LMFDB - Embedded newform 65.2.t.a.37.2

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			37.2
Root			$1.02262i$ of defining polynomial
Character	$\chi$	$=$	65.37
Dual form			65.2.t.a.58.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.885613 + 0.511309i) q^{2} +(2.69193 + 0.721300i) q^{3} +(-0.477126 + 0.826407i) q^{4} +(-1.45744 - 1.69584i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(-0.481787 + 0.834479i) q^{7} -3.02107i q^{8} +(4.12812 + 2.38337i) q^{9} +O(q^{10})$	\(q+(-0.885613 + 0.511309i) q^{2} +(2.69193 + 0.721300i) q^{3} +(-0.477126 + 0.826407i) q^{4} +(-1.45744 - 1.69584i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(-0.481787 + 0.834479i) q^{7} -3.02107i q^{8} +(4.12812 + 2.38337i) q^{9} +(2.15782 + 0.756660i) q^{10} +(1.60661 + 0.430490i) q^{11} +(-1.88048 + 1.88048i) q^{12} +(-3.11175 - 1.82127i) q^{13} -0.985368i q^{14} +(-2.70010 - 5.61633i) q^{15} +(0.590448 + 1.02269i) q^{16} +(-1.87656 - 7.00342i) q^{17} -4.87456 q^{18} +(0.707496 + 2.64041i) q^{19} +(2.09684 - 0.395304i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(-1.64295 + 0.440226i) q^{22} +(-0.997344 + 3.72214i) q^{23} +(2.17910 - 8.13250i) q^{24} +(-0.751762 + 4.94316i) q^{25} +(3.68704 + 0.0218799i) q^{26} +(3.48159 + 3.48159i) q^{27} +(-0.459747 - 0.796304i) q^{28} +(-0.253107 + 0.146132i) q^{29} +(5.26292 + 3.59331i) q^{30} +(-0.125649 - 0.125649i) q^{31} +(4.18683 + 2.41727i) q^{32} +(4.01436 + 2.31769i) q^{33} +(5.24282 + 5.24282i) q^{34} +(2.11732 - 0.399166i) q^{35} +(-3.93927 + 2.27434i) q^{36} +(2.04061 + 3.53443i) q^{37} +(-1.97663 - 1.97663i) q^{38} +(-7.06291 - 7.14724i) q^{39} +(-5.12326 + 4.40302i) q^{40} +(-1.79277 + 6.69071i) q^{41} +(0.710745 - 2.65254i) q^{42} +(7.67707 - 2.05706i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(-1.97465 - 10.4743i) q^{45} +(-1.01990 - 3.80633i) q^{46} -7.84582 q^{47} +(0.851780 + 3.17888i) q^{48} +(3.03576 + 5.25810i) q^{49} +(-1.86171 - 4.76211i) q^{50} -20.2063i q^{51} +(2.98981 - 1.70259i) q^{52} +(-1.99855 + 1.99855i) q^{53} +(-4.86351 - 1.30317i) q^{54} +(-1.61149 - 3.35197i) q^{55} +(2.52102 + 1.45551i) q^{56} +7.61811i q^{57} +(0.149437 - 0.258832i) q^{58} +(-4.87924 + 1.30739i) q^{59} +(5.92967 + 0.448318i) q^{60} +(-1.04169 + 1.80425i) q^{61} +(0.175522 + 0.0470311i) q^{62} +(-3.97775 + 2.29655i) q^{63} -7.30568 q^{64} +(1.44658 + 7.93142i) q^{65} -4.74023 q^{66} +(6.32050 - 3.64915i) q^{67} +(6.68304 + 1.79071i) q^{68} +(-5.36956 + 9.30034i) q^{69} +(-1.67103 + 1.43611i) q^{70} +(12.6082 - 3.37837i) q^{71} +(7.20034 - 12.4713i) q^{72} -3.22747i q^{73} +(-3.61437 - 2.08676i) q^{74} +(-5.58919 + 12.7644i) q^{75} +(-2.51962 - 0.675130i) q^{76} +(-1.13328 + 1.13328i) q^{77} +(9.90945 + 2.71836i) q^{78} -13.5845i q^{79} +(0.873774 - 2.49180i) q^{80} +(-0.289196 - 0.500902i) q^{81} +(-1.83332 - 6.84204i) q^{82} -8.56854 q^{83} +(-0.663230 - 2.47521i) q^{84} +(-9.14173 + 13.3894i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(-0.786751 + 0.210809i) q^{87} +(1.30054 - 4.85368i) q^{88} +(-0.134207 + 0.500868i) q^{89} +(7.10435 + 8.26648i) q^{90} +(3.01901 - 1.71922i) q^{91} +(-2.60014 - 2.60014i) q^{92} +(-0.247608 - 0.428870i) q^{93} +(6.94836 - 4.01164i) q^{94} +(3.44659 - 5.04803i) q^{95} +(9.52707 + 9.52707i) q^{96} +(-6.50662 - 3.75660i) q^{97} +(-5.37702 - 3.10442i) q^{98} +(5.60626 + 5.60626i) 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 $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.885613	+	0.511309i	−0.626223	+	0.361550i	−0.779288	−	0.626666i	$-0.784419\pi$
$2$	−0.885613	+	0.511309i	−0.626223	+	0.361550i	0.153065	+	0.988216i	$0.451086\pi$
$3$	2.69193	+	0.721300i	1.55418	+	0.416443i	0.930817	−	0.365486i	$-0.119097\pi$
$3$	2.69193	+	0.721300i	1.55418	+	0.416443i	0.623368	+	0.781929i	$0.285764\pi$
$4$	−0.477126	+	0.826407i	−0.238563	+	0.413204i
$5$	−1.45744	−	1.69584i	−0.651785	−	0.758404i
$5$	−1.45744	−	1.69584i	−0.651785	−	0.758404i
$6$	−2.75281	+	0.737614i	−1.12383	+	0.301130i
$7$	−0.481787	+	0.834479i	−0.182098	+	0.315404i	−0.942595	−	0.333938i	$-0.891622\pi$
$7$	−0.481787	+	0.834479i	−0.182098	+	0.315404i	0.760497	+	0.649342i	$0.224956\pi$
$8$		−	3.02107i		−	1.06811i
$9$	4.12812	+	2.38337i	1.37604	+	0.794457i
$10$	2.15782	+	0.756660i	0.682364	+	0.239277i
$11$	1.60661	+	0.430490i	0.484411	+	0.129797i	0.492756	−	0.870168i	$-0.335990\pi$
$11$	1.60661	+	0.430490i	0.484411	+	0.129797i	−0.00834492	+	0.999965i	$0.502656\pi$
$12$	−1.88048	+	1.88048i	−0.542847	+	0.542847i
$13$	−3.11175	−	1.82127i	−0.863043	−	0.505130i
$13$	−3.11175	−	1.82127i	−0.863043	−	0.505130i
$14$		−	0.985368i		−	0.263351i
$15$	−2.70010	−	5.61633i	−0.697163	−	1.45013i
$16$	0.590448	+	1.02269i	0.147612	+	0.255671i
$17$	−1.87656	−	7.00342i	−0.455133	−	1.69858i	−0.687697	−	0.725998i	$-0.741378\pi$
$17$	−1.87656	−	7.00342i	−0.455133	−	1.69858i	0.232564	−	0.972581i	$-0.425289\pi$
$18$	−4.87456			−1.14894
$19$	0.707496	+	2.64041i	0.162311	+	0.605752i	0.998368	+	0.0571095i	$0.0181884\pi$
$19$	0.707496	+	2.64041i	0.162311	+	0.605752i	−0.836057	+	0.548642i	$0.815145\pi$
$20$	2.09684	−	0.395304i	0.468867	−	0.0883927i
$21$	−1.89884	+	1.89884i	−0.414362	+	0.414362i
$22$	−1.64295	+	0.440226i	−0.350277	+	0.0938565i
$23$	−0.997344	+	3.72214i	−0.207961	+	0.776120i	0.780566	+	0.625073i	$0.214931\pi$
$23$	−0.997344	+	3.72214i	−0.207961	+	0.776120i	−0.988527	+	0.151046i	$0.951736\pi$
$24$	2.17910	−	8.13250i	0.444806	−	1.66004i
$25$	−0.751762	+	4.94316i	−0.150352	+	0.988632i
$26$	3.68704	+	0.0218799i	0.723087	+	0.00429099i
$27$	3.48159	+	3.48159i	0.670033	+	0.670033i
$28$	−0.459747	−	0.796304i	−0.0868839	−	0.150487i
$29$	−0.253107	+	0.146132i	−0.0470008	+	0.0271360i	−0.523316	−	0.852139i	$-0.675305\pi$
$29$	−0.253107	+	0.146132i	−0.0470008	+	0.0271360i	0.476315	+	0.879274i	$0.341972\pi$
$30$	5.26292	+	3.59331i	0.960874	+	0.656046i
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	0.695733	−	0.718300i	$-0.255080\pi$
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	−0.718300	+	0.695733i	$0.755080\pi$
$32$	4.18683	+	2.41727i	0.740134	+	0.427317i
$33$	4.01436	+	2.31769i	0.698811	+	0.403458i
$34$	5.24282	+	5.24282i	0.899136	+	0.899136i
$35$	2.11732	−	0.399166i	0.357892	−	0.0674713i
$36$	−3.93927	+	2.27434i	−0.656545	+	0.379057i
$37$	2.04061	+	3.53443i	0.335474	+	0.581057i	0.983576	−	0.180496i	$-0.0577703\pi$
$37$	2.04061	+	3.53443i	0.335474	+	0.581057i	−0.648102	+	0.761553i	$0.724437\pi$
$38$	−1.97663	−	1.97663i	−0.320652	−	0.320652i
$39$	−7.06291	−	7.14724i	−1.13097	−	1.14447i
$40$	−5.12326	+	4.40302i	−0.810059	+	0.696178i
$41$	−1.79277	+	6.69071i	−0.279984	+	1.04491i	0.672444	+	0.740148i	$0.265245\pi$
$41$	−1.79277	+	6.69071i	−0.279984	+	1.04491i	−0.952427	+	0.304765i	$0.901422\pi$
$42$	0.710745	−	2.65254i	0.109670	−	0.409295i
$43$	7.67707	−	2.05706i	1.17074	−	0.313699i	0.379494	−	0.925194i	$-0.376098\pi$
$43$	7.67707	−	2.05706i	1.17074	−	0.313699i	0.791248	+	0.611495i	$0.209432\pi$
$44$	−1.12232	+	1.12232i	−0.169195	+	0.169195i
$45$	−1.97465	−	10.4743i	−0.294363	−	1.56141i
$46$	−1.01990	−	3.80633i	−0.150376	−	0.561212i
$47$	−7.84582			−1.14443			−0.572215	−	0.820103i	$-0.693916\pi$
$47$	−7.84582			−1.14443			−0.572215	+	0.820103i	$0.693916\pi$
$48$	0.851780	+	3.17888i	0.122944	+	0.458832i
$49$	3.03576	+	5.25810i	0.433680	+	0.751156i
$50$	−1.86171	−	4.76211i	−0.263286	−	0.673464i
$51$		−	20.2063i		−	2.82944i
$52$	2.98981	−	1.70259i	0.414612	−	0.236107i
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	−0.830918	−	0.556395i	$-0.812184\pi$
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	0.556395	+	0.830918i	$0.312184\pi$
$54$	−4.86351	−	1.30317i	−0.661840	−	0.177339i
$55$	−1.61149	−	3.35197i	−0.217293	−	0.451979i
$56$	2.52102	+	1.45551i	0.336886	+	0.194501i
$57$			7.61811i			1.00904i
$58$	0.149437	−	0.258832i	0.0196220	−	0.0339863i
$59$	−4.87924	+	1.30739i	−0.635223	+	0.170207i	−0.562039	−	0.827111i	$-0.689983\pi$
$59$	−4.87924	+	1.30739i	−0.635223	+	0.170207i	−0.0731843	+	0.997318i	$0.523316\pi$
$60$	5.92967	+	0.448318i	0.765517	+	0.0578776i
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	−0.924975	−	0.380027i	$-0.875915\pi$
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	0.791601	+	0.611038i	$0.209248\pi$
$62$	0.175522	+	0.0470311i	0.0222914	+	0.00597296i
$63$	−3.97775	+	2.29655i	−0.501149	+	0.289339i
$64$	−7.30568			−0.913209
$65$	1.44658	+	7.93142i	0.179426	+	0.983771i
$66$	−4.74023			−0.583482
$67$	6.32050	−	3.64915i	0.772173	−	0.445814i	−0.0614765	−	0.998109i	$-0.519581\pi$
$67$	6.32050	−	3.64915i	0.772173	−	0.445814i	0.833649	+	0.552294i	$0.186248\pi$
$68$	6.68304	+	1.79071i	0.810437	+	0.217156i
$69$	−5.36956	+	9.30034i	−0.646419	+	1.11963i
$70$	−1.67103	+	1.43611i	−0.199726	+	0.171648i
$71$	12.6082	−	3.37837i	1.49632	−	0.400939i	0.584457	−	0.811425i	$-0.301308\pi$
$71$	12.6082	−	3.37837i	1.49632	−	0.400939i	0.911867	+	0.410486i	$0.134641\pi$
$72$	7.20034	−	12.4713i	0.848568	−	1.46976i
$73$		−	3.22747i		−	0.377746i	−0.982001	−	0.188873i	$-0.939517\pi$
$73$		−	3.22747i		−	0.377746i	0.982001	−	0.188873i	$-0.0604835\pi$
$74$	−3.61437	−	2.08676i	−0.420163	−	0.242581i
$75$	−5.58919	+	12.7644i	−0.645384	+	1.47390i
$76$	−2.51962	−	0.675130i	−0.289020	−	0.0774427i
$77$	−1.13328	+	1.13328i	−0.129149	+	0.129149i
$78$	9.90945	+	2.71836i	1.12202	+	0.307793i
$79$		−	13.5845i		−	1.52838i	−0.644992	−	0.764190i	$-0.723139\pi$
$79$		−	13.5845i		−	1.52838i	0.644992	−	0.764190i	$-0.276861\pi$
$80$	0.873774	−	2.49180i	0.0976909	−	0.278592i
$81$	−0.289196	−	0.500902i	−0.0321329	−	0.0556558i
$82$	−1.83332	−	6.84204i	−0.202456	−	0.755577i
$83$	−8.56854			−0.940519			−0.470260	−	0.882528i	$-0.655840\pi$
$83$	−8.56854			−0.940519			−0.470260	+	0.882528i	$0.655840\pi$
$84$	−0.663230	−	2.47521i	−0.0723643	−	0.270067i
$85$	−9.14173	+	13.3894i	−0.991560	+	1.45228i
$86$	−5.74712	+	5.74712i	−0.619728	+	0.619728i
$87$	−0.786751	+	0.210809i	−0.0843486	+	0.0226011i
$88$	1.30054	−	4.85368i	0.138638	−	0.517404i
$89$	−0.134207	+	0.500868i	−0.0142259	+	0.0530919i	−0.972674	−	0.232175i	$-0.925416\pi$
$89$	−0.134207	+	0.500868i	−0.0142259	+	0.0530919i	0.958448	+	0.285267i	$0.0920823\pi$
$90$	7.10435	+	8.26648i	0.748864	+	0.871363i
$91$	3.01901	−	1.71922i	0.316479	−	0.180223i
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$	−0.247608	−	0.428870i	−0.0256758	−	0.0444718i
$94$	6.94836	−	4.01164i	0.716669	−	0.413769i
$95$	3.44659	−	5.04803i	0.353613	−	0.517917i
$96$	9.52707	+	9.52707i	0.972353	+	0.972353i
$97$	−6.50662	−	3.75660i	−0.660648	−	0.381425i	0.131876	−	0.991266i	$-0.457900\pi$
$97$	−6.50662	−	3.75660i	−0.660648	−	0.381425i	−0.792524	+	0.609841i	$0.791233\pi$
$98$	−5.37702	−	3.10442i	−0.543161	−	0.313594i
$99$	5.60626	+	5.60626i	0.563450	+	0.563450i
$100$	−3.72638	−	2.97978i	−0.372638	−	0.297978i
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	−0.0169388	−	0.999857i	$-0.505392\pi$
$101$	8.44685	−	4.87679i	0.840493	−	0.485259i	0.857432	+	0.514598i	$0.172059\pi$
$102$	10.3316	+	17.8949i	1.02298	+	1.77186i
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	0.820404	−	0.571784i	$-0.193749\pi$
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	−0.571784	+	0.820404i	$0.693749\pi$
$104$	−5.50220	+	9.40081i	−0.539535	+	0.921825i
$105$	5.98759	+	0.452697i	0.584329	+	0.0441787i
$106$	0.748066	−	2.79182i	0.0726586	−	0.271166i
$107$	−0.115046	+	0.429359i	−0.0111220	+	0.0415077i	−0.971264	−	0.238005i	$-0.923506\pi$
$107$	−0.115046	+	0.429359i	−0.0111220	+	0.0415077i	0.960142	+	0.279513i	$0.0901731\pi$
$108$	−4.53837	+	1.21605i	−0.436705	+	0.117015i
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	−0.329206	−	0.944258i	$-0.606781\pi$
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	0.944258	+	0.329206i	$0.106781\pi$
$110$	3.14104	+	2.14458i	0.299487	+	0.204477i
$111$	2.94378	+	10.9863i	0.279411	+	1.04278i
$112$	−1.13788			−0.107520
$113$	0.500704	+	1.86865i	0.0471023	+	0.175788i	0.985470	−	0.169851i	$-0.0543287\pi$
$113$	0.500704	+	1.86865i	0.0471023	+	0.175788i	−0.938367	+	0.345639i	$0.887662\pi$
$114$	−3.89521	−	6.74670i	−0.364820	−	0.631886i
$115$	7.76573	−	3.73344i	0.724158	−	0.348145i
$116$		−	0.278893i		−	0.0258946i
$117$	−8.50489	−	14.9349i	−0.786277	−	1.38073i
$118$	3.65264	−	3.65264i	0.336253	−	0.336253i
$119$	6.74831	+	1.80821i	0.618617	+	0.165758i
$120$	−16.9673	+	8.15720i	−1.54890	+	0.744647i
$121$	−7.13041	−	4.11674i	−0.648219	−	0.374249i
$122$		−	2.13050i		−	0.192886i
$123$	−9.65202	+	16.7178i	−0.870293	+	1.50739i
$124$	0.163788	−	0.0438869i	0.0147086	−	0.00394116i
$125$	9.47847	−	5.92947i	0.847780	−	0.530348i
$126$	2.34850	−	4.06772i	0.209221	−	0.362381i
$127$	−2.10102	−	0.562967i	−0.186436	−	0.0499553i	0.164393	−	0.986395i	$-0.447433\pi$
$127$	−2.10102	−	0.562967i	−0.186436	−	0.0499553i	−0.350829	+	0.936440i	$0.614100\pi$
$128$	−1.90366	+	1.09908i	−0.168262	+	0.0971460i
$129$	22.1499			1.95019
$130$	−5.33651	−	6.28452i	−0.468043	−	0.551189i
$131$	−0.0622493			−0.00543874			−0.00271937	−	0.999996i	$-0.500866\pi$
$131$	−0.0622493			−0.00543874			−0.00271937	+	0.999996i	$0.500866\pi$
$132$	−3.83072	+	2.21166i	−0.333421	+	0.192501i
$133$	−2.54423	−	0.681725i	−0.220613	−	0.0591130i
$134$	−3.73168	+	6.46346i	−0.322368	+	0.558358i
$135$	0.830034	−	10.9784i	0.0714380	−	0.944872i
$136$	−21.1578	+	5.66923i	−1.81427	+	0.486132i
$137$	2.20873	−	3.82564i	0.188705	−	0.326846i	−0.756114	−	0.654440i	$-0.772904\pi$
$137$	2.20873	−	3.82564i	0.188705	−	0.326846i	0.944819	+	0.327594i	$0.106238\pi$
$138$		−	10.9820i		−	0.934850i
$139$	−11.9066	−	6.87430i	−1.00991	−	0.583070i	−0.0987430	−	0.995113i	$-0.531482\pi$
$139$	−11.9066	−	6.87430i	−1.00991	−	0.583070i	−0.911165	+	0.412043i	$0.864816\pi$
$140$	−0.680356	+	1.94022i	−0.0575005	+	0.163979i
$141$	−21.1204	−	5.65919i	−1.77866	−	0.476590i
$142$	−9.43864	+	9.43864i	−0.792073	+	0.792073i
$143$	−4.21532	−	4.26565i	−0.352503	−	0.356711i
$144$			5.62903i			0.469085i
$145$	0.616704	+	0.216253i	0.0512145	+	0.0179588i
$146$	1.65023	+	2.85829i	0.136574	+	0.236553i
$147$	4.37939	+	16.3441i	0.361206	+	1.34804i
$148$	−3.89451			−0.320127
$149$	1.12129	+	4.18471i	0.0918596	+	0.342825i	0.996525	−	0.0832987i	$-0.0265456\pi$
$149$	1.12129	+	4.18471i	0.0918596	+	0.342825i	−0.904665	+	0.426124i	$0.859879\pi$
$150$	−1.57669	−	14.1621i	−0.128736	−	1.15633i
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	−0.486910	−	0.873452i	$-0.661876\pi$
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	0.873452	+	0.486910i	$0.161876\pi$
$152$	7.97687	−	2.13740i	0.647010	−	0.173366i
$153$	8.94508	−	33.3835i	0.723167	−	2.69890i
$154$	0.424190	−	1.58310i	0.0341822	−	0.127570i
$155$	−0.0299556	+	0.396208i	−0.00240610	+	0.0318242i
$156$	9.27643	−	2.42670i	0.742709	−	0.194292i
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.985920	+	0.167218i	$0.0534784\pi$
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.167218	+	0.985920i	$0.446522\pi$
$158$	6.94589	+	12.0306i	0.552586	+	0.957106i
$159$	−6.82151	+	3.93840i	−0.540981	+	0.312336i
$160$	−2.00273	−	10.6232i	−0.158330	−	0.839839i
$161$	−2.62554	−	2.62554i	−0.206922	−	0.206922i
$162$	0.512231	+	0.295737i	0.0402447	+	0.0232353i
$163$	18.5201	+	10.6926i	1.45061	+	0.837508i	0.998516	−	0.0544633i	$-0.0173448\pi$
$163$	18.5201	+	10.6926i	1.45061	+	0.837508i	0.452091	+	0.891972i	$0.350678\pi$
$164$	−4.67387	−	4.67387i	−0.364968	−	0.364968i
$165$	−1.92023	−	10.1856i	−0.149490	−	0.792949i
$166$	7.58841	−	4.38117i	0.588975	−	0.340045i
$167$	0.857220	+	1.48475i	0.0663337	+	0.114893i	0.897285	−	0.441452i	$-0.145536\pi$
$167$	0.857220	+	1.48475i	0.0663337	+	0.114893i	−0.830951	+	0.556345i	$0.812203\pi$
$168$	5.73655	+	5.73655i	0.442584	+	0.442584i
$169$	6.36593	+	11.3347i	0.489687	+	0.871898i
$170$	1.24992	−	16.5321i	0.0958646	−	1.26795i
$171$	−3.37245	+	12.5862i	−0.257898	+	0.962488i
$172$	−1.96296	+	7.32587i	−0.149674	+	0.558592i
$173$	−14.6596	+	3.92804i	−1.11455	+	0.298643i	−0.768677	−	0.639638i	$-0.779084\pi$
$173$	−14.6596	+	3.92804i	−1.11455	+	0.298643i	−0.345875	+	0.938281i	$0.612418\pi$
$174$	0.588968	−	0.588968i	0.0446496	−	0.0446496i
$175$	−3.76278	−	3.00888i	−0.284439	−	0.227450i
$176$	0.508363	+	1.89724i	0.0383193	+	0.143010i
$177$	−14.0776			−1.05814
$178$	−0.137243	−	0.512196i	−0.0102868	−	0.0383907i
$179$	−1.37961	−	2.38956i	−0.103117	−	0.178604i	0.809850	−	0.586637i	$-0.199548\pi$
$179$	−1.37961	−	2.38956i	−0.103117	−	0.178604i	−0.912967	+	0.408033i	$0.866215\pi$
$180$	9.59815	+	3.36568i	0.715404	+	0.250863i
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$	−1.79462	+	3.06621i	−0.133026	+	0.227283i
$183$	−4.10555	+	4.10555i	−0.303491	+	0.303491i
$184$	11.2449	+	3.01305i	0.828981	+	0.222125i
$185$	3.01979	−	8.61176i	0.222019	−	0.633149i
$186$	0.438570	+	0.253209i	0.0321575	+	0.0185662i
$187$		−	12.0596i		−	0.881885i
$188$	3.74345	−	6.48384i	0.273019	−	0.472883i
$189$	−4.58270	+	1.22793i	−0.333342	+	0.0893188i
$190$	−0.471242	+	6.23287i	−0.0341875	+	0.452180i
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	0.305093	+	0.952322i	$0.401312\pi$
$191$	−9.28983	+	16.0905i	−0.672189	+	1.16427i	−0.977282	+	0.211943i	$0.932021\pi$
$192$	−19.6663	−	5.26958i	−1.41930	−	0.380299i
$193$	−10.8872	+	6.28576i	−0.783681	+	0.452459i	−0.837733	−	0.546079i	$-0.816120\pi$
$193$	−10.8872	+	6.28576i	−0.783681	+	0.452459i	0.0540520	+	0.998538i	$0.482786\pi$
$194$	7.68313			0.551617
$195$	−1.82685	+	22.3942i	−0.130823	+	1.60368i
$196$	−5.79377			−0.413841
$197$	12.3722	−	7.14308i	0.881481	−	0.508924i	0.0103349	−	0.999947i	$-0.496710\pi$
$197$	12.3722	−	7.14308i	0.881481	−	0.508924i	0.871147	+	0.491023i	$0.163377\pi$
$198$	−7.83150	−	2.09845i	−0.556561	−	0.149130i
$199$	7.36781	−	12.7614i	0.522291	−	0.904634i	−0.477373	−	0.878701i	$-0.658411\pi$
$199$	7.36781	−	12.7614i	0.522291	−	0.904634i	0.999664	−	0.0259331i	$-0.00825568\pi$
$200$	14.9336	+	2.27113i	1.05597	+	0.160593i
$201$	19.6465	−	5.26425i	1.38575	−	0.371312i
$202$	−4.98709	+	8.63790i	−0.350891	+	0.607760i
$203$		−	0.281617i		−	0.0197656i
$204$	16.6986	+	9.64094i	1.16914	+	0.675001i
$205$	13.9592	−	6.71103i	0.974956	−	0.468718i
$206$	−3.52473	−	0.944449i	−0.245580	−	0.0658029i
$207$	−12.9884	+	12.9884i	−0.902756	+	0.902756i
$208$	0.0252664	−	4.25770i	0.00175191	−	0.295219i
$209$			4.54668i			0.314500i
$210$	−5.53415	+	2.66059i	−0.381893	+	0.183598i
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	0.974678	−	0.223611i	$-0.0717845\pi$
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	−0.680992	+	0.732291i	$0.738451\pi$
$212$	−0.698056	−	2.60518i	−0.0479427	−	0.178925i
$213$	36.3773			2.49253
$214$	−0.117649	−	0.439070i	−0.00804229	−	0.0300142i
$215$	−14.6773	−	10.0211i	−1.00098	−	0.683431i
$216$	10.5181	−	10.5181i	0.715669	−	0.715669i
$217$	0.165388	−	0.0443156i	0.0112273	−	0.00300834i
$218$	−2.40353	+	8.97011i	−0.162788	+	0.607532i
$219$	2.32797	−	8.68810i	0.157310	−	0.587087i
$220$	3.53897	+	0.267567i	0.238597	+	0.0180394i
$221$	−6.91576	+	25.2106i	−0.465205	+	1.69585i
$222$	−8.22445	−	8.22445i	−0.551989	−	0.551989i
$223$	−3.53040	−	6.11483i	−0.236413	−	0.409479i	0.723269	−	0.690566i	$-0.242638\pi$
$223$	−3.53040	−	6.11483i	−0.236413	−	0.409479i	−0.959682	+	0.281087i	$0.909305\pi$
$224$	−4.03432	+	2.32922i	−0.269555	+	0.155627i
$225$	−14.8848	+	18.6142i	−0.992317	+	1.24095i
$226$	−1.39889	−	1.39889i	−0.0930527	−	0.0930527i
$227$	14.8744	+	8.58775i	0.987249	+	0.569989i	0.904451	−	0.426578i	$-0.140281\pi$
$227$	14.8744	+	8.58775i	0.987249	+	0.569989i	0.0827985	+	0.996566i	$0.473614\pi$
$228$	−6.29566	−	3.63480i	−0.416940	−	0.240721i
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	0.348684	−	0.937240i	$-0.386629\pi$
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	−0.937240	+	0.348684i	$0.886629\pi$
$230$	−4.96849	+	7.27707i	−0.327612	+	0.479836i
$231$	−3.86813	+	2.23327i	−0.254504	+	0.146938i
$232$	0.441474	+	0.764655i	0.0289842	+	0.0502021i
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.986182	−	0.165666i	$-0.947023\pi$
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.165666	−	0.986182i	$-0.552977\pi$
$234$	15.1684	+	8.87790i	0.991588	+	0.580366i
$235$	11.4348	+	13.3053i	0.745923	+	0.867940i
$236$	1.24758	−	4.65603i	0.0812105	−	0.303082i
$237$	9.79852	−	36.5686i	0.636482	−	2.37538i
$238$	−6.90095	+	1.84910i	−0.447322	+	0.119860i
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	−0.775684	−	0.631122i	$-0.782595\pi$
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	0.631122	+	0.775684i	$0.282595\pi$
$240$	4.14947	−	6.07750i	0.267847	−	0.392301i
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	−0.936825	−	0.349797i	$-0.886250\pi$
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	0.636416	−	0.771346i	$-0.280416\pi$
$242$	8.41971			0.541239
$243$	−4.24025	−	15.8248i	−0.272012	−	1.01516i
$244$	−0.994033	−	1.72172i	−0.0636364	−	0.110222i
$245$	4.49247	−	12.8115i	0.287013	−	0.818497i
$246$		−	19.7406i		−	1.25862i
$247$	2.60736	−	9.50483i	0.165902	−	0.604778i
$248$	−0.379596	+	0.379596i	−0.0241044	+	0.0241044i
$249$	−23.0659	−	6.18048i	−1.46174	−	0.391672i
$250$	−5.36246	+	10.0976i	−0.339152	+	0.638631i
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	0.830658	−	0.556782i	$-0.187964\pi$
$251$	12.1009	+	6.98644i	0.763800	+	0.440980i	−0.0668586	+	0.997762i	$0.521298\pi$
$252$		−	4.38299i		−	0.276102i
$253$	−3.20468	+	5.55068i	−0.201477	+	0.348968i
$254$	2.14854	−	0.575700i	0.134812	−	0.0361227i
$255$	−34.2666	+	29.4493i	−2.14586	+	1.84419i
$256$	8.42962	−	14.6005i	0.526851	−	0.912533i
$257$	−22.3881	−	5.99887i	−1.39653	−	0.374199i	−0.519433	−	0.854511i	$-0.673857\pi$
$257$	−22.3881	−	5.99887i	−1.39653	−	0.374199i	−0.877098	+	0.480312i	$0.840524\pi$
$258$	−19.6162	+	11.3254i	−1.22125	+	0.705090i
$259$	−3.93255			−0.244357
$260$	−7.24478	−	2.58883i	−0.449302	−	0.160552i
$261$	−1.39314			−0.0862334
$262$	0.0551288	−	0.0318286i	0.00340587	−	0.00196638i
$263$	−1.25672	−	0.336737i	−0.0774926	−	0.0207641i	0.219864	−	0.975530i	$-0.429438\pi$
$263$	−1.25672	−	0.336737i	−0.0774926	−	0.0207641i	−0.297357	+	0.954766i	$0.596105\pi$
$264$	7.00191	−	12.1277i	0.430938	−	0.746407i
$265$	6.30199	+	0.476468i	0.387128	+	0.0292692i
$266$	2.60178	−	0.697144i	0.159525	−	0.0427446i
$267$	−0.722551	+	1.25150i	−0.0442194	+	0.0765903i
$268$			6.96441i			0.425419i
$269$	−6.87429	−	3.96887i	−0.419133	−	0.241986i	0.275574	−	0.961280i	$-0.411132\pi$
$269$	−6.87429	−	3.96887i	−0.419133	−	0.241986i	−0.694706	+	0.719294i	$0.744466\pi$
$270$	4.87828	+	10.1470i	0.296883	+	0.617529i
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	0.232450	−	0.972608i	$-0.425326\pi$
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	−0.284997	+	0.958528i	$0.591993\pi$
$272$	6.05429	−	6.05429i	0.367095	−	0.367095i
$273$	9.36704	−	2.45041i	0.566919	−	0.148305i
$274$			4.51738i			0.272905i
$275$	−3.33577	+	7.61810i	−0.201154	+	0.459389i
$276$	−5.12391	−	8.87488i	−0.308423	−	0.534205i
$277$	2.47298	+	9.22930i	0.148587	+	0.554535i	0.999569	+	0.0293404i	$0.00934068\pi$
$277$	2.47298	+	9.22930i	0.148587	+	0.554535i	−0.850982	+	0.525194i	$0.823993\pi$
$278$	14.0596			0.843236
$279$	−0.219227	−	0.818165i	−0.0131248	−	0.0489823i
$280$	−1.20591	−	6.39657i	−0.0720668	−	0.382268i
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	−0.520651	−	0.853769i	$-0.674311\pi$
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	0.853769	+	0.520651i	$0.174311\pi$
$282$	21.5981	−	5.78719i	1.28615	−	0.344622i
$283$	−5.46218	+	20.3851i	−0.324693	+	1.21177i	0.589927	+	0.807457i	$0.299157\pi$
$283$	−5.46218	+	20.3851i	−0.324693	+	1.21177i	−0.914620	+	0.404314i	$0.867510\pi$
$284$	−3.22382	+	12.0315i	−0.191298	+	0.713936i
$285$	12.9191	−	11.1029i	0.765262	−	0.657679i
$286$	5.91420	+	1.62238i	0.349714	+	0.0959335i
$287$	−4.71953	−	4.71953i	−0.278585	−	0.278585i
$288$	11.5225	+	19.9576i	0.678970	+	1.17601i
$289$	−30.8040	+	17.7847i	−1.81200	+	1.04616i
$290$	−0.656733	+	0.123810i	−0.0385647	+	0.00727037i
$291$	−14.8057	−	14.8057i	−0.867927	−	0.867927i
$292$	2.66720	+	1.53991i	0.156086	+	0.0901164i
$293$	3.48280	+	2.01079i	0.203467	+	0.117472i	0.598272	−	0.801293i	$-0.295854\pi$
$293$	3.48280	+	2.01079i	0.203467	+	0.117472i	−0.394805	+	0.918765i	$0.629188\pi$
$294$	−12.2353	−	12.2353i	−0.713579	−	0.713579i
$295$	9.32830	+	6.36899i	0.543115	+	0.370817i
$296$	10.6778	−	6.16482i	0.620633	−	0.358323i
$297$	4.09477	+	7.09234i	0.237602	+	0.411539i
$298$	−3.13271	−	3.13271i	−0.181473	−	0.181473i
$299$	9.88252	−	9.76592i	0.571521	−	0.564778i
$300$	−7.88183	−	10.7092i	−0.455058	−	0.618294i
$301$	−1.98213	+	7.39742i	−0.114248	+	0.426380i
$302$	−1.77791	+	6.63524i	−0.102307	+	0.381815i
$303$	26.2559	−	7.03525i	1.50836	−	0.404165i
$304$	−2.28257	+	2.28257i	−0.130914	+	0.130914i
$305$	4.57792	−	0.863049i	0.262131	−	0.0494180i
$306$	9.14740	+	34.1386i	0.522922	+	1.95157i
$307$	24.2191			1.38226			0.691128	−	0.722732i	$-0.257114\pi$
$307$	24.2191			1.38226			0.691128	+	0.722732i	$0.257114\pi$
$308$	−0.395832	−	1.47727i	−0.0225546	−	0.0841750i
$309$	4.97231	+	8.61229i	0.282865	+	0.489936i
$310$	−0.176055	−	0.366203i	−0.00999927	−	0.0207989i
$311$		−	7.87243i		−	0.446405i	−0.974772	−	0.223202i	$-0.928349\pi$
$311$		−	7.87243i		−	0.446405i	0.974772	−	0.223202i	$-0.0716511\pi$
$312$	−21.5923	+	21.3376i	−1.22242	+	1.20800i
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	−0.604740	−	0.796423i	$-0.706723\pi$
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	0.796423	+	0.604740i	$0.206723\pi$
$314$	−20.1838	−	5.40824i	−1.13904	−	0.305204i
$315$	9.69191	+	3.39855i	0.546077	+	0.191487i
$316$	11.2264	+	6.48154i	0.631532	+	0.364615i
$317$			22.9255i			1.28762i	0.765184	+	0.643812i	$0.222648\pi$
$317$			22.9255i			1.28762i	−0.765184	+	0.643812i	$0.777352\pi$
$318$	4.02748	−	6.97580i	0.225850	−	0.391183i
$319$	−0.469553	+	0.125816i	−0.0262899	+	0.00704436i
$320$	10.6476	+	12.3893i	0.595216	+	0.692581i
$321$	−0.619393	+	1.07282i	−0.0345712	+	0.0598790i
$322$	3.66768	+	0.982751i	0.204392	+	0.0547666i
$323$	17.1643	−	9.90979i	0.955044	−	0.551395i
$324$	0.551932			0.0306629
$325$	11.3421	−	14.0127i	0.629149	−	0.777285i
$326$	−21.8689			−1.21120
$327$	21.9175	−	12.6541i	1.21204	−	0.699771i
$328$	20.2131	+	5.41609i	1.11608	+	0.299053i
$329$	3.78001	−	6.54718i	0.208399	−	0.360958i
$330$	6.90858	+	8.03868i	0.380305	+	0.442515i
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.990858	−	0.134910i	$-0.956925\pi$
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.790653	+	0.612264i	$0.790259\pi$
$332$	4.08828	−	7.08110i	0.224373	−	0.388626i
$333$			19.4541i			1.06608i
$334$	−1.51833	−	0.876609i	−0.0830794	−	0.0479659i
$335$	−15.4001	−	5.40018i	−0.841398	−	0.295044i
$336$	−3.06309	−	0.820752i	−0.167105	−	0.0447757i
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	−0.981953	−	0.189126i	$-0.939434\pi$
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	0.189126	+	0.981953i	$0.439434\pi$
$338$	−11.4333	−	6.78318i	−0.621888	−	0.368957i
$339$			5.39143i			0.292822i
$340$	−6.70333	−	13.9432i	−0.363539	−	0.756178i
$341$	−0.147779	−	0.255960i	−0.00800267	−	0.0138610i
$342$	−3.44873	−	12.8708i	−0.186486	−	0.695975i
$343$	−12.5954			−0.680087
$344$	−6.21454	−	23.1930i	−0.335065	−	1.25048i
$345$	23.5977	−	4.44873i	1.27046	−	0.239512i
$346$	10.9743	−	10.9743i	0.589983	−	0.589983i
$347$	−22.0356	+	5.90442i	−1.18293	+	0.316966i	−0.796089	−	0.605179i	$-0.793101\pi$
$347$	−22.0356	+	5.90442i	−1.18293	+	0.316966i	−0.386844	+	0.922145i	$0.626435\pi$
$348$	0.201165	−	0.750759i	0.0107836	−	0.0402449i
$349$	−2.68798	+	10.0317i	−0.143884	+	0.536983i	0.855918	+	0.517111i	$0.172992\pi$
$349$	−2.68798	+	10.0317i	−0.143884	+	0.536983i	−0.999803	+	0.0198718i	$0.993674\pi$
$350$	4.87083	+	0.740762i	0.260357	+	0.0395954i
$351$	−4.49290	−	17.1748i	−0.239813	−	0.916721i
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$	−2.15017	−	3.72420i	−0.114442	−	0.198219i	0.803115	−	0.595825i	$-0.203175\pi$
$353$	−2.15017	−	3.72420i	−0.114442	−	0.198219i	−0.917556	+	0.397605i	$0.869841\pi$
$354$	12.4673	−	7.19799i	0.662629	−	0.382569i
$355$	−24.1049	−	16.4578i	−1.27935	−	0.873491i
$356$	−0.349887	−	0.349887i	−0.0185440	−	0.0185440i
$357$	16.8617	+	9.73511i	0.892416	+	0.515237i
$358$	2.44361	+	1.41082i	0.129149	+	0.0745640i
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	0.376204	−	0.926537i	$-0.377229\pi$
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	−0.926537	+	0.376204i	$0.877229\pi$
$360$	−31.6435	+	5.96555i	−1.66776	+	0.314412i
$361$	9.98326	−	5.76384i	0.525435	−	0.303360i
$362$	−5.29555	−	9.17216i	−0.278328	−	0.482078i
$363$	−16.2251	−	16.2251i	−0.851599	−	0.851599i
$364$	−0.0196734	+	3.31522i	−0.00103117	+	0.173765i
$365$	−5.47327	+	4.70382i	−0.286484	+	0.246209i
$366$	1.53673	−	5.73514i	0.0803259	−	0.299780i
$367$	2.95657	−	11.0341i	0.154331	−	0.575973i	−0.844830	−	0.535034i	$-0.820299\pi$
$367$	2.95657	−	11.0341i	0.154331	−	0.575973i	0.999162	−	0.0409383i	$-0.0130347\pi$
$368$	−4.39546	+	1.17776i	−0.229129	+	0.0613950i
$369$	−23.3472	+	23.3472i	−1.21541	+	1.21541i
$370$	1.72890	+	9.17073i	0.0898814	+	0.476763i
$371$	−0.704874	−	2.63063i	−0.0365953	−	0.136575i
$372$	0.472562			0.0245012
$373$	7.28755	+	27.1975i	0.377335	+	1.40823i	0.849903	+	0.526939i	$0.176661\pi$
$373$	7.28755	+	27.1975i	0.377335	+	1.40823i	−0.472568	+	0.881294i	$0.656673\pi$
$374$	6.16618	+	10.6801i	0.318846	+	0.552257i
$375$	29.7923	−	9.12489i	1.53847	−	0.471207i
$376$			23.7028i			1.22238i
$377$	1.05375	+	0.00625324i	0.0542709	+	0.000322058i
$378$	3.43065	−	3.43065i	0.176453	−	0.176453i
$379$	16.3551	+	4.38232i	0.840103	+	0.225105i	0.653116	−	0.757258i	$-0.273461\pi$
$379$	16.3551	+	4.38232i	0.840103	+	0.225105i	0.186987	+	0.982362i	$0.440128\pi$
$380$	2.52727	+	5.25684i	0.129646	+	0.269670i
$381$	−5.24973	−	3.03093i	−0.268952	−	0.155279i
$382$		−	18.9999i		−	0.972119i
$383$	−3.30197	+	5.71918i	−0.168723	+	0.292236i	−0.937971	−	0.346714i	$-0.887298\pi$
$383$	−3.30197	+	5.71918i	−0.168723	+	0.292236i	0.769248	+	0.638950i	$0.220631\pi$
$384$	−5.91729	+	1.58553i	−0.301966	+	0.0809114i
$385$	3.57354	+	0.270181i	0.182124	+	0.0137697i
$386$	6.42793	−	11.1335i	0.327173	−	0.566680i
$387$	36.5946	+	9.80550i	1.86021	+	0.498441i
$388$	6.20897	−	3.58475i	0.315212	−	0.181988i
$389$	33.6949			1.70840			0.854199	−	0.519946i	$-0.174048\pi$
$389$	33.6949			1.70840			0.854199	+	0.519946i	$0.174048\pi$
$390$	−9.83248	−	20.7667i	−0.497887	−	1.05156i
$391$	27.9393			1.41295
$392$	15.8851	−	9.17126i	0.802318	−	0.463218i
$393$	−0.167570	−	0.0449004i	−0.00845281	−	0.00226492i
$394$	−7.30464	+	12.6520i	−0.368003	+	0.637399i
$395$	−23.0372	+	19.7986i	−1.15913	+	0.996175i
$396$	−7.30795	+	1.95816i	−0.367238	+	0.0984012i
$397$	−2.91045	+	5.04104i	−0.146071	+	0.253002i	−0.929772	−	0.368136i	$-0.879996\pi$
$397$	−2.91045	+	5.04104i	−0.146071	+	0.253002i	0.783701	+	0.621138i	$0.213329\pi$
$398$			15.0689i			0.755337i
$399$	−6.35716	−	3.67031i	−0.318256	−	0.183745i
$400$	−5.49918	+	2.14986i	−0.274959	+	0.107493i
$401$	0.255004	+	0.0683280i	0.0127343	+	0.00341214i	0.265181	−	0.964199i	$-0.414568\pi$
$401$	0.255004	+	0.0683280i	0.0127343	+	0.00341214i	−0.252446	+	0.967611i	$0.581235\pi$
$402$	−14.7075	+	14.7075i	−0.733544	+	0.733544i
$403$	0.162147	+	0.619831i	0.00807713	+	0.0308760i
$404$			9.30738i			0.463060i
$405$	−0.427966	+	1.22046i	−0.0212658	+	0.0606453i
$406$	0.143993	+	0.249404i	0.00714627	+	0.0123777i
$407$	1.75692	+	6.55691i	0.0870872	+	0.325014i
$408$	−61.0446			−3.02216
$409$	−9.61872	−	35.8975i	−0.475615	−	1.77502i	−0.619042	−	0.785358i	$-0.712479\pi$
$409$	−9.61872	−	35.8975i	−0.475615	−	1.77502i	0.143427	−	0.989661i	$-0.454188\pi$
$410$	−8.93108	+	13.0809i	−0.441074	+	0.646017i
$411$	8.70518	−	8.70518i	0.429395	−	0.429395i
$412$	−3.28909	+	0.881310i	−0.162042	+	0.0434190i
$413$	1.25977	−	4.70151i	0.0619890	−	0.231346i
$414$	4.86161	−	18.1438i	0.238935	−	0.891718i
$415$	12.4881	+	14.5309i	0.613016	+	0.713293i
$416$	−8.62585	−	15.1473i	−0.422917	−	0.742657i
$417$	−27.0934	−	27.0934i	−1.32677	−	1.32677i
$418$	−2.32476	−	4.02660i	−0.113708	−	0.196947i
$419$	29.3721	−	16.9580i	1.43492	−	0.828451i	0.437428	−	0.899253i	$-0.355889\pi$
$419$	29.3721	−	16.9580i	1.43492	−	0.828451i	0.997490	+	0.0708027i	$0.0225561\pi$
$420$	−3.23095	+	4.73219i	−0.157654	+	0.230907i
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.998641	−	0.0521230i	$-0.983401\pi$
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.0521230	−	0.998641i	$-0.516599\pi$
$422$	−7.55613	−	4.36253i	−0.367826	−	0.212365i
$423$	−32.3885	−	18.6995i	−1.57478	−	0.909201i
$424$	6.03777	+	6.03777i	0.293220	+	0.293220i
$425$	36.0298	−	4.01124i	1.74770	−	0.194574i
$426$	−32.2162	+	18.6000i	−1.56088	+	0.901175i
$427$	−1.00374	−	1.73853i	−0.0485745	−	0.0841335i
$428$	−0.299934	−	0.299934i	−0.0144979	−	0.0144979i
$429$	−8.27052	−	14.5233i	−0.399305	−	0.701192i
$430$	18.1223	+	1.37015i	0.873933	+	0.0660745i
$431$	1.19014	−	4.44167i	0.0573271	−	0.213948i	−0.931320	−	0.364201i	$-0.881342\pi$
$431$	1.19014	−	4.44167i	0.0573271	−	0.213948i	0.988648	+	0.150253i	$0.0480089\pi$
$432$	−1.50488	+	5.61627i	−0.0724033	+	0.270213i
$433$	−3.86627	+	1.03596i	−0.185801	+	0.0497853i	−0.350520	−	0.936555i	$-0.613995\pi$
$433$	−3.86627	+	1.03596i	−0.185801	+	0.0497853i	0.164719	+	0.986341i	$0.447328\pi$
$434$	−0.123811	+	0.123811i	−0.00594311	+	0.00594311i
$435$	1.50414	+	1.02696i	0.0721179	+	0.0492392i
$436$	2.24285	+	8.37043i	0.107413	+	0.400871i
$437$	−10.5336			−0.503890
$438$	2.38062	+	8.88461i	0.113751	+	0.424523i
$439$	11.3618	+	19.6793i	0.542271	+	0.939242i	0.998773	+	0.0495192i	$0.0157689\pi$
$439$	11.3618	+	19.6793i	0.542271	+	0.939242i	−0.456502	+	0.889723i	$0.650898\pi$
$440$	−10.1265	+	4.86842i	−0.482763	+	0.232093i
$441$			28.9414i			1.37816i
$442$	−6.76571	−	25.8629i	−0.321812	−	1.23017i
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	−0.661824	−	0.749660i	$-0.730217\pi$
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	0.749660	+	0.661824i	$0.230217\pi$
$444$	−10.4837	−	2.80911i	−0.497536	−	0.133314i
$445$	1.04499	−	0.502388i	0.0495373	−	0.0238155i
$446$	6.25313	+	3.61025i	0.296094	+	0.170950i
$447$			12.0737i			0.571067i
$448$	3.51978	−	6.09644i	0.166294	−	0.288030i
$449$	31.0770	−	8.32705i	1.46661	−	0.392978i	0.564845	−	0.825197i	$-0.308936\pi$
$449$	31.0770	−	8.32705i	1.46661	−	0.392978i	0.901769	+	0.432219i	$0.142269\pi$
$450$	3.66451	−	24.0957i	0.172746	−	1.13588i
$451$	−5.76056	+	9.97759i	−0.271254	+	0.469826i
$452$	−1.78317	−	0.477798i	−0.0838731	−	0.0224737i
$453$	16.2125	−	9.36029i	0.761729	−	0.439785i
$454$	−17.5640			−0.824318
$455$	−7.31555	−	2.61411i	−0.342958	−	0.122552i
$456$	23.0149			1.07777
$457$	−24.5669	+	14.1837i	−1.14919	+	0.663486i	−0.948690	−	0.316208i	$-0.897590\pi$
$457$	−24.5669	+	14.1837i	−1.14919	+	0.663486i	−0.200501	+	0.979693i	$0.564257\pi$
$458$	12.4416	+	3.33373i	0.581360	+	0.155775i
$459$	17.8496	−	30.9165i	0.833149	−	1.44306i
$460$	−0.619891	+	8.19898i	−0.0289026	+	0.382279i
$461$	−11.1174	+	2.97890i	−0.517790	+	0.138741i	−0.508244	−	0.861213i	$-0.669705\pi$
$461$	−11.1174	+	2.97890i	−0.517790	+	0.138741i	−0.00954570	+	0.999954i	$0.503039\pi$
$462$	2.28378	−	3.95562i	0.106251	−	0.184032i
$463$		−	29.9456i		−	1.39169i	−0.718192	−	0.695845i	$-0.755030\pi$
$463$		−	29.9456i		−	1.39169i	0.718192	−	0.695845i	$-0.244970\pi$
$464$	−0.298893	−	0.172566i	−0.0138758	−	0.00801118i
$465$	−0.366423	+	1.04496i	−0.0169925	+	0.0484586i
$466$	24.5609	+	6.58109i	1.13776	+	0.304863i
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	−0.227274	−	0.973831i	$-0.572981\pi$
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	0.973831	+	0.227274i	$0.0729812\pi$
$468$	16.4002	+	0.0973232i	0.758100	+	0.00449877i
$469$			7.03244i			0.324728i
$470$	−16.9299	−	5.93662i	−0.780918	−	0.273836i
$471$	28.4732	+	49.3170i	1.31197	+	2.27241i
$472$	3.94971	+	14.7405i	0.181800	+	0.678488i
$473$	13.2196			0.607837
$474$	10.0201	+	37.3957i	0.460240	+	1.71764i
$475$	−13.5838	+	1.51231i	−0.623270	+	0.0693894i
$476$	−4.71411	+	4.71411i	−0.216071	+	0.216071i
$477$	−13.0136	+	3.48697i	−0.595850	+	0.159657i
$478$	0.836524	−	3.12195i	0.0382617	−	0.142795i
$479$	−10.0493	+	37.5043i	−0.459162	+	1.71362i	0.216393	+	0.976306i	$0.430571\pi$
$479$	−10.0493	+	37.5043i	−0.459162	+	1.71362i	−0.675555	+	0.737309i	$0.736096\pi$
$480$	2.27132	−	30.0415i	0.103671	−	1.37120i
$481$	0.0873213	−	14.7148i	0.00398151	−	0.670935i
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$	−5.17396	−	8.96157i	−0.235424	−	0.407765i
$484$	6.80421	−	3.92841i	0.309282	−	0.178564i
$485$	3.11238	+	16.5092i	0.141326	+	0.749645i
$486$	11.8466	+	11.8466i	0.537372	+	0.537372i
$487$	−25.0660	−	14.4718i	−1.13585	−	0.655782i	−0.190448	−	0.981697i	$-0.560994\pi$
$487$	−25.0660	−	14.4718i	−1.13585	−	0.655782i	−0.945399	+	0.325916i	$0.894327\pi$
$488$	5.45078	+	3.14701i	0.246745	+	0.142458i
$489$	42.1422	+	42.1422i	1.90574	+	1.90574i
$490$	2.57205	+	13.6431i	0.116193	+	0.616332i
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	−0.351059	−	0.936353i	$-0.614178\pi$
$491$	6.30003	−	3.63733i	0.284317	−	0.164150i	0.635376	+	0.772203i	$0.280845\pi$
$492$	−9.21046	−	15.9530i	−0.415240	−	0.719216i
$493$	1.49839	+	1.49839i	0.0674842	+	0.0674842i
$494$	2.55079	+	9.75077i	0.114766	+	0.438708i
$495$	1.33657	−	17.6781i	0.0600743	−	0.794571i
$496$	0.0543104	−	0.202689i	0.00243861	−	0.00910102i
$497$	−3.25531	+	12.1490i	−0.146021	+	0.544956i
$498$	23.5876	−	6.32027i	1.05698	−	0.283218i
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	−0.605754	−	0.795652i	$-0.707128\pi$
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	0.795652	+	0.605754i	$0.207128\pi$
$500$	0.377731	+	10.6622i	0.0168926	+	0.476827i
$501$	1.23663	+	4.61515i	0.0552483	+	0.206190i
$502$	−14.2889			−0.637745
$503$	0.939636	+	3.50677i	0.0418963	+	0.156359i	0.983705	−	0.179790i	$-0.0575419\pi$
$503$	0.939636	+	3.50677i	0.0418963	+	0.156359i	−0.941809	+	0.336149i	$0.890875\pi$
$504$	6.93805	+	12.0171i	0.309046	+	0.535283i
$505$	−20.5810	−	7.21692i	−0.915843	−	0.321149i
$506$		−	6.55433i		−	0.291376i
$507$	8.96091	+	35.1039i	0.397968	+	1.55902i
$508$	1.46769	−	1.46769i	0.0651184	−	0.0651184i
$509$	−22.5037	−	6.02986i	−0.997460	−	0.267269i	−0.277079	−	0.960847i	$-0.589366\pi$
$509$	−22.5037	−	6.02986i	−0.997460	−	0.267269i	−0.720381	+	0.693578i	$0.756033\pi$
$510$	15.2893	−	43.6015i	0.677020	−	1.93071i
$511$	2.69325	+	1.55495i	0.119143	+	0.0687870i
$512$			12.8442i			0.567640i
$513$	−6.72962	+	11.6560i	−0.297120	+	0.514627i
$514$	22.8945	−	6.13455i	1.00983	−	0.270584i
$515$	0.601550	−	7.95639i	0.0265075	−	0.350600i
$516$	−10.5683	+	18.3048i	−0.465243	+	0.805824i
$517$	−12.6052	−	3.37754i	−0.554375	−	0.148544i
$518$	3.48272	−	2.01075i	0.153022	−	0.0883472i
$519$	−42.2960			−1.85659
$520$	23.9614	−	4.37021i	1.05078	−	0.191647i
$521$	−13.0530			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$521$	−13.0530			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$522$	1.23379	−	0.712327i	0.0540013	−	0.0311777i
$523$	−16.4404	−	4.40520i	−0.718890	−	0.192626i	−0.119214	−	0.992869i	$-0.538037\pi$
$523$	−16.4404	−	4.40520i	−0.718890	−	0.192626i	−0.599677	+	0.800243i	$0.704704\pi$
$524$	0.0297008	−	0.0514432i	0.00129748	−	0.00224731i
$525$	−7.95882	−	10.8138i	−0.347351	−	0.471952i
$526$	1.28514	−	0.344353i	0.0560349	−	0.0150145i
$527$	−0.644187	+	1.11577i	−0.0280612	+	0.0486035i
$528$			5.47391i			0.238221i
$529$	7.05896	+	4.07549i	0.306911	+	0.177195i
$530$	−5.82475	+	2.80030i	−0.253011	+	0.121637i
$531$	−23.2581	−	6.23198i	−1.00931	−	0.270445i
$532$	1.77730	−	1.77730i	0.0770558	−	0.0770558i
$533$	17.7643	−	17.5547i	0.769456	−	0.760377i
$534$		−	1.47779i		−	0.0639501i
$535$	0.895798	−	0.430663i	0.0387287	−	0.0186192i
$536$	−11.0243	−	19.0947i	−0.476178	−	0.824765i
$537$	−1.99023	−	7.42764i	−0.0858847	−	0.320526i
$538$	8.11728			0.349961
$539$	2.61373	+	9.75457i	0.112581	+	0.420159i
$540$	8.67662	+	5.92404i	0.373382	+	0.254930i
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	−0.902483	−	0.430727i	$-0.858257\pi$
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	0.430727	+	0.902483i	$0.358257\pi$
$542$	0.884606	−	0.237029i	0.0379971	−	0.0101813i
$543$	−7.47039	+	27.8799i	−0.320585	+	1.19644i
$544$	9.07231	−	33.8583i	0.388972	−	1.45166i
$545$	−20.2483	−	1.53089i	−0.867340	−	0.0655761i
$546$	−7.04266	+	6.95956i	−0.301398	+	0.297842i
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	0.118756	−	0.992923i	$-0.462109\pi$
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	−0.992923	+	0.118756i	$0.962109\pi$
$548$	2.10769	+	3.65063i	0.0900361	+	0.155947i
$549$	−8.60042	+	4.96545i	−0.367057	+	0.211920i
$550$	−0.941005	−	8.45230i	−0.0401246	−	0.360407i
$551$	−0.564920	−	0.564920i	−0.0240664	−	0.0240664i
$552$	28.0970	+	16.2218i	1.19589	+	0.690446i
$553$	11.3360	+	6.54485i	0.482056	+	0.278315i
$554$	−6.90913	−	6.90913i	−0.293541	−	0.293541i
$555$	14.3407	−	21.0040i	0.608729	−	0.891572i
$556$	11.3619	−	6.55982i	0.481854	−	0.278198i
$557$	6.79015	+	11.7609i	0.287708	+	0.498324i	0.973262	−	0.229697i	$-0.0737735\pi$
$557$	6.79015	+	11.7609i	0.287708	+	0.498324i	−0.685555	+	0.728021i	$0.740440\pi$
$558$	0.612485	+	0.612485i	0.0259286	+	0.0259286i
$559$	−27.6356	−	7.58098i	−1.16886	−	0.320641i
$560$	1.65839	+	1.92967i	0.0700797	+	0.0815432i
$561$	8.69858	−	32.4636i	0.367254	−	1.37061i
$562$	−2.09014	+	7.80052i	−0.0881673	+	0.329045i
$563$	4.68514	−	1.25538i	0.197455	−	0.0529080i	−0.158736	−	0.987321i	$-0.550742\pi$
$563$	4.68514	−	1.25538i	0.197455	−	0.0529080i	0.356191	+	0.934413i	$0.384075\pi$
$564$	14.7539	−	14.7539i	0.621251	−	0.621251i
$565$	2.43920	−	3.57256i	0.102618	−	0.150299i
$566$	−5.58573	−	20.8462i	−0.234786	−	0.876232i
$567$	0.557323			0.0234054
$568$	−10.2063	−	38.0904i	−0.428247	−	1.59824i
$569$	0.124396	+	0.215461i	0.00521497	+	0.00903259i	0.868621	−	0.495477i	$-0.165007\pi$
$569$	0.124396	+	0.215461i	0.00521497	+	0.00903259i	−0.863406	+	0.504509i	$0.831673\pi$
$570$	−5.76432	+	16.4385i	−0.241441	+	0.688534i
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$	5.53640	−	1.44832i	0.231489	−	0.0605572i
$573$	−36.6136	+	36.6136i	−1.52955	+	1.52955i
$574$	6.59281	+	1.76654i	0.275179	+	0.0737339i
$575$	−17.6494	−	7.72820i	−0.736030	−	0.322288i
$576$	−30.1587	−	17.4121i	−1.25661	−	0.725506i
$577$		−	12.1339i		−	0.505141i	−0.967578	−	0.252570i	$-0.918724\pi$
$577$		−	12.1339i		−	0.505141i	0.967578	−	0.252570i	$-0.0812760\pi$
$578$	18.1869	−	31.5007i	0.756477	−	1.31026i
$579$	−33.8416	+	9.06783i	−1.40641	+	0.376846i
$580$	−0.472958	+	0.406469i	−0.0196385	+	0.0168777i
$581$	4.12821	−	7.15027i	0.171267	−	0.296643i
$582$	20.6824	+	5.54184i	0.857315	+	0.229717i
$583$	−4.07125	+	2.35054i	−0.168614	+	0.0973492i
$584$	−9.75040			−0.403475
$585$	−12.9319	+	36.1896i	−0.534667	+	1.49626i
$586$	−4.11255			−0.169888
$587$	−31.6354	+	18.2647i	−1.30573	+	0.753865i	−0.981381	−	0.192072i	$-0.938479\pi$
$587$	−31.6354	+	18.2647i	−1.30573	+	0.753865i	−0.324351	+	0.945937i	$0.605146\pi$
$588$	−15.5964	−	4.17904i	−0.643185	−	0.172341i
$589$	0.242870	−	0.420663i	0.0100073	−	0.0173331i
$590$	−11.5178	−	0.870813i	−0.474180	−	0.0358508i
$591$	38.4573	−	10.3046i	1.58192	−	0.423875i
$592$	−2.40974	+	4.17380i	−0.0990398	+	0.171542i
$593$			16.6936i			0.685525i	0.939422	+	0.342762i	$0.111363\pi$
$593$			16.6936i			0.685525i	−0.939422	+	0.342762i	$0.888637\pi$
$594$	−7.25276	−	4.18738i	−0.297584	−	0.171810i
$595$	−6.76880	−	14.0794i	−0.277494	−	0.577200i
$596$	−3.99327	−	1.06999i	−0.163571	−	0.0438287i
$597$	29.0384	−	29.0384i	1.18846	−	1.18846i
$598$	−3.75868	+	13.7018i	−0.153704	+	0.560310i
$599$		−	13.2549i		−	0.541579i	−0.962639	−	0.270789i	$-0.912715\pi$
$599$		−	13.2549i		−	0.541579i	0.962639	−	0.270789i	$-0.0872847\pi$
$600$	38.5621	+	16.8853i	1.57429	+	0.689341i
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	0.854662	−	0.519185i	$-0.173764\pi$
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	−0.876958	+	0.480566i	$0.840431\pi$
$602$	−2.02696	−	7.56474i	−0.0826129	−	0.308316i
$603$	34.7891			1.41672
$604$	1.65905	+	6.19166i	0.0675058	+	0.251935i
$605$	3.41077	+	18.0919i	0.138667	+	0.735542i
$606$	−19.6554	+	19.6554i	−0.798446	+	0.798446i
$607$	40.4361	−	10.8348i	1.64125	−	0.439771i	0.684105	−	0.729384i	$-0.260193\pi$
$607$	40.4361	−	10.8348i	1.64125	−	0.439771i	0.957144	+	0.289612i	$0.0935263\pi$
$608$	−3.42042	+	12.7652i	−0.138716	+	0.517696i
$609$	0.203130	−	0.758093i	0.00823126	−	0.0307195i
$610$	−3.61298	+	3.10506i	−0.146285	+	0.125720i
$611$	24.4142	+	14.2894i	0.987693	+	0.578087i
$612$	23.3204	+	23.3204i	0.942673	+	0.942673i
$613$	−13.9548	−	24.1705i	−0.563630	−	0.976235i	−0.997176	−	0.0751039i	$-0.976071\pi$
$613$	−13.9548	−	24.1705i	−0.563630	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$614$	−21.4487	+	12.3834i	−0.865601	+	0.499755i
$615$	42.4179	−	7.99680i	1.71046	−	0.322462i
$616$	3.42371	+	3.42371i	0.137945	+	0.137945i
$617$	−3.79548	−	2.19132i	−0.152800	−	0.0882193i	0.421650	−	0.906758i	$-0.361451\pi$
$617$	−3.79548	−	2.19132i	−0.152800	−	0.0882193i	−0.574451	+	0.818539i	$0.694784\pi$
$618$	−8.80708	−	5.08477i	−0.354273	−	0.204540i
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	0.859582	−	0.510998i	$-0.170724\pi$
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	−0.510998	+	0.859582i	$0.670724\pi$
$620$	−0.313136	−	0.213797i	−0.0125759	−	0.00858628i
$621$	−16.4313	+	9.48662i	−0.659366	+	0.380685i
$622$	4.02525	+	6.97193i	0.161398	+	0.279549i
$623$	−0.353304	−	0.353304i	−0.0141548	−	0.0141548i
$624$	3.13910	−	11.4432i	0.125664	−	0.458095i
$625$	−23.8697	−	7.43216i	−0.954788	−	0.297287i
$626$	−1.26934	+	4.73726i	−0.0507332	+	0.189339i
$627$	−3.27952	+	12.2393i	−0.130971	+	0.488791i
$628$	−18.8345	+	5.04668i	−0.751577	+	0.201385i
$629$	20.9238	−	20.9238i	0.834287	−	0.834287i
$630$	−10.3210	+	1.94575i	−0.411198	+	0.0775207i
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	−0.964612	−	0.263673i	$-0.915066\pi$
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	0.703542	−	0.710653i	$-0.251601\pi$
$632$	−41.0398			−1.63248
$633$	6.15419	+	22.9677i	0.244607	+	0.912886i
$634$	−11.7220	−	20.3031i	−0.465540	−	0.806340i
$635$	2.10740	+	4.38349i	0.0836297	+	0.173954i
$636$		−	7.51646i		−	0.298047i
$637$	0.129906	−	21.8908i	0.00514706	−	0.867345i
$638$	0.351511	−	0.351511i	0.0139164	−	0.0139164i
$639$	60.1003	+	16.1038i	2.37753	+	0.637057i
$640$	4.63834	+	1.62647i	0.183346	+	0.0642920i
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	0.471760	−	0.881727i	$-0.343619\pi$
$641$	−1.41675	−	0.817961i	−0.0559582	−	0.0323075i	−0.527718	+	0.849420i	$0.676952\pi$
$642$		−	1.26681i		−	0.0499968i
$643$	19.8344	−	34.3541i	0.782191	−	1.35479i	−0.148472	−	0.988917i	$-0.547435\pi$
$643$	19.8344	−	34.3541i	0.782191	−	1.35479i	0.930663	−	0.365878i	$-0.119231\pi$
$644$	3.42248	−	0.917051i	0.134865	−	0.0361369i
$645$	−32.2820	−	37.5627i	−1.27110	−	1.47903i
$646$	−10.1339	+	17.5525i	−0.398714	+	0.690593i
$647$	−14.3588	−	3.84742i	−0.564501	−	0.151258i	−0.0347277	−	0.999397i	$-0.511056\pi$
$647$	−14.3588	−	3.84742i	−0.564501	−	0.151258i	−0.529773	+	0.848139i	$0.677723\pi$
$648$	−1.51326	+	0.873682i	−0.0594465	+	0.0343215i
$649$	−8.40185			−0.329801
$650$	−2.87993	+	18.2092i	−0.112960	+	0.714222i
$651$	0.477178			0.0187021
$652$	−17.6729	+	10.2034i	−0.692123	+	0.399597i
$653$	−12.4172	−	3.32718i	−0.485922	−	0.130203i	0.00753655	−	0.999972i	$-0.497601\pi$
$653$	−12.4172	−	3.32718i	−0.485922	−	0.130203i	−0.493459	+	0.869769i	$0.664268\pi$
$654$	−12.9403	+	22.4132i	−0.506005	+	0.876426i
$655$	0.0907243	+	0.105565i	0.00354489	+	0.00412476i
$656$	−7.90103	+	2.11708i	−0.308483	+	0.0826579i
$657$	7.69225	−	13.3234i	0.300103	−	0.519794i
$658$			7.73102i			0.301387i
$659$	20.8742	+	12.0517i	0.813144	+	0.469469i	0.848047	−	0.529922i	$-0.177779\pi$
$659$	20.8742	+	12.0517i	0.813144	+	0.469469i	−0.0349025	+	0.999391i	$0.511112\pi$
$660$	9.33366	+	3.27293i	0.363312	+	0.127399i
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.903217	−	0.429185i	$-0.141199\pi$
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.567616	+	0.823293i	$0.307866\pi$
$662$	24.2637	−	24.2637i	0.943036	−	0.943036i
$663$	−36.8011	+	62.8768i	−1.42924	+	2.44193i
$664$			25.8862i			1.00458i
$665$	2.55196	+	5.30818i	0.0989606	+	0.205843i
$666$	−9.94705	−	17.2288i	−0.385440	−	0.667602i
$667$	−0.291487	−	1.08784i	−0.0112864	−	0.0421215i
$668$	−1.63601			−0.0632991
$669$	−5.09295	−	19.0071i	−0.196905	−	0.734858i
$670$	16.3997	−	3.09174i	0.633575	−	0.119444i
$671$	−2.45030	+	2.45030i	−0.0945926	+	0.0945926i
$672$	−12.5402	+	3.36013i	−0.483747	+	0.129620i
$673$	−2.64660	+	9.87723i	−0.102019	+	0.380739i	−0.997990	−	0.0633730i	$-0.979814\pi$
$673$	−2.64660	+	9.87723i	−0.102019	+	0.380739i	0.895971	+	0.444112i	$0.146481\pi$
$674$	5.44776	−	20.3313i	0.209840	−	0.783132i
$675$	−19.8274	+	14.5927i	−0.763157	+	0.561675i
$676$	−12.4044	−	0.147227i	−0.477093	−	0.00566259i
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.986771	+	0.162121i	$0.0518333\pi$
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.162121	+	0.986771i	$0.448167\pi$
$678$	−2.75669	−	4.77472i	−0.105870	−	0.183372i
$679$	6.26961	−	3.61976i	0.240606	−	0.138914i
$680$	40.4503	+	27.6178i	1.55120	+	1.05910i
$681$	33.8465	+	33.8465i	1.29700	+	1.29700i
$682$	0.261750	+	0.151121i	0.0100229	+	0.00578673i
$683$	17.3384	+	10.0103i	0.663436	+	0.383035i	0.793585	−	0.608459i	$-0.208212\pi$
$683$	17.3384	+	10.0103i	0.663436	+	0.383035i	−0.130149	+	0.991494i	$0.541545\pi$
$684$	−8.79221	−	8.79221i	−0.336178	−	0.336178i
$685$	−9.70677	+	1.82996i	−0.370876	+	0.0699191i
$686$	11.1546	−	6.44013i	0.425886	−	0.245885i
$687$	−17.5513	−	30.3998i	−0.669625	−	1.15983i
$688$	6.63664	+	6.63664i	0.253019	+	0.253019i
$689$	9.85890	−	2.57908i	0.375594	−	0.0982550i
$690$	−18.6238	+	16.0056i	−0.708994	+	0.609322i
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	0.540147	+	0.841571i	$0.318369\pi$
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	−0.888566	+	0.458749i	$0.848298\pi$
$692$	3.74834	−	13.9890i	0.142491	−	0.531782i
$693$	−7.37933	+	1.97729i	−0.280318	+	0.0751109i
$694$	16.4960	−	16.4960i	0.626181	−	0.626181i
$695$	5.69543	+	30.2106i	0.216040	+	1.14595i
$696$	0.636870	+	2.37683i	0.0241405	+	0.0900935i
$697$	50.2221			1.90230
$698$	−2.74877	−	10.2586i	−0.104043	−	0.388292i
$699$	−34.6479	−	60.0120i	−1.31051	−	2.26986i
$700$	4.28188	−	1.67397i	0.161840	−	0.0632701i
$701$			37.1781i			1.40420i	0.712080	+	0.702098i	$0.247753\pi$
$701$			37.1781i			1.40420i	−0.712080	+	0.702098i	$0.752247\pi$
$702$	12.7606	+	12.9129i	0.481617	+	0.487367i
$703$	−7.88864	+	7.88864i	−0.297526	+	0.297526i
$704$	−11.7374	−	3.14502i	−0.442368	−	0.118532i
$705$	21.1845	+	44.0647i	0.797854	+	1.65957i
$706$	3.80843	+	2.19880i	0.143332	+	0.0827529i
$707$			9.39830i			0.353459i
$708$	6.71678	−	11.6338i	0.252432	−	0.437225i
$709$	−46.5506	+	12.4732i	−1.74824	+	0.468440i	−0.984250	−	0.176783i	$-0.943431\pi$
$709$	−46.5506	+	12.4732i	−1.74824	+	0.468440i	−0.763994	+	0.645224i	$0.776764\pi$
$710$	29.7626	+	2.25023i	1.11697	+	0.0844497i
$711$	32.3770	−	56.0786i	1.21423	−	2.10311i
$712$	1.51316	+	0.405449i	0.0567079	+	0.0151948i
$713$	0.593001	−	0.342369i	0.0222080	−	0.0128218i
$714$	−19.9106			−0.745135
$715$	−1.09031	+	13.3654i	−0.0407752	+	0.499839i
$716$	2.63300			0.0983998
$717$	−7.62814	+	4.40411i	−0.284878	+	0.164474i
$718$	14.5662	+	3.90299i	0.543604	+	0.145658i
$719$	−16.6992	+	28.9239i	−0.622777	+	1.07868i	0.366190	+	0.930540i	$0.380662\pi$
$719$	−16.6992	+	28.9239i	−0.622777	+	1.07868i	−0.988966	+	0.148141i	$0.952671\pi$
$720$	9.54594	−	8.20394i	0.355756	−	0.305743i
$721$	−3.32122	+	0.889918i	−0.123689	+	0.0331423i
$722$	−5.89421	+	10.2091i	−0.219360	+	0.379942i
$723$		−	50.2164i		−	1.86757i
$724$	−8.55897	−	4.94153i	−0.318092	−	0.183650i
$725$	−0.532076	−	1.36101i	−0.0197608	−	0.0505465i
$726$	22.6652	+	6.07313i	0.841186	+	0.225395i
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	−0.116149	−	0.993232i	$-0.537055\pi$
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	0.993232	+	0.116149i	$0.0370549\pi$
$728$	−5.19389	−	9.12066i	−0.192499	−	0.338034i
$729$		−	43.9226i		−	1.62676i
$730$	2.44209	−	6.96430i	0.0903860	−	0.257760i
$731$	−28.8130	−	49.9055i	−1.06569	−	1.84582i
$732$	−1.43399	−	5.35173i	−0.0530018	−	0.197806i
$733$	−14.7049			−0.543138			−0.271569	−	0.962419i	$-0.587542\pi$
$733$	−14.7049			−0.543138			−0.271569	+	0.962419i	$0.587542\pi$
$734$	3.02344	+	11.2836i	0.111597	+	0.416486i
$735$	21.3343	−	31.2472i	0.786929	−	1.15257i
$736$	−13.1731	+	13.1731i	−0.485568	+	0.485568i
$737$	11.7255	−	3.14184i	0.431914	−	0.115731i
$738$	8.73896	−	32.6142i	0.321686	−	1.20055i
$739$	−5.32432	+	19.8706i	−0.195858	+	0.730953i	0.796185	+	0.605054i	$0.206848\pi$
$739$	−5.32432	+	19.8706i	−0.195858	+	0.730953i	−0.992043	+	0.125900i	$0.959818\pi$
$740$	5.67600	+	6.60447i	0.208654	+	0.242785i
$741$	13.8747	−	23.7056i	0.509698	−	0.870848i
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$	22.3204	+	38.6601i	0.818856	+	1.41830i	0.906526	+	0.422151i	$0.138725\pi$
$743$	22.3204	+	38.6601i	0.818856	+	1.41830i	−0.0876692	+	0.996150i	$0.527942\pi$
$744$	−1.29565	+	0.748042i	−0.0475007	+	0.0274246i
$745$	5.46240	−	8.00048i	0.200127	−	0.293115i
$746$	−20.3603	−	20.3603i	−0.745443	−	0.745443i
$747$	−35.3720	−	20.4220i	−1.29419	−	0.747202i
$748$	9.96614	+	5.75395i	0.364398	+	0.210385i
$749$	−0.302864	−	0.302864i	−0.0110664	−	0.0110664i
$750$	−21.7188	+	23.3142i	−0.793058	+	0.851313i
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	−0.195804	−	0.980643i	$-0.562732\pi$
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	0.751360	+	0.659893i	$0.229398\pi$
$752$	−4.63255	−	8.02381i	−0.168932	−	0.292598i
$753$	27.5353	+	27.5353i	1.00344	+	1.00344i
$754$	−0.936413	+	0.533254i	−0.0341022	+	0.0194200i
$755$	−14.9778	−	1.13241i	−0.545097	−	0.0412125i
$756$	1.17176	−	4.37306i	0.0426164	−	0.159047i
$757$	−9.10848	+	33.9933i	−0.331053	+	1.23551i	0.577032	+	0.816722i	$0.304211\pi$
$757$	−9.10848	+	33.9933i	−0.331053	+	1.23551i	−0.908085	+	0.418786i	$0.862456\pi$
$758$	−16.7250	+	4.48144i	−0.607478	+	0.162773i
$759$	−12.6305	+	12.6305i	−0.458457	+	0.458457i
$760$	−15.2505	−	10.4124i	−0.553192	−	0.377697i
$761$	−3.03122	−	11.3127i	−0.109882	−	0.410084i	0.888972	−	0.457962i	$-0.151421\pi$
$761$	−3.03122	−	11.3127i	−0.109882	−	0.410084i	−0.998853	+	0.0478787i	$0.984754\pi$
$762$	6.19897			0.224565
$763$	2.26476	+	8.45219i	0.0819897	+	0.305990i
$764$	−8.86485	−	15.3544i	−0.320719	−	0.555502i
$765$	−69.6501	+	33.4849i	−2.51820	+	1.21065i
$766$		−	6.75331i		−	0.244007i
$767$	17.5641	+	4.81817i	0.634202	+	0.173974i
$768$	33.2233	−	33.2233i	1.19884	−	1.19884i
$769$	18.3227	+	4.90954i	0.660732	+	0.177043i	0.573576	−	0.819152i	$-0.305556\pi$
$769$	18.3227	+	4.90954i	0.660732	+	0.177043i	0.0871555	+	0.996195i	$0.472222\pi$
$770$	−3.30292	+	1.58791i	−0.119029	+	0.0572242i
$771$	−55.9401	−	32.2971i	−2.01463	−	1.16315i
$772$		−	11.9964i		−	0.431760i
$773$	−8.20497	+	14.2114i	−0.295112	+	0.511149i	−0.975011	−	0.222157i	$-0.928690\pi$
$773$	−8.20497	+	14.2114i	−0.295112	+	0.511149i	0.679899	+	0.733306i	$0.262024\pi$
$774$	−37.4223	+	10.0273i	−1.34512	+	0.360423i
$775$	0.715564	−	0.526647i	0.0257038	−	0.0189177i
$776$	−11.3490	+	19.6570i	−0.407404	+	0.705644i
$777$	−10.5861	−	2.83655i	−0.379775	−	0.101761i
$778$	−29.8406	+	17.2285i	−1.06984	+	0.617671i
$779$	−18.9346			−0.678403
$780$	−17.6351	−	12.1946i	−0.631438	−	0.436636i
$781$	21.7109			0.776876
$782$	−24.7434	+	14.2856i	−0.884822	+	0.510852i
$783$	−1.38999	−	0.372446i	−0.0496741	−	0.0133101i
$784$	−3.58492	+	6.20926i	−0.128033	+	0.221759i
$785$	3.44468	−	45.5610i	0.122946	−	1.62614i
$786$	0.171361	−	0.0459159i	0.00611223	−	0.00163777i
$787$	6.80008	−	11.7781i	0.242397	−	0.419844i	−0.719000	−	0.695010i	$-0.755400\pi$
$787$	6.80008	−	11.7781i	0.242397	−	0.419844i	0.961396	+	0.275167i	$0.0887331\pi$
$788$			13.6326i			0.485642i
$789$	−3.14011	−	1.81294i	−0.111791	−	0.0645424i
$790$	10.2789	−	29.3130i	0.365706	−	1.04291i
$791$	−1.80058	−	0.482465i	−0.0640214	−	0.0171545i
$792$	16.9369	−	16.9369i	0.601827	−	0.601827i
$793$	6.52751	−	3.71719i	0.231799	−	0.132001i
$794$		−	5.95255i		−	0.211248i
$795$	16.6208	+	5.82824i	0.589480	+	0.206706i
$796$	7.03076	+	12.1776i	0.249199	+	0.431625i
$797$	−7.74769	−	28.9148i	−0.274437	−	1.02421i	−0.956218	−	0.292657i	$-0.905461\pi$
$797$	−7.74769	−	28.9148i	−0.274437	−	1.02421i	0.681780	−	0.731557i	$-0.261206\pi$
$798$	7.50664			0.265732
$799$	14.7232	+	54.9476i	0.520868	+	1.94391i
$800$	−15.0965	+	18.8790i	−0.533740	+	0.667473i
$801$	−1.74778	+	1.74778i	−0.0617546	+	0.0617546i
$802$	−0.260771	+	0.0698734i	−0.00920815	+	0.00246732i
$803$	1.38939	−	5.18527i	0.0490305	−	0.182984i
$804$	−5.02343	+	18.7477i	−0.177163	+	0.661180i
$805$	−0.625946	+	8.27906i	−0.0220617	+	0.291799i
$806$	−0.460525	−	0.466023i	−0.0162213	−	0.0164150i
$807$	−15.6423	−	15.6423i	−0.550636	−	0.550636i
$808$	−14.7331	−	25.5185i	−0.518310	−	0.897739i
$809$	−2.54661	+	1.47029i	−0.0895342	+	0.0516926i	−0.544099	−	0.839021i	$-0.683128\pi$
$809$	−2.54661	+	1.47029i	−0.0895342	+	0.0516926i	0.454564	+	0.890714i	$0.349795\pi$
$810$	−0.245021	−	1.29968i	−0.00860916	−	0.0456661i
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	0.933148	−	0.359492i	$-0.117050\pi$
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	−0.359492	+	0.933148i	$0.617050\pi$
$812$	0.232730	+	0.134367i	0.00816724	+	0.00471536i
$813$	−2.16144	−	1.24791i	−0.0758050	−	0.0437660i
$814$	−4.90856	−	4.90856i	−0.172045	−	0.172045i
$815$	−8.85892	−	46.9910i	−0.310315	−	1.64602i
$816$	20.6647	−	11.9307i	0.723408	−	0.417660i
$817$	10.8630	+	18.8153i	0.380048	+	0.658262i
$818$	26.8732	+	26.8732i	0.939599	+	0.939599i
$819$	16.5604	+	0.0982738i	0.578667	+	0.00343397i
$820$	−1.11428	+	14.7380i	−0.0389124	+	0.514674i
$821$	11.8735	−	44.3125i	0.414388	−	1.54652i	−0.371672	−	0.928364i	$-0.621215\pi$
$821$	11.8735	−	44.3125i	0.414388	−	1.54652i	0.786059	−	0.618151i	$-0.212118\pi$
$822$	−3.25838	+	12.1605i	−0.113649	+	0.424145i
$823$	−17.1209	+	4.58752i	−0.596796	+	0.159911i	−0.544557	−	0.838724i	$-0.683302\pi$
$823$	−17.1209	+	4.58752i	−0.596796	+	0.159911i	−0.0522385	+	0.998635i	$0.516636\pi$
$824$	7.62280	−	7.62280i	0.265553	−	0.265553i
$825$	−14.4746	+	18.1013i	−0.503940	+	0.630206i
$826$	1.28826	+	4.80785i	0.0448242	+	0.167286i
$827$	5.79276			0.201434			0.100717	−	0.994915i	$-0.467886\pi$
$827$	5.79276			0.201434			0.100717	+	0.994915i	$0.467886\pi$
$828$	−4.53660	−	16.9308i	−0.157658	−	0.588387i
$829$	16.8799	+	29.2368i	0.586262	+	1.01544i	0.994717	+	0.102657i	$0.0327346\pi$
$829$	16.8799	+	29.2368i	0.586262	+	1.01544i	−0.408454	+	0.912779i	$0.633932\pi$
$830$	−18.4894	−	6.48347i	−0.641776	−	0.225045i
$831$			26.6284i			0.923727i
$832$	22.7334	+	13.3056i	0.788139	+	0.461290i
$833$	31.1279	−	31.1279i	1.07852	−	1.07852i
$834$	37.8473	+	10.1412i	1.31055	+	0.351160i
$835$	1.26856	−	3.61764i	0.0439002	−	0.125193i
$836$	−3.75741	−	2.16934i	−0.129953	−	0.0750282i
$837$		−	0.874920i		−	0.0302417i
$838$	−17.3415	+	30.0364i	−0.599053	+	1.03759i
$839$	37.8626	−	10.1452i	1.30716	−	0.350253i	0.463008	−	0.886354i	$-0.346770\pi$
$839$	37.8626	−	10.1452i	1.30716	−	0.350253i	0.844154	+	0.536101i	$0.180103\pi$
$840$	1.36763	−	18.0889i	0.0471877	−	0.624127i
$841$	−14.4573	+	25.0408i	−0.498527	+	0.863475i
$842$	30.1175	+	8.06995i	1.03792	+	0.278109i
$843$	19.0597	−	11.0041i	0.656451	−	0.379002i
$844$	−8.14177			−0.280251
$845$	9.94390	−	27.3152i	0.342081	−	0.939671i
$846$	38.2449			1.31489
$847$	6.87068	−	3.96679i	0.236079	−	0.136300i
$848$	−3.22393	−	0.863850i	−0.110710	−	0.0296647i
$849$	−29.4076	+	50.9354i	−1.00927	+	1.74810i
$850$	−29.8575	+	21.9748i	−1.02410	+	0.753728i
$851$	−15.1908	+	4.07037i	−0.520735	+	0.139531i
$852$	−17.3566	+	30.0625i	−0.594626	+	1.02992i
$853$		−	40.6417i		−	1.39154i	−0.718262	−	0.695772i	$-0.755062\pi$
$853$		−	40.6417i		−	1.39154i	0.718262	−	0.695772i	$-0.244938\pi$
$854$	1.77785	+	1.02644i	0.0608369	+	0.0351242i
$855$	26.2593	−	12.6244i	0.898048	−	0.431744i
$856$	1.29713	+	0.347564i	0.0443348	+	0.0118795i
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	−0.997721	−	0.0674695i	$-0.978507\pi$
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	0.0674695	+	0.997721i	$0.478507\pi$
$858$	14.7504	+	8.63325i	0.503570	+	0.294734i
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	15.2844	−	7.34811i	0.521194	−	0.250568i
$861$	−9.30043	−	16.1088i	−0.316958	−	0.548987i
$862$	1.21706	+	4.54213i	0.0414532	+	0.154706i
$863$	55.4497			1.88753			0.943766	−	0.330615i	$-0.107256\pi$
$863$	55.4497			1.88753			0.943766	+	0.330615i	$0.107256\pi$
$864$	6.16090	+	22.9928i	0.209598	+	0.782230i
$865$	28.0268	+	19.1356i	0.952940	+	0.650629i
$866$	2.89432	−	2.89432i	0.0983531	−	0.0983531i
$867$	−95.7502	+	25.6562i	−3.25185	+	0.871330i
$868$	−0.0422883	+	0.157822i	−0.00143536	+	0.00535683i
$869$	5.84800	−	21.8250i	0.198380	−	0.740363i
$870$	−1.85718	−	0.140414i	−0.0629643	−	0.00476048i
$871$	−26.3139	−	0.156154i	−0.891612	−	0.00529107i
$872$	−19.3993	−	19.3993i	−0.656944	−	0.656944i
$873$	−17.9068	−	31.0154i	−0.606052	−	1.04971i
$874$	9.32869	−	5.38592i	0.315548	−	0.182181i
$875$	0.381420	+	10.7663i	0.0128944	+	0.363968i
$876$	6.06917	+	6.06917i	0.205058	+	0.205058i
$877$	−4.65661	−	2.68849i	−0.157242	−	0.0907839i	0.419314	−	0.907841i	$-0.362271\pi$
$877$	−4.65661	−	2.68849i	−0.157242	−	0.0907839i	−0.576557	+	0.817057i	$0.695604\pi$
$878$	−20.1244	−	11.6188i	−0.679166	−	0.392116i
$879$	7.92505	+	7.92505i	0.267305	+	0.267305i
$880$	2.47651	−	3.62721i	0.0834831	−	0.122273i
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.971022	−	0.238992i	$-0.923183\pi$
$881$	−37.0890	+	21.4133i	−1.24956	+	0.721434i	−0.278538	+	0.960425i	$0.589850\pi$
$882$	−14.7980	−	25.6309i	−0.498274	−	0.863037i
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.993271	+	0.115813i	$0.0369473\pi$
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.115813	+	0.993271i	$0.463053\pi$
$884$	−17.5345	−	17.7439i	−0.589750	−	0.596791i
$885$	20.5172	+	23.8733i	0.689677	+	0.802494i
$886$	−0.691990	+	2.58254i	−0.0232478	+	0.0867622i
$887$	−5.47136	+	20.4194i	−0.183710	+	0.685616i	0.811193	+	0.584779i	$0.198819\pi$
$887$	−5.47136	+	20.4194i	−0.183710	+	0.685616i	−0.994903	+	0.100837i	$0.967848\pi$
$888$	33.1905	−	8.89336i	1.11380	−	0.298442i
$889$	1.48203	−	1.48203i	0.0497057	−	0.0497057i
$890$	−0.668582	+	0.979235i	−0.0224109	+	0.0328240i
$891$	−0.248992	−	0.929249i	−0.00834153	−	0.0311310i
$892$	6.73778			0.225598
$893$	−5.55089	−	20.7162i	−0.185753	−	0.693241i
$894$	−6.17340	−	10.6926i	−0.206469	−	0.357616i
$895$	−2.04162	+	5.82224i	−0.0682438	+	0.194616i
$896$		−	2.11809i		−	0.0707605i
$897$	33.6472	−	19.1609i	1.12345	−	0.639763i
$898$	−23.2645	+	23.2645i	−0.776346	+	0.776346i
$899$	0.0501642	+	0.0134414i	0.00167307	+	0.000448297i
$900$	−8.28103	−	21.1822i	−0.276034	−	0.706074i
$901$	17.7471	+	10.2463i	0.591242	+	0.341354i
$902$		−	11.7817i		−	0.392288i
$903$	−10.6715	+	18.4836i	−0.355126	+	0.615096i
$904$	5.64533	−	1.51266i	0.187761	−	0.0503104i
$905$	17.5636	−	15.0944i	0.583833	−	0.501756i
$906$	−9.57200	+	16.5792i	−0.318008	+	0.550807i
$907$	10.6869	+	2.86355i	0.354853	+	0.0950825i	0.431842	−	0.901949i	$-0.357864\pi$
$907$	10.6869	+	2.86355i	0.354853	+	0.0950825i	−0.0769889	+	0.997032i	$0.524531\pi$
$908$	−14.1940	+	8.19488i	−0.471043	+	0.271957i
$909$	46.4928			1.54207
$910$	7.81536	−	1.42541i	0.259077	−	0.0472519i
$911$	−15.0479			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$911$	−15.0479			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$912$	−7.79093	+	4.49810i	−0.257983	+	0.148947i
$913$	−13.7663	−	3.68867i	−0.455598	−	0.122077i
$914$	14.5045	−	25.1226i	0.479767	−	0.830980i
$915$	12.9459	+	0.978791i	0.427980	+	0.0323578i
$916$	11.6099	−	3.11086i	0.383602	−	0.102786i
$917$	0.0299909	−	0.0519457i	0.000990386	−	0.00171540i
$918$			36.5067i			1.20490i
$919$	−10.8342	−	6.25513i	−0.357388	−	0.206338i	0.310547	−	0.950558i	$-0.399488\pi$
$919$	−10.8342	−	6.25513i	−0.357388	−	0.206338i	−0.667934	+	0.744220i	$0.732821\pi$
$920$	−11.2790	−	23.4608i	−0.371857	−	0.773480i
$921$	65.1960	+	17.4692i	2.14828	+	0.575630i
$922$	8.32259	−	8.32259i	0.274090	−	0.274090i
$923$	−45.3866	−	12.4504i	−1.49392	−	0.409811i
$924$		−	4.26220i		−	0.140216i
$925$	−19.0053	+	7.42999i	−0.624891	+	0.244297i
$926$	15.3114	+	26.5202i	0.503165	+	0.871508i
$927$	4.40237	+	16.4299i	0.144593	+	0.539628i
$928$	−1.41296			−0.0463826
$929$	−12.6170	−	47.0874i	−0.413952	−	1.54489i	−0.786926	−	0.617047i	$-0.788329\pi$
$929$	−12.6170	−	47.0874i	−0.413952	−	1.54489i	0.372975	−	0.927841i	$-0.378338\pi$
$930$	−0.209786	−	1.11278i	−0.00687915	−	0.0364895i
$931$	−11.7357	+	11.7357i	−0.384623	+	0.384623i
$932$	22.9190	−	6.14112i	0.750736	−	0.201159i
$933$	5.67838	−	21.1920i	0.185902	−	0.693795i
$934$	−6.03874	+	22.5369i	−0.197594	+	0.737429i
$935$	−20.4512	+	17.5761i	−0.668825	+	0.574800i
$936$	−45.1193	+	25.6939i	−1.47477	+	0.839831i
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	0.817306	−	0.576203i	$-0.195466\pi$
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	−0.576203	+	0.817306i	$0.695466\pi$
$938$	−3.59575	−	6.22802i	−0.117405	−	0.203352i
$939$	11.5750	−	6.68281i	0.377735	−	0.218085i
$940$	−16.4514	+	3.10149i	−0.536586	+	0.101159i
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	0.681491	−	0.731827i	$-0.261332\pi$
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	−0.731827	+	0.681491i	$0.761332\pi$
$942$	−50.4324	−	29.1172i	−1.64318	−	0.948688i
$943$	−23.1158	−	13.3459i	−0.752753	−	0.434602i
$944$	−4.21798	−	4.21798i	−0.137284	−	0.137284i
$945$	8.76137	+	5.98191i	0.285007	+	0.194591i
$946$	−11.7074	+	6.75929i	−0.380642	+	0.219764i
$947$	3.35827	+	5.81670i	0.109129	+	0.189017i	0.915418	−	0.402505i	$-0.131860\pi$
$947$	3.35827	+	5.81670i	0.109129	+	0.189017i	−0.806289	+	0.591522i	$0.798527\pi$
$948$	25.5454	+	25.5454i	0.829676	+	0.829676i
$949$	−5.87810	+	10.0431i	−0.190811	+	0.326011i
$950$	11.2568	−	8.28486i	0.365218	−	0.268796i
$951$	−16.5361	+	61.7137i	−0.536221	+	2.00121i
$952$	5.46272	−	20.3871i	0.177048	−	0.660751i
$953$	−17.4402	+	4.67309i	−0.564944	+	0.151376i	−0.529977	−	0.848012i	$-0.677799\pi$
$953$	−17.4402	+	4.67309i	−0.564944	+	0.151376i	−0.0349673	+	0.999388i	$0.511133\pi$
$954$	9.74205	−	9.74205i	0.315411	−	0.315411i
$955$	40.8262	−	7.69672i	1.32111	−	0.249060i
$956$	−0.780600	−	2.91324i	−0.0252464	−	0.0942208i
$957$	−1.35475			−0.0437929
$958$	−10.2765	−	38.3526i	−0.332020	−	1.23912i
$959$	2.12828	+	3.68629i	0.0687257	+	0.119036i
$960$	19.7261	+	41.0311i	0.636656	+	1.32427i
$961$		−	30.9684i		−	0.998981i
$962$	7.44646	+	13.0762i	0.240083	+	0.421595i
$963$	−1.49825	+	1.49825i	−0.0482804	+	0.0482804i
$964$	16.6086	+	4.45026i	0.534927	+	0.143333i
$965$	26.5271	+	9.30197i	0.853938	+	0.299441i
$966$	9.16426	+	5.29099i	0.294855	+	0.170235i
$967$			60.0570i			1.93130i	0.259841	+	0.965651i	$0.416330\pi$
$967$			60.0570i			1.93130i	−0.259841	+	0.965651i	$0.583670\pi$
$968$	−12.4370	+	21.5415i	−0.399740	+	0.692369i
$969$	53.3528	−	14.2958i	1.71394	−	0.459249i
$970$	−11.1977	−	13.0294i	−0.359536	−	0.418348i
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	−0.324942	−	0.945734i	$-0.605345\pi$
$971$	20.4589	−	35.4359i	0.656558	−	1.13719i	0.981501	−	0.191459i	$-0.0613218\pi$
$972$	15.1009	+	4.04627i	0.484361	+	0.129784i
$973$	11.4729	−	6.62390i	0.367805	−	0.212352i
$974$	29.5983			0.948391
$975$	40.6396	−	29.5401i	1.30151	−	0.946040i
$976$	−2.46025			−0.0787506
$977$	32.4724	−	18.7479i	1.03888	−	0.599800i	0.119367	−	0.992850i	$-0.461913\pi$
$977$	32.4724	−	18.7479i	1.03888	−	0.599800i	0.919517	+	0.393050i	$0.128580\pi$
$978$	−58.8694	−	15.7740i	−1.88244	−	0.504397i
$979$	−0.431236	+	0.746923i	−0.0137824	+	0.0238718i
$980$	8.44405	+	9.82532i	0.269735	+	0.313858i
$981$	41.8125	−	11.2036i	1.33497	−	0.357704i
$982$	−3.71959	+	6.44253i	−0.118697	+	0.205589i
$983$			46.1176i			1.47092i	0.677567	+	0.735461i	$0.263034\pi$
$983$			46.1176i			1.47092i	−0.677567	+	0.735461i	$0.736966\pi$
$984$	50.5056	+	29.1594i	1.61006	+	0.929569i
$985$	−30.1452	−	10.5707i	−0.960506	−	0.336810i
$986$	−2.09314	−	0.560854i	−0.0666591	−	0.0178612i
$987$	14.8980	−	14.8980i	0.474208	−	0.474208i
$988$	6.61082	+	6.68975i	0.210318	+	0.212829i
$989$			30.6267i			0.973873i
$990$	7.85528	+	16.3393i	0.249657	+	0.519298i
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	0.859584	−	0.510994i	$-0.170722\pi$
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	−0.872326	+	0.488925i	$0.837389\pi$
$992$	−0.222345	−	0.829802i	−0.00705945	−	0.0263462i
$993$	−93.5143			−2.96759
$994$	−3.32894	−	12.4238i	−0.105587	−	0.394058i
$995$	−32.3795	+	6.10431i	−1.02650	+	0.193520i
$996$	16.1129	−	16.1129i	0.510558	−	0.510558i
$997$	−15.0779	+	4.04012i	−0.477522	+	0.127952i	−0.489549	−	0.871976i	$-0.662838\pi$
$997$	−15.0779	+	4.04012i	−0.477522	+	0.127952i	0.0120264	+	0.999928i	$0.496172\pi$
$998$	−1.58780	+	5.92576i	−0.0502610	+	0.187577i
$999$	−5.20090	+	19.4100i	−0.164549	+	0.614106i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.t.a.37.2	yes	20
3.2	odd	2		585.2.dp.a.37.4		20
5.2	odd	4		325.2.s.b.193.2		20
5.3	odd	4		65.2.o.a.63.4	yes	20
5.4	even	2		325.2.x.b.232.4		20
13.2	odd	12		845.2.k.e.577.3		20
13.3	even	3		845.2.f.e.437.3		20
13.4	even	6		845.2.t.e.657.2		20
13.5	odd	4		845.2.o.e.587.4		20
13.6	odd	12		65.2.o.a.32.4	✓	20
13.7	odd	12		845.2.o.g.357.2		20
13.8	odd	4		845.2.o.f.587.2		20
13.9	even	3		845.2.t.f.657.4		20
13.10	even	6		845.2.f.d.437.8		20
13.11	odd	12		845.2.k.d.577.8		20
13.12	even	2		845.2.t.g.427.4		20
15.8	even	4		585.2.cf.a.388.2		20
39.32	even	12		585.2.cf.a.487.2		20
65.3	odd	12		845.2.k.e.268.3		20
65.8	even	4		845.2.t.e.418.2		20
65.18	even	4		845.2.t.f.418.4		20
65.19	odd	12		325.2.s.b.32.2		20
65.23	odd	12		845.2.k.d.268.8		20
65.28	even	12		845.2.f.e.408.8		20
65.32	even	12		325.2.x.b.318.4		20
65.33	even	12		845.2.t.g.188.4		20
65.38	odd	4		845.2.o.g.258.2		20
65.43	odd	12		845.2.o.f.488.2		20
65.48	odd	12		845.2.o.e.488.4		20
65.58	even	12	inner	65.2.t.a.58.2	yes	20
65.63	even	12		845.2.f.d.408.3		20
195.188	odd	12		585.2.dp.a.253.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	13.6	odd	12
65.2.o.a.63.4	yes	20	5.3	odd	4
65.2.t.a.37.2	yes	20	1.1	even	1	trivial
65.2.t.a.58.2	yes	20	65.58	even	12	inner
325.2.s.b.32.2		20	65.19	odd	12
325.2.s.b.193.2		20	5.2	odd	4
325.2.x.b.232.4		20	5.4	even	2
325.2.x.b.318.4		20	65.32	even	12
585.2.cf.a.388.2		20	15.8	even	4
585.2.cf.a.487.2		20	39.32	even	12
585.2.dp.a.37.4		20	3.2	odd	2
585.2.dp.a.253.4		20	195.188	odd	12
845.2.f.d.408.3		20	65.63	even	12
845.2.f.d.437.8		20	13.10	even	6
845.2.f.e.408.8		20	65.28	even	12
845.2.f.e.437.3		20	13.3	even	3
845.2.k.d.268.8		20	65.23	odd	12
845.2.k.d.577.8		20	13.11	odd	12
845.2.k.e.268.3		20	65.3	odd	12
845.2.k.e.577.3		20	13.2	odd	12
845.2.o.e.488.4		20	65.48	odd	12
845.2.o.e.587.4		20	13.5	odd	4
845.2.o.f.488.2		20	65.43	odd	12
845.2.o.f.587.2		20	13.8	odd	4
845.2.o.g.258.2		20	65.38	odd	4
845.2.o.g.357.2		20	13.7	odd	12
845.2.t.e.418.2		20	65.8	even	4
845.2.t.e.657.2		20	13.4	even	6
845.2.t.f.418.4		20	65.18	even	4
845.2.t.f.657.4		20	13.9	even	3
845.2.t.g.188.4		20	65.33	even	12
845.2.t.g.427.4		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)

\(f(q)\)	\(=\)	\(q+(-0.885613 + 0.511309i) q^{2} +(2.69193 + 0.721300i) q^{3} +(-0.477126 + 0.826407i) q^{4} +(-1.45744 - 1.69584i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(-0.481787 + 0.834479i) q^{7} -3.02107i q^{8} +(4.12812 + 2.38337i) q^{9} +O(q^{10})\)	\(q+(-0.885613 + 0.511309i) q^{2} +(2.69193 + 0.721300i) q^{3} +(-0.477126 + 0.826407i) q^{4} +(-1.45744 - 1.69584i) q^{5} +(-2.75281 + 0.737614i) q^{6} +(-0.481787 + 0.834479i) q^{7} -3.02107i q^{8} +(4.12812 + 2.38337i) q^{9} +(2.15782 + 0.756660i) q^{10} +(1.60661 + 0.430490i) q^{11} +(-1.88048 + 1.88048i) q^{12} +(-3.11175 - 1.82127i) q^{13} -0.985368i q^{14} +(-2.70010 - 5.61633i) q^{15} +(0.590448 + 1.02269i) q^{16} +(-1.87656 - 7.00342i) q^{17} -4.87456 q^{18} +(0.707496 + 2.64041i) q^{19} +(2.09684 - 0.395304i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(-1.64295 + 0.440226i) q^{22} +(-0.997344 + 3.72214i) q^{23} +(2.17910 - 8.13250i) q^{24} +(-0.751762 + 4.94316i) q^{25} +(3.68704 + 0.0218799i) q^{26} +(3.48159 + 3.48159i) q^{27} +(-0.459747 - 0.796304i) q^{28} +(-0.253107 + 0.146132i) q^{29} +(5.26292 + 3.59331i) q^{30} +(-0.125649 - 0.125649i) q^{31} +(4.18683 + 2.41727i) q^{32} +(4.01436 + 2.31769i) q^{33} +(5.24282 + 5.24282i) q^{34} +(2.11732 - 0.399166i) q^{35} +(-3.93927 + 2.27434i) q^{36} +(2.04061 + 3.53443i) q^{37} +(-1.97663 - 1.97663i) q^{38} +(-7.06291 - 7.14724i) q^{39} +(-5.12326 + 4.40302i) q^{40} +(-1.79277 + 6.69071i) q^{41} +(0.710745 - 2.65254i) q^{42} +(7.67707 - 2.05706i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(-1.97465 - 10.4743i) q^{45} +(-1.01990 - 3.80633i) q^{46} -7.84582 q^{47} +(0.851780 + 3.17888i) q^{48} +(3.03576 + 5.25810i) q^{49} +(-1.86171 - 4.76211i) q^{50} -20.2063i q^{51} +(2.98981 - 1.70259i) q^{52} +(-1.99855 + 1.99855i) q^{53} +(-4.86351 - 1.30317i) q^{54} +(-1.61149 - 3.35197i) q^{55} +(2.52102 + 1.45551i) q^{56} +7.61811i q^{57} +(0.149437 - 0.258832i) q^{58} +(-4.87924 + 1.30739i) q^{59} +(5.92967 + 0.448318i) q^{60} +(-1.04169 + 1.80425i) q^{61} +(0.175522 + 0.0470311i) q^{62} +(-3.97775 + 2.29655i) q^{63} -7.30568 q^{64} +(1.44658 + 7.93142i) q^{65} -4.74023 q^{66} +(6.32050 - 3.64915i) q^{67} +(6.68304 + 1.79071i) q^{68} +(-5.36956 + 9.30034i) q^{69} +(-1.67103 + 1.43611i) q^{70} +(12.6082 - 3.37837i) q^{71} +(7.20034 - 12.4713i) q^{72} -3.22747i q^{73} +(-3.61437 - 2.08676i) q^{74} +(-5.58919 + 12.7644i) q^{75} +(-2.51962 - 0.675130i) q^{76} +(-1.13328 + 1.13328i) q^{77} +(9.90945 + 2.71836i) q^{78} -13.5845i q^{79} +(0.873774 - 2.49180i) q^{80} +(-0.289196 - 0.500902i) q^{81} +(-1.83332 - 6.84204i) q^{82} -8.56854 q^{83} +(-0.663230 - 2.47521i) q^{84} +(-9.14173 + 13.3894i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(-0.786751 + 0.210809i) q^{87} +(1.30054 - 4.85368i) q^{88} +(-0.134207 + 0.500868i) q^{89} +(7.10435 + 8.26648i) q^{90} +(3.01901 - 1.71922i) q^{91} +(-2.60014 - 2.60014i) q^{92} +(-0.247608 - 0.428870i) q^{93} +(6.94836 - 4.01164i) q^{94} +(3.44659 - 5.04803i) q^{95} +(9.52707 + 9.52707i) q^{96} +(-6.50662 - 3.75660i) q^{97} +(-5.37702 - 3.10442i) q^{98} +(5.60626 + 5.60626i) 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

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