LMFDB - Embedded newform 462.2.bc.a.107.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.16
Character	$\chi$	$=$	462.107
Dual form			462.2.bc.a.95.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(1.70747 - 0.290781i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.75629 + 3.94468i) q^{5} +(0.467667 + 1.66772i) q^{6} +(2.64495 - 0.0650804i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.83089 - 0.992999i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(1.70747 - 0.290781i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.75629 + 3.94468i) q^{5} +(0.467667 + 1.66772i) q^{6} +(2.64495 - 0.0650804i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.83089 - 0.992999i) q^{9} +(-3.73949 + 2.15900i) q^{10} +(-3.29397 + 0.387016i) q^{11} +(-1.60970 + 0.639429i) q^{12} +(-2.24820 - 3.09438i) q^{13} +(0.341197 + 2.62366i) q^{14} +(4.14584 + 6.22472i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.195558 - 1.86061i) q^{17} +(1.28347 + 2.71159i) q^{18} +(0.385005 - 1.81130i) q^{19} +(-2.53805 - 3.49333i) q^{20} +(4.49724 - 0.880225i) q^{21} +(-0.729209 - 3.23547i) q^{22} +(-5.76787 - 3.33008i) q^{23} +(-0.804186 - 1.53404i) q^{24} +(-9.13033 + 10.1403i) q^{25} +(2.84243 - 2.55934i) q^{26} +(4.54491 - 2.51868i) q^{27} +(-2.57362 + 0.613574i) q^{28} +(1.60027 - 4.92514i) q^{29} +(-5.75727 + 4.77379i) q^{30} +(1.16659 + 0.519398i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.51181 + 1.61864i) q^{33} +1.87086 q^{34} +(4.90201 + 10.3192i) q^{35} +(-2.56257 + 1.55988i) q^{36} +(3.11006 + 3.45407i) q^{37} +(1.84163 + 0.193563i) q^{38} +(-4.73852 - 4.62982i) q^{39} +(3.20889 - 2.88930i) q^{40} +(2.90786 + 8.94949i) q^{41} +(1.34549 + 4.38060i) q^{42} -2.90165i q^{43} +(3.14152 - 1.06341i) q^{44} +(8.88892 + 9.42298i) q^{45} +(2.70893 - 6.08437i) q^{46} +(1.28772 - 6.05823i) q^{47} +(1.44158 - 0.960132i) q^{48} +(6.99153 - 0.344269i) q^{49} +(-11.0391 - 8.02037i) q^{50} +(-0.207122 - 3.23380i) q^{51} +(2.84243 + 2.55934i) q^{52} +(-5.16057 + 11.5908i) q^{53} +(2.97996 + 4.25674i) q^{54} +(-7.31180 - 12.3139i) q^{55} +(-0.879230 - 2.49539i) q^{56} +(0.130690 - 3.20469i) q^{57} +(5.06543 + 1.07669i) q^{58} +(-0.0588568 - 0.276899i) q^{59} +(-5.34944 - 5.22673i) q^{60} +(-3.90556 - 8.77203i) q^{61} +(-0.394611 + 1.21449i) q^{62} +(7.42295 - 2.81067i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(8.25787 - 14.3031i) q^{65} +(-2.18591 - 5.31242i) q^{66} +(-3.82181 - 6.61957i) q^{67} +(0.195558 + 1.86061i) q^{68} +(-10.8168 - 4.00882i) q^{69} +(-9.75026 + 5.95381i) q^{70} +(-0.878299 + 1.20888i) q^{71} +(-1.81919 - 2.38549i) q^{72} +(1.25945 + 5.92524i) q^{73} +(-3.11006 + 3.45407i) q^{74} +(-12.6411 + 19.9691i) q^{75} +1.85177i q^{76} +(-8.68719 + 1.23801i) q^{77} +(4.10915 - 5.19651i) q^{78} +(4.12085 - 0.433118i) q^{79} +(3.20889 + 2.88930i) q^{80} +(7.02791 - 5.62215i) q^{81} +(-8.59651 + 3.82741i) q^{82} +(4.25224 + 3.08943i) q^{83} +(-4.21596 + 1.79602i) q^{84} +(7.68299 - 2.49635i) q^{85} +(2.88576 - 0.303305i) q^{86} +(1.30028 - 8.87484i) q^{87} +(1.38597 + 3.01315i) q^{88} +(-0.326895 - 0.188733i) q^{89} +(-8.44222 + 9.82520i) q^{90} +(-6.14776 - 8.03817i) q^{91} +(6.33420 + 2.05810i) q^{92} +(2.14294 + 0.547634i) q^{93} +(6.15965 + 0.647405i) q^{94} +(7.82120 - 1.66245i) q^{95} +(1.10556 + 1.33332i) q^{96} +(-3.32691 + 2.41714i) q^{97} +(1.07320 + 6.91724i) q^{98} +(-8.94056 + 4.36651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$3$	1.70747	−	0.290781i	0.985807	−	0.167883i
$3$	1.70747	−	0.290781i	0.985807	−	0.167883i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	1.75629	+	3.94468i	0.785435	+	1.76412i	0.630497	+	0.776192i	$0.282851\pi$
$5$	1.75629	+	3.94468i	0.785435	+	1.76412i	0.154938	+	0.987924i	$0.450482\pi$
$6$	0.467667	+	1.66772i	0.190924	+	0.680844i
$7$	2.64495	−	0.0650804i	0.999697	−	0.0245981i
$7$	2.64495	−	0.0650804i	0.999697	−	0.0245981i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	2.83089	−	0.992999i	0.943631	−	0.331000i
$10$	−3.73949	+	2.15900i	−1.18253	+	0.682735i
$11$	−3.29397	+	0.387016i	−0.993168	+	0.116690i
$11$	−3.29397	+	0.387016i	−0.993168	+	0.116690i
$12$	−1.60970	+	0.639429i	−0.464680	+	0.184587i
$13$	−2.24820	−	3.09438i	−0.623538	−	0.858227i	0.374066	−	0.927402i	$-0.377963\pi$
$13$	−2.24820	−	3.09438i	−0.623538	−	0.858227i	−0.997605	+	0.0691750i	$0.977963\pi$
$14$	0.341197	+	2.62366i	0.0911886	+	0.701202i
$15$	4.14584	+	6.22472i	1.07045	+	1.60722i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.195558	−	1.86061i	0.0474299	−	0.451265i	−0.944874	−	0.327435i	$-0.893816\pi$
$17$	0.195558	−	1.86061i	0.0474299	−	0.451265i	0.992303	−	0.123830i	$-0.0395177\pi$
$18$	1.28347	+	2.71159i	0.302516	+	0.639127i
$19$	0.385005	−	1.81130i	0.0883261	−	0.415542i	−0.911663	−	0.410938i	$-0.865201\pi$
$19$	0.385005	−	1.81130i	0.0883261	−	0.415542i	0.999989	−	0.00460363i	$-0.00146539\pi$
$20$	−2.53805	−	3.49333i	−0.567526	−	0.781132i
$21$	4.49724	−	0.880225i	0.981379	−	0.192081i
$22$	−0.729209	−	3.23547i	−0.155468	−	0.689804i
$23$	−5.76787	−	3.33008i	−1.20268	−	0.694370i	−0.241534	−	0.970392i	$-0.577650\pi$
$23$	−5.76787	−	3.33008i	−1.20268	−	0.694370i	−0.961151	+	0.276022i	$0.910984\pi$
$24$	−0.804186	−	1.53404i	−0.164154	−	0.313135i
$25$	−9.13033	+	10.1403i	−1.82607	+	2.02805i
$26$	2.84243	−	2.55934i	0.557446	−	0.501927i
$27$	4.54491	−	2.51868i	0.874669	−	0.484721i
$28$	−2.57362	+	0.613574i	−0.486369	+	0.115955i
$29$	1.60027	−	4.92514i	0.297163	−	0.914575i	−0.685323	−	0.728239i	$-0.740339\pi$
$29$	1.60027	−	4.92514i	0.297163	−	0.914575i	0.982486	−	0.186335i	$-0.0596611\pi$
$30$	−5.75727	+	4.77379i	−1.05113	+	0.871571i
$31$	1.16659	+	0.519398i	0.209525	+	0.0932866i	0.508816	−	0.860875i	$-0.330083\pi$
$31$	1.16659	+	0.519398i	0.209525	+	0.0932866i	−0.299291	+	0.954162i	$0.596750\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−5.51181	+	1.61864i	−0.959482	+	0.281769i
$34$	1.87086			0.320850
$35$	4.90201	+	10.3192i	0.828591	+	1.74426i
$36$	−2.56257	+	1.55988i	−0.427096	+	0.259979i
$37$	3.11006	+	3.45407i	0.511290	+	0.567845i	0.942414	−	0.334447i	$-0.108550\pi$
$37$	3.11006	+	3.45407i	0.511290	+	0.567845i	−0.431124	+	0.902292i	$0.641883\pi$
$38$	1.84163	+	0.193563i	0.298751	+	0.0314000i
$39$	−4.73852	−	4.62982i	−0.758770	−	0.741365i
$40$	3.20889	−	2.88930i	0.507371	−	0.456839i
$41$	2.90786	+	8.94949i	0.454132	+	1.39768i	0.872151	+	0.489237i	$0.162725\pi$
$41$	2.90786	+	8.94949i	0.454132	+	1.39768i	−0.418019	+	0.908438i	$0.637275\pi$
$42$	1.34549	+	4.38060i	0.207614	+	0.675941i
$43$		−	2.90165i		−	0.442498i	−0.975217	−	0.221249i	$-0.928987\pi$
$43$		−	2.90165i		−	0.442498i	0.975217	−	0.221249i	$-0.0710134\pi$
$44$	3.14152	−	1.06341i	0.473602	−	0.160316i
$45$	8.88892	+	9.42298i	1.32508	+	1.40470i
$46$	2.70893	−	6.08437i	0.399411	−	0.897091i
$47$	1.28772	−	6.05823i	0.187833	−	0.883684i	−0.778751	−	0.627333i	$-0.784146\pi$
$47$	1.28772	−	6.05823i	0.187833	−	0.883684i	0.966584	−	0.256351i	$-0.0825203\pi$
$48$	1.44158	−	0.960132i	0.208074	−	0.138583i
$49$	6.99153	−	0.344269i	0.998790	−	0.0491813i
$50$	−11.0391	−	8.02037i	−1.56116	−	1.13425i
$51$	−0.207122	−	3.23380i	−0.0290029	−	0.452823i
$52$	2.84243	+	2.55934i	0.394174	+	0.354916i
$53$	−5.16057	+	11.5908i	−0.708859	+	1.59212i	0.0937353	+	0.995597i	$0.470119\pi$
$53$	−5.16057	+	11.5908i	−0.708859	+	1.59212i	−0.802594	+	0.596526i	$0.796547\pi$
$54$	2.97996	+	4.25674i	0.405521	+	0.579269i
$55$	−7.31180	−	12.3139i	−0.985923	−	1.66041i
$56$	−0.879230	−	2.49539i	−0.117492	−	0.333460i
$57$	0.130690	−	3.20469i	0.0173103	−	0.424472i
$58$	5.06543	+	1.07669i	0.665124	+	0.141376i
$59$	−0.0588568	−	0.276899i	−0.00766250	−	0.0360492i	0.974150	−	0.225901i	$-0.0725326\pi$
$59$	−0.0588568	−	0.276899i	−0.00766250	−	0.0360492i	−0.981813	+	0.189852i	$0.939199\pi$
$60$	−5.34944	−	5.22673i	−0.690609	−	0.674768i
$61$	−3.90556	−	8.77203i	−0.500055	−	1.12314i	−0.970585	−	0.240759i	$-0.922604\pi$
$61$	−3.90556	−	8.77203i	−0.500055	−	1.12314i	0.470530	−	0.882384i	$-0.344063\pi$
$62$	−0.394611	+	1.21449i	−0.0501157	+	0.154240i
$63$	7.42295	−	2.81067i	0.935203	−	0.354111i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	8.25787	−	14.3031i	1.02426	−	1.77408i
$66$	−2.18591	−	5.31242i	−0.269067	−	0.653913i
$67$	−3.82181	−	6.61957i	−0.466908	−	0.808709i	0.532377	−	0.846507i	$-0.321299\pi$
$67$	−3.82181	−	6.61957i	−0.466908	−	0.808709i	−0.999285	+	0.0377985i	$0.987966\pi$
$68$	0.195558	+	1.86061i	0.0237149	+	0.225633i
$69$	−10.8168	−	4.00882i	−1.30219	−	0.482605i
$70$	−9.75026	+	5.95381i	−1.16538	+	0.711616i
$71$	−0.878299	+	1.20888i	−0.104235	+	0.143467i	−0.857948	−	0.513737i	$-0.828261\pi$
$71$	−0.878299	+	1.20888i	−0.104235	+	0.143467i	0.753713	+	0.657204i	$0.228261\pi$
$72$	−1.81919	−	2.38549i	−0.214394	−	0.281132i
$73$	1.25945	+	5.92524i	0.147407	+	0.693496i	0.988328	+	0.152339i	$0.0486805\pi$
$73$	1.25945	+	5.92524i	0.147407	+	0.693496i	−0.840921	+	0.541158i	$0.817986\pi$
$74$	−3.11006	+	3.45407i	−0.361537	+	0.401527i
$75$	−12.6411	+	19.9691i	−1.45967	+	2.30583i
$76$			1.85177i			0.212413i
$77$	−8.68719	+	1.23801i	−0.989998	+	0.141084i
$78$	4.10915	−	5.19651i	0.465270	−	0.588389i
$79$	4.12085	−	0.433118i	0.463631	−	0.0487296i	0.130167	−	0.991492i	$-0.458449\pi$
$79$	4.12085	−	0.433118i	0.463631	−	0.0487296i	0.333465	+	0.942763i	$0.391782\pi$
$80$	3.20889	+	2.88930i	0.358765	+	0.323034i
$81$	7.02791	−	5.62215i	0.780878	−	0.624683i
$82$	−8.59651	+	3.82741i	−0.949325	+	0.422667i
$83$	4.25224	+	3.08943i	0.466744	+	0.339109i	0.796171	−	0.605072i	$-0.206856\pi$
$83$	4.25224	+	3.08943i	0.466744	+	0.339109i	−0.329427	+	0.944181i	$0.606856\pi$
$84$	−4.21596	+	1.79602i	−0.459999	+	0.195962i
$85$	7.68299	−	2.49635i	0.833337	−	0.270768i
$86$	2.88576	−	0.303305i	0.311179	−	0.0327063i
$87$	1.30028	−	8.87484i	0.139405	−	0.951483i
$88$	1.38597	+	3.01315i	0.147744	+	0.321203i
$89$	−0.326895	−	0.188733i	−0.0346508	−	0.0200056i	0.482575	−	0.875855i	$-0.339702\pi$
$89$	−0.326895	−	0.188733i	−0.0346508	−	0.0200056i	−0.517225	+	0.855849i	$0.673035\pi$
$90$	−8.44222	+	9.82520i	−0.889888	+	1.03567i
$91$	−6.14776	−	8.03817i	−0.644461	−	0.842630i
$92$	6.33420	+	2.05810i	0.660386	+	0.214572i
$93$	2.14294	+	0.547634i	0.222213	+	0.0567870i
$94$	6.15965	+	0.647405i	0.635319	+	0.0667748i
$95$	7.82120	−	1.66245i	0.802438	−	0.170563i
$96$	1.10556	+	1.33332i	0.112836	+	0.136081i
$97$	−3.32691	+	2.41714i	−0.337797	+	0.245424i	−0.743732	−	0.668478i	$-0.766946\pi$
$97$	−3.32691	+	2.41714i	−0.337797	+	0.245424i	0.405935	+	0.913902i	$0.366946\pi$
$98$	1.07320	+	6.91724i	0.108409	+	0.698747i
$99$	−8.94056	+	4.36651i	−0.898560	+	0.438850i
$100$	6.82253	−	11.8170i	0.682253	−	1.18170i
$101$	−18.2429	−	8.12225i	−1.81523	−	0.808194i	−0.953880	−	0.300188i	$-0.902950\pi$
$101$	−18.2429	−	8.12225i	−1.81523	−	0.808194i	−0.861354	−	0.508006i	$-0.830383\pi$
$102$	3.19444	−	0.544012i	0.316296	−	0.0538652i
$103$	−6.69173	−	7.43192i	−0.659356	−	0.732289i	0.317008	−	0.948423i	$-0.397322\pi$
$103$	−6.69173	−	7.43192i	−0.659356	−	0.732289i	−0.976364	+	0.216134i	$0.930655\pi$
$104$	−2.24820	+	3.09438i	−0.220454	+	0.303429i
$105$	11.3707	+	16.1943i	1.10966	+	1.58040i
$106$	−12.0668	−	3.92073i	−1.17203	−	0.380815i
$107$	8.33745	+	1.77218i	0.806012	+	0.171323i	0.592451	−	0.805607i	$-0.298160\pi$
$107$	8.33745	+	1.77218i	0.806012	+	0.171323i	0.213561	+	0.976930i	$0.431494\pi$
$108$	−3.92193	+	3.40859i	−0.377388	+	0.327991i
$109$	0.521271	−	0.300956i	0.0499287	−	0.0288263i	−0.474828	−	0.880079i	$-0.657490\pi$
$109$	0.521271	−	0.300956i	0.0499287	−	0.0288263i	0.524757	+	0.851252i	$0.324156\pi$
$110$	11.4822	−	8.55891i	1.09478	−	0.816060i
$111$	6.31470	+	4.99336i	0.599364	+	0.473949i
$112$	2.38981	−	1.13525i	0.225816	−	0.107271i
$113$	−2.79358	+	0.907689i	−0.262798	+	0.0853882i	−0.437452	−	0.899242i	$-0.644119\pi$
$113$	−2.79358	+	0.907689i	−0.262798	+	0.0853882i	0.174655	+	0.984630i	$0.444119\pi$
$114$	3.20080	−	0.205008i	0.299782	−	0.0192008i
$115$	3.00609	−	28.6010i	0.280319	−	2.66706i
$116$	−0.541311	+	5.15023i	−0.0502594	+	0.478186i
$117$	−9.43713	−	6.52740i	−0.872463	−	0.603459i
$118$	0.269230	−	0.0874782i	0.0247846	−	0.00805302i
$119$	0.396153	−	4.93396i	0.0363153	−	0.452295i
$120$	4.63893	−	5.86648i	0.423474	−	0.535533i
$121$	10.7004	−	2.54964i	0.972767	−	0.231785i
$122$	8.31573	−	4.80109i	0.752871	−	0.434670i
$123$	7.56743	+	14.4354i	0.682332	+	1.30160i
$124$	−1.24908	−	0.265501i	−0.112171	−	0.0238427i
$125$	−35.5023	−	11.5354i	−3.17542	−	1.03176i
$126$	3.57118	+	7.08849i	0.318146	+	0.631493i
$127$	4.41242	−	6.07317i	0.391539	−	0.538907i	−0.567057	−	0.823679i	$-0.691918\pi$
$127$	4.41242	−	6.07317i	0.391539	−	0.538907i	0.958595	+	0.284772i	$0.0919179\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	−0.843746	−	4.95448i	−0.0742877	−	0.436218i
$130$	15.0879	+	6.71756i	1.32330	+	0.589169i
$131$	−2.19833	+	3.80762i	−0.192069	+	0.332673i	−0.945936	−	0.324354i	$-0.894853\pi$
$131$	−2.19833	+	3.80762i	−0.192069	+	0.332673i	0.753867	+	0.657027i	$0.228186\pi$
$132$	5.05483	−	2.72924i	0.439966	−	0.237550i
$133$	0.900438	−	4.81587i	0.0780778	−	0.417589i
$134$	6.18382	−	4.49281i	0.534200	−	0.388119i
$135$	17.9176	+	13.5047i	1.54210	+	1.16230i
$136$	−1.82998	+	0.388974i	−0.156919	+	0.0333543i
$137$	13.2270	+	1.39021i	1.13006	+	0.118774i	0.651047	−	0.759037i	$-0.274330\pi$
$137$	13.2270	+	1.39021i	1.13006	+	0.118774i	0.479008	+	0.877811i	$0.340997\pi$
$138$	2.85620	−	11.1766i	0.243136	−	0.951412i
$139$	8.53433	+	2.77297i	0.723873	+	0.235200i	0.647701	−	0.761894i	$-0.275730\pi$
$139$	8.53433	+	2.77297i	0.723873	+	0.235200i	0.0761713	+	0.997095i	$0.475730\pi$
$140$	−6.94037	−	9.07451i	−0.586568	−	0.766936i
$141$	0.437116	−	10.7187i	0.0368118	−	0.902676i
$142$	−1.29406	−	0.747126i	−0.108595	−	0.0626974i
$143$	8.60307	+	9.32270i	0.719425	+	0.779604i
$144$	2.18226	−	2.05858i	0.181855	−	0.171548i
$145$	22.2386	−	2.33738i	1.84682	−	0.194108i
$146$	−5.76113	+	1.87190i	−0.476794	+	0.154920i
$147$	11.8377	−	2.62083i	0.976357	−	0.216163i
$148$	−3.76023	−	2.73197i	−0.309089	−	0.224567i
$149$	4.03330	−	1.79574i	0.330421	−	0.147113i	−0.234820	−	0.972039i	$-0.575450\pi$
$149$	4.03330	−	1.79574i	0.330421	−	0.147113i	0.565241	+	0.824926i	$0.308783\pi$
$150$	−21.1811	−	10.4846i	−1.72943	−	0.856061i
$151$	4.14869	+	3.73550i	0.337616	+	0.303991i	0.820447	−	0.571723i	$-0.193725\pi$
$151$	4.14869	+	3.73550i	0.337616	+	0.303991i	−0.482831	+	0.875714i	$0.660391\pi$
$152$	−1.84163	+	0.193563i	−0.149376	+	0.0157000i
$153$	−1.29398	−	5.46139i	−0.104612	−	0.441527i
$154$	−2.13929	−	8.51020i	−0.172389	−	0.685771i
$155$			5.51403i			0.442897i
$156$	5.59756	+	3.54346i	0.448164	+	0.283704i
$157$	−6.00875	+	6.67339i	−0.479551	+	0.532595i	−0.933569	−	0.358397i	$-0.883323\pi$
$157$	−6.00875	+	6.67339i	−0.479551	+	0.532595i	0.454019	+	0.890992i	$0.349990\pi$
$158$	0.861491	+	4.05300i	0.0685366	+	0.322439i
$159$	−5.44111	+	21.2916i	−0.431508	+	1.68853i
$160$	−2.53805	+	3.49333i	−0.200651	+	0.276172i
$161$	−15.4725	−	8.43253i	−1.21940	−	0.664577i
$162$	6.32596	+	6.40173i	0.497015	+	0.502968i
$163$	1.73933	+	16.5486i	0.136234	+	1.29618i	0.822471	+	0.568806i	$0.192595\pi$
$163$	1.73933	+	16.5486i	0.136234	+	1.29618i	−0.686237	+	0.727378i	$0.740739\pi$
$164$	−4.70502	−	8.14934i	−0.367401	−	0.636357i
$165$	−16.0653	−	18.8995i	−1.25068	−	1.47133i
$166$	−2.62803	+	4.55188i	−0.203975	+	0.353294i
$167$	3.93748	−	2.86075i	0.304691	−	0.221371i	−0.424924	−	0.905229i	$-0.639699\pi$
$167$	3.93748	−	2.86075i	0.304691	−	0.221371i	0.729615	+	0.683858i	$0.239699\pi$
$168$	−2.22687	−	4.00513i	−0.171807	−	0.309002i
$169$	−0.503574	+	1.54984i	−0.0387365	+	0.119219i
$170$	3.28577	+	7.37996i	0.252007	+	0.566017i
$171$	−0.708717	−	5.50992i	−0.0541969	−	0.421354i
$172$	0.603288	+	2.83825i	0.0460003	+	0.216414i
$173$	−14.1785	−	3.01373i	−1.07797	−	0.229130i	−0.365485	−	0.930817i	$-0.619097\pi$
$173$	−14.1785	−	3.01373i	−1.07797	−	0.229130i	−0.712485	+	0.701688i	$0.752430\pi$
$174$	8.96214	+	0.365482i	0.679418	+	0.0277071i
$175$	−23.4893	+	27.4147i	−1.77563	+	2.07236i
$176$	−2.85178	+	1.69333i	−0.214961	+	0.127640i
$177$	−0.181013	−	0.455682i	−0.0136058	−	0.0342512i
$178$	0.153529	−	0.344832i	0.0115075	−	0.0258462i
$179$	−1.69852	−	1.52935i	−0.126953	−	0.114309i	0.603209	−	0.797584i	$-0.293889\pi$
$179$	−1.69852	−	1.52935i	−0.126953	−	0.114309i	−0.730162	+	0.683274i	$0.760555\pi$
$180$	−10.6538	−	7.36896i	−0.794089	−	0.549250i
$181$	1.13997	+	0.828240i	0.0847337	+	0.0615626i	0.629346	−	0.777126i	$-0.283323\pi$
$181$	1.13997	+	0.828240i	0.0847337	+	0.0615626i	−0.544612	+	0.838688i	$0.683323\pi$
$182$	7.35152	−	6.95430i	0.544931	−	0.515487i
$183$	−9.21935	−	13.8423i	−0.681514	−	1.02325i
$184$	−1.38473	+	6.51463i	−0.102083	+	0.480265i
$185$	−8.16305	+	18.3345i	−0.600159	+	1.34798i
$186$	−0.320635	+	2.18844i	−0.0235101	+	0.160465i
$187$	0.0759244	+	6.20449i	0.00555214	+	0.453717i
$188$			6.19358i			0.451713i
$189$	11.8572	−	6.95758i	0.862481	−	0.506090i
$190$	2.47088	+	7.60458i	0.179256	+	0.551694i
$191$	−3.21681	+	2.89643i	−0.232760	+	0.209578i	−0.777254	−	0.629186i	$-0.783388\pi$
$191$	−3.21681	+	2.89643i	−0.232760	+	0.209578i	0.544494	+	0.838764i	$0.316722\pi$
$192$	−1.21045	+	1.23887i	−0.0873570	+	0.0894078i
$193$	−17.6146	−	1.85137i	−1.26793	−	0.133264i	−0.553425	−	0.832899i	$-0.686680\pi$
$193$	−17.6146	−	1.85137i	−1.26793	−	0.133264i	−0.714501	+	0.699634i	$0.753346\pi$
$194$	−2.75166	−	3.05603i	−0.197558	−	0.219410i
$195$	9.94099	−	26.8232i	0.711889	−	1.92085i
$196$	−6.76717	+	1.79037i	−0.483369	+	0.127883i
$197$	20.8535			1.48575			0.742873	−	0.669432i	$-0.233462\pi$
$197$	20.8535			1.48575			0.742873	+	0.669432i	$0.233462\pi$
$198$	−5.27713	−	8.43516i	−0.375029	−	0.599461i
$199$	8.32060	+	14.4117i	0.589831	+	1.02162i	0.994254	+	0.107046i	$0.0341391\pi$
$199$	8.32060	+	14.4117i	0.589831	+	1.02162i	−0.404423	+	0.914572i	$0.632528\pi$
$200$	12.4654	+	5.54995i	0.881436	+	0.392441i
$201$	−8.45046	−	10.1914i	−0.596050	−	0.718845i
$202$	6.17086	−	18.9919i	0.434180	−	1.33627i
$203$	3.91212	−	13.1309i	0.274577	−	0.921608i
$204$	0.874941	+	3.12007i	0.0612581	+	0.218449i
$205$	−30.1958	+	27.1885i	−2.10897	+	1.89892i
$206$	6.69173	−	7.43192i	0.466235	−	0.517807i
$207$	−19.6350	−	3.69962i	−1.36473	−	0.257141i
$208$	−3.31243	−	1.91243i	−0.229676	−	0.132603i
$209$	−0.567189	+	6.11538i	−0.0392333	+	0.423010i
$210$	−14.9170	+	13.0011i	−1.02937	+	0.897163i
$211$	−7.10704	−	9.78201i	−0.489269	−	0.673421i	0.490984	−	0.871169i	$-0.336637\pi$
$211$	−7.10704	−	9.78201i	−0.489269	−	0.673421i	−0.980253	+	0.197748i	$0.936637\pi$
$212$	2.63793	−	12.4105i	0.181174	−	0.852356i
$213$	−1.14815	+	2.31951i	−0.0786699	+	0.158930i
$214$	−0.890971	+	8.47702i	−0.0609055	+	0.579477i
$215$	11.4461	−	5.09613i	0.780618	−	0.347553i
$216$	−3.79987	−	3.54415i	−0.258548	−	0.241149i
$217$	3.11937	+	1.29786i	0.211756	+	0.0881045i
$218$	0.353795	+	0.486957i	0.0239620	+	0.0329809i
$219$	3.87341	+	9.75093i	0.261741	+	0.658906i
$220$	9.71224	+	10.5246i	0.654799	+	0.709572i
$221$	−6.19710	+	3.57790i	−0.416862	+	0.240676i
$222$	−4.30594	+	6.80205i	−0.288996	+	0.456524i
$223$	4.63157	+	14.2545i	0.310153	+	0.954552i	0.977704	+	0.209988i	$0.0673426\pi$
$223$	4.63157	+	14.2545i	0.310153	+	0.954552i	−0.667551	+	0.744564i	$0.732657\pi$
$224$	1.37884	+	2.25805i	0.0921274	+	0.150873i
$225$	−15.7777	+	37.7724i	−1.05185	+	2.51816i
$226$	−1.19472	−	2.68340i	−0.0794719	−	0.178497i
$227$	−7.17181	+	1.52442i	−0.476010	+	0.101179i	−0.439668	−	0.898160i	$-0.644904\pi$
$227$	−7.17181	+	1.52442i	−0.476010	+	0.101179i	−0.0363419	+	0.999339i	$0.511571\pi$
$228$	0.538460	+	3.16184i	0.0356604	+	0.209398i
$229$	1.63005	+	15.5088i	0.107716	+	1.02485i	0.906204	+	0.422842i	$0.138967\pi$
$229$	1.63005	+	15.5088i	0.107716	+	1.02485i	−0.798487	+	0.602012i	$0.794366\pi$
$230$	28.7586			1.89628
$231$	−14.4731	+	4.63994i	−0.952261	+	0.305285i
$232$	−5.17859			−0.339991
$233$	1.36272	+	12.9655i	0.0892750	+	0.849395i	0.943918	+	0.330179i	$0.107109\pi$
$233$	1.36272	+	12.9655i	0.0892750	+	0.849395i	−0.854643	+	0.519216i	$0.826224\pi$
$234$	5.50520	−	10.0677i	0.359886	−	0.658148i
$235$	26.1594	−	5.56036i	1.70645	−	0.362718i
$236$	0.115141	+	0.258611i	0.00749505	+	0.0168342i
$237$	6.91027	−	1.93780i	0.448870	−	0.125874i
$238$	4.94834	−	0.121756i	0.320753	−	0.00789230i
$239$	1.99602	+	6.14310i	0.129111	+	0.397364i	0.994628	−	0.103517i	$-0.0330095\pi$
$239$	1.99602	+	6.14310i	0.129111	+	0.397364i	−0.865516	+	0.500881i	$0.833009\pi$
$240$	6.31924	+	4.00030i	0.407905	+	0.258218i
$241$	−13.3575	+	7.71194i	−0.860430	+	0.496770i	−0.864156	−	0.503223i	$-0.832147\pi$
$241$	−13.3575	+	7.71194i	−0.860430	+	0.496770i	0.00372601	+	0.999993i	$0.498814\pi$
$242$	3.65417	+	10.3753i	0.234899	+	0.666950i
$243$	10.3651	−	11.6432i	0.664922	−	0.746913i
$244$	5.64402	+	7.76833i	0.361321	+	0.497316i
$245$	13.6372	+	26.9747i	0.871246	+	1.72335i
$246$	−13.5653	+	9.03488i	−0.864893	+	0.576043i
$247$	−6.47043	+	2.88082i	−0.411704	+	0.183302i
$248$	0.133482	−	1.26999i	0.00847609	−	0.0806446i
$249$	8.15891	+	4.03863i	0.517050	+	0.255938i
$250$	7.76120	−	36.5136i	0.490862	−	2.30932i
$251$	−7.68813	−	10.5818i	−0.485270	−	0.667917i	0.494237	−	0.869327i	$-0.335448\pi$
$251$	−7.68813	−	10.5818i	−0.485270	−	0.667917i	−0.979507	+	0.201410i	$0.935448\pi$
$252$	−6.67637	+	4.29257i	−0.420572	+	0.270406i
$253$	20.2880	+	8.73693i	1.27549	+	0.549286i
$254$	6.50113	+	3.75343i	0.407917	+	0.235511i
$255$	12.3926	−	6.49651i	0.776052	−	0.406827i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−12.1156	+	10.9090i	−0.755752	+	0.680482i	−0.954046	−	0.299660i	$-0.903127\pi$
$257$	−12.1156	+	10.9090i	−0.755752	+	0.680482i	0.198294	+	0.980143i	$0.436460\pi$
$258$	4.83914	−	1.35701i	0.301272	−	0.0844837i
$259$	8.45073	+	8.93343i	0.525103	+	0.555096i
$260$	−5.10365	+	15.7074i	−0.316515	+	0.974132i
$261$	−0.360452	−	15.5316i	−0.0223114	−	0.961382i
$262$	−4.01655	−	1.78828i	−0.248143	−	0.110481i
$263$	−10.1504	−	17.5810i	−0.625901	−	1.08409i	−0.988366	−	0.152094i	$-0.951398\pi$
$263$	−10.1504	−	17.5810i	−0.625901	−	1.08409i	0.362465	−	0.931997i	$-0.381935\pi$
$264$	3.24266	+	4.74185i	0.199572	+	0.291841i
$265$	−54.7856			−3.36545
$266$	4.88361	+	0.392110i	0.299433	+	0.0240418i
$267$	−0.613042	−	0.227200i	−0.0375176	−	0.0139044i
$268$	5.11458	+	5.68031i	0.312423	+	0.346980i
$269$	−10.6458	−	1.11891i	−0.649084	−	0.0682215i	−0.225736	−	0.974189i	$-0.572479\pi$
$269$	−10.6458	−	1.11891i	−0.649084	−	0.0682215i	−0.423348	+	0.905967i	$0.639145\pi$
$270$	−11.5578	+	19.2310i	−0.703387	+	1.17036i
$271$	−3.10292	+	2.79389i	−0.188489	+	0.169716i	−0.757973	−	0.652286i	$-0.773810\pi$
$271$	−3.10292	+	2.79389i	−0.188489	+	0.169716i	0.569483	+	0.822003i	$0.307143\pi$
$272$	−0.578128	−	1.77930i	−0.0350542	−	0.107886i
$273$	−12.8345	−	11.9373i	−0.776777	−	0.722476i
$274$			13.2998i			0.803471i
$275$	26.1506	−	36.9353i	1.57694	−	2.22728i
$276$	11.4139	+	1.67228i	0.687036	+	0.100660i
$277$	−4.95199	+	11.1223i	−0.297536	+	0.668277i	−0.999013	−	0.0444150i	$-0.985858\pi$
$277$	−4.95199	+	11.1223i	−0.297536	+	0.668277i	0.701477	+	0.712692i	$0.252524\pi$
$278$	−1.86570	+	8.77744i	−0.111897	+	0.526436i
$279$	3.81824	+	0.311940i	0.228592	+	0.0186754i
$280$	8.29933	−	7.85090i	0.495980	−	0.469181i
$281$	−2.59579	−	1.88595i	−0.154852	−	0.112507i	0.507661	−	0.861557i	$-0.330510\pi$
$281$	−2.59579	−	1.88595i	−0.154852	−	0.112507i	−0.662513	+	0.749050i	$0.730510\pi$
$282$	10.7057	−	0.685687i	0.637513	−	0.0408320i
$283$	−14.9341	−	13.4467i	−0.887738	−	0.799323i	0.0927932	−	0.995685i	$-0.470420\pi$
$283$	−14.9341	−	13.4467i	−0.887738	−	0.799323i	−0.980531	+	0.196362i	$0.937087\pi$
$284$	0.607767	−	1.36507i	0.0360643	−	0.0810018i
$285$	12.8710	−	5.11283i	0.762414	−	0.302858i
$286$	−8.37237	+	9.53043i	−0.495068	+	0.563546i
$287$	8.27360	+	23.4817i	0.488375	+	1.38608i
$288$	2.27541	+	1.95513i	0.134080	+	0.115207i
$289$	13.2049	+	2.80678i	0.776757	+	0.165105i
$290$	4.64914	+	21.8725i	0.273007	+	1.28440i
$291$	−4.97774	+	5.09460i	−0.291800	+	0.298651i
$292$	−2.46385	−	5.53390i	−0.144186	−	0.323847i
$293$	1.89733	−	5.83938i	0.110843	−	0.341141i	−0.880214	−	0.474577i	$-0.842601\pi$
$293$	1.89733	−	5.83938i	0.110843	−	0.341141i	0.991057	+	0.133436i	$0.0426011\pi$
$294$	3.84385	+	11.4989i	0.224178	+	0.670630i
$295$	0.988911	−	0.718486i	0.0575766	−	0.0418318i
$296$	2.32395	−	4.02520i	0.135077	−	0.233960i
$297$	−13.9960	+	10.0554i	−0.812132	+	0.583474i
$298$	2.20750	+	3.82350i	0.127877	+	0.221490i
$299$	2.66278	+	25.3347i	0.153993	+	1.46514i
$300$	8.21310	−	22.1610i	0.474184	−	1.27946i
$301$	−0.188841	−	7.67473i	−0.0108846	−	0.442364i
$302$	−3.28138	+	4.51643i	−0.188822	+	0.259891i
$303$	−33.5109	−	8.56380i	−1.92515	−	0.491977i
$304$	−0.385005	−	1.81130i	−0.0220815	−	0.103885i
$305$	27.7436	−	30.8124i	1.58859	−	1.76431i
$306$	5.29621	−	1.85776i	0.302764	−	0.106201i
$307$		−	20.2358i		−	1.15492i	−0.816419	−	0.577460i	$-0.804044\pi$
$307$		−	20.2358i		−	1.15492i	0.816419	−	0.577460i	$-0.195956\pi$
$308$	8.23996	−	3.01713i	0.469515	−	0.171917i
$309$	−13.5870	−	10.7439i	−0.772936	−	0.611201i
$310$	−5.48382	+	0.576373i	−0.311460	+	0.0327358i
$311$	8.41084	+	7.57316i	0.476935	+	0.429434i	0.872212	−	0.489128i	$-0.162685\pi$
$311$	8.41084	+	7.57316i	0.476935	+	0.429434i	−0.395277	+	0.918562i	$0.629351\pi$
$312$	−2.93894	+	5.93729i	−0.166385	+	0.336133i
$313$	7.01174	−	3.12183i	0.396327	−	0.176456i	−0.198889	−	0.980022i	$-0.563733\pi$
$313$	7.01174	−	3.12183i	0.396327	−	0.176456i	0.595216	+	0.803566i	$0.297067\pi$
$314$	−7.26492	−	5.27827i	−0.409983	−	0.297870i
$315$	24.1240	+	24.3448i	1.35923	+	1.37168i
$316$	−3.94075	+	1.28043i	−0.221684	+	0.0720296i
$317$	−29.0730	+	3.05569i	−1.63290	+	0.171625i	−0.876137	−	0.482063i	$-0.839888\pi$
$317$	−29.0730	+	3.05569i	−1.63290	+	0.171625i	−0.756765	+	0.653688i	$0.773221\pi$
$318$	−21.7437	−	3.18573i	−1.21932	−	0.178647i
$319$	−3.36514	+	16.8426i	−0.188412	+	0.943003i
$320$	−3.73949	−	2.15900i	−0.209044	−	0.120692i
$321$	14.7512	+	0.601566i	0.823334	+	0.0335761i
$322$	6.76902	−	16.2691i	0.377223	−	0.906644i
$323$	−3.29485	−	1.07056i	−0.183330	−	0.0595676i
$324$	−5.70542	+	6.96047i	−0.316968	+	0.386693i
$325$	51.9046	+	5.45540i	2.87915	+	0.302611i
$326$	−16.2761	+	3.45959i	−0.901450	+	0.191609i
$327$	0.802541	−	0.665448i	0.0443806	−	0.0367994i
$328$	7.61289	−	5.53109i	0.420351	−	0.305403i
$329$	3.01168	−	16.1075i	0.166039	−	0.888037i
$330$	17.1167	−	17.9529i	0.942244	−	0.988273i
$331$	8.06414	−	13.9675i	0.443245	−	0.767723i	−0.554683	−	0.832062i	$-0.687161\pi$
$331$	8.06414	−	13.9675i	0.443245	−	0.767723i	0.997928	+	0.0643388i	$0.0204938\pi$
$332$	−4.80165	−	2.13783i	−0.263525	−	0.117329i
$333$	12.2341	+	6.68981i	0.670425	+	0.366599i
$334$	3.25665	+	3.61688i	0.178196	+	0.197907i
$335$	19.3999	−	26.7017i	1.05993	−	1.45887i
$336$	3.75042	−	2.63332i	0.204602	−	0.143659i
$337$	17.8788	+	5.80917i	0.973920	+	0.316446i	0.752397	−	0.658709i	$-0.228897\pi$
$337$	17.8788	+	5.80917i	0.973920	+	0.316446i	0.221523	+	0.975155i	$0.428897\pi$
$338$	−1.59399	−	0.338813i	−0.0867017	−	0.0184290i
$339$	−4.50601	+	2.36217i	−0.244733	+	0.128295i
$340$	−6.99608	+	4.03919i	−0.379415	+	0.219056i
$341$	−4.04371	−	1.25939i	−0.218979	−	0.0681999i
$342$	5.40565	−	1.28078i	0.292304	−	0.0692565i
$343$	18.4698	−	1.36559i	0.997278	−	0.0737347i
$344$	−2.75964	+	0.896660i	−0.148790	+	0.0483447i
$345$	−3.18384	−	49.7094i	−0.171412	−	2.67627i
$346$	1.51516	−	14.4158i	0.0814557	−	0.775000i
$347$	0.842256	−	8.01353i	0.0452147	−	0.430189i	−0.948376	−	0.317149i	$-0.897274\pi$
$347$	0.842256	−	8.01353i	0.0452147	−	0.430189i	0.993590	−	0.113040i	$-0.0360588\pi$
$348$	0.573318	+	8.95125i	0.0307331	+	0.479837i
$349$	−29.0378	+	9.43496i	−1.55436	+	0.505042i	−0.955294	−	0.295659i	$-0.904461\pi$
$349$	−29.0378	+	9.43496i	−1.55436	+	0.505042i	−0.599065	+	0.800701i	$0.704461\pi$
$350$	−29.7198	−	20.4950i	−1.58859	−	1.09551i
$351$	−18.0116	−	8.40119i	−0.961390	−	0.448422i
$352$	−1.98215	−	2.65915i	−0.105649	−	0.141733i
$353$	11.9037	−	6.87258i	0.633568	−	0.365791i	−0.148565	−	0.988903i	$-0.547465\pi$
$353$	11.9037	−	6.87258i	0.633568	−	0.365791i	0.782133	+	0.623112i	$0.214132\pi$
$354$	0.434265	−	0.227653i	0.0230809	−	0.0120996i
$355$	−6.31117	−	1.34148i	−0.334962	−	0.0711984i
$356$	0.358991	+	0.116643i	0.0190265	+	0.00618208i
$357$	−0.758284	−	8.53977i	−0.0401327	−	0.451973i
$358$	1.34343	−	1.84908i	0.0710026	−	0.0977267i
$359$	1.72698	+	1.91800i	0.0911463	+	0.101228i	0.786992	−	0.616963i	$-0.211637\pi$
$359$	1.72698	+	1.91800i	0.0911463	+	0.101228i	−0.695846	+	0.718191i	$0.744970\pi$
$360$	6.21496	−	11.3657i	0.327557	−	0.599027i
$361$	14.2248	+	6.33328i	0.748672	+	0.333330i
$362$	−0.704543	+	1.22030i	−0.0370300	+	0.0641378i
$363$	17.5293	−	7.46491i	0.920048	−	0.391806i
$364$	7.68465	+	6.58433i	0.402785	+	0.345113i
$365$	−21.1612	+	15.3745i	−1.10763	+	0.804740i
$366$	12.8028	−	10.6158i	0.669212	−	0.554895i
$367$	−0.145281	+	0.0308803i	−0.00758358	+	0.00161194i	−0.211702	−	0.977334i	$-0.567901\pi$
$367$	−0.145281	+	0.0308803i	−0.00758358	+	0.00161194i	0.204118	+	0.978946i	$0.434567\pi$
$368$	−6.62368	−	0.696177i	−0.345283	−	0.0362907i
$369$	17.1187	+	22.4475i	0.891163	+	1.16857i
$370$	−19.0873	−	6.20185i	−0.992304	−	0.322419i
$371$	−12.8951	+	30.9930i	−0.669481	+	1.60908i
$372$	−2.20997	−	0.0901242i	−0.114582	−	0.00467272i
$373$	3.03976	+	1.75501i	0.157393	+	0.0908707i	0.576628	−	0.817007i	$-0.304368\pi$
$373$	3.03976	+	1.75501i	0.157393	+	0.0908707i	−0.419235	+	0.907878i	$0.637702\pi$
$374$	−6.16256	+	0.724054i	−0.318658	+	0.0374399i
$375$	−63.9733	−	9.37292i	−3.30357	−	0.484015i
$376$	−6.15965	+	0.647405i	−0.317660	+	0.0333874i
$377$	−18.8380	+	6.12083i	−0.970206	+	0.315239i
$378$	8.15888	+	11.0649i	0.419647	+	0.569119i
$379$	10.3794	+	7.54109i	0.533155	+	0.387360i	0.821537	−	0.570156i	$-0.193117\pi$
$379$	10.3794	+	7.54109i	0.533155	+	0.387360i	−0.288382	+	0.957516i	$0.593117\pi$
$380$	−7.30464	+	3.25224i	−0.374720	+	0.166836i
$381$	5.76810	−	11.6528i	0.295509	−	0.596991i
$382$	−3.21681	−	2.89643i	−0.164586	−	0.148194i
$383$	−14.5926	+	1.53374i	−0.745645	+	0.0783705i	−0.469728	−	0.882811i	$-0.655648\pi$
$383$	−14.5926	+	1.53374i	−0.745645	+	0.0783705i	−0.275917	+	0.961181i	$0.588981\pi$
$384$	−1.35861	−	1.07433i	−0.0693314	−	0.0548239i
$385$	−20.1408	−	32.0939i	−1.02647	−	1.63566i
$386$		−	17.7116i		−	0.901498i
$387$	−2.88134	−	8.21427i	−0.146467	−	0.417555i
$388$	2.75166	−	3.05603i	0.139694	−	0.155146i
$389$	−1.94848	−	9.16687i	−0.0987917	−	0.464779i	−0.999537	−	0.0304306i	$-0.990312\pi$
$389$	−1.94848	−	9.16687i	−0.0987917	−	0.464779i	0.900745	−	0.434348i	$-0.143021\pi$
$390$	27.7154	+	7.08274i	1.40342	+	0.358649i
$391$	−7.32396	+	10.0806i	−0.370388	+	0.509796i
$392$	−2.48792	−	6.54295i	−0.125659	−	0.330469i
$393$	−2.64640	+	7.14062i	−0.133493	+	0.360197i
$394$	2.17978	+	20.7392i	0.109816	+	1.04483i
$395$	8.94590	+	15.4948i	0.450117	+	0.779626i
$396$	7.83734	−	6.12994i	0.393841	−	0.308041i
$397$	−0.775753	+	1.34364i	−0.0389339	+	0.0674356i	−0.884836	−	0.465903i	$-0.845730\pi$
$397$	−0.775753	+	1.34364i	−0.0389339	+	0.0674356i	0.845902	+	0.533339i	$0.179063\pi$
$398$	−13.4630	+	9.78145i	−0.674839	+	0.490300i
$399$	0.137105	−	8.48477i	0.00686384	−	0.424770i
$400$	−4.21656	+	12.9772i	−0.210828	+	0.648861i
$401$	−3.46856	−	7.79050i	−0.173211	−	0.389039i	0.805990	−	0.591929i	$-0.201633\pi$
$401$	−3.46856	−	7.79050i	−0.173211	−	0.389039i	−0.979202	+	0.202890i	$0.934967\pi$
$402$	9.25224	−	9.46946i	0.461460	−	0.472294i
$403$	−1.01550	−	4.77758i	−0.0505859	−	0.237988i
$404$	19.5329	+	4.15185i	0.971800	+	0.206562i
$405$	34.5206	+	17.8488i	1.71534	+	0.886912i
$406$	13.4679	+	2.51813i	0.668400	+	0.124973i
$407$	−11.5812	−	10.1739i	−0.574059	−	0.504303i
$408$	−3.01153	+	1.19628i	−0.149093	+	0.0592249i
$409$	−0.531107	+	1.19289i	−0.0262615	+	0.0589844i	−0.926200	−	0.377032i	$-0.876945\pi$
$409$	−0.531107	+	1.19289i	−0.0262615	+	0.0589844i	0.899939	+	0.436017i	$0.143611\pi$
$410$	−30.1958	−	27.1885i	−1.49127	−	1.34274i
$411$	22.9889	−	1.47241i	1.13396	−	0.0726288i
$412$	8.09069	+	5.87823i	0.398599	+	0.289599i
$413$	−0.173694	−	0.728554i	−0.00854692	−	0.0358498i
$414$	1.62693	−	19.9142i	0.0799594	−	0.978727i
$415$	−4.71868	+	22.1997i	−0.231631	+	1.08974i
$416$	1.55571	−	3.49419i	0.0762751	−	0.171317i
$417$	15.3784	+	2.25314i	0.753085	+	0.110337i
$418$	−6.14116	+	0.0751495i	−0.300374	+	0.00367568i
$419$		−	13.8898i		−	0.678560i	−0.940685	−	0.339280i	$-0.889817\pi$
$419$		−	13.8898i		−	0.678560i	0.940685	−	0.339280i	$-0.110183\pi$
$420$	−14.4892	−	13.4763i	−0.706998	−	0.657576i
$421$	2.64867	+	8.15177i	0.129088	+	0.397293i	0.994624	−	0.103555i	$-0.0330217\pi$
$421$	2.64867	+	8.15177i	0.129088	+	0.397293i	−0.865535	+	0.500848i	$0.833022\pi$
$422$	8.98553	−	8.09061i	0.437409	−	0.393845i
$423$	−2.37043	−	18.4289i	−0.115254	−	0.896044i
$424$	12.6182	+	1.32623i	0.612796	+	0.0644074i
$425$	17.0816	+	18.9710i	0.828579	+	0.920230i
$426$	−2.42682	−	0.899405i	−0.117580	−	0.0435763i
$427$	−10.9009	−	22.9474i	−0.527531	−	1.11050i
$428$	−8.52371			−0.412009
$429$	17.4003	+	13.4166i	0.840096	+	0.647760i
$430$	6.26466	+	10.8507i	0.302109	+	0.523268i
$431$	3.14269	+	1.39921i	0.151378	+	0.0673978i	0.481027	−	0.876706i	$-0.340264\pi$
$431$	3.14269	+	1.39921i	0.151378	+	0.0673978i	−0.329649	+	0.944103i	$0.606930\pi$
$432$	3.12754	−	4.14951i	0.150474	−	0.199644i
$433$	2.61109	−	8.03611i	0.125481	−	0.386191i	−0.868507	−	0.495676i	$-0.834920\pi$
$433$	2.61109	−	8.03611i	0.125481	−	0.386191i	0.993988	+	0.109485i	$0.0349203\pi$
$434$	−0.964688	+	3.23794i	−0.0463065	+	0.155426i
$435$	37.2921	−	10.4576i	1.78802	−	0.501402i
$436$	−0.447308	+	0.402758i	−0.0214221	+	0.0192886i
$437$	−8.25245	+	9.16528i	−0.394768	+	0.438435i
$438$	−9.29263	+	4.87144i	−0.444019	+	0.232767i
$439$	14.2511	+	8.22787i	0.680168	+	0.392695i	0.799918	−	0.600109i	$-0.204876\pi$
$439$	14.2511	+	8.22787i	0.680168	+	0.392695i	−0.119751	+	0.992804i	$0.538209\pi$
$440$	−9.45179	+	10.7592i	−0.450596	+	0.512923i
$441$	19.4504	−	7.91717i	0.926210	−	0.377008i
$442$	−4.20607	−	5.78916i	−0.200063	−	0.275362i
$443$	−5.48140	+	25.7880i	−0.260429	+	1.22522i	0.632334	+	0.774696i	$0.282097\pi$
$443$	−5.48140	+	25.7880i	−0.260429	+	1.22522i	−0.892763	+	0.450527i	$0.851236\pi$
$444$	−7.21488	−	3.57135i	−0.342403	−	0.169489i
$445$	0.170370	−	1.62096i	0.00807632	−	0.0768411i
$446$	−13.6923	+	6.09620i	−0.648348	+	0.288663i
$447$	6.36457	−	4.23898i	0.301034	−	0.200497i
$448$	−2.10156	+	1.60731i	−0.0992892	+	0.0759385i
$449$	18.2425	+	25.1086i	0.860917	+	1.18495i	0.981350	+	0.192229i	$0.0615716\pi$
$449$	18.2425	+	25.1086i	0.860917	+	1.18495i	−0.120433	+	0.992721i	$0.538428\pi$
$450$	−39.2147	−	11.7430i	−1.84860	−	0.553570i
$451$	−13.0420	−	28.3539i	−0.614124	−	1.33513i
$452$	2.54381	−	1.46867i	0.119651	−	0.0690805i
$453$	8.16997	+	5.17188i	0.383859	+	0.242996i
$454$	−2.26572	−	6.97318i	−0.106336	−	0.327267i
$455$	20.9108	−	38.3683i	0.980314	−	1.79873i
$456$	−3.08823	+	0.866012i	−0.144620	+	0.0405547i
$457$	−2.98129	−	6.69610i	−0.139459	−	0.313230i	0.830291	−	0.557330i	$-0.188174\pi$
$457$	−2.98129	−	6.69610i	−0.139459	−	0.313230i	−0.969750	+	0.244100i	$0.921508\pi$
$458$	−15.2535	+	3.24223i	−0.712749	+	0.151500i
$459$	−3.79750	−	8.94888i	−0.177252	−	0.417698i
$460$	3.00609	+	28.6010i	0.140160	+	1.33353i
$461$	−15.0082			−0.699002			−0.349501	−	0.936936i	$-0.613649\pi$
$461$	−15.0082			−0.699002			−0.349501	+	0.936936i	$0.613649\pi$
$462$	−6.12737	−	13.9088i	−0.285071	−	0.647097i
$463$	26.8294			1.24687			0.623434	−	0.781876i	$-0.285737\pi$
$463$	26.8294			1.24687			0.623434	+	0.781876i	$0.285737\pi$
$464$	−0.541311	−	5.15023i	−0.0251297	−	0.239093i
$465$	1.60338	+	9.41502i	0.0743547	+	0.436611i
$466$	−12.7520	+	2.71052i	−0.590724	+	0.125562i
$467$	−0.289655	−	0.650576i	−0.0134036	−	0.0301051i	0.906720	−	0.421734i	$-0.138578\pi$
$467$	−0.289655	−	0.650576i	−0.0134036	−	0.0301051i	−0.920123	+	0.391629i	$0.871912\pi$
$468$	10.5880	+	4.42267i	0.489432	+	0.204438i
$469$	−10.5393	−	17.2597i	−0.486660	−	0.796979i
$470$	8.26430	+	25.4349i	0.381204	+	1.17322i
$471$	−8.31925	+	13.1418i	−0.383331	+	0.605544i
$472$	−0.245159	+	0.141543i	−0.0112844	+	0.00651503i
$473$	1.12299	+	9.55795i	0.0516350	+	0.439475i
$474$	2.64950	+	6.66986i	0.121696	+	0.306357i
$475$	14.8519	+	20.4418i	0.681451	+	0.937936i
$476$	0.638332	+	4.90851i	0.0292579	+	0.224981i
$477$	−3.09934	+	37.9368i	−0.141909	+	1.73701i
$478$	−5.90081	+	2.62721i	−0.269897	+	0.120166i
$479$	2.82997	−	26.9253i	0.129305	−	1.23025i	−0.716817	−	0.697261i	$-0.754402\pi$
$479$	2.82997	−	26.9253i	0.129305	−	1.23025i	0.846122	−	0.532989i	$-0.178931\pi$
$480$	−3.31785	+	6.70277i	−0.151438	+	0.305938i
$481$	3.69617	−	17.3891i	0.168531	−	0.792876i
$482$	−9.06593	−	12.4782i	−0.412942	−	0.568366i
$483$	−28.8708	−	9.89917i	−1.31367	−	0.450428i
$484$	−9.93651	+	4.71867i	−0.451659	+	0.214485i
$485$	−15.3779	−	8.87842i	−0.698273	−	0.403148i
$486$	12.6629	+	9.09128i	0.574400	+	0.412389i
$487$	24.2545	−	26.9374i	1.09908	−	1.22065i	0.125547	−	0.992088i	$-0.459931\pi$
$487$	24.2545	−	26.9374i	1.09908	−	1.22065i	0.973530	−	0.228561i	$-0.0734019\pi$
$488$	−7.13581	+	6.42511i	−0.323023	+	0.290851i
$489$	7.78186	+	27.7504i	0.351908	+	1.25492i
$490$	−25.4015	+	16.3821i	−1.14752	+	0.740067i
$491$	−6.19751	+	19.0740i	−0.279690	+	0.860797i	0.708250	+	0.705961i	$0.249485\pi$
$491$	−6.19751	+	19.0740i	−0.279690	+	0.860797i	−0.987940	+	0.154836i	$0.950515\pi$
$492$	−10.4034	−	12.5466i	−0.469019	−	0.565645i
$493$	−8.85083	−	3.94064i	−0.398621	−	0.177478i
$494$	−3.54139	−	6.13386i	−0.159334	−	0.275975i
$495$	−32.9267	−	27.5988i	−1.47994	−	1.24048i
$496$	1.27699			0.0573385
$497$	−2.24438	+	3.25457i	−0.100674	+	0.145988i
$498$	−3.16367	+	8.53637i	−0.141768	+	0.382524i
$499$	29.2875	+	32.5271i	1.31109	+	1.45611i	0.804537	+	0.593902i	$0.202413\pi$
$499$	29.2875	+	32.5271i	1.31109	+	1.45611i	0.506551	+	0.862210i	$0.330920\pi$
$500$	37.1248	+	3.90198i	1.66027	+	0.174502i
$501$	5.89127	−	6.02958i	0.263203	−	0.269382i
$502$	9.72020	−	8.75211i	0.433834	−	0.390626i
$503$	6.83567	+	21.0380i	0.304788	+	0.938040i	0.979756	+	0.200193i	$0.0641571\pi$
$503$	6.83567	+	21.0380i	0.304788	+	0.938040i	−0.674969	+	0.737846i	$0.735843\pi$
$504$	−4.96692	−	6.19110i	−0.221244	−	0.275773i
$505$		−	86.2273i		−	3.83707i
$506$	−6.56839	+	21.0901i	−0.292001	+	0.937569i
$507$	−0.409172	+	2.79274i	−0.0181720	+	0.124030i
$508$	−3.05331	+	6.85785i	−0.135469	+	0.304268i
$509$	1.91402	−	9.00475i	0.0848374	−	0.399129i	−0.915155	−	0.403103i	$-0.867932\pi$
$509$	1.91402	−	9.00475i	0.0848374	−	0.399129i	0.999992	+	0.00397414i	$0.00126501\pi$
$510$	7.75630	+	11.6456i	0.343455	+	0.515676i
$511$	3.71679	+	15.5900i	0.164421	+	0.689661i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−2.81229	−	9.20192i	−0.124166	−	0.406275i
$514$	−12.1156	−	10.9090i	−0.534397	−	0.481174i
$515$	17.5640	−	39.4493i	0.773961	−	1.73835i
$516$	1.85540	+	4.67079i	0.0816796	+	0.205620i
$517$	−1.89707	+	20.4540i	−0.0834328	+	0.899566i
$518$	−8.00115	+	9.33824i	−0.351550	+	0.410299i
$519$	−25.0856	−	1.02301i	−1.10114	−	0.0449051i
$520$	−16.1548	−	3.43382i	−0.708436	−	0.150583i
$521$	2.87855	+	13.5425i	0.126112	+	0.593308i	0.995134	+	0.0985349i	$0.0314156\pi$
$521$	2.87855	+	13.5425i	0.126112	+	0.593308i	−0.869022	+	0.494773i	$0.835251\pi$
$522$	15.4088	−	1.98197i	0.674427	−	0.0867486i
$523$	−8.12513	−	18.2494i	−0.355287	−	0.797988i	−0.999452	−	0.0331016i	$-0.989462\pi$
$523$	−8.12513	−	18.2494i	−0.355287	−	0.797988i	0.644165	−	0.764887i	$-0.277205\pi$
$524$	1.35864	−	4.18147i	0.0593526	−	0.182669i
$525$	−32.1356	+	53.6400i	−1.40251	+	2.34104i
$526$	16.4237	−	11.9325i	0.716107	−	0.520282i
$527$	1.19453	−	2.06900i	0.0520348	−	0.0901268i
$528$	−4.37692	+	3.72056i	−0.190481	+	0.161916i
$529$	10.6789	+	18.4964i	0.464301	+	0.804192i
$530$	−5.72665	−	54.4855i	−0.248750	−	2.36670i
$531$	−0.441578	−	0.725427i	−0.0191628	−	0.0314809i
$532$	0.120514	+	4.89784i	0.00522494	+	0.212348i
$533$	21.1557	−	29.1183i	0.916354	−	1.26125i
$534$	0.161875	−	0.633433i	0.00700503	−	0.0274113i
$535$	7.65226	+	36.0010i	0.330836	+	1.55646i
$536$	−5.11458	+	5.68031i	−0.220916	+	0.245352i
$537$	−3.34487	−	2.11742i	−0.144342	−	0.0913736i
$538$		−	10.7044i		−	0.461500i
$539$	−22.8966	+	3.83984i	−0.986228	+	0.165394i
$540$	−20.3338	−	9.48433i	−0.875028	−	0.408140i
$541$	−21.3541	+	2.24440i	−0.918082	+	0.0964944i	−0.551769	−	0.833997i	$-0.686047\pi$
$541$	−21.3541	+	2.24440i	−0.918082	+	0.0964944i	−0.366314	+	0.930491i	$0.619380\pi$
$542$	−3.10292	−	2.79389i	−0.133282	−	0.120008i
$543$	2.18731	+	1.08271i	0.0938663	+	0.0464635i
$544$	1.70912	−	0.760948i	0.0732778	−	0.0326254i
$545$	2.10268	+	1.52768i	0.0900687	+	0.0654388i
$546$	10.5303	−	14.0119i	0.450656	−	0.599655i
$547$	−29.3339	+	9.53116i	−1.25423	+	0.407523i	−0.859434	−	0.511247i	$-0.829184\pi$
$547$	−29.3339	+	9.53116i	−1.25423	+	0.407523i	−0.394793	+	0.918770i	$0.629184\pi$
$548$	−13.2270	+	1.39021i	−0.565028	+	0.0593868i
$549$	−19.7668	−	20.9545i	−0.843628	−	0.894314i
$550$	39.4664	+	22.1465i	1.68285	+	0.944331i
$551$	−8.30481	−	4.79478i	−0.353797	−	0.204265i
$552$	−0.470045	+	11.5262i	−0.0200065	+	0.490586i
$553$	10.8712	−	1.41376i	0.462292	−	0.0601193i
$554$	−11.5790	−	3.76226i	−0.491946	−	0.159843i
$555$	−8.60681	+	33.6792i	−0.365339	+	1.42960i
$556$	−8.92437	−	0.937989i	−0.378478	−	0.0397796i
$557$	−15.3305	+	3.25860i	−0.649575	+	0.138071i	−0.520903	−	0.853616i	$-0.674405\pi$
$557$	−15.3305	+	3.25860i	−0.649575	+	0.138071i	−0.128672	+	0.991687i	$0.541071\pi$
$558$	0.0888839	+	3.82993i	0.00376275	+	0.162134i
$559$	−8.97882	+	6.52350i	−0.379764	+	0.275915i
$560$	8.67540	+	7.43322i	0.366603	+	0.314111i
$561$	1.93379	+	10.5719i	0.0816445	+	0.446345i
$562$	1.60429	−	2.77871i	0.0676728	−	0.117213i
$563$	−5.03519	−	2.24181i	−0.212208	−	0.0944811i	0.297880	−	0.954603i	$-0.403721\pi$
$563$	−5.03519	−	2.24181i	−0.212208	−	0.0944811i	−0.510088	+	0.860122i	$0.670387\pi$
$564$	1.80098	+	10.5753i	0.0758348	+	0.445302i
$565$	−8.48687	−	9.42562i	−0.357045	−	0.396539i
$566$	11.8120	−	16.2578i	0.496495	−	0.683367i
$567$	18.2226	−	15.3277i	0.765276	−	0.643702i
$568$	1.42112	+	0.461749i	0.0596288	+	0.0193746i
$569$	−16.1198	−	3.42637i	−0.675778	−	0.143641i	−0.142776	−	0.989755i	$-0.545603\pi$
$569$	−16.1198	−	3.42637i	−0.675778	−	0.143641i	−0.533002	+	0.846114i	$0.678936\pi$
$570$	6.43021	+	12.2661i	0.269332	+	0.513770i
$571$	12.5956	−	7.27209i	0.527111	−	0.304328i	−0.212728	−	0.977111i	$-0.568235\pi$
$571$	12.5956	−	7.27209i	0.527111	−	0.304328i	0.739839	+	0.672784i	$0.234902\pi$
$572$	−10.3534	−	7.33030i	−0.432896	−	0.306495i
$573$	−4.65037	+	5.88094i	−0.194272	+	0.245680i
$574$	−22.4882	+	10.6828i	−0.938641	+	0.445891i
$575$	86.4305	−	28.0830i	3.60440	−	1.17114i
$576$	−1.70657	+	2.46731i	−0.0711071	+	0.102805i
$577$	2.30481	−	21.9288i	0.0959507	−	0.912910i	−0.835610	−	0.549323i	$-0.814886\pi$
$577$	2.30481	−	21.9288i	0.0959507	−	0.912910i	0.931561	−	0.363586i	$-0.118448\pi$
$578$	−1.41112	+	13.4259i	−0.0586949	+	0.558445i
$579$	−30.6147	+	1.96084i	−1.27230	+	0.0814898i
$580$	−21.2667	+	6.90997i	−0.883052	+	0.286921i
$581$	11.4480	+	7.89466i	0.474944	+	0.327526i
$582$	−5.58700	−	4.41794i	−0.231589	−	0.183129i
$583$	12.5129	−	40.1770i	0.518232	−	1.66396i
$584$	5.24604	−	3.02880i	0.217083	−	0.125333i
$585$	9.17423	−	48.6905i	0.379308	−	2.01310i
$586$	6.00572	+	1.27656i	0.248094	+	0.0527340i
$587$	24.3744	+	7.91972i	1.00604	+	0.326882i	0.765276	−	0.643702i	$-0.222603\pi$
$587$	24.3744	+	7.91972i	1.00604	+	0.326882i	0.240762	+	0.970584i	$0.422603\pi$
$588$	−11.0341	+	5.02476i	−0.455039	+	0.207218i
$589$	1.38993	−	1.91307i	0.0572710	−	0.0788268i
$590$	0.817919	+	0.908391i	0.0336732	+	0.0373979i
$591$	35.6066	−	6.06379i	1.46466	−	0.249431i
$592$	4.24607	+	1.89047i	0.174512	+	0.0776980i
$593$	5.51747	−	9.55654i	0.226575	−	0.392440i	−0.730215	−	0.683217i	$-0.760580\pi$
$593$	5.51747	−	9.55654i	0.226575	−	0.392440i	0.956791	+	0.290777i	$0.0939137\pi$
$594$	−11.4633	−	12.8683i	−0.470345	−	0.527992i
$595$	20.1587	−	7.10275i	0.826425	−	0.291184i
$596$	−3.57181	+	2.59507i	−0.146307	+	0.106298i
$597$	18.3978	+	22.1880i	0.752972	+	0.908096i
$598$	−24.9176	+	5.29639i	−1.01896	+	0.216586i
$599$	−24.6888	−	2.59489i	−1.00876	−	0.106025i	−0.414290	−	0.910145i	$-0.635970\pi$
$599$	−24.6888	−	2.59489i	−1.00876	−	0.106025i	−0.594466	+	0.804121i	$0.702637\pi$
$600$	22.8981	+	5.85166i	0.934810	+	0.238893i
$601$	36.2245	+	11.7701i	1.47763	+	0.480111i	0.933404	−	0.358828i	$-0.116823\pi$
$601$	36.2245	+	11.7701i	1.47763	+	0.480111i	0.544226	+	0.838939i	$0.316823\pi$
$602$	7.61295	−	0.990034i	0.310281	−	0.0403508i
$603$	−17.3924	−	14.9442i	−0.708271	−	0.608576i
$604$	−4.83469	−	2.79131i	−0.196721	−	0.113577i
$605$	28.8505	+	37.7319i	1.17294	+	1.53402i
$606$	5.01404	−	34.2225i	0.203681	−	1.39019i
$607$	−43.5289	+	4.57507i	−1.76678	+	0.185696i	−0.931406	−	0.363981i	$-0.881417\pi$
$607$	−43.5289	+	4.57507i	−1.76678	+	0.185696i	−0.835377	+	0.549677i	$0.814751\pi$
$608$	1.76114	−	0.572228i	0.0714236	−	0.0232069i
$609$	2.86160	−	23.5581i	0.115958	−	0.954624i
$610$	33.5436	+	24.3708i	1.35814	+	0.986746i
$611$	−21.6415	+	9.63543i	−0.875523	+	0.389808i
$612$	2.40119	+	5.07301i	0.0970625	+	0.205064i
$613$	−22.1356	−	19.9310i	−0.894047	−	0.805004i	0.0875119	−	0.996163i	$-0.472108\pi$
$613$	−22.1356	−	19.9310i	−0.894047	−	0.805004i	−0.981559	+	0.191160i	$0.938775\pi$
$614$	20.1250	−	2.11522i	0.812178	−	0.0853633i
$615$	−43.6525	+	55.2038i	−1.76024	+	2.22603i
$616$	3.86191	+	7.87945i	0.155601	+	0.317472i
$617$		−	39.8641i		−	1.60487i	−0.596742	−	0.802433i	$-0.703538\pi$
$617$		−	39.8641i		−	1.60487i	0.596742	−	0.802433i	$-0.296462\pi$
$618$	9.26485	−	14.6356i	0.372687	−	0.588730i
$619$	−18.3614	+	20.3924i	−0.738006	+	0.819639i	−0.988932	−	0.148367i	$-0.952598\pi$
$619$	−18.3614	+	20.3924i	−0.738006	+	0.819639i	0.250926	+	0.968006i	$0.419265\pi$
$620$	−1.14643	−	5.39353i	−0.0460418	−	0.216609i
$621$	−34.6019	−	0.607486i	−1.38853	−	0.0243776i
$622$	−6.65250	+	9.15638i	−0.266741	+	0.367137i
$623$	−0.876903	−	0.477914i	−0.0351324	−	0.0191472i
$624$	−6.21197	−	2.30223i	−0.248678	−	0.0921628i
$625$	−9.71722	−	92.4532i	−0.388689	−	3.69813i
$626$	3.83765	+	6.64701i	0.153383	+	0.265668i
$627$	0.809781	+	10.6067i	0.0323395	+	0.423592i
$628$	4.48997	−	7.77685i	0.179169	−	0.310330i
$629$	7.03488	−	5.11114i	0.280499	−	0.203795i
$630$	−21.6898	+	26.5366i	−0.864143	+	1.05724i
$631$	−5.16165	+	15.8859i	−0.205482	+	0.632409i	0.794211	+	0.607642i	$0.207884\pi$
$631$	−5.16165	+	15.8859i	−0.205482	+	0.632409i	−0.999693	+	0.0247669i	$0.992116\pi$
$632$	−1.68533	−	3.78532i	−0.0670389	−	0.150572i
$633$	−14.9795	−	14.6359i	−0.595381	−	0.581723i
$634$	−6.07791	−	28.5943i	−0.241385	−	1.13563i
$635$	31.7062	+	6.73936i	1.25822	+	0.267443i
$636$	0.895445	−	21.9576i	0.0355067	−	0.870674i
$637$	−16.7837	−	20.8605i	−0.664993	−	0.826522i
$638$	−17.1021	−	1.58618i	−0.677077	−	0.0627975i
$639$	−1.28596	+	4.29435i	−0.0508717	+	0.169882i
$640$	1.75629	−	3.94468i	0.0694233	−	0.155927i
$641$	19.4621	+	17.5237i	0.768706	+	0.692146i	0.957039	−	0.289959i	$-0.0936417\pi$
$641$	19.4621	+	17.5237i	0.768706	+	0.692146i	−0.188333	+	0.982105i	$0.560308\pi$
$642$	0.943654	+	14.7333i	0.0372431	+	0.581477i
$643$	−32.7834	−	23.8185i	−1.29285	−	0.939310i	−0.292991	−	0.956115i	$-0.594650\pi$
$643$	−32.7834	−	23.8185i	−1.29285	−	0.939310i	−0.999859	+	0.0168053i	$0.994650\pi$
$644$	16.8876	+	5.03135i	0.665464	+	0.198263i
$645$	18.0620	−	12.0298i	0.711190	−	0.473673i
$646$	0.720291	−	3.38870i	0.0283395	−	0.133327i
$647$	9.93730	−	22.3195i	0.390676	−	0.877472i	−0.605959	−	0.795496i	$-0.707210\pi$
$647$	9.93730	−	22.3195i	0.390676	−	0.877472i	0.996634	−	0.0819756i	$-0.0261230\pi$
$648$	−7.51872	−	4.94660i	−0.295363	−	0.194321i
$649$	0.301037	+	0.889319i	0.0118167	+	0.0349088i
$650$			52.1905i			2.04708i
$651$	5.70361	+	1.30900i	0.223542	+	0.0513038i
$652$	−5.14196	−	15.8253i	−0.201375	−	0.619767i
$653$	7.12248	−	6.41311i	0.278724	−	0.250965i	−0.517897	−	0.855443i	$-0.673285\pi$
$653$	7.12248	−	6.41311i	0.278724	−	0.250965i	0.796622	+	0.604478i	$0.206618\pi$
$654$	0.745691	+	0.728586i	0.0291588	+	0.0284900i
$655$	−18.8808	−	1.98445i	−0.737732	−	0.0775388i
$656$	6.29655	+	6.99303i	0.245839	+	0.273032i
$657$	9.44911	+	15.5231i	0.368645	+	0.605613i
$658$	16.3341	+	1.31148i	0.636770	+	0.0511269i
$659$	20.2379			0.788355			0.394177	−	0.919034i	$-0.371030\pi$
$659$	20.2379			0.788355			0.394177	+	0.919034i	$0.371030\pi$
$660$	19.6437	+	15.1464i	0.764630	+	0.589571i
$661$	18.5004	+	32.0436i	0.719582	+	1.24635i	0.961165	+	0.275973i	$0.0890000\pi$
$661$	18.5004	+	32.0436i	0.719582	+	1.24635i	−0.241583	+	0.970380i	$0.577667\pi$
$662$	14.7339	+	6.55996i	0.572650	+	0.254960i
$663$	−9.54097	+	7.91115i	−0.370541	+	0.307244i
$664$	1.62421	−	4.99881i	0.0630316	−	0.193991i
$665$	20.5785	−	4.90610i	0.798000	−	0.190250i
$666$	−5.37435	+	12.8664i	−0.208252	+	0.498562i
$667$	−25.6313	+	23.0785i	−0.992448	+	0.893604i
$668$	−3.25665	+	3.61688i	−0.126004	+	0.139941i
$669$	12.0532	+	22.9923i	0.466003	+	0.888935i
$670$	28.5832	+	16.5025i	1.10427	+	0.637549i
$671$	16.2597	+	27.3833i	0.627699	+	1.05712i
$672$	3.01092	+	3.45462i	0.116149	+	0.133265i
$673$	18.7665	+	25.8299i	0.723396	+	0.995669i	0.999404	+	0.0345139i	$0.0109883\pi$
$673$	18.7665	+	25.8299i	0.723396	+	0.995669i	−0.276008	+	0.961155i	$0.589012\pi$
$674$	−3.90851	+	18.3881i	−0.150550	+	0.708282i
$675$	−15.9564	+	69.0830i	−0.614164	+	2.65901i
$676$	0.170340	−	1.62067i	0.00655153	−	0.0623336i
$677$	−24.1465	+	10.7507i	−0.928027	+	0.413184i	−0.814377	−	0.580337i	$-0.802921\pi$
$677$	−24.1465	+	10.7507i	−0.928027	+	0.413184i	−0.113650	+	0.993521i	$0.536254\pi$
$678$	−2.82023	−	4.23441i	−0.108310	−	0.162621i
$679$	−8.64221	+	6.60974i	−0.331658	+	0.253659i
$680$	−4.74835	−	6.53554i	−0.182091	−	0.250627i
$681$	−11.8024	+	4.68832i	−0.452268	+	0.179657i
$682$	0.829810	−	4.15320i	0.0317751	−	0.159034i
$683$	17.5805	−	10.1501i	0.672698	−	0.388383i	−0.124400	−	0.992232i	$-0.539701\pi$
$683$	17.5805	−	10.1501i	0.672698	−	0.388383i	0.797098	+	0.603850i	$0.206367\pi$
$684$	1.83881	+	5.24216i	0.0703085	+	0.200439i
$685$	17.7464	+	54.6178i	0.678055	+	2.08684i
$686$	3.28873	+	18.2259i	0.125564	+	0.695869i
$687$	7.29293	+	26.0069i	0.278243	+	0.992224i
$688$	−1.18021	−	2.65079i	−0.0449950	−	0.101061i
$689$	47.4684	−	10.0897i	1.80840	−	0.384388i
$690$	49.1043	−	8.36245i	1.86937	−	0.318353i
$691$	−2.04034	−	19.4126i	−0.0776183	−	0.738489i	−0.962244	−	0.272188i	$-0.912253\pi$
$691$	−2.04034	−	19.4126i	−0.0776183	−	0.738489i	0.884626	−	0.466301i	$-0.154414\pi$
$692$	14.4952			0.551026
$693$	−23.3632	+	12.1311i	−0.887493	+	0.460820i
$694$	8.05767			0.305865
$695$	4.05023	+	38.5354i	0.153634	+	1.46173i
$696$	−8.84228	+	1.50584i	−0.335166	+	0.0570786i
$697$	17.2202	−	3.66027i	0.652262	−	0.138642i
$698$	−12.4185	−	27.8925i	−0.470049	−	1.05575i
$699$	6.09692	+	21.7418i	0.230607	+	0.822352i
$700$	17.2762	−	31.6993i	0.652979	−	1.19812i
$701$	13.7758	+	42.3975i	0.520305	+	1.60133i	0.773418	+	0.633896i	$0.218545\pi$
$701$	13.7758	+	42.3975i	0.520305	+	1.60133i	−0.253114	+	0.967437i	$0.581455\pi$
$702$	6.47244	−	18.7911i	0.244286	−	0.709226i
$703$	7.45375	−	4.30342i	0.281123	−	0.162307i
$704$	2.43739	−	2.24925i	0.0918627	−	0.0847717i
$705$	43.0495	−	17.1008i	1.62134	−	0.644053i
$706$	8.07920	+	11.1201i	0.304065	+	0.418509i
$707$	−48.7801	−	20.2957i	−1.83456	−	0.763298i
$708$	0.271799	+	0.408090i	0.0102148	+	0.0153369i
$709$	26.8623	−	11.9599i	1.00884	−	0.449162i	0.165304	−	0.986243i	$-0.447139\pi$
$709$	26.8623	−	11.9599i	1.00884	−	0.449162i	0.843531	+	0.537080i	$0.180473\pi$
$710$	0.674435	−	6.41682i	0.0253111	−	0.240819i
$711$	11.2356	−	5.31811i	0.421367	−	0.199445i
$712$	−0.0784795	+	0.369217i	−0.00294114	+	0.0138370i
$713$	−4.99909	−	6.88065i	−0.187217	−	0.257683i
$714$	8.41373	−	1.64678i	0.314876	−	0.0616292i
$715$	−21.6656	+	50.3097i	−0.810249	+	1.88148i
$716$	1.97937	+	1.14279i	0.0739726	+	0.0427081i
$717$	5.19443	+	9.90875i	0.193990	+	0.370049i
$718$	−1.72698	+	1.91800i	−0.0644502	+	0.0715792i
$719$	−21.2977	+	19.1765i	−0.794269	+	0.715163i	−0.962706	−	0.270550i	$-0.912795\pi$
$719$	−21.2977	+	19.1765i	−0.794269	+	0.715163i	0.168437	+	0.985712i	$0.446128\pi$
$720$	11.9531	+	4.99287i	0.445466	+	0.186073i
$721$	−18.1830	−	19.2216i	−0.677169	−	0.715849i
$722$	−4.81169	+	14.8089i	−0.179072	+	0.551128i
$723$	−20.5650	+	17.0520i	−0.764819	+	0.634170i
$724$	−1.28726	−	0.573127i	−0.0478408	−	0.0213001i
$725$	35.3311	+	61.1953i	1.31217	+	2.27274i
$726$	9.25632	+	16.6529i	0.343534	+	0.618049i
$727$	−14.7463			−0.546910			−0.273455	−	0.961885i	$-0.588166\pi$
$727$	−14.7463			−0.546910			−0.273455	+	0.961885i	$0.588166\pi$
$728$	−5.74499	+	8.33080i	−0.212924	+	0.308760i
$729$	14.3125	−	22.8944i	0.530091	−	0.847941i
$730$	−17.5023	−	19.4382i	−0.647788	−	0.719441i
$731$	−5.39886	−	0.567443i	−0.199684	−	0.0209876i
$732$	11.8959	+	11.6230i	0.439684	+	0.429598i
$733$	15.9877	−	14.3954i	0.590519	−	0.531706i	−0.318791	−	0.947825i	$-0.603277\pi$
$733$	15.9877	−	14.3954i	0.590519	−	0.531706i	0.909310	+	0.416119i	$0.136610\pi$
$734$	−0.0458971	−	0.141257i	−0.00169409	−	0.00521388i
$735$	31.1287	+	42.0931i	1.14820	+	1.55263i
$736$		−	6.66017i		−	0.245497i
$737$	15.1508	+	20.3255i	0.558087	+	0.748701i
$738$	−20.5352	+	19.3713i	−0.755910	+	0.713068i
$739$	−20.7536	+	46.6133i	−0.763433	+	1.71470i	−0.0662536	+	0.997803i	$0.521105\pi$
$739$	−20.7536	+	46.6133i	−0.763433	+	1.71470i	−0.697180	+	0.716896i	$0.745562\pi$
$740$	4.17271	−	19.6311i	0.153392	−	0.721652i
$741$	−10.2104	+	6.80039i	−0.375087	+	0.249819i
$742$	−32.1711	−	9.58482i	−1.18104	−	0.351870i
$743$	−38.3659	−	27.8744i	−1.40751	−	1.02261i	−0.993679	−	0.112258i	$-0.964192\pi$
$743$	−38.3659	−	27.8744i	−1.40751	−	1.02261i	−0.413827	−	0.910355i	$-0.635808\pi$
$744$	−0.141374	−	2.20729i	−0.00518304	−	0.0809230i
$745$	14.1673	+	12.7563i	0.519049	+	0.467354i
$746$	−1.42765	+	3.20655i	−0.0522700	+	0.117400i
$747$	15.1054	+	4.52338i	0.552679	+	0.165502i
$748$	−1.36425	−	6.05312i	−0.0498819	−	0.221324i
$749$	22.1675	+	4.14472i	0.809982	+	0.151445i
$750$	2.63454	−	64.6026i	0.0961998	−	2.35895i
$751$	−37.0996	−	7.88576i	−1.35378	−	0.287755i	−0.526803	−	0.849987i	$-0.676610\pi$
$751$	−37.0996	−	7.88576i	−1.35378	−	0.287755i	−0.826980	+	0.562232i	$0.809943\pi$
$752$	−1.28772	−	6.05823i	−0.0469582	−	0.220921i
$753$	−16.2042	−	15.8325i	−0.590515	−	0.576969i
$754$	−8.05641	−	18.0950i	−0.293397	−	0.658981i
$755$	−7.44907	+	22.9259i	−0.271099	+	0.834358i
$756$	−10.1515	+	9.27078i	−0.369206	+	0.337175i
$757$	−39.1289	+	28.4288i	−1.42216	+	1.03326i	−0.430754	+	0.902469i	$0.641752\pi$
$757$	−39.1289	+	28.4288i	−1.42216	+	1.03326i	−0.991410	+	0.130793i	$0.958248\pi$
$758$	−6.41483	+	11.1108i	−0.232997	+	0.403563i
$759$	37.1816	+	9.01866i	1.34961	+	0.327356i
$760$	−3.99796	−	6.92468i	−0.145021	−	0.251184i
$761$	−1.35625	−	12.9038i	−0.0491640	−	0.467764i	−0.991212	−	0.132285i	$-0.957769\pi$
$761$	−1.35625	−	12.9038i	−0.0491640	−	0.467764i	0.942048	−	0.335479i	$-0.108898\pi$
$762$	12.1919	+	4.51845i	0.441666	+	0.163686i
$763$	1.35915	−	0.829938i	0.0492045	−	0.0300458i
$764$	2.54431	−	3.50194i	0.0920499	−	0.126696i
$765$	19.2708	−	14.6961i	0.696739	−	0.531339i
$766$	−3.05068	−	14.3523i	−0.110225	−	0.518570i
$767$	−0.724510	+	0.804650i	−0.0261605	+	0.0290542i
$768$	0.926426	−	1.46347i	0.0334295	−	0.0528083i
$769$			23.5374i			0.848781i	0.905479	+	0.424390i	$0.139512\pi$
$769$			23.5374i			0.848781i	−0.905479	+	0.424390i	$0.860488\pi$
$770$	29.8128	−	23.3852i	1.07438	−	0.842742i
$771$	−17.5149	+	22.1497i	−0.630785	+	0.797702i
$772$	17.6146	−	1.85137i	0.633963	−	0.0666322i
$773$	−36.5925	−	32.9480i	−1.31614	−	1.18506i	−0.968948	−	0.247264i	$-0.920468\pi$
$773$	−36.5925	−	32.9480i	−1.31614	−	1.18506i	−0.347192	−	0.937794i	$-0.612865\pi$
$774$	7.86809	−	3.72418i	0.282813	−	0.133863i
$775$	−15.9182	+	7.08722i	−0.571797	+	0.254580i
$776$	3.32691	+	2.41714i	0.119429	+	0.0867704i
$777$	17.0270	+	12.7962i	0.610841	+	0.459062i
$778$	8.91298	−	2.89600i	0.319546	−	0.103827i
$779$	17.3298	−	1.82143i	0.620904	−	0.0652596i
$780$	−4.14689	+	28.3039i	−0.148483	+	1.01344i
$781$	2.42523	−	4.32191i	0.0867817	−	0.154650i
$782$	−10.7909	−	6.23013i	−0.385882	−	0.222789i
$783$	−5.13176	−	26.4149i	−0.183394	−	0.943991i
$784$	6.24705	−	3.15822i	0.223109	−	0.112793i
$785$	−36.8775	−	11.9822i	−1.31621	−	0.427664i
$786$	−7.37813	−	1.88550i	−0.263169	−	0.0672535i
$787$	−28.3147	−	2.97600i	−1.00931	−	0.106083i	−0.414584	−	0.910011i	$-0.636073\pi$
$787$	−28.3147	−	2.97600i	−1.00931	−	0.106083i	−0.594726	+	0.803928i	$0.702740\pi$
$788$	−20.3978	+	4.33568i	−0.726640	+	0.154452i
$789$	−22.4437	−	27.0675i	−0.799017	−	0.963627i
$790$	−14.4748	+	10.5165i	−0.514989	+	0.374162i
$791$	−7.32980	+	2.58260i	−0.260618	+	0.0918266i
$792$	6.91558	+	7.15365i	0.245734	+	0.254194i
$793$	−18.3635	+	31.8066i	−0.652108	+	1.12948i
$794$	−1.41737	−	0.631055i	−0.0503007	−	0.0223953i
$795$	−93.5446	+	15.9306i	−3.31769	+	0.565001i
$796$	−11.1351	−	12.3668i	−0.394674	−	0.438330i
$797$	28.4681	−	39.1830i	1.00839	−	1.38793i	0.0883592	−	0.996089i	$-0.471838\pi$
$797$	28.4681	−	39.1830i	1.00839	−	1.38793i	0.920032	−	0.391843i	$-0.128162\pi$
$798$	8.45262	−	0.750545i	0.299219	−	0.0265690i
$799$	−11.0202	−	3.58068i	−0.389867	−	0.126675i
$800$	−13.3469	−	2.83697i	−0.471884	−	0.100302i
$801$	−1.11282	−	0.209676i	−0.0393194	−	0.00740854i
$802$	7.38526	−	4.26388i	0.260783	−	0.150563i
$803$	−6.44174	−	19.0301i	−0.227324	−	0.671558i
$804$	10.3847	+	8.21173i	0.366240	+	0.289605i
$805$	6.08959	−	75.8439i	0.214630	−	2.67315i
$806$	4.64525	−	1.50933i	0.163622	−	0.0531640i
$807$	−18.5027	+	1.18508i	−0.651324	+	0.0417167i
$808$	−2.08736	+	19.8599i	−0.0734331	+	0.698669i
$809$	1.33421	−	12.6942i	0.0469083	−	0.446303i	−0.945709	−	0.325014i	$-0.894631\pi$
$809$	1.33421	−	12.6942i	0.0469083	−	0.446303i	0.992617	−	0.121288i	$-0.0387025\pi$
$810$	−14.1426	+	36.1972i	−0.496920	+	1.27184i
$811$	45.8517	−	14.8981i	1.61007	−	0.523143i	0.640500	−	0.767958i	$-0.278727\pi$
$811$	45.8517	−	14.8981i	1.61007	−	0.523143i	0.969570	+	0.244815i	$0.0787271\pi$
$812$	−1.09656	+	13.6573i	−0.0384817	+	0.479278i
$813$	−4.48573	+	5.67274i	−0.157322	+	0.198952i
$814$	8.90764	−	12.5812i	0.312213	−	0.440972i
$815$	−62.2241	+	35.9251i	−2.17962	+	1.25840i
$816$	−1.50452	−	2.86998i	−0.0526688	−	0.100469i
$817$	−5.25578	−	1.11715i	−0.183876	−	0.0390841i
$818$	−1.24187	−	0.403507i	−0.0434209	−	0.0141083i
$819$	−25.3856	−	16.6505i	−0.887043	−	0.581815i
$820$	23.8832	−	32.8724i	0.834037	−	1.14795i
$821$	−7.62406	−	8.46737i	−0.266081	−	0.295513i	0.595267	−	0.803528i	$-0.297046\pi$
$821$	−7.62406	−	8.46737i	−0.266081	−	0.295513i	−0.861348	+	0.508015i	$0.830380\pi$
$822$	3.86734	+	22.7090i	0.134889	+	0.792068i
$823$	51.3158	+	22.8473i	1.78876	+	0.796406i	0.977258	+	0.212052i	$0.0680145\pi$
$823$	51.3158	+	22.8473i	1.78876	+	0.796406i	0.811499	+	0.584354i	$0.198652\pi$
$824$	−5.00032	+	8.66081i	−0.174194	+	0.301713i
$825$	33.9112	−	70.6699i	1.18064	−	2.46041i
$826$	0.706407	−	0.248897i	0.0245791	−	0.00866024i
$827$	32.4296	−	23.5615i	1.12769	−	0.819313i	0.142331	−	0.989819i	$-0.454540\pi$
$827$	32.4296	−	23.5615i	1.12769	−	0.819313i	0.985357	+	0.170506i	$0.0545402\pi$
$828$	19.9751	−	0.463576i	0.694184	−	0.0161104i
$829$	45.9785	−	9.77303i	1.59690	−	0.339432i	0.678351	−	0.734738i	$-0.262695\pi$
$829$	45.9785	−	9.77303i	1.59690	−	0.339432i	0.918549	+	0.395307i	$0.129362\pi$
$830$	−22.5713	−	2.37234i	−0.783461	−	0.0823450i
$831$	−5.22119	+	20.4310i	−0.181121	+	0.708743i
$832$	3.63766	+	1.18195i	0.126113	+	0.0409767i
$833$	0.726701	−	13.0759i	0.0251787	−	0.453052i
$834$	−0.633312	+	15.5297i	−0.0219298	+	0.537750i
$835$	18.2001	+	10.5078i	0.629840	+	0.363638i
$836$	−0.716664	−	6.09967i	−0.0247864	−	0.210961i
$837$	6.61023	−	0.577646i	0.228483	−	0.0199664i
$838$	13.8137	−	1.45188i	0.477186	−	0.0501543i
$839$	13.3373	−	4.33355i	0.460455	−	0.149611i	−0.0695986	−	0.997575i	$-0.522172\pi$
$839$	13.3373	−	4.33355i	0.460455	−	0.149611i	0.530053	+	0.847964i	$0.322172\pi$
$840$	11.8879	−	15.8184i	0.410173	−	0.545788i
$841$	1.76540	+	1.28264i	0.0608759	+	0.0442290i
$842$	−7.83025	+	3.48625i	−0.269848	+	0.120144i
$843$	−4.98063	−	2.46540i	−0.171542	−	0.0849128i
$844$	8.98553	+	8.09061i	0.309295	+	0.278490i
$845$	−6.99806	+	0.735526i	−0.240741	+	0.0253029i
$846$	18.0802	−	4.28379i	0.621609	−	0.147280i
$847$	28.1362	−	7.44005i	0.966771	−	0.255643i
$848$			12.6877i			0.435699i
$849$	−29.4095	−	18.6173i	−1.00933	−	0.638942i
$850$	−17.0816	+	18.9710i	−0.585894	+	0.650701i
$851$	−6.43608	−	30.2794i	−0.220626	−	1.03796i
$852$	0.640807	−	2.50753i	0.0219537	−	0.0859067i
$853$	−11.7929	+	16.2316i	−0.403783	+	0.555759i	−0.961688	−	0.274145i	$-0.911605\pi$
$853$	−11.7929	+	16.2316i	−0.403783	+	0.555759i	0.557906	+	0.829904i	$0.311605\pi$
$854$	21.6822	−	13.2398i	0.741951	−	0.453058i
$855$	20.4902	−	12.4726i	0.700749	−	0.426556i
$856$	−0.890971	−	8.47702i	−0.0304527	−	0.289739i
$857$	−14.7710	−	25.5842i	−0.504568	−	0.873938i	−0.999986	−	0.00528309i	$-0.998318\pi$
$857$	−14.7710	−	25.5842i	−0.504568	−	0.873938i	0.495418	−	0.868655i	$-0.335015\pi$
$858$	−11.5243	+	18.7074i	−0.393432	+	0.638661i
$859$	0.316537	−	0.548259i	0.0108001	−	0.0187063i	−0.860575	−	0.509324i	$-0.829895\pi$
$859$	0.316537	−	0.548259i	0.0108001	−	0.0187063i	0.871375	+	0.490618i	$0.163229\pi$
$860$	−10.1364	+	7.36455i	−0.345650	+	0.251129i
$861$	20.9549	+	37.6885i	0.714142	+	1.28442i
$862$	−1.06305	+	3.27173i	−0.0362076	+	0.111436i
$863$	−2.94457	−	6.61362i	−0.100234	−	0.225130i	0.856467	−	0.516202i	$-0.172655\pi$
$863$	−2.94457	−	6.61362i	−0.100234	−	0.225130i	−0.956701	+	0.291072i	$0.905988\pi$
$864$	4.45370	+	2.67667i	0.151518	+	0.0910621i
$865$	−13.0133	−	61.2226i	−0.442464	−	2.08163i
$866$	8.26502	+	1.75678i	0.280857	+	0.0596980i
$867$	23.3630	+	0.952762i	0.793451	+	0.0323575i
$868$	−3.32104	−	0.620946i	−0.112724	−	0.0210763i
$869$	−13.4063	+	3.02151i	−0.454778	+	0.102498i
$870$	14.2984	+	35.9947i	0.484760	+	1.22033i
$871$	−11.8913	+	26.7082i	−0.402921	+	0.904974i
$872$	−0.447308	−	0.402758i	−0.0151477	−	0.0136391i
$873$	−7.01791	+	10.1463i	−0.237520	+	0.343400i
$874$	−9.97768	−	7.24921i	−0.337500	−	0.245208i
$875$	−94.6526	−	28.2001i	−3.19984	−	0.953336i
$876$	−5.81610	−	8.73252i	−0.196508	−	0.295044i
$877$	−5.53107	+	26.0217i	−0.186771	+	0.878689i	0.780542	+	0.625103i	$0.214943\pi$
$877$	−5.53107	+	26.0217i	−0.186771	+	0.878689i	−0.967313	+	0.253585i	$0.918390\pi$
$878$	−6.69316	+	15.0331i	−0.225883	+	0.507342i
$879$	1.54165	−	10.5223i	0.0519985	−	0.354907i
$880$	−11.6882	−	8.27537i	−0.394009	−	0.278963i
$881$			7.71388i			0.259887i	0.991521	+	0.129944i	$0.0414796\pi$
$881$			7.71388i			0.259887i	−0.991521	+	0.129944i	$0.958520\pi$
$882$	9.90692	+	18.5163i	0.333583	+	0.623476i
$883$	−4.37770	−	13.4732i	−0.147321	−	0.453408i	0.849981	−	0.526813i	$-0.176613\pi$
$883$	−4.37770	−	13.4732i	−0.147321	−	0.453408i	−0.997302	+	0.0734053i	$0.976613\pi$
$884$	5.31780	−	4.78816i	0.178857	−	0.161043i
$885$	1.47961	−	1.51435i	0.0497366	−	0.0509042i
$886$	−26.2197	−	2.75580i	−0.880867	−	0.0925828i
$887$	31.4042	+	34.8779i	1.05445	+	1.17109i	0.984832	+	0.173512i	$0.0555116\pi$
$887$	31.4042	+	34.8779i	1.05445	+	1.17109i	0.0696188	+	0.997574i	$0.477822\pi$
$888$	2.79762	−	7.54867i	0.0938820	−	0.253317i
$889$	11.2754	−	16.3504i	0.378164	−	0.548375i
$890$	1.62989			0.0546342
$891$	−20.9738	+	21.2391i	−0.702650	+	0.711536i
$892$	−7.49404	−	12.9801i	−0.250919	−	0.434604i
$893$	−10.4775	−	4.66490i	−0.350617	−	0.156105i
$894$	4.88104	+	5.88661i	0.163246	+	0.196878i
$895$	3.04973	−	9.38610i	0.101941	−	0.313743i
$896$	−1.81818	−	1.92203i	−0.0607412	−	0.0642107i
$897$	11.9135	+	42.4839i	0.397779	+	1.41850i
$898$	−23.0642	+	20.7671i	−0.769664	+	0.693008i
$899$	4.42496	−	4.91442i	0.147581	−	0.163905i
$900$	7.57961	−	40.2273i	0.252654	−	1.34091i
$901$	20.5569	+	11.8685i	0.684848	+	0.395397i
$902$	26.8353	−	15.9344i	0.893519	−	0.530556i
$903$	−2.55411	−	13.0494i	−0.0849954	−	0.434258i
$904$	1.72653	+	2.37636i	0.0574234	+	0.0790365i
$905$	−1.26502	+	5.95147i	−0.0420508	+	0.197833i
$906$	−4.28956	+	8.66582i	−0.142511	+	0.287903i
$907$	−2.54162	+	24.1819i	−0.0843930	+	0.802946i	0.867690	+	0.497106i	$0.165604\pi$
$907$	−2.54162	+	24.1819i	−0.0843930	+	0.802946i	−0.952083	+	0.305840i	$0.901063\pi$
$908$	6.69815	−	2.98221i	0.222286	−	0.0989680i
$909$	−59.7090	−	4.87806i	−1.98042	−	0.161795i
$910$	40.3439	+	16.7857i	1.33739	+	0.556440i
$911$	−25.8939	−	35.6399i	−0.857904	−	1.18080i	−0.982065	−	0.188541i	$-0.939624\pi$
$911$	−25.8939	−	35.6399i	−0.857904	−	1.18080i	0.124161	−	0.992262i	$-0.460376\pi$
$912$	−1.18408	−	2.98079i	−0.0392087	−	0.0987038i
$913$	−15.2024	−	8.53080i	−0.503126	−	0.282328i
$914$	6.34778	−	3.66489i	0.209966	−	0.121224i
$915$	38.4116	−	60.6785i	1.26985	−	2.00597i
$916$	−4.81890	−	14.8310i	−0.159221	−	0.490031i
$917$	−5.56668	+	10.2140i	−0.183828	+	0.337297i
$918$	8.50291	−	4.71211i	0.280638	−	0.155523i
$919$	−7.58142	−	17.0282i	−0.250088	−	0.561707i	0.744258	−	0.667892i	$-0.232803\pi$
$919$	−7.58142	−	17.0282i	−0.250088	−	0.561707i	−0.994346	+	0.106185i	$0.966136\pi$
$920$	−28.1301	+	5.97924i	−0.927422	+	0.197130i
$921$	−5.88420	−	34.5520i	−0.193891	−	1.13853i
$922$	−1.56879	−	14.9260i	−0.0516652	−	0.491562i
$923$	5.71531			0.188122
$924$	13.1921	−	7.54767i	0.433990	−	0.248300i
$925$	−63.4210			−2.08527
$926$	2.80444	+	26.6824i	0.0921596	+	0.876840i
$927$	−26.3235	−	14.3941i	−0.864576	−	0.472764i
$928$	5.06543	−	1.07669i	0.166281	−	0.0353441i
$929$	21.3577	+	47.9702i	0.700724	+	1.57385i	0.814380	+	0.580332i	$0.197077\pi$
$929$	21.3577	+	47.9702i	0.700724	+	1.57385i	−0.113656	+	0.993520i	$0.536256\pi$
$930$	−9.19585	+	2.57873i	−0.301544	+	0.0845599i
$931$	2.06819	−	12.7963i	0.0677823	−	0.419383i
$932$	−4.02862	−	12.3988i	−0.131962	−	0.406136i
$933$	16.5634	+	10.4852i	0.542261	+	0.343270i
$934$	0.616735	−	0.356072i	0.0201802	−	0.0116510i
$935$	−24.3414	+	11.1963i	−0.796048	+	0.366160i
$936$	−3.29169	+	10.9923i	−0.107592	+	0.359295i
$937$	3.78576	+	5.21065i	0.123675	+	0.170224i	0.866365	−	0.499411i	$-0.166450\pi$
$937$	3.78576	+	5.21065i	0.123675	+	0.170224i	−0.742690	+	0.669636i	$0.766450\pi$
$938$	16.0635	−	12.2857i	0.524492	−	0.401142i
$939$	11.0645	−	7.36930i	0.361078	−	0.240488i
$940$	−24.4317	+	10.8777i	−0.796874	+	0.354791i
$941$	−4.03671	+	38.4067i	−0.131593	+	1.25202i	0.706980	+	0.707233i	$0.250057\pi$
$941$	−4.03671	+	38.4067i	−0.131593	+	1.25202i	−0.838573	+	0.544789i	$0.816610\pi$
$942$	−13.9394	−	6.89998i	−0.454172	−	0.224814i
$943$	13.0303	−	61.3030i	0.424326	−	1.99630i
$944$	−0.166393	−	0.229021i	−0.00541564	−	0.00745399i
$945$	48.2700	+	34.5532i	1.57022	+	1.12402i
$946$	−9.38821	+	2.11591i	−0.305237	+	0.0687943i
$947$	13.7152	+	7.91848i	0.445685	+	0.257316i	0.706006	−	0.708206i	$-0.250495\pi$
$947$	13.7152	+	7.91848i	0.445685	+	0.257316i	−0.260321	+	0.965522i	$0.583828\pi$
$948$	−6.35637	+	3.33218i	−0.206445	+	0.108224i
$949$	15.5035	−	17.2183i	0.503263	−	0.558931i
$950$	−18.7774	+	16.9073i	−0.609220	+	0.548544i
$951$	−48.7526	+	13.6714i	−1.58091	+	0.443325i
$952$	−4.81489	+	1.14791i	−0.156052	+	0.0372041i
$953$	2.37126	−	7.29798i	0.0768126	−	0.236405i	−0.905276	−	0.424823i	$-0.860336\pi$
$953$	2.37126	−	7.29798i	0.0768126	−	0.236405i	0.982089	+	0.188419i	$0.0603362\pi$
$954$	−38.0530	+	0.883121i	−1.23201	+	0.0285921i
$955$	−17.0751	−	7.60233i	−0.552538	−	0.246006i
$956$	−3.22962	−	5.59387i	−0.104453	−	0.180919i
$957$	−0.848371	+	29.7367i	−0.0274239	+	0.961250i
$958$	27.0737			0.874710
$959$	35.0751	+	2.81622i	1.13263	+	0.0909405i
$960$	−7.01286	−	2.59904i	−0.226339	−	0.0838838i
$961$	−19.6519	−	21.8256i	−0.633932	−	0.704053i
$962$	17.6802	+	1.85827i	0.570033	+	0.0599129i
$963$	25.3622	−	3.26223i	0.817285	−	0.105124i
$964$	11.4622	−	10.3206i	0.369172	−	0.332404i
$965$	−23.6332	−	72.7355i	−0.760780	−	2.34144i
$966$	6.82713	−	29.7473i	0.219659	−	0.957105i
$967$		−	18.8028i		−	0.604656i	−0.953204	−	0.302328i	$-0.902236\pi$
$967$		−	18.8028i		−	0.604656i	0.953204	−	0.302328i	$-0.0977638\pi$
$968$	−5.73146	−	9.38884i	−0.184216	−	0.301769i
$969$	−5.93714	−	0.869868i	−0.190728	−	0.0279442i
$970$	7.22236	−	16.2217i	0.231896	−	0.520847i
$971$	8.23654	−	38.7499i	0.264323	−	1.24354i	−0.622937	−	0.782272i	$-0.714061\pi$
$971$	8.23654	−	38.7499i	0.264323	−	1.24354i	0.887260	−	0.461270i	$-0.152606\pi$
$972$	−7.71784	+	13.5438i	−0.247550	+	0.434418i
$973$	22.7534	+	6.77896i	0.729439	+	0.217323i
$974$	29.3251	+	21.3059i	0.939636	+	0.682686i
$975$	90.2118	−	5.77798i	2.88909	−	0.185043i
$976$	−7.13581	−	6.42511i	−0.228412	−	0.205663i
$977$	−5.12931	+	11.5206i	−0.164101	+	0.368577i	−0.976815	−	0.214086i	$-0.931323\pi$
$977$	−5.12931	+	11.5206i	−0.164101	+	0.368577i	0.812714	+	0.582663i	$0.197989\pi$
$978$	−26.7850	+	10.6399i	−0.856488	+	0.340228i
$979$	1.14982	+	0.495166i	0.0367485	+	0.0158256i
$980$	−18.9475	−	23.5499i	−0.605256	−	0.752275i
$981$	1.17681	−	1.36959i	0.0375727	−	0.0437278i
$982$	−19.6173	−	4.16979i	−0.626014	−	0.133063i
$983$	−12.9052	−	60.7141i	−0.411611	−	1.93648i	−0.344674	−	0.938722i	$-0.612011\pi$
$983$	−12.9052	−	60.7141i	−0.411611	−	1.93648i	−0.0669372	−	0.997757i	$-0.521323\pi$
$984$	11.3904	−	11.6578i	0.363114	−	0.371638i
$985$	36.6246	+	82.2603i	1.16696	+	2.62103i
$986$	2.99389	−	9.21425i	0.0953450	−	0.293442i
$987$	0.458573	−	28.3788i	0.0145965	−	0.903308i
$988$	5.73008	−	4.16315i	0.182298	−	0.132447i
$989$	−9.66275	+	16.7364i	−0.307258	+	0.532186i
$990$	24.0059	−	35.6312i	0.762957	−	1.13243i
$991$	20.6992	+	35.8521i	0.657533	+	1.13888i	0.981252	+	0.192727i	$0.0617332\pi$
$991$	20.6992	+	35.8521i	0.657533	+	1.13888i	−0.323720	+	0.946153i	$0.604933\pi$
$992$	0.133482	+	1.26999i	0.00423805	+	0.0403223i
$993$	9.70777	−	26.1939i	0.308067	−	0.831240i
$994$	−3.47135	−	1.89189i	−0.110104	−	0.0600072i
$995$	−42.2362	+	58.1332i	−1.33898	+	1.84295i
$996$	−8.82030	−	2.25405i	−0.279482	−	0.0714223i
$997$	−0.548307	−	2.57958i	−0.0173651	−	0.0816962i	0.968612	−	0.248578i	$-0.0799634\pi$
$997$	−0.548307	−	2.57958i	−0.0173651	−	0.0816962i	−0.985977	+	0.166882i	$0.946630\pi$
$998$	−29.2875	+	32.5271i	−0.927080	+	1.02963i
$999$	22.8346	+	7.86518i	0.722456	+	0.248843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.107.16	yes	128
3.2	odd	2		462.2.bc.b.107.8	yes	128
7.4	even	3	inner	462.2.bc.a.305.5	yes	128
11.7	odd	10		462.2.bc.b.359.4	yes	128
21.11	odd	6		462.2.bc.b.305.4	yes	128
33.29	even	10	inner	462.2.bc.a.359.5	yes	128
77.18	odd	30		462.2.bc.b.95.8	yes	128
231.95	even	30	inner	462.2.bc.a.95.16	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.16	✓	128	231.95	even	30	inner
462.2.bc.a.107.16	yes	128	1.1	even	1	trivial
462.2.bc.a.305.5	yes	128	7.4	even	3	inner
462.2.bc.a.359.5	yes	128	33.29	even	10	inner
462.2.bc.b.95.8	yes	128	77.18	odd	30
462.2.bc.b.107.8	yes	128	3.2	odd	2
462.2.bc.b.305.4	yes	128	21.11	odd	6
462.2.bc.b.359.4	yes	128	11.7	odd	10

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(1.70747 - 0.290781i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.75629 + 3.94468i) q^{5} +(0.467667 + 1.66772i) q^{6} +(2.64495 - 0.0650804i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.83089 - 0.992999i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(1.70747 - 0.290781i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(1.75629 + 3.94468i) q^{5} +(0.467667 + 1.66772i) q^{6} +(2.64495 - 0.0650804i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(2.83089 - 0.992999i) q^{9} +(-3.73949 + 2.15900i) q^{10} +(-3.29397 + 0.387016i) q^{11} +(-1.60970 + 0.639429i) q^{12} +(-2.24820 - 3.09438i) q^{13} +(0.341197 + 2.62366i) q^{14} +(4.14584 + 6.22472i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.195558 - 1.86061i) q^{17} +(1.28347 + 2.71159i) q^{18} +(0.385005 - 1.81130i) q^{19} +(-2.53805 - 3.49333i) q^{20} +(4.49724 - 0.880225i) q^{21} +(-0.729209 - 3.23547i) q^{22} +(-5.76787 - 3.33008i) q^{23} +(-0.804186 - 1.53404i) q^{24} +(-9.13033 + 10.1403i) q^{25} +(2.84243 - 2.55934i) q^{26} +(4.54491 - 2.51868i) q^{27} +(-2.57362 + 0.613574i) q^{28} +(1.60027 - 4.92514i) q^{29} +(-5.75727 + 4.77379i) q^{30} +(1.16659 + 0.519398i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-5.51181 + 1.61864i) q^{33} +1.87086 q^{34} +(4.90201 + 10.3192i) q^{35} +(-2.56257 + 1.55988i) q^{36} +(3.11006 + 3.45407i) q^{37} +(1.84163 + 0.193563i) q^{38} +(-4.73852 - 4.62982i) q^{39} +(3.20889 - 2.88930i) q^{40} +(2.90786 + 8.94949i) q^{41} +(1.34549 + 4.38060i) q^{42} -2.90165i q^{43} +(3.14152 - 1.06341i) q^{44} +(8.88892 + 9.42298i) q^{45} +(2.70893 - 6.08437i) q^{46} +(1.28772 - 6.05823i) q^{47} +(1.44158 - 0.960132i) q^{48} +(6.99153 - 0.344269i) q^{49} +(-11.0391 - 8.02037i) q^{50} +(-0.207122 - 3.23380i) q^{51} +(2.84243 + 2.55934i) q^{52} +(-5.16057 + 11.5908i) q^{53} +(2.97996 + 4.25674i) q^{54} +(-7.31180 - 12.3139i) q^{55} +(-0.879230 - 2.49539i) q^{56} +(0.130690 - 3.20469i) q^{57} +(5.06543 + 1.07669i) q^{58} +(-0.0588568 - 0.276899i) q^{59} +(-5.34944 - 5.22673i) q^{60} +(-3.90556 - 8.77203i) q^{61} +(-0.394611 + 1.21449i) q^{62} +(7.42295 - 2.81067i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(8.25787 - 14.3031i) q^{65} +(-2.18591 - 5.31242i) q^{66} +(-3.82181 - 6.61957i) q^{67} +(0.195558 + 1.86061i) q^{68} +(-10.8168 - 4.00882i) q^{69} +(-9.75026 + 5.95381i) q^{70} +(-0.878299 + 1.20888i) q^{71} +(-1.81919 - 2.38549i) q^{72} +(1.25945 + 5.92524i) q^{73} +(-3.11006 + 3.45407i) q^{74} +(-12.6411 + 19.9691i) q^{75} +1.85177i q^{76} +(-8.68719 + 1.23801i) q^{77} +(4.10915 - 5.19651i) q^{78} +(4.12085 - 0.433118i) q^{79} +(3.20889 + 2.88930i) q^{80} +(7.02791 - 5.62215i) q^{81} +(-8.59651 + 3.82741i) q^{82} +(4.25224 + 3.08943i) q^{83} +(-4.21596 + 1.79602i) q^{84} +(7.68299 - 2.49635i) q^{85} +(2.88576 - 0.303305i) q^{86} +(1.30028 - 8.87484i) q^{87} +(1.38597 + 3.01315i) q^{88} +(-0.326895 - 0.188733i) q^{89} +(-8.44222 + 9.82520i) q^{90} +(-6.14776 - 8.03817i) q^{91} +(6.33420 + 2.05810i) q^{92} +(2.14294 + 0.547634i) q^{93} +(6.15965 + 0.647405i) q^{94} +(7.82120 - 1.66245i) q^{95} +(1.10556 + 1.33332i) q^{96} +(-3.32691 + 2.41714i) q^{97} +(1.07320 + 6.91724i) q^{98} +(-8.94056 + 4.36651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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