LMFDB - Embedded newform 189.2.be.a.20.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(20,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

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

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

chi := DirichletCharacter("189.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.11
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0448460 - 0.123213i) q^{2} +(-1.62941 - 0.587383i) q^{3} +(1.51892 - 1.27452i) q^{4} +(-0.231324 - 1.31190i) q^{5} +(0.000699206 + 0.227107i) q^{6} +(-2.62614 - 0.321557i) q^{7} +(-0.452264 - 0.261115i) q^{8} +(2.30996 + 1.91418i) q^{9} +O(q^{10})$	\(q+(-0.0448460 - 0.123213i) q^{2} +(-1.62941 - 0.587383i) q^{3} +(1.51892 - 1.27452i) q^{4} +(-0.231324 - 1.31190i) q^{5} +(0.000699206 + 0.227107i) q^{6} +(-2.62614 - 0.321557i) q^{7} +(-0.452264 - 0.261115i) q^{8} +(2.30996 + 1.91418i) q^{9} +(-0.151270 + 0.0873359i) q^{10} +(-4.31014 - 0.759994i) q^{11} +(-3.22358 + 1.18454i) q^{12} +(1.38870 - 3.81541i) q^{13} +(0.0781517 + 0.337996i) q^{14} +(-0.393667 + 2.27351i) q^{15} +(0.676731 - 3.83793i) q^{16} +(-1.85685 - 3.21617i) q^{17} +(0.132259 - 0.370462i) q^{18} +(4.31784 + 2.49291i) q^{19} +(-2.02342 - 1.69785i) q^{20} +(4.09018 + 2.06650i) q^{21} +(0.0996512 + 0.565150i) q^{22} +(0.242663 + 0.289194i) q^{23} +(0.583550 + 0.691115i) q^{24} +(3.03088 - 1.10315i) q^{25} -0.532388 q^{26} +(-2.63953 - 4.47581i) q^{27} +(-4.39872 + 2.85866i) q^{28} +(1.57190 + 4.31876i) q^{29} +(0.297781 - 0.0534526i) q^{30} +(0.693448 + 0.826419i) q^{31} +(-1.53182 + 0.270102i) q^{32} +(6.57659 + 3.77004i) q^{33} +(-0.313002 + 0.373021i) q^{34} +(0.185638 + 3.51963i) q^{35} +(5.94831 - 0.0366271i) q^{36} +(-0.172576 - 0.298911i) q^{37} +(0.113522 - 0.643813i) q^{38} +(-4.50387 + 5.40118i) q^{39} +(-0.237938 + 0.653729i) q^{40} +(5.09719 + 1.85523i) q^{41} +(0.0711916 - 0.596639i) q^{42} +(-0.390810 + 2.21639i) q^{43} +(-7.51538 + 4.33901i) q^{44} +(1.97686 - 3.47325i) q^{45} +(0.0247502 - 0.0428686i) q^{46} +(9.77186 + 8.19957i) q^{47} +(-3.35701 + 5.85607i) q^{48} +(6.79320 + 1.68890i) q^{49} +(-0.271846 - 0.323973i) q^{50} +(1.13646 + 6.33114i) q^{51} +(-2.75352 - 7.56523i) q^{52} -9.19872i q^{53} +(-0.433108 + 0.525947i) q^{54} +5.83030i q^{55} +(1.10374 + 0.831152i) q^{56} +(-5.57125 - 6.59819i) q^{57} +(0.461636 - 0.387359i) q^{58} +(-2.24314 - 12.7215i) q^{59} +(2.29969 + 3.95501i) q^{60} +(-1.14717 + 1.36715i) q^{61} +(0.0707275 - 0.122504i) q^{62} +(-5.45077 - 5.76967i) q^{63} +(-3.79516 - 6.57342i) q^{64} +(-5.32670 - 0.939241i) q^{65} +(0.169586 - 0.979395i) q^{66} +(5.40821 + 1.96843i) q^{67} +(-6.91949 - 2.51849i) q^{68} +(-0.225530 - 0.613753i) q^{69} +(0.425340 - 0.180714i) q^{70} +(2.30444 - 1.33047i) q^{71} +(-0.544894 - 1.46888i) q^{72} +(-4.63485 - 2.67593i) q^{73} +(-0.0290904 + 0.0346686i) q^{74} +(-5.58652 + 0.0171995i) q^{75} +(9.73572 - 1.71667i) q^{76} +(11.0746 + 3.38180i) q^{77} +(0.867479 + 0.312715i) q^{78} +(5.48206 - 1.99531i) q^{79} -5.19155 q^{80} +(1.67186 + 8.84335i) q^{81} -0.711242i q^{82} +(-4.03800 + 1.46971i) q^{83} +(8.84645 - 2.07420i) q^{84} +(-3.78977 + 3.17999i) q^{85} +(0.290615 - 0.0512433i) q^{86} +(-0.0245079 - 7.96035i) q^{87} +(1.75088 + 1.46916i) q^{88} +(-5.59352 + 9.68826i) q^{89} +(-0.516605 - 0.0878150i) q^{90} +(-4.87378 + 9.57326i) q^{91} +(0.737171 + 0.129983i) q^{92} +(-0.644488 - 1.75390i) q^{93} +(0.572067 - 1.57174i) q^{94} +(2.27163 - 6.24126i) q^{95} +(2.65463 + 0.459660i) q^{96} +(-14.5132 - 2.55906i) q^{97} +(-0.0965524 - 0.912754i) q^{98} +(-8.50151 - 10.0059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.0448460	−	0.123213i	−0.0317109	−	0.0871250i	0.922827	−	0.385215i	$-0.125873\pi$
$2$	−0.0448460	−	0.123213i	−0.0317109	−	0.0871250i	−0.954538	+	0.298090i	$0.903650\pi$
$3$	−1.62941	−	0.587383i	−0.940741	−	0.339125i
$3$	−1.62941	−	0.587383i	−0.940741	−	0.339125i
$4$	1.51892	−	1.27452i	0.759459	−	0.637262i
$5$	−0.231324	−	1.31190i	−0.103451	−	0.586701i	−0.991828	−	0.127585i	$-0.959277\pi$
$5$	−0.231324	−	1.31190i	−0.103451	−	0.586701i	0.888376	−	0.459116i	$-0.151834\pi$
$6$	0.000699206		0.227107i	0.000285450		0.0927161i
$7$	−2.62614	−	0.321557i	−0.992587	−	0.121537i
$7$	−2.62614	−	0.321557i	−0.992587	−	0.121537i
$8$	−0.452264	−	0.261115i	−0.159899	−	0.0923180i
$9$	2.30996	+	1.91418i	0.769988	+	0.638059i
$10$	−0.151270	+	0.0873359i	−0.0478358	+	0.0276180i
$11$	−4.31014	−	0.759994i	−1.29956	−	0.229147i	−0.519292	−	0.854597i	$-0.673804\pi$
$11$	−4.31014	−	0.759994i	−1.29956	−	0.229147i	−0.780264	+	0.625450i	$0.784915\pi$
$12$	−3.22358	+	1.18454i	−0.930566	+	0.341947i
$13$	1.38870	−	3.81541i	0.385155	−	1.05821i	−0.584000	−	0.811754i	$-0.698513\pi$
$13$	1.38870	−	3.81541i	0.385155	−	1.05821i	0.969155	−	0.246452i	$-0.0792647\pi$
$14$	0.0781517	+	0.337996i	0.0208869	+	0.0903332i
$15$	−0.393667	+	2.27351i	−0.101645	+	0.587017i
$16$	0.676731	−	3.83793i	0.169183	−	0.959483i
$17$	−1.85685	−	3.21617i	−0.450353	−	0.780035i	0.548055	−	0.836443i	$-0.315369\pi$
$17$	−1.85685	−	3.21617i	−0.450353	−	0.780035i	−0.998408	+	0.0564079i	$0.982035\pi$
$18$	0.132259	−	0.370462i	0.0311738	−	0.0873186i
$19$	4.31784	+	2.49291i	0.990581	+	0.571912i	0.905448	−	0.424458i	$-0.139535\pi$
$19$	4.31784	+	2.49291i	0.990581	+	0.571912i	0.0851328	+	0.996370i	$0.472869\pi$
$20$	−2.02342	−	1.69785i	−0.452450	−	0.379650i
$21$	4.09018	+	2.06650i	0.892551	+	0.450946i
$22$	0.0996512	+	0.565150i	0.0212457	+	0.120490i
$23$	0.242663	+	0.289194i	0.0505987	+	0.0603012i	0.790750	−	0.612139i	$-0.209691\pi$
$23$	0.242663	+	0.289194i	0.0505987	+	0.0603012i	−0.740152	+	0.672440i	$0.765246\pi$
$24$	0.583550	+	0.691115i	0.119117	+	0.141073i
$25$	3.03088	−	1.10315i	0.606176	−	0.220630i
$26$	−0.532388			−0.104410
$27$	−2.63953	−	4.47581i	−0.507977	−	0.861370i
$28$	−4.39872	+	2.85866i	−0.831280	+	0.540236i
$29$	1.57190	+	4.31876i	0.291895	+	0.801974i	0.995789	+	0.0916699i	$0.0292204\pi$
$29$	1.57190	+	4.31876i	0.291895	+	0.801974i	−0.703895	+	0.710304i	$0.748557\pi$
$30$	0.297781	−	0.0534526i	0.0543671	−	0.00975907i
$31$	0.693448	+	0.826419i	0.124547	+	0.148429i	0.824714	−	0.565549i	$-0.191336\pi$
$31$	0.693448	+	0.826419i	0.124547	+	0.148429i	−0.700168	+	0.713979i	$0.746891\pi$
$32$	−1.53182	+	0.270102i	−0.270791	+	0.0477477i
$33$	6.57659	+	3.77004i	1.14484	+	0.656281i
$34$	−0.313002	+	0.373021i	−0.0536794	+	0.0639727i
$35$	0.185638	+	3.51963i	0.0313785	+	0.594925i
$36$	5.94831	−	0.0366271i	0.991385	−	0.00610451i
$37$	−0.172576	−	0.298911i	−0.0283713	−	0.0491406i	0.851491	−	0.524369i	$-0.175699\pi$
$37$	−0.172576	−	0.298911i	−0.0283713	−	0.0491406i	−0.879862	+	0.475228i	$0.842365\pi$
$38$	0.113522	−	0.643813i	0.0184156	−	0.104440i
$39$	−4.50387	+	5.40118i	−0.721196	+	0.864882i
$40$	−0.237938	+	0.653729i	−0.0376213	+	0.103364i
$41$	5.09719	+	1.85523i	0.796047	+	0.289738i	0.707848	−	0.706365i	$-0.249666\pi$
$41$	5.09719	+	1.85523i	0.796047	+	0.289738i	0.0881999	+	0.996103i	$0.471889\pi$
$42$	0.0711916	−	0.596639i	0.0109851	−	0.0920635i
$43$	−0.390810	+	2.21639i	−0.0595979	+	0.337997i	−0.999998	−	0.00207394i	$-0.999340\pi$
$43$	−0.390810	+	2.21639i	−0.0595979	+	0.337997i	0.940400	+	0.340071i	$0.110451\pi$
$44$	−7.51538	+	4.33901i	−1.13299	+	0.654130i
$45$	1.97686	−	3.47325i	0.294694	−	0.517761i
$46$	0.0247502	−	0.0428686i	0.00364921	−	0.00632062i
$47$	9.77186	+	8.19957i	1.42537	+	1.19603i	0.948386	+	0.317119i	$0.102716\pi$
$47$	9.77186	+	8.19957i	1.42537	+	1.19603i	0.476987	+	0.878910i	$0.341729\pi$
$48$	−3.35701	+	5.85607i	−0.484542	+	0.845251i
$49$	6.79320	+	1.68890i	0.970458	+	0.241272i
$50$	−0.271846	−	0.323973i	−0.0384448	−	0.0458167i
$51$	1.13646	+	6.33114i	0.159136	+	0.886537i
$52$	−2.75352	−	7.56523i	−0.381844	−	1.04911i
$53$		−	9.19872i		−	1.26354i	−0.775155	−	0.631771i	$-0.782328\pi$
$53$		−	9.19872i		−	1.26354i	0.775155	−	0.631771i	$-0.217672\pi$
$54$	−0.433108	+	0.525947i	−0.0589385	+	0.0715724i
$55$			5.83030i			0.786157i
$56$	1.10374	+	0.831152i	0.147494	+	0.111067i
$57$	−5.57125	−	6.59819i	−0.737930	−	0.873952i
$58$	0.461636	−	0.387359i	0.0606158	−	0.0508627i
$59$	−2.24314	−	12.7215i	−0.292032	−	1.65620i	−0.679026	−	0.734115i	$-0.737597\pi$
$59$	−2.24314	−	12.7215i	−0.292032	−	1.65620i	0.386993	−	0.922082i	$-0.373514\pi$
$60$	2.29969	+	3.95501i	0.296889	+	0.510590i
$61$	−1.14717	+	1.36715i	−0.146880	+	0.175045i	−0.834468	−	0.551056i	$-0.814225\pi$
$61$	−1.14717	+	1.36715i	−0.146880	+	0.175045i	0.687588	+	0.726101i	$0.258670\pi$
$62$	0.0707275	−	0.122504i	0.00898240	−	0.0155580i
$63$	−5.45077	−	5.76967i	−0.686732	−	0.726911i
$64$	−3.79516	−	6.57342i	−0.474395	−	0.821677i
$65$	−5.32670	−	0.939241i	−0.660696	−	0.116498i
$66$	0.169586	−	0.979395i	0.0208746	−	0.120555i
$67$	5.40821	+	1.96843i	0.660718	+	0.240482i	0.650546	−	0.759467i	$-0.274540\pi$
$67$	5.40821	+	1.96843i	0.660718	+	0.240482i	0.0101714	+	0.999948i	$0.496762\pi$
$68$	−6.91949	−	2.51849i	−0.839111	−	0.305412i
$69$	−0.225530	−	0.613753i	−0.0271506	−	0.0738872i
$70$	0.425340	−	0.180714i	0.0508378	−	0.0215995i
$71$	2.30444	−	1.33047i	0.273487	−	0.157898i	−0.356984	−	0.934110i	$-0.616195\pi$
$71$	2.30444	−	1.33047i	0.273487	−	0.157898i	0.630471	+	0.776213i	$0.282862\pi$
$72$	−0.544894	−	1.46888i	−0.0642164	−	0.173109i
$73$	−4.63485	−	2.67593i	−0.542469	−	0.313194i	0.203610	−	0.979052i	$-0.434732\pi$
$73$	−4.63485	−	2.67593i	−0.542469	−	0.313194i	−0.746079	+	0.665858i	$0.768066\pi$
$74$	−0.0290904	+	0.0346686i	−0.00338169	+	0.00403015i
$75$	−5.58652	+	0.0171995i	−0.645076	+	0.00198603i
$76$	9.73572	−	1.71667i	1.11676	−	0.196916i
$77$	11.0746	+	3.38180i	1.26207	+	0.385392i
$78$	0.867479	+	0.312715i	0.0982226	+	0.0354080i
$79$	5.48206	−	1.99531i	0.616780	−	0.224489i	−0.0146875	−	0.999892i	$-0.504675\pi$
$79$	5.48206	−	1.99531i	0.616780	−	0.224489i	0.631467	+	0.775403i	$0.282453\pi$
$80$	−5.19155			−0.580432
$81$	1.67186	+	8.84335i	0.185763	+	0.982595i
$82$		−	0.711242i		−	0.0785435i
$83$	−4.03800	+	1.46971i	−0.443228	+	0.161322i	−0.553987	−	0.832526i	$-0.686894\pi$
$83$	−4.03800	+	1.46971i	−0.443228	+	0.161322i	0.110759	+	0.993847i	$0.464672\pi$
$84$	8.84645	−	2.07420i	0.965227	−	0.226314i
$85$	−3.78977	+	3.17999i	−0.411058	+	0.344918i
$86$	0.290615	−	0.0512433i	0.0313379	−	0.00552571i
$87$	−0.0245079	−	7.96035i	−0.00262753	−	0.853439i
$88$	1.75088	+	1.46916i	0.186644	+	0.156613i
$89$	−5.59352	+	9.68826i	−0.592912	+	1.02695i	0.400926	+	0.916110i	$0.368688\pi$
$89$	−5.59352	+	9.68826i	−0.592912	+	1.02695i	−0.993838	+	0.110843i	$0.964645\pi$
$90$	−0.516605	−	0.0878150i	−0.0544549	−	0.00925652i
$91$	−4.87378	+	9.57326i	−0.510911	+	1.00355i
$92$	0.737171	+	0.129983i	0.0768554	+	0.0135517i
$93$	−0.644488	−	1.75390i	−0.0668303	−	0.181871i
$94$	0.572067	−	1.57174i	0.0590042	−	0.162113i
$95$	2.27163	−	6.24126i	0.233065	−	0.640340i
$96$	2.65463	+	0.459660i	0.270937	+	0.0469138i
$97$	−14.5132	−	2.55906i	−1.47359	−	0.259833i	−0.621575	−	0.783354i	$-0.713507\pi$
$97$	−14.5132	−	2.55906i	−1.47359	−	0.259833i	−0.852013	+	0.523521i	$0.824618\pi$
$98$	−0.0965524	−	0.912754i	−0.00975327	−	0.0922021i
$99$	−8.50151	−	10.0059i	−0.854434	−	1.00563i
$100$	3.19767	−	5.53853i	0.319767	−	0.553853i
$101$	9.33893	+	7.83629i	0.929258	+	0.779740i	0.975684	−	0.219182i	$-0.0703388\pi$
$101$	9.33893	+	7.83629i	0.929258	+	0.779740i	−0.0464262	+	0.998922i	$0.514783\pi$
$102$	0.729116	−	0.423953i	0.0721932	−	0.0419776i
$103$	−8.85590	+	1.56153i	−0.872597	+	0.153862i	−0.591976	−	0.805956i	$-0.701652\pi$
$103$	−8.85590	+	1.56153i	−0.872597	+	0.153862i	−0.280622	+	0.959818i	$0.590541\pi$
$104$	−1.62432	+	1.36297i	−0.159278	+	0.133650i
$105$	1.76489	−	5.84396i	0.172235	−	0.570312i
$106$	−1.13341	+	0.412526i	−0.110086	+	0.0400680i
$107$		−	18.2346i		−	1.76280i	−0.472370	−	0.881401i	$-0.656601\pi$
$107$		−	18.2346i		−	1.76280i	0.472370	−	0.881401i	$-0.343399\pi$
$108$	−9.71376	−	3.43425i	−0.934707	−	0.330461i
$109$	−10.0889			−0.966342			−0.483171	−	0.875526i	$-0.660515\pi$
$109$	−10.0889			−0.966342			−0.483171	+	0.875526i	$0.660515\pi$
$110$	0.718371	−	0.261466i	0.0684940	−	0.0249298i
$111$	0.105623	+	0.588416i	0.0100253	+	0.0558500i
$112$	−3.01130	+	9.86133i	−0.284541	+	0.931809i
$113$	16.1779	−	2.85260i	1.52189	−	0.268350i	0.650714	−	0.759323i	$-0.274470\pi$
$113$	16.1779	−	2.85260i	1.52189	−	0.268350i	0.871175	+	0.490973i	$0.163359\pi$
$114$	−0.563138	+	0.982355i	−0.0527427	+	0.0920060i
$115$	0.323262	−	0.385248i	0.0301443	−	0.0359246i
$116$	7.89196	+	4.55642i	0.732750	+	0.423053i
$117$	10.5112	−	6.15526i	0.971762	−	0.569054i
$118$	−1.46686	+	0.846893i	−0.135036	+	0.0779628i
$119$	3.84218	+	9.04318i	0.352212	+	0.828987i
$120$	0.771688	−	0.925433i	0.0704452	−	0.0844801i
$121$	7.66310	+	2.78914i	0.696646	+	0.253558i
$122$	0.219897	+	0.0800359i	0.0199085	+	0.00724611i
$123$	−7.21569	−	6.01693i	−0.650617	−	0.542528i
$124$	2.10658	+	0.371447i	0.189177	+	0.0333569i
$125$	−5.47870	−	9.48939i	−0.490030	−	0.848757i
$126$	−0.466456	+	0.930354i	−0.0415552	+	0.0828826i
$127$	−10.9612	+	18.9854i	−0.972652	+	1.68468i	−0.285175	+	0.958475i	$0.592052\pi$
$127$	−10.9612	+	18.9854i	−0.972652	+	1.68468i	−0.687476	+	0.726207i	$0.741281\pi$
$128$	−2.63939	+	3.14550i	−0.233291	+	0.278026i
$129$	1.93866	−	3.38186i	0.170689	−	0.297756i
$130$	0.123154	+	0.698442i	0.0108013	+	0.0612574i
$131$	8.67264	−	7.27721i	0.757732	−	0.635813i	−0.179803	−	0.983703i	$-0.557546\pi$
$131$	8.67264	−	7.27721i	0.757732	−	0.635813i	0.937535	+	0.347890i	$0.113102\pi$
$132$	14.7943	−	2.65563i	1.28768	−	0.231143i
$133$	−10.5376	−	7.93515i	−0.913729	−	0.688064i
$134$		−	0.754639i		−	0.0651909i
$135$	−5.26125	+	4.49817i	−0.452816	+	0.387141i
$136$			1.93941i			0.166303i
$137$	3.91826	+	10.7653i	0.334760	+	0.919745i	0.986855	+	0.161608i	$0.0516680\pi$
$137$	3.91826	+	10.7653i	0.334760	+	0.919745i	−0.652095	+	0.758137i	$0.726110\pi$
$138$	−0.0655084	+	0.0553127i	−0.00557645	+	0.00470853i
$139$	−9.59685	−	11.4371i	−0.813994	−	0.970081i	0.185928	−	0.982563i	$-0.440471\pi$
$139$	−9.59685	−	11.4371i	−0.813994	−	0.970081i	−0.999922	+	0.0124827i	$0.996027\pi$
$140$	4.76782	+	5.10942i	0.402954	+	0.431825i
$141$	−11.1061	−	19.1003i	−0.935303	−	1.60853i
$142$	−0.267277	−	0.224272i	−0.0224294	−	0.0188205i
$143$	−8.88517	+	15.3896i	−0.743016	+	1.28694i
$144$	8.90970	−	7.57010i	0.742475	−	0.630842i
$145$	5.30219	−	3.06122i	0.440322	−	0.254220i
$146$	−0.121856	+	0.691081i	−0.0100849	+	0.0571943i
$147$	−10.0769	−	6.74213i	−0.831128	−	0.556081i
$148$	−0.643098	−	0.234068i	−0.0528623	−	0.0192403i
$149$	−1.04227	+	2.86360i	−0.0853857	+	0.234595i	−0.975036	−	0.222047i	$-0.928726\pi$
$149$	−1.04227	+	2.86360i	−0.0853857	+	0.234595i	0.889650	+	0.456643i	$0.150948\pi$
$150$	0.252653	+	0.687563i	0.0206290	+	0.0561393i
$151$	−0.106414	+	0.603503i	−0.00865984	+	0.0491124i	−0.988831	−	0.149038i	$-0.952382\pi$
$151$	−0.106414	+	0.603503i	−0.00865984	+	0.0491124i	0.980172	+	0.198150i	$0.0634934\pi$
$152$	−1.30187	−	2.25490i	−0.105596	−	0.182897i
$153$	1.86704	−	10.9836i	0.150941	−	0.887969i
$154$	−0.0799700	−	1.51620i	−0.00644417	−	0.122179i
$155$	0.923771	−	1.10091i	0.0741991	−	0.0884270i
$156$	0.0429309	+	13.9442i	0.00343722	+	1.11643i
$157$	1.89383	−	0.333933i	0.151144	−	0.0266507i	−0.0975643	−	0.995229i	$-0.531105\pi$
$157$	1.89383	−	0.333933i	0.151144	−	0.0266507i	0.248708	+	0.968579i	$0.419994\pi$
$158$	−0.491697	−	0.585981i	−0.0391173	−	0.0466182i
$159$	−5.40317	+	14.9885i	−0.428499	+	1.18867i
$160$	0.708696	+	1.94713i	0.0560273	+	0.153934i
$161$	−0.544274	−	0.837495i	−0.0428948	−	0.0660038i
$162$	1.01464	−	0.602585i	0.0797179	−	0.0473435i
$163$	14.3745			1.12590			0.562949	−	0.826492i	$-0.309667\pi$
$163$	14.3745			1.12590			0.562949	+	0.826492i	$0.309667\pi$
$164$	10.1067	−	3.67856i	0.789204	−	0.287247i
$165$	3.42461	−	9.49995i	0.266606	−	0.739570i
$166$	0.362176	+	0.431625i	0.0281103	+	0.0335006i
$167$	2.72667	+	15.4637i	0.210996	+	1.19662i	0.887720	+	0.460383i	$0.152288\pi$
$167$	2.72667	+	15.4637i	0.210996	+	1.19662i	−0.676724	+	0.736237i	$0.736601\pi$
$168$	−1.31025	−	2.00261i	−0.101088	−	0.154505i
$169$	−2.67033	−	2.24067i	−0.205410	−	0.172359i
$170$	0.561773	+	0.324340i	0.0430861	+	0.0248757i
$171$	5.20219	+	14.0236i	0.397822	+	1.07241i
$172$	2.23124	+	3.86462i	0.170130	+	0.294674i
$173$	0.759414	−	4.30685i	0.0577372	−	0.327444i	−0.942235	−	0.334954i	$-0.891279\pi$
$173$	0.759414	−	4.30685i	0.0577372	−	0.327444i	0.999972	+	0.00750984i	$0.00239048\pi$
$174$	−0.979723	+	0.360010i	−0.0742726	+	0.0272923i
$175$	−8.31424	+	1.92243i	−0.628497	+	0.145322i
$176$	−5.83361	+	16.0277i	−0.439725	+	1.20813i
$177$	−3.81738	+	22.0461i	−0.286932	+	1.65709i
$178$	1.44457	+	0.254717i	0.108275	+	0.0190918i
$179$	−12.1181	+	6.99637i	−0.905747	+	0.522933i	−0.879060	−	0.476710i	$-0.841829\pi$
$179$	−12.1181	+	6.99637i	−0.905747	+	0.522933i	−0.0266868	+	0.999644i	$0.508496\pi$
$180$	−1.42404	−	7.79514i	−0.106142	−	0.581015i
$181$	18.7936	+	10.8505i	1.39691	+	0.806509i	0.994068	−	0.108759i	$-0.0346878\pi$
$181$	18.7936	+	10.8505i	1.39691	+	0.806509i	0.402846	+	0.915268i	$0.368021\pi$
$182$	1.39812	+	0.171193i	0.103636	+	0.0126897i
$183$	2.67225	−	1.55381i	0.197539	−	0.114861i
$184$	−0.0342348	−	0.194155i	−0.00252382	−	0.0143133i
$185$	−0.352221	+	0.295548i	−0.0258958	+	0.0217292i
$186$	−0.187201	+	0.158065i	−0.0137262	+	0.0115899i
$187$	5.55904	+	15.2733i	0.406517	+	1.11690i
$188$	25.2932			1.84470
$189$	5.49254	+	12.6029i	0.399523	+	0.916723i
$190$	−0.870881			−0.0631803
$191$	−7.16981	−	19.6989i	−0.518789	−	1.42536i	−0.871855	−	0.489763i	$-0.837083\pi$
$191$	−7.16981	−	19.6989i	−0.518789	−	1.42536i	0.353066	−	0.935598i	$-0.385139\pi$
$192$	2.32277	+	12.9400i	0.167632	+	0.933865i
$193$	1.16810	−	0.980152i	0.0840817	−	0.0705529i	−0.599778	−	0.800166i	$-0.704744\pi$
$193$	1.16810	−	0.980152i	0.0840817	−	0.0705529i	0.683860	+	0.729614i	$0.260300\pi$
$194$	0.335547	+	1.90298i	0.0240908	+	0.136626i
$195$	8.12769	+	4.65922i	0.582036	+	0.333654i
$196$	12.4709	−	6.09279i	0.890776	−	0.435199i
$197$	21.6293	+	12.4877i	1.54102	+	0.889709i	0.998775	+	0.0494899i	$0.0157596\pi$
$197$	21.6293	+	12.4877i	1.54102	+	0.889709i	0.542247	+	0.840219i	$0.317574\pi$
$198$	−0.851605	+	1.49623i	−0.0605210	+	0.106332i
$199$	−0.716693	+	0.413783i	−0.0508050	+	0.0293323i	−0.525187	−	0.850987i	$-0.676005\pi$
$199$	−0.716693	+	0.413783i	−0.0508050	+	0.0293323i	0.474382	+	0.880319i	$0.342671\pi$
$200$	−1.65881	−	0.292492i	−0.117295	−	0.0206823i
$201$	−7.65597	−	6.38406i	−0.540011	−	0.450297i
$202$	0.546722	−	1.50211i	0.0384672	−	0.105688i
$203$	−2.73930	−	11.8471i	−0.192261	−	0.831505i
$204$	9.79538	+	8.16804i	0.685814	+	0.571877i
$205$	1.25478	−	7.11618i	0.0876373	−	0.497016i
$206$	0.589553	+	1.02114i	0.0410761	+	0.0711460i
$207$	0.00697361	+	1.13253i	0.000484700	+	0.0787162i
$208$	−13.7035	−	7.91174i	−0.950169	−	0.548580i
$209$	−16.7159	−	14.0263i	−1.15626	−	0.970220i
$210$	−0.799202	+	0.0446206i	−0.0551502	+	0.00307911i
$211$	1.02986	+	5.84064i	0.0708987	+	0.402086i	0.999518	+	0.0310519i	$0.00988572\pi$
$211$	1.02986	+	5.84064i	0.0708987	+	0.402086i	−0.928619	+	0.371034i	$0.879003\pi$
$212$	−11.7240	−	13.9721i	−0.805207	−	0.959608i
$213$	−4.53638	+	0.814294i	−0.310827	+	0.0557945i
$214$	−2.24674	+	0.817747i	−0.153584	+	0.0559000i
$215$	2.99810			0.204469
$216$	0.0250629	+	2.71347i	0.00170532	+	0.184628i
$217$	−1.55535	−	2.39327i	−0.105584	−	0.162466i
$218$	0.452447	+	1.24309i	0.0306436	+	0.0841926i
$219$	5.98029	+	7.08263i	0.404110	+	0.478600i
$220$	7.43085	+	8.85575i	0.500988	+	0.597054i
$221$	−14.8496	+	2.61839i	−0.998893	+	0.176132i
$222$	0.0677640	−	0.0394022i	0.00454802	−	0.00264451i
$223$	−9.34376	+	11.1355i	−0.625705	+	0.745686i	−0.982040	−	0.188672i	$-0.939582\pi$
$223$	−9.34376	+	11.1355i	−0.625705	+	0.745686i	0.356336	+	0.934358i	$0.384026\pi$
$224$	4.10964	−	0.216757i	0.274587	−	0.0144827i
$225$	9.11285	+	3.25340i	0.607523	+	0.216893i
$226$	−1.07699	−	1.86541i	−0.0716405	−	0.124085i
$227$	−1.15766	+	6.56541i	−0.0768366	+	0.435762i	0.921985	+	0.387226i	$0.126567\pi$
$227$	−1.15766	+	6.56541i	−0.0768366	+	0.435762i	−0.998821	+	0.0485359i	$0.984544\pi$
$228$	−16.8718	−	2.92143i	−1.11736	−	0.193476i
$229$	6.09035	−	16.7331i	0.402462	−	1.10575i	−0.558604	−	0.829434i	$-0.688663\pi$
$229$	6.09035	−	16.7331i	0.402462	−	1.10575i	0.961066	−	0.276320i	$-0.0891149\pi$
$230$	−0.0619647	−	0.0225533i	−0.00408583	−	0.00148712i
$231$	−16.0587	−	12.0154i	−1.05659	−	0.790555i
$232$	0.416778	−	2.36367i	0.0273628	−	0.155182i
$233$	−13.8987	+	8.02444i	−0.910537	+	0.525699i	−0.880604	−	0.473853i	$-0.842863\pi$
$233$	−13.8987	+	8.02444i	−0.910537	+	0.525699i	−0.0299330	+	0.999552i	$0.509529\pi$
$234$	−1.22980	−	1.01908i	−0.0803943	−	0.0666196i
$235$	8.49658	−	14.7165i	0.554256	−	0.959999i
$236$	−19.6210	−	16.4640i	−1.27722	−	1.07171i
$237$	−10.1045	+	0.0311094i	−0.656360	+	0.00202077i
$238$	0.941934	−	0.878958i	0.0610565	−	0.0569744i
$239$	−1.31201	−	1.56359i	−0.0848668	−	0.101140i	0.721940	−	0.691956i	$-0.243251\pi$
$239$	−1.31201	−	1.56359i	−0.0848668	−	0.101140i	−0.806807	+	0.590815i	$0.798806\pi$
$240$	8.45916	+	3.04942i	0.546037	+	0.196839i
$241$	3.55423	+	9.76517i	0.228948	+	0.629030i	0.999970	−	0.00777897i	$-0.00247615\pi$
$241$	3.55423	+	9.76517i	0.228948	+	0.629030i	−0.771021	+	0.636809i	$0.780254\pi$
$242$		−	1.06928i		−	0.0687359i
$243$	2.47028	−	15.3915i	0.158468	−	0.987364i
$244$			3.53868i			0.226541i
$245$	0.644249	−	9.30272i	0.0411596	−	0.594329i
$246$	−0.417771	+	1.15891i	−0.0266361	+	0.0738891i
$247$	15.5076	−	13.0125i	0.986728	−	0.827963i
$248$	−0.0978313	−	0.554829i	−0.00621230	−	0.0352317i
$249$	7.44285	−	0.0229147i	0.471671	−	0.00145216i
$250$	−0.923522	+	1.10061i	−0.0584086	+	0.0696087i
$251$	11.7343	−	20.3243i	0.740660	−	1.28286i	−0.211535	−	0.977370i	$-0.567846\pi$
$251$	11.7343	−	20.3243i	0.740660	−	1.28286i	0.952195	−	0.305490i	$-0.0988203\pi$
$252$	−15.6329	−	1.81653i	−0.984778	−	0.114431i
$253$	−0.826126	−	1.43089i	−0.0519381	−	0.0899594i
$254$	2.83082	+	0.499151i	0.177622	+	0.0313195i
$255$	8.04296	−	2.95547i	0.503670	−	0.185079i
$256$	−13.7592	−	5.00794i	−0.859951	−	0.312996i
$257$	4.71223	+	1.71511i	0.293941	+	0.106986i	0.484781	−	0.874635i	$-0.338899\pi$
$257$	4.71223	+	1.71511i	0.293941	+	0.106986i	−0.190841	+	0.981621i	$0.561121\pi$
$258$	−0.503632	−	0.0872059i	−0.0313547	−	0.00542920i
$259$	0.357092	+	0.840473i	0.0221886	+	0.0522245i
$260$	−9.28790	+	5.36237i	−0.576011	+	0.332560i
$261$	−4.63584	+	12.9851i	−0.286951	+	0.803756i
$262$	−1.28558	−	0.742232i	−0.0794236	−	0.0458552i
$263$	3.92830	−	4.68156i	0.242229	−	0.288678i	−0.631209	−	0.775613i	$-0.717441\pi$
$263$	3.92830	−	4.68156i	0.242229	−	0.288678i	0.873438	+	0.486935i	$0.161885\pi$
$264$	−1.98994	−	3.42230i	−0.122472	−	0.210628i
$265$	−12.0678	+	2.12789i	−0.741321	+	0.130715i
$266$	−0.505146	+	1.65424i	−0.0309725	+	0.101428i
$267$	14.8049	−	12.5006i	0.906042	−	0.765026i
$268$	10.7234	−	3.90301i	0.655038	−	0.238414i
$269$	4.75791			0.290095			0.145048	−	0.989425i	$-0.453666\pi$
$269$	4.75791			0.290095			0.145048	+	0.989425i	$0.453666\pi$
$270$	0.790181	+	0.446532i	0.0480889	+	0.0271750i
$271$		−	11.7607i		−	0.714413i	−0.934025	−	0.357206i	$-0.883729\pi$
$271$		−	11.7607i		−	0.714413i	0.934025	−	0.357206i	$-0.116271\pi$
$272$	−13.6000	+	4.95000i	−0.824622	+	0.300138i
$273$	13.5646	−	12.7360i	0.820965	−	0.770818i
$274$	1.15072	−	0.965565i	0.0695173	−	0.0583319i
$275$	−13.9019	+	2.45128i	−0.838317	+	0.147818i
$276$	−1.12480	−	0.644797i	−0.0677053	−	0.0388122i
$277$	−3.40027	−	2.85316i	−0.204302	−	0.171430i	0.534896	−	0.844918i	$-0.320351\pi$
$277$	−3.40027	−	2.85316i	−0.204302	−	0.171430i	−0.739198	+	0.673488i	$0.764795\pi$
$278$	−0.978821	+	1.69537i	−0.0587058	+	0.101681i
$279$	0.0199282	+	3.23638i	0.00119307	+	0.193757i
$280$	0.835069	−	1.64027i	0.0499049	−	0.0980250i
$281$	8.77039	+	1.54646i	0.523198	+	0.0922539i	0.429009	−	0.903300i	$-0.358863\pi$
$281$	8.77039	+	1.54646i	0.523198	+	0.0922539i	0.0941892	+	0.995554i	$0.469974\pi$
$282$	−1.85535	+	2.22499i	−0.110484	+	0.132496i
$283$	−8.13265	+	22.3443i	−0.483436	+	1.32823i	0.423093	+	0.906086i	$0.360944\pi$
$283$	−8.13265	+	22.3443i	−0.483436	+	1.32823i	−0.906529	+	0.422143i	$0.861278\pi$
$284$	1.80454	−	4.95794i	0.107080	−	0.294200i
$285$	−7.36744	+	8.83527i	−0.436409	+	0.523356i
$286$	2.29467	+	0.404612i	0.135686	+	0.0239252i
$287$	−12.7894	−	6.51111i	−0.754932	−	0.384339i
$288$	−4.05548	−	2.30826i	−0.238972	−	0.136015i
$289$	1.60419	−	2.77853i	0.0943639	−	0.163443i
$290$	−0.614965	−	0.516017i	−0.0361120	−	0.0303016i
$291$	22.1448	+	12.6945i	1.29815	+	0.744167i
$292$	−10.4505	+	1.84271i	−0.611570	+	0.107836i
$293$	−20.3420	+	17.0689i	−1.18839	+	0.997178i	−0.188505	+	0.982072i	$0.560364\pi$
$293$	−20.3420	+	17.0689i	−1.18839	+	0.997178i	−0.999886	+	0.0151056i	$0.995192\pi$
$294$	−0.378812	+	1.54397i	−0.0220928	+	0.0900459i
$295$	−16.1705	+	5.88558i	−0.941482	+	0.342671i
$296$			0.180249i			0.0104767i
$297$	7.97515	+	21.2974i	0.462765	+	1.23580i
$298$	0.399576			0.0231468
$299$	1.44038	−	0.524256i	0.0832995	−	0.0303185i
$300$	−8.46355	+	7.14628i	−0.488643	+	0.412591i
$301$	1.73902	−	5.69488i	0.100235	−	0.328248i
$302$	0.0791319	−	0.0139531i	0.00455353	−	0.000802910i
$303$	−10.6141	−	18.2541i	−0.609761	−	1.04867i
$304$	12.4896	−	14.8846i	0.716329	−	0.853688i
$305$	2.05893	+	1.18873i	0.117894	+	0.0680662i
$306$	−1.43705	+	0.262525i	−0.0821508	+	0.0150075i
$307$	27.6153	−	15.9437i	1.57609	−	0.909956i	0.580693	−	0.814123i	$-0.302782\pi$
$307$	27.6153	−	15.9437i	1.57609	−	0.909956i	0.995397	−	0.0958335i	$-0.0305517\pi$
$308$	21.1317	−	8.97821i	1.20409	−	0.511581i
$309$	15.3471	+	2.65742i	0.873067	+	0.151175i
$310$	−0.177074	−	0.0644497i	−0.0100571	−	0.00366050i
$311$	5.67000	+	2.06371i	0.321516	+	0.117022i	0.497736	−	0.867328i	$-0.334165\pi$
$311$	5.67000	+	2.06371i	0.321516	+	0.117022i	−0.176220	+	0.984351i	$0.556387\pi$
$312$	3.44727	−	1.26673i	0.195163	−	0.0717147i
$313$	4.63763	+	0.817739i	0.262134	+	0.0462213i	0.303170	−	0.952936i	$-0.401955\pi$
$313$	4.63763	+	0.817739i	0.262134	+	0.0462213i	−0.0410364	+	0.999158i	$0.513066\pi$
$314$	−0.126076	−	0.218369i	−0.00711485	−	0.0123233i
$315$	−6.30837	+	8.48555i	−0.355436	+	0.478107i
$316$	5.78373	−	10.0177i	0.325360	−	0.563541i
$317$	−9.57584	+	11.4120i	−0.537833	+	0.640964i	−0.964700	−	0.263350i	$-0.915173\pi$
$317$	−9.57584	+	11.4120i	−0.537833	+	0.640964i	0.426867	+	0.904314i	$0.359617\pi$
$318$	2.08909	−	0.00643180i	0.117151	−	0.000360678i
$319$	−3.49288	−	19.8091i	−0.195564	−	1.10910i
$320$	−7.74578	+	6.49948i	−0.433002	+	0.363332i
$321$	−10.7107	+	29.7116i	−0.597811	+	1.65834i
$322$	−0.0787820	+	0.104620i	−0.00439035	+	0.00583025i
$323$		−	18.5159i		−	1.03025i
$324$	13.8105	+	11.3015i	0.767249	+	0.627861i
$325$		−	13.0960i		−	0.726436i
$326$	−0.644639	−	1.77113i	−0.0357032	−	0.0980938i
$327$	16.4390	+	5.92605i	0.909078	+	0.327711i
$328$	−1.82085	−	2.17000i	−0.100540	−	0.119818i
$329$	−23.0256	−	24.6754i	−1.26944	−	1.36040i
$330$	−1.32410	+	0.00407658i	−0.0728894	+	0.000224408i
$331$	8.22997	+	6.90576i	0.452360	+	0.379575i	0.840311	−	0.542105i	$-0.182373\pi$
$331$	8.22997	+	6.90576i	0.452360	+	0.379575i	−0.387951	+	0.921680i	$0.626817\pi$
$332$	−4.26021	+	7.37890i	−0.233809	+	0.404970i
$333$	0.173523	−	1.02081i	0.00950899	−	0.0559402i
$334$	1.78306	−	1.02945i	0.0975646	−	0.0563290i
$335$	1.33134	−	7.55039i	0.0727388	−	0.412522i
$336$	10.6990	−	14.2994i	0.583680	−	0.780095i
$337$	−8.99836	−	3.27514i	−0.490172	−	0.178408i	0.0850964	−	0.996373i	$-0.472880\pi$
$337$	−8.99836	−	3.27514i	−0.490172	−	0.178408i	−0.575268	+	0.817965i	$0.695102\pi$
$338$	−0.156327	+	0.429506i	−0.00850308	+	0.0233620i
$339$	−28.0360	−	4.85455i	−1.52271	−	0.263663i
$340$	−1.70337	+	9.66030i	−0.0923782	+	0.523903i
$341$	−2.36078	−	4.08900i	−0.127844	−	0.221432i
$342$	1.49460	−	1.26988i	0.0808188	−	0.0686674i
$343$	−17.2968	−	6.61969i	−0.933940	−	0.357430i
$344$	0.755482	−	0.900348i	0.0407328	−	0.0485435i
$345$	−0.753014	+	0.437850i	−0.0405409	+	0.0235730i
$346$	−0.564718	+	0.0995751i	−0.0303594	+	0.00535319i
$347$	14.4006	+	17.1620i	0.773065	+	0.921303i	0.998598	−	0.0529329i	$-0.0168569\pi$
$347$	14.4006	+	17.1620i	0.773065	+	0.921303i	−0.225533	+	0.974235i	$0.572412\pi$
$348$	−10.1829	−	12.0599i	−0.545860	−	0.646478i
$349$	4.98766	+	13.7035i	0.266983	+	0.733531i	0.998654	+	0.0518722i	$0.0165189\pi$
$349$	4.98766	+	13.7035i	0.266983	+	0.733531i	−0.731670	+	0.681659i	$0.761259\pi$
$350$	0.609729	+	0.938212i	0.0325914	+	0.0501496i
$351$	−20.7426	+	3.85534i	−1.10716	+	0.205783i
$352$	6.80766			0.362849
$353$	7.53944	−	2.74413i	0.401284	−	0.146055i	−0.133491	−	0.991050i	$-0.542619\pi$
$353$	7.53944	−	2.74413i	0.401284	−	0.146055i	0.534775	+	0.844995i	$0.320396\pi$
$354$	2.88757	−	0.518328i	0.153473	−	0.0275488i
$355$	−2.27852	−	2.71544i	−0.120931	−	0.144120i
$356$	3.85182	+	21.8447i	0.204146	+	1.15777i
$357$	−0.948680	−	16.9919i	−0.0502095	−	0.899306i
$358$	1.40549	+	1.17935i	0.0742827	+	0.0623305i
$359$	−1.26586	−	0.730844i	−0.0668095	−	0.0385725i	0.466223	−	0.884667i	$-0.345614\pi$
$359$	−1.26586	−	0.730844i	−0.0668095	−	0.0385725i	−0.533033	+	0.846095i	$0.678948\pi$
$360$	−1.80098	+	1.05464i	−0.0949200	+	0.0555842i
$361$	2.92916	+	5.07346i	0.154167	+	0.267024i
$362$	0.494107	−	2.80222i	0.0259697	−	0.147281i
$363$	−10.8481	−	9.04583i	−0.569375	−	0.474783i
$364$	4.79847	+	20.7528i	0.251508	+	1.08774i
$365$	−2.43842	+	6.69949i	−0.127633	+	0.350668i
$366$	−0.311291	−	0.259575i	−0.0162714	−	0.0135682i
$367$	25.7879	+	4.54711i	1.34612	+	0.237357i	0.799824	−	0.600235i	$-0.204926\pi$
$367$	25.7879	+	4.54711i	1.34612	+	0.237357i	0.546296	+	0.837592i	$0.316037\pi$
$368$	1.27413	−	0.735617i	0.0664184	−	0.0383467i
$369$	8.22310	+	14.0424i	0.428077	+	0.731019i
$370$	0.0522112	+	0.0301442i	0.00271433	+	0.00156712i
$371$	−2.95791	+	24.1571i	−0.153567	+	1.25417i
$372$	−3.21431	−	1.84261i	−0.166654	−	0.0955349i
$373$	−2.15588	−	12.2266i	−0.111627	−	0.633069i	−0.988365	−	0.152101i	$-0.951396\pi$
$373$	−2.15588	−	12.2266i	−0.111627	−	0.633069i	0.876738	−	0.480969i	$-0.159715\pi$
$374$	1.63258	−	1.36990i	0.0844186	−	0.0708356i
$375$	3.35316	+	18.6802i	0.173156	+	0.964642i
$376$	−2.27843	−	6.25995i	−0.117501	−	0.322832i
$377$	18.6608			0.961078
$378$	1.30652	−	1.24194i	0.0672003	−	0.0638786i
$379$	7.53240			0.386913			0.193457	−	0.981109i	$-0.438030\pi$
$379$	7.53240			0.386913			0.193457	+	0.981109i	$0.438030\pi$
$380$	−4.50421	−	12.3752i	−0.231061	−	0.634835i
$381$	29.0120	−	24.4966i	1.48633	−	1.25500i
$382$	−2.10563	+	1.76683i	−0.107733	+	0.0903991i
$383$	−0.508365	−	2.88308i	−0.0259762	−	0.147319i	0.969061	−	0.246821i	$-0.0793860\pi$
$383$	−0.508365	−	2.88308i	−0.0259762	−	0.147319i	−0.995037	+	0.0995025i	$0.968275\pi$
$384$	6.14827	−	3.57499i	0.313752	−	0.182435i
$385$	1.87477	−	15.3112i	0.0955472	−	0.780329i
$386$	−0.173152	−	0.0999696i	−0.00881323	−	0.00508832i
$387$	−5.14532	+	4.37171i	−0.261551	+	0.222226i
$388$	−25.3059	+	14.6104i	−1.28471	+	0.741729i
$389$	−24.4465	−	4.31058i	−1.23949	−	0.218555i	−0.484791	−	0.874630i	$-0.661104\pi$
$389$	−24.4465	−	4.31058i	−1.23949	−	0.218555i	−0.754696	+	0.656075i	$0.772216\pi$
$390$	0.209584	−	1.21039i	0.0106127	−	0.0612904i
$391$	0.479508	−	1.31744i	0.0242497	−	0.0666256i
$392$	−2.63132	−	2.53764i	−0.132902	−	0.128170i
$393$	−18.4058	+	6.76341i	−0.928450	+	0.341169i
$394$	0.568661	−	3.22504i	0.0286487	−	0.162475i
$395$	−3.88578	−	6.73037i	−0.195515	−	0.338642i
$396$	−25.6659	−	4.36281i	−1.28976	−	0.219240i
$397$	18.3498	+	10.5942i	0.920948	+	0.531710i	0.883937	−	0.467605i	$-0.154883\pi$
$397$	18.3498	+	10.5942i	0.920948	+	0.531710i	0.0370106	+	0.999315i	$0.488216\pi$
$398$	0.0831244	+	0.0697497i	0.00416665	+	0.00349624i
$399$	12.5092	+	19.1192i	0.626242	+	0.957159i
$400$	−2.18273	−	12.3789i	−0.109136	−	0.618943i
$401$	−0.873706	−	1.04124i	−0.0436308	−	0.0519972i	0.743788	−	0.668416i	$-0.233027\pi$
$401$	−0.873706	−	1.04124i	−0.0436308	−	0.0519972i	−0.787419	+	0.616419i	$0.788583\pi$
$402$	−0.443262	+	1.22962i	−0.0221079	+	0.0613278i
$403$	4.11612	−	1.49815i	0.205039	−	0.0746279i
$404$	24.1726			1.20263
$405$	11.2149	−	4.23901i	0.557272	−	0.210638i
$406$	−1.33688	+	0.868815i	−0.0663481	+	0.0431186i
$407$	0.516657	+	1.41950i	0.0256097	+	0.0703622i
$408$	1.13917	−	3.16009i	0.0563975	−	0.156448i
$409$	17.0261	+	20.2910i	0.841889	+	1.00332i	0.999874	+	0.0158823i	$0.00505571\pi$
$409$	17.0261	+	20.2910i	0.841889	+	1.00332i	−0.157985	+	0.987441i	$0.550500\pi$
$410$	−0.933081	+	0.164527i	−0.0460816	+	0.00812543i
$411$	−0.0610907	−	19.8427i	−0.00301338	−	0.978768i
$412$	−11.4612	+	13.6589i	−0.564651	+	0.672925i
$413$	1.80012	+	34.1297i	0.0885782	+	1.67941i
$414$	0.139230	−	0.0516486i	0.00684278	−	0.00253839i
$415$	2.86221	+	4.95749i	0.140500	+	0.243354i
$416$	−1.09669	+	6.21964i	−0.0537696	+	0.304943i
$417$	8.91928	+	24.2727i	0.436779	+	1.18864i
$418$	−0.978588	+	2.68865i	−0.0478643	+	0.131506i
$419$	16.0247	+	5.83250i	0.782856	+	0.284936i	0.702363	−	0.711819i	$-0.252128\pi$
$419$	16.0247	+	5.83250i	0.782856	+	0.284936i	0.0804931	+	0.996755i	$0.474351\pi$
$420$	−4.76755	−	11.1259i	−0.232632	−	0.542888i
$421$	−3.15843	+	17.9124i	−0.153933	+	0.872995i	0.805823	+	0.592157i	$0.201724\pi$
$421$	−3.15843	+	17.9124i	−0.153933	+	0.872995i	−0.959755	+	0.280838i	$0.909388\pi$
$422$	0.673460	−	0.388822i	0.0327835	−	0.0189276i
$423$	6.87724	+	37.6458i	0.334383	+	1.83040i
$424$	−2.40192	+	4.16025i	−0.116648	+	0.202040i
$425$	−9.17582	−	7.69943i	−0.445093	−	0.373477i
$426$	0.303770	+	0.522425i	0.0147177	+	0.0253116i
$427$	3.45225	−	3.22143i	0.167066	−	0.155896i
$428$	−23.2404	−	27.6968i	−1.12337	−	1.33878i
$429$	23.5172	−	19.8570i	1.13542	−	0.958703i
$430$	−0.134453	−	0.369406i	−0.00648389	−	0.0178143i
$431$			3.52787i			0.169932i	0.996384	+	0.0849658i	$0.0270781\pi$
$431$			3.52787i			0.169932i	−0.996384	+	0.0849658i	$0.972922\pi$
$432$	−18.9641	+	7.10141i	−0.912412	+	0.341667i
$433$		−	19.5602i		−	0.940001i	−0.882666	−	0.470001i	$-0.844254\pi$
$433$		−	19.5602i		−	0.940001i	0.882666	−	0.470001i	$-0.155746\pi$
$434$	−0.225132	+	0.298969i	−0.0108067	+	0.0143510i
$435$	−10.4375	+	1.87357i	−0.500442	+	0.0898309i
$436$	−15.3242	+	12.8586i	−0.733897	+	0.615813i
$437$	0.326845	+	1.85363i	0.0156351	+	0.0886712i
$438$	0.604483	−	1.05448i	0.0288833	−	0.0503850i
$439$	−5.11723	+	6.09848i	−0.244232	+	0.291064i	−0.874209	−	0.485549i	$-0.838620\pi$
$439$	−5.11723	+	6.09848i	−0.244232	+	0.291064i	0.629977	+	0.776613i	$0.283064\pi$
$440$	1.52238	−	2.63683i	0.0725765	−	0.125706i
$441$	12.4592	+	16.9047i	0.593295	+	0.804985i
$442$	0.988566	+	1.71225i	0.0470213	+	0.0814433i
$443$	27.4654	+	4.84288i	1.30492	+	0.230092i	0.782529	−	0.622614i	$-0.213929\pi$
$443$	27.4654	+	4.84288i	1.30492	+	0.230092i	0.522390	+	0.852707i	$0.325041\pi$
$444$	0.910383	+	0.759138i	0.0432049	+	0.0360271i
$445$	14.0040	+	5.09703i	0.663852	+	0.241622i
$446$	1.79107	+	0.651896i	0.0848095	+	0.0308681i
$447$	3.38031	−	4.05378i	0.159883	−	0.191737i
$448$	7.85290	+	18.4831i	0.371015	+	0.873242i
$449$	−15.1431	+	8.74287i	−0.714647	+	0.412602i	−0.812779	−	0.582572i	$-0.802047\pi$
$449$	−15.1431	+	8.74287i	−0.714647	+	0.412602i	0.0981322	+	0.995173i	$0.468713\pi$
$450$	−0.00781227	−	1.26873i	−0.000368274	−	0.0598084i
$451$	−20.5596	−	11.8701i	−0.968116	−	0.558942i
$452$	20.9372	−	24.9520i	0.984803	−	1.17364i
$453$	0.527879	−	0.920849i	0.0248019	−	0.0432653i
$454$	0.860863	−	0.151793i	0.0404023	−	0.00712402i
$455$	13.6866	+	4.17941i	0.641639	+	0.195934i
$456$	0.796790	+	4.43886i	0.0373131	+	0.207869i
$457$	−25.2787	+	9.20069i	−1.18249	+	0.430390i	−0.857080	−	0.515184i	$-0.827724\pi$
$457$	−25.2787	+	9.20069i	−1.18249	+	0.430390i	−0.325407	+	0.945574i	$0.605501\pi$
$458$	−2.33487			−0.109101
$459$	−9.49373	+	16.8001i	−0.443130	+	0.784161i
$460$		−	0.997166i		−	0.0464931i
$461$	−17.3925	+	6.33036i	−0.810050	+	0.294834i	−0.713645	−	0.700508i	$-0.752957\pi$
$461$	−17.3925	+	6.33036i	−0.810050	+	0.294834i	−0.0964058	+	0.995342i	$0.530735\pi$
$462$	−0.760288	+	2.51749i	−0.0353718	+	0.117124i
$463$	−11.6402	+	9.76728i	−0.540966	+	0.453924i	−0.871868	−	0.489741i	$-0.837091\pi$
$463$	−11.6402	+	9.76728i	−0.540966	+	0.453924i	0.330902	+	0.943665i	$0.392647\pi$
$464$	17.6389	−	3.11021i	0.818864	−	0.144388i
$465$	−2.15186	+	1.25122i	−0.0997900	+	0.0580242i
$466$	1.61202	+	1.35265i	0.0746755	+	0.0626602i
$467$	12.8706	−	22.2926i	0.595581	−	1.03158i	−0.397884	−	0.917436i	$-0.630255\pi$
$467$	12.8706	−	22.2926i	0.595581	−	1.03158i	0.993465	−	0.114140i	$-0.0364114\pi$
$468$	8.12065	−	22.7461i	0.375377	−	1.05144i
$469$	−13.5697	−	6.90840i	−0.626592	−	0.319000i
$470$	−2.19431	−	0.386916i	−0.101216	−	0.0178471i
$471$	−3.28197	−	0.568287i	−0.151225	−	0.0261853i
$472$	−2.30728	+	6.33919i	−0.106201	+	0.291785i
$473$	3.36889	−	9.25595i	0.154902	−	0.425589i
$474$	0.456981	+	1.24362i	0.0209898	+	0.0571213i
$475$	15.8369	+	2.79247i	0.726647	+	0.128128i
$476$	17.3617	+	8.83891i	0.795772	+	0.405131i
$477$	17.6080	−	21.2487i	0.806213	−	0.972911i
$478$	−0.133817	+	0.231778i	−0.00612065	+	0.0106013i
$479$	1.75513	+	1.47273i	0.0801939	+	0.0672907i	0.682003	−	0.731349i	$-0.261109\pi$
$479$	1.75513	+	1.47273i	0.0801939	+	0.0672907i	−0.601810	+	0.798640i	$0.705553\pi$
$480$	−0.0110495	−	3.58895i	−0.000504337	−	0.163812i
$481$	−1.38012	+	0.243353i	−0.0629282	+	0.0110959i
$482$	1.04381	−	0.875858i	0.0475441	−	0.0398942i
$483$	0.394917	+	1.68432i	0.0179693	+	0.0766392i
$484$	15.1945	−	5.53033i	0.690657	−	0.251379i
$485$			19.6319i			0.891436i
$486$	−2.00722	+	0.385875i	−0.0910493	+	0.0175037i
$487$	35.0917			1.59016			0.795078	−	0.606507i	$-0.207430\pi$
$487$	35.0917			1.59016			0.795078	+	0.606507i	$0.207430\pi$
$488$	0.875806	−	0.318767i	0.0396459	−	0.0144299i
$489$	−23.4220	−	8.44333i	−1.05918	−	0.381820i
$490$	−1.17511	+	0.337810i	−0.0530861	+	0.0152607i
$491$	22.3682	−	3.94412i	1.00946	−	0.177996i	0.355624	−	0.934629i	$-0.384268\pi$
$491$	22.3682	−	3.94412i	1.00946	−	0.177996i	0.653840	+	0.756633i	$0.273157\pi$
$492$	−18.6288	+	0.0573534i	−0.839850	+	0.00258569i
$493$	10.9711	−	13.0748i	0.494112	−	0.588860i
$494$	−2.29877	−	1.32719i	−0.103426	−	0.0597132i
$495$	−11.1602	+	13.4678i	−0.501614	+	0.605331i
$496$	3.64102	−	2.10214i	0.163487	−	0.0943890i
$497$	−6.47960	+	2.75299i	−0.290650	+	0.123488i
$498$	−0.336605	−	0.916031i	−0.0150836	−	0.0410483i
$499$	−18.3536	−	6.68017i	−0.821621	−	0.299046i	−0.103206	−	0.994660i	$-0.532910\pi$
$499$	−18.3536	−	6.68017i	−0.821621	−	0.299046i	−0.718415	+	0.695615i	$0.755132\pi$
$500$	−20.4161	−	7.43087i	−0.913038	−	0.332319i
$501$	4.64025	−	26.7984i	0.207311	−	1.19726i
$502$	−3.03046	−	0.534353i	−0.135256	−	0.0238493i
$503$	6.03294	+	10.4494i	0.268995	+	0.465914i	0.968603	−	0.248614i	$-0.0799750\pi$
$503$	6.03294	+	10.4494i	0.268995	+	0.465914i	−0.699607	+	0.714528i	$0.746642\pi$
$504$	0.958639	+	4.03269i	0.0427012	+	0.179630i
$505$	8.12014	−	14.0645i	0.361342	−	0.625862i
$506$	−0.139257	+	0.165960i	−0.00619071	+	0.00737780i
$507$	3.03493	+	5.21948i	0.134786	+	0.231805i
$508$	7.54814	+	42.8076i	0.334895	+	1.89928i
$509$	−25.0698	+	21.0360i	−1.11120	+	0.932406i	−0.998127	−	0.0611805i	$-0.980513\pi$
$509$	−25.0698	+	21.0360i	−1.11120	+	0.932406i	−0.113072	+	0.993587i	$0.536069\pi$
$510$	−0.724848	−	0.858459i	−0.0320968	−	0.0380132i
$511$	11.3113	+	8.51774i	0.500383	+	0.376803i
$512$			10.1322i			0.447786i
$513$	−0.239280	−	25.9059i	−0.0105645	−	1.14378i
$514$		−	0.657525i		−	0.0290022i
$515$	4.09716	+	11.2569i	0.180543	+	0.496037i
$516$	−1.36560	−	7.60764i	−0.0601170	−	0.334908i
$517$	−35.8865	−	42.7678i	−1.57829	−	1.88093i
$518$	0.0875434	−	0.0816904i	0.00384644	−	0.00358927i
$519$	−3.76717	+	6.57156i	−0.165360	+	0.288460i
$520$	2.16382	+	1.81566i	0.0948900	+	0.0796221i
$521$	0.373097	−	0.646223i	0.0163457	−	0.0283115i	−0.857737	−	0.514089i	$-0.828130\pi$
$521$	0.373097	−	0.646223i	0.0163457	−	0.0283115i	0.874083	+	0.485777i	$0.161463\pi$
$522$	1.80783	−	0.0111319i	0.0791268	−	0.000487228i
$523$	−0.0341810	+	0.0197344i	−0.00149463	+	0.000862925i	−0.500747	−	0.865594i	$-0.666941\pi$
$523$	−0.0341810	+	0.0197344i	−0.00149463	+	0.000862925i	0.499252	+	0.866457i	$0.333608\pi$
$524$	3.89806	−	22.1070i	0.170287	−	0.965748i
$525$	14.6765	+	1.75122i	0.640536	+	0.0764293i
$526$	−0.753000	−	0.274070i	−0.0328324	−	0.0119500i
$527$	1.37027	−	3.76478i	0.0596898	−	0.163996i
$528$	18.9198	−	22.6892i	0.823377	−	0.987420i
$529$	3.96916	−	22.5102i	0.172572	−	0.978705i
$530$	0.803378	+	1.39149i	0.0348965	+	0.0604426i
$531$	19.1696	−	33.6799i	0.831889	−	1.46159i
$532$	−26.1193	+	1.37763i	−1.13242	+	0.0597277i
$533$	14.1569	−	16.8715i	0.613204	−	0.730788i
$534$	−2.20418	−	1.26355i	−0.0953843	−	0.0546793i
$535$	−23.9220	+	4.21809i	−1.03424	+	0.182364i
$536$	−1.93195	−	2.30241i	−0.0834476	−	0.0994490i
$537$	23.8549	−	4.28202i	1.02941	−	0.184783i
$538$	−0.213373	−	0.586239i	−0.00919918	−	0.0252745i
$539$	−27.9961	−	12.4422i	−1.20588	−	0.535924i
$540$	−2.25838	+	13.5379i	−0.0971854	+	0.582580i
$541$	−44.3075			−1.90493			−0.952465	−	0.304648i	$-0.901461\pi$
$541$	−44.3075			−1.90493			−0.952465	+	0.304648i	$0.901461\pi$
$542$	−1.44908	+	0.527421i	−0.0622432	+	0.0226547i
$543$	−24.2491	−	28.7189i	−1.04063	−	1.23244i
$544$	3.71307	+	4.42506i	0.159196	+	0.189723i
$545$	2.33381	+	13.2357i	0.0999693	+	0.566954i
$546$	−2.17756	−	1.10018i	−0.0931911	−	0.0470832i
$547$	1.85944	+	1.56025i	0.0795038	+	0.0667116i	0.681673	−	0.731657i	$-0.261252\pi$
$547$	1.85944	+	1.56025i	0.0795038	+	0.0667116i	−0.602170	+	0.798368i	$0.705697\pi$
$548$	19.6722	+	11.3578i	0.840355	+	0.485179i
$549$	−5.26688	+	0.962169i	−0.224785	+	0.0410644i
$550$	0.925476	+	1.60297i	0.0394624	+	0.0683509i
$551$	−3.97905	+	22.5663i	−0.169513	+	0.961358i
$552$	−0.0582608	+	0.336468i	−0.00247974	+	0.0143210i
$553$	−15.0382	+	3.47716i	−0.639491	+	0.147864i
$554$	−0.199059	+	0.546911i	−0.00845722	+	0.0232360i
$555$	0.747513	−	0.274682i	0.0317302	−	0.0116596i
$556$	−29.1537	−	5.14058i	−1.23639	−	0.218009i
$557$	−0.292925	+	0.169120i	−0.0124116	+	0.00716586i	−0.506193	−	0.862420i	$-0.668948\pi$
$557$	−0.292925	+	0.169120i	−0.0124116	+	0.00716586i	0.493781	+	0.869586i	$0.335614\pi$
$558$	0.397872	−	0.147594i	0.0168432	−	0.00624816i
$559$	7.91374	+	4.56900i	0.334715	+	0.193248i
$560$	13.6337	+	1.66938i	0.576130	+	0.0705440i
$561$	−0.0866724	−	28.1518i	−0.00365931	−	1.18857i
$562$	−0.202773	−	1.14998i	−0.00855346	−	0.0485091i
$563$	12.3087	−	10.3282i	0.518748	−	0.435282i	−0.345447	−	0.938438i	$-0.612273\pi$
$563$	12.3087	−	10.3282i	0.518748	−	0.435282i	0.864195	+	0.503157i	$0.167828\pi$
$564$	−41.2130	−	14.8568i	−1.73538	−	0.625584i
$565$	−7.48467	−	20.5640i	−0.314883	−	0.865133i
$566$	3.11783			0.131052
$567$	−1.54691	−	23.7615i	−0.0649639	−	0.997888i
$568$	−1.38962			−0.0583072
$569$	8.08739	+	22.2199i	0.339041	+	0.931507i	0.985667	+	0.168700i	$0.0539570\pi$
$569$	8.08739	+	22.2199i	0.339041	+	0.931507i	−0.646627	+	0.762807i	$0.723821\pi$
$570$	1.41902	+	0.511540i	0.0594363	+	0.0214261i
$571$	−0.278581	+	0.233758i	−0.0116583	+	0.00978245i	−0.648598	−	0.761131i	$-0.724644\pi$
$571$	−0.278581	+	0.233758i	−0.0116583	+	0.00978245i	0.636940	+	0.770913i	$0.280200\pi$
$572$	6.11852	+	34.6999i	0.255828	+	1.45087i
$573$	0.111786	+	36.3090i	0.00466995	+	1.51683i
$574$	−0.228704	+	1.86782i	−0.00954594	+	0.0779613i
$575$	1.05451	+	0.608820i	0.0439760	+	0.0253896i
$576$	3.81598	−	22.4490i	0.158999	−	0.935373i
$577$	7.66829	−	4.42729i	0.319235	−	0.184310i	−0.331817	−	0.943344i	$-0.607661\pi$
$577$	7.66829	−	4.42729i	0.319235	−	0.184310i	0.651052	+	0.759034i	$0.274328\pi$
$578$	−0.414294	−	0.0730512i	−0.0172324	−	0.00303853i
$579$	−2.47904	+	0.910950i	−0.103025	+	0.0378578i
$580$	4.15199	−	11.4075i	0.172402	−	0.473671i
$581$	11.0769	−	2.56122i	0.459549	−	0.106257i
$582$	0.571033	−	3.29783i	0.0236701	−	0.136700i
$583$	−6.99097	+	39.6478i	−0.289536	+	1.64204i
$584$	1.39745	+	2.42046i	0.0578270	+	0.100159i
$585$	−10.5066	−	12.3658i	−0.434395	−	0.511265i
$586$	3.01538	+	1.74093i	0.124564	+	0.0719171i
$587$	−22.0136	−	18.4716i	−0.908598	−	0.762405i	0.0632534	−	0.997997i	$-0.479852\pi$
$587$	−22.0136	−	18.4716i	−0.908598	−	0.762405i	−0.971852	+	0.235593i	$0.924297\pi$
$588$	−23.8990	+	2.60249i	−0.985577	+	0.107325i
$589$	0.934012	+	5.29705i	0.0384853	+	0.218261i
$590$	1.45036	+	1.72848i	0.0597105	+	0.0711602i
$591$	−27.9079	−	33.0522i	−1.14798	−	1.35959i
$592$	−1.26399	+	0.460053i	−0.0519495	+	0.0189081i
$593$	7.83158			0.321605			0.160802	−	0.986987i	$-0.448592\pi$
$593$	7.83158			0.321605			0.160802	+	0.986987i	$0.448592\pi$
$594$	2.26647	−	1.93775i	0.0929945	−	0.0795068i
$595$	10.9750	−	7.13247i	0.449931	−	0.292403i
$596$	2.06661	+	5.67797i	0.0846517	+	0.232579i
$597$	1.41084	−	0.253250i	0.0577417	−	0.0103648i
$598$	−0.129191	−	0.153964i	−0.00528300	−	0.00629604i
$599$	−25.0073	+	4.40946i	−1.02177	+	0.180166i	−0.659339	−	0.751845i	$-0.729164\pi$
$599$	−25.0073	+	4.40946i	−1.02177	+	0.180166i	−0.362430	+	0.932011i	$0.618053\pi$
$600$	2.53107	+	1.45095i	0.103331	+	0.0592346i
$601$	−28.8206	+	34.3470i	−1.17562	+	1.40104i	−0.277819	+	0.960633i	$0.589612\pi$
$601$	−28.8206	+	34.3470i	−1.17562	+	1.40104i	−0.897796	+	0.440411i	$0.854833\pi$
$602$	−0.779674	+	0.0411228i	−0.0317771	+	0.00167604i
$603$	8.72485	+	14.8992i	0.355303	+	0.606744i
$604$	0.607545	+	1.05230i	0.0247207	+	0.0428174i
$605$	1.88643	−	10.6985i	0.0766941	−	0.434954i
$606$	−1.77315	+	2.12642i	−0.0720292	+	0.0863797i
$607$	3.35939	−	9.22986i	0.136354	−	0.374628i	−0.852657	−	0.522470i	$-0.825010\pi$
$607$	3.35939	−	9.22986i	0.136354	−	0.374628i	0.989011	+	0.147842i	$0.0472327\pi$
$608$	−7.28751	−	2.65244i	−0.295548	−	0.107571i
$609$	−2.49534	+	20.9129i	−0.101116	+	0.847432i
$610$	0.0541320	−	0.306998i	0.00219174	−	0.0124300i
$611$	44.8549	−	25.8970i	1.81464	−	1.04768i
$612$	−11.1629	−	19.0627i	−0.451235	−	0.770565i
$613$	−16.3106	+	28.2507i	−0.658778	+	1.14104i	0.322154	+	0.946687i	$0.395593\pi$
$613$	−16.3106	+	28.2507i	−0.658778	+	1.14104i	−0.980932	+	0.194350i	$0.937740\pi$
$614$	−3.20292	−	2.68757i	−0.129259	−	0.108461i
$615$	−6.22447	+	10.8582i	−0.250995	+	0.437843i
$616$	−4.12562	−	4.42122i	−0.166226	−	0.178136i
$617$	0.764441	+	0.911025i	0.0307752	+	0.0366765i	0.781213	−	0.624265i	$-0.214602\pi$
$617$	0.764441	+	0.911025i	0.0307752	+	0.0366765i	−0.750437	+	0.660942i	$0.770157\pi$
$618$	−0.360827	−	2.01015i	−0.0145146	−	0.0808599i
$619$	−12.4466	−	34.1968i	−0.500271	−	1.37448i	−0.891011	−	0.453982i	$-0.850003\pi$
$619$	−12.4466	−	34.1968i	−0.500271	−	1.37448i	0.390740	−	0.920501i	$-0.372219\pi$
$620$		−	2.84956i		−	0.114441i
$621$	0.653864	−	1.84945i	0.0262387	−	0.0742159i
$622$		−	0.791169i		−	0.0317230i
$623$	17.8047	−	23.6441i	0.713329	−	0.947279i
$624$	17.6815	+	20.9407i	0.707825	+	0.838299i
$625$	1.17217	−	0.983570i	0.0468869	−	0.0393428i
$626$	−0.107223	−	0.608090i	−0.00428548	−	0.0243042i
$627$	18.9983	+	32.6733i	0.758718	+	1.30484i
$628$	2.45096	−	2.92094i	0.0978040	−	0.116558i
$629$	−0.640897	+	1.11007i	−0.0255542	+	0.0442612i
$630$	1.32844	+	0.396732i	0.0529263	+	0.0158062i
$631$	17.0123	+	29.4661i	0.677248	+	1.17303i	0.975806	+	0.218637i	$0.0701610\pi$
$631$	17.0123	+	29.4661i	0.677248	+	1.17303i	−0.298558	+	0.954391i	$0.596506\pi$
$632$	−3.00034	−	0.529041i	−0.119347	−	0.0210441i
$633$	1.75262	−	10.1217i	0.0696604	−	0.402303i
$634$	1.83556	+	0.668088i	0.0728992	+	0.0265331i
$635$	27.4426	+	9.98830i	1.08903	+	0.396374i
$636$	10.8962	+	29.6528i	0.432064	+	1.17581i
$637$	15.8776	−	23.5735i	0.629092	−	0.934016i
$638$	−2.28411	+	1.31873i	−0.0904286	+	0.0522090i
$639$	7.86993	+	1.33777i	0.311329	+	0.0529213i
$640$	4.73715	+	2.73500i	0.187252	+	0.108110i
$641$	25.3403	−	30.1994i	1.00088	−	1.19280i	0.0196832	−	0.999806i	$-0.493734\pi$
$641$	25.3403	−	30.1994i	1.00088	−	1.19280i	0.981199	−	0.192999i	$-0.0618213\pi$
$642$	4.14120	−	0.0127497i	0.163440	−	0.000503191i
$643$	−1.58947	+	0.280266i	−0.0626824	+	0.0110526i	−0.204901	−	0.978783i	$-0.565687\pi$
$643$	−1.58947	+	0.280266i	−0.0626824	+	0.0110526i	0.142219	+	0.989835i	$0.454576\pi$
$644$	−1.89411	−	0.578396i	−0.0746386	−	0.0227920i
$645$	−4.88513	−	1.76103i	−0.192352	−	0.0693405i
$646$	−2.28140	+	0.830362i	−0.0897605	+	0.0326702i
$647$	−20.9883			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$647$	−20.9883			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$648$	1.55301	−	4.43608i	0.0610078	−	0.174266i
$649$			56.5362i			2.21924i
$650$	−1.61360	+	0.587304i	−0.0632908	+	0.0230360i
$651$	1.12854	+	4.81321i	0.0442309	+	0.188645i
$652$	21.8337	−	18.3206i	0.855073	−	0.717492i
$653$	7.06142	−	1.24512i	0.276335	−	0.0487253i	−0.0337633	−	0.999430i	$-0.510749\pi$
$653$	7.06142	−	1.24512i	0.276335	−	0.0487253i	0.310098	+	0.950705i	$0.399638\pi$
$654$	−0.00705423	−	2.29126i	−0.000275842	−	0.0895954i
$655$	−11.5532	−	9.69428i	−0.451421	−	0.378787i
$656$	10.5697	−	18.3072i	0.412676	−	0.714776i
$657$	−5.58414	−	15.0532i	−0.217858	−	0.587283i
$658$	−2.00773	+	3.94366i	−0.0782695	+	0.153740i
$659$	−29.4274	−	5.18885i	−1.14633	−	0.202129i	−0.431957	−	0.901894i	$-0.642177\pi$
$659$	−29.4274	−	5.18885i	−1.14633	−	0.202129i	−0.714372	+	0.699766i	$0.753288\pi$
$660$	−6.90621	−	18.7944i	−0.268824	−	0.731571i
$661$	8.06882	−	22.1689i	0.313841	−	0.862270i	−0.678032	−	0.735033i	$-0.737167\pi$
$661$	8.06882	−	22.1689i	0.313841	−	0.862270i	0.991872	−	0.127238i	$-0.0406110\pi$
$662$	0.481801	−	1.32374i	0.0187257	−	0.0514485i
$663$	25.7341	+	4.45597i	0.999431	+	0.173056i
$664$	2.21001	+	0.389684i	0.0857649	+	0.0151227i
$665$	−7.97254	+	15.6600i	−0.309162	+	0.607267i
$666$	−0.133560	+	0.0243991i	−0.00517533	+	0.000945445i
$667$	−0.867520	+	1.50259i	−0.0335905	+	0.0581805i
$668$	23.8505	+	20.0129i	0.922803	+	0.774324i
$669$	21.7656	−	12.6559i	0.841507	−	0.489305i
$670$	−0.990015	+	0.174566i	−0.0382476	+	0.00674409i
$671$	5.98349	−	5.02075i	0.230990	−	0.193824i
$672$	−6.82361	−	2.06074i	−0.263226	−	0.0794949i
$673$	14.5070	−	5.28011i	0.559203	−	0.203533i	−0.0469277	−	0.998898i	$-0.514943\pi$
$673$	14.5070	−	5.28011i	0.559203	−	0.203533i	0.606131	+	0.795365i	$0.292721\pi$
$674$			1.25560i			0.0483637i
$675$	−12.9376	−	10.6539i	−0.497968	−	0.410067i
$676$	−6.91181			−0.265839
$677$	−35.5524	+	12.9400i	−1.36639	+	0.497325i	−0.918024	−	0.396525i	$-0.870216\pi$
$677$	−35.5524	+	12.9400i	−1.36639	+	0.497325i	−0.448366	+	0.893850i	$0.647994\pi$
$678$	0.659157	+	3.67212i	0.0253148	+	0.141027i
$679$	37.2907	+	11.3873i	1.43109	+	0.437003i
$680$	2.54432	−	0.448632i	0.0975701	−	0.0172042i
$681$	5.74271	−	10.0178i	0.220061	−	0.383882i
$682$	−0.397948	+	0.474256i	−0.0152382	+	0.0181602i
$683$	−13.2112	−	7.62750i	−0.505513	−	0.291858i	0.225474	−	0.974249i	$-0.427607\pi$
$683$	−13.2112	−	7.62750i	−0.505513	−	0.291858i	−0.730987	+	0.682391i	$0.760940\pi$
$684$	25.7752	+	14.6704i	0.985538	+	0.560938i
$685$	13.2167	−	7.63067i	0.504985	−	0.291553i
$686$	−0.0399422	+	2.42807i	−0.00152500	+	0.0927040i
$687$	−19.7524	+	23.6877i	−0.753601	+	0.903743i
$688$	8.24189	+	2.99980i	0.314219	+	0.114366i
$689$	−35.0969	−	12.7742i	−1.33709	−	0.486660i
$690$	0.0877186	+	0.0731457i	0.00333939	+	0.00278461i
$691$	−32.7662	−	5.77757i	−1.24649	−	0.219789i	−0.488792	−	0.872400i	$-0.662562\pi$
$691$	−32.7662	−	5.77757i	−1.24649	−	0.219789i	−0.757693	+	0.652611i	$0.773674\pi$
$692$	−4.33570	−	7.50964i	−0.164818	−	0.285474i
$693$	19.1087	+	29.0107i	0.725878	+	1.10202i
$694$	1.46877	−	2.54399i	0.0557539	−	0.0965686i
$695$	−12.7844	+	15.2358i	−0.484939	+	0.577928i
$696$	−2.06748	+	3.60658i	−0.0783676	+	0.136707i
$697$	−3.49803	−	19.8383i	−0.132497	−	0.751429i
$698$	1.46478	−	1.22909i	0.0554426	−	0.0465219i
$699$	27.3602	−	4.91124i	1.03486	−	0.185760i
$700$	−10.1785	+	13.5167i	−0.384710	+	0.510883i
$701$			1.67746i			0.0633567i	0.999498	+	0.0316783i	$0.0100852\pi$
$701$			1.67746i			0.0633567i	−0.999498	+	0.0316783i	$0.989915\pi$
$702$	1.40525	+	2.38287i	0.0530378	+	0.0899355i
$703$		−	1.72086i		−	0.0649036i
$704$	11.3619	+	31.2166i	0.428219	+	1.17652i
$705$	−22.4886	+	18.9885i	−0.846971	+	0.715148i
$706$	−0.676227	−	0.805896i	−0.0254501	−	0.0303303i
$707$	−22.0055	−	23.5822i	−0.827602	−	0.886899i
$708$	22.3000	+	38.3516i	0.838086	+	1.44134i
$709$	−21.9319	−	18.4031i	−0.823671	−	0.691142i	0.130158	−	0.991493i	$-0.458452\pi$
$709$	−21.9319	−	18.4031i	−0.823671	−	0.691142i	−0.953829	+	0.300351i	$0.902896\pi$
$710$	−0.232395	+	0.402521i	−0.00872165	+	0.0151063i
$711$	16.4827	+	5.88454i	0.618150	+	0.220687i
$712$	5.05949	−	2.92110i	0.189613	−	0.109473i
$713$	−0.0707217	+	0.401083i	−0.00264855	+	0.0150207i
$714$	−2.05108	+	0.878908i	−0.0767599	+	0.0328923i
$715$	22.2450	+	8.09652i	0.831916	+	0.302793i
$716$	−9.48932	+	26.0717i	−0.354633	+	0.974345i
$717$	1.21938	+	3.31839i	0.0455384	+	0.123927i
$718$	−0.0332810	+	0.188746i	−0.00124204	+	0.00704395i
$719$	−6.37063	−	11.0343i	−0.237584	−	0.411508i	0.722436	−	0.691438i	$-0.243022\pi$
$719$	−6.37063	−	11.0343i	−0.237584	−	0.411508i	−0.960021	+	0.279929i	$0.909689\pi$
$720$	−11.9923	−	9.93753i	−0.446926	−	0.370350i
$721$	23.7589	−	1.25313i	0.884829	−	0.0466690i
$722$	0.493757	−	0.588437i	0.0183757	−	0.0218994i
$723$	−0.0554150	−	17.9992i	−0.00206091	−	0.669397i
$724$	42.3750	−	7.47186i	1.57486	−	0.277690i
$725$	9.52849	+	11.3556i	0.353879	+	0.421737i
$726$	−0.628076	+	1.74230i	−0.0233101	+	0.0646627i
$727$	15.1297	+	41.5685i	0.561129	+	1.54169i	0.817985	+	0.575240i	$0.195091\pi$
$727$	15.1297	+	41.5685i	0.561129	+	1.54169i	−0.256856	+	0.966450i	$0.582687\pi$
$728$	4.70396	−	3.05702i	0.174340	−	0.113301i
$729$	−13.0658	+	23.6281i	−0.483918	+	0.875113i
$730$	0.934821			0.0345993
$731$	7.85396	−	2.85861i	0.290489	−	0.105729i
$732$	2.07856	−	5.76597i	0.0768258	−	0.213116i
$733$	13.1054	+	15.6184i	0.484060	+	0.576880i	0.951696	−	0.307041i	$-0.0993388\pi$
$733$	13.1054	+	15.6184i	0.484060	+	0.576880i	−0.467637	+	0.883921i	$0.654894\pi$
$734$	−0.596221	−	3.38134i	−0.0220069	−	0.124807i
$735$	−6.51400	+	14.7795i	−0.240272	+	0.545151i
$736$	−0.449829	−	0.377452i	−0.0165809	−	0.0139130i
$737$	−21.8141	−	12.5944i	−0.803534	−	0.463921i
$738$	1.36144	−	1.64294i	0.0501154	−	0.0604775i
$739$	−20.0545	−	34.7355i	−0.737718	−	1.27777i	−0.953520	−	0.301328i	$-0.902570\pi$
$739$	−20.0545	−	34.7355i	−0.737718	−	1.27777i	0.215802	−	0.976437i	$-0.430763\pi$
$740$	−0.158311	+	0.897828i	−0.00581964	+	0.0330048i
$741$	−32.9116	+	12.0937i	−1.20904	+	0.444274i
$742$	3.10913	−	0.718896i	0.114140	−	0.0263915i
$743$	−3.63149	+	9.97743i	−0.133226	+	0.366037i	−0.988311	−	0.152452i	$-0.951283\pi$
$743$	−3.63149	+	9.97743i	−0.133226	+	0.366037i	0.855084	+	0.518489i	$0.173505\pi$
$744$	−0.166489	+	0.961509i	−0.00610380	+	0.0352506i
$745$	3.99787	+	0.704933i	0.146471	+	0.0258267i
$746$	−1.40980	+	0.813947i	−0.0516164	+	0.0298007i
$747$	−12.1409	−	4.33446i	−0.444213	−	0.158590i
$748$	27.9099	+	16.1138i	1.02049	+	0.589179i
$749$	−5.86344	+	47.8865i	−0.214246	+	1.74973i
$750$	2.15128	−	1.25089i	0.0785535	−	0.0456759i
$751$	7.18177	+	40.7298i	0.262066	+	1.48625i	0.777260	+	0.629179i	$0.216609\pi$
$751$	7.18177	+	40.7298i	0.262066	+	1.48625i	−0.515194	+	0.857074i	$0.672280\pi$
$752$	38.0823	−	31.9549i	1.38872	−	1.16527i
$753$	−31.0581	+	26.2242i	−1.13182	+	0.955663i
$754$	−0.836861	−	2.29926i	−0.0304767	−	0.0837340i
$755$	0.816354			0.0297102
$756$	24.4054	+	12.1423i	0.887614	+	0.441613i
$757$	−23.7006			−0.861412			−0.430706	−	0.902492i	$-0.641735\pi$
$757$	−23.7006			−0.861412			−0.430706	+	0.902492i	$0.641735\pi$
$758$	−0.337798	−	0.928092i	−0.0122694	−	0.0337098i
$759$	0.505618	+	2.81676i	0.0183528	+	0.102242i
$760$	−2.65706	+	2.22954i	−0.0963818	+	0.0808740i
$761$	−2.04815	−	11.6156i	−0.0742454	−	0.421066i	−0.999163	−	0.0408995i	$-0.986978\pi$
$761$	−2.04815	−	11.6156i	−0.0742454	−	0.421066i	0.924918	−	0.380167i	$-0.124133\pi$
$762$	−4.31938	−	2.47610i	−0.156475	−	0.0896996i
$763$	26.4949	+	3.24415i	0.959178	+	0.117446i
$764$	−35.9971	−	20.7829i	−1.30233	−	0.751899i
$765$	−14.8413	+	0.0913861i	−0.536588	+	0.00330407i
$766$	−0.332436	+	0.191932i	−0.0120114	+	0.00693479i
$767$	−51.6528	−	9.10778i	−1.86507	−	0.328863i
$768$	19.4778	+	16.2419i	0.702846	+	0.586080i
$769$	8.33433	−	22.8984i	0.300544	−	0.825737i	−0.693862	−	0.720108i	$-0.744092\pi$
$769$	8.33433	−	22.8984i	0.300544	−	0.825737i	0.994406	−	0.105629i	$-0.0336855\pi$
$770$	−1.97062	+	0.455648i	−0.0710161	+	0.0164204i
$771$	−6.67073	−	5.56250i	−0.240240	−	0.200328i
$772$	0.525021	−	2.97754i	0.0188959	−	0.107164i
$773$	1.44939	+	2.51041i	0.0521309	+	0.0902933i	0.890913	−	0.454173i	$-0.150065\pi$
$773$	1.44939	+	2.51041i	0.0521309	+	0.0902933i	−0.838782	+	0.544467i	$0.816732\pi$
$774$	0.769400	+	0.437919i	0.0276555	+	0.0157407i
$775$	3.01342	+	1.73980i	0.108245	+	0.0624955i
$776$	5.89557	+	4.94697i	0.211639	+	0.177586i
$777$	−0.0881704	−	1.57923i	−0.00316309	−	0.0566544i
$778$	0.565207	+	3.20545i	0.0202637	+	0.114921i
$779$	17.3840	+	20.7174i	0.622845	+	0.742277i
$780$	18.2836	−	3.28196i	0.654657	−	0.117513i
$781$	−10.9436	+	3.98315i	−0.391593	+	0.142528i
$782$	−0.183830			−0.00657374
$783$	15.1809	−	18.4350i	0.542521	−	0.658814i
$784$	11.0791	−	24.9289i	0.395681	−	0.890319i
$785$	−0.876175	−	2.40727i	−0.0312720	−	0.0859192i
$786$	1.65877	+	1.96453i	0.0591664	+	0.0700725i
$787$	−5.60311	−	6.67753i	−0.199729	−	0.238028i	0.656878	−	0.753997i	$-0.271877\pi$
$787$	−5.60311	−	6.67753i	−0.199729	−	0.238028i	−0.856608	+	0.515969i	$0.827432\pi$
$788$	48.7689	−	8.59928i	1.73732	−	0.306337i
$789$	−9.15068	+	5.32078i	−0.325773	+	0.189425i
$790$	−0.655010	+	0.780611i	−0.0233042	+	0.0277729i
$791$	−43.4027	+	2.28921i	−1.54322	+	0.0813950i
$792$	1.23223	+	6.74519i	0.0437854	+	0.239680i
$793$	3.62315	+	6.27549i	0.128662	+	0.222849i
$794$	0.482439	−	2.73605i	0.0171211	−	0.0970986i
$795$	20.9134	+	3.62124i	0.741720	+	0.128432i
$796$	−0.561222	+	1.54195i	−0.0198920	+	0.0546528i
$797$	−11.0381	−	4.01755i	−0.390990	−	0.142309i	0.139042	−	0.990287i	$-0.455598\pi$
$797$	−11.0381	−	4.01755i	−0.390990	−	0.142309i	−0.530032	+	0.847978i	$0.677820\pi$
$798$	1.79476	−	2.39872i	0.0635338	−	0.0849138i
$799$	8.22624	−	46.6533i	0.291023	−	1.65048i
$800$	−4.34482	+	2.50848i	−0.153612	+	0.0886882i
$801$	−31.4658	+	11.6725i	−1.11179	+	0.412429i
$802$	−0.0891128	+	0.154348i	−0.00314668	+	0.00545021i
$803$	17.9432	+	15.0561i	0.633201	+	0.531319i
$804$	−19.7654	+	0.0608529i	−0.697073	+	0.00214612i
$805$	−0.972809	+	0.907768i	−0.0342870	+	0.0319946i
$806$	−0.369183	−	0.439975i	−0.0130039	−	0.0154975i
$807$	−7.75260	−	2.79471i	−0.272904	−	0.0983786i
$808$	−2.17749	−	5.98260i	−0.0766038	−	0.210467i
$809$			13.3913i			0.470814i	0.971897	+	0.235407i	$0.0756423\pi$
$809$			13.3913i			0.470814i	−0.971897	+	0.235407i	$0.924358\pi$
$810$	−1.02525	−	1.19172i	−0.0360234	−	0.0418728i
$811$			14.2545i			0.500543i	0.968176	+	0.250272i	$0.0805200\pi$
$811$			14.2545i			0.500543i	−0.968176	+	0.250272i	$0.919480\pi$
$812$	−19.2602	−	14.5035i	−0.675901	−	0.508973i
$813$	−6.90804	+	19.1631i	−0.242276	+	0.672078i
$814$	0.151732	−	0.127318i	0.00531820	−	0.00446250i
$815$	−3.32517	−	18.8580i	−0.116476	−	0.660566i
$816$	25.0676	−	0.0771768i	0.877540	−	0.00270173i
$817$	−7.21271	+	8.59577i	−0.252341	+	0.300728i
$818$	1.73656	−	3.00782i	0.0607176	−	0.105166i
$819$	−29.5832	+	12.7846i	−1.03372	+	0.446730i
$820$	−7.16385	−	12.4081i	−0.250172	−	0.433311i
$821$	53.2811	+	9.39490i	1.85952	+	0.327884i	0.987004	−	0.160695i	$-0.0513735\pi$
$821$	53.2811	+	9.39490i	1.85952	+	0.327884i	0.872520	+	0.488579i	$0.162485\pi$
$822$	−2.44215	+	0.897393i	−0.0851796	+	0.0313002i
$823$	−24.0026	−	8.73623i	−0.836678	−	0.304526i	−0.112081	−	0.993699i	$-0.535752\pi$
$823$	−24.0026	−	8.73623i	−0.836678	−	0.304526i	−0.724597	+	0.689173i	$0.757974\pi$
$824$	4.41294	+	1.60618i	0.153732	+	0.0559539i
$825$	24.0918	+	4.17159i	0.838768	+	0.145236i
$826$	4.12451	−	1.75238i	0.143510	−	0.0609731i
$827$	35.7068	−	20.6154i	1.24165	−	0.716866i	0.272219	−	0.962235i	$-0.412243\pi$
$827$	35.7068	−	20.6154i	1.24165	−	0.716866i	0.969430	+	0.245369i	$0.0789092\pi$
$828$	1.45403	+	1.71133i	0.0505309	+	0.0594728i
$829$	−19.7340	−	11.3934i	−0.685389	−	0.395710i	0.116493	−	0.993191i	$-0.462835\pi$
$829$	−19.7340	−	11.3934i	−0.685389	−	0.395710i	−0.801883	+	0.597482i	$0.796168\pi$
$830$	0.482471	−	0.574986i	0.0167468	−	0.0199581i
$831$	3.86454	+	6.64623i	0.134059	+	0.230555i
$832$	−30.3506	+	5.35164i	−1.05222	+	0.185535i
$833$	−7.18219	−	24.9841i	−0.248848	−	0.865648i
$834$	2.59073	−	2.18751i	0.0897097	−	0.0757473i
$835$	19.6562	−	7.15427i	0.680231	−	0.247584i
$836$	−43.2670			−1.49642
$837$	1.86852	−	5.28510i	0.0645855	−	0.182680i
$838$		−	2.23602i		−	0.0772420i
$839$	17.3731	−	6.32330i	0.599786	−	0.218304i	−0.0242419	−	0.999706i	$-0.507717\pi$
$839$	17.3731	−	6.32330i	0.599786	−	0.218304i	0.624028	+	0.781402i	$0.285495\pi$
$840$	−2.32414	+	2.18217i	−0.0801904	+	0.0752922i
$841$	6.03445	−	5.06350i	0.208084	−	0.174604i
$842$	2.34869	−	0.414137i	0.0809411	−	0.0142721i
$843$	−13.3822	−	7.67139i	−0.460908	−	0.264217i
$844$	9.00832	+	7.55887i	0.310079	+	0.260187i
$845$	−2.32184	+	4.02154i	−0.0798736	+	0.138345i
$846$	4.33005	−	2.53563i	0.148870	−	0.0871768i
$847$	−19.2275	−	9.78879i	−0.660665	−	0.336347i
$848$	−35.3041	−	6.22506i	−1.21235	−	0.213769i
$849$	26.3761	−	31.6311i	0.905225	−	1.08557i
$850$	−0.537174	+	1.47587i	−0.0184249	+	0.0506220i
$851$	0.0445655	−	0.122443i	0.00152768	−	0.00419728i
$852$	−5.85255	+	7.01857i	−0.200505	+	0.240452i
$853$	−52.2825	−	9.21881i	−1.79012	−	0.315646i	−0.822633	−	0.568573i	$-0.807496\pi$
$853$	−52.2825	−	9.21881i	−1.79012	−	0.315646i	−0.967485	+	0.252927i	$0.918607\pi$
$854$	−0.551743	−	0.280894i	−0.0188803	−	0.00961201i
$855$	17.1943	−	10.0688i	0.588031	−	0.344345i
$856$	−4.76131	+	8.24683i	−0.162738	+	0.281871i
$857$	5.81262	+	4.87737i	0.198555	+	0.166608i	0.736644	−	0.676280i	$-0.236409\pi$
$857$	5.81262	+	4.87737i	0.198555	+	0.166608i	−0.538089	+	0.842888i	$0.680854\pi$
$858$	−3.50129	−	2.00713i	−0.119532	−	0.0685221i
$859$	53.9268	−	9.50876i	1.83996	−	0.324435i	0.858018	−	0.513619i	$-0.171695\pi$
$859$	53.9268	−	9.50876i	1.83996	−	0.324435i	0.981942	+	0.189184i	$0.0605843\pi$
$860$	4.55387	−	3.82115i	0.155286	−	0.130300i
$861$	17.0146	+	18.1215i	0.579857	+	0.617580i
$862$	0.434681	−	0.158211i	0.0148053	−	0.00538869i
$863$			17.9590i			0.611331i	0.952139	+	0.305666i	$0.0988789\pi$
$863$			17.9590i			0.611331i	−0.952139	+	0.305666i	$0.901121\pi$
$864$	5.25222	+	6.14322i	0.178684	+	0.208997i
$865$	−5.82585			−0.198085
$866$	−2.41007	+	0.877195i	−0.0818976	+	0.0298083i
$867$	−4.24594	+	3.58510i	−0.144200	+	0.121756i
$868$	−5.41273	−	1.65286i	−0.183720	−	0.0561016i
$869$	−25.1449	+	4.43372i	−0.852981	+	0.150404i
$870$	0.698932	+	1.20202i	0.0236960	+	0.0407524i
$871$	15.0207	−	17.9010i	0.508958	−	0.606552i
$872$	4.56285	+	2.63436i	0.154518	+	0.0892108i
$873$	−28.6264	−	33.6921i	−0.968856	−	1.14030i
$874$	0.213735	−	0.123400i	0.00722968	−	0.00417406i
$875$	11.3364	+	26.6822i	0.383242	+	0.902021i
$876$	18.1106	+	3.13592i	0.611899	+	0.105953i
$877$	4.40950	+	1.60493i	0.148898	+	0.0541946i	0.415394	−	0.909642i	$-0.363644\pi$
$877$	4.40950	+	1.60493i	0.148898	+	0.0541946i	−0.266496	+	0.963836i	$0.585866\pi$
$878$	0.980901	+	0.357019i	0.0331038	+	0.0120488i
$879$	43.1714	−	15.8638i	1.45614	−	0.535073i
$880$	22.3763	+	3.94554i	0.754305	+	0.133004i
$881$	2.44317	+	4.23170i	0.0823125	+	0.142569i	0.904243	−	0.427019i	$-0.140436\pi$
$881$	2.44317	+	4.23170i	0.0823125	+	0.142569i	−0.821930	+	0.569588i	$0.807103\pi$
$882$	1.52414	−	2.29325i	0.0513204	−	0.0772176i
$883$	11.8954	−	20.6034i	0.400312	−	0.693361i	−0.593451	−	0.804870i	$-0.702235\pi$
$883$	11.8954	−	20.6034i	0.400312	−	0.693361i	0.993763	+	0.111509i	$0.0355684\pi$
$884$	−19.2182	+	22.9033i	−0.646376	+	0.770321i
$885$	29.8055	−	0.0917636i	1.00190	−	0.00308460i
$886$	−0.635004	−	3.60128i	−0.0213334	−	0.120988i
$887$	17.0442	−	14.3018i	0.572290	−	0.480208i	−0.310115	−	0.950699i	$-0.600368\pi$
$887$	17.0442	−	14.3018i	0.572290	−	0.480208i	0.882405	+	0.470491i	$0.155923\pi$
$888$	0.105875	−	0.293699i	0.00355293	−	0.00985590i
$889$	34.8906	−	46.3336i	1.17019	−	1.55398i
$890$		−	1.95406i		−	0.0655002i
$891$	−0.485071	−	39.3867i	−0.0162505	−	1.31950i
$892$			28.8227i			0.965056i
$893$	21.7526	+	59.7648i	0.727923	+	1.99995i
$894$	−0.651073	−	0.234704i	−0.0217751	−	0.00784967i
$895$	11.9818	+	14.2793i	0.400506	+	0.477305i
$896$	7.94286	−	7.41181i	0.265352	−	0.247611i
$897$	−2.65491	+	0.00817382i	−0.0886450	+	0.000272916i
$898$	1.75635	+	1.47375i	0.0586100	+	0.0491797i
$899$	−2.47908	+	4.29389i	−0.0826818	+	0.143209i
$900$	17.9882	−	6.67289i	0.599607	−	0.222430i
$901$	−29.5846	+	17.0807i	−0.985606	+	0.569040i
$902$	−0.540539	+	3.06555i	−0.0179980	+	0.102072i
$903$	−6.17865	+	8.25784i	−0.205613	+	0.274804i
$904$	−8.06153	−	2.93416i	−0.268123	−	0.0975887i
$905$	9.88737	−	27.1653i	0.328667	−	0.903006i
$906$	−0.137134	−	0.0237454i	−0.00455598	−	0.000788887i
$907$	−3.61323	+	20.4917i	−0.119975	+	0.680414i	0.864191	+	0.503165i	$0.167831\pi$
$907$	−3.61323	+	20.4917i	−0.119975	+	0.680414i	−0.984166	+	0.177249i	$0.943280\pi$
$908$	6.60939	+	11.4478i	0.219340	+	0.379908i
$909$	6.57254	+	35.9779i	0.217998	+	1.19331i
$910$	−0.0988312	−	1.87381i	−0.00327622	−	0.0621160i
$911$	−9.26438	+	11.0409i	−0.306942	+	0.365800i	−0.897361	−	0.441298i	$-0.854518\pi$
$911$	−9.26438	+	11.0409i	−0.306942	+	0.365800i	0.590418	+	0.807097i	$0.298963\pi$
$912$	−29.0937	+	16.9169i	−0.963388	+	0.560174i
$913$	18.5213	−	3.26581i	0.612966	−	0.108082i
$914$	2.26730	+	2.70206i	0.0749955	+	0.0893761i
$915$	−2.65661	−	3.14630i	−0.0878249	−	0.104014i
$916$	−12.0760	−	33.1785i	−0.399002	−	1.09625i
$917$	−25.1156	+	16.3222i	−0.829390	+	0.539007i
$918$	2.49575	+	0.416338i	0.0823721	+	0.0137412i
$919$	−23.8940			−0.788192			−0.394096	−	0.919069i	$-0.628942\pi$
$919$	−23.8940			−0.788192			−0.394096	+	0.919069i	$0.628942\pi$
$920$	−0.246794	+	0.0898255i	−0.00813655	+	0.00296146i
$921$	−54.3618	+	9.75812i	−1.79128	+	0.321541i
$922$	1.55997	+	1.85910i	0.0513749	+	0.0612262i
$923$	−1.87612	−	10.6400i	−0.0617533	−	0.350220i
$924$	−39.7058	+	2.21683i	−1.30623	+	0.0729284i
$925$	−0.852801	−	0.715585i	−0.0280399	−	0.0235283i
$926$	1.72548	+	0.996204i	0.0567027	+	0.0327373i
$927$	−23.4458	−	13.3447i	−0.770063	−	0.438296i
$928$	−3.57438	−	6.19101i	−0.117335	−	0.203230i
$929$	8.22973	−	46.6731i	0.270009	−	1.53129i	−0.484375	−	0.874861i	$-0.660953\pi$
$929$	8.22973	−	46.6731i	0.270009	−	1.53129i	0.754383	−	0.656434i	$-0.227936\pi$
$930$	0.250670	+	0.209025i	0.00821979	+	0.00685421i
$931$	25.1217	+	24.2272i	0.823330	+	0.794016i
$932$	−10.8837	+	29.9028i	−0.356508	+	0.979497i
$933$	−8.02658	−	6.69309i	−0.262778	−	0.219122i
$934$	−3.32394	−	0.586100i	−0.108763	−	0.0191778i
$935$	18.7512	−	10.8260i	0.613230	−	0.354048i
$936$	−6.36107	+	0.0391687i	−0.207918	+	0.00128027i
$937$	3.48018	+	2.00928i	0.113693	+	0.0656404i	0.555768	−	0.831337i	$-0.312424\pi$
$937$	3.48018	+	2.00928i	0.113693	+	0.0656404i	−0.442075	+	0.896978i	$0.645758\pi$
$938$	−0.242659	+	1.98179i	−0.00792311	+	0.0647077i
$939$	−7.07628	−	4.05649i	−0.230926	−	0.132379i
$940$	−5.85093	−	33.1823i	−0.190836	−	1.08229i
$941$	−17.4001	+	14.6004i	−0.567227	+	0.475960i	−0.880725	−	0.473629i	$-0.842944\pi$
$941$	−17.4001	+	14.6004i	−0.567227	+	0.475960i	0.313497	+	0.949589i	$0.398499\pi$
$942$	0.0771626	+	0.429868i	0.00251409	+	0.0140058i
$943$	0.700379	+	1.92427i	0.0228075	+	0.0626630i
$944$	−50.3422			−1.63850
$945$	15.2632	−	10.1210i	0.496512	−	0.329237i
$946$	−1.29154			−0.0419915
$947$	−16.2795	−	44.7277i	−0.529014	−	1.45345i	−0.860234	−	0.509900i	$-0.829682\pi$
$947$	−16.2795	−	44.7277i	−0.529014	−	1.45345i	0.331220	−	0.943554i	$-0.392540\pi$
$948$	−15.3083	+	12.9257i	−0.497191	+	0.419808i
$949$	−16.6462	+	13.9678i	−0.540359	+	0.453415i
$950$	−0.366152	−	2.07655i	−0.0118795	−	0.0673722i
$951$	22.3062	−	12.9702i	0.723329	−	0.420589i
$952$	0.623629	−	5.09315i	0.0202119	−	0.165070i
$953$	−33.3461	−	19.2524i	−1.08019	−	0.623646i	−0.149240	−	0.988801i	$-0.547683\pi$
$953$	−33.3461	−	19.2524i	−1.08019	−	0.623646i	−0.930947	+	0.365155i	$0.881016\pi$
$954$	−3.40777	−	1.21662i	−0.110331	−	0.0393894i
$955$	−24.1845	+	13.9629i	−0.782592	+	0.451830i
$956$	−3.98567	−	0.702781i	−0.128906	−	0.0227296i
$957$	−5.94419	+	34.3289i	−0.192148	+	1.10969i
$958$	0.102749	−	0.282301i	0.00331968	−	0.00912074i
$959$	−6.82824	−	29.5312i	−0.220495	−	0.953613i
$960$	16.4387	−	6.04059i	0.530558	−	0.194959i
$961$	5.18100	−	29.3829i	0.167129	−	0.947835i
$962$	0.0918774	+	0.159136i	0.00296225	+	0.00513076i
$963$	34.9041	−	42.1212i	1.12477	−	1.35734i
$964$	17.8445	+	10.3025i	0.574734	+	0.331823i
$965$	−1.55608	−	1.30570i	−0.0500918	−	0.0420320i
$966$	0.189820	−	0.124194i	0.00610737	−	0.00399588i
$967$	0.214600	+	1.21706i	0.00690107	+	0.0391379i	0.988064	−	0.154045i	$-0.0492301\pi$
$967$	0.214600	+	1.21706i	0.00690107	+	0.0391379i	−0.981163	+	0.193183i	$0.938119\pi$
$968$	−2.73746	−	3.26238i	−0.0879853	−	0.104857i
$969$	−10.8759	+	30.1699i	−0.349384	+	0.969198i
$970$	2.41891	−	0.880410i	0.0776664	−	0.0282683i
$971$	−55.5761			−1.78352			−0.891761	−	0.452507i	$-0.850530\pi$
$971$	−55.5761			−1.78352			−0.891761	+	0.452507i	$0.850530\pi$
$972$	−15.8647	−	26.5268i	−0.508859	−	0.850849i
$973$	21.5250	+	33.1213i	0.690059	+	1.06182i
$974$	−1.57372	−	4.32376i	−0.0504253	−	0.138542i
$975$	−7.69237	+	21.3388i	−0.246353	+	0.683388i
$976$	4.47069	+	5.32796i	0.143103	+	0.170544i
$977$	−13.4072	+	2.36405i	−0.428933	+	0.0756325i	−0.383947	−	0.923355i	$-0.625436\pi$
$977$	−13.4072	+	2.36405i	−0.428933	+	0.0756325i	−0.0449862	+	0.998988i	$0.514324\pi$
$978$	0.0100507	+	3.26455i	0.000321387	+	0.104389i
$979$	31.4719	−	37.5067i	1.00585	−	1.19872i
$980$	−10.8780	−	14.9512i	−0.347484	−	0.477598i
$981$	−23.3050	−	19.3119i	−0.744072	−	0.616583i
$982$	−1.48909	−	2.57919i	−0.0475189	−	0.0823052i
$983$	−1.53261	+	8.69187i	−0.0488827	+	0.277228i	−0.999445	−	0.0333057i	$-0.989397\pi$
$983$	−1.53261	+	8.69187i	−0.0488827	+	0.277228i	0.950563	+	0.310533i	$0.100508\pi$
$984$	1.69229	+	4.60536i	0.0539482	+	0.146814i
$985$	11.3792	−	31.2642i	0.362573	−	0.996161i
$986$	−2.10300	−	0.765429i	−0.0669732	−	0.0243762i
$987$	23.0243	+	53.7312i	0.732873	+	1.71028i
$988$	6.97016	−	39.5297i	0.221750	−	1.25761i
$989$	−0.735803	+	0.424816i	−0.0233972	+	0.0135084i
$990$	2.15990	+	0.771112i	0.0686462	+	0.0245075i
$991$	7.38836	−	12.7970i	0.234699	−	0.406511i	−0.724486	−	0.689289i	$-0.757923\pi$
$991$	7.38836	−	12.7970i	0.234699	−	0.406511i	0.959185	+	0.282779i	$0.0912562\pi$
$992$	−1.28546	−	1.07863i	−0.0408133	−	0.0342465i
$993$	−9.35368	−	16.0865i	−0.296830	−	0.510489i
$994$	0.629789	+	0.674913i	0.0199757	+	0.0214069i
$995$	0.708632	+	0.844515i	0.0224651	+	0.0267729i
$996$	11.2759	−	9.52089i	0.357290	−	0.301681i
$997$	0.491617	+	1.35071i	0.0155697	+	0.0427773i	0.947234	−	0.320543i	$-0.103865\pi$
$997$	0.491617	+	1.35071i	0.0155697	+	0.0427773i	−0.931664	+	0.363320i	$0.881643\pi$
$998$			2.56099i			0.0810667i
$999$	−0.882348	+	1.56140i	−0.0279163	+	0.0494005i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.20.11	✓	132
3.2	odd	2		567.2.be.a.62.12		132
7.6	odd	2	inner	189.2.be.a.20.12	yes	132
21.20	even	2		567.2.be.a.62.11		132
27.4	even	9		567.2.be.a.503.11		132
27.23	odd	18	inner	189.2.be.a.104.12	yes	132
189.104	even	18	inner	189.2.be.a.104.11	yes	132
189.139	odd	18		567.2.be.a.503.12		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.11	✓	132	1.1	even	1	trivial
189.2.be.a.20.12	yes	132	7.6	odd	2	inner
189.2.be.a.104.11	yes	132	189.104	even	18	inner
189.2.be.a.104.12	yes	132	27.23	odd	18	inner
567.2.be.a.62.11		132	21.20	even	2
567.2.be.a.62.12		132	3.2	odd	2
567.2.be.a.503.11		132	27.4	even	9
567.2.be.a.503.12		132	189.139	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0448460 - 0.123213i) q^{2} +(-1.62941 - 0.587383i) q^{3} +(1.51892 - 1.27452i) q^{4} +(-0.231324 - 1.31190i) q^{5} +(0.000699206 + 0.227107i) q^{6} +(-2.62614 - 0.321557i) q^{7} +(-0.452264 - 0.261115i) q^{8} +(2.30996 + 1.91418i) q^{9} +O(q^{10})\)	\(q+(-0.0448460 - 0.123213i) q^{2} +(-1.62941 - 0.587383i) q^{3} +(1.51892 - 1.27452i) q^{4} +(-0.231324 - 1.31190i) q^{5} +(0.000699206 + 0.227107i) q^{6} +(-2.62614 - 0.321557i) q^{7} +(-0.452264 - 0.261115i) q^{8} +(2.30996 + 1.91418i) q^{9} +(-0.151270 + 0.0873359i) q^{10} +(-4.31014 - 0.759994i) q^{11} +(-3.22358 + 1.18454i) q^{12} +(1.38870 - 3.81541i) q^{13} +(0.0781517 + 0.337996i) q^{14} +(-0.393667 + 2.27351i) q^{15} +(0.676731 - 3.83793i) q^{16} +(-1.85685 - 3.21617i) q^{17} +(0.132259 - 0.370462i) q^{18} +(4.31784 + 2.49291i) q^{19} +(-2.02342 - 1.69785i) q^{20} +(4.09018 + 2.06650i) q^{21} +(0.0996512 + 0.565150i) q^{22} +(0.242663 + 0.289194i) q^{23} +(0.583550 + 0.691115i) q^{24} +(3.03088 - 1.10315i) q^{25} -0.532388 q^{26} +(-2.63953 - 4.47581i) q^{27} +(-4.39872 + 2.85866i) q^{28} +(1.57190 + 4.31876i) q^{29} +(0.297781 - 0.0534526i) q^{30} +(0.693448 + 0.826419i) q^{31} +(-1.53182 + 0.270102i) q^{32} +(6.57659 + 3.77004i) q^{33} +(-0.313002 + 0.373021i) q^{34} +(0.185638 + 3.51963i) q^{35} +(5.94831 - 0.0366271i) q^{36} +(-0.172576 - 0.298911i) q^{37} +(0.113522 - 0.643813i) q^{38} +(-4.50387 + 5.40118i) q^{39} +(-0.237938 + 0.653729i) q^{40} +(5.09719 + 1.85523i) q^{41} +(0.0711916 - 0.596639i) q^{42} +(-0.390810 + 2.21639i) q^{43} +(-7.51538 + 4.33901i) q^{44} +(1.97686 - 3.47325i) q^{45} +(0.0247502 - 0.0428686i) q^{46} +(9.77186 + 8.19957i) q^{47} +(-3.35701 + 5.85607i) q^{48} +(6.79320 + 1.68890i) q^{49} +(-0.271846 - 0.323973i) q^{50} +(1.13646 + 6.33114i) q^{51} +(-2.75352 - 7.56523i) q^{52} -9.19872i q^{53} +(-0.433108 + 0.525947i) q^{54} +5.83030i q^{55} +(1.10374 + 0.831152i) q^{56} +(-5.57125 - 6.59819i) q^{57} +(0.461636 - 0.387359i) q^{58} +(-2.24314 - 12.7215i) q^{59} +(2.29969 + 3.95501i) q^{60} +(-1.14717 + 1.36715i) q^{61} +(0.0707275 - 0.122504i) q^{62} +(-5.45077 - 5.76967i) q^{63} +(-3.79516 - 6.57342i) q^{64} +(-5.32670 - 0.939241i) q^{65} +(0.169586 - 0.979395i) q^{66} +(5.40821 + 1.96843i) q^{67} +(-6.91949 - 2.51849i) q^{68} +(-0.225530 - 0.613753i) q^{69} +(0.425340 - 0.180714i) q^{70} +(2.30444 - 1.33047i) q^{71} +(-0.544894 - 1.46888i) q^{72} +(-4.63485 - 2.67593i) q^{73} +(-0.0290904 + 0.0346686i) q^{74} +(-5.58652 + 0.0171995i) q^{75} +(9.73572 - 1.71667i) q^{76} +(11.0746 + 3.38180i) q^{77} +(0.867479 + 0.312715i) q^{78} +(5.48206 - 1.99531i) q^{79} -5.19155 q^{80} +(1.67186 + 8.84335i) q^{81} -0.711242i q^{82} +(-4.03800 + 1.46971i) q^{83} +(8.84645 - 2.07420i) q^{84} +(-3.78977 + 3.17999i) q^{85} +(0.290615 - 0.0512433i) q^{86} +(-0.0245079 - 7.96035i) q^{87} +(1.75088 + 1.46916i) q^{88} +(-5.59352 + 9.68826i) q^{89} +(-0.516605 - 0.0878150i) q^{90} +(-4.87378 + 9.57326i) q^{91} +(0.737171 + 0.129983i) q^{92} +(-0.644488 - 1.75390i) q^{93} +(0.572067 - 1.57174i) q^{94} +(2.27163 - 6.24126i) q^{95} +(2.65463 + 0.459660i) q^{96} +(-14.5132 - 2.55906i) q^{97} +(-0.0965524 - 0.912754i) q^{98} +(-8.50151 - 10.0059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

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