LMFDB - Embedded newform 378.2.w.a.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	378.25
Dual form			378.2.w.a.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.06159 - 1.36859i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.03287 - 0.375933i) q^{5} +(-0.529482 + 1.64914i) q^{6} +(2.42642 - 1.05474i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.746062 - 2.90575i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.06159 - 1.36859i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.03287 - 0.375933i) q^{5} +(-0.529482 + 1.64914i) q^{6} +(2.42642 - 1.05474i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.746062 - 2.90575i) q^{9} +1.09915 q^{10} +(-0.159233 + 0.0579560i) q^{11} +(-0.0664874 - 1.73077i) q^{12} +(-0.287618 - 1.63116i) q^{13} +(-1.91935 + 1.82102i) q^{14} +(-1.61098 + 1.01448i) q^{15} +(0.173648 - 0.984808i) q^{16} -0.472564 q^{17} +(1.69489 + 2.47534i) q^{18} +3.44629 q^{19} +(-1.03287 + 0.375933i) q^{20} +(1.13235 - 4.44047i) q^{21} +(0.129808 - 0.108922i) q^{22} +(-0.542547 - 3.07694i) q^{23} +(0.654437 + 1.60366i) q^{24} +(-2.90473 - 2.43736i) q^{25} +(0.828163 + 1.43442i) q^{26} +(-4.76878 - 2.06366i) q^{27} +(1.18077 - 2.36765i) q^{28} +(-0.0779750 + 0.442218i) q^{29} +(1.16685 - 1.50429i) q^{30} +(-0.580032 + 0.486705i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.0897218 + 0.279450i) q^{33} +(0.444065 - 0.161626i) q^{34} +(-2.90268 + 0.177240i) q^{35} +(-2.43930 - 1.74638i) q^{36} +(1.51353 - 2.62151i) q^{37} +(-3.23845 + 1.17870i) q^{38} +(-2.53772 - 1.33799i) q^{39} +(0.842001 - 0.706523i) q^{40} +(-0.223307 - 1.26644i) q^{41} +(0.454672 + 4.55996i) q^{42} +(4.12401 + 3.46045i) q^{43} +(-0.0847261 + 0.146750i) q^{44} +(-0.321785 + 3.28172i) q^{45} +(1.56220 + 2.70581i) q^{46} +(3.68973 + 3.09605i) q^{47} +(-1.16345 - 1.28311i) q^{48} +(4.77503 - 5.11851i) q^{49} +(3.56318 + 1.29689i) q^{50} +(-0.501668 + 0.646745i) q^{51} +(-1.26882 - 1.06467i) q^{52} +(1.65864 - 2.87284i) q^{53} +(5.18701 + 0.308185i) q^{54} +0.186254 q^{55} +(-0.299774 + 2.62871i) q^{56} +(3.65854 - 4.71655i) q^{57} +(-0.0779750 - 0.442218i) q^{58} +(-0.668971 - 3.79392i) q^{59} +(-0.581982 + 1.81265i) q^{60} +(10.4214 + 8.74459i) q^{61} +(0.378589 - 0.655736i) q^{62} +(-4.87509 - 6.26367i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.316137 + 1.79290i) q^{65} +(-0.0112664 - 0.293283i) q^{66} +(-12.6258 - 4.59541i) q^{67} +(-0.362005 + 0.303758i) q^{68} +(-4.78702 - 2.52392i) q^{69} +(2.66701 - 1.15933i) q^{70} +(6.29081 + 10.8960i) q^{71} +(2.88949 + 0.806767i) q^{72} +(6.92519 + 11.9948i) q^{73} +(-0.525642 + 2.98107i) q^{74} +(-6.41937 + 1.38791i) q^{75} +(2.64001 - 2.21523i) q^{76} +(-0.325237 + 0.308576i) q^{77} +(2.84230 + 0.389350i) q^{78} +(-2.28827 + 0.832864i) q^{79} +(-0.549577 + 0.951896i) q^{80} +(-7.88678 + 4.33574i) q^{81} +(0.642986 + 1.11368i) q^{82} +(-2.32492 + 13.1853i) q^{83} +(-1.98685 - 4.12946i) q^{84} +(0.488096 + 0.177652i) q^{85} +(-5.05885 - 1.84127i) q^{86} +(0.522437 + 0.576169i) q^{87} +(0.0294251 - 0.166878i) q^{88} +0.874725 q^{89} +(-0.820037 - 3.19387i) q^{90} +(-2.41834 - 3.65452i) q^{91} +(-2.39343 - 2.00833i) q^{92} +(0.0503428 + 1.31050i) q^{93} +(-4.52612 - 1.64737i) q^{94} +(-3.55956 - 1.29557i) q^{95} +(1.53214 + 0.807807i) q^{96} +(3.50823 + 2.94375i) q^{97} +(-2.73643 + 6.44298i) q^{98} +(0.287203 + 0.419452i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.06159	−	1.36859i	0.612908	−	0.790154i
$3$	1.06159	−	1.36859i	0.612908	−	0.790154i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−1.03287	−	0.375933i	−0.461912	−	0.168122i	0.100573	−	0.994930i	$-0.467932\pi$
$5$	−1.03287	−	0.375933i	−0.461912	−	0.168122i	−0.562485	+	0.826807i	$0.690155\pi$
$6$	−0.529482	+	1.64914i	−0.216160	+	0.673257i
$7$	2.42642	−	1.05474i	0.917101	−	0.398656i
$7$	2.42642	−	1.05474i	0.917101	−	0.398656i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.746062	−	2.90575i	−0.248687	−	0.968584i
$10$	1.09915			0.347583
$11$	−0.159233	+	0.0579560i	−0.0480105	+	0.0174744i	−0.365914	−	0.930649i	$-0.619243\pi$
$11$	−0.159233	+	0.0579560i	−0.0480105	+	0.0174744i	0.317903	+	0.948123i	$0.397021\pi$
$12$	−0.0664874	−	1.73077i	−0.0191933	−	0.499631i
$13$	−0.287618	−	1.63116i	−0.0797709	−	0.452403i	−0.998363	−	0.0571961i	$-0.981784\pi$
$13$	−0.287618	−	1.63116i	−0.0797709	−	0.452403i	0.918592	−	0.395207i	$-0.129327\pi$
$14$	−1.91935	+	1.82102i	−0.512967	+	0.486688i
$15$	−1.61098	+	1.01448i	−0.415952	+	0.261938i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.472564			−0.114614			−0.0573068	−	0.998357i	$-0.518251\pi$
$17$	−0.472564			−0.114614			−0.0573068	+	0.998357i	$0.518251\pi$
$18$	1.69489	+	2.47534i	0.399490	+	0.583444i
$19$	3.44629			0.790633			0.395316	−	0.918545i	$-0.370635\pi$
$19$	3.44629			0.790633			0.395316	+	0.918545i	$0.370635\pi$
$20$	−1.03287	+	0.375933i	−0.230956	+	0.0840612i
$21$	1.13235	−	4.44047i	0.247099	−	0.968990i
$22$	0.129808	−	0.108922i	0.0276751	−	0.0232222i
$23$	−0.542547	−	3.07694i	−0.113129	−	0.641585i	−0.987660	−	0.156616i	$-0.949942\pi$
$23$	−0.542547	−	3.07694i	−0.113129	−	0.641585i	0.874531	−	0.484970i	$-0.161169\pi$
$24$	0.654437	+	1.60366i	0.133586	+	0.327345i
$25$	−2.90473	−	2.43736i	−0.580947	−	0.487472i
$26$	0.828163	+	1.43442i	0.162416	+	0.281313i
$27$	−4.76878	−	2.06366i	−0.917753	−	0.397151i
$28$	1.18077	−	2.36765i	0.223144	−	0.447445i
$29$	−0.0779750	+	0.442218i	−0.0144796	+	0.0821179i	−0.991191	−	0.132438i	$-0.957719\pi$
$29$	−0.0779750	+	0.442218i	−0.0144796	+	0.0821179i	0.976712	+	0.214556i	$0.0688305\pi$
$30$	1.16685	−	1.50429i	0.213037	−	0.274644i
$31$	−0.580032	+	0.486705i	−0.104177	+	0.0874148i	−0.693388	−	0.720564i	$-0.743883\pi$
$31$	−0.580032	+	0.486705i	−0.104177	+	0.0874148i	0.589211	+	0.807979i	$0.299438\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−0.0897218	+	0.279450i	−0.0156186	+	0.0486459i
$34$	0.444065	−	0.161626i	0.0761565	−	0.0277187i
$35$	−2.90268	+	0.177240i	−0.490643	+	0.0299590i
$36$	−2.43930	−	1.74638i	−0.406550	−	0.291063i
$37$	1.51353	−	2.62151i	0.248822	−	0.430973i	−0.714377	−	0.699761i	$-0.753290\pi$
$37$	1.51353	−	2.62151i	0.248822	−	0.430973i	0.963199	+	0.268788i	$0.0866231\pi$
$38$	−3.23845	+	1.17870i	−0.525346	+	0.191210i
$39$	−2.53772	−	1.33799i	−0.406360	−	0.214250i
$40$	0.842001	−	0.706523i	0.133132	−	0.111711i
$41$	−0.223307	−	1.26644i	−0.0348747	−	0.197784i	0.962393	−	0.271662i	$-0.0875734\pi$
$41$	−0.223307	−	1.26644i	−0.0348747	−	0.197784i	−0.997267	+	0.0738784i	$0.976462\pi$
$42$	0.454672	+	4.55996i	0.0701574	+	0.703618i
$43$	4.12401	+	3.46045i	0.628905	+	0.527714i	0.900589	−	0.434672i	$-0.143136\pi$
$43$	4.12401	+	3.46045i	0.628905	+	0.527714i	−0.271683	+	0.962387i	$0.587580\pi$
$44$	−0.0847261	+	0.146750i	−0.0127729	+	0.0221234i
$45$	−0.321785	+	3.28172i	−0.0479688	+	0.489211i
$46$	1.56220	+	2.70581i	0.230334	+	0.398950i
$47$	3.68973	+	3.09605i	0.538202	+	0.451605i	0.870923	−	0.491420i	$-0.163522\pi$
$47$	3.68973	+	3.09605i	0.538202	+	0.451605i	−0.332720	+	0.943026i	$0.607966\pi$
$48$	−1.16345	−	1.28311i	−0.167930	−	0.185201i
$49$	4.77503	−	5.11851i	0.682147	−	0.731215i
$50$	3.56318	+	1.29689i	0.503910	+	0.183408i
$51$	−0.501668	+	0.646745i	−0.0702476	+	0.0905624i
$52$	−1.26882	−	1.06467i	−0.175954	−	0.147643i
$53$	1.65864	−	2.87284i	0.227831	−	0.394616i	−0.729334	−	0.684158i	$-0.760170\pi$
$53$	1.65864	−	2.87284i	0.227831	−	0.394616i	0.957165	+	0.289543i	$0.0935032\pi$
$54$	5.18701	+	0.308185i	0.705862	+	0.0419387i
$55$	0.186254			0.0251145
$56$	−0.299774	+	2.62871i	−0.0400590	+	0.351277i
$57$	3.65854	−	4.71655i	0.484585	−	0.624722i
$58$	−0.0779750	−	0.442218i	−0.0102386	−	0.0580661i
$59$	−0.668971	−	3.79392i	−0.0870926	−	0.493927i	−0.996885	−	0.0788639i	$-0.974871\pi$
$59$	−0.668971	−	3.79392i	−0.0870926	−	0.493927i	0.909793	−	0.415063i	$-0.136240\pi$
$60$	−0.581982	+	1.81265i	−0.0751336	+	0.234013i
$61$	10.4214	+	8.74459i	1.33432	+	1.11963i	0.983046	+	0.183359i	$0.0586969\pi$
$61$	10.4214	+	8.74459i	1.33432	+	1.11963i	0.351277	+	0.936272i	$0.385748\pi$
$62$	0.378589	−	0.655736i	0.0480809	−	0.0832785i
$63$	−4.87509	−	6.26367i	−0.614203	−	0.789148i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.316137	+	1.79290i	−0.0392119	+	0.222382i
$66$	−0.0112664	−	0.293283i	−0.00138680	−	0.0361007i
$67$	−12.6258	−	4.59541i	−1.54248	−	0.561418i	−0.575844	−	0.817559i	$-0.695327\pi$
$67$	−12.6258	−	4.59541i	−1.54248	−	0.561418i	−0.966639	+	0.256141i	$0.917549\pi$
$68$	−0.362005	+	0.303758i	−0.0438996	+	0.0368361i
$69$	−4.78702	−	2.52392i	−0.576289	−	0.303844i
$70$	2.66701	−	1.15933i	0.318769	−	0.138566i
$71$	6.29081	+	10.8960i	0.746581	+	1.29312i	0.949452	+	0.313911i	$0.101639\pi$
$71$	6.29081	+	10.8960i	0.746581	+	1.29312i	−0.202871	+	0.979205i	$0.565027\pi$
$72$	2.88949	+	0.806767i	0.340529	+	0.0950784i
$73$	6.92519	+	11.9948i	0.810532	+	1.40388i	0.912492	+	0.409094i	$0.134155\pi$
$73$	6.92519	+	11.9948i	0.810532	+	1.40388i	−0.101960	+	0.994788i	$0.532511\pi$
$74$	−0.525642	+	2.98107i	−0.0611047	+	0.346542i
$75$	−6.41937	+	1.38791i	−0.741245	+	0.160262i
$76$	2.64001	−	2.21523i	0.302830	−	0.254105i
$77$	−0.325237	+	0.308576i	−0.0370642	+	0.0351655i
$78$	2.84230	+	0.389350i	0.321827	+	0.0440852i
$79$	−2.28827	+	0.832864i	−0.257451	+	0.0937045i	−0.467521	−	0.883982i	$-0.654853\pi$
$79$	−2.28827	+	0.832864i	−0.257451	+	0.0937045i	0.210070	+	0.977686i	$0.432631\pi$
$80$	−0.549577	+	0.951896i	−0.0614446	+	0.106425i
$81$	−7.88678	+	4.33574i	−0.876309	+	0.481749i
$82$	0.642986	+	1.11368i	0.0710060	+	0.122986i
$83$	−2.32492	+	13.1853i	−0.255193	+	1.44727i	0.540383	+	0.841419i	$0.318279\pi$
$83$	−2.32492	+	13.1853i	−0.255193	+	1.44727i	−0.795576	+	0.605853i	$0.792832\pi$
$84$	−1.98685	−	4.12946i	−0.216783	−	0.450561i
$85$	0.488096	+	0.177652i	0.0529414	+	0.0192691i
$86$	−5.05885	−	1.84127i	−0.545509	−	0.198549i
$87$	0.522437	+	0.576169i	0.0560111	+	0.0617718i
$88$	0.0294251	−	0.166878i	0.00313672	−	0.0177892i
$89$	0.874725			0.0927207			0.0463603	−	0.998925i	$-0.485238\pi$
$89$	0.874725			0.0927207			0.0463603	+	0.998925i	$0.485238\pi$
$90$	−0.820037	−	3.19387i	−0.0864395	−	0.336663i
$91$	−2.41834	−	3.65452i	−0.253511	−	0.383098i
$92$	−2.39343	−	2.00833i	−0.249532	−	0.209383i
$93$	0.0503428	+	1.31050i	0.00522031	+	0.135893i
$94$	−4.52612	−	1.64737i	−0.466834	−	0.169914i
$95$	−3.55956	−	1.29557i	−0.365203	−	0.132923i
$96$	1.53214	+	0.807807i	0.156373	+	0.0824465i
$97$	3.50823	+	2.94375i	0.356207	+	0.298893i	0.803277	−	0.595606i	$-0.203088\pi$
$97$	3.50823	+	2.94375i	0.356207	+	0.298893i	−0.447070	+	0.894499i	$0.647533\pi$
$98$	−2.73643	+	6.44298i	−0.276421	+	0.650839i
$99$	0.287203	+	0.419452i	0.0288650	+	0.0421566i
$100$	−3.79186			−0.379186
$101$	−3.07689	+	17.4499i	−0.306162	+	1.73633i	0.311820	+	0.950141i	$0.399061\pi$
$101$	−3.07689	+	17.4499i	−0.306162	+	1.73633i	−0.617982	+	0.786192i	$0.712050\pi$
$102$	0.250214	−	0.779322i	0.0247749	−	0.0771644i
$103$	4.97210	+	1.80970i	0.489916	+	0.178315i	0.575153	−	0.818046i	$-0.304943\pi$
$103$	4.97210	+	1.80970i	0.489916	+	0.178315i	−0.0852371	+	0.996361i	$0.527165\pi$
$104$	1.55644	+	0.566497i	0.152621	+	0.0555496i
$105$	−2.83888	+	4.16073i	−0.277047	+	0.406046i
$106$	−0.576039	+	3.26688i	−0.0559498	+	0.317307i
$107$	−3.85697	−	6.68047i	−0.372867	−	0.645825i	0.617138	−	0.786855i	$-0.288292\pi$
$107$	−3.85697	−	6.68047i	−0.372867	−	0.645825i	−0.990005	+	0.141030i	$0.954959\pi$
$108$	−4.97960	+	1.48446i	−0.479162	+	0.142842i
$109$	−7.36169	+	12.7508i	−0.705122	+	1.22131i	0.261525	+	0.965197i	$0.415774\pi$
$109$	−7.36169	+	12.7508i	−0.705122	+	1.22131i	−0.966647	+	0.256111i	$0.917559\pi$
$110$	−0.175022	+	0.0637026i	−0.0166876	+	0.00607381i
$111$	−1.98102	−	4.85435i	−0.188030	−	0.460755i
$112$	−0.617377	−	2.57271i	−0.0583367	−	0.243098i
$113$	9.21111	−	7.72904i	0.866508	−	0.727087i	−0.0968515	−	0.995299i	$-0.530877\pi$
$113$	9.21111	−	7.72904i	0.866508	−	0.727087i	0.963360	+	0.268212i	$0.0864327\pi$
$114$	−1.82475	+	5.68340i	−0.170903	+	0.532299i
$115$	−0.596343	+	3.38203i	−0.0556092	+	0.315376i
$116$	0.224520	+	0.388880i	0.0208462	+	0.0361066i
$117$	−4.52517	+	2.05269i	−0.418352	+	0.189772i
$118$	1.92623	+	3.33632i	0.177323	+	0.307133i
$119$	−1.14664	+	0.498434i	−0.105112	+	0.0456914i
$120$	−0.0730799	−	1.90239i	−0.00667125	−	0.173663i
$121$	−8.40449	+	7.05221i	−0.764045	+	0.641110i
$122$	−12.7837	−	4.65290i	−1.15739	−	0.421254i
$123$	−1.97029	−	1.03882i	−0.177655	−	0.0936671i
$124$	−0.131483	+	0.745675i	−0.0118075	+	0.0669636i
$125$	4.83181	+	8.36893i	0.432170	+	0.748540i
$126$	6.72338	+	4.21855i	0.598967	+	0.375818i
$127$	−3.22819	+	5.59139i	−0.286455	+	0.496155i	−0.972961	−	0.230969i	$-0.925810\pi$
$127$	−3.22819	+	5.59139i	−0.286455	+	0.496155i	0.686506	+	0.727125i	$0.259144\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	9.11393	−	1.97049i	0.802437	−	0.173492i
$130$	−0.316137	−	1.79290i	−0.0277270	−	0.157248i
$131$	−1.34999	−	7.65619i	−0.117949	−	0.668924i	−0.985248	−	0.171135i	$-0.945256\pi$
$131$	−1.34999	−	7.65619i	−0.117949	−	0.668924i	0.867298	−	0.497789i	$-0.165855\pi$
$132$	0.110896	+	0.271743i	0.00965224	+	0.0236522i
$133$	8.36214	−	3.63495i	0.725090	−	0.315191i
$134$	13.4361			1.16070
$135$	4.14972	+	3.92423i	0.357151	+	0.337744i
$136$	0.236282	−	0.409253i	0.0202610	−	0.0350931i
$137$	6.98707	+	5.86284i	0.596945	+	0.500897i	0.890462	−	0.455057i	$-0.150381\pi$
$137$	6.98707	+	5.86284i	0.596945	+	0.500897i	−0.293517	+	0.955954i	$0.594826\pi$
$138$	5.36155	+	0.734449i	0.456406	+	0.0625204i
$139$	−13.1927	−	4.80175i	−1.11899	−	0.407279i	−0.284706	−	0.958615i	$-0.591896\pi$
$139$	−13.1927	−	4.80175i	−1.11899	−	0.407279i	−0.834283	+	0.551336i	$0.814118\pi$
$140$	−2.10966	+	2.00158i	−0.178299	+	0.169165i
$141$	8.15419	−	1.76299i	0.686707	−	0.148470i
$142$	−9.63807	−	8.08730i	−0.808809	−	0.678671i
$143$	0.140334	+	0.243066i	0.0117353	+	0.0203262i
$144$	−2.99116	+	0.230149i	−0.249263	+	0.0191791i
$145$	0.246782	−	0.427439i	0.0204941	−	0.0354969i
$146$	−10.6100	−	8.90285i	−0.878090	−	0.736805i
$147$	−1.93601	−	11.9688i	−0.159680	−	0.987169i
$148$	−0.525642	−	2.98107i	−0.0432075	−	0.245042i
$149$	14.5467	−	12.2061i	1.19171	−	0.999963i	0.191881	−	0.981418i	$-0.438541\pi$
$149$	14.5467	−	12.2061i	1.19171	−	0.999963i	0.999828	−	0.0185445i	$-0.00590323\pi$
$150$	5.55754	−	3.49976i	0.453771	−	0.285754i
$151$	9.41977	−	3.42852i	0.766570	−	0.279009i	0.0710089	−	0.997476i	$-0.477378\pi$
$151$	9.41977	−	3.42852i	0.766570	−	0.279009i	0.695561	+	0.718467i	$0.255156\pi$
$152$	−1.72314	+	2.98457i	−0.139765	+	0.242081i
$153$	0.352562	+	1.37315i	0.0285030	+	0.111013i
$154$	0.200084	−	0.401204i	0.0161232	−	0.0323299i
$155$	0.782065	−	0.284648i	0.0628169	−	0.0228635i
$156$	−2.80405	+	0.606253i	−0.224504	+	0.0485391i
$157$	2.23334	+	12.6659i	0.178240	+	1.01085i	0.934337	+	0.356391i	$0.115993\pi$
$157$	2.23334	+	12.6659i	0.178240	+	1.01085i	−0.756097	+	0.654460i	$0.772896\pi$
$158$	1.86542	−	1.56527i	0.148405	−	0.124526i
$159$	−2.17095	−	5.31977i	−0.172167	−	0.421885i
$160$	0.190866	−	1.08246i	0.0150893	−	0.0855756i
$161$	−4.56183	−	6.89369i	−0.359522	−	0.543299i
$162$	5.92824	−	6.77170i	0.465767	−	0.532035i
$163$	−8.42123	−	14.5860i	−0.659601	−	1.14246i	−0.980719	−	0.195424i	$-0.937392\pi$
$163$	−8.42123	−	14.5860i	−0.659601	−	1.14246i	0.321117	−	0.947039i	$-0.395942\pi$
$164$	−0.985112	−	0.826607i	−0.0769243	−	0.0645472i
$165$	0.197725	−	0.254905i	0.0153929	−	0.0198443i
$166$	−2.32492	−	13.1853i	−0.180449	−	1.02338i
$167$	15.0551	−	12.6327i	1.16500	−	0.977551i	0.165038	−	0.986287i	$-0.447225\pi$
$167$	15.0551	−	12.6327i	1.16500	−	0.977551i	0.999962	+	0.00873601i	$0.00278079\pi$
$168$	3.27939	+	3.20088i	0.253010	+	0.246953i
$169$	9.63804	−	3.50796i	0.741387	−	0.269843i
$170$	−0.519421			−0.0398378
$171$	−2.57115	−	10.0141i	−0.196620	−	0.765794i
$172$	5.38351			0.410489
$173$	2.73809	−	15.5285i	0.208173	−	1.18061i	−0.684195	−	0.729299i	$-0.739846\pi$
$173$	2.73809	−	15.5285i	0.208173	−	1.18061i	0.892368	−	0.451308i	$-0.149043\pi$
$174$	−0.687992	−	0.362738i	−0.0521565	−	0.0274991i
$175$	−9.61890	−	2.85031i	−0.727120	−	0.215463i
$176$	0.0294251	+	0.166878i	0.00221800	+	0.0125789i
$177$	−5.90249	−	3.11204i	−0.443658	−	0.233915i
$178$	−0.821973	+	0.299174i	−0.0616095	+	0.0224240i
$179$	12.2917			0.918727			0.459364	−	0.888248i	$-0.348077\pi$
$179$	12.2917			0.918727			0.459364	+	0.888248i	$0.348077\pi$
$180$	1.86295	+	2.72079i	0.138856	+	0.202795i
$181$	−9.45246	+	16.3721i	−0.702595	+	1.21693i	0.264957	+	0.964260i	$0.414642\pi$
$181$	−9.45246	+	16.3721i	−0.702595	+	1.21693i	−0.967552	+	0.252671i	$0.918691\pi$
$182$	3.52242	+	2.60701i	0.261099	+	0.193244i
$183$	23.0310	−	4.97944i	1.70250	−	0.368091i
$184$	2.93598	+	1.06861i	0.216443	+	0.0787789i
$185$	−2.54878	+	2.13868i	−0.187390	+	0.157239i
$186$	−0.495526	−	1.21425i	−0.0363337	−	0.0890334i
$187$	0.0752478	−	0.0273879i	0.00550266	−	0.00200280i
$188$	4.81660			0.351287
$189$	−13.7477	+	0.0225456i	−0.999999	+	0.00163995i
$190$	3.78800			0.274811
$191$	−4.83956	+	1.76146i	−0.350178	+	0.127455i	−0.511120	−	0.859509i	$-0.670769\pi$
$191$	−4.83956	+	1.76146i	−0.350178	+	0.127455i	0.160941	+	0.986964i	$0.448547\pi$
$192$	−1.71603	−	0.235068i	−0.123843	−	0.0169646i
$193$	8.91438	−	7.48006i	0.641671	−	0.538426i	−0.262860	−	0.964834i	$-0.584666\pi$
$193$	8.91438	−	7.48006i	0.641671	−	0.538426i	0.904531	+	0.426408i	$0.140221\pi$
$194$	−4.30348	−	1.56634i	−0.308972	−	0.112457i
$195$	2.11813	+	2.33598i	0.151683	+	0.167283i
$196$	0.367771	−	6.99033i	0.0262693	−	0.499309i
$197$	6.23368	−	10.7971i	0.444132	−	0.769258i	−0.553860	−	0.832610i	$-0.686846\pi$
$197$	6.23368	−	10.7971i	0.444132	−	0.769258i	0.997991	+	0.0633516i	$0.0201790\pi$
$198$	−0.413344	−	0.295927i	−0.0293751	−	0.0210306i
$199$	6.55178			0.464444			0.232222	−	0.972663i	$-0.425400\pi$
$199$	6.55178			0.464444			0.232222	+	0.972663i	$0.425400\pi$
$200$	3.56318	−	1.29689i	0.251955	−	0.0917041i
$201$	−19.6926	+	12.4010i	−1.38901	+	0.874702i
$202$	−3.07689	−	17.4499i	−0.216490	−	1.22777i
$203$	0.277227	+	1.15525i	0.0194575	+	0.0810827i
$204$	0.0314196	+	0.817902i	0.00219981	+	0.0572646i
$205$	−0.245449	+	1.39201i	−0.0171429	+	0.0972221i
$206$	−5.29120			−0.368655
$207$	−8.53604	+	3.87209i	−0.593296	+	0.269129i
$208$	−1.65633			−0.114846
$209$	−0.548763	+	0.199733i	−0.0379587	+	0.0138158i
$210$	1.24463	−	4.88076i	0.0858873	−	0.336805i
$211$	−17.6296	+	14.7930i	−1.21367	+	1.01839i	−0.214539	+	0.976715i	$0.568825\pi$
$211$	−17.6296	+	14.7930i	−1.21367	+	1.01839i	−0.999131	+	0.0416751i	$0.986731\pi$
$212$	−0.576039	−	3.26688i	−0.0395625	−	0.224370i
$213$	21.5904	+	2.95754i	1.47935	+	0.202647i
$214$	5.90922	+	4.95842i	0.403946	+	0.338951i
$215$	−2.95865	−	5.12454i	−0.201779	−	0.349491i
$216$	4.17157	−	3.09806i	0.283840	−	0.210796i
$217$	−0.894052	+	1.79274i	−0.0606922	+	0.121699i
$218$	2.55669	−	14.4997i	0.173161	−	0.982044i
$219$	23.7676	+	3.25579i	1.60607	+	0.220006i
$220$	0.142679	−	0.119722i	0.00961941	−	0.00807164i
$221$	0.135918	+	0.770829i	0.00914283	+	0.0518516i
$222$	3.52183	+	3.88405i	0.236370	+	0.260680i
$223$	7.96272	−	2.89819i	0.533223	−	0.194077i	−0.0613537	−	0.998116i	$-0.519542\pi$
$223$	7.96272	−	2.89819i	0.533223	−	0.194077i	0.594577	+	0.804039i	$0.297320\pi$
$224$	1.46006	+	2.20640i	0.0975546	+	0.147421i
$225$	−4.91525	+	10.2589i	−0.327683	+	0.683924i
$226$	−6.01213	+	10.4133i	−0.399921	+	0.692683i
$227$	−14.3748	+	5.23198i	−0.954086	+	0.347259i	−0.771713	−	0.635971i	$-0.780600\pi$
$227$	−14.3748	+	5.23198i	−0.954086	+	0.347259i	−0.182373	+	0.983229i	$0.558378\pi$
$228$	−0.229135	−	5.96475i	−0.0151748	−	0.395025i
$229$	−15.5586	+	13.0552i	−1.02814	+	0.862711i	−0.990628	−	0.136585i	$-0.956387\pi$
$229$	−15.5586	+	13.0552i	−1.02814	+	0.862711i	−0.0375109	+	0.999296i	$0.511943\pi$
$230$	−0.596343	−	3.38203i	−0.0393217	−	0.223004i
$231$	0.0770451	+	0.772696i	0.00506919	+	0.0508396i
$232$	−0.343985	−	0.288637i	−0.0225837	−	0.0189500i
$233$	13.1134	−	22.7131i	0.859090	−	1.48799i	−0.0137081	−	0.999906i	$-0.504364\pi$
$233$	13.1134	−	22.7131i	0.859090	−	1.48799i	0.872798	−	0.488081i	$-0.162303\pi$
$234$	3.55021	−	3.47660i	0.232084	−	0.227273i
$235$	−2.64709	−	4.58490i	−0.172677	−	0.299086i
$236$	−2.95115	−	2.47631i	−0.192103	−	0.161194i
$237$	−1.28936	+	4.01586i	−0.0837528	+	0.260858i
$238$	0.907014	−	0.860549i	0.0587930	−	0.0557811i
$239$	−0.506479	−	0.184343i	−0.0327614	−	0.0119242i	0.325587	−	0.945512i	$-0.394438\pi$
$239$	−0.506479	−	0.184343i	−0.0327614	−	0.0119242i	−0.358349	+	0.933588i	$0.616660\pi$
$240$	0.719328	+	1.76267i	0.0464324	+	0.113780i
$241$	0.219569	+	0.184241i	0.0141437	+	0.0118680i	0.649832	−	0.760078i	$-0.274839\pi$
$241$	0.219569	+	0.184241i	0.0141437	+	0.0118680i	−0.635688	+	0.771946i	$0.719284\pi$
$242$	5.48564	−	9.50141i	0.352630	−	0.610774i
$243$	−2.43867	+	15.3965i	−0.156441	+	0.987687i
$244$	13.6042			0.870918
$245$	−6.85618	+	3.49165i	−0.438026	+	0.223073i
$246$	2.20676	+	0.302292i	0.140698	+	0.0192734i
$247$	−0.991215	−	5.62146i	−0.0630695	−	0.357685i
$248$	−0.131483	−	0.745675i	−0.00834915	−	0.0473504i
$249$	15.5771	+	17.1792i	0.987158	+	1.08869i
$250$	−7.40276	−	6.21165i	−0.468191	−	0.392859i
$251$	−12.1666	+	21.0732i	−0.767952	+	1.33013i	0.170720	+	0.985320i	$0.445391\pi$
$251$	−12.1666	+	21.0732i	−0.767952	+	1.33013i	−0.938672	+	0.344812i	$0.887943\pi$
$252$	−7.76074	−	1.66460i	−0.488881	−	0.104860i
$253$	0.264718	+	0.458506i	0.0166427	+	0.0288260i
$254$	1.12114	−	6.35829i	0.0703465	−	0.398955i
$255$	0.761290	−	0.479408i	0.0476738	−	0.0300217i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	7.99484	−	6.70847i	0.498704	−	0.418463i	−0.358429	−	0.933557i	$-0.616688\pi$
$257$	7.99484	−	6.70847i	0.498704	−	0.418463i	0.857134	+	0.515094i	$0.172243\pi$
$258$	−7.89035	+	4.96880i	−0.491232	+	0.309344i
$259$	0.907433	−	7.95726i	0.0563852	−	0.494440i
$260$	0.910279	+	1.57665i	0.0564531	+	0.0977796i
$261$	1.34315	−	0.103346i	0.0831389	−	0.00639698i
$262$	3.88715	+	6.73274i	0.240149	+	0.415950i
$263$	2.89112	−	16.3964i	0.178274	−	1.01104i	−0.756022	−	0.654546i	$-0.772860\pi$
$263$	2.89112	−	16.3964i	0.178274	−	1.01104i	0.934296	−	0.356498i	$-0.116029\pi$
$264$	−0.197149	−	0.217426i	−0.0121337	−	0.0133817i
$265$	−2.79315	+	2.34373i	−0.171582	+	0.143974i
$266$	−6.61462	+	6.27576i	−0.405568	+	0.384792i
$267$	0.928598	−	1.19714i	0.0568293	−	0.0732636i
$268$	−12.6258	+	4.59541i	−0.771242	+	0.280709i
$269$	−13.2443	+	22.9398i	−0.807520	+	1.39867i	0.107056	+	0.994253i	$0.465858\pi$
$269$	−13.2443	+	22.9398i	−0.807520	+	1.39867i	−0.914576	+	0.404413i	$0.867476\pi$
$270$	−5.24163	−	2.26828i	−0.318995	−	0.138043i
$271$	−5.73988	−	9.94176i	−0.348673	−	0.603919i	0.637341	−	0.770582i	$-0.280034\pi$
$271$	−5.73988	−	9.94176i	−0.348673	−	0.603919i	−0.986014	+	0.166663i	$0.946701\pi$
$272$	−0.0820599	+	0.465385i	−0.00497561	+	0.0282181i
$273$	−7.56881	−	0.569884i	−0.458085	−	0.0344910i
$274$	−8.57091	−	3.11955i	−0.517787	−	0.188459i
$275$	0.603789	+	0.219761i	0.0364098	+	0.0132521i
$276$	−5.28941	+	1.14360i	−0.318385	+	0.0688368i
$277$	2.90525	−	16.4765i	0.174560	−	0.989977i	−0.764091	−	0.645108i	$-0.776812\pi$
$277$	2.90525	−	16.4765i	0.174560	−	0.989977i	0.938651	−	0.344869i	$-0.112077\pi$
$278$	14.0394			0.842026
$279$	1.84698	+	1.32232i	0.110576	+	0.0791651i
$280$	1.29785	−	2.60242i	0.0775612	−	0.155524i
$281$	−21.5705	−	18.0998i	−1.28679	−	1.07974i	−0.992270	−	0.124096i	$-0.960397\pi$
$281$	−21.5705	−	18.0998i	−1.28679	−	1.07974i	−0.294516	−	0.955646i	$-0.595159\pi$
$282$	−7.05945	+	4.44556i	−0.420384	+	0.264729i
$283$	−7.20071	−	2.62084i	−0.428038	−	0.155793i	0.119012	−	0.992893i	$-0.462027\pi$
$283$	−7.20071	−	2.62084i	−0.428038	−	0.155793i	−0.547050	+	0.837100i	$0.684249\pi$
$284$	11.8228	+	4.30316i	0.701557	+	0.255346i
$285$	−5.55189	+	3.49620i	−0.328866	+	0.207097i
$286$	−0.215004	−	0.180410i	−0.0127135	−	0.0106679i
$287$	−1.87760	−	2.83737i	−0.110831	−	0.167485i
$288$	2.73205	−	1.23931i	0.160988	−	0.0730268i
$289$	−16.7767			−0.986864
$290$	−0.0857066	+	0.486066i	−0.00503286	+	0.0285428i
$291$	7.75307	−	1.67626i	0.454493	−	0.0982643i
$292$	13.0151	+	4.73711i	0.761651	+	0.277218i
$293$	13.7871	+	5.01809i	0.805450	+	0.293160i	0.711743	−	0.702440i	$-0.247906\pi$
$293$	13.7871	+	5.01809i	0.805450	+	0.293160i	0.0937071	+	0.995600i	$0.470128\pi$
$294$	5.91282	+	10.5848i	0.344843	+	0.617320i
$295$	−0.735302	+	4.17011i	−0.0428110	+	0.242793i
$296$	1.51353	+	2.62151i	0.0879720	+	0.152372i
$297$	0.878949	+	0.0522226i	0.0510018	+	0.00303026i
$298$	−9.49466	+	16.4452i	−0.550011	+	0.952647i
$299$	−4.86294	+	1.76996i	−0.281231	+	0.102360i
$300$	−4.02539	+	5.18949i	−0.232406	+	0.299615i
$301$	13.6565	+	4.04674i	0.787146	+	0.233250i
$302$	−7.67907	+	6.44350i	−0.441881	+	0.370782i
$303$	20.6154	+	22.7356i	1.18432	+	1.30613i
$304$	0.598442	−	3.39393i	0.0343230	−	0.194655i
$305$	−7.47654	−	12.9497i	−0.428105	−	0.741500i
$306$	−0.800946	−	1.16976i	−0.0457871	−	0.0668707i
$307$	−1.07222	−	1.85714i	−0.0611948	−	0.105993i	0.833805	−	0.552059i	$-0.186158\pi$
$307$	−1.07222	−	1.85714i	−0.0611948	−	0.105993i	−0.895000	+	0.446067i	$0.852824\pi$
$308$	−0.0507974	+	0.445441i	−0.00289445	+	0.0253814i
$309$	7.75505	−	4.88360i	0.441169	−	0.277818i
$310$	−0.637545	+	0.534964i	−0.0362101	+	0.0303839i
$311$	−30.7322	−	11.1856i	−1.74266	−	0.634278i	−0.743267	−	0.668994i	$-0.766725\pi$
$311$	−30.7322	−	11.1856i	−1.74266	−	0.634278i	−0.999397	+	0.0347164i	$0.988947\pi$
$312$	2.42760	−	1.52873i	0.137436	−	0.0865475i
$313$	−1.68690	+	9.56689i	−0.0953493	+	0.540752i	0.899291	+	0.437352i	$0.144084\pi$
$313$	−1.68690	+	9.56689i	−0.0953493	+	0.540752i	−0.994640	+	0.103401i	$0.967028\pi$
$314$	−6.43066	−	11.1382i	−0.362903	−	0.628567i
$315$	2.68060	+	8.30224i	0.151035	+	0.467778i
$316$	−1.21757	+	2.10889i	−0.0684934	+	0.118634i
$317$	16.4989	+	13.8442i	0.926668	+	0.777567i	0.975216	−	0.221254i	$-0.0710149\pi$
$317$	16.4989	+	13.8442i	0.926668	+	0.777567i	−0.0485479	+	0.998821i	$0.515459\pi$
$318$	3.85949	+	4.25644i	0.216430	+	0.238689i
$319$	−0.0132130	−	0.0749348i	−0.000739788	−	0.00419554i
$320$	0.190866	+	1.08246i	0.0106697	+	0.0605111i
$321$	−13.2373	−	1.81330i	−0.738835	−	0.101209i
$322$	6.64450	+	4.91771i	0.370283	+	0.274053i
$323$	−1.62859			−0.0906173
$324$	−3.25466	+	8.39090i	−0.180815	+	0.466161i
$325$	−3.14028	+	5.43912i	−0.174191	+	0.301708i
$326$	12.9021	+	10.8261i	0.714580	+	0.599603i
$327$	9.63553	+	23.6112i	0.532846	+	1.30570i
$328$	1.20842	+	0.439828i	0.0667238	+	0.0242855i
$329$	12.2184	+	3.62060i	0.673621	+	0.199610i
$330$	−0.0986181	+	0.307158i	−0.00542875	+	0.0169085i
$331$	−19.9460	−	16.7367i	−1.09633	−	0.919931i	−0.0991579	−	0.995072i	$-0.531615\pi$
$331$	−19.9460	−	16.7367i	−1.09633	−	0.919931i	−0.997173	+	0.0751409i	$0.976059\pi$
$332$	6.69434	+	11.5949i	0.367400	+	0.636355i
$333$	−8.74663	−	2.44213i	−0.479312	−	0.133828i
$334$	−9.82653	+	17.0201i	−0.537684	+	0.931296i
$335$	11.3132	+	9.49289i	0.618105	+	0.518652i
$336$	−4.17638	−	1.88622i	−0.227840	−	0.102902i
$337$	1.28273	+	7.27473i	0.0698749	+	0.396280i	0.999607	+	0.0280428i	$0.00892747\pi$
$337$	1.28273	+	7.27473i	0.0698749	+	0.396280i	−0.929732	+	0.368237i	$0.879961\pi$
$338$	−7.85700	+	6.59281i	−0.427364	+	0.358601i
$339$	−0.799461	−	20.8113i	−0.0434208	−	1.13031i
$340$	0.488096	−	0.177652i	0.0264707	−	0.00963455i
$341$	0.0641527	−	0.111116i	0.00347406	−	0.00601726i
$342$	5.84110	+	8.53075i	0.315850	+	0.461290i
$343$	6.18750	−	17.4561i	0.334094	−	0.942540i
$344$	−5.05885	+	1.84127i	−0.272755	+	0.0992746i
$345$	3.99553	+	4.40647i	0.215112	+	0.237236i
$346$	2.73809	+	15.5285i	0.147200	+	0.834815i
$347$	−25.7687	+	21.6225i	−1.38334	+	1.16076i	−0.415377	+	0.909649i	$0.636350\pi$
$347$	−25.7687	+	21.6225i	−1.38334	+	1.16076i	−0.967959	+	0.251108i	$0.919205\pi$
$348$	0.770564	+	0.105555i	0.0413066	+	0.00565835i
$349$	3.70140	−	20.9917i	0.198132	−	1.12366i	−0.709756	−	0.704447i	$-0.751195\pi$
$349$	3.70140	−	20.9917i	0.198132	−	1.12366i	0.907888	−	0.419213i	$-0.137694\pi$
$350$	10.0137	−	0.611442i	0.535253	−	0.0326830i
$351$	−1.99458	+	8.37221i	−0.106463	+	0.446875i
$352$	−0.0847261	−	0.146750i	−0.00451591	−	0.00782179i
$353$	−15.9423	−	13.3772i	−0.848521	−	0.711994i	0.110942	−	0.993827i	$-0.464613\pi$
$353$	−15.9423	−	13.3772i	−0.848521	−	0.711994i	−0.959463	+	0.281833i	$0.909058\pi$
$354$	6.61090	+	0.905590i	0.351365	+	0.0481315i
$355$	−2.40140	−	13.6190i	−0.127453	−	0.722823i
$356$	0.670078	−	0.562263i	0.0355141	−	0.0297999i
$357$	−0.535107	+	2.09841i	−0.0283209	+	0.111060i
$358$	−11.5505	+	4.20402i	−0.610460	+	0.222189i
$359$	23.3423			1.23196			0.615979	−	0.787762i	$-0.288761\pi$
$359$	23.3423			1.23196			0.615979	+	0.787762i	$0.288761\pi$
$360$	−2.68116	−	1.91954i	−0.141310	−	0.101168i
$361$	−7.12309			−0.374900
$362$	3.28280	−	18.6177i	0.172540	−	0.978525i
$363$	0.729452	+	18.9888i	0.0382863	+	0.996655i
$364$	−4.20164	−	1.24505i	−0.220226	−	0.0652581i
$365$	−2.64357	−	14.9924i	−0.138371	−	0.784739i
$366$	−19.9390	+	12.5562i	−1.04223	+	0.656323i
$367$	−7.36454	+	2.68047i	−0.384426	+	0.139920i	−0.527002	−	0.849864i	$-0.676684\pi$
$367$	−7.36454	+	2.68047i	−0.384426	+	0.139920i	0.142576	+	0.989784i	$0.454462\pi$
$368$	−3.12440			−0.162871
$369$	−3.51335	+	1.59371i	−0.182898	+	0.0829654i
$370$	1.66360	−	2.88144i	0.0864864	−	0.149799i
$371$	0.994434	−	8.72017i	0.0516284	−	0.452728i
$372$	0.880941	+	0.971545i	0.0456747	+	0.0503723i
$373$	22.8581	+	8.31966i	1.18355	+	0.430776i	0.857453	−	0.514562i	$-0.172045\pi$
$373$	22.8581	+	8.31966i	1.18355	+	0.430776i	0.326093	+	0.945338i	$0.394268\pi$
$374$	−0.0613425	+	0.0514725i	−0.00317195	+	0.00266158i
$375$	16.5830	+	2.27161i	0.856342	+	0.117305i
$376$	−4.52612	+	1.64737i	−0.233417	+	0.0849568i
$377$	0.743757			0.0383054
$378$	12.9109	−	4.72318i	0.664066	−	0.242934i
$379$	−8.45188			−0.434144			−0.217072	−	0.976156i	$-0.569651\pi$
$379$	−8.45188			−0.434144			−0.217072	+	0.976156i	$0.569651\pi$
$380$	−3.55956	+	1.29557i	−0.182602	+	0.0664615i
$381$	4.22530	+	10.3538i	0.216468	+	0.530442i
$382$	3.94525	−	3.31046i	0.201856	−	0.169378i
$383$	−2.56743	−	0.934469i	−0.131190	−	0.0477491i	0.275591	−	0.961275i	$-0.411126\pi$
$383$	−2.56743	−	0.934469i	−0.131190	−	0.0477491i	−0.406781	+	0.913526i	$0.633349\pi$
$384$	1.69293	−	0.366023i	0.0863922	−	0.0186785i
$385$	0.451930	−	0.196450i	0.0230325	−	0.0100120i
$386$	−5.81845	+	10.0779i	−0.296151	+	0.512949i
$387$	6.97845	−	14.5651i	0.354735	−	0.740383i
$388$	4.57967			0.232497
$389$	9.54703	−	3.47483i	0.484053	−	0.176181i	−0.0884545	−	0.996080i	$-0.528193\pi$
$389$	9.54703	−	3.47483i	0.484053	−	0.176181i	0.572508	+	0.819899i	$0.305971\pi$
$390$	−2.78935	−	1.47066i	−0.141244	−	0.0744698i
$391$	0.256388	+	1.45405i	0.0129661	+	0.0735344i
$392$	2.04524	+	6.69455i	0.103300	+	0.338126i
$393$	−11.9113	−	6.28014i	−0.600846	−	0.316791i
$394$	−2.16494	+	12.2780i	−0.109068	+	0.618555i
$395$	2.67658			0.134674
$396$	0.489629	+	0.136708i	0.0246048	+	0.00686985i
$397$	13.4477			0.674920			0.337460	−	0.941340i	$-0.390432\pi$
$397$	13.4477			0.674920			0.337460	+	0.941340i	$0.390432\pi$
$398$	−6.15666	+	2.24084i	−0.308606	+	0.112323i
$399$	3.90240	−	15.3031i	0.195364	−	0.766116i
$400$	−2.90473	+	2.43736i	−0.145237	+	0.121868i
$401$	0.634289	+	3.59723i	0.0316749	+	0.179637i	0.996541	−	0.0831058i	$-0.0264839\pi$
$401$	0.634289	+	3.59723i	0.0316749	+	0.179637i	−0.964866	+	0.262743i	$0.915373\pi$
$402$	14.2636	−	18.3884i	0.711402	−	0.917132i
$403$	0.960722	+	0.806142i	0.0478570	+	0.0401568i
$404$	8.85956	+	15.3452i	0.440780	+	0.763453i
$405$	9.77595	−	1.51334i	0.485771	−	0.0751987i
$406$	−0.655627	−	0.990764i	−0.0325382	−	0.0491708i
$407$	−0.0890712	+	0.505148i	−0.00441510	+	0.0250393i
$408$	−0.309264	−	0.757830i	−0.0153108	−	0.0375182i
$409$	25.9724	−	21.7935i	1.28425	−	1.07762i	0.291612	−	0.956537i	$-0.405809\pi$
$409$	25.9724	−	21.7935i	1.28425	−	1.07762i	0.992643	−	0.121080i	$-0.0386359\pi$
$410$	−0.245449	−	1.39201i	−0.0121218	−	0.0687464i
$411$	15.4412	−	3.33848i	0.761658	−	0.164675i
$412$	4.97210	−	1.80970i	0.244958	−	0.0891574i
$413$	−5.62482	−	8.50006i	−0.276780	−	0.418260i
$414$	6.69692	−	6.55807i	0.329136	−	0.322312i
$415$	7.35811	−	12.7446i	0.361196	−	0.625609i
$416$	1.55644	−	0.566497i	0.0763106	−	0.0277748i
$417$	−20.5768	+	12.9579i	−1.00765	+	0.634550i
$418$	0.447355	−	0.375376i	0.0218809	−	0.0183602i
$419$	2.40176	+	13.6211i	0.117334	+	0.665432i	0.985568	+	0.169278i	$0.0541437\pi$
$419$	2.40176	+	13.6211i	0.117334	+	0.665432i	−0.868235	+	0.496154i	$0.834745\pi$
$420$	0.499754	+	5.01210i	0.0243855	+	0.244566i
$421$	5.63925	+	4.73189i	0.274840	+	0.230618i	0.769781	−	0.638309i	$-0.220366\pi$
$421$	5.63925	+	4.73189i	0.274840	+	0.230618i	−0.494940	+	0.868927i	$0.664810\pi$
$422$	11.5069	−	19.9305i	0.560147	−	0.970203i
$423$	6.24359	−	13.0313i	0.303574	−	0.633603i
$424$	1.65864	+	2.87284i	0.0805506	+	0.139518i
$425$	1.37267	+	1.15181i	0.0665844	+	0.0558709i
$426$	−21.2998	+	4.60516i	−1.03198	+	0.223121i
$427$	34.5100	+	10.2261i	1.67006	+	0.494877i
$428$	−7.24873	−	2.63832i	−0.350381	−	0.127528i
$429$	0.481633	+	0.0659762i	0.0232535	+	0.00318536i
$430$	4.53292	+	3.80357i	0.218597	+	0.183425i
$431$	−5.43317	+	9.41053i	−0.261707	+	0.453289i	−0.966696	−	0.255929i	$-0.917619\pi$
$431$	−5.43317	+	9.41053i	−0.261707	+	0.453289i	0.704989	+	0.709218i	$0.250952\pi$
$432$	−2.86040	+	4.33799i	−0.137621	+	0.208711i
$433$	10.2657			0.493337			0.246669	−	0.969100i	$-0.420664\pi$
$433$	10.2657			0.493337			0.246669	+	0.969100i	$0.420664\pi$
$434$	0.226983	−	1.99040i	0.0108955	−	0.0955425i
$435$	−0.323007	−	0.791508i	−0.0154870	−	0.0379499i
$436$	2.55669	+	14.4997i	0.122443	+	0.694410i
$437$	−1.86977	−	10.6040i	−0.0894434	−	0.507259i
$438$	−23.4478	+	5.06956i	−1.12038	+	0.242233i
$439$	11.1094	+	9.32191i	0.530224	+	0.444911i	0.868179	−	0.496252i	$-0.165291\pi$
$439$	11.1094	+	9.32191i	0.530224	+	0.444911i	−0.337955	+	0.941162i	$0.609735\pi$
$440$	−0.0931270	+	0.161301i	−0.00443966	+	0.00768971i
$441$	−18.4356	−	10.0563i	−0.877885	−	0.478872i
$442$	−0.391360	−	0.677856i	−0.0186151	−	0.0322423i
$443$	−4.67429	+	26.5092i	−0.222082	+	1.25949i	0.646103	+	0.763251i	$0.276398\pi$
$443$	−4.67429	+	26.5092i	−0.222082	+	1.25949i	−0.868185	+	0.496241i	$0.834713\pi$
$444$	−4.63787	−	2.44528i	−0.220103	−	0.116048i
$445$	−0.903475	−	0.328838i	−0.0428288	−	0.0155884i
$446$	−6.49127	+	5.44682i	−0.307371	+	0.257914i
$447$	−1.26255	−	32.8662i	−0.0597166	−	1.55452i
$448$	−2.12665	−	1.57397i	−0.100475	−	0.0743630i
$449$	−6.94314	−	12.0259i	−0.327667	−	0.567536i	0.654382	−	0.756165i	$-0.272929\pi$
$449$	−6.94314	−	12.0259i	−0.327667	−	0.567536i	−0.982048	+	0.188629i	$0.939596\pi$
$450$	1.11009	−	11.3213i	0.0523302	−	0.533691i
$451$	0.108955	+	0.188716i	0.00513051	+	0.00888630i
$452$	2.08799	−	11.8416i	0.0982108	−	0.556981i
$453$	5.30769	−	16.5314i	0.249377	−	0.776715i
$454$	11.7184	−	9.83291i	0.549972	−	0.461481i
$455$	1.12397	+	4.68377i	0.0526926	+	0.219579i
$456$	2.25538	+	5.52666i	0.105618	+	0.258810i
$457$	−11.5787	+	4.21431i	−0.541629	+	0.197137i	−0.598323	−	0.801255i	$-0.704166\pi$
$457$	−11.5787	+	4.21431i	−0.541629	+	0.197137i	0.0566942	+	0.998392i	$0.481944\pi$
$458$	10.1551	−	17.5892i	0.474518	−	0.821890i
$459$	2.25356	+	0.975211i	0.105187	+	0.0455190i
$460$	1.71710	+	2.97411i	0.0800602	+	0.138668i
$461$	−4.32477	+	24.5270i	−0.201424	+	1.14233i	0.701543	+	0.712627i	$0.252495\pi$
$461$	−4.32477	+	24.5270i	−0.201424	+	1.14233i	−0.902968	+	0.429708i	$0.858616\pi$
$462$	−0.336676	−	0.699745i	−0.0156636	−	0.0325551i
$463$	−18.9395	−	6.89342i	−0.880194	−	0.320364i	−0.137906	−	0.990445i	$-0.544037\pi$
$463$	−18.9395	−	6.89342i	−0.880194	−	0.320364i	−0.742288	+	0.670081i	$0.766259\pi$
$464$	0.421960	+	0.153581i	0.0195890	+	0.00712981i
$465$	0.440664	−	1.37250i	0.0204353	−	0.0636483i
$466$	−4.55425	+	25.8284i	−0.210972	+	1.19648i
$467$	−15.6670			−0.724984			−0.362492	−	0.931987i	$-0.618074\pi$
$467$	−15.6670			−0.724984			−0.362492	+	0.931987i	$0.618074\pi$
$468$	−2.14704	+	4.48118i	−0.0992468	+	0.207143i
$469$	−35.4824	+	2.16658i	−1.63843	+	0.100043i
$470$	4.05558	+	3.40304i	0.187070	+	0.156970i
$471$	19.7053	+	10.3895i	0.907973	+	0.478721i
$472$	3.62012	+	1.31762i	0.166629	+	0.0606482i
$473$	−0.857232	−	0.312007i	−0.0394156	−	0.0143461i
$474$	−0.161906	−	4.21466i	−0.00743657	−	0.193586i
$475$	−10.0105	−	8.39985i	−0.459316	−	0.385411i
$476$	−0.557989	+	1.11887i	−0.0255754	+	0.0512832i
$477$	−9.58522	−	2.67627i	−0.438877	−	0.122538i
$478$	0.538983			0.0246525
$479$	2.35916	−	13.3795i	0.107793	−	0.611324i	−0.882275	−	0.470734i	$-0.843989\pi$
$479$	2.35916	−	13.3795i	0.107793	−	0.611324i	0.990068	−	0.140590i	$-0.0448998\pi$
$480$	−1.27881	−	1.41034i	−0.0583696	−	0.0643729i
$481$	−4.71142	−	1.71482i	−0.214822	−	0.0781889i
$482$	−0.269342	−	0.0980323i	−0.0122682	−	0.00446525i
$483$	−14.2774	−	1.07500i	−0.649644	−	0.0489141i
$484$	−1.90514	+	10.8046i	−0.0865974	+	0.491119i
$485$	−2.51688	−	4.35936i	−0.114286	−	0.197948i
$486$	−2.97432	−	15.3021i	−0.134918	−	0.694116i
$487$	0.510615	−	0.884411i	0.0231382	−	0.0400765i	−0.854224	−	0.519904i	$-0.825968\pi$
$487$	0.510615	−	0.884411i	0.0231382	−	0.0400765i	0.877363	+	0.479828i	$0.159301\pi$
$488$	−12.7837	+	4.65290i	−0.578693	+	0.210627i
$489$	−28.9021	−	3.95913i	−1.30700	−	0.179038i
$490$	5.24849	−	5.62603i	0.237103	−	0.254158i
$491$	−28.8407	+	24.2002i	−1.30156	+	1.09214i	−0.311691	+	0.950184i	$0.600895\pi$
$491$	−28.8407	+	24.2002i	−1.30156	+	1.09214i	−0.989873	+	0.141958i	$0.954660\pi$
$492$	−2.17707	+	0.470696i	−0.0981498	+	0.0212206i
$493$	0.0368482	−	0.208976i	0.00165956	−	0.00941183i
$494$	2.85409	+	4.94343i	0.128412	+	0.222415i
$495$	−0.138957	−	0.541208i	−0.00624566	−	0.0243255i
$496$	0.378589	+	0.655736i	0.0169992	+	0.0294434i
$497$	26.7566	+	19.8031i	1.20020	+	0.888289i
$498$	−20.5133	−	10.8155i	−0.919223	−	0.484653i
$499$	−16.2299	+	13.6185i	−0.726551	+	0.609649i	−0.929189	−	0.369605i	$-0.879493\pi$
$499$	−16.2299	+	13.6185i	−0.726551	+	0.609649i	0.202638	+	0.979254i	$0.435048\pi$
$500$	9.08082	+	3.30515i	0.406107	+	0.147811i
$501$	−1.30668	−	34.0150i	−0.0583782	−	1.51968i
$502$	4.22543	−	23.9636i	0.188590	−	1.06955i
$503$	19.9652	+	34.5807i	0.890202	+	1.54188i	0.839633	+	0.543155i	$0.182770\pi$
$503$	19.9652	+	34.5807i	0.890202	+	1.54188i	0.0505696	+	0.998721i	$0.483896\pi$
$504$	7.86204	−	1.09011i	0.350203	−	0.0485575i
$505$	9.73803	−	16.8668i	0.433337	−	0.750561i
$506$	−0.405572	−	0.340315i	−0.0180299	−	0.0151289i
$507$	5.43068	−	16.9145i	0.241185	−	0.751199i
$508$	1.12114	+	6.35829i	0.0497425	+	0.282104i
$509$	−0.476099	−	2.70009i	−0.0211027	−	0.119680i	0.972437	−	0.233167i	$-0.0749089\pi$
$509$	−0.476099	−	2.70009i	−0.0211027	−	0.119680i	−0.993539	+	0.113488i	$0.963798\pi$
$510$	−0.551411	+	0.710873i	−0.0244169	+	0.0314780i
$511$	29.4548	+	21.8001i	1.30301	+	0.964378i
$512$	1.00000			0.0441942
$513$	−16.4346	−	7.11197i	−0.725606	−	0.314001i
$514$	−5.21826	+	9.03829i	−0.230168	+	0.398662i
$515$	−4.45520	−	3.73835i	−0.196319	−	0.164732i
$516$	5.71507	−	7.36780i	0.251592	−	0.324350i
$517$	−0.766961	−	0.279151i	−0.0337309	−	0.0122771i
$518$	1.86883	+	7.78774i	0.0821119	+	0.342174i
$519$	−18.3453	−	20.2321i	−0.805271	−	0.888093i
$520$	−1.39463	−	1.17023i	−0.0611585	−	0.0513181i
$521$	−8.09607	−	14.0228i	−0.354695	−	0.614350i	0.632371	−	0.774666i	$-0.282082\pi$
$521$	−8.09607	−	14.0228i	−0.354695	−	0.614350i	−0.987066	+	0.160316i	$0.948749\pi$
$522$	−1.22680	+	0.556498i	−0.0536957	+	0.0243573i
$523$	2.04571	−	3.54327i	0.0894525	−	0.154936i	−0.817827	−	0.575464i	$-0.804822\pi$
$523$	2.04571	−	3.54327i	0.0894525	−	0.154936i	0.907280	+	0.420527i	$0.138155\pi$
$524$	−5.95546	−	4.99722i	−0.260165	−	0.218305i
$525$	−14.1122	+	10.1384i	−0.615907	+	0.442478i
$526$	2.89112	+	16.3964i	0.126059	+	0.714916i
$527$	0.274102	−	0.229999i	0.0119401	−	0.0100189i
$528$	0.259624	+	0.136885i	0.0112987	+	0.00595714i
$529$	12.4398	−	4.52770i	0.540859	−	0.196857i
$530$	1.82310	−	3.15770i	0.0791903	−	0.137162i
$531$	−10.5251	+	4.77437i	−0.456751	+	0.207190i
$532$	4.06927	−	8.15962i	0.176425	−	0.353764i
$533$	−2.00154	+	0.728499i	−0.0866961	+	0.0315548i
$534$	−0.463151	+	1.44254i	−0.0200425	+	0.0624248i
$535$	1.47233	+	8.35000i	0.0636544	+	0.361002i
$536$	10.2926	−	8.63654i	0.444574	−	0.373042i
$537$	13.0488	−	16.8223i	0.563096	−	0.725936i
$538$	4.59970	−	26.0862i	0.198307	−	1.12466i
$539$	−0.463693	+	1.09178i	−0.0199727	+	0.0470261i
$540$	5.70132	+	0.338743i	0.245346	+	0.0145772i
$541$	−6.03152	−	10.4469i	−0.259315	−	0.449148i	0.706743	−	0.707470i	$-0.250164\pi$
$541$	−6.03152	−	10.4469i	−0.259315	−	0.449148i	−0.966059	+	0.258323i	$0.916830\pi$
$542$	8.79400	+	7.37904i	0.377735	+	0.316957i
$543$	12.3721	+	30.3170i	0.530937	+	1.30103i
$544$	−0.0820599	−	0.465385i	−0.00351829	−	0.0199532i
$545$	12.3971	−	10.4024i	0.531034	−	0.445590i
$546$	7.30727	−	2.05317i	0.312722	−	0.0878676i
$547$	−16.1406	+	5.87469i	−0.690121	+	0.251184i	−0.663187	−	0.748454i	$-0.730797\pi$
$547$	−16.1406	+	5.87469i	−0.690121	+	0.251184i	−0.0269342	+	0.999637i	$0.508574\pi$
$548$	9.12097			0.389628
$549$	17.6346	−	36.8060i	0.752626	−	1.57084i
$550$	−0.642539			−0.0273979
$551$	−0.268724	+	1.52401i	−0.0114480	+	0.0649251i
$552$	4.57928	−	2.88372i	0.194907	−	0.122739i
$553$	−4.67386	+	4.43442i	−0.198753	+	0.188571i
$554$	2.90525	+	16.4765i	0.123432	+	0.700019i
$555$	0.221217	+	5.75863i	0.00939013	+	0.244440i
$556$	−13.1927	+	4.80175i	−0.559495	+	0.203639i
$557$	−23.3719			−0.990298			−0.495149	−	0.868808i	$-0.664886\pi$
$557$	−23.3719			−0.990298			−0.495149	+	0.868808i	$0.664886\pi$
$558$	−2.18786	−	0.610866i	−0.0926193	−	0.0258600i
$559$	4.45842	−	7.72222i	0.188571	−	0.326615i
$560$	−0.329498	+	2.88936i	−0.0139238	+	0.122098i
$561$	0.0423993	−	0.132058i	0.00179010	−	0.00557549i
$562$	26.4601	+	9.63069i	1.11615	+	0.406246i
$563$	27.7738	−	23.3050i	1.17053	−	0.982188i	0.170531	−	0.985352i	$-0.445452\pi$
$563$	27.7738	−	23.3050i	1.17053	−	0.982188i	0.999995	+	0.00316416i	$0.00100718\pi$
$564$	5.11325	−	6.59194i	0.215306	−	0.277571i
$565$	−12.4195	+	4.52031i	−0.522490	+	0.190171i
$566$	7.66284			0.322093
$567$	−14.5635	+	18.8389i	−0.611611	+	0.791158i
$568$	−12.5816			−0.527913
$569$	−21.4811	+	7.81848i	−0.900535	+	0.327768i	−0.750467	−	0.660908i	$-0.770171\pi$
$569$	−21.4811	+	7.81848i	−0.900535	+	0.327768i	−0.150068	+	0.988676i	$0.547949\pi$
$570$	4.02130	−	5.18421i	0.168434	−	0.217143i
$571$	28.8330	−	24.1938i	1.20662	−	1.01248i	0.207208	−	0.978297i	$-0.433562\pi$
$571$	28.8330	−	24.1938i	1.20662	−	1.01248i	0.999416	−	0.0341810i	$-0.0108823\pi$
$572$	0.263742	+	0.0959941i	0.0110276	+	0.00401371i
$573$	−2.72691	+	8.49330i	−0.113918	+	0.354813i
$574$	2.73481	+	2.02408i	0.114149	+	0.0844835i
$575$	−5.92365	+	10.2601i	−0.247033	+	0.427874i
$576$	−2.14342	+	2.09898i	−0.0893093	+	0.0874577i
$577$	38.6996			1.61109			0.805543	−	0.592537i	$-0.201874\pi$
$577$	38.6996			1.61109			0.805543	+	0.592537i	$0.201874\pi$
$578$	15.7649	−	5.73796i	0.655734	−	0.238668i
$579$	−0.773707	−	20.1408i	−0.0321542	−	0.837025i
$580$	−0.0857066	−	0.486066i	−0.00355877	−	0.0201828i
$581$	8.26587	+	34.4452i	0.342926	+	1.42903i
$582$	−6.71219	+	4.22688i	−0.278229	+	0.175210i
$583$	−0.0976110	+	0.553579i	−0.00404263	+	0.0229269i
$584$	−13.8504			−0.573133
$585$	5.44558	−	0.419000i	0.225147	−	0.0173235i
$586$	−14.6719			−0.606091
$587$	17.1717	−	6.24998i	0.708752	−	0.257964i	0.0376087	−	0.999293i	$-0.488026\pi$
$587$	17.1717	−	6.24998i	0.708752	−	0.257964i	0.671143	+	0.741328i	$0.265804\pi$
$588$	−9.17646	−	7.92418i	−0.378431	−	0.326788i
$589$	−1.99896	+	1.67733i	−0.0823656	+	0.0691130i
$590$	−0.735302	−	4.17011i	−0.0302719	−	0.171681i
$591$	−8.15911	−	19.9934i	−0.335621	−	0.822417i
$592$	−2.31886	−	1.94575i	−0.0953045	−	0.0799700i
$593$	−5.46834	−	9.47145i	−0.224558	−	0.388946i	0.731629	−	0.681703i	$-0.238760\pi$
$593$	−5.46834	−	9.47145i	−0.224558	−	0.388946i	−0.956187	+	0.292757i	$0.905427\pi$
$594$	−0.843803	+	0.251545i	−0.0346217	+	0.0103210i
$595$	1.37170	−	0.0837573i	0.0562344	−	0.00343371i
$596$	3.29746	−	18.7008i	0.135069	−	0.766016i
$597$	6.95530	−	8.96669i	0.284661	−	0.366982i
$598$	3.96430	−	3.32644i	0.162112	−	0.136028i
$599$	6.79812	+	38.5541i	0.277764	+	1.57528i	0.730044	+	0.683400i	$0.239500\pi$
$599$	6.79812	+	38.5541i	0.277764	+	1.57528i	−0.452280	+	0.891876i	$0.649389\pi$
$600$	2.00772	−	6.25329i	0.0819649	−	0.255290i
$601$	6.55427	−	2.38556i	0.267354	−	0.0973090i	−0.204865	−	0.978790i	$-0.565675\pi$
$601$	6.55427	−	2.38556i	0.267354	−	0.0973090i	0.472219	+	0.881481i	$0.343453\pi$
$602$	−14.2170	+	0.868098i	−0.579440	+	0.0353810i
$603$	−3.93350	+	40.1158i	−0.160184	+	1.63364i
$604$	5.01215	−	8.68131i	0.203942	−	0.353237i
$605$	11.3319	−	4.12447i	0.460707	−	0.167683i
$606$	−27.1481	−	14.3136i	−1.10282	−	0.581452i
$607$	−1.72282	+	1.44562i	−0.0699270	+	0.0586757i	−0.677081	−	0.735908i	$-0.736755\pi$
$607$	−1.72282	+	1.44562i	−0.0699270	+	0.0586757i	0.607154	+	0.794584i	$0.292311\pi$
$608$	0.598442	+	3.39393i	0.0242700	+	0.137642i
$609$	1.87536	+	0.846991i	0.0759935	+	0.0343218i
$610$	11.4547	+	9.61165i	0.463788	+	0.389165i
$611$	3.98893	−	6.90903i	0.161375	−	0.279509i
$612$	1.15272	+	0.825274i	0.0465961	+	0.0333597i
$613$	−23.5569	−	40.8018i	−0.951455	−	1.64797i	−0.742281	−	0.670089i	$-0.766256\pi$
$613$	−23.5569	−	40.8018i	−0.951455	−	1.64797i	−0.209174	−	0.977878i	$-0.567078\pi$
$614$	1.64274	+	1.37842i	0.0662954	+	0.0556285i
$615$	1.64452	+	1.81366i	0.0663134	+	0.0731337i
$616$	−0.104616	−	0.435951i	−0.00421509	−	0.0175650i
$617$	5.22382	+	1.90131i	0.210303	+	0.0765440i	0.445024	−	0.895519i	$-0.353195\pi$
$617$	5.22382	+	1.90131i	0.210303	+	0.0765440i	−0.234721	+	0.972063i	$0.575418\pi$
$618$	−5.61707	+	7.24147i	−0.225952	+	0.291295i
$619$	0.855491	+	0.717842i	0.0343851	+	0.0288525i	0.659818	−	0.751425i	$-0.270633\pi$
$619$	0.855491	+	0.717842i	0.0343851	+	0.0288525i	−0.625433	+	0.780278i	$0.715078\pi$
$620$	0.416128	−	0.720755i	0.0167121	−	0.0289462i
$621$	−3.76246	+	15.7929i	−0.150982	+	0.633746i
$622$	32.7046			1.31133
$623$	2.12245	−	0.922612i	0.0850342	−	0.0369637i
$624$	−1.75834	+	2.26683i	−0.0703898	+	0.0907457i
$625$	1.44779	+	8.21083i	0.0579117	+	0.328433i
$626$	−1.68690	−	9.56689i	−0.0674221	−	0.382370i
$627$	−0.309207	+	0.963064i	−0.0123486	+	0.0384611i
$628$	9.85234	+	8.26710i	0.393151	+	0.329893i
$629$	−0.715239	+	1.23883i	−0.0285184	+	0.0493954i
$630$	−5.35847	−	6.88474i	−0.213487	−	0.274295i
$631$	5.46231	+	9.46100i	0.217451	+	0.376636i	0.954028	−	0.299717i	$-0.0968924\pi$
$631$	5.46231	+	9.46100i	0.217451	+	0.376636i	−0.736577	+	0.676354i	$0.763559\pi$
$632$	0.422856	−	2.39814i	0.0168203	−	0.0953927i
$633$	1.53013	+	39.8317i	0.0608171	+	1.58317i
$634$	−20.2388	−	7.36634i	−0.803787	−	0.292555i
$635$	5.43628	−	4.56158i	0.215732	−	0.181021i
$636$	−5.08252	−	2.67972i	−0.201535	−	0.106258i
$637$	−9.72250	−	6.31667i	−0.385219	−	0.250276i
$638$	0.0380454	+	0.0658966i	0.00150623	+	0.00260887i
$639$	26.9677	−	26.4086i	1.06683	−	1.04471i
$640$	−0.549577	−	0.951896i	−0.0217239	−	0.0376270i
$641$	2.13971	−	12.1349i	0.0845136	−	0.479300i	−0.912947	−	0.408078i	$-0.866199\pi$
$641$	2.13971	−	12.1349i	0.0845136	−	0.479300i	0.997460	−	0.0712219i	$-0.0226898\pi$
$642$	13.0592	−	2.82348i	0.515405	−	0.111434i
$643$	−16.1026	+	13.5117i	−0.635025	+	0.532849i	−0.902486	−	0.430720i	$-0.858260\pi$
$643$	−16.1026	+	13.5117i	−0.635025	+	0.532849i	0.267461	+	0.963569i	$0.413815\pi$
$644$	−7.92574	−	2.34859i	−0.312318	−	0.0925473i
$645$	−10.1543	−	1.39097i	−0.399823	−	0.0547695i
$646$	1.53038	−	0.557011i	0.0602119	−	0.0219153i
$647$	−11.3848	+	19.7191i	−0.447584	+	0.775238i	−0.998228	−	0.0595021i	$-0.981049\pi$
$647$	−11.3848	+	19.7191i	−0.447584	+	0.775238i	0.550644	+	0.834740i	$0.314382\pi$
$648$	0.188528	−	8.99803i	0.00740610	−	0.353476i
$649$	0.326403	+	0.565346i	0.0128124	+	0.0221918i
$650$	1.09061	−	6.18514i	0.0427771	−	0.242601i
$651$	1.50440	+	3.12674i	0.0589621	+	0.122546i
$652$	−15.8267	−	5.76046i	−0.619823	−	0.225597i
$653$	−37.8717	−	13.7842i	−1.48203	−	0.539417i	−0.530696	−	0.847562i	$-0.678069\pi$
$653$	−37.8717	−	13.7842i	−1.48203	−	0.539417i	−0.951339	+	0.308146i	$0.900291\pi$
$654$	−17.1300	−	18.8918i	−0.669834	−	0.738726i
$655$	−1.48385	+	8.41533i	−0.0579788	+	0.328814i
$656$	−1.28597			−0.0502088
$657$	29.6872	−	29.0717i	1.15821	−	1.13420i
$658$	−12.7198	+	0.776683i	−0.495871	+	0.0302783i
$659$	−1.50385	−	1.26188i	−0.0585815	−	0.0491557i	0.613027	−	0.790062i	$-0.289952\pi$
$659$	−1.50385	−	1.26188i	−0.0585815	−	0.0491557i	−0.671608	+	0.740906i	$0.734396\pi$
$660$	−0.0123835	−	0.322364i	−0.000482029	−	0.0125480i
$661$	12.3055	+	4.47885i	0.478630	+	0.174207i	0.570058	−	0.821605i	$-0.306921\pi$
$661$	12.3055	+	4.47885i	0.478630	+	0.174207i	−0.0914280	+	0.995812i	$0.529143\pi$
$662$	24.4674	+	8.90540i	0.950952	+	0.346118i
$663$	1.19924	+	0.632287i	0.0465744	+	0.0245560i
$664$	−10.2563	−	8.60608i	−0.398023	−	0.333981i
$665$	−10.0035	+	0.610820i	−0.387918	+	0.0236866i
$666$	9.05440	−	0.696675i	0.350851	−	0.0269956i
$667$	1.40298			0.0543237
$668$	3.41272	−	19.3545i	0.132042	−	0.748848i
$669$	4.48670	−	13.9744i	0.173466	−	0.540280i
$670$	−13.8777	−	5.05106i	−0.536141	−	0.195139i
$671$	−2.16623	−	0.788444i	−0.0836264	−	0.0304375i
$672$	4.56964	+	0.344065i	0.176278	+	0.0132726i
$673$	4.13347	−	23.4421i	0.159333	−	0.903625i	−0.795383	−	0.606107i	$-0.792730\pi$
$673$	4.13347	−	23.4421i	0.159333	−	0.903625i	0.954716	−	0.297518i	$-0.0961587\pi$
$674$	−3.69348	−	6.39729i	−0.142268	−	0.246415i
$675$	8.82217	+	17.6176i	0.339565	+	0.678103i
$676$	5.12829	−	8.88246i	0.197242	−	0.341633i
$677$	29.1578	−	10.6126i	1.12062	−	0.407874i	0.285745	−	0.958306i	$-0.407759\pi$
$677$	29.1578	−	10.6126i	1.12062	−	0.407874i	0.834880	+	0.550432i	$0.185537\pi$
$678$	7.86912	+	19.2828i	0.302212	+	0.740550i
$679$	11.6173	+	3.44250i	0.445833	+	0.132111i
$680$	−0.397899	+	0.333877i	−0.0152587	+	0.0128036i
$681$	−8.09964	+	25.2273i	−0.310379	+	0.966713i
$682$	−0.0222800	+	0.126356i	−0.000853146	+	0.00483843i
$683$	−16.8297	−	29.1498i	−0.643969	−	1.11539i	−0.984539	−	0.175168i	$-0.943953\pi$
$683$	−16.8297	−	29.1498i	−0.643969	−	1.11539i	0.340570	−	0.940219i	$-0.389380\pi$
$684$	−8.40652	−	6.01851i	−0.321432	−	0.230124i
$685$	−5.01268	−	8.68221i	−0.191524	−	0.331730i
$686$	0.155979	+	18.5196i	0.00595532	+	0.707082i
$687$	1.35038	+	35.1525i	0.0515201	+	1.34115i
$688$	4.12401	−	3.46045i	0.157226	−	0.131929i
$689$	−5.16313	−	1.87923i	−0.196700	−	0.0715928i
$690$	−5.26167	−	2.77417i	−0.200308	−	0.105611i
$691$	0.429253	−	2.43441i	0.0163295	−	0.0926095i	−0.975554	−	0.219761i	$-0.929472\pi$
$691$	0.429253	−	2.43441i	0.0163295	−	0.0926095i	0.991883	+	0.127151i	$0.0405834\pi$
$692$	−7.88401	−	13.6555i	−0.299705	−	0.519104i
$693$	1.13929	+	0.714841i	0.0432781	+	0.0271546i
$694$	16.8193	−	29.1319i	0.638453	−	1.10583i
$695$	11.8212	+	9.91914i	0.448402	+	0.376254i
$696$	−0.760196	+	0.164359i	−0.0288151	+	0.00623001i
$697$	0.105527	+	0.598472i	0.00399711	+	0.0226687i
$698$	3.70140	+	20.9917i	0.140100	+	0.794548i
$699$	−17.1638	−	42.0589i	−0.649196	−	1.59081i
$700$	−9.20064	+	3.99944i	−0.347752	+	0.151165i
$701$	−27.5480			−1.04047			−0.520237	−	0.854022i	$-0.674157\pi$
$701$	−27.5480			−1.04047			−0.520237	+	0.854022i	$0.674157\pi$
$702$	−0.989176	−	8.54949i	−0.0373340	−	0.322680i
$703$	5.21605	−	9.03447i	0.196727	−	0.340741i
$704$	0.129808	+	0.108922i	0.00489232	+	0.00410514i
$705$	−9.08496	−	1.24450i	−0.342159	−	0.0468705i
$706$	19.5561	+	7.11783i	0.736003	+	0.267883i
$707$	10.9394	+	45.5862i	0.411418	+	1.71445i
$708$	−6.52195	+	1.41009i	−0.245110	+	0.0529943i
$709$	4.24593	+	3.56276i	0.159459	+	0.133802i	0.719026	−	0.694983i	$-0.244588\pi$
$709$	4.24593	+	3.56276i	0.159459	+	0.133802i	−0.559567	+	0.828785i	$0.689033\pi$
$710$	6.91457	+	11.9764i	0.259499	+	0.449466i
$711$	4.12729	+	6.02779i	0.154785	+	0.226060i
$712$	−0.437363	+	0.757534i	−0.0163909	+	0.0283898i
$713$	1.81225	+	1.52066i	0.0678694	+	0.0569492i
$714$	−0.214861	−	2.15488i	−0.00804099	−	0.0806442i
$715$	−0.0535700	−	0.303811i	−0.00200340	−	0.0113619i
$716$	9.41602	−	7.90098i	0.351893	−	0.295273i
$717$	−0.789961	+	0.497464i	−0.0295016	+	0.0185781i
$718$	−21.9346	+	7.98353i	−0.818591	+	0.297943i
$719$	−12.7704	+	22.1190i	−0.476255	+	0.824898i	−0.999630	−	0.0272047i	$-0.991339\pi$
$719$	−12.7704	+	22.1190i	−0.476255	+	0.824898i	0.523375	+	0.852103i	$0.324673\pi$
$720$	3.17599	+	0.886761i	0.118362	+	0.0330476i
$721$	13.9732	−	0.853213i	0.520388	−	0.0317753i
$722$	6.69352	−	2.43624i	0.249107	−	0.0906675i
$723$	0.485241	−	0.104912i	0.0180463	−	0.00390173i
$724$	3.28280	+	18.6177i	0.122004	+	0.691921i
$725$	1.30434	−	1.09447i	0.0484420	−	0.0406477i
$726$	−7.18002	−	17.5942i	−0.266476	−	0.652981i
$727$	4.70090	−	26.6601i	0.174347	−	0.988770i	−0.764548	−	0.644567i	$-0.777038\pi$
$727$	4.70090	−	26.6601i	0.174347	−	0.988770i	0.938895	−	0.344204i	$-0.111851\pi$
$728$	4.37408	−	0.267085i	0.162114	−	0.00989881i
$729$	18.4826	+	19.6823i	0.684541	+	0.728974i
$730$	7.61185	+	13.1841i	0.281727	+	0.487966i
$731$	−1.94886	−	1.63529i	−0.0720811	−	0.0604833i
$732$	14.4420	−	18.6185i	0.533792	−	0.688159i
$733$	−3.77026	−	21.3822i	−0.139258	−	0.789770i	−0.971800	−	0.235808i	$-0.924226\pi$
$733$	−3.77026	−	21.3822i	−0.139258	−	0.789770i	0.832542	−	0.553962i	$-0.186885\pi$
$734$	6.00363	−	5.03764i	0.221598	−	0.185943i
$735$	−2.49982	+	13.0900i	−0.0922072	+	0.482831i
$736$	2.93598	−	1.06861i	0.108222	−	0.0393894i
$737$	2.27677			0.0838659
$738$	2.75638	−	2.69924i	0.101464	−	0.0993603i
$739$	4.98747			0.183467			0.0917336	−	0.995784i	$-0.470759\pi$
$739$	4.98747			0.183467			0.0917336	+	0.995784i	$0.470759\pi$
$740$	−0.577762	+	3.27665i	−0.0212390	+	0.120452i
$741$	−8.74572	−	4.61111i	−0.321282	−	0.169393i
$742$	2.04801	+	8.53439i	0.0751848	+	0.313307i
$743$	3.58890	+	20.3536i	0.131664	+	0.746703i	0.977125	+	0.212666i	$0.0682146\pi$
$743$	3.58890	+	20.3536i	0.131664	+	0.746703i	−0.845461	+	0.534037i	$0.820674\pi$
$744$	−1.16010	−	0.611654i	−0.0425314	−	0.0224243i
$745$	−19.6134	+	7.13871i	−0.718581	+	0.261542i
$746$	−24.3251			−0.890604
$747$	40.0477	−	3.08140i	1.46527	−	0.112742i
$748$	0.0400385	−	0.0693487i	0.00146395	−	0.00253564i
$749$	−16.4048	−	12.1415i	−0.599419	−	0.443641i
$750$	−16.3599	+	3.53710i	−0.597378	+	0.129157i
$751$	34.3493	+	12.5021i	1.25343	+	0.456209i	0.881558	−	0.472076i	$-0.156495\pi$
$751$	34.3493	+	12.5021i	1.25343	+	0.456209i	0.371868	+	0.928286i	$0.378718\pi$
$752$	3.68973	−	3.09605i	0.134551	−	0.112901i
$753$	15.9246	+	39.0222i	0.580325	+	1.42205i
$754$	−0.698903	+	0.254380i	−0.0254525	+	0.00926397i
$755$	−11.0183			−0.400996
$756$	−10.5169	+	8.85413i	−0.382495	+	0.322022i
$757$	17.3561			0.630816			0.315408	−	0.948956i	$-0.397859\pi$
$757$	17.3561			0.630816			0.315408	+	0.948956i	$0.397859\pi$
$758$	7.94217	−	2.89071i	0.288472	−	0.104995i
$759$	0.908527	+	0.124454i	0.0329774	+	0.00451739i
$760$	2.90178	−	2.43488i	0.105259	−	0.0883224i
$761$	3.13397	+	1.14067i	0.113606	+	0.0413493i	0.398198	−	0.917300i	$-0.369636\pi$
$761$	3.13397	+	1.14067i	0.113606	+	0.0413493i	−0.284592	+	0.958649i	$0.591858\pi$
$762$	−7.51169	−	8.28426i	−0.272120	−	0.300107i
$763$	−4.41369	+	38.7036i	−0.159786	+	1.40116i
$764$	−2.57508	+	4.46016i	−0.0931630	+	0.161363i
$765$	0.152064	−	1.55083i	0.00549788	−	0.0560702i
$766$	2.73221			0.0987186
$767$	−5.99610	+	2.18240i	−0.216507	+	0.0788019i
$768$	−1.46565	+	0.922967i	−0.0528871	+	0.0333047i
$769$	5.54534	+	31.4492i	0.199970	+	1.13409i	0.905161	+	0.425069i	$0.139750\pi$
$769$	5.54534	+	31.4492i	0.199970	+	1.13409i	−0.705191	+	0.709018i	$0.749139\pi$
$770$	−0.357486	+	0.339172i	−0.0128829	+	0.0122229i
$771$	−0.693897	−	18.0633i	−0.0249901	−	0.650533i
$772$	2.02073	−	11.4601i	0.0727275	−	0.412458i
$773$	−17.7599			−0.638781			−0.319390	−	0.947623i	$-0.603478\pi$
$773$	−17.7599			−0.638781			−0.319390	+	0.947623i	$0.603478\pi$
$774$	−1.57606	+	16.0734i	−0.0566502	+	0.577748i
$775$	2.87111			0.103133
$776$	−4.30348	+	1.56634i	−0.154486	+	0.0562283i
$777$	−9.92688	−	9.68923i	−0.356125	−	0.347599i
$778$	−7.78281	+	6.53055i	−0.279027	+	0.234132i
$779$	−0.769580	−	4.36450i	−0.0275731	−	0.156375i
$780$	3.12412	+	0.427956i	0.111862	+	0.0153233i
$781$	−1.63319	−	1.37041i	−0.0584402	−	0.0490372i
$782$	−0.738240	−	1.27867i	−0.0263994	−	0.0457251i
$783$	1.28443	−	1.94793i	0.0459019	−	0.0696133i
$784$	−4.21157	−	5.59130i	−0.150413	−	0.199689i
$785$	2.45479	−	13.9218i	0.0876152	−	0.496891i
$786$	13.3409	+	1.82749i	0.475854	+	0.0651845i
$787$	−3.89546	+	3.26868i	−0.138858	+	0.116516i	−0.709571	−	0.704634i	$-0.751111\pi$
$787$	−3.89546	+	3.26868i	−0.138858	+	0.116516i	0.570713	+	0.821150i	$0.306667\pi$
$788$	−2.16494	−	12.2780i	−0.0771226	−	0.437384i
$789$	−19.3707	−	21.3630i	−0.689615	−	0.760541i
$790$	−2.51517	+	0.915446i	−0.0894856	+	0.0325701i
$791$	14.1979	−	28.4693i	0.504818	−	1.01225i
$792$	−0.506858	+	0.0389993i	−0.0180104	+	0.00138578i
$793$	11.2665	−	19.5141i	0.400084	−	0.692966i
$794$	−12.6367	+	4.59938i	−0.448459	+	0.163226i
$795$	0.242426	+	6.31074i	0.00859797	+	0.223819i
$796$	5.01896	−	4.21141i	0.177892	−	0.149269i
$797$	1.51369	+	8.58459i	0.0536178	+	0.304082i	0.999809	−	0.0195254i	$-0.00621552\pi$
$797$	1.51369	+	8.58459i	0.0536178	+	0.304082i	−0.946192	+	0.323607i	$0.895104\pi$
$798$	1.56693	+	15.7150i	0.0554687	+	0.556303i
$799$	−1.74363	−	1.46308i	−0.0616853	−	0.0517601i
$800$	1.89593	−	3.28385i	0.0670312	−	0.116102i
$801$	−0.652599	−	2.54173i	−0.0230585	−	0.0898078i
$802$	−1.82636	−	3.16335i	−0.0644911	−	0.111702i
$803$	−1.79789	−	1.50861i	−0.0634461	−	0.0532376i
$804$	−7.11416	+	22.1579i	−0.250897	+	0.781449i
$805$	2.12020	+	8.83521i	0.0747271	+	0.311400i
$806$	−1.17850	−	0.428939i	−0.0415109	−	0.0151087i
$807$	17.3352	+	42.4787i	0.610226	+	1.49532i
$808$	−13.5736	−	11.3896i	−0.477519	−	0.400686i
$809$	−26.7142	+	46.2704i	−0.939222	+	1.62678i	−0.172296	+	0.985045i	$0.555119\pi$
$809$	−26.7142	+	46.2704i	−0.939222	+	1.62678i	−0.766926	+	0.641735i	$0.778215\pi$
$810$	−8.66879	+	4.76565i	−0.304590	+	0.167448i
$811$	37.7040			1.32397			0.661983	−	0.749519i	$-0.269715\pi$
$811$	37.7040			1.32397			0.661983	+	0.749519i	$0.269715\pi$
$812$	0.954949	+	0.706775i	0.0335122	+	0.0248030i
$813$	−19.6995	−	2.69853i	−0.690893	−	0.0946415i
$814$	−0.0890712	−	0.505148i	−0.00312194	−	0.0177054i
$815$	3.21465	+	18.2312i	0.112604	+	0.638611i
$816$	0.549806	+	0.606353i	0.0192471	+	0.0212266i
$817$	14.2125	+	11.9257i	0.497233	+	0.417228i
$818$	−16.9523	+	29.3622i	−0.592723	+	1.02663i
$819$	−8.81490	+	9.75360i	−0.308017	+	0.340818i
$820$	0.706741	+	1.22411i	0.0246805	+	0.0427478i
$821$	−4.36687	+	24.7657i	−0.152405	+	0.864331i	0.808715	+	0.588200i	$0.200163\pi$
$821$	−4.36687	+	24.7657i	−0.152405	+	0.864331i	−0.961120	+	0.276130i	$0.910948\pi$
$822$	−13.3682	+	8.41835i	−0.466268	+	0.293624i
$823$	−10.4272	−	3.79521i	−0.363471	−	0.132293i	0.153827	−	0.988098i	$-0.450840\pi$
$823$	−10.4272	−	3.79521i	−0.363471	−	0.132293i	−0.517298	+	0.855805i	$0.673062\pi$
$824$	−4.05329	+	3.40112i	−0.141203	+	0.118484i
$825$	0.941737	−	0.593042i	0.0327871	−	0.0206471i
$826$	8.19280	+	6.06364i	0.285064	+	0.210981i
$827$	4.13487	+	7.16181i	0.143784	+	0.249041i	0.928918	−	0.370284i	$-0.120740\pi$
$827$	4.13487	+	7.16181i	0.143784	+	0.249041i	−0.785135	+	0.619325i	$0.787406\pi$
$828$	−4.05005	+	8.45305i	−0.140749	+	0.293764i
$829$	5.07141	+	8.78395i	0.176137	+	0.305079i	0.940554	−	0.339643i	$-0.110306\pi$
$829$	5.07141	+	8.78395i	0.176137	+	0.305079i	−0.764417	+	0.644722i	$0.776973\pi$
$830$	−2.55545	+	14.4927i	−0.0887008	+	0.503047i
$831$	−19.4653	−	21.4673i	−0.675246	−	0.744694i
$832$	−1.26882	+	1.06467i	−0.0439884	+	0.0369106i
$833$	−2.25651	+	2.41882i	−0.0781833	+	0.0838072i
$834$	14.9040	−	19.2141i	0.516084	−	0.665330i
$835$	−20.2990	+	7.38823i	−0.702476	+	0.255680i
$836$	−0.291990	+	0.505742i	−0.0100987	+	0.0174915i
$837$	3.77044	−	1.12400i	0.130326	−	0.0388512i
$838$	−6.91559	−	11.9782i	−0.238895	−	0.413779i
$839$	8.75012	−	49.6244i	0.302088	−	1.71322i	−0.334819	−	0.942282i	$-0.608675\pi$
$839$	8.75012	−	49.6244i	0.302088	−	1.71322i	0.636907	−	0.770941i	$-0.280214\pi$
$840$	−2.18386	−	4.53891i	−0.0753502	−	0.156607i
$841$	27.0616	+	9.84962i	0.933159	+	0.339642i
$842$	−6.91756	−	2.51779i	−0.238395	−	0.0867687i
$843$	−47.6701	+	10.3066i	−1.64184	+	0.354977i
$844$	−3.99630	+	22.6642i	−0.137558	+	0.780132i
$845$	−11.2736			−0.387823
$846$	−1.41009	+	14.3808i	−0.0484799	+	0.494423i
$847$	−12.9546	+	25.9762i	−0.445124	+	0.892553i
$848$	−2.54118	−	2.13230i	−0.0872645	−	0.0732236i
$849$	−11.2310	+	7.07254i	−0.385448	+	0.242729i
$850$	−1.68383	−	0.612865i	−0.0577550	−	0.0210211i
$851$	−8.88737	−	3.23474i	−0.304655	−	0.110885i
$852$	18.4402	−	11.6124i	0.631752	−	0.397835i
$853$	−21.9482	−	18.4167i	−0.751491	−	0.630576i	0.184406	−	0.982850i	$-0.440964\pi$
$853$	−21.9482	−	18.4167i	−0.751491	−	0.630576i	−0.935897	+	0.352275i	$0.885408\pi$
$854$	−35.9263	+	2.19369i	−1.22937	+	0.0750665i
$855$	−1.10896	+	11.3098i	−0.0379257	+	0.386786i
$856$	7.71394			0.263657
$857$	−3.08192	+	17.4785i	−0.105277	+	0.597053i	0.885833	+	0.464004i	$0.153588\pi$
$857$	−3.08192	+	17.4785i	−0.105277	+	0.597053i	−0.991110	+	0.133049i	$0.957523\pi$
$858$	−0.475152	+	0.102731i	−0.0162214	+	0.00350718i
$859$	−37.7140	−	13.7268i	−1.28678	−	0.468351i	−0.394113	−	0.919062i	$-0.628948\pi$
$859$	−37.7140	−	13.7268i	−1.28678	−	0.468351i	−0.892670	+	0.450711i	$0.851171\pi$
$860$	−5.56045	−	2.02384i	−0.189610	−	0.0690123i
$861$	−5.87643	−	0.442459i	−0.200268	−	0.0150789i
$862$	1.88692	−	10.7013i	0.0642688	−	0.364486i
$863$	2.26607	+	3.92495i	0.0771380	+	0.133607i	0.902014	−	0.431707i	$-0.142088\pi$
$863$	2.26607	+	3.92495i	0.0771380	+	0.133607i	−0.824876	+	0.565314i	$0.808755\pi$
$864$	1.20422	−	5.05469i	0.0409683	−	0.171964i
$865$	−8.66574	+	15.0095i	−0.294644	+	0.510339i
$866$	−9.64659	+	3.51107i	−0.327804	+	0.119311i
$867$	−17.8099	+	22.9604i	−0.604857	+	0.779775i
$868$	0.467465	+	1.94800i	0.0158668	+	0.0661195i
$869$	0.316099	−	0.265239i	0.0107229	−	0.00899761i
$870$	0.574239	+	0.633299i	0.0194685	+	0.0214708i
$871$	−3.86445	+	21.9164i	−0.130942	+	0.742609i
$872$	−7.36169	−	12.7508i	−0.249298	−	0.431797i
$873$	5.93646	−	12.3903i	0.200919	−	0.419347i
$874$	5.38380	+	9.32501i	0.182110	+	0.315423i
$875$	20.5511	+	15.2102i	0.694753	+	0.514199i
$876$	20.2998	−	12.7834i	0.685867	−	0.431912i
$877$	−18.7692	+	15.7493i	−0.633792	+	0.531815i	−0.902105	−	0.431517i	$-0.857978\pi$
$877$	−18.7692	+	15.7493i	−0.633792	+	0.531815i	0.268313	+	0.963332i	$0.413534\pi$
$878$	−13.6277	−	4.96009i	−0.459913	−	0.167395i
$879$	21.5039	−	13.5417i	0.725308	−	0.456750i
$880$	0.0323427	−	0.183424i	0.00109027	−	0.00618324i
$881$	1.52565	+	2.64250i	0.0514004	+	0.0890281i	0.890581	−	0.454825i	$-0.150298\pi$
$881$	1.52565	+	2.64250i	0.0514004	+	0.0890281i	−0.839180	+	0.543853i	$0.816965\pi$
$882$	20.7632	+	3.14451i	0.699135	+	0.105881i
$883$	11.3430	−	19.6466i	0.381721	−	0.661161i	−0.609587	−	0.792719i	$-0.708665\pi$
$883$	11.3430	−	19.6466i	0.381721	−	0.661161i	0.991308	+	0.131558i	$0.0419980\pi$
$884$	0.599598	+	0.503123i	0.0201667	+	0.0169219i
$885$	4.92657	+	5.43326i	0.165605	+	0.182637i
$886$	−4.67429	−	26.5092i	−0.157036	−	0.890595i
$887$	0.262124	+	1.48658i	0.00880126	+	0.0499144i	0.988892	−	0.148635i	$-0.0474880\pi$
$887$	0.262124	+	1.48658i	0.00880126	+	0.0499144i	−0.980091	+	0.198550i	$0.936377\pi$
$888$	5.19450	+	0.711565i	0.174316	+	0.0238786i
$889$	−1.93546	+	16.9720i	−0.0649131	+	0.569222i
$890$	0.961458			0.0322281
$891$	1.00455	−	1.14748i	0.0336538	−	0.0384420i
$892$	4.23688	−	7.33848i	0.141861	−	0.245711i
$893$	12.7159	+	10.6699i	0.425521	+	0.357054i
$894$	12.4273	+	30.4523i	0.415632	+	1.01848i
$895$	−12.6957	−	4.62087i	−0.424372	−	0.154459i
$896$	2.53672	+	0.751691i	0.0847459	+	0.0251122i
$897$	−2.74008	+	8.53433i	−0.0914888	+	0.284953i
$898$	10.6375	+	8.92593i	0.354978	+	0.297862i
$899$	−0.170002	−	0.294452i	−0.00566987	−	0.00982051i
$900$	2.82896	+	11.0182i	0.0942988	+	0.367273i
$901$	−0.783813	+	1.35760i	−0.0261126	+	0.0452283i
$902$	−0.166929	−	0.140070i	−0.00555814	−	0.00466383i
$903$	20.0359	−	14.3941i	0.666752	−	0.479006i
$904$	2.08799	+	11.8416i	0.0694455	+	0.393845i
$905$	15.9180	−	13.3567i	0.529131	−	0.443993i
$906$	0.666490	+	17.3498i	0.0221426	+	0.576409i
$907$	10.5449	−	3.83804i	0.350139	−	0.127440i	−0.160963	−	0.986961i	$-0.551460\pi$
$907$	10.5449	−	3.83804i	0.350139	−	0.127440i	0.511101	+	0.859520i	$0.329238\pi$
$908$	−7.64865	+	13.2478i	−0.253829	+	0.439645i
$909$	53.0007	−	4.07805i	1.75792	−	0.135260i
$910$	−2.65813	−	4.01688i	−0.0881162	−	0.133158i
$911$	−25.9761	+	9.45454i	−0.860628	+	0.313243i	−0.734366	−	0.678754i	$-0.762520\pi$
$911$	−25.9761	+	9.45454i	−0.860628	+	0.313243i	−0.126262	+	0.991997i	$0.540298\pi$
$912$	−4.00959	−	4.42198i	−0.132771	−	0.146426i
$913$	−0.393963	−	2.23427i	−0.0130383	−	0.0739437i
$914$	9.43905	−	7.92031i	0.312216	−	0.261980i
$915$	−25.6599	−	3.51500i	−0.848289	−	0.116202i
$916$	−3.52684	+	20.0017i	−0.116530	+	0.660875i
$917$	−11.3510	−	17.1532i	−0.374842	−	0.566450i
$918$	−2.45119	−	0.145637i	−0.0809014	−	0.00480674i
$919$	−4.05522	−	7.02385i	−0.133769	−	0.231695i	0.791357	−	0.611354i	$-0.209375\pi$
$919$	−4.05522	−	7.02385i	−0.133769	−	0.231695i	−0.925127	+	0.379659i	$0.876041\pi$
$920$	−2.63075	−	2.20746i	−0.0867333	−	0.0727779i
$921$	−3.67991	−	0.504090i	−0.121257	−	0.0166103i
$922$	−4.32477	−	24.5270i	−0.142429	−	0.807753i
$923$	15.9638	−	13.3952i	0.525455	−	0.440909i
$924$	0.555699	+	0.542396i	0.0182812	+	0.0178435i
$925$	−10.7859	+	3.92576i	−0.354640	+	0.129078i
$926$	20.1550			0.662335
$927$	1.54903	−	15.7978i	0.0508769	−	0.518869i
$928$	−0.449040			−0.0147405
$929$	2.34960	−	13.3252i	0.0770878	−	0.437187i	−0.921697	−	0.387910i	$-0.873197\pi$
$929$	2.34960	−	13.3252i	0.0770878	−	0.437187i	0.998785	−	0.0492770i	$-0.0156917\pi$
$930$	0.0553345	+	1.44045i	0.00181449	+	0.0472341i
$931$	16.4561	−	17.6399i	0.539328	−	0.578123i
$932$	−4.55425	−	25.8284i	−0.149179	−	0.846038i
$933$	−47.9335	+	30.1852i	−1.56927	+	0.988220i
$934$	14.7222	−	5.35844i	0.481725	−	0.175334i
$935$	−0.0880170			−0.00287846
$936$	0.484900	−	4.94526i	0.0158495	−	0.161641i
$937$	−29.3161	+	50.7769i	−0.957714	+	1.65881i	−0.229683	+	0.973266i	$0.573769\pi$
$937$	−29.3161	+	50.7769i	−0.957714	+	1.65881i	−0.728031	+	0.685544i	$0.759564\pi$
$938$	32.6015	−	14.1716i	1.06448	−	0.462720i
$939$	11.3023	+	12.4648i	0.368838	+	0.406772i
$940$	−4.97491	−	1.81072i	−0.162264	−	0.0590591i
$941$	16.1212	−	13.5273i	0.525537	−	0.440978i	−0.341020	−	0.940056i	$-0.610772\pi$
$941$	16.1212	−	13.5273i	0.525537	−	0.440978i	0.866557	+	0.499078i	$0.166328\pi$
$942$	−22.0703	−	3.02329i	−0.719091	−	0.0985041i
$943$	−3.77559	+	1.37420i	−0.122950	+	0.0447502i
$944$	−3.85245			−0.125387
$945$	14.2080	+	5.14493i	0.462187	+	0.167365i
$946$	0.912247			0.0296597
$947$	6.82641	−	2.48461i	0.221829	−	0.0807390i	−0.228715	−	0.973493i	$-0.573452\pi$
$947$	6.82641	−	2.48461i	0.221829	−	0.0807390i	0.450544	+	0.892754i	$0.351230\pi$
$948$	1.59364	+	3.90511i	0.0517590	+	0.126832i
$949$	17.5736	−	14.7460i	0.570464	−	0.478676i
$950$	12.2798	+	4.46947i	0.398408	+	0.145009i
$951$	36.4620	−	7.88331i	1.18236	−	0.255634i
$952$	0.141663	−	1.24224i	0.00459131	−	0.0402611i
$953$	30.5367	−	52.8911i	0.989180	−	1.71331i	0.367540	−	0.930008i	$-0.380200\pi$
$953$	30.5367	−	52.8911i	0.989180	−	1.71331i	0.621641	−	0.783303i	$-0.286466\pi$
$954$	9.92250	−	0.763469i	0.321253	−	0.0247182i
$955$	5.66081			0.183180
$956$	−0.506479	+	0.184343i	−0.0163807	+	0.00596208i
$957$	−0.116582	−	0.0614667i	−0.00376855	−	0.00198694i
$958$	2.35916	+	13.3795i	0.0762211	+	0.432271i
$959$	23.1374	+	6.85615i	0.747144	+	0.221397i
$960$	1.68406	+	0.887905i	0.0543527	+	0.0286570i
$961$	−5.28354	+	29.9644i	−0.170437	+	0.966595i
$962$	5.01379			0.161651
$963$	−16.5342	+	16.1914i	−0.532808	+	0.521762i
$964$	0.286627			0.00923165
$965$	−12.0194	+	4.37469i	−0.386917	+	0.140826i
$966$	13.7840	−	3.87299i	0.443494	−	0.124611i
$967$	8.31882	−	6.98032i	0.267515	−	0.224472i	−0.499155	−	0.866512i	$-0.666356\pi$
$967$	8.31882	−	6.98032i	0.267515	−	0.224472i	0.766671	+	0.642040i	$0.221912\pi$
$968$	−1.90514	−	10.8046i	−0.0612336	−	0.347273i
$969$	−1.72889	+	2.22887i	−0.0555401	+	0.0716016i
$970$	3.85608	+	3.23564i	0.123811	+	0.103890i
$971$	−0.641357	−	1.11086i	−0.0205821	−	0.0356493i	0.855551	−	0.517719i	$-0.173219\pi$
$971$	−0.641357	−	1.11086i	−0.0205821	−	0.0356493i	−0.876133	+	0.482069i	$0.839885\pi$
$972$	8.02856	+	13.3620i	0.257516	+	0.428585i
$973$	−37.0756	+	2.26387i	−1.18859	+	0.0725762i
$974$	−0.177335	+	1.00571i	−0.00568217	+	0.0322252i
$975$	4.11023	+	10.0718i	0.131633	+	0.322557i
$976$	10.4214	−	8.74459i	0.333581	−	0.279908i
$977$	−1.57160	−	8.91299i	−0.0502799	−	0.285152i	0.949292	−	0.314395i	$-0.101801\pi$
$977$	−1.57160	−	8.91299i	−0.0502799	−	0.285152i	−0.999572	+	0.0292429i	$0.990690\pi$
$978$	28.5132	−	6.16473i	0.911751	−	0.197126i
$979$	−0.139285	+	0.0506956i	−0.00445157	+	0.00162024i
$980$	−3.00775	+	7.08183i	−0.0960792	+	0.226221i
$981$	42.5430	+	11.8783i	1.35829	+	0.379246i
$982$	18.8244	−	32.6049i	0.600712	−	1.04046i
$983$	36.1142	−	13.1445i	1.15186	−	0.419244i	0.305680	−	0.952134i	$-0.401116\pi$
$983$	36.1142	−	13.1445i	1.15186	−	0.419244i	0.846185	+	0.532890i	$0.178894\pi$
$984$	1.88479	−	1.18691i	0.0600848	−	0.0378373i
$985$	−10.4975	+	8.80848i	−0.334479	+	0.280661i
$986$	0.0368482	+	0.208976i	0.00117349	+	0.00665517i
$987$	17.9260	−	12.8783i	0.570590	−	0.409922i
$988$	−4.37272	−	3.66915i	−0.139115	−	0.116731i
$989$	8.41013	−	14.5668i	0.267427	−	0.463196i
$990$	0.315681	+	0.461043i	0.0100330	+	0.0146529i
$991$	−21.2424	−	36.7930i	−0.674788	−	1.16877i	−0.976531	−	0.215378i	$-0.930902\pi$
$991$	−21.2424	−	36.7930i	−0.674788	−	1.16877i	0.301742	−	0.953390i	$-0.402432\pi$
$992$	−0.580032	−	0.486705i	−0.0184160	−	0.0154529i
$993$	−44.0800	+	9.53038i	−1.39884	+	0.302437i
$994$	−31.9161	−	9.45749i	−1.01232	−	0.299973i
$995$	−6.76712	−	2.46303i	−0.214532	−	0.0780833i
$996$	22.9753	+	3.14726i	0.728001	+	0.0997247i
$997$	−8.67674	−	7.28065i	−0.274795	−	0.230581i	0.494966	−	0.868912i	$-0.335180\pi$
$997$	−8.67674	−	7.28065i	−0.274795	−	0.230581i	−0.769761	+	0.638332i	$0.779625\pi$
$998$	10.5933	−	18.3482i	0.335326	−	0.580801i
$999$	−12.6276	+	9.37799i	−0.399519	+	0.296707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.25.9	yes	72
7.2	even	3		378.2.v.b.79.8	yes	72
27.13	even	9		378.2.v.b.67.8	✓	72
189.121	even	9	inner	378.2.w.a.121.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.8	✓	72	27.13	even	9
378.2.v.b.79.8	yes	72	7.2	even	3
378.2.w.a.25.9	yes	72	1.1	even	1	trivial
378.2.w.a.121.9	yes	72	189.121	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.06159 - 1.36859i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.03287 - 0.375933i) q^{5} +(-0.529482 + 1.64914i) q^{6} +(2.42642 - 1.05474i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.746062 - 2.90575i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.06159 - 1.36859i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-1.03287 - 0.375933i) q^{5} +(-0.529482 + 1.64914i) q^{6} +(2.42642 - 1.05474i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.746062 - 2.90575i) q^{9} +1.09915 q^{10} +(-0.159233 + 0.0579560i) q^{11} +(-0.0664874 - 1.73077i) q^{12} +(-0.287618 - 1.63116i) q^{13} +(-1.91935 + 1.82102i) q^{14} +(-1.61098 + 1.01448i) q^{15} +(0.173648 - 0.984808i) q^{16} -0.472564 q^{17} +(1.69489 + 2.47534i) q^{18} +3.44629 q^{19} +(-1.03287 + 0.375933i) q^{20} +(1.13235 - 4.44047i) q^{21} +(0.129808 - 0.108922i) q^{22} +(-0.542547 - 3.07694i) q^{23} +(0.654437 + 1.60366i) q^{24} +(-2.90473 - 2.43736i) q^{25} +(0.828163 + 1.43442i) q^{26} +(-4.76878 - 2.06366i) q^{27} +(1.18077 - 2.36765i) q^{28} +(-0.0779750 + 0.442218i) q^{29} +(1.16685 - 1.50429i) q^{30} +(-0.580032 + 0.486705i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-0.0897218 + 0.279450i) q^{33} +(0.444065 - 0.161626i) q^{34} +(-2.90268 + 0.177240i) q^{35} +(-2.43930 - 1.74638i) q^{36} +(1.51353 - 2.62151i) q^{37} +(-3.23845 + 1.17870i) q^{38} +(-2.53772 - 1.33799i) q^{39} +(0.842001 - 0.706523i) q^{40} +(-0.223307 - 1.26644i) q^{41} +(0.454672 + 4.55996i) q^{42} +(4.12401 + 3.46045i) q^{43} +(-0.0847261 + 0.146750i) q^{44} +(-0.321785 + 3.28172i) q^{45} +(1.56220 + 2.70581i) q^{46} +(3.68973 + 3.09605i) q^{47} +(-1.16345 - 1.28311i) q^{48} +(4.77503 - 5.11851i) q^{49} +(3.56318 + 1.29689i) q^{50} +(-0.501668 + 0.646745i) q^{51} +(-1.26882 - 1.06467i) q^{52} +(1.65864 - 2.87284i) q^{53} +(5.18701 + 0.308185i) q^{54} +0.186254 q^{55} +(-0.299774 + 2.62871i) q^{56} +(3.65854 - 4.71655i) q^{57} +(-0.0779750 - 0.442218i) q^{58} +(-0.668971 - 3.79392i) q^{59} +(-0.581982 + 1.81265i) q^{60} +(10.4214 + 8.74459i) q^{61} +(0.378589 - 0.655736i) q^{62} +(-4.87509 - 6.26367i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.316137 + 1.79290i) q^{65} +(-0.0112664 - 0.293283i) q^{66} +(-12.6258 - 4.59541i) q^{67} +(-0.362005 + 0.303758i) q^{68} +(-4.78702 - 2.52392i) q^{69} +(2.66701 - 1.15933i) q^{70} +(6.29081 + 10.8960i) q^{71} +(2.88949 + 0.806767i) q^{72} +(6.92519 + 11.9948i) q^{73} +(-0.525642 + 2.98107i) q^{74} +(-6.41937 + 1.38791i) q^{75} +(2.64001 - 2.21523i) q^{76} +(-0.325237 + 0.308576i) q^{77} +(2.84230 + 0.389350i) q^{78} +(-2.28827 + 0.832864i) q^{79} +(-0.549577 + 0.951896i) q^{80} +(-7.88678 + 4.33574i) q^{81} +(0.642986 + 1.11368i) q^{82} +(-2.32492 + 13.1853i) q^{83} +(-1.98685 - 4.12946i) q^{84} +(0.488096 + 0.177652i) q^{85} +(-5.05885 - 1.84127i) q^{86} +(0.522437 + 0.576169i) q^{87} +(0.0294251 - 0.166878i) q^{88} +0.874725 q^{89} +(-0.820037 - 3.19387i) q^{90} +(-2.41834 - 3.65452i) q^{91} +(-2.39343 - 2.00833i) q^{92} +(0.0503428 + 1.31050i) q^{93} +(-4.52612 - 1.64737i) q^{94} +(-3.55956 - 1.29557i) q^{95} +(1.53214 + 0.807807i) q^{96} +(3.50823 + 2.94375i) q^{97} +(-2.73643 + 6.44298i) q^{98} +(0.287203 + 0.419452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Introduction

L-functions

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