LMFDB - Embedded newform 114.2.l.b.53.1

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			53.1
Root			$-0.363139 + 1.69356i$ of defining polynomial
Character	$\chi$	$=$	114.53
Dual form			114.2.l.b.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-1.36678 + 1.06392i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.20556 - 2.62849i) q^{5} +(1.64823 - 0.532290i) q^{6} +(1.68651 - 2.92113i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.736160 - 2.90828i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.36678 + 1.06392i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.20556 - 2.62849i) q^{5} +(1.64823 - 0.532290i) q^{6} +(1.68651 - 2.92113i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.736160 - 2.90828i) q^{9} +(1.17355 + 3.22432i) q^{10} +(2.33635 - 1.34889i) q^{11} +(-1.73088 - 0.0635395i) q^{12} +(-5.05419 - 0.891189i) q^{13} +(-2.58389 + 2.16814i) q^{14} +(5.81100 + 1.24602i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.44531 + 3.97095i) q^{17} +(-1.68645 + 2.48110i) q^{18} +(-2.73048 - 3.39772i) q^{19} -3.43124i q^{20} +(0.802750 + 5.78684i) q^{21} +(-2.65680 + 0.468466i) q^{22} +(1.69398 - 2.01881i) q^{23} +(1.60477 + 0.651705i) q^{24} +(-1.17620 + 6.67054i) q^{25} +(4.44458 + 2.56608i) q^{26} +(2.08800 + 4.75818i) q^{27} +(3.16961 - 1.15364i) q^{28} +(3.54249 - 1.28936i) q^{29} +(-5.03439 - 3.15836i) q^{30} +(4.78254 + 2.76120i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-1.75816 + 4.32933i) q^{33} +(2.71629 - 3.23715i) q^{34} +(-11.3979 + 2.00975i) q^{35} +(2.43333 - 1.75467i) q^{36} -5.17636i q^{37} +(1.40372 + 4.12669i) q^{38} +(7.85610 - 4.15918i) q^{39} +(-1.17355 + 3.22432i) q^{40} +(0.289735 + 1.64317i) q^{41} +(1.22488 - 5.71241i) q^{42} +(1.85806 - 1.55910i) q^{43} +(2.65680 + 0.468466i) q^{44} +(-9.26801 + 4.47940i) q^{45} +(-2.28230 + 1.31768i) q^{46} +(0.0440069 + 0.120908i) q^{47} +(-1.28509 - 1.16127i) q^{48} +(-2.18866 - 3.79087i) q^{49} +(3.38672 - 5.86597i) q^{50} +(-2.24935 - 6.96509i) q^{51} +(-3.29889 - 3.93146i) q^{52} +(-6.53342 - 5.48219i) q^{53} +(-0.334684 - 5.18536i) q^{54} +(-8.69853 - 3.16600i) q^{55} -3.37303 q^{56} +(7.34685 + 1.73892i) q^{57} -3.76983 q^{58} +(3.87665 + 1.41099i) q^{59} +(3.65056 + 4.68975i) q^{60} +(3.53369 + 2.96512i) q^{61} +(-3.54973 - 4.23041i) q^{62} +(-7.25390 - 7.05526i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(8.80484 + 15.2504i) q^{65} +(3.13285 - 3.46691i) q^{66} +(3.81629 + 10.4852i) q^{67} +(-3.65965 + 2.11290i) q^{68} +(-0.167450 + 4.56152i) q^{69} +(11.3979 + 2.00975i) q^{70} +(9.91131 - 8.31658i) q^{71} +(-2.88672 + 0.816605i) q^{72} +(-0.414656 - 2.35163i) q^{73} +(-1.77042 + 4.86419i) q^{74} +(-5.48930 - 10.3685i) q^{75} +(0.0923461 - 4.35792i) q^{76} -9.09972i q^{77} +(-8.80484 + 1.22141i) q^{78} +(2.22246 - 0.391880i) q^{79} +(2.20556 - 2.62849i) q^{80} +(-7.91614 - 4.28191i) q^{81} +(0.289735 - 1.64317i) q^{82} +(6.27861 + 3.62496i) q^{83} +(-3.10477 + 4.94898i) q^{84} +(13.6253 - 4.95920i) q^{85} +(-2.27924 + 0.829577i) q^{86} +(-3.47002 + 5.53118i) q^{87} +(-2.33635 - 1.34889i) q^{88} +(0.209662 - 1.18905i) q^{89} +(10.2411 - 1.03941i) q^{90} +(-11.1272 + 13.2609i) q^{91} +(2.59533 - 0.457627i) q^{92} +(-9.47436 + 1.31428i) q^{93} -0.128667i q^{94} +(-2.90863 + 14.6709i) q^{95} +(0.810416 + 1.53076i) q^{96} +(3.13271 - 8.60706i) q^{97} +(0.760113 + 4.31081i) q^{98} +(-2.20303 - 7.78777i) 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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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
$3$	−1.36678	+	1.06392i	−0.789109	+	0.614253i
$3$	−1.36678	+	1.06392i	−0.789109	+	0.614253i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−2.20556	−	2.62849i	−0.986357	−	1.17549i	−0.984480	−	0.175496i	$-0.943847\pi$
$5$	−2.20556	−	2.62849i	−0.986357	−	1.17549i	−0.00187711	−	0.999998i	$-0.500598\pi$
$6$	1.64823	−	0.532290i	0.672888	−	0.217306i
$7$	1.68651	−	2.92113i	0.637442	−	1.10408i	−0.348550	−	0.937290i	$-0.613326\pi$
$7$	1.68651	−	2.92113i	0.637442	−	1.10408i	0.985992	−	0.166792i	$-0.0533409\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	0.736160	−	2.90828i	0.245387	−	0.969425i
$10$	1.17355	+	3.22432i	0.371111	+	1.01962i
$11$	2.33635	−	1.34889i	0.704437	−	0.406707i	−0.104561	−	0.994519i	$-0.533344\pi$
$11$	2.33635	−	1.34889i	0.704437	−	0.406707i	0.808998	+	0.587811i	$0.200010\pi$
$12$	−1.73088	−	0.0635395i	−0.499663	−	0.0183423i
$13$	−5.05419	−	0.891189i	−1.40178	−	0.247171i	−0.578905	−	0.815395i	$-0.696520\pi$
$13$	−5.05419	−	0.891189i	−1.40178	−	0.247171i	−0.822874	+	0.568224i	$0.807631\pi$
$14$	−2.58389	+	2.16814i	−0.690573	+	0.579460i
$15$	5.81100	+	1.24602i	1.50039	+	0.321721i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.44531	+	3.97095i	−0.350538	+	0.963096i	0.631659	+	0.775246i	$0.282374\pi$
$17$	−1.44531	+	3.97095i	−0.350538	+	0.963096i	−0.982198	+	0.187850i	$0.939848\pi$
$18$	−1.68645	+	2.48110i	−0.397501	+	0.584802i
$19$	−2.73048	−	3.39772i	−0.626414	−	0.779490i
$19$	−2.73048	−	3.39772i	−0.626414	−	0.779490i
$20$		−	3.43124i		−	0.767250i
$21$	0.802750	+	5.78684i	0.175174	+	1.26279i
$22$	−2.65680	+	0.468466i	−0.566433	+	0.0998773i
$23$	1.69398	−	2.01881i	0.353220	−	0.420951i	−0.559952	−	0.828525i	$-0.689181\pi$
$23$	1.69398	−	2.01881i	0.353220	−	0.420951i	0.913172	+	0.407574i	$0.133625\pi$
$24$	1.60477	+	0.651705i	0.327572	+	0.133029i
$25$	−1.17620	+	6.67054i	−0.235239	+	1.33411i
$26$	4.44458	+	2.56608i	0.871653	+	0.503249i
$27$	2.08800	+	4.75818i	0.401836	+	0.915712i
$28$	3.16961	−	1.15364i	0.599000	−	0.218018i
$29$	3.54249	−	1.28936i	0.657823	−	0.239428i	0.00852691	−	0.999964i	$-0.497286\pi$
$29$	3.54249	−	1.28936i	0.657823	−	0.239428i	0.649296	+	0.760536i	$0.275064\pi$
$30$	−5.03439	−	3.15836i	−0.919150	−	0.576634i
$31$	4.78254	+	2.76120i	0.858970	+	0.495927i	0.863667	−	0.504062i	$-0.168162\pi$
$31$	4.78254	+	2.76120i	0.858970	+	0.495927i	−0.00469717	+	0.999989i	$0.501495\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−1.75816	+	4.32933i	−0.306057	+	0.753639i
$34$	2.71629	−	3.23715i	0.465840	−	0.555166i
$35$	−11.3979	+	2.00975i	−1.92659	+	0.339710i
$36$	2.43333	−	1.75467i	0.405556	−	0.292446i
$37$		−	5.17636i		−	0.850989i	−0.904961	−	0.425494i	$-0.860100\pi$
$37$		−	5.17636i		−	0.850989i	0.904961	−	0.425494i	$-0.139900\pi$
$38$	1.40372	+	4.12669i	0.227713	+	0.669438i
$39$	7.85610	−	4.15918i	1.25798	−	0.666002i
$40$	−1.17355	+	3.22432i	−0.185555	+	0.509809i
$41$	0.289735	+	1.64317i	0.0452490	+	0.256620i	0.999038	−	0.0438581i	$-0.0139649\pi$
$41$	0.289735	+	1.64317i	0.0452490	+	0.256620i	−0.953789	+	0.300478i	$0.902854\pi$
$42$	1.22488	−	5.71241i	0.189003	−	0.881444i
$43$	1.85806	−	1.55910i	0.283351	−	0.237760i	−0.490023	−	0.871709i	$-0.663012\pi$
$43$	1.85806	−	1.55910i	0.283351	−	0.237760i	0.773374	+	0.633950i	$0.218567\pi$
$44$	2.65680	+	0.468466i	0.400528	+	0.0706240i
$45$	−9.26801	+	4.47940i	−1.38159	+	0.667749i
$46$	−2.28230	+	1.31768i	−0.336506	+	0.194282i
$47$	0.0440069	+	0.120908i	0.00641906	+	0.0176362i	0.942861	−	0.333187i	$-0.108124\pi$
$47$	0.0440069	+	0.120908i	0.00641906	+	0.0176362i	−0.936442	+	0.350823i	$0.885902\pi$
$48$	−1.28509	−	1.16127i	−0.185487	−	0.167614i
$49$	−2.18866	−	3.79087i	−0.312665	−	0.541552i
$50$	3.38672	−	5.86597i	0.478955	−	0.829574i
$51$	−2.24935	−	6.96509i	−0.314972	−	0.975307i
$52$	−3.29889	−	3.93146i	−0.457473	−	0.545195i
$53$	−6.53342	−	5.48219i	−0.897434	−	0.753036i	0.0722533	−	0.997386i	$-0.476981\pi$
$53$	−6.53342	−	5.48219i	−0.897434	−	0.753036i	−0.969687	+	0.244350i	$0.921425\pi$
$54$	−0.334684	−	5.18536i	−0.0455448	−	0.705638i
$55$	−8.69853	−	3.16600i	−1.17291	−	0.426904i
$56$	−3.37303			−0.450740
$57$	7.34685	+	1.73892i	0.973113	+	0.230326i
$58$	−3.76983			−0.495004
$59$	3.87665	+	1.41099i	0.504697	+	0.183695i	0.581805	−	0.813328i	$-0.302347\pi$
$59$	3.87665	+	1.41099i	0.504697	+	0.183695i	−0.0771085	+	0.997023i	$0.524569\pi$
$60$	3.65056	+	4.68975i	0.471285	+	0.605444i
$61$	3.53369	+	2.96512i	0.452443	+	0.379645i	0.840342	−	0.542057i	$-0.182354\pi$
$61$	3.53369	+	2.96512i	0.452443	+	0.379645i	−0.387898	+	0.921702i	$0.626799\pi$
$62$	−3.54973	−	4.23041i	−0.450817	−	0.537262i
$63$	−7.25390	−	7.05526i	−0.913906	−	0.888880i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	8.80484	+	15.2504i	1.09211	+	1.89158i
$66$	3.13285	−	3.46691i	0.385627	−	0.426747i
$67$	3.81629	+	10.4852i	0.466234	+	1.28097i	0.920724	+	0.390215i	$0.127599\pi$
$67$	3.81629	+	10.4852i	0.466234	+	1.28097i	−0.454490	+	0.890752i	$0.650179\pi$
$68$	−3.65965	+	2.11290i	−0.443797	+	0.256226i
$69$	−0.167450	+	4.56152i	−0.0201586	+	0.549143i
$70$	11.3979	+	2.00975i	1.36230	+	0.240211i
$71$	9.91131	−	8.31658i	1.17626	−	0.986996i	0.176260	−	0.984344i	$-0.443600\pi$
$71$	9.91131	−	8.31658i	1.17626	−	0.986996i	0.999996	−	0.00265261i	$-0.000844352\pi$
$72$	−2.88672	+	0.816605i	−0.340203	+	0.0962378i
$73$	−0.414656	−	2.35163i	−0.0485318	−	0.275238i	0.950879	−	0.309563i	$-0.100183\pi$
$73$	−0.414656	−	2.35163i	−0.0485318	−	0.275238i	−0.999411	+	0.0343255i	$0.989072\pi$
$74$	−1.77042	+	4.86419i	−0.205807	+	0.565450i
$75$	−5.48930	−	10.3685i	−0.633850	−	1.19725i
$76$	0.0923461	−	4.35792i	0.0105928	−	0.499888i
$77$		−	9.09972i		−	1.03701i
$78$	−8.80484	+	1.22141i	−0.996952	+	0.138297i
$79$	2.22246	−	0.391880i	0.250046	−	0.0440899i	−0.0472200	−	0.998885i	$-0.515036\pi$
$79$	2.22246	−	0.391880i	0.250046	−	0.0440899i	0.297266	+	0.954795i	$0.403925\pi$
$80$	2.20556	−	2.62849i	0.246589	−	0.293874i
$81$	−7.91614	−	4.28191i	−0.879571	−	0.475768i
$82$	0.289735	−	1.64317i	0.0319959	−	0.181458i
$83$	6.27861	+	3.62496i	0.689167	+	0.397891i	0.803300	−	0.595575i	$-0.203076\pi$
$83$	6.27861	+	3.62496i	0.689167	+	0.397891i	−0.114133	+	0.993465i	$0.536409\pi$
$84$	−3.10477	+	4.94898i	−0.338758	+	0.539977i
$85$	13.6253	−	4.95920i	1.47787	−	0.537901i
$86$	−2.27924	+	0.829577i	−0.245777	+	0.0894556i
$87$	−3.47002	+	5.53118i	−0.372025	+	0.593005i
$88$	−2.33635	−	1.34889i	−0.249056	−	0.143793i
$89$	0.209662	−	1.18905i	0.0222241	−	0.126039i	−0.971677	−	0.236312i	$-0.924061\pi$
$89$	0.209662	−	1.18905i	0.0222241	−	0.126039i	0.993901	+	0.110273i	$0.0351724\pi$
$90$	10.2411	−	1.03941i	1.07951	−	0.109563i
$91$	−11.1272	+	13.2609i	−1.16645	+	1.39012i
$92$	2.59533	−	0.457627i	0.270582	−	0.0477109i
$93$	−9.47436	+	1.31428i	−0.982446	+	0.136285i
$94$		−	0.128667i		−	0.0132710i
$95$	−2.90863	+	14.6709i	−0.298419	+	1.50520i
$96$	0.810416	+	1.53076i	0.0827127	+	0.156233i
$97$	3.13271	−	8.60706i	0.318079	−	0.873914i	−0.672880	−	0.739751i	$-0.734943\pi$
$97$	3.13271	−	8.60706i	0.318079	−	0.873914i	0.990959	−	0.134163i	$-0.0428346\pi$
$98$	0.760113	+	4.31081i	0.0767830	+	0.435458i
$99$	−2.20303	−	7.78777i	−0.221413	−	0.782700i
$100$	−5.18876	+	4.35388i	−0.518876	+	0.435388i
$101$	5.56915	+	0.981991i	0.554151	+	0.0977117i	0.443709	−	0.896171i	$-0.353662\pi$
$101$	5.56915	+	0.981991i	0.554151	+	0.0977117i	0.110442	+	0.993883i	$0.464773\pi$
$102$	−0.268505	+	7.31436i	−0.0265859	+	0.724230i
$103$	3.35680	−	1.93805i	0.330755	−	0.190961i	−0.325421	−	0.945569i	$-0.605506\pi$
$103$	3.35680	−	1.93805i	0.330755	−	0.190961i	0.656176	+	0.754608i	$0.272173\pi$
$104$	1.75530	+	4.82265i	0.172121	+	0.472900i
$105$	13.4401	−	14.8733i	1.31162	−	1.45148i
$106$	4.26438	+	7.38613i	0.414194	+	0.717404i
$107$	−3.48940	+	6.04382i	−0.337333	+	0.584278i	−0.983930	−	0.178554i	$-0.942858\pi$
$107$	−3.48940	+	6.04382i	−0.337333	+	0.584278i	0.646597	+	0.762832i	$0.276191\pi$
$108$	−1.45900	+	4.98712i	−0.140392	+	0.479885i
$109$	3.68457	+	4.39110i	0.352918	+	0.420591i	0.913073	−	0.407797i	$-0.133703\pi$
$109$	3.68457	+	4.39110i	0.352918	+	0.420591i	−0.560155	+	0.828388i	$0.689258\pi$
$110$	7.09110	+	5.95014i	0.676110	+	0.567324i
$111$	5.50722	+	7.07493i	0.522722	+	0.671523i
$112$	3.16961	+	1.15364i	0.299500	+	0.109009i
$113$	−16.8907			−1.58895			−0.794474	−	0.607298i	$-0.792253\pi$
$113$	−16.8907			−1.58895			−0.794474	+	0.607298i	$0.792253\pi$
$114$	−6.30903	−	4.14682i	−0.590895	−	0.388386i
$115$	−9.04260			−0.843227
$116$	3.54249	+	1.28936i	0.328912	+	0.119714i
$117$	−6.31251	+	14.0429i	−0.583592	+	1.29827i
$118$	−3.16027	−	2.65178i	−0.290927	−	0.244117i
$119$	9.16212	+	10.9190i	0.839890	+	1.00094i
$120$	−1.82642	−	5.65549i	−0.166728	−	0.516273i
$121$	−1.86097	+	3.22329i	−0.169179	+	0.293026i
$122$	−2.30645	−	3.99490i	−0.208817	−	0.361681i
$123$	−2.14420	−	1.93759i	−0.193336	−	0.174707i
$124$	1.88877	+	5.18936i	0.169617	+	0.466019i
$125$	5.26986	−	3.04256i	0.471351	−	0.272134i
$126$	4.40340	+	9.11076i	0.392286	+	0.811651i
$127$	5.44679	+	0.960416i	0.483324	+	0.0852231i	0.410001	−	0.912085i	$-0.365528\pi$
$127$	5.44679	+	0.960416i	0.483324	+	0.0852231i	0.0733234	+	0.997308i	$0.476639\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−0.880802	+	4.10776i	−0.0775503	+	0.361668i
$130$	−3.05789	−	17.3422i	−0.268195	−	1.52101i
$131$	5.04199	−	13.8528i	0.440521	−	1.21032i	−0.498629	−	0.866815i	$-0.666163\pi$
$131$	5.04199	−	13.8528i	0.440521	−	1.21032i	0.939150	−	0.343506i	$-0.111615\pi$
$132$	−4.12967	+	2.18633i	−0.359442	+	0.190296i
$133$	−14.5302	+	2.24577i	−1.25992	+	0.194733i
$134$		−	11.1581i		−	0.963911i
$135$	7.90159	−	15.9827i	0.680061	−	1.37557i
$136$	4.16160	−	0.733802i	0.356854	−	0.0629230i
$137$	12.8171	−	15.2748i	1.09503	−	1.30501i	0.146195	−	0.989256i	$-0.453297\pi$
$137$	12.8171	−	15.2748i	1.09503	−	1.30501i	0.948840	−	0.315756i	$-0.102258\pi$
$138$	1.71748	−	4.22916i	0.146202	−	0.360010i
$139$	−0.280984	+	1.59354i	−0.0238328	+	0.135162i	−0.994403	−	0.105658i	$-0.966305\pi$
$139$	−0.280984	+	1.59354i	−0.0238328	+	0.135162i	0.970570	+	0.240820i	$0.0774164\pi$
$140$	−10.0231	−	5.78684i	−0.847107	−	0.489077i
$141$	−0.188784	−	0.118434i	−0.0158984	−	0.00997398i
$142$	−12.1580	+	4.42516i	−1.02028	+	0.371351i
$143$	−13.0105	+	4.73543i	−1.08799	+	0.395997i
$144$	2.99193	+	0.219959i	0.249327	+	0.0183299i
$145$	−11.2022	−	6.46761i	−0.930295	−	0.537106i
$146$	−0.414656	+	2.35163i	−0.0343172	+	0.194622i
$147$	7.02457	+	2.85272i	0.579377	+	0.235288i
$148$	3.32730	−	3.96532i	0.273502	−	0.325948i
$149$	−23.7332	+	4.18480i	−1.94430	+	0.342832i	−0.944394	+	0.328815i	$0.893351\pi$
$149$	−23.7332	+	4.18480i	−1.94430	+	0.342832i	−0.999902	+	0.0140170i	$0.995538\pi$
$150$	1.61202	+	11.6207i	0.131621	+	0.948824i
$151$		−	14.7053i		−	1.19670i	−0.801235	−	0.598349i	$-0.795824\pi$
$151$		−	14.7053i		−	1.19670i	0.801235	−	0.598349i	$-0.204176\pi$
$152$	−1.57727	+	4.06352i	−0.127934	+	0.329595i
$153$	10.4846	+	7.12660i	0.847633	+	0.576152i
$154$	−3.11229	+	8.55094i	−0.250795	+	0.689054i
$155$	−3.29041	−	18.6609i	−0.264292	−	1.49888i
$156$	8.69159	+	1.86369i	0.695884	+	0.149214i
$157$	11.7536	−	9.86243i	0.938038	−	0.787108i	−0.0392046	−	0.999231i	$-0.512482\pi$
$157$	11.7536	−	9.86243i	0.938038	−	0.787108i	0.977243	+	0.212124i	$0.0680380\pi$
$158$	−2.22246	−	0.391880i	−0.176810	−	0.0311763i
$159$	14.7623	+	0.541913i	1.17073	+	0.0429765i
$160$	−2.97155	+	1.71562i	−0.234921	+	0.135632i
$161$	−3.04028	−	8.35309i	−0.239607	−	0.658316i
$162$	5.97424	+	6.73116i	0.469380	+	0.528850i
$163$	5.96235	+	10.3271i	0.467007	+	0.808880i	0.999290	−	0.0376868i	$-0.0119989\pi$
$163$	5.96235	+	10.3271i	0.467007	+	0.808880i	−0.532283	+	0.846567i	$0.678666\pi$
$164$	−0.834259	+	1.44498i	−0.0651447	+	0.112834i
$165$	15.2573	−	4.92729i	1.18778	−	0.383589i
$166$	−4.66016	−	5.55376i	−0.361698	−	0.431055i
$167$	−1.37759	−	1.15593i	−0.106601	−	0.0894489i	0.587929	−	0.808912i	$-0.299943\pi$
$167$	−1.37759	−	1.15593i	−0.106601	−	0.0894489i	−0.694530	+	0.719463i	$0.744388\pi$
$168$	4.61018	−	3.58862i	0.355683	−	0.276868i
$169$	12.5346	+	4.56221i	0.964198	+	0.350939i
$170$	−14.4997			−1.11208
$171$	−11.8916	+	5.43971i	−0.909371	+	0.415985i
$172$	2.42552			0.184944
$173$	6.36766	+	2.31764i	0.484124	+	0.176207i	0.572540	−	0.819877i	$-0.305958\pi$
$173$	6.36766	+	2.31764i	0.484124	+	0.176207i	−0.0884156	+	0.996084i	$0.528180\pi$
$174$	5.15252	−	4.01079i	0.390612	−	0.304057i
$175$	17.5018	+	14.6858i	1.32301	+	1.11014i
$176$	1.73411	+	2.06663i	0.130713	+	0.155778i
$177$	−6.79969	+	2.19593i	−0.511096	+	0.165056i
$178$	−0.603697	+	1.04563i	−0.0452490	+	0.0783735i
$179$	−7.17879	−	12.4340i	−0.536568	−	0.929363i	−0.999086	−	0.0427531i	$-0.986387\pi$
$179$	−7.17879	−	12.4340i	−0.536568	−	0.929363i	0.462518	−	0.886610i	$-0.346946\pi$
$180$	−9.97901	−	2.52594i	−0.743791	−	0.188273i
$181$	−4.09139	−	11.2410i	−0.304111	−	0.835537i	−0.993775	−	0.111408i	$-0.964464\pi$
$181$	−4.09139	−	11.2410i	−0.304111	−	0.835537i	0.689664	−	0.724129i	$-0.257758\pi$
$182$	14.9917	−	8.65545i	1.11126	−	0.641585i
$183$	−7.98441	−	0.293102i	−0.590225	−	0.0216667i
$184$	−2.59533	−	0.457627i	−0.191330	−	0.0337367i
$185$	−13.6060	+	11.4168i	−1.00033	+	0.839379i
$186$	9.35250	+	2.00540i	0.685759	+	0.147043i
$187$	1.97964	+	11.2271i	0.144766	+	0.821008i
$188$	−0.0440069	+	0.120908i	−0.00320953	+	0.00881811i
$189$	17.4207	+	1.92542i	1.26717	+	0.140054i
$190$	7.75096	−	12.7913i	0.562314	−	0.927980i
$191$			10.1652i			0.735526i	0.929919	+	0.367763i	$0.119876\pi$
$191$			10.1652i			0.735526i	−0.929919	+	0.367763i	$0.880124\pi$
$192$	−0.237991	−	1.71562i	−0.0171755	−	0.123814i
$193$	−12.3371	+	2.17537i	−0.888046	+	0.156587i	−0.599019	−	0.800734i	$-0.704443\pi$
$193$	−12.3371	+	2.17537i	−0.888046	+	0.156587i	−0.289027	+	0.957321i	$0.593332\pi$
$194$	−5.88758	+	7.01654i	−0.422703	+	0.503758i
$195$	−28.2595	−	11.4763i	−2.02370	−	0.821836i
$196$	0.760113	−	4.31081i	0.0542938	−	0.307915i
$197$	19.9041	+	11.4916i	1.41811	+	0.818744i	0.996132	−	0.0878643i	$-0.0280042\pi$
$197$	19.9041	+	11.4916i	1.41811	+	0.818744i	0.421974	+	0.906608i	$0.361338\pi$
$198$	−0.593403	+	8.07159i	−0.0421713	+	0.573623i
$199$	−23.8117	+	8.66676i	−1.68797	+	0.614370i	−0.994367	−	0.105990i	$-0.966199\pi$
$199$	−23.8117	+	8.66676i	−1.68797	+	0.614370i	−0.693601	+	0.720360i	$0.743977\pi$
$200$	6.36495	−	2.31665i	0.450070	−	0.163812i
$201$	−16.3714	−	10.2707i	−1.15475	−	0.724437i
$202$	−4.89743	−	2.82753i	−0.344582	−	0.198944i
$203$	2.20807	−	12.5226i	0.154976	−	0.878913i
$204$	2.75397	−	6.78142i	0.192817	−	0.474794i
$205$	3.68002	−	4.38567i	0.257024	−	0.306309i
$206$	−3.81721	+	0.673077i	−0.265957	+	0.0468955i
$207$	−4.62422	−	6.41274i	−0.321405	−	0.445716i
$208$		−	5.13216i		−	0.355851i
$209$	−10.9625	−	4.25515i	−0.758294	−	0.294335i
$210$	−17.7165	+	9.37949i	−1.22256	+	0.647247i
$211$	−4.07273	+	11.1897i	−0.280378	+	0.770333i	0.716939	+	0.697136i	$0.245542\pi$
$211$	−4.07273	+	11.1897i	−0.280378	+	0.770333i	−0.997317	+	0.0731972i	$0.976680\pi$
$212$	−1.48101	−	8.39920i	−0.101716	−	0.576859i
$213$	−4.69840	+	21.9117i	−0.321929	+	1.50137i
$214$	5.34607	−	4.48588i	0.365450	−	0.306649i
$215$	−8.19612	−	1.44520i	−0.558971	−	0.0985616i
$216$	3.07670	−	4.18735i	0.209343	−	0.284913i
$217$	16.1316	−	9.31361i	1.09509	−	0.632249i
$218$	−1.96052	−	5.38648i	−0.132783	−	0.364818i
$219$	3.06868	+	2.77300i	0.207362	+	0.187382i
$220$	−4.62839	−	8.01660i	−0.312046	−	0.540479i
$221$	10.8437	−	18.7819i	0.729427	−	1.26341i
$222$	−2.75533	−	8.53184i	−0.184925	−	0.572620i
$223$	8.14222	+	9.70352i	0.545243	+	0.649796i	0.966355	−	0.257213i	$-0.0828043\pi$
$223$	8.14222	+	9.70352i	0.545243	+	0.649796i	−0.421111	+	0.907009i	$0.638360\pi$
$224$	−2.58389	−	2.16814i	−0.172643	−	0.144865i
$225$	18.5339	+	8.33128i	1.23559	+	0.555419i
$226$	15.8721	+	5.77698i	1.05580	+	0.384279i
$227$	−3.77953			−0.250857			−0.125428	−	0.992103i	$-0.540030\pi$
$227$	−3.77953			−0.250857			−0.125428	+	0.992103i	$0.540030\pi$
$228$	4.51025	+	6.05456i	0.298699	+	0.400973i
$229$	15.3222			1.01252			0.506259	−	0.862381i	$-0.331028\pi$
$229$	15.3222			1.01252			0.506259	+	0.862381i	$0.331028\pi$
$230$	8.49726	+	3.09275i	0.560293	+	0.203930i
$231$	9.68135	+	12.4373i	0.636986	+	0.818313i
$232$	−2.88786	−	2.42320i	−0.189597	−	0.159091i
$233$	15.6260	+	18.6223i	1.02369	+	1.21999i	0.975236	+	0.221165i	$0.0709860\pi$
$233$	15.6260	+	18.6223i	1.02369	+	1.21999i	0.0484572	+	0.998825i	$0.484570\pi$
$234$	10.7348	−	11.0370i	0.701755	−	0.721512i
$235$	0.220745	−	0.382341i	0.0143998	−	0.0249412i
$236$	2.06272	+	3.57274i	0.134272	+	0.232566i
$237$	−2.62068	+	2.90013i	−0.170232	+	0.188384i
$238$	−4.87506	−	13.3941i	−0.316003	−	0.868212i
$239$	−11.5689	+	6.67933i	−0.748332	+	0.432050i	−0.825091	−	0.565000i	$-0.808876\pi$
$239$	−11.5689	+	6.67933i	−0.748332	+	0.432050i	0.0767587	+	0.997050i	$0.475543\pi$
$240$	−0.218019	+	5.93909i	−0.0140731	+	0.383367i
$241$	−21.6352	−	3.81487i	−1.39365	−	0.245737i	−0.574116	−	0.818774i	$-0.694654\pi$
$241$	−21.6352	−	3.81487i	−1.39365	−	0.245737i	−0.819530	+	0.573037i	$0.805765\pi$
$242$	2.85116	−	2.39241i	0.183280	−	0.153790i
$243$	15.3752	−	2.56970i	0.986319	−	0.164846i
$244$	0.801023	+	4.54283i	0.0512803	+	0.290825i
$245$	−5.13702	+	14.1138i	−0.328192	+	0.901700i
$246$	1.35219	+	2.55410i	0.0862126	+	0.162843i
$247$	10.7723	+	19.6061i	0.685427	+	1.24751i
$248$		−	5.52241i		−	0.350673i
$249$	−12.4381	+	1.72541i	−0.788234	+	0.109344i
$250$	−5.99267	+	1.05667i	−0.379009	+	0.0668296i
$251$	−4.35873	+	5.19453i	−0.275121	+	0.327876i	−0.885857	−	0.463958i	$-0.846429\pi$
$251$	−4.35873	+	5.19453i	−0.275121	+	0.327876i	0.610737	+	0.791834i	$0.290873\pi$
$252$	−1.02177	−	10.0674i	−0.0643658	−	0.634184i
$253$	1.23458	−	7.00166i	0.0776175	−	0.440191i
$254$	−4.78983	−	2.76541i	−0.300540	−	0.173517i
$255$	−13.3466	+	21.2743i	−0.835794	+	1.33225i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	16.7251	−	6.08743i	1.04328	−	0.379724i	0.237158	−	0.971471i	$-0.423784\pi$
$257$	16.7251	−	6.08743i	1.04328	−	0.379724i	0.806123	+	0.591747i	$0.201562\pi$
$258$	2.23262	−	3.55878i	0.138997	−	0.221560i
$259$	−15.1208	−	8.73000i	−0.939561	−	0.542456i
$260$	−3.05789	+	17.3422i	−0.189642	+	1.07551i
$261$	−1.14198	−	11.2517i	−0.0706866	−	0.696463i
$262$	−9.47585	+	11.2929i	−0.585420	+	0.697676i
$263$	3.78041	−	0.666587i	0.233110	−	0.0411035i	−0.0558728	−	0.998438i	$-0.517794\pi$
$263$	3.78041	−	0.666587i	0.233110	−	0.0411035i	0.288983	+	0.957334i	$0.406683\pi$
$264$	4.62839	−	0.642049i	0.284858	−	0.0395154i
$265$			29.2643i			1.79769i
$266$	14.4220	+	2.85928i	0.884268	+	0.175313i
$267$	0.978490	+	1.84823i	0.0598826	+	0.113110i
$268$	−3.81629	+	10.4852i	−0.233117	+	0.640483i
$269$	0.457985	+	2.59736i	0.0279239	+	0.158364i	0.995581	−	0.0939040i	$-0.0299347\pi$
$269$	0.457985	+	2.59736i	0.0279239	+	0.158364i	−0.967657	+	0.252268i	$0.918824\pi$
$270$	−12.8915	+	12.3164i	−0.784551	+	0.749549i
$271$	10.7222	−	8.99702i	0.651329	−	0.546530i	−0.256145	−	0.966638i	$-0.582452\pi$
$271$	10.7222	−	8.99702i	0.651329	−	0.546530i	0.907474	+	0.420108i	$0.138008\pi$
$272$	−4.16160	−	0.733802i	−0.252334	−	0.0444933i
$273$	1.09993	−	29.9632i	0.0665705	−	1.81345i
$274$	−17.2684	+	9.96990i	−1.04322	+	0.602304i
$275$	6.24984	+	17.1713i	0.376880	+	1.03547i
$276$	−3.06036	+	3.38669i	−0.184212	+	0.203855i
$277$	−0.166629	−	0.288609i	−0.0100117	−	0.0173408i	0.860976	−	0.508645i	$-0.169854\pi$
$277$	−0.166629	−	0.288609i	−0.0100117	−	0.0173408i	−0.870988	+	0.491305i	$0.836520\pi$
$278$	0.809062	−	1.40134i	0.0485243	−	0.0840466i
$279$	11.5511	−	11.8763i	0.691544	−	0.711014i
$280$	7.43942	+	8.86596i	0.444590	+	0.529842i
$281$	1.92247	+	1.61315i	0.114685	+	0.0962323i	0.698327	−	0.715779i	$-0.253928\pi$
$281$	1.92247	+	1.61315i	0.114685	+	0.0962323i	−0.583642	+	0.812011i	$0.698373\pi$
$282$	0.136892	+	0.175860i	0.00815177	+	0.0104723i
$283$	−24.7578	−	9.01110i	−1.47170	−	0.535655i	−0.523138	−	0.852248i	$-0.675239\pi$
$283$	−24.7578	−	9.01110i	−1.47170	−	0.535655i	−0.948561	+	0.316594i	$0.897461\pi$
$284$	12.9383			0.767747
$285$	−11.6332	−	23.1464i	−0.689090	−	1.37107i
$286$	13.8455			0.818700
$287$	5.28855	+	1.92487i	0.312173	+	0.113622i
$288$	−2.73626	−	1.22999i	−0.161236	−	0.0724780i
$289$	−0.656761	−	0.551088i	−0.0386330	−	0.0324169i
$290$	8.31460	+	9.90896i	0.488250	+	0.581874i
$291$	4.87548	+	15.0969i	0.285806	+	0.884995i
$292$	1.19395	−	2.06799i	0.0698709	−	0.121020i
$293$	−6.53329	−	11.3160i	−0.381679	−	0.661087i	0.609624	−	0.792691i	$-0.291321\pi$
$293$	−6.53329	−	11.3160i	−0.381679	−	0.661087i	−0.991302	+	0.131604i	$0.957987\pi$
$294$	−5.62525	−	5.08322i	−0.328071	−	0.296460i
$295$	−4.84144	−	13.3017i	−0.281879	−	0.774457i
$296$	−4.48286	+	2.58818i	−0.260561	+	0.150435i
$297$	11.2966	+	8.30030i	0.655495	+	0.481632i
$298$	23.7332	+	4.18480i	1.37482	+	0.242419i
$299$	−10.3608	+	8.69378i	−0.599183	+	0.502775i
$300$	2.45970	−	11.4712i	0.142011	−	0.662290i
$301$	−1.42068	−	8.05706i	−0.0818864	−	0.464401i
$302$	−5.02950	+	13.8184i	−0.289415	+	0.795162i
$303$	−8.65654	+	4.58295i	−0.497305	+	0.263284i
$304$	2.87196	−	3.27900i	0.164718	−	0.188064i
$305$		−	15.8280i		−	0.906310i
$306$	−7.41489	−	10.2828i	−0.423881	−	0.587827i
$307$	7.06477	−	1.24571i	0.403208	−	0.0710964i	0.0316333	−	0.999500i	$-0.489929\pi$
$307$	7.06477	−	1.24571i	0.403208	−	0.0710964i	0.371575	+	0.928403i	$0.378818\pi$
$308$	5.84919	−	6.97079i	0.333288	−	0.397198i
$309$	−2.52607	+	6.22023i	−0.143703	+	0.353857i
$310$	−3.29041	+	18.6609i	−0.186883	+	1.05987i
$311$	−9.96292	−	5.75210i	−0.564945	−	0.326171i	0.190183	−	0.981749i	$-0.439092\pi$
$311$	−9.96292	−	5.75210i	−0.564945	−	0.326171i	−0.755128	+	0.655577i	$0.772425\pi$
$312$	−7.53000	−	4.72399i	−0.426303	−	0.267443i
$313$	16.6644	−	6.06533i	0.941925	−	0.342833i	0.174999	−	0.984569i	$-0.444008\pi$
$313$	16.6644	−	6.06533i	0.941925	−	0.342833i	0.766926	+	0.641736i	$0.221785\pi$
$314$	−14.4179	+	5.24769i	−0.813650	+	0.296144i
$315$	−2.54574	+	34.6276i	−0.143436	+	1.95104i
$316$	1.95440	+	1.12837i	0.109944	+	0.0634759i
$317$	−5.91797	+	33.5625i	−0.332386	+	1.88506i	0.119267	+	0.992862i	$0.461946\pi$
$317$	−5.91797	+	33.5625i	−0.332386	+	1.88506i	−0.451653	+	0.892194i	$0.649165\pi$
$318$	−13.6867	−	5.55824i	−0.767512	−	0.311691i
$319$	6.53729	−	7.79084i	0.366018	−	0.436203i
$320$	3.37912	−	0.595829i	0.188898	−	0.0333079i
$321$	−1.66089	−	11.9730i	−0.0927019	−	0.668267i
$322$			8.88918i			0.495374i
$323$	17.4385	−	5.93183i	0.970307	−	0.330056i
$324$	−3.31175	−	8.36853i	−0.183986	−	0.464918i
$325$	11.8894	−	32.6659i	0.659507	−	1.81198i
$326$	−2.07070	−	11.7435i	−0.114686	−	0.650414i
$327$	−9.70775	−	2.08158i	−0.536840	−	0.115111i
$328$	1.27816	−	1.07250i	0.0705745	−	0.0592190i
$329$	0.427405	+	0.0753631i	0.0235636	+	0.00415490i
$330$	−16.0224	−	0.588171i	−0.882005	−	0.0323777i
$331$	18.0961	−	10.4478i	0.994652	−	0.574263i	0.0879907	−	0.996121i	$-0.471955\pi$
$331$	18.0961	−	10.4478i	0.994652	−	0.574263i	0.906662	+	0.421858i	$0.138622\pi$
$332$	2.47962	+	6.81269i	0.136087	+	0.373895i
$333$	−15.0543	−	3.81063i	−0.824970	−	0.208821i
$334$	0.899158	+	1.55739i	0.0491997	+	0.0852164i
$335$	19.1430	−	33.1567i	1.04590	−	1.81155i
$336$	−5.55953	+	1.79543i	−0.303297	+	0.0979487i
$337$	−19.1366	−	22.8061i	−1.04244	−	1.24233i	−0.969526	−	0.244988i	$-0.921216\pi$
$337$	−19.1366	−	22.8061i	−1.04244	−	1.24233i	−0.0729092	−	0.997339i	$-0.523228\pi$
$338$	−10.2183	−	8.57416i	−0.555801	−	0.466373i
$339$	23.0859	−	17.9704i	1.25385	−	0.976016i
$340$	13.6253	+	4.95920i	0.738935	+	0.268950i
$341$	14.8983			0.806788
$342$	13.0349	−	1.04450i	0.704847	−	0.0564802i
$343$	8.84639			0.477660
$344$	−2.27924	−	0.829577i	−0.122889	−	0.0447278i
$345$	12.3592	−	9.62058i	0.665398	−	0.517955i
$346$	−5.19097	−	4.35574i	−0.279068	−	0.234166i
$347$	3.49226	+	4.16191i	0.187474	+	0.223423i	0.851592	−	0.524204i	$-0.175637\pi$
$347$	3.49226	+	4.16191i	0.187474	+	0.223423i	−0.664118	+	0.747628i	$0.731193\pi$
$348$	−6.21356	+	2.00665i	−0.333082	+	0.107567i
$349$	−8.07643	+	13.9888i	−0.432322	+	0.748803i	−0.997073	−	0.0764582i	$-0.975639\pi$
$349$	−8.07643	+	13.9888i	−0.432322	+	0.748803i	0.564751	+	0.825261i	$0.308972\pi$
$350$	−11.4235	−	19.7861i	−0.610612	−	1.05761i
$351$	−6.31270	−	25.9095i	−0.336947	−	1.38295i
$352$	−0.922698	−	2.53509i	−0.0491800	−	0.135121i
$353$	18.1153	−	10.4589i	0.964180	−	0.556670i	0.0667232	−	0.997772i	$-0.478746\pi$
$353$	18.1153	−	10.4589i	0.964180	−	0.556670i	0.897457	+	0.441102i	$0.145412\pi$
$354$	7.14067	+	0.262129i	0.379522	+	0.0139320i
$355$	−43.7200	−	7.70902i	−2.32042	−	0.409152i
$356$	0.924917	−	0.776097i	0.0490205	−	0.0411331i
$357$	−24.1395	−	5.17608i	−1.27760	−	0.273947i
$358$	2.49317	+	14.1395i	0.131768	+	0.747294i
$359$	8.05343	−	22.1266i	0.425044	−	1.16780i	−0.523741	−	0.851877i	$-0.675464\pi$
$359$	8.05343	−	22.1266i	0.425044	−	1.16780i	0.948785	−	0.315921i	$-0.102314\pi$
$360$	8.51328	+	5.78663i	0.448689	+	0.304982i
$361$	−4.08900	+	18.5548i	−0.215211	+	0.976568i
$362$			11.9624i			0.628731i
$363$	−0.885785	−	6.38543i	−0.0464917	−	0.335148i
$364$	−17.0479	+	3.00601i	−0.893553	+	0.157558i
$365$	−5.26668	+	6.27659i	−0.275671	+	0.328532i
$366$	7.40265	+	3.00626i	0.386943	+	0.157140i
$367$	3.11469	−	17.6643i	0.162586	−	0.922069i	−0.788933	−	0.614479i	$-0.789366\pi$
$367$	3.11469	−	17.6643i	0.162586	−	0.922069i	0.951519	−	0.307590i	$-0.0995226\pi$
$368$	2.28230	+	1.31768i	0.118973	+	0.0686891i
$369$	4.99208	+	0.367005i	0.259877	+	0.0191055i
$370$	16.6902	−	6.07474i	0.867683	−	0.315811i
$371$	−27.0329	+	9.83916i	−1.40348	+	0.510824i
$372$	−8.10259	−	5.08320i	−0.420100	−	0.263552i
$373$	12.2615	+	7.07917i	0.634876	+	0.366546i	0.782638	−	0.622477i	$-0.213874\pi$
$373$	12.2615	+	7.07917i	0.634876	+	0.366546i	−0.147762	+	0.989023i	$0.547207\pi$
$374$	1.97964	−	11.2271i	0.102365	−	0.580540i
$375$	−3.96570	+	9.76519i	−0.204788	+	0.504272i
$376$	0.0827058	−	0.0985650i	0.00426523	−	0.00508310i
$377$	−19.0534	+	3.35964i	−0.981303	+	0.173030i
$378$	−15.7116	−	7.76753i	−0.808115	−	0.399519i
$379$			1.25595i			0.0645137i	0.999480	+	0.0322569i	$0.0102695\pi$
$379$			1.25595i			0.0645137i	−0.999480	+	0.0322569i	$0.989731\pi$
$380$	−11.6584	+	9.36893i	−0.598064	+	0.480616i
$381$	−8.46635	+	4.48226i	−0.433744	+	0.229633i
$382$	3.47670	−	9.55214i	0.177883	−	0.488730i
$383$	0.465296	+	2.63882i	0.0237755	+	0.134838i	0.994385	−	0.105822i	$-0.0337474\pi$
$383$	0.465296	+	2.63882i	0.0237755	+	0.134838i	−0.970610	+	0.240660i	$0.922636\pi$
$384$	−0.363139	+	1.69356i	−0.0185314	+	0.0864239i
$385$	−23.9185	+	20.0700i	−1.21900	+	1.02286i
$386$	12.3371	+	2.17537i	0.627944	+	0.110723i
$387$	−3.16645	−	6.55149i	−0.160960	−	0.333031i
$388$	7.93231	−	4.57972i	0.402702	−	0.232500i
$389$	11.2472	+	30.9013i	0.570253	+	1.56676i	0.804106	+	0.594486i	$0.202645\pi$
$389$	11.2472	+	30.9013i	0.570253	+	1.56676i	−0.233852	+	0.972272i	$0.575133\pi$
$390$	22.6301	+	20.4495i	1.14592	+	1.03550i
$391$	5.56827	+	9.64452i	0.281599	+	0.487744i
$392$	−2.18866	+	3.79087i	−0.110544	+	0.191468i
$393$	7.84692	+	24.2979i	0.395825	+	1.22567i
$394$	−14.7733	−	17.6062i	−0.744270	−	0.886987i
$395$	−5.93183	−	4.97739i	−0.298463	−	0.250440i
$396$	3.31826	−	7.38185i	0.166749	−	0.370952i
$397$	−2.19998	−	0.800726i	−0.110414	−	0.0401873i	0.286223	−	0.958163i	$-0.407600\pi$
$397$	−2.19998	−	0.800726i	−0.110414	−	0.0401873i	−0.396636	+	0.917976i	$0.629823\pi$
$398$	25.3399			1.27017
$399$	17.4702	−	18.5284i	0.874603	−	0.927578i
$400$	−6.77344			−0.338672
$401$	12.8782	+	4.68726i	0.643104	+	0.234071i	0.642925	−	0.765929i	$-0.277721\pi$
$401$	12.8782	+	4.68726i	0.643104	+	0.234071i	0.000179351		1.00000i	$0.499943\pi$
$402$	11.8713	+	15.2506i	0.592085	+	0.760631i
$403$	−21.7111	−	18.2178i	−1.08151	−	0.907492i
$404$	3.63500	+	4.33203i	0.180848	+	0.215526i
$405$	6.20459	+	30.2515i	0.308308	+	1.50321i
$406$	−6.35788	+	11.0122i	−0.315536	+	0.546525i
$407$	−6.98237	−	12.0938i	−0.346103	−	0.599468i
$408$	−4.90727	+	5.43054i	−0.242946	+	0.268852i
$409$	7.27394	+	19.9850i	0.359673	+	0.988194i	0.979143	+	0.203173i	$0.0651254\pi$
$409$	7.27394	+	19.9850i	0.359673	+	0.988194i	−0.619470	+	0.785020i	$0.712652\pi$
$410$	−4.95807	+	2.86255i	−0.244862	+	0.141371i
$411$	−1.26696	+	34.5135i	−0.0624947	+	1.70243i
$412$	3.81721	+	0.673077i	0.188060	+	0.0331601i
$413$	10.6597	−	8.94454i	0.524529	−	0.440132i
$414$	2.15206	+	7.60758i	0.105768	+	0.373892i
$415$	−4.31971	−	24.4983i	−0.212046	−	1.20257i
$416$	−1.75530	+	4.82265i	−0.0860607	+	0.236450i
$417$	−1.31135	−	2.47696i	−0.0642173	−	0.121297i
$418$	8.84606	+	7.74794i	0.432675	+	0.378964i
$419$			29.1990i			1.42646i	0.700928	+	0.713232i	$0.252770\pi$
$419$			29.1990i			1.42646i	−0.700928	+	0.713232i	$0.747230\pi$
$420$	19.8561	−	2.75443i	0.968877	−	0.134402i
$421$	7.45681	−	1.31484i	0.363423	−	0.0640812i	0.0110448	−	0.999939i	$-0.496484\pi$
$421$	7.45681	−	1.31484i	0.363423	−	0.0640812i	0.352378	+	0.935858i	$0.385373\pi$
$422$	7.65423	−	9.12195i	0.372602	−	0.444050i
$423$	0.384029	−	0.0389766i	0.0186722	−	0.00189511i
$424$	−1.48101	+	8.39920i	−0.0719240	+	0.407901i
$425$	−24.7884	−	14.3116i	−1.20241	−	0.694214i
$426$	11.9093	−	18.9833i	0.577008	−	0.919746i
$427$	14.6211	−	5.32165i	0.707565	−	0.257533i
$428$	−6.55793	+	2.38689i	−0.316989	+	0.115375i
$429$	12.7443	−	20.3144i	0.615302	−	0.980787i
$430$	7.20755	+	4.16128i	0.347579	+	0.200675i
$431$	−4.16028	+	23.5941i	−0.200394	+	1.13649i	0.704132	+	0.710069i	$0.251336\pi$
$431$	−4.16028	+	23.5941i	−0.200394	+	1.13649i	−0.904526	+	0.426419i	$0.859775\pi$
$432$	−4.32331	+	2.88253i	−0.208006	+	0.138686i
$433$	−9.89407	+	11.7913i	−0.475479	+	0.566654i	−0.949463	−	0.313880i	$-0.898371\pi$
$433$	−9.89407	+	11.7913i	−0.475479	+	0.566654i	0.473984	+	0.880534i	$0.342816\pi$
$434$	−18.3442	+	3.23458i	−0.880551	+	0.155265i
$435$	22.1920	−	3.07847i	1.06402	−	0.147601i
$436$			5.73217i			0.274521i
$437$	−11.4847	−	0.243366i	−0.549389	−	0.0116418i
$438$	−1.93520	−	3.65532i	−0.0924674	−	0.174658i
$439$	−7.60564	+	20.8963i	−0.362997	+	0.997327i	0.614967	+	0.788553i	$0.289169\pi$
$439$	−7.60564	+	20.8963i	−0.362997	+	0.997327i	−0.977964	+	0.208774i	$0.933053\pi$
$440$	1.60742	+	9.11615i	0.0766309	+	0.434595i
$441$	−12.6361	+	3.57454i	−0.601718	+	0.170216i
$442$	−16.6135	+	13.9404i	−0.790225	+	0.663078i
$443$	30.8547	+	5.44051i	1.46595	+	0.258486i	0.848948	−	0.528476i	$-0.177236\pi$
$443$	30.8547	+	5.44051i	1.46595	+	0.258486i	0.617001	+	0.786963i	$0.288348\pi$
$444$	−0.328903	+	8.95969i	−0.0156091	+	0.425208i
$445$	−3.58782	+	2.07143i	−0.170079	+	0.0981952i
$446$	−4.33238	−	11.9031i	−0.205144	−	0.563629i
$447$	27.9857	−	30.9698i	1.32368	−	1.46482i
$448$	1.68651	+	2.92113i	0.0796803	+	0.138010i
$449$	−6.15216	+	10.6559i	−0.290338	+	0.502881i	−0.973890	−	0.227022i	$-0.927101\pi$
$449$	−6.15216	+	10.6559i	−0.290338	+	0.502881i	0.683551	+	0.729902i	$0.260435\pi$
$450$	−14.5667	−	14.1678i	−0.686681	−	0.667877i
$451$	2.89339	+	3.44820i	0.136244	+	0.162370i
$452$	−12.9391	−	10.8572i	−0.608602	−	0.510678i
$453$	15.6452	+	20.0988i	0.735076	+	0.944326i
$454$	3.55160	+	1.29268i	0.166685	+	0.0606683i
$455$	59.3979			2.78462
$456$	−2.16747	−	7.23202i	−0.101501	−	0.338670i
$457$	−37.8216			−1.76922			−0.884609	−	0.466334i	$-0.845575\pi$
$457$	−37.8216			−1.76922			−0.884609	+	0.466334i	$0.845575\pi$
$458$	−14.3981	−	5.24049i	−0.672781	−	0.244872i
$459$	−21.9123	+	1.41431i	−1.02278	+	0.0660142i
$460$	−6.92703	−	5.81247i	−0.322975	−	0.271008i
$461$	−24.9818	−	29.7722i	−1.16352	−	1.38663i	−0.907550	−	0.419945i	$-0.862050\pi$
$461$	−24.9818	−	29.7722i	−1.16352	−	1.38663i	−0.255970	−	0.966685i	$-0.582395\pi$
$462$	−4.84369	−	14.9984i	−0.225349	−	0.697791i
$463$	12.3259	−	21.3492i	0.572835	−	0.992180i	−0.423438	−	0.905925i	$-0.639177\pi$
$463$	12.3259	−	21.3492i	0.572835	−	0.992180i	0.996273	−	0.0862548i	$-0.0274899\pi$
$464$	1.88492	+	3.26477i	0.0875051	+	0.151563i
$465$	24.3509	+	22.0045i	1.12924	+	1.02043i
$466$	−8.31442	−	22.8437i	−0.385158	−	1.05821i
$467$	3.17931	−	1.83558i	0.147121	−	0.0849404i	−0.424632	−	0.905366i	$-0.639597\pi$
$467$	3.17931	−	1.83558i	0.147121	−	0.0849404i	0.571754	+	0.820425i	$0.306263\pi$
$468$	−13.8623	+	6.69989i	−0.640784	+	0.309702i
$469$	37.0647	+	6.53551i	1.71149	+	0.301782i
$470$	−0.338201	+	0.283784i	−0.0156000	+	0.0130900i
$471$	−5.57172	+	25.9846i	−0.256731	+	1.19731i
$472$	−0.716376	−	4.06277i	−0.0329739	−	0.187004i
$473$	2.23803	−	6.14892i	0.102905	−	0.282728i
$474$	3.45454	−	1.82890i	0.158672	−	0.0840043i
$475$	25.8762	−	14.2174i	1.18728	−	0.652337i
$476$			14.2537i			0.653318i
$477$	−20.7534	+	14.9652i	−0.950231	+	0.685210i
$478$	13.1557	−	2.31971i	0.601728	−	0.106101i
$479$	−16.6874	+	19.8872i	−0.762465	+	0.908670i	−0.998001	−	0.0631952i	$-0.979871\pi$
$479$	−16.6874	+	19.8872i	−0.762465	+	0.908670i	0.235536	+	0.971866i	$0.424315\pi$
$480$	2.23616	−	5.50635i	0.102066	−	0.251329i
$481$	−4.61312	+	26.1623i	−0.210340	+	1.19290i
$482$	19.0257	+	10.9845i	0.866596	+	0.500329i
$483$	13.0424	+	8.18221i	0.593449	+	0.372304i
$484$	−3.49747	+	1.27298i	−0.158976	+	0.0578625i
$485$	−29.5329	+	10.7491i	−1.34102	+	0.488092i
$486$	−15.3268	−	2.84390i	−0.695240	−	0.129002i
$487$	8.59327	+	4.96133i	0.389398	+	0.224819i	0.681899	−	0.731446i	$-0.261154\pi$
$487$	8.59327	+	4.96133i	0.389398	+	0.224819i	−0.292501	+	0.956265i	$0.594488\pi$
$488$	0.801023	−	4.54283i	0.0362606	−	0.205644i
$489$	−19.1364	−	7.77138i	−0.865376	−	0.351434i
$490$	9.65444	−	11.5057i	0.436143	−	0.519775i
$491$	14.8971	−	2.62676i	0.672296	−	0.118544i	0.172929	−	0.984934i	$-0.444677\pi$
$491$	14.8971	−	2.62676i	0.672296	−	0.118544i	0.499367	+	0.866391i	$0.333566\pi$
$492$	−0.397092	−	2.86255i	−0.0179023	−	0.129054i
$493$			15.9305i			0.717476i
$494$	−3.41700	−	22.1080i	−0.153738	−	0.994688i
$495$	−15.6111	+	22.9670i	−0.701668	+	1.03229i
$496$	−1.88877	+	5.18936i	−0.0848084	+	0.233009i
$497$	−7.57822	−	42.9782i	−0.339930	−	1.92784i
$498$	12.2781	+	2.63273i	0.550196	+	0.117975i
$499$	16.3136	−	13.6887i	0.730296	−	0.612791i	−0.199917	−	0.979813i	$-0.564067\pi$
$499$	16.3136	−	13.6887i	0.730296	−	0.612791i	0.930212	+	0.367022i	$0.119623\pi$
$500$	5.99267	+	1.05667i	0.268000	+	0.0472557i
$501$	3.11268	+	0.114264i	0.139064	+	0.00510494i
$502$	5.87250	−	3.39049i	0.262103	−	0.151325i
$503$	−1.99181	−	5.47245i	−0.0888104	−	0.244004i	0.887334	−	0.461128i	$-0.152555\pi$
$503$	−1.99181	−	5.47245i	−0.0888104	−	0.244004i	−0.976144	+	0.217123i	$0.930333\pi$
$504$	−2.48309	+	9.80969i	−0.110605	+	0.436959i
$505$	−9.70195	−	16.8043i	−0.431731	−	0.747780i
$506$	−3.55484	+	6.15716i	−0.158032	+	0.273719i
$507$	−21.9858	+	7.10023i	−0.976423	+	0.315332i
$508$	3.55514	+	4.23685i	0.157734	+	0.187980i
$509$	−10.9586	−	9.19535i	−0.485731	−	0.407577i	0.366763	−	0.930315i	$-0.380466\pi$
$509$	−10.9586	−	9.19535i	−0.485731	−	0.407577i	−0.852493	+	0.522738i	$0.824911\pi$
$510$	19.8179	−	15.4265i	0.877552	−	0.683098i
$511$	−7.56874	−	2.75480i	−0.334821	−	0.121865i
$512$	1.00000			0.0441942
$513$	10.4657	−	20.0865i	0.462073	−	0.886842i
$514$	−17.7985			−0.785056
$515$	−12.4977	−	4.54881i	−0.550717	−	0.200444i
$516$	−3.31515	+	2.58055i	−0.145941	+	0.113603i
$517$	0.265908	+	0.223123i	0.0116946	+	0.00981294i
$518$	11.2231	+	13.3751i	0.493114	+	0.587670i
$519$	−11.1690	+	3.60697i	−0.490263	+	0.158328i
$520$	8.80484	−	15.2504i	0.386118	−	0.668776i
$521$	−5.93133	−	10.2734i	−0.259856	−	0.450084i	0.706347	−	0.707866i	$-0.250342\pi$
$521$	−5.93133	−	10.2734i	−0.259856	−	0.450084i	−0.966203	+	0.257781i	$0.917009\pi$
$522$	−2.77520	+	10.9637i	−0.121467	+	0.479869i
$523$	10.6971	+	29.3899i	0.467750	+	1.28513i	0.919536	+	0.393005i	$0.128565\pi$
$523$	10.6971	+	29.3899i	0.467750	+	1.28513i	−0.451787	+	0.892126i	$0.649213\pi$
$524$	12.7668	−	7.37090i	0.557719	−	0.321999i
$525$	−39.5455	−	1.45169i	−1.72591	−	0.0633568i
$526$	−3.78041	−	0.666587i	−0.164834	−	0.0290646i
$527$	−17.8768	+	15.0004i	−0.778727	+	0.653430i
$528$	−4.56886	−	0.979673i	−0.198834	−	0.0426348i
$529$	2.78789	+	15.8109i	0.121213	+	0.687431i
$530$	10.0090	−	27.4994i	0.434762	−	1.19450i
$531$	6.95737	−	10.2357i	0.301924	−	0.444190i
$532$	−12.5743	−	7.61945i	−0.545165	−	0.330345i
$533$		−	8.56309i		−	0.370909i
$534$	−0.287349	−	2.07143i	−0.0124348	−	0.0896396i
$535$	23.5822	−	4.15817i	1.01955	−	0.179774i
$536$	7.17227	−	8.54758i	0.309795	−	0.369199i
$537$	23.0406	+	9.35691i	0.994275	+	0.403780i
$538$	0.457985	−	2.59736i	0.0197451	−	0.111980i
$539$	−10.2270	−	5.90454i	−0.440506	−	0.254326i
$540$	16.3265	−	7.16444i	0.702580	−	0.308308i
$541$	−26.2388	+	9.55016i	−1.12810	+	0.410593i	−0.837601	−	0.546283i	$-0.816042\pi$
$541$	−26.2388	+	9.55016i	−1.12810	+	0.410593i	−0.290495	+	0.956876i	$0.593820\pi$
$542$	−13.1528	+	4.78721i	−0.564960	+	0.205628i
$543$	17.5515	+	11.0110i	0.753207	+	0.472529i
$544$	3.65965	+	2.11290i	0.156906	+	0.0905897i
$545$	3.41540	−	19.3697i	0.146300	−	0.829706i
$546$	−11.2816	+	27.7800i	−0.482808	+	1.18887i
$547$	12.0859	−	14.4034i	0.516757	−	0.615847i	−0.443054	−	0.896495i	$-0.646105\pi$
$547$	12.0859	−	14.4034i	0.516757	−	0.615847i	0.959811	+	0.280648i	$0.0905494\pi$
$548$	19.6369	−	3.46251i	0.838845	−	0.147911i
$549$	11.2248	−	8.09415i	0.479061	−	0.345450i
$550$		−	18.2733i		−	0.779177i
$551$	−14.0536	−	8.51581i	−0.598702	−	0.362786i
$552$	4.03412	−	2.13575i	0.171704	−	0.0909034i
$553$	2.60348	−	7.15300i	0.110711	−	0.304177i
$554$	0.0578695	+	0.328194i	0.00245864	+	0.0139436i
$555$	6.44985	−	30.0799i	0.273781	−	1.27682i
$556$	−1.23956	+	1.04011i	−0.0525689	+	0.0441105i
$557$	−22.6372	−	3.99155i	−0.959170	−	0.169128i	−0.327919	−	0.944706i	$-0.606347\pi$
$557$	−22.6372	−	3.99155i	−0.959170	−	0.169128i	−0.631251	+	0.775578i	$0.717458\pi$
$558$	−14.9164	+	7.20935i	−0.631460	+	0.305196i
$559$	−10.7804	+	6.22408i	−0.455963	+	0.263250i
$560$	−3.95843	−	10.8757i	−0.167274	−	0.459582i
$561$	−14.6504	−	13.2388i	−0.618542	−	0.558942i
$562$	−1.25481	−	2.17339i	−0.0529308	−	0.0916788i
$563$	6.45057	−	11.1727i	0.271859	−	0.470874i	−0.697479	−	0.716605i	$-0.745695\pi$
$563$	6.45057	−	11.1727i	0.271859	−	0.470874i	0.969338	+	0.245732i	$0.0790282\pi$
$564$	−0.0684884	−	0.212074i	−0.00288388	−	0.00892992i
$565$	37.2536	+	44.3971i	1.56727	+	1.86780i
$566$	20.1827	+	16.9353i	0.848344	+	0.711845i
$567$	−25.8587	+	15.9025i	−1.08596	+	0.667844i
$568$	−12.1580	−	4.42516i	−0.510139	−	0.185676i
$569$	−37.8380			−1.58625			−0.793125	−	0.609059i	$-0.791547\pi$
$569$	−37.8380			−1.58625			−0.793125	+	0.609059i	$0.791547\pi$
$570$	3.01508	+	25.7293i	0.126288	+	1.07768i
$571$	20.7087			0.866632			0.433316	−	0.901242i	$-0.357343\pi$
$571$	20.7087			0.866632			0.433316	+	0.901242i	$0.357343\pi$
$572$	−13.0105	−	4.73543i	−0.543996	−	0.197998i
$573$	−10.8149	−	13.8935i	−0.451799	−	0.580411i
$574$	−4.31126	−	3.61758i	−0.179949	−	0.150995i
$575$	11.4741	+	13.6743i	0.478503	+	0.570258i
$576$	2.15056	+	2.09167i	0.0896067	+	0.0871530i
$577$	−8.69281	+	15.0564i	−0.361886	+	0.626805i	−0.988271	−	0.152708i	$-0.951200\pi$
$577$	−8.69281	+	15.0564i	−0.361886	+	0.626805i	0.626385	+	0.779514i	$0.284534\pi$
$578$	0.428670	+	0.742479i	0.0178303	+	0.0308830i
$579$	14.5477	−	16.0989i	0.604582	−	0.669049i
$580$	−4.42411	−	12.1551i	−0.183701	−	0.504715i
$581$	21.1779	−	12.2271i	0.878608	−	0.507265i
$582$	0.581986	−	15.8539i	0.0241241	−	0.657167i
$583$	−22.6593	−	3.99544i	−0.938451	−	0.165474i
$584$	−1.82924	+	1.53492i	−0.0756947	+	0.0635154i
$585$	50.8342	−	14.3802i	2.10174	−	0.594546i
$586$	2.26899	+	12.8681i	0.0937310	+	0.531575i
$587$	−10.0782	+	27.6896i	−0.415971	+	1.14287i	0.537992	+	0.842950i	$0.319183\pi$
$587$	−10.0782	+	27.6896i	−0.415971	+	1.14287i	−0.953964	+	0.299922i	$0.903039\pi$
$588$	3.54744	+	6.70062i	0.146294	+	0.276329i
$589$	−3.67683	−	23.7891i	−0.151501	−	0.980214i
$590$			14.1554i			0.582769i
$591$	−39.4306	+	5.46980i	−1.62196	+	0.224998i
$592$	5.09772	−	0.898866i	0.209515	−	0.0369432i
$593$	−8.16230	+	9.72745i	−0.335185	+	0.399458i	−0.907141	−	0.420826i	$-0.861740\pi$
$593$	−8.16230	+	9.72745i	−0.335185	+	0.399458i	0.571956	+	0.820284i	$0.306185\pi$
$594$	−7.77645	−	11.6634i	−0.319072	−	0.478555i
$595$	8.49279	−	48.1650i	0.348170	−	1.97457i
$596$	−20.8706	−	12.0496i	−0.854893	−	0.493573i
$597$	23.3246	−	37.1792i	0.954612	−	1.52164i
$598$	12.7095	−	4.62587i	0.519729	−	0.189166i
$599$	−16.8817	+	6.14443i	−0.689767	+	0.251055i	−0.663035	−	0.748588i	$-0.730732\pi$
$599$	−16.8817	+	6.14443i	−0.689767	+	0.251055i	−0.0267313	+	0.999643i	$0.508510\pi$
$600$	−6.23474	+	9.93813i	−0.254532	+	0.405723i
$601$	8.14038	+	4.69985i	0.332053	+	0.191711i	0.656752	−	0.754106i	$-0.271930\pi$
$601$	8.14038	+	4.69985i	0.332053	+	0.191711i	−0.324699	+	0.945817i	$0.605263\pi$
$602$	−1.42068	+	8.05706i	−0.0579025	+	0.328381i
$603$	33.3031	−	3.38006i	1.35621	−	0.137647i
$604$	9.45237	−	11.2649i	0.384611	−	0.458362i
$605$	12.5768	−	2.21764i	0.511321	−	0.0901597i
$606$	9.70195	−	1.34585i	0.394115	−	0.0546715i
$607$			9.88885i			0.401376i	0.979655	+	0.200688i	$0.0643177\pi$
$607$			9.88885i			0.401376i	−0.979655	+	0.200688i	$0.935682\pi$
$608$	−3.82024	+	2.09899i	−0.154931	+	0.0851251i
$609$	10.3050	+	19.4648i	0.417582	+	0.788752i
$610$	−5.41350	+	14.8735i	−0.219186	+	0.602209i
$611$	−0.114667	−	0.650309i	−0.00463893	−	0.0263087i
$612$	3.45080	+	12.1987i	0.139491	+	0.493103i
$613$	−24.8777	+	20.8749i	−1.00480	+	0.843129i	−0.987642	−	0.156724i	$-0.949907\pi$
$613$	−24.8777	+	20.8749i	−1.00480	+	0.843129i	−0.0171592	+	0.999853i	$0.505462\pi$
$614$	−7.06477	−	1.24571i	−0.285111	−	0.0502728i
$615$	−0.363769	+	9.90947i	−0.0146686	+	0.399589i
$616$	−7.88059	+	4.54986i	−0.317518	+	0.183319i
$617$	7.64721	+	21.0105i	0.307865	+	0.845852i	0.993072	+	0.117504i	$0.0374893\pi$
$617$	7.64721	+	21.0105i	0.307865	+	0.845852i	−0.685207	+	0.728348i	$0.740288\pi$
$618$	4.50117	−	4.98114i	0.181064	−	0.200371i
$619$	−9.39662	−	16.2754i	−0.377682	−	0.654164i	0.613043	−	0.790050i	$-0.289945\pi$
$619$	−9.39662	−	16.2754i	−0.377682	−	0.654164i	−0.990725	+	0.135886i	$0.956612\pi$
$620$	9.47436	−	16.4101i	0.380500	−	0.659045i
$621$	13.1429	+	3.84500i	0.527406	+	0.154295i
$622$	7.39475	+	8.81272i	0.296503	+	0.353358i
$623$	−3.11977	−	2.61780i	−0.124991	−	0.104880i
$624$	5.46019	+	7.01451i	0.218583	+	0.280805i
$625$	12.2044	+	4.44205i	0.488178	+	0.177682i
$626$	−17.7338			−0.708787
$627$	19.5105	−	5.84738i	0.779173	−	0.233522i
$628$	15.3432			0.612261
$629$	20.5551	+	7.48143i	0.819584	+	0.298304i
$630$	14.2355	−	31.6686i	0.567158	−	1.26171i
$631$	−22.1517	−	18.5875i	−0.881846	−	0.739956i	0.0847122	−	0.996405i	$-0.473003\pi$
$631$	−22.1517	−	18.5875i	−0.881846	−	0.739956i	−0.966558	+	0.256449i	$0.917447\pi$
$632$	−1.45061	−	1.72877i	−0.0577021	−	0.0687667i
$633$	−6.33844	−	19.6269i	−0.251930	−	0.780100i
$634$	17.0401	−	29.5143i	0.676749	−	1.17216i
$635$	−9.48879	−	16.4351i	−0.376551	−	0.652206i
$636$	10.9603	+	9.90417i	0.434602	+	0.392726i
$637$	7.68350	+	21.1102i	0.304431	+	0.836418i
$638$	−8.80767	+	5.08511i	−0.348699	+	0.201321i
$639$	−16.8906	−	34.9472i	−0.668182	−	1.38249i
$640$	−3.37912	−	0.595829i	−0.133571	−	0.0235522i
$641$	18.2950	−	15.3513i	0.722609	−	0.606341i	−0.205497	−	0.978658i	$-0.565881\pi$
$641$	18.2950	−	15.3513i	0.722609	−	0.606341i	0.928106	+	0.372317i	$0.121437\pi$
$642$	−2.53427	+	11.8190i	−0.100020	+	0.466458i
$643$	6.83453	+	38.7606i	0.269528	+	1.52857i	0.755825	+	0.654774i	$0.227236\pi$
$643$	6.83453	+	38.7606i	0.269528	+	1.52857i	−0.486297	+	0.873793i	$0.661653\pi$
$644$	3.04028	−	8.35309i	0.119804	−	0.329158i
$645$	12.7398	−	6.74473i	0.501631	−	0.265574i
$646$	−18.4157	−	0.390236i	−0.724555	−	0.0153536i
$647$		−	24.3840i		−	0.958633i	−0.877642	−	0.479317i	$-0.840885\pi$
$647$		−	24.3840i		−	0.958633i	0.877642	−	0.479317i	$-0.159115\pi$
$648$	0.249825	+	8.99653i	0.00981406	+	0.353417i
$649$	10.9605	−	1.93263i	0.430237	−	0.0758624i
$650$	−22.3448	+	26.6295i	−0.876436	+	1.04450i
$651$	−12.1395	+	29.8924i	−0.475783	+	1.17157i
$652$	−2.07070	+	11.7435i	−0.0810949	+	0.459912i
$653$	20.0643	+	11.5841i	0.785178	+	0.453323i	0.838262	−	0.545268i	$-0.183572\pi$
$653$	20.0643	+	11.5841i	0.785178	+	0.453323i	−0.0530845	+	0.998590i	$0.516905\pi$
$654$	8.41036	+	5.27629i	0.328871	+	0.206319i
$655$	−47.5322	+	17.3003i	−1.85724	+	0.675979i
$656$	−1.56789	+	0.570666i	−0.0612159	+	0.0222808i
$657$	−7.14445	−	0.525242i	−0.278731	−	0.0204916i
$658$	−0.375854	−	0.216999i	−0.0146523	−	0.00845952i
$659$	3.15401	−	17.8873i	0.122863	−	0.696790i	−0.859691	−	0.510814i	$-0.829344\pi$
$659$	3.15401	−	17.8873i	0.122863	−	0.696790i	0.982554	−	0.185976i	$-0.0595448\pi$
$660$	14.8550	+	6.03269i	0.578229	+	0.234822i
$661$	22.4662	−	26.7742i	0.873835	−	1.04140i	−0.124952	−	0.992163i	$-0.539878\pi$
$661$	22.4662	−	26.7742i	0.873835	−	1.04140i	0.998787	−	0.0492336i	$-0.0156779\pi$
$662$	−20.5781	+	3.62848i	−0.799792	+	0.141025i
$663$	5.16141	+	37.2074i	0.200453	+	1.44502i
$664$		−	7.24992i		−	0.281351i
$665$	37.9501	+	33.2391i	1.47164	+	1.28896i
$666$	12.8431	+	8.72969i	0.497660	+	0.338269i
$667$	3.39794	−	9.33576i	0.131569	−	0.361482i
$668$	−0.312274	−	1.77099i	−0.0120823	−	0.0685218i
$669$	−21.4523	−	4.59990i	−0.829395	−	0.177842i
$670$	−29.3288	+	24.6098i	−1.13307	+	0.950760i
$671$	12.2556	+	2.16099i	0.473122	+	0.0834242i
$672$	5.83832	+	0.214320i	0.225218	+	0.00826759i
$673$	−8.97335	+	5.18077i	−0.345897	+	0.199704i	−0.662877	−	0.748729i	$-0.730665\pi$
$673$	−8.97335	+	5.18077i	−0.345897	+	0.199704i	0.316980	+	0.948432i	$0.397331\pi$
$674$	10.1824	+	27.9758i	0.392210	+	1.07759i
$675$	−34.1955	+	8.33153i	−1.31619	+	0.320681i
$676$	6.66951	+	11.5519i	0.256520	+	0.444305i
$677$	2.66151	−	4.60988i	0.102290	−	0.177172i	−0.810338	−	0.585963i	$-0.800716\pi$
$677$	2.66151	−	4.60988i	0.102290	−	0.177172i	0.912628	+	0.408791i	$0.134050\pi$
$678$	−27.8399	+	8.99077i	−1.06918	+	0.345289i
$679$	−19.8590	−	23.6670i	−0.762117	−	0.908255i
$680$	−11.1074	−	9.32025i	−0.425951	−	0.357415i
$681$	5.16578	−	4.02111i	0.197953	−	0.154089i
$682$	−13.9998	−	5.09551i	−0.536080	−	0.195117i
$683$	29.5958			1.13245			0.566226	−	0.824250i	$-0.308403\pi$
$683$	29.5958			1.13245			0.566226	+	0.824250i	$0.308403\pi$
$684$	−12.6061	−	3.47669i	−0.482005	−	0.132935i
$685$	−68.4183			−2.61413
$686$	−8.31289	−	3.02564i	−0.317388	−	0.115520i
$687$	−20.9420	+	16.3015i	−0.798987	+	0.621942i
$688$	1.85806	+	1.55910i	0.0708378	+	0.0594400i
$689$	28.1354	+	33.5305i	1.07187	+	1.27741i
$690$	−14.9043	+	4.81329i	−0.567397	+	0.183239i
$691$	9.35680	−	16.2065i	0.355950	−	0.616523i	−0.631330	−	0.775514i	$-0.717491\pi$
$691$	9.35680	−	16.2065i	0.355950	−	0.616523i	0.987280	+	0.158991i	$0.0508241\pi$
$692$	3.38816	+	5.86847i	0.128799	+	0.223086i
$693$	−26.4645	−	6.69885i	−1.00530	−	0.254468i
$694$	−1.85819	−	5.10534i	−0.0705361	−	0.193796i
$695$	4.80833	−	2.77609i	0.182390	−	0.105303i
$696$	6.52515	+	0.239533i	0.247335	+	0.00907948i
$697$	−6.94369	−	1.22436i	−0.263011	−	0.0463760i
$698$	12.3738	−	10.3829i	0.468356	−	0.392997i
$699$	−41.1699	−	8.82782i	−1.55719	−	0.333899i
$700$	3.96734	+	22.4999i	0.149951	+	0.850417i
$701$	−9.40339	+	25.8356i	−0.355161	+	0.975798i	0.625524	+	0.780205i	$0.284885\pi$
$701$	−9.40339	+	25.8356i	−0.355161	+	0.975798i	−0.980685	+	0.195593i	$0.937337\pi$
$702$	−2.92958	+	26.5061i	−0.110570	+	1.00041i
$703$	−17.5878	+	14.1339i	−0.663337	+	0.533071i
$704$			2.69779i			0.101677i
$705$	0.105070	+	0.757429i	0.00395718	+	0.0285264i
$706$	−20.6000	+	3.63233i	−0.775290	+	0.136705i
$707$	12.2610	−	14.6120i	0.461121	−	0.549543i
$708$	−6.62038	−	2.68857i	−0.248809	−	0.101043i
$709$	7.22305	−	40.9640i	0.271267	−	1.53843i	−0.479307	−	0.877647i	$-0.659112\pi$
$709$	7.22305	−	40.9640i	0.271267	−	1.53843i	0.750574	−	0.660786i	$-0.229777\pi$
$710$	38.4467	+	22.1972i	1.44288	+	0.833047i
$711$	0.496392	−	6.75202i	0.0186161	−	0.253220i
$712$	−1.13458	+	0.412953i	−0.0425201	+	0.0154761i
$713$	13.6759	−	4.97762i	0.512166	−	0.186413i
$714$	20.9134	+	13.1201i	0.782663	+	0.491008i
$715$	41.1425	+	23.7536i	1.53864	+	0.888335i
$716$	2.49317	−	14.1395i	0.0931741	−	0.528416i
$717$	8.70590	−	21.4375i	0.325128	−	0.800600i
$718$	−15.1355	+	18.0378i	−0.564852	+	0.673164i
$719$	26.6001	−	4.69031i	0.992015	−	0.174919i	0.345992	−	0.938237i	$-0.387542\pi$
$719$	26.6001	−	4.69031i	0.992015	−	0.174919i	0.646022	+	0.763318i	$0.276431\pi$
$720$	−6.02072	−	8.34937i	−0.224379	−	0.311163i
$721$		−	13.0742i		−	0.486908i
$722$	10.1885	−	16.0373i	0.379177	−	0.596846i
$723$	33.6292	−	17.8040i	1.25068	−	0.662137i
$724$	4.09139	−	11.2410i	0.152055	−	0.417768i
$725$	4.43406	+	25.1468i	0.164677	+	0.933930i
$726$	−1.35158	+	6.30329i	−0.0501618	+	0.233937i
$727$	23.4708	−	19.6943i	0.870483	−	0.730422i	−0.0937165	−	0.995599i	$-0.529875\pi$
$727$	23.4708	−	19.6943i	0.870483	−	0.730422i	0.964200	+	0.265177i	$0.0854303\pi$
$728$	17.0479	+	3.00601i	0.631838	+	0.111410i
$729$	−18.2805	+	19.8701i	−0.677056	+	0.735931i
$730$	7.09578	−	4.09675i	0.262627	−	0.151628i
$731$	3.50562	+	9.63162i	0.129660	+	0.356238i
$732$	−5.92801	−	5.35681i	−0.219106	−	0.197993i
$733$	−24.9658	−	43.2420i	−0.922132	−	1.59718i	−0.796110	−	0.605152i	$-0.793112\pi$
$733$	−24.9658	−	43.2420i	−0.922132	−	1.59718i	−0.126023	−	0.992027i	$-0.540221\pi$
$734$	−8.96840	+	15.5337i	−0.331030	+	0.573361i
$735$	−7.99480	−	24.7558i	−0.294893	−	0.913133i
$736$	−1.69398	−	2.01881i	−0.0624410	−	0.0744143i
$737$	23.0596	+	19.3493i	0.849410	+	0.712740i
$738$	−4.56550	−	2.05226i	−0.168058	−	0.0755449i
$739$	32.2619	+	11.7424i	1.18677	+	0.431950i	0.858589	−	0.512664i	$-0.171341\pi$
$739$	32.2619	+	11.7424i	1.18677	+	0.431950i	0.328183	+	0.944614i	$0.393564\pi$
$740$	−17.7614			−0.652921
$741$	−35.5826	−	15.3363i	−1.30716	−	0.563392i
$742$	28.7678			1.05610
$743$	−27.6540	−	10.0652i	−1.01453	−	0.369257i	−0.219357	−	0.975645i	$-0.570396\pi$
$743$	−27.6540	−	10.0652i	−1.01453	−	0.369257i	−0.795169	+	0.606387i	$0.792618\pi$
$744$	5.87538	+	7.54790i	0.215402	+	0.276719i
$745$	63.3446	+	53.1525i	2.32077	+	1.94736i
$746$	−9.10081	−	10.8459i	−0.333204	−	0.397097i
$747$	15.1644	−	15.5914i	0.554838	−	0.570459i
$748$	−5.70015	+	9.87295i	−0.208418	+	0.360991i
$749$	11.7698	+	20.3860i	0.430061	+	0.744887i
$750$	7.06643	−	7.81993i	0.258030	−	0.285544i
$751$	0.559448	+	1.53707i	0.0204145	+	0.0560885i	0.949481	−	0.313824i	$-0.101610\pi$
$751$	0.559448	+	1.53707i	0.0204145	+	0.0560885i	−0.929067	+	0.369912i	$0.879388\pi$
$752$	−0.111429	+	0.0643337i	−0.00406341	+	0.00234601i
$753$	0.430860	−	11.7371i	0.0157014	−	0.427724i
$754$	19.0534	+	3.35964i	0.693886	+	0.122351i
$755$	−38.6526	+	32.4334i	−1.40671	+	1.18037i
$756$	12.1074	+	12.6728i	0.440341	+	0.460904i
$757$	4.17165	+	23.6586i	0.151621	+	0.859887i	0.961810	+	0.273718i	$0.0882534\pi$
$757$	4.17165	+	23.6586i	0.151621	+	0.859887i	−0.810189	+	0.586169i	$0.800635\pi$
$758$	0.429560	−	1.18021i	0.0156023	−	0.0428670i
$759$	5.76179	+	10.8832i	0.209140	+	0.395035i
$760$	14.1597	−	4.81651i	0.513626	−	0.174713i
$761$			12.8974i			0.467530i	0.972293	+	0.233765i	$0.0751047\pi$
$761$			12.8974i			0.467530i	−0.972293	+	0.233765i	$0.924895\pi$
$762$	9.48879	−	1.31628i	0.343743	−	0.0476839i
$763$	19.0410	−	3.35745i	0.689332	−	0.121548i
$764$	−6.53405	+	7.78698i	−0.236394	+	0.281723i
$765$	−4.39233	−	43.2769i	−0.158805	−	1.56468i
$766$	0.465296	−	2.63882i	0.0168118	−	0.0953446i
$767$	−18.3359	−	10.5862i	−0.662069	−	0.382246i
$768$	0.920469	−	1.46722i	0.0332146	−	0.0529438i
$769$	21.8210	−	7.94220i	0.786886	−	0.286403i	0.0828452	−	0.996562i	$-0.473599\pi$
$769$	21.8210	−	7.94220i	0.786886	−	0.286403i	0.704041	+	0.710159i	$0.251377\pi$
$770$	29.3404	−	10.6790i	1.05735	−	0.384845i
$771$	−16.3829	+	26.1143i	−0.590017	+	0.940482i
$772$	−10.8491	−	6.26373i	−0.390467	−	0.225436i
$773$	6.98308	−	39.6030i	0.251164	−	1.42442i	−0.554566	−	0.832140i	$-0.687116\pi$
$773$	6.98308	−	39.6030i	0.251164	−	1.42442i	0.805730	−	0.592283i	$-0.201773\pi$
$774$	0.734751	+	7.23937i	0.0264101	+	0.260214i
$775$	−24.0439	+	28.6544i	−0.863683	+	1.02930i
$776$	−9.02029	+	1.59052i	−0.323809	+	0.0570964i
$777$	29.9548	−	4.15532i	1.07462	−	0.149071i
$778$		−	32.8845i		−	1.17897i
$779$	4.79191	−	5.47107i	0.171688	−	0.196021i
$780$	−14.2712	−	26.9562i	−0.510990	−	0.965187i
$781$	11.9381	−	32.7998i	0.427181	−	1.17367i
$782$	−1.93384	−	10.9673i	−0.0691539	−	0.392191i
$783$	13.5317	+	14.1636i	0.483584	+	0.506166i
$784$	3.35322	−	2.81368i	0.119758	−	0.100489i
$785$	−51.8465	−	9.14194i	−1.85048	−	0.326290i
$786$	0.936686	−	25.5164i	0.0334105	−	0.910139i
$787$	−40.4947	+	23.3796i	−1.44348	+	0.833393i	−0.998080	−	0.0619383i	$-0.980272\pi$
$787$	−40.4947	+	23.3796i	−1.44348	+	0.833393i	−0.445400	+	0.895332i	$0.646938\pi$
$788$	7.86073	+	21.5972i	0.280027	+	0.769368i
$789$	−4.45778	+	4.93312i	−0.158701	+	0.175624i
$790$	3.87172	+	6.70602i	0.137750	+	0.238590i
$791$	−28.4865	+	49.3400i	−1.01286	+	1.75433i
$792$	−5.64289	+	5.80176i	−0.200511	+	0.206157i
$793$	−15.2175	−	18.1355i	−0.540388	−	0.644009i
$794$	1.79344	+	1.50487i	0.0636467	+	0.0534059i
$795$	−31.1348	−	39.9978i	−1.10424	−	1.41857i
$796$	−23.8117	−	8.66676i	−0.843984	−	0.307185i
$797$	−6.73284			−0.238489			−0.119245	−	0.992865i	$-0.538047\pi$
$797$	−6.73284			−0.238489			−0.119245	+	0.992865i	$0.538047\pi$
$798$	−22.7537	+	11.4358i	−0.805471	+	0.404823i
$799$	−0.543722			−0.0192355
$800$	6.36495	+	2.31665i	0.225035	+	0.0819061i
$801$	−3.30374	−	1.48508i	−0.116732	−	0.0524729i
$802$	−10.4984	−	8.80918i	−0.370710	−	0.311063i
$803$	−4.14089	−	4.93492i	−0.146129	−	0.174149i
$804$	−5.93933	−	18.3911i	−0.209464	−	0.648604i
$805$	−15.2505	+	26.4146i	−0.537508	+	0.930992i
$806$	14.1709	+	24.5448i	0.499149	+	0.864552i
$807$	−3.38934	−	3.06276i	−0.119311	−	0.107814i
$808$	−1.93414	−	5.31402i	−0.0680430	−	0.186947i
$809$	−7.36554	+	4.25250i	−0.258959	+	0.149510i	−0.623859	−	0.781537i	$-0.714436\pi$
$809$	−7.36554	+	4.25250i	−0.258959	+	0.149510i	0.364901	+	0.931046i	$0.381103\pi$
$810$	4.51621	−	30.5492i	0.158683	−	1.07339i
$811$	28.9589	+	5.10623i	1.01688	+	0.179304i	0.657157	−	0.753753i	$-0.271759\pi$
$811$	28.9589	+	5.10623i	1.01688	+	0.179304i	0.359727	+	0.933058i	$0.382870\pi$
$812$	9.74083	−	8.17353i	0.341836	−	0.286835i
$813$	−5.08282	+	23.7045i	−0.178262	+	0.831353i
$814$	2.42495	+	13.7526i	0.0849945	+	0.482028i
$815$	13.9943	−	38.4490i	0.490198	−	1.34681i
$816$	6.46868	−	3.42465i	0.226449	−	0.119887i
$817$	−10.3708	−	2.05609i	−0.362827	−	0.0719333i
$818$		−	21.2676i		−	0.743603i
$819$	30.3750	+	42.1232i	1.06139	+	1.47190i
$820$	5.63811	−	0.994152i	0.196891	−	0.0347173i
$821$	−6.42410	+	7.65594i	−0.224203	+	0.267194i	−0.866406	−	0.499340i	$-0.833576\pi$
$821$	−6.42410	+	7.65594i	−0.224203	+	0.267194i	0.642204	+	0.766534i	$0.278020\pi$
$822$	12.9949	−	31.9988i	0.453248	−	1.11608i
$823$	−8.07641	+	45.8036i	−0.281526	+	1.59661i	0.435911	+	0.899990i	$0.356426\pi$
$823$	−8.07641	+	45.8036i	−0.281526	+	1.59661i	−0.717437	+	0.696623i	$0.754685\pi$
$824$	−3.35680	−	1.93805i	−0.116940	−	0.0675151i
$825$	−26.8110	−	16.8200i	−0.933439	−	0.585598i
$826$	−13.0760	+	4.75929i	−0.454974	+	0.165597i
$827$	46.9782	−	17.0987i	1.63359	−	0.594579i	0.647690	−	0.761904i	$-0.275735\pi$
$827$	46.9782	−	17.0987i	1.63359	−	0.594579i	0.985902	+	0.167325i	$0.0535131\pi$
$828$	0.579673	−	7.88483i	0.0201450	−	0.274017i
$829$	16.9994	+	9.81460i	0.590413	+	0.340875i	0.765261	−	0.643720i	$-0.222610\pi$
$829$	16.9994	+	9.81460i	0.590413	+	0.340875i	−0.174848	+	0.984595i	$0.555943\pi$
$830$	−4.31971	+	24.4983i	−0.149939	+	0.850349i
$831$	0.534800	+	0.217185i	0.0185520	+	0.00753408i
$832$	3.29889	−	3.93146i	0.114368	−	0.136299i
$833$	18.2166	−	3.21208i	0.631168	−	0.111292i
$834$	0.385099	+	2.77609i	0.0133349	+	0.0961282i
$835$			6.17046i			0.213538i
$836$	−5.66262	−	10.3062i	−0.195846	−	0.356448i
$837$	−3.15235	+	28.5216i	−0.108961	+	0.985850i
$838$	9.98665	−	27.4381i	0.344983	−	0.947833i
$839$	2.71691	+	15.4084i	0.0937982	+	0.531956i	0.995109	+	0.0987829i	$0.0314949\pi$
$839$	2.71691	+	15.4084i	0.0937982	+	0.531956i	−0.901311	+	0.433173i	$0.857394\pi$
$840$	−19.6007	−	4.20286i	−0.676287	−	0.145012i
$841$	−11.3285	+	9.50576i	−0.390639	+	0.327785i
$842$	−7.45681	−	1.31484i	−0.256979	−	0.0453123i
$843$	−4.34385	−	0.159459i	−0.149610	−	0.00549207i
$844$	−10.3125	+	5.95393i	−0.354971	+	0.204943i
$845$	−15.6541	−	43.0092i	−0.538516	−	1.47956i
$846$	−0.374200	−	0.0947198i	−0.0128653	−	0.00325653i
$847$	6.27709	+	10.8722i	0.215683	+	0.373574i
$848$	4.26438	−	7.38613i	0.146440	−	0.253641i
$849$	43.4255	−	14.0241i	1.49036	−	0.481305i
$850$	18.3986	+	21.9266i	0.631067	+	0.752077i
$851$	−10.4501	−	8.76867i	−0.358225	−	0.300586i
$852$	−17.6838	+	13.7653i	−0.605836	+	0.471591i
$853$	6.82954	+	2.48575i	0.233839	+	0.0851104i	0.456282	−	0.889835i	$-0.349181\pi$
$853$	6.82954	+	2.48575i	0.233839	+	0.0851104i	−0.222443	+	0.974946i	$0.571403\pi$
$854$	−15.5595			−0.532434
$855$	40.5258	+	19.2592i	1.38595	+	0.658651i
$856$	6.97880			0.238530
$857$	10.7658	+	3.91845i	0.367754	+	0.133852i	0.519285	−	0.854601i	$-0.326198\pi$
$857$	10.7658	+	3.91845i	0.367754	+	0.133852i	−0.151531	+	0.988452i	$0.548420\pi$
$858$	−18.9237	+	14.7304i	−0.646044	+	0.502889i
$859$	−38.6125	−	32.3998i	−1.31744	−	1.10547i	−0.986841	−	0.161695i	$-0.948304\pi$
$859$	−38.6125	−	32.3998i	−1.31744	−	1.10547i	−0.330602	−	0.943770i	$-0.607252\pi$
$860$	−5.34964	−	6.37545i	−0.182421	−	0.217401i
$861$	−9.27617	+	2.99570i	−0.316131	+	0.102093i
$862$	11.9790	−	20.7483i	0.408008	−	0.706690i
$863$	−13.4511	−	23.2980i	−0.457882	−	0.793075i	0.540967	−	0.841044i	$-0.318058\pi$
$863$	−13.4511	−	23.2980i	−0.457882	−	0.793075i	−0.998849	+	0.0479693i	$0.984725\pi$
$864$	5.04847	−	1.23003i	0.171752	−	0.0418464i
$865$	−7.95239	−	21.8490i	−0.270389	−	0.742889i
$866$	13.3303	−	7.69622i	0.452980	−	0.261528i
$867$	1.48396	+	0.0544750i	0.0503979	+	0.00185007i
$868$	18.3442	+	3.23458i	0.622644	+	0.109789i
$869$	4.66385	−	3.91344i	0.158210	−	0.132754i
$870$	−21.9065	−	4.69729i	−0.742701	−	0.159253i
$871$	−9.94396	−	56.3950i	−0.336938	−	1.91087i
$872$	1.96052	−	5.38648i	0.0663915	−	0.182409i
$873$	−22.7255	−	15.4470i	−0.769143	−	0.522801i
$874$	10.7089	+	4.15670i	0.362233	+	0.140602i
$875$		−	20.5252i		−	0.693880i
$876$	0.568301	+	4.09675i	0.0192011	+	0.138416i
$877$	3.93346	−	0.693575i	0.132823	−	0.0234204i	−0.106841	−	0.994276i	$-0.534074\pi$
$877$	3.93346	−	0.693575i	0.132823	−	0.0234204i	0.239665	+	0.970856i	$0.422963\pi$
$878$	14.2939	−	17.0348i	0.482397	−	0.574898i
$879$	20.9688	+	8.51555i	0.707261	+	0.287223i
$880$	1.60742	−	9.11615i	0.0541862	−	0.307305i
$881$	−27.5291	−	15.8939i	−0.927479	−	0.535480i	−0.0414655	−	0.999140i	$-0.513203\pi$
$881$	−27.5291	−	15.8939i	−0.927479	−	0.535480i	−0.886013	+	0.463660i	$0.846536\pi$
$882$	13.0966	+	0.962829i	0.440985	+	0.0324202i
$883$	14.7726	−	5.37678i	0.497136	−	0.180943i	−0.0812691	−	0.996692i	$-0.525897\pi$
$883$	14.7726	−	5.37678i	0.497136	−	0.180943i	0.578406	+	0.815749i	$0.303675\pi$
$884$	20.3795	−	7.41754i	0.685438	−	0.249479i
$885$	20.7691	+	13.0296i	0.698146	+	0.437986i
$886$	−27.1331	−	15.6653i	−0.911555	−	0.526287i
$887$	−7.99628	+	45.3492i	−0.268489	+	1.52268i	0.490424	+	0.871484i	$0.336842\pi$
$887$	−7.99628	+	45.3492i	−0.268489	+	1.52268i	−0.758913	+	0.651192i	$0.774269\pi$
$888$	3.37346	−	8.30686i	0.113206	−	0.278760i
$889$	11.9916	−	14.2910i	0.402185	−	0.479305i
$890$	4.07992	−	0.719400i	0.136759	−	0.0241144i
$891$	−24.2708	+	0.673976i	−0.813101	+	0.0225790i
$892$			12.6670i			0.424124i
$893$	0.290651	−	0.479659i	0.00972628	−	0.0160512i
$894$	−36.8902	+	19.5304i	−1.23379	+	0.653195i
$895$	−16.8494	+	46.2934i	−0.563214	+	1.54742i
$896$	−0.585720	−	3.32178i	−0.0195675	−	0.110973i
$897$	4.91150	−	22.9056i	0.163990	−	0.764794i
$898$	9.42566	−	7.90907i	0.314538	−	0.263929i
$899$	20.5023	+	3.61510i	0.683789	+	0.120570i
$900$	8.84254	+	18.2955i	0.294751	+	0.609850i
$901$	31.2123	−	18.0204i	1.03983	−	0.600347i
$902$	−1.53954	−	4.22985i	−0.0512610	−	0.140838i
$903$	10.5138	+	9.50072i	0.349877	+	0.316164i
$904$	8.44537	+	14.6278i	0.280889	+	0.486514i
$905$	−20.5230	+	35.5469i	−0.682208	+	1.18162i
$906$	−7.82747	−	24.2377i	−0.260050	−	0.805244i
$907$	−0.695285	−	0.828609i	−0.0230866	−	0.0275135i	0.754378	−	0.656441i	$-0.227939\pi$
$907$	−0.695285	−	0.828609i	−0.0230866	−	0.0275135i	−0.777464	+	0.628927i	$0.783494\pi$
$908$	−2.89529	−	2.42944i	−0.0960836	−	0.0806237i
$909$	6.95568	−	15.4737i	0.230705	−	0.513231i
$910$	−55.8158	−	20.3153i	−1.85028	−	0.673445i
$911$	−45.4512			−1.50587			−0.752933	−	0.658098i	$-0.771361\pi$
$911$	−45.4512			−1.50587			−0.752933	+	0.658098i	$0.771361\pi$
$912$	−0.436740	+	7.53719i	−0.0144619	+	0.249581i
$913$	19.5587			0.647300
$914$	35.5406	+	12.9357i	1.17558	+	0.427876i
$915$	16.8397	+	21.6334i	0.556704	+	0.715177i
$916$	11.7375	+	9.84891i	0.387817	+	0.325417i
$917$	−31.9623	−	38.0912i	−1.05549	−	1.25788i
$918$	21.0745	+	6.16543i	0.695563	+	0.203489i
$919$	−10.4915	+	18.1717i	−0.346081	+	0.599430i	−0.985550	−	0.169387i	$-0.945821\pi$
$919$	−10.4915	+	18.1717i	−0.346081	+	0.599430i	0.639468	+	0.768817i	$0.279155\pi$
$920$	4.52130	+	7.83112i	0.149063	+	0.258184i
$921$	−8.33064	+	9.21894i	−0.274504	+	0.303774i
$922$	13.2926	+	36.5210i	0.437767	+	1.20276i
$923$	−57.5053	+	33.2007i	−1.89281	+	1.09281i
$924$	−0.578191	+	15.7506i	−0.0190211	+	0.518156i
$925$	34.5291	+	6.08841i	1.13531	+	0.200186i
$926$	−18.8844	+	15.8459i	−0.620581	+	0.520730i
$927$	−3.16524	−	11.1892i	−0.103960	−	0.367502i
$928$	−0.654625	−	3.71256i	−0.0214891	−	0.121871i
$929$	10.4843	−	28.8055i	0.343980	−	0.945077i	−0.640247	−	0.768169i	$-0.721168\pi$
$929$	10.4843	−	28.8055i	0.343980	−	0.945077i	0.984227	−	0.176908i	$-0.0566096\pi$
$930$	−15.3563	−	29.0060i	−0.503554	−	0.951143i
$931$	−6.90422	+	17.7873i	−0.226277	+	0.582956i
$932$			24.3097i			0.796292i
$933$	19.7368	−	2.73789i	0.646155	−	0.0896346i
$934$	−3.61538	+	0.637489i	−0.118299	+	0.0208593i
$935$	25.1441	−	29.9655i	0.822299	−	0.979978i
$936$	15.3178	−	1.55466i	0.500677	−	0.0508156i
$937$	−0.894500	+	5.07296i	−0.0292221	+	0.165726i	−0.995926	−	0.0901691i	$-0.971259\pi$
$937$	−0.894500	+	5.07296i	−0.0292221	+	0.165726i	0.966704	+	0.255896i	$0.0823703\pi$
$938$	−32.5942	−	18.8182i	−1.06424	−	0.614438i
$939$	−16.3235	+	26.0195i	−0.532696	+	0.849113i
$940$	0.414864	−	0.150998i	0.0135314	−	0.00492502i
$941$	23.0587	−	8.39267i	0.751691	−	0.273593i	0.0623740	−	0.998053i	$-0.480133\pi$
$941$	23.0587	−	8.39267i	0.751691	−	0.273593i	0.689317	+	0.724460i	$0.257911\pi$
$942$	14.1230	−	22.5119i	0.460151	−	0.733477i
$943$	3.80805	+	2.19858i	0.124007	+	0.0715956i
$944$	−0.716376	+	4.06277i	−0.0233161	+	0.132232i
$945$	−33.3614	−	50.0367i	−1.08525	−	1.62769i
$946$	−4.20611	+	5.01265i	−0.136752	+	0.162975i
$947$	−23.9834	+	4.22892i	−0.779357	+	0.137422i	−0.549154	−	0.835721i	$-0.685050\pi$
$947$	−23.9834	+	4.22892i	−0.779357	+	0.137422i	−0.230203	+	0.973143i	$0.573939\pi$
$948$	−3.87172	+	0.537085i	−0.125748	+	0.0174437i
$949$			12.2551i			0.397818i
$950$	−29.1783	+	4.50977i	−0.946669	+	0.146316i
$951$	−27.6191	−	52.1686i	−0.895612	−	1.69168i
$952$	4.87506	−	13.3941i	0.158002	−	0.434106i
$953$	0.495016	+	2.80737i	0.0160351	+	0.0909398i	0.991775	−	0.127993i	$-0.0408535\pi$
$953$	0.495016	+	2.80737i	0.0160351	+	0.0909398i	−0.975740	+	0.218933i	$0.929742\pi$
$954$	24.6202	−	6.96464i	0.797108	−	0.225488i
$955$	26.7190	−	22.4199i	0.864607	−	0.725492i
$956$	−13.1557	−	2.31971i	−0.425486	−	0.0750247i
$957$	−0.646210	+	17.6035i	−0.0208890	+	0.569040i
$958$	22.4828	−	12.9805i	0.726387	−	0.419380i
$959$	−23.0034	−	63.2014i	−0.742819	−	2.04088i
$960$	−3.98459	+	4.40947i	−0.128602	+	0.142315i
$961$	−0.251521	−	0.435647i	−0.00811358	−	0.0140531i
$962$	13.2829	−	23.0067i	0.428259	−	0.741767i
$963$	15.0083	+	14.5973i	0.483637	+	0.470393i
$964$	−14.1214	−	16.8292i	−0.454819	−	0.542032i
$965$	32.9282	+	27.6301i	1.06000	+	0.889444i
$966$	−9.45735	−	12.1495i	−0.304285	−	0.390904i
$967$	−24.1580	−	8.79281i	−0.776870	−	0.282758i	−0.0770033	−	0.997031i	$-0.524535\pi$
$967$	−24.1580	−	8.79281i	−0.776870	−	0.282758i	−0.699867	+	0.714273i	$0.746757\pi$
$968$	3.72193			0.119627
$969$	−17.5236	+	26.6607i	−0.562940	+	0.856464i
$970$	31.4283			1.00910
$971$	8.94724	+	3.25653i	0.287131	+	0.104507i	0.481570	−	0.876407i	$-0.340067\pi$
$971$	8.94724	+	3.25653i	0.287131	+	0.104507i	−0.194440	+	0.980914i	$0.562289\pi$
$972$	13.4299	+	7.91448i	0.430763	+	0.253857i
$973$	4.18105	+	3.50832i	0.134038	+	0.112472i
$974$	−6.37816	−	7.60120i	−0.204369	−	0.243558i
$975$	18.5037	+	57.2964i	0.592591	+	1.83495i
$976$	−2.30645	+	3.99490i	−0.0738278	+	0.127874i
$977$	11.2275	+	19.4466i	0.359199	+	0.622151i	0.987827	−	0.155555i	$-0.0497166\pi$
$977$	11.2275	+	19.4466i	0.359199	+	0.622151i	−0.628628	+	0.777706i	$0.716383\pi$
$978$	15.3243	+	13.8477i	0.490018	+	0.442802i
$979$	−1.11406	−	3.06085i	−0.0356055	−	0.0978253i
$980$	−13.0074	+	7.50982i	−0.415506	+	0.239892i
$981$	15.4830	−	7.48319i	0.494333	−	0.238920i
$982$	−14.8971	−	2.62676i	−0.475385	−	0.0838232i
$983$	15.1924	−	12.7479i	0.484561	−	0.406595i	−0.367511	−	0.930019i	$-0.619790\pi$
$983$	15.1924	−	12.7479i	0.484561	−	0.406595i	0.852072	+	0.523424i	$0.175346\pi$
$984$	−0.605904	+	2.82573i	−0.0193155	+	0.0900809i
$985$	−13.6941	−	77.6630i	−0.436330	−	2.47455i
$986$	5.44857	−	14.9698i	0.173518	−	0.476736i
$987$	−0.664348	+	0.351719i	−0.0211464	+	0.0111954i
$988$	−4.35047	+	21.9434i	−0.138407	+	0.698114i
$989$		−	6.39215i		−	0.203258i
$990$	22.5248	−	16.2426i	0.715886	−	0.516225i
$991$	11.0355	−	1.94586i	0.350556	−	0.0618124i	0.00440221	−	0.999990i	$-0.498599\pi$
$991$	11.0355	−	1.94586i	0.350556	−	0.0618124i	0.346154	+	0.938178i	$0.387488\pi$
$992$	3.54973	−	4.23041i	0.112704	−	0.134316i
$993$	−13.6178	+	33.5326i	−0.432147	+	1.06412i
$994$	−7.57822	+	42.9782i	−0.240367	+	1.36319i
$995$	75.2987	+	43.4737i	2.38713	+	1.37821i
$996$	−10.6372	−	6.67332i	−0.337053	−	0.211452i
$997$	−6.92900	+	2.52195i	−0.219444	+	0.0798710i	−0.449402	−	0.893329i	$-0.648363\pi$
$997$	−6.92900	+	2.52195i	−0.219444	+	0.0798710i	0.229959	+	0.973200i	$0.426141\pi$
$998$	−20.0116	+	7.28361i	−0.633455	+	0.230559i
$999$	24.6300	−	10.8082i	0.779260	−	0.341957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.b.53.1	yes	18
3.2	odd	2		114.2.l.a.53.1	✓	18
4.3	odd	2		912.2.cc.c.737.3		18
12.11	even	2		912.2.cc.d.737.3		18
19.14	odd	18		114.2.l.a.71.1	yes	18
57.14	even	18	inner	114.2.l.b.71.1	yes	18
76.71	even	18		912.2.cc.d.641.3		18
228.71	odd	18		912.2.cc.c.641.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.53.1	✓	18	3.2	odd	2
114.2.l.a.71.1	yes	18	19.14	odd	18
114.2.l.b.53.1	yes	18	1.1	even	1	trivial
114.2.l.b.71.1	yes	18	57.14	even	18	inner
912.2.cc.c.641.3		18	228.71	odd	18
912.2.cc.c.737.3		18	4.3	odd	2
912.2.cc.d.641.3		18	76.71	even	18
912.2.cc.d.737.3		18	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.36678 + 1.06392i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.20556 - 2.62849i) q^{5} +(1.64823 - 0.532290i) q^{6} +(1.68651 - 2.92113i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.736160 - 2.90828i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-1.36678 + 1.06392i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-2.20556 - 2.62849i) q^{5} +(1.64823 - 0.532290i) q^{6} +(1.68651 - 2.92113i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(0.736160 - 2.90828i) q^{9} +(1.17355 + 3.22432i) q^{10} +(2.33635 - 1.34889i) q^{11} +(-1.73088 - 0.0635395i) q^{12} +(-5.05419 - 0.891189i) q^{13} +(-2.58389 + 2.16814i) q^{14} +(5.81100 + 1.24602i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.44531 + 3.97095i) q^{17} +(-1.68645 + 2.48110i) q^{18} +(-2.73048 - 3.39772i) q^{19} -3.43124i q^{20} +(0.802750 + 5.78684i) q^{21} +(-2.65680 + 0.468466i) q^{22} +(1.69398 - 2.01881i) q^{23} +(1.60477 + 0.651705i) q^{24} +(-1.17620 + 6.67054i) q^{25} +(4.44458 + 2.56608i) q^{26} +(2.08800 + 4.75818i) q^{27} +(3.16961 - 1.15364i) q^{28} +(3.54249 - 1.28936i) q^{29} +(-5.03439 - 3.15836i) q^{30} +(4.78254 + 2.76120i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-1.75816 + 4.32933i) q^{33} +(2.71629 - 3.23715i) q^{34} +(-11.3979 + 2.00975i) q^{35} +(2.43333 - 1.75467i) q^{36} -5.17636i q^{37} +(1.40372 + 4.12669i) q^{38} +(7.85610 - 4.15918i) q^{39} +(-1.17355 + 3.22432i) q^{40} +(0.289735 + 1.64317i) q^{41} +(1.22488 - 5.71241i) q^{42} +(1.85806 - 1.55910i) q^{43} +(2.65680 + 0.468466i) q^{44} +(-9.26801 + 4.47940i) q^{45} +(-2.28230 + 1.31768i) q^{46} +(0.0440069 + 0.120908i) q^{47} +(-1.28509 - 1.16127i) q^{48} +(-2.18866 - 3.79087i) q^{49} +(3.38672 - 5.86597i) q^{50} +(-2.24935 - 6.96509i) q^{51} +(-3.29889 - 3.93146i) q^{52} +(-6.53342 - 5.48219i) q^{53} +(-0.334684 - 5.18536i) q^{54} +(-8.69853 - 3.16600i) q^{55} -3.37303 q^{56} +(7.34685 + 1.73892i) q^{57} -3.76983 q^{58} +(3.87665 + 1.41099i) q^{59} +(3.65056 + 4.68975i) q^{60} +(3.53369 + 2.96512i) q^{61} +(-3.54973 - 4.23041i) q^{62} +(-7.25390 - 7.05526i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(8.80484 + 15.2504i) q^{65} +(3.13285 - 3.46691i) q^{66} +(3.81629 + 10.4852i) q^{67} +(-3.65965 + 2.11290i) q^{68} +(-0.167450 + 4.56152i) q^{69} +(11.3979 + 2.00975i) q^{70} +(9.91131 - 8.31658i) q^{71} +(-2.88672 + 0.816605i) q^{72} +(-0.414656 - 2.35163i) q^{73} +(-1.77042 + 4.86419i) q^{74} +(-5.48930 - 10.3685i) q^{75} +(0.0923461 - 4.35792i) q^{76} -9.09972i q^{77} +(-8.80484 + 1.22141i) q^{78} +(2.22246 - 0.391880i) q^{79} +(2.20556 - 2.62849i) q^{80} +(-7.91614 - 4.28191i) q^{81} +(0.289735 - 1.64317i) q^{82} +(6.27861 + 3.62496i) q^{83} +(-3.10477 + 4.94898i) q^{84} +(13.6253 - 4.95920i) q^{85} +(-2.27924 + 0.829577i) q^{86} +(-3.47002 + 5.53118i) q^{87} +(-2.33635 - 1.34889i) q^{88} +(0.209662 - 1.18905i) q^{89} +(10.2411 - 1.03941i) q^{90} +(-11.1272 + 13.2609i) q^{91} +(2.59533 - 0.457627i) q^{92} +(-9.47436 + 1.31428i) q^{93} -0.128667i q^{94} +(-2.90863 + 14.6709i) q^{95} +(0.810416 + 1.53076i) q^{96} +(3.13271 - 8.60706i) q^{97} +(0.760113 + 4.31081i) q^{98} +(-2.20303 - 7.78777i) 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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