LMFDB - Embedded newform 189.2.bd.a.185.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (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			185.18
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.66985 - 0.294440i) q^{2} +(0.685602 + 1.59058i) q^{3} +(0.822331 - 0.299304i) q^{4} +(1.39543 - 0.507895i) q^{5} +(1.61319 + 2.45417i) q^{6} +(-0.356869 - 2.62157i) q^{7} +(-1.65184 + 0.953692i) q^{8} +(-2.05990 + 2.18101i) q^{9} +O(q^{10})$	\(q+(1.66985 - 0.294440i) q^{2} +(0.685602 + 1.59058i) q^{3} +(0.822331 - 0.299304i) q^{4} +(1.39543 - 0.507895i) q^{5} +(1.61319 + 2.45417i) q^{6} +(-0.356869 - 2.62157i) q^{7} +(-1.65184 + 0.953692i) q^{8} +(-2.05990 + 2.18101i) q^{9} +(2.18062 - 1.25898i) q^{10} +(-0.0445037 + 0.122273i) q^{11} +(1.03986 + 1.10278i) q^{12} +(0.311287 + 0.855253i) q^{13} +(-1.36782 - 4.27257i) q^{14} +(1.76456 + 1.87133i) q^{15} +(-3.81827 + 3.20391i) q^{16} +(-2.81624 - 4.87788i) q^{17} +(-2.79755 + 4.24849i) q^{18} +(-0.0831162 - 0.0479872i) q^{19} +(0.995491 - 0.835316i) q^{20} +(3.92516 - 2.36499i) q^{21} +(-0.0383126 + 0.217282i) q^{22} +(6.39659 + 1.12789i) q^{23} +(-2.64943 - 1.97354i) q^{24} +(-2.14095 + 1.79647i) q^{25} +(0.771624 + 1.33649i) q^{26} +(-4.88135 - 1.78113i) q^{27} +(-1.07811 - 2.04899i) q^{28} +(0.238914 - 0.656410i) q^{29} +(3.49755 + 2.60529i) q^{30} +(-3.11204 - 8.55026i) q^{31} +(-2.98051 + 3.55203i) q^{32} +(-0.224997 + 0.0130438i) q^{33} +(-6.13896 - 7.31613i) q^{34} +(-1.82947 - 3.47697i) q^{35} +(-1.04113 + 2.41005i) q^{36} -3.45015 q^{37} +(-0.152921 - 0.0556588i) q^{38} +(-1.14693 + 1.08149i) q^{39} +(-1.82066 + 2.16977i) q^{40} +(2.04536 - 0.744450i) q^{41} +(5.85809 - 5.10490i) q^{42} +(1.37972 + 7.82480i) q^{43} +0.113869i q^{44} +(-1.76672 + 4.08966i) q^{45} +11.0135 q^{46} +(11.8044 + 4.29647i) q^{47} +(-7.71390 - 3.87667i) q^{48} +(-6.74529 + 1.87112i) q^{49} +(-3.04613 + 3.63023i) q^{50} +(5.82784 - 7.82375i) q^{51} +(0.511962 + 0.610132i) q^{52} +(-1.26661 - 0.731275i) q^{53} +(-8.67558 - 1.53696i) q^{54} +0.193227i q^{55} +(3.08967 + 3.99009i) q^{56} +(0.0193428 - 0.165103i) q^{57} +(0.205677 - 1.16645i) q^{58} +(4.86491 + 4.08214i) q^{59} +(2.01115 + 1.01071i) q^{60} +(-2.67073 + 7.33778i) q^{61} +(-7.71419 - 13.3614i) q^{62} +(6.45280 + 4.62184i) q^{63} +(1.05325 - 1.82428i) q^{64} +(0.868757 + 1.03534i) q^{65} +(-0.371871 + 0.0880294i) q^{66} +(-2.49984 + 14.1773i) q^{67} +(-3.77586 - 3.16832i) q^{68} +(2.59151 + 10.9476i) q^{69} +(-4.07871 - 5.26736i) q^{70} +(2.38823 + 1.37884i) q^{71} +(1.32262 - 5.56720i) q^{72} -8.02256i q^{73} +(-5.76125 + 1.01586i) q^{74} +(-4.32528 - 2.17370i) q^{75} +(-0.0827118 - 0.0145843i) q^{76} +(0.336429 + 0.0730343i) q^{77} +(-1.59677 + 2.14363i) q^{78} +(0.0703241 + 0.398828i) q^{79} +(-3.70088 + 6.41012i) q^{80} +(-0.513631 - 8.98533i) q^{81} +(3.19626 - 1.84536i) q^{82} +(4.54412 + 1.65393i) q^{83} +(2.51993 - 3.11962i) q^{84} +(-6.40732 - 5.37638i) q^{85} +(4.60787 + 12.6600i) q^{86} +(1.20787 - 0.0700244i) q^{87} +(-0.0430976 - 0.244419i) q^{88} +(7.98594 - 13.8321i) q^{89} +(-1.74600 + 7.34933i) q^{90} +(2.13102 - 1.12127i) q^{91} +(5.59770 - 0.987026i) q^{92} +(11.4663 - 10.8120i) q^{93} +(20.9768 + 3.69877i) q^{94} +(-0.140355 - 0.0247484i) q^{95} +(-7.69325 - 2.30546i) q^{96} +(-10.2887 + 1.81418i) q^{97} +(-10.7127 + 5.11057i) q^{98} +(-0.175006 - 0.348933i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.66985	−	0.294440i	1.18076	−	0.208201i	0.451398	−	0.892323i	$-0.350926\pi$
$2$	1.66985	−	0.294440i	1.18076	−	0.208201i	0.729367	+	0.684122i	$0.239815\pi$
$3$	0.685602	+	1.59058i	0.395833	+	0.918323i
$3$	0.685602	+	1.59058i	0.395833	+	0.918323i
$4$	0.822331	−	0.299304i	0.411166	−	0.149652i
$5$	1.39543	−	0.507895i	0.624055	−	0.227138i	−0.0105866	−	0.999944i	$-0.503370\pi$
$5$	1.39543	−	0.507895i	0.624055	−	0.227138i	0.634642	+	0.772806i	$0.281148\pi$
$6$	1.61319	+	2.45417i	0.658581	+	1.00191i
$7$	−0.356869	−	2.62157i	−0.134884	−	0.990861i
$7$	−0.356869	−	2.62157i	−0.134884	−	0.990861i
$8$	−1.65184	+	0.953692i	−0.584015	+	0.337181i
$9$	−2.05990	+	2.18101i	−0.686633	+	0.727004i
$10$	2.18062	−	1.25898i	0.689572	−	0.398125i
$11$	−0.0445037	+	0.122273i	−0.0134184	+	0.0368667i	−0.946221	−	0.323521i	$-0.895133\pi$
$11$	−0.0445037	+	0.122273i	−0.0134184	+	0.0368667i	0.932803	+	0.360388i	$0.117356\pi$
$12$	1.03986	+	1.10278i	0.300182	+	0.318346i
$13$	0.311287	+	0.855253i	0.0863354	+	0.237205i	0.975346	−	0.220683i	$-0.0708285\pi$
$13$	0.311287	+	0.855253i	0.0863354	+	0.237205i	−0.889010	+	0.457887i	$0.848606\pi$
$14$	−1.36782	−	4.27257i	−0.365564	−	1.14189i
$15$	1.76456	+	1.87133i	0.455607	+	0.483176i
$16$	−3.81827	+	3.20391i	−0.954568	+	0.800978i
$17$	−2.81624	−	4.87788i	−0.683040	−	1.18306i	−0.974049	−	0.226339i	$-0.927324\pi$
$17$	−2.81624	−	4.87788i	−0.683040	−	1.18306i	0.291009	−	0.956720i	$-0.406009\pi$
$18$	−2.79755	+	4.24849i	−0.659389	+	1.00138i
$19$	−0.0831162	−	0.0479872i	−0.0190682	−	0.0110090i	0.490436	−	0.871477i	$-0.336838\pi$
$19$	−0.0831162	−	0.0479872i	−0.0190682	−	0.0110090i	−0.509504	+	0.860468i	$0.670171\pi$
$20$	0.995491	−	0.835316i	0.222598	−	0.186782i
$21$	3.92516	−	2.36499i	0.856539	−	0.516082i
$22$	−0.0383126	+	0.217282i	−0.00816828	+	0.0463246i
$23$	6.39659	+	1.12789i	1.33378	+	0.235182i	0.794664	−	0.607049i	$-0.207647\pi$
$23$	6.39659	+	1.12789i	1.33378	+	0.235182i	0.539117	+	0.842231i	$0.318758\pi$
$24$	−2.64943	−	1.97354i	−0.540813	−	0.402847i
$25$	−2.14095	+	1.79647i	−0.428191	+	0.359295i
$26$	0.771624	+	1.33649i	0.151328	+	0.262108i
$27$	−4.88135	−	1.78113i	−0.939416	−	0.342779i
$28$	−1.07811	−	2.04899i	−0.203744	−	0.387223i
$29$	0.238914	−	0.656410i	0.0443651	−	0.121892i	−0.915532	−	0.402246i	$-0.868230\pi$
$29$	0.238914	−	0.656410i	0.0443651	−	0.121892i	0.959897	+	0.280354i	$0.0904518\pi$
$30$	3.49755	+	2.60529i	0.638562	+	0.475659i
$31$	−3.11204	−	8.55026i	−0.558939	−	1.53567i	−0.821180	−	0.570669i	$-0.806684\pi$
$31$	−3.11204	−	8.55026i	−0.558939	−	1.53567i	0.262242	−	0.965002i	$-0.415538\pi$
$32$	−2.98051	+	3.55203i	−0.526885	+	0.627917i
$33$	−0.224997	+	0.0130438i	−0.0391669	+	0.00227064i
$34$	−6.13896	−	7.31613i	−1.05282	−	1.25471i
$35$	−1.82947	−	3.47697i	−0.309237	−	0.587715i
$36$	−1.04113	+	2.41005i	−0.173522	+	0.401675i
$37$	−3.45015			−0.567202			−0.283601	−	0.958942i	$-0.591529\pi$
$37$	−3.45015			−0.567202			−0.283601	+	0.958942i	$0.591529\pi$
$38$	−0.152921	−	0.0556588i	−0.0248071	−	0.00902905i
$39$	−1.14693	+	1.08149i	−0.183656	+	0.173177i
$40$	−1.82066	+	2.16977i	−0.287871	+	0.343071i
$41$	2.04536	−	0.744450i	0.319432	−	0.116264i	−0.177328	−	0.984152i	$-0.556745\pi$
$41$	2.04536	−	0.744450i	0.319432	−	0.116264i	0.496760	+	0.867888i	$0.334523\pi$
$42$	5.85809	−	5.10490i	0.903923	−	0.787704i
$43$	1.37972	+	7.82480i	0.210406	+	1.19327i	0.888703	+	0.458483i	$0.151607\pi$
$43$	1.37972	+	7.82480i	0.210406	+	1.19327i	−0.678297	+	0.734788i	$0.737282\pi$
$44$			0.113869i			0.0171664i
$45$	−1.76672	+	4.08966i	−0.263367	+	0.609651i
$46$	11.0135			1.62385
$47$	11.8044	+	4.29647i	1.72186	+	0.626704i	0.997998	−	0.0632455i	$-0.0201451\pi$
$47$	11.8044	+	4.29647i	1.72186	+	0.626704i	0.723857	+	0.689950i	$0.242367\pi$
$48$	−7.71390	−	3.87667i	−1.11341	−	0.559549i
$49$	−6.74529	+	1.87112i	−0.963613	+	0.267302i
$50$	−3.04613	+	3.63023i	−0.430787	+	0.513392i
$51$	5.82784	−	7.82375i	0.816061	−	1.09554i
$52$	0.511962	+	0.610132i	0.0709963	+	0.0846101i
$53$	−1.26661	−	0.731275i	−0.173982	−	0.100448i	0.410480	−	0.911869i	$-0.365361\pi$
$53$	−1.26661	−	0.731275i	−0.173982	−	0.100448i	−0.584462	+	0.811421i	$0.698694\pi$
$54$	−8.67558	−	1.53696i	−1.18060	−	0.209154i
$55$			0.193227i			0.0260547i
$56$	3.08967	+	3.99009i	0.412874	+	0.533198i
$57$	0.0193428	−	0.165103i	0.00256202	−	0.0218685i
$58$	0.205677	−	1.16645i	0.0270068	−	0.153163i
$59$	4.86491	+	4.08214i	0.633357	+	0.531450i	0.901970	−	0.431798i	$-0.142121\pi$
$59$	4.86491	+	4.08214i	0.633357	+	0.531450i	−0.268613	+	0.963248i	$0.586565\pi$
$60$	2.01115	+	1.01071i	0.259638	+	0.130483i
$61$	−2.67073	+	7.33778i	−0.341952	+	0.939506i	0.642875	+	0.765971i	$0.277741\pi$
$61$	−2.67073	+	7.33778i	−0.341952	+	0.939506i	−0.984828	+	0.173536i	$0.944481\pi$
$62$	−7.71419	−	13.3614i	−0.979703	−	1.69690i
$63$	6.45280	+	4.62184i	0.812976	+	0.582297i
$64$	1.05325	−	1.82428i	0.131656	−	0.228035i
$65$	0.868757	+	1.03534i	0.107756	+	0.128419i
$66$	−0.371871	+	0.0880294i	−0.0457742	+	0.0108357i
$67$	−2.49984	+	14.1773i	−0.305404	+	1.73203i	0.316192	+	0.948695i	$0.397596\pi$
$67$	−2.49984	+	14.1773i	−0.305404	+	1.73203i	−0.621596	+	0.783338i	$0.713515\pi$
$68$	−3.77586	−	3.16832i	−0.457890	−	0.384215i
$69$	2.59151	+	10.9476i	0.311982	+	1.31793i
$70$	−4.07871	−	5.26736i	−0.487499	−	0.629570i
$71$	2.38823	+	1.37884i	0.283431	+	0.163639i	0.634975	−	0.772532i	$-0.281010\pi$
$71$	2.38823	+	1.37884i	0.283431	+	0.163639i	−0.351545	+	0.936171i	$0.614344\pi$
$72$	1.32262	−	5.56720i	0.155872	−	0.656101i
$73$		−	8.02256i		−	0.938969i	−0.882941	−	0.469485i	$-0.844440\pi$
$73$		−	8.02256i		−	0.938969i	0.882941	−	0.469485i	$-0.155560\pi$
$74$	−5.76125	+	1.01586i	−0.669732	+	0.118092i
$75$	−4.32528	−	2.17370i	−0.499441	−	0.250997i
$76$	−0.0827118	−	0.0145843i	−0.00948770	−	0.00167294i
$77$	0.336429	+	0.0730343i	0.0383397	+	0.00832303i
$78$	−1.59677	+	2.14363i	−0.180799	+	0.242719i
$79$	0.0703241	+	0.398828i	0.00791207	+	0.0448716i	0.988508	−	0.151167i	$-0.0483032\pi$
$79$	0.0703241	+	0.398828i	0.00791207	+	0.0448716i	−0.980596	+	0.196039i	$0.937192\pi$
$80$	−3.70088	+	6.41012i	−0.413771	+	0.716673i
$81$	−0.513631	−	8.98533i	−0.0570701	−	0.998370i
$82$	3.19626	−	1.84536i	0.352968	−	0.203786i
$83$	4.54412	+	1.65393i	0.498782	+	0.181542i	0.579146	−	0.815224i	$-0.303386\pi$
$83$	4.54412	+	1.65393i	0.498782	+	0.181542i	−0.0803638	+	0.996766i	$0.525608\pi$
$84$	2.51993	−	3.11962i	0.274947	−	0.340378i
$85$	−6.40732	−	5.37638i	−0.694972	−	0.583150i
$86$	4.60787	+	12.6600i	0.496880	+	1.36517i
$87$	1.20787	−	0.0700244i	0.129498	−	0.00750740i
$88$	−0.0430976	−	0.244419i	−0.00459422	−	0.0260551i
$89$	7.98594	−	13.8321i	0.846508	−	1.46619i	−0.0377975	−	0.999285i	$-0.512034\pi$
$89$	7.98594	−	13.8321i	0.846508	−	1.46619i	0.884305	−	0.466909i	$-0.154632\pi$
$90$	−1.74600	+	7.34933i	−0.184045	+	0.774688i
$91$	2.13102	−	1.12127i	0.223392	−	0.117541i
$92$	5.59770	−	0.987026i	0.583601	−	0.102905i
$93$	11.4663	−	10.8120i	1.18900	−	1.12115i
$94$	20.9768	+	3.69877i	2.16359	+	0.381499i
$95$	−0.140355	−	0.0247484i	−0.0144001	−	0.00253913i
$96$	−7.69325	−	2.30546i	−0.785189	−	0.235300i
$97$	−10.2887	+	1.81418i	−1.04466	+	0.184202i	−0.669541	−	0.742775i	$-0.733509\pi$
$97$	−10.2887	+	1.81418i	−1.04466	+	0.184202i	−0.375118	+	0.926977i	$0.622398\pi$
$98$	−10.7127	+	5.11057i	−1.08215	+	0.516246i
$99$	−0.175006	−	0.348933i	−0.0175887	−	0.0350691i
$100$	−1.22288	+	2.11809i	−0.122288	+	0.211809i
$101$	0.741078	+	4.20286i	0.0737400	+	0.418200i	0.999223	+	0.0394113i	$0.0125482\pi$
$101$	0.741078	+	4.20286i	0.0737400	+	0.418200i	−0.925483	+	0.378789i	$0.876341\pi$
$102$	7.42801	−	14.7805i	0.735483	−	1.46348i
$103$	1.38685	+	3.81033i	0.136650	+	0.375443i	0.989076	−	0.147404i	$-0.0470919\pi$
$103$	1.38685	+	3.81033i	0.136650	+	0.375443i	−0.852426	+	0.522848i	$0.824870\pi$
$104$	−1.32985	−	1.11587i	−0.130402	−	0.109420i
$105$	4.27612	−	5.29374i	0.417306	−	0.516616i
$106$	−2.33036	−	0.848183i	−0.226345	−	0.0823828i
$107$	8.99730	−	5.19460i	0.869802	−	0.502181i	0.00251969	−	0.999997i	$-0.499198\pi$
$107$	8.99730	−	5.19460i	0.869802	−	0.502181i	0.867283	+	0.497816i	$0.165865\pi$
$108$	−4.54719	−	0.00367129i	−0.437553	−	0.000353270i
$109$	2.59277	−	4.49081i	0.248342	−	0.430142i	−0.714724	−	0.699407i	$-0.753447\pi$
$109$	2.59277	−	4.49081i	0.248342	−	0.430142i	0.963066	+	0.269265i	$0.0867808\pi$
$110$	0.0568937	+	0.322660i	0.00542460	+	0.0307644i
$111$	−2.36543	−	5.48775i	−0.224517	−	0.520874i
$112$	9.76191	+	8.86651i	0.922414	+	0.837806i
$113$	−15.1938	−	2.67908i	−1.42931	−	0.252026i	−0.595181	−	0.803592i	$-0.702920\pi$
$113$	−15.1938	−	2.67908i	−1.42931	−	0.252026i	−0.834132	+	0.551565i	$0.814031\pi$
$114$	−0.0163133	−	0.281394i	−0.00152788	−	0.0263549i
$115$	9.49885	−	1.67490i	0.885772	−	0.156186i
$116$		−	0.611294i		−	0.0567572i
$117$	−2.50654	−	1.08281i	−0.231729	−	0.100106i
$118$	9.32564	+	5.38416i	0.858494	+	0.495652i
$119$	−11.7827	+	9.12375i	−1.08012	+	0.836373i
$120$	−4.69945	−	1.40830i	−0.428999	−	0.128560i
$121$	8.41352	+	7.05978i	0.764865	+	0.641798i
$122$	−2.29920	+	13.0394i	−0.208159	+	1.18053i
$123$	2.58641	+	2.74292i	0.233209	+	0.247320i
$124$	−5.11825	−	6.09970i	−0.459633	−	0.547769i
$125$	−5.78760	+	10.0244i	−0.517658	+	0.896611i
$126$	12.1361	+	5.81783i	1.08117	+	0.518294i
$127$	−0.565054	−	0.978702i	−0.0501404	−	0.0868458i	0.839866	−	0.542794i	$-0.182634\pi$
$127$	−0.565054	−	0.978702i	−0.0501404	−	0.0868458i	−0.890006	+	0.455948i	$0.849300\pi$
$128$	4.39342	−	12.0708i	0.388327	−	1.06692i
$129$	−11.5000	+	7.55926i	−1.01252	+	0.665556i
$130$	1.75555	+	1.47308i	0.153971	+	0.129197i
$131$	1.13648	−	6.44529i	0.0992945	−	0.563127i	−0.894052	−	0.447963i	$-0.852150\pi$
$131$	1.13648	−	6.44529i	0.0992945	−	0.563127i	0.993346	−	0.115164i	$-0.0367393\pi$
$132$	−0.181118	+	0.0780688i	−0.0157643	+	0.00679502i
$133$	−0.0961403	+	0.235020i	−0.00833642	+	0.0203788i
$134$			24.4101i			2.10871i
$135$	−7.71621	−	0.00622987i	−0.664105	−	0.000536182i
$136$	9.30399	+	5.37166i	0.797811	+	0.460616i
$137$	−2.98891	−	3.56205i	−0.255360	−	0.304326i	0.623100	−	0.782142i	$-0.285873\pi$
$137$	−2.98891	−	3.56205i	−0.255360	−	0.304326i	−0.878460	+	0.477816i	$0.841429\pi$
$138$	7.55086	+	17.5178i	0.642772	+	1.49122i
$139$	8.26472	−	9.84951i	0.701005	−	0.835425i	−0.291635	−	0.956530i	$-0.594199\pi$
$139$	8.26472	−	9.84951i	0.701005	−	0.835425i	0.992640	+	0.121105i	$0.0386437\pi$
$140$	−2.54510	−	2.31165i	−0.215100	−	0.195370i
$141$	1.25927	+	21.7216i	0.106050	+	1.82929i
$142$	4.39398	+	1.59928i	0.368735	+	0.134208i
$143$	−0.118428			−0.00990342
$144$	0.877486	−	14.9274i	0.0731239	−	1.24395i
$145$		−	1.03732i		−	0.0861445i
$146$	−2.36216	−	13.3965i	−0.195494	−	1.10870i
$147$	−7.60075	−	9.44609i	−0.626899	−	0.779100i
$148$	−2.83717	+	1.03265i	−0.233214	+	0.0848829i
$149$	−13.1499	+	15.6715i	−1.07728	+	1.28386i	−0.120608	+	0.992700i	$0.538484\pi$
$149$	−13.1499	+	15.6715i	−1.07728	+	1.28386i	−0.956676	+	0.291156i	$0.905960\pi$
$150$	−7.86261	−	2.35622i	−0.641980	−	0.192384i
$151$	12.8057	+	4.66088i	1.04211	+	0.379297i	0.805679	−	0.592352i	$-0.201800\pi$
$151$	12.8057	+	4.66088i	1.04211	+	0.379297i	0.236430	+	0.971649i	$0.424023\pi$
$152$	0.183060			0.0148481
$153$	16.4399	+	3.90567i	1.32909	+	0.315755i
$154$	0.583292	+	0.0228982i	0.0470030	+	0.00184519i
$155$	−8.68526	−	10.3507i	−0.697617	−	0.831388i
$156$	−0.619463	+	1.23262i	−0.0495967	+	0.0986889i
$157$	−2.56097	+	3.05204i	−0.204387	+	0.243579i	−0.858495	−	0.512822i	$-0.828600\pi$
$157$	−2.56097	+	3.05204i	−0.204387	+	0.243579i	0.654107	+	0.756402i	$0.273044\pi$
$158$	0.234862	+	0.645277i	0.0186846	+	0.0513355i
$159$	0.294765	−	2.51600i	0.0233764	−	0.199532i
$160$	−2.35503	+	6.47040i	−0.186182	+	0.511530i
$161$	0.674106	−	17.1716i	0.0531270	−	1.35332i
$162$	−3.50333	−	14.8530i	−0.275248	−	1.16696i
$163$	−12.3022	−	21.3081i	−0.963584	−	1.66898i	−0.713372	−	0.700785i	$-0.752833\pi$
$163$	−12.3022	−	21.3081i	−0.963584	−	1.66898i	−0.250212	−	0.968191i	$-0.580500\pi$
$164$	1.45915	−	1.22437i	0.113940	−	0.0956072i
$165$	−0.307343	+	0.132477i	−0.0239266	+	0.0103133i
$166$	8.07501	+	1.42384i	0.626742	+	0.110512i
$167$	3.18840	−	18.0823i	0.246726	−	1.39925i	−0.569724	−	0.821836i	$-0.692950\pi$
$167$	3.18840	−	18.0823i	0.246726	−	1.39925i	0.816450	−	0.577417i	$-0.195939\pi$
$168$	−4.22827	+	7.64998i	−0.326218	+	0.590209i
$169$	9.32402	−	7.82378i	0.717232	−	0.601829i
$170$	−12.2823	−	7.09120i	−0.942010	−	0.543870i
$171$	0.275872	−	0.0824288i	0.0210964	−	0.00630349i
$172$	3.47659	+	6.02162i	0.265087	+	0.459144i
$173$	−2.48370	+	2.08407i	−0.188832	+	0.158449i	−0.732303	−	0.680979i	$-0.761554\pi$
$173$	−2.48370	+	2.08407i	−0.188832	+	0.158449i	0.543470	+	0.839428i	$0.317110\pi$
$174$	1.99635	−	0.472577i	0.151343	−	0.0358260i
$175$	5.47363	+	4.97156i	0.413767	+	0.375815i
$176$	−0.221824	−	0.609457i	−0.0167206	−	0.0459396i
$177$	−3.15759	+	10.5368i	−0.237339	+	0.791992i
$178$	9.26264	−	25.4489i	0.694264	−	1.90747i
$179$	−17.0391	+	9.83754i	−1.27356	+	0.735292i	−0.975657	−	0.219303i	$-0.929622\pi$
$179$	−17.0391	+	9.83754i	−1.27356	+	0.735292i	−0.297907	+	0.954595i	$0.596288\pi$
$180$	−0.228776	+	3.89184i	−0.0170520	+	0.290081i
$181$	−14.9844	+	8.65126i	−1.11378	+	0.643043i	−0.939806	−	0.341707i	$-0.888995\pi$
$181$	−14.9844	+	8.65126i	−1.11378	+	0.643043i	−0.173976	+	0.984750i	$0.555662\pi$
$182$	3.22834	−	2.49982i	0.239301	−	0.185299i
$183$	−13.5024	+	0.782779i	−0.998126	+	0.0578647i
$184$	−11.6418	+	4.23728i	−0.858247	+	0.312376i
$185$	−4.81445	+	1.75232i	−0.353965	+	0.128833i
$186$	15.9635	−	21.4306i	1.17050	−	1.57137i
$187$	0.721766	−	0.127267i	0.0527807	−	0.00930667i
$188$	10.9931			0.801755
$189$	−2.92736	+	13.4324i	−0.212934	+	0.977067i
$190$	−0.241660			−0.0175318
$191$	−5.21186	+	0.918991i	−0.377117	+	0.0664959i	−0.358994	−	0.933340i	$-0.616880\pi$
$191$	−5.21186	+	0.918991i	−0.377117	+	0.0664959i	−0.0181229	+	0.999836i	$0.505769\pi$
$192$	3.62377	+	0.424546i	0.261523	+	0.0306390i
$193$	−16.6028	+	6.04294i	−1.19510	+	0.434980i	−0.861511	−	0.507739i	$-0.830481\pi$
$193$	−16.6028	+	6.04294i	−1.19510	+	0.434980i	−0.333587	+	0.942719i	$0.608259\pi$
$194$	−16.6465	+	6.05881i	−1.19515	+	0.434998i
$195$	−1.05118	+	2.09166i	−0.0752764	+	0.149787i
$196$	−4.98683	+	3.55757i	−0.356202	+	0.254112i
$197$	17.9168	−	10.3443i	1.27652	−	0.736997i	0.300311	−	0.953841i	$-0.402910\pi$
$197$	17.9168	−	10.3443i	1.27652	−	0.736997i	0.976206	+	0.216844i	$0.0695763\pi$
$198$	−0.394974	−	0.531138i	−0.0280696	−	0.0377464i
$199$	−11.0639	+	6.38777i	−0.784302	+	0.452817i	−0.837953	−	0.545743i	$-0.816247\pi$
$199$	−11.0639	+	6.38777i	−0.784302	+	0.452817i	0.0536510	+	0.998560i	$0.482914\pi$
$200$	1.82324	−	5.00931i	0.128922	−	0.354211i
$201$	−24.2641	+	5.74379i	−1.71145	+	0.405136i
$202$	2.47498	+	6.79996i	0.174139	+	0.478443i
$203$	−1.80609	−	0.392077i	−0.126762	−	0.0275184i
$204$	2.45073	−	8.17801i	0.171586	−	0.572575i
$205$	2.47605	−	2.07766i	0.172935	−	0.145110i
$206$	3.43775	+	5.95436i	0.239519	+	0.414860i
$207$	−15.6363	+	11.6277i	−1.08680	+	0.808181i
$208$	−3.92873	−	2.26825i	−0.272409	−	0.157275i
$209$	0.00956651	−	0.00802726i	0.000661729	−	0.000555257i
$210$	5.58180	−	10.0988i	0.385181	−	0.696885i
$211$	3.56749	−	20.2322i	0.245596	−	1.39284i	−0.573508	−	0.819200i	$-0.694418\pi$
$211$	3.56749	−	20.2322i	0.245596	−	1.39284i	0.819104	−	0.573645i	$-0.194471\pi$
$212$	−1.26044	−	0.222250i	−0.0865676	−	0.0152642i
$213$	−0.555790	+	4.74401i	−0.0380821	+	0.325054i
$214$	13.4947	−	11.3234i	0.922478	−	0.774051i
$215$	5.89948	+	10.2182i	0.402341	+	0.696876i
$216$	9.76188	−	1.71316i	0.664212	−	0.116566i
$217$	−21.3045	+	11.2098i	−1.44625	+	0.760968i
$218$	3.00727	−	8.26242i	0.203678	−	0.559601i
$219$	12.7605	−	5.50028i	0.862277	−	0.371675i
$220$	0.0578335	+	0.158896i	0.00389913	+	0.0107128i
$221$	3.29516	−	3.92702i	0.221657	−	0.264160i
$222$	−5.56574	−	8.46726i	−0.373548	−	0.568285i
$223$	−12.6494	−	15.0750i	−0.847070	−	1.00950i	−0.999775	−	0.0212263i	$-0.993243\pi$
$223$	−12.6494	−	15.0750i	−0.847070	−	1.00950i	0.152705	−	0.988272i	$-0.451202\pi$
$224$	10.3756	+	6.54602i	0.693247	+	0.437374i
$225$	0.492018	−	8.37001i	0.0328012	−	0.558000i
$226$	−26.1603			−1.74015
$227$	−0.299457	−	0.108994i	−0.0198757	−	0.00723416i	0.332063	−	0.943257i	$-0.392255\pi$
$227$	−0.299457	−	0.108994i	−0.0198757	−	0.00723416i	−0.351939	+	0.936023i	$0.614478\pi$
$228$	−0.0335099	−	0.141559i	−0.00221924	−	0.00937497i
$229$	5.56696	−	6.63444i	0.367875	−	0.438416i	−0.550073	−	0.835116i	$-0.685400\pi$
$229$	5.56696	−	6.63444i	0.367875	−	0.438416i	0.917948	+	0.396700i	$0.129845\pi$
$230$	15.3685	−	5.59369i	1.01337	−	0.368837i
$231$	0.114490	+	0.585191i	0.00753287	+	0.0385027i
$232$	0.231365	+	1.31214i	0.0151899	+	0.0861460i
$233$		−	7.34274i		−	0.481039i	−0.970644	−	0.240520i	$-0.922682\pi$
$233$		−	7.34274i		−	0.481039i	0.970644	−	0.240520i	$-0.0773178\pi$
$234$	−4.50437	−	1.07012i	−0.294460	−	0.0699558i
$235$	18.6544			1.21688
$236$	5.22237	+	1.90079i	0.339947	+	0.123731i
$237$	−0.586153	+	0.385293i	−0.0380748	+	0.0250275i
$238$	−16.9890	+	18.7046i	−1.10123	+	1.21244i
$239$	−3.02456	+	3.60453i	−0.195642	+	0.233157i	−0.854943	−	0.518722i	$-0.826408\pi$
$239$	−3.02456	+	3.60453i	−0.195642	+	0.233157i	0.659301	+	0.751879i	$0.270852\pi$
$240$	−12.7331	−	1.49176i	−0.821921	−	0.0962930i
$241$	−4.26262	−	5.07999i	−0.274579	−	0.327231i	0.611078	−	0.791571i	$-0.290736\pi$
$241$	−4.26262	−	5.07999i	−0.274579	−	0.327231i	−0.885657	+	0.464339i	$0.846292\pi$
$242$	16.1280	+	9.31152i	1.03675	+	0.598567i
$243$	13.9398	−	6.97734i	0.894236	−	0.447596i
$244$			6.83345i			0.437467i
$245$	−8.46225	+	6.03691i	−0.540633	+	0.385684i
$246$	5.12656	+	3.81872i	0.326857	+	0.243473i
$247$	0.0151682	−	0.0860232i	0.000965130	−	0.00547352i
$248$	13.2949	+	11.1558i	0.844228	+	0.708391i
$249$	0.484758	+	8.36174i	0.0307203	+	0.529903i
$250$	−6.71285	+	18.4434i	−0.424558	+	1.16646i
$251$	7.34905	+	12.7289i	0.463868	+	0.803443i	0.999150	−	0.0412308i	$-0.0131279\pi$
$251$	7.34905	+	12.7289i	0.463868	+	0.803443i	−0.535282	+	0.844674i	$0.679795\pi$
$252$	6.68967	+	1.86934i	0.421410	+	0.117757i
$253$	−0.422583	+	0.731935i	−0.0265675	+	0.0460163i
$254$	−1.23173	−	1.46792i	−0.0772854	−	0.0921052i
$255$	4.15870	−	13.8774i	0.260428	−	0.869038i
$256$	3.05066	−	17.3011i	0.190666	−	1.08132i
$257$	10.8180	+	9.07738i	0.674808	+	0.566231i	0.914484	−	0.404621i	$-0.132597\pi$
$257$	10.8180	+	9.07738i	0.674808	+	0.566231i	−0.239676	+	0.970853i	$0.577041\pi$
$258$	−16.9776	+	16.0089i	−1.05698	+	0.996673i
$259$	1.23125	+	9.04483i	0.0765063	+	0.562018i
$260$	1.02429	+	0.591374i	0.0635237	+	0.0366754i
$261$	0.939500	+	1.87321i	0.0581536	+	0.115949i
$262$		−	11.0973i		−	0.685594i
$263$	−15.4018	+	2.71576i	−0.949718	+	0.167461i	−0.626987	−	0.779030i	$-0.715712\pi$
$263$	−15.4018	+	2.71576i	−0.949718	+	0.167461i	−0.322731	+	0.946491i	$0.604601\pi$
$264$	0.359220	−	0.236124i	0.0221085	−	0.0145324i
$265$	−2.13887	−	0.377141i	−0.131390	−	0.0231676i
$266$	−0.0913407	+	0.420757i	−0.00560046	+	0.0257983i
$267$	27.4762	+	3.21900i	1.68152	+	0.197000i
$268$	2.18763	+	12.4067i	0.133631	+	0.757857i
$269$	2.15558	−	3.73358i	0.131428	−	0.227640i	−0.792799	−	0.609483i	$-0.791377\pi$
$269$	2.15558	−	3.73358i	0.131428	−	0.227640i	0.924227	+	0.381843i	$0.124710\pi$
$270$	−12.8868	+	2.26156i	−0.784264	+	0.137634i
$271$	16.1867	−	9.34540i	0.983272	−	0.567692i	0.0800157	−	0.996794i	$-0.474503\pi$
$271$	16.1867	−	9.34540i	0.983272	−	0.567692i	0.903256	+	0.429101i	$0.141170\pi$
$272$	26.3815	+	9.60207i	1.59961	+	0.582211i
$273$	3.24451	+	2.62081i	0.196367	+	0.158619i
$274$	−6.03986	−	5.06804i	−0.364881	−	0.306172i
$275$	−0.124380	−	0.341731i	−0.00750038	−	0.0206071i
$276$	5.40774	+	8.22689i	0.325508	+	0.495201i
$277$	1.63206	+	9.25587i	0.0980609	+	0.556131i	0.993766	+	0.111483i	$0.0355601\pi$
$277$	1.63206	+	9.25587i	0.0980609	+	0.556131i	−0.895705	+	0.444648i	$0.853329\pi$
$278$	10.9008	−	18.8807i	0.653786	−	1.13239i
$279$	25.0587	+	10.8253i	1.50023	+	0.648092i
$280$	6.33796	+	3.99866i	0.378765	+	0.238966i
$281$	27.0442	−	4.76862i	1.61332	−	0.284472i	0.707048	−	0.707166i	$-0.250027\pi$
$281$	27.0442	−	4.76862i	1.61332	−	0.284472i	0.906272	+	0.422694i	$0.138916\pi$
$282$	8.49852	+	35.9011i	0.506079	+	2.13788i
$283$	−21.3585	−	3.76609i	−1.26963	−	0.223871i	−0.502060	−	0.864833i	$-0.667424\pi$
$283$	−21.3585	−	3.76609i	−1.26963	−	0.223871i	−0.767573	+	0.640962i	$0.778536\pi$
$284$	2.37661	+	0.419060i	0.141026	+	0.0248667i
$285$	−0.0568635	−	0.240214i	−0.00336830	−	0.0142291i
$286$	−0.197757	+	0.0348699i	−0.0116936	+	0.00206190i
$287$	−2.68156	−	5.09639i	−0.158287	−	0.300830i
$288$	−1.60748	−	13.8174i	−0.0947217	−	0.814196i
$289$	−7.36246	+	12.7522i	−0.433086	+	0.750127i
$290$	−0.305428	−	1.73217i	−0.0179353	−	0.101716i
$291$	−9.93955	−	15.1212i	−0.582667	−	0.886421i
$292$	−2.40118	−	6.59720i	−0.140519	−	0.386072i
$293$	−7.22978	−	6.06651i	−0.422368	−	0.354409i	0.406695	−	0.913564i	$-0.366681\pi$
$293$	−7.22978	−	6.06651i	−0.422368	−	0.354409i	−0.829063	+	0.559155i	$0.811126\pi$
$294$	−15.4734	−	13.5356i	−0.902430	−	0.789414i
$295$	8.86194	+	3.22548i	0.515962	+	0.187795i
$296$	5.69911	−	3.29038i	0.331254	−	0.191250i
$297$	0.435022	−	0.517590i	0.0252425	−	0.0300336i
$298$	−17.3441	+	30.0409i	−1.00472	+	1.74022i
$299$	1.02654	+	5.82180i	0.0593664	+	0.336684i
$300$	−4.20741	−	0.492924i	−0.242915	−	0.0284590i
$301$	20.0209	−	6.40947i	1.15399	−	0.369436i
$302$	22.7559	+	4.01248i	1.30946	+	0.230892i
$303$	−6.17691	+	4.06023i	−0.354854	+	0.233254i
$304$	0.471107	−	0.0830689i	0.0270198	−	0.00476433i
$305$			11.5958i			0.663974i
$306$	28.6022	+	1.68134i	1.63508	+	0.0961156i
$307$	4.86656	+	2.80971i	0.277749	+	0.160358i	0.632404	−	0.774639i	$-0.282068\pi$
$307$	4.86656	+	2.80971i	0.277749	+	0.160358i	−0.354655	+	0.934997i	$0.615402\pi$
$308$	0.298516	−	0.0406363i	0.0170095	−	0.00231547i
$309$	−5.10982	+	4.81827i	−0.290687	+	0.274102i
$310$	−17.5508	−	14.7269i	−0.996817	−	0.836429i
$311$	3.03101	−	17.1897i	0.171873	−	0.974740i	−0.769819	−	0.638263i	$-0.779653\pi$
$311$	3.03101	−	17.1897i	0.171873	−	0.974740i	0.941692	−	0.336477i	$-0.109236\pi$
$312$	0.863141	−	2.88027i	0.0488658	−	0.163063i
$313$	−0.321001	−	0.382554i	−0.0181440	−	0.0216232i	0.756896	−	0.653535i	$-0.226715\pi$
$313$	−0.321001	−	0.382554i	−0.0181440	−	0.0216232i	−0.775040	+	0.631912i	$0.782270\pi$
$314$	−3.37779	+	5.85051i	−0.190620	+	0.330163i
$315$	11.3518	+	3.17211i	0.639603	+	0.178728i
$316$	0.177200	+	0.306920i	0.00996830	+	0.0172656i
$317$	−2.67158	+	7.34010i	−0.150051	+	0.412261i	−0.991831	−	0.127559i	$-0.959286\pi$
$317$	−2.67158	+	7.34010i	−0.150051	+	0.412261i	0.841780	+	0.539820i	$0.181508\pi$
$318$	−0.248598	−	4.28815i	−0.0139407	−	0.240467i
$319$	0.0696286	+	0.0584253i	0.00389845	+	0.00327119i
$320$	0.543191	−	3.08059i	0.0303653	−	0.172210i
$321$	14.4310	+	10.7495i	0.805460	+	0.599980i
$322$	−3.93037	−	28.8726i	−0.219031	−	1.60901i
$323$			0.540574i			0.0300784i
$324$	−3.11172	−	7.23519i	−0.172873	−	0.401955i
$325$	−2.20289	−	1.27184i	−0.122194	−	0.0705490i
$326$	−26.8169	−	31.9591i	−1.48525	−	1.77005i
$327$	8.92061	+	1.04510i	0.493311	+	0.0577944i
$328$	−2.66864	+	3.18036i	−0.147351	+	0.175606i
$329$	7.05086	−	32.4795i	0.388727	−	1.79065i
$330$	−0.474211	+	0.311710i	−0.0261044	+	0.0171591i
$331$	29.7049	+	10.8117i	1.63273	+	0.594265i	0.985746	−	0.168238i	$-0.0538077\pi$
$331$	29.7049	+	10.8117i	1.63273	+	0.594265i	0.646984	+	0.762503i	$0.276030\pi$
$332$	4.23180			0.232250
$333$	7.10697	−	7.52483i	0.389459	−	0.412358i
$334$		−	31.1336i		−	1.70356i
$335$	3.71223	+	21.0531i	0.202821	+	1.15025i
$336$	−7.41011	+	21.6060i	−0.404255	+	1.17870i
$337$	−6.59007	+	2.39859i	−0.358984	+	0.130659i	−0.515215	−	0.857061i	$-0.672288\pi$
$337$	−6.59007	+	2.39859i	−0.358984	+	0.130659i	0.156231	+	0.987721i	$0.450066\pi$
$338$	13.2661	−	15.8099i	0.721581	−	0.859947i
$339$	−6.15561	−	26.0038i	−0.334327	−	1.41233i
$340$	−6.87811	−	2.50343i	−0.373018	−	0.135767i
$341$	1.18396			0.0641151
$342$	0.436395	−	0.218872i	0.0235975	−	0.0118352i
$343$	7.31245	+	17.0155i	0.394835	+	0.918752i
$344$	−9.74154	−	11.6095i	−0.525229	−	0.625943i
$345$	9.17650	+	13.9604i	0.494046	+	0.751601i
$346$	−3.53378	+	4.21140i	−0.189977	+	0.226406i
$347$	3.63535	+	9.98804i	0.195156	+	0.536186i	0.998216	−	0.0597122i	$-0.0190183\pi$
$347$	3.63535	+	9.98804i	0.195156	+	0.536186i	−0.803060	+	0.595898i	$0.796796\pi$
$348$	0.972313	−	0.419105i	0.0521215	−	0.0224664i
$349$	2.52401	−	6.93467i	0.135107	−	0.371204i	−0.853627	−	0.520885i	$-0.825602\pi$
$349$	2.52401	−	6.93467i	0.135107	−	0.371204i	0.988734	+	0.149680i	$0.0478244\pi$
$350$	10.6040	+	6.69013i	0.566807	+	0.357602i
$351$	0.00381826	−	4.72923i	0.000203804	−	0.252428i
$352$	−0.301674	−	0.522514i	−0.0160793	−	0.0278501i
$353$	−12.7574	+	10.7047i	−0.679007	+	0.569754i	−0.915716	−	0.401826i	$-0.868376\pi$
$353$	−12.7574	+	10.7047i	−0.679007	+	0.569754i	0.236709	+	0.971581i	$0.423931\pi$
$354$	−2.17027	+	18.5246i	−0.115348	+	0.984570i
$355$	4.03291	+	0.711112i	0.214045	+	0.0377419i
$356$	2.42710	−	13.7648i	0.128636	−	0.729531i
$357$	−22.5903	−	12.4861i	−1.19561	−	0.660832i
$358$	−25.5563	+	21.4443i	−1.35069	+	1.13336i
$359$	−15.0167	−	8.66990i	−0.792552	−	0.457580i	0.0483084	−	0.998832i	$-0.484617\pi$
$359$	−15.0167	−	8.66990i	−0.792552	−	0.457580i	−0.840860	+	0.541253i	$0.817950\pi$
$360$	−0.981935	−	8.44039i	−0.0517525	−	0.444848i
$361$	−9.49539	−	16.4465i	−0.499758	−	0.865606i
$362$	−22.4745	+	18.8583i	−1.18123	+	0.991173i
$363$	−5.46083	+	18.2226i	−0.286619	+	0.956438i
$364$	1.41680	−	1.55988i	0.0742606	−	0.0817600i
$365$	−4.07462	−	11.1949i	−0.213275	−	0.585969i
$366$	−22.3165	+	5.28278i	−1.16650	+	0.276135i
$367$	−9.14036	+	25.1129i	−0.477123	+	1.31088i	0.434801	+	0.900526i	$0.356819\pi$
$367$	−9.14036	+	25.1129i	−0.477123	+	1.31088i	−0.911924	+	0.410358i	$0.865404\pi$
$368$	−28.0376	+	16.1875i	−1.46156	+	0.843833i
$369$	−2.58958	+	5.99445i	−0.134808	+	0.312059i
$370$	−7.52347	+	4.34368i	−0.391127	+	0.225817i
$371$	−1.46508	+	3.58147i	−0.0760631	+	0.185941i
$372$	6.19298	−	12.3230i	0.321091	−	0.638916i
$373$	17.3964	−	6.33178i	0.900752	−	0.327847i	0.150198	−	0.988656i	$-0.452009\pi$
$373$	17.3964	−	6.33178i	0.900752	−	0.327847i	0.750554	+	0.660809i	$0.229787\pi$
$374$	1.16777	−	0.425034i	0.0603840	−	0.0219780i
$375$	−19.9126	−	2.33289i	−1.02828	−	0.120470i
$376$	−23.5966	+	4.16072i	−1.21690	+	0.214573i
$377$	0.635767			0.0327437
$378$	−0.933213	+	23.2922i	−0.0479993	+	1.19802i
$379$	35.2309			1.80969			0.904846	−	0.425739i	$-0.139986\pi$
$379$	35.2309			1.80969			0.904846	+	0.425739i	$0.139986\pi$
$380$	−0.122826	+	0.0216575i	−0.00630083	+	0.00111101i
$381$	1.16930	−	1.56977i	0.0599052	−	0.0804215i
$382$	−8.43245	+	3.06916i	−0.431442	+	0.157032i
$383$	−15.7009	+	5.71465i	−0.802277	+	0.292005i	−0.710430	−	0.703768i	$-0.751499\pi$
$383$	−15.7009	+	5.71465i	−0.802277	+	0.292005i	−0.0918471	+	0.995773i	$0.529277\pi$
$384$	22.2118	−	1.28769i	1.13349	−	0.0657122i
$385$	0.506557	−	0.0689565i	0.0258166	−	0.00351435i
$386$	−25.9450	+	14.9794i	−1.32057	+	0.762429i
$387$	−19.9081	−	13.1091i	−1.01198	−	0.666373i
$388$	−7.91773	+	4.57130i	−0.401962	+	0.232073i
$389$	3.24562	−	8.91727i	0.164560	−	0.452124i	−0.829816	−	0.558037i	$-0.811555\pi$
$389$	3.24562	−	8.91727i	0.164560	−	0.452124i	0.994375	+	0.105914i	$0.0337767\pi$
$390$	−1.13944	+	3.80228i	−0.0576980	+	0.192536i
$391$	−12.5126	−	34.3782i	−0.632792	−	1.73858i
$392$	9.35769	−	9.52372i	0.472635	−	0.481021i
$393$	11.0309	−	2.61124i	0.556436	−	0.131720i
$394$	26.8726	−	22.5488i	1.35382	−	1.13599i
$395$	0.300695	+	0.520819i	0.0151296	+	0.0262052i
$396$	−0.248350	−	0.234559i	−0.0124800	−	0.0117870i
$397$	−32.9549	−	19.0265i	−1.65396	−	0.954913i	−0.975422	−	0.220346i	$-0.929281\pi$
$397$	−32.9549	−	19.0265i	−1.65396	−	0.954913i	−0.678536	−	0.734567i	$-0.737385\pi$
$398$	−16.5943	+	13.9243i	−0.831799	+	0.697962i
$399$	−0.439733	+	0.00821154i	−0.0220142	+	0.000411091i
$400$	2.41901	−	13.7189i	0.120950	−	0.685943i
$401$	5.53925	+	0.976719i	0.276617	+	0.0487750i	0.310236	−	0.950660i	$-0.399592\pi$
$401$	5.53925	+	0.976719i	0.276617	+	0.0487750i	−0.0336187	+	0.999435i	$0.510703\pi$
$402$	−38.8262	+	16.7356i	−1.93648	+	0.834696i
$403$	6.34390	−	5.32316i	0.316012	−	0.265166i
$404$	1.86734	+	3.23434i	0.0929039	+	0.160914i
$405$	−5.28034	−	12.2775i	−0.262382	−	0.610075i
$406$	−3.13134	−	0.122927i	−0.155406	−	0.00610076i
$407$	0.153545	−	0.421860i	0.00761092	−	0.0209108i
$408$	−2.16523	+	18.4816i	−0.107195	+	0.914974i
$409$	−0.754389	−	2.07267i	−0.0373022	−	0.102487i	0.919643	−	0.392755i	$-0.128478\pi$
$409$	−0.754389	−	2.07267i	−0.0373022	−	0.102487i	−0.956945	+	0.290268i	$0.906256\pi$
$410$	3.52290	−	4.19843i	0.173984	−	0.207346i
$411$	3.61652	−	7.19626i	0.178390	−	0.354965i
$412$	2.28090	+	2.71827i	0.112372	+	0.133919i
$413$	8.96550	−	14.2105i	0.441164	−	0.699253i
$414$	−22.6866	+	24.0205i	−1.11499	+	1.18054i
$415$	7.18103			0.352503
$416$	−3.96568	−	1.44339i	−0.194434	−	0.0707680i
$417$	21.3328	+	6.39287i	1.04467	+	0.313060i
$418$	0.0136111	−	0.0162211i	0.000665742	−	0.000793400i
$419$	11.5894	−	4.21819i	0.566178	−	0.206072i	−0.0430419	−	0.999073i	$-0.513705\pi$
$419$	11.5894	−	4.21819i	0.566178	−	0.206072i	0.609220	+	0.793001i	$0.291483\pi$
$420$	1.93195	−	5.63307i	0.0942693	−	0.274865i
$421$	3.05146	+	17.3057i	0.148719	+	0.843427i	0.964306	+	0.264792i	$0.0853034\pi$
$421$	3.05146	+	17.3057i	0.148719	+	0.843427i	−0.815587	+	0.578635i	$0.803586\pi$
$422$		−	34.8353i		−	1.69576i
$423$	−33.6866	+	16.8954i	−1.63790	+	0.821480i
$424$	2.78965			0.135477
$425$	14.7924	+	5.38401i	0.717538	+	0.261163i
$426$	0.468741	+	8.08545i	0.0227106	+	0.391742i
$427$	20.1896	+	4.38290i	0.977045	+	0.212103i
$428$	5.84400	−	6.96461i	0.282480	−	0.336647i
$429$	−0.0811943	−	0.188369i	−0.00392010	−	0.00909454i
$430$	12.8599	+	15.3259i	0.620161	+	0.739079i
$431$	30.8867	+	17.8324i	1.48776	+	0.858957i	0.999902	−	0.0139669i	$-0.00444595\pi$
$431$	30.8867	+	17.8324i	1.48776	+	0.858957i	0.487856	+	0.872924i	$0.337779\pi$
$432$	24.3449	−	8.83857i	1.17130	−	0.425246i
$433$			7.92231i			0.380722i	0.981714	+	0.190361i	$0.0609659\pi$
$433$			7.92231i			0.380722i	−0.981714	+	0.190361i	$0.939034\pi$
$434$	−32.2748	+	24.9916i	−1.54924	+	1.19963i
$435$	1.64994	−	0.711187i	0.0791084	−	0.0340988i
$436$	0.787999	−	4.46896i	0.0377383	−	0.214025i
$437$	−0.477536	−	0.400700i	−0.0228437	−	0.0191681i
$438$	19.6887	−	12.9419i	0.940763	−	0.618387i
$439$	5.74325	−	15.7794i	0.274110	−	0.753111i	−0.723891	−	0.689914i	$-0.757648\pi$
$439$	5.74325	−	15.7794i	0.274110	−	0.753111i	0.998001	−	0.0631970i	$-0.0201297\pi$
$440$	−0.184279	−	0.319180i	−0.00878514	−	0.0152163i
$441$	9.81369	−	18.5659i	0.467318	−	0.884089i
$442$	4.34616	−	7.52778i	0.206726	−	0.358060i
$443$	−11.1554	−	13.2945i	−0.530011	−	0.631642i	0.432907	−	0.901439i	$-0.357488\pi$
$443$	−11.1554	−	13.2945i	−0.530011	−	0.631642i	−0.962917	+	0.269797i	$0.913044\pi$
$444$	−3.58768	−	3.80477i	−0.170264	−	0.180566i
$445$	4.11859	−	23.3577i	0.195240	−	1.10726i
$446$	−25.5614	−	21.4486i	−1.21037	−	1.01562i
$447$	−33.9424	−	10.1716i	−1.60542	−	0.481101i
$448$	−5.15834	−	2.11013i	−0.243709	−	0.0996945i
$449$	−6.63080	−	3.82829i	−0.312927	−	0.180668i	0.335309	−	0.942108i	$-0.391159\pi$
$449$	−6.63080	−	3.82829i	−0.312927	−	0.180668i	−0.648235	+	0.761440i	$0.724493\pi$
$450$	−1.64287	−	14.1216i	−0.0774456	−	0.665696i
$451$			0.283223i			0.0133365i
$452$	−13.2962	+	2.34448i	−0.625401	+	0.110275i
$453$	1.36608	+	23.5639i	0.0641841	+	1.10713i
$454$	−0.532142	−	0.0938310i	−0.0249747	−	0.00440371i
$455$	2.40420	−	2.64699i	0.112711	−	0.124093i
$456$	0.125506	+	0.291172i	0.00587737	+	0.0136354i
$457$	5.16588	+	29.2972i	0.241650	+	1.37046i	0.828146	+	0.560512i	$0.189396\pi$
$457$	5.16588	+	29.2972i	0.241650	+	1.37046i	−0.586496	+	0.809952i	$0.699493\pi$
$458$	7.34256	−	12.7177i	0.343095	−	0.594258i
$459$	5.05894	+	28.8267i	0.236131	+	1.34552i
$460$	7.30989	−	4.22037i	0.340826	−	0.196776i
$461$	−0.444066	−	0.161627i	−0.0206822	−	0.00752772i	0.331658	−	0.943400i	$-0.392392\pi$
$461$	−0.444066	−	0.161627i	−0.0206822	−	0.00752772i	−0.352341	+	0.935872i	$0.614614\pi$
$462$	0.363485	+	0.943473i	0.0169108	+	0.0438943i
$463$	1.97532	+	1.65749i	0.0918008	+	0.0770300i	0.687533	−	0.726153i	$-0.258694\pi$
$463$	1.97532	+	1.65749i	0.0918008	+	0.0770300i	−0.595732	+	0.803183i	$0.703138\pi$
$464$	1.19084	+	3.27181i	0.0552834	+	0.151890i
$465$	10.5090	−	20.9111i	0.487343	−	0.969728i
$466$	−2.16200	−	12.2613i	−0.100153	−	0.567994i
$467$	−2.65563	+	4.59968i	−0.122888	+	0.212848i	−0.920905	−	0.389786i	$-0.872549\pi$
$467$	−2.65563	+	4.59968i	−0.122888	+	0.212848i	0.798018	+	0.602634i	$0.205882\pi$
$468$	−2.38529	−	0.140216i	−0.110260	−	0.00648148i
$469$	38.0589	+	1.49408i	1.75740	+	0.0689900i
$470$	31.1502	−	5.49262i	1.43685	−	0.253355i
$471$	−6.61032	−	1.98094i	−0.304588	−	0.0912768i
$472$	−11.9292	−	2.10344i	−0.549085	−	0.0968185i
$473$	−1.01816	−	0.179530i	−0.0468152	−	0.00825479i
$474$	−0.865345	+	0.815970i	−0.0397466	+	0.0374788i
$475$	0.264156	−	0.0465778i	0.0121203	−	0.00213714i
$476$	−6.95849	+	11.0294i	−0.318942	+	0.505530i
$477$	4.20400	−	1.25613i	0.192488	−	0.0575142i
$478$	−3.98925	+	6.90958i	−0.182464	+	0.316037i
$479$	5.71953	+	32.4371i	0.261332	+	1.48209i	0.779280	+	0.626675i	$0.215585\pi$
$479$	5.71953	+	32.4371i	0.261332	+	1.48209i	−0.517948	+	0.855412i	$0.673304\pi$
$480$	−11.9063	+	0.690249i	−0.543447	+	0.0315054i
$481$	−1.07399	−	2.95075i	−0.0489696	−	0.134543i
$482$	−8.61371	−	7.22776i	−0.392344	−	0.329215i
$483$	27.7751	−	10.7007i	1.26381	−	0.486899i
$484$	9.03172	+	3.28728i	0.410533	+	0.149422i
$485$	−13.4357	+	7.75713i	−0.610086	+	0.352233i
$486$	21.2229	−	15.7556i	0.962692	−	0.714687i
$487$	−12.1204	+	20.9931i	−0.549226	+	0.951288i	0.449101	+	0.893481i	$0.351744\pi$
$487$	−12.1204	+	20.9931i	−0.549226	+	0.951288i	−0.998328	+	0.0578073i	$0.981589\pi$
$488$	−2.58635	−	14.6679i	−0.117079	−	0.663986i
$489$	25.4578	−	34.1765i	1.15124	−	1.54552i
$490$	−12.3532	+	12.5724i	−0.558061	+	0.567962i
$491$	−11.3569	−	2.00253i	−0.512529	−	0.0903727i	−0.0885987	−	0.996067i	$-0.528239\pi$
$491$	−11.3569	−	2.00253i	−0.512529	−	0.0903727i	−0.423931	+	0.905695i	$0.639350\pi$
$492$	2.94785	+	1.48146i	0.132900	+	0.0667895i
$493$	−3.87473	+	0.683219i	−0.174509	+	0.0307706i
$494$		−	0.148112i		−	0.00666388i
$495$	−0.421429	−	0.398027i	−0.0189418	−	0.0178900i
$496$	39.2769	+	22.6765i	1.76358	+	1.01821i
$497$	2.76246	−	6.75298i	0.123913	−	0.302913i
$498$	3.27151	+	13.8201i	0.146600	+	0.619295i
$499$	3.90881	+	3.27988i	0.174983	+	0.146828i	0.726073	−	0.687618i	$-0.241344\pi$
$499$	3.90881	+	3.27988i	0.174983	+	0.146828i	−0.551090	+	0.834446i	$0.685788\pi$
$500$	−1.75897	+	9.97564i	−0.0786637	+	0.446124i
$501$	30.9474	−	7.32587i	1.38263	−	0.327296i
$502$	16.0197	+	19.0916i	0.714996	+	0.852099i
$503$	−12.9688	+	22.4626i	−0.578251	+	1.00156i	0.417429	+	0.908709i	$0.362931\pi$
$503$	−12.9688	+	22.4626i	−0.578251	+	1.00156i	−0.995680	+	0.0928501i	$0.970402\pi$
$504$	−15.0668	−	1.48057i	−0.671130	−	0.0659500i
$505$	3.16873	+	5.48841i	0.141007	+	0.244231i
$506$	−0.490140	+	1.34665i	−0.0217894	+	0.0598659i
$507$	18.8369	+	9.46661i	0.836577	+	0.420427i
$508$	−0.757591	−	0.635695i	−0.0336127	−	0.0282044i
$509$	−4.78794	+	27.1537i	−0.212222	+	1.20357i	0.673442	+	0.739240i	$0.264815\pi$
$509$	−4.78794	+	27.1537i	−0.212222	+	1.20357i	−0.885663	+	0.464328i	$0.846296\pi$
$510$	2.85835	−	24.3978i	0.126570	−	1.08035i
$511$	−21.0317	+	2.86300i	−0.930388	+	0.126652i
$512$		−	4.09759i		−	0.181090i
$513$	0.320248	+	0.382283i	0.0141393	+	0.0168782i
$514$	20.7372	+	11.9726i	0.914680	+	0.528091i
$515$	3.87050	+	4.61268i	0.170555	+	0.203259i
$516$	−7.19433	+	9.65823i	−0.316713	+	0.425180i
$517$	−1.05068	+	1.25216i	−0.0462090	+	0.0550697i
$518$	4.71917	+	14.7410i	0.207349	+	0.647683i
$519$	−5.01772	−	2.52168i	−0.220253	−	0.110690i
$520$	−2.42245	−	0.881700i	−0.106232	−	0.0386651i
$521$	−12.5739			−0.550874			−0.275437	−	0.961319i	$-0.588823\pi$
$521$	−12.5739			−0.550874			−0.275437	+	0.961319i	$0.588823\pi$
$522$	2.12038	+	2.85136i	0.0928063	+	0.124801i
$523$		−	3.41897i		−	0.149501i	−0.997202	−	0.0747507i	$-0.976184\pi$
$523$		−	3.41897i		−	0.149501i	0.997202	−	0.0747507i	$-0.0238161\pi$
$524$	−0.994539	−	5.64031i	−0.0434467	−	0.246398i
$525$	−4.15494	+	12.1148i	−0.181337	+	0.528732i
$526$	−24.9192	+	9.06984i	−1.08653	+	0.395464i
$527$	−32.9428	+	39.2598i	−1.43501	+	1.71018i
$528$	0.817308	−	0.770675i	0.0355688	−	0.0335393i
$529$	18.0313	+	6.56287i	0.783971	+	0.285342i
$530$	−3.68265			−0.159964
$531$	−18.9244	+	2.20162i	−0.821250	+	0.0955423i
$532$	−0.00871659	+	0.222040i	−0.000377912	+	0.00962664i
$533$	1.27339	+	1.51756i	0.0551565	+	0.0657330i
$534$	46.8290	−	2.71483i	2.02649	−	0.117482i
$535$	9.91680	−	11.8184i	0.428741	−	0.510953i
$536$	−9.39144	−	25.8028i	−0.405648	−	1.11451i
$537$	−27.3295	−	20.3575i	−1.17935	−	0.878490i
$538$	2.50019	−	6.86922i	0.107791	−	0.296153i
$539$	0.0714035	−	0.908038i	0.00307557	−	0.0391120i
$540$	−6.34714	+	2.30437i	−0.273138	+	0.0991643i
$541$	−1.35102	−	2.34004i	−0.0580850	−	0.100606i	0.835521	−	0.549459i	$-0.185166\pi$
$541$	−1.35102	−	2.34004i	−0.0580850	−	0.100606i	−0.893606	+	0.448853i	$0.851833\pi$
$542$	24.2778	−	20.3715i	1.04282	−	0.875029i
$543$	−24.0339	−	17.9026i	−1.03139	−	0.768275i
$544$	25.7202	+	4.53517i	1.10275	+	0.194444i
$545$	1.33717	−	7.58347i	0.0572781	−	0.324840i
$546$	6.18953	+	3.42106i	0.264887	+	0.146408i
$547$	23.8134	−	19.9818i	1.01819	−	0.854362i	0.0287897	−	0.999585i	$-0.490835\pi$
$547$	23.8134	−	19.9818i	1.01819	−	0.854362i	0.989399	+	0.145224i	$0.0463903\pi$
$548$	−3.52401	−	2.03459i	−0.150538	−	0.0869134i
$549$	−10.5023	−	20.9400i	−0.448229	−	0.893697i
$550$	−0.308315	−	0.534018i	−0.0131466	−	0.0227706i
$551$	−0.0513568	+	0.0430935i	−0.00218787	+	0.00183584i
$552$	−14.7214	−	15.6122i	−0.626585	−	0.664499i
$553$	1.02046	−	0.326689i	0.0433943	−	0.0138922i
$554$	5.45060	+	14.9754i	0.231574	+	0.636244i
$555$	−6.08800	−	6.45638i	−0.258421	−	0.274058i
$556$	3.84834	−	10.5732i	0.163206	−	0.448405i
$557$	27.0000	−	15.5885i	1.14403	−	0.660504i	0.196602	−	0.980483i	$-0.437009\pi$
$557$	27.0000	−	15.5885i	1.14403	−	0.660504i	0.947425	+	0.319979i	$0.103676\pi$
$558$	45.0318	+	10.6983i	1.90635	+	0.452896i
$559$	−6.26269	+	3.61577i	−0.264884	+	0.152931i
$560$	18.1253	+	7.41456i	0.765934	+	0.313322i
$561$	0.697272	+	1.06077i	0.0294389	+	0.0447859i
$562$	43.7557	−	15.9258i	1.84572	−	0.671789i
$563$	25.5339	−	9.29359i	1.07613	−	0.391678i	0.257662	−	0.966235i	$-0.417048\pi$
$563$	25.5339	−	9.29359i	1.07613	−	0.391678i	0.818465	+	0.574557i	$0.194826\pi$
$564$	7.53691	+	17.4854i	0.317361	+	0.736270i
$565$	−22.5626	+	3.97839i	−0.949215	+	0.167372i
$566$	−36.7745			−1.54575
$567$	−23.3724	+	4.55311i	−0.981549	+	0.191213i
$568$	−5.25997			−0.220704
$569$	15.9607	−	2.81430i	0.669107	−	0.117982i	0.171233	−	0.985231i	$-0.445225\pi$
$569$	15.9607	−	2.81430i	0.669107	−	0.117982i	0.497875	+	0.867249i	$0.334114\pi$
$570$	−0.165682	−	0.384380i	−0.00693967	−	0.0160999i
$571$	−34.7802	+	12.6590i	−1.45551	+	0.529761i	−0.944123	−	0.329592i	$-0.893089\pi$
$571$	−34.7802	+	12.6590i	−1.45551	+	0.529761i	−0.511383	+	0.859353i	$0.670867\pi$
$572$	−0.0973868	+	0.0354459i	−0.00407195	+	0.00148207i
$573$	−5.03499	−	7.65982i	−0.210340	−	0.319994i
$574$	−5.97839	−	7.72067i	−0.249533	−	0.322255i
$575$	−15.7210	+	9.07655i	−0.655613	+	0.378518i
$576$	1.80919	+	6.05497i	0.0753828	+	0.252290i
$577$	−37.5446	+	21.6764i	−1.56300	+	0.902400i	−0.566052	+	0.824370i	$0.691530\pi$
$577$	−37.5446	+	21.6764i	−1.56300	+	0.902400i	−0.996951	+	0.0780301i	$0.975137\pi$
$578$	−8.53949	+	23.4621i	−0.355196	+	0.975893i
$579$	−20.9947	−	22.2651i	−0.872511	−	0.925306i
$580$	−0.310473	−	0.853018i	−0.0128917	−	0.0354196i
$581$	2.71423	−	12.5030i	0.112605	−	0.518711i
$582$	−21.0499	−	22.3236i	−0.872546	−	0.925343i
$583$	0.145784	−	0.122327i	0.00603775	−	0.00506627i
$584$	7.65105	+	13.2520i	0.316603	+	0.548372i
$585$	−4.04765	−	0.237935i	−0.167350	−	0.00983740i
$586$	−13.8589	−	8.00144i	−0.572506	−	0.330536i
$587$	−26.0768	+	21.8811i	−1.07631	+	0.903128i	−0.995609	−	0.0936106i	$-0.970159\pi$
$587$	−26.0768	+	21.8811i	−1.07631	+	0.903128i	−0.0806972	+	0.996739i	$0.525715\pi$
$588$	−9.07759	−	5.49288i	−0.374353	−	0.226523i
$589$	−0.151642	+	0.860003i	−0.00624829	+	0.0354358i
$590$	15.7479	+	2.77677i	0.648329	+	0.114318i
$591$	28.7372	+	21.4060i	1.18209	+	0.880527i
$592$	13.1736	−	11.0540i	0.541433	−	0.454316i
$593$	−1.09399	−	1.89484i	−0.0449246	−	0.0778118i	0.842689	−	0.538401i	$-0.180971\pi$
$593$	−1.09399	−	1.89484i	−0.0449246	−	0.0778118i	−0.887613	+	0.460589i	$0.847638\pi$
$594$	0.574024	−	0.992388i	0.0235525	−	0.0407182i
$595$	−11.8080	+	18.7159i	−0.484081	+	0.767278i
$596$	−6.12306	+	16.8230i	−0.250810	+	0.689095i
$597$	−17.7457	−	13.2186i	−0.726284	−	0.541002i
$598$	3.42835	+	9.41930i	0.140196	+	0.385184i
$599$	1.54058	−	1.83600i	0.0629466	−	0.0750168i	−0.733652	−	0.679525i	$-0.762186\pi$
$599$	1.54058	−	1.83600i	0.0629466	−	0.0750168i	0.796599	+	0.604508i	$0.206630\pi$
$600$	9.21773	−	0.534382i	0.376312	−	0.0218161i
$601$	9.51673	+	11.3416i	0.388196	+	0.462634i	0.924383	−	0.381465i	$-0.124580\pi$
$601$	9.51673	+	11.3416i	0.388196	+	0.462634i	−0.536187	+	0.844099i	$0.680136\pi$
$602$	31.5448	−	16.5978i	1.28567	−	0.676478i
$603$	−25.7715	−	34.6560i	−1.04949	−	1.41130i
$604$	11.9255			0.485242
$605$	15.3261	+	5.57825i	0.623095	+	0.226788i
$606$	−9.11903	+	8.59873i	−0.370435	+	0.349299i
$607$	0.668099	−	0.796209i	0.0271173	−	0.0323171i	−0.752315	−	0.658803i	$-0.771063\pi$
$607$	0.668099	−	0.796209i	0.0271173	−	0.0323171i	0.779433	+	0.626486i	$0.215507\pi$
$608$	0.418181	−	0.152205i	0.0169595	−	0.00617274i
$609$	−0.614626	−	3.14154i	−0.0249059	−	0.127302i
$610$	3.41427	+	19.3633i	0.138240	+	0.783997i
$611$			11.4332i			0.462539i
$612$	14.6880	−	1.70877i	0.593728	−	0.0690729i
$613$	24.0367			0.970835			0.485417	−	0.874282i	$-0.338668\pi$
$613$	24.0367			0.970835			0.485417	+	0.874282i	$0.338668\pi$
$614$	8.95373	+	3.25889i	0.361343	+	0.131518i
$615$	5.00227	+	2.51392i	0.201711	+	0.101371i
$616$	−0.625381	+	0.200209i	−0.0251973	+	0.00806665i
$617$	−10.4252	+	12.4243i	−0.419702	+	0.500182i	−0.933922	−	0.357477i	$-0.883637\pi$
$617$	−10.4252	+	12.4243i	−0.419702	+	0.500182i	0.514220	+	0.857659i	$0.328082\pi$
$618$	−7.11396	+	9.55034i	−0.286165	+	0.384171i
$619$	1.86551	+	2.22322i	0.0749810	+	0.0893589i	0.802231	−	0.597014i	$-0.203646\pi$
$619$	1.86551	+	2.22322i	0.0749810	+	0.0893589i	−0.727250	+	0.686373i	$0.759202\pi$
$620$	−10.2402	−	5.91216i	−0.411255	−	0.237438i
$621$	−29.2151	−	16.8988i	−1.17236	−	0.678125i
$622$		−	29.5968i		−	1.18672i
$623$	−39.1117	−	15.9995i	−1.56698	−	0.641006i
$624$	0.914296	−	7.80409i	0.0366011	−	0.312414i
$625$	−0.558262	+	3.16606i	−0.0223305	+	0.126642i
$626$	−0.648663	−	0.544293i	−0.0259258	−	0.0217543i
$627$	0.0193268	+	0.00971281i	0.000771839	+	0.000387892i
$628$	−1.19247	+	3.27630i	−0.0475849	+	0.130738i
$629$	9.71647	+	16.8294i	0.387421	+	0.671033i
$630$	19.8899	+	1.95452i	0.792433	+	0.0778701i
$631$	−23.7928	+	41.2104i	−0.947177	+	1.64056i	−0.195844	+	0.980635i	$0.562745\pi$
$631$	−23.7928	+	41.2104i	−0.947177	+	1.64056i	−0.751333	+	0.659923i	$0.770589\pi$
$632$	−0.496523	−	0.591733i	−0.0197506	−	0.0235379i
$633$	34.6269	−	8.19689i	1.37630	−	0.325797i
$634$	−2.29992	+	13.0435i	−0.0913416	+	0.518024i
$635$	−1.28557	−	1.07872i	−0.0510163	−	0.0428078i
$636$	−0.510656	−	2.15721i	−0.0202488	−	0.0855391i
$637$	−3.70000	−	5.18648i	−0.146599	−	0.205496i
$638$	0.133472	+	0.0770603i	0.00528422	+	0.00305085i
$639$	−7.92679	+	2.36848i	−0.313579	+	0.0936955i
$640$		−	19.0754i		−	0.754021i
$641$	38.3227	−	6.75732i	1.51365	−	0.266898i	0.645719	−	0.763575i	$-0.276558\pi$
$641$	38.3227	−	6.75732i	1.51365	−	0.266898i	0.867935	+	0.496677i	$0.165447\pi$
$642$	27.2628	+	13.7011i	1.07597	+	0.540738i
$643$	11.9667	+	2.11005i	0.471919	+	0.0832121i	0.404550	−	0.914516i	$-0.367428\pi$
$643$	11.9667	+	2.11005i	0.471919	+	0.0832121i	0.0673696	+	0.997728i	$0.478539\pi$
$644$	−4.58521	−	14.3225i	−0.180682	−	0.564387i
$645$	−12.2082	+	16.3892i	−0.480697	+	0.645326i
$646$	0.159167	+	0.902680i	0.00626234	+	0.0355155i
$647$	−1.58605	+	2.74713i	−0.0623542	+	0.108001i	−0.895517	−	0.445027i	$-0.853194\pi$
$647$	−1.58605	+	2.74713i	−0.0623542	+	0.108001i	0.833163	+	0.553027i	$0.186528\pi$
$648$	9.41768	+	14.3525i	0.369961	+	0.563820i
$649$	−0.715642	+	0.413176i	−0.0280914	+	0.0162186i
$650$	−4.05299	−	1.47517i	−0.158971	−	0.0578608i
$651$	−32.4365	−	26.2012i	−1.27129	−	1.02690i
$652$	−16.4941	−	13.8402i	−0.645958	−	0.542023i
$653$	−0.519398	−	1.42703i	−0.0203256	−	0.0558441i	0.929115	−	0.369791i	$-0.120571\pi$
$653$	−0.519398	−	1.42703i	−0.0203256	−	0.0558441i	−0.949440	+	0.313947i	$0.898349\pi$
$654$	15.2038	−	0.881417i	0.594517	−	0.0344661i
$655$	−1.68765	−	9.57116i	−0.0659421	−	0.373976i
$656$	−5.42459	+	9.39567i	−0.211795	+	0.366839i
$657$	17.4973	+	16.5257i	0.682635	+	0.644727i
$658$	2.21064	−	56.3121i	0.0861796	−	2.19527i
$659$	−37.4050	+	6.59551i	−1.45709	+	0.256925i	−0.845384	−	0.534159i	$-0.820628\pi$
$659$	−37.4050	+	6.59551i	−1.45709	+	0.256925i	−0.611708	+	0.791083i	$0.709517\pi$
$660$	−0.213087	+	0.200928i	−0.00829439	+	0.00782113i
$661$	25.5835	+	4.51107i	0.995085	+	0.175460i	0.647399	−	0.762151i	$-0.275857\pi$
$661$	25.5835	+	4.51107i	0.995085	+	0.175460i	0.347685	+	0.937611i	$0.386968\pi$
$662$	52.7863	+	9.30765i	2.05160	+	0.361752i
$663$	8.50541	+	2.54885i	0.330323	+	0.0989891i
$664$	−9.08352	+	1.60167i	−0.352509	+	0.0621568i
$665$	−0.0147914	+	0.376784i	−0.000573584	+	0.0146110i
$666$	9.65198	−	14.6579i	0.374007	−	0.567984i
$667$	2.26859	−	3.92932i	0.0878402	−	0.152144i
$668$	−2.79019	−	15.8240i	−0.107956	−	0.612248i
$669$	15.3056	−	30.4554i	0.591747	−	1.17748i
$670$	12.3978	+	34.0626i	0.478967	+	1.31595i
$671$	−0.778354	−	0.653117i	−0.0300480	−	0.0252133i
$672$	−3.29846	+	20.9912i	−0.127241	+	0.809751i
$673$	−27.9585	−	10.1760i	−1.07772	−	0.392258i	−0.258661	−	0.965968i	$-0.583281\pi$
$673$	−27.9585	−	10.1760i	−1.07772	−	0.392258i	−0.819058	+	0.573710i	$0.805503\pi$
$674$	−10.2982	+	5.94568i	−0.396672	+	0.229019i
$675$	13.6505	−	4.95590i	0.525408	−	0.190753i
$676$	5.32574	−	9.22446i	0.204836	−	0.354787i
$677$	3.13508	+	17.7799i	0.120491	+	0.683339i	0.983884	+	0.178807i	$0.0572237\pi$
$677$	3.13508	+	17.7799i	0.120491	+	0.683339i	−0.863393	+	0.504532i	$0.831665\pi$
$678$	−17.9355	−	41.6100i	−0.688810	−	1.59802i
$679$	8.42771	+	26.3252i	0.323426	+	1.01027i
$680$	15.7113	+	2.77033i	0.602501	+	0.106237i
$681$	−0.0319455	−	0.551038i	−0.00122415	−	0.0211158i
$682$	1.97704	−	0.348606i	0.0757049	−	0.0133488i
$683$		−	6.39465i		−	0.244684i	−0.992488	−	0.122342i	$-0.960959\pi$
$683$		−	6.39465i		−	0.244684i	0.992488	−	0.122342i	$-0.0390406\pi$
$684$	0.202187	−	0.150353i	0.00773080	−	0.00574890i
$685$	−5.97996	−	3.45253i	−0.228483	−	0.131915i
$686$	17.2208	+	26.2604i	0.657492	+	1.00263i
$687$	14.3693	+	4.30611i	0.548224	+	0.164288i
$688$	−30.3381	−	25.4567i	−1.15663	−	0.970528i
$689$	0.231148	−	1.31090i	0.00880603	−	0.0499415i
$690$	19.4339	+	20.6099i	0.739836	+	0.784604i
$691$	−15.3397	−	18.2811i	−0.583548	−	0.695446i	0.390804	−	0.920474i	$-0.372197\pi$
$691$	−15.3397	−	18.2811i	−0.583548	−	0.695446i	−0.974352	+	0.225028i	$0.927753\pi$
$692$	−1.41865	+	2.45718i	−0.0539291	+	0.0934080i
$693$	−0.852299	+	0.583313i	−0.0323762	+	0.0221582i
$694$	9.01139	+	15.6082i	0.342068	+	0.592478i
$695$	6.53032	−	17.9419i	0.247709	−	0.680576i
$696$	−1.92844	+	1.26761i	−0.0730971	+	0.0480486i
$697$	−9.39157	−	7.88047i	−0.355731	−	0.298494i
$698$	2.17289	−	12.3231i	0.0822450	−	0.466434i
$699$	11.6792	−	5.03420i	0.441749	−	0.190411i
$700$	5.98915	+	2.44999i	0.226368	+	0.0926010i
$701$			7.66638i			0.289555i	0.989464	+	0.144778i	$0.0462467\pi$
$701$			7.66638i			0.289555i	−0.989464	+	0.144778i	$0.953753\pi$
$702$	−1.38610	−	7.89825i	−0.0523150	−	0.298100i
$703$	0.286764	+	0.165563i	0.0108155	+	0.00624433i
$704$	0.176186	+	0.209971i	0.00664027	+	0.00791356i
$705$	12.7895	+	29.6714i	0.481681	+	1.11749i
$706$	−18.1511	+	21.6316i	−0.683124	+	0.814116i
$707$	10.7536	−	3.44266i	0.404432	−	0.129475i
$708$	0.557112	+	9.60979i	0.0209375	+	0.361158i
$709$	15.4611	+	5.62740i	0.580656	+	0.211341i	0.615615	−	0.788047i	$-0.288908\pi$
$709$	15.4611	+	5.62740i	0.580656	+	0.211341i	−0.0349590	+	0.999389i	$0.511130\pi$
$710$	6.94376			0.260595
$711$	−1.01471	−	0.668167i	−0.0380545	−	0.0250582i
$712$			30.4645i			1.14171i
$713$	−10.2627	−	58.2025i	−0.384340	−	2.17970i
$714$	−41.3989	−	14.1984i	−1.54932	−	0.531361i
$715$	−0.165258	+	0.0601488i	−0.00618028	+	0.00224944i
$716$	−11.0674	+	13.1896i	−0.413608	+	0.492918i
$717$	−7.80693	−	2.33953i	−0.291555	−	0.0873714i
$718$	−27.6285	−	10.0559i	−1.03109	−	0.375284i
$719$	46.7348			1.74291			0.871457	−	0.490472i	$-0.163176\pi$
$719$	46.7348			1.74291			0.871457	+	0.490472i	$0.163176\pi$
$720$	−6.35710	−	21.2759i	−0.236915	−	0.792905i
$721$	9.49414	−	4.99551i	0.353580	−	0.186043i
$722$	−20.6984	−	24.6674i	−0.770316	−	0.918027i
$723$	5.15768	−	10.2629i	0.191816	−	0.381681i
$724$	−9.73280	+	11.5991i	−0.361717	+	0.431077i
$725$	0.667720	+	1.83455i	0.0247985	+	0.0681333i
$726$	−3.75332	+	32.0369i	−0.139299	+	1.18900i
$727$	2.15305	−	5.91545i	0.0798522	−	0.219392i	−0.893342	−	0.449378i	$-0.851646\pi$
$727$	2.15305	−	5.91545i	0.0798522	−	0.219392i	0.973194	+	0.229986i	$0.0738679\pi$
$728$	−2.45076	+	3.88451i	−0.0908312	+	0.143969i
$729$	20.6551	+	17.3886i	0.765006	+	0.644024i
$730$	−10.1002	−	17.4941i	−0.373827	−	0.647487i
$731$	34.2828	−	28.7667i	1.26799	−	1.06397i
$732$	−10.8692	+	4.68503i	−0.401736	+	0.173164i
$733$	13.4040	+	2.36349i	0.495090	+	0.0872977i	0.415618	−	0.909539i	$-0.363565\pi$
$733$	13.4040	+	2.36349i	0.495090	+	0.0872977i	0.0794720	+	0.996837i	$0.474677\pi$
$734$	−7.86881	+	44.6262i	−0.290443	+	1.64718i
$735$	−15.4039	−	9.32098i	−0.568183	−	0.343809i
$736$	−23.0714	+	19.3592i	−0.850424	+	0.713590i
$737$	−1.62225	−	0.936605i	−0.0597563	−	0.0345003i
$738$	−2.55921	+	10.7723i	−0.0942060	+	0.396535i
$739$	−12.6640	−	21.9347i	−0.465852	−	0.806880i	0.533387	−	0.845871i	$-0.320919\pi$
$739$	−12.6640	−	21.9347i	−0.465852	−	0.806880i	−0.999240	+	0.0389914i	$0.987586\pi$
$740$	−3.43460	+	2.88197i	−0.126258	+	0.105943i
$741$	0.147226	−	0.0348514i	0.00540849	−	0.00128030i
$742$	−1.39194	+	6.41191i	−0.0510997	+	0.235389i
$743$	7.84457	+	21.5528i	0.287789	+	0.790695i	0.996375	+	0.0850699i	$0.0271114\pi$
$743$	7.84457	+	21.5528i	0.287789	+	0.790695i	−0.708586	+	0.705625i	$0.750666\pi$
$744$	−8.62912	+	28.7951i	−0.316359	+	1.05568i
$745$	−10.3903	+	28.5472i	−0.380672	+	1.04589i
$746$	27.1851	−	15.6954i	0.995319	−	0.574648i
$747$	−12.9677	+	6.50387i	−0.474462	+	0.237964i
$748$	0.555439	−	0.320683i	0.0203089	−	0.0117253i
$749$	−16.8289	−	21.7333i	−0.614914	−	0.794117i
$750$	−33.9381	+	1.96750i	−1.23924	+	0.0718431i
$751$	−0.189300	+	0.0688994i	−0.00690764	+	0.00251417i	−0.345472	−	0.938429i	$-0.612281\pi$
$751$	−0.189300	+	0.0688994i	−0.00690764	+	0.00251417i	0.338564	+	0.940943i	$0.390059\pi$
$752$	−58.8381	+	21.4153i	−2.14560	+	0.780936i
$753$	−15.2079	+	20.4162i	−0.554206	+	0.744009i
$754$	1.06164	−	0.187195i	0.0386626	−	0.00681725i
$755$	20.2366			0.736486
$756$	1.61313	+	11.9221i	0.0586688	+	0.433602i
$757$	−32.2011			−1.17037			−0.585184	−	0.810901i	$-0.698978\pi$
$757$	−32.2011			−1.17037			−0.585184	+	0.810901i	$0.698978\pi$
$758$	58.8305	−	10.3734i	2.13682	−	0.376779i
$759$	−1.45393	−	0.170336i	−0.0527742	−	0.00618281i
$760$	0.255447	−	0.0929752i	0.00926605	−	0.00337257i
$761$	−49.9235	+	18.1707i	−1.80973	+	0.658686i	−0.812608	+	0.582811i	$0.801953\pi$
$761$	−49.9235	+	18.1707i	−1.80973	+	0.658686i	−0.997117	+	0.0758754i	$0.975825\pi$
$762$	1.49036	−	2.96557i	0.0539902	−	0.107431i
$763$	−12.6983	−	5.19451i	−0.459708	−	0.188054i
$764$	−4.01082	+	2.31565i	−0.145106	+	0.0837772i
$765$	24.9244	−	2.89965i	0.901143	−	0.104837i
$766$	−24.5355	+	14.1656i	−0.886505	+	0.511824i
$767$	−1.97688	+	5.43145i	−0.0713812	+	0.196118i
$768$	29.6104	−	7.00938i	1.06847	−	0.252929i
$769$	−2.05952	−	5.65850i	−0.0742683	−	0.204051i	0.897003	−	0.442024i	$-0.145739\pi$
$769$	−2.05952	−	5.65850i	−0.0742683	−	0.204051i	−0.971272	+	0.237973i	$0.923517\pi$
$770$	0.825573	−	0.264298i	0.0297516	−	0.00952465i
$771$	−7.02147	+	23.4304i	−0.252872	+	0.843825i
$772$	−11.8444	+	9.93859i	−0.426288	+	0.357698i
$773$	−15.0058	−	25.9909i	−0.539722	−	0.934827i	−0.998919	−	0.0464918i	$-0.985196\pi$
$773$	−15.0058	−	25.9909i	−0.539722	−	0.934827i	0.459196	−	0.888335i	$-0.348137\pi$
$774$	−37.1034	−	16.0285i	−1.33366	−	0.576134i
$775$	22.0230	+	12.7150i	0.791091	+	0.456737i
$776$	15.2652	−	12.8090i	0.547987	−	0.459816i
$777$	−13.5424	+	8.15956i	−0.485830	+	0.292723i
$778$	2.79411	−	15.8462i	0.100174	−	0.568113i
$779$	−0.205727	−	0.0362752i	−0.00737092	−	0.00129969i
$780$	−0.238373	+	2.03466i	−0.00853513	+	0.0728526i
$781$	−0.274880	+	0.230652i	−0.00983600	+	0.00825338i
$782$	−31.0166	−	53.7224i	−1.10915	−	1.92111i
$783$	−2.33537	+	2.77863i	−0.0834594	+	0.0993001i
$784$	19.7605	−	28.7557i	0.705731	−	1.02699i
$785$	−2.02353	+	5.55961i	−0.0722230	+	0.198431i
$786$	17.6512	−	7.60834i	0.629597	−	0.271381i
$787$	7.41173	+	20.3636i	0.264200	+	0.725883i	0.998873	+	0.0474619i	$0.0151133\pi$
$787$	7.41173	+	20.3636i	0.264200	+	0.725883i	−0.734673	+	0.678421i	$0.762665\pi$
$788$	11.6374	−	13.8690i	0.414567	−	0.494061i
$789$	−14.8792	−	22.6360i	−0.529713	−	0.805861i
$790$	0.655466	+	0.781154i	0.0233204	+	0.0277922i
$791$	−1.60120	+	40.7877i	−0.0569321	+	1.45024i
$792$	0.621857	+	0.409481i	0.0220967	+	0.0145503i
$793$	−7.10702			−0.252378
$794$	−60.6320	−	22.0682i	−2.15175	−	0.783173i
$795$	−0.866542	−	3.66062i	−0.0307331	−	0.129829i
$796$	−7.18634	+	8.56434i	−0.254713	+	0.303555i
$797$	−24.4999	+	8.91724i	−0.867832	+	0.315865i	−0.737289	−	0.675578i	$-0.763894\pi$
$797$	−24.4999	+	8.91724i	−0.867832	+	0.315865i	−0.130543	+	0.991443i	$0.541672\pi$
$798$	−0.731872	+	0.143187i	−0.0259080	+	0.00506877i
$799$	−12.2866	−	69.6805i	−0.434667	−	2.46512i
$800$		−	12.9592i		−	0.458175i
$801$	13.7176	+	45.9101i	0.484689	+	1.62215i
$802$	9.53732			0.336774
$803$	0.980941	+	0.357033i	0.0346167	+	0.0125994i
$804$	−18.2340	+	11.9856i	−0.643062	+	0.422701i
$805$	−7.78072	−	24.3042i	−0.274234	−	0.856610i
$806$	9.02603	−	10.7568i	0.317928	−	0.378892i
$807$	7.41644	+	0.868880i	0.261071	+	0.0305860i
$808$	−5.23238	−	6.23571i	−0.184074	−	0.219371i
$809$	−27.9055	−	16.1113i	−0.981106	−	0.566442i	−0.0785018	−	0.996914i	$-0.525014\pi$
$809$	−27.9055	−	16.1113i	−0.981106	−	0.566442i	−0.902604	+	0.430472i	$0.858347\pi$
$810$	−12.4324	−	18.9469i	−0.436830	−	0.665727i
$811$		−	40.6903i		−	1.42883i	−0.699722	−	0.714415i	$-0.746693\pi$
$811$		−	40.6903i		−	1.42883i	0.699722	−	0.714415i	$-0.253307\pi$
$812$	−1.60255	+	0.218152i	−0.0562386	+	0.00765563i
$813$	25.9623	+	19.3390i	0.910536	+	0.678250i
$814$	0.132184	−	0.749655i	0.00463306	−	0.0262754i
$815$	−27.9891	−	23.4857i	−0.980417	−	0.822667i
$816$	2.81432	+	48.5451i	0.0985210	+	1.69942i
$817$	0.260813	−	0.716577i	0.00912468	−	0.0250698i
$818$	−1.87000	−	3.23893i	−0.0653829	−	0.113247i
$819$	−1.94417	+	6.95749i	−0.0679349	+	0.243114i
$820$	1.41429	−	2.44962i	0.0493890	−	0.0855443i
$821$	10.0437	+	11.9696i	0.350526	+	0.417741i	0.912282	−	0.409562i	$-0.134318\pi$
$821$	10.0437	+	11.9696i	0.350526	+	0.417741i	−0.561756	+	0.827303i	$0.689874\pi$
$822$	3.92019	−	13.0815i	0.136732	−	0.456271i
$823$	−3.98182	+	22.5820i	−0.138797	+	0.787160i	0.833342	+	0.552757i	$0.186424\pi$
$823$	−3.98182	+	22.5820i	−0.138797	+	0.787160i	−0.972140	+	0.234402i	$0.924687\pi$
$824$	−5.92474	−	4.97145i	−0.206398	−	0.173189i
$825$	0.458275	−	0.432127i	0.0159551	−	0.0150447i
$826$	10.7869	−	26.3693i	0.375325	−	0.917504i
$827$	−10.7093	−	6.18300i	−0.372398	−	0.215004i	0.302108	−	0.953274i	$-0.402310\pi$
$827$	−10.7093	−	6.18300i	−0.372398	−	0.215004i	−0.674506	+	0.738270i	$0.735643\pi$
$828$	−9.37798	+	14.2418i	−0.325907	+	0.494938i
$829$		−	51.7704i		−	1.79806i	−0.437886	−	0.899030i	$-0.644273\pi$
$829$		−	51.7704i		−	1.79806i	0.437886	−	0.899030i	$-0.355727\pi$
$830$	11.9913	−	2.11438i	0.416223	−	0.0733913i
$831$	−13.6033	+	8.94176i	−0.471892	+	0.310186i
$832$	1.88808	+	0.332919i	0.0654574	+	0.0115419i
$833$	28.1235	+	27.6332i	0.974420	+	0.957433i
$834$	37.5049	+	4.39393i	1.29869	+	0.152149i
$835$	−4.73473	−	26.8520i	−0.163852	−	0.929252i
$836$	0.00546425	−	0.00946436i	0.000188985	−	0.000327332i
$837$	−0.0381725	+	47.2797i	−0.00131943	+	1.63423i
$838$	18.1106	−	10.4561i	0.625619	−	0.361201i
$839$	21.8923	+	7.96815i	0.755806	+	0.275091i	0.691047	−	0.722810i	$-0.257150\pi$
$839$	21.8923	+	7.96815i	0.755806	+	0.275091i	0.0647595	+	0.997901i	$0.479372\pi$
$840$	−2.01488	+	12.8225i	−0.0695198	+	0.442419i
$841$	21.8415	+	18.3272i	0.753155	+	0.631972i
$842$	10.1910	+	27.9995i	0.351204	+	0.964926i
$843$	26.1264	+	39.7466i	0.899842	+	1.36895i
$844$	−3.12193	−	17.7054i	−0.107461	−	0.609444i
$845$	9.03736	−	15.6532i	0.310895	−	0.538485i
$846$	−51.2771	+	38.1315i	−1.76294	+	1.31099i
$847$	15.5052	−	24.5761i	0.532765	−	0.844444i
$848$	7.17919	−	1.26588i	0.246534	−	0.0434706i
$849$	−8.65319	−	36.5545i	−0.296977	−	1.25455i
$850$	26.2865	+	4.63501i	0.901619	+	0.158980i
$851$	−22.0692	−	3.89140i	−0.756523	−	0.133395i
$852$	0.962859	+	4.06750i	0.0329870	+	0.139350i
$853$	33.4290	−	5.89444i	1.14459	−	0.201822i	0.430976	−	0.902363i	$-0.358169\pi$
$853$	33.4290	−	5.89444i	1.14459	−	0.201822i	0.713612	+	0.700541i	$0.247058\pi$
$854$	35.0042	+	1.37416i	1.19782	+	0.0470227i
$855$	0.343094	−	0.255137i	0.0117336	−	0.00872551i
$856$	−9.90809	+	17.1613i	−0.338652	+	0.586562i
$857$	−5.27816	−	29.9339i	−0.180298	−	1.02252i	−0.931849	−	0.362847i	$-0.881805\pi$
$857$	−5.27816	−	29.9339i	−0.180298	−	1.02252i	0.751550	−	0.659676i	$-0.229306\pi$
$858$	−0.191046	−	0.290642i	−0.00652220	−	0.00992234i
$859$	12.1783	+	33.4596i	0.415518	+	1.14163i	0.954214	+	0.299126i	$0.0966952\pi$
$859$	12.1783	+	33.4596i	0.415518	+	1.14163i	−0.538695	+	0.842501i	$0.681083\pi$
$860$	7.90968	+	6.63701i	0.269718	+	0.226320i
$861$	6.26774	−	7.75933i	0.213604	−	0.264437i
$862$	56.8268	+	20.6833i	1.93553	+	0.704475i
$863$	−0.566188	+	0.326889i	−0.0192733	+	0.0111274i	−0.509606	−	0.860408i	$-0.670209\pi$
$863$	−0.566188	+	0.326889i	−0.0192733	+	0.0111274i	0.490332	+	0.871535i	$0.336875\pi$
$864$	20.8756	−	12.0300i	0.710201	−	0.409270i
$865$	−2.40734	+	4.16964i	−0.0818521	+	0.141772i
$866$	2.33265	+	13.2291i	0.0792666	+	0.449543i
$867$	−25.3311	−	2.96769i	−0.860288	−	0.100788i
$868$	−14.1643	+	15.5947i	−0.480766	+	0.529318i
$869$	−0.0518955	−	0.00915058i	−0.00176043	−	0.000310412i
$870$	2.54575	−	1.67339i	0.0863090	−	0.0567331i
$871$	−12.9033	+	2.27521i	−0.437213	+	0.0770925i
$872$			9.89083i			0.334946i
$873$	17.2369	−	26.1768i	0.583382	−	0.885950i
$874$	−0.915398	−	0.528505i	−0.0309638	−	0.0178770i
$875$	28.3451	+	11.5952i	0.958240	+	0.391989i
$876$	8.84713	−	8.34233i	0.298917	−	0.281861i
$877$	27.2881	+	22.8974i	0.921453	+	0.773191i	0.974263	−	0.225414i	$-0.0723734\pi$
$877$	27.2881	+	22.8974i	0.921453	+	0.773191i	−0.0528103	+	0.998605i	$0.516818\pi$
$878$	4.94428	−	28.0404i	0.166861	−	0.946318i
$879$	4.69252	−	15.6588i	0.158275	−	0.528157i
$880$	−0.619081	−	0.737792i	−0.0208692	−	0.0248710i
$881$	23.1789	−	40.1470i	0.780916	−	1.35259i	−0.150492	−	0.988611i	$-0.548086\pi$
$881$	23.1789	−	40.1470i	0.780916	−	1.35259i	0.931409	−	0.363975i	$-0.118581\pi$
$882$	10.9209	−	33.8918i	0.367725	−	1.14120i
$883$	7.99748	+	13.8520i	0.269137	+	0.466158i	0.968639	−	0.248472i	$-0.0799284\pi$
$883$	7.99748	+	13.8520i	0.269137	+	0.466158i	−0.699503	+	0.714630i	$0.746595\pi$
$884$	1.53434	−	4.21557i	0.0516055	−	0.141785i
$885$	0.945373	+	16.3070i	0.0317784	+	0.548155i
$886$	−22.5424	−	18.9153i	−0.757327	−	0.635472i
$887$	3.85899	−	21.8854i	0.129572	−	0.734841i	−0.848914	−	0.528530i	$-0.822743\pi$
$887$	3.85899	−	21.8854i	0.129572	−	0.734841i	0.978487	−	0.206310i	$-0.0661456\pi$
$888$	9.14095	+	6.80901i	0.306750	+	0.228495i
$889$	−2.36409	+	1.83060i	−0.0792890	+	0.0613963i
$890$		−	40.2166i		−	1.34806i
$891$	1.12152	+	0.337077i	0.0375724	+	0.0112925i
$892$	−14.9141	−	8.61063i	−0.499359	−	0.288305i
$893$	−0.774966	−	0.923568i	−0.0259332	−	0.0309060i
$894$	−59.6737	−	6.99114i	−1.99579	−	0.233819i
$895$	−18.7805	+	22.3817i	−0.627762	+	0.748137i
$896$	−33.2124	−	7.20997i	−1.10955	−	0.240868i
$897$	−8.55625	+	5.62424i	−0.285685	+	0.187788i
$898$	−12.1997	−	4.44031i	−0.407108	−	0.148175i
$899$	−6.35598			−0.211984
$900$	−2.10058	−	7.03018i	−0.0700192	−	0.234339i
$901$			8.23780i			0.274441i
$902$	0.0833923	+	0.472941i	0.00277666	+	0.0157472i
$903$	23.9212	+	27.4505i	0.796047	+	0.913496i
$904$	27.6528	−	10.0648i	0.919718	−	0.334750i
$905$	−16.5158	+	19.6827i	−0.549003	+	0.654276i
$906$	9.21933	+	38.9461i	0.306292	+	1.29390i
$907$	−21.5058	−	7.82747i	−0.714089	−	0.259907i	−0.0406744	−	0.999172i	$-0.512951\pi$
$907$	−21.5058	−	7.82747i	−0.714089	−	0.259907i	−0.673414	+	0.739265i	$0.735173\pi$
$908$	−0.278876			−0.00925481
$909$	−10.6930	−	7.04117i	−0.354666	−	0.233541i
$910$	3.23528	−	5.12798i	0.107248	−	0.169991i
$911$	−18.2077	−	21.6991i	−0.603248	−	0.718923i	0.374846	−	0.927087i	$-0.377696\pi$
$911$	−18.2077	−	21.6991i	−0.603248	−	0.718923i	−0.978094	+	0.208164i	$0.933251\pi$
$912$	0.455120	+	0.692382i	0.0150705	+	0.0229271i
$913$	−0.404461	+	0.482018i	−0.0133857	+	0.0159525i
$914$	17.2525	+	47.4010i	0.570663	+	1.56788i
$915$	−18.4441	+	7.95011i	−0.609742	+	0.262823i
$916$	2.59217	−	7.12192i	0.0856476	−	0.235315i
$917$	−17.3024	−	0.679237i	−0.571374	−	0.0224304i
$918$	16.9354	+	46.6469i	0.558953	+	1.53958i
$919$	0.486170	+	0.842071i	0.0160373	+	0.0277774i	0.873933	−	0.486047i	$-0.161562\pi$
$919$	0.486170	+	0.842071i	0.0160373	+	0.0277774i	−0.857895	+	0.513824i	$0.828228\pi$
$920$	−14.0933	+	11.8257i	−0.464641	+	0.389880i
$921$	−1.13255	+	9.66700i	−0.0373187	+	0.318538i
$922$	−0.789115	−	0.139142i	−0.0259881	−	0.00458241i
$923$	−0.435837	+	2.47176i	−0.0143458	+	0.0813588i
$924$	0.269299	+	0.446954i	0.00885927	+	0.0147037i
$925$	7.38662	−	6.19811i	0.242871	−	0.203793i
$926$	3.78652	+	2.18615i	0.124433	+	0.0718413i
$927$	−11.1672	−	4.82417i	−0.366777	−	0.158447i
$928$	1.61951	+	2.80507i	0.0531629	+	0.0920808i
$929$	−1.92286	+	1.61347i	−0.0630869	+	0.0529362i	−0.673786	−	0.738927i	$-0.735333\pi$
$929$	−1.92286	+	1.61347i	−0.0630869	+	0.0529362i	0.610699	+	0.791863i	$0.290889\pi$
$930$	11.3914	−	38.0127i	0.373539	−	1.24649i
$931$	0.650432	+	0.168167i	0.0213171	+	0.00551146i
$932$	−2.19771	−	6.03817i	−0.0719885	−	0.197787i
$933$	29.4197	−	6.96424i	0.963159	−	0.227999i
$934$	−3.08018	+	8.46272i	−0.100786	+	0.276909i
$935$	0.942535	−	0.544173i	0.0308242	−	0.0177964i
$936$	5.17308	−	0.601824i	0.169087	−	0.0196712i
$937$	−6.98943	+	4.03535i	−0.228335	+	0.131829i	−0.609804	−	0.792553i	$-0.708752\pi$
$937$	−6.98943	+	4.03535i	−0.228335	+	0.131829i	0.381469	+	0.924382i	$0.375418\pi$
$938$	63.9928	−	8.71120i	2.08944	−	0.284431i
$939$	0.388404	−	0.772857i	0.0126751	−	0.0252212i
$940$	15.3401	−	5.58335i	0.500340	−	0.182109i
$941$	44.2254	−	16.0967i	1.44171	−	0.524738i	0.501444	−	0.865190i	$-0.332802\pi$
$941$	44.2254	−	16.0967i	1.44171	−	0.524738i	0.940262	+	0.340452i	$0.110580\pi$
$942$	−11.6215	−	1.36153i	−0.378650	−	0.0443612i
$943$	13.9230	−	2.45500i	0.453395	−	0.0799458i
$944$	−31.6544			−1.03026
$945$	2.73734	+	20.2308i	0.0890458	+	0.658109i
$946$	−1.75305			−0.0569964
$947$	35.6317	−	6.28283i	1.15788	−	0.204165i	0.438464	−	0.898749i	$-0.355523\pi$
$947$	35.6317	−	6.28283i	1.15788	−	0.204165i	0.719411	+	0.694584i	$0.244412\pi$
$948$	−0.366692	+	0.492277i	−0.0119096	+	0.0159884i
$949$	6.86132	−	2.49731i	0.222728	−	0.0810663i
$950$	0.427387	−	0.155556i	0.0138663	−	0.00504691i
$951$	−13.5067	+	0.783026i	−0.437984	+	0.0253914i
$952$	10.7619	−	26.3081i	0.348795	−	0.852649i
$953$	41.0448	−	23.6972i	1.32957	−	0.767629i	0.344339	−	0.938845i	$-0.388103\pi$
$953$	41.0448	−	23.6972i	1.32957	−	0.767629i	0.985233	+	0.171216i	$0.0547697\pi$
$954$	6.65021	−	3.33538i	0.215309	−	0.107987i
$955$	−6.80603	+	3.92947i	−0.220238	+	0.127155i
$956$	−1.40834	+	3.86938i	−0.0455489	+	0.125145i
$957$	−0.0451927	+	0.150806i	−0.00146087	+	0.00487488i
$958$	19.1016	+	52.4811i	0.617143	+	1.69559i
$959$	−8.27152	+	9.10684i	−0.267101	+	0.294075i
$960$	5.27234	−	1.24807i	0.170164	−	0.0402812i
$961$	−39.6747	+	33.2910i	−1.27983	+	1.07390i
$962$	−2.66222	−	4.61110i	−0.0858335	−	0.148668i
$963$	−7.20406	+	30.3236i	−0.232148	+	0.977164i
$964$	−5.02575	−	2.90162i	−0.161868	−	0.0934548i
$965$	−20.0989	+	16.8650i	−0.647007	+	0.542903i
$966$	43.2296	−	26.0467i	1.39089	−	0.838039i
$967$	−9.82570	+	55.7243i	−0.315973	+	1.79197i	0.250736	+	0.968055i	$0.419327\pi$
$967$	−9.82570	+	55.7243i	−0.315973	+	1.79197i	−0.566710	+	0.823918i	$0.691784\pi$
$968$	−20.6307	−	3.63774i	−0.663095	−	0.116922i
$969$	−0.859828	+	0.370619i	−0.0276216	+	0.0119060i
$970$	−20.1517	+	16.9093i	−0.647033	+	0.542925i
$971$	−3.04373	−	5.27190i	−0.0976780	−	0.169183i	0.813045	−	0.582201i	$-0.197808\pi$
$971$	−3.04373	−	5.27190i	−0.0976780	−	0.169183i	−0.910723	+	0.413017i	$0.864475\pi$
$972$	9.37475	−	9.90991i	0.300695	−	0.317860i
$973$	−28.7706	−	18.1516i	−0.922344	−	0.581913i
$974$	−14.0580	+	38.6241i	−0.450448	+	1.23760i
$975$	0.512658	−	4.37585i	0.0164182	−	0.140139i
$976$	−13.3120	−	36.5744i	−0.426107	−	1.17072i
$977$	11.0654	−	13.1873i	0.354015	−	0.421898i	−0.559420	−	0.828885i	$-0.688976\pi$
$977$	11.0654	−	13.1873i	0.354015	−	0.421898i	0.913434	+	0.406986i	$0.133420\pi$
$978$	32.4478	−	64.5656i	1.03757	−	2.06458i
$979$	1.33588	+	1.59204i	0.0426950	+	0.0508819i
$980$	−5.15190	+	7.49713i	−0.164571	+	0.239487i
$981$	4.45367	+	14.9055i	0.142195	+	0.475896i
$982$	−19.5540			−0.623992
$983$	−10.5976	−	3.85723i	−0.338012	−	0.123026i	0.167437	−	0.985883i	$-0.446451\pi$
$983$	−10.5976	−	3.85723i	−0.338012	−	0.123026i	−0.505449	+	0.862856i	$0.668673\pi$
$984$	−6.88825	−	2.06423i	−0.219589	−	0.0658051i
$985$	19.7478	−	23.5345i	0.629217	−	0.749872i
$986$	−6.26906	+	2.28175i	−0.199647	+	0.0726657i
$987$	56.4954	−	11.0530i	1.79827	−	0.351822i
$988$	−0.0132738	−	0.0752794i	−0.000422296	−	0.00239496i
$989$			51.6082i			1.64105i
$990$	−0.820921	−	0.540561i	−0.0260906	−	0.0171802i
$991$	35.3069			1.12156			0.560780	−	0.827965i	$-0.310501\pi$
$991$	35.3069			1.12156			0.560780	+	0.827965i	$0.310501\pi$
$992$	39.6463	+	14.4301i	1.25877	+	0.458155i
$993$	3.16886	+	54.6606i	0.100561	+	1.73460i
$994$	2.62455	−	12.0899i	0.0832456	−	0.383468i
$995$	−12.1946	+	14.5330i	−0.386596	+	0.460727i
$996$	2.90133	+	6.73103i	0.0919323	+	0.213281i
$997$	1.04902	+	1.25017i	0.0332227	+	0.0395932i	0.782400	−	0.622776i	$-0.213995\pi$
$997$	1.04902	+	1.25017i	0.0332227	+	0.0395932i	−0.749177	+	0.662370i	$0.769551\pi$
$998$	7.49288	+	4.32601i	0.237183	+	0.136938i
$999$	16.8414	+	6.14517i	0.532838	+	0.194425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.18	yes	132
3.2	odd	2		567.2.bd.a.17.5		132
7.5	odd	6		189.2.ba.a.131.5	yes	132
21.5	even	6		567.2.ba.a.341.18		132
27.7	even	9		567.2.ba.a.143.18		132
27.20	odd	18		189.2.ba.a.101.5	✓	132
189.47	even	18	inner	189.2.bd.a.47.18	yes	132
189.61	odd	18		567.2.bd.a.467.5		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.5	✓	132	27.20	odd	18
189.2.ba.a.131.5	yes	132	7.5	odd	6
189.2.bd.a.47.18	yes	132	189.47	even	18	inner
189.2.bd.a.185.18	yes	132	1.1	even	1	trivial
567.2.ba.a.143.18		132	27.7	even	9
567.2.ba.a.341.18		132	21.5	even	6
567.2.bd.a.17.5		132	3.2	odd	2
567.2.bd.a.467.5		132	189.61	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.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.66985 - 0.294440i) q^{2} +(0.685602 + 1.59058i) q^{3} +(0.822331 - 0.299304i) q^{4} +(1.39543 - 0.507895i) q^{5} +(1.61319 + 2.45417i) q^{6} +(-0.356869 - 2.62157i) q^{7} +(-1.65184 + 0.953692i) q^{8} +(-2.05990 + 2.18101i) q^{9} +O(q^{10})\)	\(q+(1.66985 - 0.294440i) q^{2} +(0.685602 + 1.59058i) q^{3} +(0.822331 - 0.299304i) q^{4} +(1.39543 - 0.507895i) q^{5} +(1.61319 + 2.45417i) q^{6} +(-0.356869 - 2.62157i) q^{7} +(-1.65184 + 0.953692i) q^{8} +(-2.05990 + 2.18101i) q^{9} +(2.18062 - 1.25898i) q^{10} +(-0.0445037 + 0.122273i) q^{11} +(1.03986 + 1.10278i) q^{12} +(0.311287 + 0.855253i) q^{13} +(-1.36782 - 4.27257i) q^{14} +(1.76456 + 1.87133i) q^{15} +(-3.81827 + 3.20391i) q^{16} +(-2.81624 - 4.87788i) q^{17} +(-2.79755 + 4.24849i) q^{18} +(-0.0831162 - 0.0479872i) q^{19} +(0.995491 - 0.835316i) q^{20} +(3.92516 - 2.36499i) q^{21} +(-0.0383126 + 0.217282i) q^{22} +(6.39659 + 1.12789i) q^{23} +(-2.64943 - 1.97354i) q^{24} +(-2.14095 + 1.79647i) q^{25} +(0.771624 + 1.33649i) q^{26} +(-4.88135 - 1.78113i) q^{27} +(-1.07811 - 2.04899i) q^{28} +(0.238914 - 0.656410i) q^{29} +(3.49755 + 2.60529i) q^{30} +(-3.11204 - 8.55026i) q^{31} +(-2.98051 + 3.55203i) q^{32} +(-0.224997 + 0.0130438i) q^{33} +(-6.13896 - 7.31613i) q^{34} +(-1.82947 - 3.47697i) q^{35} +(-1.04113 + 2.41005i) q^{36} -3.45015 q^{37} +(-0.152921 - 0.0556588i) q^{38} +(-1.14693 + 1.08149i) q^{39} +(-1.82066 + 2.16977i) q^{40} +(2.04536 - 0.744450i) q^{41} +(5.85809 - 5.10490i) q^{42} +(1.37972 + 7.82480i) q^{43} +0.113869i q^{44} +(-1.76672 + 4.08966i) q^{45} +11.0135 q^{46} +(11.8044 + 4.29647i) q^{47} +(-7.71390 - 3.87667i) q^{48} +(-6.74529 + 1.87112i) q^{49} +(-3.04613 + 3.63023i) q^{50} +(5.82784 - 7.82375i) q^{51} +(0.511962 + 0.610132i) q^{52} +(-1.26661 - 0.731275i) q^{53} +(-8.67558 - 1.53696i) q^{54} +0.193227i q^{55} +(3.08967 + 3.99009i) q^{56} +(0.0193428 - 0.165103i) q^{57} +(0.205677 - 1.16645i) q^{58} +(4.86491 + 4.08214i) q^{59} +(2.01115 + 1.01071i) q^{60} +(-2.67073 + 7.33778i) q^{61} +(-7.71419 - 13.3614i) q^{62} +(6.45280 + 4.62184i) q^{63} +(1.05325 - 1.82428i) q^{64} +(0.868757 + 1.03534i) q^{65} +(-0.371871 + 0.0880294i) q^{66} +(-2.49984 + 14.1773i) q^{67} +(-3.77586 - 3.16832i) q^{68} +(2.59151 + 10.9476i) q^{69} +(-4.07871 - 5.26736i) q^{70} +(2.38823 + 1.37884i) q^{71} +(1.32262 - 5.56720i) q^{72} -8.02256i q^{73} +(-5.76125 + 1.01586i) q^{74} +(-4.32528 - 2.17370i) q^{75} +(-0.0827118 - 0.0145843i) q^{76} +(0.336429 + 0.0730343i) q^{77} +(-1.59677 + 2.14363i) q^{78} +(0.0703241 + 0.398828i) q^{79} +(-3.70088 + 6.41012i) q^{80} +(-0.513631 - 8.98533i) q^{81} +(3.19626 - 1.84536i) q^{82} +(4.54412 + 1.65393i) q^{83} +(2.51993 - 3.11962i) q^{84} +(-6.40732 - 5.37638i) q^{85} +(4.60787 + 12.6600i) q^{86} +(1.20787 - 0.0700244i) q^{87} +(-0.0430976 - 0.244419i) q^{88} +(7.98594 - 13.8321i) q^{89} +(-1.74600 + 7.34933i) q^{90} +(2.13102 - 1.12127i) q^{91} +(5.59770 - 0.987026i) q^{92} +(11.4663 - 10.8120i) q^{93} +(20.9768 + 3.69877i) q^{94} +(-0.140355 - 0.0247484i) q^{95} +(-7.69325 - 2.30546i) q^{96} +(-10.2887 + 1.81418i) q^{97} +(-10.7127 + 5.11057i) q^{98} +(-0.175006 - 0.348933i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more