LMFDB - Embedded newform 114.2.l.b.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.3
Root			$1.69944 - 0.334495i$ of defining polynomial
Character	$\chi$	$=$	114.71
Dual form			114.2.l.b.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(1.08684 - 1.34862i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.343148 - 0.408948i) q^{5} +(-0.560041 + 1.63901i) q^{6} +(-0.716507 - 1.24103i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.637553 - 2.93147i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(1.08684 - 1.34862i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.343148 - 0.408948i) q^{5} +(-0.560041 + 1.63901i) q^{6} +(-0.716507 - 1.24103i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.637553 - 2.93147i) q^{9} +(-0.182585 + 0.501649i) q^{10} +(1.25645 + 0.725411i) q^{11} +(-0.0343077 - 1.73171i) q^{12} +(2.94737 - 0.519701i) q^{13} +(1.09775 + 0.921124i) q^{14} +(-0.178568 - 0.907238i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.89590 + 5.20894i) q^{17} +(1.60173 + 2.53663i) q^{18} +(-4.35653 + 0.143752i) q^{19} -0.533844i q^{20} +(-2.45240 - 0.382503i) q^{21} +(-1.42878 - 0.251933i) q^{22} +(0.396438 + 0.472456i) q^{23} +(0.624519 + 1.61554i) q^{24} +(0.818753 + 4.64338i) q^{25} +(-2.59188 + 1.49642i) q^{26} +(-4.64636 - 2.32623i) q^{27} +(-1.34659 - 0.490120i) q^{28} +(-4.97822 - 1.81193i) q^{29} +(0.478093 + 0.791451i) q^{30} +(-4.28601 + 2.47453i) q^{31} +(0.173648 + 0.984808i) q^{32} +(2.34386 - 0.906066i) q^{33} +(-3.56312 - 4.24636i) q^{34} +(-0.753384 - 0.132842i) q^{35} +(-2.37271 - 1.83583i) q^{36} +6.41883i q^{37} +(4.04463 - 1.62510i) q^{38} +(2.50245 - 4.53972i) q^{39} +(0.182585 + 0.501649i) q^{40} +(-1.37347 + 7.78933i) q^{41} +(2.43533 - 0.479336i) q^{42} +(4.88757 + 4.10116i) q^{43} +(1.42878 - 0.251933i) q^{44} +(-1.41759 - 0.745203i) q^{45} +(-0.534119 - 0.308374i) q^{46} +(4.37381 - 12.0169i) q^{47} +(-1.13940 - 1.30452i) q^{48} +(2.47323 - 4.28377i) q^{49} +(-2.35751 - 4.08332i) q^{50} +(9.08542 + 3.10444i) q^{51} +(1.92376 - 2.29265i) q^{52} +(-1.41439 + 1.18682i) q^{53} +(5.16177 + 0.596790i) q^{54} +(0.727804 - 0.264899i) q^{55} +1.43301 q^{56} +(-4.54099 + 6.03154i) q^{57} +5.29771 q^{58} +(-1.75650 + 0.639313i) q^{59} +(-0.719953 - 0.580203i) q^{60} +(9.02625 - 7.57392i) q^{61} +(3.18119 - 3.79120i) q^{62} +(-3.18122 + 2.89164i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.798855 - 1.38366i) q^{65} +(-1.89262 + 1.65307i) q^{66} +(3.17216 - 8.71543i) q^{67} +(4.80058 + 2.77162i) q^{68} +(1.06803 - 0.0211592i) q^{69} +(0.753384 - 0.132842i) q^{70} +(-9.59384 - 8.05019i) q^{71} +(2.85751 + 0.913599i) q^{72} +(-2.80621 + 15.9148i) q^{73} +(-2.19537 - 6.03173i) q^{74} +(7.15201 + 3.94243i) q^{75} +(-3.24489 + 2.91044i) q^{76} -2.07905i q^{77} +(-0.798855 + 5.12183i) q^{78} +(-7.87896 - 1.38927i) q^{79} +(-0.343148 - 0.408948i) q^{80} +(-8.18705 + 3.73794i) q^{81} +(-1.37347 - 7.78933i) q^{82} +(4.29627 - 2.48045i) q^{83} +(-2.12452 + 1.28336i) q^{84} +(2.78076 + 1.01211i) q^{85} +(-5.99550 - 2.18218i) q^{86} +(-7.85414 + 4.74446i) q^{87} +(-1.25645 + 0.725411i) q^{88} +(-0.832120 - 4.71919i) q^{89} +(1.58698 + 0.215416i) q^{90} +(-2.75678 - 3.28540i) q^{91} +(0.607378 + 0.107097i) q^{92} +(-1.32101 + 8.46962i) q^{93} +12.7882i q^{94} +(-1.43615 + 1.83092i) q^{95} +(1.51686 + 0.836144i) q^{96} +(-2.83601 - 7.79188i) q^{97} +(-0.858945 + 4.87132i) q^{98} +(1.32547 - 4.14573i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	1.08684	−	1.34862i	0.627488	−	0.778626i
$3$	1.08684	−	1.34862i	0.627488	−	0.778626i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.343148	−	0.408948i	0.153461	−	0.182887i	−0.683837	−	0.729635i	$-0.739690\pi$
$5$	0.343148	−	0.408948i	0.153461	−	0.182887i	0.837297	+	0.546748i	$0.184134\pi$
$6$	−0.560041	+	1.63901i	−0.228636	+	0.669123i
$7$	−0.716507	−	1.24103i	−0.270814	−	0.469064i	0.698256	−	0.715848i	$-0.253960\pi$
$7$	−0.716507	−	1.24103i	−0.270814	−	0.469064i	−0.969071	+	0.246784i	$0.920626\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.637553	−	2.93147i	−0.212518	−	0.977157i
$10$	−0.182585	+	0.501649i	−0.0577386	+	0.158635i
$11$	1.25645	+	0.725411i	0.378834	+	0.218720i	0.677311	−	0.735697i	$-0.263145\pi$
$11$	1.25645	+	0.725411i	0.378834	+	0.218720i	−0.298477	+	0.954417i	$0.596479\pi$
$12$	−0.0343077	−	1.73171i	−0.00990379	−	0.499902i
$13$	2.94737	−	0.519701i	0.817454	−	0.144139i	0.250741	−	0.968054i	$-0.419326\pi$
$13$	2.94737	−	0.519701i	0.817454	−	0.144139i	0.566713	+	0.823915i	$0.308215\pi$
$14$	1.09775	+	0.921124i	0.293387	+	0.246181i
$15$	−0.178568	−	0.907238i	−0.0461061	−	0.234248i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	1.89590	+	5.20894i	0.459823	+	1.26335i	0.925618	+	0.378460i	$0.123546\pi$
$17$	1.89590	+	5.20894i	0.459823	+	1.26335i	−0.465795	+	0.884893i	$0.654232\pi$
$18$	1.60173	+	2.53663i	0.377530	+	0.597889i
$19$	−4.35653	+	0.143752i	−0.999456	+	0.0329790i
$19$	−4.35653	+	0.143752i	−0.999456	+	0.0329790i
$20$		−	0.533844i		−	0.119371i
$21$	−2.45240	−	0.382503i	−0.535158	−	0.0834690i
$22$	−1.42878	−	0.251933i	−0.304617	−	0.0537122i
$23$	0.396438	+	0.472456i	0.0826630	+	0.0985139i	0.805791	−	0.592200i	$-0.201741\pi$
$23$	0.396438	+	0.472456i	0.0826630	+	0.0985139i	−0.723128	+	0.690714i	$0.757296\pi$
$24$	0.624519	+	1.61554i	0.127479	+	0.329771i
$25$	0.818753	+	4.64338i	0.163751	+	0.928676i
$26$	−2.59188	+	1.49642i	−0.508309	+	0.293472i
$27$	−4.64636	−	2.32623i	−0.894192	−	0.447683i
$28$	−1.34659	−	0.490120i	−0.254482	−	0.0926240i
$29$	−4.97822	−	1.81193i	−0.924433	−	0.336466i	−0.164432	−	0.986388i	$-0.552579\pi$
$29$	−4.97822	−	1.81193i	−0.924433	−	0.336466i	−0.760001	+	0.649922i	$0.774801\pi$
$30$	0.478093	+	0.791451i	0.0872874	+	0.144499i
$31$	−4.28601	+	2.47453i	−0.769790	+	0.444439i	−0.832800	−	0.553574i	$-0.813263\pi$
$31$	−4.28601	+	2.47453i	−0.769790	+	0.444439i	0.0630096	+	0.998013i	$0.479930\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	2.34386	−	0.906066i	0.408014	−	0.157726i
$34$	−3.56312	−	4.24636i	−0.611071	−	0.728245i
$35$	−0.753384	−	0.132842i	−0.127345	−	0.0224544i
$36$	−2.37271	−	1.83583i	−0.395451	−	0.305971i
$37$			6.41883i			1.05525i	0.849478	+	0.527625i	$0.176917\pi$
$37$			6.41883i			1.05525i	−0.849478	+	0.527625i	$0.823083\pi$
$38$	4.04463	−	1.62510i	0.656126	−	0.263627i
$39$	2.50245	−	4.53972i	0.400712	−	0.726937i
$40$	0.182585	+	0.501649i	0.0288693	+	0.0793177i
$41$	−1.37347	+	7.78933i	−0.214500	+	1.21649i	0.667273	+	0.744814i	$0.267462\pi$
$41$	−1.37347	+	7.78933i	−0.214500	+	1.21649i	−0.881772	+	0.471675i	$0.843650\pi$
$42$	2.43533	−	0.479336i	0.375780	−	0.0739632i
$43$	4.88757	+	4.10116i	0.745348	+	0.625421i	0.934268	−	0.356571i	$-0.116054\pi$
$43$	4.88757	+	4.10116i	0.745348	+	0.625421i	−0.188920	+	0.981992i	$0.560499\pi$
$44$	1.42878	−	0.251933i	0.215397	−	0.0379803i
$45$	−1.41759	−	0.745203i	−0.211323	−	0.111088i
$46$	−0.534119	−	0.308374i	−0.0787516	−	0.0454672i
$47$	4.37381	−	12.0169i	0.637985	−	1.75285i	−0.0199780	−	0.999800i	$-0.506360\pi$
$47$	4.37381	−	12.0169i	0.637985	−	1.75285i	0.657963	−	0.753050i	$-0.271418\pi$
$48$	−1.13940	−	1.30452i	−0.164459	−	0.188291i
$49$	2.47323	−	4.28377i	0.353319	−	0.611967i
$50$	−2.35751	−	4.08332i	−0.333402	−	0.577469i
$51$	9.08542	+	3.10444i	1.27221	+	0.434709i
$52$	1.92376	−	2.29265i	0.266778	−	0.317933i
$53$	−1.41439	+	1.18682i	−0.194282	+	0.163022i	−0.734739	−	0.678349i	$-0.762696\pi$
$53$	−1.41439	+	1.18682i	−0.194282	+	0.163022i	0.540458	+	0.841371i	$0.318251\pi$
$54$	5.16177	+	0.596790i	0.702428	+	0.0812128i
$55$	0.727804	−	0.264899i	0.0981370	−	0.0357190i
$56$	1.43301			0.191495
$57$	−4.54099	+	6.03154i	−0.601468	+	0.798897i
$58$	5.29771			0.695624
$59$	−1.75650	+	0.639313i	−0.228676	+	0.0832314i	−0.453817	−	0.891095i	$-0.649938\pi$
$59$	−1.75650	+	0.639313i	−0.228676	+	0.0832314i	0.225141	+	0.974326i	$0.427716\pi$
$60$	−0.719953	−	0.580203i	−0.0929455	−	0.0749039i
$61$	9.02625	−	7.57392i	1.15569	−	0.969742i	0.155856	−	0.987780i	$-0.450186\pi$
$61$	9.02625	−	7.57392i	1.15569	−	0.969742i	0.999837	+	0.0180382i	$0.00574206\pi$
$62$	3.18119	−	3.79120i	0.404012	−	0.481483i
$63$	−3.18122	+	2.89164i	−0.400797	+	0.364313i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.798855	−	1.38366i	0.0990857	−	0.171622i
$66$	−1.89262	+	1.65307i	−0.232965	+	0.203479i
$67$	3.17216	−	8.71543i	0.387541	−	1.06476i	−0.580564	−	0.814215i	$-0.697168\pi$
$67$	3.17216	−	8.71543i	0.387541	−	1.06476i	0.968105	−	0.250545i	$-0.0806099\pi$
$68$	4.80058	+	2.77162i	0.582156	+	0.336108i
$69$	1.06803	−	0.0211592i	0.128576	−	0.00254727i
$70$	0.753384	−	0.132842i	0.0900466	−	0.0158776i
$71$	−9.59384	−	8.05019i	−1.13858	−	0.955382i	−0.139188	−	0.990266i	$-0.544449\pi$
$71$	−9.59384	−	8.05019i	−1.13858	−	0.955382i	−0.999391	+	0.0348843i	$0.988894\pi$
$72$	2.85751	+	0.913599i	0.336760	+	0.107669i
$73$	−2.80621	+	15.9148i	−0.328442	+	1.86269i	0.155852	+	0.987780i	$0.450188\pi$
$73$	−2.80621	+	15.9148i	−0.328442	+	1.86269i	−0.484294	+	0.874905i	$0.660923\pi$
$74$	−2.19537	−	6.03173i	−0.255207	−	0.701174i
$75$	7.15201	+	3.94243i	0.825843	+	0.455232i
$76$	−3.24489	+	2.91044i	−0.372215	+	0.333851i
$77$		−	2.07905i		−	0.236930i
$78$	−0.798855	+	5.12183i	−0.0904525	+	0.579933i
$79$	−7.87896	−	1.38927i	−0.886452	−	0.156305i	−0.288159	−	0.957583i	$-0.593043\pi$
$79$	−7.87896	−	1.38927i	−0.886452	−	0.156305i	−0.598293	+	0.801277i	$0.704154\pi$
$80$	−0.343148	−	0.408948i	−0.0383651	−	0.0457218i
$81$	−8.18705	+	3.73794i	−0.909673	+	0.415326i
$82$	−1.37347	−	7.78933i	−0.151674	−	0.860187i
$83$	4.29627	−	2.48045i	0.471577	−	0.272265i	−0.245323	−	0.969442i	$-0.578894\pi$
$83$	4.29627	−	2.48045i	0.471577	−	0.272265i	0.716900	+	0.697176i	$0.245561\pi$
$84$	−2.12452	+	1.28336i	−0.231804	+	0.140026i
$85$	2.78076	+	1.01211i	0.301616	+	0.109779i
$86$	−5.99550	−	2.18218i	−0.646511	−	0.235311i
$87$	−7.85414	+	4.74446i	−0.842052	+	0.508659i
$88$	−1.25645	+	0.725411i	−0.133938	+	0.0773291i
$89$	−0.832120	−	4.71919i	−0.0882046	−	0.500233i	−0.996619	−	0.0821621i	$-0.973817\pi$
$89$	−0.832120	−	4.71919i	−0.0882046	−	0.500233i	0.908414	−	0.418071i	$-0.137294\pi$
$90$	1.58698	+	0.215416i	0.167282	+	0.0227068i
$91$	−2.75678	−	3.28540i	−0.288989	−	0.344403i
$92$	0.607378	+	0.107097i	0.0633235	+	0.0111656i
$93$	−1.32101	+	8.46962i	−0.136983	+	0.878259i
$94$			12.7882i			1.31900i
$95$	−1.43615	+	1.83092i	−0.147346	+	0.187849i
$96$	1.51686	+	0.836144i	0.154814	+	0.0853386i
$97$	−2.83601	−	7.79188i	−0.287954	−	0.791146i	−0.996352	−	0.0853335i	$-0.972804\pi$
$97$	−2.83601	−	7.79188i	−0.287954	−	0.791146i	0.708399	−	0.705812i	$-0.249418\pi$
$98$	−0.858945	+	4.87132i	−0.0867666	+	0.492078i
$99$	1.32547	−	4.14573i	0.133215	−	0.416662i
$100$	3.61191	+	3.03075i	0.361191	+	0.303075i
$101$	3.10192	−	0.546953i	0.308653	−	0.0544238i	−0.0171763	−	0.999852i	$-0.505468\pi$
$101$	3.10192	−	0.546953i	0.308653	−	0.0544238i	0.325829	+	0.945429i	$0.394357\pi$
$102$	−9.59928	+	0.190176i	−0.950470	+	0.0188302i
$103$	−8.85438	−	5.11208i	−0.872448	−	0.503708i	−0.00428731	−	0.999991i	$-0.501365\pi$
$103$	−8.85438	−	5.11208i	−0.872448	−	0.503708i	−0.868161	+	0.496282i	$0.834698\pi$
$104$	−1.02361	+	2.81235i	−0.100373	+	0.275774i
$105$	−0.997962	+	0.871651i	−0.0973911	+	0.0850644i
$106$	0.923180	−	1.59899i	0.0896672	−	0.155308i
$107$	5.80970	+	10.0627i	0.561645	+	0.972798i	0.997353	+	0.0727101i	$0.0231648\pi$
$107$	5.80970	+	10.0627i	0.561645	+	0.972798i	−0.435708	+	0.900088i	$0.643502\pi$
$108$	−5.05459	+	1.20463i	−0.486378	+	0.115916i
$109$	−0.0205152	+	0.0244490i	−0.00196500	+	0.00234179i	−0.767026	−	0.641616i	$-0.778264\pi$
$109$	−0.0205152	+	0.0244490i	−0.00196500	+	0.00234179i	0.765061	+	0.643958i	$0.222709\pi$
$110$	−0.593311	+	0.497847i	−0.0565700	+	0.0474678i
$111$	8.65657	+	6.97625i	0.821645	+	0.662156i
$112$	−1.34659	+	0.490120i	−0.127241	+	0.0463120i
$113$	10.3475			0.973413			0.486706	−	0.873566i	$-0.338198\pi$
$113$	10.3475			0.973413			0.486706	+	0.873566i	$0.338198\pi$
$114$	2.20422	−	7.22090i	0.206445	−	0.676299i
$115$	0.329247			0.0307024
$116$	−4.97822	+	1.81193i	−0.462216	+	0.168233i
$117$	−3.40259	−	8.30880i	−0.314570	−	0.768149i
$118$	1.43191	−	1.20152i	0.131818	−	0.110608i
$119$	5.10601	−	6.08510i	0.468067	−	0.557820i
$120$	0.874975	+	0.298975i	0.0798740	+	0.0272925i
$121$	−4.44756	−	7.70340i	−0.404323	−	0.700309i
$122$	−5.89147	+	10.2043i	−0.533388	+	0.923856i
$123$	9.01210	+	10.3180i	0.812594	+	0.930347i
$124$	−1.69268	+	4.65059i	−0.152007	+	0.417636i
$125$	4.49147	+	2.59315i	0.401729	+	0.231938i
$126$	2.00037	−	3.80530i	0.178207	−	0.339003i
$127$	−0.772141	+	0.136149i	−0.0685165	+	0.0120813i	−0.207801	−	0.978171i	$-0.566631\pi$
$127$	−0.772141	+	0.136149i	−0.0685165	+	0.0120813i	0.139285	+	0.990252i	$0.455520\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	10.8429	−	2.13417i	0.954666	−	0.187903i
$130$	−0.277439	+	1.57344i	−0.0243330	+	0.138000i
$131$	3.93973	+	10.8243i	0.344216	+	0.945726i	0.984157	+	0.177301i	$0.0567367\pi$
$131$	3.93973	+	10.8243i	0.344216	+	0.945726i	−0.639941	+	0.768424i	$0.721041\pi$
$132$	1.21310	−	2.20069i	0.105586	−	0.191546i
$133$	3.29988	+	5.30357i	0.286136	+	0.459878i
$134$			9.27477i			0.801218i
$135$	−2.54570	+	1.10188i	−0.219099	+	0.0948347i
$136$	−5.45902	−	0.962573i	−0.468107	−	0.0825399i
$137$	−8.70595	−	10.3754i	−0.743800	−	0.886426i	0.252909	−	0.967490i	$-0.418613\pi$
$137$	−8.70595	−	10.3754i	−0.743800	−	0.886426i	−0.996709	+	0.0810638i	$0.974168\pi$
$138$	−0.996382	+	0.385171i	−0.0848177	+	0.0327879i
$139$	−1.25656	−	7.12628i	−0.106580	−	0.604444i	−0.990578	−	0.136953i	$-0.956269\pi$
$139$	−1.25656	−	7.12628i	−0.106580	−	0.604444i	0.883998	−	0.467491i	$-0.154842\pi$
$140$	−0.662515	+	0.382503i	−0.0559927	+	0.0323274i
$141$	−11.4526	−	18.9591i	−0.964487	−	1.59664i
$142$	11.7686	+	4.28342i	0.987598	+	0.359456i
$143$	4.08022	+	1.48508i	0.341205	+	0.124188i
$144$	−2.99765	+	0.118822i	−0.249804	+	0.00990185i
$145$	−2.44925	+	1.41408i	−0.203399	+	0.117433i
$146$	−2.80621	−	15.9148i	−0.232243	−	1.31712i
$147$	−3.08916	−	7.99123i	−0.254790	−	0.659105i
$148$	4.12595	+	4.91711i	0.339151	+	0.404184i
$149$	−19.4195	−	3.42419i	−1.59091	−	0.280520i	−0.693079	−	0.720861i	$-0.743746\pi$
$149$	−19.4195	−	3.42419i	−1.59091	−	0.280520i	−0.897831	+	0.440341i	$0.854858\pi$
$150$	−8.06908	−	1.25854i	−0.658838	−	0.102759i
$151$		−	4.23079i		−	0.344297i	−0.985071	−	0.172148i	$-0.944929\pi$
$151$		−	4.23079i		−	0.344297i	0.985071	−	0.172148i	$-0.0550709\pi$
$152$	2.05377	−	3.84474i	0.166583	−	0.311850i
$153$	14.0611	−	8.87874i	1.13677	−	0.717804i
$154$	0.711077	+	1.95367i	0.0573002	+	0.157431i
$155$	−0.458783	+	2.60189i	−0.0368503	+	0.208989i
$156$	−1.00109	−	5.08617i	−0.0801513	−	0.407219i
$157$	7.78482	+	6.53224i	0.621296	+	0.521330i	0.898211	−	0.439565i	$-0.144867\pi$
$157$	7.78482	+	6.53224i	0.621296	+	0.521330i	−0.276914	+	0.960895i	$0.589312\pi$
$158$	7.87896	−	1.38927i	0.626817	−	0.110525i
$159$	0.0633444	+	3.19736i	0.00502354	+	0.253567i
$160$	0.462322	+	0.266922i	0.0365498	+	0.0211020i
$161$	0.302280	−	0.830508i	0.0238230	−	0.0654532i
$162$	6.41486	−	6.31265i	0.503999	−	0.495968i
$163$	−5.20216	+	9.01041i	−0.407465	+	0.705750i	−0.994605	−	0.103735i	$-0.966920\pi$
$163$	−5.20216	+	9.01041i	−0.407465	+	0.705750i	0.587140	+	0.809485i	$0.300254\pi$
$164$	3.95475	+	6.84982i	0.308814	+	0.534881i
$165$	0.433759	−	1.26943i	0.0337681	−	0.0988253i
$166$	−3.18881	+	3.80028i	−0.247500	+	0.294959i
$167$	−18.2265	+	15.2939i	−1.41041	+	1.18347i	−0.454162	+	0.890919i	$0.650061\pi$
$167$	−18.2265	+	15.2939i	−1.41041	+	1.18347i	−0.956249	+	0.292555i	$0.905494\pi$
$168$	1.55746	−	1.93259i	0.120161	−	0.149103i
$169$	−3.79909	+	1.38276i	−0.292238	+	0.106366i
$170$	−2.95922			−0.226962
$171$	3.19892	+	12.6794i	0.244628	+	0.969617i
$172$	6.38027			0.486491
$173$	23.5435	−	8.56912i	1.78998	−	0.651498i	0.790752	−	0.612137i	$-0.209690\pi$
$173$	23.5435	−	8.56912i	1.78998	−	0.651498i	0.999225	−	0.0393612i	$-0.0125323\pi$
$174$	5.75777	−	7.14460i	0.436496	−	0.541631i
$175$	5.17592	−	4.34311i	0.391263	−	0.328308i
$176$	0.932570	−	1.11139i	0.0702951	−	0.0837745i
$177$	−1.04684	+	3.06368i	−0.0786856	+	0.230280i
$178$	2.39599	+	4.14998i	0.179587	+	0.311054i
$179$	−7.77173	+	13.4610i	−0.580886	+	1.00612i	0.414488	+	0.910055i	$0.363961\pi$
$179$	−7.77173	+	13.4610i	−0.580886	+	1.00612i	−0.995375	+	0.0960699i	$0.969373\pi$
$180$	−1.56495	+	0.340354i	−0.116644	+	0.0253685i
$181$	7.17064	−	19.7012i	0.532990	−	1.46438i	−0.322506	−	0.946567i	$-0.604525\pi$
$181$	7.17064	−	19.7012i	0.532990	−	1.46438i	0.855496	−	0.517810i	$-0.173252\pi$
$182$	3.71420	+	2.14439i	0.275315	+	0.158953i
$183$	−0.404246	−	20.4046i	−0.0298827	−	1.50835i
$184$	−0.607378	+	0.107097i	−0.0447765	+	0.00789530i
$185$	2.62497	+	2.20261i	0.192992	+	0.161939i
$186$	−1.65544	−	8.41065i	−0.121382	−	0.616699i
$187$	−1.39652	+	7.92007i	−0.102124	+	0.579173i
$188$	−4.37381	−	12.0169i	−0.318993	−	0.876425i
$189$	0.442240	+	7.43302i	0.0321682	+	0.540673i
$190$	0.723325	−	2.21170i	0.0524755	−	0.160453i
$191$		−	1.59398i		−	0.115336i	−0.998336	−	0.0576682i	$-0.981633\pi$
$191$		−	1.59398i		−	0.115336i	0.998336	−	0.0576682i	$-0.0183665\pi$
$192$	−1.71136	−	0.266922i	−0.123507	−	0.0192634i
$193$	4.28991	+	0.756427i	0.308795	+	0.0544488i	0.325898	−	0.945405i	$-0.394333\pi$
$193$	4.28991	+	0.756427i	0.308795	+	0.0544488i	−0.0171035	+	0.999854i	$0.505444\pi$
$194$	5.32996	+	6.35200i	0.382669	+	0.456047i
$195$	−0.997799	−	2.58117i	−0.0714539	−	0.184841i
$196$	−0.858945	−	4.87132i	−0.0613532	−	0.347951i
$197$	−5.69700	+	3.28916i	−0.405894	+	0.234343i	−0.689024	−	0.724738i	$-0.741961\pi$
$197$	−5.69700	+	3.28916i	−0.405894	+	0.234343i	0.283130	+	0.959082i	$0.408627\pi$
$198$	0.172390	+	4.34905i	0.0122512	+	0.309074i
$199$	10.2412	+	3.72750i	0.725981	+	0.264235i	0.678463	−	0.734635i	$-0.262647\pi$
$199$	10.2412	+	3.72750i	0.725981	+	0.264235i	0.0475182	+	0.998870i	$0.484869\pi$
$200$	−4.43066	−	1.61263i	−0.313295	−	0.114030i
$201$	−8.30618	−	13.7503i	−0.585873	−	0.969873i
$202$	−2.72779	+	1.57489i	−0.191926	+	0.110809i
$203$	1.31829	+	7.47637i	0.0925255	+	0.524738i
$204$	8.95533	−	3.46185i	0.626998	−	0.242378i
$205$	2.71413	+	3.23457i	0.189563	+	0.225912i
$206$	10.0688	+	1.77541i	0.701529	+	0.123698i
$207$	1.13224	−	1.46336i	0.0786962	−	0.101711i
$208$		−	2.99284i		−	0.207516i
$209$	−5.57803	−	2.97966i	−0.385841	−	0.206107i
$210$	0.639655	−	1.16041i	0.0441404	−	0.0800757i
$211$	−2.58901	−	7.11324i	−0.178235	−	0.489695i	0.818116	−	0.575054i	$-0.195019\pi$
$211$	−2.58901	−	7.11324i	−0.178235	−	0.489695i	−0.996350	+	0.0853581i	$0.972797\pi$
$212$	−0.320617	+	1.81831i	−0.0220201	+	0.124882i
$213$	−21.2836	+	4.18917i	−1.45833	+	0.287037i
$214$	−8.90098	−	7.46881i	−0.608459	−	0.510558i
$215$	3.35432	−	0.591458i	0.228763	−	0.0403371i
$216$	4.33775	−	2.86075i	0.295147	−	0.194650i
$217$	6.14192	+	3.54604i	0.416940	+	0.240721i
$218$	0.0109159	−	0.0299912i	0.000739318	−	0.00203126i
$219$	18.4131	+	21.0814i	1.24424	+	1.42455i
$220$	0.387256	−	0.670747i	0.0261088	−	0.0452218i
$221$	8.29501	+	14.3674i	0.557983	+	0.966454i
$222$	−10.5205	−	3.59481i	−0.706092	−	0.241268i
$223$	−7.40150	+	8.82076i	−0.495641	+	0.590682i	−0.954643	−	0.297753i	$-0.903763\pi$
$223$	−7.40150	+	8.82076i	−0.495641	+	0.590682i	0.459002	+	0.888435i	$0.348207\pi$
$224$	1.09775	−	0.921124i	0.0733467	−	0.0615452i
$225$	13.0899	−	5.36055i	0.872662	−	0.357370i
$226$	−9.72349	+	3.53906i	−0.646797	+	0.235415i
$227$	1.54291			0.102407			0.0512033	−	0.998688i	$-0.483694\pi$
$227$	1.54291			0.102407			0.0512033	+	0.998688i	$0.483694\pi$
$228$	0.398399	+	7.53932i	0.0263846	+	0.499303i
$229$	−8.17334			−0.540110			−0.270055	−	0.962845i	$-0.587042\pi$
$229$	−8.17334			−0.540110			−0.270055	+	0.962845i	$0.587042\pi$
$230$	−0.309391	+	0.112609i	−0.0204006	+	0.00742522i
$231$	−2.80385	−	2.25960i	−0.184480	−	0.148671i
$232$	4.05828	−	3.40531i	0.266439	−	0.223569i
$233$	5.39612	−	6.43084i	0.353511	−	0.421298i	−0.559757	−	0.828657i	$-0.689106\pi$
$233$	5.39612	−	6.43084i	0.353511	−	0.421298i	0.913268	+	0.407358i	$0.133550\pi$
$234$	6.03917	+	6.64396i	0.394793	+	0.434329i
$235$	−3.41344	−	5.91225i	−0.222668	−	0.385673i
$236$	−0.934613	+	1.61880i	−0.0608381	+	0.105375i
$237$	−10.4368	+	9.11581i	−0.677942	+	0.592135i
$238$	−2.71685	+	7.46448i	−0.176107	+	0.483851i
$239$	−7.60840	−	4.39271i	−0.492147	−	0.284141i	0.233318	−	0.972401i	$-0.425042\pi$
$239$	−7.60840	−	4.39271i	−0.492147	−	0.284141i	−0.725465	+	0.688260i	$0.758375\pi$
$240$	−0.924463	+	0.0183150i	−0.0596739	+	0.00118223i
$241$	−13.2349	+	2.33367i	−0.852536	+	0.150325i	−0.582806	−	0.812611i	$-0.698045\pi$
$241$	−13.2349	+	2.33367i	−0.852536	+	0.150325i	−0.269730	+	0.962936i	$0.586934\pi$
$242$	6.81405	+	5.71767i	0.438024	+	0.367546i
$243$	−3.85697	+	15.1038i	−0.247425	+	0.968907i
$244$	2.04609	−	11.6039i	0.130987	−	0.742865i
$245$	−0.903153	−	2.48139i	−0.0577003	−	0.158530i
$246$	−11.9976	−	6.61347i	−0.764938	−	0.421660i
$247$	−12.7656	+	2.68778i	−0.812256	+	0.171020i
$248$		−	4.94906i		−	0.314265i
$249$	1.32418	−	8.48990i	0.0839162	−	0.538026i
$250$	−5.10751	−	0.900591i	−0.323027	−	0.0569584i
$251$	5.05003	+	6.01839i	0.318755	+	0.379877i	0.901501	−	0.432777i	$-0.142466\pi$
$251$	5.05003	+	6.01839i	0.318755	+	0.379877i	−0.582746	+	0.812654i	$0.698022\pi$
$252$	−0.578248	+	4.25998i	−0.0364262	+	0.268353i
$253$	0.155379	+	0.881197i	0.00976858	+	0.0554004i
$254$	0.679010	−	0.392026i	0.0426049	−	0.0245979i
$255$	4.38720	−	2.65018i	0.274737	−	0.165961i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−11.5445	−	4.20184i	−0.720123	−	0.262103i	−0.0441451	−	0.999025i	$-0.514056\pi$
$257$	−11.5445	−	4.20184i	−0.720123	−	0.262103i	−0.675978	+	0.736922i	$0.736279\pi$
$258$	−9.45909	+	5.71396i	−0.588897	+	0.355736i
$259$	7.96595	−	4.59914i	0.494980	−	0.285777i
$260$	−0.277439	−	1.57344i	−0.0172061	−	0.0975804i
$261$	−2.13773	+	15.7487i	−0.132322	+	0.974821i
$262$	−7.40427	−	8.82407i	−0.457438	−	0.545153i
$263$	−23.4707	−	4.13852i	−1.44727	−	0.255192i	−0.605849	−	0.795579i	$-0.707167\pi$
$263$	−23.4707	−	4.13852i	−1.44727	−	0.255192i	−0.841416	+	0.540387i	$0.818278\pi$
$264$	−0.387256	+	2.48288i	−0.0238340	+	0.152811i
$265$			0.985668i			0.0605491i
$266$	−4.91481	−	3.85510i	−0.301346	−	0.236371i
$267$	−7.26877	−	4.00679i	−0.444842	−	0.245212i
$268$	−3.17216	−	8.71543i	−0.193770	−	0.532380i
$269$	−3.30229	+	18.7282i	−0.201344	+	1.14188i	0.701745	+	0.712428i	$0.252404\pi$
$269$	−3.30229	+	18.7282i	−0.201344	+	1.14188i	−0.903090	+	0.429452i	$0.858707\pi$
$270$	2.01531	−	1.90611i	0.122648	−	0.116002i
$271$	4.13554	+	3.47013i	0.251216	+	0.210795i	0.759696	−	0.650279i	$-0.225348\pi$
$271$	4.13554	+	3.47013i	0.251216	+	0.210795i	−0.508480	+	0.861074i	$0.669792\pi$
$272$	5.45902	−	0.962573i	0.331002	−	0.0583645i
$273$	−7.42693	+	0.147138i	−0.449499	+	0.00890522i
$274$	11.7295	+	6.77203i	0.708605	+	0.409113i
$275$	−2.33964	+	6.42810i	−0.141085	+	0.387629i
$276$	0.804557	−	0.702725i	0.0484286	−	0.0422990i
$277$	0.0466956	−	0.0808791i	0.00280567	−	0.00485956i	−0.864619	−	0.502428i	$-0.832440\pi$
$277$	0.0466956	−	0.0808791i	0.00280567	−	0.00485956i	0.867425	+	0.497568i	$0.165774\pi$
$278$	3.61811	+	6.26675i	0.217000	+	0.375855i
$279$	9.98657	+	10.9867i	0.597880	+	0.657755i
$280$	0.491736	−	0.586029i	0.0293869	−	0.0350219i
$281$	7.81505	−	6.55760i	0.466207	−	0.391194i	−0.379202	−	0.925314i	$-0.623801\pi$
$281$	7.81505	−	6.55760i	0.466207	−	0.391194i	0.845409	+	0.534120i	$0.179357\pi$
$282$	17.2464	+	13.8987i	1.02701	+	0.827655i
$283$	18.1732	−	6.61449i	1.08028	−	0.393190i	0.260269	−	0.965536i	$-0.416189\pi$
$283$	18.1732	−	6.61449i	1.08028	−	0.393190i	0.820013	+	0.572346i	$0.193966\pi$
$284$	−12.5239			−0.743155
$285$	0.908354	+	3.92674i	0.0538063	+	0.232600i
$286$	−4.34208			−0.256752
$287$	10.6509	−	3.87660i	0.628701	−	0.228828i
$288$	2.77623	−	1.13691i	0.163591	−	0.0669932i
$289$	−10.5158	+	8.82384i	−0.618579	+	0.519049i
$290$	1.81790	−	2.16649i	0.106751	−	0.127221i
$291$	−13.5906	−	4.64383i	−0.796694	−	0.272226i
$292$	8.08015	+	13.9952i	0.472855	+	0.819009i
$293$	8.09268	−	14.0169i	0.472780	−	0.818878i	−0.526735	−	0.850030i	$-0.676584\pi$
$293$	8.09268	−	14.0169i	0.472780	−	0.818878i	0.999515	+	0.0311512i	$0.00991734\pi$
$294$	5.63602	+	6.45274i	0.328700	+	0.376332i
$295$	−0.341293	+	0.937695i	−0.0198709	+	0.0545947i
$296$	−5.55887	−	3.20942i	−0.323103	−	0.186544i
$297$	−4.15044	−	6.29331i	−0.240833	−	0.365175i
$298$	19.4195	−	3.42419i	1.12494	−	0.198358i
$299$	1.41399	+	1.18647i	0.0817729	+	0.0686156i
$300$	8.01290	−	1.57715i	0.462625	−	0.0910566i
$301$	1.58767	−	9.00413i	0.0915118	−	0.518989i
$302$	1.44702	+	3.97564i	0.0832664	+	0.228772i
$303$	2.63367	−	4.77777i	0.151300	−	0.274476i
$304$	−0.614935	+	4.31530i	−0.0352689	+	0.247500i
$305$		−	6.29025i		−	0.360179i
$306$	−10.1764	+	13.1525i	−0.581747	+	0.751877i
$307$	17.5661	+	3.09738i	1.00255	+	0.176777i	0.650745	−	0.759296i	$-0.274457\pi$
$307$	17.5661	+	3.09738i	1.00255	+	0.176777i	0.351806	+	0.936073i	$0.385568\pi$
$308$	−1.33639	−	1.59264i	−0.0761477	−	0.0907493i
$309$	−16.5176	+	6.38518i	−0.939651	+	0.363240i
$310$	−0.458783	−	2.60189i	−0.0260571	−	0.147777i
$311$	28.3493	−	16.3675i	1.60754	−	0.928114i	0.617622	−	0.786475i	$-0.288096\pi$
$311$	28.3493	−	16.3675i	1.60754	−	0.928114i	0.989918	−	0.141639i	$-0.0452373\pi$
$312$	2.68029	+	4.43704i	0.151741	+	0.251198i
$313$	−24.8285	−	9.03684i	−1.40339	−	0.510792i	−0.474208	−	0.880413i	$-0.657265\pi$
$313$	−24.8285	−	9.03684i	−1.40339	−	0.510792i	−0.929183	+	0.369621i	$0.879488\pi$
$314$	−9.54950	−	3.47573i	−0.538909	−	0.196147i
$315$	0.0908997	+	2.29322i	0.00512162	+	0.129208i
$316$	−6.92864	+	4.00025i	−0.389767	+	0.225032i
$317$	−2.32840	−	13.2050i	−0.130776	−	0.741669i	−0.977708	−	0.209968i	$-0.932664\pi$
$317$	−2.32840	−	13.2050i	−0.130776	−	0.741669i	0.846932	−	0.531701i	$-0.178447\pi$
$318$	−1.15309	−	2.98287i	−0.0646619	−	0.167271i
$319$	−4.94049	−	5.88785i	−0.276614	−	0.329656i
$320$	−0.525734	−	0.0927010i	−0.0293894	−	0.00518214i
$321$	19.8850	+	3.10148i	1.10987	+	0.173107i
$322$			0.883809i			0.0492527i
$323$	−9.00833	−	22.4203i	−0.501237	−	1.24750i
$324$	−3.86895	+	8.12596i	−0.214942	+	0.451442i
$325$	4.82634	+	13.2603i	0.267717	+	0.735547i
$326$	1.80669	−	10.2463i	0.100063	−	0.567488i
$327$	0.0106757	+	0.0542394i	0.000590369	+	0.00299945i
$328$	−6.05902	−	5.08412i	−0.334554	−	0.280724i
$329$	−18.0472	+	3.18221i	−0.994975	+	0.175441i
$330$	0.0265718	+	1.34123i	0.00146273	+	0.0738324i
$331$	21.6450	+	12.4967i	1.18971	+	0.686882i	0.958242	−	0.285959i	$-0.0923121\pi$
$331$	21.6450	+	12.4967i	1.18971	+	0.686882i	0.231473	+	0.972841i	$0.425645\pi$
$332$	1.69673	−	4.66173i	0.0931202	−	0.255846i
$333$	18.8166	−	4.09234i	1.03114	−	0.224259i
$334$	11.8965	−	20.6054i	0.650948	−	1.12748i
$335$	−2.47564	−	4.28793i	−0.135259	−	0.234275i
$336$	−0.802548	+	2.34873i	−0.0437826	+	0.128133i
$337$	10.7174	−	12.7725i	0.583815	−	0.695764i	−0.390589	−	0.920565i	$-0.627729\pi$
$337$	10.7174	−	12.7725i	0.583815	−	0.695764i	0.974405	+	0.224801i	$0.0721732\pi$
$338$	3.09705	−	2.59873i	0.168457	−	0.141352i
$339$	11.2461	−	13.9549i	0.610805	−	0.757925i
$340$	2.78076	−	1.01211i	0.150808	−	0.0548896i
$341$	−7.18020			−0.388830
$342$	−7.34261	−	10.8206i	−0.397043	−	0.585113i
$343$	−17.1195			−0.924364
$344$	−5.99550	+	2.18218i	−0.323256	+	0.117655i
$345$	0.357839	−	0.444029i	0.0192654	−	0.0239057i
$346$	−19.1928	+	16.1047i	−1.03181	+	0.865793i
$347$	23.0175	−	27.4312i	1.23564	−	1.47258i	0.406399	−	0.913696i	$-0.366784\pi$
$347$	23.0175	−	27.4312i	1.23564	−	1.47258i	0.829244	−	0.558886i	$-0.188771\pi$
$348$	−2.96694	+	8.68301i	−0.159045	+	0.465458i
$349$	9.77902	+	16.9378i	0.523459	+	0.906657i	0.999627	+	0.0273031i	$0.00869193\pi$
$349$	9.77902	+	16.9378i	0.523459	+	0.906657i	−0.476168	+	0.879354i	$0.657975\pi$
$350$	−3.37834	+	5.85146i	−0.180580	+	0.312774i
$351$	−14.9035	−	4.44154i	−0.795490	−	0.237072i
$352$	−0.496210	+	1.36333i	−0.0264481	+	0.0726656i
$353$	27.9356	+	16.1286i	1.48686	+	0.858441i	0.999888	−	0.0149745i	$-0.00476672\pi$
$353$	27.9356	+	16.1286i	1.48686	+	0.858441i	0.486976	+	0.873416i	$0.338100\pi$
$354$	−0.0641289	−	3.23696i	−0.00340841	−	0.172042i
$355$	−6.58422	+	1.16098i	−0.349454	+	0.0616182i
$356$	−3.67088	−	3.08023i	−0.194556	−	0.163252i
$357$	−2.65707	−	13.4996i	−0.140627	−	0.714475i
$358$	2.69909	−	15.3073i	0.142651	−	0.809017i
$359$	−5.99057	−	16.4590i	−0.316170	−	0.868671i	−0.991377	−	0.131042i	$-0.958168\pi$
$359$	−5.99057	−	16.4590i	−0.316170	−	0.868671i	0.675206	−	0.737629i	$-0.264055\pi$
$360$	1.35416	−	0.855072i	0.0713706	−	0.0450662i
$361$	18.9587	−	1.25252i	0.997825	−	0.0659220i
$362$			20.9656i			1.10193i
$363$	−15.2227	−	2.37430i	−0.798987	−	0.124619i
$364$	−4.22363	−	0.744740i	−0.221378	−	0.0390350i
$365$	5.54538	+	6.60873i	0.290258	+	0.345917i
$366$	7.35866	+	19.0358i	0.384644	+	0.995019i
$367$	3.59236	+	20.3733i	0.187520	+	1.06348i	0.922675	+	0.385578i	$0.125998\pi$
$367$	3.59236	+	20.3733i	0.187520	+	1.06348i	−0.735155	+	0.677899i	$0.762891\pi$
$368$	0.534119	−	0.308374i	0.0278429	−	0.0160751i
$369$	23.7099	−	0.939823i	1.23429	−	0.0489252i
$370$	−3.22000	−	1.17198i	−0.167400	−	0.0609286i
$371$	2.48630	+	0.904938i	0.129082	+	0.0469820i
$372$	4.43221	+	7.33724i	0.229800	+	0.380418i
$373$	2.46819	−	1.42501i	0.127798	−	0.0737843i	−0.434738	−	0.900557i	$-0.643159\pi$
$373$	2.46819	−	1.42501i	0.127798	−	0.0737843i	0.562536	+	0.826773i	$0.309826\pi$
$374$	−1.39652	−	7.92007i	−0.0722124	−	0.409537i
$375$	8.37868	−	3.23894i	0.432673	−	0.167258i
$376$	8.22007	+	9.79630i	0.423918	+	0.505205i
$377$	−15.6143	−	2.75323i	−0.804179	−	0.141798i
$378$	−2.95781	−	6.83350i	−0.152133	−	0.351477i
$379$		−	15.1648i		−	0.778963i	−0.921034	−	0.389482i	$-0.872654\pi$
$379$		−	15.1648i		−	0.778963i	0.921034	−	0.389482i	$-0.127346\pi$
$380$	0.0767411	+	2.32571i	0.00393673	+	0.119306i
$381$	−0.655581	+	1.18930i	−0.0335864	+	0.0609296i
$382$	0.545173	+	1.49785i	0.0278935	+	0.0766368i
$383$	0.366876	−	2.08066i	0.0187465	−	0.106317i	−0.973999	−	0.226553i	$-0.927254\pi$
$383$	0.366876	−	2.08066i	0.0187465	−	0.106317i	0.992745	+	0.120237i	$0.0383653\pi$
$384$	1.69944	−	0.334495i	0.0867244	−	0.0170696i
$385$	−0.850223	−	0.713422i	−0.0433314	−	0.0363594i
$386$	−4.28991	+	0.756427i	−0.218351	+	0.0385011i
$387$	8.90635	−	16.9425i	0.452735	−	0.861235i
$388$	−7.18104	−	4.14597i	−0.364562	−	0.210480i
$389$	1.43738	−	3.94918i	0.0728783	−	0.200231i	−0.897905	−	0.440189i	$-0.854911\pi$
$389$	1.43738	−	3.94918i	0.0728783	−	0.200231i	0.970783	+	0.239958i	$0.0771336\pi$
$390$	1.82044	+	2.08424i	0.0921813	+	0.105539i
$391$	−1.70939	+	2.96075i	−0.0864475	+	0.149731i
$392$	2.47323	+	4.28377i	0.124917	+	0.216363i
$393$	18.8798	+	6.45112i	0.952358	+	0.325416i
$394$	4.22847	−	5.03929i	0.213027	−	0.253876i
$395$	−3.27179	+	2.74536i	−0.164622	+	0.138134i
$396$	−1.64946	−	4.02781i	−0.0828883	−	0.202405i
$397$	0.284948	−	0.103713i	0.0143011	−	0.00520518i	−0.334860	−	0.942268i	$-0.608689\pi$
$397$	0.284948	−	0.103713i	0.0143011	−	0.00520518i	0.349161	+	0.937063i	$0.386467\pi$
$398$	−10.8985			−0.546291
$399$	10.7390	+	1.31385i	0.537620	+	0.0657747i
$400$	4.71501			0.235751
$401$	11.8640	−	4.31814i	0.592460	−	0.215638i	−0.0283512	−	0.999598i	$-0.509026\pi$
$401$	11.8640	−	4.31814i	0.592460	−	0.215638i	0.620811	+	0.783960i	$0.286803\pi$
$402$	12.5081	+	10.0802i	0.623850	+	0.502755i
$403$	−11.3464	+	9.52080i	−0.565207	+	0.474265i
$404$	2.02464	−	2.41287i	0.100729	−	0.120045i
$405$	−1.28075	+	4.63075i	−0.0636410	+	0.230104i
$406$	−3.79585	−	6.57461i	−0.188385	−	0.326292i
$407$	−4.65629	+	8.06493i	−0.230804	+	0.399764i
$408$	−7.23123	+	6.31598i	−0.357999	+	0.312688i
$409$	−6.63505	+	18.2296i	−0.328082	+	0.901398i	0.660515	+	0.750813i	$0.270338\pi$
$409$	−6.63505	+	18.2296i	−0.328082	+	0.901398i	−0.988597	+	0.150585i	$0.951884\pi$
$410$	−3.65673	−	2.11122i	−0.180593	−	0.104266i
$411$	−23.4544	+	0.464666i	−1.15692	+	0.0229203i
$412$	−10.0688	+	1.77541i	−0.496056	+	0.0874680i
$413$	2.05195	+	1.72179i	0.100970	+	0.0847237i
$414$	−0.563460	+	1.76236i	−0.0276926	+	0.0866153i
$415$	0.459881	−	2.60812i	0.0225747	−	0.128027i
$416$	1.02361	+	2.81235i	0.0501867	+	0.137887i
$417$	−10.9763	−	6.05052i	−0.537513	−	0.296295i
$418$	6.26074	+	0.892161i	0.306223	+	0.0436370i
$419$			15.4879i			0.756633i	0.925676	+	0.378316i	$0.123497\pi$
$419$			15.4879i			0.756633i	−0.925676	+	0.378316i	$0.876503\pi$
$420$	−0.204197	+	1.30920i	−0.00996379	+	0.0638825i
$421$	13.7766	+	2.42919i	0.671431	+	0.118391i	0.498962	−	0.866624i	$-0.333715\pi$
$421$	13.7766	+	2.42919i	0.671431	+	0.118391i	0.172468	+	0.985015i	$0.444826\pi$
$422$	4.86574	+	5.79876i	0.236861	+	0.282279i
$423$	−38.0158	−	5.16026i	−1.84839	−	0.250901i
$424$	−0.320617	−	1.81831i	−0.0155705	−	0.0883049i
$425$	−22.6348	+	13.0682i	−1.09795	+	0.633901i
$426$	18.5673	−	11.2160i	0.899588	−	0.543415i
$427$	−15.8668	−	5.77505i	−0.767849	−	0.279474i
$428$	10.9187	+	3.97407i	0.527774	+	0.192094i
$429$	6.43736	−	3.88862i	0.310798	−	0.187744i
$430$	−2.94974	+	1.70304i	−0.142249	+	0.0821277i
$431$	4.86245	+	27.5763i	0.234216	+	1.32831i	0.844258	+	0.535936i	$0.180041\pi$
$431$	4.86245	+	27.5763i	0.234216	+	1.32831i	−0.610042	+	0.792369i	$0.708848\pi$
$432$	−3.09772	+	4.17183i	−0.149039	+	0.200717i
$433$	−3.78152	−	4.50664i	−0.181728	−	0.216575i	0.667488	−	0.744621i	$-0.267370\pi$
$433$	−3.78152	−	4.50664i	−0.181728	−	0.216575i	−0.849216	+	0.528045i	$0.822925\pi$
$434$	−6.98433	−	1.23153i	−0.335259	−	0.0591151i
$435$	−0.754896	+	4.83999i	−0.0361945	+	0.232060i
$436$			0.0319160i			0.00152850i
$437$	−1.79501	−	2.00128i	−0.0858669	−	0.0957342i
$438$	−24.5129	−	13.5123i	−1.17127	−	0.645645i
$439$	7.65568	+	21.0338i	0.365386	+	1.00389i	0.977094	+	0.212806i	$0.0682602\pi$
$439$	7.65568	+	21.0338i	0.365386	+	1.00389i	−0.611709	+	0.791083i	$0.709518\pi$
$440$	−0.134493	+	0.762746i	−0.00641169	+	0.0363625i
$441$	−14.1346	−	4.51909i	−0.673074	−	0.215195i
$442$	−12.7087	−	10.6639i	−0.604491	−	0.507228i
$443$	−14.6859	+	2.58952i	−0.697748	+	0.123032i	−0.511261	−	0.859426i	$-0.670821\pi$
$443$	−14.6859	+	2.58952i	−0.697748	+	0.123032i	−0.186487	+	0.982457i	$0.559710\pi$
$444$	11.1156	−	0.220216i	0.527521	−	0.0104510i
$445$	−2.21544	−	1.27909i	−0.105022	−	0.0606345i
$446$	3.93825	−	10.8203i	0.186482	−	0.512354i
$447$	−25.7239	+	22.4680i	−1.21670	+	1.06270i
$448$	−0.716507	+	1.24103i	−0.0338518	+	0.0586330i
$449$	2.44541	+	4.23557i	0.115406	+	0.199889i	0.917942	−	0.396715i	$-0.129850\pi$
$449$	2.44541	+	4.23557i	0.115406	+	0.199889i	−0.802536	+	0.596604i	$0.796516\pi$
$450$	−10.4671	+	9.51429i	−0.493424	+	0.448508i
$451$	−7.37616	+	8.79056i	−0.347330	+	0.413931i
$452$	7.92666	−	6.65126i	0.372839	−	0.312849i
$453$	−5.70573	−	4.59820i	−0.268078	−	0.216042i
$454$	−1.44986	+	0.527706i	−0.0680453	+	0.0247665i
$455$	−2.28954			−0.107335
$456$	−2.95297	−	6.94838i	−0.138286	−	0.325388i
$457$	−30.3578			−1.42008			−0.710039	−	0.704162i	$-0.751323\pi$
$457$	−30.3578			−1.42008			−0.710039	+	0.704162i	$0.751323\pi$
$458$	7.68043	−	2.79545i	0.358883	−	0.130623i
$459$	3.30815	−	28.6129i	0.154411	−	1.33554i
$460$	0.252218	−	0.211636i	0.0117597	−	0.00986757i
$461$	−16.0576	+	19.1367i	−0.747879	+	0.891287i	−0.997017	−	0.0771808i	$-0.975408\pi$
$461$	−16.0576	+	19.1367i	−0.747879	+	0.891287i	0.249138	+	0.968468i	$0.419853\pi$
$462$	3.40758	+	1.16435i	0.158535	+	0.0541706i
$463$	−2.94958	−	5.10883i	−0.137079	−	0.237427i	0.789311	−	0.613994i	$-0.210438\pi$
$463$	−2.94958	−	5.10883i	−0.137079	−	0.237427i	−0.926390	+	0.376566i	$0.877105\pi$
$464$	−2.64886	+	4.58796i	−0.122970	+	0.212990i
$465$	3.01033	+	3.44656i	0.139601	+	0.159830i
$466$	−2.87121	+	7.88859i	−0.133006	+	0.365432i
$467$	−4.76849	−	2.75309i	−0.220659	−	0.127398i	0.385596	−	0.922668i	$-0.373996\pi$
$467$	−4.76849	−	2.75309i	−0.220659	−	0.127398i	−0.606256	+	0.795270i	$0.707329\pi$
$468$	−7.94733	−	4.17777i	−0.367366	−	0.193117i
$469$	−13.0890	+	2.30794i	−0.604392	+	0.106571i
$470$	5.22969	+	4.38823i	0.241228	+	0.202414i
$471$	17.2704	−	3.39926i	0.795777	−	0.156630i
$472$	0.324588	−	1.84083i	0.0149404	−	0.0847310i
$473$	3.16596	+	8.69840i	0.145571	+	0.399953i
$474$	6.68958	−	12.1356i	0.307262	−	0.557409i
$475$	−4.23442	−	20.1113i	−0.194288	−	0.922770i
$476$		−	7.94354i		−	0.364091i
$477$	4.38087	+	3.38960i	0.200586	+	0.155199i
$478$	8.65196	+	1.52557i	0.395731	+	0.0697781i
$479$	21.4896	+	25.6103i	0.981884	+	1.17016i	0.985415	+	0.170170i	$0.0544317\pi$
$479$	21.4896	+	25.6103i	0.981884	+	1.17016i	−0.00353081	+	0.999994i	$0.501124\pi$
$480$	0.862447	−	0.333396i	0.0393652	−	0.0152174i
$481$	3.33588	+	18.9187i	0.152103	+	0.862618i
$482$	11.6386	−	6.71954i	0.530123	−	0.306067i
$483$	−0.791510	−	1.31029i	−0.0360149	−	0.0596204i
$484$	−8.35867	−	3.04231i	−0.379940	−	0.138287i
$485$	−4.15965	−	1.51399i	−0.188880	−	0.0687467i
$486$	−1.54143	−	15.5121i	−0.0699205	−	0.703641i
$487$	21.9456	−	12.6703i	0.994448	−	0.574145i	0.0878470	−	0.996134i	$-0.472001\pi$
$487$	21.9456	−	12.6703i	0.994448	−	0.574145i	0.906601	+	0.421989i	$0.138668\pi$
$488$	2.04609	+	11.6039i	0.0926219	+	0.525285i
$489$	6.49770	+	16.8086i	0.293836	+	0.760112i
$490$	1.69737	+	2.02285i	0.0766794	+	0.0913830i
$491$	−7.76474	−	1.36913i	−0.350418	−	0.0617881i	−0.00433112	−	0.999991i	$-0.501379\pi$
$491$	−7.76474	−	1.36913i	−0.350418	−	0.0617881i	−0.346087	+	0.938202i	$0.612490\pi$
$492$	13.5360	+	2.11122i	0.610249	+	0.0951810i
$493$		−	29.3665i		−	1.32260i
$494$	11.0765	−	6.89178i	0.498354	−	0.310076i
$495$	−1.24056	−	1.96465i	−0.0557589	−	0.0883044i
$496$	1.69268	+	4.65059i	0.0760035	+	0.208818i
$497$	−3.11645	+	17.6742i	−0.139792	+	0.792798i
$498$	1.65940	+	8.43079i	0.0743594	+	0.377793i
$499$	−9.89069	−	8.29927i	−0.442768	−	0.371526i	0.393976	−	0.919121i	$-0.371099\pi$
$499$	−9.89069	−	8.29927i	−0.442768	−	0.371526i	−0.836744	+	0.547594i	$0.815544\pi$
$500$	5.10751	−	0.900591i	0.228415	−	0.0402757i
$501$	0.816285	+	41.2026i	0.0364689	+	1.84080i
$502$	−6.80388	−	3.92822i	−0.303672	−	0.175325i
$503$	2.85952	−	7.85647i	0.127500	−	0.350303i	−0.859475	−	0.511178i	$-0.829209\pi$
$503$	2.85952	−	7.85647i	0.127500	−	0.350303i	0.986975	+	0.160875i	$0.0514316\pi$
$504$	−0.913623	−	4.20084i	−0.0406960	−	0.187120i
$505$	0.840744	−	1.45621i	0.0374126	−	0.0648006i
$506$	−0.447396	−	0.774912i	−0.0198892	−	0.0344490i
$507$	−2.26420	+	6.62637i	−0.100556	+	0.294287i
$508$	−0.503979	+	0.600619i	−0.0223605	+	0.0266482i
$509$	5.11088	−	4.28853i	0.226536	−	0.190086i	−0.522454	−	0.852667i	$-0.674984\pi$
$509$	5.11088	−	4.28853i	0.226536	−	0.190086i	0.748990	+	0.662581i	$0.230539\pi$
$510$	−3.21620	+	3.99087i	−0.142416	+	0.176719i
$511$	21.7614	−	7.92049i	0.962666	−	0.350382i
$512$	1.00000			0.0441942
$513$	20.5764	+	9.46635i	0.908470	+	0.417950i
$514$	12.2853			0.541884
$515$	−5.12894	+	1.86678i	−0.226008	+	0.0822603i
$516$	6.93435	−	8.60457i	0.305268	−	0.378795i
$517$	14.2127	−	11.9259i	0.625073	−	0.524499i
$518$	−5.91254	+	7.04629i	−0.259782	+	0.309596i
$519$	14.0315	−	41.0645i	0.615915	−	1.80253i
$520$	0.798855	+	1.38366i	0.0350321	+	0.0606774i
$521$	7.75609	−	13.4339i	0.339800	−	0.588552i	−0.644595	−	0.764525i	$-0.722974\pi$
$521$	7.75609	−	13.4339i	0.339800	−	0.588552i	0.984395	+	0.175973i	$0.0563071\pi$
$522$	−3.37757	−	15.5301i	−0.147832	−	0.679734i
$523$	−7.60779	+	20.9022i	−0.332666	+	0.913991i	0.654750	+	0.755845i	$0.272774\pi$
$523$	−7.60779	+	20.9022i	−0.332666	+	0.913991i	−0.987416	+	0.158146i	$0.949448\pi$
$524$	9.97575	+	5.75950i	0.435793	+	0.251605i
$525$	−0.231806	−	11.7006i	−0.0101169	−	0.510657i
$526$	23.4707	−	4.13852i	1.02337	−	0.180448i
$527$	−21.0155	−	17.6341i	−0.915450	−	0.768154i
$528$	−0.485293	−	2.46559i	−0.0211197	−	0.107301i
$529$	3.92786	−	22.2760i	0.170776	−	0.968521i
$530$	−0.337118	−	0.926225i	−0.0146435	−	0.0402326i
$531$	2.99399	+	4.74153i	0.129928	+	0.205765i
$532$	5.93693	+	1.94165i	0.257398	+	0.0841810i
$533$			23.6718i			1.02534i
$534$	8.20082	+	1.27909i	0.354884	+	0.0553515i
$535$	6.10871	+	1.07713i	0.264103	+	0.0465684i
$536$	5.96171	+	7.10489i	0.257507	+	0.306884i
$537$	9.70718	+	25.1111i	0.418896	+	1.08362i
$538$	−3.30229	−	18.7282i	−0.142372	−	0.807431i
$539$	6.21498	−	3.58822i	0.267698	−	0.154556i
$540$	−1.24184	+	2.48043i	−0.0534404	+	0.106741i
$541$	7.24376	+	2.63651i	0.311433	+	0.113352i	0.493008	−	0.870025i	$-0.335897\pi$
$541$	7.24376	+	2.63651i	0.311433	+	0.113352i	−0.181575	+	0.983377i	$0.558119\pi$
$542$	−5.07299	−	1.84642i	−0.217904	−	0.0793104i
$543$	−18.7761	−	31.0825i	−0.805758	−	1.33388i
$544$	−4.80058	+	2.77162i	−0.205823	+	0.118832i
$545$	0.00295864	+	0.0167793i	0.000126734	+	0.000718746i
$546$	6.92871	−	2.67843i	0.296521	−	0.114626i
$547$	18.1301	+	21.6066i	0.775188	+	0.923833i	0.998705	−	0.0508673i	$-0.0161986\pi$
$547$	18.1301	+	21.6066i	0.775188	+	0.923833i	−0.223518	+	0.974700i	$0.571754\pi$
$548$	−13.3383	−	2.35190i	−0.569784	−	0.100468i
$549$	−27.9575	−	21.6314i	−1.19320	−	0.923207i
$550$		−	6.84064i		−	0.291686i
$551$	21.9482	+	7.17807i	0.935026	+	0.305796i
$552$	−0.515690	+	0.935520i	−0.0219492	+	0.0398184i
$553$	3.92121	+	10.7734i	0.166747	+	0.458133i
$554$	−0.0162172	+	0.0919724i	−0.000689003	+	0.00390753i
$555$	5.82341	−	1.14620i	0.247190	−	0.0486534i
$556$	−5.54326	−	4.65135i	−0.235087	−	0.197261i
$557$	30.7949	−	5.42997i	1.30482	−	0.230075i	0.522333	−	0.852741i	$-0.325062\pi$
$557$	30.7949	−	5.42997i	1.30482	−	0.230075i	0.782487	+	0.622666i	$0.213951\pi$
$558$	−13.1420	−	6.90849i	−0.556344	−	0.292460i
$559$	16.5369	+	9.54757i	0.699435	+	0.403819i
$560$	−0.261648	+	0.718871i	−0.0110566	+	0.0303778i
$561$	9.16337	+	10.4912i	0.386878	+	0.442940i
$562$	−5.10091	+	8.83503i	−0.215169	+	0.372683i
$563$	−4.37942	−	7.58538i	−0.184571	−	0.319686i	0.758861	−	0.651252i	$-0.225756\pi$
$563$	−4.37942	−	7.58538i	−0.184571	−	0.319686i	−0.943432	+	0.331567i	$0.892423\pi$
$564$	−20.9599	−	7.16190i	−0.882572	−	0.301570i
$565$	3.55073	−	4.23160i	0.149380	−	0.178025i
$566$	−14.8149	+	12.4312i	−0.622716	+	0.522521i
$567$	10.5050	+	7.48210i	0.441167	+	0.314219i
$568$	11.7686	−	4.28342i	0.493799	−	0.179728i
$569$	−39.4950			−1.65572			−0.827859	−	0.560936i	$-0.810441\pi$
$569$	−39.4950			−1.65572			−0.827859	+	0.560936i	$0.810441\pi$
$570$	−2.19660	−	3.37925i	−0.0920054	−	0.141541i
$571$	−1.49689			−0.0626431			−0.0313215	−	0.999509i	$-0.509972\pi$
$571$	−1.49689			−0.0626431			−0.0313215	+	0.999509i	$0.509972\pi$
$572$	4.08022	−	1.48508i	0.170603	−	0.0620942i
$573$	−2.14967	−	1.73240i	−0.0898039	−	0.0723722i
$574$	−8.68267	+	7.28562i	−0.362408	+	0.304096i
$575$	−1.86921	+	2.22764i	−0.0779514	+	0.0928988i
$576$	−2.21995	+	2.01787i	−0.0924980	+	0.0840780i
$577$	−5.32793	−	9.22825i	−0.221805	−	0.384177i	0.733551	−	0.679634i	$-0.237861\pi$
$577$	−5.32793	−	9.22825i	−0.221805	−	0.384177i	−0.955356	+	0.295457i	$0.904528\pi$
$578$	6.86373	−	11.8883i	0.285493	−	0.494489i
$579$	5.68259	−	4.96335i	0.236160	−	0.206270i
$580$	−0.967285	+	2.65759i	−0.0401643	+	0.110351i
$581$	−6.15662	−	3.55453i	−0.255420	−	0.147467i
$582$	14.3593	−	0.284478i	0.595210	−	0.0117920i
$583$	−2.63804	+	0.465158i	−0.109257	+	0.0192649i
$584$	−12.3795	−	10.3876i	−0.512268	−	0.429844i
$585$	−4.56546	−	1.45967i	−0.188759	−	0.0603497i
$586$	−2.81056	+	15.9395i	−0.116103	+	0.658454i
$587$	0.0214414	+	0.0589098i	0.000884983	+	0.00243147i	0.940134	−	0.340804i	$-0.110699\pi$
$587$	0.0214414	+	0.0589098i	0.000884983	+	0.00243147i	−0.939249	+	0.343236i	$0.888477\pi$
$588$	−7.50310	−	4.13596i	−0.309423	−	0.170564i
$589$	18.3164	−	11.3965i	0.754714	−	0.469584i
$590$		−	0.997875i		−	0.0410818i
$591$	−1.75590	+	11.2579i	−0.0722280	+	0.463087i
$592$	6.32132	+	1.11462i	0.259804	+	0.0458105i
$593$	10.0616	+	11.9910i	0.413181	+	0.492409i	0.931992	−	0.362479i	$-0.118070\pi$
$593$	10.0616	+	11.9910i	0.413181	+	0.492409i	−0.518811	+	0.854889i	$0.673625\pi$
$594$	6.05258	+	4.49424i	0.248340	+	0.184401i
$595$	−0.736374	−	4.17618i	−0.0301884	−	0.171207i
$596$	−17.0772	+	9.85955i	−0.699511	+	0.403863i
$597$	16.1576	−	9.76032i	0.661285	−	0.399463i
$598$	−1.73451	−	0.631310i	−0.0709294	−	0.0258162i
$599$	−2.10138	−	0.764839i	−0.0858600	−	0.0312505i	0.298733	−	0.954337i	$-0.403436\pi$
$599$	−2.10138	−	0.764839i	−0.0858600	−	0.0312505i	−0.384593	+	0.923086i	$0.625658\pi$
$600$	−6.99025	+	4.22261i	−0.285376	+	0.172387i
$601$	−16.1749	+	9.33861i	−0.659790	+	0.380930i	−0.792197	−	0.610266i	$-0.791063\pi$
$601$	−16.1749	+	9.33861i	−0.659790	+	0.380930i	0.132407	+	0.991195i	$0.457729\pi$
$602$	1.58767	+	9.00413i	0.0647086	+	0.366981i
$603$	−27.5715	−	3.74254i	−1.12280	−	0.152408i
$604$	−2.71950	−	3.24097i	−0.110655	−	0.131873i
$605$	−4.67646	−	0.824586i	−0.190125	−	0.0335242i
$606$	−0.840744	+	5.39040i	−0.0341529	+	0.218970i
$607$		−	43.2872i		−	1.75697i	−0.477766	−	0.878487i	$-0.658553\pi$
$607$		−	43.2872i		−	1.75697i	0.477766	−	0.878487i	$-0.341447\pi$
$608$	−0.898071	−	4.26538i	−0.0364216	−	0.172984i
$609$	11.5155	+	6.34776i	0.466634	+	0.257224i
$610$	2.15139	+	5.91090i	0.0871073	+	0.239325i
$611$	6.64602	−	37.6915i	0.268869	−	1.52483i
$612$	5.06429	−	15.8398i	0.204712	−	0.640287i
$613$	−6.84929	−	5.74724i	−0.276640	−	0.232129i	0.493902	−	0.869518i	$-0.335570\pi$
$613$	−6.84929	−	5.74724i	−0.276640	−	0.232129i	−0.770542	+	0.637389i	$0.780015\pi$
$614$	−17.5661	+	3.09738i	−0.708911	+	0.125000i
$615$	7.31203	−	0.144862i	0.294850	−	0.00584140i
$616$	1.80051	+	1.03952i	0.0725446	+	0.0418836i
$617$	8.89796	−	24.4469i	0.358218	−	0.984197i	−0.621429	−	0.783470i	$-0.713448\pi$
$617$	8.89796	−	24.4469i	0.358218	−	0.984197i	0.979647	−	0.200726i	$-0.0643302\pi$
$618$	13.3376	−	11.6494i	0.536516	−	0.468610i
$619$	−9.72654	+	16.8469i	−0.390943	+	0.677133i	−0.992574	−	0.121641i	$-0.961184\pi$
$619$	−9.72654	+	16.8469i	−0.390943	+	0.677133i	0.601631	+	0.798774i	$0.294518\pi$
$620$	1.32101	+	2.28806i	0.0530531	+	0.0918907i
$621$	−0.742952	−	3.11741i	−0.0298136	−	0.125097i
$622$	−21.0416	+	25.0764i	−0.843692	+	1.00547i
$623$	−5.26042	+	4.41402i	−0.210754	+	0.176844i
$624$	−4.03620	−	3.25274i	−0.161577	−	0.130214i
$625$	−19.5516	+	7.11620i	−0.782064	+	0.284648i
$626$	26.4219			1.05603
$627$	−10.0809	+	4.28423i	−0.402591	+	0.171096i
$628$	10.1624			0.405522
$629$	−33.4353	+	12.1695i	−1.33315	+	0.485228i
$630$	−0.869744	−	2.12383i	−0.0346514	−	0.0846154i
$631$	−11.6007	+	9.73414i	−0.461816	+	0.387510i	−0.843799	−	0.536660i	$-0.819686\pi$
$631$	−11.6007	+	9.73414i	−0.461816	+	0.387510i	0.381982	+	0.924170i	$0.375241\pi$
$632$	5.14263	−	6.12874i	0.204563	−	0.243788i
$633$	−12.4069	−	4.23937i	−0.493130	−	0.168500i
$634$	6.70437	+	11.6123i	0.266265	+	0.461184i
$635$	−0.209281	+	0.362485i	−0.00830506	+	0.0143848i
$636$	2.10375	+	2.40860i	0.0834191	+	0.0955074i
$637$	5.06326	−	13.9112i	0.200614	−	0.551182i
$638$	6.65631	+	3.84302i	0.263526	+	0.152147i
$639$	−17.4823	+	33.2565i	−0.691590	+	1.31561i
$640$	0.525734	−	0.0927010i	0.0207814	−	0.00366433i
$641$	28.6682	+	24.0555i	1.13233	+	0.950135i	0.999161	−	0.0409586i	$-0.0130412\pi$
$641$	28.6682	+	24.0555i	1.13233	+	0.950135i	0.133166	+	0.991094i	$0.457486\pi$
$642$	−19.7465	+	3.88663i	−0.779334	+	0.153393i
$643$	1.81700	−	10.3047i	0.0716554	−	0.406378i	−0.927791	−	0.373101i	$-0.878295\pi$
$643$	1.81700	−	10.3047i	0.0716554	−	0.406378i	0.999446	−	0.0332769i	$-0.0105943\pi$
$644$	−0.302280	−	0.830508i	−0.0119115	−	0.0327266i
$645$	2.84797	−	5.16653i	0.112139	−	0.203432i
$646$	16.1333	+	17.9872i	0.634755	+	0.707697i
$647$			15.2706i			0.600348i	0.953884	+	0.300174i	$0.0970448\pi$
$647$			15.2706i			0.600348i	−0.953884	+	0.300174i	$0.902955\pi$
$648$	0.856379	−	8.95916i	0.0336418	−	0.351949i
$649$	−2.67071	−	0.470919i	−0.104835	−	0.0184852i
$650$	−9.07055	−	10.8099i	−0.355776	−	0.423998i
$651$	11.4575	−	4.42913i	0.449057	−	0.173591i
$652$	1.80669	+	10.2463i	0.0707555	+	0.401275i
$653$	2.32583	−	1.34282i	0.0910168	−	0.0525486i	−0.453801	−	0.891103i	$-0.649932\pi$
$653$	2.32583	−	1.34282i	0.0910168	−	0.0525486i	0.544818	+	0.838555i	$0.316599\pi$
$654$	−0.0285829	−	0.0473171i	−0.00111768	−	0.00185024i
$655$	5.77850	+	2.10320i	0.225785	+	0.0821789i
$656$	7.43249	+	2.70521i	0.290190	+	0.105621i
$657$	48.4429	−	1.92020i	1.88994	−	0.0749142i
$658$	15.8705	−	9.16281i	0.618695	−	0.357203i
$659$	−5.97002	−	33.8577i	−0.232559	−	1.31891i	−0.847694	−	0.530486i	$-0.822009\pi$
$659$	−5.97002	−	33.8577i	−0.232559	−	1.31891i	0.615134	−	0.788422i	$-0.289102\pi$
$660$	−0.483698	−	1.25126i	−0.0188279	−	0.0487051i
$661$	11.2236	+	13.3757i	0.436546	+	0.520256i	0.938799	−	0.344465i	$-0.111940\pi$
$661$	11.2236	+	13.3757i	0.436546	+	0.520256i	−0.502253	+	0.864721i	$0.667495\pi$
$662$	−24.6137	−	4.34007i	−0.956640	−	0.168682i
$663$	28.3915	+	4.42824i	1.10263	+	0.171979i
$664$			4.96091i			0.192521i
$665$	3.30123	+	0.470429i	0.128016	+	0.0182425i
$666$	−16.2822	+	10.2812i	−0.630922	+	0.398389i
$667$	−1.11750	−	3.07031i	−0.0432698	−	0.118883i
$668$	−4.13162	+	23.4316i	−0.159857	+	0.906594i
$669$	3.85160	+	19.5686i	0.148912	+	0.756565i
$670$	3.79290	+	3.18262i	0.146533	+	0.122955i
$671$	16.8352	−	2.96851i	0.649917	−	0.114598i
$672$	−0.0491635	−	2.48157i	−0.00189652	−	0.0957285i
$673$	−38.2505	−	22.0839i	−1.47445	−	0.851273i	−0.474863	−	0.880060i	$-0.657502\pi$
$673$	−38.2505	−	22.0839i	−1.47445	−	0.851273i	−0.999586	+	0.0287864i	$0.990836\pi$
$674$	−5.70262	+	15.6678i	−0.219657	+	0.603502i
$675$	6.99733	−	23.4794i	0.269328	−	0.903723i
$676$	−2.02145	+	3.50126i	−0.0777483	+	0.134664i
$677$	9.28464	+	16.0815i	0.356838	+	0.618061i	0.987431	−	0.158053i	$-0.0505216\pi$
$677$	9.28464	+	16.0815i	0.356838	+	0.618061i	−0.630593	+	0.776114i	$0.717188\pi$
$678$	−5.79504	+	16.9597i	−0.222557	+	0.651333i
$679$	−7.63791	+	9.10251i	−0.293116	+	0.349322i
$680$	−2.26690	+	1.90215i	−0.0869315	+	0.0729442i
$681$	1.67690	−	2.08080i	0.0642589	−	0.0797364i
$682$	6.74718	−	2.45577i	0.258363	−	0.0940364i
$683$	18.9873			0.726527			0.363264	−	0.931686i	$-0.381662\pi$
$683$	18.9873			0.726527			0.363264	+	0.931686i	$0.381662\pi$
$684$	10.6007	+	7.65675i	0.405327	+	0.292763i
$685$	−7.23041			−0.276260
$686$	16.0870	−	5.85520i	0.614206	−	0.223553i
$687$	−8.88312	+	11.0227i	−0.338912	+	0.420544i
$688$	4.88757	−	4.10116i	0.186337	−	0.156355i
$689$	−3.55195	+	4.23305i	−0.135319	+	0.161266i
$690$	−0.184392	+	0.539639i	−0.00701968	+	0.0205437i
$691$	7.53839	+	13.0569i	0.286774	+	0.496707i	0.973038	−	0.230646i	$-0.0740839\pi$
$691$	7.53839	+	13.0569i	0.286774	+	0.496707i	−0.686264	+	0.727352i	$0.740751\pi$
$692$	12.5272	−	21.6978i	0.476213	−	0.824826i
$693$	−6.09467	+	1.32550i	−0.231518	+	0.0503517i
$694$	−12.2473	+	33.6493i	−0.464903	+	1.27731i
$695$	−3.34547	−	1.93151i	−0.126901	−	0.0732662i
$696$	−0.181753	−	9.17411i	−0.00688931	−	0.347744i
$697$	−43.1781	+	7.61346i	−1.63549	+	0.288380i
$698$	−14.9823	−	12.5717i	−0.567089	−	0.475844i
$699$	−2.80804	−	14.2666i	−0.106210	−	0.539613i
$700$	1.17329	−	6.65403i	0.0443460	−	0.251499i
$701$	−4.16179	−	11.4344i	−0.157189	−	0.431872i	0.835951	−	0.548804i	$-0.184917\pi$
$701$	−4.16179	−	11.4344i	−0.157189	−	0.431872i	−0.993140	+	0.116931i	$0.962694\pi$
$702$	15.5238	−	0.923615i	0.585908	−	0.0348596i
$703$	−0.922720	−	27.9638i	−0.0348010	−	1.05468i
$704$		−	1.45082i		−	0.0546799i
$705$	−11.6832	−	1.82224i	−0.440017	−	0.0686297i
$706$	−31.7672	−	5.60142i	−1.19558	−	0.210812i
$707$	−2.90133	−	3.45768i	−0.109116	−	0.130039i
$708$	1.16737	+	3.01981i	0.0438723	+	0.113492i
$709$	−6.71310	−	38.0719i	−0.252116	−	1.42982i	−0.803369	−	0.595481i	$-0.796961\pi$
$709$	−6.71310	−	38.0719i	−0.252116	−	1.42982i	0.551253	−	0.834338i	$-0.314150\pi$
$710$	5.79007	−	3.34290i	0.217297	−	0.125457i
$711$	0.950637	+	23.9827i	0.0356517	+	0.899421i
$712$	4.50300	+	1.63896i	0.168757	+	0.0614225i
$713$	−2.86824	−	1.04395i	−0.107417	−	0.0390964i
$714$	7.11397	+	11.7767i	0.266234	+	0.440732i
$715$	2.00744	−	1.15900i	0.0750740	−	0.0433440i
$716$	2.69909	+	15.3073i	0.100870	+	0.572061i
$717$	−14.1932	+	5.48666i	−0.530056	+	0.204903i
$718$	11.2586	+	13.4175i	0.420167	+	0.500736i
$719$	26.0696	+	4.59678i	0.972233	+	0.171431i	0.637135	−	0.770752i	$-0.280119\pi$
$719$	26.0696	+	4.59678i	0.972233	+	0.171431i	0.335098	+	0.942183i	$0.391231\pi$
$720$	−0.980045	+	1.26666i	−0.0365241	+	0.0472055i
$721$			14.6514i			0.545646i
$722$	−17.3869	+	7.66123i	−0.647075	+	0.285121i
$723$	−11.2370	+	20.3852i	−0.417909	+	0.758134i
$724$	−7.17064	−	19.7012i	−0.266495	−	0.732188i
$725$	4.33752	−	24.5993i	0.161091	−	0.913595i
$726$	15.1168	−	2.97537i	0.561036	−	0.110426i
$727$	23.0429	+	19.3353i	0.854614	+	0.717107i	0.960801	−	0.277240i	$-0.0894196\pi$
$727$	23.0429	+	19.3353i	0.854614	+	0.717107i	−0.106187	+	0.994346i	$0.533864\pi$
$728$	4.22363	−	0.744740i	0.156538	−	0.0276019i
$729$	16.1773	+	21.6170i	0.599160	+	0.800629i
$730$	−7.47127	−	4.31354i	−0.276524	−	0.159651i
$731$	−12.0964	+	33.2345i	−0.447400	+	1.22922i
$732$	−13.4255	−	15.3710i	−0.496221	−	0.568129i
$733$	4.85445	−	8.40816i	0.179303	−	0.310563i	−0.762339	−	0.647178i	$-0.775949\pi$
$733$	4.85445	−	8.40816i	0.179303	−	0.310563i	0.941642	+	0.336616i	$0.109282\pi$
$734$	−10.3438	−	17.9160i	−0.381796	−	0.661291i
$735$	−4.32804	−	1.47887i	−0.159642	−	0.0545489i
$736$	−0.396438	+	0.472456i	−0.0146129	+	0.0174150i
$737$	10.3079	−	8.64938i	0.379697	−	0.318604i
$738$	−21.9585	+	8.99239i	−0.808305	+	0.331015i
$739$	−46.3353	+	16.8647i	−1.70447	+	0.620377i	−0.996322	−	0.0856846i	$-0.972692\pi$
$739$	−46.3353	+	16.8647i	−1.70447	+	0.620377i	−0.708150	+	0.706062i	$0.750470\pi$
$740$	3.42665			0.125966
$741$	−10.2494	+	20.1371i	−0.376520	+	0.739756i
$742$	−2.64586			−0.0971326
$743$	−6.36036	+	2.31498i	−0.233339	+	0.0849285i	−0.456043	−	0.889958i	$-0.650734\pi$
$743$	−6.36036	+	2.31498i	−0.233339	+	0.0849285i	0.222704	+	0.974886i	$0.428512\pi$
$744$	−6.67440	−	5.37884i	−0.244695	−	0.197198i
$745$	−8.06409	+	6.76658i	−0.295445	+	0.247908i
$746$	−1.83196	+	2.18324i	−0.0670728	+	0.0799342i
$747$	−10.0105	−	11.0130i	−0.366264	−	0.402944i
$748$	4.02112	+	6.96479i	0.147027	+	0.254658i
$749$	8.32539	−	14.4200i	0.304203	−	0.526895i
$750$	−6.76560	+	5.90929i	−0.247045	+	0.215777i
$751$	7.71871	−	21.2070i	0.281660	−	0.773853i	−0.715505	−	0.698607i	$-0.753804\pi$
$751$	7.71871	−	21.2070i	0.281660	−	0.773853i	0.997165	−	0.0752462i	$-0.0239743\pi$
$752$	−11.0749	−	6.39408i	−0.403859	−	0.233168i
$753$	13.6051	−	0.269537i	0.495797	−	0.00982247i
$754$	15.6143	−	2.75323i	0.568641	−	0.100267i
$755$	−1.73017	−	1.45179i	−0.0629675	−	0.0528360i
$756$	5.11663	+	5.40976i	0.186090	+	0.196751i
$757$	−9.07767	+	51.4820i	−0.329933	+	1.87115i	0.142523	+	0.989791i	$0.454478\pi$
$757$	−9.07767	+	51.4820i	−0.329933	+	1.87115i	−0.472457	+	0.881354i	$0.656633\pi$
$758$	5.18667	+	14.2502i	0.188388	+	0.517592i
$759$	1.35727	+	0.748174i	0.0492659	+	0.0271570i
$760$	−0.867551	−	2.15920i	−0.0314694	−	0.0783225i
$761$		−	16.8329i		−	0.610193i	−0.952321	−	0.305097i	$-0.901311\pi$
$761$		−	16.8329i		−	0.610193i	0.952321	−	0.305097i	$-0.0986888\pi$
$762$	0.209281	−	1.34180i	0.00758145	−	0.0486082i
$763$	0.0450412	+	0.00794198i	0.00163060	+	0.000287519i
$764$	−1.02459	−	1.22106i	−0.0370684	−	0.0441764i
$765$	1.19410	−	8.79699i	0.0431728	−	0.318056i
$766$	0.366876	+	2.08066i	0.0132558	+	0.0751772i
$767$	−4.84480	+	2.79715i	−0.174936	+	0.100999i
$768$	−1.48255	+	0.895567i	−0.0534970	+	0.0323160i
$769$	2.83204	+	1.03078i	0.102126	+	0.0371708i	0.392578	−	0.919719i	$-0.371583\pi$
$769$	2.83204	+	1.03078i	0.102126	+	0.0371708i	−0.290452	+	0.956890i	$0.593806\pi$
$770$	1.04295	+	0.379604i	0.0375854	+	0.0136800i
$771$	−18.2137	+	11.0024i	−0.655949	+	0.396240i
$772$	3.77249	−	2.17805i	0.135775	−	0.0783896i
$773$	−8.98386	−	50.9500i	−0.323127	−	1.83254i	−0.522523	−	0.852625i	$-0.675009\pi$
$773$	−8.98386	−	50.9500i	−0.323127	−	1.83254i	0.199396	−	0.979919i	$-0.436102\pi$
$774$	−2.57456	+	18.9669i	−0.0925407	+	0.681751i
$775$	−14.9994	−	17.8755i	−0.538793	−	0.642108i
$776$	8.16597	+	1.43988i	0.293141	+	0.0516887i
$777$	2.45522	−	15.7416i	0.0880806	−	0.564726i
$778$			4.20263i			0.150672i
$779$	4.86382	−	34.1319i	0.174265	−	1.22290i
$780$	−2.42350	−	1.33592i	−0.0867752	−	0.0478334i
$781$	−6.21447	−	17.0741i	−0.222371	−	0.610960i
$782$	0.593664	−	3.36684i	0.0212294	−	0.120398i
$783$	18.9157	+	19.9993i	0.675991	+	0.714718i
$784$	−3.78921	−	3.17953i	−0.135329	−	0.113555i
$785$	5.34270	−	0.942061i	0.190689	−	0.0336236i
$786$	−19.9476	+	0.395191i	−0.711507	+	0.0140960i
$787$	14.8092	+	8.55010i	0.527891	+	0.304778i	0.740157	−	0.672434i	$-0.234751\pi$
$787$	14.8092	+	8.55010i	0.527891	+	0.304778i	−0.212266	+	0.977212i	$0.568084\pi$
$788$	−2.24992	+	6.18160i	−0.0801501	+	0.220210i
$789$	−31.0902	+	27.1552i	−1.10684	+	0.966749i
$790$	2.13551	−	3.69881i	0.0759781	−	0.131598i
$791$	−7.41407	−	12.8416i	−0.263614	−	0.456593i
$792$	2.92757	+	3.22076i	0.104027	+	0.114445i
$793$	22.6675	−	27.0141i	0.804948	−	0.959300i
$794$	−0.232292	+	0.194916i	−0.00824372	+	0.00691731i
$795$	1.32929	+	1.07126i	0.0471451	+	0.0379938i
$796$	10.2412	−	3.72750i	0.362990	−	0.132118i
$797$	7.92776			0.280816			0.140408	−	0.990094i	$-0.455159\pi$
$797$	7.92776			0.280816			0.140408	+	0.990094i	$0.455159\pi$
$798$	−10.5407	+	2.43833i	−0.373136	+	0.0863158i
$799$	70.8878			2.50783
$800$	−4.43066	+	1.61263i	−0.156648	+	0.0570150i
$801$	−13.3036	+	5.44807i	−0.470061	+	0.192498i
$802$	−9.67162	+	8.11545i	−0.341517	+	0.286567i
$803$	−15.0706	+	17.9605i	−0.531831	+	0.633811i
$804$	−15.2014	−	5.19426i	−0.536114	−	0.183187i
$805$	−0.235908	−	0.408604i	−0.00831466	−	0.0144014i
$806$	7.40587	−	12.8273i	0.260861	−	0.451824i
$807$	21.6682	+	24.8081i	0.762757	+	0.873288i
$808$	−1.07729	+	2.95982i	−0.0378988	+	0.104126i
$809$	3.32547	+	1.91996i	0.116917	+	0.0675022i	0.557318	−	0.830299i	$-0.311830\pi$
$809$	3.32547	+	1.91996i	0.116917	+	0.0675022i	−0.440401	+	0.897801i	$0.645164\pi$
$810$	−0.380296	−	4.78952i	−0.0133622	−	0.168287i
$811$	27.5374	−	4.85558i	0.966968	−	0.170503i	0.332203	−	0.943208i	$-0.392208\pi$
$811$	27.5374	−	4.85558i	0.966968	−	0.170503i	0.634765	+	0.772705i	$0.281097\pi$
$812$	5.81558	+	4.87985i	0.204087	+	0.171249i
$813$	9.17456	−	1.80579i	0.321766	−	0.0633319i
$814$	1.61711	−	9.17110i	0.0566798	−	0.321447i
$815$	1.89968	+	5.21932i	0.0665428	+	0.182825i
$816$	4.63494	−	8.40831i	0.162255	−	0.294350i
$817$	−21.8824	−	17.1642i	−0.765568	−	0.600500i
$818$		−	19.3996i		−	0.678291i
$819$	−7.87346	+	10.1760i	−0.275121	+	0.355579i
$820$	4.15829	+	0.733218i	0.145214	+	0.0256051i
$821$	−31.0592	−	37.0149i	−1.08397	−	1.29183i	−0.953834	−	0.300333i	$-0.902902\pi$
$821$	−31.0592	−	37.0149i	−1.08397	−	1.29183i	−0.130139	−	0.991496i	$-0.541542\pi$
$822$	21.8810	−	8.45852i	0.763188	−	0.295025i
$823$	7.99935	+	45.3666i	0.278840	+	1.58138i	0.726494	+	0.687173i	$0.241149\pi$
$823$	7.99935	+	45.3666i	0.278840	+	1.58138i	−0.447654	+	0.894207i	$0.647740\pi$
$824$	8.85438	−	5.11208i	0.308457	−	0.178088i
$825$	6.12625	+	10.1416i	0.213289	+	0.353085i
$826$	−2.51709	−	0.916145i	−0.0875807	−	0.0318768i
$827$	−26.1088	−	9.50281i	−0.907891	−	0.330445i	−0.154480	−	0.987996i	$-0.549370\pi$
$827$	−26.1088	−	9.50281i	−0.907891	−	0.330445i	−0.753410	+	0.657551i	$0.771593\pi$
$828$	−0.0732833	−	1.84879i	−0.00254677	−	0.0642499i
$829$	18.4501	−	10.6521i	0.640797	−	0.369964i	−0.144125	−	0.989560i	$-0.546037\pi$
$829$	18.4501	−	10.6521i	0.640797	−	0.369964i	0.784921	+	0.619595i	$0.212703\pi$
$830$	0.459881	+	2.60812i	0.0159627	+	0.0905290i
$831$	−0.0583245	−	0.150877i	−0.00202326	−	0.00523388i
$832$	−1.92376	−	2.29265i	−0.0666944	−	0.0794833i
$833$	27.0029	+	4.76134i	0.935594	+	0.164970i
$834$	12.3838	+	1.93151i	0.428815	+	0.0668826i
$835$			12.7018i			0.439563i
$836$	−6.18831	+	1.30294i	−0.214027	+	0.0450632i
$837$	25.6707	−	1.52732i	0.887308	−	0.0527919i
$838$	−5.29717	−	14.5539i	−0.182988	−	0.502755i
$839$	−6.05886	+	34.3615i	−0.209175	+	1.18629i	0.681558	+	0.731765i	$0.261303\pi$
$839$	−6.05886	+	34.3615i	−0.209175	+	1.18629i	−0.890733	+	0.454527i	$0.849808\pi$
$840$	−0.255891	−	1.30009i	−0.00882907	−	0.0448572i
$841$	−0.715656	−	0.600507i	−0.0246778	−	0.0207071i
$842$	−13.7766	+	2.42919i	−0.474773	+	0.0837153i
$843$	−0.350001	−	17.6666i	−0.0120547	−	0.608470i
$844$	−6.55559	−	3.78487i	−0.225653	−	0.130281i
$845$	−0.738176	+	2.02812i	−0.0253940	+	0.0697695i
$846$	37.4881	−	8.15312i	1.28887	−	0.280310i
$847$	−6.37342	+	11.0391i	−0.218993	+	0.379307i
$848$	0.923180	+	1.59899i	0.0317021	+	0.0549097i
$849$	10.8309	−	31.6976i	0.371716	−	1.08786i
$850$	16.8002	−	20.0217i	0.576241	−	0.686737i
$851$	−3.03262	+	2.54467i	−0.103957	+	0.0872301i
$852$	−13.6115	+	16.8899i	−0.466321	+	0.578640i
$853$	−0.565541	+	0.205840i	−0.0193638	+	0.00704783i	−0.351684	−	0.936119i	$-0.614391\pi$
$853$	−0.565541	+	0.205840i	−0.0193638	+	0.00704783i	0.332320	+	0.943167i	$0.392169\pi$
$854$	16.8851			0.577797
$855$	6.28292	+	3.04272i	0.214871	+	0.104059i
$856$	−11.6194			−0.397143
$857$	4.78193	−	1.74048i	0.163348	−	0.0594537i	−0.259052	−	0.965863i	$-0.583410\pi$
$857$	4.78193	−	1.74048i	0.163348	−	0.0594537i	0.422400	+	0.906410i	$0.361188\pi$
$858$	−4.71915	+	5.85581i	−0.161109	+	0.199914i
$859$	23.1806	−	19.4509i	0.790913	−	0.663655i	−0.155058	−	0.987905i	$-0.549556\pi$
$859$	23.1806	−	19.4509i	0.790913	−	0.663655i	0.945971	+	0.324250i	$0.105112\pi$
$860$	2.18938	−	2.60920i	0.0746572	−	0.0889730i
$861$	6.34774	−	18.5772i	0.216330	−	0.633110i
$862$	−14.0009	−	24.2502i	−0.476871	−	0.825966i
$863$	−20.1792	+	34.9514i	−0.686908	+	1.18976i	0.285925	+	0.958252i	$0.407699\pi$
$863$	−20.1792	+	34.9514i	−0.686908	+	1.18976i	−0.972833	+	0.231508i	$0.925634\pi$
$864$	1.48405	−	4.97972i	0.0504886	−	0.169413i
$865$	4.57457	−	12.5685i	0.155540	−	0.427343i
$866$	5.09482	+	2.94150i	0.173129	+	0.0999562i
$867$	0.470958	+	23.7720i	0.0159946	+	0.807339i
$868$	6.98433	−	1.23153i	0.237064	−	0.0418007i
$869$	−8.89172	−	7.46104i	−0.301631	−	0.253098i
$870$	−0.946003	−	4.80629i	−0.0320725	−	0.162948i
$871$	4.82011	−	27.3362i	0.163323	−	0.926252i
$872$	−0.0109159	−	0.0299912i	−0.000369659	−	0.00101563i
$873$	−21.0336	+	13.2814i	−0.711879	+	0.449508i
$874$	2.37123	+	1.26666i	0.0802082	+	0.0428454i
$875$		−	7.43204i		−	0.251249i
$876$	27.6561	+	4.31354i	0.934413	+	0.145741i
$877$	34.2610	+	6.04114i	1.15691	+	0.203995i	0.718992	−	0.695019i	$-0.244604\pi$
$877$	34.2610	+	6.04114i	1.15691	+	0.203995i	0.437921	+	0.899014i	$0.355715\pi$
$878$	−14.3880	−	17.1469i	−0.485571	−	0.578681i
$879$	−10.1081	−	26.1481i	−0.340937	−	0.881955i
$880$	−0.134493	−	0.762746i	−0.00453375	−	0.0257122i
$881$	9.93336	−	5.73503i	0.334663	−	0.193218i	−0.323246	−	0.946315i	$-0.604774\pi$
$881$	9.93336	−	5.73503i	0.334663	−	0.193218i	0.657910	+	0.753097i	$0.271441\pi$
$882$	14.8278	−	0.587750i	0.499277	−	0.0197906i
$883$	4.25598	+	1.54905i	0.143225	+	0.0521297i	0.412638	−	0.910895i	$-0.364607\pi$
$883$	4.25598	+	1.54905i	0.143225	+	0.0521297i	−0.269413	+	0.963025i	$0.586830\pi$
$884$	15.5895	+	5.67412i	0.524332	+	0.190841i
$885$	0.893663	+	1.47940i	0.0300402	+	0.0497295i
$886$	12.9146	−	7.45622i	0.433873	−	0.250497i
$887$	9.37732	+	53.1814i	0.314859	+	1.78566i	0.573006	+	0.819551i	$0.305777\pi$
$887$	9.37732	+	53.1814i	0.314859	+	1.78566i	−0.258147	+	0.966106i	$0.583112\pi$
$888$	−10.3699	+	4.00868i	−0.347991	+	0.134523i
$889$	0.722210	+	0.860696i	0.0242221	+	0.0288668i
$890$	2.51931	+	0.444222i	0.0844475	+	0.0148904i
$891$	−12.9982	−	1.24245i	−0.435454	−	0.0416238i
$892$			11.5147i			0.385540i
$893$	−17.3272	+	52.9809i	−0.579831	+	1.77294i
$894$	16.4880	−	29.9111i	0.551442	−	1.00038i
$895$	2.83801	+	7.79736i	0.0948641	+	0.260637i
$896$	0.248840	−	1.41124i	0.00831317	−	0.0471464i
$897$	3.13688	−	0.617420i	0.104737	−	0.0206151i
$898$	−3.74659	−	3.14376i	−0.125025	−	0.104909i
$899$	25.8204	−	4.55283i	0.861158	−	0.151845i
$900$	6.58178	−	12.5205i	0.219393	−	0.417349i
$901$	−8.86360	−	5.11740i	−0.295289	−	0.170485i
$902$	3.92477	−	10.7832i	0.130681	−	0.359042i
$903$	−10.4176	−	11.9272i	−0.346676	−	0.396913i
$904$	−5.17376	+	8.96121i	−0.172077	+	0.298046i
$905$	−5.59617	−	9.69284i	−0.186023	−	0.322201i
$906$	6.93431	+	2.36942i	0.230377	+	0.0787186i
$907$	4.49918	−	5.36192i	0.149393	−	0.178039i	−0.686158	−	0.727452i	$-0.740704\pi$
$907$	4.49918	−	5.36192i	0.149393	−	0.178039i	0.835551	+	0.549413i	$0.185149\pi$
$908$	1.18194	−	0.991763i	0.0392240	−	0.0329128i
$909$	−3.58102	−	8.74449i	−0.118775	−	0.290036i
$910$	2.15146	−	0.783069i	0.0713204	−	0.0259585i
$911$	−13.0438			−0.432160			−0.216080	−	0.976376i	$-0.569327\pi$
$911$	−13.0438			−0.432160			−0.216080	+	0.976376i	$0.569327\pi$
$912$	5.15137	+	5.51936i	0.170579	+	0.182764i
$913$	7.19739			0.238199
$914$	28.5270	−	10.3830i	0.943590	−	0.343439i
$915$	−8.48315	−	6.83650i	−0.280444	−	0.226008i
$916$	−6.26114	+	5.25372i	−0.206874	+	0.173588i
$917$	10.6104	−	12.6450i	0.350387	−	0.417575i
$918$	6.67754	+	28.0188i	0.220392	+	0.924757i
$919$	−3.44700	−	5.97038i	−0.113706	−	0.196945i	0.803556	−	0.595229i	$-0.202939\pi$
$919$	−3.44700	−	5.97038i	−0.113706	−	0.196945i	−0.917262	+	0.398285i	$0.869606\pi$
$920$	−0.164623	+	0.285136i	−0.00542748	+	0.00940066i
$921$	23.2688	−	20.3237i	0.766732	−	0.669687i
$922$	8.54409	−	23.4747i	0.281385	−	0.773098i
$923$	−32.4603	−	18.7410i	−1.06844	−	0.616867i
$924$	−3.60031	+	0.0713275i	−0.118442	+	0.00234650i
$925$	−29.8051	+	5.25544i	−0.979985	+	0.172798i
$926$	4.51902	+	3.79191i	0.148504	+	0.124610i
$927$	−9.34078	+	29.2156i	−0.306792	+	0.959566i
$928$	0.919938	−	5.21723i	0.0301985	−	0.171264i
$929$	−13.7442	−	37.7618i	−0.450931	−	1.23892i	−0.932070	−	0.362279i	$-0.881999\pi$
$929$	−13.7442	−	37.7618i	−0.450931	−	1.23892i	0.481139	−	0.876645i	$-0.340223\pi$
$930$	−4.00758	−	2.20911i	−0.131414	−	0.0724397i
$931$	−10.1589	+	19.0179i	−0.332945	+	0.623286i
$932$		−	8.39487i		−	0.274983i
$933$	8.73767	−	56.0213i	0.286059	−	1.83405i
$934$	5.42253	+	0.956138i	0.177431	+	0.0312858i
$935$	2.75968	+	3.28886i	0.0902513	+	0.107557i
$936$	8.89693	+	1.20767i	0.290805	+	0.0394738i
$937$	3.70352	+	21.0037i	0.120989	+	0.686161i	0.983610	+	0.180310i	$0.0577101\pi$
$937$	3.70352	+	21.0037i	0.120989	+	0.686161i	−0.862621	+	0.505850i	$0.831179\pi$
$938$	11.5102	−	6.64544i	0.375823	−	0.216981i
$939$	−39.1719	+	23.6626i	−1.27833	+	0.772201i
$940$	−6.41517	−	2.33493i	−0.209240	−	0.0761570i
$941$	33.1057	+	12.0495i	1.07922	+	0.392802i	0.819616	−	0.572914i	$-0.194187\pi$
$941$	33.1057	+	12.0495i	1.07922	+	0.392802i	0.259600	+	0.965716i	$0.416409\pi$
$942$	−15.0662	+	9.10108i	−0.490884	+	0.296529i
$943$	−4.22461	+	2.43908i	−0.137572	+	0.0794274i
$944$	0.324588	+	1.84083i	0.0105644	+	0.0599138i
$945$	3.19147	+	2.36977i	0.103819	+	0.0770888i
$946$	−5.95006	−	7.09100i	−0.193453	−	0.230548i
$947$	26.6972	+	4.70744i	0.867542	+	0.152971i	0.589667	−	0.807646i	$-0.299259\pi$
$947$	26.6972	+	4.70744i	0.867542	+	0.152971i	0.277875	+	0.960617i	$0.410370\pi$
$948$	−2.13551	+	13.6917i	−0.0693582	+	0.444687i
$949$			48.3652i			1.57000i
$950$	10.8575	+	17.4502i	0.352265	+	0.566159i
$951$	−20.3392	−	11.2116i	−0.659543	−	0.363562i
$952$	2.71685	+	7.46448i	0.0880536	+	0.241925i
$953$	−1.20982	+	6.86124i	−0.0391900	+	0.222258i	−0.998113	−	0.0614103i	$-0.980440\pi$
$953$	−1.20982	+	6.86124i	−0.0391900	+	0.222258i	0.958923	+	0.283668i	$0.0915513\pi$
$954$	−5.27598	−	1.68683i	−0.170816	−	0.0546132i
$955$	−0.651855	−	0.546972i	−0.0210935	−	0.0176996i
$956$	−8.65196	+	1.52557i	−0.279824	+	0.0493406i
$957$	−13.3100	+	0.263691i	−0.430251	+	0.00852391i
$958$	−28.9528	−	16.7159i	−0.935424	−	0.540067i
$959$	−6.63821	+	18.2383i	−0.214359	+	0.588947i
$960$	−0.696407	+	0.608264i	−0.0224765	+	0.0196316i
$961$	−3.25341	+	5.63508i	−0.104949	+	0.181777i
$962$	−9.60527	−	16.6368i	−0.309686	−	0.536392i
$963$	25.7945	−	23.4465i	0.831217	−	0.755553i
$964$	−8.63848	+	10.2949i	−0.278227	+	0.331578i
$965$	1.78142	−	1.49479i	0.0573458	−	0.0481188i
$966$	1.19192	+	0.960560i	0.0383495	+	0.0309055i
$967$	−37.2609	+	13.5619i	−1.19823	+	0.436120i	−0.862606	−	0.505876i	$-0.831169\pi$
$967$	−37.2609	+	13.5619i	−1.19823	+	0.436120i	−0.335623	+	0.941996i	$0.608947\pi$
$968$	8.89512			0.285900
$969$	−40.0271	−	12.2185i	−1.28586	−	0.392516i
$970$	4.42661			0.142130
$971$	−48.3722	+	17.6060i	−1.55234	+	0.565004i	−0.968964	−	0.247201i	$-0.920489\pi$
$971$	−48.3722	+	17.6060i	−1.55234	+	0.565004i	−0.583372	+	0.812205i	$0.698267\pi$
$972$	6.75390	+	14.0494i	0.216632	+	0.450634i
$973$	−7.94358	+	6.66546i	−0.254660	+	0.213685i
$974$	−16.2886	+	19.4120i	−0.521920	+	0.622000i
$975$	23.1285	+	7.90290i	0.740705	+	0.253095i
$976$	−5.89147	−	10.2043i	−0.188581	−	0.326632i
$977$	−29.8636	+	51.7252i	−0.955421	+	1.65484i	−0.222018	+	0.975042i	$0.571264\pi$
$977$	−29.8636	+	51.7252i	−0.955421	+	1.65484i	−0.733402	+	0.679795i	$0.762069\pi$
$978$	−11.8547	−	13.5726i	−0.379072	−	0.434004i
$979$	2.37783	−	6.53305i	0.0759959	−	0.208797i
$980$	−2.28686	−	1.32032i	−0.0730512	−	0.0421761i
$981$	0.0847512	+	0.0445521i	0.00270590	+	0.00142244i
$982$	7.76474	−	1.36913i	0.247783	−	0.0436908i
$983$	27.8849	+	23.3982i	0.889391	+	0.746288i	0.968088	−	0.250611i	$-0.0806315\pi$
$983$	27.8849	+	23.3982i	0.889391	+	0.746288i	−0.0786969	+	0.996899i	$0.525076\pi$
$984$	−13.4417	+	2.64569i	−0.428507	+	0.0843414i
$985$	−0.609817	+	3.45845i	−0.0194304	+	0.110195i
$986$	10.0439	+	27.5955i	0.319864	+	0.878818i
$987$	−15.3229	+	27.7974i	−0.487732	+	0.884801i
$988$	−8.05134	+	10.2645i	−0.256147	+	0.326558i
$989$			3.93502i			0.125126i
$990$	1.83769	+	1.42187i	0.0584057	+	0.0451900i
$991$	−45.8935	−	8.09227i	−1.45786	−	0.257059i	−0.612164	−	0.790730i	$-0.709701\pi$
$991$	−45.8935	−	8.09227i	−1.45786	−	0.257059i	−0.845692	+	0.533671i	$0.820812\pi$
$992$	−3.18119	−	3.79120i	−0.101003	−	0.120371i
$993$	40.3780	−	15.6089i	1.28136	−	0.495333i
$994$	−3.11645	−	17.6742i	−0.0988476	−	0.560593i
$995$	5.03861	−	2.90904i	0.159735	−	0.0922229i
$996$	−4.44282	−	7.35480i	−0.140776	−	0.233046i
$997$	6.98731	+	2.54317i	0.221290	+	0.0805430i	0.450286	−	0.892884i	$-0.351322\pi$
$997$	6.98731	+	2.54317i	0.221290	+	0.0805430i	−0.228996	+	0.973427i	$0.573544\pi$
$998$	12.1327	+	4.41595i	0.384055	+	0.139784i
$999$	14.9317	−	29.8242i	0.472417	−	0.943596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.b.71.3	yes	18
3.2	odd	2		114.2.l.a.71.2	yes	18
4.3	odd	2		912.2.cc.c.641.1		18
12.11	even	2		912.2.cc.d.641.2		18
19.15	odd	18		114.2.l.a.53.2	✓	18
57.53	even	18	inner	114.2.l.b.53.3	yes	18
76.15	even	18		912.2.cc.d.737.2		18
228.167	odd	18		912.2.cc.c.737.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.2	✓	18	19.15	odd	18
114.2.l.a.71.2	yes	18	3.2	odd	2
114.2.l.b.53.3	yes	18	57.53	even	18	inner
114.2.l.b.71.3	yes	18	1.1	even	1	trivial
912.2.cc.c.641.1		18	4.3	odd	2
912.2.cc.c.737.1		18	228.167	odd	18
912.2.cc.d.641.2		18	12.11	even	2
912.2.cc.d.737.2		18	76.15	even	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.08684 - 1.34862i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.343148 - 0.408948i) q^{5} +(-0.560041 + 1.63901i) q^{6} +(-0.716507 - 1.24103i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.637553 - 2.93147i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(1.08684 - 1.34862i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.343148 - 0.408948i) q^{5} +(-0.560041 + 1.63901i) q^{6} +(-0.716507 - 1.24103i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.637553 - 2.93147i) q^{9} +(-0.182585 + 0.501649i) q^{10} +(1.25645 + 0.725411i) q^{11} +(-0.0343077 - 1.73171i) q^{12} +(2.94737 - 0.519701i) q^{13} +(1.09775 + 0.921124i) q^{14} +(-0.178568 - 0.907238i) q^{15} +(0.173648 - 0.984808i) q^{16} +(1.89590 + 5.20894i) q^{17} +(1.60173 + 2.53663i) q^{18} +(-4.35653 + 0.143752i) q^{19} -0.533844i q^{20} +(-2.45240 - 0.382503i) q^{21} +(-1.42878 - 0.251933i) q^{22} +(0.396438 + 0.472456i) q^{23} +(0.624519 + 1.61554i) q^{24} +(0.818753 + 4.64338i) q^{25} +(-2.59188 + 1.49642i) q^{26} +(-4.64636 - 2.32623i) q^{27} +(-1.34659 - 0.490120i) q^{28} +(-4.97822 - 1.81193i) q^{29} +(0.478093 + 0.791451i) q^{30} +(-4.28601 + 2.47453i) q^{31} +(0.173648 + 0.984808i) q^{32} +(2.34386 - 0.906066i) q^{33} +(-3.56312 - 4.24636i) q^{34} +(-0.753384 - 0.132842i) q^{35} +(-2.37271 - 1.83583i) q^{36} +6.41883i q^{37} +(4.04463 - 1.62510i) q^{38} +(2.50245 - 4.53972i) q^{39} +(0.182585 + 0.501649i) q^{40} +(-1.37347 + 7.78933i) q^{41} +(2.43533 - 0.479336i) q^{42} +(4.88757 + 4.10116i) q^{43} +(1.42878 - 0.251933i) q^{44} +(-1.41759 - 0.745203i) q^{45} +(-0.534119 - 0.308374i) q^{46} +(4.37381 - 12.0169i) q^{47} +(-1.13940 - 1.30452i) q^{48} +(2.47323 - 4.28377i) q^{49} +(-2.35751 - 4.08332i) q^{50} +(9.08542 + 3.10444i) q^{51} +(1.92376 - 2.29265i) q^{52} +(-1.41439 + 1.18682i) q^{53} +(5.16177 + 0.596790i) q^{54} +(0.727804 - 0.264899i) q^{55} +1.43301 q^{56} +(-4.54099 + 6.03154i) q^{57} +5.29771 q^{58} +(-1.75650 + 0.639313i) q^{59} +(-0.719953 - 0.580203i) q^{60} +(9.02625 - 7.57392i) q^{61} +(3.18119 - 3.79120i) q^{62} +(-3.18122 + 2.89164i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.798855 - 1.38366i) q^{65} +(-1.89262 + 1.65307i) q^{66} +(3.17216 - 8.71543i) q^{67} +(4.80058 + 2.77162i) q^{68} +(1.06803 - 0.0211592i) q^{69} +(0.753384 - 0.132842i) q^{70} +(-9.59384 - 8.05019i) q^{71} +(2.85751 + 0.913599i) q^{72} +(-2.80621 + 15.9148i) q^{73} +(-2.19537 - 6.03173i) q^{74} +(7.15201 + 3.94243i) q^{75} +(-3.24489 + 2.91044i) q^{76} -2.07905i q^{77} +(-0.798855 + 5.12183i) q^{78} +(-7.87896 - 1.38927i) q^{79} +(-0.343148 - 0.408948i) q^{80} +(-8.18705 + 3.73794i) q^{81} +(-1.37347 - 7.78933i) q^{82} +(4.29627 - 2.48045i) q^{83} +(-2.12452 + 1.28336i) q^{84} +(2.78076 + 1.01211i) q^{85} +(-5.99550 - 2.18218i) q^{86} +(-7.85414 + 4.74446i) q^{87} +(-1.25645 + 0.725411i) q^{88} +(-0.832120 - 4.71919i) q^{89} +(1.58698 + 0.215416i) q^{90} +(-2.75678 - 3.28540i) q^{91} +(0.607378 + 0.107097i) q^{92} +(-1.32101 + 8.46962i) q^{93} +12.7882i q^{94} +(-1.43615 + 1.83092i) q^{95} +(1.51686 + 0.836144i) q^{96} +(-2.83601 - 7.79188i) q^{97} +(-0.858945 + 4.87132i) q^{98} +(1.32547 - 4.14573i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Introduction

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