LMFDB - Embedded newform 216.2.v.b.83.1

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			83.1
Character	$\chi$	$=$	216.83
Dual form			216.2.v.b.203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41378 + 0.0350966i) q^{2} +(1.62005 - 0.612720i) q^{3} +(1.99754 - 0.0992376i) q^{4} +(1.31649 - 1.10467i) q^{5} +(-2.26889 + 0.923108i) q^{6} +(1.63653 + 4.49634i) q^{7} +(-2.82059 + 0.210407i) q^{8} +(2.24915 - 1.98528i) q^{9} +O(q^{10})$	\(q+(-1.41378 + 0.0350966i) q^{2} +(1.62005 - 0.612720i) q^{3} +(1.99754 - 0.0992376i) q^{4} +(1.31649 - 1.10467i) q^{5} +(-2.26889 + 0.923108i) q^{6} +(1.63653 + 4.49634i) q^{7} +(-2.82059 + 0.210407i) q^{8} +(2.24915 - 1.98528i) q^{9} +(-1.82246 + 1.60796i) q^{10} +(0.757427 - 0.902667i) q^{11} +(3.17531 - 1.38470i) q^{12} +(-5.36812 + 0.946545i) q^{13} +(-2.47150 - 6.29938i) q^{14} +(1.45594 - 2.59627i) q^{15} +(3.98030 - 0.396461i) q^{16} +(-0.394582 + 0.227812i) q^{17} +(-3.11012 + 2.88568i) q^{18} +(1.73047 - 2.99726i) q^{19} +(2.52012 - 2.33726i) q^{20} +(5.40626 + 6.28157i) q^{21} +(-1.03915 + 1.30275i) q^{22} +(-1.07038 - 0.389588i) q^{23} +(-4.44059 + 2.06910i) q^{24} +(-0.355379 + 2.01545i) q^{25} +(7.55611 - 1.52661i) q^{26} +(2.42732 - 4.59435i) q^{27} +(3.71524 + 8.81919i) q^{28} +(0.152108 - 0.862650i) q^{29} +(-1.96725 + 3.72164i) q^{30} +(2.15993 - 5.93437i) q^{31} +(-5.61335 + 0.700203i) q^{32} +(0.673992 - 1.92646i) q^{33} +(0.549855 - 0.335924i) q^{34} +(7.12145 + 4.11157i) q^{35} +(4.29574 - 4.18886i) q^{36} +(5.49344 - 3.17164i) q^{37} +(-2.34131 + 4.29820i) q^{38} +(-8.11668 + 4.82261i) q^{39} +(-3.48086 + 3.39282i) q^{40} +(-11.4320 + 2.01577i) q^{41} +(-7.86372 - 8.69100i) q^{42} +(-1.41495 - 1.18728i) q^{43} +(1.42341 - 1.87827i) q^{44} +(0.767916 - 5.09817i) q^{45} +(1.52696 + 0.513224i) q^{46} +(-2.28362 + 0.831169i) q^{47} +(6.20539 - 3.08110i) q^{48} +(-12.1765 + 10.2173i) q^{49} +(0.431691 - 2.86188i) q^{50} +(-0.499659 + 0.610835i) q^{51} +(-10.6291 + 2.42348i) q^{52} -12.1387 q^{53} +(-3.27045 + 6.58059i) q^{54} -2.02506i q^{55} +(-5.56205 - 12.3380i) q^{56} +(0.966974 - 5.91602i) q^{57} +(-0.184772 + 1.22493i) q^{58} +(3.18940 + 3.80098i) q^{59} +(2.65064 - 5.33062i) q^{60} +(-2.41946 - 6.64740i) q^{61} +(-2.84539 + 8.46569i) q^{62} +(12.6073 + 6.86396i) q^{63} +(7.91146 - 1.18694i) q^{64} +(-6.02148 + 7.17612i) q^{65} +(-0.885262 + 2.74724i) q^{66} +(0.600205 + 3.40393i) q^{67} +(-0.765584 + 0.494220i) q^{68} +(-1.97279 + 0.0246918i) q^{69} +(-10.2125 - 5.56291i) q^{70} +(3.41347 + 5.91231i) q^{71} +(-5.92621 + 6.07289i) q^{72} +(-0.407067 + 0.705061i) q^{73} +(-7.65520 + 4.67680i) q^{74} +(0.659175 + 3.48289i) q^{75} +(3.15924 - 6.15887i) q^{76} +(5.29825 + 1.92840i) q^{77} +(11.3059 - 7.10296i) q^{78} +(-12.8555 - 2.26677i) q^{79} +(4.80209 - 4.91886i) q^{80} +(1.11735 - 8.93037i) q^{81} +(16.0916 - 3.25107i) q^{82} +(10.5557 + 1.86125i) q^{83} +(11.4226 + 12.0112i) q^{84} +(-0.267808 + 0.735795i) q^{85} +(2.04209 + 1.62889i) q^{86} +(-0.282139 - 1.49074i) q^{87} +(-1.94646 + 2.70542i) q^{88} +(7.03637 + 4.06245i) q^{89} +(-0.906734 + 7.23464i) q^{90} +(-13.0411 - 22.5878i) q^{91} +(-2.17679 - 0.671994i) q^{92} +(-0.136895 - 10.9374i) q^{93} +(3.19936 - 1.25524i) q^{94} +(-1.03283 - 5.85748i) q^{95} +(-8.66490 + 4.57378i) q^{96} +(-1.18161 - 0.991491i) q^{97} +(16.8563 - 14.8723i) q^{98} +(-0.0884767 - 3.53394i) 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41378	+	0.0350966i	−0.999692	+	0.0248170i
$2$	−1.41378	+	0.0350966i	−0.999692	+	0.0248170i
$3$	1.62005	−	0.612720i	0.935339	−	0.353754i
$3$	1.62005	−	0.612720i	0.935339	−	0.353754i
$4$	1.99754	−	0.0992376i	0.998768	−	0.0496188i
$5$	1.31649	−	1.10467i	0.588754	−	0.494023i	−0.299055	−	0.954236i	$-0.596671\pi$
$5$	1.31649	−	1.10467i	0.588754	−	0.494023i	0.887809	+	0.460213i	$0.152227\pi$
$6$	−2.26889	+	0.923108i	−0.926271	+	0.376857i
$7$	1.63653	+	4.49634i	0.618551	+	1.69946i	0.710505	+	0.703692i	$0.248466\pi$
$7$	1.63653	+	4.49634i	0.618551	+	1.69946i	−0.0919543	+	0.995763i	$0.529311\pi$
$8$	−2.82059	+	0.210407i	−0.997229	+	0.0743900i
$9$	2.24915	−	1.98528i	0.749716	−	0.661759i
$10$	−1.82246	+	1.60796i	−0.576313	+	0.508482i
$11$	0.757427	−	0.902667i	0.228373	−	0.272164i	−0.639674	−	0.768646i	$-0.720931\pi$
$11$	0.757427	−	0.902667i	0.228373	−	0.272164i	0.868047	+	0.496482i	$0.165375\pi$
$12$	3.17531	−	1.38470i	0.916634	−	0.399728i
$13$	−5.36812	+	0.946545i	−1.48885	+	0.262524i	−0.858108	−	0.513469i	$-0.828360\pi$
$13$	−5.36812	+	0.946545i	−1.48885	+	0.262524i	−0.630741	+	0.775993i	$0.717249\pi$
$14$	−2.47150	−	6.29938i	−0.660536	−	1.68358i
$15$	1.45594	−	2.59627i	0.375922	−	0.670353i
$16$	3.98030	−	0.396461i	0.995076	−	0.0991153i
$17$	−0.394582	+	0.227812i	−0.0957001	+	0.0552525i	−0.547086	−	0.837076i	$-0.684263\pi$
$17$	−0.394582	+	0.227812i	−0.0957001	+	0.0552525i	0.451386	+	0.892329i	$0.350930\pi$
$18$	−3.11012	+	2.88568i	−0.733063	+	0.680161i
$19$	1.73047	−	2.99726i	0.396997	−	0.687619i	−0.596357	−	0.802720i	$-0.703386\pi$
$19$	1.73047	−	2.99726i	0.396997	−	0.687619i	0.993354	+	0.115100i	$0.0367189\pi$
$20$	2.52012	−	2.33726i	0.563516	−	0.522628i
$21$	5.40626	+	6.28157i	1.17974	+	1.37075i
$22$	−1.03915	+	1.30275i	−0.221548	+	0.277748i
$23$	−1.07038	−	0.389588i	−0.223191	−	0.0812347i	0.228004	−	0.973660i	$-0.426780\pi$
$23$	−1.07038	−	0.389588i	−0.223191	−	0.0812347i	−0.451195	+	0.892425i	$0.649002\pi$
$24$	−4.44059	+	2.06910i	−0.906431	+	0.422353i
$25$	−0.355379	+	2.01545i	−0.0710758	+	0.403091i
$26$	7.55611	−	1.52661i	1.48188	−	0.299392i
$27$	2.42732	−	4.59435i	0.467139	−	0.884184i
$28$	3.71524	+	8.81919i	0.702114	+	1.66667i
$29$	0.152108	−	0.862650i	0.0282458	−	0.160190i	−0.967422	−	0.253168i	$-0.918527\pi$
$29$	0.152108	−	0.862650i	0.0282458	−	0.160190i	0.995668	+	0.0929779i	$0.0296386\pi$
$30$	−1.96725	+	3.72164i	−0.359170	+	0.679476i
$31$	2.15993	−	5.93437i	0.387935	−	1.06584i	−0.579994	−	0.814621i	$-0.696945\pi$
$31$	2.15993	−	5.93437i	0.387935	−	1.06584i	0.967929	−	0.251223i	$-0.0808328\pi$
$32$	−5.61335	+	0.700203i	−0.992310	+	0.123780i
$33$	0.673992	−	1.92646i	0.117327	−	0.335354i
$34$	0.549855	−	0.335924i	0.0942994	−	0.0576105i
$35$	7.12145	+	4.11157i	1.20375	+	0.694983i
$36$	4.29574	−	4.18886i	0.715957	−	0.698144i
$37$	5.49344	−	3.17164i	0.903117	−	0.521415i	0.0249066	−	0.999690i	$-0.492071\pi$
$37$	5.49344	−	3.17164i	0.903117	−	0.521415i	0.878210	+	0.478275i	$0.158738\pi$
$38$	−2.34131	+	4.29820i	−0.379810	+	0.697260i
$39$	−8.11668	+	4.82261i	−1.29971	+	0.772235i
$40$	−3.48086	+	3.39282i	−0.550373	+	0.536452i
$41$	−11.4320	+	2.01577i	−1.78538	+	0.314810i	−0.966019	−	0.258472i	$-0.916781\pi$
$41$	−11.4320	+	2.01577i	−1.78538	+	0.314810i	−0.819358	+	0.573282i	$0.805670\pi$
$42$	−7.86372	−	8.69100i	−1.21340	−	1.34105i
$43$	−1.41495	−	1.18728i	−0.215777	−	0.181059i	0.528492	−	0.848938i	$-0.322758\pi$
$43$	−1.41495	−	1.18728i	−0.215777	−	0.181059i	−0.744269	+	0.667880i	$0.767202\pi$
$44$	1.42341	−	1.87827i	0.214587	−	0.283161i
$45$	0.767916	−	5.09817i	0.114474	−	0.759991i
$46$	1.52696	+	0.513224i	0.225138	+	0.0756708i
$47$	−2.28362	+	0.831169i	−0.333100	+	0.121239i	−0.503155	−	0.864196i	$-0.667828\pi$
$47$	−2.28362	+	0.831169i	−0.333100	+	0.121239i	0.170055	+	0.985435i	$0.445605\pi$
$48$	6.20539	−	3.08110i	0.895670	−	0.444718i
$49$	−12.1765	+	10.2173i	−1.73950	+	1.45961i
$50$	0.431691	−	2.86188i	0.0610504	−	0.404731i
$51$	−0.499659	+	0.610835i	−0.0699662	+	0.0855340i
$52$	−10.6291	+	2.42348i	−1.47399	+	0.336076i
$53$	−12.1387			−1.66737			−0.833687	−	0.552237i	$-0.813774\pi$
$53$	−12.1387			−1.66737			−0.833687	+	0.552237i	$0.813774\pi$
$54$	−3.27045	+	6.58059i	−0.445052	+	0.895505i
$55$		−	2.02506i		−	0.273059i
$56$	−5.56205	−	12.3380i	−0.743260	−	1.64873i
$57$	0.966974	−	5.91602i	0.128079	−	0.783596i
$58$	−0.184772	+	1.22493i	−0.0242617	+	0.160842i
$59$	3.18940	+	3.80098i	0.415225	+	0.494846i	0.932599	−	0.360913i	$-0.117535\pi$
$59$	3.18940	+	3.80098i	0.415225	+	0.494846i	−0.517374	+	0.855759i	$0.673091\pi$
$60$	2.65064	−	5.33062i	0.342197	−	0.688180i
$61$	−2.41946	−	6.64740i	−0.309780	−	0.851112i	−0.992699	−	0.120619i	$-0.961512\pi$
$61$	−2.41946	−	6.64740i	−0.309780	−	0.851112i	0.682919	−	0.730494i	$-0.260710\pi$
$62$	−2.84539	+	8.46569i	−0.361365	+	1.07514i
$63$	12.6073	+	6.86396i	1.58837	+	0.864778i
$64$	7.91146	−	1.18694i	0.988932	−	0.148368i
$65$	−6.02148	+	7.17612i	−0.746873	+	0.890089i
$66$	−0.885262	+	2.74724i	−0.108968	+	0.338162i
$67$	0.600205	+	3.40393i	0.0733267	+	0.415856i	0.999270	+	0.0381946i	$0.0121607\pi$
$67$	0.600205	+	3.40393i	0.0733267	+	0.415856i	−0.925944	+	0.377662i	$0.876728\pi$
$68$	−0.765584	+	0.494220i	−0.0928407	+	0.0599329i
$69$	−1.97279	+	0.0246918i	−0.237496	+	0.00297255i
$70$	−10.2125	−	5.56291i	−1.22062	−	0.664895i
$71$	3.41347	+	5.91231i	0.405105	+	0.701662i	0.994334	−	0.106304i	$-0.0339017\pi$
$71$	3.41347	+	5.91231i	0.405105	+	0.701662i	−0.589229	+	0.807966i	$0.700568\pi$
$72$	−5.92621	+	6.07289i	−0.698411	+	0.715697i
$73$	−0.407067	+	0.705061i	−0.0476436	+	0.0825211i	−0.888864	−	0.458172i	$-0.848505\pi$
$73$	−0.407067	+	0.705061i	−0.0476436	+	0.0825211i	0.841220	+	0.540693i	$0.181838\pi$
$74$	−7.65520	+	4.67680i	−0.889899	+	0.543667i
$75$	0.659175	+	3.48289i	0.0761150	+	0.402170i
$76$	3.15924	−	6.15887i	0.362389	−	0.706471i
$77$	5.29825	+	1.92840i	0.603791	+	0.219762i
$78$	11.3059	−	7.10296i	1.28014	−	0.804252i
$79$	−12.8555	−	2.26677i	−1.44636	−	0.255032i	−0.605308	−	0.795991i	$-0.706950\pi$
$79$	−12.8555	−	2.26677i	−1.44636	−	0.255032i	−0.841049	+	0.540959i	$0.818061\pi$
$80$	4.80209	−	4.91886i	0.536890	−	0.549945i
$81$	1.11735	−	8.93037i	0.124150	−	0.992264i
$82$	16.0916	−	3.25107i	1.77701	−	0.359021i
$83$	10.5557	+	1.86125i	1.15864	+	0.204299i	0.719743	−	0.694241i	$-0.244260\pi$
$83$	10.5557	+	1.86125i	1.15864	+	0.204299i	0.438893	+	0.898539i	$0.355371\pi$
$84$	11.4226	+	12.0112i	1.24631	+	1.31053i
$85$	−0.267808	+	0.735795i	−0.0290478	+	0.0798082i
$86$	2.04209	+	1.62889i	0.220204	+	0.175648i
$87$	−0.282139	−	1.49074i	−0.0302484	−	0.159824i
$88$	−1.94646	+	2.70542i	−0.207494	+	0.288399i
$89$	7.03637	+	4.06245i	0.745853	+	0.430619i	0.824194	−	0.566308i	$-0.191629\pi$
$89$	7.03637	+	4.06245i	0.745853	+	0.430619i	−0.0783403	+	0.996927i	$0.524962\pi$
$90$	−0.906734	+	7.23464i	−0.0955782	+	0.762598i
$91$	−13.0411	−	22.5878i	−1.36708	−	2.36785i
$92$	−2.17679	−	0.671994i	−0.226946	−	0.0700602i
$93$	−0.136895	−	10.9374i	−0.0141954	−	1.13416i
$94$	3.19936	−	1.25524i	0.329989	−	0.129468i
$95$	−1.03283	−	5.85748i	−0.105966	−	0.600965i
$96$	−8.66490	+	4.57378i	−0.884358	+	0.466809i
$97$	−1.18161	−	0.991491i	−0.119975	−	0.100671i	0.580826	−	0.814027i	$-0.302729\pi$
$97$	−1.18161	−	0.991491i	−0.119975	−	0.100671i	−0.700801	+	0.713357i	$0.747174\pi$
$98$	16.8563	−	14.8723i	1.70274	−	1.50233i
$99$	−0.0884767	−	3.53394i	−0.00889225	−	0.355174i
$100$	−0.509874	+	4.06121i	−0.0509874	+	0.406121i
$101$	2.31957	−	0.844254i	0.230806	−	0.0840064i	−0.224028	−	0.974583i	$-0.571921\pi$
$101$	2.31957	−	0.844254i	0.230806	−	0.0840064i	0.454834	+	0.890576i	$0.349699\pi$
$102$	0.684968	−	0.881122i	0.0678220	−	0.0872441i
$103$	1.22953	+	1.46530i	0.121149	+	0.144380i	0.823210	−	0.567737i	$-0.192181\pi$
$103$	1.22953	+	1.46530i	0.121149	+	0.144380i	−0.702061	+	0.712117i	$0.747736\pi$
$104$	14.9421	−	3.79930i	1.46519	−	0.372552i
$105$	14.0564	+	2.29752i	1.37176	+	0.224215i
$106$	17.1614	−	0.426026i	1.66686	−	0.0413793i
$107$			16.8797i			1.63182i	0.578175	+	0.815912i	$0.303765\pi$
$107$			16.8797i			1.63182i	−0.578175	+	0.815912i	$0.696235\pi$
$108$	4.39274	−	9.41827i	0.422691	−	0.906274i
$109$			11.1831i			1.07115i	0.844489	+	0.535573i	$0.179905\pi$
$109$			11.1831i			1.07115i	−0.844489	+	0.535573i	$0.820095\pi$
$110$	0.0710728	+	2.86299i	0.00677653	+	0.272975i
$111$	6.95635	−	8.50417i	0.660267	−	0.807180i
$112$	8.29652	+	17.2480i	0.783947	+	1.62978i
$113$	−11.3884	−	13.5722i	−1.07133	−	1.27676i	−0.959096	−	0.283080i	$-0.908644\pi$
$113$	−11.3884	−	13.5722i	−1.07133	−	1.27676i	−0.112234	−	0.993682i	$-0.535801\pi$
$114$	−1.15945	+	8.39788i	−0.108593	+	0.786534i
$115$	−1.83952	+	0.669531i	−0.171536	+	0.0624341i
$116$	0.218235	−	1.73827i	0.0202626	−	0.161394i
$117$	−10.1946	+	12.7861i	−0.942487	+	1.18208i
$118$	−4.64251	−	5.26181i	−0.427378	−	0.484389i
$119$	−1.67006	−	1.40135i	−0.153094	−	0.128462i
$120$	−3.56034	+	7.62934i	−0.325013	+	0.696461i
$121$	1.66902	+	9.46548i	0.151729	+	0.860498i
$122$	3.65387	+	9.31303i	0.330806	+	0.843162i
$123$	−17.2853	+	10.2703i	−1.55857	+	0.926038i
$124$	3.72563	−	12.0685i	0.334572	−	1.08378i
$125$	6.05496	+	10.4875i	0.541572	+	0.938031i
$126$	−18.0648	−	9.26164i	−1.60934	−	0.825093i
$127$	9.67865	+	5.58797i	0.858841	+	0.495852i	0.863624	−	0.504136i	$-0.168189\pi$
$127$	9.67865	+	5.58797i	0.858841	+	0.495852i	−0.00478302	+	0.999989i	$0.501522\pi$
$128$	−11.1434	+	1.95574i	−0.984946	+	0.172864i
$129$	−3.01976	−	1.05649i	−0.265875	−	0.0930190i
$130$	8.26118	−	10.3568i	0.724554	−	0.908350i
$131$	3.76485	−	10.3438i	0.328936	−	0.903744i	−0.659446	−	0.751752i	$-0.729209\pi$
$131$	3.76485	−	10.3438i	0.328936	−	0.903744i	0.988382	−	0.151992i	$-0.0485689\pi$
$132$	1.15515	−	3.91506i	0.100543	−	0.340762i
$133$	16.3087	+	2.87566i	1.41414	+	0.249351i
$134$	−0.968023	−	4.79134i	−0.0836245	−	0.413909i
$135$	−1.87969	−	8.72984i	−0.161778	−	0.751345i
$136$	1.06502	−	0.725586i	0.0913247	−	0.0622185i
$137$	13.8815	+	2.44768i	1.18598	+	0.209119i	0.731627	−	0.681705i	$-0.238761\pi$
$137$	13.8815	+	2.44768i	1.18598	+	0.209119i	0.454348	+	0.890824i	$0.349872\pi$
$138$	2.78822	−	0.104147i	0.237349	−	0.00886557i
$139$	−5.23084	−	1.90387i	−0.443674	−	0.161484i	0.110516	−	0.993874i	$-0.464750\pi$
$139$	−5.23084	−	1.90387i	−0.443674	−	0.161484i	−0.554190	+	0.832390i	$0.686972\pi$
$140$	14.6334	+	7.50630i	1.23675	+	0.634398i
$141$	−3.19031	+	2.74576i	−0.268673	+	0.231235i
$142$	−5.03340	−	8.23889i	−0.422393	−	0.691392i
$143$	−3.21155	+	5.56256i	−0.268563	+	0.465165i
$144$	8.16521	−	8.79371i	0.680434	−	0.732809i
$145$	−0.752694	−	1.30370i	−0.0625078	−	0.108267i
$146$	0.550757	−	1.01109i	0.0455810	−	0.0836781i
$147$	−13.4662	+	24.0133i	−1.11068	+	1.98059i
$148$	10.6586	−	6.88063i	0.876132	−	0.565584i
$149$	−2.58539	−	14.6625i	−0.211803	−	1.20120i	−0.886368	−	0.462981i	$-0.846780\pi$
$149$	−2.58539	−	14.6625i	−0.211803	−	1.20120i	0.674565	−	0.738216i	$-0.264331\pi$
$150$	−1.05417	−	4.90090i	−0.0860722	−	0.400157i
$151$	11.9983	−	14.2990i	0.976405	−	1.16363i	−0.0101076	−	0.999949i	$-0.503217\pi$
$151$	11.9983	−	14.2990i	0.976405	−	1.16363i	0.986513	−	0.163685i	$-0.0523382\pi$
$152$	−4.25031	+	8.81816i	−0.344745	+	0.715247i
$153$	−0.435203	+	1.29574i	−0.0351841	+	0.104754i
$154$	−7.55822	−	2.54038i	−0.609059	−	0.204710i
$155$	−3.71198	−	10.1986i	−0.298153	−	0.819169i
$156$	−15.7348	+	10.4388i	−1.25979	+	0.835774i
$157$	−4.95279	−	5.90251i	−0.395276	−	0.471071i	0.531298	−	0.847185i	$-0.321705\pi$
$157$	−4.95279	−	5.90251i	−0.395276	−	0.471071i	−0.926573	+	0.376114i	$0.877260\pi$
$158$	18.2544	+	2.75353i	1.45224	+	0.219059i
$159$	−19.6653	+	7.43760i	−1.55956	+	0.589840i
$160$	−6.61645	+	7.12272i	−0.523077	+	0.563100i
$161$		−	5.45038i		−	0.429550i
$162$	−1.26625	+	12.6648i	−0.0994863	+	0.995039i
$163$	−4.86594			−0.381130			−0.190565	−	0.981675i	$-0.561032\pi$
$163$	−4.86594			−0.381130			−0.190565	+	0.981675i	$0.561032\pi$
$164$	−22.6358	+	5.16105i	−1.76756	+	0.403011i
$165$	−1.24080	−	3.28071i	−0.0965958	−	0.255403i
$166$	−14.9887	−	2.26093i	−1.16335	−	0.175482i
$167$	−5.93958	+	4.98390i	−0.459619	+	0.385666i	−0.842991	−	0.537928i	$-0.819207\pi$
$167$	−5.93958	+	4.98390i	−0.459619	+	0.385666i	0.383372	+	0.923594i	$0.374763\pi$
$168$	−16.5705	−	16.5802i	−1.27844	−	1.27919i
$169$	15.7048	−	5.71607i	1.20806	−	0.439698i
$170$	0.352797	−	1.04965i	0.0270583	−	0.0805045i
$171$	−2.05831	−	10.1768i	−0.157403	−	0.778236i
$172$	−2.94423	−	2.23122i	−0.224495	−	0.170129i
$173$	−2.39480	−	2.00948i	−0.182073	−	0.152778i	0.547196	−	0.837005i	$-0.315695\pi$
$173$	−2.39480	−	2.00948i	−0.182073	−	0.152778i	−0.729269	+	0.684227i	$0.760140\pi$
$174$	0.451201	+	2.09767i	0.0342055	+	0.159024i
$175$	−9.64375	+	1.70045i	−0.728999	+	0.128542i
$176$	2.65692	−	3.89318i	0.200273	−	0.293459i
$177$	7.49594	+	4.20359i	0.563429	+	0.315961i
$178$	−10.0904	−	5.49645i	−0.756310	−	0.411976i
$179$	−9.72475	+	5.61459i	−0.726862	+	0.419654i	−0.817273	−	0.576250i	$-0.804515\pi$
$179$	−9.72475	+	5.61459i	−0.726862	+	0.419654i	0.0904110	+	0.995905i	$0.471182\pi$
$180$	1.02801	−	10.2600i	0.0766234	−	0.764735i
$181$	−12.9165	−	7.45734i	−0.960075	−	0.554300i	−0.0638789	−	0.997958i	$-0.520347\pi$
$181$	−12.9165	−	7.45734i	−0.960075	−	0.554300i	−0.896196	+	0.443658i	$0.853680\pi$
$182$	19.2300	+	31.4765i	1.42542	+	2.33319i
$183$	−7.99264	−	9.28670i	−0.590833	−	0.686493i
$184$	3.10109	+	0.873652i	0.228615	+	0.0644065i
$185$	3.72847	−	10.2439i	0.274123	−	0.753146i
$186$	0.577406	+	15.4583i	0.0423374	+	1.13346i
$187$	−0.0932288	+	0.528727i	−0.00681756	+	0.0386643i
$188$	−4.47913	+	1.88691i	−0.326674	+	0.137617i
$189$	24.6302	+	3.39526i	1.79158	+	0.246969i
$190$	1.66577	+	8.24493i	0.120848	+	0.598150i
$191$	−1.67647	+	9.50775i	−0.121305	+	0.687957i	0.862129	+	0.506690i	$0.169131\pi$
$191$	−1.67647	+	9.50775i	−0.121305	+	0.687957i	−0.983434	+	0.181267i	$0.941980\pi$
$192$	12.0897	−	6.77041i	0.872501	−	0.488613i
$193$	5.42295	+	1.97379i	0.390352	+	0.142077i	0.529738	−	0.848162i	$-0.322290\pi$
$193$	5.42295	+	1.97379i	0.390352	+	0.142077i	−0.139385	+	0.990238i	$0.544513\pi$
$194$	1.70534	+	1.36028i	0.122436	+	0.0976622i
$195$	−5.35818	+	15.3152i	−0.383707	+	1.09674i
$196$	−23.3090	+	21.6178i	−1.66493	+	1.54413i
$197$	7.24542	−	12.5494i	0.516215	−	0.894110i	−0.483608	−	0.875285i	$-0.660674\pi$
$197$	7.24542	−	12.5494i	0.516215	−	0.894110i	0.999823	−	0.0188255i	$-0.00599269\pi$
$198$	0.249116	+	4.99310i	0.0177039	+	0.354844i
$199$	12.3632	−	7.13788i	0.876402	−	0.505991i	0.00693173	−	0.999976i	$-0.497794\pi$
$199$	12.3632	−	7.13788i	0.876402	−	0.505991i	0.869470	+	0.493985i	$0.164460\pi$
$200$	0.578314	−	5.75955i	0.0408930	−	0.407261i
$201$	3.05802	+	5.14680i	0.215696	+	0.363027i
$202$	−3.24973	+	1.27500i	−0.228650	+	0.0897085i
$203$	4.12769	−	0.727824i	0.289707	−	0.0510832i
$204$	−0.937469	+	1.26975i	−0.0656359	+	0.0889003i
$205$	−12.8234	+	15.2823i	−0.895625	+	1.06736i
$206$	−1.78971	−	2.02845i	−0.124695	−	0.141329i
$207$	−3.18089	+	1.24877i	−0.221087	+	0.0867954i
$208$	−20.9915	+	5.89579i	−1.45550	+	0.408799i
$209$	−1.39482	−	3.83225i	−0.0964820	−	0.265082i
$210$	−19.9532	−	2.75485i	−1.37690	−	0.190102i
$211$	13.8816	−	11.6480i	0.955649	−	0.801885i	−0.0245907	−	0.999698i	$-0.507828\pi$
$211$	13.8816	−	11.6480i	0.955649	−	0.801885i	0.980240	+	0.197813i	$0.0633838\pi$
$212$	−24.2474	+	1.20461i	−1.66532	+	0.0827331i
$213$	9.15260	+	7.48676i	0.627126	+	0.512984i
$214$	−0.592421	−	23.8642i	−0.0404971	−	1.63132i
$215$	−3.17432			−0.216487
$216$	−5.87981	+	13.4695i	−0.400070	+	0.916485i
$217$	30.2177			2.05131
$218$	−0.392489	−	15.8104i	−0.0265827	−	1.07082i
$219$	−0.227466	+	1.39165i	−0.0153707	+	0.0940393i
$220$	−0.200962	−	4.04514i	−0.0135489	−	0.272723i
$221$	1.90253	−	1.59641i	0.127978	−	0.107386i
$222$	−9.53627	+	12.2672i	−0.640032	+	0.823317i
$223$	3.12879	+	8.59628i	0.209519	+	0.575650i	0.999287	−	0.0377565i	$-0.0120211\pi$
$223$	3.12879	+	8.59628i	0.209519	+	0.575650i	−0.789768	+	0.613406i	$0.789799\pi$
$224$	−12.3348	−	24.0936i	−0.824152	−	1.60982i
$225$	3.20194	+	5.23858i	0.213462	+	0.349239i
$226$	16.5770	+	18.7883i	1.10269	+	1.24978i
$227$	6.66470	−	7.94268i	0.442352	−	0.527174i	−0.498092	−	0.867124i	$-0.665966\pi$
$227$	6.66470	−	7.94268i	0.442352	−	0.527174i	0.940443	+	0.339950i	$0.110410\pi$
$228$	1.34447	−	11.9134i	0.0890400	−	0.788986i
$229$	5.01320	−	0.883963i	0.331282	−	0.0584139i	−0.00553340	−	0.999985i	$-0.501761\pi$
$229$	5.01320	−	0.883963i	0.331282	−	0.0584139i	0.336815	+	0.941571i	$0.390650\pi$
$230$	2.57718	−	1.01113i	0.169934	−	0.0666719i
$231$	9.76502	−	0.122221i	0.642491	−	0.00804154i
$232$	−0.247528	+	2.46519i	−0.0162510	+	0.161847i
$233$	8.21403	−	4.74237i	0.538119	−	0.310683i	−0.206197	−	0.978510i	$-0.566109\pi$
$233$	8.21403	−	4.74237i	0.538119	−	0.310683i	0.744316	+	0.667827i	$0.232775\pi$
$234$	13.9641	−	18.4345i	0.912861	−	1.20510i
$235$	−2.08820	+	3.61688i	−0.136219	+	0.235939i
$236$	6.74815	+	7.27609i	0.439267	+	0.473633i
$237$	−22.2155	+	4.20453i	−1.44305	+	0.273113i
$238$	2.41028	+	1.92258i	0.156235	+	0.124623i
$239$	22.5356	+	8.20228i	1.45771	+	0.530561i	0.944732	−	0.327843i	$-0.106322\pi$
$239$	22.5356	+	8.20228i	1.45771	+	0.530561i	0.512973	+	0.858405i	$0.328544\pi$
$240$	4.76576	−	10.9112i	0.307629	−	0.704312i
$241$	3.02186	−	17.1378i	0.194655	−	1.10394i	−0.718255	−	0.695780i	$-0.755059\pi$
$241$	3.02186	−	17.1378i	0.194655	−	1.10394i	0.912909	−	0.408162i	$-0.133830\pi$
$242$	−2.69183	−	13.3235i	−0.173037	−	0.856467i
$243$	−3.66165	−	15.1523i	−0.234895	−	0.972021i
$244$	−5.49262	−	13.0383i	−0.351629	−	0.834693i
$245$	−4.74355	+	26.9020i	−0.303054	+	1.71871i
$246$	24.0772	−	15.1265i	1.53511	−	0.964432i
$247$	−6.45233	+	17.7276i	−0.410552	+	1.12798i
$248$	−4.84366	+	17.1929i	−0.307572	+	1.09175i
$249$	18.2412	−	3.45234i	1.15599	−	0.218783i
$250$	−8.92845	−	14.6145i	−0.564685	−	0.924302i
$251$	−9.03981	−	5.21914i	−0.570588	−	0.329429i	0.186796	−	0.982399i	$-0.440190\pi$
$251$	−9.03981	−	5.21914i	−0.570588	−	0.329429i	−0.757384	+	0.652970i	$0.773523\pi$
$252$	25.8647	+	12.4599i	1.62932	+	0.784900i
$253$	−1.16241	+	0.671116i	−0.0730799	+	0.0421927i
$254$	−13.8796	−	7.56046i	−0.870882	−	0.474385i
$255$	0.0169735	+	1.35612i	0.00106292	+	0.0849235i
$256$	15.6856	−	3.15607i	0.980352	−	0.197255i
$257$	−20.2320	+	3.56745i	−1.26204	+	0.222532i	−0.764338	−	0.644816i	$-0.776934\pi$
$257$	−20.2320	+	3.56745i	−1.26204	+	0.222532i	−0.497702	+	0.867348i	$0.665823\pi$
$258$	4.30635	+	1.38766i	0.268101	+	0.0863921i
$259$	23.2510	+	19.5099i	1.44474	+	1.21228i
$260$	−11.3160	+	14.9321i	−0.701788	+	0.926051i
$261$	−1.37048	−	2.24221i	−0.0848309	−	0.138789i
$262$	−4.95962	+	14.7560i	−0.306407	+	0.911629i
$263$	23.8393	−	8.67678i	1.46999	−	0.535033i	0.521893	−	0.853011i	$-0.325226\pi$
$263$	23.8393	−	8.67678i	1.46999	−	0.535033i	0.948098	+	0.317978i	$0.103004\pi$
$264$	−1.49571	+	5.57556i	−0.0920548	+	0.343152i
$265$	−15.9805	+	13.4092i	−0.981674	+	0.823722i
$266$	−23.1578	−	3.49317i	−1.41989	−	0.214180i
$267$	13.8884	+	2.27007i	0.849958	+	0.138926i
$268$	1.53673	+	6.73991i	0.0938707	+	0.411706i
$269$	19.8102			1.20785			0.603926	−	0.797040i	$-0.293602\pi$
$269$	19.8102			1.20785			0.603926	+	0.797040i	$0.293602\pi$
$270$	2.96385	+	12.2761i	0.180374	+	0.747098i
$271$			12.1420i			0.737573i	0.929514	+	0.368787i	$0.120227\pi$
$271$			12.1420i			0.737573i	−0.929514	+	0.368787i	$0.879773\pi$
$272$	−1.48024	+	1.06320i	−0.0897525	+	0.0644658i
$273$	−34.9673	−	28.6030i	−2.11632	−	1.73113i
$274$	−19.7112	−	2.97328i	−1.19080	−	0.179623i
$275$	1.55011	+	1.84735i	0.0934752	+	0.111399i
$276$	−3.93827	+	0.245098i	−0.237056	+	0.0147531i
$277$	1.79216	+	4.92392i	0.107681	+	0.295850i	0.981817	−	0.189831i	$-0.0607940\pi$
$277$	1.79216	+	4.92392i	0.107681	+	0.295850i	−0.874136	+	0.485681i	$0.838572\pi$
$278$	7.46206	+	2.50806i	0.447545	+	0.150424i
$279$	−6.92335	−	17.6353i	−0.414490	−	1.05580i
$280$	−20.9518	−	10.0987i	−1.25211	−	0.603510i
$281$	−0.727805	+	0.867364i	−0.0434172	+	0.0517426i	−0.787316	−	0.616550i	$-0.788530\pi$
$281$	−0.727805	+	0.867364i	−0.0434172	+	0.0517426i	0.743899	+	0.668292i	$0.232974\pi$
$282$	4.41403	−	3.99386i	0.262852	−	0.237831i
$283$	1.23962	+	7.03026i	0.0736880	+	0.417905i	0.999229	+	0.0392582i	$0.0124995\pi$
$283$	1.23962	+	7.03026i	0.0736880	+	0.417905i	−0.925541	+	0.378647i	$0.876389\pi$
$284$	7.40526	+	11.4713i	0.439421	+	0.680697i
$285$	−5.26224	−	8.85660i	−0.311708	−	0.524620i
$286$	4.34519	−	7.97694i	0.256936	−	0.471687i
$287$	−27.7724	−	48.1032i	−1.63935	−	2.83944i
$288$	−11.2352	+	12.7189i	−0.662039	+	0.749470i
$289$	−8.39620	+	14.5427i	−0.493894	+	0.855450i
$290$	1.10990	+	1.81673i	0.0651754	+	0.106682i
$291$	−2.52178	−	0.882271i	−0.147829	−	0.0517196i
$292$	−0.743163	+	1.44878i	−0.0434903	+	0.0847835i
$293$	−2.36358	−	0.860272i	−0.138082	−	0.0502576i	0.272055	−	0.962282i	$-0.412297\pi$
$293$	−2.36358	−	0.860272i	−0.138082	−	0.0502576i	−0.410137	+	0.912024i	$0.634519\pi$
$294$	18.1955	−	34.4221i	1.06118	−	2.00754i
$295$	8.39766	+	1.48073i	0.488931	+	0.0862117i
$296$	−14.8274	+	10.1018i	−0.861826	+	0.587153i
$297$	−2.30865	−	5.67096i	−0.133961	−	0.329062i
$298$	4.16977	+	20.6388i	0.241548	+	1.19557i
$299$	6.11472	+	1.07819i	0.353623	+	0.0623533i
$300$	1.66236	+	6.89179i	0.0959764	+	0.397898i
$301$	3.02281	−	8.30509i	0.174232	−	0.478697i
$302$	−16.4610	+	20.6367i	−0.947226	+	1.18751i
$303$	3.24054	−	2.78898i	0.186164	−	0.160223i
$304$	5.69950	−	12.6161i	0.326889	−	0.723582i
$305$	−10.5284	−	6.07857i	−0.602854	−	0.348058i
$306$	0.569805	−	1.84716i	0.0325736	−	0.105595i
$307$	−5.71371	−	9.89644i	−0.326099	−	0.564820i	0.655635	−	0.755078i	$-0.272401\pi$
$307$	−5.71371	−	9.89644i	−0.326099	−	0.564820i	−0.981734	+	0.190258i	$0.939068\pi$
$308$	10.7748	+	3.32627i	0.613952	+	0.189532i
$309$	2.88972	+	1.62050i	0.164391	+	0.0921873i
$310$	5.60585	+	14.2882i	0.318391	+	0.811518i
$311$	1.99125	+	11.2930i	0.112914	+	0.640365i	0.987762	+	0.155968i	$0.0498497\pi$
$311$	1.99125	+	11.2930i	0.112914	+	0.640365i	−0.874849	+	0.484397i	$0.839039\pi$
$312$	21.8791	−	15.3104i	1.23866	−	0.866781i
$313$	6.15688	+	5.16624i	0.348008	+	0.292013i	0.799989	−	0.600014i	$-0.204838\pi$
$313$	6.15688	+	5.16624i	0.348008	+	0.292013i	−0.451982	+	0.892027i	$0.649283\pi$
$314$	7.20931	+	8.17101i	0.406845	+	0.461117i
$315$	24.1798	−	4.89052i	1.36238	−	0.275550i
$316$	−25.9043	−	3.25221i	−1.45723	−	0.182951i
$317$	−10.7435	+	3.91031i	−0.603415	+	0.219625i	−0.625620	−	0.780128i	$-0.715154\pi$
$317$	−10.7435	+	3.91031i	−0.603415	+	0.219625i	0.0222044	+	0.999753i	$0.492932\pi$
$318$	27.5413	−	11.2053i	1.54444	−	0.628362i
$319$	−0.663474	−	0.790698i	−0.0371474	−	0.0442706i
$320$	9.10421	−	10.3022i	0.508941	−	0.575908i
$321$	10.3425	+	27.3461i	0.577264	+	1.52631i
$322$	0.191290	+	7.70563i	0.0106602	+	0.429418i
$323$			1.57689i			0.0877403i
$324$	1.34571	−	17.9496i	0.0747618	−	0.997201i
$325$		−	11.1556i		−	0.618801i
$326$	6.87936	−	0.170778i	0.381012	−	0.00945851i
$327$	6.85211	+	18.1172i	0.378922	+	1.00189i
$328$	31.8208	−	8.09102i	1.75701	−	0.446752i
$329$	−7.47443	−	8.90768i	−0.412079	−	0.491096i
$330$	1.86935	+	4.59465i	0.102904	+	0.252927i
$331$	0.710903	−	0.258748i	0.0390748	−	0.0142221i	−0.322409	−	0.946601i	$-0.604493\pi$
$331$	0.710903	−	0.258748i	0.0390748	−	0.0142221i	0.361484	+	0.932378i	$0.382270\pi$
$332$	21.2700	+	2.67040i	1.16735	+	0.146557i
$333$	6.05899	−	18.0395i	0.332030	−	0.988559i
$334$	8.22233	−	7.25459i	0.449906	−	0.396953i
$335$	4.55039	+	3.81823i	0.248614	+	0.208612i
$336$	24.0090	+	22.8592i	1.30980	+	1.24707i
$337$	−2.31594	−	13.1343i	−0.126157	−	0.715473i	−0.980614	−	0.195950i	$-0.937221\pi$
$337$	−2.31594	−	13.1343i	−0.126157	−	0.715473i	0.854457	−	0.519523i	$-0.173890\pi$
$338$	−22.0025	+	8.63244i	−1.19678	+	0.469543i
$339$	−26.7657	−	15.0097i	−1.45372	−	0.815217i
$340$	−0.461937	+	1.49635i	−0.0250520	+	0.0811512i
$341$	−3.72076	−	6.44455i	−0.201491	−	0.348992i
$342$	3.26717	+	14.3154i	0.176668	+	0.774090i
$343$	−36.8606	−	21.2815i	−1.99029	−	1.14909i
$344$	4.24079	+	3.05112i	0.228648	+	0.164505i
$345$	−2.56989	+	2.21179i	−0.138358	+	0.119079i
$346$	3.45624	+	2.75690i	0.185809	+	0.148212i
$347$	−6.31721	+	17.3564i	−0.339126	+	0.931740i	0.646518	+	0.762899i	$0.276225\pi$
$347$	−6.31721	+	17.3564i	−0.339126	+	0.931740i	−0.985643	+	0.168841i	$0.945998\pi$
$348$	−0.711519	−	2.94981i	−0.0381414	−	0.158126i
$349$	−2.00043	−	0.352730i	−0.107081	−	0.0188812i	0.119851	−	0.992792i	$-0.461758\pi$
$349$	−2.00043	−	0.352730i	−0.107081	−	0.0188812i	−0.226932	+	0.973911i	$0.572869\pi$
$350$	13.5744	−	2.74253i	0.725584	−	0.146594i
$351$	−8.68141	+	26.9606i	−0.463380	+	1.43905i
$352$	−3.61966	+	5.59734i	−0.192928	+	0.298339i
$353$	14.8073	+	2.61092i	0.788111	+	0.138965i	0.553196	−	0.833051i	$-0.313408\pi$
$353$	14.8073	+	2.61092i	0.788111	+	0.138965i	0.234914	+	0.972016i	$0.424519\pi$
$354$	−10.7451	−	5.67986i	−0.571097	−	0.301881i
$355$	11.0250	+	4.01276i	0.585145	+	0.212975i
$356$	14.4585	+	7.41662i	0.766301	+	0.393080i
$357$	−3.56423	−	1.24698i	−0.188639	−	0.0659973i
$358$	13.5516	−	8.27909i	0.716224	−	0.437563i
$359$	−6.75445	+	11.6991i	−0.356486	+	0.617453i	−0.987371	−	0.158424i	$-0.949359\pi$
$359$	−6.75445	+	11.6991i	−0.356486	+	0.617453i	0.630885	+	0.775877i	$0.282692\pi$
$360$	−1.09329	+	14.5414i	−0.0576213	+	0.766401i
$361$	3.51094	+	6.08113i	0.184786	+	0.320059i
$362$	18.5228	+	10.0897i	0.973535	+	0.530303i
$363$	8.50358	+	14.3119i	0.446322	+	0.751182i
$364$	−28.2916	−	43.8258i	−1.48288	−	2.29710i
$365$	0.242958	+	1.37788i	0.0127170	+	0.0721217i
$366$	11.6258	+	12.8488i	0.607688	+	0.671618i
$367$	−19.2060	+	22.8888i	−1.00254	+	1.19478i	−0.0217439	+	0.999764i	$0.506922\pi$
$367$	−19.2060	+	22.8888i	−1.00254	+	1.19478i	−0.980799	+	0.195021i	$0.937523\pi$
$368$	−4.41491	−	1.12631i	−0.230143	−	0.0587131i
$369$	−21.7104	+	27.2294i	−1.13020	+	1.41751i
$370$	−4.91171	+	14.6134i	−0.255347	+	0.759717i
$371$	−19.8653	−	54.5795i	−1.03136	−	2.83363i
$372$	−1.35886	−	21.8343i	−0.0704534	−	1.13206i
$373$	1.28233	+	1.52822i	0.0663966	+	0.0791284i	0.798220	−	0.602366i	$-0.205775\pi$
$373$	1.28233	+	1.52822i	0.0663966	+	0.0791284i	−0.731824	+	0.681494i	$0.761331\pi$
$374$	0.113248	−	0.750774i	0.00585593	−	0.0388216i
$375$	16.2353	+	13.2803i	0.838385	+	0.685793i
$376$	6.26627	−	2.82488i	0.323158	−	0.145682i
$377$			4.77479i			0.245914i
$378$	−34.9407	−	3.93571i	−1.79716	−	0.202431i
$379$	−2.60318			−0.133716			−0.0668581	−	0.997762i	$-0.521297\pi$
$379$	−2.60318			−0.133716			−0.0668581	+	0.997762i	$0.521297\pi$
$380$	−2.64440	−	11.5980i	−0.135655	−	0.594967i
$381$	19.1038	+	3.12252i	0.978717	+	0.159971i
$382$	2.03647	−	13.5007i	0.104195	−	0.690755i
$383$	13.6082	−	11.4186i	0.695347	−	0.583465i	−0.225099	−	0.974336i	$-0.572271\pi$
$383$	13.6082	−	11.4186i	0.695347	−	0.583465i	0.920446	+	0.390871i	$0.127826\pi$
$384$	−16.8546	+	9.99617i	−0.860106	+	0.510115i
$385$	9.10536	−	3.31408i	0.464052	−	0.168901i
$386$	−7.73612	−	2.60018i	−0.393758	−	0.132345i
$387$	−5.53950	+	0.138689i	−0.281589	+	0.00704995i
$388$	−2.45871	−	1.86328i	−0.124822	−	0.0945936i
$389$	−10.4996	−	8.81024i	−0.532353	−	0.446697i	0.336560	−	0.941662i	$-0.390736\pi$
$389$	−10.4996	−	8.81024i	−0.532353	−	0.446697i	−0.868913	+	0.494965i	$0.835181\pi$
$390$	7.03776	−	21.8403i	0.356371	−	1.10593i
$391$	0.511107	−	0.0901219i	0.0258478	−	0.00455766i
$392$	32.1951	−	31.3808i	1.62610	−	1.58497i
$393$	−0.238613	−	19.0644i	−0.0120364	−	0.961669i
$394$	−9.80297	+	17.9964i	−0.493867	+	0.906646i
$395$	−19.4282	+	11.2169i	−0.977541	+	0.564383i
$396$	−0.527435	−	7.05039i	−0.0265046	−	0.354295i
$397$	22.3133	+	12.8826i	1.11987	+	0.646560i	0.941369	−	0.337379i	$-0.109540\pi$
$397$	22.3133	+	12.8826i	1.11987	+	0.646560i	0.178505	+	0.983939i	$0.442874\pi$
$398$	−17.2283	+	10.5253i	−0.863575	+	0.527585i
$399$	28.1829	−	5.33392i	1.41091	−	0.267030i
$400$	−0.615467	+	8.16302i	−0.0307733	+	0.408151i
$401$	−3.91465	+	10.7554i	−0.195488	+	0.537100i	−0.998246	−	0.0592057i	$-0.981143\pi$
$401$	−3.91465	+	10.7554i	−0.195488	+	0.537100i	0.802757	+	0.596306i	$0.203365\pi$
$402$	−4.50400	−	7.16910i	−0.224639	−	0.357562i
$403$	−5.97764	+	33.9009i	−0.297767	+	1.68872i
$404$	4.54964	−	1.91662i	0.226353	−	0.0953553i
$405$	−8.39413	−	12.9911i	−0.417108	−	0.645532i
$406$	−5.81010	+	1.17385i	−0.288350	+	0.0582572i
$407$	1.29795	−	7.36104i	0.0643370	−	0.364873i
$408$	1.28081	−	1.82805i	0.0634095	−	0.0905018i
$409$	−8.73375	−	3.17883i	−0.431856	−	0.157183i	0.116940	−	0.993139i	$-0.462691\pi$
$409$	−8.73375	−	3.17883i	−0.431856	−	0.157183i	−0.548796	+	0.835956i	$0.684914\pi$
$410$	17.5931	−	22.0559i	0.868860	−	1.08926i
$411$	23.9885	−	4.54008i	1.18327	−	0.223946i
$412$	2.60145	+	2.80497i	0.128164	+	0.138191i
$413$	−11.8709	+	20.5611i	−0.584130	+	1.01174i
$414$	4.45325	−	1.87712i	0.218865	−	0.0922554i
$415$	15.9526	−	9.21021i	0.783080	−	0.452111i
$416$	29.4704	−	9.07206i	1.44490	−	0.444795i
$417$	−9.64078	+	0.120666i	−0.472111	+	0.00590903i
$418$	2.10647	+	5.36899i	0.103031	+	0.262606i
$419$	13.8643	−	2.44465i	0.677314	−	0.119429i	0.175599	−	0.984462i	$-0.443814\pi$
$419$	13.8643	−	2.44465i	0.677314	−	0.119429i	0.501715	+	0.865033i	$0.332703\pi$
$420$	28.3061	+	3.19445i	1.38120	+	0.155873i
$421$	−6.70587	+	7.99174i	−0.326824	+	0.389494i	−0.904288	−	0.426922i	$-0.859598\pi$
$421$	−6.70587	+	7.99174i	−0.326824	+	0.389494i	0.577464	+	0.816416i	$0.304042\pi$
$422$	−19.2167	+	16.9550i	−0.935454	+	0.825354i
$423$	−3.48610	+	6.40304i	−0.169500	+	0.311327i
$424$	34.2382	−	2.55406i	1.66275	−	0.124036i
$425$	−0.318918	−	0.876221i	−0.0154698	−	0.0425030i
$426$	−13.2025	−	10.2634i	−0.639663	−	0.497263i
$427$	25.9294	−	21.7574i	1.25481	−	1.05291i
$428$	1.67510	+	33.7179i	0.0809692	+	1.62981i
$429$	−1.79459	+	10.9794i	−0.0866436	+	0.530092i
$430$	4.48778	−	0.111408i	0.216420	−	0.00537256i
$431$	16.0211			0.771709			0.385855	−	0.922560i	$-0.373907\pi$
$431$	16.0211			0.771709			0.385855	+	0.922560i	$0.373907\pi$
$432$	7.84001	−	19.2493i	0.377202	−	0.926131i
$433$	−8.60544			−0.413551			−0.206775	−	0.978388i	$-0.566297\pi$
$433$	−8.60544			−0.413551			−0.206775	+	0.978388i	$0.566297\pi$
$434$	−42.7211	+	1.06054i	−2.05068	+	0.0509075i
$435$	−2.01821	−	1.65088i	−0.0967657	−	0.0791536i
$436$	1.10978	+	22.3387i	0.0531490	+	1.06983i
$437$	−3.01997	+	2.53405i	−0.144465	+	0.121220i
$438$	0.272744	−	1.97547i	0.0130322	−	0.0943918i
$439$	−3.25240	−	8.93590i	−0.155229	−	0.426487i	0.837563	−	0.546341i	$-0.183980\pi$
$439$	−3.25240	−	8.93590i	−0.155229	−	0.426487i	−0.992792	+	0.119854i	$0.961757\pi$
$440$	0.426087	+	5.71187i	0.0203129	+	0.272303i
$441$	−7.10259	+	47.1539i	−0.338219	+	2.24542i
$442$	−2.63372	+	2.32374i	−0.125273	+	0.110529i
$443$	−8.64715	+	10.3053i	−0.410838	+	0.489618i	−0.931293	−	0.364271i	$-0.881318\pi$
$443$	−8.64715	+	10.3053i	−0.410838	+	0.489618i	0.520454	+	0.853889i	$0.325763\pi$
$444$	13.0516	−	17.6777i	0.619403	−	0.838948i
$445$	13.7510	−	2.42467i	0.651860	−	0.114941i
$446$	−4.72512	−	12.0434i	−0.223741	−	0.570273i
$447$	−13.1725	−	22.1699i	−0.623036	−	1.04860i
$448$	18.2842	+	33.6301i	0.863849	+	1.58887i
$449$	8.35608	−	4.82439i	0.394348	−	0.227677i	−0.289694	−	0.957119i	$-0.593554\pi$
$449$	8.35608	−	4.82439i	0.394348	−	0.227677i	0.684042	+	0.729442i	$0.260220\pi$
$450$	−4.71068	−	7.29382i	−0.222064	−	0.343834i
$451$	−6.83934	+	11.8461i	−0.322052	+	0.557810i
$452$	−24.0956	−	25.9807i	−1.13336	−	1.22203i
$453$	10.6766	−	30.5167i	0.501629	−	1.43380i
$454$	−9.14364	+	11.4631i	−0.429132	+	0.537990i
$455$	−42.1206	−	15.3306i	−1.97464	−	0.718712i
$456$	−1.48267	+	16.8901i	−0.0694323	+	0.790953i
$457$	2.34734	−	13.3124i	0.109804	−	0.622730i	−0.879388	−	0.476106i	$-0.842048\pi$
$457$	2.34734	−	13.3124i	0.109804	−	0.622730i	0.989192	−	0.146624i	$-0.0468409\pi$
$458$	−7.05653	+	1.42567i	−0.329730	+	0.0666174i
$459$	0.0888704	+	2.36582i	0.00414811	+	0.110427i
$460$	−3.60807	+	1.51996i	−0.168227	+	0.0708686i
$461$	7.09030	−	40.2111i	0.330228	−	1.87282i	−0.139822	−	0.990177i	$-0.544653\pi$
$461$	7.09030	−	40.2111i	0.330228	−	1.87282i	0.470050	−	0.882640i	$-0.344236\pi$
$462$	−13.8013	+	0.515512i	−0.642093	+	0.0239838i
$463$	7.18260	−	19.7340i	0.333804	−	0.917118i	−0.653309	−	0.757091i	$-0.726620\pi$
$463$	7.18260	−	19.7340i	0.333804	−	0.917118i	0.987113	−	0.160027i	$-0.0511581\pi$
$464$	0.263431	−	3.49391i	0.0122295	−	0.162201i
$465$	−12.2625	−	14.2478i	−0.568659	−	0.660728i
$466$	−11.4464	+	6.99295i	−0.530243	+	0.323942i
$467$	−25.7460	−	14.8645i	−1.19138	−	0.687846i	−0.232763	−	0.972533i	$-0.574777\pi$
$467$	−25.7460	−	14.8645i	−1.19138	−	0.687846i	−0.958620	+	0.284688i	$0.908110\pi$
$468$	−19.0951	+	26.5524i	−0.882673	+	1.22739i
$469$	−14.3230	+	8.26937i	−0.661373	+	0.381844i
$470$	2.82532	−	5.18675i	0.130322	−	0.239247i
$471$	−11.6404	−	6.52771i	−0.536360	−	0.300781i
$472$	−9.79575	−	10.0499i	−0.450886	−	0.462586i
$473$	−2.14344	+	0.377946i	−0.0985553	+	0.0173780i
$474$	31.2602	−	6.72395i	1.43583	−	0.308841i
$475$	5.42588	+	4.55285i	0.248956	+	0.208899i
$476$	−3.47508	−	2.63351i	−0.159280	−	0.120707i
$477$	−27.3017	+	24.0986i	−1.25006	+	1.10340i
$478$	−32.1482	−	10.8053i	−1.47042	−	0.494222i
$479$	−3.00899	+	1.09518i	−0.137484	+	0.0500401i	−0.409846	−	0.912155i	$-0.634417\pi$
$479$	−3.00899	+	1.09518i	−0.137484	+	0.0500401i	0.272362	+	0.962195i	$0.412195\pi$
$480$	−6.35478	+	15.5932i	−0.290055	+	0.711730i
$481$	−26.4874	+	22.2255i	−1.20772	+	1.01340i
$482$	−3.67075	+	24.3351i	−0.167198	+	1.10843i
$483$	−3.33955	−	8.82991i	−0.151955	−	0.401775i
$484$	4.27326	+	18.7420i	0.194239	+	0.851909i
$485$	−2.65086			−0.120369
$486$	5.70856	+	21.2935i	0.258945	+	0.965892i
$487$		−	0.767571i		−	0.0347819i	−0.999849	−	0.0173910i	$-0.994464\pi$
$487$		−	0.767571i		−	0.0347819i	0.999849	−	0.0173910i	$-0.00553600\pi$
$488$	8.22295	+	18.2405i	0.372235	+	0.825710i
$489$	−7.88309	+	2.98146i	−0.356485	+	0.134826i
$490$	5.76215	−	38.1999i	0.260308	−	1.72570i
$491$	10.2907	+	12.2639i	0.464411	+	0.553463i	0.946519	−	0.322648i	$-0.104573\pi$
$491$	10.2907	+	12.2639i	0.464411	+	0.553463i	−0.482108	+	0.876112i	$0.660129\pi$
$492$	−33.5089	+	22.2306i	−1.51070	+	1.00223i
$493$	0.136503	+	0.375038i	0.00614777	+	0.0168909i
$494$	8.49999	−	25.2894i	0.382433	−	1.13782i
$495$	−4.02031	−	4.55467i	−0.180700	−	0.204717i
$496$	6.24444	−	24.4769i	0.280384	−	1.09905i
$497$	−20.9975	+	25.0238i	−0.941865	+	1.12247i
$498$	−25.6678	+	5.52105i	−1.15020	+	0.247404i
$499$	4.92918	+	27.9548i	0.220661	+	1.25143i	0.870809	+	0.491621i	$0.163596\pi$
$499$	4.92918	+	27.9548i	0.220661	+	1.25143i	−0.650148	+	0.759807i	$0.725293\pi$
$500$	13.1358	+	20.3483i	0.587449	+	0.910003i
$501$	−6.56871	+	11.7135i	−0.293468	+	0.523320i
$502$	12.9635	+	7.06144i	0.578588	+	0.315167i
$503$	22.0465	+	38.1856i	0.983004	+	1.70261i	0.650489	+	0.759516i	$0.274564\pi$
$503$	22.0465	+	38.1856i	0.983004	+	1.70261i	0.332515	+	0.943098i	$0.392103\pi$
$504$	−37.0042	−	16.7078i	−1.64830	−	0.744223i
$505$	2.12108	−	3.67381i	0.0943867	−	0.163483i
$506$	1.61983	−	0.989605i	0.0720103	−	0.0439933i
$507$	21.9402	−	18.8830i	0.974400	−	0.838622i
$508$	19.8880	+	10.2017i	0.882387	+	0.452627i
$509$	−18.6141	−	6.77499i	−0.825057	−	0.300296i	−0.105228	−	0.994448i	$-0.533557\pi$
$509$	−18.6141	−	6.77499i	−0.825057	−	0.300296i	−0.719828	+	0.694152i	$0.755780\pi$
$510$	−0.0715919	−	1.91666i	−0.00317014	−	0.0848709i
$511$	−3.83637	−	0.676455i	−0.169711	−	0.0299246i
$512$	−22.0652	+	5.01250i	−0.975155	+	0.221523i
$513$	−9.57008	−	15.2257i	−0.422529	−	0.672232i
$514$	28.4784	−	5.75366i	1.25613	−	0.253783i
$515$	3.23734	+	0.570831i	0.142654	+	0.0251538i
$516$	−6.13692	−	1.81071i	−0.270163	−	0.0797121i
$517$	−0.979407	+	2.69090i	−0.0430743	+	0.118346i
$518$	−33.5564	−	26.7666i	−1.47438	−	1.17606i
$519$	−5.11095	−	1.78812i	−0.224346	−	0.0784897i
$520$	15.4742	−	21.5079i	0.678590	−	0.943182i
$521$	21.7137	+	12.5364i	0.951292	+	0.549229i	0.893482	−	0.449099i	$-0.148255\pi$
$521$	21.7137	+	12.5364i	0.951292	+	0.549229i	0.0578103	+	0.998328i	$0.481588\pi$
$522$	2.01625	+	3.12188i	0.0882491	+	0.136641i
$523$	−1.30383	−	2.25830i	−0.0570126	−	0.0987487i	0.836110	−	0.548561i	$-0.184824\pi$
$523$	−1.30383	−	2.25830i	−0.0570126	−	0.0987487i	−0.893123	+	0.449812i	$0.851491\pi$
$524$	6.49392	−	21.0358i	0.283688	−	0.918953i
$525$	−14.5815	+	8.66374i	−0.636389	+	0.378117i
$526$	−33.3989	+	13.1037i	−1.45626	+	0.571349i
$527$	0.499649	+	2.83365i	0.0217651	+	0.123436i
$528$	1.91892	−	7.93510i	0.0835105	−	0.345331i
$529$	−16.6251	−	13.9501i	−0.722829	−	0.606526i
$530$	22.1223	−	19.5185i	0.960929	−	0.847831i
$531$	14.7194	+	2.21713i	0.638770	+	0.0962151i
$532$	32.8625	+	4.12580i	1.42477	+	0.178876i
$533$	59.4603	−	21.6418i	2.57551	−	0.937410i
$534$	−19.7148	−	2.72193i	−0.853144	−	0.117790i
$535$	18.6465	+	22.2221i	0.806160	+	0.960744i
$536$	−2.40914	−	9.47481i	−0.104059	−	0.409249i
$537$	−12.3145	+	15.0545i	−0.531408	+	0.649649i
$538$	−28.0073	+	0.695272i	−1.20748	+	0.0299753i
$539$			18.7302i			0.806765i
$540$	−4.62107	−	17.2516i	−0.198859	−	0.742392i
$541$			5.42107i			0.233070i	0.993187	+	0.116535i	$0.0371787\pi$
$541$			5.42107i			0.233070i	−0.993187	+	0.116535i	$0.962821\pi$
$542$	−0.426142	−	17.1661i	−0.0183044	−	0.737346i
$543$	−25.4947	−	4.16710i	−1.09408	−	0.178828i
$544$	2.05541	−	1.55508i	0.0881250	−	0.0666733i
$545$	12.3536	+	14.7225i	0.529172	+	0.630642i
$546$	50.4398	+	39.2110i	2.15862	+	1.67808i
$547$	6.73827	−	2.45253i	0.288107	−	0.104863i	−0.193924	−	0.981017i	$-0.562121\pi$
$547$	6.73827	−	2.45253i	0.288107	−	0.104863i	0.482031	+	0.876154i	$0.339899\pi$
$548$	27.9717	+	3.51177i	1.19489	+	0.150015i
$549$	−18.6387	−	10.1477i	−0.795478	−	0.433094i
$550$	−2.25635	−	2.55734i	−0.0962110	−	0.109045i
$551$	−2.32237	−	1.94870i	−0.0989363	−	0.0830174i
$552$	5.55923	−	0.484733i	0.236617	−	0.0206316i
$553$	−10.8463	−	61.5123i	−0.461231	−	2.61577i
$554$	−2.70653	−	6.89843i	−0.114989	−	0.293086i
$555$	−0.236308	−	18.8802i	−0.0100307	−	0.801418i
$556$	−10.6377	−	3.28395i	−0.451140	−	0.139271i
$557$	−5.53410	−	9.58535i	−0.234487	−	0.406144i	0.724636	−	0.689132i	$-0.242008\pi$
$557$	−5.53410	−	9.58535i	−0.234487	−	0.406144i	−0.959124	+	0.282987i	$0.908675\pi$
$558$	10.4070	+	24.6895i	0.440565	+	1.04519i
$559$	8.71941	+	5.03415i	0.368792	+	0.212922i
$560$	29.9756	+	13.5419i	1.26670	+	0.572251i
$561$	0.172925	+	0.913689i	0.00730092	+	0.0385760i
$562$	0.998513	−	1.25180i	0.0421197	−	0.0528042i
$563$	5.06217	−	13.9082i	0.213345	−	0.586160i	−0.786147	−	0.618040i	$-0.787927\pi$
$563$	5.06217	−	13.9082i	0.213345	−	0.586160i	0.999492	+	0.0318795i	$0.0101493\pi$
$564$	−6.10028	+	5.80135i	−0.256868	+	0.244281i
$565$	−29.9855	−	5.28726i	−1.26150	−	0.222437i
$566$	−1.99929	−	9.89572i	−0.0840365	−	0.415948i
$567$	41.9825	−	9.59088i	1.76310	−	0.402779i
$568$	−10.8720	−	15.9580i	−0.456179	−	0.669582i
$569$	44.3139	+	7.81374i	1.85774	+	0.327569i	0.986560	−	0.163401i	$-0.0522466\pi$
$569$	44.3139	+	7.81374i	1.85774	+	0.327569i	0.871176	+	0.490970i	$0.163358\pi$
$570$	7.75047	+	12.3366i	0.324631	+	0.516722i
$571$	−36.4607	−	13.2706i	−1.52583	−	0.555357i	−0.563235	−	0.826296i	$-0.690444\pi$
$571$	−36.4607	−	13.2706i	−1.52583	−	0.555357i	−0.962596	+	0.270939i	$0.912666\pi$
$572$	−5.86317	+	11.4301i	−0.245151	+	0.477918i
$573$	3.10961	+	16.4303i	0.129906	+	0.686385i
$574$	40.9523	+	67.0325i	1.70931	+	2.79788i
$575$	1.16559	−	2.01886i	0.0486084	−	0.0841923i
$576$	15.4376	−	18.3760i	0.643235	−	0.765669i
$577$	−8.27041	−	14.3248i	−0.344302	−	0.596348i	0.640925	−	0.767603i	$-0.278551\pi$
$577$	−8.27041	−	14.3248i	−0.344302	−	0.596348i	−0.985227	+	0.171256i	$0.945218\pi$
$578$	11.3600	−	20.8548i	0.472512	−	0.867444i
$579$	9.99485	−	0.125097i	0.415372	−	0.00519887i
$580$	−1.63291	−	2.52950i	−0.0678029	−	0.105032i
$581$	8.90589	+	50.5078i	0.369479	+	2.09542i
$582$	3.59620	+	1.15883i	0.149067	+	0.0480350i
$583$	−9.19416	+	10.9572i	−0.380783	+	0.453800i
$584$	0.999820	−	2.07434i	0.0413728	−	0.0858367i
$585$	0.703383	+	28.0945i	0.0290813	+	1.16156i
$586$	3.37177	+	1.13328i	0.139286	+	0.0468154i
$587$	−3.92702	−	10.7894i	−0.162085	−	0.445326i	0.831888	−	0.554943i	$-0.187260\pi$
$587$	−3.92702	−	10.7894i	−0.162085	−	0.445326i	−0.993974	+	0.109617i	$0.965038\pi$
$588$	−24.5163	+	49.3038i	−1.01103	+	2.03326i
$589$	−14.0492	−	16.7431i	−0.578886	−	0.689889i
$590$	−11.9244	−	1.79870i	−0.490920	−	0.0740513i
$591$	4.04869	−	24.7702i	0.166541	−	1.01891i
$592$	20.6081	−	14.8020i	0.846989	−	0.608360i
$593$		−	28.6932i		−	1.17829i	−0.808028	−	0.589145i	$-0.799465\pi$
$593$		−	28.6932i		−	1.17829i	0.808028	−	0.589145i	$-0.200535\pi$
$594$	3.46295	+	7.93645i	0.142086	+	0.325636i
$595$	−3.74666			−0.153598
$596$	−6.61948	−	29.0323i	−0.271144	−	1.18921i
$597$	15.6555	−	19.1389i	0.640737	−	0.783304i
$598$	−8.68269	−	1.30971i	−0.355062	−	0.0535582i
$599$	−10.2334	+	8.58682i	−0.418124	+	0.350848i	−0.827449	−	0.561541i	$-0.810209\pi$
$599$	−10.2334	+	8.58682i	−0.418124	+	0.350848i	0.409325	+	0.912389i	$0.365764\pi$
$600$	−2.59209	−	9.68512i	−0.105822	−	0.395393i
$601$	−18.0827	+	6.58157i	−0.737610	+	0.268468i	−0.683382	−	0.730061i	$-0.739492\pi$
$601$	−18.0827	+	6.58157i	−0.737610	+	0.268468i	−0.0542273	+	0.998529i	$0.517270\pi$
$602$	−3.98210	+	11.8476i	−0.162298	+	0.482874i
$603$	8.10770	+	6.46438i	0.330171	+	0.263250i
$604$	22.5480	−	29.7534i	0.917464	−	1.21065i
$605$	12.6535	+	10.6175i	0.514437	+	0.431664i
$606$	−4.48351	+	4.05673i	−0.182130	+	0.164794i
$607$	33.3808	−	5.88593i	1.35488	−	0.238903i	0.551406	−	0.834237i	$-0.314092\pi$
$607$	33.3808	−	5.88593i	1.35488	−	0.238903i	0.803478	+	0.595334i	$0.202980\pi$
$608$	−7.61505	+	18.0364i	−0.308831	+	0.731472i
$609$	6.24113	−	3.70823i	0.252904	−	0.150265i
$610$	15.0981	+	8.22423i	0.611306	+	0.332989i
$611$	11.4720	−	6.62337i	0.464108	−	0.267953i
$612$	−0.740749	+	2.63147i	−0.0299430	+	0.106371i
$613$	−5.44638	−	3.14447i	−0.219977	−	0.127004i	0.385963	−	0.922514i	$-0.373869\pi$
$613$	−5.44638	−	3.14447i	−0.219977	−	0.127004i	−0.605940	+	0.795511i	$0.707203\pi$
$614$	8.42525	+	13.7908i	0.340016	+	0.556553i
$615$	−11.4108	+	32.6153i	−0.460128	+	1.31518i
$616$	−15.3499	−	4.32445i	−0.618466	−	0.174237i
$617$	−9.83236	+	27.0142i	−0.395836	+	1.08755i	0.568457	+	0.822713i	$0.307541\pi$
$617$	−9.83236	+	27.0142i	−0.395836	+	1.08755i	−0.964293	+	0.264838i	$0.914682\pi$
$618$	−4.14230	−	2.18961i	−0.166628	−	0.0880792i
$619$	−1.65721	+	9.39848i	−0.0666087	+	0.377757i	0.933221	+	0.359303i	$0.116986\pi$
$619$	−1.65721	+	9.39848i	−0.0666087	+	0.377757i	−0.999830	+	0.0184539i	$0.994126\pi$
$620$	−8.42689	−	20.0037i	−0.338432	−	0.803366i
$621$	−4.38808	+	3.97207i	−0.176087	+	0.159394i
$622$	−3.21153	−	15.8958i	−0.128771	−	0.637365i
$623$	−6.75089	+	38.2862i	−0.270469	+	1.53390i
$624$	−30.3949	+	22.4134i	−1.21677	+	0.897254i
$625$	9.94093	+	3.61820i	0.397637	+	0.144728i
$626$	−8.88578	−	7.08783i	−0.355147	−	0.283287i
$627$	−4.60778	−	5.35381i	−0.184017	−	0.213811i
$628$	−10.4791	−	11.2990i	−0.418163	−	0.450878i
$629$	−1.44507	+	2.50294i	−0.0576189	+	0.0997989i
$630$	−34.0133	+	7.76274i	−1.35512	+	0.309275i
$631$	−18.9384	+	10.9341i	−0.753925	+	0.435279i	−0.827110	−	0.562040i	$-0.810017\pi$
$631$	−18.9384	+	10.9341i	−0.753925	+	0.435279i	0.0731856	+	0.997318i	$0.476683\pi$
$632$	36.7371	+	3.68875i	1.46132	+	0.146731i
$633$	15.3520	−	27.3760i	0.610186	−	1.08810i
$634$	15.0517	−	5.90538i	0.597779	−	0.234532i
$635$	18.9147	−	3.33518i	0.750609	−	0.132353i
$636$	−38.5441	+	16.8084i	−1.52837	+	0.666497i
$637$	55.6937	−	66.3732i	2.20667	−	2.62980i
$638$	0.965756	+	1.09459i	0.0382346	+	0.0433351i
$639$	19.4150	+	6.52097i	0.768045	+	0.257966i
$640$	−12.5098	+	14.8845i	−0.494492	+	0.588361i
$641$	5.37663	+	14.7722i	0.212364	+	0.583466i	0.999442	−	0.0333872i	$-0.0106295\pi$
$641$	5.37663	+	14.7722i	0.212364	+	0.583466i	−0.787078	+	0.616853i	$0.788407\pi$
$642$	−15.5818	−	38.2983i	−0.614965	−	1.51151i
$643$	21.2643	−	17.8429i	0.838584	−	0.703655i	−0.118661	−	0.992935i	$-0.537860\pi$
$643$	21.2643	−	17.8429i	0.838584	−	0.703655i	0.957245	+	0.289280i	$0.0934157\pi$
$644$	−0.540883	−	10.8873i	−0.0213138	−	0.429021i
$645$	−5.14257	+	1.94497i	−0.202488	+	0.0765830i
$646$	−0.0553434	−	2.22937i	−0.00217746	−	0.0877133i
$647$	−1.38696			−0.0545272			−0.0272636	−	0.999628i	$-0.508679\pi$
$647$	−1.38696			−0.0545272			−0.0272636	+	0.999628i	$0.508679\pi$
$648$	−1.27257	+	25.4240i	−0.0499911	+	0.998750i
$649$	5.84676			0.229505
$650$	0.391523	+	15.7715i	0.0153568	+	0.618610i
$651$	48.9543	−	18.5150i	1.91867	−	0.725659i
$652$	−9.71989	+	0.482884i	−0.380660	+	0.0189112i
$653$	5.23172	−	4.38994i	0.204733	−	0.171792i	−0.534656	−	0.845070i	$-0.679559\pi$
$653$	5.23172	−	4.38994i	0.204733	−	0.171792i	0.739389	+	0.673278i	$0.235114\pi$
$654$	−10.3232	−	25.3733i	−0.403669	−	0.992173i
$655$	−6.47012	−	17.7765i	−0.252808	−	0.694586i
$656$	−44.7036	+	12.5557i	−1.74538	+	0.490218i
$657$	0.484187	+	2.39393i	0.0188899	+	0.0933960i
$658$	10.8798	+	12.3312i	0.424140	+	0.480719i
$659$	−16.7924	+	20.0124i	−0.654141	+	0.779574i	−0.986532	−	0.163567i	$-0.947700\pi$
$659$	−16.7924	+	20.0124i	−0.654141	+	0.779574i	0.332392	+	0.943141i	$0.392144\pi$
$660$	−2.80410	−	6.43021i	−0.109150	−	0.250295i
$661$	11.4759	−	2.02351i	0.446361	−	0.0787056i	0.0540505	−	0.998538i	$-0.482787\pi$
$661$	11.4759	−	2.02351i	0.446361	−	0.0787056i	0.392311	+	0.919833i	$0.371676\pi$
$662$	−0.995978	+	0.390762i	−0.0387098	+	0.0151874i
$663$	2.10405	−	3.75199i	0.0817144	−	0.145715i
$664$	−30.1648	−	3.02884i	−1.17062	−	0.117542i
$665$	24.6469	−	14.2299i	0.955767	−	0.551812i
$666$	−7.93294	+	25.7165i	−0.307395	+	0.996494i
$667$	−0.498893	+	0.864107i	−0.0193172	+	0.0334584i
$668$	−11.3699	+	10.5450i	−0.439916	+	0.407996i
$669$	10.3359	+	12.0094i	0.399610	+	0.464309i
$670$	−6.56725	−	5.23842i	−0.253715	−	0.202378i
$671$	−7.83295	−	2.85096i	−0.302388	−	0.110060i
$672$	−34.7456	−	31.4752i	−1.34034	−	1.21418i
$673$	6.57735	−	37.3020i	0.253538	−	1.43789i	−0.546259	−	0.837617i	$-0.683948\pi$
$673$	6.57735	−	37.3020i	0.253538	−	1.43789i	0.799797	−	0.600271i	$-0.204940\pi$
$674$	3.73519	+	18.4878i	0.143874	+	0.712122i
$675$	8.39709	+	6.52490i	0.323204	+	0.251144i
$676$	30.8036	−	12.9766i	1.18475	−	0.499099i
$677$	−7.47059	+	42.3678i	−0.287118	+	1.62833i	0.410502	+	0.911860i	$0.365354\pi$
$677$	−7.47059	+	42.3678i	−0.287118	+	1.62833i	−0.697620	+	0.716468i	$0.745758\pi$
$678$	38.3676	+	20.2811i	1.47350	+	0.778889i
$679$	2.52433	−	6.93553i	0.0968748	−	0.266161i
$680$	0.600559	−	2.13173i	0.0230304	−	0.0817480i
$681$	5.93054	−	16.9512i	0.227259	−	0.649570i
$682$	5.48652	+	8.98058i	0.210090	+	0.343884i
$683$	15.8827	+	9.16986i	0.607733	+	0.350875i	0.772078	−	0.635528i	$-0.219218\pi$
$683$	15.8827	+	9.16986i	0.607733	+	0.350875i	−0.164345	+	0.986403i	$0.552551\pi$
$684$	−5.12147	−	20.1242i	−0.195824	−	0.769467i
$685$	20.9788	−	12.1121i	0.801558	−	0.462780i
$686$	52.8596	+	28.7936i	2.01819	+	1.09935i
$687$	7.58004	−	4.50376i	0.289197	−	0.171829i
$688$	−6.10262	−	4.16476i	−0.232660	−	0.158780i
$689$	65.1619	−	11.4898i	2.48247	−	0.437726i
$690$	3.55563	−	3.21717i	0.135360	−	0.122476i
$691$	−14.5270	−	12.1896i	−0.552634	−	0.463715i	0.323198	−	0.946331i	$-0.395242\pi$
$691$	−14.5270	−	12.1896i	−0.552634	−	0.463715i	−0.875832	+	0.482617i	$0.839686\pi$
$692$	−4.98312	−	3.77635i	−0.189430	−	0.143555i
$693$	15.7450	−	6.18122i	0.598102	−	0.234805i
$694$	8.32198	−	24.7598i	0.315898	−	0.939869i
$695$	−8.98952	+	3.27192i	−0.340992	+	0.124111i
$696$	1.10946	+	4.14540i	0.0420539	+	0.157131i
$697$	4.05164	−	3.39973i	0.153467	−	0.128774i
$698$	2.84054	+	0.428473i	0.107516	+	0.0162179i
$699$	10.4014	−	12.7158i	0.393418	−	0.480956i
$700$	−19.0950	+	4.35374i	−0.721723	+	0.164556i
$701$	−34.7772			−1.31352			−0.656759	−	0.754101i	$-0.728073\pi$
$701$	−34.7772			−1.31352			−0.656759	+	0.754101i	$0.728073\pi$
$702$	11.3274	−	38.4210i	0.427524	−	1.45011i
$703$		−	21.9537i		−	0.828001i
$704$	4.92094	−	8.04043i	0.185465	−	0.303035i
$705$	−1.16687	+	7.13902i	−0.0439470	+	0.268871i
$706$	−21.0258	−	3.17158i	−0.791317	−	0.119364i
$707$	7.59210	+	9.04791i	0.285530	+	0.340282i
$708$	15.3906	+	7.65294i	0.578413	+	0.287615i
$709$	9.57106	+	26.2963i	0.359449	+	0.987578i	0.979221	+	0.202796i	$0.0650028\pi$
$709$	9.57106	+	26.2963i	0.359449	+	0.987578i	−0.619772	+	0.784782i	$0.712775\pi$
$710$	−15.7277	−	5.28621i	−0.590250	−	0.198388i
$711$	−33.4141	+	20.4234i	−1.25313	+	0.765939i
$712$	−20.7015	−	9.97800i	−0.775820	−	0.373941i
$713$	−4.62392	+	5.51057i	−0.173167	+	0.206372i
$714$	5.08279	+	1.63786i	0.190219	+	0.0612955i
$715$	1.91681	+	10.8708i	0.0716847	+	0.406544i
$716$	−18.8684	+	12.1804i	−0.705144	+	0.455203i
$717$	41.5346	−	0.519855i	1.55114	−	0.0194143i
$718$	9.13870	−	16.7769i	0.341053	−	0.626109i
$719$	7.82104	+	13.5464i	0.291676	+	0.505197i	0.974206	−	0.225660i	$-0.0724539\pi$
$719$	7.82104	+	13.5464i	0.291676	+	0.505197i	−0.682530	+	0.730857i	$0.739121\pi$
$720$	1.03531	−	20.5967i	0.0385837	−	0.767595i
$721$	−4.57631	+	7.92639i	−0.170431	+	0.295194i
$722$	−5.17712	−	8.47414i	−0.192672	−	0.315375i
$723$	−5.60509	−	29.6157i	−0.208456	−	1.10142i
$724$	−26.5412	−	13.6145i	−0.986396	−	0.505979i
$725$	1.68458	+	0.613135i	0.0625636	+	0.0227713i
$726$	−12.5245	−	19.9355i	−0.464827	−	0.739874i
$727$	22.5584	+	3.97765i	0.836643	+	0.147523i	0.575525	−	0.817784i	$-0.304798\pi$
$727$	22.5584	+	3.97765i	0.836643	+	0.147523i	0.261118	+	0.965307i	$0.415909\pi$
$728$	41.5362	+	60.9671i	1.53943	+	2.25959i
$729$	−15.2162	−	22.3040i	−0.563562	−	0.826073i
$730$	−0.391848	−	1.93949i	−0.0145029	−	0.0717839i
$731$	0.828788	+	0.146138i	0.0306538	+	0.00540510i
$732$	−16.8872	−	17.7574i	−0.624168	−	0.656331i
$733$	−14.5646	+	40.0158i	−0.537954	+	1.47802i	0.311444	+	0.950265i	$0.399188\pi$
$733$	−14.5646	+	40.0158i	−0.537954	+	1.47802i	−0.849398	+	0.527753i	$0.823035\pi$
$734$	26.3496	−	33.0337i	0.972583	−	1.21930i
$735$	8.79858	+	46.4891i	0.324540	+	1.71478i
$736$	6.28123	+	1.43741i	0.231529	+	0.0529836i
$737$	3.52723	+	2.03645i	0.129927	+	0.0750134i
$738$	29.7380	−	39.2583i	1.09467	−	1.44512i
$739$	16.7732	+	29.0520i	0.617011	+	1.06870i	0.990028	+	0.140871i	$0.0449901\pi$
$739$	16.7732	+	29.0520i	0.617011	+	1.06870i	−0.373017	+	0.927825i	$0.621677\pi$
$740$	6.43118	−	20.8326i	0.236415	−	0.765820i
$741$	0.408944	+	32.6732i	0.0150229	+	1.20028i
$742$	30.0007	+	76.4661i	1.10136	+	2.80716i
$743$	−3.95562	−	22.4334i	−0.145118	−	0.823002i	−0.967273	−	0.253739i	$-0.918340\pi$
$743$	−3.95562	−	22.4334i	−0.145118	−	0.823002i	0.822155	−	0.569263i	$-0.192772\pi$
$744$	2.68743	+	30.8212i	0.0985260	+	1.12996i
$745$	−19.6009	−	16.4471i	−0.718120	−	0.602574i
$746$	−1.86657	−	2.11556i	−0.0683399	−	0.0774562i
$747$	27.4364	−	16.7697i	1.00384	−	0.613572i
$748$	−0.133758	+	1.06540i	−0.00489069	+	0.0389550i
$749$	−75.8969	+	27.6242i	−2.77321	+	1.00937i
$750$	−23.4191	−	18.2056i	−0.855146	−	0.664776i
$751$	−25.7667	−	30.7076i	−0.940242	−	1.12054i	−0.992542	−	0.121905i	$-0.961100\pi$
$751$	−25.7667	−	30.7076i	−0.940242	−	1.12054i	0.0522997	−	0.998631i	$-0.483345\pi$
$752$	−8.75997	+	4.21367i	−0.319443	+	0.153657i
$753$	−17.8429	−	2.91642i	−0.650230	−	0.106280i
$754$	−0.167579	−	6.75049i	−0.00610286	−	0.245838i
$755$		−	32.0786i		−	1.16746i
$756$	49.5366	+	4.33791i	1.80163	+	0.157768i
$757$			18.0630i			0.656512i	0.944589	+	0.328256i	$0.106461\pi$
$757$			18.0630i			0.656512i	−0.944589	+	0.328256i	$0.893539\pi$
$758$	3.68031	−	0.0913626i	0.133675	−	0.00331844i
$759$	−1.47196	+	1.79947i	−0.0534286	+	0.0653167i
$760$	4.14565	+	16.3042i	0.150378	+	0.591417i
$761$	6.35846	+	7.57772i	0.230494	+	0.274692i	0.868878	−	0.495026i	$-0.164841\pi$
$761$	6.35846	+	7.57772i	0.230494	+	0.274692i	−0.638384	+	0.769718i	$0.720397\pi$
$762$	−27.1181	−	3.74407i	−0.982385	−	0.135633i
$763$	−50.2830	+	18.3015i	−1.82037	+	0.662559i
$764$	−2.40529	+	19.1585i	−0.0870203	+	0.693128i
$765$	0.858419	+	2.18659i	0.0310362	+	0.0790562i
$766$	−18.8382	+	16.6210i	−0.680653	+	0.600542i
$767$	−20.7189	−	17.3852i	−0.748116	−	0.627744i
$768$	23.4778	−	14.7239i	0.847182	−	0.531303i
$769$	−2.24867	−	12.7528i	−0.0810890	−	0.459879i	−0.998132	−	0.0610908i	$-0.980542\pi$
$769$	−2.24867	−	12.7528i	−0.0810890	−	0.459879i	0.917043	−	0.398788i	$-0.130569\pi$
$770$	−12.7566	+	5.00494i	−0.459718	+	0.180366i
$771$	−30.5911	+	18.1760i	−1.10171	+	0.654594i
$772$	11.0284	+	3.40456i	0.396921	+	0.122533i
$773$	11.3665	+	19.6874i	0.408825	+	0.708106i	0.994758	−	0.102254i	$-0.0326053\pi$
$773$	11.3665	+	19.6874i	0.408825	+	0.708106i	−0.585933	+	0.810359i	$0.699272\pi$
$774$	7.82676	−	0.390493i	0.281327	−	0.0140360i
$775$	11.1929	+	6.46220i	0.402059	+	0.232129i
$776$	3.54146	+	2.54797i	0.127131	+	0.0914668i
$777$	49.6219	+	17.3607i	1.78018	+	0.622813i
$778$	15.1534	+	12.0872i	0.543274	+	0.433348i
$779$	−13.7409	+	37.7529i	−0.492320	+	1.35264i
$780$	−9.18331	+	31.1244i	−0.328815	+	1.11443i
$781$	7.92230	+	1.39692i	0.283482	+	0.0499856i
$782$	−0.719428	+	0.145350i	−0.0257267	+	0.00519772i
$783$	−3.59410	−	2.79277i	−0.128443	−	0.0998055i
$784$	−44.4153	+	45.4954i	−1.58626	+	1.62484i
$785$	−13.0406	−	2.29942i	−0.465441	−	0.0820697i
$786$	1.00644	+	26.9444i	0.0358985	+	0.961075i
$787$	−19.7167	−	7.17628i	−0.702823	−	0.255807i	−0.0342072	−	0.999415i	$-0.510891\pi$
$787$	−19.7167	−	7.17628i	−0.702823	−	0.255807i	−0.668616	+	0.743608i	$0.733113\pi$
$788$	13.2276	−	25.7870i	0.471214	−	0.918623i
$789$	33.3044	−	28.6636i	1.18567	−	1.02045i
$790$	27.0735	−	16.5401i	0.963233	−	0.588469i
$791$	42.3875	−	73.4173i	1.50713	−	2.61042i
$792$	0.993120	+	9.94917i	0.0352890	+	0.353528i
$793$	19.2800	+	33.3939i	0.684653	+	1.18585i
$794$	−31.9982	−	17.4300i	−1.13558	−	0.618569i
$795$	−17.6732	+	31.5152i	−0.626803	+	1.11773i
$796$	23.9875	−	15.4851i	0.850216	−	0.548854i
$797$	−5.29392	−	30.0233i	−0.187520	−	1.06348i	−0.922674	−	0.385580i	$-0.874001\pi$
$797$	−5.29392	−	30.0233i	−0.187520	−	1.06348i	0.735154	−	0.677900i	$-0.237110\pi$
$798$	−39.6572	+	8.53010i	−1.40385	+	0.301962i
$799$	0.711724	−	0.848200i	0.0251790	−	0.0300071i
$800$	0.583639	−	11.5623i	0.0206348	−	0.408789i
$801$	23.8909	−	4.83209i	0.844144	−	0.170733i
$802$	5.15697	−	15.3432i	0.182099	−	0.541786i
$803$	0.328111	+	0.901478i	0.0115788	+	0.0318125i
$804$	6.61926	+	9.97744i	0.233443	+	0.351877i
$805$	−6.02087	−	7.17540i	−0.212208	−	0.252899i
$806$	7.26125	−	48.1381i	0.255767	−	1.69559i
$807$	32.0937	−	12.1381i	1.12975	−	0.427282i
$808$	−6.36492	+	2.86935i	−0.223917	+	0.100943i
$809$			12.1921i			0.428652i	0.976762	+	0.214326i	$0.0687555\pi$
$809$			12.1921i			0.428652i	−0.976762	+	0.214326i	$0.931244\pi$
$810$	12.3234	+	18.0719i	0.433000	+	0.634982i
$811$	−32.9198			−1.15597			−0.577985	−	0.816048i	$-0.696161\pi$
$811$	−32.9198			−1.15597			−0.577985	+	0.816048i	$0.696161\pi$
$812$	8.17299	−	1.86348i	0.286816	−	0.0653952i
$813$	7.43963	+	19.6707i	0.260919	+	0.689881i
$814$	−1.57666	+	10.4524i	−0.0552621	+	0.366357i
$815$	−6.40598	+	5.37526i	−0.224392	+	0.188287i
$816$	−1.74662	+	2.62941i	−0.0611440	+	0.0920476i
$817$	−6.00711	+	2.18641i	−0.210162	+	0.0764928i
$818$	12.4592	+	4.18763i	0.435624	+	0.146417i
$819$	−74.1745	−	24.9132i	−2.59187	−	0.870538i
$820$	−24.0986	+	31.7996i	−0.841560	+	1.11049i
$821$	−23.5767	−	19.7832i	−0.822832	−	0.690438i	0.130802	−	0.991409i	$-0.458245\pi$
$821$	−23.5767	−	19.7832i	−0.822832	−	0.690438i	−0.953633	+	0.300971i	$0.902689\pi$
$822$	−33.7551	+	7.26059i	−1.17734	+	0.253242i
$823$	−32.9923	+	5.81743i	−1.15004	+	0.202783i	−0.715992	−	0.698108i	$-0.754026\pi$
$823$	−32.9923	+	5.81743i	−1.15004	+	0.202783i	−0.434046	+	0.900891i	$0.642914\pi$
$824$	−3.77631	−	3.87430i	−0.131554	−	0.134968i
$825$	3.64317	+	2.04302i	0.126839	+	0.0711289i
$826$	16.0612	−	29.4854i	0.558842	−	1.02593i
$827$	−45.1216	+	26.0510i	−1.56903	+	0.905882i	−0.572751	+	0.819729i	$0.694124\pi$
$827$	−45.1216	+	26.0510i	−1.56903	+	0.905882i	−0.996282	+	0.0861526i	$0.972543\pi$
$828$	−6.23003	+	2.81012i	−0.216508	+	0.0976586i
$829$	−25.6067	−	14.7840i	−0.889357	−	0.513471i	−0.0156251	−	0.999878i	$-0.504974\pi$
$829$	−25.6067	−	14.7840i	−0.889357	−	0.513471i	−0.873732	+	0.486407i	$0.838307\pi$
$830$	−22.2301	+	13.5811i	−0.771619	+	0.471406i
$831$	5.92038	+	6.87893i	0.205376	+	0.238627i
$832$	−41.3462	+	13.8602i	−1.43342	+	0.480516i
$833$	2.47700	−	6.80550i	0.0858229	−	0.235797i
$834$	13.6257	−	0.508953i	0.471819	−	0.0176236i
$835$	−2.31386	+	13.1226i	−0.0800744	+	0.454125i
$836$	−3.16652	−	7.51664i	−0.109516	−	0.259968i
$837$	−22.0217	−	24.3281i	−0.761182	−	0.840903i
$838$	−19.5152	+	3.94278i	−0.674142	+	0.136201i
$839$	7.95080	−	45.0912i	0.274492	−	1.55672i	−0.466078	−	0.884743i	$-0.654334\pi$
$839$	7.95080	−	45.0912i	0.274492	−	1.55672i	0.740571	−	0.671979i	$-0.234555\pi$
$840$	−40.1307	−	3.52280i	−1.38464	−	0.121548i
$841$	26.5301	+	9.65615i	0.914830	+	0.332971i
$842$	9.20013	−	11.5339i	0.317057	−	0.397485i
$843$	−0.647632	+	1.85112i	−0.0223056	+	0.0637559i
$844$	26.5731	−	24.6450i	0.914683	−	0.848315i
$845$	14.3609	−	24.8738i	0.494029	−	0.855684i
$846$	4.70385	−	9.17483i	0.161722	−	0.315437i
$847$	−39.8286	+	22.9950i	−1.36853	+	0.790118i
$848$	−48.3156	+	4.81251i	−1.65916	+	0.165262i
$849$	6.31583	+	10.6299i	0.216759	+	0.364816i
$850$	0.481632	+	1.22759i	0.0165198	+	0.0421060i
$851$	−7.11573	+	1.25470i	−0.243924	+	0.0430104i
$852$	19.0256	+	14.0468i	0.651807	+	0.481235i
$853$	7.00400	−	8.34705i	0.239813	−	0.285797i	−0.632692	−	0.774404i	$-0.718050\pi$
$853$	7.00400	−	8.34705i	0.239813	−	0.285797i	0.872504	+	0.488606i	$0.162494\pi$
$854$	−35.8948	+	31.6701i	−1.22830	+	1.08373i
$855$	−13.9517	−	11.1239i	−0.477139	−	0.380429i
$856$	−3.55161	−	47.6108i	−0.121391	−	1.62730i
$857$	−6.47755	−	17.7969i	−0.221269	−	0.607931i	0.778538	−	0.627598i	$-0.215962\pi$
$857$	−6.47755	−	17.7969i	−0.221269	−	0.607931i	−0.999807	+	0.0196666i	$0.993740\pi$
$858$	2.15181	−	15.5855i	0.0734616	−	0.532079i
$859$	30.2186	−	25.3564i	1.03105	−	0.865150i	0.0400702	−	0.999197i	$-0.487242\pi$
$859$	30.2186	−	25.3564i	1.03105	−	0.865150i	0.990975	+	0.134047i	$0.0427974\pi$
$860$	−6.34082	+	0.315012i	−0.216220	+	0.0107418i
$861$	−74.4665	−	60.9131i	−2.53781	−	2.07591i
$862$	−22.6503	+	0.562286i	−0.771472	+	0.0191515i
$863$	−16.4124			−0.558684			−0.279342	−	0.960192i	$-0.590116\pi$
$863$	−16.4124			−0.558684			−0.279342	+	0.960192i	$0.590116\pi$
$864$	−10.4084	+	27.4893i	−0.354103	+	0.935207i
$865$	−5.37255			−0.182672
$866$	12.1662	−	0.302022i	0.413424	−	0.0102631i
$867$	−4.69174	+	28.7044i	−0.159340	+	0.974852i
$868$	60.3610	−	2.99873i	2.04878	−	0.101784i
$869$	−11.7833	+	9.88732i	−0.399719	+	0.335404i
$870$	2.91124	+	2.26315i	0.0987003	+	0.0767278i
$871$	−6.44395	−	17.7046i	−0.218345	−	0.599897i
$872$	−2.35300	−	31.5429i	−0.0796826	−	1.06818i
$873$	−4.62601	+	0.115818i	−0.156567	+	0.00391985i
$874$	4.18063	−	3.68858i	0.141412	−	0.124768i
$875$	−37.2462	+	44.3883i	−1.25915	+	1.50060i
$876$	−0.316267	+	2.80245i	−0.0106857	+	0.0946861i
$877$	−18.5740	+	3.27509i	−0.627198	+	0.110592i	−0.478208	−	0.878247i	$-0.658713\pi$
$877$	−18.5740	+	3.27509i	−0.627198	+	0.110592i	−0.148990	+	0.988839i	$0.547602\pi$
$878$	4.91179	+	12.5192i	0.165765	+	0.422503i
$879$	−4.35623	+	0.0545234i	−0.146932	+	0.00183903i
$880$	−0.802859	−	8.06037i	−0.0270644	−	0.271715i
$881$	10.7069	−	6.18163i	0.360725	−	0.208265i	−0.308674	−	0.951168i	$-0.599885\pi$
$881$	10.7069	−	6.18163i	0.360725	−	0.208265i	0.669399	+	0.742903i	$0.266552\pi$
$882$	8.38654	−	66.9144i	0.282390	−	2.25313i
$883$	−11.5774	+	20.0526i	−0.389610	+	0.674824i	−0.992397	−	0.123078i	$-0.960723\pi$
$883$	−11.5774	+	20.0526i	−0.389610	+	0.674824i	0.602787	+	0.797902i	$0.294057\pi$
$884$	3.64195	−	3.37769i	0.122492	−	0.113604i
$885$	14.5119	−	2.74654i	0.487814	−	0.0923240i
$886$	11.8635	−	14.8728i	0.398561	−	0.499663i
$887$	44.9592	+	16.3638i	1.50958	+	0.549443i	0.958521	−	0.285022i	$-0.0920010\pi$
$887$	44.9592	+	16.3638i	1.50958	+	0.549443i	0.551061	+	0.834465i	$0.314223\pi$
$888$	−17.8317	+	25.4504i	−0.598392	+	0.854061i
$889$	−9.28597	+	52.6633i	−0.311441	+	1.76627i
$890$	−19.3558	+	3.91056i	−0.648807	+	0.131082i
$891$	−7.21484	−	7.77270i	−0.241706	−	0.260395i
$892$	7.10295	+	16.8609i	0.237824	+	0.564544i
$893$	−1.46050	+	8.28292i	−0.0488739	+	0.277178i
$894$	19.4010	+	30.8810i	0.648867	+	1.03281i
$895$	−6.60032	+	18.1342i	−0.220624	+	0.606160i
$896$	−27.0302	−	46.9038i	−0.903014	−	1.56695i
$897$	10.5668	−	1.99988i	0.352815	−	0.0667741i
$898$	−11.6443	+	7.11388i	−0.388576	+	0.237393i
$899$	−4.79074	−	2.76593i	−0.159780	−	0.0922490i
$900$	6.91585	+	10.1465i	0.230528	+	0.338217i
$901$	4.78970	−	2.76533i	0.159568	−	0.0921266i
$902$	9.25355	−	16.9878i	0.308109	−	0.565631i
$903$	−0.191583	−	15.3068i	−0.00637549	−	0.509379i
$904$	34.9777	+	35.8853i	1.16334	+	1.19353i
$905$	−25.2424	+	4.45091i	−0.839085	+	0.147953i
$906$	−14.0233	+	43.5185i	−0.465892	+	1.44581i
$907$	−45.8690	−	38.4887i	−1.52306	−	1.27800i	−0.831223	−	0.555939i	$-0.812359\pi$
$907$	−45.8690	−	38.4887i	−1.52306	−	1.27800i	−0.691834	−	0.722057i	$-0.743197\pi$
$908$	12.5248	−	16.5272i	0.415649	−	0.548474i
$909$	3.54098	−	6.50384i	0.117447	−	0.215719i
$910$	60.0872	+	20.1958i	1.99187	+	0.669486i
$911$	5.57494	−	2.02911i	0.184706	−	0.0672275i	−0.248011	−	0.968757i	$-0.579777\pi$
$911$	5.57494	−	2.02911i	0.184706	−	0.0672275i	0.432717	+	0.901530i	$0.357555\pi$
$912$	1.50338	−	23.9309i	0.0497818	−	0.792432i
$913$	9.67524	−	8.11849i	0.320204	−	0.268683i
$914$	−2.85140	+	18.9032i	−0.0943160	+	0.625263i
$915$	−20.7810	−	3.39666i	−0.686999	−	0.112290i
$916$	9.92633	−	2.26325i	0.327975	−	0.0747798i
$917$	52.6706			1.73934
$918$	−0.208675	−	3.34163i	−0.00688731	−	0.110290i
$919$			16.2524i			0.536116i	0.963403	+	0.268058i	$0.0863819\pi$
$919$			16.2524i			0.536116i	−0.963403	+	0.268058i	$0.913618\pi$
$920$	5.04766	−	2.27552i	0.166416	−	0.0750217i
$921$	−15.3203	−	12.5319i	−0.504820	−	0.412939i
$922$	−8.61284	+	57.0984i	−0.283649	+	1.88044i
$923$	−23.9202	−	28.5070i	−0.787343	−	0.938319i
$924$	19.4938	−	1.21320i	0.641300	−	0.0399113i
$925$	4.44004	+	12.1989i	0.145988	+	0.401098i
$926$	−9.46201	+	28.1516i	−0.310941	+	0.925120i
$927$	5.67442	+	0.854714i	0.186373	+	0.0280725i
$928$	−0.249808	+	4.94886i	−0.00820034	+	0.162454i
$929$	−35.2810	+	42.0462i	−1.15753	+	1.37949i	−0.245486	+	0.969400i	$0.578948\pi$
$929$	−35.2810	+	42.0462i	−1.15753	+	1.37949i	−0.912044	+	0.410092i	$0.865497\pi$
$930$	17.8365	+	19.7129i	0.584881	+	0.646412i
$931$	9.55284	+	54.1768i	0.313082	+	1.77557i
$932$	15.9372	−	10.2882i	0.522041	−	0.337001i
$933$	10.1453	+	17.0751i	0.332144	+	0.559014i
$934$	36.9209	+	20.1115i	1.20809	+	0.658067i
$935$	0.461333	+	0.799053i	0.0150872	+	0.0261318i
$936$	26.0644	−	38.2094i	0.851941	−	1.24891i
$937$	17.4404	−	30.2077i	0.569753	−	0.986841i	−0.426837	−	0.904329i	$-0.640372\pi$
$937$	17.4404	−	30.2077i	0.569753	−	0.986841i	0.996590	−	0.0825128i	$-0.0262945\pi$
$938$	19.9593	−	12.1937i	0.651693	−	0.398140i
$939$	13.1399	+	4.59714i	0.428806	+	0.150022i
$940$	−3.81233	+	7.43207i	−0.124345	+	0.242407i
$941$	41.1785	+	14.9877i	1.34238	+	0.488586i	0.910561	−	0.413374i	$-0.135650\pi$
$941$	41.1785	+	14.9877i	1.34238	+	0.488586i	0.431818	+	0.901961i	$0.357872\pi$
$942$	16.6860	+	8.82019i	0.543659	+	0.287377i
$943$	13.0219	+	2.29612i	0.424053	+	0.0747720i
$944$	14.2017	+	13.8646i	0.462227	+	0.451254i
$945$	36.1761	−	22.7384i	1.17681	−	0.739679i
$946$	3.01708	−	0.609559i	0.0980937	−	0.0198185i
$947$	−18.8196	−	3.31841i	−0.611556	−	0.107834i	−0.140713	−	0.990050i	$-0.544939\pi$
$947$	−18.8196	−	3.31841i	−0.611556	−	0.107834i	−0.470844	+	0.882217i	$0.656050\pi$
$948$	−43.9590	+	10.6033i	−1.42772	+	0.344379i
$949$	1.51781	−	4.17016i	0.0492703	−	0.135369i
$950$	−7.83077	−	6.24629i	−0.254064	−	0.202656i
$951$	−15.0091	+	12.9177i	−0.486704	+	0.418884i
$952$	5.00542	+	3.60124i	0.162227	+	0.116717i
$953$	−12.5264	−	7.23211i	−0.405769	−	0.234271i	0.283201	−	0.959061i	$-0.408604\pi$
$953$	−12.5264	−	7.23211i	−0.405769	−	0.234271i	−0.688970	+	0.724790i	$0.741937\pi$
$954$	37.7527	−	35.0283i	1.22229	−	1.13408i
$955$	8.29586	+	14.3689i	0.268448	+	0.464965i
$956$	45.8296	+	14.1480i	1.48224	+	0.457578i
$957$	−1.55934	−	0.874449i	−0.0504063	−	0.0282669i
$958$	4.21560	−	1.65395i	0.136200	−	0.0534367i
$959$	11.7119	+	66.4215i	0.378197	+	2.14486i
$960$	8.43698	−	22.2684i	0.272302	−	0.718709i
$961$	−6.80403	−	5.70926i	−0.219485	−	0.184170i
$962$	36.6672	−	32.3516i	1.18220	−	1.04306i
$963$	33.5109	+	37.9650i	1.07988	+	1.22341i
$964$	4.33555	−	34.5332i	0.139639	−	1.11224i
$965$	9.31967	−	3.39208i	0.300011	−	0.109195i
$966$	5.03129	+	12.3663i	0.161879	+	0.397880i
$967$	8.91628	+	10.6260i	0.286728	+	0.341709i	0.890112	−	0.455741i	$-0.150626\pi$
$967$	8.91628	+	10.6260i	0.286728	+	0.341709i	−0.603384	+	0.797451i	$0.706181\pi$
$968$	−6.69922	−	26.3471i	−0.215321	−	0.846826i
$969$	0.966189	+	2.55464i	0.0310385	+	0.0820669i
$970$	3.74772	−	0.0930360i	0.120332	−	0.00298721i
$971$		−	35.7599i		−	1.14759i	−0.818999	−	0.573795i	$-0.805470\pi$
$971$		−	35.7599i		−	1.14759i	0.818999	−	0.573795i	$-0.194530\pi$
$972$	−8.81796	−	29.9039i	−0.282836	−	0.959168i
$973$		−	26.6353i		−	0.853890i
$974$	0.0269391	+	1.08517i	0.000863185	+	0.0347712i
$975$	−6.83525	−	18.0727i	−0.218903	−	0.578788i
$976$	−12.2656	−	25.4995i	−0.392613	−	0.816218i
$977$	−3.44365	−	4.10398i	−0.110172	−	0.131298i	0.708140	−	0.706072i	$-0.249534\pi$
$977$	−3.44365	−	4.10398i	−0.110172	−	0.131298i	−0.818312	+	0.574774i	$0.805090\pi$
$978$	11.0403	−	4.49179i	0.353030	−	0.143632i
$979$	8.99657	−	3.27448i	0.287532	−	0.104653i
$980$	−6.80572	+	54.2084i	−0.217401	+	1.73163i
$981$	22.2016	+	25.1525i	0.708841	+	0.803057i
$982$	−14.9791	−	16.9773i	−0.478003	−	0.541768i
$983$	−20.2989	−	17.0328i	−0.647436	−	0.543263i	0.258856	−	0.965916i	$-0.416655\pi$
$983$	−20.2989	−	17.0328i	−0.647436	−	0.543263i	−0.906292	+	0.422653i	$0.861099\pi$
$984$	46.5939	−	32.6051i	1.48536	−	1.03941i
$985$	−4.32443	−	24.5251i	−0.137788	−	0.781433i
$986$	−0.206147	−	0.525429i	−0.00656506	−	0.0167331i
$987$	−17.5669	−	9.85120i	−0.559161	−	0.313567i
$988$	−11.1295	+	36.0519i	−0.354077	+	1.14696i
$989$	1.05199	+	1.82209i	0.0334512	+	0.0579391i
$990$	5.84368	+	6.29819i	0.185724	+	0.200170i
$991$	41.5804	+	24.0065i	1.32085	+	0.762590i	0.983863	−	0.178921i	$-0.0572606\pi$
$991$	41.5804	+	24.0065i	1.32085	+	0.762590i	0.336982	+	0.941511i	$0.390594\pi$
$992$	−7.96920	+	34.8241i	−0.253022	+	1.10567i
$993$	0.993162	−	0.854769i	0.0315170	−	0.0271253i
$994$	28.8075	−	36.1150i	0.913719	−	1.14550i
$995$	8.39105	−	23.0542i	0.266014	−	0.730868i
$996$	36.0948	−	8.70639i	1.14371	−	0.275873i
$997$	−26.4974	−	4.67220i	−0.839180	−	0.147970i	−0.262492	−	0.964934i	$-0.584544\pi$
$997$	−26.4974	−	4.67220i	−0.839180	−	0.147970i	−0.576689	+	0.816964i	$0.695655\pi$
$998$	−7.94989	−	39.3489i	−0.251649	−	1.24557i
$999$	−1.23727	−	32.9374i	−0.0391455	−	1.04209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.83.1	✓	192
3.2	odd	2		648.2.v.b.251.32		192
4.3	odd	2		864.2.bh.b.623.4		192
8.3	odd	2	inner	216.2.v.b.83.4	yes	192
8.5	even	2		864.2.bh.b.623.3		192
24.11	even	2		648.2.v.b.251.29		192
27.13	even	9		648.2.v.b.395.29		192
27.14	odd	18	inner	216.2.v.b.203.4	yes	192
108.95	even	18		864.2.bh.b.527.3		192
216.67	odd	18		648.2.v.b.395.32		192
216.149	odd	18		864.2.bh.b.527.4		192
216.203	even	18	inner	216.2.v.b.203.1	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.83.1	✓	192	1.1	even	1	trivial
216.2.v.b.83.4	yes	192	8.3	odd	2	inner
216.2.v.b.203.1	yes	192	216.203	even	18	inner
216.2.v.b.203.4	yes	192	27.14	odd	18	inner
648.2.v.b.251.29		192	24.11	even	2
648.2.v.b.251.32		192	3.2	odd	2
648.2.v.b.395.29		192	27.13	even	9
648.2.v.b.395.32		192	216.67	odd	18
864.2.bh.b.527.3		192	108.95	even	18
864.2.bh.b.527.4		192	216.149	odd	18
864.2.bh.b.623.3		192	8.5	even	2
864.2.bh.b.623.4		192	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-1.41378 + 0.0350966i) q^{2} +(1.62005 - 0.612720i) q^{3} +(1.99754 - 0.0992376i) q^{4} +(1.31649 - 1.10467i) q^{5} +(-2.26889 + 0.923108i) q^{6} +(1.63653 + 4.49634i) q^{7} +(-2.82059 + 0.210407i) q^{8} +(2.24915 - 1.98528i) q^{9} +O(q^{10})\)	\(q+(-1.41378 + 0.0350966i) q^{2} +(1.62005 - 0.612720i) q^{3} +(1.99754 - 0.0992376i) q^{4} +(1.31649 - 1.10467i) q^{5} +(-2.26889 + 0.923108i) q^{6} +(1.63653 + 4.49634i) q^{7} +(-2.82059 + 0.210407i) q^{8} +(2.24915 - 1.98528i) q^{9} +(-1.82246 + 1.60796i) q^{10} +(0.757427 - 0.902667i) q^{11} +(3.17531 - 1.38470i) q^{12} +(-5.36812 + 0.946545i) q^{13} +(-2.47150 - 6.29938i) q^{14} +(1.45594 - 2.59627i) q^{15} +(3.98030 - 0.396461i) q^{16} +(-0.394582 + 0.227812i) q^{17} +(-3.11012 + 2.88568i) q^{18} +(1.73047 - 2.99726i) q^{19} +(2.52012 - 2.33726i) q^{20} +(5.40626 + 6.28157i) q^{21} +(-1.03915 + 1.30275i) q^{22} +(-1.07038 - 0.389588i) q^{23} +(-4.44059 + 2.06910i) q^{24} +(-0.355379 + 2.01545i) q^{25} +(7.55611 - 1.52661i) q^{26} +(2.42732 - 4.59435i) q^{27} +(3.71524 + 8.81919i) q^{28} +(0.152108 - 0.862650i) q^{29} +(-1.96725 + 3.72164i) q^{30} +(2.15993 - 5.93437i) q^{31} +(-5.61335 + 0.700203i) q^{32} +(0.673992 - 1.92646i) q^{33} +(0.549855 - 0.335924i) q^{34} +(7.12145 + 4.11157i) q^{35} +(4.29574 - 4.18886i) q^{36} +(5.49344 - 3.17164i) q^{37} +(-2.34131 + 4.29820i) q^{38} +(-8.11668 + 4.82261i) q^{39} +(-3.48086 + 3.39282i) q^{40} +(-11.4320 + 2.01577i) q^{41} +(-7.86372 - 8.69100i) q^{42} +(-1.41495 - 1.18728i) q^{43} +(1.42341 - 1.87827i) q^{44} +(0.767916 - 5.09817i) q^{45} +(1.52696 + 0.513224i) q^{46} +(-2.28362 + 0.831169i) q^{47} +(6.20539 - 3.08110i) q^{48} +(-12.1765 + 10.2173i) q^{49} +(0.431691 - 2.86188i) q^{50} +(-0.499659 + 0.610835i) q^{51} +(-10.6291 + 2.42348i) q^{52} -12.1387 q^{53} +(-3.27045 + 6.58059i) q^{54} -2.02506i q^{55} +(-5.56205 - 12.3380i) q^{56} +(0.966974 - 5.91602i) q^{57} +(-0.184772 + 1.22493i) q^{58} +(3.18940 + 3.80098i) q^{59} +(2.65064 - 5.33062i) q^{60} +(-2.41946 - 6.64740i) q^{61} +(-2.84539 + 8.46569i) q^{62} +(12.6073 + 6.86396i) q^{63} +(7.91146 - 1.18694i) q^{64} +(-6.02148 + 7.17612i) q^{65} +(-0.885262 + 2.74724i) q^{66} +(0.600205 + 3.40393i) q^{67} +(-0.765584 + 0.494220i) q^{68} +(-1.97279 + 0.0246918i) q^{69} +(-10.2125 - 5.56291i) q^{70} +(3.41347 + 5.91231i) q^{71} +(-5.92621 + 6.07289i) q^{72} +(-0.407067 + 0.705061i) q^{73} +(-7.65520 + 4.67680i) q^{74} +(0.659175 + 3.48289i) q^{75} +(3.15924 - 6.15887i) q^{76} +(5.29825 + 1.92840i) q^{77} +(11.3059 - 7.10296i) q^{78} +(-12.8555 - 2.26677i) q^{79} +(4.80209 - 4.91886i) q^{80} +(1.11735 - 8.93037i) q^{81} +(16.0916 - 3.25107i) q^{82} +(10.5557 + 1.86125i) q^{83} +(11.4226 + 12.0112i) q^{84} +(-0.267808 + 0.735795i) q^{85} +(2.04209 + 1.62889i) q^{86} +(-0.282139 - 1.49074i) q^{87} +(-1.94646 + 2.70542i) q^{88} +(7.03637 + 4.06245i) q^{89} +(-0.906734 + 7.23464i) q^{90} +(-13.0411 - 22.5878i) q^{91} +(-2.17679 - 0.671994i) q^{92} +(-0.136895 - 10.9374i) q^{93} +(3.19936 - 1.25524i) q^{94} +(-1.03283 - 5.85748i) q^{95} +(-8.66490 + 4.57378i) q^{96} +(-1.18161 - 0.991491i) q^{97} +(16.8563 - 14.8723i) q^{98} +(-0.0884767 - 3.53394i) 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

Related objects

Downloads

Learn more