LMFDB - Embedded newform 57.2.j.b.14.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.2
Character	$\chi$	$=$	57.14
Dual form			57.2.j.b.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.886259 + 0.322572i) q^{2} +(-0.858393 + 1.50438i) q^{3} +(-0.850687 + 0.713811i) q^{4} +(-0.485824 + 0.578982i) q^{5} +(0.275488 - 1.61016i) q^{6} +(1.38278 + 2.39504i) q^{7} +(1.46681 - 2.54059i) q^{8} +(-1.52632 - 2.58270i) q^{9} +O(q^{10})$	\(q+(-0.886259 + 0.322572i) q^{2} +(-0.858393 + 1.50438i) q^{3} +(-0.850687 + 0.713811i) q^{4} +(-0.485824 + 0.578982i) q^{5} +(0.275488 - 1.61016i) q^{6} +(1.38278 + 2.39504i) q^{7} +(1.46681 - 2.54059i) q^{8} +(-1.52632 - 2.58270i) q^{9} +(0.243802 - 0.669841i) q^{10} +(2.28018 + 1.31646i) q^{11} +(-0.343620 - 1.89249i) q^{12} +(1.90254 - 0.335470i) q^{13} +(-1.99807 - 1.67658i) q^{14} +(-0.453982 - 1.22786i) q^{15} +(-0.0947805 + 0.537527i) q^{16} +(-0.220652 - 0.606237i) q^{17} +(2.18582 + 1.79659i) q^{18} +(-1.94082 - 3.90298i) q^{19} -0.839319i q^{20} +(-4.79001 + 0.0243368i) q^{21} +(-2.44549 - 0.431205i) q^{22} +(5.61638 + 6.69334i) q^{23} +(2.56291 + 4.38747i) q^{24} +(0.769045 + 4.36147i) q^{25} +(-1.57793 + 0.911019i) q^{26} +(5.19555 - 0.0791971i) q^{27} +(-2.88591 - 1.05039i) q^{28} +(-8.33804 - 3.03480i) q^{29} +(0.798418 + 0.941759i) q^{30} +(2.10245 - 1.21385i) q^{31} +(0.929445 + 5.27114i) q^{32} +(-3.93776 + 2.30022i) q^{33} +(0.391110 + 0.466106i) q^{34} +(-2.05847 - 0.362964i) q^{35} +(3.14198 + 1.10756i) q^{36} -6.09943i q^{37} +(2.97906 + 2.83300i) q^{38} +(-1.12846 + 3.15011i) q^{39} +(0.758345 + 2.08354i) q^{40} +(0.930968 - 5.27978i) q^{41} +(4.23734 - 1.56669i) q^{42} +(-1.12968 - 0.947914i) q^{43} +(-2.87943 + 0.507721i) q^{44} +(2.23686 + 0.371024i) q^{45} +(-7.13664 - 4.12034i) q^{46} +(3.48030 - 9.56204i) q^{47} +(-0.727286 - 0.603995i) q^{48} +(-0.324139 + 0.561425i) q^{49} +(-2.08846 - 3.61732i) q^{50} +(1.10142 + 0.188445i) q^{51} +(-1.37901 + 1.64344i) q^{52} +(4.16382 - 3.49386i) q^{53} +(-4.57905 + 1.74613i) q^{54} +(-1.86998 + 0.680616i) q^{55} +8.11308 q^{56} +(7.53755 + 0.430564i) q^{57} +8.36860 q^{58} +(-7.06560 + 2.57167i) q^{59} +(1.26266 + 0.720466i) q^{60} +(-1.37444 + 1.15329i) q^{61} +(-1.47176 + 1.75398i) q^{62} +(4.07510 - 7.22690i) q^{63} +(-3.06987 - 5.31717i) q^{64} +(-0.730070 + 1.26452i) q^{65} +(2.74788 - 3.30880i) q^{66} +(-3.35090 + 9.20653i) q^{67} +(0.620444 + 0.358214i) q^{68} +(-14.8904 + 2.70365i) q^{69} +(1.94142 - 0.342325i) q^{70} +(2.08521 + 1.74970i) q^{71} +(-8.80041 + 0.0894274i) q^{72} +(0.952144 - 5.39988i) q^{73} +(1.96750 + 5.40567i) q^{74} +(-7.22146 - 2.58692i) q^{75} +(4.43702 + 1.93484i) q^{76} +7.28150i q^{77} +(-0.0160339 - 3.15582i) q^{78} +(9.22088 + 1.62589i) q^{79} +(-0.265172 - 0.316020i) q^{80} +(-4.34068 + 7.88407i) q^{81} +(0.878031 + 4.97956i) q^{82} +(-7.02840 + 4.05785i) q^{83} +(4.05743 - 3.43987i) q^{84} +(0.458198 + 0.166771i) q^{85} +(1.30696 + 0.475694i) q^{86} +(11.7228 - 9.93854i) q^{87} +(6.68919 - 3.86200i) q^{88} +(-0.233188 - 1.32248i) q^{89} +(-2.10212 + 0.392725i) q^{90} +(3.43425 + 4.09278i) q^{91} +(-9.55556 - 1.68490i) q^{92} +(0.0213637 + 4.20485i) q^{93} +9.59708i q^{94} +(3.20265 + 0.772462i) q^{95} +(-8.72763 - 3.12647i) q^{96} +(4.64863 + 12.7720i) q^{97} +(0.106171 - 0.602125i) q^{98} +(-0.0802612 - 7.89837i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.886259	+	0.322572i	−0.626679	+	0.228093i	−0.635785	−	0.771866i	$-0.719324\pi$
$2$	−0.886259	+	0.322572i	−0.626679	+	0.228093i	0.00910593	+	0.999959i	$0.497101\pi$
$3$	−0.858393	+	1.50438i	−0.495594	+	0.868555i
$3$	−0.858393	+	1.50438i	−0.495594	+	0.868555i
$4$	−0.850687	+	0.713811i	−0.425344	+	0.356906i
$5$	−0.485824	+	0.578982i	−0.217267	+	0.258929i	−0.863659	−	0.504077i	$-0.831833\pi$
$5$	−0.485824	+	0.578982i	−0.217267	+	0.258929i	0.646392	+	0.763006i	$0.276277\pi$
$6$	0.275488	−	1.61016i	0.112467	−	0.657347i
$7$	1.38278	+	2.39504i	0.522640	+	0.905239i	0.999653	+	0.0263430i	$0.00838621\pi$
$7$	1.38278	+	2.39504i	0.522640	+	0.905239i	−0.477013	+	0.878896i	$0.658280\pi$
$8$	1.46681	−	2.54059i	0.518596	−	0.898234i
$9$	−1.52632	−	2.58270i	−0.508774	−	0.860900i
$10$	0.243802	−	0.669841i	0.0770971	−	0.211822i
$11$	2.28018	+	1.31646i	0.687501	+	0.396929i	0.802675	−	0.596417i	$-0.203409\pi$
$11$	2.28018	+	1.31646i	0.687501	+	0.396929i	−0.115174	+	0.993345i	$0.536743\pi$
$12$	−0.343620	−	1.89249i	−0.0991945	−	0.546314i
$13$	1.90254	−	0.335470i	0.527670	−	0.0930425i	0.0965347	−	0.995330i	$-0.469224\pi$
$13$	1.90254	−	0.335470i	0.527670	−	0.0930425i	0.431136	+	0.902287i	$0.358113\pi$
$14$	−1.99807	−	1.67658i	−0.534006	−	0.448085i
$15$	−0.453982	−	1.22786i	−0.117218	−	0.317032i
$16$	−0.0947805	+	0.537527i	−0.0236951	+	0.134382i
$17$	−0.220652	−	0.606237i	−0.0535160	−	0.147034i	0.910054	−	0.414489i	$-0.136040\pi$
$17$	−0.220652	−	0.606237i	−0.0535160	−	0.147034i	−0.963570	+	0.267455i	$0.913817\pi$
$18$	2.18582	+	1.79659i	0.515203	+	0.423461i
$19$	−1.94082	−	3.90298i	−0.445254	−	0.895404i
$19$	−1.94082	−	3.90298i	−0.445254	−	0.895404i
$20$		−	0.839319i		−	0.187678i
$21$	−4.79001	+	0.0243368i	−1.04527	+	0.00531073i
$22$	−2.44549	−	0.431205i	−0.521379	−	0.0919332i
$23$	5.61638	+	6.69334i	1.17110	+	1.39566i	0.901553	+	0.432668i	$0.142428\pi$
$23$	5.61638	+	6.69334i	1.17110	+	1.39566i	0.269542	+	0.962989i	$0.413128\pi$
$24$	2.56291	+	4.38747i	0.523153	+	0.895588i
$25$	0.769045	+	4.36147i	0.153809	+	0.872294i
$26$	−1.57793	+	0.911019i	−0.309458	+	0.178666i
$27$	5.19555	−	0.0791971i	0.999884	−	0.0152415i
$28$	−2.88591	−	1.05039i	−0.545387	−	0.198504i
$29$	−8.33804	−	3.03480i	−1.54834	−	0.563548i	−0.580309	−	0.814397i	$-0.697068\pi$
$29$	−8.33804	−	3.03480i	−1.54834	−	0.563548i	−0.968026	+	0.250849i	$0.919290\pi$
$30$	0.798418	+	0.941759i	0.145771	+	0.171941i
$31$	2.10245	−	1.21385i	0.377611	−	0.218014i	−0.299167	−	0.954201i	$-0.596709\pi$
$31$	2.10245	−	1.21385i	0.377611	−	0.218014i	0.676778	+	0.736187i	$0.263375\pi$
$32$	0.929445	+	5.27114i	0.164304	+	0.931815i
$33$	−3.93776	+	2.30022i	−0.685475	+	0.400417i
$34$	0.391110	+	0.466106i	0.0670747	+	0.0799366i
$35$	−2.05847	−	0.362964i	−0.347945	−	0.0613521i
$36$	3.14198	+	1.10756i	0.523664	+	0.184594i
$37$		−	6.09943i		−	1.00274i	−0.865233	−	0.501370i	$-0.832829\pi$
$37$		−	6.09943i		−	1.00274i	0.865233	−	0.501370i	$-0.167171\pi$
$38$	2.97906	+	2.83300i	0.483267	+	0.459573i
$39$	−1.12846	+	3.15011i	−0.180698	+	0.504422i
$40$	0.758345	+	2.08354i	0.119905	+	0.329436i
$41$	0.930968	−	5.27978i	0.145393	−	0.824564i	−0.821658	−	0.569981i	$-0.806951\pi$
$41$	0.930968	−	5.27978i	0.145393	−	0.824564i	0.967051	−	0.254583i	$-0.0819382\pi$
$42$	4.23734	−	1.56669i	0.653836	−	0.241746i
$43$	−1.12968	−	0.947914i	−0.172275	−	0.144556i	0.552574	−	0.833464i	$-0.313646\pi$
$43$	−1.12968	−	0.947914i	−0.172275	−	0.144556i	−0.724848	+	0.688908i	$0.758090\pi$
$44$	−2.87943	+	0.507721i	−0.434090	+	0.0765418i
$45$	2.23686	+	0.371024i	0.333452	+	0.0553090i
$46$	−7.13664	−	4.12034i	−1.05224	−	0.607511i
$47$	3.48030	−	9.56204i	0.507653	−	1.39477i	−0.375998	−	0.926621i	$-0.622700\pi$
$47$	3.48030	−	9.56204i	0.507653	−	1.39477i	0.883651	−	0.468146i	$-0.155078\pi$
$48$	−0.727286	−	0.603995i	−0.104975	−	0.0871792i
$49$	−0.324139	+	0.561425i	−0.0463055	+	0.0802035i
$50$	−2.08846	−	3.61732i	−0.295353	−	0.511566i
$51$	1.10142	+	0.188445i	0.154229	+	0.0263875i
$52$	−1.37901	+	1.64344i	−0.191234	+	0.227904i
$53$	4.16382	−	3.49386i	0.571945	−	0.479919i	−0.310346	−	0.950624i	$-0.600445\pi$
$53$	4.16382	−	3.49386i	0.571945	−	0.479919i	0.882291	+	0.470705i	$0.156000\pi$
$54$	−4.57905	+	1.74613i	−0.623130	+	0.237618i
$55$	−1.86998	+	0.680616i	−0.252148	+	0.0917742i
$56$	8.11308			1.08416
$57$	7.53755	+	0.430564i	0.998372	+	0.0570296i
$58$	8.36860			1.09885
$59$	−7.06560	+	2.57167i	−0.919863	+	0.334803i	−0.758184	−	0.652041i	$-0.773913\pi$
$59$	−7.06560	+	2.57167i	−0.919863	+	0.334803i	−0.161679	+	0.986843i	$0.551691\pi$
$60$	1.26266	+	0.720466i	0.163008	+	0.0930118i
$61$	−1.37444	+	1.15329i	−0.175979	+	0.147664i	−0.726523	−	0.687142i	$-0.758865\pi$
$61$	−1.37444	+	1.15329i	−0.175979	+	0.147664i	0.550544	+	0.834806i	$0.314420\pi$
$62$	−1.47176	+	1.75398i	−0.186914	+	0.222755i
$63$	4.07510	−	7.22690i	0.513415	−	0.910503i
$64$	−3.06987	−	5.31717i	−0.383734	−	0.664646i
$65$	−0.730070	+	1.26452i	−0.0905540	+	0.156844i
$66$	2.74788	−	3.30880i	0.338241	−	0.407285i
$67$	−3.35090	+	9.20653i	−0.409378	+	1.12476i	0.548141	+	0.836386i	$0.315336\pi$
$67$	−3.35090	+	9.20653i	−0.409378	+	1.12476i	−0.957519	+	0.288371i	$0.906886\pi$
$68$	0.620444	+	0.358214i	0.0752399	+	0.0434398i
$69$	−14.8904	+	2.70365i	−1.79259	+	0.325482i
$70$	1.94142	−	0.342325i	0.232044	−	0.0409156i
$71$	2.08521	+	1.74970i	0.247469	+	0.207651i	0.758082	−	0.652160i	$-0.226137\pi$
$71$	2.08521	+	1.74970i	0.247469	+	0.207651i	−0.510613	+	0.859811i	$0.670581\pi$
$72$	−8.80041	+	0.0894274i	−1.03714	+	0.0105391i
$73$	0.952144	−	5.39988i	0.111440	−	0.632008i	−0.877011	−	0.480470i	$-0.840466\pi$
$73$	0.952144	−	5.39988i	0.111440	−	0.632008i	0.988451	−	0.151538i	$-0.0484226\pi$
$74$	1.96750	+	5.40567i	0.228718	+	0.628397i
$75$	−7.22146	−	2.58692i	−0.833862	−	0.298712i
$76$	4.43702	+	1.93484i	0.508961	+	0.221941i
$77$			7.28150i			0.829804i
$78$	−0.0160339	−	3.15582i	−0.00181548	−	0.357327i
$79$	9.22088	+	1.62589i	1.03743	+	0.182927i	0.666323	−	0.745663i	$-0.267867\pi$
$79$	9.22088	+	1.62589i	1.03743	+	0.182927i	0.371107	+	0.928590i	$0.378978\pi$
$80$	−0.265172	−	0.316020i	−0.0296471	−	0.0353321i
$81$	−4.34068	+	7.88407i	−0.482298	+	0.876007i
$82$	0.878031	+	4.97956i	0.0969622	+	0.549900i
$83$	−7.02840	+	4.05785i	−0.771467	+	0.445406i	−0.833398	−	0.552674i	$-0.813607\pi$
$83$	−7.02840	+	4.05785i	−0.771467	+	0.445406i	0.0619310	+	0.998080i	$0.480274\pi$
$84$	4.05743	−	3.43987i	0.442702	−	0.375320i
$85$	0.458198	+	0.166771i	0.0496986	+	0.0180888i
$86$	1.30696	+	0.475694i	0.140933	+	0.0512954i
$87$	11.7228	−	9.93854i	1.25682	−	1.06552i
$88$	6.68919	−	3.86200i	0.713070	−	0.411691i
$89$	−0.233188	−	1.32248i	−0.0247179	−	0.140182i	0.969951	−	0.243299i	$-0.0782296\pi$
$89$	−0.233188	−	1.32248i	−0.0247179	−	0.140182i	−0.994669	+	0.103117i	$0.967118\pi$
$90$	−2.10212	+	0.392725i	−0.221583	+	0.0413969i
$91$	3.43425	+	4.09278i	0.360008	+	0.429040i
$92$	−9.55556	−	1.68490i	−0.996236	−	0.175663i
$93$	0.0213637	+	4.20485i	0.00221531	+	0.436022i
$94$			9.59708i			0.989863i
$95$	3.20265	+	0.772462i	0.328585	+	0.0792529i
$96$	−8.72763	−	3.12647i	−0.890760	−	0.319094i
$97$	4.64863	+	12.7720i	0.471997	+	1.29680i	0.916145	+	0.400847i	$0.131284\pi$
$97$	4.64863	+	12.7720i	0.471997	+	1.29680i	−0.444148	+	0.895953i	$0.646494\pi$
$98$	0.106171	−	0.602125i	0.0107249	−	0.0608239i
$99$	−0.0802612	−	7.89837i	−0.00806655	−	0.793817i
$100$	−3.76748	−	3.16129i	−0.376748	−	0.316129i
$101$	2.06421	−	0.363975i	0.205396	−	0.0362169i	−0.0700033	−	0.997547i	$-0.522301\pi$
$101$	2.06421	−	0.363975i	0.205396	−	0.0362169i	0.275400	+	0.961330i	$0.411190\pi$
$102$	−1.03693	+	0.188275i	−0.102671	+	0.0186420i
$103$	−10.4189	−	6.01535i	−1.02660	−	0.592710i	−0.110594	−	0.993866i	$-0.535275\pi$
$103$	−10.4189	−	6.01535i	−1.02660	−	0.592710i	−0.916010	+	0.401155i	$0.868609\pi$
$104$	1.93838	−	5.32565i	0.190074	−	0.522223i
$105$	2.31301	−	2.78516i	0.225727	−	0.271804i
$106$	−2.56320	+	4.43960i	−0.248960	+	0.431212i
$107$	3.41283	+	5.91119i	0.329930	+	0.571456i	0.982498	−	0.186275i	$-0.0596414\pi$
$107$	3.41283	+	5.91119i	0.329930	+	0.571456i	−0.652567	+	0.757731i	$0.726308\pi$
$108$	−4.36325	+	3.77601i	−0.419854	+	0.363347i
$109$	7.55399	−	9.00250i	0.723541	−	0.862283i	−0.271429	−	0.962459i	$-0.587496\pi$
$109$	7.55399	−	9.00250i	0.723541	−	0.862283i	0.994970	+	0.100176i	$0.0319405\pi$
$110$	1.43774	−	1.20640i	0.137083	−	0.115026i
$111$	9.17587	+	5.23571i	0.870935	+	0.496952i
$112$	−1.41846	+	0.516276i	−0.134032	+	0.0487835i
$113$	−1.98486			−0.186720			−0.0933599	−	0.995632i	$-0.529761\pi$
$113$	−1.98486			−0.186720			−0.0933599	+	0.995632i	$0.529761\pi$
$114$	−6.81910	+	2.04981i	−0.638668	+	0.191982i
$115$	−6.60389			−0.615816
$116$	9.25934	−	3.37012i	0.859708	−	0.312908i
$117$	−3.77031	−	4.40166i	−0.348565	−	0.406934i
$118$	5.43240	−	4.55833i	0.500093	−	0.419628i
$119$	1.14685	−	1.36676i	0.105131	−	0.125291i
$120$	−3.78539	−	0.647654i	−0.345557	−	0.0591224i
$121$	−2.03385	−	3.52273i	−0.184895	−	0.320248i
$122$	0.846091	−	1.46547i	0.0766015	−	0.132678i
$123$	7.14367	+	5.93266i	0.644123	+	0.534930i
$124$	−0.922067	+	2.53336i	−0.0828041	+	0.227502i
$125$	−6.17158	−	3.56316i	−0.552003	−	0.318699i
$126$	−1.28040	+	7.71941i	−0.114067	+	0.687700i
$127$	−11.1687	+	1.96935i	−0.991065	+	0.174751i	−0.645596	−	0.763679i	$-0.723391\pi$
$127$	−11.1687	+	1.96935i	−0.991065	+	0.174751i	−0.345468	+	0.938430i	$0.612280\pi$
$128$	−3.76458	−	3.15885i	−0.332745	−	0.279206i
$129$	2.39573	−	0.885786i	0.210933	−	0.0779891i
$130$	0.239133	−	1.35619i	0.0209733	−	0.118946i
$131$	−6.23539	−	17.1316i	−0.544789	−	1.49679i	−0.840658	−	0.541566i	$-0.817832\pi$
$131$	−6.23539	−	17.1316i	−0.544789	−	1.49679i	0.295869	−	0.955228i	$-0.404391\pi$
$132$	1.70788	−	4.76758i	0.148652	−	0.414965i
$133$	6.66407	−	10.0453i	0.577848	−	0.871035i
$134$		−	9.24028i		−	0.798238i
$135$	−2.47827	+	3.04661i	−0.213295	+	0.262210i
$136$	−1.86385	−	0.328648i	−0.159824	−	0.0281813i
$137$	5.03788	+	6.00391i	0.430415	+	0.512949i	0.937042	−	0.349217i	$-0.113552\pi$
$137$	5.03788	+	6.00391i	0.430415	+	0.512949i	−0.506627	+	0.862165i	$0.669108\pi$
$138$	12.3246	−	7.19935i	1.04914	−	0.612850i
$139$	−0.0146771	−	0.0832380i	−0.00124490	−	0.00706015i	0.984179	−	0.177177i	$-0.0566966\pi$
$139$	−0.0146771	−	0.0832380i	−0.00124490	−	0.00706015i	−0.985424	+	0.170117i	$0.945585\pi$
$140$	2.01020	−	1.16059i	0.169893	−	0.0980878i
$141$	11.3975	+	13.4437i	0.959841	+	1.13216i
$142$	−2.41244	−	0.878056i	−0.202447	−	0.0736849i
$143$	4.77978	+	1.73970i	0.399705	+	0.145481i
$144$	1.53294	−	0.575649i	0.127745	−	0.0479708i
$145$	5.80791	−	3.35320i	0.482321	−	0.278468i
$146$	0.898002	+	5.09282i	0.0743192	+	0.421485i
$147$	−0.566358	−	0.969551i	−0.0467124	−	0.0799672i
$148$	4.35384	+	5.18871i	0.357884	+	0.426509i
$149$	11.7508	+	2.07199i	0.962664	+	0.169744i	0.632826	−	0.774294i	$-0.281895\pi$
$149$	11.7508	+	2.07199i	0.962664	+	0.169744i	0.329838	+	0.944038i	$0.393006\pi$
$150$	7.23455	−	0.0367568i	0.590698	−	0.00300118i
$151$		−	2.63924i		−	0.214778i	−0.994217	−	0.107389i	$-0.965751\pi$
$151$		−	2.63924i		−	0.214778i	0.994217	−	0.107389i	$-0.0342491\pi$
$152$	−12.7627	−	0.794111i	−1.03519	−	0.0644109i
$153$	−1.22894	+	1.49519i	−0.0993540	+	0.120879i
$154$	−2.34881	−	6.45329i	−0.189272	−	0.520021i
$155$	−0.318623	+	1.80700i	−0.0255924	+	0.145142i
$156$	−1.28862	−	3.48527i	−0.103172	−	0.279045i
$157$	−10.0279	−	8.41440i	−0.800313	−	0.671543i	0.147962	−	0.988993i	$-0.452729\pi$
$157$	−10.0279	−	8.41440i	−0.800313	−	0.671543i	−0.948275	+	0.317451i	$0.897173\pi$
$158$	−8.69655	+	1.53344i	−0.691861	+	0.121994i
$159$	1.68190	+	9.26308i	0.133383	+	0.734610i
$160$	−3.50345	−	2.02272i	−0.276972	−	0.159910i
$161$	−8.26461	+	22.7068i	−0.651342	+	1.78955i
$162$	1.30379	−	8.38750i	0.102435	−	0.658984i
$163$	−10.9580	+	18.9799i	−0.858299	+	1.48662i	0.0152513	+	0.999884i	$0.495145\pi$
$163$	−10.9580	+	18.9799i	−0.858299	+	1.48662i	−0.873550	+	0.486734i	$0.838188\pi$
$164$	2.97681	+	5.15598i	0.232450	+	0.402614i
$165$	0.581270	−	3.39739i	0.0452518	−	0.264487i
$166$	4.92003	−	5.86346i	0.381868	−	0.455093i
$167$	0.977437	−	0.820167i	0.0756363	−	0.0634664i	−0.604186	−	0.796844i	$-0.706501\pi$
$167$	0.977437	−	0.820167i	0.0756363	−	0.0634664i	0.679822	+	0.733377i	$0.262057\pi$
$168$	−6.96421	+	12.2052i	−0.537301	+	0.941648i
$169$	−8.70887	+	3.16977i	−0.669913	+	0.243829i
$170$	−0.459878			−0.0352710
$171$	−7.11791	+	10.9697i	−0.544320	+	0.838877i
$172$	1.63764			0.124869
$173$	2.84010	−	1.03371i	0.215929	−	0.0785917i	−0.231791	−	0.972766i	$-0.574458\pi$
$173$	2.84010	−	1.03371i	0.215929	−	0.0785917i	0.447720	+	0.894174i	$0.352236\pi$
$174$	−7.18355	+	12.5896i	−0.544583	+	0.954412i
$175$	−9.38247	+	7.87283i	−0.709248	+	0.595130i
$176$	−0.923751	+	1.10088i	−0.0696304	+	0.0829822i
$177$	2.19630	−	12.8369i	0.165084	−	0.964877i
$178$	0.633259	+	1.09684i	0.0474647	+	0.0822113i
$179$	−6.00020	+	10.3927i	−0.448476	+	0.776784i	−0.998287	−	0.0585055i	$-0.981366\pi$
$179$	−6.00020	+	10.3927i	−0.448476	+	0.776784i	0.549811	+	0.835289i	$0.314700\pi$
$180$	−2.16771	+	1.28107i	−0.161572	+	0.0954855i
$181$	2.65765	−	7.30183i	0.197542	−	0.542741i	−0.800885	−	0.598818i	$-0.795637\pi$
$181$	2.65765	−	7.30183i	0.197542	−	0.542741i	0.998426	+	0.0560773i	$0.0178593\pi$
$182$	−4.36385	−	2.51947i	−0.323470	−	0.186756i
$183$	−0.555181	−	3.05766i	−0.0410402	−	0.226029i
$184$	25.2432	−	4.45105i	1.86095	−	0.328136i
$185$	3.53146	+	2.96325i	0.259638	+	0.217863i
$186$	−1.37530	−	3.71969i	−0.100842	−	0.272741i
$187$	0.294962	−	1.67281i	0.0215697	−	0.122328i
$188$	3.86485	+	10.6186i	0.281873	+	0.774439i
$189$	7.37396	+	12.3340i	0.536377	+	0.897168i
$190$	−3.08755	+	0.348484i	−0.223994	+	0.0252817i
$191$		−	1.07540i		−	0.0778132i	−0.999243	−	0.0389066i	$-0.987613\pi$
$191$		−	1.07540i		−	0.0778132i	0.999243	−	0.0389066i	$-0.0123875\pi$
$192$	10.6342	−	0.0540296i	0.767457	−	0.00389925i
$193$	−1.90955	−	0.336705i	−0.137452	−	0.0242366i	0.104499	−	0.994525i	$-0.466676\pi$
$193$	−1.90955	−	0.336705i	−0.137452	−	0.0242366i	−0.241951	+	0.970288i	$0.577787\pi$
$194$	−8.23978	−	9.81978i	−0.591581	−	0.705019i
$195$	−1.27563	−	2.18376i	−0.0913497	−	0.156382i
$196$	−0.125011	−	0.708971i	−0.00892933	−	0.0506408i
$197$	13.7608	−	7.94478i	0.980414	−	0.566042i	0.0780187	−	0.996952i	$-0.475141\pi$
$197$	13.7608	−	7.94478i	0.980414	−	0.566042i	0.902395	+	0.430910i	$0.141807\pi$
$198$	2.61892	+	6.97411i	0.186119	+	0.495629i
$199$	−2.60596	−	0.948493i	−0.184732	−	0.0672369i	0.247998	−	0.968761i	$-0.420227\pi$
$199$	−2.60596	−	0.948493i	−0.184732	−	0.0672369i	−0.432730	+	0.901524i	$0.642450\pi$
$200$	12.2088	+	4.44362i	0.863289	+	0.314212i
$201$	−10.9737	−	12.9439i	−0.774028	−	0.912990i
$202$	−1.71201	+	0.988431i	−0.120457	+	0.0695458i
$203$	−4.26118	−	24.1664i	−0.299076	−	1.69615i
$204$	−1.07148	+	0.625896i	−0.0750183	+	0.0438215i
$205$	2.60462	+	3.10406i	0.181914	+	0.216797i
$206$	11.1742	+	1.97032i	0.778545	+	0.137278i
$207$	8.71448	−	24.7216i	0.605698	−	1.71827i
$208$			1.05446i			0.0731139i
$209$	0.712715	−	11.4545i	0.0492996	−	0.792325i
$210$	−1.15151	+	3.21448i	−0.0794621	+	0.221820i
$211$	−4.07334	−	11.1914i	−0.280420	−	0.770449i	−0.997313	−	0.0732647i	$-0.976658\pi$
$211$	−4.07334	−	11.1914i	−0.280420	−	0.770449i	0.716892	−	0.697184i	$-0.245564\pi$
$212$	−1.04815	+	5.94436i	−0.0719874	+	0.408261i
$213$	−4.42215	+	1.63502i	−0.303000	+	0.112030i
$214$	−4.93143	−	4.13796i	−0.337105	−	0.282865i
$215$	1.09765	−	0.193546i	0.0748592	−	0.0131997i
$216$	7.41968	−	13.3159i	0.504845	−	0.906034i
$217$	5.81444	+	3.35697i	0.394710	+	0.227886i
$218$	−3.79084	+	10.4152i	−0.256748	+	0.705409i
$219$	7.30616	+	6.06760i	0.493704	+	0.410011i
$220$	1.10493	−	1.91380i	0.0744946	−	0.129028i
$221$	−0.623174	−	1.07937i	−0.0419192	−	0.0726062i
$222$	−9.82109	−	1.68032i	−0.659148	−	0.112776i
$223$	4.22862	−	5.03948i	0.283170	−	0.337468i	−0.605645	−	0.795735i	$-0.707085\pi$
$223$	4.22862	−	5.03948i	0.283170	−	0.337468i	0.888815	+	0.458266i	$0.151529\pi$
$224$	−11.3394	+	9.51487i	−0.757644	+	0.635739i
$225$	10.0906	−	8.64322i	0.672704	−	0.576215i
$226$	1.75910	−	0.640260i	0.117013	−	0.0425894i
$227$	−18.9131			−1.25531			−0.627655	−	0.778492i	$-0.715985\pi$
$227$	−18.9131			−1.25531			−0.627655	+	0.778492i	$0.715985\pi$
$228$	−6.71944	+	5.01411i	−0.445005	+	0.332068i
$229$	9.56916			0.632348			0.316174	−	0.948701i	$-0.397602\pi$
$229$	9.56916			0.632348			0.316174	+	0.948701i	$0.397602\pi$
$230$	5.85276	−	2.13023i	0.385919	−	0.140463i
$231$	−10.9541	−	6.25039i	−0.720730	−	0.411245i
$232$	−19.9405	+	16.7321i	−1.30916	+	1.09851i
$233$	10.9126	−	13.0052i	0.714910	−	0.851997i	−0.279216	−	0.960228i	$-0.590074\pi$
$233$	10.9126	−	13.0052i	0.714910	−	0.851997i	0.994126	+	0.108232i	$0.0345189\pi$
$234$	4.76132	+	2.68482i	0.311257	+	0.175512i
$235$	3.84544	+	6.66050i	0.250849	+	0.434483i
$236$	4.17493	−	7.23119i	0.271765	−	0.470710i
$237$	−10.3611	+	12.4761i	−0.673026	+	0.810408i
$238$	−0.575525	+	1.58124i	−0.0373058	+	0.102497i
$239$	15.3984	+	8.89028i	0.996041	+	0.575064i	0.907074	−	0.420970i	$-0.138310\pi$
$239$	15.3984	+	8.89028i	0.996041	+	0.575064i	0.0889661	+	0.996035i	$0.471644\pi$
$240$	0.703035	−	0.127650i	0.0453807	−	0.00823980i
$241$	−6.54342	+	1.15378i	−0.421499	+	0.0743216i	−0.380375	−	0.924832i	$-0.624205\pi$
$241$	−6.54342	+	1.15378i	−0.421499	+	0.0743216i	−0.0411240	+	0.999154i	$0.513094\pi$
$242$	2.93885	+	2.46598i	0.188916	+	0.158519i
$243$	−8.13462	−	13.2977i	−0.521836	−	0.853046i
$244$	0.345986	−	1.96218i	0.0221495	−	0.125616i
$245$	−0.167581	−	0.460424i	−0.0107063	−	0.0294154i
$246$	−8.24485	−	2.95353i	−0.525672	−	0.188310i
$247$	−5.00182	−	6.77450i	−0.318258	−	0.431051i
$248$		−	7.12195i		−	0.452244i
$249$	−0.0714179	−	14.0566i	−0.00452593	−	0.890801i
$250$	6.61899	+	1.16711i	0.418622	+	0.0738143i
$251$	−18.5555	−	22.1135i	−1.17121	−	1.39579i	−0.901459	−	0.432864i	$-0.857503\pi$
$251$	−18.5555	−	22.1135i	−1.17121	−	1.39579i	−0.269751	−	0.962930i	$-0.586941\pi$
$252$	1.69200	+	9.05668i	0.106586	+	0.570517i
$253$	3.99483	+	22.6558i	0.251153	+	1.42436i
$254$	9.26313	−	5.34807i	0.581220	−	0.335568i
$255$	−0.644201	+	0.546150i	−0.0403414	+	0.0342012i
$256$	15.8943	+	5.78504i	0.993392	+	0.361565i
$257$	−6.67388	−	2.42909i	−0.416305	−	0.151523i	0.125371	−	0.992110i	$-0.459988\pi$
$257$	−6.67388	−	2.42909i	−0.416305	−	0.151523i	−0.541676	+	0.840587i	$0.682210\pi$
$258$	−1.83751	+	1.55783i	−0.114398	+	0.0969863i
$259$	14.6084	−	8.43415i	0.907720	−	0.524073i
$260$	−0.281566	−	1.59684i	−0.0174620	−	0.0990319i
$261$	4.88856	+	26.1667i	0.302594	+	1.61968i
$262$	11.0523	+	13.1717i	0.682816	+	0.813748i
$263$	−1.50286	−	0.264995i	−0.0926703	−	0.0163403i	0.127121	−	0.991887i	$-0.459426\pi$
$263$	−1.50286	−	0.264995i	−0.0926703	−	0.0163403i	−0.219791	+	0.975547i	$0.570538\pi$
$264$	0.0679711	+	13.3782i	0.00418333	+	0.823372i
$265$			4.10818i			0.252364i
$266$	−2.66577	+	11.0523i	−0.163449	+	0.677663i
$267$	2.18967	+	0.784401i	0.134006	+	0.0480045i
$268$	−3.72116	−	10.2238i	−0.227306	−	0.624518i
$269$	−2.20000	+	12.4768i	−0.134136	+	0.760726i	0.841321	+	0.540536i	$0.181779\pi$
$269$	−2.20000	+	12.4768i	−0.134136	+	0.760726i	−0.975457	+	0.220189i	$0.929332\pi$
$270$	1.21364	−	3.49950i	0.0738596	−	0.212973i
$271$	17.4285	+	14.6242i	1.05871	+	0.888359i	0.993982	−	0.109544i	$-0.0349391\pi$
$271$	17.4285	+	14.6242i	1.05871	+	0.888359i	0.0647232	+	0.997903i	$0.479384\pi$
$272$	0.346782	−	0.0611470i	0.0210267	−	0.00370758i
$273$	−9.10504	+	1.65321i	−0.551062	+	0.100057i
$274$	−6.40155	−	3.69594i	−0.386732	−	0.223280i
$275$	−3.98816	+	10.9574i	−0.240495	+	0.660754i
$276$	10.7372	−	12.9289i	0.646301	−	0.778227i
$277$	1.84387	−	3.19367i	0.110787	−	0.191889i	−0.805301	−	0.592867i	$-0.797996\pi$
$277$	1.84387	−	3.19367i	0.110787	−	0.191889i	0.916088	+	0.400978i	$0.131329\pi$
$278$	0.0398579	+	0.0690360i	0.00239052	+	0.00414050i
$279$	−6.34403	−	3.57727i	−0.379807	−	0.214166i
$280$	−3.94153	+	4.69733i	−0.235551	+	0.280719i
$281$	−7.23561	+	6.07140i	−0.431640	+	0.362189i	−0.832570	−	0.553919i	$-0.813132\pi$
$281$	−7.23561	+	6.07140i	−0.431640	+	0.362189i	0.400930	+	0.916109i	$0.368687\pi$
$282$	−14.4377	−	8.23807i	−0.859750	−	0.490570i
$283$	−15.5216	+	5.64941i	−0.922665	+	0.335823i	−0.759298	−	0.650743i	$-0.774458\pi$
$283$	−15.5216	+	5.64941i	−0.922665	+	0.335823i	−0.163367	+	0.986565i	$0.552235\pi$
$284$	−3.02282			−0.179371
$285$	−3.91121	+	4.15493i	−0.231680	+	0.246117i
$286$	−4.79730			−0.283670
$287$	13.9326	−	5.07105i	0.822416	−	0.299335i
$288$	12.1952	−	10.4459i	0.718606	−	0.615533i
$289$	12.7039	−	10.6599i	0.747289	−	0.627050i
$290$	−4.06567	+	4.84527i	−0.238744	+	0.284524i
$291$	−23.2043	−	3.97009i	−1.36026	−	0.232731i
$292$	3.04452	+	5.27326i	0.178167	+	0.308594i
$293$	−12.9655	+	22.4569i	−0.757453	+	1.31195i	0.186692	+	0.982418i	$0.440223\pi$
$293$	−12.9655	+	22.4569i	−0.757453	+	1.31195i	−0.944145	+	0.329529i	$0.893110\pi$
$294$	0.814689	+	0.676582i	0.0475137	+	0.0394591i
$295$	1.94369	−	5.34024i	0.113166	−	0.310921i
$296$	−15.4962	−	8.94671i	−0.900696	−	0.520017i
$297$	11.9511	+	6.65917i	0.693471	+	0.386404i
$298$	−11.0826	+	1.95417i	−0.641999	+	0.113202i
$299$	12.9308	+	10.8502i	0.747808	+	0.627485i
$300$	7.98977	−	2.95410i	0.461290	−	0.170555i
$301$	0.708196	−	4.01638i	0.0408197	−	0.231500i
$302$	0.851345	+	2.33905i	0.0489894	+	0.134597i
$303$	−1.22434	+	3.41779i	−0.0703367	+	0.196347i
$304$	2.28191	−	0.673314i	0.130876	−	0.0386172i
$305$		−	1.35608i		−	0.0776487i
$306$	0.606854	−	1.72155i	0.0346915	−	0.0984143i
$307$	11.7253	+	2.06749i	0.669199	+	0.117998i	0.497917	−	0.867224i	$-0.334098\pi$
$307$	11.7253	+	2.06749i	0.669199	+	0.117998i	0.171281	+	0.985222i	$0.445209\pi$
$308$	−5.19761	−	6.19428i	−0.296162	−	0.352952i
$309$	17.9929	−	10.5104i	1.02358	−	0.597918i
$310$	−0.300505	−	1.70425i	−0.0170675	−	0.0967948i
$311$	−11.8340	+	6.83236i	−0.671045	+	0.387428i	−0.796472	−	0.604675i	$-0.793303\pi$
$311$	−11.8340	+	6.83236i	−0.671045	+	0.387428i	0.125428	+	0.992103i	$0.459970\pi$
$312$	6.34792	+	7.48756i	0.359380	+	0.423900i
$313$	−0.501783	−	0.182634i	−0.0283624	−	0.0103231i	0.327800	−	0.944747i	$-0.393693\pi$
$313$	−0.501783	−	0.182634i	−0.0283624	−	0.0103231i	−0.356162	+	0.934424i	$0.615915\pi$
$314$	11.6016	+	4.22262i	0.654714	+	0.238296i
$315$	2.20446	+	5.87041i	0.124207	+	0.330760i
$316$	−9.00467	+	5.19885i	−0.506552	+	0.292458i
$317$	1.24799	+	7.07772i	0.0700943	+	0.397525i	0.999588	+	0.0286876i	$0.00913281\pi$
$317$	1.24799	+	7.07772i	0.0700943	+	0.397525i	−0.929494	+	0.368837i	$0.879756\pi$
$318$	−4.47861	−	7.66695i	−0.251148	−	0.429941i
$319$	−15.0170	−	17.8966i	−0.840793	−	1.00202i
$320$	4.56996	+	0.805808i	0.255469	+	0.0450460i
$321$	−11.8222	+	0.0600656i	−0.659852	+	0.00335253i
$322$		−	22.7900i		−	1.27004i
$323$	−1.93788	+	2.03779i	−0.107827	+	0.113386i
$324$	−1.93517	−	9.80530i	−0.107510	−	0.544739i
$325$	2.92628	+	8.03990i	0.162321	+	0.445973i
$326$	3.58928	−	20.3558i	0.198792	−	1.12740i
$327$	7.05889	+	19.0918i	0.390357	+	1.05578i
$328$	−12.0482	−	10.1096i	−0.665251	−	0.558212i
$329$	27.7139	−	4.88671i	1.52792	−	0.269413i
$330$	0.580747	+	3.19847i	0.0319691	+	0.176070i
$331$	10.8346	+	6.25537i	0.595524	+	0.343826i	0.767279	−	0.641314i	$-0.221610\pi$
$331$	10.8346	+	6.25537i	0.595524	+	0.343826i	−0.171755	+	0.985140i	$0.554944\pi$
$332$	3.08243	−	8.46890i	0.169170	−	0.464791i
$333$	−15.7530	+	9.30970i	−0.863259	+	0.510168i
$334$	−0.601699	+	1.04217i	−0.0329235	+	0.0570252i
$335$	−3.70247	−	6.41287i	−0.202288	−	0.350373i
$336$	0.440918	−	2.57707i	0.0240541	−	0.140591i
$337$	−10.1355	+	12.0790i	−0.552114	+	0.657984i	−0.967858	−	0.251498i	$-0.919077\pi$
$337$	−10.1355	+	12.0790i	−0.552114	+	0.657984i	0.415744	+	0.909482i	$0.363521\pi$
$338$	6.69584	−	5.61847i	0.364205	−	0.305605i
$339$	1.70379	−	2.98598i	0.0925372	−	0.162176i
$340$	−0.508826	+	0.185198i	−0.0275950	+	0.0100437i
$341$	6.39196			0.346144
$342$	2.76978	−	12.0181i	0.149773	−	0.649863i
$343$	17.5660			0.948476
$344$	−4.06529	+	1.47964i	−0.219186	+	0.0797770i
$345$	5.66874	−	9.93477i	0.305195	−	0.534870i
$346$	−2.18362	+	1.83227i	−0.117392	+	0.0985036i
$347$	6.99541	−	8.33680i	0.375533	−	0.447543i	−0.544866	−	0.838523i	$-0.683419\pi$
$347$	6.99541	−	8.33680i	0.375533	−	0.447543i	0.920399	+	0.390980i	$0.127864\pi$
$348$	−2.87820	+	16.8225i	−0.154288	+	0.901778i
$349$	−15.3337	−	26.5588i	−0.820796	−	1.42166i	−0.905090	−	0.425219i	$-0.860197\pi$
$349$	−15.3337	−	26.5588i	−0.820796	−	1.42166i	0.0842943	−	0.996441i	$-0.473136\pi$
$350$	5.77575	−	10.0039i	0.308727	−	0.534730i
$351$	9.85819	−	1.89362i	0.526191	−	0.101074i
$352$	−4.81997	+	13.2427i	−0.256905	+	0.705841i
$353$	−9.45086	−	5.45646i	−0.503018	−	0.290418i	0.226941	−	0.973909i	$-0.427128\pi$
$353$	−9.45086	−	5.45646i	−0.503018	−	0.290418i	−0.729959	+	0.683491i	$0.760461\pi$
$354$	2.19432	+	12.0852i	0.116627	+	0.642323i
$355$	−2.02609	+	0.357255i	−0.107534	+	0.0189611i
$356$	1.14237	+	0.958561i	0.0605454	+	0.0508036i
$357$	1.07168	+	2.89851i	0.0567193	+	0.153406i
$358$	1.96535	−	11.1461i	0.103872	−	0.589089i
$359$	0.231280	+	0.635437i	0.0122065	+	0.0335371i	0.945646	−	0.325197i	$-0.105431\pi$
$359$	0.231280	+	0.635437i	0.0122065	+	0.0335371i	−0.933440	+	0.358734i	$0.883208\pi$
$360$	4.22367	−	5.13873i	0.222607	−	0.270835i
$361$	−11.4665	+	15.1499i	−0.603498	+	0.797364i
$362$			7.32860i			0.385183i
$363$	7.04536	−	0.0357956i	0.369785	−	0.00187878i
$364$	−5.84295	−	1.03027i	−0.306254	−	0.0540008i
$365$	2.66386	+	3.17466i	0.139433	+	0.166170i
$366$	1.47835	+	2.53080i	0.0772746	+	0.132287i
$367$	−0.213597	−	1.21137i	−0.0111497	−	0.0632330i	0.978725	−	0.205175i	$-0.0657764\pi$
$367$	−0.213597	−	1.21137i	−0.0111497	−	0.0632330i	−0.989875	+	0.141942i	$0.954665\pi$
$368$	−4.13017	+	2.38455i	−0.215300	+	0.124303i
$369$	−15.0571	+	5.65424i	−0.783839	+	0.294348i
$370$	−4.08565	−	1.48706i	−0.212403	−	0.0773083i
$371$	14.1256	+	5.14128i	0.733363	+	0.266922i
$372$	−3.01964	−	3.56176i	−0.156561	−	0.184669i
$373$	5.13058	−	2.96214i	0.265652	−	0.153374i	−0.361258	−	0.932466i	$-0.617653\pi$
$373$	5.13058	−	2.96214i	0.265652	−	0.153374i	0.626910	+	0.779092i	$0.284319\pi$
$374$	0.278189	+	1.57769i	0.0143848	+	0.0815803i
$375$	10.6580	−	6.22581i	0.550377	−	0.321499i
$376$	−19.1883	−	22.8677i	−0.989560	−	1.17931i
$377$	−16.8816	−	2.97667i	−0.869445	−	0.153307i
$378$	−10.5138	−	8.55251i	−0.540774	−	0.439893i
$379$			10.4298i			0.535745i	0.963454	+	0.267872i	$0.0863205\pi$
$379$			10.4298i			0.535745i	−0.963454	+	0.267872i	$0.913679\pi$
$380$	−3.27585	+	1.62896i	−0.168047	+	0.0835641i
$381$	6.62451	−	18.4925i	0.339384	−	0.947399i
$382$	0.346894	+	0.953083i	0.0177486	+	0.0487640i
$383$	−2.22181	+	12.6005i	−0.113529	+	0.643855i	0.873939	+	0.486036i	$0.161558\pi$
$383$	−2.22181	+	12.6005i	−0.113529	+	0.643855i	−0.987468	+	0.157820i	$0.949554\pi$
$384$	7.98361	−	2.95182i	0.407412	−	0.150634i
$385$	−4.21586	−	3.53753i	−0.214860	−	0.180289i
$386$	1.80097	−	0.317559i	0.0916668	−	0.0161633i
$387$	−0.723922	+	4.36445i	−0.0367990	+	0.221857i
$388$	−13.0713	−	7.54673i	−0.663596	−	0.383127i
$389$	5.42537	−	14.9061i	0.275077	−	0.755768i	−0.722825	−	0.691031i	$-0.757157\pi$
$389$	5.42537	−	14.9061i	0.275077	−	0.755768i	0.997902	−	0.0647371i	$-0.0206209\pi$
$390$	1.83496	+	1.52389i	0.0929166	+	0.0771652i
$391$	2.81848	−	4.88175i	0.142537	−	0.246881i
$392$	0.950900	+	1.64701i	0.0480277	+	0.0831864i
$393$	31.1249	+	5.32525i	1.57004	+	0.268623i
$394$	−9.63283	+	11.4800i	−0.485295	+	0.578352i
$395$	−5.42109	+	4.54883i	−0.272765	+	0.228877i
$396$	5.70623	+	6.66175i	0.286749	+	0.334766i
$397$	17.4496	−	6.35113i	0.875770	−	0.318754i	0.135269	−	0.990809i	$-0.456810\pi$
$397$	17.4496	−	6.35113i	0.875770	−	0.318754i	0.740501	+	0.672055i	$0.234588\pi$
$398$	2.61552			0.131104
$399$	9.39152	+	18.6481i	0.470164	+	0.933572i
$400$	−2.41730			−0.120865
$401$	−30.7150	+	11.1794i	−1.53384	+	0.558271i	−0.964557	−	0.263874i	$-0.915000\pi$
$401$	−30.7150	+	11.1794i	−1.53384	+	0.558271i	−0.569279	+	0.822144i	$0.692778\pi$
$402$	13.9009	+	7.93179i	0.693314	+	0.395602i
$403$	3.59279	−	3.01471i	0.178970	−	0.150173i
$404$	−1.49618	+	1.78308i	−0.0744379	+	0.0887117i
$405$	−2.45593	−	6.34345i	−0.122036	−	0.315208i
$406$	11.5719	+	20.0431i	0.574304	+	0.994723i
$407$	8.02968	−	13.9078i	0.398017	−	0.689385i
$408$	2.09433	−	2.52184i	0.103685	−	0.124849i
$409$	6.25333	−	17.1809i	0.309207	−	0.849540i	−0.683605	−	0.729853i	$-0.739589\pi$
$409$	6.25333	−	17.1809i	0.309207	−	0.849540i	0.992812	−	0.119687i	$-0.0381891\pi$
$410$	−3.30965	−	1.91082i	−0.163452	−	0.0943689i
$411$	−13.3566	+	2.42517i	−0.658835	+	0.119625i
$412$	13.1570	−	2.31994i	0.648201	−	0.114295i
$413$	−15.9294	−	13.3663i	−0.783834	−	0.657715i
$414$	0.251206	+	24.7208i	0.0123461	+	1.21496i
$415$	1.06514	−	6.04072i	0.0522857	−	0.296527i
$416$	3.53662	+	9.71678i	0.173397	+	0.476404i
$417$	0.137820	+	0.0493710i	0.00674909	+	0.00241771i
$418$	3.06325	+	10.3816i	0.149829	+	0.507779i
$419$			23.0832i			1.12769i	0.825882	+	0.563843i	$0.190678\pi$
$419$			23.0832i			1.12769i	−0.825882	+	0.563843i	$0.809322\pi$
$420$	0.0204264	+	4.02035i	0.000996704	+	0.196173i
$421$	−11.4247	−	2.01448i	−0.556804	−	0.0981796i	−0.111837	−	0.993727i	$-0.535674\pi$
$421$	−11.4247	−	2.01448i	−0.556804	−	0.0981796i	−0.444967	+	0.895547i	$0.646785\pi$
$422$	7.22007	+	8.60454i	0.351467	+	0.418863i
$423$	−30.0079	+	5.60619i	−1.45904	+	0.272582i
$424$	−2.76893	−	15.7034i	−0.134471	−	0.762624i
$425$	2.47439	−	1.42859i	0.120026	−	0.0692968i
$426$	3.39175	−	2.87551i	0.164331	−	0.139319i
$427$	−4.66273	−	1.69709i	−0.225645	−	0.0821282i
$428$	−7.12272	−	2.59246i	−0.344290	−	0.125311i
$429$	−6.72010	+	5.69726i	−0.324449	+	0.275066i
$430$	−0.910371	+	0.525603i	−0.0439020	+	0.0253468i
$431$	1.52061	+	8.62379i	0.0732450	+	0.415393i	0.999279	+	0.0379542i	$0.0120841\pi$
$431$	1.52061	+	8.62379i	0.0732450	+	0.415393i	−0.926034	+	0.377439i	$0.876805\pi$
$432$	−0.449866	+	2.80025i	−0.0216442	+	0.134727i
$433$	22.4687	+	26.7771i	1.07977	+	1.28683i	0.955633	+	0.294561i	$0.0951734\pi$
$433$	22.4687	+	26.7771i	1.07977	+	1.28683i	0.124142	+	0.992264i	$0.460382\pi$
$434$	−6.23596	−	1.09957i	−0.299335	−	0.0527809i
$435$	0.0590162	+	11.6157i	0.00282961	+	0.556929i
$436$			13.0504i			0.625002i
$437$	15.2236	−	34.9111i	0.728243	−	1.67003i
$438$	−8.43238	−	3.02071i	−0.402915	−	0.144335i
$439$	7.13625	+	19.6067i	0.340595	+	0.935777i	0.985222	+	0.171280i	$0.0547902\pi$
$439$	7.13625	+	19.6067i	0.340595	+	0.935777i	−0.644628	+	0.764497i	$0.722988\pi$
$440$	−1.01374	+	5.74918i	−0.0483279	+	0.274081i
$441$	1.94473	−	0.0197619i	0.0926063	−	0.000941041i
$442$	0.900467	+	0.755582i	0.0428309	+	0.0359394i
$443$	−3.66884	+	0.646915i	−0.174312	+	0.0307359i	−0.260123	−	0.965576i	$-0.583763\pi$
$443$	−3.66884	+	0.646915i	−0.174312	+	0.0307359i	0.0858110	+	0.996311i	$0.472652\pi$
$444$	−11.5431	+	2.09589i	−0.547811	+	0.0994663i
$445$	0.878979	+	0.507479i	0.0416676	+	0.0240568i
$446$	−2.12206	+	5.83032i	−0.100483	+	0.276073i
$447$	−13.2039	+	15.8991i	−0.624522	+	0.752002i
$448$	8.48988	−	14.7049i	0.401109	−	0.694742i
$449$	−3.50765	−	6.07543i	−0.165536	−	0.286717i	0.771309	−	0.636461i	$-0.219602\pi$
$449$	−3.50765	−	6.07543i	−0.165536	−	0.286717i	−0.936846	+	0.349743i	$0.886269\pi$
$450$	−6.15479	+	10.9151i	−0.290140	+	0.514541i
$451$	9.07342	−	10.8133i	0.427251	−	0.509178i
$452$	1.68849	−	1.41681i	0.0794201	−	0.0666414i
$453$	3.97042	+	2.26551i	0.186547	+	0.106443i
$454$	16.7619	−	6.10085i	0.786677	−	0.286327i
$455$	−4.03809			−0.189309
$456$	12.1500	−	18.5183i	0.568978	−	0.867197i
$457$	−30.3503			−1.41973			−0.709864	−	0.704339i	$-0.751243\pi$
$457$	−30.3503			−1.41973			−0.709864	+	0.704339i	$0.751243\pi$
$458$	−8.48075	+	3.08674i	−0.396280	+	0.144234i
$459$	−1.19442	−	3.13226i	−0.0557508	−	0.146201i
$460$	5.61785	−	4.71393i	0.261933	−	0.219788i
$461$	−12.4414	+	14.8271i	−0.579453	+	0.690565i	−0.973542	−	0.228507i	$-0.926616\pi$
$461$	−12.4414	+	14.8271i	−0.579453	+	0.690565i	0.394089	+	0.919072i	$0.371060\pi$
$462$	11.7244	+	2.00596i	0.545469	+	0.0933258i
$463$	−6.55643	−	11.3561i	−0.304703	−	0.527761i	0.672492	−	0.740104i	$-0.265224\pi$
$463$	−6.55643	−	11.3561i	−0.304703	−	0.527761i	−0.977195	+	0.212343i	$0.931891\pi$
$464$	2.42157	−	4.19428i	0.112418	−	0.194715i
$465$	−2.44491	−	2.03045i	−0.113380	−	0.0941597i
$466$	−5.47631	+	15.0460i	−0.253685	+	0.696995i
$467$	31.3996	+	18.1286i	1.45300	+	0.838891i	0.998651	−	0.0519317i	$-0.0165378\pi$
$467$	31.3996	+	18.1286i	1.45300	+	0.838891i	0.454351	+	0.890823i	$0.349871\pi$
$468$	6.34931	+	1.05315i	0.293497	+	0.0486818i
$469$	−26.6836	+	4.70503i	−1.23213	+	0.217258i
$470$	−5.55654	−	4.66249i	−0.256304	−	0.215065i
$471$	21.2663	−	7.86291i	0.979902	−	0.362304i
$472$	−3.83034	+	21.7229i	−0.176306	+	0.999880i
$473$	−1.32798	−	3.64860i	−0.0610607	−	0.167763i
$474$	5.15819	−	14.3992i	0.236924	−	0.661378i
$475$	15.5302	−	11.4664i	0.712572	−	0.526114i
$476$			1.98132i			0.0908135i
$477$	−15.3789	−	5.42114i	−0.704153	−	0.248217i
$478$	−16.5147	−	2.91199i	−0.755366	−	0.133191i
$479$	−7.11537	−	8.47977i	−0.325110	−	0.387451i	0.578589	−	0.815619i	$-0.303603\pi$
$479$	−7.11537	−	8.47977i	−0.325110	−	0.387451i	−0.903699	+	0.428169i	$0.859159\pi$
$480$	6.05027	−	3.53423i	0.276156	−	0.161315i
$481$	−2.04617	−	11.6044i	−0.0932975	−	0.529117i
$482$	5.42698	−	3.13327i	0.247192	−	0.142717i
$483$	−27.0654	−	31.9245i	−1.23152	−	1.45261i
$484$	4.24473	+	1.54495i	0.192942	+	0.0702252i
$485$	−9.65318	−	3.51347i	−0.438328	−	0.159538i
$486$	11.4988	+	9.16117i	0.521598	+	0.415559i
$487$	−16.7012	+	9.64242i	−0.756802	+	0.436940i	−0.828146	−	0.560512i	$-0.810604\pi$
$487$	−16.7012	+	9.64242i	−0.756802	+	0.436940i	0.0713444	+	0.997452i	$0.477271\pi$
$488$	0.914001	+	5.18356i	0.0413749	+	0.234649i
$489$	−19.1466	−	32.7772i	−0.865841	−	1.48224i
$490$	0.297040	+	0.353998i	0.0134189	+	0.0159920i
$491$	20.1391	+	3.55106i	0.908864	+	0.160257i	0.608488	−	0.793563i	$-0.291776\pi$
$491$	20.1391	+	3.55106i	0.908864	+	0.160257i	0.300377	+	0.953821i	$0.402888\pi$
$492$	−10.3118	+	0.0523917i	−0.464893	+	0.00236200i
$493$			5.72446i			0.257817i
$494$	6.61816	+	4.39051i	0.297765	+	0.197538i
$495$	4.61201	+	3.79075i	0.207295	+	0.170382i
$496$	0.453206	+	1.24517i	0.0203495	+	0.0559099i
$497$	−1.30722	+	7.41360i	−0.0586368	+	0.332546i
$498$	4.59756	+	12.4348i	0.206022	+	0.557215i
$499$	26.4116	+	22.1619i	1.18234	+	0.992104i	0.999961	+	0.00887695i	$0.00282566\pi$
$499$	26.4116	+	22.1619i	1.18234	+	0.992104i	0.182383	+	0.983227i	$0.441619\pi$
$500$	7.79351	−	1.37421i	0.348536	−	0.0614564i
$501$	0.394818	+	2.17446i	0.0176392	+	0.0971478i
$502$	23.5781	+	13.6128i	1.05234	+	0.607571i
$503$	14.2850	−	39.2477i	0.636936	−	1.74997i	−0.0242047	−	0.999707i	$-0.507705\pi$
$503$	14.2850	−	39.2477i	0.636936	−	1.74997i	0.661141	−	0.750262i	$-0.270072\pi$
$504$	−12.3832	−	20.9537i	−0.551590	−	0.933350i
$505$	−0.792106	+	1.37197i	−0.0352482	+	0.0610517i
$506$	−10.8486	−	18.7903i	−0.482277	−	0.835329i
$507$	2.70710	−	15.8224i	0.120226	−	0.702696i
$508$	8.09535	−	9.64767i	0.359173	−	0.428046i
$509$	2.29929	−	1.92934i	0.101914	−	0.0855163i	−0.590407	−	0.807106i	$-0.701033\pi$
$509$	2.29929	−	1.92934i	0.101914	−	0.0855163i	0.692321	+	0.721590i	$0.256588\pi$
$510$	0.394756	−	0.691831i	0.0174801	−	0.0306348i
$511$	14.2495	−	5.18640i	0.630361	−	0.229433i
$512$	−6.12392			−0.270642
$513$	−10.3927	−	20.1244i	−0.458849	−	0.888514i
$514$	6.69834			0.295451
$515$	8.54453	−	3.10996i	0.376517	−	0.137041i
$516$	−1.40574	+	2.46363i	−0.0618841	+	0.108455i
$517$	20.5238	−	17.2215i	0.902635	−	0.757401i
$518$	−10.2262	+	12.1871i	−0.449313	+	0.535470i
$519$	−0.882826	+	5.15992i	−0.0387518	+	0.226495i
$520$	2.14175	+	3.70962i	0.0939219	+	0.162677i
$521$	15.2958	−	26.4931i	0.670121	−	1.16068i	−0.307748	−	0.951468i	$-0.599575\pi$
$521$	15.2958	−	26.4931i	0.670121	−	1.16068i	0.977869	−	0.209216i	$-0.0670913\pi$
$522$	−12.7732	−	21.6136i	−0.559067	−	0.946001i
$523$	6.27523	−	17.2410i	0.274397	−	0.753898i	−0.723576	−	0.690245i	$-0.757503\pi$
$523$	6.27523	−	17.2410i	0.274397	−	0.753898i	0.997972	−	0.0636530i	$-0.0202751\pi$
$524$	17.5331	+	10.1227i	0.765937	+	0.442214i
$525$	−3.78988	−	20.8728i	−0.165404	−	0.910964i
$526$	1.41740	−	0.249926i	0.0618016	−	0.0108973i
$527$	−1.19979	−	1.00674i	−0.0522637	−	0.0438545i
$528$	−0.863206	−	2.33466i	−0.0375662	−	0.101603i
$529$	−9.26316	+	52.5340i	−0.402746	+	2.28409i
$530$	−1.32518	−	3.64091i	−0.0575623	−	0.158151i
$531$	17.4262	+	14.3231i	0.756234	+	0.621571i
$532$	1.50139	+	13.3023i	0.0650936	+	0.576726i
$533$		−	10.3573i		−	0.448626i
$534$	−2.19364	+	0.0111453i	−0.0949282	+	0.000482306i
$535$	−5.08051	−	0.895830i	−0.219649	−	0.0387301i
$536$	18.4749	+	22.0175i	0.797994	+	0.951012i
$537$	−10.4840	−	17.9476i	−0.452417	−	0.774495i
$538$	−2.07490	−	11.7674i	−0.0894554	−	0.507327i
$539$	−1.47819	+	0.853434i	−0.0636702	+	0.0367600i
$540$	−0.0664717	−	4.36073i	−0.00286049	−	0.187656i
$541$	−11.3765	−	4.14071i	−0.489114	−	0.178023i	0.0856773	−	0.996323i	$-0.472695\pi$
$541$	−11.3765	−	4.14071i	−0.489114	−	0.178023i	−0.574791	+	0.818300i	$0.694917\pi$
$542$	−20.1635	−	7.33892i	−0.866097	−	0.315234i
$543$	8.70343	+	10.2660i	0.373500	+	0.440555i
$544$	2.99048	−	1.72655i	0.128216	−	0.0740253i
$545$	1.54238	+	8.74726i	0.0660682	+	0.374691i
$546$	7.53615	−	4.40220i	0.322517	−	0.188397i
$547$	−14.0778	−	16.7773i	−0.601923	−	0.717344i	0.375927	−	0.926649i	$-0.377324\pi$
$547$	−14.0778	−	16.7773i	−0.601923	−	0.717344i	−0.977850	+	0.209305i	$0.932880\pi$
$548$	−8.57132	−	1.51135i	−0.366148	−	0.0645618i
$549$	5.07645	+	1.78947i	0.216658	+	0.0763729i
$550$		−	10.9975i		−	0.468936i
$551$	4.33785	+	38.4332i	0.184799	+	1.63731i
$552$	−14.9725	+	41.7961i	−0.637272	+	1.77896i
$553$	8.85635	+	24.3326i	0.376610	+	1.03473i
$554$	−0.603955	+	3.42520i	−0.0256596	+	0.145523i
$555$	−7.48924	+	2.76903i	−0.317901	+	0.117539i
$556$	0.0719018	+	0.0603328i	0.00304932	+	0.00255868i
$557$	−26.7456	+	4.71596i	−1.13325	+	0.199822i	−0.708649	−	0.705561i	$-0.750695\pi$
$557$	−26.7456	+	4.71596i	−1.13325	+	0.199822i	−0.424596	+	0.905383i	$0.639584\pi$
$558$	6.77638	+	1.12398i	0.286867	+	0.0475821i
$559$	−2.46726	−	1.42447i	−0.104354	−	0.0602488i
$560$	0.390206	−	1.07208i	0.0164892	−	0.0453037i
$561$	2.26335	+	1.87966i	0.0955587	+	0.0793595i
$562$	4.45416	−	7.71484i	0.187887	−	0.325431i
$563$	0.218964	+	0.379256i	0.00922822	+	0.0159837i	0.870603	−	0.491987i	$-0.163729\pi$
$563$	0.218964	+	0.379256i	0.00922822	+	0.0159837i	−0.861374	+	0.507971i	$0.830396\pi$
$564$	−19.2919	−	3.30071i	−0.812337	−	0.138985i
$565$	0.964292	−	1.14920i	0.0405681	−	0.0483472i
$566$	11.9338	−	10.0137i	0.501617	−	0.420906i
$567$	−24.8848	+	0.505798i	−1.04506	+	0.0212415i
$568$	7.50388	−	2.73119i	0.314856	−	0.114598i
$569$	32.6261			1.36776			0.683878	−	0.729596i	$-0.260292\pi$
$569$	32.6261			1.36776			0.683878	+	0.729596i	$0.260292\pi$
$570$	2.12608	−	4.94399i	0.0890517	−	0.207081i
$571$	−22.3986			−0.937353			−0.468676	−	0.883370i	$-0.655269\pi$
$571$	−22.3986			−0.937353			−0.468676	+	0.883370i	$0.655269\pi$
$572$	−5.30791	+	1.93192i	−0.221935	+	0.0807777i
$573$	1.61781	+	0.923116i	0.0675851	+	0.0385637i
$574$	−10.7121	+	8.98853i	−0.447115	+	0.375174i
$575$	−24.8735	+	29.6431i	−1.03730	+	1.23620i
$576$	−9.04705	+	16.0443i	−0.376960	+	0.668511i
$577$	11.7982	+	20.4351i	0.491165	+	0.850723i	0.999948	−	0.0101715i	$-0.00323775\pi$
$577$	11.7982	+	20.4351i	0.491165	+	0.850723i	−0.508783	+	0.860895i	$0.669904\pi$
$578$	−7.82039	+	13.5453i	−0.325285	+	0.563411i
$579$	2.14568	−	2.58366i	0.0891713	−	0.107373i
$580$	−2.54717	+	6.99828i	−0.105765	+	0.290588i
$581$	−19.4374	−	11.2222i	−0.806399	−	0.465575i
$582$	21.8457	−	3.96652i	0.905532	−	0.164418i
$583$	14.0938	−	2.48512i	0.583706	−	0.102923i
$584$	−12.3223	−	10.3396i	−0.509899	−	0.427856i
$585$	4.38019	−	0.0445104i	0.181099	−	0.00184028i
$586$	4.24683	−	24.0849i	0.175435	−	0.994940i
$587$	5.00085	+	13.7397i	0.206407	+	0.567099i	0.999095	−	0.0425285i	$-0.0135413\pi$
$587$	5.00085	+	13.7397i	0.206407	+	0.567099i	−0.792688	+	0.609627i	$0.791319\pi$
$588$	1.17387	+	0.420512i	0.0484096	+	0.0173416i
$589$	−8.81810	−	5.84996i	−0.363343	−	0.241043i
$590$			5.35981i			0.220660i
$591$	0.139828	+	27.5212i	0.00575175	+	1.13207i
$592$	3.27861	+	0.578107i	0.134750	+	0.0237601i
$593$	25.5787	+	30.4835i	1.05039	+	1.25181i	0.966861	+	0.255302i	$0.0821749\pi$
$593$	25.5787	+	30.4835i	1.05039	+	1.25181i	0.0835298	+	0.996505i	$0.473381\pi$
$594$	−12.7398	−	2.04667i	−0.522720	−	0.0839759i
$595$	0.234164	+	1.32801i	0.00959978	+	0.0544431i
$596$	−11.4753	+	6.62525i	−0.470045	+	0.271381i
$597$	3.66384	−	3.10618i	0.149951	−	0.127128i
$598$	−14.9600	−	5.44500i	−0.611761	−	0.222663i
$599$	−38.7502	−	14.1039i	−1.58329	−	0.576270i	−0.607374	−	0.794416i	$-0.707777\pi$
$599$	−38.7502	−	14.1039i	−1.58329	−	0.576270i	−0.975916	+	0.218146i	$0.929999\pi$
$600$	−17.1648	+	14.5522i	−0.700750	+	0.594093i
$601$	−33.4472	+	19.3108i	−1.36434	+	0.787703i	−0.990198	−	0.139669i	$-0.955396\pi$
$601$	−33.4472	+	19.3108i	−1.36434	+	0.787703i	−0.374143	+	0.927371i	$0.622063\pi$
$602$	0.667926	+	3.78800i	0.0272226	+	0.154387i
$603$	28.8923	−	5.39776i	1.17658	−	0.219814i
$604$	1.88392	+	2.24517i	0.0766556	+	0.0913546i
$605$	3.02769	+	0.533863i	0.123093	+	0.0217046i
$606$	−0.0173963	−	3.42398i	−0.000706678	−	0.139090i
$607$		−	14.1262i		−	0.573366i	−0.958026	−	0.286683i	$-0.907447\pi$
$607$		−	14.1262i		−	0.573366i	0.958026	−	0.286683i	$-0.0925526\pi$
$608$	18.7693	−	13.8579i	0.761194	−	0.562013i
$609$	40.0132	+	14.3338i	1.62142	+	0.580835i
$610$	0.437432	+	1.20183i	0.0177111	+	0.0486608i
$611$	3.41364	−	19.3597i	0.138101	−	0.783210i
$612$	−0.0218393	−	2.14917i	−0.000882802	−	0.0868751i
$613$	−3.94393	−	3.30935i	−0.159294	−	0.133663i	0.559657	−	0.828724i	$-0.310933\pi$
$613$	−3.94393	−	3.30935i	−0.159294	−	0.133663i	−0.718951	+	0.695061i	$0.755377\pi$
$614$	−11.0586	+	1.94992i	−0.446287	+	0.0786925i
$615$	−6.90547	+	1.25383i	−0.278456	+	0.0505593i
$616$	18.4993	+	10.6806i	0.745358	+	0.430333i
$617$	−0.607820	+	1.66997i	−0.0244699	+	0.0672305i	−0.951326	−	0.308186i	$-0.900278\pi$
$617$	−0.607820	+	1.66997i	−0.0244699	+	0.0672305i	0.926856	+	0.375416i	$0.122500\pi$
$618$	−12.5560	+	15.1190i	−0.505076	+	0.608174i
$619$	11.8880	−	20.5906i	0.477819	−	0.827606i	−0.521858	−	0.853032i	$-0.674761\pi$
$619$	11.8880	−	20.5906i	0.477819	−	0.827606i	0.999677	+	0.0254261i	$0.00809425\pi$
$620$	−1.01881	−	1.76463i	−0.0409163	−	0.0708692i
$621$	29.7102	+	34.3308i	1.19223	+	1.37765i
$622$	8.28406	−	9.87256i	0.332161	−	0.395853i
$623$	2.84493	−	2.38718i	0.113980	−	0.0956405i
$624$	−1.58631	−	0.905144i	−0.0635034	−	0.0362348i
$625$	−15.7470	+	5.73145i	−0.629881	+	0.229258i
$626$	0.503622			0.0201288
$627$	16.6202	+	10.9047i	0.663745	+	0.435491i
$628$	14.5369			0.580085
$629$	−3.69770	+	1.34585i	−0.147437	+	0.0536627i
$630$	−3.84735	−	4.49161i	−0.153282	−	0.178950i
$631$	21.9849	−	18.4475i	0.875205	−	0.734385i	−0.0899821	−	0.995943i	$-0.528681\pi$
$631$	21.9849	−	18.4475i	0.875205	−	0.734385i	0.965188	+	0.261559i	$0.0842365\pi$
$632$	17.6560	−	21.0416i	0.702318	−	0.836990i
$633$	20.3327	+	3.47878i	0.808151	+	0.138269i
$634$	−3.38912	−	5.87013i	−0.134599	−	0.233132i
$635$	4.28582	−	7.42326i	0.170078	−	0.294583i
$636$	−8.04286	−	6.67942i	−0.318920	−	0.264856i
$637$	−0.428347	+	1.17687i	−0.0169717	+	0.0466294i
$638$	19.0819	+	11.0170i	0.755461	+	0.436166i
$639$	1.33625	−	8.05608i	0.0528611	−	0.318694i
$640$	3.65784	−	0.644976i	0.144589	−	0.0254949i
$641$	−23.9818	−	20.1231i	−0.947225	−	0.794816i	0.0316033	−	0.999500i	$-0.489939\pi$
$641$	−23.9818	−	20.1231i	−0.947225	−	0.794816i	−0.978828	+	0.204685i	$0.934383\pi$
$642$	10.4582	−	3.86675i	0.412751	−	0.152608i
$643$	−2.95925	+	16.7827i	−0.116701	+	0.661846i	0.869192	+	0.494474i	$0.164639\pi$
$643$	−2.95925	+	16.7827i	−0.116701	+	0.661846i	−0.985894	+	0.167372i	$0.946472\pi$
$644$	−9.17779	−	25.2158i	−0.361656	−	0.993640i
$645$	−0.651050	+	1.81742i	−0.0256351	+	0.0715610i
$646$	1.06013	−	2.43112i	0.0417103	−	0.0956511i
$647$		−	3.40639i		−	0.133919i	−0.997756	−	0.0669596i	$-0.978670\pi$
$647$		−	3.40639i		−	0.133919i	0.997756	−	0.0669596i	$-0.0213299\pi$
$648$	13.6632	+	22.5923i	0.536742	+	0.887510i
$649$	−19.4964	−	3.43774i	−0.765299	−	0.134943i
$650$	−5.18689	−	6.18149i	−0.203446	−	0.242458i
$651$	−10.0412	+	5.86553i	−0.393547	+	0.229888i
$652$	−4.22619	−	23.9679i	−0.165510	−	0.938655i
$653$	4.29421	−	2.47926i	0.168045	−	0.0970211i	−0.413618	−	0.910450i	$-0.635735\pi$
$653$	4.29421	−	2.47926i	0.168045	−	0.0970211i	0.581664	+	0.813429i	$0.302402\pi$
$654$	−12.4145	−	14.6432i	−0.485444	−	0.572596i
$655$	12.9482	+	4.71276i	0.505928	+	0.184143i
$656$	2.74979	+	1.00084i	0.107361	+	0.0390763i
$657$	−15.3995	+	5.78285i	−0.600793	+	0.225610i
$658$	−22.9854	+	13.2706i	−0.896063	+	0.517342i
$659$	−2.99511	−	16.9861i	−0.116673	−	0.661686i	−0.985908	−	0.167287i	$-0.946499\pi$
$659$	−2.99511	−	16.9861i	−0.116673	−	0.661686i	0.869235	−	0.494399i	$-0.164612\pi$
$660$	1.93062	+	3.30503i	0.0751492	+	0.128648i
$661$	−15.2930	−	18.2255i	−0.594830	−	0.708891i	0.381696	−	0.924288i	$-0.375340\pi$
$661$	−15.2930	−	18.2255i	−0.594830	−	0.708891i	−0.976527	+	0.215397i	$0.930896\pi$
$662$	−11.6201	−	2.04893i	−0.451627	−	0.0796340i
$663$	2.15871	−	0.0109678i	0.0838374	−	0.000425956i
$664$			23.8084i			0.923943i
$665$	2.57847	+	8.73861i	0.0999889	+	0.338869i
$666$	10.9582	−	13.3323i	0.424621	−	0.516615i
$667$	−26.5166	−	72.8539i	−1.02673	−	2.82091i
$668$	−0.246049	+	1.39541i	−0.00951991	+	0.0539901i
$669$	3.95147	+	10.6873i	0.152773	+	0.413195i
$670$	5.34996	+	4.48915i	0.206687	+	0.173431i
$671$	−4.65225	+	0.820317i	−0.179598	+	0.0316680i
$672$	−4.58034	−	25.2262i	−0.176690	−	0.973123i
$673$	9.66092	+	5.57774i	0.372401	+	0.215006i	0.674507	−	0.738268i	$-0.264356\pi$
$673$	9.66092	+	5.57774i	0.372401	+	0.215006i	−0.302106	+	0.953274i	$0.597690\pi$
$674$	5.08631	−	13.9745i	0.195917	−	0.538278i
$675$	4.34103	+	22.5993i	0.167086	+	0.869849i
$676$	5.14591	−	8.91298i	0.197920	−	0.342807i
$677$	12.7624	+	22.1050i	0.490497	+	0.849566i	0.999940	−	0.0109384i	$-0.00348188\pi$
$677$	12.7624	+	22.1050i	0.490497	+	0.849566i	−0.509443	+	0.860504i	$0.670149\pi$
$678$	−0.546804	+	3.19595i	−0.0209999	+	0.122740i
$679$	−24.1614	+	28.7945i	−0.927230	+	1.10503i
$680$	1.09579	−	0.919473i	0.0420215	−	0.0352602i
$681$	16.2349	−	28.4526i	0.622123	−	1.09030i
$682$	−5.66493	+	2.06187i	−0.216921	+	0.0789529i
$683$	19.7577			0.756007			0.378004	−	0.925804i	$-0.376611\pi$
$683$	19.7577			0.756007			0.378004	+	0.925804i	$0.376611\pi$
$684$	−1.77521	−	14.4127i	−0.0678770	−	0.551082i
$685$	−5.92368			−0.226332
$686$	−15.5680	+	5.66630i	−0.594390	+	0.216340i
$687$	−8.21411	+	14.3957i	−0.313388	+	0.549229i
$688$	0.616601	−	0.517389i	0.0235077	−	0.0197253i
$689$	6.74976	−	8.04406i	0.257146	−	0.306454i
$690$	−1.81929	+	10.6334i	−0.0692592	+	0.404805i
$691$	6.70762	+	11.6179i	0.255170	+	0.441967i	0.964942	−	0.262465i	$-0.0845353\pi$
$691$	6.70762	+	11.6179i	0.255170	+	0.441967i	−0.709772	+	0.704432i	$0.751202\pi$
$692$	−1.67816	+	2.90666i	−0.0637941	+	0.110495i
$693$	18.8059	−	11.1139i	0.714378	−	0.422183i
$694$	−3.51052	+	9.64508i	−0.133258	+	0.366122i
$695$	0.0553238	+	0.0319412i	0.00209855	+	0.00121160i
$696$	−8.05461	−	44.3608i	−0.305309	−	1.68149i
$697$	−3.40622	+	0.600608i	−0.129020	+	0.0227497i
$698$	22.1568	+	18.5917i	0.838646	+	0.703708i
$699$	10.1974	+	27.5803i	0.385701	+	1.04318i
$700$	2.36183	−	13.3946i	0.0892690	−	0.506269i
$701$	14.9221	+	40.9982i	0.563601	+	1.54848i	0.814318	+	0.580420i	$0.197111\pi$
$701$	14.9221	+	40.9982i	0.563601	+	1.54848i	−0.250717	+	0.968060i	$0.580666\pi$
$702$	−8.12607	+	4.85821i	−0.306699	+	0.183361i
$703$	−23.8059	+	11.8379i	−0.897858	+	0.446474i
$704$		−	16.1655i		−	0.609260i
$705$	−13.3208	+	0.0676796i	−0.501691	+	0.00254896i
$706$	10.1360	+	1.78725i	0.381474	+	0.0672641i
$707$	3.72607	+	4.44056i	0.140133	+	0.167004i
$708$	7.29473	+	12.4879i	0.274153	+	0.469324i
$709$	−2.60312	−	14.7630i	−0.0977623	−	0.554438i	−0.993866	−	0.110593i	$-0.964725\pi$
$709$	−2.60312	−	14.7630i	−0.0977623	−	0.554438i	0.896104	−	0.443845i	$-0.146386\pi$
$710$	1.68040	−	0.970180i	0.0630643	−	0.0364102i
$711$	−9.87485	−	26.2964i	−0.370336	−	0.986192i
$712$	−3.70191	−	1.34739i	−0.138735	−	0.0504954i
$713$	19.9329	+	7.25497i	0.746491	+	0.271701i
$714$	−1.88476	−	2.22314i	−0.0705355	−	0.0831988i
$715$	−3.32938	+	1.92222i	−0.124512	+	0.0718870i
$716$	−2.31410	−	13.1239i	−0.0864820	−	0.490464i
$717$	−26.5923	+	15.5337i	−0.993106	+	0.580117i
$718$	−0.409948	−	0.488557i	−0.0152991	−	0.0182328i
$719$	−41.3087	−	7.28384i	−1.54056	−	0.271642i	−0.662082	−	0.749432i	$-0.730327\pi$
$719$	−41.3087	−	7.28384i	−1.54056	−	0.271642i	−0.878474	+	0.477790i	$0.841438\pi$
$720$	−0.411446	+	1.16721i	−0.0153337	+	0.0434992i
$721$		−	33.2715i		−	1.23910i
$722$	5.27532	−	17.1255i	0.196327	−	0.637345i
$723$	3.88110	−	10.8342i	0.144340	−	0.402928i
$724$	2.95130	+	8.10864i	0.109684	+	0.301355i
$725$	6.82386	−	38.7000i	0.253432	−	1.43728i
$726$	−6.23246	+	2.30436i	−0.231308	+	0.0855228i
$727$	11.3609	+	9.53290i	0.421351	+	0.353556i	0.828677	−	0.559727i	$-0.189094\pi$
$727$	11.3609	+	9.53290i	0.421351	+	0.353556i	−0.407326	+	0.913283i	$0.633539\pi$
$728$	15.4355	−	2.72169i	0.572077	−	0.100873i
$729$	26.9875	−	0.822945i	0.999535	−	0.0304794i
$730$	−3.38493	−	1.95429i	−0.125282	−	0.0723314i
$731$	−0.325394	+	0.894013i	−0.0120351	+	0.0330663i
$732$	2.65488	+	2.20482i	0.0981272	+	0.0814925i
$733$	−0.804203	+	1.39292i	−0.0297039	+	0.0514487i	−0.880495	−	0.474055i	$-0.842790\pi$
$733$	−0.804203	+	1.39292i	−0.0297039	+	0.0514487i	0.850791	+	0.525504i	$0.176123\pi$
$734$	0.580056	+	1.00469i	0.0214103	+	0.0370836i
$735$	0.836503	+	0.143120i	0.0308549	+	0.00527905i
$736$	−30.0614	+	35.8258i	−1.10808	+	1.32056i
$737$	−19.7607	+	16.5812i	−0.727896	+	0.610778i
$738$	11.5205	−	9.86810i	0.424077	−	0.363250i
$739$	1.21979	−	0.443965i	0.0448705	−	0.0163315i	−0.319487	−	0.947591i	$-0.603511\pi$
$739$	1.21979	−	0.443965i	0.0448705	−	0.0163315i	0.364358	+	0.931259i	$0.381288\pi$
$740$	−5.11937			−0.188192
$741$	14.4849	−	1.70945i	0.532118	−	0.0627983i
$742$	−14.1773			−0.520466
$743$	8.68786	−	3.16212i	0.318727	−	0.116007i	−0.177703	−	0.984084i	$-0.556866\pi$
$743$	8.68786	−	3.16212i	0.318727	−	0.116007i	0.496429	+	0.868077i	$0.334644\pi$
$744$	10.7141	+	6.11344i	0.392799	+	0.224129i
$745$	−6.90847	+	5.79689i	−0.253107	+	0.212382i
$746$	−3.59152	+	4.28021i	−0.131495	+	0.156710i
$747$	21.2078	+	11.9587i	0.775953	+	0.437544i
$748$	0.943151	+	1.63358i	0.0344850	+	0.0597298i
$749$	−9.43835	+	16.3477i	−0.344870	+	0.597332i
$750$	−7.43747	+	8.95565i	−0.271578	+	0.327014i
$751$	9.38727	−	25.7913i	0.342546	−	0.941138i	−0.642107	−	0.766615i	$-0.721939\pi$
$751$	9.38727	−	25.7913i	0.342546	−	0.941138i	0.984653	−	0.174523i	$-0.0558383\pi$
$752$	4.80999	+	2.77705i	0.175402	+	0.101268i
$753$	49.1951	−	8.93236i	1.79277	−	0.325513i
$754$	15.9216	−	2.80741i	0.579831	−	0.102240i
$755$	1.52807	+	1.28221i	0.0556123	+	0.0466643i
$756$	−15.0771	−	5.22878i	−0.548349	−	0.190169i
$757$	3.02250	−	17.1414i	0.109855	−	0.623016i	−0.879315	−	0.476240i	$-0.841999\pi$
$757$	3.02250	−	17.1414i	0.109855	−	0.623016i	0.989170	−	0.146776i	$-0.0468897\pi$
$758$	−3.36437	−	9.24353i	−0.122199	−	0.335740i
$759$	−37.5120	−	13.4378i	−1.36160	−	0.487762i
$760$	6.66019	−	7.00357i	0.241590	−	0.254046i
$761$		−	8.35519i		−	0.302875i	−0.988467	−	0.151438i	$-0.951610\pi$
$761$		−	8.35519i		−	0.302875i	0.988467	−	0.151438i	$-0.0483903\pi$
$762$	0.0941258	+	18.5260i	0.00340982	+	0.671127i
$763$	32.0068	+	5.64366i	1.15872	+	0.204314i
$764$	0.767633	+	0.914829i	0.0277720	+	0.0330974i
$765$	−0.268640	−	1.43793i	−0.00971270	−	0.0519886i
$766$	−2.09547	−	11.8840i	−0.0757124	−	0.429386i
$767$	−12.5799	+	7.26301i	−0.454234	+	0.262252i
$768$	−22.3464	+	18.9452i	−0.806358	+	0.683626i
$769$	31.8082	+	11.5772i	1.14703	+	0.417486i	0.844449	−	0.535636i	$-0.179928\pi$
$769$	31.8082	+	11.5772i	1.14703	+	0.417486i	0.302585	+	0.953122i	$0.402150\pi$
$770$	4.87745	+	1.77525i	0.175771	+	0.0639754i
$771$	9.38309	−	7.95494i	0.337924	−	0.286490i
$772$	1.86477	−	1.07663i	0.0671146	−	0.0387487i
$773$	7.25002	+	41.1169i	0.260765	+	1.47887i	0.780829	+	0.624744i	$0.214797\pi$
$773$	7.25002	+	41.1169i	0.260765	+	1.47887i	−0.520064	+	0.854127i	$0.674092\pi$
$774$	−0.766265	−	4.10155i	−0.0275428	−	0.147427i
$775$	6.91105	+	8.23627i	0.248252	+	0.295856i
$776$	39.2671	+	6.92385i	1.40961	+	0.248552i
$777$	0.148441	+	29.2164i	0.00532528	+	1.04813i
$778$			14.9607i			0.536367i
$779$	−22.4137	+	6.61354i	−0.803055	+	0.236955i
$780$	2.64395	+	0.947135i	0.0946687	+	0.0339129i
$781$	2.45124	+	6.73474i	0.0877124	+	0.240988i
$782$	−0.923187	+	5.23566i	−0.0330131	+	0.187227i
$783$	−43.5610	−	15.1071i	−1.55674	−	0.539884i
$784$	−0.271059	−	0.227445i	−0.00968067	−	0.00812305i
$785$	9.74359	−	1.71806i	0.347763	−	0.0613201i
$786$	−29.3025	+	5.32046i	−1.04518	+	0.189774i
$787$	26.7581	+	15.4488i	0.953822	+	0.550689i	0.894266	−	0.447536i	$-0.147698\pi$
$787$	26.7581	+	15.4488i	0.953822	+	0.550689i	0.0595556	+	0.998225i	$0.481032\pi$
$788$	−6.03503	+	16.5811i	−0.214989	+	0.590678i
$789$	1.68870	−	2.03340i	0.0601192	−	0.0723910i
$790$	3.33716	−	5.78013i	0.118731	−	0.205648i
$791$	−2.74462	−	4.75381i	−0.0975873	−	0.169026i
$792$	−20.1843	−	11.3815i	−0.717216	−	0.404424i
$793$	−2.22804	+	2.65528i	−0.0791200	+	0.0942916i
$794$	−13.4162	+	11.2575i	−0.476122	+	0.399513i
$795$	−6.18027	−	3.52643i	−0.219192	−	0.125070i
$796$	2.89391	−	1.05330i	0.102572	−	0.0373331i
$797$	−24.5528			−0.869703			−0.434852	−	0.900502i	$-0.643199\pi$
$797$	−24.5528			−0.869703			−0.434852	+	0.900502i	$0.643199\pi$
$798$	−14.3387	−	13.4976i	−0.507583	−	0.477809i
$799$	−6.56479			−0.232246
$800$	−22.2752	+	8.10749i	−0.787546	+	0.286643i
$801$	−3.05964	+	2.62078i	−0.108107	+	0.0926007i
$802$	23.6153	−	19.8156i	0.833886	−	0.699714i
$803$	9.27980	−	11.0592i	0.327477	−	0.390272i
$804$	18.5747	+	3.17800i	0.655079	+	0.112079i
$805$	−9.13171	−	15.8166i	−0.321850	−	0.557461i
$806$	−2.21168	+	3.83075i	−0.0779032	+	0.134932i
$807$	−16.8814	−	14.0197i	−0.594255	−	0.493516i
$808$	2.10309	−	5.77818i	0.0739863	−	0.203276i
$809$	−34.4237	−	19.8745i	−1.21027	−	0.698751i	−0.247454	−	0.968900i	$-0.579594\pi$
$809$	−34.4237	−	19.8745i	−1.21027	−	0.698751i	−0.962819	+	0.270148i	$0.912927\pi$
$810$	4.22280	+	4.82972i	0.148374	+	0.169699i
$811$	−24.3550	+	4.29445i	−0.855221	+	0.150799i	−0.584035	−	0.811728i	$-0.698527\pi$
$811$	−24.3550	+	4.29445i	−0.855221	+	0.150799i	−0.271186	+	0.962527i	$0.587416\pi$
$812$	20.8752	+	17.5163i	0.732574	+	0.614703i
$813$	−36.9609	+	13.6657i	−1.29628	+	0.479278i
$814$	−2.63011	+	14.9161i	−0.0921852	+	0.522808i
$815$	−5.66533	−	15.5654i	−0.198448	−	0.545231i
$816$	−0.205687	+	0.574180i	−0.00720048	+	0.0201003i
$817$	−1.50719	+	6.24884i	−0.0527298	+	0.218619i
$818$			17.2438i			0.602917i
$819$	5.32866	−	15.1166i	0.186198	−	0.528215i
$820$	−4.43143	−	0.781380i	−0.154752	−	0.0272870i
$821$	−0.437587	−	0.521496i	−0.0152719	−	0.0182003i	0.758354	−	0.651842i	$-0.226004\pi$
$821$	−0.437587	−	0.521496i	−0.0152719	−	0.0182003i	−0.773626	+	0.633642i	$0.781559\pi$
$822$	11.0552	−	6.45781i	0.385593	−	0.225242i
$823$	8.74011	+	49.5676i	0.304661	+	1.72782i	0.625096	+	0.780548i	$0.285060\pi$
$823$	8.74011	+	49.5676i	0.304661	+	1.72782i	−0.320435	+	0.947270i	$0.603829\pi$
$824$	−30.5651	+	17.6468i	−1.06479	+	0.614754i
$825$	−13.0606	−	15.4054i	−0.454713	−	0.536348i
$826$	18.4292	+	6.70767i	0.641233	+	0.233390i
$827$	10.4120	+	3.78966i	0.362061	+	0.131779i	0.516644	−	0.856201i	$-0.327181\pi$
$827$	10.4120	+	3.78966i	0.362061	+	0.131779i	−0.154583	+	0.987980i	$0.549403\pi$
$828$	10.2333	+	27.2508i	0.355630	+	0.947032i
$829$	−15.6901	+	9.05871i	−0.544941	+	0.314622i	−0.747079	−	0.664735i	$-0.768544\pi$
$829$	−15.6901	+	9.05871i	−0.544941	+	0.314622i	0.202138	+	0.979357i	$0.435211\pi$
$830$	1.00457	+	5.69722i	0.0348693	+	0.197753i
$831$	3.22173	+	5.51530i	0.111761	+	0.191324i
$832$	−7.62431	−	9.08629i	−0.264325	−	0.315011i
$833$	0.411878	+	0.0726252i	0.0142707	+	0.00251631i
$834$	−0.138070		0.000701498i	−0.00478098		2.42909e-5i
$835$			0.964376i			0.0333736i
$836$	7.57006	+	10.2530i	0.261816	+	0.354606i
$837$	10.8273	−	6.47313i	0.374245	−	0.223744i
$838$	−7.44597	−	20.4576i	−0.257217	−	0.706698i
$839$	−4.98678	+	28.2814i	−0.172163	+	0.976384i	0.769205	+	0.639002i	$0.220652\pi$
$839$	−4.98678	+	28.2814i	−0.172163	+	0.976384i	−0.941368	+	0.337382i	$0.890459\pi$
$840$	−3.68319	−	9.96172i	−0.127082	−	0.343712i
$841$	38.0976	+	31.9677i	1.31371	+	1.10233i
$842$	10.7750	−	1.89993i	0.371332	−	0.0654758i
$843$	−2.92270	−	16.0968i	−0.100663	−	0.554402i
$844$	11.4537	+	6.61279i	0.394253	+	0.227622i
$845$	2.39574	−	6.58224i	0.0824159	−	0.226436i
$846$	24.7864	−	14.6482i	0.852174	−	0.503617i
$847$	5.62471	−	9.74228i	0.193267	−	0.334749i
$848$	1.48339	+	2.56931i	0.0509400	+	0.0882306i
$849$	4.82480	−	28.1999i	0.165587	−	0.967817i
$850$	−1.73213	+	2.06427i	−0.0594115	+	0.0708039i
$851$	40.8256	−	34.2567i	1.39948	−	1.17430i
$852$	2.59477	−	4.54747i	0.0888952	−	0.155794i
$853$	−4.18389	+	1.52281i	−0.143254	+	0.0521401i	−0.412652	−	0.910889i	$-0.635397\pi$
$853$	−4.18389	+	1.52281i	−0.143254	+	0.0521401i	0.269398	+	0.963029i	$0.413175\pi$
$854$	4.67982			0.160140
$855$	−2.89324	−	9.45051i	−0.0989467	−	0.323201i
$856$	20.0239			0.684402
$857$	39.7782	−	14.4781i	1.35880	−	0.494562i	0.443116	−	0.896464i	$-0.353873\pi$
$857$	39.7782	−	14.4781i	1.35880	−	0.494562i	0.915683	+	0.401902i	$0.131651\pi$
$858$	4.11797	−	7.21696i	0.140585	−	0.246383i
$859$	−16.2198	+	13.6100i	−0.553411	+	0.464367i	−0.876094	−	0.482140i	$-0.839860\pi$
$859$	−16.2198	+	13.6100i	−0.553411	+	0.464367i	0.322683	+	0.946507i	$0.395415\pi$
$860$	−0.795603	+	0.948162i	−0.0271298	+	0.0323321i
$861$	−4.33086	+	25.3129i	−0.147595	+	0.862661i
$862$	−4.12944	−	7.15240i	−0.140649	−	0.243612i
$863$	12.2868	−	21.2813i	0.418246	−	0.724424i	−0.577517	−	0.816379i	$-0.695978\pi$
$863$	12.2868	−	21.2813i	0.418246	−	0.724424i	0.995763	+	0.0919547i	$0.0293115\pi$
$864$	5.24643	+	27.3129i	0.178487	+	0.929203i
$865$	−0.781288	+	2.14657i	−0.0265646	+	0.0729856i
$866$	−28.5506	−	16.4837i	−0.970188	−	0.560138i
$867$	5.13152	+	28.2619i	0.174276	+	0.959824i
$868$	−7.34251	+	1.29468i	−0.249221	+	0.0439444i
$869$	18.8849	+	15.8463i	0.640625	+	0.537548i
$870$	−3.79919	−	10.2755i	−0.128805	−	0.348371i
$871$	−3.28673	+	18.6400i	−0.111366	+	0.631591i
$872$	−11.7914	−	32.3965i	−0.399306	−	1.09709i
$873$	25.8910	−	31.5002i	0.876276	−	1.06612i
$874$	−2.23070	+	35.8510i	−0.0754545	+	1.21268i
$875$		−	19.7082i		−	0.666260i
$876$	−10.5464	+	0.0535834i	−0.356329	+	0.00181041i
$877$	51.5733	+	9.09377i	1.74151	+	0.307075i	0.951871	−	0.306499i	$-0.0991577\pi$
$877$	51.5733	+	9.09377i	1.74151	+	0.307075i	0.789637	+	0.613574i	$0.210269\pi$
$878$	−12.6491	−	15.0747i	−0.426888	−	0.508745i
$879$	−22.6543	−	38.7819i	−0.764109	−	1.30808i
$880$	−0.188612	−	1.06967i	−0.00635811	−	0.0360586i
$881$	11.8654	−	6.85051i	0.399756	−	0.230799i	−0.286623	−	0.958044i	$-0.592533\pi$
$881$	11.8654	−	6.85051i	0.399756	−	0.230799i	0.686379	+	0.727244i	$0.259199\pi$
$882$	−1.71716	+	0.644830i	−0.0578198	+	0.0217125i
$883$	−50.1392	−	18.2492i	−1.68732	−	0.614134i	−0.693036	−	0.720903i	$-0.743727\pi$
$883$	−50.1392	−	18.2492i	−1.68732	−	0.614134i	−0.994284	+	0.106769i	$0.965950\pi$
$884$	1.30059	+	0.473377i	0.0437436	+	0.0159214i
$885$	6.36530	+	7.50807i	0.213967	+	0.252381i
$886$	3.04286	−	1.75680i	0.102227	−	0.0590208i
$887$	−5.01003	−	28.4133i	−0.168220	−	0.954025i	−0.945682	−	0.325094i	$-0.894604\pi$
$887$	−5.01003	−	28.4133i	−0.168220	−	0.954025i	0.777461	−	0.628931i	$-0.216507\pi$
$888$	26.7611	−	15.6323i	0.898042	−	0.524586i
$889$	−20.1605	−	24.0264i	−0.676162	−	0.805819i
$890$	−0.942701	−	0.166224i	−0.0315994	−	0.00557183i
$891$	−20.2766	+	12.2628i	−0.679293	+	0.410818i
$892$			7.30546i			0.244605i
$893$	−44.0750	+	4.97463i	−1.47491	+	0.166470i
$894$	6.57344	−	18.3499i	0.219849	−	0.613713i
$895$	−3.10212	−	8.52301i	−0.103693	−	0.284893i
$896$	2.36001	−	13.3843i	0.0788425	−	0.447138i
$897$	−27.4226	+	10.1391i	−0.915614	+	0.338534i
$898$	5.06845	+	4.25293i	0.169136	+	0.141922i
$899$	−21.2141	+	3.74062i	−0.707530	+	0.124757i
$900$	−2.41428	+	14.5554i	−0.0804761	+	0.485181i
$901$	−3.03686	−	1.75333i	−0.101173	−	0.0584120i
$902$	−4.55334	+	12.5102i	−0.151610	+	0.416544i
$903$	5.43425	+	4.51303i	0.180841	+	0.150184i
$904$	−2.91141	+	5.04271i	−0.0968321	+	0.167718i
$905$	2.93648	+	5.08614i	0.0976120	+	0.169069i
$906$	−4.24961	−	0.727078i	−0.141184	−	0.0241556i
$907$	−4.09841	+	4.88429i	−0.136085	+	0.162180i	−0.829783	−	0.558086i	$-0.811536\pi$
$907$	−4.09841	+	4.88429i	−0.136085	+	0.162180i	0.693698	+	0.720266i	$0.255980\pi$
$908$	16.0892	−	13.5004i	0.533938	−	0.448027i
$909$	−4.09068	−	4.77568i	−0.135679	−	0.158399i
$910$	3.57879	−	1.30257i	0.118636	−	0.0431799i
$911$	−20.6085			−0.682792			−0.341396	−	0.939920i	$-0.610900\pi$
$911$	−20.6085			−0.682792			−0.341396	+	0.939920i	$0.610900\pi$
$912$	−0.945852	+	4.01082i	−0.0313203	+	0.132812i
$913$	−21.3680			−0.707178
$914$	26.8982	−	9.79015i	0.889714	−	0.323829i
$915$	2.04005	+	1.16405i	0.0674421	+	0.0384822i
$916$	−8.14036	+	6.83058i	−0.268965	+	0.225689i
$917$	32.4087	−	38.6232i	1.07023	−	1.27545i
$918$	2.06894	+	2.39070i	0.0682853	+	0.0789050i
$919$	19.9111	+	34.4870i	0.656806	+	1.13762i	0.981438	+	0.191781i	$0.0614264\pi$
$919$	19.9111	+	34.4870i	0.656806	+	1.13762i	−0.324631	+	0.945841i	$0.605240\pi$
$920$	−9.68666	+	16.7778i	−0.319360	+	0.553147i
$921$	−13.1752	+	15.8646i	−0.434138	+	0.522757i
$922$	6.24349	−	17.1539i	0.205618	−	0.564932i
$923$	4.55417	+	2.62935i	0.149902	+	0.0865462i
$924$	13.7801	−	2.50207i	0.453334	−	0.0823119i
$925$	26.6025	−	4.69074i	0.874685	−	0.154231i
$926$	9.47384	+	7.94949i	0.311330	+	0.261237i
$927$	0.366740	+	36.0903i	0.0120453	+	1.18536i
$928$	8.24711	−	46.7717i	0.270725	−	1.53536i
$929$	−3.83622	−	10.5399i	−0.125862	−	0.345804i	0.860718	−	0.509083i	$-0.170015\pi$
$929$	−3.83622	−	10.5399i	−0.125862	−	0.345804i	−0.986580	+	0.163279i	$0.947793\pi$
$930$	2.82179	+	1.01084i	0.0925301	+	0.0331468i
$931$	2.82032	+	0.175484i	0.0924323	+	0.00575126i
$932$			18.8529i			0.617547i
$933$	−0.120249	−	23.6677i	−0.00393679	−	0.774846i
$934$	−33.6760	−	5.93798i	−1.10191	−	0.194297i
$935$	0.825228	+	0.983469i	0.0269879	+	0.0321629i
$936$	−16.7132	+	3.12241i	−0.546286	+	0.102059i
$937$	−7.56135	−	42.8826i	−0.247019	−	1.40091i	−0.815757	−	0.578394i	$-0.803680\pi$
$937$	−7.56135	−	42.8826i	−0.247019	−	1.40091i	0.568739	−	0.822518i	$-0.307432\pi$
$938$	22.1308	−	12.7772i	0.722597	−	0.417191i
$939$	0.705478	−	0.598100i	0.0230224	−	0.0195183i
$940$	−8.02560	−	2.92108i	−0.261766	−	0.0952751i
$941$	36.3696	+	13.2374i	1.18561	+	0.431529i	0.858182	−	0.513346i	$-0.171594\pi$
$941$	36.3696	+	13.2374i	1.18561	+	0.431529i	0.327433	+	0.944874i	$0.393816\pi$
$942$	−16.3111	+	13.8285i	−0.531445	+	0.450557i
$943$	40.5680	−	23.4220i	1.32108	−	0.762724i
$944$	−0.712660	−	4.04169i	−0.0231951	−	0.131546i
$945$	−10.7236	−	1.72277i	−0.348840	−	0.0560418i
$946$	2.35387	+	2.80523i	0.0765309	+	0.0912060i
$947$	−39.6810	−	6.99682i	−1.28946	−	0.227366i	−0.513466	−	0.858110i	$-0.671639\pi$
$947$	−39.6810	−	6.99682i	−1.28946	−	0.227366i	−0.775991	+	0.630743i	$0.782750\pi$
$948$	−0.0914995	−	18.0091i	−0.00297177	−	0.584908i
$949$		−	10.5929i		−	0.343860i
$950$	−10.0650	+	15.1718i	−0.326552	+	0.492237i
$951$	−11.7189	−	4.19801i	−0.380010	−	0.136130i
$952$	−1.79017	−	4.91845i	−0.0580197	−	0.159408i
$953$	2.40512	−	13.6401i	0.0779096	−	0.441847i	−0.920753	−	0.390146i	$-0.872425\pi$
$953$	2.40512	−	13.6401i	0.0779096	−	0.441847i	0.998663	−	0.0517013i	$-0.0164644\pi$
$954$	15.3784	−	0.156271i	0.497895	−	0.00505947i
$955$	0.622638	+	0.522455i	0.0201481	+	0.0169063i
$956$	−19.4452	+	3.42872i	−0.628903	+	0.110893i
$957$	39.8139	−	7.22902i	1.28700	−	0.233681i
$958$	9.04139	+	5.22005i	0.292114	+	0.168652i
$959$	−7.41334	+	20.3680i	−0.239389	+	0.657716i
$960$	−5.13507	+	6.18326i	−0.165734	+	0.199564i
$961$	−12.5531	+	21.7427i	−0.404940	+	0.701376i
$962$	5.55670	+	9.62449i	0.179155	+	0.310306i
$963$	10.0578	−	17.8367i	0.324107	−	0.574779i
$964$	4.74282	−	5.65227i	0.152756	−	0.182047i
$965$	1.12265	−	0.942016i	0.0361394	−	0.0303246i
$966$	34.2849	+	19.5628i	1.10310	+	0.629423i
$967$	7.29648	−	2.65570i	0.234639	−	0.0854016i	−0.222025	−	0.975041i	$-0.571267\pi$
$967$	7.29648	−	2.65570i	0.234639	−	0.0854016i	0.456664	+	0.889639i	$0.349044\pi$
$968$	−11.9331			−0.383543
$969$	−1.40215	−	4.66454i	−0.0450436	−	0.149847i
$970$	9.68856			0.311081
$971$	19.9285	−	7.25337i	0.639535	−	0.232772i	−0.00184129	−	0.999998i	$-0.500586\pi$
$971$	19.9285	−	7.25337i	0.639535	−	0.232772i	0.641376	+	0.767227i	$0.278364\pi$
$972$	16.4120	+	5.50557i	0.526416	+	0.176591i
$973$	0.179063	−	0.150252i	0.00574050	−	0.00481685i
$974$	11.6912	−	13.9330i	0.374609	−	0.446442i
$975$	−14.6070	−	2.49915i	−0.467797	−	0.0800368i
$976$	−0.489656	−	0.848109i	−0.0156735	−	0.0271473i
$977$	−29.9393	+	51.8564i	−0.957844	+	1.65903i	−0.230121	+	0.973162i	$0.573912\pi$
$977$	−29.9393	+	51.8564i	−0.957844	+	1.65903i	−0.727722	+	0.685872i	$0.759421\pi$
$978$	27.5419	+	22.8729i	0.880692	+	0.731396i
$979$	1.20928	−	3.32247i	0.0386488	−	0.106187i
$980$	0.471215	+	0.272056i	0.0150524	+	0.00869051i
$981$	−34.7806	−	5.76899i	−1.11046	−	0.184190i
$982$	−18.9939	+	3.34914i	−0.606120	+	0.106875i
$983$	1.76552	+	1.48145i	0.0563114	+	0.0472509i	0.670509	−	0.741901i	$-0.266076\pi$
$983$	1.76552	+	1.48145i	0.0563114	+	0.0472509i	−0.614198	+	0.789152i	$0.710520\pi$
$984$	25.5509	−	9.44704i	0.814532	−	0.301161i
$985$	−2.08542	+	11.8270i	−0.0664470	+	0.376840i
$986$	−1.84655	−	5.07335i	−0.0588061	−	0.161568i
$987$	−16.4380	+	45.8870i	−0.523226	+	1.46060i
$988$	9.09069	+	2.19263i	0.289213	+	0.0697567i
$989$		−	12.8852i		−	0.409725i
$990$	−5.31023	−	1.87188i	−0.168770	−	0.0594922i
$991$	−47.0657	−	8.29896i	−1.49509	−	0.263625i	−0.634501	−	0.772922i	$-0.718795\pi$
$991$	−47.0657	−	8.29896i	−1.49509	−	0.263625i	−0.860591	+	0.509297i	$0.829906\pi$
$992$	8.35249	+	9.95411i	0.265192	+	0.316043i
$993$	−18.7108	+	10.9298i	−0.593770	+	0.346847i
$994$	−1.23289	−	6.99204i	−0.0391048	−	0.221774i
$995$	1.81520	−	1.04801i	0.0575457	−	0.0332240i
$996$	10.0945	+	11.9068i	0.319857	+	0.377281i
$997$	32.6262	+	11.8750i	1.03328	+	0.376084i	0.802329	−	0.596882i	$-0.203594\pi$
$997$	32.6262	+	11.8750i	1.03328	+	0.376084i	0.230952	+	0.972965i	$0.425816\pi$
$998$	−30.5563	−	11.1216i	−0.967243	−	0.352047i
$999$	−0.483057	−	31.6899i	−0.0152833	−	1.00262i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.14.2	✓	24
3.2	odd	2	inner	57.2.j.b.14.3	yes	24
4.3	odd	2		912.2.cc.e.641.2		24
12.11	even	2		912.2.cc.e.641.1		24
19.2	odd	18		1083.2.d.d.1082.12		24
19.15	odd	18	inner	57.2.j.b.53.3	yes	24
19.17	even	9		1083.2.d.d.1082.14		24
57.2	even	18		1083.2.d.d.1082.13		24
57.17	odd	18		1083.2.d.d.1082.11		24
57.53	even	18	inner	57.2.j.b.53.2	yes	24
76.15	even	18		912.2.cc.e.737.1		24
228.167	odd	18		912.2.cc.e.737.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.14.2	✓	24	1.1	even	1	trivial
57.2.j.b.14.3	yes	24	3.2	odd	2	inner
57.2.j.b.53.2	yes	24	57.53	even	18	inner
57.2.j.b.53.3	yes	24	19.15	odd	18	inner
912.2.cc.e.641.1		24	12.11	even	2
912.2.cc.e.641.2		24	4.3	odd	2
912.2.cc.e.737.1		24	76.15	even	18
912.2.cc.e.737.2		24	228.167	odd	18
1083.2.d.d.1082.11		24	57.17	odd	18
1083.2.d.d.1082.12		24	19.2	odd	18
1083.2.d.d.1082.13		24	57.2	even	18
1083.2.d.d.1082.14		24	19.17	even	9

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.886259 + 0.322572i) q^{2} +(-0.858393 + 1.50438i) q^{3} +(-0.850687 + 0.713811i) q^{4} +(-0.485824 + 0.578982i) q^{5} +(0.275488 - 1.61016i) q^{6} +(1.38278 + 2.39504i) q^{7} +(1.46681 - 2.54059i) q^{8} +(-1.52632 - 2.58270i) q^{9} +O(q^{10})\)	\(q+(-0.886259 + 0.322572i) q^{2} +(-0.858393 + 1.50438i) q^{3} +(-0.850687 + 0.713811i) q^{4} +(-0.485824 + 0.578982i) q^{5} +(0.275488 - 1.61016i) q^{6} +(1.38278 + 2.39504i) q^{7} +(1.46681 - 2.54059i) q^{8} +(-1.52632 - 2.58270i) q^{9} +(0.243802 - 0.669841i) q^{10} +(2.28018 + 1.31646i) q^{11} +(-0.343620 - 1.89249i) q^{12} +(1.90254 - 0.335470i) q^{13} +(-1.99807 - 1.67658i) q^{14} +(-0.453982 - 1.22786i) q^{15} +(-0.0947805 + 0.537527i) q^{16} +(-0.220652 - 0.606237i) q^{17} +(2.18582 + 1.79659i) q^{18} +(-1.94082 - 3.90298i) q^{19} -0.839319i q^{20} +(-4.79001 + 0.0243368i) q^{21} +(-2.44549 - 0.431205i) q^{22} +(5.61638 + 6.69334i) q^{23} +(2.56291 + 4.38747i) q^{24} +(0.769045 + 4.36147i) q^{25} +(-1.57793 + 0.911019i) q^{26} +(5.19555 - 0.0791971i) q^{27} +(-2.88591 - 1.05039i) q^{28} +(-8.33804 - 3.03480i) q^{29} +(0.798418 + 0.941759i) q^{30} +(2.10245 - 1.21385i) q^{31} +(0.929445 + 5.27114i) q^{32} +(-3.93776 + 2.30022i) q^{33} +(0.391110 + 0.466106i) q^{34} +(-2.05847 - 0.362964i) q^{35} +(3.14198 + 1.10756i) q^{36} -6.09943i q^{37} +(2.97906 + 2.83300i) q^{38} +(-1.12846 + 3.15011i) q^{39} +(0.758345 + 2.08354i) q^{40} +(0.930968 - 5.27978i) q^{41} +(4.23734 - 1.56669i) q^{42} +(-1.12968 - 0.947914i) q^{43} +(-2.87943 + 0.507721i) q^{44} +(2.23686 + 0.371024i) q^{45} +(-7.13664 - 4.12034i) q^{46} +(3.48030 - 9.56204i) q^{47} +(-0.727286 - 0.603995i) q^{48} +(-0.324139 + 0.561425i) q^{49} +(-2.08846 - 3.61732i) q^{50} +(1.10142 + 0.188445i) q^{51} +(-1.37901 + 1.64344i) q^{52} +(4.16382 - 3.49386i) q^{53} +(-4.57905 + 1.74613i) q^{54} +(-1.86998 + 0.680616i) q^{55} +8.11308 q^{56} +(7.53755 + 0.430564i) q^{57} +8.36860 q^{58} +(-7.06560 + 2.57167i) q^{59} +(1.26266 + 0.720466i) q^{60} +(-1.37444 + 1.15329i) q^{61} +(-1.47176 + 1.75398i) q^{62} +(4.07510 - 7.22690i) q^{63} +(-3.06987 - 5.31717i) q^{64} +(-0.730070 + 1.26452i) q^{65} +(2.74788 - 3.30880i) q^{66} +(-3.35090 + 9.20653i) q^{67} +(0.620444 + 0.358214i) q^{68} +(-14.8904 + 2.70365i) q^{69} +(1.94142 - 0.342325i) q^{70} +(2.08521 + 1.74970i) q^{71} +(-8.80041 + 0.0894274i) q^{72} +(0.952144 - 5.39988i) q^{73} +(1.96750 + 5.40567i) q^{74} +(-7.22146 - 2.58692i) q^{75} +(4.43702 + 1.93484i) q^{76} +7.28150i q^{77} +(-0.0160339 - 3.15582i) q^{78} +(9.22088 + 1.62589i) q^{79} +(-0.265172 - 0.316020i) q^{80} +(-4.34068 + 7.88407i) q^{81} +(0.878031 + 4.97956i) q^{82} +(-7.02840 + 4.05785i) q^{83} +(4.05743 - 3.43987i) q^{84} +(0.458198 + 0.166771i) q^{85} +(1.30696 + 0.475694i) q^{86} +(11.7228 - 9.93854i) q^{87} +(6.68919 - 3.86200i) q^{88} +(-0.233188 - 1.32248i) q^{89} +(-2.10212 + 0.392725i) q^{90} +(3.43425 + 4.09278i) q^{91} +(-9.55556 - 1.68490i) q^{92} +(0.0213637 + 4.20485i) q^{93} +9.59708i q^{94} +(3.20265 + 0.772462i) q^{95} +(-8.72763 - 3.12647i) q^{96} +(4.64863 + 12.7720i) q^{97} +(0.106171 - 0.602125i) q^{98} +(-0.0802612 - 7.89837i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

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