LMFDB - Embedded newform 76.2.k.a.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.1
Character	$\chi$	$=$	76.71
Dual form			76.2.k.a.15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37896 - 0.313814i) q^{2} +(-0.00846870 + 0.0480284i) q^{3} +(1.80304 + 0.865472i) q^{4} +(0.579816 + 0.486524i) q^{5} +(0.0267499 - 0.0635714i) q^{6} +(2.62687 - 1.51662i) q^{7} +(-2.21472 - 1.75927i) q^{8} +(2.81684 + 1.02525i) q^{9} +O(q^{10})$	\(q+(-1.37896 - 0.313814i) q^{2} +(-0.00846870 + 0.0480284i) q^{3} +(1.80304 + 0.865472i) q^{4} +(0.579816 + 0.486524i) q^{5} +(0.0267499 - 0.0635714i) q^{6} +(2.62687 - 1.51662i) q^{7} +(-2.21472 - 1.75927i) q^{8} +(2.81684 + 1.02525i) q^{9} +(-0.646863 - 0.852849i) q^{10} +(-0.655865 - 0.378664i) q^{11} +(-0.0568366 + 0.0792677i) q^{12} +(-1.53562 + 0.270771i) q^{13} +(-4.09827 + 1.26701i) q^{14} +(-0.0282772 + 0.0237274i) q^{15} +(2.50192 + 3.12096i) q^{16} +(-4.84662 + 1.76403i) q^{17} +(-3.56257 - 2.29774i) q^{18} +(-4.29322 + 0.753853i) q^{19} +(0.624360 + 1.37904i) q^{20} +(0.0505948 + 0.139008i) q^{21} +(0.785579 + 0.727981i) q^{22} +(-1.13123 - 1.34815i) q^{23} +(0.103251 - 0.0914706i) q^{24} +(-0.768759 - 4.35985i) q^{25} +(2.20252 + 0.108518i) q^{26} +(-0.146250 + 0.253312i) q^{27} +(6.04894 - 0.461053i) q^{28} +(-0.178978 + 0.491737i) q^{29} +(0.0464391 - 0.0238453i) q^{30} +(3.59957 + 6.23464i) q^{31} +(-2.47063 - 5.08881i) q^{32} +(0.0237409 - 0.0282933i) q^{33} +(7.23685 - 0.911576i) q^{34} +(2.26097 + 0.398670i) q^{35} +(4.19156 + 4.28646i) q^{36} -8.80926i q^{37} +(6.15673 + 0.307741i) q^{38} -0.0760464i q^{39} +(-0.428204 - 2.09756i) q^{40} +(-2.56508 - 0.452292i) q^{41} +(-0.0261453 - 0.207563i) q^{42} +(-6.43028 + 7.66330i) q^{43} +(-0.854829 - 1.25038i) q^{44} +(1.13444 + 1.96492i) q^{45} +(1.13685 + 2.21404i) q^{46} +(3.62828 - 9.96861i) q^{47} +(-0.171083 + 0.0937325i) q^{48} +(1.10029 - 1.90575i) q^{49} +(-0.308097 + 6.25329i) q^{50} +(-0.0436787 - 0.247714i) q^{51} +(-3.00313 - 0.840824i) q^{52} +(5.23679 + 6.24096i) q^{53} +(0.281165 - 0.303411i) q^{54} +(-0.196052 - 0.538649i) q^{55} +(-8.48591 - 1.26247i) q^{56} +(0.000151609 - 0.212580i) q^{57} +(0.401117 - 0.621918i) q^{58} +(-7.79113 + 2.83574i) q^{59} +(-0.0715204 + 0.0183083i) q^{60} +(-2.83699 + 2.38052i) q^{61} +(-3.00713 - 9.72690i) q^{62} +(8.95438 - 1.57890i) q^{63} +(1.80995 + 7.79257i) q^{64} +(-1.02211 - 0.590117i) q^{65} +(-0.0416166 + 0.0315651i) q^{66} +(-8.84545 - 3.21948i) q^{67} +(-10.2654 - 1.01400i) q^{68} +(0.0743296 - 0.0429142i) q^{69} +(-2.99267 - 1.25927i) q^{70} +(6.90158 + 5.79111i) q^{71} +(-4.43483 - 7.22621i) q^{72} +(-1.69979 + 9.64000i) q^{73} +(-2.76447 + 12.1476i) q^{74} +0.215907 q^{75} +(-8.39329 - 2.35643i) q^{76} -2.29716 q^{77} +(-0.0238644 + 0.104865i) q^{78} +(2.62972 - 14.9139i) q^{79} +(-0.0677710 + 3.02683i) q^{80} +(6.87801 + 5.77133i) q^{81} +(3.39519 + 1.42865i) q^{82} +(10.6616 - 6.15546i) q^{83} +(-0.0290831 + 0.294425i) q^{84} +(-3.66839 - 1.33518i) q^{85} +(11.2719 - 8.54945i) q^{86} +(-0.0221016 - 0.0127604i) q^{87} +(0.786385 + 1.99248i) q^{88} +(13.0613 - 2.30306i) q^{89} +(-0.947731 - 3.06554i) q^{90} +(-3.62321 + 3.04023i) q^{91} +(-0.872873 - 3.40982i) q^{92} +(-0.329923 + 0.120082i) q^{93} +(-8.13153 + 12.6077i) q^{94} +(-2.85604 - 1.65165i) q^{95} +(0.265330 - 0.0755648i) q^{96} +(-1.74814 - 4.80298i) q^{97} +(-2.11530 + 2.28266i) q^{98} +(-1.45925 - 1.73906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−1.37896	−	0.313814i	−0.975069	−	0.221900i
$2$	−1.37896	−	0.313814i	−0.975069	−	0.221900i
$3$	−0.00846870	+	0.0480284i	−0.00488941	+	0.0277292i	−0.987155	−	0.159766i	$-0.948926\pi$
$3$	−0.00846870	+	0.0480284i	−0.00488941	+	0.0277292i	0.982265	+	0.187496i	$0.0600370\pi$
$4$	1.80304	+	0.865472i	0.901521	+	0.432736i
$5$	0.579816	+	0.486524i	0.259302	+	0.217580i	0.763165	−	0.646203i	$-0.223644\pi$
$5$	0.579816	+	0.486524i	0.259302	+	0.217580i	−0.503864	+	0.863783i	$0.668089\pi$
$6$	0.0267499	−	0.0635714i	0.0109206	−	0.0259529i
$7$	2.62687	−	1.51662i	0.992862	−	0.573229i	0.0867337	−	0.996232i	$-0.472357\pi$
$7$	2.62687	−	1.51662i	0.992862	−	0.573229i	0.906129	+	0.423002i	$0.139024\pi$
$8$	−2.21472	−	1.75927i	−0.783021	−	0.621995i
$9$	2.81684	+	1.02525i	0.938948	+	0.341749i
$10$	−0.646863	−	0.852849i	−0.204556	−	0.269695i
$11$	−0.655865	−	0.378664i	−0.197751	−	0.114171i	0.397855	−	0.917448i	$-0.369755\pi$
$11$	−0.655865	−	0.378664i	−0.197751	−	0.114171i	−0.595606	+	0.803277i	$0.703088\pi$
$12$	−0.0568366	+	0.0792677i	−0.0164073	+	0.0228826i
$13$	−1.53562	+	0.270771i	−0.425904	+	0.0750984i	−0.382492	−	0.923959i	$-0.624934\pi$
$13$	−1.53562	+	0.270771i	−0.425904	+	0.0750984i	−0.0434122	+	0.999057i	$0.513823\pi$
$14$	−4.09827	+	1.26701i	−1.09531	+	0.338622i
$15$	−0.0282772	+	0.0237274i	−0.00730115	+	0.00612639i
$16$	2.50192	+	3.12096i	0.625479	+	0.780241i
$17$	−4.84662	+	1.76403i	−1.17548	+	0.427839i	−0.854603	−	0.519282i	$-0.826199\pi$
$17$	−4.84662	+	1.76403i	−1.17548	+	0.427839i	−0.320875	+	0.947121i	$0.603977\pi$
$18$	−3.56257	−	2.29774i	−0.839705	−	0.541582i
$19$	−4.29322	+	0.753853i	−0.984931	+	0.172946i
$19$	−4.29322	+	0.753853i	−0.984931	+	0.172946i
$20$	0.624360	+	1.37904i	0.139611	+	0.308362i
$21$	0.0505948	+	0.139008i	0.0110407	+	0.0303340i
$22$	0.785579	+	0.727981i	0.167486	+	0.155206i
$23$	−1.13123	−	1.34815i	−0.235879	−	0.281109i	0.635100	−	0.772430i	$-0.280959\pi$
$23$	−1.13123	−	1.34815i	−0.235879	−	0.281109i	−0.870979	+	0.491321i	$0.836514\pi$
$24$	0.103251	−	0.0914706i	0.0210759	−	0.0186714i
$25$	−0.768759	−	4.35985i	−0.153752	−	0.871970i
$26$	2.20252	+	0.108518i	0.431950	+	0.0212820i
$27$	−0.146250	+	0.253312i	−0.0281458	+	0.0487500i
$28$	6.04894	−	0.461053i	1.14314	−	0.0871308i
$29$	−0.178978	+	0.491737i	−0.0332353	+	0.0913133i	−0.955200	−	0.295960i	$-0.904361\pi$
$29$	−0.178978	+	0.491737i	−0.0332353	+	0.0913133i	0.921965	+	0.387273i	$0.126583\pi$
$30$	0.0464391	−	0.0238453i	0.00847857	−	0.00435353i
$31$	3.59957	+	6.23464i	0.646502	+	1.11978i	0.983952	+	0.178432i	$0.0571023\pi$
$31$	3.59957	+	6.23464i	0.646502	+	1.11978i	−0.337450	+	0.941343i	$0.609564\pi$
$32$	−2.47063	−	5.08881i	−0.436750	−	0.899583i
$33$	0.0237409	−	0.0282933i	0.00413277	−	0.00492524i
$34$	7.23685	−	0.911576i	1.24111	−	0.156334i
$35$	2.26097	+	0.398670i	0.382174	+	0.0673876i
$36$	4.19156	+	4.28646i	0.698594	+	0.714410i
$37$		−	8.80926i		−	1.44823i	−0.689678	−	0.724116i	$-0.742248\pi$
$37$		−	8.80926i		−	1.44823i	0.689678	−	0.724116i	$-0.257752\pi$
$38$	6.15673	+	0.307741i	0.998753	+	0.0499223i
$39$		−	0.0760464i		−	0.0121772i
$40$	−0.428204	−	2.09756i	−0.0677050	−	0.331654i
$41$	−2.56508	−	0.452292i	−0.400598	−	0.0706361i	−0.0302802	−	0.999541i	$-0.509640\pi$
$41$	−2.56508	−	0.452292i	−0.400598	−	0.0706361i	−0.370317	+	0.928905i	$0.620751\pi$
$42$	−0.0261453	−	0.207563i	−0.00403431	−	0.0320277i
$43$	−6.43028	+	7.66330i	−0.980608	+	1.16864i	0.00506711	+	0.999987i	$0.498387\pi$
$43$	−6.43028	+	7.66330i	−0.980608	+	1.16864i	−0.985675	+	0.168656i	$0.946057\pi$
$44$	−0.854829	−	1.25038i	−0.128870	−	0.188502i
$45$	1.13444	+	1.96492i	0.169113	+	0.292912i
$46$	1.13685	+	2.21404i	0.167620	+	0.326442i
$47$	3.62828	−	9.96861i	0.529239	−	1.45407i	−0.330730	−	0.943725i	$-0.607295\pi$
$47$	3.62828	−	9.96861i	0.529239	−	1.45407i	0.859969	−	0.510346i	$-0.170483\pi$
$48$	−0.171083	+	0.0937325i	−0.0246937	+	0.0135291i
$49$	1.10029	−	1.90575i	0.157184	−	0.272250i
$50$	−0.308097	+	6.25329i	−0.0435715	+	0.884349i
$51$	−0.0436787	−	0.247714i	−0.00611624	−	0.0346869i
$52$	−3.00313	−	0.840824i	−0.416459	−	0.116601i
$53$	5.23679	+	6.24096i	0.719328	+	0.857262i	0.994565	−	0.104114i	$-0.0332007\pi$
$53$	5.23679	+	6.24096i	0.719328	+	0.857262i	−0.275237	+	0.961376i	$0.588756\pi$
$54$	0.281165	−	0.303411i	0.0382617	−	0.0412890i
$55$	−0.196052	−	0.538649i	−0.0264357	−	0.0726315i
$56$	−8.48591	−	1.26247i	−1.13398	−	0.168705i
$57$	0.000151609	−	0.212580i	2.00811e−5	−	0.0281570i
$58$	0.401117	−	0.621918i	0.0526692	−	0.0816619i
$59$	−7.79113	+	2.83574i	−1.01432	+	0.369182i	−0.795090	−	0.606492i	$-0.792576\pi$
$59$	−7.79113	+	2.83574i	−1.01432	+	0.369182i	−0.219228	+	0.975674i	$0.570354\pi$
$60$	−0.0715204	+	0.0183083i	−0.00923325	+	0.00236360i
$61$	−2.83699	+	2.38052i	−0.363239	+	0.304794i	−0.806080	−	0.591806i	$-0.798415\pi$
$61$	−2.83699	+	2.38052i	−0.363239	+	0.304794i	0.442841	+	0.896600i	$0.353971\pi$
$62$	−3.00713	−	9.72690i	−0.381907	−	1.23532i
$63$	8.95438	−	1.57890i	1.12815	−	0.198923i
$64$	1.80995	+	7.79257i	0.226244	+	0.974071i
$65$	−1.02211	−	0.590117i	−0.126778	−	0.0731951i
$66$	−0.0416166	+	0.0315651i	−0.00512265	+	0.00388539i
$67$	−8.84545	−	3.21948i	−1.08064	−	0.393322i	−0.260497	−	0.965475i	$-0.583886\pi$
$67$	−8.84545	−	3.21948i	−1.08064	−	0.393322i	−0.820147	+	0.572152i	$0.806109\pi$
$68$	−10.2654	−	1.01400i	−1.24486	−	0.122966i
$69$	0.0743296	−	0.0429142i	0.00894823	−	0.00516627i
$70$	−2.99267	−	1.25927i	−0.357693	−	0.150512i
$71$	6.90158	+	5.79111i	0.819067	+	0.687279i	0.952753	−	0.303745i	$-0.0982371\pi$
$71$	6.90158	+	5.79111i	0.819067	+	0.687279i	−0.133687	+	0.991024i	$0.542682\pi$
$72$	−4.43483	−	7.22621i	−0.522649	−	0.851618i
$73$	−1.69979	+	9.64000i	−0.198946	+	1.12828i	0.707741	+	0.706472i	$0.249714\pi$
$73$	−1.69979	+	9.64000i	−0.198946	+	1.12828i	−0.906687	+	0.421805i	$0.861397\pi$
$74$	−2.76447	+	12.1476i	−0.321363	+	1.41213i
$75$	0.215907			0.0249308
$76$	−8.39329	−	2.35643i	−0.962776	−	0.270301i
$77$	−2.29716			−0.261786
$78$	−0.0238644	+	0.104865i	−0.00270211	+	0.0118736i
$79$	2.62972	−	14.9139i	0.295866	−	1.67794i	−0.367794	−	0.929907i	$-0.619887\pi$
$79$	2.62972	−	14.9139i	0.295866	−	1.67794i	0.663660	−	0.748034i	$-0.269002\pi$
$80$	−0.0677710	+	3.02683i	−0.00757703	+	0.338409i
$81$	6.87801	+	5.77133i	0.764223	+	0.641259i
$82$	3.39519	+	1.42865i	0.374936	+	0.157768i
$83$	10.6616	−	6.15546i	1.17026	−	0.675650i	0.216519	−	0.976279i	$-0.430530\pi$
$83$	10.6616	−	6.15546i	1.17026	−	0.675650i	0.953741	+	0.300629i	$0.0971965\pi$
$84$	−0.0290831	+	0.294425i	−0.00317322	+	0.0321244i
$85$	−3.66839	−	1.33518i	−0.397893	−	0.144821i
$86$	11.2719	−	8.54945i	1.21548	−	0.921911i
$87$	−0.0221016	−	0.0127604i	−0.00236954	−	0.00136806i
$88$	0.786385	+	1.99248i	0.0838289	+	0.212399i
$89$	13.0613	−	2.30306i	1.38450	−	0.244124i	0.568739	−	0.822518i	$-0.307432\pi$
$89$	13.0613	−	2.30306i	1.38450	−	0.244124i	0.815757	+	0.578394i	$0.196321\pi$
$90$	−0.947731	−	3.06554i	−0.0998996	−	0.323136i
$91$	−3.62321	+	3.04023i	−0.379816	+	0.318703i
$92$	−0.872873	−	3.40982i	−0.0910033	−	0.355499i
$93$	−0.329923	+	0.120082i	−0.0342115	+	0.0124520i
$94$	−8.13153	+	12.6077i	−0.838703	+	1.30038i
$95$	−2.85604	−	1.65165i	−0.293024	−	0.169456i
$96$	0.265330	−	0.0755648i	0.0270802	−	0.00771230i
$97$	−1.74814	−	4.80298i	−0.177497	−	0.487669i	0.818757	−	0.574140i	$-0.194663\pi$
$97$	−1.74814	−	4.80298i	−0.177497	−	0.487669i	−0.996254	+	0.0864706i	$0.972441\pi$
$98$	−2.11530	+	2.28266i	−0.213677	+	0.230584i
$99$	−1.45925	−	1.73906i	−0.146660	−	0.174782i
$100$	2.38722	−	8.52633i	0.238722	−	0.852633i
$101$	1.38063	+	7.82996i	0.137378	+	0.779110i	0.973174	+	0.230070i	$0.0738955\pi$
$101$	1.38063	+	7.82996i	0.137378	+	0.779110i	−0.835796	+	0.549040i	$0.814993\pi$
$102$	−0.0175052	+	0.355294i	−0.00173327	+	0.0351794i
$103$	−3.24938	+	5.62810i	−0.320171	+	0.554553i	−0.980523	−	0.196403i	$-0.937074\pi$
$103$	−3.24938	+	5.62810i	−0.320171	+	0.554553i	0.660352	+	0.750956i	$0.270407\pi$
$104$	3.87732	+	2.10188i	0.380203	+	0.206107i
$105$	−0.0382950	+	0.105215i	−0.00373721	+	0.0102679i
$106$	−5.26280	−	10.2494i	−0.511169	−	0.995509i
$107$	6.67434	+	11.5603i	0.645233	+	1.11758i	0.984248	+	0.176795i	$0.0565731\pi$
$107$	6.67434	+	11.5603i	0.645233	+	1.11758i	−0.339015	+	0.940781i	$0.610094\pi$
$108$	−0.482929	+	0.330157i	−0.0464699	+	0.0317694i
$109$	7.71028	−	9.18876i	0.738511	−	0.880124i	−0.257777	−	0.966204i	$-0.582990\pi$
$109$	7.71028	−	9.18876i	0.738511	−	0.880124i	0.996288	+	0.0860809i	$0.0274344\pi$
$110$	0.101312	+	0.804298i	0.00965970	+	0.0766868i
$111$	0.423094	+	0.0746029i	0.0401583	+	0.00708100i
$112$	11.3055	+	4.40389i	1.06827	+	0.416129i
$113$		−	0.773048i		−	0.0727222i	−0.999339	−	0.0363611i	$-0.988423\pi$
$113$		−	0.773048i		−	0.0727222i	0.999339	−	0.0363611i	$-0.0115766\pi$
$114$	−0.0669198	+	0.293091i	−0.00626761	+	0.0274505i
$115$		−	1.33205i		−	0.124214i
$116$	−0.748289	+	0.731722i	−0.0694769	+	0.0679387i
$117$	−4.60320	−	0.811669i	−0.425566	−	0.0750388i
$118$	11.6335	−	1.46539i	1.07095	−	0.134900i
$119$	−10.0561	+	11.9844i	−0.921838	+	1.09860i
$120$	0.104369	−	0.00280230i	0.00952754	−	0.000255813i
$121$	−5.21323	−	9.02957i	−0.473930	−	0.820870i
$122$	4.65913	−	2.39234i	0.421817	−	0.216592i
$123$	0.0434457	−	0.119366i	0.00391737	−	0.0107629i
$124$	1.09427	+	14.3567i	0.0982683	+	1.28927i
$125$	3.56767	−	6.17939i	0.319102	−	0.552701i
$126$	−12.8432	−	0.632779i	−1.14416	−	0.0563724i
$127$	0.599259	+	3.39856i	0.0531756	+	0.301574i	0.999783	−	0.0208137i	$-0.00662569\pi$
$127$	0.599259	+	3.39856i	0.0531756	+	0.301574i	−0.946608	+	0.322388i	$0.895515\pi$
$128$	−0.0504258	−	11.3136i	−0.00445705	−	0.999990i
$129$	−0.313600	−	0.373734i	−0.0276109	−	0.0329054i
$130$	1.22426	+	1.13450i	0.107375	+	0.0995022i
$131$	−5.11120	−	14.0429i	−0.446568	−	1.22694i	−0.935098	−	0.354389i	$-0.884689\pi$
$131$	−5.11120	−	14.0429i	−0.446568	−	1.22694i	0.488530	−	0.872547i	$-0.337533\pi$
$132$	0.0672930	−	0.0304670i	0.00585710	−	0.00265181i
$133$	−10.1344	+	8.49146i	−0.878764	+	0.736303i
$134$	11.1872	+	7.21535i	0.966425	+	0.623312i
$135$	−0.208040	+	0.0757205i	−0.0179053	+	0.00651698i
$136$	13.8373	+	4.61969i	1.18654	+	0.396135i
$137$	−4.04425	+	3.39353i	−0.345524	+	0.289929i	−0.798990	−	0.601345i	$-0.794632\pi$
$137$	−4.04425	+	3.39353i	−0.345524	+	0.289929i	0.453466	+	0.891274i	$0.350187\pi$
$138$	−0.115964	+	0.0358512i	−0.00987154	+	0.00305185i
$139$	2.03176	−	0.358254i	0.172332	−	0.0303867i	−0.0868164	−	0.996224i	$-0.527669\pi$
$139$	2.03176	−	0.358254i	0.172332	−	0.0303867i	0.259148	+	0.965838i	$0.416558\pi$
$140$	3.73159	+	2.67563i	0.315377	+	0.226132i
$141$	0.448050	+	0.258682i	0.0377326	+	0.0217849i
$142$	−7.69964	−	10.1515i	−0.646140	−	0.851895i
$143$	1.10969	+	0.403894i	0.0927970	+	0.0337753i
$144$	3.84775	+	11.3563i	0.320645	+	0.946362i
$145$	−0.343016	+	0.198040i	−0.0284859	+	0.0164464i
$146$	5.36911	−	12.7597i	0.444351	−	1.05600i
$147$	0.0822122	+	0.0689842i	0.00678074	+	0.00568972i
$148$	7.62417	−	15.8835i	0.626703	−	1.30561i
$149$	2.62167	−	14.8682i	0.214776	−	1.21805i	−0.666520	−	0.745487i	$-0.732217\pi$
$149$	2.62167	−	14.8682i	0.214776	−	1.21805i	0.881295	−	0.472566i	$-0.156672\pi$
$150$	−0.297726	−	0.0677546i	−0.0243092	−	0.00553214i
$151$	6.29994			0.512682			0.256341	−	0.966586i	$-0.417483\pi$
$151$	6.29994			0.512682			0.256341	+	0.966586i	$0.417483\pi$
$152$	10.8345	+	5.88335i	0.878793	+	0.477202i
$153$	−15.4607			−1.24993
$154$	3.16768	+	0.720882i	0.255259	+	0.0580903i
$155$	−0.946210	+	5.36622i	−0.0760014	+	0.431026i
$156$	0.0658160	−	0.137115i	0.00526950	−	0.0109780i
$157$	−0.586898	−	0.492466i	−0.0468395	−	0.0393030i	0.619067	−	0.785338i	$-0.287511\pi$
$157$	−0.586898	−	0.492466i	−0.0468395	−	0.0393030i	−0.665907	+	0.746035i	$0.731955\pi$
$158$	−8.30645	+	19.7403i	−0.660826	+	1.57046i
$159$	−0.344092	+	0.198662i	−0.0272883	+	0.0157549i
$160$	1.04331	−	4.15259i	0.0824812	−	0.328291i
$161$	−5.01624	−	1.82576i	−0.395335	−	0.143890i
$162$	−7.67334	−	10.1168i	−0.602875	−	0.794853i
$163$	10.9317	+	6.31140i	0.856234	+	0.494347i	0.862749	−	0.505632i	$-0.168741\pi$
$163$	10.9317	+	6.31140i	0.856234	+	0.494347i	−0.00651568	+	0.999979i	$0.502074\pi$
$164$	−4.23349	−	3.03550i	−0.330580	−	0.237033i
$165$	0.0275308	−	0.00485442i	0.00214327	−	0.000377916i
$166$	−16.6335	+	5.14236i	−1.29101	+	0.399125i
$167$	−10.1626	+	8.52746i	−0.786408	+	0.659875i	−0.944854	−	0.327493i	$-0.893796\pi$
$167$	−10.1626	+	8.52746i	−0.786408	+	0.659875i	0.158446	+	0.987368i	$0.449352\pi$
$168$	0.132499	−	0.396873i	0.0102225	−	0.0306194i
$169$	−9.93120	+	3.61466i	−0.763938	+	0.278051i
$170$	4.63955	+	2.99235i	0.355837	+	0.229503i
$171$	−12.8662	−	2.27812i	−0.983903	−	0.174212i
$172$	−18.2264	+	8.25203i	−1.38975	+	0.629211i
$173$	3.89414	+	10.6990i	0.296066	+	0.813434i	0.995148	+	0.0983922i	$0.0313700\pi$
$173$	3.89414	+	10.6990i	0.296066	+	0.813434i	−0.699082	+	0.715041i	$0.746408\pi$
$174$	0.0264728	+	0.0245318i	0.00200690	+	0.00185975i
$175$	−8.63167	−	10.2868i	−0.652493	−	0.777611i
$176$	−0.459123	−	2.99432i	−0.0346077	−	0.225705i
$177$	−0.0702152	−	0.398210i	−0.00527770	−	0.0299313i
$178$	−18.7337	−	0.923003i	−1.40415	−	0.0691820i
$179$	3.55631	−	6.15972i	0.265811	−	0.460399i	−0.701964	−	0.712212i	$-0.747693\pi$
$179$	3.55631	−	6.15972i	0.265811	−	0.460399i	0.967776	+	0.251813i	$0.0810268\pi$
$180$	0.344871	+	4.52465i	0.0257051	+	0.337248i
$181$	−3.43948	+	9.44990i	−0.255655	+	0.702405i	0.743768	+	0.668438i	$0.233037\pi$
$181$	−3.43948	+	9.44990i	−0.255655	+	0.702405i	−0.999423	+	0.0339678i	$0.989186\pi$
$182$	5.95032	−	3.05534i	0.441067	−	0.226477i
$183$	−0.0903068	−	0.156416i	−0.00667567	−	0.0115626i
$184$	0.133603	+	4.97592i	0.00984934	+	0.366830i
$185$	4.28591	−	5.10775i	0.315106	−	0.375529i
$186$	0.492634	−	0.0620536i	0.0361217	−	0.00454999i
$187$	3.84670	+	0.678278i	0.281299	+	0.0496006i
$188$	15.1695	−	14.8336i	1.10635	−	1.08186i
$189$			0.887223i			0.0645360i
$190$	3.42005	+	3.17383i	0.248116	+	0.230254i
$191$		−	8.64923i		−	0.625836i	−0.949780	−	0.312918i	$-0.898693\pi$
$191$		−	8.64923i		−	0.625836i	0.949780	−	0.312918i	$-0.101307\pi$
$192$	−0.389592	+	0.0209361i	−0.0281164	+	0.00151093i
$193$	14.2454	+	2.51184i	1.02540	+	0.180806i	0.660962	−	0.750420i	$-0.270149\pi$
$193$	14.2454	+	2.51184i	1.02540	+	0.180806i	0.364442	+	0.931226i	$0.381260\pi$
$194$	0.903369	+	7.17170i	0.0648581	+	0.514898i
$195$	0.0369983	−	0.0440929i	0.00264951	−	0.00315756i
$196$	3.63324	−	2.48388i	0.259517	−	0.177420i
$197$	−1.14351	−	1.98061i	−0.0814716	−	0.141113i	0.822411	−	0.568894i	$-0.192629\pi$
$197$	−1.14351	−	1.98061i	−0.0814716	−	0.141113i	−0.903882	+	0.427781i	$0.859295\pi$
$198$	1.46649	+	2.85602i	0.104219	+	0.202969i
$199$	−2.83294	+	7.78345i	−0.200822	+	0.551754i	−0.998695	−	0.0510715i	$-0.983736\pi$
$199$	−2.83294	+	7.78345i	−0.200822	+	0.551754i	0.797873	+	0.602826i	$0.205959\pi$
$200$	−5.96756	+	11.0083i	−0.421970	+	0.778404i
$201$	0.229536	−	0.397568i	0.0161902	−	0.0280423i
$202$	0.553319	−	11.2304i	0.0389314	−	0.790170i
$203$	0.275629	+	1.56317i	0.0193454	+	0.109713i
$204$	0.135635	−	0.484442i	0.00949637	−	0.0339177i
$205$	−1.26722	−	1.51022i	−0.0885066	−	0.105478i
$206$	6.24693	−	6.74120i	0.435245	−	0.469681i
$207$	−1.80432	−	4.95733i	−0.125409	−	0.344558i
$208$	−4.68706	−	4.11517i	−0.324989	−	0.285335i
$209$	3.10123	+	1.13126i	0.214516	+	0.0782509i
$210$	0.0858249	−	0.133069i	0.00592248	−	0.00918262i
$211$	13.0032	−	4.73277i	0.895175	−	0.325817i	0.146857	−	0.989158i	$-0.453084\pi$
$211$	13.0032	−	4.73277i	0.895175	−	0.325817i	0.748318	+	0.663341i	$0.230862\pi$
$212$	4.04077	+	15.7850i	0.277521	+	1.08412i
$213$	−0.336585	+	0.282428i	−0.0230624	+	0.0193517i
$214$	−5.57584	−	18.0357i	−0.381157	−	1.23289i
$215$	−7.45676	+	1.31483i	−0.508547	+	0.0896705i
$216$	0.769546	−	0.303722i	0.0523610	−	0.0206657i
$217$	18.9112	+	10.9184i	1.28378	+	0.741188i
$218$	−13.5157	+	10.2513i	−0.915399	+	0.694306i
$219$	−0.448599	−	0.163277i	−0.0303135	−	0.0110332i
$220$	0.112696	−	1.14088i	0.00759793	−	0.0769184i
$221$	6.96492	−	4.02120i	0.468511	−	0.270495i
$222$	−0.560017	−	0.235647i	−0.0375859	−	0.0158156i
$223$	7.16674	+	6.01361i	0.479921	+	0.402701i	0.850398	−	0.526140i	$-0.176361\pi$
$223$	7.16674	+	6.01361i	0.479921	+	0.402701i	−0.370477	+	0.928842i	$0.620806\pi$
$224$	−14.2078	−	9.62061i	−0.949300	−	0.642804i
$225$	2.30445	−	13.0692i	0.153630	−	0.871279i
$226$	−0.242593	+	1.06600i	−0.0161371	+	0.0709092i
$227$	28.0188			1.85967			0.929837	−	0.367972i	$-0.119948\pi$
$227$	28.0188			1.85967			0.929837	+	0.367972i	$0.119948\pi$
$228$	0.184256	−	0.383160i	0.0122026	−	0.0253754i
$229$	21.2119			1.40172			0.700861	−	0.713298i	$-0.252799\pi$
$229$	21.2119			1.40172			0.700861	+	0.713298i	$0.252799\pi$
$230$	−0.418017	+	1.83684i	−0.0275632	+	0.121118i
$231$	0.0194540	−	0.110329i	0.00127998	−	0.00725911i
$232$	1.26148	−	0.774189i	0.0828204	−	0.0508280i
$233$	7.85528	+	6.59136i	0.514617	+	0.431815i	0.862750	−	0.505630i	$-0.168740\pi$
$233$	7.85528	+	6.59136i	0.514617	+	0.431815i	−0.348134	+	0.937445i	$0.613184\pi$
$234$	6.09291	+	2.56381i	0.398306	+	0.167601i
$235$	6.95370	−	4.01472i	0.453609	−	0.261891i
$236$	−16.5020	−	1.63005i	−1.07419	−	0.106107i
$237$	0.694019	+	0.252602i	0.0450814	+	0.0164083i
$238$	17.6277	−	13.3702i	1.14264	−	0.866659i
$239$	−3.59307	−	2.07446i	−0.232416	−	0.134186i	0.379270	−	0.925286i	$-0.376175\pi$
$239$	−3.59307	−	2.07446i	−0.232416	−	0.134186i	−0.611686	+	0.791100i	$0.709509\pi$
$240$	−0.144800	−	0.0288882i	−0.00934678	−	0.00186473i
$241$	−7.29483	+	1.28628i	−0.469902	+	0.0828563i	−0.403585	−	0.914942i	$-0.632236\pi$
$241$	−7.29483	+	1.28628i	−0.469902	+	0.0828563i	−0.0663169	+	0.997799i	$0.521125\pi$
$242$	4.35520	+	14.0874i	0.279963	+	0.905571i
$243$	−1.00764	+	0.845509i	−0.0646401	+	0.0542395i
$244$	−7.17548	+	1.83684i	−0.459363	+	0.117591i
$245$	1.56516	−	0.569670i	0.0999942	−	0.0363949i
$246$	−0.0973685	+	0.150967i	−0.00620799	+	0.00962529i
$247$	6.38862	−	2.32011i	0.406498	−	0.147625i
$248$	2.99637	−	20.1406i	0.190270	−	1.27893i
$249$	0.205347	+	0.564187i	0.0130133	+	0.0357539i
$250$	−6.85884	+	7.40152i	−0.433791	+	0.468113i
$251$	5.06780	+	6.03957i	0.319877	+	0.381214i	0.901891	−	0.431965i	$-0.142179\pi$
$251$	5.06780	+	6.03957i	0.319877	+	0.381214i	−0.582014	+	0.813179i	$0.697735\pi$
$252$	17.5116	+	4.90295i	1.10313	+	0.308857i
$253$	0.231440	+	1.31256i	0.0145505	+	0.0825202i
$254$	0.240166	−	4.87453i	0.0150694	−	0.305855i
$255$	0.0951932	−	0.164879i	0.00596123	−	0.0103252i
$256$	−3.48083	+	15.6168i	−0.217552	+	0.976049i
$257$	−2.87499	+	7.89897i	−0.179337	+	0.492724i	−0.996491	−	0.0836944i	$-0.973328\pi$
$257$	−2.87499	+	7.89897i	−0.179337	+	0.492724i	0.817154	+	0.576419i	$0.195550\pi$
$258$	0.315158	+	0.613775i	0.0196209	+	0.0382120i
$259$	−13.3603	−	23.1407i	−0.830170	−	1.43790i
$260$	−1.33218	−	1.94862i	−0.0826184	−	0.120848i
$261$	−1.00830	+	1.20165i	−0.0624125	+	0.0743803i
$262$	2.64126	+	20.9685i	0.163178	+	1.29544i
$263$	−22.8569	−	4.03030i	−1.40942	−	0.248519i	−0.583411	−	0.812177i	$-0.698282\pi$
$263$	−22.8569	−	4.03030i	−1.40942	−	0.248519i	−0.826008	+	0.563658i	$0.809393\pi$
$264$	−0.102355	+	0.0208951i	−0.00629952	+	0.00128601i
$265$			6.16643i			0.378801i
$266$	16.6396	−	8.52903i	1.02024	−	0.522949i
$267$			0.646817i			0.0395846i
$268$	−13.1623	−	13.4604i	−0.804018	−	0.822222i
$269$	−22.6141	−	3.98747i	−1.37880	−	0.243120i	−0.565398	−	0.824818i	$-0.691277\pi$
$269$	−22.6141	−	3.98747i	−1.37880	−	0.243120i	−0.813405	+	0.581698i	$0.802389\pi$
$270$	0.310641	−	0.0391293i	0.0189050	−	0.00238133i
$271$	1.64574	−	1.96132i	0.0999715	−	0.119141i	−0.713739	−	0.700412i	$-0.753000\pi$
$271$	1.64574	−	1.96132i	0.0999715	−	0.119141i	0.813710	+	0.581270i	$0.197444\pi$
$272$	−17.6313	−	10.7127i	−1.06905	−	0.649552i
$273$	−0.115334	−	0.199764i	−0.00698031	−	0.0120902i
$274$	6.64178	−	3.41039i	0.401245	−	0.206029i
$275$	−1.14672	+	3.15058i	−0.0691496	+	0.189987i
$276$	0.171160	−	0.0130459i	0.0103026	−	0.000785272i
$277$	0.506680	−	0.877596i	0.0304435	−	0.0527296i	−0.850402	−	0.526133i	$-0.823641\pi$
$277$	0.506680	−	0.877596i	0.0304435	−	0.0527296i	0.880846	+	0.473403i	$0.156975\pi$
$278$	−2.91414	−	0.143578i	−0.174778	−	0.00861126i
$279$	3.74738	+	21.2525i	0.224350	+	1.27235i
$280$	−4.30605	−	4.86060i	−0.257336	−	0.290476i
$281$	−0.958866	−	1.14273i	−0.0572011	−	0.0681697i	0.736685	−	0.676236i	$-0.236390\pi$
$281$	−0.958866	−	1.14273i	−0.0572011	−	0.0681697i	−0.793886	+	0.608066i	$0.791946\pi$
$282$	−0.536663	−	0.497315i	−0.0319578	−	0.0296147i
$283$	−0.620886	−	1.70587i	−0.0369078	−	0.101403i	0.919870	−	0.392224i	$-0.128294\pi$
$283$	−0.620886	−	1.70587i	−0.0369078	−	0.101403i	−0.956778	+	0.290820i	$0.906072\pi$
$284$	7.43179	+	16.4147i	0.440995	+	0.974036i
$285$	0.103513	−	0.123184i	0.00613160	−	0.00729678i
$286$	−1.40347	−	0.905189i	−0.0829887	−	0.0535250i
$287$	−7.42407	+	2.70214i	−0.438229	+	0.159502i
$288$	−1.74209	−	16.8674i	−0.102654	−	0.993920i
$289$	7.35519	−	6.17174i	0.432658	−	0.363043i
$290$	0.535152	−	0.165446i	0.0314252	−	0.00971531i
$291$	0.245484	−	0.0432854i	0.0143905	−	0.00253744i
$292$	−11.4079	+	15.9102i	−0.667600	+	0.931074i
$293$	−22.4015	−	12.9335i	−1.30871	−	0.755585i	−0.326831	−	0.945083i	$-0.605981\pi$
$293$	−22.4015	−	12.9335i	−1.30871	−	0.755585i	−0.981881	+	0.189498i	$0.939314\pi$
$294$	−0.0917188	−	0.120926i	−0.00534915	−	0.00705252i
$295$	−5.89707	−	2.14636i	−0.343341	−	0.124966i
$296$	−15.4978	+	19.5100i	−0.900794	+	1.13400i
$297$	0.191840	−	0.110759i	0.0111317	−	0.00642690i
$298$	−8.28103	+	19.6799i	−0.479707	+	1.14003i
$299$	2.10218	+	1.76394i	0.121572	+	0.102011i
$300$	0.389289	+	0.186861i	0.0224756	+	0.0107884i
$301$	−5.26914	+	29.8828i	−0.303708	+	1.72241i
$302$	−8.68735	−	1.97701i	−0.499901	−	0.113764i
$303$	−0.387752			−0.0222758
$304$	−13.0940	−	11.5129i	−0.750993	−	0.660310i
$305$	−2.80311			−0.160506
$306$	21.3197	+	4.85180i	1.21876	+	0.277359i
$307$	0.350833	−	1.98967i	0.0200231	−	0.113557i	−0.973158	−	0.230138i	$-0.926082\pi$
$307$	0.350833	−	1.98967i	0.0200231	−	0.113557i	0.993181	+	0.116581i	$0.0371935\pi$
$308$	−4.14188	−	1.98813i	−0.236005	−	0.113284i
$309$	−0.242790	−	0.203725i	−0.0138119	−	0.0115895i
$310$	2.98878	−	7.10286i	0.169751	−	0.403415i
$311$	−23.8648	+	13.7783i	−1.35325	+	0.781298i	−0.988703	−	0.149887i	$-0.952109\pi$
$311$	−23.8648	+	13.7783i	−1.35325	+	0.781298i	−0.364545	+	0.931186i	$0.618776\pi$
$312$	−0.133786	+	0.168421i	−0.00757414	+	0.00953498i
$313$	−15.2863	−	5.56377i	−0.864034	−	0.314483i	−0.128285	−	0.991737i	$-0.540947\pi$
$313$	−15.2863	−	5.56377i	−0.864034	−	0.314483i	−0.735749	+	0.677255i	$0.763170\pi$
$314$	0.654764	+	0.863266i	0.0369505	+	0.0487169i
$315$	5.96007	+	3.44105i	0.335812	+	0.193881i
$316$	17.6490	−	24.6144i	0.992835	−	1.38467i
$317$	−3.12323	+	0.550709i	−0.175418	+	0.0309309i	−0.260667	−	0.965429i	$-0.583942\pi$
$317$	−3.12323	+	0.550709i	−0.175418	+	0.0309309i	0.0852491	+	0.996360i	$0.472831\pi$
$318$	0.536831	−	0.165965i	0.0301040	−	0.00930684i
$319$	0.303588	−	0.254741i	0.0169977	−	0.0142628i
$320$	−2.74183	+	5.39884i	−0.153273	+	0.301804i
$321$	−0.611745	+	0.222657i	−0.0341443	+	0.0124275i
$322$	6.34422	+	4.09181i	0.353550	+	0.228028i
$323$	19.4778	−	11.2270i	1.08377	−	0.624686i
$324$	7.40640	+	16.3587i	0.411467	+	0.908815i
$325$	2.36104	+	6.48691i	0.130967	+	0.359829i
$326$	−13.0937	−	12.1336i	−0.725192	−	0.672021i
$327$	0.376025	+	0.448129i	0.0207942	+	0.0247816i
$328$	4.88522	+	5.51436i	0.269741	+	0.304479i
$329$	−5.58762	−	31.6889i	−0.308055	−	1.74707i
$330$	−0.0394871	−	0.00194552i	−0.00217369	−	0.000107097i
$331$	−0.852024	+	1.47575i	−0.0468315	+	0.0811145i	−0.888491	−	0.458894i	$-0.848246\pi$
$331$	−0.852024	+	1.47575i	−0.0468315	+	0.0811145i	0.841659	+	0.540009i	$0.181579\pi$
$332$	24.5506	−	1.87126i	1.34739	−	0.102699i
$333$	9.03166	−	24.8143i	0.494932	−	1.35981i
$334$	16.6899	−	8.56982i	0.913229	−	0.468920i
$335$	−3.56238	−	6.17023i	−0.194634	−	0.337116i
$336$	−0.307255	+	0.505691i	−0.0167621	+	0.0275877i
$337$	−7.69079	+	9.16552i	−0.418944	+	0.499278i	−0.933699	−	0.358060i	$-0.883438\pi$
$337$	−7.69079	+	9.16552i	−0.418944	+	0.499278i	0.514755	+	0.857337i	$0.327883\pi$
$338$	14.8290	−	1.86791i	0.806592	−	0.101601i
$339$	0.0371282	+	0.00654671i	0.00201653	+	0.000355568i
$340$	−5.45869	−	5.58228i	−0.296039	−	0.302742i
$341$		−	5.45211i		−	0.295249i
$342$	17.0270	+	7.17903i	0.920716	+	0.388197i
$343$			14.5578i			0.786049i
$344$	27.7231	−	5.65948i	1.49473	−	0.305139i
$345$	0.0639763	+	0.0112807i	0.00344437	+	0.000607335i
$346$	−2.01233	−	15.9756i	−0.108184	−	0.858851i
$347$	3.49270	−	4.16244i	0.187498	−	0.223451i	−0.664104	−	0.747640i	$-0.731187\pi$
$347$	3.49270	−	4.16244i	0.187498	−	0.223451i	0.851602	+	0.524189i	$0.175631\pi$
$348$	−0.0288064	−	0.0421358i	−0.00154419	−	0.00225872i
$349$	−3.58269	−	6.20540i	−0.191777	−	0.332167i	0.754062	−	0.656803i	$-0.228092\pi$
$349$	−3.58269	−	6.20540i	−0.191777	−	0.332167i	−0.945839	+	0.324636i	$0.894758\pi$
$350$	8.67455	+	16.8938i	0.463674	+	0.903013i
$351$	0.155994	−	0.428591i	0.00832637	−	0.0228765i
$352$	−0.306548	+	4.27311i	−0.0163391	+	0.227758i
$353$	−12.4326	+	21.5339i	−0.661721	+	1.14614i	0.318442	+	0.947942i	$0.396840\pi$
$353$	−12.4326	+	21.5339i	−0.661721	+	1.14614i	−0.980163	+	0.198193i	$0.936493\pi$
$354$	−0.0281403	+	0.571149i	−0.00149564	+	0.0303562i
$355$	1.18413	+	6.71556i	0.0628473	+	0.356425i
$356$	25.5433	+	7.15168i	1.35379	+	0.379038i
$357$	−0.490427	−	0.584468i	−0.0259562	−	0.0309333i
$358$	−6.83701	+	7.37796i	−0.361347	+	0.389937i
$359$	−2.84636	−	7.82030i	−0.150225	−	0.412740i	0.841639	−	0.540040i	$-0.181591\pi$
$359$	−2.84636	−	7.82030i	−0.150225	−	0.412740i	−0.991864	+	0.127301i	$0.959369\pi$
$360$	0.944339	−	6.34752i	0.0497710	−	0.334544i
$361$	17.8634	−	6.47291i	0.940180	−	0.340679i
$362$	7.70841	−	11.9516i	0.405145	−	0.628164i
$363$	0.477825	−	0.173914i	0.0250793	−	0.00912812i
$364$	−9.16403	+	2.34588i	−0.480326	+	0.122958i
$365$	−5.67566	+	4.76244i	−0.297077	+	0.249278i
$366$	0.0754436	+	0.244030i	0.00394350	+	0.0127557i
$367$	−5.79355	+	1.02156i	−0.302421	+	0.0533249i	−0.322799	−	0.946467i	$-0.604624\pi$
$367$	−5.79355	+	1.02156i	−0.302421	+	0.0533249i	0.0203787	+	0.999792i	$0.493513\pi$
$368$	1.37728	−	6.90350i	0.0717958	−	0.359870i
$369$	−6.76170	−	3.90387i	−0.352000	−	0.203227i
$370$	−7.51297	+	5.69838i	−0.390581	+	0.296245i
$371$	23.2215	+	8.45195i	1.20560	+	0.438803i
$372$	−0.698794	−	0.0690262i	−0.0362308	−	0.00357884i
$373$	18.2764	−	10.5519i	0.946317	−	0.546356i	0.0543820	−	0.998520i	$-0.482681\pi$
$373$	18.2764	−	10.5519i	0.946317	−	0.546356i	0.891935	+	0.452164i	$0.149348\pi$
$374$	−5.09158	−	2.14247i	−0.263279	−	0.110784i
$375$	0.266572	+	0.223681i	0.0137657	+	0.0115508i
$376$	−25.5731	+	15.6946i	−1.31883	+	0.809385i
$377$	0.141693	−	0.803583i	0.00729758	−	0.0413866i
$378$	0.278423	−	1.22344i	0.0143205	−	0.0629271i
$379$	−12.0168			−0.617263			−0.308631	−	0.951182i	$-0.599871\pi$
$379$	−12.0168			−0.617263			−0.308631	+	0.951182i	$0.599871\pi$
$380$	−3.72010	−	5.44983i	−0.190837	−	0.279570i
$381$	−0.168302			−0.00862240
$382$	−2.71425	+	11.9269i	−0.138873	+	0.610234i
$383$	−3.07265	+	17.4259i	−0.157005	+	0.890419i	0.799925	+	0.600100i	$0.204873\pi$
$383$	−3.07265	+	17.4259i	−0.157005	+	0.890419i	−0.956930	+	0.290319i	$0.906238\pi$
$384$	0.543801	+	0.0933896i	0.0277507	+	0.00476577i
$385$	−1.33193	−	1.11762i	−0.0678815	−	0.0569593i
$386$	−18.8555	−	7.93412i	−0.959719	−	0.403836i
$387$	−25.9699	+	14.9937i	−1.32012	+	0.762173i
$388$	1.00487	−	10.1729i	0.0510147	−	0.516453i
$389$	22.3252	+	8.12572i	1.13193	+	0.411991i	0.838994	−	0.544140i	$-0.183144\pi$
$389$	22.3252	+	8.12572i	1.13193	+	0.411991i	0.292940	+	0.956131i	$0.405366\pi$
$390$	−0.0648561	+	0.0491916i	−0.00328412	+	0.00249091i
$391$	7.86084	+	4.53846i	0.397540	+	0.229520i
$392$	−5.78955	+	2.28500i	−0.292417	+	0.115410i
$393$	0.717744	−	0.126558i	0.0362054	−	0.00638399i
$394$	0.955303	+	3.09003i	0.0481275	+	0.155673i
$395$	8.78070	−	7.36788i	0.441805	−	0.370718i
$396$	−1.12597	−	4.39853i	−0.0565822	−	0.221035i
$397$	26.0487	−	9.48094i	1.30734	−	0.475835i	0.407963	−	0.912999i	$-0.366239\pi$
$397$	26.0487	−	9.48094i	1.30734	−	0.475835i	0.899382	+	0.437164i	$0.144017\pi$
$398$	6.34906	−	9.84402i	0.318250	−	0.493436i
$399$	−0.322006	−	0.558650i	−0.0161205	−	0.0279675i
$400$	11.6836	−	13.3072i	0.584178	−	0.665362i
$401$	−8.35712	−	22.9610i	−0.417334	−	1.14662i	−0.953207	−	0.302318i	$-0.902239\pi$
$401$	−8.35712	−	22.9610i	−0.417334	−	1.14662i	0.535873	−	0.844299i	$-0.319983\pi$
$402$	−0.441283	+	0.476197i	−0.0220092	+	0.0237506i
$403$	−7.21573	−	8.59938i	−0.359441	−	0.428366i
$404$	−4.28727	+	15.3126i	−0.213300	+	0.761832i
$405$	1.18009	+	6.69262i	0.0586392	+	0.332559i
$406$	0.110464	−	2.24204i	0.00548226	−	0.111271i
$407$	−3.33575	+	5.77769i	−0.165347	+	0.286389i
$408$	−0.339060	+	0.625460i	−0.0167860	+	0.0309649i
$409$	−2.46916	+	6.78397i	−0.122092	+	0.335446i	−0.985649	−	0.168805i	$-0.946009\pi$
$409$	−2.46916	+	6.78397i	−0.122092	+	0.335446i	0.863557	+	0.504251i	$0.168231\pi$
$410$	1.27352	+	2.48019i	0.0628945	+	0.122488i
$411$	−0.128736	−	0.222978i	−0.00635009	−	0.0109987i
$412$	−10.7297	+	7.33544i	−0.528616	+	0.361391i
$413$	−16.1655	+	19.2653i	−0.795453	+	0.947983i
$414$	0.932398	+	7.40216i	0.0458249	+	0.363796i
$415$	9.17653	+	1.61807i	0.450458	+	0.0794279i
$416$	5.17185	+	7.14550i	0.253571	+	0.350337i
$417$			0.100616i			0.00492719i
$418$	−3.92145	−	2.53317i	−0.191805	−	0.123901i
$419$		−	14.7450i		−	0.720341i	−0.932887	−	0.360170i	$-0.882719\pi$
$419$		−	14.7450i		−	0.720341i	0.932887	−	0.360170i	$-0.117281\pi$
$420$	−0.160108	+	0.156563i	−0.00781246	+	0.00763949i
$421$	−2.41752	−	0.426275i	−0.117823	−	0.0207754i	0.114426	−	0.993432i	$-0.463497\pi$
$421$	−2.41752	−	0.426275i	−0.117823	−	0.0207754i	−0.232249	+	0.972656i	$0.574608\pi$
$422$	−19.4160	+	2.44570i	−0.945156	+	0.119055i
$423$	20.4406	−	24.3601i	0.993855	−	1.18443i
$424$	−0.618485	−	23.0349i	−0.0300363	−	1.11867i
$425$	11.4168	+	19.7744i	0.553795	+	0.959201i
$426$	0.552766	−	0.283831i	0.0267816	−	0.0137517i
$427$	−3.84205	+	10.5559i	−0.185930	+	0.510838i
$428$	2.02900	+	26.6202i	0.0980753	+	1.28673i
$429$	−0.0287960	+	0.0498762i	−0.00139028	+	0.00240804i
$430$	10.6952	+	0.526946i	0.515766	+	0.0254116i
$431$	−5.88885	−	33.3973i	−0.283656	−	1.60869i	−0.710047	−	0.704154i	$-0.751326\pi$
$431$	−5.88885	−	33.3973i	−0.283656	−	1.60869i	0.426391	−	0.904539i	$-0.359785\pi$
$432$	−1.15648	+	0.177325i	−0.0556413	+	0.00853157i
$433$	12.1460	+	14.4750i	0.583698	+	0.695624i	0.974382	−	0.224901i	$-0.0722059\pi$
$433$	12.1460	+	14.4750i	0.583698	+	0.695624i	−0.390684	+	0.920525i	$0.627761\pi$
$434$	−22.6514	−	20.9906i	−1.08730	−	1.00758i
$435$	−0.00660666	−	0.0181516i	−0.000316765	−	0.000870305i
$436$	21.8546	−	9.89468i	1.04664	−	0.473869i
$437$	5.87294	+	4.93512i	0.280941	+	0.236079i
$438$	0.567359	+	0.365928i	0.0271095	+	0.0174847i
$439$	18.3905	−	6.69359i	0.877730	−	0.319468i	0.136437	−	0.990649i	$-0.456435\pi$
$439$	18.3905	−	6.69359i	0.877730	−	0.319468i	0.741293	+	0.671181i	$0.234213\pi$
$440$	−0.513428	+	1.53787i	−0.0244767	+	0.0733148i
$441$	5.05320	−	4.24014i	0.240629	−	0.201911i
$442$	−10.8662	+	3.35936i	−0.516854	+	0.159789i
$443$	−10.5778	+	1.86515i	−0.502567	+	0.0886161i	−0.419184	−	0.907901i	$-0.637684\pi$
$443$	−10.5778	+	1.86515i	−0.502567	+	0.0886161i	−0.0833832	+	0.996518i	$0.526573\pi$
$444$	0.698290	+	0.500688i	0.0331394	+	0.0237616i
$445$	8.69365	+	5.01928i	0.412119	+	0.237937i
$446$	−7.99547	−	10.5415i	−0.378596	−	0.499156i
$447$	0.691895	+	0.251829i	0.0327255	+	0.0119111i
$448$	16.5729	+	17.7250i	0.782995	+	0.837428i
$449$	−12.5426	+	7.24145i	−0.591920	+	0.341745i	−0.765856	−	0.643012i	$-0.777685\pi$
$449$	−12.5426	+	7.24145i	−0.591920	+	0.341745i	0.173936	+	0.984757i	$0.444351\pi$
$450$	−7.27903	+	17.2987i	−0.343137	+	0.815467i
$451$	1.51108	+	1.26794i	0.0711538	+	0.0597052i
$452$	0.669051	−	1.39384i	0.0314695	−	0.0655606i
$453$	−0.0533523	+	0.302576i	−0.00250671	+	0.0142163i
$454$	−38.6367	−	8.79270i	−1.81331	−	0.412662i
$455$	−3.57994			−0.167830
$456$	−0.374322	+	0.470539i	−0.0175292	+	0.0220350i
$457$	1.91109			0.0893972			0.0446986	−	0.999001i	$-0.485767\pi$
$457$	1.91109			0.0893972			0.0446986	+	0.999001i	$0.485767\pi$
$458$	−29.2503	−	6.65659i	−1.36678	−	0.311042i
$459$	0.261968	−	1.48570i	0.0122276	−	0.0693464i
$460$	1.15285	−	2.40174i	0.0537521	−	0.111982i
$461$	−12.8228	−	10.7596i	−0.597218	−	0.501125i	0.293332	−	0.956011i	$-0.405236\pi$
$461$	−12.8228	−	10.7596i	−0.597218	−	0.501125i	−0.890550	+	0.454885i	$0.849680\pi$
$462$	−0.0614489	+	0.146034i	−0.00285886	+	0.00679411i
$463$	23.6906	−	13.6778i	1.10100	−	0.635660i	0.164513	−	0.986375i	$-0.447395\pi$
$463$	23.6906	−	13.6778i	1.10100	−	0.635660i	0.936482	+	0.350715i	$0.114061\pi$
$464$	−1.98248	+	0.671702i	−0.0920344	+	0.0311830i
$465$	−0.249718	−	0.0908899i	−0.0115804	−	0.00421492i
$466$	−8.76363	−	11.5543i	−0.405967	−	0.535243i
$467$	−15.5831	−	8.99692i	−0.721101	−	0.416328i	0.0940567	−	0.995567i	$-0.470017\pi$
$467$	−15.5831	−	8.99692i	−0.721101	−	0.416328i	−0.815158	+	0.579239i	$0.803350\pi$
$468$	−7.59729	−	5.44742i	−0.351185	−	0.251807i
$469$	−28.1186	+	4.95806i	−1.29839	+	0.228942i
$470$	−10.8487	+	3.35395i	−0.500414	+	0.154706i
$471$	0.0286226	−	0.0240172i	0.00131886	−	0.00110665i
$472$	22.2440	+	7.42632i	1.02386	+	0.341824i
$473$	7.11921	−	2.59118i	0.327342	−	0.119143i
$474$	−0.877751	−	0.566120i	−0.0403165	−	0.0260028i
$475$	6.58714	+	18.1382i	0.302239	+	0.832240i
$476$	−28.5036	+	12.9050i	−1.30646	+	0.591502i
$477$	8.35269	+	22.9488i	0.382443	+	1.05075i
$478$	4.30369	+	3.98815i	0.196846	+	0.182414i
$479$	18.4519	+	21.9901i	0.843087	+	1.00475i	0.999853	+	0.0171167i	$0.00544868\pi$
$479$	18.4519	+	21.9901i	0.843087	+	1.00475i	−0.156766	+	0.987636i	$0.550107\pi$
$480$	0.190607	+	0.0852758i	0.00869997	+	0.00389229i
$481$	2.38529	+	13.5277i	0.108760	+	0.616808i
$482$	10.4629	+	0.515504i	0.476572	+	0.0234806i
$483$	0.130169	−	0.225460i	0.00592291	−	0.0102588i
$484$	−1.58482	−	20.7926i	−0.0720372	−	0.945118i
$485$	1.32316	−	3.63536i	0.0600817	−	0.165073i
$486$	1.65482	−	0.849709i	0.0750643	−	0.0385436i
$487$	−14.1294	−	24.4728i	−0.640263	−	1.10897i	−0.985374	−	0.170406i	$-0.945492\pi$
$487$	−14.1294	−	24.4728i	−0.640263	−	1.10897i	0.345111	−	0.938562i	$-0.387841\pi$
$488$	10.4711	−	0.281148i	0.474005	−	0.0127270i
$489$	−0.395703	+	0.471580i	−0.0178943	+	0.0213256i
$490$	−2.33705	+	0.294382i	−0.105577	+	0.0132988i
$491$	3.11289	+	0.548887i	0.140483	+	0.0247709i	0.243447	−	0.969914i	$-0.421722\pi$
$491$	3.11289	+	0.548887i	0.140483	+	0.0247709i	−0.102964	+	0.994685i	$0.532833\pi$
$492$	0.181642	−	0.177621i	0.00818907	−	0.00800777i
$493$		−	2.69899i		−	0.121556i
$494$	−9.53772	+	1.19449i	−0.429122	+	0.0537427i
$495$		−	1.71829i		−	0.0772315i
$496$	−10.4523	+	26.8327i	−0.469321	+	1.20482i
$497$	26.9125	+	4.74539i	1.20719	+	0.212860i
$498$	−0.106115	−	0.842430i	−0.00475513	−	0.0377502i
$499$	13.2403	−	15.7791i	0.592715	−	0.706371i	−0.383410	−	0.923578i	$-0.625250\pi$
$499$	13.2403	−	15.7791i	0.592715	−	0.706371i	0.976125	+	0.217207i	$0.0696948\pi$
$500$	11.7807	−	8.05397i	0.526851	−	0.360185i
$501$	−0.323496	−	0.560311i	−0.0144527	−	0.0250329i
$502$	−5.09298	−	9.91865i	−0.227311	−	0.442691i
$503$	−6.36560	+	17.4893i	−0.283828	+	0.779811i	0.713069	+	0.701094i	$0.247305\pi$
$503$	−6.36560	+	17.4893i	−0.283828	+	0.779811i	−0.996897	+	0.0787173i	$0.974918\pi$
$504$	−22.6091	−	12.2563i	−1.00709	−	0.545941i
$505$	−3.00895	+	5.21165i	−0.133896	+	0.231915i
$506$	0.0927549	−	1.88260i	0.00412346	−	0.0836916i
$507$	−0.0895019	−	0.507591i	−0.00397492	−	0.0225429i
$508$	−1.86087	+	6.64639i	−0.0825630	+	0.294886i
$509$	−20.1592	−	24.0248i	−0.893543	−	1.06488i	−0.997526	−	0.0703037i	$-0.977603\pi$
$509$	−20.1592	−	24.0248i	−0.893543	−	1.06488i	0.103983	−	0.994579i	$-0.466841\pi$
$510$	−0.183009	+	0.197489i	−0.00810377	+	0.00874494i
$511$	10.1551	+	27.9009i	0.449236	+	1.23427i
$512$	9.70068	−	20.4425i	0.428714	−	0.903440i
$513$	0.436922	−	1.19777i	0.0192906	−	0.0528831i
$514$	6.44330	−	9.99013i	0.284202	−	0.440646i
$515$	−4.62225	+	1.68236i	−0.203681	+	0.0741336i
$516$	−0.241977	−	0.945270i	−0.0106525	−	0.0416132i
$517$	−6.15442	+	5.16417i	−0.270671	+	0.227120i
$518$	11.1614	+	36.1027i	0.490404	+	1.58626i
$519$	−0.546836	+	0.0964220i	−0.0240034	+	0.00423246i
$520$	1.22552	+	3.10511i	0.0537425	+	0.136168i
$521$	0.219847	+	0.126929i	0.00963168	+	0.00556085i	0.504808	−	0.863232i	$-0.331563\pi$
$521$	0.219847	+	0.126929i	0.00963168	+	0.00556085i	−0.495176	+	0.868792i	$0.664897\pi$
$522$	1.76750	−	1.34060i	0.0773615	−	0.0586766i
$523$	−16.5515	−	6.02425i	−0.723746	−	0.263422i	−0.0462307	−	0.998931i	$-0.514721\pi$
$523$	−16.5515	−	6.02425i	−0.723746	−	0.263422i	−0.677515	+	0.735509i	$0.736943\pi$
$524$	2.93804	−	29.7436i	0.128349	−	1.29935i
$525$	0.567159	−	0.327449i	0.0247528	−	0.0142911i
$526$	30.2540	+	12.7304i	1.31914	+	0.555073i
$527$	−28.4438	−	23.8672i	−1.23903	−	1.03967i
$528$	0.147700	+	0.00330703i	0.00642783	+	0.000143920i
$529$	3.45608	−	19.6004i	0.150265	−	0.852193i
$530$	1.93511	−	8.50324i	0.0840560	−	0.369357i
$531$	−24.8537			−1.07856
$532$	−25.6219	+	6.53941i	−1.11085	+	0.283520i
$533$	4.06145			0.175921
$534$	0.202980	−	0.891933i	0.00878382	−	0.0385977i
$535$	−1.75447	+	9.95007i	−0.0758522	+	0.430179i
$536$	13.9263	+	22.6918i	0.601522	+	0.980135i
$537$	0.265724	+	0.222969i	0.0114668	+	0.00962181i
$538$	29.9325	+	12.5952i	1.29048	+	0.543016i
$539$	−1.44328	+	0.833278i	−0.0621664	+	0.0358918i
$540$	−0.440639	−	0.0435259i	−0.0189621	−	0.00187306i
$541$	17.7401	+	6.45689i	0.762709	+	0.277603i	0.693943	−	0.720030i	$-0.255872\pi$
$541$	17.7401	+	6.45689i	0.762709	+	0.277603i	0.0687653	+	0.997633i	$0.478094\pi$
$542$	−2.88489	+	2.18811i	−0.123917	+	0.0939875i
$543$	−0.424735	−	0.245221i	−0.0182271	−	0.0105234i
$544$	20.9510	+	20.3053i	0.898267	+	0.870582i
$545$	8.94110	−	1.57656i	0.382994	−	0.0675323i
$546$	0.0963513	+	0.311659i	0.00412346	+	0.0133378i
$547$	2.04894	−	1.71927i	0.0876065	−	0.0735106i	−0.597933	−	0.801546i	$-0.704011\pi$
$547$	2.04894	−	1.71927i	0.0876065	−	0.0735106i	0.685539	+	0.728036i	$0.259567\pi$
$548$	−10.2290	+	2.61849i	−0.436959	+	0.111856i
$549$	−10.4320	+	3.79693i	−0.445226	+	0.162049i
$550$	2.56997	−	3.98465i	0.109584	−	0.169906i
$551$	0.397692	−	2.24606i	0.0169423	−	0.0956853i
$552$	−0.240117	−	0.0357228i	−0.0102200	−	0.00152046i
$553$	−15.7108	−	43.1650i	−0.668091	−	1.83556i
$554$	−0.974092	+	1.05116i	−0.0413852	+	0.0446597i
$555$	0.209021	+	0.249101i	0.00887244	+	0.0105738i
$556$	3.97341	+	1.11249i	0.168510	+	0.0471799i
$557$	1.36362	+	7.73347i	0.0577784	+	0.327678i	0.999973	−	0.00738933i	$-0.00235212\pi$
$557$	1.36362	+	7.73347i	0.0577784	+	0.327678i	−0.942194	+	0.335067i	$0.891241\pi$
$558$	1.50185	−	30.4822i	0.0635782	−	1.29041i
$559$	7.79945	−	13.5090i	0.329882	−	0.571372i
$560$	4.41253	+	8.05385i	0.186463	+	0.340337i
$561$	−0.0651531	+	0.179007i	−0.00275077	+	0.00755767i
$562$	0.963629	+	1.87668i	0.0406482	+	0.0791631i
$563$	9.25757	+	16.0346i	0.390160	+	0.675777i	0.992470	−	0.122485i	$-0.0390864\pi$
$563$	9.25757	+	16.0346i	0.390160	+	0.675777i	−0.602310	+	0.798262i	$0.705753\pi$
$564$	0.583970	+	0.854188i	0.0245896	+	0.0359678i
$565$	0.376106	−	0.448225i	0.0158229	−	0.0188570i
$566$	0.320848	+	2.54716i	0.0134863	+	0.107065i
$567$	26.8205	+	4.72918i	1.12636	+	0.198607i
$568$	−5.09693	−	24.9674i	−0.213862	−	1.04761i
$569$			42.7241i			1.79109i	0.444972	+	0.895544i	$0.353214\pi$
$569$			42.7241i			1.79109i	−0.444972	+	0.895544i	$0.646786\pi$
$570$	−0.181397	+	0.137381i	−0.00759789	+	0.00575426i
$571$			32.7962i			1.37248i	0.727376	+	0.686239i	$0.240740\pi$
$571$			32.7962i			1.37248i	−0.727376	+	0.686239i	$0.759260\pi$
$572$	1.65126	+	1.68864i	0.0690426	+	0.0706058i
$573$	0.415408	+	0.0732477i	0.0173539	+	0.00305997i
$574$	11.0854	−	1.39636i	0.462697	−	0.0582827i
$575$	−5.00809	+	5.96841i	−0.208852	+	0.248900i
$576$	−2.89096	+	23.8061i	−0.120457	+	0.991920i
$577$	−11.0125	−	19.0742i	−0.458457	−	0.794071i	0.540422	−	0.841394i	$-0.318264\pi$
$577$	−11.0125	−	19.0742i	−0.458457	−	0.794071i	−0.998880	+	0.0473226i	$0.984931\pi$
$578$	−12.0793	+	6.20239i	−0.502431	+	0.257986i
$579$	−0.241279	+	0.662910i	−0.0100272	+	0.0275496i
$580$	−0.789870	+	0.0602042i	−0.0327976	+	0.00249984i
$581$	18.6710	−	32.3392i	0.774605	−	1.34165i
$582$	−0.352095	−	0.0173476i	−0.0145948	−	0.000719081i
$583$	−1.07140	−	6.07622i	−0.0443729	−	0.251651i
$584$	20.7239	−	18.3595i	0.857562	−	0.759721i
$585$	−2.27412	−	2.71019i	−0.0940231	−	0.112052i
$586$	26.8320	+	24.8647i	1.10842	+	1.02715i
$587$	13.7736	+	37.8426i	0.568497	+	1.56193i	0.806851	+	0.590754i	$0.201170\pi$
$587$	13.7736	+	37.8426i	0.568497	+	1.56193i	−0.238354	+	0.971178i	$0.576608\pi$
$588$	0.0885280	+	0.195534i	0.00365083	+	0.00806367i
$589$	−20.1538	−	24.0531i	−0.830421	−	0.991092i
$590$	7.45825	+	4.81032i	0.307051	+	0.198038i
$591$	0.104810	−	0.0381476i	0.00431130	−	0.00156918i
$592$	27.4934	−	22.0400i	1.12997	−	0.905839i
$593$	26.7671	−	22.4603i	1.09919	−	0.922332i	0.101822	−	0.994803i	$-0.467533\pi$
$593$	26.7671	−	22.4603i	1.09919	−	0.922332i	0.997371	+	0.0724705i	$0.0230883\pi$
$594$	−0.299297	+	0.0925297i	−0.0122803	+	0.00379654i
$595$	−11.6613	+	2.05621i	−0.478068	+	0.0842963i
$596$	17.5950	−	24.5391i	0.720720	−	1.00516i
$597$	−0.349835	−	0.201977i	−0.0143178	−	0.00826639i
$598$	−2.34527	−	3.09209i	−0.0959053	−	0.126445i
$599$	30.0126	+	10.9237i	1.22628	+	0.446331i	0.872323	−	0.488930i	$-0.162613\pi$
$599$	30.0126	+	10.9237i	1.22628	+	0.446331i	0.353960	+	0.935261i	$0.384835\pi$
$600$	−0.478173	−	0.379838i	−0.0195213	−	0.0155068i
$601$	−30.8953	+	17.8374i	−1.26024	+	0.727602i	−0.973122	−	0.230292i	$-0.926032\pi$
$601$	−30.8953	+	17.8374i	−1.26024	+	0.727602i	−0.287122	+	0.957894i	$0.592699\pi$
$602$	16.6436	−	39.5535i	0.678341	−	1.61208i
$603$	−21.6155	−	18.1375i	−0.880251	−	0.738618i
$604$	11.3591	+	5.45242i	0.462193	+	0.221856i
$605$	1.37039	−	7.77185i	0.0557142	−	0.315971i
$606$	0.534693	+	0.121682i	0.0217204	+	0.00494300i
$607$	−15.1801			−0.616142			−0.308071	−	0.951363i	$-0.599683\pi$
$607$	−15.1801			−0.616142			−0.308071	+	0.951363i	$0.599683\pi$
$608$	14.4432	+	19.9849i	0.585748	+	0.810493i
$609$	−0.0774107			−0.00313684
$610$	3.86537	+	0.879656i	0.156504	+	0.0356162i
$611$	−2.87244	+	16.2904i	−0.116207	+	0.659040i
$612$	−27.8763	−	13.3808i	−1.12683	−	0.540888i
$613$	−25.6192	−	21.4971i	−1.03475	−	0.868260i	−0.0433427	−	0.999060i	$-0.513801\pi$
$613$	−25.6192	−	21.4971i	−1.03475	−	0.868260i	−0.991409	+	0.130801i	$0.958245\pi$
$614$	−1.10817	+	2.63358i	−0.0447222	+	0.106283i
$615$	0.0832649	−	0.0480730i	0.00335757	−	0.00193849i
$616$	5.08756	+	4.04132i	0.204984	+	0.162830i
$617$	−12.4136	−	4.51818i	−0.499752	−	0.181895i	0.0798303	−	0.996808i	$-0.474562\pi$
$617$	−12.4136	−	4.51818i	−0.499752	−	0.181895i	−0.579583	+	0.814914i	$0.696784\pi$
$618$	0.270865	+	0.357119i	0.0108958	+	0.0143654i
$619$	−26.2189	−	15.1375i	−1.05383	−	0.608427i	−0.130109	−	0.991500i	$-0.541533\pi$
$619$	−26.2189	−	15.1375i	−1.05383	−	0.608427i	−0.923718	+	0.383072i	$0.874866\pi$
$620$	−6.35037	+	8.85661i	−0.255037	+	0.355690i
$621$	0.506946	−	0.0893883i	0.0203430	−	0.00358703i
$622$	37.2324	−	11.5106i	1.49288	−	0.461534i
$623$	30.8174	−	25.8589i	1.23467	−	1.03602i
$624$	0.237338	−	0.190262i	0.00950112	−	0.00761656i
$625$	−15.7256	+	5.72365i	−0.629024	+	0.228946i
$626$	19.3332	+	12.4693i	0.772709	+	0.498372i
$627$	−0.0805960	+	0.139367i	−0.00321869	+	0.00556577i
$628$	−0.631986	−	1.39588i	−0.0252190	−	0.0557017i
$629$	15.5398	+	42.6951i	0.619611	+	1.70237i
$630$	−7.13882	−	6.61541i	−0.284418	−	0.263564i
$631$	5.39835	+	6.43350i	0.214905	+	0.256114i	0.862718	−	0.505686i	$-0.168761\pi$
$631$	5.39835	+	6.43350i	0.214905	+	0.256114i	−0.647813	+	0.761800i	$0.724316\pi$
$632$	−32.0616	+	28.4036i	−1.27534	+	1.12984i
$633$	0.117187	+	0.664601i	0.00465777	+	0.0264155i
$634$	4.47962	+	0.220709i	0.177908	+	0.00876548i
$635$	−1.30602	+	2.26210i	−0.0518279	+	0.0897686i
$636$	−0.792348	+	0.0603931i	−0.0314187	+	0.00239474i
$637$	−1.17360	+	3.22443i	−0.0464996	+	0.127757i
$638$	−0.498577	+	0.256006i	−0.0197388	+	0.0101354i
$639$	13.5033	+	23.3885i	0.534184	+	0.925234i
$640$	5.47509	−	6.58434i	0.216422	−	0.260269i
$641$	8.67553	−	10.3391i	0.342663	−	0.408370i	−0.567000	−	0.823718i	$-0.691896\pi$
$641$	8.67553	−	10.3391i	0.342663	−	0.408370i	0.909662	+	0.415348i	$0.136340\pi$
$642$	0.913443	−	0.115060i	0.0360507	−	0.00454106i
$643$	−32.2342	−	5.68376i	−1.27119	−	0.224146i	−0.502957	−	0.864312i	$-0.667754\pi$
$643$	−32.2342	−	5.68376i	−1.27119	−	0.224146i	−0.768237	+	0.640166i	$0.778866\pi$
$644$	−7.46434	−	7.63334i	−0.294136	−	0.300796i
$645$		−	0.369271i		−	0.0145400i
$646$	−30.3822	+	9.36912i	−1.19537	+	0.368623i
$647$		−	27.0952i		−	1.06522i	−0.846360	−	0.532611i	$-0.821211\pi$
$647$		−	27.0952i		−	1.06522i	0.846360	−	0.532611i	$-0.178789\pi$
$648$	−5.07952	−	24.8821i	−0.199542	−	0.977462i
$649$	6.18372	+	1.09036i	0.242732	+	0.0428002i
$650$	−1.22009	−	9.68610i	−0.0478559	−	0.379920i
$651$	−0.684546	+	0.815810i	−0.0268295	+	0.0319741i
$652$	14.2479	+	20.8408i	0.557991	+	0.816187i
$653$	17.7481	+	30.7407i	0.694539	+	1.20298i	0.970336	+	0.241760i	$0.0777248\pi$
$653$	17.7481	+	30.7407i	0.694539	+	1.20298i	−0.275797	+	0.961216i	$0.588942\pi$
$654$	−0.377893	−	0.735953i	−0.0147768	−	0.0287780i
$655$	3.86865	−	10.6290i	0.151161	−	0.415311i
$656$	−5.00602	−	9.13711i	−0.195452	−	0.356744i
$657$	−14.6714	+	25.4117i	−0.572387	+	0.991403i
$658$	−2.23936	+	45.4512i	−0.0872994	+	1.77187i
$659$	−2.56553	−	14.5498i	−0.0999388	−	0.566781i	−0.993122	−	0.117087i	$-0.962644\pi$
$659$	−2.56553	−	14.5498i	−0.0999388	−	0.566781i	0.893183	−	0.449694i	$-0.148467\pi$
$660$	0.0538405	+	0.0150744i	0.00209574	+	0.000586770i
$661$	−16.8005	−	20.0220i	−0.653462	−	0.778766i	0.332970	−	0.942938i	$-0.391949\pi$
$661$	−16.8005	−	20.0220i	−0.653462	−	0.778766i	−0.986432	+	0.164172i	$0.947505\pi$
$662$	1.63802	−	1.76762i	0.0636633	−	0.0687004i
$663$	0.134148	+	0.368568i	0.00520987	+	0.0143140i
$664$	−34.4415	−	5.12395i	−1.33659	−	0.198848i
$665$	−10.0074	−	0.00713711i	−0.388070	−	0.000276765i
$666$	−20.2413	+	31.3836i	−0.784336	+	1.21609i
$667$	0.865402	−	0.314981i	0.0335085	−	0.0121961i
$668$	−25.7039	+	6.57989i	−0.994515	+	0.254584i
$669$	−0.349517	+	0.293280i	−0.0135131	+	0.0113388i
$670$	2.97607	+	9.62640i	0.114975	+	0.371900i
$671$	2.76210	−	0.487033i	0.106630	−	0.0188017i
$672$	0.582384	−	0.600904i	0.0224660	−	0.0231804i
$673$	−8.55734	−	4.94058i	−0.329861	−	0.190446i	0.325918	−	0.945398i	$-0.394327\pi$
$673$	−8.55734	−	4.94058i	−0.329861	−	0.190446i	−0.655780	+	0.754952i	$0.727660\pi$
$674$	13.4815	−	10.2254i	0.519289	−	0.393867i
$675$	1.21683	+	0.442891i	0.0468360	+	0.0170469i
$676$	−21.0347	−	2.07779i	−0.809029	−	0.0799151i
$677$	−10.8961	+	6.29088i	−0.418772	+	0.241778i	−0.694552	−	0.719443i	$-0.744397\pi$
$677$	−10.8961	+	6.29088i	−0.418772	+	0.241778i	0.275780	+	0.961221i	$0.411064\pi$
$678$	−0.0491437	−	0.0206790i	−0.00188735	−	0.000794172i
$679$	−11.8764	−	9.96552i	−0.455776	−	0.382442i
$680$	5.77550	+	9.41074i	0.221480	+	0.360885i
$681$	−0.237283	+	1.34570i	−0.00909270	+	0.0515673i
$682$	−1.71095	+	7.51823i	−0.0655157	+	0.287888i
$683$	−40.5886			−1.55308			−0.776540	−	0.630068i	$-0.783027\pi$
$683$	−40.5886			−1.55308			−0.776540	+	0.630068i	$0.783027\pi$
$684$	−21.2266	−	15.2429i	−0.811621	−	0.582826i
$685$	−3.99595			−0.152678
$686$	4.56846	−	20.0746i	0.174424	−	0.766453i
$687$	−0.179637	+	1.01877i	−0.00685358	+	0.0388686i
$688$	−40.0049	−	0.895715i	−1.52517	−	0.0341488i
$689$	−9.73159	−	8.16577i	−0.370744	−	0.311091i
$690$	−0.0846805	−	0.0356323i	−0.00322373	−	0.00135650i
$691$	−20.0557	+	11.5792i	−0.762956	+	0.440493i	−0.830356	−	0.557233i	$-0.811863\pi$
$691$	−20.0557	+	11.5792i	−0.762956	+	0.440493i	0.0674004	+	0.997726i	$0.478530\pi$
$692$	−2.23844	+	22.6611i	−0.0850928	+	0.861446i
$693$	−6.47074	−	2.35516i	−0.245803	−	0.0894650i
$694$	−6.12251	+	4.64376i	−0.232407	+	0.176275i
$695$	1.35235	+	0.780778i	0.0512975	+	0.0296166i
$696$	0.0264999	+	0.0671433i	0.00100448	+	0.00254506i
$697$	13.2298	−	2.33277i	0.501115	−	0.0883600i
$698$	2.99303	+	9.68127i	0.113288	+	0.366441i
$699$	−0.383096	+	0.321456i	−0.0144900	+	0.0121586i
$700$	−6.66030	−	26.0181i	−0.251736	−	0.983390i
$701$	30.4371	−	11.0782i	1.14959	−	0.418418i	0.304224	−	0.952601i	$-0.401603\pi$
$701$	30.4371	−	11.0782i	1.14959	−	0.418418i	0.845369	+	0.534183i	$0.179381\pi$
$702$	−0.349608	+	0.542055i	−0.0131951	+	0.0204586i
$703$	6.64089	+	37.8200i	0.250466	+	1.42641i
$704$	1.76368	−	5.79624i	0.0664712	−	0.218454i
$705$	0.133932	+	0.367974i	0.00504416	+	0.0138587i
$706$	23.9017	−	25.7928i	0.899552	−	0.970725i
$707$	15.5018	+	18.4744i	0.583006	+	0.694800i
$708$	0.218039	−	0.778758i	0.00819440	−	0.0292675i
$709$	7.62702	+	43.2550i	0.286439	+	1.62448i	0.700100	+	0.714045i	$0.253139\pi$
$709$	7.62702	+	43.2550i	0.286439	+	1.62448i	−0.413661	+	0.910431i	$0.635750\pi$
$710$	0.474568	−	9.63206i	0.0178102	−	0.361485i
$711$	22.6979	−	39.3139i	0.851238	−	1.47439i
$712$	−32.9788	−	17.8777i	−1.23593	−	0.669996i
$713$	4.33329	−	11.9056i	0.162283	−	0.445869i
$714$	0.492863	+	0.959859i	0.0184449	+	0.0359218i
$715$	0.446912	+	0.774075i	0.0167136	+	0.0289488i
$716$	11.7432	−	8.02833i	0.438866	−	0.300033i
$717$	0.130062	−	0.155001i	0.00485724	−	0.00578863i
$718$	1.47088	+	11.6771i	0.0548928	+	0.435785i
$719$	12.5454	+	2.21209i	0.467864	+	0.0824971i	0.402610	−	0.915372i	$-0.368103\pi$
$719$	12.5454	+	2.21209i	0.467864	+	0.0824971i	0.0652543	+	0.997869i	$0.479214\pi$
$720$	−3.29414	+	8.45661i	−0.122766	+	0.315159i
$721$			19.7123i			0.734126i
$722$	−26.6642	+	3.32007i	−0.992337	+	0.123560i
$723$		−	0.361252i		−	0.0134351i
$724$	−14.3801	+	14.0618i	−0.534434	+	0.522602i
$725$	2.28149	+	0.402289i	0.0847325	+	0.0149406i
$726$	−0.713477	+	0.0898717i	−0.0264796	+	0.00333545i
$727$	14.5133	−	17.2962i	0.538267	−	0.641481i	−0.426531	−	0.904473i	$-0.640265\pi$
$727$	14.5133	−	17.2962i	0.538267	−	0.641481i	0.964798	+	0.262991i	$0.0847091\pi$
$728$	13.3730	−	0.359063i	0.495635	−	0.0133078i
$729$	13.4358	+	23.2715i	0.497623	+	0.861909i
$730$	9.32100	−	4.78610i	0.344986	−	0.177141i
$731$	17.6468	−	48.4843i	0.652692	−	1.79326i
$732$	−0.0274532	−	0.360182i	−0.00101470	−	0.0133127i
$733$	13.0679	−	22.6343i	0.482675	−	0.836017i	−0.517127	−	0.855908i	$-0.672999\pi$
$733$	13.0679	−	22.6343i	0.482675	−	0.836017i	0.999802	+	0.0198913i	$0.00633202\pi$
$734$	8.30963	+	0.409412i	0.306714	+	0.0151117i
$735$	0.0141055	+	0.0799963i	0.000520289	+	0.00295071i
$736$	−4.06563	+	9.08742i	−0.149861	+	0.334967i
$737$	4.58232	+	5.46100i	0.168792	+	0.201159i
$738$	8.09900	+	7.50519i	0.298128	+	0.276270i
$739$	13.7325	+	37.7299i	0.505160	+	1.38792i	0.886177	+	0.463347i	$0.153352\pi$
$739$	13.7325	+	37.7299i	0.505160	+	1.38792i	−0.381017	+	0.924568i	$0.624426\pi$
$740$	12.1483	−	5.50015i	0.446580	−	0.202189i
$741$	0.0573278	+	0.326483i	0.00210599	+	0.0119937i
$742$	−29.3691	−	18.9421i	−1.07818	−	0.695387i
$743$	−19.0012	+	6.91587i	−0.697086	+	0.253719i	−0.666166	−	0.745803i	$-0.732066\pi$
$743$	−19.0012	+	6.91587i	−0.697086	+	0.253719i	−0.0309197	+	0.999522i	$0.509844\pi$
$744$	0.941944	+	0.314475i	0.0345334	+	0.0115292i
$745$	8.75383	−	7.34534i	0.320716	−	0.269112i
$746$	−28.5137	+	8.81520i	−1.04396	+	0.322747i
$747$	36.3428	−	6.40822i	1.32972	−	0.234465i
$748$	6.34873	+	4.55218i	0.232133	+	0.166444i
$749$	35.0652	+	20.2449i	1.28126	+	0.739733i
$750$	−0.297398	−	0.392100i	−0.0108594	−	0.0143175i
$751$	−30.8187	−	11.2171i	−1.12459	−	0.409318i	−0.288265	−	0.957551i	$-0.593078\pi$
$751$	−30.8187	−	11.2171i	−1.12459	−	0.409318i	−0.836326	+	0.548233i	$0.815301\pi$
$752$	40.1893	−	13.6169i	1.46555	−	0.496558i
$753$	−0.332988	+	0.192251i	−0.0121348	+	0.00700602i
$754$	−0.447565	+	1.06364i	−0.0162993	+	0.0387355i
$755$	3.65281	+	3.06507i	0.132939	+	0.111549i
$756$	−0.767867	+	1.59970i	−0.0279271	+	0.0581805i
$757$	−0.0728195	+	0.412980i	−0.00264667	+	0.0150100i	−0.986102	−	0.166138i	$-0.946870\pi$
$757$	−0.0728195	+	0.412980i	−0.00264667	+	0.0150100i	0.983456	+	0.181148i	$0.0579814\pi$
$758$	16.5707	+	3.77105i	0.601874	+	0.136971i
$759$	−0.0650003			−0.00235936
$760$	3.41963	+	8.68250i	0.124043	+	0.314947i
$761$	−5.25859			−0.190624			−0.0953119	−	0.995447i	$-0.530385\pi$
$761$	−5.25859			−0.190624			−0.0953119	+	0.995447i	$0.530385\pi$
$762$	0.232082	+	0.0528157i	0.00840744	+	0.00191331i
$763$	6.31801	−	35.8312i	0.228727	−	1.29718i
$764$	7.48567	−	15.5949i	0.270822	−	0.564204i
$765$	−8.96438	−	7.52201i	−0.324108	−	0.271959i
$766$	9.70553	−	23.0653i	0.350675	−	0.833381i
$767$	11.1964	−	6.46422i	0.404277	−	0.233410i
$768$	−0.720570	−	0.299432i	−0.0260013	−	0.0108048i
$769$	0.0384186	+	0.0139832i	0.00138541	+	0.000504249i	0.342713	−	0.939440i	$-0.388654\pi$
$769$	0.0384186	+	0.0139832i	0.00138541	+	0.000504249i	−0.341327	+	0.939944i	$0.610876\pi$
$770$	1.48595	+	1.95913i	0.0535499	+	0.0706022i
$771$	−0.355027	−	0.204975i	−0.0127860	−	0.00738200i
$772$	23.5110	+	16.8579i	0.846181	+	0.606730i
$773$	25.9276	−	4.57173i	0.932550	−	0.164434i	0.313324	−	0.949646i	$-0.398558\pi$
$773$	25.9276	−	4.57173i	0.932550	−	0.164434i	0.619226	+	0.785213i	$0.287446\pi$
$774$	40.5165	−	12.5260i	1.45634	−	0.450236i
$775$	24.4149	−	20.4865i	0.877009	−	0.735898i
$776$	−4.57809	+	13.7127i	−0.164344	+	0.492257i
$777$	1.22456	−	0.445702i	0.0439307	−	0.0159895i
$778$	−28.2356	−	18.2110i	−1.01229	−	0.652896i
$779$	11.3534	+	0.00809706i	0.406777	+	0.000290107i
$780$	0.104871	−	0.0474803i	0.00375497	−	0.00170007i
$781$	−2.33362	−	6.41157i	−0.0835035	−	0.229424i
$782$	−9.41552	−	8.72517i	−0.336698	−	0.312012i
$783$	−0.0983876	−	0.117254i	−0.00351609	−	0.00419031i
$784$	8.70061	−	1.33408i	0.310736	−	0.0476456i
$785$	−0.100697	−	0.571079i	−0.00359402	−	0.0203827i
$786$	−1.02945	−	0.0507208i	−0.0367194	−	0.00180915i
$787$	−19.4995	+	33.7741i	−0.695081	+	1.20392i	0.275072	+	0.961423i	$0.411298\pi$
$787$	−19.4995	+	33.7741i	−0.695081	+	1.20392i	−0.970153	+	0.242492i	$0.922035\pi$
$788$	−0.347626	−	4.56080i	−0.0123837	−	0.162472i
$789$	0.387137	−	1.06365i	0.0137824	−	0.0378670i
$790$	−14.4204	+	7.40448i	−0.513053	+	0.263440i
$791$	−1.17242	−	2.03069i	−0.0416865	−	0.0722031i
$792$	0.172342	+	6.41873i	0.00612392	+	0.228080i
$793$	3.71196	−	4.42374i	0.131816	−	0.157092i
$794$	−38.8952	+	4.89936i	−1.38034	+	0.173872i
$795$	−0.296164	−	0.0522217i	−0.0105038	−	0.00185211i
$796$	−11.8443	+	11.5820i	−0.419809	+	0.410515i
$797$		−	23.6830i		−	0.838894i	−0.907780	−	0.419447i	$-0.862224\pi$
$797$		−	23.6830i		−	0.838894i	0.907780	−	0.419447i	$-0.137776\pi$
$798$	0.268720	+	0.871404i	0.00951257	+	0.0308474i
$799$			54.7145i			1.93566i
$800$	−20.2871	+	14.6836i	−0.717258	+	0.519145i
$801$	39.1529	+	6.90370i	1.38340	+	0.243930i
$802$	4.31862	+	34.2848i	0.152496	+	1.21064i
$803$	4.76516	−	5.67889i	0.168159	−	0.200404i
$804$	0.757947	−	0.518174i	0.0267307	−	0.0182746i
$805$	−2.02022	−	3.49912i	−0.0712034	−	0.123328i
$806$	7.25158	+	14.1226i	0.255426	+	0.497446i
$807$	0.383023	−	1.05235i	0.0134831	−	0.0370444i
$808$	10.7173	−	19.7700i	0.377033	−	0.695508i
$809$	−11.3880	+	19.7247i	−0.400382	+	0.693483i	−0.993772	−	0.111433i	$-0.964456\pi$
$809$	−11.3880	+	19.7247i	−0.400382	+	0.693483i	0.593390	+	0.804915i	$0.297789\pi$
$810$	0.472947	−	9.59917i	0.0166177	−	0.337280i
$811$	−6.60869	−	37.4798i	−0.232063	−	1.31609i	−0.848712	−	0.528855i	$-0.822622\pi$
$811$	−6.60869	−	37.4798i	−0.232063	−	1.31609i	0.616650	−	0.787238i	$-0.288490\pi$
$812$	−0.855909	+	3.05701i	−0.0300365	+	0.107280i
$813$	0.0802615	+	0.0956519i	0.00281489	+	0.00335466i
$814$	6.41297	−	6.92037i	0.224775	−	0.242559i
$815$	3.26771	+	8.97796i	0.114463	+	0.314484i
$816$	0.663827	−	0.756080i	0.0232386	−	0.0264681i
$817$	21.8296	−	37.7477i	0.763720	−	1.32063i
$818$	5.53377	−	8.57994i	0.193484	−	0.299990i
$819$	−13.3230	+	4.84918i	−0.465543	+	0.169444i
$820$	−0.977803	−	3.81973i	−0.0341464	−	0.133391i
$821$	−32.3816	+	27.1714i	−1.13013	+	0.948289i	−0.999071	−	0.0430862i	$-0.986281\pi$
$821$	−32.3816	+	27.1714i	−1.13013	+	0.948289i	−0.131055	+	0.991375i	$0.541837\pi$
$822$	0.107548	+	0.347876i	0.00375117	+	0.0121336i
$823$	−5.80436	+	1.02346i	−0.202327	+	0.0356757i	−0.273893	−	0.961760i	$-0.588311\pi$
$823$	−5.80436	+	1.02346i	−0.202327	+	0.0356757i	0.0715660	+	0.997436i	$0.477200\pi$
$824$	17.0978	−	6.74811i	0.595630	−	0.235082i
$825$	−0.141606	−	0.0817562i	−0.00493008	−	0.00284638i
$826$	28.3372	−	21.4930i	0.985979	−	0.747839i
$827$	32.1283	+	11.6937i	1.11721	+	0.406631i	0.833633	−	0.552318i	$-0.186257\pi$
$827$	32.1283	+	11.6937i	1.11721	+	0.406631i	0.283577	+	0.958950i	$0.408479\pi$
$828$	1.03717	−	10.4999i	0.0360440	−	0.364895i
$829$	−16.6326	+	9.60285i	−0.577675	+	0.333521i	−0.760209	−	0.649679i	$-0.774903\pi$
$829$	−16.6326	+	9.60285i	−0.577675	+	0.333521i	0.182534	+	0.983200i	$0.441570\pi$
$830$	−12.1463	−	5.11097i	−0.421603	−	0.177404i
$831$	0.0378586	+	0.0317671i	0.00131330	+	0.00110199i
$832$	−4.88940	−	11.4763i	−0.169509	−	0.397870i
$833$	−1.97088	+	11.1774i	−0.0682868	+	0.387274i
$834$	0.0315748	−	0.138745i	0.00109334	−	0.00480436i
$835$	−10.0413			−0.347492
$836$	4.61257	+	4.72374i	0.159529	+	0.163374i
$837$	−2.10575			−0.0727853
$838$	−4.62719	+	20.3327i	−0.159844	+	0.702382i
$839$	−2.76417	+	15.6764i	−0.0954297	+	0.541209i	0.899185	+	0.437569i	$0.144160\pi$
$839$	−2.76417	+	15.6764i	−0.0954297	+	0.541209i	−0.994615	+	0.103640i	$0.966951\pi$
$840$	0.269913	−	0.165650i	0.00931289	−	0.00571545i
$841$	22.0055	+	18.4648i	0.758811	+	0.636718i
$842$	3.19989	+	1.34647i	0.110275	+	0.0464023i
$843$	0.0630039	−	0.0363753i	0.00216997	−	0.00125283i
$844$	27.5413	+	2.72051i	0.948011	+	0.0936437i
$845$	−7.51688	−	2.73592i	−0.258589	−	0.0941186i
$846$	−35.8312	+	27.1770i	−1.23190	+	0.934365i
$847$	−27.3889	−	15.8130i	−0.941094	−	0.543341i
$848$	−6.37581	+	31.9582i	−0.218946	+	1.09745i
$849$	0.0871882	−	0.0153736i	0.00299229	−	0.000527622i
$850$	−9.53773	−	30.8508i	−0.327142	−	1.05817i
$851$	−11.8762	+	9.96533i	−0.407111	+	0.341607i
$852$	−0.851311	+	0.217925i	−0.0291654	+	0.00746599i
$853$	49.7520	−	18.1082i	1.70348	−	0.620014i	0.707261	−	0.706952i	$-0.249930\pi$
$853$	49.7520	−	18.1082i	1.70348	−	0.620014i	0.996214	+	0.0869379i	$0.0277082\pi$
$854$	8.61062	−	13.3505i	0.294649	−	0.456845i
$855$	−6.35167	−	7.58060i	−0.217223	−	0.259251i
$856$	5.55588	−	37.3448i	0.189896	−	1.27642i
$857$	−14.6168	−	40.1592i	−0.499299	−	1.37181i	−0.891953	−	0.452127i	$-0.850665\pi$
$857$	−14.6168	−	40.1592i	−0.499299	−	1.37181i	0.392654	−	0.919686i	$-0.371557\pi$
$858$	0.0553603	−	0.0597405i	0.00188997	−	0.00203951i
$859$	−7.20171	−	8.58266i	−0.245719	−	0.292837i	0.629062	−	0.777355i	$-0.283439\pi$
$859$	−7.20171	−	8.58266i	−0.245719	−	0.292837i	−0.874781	+	0.484519i	$0.838995\pi$
$860$	−14.5828	−	4.08293i	−0.497269	−	0.139227i
$861$	−0.0669072	−	0.379450i	−0.00228019	−	0.0129316i
$862$	−2.36009	+	47.9015i	−0.0803849	+	1.63153i
$863$	−18.3713	+	31.8200i	−0.625367	+	1.08317i	0.363103	+	0.931749i	$0.381717\pi$
$863$	−18.3713	+	31.8200i	−0.625367	+	1.08317i	−0.988470	+	0.151418i	$0.951616\pi$
$864$	1.65039	+	0.118397i	0.0561473	+	0.00402795i
$865$	−2.94746	+	8.09807i	−0.100217	+	0.275343i
$866$	−12.2063	−	23.7720i	−0.414787	−	0.807804i
$867$	0.234130	+	0.405524i	0.00795146	+	0.0137723i
$868$	24.6481	+	36.0534i	0.836612	+	1.22373i
$869$	−7.37209	+	8.78571i	−0.250081	+	0.298035i
$870$	0.00341405	+	0.0271036i	0.000115747	+	0.000918898i
$871$	14.4550	+	2.54880i	0.489789	+	0.0863630i
$872$	−33.2416	+	6.78605i	−1.12570	+	0.229805i
$873$		−	15.3215i		−	0.518555i
$874$	−6.54982	−	8.64833i	−0.221551	−	0.292534i
$875$		−	21.6432i		−	0.731675i
$876$	−0.667531	−	0.682644i	−0.0225538	−	0.0230644i
$877$	−42.8083	−	7.54826i	−1.44553	−	0.254887i	−0.604818	−	0.796364i	$-0.706754\pi$
$877$	−42.8083	−	7.54826i	−1.44553	−	0.254887i	−0.840716	+	0.541477i	$0.817865\pi$
$878$	−27.4602	+	3.45897i	−0.926738	+	0.116735i
$879$	0.810888	−	0.966379i	0.0273506	−	0.0325952i
$880$	1.19060	−	1.95953i	0.0401351	−	0.0660557i
$881$	−4.25465	−	7.36927i	−0.143343	−	0.248277i	0.785411	−	0.618975i	$-0.212452\pi$
$881$	−4.25465	−	7.36927i	−0.143343	−	0.248277i	−0.928753	+	0.370698i	$0.879118\pi$
$882$	−8.29876	+	4.26120i	−0.279434	+	0.143482i
$883$	−6.94077	+	19.0696i	−0.233575	+	0.641743i	−1.00000		0.000591383i	$-0.999812\pi$
$883$	−6.94077	+	19.0696i	−0.233575	+	0.641743i	0.766424	+	0.642334i	$0.222034\pi$
$884$	16.0383	−	1.22244i	0.539425	−	0.0411152i
$885$	0.153027	−	0.265050i	0.00514394	−	0.00890956i
$886$	15.1716	+	0.747501i	0.509701	+	0.0251128i
$887$	−3.85358	−	21.8547i	−0.129390	−	0.733810i	−0.978603	−	0.205758i	$-0.934034\pi$
$887$	−3.85358	−	21.8547i	−0.129390	−	0.733810i	0.849212	−	0.528051i	$-0.177077\pi$
$888$	−0.805788	−	0.909561i	−0.0270405	−	0.0305229i
$889$	6.72851	+	8.01873i	0.225667	+	0.268940i
$890$	−10.4130	−	9.64956i	−0.349046	−	0.323454i
$891$	−2.32565	−	6.38967i	−0.0779122	−	0.214062i
$892$	7.71732	+	17.0454i	0.258395	+	0.570722i
$893$	−8.06211	+	45.5326i	−0.269788	+	1.52369i
$894$	−0.875065	−	0.564388i	−0.0292666	−	0.0188760i
$895$	5.05886	−	1.84127i	0.169099	−	0.0615470i
$896$	−17.2909	−	29.6428i	−0.577649	−	0.990298i
$897$	−0.102522	+	0.0860262i	−0.00342311	+	0.00287233i
$898$	19.5681	−	6.04961i	0.652996	−	0.201878i
$899$	−3.71005	+	0.654182i	−0.123737	+	0.0218182i
$900$	15.4660	−	21.5698i	0.515534	−	0.718995i
$901$	−36.3900	−	21.0098i	−1.21233	−	0.699936i
$902$	−1.68581	−	2.22264i	−0.0561314	−	0.0740057i
$903$	−1.39060	−	0.506136i	−0.0462762	−	0.0168432i
$904$	−1.36000	+	1.71208i	−0.0452329	+	0.0569430i
$905$	−6.59186	+	3.80581i	−0.219121	+	0.126510i
$906$	0.168523	−	0.400496i	0.00559881	−	0.0133056i
$907$	14.1086	+	11.8385i	0.468467	+	0.393091i	0.846235	−	0.532810i	$-0.178864\pi$
$907$	14.1086	+	11.8385i	0.468467	+	0.393091i	−0.377768	+	0.925900i	$0.623308\pi$
$908$	50.5191	+	24.2495i	1.67653	+	0.804748i
$909$	−4.13861	+	23.4712i	−0.137269	+	0.778492i
$910$	4.93658	+	1.12344i	0.163646	+	0.0372415i
$911$	−24.3324			−0.806168			−0.403084	−	0.915163i	$-0.632062\pi$
$911$	−24.3324			−0.806168			−0.403084	+	0.915163i	$0.632062\pi$
$912$	0.663835	−	0.531385i	0.0219818	−	0.0175959i
$913$	−9.32341			−0.308560
$914$	−2.63531	−	0.599728i	−0.0871684	−	0.0198372i
$915$	0.0237387	−	0.134629i	0.000784777	−	0.00445069i
$916$	38.2459	+	18.3583i	1.26368	+	0.606575i
$917$	−34.7243	−	29.1371i	−1.14670	−	0.962192i
$918$	−0.827476	+	1.96650i	−0.0273108	+	0.0649042i
$919$	25.1161	−	14.5008i	0.828504	−	0.478337i	−0.0248364	−	0.999692i	$-0.507906\pi$
$919$	25.1161	−	14.5008i	0.828504	−	0.478337i	0.853340	+	0.521355i	$0.174573\pi$
$920$	−2.34344	+	2.95012i	−0.0772608	+	0.0972626i
$921$	0.0925897	+	0.0336999i	0.00305093	+	0.00111045i
$922$	14.3056	+	18.8610i	0.471129	+	0.621155i
$923$	−12.1663	−	7.02420i	−0.400457	−	0.231204i
$924$	0.130563	−	0.182091i	0.00429520	−	0.00599034i
$925$	−38.4070	+	6.77220i	−1.26282	+	0.222668i
$926$	−36.9606	+	11.4266i	−1.21460	+	0.375502i
$927$	−14.9232	+	12.5220i	−0.490142	+	0.411278i
$928$	2.94455	−	0.304117i	0.0966594	−	0.00998314i
$929$	−51.4833	+	18.7384i	−1.68911	+	0.614787i	−0.994513	−	0.104609i	$-0.966641\pi$
$929$	−51.4833	+	18.7384i	−1.68911	+	0.614787i	−0.694600	+	0.719396i	$0.744419\pi$
$930$	0.315827	+	0.203698i	0.0103564	+	0.00667953i
$931$	−3.28711	+	9.01126i	−0.107731	+	0.295332i
$932$	8.45875	+	18.6830i	0.277076	+	0.611983i
$933$	−0.459648	−	1.26287i	−0.0150482	−	0.0413446i
$934$	18.6651	+	17.2966i	0.610740	+	0.565961i
$935$	1.90038	+	2.26479i	0.0621492	+	0.0740665i
$936$	8.76686	+	9.89589i	0.286554	+	0.323457i
$937$	−3.50848	−	19.8976i	−0.114617	−	0.650026i	−0.986939	−	0.161094i	$-0.948498\pi$
$937$	−3.50848	−	19.8976i	−0.114617	−	0.650026i	0.872322	−	0.488932i	$-0.162613\pi$
$938$	40.3302	+	1.98705i	1.31683	+	0.0648796i
$939$	0.396674	−	0.687059i	0.0129450	−	0.0224213i
$940$	16.0124	−	1.22047i	0.522268	−	0.0398075i
$941$	13.2176	−	36.3151i	0.430882	−	1.18384i	−0.514390	−	0.857557i	$-0.671981\pi$
$941$	13.2176	−	36.3151i	0.430882	−	1.18384i	0.945272	−	0.326283i	$-0.105796\pi$
$942$	−0.0470062	+	0.0241365i	−0.00153155	+	0.000786410i
$943$	2.29194	+	3.96976i	0.0746359	+	0.129273i
$944$	−28.3430	−	17.2210i	−0.922485	−	0.560497i
$945$	−0.431655	+	0.514426i	−0.0140417	+	0.0167343i
$946$	−10.6302	+	1.33902i	−0.345619	+	0.0435352i
$947$	20.9978	+	3.70248i	0.682338	+	0.120315i	0.504064	−	0.863666i	$-0.331838\pi$
$947$	20.9978	+	3.70248i	0.682338	+	0.120315i	0.178274	+	0.983981i	$0.442949\pi$
$948$	1.03272	+	1.05611i	0.0335413	+	0.0343007i
$949$		−	15.2636i		−	0.495478i
$950$	−3.39133	−	27.0790i	−0.110029	−	0.878558i
$951$		−	0.154667i		−	0.00501543i
$952$	43.3550	−	8.85064i	1.40514	−	0.286851i
$953$	9.61564	+	1.69550i	0.311481	+	0.0549225i	0.327204	−	0.944954i	$-0.393894\pi$
$953$	9.61564	+	1.69550i	0.311481	+	0.0549225i	−0.0157225	+	0.999876i	$0.505005\pi$
$954$	−4.31633	−	34.2666i	−0.139746	−	1.10942i
$955$	4.20805	−	5.01496i	0.136169	−	0.162280i
$956$	−4.68307	−	6.85004i	−0.151461	−	0.221546i
$957$	0.00966379	+	0.0167382i	0.000312386	+	0.000541069i
$958$	−18.5435	−	36.1138i	−0.599114	−	1.16678i
$959$	−5.47701	+	15.0480i	−0.176862	+	0.485924i
$960$	−0.236078	−	0.177407i	−0.00761938	−	0.00572578i
$961$	−10.4139	+	18.0373i	−0.335931	+	0.581849i
$962$	0.955959	−	19.4026i	0.0308213	−	0.625565i
$963$	6.94841	+	39.4064i	0.223909	+	1.26985i
$964$	−14.2661	−	3.99427i	−0.459481	−	0.128647i
$965$	7.03762	+	8.38711i	0.226549	+	0.269991i
$966$	−0.250250	+	0.270050i	−0.00805167	+	0.00868873i
$967$	−3.34004	−	9.17669i	−0.107408	−	0.295102i	0.874332	−	0.485329i	$-0.161300\pi$
$967$	−3.34004	−	9.17669i	−0.107408	−	0.295102i	−0.981740	+	0.190226i	$0.939078\pi$
$968$	−4.33962	+	29.1694i	−0.139481	+	0.937541i
$969$	0.374262	+	1.03056i	0.0120230	+	0.0331065i
$970$	−2.96541	+	4.59778i	−0.0952136	+	0.147626i
$971$	6.46943	−	2.35468i	0.207614	−	0.0755653i	−0.236120	−	0.971724i	$-0.575876\pi$
$971$	6.46943	−	2.35468i	0.207614	−	0.0755653i	0.443734	+	0.896159i	$0.353654\pi$
$972$	−2.54858	+	0.652405i	−0.0817457	+	0.0209259i
$973$	4.79383	−	4.02250i	0.153683	−	0.128955i
$974$	11.8039	+	38.1809i	0.378221	+	1.22339i
$975$	−0.331551	+	0.0584613i	−0.0106181	+	0.00187226i
$976$	−14.5274	−	2.89829i	−0.465011	−	0.0927720i
$977$	−18.1282	−	10.4663i	−0.579973	−	0.334848i	0.181149	−	0.983456i	$-0.442018\pi$
$977$	−18.1282	−	10.4663i	−0.579973	−	0.334848i	−0.761123	+	0.648608i	$0.775352\pi$
$978$	0.693646	−	0.526112i	0.0221803	−	0.0168232i
$979$	−9.43854	−	3.43535i	−0.301657	−	0.109794i
$980$	3.31508	+	0.327460i	0.105896	+	0.0104603i
$981$	31.1394	−	17.9783i	0.994205	−	0.574004i
$982$	−4.12029	−	1.73376i	−0.131484	−	0.0553265i
$983$	−13.8631	−	11.6325i	−0.442164	−	0.371020i	0.394354	−	0.918959i	$-0.370968\pi$
$983$	−13.8631	−	11.6325i	−0.442164	−	0.371020i	−0.836519	+	0.547939i	$0.815413\pi$
$984$	−0.306217	+	0.187930i	−0.00976184	+	0.00599098i
$985$	0.300591	−	1.70474i	0.00957763	−	0.0543174i
$986$	−0.846980	+	3.72178i	−0.0269733	+	0.118526i
$987$	1.56929			0.0499510
$988$	13.5269	+	1.34592i	0.430349	+	0.0428194i
$989$	17.6054			0.559821
$990$	−0.539225	+	2.36945i	−0.0171377	+	0.0753061i
$991$	−1.80534	+	10.2386i	−0.0573485	+	0.325240i	−0.999963	−	0.00864445i	$-0.997248\pi$
$991$	−1.80534	+	10.2386i	−0.0573485	+	0.325240i	0.942614	+	0.333884i	$0.108359\pi$
$992$	22.8337	−	33.7210i	0.724971	−	1.07064i
$993$	−0.0636623	−	0.0534190i	−0.00202026	−	0.00169520i
$994$	−35.6219	−	14.9892i	−1.12986	−	0.475429i
$995$	−5.42942	+	3.13468i	−0.172124	+	0.0993759i
$996$	−0.118038	+	1.19497i	−0.00374019	+	0.0378642i
$997$	51.1244	+	18.6078i	1.61913	+	0.589313i	0.983215	−	0.182450i	$-0.0584026\pi$
$997$	51.1244	+	18.6078i	1.61913	+	0.589313i	0.635910	+	0.771763i	$0.280625\pi$
$998$	−23.2095	+	17.6037i	−0.734683	+	0.557237i
$999$	2.23149	+	1.28835i	0.0706013	+	0.0407617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.71.1	yes	48
3.2	odd	2		684.2.cf.a.451.8		48
4.3	odd	2	inner	76.2.k.a.71.6	yes	48
12.11	even	2		684.2.cf.a.451.3		48
19.15	odd	18	inner	76.2.k.a.15.6	yes	48
57.53	even	18		684.2.cf.a.91.3		48
76.15	even	18	inner	76.2.k.a.15.1	✓	48
228.167	odd	18		684.2.cf.a.91.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.15.1	✓	48	76.15	even	18	inner
76.2.k.a.15.6	yes	48	19.15	odd	18	inner
76.2.k.a.71.1	yes	48	1.1	even	1	trivial
76.2.k.a.71.6	yes	48	4.3	odd	2	inner
684.2.cf.a.91.3		48	57.53	even	18
684.2.cf.a.91.8		48	228.167	odd	18
684.2.cf.a.451.3		48	12.11	even	2
684.2.cf.a.451.8		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37896 - 0.313814i) q^{2} +(-0.00846870 + 0.0480284i) q^{3} +(1.80304 + 0.865472i) q^{4} +(0.579816 + 0.486524i) q^{5} +(0.0267499 - 0.0635714i) q^{6} +(2.62687 - 1.51662i) q^{7} +(-2.21472 - 1.75927i) q^{8} +(2.81684 + 1.02525i) q^{9} +O(q^{10})\)	\(q+(-1.37896 - 0.313814i) q^{2} +(-0.00846870 + 0.0480284i) q^{3} +(1.80304 + 0.865472i) q^{4} +(0.579816 + 0.486524i) q^{5} +(0.0267499 - 0.0635714i) q^{6} +(2.62687 - 1.51662i) q^{7} +(-2.21472 - 1.75927i) q^{8} +(2.81684 + 1.02525i) q^{9} +(-0.646863 - 0.852849i) q^{10} +(-0.655865 - 0.378664i) q^{11} +(-0.0568366 + 0.0792677i) q^{12} +(-1.53562 + 0.270771i) q^{13} +(-4.09827 + 1.26701i) q^{14} +(-0.0282772 + 0.0237274i) q^{15} +(2.50192 + 3.12096i) q^{16} +(-4.84662 + 1.76403i) q^{17} +(-3.56257 - 2.29774i) q^{18} +(-4.29322 + 0.753853i) q^{19} +(0.624360 + 1.37904i) q^{20} +(0.0505948 + 0.139008i) q^{21} +(0.785579 + 0.727981i) q^{22} +(-1.13123 - 1.34815i) q^{23} +(0.103251 - 0.0914706i) q^{24} +(-0.768759 - 4.35985i) q^{25} +(2.20252 + 0.108518i) q^{26} +(-0.146250 + 0.253312i) q^{27} +(6.04894 - 0.461053i) q^{28} +(-0.178978 + 0.491737i) q^{29} +(0.0464391 - 0.0238453i) q^{30} +(3.59957 + 6.23464i) q^{31} +(-2.47063 - 5.08881i) q^{32} +(0.0237409 - 0.0282933i) q^{33} +(7.23685 - 0.911576i) q^{34} +(2.26097 + 0.398670i) q^{35} +(4.19156 + 4.28646i) q^{36} -8.80926i q^{37} +(6.15673 + 0.307741i) q^{38} -0.0760464i q^{39} +(-0.428204 - 2.09756i) q^{40} +(-2.56508 - 0.452292i) q^{41} +(-0.0261453 - 0.207563i) q^{42} +(-6.43028 + 7.66330i) q^{43} +(-0.854829 - 1.25038i) q^{44} +(1.13444 + 1.96492i) q^{45} +(1.13685 + 2.21404i) q^{46} +(3.62828 - 9.96861i) q^{47} +(-0.171083 + 0.0937325i) q^{48} +(1.10029 - 1.90575i) q^{49} +(-0.308097 + 6.25329i) q^{50} +(-0.0436787 - 0.247714i) q^{51} +(-3.00313 - 0.840824i) q^{52} +(5.23679 + 6.24096i) q^{53} +(0.281165 - 0.303411i) q^{54} +(-0.196052 - 0.538649i) q^{55} +(-8.48591 - 1.26247i) q^{56} +(0.000151609 - 0.212580i) q^{57} +(0.401117 - 0.621918i) q^{58} +(-7.79113 + 2.83574i) q^{59} +(-0.0715204 + 0.0183083i) q^{60} +(-2.83699 + 2.38052i) q^{61} +(-3.00713 - 9.72690i) q^{62} +(8.95438 - 1.57890i) q^{63} +(1.80995 + 7.79257i) q^{64} +(-1.02211 - 0.590117i) q^{65} +(-0.0416166 + 0.0315651i) q^{66} +(-8.84545 - 3.21948i) q^{67} +(-10.2654 - 1.01400i) q^{68} +(0.0743296 - 0.0429142i) q^{69} +(-2.99267 - 1.25927i) q^{70} +(6.90158 + 5.79111i) q^{71} +(-4.43483 - 7.22621i) q^{72} +(-1.69979 + 9.64000i) q^{73} +(-2.76447 + 12.1476i) q^{74} +0.215907 q^{75} +(-8.39329 - 2.35643i) q^{76} -2.29716 q^{77} +(-0.0238644 + 0.104865i) q^{78} +(2.62972 - 14.9139i) q^{79} +(-0.0677710 + 3.02683i) q^{80} +(6.87801 + 5.77133i) q^{81} +(3.39519 + 1.42865i) q^{82} +(10.6616 - 6.15546i) q^{83} +(-0.0290831 + 0.294425i) q^{84} +(-3.66839 - 1.33518i) q^{85} +(11.2719 - 8.54945i) q^{86} +(-0.0221016 - 0.0127604i) q^{87} +(0.786385 + 1.99248i) q^{88} +(13.0613 - 2.30306i) q^{89} +(-0.947731 - 3.06554i) q^{90} +(-3.62321 + 3.04023i) q^{91} +(-0.872873 - 3.40982i) q^{92} +(-0.329923 + 0.120082i) q^{93} +(-8.13153 + 12.6077i) q^{94} +(-2.85604 - 1.65165i) q^{95} +(0.265330 - 0.0755648i) q^{96} +(-1.74814 - 4.80298i) q^{97} +(-2.11530 + 2.28266i) q^{98} +(-1.45925 - 1.73906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Introduction

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