943952	−	0.402180i
$268$	−5.50546	−	14.5167i	−0.336300	−	0.886749i
$269$	−15.4543	−	8.11107i	−0.942268	−	0.494540i	−0.0776558	−	0.996980i	$-0.524744\pi$
$269$	−15.4543	−	8.11107i	−0.942268	−	0.494540i	−0.864612	+	0.502440i	$0.832436\pi$
$270$	0.205427	+	0.709216i	0.0125019	+	0.0431615i
$271$	19.3404	−	12.2301i	1.17485	−	0.742928i	0.203147	−	0.979148i	$-0.434883\pi$
$271$	19.3404	−	12.2301i	1.17485	−	0.742928i	0.971699	+	0.236220i	$0.0759088\pi$
$272$	6.12010	+	2.04319i	0.371085	+	0.123886i
$273$	−9.34873	+	13.5440i	−0.565811	+	0.819719i
$274$	48.0719	+	3.88076i	2.90413	+	0.234446i
$275$	−14.8693	+	7.80400i	−0.896651	+	0.470599i
$276$	8.19343	−	17.2673i	0.493187	−	1.03937i
$277$	16.3912	+	12.3172i	0.984854	+	0.740070i	0.965677	−	0.259746i	$-0.0836390\pi$
$277$	16.3912	+	12.3172i	0.984854	+	0.740070i	0.0191771	+	0.999816i	$0.493895\pi$
$278$	1.71374	−	42.5260i	0.102783	−	2.55054i
$279$	4.42241	−	9.32003i	0.264763	−	0.557976i
$280$	−1.56478	+	0.666690i	−0.0935134	+	0.0398423i
$281$	5.19257	+	25.4349i	0.309762	+	1.51732i	0.774903	+	0.632080i	$0.217799\pi$
$281$	5.19257	+	25.4349i	0.309762	+	1.51732i	−0.465141	+	0.885237i	$0.653996\pi$
$282$	5.00400	+	13.1945i	0.297984	+	0.785718i
$283$	−13.4985	−	16.5327i	−0.802405	−	0.982768i	−0.999997	−	0.00248377i	$-0.999209\pi$
$283$	−13.4985	−	16.5327i	−0.802405	−	0.982768i	0.197591	−	0.980284i	$-0.436688\pi$
$284$	−28.1544	−	4.57554i	−1.67066	−	0.271508i
$285$	−0.0921985	+	0.759323i	−0.00546137	+	0.0449784i
$286$	37.0744			2.19225
$287$	1.47543	−	12.1513i	0.0870919	−	0.717266i
$288$	5.27676	−	5.49369i	0.310936	−	0.323719i
$289$	−2.15776	+	7.44947i	−0.126927	+	0.438204i
$290$	0.0569624	+	0.196657i	0.00334494	+	0.0115481i
$291$	−10.7647	−	15.5953i	−0.631037	−	0.914215i
$292$	−8.37030	−	14.4978i	−0.489835	−	0.848419i
$293$	4.32157	+	0.348874i	0.252469	+	0.0203814i	0.206053	−	0.978541i	$-0.433938\pi$
$293$	4.32157	+	0.348874i	0.252469	+	0.0203814i	0.0464159	+	0.998922i	$0.485220\pi$
$294$	−8.42915	+	1.36987i	−0.491598	+	0.0798925i
$295$	0.0846438	−	0.414613i	0.00492816	−	0.0241397i
$296$	−0.821771	−	4.02530i	−0.0477645	−	0.233966i
$297$	2.74879	−	2.06559i	0.159501	−	0.119857i
$298$	9.07733	+	13.1508i	0.525835	+	0.761804i
$299$	35.1523	−	2.83779i	2.03291	−	0.164114i
$300$	12.7865	−	3.15159i	0.738229	−	0.181957i
$301$	−1.49415	+	2.58795i	−0.0861216	+	0.149167i
$302$	−8.58161	−	14.8638i	−0.493816	−	0.855315i
$303$	8.40832	+	8.75399i	0.483046	+	0.502904i
$304$	4.38289	−	1.86737i	0.251376	−	0.107101i
$305$	−1.92773	−	4.06260i	−0.110381	−	0.232624i
$306$	−4.93196	−	4.36934i	−0.281942	−	0.249778i
$307$	17.1897	−	9.02187i	0.981070	−	0.514905i	0.103643	−	0.994615i	$-0.466950\pi$
$307$	17.1897	−	9.02187i	0.981070	−	0.514905i	0.877428	+	0.479709i	$0.159258\pi$
$308$	21.2435	+	22.1168i	1.21046	+	1.26022i
$309$	7.58346	−	5.69860i	0.431408	−	0.324182i
$310$	6.74455	+	3.53981i	0.383065	+	0.201048i
$311$	−14.9218	−	9.43596i	−0.846137	−	0.535064i	0.0396197	−	0.999215i	$-0.487385\pi$
$311$	−14.9218	−	9.43596i	−0.846137	−	0.535064i	−0.885756	+	0.464150i	$0.846360\pi$
$312$	−7.29111	−	1.79710i	−0.412778	−	0.101741i
$313$	−9.94580			−0.562170			−0.281085	−	0.959683i	$-0.590694\pi$
$313$	−9.94580			−0.562170			−0.281085	+	0.959683i	$0.590694\pi$
$314$	6.47336	−	26.3711i	0.365313	−	1.48821i
$315$	−1.12696			−0.0634971
$316$	−5.62179	−	1.38565i	−0.316250	−	0.0779487i
$317$	−4.23673	−	2.67915i	−0.237959	−	0.150476i	0.410164	−	0.912012i	$-0.365471\pi$
$317$	−4.23673	−	2.67915i	−0.237959	−	0.150476i	−0.648123	+	0.761536i	$0.724446\pi$
$318$	15.1985	+	7.97676i	0.852287	+	0.447315i
$319$	0.762207	−	0.572761i	0.0426754	−	0.0320685i
$320$	2.89447	+	3.01346i	0.161806	+	0.168458i
$321$	−9.48505	+	4.97814i	−0.529404	+	0.277853i
$322$	38.0305	+	33.6921i	2.11936	+	1.87759i
$323$	−2.92617	−	6.16677i	−0.162816	−	0.343128i
$324$	−2.48067	+	1.05691i	−0.137815	+	0.0587174i
$325$	16.8331	+	17.5251i	0.933730	+	0.972116i
$326$	10.3631	+	17.9495i	0.573962	+	0.994131i
$327$	−1.69902	+	2.94279i	−0.0939561	+	0.162737i
$328$	5.42298	−	1.33664i	0.299434	−	0.0738039i
$329$	−21.4683	+	1.73310i	−1.18359	+	0.0955489i
$330$	1.44220	+	2.08939i	0.0793905	+	0.115017i
$331$	18.6620	−	14.0236i	1.02576	−	0.770805i	0.0520569	−	0.998644i	$-0.483422\pi$
$331$	18.6620	−	14.0236i	1.02576	−	0.770805i	0.973699	+	0.227839i	$0.0731659\pi$
$332$	3.23606	+	15.8513i	0.177602	+	0.869951i
$333$	0.544484	−	2.66706i	0.0298375	−	0.146154i
$334$	16.0735	−	2.61220i	0.879505	−	0.142933i
$335$	1.95541	+	0.157857i	0.106835	+	0.00862463i
$336$	3.50959	+	6.07879i	0.191464	+	0.331625i
$337$	7.95544	+	11.5254i	0.433361	+	0.627831i	0.977443	−	0.211201i	$-0.0677374\pi$
$337$	7.95544	+	11.5254i	0.433361	+	0.627831i	−0.544082	+	0.839032i	$0.683122\pi$
$338$	−7.08769	−	24.4695i	−0.385520	−	1.33097i
$339$	5.40024	−	18.6438i	0.293301	−	1.01259i
$340$	1.93498	−	2.01453i	0.104939	−	0.109253i
$341$	4.27550	−	35.2119i	0.231531	−	1.90683i
$342$	−4.86519			−0.263079
$343$	−1.21977	+	10.0457i	−0.0658614	+	0.542418i
$344$	−1.34589	−	0.218729i	−0.0725656	−	0.0117931i
$345$	1.52736	+	1.87068i	0.0822303	+	0.100714i
$346$	5.78651	+	15.2578i	0.311085	+	0.820263i
$347$	−2.16386	−	10.5993i	−0.116162	−	0.568999i	−0.995658	−	0.0930916i	$-0.970325\pi$
$347$	−2.16386	−	10.5993i	−0.116162	−	0.568999i	0.879496	−	0.475907i	$-0.157880\pi$
$348$	−0.687858	+	0.293069i	−0.0368731	+	0.0157101i
$349$	9.84783	−	20.7539i	0.527142	−	1.11093i	−0.448947	−	0.893558i	$-0.648201\pi$
$349$	9.84783	−	20.7539i	0.527142	−	1.11093i	0.976089	−	0.217370i	$-0.0697478\pi$
$350$	−1.40965	+	34.9800i	−0.0753488	+	1.86976i
$351$	−3.97761	−	2.98898i	−0.212309	−	0.159540i
$352$	11.2281	−	23.6628i	0.598461	−	1.26123i
$353$	−7.46224	+	3.91648i	−0.397175	+	0.208453i	−0.651472	−	0.758673i	$-0.725848\pi$
$353$	−7.46224	+	3.91648i	−0.397175	+	0.208453i	0.254297	+	0.967126i	$0.418156\pi$
$354$	2.68284	+	0.216581i	0.142591	+	0.0115112i
$355$	2.04740	−	2.96618i	0.108665	−	0.157428i
$356$	42.8817	+	14.3160i	2.27272	+	0.758747i
$357$	8.49987	−	5.37499i	0.449861	−	0.284475i
$358$	1.28481	+	4.43569i	0.0679045	+	0.234433i
$359$	−3.82382	−	2.00690i	−0.201814	−	0.105920i	0.360789	−	0.932648i	$-0.382508\pi$
$359$	−3.82382	−	2.00690i	−0.201814	−	0.105920i	−0.562602	+	0.826728i	$0.690200\pi$
$360$	−0.182347	−	0.480810i	−0.00961054	−	0.0253409i
$361$	12.8429	+	5.47185i	0.675942	+	0.287992i
$362$	−0.316100	−	7.84395i	−0.0166139	−	0.412269i
$363$	0.467241	−	0.676915i	0.0245238	−	0.0355288i
$364$	22.1878	−	38.4305i	1.16296	−	2.01430i
$365$	2.10843	−	0.170210i	0.110360	−	0.00890920i
$366$	24.1741	−	15.2868i	1.26360	−	0.799052i
$367$	−3.39510	+	1.13345i	−0.177223	+	0.0591656i	−0.403895	−	0.914806i	$-0.632344\pi$
$367$	−3.39510	+	1.13345i	−0.177223	+	0.0591656i	0.226672	+	0.973971i	$0.427216\pi$
$368$	5.33385	−	14.0642i	0.278046	−	0.733148i
$369$	3.65274	+	0.593628i	0.190154	+	0.0309030i
$370$	1.95149	+	0.480998i	0.101453	+	0.0250059i
$371$	−18.1480	+	18.8941i	−0.942197	+	0.980931i
$372$	−9.86388	+	26.0089i	−0.511418	+	1.34850i
$373$	3.57864	−	3.17040i	0.185295	−	0.164157i	−0.565376	−	0.824833i	$-0.691269\pi$
$373$	3.57864	−	3.17040i	0.185295	−	0.164157i	0.750671	+	0.660676i	$0.229730\pi$
$374$	−20.8427	−	8.88026i	−1.07775	−	0.459187i
$375$	−0.673602	+	3.29952i	−0.0347847	+	0.170387i
$376$	−4.21308	−	8.87888i	−0.217273	−	0.457893i
$377$	−1.10294	−	0.828807i	−0.0568044	−	0.0426857i
$378$	−0.864020	−	7.11584i	−0.0444404	−	0.365999i
$379$	1.33647	+	11.0069i	0.0686500	+	0.565384i	0.985932	+	0.167146i	$0.0534551\pi$
$379$	1.33647	+	11.0069i	0.0686500	+	0.565384i	−0.917282	+	0.398238i	$0.869622\pi$
$380$	0.0830486	−	2.06083i	0.00426030	−	0.105718i
$381$	−0.418255	−	0.370541i	−0.0214278	−	0.0189834i
$382$	−19.7816	+	3.21483i	−1.01212	+	0.164485i
$383$	0.156038	+	3.87204i	0.00797316	+	0.197852i	0.998266	+	0.0588578i	$0.0187459\pi$
$383$	0.156038	+	3.87204i	0.00797316	+	0.197852i	−0.990293	+	0.138994i	$0.955613\pi$
$384$	−7.17326	+	8.78564i	−0.366059	+	0.448340i
$385$	−3.67551	+	1.22707i	−0.187321	+	0.0625371i
$386$	−7.73349	+	26.6991i	−0.393624	+	1.35895i
$387$	−0.763589	−	0.482864i	−0.0388154	−	0.0245454i
$388$	32.3159	+	39.5798i	1.64059	+	2.00936i
$389$	−8.94487	+	7.92447i	−0.453523	+	0.401786i	−0.858722	−	0.512442i	$-0.828741\pi$
$389$	−8.94487	+	7.92447i	−0.453523	+	0.401786i	0.405199	+	0.914229i	$0.367202\pi$
$390$	2.32344	−	2.84569i	0.117652	−	0.144097i
$391$	−20.4419	−	6.82451i	−1.03379	−	0.345130i
$392$	5.77457	−	1.42330i	0.291660	−	0.0718876i
$393$	2.29682	−	0.566116i	0.115859	−	0.0285568i
$394$	−10.0409	−	3.35213i	−0.505852	−	0.168878i
$395$	0.462704	−	0.566709i	0.0232811	−	0.0285142i
$396$	−6.93974	+	6.14807i	−0.348735	+	0.308952i
$397$	−14.7792	−	18.1012i	−0.741746	−	0.908474i	0.256568	−	0.966526i	$-0.417408\pi$
$397$	−14.7792	−	18.1012i	−0.741746	−	0.908474i	−0.998314	+	0.0580527i	$0.981511\pi$
$398$	−23.3770	−	14.7827i	−1.17178	−	0.740992i
$399$	2.06595	−	7.13250i	0.103427	−	0.357071i
$400$	9.83080	−	3.28200i	0.491540	−	0.164100i
$401$	4.38595	−	5.37181i	0.219024	−	0.268255i	−0.653392	−	0.757020i	$-0.726655\pi$
$401$	4.38595	−	5.37181i	0.219024	−	0.268255i	0.872416	+	0.488764i	$0.162552\pi$
$402$	0.502436	+	12.4678i	0.0250592	+	0.621839i
$403$	−50.6625	+	8.23346i	−2.52368	+	0.410138i
$404$	−24.4984	−	21.7037i	−1.21884	−	1.07980i
$405$	0.0137191	−	0.340437i	0.000681709	−	0.0169164i
$406$	−0.239582	−	1.97314i	−0.0118903	−	0.0979251i
$407$	−1.12817	−	9.29129i	−0.0559212	−	0.460552i
$408$	3.66852	+	2.75671i	0.181619	+	0.136478i
$409$	11.1542	+	23.5070i	0.551539	+	1.16234i	0.967479	+	0.252952i	$0.0814015\pi$
$409$	11.1542	+	23.5070i	0.551539	+	1.16234i	−0.415940	+	0.909392i	$0.636547\pi$
$410$	−0.546560	+	2.67723i	−0.0269927	+	0.132219i
$411$	−20.4737	−	8.72301i	−1.00989	−	0.430275i
$412$	−19.1456	+	16.9615i	−0.943234	+	0.835632i
$413$	−1.45675	+	3.84114i	−0.0716821	+	0.189010i
$414$	−10.6408	+	11.0783i	−0.522967	+	0.544466i
$415$	−1.98482	−	0.489215i	−0.0974312	−	0.0240146i
$416$	−37.4094	−	6.07962i	−1.83415	−	0.298078i
$417$	−6.96414	+	18.3629i	−0.341035	+	0.899236i
$418$	−15.8675	+	5.29736i	−0.776106	+	0.259102i
$419$	−12.2625	+	7.75431i	−0.599060	+	0.378823i	−0.799307	−	0.600923i	$-0.794800\pi$
$419$	−12.2625	+	7.75431i	−0.599060	+	0.378823i	0.200247	+	0.979745i	$0.435826\pi$
$420$	3.02892	−	0.244520i	0.147796	−	0.0119314i
$421$	14.1320	−	24.4774i	0.688754	−	1.19296i	−0.283487	−	0.958976i	$-0.591491\pi$
$421$	14.1320	−	24.4774i	0.688754	−	1.19296i	0.972241	−	0.233981i	$-0.0751752\pi$
$422$	13.3084	−	19.2805i	0.647843	−	0.938562i
$423$	−0.262196	−	6.50633i	−0.0127484	−	0.316348i
$424$	−10.9974	−	4.68557i	−0.534083	−	0.227552i
$425$	−5.26563	−	13.8843i	−0.255421	−	0.673489i
$426$	20.2987	+	10.6536i	0.983475	+	0.516167i
$427$	12.1455	+	41.9312i	0.587763	+	2.02919i
$428$	24.4128	−	15.4377i	1.18004	−	0.746210i
$429$	−16.2272	−	5.41744i	−0.783457	−	0.261556i
$430$	0.378945	−	0.548996i	0.0182743	−	0.0264749i
$431$	3.08440	+	0.248998i	0.148570	+	0.0119938i	0.154528	−	0.987988i	$-0.450614\pi$
$431$	3.08440	+	0.248998i	0.148570	+	0.0119938i	−0.00595770	+	0.999982i	$0.501896\pi$
$432$	−1.87903	+	0.986191i	−0.0904048	+	0.0474481i
$433$	−10.5089	+	22.1470i	−0.505025	+	1.06432i	0.477577	+	0.878590i	$0.341515\pi$
$433$	−10.5089	+	22.1470i	−0.505025	+	1.06432i	−0.982601	+	0.185727i	$0.940536\pi$
$434$	−59.1160	−	44.4228i	−2.83766	−	2.13236i
$435$	0.00380415	−	0.0943989i	0.000182395	−	0.00452608i
$436$	3.92794	−	8.27796i	0.188114	−	0.396442i
$437$	−14.6394	+	6.23727i	−0.700298	+	0.298369i
$438$	2.69123	+	13.1825i	0.128592	+	0.629885i
$439$	−3.81114	−	10.0492i	−0.181896	−	0.479620i	0.812792	−	0.582554i	$-0.197946\pi$
$439$	−3.81114	−	10.0492i	−0.181896	−	0.479620i	−0.994688	+	0.102933i	$0.967177\pi$
$440$	−1.11823	−	1.36959i	−0.0533097	−	0.0652925i
$441$	3.88955	+	0.632114i	0.185217	+	0.0301007i
$442$	−3.95163	+	32.5446i	−0.187960	+	1.54799i
$443$	0.435900			0.0207102			0.0103551	−	0.999946i	$-0.496704\pi$
$443$	0.435900			0.0207102			0.0103551	+	0.999946i	$0.496704\pi$
$444$	−0.884726	+	7.28637i	−0.0419872	+	0.345796i
$445$	−3.95710	+	4.11977i	−0.187584	+	0.195296i
$446$	6.16645	−	21.2891i	0.291990	−	1.00807i
$447$	−2.05145	−	7.08242i	−0.0970301	−	0.334987i
$448$	−23.0429	−	33.3835i	−1.08868	−	1.57722i
$449$	−17.8904	−	30.9871i	−0.844302	−	1.46237i	−0.886226	−	0.463253i	$-0.846682\pi$
$449$	−17.8904	−	30.9871i	−0.844302	−	1.46237i	0.0419247	−	0.999121i	$-0.486651\pi$
$450$	−10.5497	−	0.851663i	−0.497319	−	0.0401478i
$451$	12.5595	−	2.04112i	0.591405	−	0.0961127i
$452$	−10.4690	+	51.2805i	−0.492420	+	2.41203i
$453$	1.58417	+	7.75975i	0.0744306	+	0.364585i
$454$	43.5833	−	32.7507i	2.04547	−	1.53707i
$455$	3.18523	+	4.61461i	0.149326	+	0.216336i
$456$	3.37731	−	0.272645i	0.158157	−	0.0127678i
$457$	−2.10118	+	0.517894i	−0.0982889	+	0.0242260i	−0.288153	−	0.957584i	$-0.593041\pi$
$457$	−2.10118	+	0.517894i	−0.0982889	+	0.0242260i	0.189864	+	0.981810i	$0.439195\pi$
$458$	17.0094	−	29.4612i	0.794798	−	1.37663i
$459$	1.52022	+	2.63311i	0.0709580	+	0.122903i
$460$	−4.51096	−	4.69641i	−0.210325	−	0.218971i
$461$	11.7752	−	5.01696i	0.548427	−	0.233663i	−0.0999365	−	0.994994i	$-0.531864\pi$
$461$	11.7752	−	5.01696i	0.548427	−	0.233663i	0.648364	+	0.761331i	$0.275454\pi$
$462$	−10.5659	−	22.2671i	−0.491569	−	1.03596i
$463$	11.7757	+	10.4323i	0.547261	+	0.484831i	0.890855	−	0.454287i	$-0.150106\pi$
$463$	11.7757	+	10.4323i	0.547261	+	0.484831i	−0.343594	+	0.939118i	$0.611644\pi$
$464$	−0.521032	+	0.273459i	−0.0241883	+	0.0126950i
$465$	−2.43479	−	2.53489i	−0.112911	−	0.117553i
$466$	3.67154	−	2.75898i	0.170081	−	0.127807i
$467$	3.04912	+	1.60030i	0.141096	+	0.0740531i	0.533794	−	0.845615i	$-0.320766\pi$
$467$	3.04912	+	1.60030i	0.141096	+	0.0740531i	−0.392698	+	0.919668i	$0.628458\pi$
$468$	11.3391	+	7.17042i	0.524151	+	0.331453i
$469$	−18.4915	−	4.55775i	−0.853858	−	0.210457i
$470$	4.80796			0.221775
$471$	−6.68678	+	10.5966i	−0.308111	+	0.488263i
$472$	−1.87451			−0.0862811
$473$	−3.01615	−	0.743415i	−0.138683	−	0.0341822i
$474$	3.93305	+	2.48711i	0.180651	+	0.114237i
$475$	−9.70847	−	5.09540i	−0.445455	−	0.233793i
$476$	−21.6788	+	16.2906i	−0.993647	+	0.746677i
$477$	−5.48667	−	5.71223i	−0.251217	−	0.261545i
$478$	−3.73260	+	1.95902i	−0.170725	+	0.0896036i
$479$	18.7222	+	16.5864i	0.855438	+	0.757851i	0.971913	−	0.235342i	$-0.0756211\pi$
$479$	18.7222	+	16.5864i	0.855438	+	0.757851i	−0.116475	+	0.993194i	$0.537160\pi$
$480$	−1.11261	−	2.34477i	−0.0507833	−	0.107023i
$481$	−12.4598	+	5.30864i	−0.568119	+	0.242053i
$482$	27.5260	+	28.6576i	1.25377	+	1.30532i
$483$	−11.7225	−	20.3040i	−0.533392	−	0.923862i
$484$	−1.10893	+	1.92072i	−0.0504058	+	0.0873053i
$485$	−6.26881	+	1.54512i	−0.284652	+	0.0701605i
$486$	2.16010	−	0.174381i	0.0979841	−	0.00791009i
$487$	−5.38190	−	7.79703i	−0.243877	−	0.353317i	0.681861	−	0.731482i	$-0.261171\pi$
$487$	−5.38190	−	7.79703i	−0.243877	−	0.353317i	−0.925738	+	0.378164i	$0.876555\pi$
$488$	−15.9245	+	11.9665i	−0.720866	+	0.541696i
$489$	−1.91304	−	9.37067i	−0.0865105	−	0.423756i
$490$	−0.581995	+	2.85080i	−0.0262918	+	0.128786i
$491$	−6.50386	+	1.05698i	−0.293515	+	0.0477008i	−0.305386	−	0.952229i	$-0.598785\pi$
$491$	−6.50386	+	1.05698i	−0.293515	+	0.0477008i	0.0118708	+	0.999930i	$0.496221\pi$
$492$	−9.94624	−	0.802943i	−0.448411	−	0.0361995i
$493$	0.421540	+	0.730128i	0.0189852	+	0.0328833i
$494$	13.7509	+	19.9217i	0.618684	+	0.896319i
$495$	−0.325933	−	1.12525i	−0.0146496	−	0.0505762i
$496$	−6.09065	+	21.0274i	−0.273478	+	0.944157i
$497$	−24.2380	+	25.2345i	−1.08722	+	1.13192i
$498$	1.56727	−	12.9076i	0.0702310	−	0.578405i
$499$	−23.3734			−1.04634			−0.523169	−	0.852229i	$-0.675250\pi$
$499$	−23.3734			−1.04634			−0.523169	+	0.852229i	$0.675250\pi$
$500$	1.09453	−	9.01425i	0.0489488	−	0.403130i
$501$	−7.41698	−	1.20538i	−0.331366	−	0.0538523i
$502$	10.8296	+	13.2639i	0.483349	+	0.591995i
$503$	0.174675	+	0.460581i	0.00778838	+	0.0205363i	0.938854	−	0.344315i	$-0.111889\pi$
$503$	0.174675	+	0.460581i	0.00778838	+	0.0205363i	−0.931066	+	0.364852i	$0.881120\pi$
$504$	0.998554	+	4.89124i	0.0444791	+	0.217873i
$505$	3.80466	−	1.62101i	0.169305	−	0.0721342i
$506$	−22.6420	+	47.7170i	−1.00656	+	2.12128i
$507$	−0.473341	+	11.7458i	−0.0210218	+	0.521651i
$508$	1.20454	+	0.905151i	0.0534427	+	0.0401596i
$509$	−0.0294320	+	0.0620267i	−0.00130455	+	0.00274928i	−0.904102	−	0.427317i	$-0.859459\pi$
$509$	−0.0294320	+	0.0620267i	−0.00130455	+	0.00274928i	0.902797	+	0.430067i	$0.141510\pi$
$510$	−1.98782	+	1.04329i	−0.0880222	+	0.0461976i
$511$	−20.4687	−	1.65241i	−0.905482	−	0.0730981i
$512$	−12.8215	+	18.5752i	−0.566637	+	0.820915i
$513$	2.12946	+	0.710919i	0.0940180	+	0.0313878i
$514$	−45.1868	+	28.5744i	−1.99310	+	1.26036i
$515$	−0.899193	−	3.10437i	−0.0396232	−	0.136795i
$516$	2.15706	+	1.13211i	0.0949593	+	0.0498385i
$517$	−7.93940	−	20.9345i	−0.349174	−	0.920697i
$518$	−17.9507	−	7.64809i	−0.788709	−	0.336038i
$519$	−0.303198	−	7.52377i	−0.0133089	−	0.330257i
$520$	−1.45341	+	2.10562i	−0.0637361	+	0.0923376i
$521$	12.1145	−	20.9829i	0.530745	−	0.919277i	−0.468612	−	0.883404i	$-0.655246\pi$
$521$	12.1145	−	20.9829i	0.530745	−	0.919277i	0.999356	−	0.0358725i	$-0.0114210\pi$
$522$	0.598969	−	0.0483538i	0.0262162	−	0.00211639i
$523$	−0.125391	+	0.0792927i	−0.00548298	+	0.00346723i	−0.537205	−	0.843452i	$-0.680520\pi$
$523$	−0.125391	+	0.0792927i	−0.00548298	+	0.00346723i	0.531722	+	0.846919i	$0.321545\pi$
$524$	−6.05032	+	2.01989i	−0.264309	+	0.0882395i
$525$	5.72840	−	15.1045i	0.250008	−	0.659216i
$526$	−62.3826	−	10.1382i	−2.72001	−	0.442045i
$527$	30.4540	+	7.50623i	1.32660	+	0.326976i
$528$	−5.05454	+	5.26234i	−0.219971	+	0.229014i
$529$	−9.65984	+	25.4709i	−0.419993	+	1.10743i
$530$	4.37743	−	3.87806i	0.190143	−	0.168452i
$531$	−1.14261	−	0.486822i	−0.0495852	−	0.0211263i
$532$	−4.00509	+	19.6182i	−0.173643	+	0.850558i
$533$	−7.89332	−	16.6348i	−0.341898	−	0.720534i
$534$	−29.0469	−	21.8273i	−1.25698	−	0.944559i
$535$	0.439927	+	3.62312i	0.0190197	+	0.156641i
$536$	−1.04748	−	8.62673i	−0.0452440	−	0.372618i
$537$	0.0858043	−	2.12921i	0.00370273	−	0.0918823i
$538$	−28.3117	−	25.0820i	−1.22060	−	1.08136i
$539$	13.3738	−	2.17345i	0.576050	−	0.0936172i
$540$	0.0369928	+	0.917966i	0.00159191	+	0.0395030i
$541$	23.3676	−	28.6201i	1.00465	−	1.23048i	0.0316938	−	0.999498i	$-0.489910\pi$
$541$	23.3676	−	28.6201i	1.00465	−	1.23048i	0.972959	−	0.230978i	$-0.0741927\pi$
$542$	47.0381	−	15.7036i	2.02046	−	0.674528i
$543$	−1.00783	+	3.47943i	−0.0432501	+	0.149317i
$544$	19.5749	+	12.3784i	0.839265	+	0.530719i
$545$	0.732218	+	0.896804i	0.0313648	+	0.0384149i
$546$	−26.6954	+	23.6501i	−1.14246	+	1.01213i
$547$	23.4735	−	28.7499i	1.00366	−	1.22926i	0.0303991	−	0.999538i	$-0.490322\pi$
$547$	23.4735	−	28.7499i	1.00366	−	1.22926i	0.973257	−	0.229718i	$-0.0737804\pi$
$548$	56.9196	+	19.0025i	2.43148	+	0.811749i
$549$	−12.8146	+	3.15851i	−0.546913	+	0.134802i
$550$	−35.3346	+	8.70920i	−1.50667	+	0.371362i
$551$	0.590474	+	0.197129i	0.0251550	+	0.00839798i
$552$	6.76579	−	8.28659i	0.287971	−	0.352701i
$553$	−5.31630	+	4.70983i	−0.226072	+	0.200282i
$554$	28.1016	+	34.4183i	1.19392	+	1.46229i
$555$	−0.783867	−	0.495687i	−0.0332733	−	0.0210408i
$556$	14.7332	−	50.8649i	0.624827	−	2.15715i
$557$	−8.54949	+	2.85424i	−0.362254	+	0.120938i	−0.491968	−	0.870613i	$-0.663722\pi$
$557$	−8.54949	+	2.85424i	−0.362254	+	0.120938i	0.129714	+	0.991551i	$0.458594\pi$
$558$	14.1390	−	17.3172i	0.598554	−	0.733095i
$559$	0.181000	+	4.49146i	0.00765547	+	0.189968i
$560$	2.36056	−	0.383628i	0.0997518	−	0.0162112i
$561$	7.82511	+	6.93244i	0.330376	+	0.292688i
$562$	−2.26526	+	56.2119i	−0.0955543	+	2.37115i
$563$	0.229974	+	1.89401i	0.00969226	+	0.0798230i	0.996752	−	0.0805277i	$-0.0256606\pi$
$563$	0.229974	+	1.89401i	0.00969226	+	0.0798230i	−0.987060	+	0.160351i	$0.948737\pi$
$564$	2.11640	+	17.4301i	0.0891165	+	0.733940i
$565$	−5.28694	−	3.97288i	−0.222423	−	0.167140i
$566$	−19.8287	−	41.7881i	−0.833462	−	1.75648i
$567$	−0.661616	+	3.24081i	−0.0277853	+	0.136101i
$568$	−14.6879	−	6.25794i	−0.616292	−	0.262577i
$569$	19.6022	−	17.3660i	0.821765	−	0.728020i	−0.143399	−	0.989665i	$-0.545803\pi$
$569$	19.6022	−	17.3660i	0.821765	−	0.728020i	0.965164	+	0.261645i	$0.0842648\pi$
$570$	−0.587805	+	1.54991i	−0.0246204	+	0.0649188i
$571$	26.1926	−	27.2694i	1.09613	−	1.14119i	0.106981	−	0.994261i	$-0.465882\pi$
$571$	26.1926	−	27.2694i	1.09613	−	1.14119i	0.989147	−	0.146929i	$-0.0469388\pi$
$572$	44.7892	+	11.0395i	1.87273	+	0.461586i
$573$	9.12805	+	1.48345i	0.381330	+	0.0619721i
$574$	9.40651	−	24.8029i	0.392620	−	1.03525i
$575$	−32.8361	+	10.9623i	−1.36936	+	0.457160i
$576$	10.3651	−	6.55450i	0.431880	−	0.273104i
$577$	−23.8763	+	1.92750i	−0.993984	+	0.0802427i	−0.566743	−	0.823895i	$-0.691797\pi$
$577$	−23.8763	+	1.92750i	−0.993984	+	0.0802427i	−0.427242	+	0.904138i	$0.640515\pi$
$578$	−8.40376	+	14.5557i	−0.349550	+	0.605439i
$579$	7.28627	−	10.5560i	0.302807	−	0.438691i
$580$	0.0102576	+	0.254541i	0.000425925	+	0.0105692i
$581$	18.2574	+	7.77875i	0.757444	+	0.322717i
$582$	−14.5624	−	38.3979i	−0.603630	−	1.59164i
$583$	−24.1140	−	12.6560i	−0.998702	−	0.524159i
$584$	−2.60694	−	9.00020i	−0.107876	−	0.372431i
$585$	−1.43277	+	0.906031i	−0.0592379	+	0.0374598i
$586$	8.91232	+	2.97537i	0.368165	+	0.122911i
$587$	−21.6276	+	31.3330i	−0.892666	+	1.29325i	0.0627627	+	0.998028i	$0.480009\pi$
$587$	−21.6276	+	31.3330i	−0.892666	+	1.29325i	−0.955429	+	0.295222i	$0.904607\pi$
$588$	−10.5911	−	0.855000i	−0.436769	−	0.0352596i
$589$	20.5067	−	10.7627i	0.844964	−	0.443471i
$590$	0.393133	−	0.828511i	0.0161850	−	0.0341092i
$591$	3.90499	+	2.93441i	0.160630	+	0.120706i
$592$	−0.232597	+	5.77183i	−0.00955967	+	0.237221i
$593$	16.5186	−	34.8121i	0.678336	−	1.42956i	−0.213381	−	0.976969i	$-0.568447\pi$
$593$	16.5186	−	34.8121i	0.678336	−	1.42956i	0.891717	−	0.452594i	$-0.149501\pi$
$594$	6.85515	−	2.92071i	0.281270	−	0.119838i
$595$	−0.685381	−	3.35722i	−0.0280979	−	0.137633i
$596$	7.05035	+	18.5903i	0.288794	+	0.761486i
$597$	8.07186	+	9.88623i	0.330359	+	0.404617i
$598$	75.4376	+	12.2598i	3.08487	+	0.501341i
$599$	−3.21910	+	26.5117i	−0.131529	+	1.08324i	0.766173	+	0.642634i	$0.222158\pi$
$599$	−3.21910	+	26.5117i	−0.131529	+	1.08324i	−0.897702	+	0.440603i	$0.854765\pi$
$600$	7.37112			0.300925
$601$	−1.68385	+	13.8678i	−0.0686859	+	0.565679i	0.917220	+	0.398380i	$0.130428\pi$
$601$	−1.68385	+	13.8678i	−0.0686859	+	0.565679i	−0.985906	+	0.167299i	$0.946496\pi$
$602$	−4.48611	+	4.67054i	−0.182840	+	0.190357i
$603$	1.60193	−	5.53050i	0.0652356	−	0.225219i
$604$	−5.94141	−	20.5121i	−0.241752	−	0.834626i
$605$	−0.159195	−	0.230634i	−0.00647219	−	0.00937659i
$606$	13.1523	+	22.7805i	0.534278	+	0.925396i
$607$	28.1275	+	2.27069i	1.14166	+	0.0921643i	0.636794	−	0.771034i	$-0.280260\pi$
$607$	28.1275	+	2.27069i	1.14166	+	0.0921643i	0.504866	+	0.863198i	$0.331542\pi$
$608$	16.8796	−	2.74320i	0.684557	−	0.111251i
$609$	−0.183458	+	0.898637i	−0.00743409	+	0.0364146i
$610$	−1.94926	−	9.54812i	−0.0789233	−	0.386592i
$611$	−25.9006	+	19.4631i	−1.04783	+	0.787391i
$612$	−4.65721	−	6.74713i	−0.188256	−	0.272737i
$613$	−18.3510	+	1.48145i	−0.741191	+	0.0598351i	−0.445294	−	0.895385i	$-0.646901\pi$
$613$	−18.3510	+	1.48145i	−0.741191	+	0.0598351i	−0.295897	+	0.955220i	$0.595619\pi$
$614$	40.8488	−	10.0683i	1.64853	−	0.406325i
$615$	0.630431	−	1.09194i	0.0254214	−	0.0440312i
$616$	8.58244	+	14.8652i	0.345796	+	0.598937i
$617$	9.10933	+	9.48382i	0.366728	+	0.381804i	0.878842	−	0.477113i	$-0.158317\pi$
$617$	9.10933	+	9.48382i	0.366728	+	0.381804i	−0.512114	+	0.858918i	$0.671137\pi$
$618$	18.9122	−	8.05774i	0.760760	−	0.324130i
$619$	−19.4844	−	41.0625i	−0.783144	−	1.65044i	−0.759313	−	0.650726i	$-0.774465\pi$
$619$	−19.4844	−	41.0625i	−0.783144	−	1.65044i	−0.0238316	−	0.999716i	$-0.507587\pi$
$620$	7.09398	+	6.28472i	0.284901	+	0.252400i
$621$	6.27620	−	3.29400i	0.251855	−	0.132184i
$622$	−26.5040	−	27.5936i	−1.06271	−	1.10640i
$623$	44.3338	−	33.3147i	1.77620	−	1.33473i
$624$	9.34907	+	4.90677i	0.374262	+	0.196428i
$625$	−19.6694	−	12.4382i	−0.786777	−	0.497528i
$626$	−20.9275	−	5.15817i	−0.836431	−	0.206162i
$627$	7.71917			0.308274
$628$	15.6729	−	29.9311i	0.625415	−	1.19438i
$629$	8.27631			0.329998
$630$	−2.37130	−	0.584473i	−0.0944748	−	0.0232859i
$631$	23.7113	+	14.9941i	0.943932	+	0.596906i	0.915339	−	0.402685i	$-0.131923\pi$
$631$	23.7113	+	14.9941i	0.943932	+	0.596906i	0.0285932	+	0.999591i	$0.490897\pi$
$632$	−2.86962	−	1.50609i	−0.114147	−	0.0599091i
$633$	−8.64234	+	6.49429i	−0.343502	+	0.258125i
$634$	−7.52526	−	7.83462i	−0.298866	−	0.311153i
$635$	−0.168577	+	0.0884760i	−0.00668978	+	0.00351106i
$636$	15.9859	+	14.1622i	0.633881	+	0.561570i
$637$	−8.40506	−	17.7133i	−0.333021	−	0.701826i
$638$	1.90085	−	0.809877i	0.0752554	−	0.0320633i
$639$	−7.32786	−	7.62911i	−0.289886	−	0.301803i
$640$	1.93220	+	3.34667i	0.0763769	+	0.132289i
$641$	23.6253	−	40.9202i	0.933142	−	1.61625i	0.155229	−	0.987879i	$-0.450389\pi$
$641$	23.6253	−	40.9202i	0.933142	−	1.61625i	0.777914	−	0.628371i	$-0.216278\pi$
$642$	−22.5398	+	5.55556i	−0.889575	+	0.219261i
$643$	−39.4617	+	3.18568i	−1.55622	+	0.125631i	−0.828400	−	0.560138i	$-0.810748\pi$
$643$	−39.4617	+	3.18568i	−1.55622	+	0.125631i	−0.727820	+	0.685769i	$0.759466\pi$
$644$	35.9119	+	52.0273i	1.41513	+	2.05016i
$645$	−0.246083	+	0.184919i	−0.00968950	+	0.00728119i
$646$	−2.95885	−	14.4934i	−0.116415	−	0.570236i
$647$	−4.93922	+	24.1939i	−0.194181	+	0.951159i	0.759539	+	0.650462i	$0.225425\pi$
$647$	−4.93922	+	24.1939i	−0.194181	+	0.951159i	−0.953720	+	0.300698i	$0.902781\pi$
$648$	−1.48972	+	0.242103i	−0.0585218	+	0.00951071i
$649$	−4.25662	−	0.343630i	−0.167087	−	0.0134887i
$650$	26.3304	+	45.6055i	1.03276	+	1.78880i
$651$	19.3834	+	28.0818i	0.759697	+	1.10061i
$652$	7.17484	+	24.7704i	0.280988	+	0.970084i
$653$	7.37553	−	25.4633i	0.288627	−	0.996455i	−0.676884	−	0.736090i	$-0.736670\pi$
$653$	7.37553	−	25.4633i	0.288627	−	0.996455i	0.965510	−	0.260365i	$-0.0838429\pi$
$654$	−5.10121	+	5.31092i	−0.199473	+	0.207674i
$655$	0.0971498	−	0.800101i	0.00379596	−	0.0312625i
$656$	−7.85318			−0.306615
$657$	0.748342	−	6.16315i	0.0291956	−	0.240447i
$658$	−46.0714	−	7.48734i	−1.79605	−	0.291887i
$659$	1.78767	+	2.18950i	0.0696378	+	0.0852908i	0.808249	−	0.588841i	$-0.200415\pi$
$659$	1.78767	+	2.18950i	0.0696378	+	0.0852908i	−0.738611	+	0.674132i	$0.764518\pi$
$660$	1.12016	+	2.95361i	0.0436020	+	0.114969i
$661$	8.71187	+	42.6736i	0.338853	+	1.65981i	0.690241	+	0.723580i	$0.257505\pi$
$661$	8.71187	+	42.6736i	0.338853	+	1.65981i	−0.351388	+	0.936230i	$0.614290\pi$
$662$	46.5407	−	19.8291i	1.80886	−	0.770681i
$663$	6.48512	−	13.6671i	0.251861	−	0.530786i
$664$	−0.364623	+	9.04802i	−0.0141501	+	0.351131i
$665$	−2.02261	−	1.51989i	−0.0784334	−	0.0589389i
$666$	2.52889	−	5.32952i	0.0979924	−	0.206515i
$667$	1.74031	−	0.913387i	0.0673852	−	0.0353665i
$668$	20.1961	+	1.63040i	0.781411	+	0.0630820i
$669$	−5.80984	+	8.41701i	−0.224622	+	0.325421i
$670$	4.03260	+	1.34628i	0.155793	+	0.0520114i
$671$	−38.3549	+	24.2542i	−1.48067	+	0.936322i
$672$	7.00989	+	24.2009i	0.270412	+	0.933572i
$673$	17.3153	+	9.08775i	0.667454	+	0.350307i	0.764179	−	0.645004i	$-0.223144\pi$
$673$	17.3153	+	9.08775i	0.667454	+	0.350307i	−0.0967249	+	0.995311i	$0.530837\pi$
$674$	10.7621	+	28.3772i	0.414539	+	1.09305i
$675$	4.49310	+	1.91433i	0.172940	+	0.0736827i
$676$	−1.27633	−	31.6719i	−0.0490897	−	1.21815i
$677$	−5.07192	+	7.34794i	−0.194930	+	0.282404i	−0.908245	−	0.418439i	$-0.862577\pi$
$677$	−5.07192	+	7.34794i	−0.194930	+	0.282404i	0.713315	+	0.700843i	$0.247193\pi$
$678$	21.0321	−	36.4287i	0.807734	−	1.39904i
$679$	62.4760	−	5.04358i	2.39761	−	0.193555i
$680$	1.32144	−	0.835626i	0.0506748	−	0.0320448i
$681$	−23.8618	+	7.96623i	−0.914385	+	0.305267i
$682$	27.2582	−	71.8739i	1.04377	−	2.75219i
$683$	−22.7845	−	3.70285i	−0.871826	−	0.141685i	−0.291992	−	0.956421i	$-0.594318\pi$
$683$	−22.7845	−	3.70285i	−0.871826	−	0.141685i	−0.579833	+	0.814735i	$0.696882\pi$
$684$	−5.87759	−	1.44870i	−0.224735	−	0.0553923i
$685$	−5.25251	+	5.46844i	−0.200688	+	0.208938i
$686$	−7.77657	+	20.5051i	−0.296911	+	0.782889i
$687$	−11.7499	+	10.4095i	−0.448286	+	0.397146i
$688$	1.76380	+	0.751486i	0.0672443	+	0.0286501i
$689$	−7.88258	+	38.6114i	−0.300303	+	1.47098i
$690$	2.24362	+	4.72832i	0.0854130	+	0.180004i
$691$	10.0941	+	7.58521i	0.383997	+	0.288555i	0.775158	−	0.631767i	$-0.217670\pi$
$691$	10.0941	+	7.58521i	0.383997	+	0.288555i	−0.391161	+	0.920322i	$0.627927\pi$
$692$	2.44736	+	20.1558i	0.0930345	+	0.766208i
$693$	1.37086	+	11.2901i	0.0520748	+	0.428875i
$694$	0.943984	−	23.4247i	0.0358331	−	0.889190i
$695$	5.00852	+	4.43716i	0.189984	+	0.168311i
$696$	−0.413081	+	0.0671323i	−0.0156578	+	0.00254464i
$697$	0.453059	+	11.2425i	0.0171608	+	0.425842i
$698$	31.4849	−	38.5619i	1.19172	−	1.45959i
$699$	−2.01016	+	0.671090i	−0.0760312	+	0.0253830i
$700$	−12.1189	+	41.8393i	−0.458051	+	1.58138i
$701$	33.9301	+	21.4561i	1.28152	+	0.810387i	0.989290	−	0.145960i	$-0.0466272\pi$
$701$	33.9301	+	21.4561i	1.28152	+	0.810387i	0.292233	+	0.956347i	$0.405602\pi$
$702$	−6.81933	−	8.35217i	−0.257379	−	0.315232i
$703$	4.57418	−	4.05237i	0.172518	−	0.152838i
$704$	26.6685	−	32.6629i	1.00511	−	1.23103i
$705$	−2.10441	−	0.702556i	−0.0792567	−	0.0264598i
$706$	−17.7329	+	4.37076i	−0.667386	+	0.164496i
$707$	−38.9818	+	9.60816i	−1.46606	+	0.361352i
$708$	3.17662	+	1.06051i	0.119385	+	0.0398565i
$709$	18.2622	−	22.3672i	0.685853	−	0.840017i	−0.307923	−	0.951411i	$-0.599634\pi$
$709$	18.2622	−	22.3672i	0.685853	−	0.840017i	0.993776	+	0.111394i	$0.0355315\pi$
$710$	5.84639	−	5.17945i	0.219411	−	0.194381i
$711$	−1.35805	−	1.66330i	−0.0509307	−	0.0623787i
$712$	21.3869	+	13.5242i	0.801508	+	0.506843i
$713$	20.3436	−	70.2341i	0.761872	−	2.63029i
$714$	20.6726	−	6.90154i	0.773654	−	0.258284i
$715$	−3.68639	+	4.51501i	−0.137863	+	0.168852i
$716$	0.231366	+	5.74129i	0.00864655	+	0.214562i
$717$	1.91999	−	0.312030i	0.0717035	−	0.0116530i
$718$	−7.00508	−	6.20596i	−0.261427	−	0.231604i
$719$	1.31884	−	32.7268i	0.0491845	−	1.22050i	−0.766592	−	0.642135i	$-0.778049\pi$
$719$	1.31884	−	32.7268i	0.0491845	−	1.22050i	0.815776	−	0.578367i	$-0.196310\pi$
$720$	0.0871514	+	0.717756i	0.00324794	+	0.0267492i
$721$	3.78198	+	31.1474i	0.140848	+	1.15999i
$722$	24.1856	+	18.1743i	0.900094	+	0.676377i
$723$	−7.86038	−	16.5654i	−0.292331	−	0.616074i
$724$	1.95380	−	9.57032i	0.0726122	−	0.355678i
$725$	1.24588	+	0.530821i	0.0462709	+	0.0197142i
$726$	1.33421	−	1.18201i	0.0495173	−	0.0438685i
$727$	−15.0197	+	39.6037i	−0.557050	+	1.46882i	0.300179	+	0.953883i	$0.402954\pi$
$727$	−15.0197	+	39.6037i	−0.557050	+	1.46882i	−0.857228	+	0.514936i	$0.827816\pi$
$728$	17.2060	−	17.9134i	0.637698	−	0.663914i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	4.52473	+	0.735341i	0.167468	+	0.0272162i
$731$	0.974064	−	2.56840i	0.0360271	−	0.0949955i
$732$	33.7564	−	11.2695i	1.24767	−	0.416534i
$733$	−42.4471	+	26.8419i	−1.56782	+	0.991428i	−0.584106	+	0.811677i	$0.698555\pi$
$733$	−42.4471	+	26.8419i	−1.56782	+	0.991428i	−0.983712	+	0.179751i	$0.942471\pi$
$734$	−7.73165	+	0.624163i	−0.285380	+	0.0230383i
$735$	0.671304	−	1.16273i	0.0247614	−	0.0428880i
$736$	30.6714	−	44.4353i	1.13056	−	1.63791i
$737$	−0.797171	−	19.7816i	−0.0293642	−	0.728664i
$738$	7.37805	+	3.14349i	0.271590	+	0.115714i
$739$	10.3721	+	27.3489i	0.381543	+	1.00605i	0.978949	+	0.204106i	$0.0654288\pi$
$739$	10.3721	+	27.3489i	0.381543	+	1.00605i	−0.597406	+	0.801939i	$0.703802\pi$
$740$	2.21434	+	1.16218i	0.0814009	+	0.0427225i
$741$	−3.10767	−	10.7289i	−0.114163	−	0.394137i
$742$	−47.9852	+	30.3440i	−1.76159	+	1.11396i
$743$	−18.2502	−	6.09283i	−0.669536	−	0.223524i	−0.0384781	−	0.999259i	$-0.512251\pi$
$743$	−18.2502	−	6.09283i	−0.669536	−	0.223524i	−0.631058	+	0.775735i	$0.717379\pi$
$744$	−8.84456	+	12.8136i	−0.324257	+	0.469768i
$745$	−2.50411	−	0.202153i	−0.0917436	−	0.00740631i
$746$	9.17427	−	4.81503i	0.335894	−	0.176291i
$747$	−2.57209	+	5.42057i	−0.0941079	+	0.198328i
$748$	−22.5356	−	16.9344i	−0.823985	−	0.619185i
$749$	1.42669	−	35.4030i	0.0521302	−	1.29360i
$750$	−3.12858	+	6.59335i	−0.114240	+	0.240755i
$751$	−18.9673	+	8.08121i	−0.692126	+	0.294887i	−0.709241	−	0.704966i	$-0.750962\pi$
$751$	−18.9673	+	8.08121i	−0.692126	+	0.294887i	0.0171148	+	0.999854i	$0.494552\pi$
$752$	2.76402	+	13.5390i	0.100793	+	0.493718i
$753$	−2.80188	−	7.38796i	−0.102106	−	0.269232i
$754$	−1.89092	−	2.31595i	−0.0688632	−	0.0843420i
$755$	2.66344	+	0.432851i	0.0969324	+	0.0157531i
$756$	1.07505	−	8.85385i	0.0390993	−	0.322012i
$757$	32.3296			1.17504			0.587519	−	0.809210i	$-0.300105\pi$
$757$	32.3296			1.17504			0.587519	+	0.809210i	$0.300105\pi$
$758$	−2.89631	+	23.8532i	−0.105199	+	0.866389i
$759$	16.8828	−	17.5769i	0.612808	−	0.638000i
$760$	0.321184	−	1.10886i	0.0116506	−	0.0402225i
$761$	5.08915	+	17.5698i	0.184482	+	0.636904i	0.998432	+	0.0559706i	$0.0178253\pi$
$761$	5.08915	+	17.5698i	0.184482	+	0.636904i	−0.813951	+	0.580934i	$0.802688\pi$
$762$	−0.687899	−	0.996594i	−0.0249200	−	0.0361028i
$763$	−5.61978	−	9.73374i	−0.203450	−	0.352385i
$764$	−24.8553	−	2.00652i	−0.899231	−	0.0725935i
$765$	1.02251	−	0.166173i	0.0369688	−	0.00600801i
$766$	−1.67982	+	8.22829i	−0.0606942	+	0.297300i
$767$	1.23607	+	6.05465i	0.0446317	+	0.218621i
$768$	−0.0419243	+	0.0315040i	−0.00151281	+	0.00113680i
$769$	22.1734	+	32.1237i	0.799593	+	1.15841i	0.984453	+	0.175646i	$0.0562013\pi$
$769$	22.1734	+	32.1237i	0.799593	+	1.15841i	−0.184860	+	0.982765i	$0.559183\pi$
$770$	−8.37023	+	0.675715i	−0.301642	+	0.0243511i
$771$	23.9533	−	5.90396i	0.862658	−	0.212626i
$772$	−17.2929	+	29.9521i	−0.622384	+	1.07800i
$773$	23.7376	+	41.1147i	0.853782	+	1.47879i	0.877770	+	0.479082i	$0.159030\pi$
$773$	23.7376	+	41.1147i	0.853782	+	1.47879i	−0.0239882	+	0.999712i	$0.507636\pi$
$774$	−1.35628	−	1.41204i	−0.0487505	−	0.0507547i
$775$	46.3510	−	19.7483i	1.66498	−	0.709380i
$776$	12.2607	+	25.8389i	0.440133	+	0.927561i
$777$	6.73934	+	5.97054i	0.241773	+	0.214192i
$778$	−22.9312	+	12.0352i	−0.822125	+	0.431484i
$779$	5.75513	+	5.99173i	0.206199	+	0.214676i
$780$	3.65427	−	2.74601i	0.130844	−	0.0983228i
$781$	−32.2061	−	16.9031i	−1.15243	−	0.604840i
$782$	−39.4735	−	24.9616i	−1.41157	−	0.892623i
$783$	−0.269230	−	0.0663593i	−0.00962150	−	0.00237149i
$784$	−8.36232			−0.298654
$785$	2.56788	+	3.41048i	0.0916515	+	0.121725i
$786$	5.12647			0.182855
$787$	12.6475	+	3.11733i	0.450834	+	0.111121i	0.458194	−	0.888852i	$-0.348497\pi$
$787$	12.6475	+	3.11733i	0.450834	+	0.111121i	−0.00735964	+	0.999973i	$0.502343\pi$
$788$	−11.1321	−	7.03952i	−0.396565	−	0.250773i
$789$	25.8230	+	13.5530i	0.919324	+	0.482498i
$790$	1.26751	−	0.952472i	0.0450960	−	0.0338874i
$791$	44.4743	+	46.3027i	1.58133	+	1.64633i
$792$	−4.59502	+	2.41165i	−0.163277	+	0.0856944i
$793$	49.1523	+	43.5452i	1.74545	+	1.54633i
$794$	−21.7099	−	45.7526i	−0.770455	−	1.62370i
$795$	−2.48265	+	1.05776i	−0.0880504	+	0.0375148i
$796$	−23.8397	−	24.8198i	−0.844977	−	0.879714i
$797$	−15.6763	−	27.1522i	−0.555285	−	0.961781i	−0.997881	−	0.0650605i	$-0.979276\pi$
$797$	−15.6763	−	27.1522i	−0.555285	−	0.961781i	0.442597	−	0.896721i	$-0.354057\pi$
$798$	8.04619	−	13.9364i	0.284832	−	0.493344i
$799$	19.2229	−	4.73802i	0.680057	−	0.167619i
$800$	37.0821	−	2.99358i	1.31105	−	0.105839i
$801$	9.52413	+	13.7981i	0.336519	+	0.487531i
$802$	12.0147	−	9.02844i	0.424253	−	0.318805i
$803$	−4.26994	−	20.9155i	−0.150683	−	0.738093i
$804$	−3.10552	+	15.2119i	−0.109523	+	0.536481i
$805$	−7.88457	+	1.28137i	−0.277895	+	0.0451623i
$806$	−110.872	−	8.95050i	−3.90529	−	0.315268i
$807$	8.72677	+	15.1152i	0.307197	+	0.532081i
$808$	−10.4067	−	15.0767i	−0.366106	−	0.530396i
$809$	4.88916	+	16.8793i	0.171894	+	0.593446i	0.999484	+	0.0321135i	$0.0102238\pi$
$809$	4.88916	+	16.8793i	0.171894	+	0.593446i	−0.827591	+	0.561332i	$0.810289\pi$
$810$	0.205427	−	0.709216i	0.00721796	−	0.0249193i
$811$	16.9103	−	17.6055i	0.593800	−	0.618211i	−0.354703	−	0.934979i	$-0.615418\pi$
$811$	16.9103	−	17.6055i	0.593800	−	0.618211i	0.948503	+	0.316768i	$0.102598\pi$
$812$	0.298099	−	2.45506i	0.0104612	−	0.0861559i
$813$	−22.8829			−0.802539
$814$	2.44488	−	20.1354i	0.0856930	−	0.705745i
$815$	−3.21636	−	0.522710i	−0.112664	−	0.0183097i
$816$	−4.08063	−	4.99786i	−0.142851	−	0.174960i
$817$	−0.719227	−	1.89644i	−0.0251626	−	0.0663482i
$818$	11.2788	+	55.2471i	0.394353	+	1.93167i
$819$	15.1402	−	6.45066i	0.529043	−	0.225404i
$820$	−1.45748	+	3.07158i	−0.0508976	+	0.107264i
$821$	1.94247	−	48.2018i	0.0677926	−	1.68226i	−0.505439	−	0.862862i	$-0.668670\pi$
$821$	1.94247	−	48.2018i	0.0677926	−	1.68226i	0.573232	−	0.819393i	$-0.305689\pi$
$822$	−38.5557	−	28.9728i	−1.34479	−	1.01054i
$823$	−8.37024	+	17.6399i	−0.291768	+	0.614889i	−0.995414	−	0.0956625i	$-0.969503\pi$
$823$	−8.37024	+	17.6399i	−0.291768	+	0.614889i	0.703645	+	0.710551i	$0.251554\pi$
$824$	−12.6769	+	6.65334i	−0.441620	+	0.231780i
$825$	16.7383	+	1.35126i	0.582754	+	0.0470448i
$826$	−5.05735	+	7.32684i	−0.175968	+	0.254933i
$827$	−42.6813	−	14.2491i	−1.48417	−	0.495490i	−0.544854	−	0.838531i	$-0.683415\pi$
$827$	−42.6813	−	14.2491i	−1.48417	−	0.495490i	−0.939320	+	0.343041i	$0.888543\pi$
$828$	−16.1538	+	10.2150i	−0.561383	+	0.354997i
$829$	−0.455865	−	1.57383i	−0.0158329	−	0.0546614i	0.952213	−	0.305436i	$-0.0988020\pi$
$829$	−0.455865	−	1.57383i	−0.0158329	−	0.0546614i	−0.968046	+	0.250774i	$0.919315\pi$
$830$	−3.92266	−	2.05877i	−0.136157	−	0.0714609i
$831$	−7.27058	−	19.1709i	−0.252214	−	0.665033i
$832$	−56.1349	−	23.9168i	−1.94613	−	0.829167i
$833$	0.482432	+	11.9714i	0.0167153	+	0.414785i
$834$	−24.1771	+	35.0266i	−0.837185	+	1.21287i
$835$	−1.28011	+	2.21721i	−0.0443000	+	0.0767298i
$836$	−20.7468	+	1.67485i	−0.717542	+	0.0579260i
$837$	−8.71901	+	5.51357i	−0.301373	+	0.190577i
$838$	−29.8237	+	9.95661i	−1.03024	+	0.343945i
$839$	−2.20847	+	5.82325i	−0.0762447	+	0.201041i	−0.967720	−	0.252029i	$-0.918902\pi$
$839$	−2.20847	+	5.82325i	−0.0762447	+	0.201041i	0.891475	+	0.453070i	$0.149671\pi$
$840$	1.67886	+	0.272841i	0.0579261	+	0.00941390i
$841$	28.0827	+	6.92175i	0.968368	+	0.238681i
$842$	42.4307	−	44.1750i	1.46226	−	1.52237i
$843$	9.20536	−	24.2725i	0.317050	−	0.835991i
$844$	21.8189	−	19.3298i	0.751036	−	0.665360i
$845$	3.68471	+	1.56991i	0.126758	+	0.0540064i
$846$	2.82266	−	13.8263i	0.0970450	−	0.475358i
$847$	1.16630	+	2.45792i	0.0400744	+	0.0844550i
$848$	13.4370	+	10.0972i	0.461428	+	0.346741i
$849$	2.57267	+	21.1878i	0.0882936	+	0.727164i
$850$	−3.87891	−	31.9457i	−0.133045	−	1.09573i
$851$	0.776903	−	19.2786i	0.0266319	−	0.660864i
$852$	21.3504	+	18.9148i	0.731451	+	0.648009i
$853$	31.3814	−	5.09997i	1.07448	−	0.174620i	0.402671	−	0.915345i	$-0.368082\pi$
$853$	31.3814	−	5.09997i	1.07448	−	0.174620i	0.671808	+	0.740725i	$0.265518\pi$
$854$	3.80938	+	94.5287i	0.130354	+	3.23471i
$855$	0.483757	−	0.592495i	0.0165441	−	0.0202629i
$856$	15.3353	−	5.11968i	0.524150	−	0.174987i
$857$	−6.59191	+	22.7579i	−0.225175	+	0.777395i	0.765768	+	0.643117i	$0.222359\pi$
$857$	−6.59191	+	22.7579i	−0.225175	+	0.777395i	−0.990944	+	0.134279i	$0.957128\pi$
$858$	−31.3349	−	19.8150i	−1.06976	−	0.676472i
$859$	16.0463	+	19.6532i	0.547494	+	0.670559i	0.972031	−	0.234852i	$-0.0754606\pi$
$859$	16.0463	+	19.6532i	0.547494	+	0.670559i	−0.424537	+	0.905411i	$0.639563\pi$
$860$	0.621272	−	0.550399i	0.0211852	−	0.0187685i
$861$	−7.74145	+	9.48156i	−0.263828	+	0.323131i
$862$	6.36091	+	2.12358i	0.216653	+	0.0723295i
$863$	20.6235	−	5.08324i	0.702033	−	0.173035i	0.127887	−	0.991789i	$-0.459181\pi$
$863$	20.6235	−	5.08324i	0.702033	−	0.173035i	0.574146	+	0.818753i	$0.305334\pi$
$864$	−7.39605	+	1.82296i	−0.251619	+	0.0620184i
$865$	−2.43350	−	0.812420i	−0.0827413	−	0.0276231i
$866$	−33.5983	+	41.1505i	−1.14172	+	1.39835i
$867$	5.80521	−	5.14296i	0.197155	−	0.174664i
$868$	−58.1897	−	71.2695i	−1.97509	−	2.41904i
$869$	−6.24023	−	3.94608i	−0.211685	−	0.133862i
$870$	0.0569624	−	0.196657i	0.00193120	−	0.00666729i
$871$	−27.1736	+	9.07189i	−0.920743	+	0.307389i
$872$	3.24353	−	3.97260i	0.109840	−	0.134529i
$873$	0.763030	+	18.9344i	0.0258246	+	0.640832i
$874$	−34.0384	+	5.53178i	−1.15137	+	0.187115i
$875$	−8.33750	−	7.38638i	−0.281859	−	0.249705i
$876$	−0.674076	+	16.7270i	−0.0227749	+	0.565154i
$877$	0.471262	+	3.88119i	0.0159134	+	0.131059i	0.998500	−	0.0547445i	$-0.0174344\pi$
$877$	0.471262	+	3.88119i	0.0159134	+	0.131059i	−0.982587	+	0.185803i	$0.940511\pi$
$878$	−2.80746	−	23.1215i	−0.0947473	−	0.780314i
$879$	−3.46609	−	2.60460i	−0.116908	−	0.0878509i
$880$	1.06575	+	2.24602i	0.0359265	+	0.0757135i
$881$	−9.92537	+	48.6177i	−0.334394	+	1.63797i	0.370624	+	0.928783i	$0.379144\pi$
$881$	−9.92537	+	48.6177i	−0.334394	+	1.63797i	−0.705019	+	0.709189i	$0.749061\pi$
$882$	7.85638	+	3.34729i	0.264538	+	0.112709i
$883$	7.07341	−	6.26650i	0.238039	−	0.210884i	−0.535666	−	0.844430i	$-0.679939\pi$
$883$	7.07341	−	6.26650i	0.238039	−	0.210884i	0.773705	+	0.633545i	$0.218401\pi$
$884$	−14.4646	+	38.1401i	−0.486498	+	1.28279i
$885$	−0.293137	+	0.305188i	−0.00985368	+	0.0102588i
$886$	0.917200	+	0.226069i	0.0308139	+	0.00759495i
$887$	13.2150	+	2.14764i	0.443715	+	0.0721107i	0.378164	−	0.925739i	$-0.376555\pi$
$887$	13.2150	+	2.14764i	0.443715	+	0.0721107i	0.0655508	+	0.997849i	$0.479120\pi$
$888$	−1.45683	+	3.84135i	−0.0488881	+	0.128907i
$889$	1.75314	−	0.585285i	0.0587985	−	0.0196298i
$890$	−10.4630	+	6.61638i	−0.350719	+	0.221782i
$891$	−3.42724	+	0.276675i	−0.114817	+	0.00926897i
$892$	13.7888	−	23.8829i	0.461684	−	0.799659i
$893$	8.30428	−	12.0308i	0.277892	−	0.402596i
$894$	−0.643425	−	15.9664i	−0.0215194	−	0.533997i
$895$	−0.667941	−	0.284583i	−0.0223268	−	0.00951256i
$896$	−13.3033	−	35.0778i	−0.444431	−	1.17187i
$897$	−31.2271	−	16.3892i	−1.04264	−	0.547221i
$898$	−21.5734	−	74.4802i	−0.719915	−	2.48543i
$899$	−2.41768	+	1.52885i	−0.0806340	+	0.0509898i
$900$	−12.4914	−	4.17025i	−0.416381	−	0.139008i
$901$	13.6799	−	19.8188i	0.455744	−	0.660260i
$902$	27.4858	+	2.21888i	0.915176	+	0.0738806i
$903$	2.64602	−	1.38874i	0.0880539	−	0.0462142i
$904$	−12.5586	+	26.4666i	−0.417692	+	0.880267i
$905$	0.986686	+	0.741447i	0.0327986	+	0.0246465i
$906$	−0.691093	+	17.1493i	−0.0229600	+	0.569748i
$907$	−15.6476	+	32.9767i	−0.519572	+	1.09497i	0.458880	+	0.888498i	$0.348251\pi$
$907$	−15.6476	+	32.9767i	−0.519572	+	1.09497i	−0.978452	+	0.206476i	$0.933801\pi$
$908$	62.4046	−	26.5881i	2.07097	−	0.882358i
$909$	−2.42792	−	11.8927i	−0.0805291	−	0.394458i
$910$	4.30896	+	11.3618i	0.142841	+	0.376640i
$911$	−1.10001	−	1.34726i	−0.0364448	−	0.0446368i	0.756061	−	0.654501i	$-0.227121\pi$
$911$	−1.10001	−	1.34726i	−0.0364448	−	0.0446368i	−0.792506	+	0.609864i	$0.791224\pi$
$912$	−4.70242	−	0.764218i	−0.155713	−	0.0253058i
$913$	−2.48665	+	20.4794i	−0.0822961	+	0.677769i
$914$	−4.68979			−0.155125
$915$	−0.542025	+	4.46398i	−0.0179188	+	0.147575i
$916$	29.3215	−	30.5269i	0.968809	−	1.00864i
$917$	−2.17690	+	7.51554i	−0.0718876	+	0.248185i
$918$	1.83318	+	6.32889i	0.0605041	+	0.208884i
$919$	3.51406	+	5.09100i	0.115918	+	0.167937i	0.876648	−	0.481132i	$-0.159774\pi$
$919$	3.51406	+	5.09100i	0.115918	+	0.167937i	−0.760730	+	0.649069i	$0.775159\pi$
$920$	−1.82244	−	3.15656i	−0.0600842	−	0.104069i
$921$	−19.3505	−	1.56213i	−0.637620	−	0.0514740i
$922$	27.3788	−	4.44949i	0.901673	−	0.146536i
$923$	−10.5278	+	51.5685i	−0.346527	+	1.69740i
$924$	−6.13410	−	30.0468i	−0.201797	−	0.988468i
$925$	10.6281	−	7.98648i	0.349449	−	0.262594i
$926$	19.3673	+	28.0584i	0.636449	+	0.922055i
$927$	−9.45517	+	0.763300i	−0.310548	+	0.0250701i
$928$	−2.05083	+	0.505485i	−0.0673219	+	0.0165934i
$929$	24.6148	−	42.6340i	0.807585	−	1.39878i	−0.106948	−	0.994265i	$-0.534108\pi$
$929$	24.6148	−	42.6340i	0.807585	−	1.39878i	0.914532	−	0.404513i	$-0.132559\pi$
$930$	−3.80852	−	6.59654i	−0.124886	−	0.216309i
$931$	6.12825	+	6.38019i	0.200845	+	0.209102i
$932$	5.25708	−	2.23983i	0.172201	−	0.0733682i
$933$	7.56854	+	15.9504i	0.247783	+	0.522192i
$934$	5.58586	+	4.94864i	0.182775	+	0.161924i
$935$	3.15390	−	1.65530i	0.103144	−	0.0541339i
$936$	5.20189	+	5.41574i	0.170029	+	0.177019i
$937$	−6.47202	+	4.86341i	−0.211432	+	0.158881i	−0.701183	−	0.712982i	$-0.747344\pi$
$937$	−6.47202	+	4.86341i	−0.211432	+	0.158881i	0.489751	+	0.871863i	$0.337088\pi$
$938$	−36.5452	−	19.1804i	−1.19324	−	0.626262i
$939$	8.40610	+	5.31569i	0.274323	+	0.173471i
$940$	5.80845	+	1.43165i	0.189451	+	0.0466954i
$941$	−11.8147			−0.385149			−0.192575	−	0.981282i	$-0.561684\pi$
$941$	−11.8147			−0.385149			−0.192575	+	0.981282i	$0.561684\pi$
$942$	−19.5657	+	18.8288i	−0.637484	+	0.613476i
$943$	26.2306			0.854187
$944$	2.55906	+	0.630752i	0.0832904	+	0.0205292i
$945$	0.952496	+	0.602322i	0.0309847	+	0.0195935i
$946$	−5.96089	−	3.12852i	−0.193805	−	0.101717i
$947$	−7.69742	+	5.78424i	−0.250133	+	0.187962i	−0.718412	−	0.695618i	$-0.755131\pi$
$947$	−7.69742	+	5.78424i	−0.250133	+	0.187962i	0.468279	+	0.883581i	$0.344874\pi$
$948$	4.01090	+	4.17579i	0.130268	+	0.135623i
$949$	−27.3516	+	14.3552i	−0.887870	+	0.465990i
$950$	−17.7855	−	15.7566i	−0.577038	−	0.511211i
$951$	2.14893	+	4.52878i	0.0696839	+	0.146856i
$952$	−13.9637	+	5.94939i	−0.452567	+	0.192821i
$953$	−26.8164	−	27.9189i	−0.868670	−	0.904381i	0.127499	−	0.991839i	$-0.459305\pi$
$953$	−26.8164	−	27.9189i	−0.868670	−	0.904381i	−0.996168	+	0.0874579i	$0.972126\pi$
$954$	−8.58227	−	14.8649i	−0.277861	−	0.481270i
$955$	1.57542	−	2.72871i	0.0509795	−	0.0882991i
$956$	−5.09265	+	1.25523i	−0.164708	+	0.0405969i
$957$	−0.950331	+	0.0767187i	−0.0307198	+	0.00247996i
$958$	30.7922	+	44.6101i	0.994849	+	1.44129i
$959$	58.8471	−	44.2207i	1.90027	−	1.42796i
$960$	−0.835785	−	4.09394i	−0.0269748	−	0.132131i
$961$	−15.0861	+	73.8964i	−0.486647	+	2.38376i
$962$	−28.9706	+	4.70818i	−0.934049	+	0.151798i
$963$	10.6773	+	0.861962i	0.344072	+	0.0277763i
$964$	24.7205	+	42.8172i	0.796195	+	1.37905i
$965$	−2.48253	−	3.59656i	−0.0799153	−	0.115777i
$966$	−14.1357	−	48.8022i	−0.454810	−	1.57019i
$967$	12.9347	−	44.6557i	0.415952	−	1.43603i	−0.430027	−	0.902816i	$-0.641496\pi$
$967$	12.9347	−	44.6557i	0.415952	−	1.43603i	0.845979	−	0.533216i	$-0.179017\pi$
$968$	−0.859941	+	0.895294i	−0.0276396	+	0.0287758i
$969$	−0.822759	+	6.77603i	−0.0264308	+	0.217677i
$970$	−13.9919			−0.449253
$971$	0.542481	−	4.46773i	0.0174090	−	0.143376i	−0.981412	−	0.191910i	$-0.938532\pi$
$971$	0.542481	−	4.46773i	0.0174090	−	0.143376i	0.998822	+	0.0485338i	$0.0154548\pi$
$972$	2.66152	+	0.432539i	0.0853682	+	0.0138737i
$973$	−41.0834	−	50.3180i	−1.31707	−	1.61312i
$974$	−7.28060	−	19.1974i	−0.233285	−	0.615123i
$975$	−4.86058	−	23.8087i	−0.155663	−	0.762489i
$976$	25.7665	−	10.9781i	0.824767	−	0.351400i
$977$	17.7328	−	37.3711i	0.567323	−	1.19561i	−0.393726	−	0.919228i	$-0.628814\pi$
$977$	17.7328	−	37.3711i	0.567323	−	1.19561i	0.961049	−	0.276379i	$-0.0891346\pi$
$978$	0.834564	−	20.7095i	0.0266864	−	0.662216i
$979$	46.0861	+	34.6314i	1.47292	+	1.10683i
$980$	−1.55198	+	3.27072i	−0.0495761	+	0.104479i
$981$	3.00882	−	1.57915i	0.0960641	−	0.0504183i
$982$	−14.2333	−	1.14903i	−0.454203	−	0.0366670i
$983$	−2.23266	+	3.23457i	−0.0712109	+	0.103167i	−0.856971	−	0.515364i	$-0.827657\pi$
$983$	−2.23266	+	3.23457i	−0.0712109	+	0.103167i	0.785760	+	0.618531i	$0.212272\pi$
$984$	−5.29784	−	1.76868i	−0.168889	−	0.0563834i
$985$	1.40662	−	0.889491i	0.0448186	−	0.0283415i
$986$	0.508320	+	1.75492i	0.0161882	+	0.0558881i
$987$	19.0711	+	10.0093i	0.607039	+	0.318599i
$988$	10.6803	+	28.1618i	0.339787	+	0.895945i
$989$	−5.89133	−	2.51006i	−0.187333	−	0.0798152i
$990$	−0.102227	−	2.53674i	−0.00324899	−	0.0806228i
$991$	17.1753	−	24.8828i	0.545592	−	0.790427i	−0.449082	−	0.893490i	$-0.648249\pi$
$991$	17.1753	−	24.8828i	0.545592	−	0.790427i	0.994675	+	0.103063i	$0.0328644\pi$
$992$	−39.2907	+	68.0535i	−1.24748	+	2.16070i
$993$	−23.2681	+	1.87839i	−0.738389	+	0.0596089i
$994$	−64.0879	+	40.5267i	−2.03274	+	1.28543i
$995$	4.12471	−	1.37703i	0.130762	−	0.0436548i
$996$	5.73687	−	15.1269i	0.181780	−	0.479314i
$997$	37.1886	+	6.04374i	1.17777	+	0.191407i	0.717622	−	0.696433i	$-0.245231\pi$
$997$	37.1886	+	6.04374i	1.17777	+	0.191407i	0.460153	+	0.887840i	$0.347795\pi$
$998$	−49.1812	−	12.1221i	−1.55681	−	0.383718i
$999$	−1.88564	+	1.96316i	−0.0596591	+	0.0621117i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.q.b.19.13	✓	336
157.124	even	39	inner	471.2.q.b.124.13	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.q.b.19.13	✓	336	1.1	even	1	trivial
471.2.q.b.124.13	yes	336	157.124	even	39	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10415 + 0.518627i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.38758 + 1.25310i) q^{4} +(-0.272381 + 0.204681i) q^{5} +(-1.50122 - 1.56294i) q^{6} +(2.92878 - 1.53714i) q^{7} +(1.12970 + 1.00083i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(2.10415 + 0.518627i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(2.38758 + 1.25310i) q^{4} +(-0.272381 + 0.204681i) q^{5} +(-1.50122 - 1.56294i) q^{6} +(2.92878 - 1.53714i) q^{7} +(1.12970 + 1.00083i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.679283 + 0.289416i) q^{10} +(2.38186 + 2.47977i) q^{11} +(-1.34822 - 2.33518i) q^{12} +(2.48774 - 4.30889i) q^{13} +(6.95981 - 1.71544i) q^{14} +(0.339608 - 0.0274160i) q^{15} +(-1.20549 - 1.74646i) q^{16} +(-2.43066 + 1.82653i) q^{17} +(0.433481 + 2.12333i) q^{18} +(-0.449057 + 2.19963i) q^{19} +(-0.906814 + 0.147372i) q^{20} +(-3.29693 - 0.266156i) q^{21} +(3.72571 + 6.45312i) q^{22} +(4.02650 + 5.83339i) q^{23} +(-0.419904 - 1.44968i) q^{24} +(-1.35879 + 4.69109i) q^{25} +(7.46929 - 7.77636i) q^{26} +(0.120537 - 0.992709i) q^{27} +8.91888 q^{28} +(0.0334233 - 0.275266i) q^{29} +(0.728806 + 0.118443i) q^{30} +(-6.52433 - 7.99085i) q^{31} +(-2.70117 - 7.12239i) q^{32} +(-0.687766 - 3.36890i) q^{33} +(-6.06178 + 2.58268i) q^{34} +(-0.483120 + 1.01815i) q^{35} +(-0.108575 + 2.69425i) q^{36} +(-2.17614 - 1.63526i) q^{37} +(-2.08567 + 4.39546i) q^{38} +(-4.40557 + 2.31222i) q^{39} +(-0.512559 - 0.0413780i) q^{40} +(2.10221 - 3.04558i) q^{41} +(-6.79921 - 2.26991i) q^{42} +(-0.763589 + 0.482864i) q^{43} +(2.57946 + 8.90534i) q^{44} +(-0.301686 - 0.158337i) q^{45} +(5.44702 + 14.3626i) q^{46} +(-5.99054 - 2.55233i) q^{47} +(0.0854485 + 2.12038i) q^{48} +(2.23851 - 3.24304i) q^{49} +(-5.29203 + 9.16606i) q^{50} +(3.03059 - 0.244654i) q^{51} +(11.3391 - 7.17042i) q^{52} +(-7.51281 + 2.50814i) q^{53} +(0.768474 - 2.02630i) q^{54} +(-1.15633 - 0.187922i) q^{55} +(4.84707 + 1.19469i) q^{56} +(1.55516 - 1.61910i) q^{57} +(0.213088 - 0.561868i) q^{58} +(-0.929649 + 0.823597i) q^{59} +(0.845195 + 0.360104i) q^{60} +(-2.63996 + 12.9314i) q^{61} +(-9.58392 - 20.1977i) q^{62} +(2.64428 + 1.98705i) q^{63} +(-1.47822 - 12.1742i) q^{64} +(0.204335 + 1.68285i) q^{65} +(0.300038 - 7.44538i) q^{66} +(-4.30980 - 3.81815i) q^{67} +(-8.09221 + 1.31511i) q^{68} +(-0.285409 - 7.08235i) q^{69} +(-1.54460 + 1.89179i) q^{70} +(-10.0339 + 3.34982i) q^{71} +(-0.419904 + 1.44968i) q^{72} +(-5.24729 - 3.31819i) q^{73} +(-3.73084 - 4.56945i) q^{74} +(3.65566 - 3.23863i) q^{75} +(-3.82850 + 4.68907i) q^{76} +(10.7877 + 3.60147i) q^{77} +(-10.4692 + 2.58042i) q^{78} +(-2.08490 + 0.513881i) q^{79} +(0.685819 + 0.228960i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(6.00290 - 5.31811i) q^{82} +(3.79458 + 4.64751i) q^{83} +(-7.53815 - 4.76684i) q^{84} +(0.288211 - 0.995020i) q^{85} +(-1.85713 + 0.620003i) q^{86} +(-0.175369 + 0.214788i) q^{87} +(0.208958 + 5.18523i) q^{88} +(16.5488 - 2.68944i) q^{89} +(-0.552676 - 0.489629i) q^{90} +(0.662663 - 16.4438i) q^{91} +(2.30377 + 18.9733i) q^{92} +(1.24346 + 10.2408i) q^{93} +(-11.2813 - 8.47736i) q^{94} +(-0.327907 - 0.691049i) q^{95} +(-1.52368 + 7.46346i) q^{96} +(17.4334 + 7.42767i) q^{97} +(6.39209 - 5.66289i) q^{98} +(-1.21927 + 3.21495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9}+O(q^{10}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9	\( 336 q - 2 q^{2} + 14 q^{3} - 26 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 14 q^{9} + q^{10} - 2 q^{11} - 182 q^{12} - 78 q^{13} - 38 q^{14} - 24 q^{15} - 14 q^{16} - 3 q^{17} + q^{18} - 2 q^{19} - q^{20} + 2 q^{21} + 2 q^{22} - 7 q^{23} + 124 q^{25} + 118 q^{26} - 28 q^{27} - 80 q^{28} + 49 q^{29} + q^{30} - 12 q^{31} - 12 q^{32} + 11 q^{33} - 63 q^{34} + 65 q^{35} + 13 q^{36} - 25 q^{37} - 5 q^{38} + 73 q^{40} - 94 q^{41} - 7 q^{42} - 10 q^{43} - 12 q^{44} - 17 q^{45} - 16 q^{46} + 29 q^{47} + 7 q^{48} - 70 q^{49} - 36 q^{50} + 101 q^{51} - 27 q^{52} - 32 q^{53} - 2 q^{54} - 23 q^{55} - 130 q^{56} - 2 q^{57} + 302 q^{58} - 18 q^{59} - q^{60} - 40 q^{61} - 130 q^{62} + 28 q^{63} - 16 q^{64} + 52 q^{65} - 24 q^{66} - 114 q^{67} + 150 q^{68} - 3 q^{69} - 15 q^{70} + 27 q^{71} - 3 q^{73} - 125 q^{74} - 40 q^{75} + 368 q^{76} - 24 q^{77} - 41 q^{78} + 55 q^{79} + 78 q^{80} + 14 q^{81} + 24 q^{82} + 40 q^{83} + 105 q^{84} - 142 q^{85} - 48 q^{86} - 5 q^{87} - 255 q^{88} - 52 q^{89} - 2 q^{90} + 130 q^{91} - 366 q^{92} - 54 q^{93} - 64 q^{94} - 58 q^{95} + 136 q^{96} - 110 q^{97} - 6 q^{98} + 4 q^{99}+O(q^{100}) \) 336 * q - 2 * q^2 + 14 * q^3 - 26 * q^4 + 2 * q^5 + q^6 - 4 * q^7 + 14 * q^9 + q^10 - 2 * q^11 - 182 * q^12 - 78 * q^13 - 38 * q^14 - 24 * q^15 - 14 * q^16 - 3 * q^17 + q^18 - 2 * q^19 - q^20 + 2 * q^21 + 2 * q^22 - 7 * q^23 + 124 * q^25 + 118 * q^26 - 28 * q^27 - 80 * q^28 + 49 * q^29 + q^30 - 12 * q^31 - 12 * q^32 + 11 * q^33 - 63 * q^34 + 65 * q^35 + 13 * q^36 - 25 * q^37 - 5 * q^38 + 73 * q^40 - 94 * q^41 - 7 * q^42 - 10 * q^43 - 12 * q^44 - 17 * q^45 - 16 * q^46 + 29 * q^47 + 7 * q^48 - 70 * q^49 - 36 * q^50 + 101 * q^51 - 27 * q^52 - 32 * q^53 - 2 * q^54 - 23 * q^55 - 130 * q^56 - 2 * q^57 + 302 * q^58 - 18 * q^59 - q^60 - 40 * q^61 - 130 * q^62 + 28 * q^63 - 16 * q^64 + 52 * q^65 - 24 * q^66 - 114 * q^67 + 150 * q^68 - 3 * q^69 - 15 * q^70 + 27 * q^71 - 3 * q^73 - 125 * q^74 - 40 * q^75 + 368 * q^76 - 24 * q^77 - 41 * q^78 + 55 * q^79 + 78 * q^80 + 14 * q^81 + 24 * q^82 + 40 * q^83 + 105 * q^84 - 142 * q^85 - 48 * q^86 - 5 * q^87 - 255 * q^88 - 52 * q^89 - 2 * q^90 + 130 * q^91 - 366 * q^92 - 54 * q^93 - 64 * q^94 - 58 * q^95 + 136 * q^96 - 110 * q^97 - 6 * q^98 + 4 * q^99

Introduction

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