LMFDB - Embedded newform 216.2.v.b.11.31

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			11.31
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41205 + 0.0781964i) q^{2} +(0.889428 + 1.48624i) q^{3} +(1.98777 + 0.220834i) q^{4} +(-0.479395 - 0.174486i) q^{5} +(1.13970 + 2.16820i) q^{6} +(-1.63176 - 0.287723i) q^{7} +(2.78956 + 0.467266i) q^{8} +(-1.41783 + 2.64381i) q^{9} +O(q^{10})$	\(q+(1.41205 + 0.0781964i) q^{2} +(0.889428 + 1.48624i) q^{3} +(1.98777 + 0.220834i) q^{4} +(-0.479395 - 0.174486i) q^{5} +(1.13970 + 2.16820i) q^{6} +(-1.63176 - 0.287723i) q^{7} +(2.78956 + 0.467266i) q^{8} +(-1.41783 + 2.64381i) q^{9} +(-0.663286 - 0.283869i) q^{10} +(-0.576981 - 1.58524i) q^{11} +(1.43977 + 3.15073i) q^{12} +(-3.81226 - 4.54327i) q^{13} +(-2.28162 - 0.533876i) q^{14} +(-0.167060 - 0.867690i) q^{15} +(3.90246 + 0.877936i) q^{16} +(5.08792 - 2.93751i) q^{17} +(-2.20879 + 3.62233i) q^{18} +(-1.91901 + 3.32382i) q^{19} +(-0.914395 - 0.452704i) q^{20} +(-1.02370 - 2.68110i) q^{21} +(-0.690766 - 2.28356i) q^{22} +(0.765923 + 4.34377i) q^{23} +(1.78665 + 4.56157i) 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} +(-0.168046 - 1.23829i) q^{30} +(6.88153 - 1.21340i) q^{31} +(5.44182 + 1.54485i) q^{32} +(1.84287 - 2.26749i) q^{33} +(7.41411 - 3.75006i) q^{34} +(0.732053 + 0.422651i) q^{35} +(-3.40217 + 4.94219i) q^{36} +(-5.88275 + 3.39641i) q^{37} +(-2.96965 + 4.54335i) q^{38} +(3.36168 - 9.70686i) q^{39} +(-1.25577 - 0.710743i) q^{40} +(-2.01755 - 2.40442i) q^{41} +(-1.23587 - 3.86589i) q^{42} +(0.826023 - 0.300648i) q^{43} +(-0.796830 - 3.27851i) q^{44} +(1.14101 - 1.02004i) q^{45} +(0.741855 + 6.19351i) q^{46} +(-0.0117553 + 0.0666674i) q^{47} +(2.16614 + 6.58087i) q^{48} +(-3.99800 - 1.45515i) q^{49} +(-4.88870 - 4.58593i) q^{50} +(8.89120 + 4.94918i) q^{51} +(-6.57458 - 9.87286i) q^{52} +5.83248 q^{53} +(-7.34822 - 0.0609986i) q^{54} +0.860632i q^{55} +(-4.41745 - 1.56508i) q^{56} +(-6.64683 + 0.104187i) q^{57} +(1.00842 + 0.945969i) q^{58} +(-0.521107 + 1.43173i) q^{59} +(-0.140461 - 1.76166i) q^{60} +(-10.6832 - 1.88373i) q^{61} +(9.81195 - 1.17527i) q^{62} +(3.07425 - 3.90612i) q^{63} +(7.56333 + 2.60693i) q^{64} +(1.03484 + 2.84321i) q^{65} +(2.77954 - 3.05771i) q^{66} +(-7.05812 + 5.92246i) q^{67} +(10.7623 - 4.71552i) q^{68} +(-5.77466 + 5.00182i) q^{69} +(1.00065 + 0.654048i) q^{70} +(8.21657 + 14.2315i) q^{71} +(-5.19050 + 6.71258i) q^{72} +(0.650656 - 1.12697i) q^{73} +(-8.57233 + 4.33589i) q^{74} +(1.29867 - 8.10609i) q^{75} +(-4.54857 + 6.18322i) q^{76} +(0.485382 + 2.75274i) q^{77} +(5.50589 - 13.4437i) 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} +(-1.44281 - 5.55547i) q^{84} +(-2.95168 + 0.520461i) q^{85} +(1.18990 - 0.359938i) q^{86} +(-0.267885 + 1.67209i) q^{87} +(-0.868796 - 4.69174i) q^{88} +(11.2944 + 6.52081i) q^{89} +(1.69093 - 1.35112i) q^{90} +(4.91348 + 8.51039i) q^{91} +(0.563227 + 8.80355i) q^{92} +(7.92403 + 9.14839i) q^{93} +(-0.0218122 + 0.0932185i) q^{94} +(1.49992 - 1.25859i) q^{95} +(2.54409 + 9.46190i) q^{96} +(13.9173 - 5.06549i) q^{97} +(-5.53159 - 2.36738i) 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 $

$2$	1.41205	+	0.0781964i	0.998470	+	0.0552932i
$2$	1.41205	+	0.0781964i	0.998470	+	0.0552932i
$3$	0.889428	+	1.48624i	0.513512	+	0.858083i
$3$	0.889428	+	1.48624i	0.513512	+	0.858083i
$4$	1.98777	+	0.220834i	0.993885	+	0.110417i
$5$	−0.479395	−	0.174486i	−0.214392	−	0.0780323i	0.232591	−	0.972575i	$-0.425280\pi$
$5$	−0.479395	−	0.174486i	−0.214392	−	0.0780323i	−0.446983	+	0.894542i	$0.647502\pi$
$6$	1.13970	+	2.16820i	0.465280	+	0.885164i
$7$	−1.63176	−	0.287723i	−0.616746	−	0.108749i	−0.143458	−	0.989656i	$-0.545822\pi$
$7$	−1.63176	−	0.287723i	−0.616746	−	0.108749i	−0.473289	+	0.880907i	$0.656933\pi$
$8$	2.78956	+	0.467266i	0.986260	+	0.165203i
$9$	−1.41783	+	2.64381i	−0.472612	+	0.881271i
$10$	−0.663286	−	0.283869i	−0.209749	−	0.0897674i
$11$	−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	$0.970741\pi$
$12$	1.43977	+	3.15073i	0.415625	+	0.909536i
$13$	−3.81226	−	4.54327i	−1.05733	−	1.26008i	−0.964412	−	0.264403i	$-0.914825\pi$
$13$	−3.81226	−	4.54327i	−1.05733	−	1.26008i	−0.0929181	−	0.995674i	$-0.529619\pi$
$14$	−2.28162	−	0.533876i	−0.609790	−	0.142684i
$15$	−0.167060	−	0.867690i	−0.0431346	−	0.224037i
$16$	3.90246	+	0.877936i	0.975616	+	0.219484i
$17$	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	$0.0809180\pi$
$18$	−2.20879	+	3.62233i	−0.520617	+	0.853790i
$19$	−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	$0.311777\pi$
$20$	−0.914395	−	0.452704i	−0.204465	−	0.101228i
$21$	−1.02370	−	2.68110i	−0.223391	−	0.585063i
$22$	−0.690766	−	2.28356i	−0.147272	−	0.486856i
$23$	0.765923	+	4.34377i	0.159706	+	0.905738i	0.954356	+	0.298670i	$0.0965431\pi$
$23$	0.765923	+	4.34377i	0.159706	+	0.905738i	−0.794650	+	0.607067i	$0.792346\pi$
$24$	1.78665	+	4.56157i	0.364698	+	0.931126i
$25$	−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	0.709673	−	0.704532i	$-0.248843\pi$
$29$	0.748958	+	0.628450i	0.139078	+	0.116700i	−0.570595	+	0.821232i	$0.693287\pi$
$30$	−0.168046	−	1.23829i	−0.0306810	−	0.226079i
$31$	6.88153	−	1.21340i	1.23596	−	0.217933i	0.482776	−	0.875744i	$-0.339628\pi$
$31$	6.88153	−	1.21340i	1.23596	−	0.217933i	0.753183	+	0.657811i	$0.228517\pi$
$32$	5.44182	+	1.54485i	0.961988	+	0.273093i
$33$	1.84287	−	2.26749i	0.320803	−	0.394720i
$34$	7.41411	−	3.75006i	1.27151	−	0.643130i
$35$	0.732053	+	0.422651i	0.123740	+	0.0714410i
$36$	−3.40217	+	4.94219i	−0.567029	+	0.823698i
$37$	−5.88275	+	3.39641i	−0.967118	+	0.558366i	−0.898357	−	0.439267i	$-0.855238\pi$
$37$	−5.88275	+	3.39641i	−0.967118	+	0.558366i	−0.0687618	+	0.997633i	$0.521905\pi$
$38$	−2.96965	+	4.54335i	−0.481741	+	0.737028i
$39$	3.36168	−	9.70686i	0.538299	−	1.55434i
$40$	−1.25577	−	0.710743i	−0.198555	−	0.112378i
$41$	−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	$0.856597\pi$
$42$	−1.23587	−	3.86589i	−0.190699	−	0.596520i
$43$	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	$0.367538\pi$
$44$	−0.796830	−	3.27851i	−0.120127	−	0.494255i
$45$	1.14101	−	1.02004i	0.170092	−	0.152058i
$46$	0.741855	+	6.19351i	0.109381	+	0.913183i
$47$	−0.0117553	+	0.0666674i	−0.00171468	+	0.00972444i	−0.985653	−	0.168784i	$-0.946016\pi$
$47$	−0.0117553	+	0.0666674i	−0.00171468	+	0.00972444i	0.983938	+	0.178508i	$0.0571271\pi$
$48$	2.16614	+	6.58087i	0.312655	+	0.949867i
$49$	−3.99800	−	1.45515i	−0.571143	−	0.207879i
$50$	−4.88870	−	4.58593i	−0.691367	−	0.648549i
$51$	8.89120	+	4.94918i	1.24502	+	0.693024i
$52$	−6.57458	−	9.87286i	−0.911731	−	1.36912i
$53$	5.83248			0.801152			0.400576	−	0.916263i	$-0.368810\pi$
$53$	5.83248			0.801152			0.400576	+	0.916263i	$0.368810\pi$
$54$	−7.34822	−	0.0609986i	−0.999966	−	0.00830086i
$55$			0.860632i			0.116048i
$56$	−4.41745	−	1.56508i	−0.590306	−	0.209143i
$57$	−6.64683	+	0.104187i	−0.880394	+	0.0138000i
$58$	1.00842	+	0.945969i	0.132412	+	0.124212i
$59$	−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	$0.142733\pi$
$60$	−0.140461	−	1.76166i	−0.0181334	−	0.227429i
$61$	−10.6832	−	1.88373i	−1.36784	−	0.241187i	−0.558976	−	0.829184i	$-0.688806\pi$
$61$	−10.6832	−	1.88373i	−1.36784	−	0.241187i	−0.808864	+	0.587996i	$0.799917\pi$
$62$	9.81195	−	1.17527i	1.24612	−	0.149259i
$63$	3.07425	−	3.90612i	0.387319	−	0.492124i
$64$	7.56333	+	2.60693i	0.945416	+	0.325867i
$65$	1.03484	+	2.84321i	0.128356	+	0.352656i
$66$	2.77954	−	3.05771i	0.342137	−	0.376378i
$67$	−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	$0.468060\pi$
$68$	10.7623	−	4.71552i	1.30512	−	0.571840i
$69$	−5.77466	+	5.00182i	−0.695187	+	0.602148i
$70$	1.00065	+	0.654048i	0.119600	+	0.0781737i
$71$	8.21657	+	14.2315i	0.975127	+	1.68897i	0.679514	+	0.733662i	$0.262191\pi$
$71$	8.21657	+	14.2315i	0.975127	+	1.68897i	0.295613	+	0.955308i	$0.404476\pi$
$72$	−5.19050	+	6.71258i	−0.611707	+	0.791085i
$73$	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	$0.142403\pi$
$74$	−8.57233	+	4.33589i	−0.996513	+	0.504037i
$75$	1.29867	−	8.10609i	0.149958	−	0.936011i
$76$	−4.54857	+	6.18322i	−0.521756	+	0.709264i
$77$	0.485382	+	2.75274i	0.0553144	+	0.313704i
$78$	5.50589	−	13.4437i	0.623420	−	1.52220i
$79$	−3.66309	+	4.36550i	−0.412130	+	0.491157i	−0.931679	−	0.363284i	$-0.881656\pi$
$79$	−3.66309	+	4.36550i	−0.412130	+	0.491157i	0.519549	+	0.854441i	$0.326100\pi$
$80$	−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	$0.261614\pi$
$84$	−1.44281	−	5.55547i	−0.157424	−	0.606152i
$85$	−2.95168	+	0.520461i	−0.320155	+	0.0564519i
$86$	1.18990	−	0.359938i	0.128310	−	0.0388131i
$87$	−0.267885	+	1.67209i	−0.0287203	+	0.179267i
$88$	−0.868796	−	4.69174i	−0.0926139	−	0.500141i
$89$	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	$0.423747\pi$
$90$	1.69093	−	1.35112i	0.178239	−	0.142421i
$91$	4.91348	+	8.51039i	0.515072	+	0.892131i
$92$	0.563227	+	8.80355i	0.0587205	+	0.917834i
$93$	7.92403	+	9.14839i	0.821684	+	0.948644i
$94$	−0.0218122	+	0.0932185i	−0.00224975	+	0.00961475i
$95$	1.49992	−	1.25859i	0.153889	−	0.129128i
$96$	2.54409	+	9.46190i	0.259655	+	0.965701i
$97$	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	$0.118032\pi$
$98$	−5.53159	−	2.36738i	−0.558775	−	0.239141i
$99$	5.00915	+	0.722182i	0.503438	+	0.0725820i
$100$	−6.54449	−	6.85784i	−0.654449	−	0.685784i
$101$	1.51077	−	8.56802i	0.150328	−	0.852550i	−0.812606	−	0.582813i	$-0.801952\pi$
$101$	1.51077	−	8.56802i	0.150328	−	0.852550i	0.962934	−	0.269737i	$-0.0869368\pi$
$102$	12.1678	+	7.68375i	1.20479	+	0.760805i
$103$	0.326997	−	0.898417i	0.0322200	−	0.0885237i	−0.922540	−	0.385902i	$-0.873890\pi$
$103$	0.326997	−	0.898417i	0.0322200	−	0.0885237i	0.954760	+	0.297379i	$0.0961124\pi$
$104$	−8.51162	−	14.4551i	−0.834633	−	1.41744i
$105$	0.0229467	+	1.46393i	0.00223937	+	0.142865i
$106$	8.23575	+	0.456078i	0.799927	+	0.0442982i
$107$		−	14.4932i		−	1.40111i	−0.713597	−	0.700557i	$-0.752935\pi$
$107$		−	14.4932i		−	1.40111i	0.713597	−	0.700557i	$-0.247065\pi$
$108$	−10.3713	−	0.660737i	−0.997977	−	0.0635794i
$109$			17.4622i			1.67258i	0.548290	+	0.836288i	$0.315279\pi$
$109$			17.4622i			1.67258i	−0.548290	+	0.836288i	$0.684721\pi$
$110$	−0.0672983	+	1.21526i	−0.00641664	+	0.115870i
$111$	−10.2802	−	5.72233i	−0.975751	−	0.543140i
$112$	−6.11527	−	2.55541i	−0.577839	−	0.241463i
$113$	−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	$0.138765\pi$
$114$	−9.39381	−	0.372640i	−0.879811	−	0.0349009i
$115$	0.390745	−	2.21602i	0.0364371	−	0.206645i
$116$	1.34997	+	1.41461i	0.125342	+	0.131343i
$117$	17.4167	−	3.63729i	1.61018	−	0.336267i
$118$	−0.847785	+	1.98092i	−0.0780449	+	0.182359i
$119$	−9.14744	+	3.32940i	−0.838545	+	0.305205i
$120$	−0.0605820	−	2.49854i	−0.00553036	−	0.228084i
$121$	6.24640	−	5.24136i	0.567855	−	0.476487i
$122$	−14.9379	−	3.49531i	−1.35241	−	0.316450i
$123$	1.77909	−	5.13714i	0.160415	−	0.463200i
$124$	13.9469	−	0.892282i	1.25247	−	0.0801293i
$125$	2.48442	+	4.30314i	0.222213	+	0.384885i
$126$	4.64643	−	5.27524i	0.413937	−	0.469955i
$127$	9.88071	+	5.70463i	0.876771	+	0.506204i	0.869592	−	0.493770i	$-0.164382\pi$
$127$	9.88071	+	5.70463i	0.876771	+	0.506204i	0.00717861	+	0.999974i	$0.497715\pi$
$128$	10.4759	+	4.27254i	0.925951	+	0.377643i
$129$	1.18152	+	0.960266i	0.104027	+	0.0845467i
$130$	1.23892	+	4.09567i	0.108661	+	0.359214i
$131$	−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	$0.497317\pi$
$132$	4.16394	−	4.10029i	0.362425	−	0.356884i
$133$	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	$0.944294\pi$
$138$	−8.54523	+	6.61126i	−0.727418	+	0.562788i
$139$	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	$0.911115\pi$
$140$	1.36182	+	1.00180i	0.115095	+	0.0846672i
$141$	−0.109539	+	0.0418247i	−0.00922488	+	0.00352228i
$142$	10.4894	+	20.7381i	0.880247	+	1.74030i
$143$	−5.00259	+	8.66473i	−0.418337	+	0.724581i
$144$	−7.85415	+	9.07262i	−0.654512	+	0.756051i
$145$	−0.249391	−	0.431958i	−0.0207108	−	0.0358722i
$146$	1.00688	−	1.54046i	0.0833302	−	0.127489i
$147$	−1.39322	−	7.23626i	−0.114911	−	0.596836i
$148$	−12.4436	+	5.45217i	−1.02286	+	0.448165i
$149$	−3.55227	+	2.98071i	−0.291013	+	0.244189i	−0.776592	−	0.630004i	$-0.783053\pi$
$149$	−3.55227	+	2.98071i	−0.291013	+	0.244189i	0.485579	+	0.874193i	$0.338609\pi$
$150$	2.46766	−	11.3447i	0.201483	−	0.926287i
$151$	−1.81281	−	4.98066i	−0.147524	−	0.405320i	0.843817	−	0.536632i	$-0.180303\pi$
$151$	−1.81281	−	4.98066i	−0.147524	−	0.405320i	−0.991341	+	0.131311i	$0.958081\pi$
$152$	−6.90631	+	8.37533i	−0.560176	+	0.679329i
$153$	0.552402	+	17.6164i	0.0446591	+	1.42420i
$154$	0.470130	+	3.92496i	0.0378841	+	0.316282i
$155$	−3.51069	−	0.619030i	−0.281986	−	0.0497217i
$156$	8.82585	−	18.5526i	0.706633	−	1.48540i
$157$	6.04596	−	16.6111i	0.482520	−	1.32571i	−0.424805	−	0.905285i	$-0.639657\pi$
$157$	6.04596	−	16.6111i	0.482520	−	1.32571i	0.907326	−	0.420429i	$-0.138120\pi$
$158$	−5.51383	+	5.87787i	−0.438657	+	0.467618i
$159$	5.18757	+	8.66847i	0.411401	+	0.687455i
$160$	−2.33923	−	1.69011i	−0.184932	−	0.133615i
$161$		−	7.30834i		−	0.575978i
$162$	−6.44505	−	10.9755i	−0.506371	−	0.862316i
$163$	21.0349			1.64758			0.823789	−	0.566896i	$-0.191856\pi$
$163$	21.0349			1.64758			0.823789	+	0.566896i	$0.191856\pi$
$164$	−3.47945	−	5.22499i	−0.271699	−	0.408003i
$165$	−1.27911	+	0.765470i	−0.0995784	+	0.0595918i
$166$	−2.17614	+	2.31982i	−0.168901	+	0.180053i
$167$	−16.2585	−	5.91760i	−1.25812	−	0.457918i	−0.374982	−	0.927032i	$-0.622351\pi$
$167$	−16.2585	−	5.91760i	−1.25812	−	0.457918i	−0.883137	+	0.469114i	$0.844573\pi$
$168$	−1.60291	−	7.95743i	−0.123667	−	0.613929i
$169$	−3.85059	+	21.8378i	−0.296199	+	1.67983i
$170$	−4.20862	+	0.504106i	−0.322786	+	0.0386632i
$171$	−6.06673	−	9.78614i	−0.463934	−	0.748365i
$172$	1.70834	−	0.415205i	0.130260	−	0.0316591i
$173$	22.9789	−	8.36365i	1.74706	−	0.635877i	0.747461	−	0.664306i	$-0.231273\pi$
$173$	22.9789	−	8.36365i	1.74706	−	0.635877i	0.999596	+	0.0284290i	$0.00905045\pi$
$174$	−0.509019	+	2.34013i	−0.0385886	+	0.177405i
$175$	5.04807	+	6.01606i	0.381598	+	0.454771i
$176$	−0.859906	−	6.69290i	−0.0648179	−	0.504496i
$177$	−2.59138	+	0.498929i	−0.194780	+	0.0375018i
$178$	15.4383	+	10.0909i	1.15715	+	0.756344i
$179$	−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	$0.492809\pi$
$180$	2.49333	−	1.77563i	0.185842	−	0.132348i
$181$	−5.53930	−	3.19811i	−0.411733	−	0.237714i	0.279801	−	0.960058i	$-0.409731\pi$
$181$	−5.53930	−	3.19811i	−0.411733	−	0.237714i	−0.691534	+	0.722344i	$0.743065\pi$
$182$	6.27259	+	12.4013i	0.464955	+	0.919246i
$183$	−6.70223	−	17.5532i	−0.495443	−	1.29757i
$184$	0.106899	+	12.4751i	0.00788069	+	0.919676i
$185$	3.41279	−	0.601766i	0.250913	−	0.0442427i
$186$	10.4738	+	13.5376i	0.767973	+	0.992626i
$187$	−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	$-0.954520\pi$
$191$	−17.9929	−	15.0978i	−1.30192	−	1.09244i	−0.312110	−	0.950046i	$-0.601036\pi$
$192$	2.85250	+	13.5596i	0.205861	+	0.978581i
$193$	−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	$-0.182924\pi$
$194$	20.0481	−	6.06444i	1.43937	−	0.435402i
$195$	−3.30528	+	4.06686i	−0.236696	+	0.291234i
$196$	−7.62576	−	3.77541i	−0.544697	−	0.269672i
$197$	11.1556	−	19.3221i	0.794806	−	1.37664i	−0.128157	−	0.991754i	$-0.540906\pi$
$197$	11.1556	−	19.3221i	0.794806	−	1.37664i	0.922963	−	0.384890i	$-0.125761\pi$
$198$	7.01669	+	1.41145i	0.498655	+	0.100308i
$199$	−1.06520	+	0.614992i	−0.0755098	+	0.0435956i	−0.537280	−	0.843404i	$-0.680548\pi$
$199$	−1.06520	+	0.614992i	−0.0755098	+	0.0435956i	0.461770	+	0.887000i	$0.347215\pi$
$200$	−8.70489	−	10.1954i	−0.615529	−	0.720922i
$201$	−15.0799	−	5.22247i	−1.06365	−	0.368364i
$202$	2.80328	−	11.9803i	0.197238	−	0.842934i
$203$	−1.04130	−	1.24097i	−0.0730848	−	0.0870990i
$204$	16.5807	+	11.8013i	1.16088	+	0.826258i
$205$	0.547667	+	1.50470i	0.0382507	+	0.105093i
$206$	0.531989	−	1.24304i	0.0370654	−	0.0866067i
$207$	−12.5701	−	4.13378i	−0.873679	−	0.287318i
$208$	−10.8885	−	21.0769i	−0.754982	−	1.46142i
$209$	6.37630	+	1.12431i	0.441058	+	0.0777704i
$210$	−0.0820718	+	2.06893i	−0.00566349	+	0.142770i
$211$	−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	$0.728734\pi$
$212$	11.5936	+	1.28801i	0.796253	+	0.0884610i
$213$	−13.8434	+	24.8697i	−0.948537	+	1.70405i
$214$	1.13332	−	20.4652i	0.0774720	−	1.39897i
$215$	−0.448450			−0.0305840
$216$	−14.5931	−	1.74399i	−0.992935	−	0.118663i
$217$	−11.5781			−0.785973
$218$	−1.36548	+	24.6575i	−0.0924821	+	1.67002i
$219$	2.25366	−	0.0353256i	0.152288	−	0.00238708i
$220$	−0.190057	+	1.71074i	−0.0128136	+	0.115338i
$221$	−32.7424	−	11.9173i	−2.20249	−	0.801642i
$222$	−14.0687	−	8.88409i	−0.944226	−	0.596261i
$223$	−16.8245	−	2.96662i	−1.12666	−	0.198660i	−0.420894	−	0.907110i	$-0.638284\pi$
$223$	−16.8245	−	2.96662i	−1.12666	−	0.198660i	−0.705761	+	0.708450i	$0.749395\pi$
$224$	−8.43525	−	4.08655i	−0.563604	−	0.273044i
$225$	13.2027	−	5.27964i	0.880180	−	0.351976i
$226$	−1.02645	+	2.39840i	−0.0682786	+	0.159539i
$227$	−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	$0.926933\pi$
$228$	−13.2354	−	1.26075i	−0.876535	−	0.0834951i
$229$	−1.03366	−	1.23187i	−0.0683063	−	0.0814042i	0.730809	−	0.682582i	$-0.239143\pi$
$229$	−1.03366	−	1.23187i	−0.0683063	−	0.0814042i	−0.799115	+	0.601178i	$0.794698\pi$
$230$	0.725036	−	3.09858i	0.0478074	−	0.204314i
$231$	−3.65953	+	3.16976i	−0.240779	+	0.208555i
$232$	1.79561	+	2.10306i	0.117888	+	0.138073i
$233$	−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	$0.439865\pi$
$234$	24.8777	−	3.77411i	1.62631	−	0.246721i
$235$	0.0172679	−	0.0299089i	0.00112643	−	0.00195104i
$236$	−1.35202	+	2.73087i	−0.0880087	+	0.177765i
$237$	−9.74625	−	1.56144i	−0.633087	−	0.101427i
$238$	−13.1770	+	3.98598i	−0.854138	+	0.258373i
$239$	1.87083	+	10.6100i	0.121014	+	0.686305i	0.983596	+	0.180387i	$0.0577351\pi$
$239$	1.87083	+	10.6100i	0.121014	+	0.686305i	−0.862582	+	0.505918i	$0.831154\pi$
$240$	0.109832	−	3.53280i	0.00708960	−	0.228041i
$241$	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
$246$	2.91387	−	7.11477i	0.185782	−	0.453621i
$247$	22.4168	−	3.95269i	1.42635	−	0.251503i
$248$	19.7634	−	0.169353i	1.25498	−	0.0107539i
$249$	−3.84655	−	0.616253i	−0.243765	−	0.0390535i
$250$	3.17164	+	6.27052i	0.200592	+	0.396583i
$251$	−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	$0.722941\pi$
$252$	6.97350	−	7.08556i	0.439289	−	0.446349i
$253$	6.44400	−	3.72044i	0.405131	−	0.233902i
$254$	13.5060	+	8.82786i	0.847440	+	0.553909i
$255$	−3.39884	−	3.92400i	−0.212844	−	0.245730i
$256$	14.4585	+	6.85223i	0.903654	+	0.428264i
$257$	−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	$0.858362\pi$
$258$	1.59328	+	1.44833i	0.0991934	+	0.0901694i
$259$	10.5764	−	3.84951i	0.657188	−	0.239197i
$260$	1.42915	+	5.88017i	0.0886323	+	0.364673i
$261$	−2.72340	+	1.08907i	−0.168574	+	0.0674115i
$262$	−5.31458	+	0.636578i	−0.328336	+	0.0393279i
$263$	5.00913	−	28.4082i	0.308876	−	1.75173i	−0.295796	−	0.955251i	$-0.595585\pi$
$263$	5.00913	−	28.4082i	0.308876	−	1.75173i	0.604673	−	0.796474i	$-0.293304\pi$
$264$	6.20033	−	5.46420i	0.381604	−	0.336298i
$265$	−2.79606	−	1.01768i	−0.171761	−	0.0625158i
$266$	6.15297	−	6.55920i	0.377263	−	0.402170i
$267$	0.354030	+	22.5860i	0.0216663	+	1.38224i
$268$	−15.3378	+	10.2138i	−0.936905	+	0.623909i
$269$	−3.32709			−0.202856			−0.101428	−	0.994843i	$-0.532341\pi$
$269$	−3.32709			−0.202856			−0.101428	+	0.994843i	$0.532341\pi$
$270$	3.51206	+	1.31140i	0.213737	+	0.0798093i
$271$		−	21.4283i		−	1.30168i	−0.759217	−	0.650838i	$-0.774418\pi$
$271$		−	21.4283i		−	1.30168i	0.759217	−	0.650838i	$-0.225582\pi$
$272$	22.4344	−	6.99667i	1.36028	−	0.424236i
$273$	−8.27832	+	14.8720i	−0.501027	+	0.900094i
$274$	−17.3576	+	18.5036i	−1.04861	+	1.11784i
$275$	−2.73474	+	7.51363i	−0.164911	+	0.453089i
$276$	−12.5833	+	8.66722i	−0.757424	+	0.521705i
$277$	20.0857	+	3.54166i	1.20684	+	0.212798i	0.740651	−	0.671890i	$-0.234517\pi$
$277$	20.0857	+	3.54166i	1.20684	+	0.212798i	0.466184	+	0.884688i	$0.345628\pi$
$278$	0.414506	+	3.46057i	0.0248604	+	0.207551i
$279$	−6.54887	+	19.9139i	−0.392071	+	1.19221i
$280$	1.84462	+	1.52107i	0.110237	+	0.0909016i
$281$	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	$0.791157\pi$
$282$	−0.157946	+	0.0504930i	−0.00940553	+	0.00300681i
$283$	−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	$0.369182\pi$
$284$	13.1898	+	30.1035i	0.782673	+	1.78631i
$285$	3.20464	+	1.10983i	0.189826	+	0.0657406i
$286$	−7.74145	+	11.8439i	−0.457762	+	0.700342i
$287$	2.60035	+	4.50393i	0.153494	+	0.265859i
$288$	−11.7999	+	12.1968i	−0.695315	+	0.718705i
$289$	8.75798	−	15.1693i	0.515175	−	0.892309i
$290$	−0.318375	−	0.629448i	−0.0186956	−	0.0369625i
$291$	19.9070	+	16.1791i	1.16697	+	0.948437i
$292$	1.54223	−	2.09647i	0.0902520	−	0.122687i
$293$	3.81617	+	21.6426i	0.222943	+	1.26437i	0.866579	+	0.499040i	$0.166314\pi$
$293$	3.81617	+	21.6426i	0.222943	+	1.26437i	−0.643636	+	0.765332i	$0.722575\pi$
$294$	−1.40145	−	10.3269i	−0.0817345	−	0.602277i
$295$	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
$300$	4.37157	−	15.8263i	0.252392	−	0.913729i
$301$	−1.43437	+	0.252918i	−0.0826758	+	0.0145780i
$302$	−2.17031	−	7.17469i	−0.124887	−	0.412857i
$303$	14.0779	−	5.37527i	0.808753	−	0.308801i
$304$	−10.4070	+	11.2863i	−0.596881	+	0.647316i
$305$	4.79278	+	2.76711i	0.274434	+	0.158444i
$306$	−0.597521	+	24.9185i	−0.0341580	+	1.42449i
$307$	−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	$-0.444083\pi$
$308$	0.356929	+	5.57900i	0.0203379	+	0.317893i
$309$	1.62611	−	0.313081i	0.0925060	−	0.0178105i
$310$	−4.90887	−	1.14862i	−0.278805	−	0.0652375i
$311$	18.4841	−	15.5100i	1.04814	−	0.879492i	0.0552415	−	0.998473i	$-0.482407\pi$
$311$	18.4841	−	15.5100i	1.04814	−	0.879492i	0.992897	+	0.118981i	$0.0379627\pi$
$312$	13.9133	−	25.5071i	0.787685	−	1.44405i
$313$	−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	$0.554945\pi$
$314$	9.83613	−	22.9830i	0.555085	−	1.29701i
$315$	−2.15534	+	1.33616i	−0.121440	+	0.0752842i
$316$	−8.24544	+	7.86868i	−0.463842	+	0.442648i
$317$	−0.661246	+	3.75011i	−0.0371393	+	0.210627i	−0.997730	−	0.0673387i	$-0.978549\pi$
$317$	−0.661246	+	3.75011i	−0.0371393	+	0.210627i	0.960591	+	0.277966i	$0.0896603\pi$
$318$	6.64726	+	12.6460i	0.372760	+	0.709151i
$319$	0.564111	−	1.54988i	0.0315842	−	0.0867768i
$320$	−3.17095	−	2.56944i	−0.177261	−	0.143636i
$321$	21.5405	−	12.8907i	1.20227	−	0.719488i
$322$	0.571486	−	10.3197i	0.0318477	−	0.575097i
$323$			22.5485i			1.25463i
$324$	−8.24249	−	16.0019i	−0.457916	−	0.888995i
$325$			28.1105i			1.55929i
$326$	29.7023	+	1.64485i	1.64506	+	0.0910998i
$327$	−25.9531	+	15.5314i	−1.43521	+	0.858888i
$328$	−4.50458	−	7.65003i	−0.248724	−	0.422402i
$329$	0.0383635	−	0.105403i	0.00211505	−	0.00581104i
$330$	−1.86602	+	0.980861i	−0.102721	+	0.0539946i
$331$	−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	$0.758705\pi$
$332$	−3.25422	+	3.10553i	−0.178599	+	0.170438i
$333$	−0.638698	−	20.3684i	−0.0350004	−	1.11618i
$334$	−22.4951	−	9.62731i	−1.23087	−	0.526783i
$335$	4.41701	−	1.60766i	0.241327	−	0.0878359i
$336$	−1.64114	−	11.3616i	−0.0895316	−	0.619828i
$337$	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	$0.168180\pi$
$338$	−7.14485	+	30.5349i	−0.388629	+	1.66088i
$339$	−3.13751	+	0.604077i	−0.170406	+	0.0328090i
$340$	−5.98220	+	0.382724i	−0.324430	+	0.0207561i
$341$	−5.89404	−	10.2088i	−0.319180	−	0.552836i
$342$	−7.80128	−	14.2929i	−0.421845	−	0.772872i
$343$	16.1497	+	9.32403i	0.872001	+	0.503450i
$344$	2.44473	−	0.452704i	0.131811	−	0.0244082i
$345$	3.64109	−	1.39025i	0.196030	−	0.0748487i
$346$	33.1014	−	10.0130i	1.77954	−	0.538304i
$347$	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	$0.148424\pi$
$348$	−0.901750	+	3.26458i	−0.0483389	+	0.175000i
$349$	6.13674	−	7.31348i	0.328492	−	0.391482i	−0.576368	−	0.817190i	$-0.695531\pi$
$349$	6.13674	−	7.31348i	0.328492	−	0.391482i	0.904860	+	0.425708i	$0.139975\pi$
$350$	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	$0.0680326\pi$
$354$	−3.69818	+	0.501876i	−0.196556	+	0.0266744i
$355$	−1.45579	−	8.25619i	−0.0772653	−	0.438193i
$356$	21.0106	+	15.4561i	1.11356	+	0.819169i
$357$	−13.0843	−	10.6341i	−0.692494	−	0.562814i
$358$	−16.2191	+	8.20362i	−0.857205	+	0.433575i
$359$	−7.81239	+	13.5314i	−0.412322	+	0.714163i	−0.995143	−	0.0984378i	$-0.968615\pi$
$359$	−7.81239	+	13.5314i	−0.412322	+	0.714163i	0.582821	+	0.812600i	$0.301949\pi$
$360$	3.65955	−	2.31231i	0.192875	−	0.121869i
$361$	2.13480	+	3.69758i	0.112358	+	0.194609i
$362$	−7.57168	−	4.94905i	−0.397959	−	0.260116i
$363$	13.3457	+	4.62186i	0.700465	+	0.242585i
$364$	7.88748	+	18.0018i	0.413416	+	0.943549i
$365$	−0.508561	+	0.426733i	−0.0266193	+	0.0223362i
$366$	−8.09129	−	25.3101i	−0.422939	−	1.32298i
$367$	4.58311	+	12.5920i	0.239236	+	0.657296i	0.999966	+	0.00822764i	$0.00261897\pi$
$367$	4.58311	+	12.5920i	0.239236	+	0.657296i	−0.760730	+	0.649069i	$0.775159\pi$
$368$	−0.824561	+	17.6238i	−0.0429832	+	0.918705i
$369$	9.21740	−	1.92495i	0.479839	−	0.100209i
$370$	4.86608	−	0.582857i	0.252976	−	0.0303013i
$371$	−9.51718	−	1.67814i	−0.494108	−	0.0871245i
$372$	13.7309	+	19.9348i	0.711913	+	1.03357i
$373$	2.05166	−	5.63688i	0.106231	−	0.291867i	−0.875176	−	0.483804i	$-0.839255\pi$
$373$	2.05166	−	5.63688i	0.106231	−	0.291867i	0.981407	+	0.191937i	$0.0614770\pi$
$374$	−10.2225	−	9.58944i	−0.528595	−	0.495858i
$375$	−4.18580	+	7.51979i	−0.216154	+	0.388320i
$376$	−0.0639434	+	0.180480i	−0.00329763	+	0.00930755i
$377$		−	5.79853i		−	0.298640i
$378$	11.9730	+	2.21378i	0.615822	+	0.113865i
$379$	7.22372			0.371057			0.185529	−	0.982639i	$-0.440600\pi$
$379$	7.22372			0.371057			0.185529	+	0.982639i	$0.440600\pi$
$380$	3.25944	−	2.17054i	0.167206	−	0.111347i
$381$	0.309717	+	19.7590i	0.0158673	+	1.01228i
$382$	−24.2263	−	22.7259i	−1.23952	−	1.16276i
$383$	−3.09179	−	1.12532i	−0.157983	−	0.0575012i	0.261818	−	0.965117i	$-0.415678\pi$
$383$	−3.09179	−	1.12532i	−0.157983	−	0.0575012i	−0.419801	+	0.907616i	$0.637900\pi$
$384$	2.96756	+	19.3699i	0.151438	+	0.988467i
$385$	0.247623	−	1.40434i	0.0126201	−	0.0715719i
$386$	−1.82042	−	15.1981i	−0.0926570	−	0.773564i
$387$	−0.376308	+	2.61012i	−0.0191288	+	0.132680i
$388$	28.7831	−	6.99561i	1.46124	−	0.355148i
$389$	−14.6598	+	5.33573i	−0.743282	+	0.270532i	−0.685776	−	0.727813i	$-0.740537\pi$
$389$	−14.6598	+	5.33573i	−0.743282	+	0.270532i	−0.0575057	+	0.998345i	$0.518315\pi$
$390$	−4.98523	+	5.48414i	−0.252437	+	0.277700i
$391$	16.6568	+	19.8508i	0.842372	+	1.00390i
$392$	−10.4727	−	5.92737i	−0.528953	−	0.299377i
$393$	−4.29200	−	4.95517i	−0.216503	−	0.249955i
$394$	17.2632	−	26.4115i	0.869709	−	1.33059i
$395$	2.51778	−	1.45364i	0.126684	−	0.0731408i
$396$	9.79755	+	2.54172i	0.492345	+	0.127726i
$397$	5.69844	+	3.28999i	0.285996	+	0.165120i	0.636135	−	0.771578i	$-0.280532\pi$
$397$	5.69844	+	3.28999i	0.285996	+	0.165120i	−0.350139	+	0.936698i	$0.613866\pi$
$398$	−1.55220	+	0.785105i	−0.0778049	+	0.0393537i
$399$	10.8760	+	1.74244i	0.544481	+	0.0872309i
$400$	−11.4945	−	15.0771i	−0.574725	−	0.753853i
$401$	−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	$0.468360\pi$
$402$	−20.8852	−	8.55358i	−1.04166	−	0.426614i
$403$	−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
$408$	22.4900	+	17.9606i	1.11342	+	0.889182i
$409$	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	$0.927430\pi$
$410$	0.655671	+	2.16754i	0.0323813	+	0.107047i
$411$	−30.6813	−	4.91543i	−1.51340	−	0.242460i
$412$	0.848397	−	1.71364i	0.0417975	−	0.0844247i
$413$	1.26226	−	2.18630i	0.0621118	−	0.107581i
$414$	−17.4263	−	6.82004i	−0.856456	−	0.335187i
$415$	0.993693	−	0.573709i	0.0487785	−	0.0281623i
$416$	−13.7270	−	30.6130i	−0.673020	−	1.50093i
$417$	−3.22655	+	2.79473i	−0.158005	+	0.136858i
$418$	8.91573	+	2.08619i	0.436083	+	0.102039i
$419$	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	$0.524223\pi$
$420$	−0.277672	+	2.91502i	−0.0135490	+	0.142238i
$421$	−3.99170	−	10.9671i	−0.194544	−	0.534504i	0.803616	−	0.595148i	$-0.202907\pi$
$421$	−3.99170	−	10.9671i	−0.194544	−	0.534504i	−0.998159	+	0.0606441i	$0.980685\pi$
$422$	−13.6420	−	5.83841i	−0.664080	−	0.284209i
$423$	−0.159589	−	0.125602i	−0.00775949	−	0.00610698i
$424$	16.2701	+	2.72532i	0.790144	+	0.132353i
$425$	−27.4230	−	4.83542i	−1.33021	−	0.234552i
$426$	−21.4923	+	34.0348i	−1.04131	+	1.64899i
$427$	16.8903	+	6.14758i	0.817381	+	0.297502i
$428$	3.20060	−	28.8092i	0.154707	−	1.39255i
$429$	−17.3273	+	0.271602i	−0.836572	+	0.0131131i
$430$	−0.633234	−	0.0350672i	−0.0305373	−	0.00169109i
$431$	20.3897			0.982136			0.491068	−	0.871121i	$-0.336607\pi$
$431$	20.3897			0.982136			0.491068	+	0.871121i	$0.336607\pi$
$432$	−20.4698	−	3.60373i	−0.984854	−	0.173384i
$433$	−38.5969			−1.85485			−0.927424	−	0.374013i	$-0.877982\pi$
$433$	−38.5969			−1.85485			−0.927424	+	0.374013i	$0.877982\pi$
$434$	−16.3489	−	0.905366i	−0.784771	−	0.0434589i
$435$	0.420179	−	0.754852i	0.0201460	−	0.0361924i
$436$	−3.85626	+	34.7109i	−0.184681	+	1.66235i
$437$	−15.9077	−	5.78994i	−0.760970	−	0.276970i
$438$	3.18504	+	0.126347i	0.152187	+	0.00603707i
$439$	−33.3328	−	5.87748i	−1.59089	−	0.280517i	−0.693066	−	0.720874i	$-0.743741\pi$
$439$	−33.3328	−	5.87748i	−1.59089	−	0.280517i	−0.897823	+	0.440357i	$0.854852\pi$
$440$	−0.402144	+	2.40079i	−0.0191714	+	0.114453i
$441$	9.51566	−	8.50680i	0.453127	−	0.405086i
$442$	−45.3020	−	19.3881i	−2.15480	−	0.922198i
$443$	−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	$0.955688\pi$
$444$	−19.1709	−	13.6449i	−0.909812	−	0.647558i
$445$	−4.27668	−	5.09675i	−0.202734	−	0.241609i
$446$	−23.5251	−	5.50464i	−1.11395	−	0.260652i
$447$	−7.58954	−	2.62841i	−0.358973	−	0.124319i
$448$	−11.5914	−	6.43002i	−0.547644	−	0.303790i
$449$	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	$0.109276\pi$
$450$	19.0557	−	6.42272i	0.898295	−	0.302770i
$451$	−2.64751	+	4.58561i	−0.124666	+	0.215928i
$452$	−1.63695	+	3.30639i	−0.0769956	+	0.155520i
$453$	5.79010	−	7.12422i	0.272043	−	0.334725i
$454$	−1.47118	−	4.86348i	−0.0690459	−	0.228255i
$455$	−0.870556	−	4.93717i	−0.0408123	−	0.231458i
$456$	−18.5904	−	2.81520i	−0.870577	−	0.131834i
$457$	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	0.849449	−	0.527671i	$-0.176935\pi$
$461$	10.2480	+	8.59913i	0.477299	+	0.400502i	−0.372150	+	0.928173i	$0.621379\pi$
$462$	−5.41530	+	4.18970i	−0.251942	+	0.194922i
$463$	−23.4427	+	4.13359i	−1.08948	+	0.192104i	−0.689402	−	0.724379i	$-0.742127\pi$
$463$	−23.4427	+	4.13359i	−1.08948	+	0.192104i	−0.400074	+	0.916483i	$0.631016\pi$
$464$	2.37104	+	3.11004i	0.110073	+	0.144380i
$465$	−2.20248	−	5.76832i	−0.102138	−	0.267500i
$466$	−12.6545	+	6.40068i	−0.586210	+	0.296506i
$467$	−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	$0.889270\pi$
$468$	35.4237	−	3.38388i	1.63746	−	0.156420i
$469$	13.2212	−	7.63324i	0.610496	−	0.352470i
$470$	0.0267219	−	0.0408826i	0.00123259	−	0.00188577i
$471$	30.0656	−	5.78865i	1.38535	−	0.266727i
$472$	−2.12266	+	3.75040i	−0.0977033	+	0.172626i
$473$	−0.953199	−	1.13598i	−0.0438281	−	0.0522323i
$474$	−13.6401	−	2.96695i	−0.626510	−	0.136277i
$475$	17.0941	−	6.22176i	0.784333	−	0.285474i
$476$	−18.9183	+	4.59801i	−0.867117	+	0.210749i
$477$	−8.26949	+	15.4200i	−0.378634	+	0.706032i
$478$	1.81204	+	15.1282i	0.0828810	+	0.691947i
$479$	−4.28076	+	24.2774i	−0.195593	+	1.10926i	0.715979	+	0.698122i	$0.245981\pi$
$479$	−4.28076	+	24.2774i	−0.195593	+	1.10926i	−0.911572	+	0.411141i	$0.865131\pi$
$480$	0.431340	−	4.97990i	0.0196879	−	0.227300i
$481$	37.8574	+	13.7790i	1.72615	+	0.628266i
$482$	1.51764	+	1.42365i	0.0691268	+	0.0648455i
$483$	10.8620	−	6.50025i	0.494237	−	0.295771i
$484$	13.5739	−	9.03919i	0.616995	−	0.410872i
$485$	−7.55575			−0.343089
$486$	10.5798	−	19.3408i	0.479911	−	0.877317i
$487$		−	27.8176i		−	1.26054i	−0.776377	−	0.630268i	$-0.782945\pi$
$487$		−	27.8176i		−	1.26054i	0.776377	−	0.630268i	$-0.217055\pi$
$488$	−28.9212	−	10.2467i	−1.30920	−	0.463845i
$489$	18.7090	+	31.2629i	0.846051	+	1.41376i
$490$	2.23874	+	2.10009i	0.101136	+	0.0948725i
$491$	−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	$0.886539\pi$
$492$	4.67088	−	9.81856i	0.210580	−	0.442655i
$493$	5.65672	+	0.997432i	0.254766	+	0.0449221i
$494$	31.9627	−	3.82848i	1.43807	−	0.172251i
$495$	−2.27535	−	1.22023i	−0.102269	−	0.0548454i
$496$	27.9202	+	1.30629i	1.25365	+	0.0586544i
$497$	−9.31271	−	25.5865i	−0.417732	−	1.14771i
$498$	−5.38333	−	1.17097i	−0.241233	−	0.0524723i
$499$	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	$0.188113\pi$
$500$	3.98818	+	9.10230i	0.178357	+	0.407067i
$501$	−5.66576	−	29.4273i	−0.253127	−	1.31472i
$502$	−6.59672	−	4.31179i	−0.294426	−	0.192445i
$503$	−4.48697	−	7.77165i	−0.200064	−	0.346521i	0.748485	−	0.663152i	$-0.230782\pi$
$503$	−4.48697	−	7.77165i	−0.200064	−	0.346521i	−0.948549	+	0.316631i	$0.897448\pi$
$504$	10.4010	−	9.45987i	0.463297	−	0.421376i
$505$	−2.21925	+	3.84386i	−0.0987555	+	0.171050i
$506$	9.39017	−	4.74955i	0.417444	−	0.211143i
$507$	−35.8810	+	13.7002i	−1.59353	+	0.608448i
$508$	18.3808	+	13.5215i	0.815516	+	0.599919i
$509$	6.33516	+	35.9285i	0.280801	+	1.59250i	0.719909	+	0.694068i	$0.244183\pi$
$509$	6.33516	+	35.9285i	0.280801	+	1.59250i	−0.439108	+	0.898434i	$0.644706\pi$
$510$	−4.49249	−	5.80666i	−0.198931	−	0.257123i
$511$	−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
$516$	2.13654	+	2.16971i	0.0940559	+	0.0955161i
$517$	0.112467	−	0.0198309i	0.00494627	−	0.000872161i
$518$	15.2355	−	4.60866i	0.669409	−	0.202493i
$519$	32.8685	+	26.7134i	1.44277	+	1.17259i
$520$	1.55823	+	8.41485i	0.0683328	+	0.369016i
$521$	−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	$0.909547\pi$
$522$	−3.93074	+	1.32485i	−0.172044	+	0.0579873i
$523$	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	$0.733180\pi$
$524$	−7.55423	+	0.483299i	−0.330008	+	0.0211130i
$525$	−4.45142	+	12.8535i	−0.194276	+	0.560973i
$526$	9.29457	−	39.7221i	0.405262	−	1.73197i
$527$	31.4483	−	26.3883i	1.36991	−	1.14949i
$528$	9.18245	−	7.23089i	0.399615	−	0.314684i
$529$	3.33127	−	1.21248i	0.144838	−	0.0527166i
$530$	−3.86860	−	1.65566i	−0.168041	−	0.0719173i
$531$	−3.04638	−	3.40766i	−0.132202	−	0.147880i
$532$	9.20121	−	8.78078i	0.398923	−	0.380695i
$533$	−3.23253	+	18.3326i	−0.140016	+	0.794072i
$534$	−1.26623	+	31.9202i	−0.0547952	+	1.38132i
$535$	−2.52886	+	6.94799i	−0.109332	+	0.300388i
$536$	−22.4564	+	13.2231i	−0.969970	+	0.571150i
$537$	−19.4504	−	10.8268i	−0.839346	−	0.467212i
$538$	−4.69802	−	0.260166i	−0.202546	−	0.0112166i
$539$			7.17740i			0.309152i
$540$	4.85665	+	2.12639i	0.208997	+	0.0915054i
$541$			9.11080i			0.391704i	0.980633	+	0.195852i	$0.0627472\pi$
$541$			9.11080i			0.391704i	−0.980633	+	0.195852i	$0.937253\pi$
$542$	1.67561	−	30.2578i	0.0719738	−	1.29968i
$543$	−0.173633	−	11.0772i	−0.00745130	−	0.475370i
$544$	32.2256	−	8.12536i	1.38166	−	0.348372i
$545$	3.04690	−	8.37130i	0.130515	−	0.358587i
$546$	−12.8523	+	20.3527i	−0.550029	+	0.871014i
$547$	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	$-0.131738\pi$
$548$	−25.9567	+	24.7707i	−1.10882	+	1.05815i
$549$	20.1272	−	25.5735i	0.859008	−	1.09145i
$550$	−4.44912	+	10.3958i	−0.189711	+	0.443277i
$551$	−3.52612	+	1.28340i	−0.150218	+	0.0546747i
$552$	−18.4459	+	11.2546i	−0.785112	+	0.479027i
$553$	7.23333	−	6.06948i	0.307592	−	0.258101i
$554$	28.0851	+	6.57163i	1.19322	+	0.279202i
$555$	3.92980	+	4.53700i	0.166811	+	0.192585i
$556$	0.314699	+	4.91892i	0.0133462	+	0.208609i
$557$	−16.1779	−	28.0210i	−0.685481	−	1.18729i	−0.973285	−	0.229598i	$-0.926259\pi$
$557$	−16.1779	−	28.0210i	−0.685481	−	1.18729i	0.287805	−	0.957689i	$-0.407075\pi$
$558$	−10.8045	+	27.6073i	−0.457392	+	1.16871i
$559$	−4.51494	−	2.60670i	−0.190962	−	0.110252i
$560$	2.48575	+	2.29208i	0.105042	+	0.0968579i
$561$	2.71560	−	16.9503i	0.114653	−	0.715642i
$562$	4.14902	+	13.7160i	0.175016	+	0.578573i
$563$	−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	$0.494586\pi$
$564$	−0.226976	+	0.0589479i	−0.00955739	+	0.00248215i
$565$	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	$0.330019\pi$
$570$	4.43832	+	1.81773i	0.185901	+	0.0761361i
$571$	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	$0.705341\pi$
$572$	−11.8575	+	16.1188i	−0.495785	+	0.673959i
$573$	6.43565	−	40.1702i	0.268853	−	1.67814i
$574$	3.31963	+	6.56312i	0.138559	+	0.273939i
$575$	10.4530	−	18.1050i	0.435918	−	0.755033i
$576$	−17.6158	+	16.2998i	−0.733991	+	0.679159i
$577$	−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	$0.899448\pi$
$578$	13.5529	−	20.7349i	0.563726	−	0.862459i
$579$	14.1703	−	12.2738i	0.588898	−	0.510084i
$580$	−0.400341	−	0.913708i	−0.0166233	−	0.0379397i
$581$	2.85477	−	2.39544i	0.118436	−	0.0993796i
$582$	26.8445	+	24.4024i	1.11274	+	1.01151i
$583$	−3.36523	−	9.24588i	−0.139373	−	0.382925i
$584$	2.34164	−	2.83972i	0.0968977	−	0.117509i
$585$	−8.98414	−	1.29527i	−0.371449	−	0.0535527i
$586$	3.69625	+	30.8588i	0.152691	+	1.27477i
$587$	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	$0.264328\pi$
$588$	−1.17140	−	14.6917i	−0.0483076	−	0.605875i
$589$	−9.17260	+	25.2015i	−0.377951	+	1.03841i
$590$	0.752067	−	0.801720i	0.0309621	−	0.0330063i
$591$	38.6395	−	0.605665i	1.58942	−	0.0249137i
$592$	−25.9391	+	8.08968i	−1.06609	+	0.332484i
$593$			46.0294i			1.89020i	0.326782	+	0.945100i	$0.394036\pi$
$593$			46.0294i			1.89020i	−0.326782	+	0.945100i	$0.605964\pi$
$594$	4.14308	+	11.6839i	0.169993	+	0.479396i
$595$	4.96617			0.203593
$596$	−7.71933	+	5.14050i	−0.316196	+	0.210563i
$597$	−1.86144	−	1.03615i	−0.0761838	−	0.0424068i
$598$	25.3106	−	26.9817i	1.03503	−	1.10336i
$599$	17.8974	+	6.51412i	0.731268	+	0.266160i	0.680702	−	0.732561i	$-0.261675\pi$
$599$	17.8974	+	6.51412i	0.731268	+	0.266160i	0.0505667	+	0.998721i	$0.483897\pi$
$600$	7.41043	−	22.0056i	0.302529	−	0.898376i
$601$	−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	$0.903156\pi$
$602$	−2.04518	+	0.244971i	−0.0833554	+	0.00998427i
$603$	−5.65064	−	27.0574i	−0.230112	−	1.10186i
$604$	−2.50355	−	10.3007i	−0.101868	−	0.419131i
$605$	−3.90904	+	1.42277i	−0.158925	+	0.0578440i
$606$	20.2990	−	6.48930i	0.824591	−	0.263610i
$607$	−8.73413	−	10.4089i	−0.354508	−	0.422486i	0.559089	−	0.829108i	$-0.311151\pi$
$607$	−8.73413	−	10.4089i	−0.354508	−	0.422486i	−0.913596	+	0.406622i	$0.866707\pi$
$608$	−15.5777	+	15.1231i	−0.631760	+	0.613322i
$609$	0.918223	−	2.65137i	0.0372083	−	0.107439i
$610$	6.55126	+	4.28208i	0.265253	+	0.173376i
$611$	0.347702	−	0.200746i	0.0140665	−	0.00812131i
$612$	−2.79226	+	35.1394i	−0.112871	+	1.42043i
$613$	−25.2780	−	14.5943i	−1.02097	−	0.589457i	−0.106584	−	0.994304i	$-0.533991\pi$
$613$	−25.2780	−	14.5943i	−1.02097	−	0.589457i	−0.914384	+	0.404847i	$0.867325\pi$
$614$	−17.1186	−	33.8445i	−0.690849	−	1.36585i
$615$	−1.74924	+	2.15229i	−0.0705363	+	0.0867888i
$616$	0.0677442	+	7.90574i	0.00272949	+	0.318531i
$617$	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	$0.382637\pi$
$618$	2.32063	−	0.314930i	0.0933492	−	0.0126683i
$619$	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
$624$	21.6408	−	34.9293i	0.866326	−	1.39829i
$625$	3.67505	+	20.8422i	0.147002	+	0.833690i
$626$	−23.8686	+	7.22015i	−0.953983	+	0.288575i
$627$	4.00026	+	10.4767i	0.159755	+	0.418400i
$628$	15.6863	−	31.6840i	0.625951	−	1.26433i
$629$	−19.9540	+	34.5613i	−0.795618	+	1.37805i
$630$	−3.14793	+	1.71819i	−0.125417	+	0.0684542i
$631$	−29.5141	+	17.0400i	−1.17494	+	0.678350i	−0.954838	−	0.297127i	$-0.903972\pi$
$631$	−29.5141	+	17.0400i	−1.17494	+	0.678350i	−0.220099	+	0.975477i	$0.570638\pi$
$632$	−12.2583	+	10.4662i	−0.487608	+	0.416323i
$633$	−3.43596	−	17.8460i	−0.136567	−	0.709314i
$634$	−1.22696	+	5.24364i	−0.0487287	+	0.208252i
$635$	−3.74139	−	4.45881i	−0.148472	−	0.176943i
$636$	8.39740	+	18.3765i	0.332979	+	0.728677i
$637$	8.63026	+	23.7114i	0.341943	+	0.939481i
$638$	0.917748	−	2.14440i	0.0363340	−	0.0848976i
$639$	−49.2752	+	1.54513i	−1.94930	+	0.0611245i
$640$	−4.27662	−	3.87614i	−0.169048	−	0.153218i
$641$	−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	$0.591387\pi$
$642$	31.4242	−	16.5179i	1.24021	−	0.651910i
$643$	−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	$0.695947\pi$
$644$	1.61393	−	14.5273i	0.0635979	−	0.572456i
$645$	−0.398864	−	0.666506i	−0.0157053	−	0.0262436i
$646$	−1.76321	+	31.8396i	−0.0693725	+	1.25271i
$647$	−9.31643			−0.366267			−0.183133	−	0.983088i	$-0.558624\pi$
$647$	−9.31643			−0.366267			−0.183133	+	0.983088i	$0.558624\pi$
$648$	−10.3875	−	23.2400i	−0.408060	−	0.912955i
$649$	2.57031			0.100893
$650$	−2.19814	+	39.6935i	−0.0862182	+	1.55691i
$651$	−10.2979	−	17.2079i	−0.403606	−	0.674430i
$652$	41.8125	+	4.64522i	1.63750	+	0.181921i
$653$	0.849632	+	0.309241i	0.0332487	+	0.0121015i	0.358591	−	0.933495i	$-0.383257\pi$
$653$	0.849632	+	0.309241i	0.0332487	+	0.0121015i	−0.325342	+	0.945596i	$0.605480\pi$
$654$	−37.8616	+	19.9017i	−1.48050	+	0.778217i
$655$	1.90154	+	0.335294i	0.0742995	+	0.0131010i
$656$	−5.76249	−	11.1545i	−0.224988	−	0.435509i
$657$	2.05697	+	3.31807i	0.0802501	+	0.129450i
$658$	0.0624132	−	0.145834i	0.00243312	−	0.00568520i
$659$	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	$0.872921\pi$
$660$	−2.71162	+	1.23911i	−0.105549	+	0.0482322i
$661$	−13.7378	−	16.3720i	−0.534337	−	0.636798i	0.429571	−	0.903033i	$-0.358665\pi$
$661$	−13.7378	−	16.3720i	−0.534337	−	0.636798i	−0.963908	+	0.266235i	$0.914220\pi$
$662$	−9.41638	+	40.2427i	−0.365978	+	1.56408i
$663$	−11.4101	−	59.2627i	−0.443131	−	2.30157i
$664$	−4.83797	+	4.13069i	−0.187750	+	0.160302i
$665$	−2.80963	+	1.62214i	−0.108953	+	0.0629040i
$666$	0.690864	−	28.8112i	0.0267705	−	1.11641i
$667$	−2.15620	+	3.73464i	−0.0834882	+	0.144606i
$668$	−31.0113	−	15.3533i	−1.19986	−	0.594036i
$669$	−10.5551	−	27.6440i	−0.408084	−	1.06878i
$670$	6.36275	−	1.92470i	0.245815	−	0.0743578i
$671$	3.17782	+	18.0223i	0.122678	+	0.695743i
$672$	−1.42894	−	16.1715i	−0.0551224	−	0.623830i
$673$	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	0.933995	−	0.357285i	$-0.116298\pi$
$677$	19.3668	+	16.2506i	0.744325	+	0.624563i	−0.189670	+	0.981848i	$0.560742\pi$
$678$	−4.47756	+	0.607645i	−0.171960	+	0.0233365i
$679$	−24.1671	+	4.26132i	−0.927450	+	0.163534i
$680$	−8.47709	+	0.0726400i	−0.325082	+	0.00278562i
$681$	3.92491	−	4.82926i	0.150403	−	0.185058i
$682$	−7.52439	−	14.8762i	−0.288124	−	0.569639i
$683$	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	$0.534627\pi$
$684$	−9.89815	−	20.7923i	−0.378465	−	0.795015i
$685$	7.92601	−	4.57608i	0.302837	−	0.174843i
$686$	22.0751	+	14.4288i	0.842830	+	0.550896i
$687$	0.911489	−	2.63193i	0.0347755	−	0.100414i
$688$	3.48748	−	0.448072i	0.132959	−	0.0170826i
$689$	−22.2349	−	26.4985i	−0.847082	−	1.00951i
$690$	5.25011	−	1.67839i	0.199868	−	0.0638951i
$691$	−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	$0.463135\pi$
$692$	47.5239	−	11.5505i	1.80659	−	0.439083i
$693$	−7.96592	−	2.61967i	−0.302600	−	0.0995130i
$694$	41.9350	−	5.02295i	1.59183	−	0.190669i
$695$	0.218326	−	1.23819i	0.00828156	−	0.0469671i
$696$	−1.52859	+	4.53924i	−0.0579412	+	0.172059i
$697$	−17.3282	−	6.30694i	−0.656352	−	0.238892i
$698$	9.23727	−	9.84713i	0.349636	−	0.372719i
$699$	−15.1757	−	8.44736i	−0.573997	−	0.319509i
$700$	8.70586	+	13.0733i	0.329050	+	0.494125i
$701$	1.58337			0.0598031			0.0299015	−	0.999553i	$-0.490481\pi$
$701$	1.58337			0.0598031			0.0299015	+	0.999553i	$0.490481\pi$
$702$	27.7362	+	33.6175i	1.04683	+	1.26881i
$703$		−	26.0710i		−	0.983285i
$704$	−0.231274	−	13.4939i	−0.00871647	−	0.508569i
$705$	0.0598105		0.000937515i	0.00225259		3.53088e-5i
$706$	16.9308	−	18.0486i	0.637198	−	0.679267i
$707$	−4.93043	+	13.5462i	−0.185428	+	0.509459i
$708$	−5.26126	+	0.419490i	−0.197730	+	0.0157654i
$709$	12.4085	+	2.18796i	0.466012	+	0.0821706i	0.401724	−	0.915761i	$-0.368411\pi$
$709$	12.4085	+	2.18796i	0.466012	+	0.0821706i	0.0642885	+	0.997931i	$0.479522\pi$
$710$	−1.41004	−	11.7720i	−0.0529180	−	0.441795i
$711$	−6.34791	−	15.8741i	−0.238065	−	0.595325i
$712$	28.4594	+	23.4677i	1.06656	+	0.879488i
$713$	10.5414	+	28.9624i	0.394780	+	1.08465i
$714$	−17.6441	−	16.0390i	−0.660315	−	0.600243i
$715$	3.91009	−	3.28095i	0.146229	−	0.122701i
$716$	−23.5436	+	10.3157i	−0.879867	+	0.385514i
$717$	−14.1051	+	12.2174i	−0.526764	+	0.456266i
$718$	−12.0896	+	18.4962i	−0.451180	+	0.690271i
$719$	−4.75877	−	8.24242i	−0.177472	−	0.307391i	0.763542	−	0.645758i	$-0.223459\pi$
$719$	−4.75877	−	8.24242i	−0.177472	−	0.307391i	−0.941014	+	0.338368i	$0.890125\pi$
$720$	5.34828	−	2.97893i	0.199319	−	0.111018i
$721$	−0.792075	+	1.37191i	−0.0294984	+	0.0510927i
$722$	2.72530	+	5.38809i	0.101425	+	0.200524i
$723$	−0.403158	+	2.51645i	−0.0149936	+	0.0935876i
$724$	−10.3046	−	7.58038i	−0.382967	−	0.281723i
$725$	−0.804688	−	4.56361i	−0.0298854	−	0.169488i
$726$	18.4833	+	7.56988i	0.685980	+	0.280945i
$727$	−19.7951	+	23.5909i	−0.734161	+	0.874939i	−0.995924	−	0.0901927i	$-0.971252\pi$
$727$	−19.7951	+	23.5909i	−0.734161	+	0.874939i	0.261763	+	0.965132i	$0.415696\pi$
$728$	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
$732$	−9.44615	−	36.3719i	−0.349140	−	1.34434i
$733$	−4.98281	+	0.878603i	−0.184044	+	0.0324519i	−0.264910	−	0.964273i	$-0.585342\pi$
$733$	−4.98281	+	0.878603i	−0.184044	+	0.0324519i	0.0808664	+	0.996725i	$0.474231\pi$
$734$	5.48693	+	18.1389i	0.202526	+	0.669519i
$735$	−0.594717	+	3.71212i	−0.0219365	+	0.136924i
$736$	−2.54244	+	24.8212i	−0.0937156	+	0.914923i
$737$	13.4609	+	7.77167i	0.495840	+	0.286273i
$738$	13.1660	−	1.99736i	0.484646	−	0.0735239i
$739$	−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	$-0.395656\pi$
$740$	6.91673	−	0.442513i	0.254264	−	0.0162671i
$741$	25.8128	+	29.8012i	0.948257	+	1.09477i
$742$	−13.3075	−	3.11382i	−0.488534	−	0.114312i
$743$	5.34278	−	4.48312i	0.196007	−	0.164470i	−0.539502	−	0.841984i	$-0.681387\pi$
$743$	5.34278	−	4.48312i	0.196007	−	0.164470i	0.735509	+	0.677515i	$0.236943\pi$
$744$	17.8299	+	29.2226i	0.653675	+	1.07135i
$745$	2.22303	−	0.809117i	0.0814455	−	0.0296437i
$746$	3.33783	−	7.79913i	0.122207	−	0.285546i
$747$	−2.50533	−	6.26502i	−0.0916651	−	0.229225i
$748$	−13.6849	−	14.3401i	−0.500369	−	0.524327i
$749$	−4.17003	+	23.6494i	−0.152370	+	0.864131i
$750$	−6.49858	+	10.2910i	−0.237294	+	0.375774i
$751$	−8.84901	+	24.3125i	−0.322905	+	0.887174i	0.666951	+	0.745101i	$0.267599\pi$
$751$	−8.84901	+	24.3125i	−0.322905	+	0.887174i	−0.989856	+	0.142073i	$0.954623\pi$
$752$	−0.104404	+	0.249847i	−0.00380723	+	0.00911098i
$753$	−0.151275	−	9.65088i	−0.00551278	−	0.351698i
$754$	0.453424	−	8.18782i	0.0165127	−	0.298183i
$755$			2.70401i			0.0984091i
$756$	16.7333	+	4.06221i	0.608584	+	0.147741i
$757$			9.14500i			0.332381i	0.986094	+	0.166190i	$0.0531466\pi$
$757$			9.14500i			0.332381i	−0.986094	+	0.166190i	$0.946853\pi$
$758$	10.2002	+	0.564868i	0.370490	+	0.0205169i
$759$	11.2610	+	6.26827i	0.408747	+	0.227524i
$760$	4.77223	−	2.81004i	0.173107	−	0.101931i
$761$	−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	$0.118140\pi$
$762$	−1.10774	+	27.9249i	−0.0401293	+	1.01161i
$763$	5.02428	−	28.4941i	0.181891	−	1.03156i
$764$	−32.4316	−	33.9845i	−1.17334	−	1.22952i
$765$	2.80899	−	8.54161i	0.101559	−	0.308823i
$766$	−4.27777	−	1.83078i	−0.154562	−	0.0661487i
$767$	8.49133	−	3.09059i	0.306604	−	0.111595i
$768$	2.67569	+	27.5833i	0.0965505	+	0.995328i
$769$	−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	$0.525170\pi$
$770$	0.459471	−	1.96364i	0.0165582	−	0.0707646i
$771$	4.55186	−	13.1435i	0.163931	−	0.473352i
$772$	−1.38209	−	21.6028i	−0.0497425	−	0.777503i
$773$	4.50449	+	7.80201i	0.162015	+	0.280619i	0.935591	−	0.353085i	$-0.114867\pi$
$773$	4.50449	+	7.80201i	0.162015	+	0.280619i	−0.773576	+	0.633704i	$0.781534\pi$
$774$	−0.735467	+	3.65619i	−0.0264358	+	0.131419i
$775$	−28.6826	−	16.5599i	−1.03031	−	0.594849i
$776$	41.1902	−	7.62742i	1.47864	−	0.273809i
$777$	15.1283	+	12.2953i	0.542725	+	0.441091i
$778$	−21.1176	+	6.38798i	−0.757103	+	0.229020i
$779$	11.8636	−	2.09187i	0.425057	−	0.0749491i
$780$	−7.46823	+	7.35406i	−0.267406	+	0.263318i
$781$	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
$786$	−5.67305	−	7.33256i	−0.202351	−	0.261544i
$787$	−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	$-0.218581\pi$
$788$	26.4418	−	35.9444i	0.941951	−	1.28047i
$789$	46.6768	−	17.8223i	1.66174	−	0.634490i
$790$	3.66891	−	1.85574i	0.130534	−	0.0660241i
$791$	1.52828	−	2.64706i	0.0543393	−	0.0941185i
$792$	13.6359	+	4.35517i	0.484530	+	0.154754i
$793$	32.1687	+	55.7178i	1.14234	+	1.97860i
$794$	7.78921	+	5.09123i	0.276429	+	0.180681i
$795$	−0.974372	−	5.06078i	−0.0345574	−	0.179487i
$796$	−2.25318	+	0.987231i	−0.0798618	+	0.0349915i
$797$	31.1047	−	26.0999i	1.10178	−	0.924506i	0.104240	−	0.994552i	$-0.466759\pi$
$797$	31.1047	−	26.0999i	1.10178	−	0.924506i	0.997544	+	0.0700458i	$0.0223145\pi$
$798$	15.2212	+	3.31087i	0.538824	+	0.117204i
$799$	0.136027	+	0.373730i	0.00481227	+	0.0132216i
$800$	−15.0518	−	22.1884i	−0.532163	−	0.784478i
$801$	−33.2533	+	20.6148i	−1.17495	+	0.728387i
$802$	−4.22136	+	0.505633i	−0.149062	+	0.0178545i
$803$	−2.16193	−	0.381207i	−0.0762930	−	0.0134525i
$804$	−28.8221	−	13.7112i	−1.01648	−	0.483558i
$805$	−1.27520	+	3.50358i	−0.0449449	+	0.123485i
$806$	−42.7453	−	40.0979i	−1.50564	−	1.41239i
$807$	−2.95921	−	4.94486i	−0.104169	−	0.174067i
$808$	8.21794	−	23.1951i	0.289106	−	0.816001i
$809$		−	37.9716i		−	1.33501i	−0.744606	−	0.667505i	$-0.767362\pi$
$809$		−	37.9716i		−	1.33501i	0.744606	−	0.667505i	$-0.232638\pi$
$810$	1.17466	+	6.38616i	0.0412734	+	0.224387i
$811$	11.0327			0.387411			0.193706	−	0.981060i	$-0.437949\pi$
$811$	11.0327			0.387411			0.193706	+	0.981060i	$0.437949\pi$
$812$	−1.79581	−	2.69672i	−0.0630206	−	0.0946362i
$813$	31.8476	−	19.0589i	1.11695	−	0.668426i
$814$	11.8195	+	11.0875i	0.414273	+	0.388616i
$815$	−10.0840	−	3.67028i	−0.353228	−	0.128564i
$816$	30.3525	+	27.1199i	1.06255	+	0.949387i
$817$	−0.585847	+	3.32250i	−0.0204962	+	0.116240i
$818$	0.363456	+	3.03438i	0.0127079	+	0.106094i
$819$	−29.4664	+	0.923984i	−1.02964	+	0.0322866i
$820$	0.756347	+	3.11195i	0.0264128	+	0.108674i
$821$	19.8243	−	7.21546i	0.691874	−	0.251821i	0.0279364	−	0.999610i	$-0.491106\pi$
$821$	19.8243	−	7.21546i	0.691874	−	0.251821i	0.663937	+	0.747788i	$0.268884\pi$
$822$	−42.9391	−	9.34000i	−1.49767	−	0.325770i
$823$	−14.2858	−	17.0252i	−0.497972	−	0.593460i	0.457254	−	0.889336i	$-0.348833\pi$
$823$	−14.2858	−	17.0252i	−0.497972	−	0.593460i	−0.955226	+	0.295876i	$0.904389\pi$
$824$	1.33198	−	2.35340i	0.0464017	−	0.0819845i
$825$	−13.5994	+	2.61835i	−0.473471	+	0.0911592i
$826$	1.95334	−	2.98846i	0.0679653	−	0.103982i
$827$	−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	$0.374168\pi$
$828$	−24.0735	−	10.9929i	−0.836612	−	0.382030i
$829$	−28.6959	−	16.5676i	−0.996649	−	0.575416i	−0.0893942	−	0.995996i	$-0.528493\pi$
$829$	−28.6959	−	16.5676i	−0.996649	−	0.575416i	−0.907255	+	0.420581i	$0.861826\pi$
$830$	1.44801	−	0.732403i	0.0502610	−	0.0254221i
$831$	12.6011	+	33.0023i	0.437126	+	1.14484i
$832$	−16.9893	−	44.3006i	−0.589000	−	1.53585i
$833$	−24.6161	+	4.34048i	−0.852896	+	0.150389i
$834$	−4.77458	+	3.69399i	−0.165330	+	0.127912i
$835$	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	0.980996	−	0.194026i	$-0.0621545\pi$
$839$	27.8146	+	23.3392i	0.960267	+	0.805759i	−0.0207297	+	0.999785i	$0.506599\pi$
$840$	−0.620031	+	4.09444i	−0.0213931	+	0.141271i
$841$	−4.86981	−	27.6181i	−0.167924	−	0.952347i
$842$	−4.77889	−	15.7982i	−0.164692	−	0.544444i
$843$	−11.0690	+	13.6195i	−0.381237	+	0.469079i
$844$	−18.8066	−	9.31088i	−0.647350	−	0.320494i
$845$	5.65633	−	9.79704i	0.194584	−	0.337029i
$846$	−0.215526	−	0.189836i	−0.00740994	−	0.00652669i
$847$	−11.7007	+	6.75539i	−0.402040	+	0.232118i
$848$	22.7610	+	5.12054i	0.781617	+	0.175840i
$849$	−15.5961	−	5.40125i	−0.535258	−	0.185370i
$850$	−38.3446	−	8.97224i	−1.31521	−	0.307745i
$851$	−19.2589	−	22.9519i	−0.660188	−	0.786781i
$852$	−33.0097	+	46.3782i	−1.13089	+	1.58889i
$853$	8.87061	+	24.3718i	0.303724	+	0.834475i	0.993845	+	0.110781i	$0.0353351\pi$
$853$	8.87061	+	24.3718i	0.303724	+	0.834475i	−0.690121	+	0.723694i	$0.742443\pi$
$854$	23.3693	+	10.0015i	0.799681	+	0.342243i
$855$	1.20082	+	5.74998i	0.0410672	+	0.196645i
$856$	6.77219	−	40.4298i	0.231469	−	1.38186i
$857$	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	$0.177879\pi$
$858$	−24.4883	−	0.971419i	−0.836017	−	0.0331637i
$859$	−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	$0.722555\pi$
$860$	−0.891416	−	0.0990332i	−0.0303970	−	0.00337700i
$861$	−4.38111	+	7.87067i	−0.149308	+	0.268232i
$862$	28.7913	+	1.59440i	0.980634	+	0.0543054i
$863$	−35.7624			−1.21737			−0.608683	−	0.793414i	$-0.708302\pi$
$863$	−35.7624			−1.21737			−0.608683	+	0.793414i	$0.708302\pi$
$864$	−28.6226	−	6.68931i	−0.973761	−	0.227575i
$865$	−12.4753			−0.424174
$866$	−54.5007	−	3.01813i	−1.85201	−	0.102560i
$867$	30.3348	−	0.475491i	1.03022	−	0.0161485i
$868$	−23.0146	−	2.55684i	−0.781167	−	0.0867849i
$869$	9.03391	+	3.28807i	0.306454	+	0.111540i
$870$	0.652341	−	1.03303i	0.0221164	−	0.0350231i
$871$	53.8147	+	9.48899i	1.82344	+	0.321522i
$872$	−8.15949	+	48.7120i	−0.276315	+	1.64959i
$873$	−6.34025	+	43.9768i	−0.214585	+	1.48839i
$874$	−22.0098	−	9.41961i	−0.744491	−	0.318623i
$875$	−2.81586	−	7.73650i	−0.0951934	−	0.261542i
$876$	4.48756	+	0.427466i	0.151621	+	0.0144428i
$877$	11.4196	+	13.6093i	0.385612	+	0.459554i	0.923577	−	0.383413i	$-0.125251\pi$
$877$	11.4196	+	13.6093i	0.385612	+	0.459554i	−0.537965	+	0.842967i	$0.680807\pi$
$878$	−46.6080	−	10.9058i	−1.57294	−	0.368053i
$879$	−28.7719	+	24.9213i	−0.970452	+	0.840573i
$880$	−0.755580	+	3.35859i	−0.0254706	+	0.113218i
$881$	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	$0.322073\pi$
$882$	14.1018	−	11.2679i	0.474832	−	0.379411i
$883$	−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	$0.327894\pi$
$884$	−62.4527	−	30.9194i	−2.10051	−	1.03993i
$885$	1.32935	+	0.212975i	0.0446857	+	0.00715907i
$886$	−3.59070	−	11.8703i	−0.120632	−	0.398790i
$887$	2.85336	+	16.1822i	0.0958066	+	0.543346i	0.994497	+	0.104763i	$0.0334084\pi$
$887$	2.85336	+	16.1822i	0.0958066	+	0.543346i	−0.898691	+	0.438583i	$0.855481\pi$
$888$	−26.0033	−	20.7664i	−0.872615	−	0.696874i
$889$	−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
$894$	−10.5113	−	4.30492i	−0.351550	−	0.143978i
$895$	6.45709	−	1.13856i	0.215837	−	0.0380578i
$896$	−15.8649	−	9.98592i	−0.530009	−	0.333606i
$897$	44.7391	+	7.16762i	1.49379	+	0.239320i
$898$	34.6127	−	17.5071i	1.15504	−	0.584220i
$899$	5.91654	+	3.41591i	0.197328	+	0.113927i
$900$	27.4099	−	7.57911i	0.913662	−	0.252637i
$901$	29.6752	−	17.1330i	0.988624	−	0.570782i
$902$	−4.09699	+	6.26809i	−0.136415	+	0.208705i
$903$	−1.65167	−	1.90687i	−0.0549641	−	0.0634567i
$904$	−2.57000	+	4.54079i	−0.0854770	+	0.151024i
$905$	2.09749	+	2.49969i	0.0697228	+	0.0830924i
$906$	8.73300	−	9.60698i	0.290135	−	0.319171i
$907$	−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	$0.550994\pi$
$908$	−1.69707	−	6.98252i	−0.0563194	−	0.231723i
$909$	20.5102	+	16.1422i	0.680281	+	0.535404i
$910$	−0.843200	−	7.03961i	−0.0279518	−	0.233361i
$911$	−4.26579	+	24.1925i	−0.141332	+	0.801533i	0.828908	+	0.559385i	$0.188963\pi$
$911$	−4.26579	+	24.1925i	−0.141332	+	0.801533i	−0.970240	+	0.242147i	$0.922148\pi$
$912$	−26.0305	−	5.42890i	−0.861956	−	0.179769i
$913$	3.56541	+	1.29770i	0.117998	+	0.0429477i
$914$	12.8059	+	12.0128i	0.423583	+	0.397349i
$915$	0.150233	+	9.58438i	0.00496654	+	0.316850i
$916$	−1.78264	−	2.67694i	−0.0589002	−	0.0884486i
$917$	6.27121			0.207094
$918$	−37.5663	+	21.2751i	−1.23987	+	0.702184i
$919$		−	38.5765i		−	1.27252i	−0.771474	−	0.636261i	$-0.780480\pi$
$919$		−	38.5765i		−	1.27252i	0.771474	−	0.636261i	$-0.219520\pi$
$920$	2.12548	−	5.99915i	0.0700749	−	0.197786i
$921$	22.5924	−	40.5873i	0.744445	−	1.33740i
$922$	13.7983	+	12.9438i	0.454424	+	0.426280i
$923$	33.3340	−	91.5843i	1.09720	−	3.01453i
$924$	−7.97429	+	5.49261i	−0.262335	+	0.180694i
$925$	31.7070	+	5.59080i	1.04252	+	0.183824i
$926$	−33.4255	+	4.00369i	−1.09843	+	0.131570i
$927$	1.91162	+	2.13833i	0.0627858	+	0.0702318i
$928$	3.10484	+	4.57694i	0.101921	+	0.150245i
$929$	−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	$0.916974\pi$
$930$	−2.65895	−	8.31739i	−0.0871904	−	0.272738i
$931$	12.5089	−	10.4962i	0.409962	−	0.343999i
$932$	−18.3694	+	8.04854i	−0.601708	+	0.263639i
$933$	39.4919	+	13.6768i	1.29291	+	0.447759i
$934$	−32.9339	−	21.5265i	−1.07763	−	0.704367i
$935$	2.52812	+	4.37883i	0.0826783	+	0.143203i
$936$	50.2846	−	2.00821i	1.64360	−	0.0656405i
$937$	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	$-0.00200211\pi$
$938$	19.2658	−	9.74467i	0.629052	−	0.318175i
$939$	−23.7007	−	19.2624i	−0.773444	−	0.628605i
$940$	0.0409296	−	0.0556387i	0.00133498	−	0.00181473i
$941$	3.69758	+	20.9700i	0.120538	+	0.683603i	0.983859	+	0.178947i	$0.0572692\pi$
$941$	3.69758	+	20.9700i	0.120538	+	0.683603i	−0.863321	+	0.504655i	$0.831620\pi$
$942$	42.9068	−	5.82285i	1.39798	−	0.189719i
$943$	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	$0.424265\pi$
$948$	−19.0285	−	5.25609i	−0.618017	−	0.170710i
$949$	−7.60059	+	1.34019i	−0.246726	+	0.0435044i
$950$	24.6243	−	7.44873i	0.798918	−	0.241669i
$951$	−6.16171	+	2.35268i	−0.199807	+	0.0762910i
$952$	−27.0731	+	5.01328i	−0.877444	+	0.162481i
$953$	−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	$0.724924\pi$
$954$	−12.8827	+	21.1271i	−0.417093	+	0.684016i
$955$	5.99135	+	10.3773i	0.193876	+	0.335802i
$956$	1.37573	+	21.5034i	0.0444943	+	0.695471i
$957$	2.80524	−	0.540103i	0.0906805	−	0.0174591i
$958$	−7.94305	+	33.9461i	−0.256628	+	1.09675i
$959$	22.7706	−	19.1068i	0.735300	−	0.616990i
$960$	0.998483	−	6.99814i	0.0322259	−	0.225864i
$961$	16.7526	−	6.09746i	0.540408	−	0.196692i
$962$	52.3790	+	22.4169i	1.68877	+	0.722749i
$963$	38.3174	+	20.5490i	1.23476	+	0.662182i
$964$	2.03166	+	2.12894i	0.0654355	+	0.0685686i
$965$	−0.958840	+	5.43785i	−0.0308661	+	0.175051i
$966$	15.8459	−	8.32931i	0.509835	−	0.267991i
$967$	−7.29159	+	20.0335i	−0.234482	+	0.644233i	0.765518	+	0.643415i	$0.222483\pi$
$967$	−7.29159	+	20.0335i	−0.234482	+	0.644233i	−1.00000		0.000818662i	$0.999739\pi$
$968$	19.8738	−	11.7024i	0.638770	−	0.376128i
$969$	−33.5125	+	20.0553i	−1.07658	+	0.644268i
$970$	−10.6691	−	0.590832i	−0.342564	−	0.0189705i
$971$		−	38.3665i		−	1.23124i	−0.788044	−	0.615619i	$-0.788906\pi$
$971$		−	38.3665i		−	1.23124i	0.788044	−	0.615619i	$-0.211094\pi$
$972$	16.4516	−	26.4829i	0.527686	−	0.849439i
$973$		−	4.08348i		−	0.130910i
$974$	2.17524	−	39.2799i	0.0696991	−	1.25861i
$975$	−41.7791	+	25.0023i	−1.33800	+	0.800714i
$976$	−40.0369	−	16.7303i	−1.28155	−	0.535525i
$977$	−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	$0.199906\pi$
$978$	23.9734	+	45.6078i	0.766585	+	1.45838i
$979$	3.82042	−	21.6667i	0.122101	−	0.692470i
$980$	2.99700	+	3.14050i	0.0957356	+	0.100320i
$981$	−46.1668	−	24.7585i	−1.47399	−	0.790479i
$982$	−15.9897	+	37.3614i	−0.510253	+	1.19225i
$983$	−41.2780	+	15.0240i	−1.31656	+	0.479190i	−0.902356	−	0.430992i	$-0.858164\pi$
$983$	−41.2780	+	15.0240i	−1.31656	+	0.479190i	−0.414208	+	0.910182i	$0.635942\pi$
$984$	7.36329	−	13.4991i	0.234733	−	0.430334i
$985$	−8.71938	+	7.31643i	−0.277823	+	0.233121i
$986$	7.90958	+	1.85076i	0.251892	+	0.0589402i
$987$	0.190776	−	0.0367308i	0.00607245	−	0.00116915i
$988$	45.4324	−	2.90664i	1.44540	−	0.0924724i
$989$	1.93861	+	3.35778i	0.0616443	+	0.106771i
$990$	−3.11749	−	1.90096i	−0.0990803	−	0.0604163i
$991$	29.3156	+	16.9254i	0.931241	+	0.537652i	0.887204	−	0.461378i	$-0.152645\pi$
$991$	29.3156	+	16.9254i	0.931241	+	0.537652i	0.0440369	+	0.999030i	$0.485978\pi$
$992$	39.3226	+	4.02781i	1.24849	+	0.127883i
$993$	−47.2885	+	18.0559i	−1.50065	+	0.572985i
$994$	−11.1492	−	36.8576i	−0.353633	−	1.16905i
$995$	0.617958	−	0.108963i	0.0195906	−	0.00345435i
$996$	−7.50997	−	2.07442i	−0.237962	−	0.0657305i
$997$	−4.25751	+	5.07390i	−0.134837	+	0.160692i	−0.829238	−	0.558896i	$-0.811225\pi$
$997$	−4.25751	+	5.07390i	−0.134837	+	0.160692i	0.694401	+	0.719588i	$0.255669\pi$
$998$	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.11.31	yes	192
3.2	odd	2		648.2.v.b.35.2		192
4.3	odd	2		864.2.bh.b.335.9		192
8.3	odd	2	inner	216.2.v.b.11.14	✓	192
8.5	even	2		864.2.bh.b.335.10		192
24.11	even	2		648.2.v.b.35.19		192
27.5	odd	18	inner	216.2.v.b.59.14	yes	192
27.22	even	9		648.2.v.b.611.19		192
108.59	even	18		864.2.bh.b.815.10		192
216.5	odd	18		864.2.bh.b.815.9		192
216.59	even	18	inner	216.2.v.b.59.31	yes	192
216.211	odd	18		648.2.v.b.611.2		192

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

\(f(q)\)	\(=\)	\(q+(1.41205 + 0.0781964i) q^{2} +(0.889428 + 1.48624i) q^{3} +(1.98777 + 0.220834i) q^{4} +(-0.479395 - 0.174486i) q^{5} +(1.13970 + 2.16820i) q^{6} +(-1.63176 - 0.287723i) q^{7} +(2.78956 + 0.467266i) q^{8} +(-1.41783 + 2.64381i) q^{9} +O(q^{10})\)	\(q+(1.41205 + 0.0781964i) q^{2} +(0.889428 + 1.48624i) q^{3} +(1.98777 + 0.220834i) q^{4} +(-0.479395 - 0.174486i) q^{5} +(1.13970 + 2.16820i) q^{6} +(-1.63176 - 0.287723i) q^{7} +(2.78956 + 0.467266i) q^{8} +(-1.41783 + 2.64381i) q^{9} +(-0.663286 - 0.283869i) q^{10} +(-0.576981 - 1.58524i) q^{11} +(1.43977 + 3.15073i) q^{12} +(-3.81226 - 4.54327i) q^{13} +(-2.28162 - 0.533876i) q^{14} +(-0.167060 - 0.867690i) q^{15} +(3.90246 + 0.877936i) q^{16} +(5.08792 - 2.93751i) q^{17} +(-2.20879 + 3.62233i) q^{18} +(-1.91901 + 3.32382i) q^{19} +(-0.914395 - 0.452704i) q^{20} +(-1.02370 - 2.68110i) q^{21} +(-0.690766 - 2.28356i) q^{22} +(0.765923 + 4.34377i) q^{23} +(1.78665 + 4.56157i) 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} +(-0.168046 - 1.23829i) q^{30} +(6.88153 - 1.21340i) q^{31} +(5.44182 + 1.54485i) q^{32} +(1.84287 - 2.26749i) q^{33} +(7.41411 - 3.75006i) q^{34} +(0.732053 + 0.422651i) q^{35} +(-3.40217 + 4.94219i) q^{36} +(-5.88275 + 3.39641i) q^{37} +(-2.96965 + 4.54335i) q^{38} +(3.36168 - 9.70686i) q^{39} +(-1.25577 - 0.710743i) q^{40} +(-2.01755 - 2.40442i) q^{41} +(-1.23587 - 3.86589i) q^{42} +(0.826023 - 0.300648i) q^{43} +(-0.796830 - 3.27851i) q^{44} +(1.14101 - 1.02004i) q^{45} +(0.741855 + 6.19351i) q^{46} +(-0.0117553 + 0.0666674i) q^{47} +(2.16614 + 6.58087i) q^{48} +(-3.99800 - 1.45515i) q^{49} +(-4.88870 - 4.58593i) q^{50} +(8.89120 + 4.94918i) q^{51} +(-6.57458 - 9.87286i) q^{52} +5.83248 q^{53} +(-7.34822 - 0.0609986i) q^{54} +0.860632i q^{55} +(-4.41745 - 1.56508i) q^{56} +(-6.64683 + 0.104187i) q^{57} +(1.00842 + 0.945969i) q^{58} +(-0.521107 + 1.43173i) q^{59} +(-0.140461 - 1.76166i) q^{60} +(-10.6832 - 1.88373i) q^{61} +(9.81195 - 1.17527i) q^{62} +(3.07425 - 3.90612i) q^{63} +(7.56333 + 2.60693i) q^{64} +(1.03484 + 2.84321i) q^{65} +(2.77954 - 3.05771i) q^{66} +(-7.05812 + 5.92246i) q^{67} +(10.7623 - 4.71552i) q^{68} +(-5.77466 + 5.00182i) q^{69} +(1.00065 + 0.654048i) q^{70} +(8.21657 + 14.2315i) q^{71} +(-5.19050 + 6.71258i) q^{72} +(0.650656 - 1.12697i) q^{73} +(-8.57233 + 4.33589i) q^{74} +(1.29867 - 8.10609i) q^{75} +(-4.54857 + 6.18322i) q^{76} +(0.485382 + 2.75274i) q^{77} +(5.50589 - 13.4437i) 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} +(-1.44281 - 5.55547i) q^{84} +(-2.95168 + 0.520461i) q^{85} +(1.18990 - 0.359938i) q^{86} +(-0.267885 + 1.67209i) q^{87} +(-0.868796 - 4.69174i) q^{88} +(11.2944 + 6.52081i) q^{89} +(1.69093 - 1.35112i) q^{90} +(4.91348 + 8.51039i) q^{91} +(0.563227 + 8.80355i) q^{92} +(7.92403 + 9.14839i) q^{93} +(-0.0218122 + 0.0932185i) q^{94} +(1.49992 - 1.25859i) q^{95} +(2.54409 + 9.46190i) q^{96} +(13.9173 - 5.06549i) q^{97} +(-5.53159 - 2.36738i) 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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