LMFDB - Embedded newform 588.2.ba.a.283.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(103,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 29]))

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

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

chi := DirichletCharacter("588.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.ba (of order $42$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			283.14
Character	$\chi$	$=$	588.283
Dual form			588.2.ba.a.187.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.109917 + 1.40994i) q^{2} +(0.988831 - 0.149042i) q^{3} +(-1.97584 - 0.309952i) q^{4} +(0.577807 + 0.226773i) q^{5} +(0.101451 + 1.41057i) q^{6} +(2.12573 + 1.57521i) q^{7} +(0.654190 - 2.75173i) q^{8} +(0.955573 - 0.294755i) q^{9} +O(q^{10})$	\(q+(-0.109917 + 1.40994i) q^{2} +(0.988831 - 0.149042i) q^{3} +(-1.97584 - 0.309952i) q^{4} +(0.577807 + 0.226773i) q^{5} +(0.101451 + 1.41057i) q^{6} +(2.12573 + 1.57521i) q^{7} +(0.654190 - 2.75173i) q^{8} +(0.955573 - 0.294755i) q^{9} +(-0.383246 + 0.789745i) q^{10} +(0.418624 - 1.35715i) q^{11} +(-1.99996 - 0.0120066i) q^{12} +(-0.804577 + 0.183639i) q^{13} +(-2.45460 + 2.82399i) q^{14} +(0.605152 + 0.138122i) q^{15} +(3.80786 + 1.22483i) q^{16} +(3.97606 + 5.83181i) q^{17} +(0.310552 + 1.37969i) q^{18} +(0.990339 + 1.71532i) q^{19} +(-1.07136 - 0.627158i) q^{20} +(2.33676 + 1.24079i) q^{21} +(1.86747 + 0.739406i) q^{22} +(2.55242 - 3.74372i) q^{23} +(0.236758 - 2.81850i) q^{24} +(-3.38282 - 3.13880i) q^{25} +(-0.170483 - 1.15459i) q^{26} +(0.900969 - 0.433884i) q^{27} +(-3.71185 - 3.77123i) q^{28} +(2.01507 + 0.970408i) q^{29} +(-0.261260 + 0.838044i) q^{30} +(-2.30045 + 3.98449i) q^{31} +(-2.14548 + 5.23421i) q^{32} +(0.211676 - 1.40438i) q^{33} +(-8.65952 + 4.96498i) q^{34} +(0.871045 + 1.39222i) q^{35} +(-1.97942 + 0.286207i) q^{36} +(0.849468 + 11.3354i) q^{37} +(-2.52734 + 1.20777i) q^{38} +(-0.768220 + 0.301504i) q^{39} +(1.00201 - 1.44162i) q^{40} +(-0.142820 + 0.113895i) q^{41} +(-2.00629 + 3.15829i) q^{42} +(-7.66154 - 6.10987i) q^{43} +(-1.24778 + 2.55175i) q^{44} +(0.618979 + 0.0463861i) q^{45} +(4.99785 + 4.01025i) q^{46} +(9.80152 - 9.09448i) q^{47} +(3.94788 + 0.643615i) q^{48} +(2.03742 + 6.69693i) q^{49} +(4.79734 - 4.42456i) q^{50} +(4.80084 + 5.17407i) q^{51} +(1.64663 - 0.113462i) q^{52} +(-0.412496 + 5.50437i) q^{53} +(0.512716 + 1.31800i) q^{54} +(0.549648 - 0.689236i) q^{55} +(5.72519 - 4.81894i) q^{56} +(1.23493 + 1.54856i) q^{57} +(-1.58970 + 2.73446i) q^{58} +(-2.34591 - 5.97729i) q^{59} +(-1.15287 - 0.460474i) q^{60} +(-9.20724 + 0.689988i) q^{61} +(-5.36502 - 3.68145i) q^{62} +(2.49559 + 0.878660i) q^{63} +(-7.14407 - 3.60031i) q^{64} +(-0.506534 - 0.0763478i) q^{65} +(1.95682 + 0.452815i) q^{66} +(-0.491853 - 0.283971i) q^{67} +(-6.04847 - 12.7551i) q^{68} +(1.96594 - 4.08232i) q^{69} +(-2.05869 + 1.07509i) q^{70} +(-3.11294 - 6.46408i) q^{71} +(-0.185962 - 2.82231i) q^{72} +(-2.32715 + 2.50808i) q^{73} +(-16.0755 - 0.0482534i) q^{74} +(-3.81285 - 2.59956i) q^{75} +(-1.42508 - 3.69614i) q^{76} +(3.02767 - 2.22550i) q^{77} +(-0.340661 - 1.11628i) q^{78} +(4.26467 - 2.46221i) q^{79} +(1.92245 + 1.57123i) q^{80} +(0.826239 - 0.563320i) q^{81} +(-0.144887 - 0.213886i) q^{82} +(-0.542153 + 2.37533i) q^{83} +(-4.23246 - 3.17589i) q^{84} +(0.974902 + 4.27132i) q^{85} +(9.45666 - 10.1307i) q^{86} +(2.13720 + 0.659238i) q^{87} +(-3.46064 - 2.03977i) q^{88} +(-0.190161 - 0.616487i) q^{89} +(-0.133438 + 0.867622i) q^{90} +(-1.99958 - 0.877011i) q^{91} +(-6.20354 + 6.60585i) q^{92} +(-1.68090 + 4.28285i) q^{93} +(11.7453 + 14.8192i) q^{94} +(0.183238 + 1.21570i) q^{95} +(-1.34139 + 5.49551i) q^{96} -17.0926i q^{97} +(-9.66619 + 2.13652i) q^{98} -1.42024i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9	$ 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9} + 41 q^{10} + 6 q^{11} + 52 q^{14} + 20 q^{16} - 6 q^{19} - 25 q^{20} + 4 q^{21} + 6 q^{22} + 9 q^{24} - 26 q^{25} - 18 q^{26} + 56 q^{27} + 5 q^{30} + 2 q^{31} + 15 q^{32} + 6 q^{33} + 44 q^{34} - 12 q^{35} + 16 q^{37} - 100 q^{38} + 8 q^{39} - 7 q^{40} - 7 q^{42} - 53 q^{44} - 10 q^{46} + 4 q^{47} + 8 q^{48} - 4 q^{49} - 114 q^{50} - 28 q^{52} - 4 q^{53} + q^{56} - 12 q^{57} + 27 q^{58} - 10 q^{59} - 7 q^{60} + 2 q^{61} - 16 q^{62} - 12 q^{63} - 84 q^{64} - 4 q^{65} + 21 q^{66} + 42 q^{67} + 26 q^{68} - 70 q^{70} + 28 q^{71} + 15 q^{72} + 18 q^{73} + 20 q^{74} + 54 q^{75} + 49 q^{76} - 8 q^{77} - 6 q^{78} - 6 q^{79} - 40 q^{80} + 28 q^{81} - 99 q^{82} + 10 q^{83} + 54 q^{84} + 24 q^{85} - 314 q^{86} - 40 q^{88} + 20 q^{90} - 34 q^{91} + 14 q^{92} - 2 q^{93} - 152 q^{94} - 24 q^{95} - 10 q^{96} - 156 q^{98}+O(q^{100}) $ 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9 + 41 * q^10 + 6 * q^11 + 52 * q^14 + 20 * q^16 - 6 * q^19 - 25 * q^20 + 4 * q^21 + 6 * q^22 + 9 * q^24 - 26 * q^25 - 18 * q^26 + 56 * q^27 + 5 * q^30 + 2 * q^31 + 15 * q^32 + 6 * q^33 + 44 * q^34 - 12 * q^35 + 16 * q^37 - 100 * q^38 + 8 * q^39 - 7 * q^40 - 7 * q^42 - 53 * q^44 - 10 * q^46 + 4 * q^47 + 8 * q^48 - 4 * q^49 - 114 * q^50 - 28 * q^52 - 4 * q^53 + q^56 - 12 * q^57 + 27 * q^58 - 10 * q^59 - 7 * q^60 + 2 * q^61 - 16 * q^62 - 12 * q^63 - 84 * q^64 - 4 * q^65 + 21 * q^66 + 42 * q^67 + 26 * q^68 - 70 * q^70 + 28 * q^71 + 15 * q^72 + 18 * q^73 + 20 * q^74 + 54 * q^75 + 49 * q^76 - 8 * q^77 - 6 * q^78 - 6 * q^79 - 40 * q^80 + 28 * q^81 - 99 * q^82 + 10 * q^83 + 54 * q^84 + 24 * q^85 - 314 * q^86 - 40 * q^88 + 20 * q^90 - 34 * q^91 + 14 * q^92 - 2 * q^93 - 152 * q^94 - 24 * q^95 - 10 * q^96 - 156 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{42}\right)$

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 $

$2$	−0.109917	+	1.40994i	−0.0777230	+	0.996975i
$2$	−0.109917	+	1.40994i	−0.0777230	+	0.996975i
$3$	0.988831	−	0.149042i	0.570902	−	0.0860496i
$3$	0.988831	−	0.149042i	0.570902	−	0.0860496i
$4$	−1.97584	−	0.309952i	−0.987918	−	0.154976i
$5$	0.577807	+	0.226773i	0.258403	+	0.101416i	0.491006	−	0.871156i	$-0.336629\pi$
$5$	0.577807	+	0.226773i	0.258403	+	0.101416i	−0.232603	+	0.972572i	$0.574724\pi$
$6$	0.101451	+	1.41057i	0.0414171	+	0.575863i
$7$	2.12573	+	1.57521i	0.803449	+	0.595374i
$7$	2.12573	+	1.57521i	0.803449	+	0.595374i
$8$	0.654190	−	2.75173i	0.231291	−	0.972885i
$9$	0.955573	−	0.294755i	0.318524	−	0.0982517i
$10$	−0.383246	+	0.789745i	−0.121193	+	0.249739i
$11$	0.418624	−	1.35715i	0.126220	−	0.409195i	−0.870303	−	0.492517i	$-0.836077\pi$
$11$	0.418624	−	1.35715i	0.126220	−	0.409195i	0.996523	+	0.0833222i	$0.0265531\pi$
$12$	−1.99996	−	0.0120066i	−0.577340	−	0.00346600i
$13$	−0.804577	+	0.183639i	−0.223149	+	0.0509324i	−0.332634	−	0.943056i	$-0.607937\pi$
$13$	−0.804577	+	0.183639i	−0.223149	+	0.0509324i	0.109484	+	0.993989i	$0.465080\pi$
$14$	−2.45460	+	2.82399i	−0.656019	+	0.754744i
$15$	0.605152	+	0.138122i	0.156250	+	0.0356630i
$16$	3.80786	+	1.22483i	0.951965	+	0.306207i
$17$	3.97606	+	5.83181i	0.964337	+	1.41442i	0.909395	+	0.415933i	$0.136545\pi$
$17$	3.97606	+	5.83181i	0.964337	+	1.41442i	0.0549414	+	0.998490i	$0.482503\pi$
$18$	0.310552	+	1.37969i	0.0731978	+	0.325197i
$19$	0.990339	+	1.71532i	0.227199	+	0.393521i	0.956977	−	0.290164i	$-0.0937098\pi$
$19$	0.990339	+	1.71532i	0.227199	+	0.393521i	−0.729778	+	0.683684i	$0.760376\pi$
$20$	−1.07136	−	0.627158i	−0.239564	−	0.140237i
$21$	2.33676	+	1.24079i	0.509922	+	0.270764i
$22$	1.86747	+	0.739406i	0.398147	+	0.157642i
$23$	2.55242	−	3.74372i	0.532217	−	0.780619i	−0.462128	−	0.886813i	$-0.652914\pi$
$23$	2.55242	−	3.74372i	0.532217	−	0.780619i	0.994345	+	0.106194i	$0.0338664\pi$
$24$	0.236758	−	2.81850i	0.0483281	−	0.575324i
$25$	−3.38282	−	3.13880i	−0.676565	−	0.627760i
$26$	−0.170483	−	1.15459i	−0.0334345	−	0.226433i
$27$	0.900969	−	0.433884i	0.173392	−	0.0835010i
$28$	−3.71185	−	3.77123i	−0.701473	−	0.712696i
$29$	2.01507	+	0.970408i	0.374190	+	0.180200i	0.611520	−	0.791229i	$-0.290558\pi$
$29$	2.01507	+	0.970408i	0.374190	+	0.180200i	−0.237331	+	0.971429i	$0.576273\pi$
$30$	−0.261260	+	0.838044i	−0.0476993	+	0.153005i
$31$	−2.30045	+	3.98449i	−0.413173	+	0.715636i	−0.995235	−	0.0975084i	$-0.968913\pi$
$31$	−2.30045	+	3.98449i	−0.413173	+	0.715636i	0.582062	+	0.813144i	$0.302246\pi$
$32$	−2.14548	+	5.23421i	−0.379270	+	0.925286i
$33$	0.211676	−	1.40438i	0.0368481	−	0.244471i
$34$	−8.65952	+	4.96498i	−1.48509	+	0.851486i
$35$	0.871045	+	1.39222i	0.147233	+	0.235329i
$36$	−1.97942	+	0.286207i	−0.329903	+	0.0477011i
$37$	0.849468	+	11.3354i	0.139652	+	1.86352i	0.425123	+	0.905135i	$0.360231\pi$
$37$	0.849468	+	11.3354i	0.139652	+	1.86352i	−0.285472	+	0.958387i	$0.592150\pi$
$38$	−2.52734	+	1.20777i	−0.409989	+	0.195926i
$39$	−0.768220	+	0.301504i	−0.123014	+	0.0482793i
$40$	1.00201	−	1.44162i	0.158432	−	0.227940i
$41$	−0.142820	+	0.113895i	−0.0223048	+	0.0177875i	−0.634579	−	0.772858i	$-0.718826\pi$
$41$	−0.142820	+	0.113895i	−0.0223048	+	0.0177875i	0.612274	+	0.790646i	$0.290255\pi$
$42$	−2.00629	+	3.15829i	−0.309577	+	0.487335i
$43$	−7.66154	−	6.10987i	−1.16837	−	0.931747i	−0.169818	−	0.985475i	$-0.554318\pi$
$43$	−7.66154	−	6.10987i	−1.16837	−	0.931747i	−0.998556	+	0.0537287i	$0.982889\pi$
$44$	−1.24778	+	2.55175i	−0.188110	+	0.384690i
$45$	0.618979	+	0.0463861i	0.0922720	+	0.00691483i
$46$	4.99785	+	4.01025i	0.736892	+	0.591279i
$47$	9.80152	−	9.09448i	1.42970	−	1.32657i	0.564217	−	0.825626i	$-0.309178\pi$
$47$	9.80152	−	9.09448i	1.42970	−	1.32657i	0.865482	−	0.500940i	$-0.167012\pi$
$48$	3.94788	+	0.643615i	0.569827	+	0.0928978i
$49$	2.03742	+	6.69693i	0.291060	+	0.956705i
$50$	4.79734	−	4.42456i	0.678446	−	0.625727i
$51$	4.80084	+	5.17407i	0.672252	+	0.724515i
$52$	1.64663	−	0.113462i	0.228347	−	0.0157343i
$53$	−0.412496	+	5.50437i	−0.0566607	+	0.756084i	0.894437	+	0.447194i	$0.147577\pi$
$53$	−0.412496	+	5.50437i	−0.0566607	+	0.756084i	−0.951098	+	0.308890i	$0.900042\pi$
$54$	0.512716	+	1.31800i	0.0697719	+	0.179357i
$55$	0.549648	−	0.689236i	0.0741145	−	0.0929366i
$56$	5.72519	−	4.81894i	0.765061	−	0.643958i
$57$	1.23493	+	1.54856i	0.163571	+	0.205111i
$58$	−1.58970	+	2.73446i	−0.208738	+	0.359052i
$59$	−2.34591	−	5.97729i	−0.305412	−	0.778176i	−0.998363	−	0.0571921i	$-0.981785\pi$
$59$	−2.34591	−	5.97729i	−0.305412	−	0.778176i	0.692951	−	0.720984i	$-0.256310\pi$
$60$	−1.15287	−	0.460474i	−0.148835	−	0.0594470i
$61$	−9.20724	+	0.689988i	−1.17887	+	0.0883439i	−0.649711	−	0.760181i	$-0.725110\pi$
$61$	−9.20724	+	0.689988i	−1.17887	+	0.0883439i	−0.529156	+	0.848525i	$0.677491\pi$
$62$	−5.36502	−	3.68145i	−0.681358	−	0.467544i
$63$	2.49559	+	0.878660i	0.314414	+	0.110701i
$64$	−7.14407	−	3.60031i	−0.893009	−	0.450039i
$65$	−0.506534	−	0.0763478i	−0.0628279	−	0.00946978i
$66$	1.95682	+	0.452815i	0.240868	+	0.0557377i
$67$	−0.491853	−	0.283971i	−0.0600894	−	0.0346926i	0.469654	−	0.882850i	$-0.344379\pi$
$67$	−0.491853	−	0.283971i	−0.0600894	−	0.0346926i	−0.529744	+	0.848158i	$0.677712\pi$
$68$	−6.04847	−	12.7551i	−0.733485	−	1.54678i
$69$	1.96594	−	4.08232i	0.236672	−	0.491454i
$70$	−2.05869	+	1.07509i	−0.246060	+	0.128498i
$71$	−3.11294	−	6.46408i	−0.369438	−	0.767145i	0.630522	−	0.776172i	$-0.282841\pi$
$71$	−3.11294	−	6.46408i	−0.369438	−	0.767145i	−0.999959	+	0.00902650i	$0.997127\pi$
$72$	−0.185962	−	2.82231i	−0.0219158	−	0.332612i
$73$	−2.32715	+	2.50808i	−0.272373	+	0.293548i	−0.854394	−	0.519625i	$-0.826072\pi$
$73$	−2.32715	+	2.50808i	−0.272373	+	0.293548i	0.582021	+	0.813173i	$0.302262\pi$
$74$	−16.0755	−	0.0482534i	−1.86874	−	0.00560935i
$75$	−3.81285	−	2.59956i	−0.440271	−	0.300171i
$76$	−1.42508	−	3.69614i	−0.163468	−	0.423977i
$77$	3.02767	−	2.22550i	0.345035	−	0.253619i
$78$	−0.340661	−	1.11628i	−0.0385723	−	0.126394i
$79$	4.26467	−	2.46221i	0.479813	−	0.277020i	−0.240526	−	0.970643i	$-0.577320\pi$
$79$	4.26467	−	2.46221i	0.479813	−	0.277020i	0.720338	+	0.693623i	$0.243987\pi$
$80$	1.92245	+	1.57123i	0.214937	+	0.175669i
$81$	0.826239	−	0.563320i	0.0918043	−	0.0625911i
$82$	−0.144887	−	0.213886i	−0.0160001	−	0.0236198i
$83$	−0.542153	+	2.37533i	−0.0595090	+	0.260726i	−0.995927	−	0.0901597i	$-0.971262\pi$
$83$	−0.542153	+	2.37533i	−0.0595090	+	0.260726i	0.936418	+	0.350886i	$0.114119\pi$
$84$	−4.23246	−	3.17589i	−0.461799	−	0.346518i
$85$	0.974902	+	4.27132i	0.105743	+	0.463290i
$86$	9.45666	−	10.1307i	1.01974	−	1.09242i
$87$	2.13720	+	0.659238i	0.229132	+	0.0706778i
$88$	−3.46064	−	2.03977i	−0.368906	−	0.217441i
$89$	−0.190161	−	0.616487i	−0.0201570	−	0.0653475i	0.944936	−	0.327257i	$-0.106124\pi$
$89$	−0.190161	−	0.616487i	−0.0201570	−	0.0653475i	−0.965093	+	0.261909i	$0.915648\pi$
$90$	−0.133438	+	0.867622i	−0.0140656	+	0.0914554i
$91$	−1.99958	−	0.877011i	−0.209613	−	0.0919358i
$92$	−6.20354	+	6.60585i	−0.646764	+	0.688707i
$93$	−1.68090	+	4.28285i	−0.174301	+	0.444111i
$94$	11.7453	+	14.8192i	1.21143	+	1.52848i
$95$	0.183238	+	1.21570i	0.0187998	+	0.124729i
$96$	−1.34139	+	5.49551i	−0.136906	+	0.560883i
$97$		−	17.0926i		−	1.73549i	−0.497007	−	0.867747i	$-0.665568\pi$
$97$		−	17.0926i		−	1.73549i	0.497007	−	0.867747i	$-0.334432\pi$
$98$	−9.66619	+	2.13652i	−0.976433	+	0.215821i
$99$		−	1.42024i		−	0.142740i
$100$	5.71103	+	7.25027i	0.571103	+	0.725027i
$101$	−1.51215	−	10.0325i	−0.150465	−	0.998269i	−0.928843	−	0.370473i	$-0.879195\pi$
$101$	−1.51215	−	10.0325i	−0.150465	−	0.998269i	0.778378	−	0.627796i	$-0.216043\pi$
$102$	−7.82281	+	6.20016i	−0.774573	+	0.613907i
$103$	5.60419	−	14.2793i	0.552198	−	1.40698i	−0.333516	−	0.942744i	$-0.608235\pi$
$103$	5.60419	−	14.2793i	0.552198	−	1.40698i	0.885714	−	0.464232i	$-0.153670\pi$
$104$	−0.0210193	+	2.33412i	−0.00206111	+	0.228879i
$105$	1.06882	+	1.24685i	0.104306	+	0.121680i
$106$	−7.71547	−	1.18662i	−0.749393	−	0.115254i
$107$	−2.80883	−	9.10602i	−0.271540	−	0.880312i	−0.983934	−	0.178532i	$-0.942865\pi$
$107$	−2.80883	−	9.10602i	−0.271540	−	0.880312i	0.712394	−	0.701780i	$-0.247611\pi$
$108$	−1.91465	+	0.578027i	−0.184237	+	0.0556206i
$109$	4.79772	+	1.47990i	0.459538	+	0.141749i	0.515876	−	0.856663i	$-0.327466\pi$
$109$	4.79772	+	1.47990i	0.459538	+	0.141749i	−0.0563385	+	0.998412i	$0.517943\pi$
$110$	0.911363	+	0.850726i	0.0868951	+	0.0811136i
$111$	2.52943	+	11.0822i	0.240083	+	1.05187i
$112$	6.16510	+	8.60183i	0.582548	+	0.812797i
$113$	1.13005	−	4.95109i	0.106307	−	0.465759i	−0.893552	−	0.448959i	$-0.851795\pi$
$113$	1.13005	−	4.95109i	0.106307	−	0.465759i	0.999859	−	0.0168004i	$-0.00534797\pi$
$114$	−2.31910	+	1.57096i	−0.217204	+	0.147134i
$115$	2.32378	−	1.58433i	0.216694	−	0.147739i
$116$	−3.68068	−	2.54194i	−0.341742	−	0.236013i
$117$	−0.714703	+	0.412634i	−0.0660743	+	0.0381480i
$118$	8.68544	−	2.65058i	0.799560	−	0.244006i
$119$	−0.734318	+	18.6600i	−0.0673149	+	1.71056i
$120$	0.775959	−	1.57486i	0.0708351	−	0.143764i
$121$	7.42203	+	5.06025i	0.674730	+	0.460023i
$122$	0.0391942	−	13.0575i	0.00354848	−	1.18217i
$123$	−0.124250	+	0.133909i	−0.0112032	+	0.0120742i
$124$	5.78031	−	7.15968i	0.519087	−	0.642958i
$125$	−2.58942	−	5.37698i	−0.231604	−	0.480931i
$126$	−1.51316	+	3.42204i	−0.134803	+	0.304859i
$127$	−6.79446	+	14.1088i	−0.602911	+	1.25196i	0.346538	+	0.938036i	$0.387357\pi$
$127$	−6.79446	+	14.1088i	−0.602911	+	1.25196i	−0.949449	+	0.313922i	$0.898357\pi$
$128$	5.86146	−	9.67695i	0.518085	−	0.855329i
$129$	−8.48659	−	4.89974i	−0.747203	−	0.431398i
$130$	0.163322	−	0.705789i	0.0143243	−	0.0619018i
$131$	2.36683	+	0.356742i	0.206791	+	0.0311687i	0.251621	−	0.967826i	$-0.419036\pi$
$131$	2.36683	+	0.356742i	0.206791	+	0.0311687i	−0.0448298	+	0.998995i	$0.514275\pi$
$132$	−0.853528	+	2.70922i	−0.0742901	+	0.235807i
$133$	−0.596798	+	5.20628i	−0.0517489	+	0.451442i
$134$	0.454444	−	0.662267i	0.0392580	−	0.0572112i
$135$	0.618979	−	0.0463861i	0.0532732	−	0.00399228i
$136$	18.6487	−	7.12595i	1.59911	−	0.611045i
$137$	−5.43351	−	13.8444i	−0.464216	−	1.18280i	−0.950975	−	0.309267i	$-0.899916\pi$
$137$	−5.43351	−	13.8444i	−0.464216	−	1.18280i	0.486759	−	0.873536i	$-0.338179\pi$
$138$	5.53972	+	3.22057i	0.471572	+	0.274153i
$139$	1.74043	+	2.18243i	0.147621	+	0.185111i	0.850144	−	0.526550i	$-0.176515\pi$
$139$	1.74043	+	2.18243i	0.147621	+	0.185111i	−0.702523	+	0.711661i	$0.747943\pi$
$140$	−1.28952	−	3.02079i	−0.108984	−	0.255303i
$141$	8.33658	−	10.4537i	0.702067	−	0.880364i
$142$	9.45610	−	3.67853i	0.793538	−	0.308695i
$143$	−0.0875897	+	1.16880i	−0.00732462	+	0.0977403i
$144$	3.99971	+	0.0480255i	0.333309	+	0.00400212i
$145$	0.944262	+	1.01767i	0.0784167	+	0.0845131i
$146$	−3.28043	−	3.55682i	−0.271490	−	0.294364i
$147$	3.01279	+	6.31847i	0.248491	+	0.521139i
$148$	1.83500	−	22.6601i	0.150836	−	1.86265i
$149$	−5.48353	+	5.08797i	−0.449228	+	0.416823i	−0.872070	−	0.489380i	$-0.837223\pi$
$149$	−5.48353	+	5.08797i	−0.449228	+	0.416823i	0.422842	+	0.906203i	$0.361032\pi$
$150$	4.08431	−	5.09014i	0.333483	−	0.415609i
$151$	−17.3860	−	1.30290i	−1.41485	−	0.106028i	−0.654755	−	0.755841i	$-0.727228\pi$
$151$	−17.3860	−	1.30290i	−1.41485	−	0.106028i	−0.760094	+	0.649813i	$0.774847\pi$
$152$	5.36796	−	1.60300i	0.435399	−	0.130021i
$153$	5.51837	+	4.40076i	0.446134	+	0.355780i
$154$	2.80502	+	4.51344i	0.226035	+	0.363704i
$155$	−2.23279	+	1.78059i	−0.179342	+	0.143020i
$156$	1.61133	−	0.357612i	0.129010	−	0.0286319i
$157$	5.84618	−	2.29446i	0.466576	−	0.183117i	−0.120394	−	0.992726i	$-0.538416\pi$
$157$	5.84618	−	2.29446i	0.466576	−	0.183117i	0.586970	+	0.809609i	$0.300321\pi$
$158$	3.00279	+	6.28355i	0.238889	+	0.499892i
$159$	0.412496	+	5.50437i	0.0327130	+	0.436525i
$160$	−2.42665	+	2.53783i	−0.191843	+	0.200633i
$161$	11.3229	−	3.93751i	0.892369	−	0.310319i
$162$	0.703427	+	1.22686i	0.0552665	+	0.0963914i
$163$	0.483252	−	3.20617i	0.0378512	−	0.251127i	−0.961901	−	0.273399i	$-0.911852\pi$
$163$	0.483252	−	3.20617i	0.0378512	−	0.251127i	0.999752	+	0.0222725i	$0.00709015\pi$
$164$	0.317491	−	0.180771i	0.0247919	−	0.0141159i
$165$	0.440783	−	0.763459i	0.0343149	−	0.0594352i
$166$	−3.28947	−	1.02549i	−0.255312	−	0.0795934i
$167$	15.6298	+	7.52690i	1.20947	+	0.582449i	0.926360	−	0.376639i	$-0.122920\pi$
$167$	15.6298	+	7.52690i	1.20947	+	0.582449i	0.283108	+	0.959088i	$0.408634\pi$
$168$	4.94302	−	5.61841i	0.381362	−	0.433470i
$169$	−11.0990	+	5.34498i	−0.853767	+	0.411153i
$170$	−6.12945	+	0.905058i	−0.470107	+	0.0694148i
$171$	1.45194	+	1.34720i	0.111033	+	0.103023i
$172$	13.2442	+	14.4468i	1.00986	+	1.10156i
$173$	8.13698	−	11.9348i	0.618643	−	0.907383i	−0.381210	−	0.924488i	$-0.624493\pi$
$173$	8.13698	−	11.9348i	0.618643	−	0.907383i	0.999854	+	0.0171052i	$0.00544503\pi$
$174$	−1.16440	+	2.94085i	−0.0882728	+	0.222945i
$175$	−2.24668	−	12.0009i	−0.169833	−	0.907182i
$176$	3.25633	−	4.65508i	0.245455	−	0.350890i
$177$	−3.21058	−	5.56088i	−0.241322	−	0.417982i
$178$	0.890109	−	0.200353i	0.0667165	−	0.0150171i
$179$	−8.29189	−	12.1620i	−0.619765	−	0.909029i	0.380108	−	0.924942i	$-0.375887\pi$
$179$	−8.29189	−	12.1620i	−0.619765	−	0.909029i	−0.999873	+	0.0159134i	$0.994934\pi$
$180$	−1.20862	−	0.283505i	−0.0900855	−	0.0211312i
$181$	6.52609	+	1.48954i	0.485081	+	0.110716i	0.458065	−	0.888919i	$-0.348543\pi$
$181$	6.52609	+	1.48954i	0.485081	+	0.110716i	0.0270153	+	0.999635i	$0.491400\pi$
$182$	1.45632	−	2.72288i	0.107949	−	0.201833i
$183$	−9.00157	+	2.05455i	−0.665415	+	0.151877i
$184$	−8.63194	−	9.47269i	−0.636355	−	0.698336i
$185$	−2.07972	+	6.74229i	−0.152904	+	0.495703i
$186$	−5.85379	−	2.84071i	−0.429220	−	0.208291i
$187$	9.57910	−	2.95476i	0.700493	−	0.216073i
$188$	−22.1851	+	14.9312i	−1.61801	+	1.08897i
$189$	2.59867	+	0.496898i	0.189026	+	0.0361440i
$190$	−1.73420	+	0.124727i	−0.125812	+	0.00904866i
$191$	5.15591	+	2.02355i	0.373069	+	0.146419i	0.544465	−	0.838783i	$-0.316733\pi$
$191$	5.15591	+	2.02355i	0.373069	+	0.146419i	−0.171396	+	0.985202i	$0.554828\pi$
$192$	−7.60088	−	2.49533i	−0.548546	−	0.180085i
$193$	−16.5352	+	2.49227i	−1.19023	+	0.179398i	−0.714142	−	0.700001i	$-0.753183\pi$
$193$	−16.5352	+	2.49227i	−1.19023	+	0.179398i	−0.476085	+	0.879399i	$0.657945\pi$
$194$	24.0995	+	1.87877i	1.73024	+	0.134888i
$195$	−0.512256			−0.0366834
$196$	−1.94988	−	13.8635i	−0.139277	−	0.990253i
$197$	3.34340			0.238208			0.119104	−	0.992882i	$-0.461998\pi$
$197$	3.34340			0.238208			0.119104	+	0.992882i	$0.461998\pi$
$198$	2.00245	+	0.156109i	0.142308	+	0.0110942i
$199$	−3.30520	+	0.498179i	−0.234300	+	0.0353150i	−0.265142	−	0.964209i	$-0.585419\pi$
$199$	−3.30520	+	0.498179i	−0.234300	+	0.0353150i	0.0308428	+	0.999524i	$0.490181\pi$
$200$	−10.8502	+	7.25526i	−0.767222	+	0.513024i
$201$	−0.528683	−	0.207493i	−0.0372904	−	0.0146354i
$202$	14.3114	−	1.02930i	1.00694	−	0.0724212i
$203$	2.75489	+	5.23699i	0.193356	+	0.367564i
$204$	−7.88196	−	11.7112i	−0.551848	−	0.819945i
$205$	−0.108351	+	0.0334218i	−0.00756755	+	0.00233428i
$206$	19.5168	+	9.47108i	1.35980	+	0.659882i
$207$	1.33555	−	4.32973i	0.0928269	−	0.300937i
$208$	−3.28864	−	0.286195i	−0.228026	−	0.0198440i
$209$	2.74251	−	0.625961i	0.189704	−	0.0432986i
$210$	−1.87546	+	1.36991i	−0.129419	+	0.0945329i
$211$	−22.5167	−	5.13929i	−1.55011	−	0.353803i	−0.640069	−	0.768317i	$-0.721094\pi$
$211$	−22.5167	−	5.13929i	−1.55011	−	0.353803i	−0.910043	+	0.414514i	$0.863952\pi$
$212$	2.52111	−	10.7479i	0.173151	−	0.738168i
$213$	−4.04159	−	5.92792i	−0.276925	−	0.406175i
$214$	13.1476	−	2.95937i	0.898754	−	0.202298i
$215$	−3.04134	−	5.26775i	−0.207418	−	0.359258i
$216$	−0.604528	−	2.76307i	−0.0411329	−	0.188003i
$217$	−11.1665	+	4.84625i	−0.758034	+	0.328985i
$218$	−2.61391	+	6.60180i	−0.177037	+	0.447131i
$219$	−1.92735	+	2.82691i	−0.130238	+	0.191025i
$220$	−1.29964	+	1.19145i	−0.0876219	+	0.0803278i
$221$	−4.27000	−	3.96198i	−0.287231	−	0.266511i
$222$	−15.9031	+	2.34822i	−1.06735	+	0.157602i
$223$	10.3800	−	4.99874i	0.695095	−	0.334740i	−0.0527554	−	0.998607i	$-0.516800\pi$
$223$	10.3800	−	4.99874i	0.695095	−	0.334740i	0.747850	+	0.663867i	$0.231086\pi$
$224$	−12.8057	+	7.74691i	−0.855615	+	0.517612i
$225$	−4.15771	−	2.00225i	−0.277181	−	0.133483i
$226$	6.85651	+	2.13751i	0.456088	+	0.142185i
$227$	−14.8268	+	25.6808i	−0.984092	+	1.70450i	−0.338189	+	0.941078i	$0.609814\pi$
$227$	−14.8268	+	25.6808i	−0.984092	+	1.70450i	−0.645903	+	0.763420i	$0.723519\pi$
$228$	−1.96005	−	3.44246i	−0.129807	−	0.227983i
$229$	1.79196	−	11.8889i	0.118416	−	0.785638i	−0.848250	−	0.529596i	$-0.822343\pi$
$229$	1.79196	−	11.8889i	0.118416	−	0.785638i	0.966666	−	0.256042i	$-0.0824184\pi$
$230$	1.97838	+	3.45053i	0.130450	+	0.227521i
$231$	2.66216	−	2.65189i	0.175157	−	0.174482i
$232$	3.98854	−	4.91011i	0.261861	−	0.322365i
$233$	−1.71189	−	22.8436i	−0.112150	−	1.49653i	−0.715250	−	0.698869i	$-0.753687\pi$
$233$	−1.71189	−	22.8436i	−0.112150	−	1.49653i	0.603100	−	0.797666i	$-0.293932\pi$
$234$	−0.503229	−	1.05304i	−0.0328971	−	0.0688394i
$235$	7.72577	−	3.03214i	0.503974	−	0.197795i
$236$	2.78247	+	12.5373i	0.181123	+	0.816106i
$237$	3.85006	−	3.07032i	0.250088	−	0.199439i
$238$	−26.2286	−	3.08639i	−1.70015	−	0.200061i
$239$	1.01055	+	0.805883i	0.0653667	+	0.0521282i	0.655628	−	0.755084i	$-0.272404\pi$
$239$	1.01055	+	0.805883i	0.0653667	+	0.0521282i	−0.590261	+	0.807212i	$0.700975\pi$
$240$	2.13516	+	1.26716i	0.137824	+	0.0817946i
$241$	−5.92591	−	0.444086i	−0.381722	−	0.0286061i	−0.117512	−	0.993071i	$-0.537492\pi$
$241$	−5.92591	−	0.444086i	−0.381722	−	0.0286061i	−0.264209	+	0.964465i	$0.585111\pi$
$242$	−7.95044	+	9.90837i	−0.511073	+	0.636934i
$243$	0.733052	−	0.680173i	0.0470253	−	0.0436331i
$244$	18.4059	+	1.49050i	1.17832	+	0.0954193i
$245$	−0.341446	+	4.33157i	−0.0218142	+	0.276734i
$246$	−0.175147	−	0.189903i	−0.0111669	−	0.0121078i
$247$	−1.11180	−	1.19824i	−0.0707423	−	0.0762421i
$248$	9.45933	+	8.93683i	0.600668	+	0.567489i
$249$	−0.182073	+	2.42960i	−0.0115384	+	0.153970i
$250$	7.86581	−	3.05989i	0.497478	−	0.193524i
$251$	−7.03991	+	8.82777i	−0.444355	+	0.557204i	−0.952685	−	0.303959i	$-0.901692\pi$
$251$	−7.03991	+	8.82777i	−0.444355	+	0.557204i	0.508330	+	0.861162i	$0.330263\pi$
$252$	−4.65853	−	2.50960i	−0.293460	−	0.158090i
$253$	−4.01227	−	5.03122i	−0.252249	−	0.316310i
$254$	−19.1457	−	11.1306i	−1.20131	−	0.698393i
$255$	1.60062	+	4.07832i	0.100235	+	0.255394i
$256$	12.9996	+	9.32794i	0.812475	+	0.582996i
$257$	3.00243	−	0.225001i	0.187287	−	0.0140352i	0.0192434	−	0.999815i	$-0.493874\pi$
$257$	3.00243	−	0.225001i	0.187287	−	0.0140352i	0.168043	+	0.985780i	$0.446255\pi$
$258$	7.84113	−	11.4270i	0.488168	−	0.711413i
$259$	−16.0499	+	25.4340i	−0.997290	+	1.58039i
$260$	0.977165	+	0.307852i	0.0606012	+	0.0190922i
$261$	2.21158	+	0.333342i	0.136893	+	0.0206334i
$262$	−0.763139	+	3.29787i	−0.0471469	+	0.203743i
$263$	12.4143	+	7.16740i	0.765499	+	0.441961i	0.831267	−	0.555874i	$-0.187616\pi$
$263$	12.4143	+	7.16740i	0.765499	+	0.441961i	−0.0657675	+	0.997835i	$0.520950\pi$
$264$	−3.72600	−	1.50121i	−0.229320	−	0.0923930i
$265$	−1.48658	+	3.08692i	−0.0913201	+	0.189628i
$266$	−7.27493	−	1.41371i	−0.446054	−	0.0866799i
$267$	−0.279920	−	0.581260i	−0.0171308	−	0.0355725i
$268$	0.883803	+	0.713531i	0.0539869	+	0.0435859i
$269$	−19.4784	+	20.9927i	−1.18762	+	1.27995i	−0.236317	+	0.971676i	$0.575940\pi$
$269$	−19.4784	+	20.9927i	−1.18762	+	1.27995i	−0.951299	+	0.308270i	$0.900250\pi$
$270$	−0.00263493	+	0.877819i	−0.000160357	+	0.0534224i
$271$	14.3291	+	9.76944i	0.870433	+	0.593451i	0.914052	−	0.405597i	$-0.132936\pi$
$271$	14.3291	+	9.76944i	0.870433	+	0.593451i	−0.0436190	+	0.999048i	$0.513889\pi$
$272$	7.99732	+	27.0767i	0.484909	+	1.64177i
$273$	−2.10796	−	0.569194i	−0.127579	−	0.0344492i
$274$	20.1169	−	6.13917i	1.21531	−	0.370881i
$275$	−5.67594	+	3.27701i	−0.342272	+	0.197611i
$276$	−5.14970	+	7.45665i	−0.309976	+	0.448838i
$277$	3.56330	−	2.42942i	0.214098	−	0.145970i	−0.451523	−	0.892259i	$-0.649119\pi$
$277$	3.56330	−	2.42942i	0.214098	−	0.145970i	0.665621	+	0.746290i	$0.268167\pi$
$278$	−3.26839	+	2.21401i	−0.196025	+	0.132787i
$279$	−1.02380	+	4.48554i	−0.0612930	+	0.268542i
$280$	4.40086	−	1.48610i	0.263002	−	0.0888117i
$281$	7.05006	+	30.8883i	0.420571	+	1.84264i	0.529113	+	0.848551i	$0.322525\pi$
$281$	7.05006	+	30.8883i	0.420571	+	1.84264i	−0.108542	+	0.994092i	$0.534618\pi$
$282$	13.8228	+	12.9031i	0.823134	+	0.768368i
$283$	−20.1599	−	6.21850i	−1.19838	−	0.369651i	−0.369582	−	0.929198i	$-0.620499\pi$
$283$	−20.1599	−	6.21850i	−1.19838	−	0.369651i	−0.828799	+	0.559547i	$0.810975\pi$
$284$	4.14710	+	13.7368i	0.246085	+	0.815131i
$285$	0.362382	+	1.17482i	0.0214657	+	0.0695900i
$286$	−1.63831	−	0.251967i	−0.0968753	−	0.0148991i
$287$	−0.483006	+	0.0171382i	−0.0285109	+	0.00101164i
$288$	−0.507349	+	5.63406i	−0.0298958	+	0.331990i
$289$	−11.9902	+	30.5504i	−0.705304	+	1.79709i
$290$	−1.53864	+	1.21949i	−0.0903522	+	0.0716108i
$291$	−2.54752	−	16.9017i	−0.149338	−	0.990796i
$292$	5.37546	−	4.23424i	0.314575	−	0.247790i
$293$			11.4174i			0.667012i	0.942748	+	0.333506i	$0.108232\pi$
$293$			11.4174i			0.667012i	−0.942748	+	0.333506i	$0.891768\pi$
$294$	−9.23980	+	3.55333i	−0.538876	+	0.207234i
$295$		−	3.98571i		−	0.232057i
$296$	31.7476	+	5.07797i	1.84529	+	0.295151i
$297$	−0.211676	−	1.40438i	−0.0122827	−	0.0814904i
$298$	−6.57098	−	8.29068i	−0.380647	−	0.480266i
$299$	−1.36613	+	3.48083i	−0.0790051	+	0.201302i
$300$	6.72784	+	6.31811i	0.388432	+	0.364776i
$301$	−6.66199	−	25.0565i	−0.383991	−	1.44423i
$302$	3.74801	−	24.3699i	0.215674	−	1.40233i
$303$	−2.99053	−	9.69505i	−0.171801	−	0.556966i
$304$	1.67010	+	7.74468i	0.0957870	+	0.444188i
$305$	−5.47648	−	1.68927i	−0.313582	−	0.0967274i
$306$	−6.81135	+	7.29683i	−0.389379	+	0.417132i
$307$	−1.61490	−	7.07536i	−0.0921675	−	0.403812i	0.907708	−	0.419603i	$-0.137831\pi$
$307$	−1.61490	−	7.07536i	−0.0921675	−	0.403812i	−0.999875	+	0.0157907i	$0.994973\pi$
$308$	−6.67198	+	3.45879i	−0.380171	+	0.197083i
$309$	3.41339	−	14.9550i	0.194181	−	0.850762i
$310$	−2.26509	−	3.34380i	−0.128649	−	0.189915i
$311$	16.8070	−	11.4588i	0.953039	−	0.649771i	0.0163252	−	0.999867i	$-0.494803\pi$
$311$	16.8070	−	11.4588i	0.953039	−	0.649771i	0.936714	+	0.350096i	$0.113851\pi$
$312$	0.327097	+	2.31118i	0.0185182	+	0.130845i
$313$	−9.81461	+	5.66647i	−0.554755	+	0.320288i	−0.751038	−	0.660260i	$-0.770446\pi$
$313$	−9.81461	+	5.66647i	−0.554755	+	0.320288i	0.196283	+	0.980547i	$0.437113\pi$
$314$	2.59244	+	8.49493i	0.146300	+	0.479397i
$315$	1.24271	+	1.07363i	0.0700189	+	0.0604920i
$316$	−9.18945	+	3.54308i	−0.516947	+	0.199314i
$317$	−10.9993	−	7.49919i	−0.617782	−	0.421197i	0.213582	−	0.976925i	$-0.431487\pi$
$317$	−10.9993	−	7.49919i	−0.617782	−	0.421197i	−0.831364	+	0.555729i	$0.812439\pi$
$318$	−7.80615	−	0.0234315i	−0.437747	−	0.00131397i
$319$	2.16054	−	2.32851i	0.120967	−	0.130372i
$320$	−3.31144	−	3.70037i	−0.185115	−	0.206857i
$321$	−4.13464	−	8.58567i	−0.230773	−	0.479206i
$322$	4.30706	+	16.3974i	0.240023	+	0.913789i
$323$	−6.06576	+	12.5957i	−0.337508	+	0.700842i
$324$	−1.80711	+	0.856934i	−0.100395	+	0.0476075i
$325$	3.29815	+	1.90419i	0.182948	+	0.105625i
$326$	4.46737	+	1.03377i	0.247425	+	0.0572550i
$327$	4.96470	+	0.748308i	0.274548	+	0.0413815i
$328$	0.219978	+	0.467512i	0.0121463	+	0.0258140i
$329$	35.1611	−	3.89291i	1.93849	−	0.214623i
$330$	1.02798	+	0.705393i	0.0565883	+	0.0388306i
$331$	−14.7413	+	1.10471i	−0.810258	+	0.0607204i	−0.473414	−	0.880840i	$-0.656979\pi$
$331$	−14.7413	+	1.10471i	−0.810258	+	0.0607204i	−0.336844	+	0.941561i	$0.609359\pi$
$332$	1.80744	−	4.52522i	0.0991963	−	0.248353i
$333$	4.15289	+	10.5814i	0.227577	+	0.579856i
$334$	−12.3304	+	21.2096i	−0.674691	+	1.16054i
$335$	−0.219799	−	0.275619i	−0.0120089	−	0.0150587i
$336$	7.37828	+	7.58689i	0.402518	+	0.413899i
$337$	−12.2912	+	15.4127i	−0.669546	+	0.839584i	−0.994345	−	0.106199i	$-0.966132\pi$
$337$	−12.2912	+	15.4127i	−0.669546	+	0.839584i	0.324799	+	0.945783i	$0.394703\pi$
$338$	−6.31612	−	16.2363i	−0.343552	−	0.883141i
$339$	0.379511	−	5.06422i	0.0206122	−	0.275051i
$340$	−0.602343	−	8.74161i	−0.0326666	−	0.474080i
$341$	4.44451	+	4.79005i	0.240684	+	0.259396i
$342$	−2.05906	+	1.89906i	−0.111341	+	0.102689i
$343$	−6.21809	+	17.4452i	−0.335745	+	0.941953i
$344$	−21.8248	+	17.0855i	−1.17672	+	0.921188i
$345$	2.06169	−	1.91297i	0.110998	−	0.102991i
$346$	15.9329	+	12.7845i	0.856555	+	0.687296i
$347$	−32.8163	−	2.45924i	−1.76167	−	0.132019i	−0.845803	−	0.533495i	$-0.820878\pi$
$347$	−32.8163	−	2.45924i	−1.76167	−	0.132019i	−0.915870	+	0.401476i	$0.868497\pi$
$348$	−4.01842	−	1.96498i	−0.215410	−	0.105334i
$349$	8.98286	+	7.16359i	0.480841	+	0.383458i	0.833699	−	0.552219i	$-0.186219\pi$
$349$	8.98286	+	7.16359i	0.480841	+	0.383458i	−0.352858	+	0.935677i	$0.614790\pi$
$350$	17.1674	−	1.84857i	0.917638	−	0.0988103i
$351$	−0.645220	+	0.514546i	−0.0344393	+	0.0274644i
$352$	6.20544	+	5.10289i	0.330751	+	0.271985i
$353$	−17.8587	+	7.00902i	−0.950522	+	0.373052i	−0.789398	−	0.613882i	$-0.789607\pi$
$353$	−17.8587	+	7.00902i	−0.950522	+	0.373052i	−0.161124	+	0.986934i	$0.551512\pi$
$354$	8.19339	−	3.91547i	0.435474	−	0.208105i
$355$	−0.332801	−	4.44092i	−0.0176632	−	0.235700i
$356$	0.184646	+	1.27702i	0.00978622	+	0.0676819i
$357$	2.05501	+	18.5610i	0.108763	+	0.982352i
$358$	18.0590	−	10.3542i	0.954449	−	0.547238i
$359$	−1.27705	+	8.47270i	−0.0674003	+	0.447172i	0.929521	+	0.368768i	$0.120220\pi$
$359$	−1.27705	+	8.47270i	−0.0674003	+	0.447172i	−0.996922	+	0.0784036i	$0.975018\pi$
$360$	0.532572	−	1.67292i	0.0280690	−	0.0881706i
$361$	7.53846	−	13.0570i	0.396761	−	0.687210i
$362$	−2.81748	+	9.03764i	−0.148083	+	0.475008i
$363$	8.09332	+	3.89754i	0.424789	+	0.204568i
$364$	3.67901	+	2.35260i	0.192833	+	0.123310i
$365$	−1.91341	+	0.921449i	−0.100152	+	0.0482309i
$366$	−1.90736	−	12.9175i	−0.0996992	−	0.675207i
$367$	−8.93750	−	8.29279i	−0.466534	−	0.432880i	0.411550	−	0.911387i	$-0.364988\pi$
$367$	−8.93750	−	8.29279i	−0.466534	−	0.432880i	−0.878084	+	0.478507i	$0.841178\pi$
$368$	14.3047	−	11.1293i	0.745683	−	0.580153i
$369$	−0.102904	+	0.150932i	−0.00535696	+	0.00785722i
$370$	−9.27760	−	3.67337i	−0.482319	−	0.190969i
$371$	−9.54740	+	11.0510i	−0.495677	+	0.573740i
$372$	4.64865	−	7.94122i	0.241021	−	0.411733i
$373$	10.7356	+	18.5947i	0.555871	+	0.962796i	0.997835	+	0.0657637i	$0.0209484\pi$
$373$	10.7356	+	18.5947i	0.555871	+	0.962796i	−0.441965	+	0.897033i	$0.645718\pi$
$374$	3.11312	+	13.8307i	0.160975	+	0.715168i
$375$	−3.36189	−	4.93099i	−0.173607	−	0.254635i
$376$	−18.6135	−	32.9207i	−0.959920	−	1.69776i
$377$	−1.79949	−	0.410721i	−0.0926782	−	0.0211532i
$378$	−0.986233	+	3.60934i	−0.0507263	+	0.185644i
$379$	13.3984	−	3.05810i	0.688230	−	0.157084i	0.135916	−	0.990720i	$-0.456602\pi$
$379$	13.3984	−	3.05810i	0.688230	−	0.157084i	0.552314	+	0.833636i	$0.313745\pi$
$380$	0.0147613	−	2.45883i	0.000757240	−	0.126135i
$381$	−4.61576	+	14.9639i	−0.236473	+	0.766625i
$382$	−3.41979	+	7.04708i	−0.174972	+	0.360560i
$383$	−7.00739	+	2.16149i	−0.358061	+	0.110447i	−0.468566	−	0.883428i	$-0.655229\pi$
$383$	−7.00739	+	2.16149i	−0.358061	+	0.110447i	0.110505	+	0.993876i	$0.464753\pi$
$384$	4.35372	−	10.4425i	0.222175	−	0.532890i
$385$	2.25409	−	0.599316i	0.114879	−	0.0305440i
$386$	−1.69645	−	23.5875i	−0.0863471	−	1.20057i
$387$	−9.12207	−	3.58015i	−0.463701	−	0.181989i
$388$	−5.29789	+	33.7722i	−0.268959	+	1.71453i
$389$	−24.9594	+	3.76203i	−1.26549	+	0.190742i	−0.747280	−	0.664509i	$-0.768641\pi$
$389$	−24.9594	+	3.76203i	−1.26549	+	0.190742i	−0.518213	+	0.855252i	$0.673403\pi$
$390$	0.0563056	−	0.722248i	0.00285115	−	0.0365724i
$391$	31.9813			1.61736
$392$	19.7610	−	1.22537i	0.998083	−	0.0618905i
$393$	2.39356			0.120739
$394$	−0.367497	+	4.71398i	−0.0185142	+	0.237487i
$395$	3.02252	−	0.455571i	0.152079	−	0.0229223i
$396$	−0.440207	+	2.80617i	−0.0221212	+	0.141015i
$397$	−15.6055	−	6.12471i	−0.783218	−	0.307390i	−0.0601698	−	0.998188i	$-0.519164\pi$
$397$	−15.6055	−	6.12471i	−0.783218	−	0.307390i	−0.723048	+	0.690798i	$0.757259\pi$
$398$	−0.339103	−	4.71488i	−0.0169977	−	0.236336i
$399$	0.185824	+	5.23708i	0.00930285	+	0.262182i
$400$	−9.03683	−	16.0955i	−0.451841	−	0.804775i
$401$	−9.77007	+	3.01367i	−0.487894	+	0.150495i	−0.528935	−	0.848662i	$-0.677409\pi$
$401$	−9.77007	+	3.01367i	−0.487894	+	0.150495i	0.0410415	+	0.999157i	$0.486932\pi$
$402$	0.350663	−	0.722602i	0.0174895	−	0.0360401i
$403$	1.11918	−	3.62828i	0.0557502	−	0.180738i
$404$	−0.121816	+	20.2912i	−0.00606059	+	1.00953i
$405$	0.605152	−	0.138122i	0.0300703	−	0.00686334i
$406$	−7.68662	+	3.30859i	−0.381481	+	0.164203i
$407$	15.7394	+	3.59240i	0.780171	+	0.178069i
$408$	17.3783	−	9.82580i	0.860356	−	0.486450i
$409$	−17.4433	−	25.5846i	−0.862514	−	1.26508i	−0.962827	−	0.270120i	$-0.912937\pi$
$409$	−17.4433	−	25.5846i	−0.862514	−	1.26508i	0.100313	−	0.994956i	$-0.468016\pi$
$410$	−0.0352130	−	0.156441i	−0.00173905	−	0.00772609i
$411$	−7.43622	−	12.8799i	−0.366802	−	0.635319i
$412$	−15.4988	+	26.4764i	−0.763573	+	1.30440i
$413$	4.42872	−	16.4014i	0.217923	−	0.807059i
$414$	5.95785	+	2.35895i	0.292812	+	0.115936i
$415$	−0.851919	+	1.24954i	−0.0418190	+	0.0613373i
$416$	0.764993	−	4.60532i	0.0375069	−	0.225794i
$417$	2.04627	+	1.89866i	0.100206	+	0.0929776i
$418$	0.581116	+	3.93557i	0.0284233	+	0.192495i
$419$	15.2156	−	7.32746i	0.743332	−	0.357970i	−0.0235800	−	0.999722i	$-0.507506\pi$
$419$	15.2156	−	7.32746i	0.743332	−	0.357970i	0.766912	+	0.641752i	$0.221792\pi$
$420$	−1.72534	−	2.79486i	−0.0841881	−	0.136375i
$421$	30.9897	+	14.9238i	1.51034	+	0.727343i	0.991811	−	0.127714i	$-0.0407641\pi$
$421$	30.9897	+	14.9238i	1.51034	+	0.727343i	0.518533	+	0.855058i	$0.326478\pi$
$422$	9.72103	−	31.1822i	0.473212	−	1.51792i
$423$	6.68542	−	11.5795i	0.325056	−	0.563014i
$424$	14.8767	+	4.73598i	0.722477	+	0.230000i
$425$	4.85459	−	32.2081i	0.235482	−	1.56232i
$426$	8.80223	−	5.04680i	0.426469	−	0.244518i
$427$	−20.6590	−	13.0366i	−0.999757	−	0.630887i
$428$	2.72737	+	18.8626i	0.131833	+	0.911758i
$429$	0.0875897	+	1.16880i	0.00422887	+	0.0564304i
$430$	7.76149	−	3.70908i	0.374292	−	0.178868i
$431$	20.7106	−	8.12830i	0.997593	−	0.391526i	0.190331	−	0.981720i	$-0.439044\pi$
$431$	20.7106	−	8.12830i	0.997593	−	0.391526i	0.807262	+	0.590194i	$0.200949\pi$
$432$	3.96220	−	0.548637i	0.190631	−	0.0263963i
$433$	19.6127	−	15.6406i	0.942528	−	0.751641i	−0.0262284	−	0.999656i	$-0.508350\pi$
$433$	19.6127	−	15.6406i	0.942528	−	0.751641i	0.968756	+	0.248015i	$0.0797783\pi$
$434$	−5.60550	−	16.2768i	−0.269073	−	0.781311i
$435$	1.08539	+	0.865571i	0.0520405	+	0.0415009i
$436$	−9.02081	−	4.41110i	−0.432018	−	0.211253i
$437$	8.94942	+	0.670667i	0.428109	+	0.0320823i
$438$	−3.77391	−	3.02817i	−0.180324	−	0.144691i
$439$	11.0750	−	10.2761i	0.528579	−	0.490449i	−0.370139	−	0.928976i	$-0.620690\pi$
$439$	11.0750	−	10.2761i	0.528579	−	0.490449i	0.898718	+	0.438527i	$0.144500\pi$
$440$	−1.53702	−	1.96337i	−0.0732746	−	0.0936002i
$441$	3.92086	+	5.79887i	0.186708	+	0.276137i
$442$	6.05548	−	5.58493i	0.288030	−	0.265648i
$443$	−1.74084	−	1.87618i	−0.0827099	−	0.0891400i	0.690341	−	0.723484i	$-0.257461\pi$
$443$	−1.74084	−	1.87618i	−0.0827099	−	0.0891400i	−0.773051	+	0.634344i	$0.781270\pi$
$444$	−1.56281	−	22.6805i	−0.0741675	−	1.07637i
$445$	0.0299260	−	0.399334i	0.00141863	−	0.0189303i
$446$	5.90696	+	15.1846i	0.279703	+	0.719009i
$447$	−4.66396	+	5.84842i	−0.220598	+	0.276621i
$448$	−9.51509	−	18.9067i	−0.449546	−	0.893257i
$449$	7.89498	+	9.89999i	0.372587	+	0.467210i	0.932410	−	0.361403i	$-0.117702\pi$
$449$	7.89498	+	9.89999i	0.372587	+	0.467210i	−0.559823	+	0.828613i	$0.689131\pi$
$450$	3.28005	−	5.64203i	0.154623	−	0.265968i
$451$	0.0947846	+	0.241507i	0.00446323	+	0.0113721i
$452$	−3.76740	+	9.43228i	−0.177204	+	0.443657i
$453$	−17.3860	+	1.30290i	−0.816864	+	0.0612155i
$454$	−34.5786	−	23.7277i	−1.62285	−	1.11359i
$455$	−0.956489	−	0.960193i	−0.0448409	−	0.0450146i
$456$	5.06909	−	2.38515i	0.237382	−	0.111695i
$457$	2.16619	+	0.326500i	0.101330	+	0.0152730i	0.199511	−	0.979895i	$-0.436064\pi$
$457$	2.16619	+	0.326500i	0.101330	+	0.0152730i	−0.0981815	+	0.995169i	$0.531303\pi$
$458$	16.5656	+	3.83333i	0.774058	+	0.179120i
$459$	6.11264	+	3.52913i	0.285313	+	0.164726i
$460$	−5.08248	+	2.41011i	−0.236972	+	0.112372i
$461$	13.8404	−	28.7399i	0.644612	−	1.33855i	−0.280866	−	0.959747i	$-0.590622\pi$
$461$	13.8404	−	28.7399i	0.644612	−	1.33855i	0.925477	−	0.378803i	$-0.123664\pi$
$462$	3.44638	+	4.04496i	0.160340	+	0.188189i
$463$	5.31504	+	11.0368i	0.247011	+	0.512924i	0.987202	−	0.159473i	$-0.0509794\pi$
$463$	5.31504	+	11.0368i	0.247011	+	0.512924i	−0.740191	+	0.672396i	$0.765265\pi$
$464$	6.48453	+	6.16329i	0.301037	+	0.286124i
$465$	−1.94247	+	2.09348i	−0.0900797	+	0.0970829i
$466$	32.3962	+	0.0972428i	1.50072	+	0.00450469i
$467$	−3.65043	−	2.48882i	−0.168922	−	0.115169i	0.475908	−	0.879495i	$-0.342119\pi$
$467$	−3.65043	−	2.48882i	−0.168922	−	0.115169i	−0.644830	+	0.764326i	$0.723072\pi$
$468$	1.54003	−	0.593774i	0.0711880	−	0.0274472i
$469$	−0.598229	−	1.37842i	−0.0276237	−	0.0636494i
$470$	3.42593	+	11.2261i	0.158026	+	0.517822i
$471$	5.43891	−	3.14016i	0.250612	−	0.144691i
$472$	−17.9826	+	2.54504i	−0.827715	+	0.117145i
$473$	−11.4993	+	7.84009i	−0.528738	+	0.360488i
$474$	3.90577	+	5.76582i	0.179398	+	0.264833i
$475$	2.03390	−	8.91109i	0.0933217	−	0.408869i
$476$	7.23458	−	36.6414i	0.331597	−	1.67946i
$477$	1.22827	+	5.38142i	0.0562388	+	0.246398i
$478$	−1.24732	+	1.33622i	−0.0570510	+	0.0611174i
$479$	24.4733	+	7.54901i	1.11821	+	0.344923i	0.798142	−	0.602470i	$-0.205817\pi$
$479$	24.4733	+	7.54901i	1.11821	+	0.344923i	0.320072	+	0.947393i	$0.396293\pi$
$480$	−2.02130	+	2.87115i	−0.0922593	+	0.131050i
$481$	−2.76508	−	8.96417i	−0.126077	−	0.408731i
$482$	1.27749	−	8.30634i	0.0581881	−	0.378344i
$483$	10.6096	−	5.58112i	0.482752	−	0.253950i
$484$	−13.0963	−	12.2987i	−0.595285	−	0.559032i
$485$	3.87614	−	9.87624i	0.176006	−	0.448457i
$486$	0.878425	+	1.10832i	0.0398462	+	0.0502743i
$487$	2.92596	+	19.4125i	0.132588	+	0.879663i	0.951921	+	0.306345i	$0.0991060\pi$
$487$	2.92596	+	19.4125i	0.132588	+	0.879663i	−0.819333	+	0.573318i	$0.805656\pi$
$488$	−4.12462	+	25.7873i	−0.186713	+	1.16733i
$489$		−	3.24238i		−	0.146626i
$490$	−6.06970	−	0.957529i	−0.274201	−	0.0432568i
$491$		−	9.88969i		−	0.446315i	−0.974782	−	0.223158i	$-0.928364\pi$
$491$		−	9.88969i		−	0.446315i	0.974782	−	0.223158i	$-0.0716365\pi$
$492$	0.287003	−	0.226072i	0.0129391	−	0.0101921i
$493$	2.35282	+	15.6099i	0.105966	+	0.703036i
$494$	1.81165	−	1.43586i	0.0815098	−	0.0646026i
$495$	0.322072	−	0.820627i	0.0144761	−	0.0368844i
$496$	−13.6401	+	12.3547i	−0.612458	+	0.554744i
$497$	3.56504	−	18.6444i	0.159914	−	0.836315i
$498$	−3.40557	−	0.523766i	−0.152607	−	0.0234705i
$499$	−7.78088	−	25.2250i	−0.348320	−	1.12923i	−0.945089	−	0.326812i	$-0.894025\pi$
$499$	−7.78088	−	25.2250i	−0.348320	−	1.12923i	0.596769	−	0.802413i	$-0.296451\pi$
$500$	3.44966	+	11.4266i	0.154273	+	0.511014i
$501$	16.5770	+	5.11334i	0.740607	+	0.228447i
$502$	−11.6728	−	10.8961i	−0.520982	−	0.486319i
$503$	5.25406	+	23.0195i	0.234267	+	1.02639i	0.946058	+	0.323999i	$0.105027\pi$
$503$	5.25406	+	23.0195i	0.234267	+	1.02639i	−0.711791	+	0.702392i	$0.752116\pi$
$504$	4.05043	−	6.29238i	0.180420	−	0.280285i
$505$	1.40136	−	6.13975i	0.0623596	−	0.273215i
$506$	7.53471	−	5.10402i	0.334959	−	0.226901i
$507$	−10.1784	+	6.93950i	−0.452038	+	0.308194i
$508$	17.7978	−	25.7708i	0.789650	−	1.14340i
$509$	−10.9194	+	6.30430i	−0.483992	+	0.279433i	−0.722079	−	0.691811i	$-0.756813\pi$
$509$	−10.9194	+	6.30430i	−0.483992	+	0.279433i	0.238087	+	0.971244i	$0.423480\pi$
$510$	−5.92610	+	1.80850i	−0.262412	+	0.0800816i
$511$	−8.89764	+	1.66572i	−0.393608	+	0.0736872i
$512$	−14.5807	+	17.3033i	−0.644381	+	0.764705i
$513$	1.63651	+	1.11576i	0.0722538	+	0.0492618i
$514$	−0.0127810	+	4.25797i	−0.000563747	+	0.187811i
$515$	6.47628	−	6.97978i	0.285379	−	0.307566i
$516$	15.2494	+	12.3115i	0.671319	+	0.541984i
$517$	−8.23939	−	17.1093i	−0.362368	−	0.752465i
$518$	−34.0961	−	25.4249i	−1.49810	−	1.11711i
$519$	6.26732	−	13.0142i	0.275105	−	0.571261i
$520$	−0.541458	+	1.34390i	−0.0237445	+	0.0589340i
$521$	28.5214	+	16.4669i	1.24955	+	0.721426i	0.971019	−	0.239002i	$-0.0768201\pi$
$521$	28.5214	+	16.4669i	1.24955	+	0.721426i	0.278528	+	0.960428i	$0.410153\pi$
$522$	−0.713082	+	3.08155i	−0.0312107	+	0.134876i
$523$	18.8375	+	2.83930i	0.823707	+	0.124154i	0.547353	−	0.836902i	$-0.315636\pi$
$523$	18.8375	+	2.83930i	0.823707	+	0.124154i	0.276354	+	0.961056i	$0.410874\pi$
$524$	−4.56590	−	1.43847i	−0.199462	−	0.0628397i
$525$	−4.01023	−	11.5320i	−0.175021	−	0.503298i
$526$	−11.4701	+	16.7156i	−0.500121	+	0.728833i
$527$	−32.3835	+	2.42681i	−1.41065	+	0.105714i
$528$	2.52616	−	5.08842i	0.109937	−	0.221445i
$529$	0.902288	+	2.29899i	0.0392299	+	0.0999561i
$530$	−4.18896	−	2.43529i	−0.181957	−	0.105782i
$531$	−4.00353	−	5.02026i	−0.173738	−	0.217861i
$532$	2.79287	−	10.1018i	0.121086	−	0.437968i
$533$	0.0939941	−	0.117865i	0.00407134	−	0.00510530i
$534$	0.850307	−	0.330779i	0.0367964	−	0.0143142i
$535$	0.442031	−	5.89849i	0.0191106	−	0.255014i
$536$	−1.10318	+	1.16768i	−0.0476500	+	0.0504359i
$537$	−10.0119	−	10.7903i	−0.432047	−	0.465636i
$538$	−27.4573	−	29.7707i	−1.18377	−	1.28350i
$539$	9.94163	+	0.0384225i	0.428216	+	0.00165497i
$540$	−1.23738	−	0.100202i	−0.0532483	−	0.00431202i
$541$	24.1032	−	22.3645i	1.03628	−	0.961526i	0.0369926	−	0.999316i	$-0.488222\pi$
$541$	24.1032	−	22.3645i	1.03628	−	0.961526i	0.999286	+	0.0377898i	$0.0120317\pi$
$542$	−15.3493	+	19.1293i	−0.659309	+	0.821675i
$543$	6.67521	+	0.500237i	0.286460	+	0.0214672i
$544$	−39.0555	+	8.29952i	−1.67449	+	0.355839i
$545$	2.43655	+	1.94309i	0.104370	+	0.0832327i
$546$	1.03423	−	2.90952i	0.0442608	−	0.124516i
$547$	−17.4024	+	13.8780i	−0.744073	+	0.593379i	−0.920411	−	0.390951i	$-0.872146\pi$
$547$	−17.4024	+	13.8780i	−0.744073	+	0.593379i	0.176338	+	0.984330i	$0.443575\pi$
$548$	6.44465	+	29.0383i	0.275302	+	1.24046i
$549$	−8.59481	+	3.37322i	−0.366818	+	0.143965i
$550$	−3.99649	−	8.36291i	−0.170411	−	0.356596i
$551$	0.331047	+	4.41752i	0.0141031	+	0.188193i
$552$	−9.94736	−	8.08036i	−0.423388	−	0.343923i
$553$	12.9440	+	1.48378i	0.550435	+	0.0630966i
$554$	3.03365	+	5.29106i	0.128888	+	0.224795i
$555$	−1.05161	+	6.97695i	−0.0446382	+	0.296155i
$556$	−2.76236	−	4.85158i	−0.117150	−	0.205753i
$557$	−1.41455	+	2.45008i	−0.0599366	+	0.103813i	−0.894437	−	0.447194i	$-0.852423\pi$
$557$	−1.41455	+	2.45008i	−0.0599366	+	0.103813i	0.834500	+	0.551008i	$0.185757\pi$
$558$	−6.21179	−	1.93652i	−0.262966	−	0.0819795i
$559$	7.28631	+	3.50890i	0.308178	+	0.148411i
$560$	1.61158	+	6.36828i	0.0681017	+	0.269109i
$561$	9.03172	−	4.34945i	0.381320	−	0.183634i
$562$	−44.3255	+	6.54498i	−1.86976	+	0.276083i
$563$	1.98536	+	1.84214i	0.0836729	+	0.0776371i	0.720901	−	0.693039i	$-0.243728\pi$
$563$	1.98536	+	1.84214i	0.0836729	+	0.0776371i	−0.637228	+	0.770676i	$0.719919\pi$
$564$	−19.7119	+	18.0710i	−0.830020	+	0.760925i
$565$	1.77573	−	2.60451i	0.0747053	−	0.109573i
$566$	10.9836	−	27.7406i	0.461675	−	1.16602i
$567$	2.64371	+	0.104037i	0.111025	+	0.00436913i
$568$	−19.8239	+	4.33724i	−0.831791	+	0.181986i
$569$	5.37683	+	9.31294i	0.225408	+	0.390419i	0.956442	−	0.291923i	$-0.0942950\pi$
$569$	5.37683	+	9.31294i	0.225408	+	0.390419i	−0.731033	+	0.682342i	$0.760962\pi$
$570$	−1.69625	+	0.381804i	−0.0710479	+	0.0159920i
$571$	12.7517	+	18.7034i	0.533644	+	0.782712i	0.994497	−	0.104765i	$-0.0334089\pi$
$571$	12.7517	+	18.7034i	0.533644	+	0.782712i	−0.460853	+	0.887476i	$0.652457\pi$
$572$	0.535336	−	2.28222i	0.0223835	−	0.0954243i
$573$	5.39992	+	1.23250i	0.225585	+	0.0514883i
$574$	0.0289268	−	0.682891i	0.00120738	−	0.0285033i
$575$	−20.3852	+	4.65279i	−0.850121	+	0.194035i
$576$	−7.88789	−	1.33461i	−0.328662	−	0.0556087i
$577$	1.93231	−	6.26441i	0.0804433	−	0.260791i	−0.906413	−	0.422393i	$-0.861190\pi$
$577$	1.93231	−	6.26441i	0.0804433	−	0.260791i	0.986856	+	0.161603i	$0.0516663\pi$
$578$	−41.7562	−	20.2634i	−1.73683	−	0.842845i
$579$	−15.9790	+	4.92888i	−0.664066	+	0.204837i
$580$	−1.55028	−	2.30343i	−0.0643718	−	0.0956447i
$581$	−4.89411	+	4.19529i	−0.203042	+	0.174050i
$582$	24.1103	−	1.73406i	0.999406	−	0.0718791i
$583$	7.29756	+	2.86408i	0.302234	+	0.118618i
$584$	5.37915	+	8.04446i	0.222591	+	0.332882i
$585$	−0.506534	+	0.0763478i	−0.0209426	+	0.00315659i
$586$	−16.0978	−	1.25497i	−0.664994	−	0.0518422i
$587$	15.9359			0.657744			0.328872	−	0.944375i	$-0.393332\pi$
$587$	15.9359			0.657744			0.328872	+	0.944375i	$0.393332\pi$
$588$	−3.99436	−	13.4181i	−0.164725	−	0.553353i
$589$	−9.11289			−0.375490
$590$	5.61959	+	0.438097i	0.231355	+	0.0180362i
$591$	3.30606	−	0.498308i	0.135993	−	0.0204977i
$592$	−10.6492	+	44.2039i	−0.437680	+	1.81677i
$593$	17.2099	+	6.75439i	0.706726	+	0.277370i	0.691358	−	0.722512i	$-0.257013\pi$
$593$	17.2099	+	6.75439i	0.706726	+	0.277370i	0.0153682	+	0.999882i	$0.495108\pi$
$594$	2.00335	−	0.144085i	0.0821986	−	0.00591187i
$595$	−4.65586	+	10.6153i	−0.190872	+	0.435187i
$596$	12.4116	−	8.35337i	0.508398	−	0.342167i
$597$	−3.19404	+	0.985230i	−0.130723	+	0.0403228i
$598$	−4.75759	−	2.30875i	−0.194552	−	0.0944119i
$599$	11.3341	−	36.7443i	0.463099	−	1.50133i	−0.359738	−	0.933053i	$-0.617134\pi$
$599$	11.3341	−	36.7443i	0.463099	−	1.50133i	0.822837	−	0.568277i	$-0.192390\pi$
$600$	−9.64763	+	8.79135i	−0.393863	+	0.358906i
$601$	25.2890	−	5.77205i	1.03156	−	0.235447i	0.326950	−	0.945042i	$-0.393979\pi$
$601$	25.2890	−	5.77205i	1.03156	−	0.235447i	0.704610	+	0.709595i	$0.251122\pi$
$602$	36.0602	−	6.63884i	1.46971	−	0.270579i
$603$	−0.553703	−	0.126379i	−0.0225485	−	0.00514655i
$604$	33.9480	+	7.96312i	1.38132	+	0.324015i
$605$	3.14097	+	4.60696i	0.127699	+	0.187300i
$606$	13.9981	−	3.15080i	0.568634	−	0.127992i
$607$	6.27497	+	10.8686i	0.254693	+	0.441142i	0.964812	−	0.262940i	$-0.0846922\pi$
$607$	6.27497	+	10.8686i	0.254693	+	0.441142i	−0.710119	+	0.704082i	$0.751359\pi$
$608$	−11.1031	+	1.50347i	−0.450289	+	0.0609736i
$609$	3.50466	+	4.76790i	0.142016	+	0.193205i
$610$	2.98372	−	7.53581i	0.120807	−	0.305116i
$611$	−6.21597	+	9.11715i	−0.251471	+	0.368841i
$612$	−9.53938	−	10.4056i	−0.385607	−	0.420622i
$613$	−23.6124	−	21.9091i	−0.953694	−	0.884899i	0.0397510	−	0.999210i	$-0.487344\pi$
$613$	−23.6124	−	21.9091i	−0.953694	−	0.884899i	−0.993445	+	0.114311i	$0.963534\pi$
$614$	10.1533	−	1.49921i	0.409754	−	0.0605032i
$615$	−0.102159	+	0.0491974i	−0.00411947	+	0.00198383i
$616$	−4.14331	−	9.78724i	−0.166939	−	0.394339i
$617$	40.1587	+	19.3394i	1.61673	+	0.778576i	0.999963	−	0.00857046i	$-0.00272810\pi$
$617$	40.1587	+	19.3394i	1.61673	+	0.778576i	0.616766	+	0.787146i	$0.288442\pi$
$618$	20.7104	+	6.45647i	0.833096	+	0.259717i
$619$	14.0111	−	24.2679i	0.563153	−	0.975409i	−0.434066	−	0.900881i	$-0.642922\pi$
$619$	14.0111	−	24.2679i	0.563153	−	0.975409i	0.997219	−	0.0745283i	$-0.0237451\pi$
$620$	4.96352	−	2.82610i	0.199340	−	0.113499i
$621$	0.675316	−	4.48043i	0.0270995	−	0.179793i
$622$	14.3088	+	24.9563i	0.573732	+	1.00066i
$623$	0.566867	−	1.61003i	0.0227111	−	0.0645044i
$624$	−3.29457	+	0.207149i	−0.131888	+	0.00829258i
$625$	1.44746	+	19.3150i	0.0578983	+	0.772599i
$626$	−6.91056	−	14.4608i	−0.276202	−	0.577970i
$627$	2.61859	−	1.02772i	0.104576	−	0.0410432i
$628$	−12.2623	+	2.72144i	−0.489317	+	0.108597i
$629$	−62.7282	+	50.0241i	−2.50114	+	1.99459i
$630$	−1.65034	+	1.63413i	−0.0657511	+	0.0651055i
$631$	30.7864	+	24.5514i	1.22559	+	0.977374i	0.999995	+	0.00315261i	$0.00100351\pi$
$631$	30.7864	+	24.5514i	1.22559	+	0.977374i	0.225593	+	0.974222i	$0.427568\pi$
$632$	−3.98544	−	13.3460i	−0.158532	−	0.530875i
$633$	−23.0312	−	1.72595i	−0.915406	−	0.0686002i
$634$	11.7824	−	14.6840i	0.467938	−	0.583176i
$635$	−7.12539	+	6.61140i	−0.282762	+	0.262365i
$636$	0.891066	−	11.0036i	0.0353330	−	0.436321i
$637$	−2.86908	−	5.01405i	−0.113677	−	0.198664i
$638$	3.04557	+	3.30217i	0.120575	+	0.130734i
$639$	−4.87996	−	5.25935i	−0.193048	−	0.208056i
$640$	5.58126	−	4.26219i	0.220619	−	0.168478i
$641$	−0.908690	+	12.1256i	−0.0358911	+	0.478934i	0.950079	+	0.312010i	$0.101002\pi$
$641$	−0.908690	+	12.1256i	−0.0358911	+	0.478934i	−0.985970	+	0.166923i	$0.946617\pi$
$642$	12.5597	−	4.88587i	0.495692	−	0.192830i
$643$	8.80422	−	11.0401i	0.347205	−	0.435381i	−0.577311	−	0.816524i	$-0.695898\pi$
$643$	8.80422	−	11.0401i	0.347205	−	0.435381i	0.924516	+	0.381143i	$0.124470\pi$
$644$	−23.5926	+	4.27033i	−0.929680	+	0.168274i
$645$	−3.79249	−	4.75563i	−0.149329	−	0.187253i
$646$	−17.0924	−	9.93680i	−0.672490	−	0.390958i
$647$	−8.22345	−	20.9530i	−0.323297	−	0.823748i	−0.996445	−	0.0842405i	$-0.973154\pi$
$647$	−8.22345	−	20.9530i	−0.323297	−	0.823748i	0.673148	−	0.739508i	$-0.264942\pi$
$648$	−1.00959	−	2.64211i	−0.0396604	−	0.103792i
$649$	−9.09411	+	0.681509i	−0.356975	+	0.0267516i
$650$	−3.04730	+	4.44087i	−0.119525	+	0.174185i
$651$	−10.3195	+	6.45640i	−0.404454	+	0.253046i
$652$	−1.94858	+	6.18508i	−0.0763125	+	0.242226i
$653$	3.42559	+	0.516325i	0.134054	+	0.0202054i	0.215726	−	0.976454i	$-0.430788\pi$
$653$	3.42559	+	0.516325i	0.134054	+	0.0202054i	−0.0816725	+	0.996659i	$0.526026\pi$
$654$	−1.60077	+	6.91765i	−0.0625951	+	0.270502i
$655$	1.28667	+	0.742861i	0.0502744	+	0.0290260i
$656$	−0.683342	+	0.258767i	−0.0266800	+	0.0101032i
$657$	−1.48450	+	3.08259i	−0.0579157	+	0.120263i
$658$	1.62395	+	50.0028i	0.0633083	+	1.94931i
$659$	5.06565	+	10.5189i	0.197330	+	0.409760i	0.976030	−	0.217637i	$-0.0698348\pi$
$659$	5.06565	+	10.5189i	0.197330	+	0.409760i	−0.778700	+	0.627396i	$0.784121\pi$
$660$	−1.10755	+	1.37185i	−0.0431113	+	0.0533991i
$661$	13.2529	−	14.2833i	0.515480	−	0.555555i	−0.420644	−	0.907226i	$-0.638196\pi$
$661$	13.2529	−	14.2833i	0.515480	−	0.555555i	0.936124	+	0.351671i	$0.114386\pi$
$662$	0.0627523	−	20.9058i	0.00243894	−	0.812526i
$663$	−4.81281	−	3.28132i	−0.186914	−	0.127436i
$664$	6.18159	+	3.04577i	0.239892	+	0.118199i
$665$	−1.52548	+	2.87289i	−0.0591555	+	0.111406i
$666$	−15.3755	+	4.69223i	−0.595790	+	0.181820i
$667$	8.77625	−	5.06697i	0.339818	−	0.196194i
$668$	−28.5489	−	19.7164i	−1.10459	−	0.762851i
$669$	9.51902	−	6.48996i	0.368027	−	0.250916i
$670$	0.412765	−	0.279607i	0.0159465	−	0.0108022i
$671$	−2.91796	+	12.7844i	−0.112647	+	0.493537i
$672$	−11.5080	+	9.56897i	−0.443932	+	0.369131i
$673$	2.19095	+	9.59916i	0.0844548	+	0.370020i	0.999440	−	0.0334673i	$-0.0106549\pi$
$673$	2.19095	+	9.59916i	0.0844548	+	0.370020i	−0.914985	+	0.403488i	$0.867798\pi$
$674$	−20.3799	−	19.0240i	−0.785005	−	0.732775i
$675$	−4.40969	−	1.36021i	−0.169729	−	0.0523545i
$676$	23.5864	−	7.12067i	0.907171	−	0.273872i
$677$	−4.23533	−	13.7306i	−0.162777	−	0.527709i	0.837034	−	0.547151i	$-0.184287\pi$
$677$	−4.23533	−	13.7306i	−0.162777	−	0.527709i	−0.999811	+	0.0194412i	$0.993811\pi$
$678$	7.09851	+	1.09173i	0.272616	+	0.0419276i
$679$	26.9245	−	36.3342i	1.03327	−	1.39438i
$680$	12.3913	+	0.111587i	0.475185	+	0.00427916i
$681$	−10.8337	+	27.6038i	−0.415149	+	1.05778i
$682$	−7.24219	+	5.73997i	−0.277318	+	0.219795i
$683$	−4.27065	−	28.3339i	−0.163412	−	1.08417i	−0.908707	−	0.417433i	$-0.862930\pi$
$683$	−4.27065	−	28.3339i	−0.163412	−	1.08417i	0.745295	−	0.666734i	$-0.232308\pi$
$684$	−2.45123	−	3.11188i	−0.0937250	−	0.118986i
$685$		−	9.23154i		−	0.352719i
$686$	−23.9131	−	10.6846i	−0.913008	−	0.407941i
$687$		−	12.0231i		−	0.458712i
$688$	−21.6905	−	32.6496i	−0.826943	−	1.24475i
$689$	−0.678935	−	4.50444i	−0.0258654	−	0.171606i
$690$	2.47055	+	3.11712i	0.0940524	+	0.118667i
$691$	−10.2607	+	26.1439i	−0.390336	+	0.994559i	0.591749	+	0.806122i	$0.298437\pi$
$691$	−10.2607	+	26.1439i	−0.390336	+	0.994559i	−0.982085	+	0.188437i	$0.939658\pi$
$692$	−19.7765	+	21.0591i	−0.751791	+	0.800546i
$693$	2.23718	−	3.01905i	0.0849836	−	0.114684i
$694$	7.07445	−	45.9986i	0.268542	−	1.74608i
$695$	0.510718	+	1.65571i	0.0193726	+	0.0628045i
$696$	3.21218	−	5.44973i	0.121757	−	0.206572i
$697$	−1.23208	−	0.380046i	−0.0466683	−	0.0143953i
$698$	−11.0876	+	11.8778i	−0.419671	+	0.449583i
$699$	−5.09744	−	22.3333i	−0.192803	−	0.844724i
$700$	0.719375	+	24.4082i	0.0271898	+	0.922542i
$701$	−5.93530	+	26.0042i	−0.224173	+	0.982167i	0.730126	+	0.683313i	$0.239461\pi$
$701$	−5.93530	+	26.0042i	−0.224173	+	0.982167i	−0.954299	+	0.298854i	$0.903396\pi$
$702$	−0.654556	−	0.966276i	−0.0247046	−	0.0364698i
$703$	−18.6025	+	12.6830i	−0.701606	+	0.478347i
$704$	−7.87683	+	8.18837i	−0.296869	+	0.308611i
$705$	7.18756	−	4.14974i	0.270699	−	0.156288i
$706$	−7.91929	−	25.9500i	−0.298046	−	0.976641i
$707$	12.5889	−	23.7083i	0.473452	−	0.891641i
$708$	4.61997	+	11.9825i	0.173629	+	0.450331i
$709$	11.8025	+	8.04682i	0.443253	+	0.302205i	0.764303	−	0.644858i	$-0.223083\pi$
$709$	11.8025	+	8.04682i	0.443253	+	0.302205i	−0.321050	+	0.947062i	$0.604036\pi$
$710$	6.29799	+	0.0189045i	0.236359	+	0.000709474i
$711$	3.34945	−	3.60985i	0.125614	−	0.135380i
$712$	−1.82081	+	0.119973i	−0.0682378	+	0.00449618i
$713$	9.04510	+	18.7823i	0.338742	+	0.703404i
$714$	−26.3957	+	0.857260i	−0.987834	+	0.0320821i
$715$	−0.315663	+	0.655480i	−0.0118051	+	0.0245136i
$716$	12.6138	+	26.6002i	0.471400	+	0.994095i
$717$	1.11937	+	0.646268i	0.0418036	+	0.0241353i
$718$	−11.8056	−	2.73186i	−0.440581	−	0.101952i
$719$	−6.13733	−	0.925053i	−0.228884	−	0.0344987i	0.0335989	−	0.999435i	$-0.489303\pi$
$719$	−6.13733	−	0.925053i	−0.228884	−	0.0344987i	−0.262483	+	0.964937i	$0.584541\pi$
$720$	2.30017	+	0.934774i	0.0857223	+	0.0348370i
$721$	34.4058	−	21.5260i	1.28134	−	0.801669i
$722$	17.5809	+	12.0639i	0.654294	+	0.448973i
$723$	−5.92591	+	0.444086i	−0.220387	+	0.0165157i
$724$	−12.4328	−	4.96586i	−0.462062	−	0.184555i
$725$	−3.77072	−	9.60763i	−0.140041	−	0.356819i
$726$	−6.38487	+	10.9827i	−0.236965	+	0.407605i
$727$	−26.9650	−	33.8130i	−1.00008	−	1.25405i	−0.967046	−	0.254600i	$-0.918056\pi$
$727$	−26.9650	−	33.8130i	−1.00008	−	1.25405i	−0.0330286	−	0.999454i	$-0.510515\pi$
$728$	−3.72141	+	4.92858i	−0.137924	+	0.182665i
$729$	0.623490	−	0.781831i	0.0230922	−	0.0289567i
$730$	−1.08887	−	2.79907i	−0.0403008	−	0.103598i
$731$	5.16888	−	68.9739i	0.191178	−	2.55109i
$732$	18.4224	−	1.26940i	0.680913	−	0.0469185i
$733$	28.5166	+	30.7335i	1.05328	+	1.13517i	0.990552	+	0.137139i	$0.0437907\pi$
$733$	28.5166	+	30.7335i	1.05328	+	1.13517i	0.0627314	+	0.998030i	$0.480019\pi$
$734$	12.6747	−	11.6898i	0.467831	−	0.431478i
$735$	0.307955	+	4.33408i	0.0113591	+	0.159865i
$736$	14.1192	+	21.3920i	0.520442	+	0.788519i
$737$	−0.591292	+	0.548639i	−0.0217805	+	0.0202094i
$738$	−0.201494	−	0.161678i	−0.00741709	−	0.00595144i
$739$	−4.01561	−	0.300928i	−0.147717	−	0.0110698i	0.000666522	−	1.00000i	$-0.499788\pi$
$739$	−4.01561	−	0.300928i	−0.147717	−	0.0110698i	−0.148383	+	0.988930i	$0.547407\pi$
$740$	6.19897	−	12.6771i	0.227879	−	0.466018i
$741$	−1.27797	−	1.01915i	−0.0469475	−	0.0374394i
$742$	−14.5318	−	14.6759i	−0.533479	−	0.538770i
$743$	5.17603	−	4.12774i	0.189890	−	0.151432i	−0.523930	−	0.851761i	$-0.675535\pi$
$743$	5.17603	−	4.12774i	0.189890	−	0.151432i	0.713820	+	0.700329i	$0.246963\pi$
$744$	10.6856	+	7.42717i	0.391755	+	0.272293i
$745$	−4.32223	+	1.69635i	−0.158354	+	0.0621495i
$746$	−27.3973	+	13.0927i	−1.00309	+	0.479358i
$747$	0.182073	+	2.42960i	0.00666172	+	0.0888944i
$748$	−19.8426	+	2.86907i	−0.725516	+	0.104903i
$749$	8.37309	−	23.7814i	0.305946	−	0.868953i
$750$	7.32191	−	4.19805i	0.267358	−	0.153291i
$751$	−0.545381	+	3.61836i	−0.0199012	+	0.132036i	−0.996575	−	0.0826917i	$-0.973648\pi$
$751$	−0.545381	+	3.61836i	−0.0199012	+	0.132036i	0.976674	+	0.214728i	$0.0688864\pi$
$752$	48.4620	−	22.6253i	1.76723	−	0.825061i
$753$	−5.64557	+	9.77841i	−0.205736	+	0.356345i
$754$	0.776884	−	2.49201i	0.0282924	−	0.0907538i
$755$	−9.75027	−	4.69548i	−0.354849	−	0.170886i
$756$	−4.98053	−	1.78725i	−0.181140	−	0.0650017i
$757$	−37.6886	+	18.1499i	−1.36982	+	0.659669i	−0.966802	−	0.255525i	$-0.917752\pi$
$757$	−37.6886	+	18.1499i	−1.36982	+	0.659669i	−0.403014	+	0.915194i	$0.632037\pi$
$758$	2.83901	+	19.2270i	0.103118	+	0.698357i
$759$	−4.71732	−	4.37703i	−0.171228	−	0.158876i
$760$	3.46516	+	0.291079i	0.125695	+	0.0105586i
$761$	23.6599	−	34.7027i	0.857670	−	1.25797i	−0.106934	−	0.994266i	$-0.534103\pi$
$761$	23.6599	−	34.7027i	0.857670	−	1.25797i	0.964604	−	0.263704i	$-0.0849443\pi$
$762$	−20.5908	−	8.15271i	−0.745927	−	0.295342i
$763$	7.86747	+	10.7033i	0.284822	+	0.387485i
$764$	−9.56004	−	5.59628i	−0.345870	−	0.202466i
$765$	2.19058	+	3.79420i	0.0792008	+	0.137180i
$766$	−2.27734	−	10.1176i	−0.0822835	−	0.365562i
$767$	2.98513	+	4.37838i	0.107787	+	0.158094i
$768$	14.2447	+	7.28627i	0.514010	+	0.262921i
$769$	22.9129	+	5.22973i	0.826262	+	0.188589i	0.614685	−	0.788772i	$-0.289283\pi$
$769$	22.9129	+	5.22973i	0.826262	+	0.188589i	0.211577	+	0.977361i	$0.432140\pi$
$770$	0.597234	+	3.24400i	0.0215228	+	0.116906i
$771$	2.93536	−	0.669977i	0.105714	−	0.0241286i
$772$	33.4433	+	0.200773i	1.20365	+	0.00722599i
$773$	−13.9847	+	45.3373i	−0.502995	+	1.63067i	0.246849	+	0.969054i	$0.420605\pi$
$773$	−13.9847	+	45.3373i	−0.502995	+	1.63067i	−0.749844	+	0.661615i	$0.769871\pi$
$774$	6.05045	−	12.4680i	0.217479	−	0.448154i
$775$	20.2885	−	6.25819i	0.728786	−	0.224801i
$776$	−47.0343	−	11.1818i	−1.68843	−	0.401404i
$777$	−12.0799	+	27.5420i	−0.433363	+	0.988064i
$778$	−2.56075	−	35.6047i	−0.0918075	−	1.27649i
$779$	−0.336807	−	0.132187i	−0.0120674	−	0.00473609i
$780$	1.01213	+	0.158775i	0.0362402	+	0.00568504i
$781$	−10.0759	+	1.51869i	−0.360542	+	0.0543430i
$782$	−3.51528	+	45.0915i	−0.125706	+	1.61247i
$783$	2.23656			0.0799282
$784$	−0.444382	+	27.9965i	−0.0158708	+	0.999874i
$785$	3.89828			0.139136
$786$	−0.263093	+	3.37477i	−0.00938423	+	0.120374i
$787$	−21.3091	+	3.21182i	−0.759586	+	0.114489i	−0.517404	−	0.855742i	$-0.673101\pi$
$787$	−21.3091	+	3.21182i	−0.759586	+	0.114489i	−0.242182	+	0.970231i	$0.577863\pi$
$788$	−6.60602	−	1.03629i	−0.235330	−	0.0369164i
$789$	13.3439	+	5.23709i	0.475055	+	0.186445i
$790$	0.310100	+	4.31163i	0.0110329	+	0.153401i
$791$	10.2012	−	8.74459i	0.362713	−	0.310922i
$792$	−3.90813	−	0.929109i	−0.138869	−	0.0330144i
$793$	7.28122	−	2.24596i	0.258564	−	0.0797564i
$794$	10.3508	−	21.3295i	0.367334	−	0.756957i
$795$	−1.00990	+	3.27401i	−0.0358174	+	0.116117i
$796$	6.68495	+	0.0401325i	0.236942	+	0.00142246i
$797$	−40.9806	+	9.35355i	−1.45161	+	0.331320i	−0.874371	−	0.485258i	$-0.838726\pi$
$797$	−40.9806	+	9.35355i	−1.45161	+	0.331320i	−0.577235	+	0.816578i	$0.695869\pi$
$798$	−7.40437	−	0.313644i	−0.262112	−	0.0111029i
$799$	92.0088	+	21.0004i	3.25504	+	0.742941i
$800$	23.6869	−	10.9722i	0.837459	−	0.387925i
$801$	−0.363426	−	0.533048i	−0.0128410	−	0.0188343i
$802$	−3.17518	−	14.1064i	−0.112119	−	0.498115i
$803$	2.42962	+	4.20823i	0.0857395	+	0.148505i
$804$	0.980278	+	0.573838i	0.0345717	+	0.0202377i
$805$	7.43537	+	0.292601i	0.262062	+	0.0103128i
$806$	4.99263	+	1.97678i	0.175858	+	0.0696290i
$807$	−16.1320	+	23.6613i	−0.567873	+	0.832917i
$808$	−28.5959	−	2.40210i	−1.00600	−	0.0845057i
$809$	−23.8983	−	22.1744i	−0.840221	−	0.779611i	0.137282	−	0.990532i	$-0.456163\pi$
$809$	−23.8983	−	22.1744i	−0.840221	−	0.779611i	−0.977503	+	0.210921i	$0.932354\pi$
$810$	0.128227	+	0.868408i	0.00450543	+	0.0305127i
$811$	−38.3027	+	18.4456i	−1.34499	+	0.647712i	−0.961237	−	0.275724i	$-0.911082\pi$
$811$	−38.3027	+	18.4456i	−1.34499	+	0.647712i	−0.383752	+	0.923436i	$0.625368\pi$
$812$	−3.82001	−	11.2013i	−0.134056	−	0.393089i
$813$	15.6252	+	7.52468i	0.547998	+	0.263902i
$814$	−6.79508	+	21.7966i	−0.238167	+	0.763971i
$815$	1.00630	−	1.74296i	0.0352491	−	0.0610532i
$816$	11.9436	+	25.5824i	0.418109	+	0.895561i
$817$	2.89285	−	19.1928i	0.101208	−	0.671471i
$818$	37.9899	−	21.7817i	1.32829	−	0.761579i
$819$	−2.16925	−	0.248662i	−0.0757997	−	0.00868894i
$820$	0.224443	−	0.0324525i	0.00783788	−	0.00113329i
$821$	−3.98359	−	53.1574i	−0.139028	−	1.85521i	−0.435532	−	0.900173i	$-0.643440\pi$
$821$	−3.98359	−	53.1574i	−0.139028	−	1.85521i	0.296503	−	0.955032i	$-0.404179\pi$
$822$	18.9772	−	9.06887i	0.661906	−	0.316313i
$823$	11.0750	−	4.34663i	0.386052	−	0.151514i	−0.164374	−	0.986398i	$-0.552561\pi$
$823$	11.0750	−	4.34663i	0.386052	−	0.151514i	0.550426	+	0.834884i	$0.314465\pi$
$824$	−35.6265	−	24.7626i	−1.24111	−	0.862645i
$825$	−5.12414	+	4.08636i	−0.178400	+	0.142269i
$826$	22.6381	+	8.04700i	0.787680	+	0.279991i
$827$	−41.5447	−	33.1308i	−1.44465	−	1.15207i	−0.960911	−	0.276858i	$-0.910707\pi$
$827$	−41.5447	−	33.1308i	−1.44465	−	1.15207i	−0.483739	−	0.875212i	$-0.660722\pi$
$828$	−3.98083	+	8.14089i	−0.138343	+	0.282916i
$829$	36.8450	+	2.76115i	1.27968	+	0.0958986i	0.697158	−	0.716918i	$-0.254448\pi$
$829$	36.8450	+	2.76115i	1.27968	+	0.0958986i	0.582520	+	0.812816i	$0.302067\pi$
$830$	−1.66812	−	1.33850i	−0.0579014	−	0.0464599i
$831$	3.16141	−	2.93336i	0.109668	−	0.101757i
$832$	6.40911	+	1.58479i	0.222196	+	0.0549428i
$833$	−30.9544	+	38.5093i	−1.07250	+	1.33427i
$834$	−2.90190	+	2.67641i	−0.100485	+	0.0926764i
$835$	7.32410	+	7.89350i	0.253461	+	0.273166i
$836$	−5.61278	+	0.386750i	−0.194122	+	0.0133760i
$837$	−0.343825	+	4.58803i	−0.0118843	+	0.158586i
$838$	8.65879	+	22.2585i	0.299113	+	0.768906i
$839$	−13.6338	+	17.0962i	−0.470691	+	0.590228i	−0.959340	−	0.282253i	$-0.908918\pi$
$839$	−13.6338	+	17.0962i	−0.470691	+	0.590228i	0.488649	+	0.872480i	$0.337490\pi$
$840$	4.13021	−	2.12542i	0.142506	−	0.0733339i
$841$	−14.9624	−	18.7622i	−0.515944	−	0.646973i
$842$	−24.4479	+	42.0530i	−0.842532	+	1.44924i
$843$	11.5750	+	29.4926i	0.398664	+	1.01578i
$844$	42.8964	+	17.1335i	1.47655	+	0.589758i
$845$	−7.62516	+	0.571427i	−0.262314	+	0.0196577i
$846$	15.5915	+	10.6988i	0.536047	+	0.367832i
$847$	7.80623	+	22.4480i	0.268225	+	0.771321i
$848$	−8.31264	+	20.4546i	−0.285457	+	0.702416i
$849$	−20.8615	−	3.14437i	−0.715966	−	0.107914i
$850$	44.8777	+	10.3849i	1.53929	+	0.356198i
$851$	44.6046	+	25.7525i	1.52903	+	0.882784i
$852$	6.14815	+	12.9653i	0.210632	+	0.444184i
$853$	3.49359	−	7.25450i	0.119618	−	0.248389i	−0.832559	−	0.553937i	$-0.813125\pi$
$853$	3.49359	−	7.25450i	0.119618	−	0.248389i	0.952177	+	0.305547i	$0.0988393\pi$
$854$	20.6516	−	27.6948i	0.706682	−	0.947698i
$855$	0.533432	+	1.10768i	0.0182430	+	0.0378820i
$856$	−26.8948	+	1.77210i	−0.919247	+	0.0605691i
$857$	19.5902	−	21.1133i	0.669190	−	0.721215i	−0.303627	−	0.952791i	$-0.598198\pi$
$857$	19.5902	−	21.1133i	0.669190	−	0.721215i	0.972817	+	0.231576i	$0.0743882\pi$
$858$	−1.65757	−	0.00497547i	−0.0565884	−	0.000169860i
$859$	22.8142	+	15.5545i	0.778411	+	0.530712i	0.886112	−	0.463472i	$-0.153396\pi$
$859$	22.8142	+	15.5545i	0.778411	+	0.530712i	−0.107701	+	0.994183i	$0.534349\pi$
$860$	4.37644	+	11.3509i	0.149235	+	0.387062i
$861$	−0.475057	+	0.0889351i	−0.0161899	+	0.00303090i
$862$	9.18393	+	30.0940i	0.312806	+	1.02501i
$863$	−28.0837	+	16.2141i	−0.955979	+	0.551935i	−0.894933	−	0.446200i	$-0.852777\pi$
$863$	−28.0837	+	16.2141i	−0.955979	+	0.551935i	−0.0610460	+	0.998135i	$0.519444\pi$
$864$	0.338030	+	5.64675i	0.0115000	+	0.192106i
$865$	7.40808	−	5.05075i	0.251882	−	0.171731i
$866$	19.8965	+	29.3719i	0.676111	+	0.998096i
$867$	−7.30294	+	31.9963i	−0.248021	+	1.08665i
$868$	23.5654	−	6.11430i	0.799860	−	0.207533i
$869$	−1.55628	−	6.81852i	−0.0527933	−	0.231302i
$870$	−1.33970	+	1.43519i	−0.0454201	+	0.0486575i
$871$	0.447881	+	0.138153i	0.0151759	+	0.00468114i
$872$	7.21090	−	12.2339i	0.244192	−	0.414292i
$873$	−5.03814	−	16.3332i	−0.170515	−	0.552797i
$874$	−1.92929	+	12.5444i	−0.0652592	+	0.424320i
$875$	2.96549	−	15.5089i	0.100252	−	0.524295i
$876$	4.68434	−	4.98812i	0.158269	−	0.168533i
$877$	−16.0880	+	40.9915i	−0.543252	+	1.38418i	0.350896	+	0.936414i	$0.385877\pi$
$877$	−16.0880	+	40.9915i	−0.543252	+	1.38418i	−0.894149	+	0.447770i	$0.852218\pi$
$878$	13.2713	+	16.7445i	0.447883	+	0.565099i
$879$	1.70168	+	11.2899i	0.0573961	+	0.380798i
$880$	2.93718	−	1.95129i	0.0990122	−	0.0657780i
$881$		−	16.2689i		−	0.548113i	−0.961714	−	0.274056i	$-0.911634\pi$
$881$		−	16.2689i		−	0.548113i	0.961714	−	0.274056i	$-0.0883655\pi$
$882$	−8.60700	+	4.89076i	−0.289813	+	0.164681i
$883$			27.8919i			0.938637i	0.883029	+	0.469319i	$0.155500\pi$
$883$			27.8919i			0.938637i	−0.883029	+	0.469319i	$0.844500\pi$
$884$	7.20879	+	9.15171i	0.242458	+	0.307805i
$885$	−0.594039	−	3.94119i	−0.0199684	−	0.132482i
$886$	2.83664	−	2.24825i	0.0952989	−	0.0755314i
$887$	8.97795	−	22.8755i	0.301450	−	0.768083i	−0.697236	−	0.716842i	$-0.745587\pi$
$887$	8.97795	−	22.8755i	0.301450	−	0.768083i	0.998686	−	0.0512411i	$-0.0163177\pi$
$888$	32.1499	+	0.289517i	1.07888	+	0.00971556i
$889$	−36.6676	+	19.2888i	−1.22979	+	0.646927i
$890$	0.559746	+	0.0860873i	0.0187627	+	0.00288565i
$891$	−0.418624	−	1.35715i	−0.0140244	−	0.0454661i
$892$	−22.0585	+	6.65939i	−0.738574	+	0.222973i
$893$	25.3067	+	7.80610i	0.846858	+	0.261221i
$894$	−7.73325	−	7.21872i	−0.258638	−	0.241430i
$895$	−2.03311	−	8.90765i	−0.0679595	−	0.297750i
$896$	27.7031	−	11.3375i	0.925495	−	0.378759i
$897$	−0.832077	+	3.64557i	−0.0277822	+	0.121722i
$898$	−14.8261	+	10.0432i	−0.494755	+	0.335147i
$899$	−8.50215	+	5.79667i	−0.283563	+	0.193330i
$900$	7.59436	+	5.24481i	0.253145	+	0.174827i
$901$	−33.7406	+	19.4801i	−1.12406	+	0.648977i
$902$	−0.350928	+	0.107094i	−0.0116846	+	0.00356585i
$903$	−10.3220	−	23.7837i	−0.343496	−	0.791471i
$904$	−12.8848	−	6.34856i	−0.428542	−	0.211150i
$905$	3.43304	+	2.34060i	0.114118	+	0.0778043i
$906$	0.0740102	−	24.6563i	0.00245882	−	0.819151i
$907$	11.5937	−	12.4951i	0.384964	−	0.414892i	−0.510605	−	0.859815i	$-0.670579\pi$
$907$	11.5937	−	12.4951i	0.384964	−	0.414892i	0.895569	+	0.444923i	$0.146769\pi$
$908$	37.2552	−	46.1456i	1.23636	−	1.53139i
$909$	−4.40210	−	9.14105i	−0.146008	−	0.303189i
$910$	1.45894	−	1.24305i	0.0483636	−	0.0412066i
$911$	−2.28826	+	4.75163i	−0.0758136	+	0.157429i	−0.935431	−	0.353510i	$-0.884988\pi$
$911$	−2.28826	+	4.75163i	−0.0758136	+	0.157429i	0.859617	+	0.510939i	$0.170702\pi$
$912$	2.80573	+	7.40926i	0.0929071	+	0.245345i
$913$	2.99671	+	1.73015i	0.0991765	+	0.0572596i
$914$	−0.698445	+	3.01830i	−0.0231025	+	0.0998363i
$915$	−5.66709	−	0.854176i	−0.187348	−	0.0282382i
$916$	−7.22559	+	22.9350i	−0.238740	+	0.757794i
$917$	4.46929	+	4.48659i	0.147589	+	0.148160i
$918$	−5.64773	+	8.23051i	−0.186403	+	0.271647i
$919$	−2.36545	+	0.177266i	−0.0780291	+	0.00584747i	−0.113687	−	0.993517i	$-0.536266\pi$
$919$	−2.36545	+	0.177266i	−0.0780291	+	0.00584747i	0.0356583	+	0.999364i	$0.488647\pi$
$920$	−2.83945	−	7.43088i	−0.0936139	−	0.244989i
$921$	−2.65139	−	6.75564i	−0.0873664	−	0.222606i
$922$	39.0001	+	22.6731i	1.28440	+	0.746698i
$923$	3.69166	+	4.62919i	0.121512	+	0.152372i
$924$	−6.08196	+	4.41457i	−0.200082	+	0.145229i
$925$	32.7059	−	41.0119i	1.07536	−	1.34846i
$926$	−16.1454	+	6.28074i	−0.530571	+	0.206398i
$927$	1.14633	−	15.2967i	0.0376505	−	0.502410i
$928$	−9.40261	+	8.46532i	−0.308656	+	0.277888i
$929$	34.7979	+	37.5032i	1.14168	+	1.23044i	0.969425	+	0.245389i	$0.0789157\pi$
$929$	34.7979	+	37.5032i	1.14168	+	1.23044i	0.172258	+	0.985052i	$0.444894\pi$
$930$	−2.73816	−	2.96886i	−0.0897879	−	0.0973528i
$931$	−9.46963	+	10.1271i	−0.310354	+	0.331901i
$932$	−3.69800	+	45.6658i	−0.121132	+	1.49583i
$933$	14.9115	−	13.8358i	0.488179	−	0.452964i
$934$	3.91032	−	4.87331i	0.127950	−	0.159460i
$935$	6.20493	+	0.464995i	0.202923	+	0.0152070i
$936$	0.667907	+	2.23661i	0.0218312	+	0.0731060i
$937$	43.9278	+	35.0312i	1.43506	+	1.14442i	0.965148	+	0.261706i	$0.0842850\pi$
$937$	43.9278	+	35.0312i	1.43506	+	1.14442i	0.469910	+	0.882714i	$0.344286\pi$
$938$	2.00923	−	0.691953i	0.0656038	−	0.0225931i
$939$	−8.86045	+	7.06597i	−0.289150	+	0.230589i
$940$	−16.2047	+	3.59640i	−0.528538	+	0.117302i
$941$	9.58793	−	3.76298i	0.312558	−	0.122670i	−0.203877	−	0.978997i	$-0.565354\pi$
$941$	9.58793	−	3.76298i	0.312558	−	0.122670i	0.516434	+	0.856327i	$0.327259\pi$
$942$	3.82959	+	8.01367i	0.124775	+	0.261099i
$943$	0.0618543	+	0.825388i	0.00201425	+	0.0268783i
$944$	−1.61176	−	25.6340i	−0.0524583	−	0.834316i
$945$	1.38885	+	0.876419i	0.0451792	+	0.0285099i
$946$	−9.79005	−	17.0750i	−0.318302	−	0.555157i
$947$	−6.87602	+	45.6194i	−0.223441	+	1.48243i	0.542791	+	0.839868i	$0.317367\pi$
$947$	−6.87602	+	45.6194i	−0.223441	+	1.48243i	−0.766232	+	0.642564i	$0.777871\pi$
$948$	−8.55875	+	4.87312i	−0.277975	+	0.158272i
$949$	1.41179	−	2.44530i	0.0458287	−	0.0793777i
$950$	12.3405	+	3.84715i	0.400379	+	0.124818i
$951$	−11.9941	−	5.77607i	−0.388936	−	0.187302i
$952$	50.8669	+	14.2278i	1.64861	+	0.461126i
$953$	−31.0713	+	14.9632i	−1.00650	+	0.484705i	−0.863139	−	0.504966i	$-0.831505\pi$
$953$	−31.0713	+	14.9632i	−1.00650	+	0.484705i	−0.143360	+	0.989671i	$0.545791\pi$
$954$	−7.72246	+	1.14028i	−0.250024	+	0.0369178i
$955$	2.52024	+	2.33844i	0.0815530	+	0.0756701i
$956$	−1.74689	−	1.90551i	−0.0564984	−	0.0616287i
$957$	1.78937	−	2.62452i	0.0578420	−	0.0848386i
$958$	−13.3337	+	33.6760i	−0.430791	+	1.08802i
$959$	10.2576	−	37.9883i	0.331237	−	1.22670i
$960$	−3.82597	−	3.16549i	−0.123483	−	0.102166i
$961$	4.91588	+	8.51456i	0.158577	+	0.274663i
$962$	12.9428	−	2.91327i	0.417294	−	0.0939277i
$963$	−5.36809	−	7.87354i	−0.172984	−	0.253721i
$964$	11.5710	+	2.71419i	0.372677	+	0.0874181i
$965$	−10.1193	−	2.30967i	−0.325752	−	0.0743508i
$966$	6.70285	+	15.5723i	0.215661	+	0.501030i
$967$	−47.2785	+	10.7910i	−1.52037	+	0.347016i	−0.899509	−	0.436902i	$-0.856076\pi$
$967$	−47.2785	+	10.7910i	−1.52037	+	0.347016i	−0.620865	+	0.783917i	$0.713219\pi$
$968$	18.7799	−	17.1131i	0.603608	−	0.550035i
$969$	−4.12072	+	13.3590i	−0.132377	+	0.429154i
$970$	13.4988	+	6.55067i	0.433421	+	0.210329i
$971$	−31.9478	+	9.85458i	−1.02525	+	0.316248i	−0.761378	−	0.648309i	$-0.775477\pi$
$971$	−31.9478	+	9.85458i	−1.02525	+	0.316248i	−0.263874	+	0.964557i	$0.585000\pi$
$972$	−1.65921	+	1.11670i	−0.0532192	+	0.0358182i
$973$	0.261888	+	7.38080i	0.00839575	+	0.236617i
$974$	−27.6919	+	1.99165i	−0.887307	+	0.0638167i
$975$	3.54512	+	1.39136i	0.113535	+	0.0445590i
$976$	−35.9050	−	8.64991i	−1.14929	−	0.276877i
$977$	15.8494	−	2.38892i	0.507068	−	0.0764282i	0.109474	−	0.993990i	$-0.465083\pi$
$977$	15.8494	−	2.38892i	0.507068	−	0.0764282i	0.397594	+	0.917561i	$0.369845\pi$
$978$	4.57155	+	0.356393i	0.146182	+	0.0113962i
$979$	−0.916269			−0.0292841
$980$	2.01722	−	8.45264i	0.0644376	−	0.270010i
$981$	5.02077			0.160301
$982$	13.9438	+	1.08704i	0.444965	+	0.0346890i
$983$	−13.2842	+	2.00227i	−0.423699	+	0.0638624i	−0.357431	−	0.933939i	$-0.616347\pi$
$983$	−13.2842	+	2.00227i	−0.423699	+	0.0638624i	−0.0662681	+	0.997802i	$0.521109\pi$
$984$	0.287200	+	0.429505i	0.00915561	+	0.0136921i
$985$	1.93184	+	0.758192i	0.0615536	+	0.0241580i
$986$	−22.2676	+	1.60153i	−0.709145	+	0.0510030i
$987$	34.1882	−	9.08992i	1.08822	−	0.289335i
$988$	1.82534	+	2.71213i	0.0580720	+	0.0862843i
$989$	−42.4291	+	13.0877i	−1.34917	+	0.416163i
$990$	1.12163	+	0.544302i	0.0356477	+	0.0172991i
$991$	−14.6780	+	47.5848i	−0.466261	+	1.51158i	0.351592	+	0.936153i	$0.385640\pi$
$991$	−14.6780	+	47.5848i	−0.466261	+	1.51158i	−0.817853	+	0.575427i	$0.804836\pi$
$992$	−15.9201	−	20.5897i	−0.505464	−	0.653722i
$993$	−14.4121	+	3.28946i	−0.457353	+	0.104388i
$994$	25.8955	+	7.07581i	0.821357	+	0.224431i
$995$	−2.02274	−	0.461678i	−0.0641253	−	0.0146362i
$996$	1.11281	−	4.74406i	0.0352606	−	0.150321i
$997$	−20.8761	−	30.6196i	−0.661152	−	0.969732i	−0.999587	−	0.0287424i	$-0.990850\pi$
$997$	−20.8761	−	30.6196i	−0.661152	−	0.969732i	0.338435	−	0.940990i	$-0.390103\pi$
$998$	36.4208	−	8.19788i	1.15288	−	0.259499i
$999$	5.68358	+	9.84424i	0.179820	+	0.311458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.ba.a.283.14	yes	336
4.3	odd	2		588.2.ba.b.283.1	yes	336
49.40	odd	42		588.2.ba.b.187.1	yes	336
196.187	even	42	inner	588.2.ba.a.187.14	✓	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.ba.a.187.14	✓	336	196.187	even	42	inner
588.2.ba.a.283.14	yes	336	1.1	even	1	trivial
588.2.ba.b.187.1	yes	336	49.40	odd	42
588.2.ba.b.283.1	yes	336	4.3	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.ba (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.109917 + 1.40994i) q^{2} +(0.988831 - 0.149042i) q^{3} +(-1.97584 - 0.309952i) q^{4} +(0.577807 + 0.226773i) q^{5} +(0.101451 + 1.41057i) q^{6} +(2.12573 + 1.57521i) q^{7} +(0.654190 - 2.75173i) q^{8} +(0.955573 - 0.294755i) q^{9} +O(q^{10})\)	\(q+(-0.109917 + 1.40994i) q^{2} +(0.988831 - 0.149042i) q^{3} +(-1.97584 - 0.309952i) q^{4} +(0.577807 + 0.226773i) q^{5} +(0.101451 + 1.41057i) q^{6} +(2.12573 + 1.57521i) q^{7} +(0.654190 - 2.75173i) q^{8} +(0.955573 - 0.294755i) q^{9} +(-0.383246 + 0.789745i) q^{10} +(0.418624 - 1.35715i) q^{11} +(-1.99996 - 0.0120066i) q^{12} +(-0.804577 + 0.183639i) q^{13} +(-2.45460 + 2.82399i) q^{14} +(0.605152 + 0.138122i) q^{15} +(3.80786 + 1.22483i) q^{16} +(3.97606 + 5.83181i) q^{17} +(0.310552 + 1.37969i) q^{18} +(0.990339 + 1.71532i) q^{19} +(-1.07136 - 0.627158i) q^{20} +(2.33676 + 1.24079i) q^{21} +(1.86747 + 0.739406i) q^{22} +(2.55242 - 3.74372i) q^{23} +(0.236758 - 2.81850i) q^{24} +(-3.38282 - 3.13880i) q^{25} +(-0.170483 - 1.15459i) q^{26} +(0.900969 - 0.433884i) q^{27} +(-3.71185 - 3.77123i) q^{28} +(2.01507 + 0.970408i) q^{29} +(-0.261260 + 0.838044i) q^{30} +(-2.30045 + 3.98449i) q^{31} +(-2.14548 + 5.23421i) q^{32} +(0.211676 - 1.40438i) q^{33} +(-8.65952 + 4.96498i) q^{34} +(0.871045 + 1.39222i) q^{35} +(-1.97942 + 0.286207i) q^{36} +(0.849468 + 11.3354i) q^{37} +(-2.52734 + 1.20777i) q^{38} +(-0.768220 + 0.301504i) q^{39} +(1.00201 - 1.44162i) q^{40} +(-0.142820 + 0.113895i) q^{41} +(-2.00629 + 3.15829i) q^{42} +(-7.66154 - 6.10987i) q^{43} +(-1.24778 + 2.55175i) q^{44} +(0.618979 + 0.0463861i) q^{45} +(4.99785 + 4.01025i) q^{46} +(9.80152 - 9.09448i) q^{47} +(3.94788 + 0.643615i) q^{48} +(2.03742 + 6.69693i) q^{49} +(4.79734 - 4.42456i) q^{50} +(4.80084 + 5.17407i) q^{51} +(1.64663 - 0.113462i) q^{52} +(-0.412496 + 5.50437i) q^{53} +(0.512716 + 1.31800i) q^{54} +(0.549648 - 0.689236i) q^{55} +(5.72519 - 4.81894i) q^{56} +(1.23493 + 1.54856i) q^{57} +(-1.58970 + 2.73446i) q^{58} +(-2.34591 - 5.97729i) q^{59} +(-1.15287 - 0.460474i) q^{60} +(-9.20724 + 0.689988i) q^{61} +(-5.36502 - 3.68145i) q^{62} +(2.49559 + 0.878660i) q^{63} +(-7.14407 - 3.60031i) q^{64} +(-0.506534 - 0.0763478i) q^{65} +(1.95682 + 0.452815i) q^{66} +(-0.491853 - 0.283971i) q^{67} +(-6.04847 - 12.7551i) q^{68} +(1.96594 - 4.08232i) q^{69} +(-2.05869 + 1.07509i) q^{70} +(-3.11294 - 6.46408i) q^{71} +(-0.185962 - 2.82231i) q^{72} +(-2.32715 + 2.50808i) q^{73} +(-16.0755 - 0.0482534i) q^{74} +(-3.81285 - 2.59956i) q^{75} +(-1.42508 - 3.69614i) q^{76} +(3.02767 - 2.22550i) q^{77} +(-0.340661 - 1.11628i) q^{78} +(4.26467 - 2.46221i) q^{79} +(1.92245 + 1.57123i) q^{80} +(0.826239 - 0.563320i) q^{81} +(-0.144887 - 0.213886i) q^{82} +(-0.542153 + 2.37533i) q^{83} +(-4.23246 - 3.17589i) q^{84} +(0.974902 + 4.27132i) q^{85} +(9.45666 - 10.1307i) q^{86} +(2.13720 + 0.659238i) q^{87} +(-3.46064 - 2.03977i) q^{88} +(-0.190161 - 0.616487i) q^{89} +(-0.133438 + 0.867622i) q^{90} +(-1.99958 - 0.877011i) q^{91} +(-6.20354 + 6.60585i) q^{92} +(-1.68090 + 4.28285i) q^{93} +(11.7453 + 14.8192i) q^{94} +(0.183238 + 1.21570i) q^{95} +(-1.34139 + 5.49551i) q^{96} -17.0926i q^{97} +(-9.66619 + 2.13652i) q^{98} -1.42024i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9	\( 336 q - 28 q^{3} + 2 q^{7} - 6 q^{8} + 28 q^{9} + 41 q^{10} + 6 q^{11} + 52 q^{14} + 20 q^{16} - 6 q^{19} - 25 q^{20} + 4 q^{21} + 6 q^{22} + 9 q^{24} - 26 q^{25} - 18 q^{26} + 56 q^{27} + 5 q^{30} + 2 q^{31} + 15 q^{32} + 6 q^{33} + 44 q^{34} - 12 q^{35} + 16 q^{37} - 100 q^{38} + 8 q^{39} - 7 q^{40} - 7 q^{42} - 53 q^{44} - 10 q^{46} + 4 q^{47} + 8 q^{48} - 4 q^{49} - 114 q^{50} - 28 q^{52} - 4 q^{53} + q^{56} - 12 q^{57} + 27 q^{58} - 10 q^{59} - 7 q^{60} + 2 q^{61} - 16 q^{62} - 12 q^{63} - 84 q^{64} - 4 q^{65} + 21 q^{66} + 42 q^{67} + 26 q^{68} - 70 q^{70} + 28 q^{71} + 15 q^{72} + 18 q^{73} + 20 q^{74} + 54 q^{75} + 49 q^{76} - 8 q^{77} - 6 q^{78} - 6 q^{79} - 40 q^{80} + 28 q^{81} - 99 q^{82} + 10 q^{83} + 54 q^{84} + 24 q^{85} - 314 q^{86} - 40 q^{88} + 20 q^{90} - 34 q^{91} + 14 q^{92} - 2 q^{93} - 152 q^{94} - 24 q^{95} - 10 q^{96} - 156 q^{98}+O(q^{100}) \) 336 * q - 28 * q^3 + 2 * q^7 - 6 * q^8 + 28 * q^9 + 41 * q^10 + 6 * q^11 + 52 * q^14 + 20 * q^16 - 6 * q^19 - 25 * q^20 + 4 * q^21 + 6 * q^22 + 9 * q^24 - 26 * q^25 - 18 * q^26 + 56 * q^27 + 5 * q^30 + 2 * q^31 + 15 * q^32 + 6 * q^33 + 44 * q^34 - 12 * q^35 + 16 * q^37 - 100 * q^38 + 8 * q^39 - 7 * q^40 - 7 * q^42 - 53 * q^44 - 10 * q^46 + 4 * q^47 + 8 * q^48 - 4 * q^49 - 114 * q^50 - 28 * q^52 - 4 * q^53 + q^56 - 12 * q^57 + 27 * q^58 - 10 * q^59 - 7 * q^60 + 2 * q^61 - 16 * q^62 - 12 * q^63 - 84 * q^64 - 4 * q^65 + 21 * q^66 + 42 * q^67 + 26 * q^68 - 70 * q^70 + 28 * q^71 + 15 * q^72 + 18 * q^73 + 20 * q^74 + 54 * q^75 + 49 * q^76 - 8 * q^77 - 6 * q^78 - 6 * q^79 - 40 * q^80 + 28 * q^81 - 99 * q^82 + 10 * q^83 + 54 * q^84 + 24 * q^85 - 314 * q^86 - 40 * q^88 + 20 * q^90 - 34 * q^91 + 14 * q^92 - 2 * q^93 - 152 * q^94 - 24 * q^95 - 10 * q^96 - 156 * q^98

Introduction

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