LMFDB - Embedded newform 57.2.j.b.32.3

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			32.3
Character	$\chi$	$=$	57.32
Dual form			57.2.j.b.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.745719 - 0.625733i) q^{2} +(1.09578 - 1.34136i) q^{3} +(-0.182741 + 1.03637i) q^{4} +(-3.79113 + 0.668479i) q^{5} +(-0.0221879 - 1.68595i) q^{6} +(-0.469963 + 0.814000i) q^{7} +(1.48569 + 2.57329i) q^{8} +(-0.598514 - 2.93969i) q^{9} +O(q^{10})$	\(q+(0.745719 - 0.625733i) q^{2} +(1.09578 - 1.34136i) q^{3} +(-0.182741 + 1.03637i) q^{4} +(-3.79113 + 0.668479i) q^{5} +(-0.0221879 - 1.68595i) q^{6} +(-0.469963 + 0.814000i) q^{7} +(1.48569 + 2.57329i) q^{8} +(-0.598514 - 2.93969i) q^{9} +(-2.40883 + 2.87073i) q^{10} +(3.44730 - 1.99030i) q^{11} +(1.18991 + 1.38076i) q^{12} +(-0.353205 - 0.970422i) q^{13} +(0.158886 + 0.901087i) q^{14} +(-3.25759 + 5.81780i) q^{15} +(0.740303 + 0.269448i) q^{16} +(-0.804427 - 0.958678i) q^{17} +(-2.28578 - 1.81767i) q^{18} +(-4.22014 + 1.09106i) q^{19} -4.05119i q^{20} +(0.576892 + 1.52236i) q^{21} +(1.32532 - 3.64129i) q^{22} +(-0.477922 - 0.0842705i) q^{23} +(5.07970 + 0.826919i) q^{24} +(9.22735 - 3.35848i) q^{25} +(-0.870616 - 0.502651i) q^{26} +(-4.59904 - 2.41844i) q^{27} +(-0.757727 - 0.635808i) q^{28} +(3.32571 + 2.79060i) q^{29} +(1.21114 + 6.37682i) q^{30} +(4.26794 + 2.46410i) q^{31} +(-4.86370 + 1.77024i) q^{32} +(1.10778 - 6.80502i) q^{33} +(-1.19975 - 0.211549i) q^{34} +(1.23755 - 3.40014i) q^{35} +(3.15599 - 0.0830829i) q^{36} -1.10257i q^{37} +(-2.46433 + 3.45430i) q^{38} +(-1.68872 - 0.589597i) q^{39} +(-7.35262 - 8.76251i) q^{40} +(2.04769 + 0.745298i) q^{41} +(1.38279 + 0.774273i) q^{42} +(-1.00316 - 5.68919i) q^{43} +(1.43273 + 3.93640i) q^{44} +(4.23417 + 10.7447i) q^{45} +(-0.409126 + 0.236209i) q^{46} +(-4.96510 + 5.91718i) q^{47} +(1.17264 - 0.697758i) q^{48} +(3.05827 + 5.29708i) q^{49} +(4.77950 - 8.27834i) q^{50} +(-2.16741 + 0.0285242i) q^{51} +(1.07026 - 0.188716i) q^{52} +(1.34079 - 7.60399i) q^{53} +(-4.94289 + 1.07429i) q^{54} +(-11.7387 + 9.84993i) q^{55} -2.79287 q^{56} +(-3.16086 + 6.85631i) q^{57} +4.22621 q^{58} +(-5.26126 + 4.41472i) q^{59} +(-5.43411 - 4.43923i) q^{60} +(0.740173 - 4.19773i) q^{61} +(4.72455 - 0.833066i) q^{62} +(2.67419 + 0.894356i) q^{63} +(-3.30707 + 5.72801i) q^{64} +(1.98775 + 3.44289i) q^{65} +(-3.43203 - 5.76781i) q^{66} +(0.918596 - 1.09474i) q^{67} +(1.14055 - 0.658497i) q^{68} +(-0.636737 + 0.548725i) q^{69} +(-1.20471 - 3.30993i) q^{70} +(0.438181 + 2.48505i) q^{71} +(6.67546 - 5.90761i) q^{72} +(8.28206 + 3.01442i) q^{73} +(-0.689912 - 0.822205i) q^{74} +(5.60624 - 16.0574i) q^{75} +(-0.359552 - 4.57302i) q^{76} +3.74147i q^{77} +(-1.62824 + 0.617017i) q^{78} +(-1.50043 + 4.12240i) q^{79} +(-2.98671 - 0.526637i) q^{80} +(-8.28356 + 3.51889i) q^{81} +(1.99336 - 0.725523i) q^{82} +(-3.66720 - 2.11726i) q^{83} +(-1.68315 + 0.319678i) q^{84} +(3.69054 + 3.09673i) q^{85} +(-4.30799 - 3.61483i) q^{86} +(7.38747 - 1.40309i) q^{87} +(10.2432 + 5.91392i) q^{88} +(7.56260 - 2.75256i) q^{89} +(9.88079 + 5.36304i) q^{90} +(0.955916 + 0.168554i) q^{91} +(0.174671 - 0.479906i) q^{92} +(7.98199 - 3.02474i) q^{93} +7.51939i q^{94} +(15.2698 - 6.95742i) q^{95} +(-2.95502 + 8.46379i) q^{96} +(-6.91522 - 8.24124i) q^{97} +(5.59517 + 2.03647i) q^{98} +(-7.91412 - 8.94277i) 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 $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.745719	−	0.625733i	0.527303	−	0.442460i	−0.339866	−	0.940474i	$-0.610382\pi$
$2$	0.745719	−	0.625733i	0.527303	−	0.442460i	0.867169	+	0.498014i	$0.165937\pi$
$3$	1.09578	−	1.34136i	0.632651	−	0.774437i
$3$	1.09578	−	1.34136i	0.632651	−	0.774437i
$4$	−0.182741	+	1.03637i	−0.0913703	+	0.518187i
$5$	−3.79113	+	0.668479i	−1.69545	+	0.298953i	−0.936100	−	0.351734i	$-0.885592\pi$
$5$	−3.79113	+	0.668479i	−1.69545	+	0.298953i	−0.759346	+	0.650687i	$0.774481\pi$
$6$	−0.0221879	−	1.68595i	−0.00905815	−	0.688286i
$7$	−0.469963	+	0.814000i	−0.177629	+	0.307663i	−0.941068	−	0.338217i	$-0.890176\pi$
$7$	−0.469963	+	0.814000i	−0.177629	+	0.307663i	0.763439	+	0.645880i	$0.223509\pi$
$8$	1.48569	+	2.57329i	0.525270	+	0.909794i
$9$	−0.598514	−	2.93969i	−0.199505	−	0.979897i
$10$	−2.40883	+	2.87073i	−0.761739	+	0.907805i
$11$	3.44730	−	1.99030i	1.03940	−	0.600098i	0.119736	−	0.992806i	$-0.461795\pi$
$11$	3.44730	−	1.99030i	1.03940	−	0.600098i	0.919663	+	0.392708i	$0.128462\pi$
$12$	1.18991	+	1.38076i	0.343497	+	0.398592i
$13$	−0.353205	−	0.970422i	−0.0979613	−	0.269147i	0.881026	−	0.473068i	$-0.156854\pi$
$13$	−0.353205	−	0.970422i	−0.0979613	−	0.269147i	−0.978987	+	0.203921i	$0.934631\pi$
$14$	0.158886	+	0.901087i	0.0424640	+	0.240826i
$15$	−3.25759	+	5.81780i	−0.841106	+	1.50215i
$16$	0.740303	+	0.269448i	0.185076	+	0.0673620i
$17$	−0.804427	−	0.958678i	−0.195102	−	0.232514i	0.659620	−	0.751599i	$-0.270717\pi$
$17$	−0.804427	−	0.958678i	−0.195102	−	0.232514i	−0.854722	+	0.519085i	$0.826273\pi$
$18$	−2.28578	−	1.81767i	−0.538764	−	0.428430i
$19$	−4.22014	+	1.09106i	−0.968167	+	0.250306i
$19$	−4.22014	+	1.09106i	−0.968167	+	0.250306i
$20$		−	4.05119i		−	0.905873i
$21$	0.576892	+	1.52236i	0.125888	+	0.332206i
$22$	1.32532	−	3.64129i	0.282560	−	0.776326i
$23$	−0.477922	−	0.0842705i	−0.0996536	−	0.0175716i	0.123599	−	0.992332i	$-0.460556\pi$
$23$	−0.477922	−	0.0842705i	−0.0996536	−	0.0175716i	−0.223253	+	0.974761i	$0.571667\pi$
$24$	5.07970	+	0.826919i	1.03689	+	0.168794i
$25$	9.22735	−	3.35848i	1.84547	−	0.671696i
$26$	−0.870616	−	0.502651i	−0.170742	−	0.0985779i
$27$	−4.59904	−	2.41844i	−0.885085	−	0.465429i
$28$	−0.757727	−	0.635808i	−0.143197	−	0.120156i
$29$	3.32571	+	2.79060i	0.617568	+	0.518201i	0.897038	−	0.441953i	$-0.145714\pi$
$29$	3.32571	+	2.79060i	0.617568	+	0.518201i	−0.279470	+	0.960155i	$0.590159\pi$
$30$	1.21114	+	6.37682i	0.221123	+	1.16424i
$31$	4.26794	+	2.46410i	0.766544	+	0.442565i	0.831641	−	0.555314i	$-0.187402\pi$
$31$	4.26794	+	2.46410i	0.766544	+	0.442565i	−0.0650961	+	0.997879i	$0.520735\pi$
$32$	−4.86370	+	1.77024i	−0.859788	+	0.312937i
$33$	1.10778	−	6.80502i	0.192840	−	1.18460i
$34$	−1.19975	−	0.211549i	−0.205756	−	0.0362803i
$35$	1.23755	−	3.40014i	0.209184	−	0.574729i
$36$	3.15599	−	0.0830829i	0.525998	−	0.0138472i
$37$		−	1.10257i		−	0.181261i	−0.995885	−	0.0906304i	$-0.971112\pi$
$37$		−	1.10257i		−	0.181261i	0.995885	−	0.0906304i	$-0.0288882\pi$
$38$	−2.46433	+	3.45430i	−0.399767	+	0.560362i
$39$	−1.68872	−	0.589597i	−0.270412	−	0.0944111i
$40$	−7.35262	−	8.76251i	−1.16255	−	1.38548i
$41$	2.04769	+	0.745298i	0.319795	+	0.116396i	0.496930	−	0.867791i	$-0.334461\pi$
$41$	2.04769	+	0.745298i	0.319795	+	0.116396i	−0.177135	+	0.984187i	$0.556683\pi$
$42$	1.38279	+	0.774273i	0.213369	+	0.119473i
$43$	−1.00316	−	5.68919i	−0.152980	−	0.867593i	−0.960609	−	0.277903i	$-0.910361\pi$
$43$	−1.00316	−	5.68919i	−0.152980	−	0.867593i	0.807629	−	0.589691i	$-0.200750\pi$
$44$	1.43273	+	3.93640i	0.215992	+	0.593434i
$45$	4.23417	+	10.7447i	0.631192	+	1.60172i
$46$	−0.409126	+	0.236209i	−0.0603224	+	0.0348271i
$47$	−4.96510	+	5.91718i	−0.724235	+	0.863110i	−0.995035	−	0.0995260i	$-0.968267\pi$
$47$	−4.96510	+	5.91718i	−0.724235	+	0.863110i	0.270800	+	0.962636i	$0.412712\pi$
$48$	1.17264	−	0.697758i	0.169256	−	0.100713i
$49$	3.05827	+	5.29708i	0.436896	+	0.756725i
$50$	4.77950	−	8.27834i	0.675924	−	1.17073i
$51$	−2.16741	+	0.0285242i	−0.303499	+	0.00399418i
$52$	1.07026	−	0.188716i	0.148419	−	0.0261703i
$53$	1.34079	−	7.60399i	0.184172	−	1.04449i	−0.742844	−	0.669465i	$-0.766523\pi$
$53$	1.34079	−	7.60399i	0.184172	−	1.04449i	0.927015	−	0.375024i	$-0.122365\pi$
$54$	−4.94289	+	1.07429i	−0.672642	+	0.146192i
$55$	−11.7387	+	9.84993i	−1.58284	+	1.32816i
$56$	−2.79287			−0.373213
$57$	−3.16086	+	6.85631i	−0.418666	+	0.908140i
$58$	4.22621			0.554929
$59$	−5.26126	+	4.41472i	−0.684958	+	0.574748i	−0.917450	−	0.397850i	$-0.869756\pi$
$59$	−5.26126	+	4.41472i	−0.684958	+	0.574748i	0.232493	+	0.972598i	$0.425312\pi$
$60$	−5.43411	−	4.43923i	−0.701541	−	0.573102i
$61$	0.740173	−	4.19773i	0.0947695	−	0.537464i	−0.900048	−	0.435790i	$-0.856469\pi$
$61$	0.740173	−	4.19773i	0.0947695	−	0.537464i	0.994818	−	0.101674i	$-0.0324199\pi$
$62$	4.72455	−	0.833066i	0.600018	−	0.105799i
$63$	2.67419	+	0.894356i	0.336916	+	0.112678i
$64$	−3.30707	+	5.72801i	−0.413384	+	0.716001i
$65$	1.98775	+	3.44289i	0.246550	+	0.427038i
$66$	−3.43203	−	5.76781i	−0.422454	−	0.709968i
$67$	0.918596	−	1.09474i	0.112224	−	0.133744i	−0.707008	−	0.707206i	$-0.749955\pi$
$67$	0.918596	−	1.09474i	0.112224	−	0.133744i	0.819232	+	0.573462i	$0.194400\pi$
$68$	1.14055	−	0.658497i	0.138312	−	0.0798545i
$69$	−0.636737	+	0.548725i	−0.0766541	+	0.0660587i
$70$	−1.20471	−	3.30993i	−0.143991	−	0.395612i
$71$	0.438181	+	2.48505i	0.0520026	+	0.294921i	0.999706	−	0.0242299i	$-0.00771337\pi$
$71$	0.438181	+	2.48505i	0.0520026	+	0.294921i	−0.947704	+	0.319151i	$0.896602\pi$
$72$	6.67546	−	5.90761i	0.786710	−	0.696218i
$73$	8.28206	+	3.01442i	0.969342	+	0.352812i	0.777688	−	0.628651i	$-0.216393\pi$
$73$	8.28206	+	3.01442i	0.969342	+	0.352812i	0.191654	+	0.981462i	$0.438615\pi$
$74$	−0.689912	−	0.822205i	−0.0802006	−	0.0955794i
$75$	5.60624	−	16.0574i	0.647353	−	1.85415i
$76$	−0.359552	−	4.57302i	−0.0412434	−	0.524562i
$77$			3.74147i			0.426380i
$78$	−1.62824	+	0.617017i	−0.184362	+	0.0698634i
$79$	−1.50043	+	4.12240i	−0.168812	+	0.463806i	−0.995034	−	0.0995383i	$-0.968263\pi$
$79$	−1.50043	+	4.12240i	−0.168812	+	0.463806i	0.826222	+	0.563345i	$0.190486\pi$
$80$	−2.98671	−	0.526637i	−0.333924	−	0.0588798i
$81$	−8.28356	+	3.51889i	−0.920396	+	0.390988i
$82$	1.99336	−	0.725523i	0.220130	−	0.0801206i
$83$	−3.66720	−	2.11726i	−0.402527	−	0.232399i	0.285047	−	0.958514i	$-0.407991\pi$
$83$	−3.66720	−	2.11726i	−0.402527	−	0.232399i	−0.687574	+	0.726114i	$0.741324\pi$
$84$	−1.68315	+	0.319678i	−0.183647	+	0.0348798i
$85$	3.69054	+	3.09673i	0.400296	+	0.335888i
$86$	−4.30799	−	3.61483i	−0.464542	−	0.389797i
$87$	7.38747	−	1.40309i	0.792020	−	0.150427i
$88$	10.2432	+	5.91392i	1.09193	+	0.630426i
$89$	7.56260	−	2.75256i	0.801634	−	0.291771i	0.0914708	−	0.995808i	$-0.470843\pi$
$89$	7.56260	−	2.75256i	0.801634	−	0.291771i	0.710164	+	0.704037i	$0.248621\pi$
$90$	9.88079	+	5.36304i	1.04153	+	0.565315i
$91$	0.955916	+	0.168554i	0.100207	+	0.0176692i
$92$	0.174671	−	0.479906i	0.0182108	−	0.0500336i
$93$	7.98199	−	3.02474i	0.827694	−	0.313651i
$94$			7.51939i			0.775565i
$95$	15.2698	−	6.95742i	1.56664	−	0.713816i
$96$	−2.95502	+	8.46379i	−0.301596	+	0.863832i
$97$	−6.91522	−	8.24124i	−0.702134	−	0.836771i	0.290632	−	0.956835i	$-0.406134\pi$
$97$	−6.91522	−	8.24124i	−0.702134	−	0.836771i	−0.992766	+	0.120064i	$0.961690\pi$
$98$	5.59517	+	2.03647i	0.565197	+	0.205715i
$99$	−7.91412	−	8.94277i	−0.795399	−	0.898782i
$100$	1.79443	+	10.1767i	0.179443	+	1.01767i
$101$	−5.98720	−	16.4497i	−0.595749	−	1.63681i	−0.759652	−	0.650329i	$-0.774631\pi$
$101$	−5.98720	−	16.4497i	−0.595749	−	1.63681i	0.163904	−	0.986476i	$-0.447591\pi$
$102$	−1.59843	+	1.37749i	−0.158269	+	0.136392i
$103$	−1.32095	+	0.762653i	−0.130157	+	0.0751464i	−0.563665	−	0.826004i	$-0.690609\pi$
$103$	−1.32095	+	0.762653i	−0.130157	+	0.0751464i	0.433508	+	0.901150i	$0.357276\pi$
$104$	1.97242	−	2.35064i	0.193412	−	0.230499i
$105$	−3.20474	−	5.38583i	−0.312750	−	0.525603i
$106$	−3.75822	−	6.50942i	−0.365030	−	0.632251i
$107$	−5.43705	+	9.41724i	−0.525619	+	0.910399i	0.473935	+	0.880560i	$0.342833\pi$
$107$	−5.43705	+	9.41724i	−0.525619	+	0.910399i	−0.999555	+	0.0298397i	$0.990500\pi$
$108$	3.34684	−	4.32437i	0.322050	−	0.416113i
$109$	−13.5446	+	2.38827i	−1.29733	+	0.228755i	−0.779324	−	0.626621i	$-0.784438\pi$
$109$	−13.5446	+	2.38827i	−1.29733	+	0.228755i	−0.518008	+	0.855376i	$0.673326\pi$
$110$	−2.59034	+	14.6906i	−0.246980	+	1.40069i
$111$	−1.47894	−	1.20817i	−0.140375	−	0.114675i
$112$	−0.567246	+	0.475976i	−0.0535997	+	0.0449755i
$113$	−9.69889			−0.912395			−0.456198	−	0.889879i	$-0.650789\pi$
$113$	−9.69889			−0.912395			−0.456198	+	0.889879i	$0.650789\pi$
$114$	1.93310	+	7.09074i	0.181052	+	0.664108i
$115$	1.86820			0.174210
$116$	−3.49985	+	2.93672i	−0.324953	+	0.272668i
$117$	−2.64134	+	1.61912i	−0.244192	+	0.149688i
$118$	−1.16099	+	6.58429i	−0.106878	+	0.606133i
$119$	1.15841	−	0.204260i	0.106192	−	0.0187245i
$120$	−19.8106	+	0.260717i	−1.80845	+	0.0238001i
$121$	2.42258	−	4.19603i	0.220234	−	0.381457i
$122$	−2.07470	−	3.59348i	−0.187834	−	0.325338i
$123$	3.24354	−	1.93001i	0.292460	−	0.174023i
$124$	−3.33365	+	3.97289i	−0.299371	+	0.356776i
$125$	−16.0677	+	9.27670i	−1.43714	+	0.829733i
$126$	2.55382	−	1.00639i	0.227512	−	0.0896562i
$127$	−3.25642	−	8.94695i	−0.288961	−	0.793913i	−0.996213	−	0.0869515i	$-0.972287\pi$
$127$	−3.25642	−	8.94695i	−0.288961	−	0.793913i	0.707252	−	0.706962i	$-0.249935\pi$
$128$	−0.679490	−	3.85358i	−0.0600590	−	0.340612i
$129$	−8.73052	−	4.88853i	−0.768679	−	0.430411i
$130$	3.63663	+	1.32363i	0.318954	+	0.116090i
$131$	10.7966	+	12.8668i	0.943299	+	1.12418i	0.992110	+	0.125372i	$0.0400126\pi$
$131$	10.7966	+	12.8668i	0.943299	+	1.12418i	−0.0488102	+	0.998808i	$0.515543\pi$
$132$	6.85010	+	2.39163i	0.596225	+	0.208164i
$133$	1.09519	−	3.94795i	0.0949650	−	0.342331i
$134$		−	1.39116i		−	0.120178i
$135$	19.0522	+	6.09427i	1.63975	+	0.524512i
$136$	1.27183	−	3.49432i	0.109058	−	0.299635i
$137$	21.0716	+	3.71550i	1.80027	+	0.317436i	0.970579	−	0.240784i	$-0.0774046\pi$
$137$	21.0716	+	3.71550i	1.80027	+	0.317436i	0.829693	+	0.558221i	$0.188516\pi$
$138$	−0.131472	+	0.807622i	−0.0111916	+	0.0687493i
$139$	6.64113	−	2.41718i	0.563294	−	0.205022i	−0.0446494	−	0.999003i	$-0.514217\pi$
$139$	6.64113	−	2.41718i	0.563294	−	0.205022i	0.607943	+	0.793981i	$0.291995\pi$
$140$	3.29767	+	1.90391i	0.278704	+	0.160910i
$141$	2.49641	+	13.1440i	0.210236	+	1.10692i
$142$	1.88174	+	1.57897i	0.157912	+	0.132504i
$143$	−3.14903	−	2.64235i	−0.263335	−	0.220964i
$144$	0.349013	−	2.33753i	0.0290844	−	0.194794i
$145$	−14.4737	−	8.35637i	−1.20197	−	0.693959i
$146$	8.06232	−	2.93444i	0.667242	−	0.242856i
$147$	10.4565	+	1.70220i	0.862439	+	0.140395i
$148$	1.14267	+	0.201484i	0.0939269	+	0.0165619i
$149$	−2.02439	+	5.56197i	−0.165845	+	0.455655i	−0.994579	−	0.103988i	$-0.966840\pi$
$149$	−2.02439	+	5.56197i	−0.165845	+	0.455655i	0.828734	+	0.559643i	$0.189062\pi$
$150$	−5.86696	−	15.4823i	−0.479036	−	1.26413i
$151$			16.2196i			1.31993i	0.751297	+	0.659964i	$0.229429\pi$
$151$			16.2196i			1.31993i	−0.751297	+	0.659964i	$0.770571\pi$
$152$	−9.07741	−	9.23866i	−0.736275	−	0.749354i
$153$	−2.33676	+	2.93855i	−0.188916	+	0.237567i
$154$	2.34116	+	2.79008i	0.188656	+	0.224831i
$155$	−17.8275	−	6.48868i	−1.43194	−	0.521184i
$156$	0.919641	−	1.64241i	0.0736302	−	0.131498i
$157$	−3.95357	−	22.4218i	−0.315529	−	1.78945i	−0.569237	−	0.822174i	$-0.692761\pi$
$157$	−3.95357	−	22.4218i	−0.315529	−	1.78945i	0.253708	−	0.967281i	$-0.418350\pi$
$158$	1.46062	+	4.01302i	0.116201	+	0.319259i
$159$	−8.73051	−	10.1308i	−0.692374	−	0.803426i
$160$	17.2555	−	9.96249i	1.36417	−	0.787604i
$161$	0.293202	−	0.349424i	0.0231075	−	0.0275385i
$162$	−3.97533	+	7.80740i	−0.312331	+	0.613407i
$163$	−1.76026	−	3.04886i	−0.137874	−	0.238805i	0.788818	−	0.614627i	$-0.210694\pi$
$163$	−1.76026	−	3.04886i	−0.137874	−	0.238805i	−0.926692	+	0.375822i	$0.877360\pi$
$164$	−1.14660	+	1.98597i	−0.0895346	+	0.155079i
$165$	0.349269	+	26.5393i	0.0271905	+	2.06608i
$166$	−4.05954	+	0.715806i	−0.315081	+	0.0555573i
$167$	1.25909	−	7.14068i	0.0974316	−	0.552562i	−0.896543	−	0.442956i	$-0.853930\pi$
$167$	1.25909	−	7.14068i	0.0974316	−	0.552562i	0.993975	−	0.109606i	$-0.0349591\pi$
$168$	−3.06039	+	3.74626i	−0.236114	+	0.289030i
$169$	9.14161	−	7.67072i	0.703201	−	0.590056i
$170$	4.68984			0.359694
$171$	5.73318	+	11.7529i	0.438428	+	0.898767i
$172$	6.07944			0.463553
$173$	11.9969	−	10.0666i	0.912110	−	0.765351i	−0.0604095	−	0.998174i	$-0.519241\pi$
$173$	11.9969	−	10.0666i	0.912110	−	0.765351i	0.972519	+	0.232823i	$0.0747962\pi$
$174$	4.63102	−	5.66889i	0.351077	−	0.429758i
$175$	−1.60271	+	9.08943i	−0.121154	+	0.687096i
$176$	3.08833	−	0.544555i	0.232791	−	0.0410474i
$177$	0.156542	+	11.8948i	0.0117664	+	0.894071i
$178$	3.91721	−	6.78481i	0.293607	−	0.508543i
$179$	−6.47528	−	11.2155i	−0.483985	−	0.838287i	0.515845	−	0.856682i	$-0.327478\pi$
$179$	−6.47528	−	11.2155i	−0.483985	−	0.838287i	−0.999831	+	0.0183944i	$0.994145\pi$
$180$	−11.9092	+	2.42469i	−0.887662	+	0.180726i
$181$	2.54385	−	3.03164i	0.189083	−	0.225340i	−0.663172	−	0.748467i	$-0.730790\pi$
$181$	2.54385	−	3.03164i	0.189083	−	0.225340i	0.852255	+	0.523127i	$0.175235\pi$
$182$	0.818315	−	0.472454i	0.0606575	−	0.0350206i
$183$	−4.81961	−	5.59265i	−0.356276	−	0.413421i
$184$	−0.493190	−	1.35503i	−0.0363585	−	0.0998941i
$185$	0.737042	+	4.17997i	0.0541884	+	0.307318i
$186$	4.05964	−	7.25020i	0.297667	−	0.531610i
$187$	−4.68115	−	1.70380i	−0.342320	−	0.124594i
$188$	−5.22508	−	6.22701i	−0.381078	−	0.454152i
$189$	4.12999	−	2.60704i	0.300412	−	0.189634i
$190$	7.03347	−	14.7431i	0.510262	−	1.06957i
$191$		−	15.8889i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$191$		−	15.8889i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$192$	4.05951	+	10.7126i	0.292970	+	0.773119i
$193$	−5.39307	+	14.8173i	−0.388202	+	1.06657i	0.579609	+	0.814895i	$0.303205\pi$
$193$	−5.39307	+	14.8173i	−0.388202	+	1.06657i	−0.967810	+	0.251680i	$0.919017\pi$
$194$	−10.3136	−	1.81857i	−0.740475	−	0.130566i
$195$	6.79631	+	1.10636i	0.486694	+	0.0792283i
$196$	−6.04862	+	2.20152i	−0.432044	+	0.157251i
$197$	3.60442	+	2.08101i	0.256804	+	0.148266i	0.622876	−	0.782321i	$-0.285964\pi$
$197$	3.60442	+	2.08101i	0.256804	+	0.148266i	−0.366072	+	0.930587i	$0.619297\pi$
$198$	−11.4975	−	1.71667i	−0.817091	−	0.121999i
$199$	17.0487	+	14.3056i	1.20855	+	1.01410i	0.999344	+	0.0362239i	$0.0115329\pi$
$199$	17.0487	+	14.3056i	1.20855	+	1.01410i	0.209208	+	0.977871i	$0.432912\pi$
$200$	22.3513	+	18.7550i	1.58047	+	1.32618i
$201$	−0.461862	−	2.43177i	−0.0325772	−	0.171524i
$202$	−14.7579	−	8.52047i	−1.03836	−	0.599498i
$203$	−3.83451	+	1.39565i	−0.269130	+	0.0979552i
$204$	0.366513	−	2.25146i	0.0256610	−	0.157634i
$205$	−8.26127	−	1.45669i	−0.576992	−	0.101739i
$206$	−0.507844	+	1.39529i	−0.0353831	+	0.0972144i
$207$	0.0383135	+	1.45538i	0.00266298	+	0.101156i
$208$		−	0.813576i		−	0.0564114i
$209$	−12.3766	+	12.1605i	−0.856104	+	0.841162i
$210$	−5.75992	−	2.01100i	−0.397472	−	0.138773i
$211$	11.8117	+	14.0766i	0.813151	+	0.969076i	0.999911	−	0.0133296i	$-0.00424307\pi$
$211$	11.8117	+	14.0766i	0.813151	+	0.969076i	−0.186760	+	0.982406i	$0.559799\pi$
$212$	7.63556	+	2.77912i	0.524412	+	0.190871i
$213$	3.81351	+	2.13532i	0.261297	+	0.146310i
$214$	1.83817	+	10.4248i	0.125654	+	0.712622i
$215$	7.60621	+	20.8979i	0.518739	+	1.42522i
$216$	−0.609387	−	15.4277i	−0.0414636	−	1.04972i
$217$	−4.01155	+	2.31607i	−0.272322	+	0.157225i
$218$	−8.60601	+	10.2562i	−0.582873	+	0.694641i
$219$	13.1188	−	7.80610i	0.886486	−	0.527487i
$220$	−8.06307	−	13.9656i	−0.543612	−	0.941564i
$221$	−0.646195	+	1.11924i	−0.0434678	+	0.0752884i
$222$	−1.85887	+	0.0244636i	−0.124759	+	0.00164189i
$223$	−25.0726	+	4.42098i	−1.67899	+	0.296051i	−0.930280	−	0.366849i	$-0.880436\pi$
$223$	−25.0726	+	4.42098i	−1.67899	+	0.296051i	−0.748708	+	0.662900i	$0.769325\pi$
$224$	0.844782	−	4.79100i	0.0564444	−	0.320112i
$225$	−15.3956	−	25.1155i	−1.02637	−	1.67436i
$226$	−7.23265	+	6.06892i	−0.481109	+	0.403698i
$227$	8.03209			0.533109			0.266554	−	0.963820i	$-0.414115\pi$
$227$	8.03209			0.533109			0.266554	+	0.963820i	$0.414115\pi$
$228$	−6.52808	−	4.52876i	−0.432333	−	0.299924i
$229$	−5.34452			−0.353176			−0.176588	−	0.984285i	$-0.556506\pi$
$229$	−5.34452			−0.353176			−0.176588	+	0.984285i	$0.556506\pi$
$230$	1.39315	−	1.16899i	0.0918617	−	0.0770811i
$231$	5.01867	+	4.09984i	0.330204	+	0.269750i
$232$	−2.24005	+	12.7040i	−0.147066	+	0.834055i
$233$	4.41323	−	0.778172i	0.289120	−	0.0509797i	−0.0272070	−	0.999630i	$-0.508661\pi$
$233$	4.41323	−	0.778172i	0.289120	−	0.0509797i	0.316327	+	0.948650i	$0.397550\pi$
$234$	−0.956561	+	2.86019i	−0.0625324	+	0.186976i
$235$	14.8679	−	25.7519i	0.969872	−	1.67987i
$236$	−3.61385	−	6.25938i	−0.235242	−	0.407451i
$237$	3.88549	+	6.52988i	0.252390	+	0.424162i
$238$	0.736040	−	0.877179i	0.0477104	−	0.0568590i
$239$	6.74189	−	3.89243i	0.436096	−	0.251780i	−0.265844	−	0.964016i	$-0.585651\pi$
$239$	6.74189	−	3.89243i	0.436096	−	0.251780i	0.701940	+	0.712236i	$0.252317\pi$
$240$	−3.97920	+	3.42918i	−0.256856	+	0.221352i
$241$	5.91131	+	16.2412i	0.380781	+	1.04619i	0.971028	+	0.238964i	$0.0768079\pi$
$241$	5.91131	+	16.2412i	0.380781	+	1.04619i	−0.590247	+	0.807222i	$0.700970\pi$
$242$	−0.819029	−	4.64495i	−0.0526492	−	0.298588i
$243$	−4.35688	+	14.9672i	−0.279494	+	0.960147i
$244$	4.21516	+	1.53419i	0.269848	+	0.0982166i
$245$	−15.1353	−	18.0375i	−0.966958	−	1.15238i
$246$	1.21110	−	3.46884i	0.0772169	−	0.221165i
$247$	2.54936	+	3.70995i	0.162212	+	0.236059i
$248$			14.6435i			0.929863i
$249$	−6.85847	+	2.59899i	−0.434638	+	0.164704i
$250$	−6.17727	+	16.9719i	−0.390685	+	1.07340i
$251$	−8.62554	−	1.52092i	−0.544439	−	0.0959994i	−0.105337	−	0.994437i	$-0.533592\pi$
$251$	−8.62554	−	1.52092i	−0.544439	−	0.0959994i	−0.439102	+	0.898437i	$0.644703\pi$
$252$	−1.41557	+	2.60802i	−0.0891725	+	0.164290i
$253$	−1.81526	+	0.660702i	−0.114125	+	0.0415380i
$254$	−8.02678	−	4.63426i	−0.503645	−	0.290779i
$255$	8.19789	−	1.55701i	0.513371	−	0.0975037i
$256$	−13.0515	−	10.9515i	−0.815717	−	0.684468i
$257$	−18.4633	−	15.4925i	−1.15171	−	0.966398i	−0.151950	−	0.988388i	$-0.548555\pi$
$257$	−18.4633	−	15.4925i	−1.15171	−	0.966398i	−0.999758	+	0.0219902i	$0.993000\pi$
$258$	−9.56943	+	1.81750i	−0.595767	+	0.113153i
$259$	0.897489	+	0.518165i	0.0557672	+	0.0321972i
$260$	−3.93136	+	1.43090i	−0.243813	+	0.0887405i
$261$	6.21302	−	11.4468i	0.384576	−	0.708537i
$262$	16.1024	+	2.83929i	0.994810	+	0.175412i
$263$	−4.76306	+	13.0864i	−0.293703	+	0.806941i	0.701814	+	0.712360i	$0.252374\pi$
$263$	−4.76306	+	13.0864i	−0.293703	+	0.806941i	−0.995517	+	0.0945816i	$0.969849\pi$
$264$	19.1571	−	7.25949i	1.17904	−	0.446791i
$265$			29.7240i			1.82593i
$266$	−1.65366	−	3.62936i	−0.101392	−	0.222530i
$267$	4.59479	−	13.1604i	0.281197	−	0.805404i
$268$	0.966694	+	1.15206i	0.0590503	+	0.0703734i
$269$	19.4257	+	7.07039i	1.18441	+	0.431089i	0.857757	−	0.514055i	$-0.171857\pi$
$269$	19.4257	+	7.07039i	1.18441	+	0.431089i	0.326652	+	0.945145i	$0.394080\pi$
$270$	18.0210	−	7.37699i	1.09672	−	0.448949i
$271$	0.727540	+	4.12608i	0.0441949	+	0.250642i	0.998899	−	0.0469156i	$-0.0149392\pi$
$271$	0.727540	+	4.12608i	0.0441949	+	0.250642i	−0.954704	+	0.297557i	$0.903828\pi$
$272$	−0.337205	−	0.926463i	−0.0204461	−	0.0561751i
$273$	1.27357	−	1.09753i	0.0770800	−	0.0664257i
$274$	18.0384	−	10.4145i	1.08974	−	0.629163i
$275$	25.1251	−	29.9429i	1.51510	−	1.80562i
$276$	−0.452326	−	0.760171i	−0.0272268	−	0.0457569i
$277$	−2.59286	−	4.49097i	−0.155790	−	0.269836i	0.777556	−	0.628813i	$-0.216459\pi$
$277$	−2.59286	−	4.49097i	−0.155790	−	0.269836i	−0.933346	+	0.358977i	$0.883126\pi$
$278$	3.43992	−	5.95811i	0.206312	−	0.357344i
$279$	4.68926	−	14.0212i	0.280739	−	0.839428i
$280$	10.5881	−	1.86698i	0.632763	−	0.111573i
$281$	−3.26188	+	18.4991i	−0.194588	+	1.10356i	0.718417	+	0.695613i	$0.244867\pi$
$281$	−3.26188	+	18.4991i	−0.194588	+	1.10356i	−0.913005	+	0.407949i	$0.866244\pi$
$282$	10.0862	+	8.23962i	0.600626	+	0.490662i
$283$	−8.43214	+	7.07541i	−0.501239	+	0.420589i	−0.858034	−	0.513593i	$-0.828314\pi$
$283$	−8.43214	+	7.07541i	−0.501239	+	0.420589i	0.356795	+	0.934183i	$0.383870\pi$
$284$	−2.65551			−0.157576
$285$	7.39994	−	28.1061i	0.438335	−	1.66486i
$286$	−4.00170			−0.236625
$287$	−1.56901	+	1.31656i	−0.0926158	+	0.0777138i
$288$	8.11495	+	13.2382i	0.478178	+	0.780071i
$289$	2.68006	−	15.1994i	0.157650	−	0.894080i
$290$	−16.0221	+	2.82513i	−0.940852	+	0.165898i
$291$	−18.6321	+	0.245207i	−1.09223	+	0.0143743i
$292$	−4.63754	+	8.03245i	−0.271391	+	0.470064i
$293$	11.4509	+	19.8336i	0.668970	+	1.15869i	0.978192	+	0.207701i	$0.0665980\pi$
$293$	11.4509	+	19.8336i	0.668970	+	1.15869i	−0.309222	+	0.950990i	$0.600069\pi$
$294$	8.86275	−	5.27362i	0.516886	−	0.307564i
$295$	16.9950	−	20.2538i	0.989486	−	1.17922i
$296$	2.83722	−	1.63807i	0.164910	−	0.0952108i
$297$	−20.6677	+	0.816365i	−1.19926	+	0.0473703i
$298$	1.97068	+	5.41440i	0.114158	+	0.313648i
$299$	0.0870263	+	0.493551i	0.00503286	+	0.0285428i
$300$	15.6170	+	8.74450i	0.901647	+	0.504864i
$301$	5.10245	+	1.85714i	0.294100	+	0.107044i
$302$	10.1491	+	12.0952i	0.584015	+	0.696002i
$303$	−28.6257	−	9.99430i	−1.64450	−	0.574158i
$304$	−3.41817	−	0.329397i	−0.196045	−	0.0188922i
$305$			16.4089i			0.939573i
$306$	0.0961806	+	3.65352i	0.00549828	+	0.208858i
$307$	7.35296	−	20.2021i	0.419655	−	1.15299i	−0.532246	−	0.846590i	$-0.678652\pi$
$307$	7.35296	−	20.2021i	0.419655	−	1.15299i	0.951902	−	0.306404i	$-0.0991259\pi$
$308$	−3.87756	−	0.683718i	−0.220944	−	0.0389584i
$309$	−0.424485	+	2.60758i	−0.0241481	+	0.148340i
$310$	−17.3545	+	6.31652i	−0.985670	+	0.358754i
$311$	6.19121	+	3.57450i	0.351071	+	0.202691i	0.665157	−	0.746704i	$-0.268365\pi$
$311$	6.19121	+	3.57450i	0.351071	+	0.202691i	−0.314086	+	0.949395i	$0.601698\pi$
$312$	−0.991715	−	5.22153i	−0.0561448	−	0.295611i
$313$	3.43872	+	2.88543i	0.194368	+	0.163094i	0.734778	−	0.678308i	$-0.237286\pi$
$313$	3.43872	+	2.88543i	0.194368	+	0.163094i	−0.540410	+	0.841402i	$0.681731\pi$
$314$	−16.9783	−	14.2465i	−0.958141	−	0.803976i
$315$	−10.7361	−	1.60298i	−0.604908	−	0.0903179i
$316$	−3.99816	−	2.30834i	−0.224914	−	0.129854i
$317$	−10.4058	+	3.78740i	−0.584448	+	0.212722i	−0.617286	−	0.786739i	$-0.711768\pi$
$317$	−10.4058	+	3.78740i	−0.584448	+	0.212722i	0.0328380	+	0.999461i	$0.489545\pi$
$318$	−12.8497	−	2.09179i	−0.720575	−	0.117302i
$319$	17.0188	+	3.00088i	0.952872	+	0.168017i
$320$	8.70848	−	23.9263i	0.486819	−	1.33752i
$321$	6.67412	+	17.6123i	0.372513	+	0.983024i
$322$		−	0.444038i		−	0.0247453i
$323$	4.44077	+	3.16808i	0.247091	+	0.176277i
$324$	−2.13314	−	9.22791i	−0.118508	−	0.512662i
$325$	−6.51829	−	7.76819i	−0.361570	−	0.430902i
$326$	−3.22043	−	1.17214i	−0.178363	−	0.0649189i
$327$	−11.6384	+	20.7852i	−0.643603	+	1.14942i
$328$	1.12436	+	6.37657i	0.0620824	+	0.352087i
$329$	−2.48317	−	6.82245i	−0.136902	−	0.376134i
$330$	16.8669	+	19.5723i	0.928494	+	1.07742i
$331$	−17.4647	+	10.0833i	−0.959948	+	0.554226i	−0.896157	−	0.443737i	$-0.853652\pi$
$331$	−17.4647	+	10.0833i	−0.959948	+	0.554226i	−0.0637910	+	0.997963i	$0.520319\pi$
$332$	2.86442	−	3.41368i	0.157205	−	0.187350i
$333$	−3.24120	+	0.659901i	−0.177617	+	0.0361624i
$334$	−3.52923	−	6.11280i	−0.193111	−	0.334477i
$335$	−2.75071	+	4.76436i	−0.150287	+	0.260305i
$336$	0.0168776	+	1.28245i	0.000920749	+	0.0699633i
$337$	7.33303	−	1.29301i	0.399455	−	0.0704348i	0.0296882	−	0.999559i	$-0.490549\pi$
$337$	7.33303	−	1.29301i	0.399455	−	0.0704348i	0.369767	+	0.929124i	$0.379437\pi$
$338$	2.01725	−	11.4404i	0.109724	−	0.622276i
$339$	−10.6279	+	13.0097i	−0.577228	+	0.706592i
$340$	−3.88378	+	3.25888i	−0.210628	+	0.176738i
$341$	19.6171			1.06233
$342$	11.6295	+	5.17692i	0.628852	+	0.279936i
$343$	−12.3286			−0.665681
$344$	13.1495	−	11.0338i	0.708975	−	0.594901i
$345$	2.04714	−	2.50593i	0.110214	−	0.134915i
$346$	2.64733	−	15.0137i	0.142321	−	0.807144i
$347$	−20.4261	+	3.60168i	−1.09653	+	0.193348i	−0.692516	−	0.721403i	$-0.743498\pi$
$347$	−20.4261	+	3.60168i	−1.09653	+	0.193348i	−0.404017	+	0.914751i	$0.632387\pi$
$348$	0.104133	+	7.91258i	0.00558212	+	0.424159i
$349$	−3.98587	+	6.90373i	−0.213359	+	0.369548i	−0.952764	−	0.303713i	$-0.901774\pi$
$349$	−3.98587	+	6.90373i	−0.213359	+	0.369548i	0.739405	+	0.673261i	$0.235107\pi$
$350$	4.49238	+	7.78103i	0.240128	+	0.415914i
$351$	−0.722508	+	5.31721i	−0.0385646	+	0.283812i
$352$	−13.2433	+	15.7828i	−0.705871	+	0.841224i
$353$	20.0695	−	11.5871i	1.06819	−	0.616721i	0.140505	−	0.990080i	$-0.455127\pi$
$353$	20.0695	−	11.5871i	1.06819	−	0.616721i	0.927687	+	0.373359i	$0.121794\pi$
$354$	7.55973	+	8.77226i	0.401795	+	0.466241i
$355$	−3.32241	−	9.12824i	−0.176335	−	0.484477i
$356$	1.47069	+	8.34069i	0.0779463	+	0.442055i
$357$	0.995386	−	1.77768i	0.0526814	−	0.0940848i
$358$	−11.8467	−	4.31183i	−0.626116	−	0.227887i
$359$	−4.97359	−	5.92729i	−0.262496	−	0.312831i	0.618658	−	0.785661i	$-0.287677\pi$
$359$	−4.97359	−	5.92729i	−0.262496	−	0.312831i	−0.881154	+	0.472830i	$0.843232\pi$
$360$	−21.3584	+	26.8589i	−1.12569	+	1.41559i
$361$	16.6192	−	9.20883i	0.874694	−	0.484675i
$362$		−	3.85252i		−	0.202484i
$363$	−2.97378	−	7.84750i	−0.156083	−	0.411887i
$364$	−0.349369	+	0.959885i	−0.0183119	+	0.0503116i
$365$	−33.4135	−	5.89170i	−1.74894	−	0.308385i
$366$	−7.09358	−	1.15476i	−0.370788	−	0.0603600i
$367$	−8.07339	+	2.93847i	−0.421427	+	0.153387i	−0.544024	−	0.839070i	$-0.683100\pi$
$367$	−8.07339	+	2.93847i	−0.421427	+	0.153387i	0.122597	+	0.992457i	$0.460878\pi$
$368$	−0.331100	−	0.191161i	−0.0172598	−	0.00996495i
$369$	0.965375	−	6.46564i	0.0502554	−	0.336588i
$370$	3.16517	+	2.65590i	0.164550	+	0.138073i
$371$	5.55953	+	4.66500i	0.288636	+	0.242195i
$372$	1.67613	+	8.82506i	0.0869032	+	0.457558i
$373$	12.7094	+	7.33779i	0.658069	+	0.379936i	0.791541	−	0.611116i	$-0.209279\pi$
$373$	12.7094	+	7.33779i	0.658069	+	0.379936i	−0.133472	+	0.991053i	$0.542613\pi$
$374$	−4.55695	+	1.65859i	−0.235634	+	0.0857639i
$375$	−5.16332	+	31.7179i	−0.266633	+	1.63791i
$376$	−22.6032	−	3.98555i	−1.16567	−	0.205539i
$377$	1.53340	−	4.21299i	0.0789743	−	0.216980i
$378$	1.44850	−	4.52839i	0.0745030	−	0.232915i
$379$		−	24.4001i		−	1.25335i	−0.779282	−	0.626674i	$-0.784416\pi$
$379$		−	24.4001i		−	1.25335i	0.779282	−	0.626674i	$-0.215584\pi$
$380$	4.42008	+	17.0966i	0.226745	+	0.877036i
$381$	−15.5694	−	5.43588i	−0.797647	−	0.278488i
$382$	−9.94220	−	11.8487i	−0.508687	−	0.606230i
$383$	0.785119	+	0.285760i	0.0401177	+	0.0146017i	0.362001	−	0.932178i	$-0.382094\pi$
$383$	0.785119	+	0.285760i	0.0401177	+	0.0146017i	−0.321883	+	0.946779i	$0.604316\pi$
$384$	−5.91363	−	3.31125i	−0.301779	−	0.168976i
$385$	−2.50109	−	14.1844i	−0.127467	−	0.722904i
$386$	5.24998	+	14.4242i	0.267217	+	0.734172i
$387$	−16.1241	+	6.35403i	−0.819632	+	0.322994i
$388$	9.80469	−	5.66074i	0.497758	−	0.287381i
$389$	2.71775	−	3.23889i	0.137795	−	0.164218i	−0.692734	−	0.721194i	$-0.743594\pi$
$389$	2.71775	−	3.23889i	0.137795	−	0.164218i	0.830529	+	0.556975i	$0.188038\pi$
$390$	5.76043	−	3.42764i	0.291691	−	0.173565i
$391$	0.303665	+	0.525963i	0.0153570	+	0.0265991i
$392$	−9.08726	+	15.7396i	−0.458976	+	0.794970i
$393$	29.0898	−	0.382835i	1.46739	−	0.0193115i
$394$	3.99005	−	0.703553i	0.201016	−	0.0354445i
$395$	2.93259	−	16.6316i	0.147555	−	0.836825i
$396$	10.7143	−	6.56777i	0.538413	−	0.330043i
$397$	19.0110	−	15.9522i	0.954137	−	0.800616i	−0.0258527	−	0.999666i	$-0.508230\pi$
$397$	19.0110	−	15.9522i	0.954137	−	0.800616i	0.979989	+	0.199050i	$0.0637857\pi$
$398$	21.6650			1.08597
$399$	−4.09555	−	5.79515i	−0.205034	−	0.290120i
$400$	7.73597			0.386799
$401$	−18.0223	+	15.1225i	−0.899990	+	0.755181i	−0.970188	−	0.242352i	$-0.922081\pi$
$401$	−18.0223	+	15.1225i	−0.899990	+	0.755181i	0.0701986	+	0.997533i	$0.477637\pi$
$402$	−1.86606	−	1.52442i	−0.0930705	−	0.0760309i
$403$	0.883756	−	5.01203i	0.0440230	−	0.249667i
$404$	18.1421	−	3.19895i	0.902605	−	0.159154i
$405$	29.0518	−	18.8780i	1.44359	−	0.938054i
$406$	−1.98616	+	3.44014i	−0.0985717	+	0.170731i
$407$	−2.19444	−	3.80087i	−0.108774	−	0.188402i
$408$	−3.29350	−	5.53500i	−0.163053	−	0.274023i
$409$	−3.18484	+	3.79554i	−0.157480	+	0.187677i	−0.839015	−	0.544108i	$-0.816868\pi$
$409$	−3.18484	+	3.79554i	−0.157480	+	0.187677i	0.681535	+	0.731785i	$0.261313\pi$
$410$	−7.07209	+	4.08307i	−0.349266	+	0.201649i
$411$	28.0738	−	24.1933i	1.38478	−	1.19337i
$412$	−0.549001	−	1.50837i	−0.0270474	−	0.0743120i
$413$	−1.12098	−	6.35742i	−0.0551601	−	0.312828i
$414$	0.939250	+	1.06133i	0.0461616	+	0.0521615i
$415$	15.3182	+	5.57536i	0.751940	+	0.273684i
$416$	3.43576	+	4.09458i	0.168452	+	0.200753i
$417$	4.03494	−	11.5569i	0.197592	−	0.565943i
$418$	−1.62019	+	16.8128i	−0.0792460	+	0.822339i
$419$			15.3248i			0.748666i	0.927294	+	0.374333i	$0.122128\pi$
$419$			15.3248i			0.748666i	−0.927294	+	0.374333i	$0.877872\pi$
$420$	6.16736	−	2.33710i	0.300936	−	0.114039i
$421$	−2.52944	+	6.94957i	−0.123277	+	0.338701i	−0.985945	−	0.167069i	$-0.946570\pi$
$421$	−2.52944	+	6.94957i	−0.123277	+	0.338701i	0.862668	+	0.505771i	$0.168792\pi$
$422$	17.6164	+	3.10625i	0.857555	+	0.151210i
$423$	20.3664	+	11.0544i	0.990247	+	0.537481i
$424$	21.5592	−	7.84692i	1.04701	−	0.381080i
$425$	−10.6424	−	6.14441i	−0.516234	−	0.298048i
$426$	4.17995	−	0.793889i	0.202519	−	0.0384641i
$427$	3.06910	+	2.57528i	0.148524	+	0.124627i
$428$	−8.76621	−	7.35572i	−0.423731	−	0.355552i
$429$	−6.99501	+	1.32855i	−0.337722	+	0.0641430i
$430$	18.7486	+	10.8245i	0.904137	+	0.522004i
$431$	−21.0743	+	7.67041i	−1.01511	+	0.369471i	−0.795394	−	0.606093i	$-0.792736\pi$
$431$	−21.0743	+	7.67041i	−1.01511	+	0.369471i	−0.219719	+	0.975563i	$0.570514\pi$
$432$	−2.75303	−	3.02958i	−0.132455	−	0.145761i
$433$	4.97197	+	0.876693i	0.238938	+	0.0421312i	0.291835	−	0.956469i	$-0.405734\pi$
$433$	4.97197	+	0.876693i	0.238938	+	0.0421312i	−0.0528968	+	0.998600i	$0.516845\pi$
$434$	−1.54225	+	4.23729i	−0.0740303	+	0.203397i
$435$	−27.0689	+	10.2577i	−1.29786	+	0.491817i
$436$		−	14.4736i		−	0.693162i
$437$	2.10884	−	0.165807i	0.100880	−	0.00793161i
$438$	4.89840	−	14.0300i	0.234055	−	0.670380i
$439$	6.97583	+	8.31347i	0.332938	+	0.396780i	0.906378	−	0.422467i	$-0.138836\pi$
$439$	6.97583	+	8.31347i	0.332938	+	0.396780i	−0.573440	+	0.819248i	$0.694391\pi$
$440$	−42.7867	−	15.5731i	−2.03978	−	0.742418i
$441$	13.7414	−	12.1607i	0.654350	−	0.579083i
$442$	0.218467	+	1.23899i	0.0103914	+	0.0589326i
$443$	0.466572	+	1.28190i	0.0221675	+	0.0609047i	0.950283	−	0.311388i	$-0.100794\pi$
$443$	0.466572	+	1.28190i	0.0221675	+	0.0609047i	−0.928115	+	0.372293i	$0.878572\pi$
$444$	1.52238	−	1.31195i	0.0722491	−	0.0622626i
$445$	−26.8308	+	15.4908i	−1.27190	+	0.734333i
$446$	−15.9308	+	18.9856i	−0.754345	+	0.898993i
$447$	5.24233	+	8.81017i	0.247954	+	0.416707i
$448$	−3.10840	−	5.38391i	−0.146858	−	0.254366i
$449$	12.5605	−	21.7554i	0.592767	−	1.02670i	−0.401091	−	0.916038i	$-0.631369\pi$
$449$	12.5605	−	21.7554i	0.592767	−	1.02670i	0.993858	−	0.110664i	$-0.0352977\pi$
$450$	−27.1964	−	9.09556i	−1.28205	−	0.428769i
$451$	8.54236	−	1.50625i	0.402244	−	0.0709265i
$452$	1.77238	−	10.0517i	0.0833658	−	0.472791i
$453$	21.7563	+	17.7731i	1.02220	+	0.835054i
$454$	5.98969	−	5.02594i	0.281110	−	0.235879i
$455$	−3.73668			−0.175178
$456$	−22.3393	+	2.05253i	−1.04613	+	0.0961187i
$457$	18.4143			0.861385			0.430692	−	0.902499i	$-0.358269\pi$
$457$	18.4143			0.861385			0.430692	+	0.902499i	$0.358269\pi$
$458$	−3.98551	+	3.34424i	−0.186231	+	0.156266i
$459$	1.38108	+	6.35446i	0.0644633	+	0.296601i
$460$	−0.341396	+	1.93615i	−0.0159177	+	0.0902735i
$461$	24.2759	−	4.28049i	1.13064	−	0.199362i	0.423132	−	0.906068i	$-0.360931\pi$
$461$	24.2759	−	4.28049i	1.13064	−	0.199362i	0.707508	+	0.706706i	$0.249819\pi$
$462$	6.30792	−	0.0830151i	0.293471	−	0.00386221i
$463$	−2.54672	+	4.41106i	−0.118356	+	0.204999i	−0.919116	−	0.393986i	$-0.871096\pi$
$463$	−2.54672	+	4.41106i	−0.118356	+	0.204999i	0.800760	+	0.598985i	$0.204429\pi$
$464$	1.71011	+	2.96199i	0.0793898	+	0.137507i
$465$	−28.2388	+	16.8030i	−1.30954	+	0.779220i
$466$	2.80410	−	3.34180i	0.129898	−	0.154806i
$467$	−2.55047	+	1.47252i	−0.118022	+	0.0681399i	−0.557849	−	0.829943i	$-0.688373\pi$
$467$	−2.55047	+	1.47252i	−0.118022	+	0.0681399i	0.439827	+	0.898083i	$0.355040\pi$
$468$	−1.19534	−	3.03330i	−0.0552544	−	0.140214i
$469$	0.459412	+	1.26222i	0.0212137	+	0.0582841i
$470$	−5.02655	−	28.5070i	−0.231857	−	1.31493i
$471$	−34.4080	−	19.2663i	−1.58544	−	0.887743i
$472$	−19.1769	−	6.97983i	−0.882690	−	0.321273i
$473$	−14.7814	−	17.6158i	−0.679648	−	0.809973i
$474$	6.98345	+	2.43818i	0.320760	+	0.111989i
$475$	−35.2764	+	24.2408i	−1.61859	+	1.11225i
$476$			1.23788i			0.0567380i
$477$	−23.1559	+	0.609589i	−1.06023	+	0.0279112i
$478$	2.59193	−	7.12128i	0.118552	−	0.325720i
$479$	37.3421	+	6.58442i	1.70620	+	0.300850i	0.939855	−	0.341574i	$-0.110960\pi$
$479$	37.3421	+	6.58442i	1.70620	+	0.300850i	0.766350	+	0.642424i	$0.222071\pi$
$480$	5.54503	−	34.0627i	0.253095	−	1.55474i
$481$	−1.06995	+	0.389432i	−0.0487857	+	0.0177565i
$482$	14.5708	+	8.41247i	0.663683	+	0.383177i
$483$	−0.147419	−	0.776184i	−0.00670781	−	0.0353176i
$484$	3.90595	+	3.27748i	0.177543	+	0.148976i
$485$	31.7256	+	26.6209i	1.44059	+	1.20879i
$486$	6.11646	+	13.8876i	0.277448	+	0.629954i
$487$	−20.3426	−	11.7448i	−0.921810	−	0.532207i	−0.0375979	−	0.999293i	$-0.511971\pi$
$487$	−20.3426	−	11.7448i	−0.921810	−	0.532207i	−0.884212	+	0.467086i	$0.845304\pi$
$488$	11.9016	−	4.33184i	0.538761	−	0.196093i
$489$	−6.01850	−	0.979744i	−0.272166	−	0.0443055i
$490$	−22.5734	−	3.98029i	−1.01976	−	0.179811i
$491$	−0.192209	+	0.528090i	−0.00867427	+	0.0238324i	−0.943954	−	0.330076i	$-0.892925\pi$
$491$	−0.192209	+	0.528090i	−0.00867427	+	0.0238324i	0.935280	+	0.353909i	$0.115148\pi$
$492$	1.40748	+	3.71421i	0.0634543	+	0.167450i
$493$		−	5.43312i		−	0.244695i
$494$	4.22254	+	1.17136i	0.189981	+	0.0527022i
$495$	35.9815	+	28.6128i	1.61725	+	1.28605i
$496$	2.49562	+	2.97416i	0.112057	+	0.133544i
$497$	−2.22876	−	0.811202i	−0.0999735	−	0.0363874i
$498$	−3.48822	+	6.22969i	−0.156311	+	0.279159i
$499$	0.766881	+	4.34920i	0.0343303	+	0.194697i	0.997150	−	0.0754493i	$-0.0240391\pi$
$499$	0.766881	+	4.34920i	0.0343303	+	0.194697i	−0.962819	+	0.270146i	$0.912928\pi$
$500$	−6.67790	−	18.3474i	−0.298645	−	0.820520i
$501$	−8.19855	−	9.51355i	−0.366284	−	0.425034i
$502$	−7.38392	+	4.26311i	−0.329560	+	0.190272i
$503$	−15.8601	+	18.9014i	−0.707168	+	0.842770i	−0.993317	−	0.115415i	$-0.963180\pi$
$503$	−15.8601	+	18.9014i	−0.707168	+	0.842770i	0.286150	+	0.958185i	$0.407625\pi$
$504$	1.67157	+	8.21018i	0.0744578	+	0.365710i
$505$	33.6945	+	58.3606i	1.49939	+	2.59701i
$506$	−0.940254	+	1.62857i	−0.0417994	+	0.0723987i
$507$	−0.271996	−	20.6677i	−0.0120798	−	0.917884i
$508$	9.86746	−	1.73990i	0.437798	−	0.0771956i
$509$	−4.61747	+	26.1870i	−0.204666	+	1.16072i	0.693299	+	0.720650i	$0.256156\pi$
$509$	−4.61747	+	26.1870i	−0.204666	+	1.16072i	−0.897965	+	0.440067i	$0.854955\pi$
$510$	5.13905	−	6.29078i	0.227561	−	0.278560i
$511$	−6.34600	+	5.32493i	−0.280731	+	0.235561i
$512$	−8.75937			−0.387113
$513$	22.0472	+	5.18835i	0.973410	+	0.229071i
$514$	−23.4626			−1.03489
$515$	4.49809	−	3.77435i	0.198210	−	0.166318i
$516$	6.66176	−	8.15475i	0.293268	−	0.358993i
$517$	−5.33924	+	30.2803i	−0.234819	+	1.33173i
$518$	0.993508	−	0.175182i	0.0436522	−	0.00769706i
$519$	−0.356952	−	27.1231i	−0.0156685	−	1.19057i
$520$	−5.90635	+	10.2301i	−0.259011	+	0.448620i
$521$	−22.0694	−	38.2253i	−0.966878	−	1.67468i	−0.704482	−	0.709722i	$-0.748821\pi$
$521$	−22.0694	−	38.2253i	−0.966878	−	1.67468i	−0.262396	−	0.964960i	$-0.584513\pi$
$522$	−2.52945	−	12.4238i	−0.110711	−	0.543773i
$523$	−25.4961	+	30.3850i	−1.11486	+	1.32864i	−0.175987	+	0.984392i	$0.556312\pi$
$523$	−25.4961	+	30.3850i	−1.11486	+	1.32864i	−0.938877	+	0.344252i	$0.888133\pi$
$524$	−15.3078	+	8.83797i	−0.668725	+	0.386089i
$525$	10.4360	+	12.1099i	0.455464	+	0.528518i
$526$	4.63668	+	12.7392i	0.202169	+	0.555454i
$527$	−1.07097	−	6.07376i	−0.0466521	−	0.264577i
$528$	2.65369	−	4.73928i	0.115487	−	0.206251i
$529$	−21.3916	−	7.78591i	−0.930071	−	0.338518i
$530$	18.5993	+	22.1658i	0.807902	+	0.962820i
$531$	16.1269	+	12.8242i	0.699846	+	0.556523i
$532$	3.89142	+	1.85648i	0.168714	+	0.0804885i
$533$		−	2.25036i		−	0.0974741i
$534$	−4.80848	−	12.6891i	−0.208083	−	0.549111i
$535$	14.3173	−	39.3366i	0.618992	−	1.70067i
$536$	4.18182	+	0.737368i	0.180627	+	0.0318495i
$537$	−22.1396	−	3.60408i	−0.955394	−	0.155527i
$538$	18.9103	−	6.88280i	0.815282	−	0.296738i
$539$	21.0855	+	12.1737i	0.908218	+	0.524360i
$540$	−9.79756	+	18.6316i	−0.421620	+	0.801774i
$541$	−27.6522	−	23.2029i	−1.18886	−	0.997573i	−0.999878	−	0.0155921i	$-0.995037\pi$
$541$	−27.6522	−	23.2029i	−1.18886	−	0.997573i	−0.188982	−	0.981980i	$-0.560519\pi$
$542$	3.12437	+	2.62165i	0.134203	+	0.112610i
$543$	−1.27902	−	6.73425i	−0.0548882	−	0.288995i
$544$	5.60958	+	3.23869i	0.240509	+	0.138858i
$545$	49.7527	−	18.1085i	2.13117	−	0.775682i
$546$	0.262963	−	1.61537i	0.0112538	−	0.0691313i
$547$	19.9934	+	3.52537i	0.854855	+	0.150734i	0.583868	−	0.811849i	$-0.301539\pi$
$547$	19.9934	+	3.52537i	0.854855	+	0.150734i	0.270988	+	0.962583i	$0.412650\pi$
$548$	−7.70129	+	21.1591i	−0.328983	+	0.903872i
$549$	−12.7830	+	0.336519i	−0.545567	+	0.0143623i
$550$		−	38.0506i		−	1.62248i
$551$	−17.0797	−	8.14819i	−0.727618	−	0.347125i
$552$	−2.35802	−	0.823272i	−0.100364	−	0.0350408i
$553$	−2.65049	−	3.15873i	−0.112710	−	0.134323i
$554$	−4.74369	−	1.72656i	−0.201540	−	0.0733547i
$555$	6.41450	+	3.59171i	0.272281	+	0.152459i
$556$	1.29149	+	7.32441i	0.0547714	+	0.310624i
$557$	−9.69201	−	26.6286i	−0.410664	−	1.12829i	−0.956839	−	0.290619i	$-0.906139\pi$
$557$	−9.69201	−	26.6286i	−0.410664	−	1.12829i	0.546175	−	0.837671i	$-0.316083\pi$
$558$	−5.27666	−	13.3901i	−0.223379	−	0.566849i
$559$	−5.16659	+	2.98293i	−0.218524	+	0.126165i
$560$	1.83232	−	2.18368i	0.0774298	−	0.0922772i
$561$	−7.41495	+	4.41213i	−0.313060	+	0.186280i
$562$	9.14302	+	15.8362i	0.385675	+	0.668009i
$563$	−7.48478	+	12.9640i	−0.315446	+	0.546368i	−0.979532	−	0.201288i	$-0.935487\pi$
$563$	−7.48478	+	12.9640i	−0.315446	+	0.546368i	0.664086	+	0.747656i	$0.268821\pi$
$564$	−14.0783	+	0.185276i	−0.592801	+	0.00780154i
$565$	36.7698	−	6.48350i	1.54692	−	0.272763i
$566$	−1.86070	+	10.5525i	−0.0782109	+	0.443556i
$567$	1.02859	−	8.39657i	0.0431968	−	0.352623i
$568$	−5.74374	+	4.81957i	−0.241002	+	0.202225i
$569$	−32.6749			−1.36980			−0.684901	−	0.728636i	$-0.740155\pi$
$569$	−32.6749			−1.36980			−0.684901	+	0.728636i	$0.740155\pi$
$570$	−12.0687	−	25.5897i	−0.505500	−	1.07183i
$571$	29.9468			1.25324			0.626618	−	0.779327i	$-0.284439\pi$
$571$	29.9468			1.25324			0.626618	+	0.779327i	$0.284439\pi$
$572$	3.31392	−	2.78071i	0.138562	−	0.116267i
$573$	−21.3128	−	17.4108i	−0.890355	−	0.727347i
$574$	−0.346229	+	1.96356i	−0.0144513	+	0.0819575i
$575$	−4.69297	+	0.827498i	−0.195711	+	0.0345091i
$576$	18.8179	+	6.29346i	0.784079	+	0.262228i
$577$	−13.5840	+	23.5283i	−0.565511	+	0.979494i	0.431491	+	0.902117i	$0.357988\pi$
$577$	−13.5840	+	23.5283i	−0.565511	+	0.979494i	−0.997002	+	0.0773769i	$0.975346\pi$
$578$	−7.51217	−	13.0115i	−0.312465	−	0.541205i
$579$	13.9658	+	23.4707i	0.580399	+	0.975408i
$580$	11.3052	−	13.4731i	0.469425	−	0.559438i
$581$	3.44690	−	1.99007i	0.143001	−	0.0825618i
$582$	−13.7409	+	11.8416i	−0.569577	+	0.490849i
$583$	−10.5121	−	28.8818i	−0.435367	−	1.19616i
$584$	4.54758	+	25.7906i	0.188180	+	1.06722i
$585$	8.93133	−	7.90399i	0.369265	−	0.326790i
$586$	20.9497	+	7.62507i	0.865424	+	0.314989i
$587$	11.5736	+	13.7929i	0.477695	+	0.569295i	0.950044	−	0.312117i	$-0.101038\pi$
$587$	11.5736	+	13.7929i	0.477695	+	0.569295i	−0.472349	+	0.881412i	$0.656594\pi$
$588$	−3.67495	+	10.5258i	−0.151552	+	0.434076i
$589$	−20.6998	−	5.74227i	−0.852919	−	0.236606i
$590$		−	25.7380i		−	1.05962i
$591$	6.74107	−	2.55450i	0.277290	−	0.105078i
$592$	0.297084	−	0.816233i	0.0122101	−	0.0335470i
$593$	−22.7215	−	4.00642i	−0.933062	−	0.164524i	−0.313604	−	0.949554i	$-0.601536\pi$
$593$	−22.7215	−	4.00642i	−0.933062	−	0.164524i	−0.619458	+	0.785030i	$0.712648\pi$
$594$	−14.9015	+	13.5412i	−0.611414	+	0.555603i
$595$	−4.25516	+	1.54875i	−0.174445	+	0.0634926i
$596$	−5.39434	−	3.11443i	−0.220961	−	0.127572i
$597$	37.8707	−	7.19271i	1.54994	−	0.294378i
$598$	0.373728	+	0.313595i	0.0152829	+	0.0128239i
$599$	−16.7485	−	14.0536i	−0.684323	−	0.574216i	0.232943	−	0.972490i	$-0.425165\pi$
$599$	−16.7485	−	14.0536i	−0.684323	−	0.574216i	−0.917266	+	0.398275i	$0.869609\pi$
$600$	49.6494	−	9.42982i	2.02693	−	0.384971i
$601$	34.1830	+	19.7356i	1.39435	+	0.805031i	0.993794	−	0.111239i	$-0.0354818\pi$
$601$	34.1830	+	19.7356i	1.39435	+	0.805031i	0.400561	+	0.916270i	$0.368815\pi$
$602$	4.96707	−	1.80786i	0.202443	−	0.0736830i
$603$	−3.76799	−	2.04517i	−0.153444	−	0.0832858i
$604$	−16.8095	−	2.96397i	−0.683969	−	0.120602i
$605$	−6.37936	+	17.5271i	−0.259358	+	0.712580i
$606$	−27.6005	+	10.4591i	−1.12119	+	0.424872i
$607$		−	19.6240i		−	0.796513i	−0.917274	−	0.398257i	$-0.869615\pi$
$607$		−	19.6240i		−	0.796513i	0.917274	−	0.398257i	$-0.130385\pi$
$608$	18.5941	−	12.7772i	0.754088	−	0.518185i
$609$	−2.32972	+	6.67280i	−0.0944052	+	0.270395i
$610$	10.2676	+	12.2365i	0.415723	+	0.495440i
$611$	7.49586	+	2.72827i	0.303250	+	0.110374i
$612$	−2.61841	−	2.95875i	−0.105843	−	0.119600i
$613$	−1.42980	−	8.10881i	−0.0577492	−	0.327512i	0.942223	−	0.334987i	$-0.108732\pi$
$613$	−1.42980	−	8.10881i	−0.0577492	−	0.327512i	−0.999972	+	0.00747482i	$0.997621\pi$
$614$	−7.15786	−	19.6661i	−0.288868	−	0.793658i
$615$	−11.0065	+	9.48516i	−0.443826	+	0.382479i
$616$	−9.62786	+	5.55865i	−0.387918	+	0.223964i
$617$	19.4518	−	23.1818i	0.783102	−	0.933264i	−0.215967	−	0.976401i	$-0.569290\pi$
$617$	19.4518	−	23.1818i	0.783102	−	0.933264i	0.999069	+	0.0431361i	$0.0137349\pi$
$618$	1.31510	+	2.21014i	0.0529012	+	0.0889048i
$619$	−1.78524	−	3.09212i	−0.0717547	−	0.124283i	0.827916	−	0.560853i	$-0.189527\pi$
$619$	−1.78524	−	3.09212i	−0.0717547	−	0.124283i	−0.899670	+	0.436570i	$0.856193\pi$
$620$	9.98251	−	17.2902i	0.400907	−	0.694392i
$621$	1.99418	+	1.54339i	0.0800236	+	0.0619341i
$622$	6.85358	−	1.20847i	0.274804	−	0.0484553i
$623$	−1.31356	+	7.44956i	−0.0526266	+	0.298460i
$624$	−1.09130	−	0.891504i	−0.0436870	−	0.0356887i
$625$	17.1025	−	14.3507i	0.684100	−	0.574028i
$626$	4.36982			0.174653
$627$	2.74968	+	29.9268i	0.109811	+	1.19516i
$628$	23.9598			0.956102
$629$	−1.05701	+	0.886934i	−0.0421456	+	0.0353644i
$630$	−9.00912	+	5.52253i	−0.358932	+	0.220023i
$631$	7.66474	−	43.4689i	0.305128	−	1.73047i	−0.317771	−	0.948167i	$-0.602934\pi$
$631$	7.66474	−	43.4689i	0.305128	−	1.73047i	0.622900	−	0.782302i	$-0.285954\pi$
$632$	−12.8373	+	2.26356i	−0.510640	+	0.0900396i
$633$	31.8250	−	0.418831i	1.26493	−	0.0166470i
$634$	−5.38990	+	9.33558i	−0.214060	+	0.370763i
$635$	18.3264	+	31.7422i	0.727260	+	1.25965i
$636$	12.0947	−	7.19675i	0.479587	−	0.285370i
$637$	4.06021	−	4.83876i	0.160871	−	0.191719i
$638$	14.5690	−	8.41143i	0.576793	−	0.333012i
$639$	7.04302	−	2.77545i	0.278618	−	0.109795i
$640$	5.15207	+	14.1552i	0.203654	+	0.559534i
$641$	6.23658	+	35.3694i	0.246330	+	1.39701i	0.817384	+	0.576094i	$0.195424\pi$
$641$	6.23658	+	35.3694i	0.246330	+	1.39701i	−0.571054	+	0.820913i	$0.693465\pi$
$642$	15.9976	+	8.95764i	0.631376	+	0.353530i
$643$	−14.3616	−	5.22718i	−0.566365	−	0.206140i	0.0429378	−	0.999078i	$-0.486328\pi$
$643$	−14.3616	−	5.22718i	−0.566365	−	0.206140i	−0.609303	+	0.792938i	$0.708551\pi$
$644$	0.308554	+	0.367721i	0.0121587	+	0.0144902i
$645$	36.3664	+	12.6969i	1.43193	+	0.499939i
$646$	5.29394	−	0.416233i	0.208287	−	0.0163765i
$647$		−	16.9968i		−	0.668212i	−0.942536	−	0.334106i	$-0.891566\pi$
$647$		−	16.9968i		−	0.668212i	0.942536	−	0.334106i	$-0.108434\pi$
$648$	−21.3619	−	16.0880i	−0.839174	−	0.631996i
$649$	−9.35052	+	25.6903i	−0.367040	+	1.00843i
$650$	−9.72163	−	1.71419i	−0.381314	−	0.0672359i
$651$	−1.28910	+	7.91885i	−0.0505238	+	0.310364i
$652$	3.48143	−	1.26714i	0.136343	−	0.0496249i
$653$	4.58433	+	2.64676i	0.179399	+	0.103576i	0.587010	−	0.809580i	$-0.300305\pi$
$653$	4.58433	+	2.64676i	0.179399	+	0.103576i	−0.407611	+	0.913155i	$0.633638\pi$
$654$	4.32703	+	22.7824i	0.169200	+	0.890864i
$655$	−49.5324	−	41.5626i	−1.93539	−	1.62399i
$656$	1.31509	+	1.10349i	0.0513457	+	0.0430841i
$657$	3.90455	−	26.1509i	0.152331	−	1.02024i
$658$	−6.12078	−	3.53383i	−0.238613	−	0.137763i
$659$	−24.0269	+	8.74509i	−0.935956	+	0.340660i	−0.764568	−	0.644543i	$-0.777048\pi$
$659$	−24.0269	+	8.74509i	−0.935956	+	0.340660i	−0.171388	+	0.985204i	$0.554825\pi$
$660$	−27.5684	−	4.48783i	−1.07310	−	0.174688i
$661$	−23.7023	−	4.17936i	−0.921913	−	0.162558i	−0.307505	−	0.951546i	$-0.599494\pi$
$661$	−23.7023	−	4.17936i	−0.921913	−	0.162558i	−0.614408	+	0.788988i	$0.710605\pi$
$662$	−6.71435	+	18.4475i	−0.260961	+	0.716984i
$663$	0.793221	+	2.09323i	0.0308062	+	0.0812944i
$664$		−	12.5823i		−	0.488289i
$665$	−1.51289	+	15.6993i	−0.0586673	+	0.608793i
$666$	−2.00411	+	2.52023i	−0.0776575	+	0.0976569i
$667$	−1.35426	−	1.61395i	−0.0524373	−	0.0624923i
$668$	7.17032	+	2.60978i	0.277428	+	0.100976i
$669$	−21.5441	+	38.4760i	−0.832941	+	1.48757i
$670$	0.929964	+	5.27409i	0.0359276	+	0.203756i
$671$	−5.80314	−	15.9440i	−0.224028	−	0.615511i
$672$	−5.50077	−	6.38306i	−0.212197	−	0.246232i
$673$	26.8141	−	15.4811i	1.03361	−	0.596754i	0.115591	−	0.993297i	$-0.463124\pi$
$673$	26.8141	−	15.4811i	1.03361	−	0.596754i	0.918016	+	0.396543i	$0.129790\pi$
$674$	4.65930	−	5.55274i	0.179470	−	0.213883i
$675$	−50.5592	−	6.87004i	−1.94603	−	0.264428i
$676$	6.27919	+	10.8759i	0.241507	+	0.418303i
$677$	4.46701	−	7.73710i	0.171681	−	0.297361i	−0.767326	−	0.641257i	$-0.778413\pi$
$677$	4.46701	−	7.73710i	0.171681	−	0.297361i	0.939008	+	0.343896i	$0.111747\pi$
$678$	0.215198	+	16.3518i	0.00826462	+	0.627989i
$679$	9.95826	−	1.75591i	0.382163	−	0.0673857i
$680$	−2.48579	+	14.0976i	−0.0953256	+	0.540618i
$681$	8.80144	−	10.7740i	0.337272	−	0.412859i
$682$	14.6289	−	12.2751i	0.560169	−	0.470038i
$683$	−44.5537			−1.70480			−0.852400	−	0.522890i	$-0.824854\pi$
$683$	−44.5537			−1.70480			−0.852400	+	0.522890i	$0.824854\pi$
$684$	−13.2281	+	3.79399i	−0.505788	+	0.145067i
$685$	−82.3691			−3.14716
$686$	−9.19366	+	7.71440i	−0.351015	+	0.294537i
$687$	−5.85644	+	7.16895i	−0.223437	+	0.273512i
$688$	0.790301	−	4.48202i	0.0301300	−	0.170875i
$689$	−7.85265	+	1.38463i	−0.299162	+	0.0527504i
$690$	−0.0414513	−	3.14969i	−0.00157802	−	0.119907i
$691$	−1.53979	+	2.66699i	−0.0585763	+	0.101457i	−0.893827	−	0.448413i	$-0.851989\pi$
$691$	−1.53979	+	2.66699i	−0.0585763	+	0.101457i	0.835250	+	0.549870i	$0.185323\pi$
$692$	8.24045	+	14.2729i	0.313255	+	0.542573i
$693$	10.9988	−	2.23932i	0.417808	−	0.0850647i
$694$	−12.9785	+	15.4672i	−0.492656	+	0.587125i
$695$	−23.5616	+	13.6033i	−0.893742	+	0.516002i
$696$	14.5860	+	16.9255i	0.552881	+	0.641560i
$697$	−0.932715	−	2.56261i	−0.0353291	−	0.0970659i
$698$	1.34755	+	7.64234i	0.0510055	+	0.289267i
$699$	3.79214	−	6.77246i	0.143432	−	0.256158i
$700$	−9.12716	−	3.32201i	−0.344974	−	0.125560i
$701$	10.2378	+	12.2010i	0.386677	+	0.460824i	0.923910	−	0.382610i	$-0.124975\pi$
$701$	10.2378	+	12.2010i	0.386677	+	0.460824i	−0.537233	+	0.843434i	$0.680530\pi$
$702$	2.78836	+	4.41724i	0.105240	+	0.166718i
$703$	1.20296	+	4.65299i	0.0453706	+	0.175491i
$704$			26.3282i			0.992282i
$705$	−18.2507	−	48.1617i	−0.687360	−	1.81387i
$706$	7.71577	−	21.1989i	0.290387	−	0.797831i
$707$	16.2038	+	2.85717i	0.609407	+	0.107455i
$708$	−12.3561	−	2.01144i	−0.464371	−	0.0755944i
$709$	−22.5919	+	8.22277i	−0.848456	+	0.308813i	−0.729411	−	0.684076i	$-0.760206\pi$
$709$	−22.5919	+	8.22277i	−0.848456	+	0.308813i	−0.119045	+	0.992889i	$0.537983\pi$
$710$	−8.18942	−	4.72816i	−0.307343	−	0.177445i
$711$	13.0166	+	1.94349i	0.488161	+	0.0728866i
$712$	18.3188	+	15.3713i	0.686526	+	0.576063i
$713$	−1.83209	−	1.53731i	−0.0686123	−	0.0575726i
$714$	−0.370074	−	1.94850i	−0.0138497	−	0.0729206i
$715$	13.7047	+	7.91244i	0.512529	+	0.295908i
$716$	12.8068	−	4.66128i	0.478611	−	0.174200i
$717$	2.16649	−	13.3086i	0.0809090	−	0.497018i
$718$	−7.41780	−	1.30796i	−0.276830	−	0.0488126i
$719$	16.7833	−	46.1117i	0.625911	−	1.71968i	−0.0661225	−	0.997812i	$-0.521063\pi$
$719$	16.7833	−	46.1117i	0.625911	−	1.71968i	0.692034	−	0.721865i	$-0.256715\pi$
$720$	0.239435	+	9.09519i	0.00892322	+	0.338958i
$721$		−	1.43367i		−	0.0533928i
$722$	6.63098	−	17.2664i	0.246780	−	0.642588i
$723$	28.2629	+	9.86762i	1.05111	+	0.366981i
$724$	2.67705	+	3.19038i	0.0994917	+	0.118570i
$725$	40.0597	+	14.5805i	1.48778	+	0.541507i
$726$	−7.12804	−	3.99124i	−0.264546	−	0.148129i
$727$	4.87540	+	27.6498i	0.180819	+	1.02547i	0.931211	+	0.364480i	$0.118753\pi$
$727$	4.87540	+	27.6498i	0.180819	+	1.02547i	−0.750393	+	0.660993i	$0.770135\pi$
$728$	0.986455	+	2.71026i	0.0365605	+	0.100449i
$729$	15.3023	+	22.2450i	0.566751	+	0.823889i
$730$	−28.6037	+	16.5144i	−1.05867	+	0.611224i
$731$	−4.64714	+	5.53824i	−0.171881	+	0.204839i
$732$	6.67681	−	3.97292i	0.246782	−	0.146843i
$733$	−0.671595	−	1.16324i	−0.0248059	−	0.0429651i	0.853356	−	0.521329i	$-0.174563\pi$
$733$	−0.671595	−	1.16324i	−0.0248059	−	0.0429651i	−0.878162	+	0.478364i	$0.841230\pi$
$734$	−4.18178	+	7.24306i	−0.154352	+	0.267346i
$735$	−40.7799	+	0.536682i	−1.50419	+	0.0197958i
$736$	2.47365	−	0.436170i	0.0911798	−	0.0160775i
$737$	0.987815	−	5.60217i	0.0363866	−	0.206359i
$738$	−3.32587	−	5.42562i	−0.122427	−	0.199720i
$739$	−0.414289	+	0.347630i	−0.0152399	+	0.0127878i	−0.650376	−	0.759613i	$-0.725389\pi$
$739$	−0.414289	+	0.347630i	−0.0152399	+	0.0127878i	0.635136	+	0.772400i	$0.280944\pi$
$740$	−4.46670			−0.164199
$741$	7.76994	+	0.645687i	0.285436	+	0.0237199i
$742$	7.06489			0.259360
$743$	26.3387	−	22.1008i	0.966272	−	0.810799i	−0.0156896	−	0.999877i	$-0.504994\pi$
$743$	26.3387	−	22.1008i	0.966272	−	0.810799i	0.981962	+	0.189078i	$0.0605499\pi$
$744$	19.6423	+	16.0461i	0.720120	+	0.588279i
$745$	3.95668	−	22.4394i	0.144961	−	0.822117i
$746$	14.0692	−	2.48077i	0.515108	−	0.0908275i
$747$	−4.02921	+	12.0476i	−0.147421	+	0.440800i
$748$	2.62121	−	4.54007i	0.0958410	−	0.166001i
$749$	−5.11042	−	8.85151i	−0.186731	−	0.323427i
$750$	15.9965	+	26.8835i	0.584111	+	0.981647i
$751$	26.1379	−	31.1499i	0.953784	−	1.13668i	−0.0367385	−	0.999325i	$-0.511697\pi$
$751$	26.1379	−	31.1499i	0.953784	−	1.13668i	0.990523	−	0.137351i	$-0.0438587\pi$
$752$	−5.27005	+	3.04267i	−0.192179	+	0.110955i
$753$	−11.4918	+	9.90339i	−0.418786	+	0.360900i
$754$	−1.49272	−	4.10121i	−0.0543616	−	0.149357i
$755$	−10.8424	−	61.4905i	−0.394596	−	2.23787i
$756$	1.94715	+	4.75662i	0.0708171	+	0.172997i
$757$	16.1453	+	5.87639i	0.586809	+	0.213581i	0.618325	−	0.785922i	$-0.287811\pi$
$757$	16.1453	+	5.87639i	0.586809	+	0.213581i	−0.0315162	+	0.999503i	$0.510034\pi$
$758$	−15.2679	−	18.1956i	−0.554556	−	0.660894i
$759$	−1.10290	+	3.15891i	−0.0400326	+	0.114661i
$760$	40.5895	+	28.9569i	1.47234	+	1.05038i
$761$		−	31.1788i		−	1.13023i	−0.825012	−	0.565116i	$-0.808832\pi$
$761$		−	31.1788i		−	1.13023i	0.825012	−	0.565116i	$-0.191168\pi$
$762$	−15.0118	+	5.68868i	−0.543822	+	0.206079i
$763$	4.42139	−	12.1477i	0.160065	−	0.439775i
$764$	16.4668	+	2.90355i	0.595749	+	0.105047i
$765$	6.89460	−	12.7025i	0.249275	−	0.459260i
$766$	0.764288	−	0.278178i	0.0276149	−	0.0100510i
$767$	6.14244	+	3.54634i	0.221791	+	0.128051i
$768$	−28.9915	+	5.50630i	−1.04614	+	0.198692i
$769$	−14.5474	−	12.2068i	−0.524594	−	0.440187i	0.341636	−	0.939832i	$-0.389019\pi$
$769$	−14.5474	−	12.2068i	−0.524594	−	0.440187i	−0.866230	+	0.499646i	$0.833464\pi$
$770$	−10.7408	−	9.01256i	−0.387070	−	0.324790i
$771$	−41.0129	+	7.78951i	−1.47704	+	0.280532i
$772$	−14.3708	−	8.29696i	−0.517215	−	0.298614i
$773$	−40.7594	+	14.8352i	−1.46601	+	0.533585i	−0.947015	−	0.321190i	$-0.895917\pi$
$773$	−40.7594	+	14.8352i	−1.46601	+	0.533585i	−0.518998	+	0.854775i	$0.673695\pi$
$774$	−8.04809	+	14.8277i	−0.289283	+	0.532970i
$775$	47.6574	+	8.40329i	1.71190	+	0.301855i
$776$	10.9332	−	30.0387i	0.392479	−	1.07833i
$777$	1.67850	−	0.636061i	0.0602159	−	0.0228186i
$778$		−	4.11588i		−	0.147562i
$779$	−9.45470	−	0.911116i	−0.338750	−	0.0326441i
$780$	−2.38857	+	6.84134i	−0.0855244	+	0.244959i
$781$	6.45653	+	7.69460i	0.231033	+	0.275334i
$782$	0.555561	+	0.202208i	0.0198668	+	0.00723093i
$783$	−8.54615	−	20.8771i	−0.305414	−	0.746087i
$784$	0.836757	+	4.74549i	0.0298842	+	0.169482i
$785$	29.9770	+	82.3611i	1.06992	+	2.93959i
$786$	21.4533	−	18.4879i	0.765213	−	0.659443i
$787$	4.96475	−	2.86640i	0.176974	−	0.102176i	−0.408896	−	0.912581i	$-0.634086\pi$
$787$	4.96475	−	2.86640i	0.176974	−	0.102176i	0.585870	+	0.810405i	$0.300753\pi$
$788$	−2.81538	+	3.35524i	−0.100294	+	0.119526i
$789$	12.3343	+	20.7289i	0.439114	+	0.737967i
$790$	−8.22003	−	14.2375i	−0.292455	−	0.506548i
$791$	4.55812	−	7.89490i	0.162068	−	0.280710i
$792$	11.2544	−	33.6514i	0.399908	−	1.19575i
$793$	−4.33500	+	0.764378i	−0.153940	+	0.0271439i
$794$	4.19511	−	23.7917i	0.148879	−	0.844334i
$795$	39.8707	+	32.5711i	1.41407	+	1.15518i
$796$	−17.9414	+	15.0546i	−0.635916	+	0.533597i
$797$	3.78719			0.134149			0.0670746	−	0.997748i	$-0.478633\pi$
$797$	3.78719			0.134149			0.0670746	+	0.997748i	$0.478633\pi$
$798$	−6.68034	−	1.75884i	−0.236482	−	0.0622622i
$799$	9.66674			0.341985
$800$	−38.9337	+	32.6693i	−1.37651	+	1.15503i
$801$	−12.6180	−	20.5843i	−0.445835	−	0.727309i
$802$	−3.97693	+	22.5543i	−0.140430	+	0.796419i
$803$	34.5503	−	6.09216i	1.21926	−	0.214988i
$804$	2.60462	−	0.0342780i	0.0918579	−	0.00120889i
$805$	−0.877984	+	1.52071i	−0.0309449	+	0.0535981i
$806$	−2.47716	−	4.29056i	−0.0872542	−	0.151129i
$807$	30.7704	−	18.3094i	1.08317	−	0.644520i
$808$	33.4347	−	39.8459i	1.17623	−	1.40177i
$809$	9.92215	−	5.72856i	0.348844	−	0.201405i	−0.315332	−	0.948981i	$-0.602116\pi$
$809$	9.92215	−	5.72856i	0.348844	−	0.201405i	0.664176	+	0.747576i	$0.268783\pi$
$810$	9.85191	−	32.2563i	0.346161	−	1.13337i
$811$	13.9130	+	38.2257i	0.488552	+	1.34229i	0.901991	+	0.431755i	$0.142105\pi$
$811$	13.9130	+	38.2257i	0.488552	+	1.34229i	−0.413439	+	0.910532i	$0.635672\pi$
$812$	−0.745691	−	4.22902i	−0.0261686	−	0.148410i
$813$	6.33181	+	3.54540i	0.222066	+	0.124343i
$814$	−4.01477	−	1.46126i	−0.140717	−	0.0512170i
$815$	8.71148	+	10.3819i	0.305150	+	0.363663i
$816$	−1.61223	−	0.562889i	−0.0564393	−	0.0197051i
$817$	10.4407	+	22.9147i	0.365274	+	0.801683i
$818$			4.82327i			0.168642i
$819$	−0.0766329	−	2.91098i	−0.00267777	−	0.101718i
$820$	3.01934	−	8.29557i	0.105440	−	0.289694i
$821$	−34.6702	−	6.11330i	−1.21000	−	0.213356i	−0.467983	−	0.883737i	$-0.655019\pi$
$821$	−34.6702	−	6.11330i	−1.21000	−	0.213356i	−0.742016	+	0.670382i	$0.766130\pi$
$822$	5.79661	−	35.6081i	0.202180	−	1.24198i
$823$	−22.3227	+	8.12480i	−0.778121	+	0.283213i	−0.700389	−	0.713762i	$-0.746990\pi$
$823$	−22.3227	+	8.12480i	−0.778121	+	0.283213i	−0.0777319	+	0.996974i	$0.524768\pi$
$824$	−3.92505	−	2.26613i	−0.136736	−	0.0789443i
$825$	−12.6327	−	66.5128i	−0.439812	−	2.31568i
$826$	−4.81399	−	4.03941i	−0.167500	−	0.140549i
$827$	36.3149	+	30.4719i	1.26279	+	1.05961i	0.995379	+	0.0960290i	$0.0306142\pi$
$827$	36.3149	+	30.4719i	1.26279	+	1.05961i	0.267416	+	0.963581i	$0.413830\pi$
$828$	−1.51532	−	0.226250i	−0.0526609	−	0.00786272i
$829$	−21.9960	−	12.6994i	−0.763951	−	0.441067i	0.0667615	−	0.997769i	$-0.478733\pi$
$829$	−21.9960	−	12.6994i	−0.763951	−	0.441067i	−0.830713	+	0.556702i	$0.812067\pi$
$830$	14.9117	−	5.42743i	0.517594	−	0.188389i
$831$	−8.86524	−	1.44316i	−0.307532	−	0.0500627i
$832$	6.72666	+	1.18609i	0.233205	+	0.0411203i
$833$	2.61804	−	7.19301i	0.0907097	−	0.249223i
$834$	−4.22259	−	11.1430i	−0.146216	−	0.385850i
$835$			27.9129i			0.965967i
$836$	−10.3412	−	15.0490i	−0.357657	−	0.520479i
$837$	−13.6691	−	21.6542i	−0.472474	−	0.748480i
$838$	9.58924	+	11.4280i	0.331255	+	0.394774i
$839$	−1.80620	−	0.657403i	−0.0623570	−	0.0226961i	0.310653	−	0.950523i	$-0.399452\pi$
$839$	−1.80620	−	0.657403i	−0.0623570	−	0.0226961i	−0.373010	+	0.927827i	$0.621674\pi$
$840$	9.09803	−	16.2484i	0.313912	−	0.560622i
$841$	−1.76291	−	9.99798i	−0.0607901	−	0.344758i
$842$	2.46232	+	6.76518i	0.0848573	+	0.233143i
$843$	21.2397	+	24.6464i	0.731533	+	0.848866i
$844$	−16.7471	+	9.66896i	−0.576460	+	0.332819i
$845$	−29.5293	+	35.1917i	−1.01584	+	1.21063i
$846$	22.1047	−	4.50046i	0.759974	−	0.154729i
$847$	2.27704	+	3.94396i	0.0782402	+	0.135516i
$848$	3.04147	−	5.26798i	0.104445	−	0.180903i
$849$	0.250887	+	19.0637i	0.00861042	+	0.654264i
$850$	−11.7810	+	2.07731i	−0.404086	+	0.0712512i
$851$	−0.0929138	+	0.526940i	−0.00318504	+	0.0180633i
$852$	−2.90987	+	3.56201i	−0.0996905	+	0.122032i
$853$	26.9920	−	22.6489i	0.924187	−	0.775485i	−0.0505775	−	0.998720i	$-0.516106\pi$
$853$	26.9920	−	22.6489i	0.924187	−	0.775485i	0.974765	+	0.223235i	$0.0716617\pi$
$854$	3.90012			0.133459
$855$	−29.5918	−	40.7243i	−1.01202	−	1.39274i
$856$	−32.3110			−1.10437
$857$	−26.1095	+	21.9085i	−0.891884	+	0.748379i	−0.968587	−	0.248675i	$-0.920005\pi$
$857$	−26.1095	+	21.9085i	−0.891884	+	0.748379i	0.0767032	+	0.997054i	$0.475561\pi$
$858$	−4.38500	+	5.36773i	−0.149701	+	0.183251i
$859$	−1.10970	+	6.29342i	−0.0378624	+	0.214729i	−0.997869	−	0.0652488i	$-0.979216\pi$
$859$	−1.10970	+	6.29342i	−0.0378624	+	0.214729i	0.960007	+	0.279977i	$0.0903270\pi$
$860$	−23.0480	+	4.06398i	−0.785929	+	0.138581i
$861$	0.0466838	+	3.54728i	0.00159098	+	0.120891i
$862$	−10.9159	+	18.9068i	−0.371796	+	0.643970i
$863$	5.52979	+	9.57787i	0.188236	+	0.326035i	0.944662	−	0.328045i	$-0.106390\pi$
$863$	5.52979	+	9.57787i	0.188236	+	0.326035i	−0.756426	+	0.654079i	$0.773056\pi$
$864$	26.6495	+	3.62117i	0.906636	+	0.123195i
$865$	−38.7526	+	46.1836i	−1.31763	+	1.57029i
$866$	4.25627	−	2.45736i	0.144634	−	0.0835045i
$867$	−17.4511	−	20.2502i	−0.592671	−	0.687731i
$868$	−1.66724	−	4.58070i	−0.0565898	−	0.155479i
$869$	3.03237	+	17.1974i	0.102866	+	0.583383i
$870$	−13.7673	+	24.5873i	−0.466754	+	0.833586i
$871$	−1.38681	−	0.504758i	−0.0469903	−	0.0171031i
$872$	−26.2687	−	31.3058i	−0.889569	−	1.06015i
$873$	−20.0878	+	25.2611i	−0.679870	+	0.854959i
$874$	1.46885	−	1.44322i	0.0496847	−	0.0488175i
$875$		−	17.4388i		−	0.589540i
$876$	5.69270	+	15.0225i	0.192338	+	0.507562i
$877$	−16.3756	+	44.9915i	−0.552963	+	1.51925i	0.276682	+	0.960962i	$0.410765\pi$
$877$	−16.3756	+	44.9915i	−0.552963	+	1.51925i	−0.829645	+	0.558292i	$0.811457\pi$
$878$	10.4040	+	1.83451i	0.351119	+	0.0619117i
$879$	39.1518	+	6.37347i	1.32056	+	0.214972i
$880$	−11.3442	+	4.12896i	−0.382414	+	0.139187i
$881$	−15.8937	−	9.17623i	−0.535472	−	0.309155i	0.207770	−	0.978178i	$-0.433380\pi$
$881$	−15.8937	−	9.17623i	−0.535472	−	0.309155i	−0.743242	+	0.669023i	$0.766713\pi$
$882$	2.63782	−	17.6669i	0.0888200	−	0.594876i
$883$	15.9103	+	13.3504i	0.535425	+	0.449275i	0.869970	−	0.493105i	$-0.164138\pi$
$883$	15.9103	+	13.3504i	0.535425	+	0.449275i	−0.334545	+	0.942380i	$0.608583\pi$
$884$	−1.04187	−	0.874231i	−0.0350418	−	0.0294036i
$885$	−8.54492	−	44.9903i	−0.287234	−	1.51233i
$886$	1.15006	+	0.663985i	0.0386369	+	0.0223070i
$887$	−19.3286	+	7.03503i	−0.648991	+	0.236213i	−0.645476	−	0.763781i	$-0.723341\pi$
$887$	−19.3286	+	7.03503i	−0.648991	+	0.236213i	−0.00351460	+	0.999994i	$0.501119\pi$
$888$	0.911733	−	5.60071i	0.0305957	−	0.187948i
$889$	8.81321	+	1.55401i	0.295586	+	0.0521197i
$890$	−10.3152	+	28.3407i	−0.345765	+	0.949981i
$891$	−21.5523	+	28.6174i	−0.722028	+	0.958720i
$892$		−	26.7925i		−	0.897080i
$893$	14.4975	−	30.3886i	0.485139	−	1.01691i
$894$	9.42212	+	3.28961i	0.315123	+	0.110021i
$895$	32.0460	+	38.1909i	1.07118	+	1.27658i
$896$	3.45615	+	1.25794i	0.115462	+	0.0420247i
$897$	0.757393	+	0.424091i	0.0252886	+	0.0141600i
$898$	−4.24648	−	24.0830i	−0.141707	−	0.803659i
$899$	7.31761	+	20.1050i	0.244056	+	0.670538i
$900$	28.8424	−	11.3660i	0.961413	−	0.378866i
$901$	−8.36835	+	4.83147i	−0.278790	+	0.160960i
$902$	5.42769	−	6.46847i	0.180722	−	0.215377i
$903$	8.08228	−	4.80921i	0.268961	−	0.160041i
$904$	−14.4095	−	24.9580i	−0.479254	−	0.830091i
$905$	−7.61748	+	13.1939i	−0.253214	+	0.438579i
$906$	27.3453	−	0.359877i	0.908488	−	0.0119561i
$907$	−17.2346	+	3.03893i	−0.572266	+	0.100906i	−0.452290	−	0.891871i	$-0.649393\pi$
$907$	−17.2346	+	3.03893i	−0.572266	+	0.100906i	−0.119976	+	0.992777i	$0.538282\pi$
$908$	−1.46779	+	8.32425i	−0.0487103	+	0.276250i
$909$	−44.7736	+	27.4459i	−1.48505	+	0.910322i
$910$	−2.78651	+	2.33816i	−0.0923720	+	0.0775093i
$911$	50.6401			1.67778			0.838891	−	0.544299i	$-0.183204\pi$
$911$	50.6401			1.67778			0.838891	+	0.544299i	$0.183204\pi$
$912$	−4.18741	+	4.22406i	−0.138659	+	0.139872i
$913$	−16.8559			−0.557849
$914$	13.7319	−	11.5224i	0.454211	−	0.381128i
$915$	22.0104	+	17.9807i	0.727640	+	0.594422i
$916$	0.976661	−	5.53892i	0.0322698	−	0.183011i
$917$	−15.5476	+	2.74146i	−0.513426	+	0.0905309i
$918$	5.00609	+	3.87445i	0.165226	+	0.127876i
$919$	13.7532	−	23.8213i	0.453677	−	0.785792i	−0.544934	−	0.838479i	$-0.683445\pi$
$919$	13.7532	−	23.8213i	0.453677	−	0.785792i	0.998611	+	0.0526868i	$0.0167785\pi$
$920$	2.77556	+	4.80741i	0.0915074	+	0.158495i
$921$	−19.0411	−	32.0001i	−0.627425	−	1.05444i
$922$	15.4245	−	18.3822i	0.507980	−	0.605387i
$923$	2.25678	−	1.30295i	0.0742828	−	0.0428872i
$924$	−5.16608	+	4.45201i	−0.169952	+	0.146460i
$925$	−3.70295	−	10.1738i	−0.121752	−	0.334511i
$926$	0.861001	+	4.88298i	0.0282943	+	0.160465i
$927$	3.03257	+	3.42674i	0.0996028	+	0.112549i
$928$	−21.1153	−	7.68533i	−0.693143	−	0.252283i
$929$	−7.33625	−	8.74300i	−0.240695	−	0.286849i	0.632151	−	0.774845i	$-0.282172\pi$
$929$	−7.33625	−	8.74300i	−0.240695	−	0.286849i	−0.872845	+	0.487997i	$0.837728\pi$
$930$	−10.5440	+	30.2003i	−0.345753	+	0.990305i
$931$	−18.6857	−	19.0177i	−0.612401	−	0.623279i
$932$			4.71596i			0.154476i
$933$	11.5789	−	4.38779i	0.379077	−	0.143650i
$934$	−0.980535	+	2.69400i	−0.0320841	+	0.0881503i
$935$	18.8858	+	3.33008i	0.617633	+	0.108905i
$936$	−8.09067	−	4.39142i	−0.264452	−	0.143538i
$937$	−28.9100	+	10.5224i	−0.944448	+	0.343751i	−0.767921	−	0.640545i	$-0.778709\pi$
$937$	−28.9100	+	10.5224i	−0.944448	+	0.343751i	−0.176527	+	0.984296i	$0.556486\pi$
$938$	1.13241	+	0.653796i	0.0369744	+	0.0213472i
$939$	7.63850	−	1.45077i	0.249273	−	0.0473440i
$940$	23.9716	+	20.1146i	0.781868	+	0.656065i
$941$	−2.17650	−	1.82630i	−0.0709518	−	0.0595356i	0.606622	−	0.794990i	$-0.292524\pi$
$941$	−2.17650	−	1.82630i	−0.0709518	−	0.0595356i	−0.677574	+	0.735455i	$0.736969\pi$
$942$	−37.7143	+	7.16301i	−1.22880	+	0.233383i
$943$	−0.915829	−	0.528754i	−0.0298235	−	0.0172186i
$944$	−5.08446	+	1.85059i	−0.165485	+	0.0602317i
$945$	−13.9146	+	12.6444i	−0.452641	+	0.411323i
$946$	−22.0455	−	3.88722i	−0.716761	−	0.126384i
$947$	10.4821	−	28.7992i	0.340621	−	0.935848i	−0.644594	−	0.764525i	$-0.722974\pi$
$947$	10.4821	−	28.7992i	0.340621	−	0.935848i	0.985215	−	0.171323i	$-0.0548043\pi$
$948$	−7.47744	+	2.83354i	−0.242856	+	0.0920292i
$949$		−	9.10180i		−	0.295457i
$950$	−11.1380	+	40.1505i	−0.361365	+	1.30265i
$951$	−6.32222	+	18.1081i	−0.205012	+	0.587196i
$952$	2.24666	+	2.67747i	0.0728147	+	0.0867772i
$953$	−5.57402	−	2.02878i	−0.180560	−	0.0657186i	0.250158	−	0.968205i	$-0.419517\pi$
$953$	−5.57402	−	2.02878i	−0.180560	−	0.0657186i	−0.430718	+	0.902486i	$0.641740\pi$
$954$	−16.8863	+	14.9440i	−0.546715	+	0.483829i
$955$	10.6214	+	60.2369i	0.343700	+	1.94922i
$956$	2.80199	+	7.69842i	0.0906230	+	0.248985i
$957$	22.6742	−	19.5401i	0.732954	−	0.631643i
$958$	31.9668	−	18.4561i	1.03280	−	0.596288i
$959$	−12.9273	+	15.4062i	−0.417444	+	0.497491i
$960$	−22.5513	−	37.8994i	−0.727841	−	1.22320i
$961$	−3.35647	−	5.81357i	−0.108273	−	0.187534i
$962$	−0.554205	+	0.959912i	−0.0178683	+	0.0309488i
$963$	30.9379	+	10.3469i	0.996961	+	0.333424i
$964$	−17.9122	+	3.15840i	−0.576912	+	0.101725i
$965$	10.5408	−	59.7796i	0.339319	−	1.92437i
$966$	−0.595617	−	0.486570i	−0.0191637	−	0.0156551i
$967$	38.7529	−	32.5176i	1.24621	−	1.04570i	0.249198	−	0.968452i	$-0.419833\pi$
$967$	38.7529	−	32.5176i	1.24621	−	1.04570i	0.997012	−	0.0772426i	$-0.0246116\pi$
$968$	14.3968			0.462730
$969$	9.11567	−	2.48515i	0.292838	−	0.0798345i
$970$	40.3160			1.29447
$971$	24.0894	−	20.2134i	0.773065	−	0.648679i	−0.168427	−	0.985714i	$-0.553869\pi$
$971$	24.0894	−	20.2134i	0.773065	−	0.648679i	0.941492	+	0.337036i	$0.109424\pi$
$972$	−14.7154	−	7.25048i	−0.471998	−	0.232559i
$973$	−1.15351	+	6.54187i	−0.0369798	+	0.209723i
$974$	−22.5189	+	3.97070i	−0.721554	+	0.127229i
$975$	−17.5626	+	0.231132i	−0.562454	+	0.00740215i
$976$	1.67902	−	2.90815i	0.0537442	−	0.0930877i
$977$	5.65819	+	9.80028i	0.181022	+	0.313539i	0.942229	−	0.334970i	$-0.108726\pi$
$977$	5.65819	+	9.80028i	0.181022	+	0.313539i	−0.761207	+	0.648509i	$0.775393\pi$
$978$	−5.10117	+	3.03536i	−0.163117	+	0.0970600i
$979$	20.5921	−	24.5407i	0.658127	−	0.784326i
$980$	21.4595	−	12.3896i	0.685497	−	0.395772i
$981$	15.1274	+	38.3874i	0.482980	+	1.22561i
$982$	0.187109	+	0.514078i	0.00597089	+	0.0164049i
$983$	2.53074	+	14.3526i	0.0807181	+	0.457775i	0.998199	+	0.0599947i	$0.0191084\pi$
$983$	2.53074	+	14.3526i	0.0807181	+	0.457775i	−0.917481	+	0.397781i	$0.869781\pi$
$984$	9.78535	+	5.47917i	0.311946	+	0.174669i
$985$	−15.0560	−	5.47992i	−0.479723	−	0.174605i
$986$	−3.39968	−	4.05158i	−0.108268	−	0.129029i
$987$	−11.8724	−	4.14510i	−0.377903	−	0.131940i
$988$	−4.31077	+	1.96413i	−0.137144	+	0.0624873i
$989$			2.80353i			0.0891469i
$990$	44.7361	−	1.17770i	1.42181	−	0.0374297i
$991$	9.66800	−	26.5626i	0.307114	−	0.843789i	−0.686102	−	0.727505i	$-0.740680\pi$
$991$	9.66800	−	26.5626i	0.307114	−	0.843789i	0.993216	−	0.116284i	$-0.0370981\pi$
$992$	−25.1200	−	4.42933i	−0.797561	−	0.140631i
$993$	−5.61225	+	34.4756i	−0.178099	+	1.09405i
$994$	−2.16962	+	0.789679i	−0.0688163	+	0.0250471i
$995$	−74.1969	−	42.8376i	−2.35220	−	1.35804i
$996$	−1.44020	−	7.58288i	−0.0456346	−	0.240273i
$997$	29.1031	+	24.4204i	0.921704	+	0.773401i	0.974309	−	0.225214i	$-0.0723081\pi$
$997$	29.1031	+	24.4204i	0.921704	+	0.773401i	−0.0526054	+	0.998615i	$0.516753\pi$
$998$	3.29331	+	2.76342i	0.104248	+	0.0874745i
$999$	−2.66649	+	5.07074i	−0.0843641	+	0.160431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.32.3	yes	24
3.2	odd	2	inner	57.2.j.b.32.2	✓	24
4.3	odd	2		912.2.cc.e.545.2		24
12.11	even	2		912.2.cc.e.545.3		24
19.3	odd	18	inner	57.2.j.b.41.2	yes	24
19.4	even	9		1083.2.d.d.1082.16		24
19.15	odd	18		1083.2.d.d.1082.10		24
57.23	odd	18		1083.2.d.d.1082.9		24
57.41	even	18	inner	57.2.j.b.41.3	yes	24
57.53	even	18		1083.2.d.d.1082.15		24
76.3	even	18		912.2.cc.e.497.3		24
228.155	odd	18		912.2.cc.e.497.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.32.2	✓	24	3.2	odd	2	inner
57.2.j.b.32.3	yes	24	1.1	even	1	trivial
57.2.j.b.41.2	yes	24	19.3	odd	18	inner
57.2.j.b.41.3	yes	24	57.41	even	18	inner
912.2.cc.e.497.2		24	228.155	odd	18
912.2.cc.e.497.3		24	76.3	even	18
912.2.cc.e.545.2		24	4.3	odd	2
912.2.cc.e.545.3		24	12.11	even	2
1083.2.d.d.1082.9		24	57.23	odd	18
1083.2.d.d.1082.10		24	19.15	odd	18
1083.2.d.d.1082.15		24	57.53	even	18
1083.2.d.d.1082.16		24	19.4	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)

\(f(q)\)	\(=\)	\(q+(0.745719 - 0.625733i) q^{2} +(1.09578 - 1.34136i) q^{3} +(-0.182741 + 1.03637i) q^{4} +(-3.79113 + 0.668479i) q^{5} +(-0.0221879 - 1.68595i) q^{6} +(-0.469963 + 0.814000i) q^{7} +(1.48569 + 2.57329i) q^{8} +(-0.598514 - 2.93969i) q^{9} +O(q^{10})\)	\(q+(0.745719 - 0.625733i) q^{2} +(1.09578 - 1.34136i) q^{3} +(-0.182741 + 1.03637i) q^{4} +(-3.79113 + 0.668479i) q^{5} +(-0.0221879 - 1.68595i) q^{6} +(-0.469963 + 0.814000i) q^{7} +(1.48569 + 2.57329i) q^{8} +(-0.598514 - 2.93969i) q^{9} +(-2.40883 + 2.87073i) q^{10} +(3.44730 - 1.99030i) q^{11} +(1.18991 + 1.38076i) q^{12} +(-0.353205 - 0.970422i) q^{13} +(0.158886 + 0.901087i) q^{14} +(-3.25759 + 5.81780i) q^{15} +(0.740303 + 0.269448i) q^{16} +(-0.804427 - 0.958678i) q^{17} +(-2.28578 - 1.81767i) q^{18} +(-4.22014 + 1.09106i) q^{19} -4.05119i q^{20} +(0.576892 + 1.52236i) q^{21} +(1.32532 - 3.64129i) q^{22} +(-0.477922 - 0.0842705i) q^{23} +(5.07970 + 0.826919i) q^{24} +(9.22735 - 3.35848i) q^{25} +(-0.870616 - 0.502651i) q^{26} +(-4.59904 - 2.41844i) q^{27} +(-0.757727 - 0.635808i) q^{28} +(3.32571 + 2.79060i) q^{29} +(1.21114 + 6.37682i) q^{30} +(4.26794 + 2.46410i) q^{31} +(-4.86370 + 1.77024i) q^{32} +(1.10778 - 6.80502i) q^{33} +(-1.19975 - 0.211549i) q^{34} +(1.23755 - 3.40014i) q^{35} +(3.15599 - 0.0830829i) q^{36} -1.10257i q^{37} +(-2.46433 + 3.45430i) q^{38} +(-1.68872 - 0.589597i) q^{39} +(-7.35262 - 8.76251i) q^{40} +(2.04769 + 0.745298i) q^{41} +(1.38279 + 0.774273i) q^{42} +(-1.00316 - 5.68919i) q^{43} +(1.43273 + 3.93640i) q^{44} +(4.23417 + 10.7447i) q^{45} +(-0.409126 + 0.236209i) q^{46} +(-4.96510 + 5.91718i) q^{47} +(1.17264 - 0.697758i) q^{48} +(3.05827 + 5.29708i) q^{49} +(4.77950 - 8.27834i) q^{50} +(-2.16741 + 0.0285242i) q^{51} +(1.07026 - 0.188716i) q^{52} +(1.34079 - 7.60399i) q^{53} +(-4.94289 + 1.07429i) q^{54} +(-11.7387 + 9.84993i) q^{55} -2.79287 q^{56} +(-3.16086 + 6.85631i) q^{57} +4.22621 q^{58} +(-5.26126 + 4.41472i) q^{59} +(-5.43411 - 4.43923i) q^{60} +(0.740173 - 4.19773i) q^{61} +(4.72455 - 0.833066i) q^{62} +(2.67419 + 0.894356i) q^{63} +(-3.30707 + 5.72801i) q^{64} +(1.98775 + 3.44289i) q^{65} +(-3.43203 - 5.76781i) q^{66} +(0.918596 - 1.09474i) q^{67} +(1.14055 - 0.658497i) q^{68} +(-0.636737 + 0.548725i) q^{69} +(-1.20471 - 3.30993i) q^{70} +(0.438181 + 2.48505i) q^{71} +(6.67546 - 5.90761i) q^{72} +(8.28206 + 3.01442i) q^{73} +(-0.689912 - 0.822205i) q^{74} +(5.60624 - 16.0574i) q^{75} +(-0.359552 - 4.57302i) q^{76} +3.74147i q^{77} +(-1.62824 + 0.617017i) q^{78} +(-1.50043 + 4.12240i) q^{79} +(-2.98671 - 0.526637i) q^{80} +(-8.28356 + 3.51889i) q^{81} +(1.99336 - 0.725523i) q^{82} +(-3.66720 - 2.11726i) q^{83} +(-1.68315 + 0.319678i) q^{84} +(3.69054 + 3.09673i) q^{85} +(-4.30799 - 3.61483i) q^{86} +(7.38747 - 1.40309i) q^{87} +(10.2432 + 5.91392i) q^{88} +(7.56260 - 2.75256i) q^{89} +(9.88079 + 5.36304i) q^{90} +(0.955916 + 0.168554i) q^{91} +(0.174671 - 0.479906i) q^{92} +(7.98199 - 3.02474i) q^{93} +7.51939i q^{94} +(15.2698 - 6.95742i) q^{95} +(-2.95502 + 8.46379i) q^{96} +(-6.91522 - 8.24124i) q^{97} +(5.59517 + 2.03647i) q^{98} +(-7.91412 - 8.94277i) 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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