LMFDB - Embedded newform 65.2.t.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(7,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("65.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.t (of order $12$, degree $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.3
Root			$-0.493902i$ of defining polynomial
Character	$\chi$	$=$	65.7
Dual form			65.2.t.a.28.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.427732 - 0.246951i) q^{2} +(-0.243392 - 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.284413 - 2.21791i) q^{5} +(-0.120212 + 0.448637i) q^{6} +(1.83775 + 3.18307i) q^{7} +1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +O(q^{10})$	\(q+(-0.427732 - 0.246951i) q^{2} +(-0.243392 - 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.284413 - 2.21791i) q^{5} +(-0.120212 + 0.448637i) q^{6} +(1.83775 + 3.18307i) q^{7} +1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +(-0.426062 + 1.01890i) q^{10} +(-0.177987 - 0.664257i) q^{11} +(-1.16771 + 1.16771i) q^{12} +(-2.92331 + 2.11051i) q^{13} -1.81533i q^{14} +(-1.94542 + 0.798168i) q^{15} +(-1.29794 + 2.24809i) q^{16} +(2.29359 + 0.614565i) q^{17} -1.04493 q^{18} +(5.29067 + 1.41763i) q^{19} +(-3.12325 + 2.37992i) q^{20} +(2.44406 - 2.44406i) q^{21} +(-0.0879082 + 0.328078i) q^{22} +(1.30811 - 0.350507i) q^{23} +(1.68511 - 0.451523i) q^{24} +(-4.83822 + 1.26160i) q^{25} +(1.77158 - 0.180816i) q^{26} +(-3.40171 - 3.40171i) q^{27} +(3.22719 - 5.58966i) q^{28} +(-8.24134 - 4.75814i) q^{29} +(1.02922 + 0.139021i) q^{30} +(4.81595 + 4.81595i) q^{31} +(4.32351 - 2.49618i) q^{32} +(-0.560059 + 0.323350i) q^{33} +(-0.829273 - 0.829273i) q^{34} +(6.53707 - 4.98125i) q^{35} +(-3.21748 - 1.85761i) q^{36} +(-0.917615 + 1.58936i) q^{37} +(-1.91290 - 1.91290i) q^{38} +(2.62860 + 2.14172i) q^{39} +(4.11449 - 0.527621i) q^{40} +(-0.534988 + 0.143350i) q^{41} +(-1.64896 + 0.441838i) q^{42} +(-0.560778 + 2.09285i) q^{43} +(-0.853919 + 0.853919i) q^{44} +(-2.86727 - 3.76281i) q^{45} +(-0.646078 - 0.173116i) q^{46} -3.80918 q^{47} +(2.35797 + 0.631815i) q^{48} +(-3.25462 + 5.63717i) q^{49} +(2.38101 + 0.655176i) q^{50} -2.23297i q^{51} +(5.77640 + 2.59266i) q^{52} +(-2.47293 + 2.47293i) q^{53} +(0.614963 + 2.29507i) q^{54} +(-1.42264 + 0.583682i) q^{55} +(-5.90499 + 3.40925i) q^{56} -5.15084i q^{57} +(2.35005 + 4.07041i) q^{58} +(-2.69310 + 10.0508i) q^{59} +(2.92199 + 2.25776i) q^{60} +(-3.09904 - 5.36770i) q^{61} +(-0.870630 - 3.24924i) q^{62} +(6.73428 + 3.88804i) q^{63} +2.72601 q^{64} +(5.51234 + 5.88338i) q^{65} +0.319406 q^{66} +(-10.6066 - 6.12371i) q^{67} +(-1.07921 - 4.02768i) q^{68} +(-0.636768 - 1.10291i) q^{69} +(-4.02624 + 0.516303i) q^{70} +(-1.73500 + 6.47512i) q^{71} +(1.96240 + 3.39898i) q^{72} -3.37642i q^{73} +(0.784986 - 0.453212i) q^{74} +(2.32356 + 4.08774i) q^{75} +(-2.48945 - 9.29074i) q^{76} +(1.78728 - 1.78728i) q^{77} +(-0.595435 - 1.56521i) q^{78} +3.12149i q^{79} +(5.35521 + 2.23932i) q^{80} +(0.911483 - 1.57873i) q^{81} +(0.264231 + 0.0708006i) q^{82} +2.13918 q^{83} +(-5.86286 - 1.57095i) q^{84} +(0.710723 - 5.26175i) q^{85} +(0.756694 - 0.756694i) q^{86} +(-2.31619 + 8.64414i) q^{87} +(1.23228 - 0.330188i) q^{88} +(3.26255 - 0.874198i) q^{89} +(0.297190 + 2.31755i) q^{90} +(-12.0902 - 5.42653i) q^{91} +(-1.68161 - 1.68161i) q^{92} +(3.20242 - 5.54675i) q^{93} +(1.62931 + 0.940681i) q^{94} +(1.63944 - 12.1374i) q^{95} +(-3.31972 - 3.31972i) q^{96} +(6.12606 - 3.53688i) q^{97} +(2.78421 - 1.60746i) q^{98} +(-1.02878 - 1.02878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	$ 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$	−0.427732	−	0.246951i	−0.302452	−	0.174621i	0.341092	−	0.940030i	$-0.389203\pi$
$2$	−0.427732	−	0.246951i	−0.302452	−	0.174621i	−0.643544	+	0.765409i	$0.722537\pi$
$3$	−0.243392	−	0.908353i	−0.140523	−	0.524438i	−0.999914	−	0.0131191i	$-0.995824\pi$
$3$	−0.243392	−	0.908353i	−0.140523	−	0.524438i	0.859391	−	0.511318i	$-0.170843\pi$
$4$	−0.878030	−	1.52079i	−0.439015	−	0.760397i
$5$	−0.284413	−	2.21791i	−0.127193	−	0.991878i
$5$	−0.284413	−	2.21791i	−0.127193	−	0.991878i
$6$	−0.120212	+	0.448637i	−0.0490763	+	0.183155i
$7$	1.83775	+	3.18307i	0.694603	+	1.20309i	0.970314	+	0.241847i	$0.0777532\pi$
$7$	1.83775	+	3.18307i	0.694603	+	1.20309i	−0.275712	+	0.961240i	$0.588914\pi$
$8$			1.85513i			0.655886i
$9$	1.83221	−	1.05783i	0.610737	−	0.352609i
$10$	−0.426062	+	1.01890i	−0.134733	+	0.322206i
$11$	−0.177987	−	0.664257i	−0.0536651	−	0.200281i	0.933888	−	0.357565i	$-0.116393\pi$
$11$	−0.177987	−	0.664257i	−0.0536651	−	0.200281i	−0.987553	+	0.157284i	$0.949726\pi$
$12$	−1.16771	+	1.16771i	−0.337089	+	0.337089i
$13$	−2.92331	+	2.11051i	−0.810781	+	0.585350i
$13$	−2.92331	+	2.11051i	−0.810781	+	0.585350i
$14$		−	1.81533i		−	0.485168i
$15$	−1.94542	+	0.798168i	−0.502305	+	0.206086i
$16$	−1.29794	+	2.24809i	−0.324484	+	0.562023i
$17$	2.29359	+	0.614565i	0.556277	+	0.149054i	0.525995	−	0.850487i	$-0.323693\pi$
$17$	2.29359	+	0.614565i	0.556277	+	0.149054i	0.0302815	+	0.999541i	$0.490360\pi$
$18$	−1.04493			−0.246291
$19$	5.29067	+	1.41763i	1.21376	+	0.325227i	0.808238	−	0.588857i	$-0.200422\pi$
$19$	5.29067	+	1.41763i	1.21376	+	0.325227i	0.405526	+	0.914084i	$0.367088\pi$
$20$	−3.12325	+	2.37992i	−0.698381	+	0.532167i
$21$	2.44406	−	2.44406i	0.533337	−	0.533337i
$22$	−0.0879082	+	0.328078i	−0.0187421	+	0.0699464i
$23$	1.30811	−	0.350507i	0.272760	−	0.0730858i	−0.119846	−	0.992792i	$-0.538240\pi$
$23$	1.30811	−	0.350507i	0.272760	−	0.0730858i	0.392606	+	0.919707i	$0.371574\pi$
$24$	1.68511	−	0.451523i	0.343971	−	0.0921668i
$25$	−4.83822	+	1.26160i	−0.967644	+	0.252320i
$26$	1.77158	−	0.180816i	0.347436	−	0.0354610i
$27$	−3.40171	−	3.40171i	−0.654659	−	0.654659i
$28$	3.22719	−	5.58966i	0.609882	−	1.05635i
$29$	−8.24134	−	4.75814i	−1.53038	−	0.883564i	−0.999344	−	0.0362142i	$-0.988470\pi$
$29$	−8.24134	−	4.75814i	−1.53038	−	0.883564i	−0.531034	−	0.847350i	$-0.678197\pi$
$30$	1.02922	+	0.139021i	0.187910	+	0.0253816i
$31$	4.81595	+	4.81595i	0.864970	+	0.864970i	0.991910	−	0.126940i	$-0.0405157\pi$
$31$	4.81595	+	4.81595i	0.864970	+	0.864970i	−0.126940	+	0.991910i	$0.540516\pi$
$32$	4.32351	−	2.49618i	0.764295	−	0.441266i
$33$	−0.560059	+	0.323350i	−0.0974937	+	0.0562880i
$34$	−0.829273	−	0.829273i	−0.142219	−	0.142219i
$35$	6.53707	−	4.98125i	1.10497	−	0.841986i
$36$	−3.21748	−	1.85761i	−0.536246	−	0.309602i
$37$	−0.917615	+	1.58936i	−0.150855	+	0.261289i	−0.931542	−	0.363634i	$-0.881536\pi$
$37$	−0.917615	+	1.58936i	−0.150855	+	0.261289i	0.780687	+	0.624922i	$0.214869\pi$
$38$	−1.91290	−	1.91290i	−0.310314	−	0.310314i
$39$	2.62860	+	2.14172i	0.420912	+	0.342949i
$40$	4.11449	−	0.527621i	0.650559	−	0.0834242i
$41$	−0.534988	+	0.143350i	−0.0835510	+	0.0223874i	−0.300352	−	0.953828i	$-0.597104\pi$
$41$	−0.534988	+	0.143350i	−0.0835510	+	0.0223874i	0.216801	+	0.976216i	$0.430438\pi$
$42$	−1.64896	+	0.441838i	−0.254440	+	0.0681771i
$43$	−0.560778	+	2.09285i	−0.0855178	+	0.319157i	−0.995412	−	0.0956841i	$-0.969496\pi$
$43$	−0.560778	+	2.09285i	−0.0855178	+	0.319157i	0.909894	+	0.414841i	$0.136163\pi$
$44$	−0.853919	+	0.853919i	−0.128733	+	0.128733i
$45$	−2.86727	−	3.76281i	−0.427427	−	0.560927i
$46$	−0.646078	−	0.173116i	−0.0952590	−	0.0255246i
$47$	−3.80918			−0.555626			−0.277813	−	0.960635i	$-0.589610\pi$
$47$	−3.80918			−0.555626			−0.277813	+	0.960635i	$0.589610\pi$
$48$	2.35797	+	0.631815i	0.340343	+	0.0911947i
$49$	−3.25462	+	5.63717i	−0.464946	+	0.805310i
$50$	2.38101	+	0.655176i	0.336726	+	0.0926559i
$51$		−	2.23297i		−	0.312678i
$52$	5.77640	+	2.59266i	0.801043	+	0.359538i
$53$	−2.47293	+	2.47293i	−0.339683	+	0.339683i	−0.856248	−	0.516565i	$-0.827211\pi$
$53$	−2.47293	+	2.47293i	−0.339683	+	0.339683i	0.516565	+	0.856248i	$0.327211\pi$
$54$	0.614963	+	2.29507i	0.0836858	+	0.312320i
$55$	−1.42264	+	0.583682i	−0.191828	+	0.0787036i
$56$	−5.90499	+	3.40925i	−0.789088	+	0.455580i
$57$		−	5.15084i		−	0.682245i
$58$	2.35005	+	4.07041i	0.308577	+	0.534471i
$59$	−2.69310	+	10.0508i	−0.350612	+	1.30850i	0.535305	+	0.844659i	$0.320197\pi$
$59$	−2.69310	+	10.0508i	−0.350612	+	1.30850i	−0.885917	+	0.463844i	$0.846470\pi$
$60$	2.92199	+	2.25776i	0.377227	+	0.291476i
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	0.596536	−	0.802586i	$-0.296543\pi$
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	−0.993328	+	0.115323i	$0.963210\pi$
$62$	−0.870630	−	3.24924i	−0.110570	−	0.412653i
$63$	6.73428	+	3.88804i	0.848439	+	0.489847i
$64$	2.72601			0.340751
$65$	5.51234	+	5.88338i	0.683721	+	0.729743i
$66$	0.319406			0.0393162
$67$	−10.6066	−	6.12371i	−1.29580	−	0.748130i	−0.316124	−	0.948718i	$-0.602381\pi$
$67$	−10.6066	−	6.12371i	−1.29580	−	0.748130i	−0.979676	+	0.200588i	$0.935715\pi$
$68$	−1.07921	−	4.02768i	−0.130874	−	0.488428i
$69$	−0.636768	−	1.10291i	−0.0766579	−	0.132775i
$70$	−4.02624	+	0.516303i	−0.481227	+	0.0617101i
$71$	−1.73500	+	6.47512i	−0.205907	+	0.768456i	0.783264	+	0.621689i	$0.213553\pi$
$71$	−1.73500	+	6.47512i	−0.205907	+	0.768456i	−0.989171	+	0.146767i	$0.953113\pi$
$72$	1.96240	+	3.39898i	0.231271	+	0.400574i
$73$		−	3.37642i		−	0.395180i	−0.980285	−	0.197590i	$-0.936688\pi$
$73$		−	3.37642i		−	0.395180i	0.980285	−	0.197590i	$-0.0633115\pi$
$74$	0.784986	−	0.453212i	0.0912528	−	0.0526848i
$75$	2.32356	+	4.08774i	0.268302	+	0.472012i
$76$	−2.48945	−	9.29074i	−0.285559	−	1.06572i
$77$	1.78728	−	1.78728i	0.203680	−	0.203680i
$78$	−0.595435	−	1.56521i	−0.0674198	−	0.177226i
$79$			3.12149i			0.351195i	0.984462	+	0.175598i	$0.0561857\pi$
$79$			3.12149i			0.351195i	−0.984462	+	0.175598i	$0.943814\pi$
$80$	5.35521	+	2.23932i	0.598730	+	0.250363i
$81$	0.911483	−	1.57873i	0.101276	−	0.175415i
$82$	0.264231	+	0.0708006i	0.0291795	+	0.00781862i
$83$	2.13918			0.234805			0.117403	−	0.993084i	$-0.462543\pi$
$83$	2.13918			0.234805			0.117403	+	0.993084i	$0.462543\pi$
$84$	−5.86286	−	1.57095i	−0.639691	−	0.171405i
$85$	0.710723	−	5.26175i	0.0770887	−	0.570717i
$86$	0.756694	−	0.756694i	0.0815964	−	0.0815964i
$87$	−2.31619	+	8.64414i	−0.248322	+	0.926749i
$88$	1.23228	−	0.330188i	0.131361	−	0.0351982i
$89$	3.26255	−	0.874198i	0.345830	−	0.0926648i	−0.0817233	−	0.996655i	$-0.526042\pi$
$89$	3.26255	−	0.874198i	0.345830	−	0.0926648i	0.427553	+	0.903990i	$0.359376\pi$
$90$	0.297190	+	2.31755i	0.0313266	+	0.244291i
$91$	−12.0902	−	5.42653i	−1.26740	−	0.568855i
$92$	−1.68161	−	1.68161i	−0.175320	−	0.175320i
$93$	3.20242	−	5.54675i	0.332075	−	0.575171i
$94$	1.62931	+	0.940681i	0.168050	+	0.0970238i
$95$	1.63944	−	12.1374i	0.168203	−	1.24527i
$96$	−3.31972	−	3.31972i	−0.338817	−	0.338817i
$97$	6.12606	−	3.53688i	0.622007	−	0.359116i	−0.155643	−	0.987813i	$-0.549745\pi$
$97$	6.12606	−	3.53688i	0.622007	−	0.359116i	0.777650	+	0.628697i	$0.216412\pi$
$98$	2.78421	−	1.60746i	0.281248	−	0.162378i
$99$	−1.02878	−	1.02878i	−0.103396	−	0.103396i
$100$	6.16674	+	6.25021i	0.616674	+	0.625021i
$101$	12.9641	+	7.48483i	1.28998	+	0.744769i	0.978650	−	0.205534i	$-0.0658932\pi$
$101$	12.9641	+	7.48483i	1.28998	+	0.744769i	0.311327	+	0.950303i	$0.399226\pi$
$102$	−0.551433	+	0.955111i	−0.0546000	+	0.0945700i
$103$	−3.17851	−	3.17851i	−0.313188	−	0.313188i	0.532956	−	0.846143i	$-0.321081\pi$
$103$	−3.17851	−	3.17851i	−0.313188	−	0.313188i	−0.846143	+	0.532956i	$0.821081\pi$
$104$	−3.91526	−	5.42311i	−0.383923	−	0.531780i
$105$	−6.11581	−	4.72557i	−0.596842	−	0.461168i
$106$	1.66844	−	0.447058i	0.162054	−	0.0434221i
$107$	14.7329	−	3.94767i	1.42428	−	0.381635i	0.537282	−	0.843403i	$-0.319451\pi$
$107$	14.7329	−	3.94767i	1.42428	−	0.381635i	0.887001	+	0.461767i	$0.152784\pi$
$108$	−2.18649	+	8.16010i	−0.210395	+	0.785206i
$109$	2.25902	−	2.25902i	0.216375	−	0.216375i	−0.590594	−	0.806969i	$-0.701107\pi$
$109$	2.25902	−	2.25902i	0.216375	−	0.216375i	0.806969	+	0.590594i	$0.201107\pi$
$110$	0.752648	+	0.101663i	0.0717622	+	0.00969315i
$111$	1.66704	+	0.446681i	0.158228	+	0.0423971i
$112$	−9.54111			−0.901550
$113$	−16.0061	−	4.28882i	−1.50573	−	0.403458i	−0.590713	−	0.806881i	$-0.701154\pi$
$113$	−16.0061	−	4.28882i	−1.50573	−	0.403458i	−0.915014	+	0.403423i	$0.867820\pi$
$114$	−1.27200	+	2.20318i	−0.119134	+	0.206346i
$115$	−1.14944	−	2.80158i	−0.107185	−	0.261248i
$116$			16.7112i			1.55159i
$117$	−3.12357	+	6.95926i	−0.288774	+	0.643384i
$118$	3.63398	−	3.63398i	0.334535	−	0.334535i
$119$	2.25883	+	8.43007i	0.207067	+	0.772783i
$120$	−1.48070	−	3.60899i	−0.135169	−	0.329455i
$121$	9.11672	−	5.26354i	0.828793	−	0.478504i
$122$			3.06124i			0.277152i
$123$	0.260424	+	0.451067i	0.0234816	+	0.0406714i
$124$	3.09551	−	11.5526i	0.277985	−	1.03746i
$125$	4.17416	+	10.3719i	0.373349	+	0.927691i
$126$	−1.92031	−	3.32607i	−0.171075	−	0.296310i
$127$	−2.14812	−	8.01688i	−0.190614	−	0.711383i	−0.993359	−	0.115059i	$-0.963294\pi$
$127$	−2.14812	−	8.01688i	−0.190614	−	0.711383i	0.802744	−	0.596324i	$-0.203372\pi$
$128$	−9.81302	−	5.66555i	−0.867356	−	0.500768i
$129$	2.03754			0.179395
$130$	−0.904895	−	3.87778i	−0.0793645	−	0.340104i
$131$	1.37409			0.120054			0.0600272	−	0.998197i	$-0.480881\pi$
$131$	1.37409			0.120054			0.0600272	+	0.998197i	$0.480881\pi$
$132$	0.983497	+	0.567822i	0.0856025	+	0.0494226i
$133$	5.21049	+	19.4458i	0.451807	+	1.68617i
$134$	3.02451	+	5.23861i	0.261278	+	0.452547i
$135$	−6.57718	+	8.51216i	−0.566074	+	0.732610i
$136$	−1.14010	+	4.25489i	−0.0977624	+	0.364854i
$137$	−6.16380	−	10.6760i	−0.526609	−	0.912114i	−0.999519	−	0.0310029i	$-0.990130\pi$
$137$	−6.16380	−	10.6760i	−0.526609	−	0.912114i	0.472910	−	0.881111i	$-0.343203\pi$
$138$			0.629002i			0.0535442i
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	−0.246107	−	0.969243i	$-0.579151\pi$
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	0.716336	+	0.697756i	$0.245818\pi$
$140$	−13.3152	−	5.56784i	−1.12534	−	0.470569i
$141$	0.927126	+	3.46008i	0.0780781	+	0.291391i
$142$	2.34115	−	2.34115i	0.196465	−	0.196465i
$143$	1.92223	+	1.56619i	0.160745	+	0.130971i
$144$			5.49197i			0.457664i
$145$	−8.20917	+	19.6318i	−0.681734	+	1.63033i
$146$	−0.833811	+	1.44420i	−0.0690067	+	0.119523i
$147$	5.91269	+	1.58430i	0.487670	+	0.130671i
$148$	3.22278			0.264911
$149$	−16.2300	−	4.34882i	−1.32961	−	0.356269i	−0.477043	−	0.878880i	$-0.658291\pi$
$149$	−16.2300	−	4.34882i	−1.32961	−	0.356269i	−0.852571	+	0.522611i	$0.824958\pi$
$150$	0.0156106	−	2.32226i	0.00127460	−	0.189612i
$151$	−3.31542	+	3.31542i	−0.269805	+	0.269805i	−0.829022	−	0.559217i	$-0.811102\pi$
$151$	−3.31542	+	3.31542i	−0.269805	+	0.269805i	0.559217	+	0.829022i	$0.311102\pi$
$152$	−2.62988	+	9.81486i	−0.213312	+	0.796090i
$153$	4.85244	−	1.30021i	0.392297	−	0.105116i
$154$	−1.20585	+	0.323106i	−0.0971699	+	0.0260366i
$155$	9.31161	−	12.0510i	0.747926	−	0.967963i
$156$	0.949120	−	5.87805i	0.0759904	−	0.470620i
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	0.981242	−	0.192779i	$-0.0617501\pi$
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	−0.192779	+	0.981242i	$0.561750\pi$
$158$	0.770855	−	1.33516i	0.0613259	−	0.106220i
$159$	2.84819	+	1.64440i	0.225876	+	0.130410i
$160$	−6.76595	−	8.87919i	−0.534895	−	0.701962i
$161$	3.51966	+	3.51966i	0.277388	+	0.277388i
$162$	−0.779740	+	0.450183i	−0.0612622	+	0.0353697i
$163$	−0.114289	+	0.0659848i	−0.00895180	+	0.00516833i	−0.504469	−	0.863430i	$-0.668312\pi$
$163$	−0.114289	+	0.0659848i	−0.00895180	+	0.00516833i	0.495517	+	0.868598i	$0.334978\pi$
$164$	0.687741	+	0.687741i	0.0537035	+	0.0537035i
$165$	0.876448	+	1.15019i	0.0682314	+	0.0895424i
$166$	−0.914995	−	0.528272i	−0.0710174	−	0.0410019i
$167$	−10.8184	+	18.7380i	−0.837152	+	1.44999i	0.0551149	+	0.998480i	$0.482447\pi$
$167$	−10.8184	+	18.7380i	−0.837152	+	1.44999i	−0.892267	+	0.451509i	$0.850886\pi$
$168$	4.53403	+	4.53403i	0.349808	+	0.349808i
$169$	4.09151	−	12.3393i	0.314731	−	0.949181i
$170$	−1.60339	+	2.07510i	−0.122975	+	0.159153i
$171$	11.1932	−	2.99922i	0.855969	−	0.229356i
$172$	3.67518	−	0.984760i	0.280230	−	0.0750873i
$173$	−2.00162	+	7.47013i	−0.152180	+	0.567943i	0.847150	+	0.531353i	$0.178316\pi$
$173$	−2.00162	+	7.47013i	−0.152180	+	0.567943i	−0.999330	+	0.0365902i	$0.988350\pi$
$174$	3.12539	−	3.12539i	0.236935	−	0.236935i
$175$	−12.9072	−	13.0819i	−0.975691	−	0.988898i
$176$	1.72433	+	0.462032i	0.129976	+	0.0348270i
$177$	9.78515			0.735497
$178$	−1.61138	−	0.431768i	−0.120778	−	0.0323624i
$179$	8.17681	−	14.1627i	0.611164	−	1.05857i	−0.379881	−	0.925035i	$-0.624035\pi$
$179$	8.17681	−	14.1627i	0.611164	−	1.05857i	0.991045	−	0.133531i	$-0.0426317\pi$
$180$	−3.20492	+	7.66439i	−0.238880	+	0.571270i
$181$		−	18.0387i		−	1.34081i	−0.741997	−	0.670403i	$-0.766121\pi$
$181$		−	18.0387i		−	1.34081i	0.741997	−	0.670403i	$-0.233879\pi$
$182$	3.83127	+	5.30678i	0.283993	+	0.393365i
$183$	−4.12148	+	4.12148i	−0.304668	+	0.304668i
$184$	0.650235	+	2.42671i	0.0479359	+	0.178899i
$185$	3.78603	+	1.58315i	0.278354	+	0.116396i
$186$	−2.73955	+	1.58168i	−0.200873	+	0.115974i
$187$		−	1.63292i		−	0.119411i
$188$	3.34458	+	5.79298i	0.243928	+	0.422496i
$189$	4.57640	−	17.0793i	0.332884	−	1.24234i
$190$	−3.69858	+	4.78669i	−0.268324	+	0.347263i
$191$	−2.59552	−	4.49557i	−0.187805	−	0.325288i	0.756713	−	0.653747i	$-0.226804\pi$
$191$	−2.59552	−	4.49557i	−0.187805	−	0.325288i	−0.944518	+	0.328459i	$0.893471\pi$
$192$	−0.663490	−	2.47618i	−0.0478833	−	0.178703i
$193$	−8.74813	−	5.05073i	−0.629704	−	0.363560i	0.150934	−	0.988544i	$-0.451772\pi$
$193$	−8.74813	−	5.05073i	−0.629704	−	0.363560i	−0.780637	+	0.624984i	$0.785105\pi$
$194$	−3.49375			−0.250836
$195$	4.00252	−	6.43912i	0.286627	−	0.461115i
$196$	11.4306			0.816473
$197$	−11.3137	−	6.53197i	−0.806068	−	0.465384i	0.0395205	−	0.999219i	$-0.487417\pi$
$197$	−11.3137	−	6.53197i	−0.806068	−	0.465384i	−0.845589	+	0.533835i	$0.820750\pi$
$198$	0.185983	+	0.694099i	0.0132173	+	0.0493275i
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	0.692707	−	0.721219i	$-0.256418\pi$
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	−0.970947	+	0.239293i	$0.923084\pi$
$200$	−2.34043	−	8.97550i	−0.165493	−	0.634664i
$201$	−2.98093	+	11.1250i	−0.210258	+	0.784695i
$202$	−3.69677	−	6.40300i	−0.260104	−	0.450513i
$203$		−	34.9770i		−	2.45491i
$204$	−3.39588	+	1.96061i	−0.237759	+	0.137270i
$205$	0.470093	+	1.14578i	0.0328327	+	0.0800249i
$206$	0.574613	+	2.14448i	0.0400352	+	0.149413i
$207$	2.02596	−	2.02596i	0.140814	−	0.140814i
$208$	−0.950343	−	9.31118i	−0.0658944	−	0.645614i
$209$		−	3.76669i		−	0.260547i
$210$	1.44894	+	3.53158i	0.0999864	+	0.243702i
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	−0.996664	−	0.0816108i	$-0.973994\pi$
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	0.569009	+	0.822331i	$0.307327\pi$
$212$	5.93213	+	1.58951i	0.407420	+	0.109168i
$213$	6.30398			0.431942
$214$	−7.27661	−	1.94976i	−0.497419	−	0.133283i
$215$	4.80124	+	0.648520i	0.327442	+	0.0442287i
$216$	6.31059	−	6.31059i	0.429382	−	0.429382i
$217$	−6.47901	+	24.1800i	−0.439824	+	1.64145i
$218$	−1.52412	+	0.408387i	−0.103226	+	0.0276594i
$219$	−3.06698	+	0.821796i	−0.207248	+	0.0555318i
$220$	2.13678	+	1.65105i	0.144062	+	0.111314i
$221$	−8.00192	+	3.04407i	−0.538267	+	0.204766i
$222$	−0.602736	−	0.602736i	−0.0404530	−	0.0404530i
$223$	−4.97247	+	8.61258i	−0.332981	+	0.576741i	−0.983095	−	0.183096i	$-0.941388\pi$
$223$	−4.97247	+	8.61258i	−0.332981	+	0.576741i	0.650114	+	0.759837i	$0.274721\pi$
$224$	15.8910	+	9.17468i	1.06176	+	0.613009i
$225$	−7.53008	+	7.42952i	−0.502006	+	0.495302i
$226$	5.78718	+	5.78718i	0.384958	+	0.384958i
$227$	12.6490	−	7.30290i	0.839543	−	0.484710i	−0.0175659	−	0.999846i	$-0.505592\pi$
$227$	12.6490	−	7.30290i	0.839543	−	0.484710i	0.857109	+	0.515135i	$0.172258\pi$
$228$	−7.83336	+	4.52259i	−0.518777	+	0.299516i
$229$	15.6183	+	15.6183i	1.03209	+	1.03209i	0.999468	+	0.0326207i	$0.0103853\pi$
$229$	15.6183	+	15.6183i	1.03209	+	1.03209i	0.0326207	+	0.999468i	$0.489615\pi$
$230$	−0.200203	+	1.48218i	−0.0132010	+	0.0977319i
$231$	−2.05849	−	1.18847i	−0.135439	−	0.0781956i
$232$	8.82695	−	15.2887i	0.579517	−	1.00375i
$233$	16.5625	+	16.5625i	1.08505	+	1.08505i	0.996030	+	0.0890148i	$0.0283719\pi$
$233$	16.5625	+	16.5625i	1.08505	+	1.08505i	0.0890148	+	0.996030i	$0.471628\pi$
$234$	3.05465	−	2.20533i	0.199688	−	0.144167i
$235$	1.08338	+	8.44841i	0.0706719	+	0.551113i
$236$	17.6498	−	4.72926i	1.14891	−	0.307848i
$237$	2.83541	−	0.759747i	0.184180	−	0.0493509i
$238$	1.11564	−	4.16362i	0.0723162	−	0.269888i
$239$	−14.6022	+	14.6022i	−0.944535	+	0.944535i	−0.998541	−	0.0540053i	$-0.982801\pi$
$239$	−14.6022	+	14.6022i	−0.944535	+	0.944535i	0.0540053	+	0.998541i	$0.482801\pi$
$240$	0.730672	−	5.40945i	0.0471647	−	0.349178i
$241$	2.99335	+	0.802065i	0.192818	+	0.0516656i	0.353936	−	0.935270i	$-0.384843\pi$
$241$	2.99335	+	0.802065i	0.192818	+	0.0516656i	−0.161117	+	0.986935i	$0.551510\pi$
$242$	−5.19935			−0.334227
$243$	−15.5964	−	4.17903i	−1.00051	−	0.268085i
$244$	−5.44211	+	9.42600i	−0.348395	+	0.603438i
$245$	13.4284	+	5.61516i	0.857907	+	0.358740i
$246$		−	0.257248i		−	0.0164015i
$247$	−18.4582	+	7.02183i	−1.17447	+	0.446788i
$248$	−8.93419	+	8.93419i	−0.567322	+	0.567322i
$249$	−0.520660	−	1.94313i	−0.0329955	−	0.123141i
$250$	0.775929	−	5.46720i	0.0490741	−	0.345776i
$251$	−25.5728	+	14.7645i	−1.61414	+	0.931925i	−0.625745	+	0.780028i	$0.715205\pi$
$251$	−25.5728	+	14.7645i	−1.61414	+	0.931925i	−0.988396	+	0.151897i	$0.951462\pi$
$252$		−	13.6553i		−	0.860201i
$253$	−0.465654	−	0.806536i	−0.0292754	−	0.0507065i
$254$	−1.06096	+	3.95955i	−0.0665704	+	0.248444i
$255$	−4.95251	+	0.635084i	−0.310138	+	0.0397705i
$256$	0.0722145	+	0.125079i	0.00451341	+	0.00781745i
$257$	−1.85447	−	6.92097i	−0.115679	−	0.431718i	0.883658	−	0.468133i	$-0.155073\pi$
$257$	−1.85447	−	6.92097i	−0.115679	−	0.431718i	−0.999337	+	0.0364143i	$0.988406\pi$
$258$	−0.871519	−	0.503172i	−0.0542584	−	0.0313261i
$259$	−6.74538			−0.419137
$260$	4.10740	−	13.5489i	0.254730	−	0.840268i
$261$	−20.1332			−1.24621
$262$	−0.587740	−	0.339332i	−0.0363107	−	0.0209640i
$263$	−3.48511	−	13.0066i	−0.214901	−	0.802023i	−0.986201	−	0.165551i	$-0.947060\pi$
$263$	−3.48511	−	13.0066i	−0.214901	−	0.802023i	0.771300	−	0.636472i	$-0.219607\pi$
$264$	−0.599855	−	1.03898i	−0.0369185	−	0.0639448i
$265$	6.18807	+	4.78140i	0.380130	+	0.293719i
$266$	2.57347	−	9.60433i	0.157790	−	0.588879i
$267$	−1.58816	−	2.75077i	−0.0971938	−	0.168345i
$268$			21.5072i			1.31376i
$269$	−7.01806	+	4.05188i	−0.427899	+	0.247047i	−0.698451	−	0.715658i	$-0.746127\pi$
$269$	−7.01806	+	4.05188i	−0.427899	+	0.247047i	0.270552	+	0.962705i	$0.412794\pi$
$270$	4.91535	−	2.01668i	0.299139	−	0.122731i
$271$	−2.38026	−	8.88325i	−0.144590	−	0.539619i	−0.999773	−	0.0212923i	$-0.993222\pi$
$271$	−2.38026	−	8.88325i	−0.144590	−	0.539619i	0.855183	−	0.518326i	$-0.173445\pi$
$272$	−4.35853	+	4.35853i	−0.264275	+	0.264275i
$273$	−1.98654	+	12.3029i	−0.120231	+	0.744608i
$274$			6.08862i			0.367827i
$275$	1.69917	+	2.98927i	0.102464	+	0.180260i
$276$	−1.11820	+	1.93679i	−0.0673080	+	0.116581i
$277$	24.9641	+	6.68911i	1.49995	+	0.401910i	0.913082	−	0.407775i	$-0.133695\pi$
$277$	24.9641	+	6.68911i	1.49995	+	0.401910i	0.586865	+	0.809685i	$0.300362\pi$
$278$	−3.16174			−0.189629
$279$	13.9183	+	3.72939i	0.833266	+	0.223273i
$280$	9.24085	+	12.1271i	0.552246	+	0.724732i
$281$	5.41928	−	5.41928i	0.323287	−	0.323287i	−0.526740	−	0.850027i	$-0.676586\pi$
$281$	5.41928	−	5.41928i	0.323287	−	0.323287i	0.850027	+	0.526740i	$0.176586\pi$
$282$	0.457909	−	1.70894i	0.0272681	−	0.101766i
$283$	8.48623	−	2.27388i	0.504454	−	0.135168i	0.00238762	−	0.999997i	$-0.499240\pi$
$283$	8.48623	−	2.27388i	0.504454	−	0.135168i	0.502066	+	0.864829i	$0.332573\pi$
$284$	11.3707	−	3.04677i	0.674728	−	0.180793i
$285$	−11.4241	+	1.46496i	−0.676704	+	0.0867769i
$286$	−0.435428	−	1.14460i	−0.0257474	−	0.0676819i
$287$	−1.43946	−	1.43946i	−0.0849688	−	0.0849688i
$288$	5.28105	−	9.14705i	0.311189	−	0.538995i
$289$	−9.83958	−	5.68088i	−0.578799	−	0.334170i
$290$	8.35941	−	6.36988i	0.490882	−	0.374052i
$291$	−4.70377	−	4.70377i	−0.275740	−	0.275740i
$292$	−5.13484	+	2.96460i	−0.300494	+	0.173490i
$293$	11.4627	−	6.61798i	0.669657	−	0.386626i	−0.126290	−	0.991993i	$-0.540307\pi$
$293$	11.4627	−	6.61798i	0.669657	−	0.386626i	0.795947	+	0.605367i	$0.206974\pi$
$294$	−2.13780	−	2.13780i	−0.124679	−	0.124679i
$295$	23.0577	+	3.11448i	1.34247	+	0.181332i
$296$	−2.94846	−	1.70229i	−0.171375	−	0.0989437i
$297$	−1.65415	+	2.86507i	−0.0959834	+	0.166248i
$298$	5.86814	+	5.86814i	0.339932	+	0.339932i
$299$	−3.08427	+	3.78542i	−0.178368	+	0.218916i
$300$	4.17646	−	7.12283i	0.241128	−	0.411237i
$301$	−7.69226	+	2.06114i	−0.443375	+	0.118802i
$302$	2.23685	−	0.599363i	0.128716	−	0.0344895i
$303$	3.64350	−	13.5977i	0.209314	−	0.781169i
$304$	−10.0539	+	10.0539i	−0.576632	+	0.576632i
$305$	−11.0236	+	8.40003i	−0.631212	+	0.480984i
$306$	−2.39663	−	0.642175i	−0.137006	−	0.0367107i
$307$	−15.4782			−0.883389			−0.441695	−	0.897165i	$-0.645623\pi$
$307$	−15.4782			−0.883389			−0.441695	+	0.897165i	$0.645623\pi$
$308$	−4.28737	−	1.14880i	−0.244296	−	0.0654588i
$309$	−2.11358	+	3.66083i	−0.120237	+	0.208257i
$310$	−6.95889	+	2.85510i	−0.395238	+	0.162159i
$311$		−	5.34922i		−	0.303326i	−0.988432	−	0.151663i	$-0.951537\pi$
$311$		−	5.34922i		−	0.303326i	0.988432	−	0.151663i	$-0.0484629\pi$
$312$	−3.97315	+	4.87638i	−0.224936	+	0.276071i
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.531967	−	0.846765i	$-0.321453\pi$
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.846765	−	0.531967i	$-0.178547\pi$
$314$	−1.78601	−	6.66547i	−0.100790	−	0.376154i
$315$	6.70799	−	16.0418i	0.377952	−	0.903854i
$316$	4.74714	−	2.74076i	0.267048	−	0.154180i
$317$		−	18.9851i		−	1.06631i	−0.846017	−	0.533156i	$-0.821006\pi$
$317$		−	18.9851i		−	1.06631i	0.846017	−	0.533156i	$-0.178994\pi$
$318$	−0.812173	−	1.40673i	−0.0455444	−	0.0788852i
$319$	−1.69378	+	6.32125i	−0.0948332	+	0.353922i
$320$	−0.775312	−	6.04604i	−0.0433412	−	0.337984i
$321$	−7.17175	−	12.4218i	−0.400288	−	0.693319i
$322$	−0.636287	−	2.37466i	−0.0354589	−	0.132334i
$323$	11.2634	+	6.50293i	0.626712	+	0.361832i
$324$	−3.20124			−0.177847
$325$	11.4810	−	13.8992i	0.636852	−	0.770986i
$326$	0.0651800			0.00360999
$327$	−2.60181	−	1.50216i	−0.143881	−	0.0830695i
$328$	−0.265931	−	0.992469i	−0.0146836	−	0.0548000i
$329$	−7.00031	−	12.1249i	−0.385940	−	0.668467i
$330$	−0.0908432	−	0.708414i	−0.00500075	−	0.0389969i
$331$	−1.81607	+	6.77766i	−0.0998202	+	0.372534i	−0.997706	−	0.0676941i	$-0.978436\pi$
$331$	−1.81607	+	6.77766i	−0.0998202	+	0.372534i	0.897886	+	0.440228i	$0.145102\pi$
$332$	−1.87826	−	3.25325i	−0.103083	−	0.178545i
$333$			3.88272i			0.212772i
$334$	9.25473	−	5.34322i	0.506396	−	0.292368i
$335$	−10.5652	+	25.2661i	−0.577237	+	1.38043i
$336$	2.32223	+	8.66669i	0.126688	+	0.472807i
$337$	−1.10195	+	1.10195i	−0.0600271	+	0.0600271i	−0.736483	−	0.676456i	$-0.763515\pi$
$337$	−1.10195	+	1.10195i	−0.0600271	+	0.0600271i	0.676456	+	0.736483i	$0.263515\pi$
$338$	−4.79728	+	4.26753i	−0.260938	+	0.232123i
$339$			15.5830i			0.846355i
$340$	−8.62608	+	3.53912i	−0.467815	+	0.191936i
$341$	2.34185	−	4.05620i	0.126818	−	0.219656i
$342$	−5.52836	−	1.48132i	−0.298940	−	0.0801006i
$343$	1.80378			0.0973947
$344$	−3.88250	−	1.04031i	−0.209331	−	0.0560899i
$345$	−2.26506	+	1.72598i	−0.121947	+	0.0929234i
$346$	2.70091	−	2.70091i	0.145202	−	0.145202i
$347$	6.68561	−	24.9510i	0.358902	−	1.33944i	−0.516600	−	0.856227i	$-0.672803\pi$
$347$	6.68561	−	24.9510i	0.358902	−	1.33944i	0.875502	−	0.483214i	$-0.160531\pi$
$348$	15.1796	−	4.06737i	0.813714	−	0.218034i
$349$	−9.07958	+	2.43287i	−0.486019	+	0.130228i	−0.493504	−	0.869744i	$-0.664284\pi$
$349$	−9.07958	+	2.43287i	−0.486019	+	0.130228i	0.00748510	+	0.999972i	$0.497617\pi$
$350$	2.29023	+	8.78298i	0.122418	+	0.469470i
$351$	17.1236	+	2.76492i	0.913989	+	0.147581i
$352$	−2.42763	−	2.42763i	−0.129393	−	0.129393i
$353$	1.63274	−	2.82798i	0.0869017	−	0.150518i	−0.819298	−	0.573368i	$-0.805637\pi$
$353$	1.63274	−	2.82798i	0.0869017	−	0.150518i	0.906200	+	0.422849i	$0.138970\pi$
$354$	−4.18542	−	2.41645i	−0.222452	−	0.128433i
$355$	14.8547	+	2.00647i	0.788404	+	0.106492i
$356$	−4.19410	−	4.19410i	−0.222287	−	0.222287i
$357$	7.10769	−	4.10363i	0.376179	−	0.217187i
$358$	−6.99496	+	4.03854i	−0.369695	+	0.213444i
$359$	3.12090	+	3.12090i	0.164715	+	0.164715i	0.784652	−	0.619937i	$-0.212842\pi$
$359$	3.12090	+	3.12090i	0.164715	+	0.164715i	−0.619937	+	0.784652i	$0.712842\pi$
$360$	6.98049	−	5.31914i	0.367904	−	0.280343i
$361$	9.52706	+	5.50045i	0.501424	+	0.289497i
$362$	−4.45468	+	7.71573i	−0.234133	+	0.405530i
$363$	−7.00009	−	7.00009i	−0.367410	−	0.367410i
$364$	2.36294	+	23.1514i	0.123852	+	1.21346i
$365$	−7.48859	+	0.960297i	−0.391971	+	0.0502643i
$366$	2.78069	−	0.745084i	0.145349	−	0.0389461i
$367$	−24.2349	+	6.49371i	−1.26505	+	0.338969i	−0.828132	−	0.560533i	$-0.810596\pi$
$367$	−24.2349	+	6.49371i	−1.26505	+	0.338969i	−0.436917	+	0.899502i	$0.643930\pi$
$368$	−0.909872	+	3.39569i	−0.0474303	+	0.177012i
$369$	−0.828572	+	0.828572i	−0.0431337	+	0.0431337i
$370$	−1.22844	−	1.61213i	−0.0638636	−	0.0838105i
$371$	−12.4161	−	3.32690i	−0.644614	−	0.172724i
$372$	−11.2473			−0.583144
$373$	11.0372	+	2.95740i	0.571483	+	0.153128i	0.532976	−	0.846130i	$-0.321073\pi$
$373$	11.0372	+	2.95740i	0.571483	+	0.153128i	0.0385061	+	0.999258i	$0.487740\pi$
$374$	−0.403250	+	0.698450i	−0.0208516	+	0.0361160i
$375$	8.40538	−	6.31605i	0.434052	−	0.326160i
$376$		−	7.06651i		−	0.364427i
$377$	34.1341	−	3.48389i	1.75800	−	0.179429i
$378$	−6.17523	+	6.17523i	−0.317620	+	0.317620i
$379$	0.520109	+	1.94107i	0.0267162	+	0.0997062i	0.977997	−	0.208621i	$-0.0668975\pi$
$379$	0.520109	+	1.94107i	0.0267162	+	0.0997062i	−0.951280	+	0.308327i	$0.900231\pi$
$380$	−19.8980	+	8.16377i	−1.02074	+	0.418792i
$381$	−6.75932	+	3.90249i	−0.346290	+	0.199931i
$382$			2.56386i			0.131179i
$383$	13.2258	+	22.9077i	0.675806	+	1.17053i	0.976233	+	0.216725i	$0.0695376\pi$
$383$	13.2258	+	22.9077i	0.675806	+	1.17053i	−0.300427	+	0.953805i	$0.597129\pi$
$384$	−2.75790	+	10.2926i	−0.140739	+	0.525244i
$385$	−4.47235	−	3.45570i	−0.227932	−	0.176119i
$386$	2.49457	+	4.32072i	0.126970	+	0.219919i
$387$	1.18641	+	4.42775i	0.0603088	+	0.225075i
$388$	−10.7577	−	6.21098i	−0.546141	−	0.315315i
$389$	−0.650094			−0.0329611			−0.0164805	−	0.999864i	$-0.505246\pi$
$389$	−0.650094			−0.0329611			−0.0164805	+	0.999864i	$0.505246\pi$
$390$	−3.30215	+	1.76579i	−0.167211	+	0.0894141i
$391$	3.21568			0.162624
$392$	−10.4577	−	6.03773i	−0.528191	−	0.304951i
$393$	−0.334442	−	1.24815i	−0.0168704	−	0.0629610i
$394$	3.22615	+	5.58786i	0.162531	+	0.281512i
$395$	6.92317	−	0.887791i	0.348343	−	0.0446696i
$396$	−0.661261	+	2.46786i	−0.0332296	+	0.124015i
$397$	13.5041	+	23.3897i	0.677750	+	1.17390i	0.975657	+	0.219303i	$0.0703782\pi$
$397$	13.5041	+	23.3897i	0.677750	+	1.17390i	−0.297907	+	0.954595i	$0.596288\pi$
$398$			3.87719i			0.194346i
$399$	16.3955	−	9.46593i	0.820800	−	0.473889i
$400$	3.44350	−	12.5142i	0.172175	−	0.625712i
$401$	−1.28339	−	4.78969i	−0.0640896	−	0.239186i	0.926449	−	0.376421i	$-0.122845\pi$
$401$	−1.28339	−	4.78969i	−0.0640896	−	0.239186i	−0.990539	+	0.137235i	$0.956179\pi$
$402$	4.02236	−	4.02236i	0.200617	−	0.200617i
$403$	−24.2426	−	3.91442i	−1.20761	−	0.194991i
$404$		−	26.2876i		−	1.30786i
$405$	−3.76072	−	1.57257i	−0.186872	−	0.0781417i
$406$	−8.63761	+	14.9608i	−0.428677	+	0.742491i
$407$	1.21906	+	0.326647i	0.0604268	+	0.0161913i
$408$	4.14243			0.205081
$409$	5.83965	+	1.56473i	0.288752	+	0.0773708i	0.400288	−	0.916390i	$-0.368910\pi$
$409$	5.83965	+	1.56473i	0.288752	+	0.0773708i	−0.111536	+	0.993760i	$0.535577\pi$
$410$	0.0818784	−	0.606177i	0.00404368	−	0.0299370i
$411$	−8.19736	+	8.19736i	−0.404346	+	0.404346i
$412$	−2.04303	+	7.62468i	−0.100653	+	0.375641i
$413$	−36.9416	+	9.89848i	−1.81778	+	0.487073i
$414$	−1.36688	+	0.366254i	−0.0671784	+	0.0180004i
$415$	−0.608410	−	4.74450i	−0.0298657	−	0.232898i
$416$	−7.37076	+	16.4219i	−0.361381	+	0.805150i
$417$	−4.25679	−	4.25679i	−0.208456	−	0.208456i
$418$	−0.930187	+	1.61113i	−0.0454969	+	0.0788030i
$419$	4.65114	+	2.68534i	0.227223	+	0.131187i	0.609290	−	0.792947i	$-0.291454\pi$
$419$	4.65114	+	2.68534i	0.227223	+	0.131187i	−0.382067	+	0.924135i	$0.624788\pi$
$420$	−1.81675	+	13.4501i	−0.0886481	+	0.656296i
$421$	14.1377	+	14.1377i	0.689029	+	0.689029i	0.962017	−	0.272988i	$-0.0880119\pi$
$421$	14.1377	+	14.1377i	0.689029	+	0.689029i	−0.272988	+	0.962017i	$0.588012\pi$
$422$	5.31418	−	3.06814i	0.258690	−	0.149355i
$423$	−6.97923	+	4.02946i	−0.339342	+	0.195919i
$424$	−4.58760	−	4.58760i	−0.222794	−	0.222794i
$425$	−11.8722	−	0.0798070i	−0.575887	−	0.00387121i
$426$	−2.69641	−	1.55677i	−0.130642	−	0.0754260i
$427$	11.3905	−	19.7289i	0.551225	−	0.954750i
$428$	−18.9395	−	18.9395i	−0.915476	−	0.915476i
$429$	0.954794	−	2.12726i	0.0460979	−	0.102705i
$430$	−1.89349	−	1.46306i	−0.0913122	−	0.0705552i
$431$	16.1219	−	4.31985i	0.776564	−	0.208080i	0.151295	−	0.988489i	$-0.451656\pi$
$431$	16.1219	−	4.31985i	0.776564	−	0.208080i	0.625269	+	0.780409i	$0.284989\pi$
$432$	12.0625	−	3.23215i	0.580360	−	0.155507i
$433$	−1.96538	+	7.33490i	−0.0944502	+	0.352493i	−0.996936	−	0.0782277i	$-0.975074\pi$
$433$	−1.96538	+	7.33490i	−0.0944502	+	0.352493i	0.902485	+	0.430721i	$0.141741\pi$
$434$	8.74255	−	8.74255i	0.419656	−	0.419656i
$435$	19.8306	+	2.67859i	0.950807	+	0.128429i
$436$	−5.41899	−	1.45201i	−0.259522	−	0.0695388i
$437$	7.41767			0.354835
$438$	1.51479	+	0.405886i	0.0723794	+	0.0193940i
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	−0.655146	−	0.755502i	$-0.727393\pi$
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	0.981857	+	0.189622i	$0.0607262\pi$
$440$	−1.08280	−	2.63917i	−0.0516206	−	0.125818i
$441$			13.7713i			0.655777i
$442$	4.17441	+	0.674036i	0.198556	+	0.0320606i
$443$	6.46290	−	6.46290i	0.307062	−	0.307062i	−0.536707	−	0.843769i	$-0.680332\pi$
$443$	6.46290	−	6.46290i	0.307062	−	0.307062i	0.843769	+	0.536707i	$0.180332\pi$
$444$	−0.784399	−	2.92742i	−0.0372259	−	0.138929i
$445$	−2.86680	−	6.98740i	−0.135899	−	0.331235i
$446$	4.25377	−	2.45591i	0.201422	−	0.116291i
$447$			15.8010i			0.747364i
$448$	5.00971	+	8.67708i	0.236687	+	0.409953i
$449$	−6.65458	+	24.8352i	−0.314049	+	1.17205i	0.610822	+	0.791768i	$0.290839\pi$
$449$	−6.65458	+	24.8352i	−0.314049	+	1.17205i	−0.924872	+	0.380280i	$0.875828\pi$
$450$	5.05558	−	1.31828i	0.238322	−	0.0621443i
$451$	0.190442	+	0.329855i	0.00896755	+	0.0155323i
$452$	7.53143	+	28.1077i	0.354249	+	1.32207i
$453$	3.81852	+	2.20462i	0.179409	+	0.103582i
$454$	−7.21383			−0.338562
$455$	−8.59693	+	28.3583i	−0.403030	+	1.32946i
$456$	9.55545			0.447475
$457$	−0.716665	−	0.413767i	−0.0335242	−	0.0193552i	0.483144	−	0.875541i	$-0.339495\pi$
$457$	−0.716665	−	0.413767i	−0.0335242	−	0.0193552i	−0.516668	+	0.856186i	$0.672828\pi$
$458$	−2.82349	−	10.5374i	−0.131933	−	0.492381i
$459$	−5.71155	−	9.89269i	−0.266592	−	0.461751i
$460$	−3.25138	+	4.20792i	−0.151596	+	0.196195i
$461$	6.23219	−	23.2589i	0.290262	−	1.08327i	−0.654646	−	0.755936i	$-0.727182\pi$
$461$	6.23219	−	23.2589i	0.290262	−	1.08327i	0.944908	−	0.327337i	$-0.106151\pi$
$462$	0.586988	+	1.01669i	0.0273091	+	0.0473008i
$463$		−	6.35566i		−	0.295373i	−0.989034	−	0.147686i	$-0.952817\pi$
$463$		−	6.35566i		−	0.295373i	0.989034	−	0.147686i	$-0.0471826\pi$
$464$	21.3935	−	12.3515i	0.993167	−	0.573405i
$465$	−13.2130	−	5.52509i	−0.612737	−	0.256220i
$466$	−2.99418	−	11.1744i	−0.138703	−	0.517645i
$467$	−15.6194	+	15.6194i	−0.722781	+	0.722781i	−0.969171	−	0.246390i	$-0.920756\pi$
$467$	−15.6194	+	15.6194i	−0.722781	+	0.722781i	0.246390	+	0.969171i	$0.420756\pi$
$468$	13.3262	−	1.36013i	0.616003	−	0.0628722i
$469$		−	45.0153i		−	2.07861i
$470$	1.62295	−	3.88119i	0.0748610	−	0.179026i
$471$	6.56942	−	11.3786i	0.302703	−	0.524297i
$472$	−18.6455	−	4.99605i	−0.858229	−	0.229962i
$473$	1.49000			0.0685104
$474$	−1.40042	−	0.375240i	−0.0643232	−	0.0172354i
$475$	−27.3859	−	0.184093i	−1.25655	−	0.00844675i
$476$	10.8371	−	10.8371i	0.496716	−	0.496716i
$477$	−1.91500	+	7.14687i	−0.0876818	+	0.327233i
$478$	9.85182	−	2.63979i	0.450612	−	0.120741i
$479$	9.14111	−	2.44935i	0.417668	−	0.111914i	−0.0438638	−	0.999038i	$-0.513967\pi$
$479$	9.14111	−	2.44935i	0.417668	−	0.111914i	0.461532	+	0.887124i	$0.347300\pi$
$480$	−6.41866	+	8.30700i	−0.292970	+	0.379161i
$481$	−0.671874	−	6.58282i	−0.0306348	−	0.300151i
$482$	−1.08228	−	1.08228i	−0.0492964	−	0.0492964i
$483$	2.34044	−	4.05375i	0.106494	−	0.184452i
$484$	−16.0095	−	9.24310i	−0.727705	−	0.420141i
$485$	−9.58681	−	12.5811i	−0.435314	−	0.571278i
$486$	5.63904	+	5.63904i	0.255792	+	0.255792i
$487$	5.33382	−	3.07948i	0.241698	−	0.139545i	−0.374259	−	0.927324i	$-0.622103\pi$
$487$	5.33382	−	3.07948i	0.241698	−	0.139545i	0.615957	+	0.787780i	$0.288769\pi$
$488$	9.95775	−	5.74911i	0.450766	−	0.260250i
$489$	0.0877545	+	0.0877545i	0.00396840	+	0.00396840i
$490$	−4.35707	−	5.71793i	−0.196832	−	0.258310i
$491$	12.8290	+	7.40681i	0.578964	+	0.334265i	0.760721	−	0.649078i	$-0.224845\pi$
$491$	12.8290	+	7.40681i	0.578964	+	0.334265i	−0.181758	+	0.983343i	$0.558179\pi$
$492$	0.457320	−	0.792102i	0.0206176	−	0.0357107i
$493$	−15.9781	−	15.9781i	−0.719615	−	0.719615i
$494$	9.62921	+	1.55481i	0.433238	+	0.0699544i
$495$	−1.98914	+	2.57433i	−0.0894051	+	0.115708i
$496$	−17.0775	+	4.57590i	−0.766802	+	0.205464i
$497$	−23.7993	+	6.37699i	−1.06754	+	0.286047i
$498$	−0.257155	+	0.959715i	−0.0115234	+	0.0430059i
$499$	21.0529	−	21.0529i	0.942459	−	0.942459i	−0.0559733	−	0.998432i	$-0.517826\pi$
$499$	21.0529	−	21.0529i	0.942459	−	0.942459i	0.998432	+	0.0559733i	$0.0178262\pi$
$500$	12.1085	−	15.4549i	0.541508	−	0.691164i
$501$	19.6538	+	5.26622i	0.878068	+	0.235278i
$502$	14.5844			0.650933
$503$	37.4393	+	10.0318i	1.66934	+	0.447297i	0.964932	−	0.262502i	$-0.0845476\pi$
$503$	37.4393	+	10.0318i	1.66934	+	0.447297i	0.704404	+	0.709799i	$0.251214\pi$
$504$	−7.21280	+	12.4929i	−0.321284	+	0.556479i
$505$	12.9135	−	30.8820i	0.574643	−	1.37423i
$506$			0.459974i			0.0204484i
$507$	−12.2043	−	0.713230i	−0.542013	−	0.0316756i
$508$	−10.3059	+	10.3059i	−0.457250	+	0.457250i
$509$	−1.43699	−	5.36291i	−0.0636933	−	0.237707i	0.926739	−	0.375706i	$-0.122600\pi$
$509$	−1.43699	−	5.36291i	−0.0636933	−	0.237707i	−0.990432	+	0.137999i	$0.955933\pi$
$510$	2.27518	+	0.951382i	0.100747	+	0.0421279i
$511$	10.7474	−	6.20501i	0.475437	−	0.274493i
$512$			22.5909i			0.998384i
$513$	−13.1750	−	22.8197i	−0.581688	−	1.00751i
$514$	−0.915926	+	3.41828i	−0.0403997	+	0.150774i
$515$	−6.14563	+	7.95364i	−0.270809	+	0.350479i
$516$	−1.78902	−	3.09867i	−0.0787572	−	0.136411i
$517$	0.677985	+	2.53028i	0.0298178	+	0.111281i
$518$	2.88521	+	1.66578i	0.126769	+	0.0731900i
$519$	7.27269			0.319236
$520$	−10.9144	+	10.2261i	−0.478628	+	0.448443i
$521$	−13.8692			−0.607619			−0.303809	−	0.952733i	$-0.598259\pi$
$521$	−13.8692			−0.607619			−0.303809	+	0.952733i	$0.598259\pi$
$522$	8.61159	+	4.97191i	0.376919	+	0.217614i
$523$	8.10818	+	30.2601i	0.354546	+	1.32318i	0.881055	+	0.473014i	$0.156834\pi$
$523$	8.10818	+	30.2601i	0.354546	+	1.32318i	−0.526509	+	0.850170i	$0.676499\pi$
$524$	−1.20649	−	2.08970i	−0.0527057	−	0.0912890i
$525$	−8.74146	+	14.9083i	−0.381508	+	0.650652i
$526$	−1.72130	+	6.42400i	−0.0750524	+	0.280100i
$527$	8.08609	+	14.0055i	0.352236	+	0.610090i
$528$		−	1.67875i		−	0.0730583i
$529$	−18.3303	+	10.5830i	−0.796969	+	0.460130i
$530$	−1.46606	−	3.57331i	−0.0636816	−	0.155214i
$531$	5.69768	+	21.2640i	0.247258	+	0.922781i
$532$	24.9981	−	24.9981i	1.08381	−	1.08381i
$533$	1.26140	−	1.54815i	0.0546371	−	0.0670579i
$534$			1.56879i			0.0678882i
$535$	−12.9458	−	31.5534i	−0.559695	−	1.36417i
$536$	11.3602	−	19.6765i	0.490688	−	0.849897i
$537$	−14.8549	−	3.98035i	−0.641035	−	0.171765i
$538$	4.00246			0.172558
$539$	4.32381	+	1.15856i	0.186240	+	0.0499028i
$540$	18.7202	+	2.52860i	0.805589	+	0.108814i
$541$	−10.7732	+	10.7732i	−0.463175	+	0.463175i	−0.899695	−	0.436520i	$-0.856211\pi$
$541$	−10.7732	+	10.7732i	−0.463175	+	0.463175i	0.436520	+	0.899695i	$0.356211\pi$
$542$	−1.17561	+	4.38745i	−0.0504969	+	0.188457i
$543$	−16.3855	+	4.39048i	−0.703170	+	0.188414i
$544$	11.4504	−	3.06813i	0.490932	−	0.131545i
$545$	−5.65278	−	4.36780i	−0.242139	−	0.187096i
$546$	3.88793	−	4.77178i	0.166388	−	0.204213i
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	0.942987	−	0.332828i	$-0.108003\pi$
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	−0.332828	+	0.942987i	$0.608003\pi$
$548$	−10.8240	+	18.7477i	−0.462379	+	0.800863i
$549$	−11.3562	−	6.55650i	−0.484671	−	0.279825i
$550$	0.0114157	−	1.69822i	0.000486767	−	0.0724122i
$551$	−36.8569	−	36.8569i	−1.57016	−	1.57016i
$552$	2.04605	−	1.18128i	0.0870855	−	0.0502788i
$553$	−9.93592	+	5.73651i	−0.422518	+	0.243941i
$554$	−9.02605	−	9.02605i	−0.383480	−	0.383480i
$555$	0.516571	−	3.82437i	0.0219272	−	0.162336i
$556$	−9.73546	−	5.62077i	−0.412875	−	0.238374i
$557$	−8.35584	+	14.4727i	−0.354048	+	0.613229i	−0.986955	−	0.160999i	$-0.948528\pi$
$557$	−8.35584	+	14.4727i	−0.354048	+	0.613229i	0.632906	+	0.774228i	$0.281862\pi$
$558$	−5.03231	−	5.03231i	−0.213035	−	0.213035i
$559$	−2.77765	−	7.30159i	−0.117482	−	0.308824i
$560$	2.71361	+	21.1613i	0.114671	+	0.894227i
$561$	−1.48326	+	0.397439i	−0.0626234	+	0.0167799i
$562$	−3.65629	+	0.979701i	−0.154231	+	0.0413262i
$563$	−5.84179	+	21.8019i	−0.246202	+	0.918839i	0.726573	+	0.687089i	$0.241112\pi$
$563$	−5.84179	+	21.8019i	−0.246202	+	0.918839i	−0.972775	+	0.231750i	$0.925555\pi$
$564$	4.44802	−	4.44802i	0.187296	−	0.187296i
$565$	−4.95987	+	36.7198i	−0.208663	+	1.54481i
$566$	−4.19136	−	1.12307i	−0.176176	−	0.0472063i
$567$	6.70030			0.281386
$568$	−12.0122	−	3.21865i	−0.504019	−	0.135052i
$569$	2.86843	−	4.96826i	0.120251	−	0.208280i	−0.799616	−	0.600512i	$-0.794963\pi$
$569$	2.86843	−	4.96826i	0.120251	−	0.208280i	0.919866	+	0.392232i	$0.128297\pi$
$570$	5.24821	+	2.19458i	0.219823	+	0.0919206i
$571$			46.5634i			1.94862i	0.225214	+	0.974309i	$0.427692\pi$
$571$			46.5634i			1.94862i	−0.225214	+	0.974309i	$0.572308\pi$
$572$	0.694069	−	4.29848i	0.0290205	−	0.179728i
$573$	−3.45183	+	3.45183i	−0.144202	+	0.144202i
$574$	0.260227	+	0.971181i	0.0108617	+	0.0405363i
$575$	−5.88672	+	3.34614i	−0.245493	+	0.139544i
$576$	4.99463	−	2.88365i	0.208109	−	0.120152i
$577$		−	28.9429i		−	1.20491i	−0.798153	−	0.602455i	$-0.794189\pi$
$577$		−	28.9429i		−	1.20491i	0.798153	−	0.602455i	$-0.205811\pi$
$578$	2.80580	+	4.85978i	0.116706	+	0.202140i
$579$	−2.45862	+	9.17569i	−0.102177	+	0.381329i
$580$	37.0638	−	4.75287i	1.53899	−	0.197352i
$581$	3.93127	+	6.80916i	0.163097	+	0.282491i
$582$	0.850351	+	3.17355i	0.0352482	+	0.131548i
$583$	2.08281	+	1.20251i	0.0862613	+	0.0498030i
$584$	6.26369			0.259193
$585$	16.3234	+	4.94849i	0.674888	+	0.204595i
$586$	−6.53726			−0.270052
$587$	17.0534	+	9.84577i	0.703868	+	0.406379i	0.808787	−	0.588102i	$-0.200125\pi$
$587$	17.0534	+	9.84577i	0.703868	+	0.406379i	−0.104918	+	0.994481i	$0.533458\pi$
$588$	−2.78213	−	10.3830i	−0.114733	−	0.428189i
$589$	18.6524	+	32.3069i	0.768558	+	1.33118i
$590$	−9.09338	−	7.02628i	−0.374368	−	0.289267i
$591$	−3.17966	+	11.8667i	−0.130794	+	0.488129i
$592$	−2.38201	−	4.12577i	−0.0979001	−	0.169568i
$593$			21.8216i			0.896106i	0.894007	+	0.448053i	$0.147882\pi$
$593$			21.8216i			0.896106i	−0.894007	+	0.448053i	$0.852118\pi$
$594$	1.41506	−	0.816987i	0.0580607	−	0.0335214i
$595$	18.0547	−	7.40749i	0.740169	−	0.303677i
$596$	7.63679	+	28.5009i	0.312815	+	1.16744i
$597$	−5.22002	+	5.22002i	−0.213641	+	0.213641i
$598$	2.25405	−	0.857481i	0.0921750	−	0.0350650i
$599$			37.6041i			1.53646i	0.640172	+	0.768232i	$0.278863\pi$
$599$			37.6041i			1.53646i	−0.640172	+	0.768232i	$0.721137\pi$
$600$	−7.58328	+	4.31050i	−0.309586	+	0.175976i
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	−0.581344	−	0.813658i	$-0.697473\pi$
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	0.995320	+	0.0966302i	$0.0308064\pi$
$602$	3.79922	+	1.01800i	0.154845	+	0.0414905i
$603$	−25.9113			−1.05519
$604$	7.95310	+	2.13103i	0.323607	+	0.0867103i
$605$	−14.2670	−	18.7230i	−0.580034	−	0.761199i
$606$	−4.91641	+	4.91641i	−0.199716	+	0.199716i
$607$	8.91757	−	33.2808i	0.361953	−	1.35083i	−0.509552	−	0.860440i	$-0.670189\pi$
$607$	8.91757	−	33.2808i	0.361953	−	1.35083i	0.871505	−	0.490387i	$-0.163144\pi$
$608$	26.4129	−	7.07732i	1.07119	−	0.287023i
$609$	−31.7715	+	8.51314i	−1.28744	+	0.344970i
$610$	6.78955	−	0.870657i	0.274901	−	0.0352519i
$611$	11.1354	−	8.03931i	0.450491	−	0.325236i
$612$	−6.23794	−	6.23794i	−0.252154	−	0.252154i
$613$	12.4332	−	21.5350i	0.502173	−	0.869790i	−0.497824	−	0.867278i	$-0.665867\pi$
$613$	12.4332	−	21.5350i	0.502173	−	0.869790i	0.999997	−	0.00251133i	$-0.000799381\pi$
$614$	6.62053	+	3.82236i	0.267183	+	0.154258i
$615$	0.926357	−	0.705885i	0.0373543	−	0.0284640i
$616$	3.31563	+	3.31563i	0.133591	+	0.133591i
$617$	−24.0895	+	13.9081i	−0.969805	+	0.559917i	−0.899177	−	0.437585i	$-0.855834\pi$
$617$	−24.0895	+	13.9081i	−0.969805	+	0.559917i	−0.0706286	+	0.997503i	$0.522501\pi$
$618$	1.80809	−	1.04390i	0.0727321	−	0.0419919i
$619$	−19.5593	−	19.5593i	−0.786156	−	0.786156i	0.194705	−	0.980862i	$-0.437625\pi$
$619$	−19.5593	−	19.5593i	−0.786156	−	0.786156i	−0.980862	+	0.194705i	$0.937625\pi$
$620$	−26.5030	−	3.57985i	−1.06439	−	0.143770i
$621$	−5.64213	−	3.25749i	−0.226411	−	0.130718i
$622$	−1.32099	+	2.28803i	−0.0529671	+	0.0917416i
$623$	8.77838	+	8.77838i	0.351698	+	0.351698i
$624$	−8.22653	+	3.12952i	−0.329325	+	0.125281i
$625$	21.8167	−	12.2078i	0.872669	−	0.488312i
$626$	−16.4570	+	4.40965i	−0.657755	+	0.176245i
$627$	−3.42148	+	0.916783i	−0.136641	+	0.0366128i
$628$	6.35012	−	23.6990i	0.253397	−	0.945692i
$629$	−3.08139	+	3.08139i	−0.122863	+	0.122863i
$630$	−6.83076	+	5.20504i	−0.272144	+	0.207374i
$631$	12.6187	+	3.38116i	0.502341	+	0.134602i	0.501086	−	0.865397i	$-0.332934\pi$
$631$	12.6187	+	3.38116i	0.502341	+	0.134602i	0.00125496	+	0.999999i	$0.499601\pi$
$632$	−5.79076			−0.230344
$633$	11.2855	+	3.02393i	0.448557	+	0.120190i
$634$	−4.68840	+	8.12054i	−0.186200	+	0.322508i
$635$	−17.1697	+	7.04442i	−0.681360	+	0.279549i
$636$		−	5.77534i		−	0.229007i
$637$	−2.38302	−	23.3481i	−0.0944186	−	0.925086i
$638$	2.28552	−	2.28552i	0.0904846	−	0.0904846i
$639$	3.67067	+	13.6991i	0.145210	+	0.541929i
$640$	−9.77471	+	23.3757i	−0.386379	+	0.924006i
$641$	23.7092	−	13.6885i	0.936456	−	0.540663i	0.0476083	−	0.998866i	$-0.484840\pi$
$641$	23.7092	−	13.6885i	0.936456	−	0.540663i	0.888848	+	0.458203i	$0.151507\pi$
$642$			7.08428i			0.279594i
$643$	−15.7510	−	27.2816i	−0.621161	−	1.07588i	−0.989270	−	0.146099i	$-0.953328\pi$
$643$	−15.7510	−	27.2816i	−0.621161	−	1.07588i	0.368109	−	0.929783i	$-0.380005\pi$
$644$	2.26231	−	8.44305i	0.0891475	−	0.332703i
$645$	−0.579501	−	4.51907i	−0.0228178	−	0.177938i
$646$	−3.21181	−	5.56301i	−0.126367	−	0.218874i
$647$	−10.8106	−	40.3457i	−0.425008	−	1.58615i	−0.763905	−	0.645329i	$-0.776720\pi$
$647$	−10.8106	−	40.3457i	−0.425008	−	1.58615i	0.338896	−	0.940824i	$-0.389946\pi$
$648$	2.92875	+	1.69092i	0.115052	+	0.0664254i
$649$	7.15565			0.280884
$650$	−8.34320	+	3.10986i	−0.327247	+	0.121979i
$651$	23.5409			0.922641
$652$	0.200698	+	0.115873i	0.00785996	+	0.00453795i
$653$	−3.93069	−	14.6695i	−0.153820	−	0.574064i	−0.999204	−	0.0399041i	$-0.987295\pi$
$653$	−3.93069	−	14.6695i	−0.153820	−	0.574064i	0.845384	−	0.534160i	$-0.179372\pi$
$654$	0.741918	+	1.28504i	0.0290113	+	0.0502490i
$655$	−0.390807	−	3.04759i	−0.0152701	−	0.119079i
$656$	0.372117	−	1.38876i	0.0145287	−	0.0542220i
$657$	−3.57167	−	6.18632i	−0.139344	−	0.241351i
$658$			6.91493i			0.269572i
$659$	−24.6914	+	14.2556i	−0.961840	+	0.555319i	−0.896739	−	0.442560i	$-0.854070\pi$
$659$	−24.6914	+	14.2556i	−0.961840	+	0.555319i	−0.0651015	+	0.997879i	$0.520737\pi$
$660$	0.979658	−	2.34280i	0.0381331	−	0.0911934i
$661$	−1.63091	−	6.08664i	−0.0634351	−	0.236743i	0.926928	−	0.375240i	$-0.122440\pi$
$661$	−1.63091	−	6.08664i	−0.0634351	−	0.236743i	−0.990363	+	0.138497i	$0.955773\pi$
$662$	2.45054	−	2.45054i	0.0952430	−	0.0952430i
$663$	4.71270	+	6.52766i	0.183026	+	0.253513i
$664$			3.96845i			0.154006i
$665$	41.6471	−	17.0870i	1.61501	−	0.662606i
$666$	0.958840	−	1.66076i	0.0371543	−	0.0643531i
$667$	−12.4483	−	3.33552i	−0.482002	−	0.129152i
$668$	37.9955			1.47009
$669$	9.03352	+	2.42052i	0.349256	+	0.0935829i
$670$	10.7585	−	8.19801i	0.415638	−	0.316717i
$671$	−3.01394	+	3.01394i	−0.116352	+	0.116352i
$672$	4.46610	−	16.6677i	0.172283	−	0.642970i
$673$	−22.1285	+	5.92931i	−0.852991	+	0.228558i	−0.658719	−	0.752389i	$-0.728901\pi$
$673$	−22.1285	+	5.92931i	−0.852991	+	0.228558i	−0.194272	+	0.980948i	$0.562235\pi$
$674$	0.743468	−	0.199212i	0.0286373	−	0.00767334i
$675$	20.7498	+	12.1666i	0.798660	+	0.468293i
$676$	−22.3581	+	4.61199i	−0.859926	+	0.177384i
$677$	−16.1247	−	16.1247i	−0.619724	−	0.619724i	0.325736	−	0.945461i	$-0.394388\pi$
$677$	−16.1247	−	16.1247i	−0.619724	−	0.619724i	−0.945461	+	0.325736i	$0.894388\pi$
$678$	3.84825	−	6.66536i	0.147791	−	0.255982i
$679$	22.5163	+	12.9998i	0.864096	+	0.498886i
$680$	9.76121	+	1.31848i	0.374325	+	0.0505614i
$681$	−9.71227	−	9.71227i	−0.372175	−	0.372175i
$682$	−2.00337	+	1.15664i	−0.0767129	+	0.0442902i
$683$	27.7544	−	16.0240i	1.06199	−	0.613142i	0.136010	−	0.990707i	$-0.456572\pi$
$683$	27.7544	−	16.0240i	1.06199	−	0.613142i	0.925983	+	0.377565i	$0.123239\pi$
$684$	−14.3892	−	14.3892i	−0.550185	−	0.550185i
$685$	−21.9253	+	16.7071i	−0.837724	+	0.638346i
$686$	−0.771532	−	0.445444i	−0.0294572	−	0.0170071i
$687$	10.3856	−	17.9883i	0.396234	−	0.686298i
$688$	−3.97707	−	3.97707i	−0.151624	−	0.151624i
$689$	2.01001	−	12.4483i	0.0765753	−	0.474243i
$690$	1.39507	−	0.178896i	0.0531093	−	0.00681046i
$691$	−0.532264	+	0.142620i	−0.0202483	+	0.00542551i	−0.268929	−	0.963160i	$-0.586670\pi$
$691$	−0.532264	+	0.142620i	−0.0202483	+	0.00542551i	0.248681	+	0.968586i	$0.420003\pi$
$692$	13.1180	−	3.51496i	0.498672	−	0.133619i
$693$	1.38404	−	5.16531i	0.0525754	−	0.196214i
$694$	−9.02132	+	9.02132i	−0.342445	+	0.342445i
$695$	−8.67580	−	11.3855i	−0.329092	−	0.431878i
$696$	−16.0360	−	4.29682i	−0.607842	−	0.162871i
$697$	−1.31514			−0.0498144
$698$	4.48442	+	1.20160i	0.169738	+	0.0454811i
$699$	11.0134	−	19.0758i	0.416565	−	0.721512i
$700$	−8.56194	+	31.1155i	−0.323611	+	1.17605i
$701$		−	9.52279i		−	0.359671i	−0.983697	−	0.179835i	$-0.942443\pi$
$701$		−	9.52279i		−	0.359671i	0.983697	−	0.179835i	$-0.0575565\pi$
$702$	−6.64150	−	5.41133i	−0.250667	−	0.204237i
$703$	−7.10792	+	7.10792i	−0.268080	+	0.268080i
$704$	−0.485195	−	1.81077i	−0.0182865	−	0.0682460i
$705$	7.41045	−	3.04037i	0.279094	−	0.114507i
$706$	−1.39674	+	0.806411i	−0.0525672	+	0.0303497i
$707$			55.0209i			2.06927i
$708$	−8.59166	−	14.8812i	−0.322894	−	0.559270i
$709$	8.39944	−	31.3471i	0.315448	−	1.17727i	−0.608124	−	0.793842i	$-0.708078\pi$
$709$	8.39944	−	31.3471i	0.315448	−	1.17727i	0.923572	−	0.383425i	$-0.125255\pi$
$710$	−5.85831	−	4.52661i	−0.219859	−	0.169881i
$711$	3.30200	+	5.71923i	0.123835	+	0.214488i
$712$	1.62175	+	6.05244i	0.0607776	+	0.226825i
$713$	7.98782	+	4.61177i	0.299146	+	0.172712i
$714$	−4.05358			−0.151701
$715$	2.92695	−	4.70877i	0.109462	−	0.176098i
$716$	−28.7180			−1.07324
$717$	16.8180	+	9.70986i	0.628079	+	0.362621i
$718$	−0.564197	−	2.10561i	−0.0210557	−	0.0785808i
$719$	4.21240	+	7.29608i	0.157096	+	0.272098i	0.933820	−	0.357743i	$-0.116454\pi$
$719$	4.21240	+	7.29608i	0.157096	+	0.272098i	−0.776724	+	0.629841i	$0.783120\pi$
$720$	12.1807	−	1.56199i	0.453947	−	0.0582118i
$721$	4.27612	−	15.9587i	0.159251	−	0.594333i
$722$	−2.71668	−	4.70543i	−0.101104	−	0.175118i
$723$		−	2.91423i		−	0.108381i
$724$	−27.4332	+	15.8385i	−1.01955	+	0.588635i
$725$	45.8763	+	12.6236i	1.70380	+	0.468830i
$726$	1.26548	+	4.72284i	0.0469664	+	0.175281i
$727$	−8.33682	+	8.33682i	−0.309195	+	0.309195i	−0.844597	−	0.535402i	$-0.820160\pi$
$727$	−8.33682	+	8.33682i	−0.309195	+	0.309195i	0.535402	+	0.844597i	$0.320160\pi$
$728$	10.0669	−	22.4288i	0.373104	−	0.831268i
$729$			9.71523i			0.359824i
$730$	3.44025	+	1.43857i	0.127329	+	0.0532437i
$731$	−2.57239	+	4.45551i	−0.0951432	+	0.164793i
$732$	9.88670	+	2.64913i	0.365423	+	0.0979148i
$733$	−18.6238			−0.687887			−0.343944	−	0.938990i	$-0.611763\pi$
$733$	−18.6238			−0.687887			−0.343944	+	0.938990i	$0.611763\pi$
$734$	11.9696	+	3.20725i	0.441807	+	0.118382i
$735$	1.83219	−	13.5644i	0.0675812	−	0.500330i
$736$	4.78070	−	4.78070i	0.176219	−	0.176219i
$737$	−2.17988	+	8.13543i	−0.0802970	+	0.299672i
$738$	0.559023	−	0.149790i	0.0205779	−	0.00551383i
$739$	−31.8740	+	8.54061i	−1.17250	+	0.314171i	−0.791949	−	0.610587i	$-0.790934\pi$
$739$	−31.8740	+	8.54061i	−1.17250	+	0.314171i	−0.380555	+	0.924758i	$0.624267\pi$
$740$	−0.916598	−	7.14782i	−0.0336948	−	0.262759i
$741$	10.8709	+	15.0575i	0.399352	+	0.553151i
$742$	4.48920	+	4.48920i	0.164804	+	0.164804i
$743$	−18.7850	+	32.5366i	−0.689155	+	1.19365i	0.282957	+	0.959133i	$0.408685\pi$
$743$	−18.7850	+	32.5366i	−0.689155	+	1.19365i	−0.972112	+	0.234518i	$0.924649\pi$
$744$	10.2899	+	5.94088i	0.377246	+	0.217803i
$745$	−5.02925	+	37.2335i	−0.184258	+	1.36413i
$746$	−3.99061	−	3.99061i	−0.146107	−	0.146107i
$747$	3.91943	−	2.26288i	0.143404	−	0.0827946i
$748$	−2.48333	+	1.43375i	−0.0907995	+	0.0524231i
$749$	39.6410	+	39.6410i	1.44845	+	1.44845i
$750$	−5.15500	+	0.625858i	−0.188234	+	0.0228531i
$751$	−29.1051	−	16.8038i	−1.06206	−	0.613181i	−0.136059	−	0.990701i	$-0.543444\pi$
$751$	−29.1051	−	16.8038i	−1.06206	−	0.613181i	−0.926001	+	0.377520i	$0.876777\pi$
$752$	4.94407	−	8.56339i	0.180292	−	0.312275i
$753$	19.6356	+	19.6356i	0.715560	+	0.715560i
$754$	−15.4606	−	6.93928i	−0.563041	−	0.252714i
$755$	8.29623	+	6.41034i	0.301931	+	0.233296i
$756$	−29.9924	+	8.03643i	−1.09081	+	0.292282i
$757$	15.5871	−	4.17654i	0.566521	−	0.151799i	0.0358205	−	0.999358i	$-0.488596\pi$
$757$	15.5871	−	4.17654i	0.566521	−	0.151799i	0.530701	+	0.847559i	$0.321929\pi$
$758$	0.256883	−	0.958699i	0.00933040	−	0.0348215i
$759$	−0.619282	+	0.619282i	−0.0224785	+	0.0224785i
$760$	22.5164	+	3.04137i	0.816756	+	0.110322i
$761$	−15.1340	−	4.05514i	−0.548606	−	0.146999i	−0.0261397	−	0.999658i	$-0.508321\pi$
$761$	−15.1340	−	4.05514i	−0.548606	−	0.146999i	−0.522467	+	0.852660i	$0.674988\pi$
$762$	3.85490			0.139648
$763$	11.3421	+	3.03911i	0.410612	+	0.110023i
$764$	−4.55789	+	7.89449i	−0.164899	+	0.285613i
$765$	−4.26384	−	10.3925i	−0.154159	−	0.375741i
$766$		−	13.0645i		−	0.472039i
$767$	−13.3395	−	35.0655i	−0.481662	−	1.26614i
$768$	0.0960396	−	0.0960396i	0.00346553	−	0.00346553i
$769$	8.43930	+	31.4959i	0.304329	+	1.13577i	0.933522	+	0.358521i	$0.116719\pi$
$769$	8.43930	+	31.4959i	0.304329	+	1.13577i	−0.629193	+	0.777249i	$0.716614\pi$
$770$	1.05958	+	2.58256i	0.0381845	+	0.0930690i
$771$	−5.83532	+	3.36902i	−0.210154	+	0.121332i
$772$			17.7388i			0.638433i
$773$	−11.9531	−	20.7033i	−0.429921	−	0.744646i	0.566944	−	0.823756i	$-0.308125\pi$
$773$	−11.9531	−	20.7033i	−0.429921	−	0.744646i	−0.996866	+	0.0791103i	$0.974792\pi$
$774$	0.585972	−	2.18688i	0.0210623	−	0.0786056i
$775$	−29.3764	−	17.2248i	−1.05523	−	0.618733i
$776$	6.56136	+	11.3646i	0.235539	+	0.407966i
$777$	1.64177	+	6.12718i	0.0588983	+	0.219811i
$778$	0.278066	+	0.160541i	0.00996914	+	0.00575569i
$779$	−3.03366			−0.108692
$780$	−13.3069	−	0.433269i	−0.476463	−	0.0155135i
$781$	4.60995			0.164957
$782$	−1.37545	−	0.794114i	−0.0491858	−	0.0283975i
$783$	11.8488	+	44.2204i	0.423443	+	1.58031i
$784$	−8.44858	−	14.6334i	−0.301735	−	0.522620i
$785$	19.1018	−	24.7214i	0.681772	−	0.882346i
$786$	−0.165181	+	0.616466i	−0.00589183	+	0.0219886i
$787$	−7.85572	−	13.6065i	−0.280026	−	0.485020i	0.691365	−	0.722506i	$-0.257010\pi$
$787$	−7.85572	−	13.6065i	−0.280026	−	0.485020i	−0.971391	+	0.237486i	$0.923676\pi$
$788$			22.9411i			0.817242i
$789$	−10.9664	+	6.33143i	−0.390412	+	0.225405i
$790$	−3.18050	−	1.32995i	−0.113157	−	0.0473174i
$791$	−15.7635	−	58.8303i	−0.560487	−	2.09176i
$792$	1.90851	−	1.90851i	0.0678161	−	0.0678161i
$793$	20.3880	+	9.15090i	0.724000	+	0.324958i
$794$		−	13.3394i		−	0.473397i
$795$	2.83707	−	6.78470i	0.100621	−	0.240629i
$796$	−6.89264	+	11.9384i	−0.244303	+	0.423146i
$797$	−30.1666	−	8.08312i	−1.06856	−	0.286319i	−0.318656	−	0.947870i	$-0.603232\pi$
$797$	−30.1666	−	8.08312i	−1.06856	−	0.286319i	−0.749900	+	0.661552i	$0.769898\pi$
$798$	−9.35048			−0.331003
$799$	−8.73669	−	2.34099i	−0.309082	−	0.0828183i
$800$	−17.7689	+	17.5316i	−0.628225	+	0.619836i
$801$	5.05293	−	5.05293i	0.178537	−	0.178537i
$802$	−0.633871	+	2.36564i	−0.0223827	+	0.0835336i
$803$	−2.24281	+	0.600960i	−0.0791471	+	0.0212074i
$804$	19.5361	−	5.23469i	0.688986	−	0.184613i
$805$	6.80525	−	8.80732i	0.239853	−	0.310417i
$806$	9.40267	+	7.66106i	0.331195	+	0.269849i
$807$	5.38868	+	5.38868i	0.189690	+	0.189690i
$808$	−13.8853	+	24.0500i	−0.488483	+	0.846078i
$809$	11.4546	+	6.61331i	0.402722	+	0.232512i	0.687658	−	0.726035i	$-0.258639\pi$
$809$	11.4546	+	6.61331i	0.402722	+	0.232512i	−0.284936	+	0.958547i	$0.591972\pi$
$810$	1.22023	+	1.60135i	0.0428746	+	0.0562658i
$811$	22.0736	+	22.0736i	0.775109	+	0.775109i	0.978995	−	0.203886i	$-0.0653572\pi$
$811$	22.0736	+	22.0736i	0.775109	+	0.775109i	−0.203886	+	0.978995i	$0.565357\pi$
$812$	−53.1928	+	30.7109i	−1.86670	+	1.07774i
$813$	−7.48978	+	4.32423i	−0.262678	+	0.151657i
$814$	−0.440767	−	0.440767i	−0.0154489	−	0.0154489i
$815$	0.178853	+	0.234715i	0.00626496	+	0.00822172i
$816$	5.01991	+	2.89825i	0.175732	+	0.101459i
$817$	−5.93379	+	10.2776i	−0.207597	+	0.359568i
$818$	−2.11139	−	2.11139i	−0.0738230	−	0.0738230i
$819$	−27.8921	+	2.84680i	−0.974630	+	0.0994754i
$820$	1.32974	−	1.72095i	0.0464366	−	0.0600981i
$821$	−8.74860	+	2.34418i	−0.305328	+	0.0818124i	−0.408230	−	0.912879i	$-0.633854\pi$
$821$	−8.74860	+	2.34418i	−0.305328	+	0.0818124i	0.102902	+	0.994692i	$0.467187\pi$
$822$	5.53062	−	1.48192i	0.192902	−	0.0516881i
$823$	10.8551	−	40.5117i	0.378384	−	1.41215i	−0.469953	−	0.882691i	$-0.655729\pi$
$823$	10.8551	−	40.5117i	0.378384	−	1.41215i	0.848337	−	0.529457i	$-0.177604\pi$
$824$	5.89653	−	5.89653i	0.205415	−	0.205415i
$825$	2.30175	−	2.27101i	0.0801366	−	0.0790664i
$826$	18.2455	+	4.88888i	0.634844	+	0.170106i
$827$	38.2009			1.32838			0.664188	−	0.747566i	$-0.268778\pi$
$827$	38.2009			1.32838			0.664188	+	0.747566i	$0.268778\pi$
$828$	−4.85992	−	1.30221i	−0.168894	−	0.0452550i
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	0.490255	+	0.871579i	$0.336904\pi$
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	−0.999937	+	0.0112165i	$0.996430\pi$
$830$	−0.911423	+	2.17962i	−0.0316359	+	0.0756557i
$831$		−	24.3043i		−	0.843106i
$832$	−7.96898	+	5.75327i	−0.276275	+	0.199459i
$833$	−10.9292	+	10.9292i	−0.378673	+	0.378673i
$834$	0.769545	+	2.87198i	0.0266471	+	0.0994485i
$835$	44.6360	+	18.6648i	1.54469	+	0.645923i
$836$	−5.72835	+	3.30726i	−0.198119	+	0.114384i
$837$		−	32.7649i		−	1.13252i
$838$	−1.32629	−	2.29721i	−0.0458161	−	0.0793557i
$839$	9.11914	−	34.0331i	0.314828	−	1.17495i	−0.609322	−	0.792923i	$-0.708558\pi$
$839$	9.11914	−	34.0331i	0.314828	−	1.17495i	0.924150	−	0.382030i	$-0.124775\pi$
$840$	8.76652	−	11.3456i	0.302474	−	0.391460i
$841$	30.7798	+	53.3122i	1.06137	+	1.83835i
$842$	−2.55582	−	9.53846i	−0.0880795	−	0.328717i
$843$	−6.24163	−	3.60361i	−0.214973	−	0.124115i
$844$	21.8175			0.750988
$845$	−28.5312	−	5.56512i	−0.981503	−	0.191446i
$846$	3.98031			0.136846
$847$	33.5084	+	19.3461i	1.15136	+	0.664740i
$848$	−2.34967	−	8.76909i	−0.0806880	−	0.301132i
$849$	−4.13097	−	7.15504i	−0.141774	−	0.245560i
$850$	5.05841	+	2.96599i	0.173502	+	0.101733i
$851$	−0.643261	+	2.40068i	−0.0220507	+	0.0822944i
$852$	−5.53509	−	9.58705i	−0.189629	−	0.328447i
$853$		−	17.6392i		−	0.603954i	−0.953315	−	0.301977i	$-0.902353\pi$
$853$		−	17.6392i		−	0.603954i	0.953315	−	0.301977i	$-0.0976465\pi$
$854$	−9.74415	+	5.62579i	−0.333438	+	0.192511i
$855$	−9.83549	−	23.9725i	−0.336367	−	0.819844i
$856$	7.32342	+	27.3314i	0.250309	+	0.934167i
$857$	6.30427	−	6.30427i	0.215350	−	0.215350i	−0.591186	−	0.806535i	$-0.701340\pi$
$857$	6.30427	−	6.30427i	0.215350	−	0.215350i	0.806535	+	0.591186i	$0.201340\pi$
$858$	−0.933725	+	0.674110i	−0.0318768	+	0.0230137i
$859$			29.2307i			0.997338i	0.866793	+	0.498669i	$0.166178\pi$
$859$			29.2307i			0.997338i	−0.866793	+	0.498669i	$0.833822\pi$
$860$	−3.22937	−	7.87112i	−0.110121	−	0.268403i
$861$	−0.957186	+	1.65789i	−0.0326208	+	0.0565009i
$862$	−7.96263	−	2.13358i	−0.271208	−	0.0726701i
$863$	−15.7688			−0.536775			−0.268387	−	0.963311i	$-0.586491\pi$
$863$	−15.7688			−0.536775			−0.268387	+	0.963311i	$0.586491\pi$
$864$	−23.1986	−	6.21604i	−0.789232	−	0.211474i
$865$	17.1373	+	2.31480i	0.582687	+	0.0787054i
$866$	2.65202	−	2.65202i	0.0901192	−	0.0901192i
$867$	−2.76537	+	10.3205i	−0.0939168	+	0.350502i
$868$	42.4615	−	11.3775i	1.44124	−	0.386179i
$869$	2.07347	−	0.555585i	0.0703377	−	0.0188469i
$870$	−7.82071	−	6.04291i	−0.265147	−	0.204874i
$871$	43.9305	−	4.48375i	1.48853	−	0.151926i
$872$	4.19076	+	4.19076i	0.141917	+	0.141917i
$873$	7.48283	−	12.9606i	0.253255	−	0.438651i
$874$	−3.17277	−	1.83180i	−0.107321	−	0.0619616i
$875$	−25.3434	+	32.3476i	−0.856764	+	1.09355i
$876$	3.94269	+	3.94269i	0.133211	+	0.133211i
$877$	−38.7309	+	22.3613i	−1.30785	+	0.755088i	−0.981737	−	0.190242i	$-0.939073\pi$
$877$	−38.7309	+	22.3613i	−1.30785	+	0.755088i	−0.326114	+	0.945331i	$0.605739\pi$
$878$	−5.85595	+	3.38094i	−0.197629	+	0.114101i
$879$	−8.80139	−	8.80139i	−0.296863	−	0.296863i
$880$	0.534323	−	3.95580i	0.0180120	−	0.133350i
$881$	−18.0323	−	10.4110i	−0.607525	−	0.350755i	0.164471	−	0.986382i	$-0.447408\pi$
$881$	−18.0323	−	10.4110i	−0.607525	−	0.350755i	−0.771996	+	0.635627i	$0.780742\pi$
$882$	3.40084	−	5.89043i	0.114512	−	0.198341i
$883$	5.33747	+	5.33747i	0.179620	+	0.179620i	0.791190	−	0.611570i	$-0.209462\pi$
$883$	5.33747	+	5.33747i	0.179620	+	0.179620i	−0.611570	+	0.791190i	$0.709462\pi$
$884$	11.6553	+	9.49648i	0.392011	+	0.319401i
$885$	−2.78302	−	21.7026i	−0.0935502	−	0.729523i
$886$	−4.36041	+	1.16837i	−0.146491	+	0.0392521i
$887$	25.8911	−	6.93749i	0.869337	−	0.232938i	0.203536	−	0.979067i	$-0.434757\pi$
$887$	25.8911	−	6.93749i	0.869337	−	0.232938i	0.665801	+	0.746129i	$0.268090\pi$
$888$	−0.828649	+	3.09256i	−0.0278077	+	0.103780i
$889$	21.5706	−	21.5706i	0.723454	−	0.723454i
$890$	−0.499324	+	3.69669i	−0.0167374	+	0.123913i
$891$	−1.21092	−	0.324464i	−0.0405673	−	0.0108700i
$892$	17.4639			0.584736
$893$	−20.1531	−	5.40002i	−0.674399	−	0.180705i
$894$	3.90208	−	6.75861i	0.130505	−	0.226042i
$895$	−33.7370	−	14.1074i	−1.12770	−	0.471557i
$896$		−	41.6474i		−	1.39134i
$897$	4.18918	+	1.88026i	0.139873	+	0.0627800i
$898$	8.97946	−	8.97946i	0.299648	−	0.299648i
$899$	−16.7749	−	62.6048i	−0.559475	−	2.08799i
$900$	17.9104	+	4.92835i	0.597014	+	0.164278i
$901$	−7.19167	+	4.15211i	−0.239589	+	0.138327i
$902$		−	0.188119i		−	0.00626368i
$903$	3.74447	+	6.48562i	0.124608	+	0.215828i
$904$	7.95630	−	29.6933i	0.264623	−	0.987585i
$905$	−40.0082	+	5.13044i	−1.32992	+	0.170542i
$906$	−1.08887	−	1.88597i	−0.0361752	−	0.0626572i
$907$	10.4931	+	39.1608i	0.348418	+	1.30031i	0.888568	+	0.458744i	$0.151701\pi$
$907$	10.4931	+	39.1608i	0.348418	+	1.30031i	−0.540151	+	0.841568i	$0.681633\pi$
$908$	−22.2124	−	12.8243i	−0.737144	−	0.425590i
$909$	31.6707			1.05045
$910$	10.6803	−	10.0067i	0.354048	−	0.331720i
$911$	8.00072			0.265076			0.132538	−	0.991178i	$-0.457687\pi$
$911$	8.00072			0.265076			0.132538	+	0.991178i	$0.457687\pi$
$912$	11.5796	+	6.68546i	0.383437	+	0.221378i
$913$	−0.380746	−	1.42096i	−0.0126009	−	0.0470271i
$914$	0.204360	+	0.353962i	0.00675963	+	0.0117080i
$915$	10.3133	+	7.96885i	0.340946	+	0.263442i
$916$	10.0389	−	37.4656i	0.331694	−	1.23790i
$917$	2.52522	+	4.37381i	0.0833901	+	0.144436i
$918$			5.64189i			0.186210i
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	−0.530079	−	0.847948i	$-0.677838\pi$
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	0.469305	+	0.883036i	$0.344504\pi$
$920$	5.19728	−	2.13235i	0.171349	−	0.0703014i
$921$	3.76728	+	14.0597i	0.124136	+	0.463283i
$922$	−8.40950	+	8.40950i	−0.276952	+	0.276952i
$923$	−8.59384	−	22.5905i	−0.282870	−	0.743577i
$924$			4.17405i			0.137316i
$925$	2.43449	−	8.84732i	0.0800455	−	0.290898i
$926$	−1.56954	+	2.71852i	−0.0515782	+	0.0893360i
$927$	−9.18601	−	2.46138i	−0.301708	−	0.0808425i
$928$	−47.5087			−1.55955
$929$	19.2515	+	5.15841i	0.631620	+	0.169242i	0.560405	−	0.828219i	$-0.310646\pi$
$929$	19.2515	+	5.15841i	0.631620	+	0.169242i	0.0712153	+	0.997461i	$0.477312\pi$
$930$	4.28718	+	5.62621i	0.140582	+	0.184491i
$931$	−25.2106	+	25.2106i	−0.826243	+	0.826243i
$932$	10.6458	−	39.7305i	0.348713	−	1.30142i
$933$	−4.85898	+	1.30196i	−0.159076	+	0.0426242i
$934$	10.5382	−	2.82369i	0.344819	−	0.0923940i
$935$	−3.62166	+	0.464422i	−0.118441	+	0.0151882i
$936$	−12.9103	−	5.79462i	−0.421986	−	0.189403i
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	0.930562	−	0.366135i	$-0.119319\pi$
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	−0.366135	+	0.930562i	$0.619319\pi$
$938$	−11.1166	+	19.2545i	−0.362969	+	0.628680i
$939$	−28.0937	−	16.2199i	−0.916802	−	0.529316i
$940$	11.8970	−	9.06556i	0.388039	−	0.295686i
$941$	24.2129	+	24.2129i	0.789319	+	0.789319i	0.981383	−	0.192063i	$-0.0615179\pi$
$941$	24.2129	+	24.2129i	0.789319	+	0.789319i	−0.192063	+	0.981383i	$0.561518\pi$
$942$	−5.61989	+	3.24465i	−0.183106	+	0.105716i
$943$	−0.649578	+	0.375034i	−0.0211532	+	0.0122128i
$944$	−19.0996	−	19.0996i	−0.621640	−	0.621640i
$945$	−39.1820	−	5.29244i	−1.27459	−	0.172163i
$946$	−0.637321	−	0.367957i	−0.0207211	−	0.0119633i
$947$	4.15045	−	7.18880i	0.134872	−	0.233605i	−0.790677	−	0.612234i	$-0.790271\pi$
$947$	4.15045	−	7.18880i	0.134872	−	0.233605i	0.925548	+	0.378629i	$0.123604\pi$
$948$	−3.64500	−	3.64500i	−0.118384	−	0.118384i
$949$	7.12597	+	9.87034i	0.231319	+	0.320405i
$950$	11.6684	+	6.84172i	0.378572	+	0.221975i
$951$	−17.2452	+	4.62084i	−0.559214	+	0.149841i
$952$	−15.6388	+	4.19041i	−0.506857	+	0.135812i
$953$	1.23858	−	4.62244i	0.0401215	−	0.149736i	−0.942959	−	0.332908i	$-0.891970\pi$
$953$	1.23858	−	4.62244i	0.0401215	−	0.149736i	0.983081	+	0.183173i	$0.0586367\pi$
$954$	2.58403	−	2.58403i	0.0836611	−	0.0836611i
$955$	−9.23255	+	7.03521i	−0.298758	+	0.227654i
$956$	35.0280	+	9.38573i	1.13289	+	0.303556i
$957$	6.15418			0.198936
$958$	−4.51481	−	1.20974i	−0.145867	−	0.0390849i
$959$	22.6550	−	39.2396i	0.731568	−	1.26711i
$960$	−5.30323	+	2.17582i	−0.171161	+	0.0702241i
$961$			15.3867i			0.496346i
$962$	−1.33825	+	2.98160i	−0.0431470	+	0.0961306i
$963$	22.8178	−	22.8178i	0.735294	−	0.735294i
$964$	−1.40848	−	5.25650i	−0.0453639	−	0.169301i
$965$	−8.71398	+	20.8390i	−0.280513	+	0.670832i
$966$	−2.00216	+	1.15595i	−0.0644183	+	0.0371919i
$967$			8.78782i			0.282597i	0.989967	+	0.141299i	$0.0451278\pi$
$967$			8.78782i			0.282597i	−0.989967	+	0.141299i	$0.954872\pi$
$968$	9.76453	+	16.9127i	0.313844	+	0.543594i
$969$	3.16552	−	11.8139i	0.101691	−	0.379517i
$970$	0.993666	+	7.74880i	0.0319047	+	0.248799i
$971$	2.71693	+	4.70586i	0.0871905	+	0.151018i	0.906323	−	0.422587i	$-0.138878\pi$
$971$	2.71693	+	4.70586i	0.0871905	+	0.151018i	−0.819132	+	0.573605i	$0.805544\pi$
$972$	7.33863	+	27.3881i	0.235387	+	0.878475i
$973$	20.3766	+	11.7645i	0.653245	+	0.377151i
$974$	−3.04192			−0.0974695
$975$	−15.4197	−	7.04585i	−0.493826	−	0.225648i
$976$	16.0894			0.515010
$977$	16.1709	+	9.33626i	0.517352	+	0.298693i	0.735851	−	0.677144i	$-0.236783\pi$
$977$	16.1709	+	9.33626i	0.517352	+	0.298693i	−0.218499	+	0.975837i	$0.570116\pi$
$978$	−0.0158643	−	0.0592064i	−0.000507285	−	0.00189321i
$979$	−1.16138	−	2.01158i	−0.0371180	−	0.0642903i
$980$	−3.25101	−	25.3521i	−0.103850	−	0.809842i
$981$	1.74935	−	6.52865i	0.0558524	−	0.208444i
$982$	−3.65824	−	6.33626i	−0.116739	−	0.202198i
$983$		−	6.62470i		−	0.211295i	−0.994404	−	0.105648i	$-0.966308\pi$
$983$		−	6.62470i		−	0.211295i	0.994404	−	0.105648i	$-0.0336915\pi$
$984$	−0.836786	+	0.483119i	−0.0266758	+	0.0154013i
$985$	−11.2695	+	26.9505i	−0.359077	+	0.858715i
$986$	2.88852	+	10.7801i	0.0919893	+	0.343309i
$987$	−9.30986	+	9.30986i	−0.296336	+	0.296336i
$988$	26.8856	+	21.9057i	0.855346	+	0.696915i
$989$			2.93424i			0.0933033i
$990$	1.48655	−	0.609904i	0.0472457	−	0.0193840i
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	−0.286362	−	0.958121i	$-0.592446\pi$
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	0.972939	−	0.231064i	$-0.0742206\pi$
$992$	32.8433	+	8.80033i	1.04277	+	0.279411i
$993$	6.59853			0.209398
$994$	11.7545	+	3.14961i	0.372830	+	0.0998995i
$995$	−13.9619	+	10.6390i	−0.442621	+	0.337278i
$996$	−2.49794	+	2.49794i	−0.0791504	+	0.0791504i
$997$	11.7001	−	43.6654i	0.370547	−	1.38290i	−0.489197	−	0.872173i	$-0.662710\pi$
$997$	11.7001	−	43.6654i	0.370547	−	1.38290i	0.859744	−	0.510725i	$-0.170623\pi$
$998$	−14.2040	+	3.80596i	−0.449621	+	0.120476i
$999$	8.52799	−	2.28507i	0.269814	−	0.0722963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.t.a.7.3	yes	20
3.2	odd	2		585.2.dp.a.397.3		20
5.2	odd	4		325.2.s.b.293.3		20
5.3	odd	4		65.2.o.a.33.3	yes	20
5.4	even	2		325.2.x.b.7.3		20
13.2	odd	12		65.2.o.a.2.3	✓	20
13.3	even	3		845.2.t.f.427.3		20
13.4	even	6		845.2.f.d.437.5		20
13.5	odd	4		845.2.o.e.357.3		20
13.6	odd	12		845.2.k.e.577.6		20
13.7	odd	12		845.2.k.d.577.5		20
13.8	odd	4		845.2.o.f.357.3		20
13.9	even	3		845.2.f.e.437.6		20
13.10	even	6		845.2.t.e.427.3		20
13.11	odd	12		845.2.o.g.587.3		20
13.12	even	2		845.2.t.g.657.3		20
15.8	even	4		585.2.cf.a.163.3		20
39.2	even	12		585.2.cf.a.262.3		20
65.2	even	12		325.2.x.b.93.3		20
65.3	odd	12		845.2.o.e.258.3		20
65.8	even	4		845.2.t.e.188.3		20
65.18	even	4		845.2.t.f.188.3		20
65.23	odd	12		845.2.o.f.258.3		20
65.28	even	12	inner	65.2.t.a.28.3	yes	20
65.33	even	12		845.2.f.d.408.6		20
65.38	odd	4		845.2.o.g.488.3		20
65.43	odd	12		845.2.k.d.268.5		20
65.48	odd	12		845.2.k.e.268.6		20
65.54	odd	12		325.2.s.b.132.3		20
65.58	even	12		845.2.f.e.408.5		20
65.63	even	12		845.2.t.g.418.3		20
195.158	odd	12		585.2.dp.a.28.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	13.2	odd	12
65.2.o.a.33.3	yes	20	5.3	odd	4
65.2.t.a.7.3	yes	20	1.1	even	1	trivial
65.2.t.a.28.3	yes	20	65.28	even	12	inner
325.2.s.b.132.3		20	65.54	odd	12
325.2.s.b.293.3		20	5.2	odd	4
325.2.x.b.7.3		20	5.4	even	2
325.2.x.b.93.3		20	65.2	even	12
585.2.cf.a.163.3		20	15.8	even	4
585.2.cf.a.262.3		20	39.2	even	12
585.2.dp.a.28.3		20	195.158	odd	12
585.2.dp.a.397.3		20	3.2	odd	2
845.2.f.d.408.6		20	65.33	even	12
845.2.f.d.437.5		20	13.4	even	6
845.2.f.e.408.5		20	65.58	even	12
845.2.f.e.437.6		20	13.9	even	3
845.2.k.d.268.5		20	65.43	odd	12
845.2.k.d.577.5		20	13.7	odd	12
845.2.k.e.268.6		20	65.48	odd	12
845.2.k.e.577.6		20	13.6	odd	12
845.2.o.e.258.3		20	65.3	odd	12
845.2.o.e.357.3		20	13.5	odd	4
845.2.o.f.258.3		20	65.23	odd	12
845.2.o.f.357.3		20	13.8	odd	4
845.2.o.g.488.3		20	65.38	odd	4
845.2.o.g.587.3		20	13.11	odd	12
845.2.t.e.188.3		20	65.8	even	4
845.2.t.e.427.3		20	13.10	even	6
845.2.t.f.188.3		20	65.18	even	4
845.2.t.f.427.3		20	13.3	even	3
845.2.t.g.418.3		20	65.63	even	12
845.2.t.g.657.3		20	13.12	even	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.427732 - 0.246951i) q^{2} +(-0.243392 - 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.284413 - 2.21791i) q^{5} +(-0.120212 + 0.448637i) q^{6} +(1.83775 + 3.18307i) q^{7} +1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +O(q^{10})\)	\(q+(-0.427732 - 0.246951i) q^{2} +(-0.243392 - 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.284413 - 2.21791i) q^{5} +(-0.120212 + 0.448637i) q^{6} +(1.83775 + 3.18307i) q^{7} +1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +(-0.426062 + 1.01890i) q^{10} +(-0.177987 - 0.664257i) q^{11} +(-1.16771 + 1.16771i) q^{12} +(-2.92331 + 2.11051i) q^{13} -1.81533i q^{14} +(-1.94542 + 0.798168i) q^{15} +(-1.29794 + 2.24809i) q^{16} +(2.29359 + 0.614565i) q^{17} -1.04493 q^{18} +(5.29067 + 1.41763i) q^{19} +(-3.12325 + 2.37992i) q^{20} +(2.44406 - 2.44406i) q^{21} +(-0.0879082 + 0.328078i) q^{22} +(1.30811 - 0.350507i) q^{23} +(1.68511 - 0.451523i) q^{24} +(-4.83822 + 1.26160i) q^{25} +(1.77158 - 0.180816i) q^{26} +(-3.40171 - 3.40171i) q^{27} +(3.22719 - 5.58966i) q^{28} +(-8.24134 - 4.75814i) q^{29} +(1.02922 + 0.139021i) q^{30} +(4.81595 + 4.81595i) q^{31} +(4.32351 - 2.49618i) q^{32} +(-0.560059 + 0.323350i) q^{33} +(-0.829273 - 0.829273i) q^{34} +(6.53707 - 4.98125i) q^{35} +(-3.21748 - 1.85761i) q^{36} +(-0.917615 + 1.58936i) q^{37} +(-1.91290 - 1.91290i) q^{38} +(2.62860 + 2.14172i) q^{39} +(4.11449 - 0.527621i) q^{40} +(-0.534988 + 0.143350i) q^{41} +(-1.64896 + 0.441838i) q^{42} +(-0.560778 + 2.09285i) q^{43} +(-0.853919 + 0.853919i) q^{44} +(-2.86727 - 3.76281i) q^{45} +(-0.646078 - 0.173116i) q^{46} -3.80918 q^{47} +(2.35797 + 0.631815i) q^{48} +(-3.25462 + 5.63717i) q^{49} +(2.38101 + 0.655176i) q^{50} -2.23297i q^{51} +(5.77640 + 2.59266i) q^{52} +(-2.47293 + 2.47293i) q^{53} +(0.614963 + 2.29507i) q^{54} +(-1.42264 + 0.583682i) q^{55} +(-5.90499 + 3.40925i) q^{56} -5.15084i q^{57} +(2.35005 + 4.07041i) q^{58} +(-2.69310 + 10.0508i) q^{59} +(2.92199 + 2.25776i) q^{60} +(-3.09904 - 5.36770i) q^{61} +(-0.870630 - 3.24924i) q^{62} +(6.73428 + 3.88804i) q^{63} +2.72601 q^{64} +(5.51234 + 5.88338i) q^{65} +0.319406 q^{66} +(-10.6066 - 6.12371i) q^{67} +(-1.07921 - 4.02768i) q^{68} +(-0.636768 - 1.10291i) q^{69} +(-4.02624 + 0.516303i) q^{70} +(-1.73500 + 6.47512i) q^{71} +(1.96240 + 3.39898i) q^{72} -3.37642i q^{73} +(0.784986 - 0.453212i) q^{74} +(2.32356 + 4.08774i) q^{75} +(-2.48945 - 9.29074i) q^{76} +(1.78728 - 1.78728i) q^{77} +(-0.595435 - 1.56521i) q^{78} +3.12149i q^{79} +(5.35521 + 2.23932i) q^{80} +(0.911483 - 1.57873i) q^{81} +(0.264231 + 0.0708006i) q^{82} +2.13918 q^{83} +(-5.86286 - 1.57095i) q^{84} +(0.710723 - 5.26175i) q^{85} +(0.756694 - 0.756694i) q^{86} +(-2.31619 + 8.64414i) q^{87} +(1.23228 - 0.330188i) q^{88} +(3.26255 - 0.874198i) q^{89} +(0.297190 + 2.31755i) q^{90} +(-12.0902 - 5.42653i) q^{91} +(-1.68161 - 1.68161i) q^{92} +(3.20242 - 5.54675i) q^{93} +(1.62931 + 0.940681i) q^{94} +(1.63944 - 12.1374i) q^{95} +(-3.31972 - 3.31972i) q^{96} +(6.12606 - 3.53688i) q^{97} +(2.78421 - 1.60746i) q^{98} +(-1.02878 - 1.02878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9	\( 20 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - 8 q^{6} - 2 q^{7} + 12 q^{9} - 2 q^{10} - 16 q^{11} - 24 q^{12} - 4 q^{13} - 20 q^{15} - 2 q^{16} + 4 q^{17} - 20 q^{19} + 4 q^{21} + 16 q^{22} - 10 q^{23} + 32 q^{24} + 18 q^{25} - 24 q^{26} + 4 q^{27} + 18 q^{28} - 26 q^{30} + 48 q^{32} + 18 q^{33} + 2 q^{34} + 40 q^{35} + 36 q^{36} - 4 q^{37} - 8 q^{38} + 4 q^{39} - 16 q^{40} + 10 q^{41} + 40 q^{42} + 10 q^{43} - 36 q^{44} + 4 q^{46} - 40 q^{47} - 56 q^{48} + 18 q^{49} + 36 q^{50} - 30 q^{52} - 10 q^{53} - 48 q^{54} - 10 q^{55} - 16 q^{59} + 28 q^{60} - 16 q^{61} - 44 q^{62} - 36 q^{63} + 20 q^{64} - 14 q^{65} - 32 q^{66} + 18 q^{67} + 22 q^{68} - 16 q^{69} - 12 q^{70} - 16 q^{71} + 4 q^{72} + 18 q^{74} - 38 q^{75} - 64 q^{76} - 28 q^{77} + 68 q^{78} - 2 q^{80} - 14 q^{81} + 56 q^{82} + 48 q^{83} - 40 q^{84} - 26 q^{85} + 60 q^{86} - 34 q^{87} + 82 q^{88} - 6 q^{89} + 46 q^{90} + 8 q^{91} - 8 q^{92} + 32 q^{93} - 48 q^{94} - 26 q^{95} + 56 q^{96} + 66 q^{97} - 30 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - 8 * q^6 - 2 * q^7 + 12 * q^9 - 2 * q^10 - 16 * q^11 - 24 * q^12 - 4 * q^13 - 20 * q^15 - 2 * q^16 + 4 * q^17 - 20 * q^19 + 4 * q^21 + 16 * q^22 - 10 * q^23 + 32 * q^24 + 18 * q^25 - 24 * q^26 + 4 * q^27 + 18 * q^28 - 26 * q^30 + 48 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 + 36 * q^36 - 4 * q^37 - 8 * q^38 + 4 * q^39 - 16 * q^40 + 10 * q^41 + 40 * q^42 + 10 * q^43 - 36 * q^44 + 4 * q^46 - 40 * q^47 - 56 * q^48 + 18 * q^49 + 36 * q^50 - 30 * q^52 - 10 * q^53 - 48 * q^54 - 10 * q^55 - 16 * q^59 + 28 * q^60 - 16 * q^61 - 44 * q^62 - 36 * q^63 + 20 * q^64 - 14 * q^65 - 32 * q^66 + 18 * q^67 + 22 * q^68 - 16 * q^69 - 12 * q^70 - 16 * q^71 + 4 * q^72 + 18 * q^74 - 38 * q^75 - 64 * q^76 - 28 * q^77 + 68 * q^78 - 2 * q^80 - 14 * q^81 + 56 * q^82 + 48 * q^83 - 40 * q^84 - 26 * q^85 + 60 * q^86 - 34 * q^87 + 82 * q^88 - 6 * q^89 + 46 * q^90 + 8 * q^91 - 8 * q^92 + 32 * q^93 - 48 * q^94 - 26 * q^95 + 56 * q^96 + 66 * q^97 - 30 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more