LMFDB - Embedded newform 722.2.i.a.501.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$16$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			501.16
Character	$\chi$	$=$	722.501
Dual form			722.2.i.a.49.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.926494 + 0.376309i) q^{2} +(2.90522 + 0.651074i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0514187 - 1.86537i) q^{5} +(2.44666 + 1.69648i) q^{6} +(-0.742684 - 2.93279i) q^{7} +(0.401695 + 0.915773i) q^{8} +(5.30331 + 2.50269i) q^{9} +O(q^{10})$	\(q+(0.926494 + 0.376309i) q^{2} +(2.90522 + 0.651074i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0514187 - 1.86537i) q^{5} +(2.44666 + 1.69648i) q^{6} +(-0.742684 - 2.93279i) q^{7} +(0.401695 + 0.915773i) q^{8} +(5.30331 + 2.50269i) q^{9} +(0.654318 - 1.74761i) q^{10} +(0.216512 - 2.61291i) q^{11} +(1.62842 + 2.49248i) q^{12} +(0.162577 + 0.519789i) q^{13} +(0.415545 - 2.99669i) q^{14} +(1.06511 - 5.45279i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-2.99652 + 2.91506i) q^{17} +(3.97170 + 4.31441i) q^{18} +(-0.717523 + 4.29944i) q^{19} +(1.26386 - 1.37292i) q^{20} +(-0.248192 - 9.00394i) q^{21} +(1.18386 - 2.33937i) q^{22} +(-5.32737 + 1.19389i) q^{23} +(0.570776 + 2.92205i) q^{24} +(1.51543 - 0.0836089i) q^{25} +(-0.0449744 + 0.542761i) q^{26} +(6.72935 + 5.23766i) q^{27} +(1.51268 - 2.62005i) q^{28} +(-1.53393 - 0.433753i) q^{29} +(3.03876 - 4.65116i) q^{30} +(-0.470692 - 0.366354i) q^{31} +(-0.350638 + 0.936511i) q^{32} +(2.33021 - 7.45011i) q^{33} +(-3.87323 + 1.57317i) q^{34} +(-5.43257 + 1.53618i) q^{35} +(2.05620 + 5.49187i) q^{36} +(-0.574887 + 6.93786i) q^{37} +(-2.28270 + 3.71339i) q^{38} +(0.133901 + 1.61595i) q^{39} +(1.68760 - 0.796400i) q^{40} +(8.71349 + 7.58858i) q^{41} +(3.15832 - 8.43549i) q^{42} +(0.214111 + 0.571866i) q^{43} +(1.97717 - 1.72192i) q^{44} +(4.39576 - 10.0213i) q^{45} +(-5.38505 - 0.898606i) q^{46} +(-6.37672 - 4.42152i) q^{47} +(-0.570776 + 2.92205i) q^{48} +(-1.89338 + 1.02465i) q^{49} +(1.43550 + 0.492809i) q^{50} +(-10.6035 + 6.51793i) q^{51} +(-0.245915 + 0.485940i) q^{52} +(-2.87371 - 1.99258i) q^{53} +(4.26372 + 7.38498i) q^{54} +(-4.88519 - 0.269523i) q^{55} +(2.38744 - 1.85822i) q^{56} +(-4.88381 + 12.0236i) q^{57} +(-1.25795 - 0.979100i) q^{58} +(5.22045 + 4.54650i) q^{59} +(4.56567 - 3.16576i) q^{60} +(-3.61905 - 4.92390i) q^{61} +(-0.298231 - 0.516551i) q^{62} +(3.40119 - 17.4122i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(0.961241 - 0.329994i) q^{65} +(4.96247 - 6.02560i) q^{66} +(-3.26793 - 0.361695i) q^{67} -4.18052 q^{68} -16.2545 q^{69} +(-5.61132 - 0.621061i) q^{70} +(-4.05297 + 5.51426i) q^{71} +(-0.161583 + 5.86195i) q^{72} +(-2.34883 + 2.28498i) q^{73} +(-3.14341 + 6.21155i) q^{74} +(4.45710 + 0.743758i) q^{75} +(-3.51229 + 2.58143i) q^{76} +(-7.82393 + 1.30558i) q^{77} +(-0.484038 + 1.54756i) q^{78} +(2.66114 + 7.10758i) q^{79} +(1.86325 - 0.102798i) q^{80} +(4.95612 + 6.01788i) q^{81} +(5.21734 + 10.3097i) q^{82} +(1.96757 - 1.06479i) q^{83} +(6.10052 - 6.62693i) q^{84} +(5.59176 + 5.43974i) q^{85} +(-0.0168256 + 0.610403i) q^{86} +(-4.17398 - 2.25884i) q^{87} +(2.47981 - 0.851319i) q^{88} +(-0.562682 - 0.547385i) q^{89} +(7.84377 - 7.63054i) q^{90} +(1.40369 - 0.862845i) q^{91} +(-4.65107 - 2.85900i) q^{92} +(-1.12894 - 1.37079i) q^{93} +(-4.24413 - 6.49613i) q^{94} +(8.05695 + 1.11738i) q^{95} +(-1.62842 + 2.49248i) q^{96} +(-13.4044 + 1.48360i) q^{97} +(-2.13979 + 0.236832i) q^{98} +(7.68754 - 13.3152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) $ 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{57}\right)$

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 $

$2$	0.926494	+	0.376309i	0.655130	+	0.266091i
$2$	0.926494	+	0.376309i	0.655130	+	0.266091i
$3$	2.90522	+	0.651074i	1.67733	+	0.375898i	0.950452	−	0.310872i	$-0.100621\pi$
$3$	2.90522	+	0.651074i	1.67733	+	0.375898i	0.726875	+	0.686770i	$0.240972\pi$
$4$	0.716783	+	0.697297i	0.358391	+	0.348648i
$5$	−0.0514187	−	1.86537i	−0.0229951	−	0.834220i	−0.919936	−	0.392069i	$-0.871759\pi$
$5$	−0.0514187	−	1.86537i	−0.0229951	−	0.834220i	0.896941	−	0.442151i	$-0.145784\pi$
$6$	2.44666	+	1.69648i	0.998845	+	0.692583i
$7$	−0.742684	−	2.93279i	−0.280708	−	1.10849i	−0.935683	−	0.352841i	$-0.885216\pi$
$7$	−0.742684	−	2.93279i	−0.280708	−	1.10849i	0.654975	−	0.755651i	$-0.272679\pi$
$8$	0.401695	+	0.915773i	0.142021	+	0.323775i
$9$	5.30331	+	2.50269i	1.76777	+	0.834231i
$10$	0.654318	−	1.74761i	0.206914	−	0.552642i
$11$	0.216512	−	2.61291i	0.0652808	−	0.787823i	−0.882791	−	0.469766i	$-0.844338\pi$
$11$	0.216512	−	2.61291i	0.0652808	−	0.787823i	0.948072	−	0.318056i	$-0.103030\pi$
$12$	1.62842	+	2.49248i	0.470083	+	0.719516i
$13$	0.162577	+	0.519789i	0.0450909	+	0.144164i	0.974225	−	0.225580i	$-0.0724278\pi$
$13$	0.162577	+	0.519789i	0.0450909	+	0.144164i	−0.929134	+	0.369744i	$0.879445\pi$
$14$	0.415545	−	2.99669i	0.111059	−	0.800900i
$15$	1.06511	−	5.45279i	0.275011	−	1.40790i
$16$	0.0275543	+	0.999620i	0.00688859	+	0.249905i
$17$	−2.99652	+	2.91506i	−0.726764	+	0.707006i	−0.964429	−	0.264340i	$-0.914846\pi$
$17$	−2.99652	+	2.91506i	−0.726764	+	0.707006i	0.237666	+	0.971347i	$0.423618\pi$
$18$	3.97170	+	4.31441i	0.936138	+	1.01692i
$19$	−0.717523	+	4.29944i	−0.164611	+	0.986359i
$19$	−0.717523	+	4.29944i	−0.164611	+	0.986359i
$20$	1.26386	−	1.37292i	0.282608	−	0.306994i
$21$	−0.248192	−	9.00394i	−0.0541599	−	1.96482i
$22$	1.18386	−	2.33937i	0.252400	−	0.498756i
$23$	−5.32737	+	1.19389i	−1.11083	+	0.248944i	−0.735217	−	0.677831i	$-0.762920\pi$
$23$	−5.32737	+	1.19389i	−1.11083	+	0.248944i	−0.375617	+	0.926775i	$0.622569\pi$
$24$	0.570776	+	2.92205i	0.116509	+	0.596461i
$25$	1.51543	−	0.0836089i	0.303087	−	0.0167218i
$26$	−0.0449744	+	0.542761i	−0.00882021	+	0.106444i
$27$	6.72935	+	5.23766i	1.29506	+	1.00799i
$28$	1.51268	−	2.62005i	0.285870	−	0.495142i
$29$	−1.53393	−	0.433753i	−0.284843	−	0.0805459i	0.126685	−	0.991943i	$-0.459566\pi$
$29$	−1.53393	−	0.433753i	−0.284843	−	0.0805459i	−0.411528	+	0.911397i	$0.635005\pi$
$30$	3.03876	−	4.65116i	0.554799	−	0.849182i
$31$	−0.470692	−	0.366354i	−0.0845388	−	0.0657992i	0.571062	−	0.820907i	$-0.306532\pi$
$31$	−0.470692	−	0.366354i	−0.0845388	−	0.0657992i	−0.655600	+	0.755108i	$0.727584\pi$
$32$	−0.350638	+	0.936511i	−0.0619845	+	0.165553i
$33$	2.33021	−	7.45011i	0.405638	−	1.29690i
$34$	−3.87323	+	1.57317i	−0.664253	+	0.269796i
$35$	−5.43257	+	1.53618i	−0.918271	+	0.259662i
$36$	2.05620	+	5.49187i	0.342700	+	0.915311i
$37$	−0.574887	+	6.93786i	−0.0945109	+	1.14058i	0.770028	+	0.638010i	$0.220242\pi$
$37$	−0.574887	+	6.93786i	−0.0945109	+	1.14058i	−0.864539	+	0.502566i	$0.832389\pi$
$38$	−2.28270	+	3.71339i	−0.370303	+	0.602392i
$39$	0.133901	+	1.61595i	0.0214414	+	0.258759i
$40$	1.68760	−	0.796400i	0.266834	−	0.125922i
$41$	8.71349	+	7.58858i	1.36082	+	1.18514i	0.963580	+	0.267422i	$0.0861718\pi$
$41$	8.71349	+	7.58858i	1.36082	+	1.18514i	0.397238	+	0.917715i	$0.369969\pi$
$42$	3.15832	−	8.43549i	0.487339	−	1.30162i
$43$	0.214111	+	0.571866i	0.0326517	+	0.0872088i	0.951821	−	0.306653i	$-0.0992091\pi$
$43$	0.214111	+	0.571866i	0.0326517	+	0.0872088i	−0.919170	+	0.393862i	$0.871139\pi$
$44$	1.97717	−	1.72192i	0.298069	−	0.259589i
$45$	4.39576	−	10.0213i	0.655282	−	1.49389i
$46$	−5.38505	−	0.898606i	−0.793983	−	0.132492i
$47$	−6.37672	−	4.42152i	−0.930140	−	0.644945i	0.00470927	−	0.999989i	$-0.498501\pi$
$47$	−6.37672	−	4.42152i	−0.930140	−	0.644945i	−0.934850	+	0.355044i	$0.884466\pi$
$48$	−0.570776	+	2.92205i	−0.0823844	+	0.421762i
$49$	−1.89338	+	1.02465i	−0.270483	+	0.146378i
$50$	1.43550	+	0.492809i	0.203011	+	0.0696937i
$51$	−10.6035	+	6.51793i	−1.48478	+	0.912692i
$52$	−0.245915	+	0.485940i	−0.0341022	+	0.0673878i
$53$	−2.87371	−	1.99258i	−0.394734	−	0.273702i	0.355763	−	0.934576i	$-0.384221\pi$
$53$	−2.87371	−	1.99258i	−0.394734	−	0.273702i	−0.750497	+	0.660874i	$0.770186\pi$
$54$	4.26372	+	7.38498i	0.580219	+	1.00497i
$55$	−4.88519	−	0.269523i	−0.658719	−	0.0363425i
$56$	2.38744	−	1.85822i	0.319035	−	0.248315i
$57$	−4.88381	+	12.0236i	−0.646877	+	1.59257i
$58$	−1.25795	−	0.979100i	−0.165177	−	0.128562i
$59$	5.22045	+	4.54650i	0.679645	+	0.591903i	0.926112	−	0.377248i	$-0.123129\pi$
$59$	5.22045	+	4.54650i	0.679645	+	0.591903i	−0.246467	+	0.969151i	$0.579270\pi$
$60$	4.56567	−	3.16576i	0.589425	−	0.408698i
$61$	−3.61905	−	4.92390i	−0.463372	−	0.630441i	0.509862	−	0.860256i	$-0.329696\pi$
$61$	−3.61905	−	4.92390i	−0.463372	−	0.630441i	−0.973234	+	0.229816i	$0.926188\pi$
$62$	−0.298231	−	0.516551i	−0.0378753	−	0.0656020i
$63$	3.40119	−	17.4122i	0.428510	−	2.19373i
$64$	−0.677282	+	0.735724i	−0.0846602	+	0.0919655i
$65$	0.961241	−	0.329994i	0.119227	−	0.0409308i
$66$	4.96247	−	6.02560i	0.610838	−	0.741700i
$67$	−3.26793	−	0.361695i	−0.399242	−	0.0441881i	−0.0918541	−	0.995772i	$-0.529279\pi$
$67$	−3.26793	−	0.361695i	−0.399242	−	0.0441881i	−0.307388	+	0.951584i	$0.599455\pi$
$68$	−4.18052			−0.506962
$69$	−16.2545			−1.95681
$70$	−5.61132	−	0.621061i	−0.670681	−	0.0742310i
$71$	−4.05297	+	5.51426i	−0.480999	+	0.654422i	−0.976835	−	0.213994i	$-0.931353\pi$
$71$	−4.05297	+	5.51426i	−0.480999	+	0.654422i	0.495836	+	0.868416i	$0.334862\pi$
$72$	−0.161583	+	5.86195i	−0.0190428	+	0.690837i
$73$	−2.34883	+	2.28498i	−0.274910	+	0.267436i	−0.821810	−	0.569761i	$-0.807036\pi$
$73$	−2.34883	+	2.28498i	−0.274910	+	0.267436i	0.546901	+	0.837198i	$0.315808\pi$
$74$	−3.14341	+	6.21155i	−0.365414	+	0.722078i
$75$	4.45710	+	0.743758i	0.514662	+	0.0858818i
$76$	−3.51229	+	2.58143i	−0.402888	+	0.296111i
$77$	−7.82393	+	1.30558i	−0.891620	+	0.148785i
$78$	−0.484038	+	1.54756i	−0.0548065	+	0.175226i
$79$	2.66114	+	7.10758i	0.299401	+	0.799666i	0.996570	+	0.0827581i	$0.0263729\pi$
$79$	2.66114	+	7.10758i	0.299401	+	0.799666i	−0.697168	+	0.716908i	$0.745557\pi$
$80$	1.86325	−	0.102798i	0.208317	−	0.0114932i
$81$	4.95612	+	6.01788i	0.550680	+	0.668653i
$82$	5.21734	+	10.3097i	0.576159	+	1.13852i
$83$	1.96757	−	1.06479i	0.215968	−	0.116876i	−0.364362	−	0.931257i	$-0.618713\pi$
$83$	1.96757	−	1.06479i	0.215968	−	0.116876i	0.580330	+	0.814381i	$0.302923\pi$
$84$	6.10052	−	6.62693i	0.665621	−	0.723057i
$85$	5.59176	+	5.43974i	0.606511	+	0.590023i
$86$	−0.0168256	+	0.610403i	−0.00181436	+	0.0658214i
$87$	−4.17398	−	2.25884i	−0.447497	−	0.242174i
$88$	2.47981	−	0.851319i	0.264348	−	0.0907509i
$89$	−0.562682	−	0.547385i	−0.0596442	−	0.0580227i	0.666871	−	0.745173i	$-0.267633\pi$
$89$	−0.562682	−	0.547385i	−0.0596442	−	0.0580227i	−0.726515	+	0.687150i	$0.758861\pi$
$90$	7.84377	−	7.63054i	0.826806	−	0.804329i
$91$	1.40369	−	0.862845i	0.147147	−	0.0904507i
$92$	−4.65107	−	2.85900i	−0.484907	−	0.298071i
$93$	−1.12894	−	1.37079i	−0.117065	−	0.142145i
$94$	−4.24413	−	6.49613i	−0.437749	−	0.670025i
$95$	8.05695	+	1.11738i	0.826625	+	0.114641i
$96$	−1.62842	+	2.49248i	−0.166199	+	0.254387i
$97$	−13.4044	+	1.48360i	−1.36101	+	0.150637i	−0.760686	−	0.649120i	$-0.775137\pi$
$97$	−13.4044	+	1.48360i	−1.36101	+	0.150637i	−0.600324	+	0.799757i	$0.704962\pi$
$98$	−2.13979	+	0.236832i	−0.216151	+	0.0239236i
$99$	7.68754	−	13.3152i	0.772627	−	1.33823i
$100$	1.14454	+	0.996778i	0.114454	+	0.0996778i
$101$	−1.87441	−	0.884557i	−0.186511	−	0.0880167i	0.331246	−	0.943544i	$-0.392531\pi$
$101$	−1.87441	−	0.884557i	−0.186511	−	0.0880167i	−0.517757	+	0.855528i	$0.673233\pi$
$102$	−12.2768	+	2.04864i	−1.21558	+	0.202845i
$103$	3.95437	−	15.6154i	0.389635	−	1.53864i	−0.395002	−	0.918680i	$-0.629256\pi$
$103$	3.95437	−	15.6154i	0.389635	−	1.53864i	0.784637	−	0.619955i	$-0.212849\pi$
$104$	−0.410702	+	0.357681i	−0.0402727	+	0.0350735i
$105$	−16.7829	+	0.925941i	−1.63785	+	0.0903626i
$106$	−1.91264	−	2.92752i	−0.185772	−	0.284346i
$107$	5.96388	−	4.64187i	0.576550	−	0.448747i	−0.283489	−	0.958975i	$-0.591492\pi$
$107$	5.96388	−	4.64187i	0.576550	−	0.448747i	0.860039	+	0.510229i	$0.170439\pi$
$108$	1.17127	+	8.44662i	0.112706	+	0.812776i
$109$	10.9539	−	7.59527i	1.04919	−	0.727495i	0.0859985	−	0.996295i	$-0.472592\pi$
$109$	10.9539	−	7.59527i	1.04919	−	0.727495i	0.963196	+	0.268800i	$0.0866270\pi$
$110$	−4.42467	−	2.08805i	−0.421876	−	0.199088i
$111$	−6.18723	+	19.7817i	−0.587266	+	1.87759i
$112$	2.91122	−	0.823213i	0.275084	−	0.0777863i
$113$	4.41101	−	17.4187i	0.414953	−	1.63861i	−0.310668	−	0.950518i	$-0.600553\pi$
$113$	4.41101	−	17.4187i	0.414953	−	1.63861i	0.725621	−	0.688094i	$-0.241552\pi$
$114$	−9.04943	+	9.30200i	−0.847557	+	0.871212i
$115$	2.50098	+	9.87615i	0.233218	+	0.920956i
$116$	−0.797036	−	1.38051i	−0.0740030	−	0.128177i
$117$	−0.438673	+	3.16348i	−0.0405554	+	0.292464i
$118$	3.12583	+	6.17681i	0.287756	+	0.568621i
$119$	10.7747	+	6.62321i	0.987719	+	0.607149i
$120$	5.42137	−	1.21496i	0.494901	−	0.110910i
$121$	4.06954	+	0.679087i	0.369959	+	0.0617352i
$122$	−1.50012	−	5.92385i	−0.135815	−	0.536320i
$123$	20.3738	+	27.7196i	1.83705	+	2.49939i
$124$	−0.0819261	−	0.590808i	−0.00735718	−	0.0530561i
$125$	−1.00438	−	12.1211i	−0.0898347	−	1.08414i
$126$	9.70357	−	14.8524i	0.864462	−	1.32316i
$127$	3.70377	−	6.41512i	0.328657	−	0.569250i	−0.653589	−	0.756850i	$-0.726737\pi$
$127$	3.70377	−	6.41512i	0.328657	−	0.569250i	0.982246	+	0.187600i	$0.0600707\pi$
$128$	−0.904357	+	0.426776i	−0.0799346	+	0.0377221i
$129$	0.249713	+	1.80080i	0.0219860	+	0.158551i
$130$	1.01476	+	0.0559861i	0.0890007	+	0.00491031i
$131$	2.38678	−	17.2122i	0.208534	−	1.50384i	−0.540520	−	0.841331i	$-0.681773\pi$
$131$	2.38678	−	17.2122i	0.208534	−	1.50384i	0.749055	−	0.662508i	$-0.230508\pi$
$132$	6.86519	−	3.71526i	0.597538	−	0.323372i
$133$	13.1423	−	1.08878i	1.13958	−	0.0944089i
$134$	−2.89161	−	1.56486i	−0.249797	−	0.135183i
$135$	9.42418	−	12.8221i	0.811104	−	1.10355i
$136$	−3.87323	−	1.57317i	−0.332126	−	0.134898i
$137$	−17.7451	−	1.96403i	−1.51607	−	0.167799i	−0.686882	−	0.726769i	$-0.741021\pi$
$137$	−17.7451	−	1.96403i	−1.51607	−	0.167799i	−0.829188	+	0.558970i	$0.811197\pi$
$138$	−15.0597	−	6.11671i	−1.28197	−	0.520689i
$139$	10.8259	−	13.1452i	0.918244	−	1.11496i	−0.0747982	−	0.997199i	$-0.523831\pi$
$139$	10.8259	−	13.1452i	0.918244	−	1.11496i	0.993042	−	0.117763i	$-0.0375722\pi$
$140$	−4.96514	−	2.68700i	−0.419631	−	0.227093i
$141$	−15.6470	−	16.9972i	−1.31772	−	1.43142i
$142$	−5.83012	+	3.58376i	−0.489253	+	0.300742i
$143$	1.39336	−	0.312260i	0.116519	−	0.0261125i
$144$	−2.35561	+	5.37025i	−0.196301	+	0.447521i
$145$	−0.730238	+	2.88365i	−0.0606430	+	0.239474i
$146$	−3.03603	+	1.23313i	−0.251264	+	0.102055i
$147$	−6.16780	+	1.74409i	−0.508712	+	0.143850i
$148$	−5.24982	+	4.57207i	−0.431532	+	0.375822i
$149$	1.74299	+	8.92315i	0.142792	+	0.731013i	0.982248	+	0.187586i	$0.0600665\pi$
$149$	1.74299	+	8.92315i	0.142792	+	0.731013i	−0.839457	+	0.543427i	$0.817127\pi$
$150$	3.84959	+	2.36634i	0.314318	+	0.193211i
$151$	17.8492	+	6.12764i	1.45255	+	0.498660i	0.934275	−	0.356554i	$-0.116049\pi$
$151$	17.8492	+	6.12764i	1.45255	+	0.498660i	0.518274	+	0.855215i	$0.326575\pi$
$152$	−4.22554	+	1.06998i	−0.342736	+	0.0867865i
$153$	−23.1870	+	7.96010i	−1.87456	+	0.643536i
$154$	−7.74013	−	1.73460i	−0.623717	−	0.139778i
$155$	−0.659185	+	0.896853i	−0.0529470	+	0.0720370i
$156$	−1.03082	+	1.25165i	−0.0825315	+	0.100212i
$157$	6.74116	+	1.51073i	0.538003	+	0.120569i	0.479209	−	0.877701i	$-0.340924\pi$
$157$	6.74116	+	1.51073i	0.538003	+	0.120569i	0.0587943	+	0.998270i	$0.481274\pi$
$158$	−0.209122	+	7.58655i	−0.0166368	+	0.603553i
$159$	−7.05142	−	7.65988i	−0.559214	−	0.607468i
$160$	1.76497	+	0.605916i	0.139533	+	0.0479018i
$161$	7.45800	+	14.7374i	0.587772	+	1.16147i
$162$	2.32723	+	7.44056i	0.182844	+	0.584586i
$163$	−17.7686	+	13.8298i	−1.39174	+	1.08324i	−0.406205	+	0.913782i	$0.633148\pi$
$163$	−17.7686	+	13.8298i	−1.39174	+	1.08324i	−0.985538	+	0.169455i	$0.945799\pi$
$164$	0.954181	+	11.5152i	0.0745090	+	0.899190i
$165$	−14.0170	−	3.96364i	−1.09123	−	0.308569i
$166$	2.22363	−	0.246111i	0.172587	−	0.0191019i
$167$	−2.64220	−	0.747143i	−0.204459	−	0.0578156i	0.168334	−	0.985730i	$-0.446161\pi$
$167$	−2.64220	−	0.747143i	−0.204459	−	0.0578156i	−0.372793	+	0.927914i	$0.621600\pi$
$168$	8.14587	−	3.84413i	0.628468	−	0.296581i
$169$	10.4394	−	7.23849i	0.803028	−	0.556807i
$170$	3.13370	+	7.14412i	0.240344	+	0.547929i
$171$	−14.5654	+	21.0055i	−1.11384	+	1.60633i
$172$	−0.245289	+	0.559203i	−0.0187031	+	0.0426388i
$173$	−0.341010	−	1.74578i	−0.0259265	−	0.132729i	0.966242	−	0.257637i	$-0.0829437\pi$
$173$	−0.341010	−	1.74578i	−0.0259265	−	0.132729i	−0.992168	+	0.124907i	$0.960137\pi$
$174$	−3.01714	−	3.66351i	−0.228729	−	0.277730i
$175$	−1.37070	−	4.38236i	−0.103615	−	0.331275i
$176$	2.61789	+	0.144433i	0.197331	+	0.0108870i
$177$	12.2064	+	16.6075i	0.917492	+	1.24829i
$178$	−0.315335	−	0.718892i	−0.0236354	−	0.0538832i
$179$	−4.52587	+	0.755234i	−0.338279	+	0.0564488i	−0.331296	−	0.943527i	$-0.607486\pi$
$179$	−4.52587	+	0.755234i	−0.338279	+	0.0564488i	−0.00698307	+	0.999976i	$0.502223\pi$
$180$	10.1387	−	4.11796i	0.755690	−	0.306935i
$181$	−20.6234	+	8.37650i	−1.53293	+	0.622620i	−0.977874	−	0.209196i	$-0.932915\pi$
$181$	−20.6234	+	8.37650i	−1.53293	+	0.622620i	−0.555051	+	0.831816i	$0.687301\pi$
$182$	1.62521	−	0.271199i	0.120468	−	0.0201026i
$183$	−7.30831	−	16.6613i	−0.540245	−	1.23164i
$184$	−3.23332	−	4.39909i	−0.238363	−	0.324305i
$185$	12.9713	+	0.715644i	0.953665	+	0.0526152i
$186$	−0.530112	−	1.69486i	−0.0388697	−	0.124273i
$187$	6.96802	+	8.46080i	0.509552	+	0.618715i
$188$	−1.48761	−	7.61574i	−0.108495	−	0.555435i
$189$	10.3632	−	23.6257i	0.753812	−	1.71852i
$190$	7.04424	+	4.06715i	0.511043	+	0.295062i
$191$	−8.32408	−	18.9770i	−0.602309	−	1.37313i	−0.907184	−	0.420735i	$-0.861772\pi$
$191$	−8.32408	−	18.9770i	−0.602309	−	1.37313i	0.304874	−	0.952393i	$-0.401386\pi$
$192$	−2.44666	+	1.69648i	−0.176572	+	0.122433i
$193$	7.99165	−	3.77135i	0.575251	−	0.271468i	−0.116991	−	0.993133i	$-0.537325\pi$
$193$	7.99165	−	3.77135i	0.575251	−	0.271468i	0.692242	+	0.721665i	$0.256623\pi$
$194$	−12.9774	−	3.66965i	−0.931722	−	0.263466i
$195$	3.00746	−	0.332866i	0.215369	−	0.0238370i
$196$	−2.07163	−	0.585800i	−0.147973	−	0.0418428i
$197$	1.30518	+	15.7512i	0.0929904	+	1.12223i	0.870104	+	0.492867i	$0.164051\pi$
$197$	1.30518	+	15.7512i	0.0929904	+	1.12223i	−0.777114	+	0.629360i	$0.783317\pi$
$198$	12.1331	−	9.44357i	0.862262	−	0.671125i
$199$	−3.52214	−	11.2609i	−0.249678	−	0.798265i	−0.991777	−	0.127975i	$-0.959152\pi$
$199$	−3.52214	−	11.2609i	−0.249678	−	0.798265i	0.742099	−	0.670290i	$-0.233830\pi$
$200$	0.685310	+	1.35421i	0.0484587	+	0.0957571i
$201$	−9.25856	−	3.17847i	−0.653049	−	0.224192i
$202$	−1.40377	−	1.52490i	−0.0987686	−	0.107291i
$203$	−0.132885	+	4.82083i	−0.00932671	+	0.338356i
$204$	−12.1453	−	2.72183i	−0.850342	−	0.190566i
$205$	13.7075	−	16.6441i	0.957373	−	1.16247i
$206$	9.53993	−	12.9795i	0.664679	−	0.904328i
$207$	−31.2406	−	7.00119i	−2.17138	−	0.486617i
$208$	−0.515112	+	0.176838i	−0.0357166	+	0.0122615i
$209$	11.0787	+	2.80571i	0.766330	+	0.194075i
$210$	−15.8977	−	5.45770i	−1.09705	−	0.376617i
$211$	4.15505	+	2.55410i	0.286045	+	0.175831i	0.659263	−	0.751912i	$-0.270868\pi$
$211$	4.15505	+	2.55410i	0.286045	+	0.175831i	−0.373218	+	0.927744i	$0.621746\pi$
$212$	−0.670400	−	3.43208i	−0.0460433	−	0.235716i
$213$	−15.3649	+	13.3813i	−1.05279	+	0.916874i
$214$	7.27227	−	2.05640i	0.497122	−	0.140573i
$215$	1.05573	−	0.428802i	0.0720005	−	0.0292441i
$216$	−2.09336	+	8.26650i	−0.142435	+	0.562464i
$217$	−0.724866	+	1.65253i	−0.0492071	+	0.112181i
$218$	13.0069	−	2.91492i	0.880939	−	0.197423i
$219$	−8.31154	+	5.10908i	−0.561642	+	0.345240i
$220$	−3.31368	−	3.59962i	−0.223408	−	0.242686i
$221$	−2.00238	−	1.08364i	−0.134695	−	0.0728933i
$222$	−13.1765	+	15.9993i	−0.884346	+	1.07380i
$223$	10.2987	+	4.18296i	0.689650	+	0.280112i	0.694100	−	0.719878i	$-0.255802\pi$
$223$	10.2987	+	4.18296i	0.689650	+	0.280112i	−0.00445015	+	0.999990i	$0.501417\pi$
$224$	3.00701	+	0.332815i	0.200914	+	0.0222372i
$225$	8.24606	+	3.34926i	0.549738	+	0.223284i
$226$	10.6416	−	14.4784i	0.707868	−	0.963089i
$227$	−11.6867	−	6.32454i	−0.775675	−	0.419774i	0.0393316	−	0.999226i	$-0.487477\pi$
$227$	−11.6867	−	6.32454i	−0.775675	−	0.419774i	−0.815006	+	0.579452i	$0.803267\pi$
$228$	−11.8847	+	5.21286i	−0.787082	+	0.345230i
$229$	3.39866	−	1.83926i	0.224590	−	0.121542i	−0.359757	−	0.933046i	$-0.617140\pi$
$229$	3.39866	−	1.83926i	0.224590	−	0.121542i	0.584347	+	0.811504i	$0.301351\pi$
$230$	−1.39934	+	10.0913i	−0.0922700	+	0.665403i
$231$	−23.5802	−	1.30096i	−1.55147	−	0.0855967i
$232$	−0.218952	−	1.57896i	−0.0143749	−	0.103664i
$233$	−3.45602	+	1.63093i	−0.226411	+	0.106846i	−0.536625	−	0.843821i	$-0.680301\pi$
$233$	−3.45602	+	1.63093i	−0.226411	+	0.106846i	0.310214	+	0.950667i	$0.399599\pi$
$234$	−1.59688	+	2.76587i	−0.104391	+	0.180811i
$235$	−7.91990	+	12.1223i	−0.516637	+	0.790772i
$236$	0.571672	+	6.89905i	0.0372127	+	0.449090i
$237$	3.10362	+	22.3817i	0.201602	+	1.45385i
$238$	7.49036	+	10.1910i	0.485528	+	0.660585i
$239$	−0.705093	−	2.78435i	−0.0456087	−	0.180105i	0.942404	−	0.334476i	$-0.108559\pi$
$239$	−0.705093	−	2.78435i	−0.0456087	−	0.180105i	−0.988013	+	0.154372i	$0.950665\pi$
$240$	5.48007	+	0.914461i	0.353737	+	0.0590282i
$241$	−3.03421	+	0.679983i	−0.195451	+	0.0438016i	−0.315307	−	0.948990i	$-0.602108\pi$
$241$	−3.03421	+	0.679983i	−0.195451	+	0.0438016i	0.119856	+	0.992791i	$0.461757\pi$
$242$	3.51486	+	2.16058i	0.225944	+	0.138887i
$243$	−1.07077	−	2.11590i	−0.0686899	−	0.135735i
$244$	0.839345	−	6.05292i	0.0537336	−	0.387498i
$245$	2.00870	+	3.47918i	0.128331	+	0.222276i
$246$	8.44509	+	33.3489i	0.538439	+	2.12625i
$247$	−2.35145	+	0.326031i	−0.149619	+	0.0207448i
$248$	0.146423	−	0.578210i	0.00929785	−	0.0367164i
$249$	6.40946	−	1.81242i	0.406183	−	0.114858i
$250$	3.63073	−	11.6081i	0.229627	−	0.734159i
$251$	−23.1735	−	10.9358i	−1.46270	−	0.690264i	−0.480307	−	0.877100i	$-0.659475\pi$
$251$	−23.1735	−	10.9358i	−1.46270	−	0.690264i	−0.982391	+	0.186837i	$0.940177\pi$
$252$	14.5794	−	10.1091i	0.918416	−	0.636815i
$253$	1.96609	+	14.1784i	0.123607	+	0.891391i
$254$	5.84560	−	4.54981i	0.366785	−	0.285480i
$255$	12.7036	+	19.4443i	0.795529	+	1.21765i
$256$	−0.998482	+	0.0550878i	−0.0624051	+	0.00344299i
$257$	−19.9256	+	17.3532i	−1.24292	+	1.08246i	−0.249452	+	0.968387i	$0.580250\pi$
$257$	−19.9256	+	17.3532i	−1.24292	+	1.08246i	−0.993472	+	0.114076i	$0.963609\pi$
$258$	−0.446300	+	1.76240i	−0.0277854	+	0.109722i
$259$	20.7743	−	3.46661i	1.29085	−	0.215405i
$260$	0.919105	+	0.433736i	0.0570005	+	0.0268992i
$261$	−7.04933	−	6.13927i	−0.436343	−	0.380011i
$262$	8.68846	−	15.0489i	0.536775	−	0.929722i
$263$	−24.4646	+	2.70774i	−1.50855	+	0.166966i	−0.825915	−	0.563794i	$-0.809341\pi$
$263$	−24.4646	+	2.70774i	−1.50855	+	0.166966i	−0.682634	+	0.730760i	$0.739166\pi$
$264$	7.75864	−	0.858727i	0.477512	−	0.0528510i
$265$	−3.56915	+	5.46299i	−0.219251	+	0.335589i
$266$	12.5859	+	3.93681i	0.771693	+	0.241381i
$267$	−1.27832	−	1.95662i	−0.0782321	−	0.119743i
$268$	−2.09019	−	2.53798i	−0.127679	−	0.155032i
$269$	−9.46357	−	5.81723i	−0.577004	−	0.354683i	0.204229	−	0.978923i	$-0.434531\pi$
$269$	−9.46357	−	5.81723i	−0.577004	−	0.354683i	−0.781232	+	0.624240i	$0.785409\pi$
$270$	13.5565	−	8.33315i	0.825023	−	0.507140i
$271$	−19.9921	+	19.4486i	−1.21443	+	1.18142i	−0.236693	+	0.971584i	$0.576064\pi$
$271$	−19.9921	+	19.4486i	−1.21443	+	1.18142i	−0.977737	+	0.209832i	$0.932708\pi$
$272$	−2.99652	−	2.91506i	−0.181691	−	0.176752i
$273$	4.63980	−	1.59284i	0.280813	−	0.0964034i
$274$	−15.7017	−	8.49733i	−0.948573	−	0.513342i
$275$	0.109647	−	3.97780i	0.00661198	−	0.239870i
$276$	−11.6509	−	11.3342i	−0.701303	−	0.682238i
$277$	9.26564	−	10.0652i	0.556718	−	0.604757i	−0.392354	−	0.919814i	$-0.628339\pi$
$277$	9.26564	−	10.0652i	0.556718	−	0.604757i	0.949073	+	0.315057i	$0.102024\pi$
$278$	14.9768	−	8.10505i	0.898250	−	0.486109i
$279$	−1.57935	−	3.12089i	−0.0945534	−	0.186843i
$280$	−3.58903	−	4.35792i	−0.214486	−	0.260436i
$281$	14.0299	−	0.774049i	0.836951	−	0.0461759i	0.368460	−	0.929644i	$-0.379885\pi$
$281$	14.0299	−	0.774049i	0.836951	−	0.0461759i	0.468492	+	0.883468i	$0.344798\pi$
$282$	−8.10066	−	21.6359i	−0.482387	−	1.28840i
$283$	0.196665	−	0.628772i	0.0116905	−	0.0373766i	−0.948377	−	0.317146i	$-0.897276\pi$
$283$	0.196665	−	0.628772i	0.0116905	−	0.0373766i	0.960067	+	0.279769i	$0.0902580\pi$
$284$	−6.75017	+	1.12640i	−0.400549	+	0.0668398i
$285$	22.6797	+	8.49189i	1.34343	+	0.503016i
$286$	1.40845	+	0.235029i	0.0832833	+	0.0138975i
$287$	15.7844	−	31.1908i	0.931722	−	1.84113i
$288$	−4.20334	+	4.08907i	−0.247684	+	0.240951i
$289$	0.0131362	−	0.476556i	0.000772716	−	0.0280327i
$290$	−1.76170	+	2.39689i	−0.103451	+	0.140750i
$291$	−39.9086	−	4.41708i	−2.33948	−	0.258934i
$292$	−3.27690			−0.191766
$293$	29.4339			1.71955			0.859775	−	0.510674i	$-0.170604\pi$
$293$	29.4339			1.71955			0.859775	+	0.510674i	$0.170604\pi$
$294$	−6.37075	−	0.705114i	−0.371550	−	0.0411231i
$295$	8.21248	−	9.97187i	0.478149	−	0.580585i
$296$	−6.58443	+	2.26044i	−0.382712	+	0.131385i
$297$	15.1425	−	16.4492i	0.878659	−	0.954478i
$298$	−1.74299	+	8.92315i	−0.100969	+	0.516904i
$299$	−1.48668	−	2.57501i	−0.0859771	−	0.148917i
$300$	2.67615	+	3.64103i	0.154508	+	0.210215i
$301$	1.51815	−	1.05266i	0.0875046	−	0.0606744i
$302$	14.2313	+	12.3941i	0.818919	+	0.713197i
$303$	−4.86966	−	3.79021i	−0.279755	−	0.217742i
$304$	−4.31758	−	0.598783i	−0.247630	−	0.0343425i
$305$	−8.99882	+	7.00406i	−0.515271	+	0.401052i
$306$	−24.4781	−	1.35049i	−1.39932	−	0.0772025i
$307$	12.9422	+	22.4166i	0.738653	+	1.27938i	0.953102	+	0.302649i	$0.0978710\pi$
$307$	12.9422	+	22.4166i	0.738653	+	1.27938i	−0.214449	+	0.976735i	$0.568796\pi$
$308$	−6.51844	−	4.51978i	−0.371422	−	0.257539i
$309$	21.6551	−	42.7916i	1.23192	−	2.43433i
$310$	−0.948225	+	0.582872i	−0.0538556	+	0.0331049i
$311$	28.3339	+	9.72706i	1.60667	+	0.551571i	0.974718	−	0.223437i	$-0.0717275\pi$
$311$	28.3339	+	9.72706i	1.60667	+	0.551571i	0.631952	+	0.775007i	$0.282254\pi$
$312$	−1.42606	+	0.771743i	−0.0807345	+	0.0436913i
$313$	−6.39496	+	32.7386i	−0.361465	+	1.85050i	0.146625	+	0.989192i	$0.453159\pi$
$313$	−6.39496	+	32.7386i	−0.361465	+	1.85050i	−0.508089	+	0.861304i	$0.669648\pi$
$314$	5.67715	+	3.93645i	0.320380	+	0.222146i
$315$	−32.6552	−	5.44918i	−1.83991	−	0.307027i
$316$	−3.04864	+	6.95020i	−0.171499	+	0.390979i
$317$	23.4064	−	20.3846i	1.31463	−	1.14491i	0.335422	−	0.942068i	$-0.391121\pi$
$317$	23.4064	−	20.3846i	1.31463	−	1.14491i	0.979210	−	0.202847i	$-0.0650194\pi$
$318$	−3.65061	−	9.75035i	−0.204716	−	0.546772i
$319$	−1.46547	+	3.91410i	−0.0820506	+	0.219147i
$320$	1.40722	+	1.22555i	0.0786662	+	0.0685105i
$321$	20.3485	−	9.60271i	1.13575	−	0.535971i
$322$	1.36397	+	16.4606i	0.0760109	+	0.917315i
$323$	−10.3831	−	14.9750i	−0.577729	−	0.833231i
$324$	−0.643790	+	7.76940i	−0.0357661	+	0.431633i
$325$	0.289834	+	0.774113i	0.0160771	+	0.0429401i
$326$	−21.6668	+	6.12678i	−1.20001	+	0.339331i
$327$	36.7686	−	14.9341i	2.03331	−	0.825858i
$328$	−3.44925	+	11.0279i	−0.190453	+	0.608913i
$329$	−8.23151	+	21.9854i	−0.453818	+	1.21209i
$330$	−11.4952	−	8.94704i	−0.632787	−	0.492518i
$331$	6.90816	−	10.5737i	0.379707	−	0.581184i	−0.595261	−	0.803533i	$-0.702951\pi$
$331$	6.90816	−	10.5737i	0.379707	−	0.581184i	0.974967	+	0.222348i	$0.0713722\pi$
$332$	2.15279	+	0.608752i	0.118150	+	0.0334096i
$333$	−20.4121	+	35.3548i	−1.11858	+	1.93743i
$334$	−2.16682	−	1.68651i	−0.118563	−	0.0922816i
$335$	−0.506663	+	6.11451i	−0.0276820	+	0.334072i
$336$	8.99368	−	0.496195i	0.490646	−	0.0270697i
$337$	0.592538	+	3.03346i	0.0322776	+	0.165243i	0.994106	−	0.108408i	$-0.0345754\pi$
$337$	0.592538	+	3.03346i	0.0322776	+	0.165243i	−0.961829	+	0.273652i	$0.911768\pi$
$338$	12.3959	−	2.77799i	0.674249	−	0.151103i
$339$	24.1558	−	47.7332i	1.31196	−	2.59251i
$340$	0.214957	+	7.79823i	0.0116577	+	0.422918i
$341$	−1.05916	+	1.15056i	−0.0573568	+	0.0623061i
$342$	−21.3993	+	13.9804i	−1.15714	+	0.755972i
$343$	−9.93193	−	10.7889i	−0.536274	−	0.582548i
$344$	−0.437692	+	0.425794i	−0.0235988	+	0.0229573i
$345$	0.835783	+	30.3207i	0.0449971	+	1.63241i
$346$	0.341010	−	1.74578i	0.0183328	−	0.0938539i
$347$	3.63369	−	26.2043i	0.195067	−	1.40672i	−0.599903	−	0.800072i	$-0.704794\pi$
$347$	3.63369	−	26.2043i	0.195067	−	1.40672i	0.794970	−	0.606648i	$-0.207486\pi$
$348$	−1.41675	−	4.52960i	−0.0759458	−	0.242812i
$349$	13.5265	+	20.7038i	0.724056	+	1.10825i	0.989557	+	0.144140i	$0.0460415\pi$
$349$	13.5265	+	20.7038i	0.724056	+	1.10825i	−0.265501	+	0.964111i	$0.585537\pi$
$350$	0.379181	−	4.57604i	0.0202681	−	0.244600i
$351$	−1.62844	+	4.34937i	−0.0869197	+	0.232152i
$352$	2.37110	+	1.11895i	0.126380	+	0.0596403i
$353$	8.08014	+	18.4209i	0.430062	+	0.980443i	0.988545	+	0.150927i	$0.0482258\pi$
$353$	8.08014	+	18.4209i	0.430062	+	0.980443i	−0.558483	+	0.829516i	$0.688616\pi$
$354$	5.05965	+	19.9801i	0.268917	+	1.06193i
$355$	10.4946	+	7.27676i	0.556993	+	0.386210i
$356$	−0.0216305	−	0.784713i	−0.00114641	−	0.0415897i
$357$	26.9908	+	26.2570i	1.42850	+	1.38967i
$358$	−4.47739	−	1.00341i	−0.236638	−	0.0530317i
$359$	−3.94780	−	1.60346i	−0.208357	−	0.0846273i	0.269744	−	0.962932i	$-0.413061\pi$
$359$	−3.94780	−	1.60346i	−0.208357	−	0.0846273i	−0.478101	+	0.878305i	$0.658675\pi$
$360$	10.9430			0.576748
$361$	−17.9703	−	6.16989i	−0.945806	−	0.324731i
$362$	−22.2596			−1.16994
$363$	11.3808	+	4.62247i	0.597335	+	0.242617i
$364$	1.60780	+	0.360316i	0.0842716	+	0.0188857i
$365$	4.38310	+	4.26395i	0.229422	+	0.223185i
$366$	−0.501314	−	18.1867i	−0.0262041	−	0.950636i
$367$	23.8569	+	16.5420i	1.24532	+	0.863486i	0.994519	−	0.104552i	$-0.0333410\pi$
$367$	23.8569	+	16.5420i	1.24532	+	0.863486i	0.250801	+	0.968039i	$0.419306\pi$
$368$	−1.34023	−	5.29245i	−0.0698644	−	0.275888i
$369$	27.2184	+	62.0518i	1.41693	+	3.23029i
$370$	11.7485	+	5.54424i	0.610775	+	0.288232i
$371$	−3.70958	+	9.90785i	−0.192592	+	0.514390i
$372$	0.146647	−	1.76977i	0.00760329	−	0.0917580i
$373$	11.1889	+	17.1259i	0.579339	+	0.886744i	0.999788	−	0.0205721i	$-0.00654877\pi$
$373$	11.1889	+	17.1259i	0.579339	+	0.886744i	−0.420450	+	0.907316i	$0.638128\pi$
$374$	3.27195	+	10.4610i	0.169189	+	0.540926i
$375$	4.97378	−	35.8683i	0.256845	−	1.85223i
$376$	1.48761	−	7.61574i	0.0767176	−	0.392752i
$377$	−0.0239217	−	0.867836i	−0.00123203	−	0.0446958i
$378$	18.4920	−	17.9893i	0.951127	−	0.925271i
$379$	16.4886	+	17.9114i	0.846961	+	0.920045i	0.997649	−	0.0685362i	$-0.0218329\pi$
$379$	16.4886	+	17.9114i	0.846961	+	0.920045i	−0.150687	+	0.988581i	$0.548149\pi$
$380$	4.99594	+	6.41900i	0.256286	+	0.329288i
$381$	14.9370	−	16.2259i	0.765245	−	0.831277i
$382$	−0.570991	−	20.7145i	−0.0292145	−	1.05985i
$383$	9.77067	−	19.3074i	0.499258	−	0.986561i	−0.493871	−	0.869535i	$-0.664418\pi$
$383$	9.77067	−	19.3074i	0.499258	−	0.986561i	0.993129	−	0.117026i	$-0.0373359\pi$
$384$	−2.90522	+	0.651074i	−0.148256	+	0.0332250i
$385$	2.83770	+	14.5274i	0.144622	+	0.740386i
$386$	8.82341	−	0.486801i	0.449100	−	0.0247775i
$387$	−0.295706	+	3.56864i	−0.0150316	+	0.181404i
$388$	−10.6425	−	8.28342i	−0.540293	−	0.420527i
$389$	−18.4099	+	31.8869i	−0.933421	+	1.61673i	−0.155995	+	0.987758i	$0.549858\pi$
$389$	−18.4099	+	31.8869i	−0.933421	+	1.61673i	−0.777426	+	0.628974i	$0.783475\pi$
$390$	2.91166	+	0.823338i	0.147437	+	0.0416914i
$391$	12.4833	−	19.1072i	0.631309	−	0.966290i
$392$	−1.69891	−	1.32231i	−0.0858077	−	0.0667868i
$393$	18.1406	−	48.4513i	0.915070	−	2.44404i
$394$	−4.71808	+	15.0846i	−0.237694	+	0.759949i
$395$	13.1215	−	5.32948i	0.660213	−	0.268155i
$396$	14.7950	−	4.18361i	0.743474	−	0.210235i
$397$	−1.79737	−	4.80056i	−0.0902074	−	0.240933i	0.883627	−	0.468191i	$-0.155094\pi$
$397$	−1.79737	−	4.80056i	−0.0902074	−	0.240933i	−0.973835	+	0.227258i	$0.927024\pi$
$398$	0.974344	−	11.7586i	0.0488394	−	0.589404i
$399$	38.8900	+	5.39345i	1.94693	+	0.270010i
$400$	0.125334	+	1.51256i	0.00626670	+	0.0756278i
$401$	−22.8329	+	10.7751i	−1.14022	+	0.538084i	−0.901403	−	0.432980i	$-0.857462\pi$
$401$	−22.8329	+	10.7751i	−1.14022	+	0.538084i	−0.238819	+	0.971064i	$0.576760\pi$
$402$	−7.38191	−	6.42892i	−0.368176	−	0.320645i
$403$	0.113903	−	0.304221i	0.00567391	−	0.0151543i
$404$	−0.726748	−	1.94106i	−0.0361571	−	0.0965712i
$405$	10.9708	−	9.55444i	0.545141	−	0.474764i
$406$	−1.93724	+	4.41646i	−0.0961436	+	0.219185i
$407$	18.0035	+	3.00426i	0.892402	+	0.148916i
$408$	−10.2283	−	7.09215i	−0.506377	−	0.351114i
$409$	0.474975	−	2.43160i	0.0234860	−	0.120235i	−0.967866	−	0.251468i	$-0.919087\pi$
$409$	0.474975	−	2.43160i	0.0234860	−	0.120235i	0.991352	+	0.131233i	$0.0418936\pi$
$410$	18.9632	−	10.2624i	0.936528	−	0.506824i
$411$	−50.2747	−	17.2593i	−2.47987	−	0.851340i
$412$	13.7230	−	8.43551i	0.676085	−	0.415588i
$413$	9.45679	−	18.6871i	0.465338	−	0.919533i
$414$	−26.3097	−	18.2427i	−1.29305	−	0.896580i
$415$	−2.08741	−	3.61549i	−0.102467	−	0.177478i
$416$	−0.543794	−	0.0300020i	−0.0266617	−	0.00147097i
$417$	40.0102	−	31.1412i	1.95931	−	1.52499i
$418$	9.20853	+	6.76849i	0.450404	+	0.331058i
$419$	13.6698	+	10.6396i	0.667813	+	0.519780i	0.890427	−	0.455127i	$-0.150406\pi$
$419$	13.6698	+	10.6396i	0.667813	+	0.519780i	−0.222613	+	0.974907i	$0.571459\pi$
$420$	−12.6754	−	11.0390i	−0.618495	−	0.538648i
$421$	7.52416	−	5.21714i	0.366705	−	0.254268i	−0.372091	−	0.928196i	$-0.621359\pi$
$421$	7.52416	−	5.21714i	0.366705	−	0.254268i	0.738797	+	0.673928i	$0.235394\pi$
$422$	2.88850	+	3.92994i	0.140610	+	0.191306i
$423$	−22.7520	−	39.4077i	−1.10624	−	1.91607i
$424$	0.670400	−	3.43208i	0.0325575	−	0.166676i
$425$	−4.29731	+	4.66812i	−0.208450	+	0.226437i
$426$	−19.2710	+	6.61576i	−0.933685	+	0.320534i
$427$	−11.7530	+	14.2708i	−0.568766	+	0.690614i
$428$	7.51156	+	0.831380i	0.363085	+	0.0401862i
$429$	4.25132			0.205256
$430$	1.13949			0.0549513
$431$	−19.1817	−	2.12303i	−0.923949	−	0.102263i	−0.364571	−	0.931176i	$-0.618784\pi$
$431$	−19.1817	−	2.12303i	−0.923949	−	0.102263i	−0.559378	+	0.828913i	$0.688960\pi$
$432$	−5.05025	+	6.87111i	−0.242980	+	0.330587i
$433$	−1.00460	+	36.4449i	−0.0482779	+	1.75143i	0.457901	+	0.889003i	$0.348601\pi$
$433$	−1.00460	+	36.4449i	−0.0482779	+	1.75143i	−0.506179	+	0.862428i	$0.668943\pi$
$434$	−1.29345	+	1.25828i	−0.0620874	+	0.0603995i
$435$	−3.99897	+	7.90217i	−0.191736	+	0.378880i
$436$	13.1477	+	2.19397i	0.629662	+	0.105072i
$437$	−1.31055	−	23.7614i	−0.0626921	−	1.13666i
$438$	−9.62319	+	1.60583i	−0.459814	+	0.0767293i
$439$	−3.74444	+	11.9716i	−0.178712	+	0.571375i	0.821287	+	0.570515i	$0.193256\pi$
$439$	−3.74444	+	11.9716i	−0.178712	+	0.571375i	−1.00000		0.000860164i	$0.999726\pi$
$440$	−1.71554	−	4.58199i	−0.0817849	−	0.218438i
$441$	−12.6056	+	0.695468i	−0.600265	+	0.0331175i
$442$	−1.44741	−	1.75750i	−0.0688465	−	0.0835957i
$443$	−12.9722	−	25.6337i	−0.616326	−	1.21789i	−0.960314	−	0.278920i	$-0.910024\pi$
$443$	−12.9722	−	25.6337i	−0.616326	−	1.21789i	0.343988	−	0.938974i	$-0.388222\pi$
$444$	−18.2286	+	9.86482i	−0.865091	+	0.468164i
$445$	−0.992146	+	1.07776i	−0.0470322	+	0.0510906i
$446$	7.96757	+	7.75097i	0.377275	+	0.367019i
$447$	−0.745862	+	27.0585i	−0.0352781	+	1.27982i
$448$	2.66073	+	1.43992i	0.125708	+	0.0680297i
$449$	15.6262	−	5.36448i	0.737446	−	0.253166i	0.0697137	−	0.997567i	$-0.477791\pi$
$449$	15.6262	−	5.36448i	0.737446	−	0.253166i	0.667732	+	0.744402i	$0.267265\pi$
$450$	6.37957	+	6.20614i	0.300736	+	0.292560i
$451$	21.7149	−	21.1246i	1.02251	−	0.994716i
$452$	15.3077	−	9.40963i	0.720015	−	0.442592i
$453$	47.8663	+	29.4233i	2.24895	+	1.38243i
$454$	−8.44769	−	10.2575i	−0.396470	−	0.481407i
$455$	−1.68170	−	2.57404i	−0.0788395	−	0.120673i
$456$	−12.9727	+	0.357373i	−0.607504	+	0.0167355i
$457$	−7.22139	+	11.0532i	−0.337802	+	0.517045i	−0.965151	−	0.261694i	$-0.915719\pi$
$457$	−7.22139	+	11.0532i	−0.337802	+	0.517045i	0.627349	+	0.778738i	$0.284140\pi$
$458$	3.84097	−	0.425118i	0.179477	−	0.0198645i
$459$	−35.4328	+	3.92170i	−1.65386	+	0.183049i
$460$	−5.09395	+	8.82298i	−0.237507	+	0.411373i
$461$	−21.1790	−	18.4448i	−0.986404	−	0.859060i	0.00361501	−	0.999993i	$-0.498849\pi$
$461$	−21.1790	−	18.4448i	−0.986404	−	0.859060i	−0.990019	+	0.140933i	$0.954990\pi$
$462$	−21.3574	−	10.0788i	−0.993635	−	0.468908i
$463$	−15.4252	+	2.57402i	−0.716871	+	0.119625i	−0.511778	−	0.859118i	$-0.671013\pi$
$463$	−15.4252	+	2.57402i	−0.716871	+	0.119625i	−0.205093	+	0.978742i	$0.565750\pi$
$464$	0.391322	−	1.54529i	0.0181667	−	0.0717385i
$465$	−2.49899	+	2.17637i	−0.115888	+	0.100927i
$466$	−3.81572	+	0.210519i	−0.176760	+	0.00975210i
$467$	−4.18927	−	6.41216i	−0.193856	−	0.296719i	0.726987	−	0.686651i	$-0.240920\pi$
$467$	−4.18927	−	6.41216i	−0.193856	−	0.296719i	−0.920844	+	0.389931i	$0.872499\pi$
$468$	−2.52032	+	1.96164i	−0.116502	+	0.0906770i
$469$	1.36627	+	9.85280i	0.0630883	+	0.454960i
$470$	−11.8995	+	8.25092i	−0.548882	+	0.380586i
$471$	18.6009	+	8.77799i	0.857086	+	0.404469i
$472$	−2.06653	+	6.60706i	−0.0951197	+	0.304115i
$473$	1.54059	−	0.435638i	0.0708366	−	0.0200307i
$474$	−5.54695	+	21.9044i	−0.254780	+	1.00610i
$475$	−0.727889	+	6.57551i	−0.0333978	+	0.301705i
$476$	3.10481	+	12.2606i	0.142309	+	0.561964i
$477$	−10.2533	−	17.7593i	−0.469468	−	0.813142i
$478$	0.394512	−	2.84502i	0.0180446	−	0.130128i
$479$	2.36682	+	4.67696i	0.108143	+	0.213696i	0.939905	−	0.341436i	$-0.110913\pi$
$479$	2.36682	+	4.67696i	0.108143	+	0.213696i	−0.831762	+	0.555132i	$0.812668\pi$
$480$	4.73313	+	2.90944i	0.216037	+	0.132797i
$481$	−3.69969	+	0.829119i	−0.168691	+	0.0378046i
$482$	−3.06706	−	0.511803i	−0.139701	−	0.0233120i
$483$	12.0719	+	47.6710i	0.549293	+	2.16911i
$484$	2.44345	+	3.32444i	0.111066	+	0.151111i
$485$	3.45670	+	24.9279i	0.156961	+	1.13192i
$486$	−0.195829	−	2.36331i	−0.00888299	−	0.107202i
$487$	−7.78162	+	11.9107i	−0.352619	+	0.539724i	−0.968788	−	0.247890i	$-0.920263\pi$
$487$	−7.78162	+	11.9107i	−0.352619	+	0.539724i	0.616169	+	0.787614i	$0.288684\pi$
$488$	3.05542	−	5.29214i	0.138312	−	0.239564i
$489$	−60.6258	+	28.6100i	−2.74159	+	1.29379i
$490$	0.551805	+	3.97933i	0.0249280	+	0.179768i
$491$	−33.4038	−	1.84294i	−1.50749	−	0.0831706i	−0.717616	−	0.696439i	$-0.754767\pi$
$491$	−33.4038	−	1.84294i	−1.50749	−	0.0831706i	−0.789875	+	0.613268i	$0.789855\pi$
$492$	−4.72518	+	34.0755i	−0.213028	+	1.53624i
$493$	5.86086	−	3.17174i	0.263960	−	0.142848i
$494$	−2.30130	−	0.582808i	−0.103540	−	0.0262218i
$495$	−25.2331	−	13.6555i	−1.13414	−	0.613768i
$496$	0.353245	−	0.480608i	0.0158612	−	0.0215799i
$497$	19.1823	+	7.79116i	0.860442	+	0.349481i
$498$	6.62036	+	0.732741i	0.296665	+	0.0328349i
$499$	9.89403	+	4.01861i	0.442918	+	0.179898i	0.586860	−	0.809688i	$-0.300364\pi$
$499$	9.89403	+	4.01861i	0.442918	+	0.179898i	−0.143942	+	0.989586i	$0.545978\pi$
$500$	7.73208	−	9.38854i	0.345789	−	0.419868i
$501$	−7.18971	−	3.89088i	−0.321213	−	0.173832i
$502$	−17.3548	−	18.8524i	−0.774585	−	0.841423i
$503$	26.2506	−	16.1362i	1.17046	−	0.719478i	0.204676	−	0.978830i	$-0.434386\pi$
$503$	26.2506	−	16.1362i	1.17046	−	0.719478i	0.965783	+	0.259352i	$0.0835089\pi$
$504$	17.3119	−	3.87969i	0.771133	−	0.172815i
$505$	−1.55365	+	3.54196i	−0.0691365	+	0.157615i
$506$	−3.51391	+	13.8761i	−0.156212	+	0.616868i
$507$	35.0414	−	14.2326i	1.55624	−	0.632091i
$508$	7.12805	−	2.01562i	0.316256	−	0.0894286i
$509$	−5.15489	+	4.48940i	−0.228487	+	0.198989i	−0.763415	−	0.645908i	$-0.776479\pi$
$509$	−5.15489	+	4.48940i	−0.228487	+	0.198989i	0.534928	+	0.844897i	$0.320339\pi$
$510$	4.45273	+	22.7955i	0.197170	+	1.00940i
$511$	8.44580	+	5.19161i	0.373620	+	0.229663i
$512$	−0.945817	−	0.324699i	−0.0417996	−	0.0143498i
$513$	−27.3475	+	25.1743i	−1.20742	+	1.11147i
$514$	−24.9911	+	8.57946i	−1.10231	+	0.378424i
$515$	−29.3320	−	6.57344i	−1.29252	−	0.289661i
$516$	−1.07670	+	1.46490i	−0.0473991	+	0.0644888i
$517$	−12.9337	+	15.7045i	−0.568823	+	0.690683i
$518$	20.5517	+	4.60575i	0.902992	+	0.202365i
$519$	0.145925	−	5.29390i	0.00640541	−	0.232376i
$520$	0.688326	+	0.747722i	0.0301851	+	0.0327898i
$521$	8.32374	+	2.85754i	0.364670	+	0.125191i	0.500944	−	0.865480i	$-0.332986\pi$
$521$	8.32374	+	2.85754i	0.364670	+	0.125191i	−0.136274	+	0.990671i	$0.543513\pi$
$522$	−4.22090	−	8.34072i	−0.184744	−	0.365064i
$523$	−2.74322	−	8.77055i	−0.119952	−	0.383509i	0.874967	−	0.484182i	$-0.160883\pi$
$523$	−2.74322	−	8.77055i	−0.119952	−	0.383509i	−0.994920	+	0.100673i	$0.967900\pi$
$524$	13.7128	−	10.6731i	0.599048	−	0.466258i
$525$	−1.12893	−	13.6241i	−0.0492704	−	0.594606i
$526$	−23.6852	−	6.69754i	−1.03272	−	0.292027i
$527$	2.47838	−	0.274307i	0.107960	−	0.0119490i
$528$	7.51149	+	2.12405i	0.326895	+	0.0924372i
$529$	6.15531	−	2.90476i	0.267622	−	0.126294i
$530$	−5.36257	+	3.71832i	−0.232935	+	0.161514i
$531$	16.3072	+	37.1767i	0.707672	+	1.61333i
$532$	10.1793	+	8.38364i	0.441330	+	0.363477i
$533$	−2.52785	+	5.76291i	−0.109493	+	0.249619i
$534$	−0.448065	−	2.29384i	−0.0193897	−	0.0992643i
$535$	−8.96547	−	10.8862i	−0.387611	−	0.470650i
$536$	−0.981484	−	3.13798i	−0.0423936	−	0.135540i
$537$	−13.6403	−	0.752558i	−0.588624	−	0.0324753i
$538$	−6.57886	−	8.95086i	−0.283635	−	0.385899i
$539$	2.26737	+	5.16909i	0.0976626	+	0.222648i
$540$	15.6959	−	2.61918i	0.675443	−	0.112711i
$541$	−0.935611	+	0.380012i	−0.0402251	+	0.0163380i	−0.396333	−	0.918107i	$-0.629718\pi$
$541$	−0.935611	+	0.380012i	−0.0402251	+	0.0163380i	0.356108	+	0.934445i	$0.384103\pi$
$542$	−25.8412	+	10.4958i	−1.10997	+	0.450833i
$543$	−65.3691	+	10.9082i	−2.80526	+	0.468115i
$544$	−1.67930	−	3.82841i	−0.0719992	−	0.164142i
$545$	−14.7313	−	20.0426i	−0.631018	−	0.858530i
$546$	4.89815	+	0.270238i	0.209621	+	0.0115651i
$547$	−10.4499	−	33.4102i	−0.446805	−	1.42852i	−0.856431	−	0.516262i	$-0.827323\pi$
$547$	−10.4499	−	33.4102i	−0.446805	−	1.42852i	0.409626	−	0.912254i	$-0.365659\pi$
$548$	−11.3499	−	13.7814i	−0.484843	−	0.588713i
$549$	−6.86995	−	35.1703i	−0.293202	−	1.50103i
$550$	1.59847	−	3.64415i	0.0681590	−	0.155387i
$551$	2.96552	−	6.28379i	0.126335	−	0.267698i
$552$	−6.52935	−	14.8854i	−0.277908	−	0.633566i
$553$	18.8687	−	13.0833i	0.802378	−	0.556357i
$554$	12.3722	−	5.83857i	0.525644	−	0.248057i
$555$	37.2183	+	10.5243i	1.57983	+	0.446734i
$556$	16.9259	−	1.87336i	0.717820	−	0.0794483i
$557$	8.36426	+	2.36519i	0.354405	+	0.100216i	0.444652	−	0.895703i	$-0.353327\pi$
$557$	8.36426	+	2.36519i	0.354405	+	0.100216i	−0.0902475	+	0.995919i	$0.528766\pi$
$558$	−0.288842	−	3.48581i	−0.0122277	−	0.147566i
$559$	−0.262440	+	0.204265i	−0.0111000	+	0.00863950i
$560$	−1.68529	−	5.38817i	−0.0712165	−	0.227692i
$561$	14.7350	+	29.1171i	0.622112	+	1.22933i
$562$	13.2899	+	4.56242i	0.560599	+	0.192454i
$563$	−16.0916	−	17.4802i	−0.678181	−	0.736701i	0.297783	−	0.954634i	$-0.403753\pi$
$563$	−16.0916	−	17.4802i	−0.678181	−	0.736701i	−0.975964	+	0.217933i	$0.930069\pi$
$564$	0.636579	−	23.0939i	0.0268048	−	0.972428i
$565$	−32.7192	−	7.33254i	−1.37651	−	0.308482i
$566$	0.418821	−	0.508547i	0.0176044	−	0.0213758i
$567$	13.9684	−	19.0047i	0.586616	−	0.798120i
$568$	−6.67787	−	1.49655i	−0.280197	−	0.0627937i
$569$	4.93160	−	1.69302i	0.206743	−	0.0709750i	−0.219383	−	0.975639i	$-0.570404\pi$
$569$	4.93160	−	1.69302i	0.206743	−	0.0709750i	0.426126	+	0.904664i	$0.359878\pi$
$570$	17.8170	+	16.4023i	0.746272	+	0.687015i
$571$	39.1271	+	13.4324i	1.63742	+	0.562127i	0.981292	−	0.192524i	$-0.0616674\pi$
$571$	39.1271	+	13.4324i	1.63742	+	0.562127i	0.656127	+	0.754651i	$0.272194\pi$
$572$	1.21648	+	0.747765i	0.0508634	+	0.0312656i
$573$	−11.8278	−	60.5519i	−0.494114	−	2.52959i
$574$	26.3615	−	22.9583i	1.10031	−	0.958259i
$575$	−7.97347	+	2.25468i	−0.332517	+	0.0940267i
$576$	−5.43312	+	2.20674i	−0.226380	+	0.0919477i
$577$	11.4005	−	45.0194i	0.474607	−	1.87418i	−0.0108875	−	0.999941i	$-0.503466\pi$
$577$	11.4005	−	45.0194i	0.474607	−	1.87418i	0.485494	−	0.874240i	$-0.338640\pi$
$578$	0.191503	−	0.436583i	0.00796548	−	0.0181595i
$579$	25.6729	−	5.75343i	1.06693	−	0.239104i
$580$	−2.53418	+	1.55775i	−0.105226	+	0.0646822i
$581$	−4.58410	−	4.97966i	−0.190180	−	0.206591i
$582$	−35.3129	−	19.1104i	−1.46377	−	0.792150i
$583$	−5.82864	+	7.07732i	−0.241397	+	0.293113i
$584$	−3.03603	−	1.23313i	−0.125632	−	0.0510273i
$585$	5.92363	+	0.655627i	0.244912	+	0.0271069i
$586$	27.2704	+	11.0763i	1.12653	+	0.457556i
$587$	−23.9912	+	32.6413i	−0.990225	+	1.34725i	−0.0529727	+	0.998596i	$0.516870\pi$
$587$	−23.9912	+	32.6413i	−0.990225	+	1.34725i	−0.937252	+	0.348653i	$0.886639\pi$
$588$	−5.63712	−	3.05066i	−0.232471	−	0.125807i
$589$	1.91285	−	1.76084i	0.0788176	−	0.0725542i
$590$	11.3613	−	6.14844i	0.467738	−	0.253127i
$591$	−6.46337	+	46.6104i	−0.265867	+	1.91730i
$592$	−6.95106	−	0.383501i	−0.285687	−	0.0157618i
$593$	3.31150	+	23.8808i	0.135987	+	0.980668i	0.928637	+	0.370990i	$0.120982\pi$
$593$	3.31150	+	23.8808i	0.135987	+	0.980668i	−0.792650	+	0.609677i	$0.791299\pi$
$594$	20.2194	−	9.54179i	0.829614	−	0.391504i
$595$	11.8007	−	20.4395i	0.483783	−	0.837937i
$596$	−4.97274	+	7.61134i	−0.203691	+	0.311773i
$597$	−2.90089	−	35.0085i	−0.118726	−	1.43280i
$598$	−0.408402	−	2.94518i	−0.0167008	−	0.120438i
$599$	−4.91577	−	6.68814i	−0.200853	−	0.273270i	0.693670	−	0.720293i	$-0.255993\pi$
$599$	−4.91577	−	6.68814i	−0.200853	−	0.273270i	−0.894522	+	0.447023i	$0.852484\pi$
$600$	1.10928	+	4.38046i	0.0452863	+	0.178831i
$601$	6.73672	+	1.12416i	0.274796	+	0.0458554i	0.300388	−	0.953817i	$-0.402884\pi$
$601$	6.73672	+	1.12416i	0.274796	+	0.0458554i	−0.0255917	+	0.999672i	$0.508147\pi$
$602$	1.80268	−	0.403990i	0.0734718	−	0.0164654i
$603$	−16.4256	−	10.0968i	−0.668904	−	0.411174i
$604$	8.52122	+	16.8384i	0.346723	+	0.685144i
$605$	1.05750	−	7.62614i	0.0429935	−	0.310047i
$606$	−3.08542	−	5.34411i	−0.125337	−	0.217089i
$607$	2.47894	+	9.78913i	0.100617	+	0.397329i	0.999134	−	0.0416109i	$-0.0132490\pi$
$607$	2.47894	+	9.78913i	0.100617	+	0.397329i	−0.898517	+	0.438939i	$0.855354\pi$
$608$	−3.77488	−	2.17951i	−0.153092	−	0.0883909i
$609$	−3.52478	+	13.9190i	−0.142831	+	0.564027i
$610$	−10.9730	+	3.10288i	−0.444286	+	0.125632i
$611$	1.26155	−	4.03339i	0.0510367	−	0.163173i
$612$	−22.1706	−	10.4625i	−0.896193	−	0.422923i
$613$	9.60351	−	6.65892i	0.387882	−	0.268951i	−0.359772	−	0.933040i	$-0.617145\pi$
$613$	9.60351	−	6.65892i	0.387882	−	0.268951i	0.747653	+	0.664089i	$0.231180\pi$
$614$	3.55533	+	25.6392i	0.143481	+	1.03471i
$615$	50.6598	−	39.4301i	2.04280	−	1.58997i
$616$	−4.33846	−	6.64050i	−0.174801	−	0.267553i
$617$	24.9460	−	1.37631i	1.00429	−	0.0554081i	0.454529	−	0.890732i	$-0.349808\pi$
$617$	24.9460	−	1.37631i	1.00429	−	0.0554081i	0.549758	+	0.835324i	$0.314720\pi$
$618$	36.1662	−	31.4972i	1.45482	−	1.26700i
$619$	−3.06103	+	12.0877i	−0.123033	+	0.485847i	0.876953	+	0.480576i	$0.159572\pi$
$619$	−3.06103	+	12.0877i	−0.123033	+	0.485847i	−0.999986	+	0.00527050i	$0.998322\pi$
$620$	−1.09787	+	0.183201i	−0.0440913	+	0.00735754i
$621$	−42.1030	−	19.8689i	−1.68953	−	0.797310i
$622$	22.5909	+	19.6744i	0.905811	+	0.788871i
$623$	−1.18747	+	2.05676i	−0.0475751	+	0.0824025i
$624$	−1.61165	+	0.178377i	−0.0645175	+	0.00714079i
$625$	−15.0161	+	1.66198i	−0.600643	+	0.0664792i
$626$	−18.2447	+	27.9257i	−0.729207	+	1.11613i
$627$	30.3593	+	15.3642i	1.21243	+	0.613588i
$628$	3.77852	+	5.78346i	0.150779	+	0.230785i
$629$	−18.5016	−	22.4653i	−0.737708	−	0.895749i
$630$	−28.2042	−	17.3371i	−1.12368	−	0.690726i
$631$	19.3411	−	11.8889i	0.769957	−	0.473291i	−0.0821750	−	0.996618i	$-0.526187\pi$
$631$	19.3411	−	11.8889i	0.769957	−	0.473291i	0.852132	+	0.523327i	$0.175309\pi$
$632$	−5.43997	+	5.29208i	−0.216390	+	0.210508i
$633$	10.4084	+	10.1254i	0.413697	+	0.402450i
$634$	29.3568	−	10.0782i	1.16591	−	0.400256i
$635$	−12.1570	−	6.57906i	−0.482438	−	0.261082i
$636$	0.286878	−	10.4074i	0.0113755	−	0.412680i
$637$	−0.840421	−	0.817574i	−0.0332987	−	0.0323935i
$638$	−2.83066	+	3.07492i	−0.112067	+	0.121737i
$639$	−35.2946	+	19.1005i	−1.39623	+	0.755604i
$640$	0.842598	+	1.66502i	0.0333066	+	0.0658157i
$641$	2.27990	+	2.76833i	0.0900507	+	0.109342i	0.815003	−	0.579456i	$-0.196735\pi$
$641$	2.27990	+	2.76833i	0.0900507	+	0.109342i	−0.724953	+	0.688799i	$0.758138\pi$
$642$	22.4664	−	1.23951i	0.886678	−	0.0489194i
$643$	−3.64915	−	9.74645i	−0.143909	−	0.384363i	0.844626	−	0.535357i	$-0.179823\pi$
$643$	−3.64915	−	9.74645i	−0.143909	−	0.384363i	−0.988535	+	0.150994i	$0.951753\pi$
$644$	−4.93058	+	15.7639i	−0.194292	+	0.621187i
$645$	3.34632	−	0.558402i	0.131761	−	0.0219871i
$646$	−3.98461	−	17.7815i	−0.156772	−	0.699603i
$647$	−1.46803	−	0.244972i	−0.0577144	−	0.00963083i	0.135667	−	0.990755i	$-0.456682\pi$
$647$	−1.46803	−	0.244972i	−0.0577144	−	0.00963083i	−0.193381	+	0.981124i	$0.561945\pi$
$648$	−3.52016	+	6.95603i	−0.138285	+	0.273259i
$649$	13.0099	−	12.6562i	0.510683	−	0.496800i
$650$	−0.0227762	+	0.826279i	−0.000893357	+	0.0324093i
$651$	−3.18181	+	4.32901i	−0.124705	+	0.169667i
$652$	−22.3797	−	2.47699i	−0.876457	−	0.0970063i
$653$	9.38200			0.367146			0.183573	−	0.983006i	$-0.441234\pi$
$653$	9.38200			0.367146			0.183573	+	0.983006i	$0.441234\pi$
$654$	39.6857			1.55183
$655$	−32.2300	−	3.56721i	−1.25933	−	0.139382i
$656$	−7.34561	+	8.91928i	−0.286798	+	0.348239i
$657$	−18.1751	+	6.23954i	−0.709080	+	0.243427i
$658$	−15.8998	+	17.2717i	−0.619837	+	0.673323i
$659$	2.53391	−	12.9722i	0.0987070	−	0.505325i	−0.899018	−	0.437911i	$-0.855718\pi$
$659$	2.53391	−	12.9722i	0.0987070	−	0.505325i	0.997725	−	0.0674133i	$-0.0214746\pi$
$660$	−7.28334	−	12.6151i	−0.283504	−	0.491042i
$661$	−8.80375	−	11.9779i	−0.342426	−	0.465887i	0.600146	−	0.799891i	$-0.295109\pi$
$661$	−8.80375	−	11.9779i	−0.342426	−	0.465887i	−0.942572	+	0.334003i	$0.891600\pi$
$662$	10.3794	−	7.19689i	0.403405	−	0.279715i
$663$	−5.11183	−	4.45190i	−0.198527	−	0.172897i
$664$	1.76547	+	1.37412i	0.0685136	+	0.0533262i
$665$	−2.70673	−	24.4592i	−0.104963	−	0.948488i
$666$	−32.2161	+	25.0748i	−1.24835	+	0.971628i
$667$	8.68965	+	0.479421i	0.336464	+	0.0185633i
$668$	−1.37290	−	2.37794i	−0.0531192	−	0.0920051i
$669$	27.1964	+	18.8576i	1.05148	+	0.729077i
$670$	−2.77037	+	5.47440i	−0.107029	+	0.211494i
$671$	−13.6493	+	8.39018i	−0.526925	+	0.323899i
$672$	8.51932	+	2.92468i	0.328640	+	0.112822i
$673$	35.2166	−	19.0583i	1.35750	−	0.734643i	0.376095	−	0.926581i	$-0.377267\pi$
$673$	35.2166	−	19.0583i	1.35750	−	0.734643i	0.981407	+	0.191938i	$0.0614773\pi$
$674$	−0.592538	+	3.03346i	−0.0228237	+	0.116845i
$675$	10.6358	+	7.37470i	0.409372	+	0.283852i
$676$	12.5301	+	2.09091i	0.481928	+	0.0804196i
$677$	−11.7128	+	26.7026i	−0.450161	+	1.02626i	0.533429	+	0.845845i	$0.320903\pi$
$677$	−11.7128	+	26.7026i	−0.450161	+	1.02626i	−0.983590	+	0.180418i	$0.942255\pi$
$678$	40.3426	−	35.1344i	1.54935	−	1.34933i
$679$	14.3063	+	38.2105i	0.549026	+	1.46638i
$680$	−2.73539	+	7.30590i	−0.104897	+	0.280169i
$681$	−29.8347	−	25.9831i	−1.14327	−	0.995673i
$682$	−1.41427	+	0.667411i	−0.0541553	+	0.0255565i
$683$	−0.100133	−	1.20842i	−0.00383147	−	0.0462390i	0.994401	−	0.105677i	$-0.0337008\pi$
$683$	−0.100133	−	1.20842i	−0.00383147	−	0.0462390i	−0.998232	+	0.0594376i	$0.981069\pi$
$684$	−25.0873	+	4.89996i	−0.959237	+	0.187355i
$685$	−2.75122	+	33.2023i	−0.105119	+	1.26859i
$686$	−5.14189	−	13.7334i	−0.196318	−	0.524343i
$687$	11.0713	−	3.13068i	0.422398	−	0.119443i
$688$	−0.565749	+	0.229788i	−0.0215690	+	0.00876057i
$689$	0.568523	−	1.81767i	0.0216590	−	0.0692477i
$690$	−10.6356	+	28.4064i	−0.404891	+	1.08141i
$691$	17.4709	+	13.5982i	0.664625	+	0.517299i	0.889410	−	0.457110i	$-0.151115\pi$
$691$	17.4709	+	13.5982i	0.664625	+	0.517299i	−0.224785	+	0.974408i	$0.572168\pi$
$692$	0.972898	−	1.48913i	0.0369840	−	0.0566083i
$693$	−44.7602	−	12.6570i	−1.70030	−	0.480799i
$694$	13.2275	−	22.9107i	0.502110	−	0.869680i
$695$	−25.0774	−	19.5185i	−0.951239	−	0.740379i
$696$	0.391921	−	4.72979i	0.0148557	−	0.179282i
$697$	−48.2314	+	2.66100i	−1.82689	+	0.100792i
$698$	4.74116	+	24.2721i	0.179456	+	0.918713i
$699$	−11.1023	+	2.48809i	−0.419929	+	0.0941083i
$700$	2.07332	−	4.09698i	0.0783639	−	0.154851i
$701$	0.247446	+	8.97689i	0.00934592	+	0.339053i	0.989813	+	0.142371i	$0.0454726\pi$
$701$	0.247446	+	8.97689i	0.00934592	+	0.339053i	−0.980467	+	0.196681i	$0.936984\pi$
$702$	−3.14545	+	3.41687i	−0.118717	+	0.128961i
$703$	−29.4164	−	7.44977i	−1.10946	−	0.280973i
$704$	1.77574	+	1.92897i	0.0669258	+	0.0727008i
$705$	−30.9015	+	30.0615i	−1.16382	+	1.13218i
$706$	0.554258	+	20.1074i	0.0208598	+	0.756754i
$707$	−1.20213	+	6.15421i	−0.0452106	+	0.231453i
$708$	−2.83097	+	20.4154i	−0.106394	+	0.767259i
$709$	4.83323	+	15.4527i	0.181516	+	0.580338i	0.999983	+	0.00578536i	$0.00184155\pi$
$709$	4.83323	+	15.4527i	0.181516	+	0.580338i	−0.818468	+	0.574553i	$0.805176\pi$
$710$	6.98483	+	10.6911i	0.262136	+	0.401229i
$711$	−3.67525	+	44.3537i	−0.137833	+	1.66339i
$712$	0.275254	−	0.735171i	0.0103156	−	0.0275517i
$713$	2.94494	+	1.38975i	0.110289	+	0.0520465i
$714$	15.1260	+	34.4838i	0.566077	+	1.29053i
$715$	−0.654126	−	2.58309i	−0.0244629	−	0.0966019i
$716$	−3.77069	−	2.61454i	−0.140917	−	0.0977098i
$717$	−0.235630	−	8.54821i	−0.00879975	−	0.319239i
$718$	−3.05422	−	2.97119i	−0.113982	−	0.110884i
$719$	−35.7573	−	8.01340i	−1.33352	−	0.298849i	−0.507093	−	0.861891i	$-0.669280\pi$
$719$	−35.7573	−	8.01340i	−1.33352	−	0.298849i	−0.826428	+	0.563042i	$0.809631\pi$
$720$	10.1387	+	4.11796i	0.377845	+	0.153467i
$721$	−48.7337			−1.81494
$722$	−14.3276	−	12.4788i	−0.533218	−	0.464412i
$723$	−9.25776			−0.344300
$724$	−20.6234	−	8.37650i	−0.766463	−	0.311310i
$725$	−2.36083	−	0.529074i	−0.0876790	−	0.0196493i
$726$	8.80474	+	8.56538i	0.326774	+	0.317891i
$727$	−1.15053	−	41.7391i	−0.0426708	−	1.54802i	−0.653910	−	0.756572i	$-0.726873\pi$
$727$	−1.15053	−	41.7391i	−0.0426708	−	1.54802i	0.611239	−	0.791446i	$-0.290671\pi$
$728$	1.35403	+	0.938861i	0.0501836	+	0.0347965i
$729$	−7.47464	−	29.5167i	−0.276839	−	1.09321i
$730$	2.45636	+	5.59993i	0.0909138	+	0.207263i
$731$	−2.30862	−	1.08946i	−0.0853872	−	0.0402952i
$732$	6.37938	−	17.0386i	0.235789	−	0.629763i
$733$	−3.41042	+	41.1576i	−0.125967	+	1.52019i	0.581560	+	0.813504i	$0.302443\pi$
$733$	−3.41042	+	41.1576i	−0.125967	+	1.52019i	−0.707526	+	0.706687i	$0.750189\pi$
$734$	15.8784	+	24.3037i	0.586081	+	0.897064i
$735$	3.57051	+	11.4156i	0.131700	+	0.421070i
$736$	0.749884	−	5.40777i	0.0276411	−	0.199333i
$737$	−1.65262	+	8.46051i	−0.0608752	+	0.311647i
$738$	1.86705	+	67.7331i	0.0687271	+	2.49329i
$739$	18.1684	−	17.6745i	0.668335	−	0.650166i	−0.282715	−	0.959204i	$-0.591235\pi$
$739$	18.1684	−	17.6745i	0.668335	−	0.650166i	0.951050	+	0.309038i	$0.100007\pi$
$740$	8.79855	+	9.55777i	0.323441	+	0.351351i
$741$	−7.04375	−	0.583781i	−0.258759	−	0.0214457i
$742$	−7.16532	+	7.78361i	−0.263047	+	0.285745i
$743$	0.583509	+	21.1686i	0.0214069	+	0.776602i	0.931824	+	0.362910i	$0.118217\pi$
$743$	0.583509	+	21.1686i	0.0214069	+	0.776602i	−0.910417	+	0.413691i	$0.864239\pi$
$744$	0.801847	−	1.58449i	0.0293971	−	0.0580903i
$745$	16.5554	−	3.71015i	0.606543	−	0.135929i
$746$	3.92181	+	20.0775i	0.143588	+	0.735089i
$747$	13.0995	−	0.722717i	0.479284	−	0.0264428i
$748$	−0.905133	+	10.9233i	−0.0330949	+	0.399396i
$749$	−18.0429	−	14.0434i	−0.659274	−	0.513134i
$750$	18.1058	−	31.3601i	0.661129	−	1.14511i
$751$	5.88112	+	1.66302i	0.214605	+	0.0606845i	0.377709	−	0.925924i	$-0.376712\pi$
$751$	5.88112	+	1.66302i	0.214605	+	0.0606845i	−0.163104	+	0.986609i	$0.552151\pi$
$752$	4.24413	−	6.49613i	0.154768	−	0.236890i
$753$	−60.2040	−	46.8586i	−2.19395	−	1.70762i
$754$	0.304411	−	0.813047i	0.0110860	−	0.0296094i
$755$	10.5126	−	33.6105i	0.382591	−	1.22321i
$756$	23.9023	−	9.70827i	0.869318	−	0.353087i
$757$	36.5974	−	10.3488i	1.33016	−	0.376132i	0.468427	−	0.883502i	$-0.344821\pi$
$757$	36.5974	−	10.3488i	1.33016	−	0.376132i	0.861728	+	0.507370i	$0.169382\pi$
$758$	8.53635	+	22.7996i	0.310054	+	0.828118i
$759$	−3.51929	+	42.4715i	−0.127742	+	1.54162i
$760$	2.21317	+	7.82718i	0.0802803	+	0.283922i
$761$	1.33047	+	16.0564i	0.0482295	+	0.582044i	0.977261	+	0.212042i	$0.0680114\pi$
$761$	1.33047	+	16.0564i	0.0482295	+	0.582044i	−0.929031	+	0.370002i	$0.879357\pi$
$762$	19.9450	−	9.41226i	0.722530	−	0.340970i
$763$	−30.4107	−	26.4847i	−1.10094	−	0.958810i
$764$	7.26604	−	19.4067i	0.262876	−	0.702111i
$765$	16.0408	+	42.8431i	0.579957	+	1.54900i
$766$	16.3180	−	14.2114i	0.589594	−	0.513478i
$767$	−1.51449	+	3.45269i	−0.0546851	+	0.124669i
$768$	−2.93667	−	0.490044i	−0.105968	−	0.0176829i
$769$	−42.4515	−	29.4352i	−1.53084	−	1.06146i	−0.972800	−	0.231645i	$-0.925589\pi$
$769$	−42.4515	−	29.4352i	−1.53084	−	1.06146i	−0.558038	−	0.829815i	$-0.688446\pi$
$770$	−2.83770	+	14.5274i	−0.102263	+	0.523532i
$771$	−69.1863	+	37.4418i	−2.49169	+	1.34843i
$772$	8.35802	+	2.86931i	0.300812	+	0.103269i
$773$	−15.1157	+	9.29158i	−0.543674	+	0.334195i	−0.768135	−	0.640288i	$-0.778815\pi$
$773$	−15.1157	+	9.29158i	−0.543674	+	0.334195i	0.224461	+	0.974483i	$0.427938\pi$
$774$	−1.61688	+	3.19505i	−0.0581176	+	0.114844i
$775$	−0.743933	−	0.515832i	−0.0267229	−	0.0185292i
$776$	−6.74312	−	11.6794i	−0.242064	−	0.419267i
$777$	62.6107	+	3.45433i	2.24615	+	0.123923i
$778$	−29.0561	+	22.6152i	−1.04171	+	0.810795i
$779$	−38.8788	+	32.0181i	−1.39298	+	1.14717i
$780$	2.38780	+	1.85850i	0.0854971	+	0.0665450i
$781$	13.5308	+	11.7839i	0.484169	+	0.421663i
$782$	18.7559	−	13.0051i	0.670711	−	0.465060i
$783$	−8.05047	−	10.9531i	−0.287700	−	0.391430i
$784$	−1.07643	−	1.86443i	−0.0384439	−	0.0665867i
$785$	2.47145	−	12.6525i	0.0882100	−	0.451586i
$786$	35.0398	−	38.0633i	1.24983	−	1.35767i
$787$	22.1018	−	7.58756i	0.787844	−	0.270467i	0.0987245	−	0.995115i	$-0.468524\pi$
$787$	22.1018	−	7.58756i	0.787844	−	0.270467i	0.689120	+	0.724648i	$0.257997\pi$
$788$	−10.0477	+	12.2003i	−0.357936	+	0.434617i
$789$	−72.8377	−	8.06168i	−2.59309	−	0.287003i
$790$	14.1625			0.503879
$791$	−54.3614			−1.93287
$792$	15.2818	+	1.69139i	0.543014	+	0.0601008i
$793$	1.97101	−	2.68166i	0.0699927	−	0.0952285i
$794$	0.141244	−	5.12406i	0.00501255	−	0.181846i
$795$	−13.9260	+	13.5474i	−0.493903	+	0.480476i
$796$	5.32759	−	10.5276i	0.188831	−	0.373141i
$797$	−34.5016	−	5.75730i	−1.22211	−	0.203934i	−0.481849	−	0.876254i	$-0.660035\pi$
$797$	−34.5016	−	5.75730i	−1.22211	−	0.203934i	−0.740261	+	0.672320i	$0.765298\pi$
$798$	34.0017	+	19.6317i	1.20365	+	0.694953i
$799$	31.9970	−	5.33935i	1.13197	−	0.188893i
$800$	−0.453068	+	1.44854i	−0.0160184	+	0.0512135i
$801$	−1.61414	−	4.31117i	−0.0570328	−	0.152328i
$802$	−25.2094	+	1.39084i	−0.890173	+	0.0491122i
$803$	5.46189	+	6.63200i	0.192746	+	0.234038i
$804$	−4.42004	−	8.73424i	−0.155883	−	0.308033i
$805$	27.1073	−	14.6697i	0.955406	−	0.517040i
$806$	0.220012	−	0.238997i	0.00774959	−	0.00841829i
$807$	−23.7063	−	23.0618i	−0.834500	−	0.811814i
$808$	0.0571104	−	2.07186i	0.00200914	−	0.0728878i
$809$	14.2782	+	7.72698i	0.501995	+	0.271666i	0.707150	−	0.707063i	$-0.249980\pi$
$809$	14.2782	+	7.72698i	0.501995	+	0.271666i	−0.205155	+	0.978729i	$0.565770\pi$
$810$	13.7598	−	4.72373i	0.483469	−	0.165975i
$811$	−1.06046	−	1.03163i	−0.0372379	−	0.0362256i	0.678443	−	0.734653i	$-0.262655\pi$
$811$	−1.06046	−	1.03163i	−0.0372379	−	0.0362256i	−0.715680	+	0.698428i	$0.753883\pi$
$812$	−3.45680	+	3.36282i	−0.121310	+	0.118012i
$813$	−70.7437	+	43.4860i	−2.48109	+	1.52512i
$814$	15.5496	+	9.55833i	0.545015	+	0.335019i
$815$	26.7115	+	32.4339i	0.935661	+	1.13611i
$816$	−6.80762	−	10.4198i	−0.238314	−	0.364767i
$817$	−2.61233	+	0.510231i	−0.0913940	+	0.0178507i
$818$	1.35510	−	2.07413i	0.0473798	−	0.0725203i
$819$	9.60364	−	1.06293i	0.335578	−	0.0371418i
$820$	21.4312	−	2.37200i	0.748409	−	0.0828339i
$821$	−21.7626	+	37.6940i	−0.759522	+	1.31553i	0.183573	+	0.983006i	$0.441234\pi$
$821$	−21.7626	+	37.6940i	−0.759522	+	1.31553i	−0.943095	+	0.332524i	$0.892100\pi$
$822$	−40.0844	−	34.9095i	−1.39810	−	1.21761i
$823$	16.2662	+	7.67619i	0.567003	+	0.267575i	0.688766	−	0.724984i	$-0.258153\pi$
$823$	16.2662	+	7.67619i	0.567003	+	0.267575i	−0.121763	+	0.992559i	$0.538855\pi$
$824$	15.8887	−	2.65135i	0.553508	−	0.0923641i
$825$	2.90839	−	11.4850i	0.101257	−	0.399856i
$826$	15.7938	−	13.7548i	0.549536	−	0.478592i
$827$	33.2803	−	1.83613i	1.15727	−	0.0638484i	0.533741	−	0.845648i	$-0.320786\pi$
$827$	33.2803	−	1.83613i	1.15727	−	0.0638484i	0.623530	+	0.781800i	$0.285698\pi$
$828$	−17.5108	−	26.8023i	−0.608544	−	0.931446i
$829$	−10.2181	+	7.95309i	−0.354890	+	0.276222i	−0.775929	−	0.630821i	$-0.782718\pi$
$829$	−10.2181	+	7.95309i	−0.354890	+	0.276222i	0.421038	+	0.907043i	$0.361666\pi$
$830$	−0.573425	−	4.13524i	−0.0199039	−	0.143536i
$831$	33.4719	−	23.2089i	1.16113	−	0.805107i
$832$	−0.492532	−	0.232431i	−0.0170755	−	0.00805811i
$833$	2.68665	−	8.58970i	0.0930869	−	0.297615i
$834$	48.7879	−	13.7959i	1.68939	−	0.477713i
$835$	−1.25784	+	4.96710i	−0.0435294	+	0.171894i
$836$	5.98461	+	9.73622i	0.206982	+	0.336734i
$837$	−1.24861	−	4.93065i	−0.0431583	−	0.170428i
$838$	8.66119	+	15.0016i	0.299196	+	0.518223i
$839$	5.33523	−	38.4749i	0.184193	−	1.32830i	−0.642777	−	0.766053i	$-0.722218\pi$
$839$	5.33523	−	38.4749i	0.184193	−	1.32830i	0.826969	−	0.562247i	$-0.190063\pi$
$840$	−7.58958	−	14.9974i	−0.261866	−	0.517460i
$841$	−22.5409	−	13.8558i	−0.777272	−	0.477787i
$842$	8.93435	−	2.00224i	0.307898	−	0.0690016i
$843$	41.2637	+	6.88570i	1.42120	+	0.237156i
$844$	1.19730	+	4.72803i	0.0412128	+	0.162746i
$845$	−14.0393	−	19.1011i	−0.482965	−	0.657098i
$846$	−6.25014	−	45.0728i	−0.214884	−	1.54963i
$847$	−1.03076	−	12.4395i	−0.0354175	−	0.427426i
$848$	1.91264	−	2.92752i	0.0656805	−	0.100531i
$849$	0.980730	−	1.69867i	0.0336586	−	0.0582984i
$850$	−5.73809	+	2.70787i	−0.196815	+	0.0928792i
$851$	−5.22042	−	37.6469i	−0.178954	−	1.29052i
$852$	−20.3441	−	1.12241i	−0.696977	−	0.0384533i
$853$	−5.59316	+	40.3349i	−0.191506	+	1.38104i	0.614399	+	0.788996i	$0.289399\pi$
$853$	−5.59316	+	40.3349i	−0.191506	+	1.38104i	−0.805905	+	0.592045i	$0.798321\pi$
$854$	−16.2593	+	8.79909i	−0.556382	+	0.301099i
$855$	39.9320	+	26.0899i	1.36565	+	0.892254i
$856$	6.64656	+	3.59694i	0.227175	+	0.122941i
$857$	1.14568	−	1.55875i	0.0391357	−	0.0532460i	−0.785757	−	0.618535i	$-0.787727\pi$
$857$	1.14568	−	1.55875i	0.0391357	−	0.0532460i	0.824893	+	0.565289i	$0.191235\pi$
$858$	3.93883	+	1.59981i	0.134469	+	0.0546167i
$859$	11.6073	+	1.28470i	0.396036	+	0.0438333i	0.305821	−	0.952089i	$-0.401069\pi$
$859$	11.6073	+	1.28470i	0.396036	+	0.0438333i	0.0902152	+	0.995922i	$0.471245\pi$
$860$	1.05573	+	0.428802i	0.0360003	+	0.0146220i
$861$	66.1645	−	80.3391i	2.25488	−	2.73795i
$862$	−16.9728	−	9.18522i	−0.578096	−	0.312850i
$863$	−5.51119	−	5.98674i	−0.187603	−	0.203791i	0.634832	−	0.772650i	$-0.281069\pi$
$863$	−5.51119	−	5.98674i	−0.187603	−	0.203791i	−0.822435	+	0.568859i	$0.807385\pi$
$864$	−7.26469	+	4.46559i	−0.247150	+	0.151922i
$865$	−3.23900	+	0.725877i	−0.110129	+	0.0246806i
$866$	−14.6453	+	33.3880i	−0.497668	+	1.13457i
$867$	0.348437	−	1.37595i	0.0118335	−	0.0467296i
$868$	−1.67187	+	0.679056i	−0.0567471	+	0.0230487i
$869$	19.1477	−	5.41444i	0.649540	−	0.183672i
$870$	−6.67868	+	5.81647i	−0.226428	+	0.197197i
$871$	−0.343287	−	1.75744i	−0.0116318	−	0.0595486i
$872$	11.3557	+	6.98031i	0.384552	+	0.236383i
$873$	−74.8006	−	25.6791i	−2.53162	−	0.869105i
$874$	7.72740	−	22.5079i	0.261383	−	0.761342i
$875$	−34.8027	+	11.9478i	−1.17655	+	0.403909i
$876$	−9.52011	−	2.13351i	−0.321655	−	0.0720845i
$877$	−1.68518	+	2.29277i	−0.0569045	+	0.0774214i	−0.833287	−	0.552841i	$-0.813544\pi$
$877$	−1.68518	+	2.29277i	−0.0569045	+	0.0774214i	0.776382	+	0.630262i	$0.217053\pi$
$878$	−7.97424	+	9.68258i	−0.269117	+	0.326771i
$879$	85.5119	+	19.1637i	2.88425	+	0.646375i
$880$	0.134813	−	4.89076i	0.00454454	−	0.164867i
$881$	−13.4278	−	14.5865i	−0.452393	−	0.491430i	0.467283	−	0.884108i	$-0.345233\pi$
$881$	−13.4278	−	14.5865i	−0.452393	−	0.491430i	−0.919676	+	0.392678i	$0.871549\pi$
$882$	−11.9407	−	4.09924i	−0.402064	−	0.138029i
$883$	−0.548592	−	1.08405i	−0.0184616	−	0.0364811i	0.882837	−	0.469680i	$-0.155631\pi$
$883$	−0.548592	−	1.08405i	−0.0184616	−	0.0364811i	−0.901299	+	0.433198i	$0.857385\pi$
$884$	−0.679658	−	2.17299i	−0.0228594	−	0.0730855i
$885$	30.3515	−	23.6235i	1.02025	−	0.794095i
$886$	−2.37243	−	28.6310i	−0.0797035	−	0.961878i
$887$	−0.154990	−	0.0438271i	−0.00520406	−	0.00147157i	0.269500	−	0.963000i	$-0.413141\pi$
$887$	−0.154990	−	0.0438271i	−0.00520406	−	0.00147157i	−0.274705	+	0.961529i	$0.588580\pi$
$888$	−20.6009	+	2.28011i	−0.691321	+	0.0765154i
$889$	−21.5650	−	6.09799i	−0.723266	−	0.204520i
$890$	−1.32479	+	0.625182i	−0.0444070	+	0.0209562i
$891$	16.7972	−	11.6470i	0.562729	−	0.390188i
$892$	4.46514	+	10.1795i	0.149504	+	0.340835i
$893$	23.5855	−	24.2438i	0.789258	−	0.811287i
$894$	−10.8734	+	24.7889i	−0.363661	+	0.829064i
$895$	1.64151	+	8.40360i	0.0548695	+	0.280901i
$896$	1.92330	+	2.33533i	0.0642529	+	0.0780180i
$897$	−2.64261	−	8.44890i	−0.0882342	−	0.282101i
$898$	16.4963	+	0.910126i	0.550488	+	0.0303713i
$899$	0.563099	+	0.766124i	0.0187804	+	0.0255517i
$900$	3.57521	+	8.15065i	0.119174	+	0.271688i
$901$	14.4196	−	2.40621i	0.480388	−	0.0801625i
$902$	28.0681	−	11.4003i	0.934564	−	0.379587i
$903$	5.09591	−	2.06978i	0.169581	−	0.0688779i
$904$	17.7235	−	2.95752i	0.589473	−	0.0983657i
$905$	16.6857	+	38.0396i	0.554652	+	1.26448i
$906$	33.2756	+	45.2730i	1.10551	+	1.50410i
$907$	1.66342	+	0.0917737i	0.0552331	+	0.00304730i	0.0826832	−	0.996576i	$-0.473651\pi$
$907$	1.66342	+	0.0917737i	0.0552331	+	0.00304730i	−0.0274501	+	0.999623i	$0.508739\pi$
$908$	−3.96676	−	12.6824i	−0.131641	−	0.420881i
$909$	−7.72682	−	9.38215i	−0.256282	−	0.311186i
$910$	−0.589454	−	3.01767i	−0.0195402	−	0.100035i
$911$	14.5468	−	33.1633i	0.481956	−	1.09875i	−0.491708	−	0.870760i	$-0.663627\pi$
$911$	14.5468	−	33.1633i	0.481956	−	1.09875i	0.973664	−	0.227989i	$-0.0732150\pi$
$912$	−12.1536	−	4.55065i	−0.402447	−	0.150687i
$913$	−2.35621	−	5.37161i	−0.0779791	−	0.177774i
$914$	−10.8500	+	7.52321i	−0.358885	+	0.248846i
$915$	−30.7037	+	14.4894i	−1.01503	+	0.479005i
$916$	3.71861	+	1.05152i	0.122866	+	0.0347433i
$917$	−52.2525	+	5.78331i	−1.72553	+	0.190982i
$918$	−34.3040	−	9.70025i	−1.13220	−	0.320156i
$919$	0.355537	+	4.29069i	0.0117281	+	0.141537i	0.999933	−	0.0116025i	$-0.00369328\pi$
$919$	0.355537	+	4.29069i	0.0117281	+	0.141537i	−0.988205	+	0.153139i	$0.951062\pi$
$920$	−8.03968	+	6.25754i	−0.265060	+	0.206305i
$921$	23.0051	+	73.5515i	0.758045	+	2.42360i
$922$	−12.6813	−	25.0589i	−0.417635	−	0.825269i
$923$	−3.52517	−	1.21019i	−0.116032	−	0.0398340i
$924$	−15.9947	−	17.3749i	−0.526189	−	0.571593i
$925$	−0.291138	+	10.5619i	−0.00957255	+	0.347274i
$926$	−15.2600	−	3.41985i	−0.501475	−	0.112383i
$927$	60.0519	−	72.9169i	1.97236	−	2.39491i
$928$	0.944066	−	1.28445i	0.0309905	−	0.0421641i
$929$	32.1942	+	7.21489i	1.05626	+	0.236713i	0.712012	−	0.702167i	$-0.247784\pi$
$929$	32.1942	+	7.21489i	1.05626	+	0.236713i	0.344245	+	0.938880i	$0.388135\pi$
$930$	−3.13429	+	1.07600i	−0.102777	+	0.0352835i
$931$	−3.04686	−	8.87568i	−0.0998568	−	0.290889i
$932$	−3.61446	−	1.24085i	−0.118396	−	0.0406452i
$933$	75.9832	+	46.7067i	2.48758	+	1.52911i
$934$	−1.46838	−	7.51729i	−0.0480469	−	0.245973i
$935$	15.4243	−	13.4330i	0.504427	−	0.439306i
$936$	−3.07325	+	0.869031i	−0.100452	+	0.0284052i
$937$	22.6858	−	9.21418i	0.741113	−	0.301014i	0.0256562	−	0.999671i	$-0.491832\pi$
$937$	22.6858	−	9.21418i	0.741113	−	0.301014i	0.715457	+	0.698657i	$0.246218\pi$
$938$	−2.44186	+	9.64270i	−0.0797297	+	0.314845i
$939$	−39.8940	+	90.9492i	−1.30189	+	2.96801i
$940$	−14.1297	+	3.16654i	−0.460860	+	0.103281i
$941$	−3.20022	+	1.96717i	−0.104324	+	0.0641279i	−0.574853	−	0.818257i	$-0.694941\pi$
$941$	−3.20022	+	1.96717i	−0.104324	+	0.0641279i	0.470528	+	0.882385i	$0.344063\pi$
$942$	13.9304	+	15.1325i	0.453878	+	0.493042i
$943$	−55.4799	−	30.0242i	−1.80668	−	0.977724i
$944$	−4.40092	+	5.34375i	−0.143238	+	0.173924i
$945$	−44.6036	−	18.1164i	−1.45096	−	0.589328i
$946$	1.59129	+	0.176123i	0.0517372	+	0.00572627i
$947$	−23.1061	−	9.38489i	−0.750847	−	0.304968i	−0.0313925	−	0.999507i	$-0.509994\pi$
$947$	−23.1061	−	9.38489i	−0.750847	−	0.304968i	−0.719455	+	0.694539i	$0.755608\pi$
$948$	−13.3820	+	18.2069i	−0.434629	+	0.591333i
$949$	−1.56957	−	0.849410i	−0.0509504	−	0.0275730i
$950$	−3.14881	+	5.81826i	−0.102161	+	0.188769i
$951$	81.2725	−	43.9825i	2.63544	−	1.42623i
$952$	−1.73719	+	12.5277i	−0.0563028	+	0.406026i
$953$	−32.2965	−	1.78185i	−1.04619	−	0.0577197i	−0.476170	−	0.879353i	$-0.657975\pi$
$953$	−32.2965	−	1.78185i	−1.04619	−	0.0577197i	−0.570016	+	0.821633i	$0.693063\pi$
$954$	−2.81666	−	20.3123i	−0.0911928	−	0.657635i
$955$	−34.9712	+	16.5033i	−1.13164	+	0.534034i
$956$	1.43612	−	2.48743i	0.0464475	−	0.0804493i
$957$	−6.80588	+	10.4172i	−0.220003	+	0.336739i
$958$	0.432859	+	5.22384i	0.0139851	+	0.168774i
$959$	7.41894	+	53.5015i	0.239570	+	1.72765i
$960$	3.29036	+	4.47670i	0.106196	+	0.144485i
$961$	−7.52271	−	29.7065i	−0.242668	−	0.958275i
$962$	−3.73974	−	0.624053i	−0.120574	−	0.0201203i
$963$	43.2454	−	9.69153i	1.39356	−	0.312305i
$964$	−2.64902	−	1.62835i	−0.0853192	−	0.0524455i
$965$	−7.44589	−	14.7135i	−0.239692	−	0.473644i
$966$	−6.75447	+	48.7097i	−0.217322	+	1.56721i
$967$	−3.93201	−	6.81044i	−0.126445	−	0.219009i	0.795852	−	0.605491i	$-0.207023\pi$
$967$	−3.93201	−	6.81044i	−0.126445	−	0.219009i	−0.922297	+	0.386482i	$0.873690\pi$
$968$	1.01283	+	3.99957i	0.0325535	+	0.128551i
$969$	−20.4152	−	50.2657i	−0.655830	−	1.61477i
$970$	−6.17799	+	24.3963i	−0.198363	+	0.783320i
$971$	−52.5507	+	14.8599i	−1.68643	+	0.476877i	−0.974316	−	0.225186i	$-0.927701\pi$
$971$	−52.5507	+	14.8599i	−1.68643	+	0.476877i	−0.712115	+	0.702063i	$0.752263\pi$
$972$	0.707900	−	2.26328i	0.0227059	−	0.0725948i
$973$	−46.5924	−	21.9875i	−1.49368	−	0.704886i
$974$	−11.6917	+	8.10686i	−0.374627	+	0.259761i
$975$	0.338026	+	2.43767i	0.0108255	+	0.0780679i
$976$	4.82231	−	3.75335i	0.154358	−	0.120142i
$977$	−2.32436	−	3.55770i	−0.0743628	−	0.113821i	0.798048	−	0.602593i	$-0.205866\pi$
$977$	−2.32436	−	3.55770i	−0.0743628	−	0.113821i	−0.872411	+	0.488773i	$0.837445\pi$
$978$	−66.9357	+	3.69294i	−2.14037	+	0.118087i
$979$	−1.55210	+	1.35172i	−0.0496052	+	0.0432012i
$980$	−0.986215	+	3.89447i	−0.0315035	+	0.124404i
$981$	77.1006	−	12.8658i	2.46163	−	0.410774i
$982$	−30.2549	−	14.2776i	−0.965472	−	0.455617i
$983$	23.9094	+	20.8227i	0.762591	+	0.664141i	0.947910	−	0.318538i	$-0.103192\pi$
$983$	23.9094	+	20.8227i	0.762591	+	0.664141i	−0.185320	+	0.982678i	$0.559332\pi$
$984$	−17.2008	+	29.7926i	−0.548341	+	0.949755i
$985$	29.3148	−	3.24456i	0.934046	−	0.103380i
$986$	6.62360	−	0.733100i	0.210939	−	0.0233467i
$987$	−38.2284	+	58.5130i	−1.21682	+	1.86249i
$988$	−1.91282	−	1.40597i	−0.0608549	−	0.0447298i
$989$	−1.82340	−	2.79092i	−0.0579807	−	0.0887461i
$990$	−18.2397	−	22.1472i	−0.579694	−	0.703884i
$991$	24.8623	+	15.2828i	0.789778	+	0.485475i	0.858906	−	0.512133i	$-0.171144\pi$
$991$	24.8623	+	15.2828i	0.789778	+	0.485475i	−0.0691280	+	0.997608i	$0.522022\pi$
$992$	0.508137	−	0.312351i	0.0161334	−	0.00991714i
$993$	26.9540	−	26.2212i	0.855358	−	0.832105i
$994$	14.8404	+	14.4369i	0.470708	+	0.457912i
$995$	−20.8247	+	7.14913i	−0.660187	+	0.226643i
$996$	5.85798	+	3.17018i	0.185617	+	0.100451i
$997$	−0.588796	+	21.3604i	−0.0186474	+	0.676491i	0.931331	+	0.364175i	$0.118649\pi$
$997$	−0.588796	+	21.3604i	−0.0186474	+	0.676491i	−0.949978	+	0.312317i	$0.898895\pi$
$998$	7.65452	+	7.44644i	0.242300	+	0.235713i
$999$	−40.2068	+	43.6762i	−1.27209	+	1.38185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.a.501.16	yes	576
361.49	even	57	inner	722.2.i.a.49.16	✓	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.a.49.16	✓	576	361.49	even	57	inner
722.2.i.a.501.16	yes	576	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926494 + 0.376309i) q^{2} +(2.90522 + 0.651074i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0514187 - 1.86537i) q^{5} +(2.44666 + 1.69648i) q^{6} +(-0.742684 - 2.93279i) q^{7} +(0.401695 + 0.915773i) q^{8} +(5.30331 + 2.50269i) q^{9} +O(q^{10})\)	\(q+(0.926494 + 0.376309i) q^{2} +(2.90522 + 0.651074i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0514187 - 1.86537i) q^{5} +(2.44666 + 1.69648i) q^{6} +(-0.742684 - 2.93279i) q^{7} +(0.401695 + 0.915773i) q^{8} +(5.30331 + 2.50269i) q^{9} +(0.654318 - 1.74761i) q^{10} +(0.216512 - 2.61291i) q^{11} +(1.62842 + 2.49248i) q^{12} +(0.162577 + 0.519789i) q^{13} +(0.415545 - 2.99669i) q^{14} +(1.06511 - 5.45279i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-2.99652 + 2.91506i) q^{17} +(3.97170 + 4.31441i) q^{18} +(-0.717523 + 4.29944i) q^{19} +(1.26386 - 1.37292i) q^{20} +(-0.248192 - 9.00394i) q^{21} +(1.18386 - 2.33937i) q^{22} +(-5.32737 + 1.19389i) q^{23} +(0.570776 + 2.92205i) q^{24} +(1.51543 - 0.0836089i) q^{25} +(-0.0449744 + 0.542761i) q^{26} +(6.72935 + 5.23766i) q^{27} +(1.51268 - 2.62005i) q^{28} +(-1.53393 - 0.433753i) q^{29} +(3.03876 - 4.65116i) q^{30} +(-0.470692 - 0.366354i) q^{31} +(-0.350638 + 0.936511i) q^{32} +(2.33021 - 7.45011i) q^{33} +(-3.87323 + 1.57317i) q^{34} +(-5.43257 + 1.53618i) q^{35} +(2.05620 + 5.49187i) q^{36} +(-0.574887 + 6.93786i) q^{37} +(-2.28270 + 3.71339i) q^{38} +(0.133901 + 1.61595i) q^{39} +(1.68760 - 0.796400i) q^{40} +(8.71349 + 7.58858i) q^{41} +(3.15832 - 8.43549i) q^{42} +(0.214111 + 0.571866i) q^{43} +(1.97717 - 1.72192i) q^{44} +(4.39576 - 10.0213i) q^{45} +(-5.38505 - 0.898606i) q^{46} +(-6.37672 - 4.42152i) q^{47} +(-0.570776 + 2.92205i) q^{48} +(-1.89338 + 1.02465i) q^{49} +(1.43550 + 0.492809i) q^{50} +(-10.6035 + 6.51793i) q^{51} +(-0.245915 + 0.485940i) q^{52} +(-2.87371 - 1.99258i) q^{53} +(4.26372 + 7.38498i) q^{54} +(-4.88519 - 0.269523i) q^{55} +(2.38744 - 1.85822i) q^{56} +(-4.88381 + 12.0236i) q^{57} +(-1.25795 - 0.979100i) q^{58} +(5.22045 + 4.54650i) q^{59} +(4.56567 - 3.16576i) q^{60} +(-3.61905 - 4.92390i) q^{61} +(-0.298231 - 0.516551i) q^{62} +(3.40119 - 17.4122i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(0.961241 - 0.329994i) q^{65} +(4.96247 - 6.02560i) q^{66} +(-3.26793 - 0.361695i) q^{67} -4.18052 q^{68} -16.2545 q^{69} +(-5.61132 - 0.621061i) q^{70} +(-4.05297 + 5.51426i) q^{71} +(-0.161583 + 5.86195i) q^{72} +(-2.34883 + 2.28498i) q^{73} +(-3.14341 + 6.21155i) q^{74} +(4.45710 + 0.743758i) q^{75} +(-3.51229 + 2.58143i) q^{76} +(-7.82393 + 1.30558i) q^{77} +(-0.484038 + 1.54756i) q^{78} +(2.66114 + 7.10758i) q^{79} +(1.86325 - 0.102798i) q^{80} +(4.95612 + 6.01788i) q^{81} +(5.21734 + 10.3097i) q^{82} +(1.96757 - 1.06479i) q^{83} +(6.10052 - 6.62693i) q^{84} +(5.59176 + 5.43974i) q^{85} +(-0.0168256 + 0.610403i) q^{86} +(-4.17398 - 2.25884i) q^{87} +(2.47981 - 0.851319i) q^{88} +(-0.562682 - 0.547385i) q^{89} +(7.84377 - 7.63054i) q^{90} +(1.40369 - 0.862845i) q^{91} +(-4.65107 - 2.85900i) q^{92} +(-1.12894 - 1.37079i) q^{93} +(-4.24413 - 6.49613i) q^{94} +(8.05695 + 1.11738i) q^{95} +(-1.62842 + 2.49248i) q^{96} +(-13.4044 + 1.48360i) q^{97} +(-2.13979 + 0.236832i) q^{98} +(7.68754 - 13.3152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Introduction

L-functions

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