LMFDB - Embedded newform 216.2.v.b.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.322208 - 1.37702i) q^{2} +(0.889428 + 1.48624i) q^{3} +(-1.79236 + 0.887374i) q^{4} +(0.479395 + 0.174486i) q^{5} +(1.76000 - 1.70364i) q^{6} +(1.63176 + 0.287723i) q^{7} +(1.79945 + 2.18220i) q^{8} +(-1.41783 + 2.64381i) q^{9} +O(q^{10})$	\(q+(-0.322208 - 1.37702i) q^{2} +(0.889428 + 1.48624i) q^{3} +(-1.79236 + 0.887374i) q^{4} +(0.479395 + 0.174486i) q^{5} +(1.76000 - 1.70364i) q^{6} +(1.63176 + 0.287723i) q^{7} +(1.79945 + 2.18220i) q^{8} +(-1.41783 + 2.64381i) q^{9} +(0.0858049 - 0.716357i) q^{10} +(-0.576981 - 1.58524i) q^{11} +(-2.91303 - 1.87463i) q^{12} +(3.81226 + 4.54327i) q^{13} +(-0.129566 - 2.33967i) q^{14} +(0.167060 + 0.867690i) q^{15} +(2.42513 - 3.18099i) q^{16} +(5.08792 - 2.93751i) q^{17} +(4.09742 + 1.10053i) q^{18} +(-1.91901 + 3.32382i) q^{19} +(-1.01408 + 0.112661i) q^{20} +(1.02370 + 2.68110i) q^{21} +(-1.99700 + 1.30529i) q^{22} +(-0.765923 - 4.34377i) q^{23} +(-1.64280 + 4.61532i) q^{24} +(-3.63085 - 3.04664i) q^{25} +(5.02783 - 6.71343i) q^{26} +(-5.19041 + 0.244235i) q^{27} +(-3.18002 + 0.932275i) q^{28} +(-0.748958 - 0.628450i) q^{29} +(1.14100 - 0.509621i) q^{30} +(-6.88153 + 1.21340i) q^{31} +(-5.16169 - 2.31451i) q^{32} +(1.84287 - 2.26749i) q^{33} +(-5.68438 - 6.05968i) q^{34} +(0.732053 + 0.422651i) q^{35} +(0.195225 - 5.99682i) q^{36} +(5.88275 - 3.39641i) q^{37} +(5.19529 + 1.57155i) q^{38} +(-3.36168 + 9.70686i) q^{39} +(0.481883 + 1.36011i) q^{40} +(-2.01755 - 2.40442i) q^{41} +(3.36207 - 2.27353i) q^{42} +(0.826023 - 0.300648i) q^{43} +(2.44086 + 2.32933i) q^{44} +(-1.14101 + 1.02004i) q^{45} +(-5.73466 + 2.45429i) q^{46} +(0.0117553 - 0.0666674i) q^{47} +(6.88471 + 0.775073i) q^{48} +(-3.99800 - 1.45515i) q^{49} +(-3.02540 + 5.98140i) q^{50} +(8.89120 + 4.94918i) q^{51} +(-10.8645 - 4.76030i) q^{52} -5.83248 q^{53} +(2.00871 + 7.06860i) q^{54} -0.860632i q^{55} +(2.30839 + 4.07856i) q^{56} +(-6.64683 + 0.104187i) q^{57} +(-0.624067 + 1.23382i) q^{58} +(-0.521107 + 1.43173i) q^{59} +(-1.06940 - 1.40697i) q^{60} +(10.6832 + 1.88373i) q^{61} +(3.88816 + 9.08503i) q^{62} +(-3.07425 + 3.90612i) q^{63} +(-1.52399 + 7.85350i) q^{64} +(1.03484 + 2.84321i) q^{65} +(-3.71617 - 1.80706i) q^{66} +(-7.05812 + 5.92246i) q^{67} +(-6.51274 + 9.77998i) q^{68} +(5.77466 - 5.00182i) q^{69} +(0.346125 - 1.14423i) q^{70} +(-8.21657 - 14.2315i) q^{71} +(-8.32064 + 1.66340i) q^{72} +(0.650656 - 1.12697i) q^{73} +(-6.57239 - 7.00631i) q^{74} +(1.29867 - 8.10609i) q^{75} +(0.490090 - 7.66038i) q^{76} +(-0.485382 - 2.75274i) q^{77} +(14.4497 + 1.50146i) q^{78} +(3.66309 - 4.36550i) q^{79} +(1.71764 - 1.10180i) q^{80} +(-4.97949 - 7.49698i) q^{81} +(-2.66087 + 3.55293i) q^{82} +(-1.44571 + 1.72293i) q^{83} +(-4.21399 - 3.89709i) q^{84} +(2.95168 - 0.520461i) q^{85} +(-0.680149 - 1.04058i) q^{86} +(0.267885 - 1.67209i) q^{87} +(2.42107 - 4.11164i) q^{88} +(11.2944 + 6.52081i) q^{89} +(1.77226 + 1.24253i) q^{90} +(4.91348 + 8.51039i) q^{91} +(5.22736 + 7.10595i) q^{92} +(-7.92403 - 9.14839i) q^{93} +(-0.0955899 + 0.00529357i) q^{94} +(-1.49992 + 1.25859i) q^{95} +(-1.15102 - 9.73012i) q^{96} +(13.9173 - 5.06549i) q^{97} +(-0.715585 + 5.97419i) q^{98} +(5.00915 + 0.722182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.322208	−	1.37702i	−0.227836	−	0.973700i
$2$	−0.322208	−	1.37702i	−0.227836	−	0.973700i
$3$	0.889428	+	1.48624i	0.513512	+	0.858083i
$3$	0.889428	+	1.48624i	0.513512	+	0.858083i
$4$	−1.79236	+	0.887374i	−0.896182	+	0.443687i
$5$	0.479395	+	0.174486i	0.214392	+	0.0780323i	0.446983	−	0.894542i	$-0.352498\pi$
$5$	0.479395	+	0.174486i	0.214392	+	0.0780323i	−0.232591	+	0.972575i	$0.574720\pi$
$6$	1.76000	−	1.70364i	0.718518	−	0.695508i
$7$	1.63176	+	0.287723i	0.616746	+	0.108749i	0.473289	−	0.880907i	$-0.343067\pi$
$7$	1.63176	+	0.287723i	0.616746	+	0.108749i	0.143458	+	0.989656i	$0.454178\pi$
$8$	1.79945	+	2.18220i	0.636200	+	0.771524i
$9$	−1.41783	+	2.64381i	−0.472612	+	0.881271i
$10$	0.0858049	−	0.716357i	0.0271339	−	0.226532i
$11$	−0.576981	−	1.58524i	−0.173966	−	0.477968i	0.821812	−	0.569759i	$-0.192963\pi$
$11$	−0.576981	−	1.58524i	−0.173966	−	0.477968i	−0.995778	+	0.0917902i	$0.970741\pi$
$12$	−2.91303	−	1.87463i	−0.840920	−	0.541160i
$13$	3.81226	+	4.54327i	1.05733	+	1.26008i	0.964412	+	0.264403i	$0.0851750\pi$
$13$	3.81226	+	4.54327i	1.05733	+	1.26008i	0.0929181	+	0.995674i	$0.470381\pi$
$14$	−0.129566	−	2.33967i	−0.0346279	−	0.625302i
$15$	0.167060	+	0.867690i	0.0431346	+	0.224037i
$16$	2.42513	−	3.18099i	0.606284	−	0.795248i
$17$	5.08792	−	2.93751i	1.23400	−	0.712452i	0.266141	−	0.963934i	$-0.414251\pi$
$17$	5.08792	−	2.93751i	1.23400	−	0.712452i	0.967862	+	0.251482i	$0.0809180\pi$
$18$	4.09742	+	1.10053i	0.965771	+	0.259397i
$19$	−1.91901	+	3.32382i	−0.440251	+	0.762538i	−0.997708	−	0.0676685i	$-0.978444\pi$
$19$	−1.91901	+	3.32382i	−0.440251	+	0.762538i	0.557457	+	0.830206i	$0.311777\pi$
$20$	−1.01408	+	0.112661i	−0.226756	+	0.0251918i
$21$	1.02370	+	2.68110i	0.223391	+	0.585063i
$22$	−1.99700	+	1.30529i	−0.425762	+	0.278289i
$23$	−0.765923	−	4.34377i	−0.159706	−	0.905738i	−0.954356	−	0.298670i	$-0.903457\pi$
$23$	−0.765923	−	4.34377i	−0.159706	−	0.905738i	0.794650	−	0.607067i	$-0.207654\pi$
$24$	−1.64280	+	4.61532i	−0.335335	+	0.942099i
$25$	−3.63085	−	3.04664i	−0.726170	−	0.609329i
$26$	5.02783	−	6.71343i	0.986039	−	1.31661i
$27$	−5.19041	+	0.244235i	−0.998895	+	0.0470031i
$28$	−3.18002	+	0.932275i	−0.600967	+	0.176183i
$29$	−0.748958	−	0.628450i	−0.139078	−	0.116700i	0.570595	−	0.821232i	$-0.306713\pi$
$29$	−0.748958	−	0.628450i	−0.139078	−	0.116700i	−0.709673	+	0.704532i	$0.751157\pi$
$30$	1.14100	−	0.509621i	0.208317	−	0.0930437i
$31$	−6.88153	+	1.21340i	−1.23596	+	0.217933i	−0.753183	−	0.657811i	$-0.771483\pi$
$31$	−6.88153	+	1.21340i	−1.23596	+	0.217933i	−0.482776	+	0.875744i	$0.660372\pi$
$32$	−5.16169	−	2.31451i	−0.912466	−	0.409152i
$33$	1.84287	−	2.26749i	0.320803	−	0.394720i
$34$	−5.68438	−	6.05968i	−0.974864	−	1.03923i
$35$	0.732053	+	0.422651i	0.123740	+	0.0714410i
$36$	0.195225	−	5.99682i	0.0325375	−	0.999471i
$37$	5.88275	−	3.39641i	0.967118	−	0.558366i	0.0687618	−	0.997633i	$-0.478095\pi$
$37$	5.88275	−	3.39641i	0.967118	−	0.558366i	0.898357	+	0.439267i	$0.144762\pi$
$38$	5.19529	+	1.57155i	0.842787	+	0.254939i
$39$	−3.36168	+	9.70686i	−0.538299	+	1.55434i
$40$	0.481883	+	1.36011i	0.0761924	+	0.215053i
$41$	−2.01755	−	2.40442i	−0.315089	−	0.375508i	0.585135	−	0.810936i	$-0.301042\pi$
$41$	−2.01755	−	2.40442i	−0.315089	−	0.375508i	−0.900224	+	0.435428i	$0.856597\pi$
$42$	3.36207	−	2.27353i	0.518779	−	0.350814i
$43$	0.826023	−	0.300648i	0.125967	−	0.0458484i	−0.278267	−	0.960504i	$-0.589760\pi$
$43$	0.826023	−	0.300648i	0.125967	−	0.0458484i	0.404235	+	0.914655i	$0.367538\pi$
$44$	2.44086	+	2.32933i	0.367974	+	0.351160i
$45$	−1.14101	+	1.02004i	−0.170092	+	0.152058i
$46$	−5.73466	+	2.45429i	−0.845530	+	0.361865i
$47$	0.0117553	−	0.0666674i	0.00171468	−	0.00972444i	−0.983938	−	0.178508i	$-0.942873\pi$
$47$	0.0117553	−	0.0666674i	0.00171468	−	0.00972444i	0.985653	+	0.168784i	$0.0539840\pi$
$48$	6.88471	+	0.775073i	0.993723	+	0.111872i
$49$	−3.99800	−	1.45515i	−0.571143	−	0.207879i
$50$	−3.02540	+	5.98140i	−0.427856	+	0.845898i
$51$	8.89120	+	4.94918i	1.24502	+	0.693024i
$52$	−10.8645	−	4.76030i	−1.50664	−	0.660135i
$53$	−5.83248			−0.801152			−0.400576	−	0.916263i	$-0.631190\pi$
$53$	−5.83248			−0.801152			−0.400576	+	0.916263i	$0.631190\pi$
$54$	2.00871	+	7.06860i	0.273351	+	0.961914i
$55$		−	0.860632i		−	0.116048i
$56$	2.30839	+	4.07856i	0.308471	+	0.545021i
$57$	−6.64683	+	0.104187i	−0.880394	+	0.0138000i
$58$	−0.624067	+	1.23382i	−0.0819441	+	0.162009i
$59$	−0.521107	+	1.43173i	−0.0678423	+	0.186395i	−0.968981	−	0.247136i	$-0.920510\pi$
$59$	−0.521107	+	1.43173i	−0.0678423	+	0.186395i	0.901138	+	0.433532i	$0.142733\pi$
$60$	−1.06940	−	1.40697i	−0.138059	−	0.181639i
$61$	10.6832	+	1.88373i	1.36784	+	0.241187i	0.808864	−	0.587996i	$-0.200083\pi$
$61$	10.6832	+	1.88373i	1.36784	+	0.241187i	0.558976	+	0.829184i	$0.311194\pi$
$62$	3.88816	+	9.08503i	0.493797	+	1.15380i
$63$	−3.07425	+	3.90612i	−0.387319	+	0.492124i
$64$	−1.52399	+	7.85350i	−0.190499	+	0.981687i
$65$	1.03484	+	2.84321i	0.128356	+	0.352656i
$66$	−3.71617	−	1.80706i	−0.457429	−	0.222434i
$67$	−7.05812	+	5.92246i	−0.862286	+	0.723544i	−0.962459	−	0.271426i	$-0.912505\pi$
$67$	−7.05812	+	5.92246i	−0.862286	+	0.723544i	0.100173	+	0.994970i	$0.468060\pi$
$68$	−6.51274	+	9.77998i	−0.789785	+	1.18600i
$69$	5.77466	−	5.00182i	0.695187	−	0.602148i
$70$	0.346125	−	1.14423i	0.0413698	−	0.136762i
$71$	−8.21657	−	14.2315i	−0.975127	−	1.68897i	−0.679514	−	0.733662i	$-0.737809\pi$
$71$	−8.21657	−	14.2315i	−0.975127	−	1.68897i	−0.295613	−	0.955308i	$-0.595524\pi$
$72$	−8.32064	+	1.66340i	−0.980597	+	0.196033i
$73$	0.650656	−	1.12697i	0.0761535	−	0.131902i	−0.825434	−	0.564499i	$-0.809069\pi$
$73$	0.650656	−	1.12697i	0.0761535	−	0.131902i	0.901587	+	0.432597i	$0.142403\pi$
$74$	−6.57239	−	7.00631i	−0.764025	−	0.814467i
$75$	1.29867	−	8.10609i	0.149958	−	0.936011i
$76$	0.490090	−	7.66038i	0.0562172	−	0.878706i
$77$	−0.485382	−	2.75274i	−0.0553144	−	0.313704i
$78$	14.4497	+	1.50146i	1.63610	+	0.170007i
$79$	3.66309	−	4.36550i	0.412130	−	0.491157i	−0.519549	−	0.854441i	$-0.673900\pi$
$79$	3.66309	−	4.36550i	0.412130	−	0.491157i	0.931679	+	0.363284i	$0.118344\pi$
$80$	1.71764	−	1.10180i	0.192037	−	0.123185i
$81$	−4.97949	−	7.49698i	−0.553277	−	0.832998i
$82$	−2.66087	+	3.55293i	−0.293844	+	0.392356i
$83$	−1.44571	+	1.72293i	−0.158687	+	0.189116i	−0.839530	−	0.543314i	$-0.817169\pi$
$83$	−1.44571	+	1.72293i	−0.158687	+	0.189116i	0.680842	+	0.732430i	$0.261614\pi$
$84$	−4.21399	−	3.89709i	−0.459784	−	0.425207i
$85$	2.95168	−	0.520461i	0.320155	−	0.0564519i
$86$	−0.680149	−	1.04058i	−0.0733424	−	0.112208i
$87$	0.267885	−	1.67209i	0.0287203	−	0.179267i
$88$	2.42107	−	4.11164i	0.258087	−	0.438303i
$89$	11.2944	+	6.52081i	1.19720	+	0.691204i	0.959930	−	0.280239i	$-0.0904139\pi$
$89$	11.2944	+	6.52081i	1.19720	+	0.691204i	0.237271	+	0.971444i	$0.423747\pi$
$90$	1.77226	+	1.24253i	0.186812	+	0.130974i
$91$	4.91348	+	8.51039i	0.515072	+	0.892131i
$92$	5.22736	+	7.10595i	0.544990	+	0.740846i
$93$	−7.92403	−	9.14839i	−0.821684	−	0.948644i
$94$	−0.0955899	+	0.00529357i	−0.00985935	+	0.000545990i
$95$	−1.49992	+	1.25859i	−0.153889	+	0.129128i
$96$	−1.15102	−	9.73012i	−0.117476	−	0.993076i
$97$	13.9173	−	5.06549i	1.41309	−	0.514323i	0.481055	−	0.876691i	$-0.340254\pi$
$97$	13.9173	−	5.06549i	1.41309	−	0.514323i	0.932035	+	0.362368i	$0.118032\pi$
$98$	−0.715585	+	5.97419i	−0.0722850	+	0.603484i
$99$	5.00915	+	0.722182i	0.503438	+	0.0725820i
$100$	9.21131	+	2.23877i	0.921131	+	0.223877i
$101$	−1.51077	+	8.56802i	−0.150328	+	0.852550i	0.812606	+	0.582813i	$0.198048\pi$
$101$	−1.51077	+	8.56802i	−0.150328	+	0.852550i	−0.962934	+	0.269737i	$0.913063\pi$
$102$	3.95030	−	13.8380i	0.391138	−	1.37017i
$103$	−0.326997	+	0.898417i	−0.0322200	+	0.0885237i	−0.954760	−	0.297379i	$-0.903888\pi$
$103$	−0.326997	+	0.898417i	−0.0322200	+	0.0885237i	0.922540	+	0.385902i	$0.126110\pi$
$104$	−3.05438	+	16.4945i	−0.299506	+	1.61742i
$105$	0.0229467	+	1.46393i	0.00223937	+	0.142865i
$106$	1.87927	+	8.03143i	0.182531	+	0.780082i
$107$		−	14.4932i		−	1.40111i	−0.713597	−	0.700557i	$-0.752935\pi$
$107$		−	14.4932i		−	1.40111i	0.713597	−	0.700557i	$-0.247065\pi$
$108$	9.08637	−	5.04359i	0.874337	−	0.485320i
$109$		−	17.4622i		−	1.67258i	−0.548290	−	0.836288i	$-0.684721\pi$
$109$		−	17.4622i		−	1.67258i	0.548290	−	0.836288i	$-0.315279\pi$
$110$	−1.18511	+	0.277303i	−0.112995	+	0.0264398i
$111$	10.2802	+	5.72233i	0.975751	+	0.543140i
$112$	4.87247	−	4.49284i	0.460406	−	0.424534i
$113$	−0.630928	+	1.73346i	−0.0593528	+	0.163070i	−0.965825	−	0.259195i	$-0.916543\pi$
$113$	−0.630928	+	1.73346i	−0.0593528	+	0.163070i	0.906472	+	0.422265i	$0.138765\pi$
$114$	2.28513	+	9.11924i	0.214022	+	0.854095i
$115$	0.390745	−	2.21602i	0.0364371	−	0.206645i
$116$	1.90007	+	0.461806i	0.176418	+	0.0428776i
$117$	−17.4167	+	3.63729i	−1.61018	+	0.336267i
$118$	2.13942	+	0.256259i	0.196950	+	0.0235906i
$119$	9.14744	−	3.32940i	0.838545	−	0.305205i
$120$	−1.59286	+	1.92592i	−0.145407	+	0.175811i
$121$	6.24640	−	5.24136i	0.567855	−	0.476487i
$122$	−0.848272	−	15.3179i	−0.0767990	−	1.38682i
$123$	1.77909	−	5.13714i	0.160415	−	0.463200i
$124$	11.2575	−	8.28134i	1.01095	−	0.743687i
$125$	−2.48442	−	4.30314i	−0.222213	−	0.384885i
$126$	6.36934	+	2.97471i	0.567426	+	0.265009i
$127$	−9.88071	−	5.70463i	−0.876771	−	0.506204i	−0.00717861	−	0.999974i	$-0.502285\pi$
$127$	−9.88071	−	5.70463i	−0.876771	−	0.506204i	−0.869592	+	0.493770i	$0.835618\pi$
$128$	11.3055	−	0.431896i	0.999271	−	0.0381746i
$129$	1.18152	+	0.960266i	0.104027	+	0.0845467i
$130$	3.58172	−	2.34110i	0.314137	−	0.205328i
$131$	−3.72734	+	0.657230i	−0.325659	+	0.0574225i	−0.334088	−	0.942542i	$-0.608428\pi$
$131$	−3.72734	+	0.657230i	−0.325659	+	0.0574225i	0.00842869	+	0.999964i	$0.497317\pi$
$132$	−1.29098	+	5.69949i	−0.112365	+	0.496077i
$133$	−4.08770	+	4.87153i	−0.354448	+	0.422415i
$134$	10.4295	+	7.81089i	0.900974	+	0.674759i
$135$	−2.53087	−	0.788566i	−0.217823	−	0.0678690i
$136$	15.5657	+	5.81697i	1.33475	+	0.498801i
$137$	−11.5314	+	13.7426i	−0.985198	+	1.17411i	−0.000471980		1.00000i	$0.500150\pi$
$137$	−11.5314	+	13.7426i	−0.985198	+	1.17411i	−0.984726	+	0.174113i	$0.944294\pi$
$138$	−8.74824	−	6.34019i	−0.744699	−	0.539712i
$139$	0.427954	+	2.42705i	0.0362986	+	0.205859i	0.997563	−	0.0697674i	$-0.0222257\pi$
$139$	0.427954	+	2.42705i	0.0362986	+	0.205859i	−0.961265	+	0.275627i	$0.911115\pi$
$140$	−1.68715	−	0.107939i	−0.142591	−	0.00912255i
$141$	0.109539	−	0.0418247i	0.00922488	−	0.00352228i
$142$	−16.9496	+	15.8999i	−1.42238	+	1.33429i
$143$	5.00259	−	8.66473i	0.418337	−	0.724581i
$144$	4.97151	+	10.9217i	0.414293	+	0.910144i
$145$	−0.249391	−	0.431958i	−0.0207108	−	0.0358722i
$146$	−1.76150	−	0.532847i	−0.145783	−	0.0440987i
$147$	−1.39322	−	7.23626i	−0.114911	−	0.596836i
$148$	−7.53015	+	11.3078i	−0.618974	+	0.929495i
$149$	3.55227	−	2.98071i	0.291013	−	0.244189i	−0.485579	−	0.874193i	$-0.661391\pi$
$149$	3.55227	−	2.98071i	0.291013	−	0.244189i	0.776592	+	0.630004i	$0.216947\pi$
$150$	−11.5807	+	0.823553i	−0.945559	+	0.0672428i
$151$	1.81281	+	4.98066i	0.147524	+	0.405320i	0.991341	−	0.131311i	$-0.0419187\pi$
$151$	1.81281	+	4.98066i	0.147524	+	0.405320i	−0.843817	+	0.536632i	$0.819697\pi$
$152$	−10.7064	+	1.79338i	−0.868404	+	0.145462i
$153$	0.552402	+	17.6164i	0.0446591	+	1.42420i
$154$	−3.63418	+	1.55534i	−0.292851	+	0.125333i
$155$	−3.51069	−	0.619030i	−0.281986	−	0.0497217i
$156$	−2.58827	−	20.3813i	−0.207227	−	1.63181i
$157$	−6.04596	+	16.6111i	−0.482520	+	1.32571i	0.424805	+	0.905285i	$0.360343\pi$
$157$	−6.04596	+	16.6111i	−0.482520	+	1.32571i	−0.907326	+	0.420429i	$0.861880\pi$
$158$	−7.19166	−	3.63755i	−0.572138	−	0.289388i
$159$	−5.18757	−	8.66847i	−0.411401	−	0.687455i
$160$	−2.07064	−	2.01021i	−0.163698	−	0.158921i
$161$		−	7.30834i		−	0.575978i
$162$	−8.71905	+	9.27244i	−0.685033	+	0.728512i
$163$	21.0349			1.64758			0.823789	−	0.566896i	$-0.191856\pi$
$163$	21.0349			1.64758			0.823789	+	0.566896i	$0.191856\pi$
$164$	5.74981	+	2.51928i	0.448985	+	0.196723i
$165$	1.27911	−	0.765470i	0.0995784	−	0.0595918i
$166$	2.83833	+	1.43563i	0.220297	+	0.111426i
$167$	16.2585	+	5.91760i	1.25812	+	0.457918i	0.883137	−	0.469114i	$-0.155427\pi$
$167$	16.2585	+	5.91760i	1.25812	+	0.457918i	0.374982	+	0.927032i	$0.377649\pi$
$168$	−4.00859	+	7.05841i	−0.309269	+	0.544568i
$169$	−3.85059	+	21.8378i	−0.296199	+	1.67983i
$170$	−1.66774	−	3.89682i	−0.127910	−	0.298873i
$171$	−6.06673	−	9.78614i	−0.463934	−	0.748365i
$172$	−1.21375	+	1.27186i	−0.0925473	+	0.0969785i
$173$	−22.9789	+	8.36365i	−1.74706	+	0.635877i	−0.999596	−	0.0284290i	$-0.990950\pi$
$173$	−22.9789	+	8.36365i	−1.74706	+	0.635877i	−0.747461	+	0.664306i	$0.768727\pi$
$174$	−2.38882	+	0.169879i	−0.181096	+	0.0128785i
$175$	−5.04807	−	6.01606i	−0.381598	−	0.454771i
$176$	−6.44190	−	2.00905i	−0.485577	−	0.151438i
$177$	−2.59138	+	0.498929i	−0.194780	+	0.0375018i
$178$	5.34014	−	17.6536i	0.400260	−	1.32319i
$179$	−11.1303	+	6.42610i	−0.831920	+	0.480309i	−0.854510	−	0.519436i	$-0.826142\pi$
$179$	−11.1303	+	6.42610i	−0.831920	+	0.480309i	0.0225897	+	0.999745i	$0.492809\pi$
$180$	1.13995	−	2.84078i	0.0849668	−	0.211740i
$181$	5.53930	+	3.19811i	0.411733	+	0.237714i	0.691534	−	0.722344i	$-0.256935\pi$
$181$	5.53930	+	3.19811i	0.411733	+	0.237714i	−0.279801	+	0.960058i	$0.590269\pi$
$182$	10.1358	−	9.50807i	0.751316	−	0.704785i
$183$	6.70223	+	17.5532i	0.495443	+	1.29757i
$184$	8.10073	−	9.48777i	0.597194	−	0.699447i
$185$	3.41279	−	0.601766i	0.250913	−	0.0442427i
$186$	−10.0443	+	13.8592i	−0.736485	+	1.01621i
$187$	−7.59230	−	6.37070i	−0.555204	−	0.465872i
$188$	0.0380892	+	0.129924i	0.00277794	+	0.00947565i
$189$	−8.53976	−	1.09487i	−0.621176	−	0.0796398i
$190$	2.21638	+	1.65990i	0.160793	+	0.120422i
$191$	17.9929	+	15.0978i	1.30192	+	1.09244i	0.989810	+	0.142395i	$0.0454803\pi$
$191$	17.9929	+	15.0978i	1.30192	+	1.09244i	0.312110	+	0.950046i	$0.398964\pi$
$192$	−13.0277	+	4.72010i	−0.940192	+	0.340644i
$193$	−1.87948	−	10.6591i	−0.135288	−	0.767257i	−0.974659	−	0.223697i	$-0.928187\pi$
$193$	−1.87948	−	10.6591i	−0.135288	−	0.767257i	0.839371	−	0.543560i	$-0.182924\pi$
$194$	−11.4596	−	17.5323i	−0.822748	−	1.25874i
$195$	−3.30528	+	4.06686i	−0.236696	+	0.291234i
$196$	8.45714	−	0.939558i	0.604081	−	0.0671113i
$197$	−11.1556	+	19.3221i	−0.794806	+	1.37664i	0.128157	+	0.991754i	$0.459094\pi$
$197$	−11.1556	+	19.3221i	−0.794806	+	1.37664i	−0.922963	+	0.384890i	$0.874239\pi$
$198$	−0.619530	−	7.13038i	−0.0440281	−	0.506734i
$199$	1.06520	−	0.614992i	0.0755098	−	0.0435956i	−0.461770	−	0.887000i	$-0.652785\pi$
$199$	1.06520	−	0.614992i	0.0755098	−	0.0435956i	0.537280	+	0.843404i	$0.319452\pi$
$200$	0.114872	−	13.4055i	0.00812264	−	0.947912i
$201$	−15.0799	−	5.22247i	−1.06365	−	0.368364i
$202$	12.2851	−	0.680324i	0.864378	−	0.0478674i
$203$	−1.04130	−	1.24097i	−0.0730848	−	0.0870990i
$204$	−20.3280	−	0.980911i	−1.42325	−	0.0686775i
$205$	−0.547667	−	1.50470i	−0.0382507	−	0.105093i
$206$	1.34250	+	0.160804i	0.0935363	+	0.0112037i
$207$	12.5701	+	4.13378i	0.873679	+	0.287318i
$208$	23.6974	−	1.10872i	1.64312	−	0.0768760i
$209$	6.37630	+	1.12431i	0.441058	+	0.0777704i
$210$	2.00846	−	0.503287i	0.138597	−	0.0347301i
$211$	−9.85984	−	3.58869i	−0.678779	−	0.247055i	−0.0204559	−	0.999791i	$-0.506512\pi$
$211$	−9.85984	−	3.58869i	−0.678779	−	0.247055i	−0.658323	+	0.752735i	$0.728734\pi$
$212$	10.4539	−	5.17559i	0.717978	−	0.355461i
$213$	13.8434	−	24.8697i	0.948537	−	1.70405i
$214$	−19.9575	+	4.66984i	−1.36426	+	0.319224i
$215$	0.448450			0.0305840
$216$	−9.87283	−	10.8870i	−0.671761	−	0.740768i
$217$	−11.5781			−0.785973
$218$	−24.0458	+	5.62647i	−1.62859	+	0.381073i
$219$	2.25366	−	0.0353256i	0.152288	−	0.00238708i
$220$	0.763702	+	1.54257i	0.0514888	+	0.104000i
$221$	32.7424	+	11.9173i	2.20249	+	0.801642i
$222$	4.56741	−	15.9998i	0.306544	−	1.07383i
$223$	16.8245	+	2.96662i	1.12666	+	0.198660i	0.705761	−	0.708450i	$-0.250605\pi$
$223$	16.8245	+	2.96662i	1.12666	+	0.198660i	0.420894	+	0.907110i	$0.361716\pi$
$224$	−7.75668	−	5.26186i	−0.518265	−	0.351573i
$225$	13.2027	−	5.27964i	0.880180	−	0.351976i
$226$	2.59030	+	0.310265i	0.172304	+	0.0206385i
$227$	−1.22884	−	3.37622i	−0.0815612	−	0.224088i	0.892208	−	0.451624i	$-0.149155\pi$
$227$	−1.22884	−	3.37622i	−0.0815612	−	0.224088i	−0.973770	+	0.227536i	$0.926933\pi$
$228$	11.8211	−	6.08497i	0.782871	−	0.402987i
$229$	1.03366	+	1.23187i	0.0683063	+	0.0814042i	0.799115	−	0.601178i	$-0.205302\pi$
$229$	1.03366	+	1.23187i	0.0683063	+	0.0814042i	−0.730809	+	0.682582i	$0.760857\pi$
$230$	−3.17741	+	0.175958i	−0.209512	+	0.0116023i
$231$	3.65953	−	3.16976i	0.240779	−	0.208555i
$232$	0.0236953	−	2.76524i	0.00155567	−	0.181547i
$233$	−8.68417	+	5.01381i	−0.568919	+	0.328465i	−0.756717	−	0.653742i	$-0.773198\pi$
$233$	−8.68417	+	5.01381i	−0.568919	+	0.328465i	0.187799	+	0.982208i	$0.439865\pi$
$234$	10.6204	+	22.8112i	0.694279	+	1.49121i
$235$	0.0172679	−	0.0299089i	0.00112643	−	0.00195104i
$236$	−0.336466	−	3.02860i	−0.0219021	−	0.197145i
$237$	9.74625	+	1.56144i	0.633087	+	0.101427i
$238$	−7.53203	−	11.5234i	−0.488229	−	0.746954i
$239$	−1.87083	−	10.6100i	−0.121014	−	0.686305i	−0.983596	−	0.180387i	$-0.942265\pi$
$239$	−1.87083	−	10.6100i	−0.121014	−	0.686305i	0.862582	−	0.505918i	$-0.168846\pi$
$240$	3.16526	+	1.57285i	0.204317	+	0.101527i
$241$	1.12716	+	0.945796i	0.0726065	+	0.0609241i	0.678369	−	0.734722i	$-0.262687\pi$
$241$	1.12716	+	0.945796i	0.0726065	+	0.0609241i	−0.605762	+	0.795646i	$0.707132\pi$
$242$	−9.23009	−	6.91261i	−0.593333	−	0.444359i
$243$	6.71343	−	14.0688i	0.430667	−	0.902511i
$244$	−20.8197	+	6.10364i	−1.33284	+	0.390745i
$245$	−1.66272	−	1.39519i	−0.106227	−	0.0891352i
$246$	−7.64717	−	0.794615i	−0.487566	−	0.0506628i
$247$	−22.4168	+	3.95269i	−1.42635	+	0.251503i
$248$	−15.0308	−	12.8334i	−0.954458	−	0.814923i
$249$	−3.84655	−	0.616253i	−0.243765	−	0.0390535i
$250$	−5.12501	+	4.80760i	−0.324134	+	0.304059i
$251$	−4.82603	−	2.78631i	−0.304616	−	0.175870i	0.339898	−	0.940462i	$-0.389607\pi$
$251$	−4.82603	−	2.78631i	−0.304616	−	0.175870i	−0.644515	+	0.764592i	$0.722941\pi$
$252$	2.04398	−	9.72919i	0.128759	−	0.612881i
$253$	−6.44400	+	3.72044i	−0.405131	+	0.233902i
$254$	−4.67174	+	15.4440i	−0.293131	+	0.969043i
$255$	3.39884	+	3.92400i	0.212844	+	0.245730i
$256$	−4.23744	−	15.4287i	−0.264840	−	0.964292i
$257$	−5.16196	−	6.15179i	−0.321995	−	0.383738i	0.580630	−	0.814168i	$-0.302806\pi$
$257$	−5.16196	−	6.15179i	−0.321995	−	0.383738i	−0.902624	+	0.430430i	$0.858362\pi$
$258$	0.941608	−	1.93639i	0.0586220	−	0.120554i
$259$	10.5764	−	3.84951i	0.657188	−	0.239197i
$260$	−4.37780	−	4.17777i	−0.271500	−	0.259094i
$261$	2.72340	−	1.08907i	0.168574	−	0.0674115i
$262$	2.10600	+	4.92085i	0.130109	+	0.304011i
$263$	−5.00913	+	28.4082i	−0.308876	+	1.75173i	0.295796	+	0.955251i	$0.404415\pi$
$263$	−5.00913	+	28.4082i	−0.308876	+	1.75173i	−0.604673	+	0.796474i	$0.706696\pi$
$264$	8.26427	−	0.0587161i	0.508630	−	0.00361373i
$265$	−2.79606	−	1.01768i	−0.171761	−	0.0625158i
$266$	8.02528	+	4.05919i	0.492062	+	0.248885i
$267$	0.354030	+	22.5860i	0.0216663	+	1.38224i
$268$	7.39527	−	16.8784i	0.451738	−	1.03101i
$269$	3.32709			0.202856			0.101428	−	0.994843i	$-0.467659\pi$
$269$	3.32709			0.202856			0.101428	+	0.994843i	$0.467659\pi$
$270$	−0.270403	+	3.73914i	−0.0164562	+	0.227557i
$271$			21.4283i			1.30168i	0.759217	+	0.650838i	$0.225582\pi$
$271$			21.4283i			1.30168i	−0.759217	+	0.650838i	$0.774418\pi$
$272$	2.99469	−	23.3085i	0.181580	−	1.41329i
$273$	−8.27832	+	14.8720i	−0.501027	+	0.900094i
$274$	22.6394	+	11.4510i	1.36770	+	0.691782i
$275$	−2.73474	+	7.51363i	−0.164911	+	0.453089i
$276$	−5.91180	+	14.0894i	−0.355849	+	0.848079i
$277$	−20.0857	−	3.54166i	−1.20684	−	0.212798i	−0.466184	−	0.884688i	$-0.654372\pi$
$277$	−20.0857	−	3.54166i	−1.20684	−	0.212798i	−0.740651	+	0.671890i	$0.765483\pi$
$278$	3.20420	−	1.37131i	0.192175	−	0.0822460i
$279$	6.54887	−	19.9139i	0.392071	−	1.19221i
$280$	0.394980	+	2.35802i	0.0236046	+	0.140919i
$281$	3.46558	+	9.52160i	0.206739	+	0.568011i	0.999117	−	0.0420199i	$-0.0133793\pi$
$281$	3.46558	+	9.52160i	0.206739	+	0.568011i	−0.792378	+	0.610031i	$0.791157\pi$
$282$	−0.0928879	−	0.137362i	−0.00553140	−	0.00817976i
$283$	−7.29974	+	6.12521i	−0.433924	+	0.364106i	−0.833430	−	0.552625i	$-0.813626\pi$
$283$	−7.29974	+	6.12521i	−0.433924	+	0.364106i	0.399506	+	0.916731i	$0.369182\pi$
$284$	27.3558	+	18.2169i	1.62327	+	1.08097i
$285$	−3.20464	−	1.10983i	−0.189826	−	0.0657406i
$286$	−13.5434	−	4.09681i	−0.800837	−	0.242249i
$287$	−2.60035	−	4.50393i	−0.153494	−	0.265859i
$288$	13.4376	−	10.3649i	0.791816	−	0.610760i
$289$	8.75798	−	15.1693i	0.515175	−	0.892309i
$290$	−0.514459	+	0.482597i	−0.0302101	+	0.0283391i
$291$	19.9070	+	16.1791i	1.16697	+	0.948437i
$292$	−0.166169	+	2.59731i	−0.00972430	+	0.151996i
$293$	−3.81617	−	21.6426i	−0.222943	−	1.26437i	−0.866579	−	0.499040i	$-0.833686\pi$
$293$	−3.81617	−	21.6426i	−0.222943	−	1.26437i	0.643636	−	0.765332i	$-0.277425\pi$
$294$	−9.51556	+	4.25008i	−0.554958	+	0.247870i
$295$	−0.499632	+	0.595438i	−0.0290897	+	0.0346678i
$296$	17.9973	+	6.72569i	1.04607	+	0.390923i
$297$	3.38194	+	8.08713i	0.196240	+	0.469263i
$298$	−5.24906	−	3.93113i	−0.304070	−	0.227724i
$299$	16.8150	−	20.0394i	0.972437	−	1.15891i
$300$	4.86544	+	15.6815i	0.280906	+	0.905370i
$301$	1.43437	−	0.252918i	0.0826758	−	0.0145780i
$302$	6.27436	−	4.10109i	0.361049	−	0.235991i
$303$	−14.0779	+	5.37527i	−0.808753	+	0.308801i
$304$	5.91920	+	14.1651i	0.339490	+	0.812423i
$305$	4.79278	+	2.76711i	0.274434	+	0.158444i
$306$	24.0802	−	6.43683i	1.37657	−	0.367969i
$307$	−13.4094	−	23.2258i	−0.765315	−	1.32556i	−0.940080	−	0.340954i	$-0.889250\pi$
$307$	−13.4094	−	23.2258i	−0.765315	−	1.32556i	0.174766	−	0.984610i	$-0.444083\pi$
$308$	3.31269	+	4.50319i	0.188758	+	0.256593i
$309$	−1.62611	+	0.313081i	−0.0925060	+	0.0178105i
$310$	0.278758	+	5.03375i	0.0158324	+	0.285898i
$311$	−18.4841	+	15.5100i	−1.04814	+	0.879492i	−0.992897	−	0.118981i	$-0.962037\pi$
$311$	−18.4841	+	15.5100i	−1.04814	+	0.879492i	−0.0552415	+	0.998473i	$0.517593\pi$
$312$	−27.2315	+	10.1311i	−1.54168	+	0.573561i
$313$	−16.5696	+	6.03083i	−0.936567	+	0.340883i	−0.764809	−	0.644257i	$-0.777167\pi$
$313$	−16.5696	+	6.03083i	−0.936567	+	0.340883i	−0.171758	+	0.985139i	$0.554945\pi$
$314$	24.8219	+	2.97316i	1.40078	+	0.167785i
$315$	−2.15534	+	1.33616i	−0.121440	+	0.0752842i
$316$	−2.69176	+	11.0751i	−0.151423	+	0.623023i
$317$	0.661246	−	3.75011i	0.0371393	−	0.210627i	−0.960591	−	0.277966i	$-0.910340\pi$
$317$	0.661246	−	3.75011i	0.0371393	−	0.210627i	0.997730	+	0.0673387i	$0.0214508\pi$
$318$	−10.2652	+	9.93644i	−0.575643	+	0.557208i
$319$	−0.564111	+	1.54988i	−0.0315842	+	0.0867768i
$320$	−2.10092	+	3.49901i	−0.117445	+	0.195601i
$321$	21.5405	−	12.8907i	1.20227	−	0.719488i
$322$	−10.0637	+	2.35481i	−0.560830	+	0.131228i
$323$			22.5485i			1.25463i
$324$	15.5777	+	9.01864i	0.865427	+	0.501036i
$325$		−	28.1105i		−	1.55929i
$326$	−6.77761	−	28.9654i	−0.375377	−	1.60425i
$327$	25.9531	−	15.5314i	1.43521	−	0.858888i
$328$	1.61646	−	8.72933i	0.0892541	−	0.481997i
$329$	0.0383635	−	0.105403i	0.00211505	−	0.00581104i
$330$	−1.46621	−	1.51472i	−0.0807120	−	0.0833823i
$331$	−5.07478	+	28.7805i	−0.278935	+	1.58192i	0.447242	+	0.894413i	$0.352406\pi$
$331$	−5.07478	+	28.7805i	−0.278935	+	1.58192i	−0.726177	+	0.687508i	$0.758705\pi$
$332$	1.06236	−	4.37100i	0.0583043	−	0.239890i
$333$	0.638698	+	20.3684i	0.0350004	+	1.11618i
$334$	2.91004	−	24.2949i	0.159230	−	1.32936i
$335$	−4.41701	+	1.60766i	−0.241327	+	0.0878359i
$336$	11.0112	+	3.24562i	0.600709	+	0.177063i
$337$	9.49374	−	7.96619i	0.517157	−	0.433946i	−0.346482	−	0.938056i	$-0.612624\pi$
$337$	9.49374	−	7.96619i	0.517157	−	0.433946i	0.863639	+	0.504110i	$0.168180\pi$
$338$	31.3117	−	1.73398i	1.70313	−	0.0943159i
$339$	−3.13751	+	0.604077i	−0.170406	+	0.0328090i
$340$	−4.82864	+	3.55210i	−0.261870	+	0.192640i
$341$	5.89404	+	10.2088i	0.319180	+	0.552836i
$342$	−11.5209	+	11.5072i	−0.622982	+	0.622237i
$343$	−16.1497	−	9.32403i	−0.872001	−	0.503450i
$344$	2.14246	+	1.26155i	0.115514	+	0.0680181i
$345$	3.64109	−	1.39025i	0.196030	−	0.0748487i
$346$	18.9209	+	28.9476i	1.01719	+	1.55623i
$347$	29.4108	−	5.18591i	1.57885	−	0.278394i	0.685610	−	0.727969i	$-0.259535\pi$
$347$	29.4108	−	5.18591i	1.57885	−	0.278394i	0.893243	+	0.449574i	$0.148424\pi$
$348$	1.00363	+	3.23472i	0.0538000	+	0.173399i
$349$	−6.13674	+	7.31348i	−0.328492	+	0.391482i	−0.904860	−	0.425708i	$-0.860025\pi$
$349$	−6.13674	+	7.31348i	−0.328492	+	0.391482i	0.576368	+	0.817190i	$0.304469\pi$
$350$	−6.65770	+	8.88972i	−0.355869	+	0.475175i
$351$	−20.8968	−	22.6504i	−1.11539	−	1.20899i
$352$	−0.690870	+	9.51795i	−0.0368235	+	0.507309i
$353$	11.2479	−	13.4047i	0.598664	−	0.713461i	−0.378582	−	0.925568i	$-0.623588\pi$
$353$	11.2479	−	13.4047i	0.598664	−	0.713461i	0.977246	+	0.212107i	$0.0680326\pi$
$354$	1.52200	+	3.40763i	0.0808934	+	0.181113i
$355$	−1.45579	−	8.25619i	−0.0772653	−	0.438193i
$356$	−26.0300	−	1.66533i	−1.37959	−	0.0882622i
$357$	13.0843	+	10.6341i	0.692494	+	0.562814i
$358$	12.4351	+	13.2561i	0.657218	+	0.700609i
$359$	7.81239	−	13.5314i	0.412322	−	0.714163i	−0.582821	−	0.812600i	$-0.698051\pi$
$359$	7.81239	−	13.5314i	0.412322	−	0.714163i	0.995143	+	0.0984378i	$0.0313845\pi$
$360$	−4.27912	−	0.654407i	−0.225529	−	0.0344903i
$361$	2.13480	+	3.69758i	0.112358	+	0.194609i
$362$	2.61906	−	8.65818i	0.137655	−	0.455064i
$363$	13.3457	+	4.62186i	0.700465	+	0.242585i
$364$	−16.3586	−	10.8936i	−0.857425	−	0.570981i
$365$	0.508561	−	0.426733i	0.0266193	−	0.0223362i
$366$	22.0116	−	14.8849i	1.15057	−	0.778046i
$367$	−4.58311	−	12.5920i	−0.239236	−	0.657296i	−0.999966	−	0.00822764i	$-0.997381\pi$
$367$	−4.58311	−	12.5920i	−0.239236	−	0.657296i	0.760730	−	0.649069i	$-0.224841\pi$
$368$	−15.6750	−	8.09782i	−0.817114	−	0.422128i
$369$	9.21740	−	1.92495i	0.479839	−	0.100209i
$370$	−1.92827	−	4.50558i	−0.100246	−	0.234234i
$371$	−9.51718	−	1.67814i	−0.494108	−	0.0871245i
$372$	22.3208	+	9.36566i	1.15728	+	0.485587i
$373$	−2.05166	+	5.63688i	−0.106231	+	0.291867i	−0.981407	−	0.191937i	$-0.938523\pi$
$373$	−2.05166	+	5.63688i	−0.106231	+	0.291867i	0.875176	+	0.483804i	$0.160745\pi$
$374$	−6.32627	+	12.5074i	−0.327124	+	0.646744i
$375$	4.18580	−	7.51979i	0.216154	−	0.388320i
$376$	0.166635	−	0.0943120i	0.00859352	−	0.00486377i
$377$		−	5.79853i		−	0.298640i
$378$	1.24393	+	12.1122i	0.0639808	+	0.622984i
$379$	7.22372			0.371057			0.185529	−	0.982639i	$-0.440600\pi$
$379$	7.22372			0.371057			0.185529	+	0.982639i	$0.440600\pi$
$380$	1.57157	−	3.58684i	0.0806200	−	0.184001i
$381$	−0.309717	−	19.7590i	−0.0158673	−	1.01228i
$382$	14.9925	−	29.6412i	0.767085	−	1.51658i
$383$	3.09179	+	1.12532i	0.157983	+	0.0575012i	0.419801	−	0.907616i	$-0.362100\pi$
$383$	3.09179	+	1.12532i	0.157983	+	0.0575012i	−0.261818	+	0.965117i	$0.584322\pi$
$384$	10.6973	+	16.4185i	0.545894	+	0.837854i
$385$	0.247623	−	1.40434i	0.0126201	−	0.0715719i
$386$	−14.0722	+	6.02252i	−0.716254	+	0.306538i
$387$	−0.376308	+	2.61012i	−0.0191288	+	0.132680i
$388$	−20.4499	+	21.4291i	−1.03819	+	1.08790i
$389$	14.6598	−	5.33573i	0.743282	−	0.270532i	0.0575057	−	0.998345i	$-0.481685\pi$
$389$	14.6598	−	5.33573i	0.743282	−	0.270532i	0.685776	+	0.727813i	$0.259463\pi$
$390$	6.66513	+	3.24106i	0.337502	+	0.164117i
$391$	−16.6568	−	19.8508i	−0.842372	−	1.00390i
$392$	−4.01875	−	11.3429i	−0.202978	−	0.572903i
$393$	−4.29200	−	4.95517i	−0.216503	−	0.249955i
$394$	30.2014	+	9.13577i	1.52152	+	0.460253i
$395$	2.51778	−	1.45364i	0.126684	−	0.0731408i
$396$	−9.61906	+	3.15057i	−0.483376	+	0.158322i
$397$	−5.69844	−	3.28999i	−0.285996	−	0.165120i	0.350139	−	0.936698i	$-0.386134\pi$
$397$	−5.69844	−	3.28999i	−0.285996	−	0.165120i	−0.636135	+	0.771578i	$0.719468\pi$
$398$	−1.19007	−	1.26864i	−0.0596529	−	0.0635913i
$399$	−10.8760	−	1.74244i	−0.544481	−	0.0872309i
$400$	−18.4966	+	4.16118i	−0.924832	+	0.208059i
$401$	−2.96062	+	0.522037i	−0.147846	+	0.0260693i	−0.247081	−	0.968995i	$-0.579472\pi$
$401$	−2.96062	+	0.522037i	−0.147846	+	0.0260693i	0.0992351	+	0.995064i	$0.468360\pi$
$402$	−2.33257	+	22.4480i	−0.116338	+	1.11961i
$403$	−31.7470	−	26.6389i	−1.58143	−	1.32698i
$404$	−4.89518	−	16.6976i	−0.243545	−	0.830738i
$405$	−1.07903	−	4.46286i	−0.0536174	−	0.221761i
$406$	−1.37332	+	1.83374i	−0.0681570	+	0.0910069i
$407$	−8.77836	−	7.36592i	−0.435127	−	0.365115i
$408$	5.19913	+	28.3082i	0.257395	+	1.40146i
$409$	0.375248	+	2.12813i	0.0185548	+	0.105229i	0.992679	−	0.120785i	$-0.0385413\pi$
$409$	0.375248	+	2.12813i	0.0185548	+	0.105229i	−0.974124	+	0.226015i	$0.927430\pi$
$410$	−1.89554	+	1.23898i	−0.0936142	+	0.0611887i
$411$	−30.6813	−	4.91543i	−1.51340	−	0.242460i
$412$	−0.211134	−	1.90046i	−0.0104018	−	0.0936289i
$413$	−1.26226	+	2.18630i	−0.0621118	+	0.107581i
$414$	1.64212	−	18.6411i	0.0807060	−	0.916162i
$415$	−0.993693	+	0.573709i	−0.0487785	+	0.0281623i
$416$	−9.16222	−	32.2745i	−0.449215	−	1.58239i
$417$	−3.22655	+	2.79473i	−0.158005	+	0.136858i
$418$	−0.506295	−	9.14255i	−0.0247637	−	0.447177i
$419$	18.8142	+	22.4219i	0.919134	+	1.09538i	0.995159	+	0.0982753i	$0.0313326\pi$
$419$	18.8142	+	22.4219i	0.919134	+	1.09538i	−0.0760253	+	0.997106i	$0.524223\pi$
$420$	−1.34018	−	2.60353i	−0.0653940	−	0.127039i
$421$	3.99170	+	10.9671i	0.194544	+	0.534504i	0.998159	−	0.0606441i	$-0.0193155\pi$
$421$	3.99170	+	10.9671i	0.194544	+	0.534504i	−0.803616	+	0.595148i	$0.797093\pi$
$422$	−1.76477	+	14.7335i	−0.0859077	+	0.717215i
$423$	0.159589	+	0.125602i	0.00775949	+	0.00610698i
$424$	−10.4952	−	12.7276i	−0.509693	−	0.618108i
$425$	−27.4230	−	4.83542i	−1.33021	−	0.234552i
$426$	−38.7066	−	11.0494i	−1.87534	−	0.535347i
$427$	16.8903	+	6.14758i	0.817381	+	0.297502i
$428$	12.8609	+	25.9771i	0.621656	+	1.25565i
$429$	17.3273	−	0.271602i	0.836572	−	0.0131131i
$430$	−0.144494	−	0.617524i	−0.00696814	−	0.0297797i
$431$	−20.3897			−0.982136			−0.491068	−	0.871121i	$-0.663393\pi$
$431$	−20.3897			−0.982136			−0.491068	+	0.871121i	$0.663393\pi$
$432$	−11.8105	+	17.1030i	−0.568234	+	0.822867i
$433$	−38.5969			−1.85485			−0.927424	−	0.374013i	$-0.877982\pi$
$433$	−38.5969			−1.85485			−0.927424	+	0.374013i	$0.877982\pi$
$434$	3.73056	+	15.9433i	0.179073	+	0.765302i
$435$	0.420179	−	0.754852i	0.0201460	−	0.0361924i
$436$	15.4955	+	31.2986i	0.742101	+	1.49893i
$437$	15.9077	+	5.78994i	0.760970	+	0.276970i
$438$	−0.774792	−	3.09195i	−0.0370210	−	0.147739i
$439$	33.3328	+	5.87748i	1.59089	+	0.280517i	0.897823	−	0.440357i	$-0.145148\pi$
$439$	33.3328	+	5.87748i	1.59089	+	0.280517i	0.693066	+	0.720874i	$0.256259\pi$
$440$	1.87807	−	1.54866i	0.0895335	−	0.0738295i
$441$	9.51566	−	8.50680i	0.453127	−	0.405086i
$442$	5.86042	−	48.9268i	0.278752	−	2.32721i
$443$	−2.99923	−	8.24032i	−0.142498	−	0.391509i	0.847828	−	0.530271i	$-0.177910\pi$
$443$	−2.99923	−	8.24032i	−0.142498	−	0.391509i	−0.990326	+	0.138762i	$0.955688\pi$
$444$	−23.5037	−	1.13415i	−1.11543	−	0.0538243i
$445$	4.27668	+	5.09675i	0.202734	+	0.241609i
$446$	−1.33591	−	24.1236i	−0.0632574	−	1.14229i
$447$	7.58954	+	2.62841i	0.358973	+	0.124319i
$448$	−4.74642	+	12.3765i	−0.224247	+	0.584735i
$449$	23.7529	−	13.7138i	1.12097	−	0.647193i	0.179322	−	0.983790i	$-0.442610\pi$
$449$	23.7529	−	13.7138i	1.12097	−	0.647193i	0.941648	+	0.336598i	$0.109276\pi$
$450$	−11.5242	−	16.4792i	−0.543256	−	0.776838i
$451$	−2.64751	+	4.58561i	−0.124666	+	0.215928i
$452$	−0.407376	−	3.66686i	−0.0191613	−	0.172475i
$453$	−5.79010	+	7.12422i	−0.272043	+	0.334725i
$454$	−4.25318	+	2.77999i	−0.199611	+	0.130471i
$455$	0.870556	+	4.93717i	0.0408123	+	0.231458i
$456$	−12.1880	−	14.3172i	−0.570754	−	0.670466i
$457$	9.51099	+	7.98067i	0.444905	+	0.373320i	0.837541	−	0.546374i	$-0.183992\pi$
$457$	9.51099	+	7.98067i	0.444905	+	0.373320i	−0.392636	+	0.919694i	$0.628437\pi$
$458$	1.36325	−	1.82029i	0.0637007	−	0.0850566i
$459$	−25.6910	+	16.4896i	−1.19915	+	0.769666i
$460$	1.26608	+	4.31866i	0.0590315	+	0.201358i
$461$	−10.2480	−	8.59913i	−0.477299	−	0.400502i	0.372150	−	0.928173i	$-0.378621\pi$
$461$	−10.2480	−	8.59913i	−0.477299	−	0.400502i	−0.849449	+	0.527671i	$0.823065\pi$
$462$	−5.54395	−	4.01792i	−0.257928	−	0.186930i
$463$	23.4427	−	4.13359i	1.08948	−	0.192104i	0.400074	−	0.916483i	$-0.368984\pi$
$463$	23.4427	−	4.13359i	1.08948	−	0.192104i	0.689402	+	0.724379i	$0.257873\pi$
$464$	−3.81542	+	0.858353i	−0.177126	+	0.0398481i
$465$	−2.20248	−	5.76832i	−0.102138	−	0.267500i
$466$	9.70222	+	10.3428i	0.449447	+	0.479120i
$467$	−24.0938	−	13.9106i	−1.11493	−	0.643704i	−0.174827	−	0.984599i	$-0.555937\pi$
$467$	−24.0938	−	13.9106i	−1.11493	−	0.643704i	−0.940101	+	0.340895i	$0.889270\pi$
$468$	27.9894	−	21.9745i	1.29381	−	1.01577i
$469$	−13.2212	+	7.63324i	−0.610496	+	0.352470i
$470$	−0.0467490	−	0.0141414i	−0.00215637	−	0.000652292i
$471$	−30.0656	+	5.78865i	−1.38535	+	0.266727i
$472$	−4.06202	+	1.43916i	−0.186970	+	0.0662427i
$473$	−0.953199	−	1.13598i	−0.0438281	−	0.0522323i
$474$	−0.990188	−	13.9239i	−0.0454809	−	0.639545i
$475$	17.0941	−	6.22176i	0.784333	−	0.285474i
$476$	−13.4411	+	14.0847i	−0.616073	+	0.645571i
$477$	8.26949	−	15.4200i	0.378634	−	0.706032i
$478$	−14.0074	+	5.99481i	−0.640684	+	0.274196i
$479$	4.28076	−	24.2774i	0.195593	−	1.10926i	−0.715979	−	0.698122i	$-0.754019\pi$
$479$	4.28076	−	24.2774i	0.195593	−	1.10926i	0.911572	−	0.411141i	$-0.134869\pi$
$480$	1.14597	−	4.86541i	0.0523062	−	0.222074i
$481$	37.8574	+	13.7790i	1.72615	+	0.628266i
$482$	0.939201	−	1.85686i	0.0427794	−	0.0845776i
$483$	10.8620	−	6.50025i	0.494237	−	0.295771i
$484$	−6.54479	+	14.9373i	−0.297490	+	0.678969i
$485$	7.55575			0.343089
$486$	−21.5361	−	4.71145i	−0.976896	−	0.213716i
$487$			27.8176i			1.26054i	0.776377	+	0.630268i	$0.217055\pi$
$487$			27.8176i			1.26054i	−0.776377	+	0.630268i	$0.782945\pi$
$488$	15.1131	+	26.7025i	0.684138	+	1.20876i
$489$	18.7090	+	31.2629i	0.846051	+	1.41376i
$490$	−1.38546	+	2.73914i	−0.0625886	+	0.123742i
$491$	−9.82839	+	27.0033i	−0.443549	+	1.21864i	0.493593	+	0.869693i	$0.335683\pi$
$491$	−9.82839	+	27.0033i	−0.443549	+	1.21864i	−0.937142	+	0.348948i	$0.886539\pi$
$492$	1.36978	+	10.7863i	0.0617546	+	0.486285i
$493$	−5.65672	−	0.997432i	−0.254766	−	0.0449221i
$494$	12.6658	+	29.5948i	0.569862	+	1.33153i
$495$	2.27535	+	1.22023i	0.102269	+	0.0548454i
$496$	−12.8288	+	24.8328i	−0.576031	+	1.11502i
$497$	−9.31271	−	25.5865i	−0.417732	−	1.14771i
$498$	0.390797	+	5.49533i	0.0175120	+	0.246252i
$499$	9.51361	−	7.98287i	0.425888	−	0.357362i	−0.404510	−	0.914534i	$-0.632558\pi$
$499$	9.51361	−	7.98287i	0.425888	−	0.357362i	0.830398	+	0.557171i	$0.188113\pi$
$500$	8.27148	+	5.50818i	0.369912	+	0.246333i
$501$	5.66576	+	29.4273i	0.253127	+	1.31472i
$502$	−2.28182	+	7.54331i	−0.101842	+	0.336674i
$503$	4.48697	+	7.77165i	0.200064	+	0.346521i	0.948549	−	0.316631i	$-0.102552\pi$
$503$	4.48697	+	7.77165i	0.200064	+	0.346521i	−0.748485	+	0.663152i	$0.769218\pi$
$504$	−14.0559	+	0.320222i	−0.626098	+	0.0142638i
$505$	−2.21925	+	3.84386i	−0.0987555	+	0.171050i
$506$	7.19943	+	7.67475i	0.320054	+	0.341184i
$507$	−35.8810	+	13.7002i	−1.59353	+	0.608448i
$508$	22.7720	+	1.45689i	1.01034	+	0.0646389i
$509$	−6.33516	−	35.9285i	−0.280801	−	1.59250i	−0.719909	−	0.694068i	$-0.755817\pi$
$509$	−6.33516	−	35.9285i	−0.280801	−	1.59250i	0.439108	−	0.898434i	$-0.355294\pi$
$510$	4.30829	−	5.94461i	0.190774	−	0.263232i
$511$	1.38597	−	1.65173i	0.0613115	−	0.0730682i
$512$	−19.8802	+	10.8063i	−0.878591	+	0.477575i
$513$	9.14866	−	17.7207i	0.403923	−	0.782388i
$514$	−6.80791	+	9.09028i	−0.300284	+	0.400955i
$515$	−0.313522	+	0.373641i	−0.0138154	+	0.0164646i
$516$	−2.96984	−	0.672692i	−0.130740	−	0.0296136i
$517$	−0.112467	+	0.0198309i	−0.00494627	+	0.000872161i
$518$	−8.70867	−	13.3236i	−0.382637	−	0.585406i
$519$	−32.8685	−	26.7134i	−1.44277	−	1.17259i
$520$	−4.34230	+	7.37443i	−0.190423	+	0.323390i
$521$	−27.3231	−	15.7750i	−1.19705	−	0.691115i	−0.237151	−	0.971473i	$-0.576214\pi$
$521$	−27.3231	−	15.7750i	−1.19705	−	0.691115i	−0.959896	+	0.280358i	$0.909547\pi$
$522$	−2.37717	−	3.39927i	−0.104046	−	0.148782i
$523$	7.07743	+	12.2585i	0.309475	+	0.536026i	0.978248	−	0.207441i	$-0.0665135\pi$
$523$	7.07743	+	12.2585i	0.309475	+	0.536026i	−0.668773	+	0.743467i	$0.733180\pi$
$524$	6.09753	−	4.48554i	0.266372	−	0.195952i
$525$	4.45142	−	12.8535i	0.194276	−	0.560973i
$526$	40.7326	−	2.25569i	1.77603	−	0.0983526i
$527$	−31.4483	+	26.3883i	−1.36991	+	1.14949i
$528$	−2.74367	−	11.3611i	−0.119403	−	0.494430i
$529$	3.33127	−	1.21248i	0.144838	−	0.0527166i
$530$	−0.500455	+	4.17814i	−0.0217384	+	0.181487i
$531$	−3.04638	−	3.40766i	−0.132202	−	0.147880i
$532$	3.00377	−	12.3589i	0.130230	−	0.535825i
$533$	3.23253	−	18.3326i	0.140016	−	0.794072i
$534$	30.9872	−	7.76489i	1.34095	−	0.336020i
$535$	2.52886	−	6.94799i	0.109332	−	0.300388i
$536$	−25.6247	−	4.74507i	−1.10682	−	0.204956i
$537$	−19.4504	−	10.8268i	−0.839346	−	0.467212i
$538$	−1.07202	−	4.58147i	−0.0462179	−	0.197521i
$539$			7.17740i			0.309152i
$540$	5.23600	−	0.832433i	0.225321	−	0.0358222i
$541$		−	9.11080i		−	0.391704i	−0.980633	−	0.195852i	$-0.937253\pi$
$541$		−	9.11080i		−	0.391704i	0.980633	−	0.195852i	$-0.0627472\pi$
$542$	29.5072	−	6.90437i	1.26744	−	0.296568i
$543$	0.173633	+	11.0772i	0.00745130	+	0.475370i
$544$	−33.0612	+	3.38646i	−1.41749	+	0.145193i
$545$	3.04690	−	8.37130i	0.130515	−	0.358587i
$546$	23.1464	+	6.60752i	0.990573	+	0.282776i
$547$	4.50829	−	25.5678i	0.192761	−	1.09320i	−0.722811	−	0.691045i	$-0.757150\pi$
$547$	4.50829	−	25.5678i	0.192761	−	1.09320i	0.915572	−	0.402154i	$-0.131738\pi$
$548$	8.47368	−	34.8645i	0.361978	−	1.48934i
$549$	−20.1272	+	25.5735i	−0.859008	+	1.09145i
$550$	11.2276	+	1.34483i	0.478745	+	0.0573438i
$551$	3.52612	−	1.28340i	0.150218	−	0.0546747i
$552$	21.3061	+	3.60096i	0.906850	+	0.153267i
$553$	7.23333	−	6.06948i	0.307592	−	0.258101i
$554$	1.59486	+	28.7996i	0.0677592	+	1.22358i
$555$	3.92980	+	4.53700i	0.166811	+	0.192585i
$556$	−2.92075	−	3.97039i	−0.123867	−	0.168382i
$557$	16.1779	+	28.0210i	0.685481	+	1.18729i	0.973285	+	0.229598i	$0.0737413\pi$
$557$	16.1779	+	28.0210i	0.685481	+	1.18729i	−0.287805	+	0.957689i	$0.592925\pi$
$558$	−29.5319	−	2.60151i	−1.25018	−	0.110131i
$559$	4.51494	+	2.60670i	0.190962	+	0.110252i
$560$	3.11978	−	1.30367i	0.131835	−	0.0550901i
$561$	2.71560	−	16.9503i	0.114653	−	0.715642i
$562$	11.9948	−	7.84011i	0.505969	−	0.330715i
$563$	−7.33135	+	1.29271i	−0.308980	+	0.0544814i	−0.325988	−	0.945374i	$-0.605697\pi$
$563$	−7.33135	+	1.29271i	−0.308980	+	0.0544814i	0.0170084	+	0.999855i	$0.494586\pi$
$564$	−0.159220	+	0.172168i	−0.00670438	+	0.00724956i
$565$	−0.604928	+	0.720925i	−0.0254495	+	0.0303296i
$566$	10.7866	+	8.07829i	0.453393	+	0.339556i
$567$	−5.96827	−	13.6660i	−0.250644	−	0.573916i
$568$	16.2707	−	43.5390i	0.682705	−	1.82686i
$569$	−10.1877	+	12.1413i	−0.427091	+	0.508988i	−0.936081	−	0.351785i	$-0.885575\pi$
$569$	−10.1877	+	12.1413i	−0.427091	+	0.508988i	0.508989	+	0.860773i	$0.330019\pi$
$570$	−0.495695	+	4.77044i	−0.0207624	+	0.199812i
$571$	5.66390	+	32.1216i	0.237027	+	1.34425i	0.838303	+	0.545204i	$0.183548\pi$
$571$	5.66390	+	32.1216i	0.237027	+	1.34425i	−0.601276	+	0.799041i	$0.705341\pi$
$572$	−1.27759	+	19.9695i	−0.0534189	+	0.834967i
$573$	−6.43565	+	40.1702i	−0.268853	+	1.67814i
$574$	−5.36415	+	5.03193i	−0.223895	+	0.210029i
$575$	−10.4530	+	18.1050i	−0.435918	+	0.755033i
$576$	−18.6024	−	15.1641i	−0.775100	−	0.631838i
$577$	−4.95348	−	8.57967i	−0.206216	−	0.357176i	0.744304	−	0.667841i	$-0.232782\pi$
$577$	−4.95348	−	8.57967i	−0.206216	−	0.357176i	−0.950519	+	0.310665i	$0.899448\pi$
$578$	−23.7103	−	7.17224i	−0.986217	−	0.298326i
$579$	14.1703	−	12.2738i	0.588898	−	0.510084i
$580$	0.830308	+	0.552923i	0.0344767	+	0.0229589i
$581$	−2.85477	+	2.39544i	−0.118436	+	0.0993796i
$582$	15.8648	−	32.6254i	0.657616	−	1.35237i
$583$	3.36523	+	9.24588i	0.139373	+	0.382925i
$584$	3.63009	−	0.608058i	0.150214	−	0.0251616i
$585$	−8.98414	−	1.29527i	−0.371449	−	0.0535527i
$586$	−28.5726	+	12.2284i	−1.18032	+	0.505149i
$587$	37.8187	+	6.66846i	1.56095	+	0.275237i	0.886373	−	0.462971i	$-0.153217\pi$
$587$	37.8187	+	6.66846i	1.56095	+	0.275237i	0.674573	+	0.738208i	$0.264328\pi$
$588$	8.91843	+	11.7337i	0.367790	+	0.483889i
$589$	9.17260	−	25.2015i	0.377951	−	1.03841i
$590$	0.980916	+	0.496148i	0.0403837	+	0.0204261i
$591$	−38.6395	+	0.605665i	−1.58942	+	0.0249137i
$592$	3.46251	−	26.9497i	0.142308	−	1.10763i
$593$			46.0294i			1.89020i	0.326782	+	0.945100i	$0.394036\pi$
$593$			46.0294i			1.89020i	−0.326782	+	0.945100i	$0.605964\pi$
$594$	10.0465	−	7.26274i	0.412211	−	0.297994i
$595$	4.96617			0.203593
$596$	−3.72195	+	8.49470i	−0.152457	+	0.347956i
$597$	1.86144	+	1.03615i	0.0761838	+	0.0424068i
$598$	−33.0125	−	16.6978i	−1.34998	−	0.682822i
$599$	−17.8974	−	6.51412i	−0.731268	−	0.266160i	−0.0505667	−	0.998721i	$-0.516103\pi$
$599$	−17.8974	−	6.51412i	−0.731268	−	0.266160i	−0.680702	+	0.732561i	$0.738325\pi$
$600$	20.0260	−	11.7525i	0.817558	−	0.479794i
$601$	−3.92238	+	22.2449i	−0.159997	+	0.907389i	0.794077	+	0.607818i	$0.207955\pi$
$601$	−3.92238	+	22.2449i	−0.159997	+	0.907389i	−0.954074	+	0.299572i	$0.903156\pi$
$602$	−0.810440	−	1.89367i	−0.0330311	−	0.0771800i
$603$	−5.65064	−	27.0574i	−0.230112	−	1.10186i
$604$	−7.66892	−	7.31851i	−0.312044	−	0.297786i
$605$	3.90904	−	1.42277i	0.158925	−	0.0578440i
$606$	11.9379	+	17.6536i	0.484942	+	0.717127i
$607$	8.73413	+	10.4089i	0.354508	+	0.422486i	0.913596	−	0.406622i	$-0.133293\pi$
$607$	8.73413	+	10.4089i	0.354508	+	0.422486i	−0.559089	+	0.829108i	$0.688849\pi$
$608$	17.5984	−	12.7150i	0.713708	−	0.515660i
$609$	0.918223	−	2.65137i	0.0372083	−	0.107439i
$610$	2.26609	−	7.49133i	0.0917514	−	0.303315i
$611$	0.347702	−	0.200746i	0.0140665	−	0.00812131i
$612$	−16.6225	−	31.0849i	−0.671923	−	1.25653i
$613$	25.2780	+	14.5943i	1.02097	+	0.589457i	0.914384	−	0.404847i	$-0.132675\pi$
$613$	25.2780	+	14.5943i	1.02097	+	0.589457i	0.106584	+	0.994304i	$0.466009\pi$
$614$	−27.6617	+	25.9485i	−1.11633	+	1.04720i
$615$	1.74924	−	2.15229i	0.0705363	−	0.0867888i
$616$	5.13361	−	6.01261i	0.206839	−	0.242255i
$617$	9.44021	−	1.66456i	0.380048	−	0.0670128i	0.0196393	−	0.999807i	$-0.493748\pi$
$617$	9.44021	−	1.66456i	0.380048	−	0.0670128i	0.360409	+	0.932794i	$0.382637\pi$
$618$	0.955063	+	2.13830i	0.0384183	+	0.0860151i
$619$	21.0382	+	17.6531i	0.845596	+	0.709539i	0.958815	−	0.284031i	$-0.0916717\pi$
$619$	21.0382	+	17.6531i	0.845596	+	0.709539i	−0.113219	+	0.993570i	$0.536116\pi$
$620$	6.84175	−	2.00577i	0.274771	−	0.0805537i
$621$	5.03636	+	22.3589i	0.202102	+	0.897230i
$622$	27.3133	+	20.4555i	1.09516	+	0.820192i
$623$	16.5535	+	13.8900i	0.663201	+	0.556492i
$624$	22.7249	+	34.2339i	0.909725	+	1.37045i
$625$	3.67505	+	20.8422i	0.147002	+	0.833690i
$626$	13.6434	+	20.8734i	0.545301	+	0.834270i
$627$	4.00026	+	10.4767i	0.159755	+	0.418400i
$628$	−3.90373	−	35.1382i	−0.155776	−	1.40217i
$629$	19.9540	−	34.5613i	0.795618	−	1.37805i
$630$	2.53439	+	2.53742i	0.100972	+	0.101093i
$631$	29.5141	−	17.0400i	1.17494	−	0.678350i	0.220099	−	0.975477i	$-0.429362\pi$
$631$	29.5141	−	17.0400i	1.17494	−	0.678350i	0.954838	+	0.297127i	$0.0960285\pi$
$632$	16.1179	+	0.138114i	0.641137	+	0.00549389i
$633$	−3.43596	−	17.8460i	−0.136567	−	0.709314i
$634$	−5.37704	+	0.297769i	−0.213549	+	0.0118259i
$635$	−3.74139	−	4.45881i	−0.148472	−	0.176943i
$636$	16.9902	+	10.9337i	0.673705	+	0.433551i
$637$	−8.63026	−	23.7114i	−0.341943	−	0.939481i
$638$	2.31598	+	0.277407i	0.0916905	+	0.0109826i
$639$	49.2752	−	1.54513i	1.94930	−	0.0611245i
$640$	5.49514	+	1.76559i	0.217215	+	0.0697911i
$641$	−5.60146	−	0.987689i	−0.221244	−	0.0390114i	0.0619270	−	0.998081i	$-0.480275\pi$
$641$	−5.60146	−	0.987689i	−0.221244	−	0.0390114i	−0.283171	+	0.959069i	$0.591387\pi$
$642$	−24.6912	−	25.5081i	−0.974486	−	1.00673i
$643$	−12.5515	−	4.56839i	−0.494984	−	0.180160i	0.0824524	−	0.996595i	$-0.473725\pi$
$643$	−12.5515	−	4.56839i	−0.494984	−	0.180160i	−0.577437	+	0.816435i	$0.695947\pi$
$644$	6.48523	+	13.0992i	0.255554	+	0.516181i
$645$	0.398864	+	0.666506i	0.0157053	+	0.0262436i
$646$	31.0497	−	7.26531i	1.22163	−	0.285850i
$647$	9.31643			0.366267			0.183133	−	0.983088i	$-0.441376\pi$
$647$	9.31643			0.366267			0.183133	+	0.983088i	$0.441376\pi$
$648$	7.39958	−	24.3566i	0.290683	−	0.956819i
$649$	2.57031			0.100893
$650$	−38.7087	+	9.05744i	−1.51828	+	0.355262i
$651$	−10.2979	−	17.2079i	−0.403606	−	0.674430i
$652$	−37.7021	+	18.6658i	−1.47653	+	0.731009i
$653$	−0.849632	−	0.309241i	−0.0332487	−	0.0121015i	0.325342	−	0.945596i	$-0.394520\pi$
$653$	−0.849632	−	0.309241i	−0.0332487	−	0.0121015i	−0.358591	+	0.933495i	$0.616743\pi$
$654$	−29.7493	−	30.7336i	−1.16329	−	1.20178i
$655$	−1.90154	−	0.335294i	−0.0742995	−	0.0131010i
$656$	−12.5413	+	0.586766i	−0.489655	+	0.0229094i
$657$	2.05697	+	3.31807i	0.0802501	+	0.129450i
$658$	−0.157503	−	0.0188656i	−0.00614009	−	0.000735457i
$659$	0.880523	+	2.41922i	0.0343003	+	0.0942394i	0.955661	−	0.294470i	$-0.0951432\pi$
$659$	0.880523	+	2.41922i	0.0343003	+	0.0942394i	−0.921360	+	0.388710i	$0.872921\pi$
$660$	−1.61337	+	2.50705i	−0.0628003	+	0.0975867i
$661$	13.7378	+	16.3720i	0.534337	+	0.636798i	0.963908	−	0.266235i	$-0.0857796\pi$
$661$	13.7378	+	16.3720i	0.534337	+	0.636798i	−0.429571	+	0.903033i	$0.641335\pi$
$662$	41.2665	−	2.28525i	1.60387	−	0.0888188i
$663$	11.4101	+	59.2627i	0.443131	+	2.30157i
$664$	−6.36126	−	0.0545095i	−0.246865	−	0.00211538i
$665$	−2.80963	+	1.62214i	−0.108953	+	0.0629040i
$666$	27.8419	−	7.44238i	1.07885	−	0.288386i
$667$	−2.15620	+	3.73464i	−0.0834882	+	0.144606i
$668$	−34.3922	+	3.82086i	−1.33068	+	0.147833i
$669$	10.5551	+	27.6440i	0.408084	+	1.06878i
$670$	3.63698	+	5.56431i	0.140509	+	0.214968i
$671$	−3.17782	−	18.0223i	−0.122678	−	0.695743i
$672$	0.921390	−	16.2084i	0.0355434	−	0.625251i
$673$	3.15078	+	2.64382i	0.121454	+	0.101912i	0.701492	−	0.712678i	$-0.252518\pi$
$673$	3.15078	+	2.64382i	0.121454	+	0.101912i	−0.580038	+	0.814590i	$0.696962\pi$
$674$	−14.0286	−	10.5063i	−0.540360	−	0.404687i
$675$	19.5897	+	14.9265i	0.754007	+	0.574523i
$676$	−12.4766	−	42.5581i	−0.479870	−	1.63685i
$677$	−19.3668	−	16.2506i	−0.744325	−	0.624563i	0.189670	−	0.981848i	$-0.439258\pi$
$677$	−19.3668	−	16.2506i	−0.744325	−	0.624563i	−0.933995	+	0.357285i	$0.883702\pi$
$678$	1.84276	+	4.12577i	0.0707707	+	0.158449i
$679$	24.1671	−	4.26132i	0.927450	−	0.163534i
$680$	6.44714	+	5.50461i	0.247236	+	0.211092i
$681$	3.92491	−	4.82926i	0.150403	−	0.185058i
$682$	12.1586	−	11.4056i	0.465576	−	0.436742i
$683$	18.2431	+	10.5327i	0.698053	+	0.403021i	0.806622	−	0.591068i	$-0.201293\pi$
$683$	18.2431	+	10.5327i	0.698053	+	0.403021i	−0.108569	+	0.994089i	$0.534627\pi$
$684$	19.5577	+	12.1569i	0.747809	+	0.464829i
$685$	−7.92601	+	4.57608i	−0.302837	+	0.174843i
$686$	−7.63580	+	25.2427i	−0.291536	+	0.963771i
$687$	−0.911489	+	2.63193i	−0.0347755	+	0.100414i
$688$	1.04686	−	3.35669i	0.0399111	−	0.127972i
$689$	−22.2349	−	26.4985i	−0.847082	−	1.00951i
$690$	−3.08759	−	4.56590i	−0.117543	−	0.173821i
$691$	−11.4191	+	4.15621i	−0.434403	+	0.158110i	−0.549960	−	0.835191i	$-0.685357\pi$
$691$	−11.4191	+	4.15621i	−0.434403	+	0.158110i	0.115557	+	0.993301i	$0.463135\pi$
$692$	33.7649	−	35.3816i	1.28355	−	1.34501i
$693$	7.96592	+	2.61967i	0.302600	+	0.0995130i
$694$	−16.6175	−	38.8283i	−0.630792	−	1.47390i
$695$	−0.218326	+	1.23819i	−0.00828156	+	0.0469671i
$696$	4.13089	−	2.42426i	0.156581	−	0.0918915i
$697$	−17.3282	−	6.30694i	−0.656352	−	0.238892i
$698$	12.0481	+	6.09394i	0.456028	+	0.230659i
$699$	−15.1757	−	8.44736i	−0.573997	−	0.319509i
$700$	14.3865	+	6.30344i	0.543758	+	0.238247i
$701$	−1.58337			−0.0598031			−0.0299015	−	0.999553i	$-0.509519\pi$
$701$	−1.58337			−0.0598031			−0.0299015	+	0.999553i	$0.509519\pi$
$702$	−24.4569	+	36.0734i	−0.923064	+	1.36150i
$703$			26.0710i			0.983285i
$704$	13.3290	−	2.11542i	0.502356	−	0.0797280i
$705$	0.0598105		0.000937515i	0.00225259		3.53088e-5i
$706$	−22.0827	−	11.1694i	−0.831093	−	0.420368i
$707$	−4.93043	+	13.5462i	−0.185428	+	0.509459i
$708$	4.20197	−	3.19379i	0.157920	−	0.120030i
$709$	−12.4085	−	2.18796i	−0.466012	−	0.0821706i	−0.0642885	−	0.997931i	$-0.520478\pi$
$709$	−12.4085	−	2.18796i	−0.466012	−	0.0821706i	−0.401724	+	0.915761i	$0.631589\pi$
$710$	−10.8999	+	4.66486i	−0.409065	+	0.175069i
$711$	6.34791	+	15.8741i	0.238065	+	0.595325i
$712$	6.09390	+	36.3804i	0.228378	+	1.36341i
$713$	10.5414	+	28.9624i	0.394780	+	1.08465i
$714$	10.4274	−	21.4437i	0.390237	−	0.802510i
$715$	3.91009	−	3.28095i	0.146229	−	0.122701i
$716$	14.2472	−	21.3947i	0.532445	−	0.799556i
$717$	14.1051	−	12.2174i	0.526764	−	0.456266i
$718$	−21.1503	−	6.39786i	−0.789322	−	0.238766i
$719$	4.75877	+	8.24242i	0.177472	+	0.307391i	0.941014	−	0.338368i	$-0.109875\pi$
$719$	4.75877	+	8.24242i	0.177472	+	0.307391i	−0.763542	+	0.645758i	$0.776541\pi$
$720$	0.477635	+	6.10328i	0.0178004	+	0.227456i
$721$	−0.792075	+	1.37191i	−0.0294984	+	0.0510927i
$722$	4.40378	−	4.13104i	0.163892	−	0.153742i
$723$	−0.403158	+	2.51645i	−0.0149936	+	0.0935876i
$724$	−12.7664	−	0.816756i	−0.474458	−	0.0303545i
$725$	0.804688	+	4.56361i	0.0298854	+	0.169488i
$726$	2.06431	−	19.8664i	0.0766138	−	0.737312i
$727$	19.7951	−	23.5909i	0.734161	−	0.874939i	−0.261763	−	0.965132i	$-0.584304\pi$
$727$	19.7951	−	23.5909i	0.734161	−	0.874939i	0.995924	+	0.0901927i	$0.0287483\pi$
$728$	−9.72984	+	26.0362i	−0.360612	+	0.964965i
$729$	26.8807	−	2.53536i	0.995581	−	0.0939023i
$730$	−0.751482	−	0.562801i	−0.0278136	−	0.0208302i
$731$	3.31959	−	3.95613i	0.122779	−	0.146323i
$732$	−27.5891	−	25.5144i	−1.01972	−	0.943039i
$733$	4.98281	−	0.878603i	0.184044	−	0.0324519i	−0.0808664	−	0.996725i	$-0.525769\pi$
$733$	4.98281	−	0.878603i	0.184044	−	0.0324519i	0.264910	+	0.964273i	$0.414658\pi$
$734$	−15.8627	+	10.3683i	−0.585503	+	0.382700i
$735$	0.594717	−	3.71212i	0.0219365	−	0.136924i
$736$	−6.10025	+	24.1939i	−0.224858	+	0.891799i
$737$	13.4609	+	7.77167i	0.495840	+	0.286273i
$738$	−5.62062	−	12.0723i	−0.206898	−	0.444388i
$739$	−17.9126	−	31.0256i	−0.658926	−	1.14129i	−0.980894	−	0.194543i	$-0.937678\pi$
$739$	−17.9126	−	31.0256i	−0.658926	−	1.14129i	0.321968	−	0.946751i	$-0.395656\pi$
$740$	−5.58296	+	4.10700i	−0.205234	+	0.150976i
$741$	−25.8128	−	29.8012i	−0.948257	−	1.09477i
$742$	0.755690	+	13.6461i	0.0277422	+	0.500962i
$743$	−5.34278	+	4.48312i	−0.196007	+	0.164470i	−0.735509	−	0.677515i	$-0.763057\pi$
$743$	−5.34278	+	4.48312i	−0.196007	+	0.164470i	0.539502	+	0.841984i	$0.318613\pi$
$744$	5.70475	−	33.7539i	0.209146	−	1.23748i
$745$	2.22303	−	0.809117i	0.0814455	−	0.0296437i
$746$	8.42316	+	1.00892i	0.308394	+	0.0369392i
$747$	−2.50533	−	6.26502i	−0.0916651	−	0.229225i
$748$	19.2614	+	4.68140i	0.704265	+	0.171169i
$749$	4.17003	−	23.6494i	0.152370	−	0.864131i
$750$	−11.7036	−	3.34099i	−0.427355	−	0.121996i
$751$	8.84901	−	24.3125i	0.322905	−	0.887174i	−0.666951	−	0.745101i	$-0.732401\pi$
$751$	8.84901	−	24.3125i	0.322905	−	0.887174i	0.989856	−	0.142073i	$-0.0453767\pi$
$752$	−0.183561	−	0.199071i	−0.00669376	−	0.00725937i
$753$	−0.151275	−	9.65088i	−0.00551278	−	0.351698i
$754$	−7.98469	+	1.86834i	−0.290785	+	0.0680408i
$755$			2.70401i			0.0984091i
$756$	16.2779	−	5.61556i	0.592022	−	0.204236i
$757$		−	9.14500i		−	0.332381i	−0.986094	−	0.166190i	$-0.946853\pi$
$757$		−	9.14500i		−	0.332381i	0.986094	−	0.166190i	$-0.0531466\pi$
$758$	−2.32754	−	9.94720i	−0.0845401	−	0.361298i
$759$	−11.2610	−	6.26827i	−0.408747	−	0.227524i
$760$	−5.44552	−	1.00838i	−0.197530	−	0.0365777i
$761$	−0.416647	+	1.14473i	−0.0151034	+	0.0414964i	−0.947015	−	0.321189i	$-0.895918\pi$
$761$	−0.416647	+	1.14473i	−0.0151034	+	0.0414964i	0.931912	+	0.362685i	$0.118140\pi$
$762$	−27.1087	+	6.79300i	−0.982045	+	0.246084i
$763$	5.02428	−	28.4941i	0.181891	−	1.03156i
$764$	−45.6472	−	11.0944i	−1.65146	−	0.401380i
$765$	−2.80899	+	8.54161i	−0.101559	+	0.308823i
$766$	0.553387	−	4.62005i	0.0199947	−	0.166929i
$767$	−8.49133	+	3.09059i	−0.306604	+	0.111595i
$768$	19.1619	−	20.0206i	0.691444	−	0.722430i
$769$	−29.7951	+	25.0010i	−1.07444	+	0.901561i	−0.995447	−	0.0953147i	$-0.969614\pi$
$769$	−29.7951	+	25.0010i	−1.07444	+	0.901561i	−0.0789909	+	0.996875i	$0.525170\pi$
$770$	−2.01359	+	0.111509i	−0.0725648	+	0.00401849i
$771$	4.55186	−	13.1435i	0.163931	−	0.473352i
$772$	12.8273	+	17.4371i	0.461665	+	0.627576i
$773$	−4.50449	−	7.80201i	−0.162015	−	0.280619i	0.773576	−	0.633704i	$-0.218466\pi$
$773$	−4.50449	−	7.80201i	−0.162015	−	0.280619i	−0.935591	+	0.353085i	$0.885133\pi$
$774$	3.71543	−	0.322819i	0.133548	−	0.0116035i
$775$	28.6826	+	16.5599i	1.03031	+	0.594849i
$776$	36.0974	+	21.2553i	1.29582	+	0.763021i
$777$	15.1283	+	12.2953i	0.542725	+	0.441091i
$778$	−12.0709	−	18.4676i	−0.432763	−	0.662096i
$779$	11.8636	−	2.09187i	0.425057	−	0.0749491i
$780$	2.31544	−	10.2223i	0.0829059	−	0.366017i
$781$	−17.8196	+	21.2366i	−0.637635	+	0.759904i
$782$	−21.9680	+	29.3329i	−0.785575	+	1.04894i
$783$	4.04089	+	3.07899i	0.144410	+	0.110034i
$784$	−14.3245	+	9.18868i	−0.511590	+	0.328167i
$785$	−5.79681	+	6.90837i	−0.206897	+	0.246570i
$786$	−5.44044	+	7.50677i	−0.194054	+	0.267757i
$787$	−4.77460	−	27.0781i	−0.170196	−	0.965230i	−0.943544	−	0.331248i	$-0.892530\pi$
$787$	−4.77460	−	27.0781i	−0.170196	−	0.965230i	0.773348	−	0.633982i	$-0.218581\pi$
$788$	2.84900	−	44.5315i	0.101491	−	1.58637i
$789$	−46.6768	+	17.8223i	−1.66174	+	0.634490i
$790$	−2.81295	−	2.99866i	−0.100080	−	0.106688i
$791$	−1.52828	+	2.64706i	−0.0543393	+	0.0941185i
$792$	7.43774	+	12.2305i	0.264289	+	0.434591i
$793$	32.1687	+	55.7178i	1.14234	+	1.97860i
$794$	−2.69430	+	8.90692i	−0.0956171	+	0.316095i
$795$	−0.974372	−	5.06078i	−0.0345574	−	0.179487i
$796$	−1.36349	+	2.04752i	−0.0483277	+	0.0725723i
$797$	−31.1047	+	26.0999i	−1.10178	+	0.924506i	−0.997544	−	0.0700458i	$-0.977685\pi$
$797$	−31.1047	+	26.0999i	−1.10178	+	0.924506i	−0.104240	+	0.994552i	$0.533241\pi$
$798$	1.10497	+	15.5379i	0.0391154	+	0.550035i
$799$	−0.136027	−	0.373730i	−0.00481227	−	0.0132216i
$800$	11.6898	+	24.1295i	0.413297	+	0.853106i
$801$	−33.2533	+	20.6148i	−1.17495	+	0.728387i
$802$	1.67279	+	3.90862i	0.0590683	+	0.138018i
$803$	−2.16193	−	0.381207i	−0.0762930	−	0.0134525i
$804$	31.6630	−	4.02095i	1.11667	−	0.141808i
$805$	1.27520	−	3.50358i	0.0449449	−	0.123485i
$806$	−26.4531	+	52.2995i	−0.931771	+	1.84217i
$807$	2.95921	+	4.94486i	0.104169	+	0.174067i
$808$	−21.4157	+	12.1209i	−0.753401	+	0.426411i
$809$		−	37.9716i		−	1.33501i	−0.744606	−	0.667505i	$-0.767362\pi$
$809$		−	37.9716i		−	1.33501i	0.744606	−	0.667505i	$-0.232638\pi$
$810$	−5.79778	+	2.92382i	−0.203713	+	0.102732i
$811$	11.0327			0.387411			0.193706	−	0.981060i	$-0.437949\pi$
$811$	11.0327			0.387411			0.193706	+	0.981060i	$0.437949\pi$
$812$	2.96759	+	1.30025i	0.104142	+	0.0456298i
$813$	−31.8476	+	19.0589i	−1.11695	+	0.668426i
$814$	−7.31455	+	14.4613i	−0.256375	+	0.506869i
$815$	10.0840	+	3.67028i	0.353228	+	0.128564i
$816$	37.3057	−	16.2804i	1.30596	−	0.569929i
$817$	−0.585847	+	3.32250i	−0.0204962	+	0.116240i
$818$	2.80957	−	1.20243i	0.0982345	−	0.0420418i
$819$	−29.4664	+	0.923984i	−1.02964	+	0.0322866i
$820$	2.31685	+	2.21099i	0.0809080	+	0.0772111i
$821$	−19.8243	+	7.21546i	−0.691874	+	0.251821i	−0.663937	−	0.747788i	$-0.731116\pi$
$821$	−19.8243	+	7.21546i	−0.691874	+	0.251821i	−0.0279364	+	0.999610i	$0.508894\pi$
$822$	3.11712	+	43.8325i	0.108722	+	1.52883i
$823$	14.2858	+	17.0252i	0.497972	+	0.593460i	0.955226	−	0.295876i	$-0.0956114\pi$
$823$	14.2858	+	17.0252i	0.497972	+	0.593460i	−0.457254	+	0.889336i	$0.651167\pi$
$824$	−2.54894	+	0.903080i	−0.0887965	+	0.0314603i
$825$	−13.5994	+	2.61835i	−0.473471	+	0.0911592i
$826$	3.41729	+	1.03371i	0.118903	+	0.0359675i
$827$	−6.37239	+	3.67910i	−0.221590	+	0.127935i	−0.606686	−	0.794942i	$-0.707501\pi$
$827$	−6.37239	+	3.67910i	−0.221590	+	0.127935i	0.385096	+	0.922876i	$0.374168\pi$
$828$	−26.1983	+	3.74509i	−0.910455	+	0.130151i
$829$	28.6959	+	16.5676i	0.996649	+	0.575416i	0.907255	−	0.420581i	$-0.138174\pi$
$829$	28.6959	+	16.5676i	0.996649	+	0.575416i	0.0893942	+	0.995996i	$0.471507\pi$
$830$	1.11018	+	1.18348i	0.0385351	+	0.0410792i
$831$	−12.6011	−	33.0023i	−0.437126	−	1.14484i
$832$	−41.4904	+	23.0157i	−1.43842	+	0.797924i
$833$	−24.6161	+	4.34048i	−0.852896	+	0.150389i
$834$	4.88801	+	3.54253i	0.169258	+	0.122668i
$835$	6.76170	+	5.67374i	0.233998	+	0.196348i
$836$	−12.4263	+	3.64298i	−0.429774	+	0.125995i
$837$	35.4216	−	7.97875i	1.22435	−	0.275786i
$838$	24.8133	−	33.1320i	0.857161	−	1.14453i
$839$	−27.8146	−	23.3392i	−0.960267	−	0.805759i	0.0207297	−	0.999785i	$-0.493401\pi$
$839$	−27.8146	−	23.3392i	−0.960267	−	0.805759i	−0.980996	+	0.194026i	$0.937845\pi$
$840$	−3.15329	+	2.68433i	−0.108799	+	0.0926182i
$841$	−4.86981	−	27.6181i	−0.167924	−	0.952347i
$842$	13.8158	−	9.03034i	0.476123	−	0.311206i
$843$	−11.0690	+	13.6195i	−0.381237	+	0.469079i
$844$	20.8569	−	2.31713i	0.717925	−	0.0797589i
$845$	−5.65633	+	9.79704i	−0.194584	+	0.337029i
$846$	0.121536	−	0.260227i	0.00417848	−	0.00894680i
$847$	11.7007	−	6.75539i	0.402040	−	0.232118i
$848$	−14.1445	+	18.5531i	−0.485726	+	0.637115i
$849$	−15.5961	−	5.40125i	−0.535258	−	0.185370i
$850$	2.17746	+	39.3201i	0.0746863	+	1.34867i
$851$	−19.2589	−	22.9519i	−0.660188	−	0.786781i
$852$	−2.74372	+	56.8599i	−0.0939984	+	1.94799i
$853$	−8.87061	−	24.3718i	−0.303724	−	0.834475i	−0.993845	−	0.110781i	$-0.964665\pi$
$853$	−8.87061	−	24.3718i	−0.303724	−	0.834475i	0.690121	−	0.723694i	$-0.257557\pi$
$854$	3.02313	−	25.2391i	0.103449	−	0.863665i
$855$	−1.20082	−	5.74998i	−0.0410672	−	0.196645i
$856$	31.6271	−	26.0798i	1.08099	−	0.891389i
$857$	53.4542	+	9.42542i	1.82596	+	0.321966i	0.978081	−	0.208223i	$-0.0667679\pi$
$857$	53.4542	+	9.42542i	1.82596	+	0.321966i	0.847880	+	0.530189i	$0.177879\pi$
$858$	−5.95701	−	23.7726i	−0.203369	−	0.811582i
$859$	−18.8934	−	6.87662i	−0.644633	−	0.234627i	−0.00104505	−	0.999999i	$-0.500333\pi$
$859$	−18.8934	−	6.87662i	−0.644633	−	0.234627i	−0.643588	+	0.765372i	$0.722555\pi$
$860$	−0.803786	+	0.397943i	−0.0274089	+	0.0135697i
$861$	4.38111	−	7.87067i	0.149308	−	0.268232i
$862$	6.56972	+	28.0770i	0.223766	+	0.956306i
$863$	35.7624			1.21737			0.608683	−	0.793414i	$-0.291698\pi$
$863$	35.7624			1.21737			0.608683	+	0.793414i	$0.291698\pi$
$864$	27.3566	+	10.7526i	0.930689	+	0.365811i
$865$	−12.4753			−0.424174
$866$	12.4362	+	53.1486i	0.422600	+	1.80606i
$867$	30.3348	−	0.475491i	1.03022	−	0.0161485i
$868$	20.7522	−	10.2741i	0.704375	−	0.348726i
$869$	−9.03391	−	3.28807i	−0.306454	−	0.111540i
$870$	−1.17483	−	0.335375i	−0.0398305	−	0.0113703i
$871$	−53.8147	−	9.48899i	−1.82344	−	0.321522i
$872$	38.1060	−	31.4223i	1.29043	−	1.06409i
$873$	−6.34025	+	43.9768i	−0.214585	+	1.48839i
$874$	2.84726	−	23.7708i	0.0963099	−	0.804060i
$875$	−2.81586	−	7.73650i	−0.0951934	−	0.261542i
$876$	−4.00803	+	2.06316i	−0.135419	+	0.0697076i
$877$	−11.4196	−	13.6093i	−0.385612	−	0.459554i	0.537965	−	0.842967i	$-0.319193\pi$
$877$	−11.4196	−	13.6093i	−0.385612	−	0.459554i	−0.923577	+	0.383413i	$0.874749\pi$
$878$	−2.64672	−	47.7937i	−0.0893223	−	1.61296i
$879$	28.7719	−	24.9213i	0.970452	−	0.840573i
$880$	−2.73767	−	2.08715i	−0.0922867	−	0.0703578i
$881$	1.81835	−	1.04983i	0.0612618	−	0.0353695i	−0.469056	−	0.883168i	$-0.655406\pi$
$881$	1.81835	−	1.04983i	0.0612618	−	0.0353695i	0.530318	+	0.847799i	$0.322073\pi$
$882$	−14.7801	−	10.3623i	−0.497670	−	0.348916i
$883$	−14.4157	+	24.9688i	−0.485128	+	0.840267i	−0.999854	−	0.0170882i	$-0.994560\pi$
$883$	−14.4157	+	24.9688i	−0.485128	+	0.840267i	0.514726	+	0.857355i	$0.327894\pi$
$884$	−69.2614	+	7.69469i	−2.32951	+	0.258801i
$885$	−1.32935	−	0.212975i	−0.0446857	−	0.00715907i
$886$	−10.3807	+	6.78510i	−0.348746	+	0.227950i
$887$	−2.85336	−	16.1822i	−0.0958066	−	0.543346i	−0.994497	−	0.104763i	$-0.966592\pi$
$887$	−2.85336	−	16.1822i	−0.0958066	−	0.543346i	0.898691	−	0.438583i	$-0.144519\pi$
$888$	6.01133	+	32.7304i	0.201727	+	1.09836i
$889$	−14.4816	−	12.1515i	−0.485696	−	0.407547i
$890$	5.64034	−	7.53128i	0.189065	−	0.252449i
$891$	−9.01145	+	12.2193i	−0.301895	+	0.409362i
$892$	−32.7882	+	9.61240i	−1.09783	+	0.321847i
$893$	0.199032	+	0.167008i	0.00666036	+	0.00558871i
$894$	1.17395	−	11.2978i	0.0392629	−	0.377856i
$895$	−6.45709	+	1.13856i	−0.215837	+	0.0380578i
$896$	18.5720	+	2.54809i	0.620448	+	0.0851257i
$897$	44.7391	+	7.16762i	1.49379	+	0.239320i
$898$	−26.5375	−	28.2896i	−0.885568	−	0.944035i
$899$	5.91654	+	3.41591i	0.197328	+	0.113927i
$900$	−18.9790	+	21.1788i	−0.632634	+	0.705959i
$901$	−29.6752	+	17.1330i	−0.988624	+	0.570782i
$902$	7.16753	+	2.16814i	0.238653	+	0.0721913i
$903$	1.65167	+	1.90687i	0.0549641	+	0.0634567i
$904$	−4.91808	+	1.74246i	−0.163573	+	0.0579533i
$905$	2.09749	+	2.49969i	0.0697228	+	0.0830924i
$906$	11.6758	+	5.67760i	0.387902	+	0.188626i
$907$	−27.5948	+	10.0437i	−0.916272	+	0.333496i	−0.756754	−	0.653699i	$-0.773216\pi$
$907$	−27.5948	+	10.0437i	−0.916272	+	0.333496i	−0.159517	+	0.987195i	$0.550994\pi$
$908$	5.19850	+	4.96097i	0.172518	+	0.164636i
$909$	−20.5102	−	16.1422i	−0.680281	−	0.535404i
$910$	6.51808	−	2.78957i	0.216072	−	0.0924733i
$911$	4.26579	−	24.1925i	0.141332	−	0.801533i	−0.828908	−	0.559385i	$-0.811037\pi$
$911$	4.26579	−	24.1925i	0.141332	−	0.801533i	0.970240	−	0.242147i	$-0.0778517\pi$
$912$	−15.7880	+	21.3962i	−0.522794	+	0.708499i
$913$	3.56541	+	1.29770i	0.117998	+	0.0429477i
$914$	7.92501	−	15.6683i	0.262136	−	0.518260i
$915$	0.150233	+	9.58438i	0.00496654	+	0.316850i
$916$	−2.94583	−	1.29071i	−0.0973328	−	0.0426464i
$917$	−6.27121			−0.207094
$918$	30.9843	+	30.0639i	1.02263	+	0.992256i
$919$			38.5765i			1.27252i	0.771474	+	0.636261i	$0.219520\pi$
$919$			38.5765i			1.27252i	−0.771474	+	0.636261i	$0.780480\pi$
$920$	5.53893	−	3.13493i	0.182613	−	0.103356i
$921$	22.5924	−	40.5873i	0.744445	−	1.33740i
$922$	−8.53917	+	16.8825i	−0.281222	+	0.555995i
$923$	33.3340	−	91.5843i	1.09720	−	3.01453i
$924$	−3.74644	+	8.92873i	−0.123249	+	0.293734i
$925$	−31.7070	−	5.59080i	−1.04252	−	0.183824i
$926$	−13.2455	−	30.9492i	−0.435273	−	1.01705i
$927$	−1.91162	−	2.13833i	−0.0627858	−	0.0702318i
$928$	2.41133	+	4.97734i	0.0791557	+	0.163389i
$929$	−1.83720	−	5.04766i	−0.0602765	−	0.165608i	0.905899	−	0.423494i	$-0.139196\pi$
$929$	−1.83720	−	5.04766i	−0.0602765	−	0.165608i	−0.966175	+	0.257886i	$0.916974\pi$
$930$	−7.23344	+	4.89146i	−0.237194	+	0.160397i
$931$	12.5089	−	10.4962i	0.409962	−	0.343999i
$932$	11.1161	−	16.6927i	0.364119	−	0.546787i
$933$	−39.4919	−	13.6768i	−1.29291	−	0.447759i
$934$	−11.3919	+	37.6597i	−0.372754	+	1.23226i
$935$	−2.52812	−	4.37883i	−0.0826783	−	0.143203i
$936$	−39.2777	−	31.4616i	−1.28383	−	1.02836i
$937$	15.4717	−	26.7977i	0.505437	−	0.875443i	−0.494543	−	0.869153i	$-0.664665\pi$
$937$	15.4717	−	26.7977i	0.505437	−	0.875443i	0.999980	−	0.00628976i	$-0.00200211\pi$
$938$	14.7711	+	15.7463i	0.482293	+	0.514135i
$939$	−23.7007	−	19.2624i	−0.773444	−	0.628605i
$940$	−0.00441000	+	0.0689307i	−0.000143838	+	0.00224827i
$941$	−3.69758	−	20.9700i	−0.120538	−	0.683603i	−0.983859	−	0.178947i	$-0.942731\pi$
$941$	−3.69758	−	20.9700i	−0.120538	−	0.683603i	0.863321	−	0.504655i	$-0.168380\pi$
$942$	17.6585	+	39.5358i	0.575345	+	1.28815i
$943$	−8.89897	+	10.6054i	−0.289790	+	0.345359i
$944$	3.29057	+	5.12977i	0.107099	+	0.166960i
$945$	−3.90288	−	2.01494i	−0.126961	−	0.0655459i
$946$	−1.25714	+	1.67859i	−0.0408730	+	0.0545758i
$947$	−23.4586	+	27.9569i	−0.762302	+	0.908476i	−0.997991	−	0.0633524i	$-0.979821\pi$
$947$	−23.4586	+	27.9569i	−0.762302	+	0.908476i	0.235689	+	0.971828i	$0.424265\pi$
$948$	−18.8544	+	5.84990i	−0.612363	+	0.189996i
$949$	7.60059	−	1.34019i	0.246726	−	0.0435044i
$950$	−14.0754	−	21.5343i	−0.456665	−	0.698664i
$951$	6.16171	−	2.35268i	0.199807	−	0.0762910i
$952$	23.7257	+	13.9705i	0.768956	+	0.452786i
$953$	−9.73145	−	5.61845i	−0.315233	−	0.182000i	0.334033	−	0.942561i	$-0.391590\pi$
$953$	−9.73145	−	5.61845i	−0.315233	−	0.182000i	−0.649266	+	0.760562i	$0.724924\pi$
$954$	−23.8981	−	6.41880i	−0.773729	−	0.207816i
$955$	5.99135	+	10.3773i	0.193876	+	0.335802i
$956$	12.7683	+	17.3569i	0.412955	+	0.561362i
$957$	−2.80524	+	0.540103i	−0.0906805	+	0.0174591i
$958$	−34.8097	+	1.92769i	−1.12465	+	0.0622808i
$959$	−22.7706	+	19.1068i	−0.735300	+	0.616990i
$960$	−7.06900	−	0.0103495i	−0.228151	−	0.000334029i
$961$	16.7526	−	6.09746i	0.540408	−	0.196692i
$962$	6.77593	−	56.5700i	0.218465	−	1.82389i
$963$	38.3174	+	20.5490i	1.23476	+	0.662182i
$964$	−2.85955	−	0.695002i	−0.0920999	−	0.0223845i
$965$	0.958840	−	5.43785i	0.0308661	−	0.175051i
$966$	−12.4508	−	12.8627i	−0.400597	−	0.413851i
$967$	7.29159	−	20.0335i	0.234482	−	0.644233i	−0.765518	−	0.643415i	$-0.777517\pi$
$967$	7.29159	−	20.0335i	0.234482	−	0.644233i	1.00000		0.000818662i	$-0.000260588\pi$
$968$	22.6777	+	4.19937i	0.728890	+	0.134973i
$969$	−33.5125	+	20.0553i	−1.07658	+	0.644268i
$970$	−2.43453	−	10.4044i	−0.0781679	−	0.334066i
$971$		−	38.3665i		−	1.23124i	−0.788044	−	0.615619i	$-0.788906\pi$
$971$		−	38.3665i		−	1.23124i	0.788044	−	0.615619i	$-0.211094\pi$
$972$	0.451339	+	31.1736i	0.0144767	+	0.999895i
$973$			4.08348i			0.130910i
$974$	38.3054	−	8.96307i	1.22738	−	0.287195i
$975$	41.7791	−	25.0023i	1.33800	−	0.800714i
$976$	31.9003	−	29.4148i	1.02110	−	0.941545i
$977$	−5.88737	+	16.1754i	−0.188354	+	0.517498i	−0.997543	−	0.0700498i	$-0.977684\pi$
$977$	−5.88737	+	16.1754i	−0.188354	+	0.517498i	0.809190	+	0.587547i	$0.199906\pi$
$978$	37.0215	−	35.8358i	1.18382	−	1.14590i
$979$	3.82042	−	21.6667i	0.122101	−	0.692470i
$980$	4.21825	+	1.02523i	0.134747	+	0.0327497i
$981$	46.1668	+	24.7585i	1.47399	+	0.790479i
$982$	40.3508	+	4.83320i	1.28765	+	0.154234i
$983$	41.2780	−	15.0240i	1.31656	−	0.479190i	0.414208	−	0.910182i	$-0.364058\pi$
$983$	41.2780	−	15.0240i	1.31656	−	0.479190i	0.902356	+	0.430992i	$0.141836\pi$
$984$	14.4116	−	5.36166i	0.459426	−	0.170924i
$985$	−8.71938	+	7.31643i	−0.277823	+	0.233121i
$986$	0.449159	+	8.11079i	0.0143041	+	0.258300i
$987$	0.190776	−	0.0367308i	0.00607245	−	0.00116915i
$988$	36.6716	−	26.9767i	1.16668	−	0.858244i
$989$	−1.93861	−	3.35778i	−0.0616443	−	0.106771i
$990$	0.947149	−	3.52637i	0.0301024	−	0.112075i
$991$	−29.3156	−	16.9254i	−0.931241	−	0.537652i	−0.0440369	−	0.999030i	$-0.514022\pi$
$991$	−29.3156	−	16.9254i	−0.931241	−	0.537652i	−0.887204	+	0.461378i	$0.847355\pi$
$992$	38.3287	+	9.66421i	1.21694	+	0.306839i
$993$	−47.2885	+	18.0559i	−1.50065	+	0.572985i
$994$	−32.2324	+	21.0680i	−1.02235	+	0.668235i
$995$	0.617958	−	0.108963i	0.0195906	−	0.00345435i
$996$	7.44126	−	2.30878i	0.235785	−	0.0731564i
$997$	4.25751	−	5.07390i	0.134837	−	0.160692i	−0.694401	−	0.719588i	$-0.744331\pi$
$997$	4.25751	−	5.07390i	0.134837	−	0.160692i	0.829238	+	0.558896i	$0.188775\pi$
$998$	−14.0579	−	10.5283i	−0.444996	−	0.333267i
$999$	−29.7044	+	19.0655i	−0.939804	+	0.603206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.14	✓	192
3.2	odd	2		648.2.v.b.35.19		192
4.3	odd	2		864.2.bh.b.335.10		192
8.3	odd	2	inner	216.2.v.b.11.31	yes	192
8.5	even	2		864.2.bh.b.335.9		192
24.11	even	2		648.2.v.b.35.2		192
27.5	odd	18	inner	216.2.v.b.59.31	yes	192
27.22	even	9		648.2.v.b.611.2		192
108.59	even	18		864.2.bh.b.815.9		192
216.5	odd	18		864.2.bh.b.815.10		192
216.59	even	18	inner	216.2.v.b.59.14	yes	192
216.211	odd	18		648.2.v.b.611.19		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.14	✓	192	1.1	even	1	trivial
216.2.v.b.11.31	yes	192	8.3	odd	2	inner
216.2.v.b.59.14	yes	192	216.59	even	18	inner
216.2.v.b.59.31	yes	192	27.5	odd	18	inner
648.2.v.b.35.2		192	24.11	even	2
648.2.v.b.35.19		192	3.2	odd	2
648.2.v.b.611.2		192	27.22	even	9
648.2.v.b.611.19		192	216.211	odd	18
864.2.bh.b.335.9		192	8.5	even	2
864.2.bh.b.335.10		192	4.3	odd	2
864.2.bh.b.815.9		192	108.59	even	18
864.2.bh.b.815.10		192	216.5	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.322208 - 1.37702i) q^{2} +(0.889428 + 1.48624i) q^{3} +(-1.79236 + 0.887374i) q^{4} +(0.479395 + 0.174486i) q^{5} +(1.76000 - 1.70364i) q^{6} +(1.63176 + 0.287723i) q^{7} +(1.79945 + 2.18220i) q^{8} +(-1.41783 + 2.64381i) q^{9} +O(q^{10})\)	\(q+(-0.322208 - 1.37702i) q^{2} +(0.889428 + 1.48624i) q^{3} +(-1.79236 + 0.887374i) q^{4} +(0.479395 + 0.174486i) q^{5} +(1.76000 - 1.70364i) q^{6} +(1.63176 + 0.287723i) q^{7} +(1.79945 + 2.18220i) q^{8} +(-1.41783 + 2.64381i) q^{9} +(0.0858049 - 0.716357i) q^{10} +(-0.576981 - 1.58524i) q^{11} +(-2.91303 - 1.87463i) q^{12} +(3.81226 + 4.54327i) q^{13} +(-0.129566 - 2.33967i) q^{14} +(0.167060 + 0.867690i) q^{15} +(2.42513 - 3.18099i) q^{16} +(5.08792 - 2.93751i) q^{17} +(4.09742 + 1.10053i) q^{18} +(-1.91901 + 3.32382i) q^{19} +(-1.01408 + 0.112661i) q^{20} +(1.02370 + 2.68110i) q^{21} +(-1.99700 + 1.30529i) q^{22} +(-0.765923 - 4.34377i) q^{23} +(-1.64280 + 4.61532i) q^{24} +(-3.63085 - 3.04664i) q^{25} +(5.02783 - 6.71343i) q^{26} +(-5.19041 + 0.244235i) q^{27} +(-3.18002 + 0.932275i) q^{28} +(-0.748958 - 0.628450i) q^{29} +(1.14100 - 0.509621i) q^{30} +(-6.88153 + 1.21340i) q^{31} +(-5.16169 - 2.31451i) q^{32} +(1.84287 - 2.26749i) q^{33} +(-5.68438 - 6.05968i) q^{34} +(0.732053 + 0.422651i) q^{35} +(0.195225 - 5.99682i) q^{36} +(5.88275 - 3.39641i) q^{37} +(5.19529 + 1.57155i) q^{38} +(-3.36168 + 9.70686i) q^{39} +(0.481883 + 1.36011i) q^{40} +(-2.01755 - 2.40442i) q^{41} +(3.36207 - 2.27353i) q^{42} +(0.826023 - 0.300648i) q^{43} +(2.44086 + 2.32933i) q^{44} +(-1.14101 + 1.02004i) q^{45} +(-5.73466 + 2.45429i) q^{46} +(0.0117553 - 0.0666674i) q^{47} +(6.88471 + 0.775073i) q^{48} +(-3.99800 - 1.45515i) q^{49} +(-3.02540 + 5.98140i) q^{50} +(8.89120 + 4.94918i) q^{51} +(-10.8645 - 4.76030i) q^{52} -5.83248 q^{53} +(2.00871 + 7.06860i) q^{54} -0.860632i q^{55} +(2.30839 + 4.07856i) q^{56} +(-6.64683 + 0.104187i) q^{57} +(-0.624067 + 1.23382i) q^{58} +(-0.521107 + 1.43173i) q^{59} +(-1.06940 - 1.40697i) q^{60} +(10.6832 + 1.88373i) q^{61} +(3.88816 + 9.08503i) q^{62} +(-3.07425 + 3.90612i) q^{63} +(-1.52399 + 7.85350i) q^{64} +(1.03484 + 2.84321i) q^{65} +(-3.71617 - 1.80706i) q^{66} +(-7.05812 + 5.92246i) q^{67} +(-6.51274 + 9.77998i) q^{68} +(5.77466 - 5.00182i) q^{69} +(0.346125 - 1.14423i) q^{70} +(-8.21657 - 14.2315i) q^{71} +(-8.32064 + 1.66340i) q^{72} +(0.650656 - 1.12697i) q^{73} +(-6.57239 - 7.00631i) q^{74} +(1.29867 - 8.10609i) q^{75} +(0.490090 - 7.66038i) q^{76} +(-0.485382 - 2.75274i) q^{77} +(14.4497 + 1.50146i) q^{78} +(3.66309 - 4.36550i) q^{79} +(1.71764 - 1.10180i) q^{80} +(-4.97949 - 7.49698i) q^{81} +(-2.66087 + 3.55293i) q^{82} +(-1.44571 + 1.72293i) q^{83} +(-4.21399 - 3.89709i) q^{84} +(2.95168 - 0.520461i) q^{85} +(-0.680149 - 1.04058i) q^{86} +(0.267885 - 1.67209i) q^{87} +(2.42107 - 4.11164i) q^{88} +(11.2944 + 6.52081i) q^{89} +(1.77226 + 1.24253i) q^{90} +(4.91348 + 8.51039i) q^{91} +(5.22736 + 7.10595i) q^{92} +(-7.92403 - 9.14839i) q^{93} +(-0.0955899 + 0.00529357i) q^{94} +(-1.49992 + 1.25859i) q^{95} +(-1.15102 - 9.73012i) q^{96} +(13.9173 - 5.06549i) q^{97} +(-0.715585 + 5.97419i) q^{98} +(5.00915 + 0.722182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25} + 18 q^{27} - 12 q^{28} - 21 q^{30} - 36 q^{32} - 30 q^{33} + 12 q^{34} - 18 q^{35} - 36 q^{36} - 102 q^{38} + 9 q^{40} + 18 q^{41} - 6 q^{42} - 42 q^{43} - 81 q^{44} - 3 q^{46} - 81 q^{48} - 12 q^{49} + 57 q^{50} - 18 q^{51} + 21 q^{52} + 78 q^{54} - 69 q^{56} - 36 q^{57} - 33 q^{58} - 84 q^{59} - 54 q^{60} + 90 q^{62} - 51 q^{64} - 12 q^{65} + 87 q^{66} + 30 q^{67} + 63 q^{68} - 33 q^{70} + 12 q^{72} - 6 q^{73} + 51 q^{74} - 96 q^{75} + 30 q^{76} + 90 q^{78} - 12 q^{81} - 12 q^{82} - 72 q^{83} - 48 q^{84} + 42 q^{86} - 78 q^{88} + 144 q^{89} + 120 q^{90} - 6 q^{91} - 3 q^{92} - 33 q^{94} - 78 q^{96} - 42 q^{97} + 162 q^{98} - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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