LMFDB - Embedded newform 483.2.q.f.85.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.3
Character	$\chi$	$=$	483.85
Dual form			483.2.q.f.358.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.723306 + 0.834739i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.111011 + 0.772099i) q^{4} +(-1.01603 - 2.22480i) q^{5} +(-0.157189 + 1.09328i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-2.58316 - 1.66009i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.723306 + 0.834739i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.111011 + 0.772099i) q^{4} +(-1.01603 - 2.22480i) q^{5} +(-0.157189 + 1.09328i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-2.58316 - 1.66009i) q^{8} +(0.415415 - 0.909632i) q^{9} +(2.59204 + 0.761090i) q^{10} +(-3.81879 - 4.40712i) q^{11} +(0.510817 + 0.589514i) q^{12} +(-5.27555 - 1.54904i) q^{13} +(-0.458834 + 1.00471i) q^{14} +(-2.05756 - 1.32232i) q^{15} +(1.75727 - 0.515982i) q^{16} +(-0.425265 + 2.95778i) q^{17} +(0.458834 + 1.00471i) q^{18} +(0.0285726 + 0.198727i) q^{19} +(1.60498 - 1.03146i) q^{20} +(0.654861 - 0.755750i) q^{21} +6.44095 q^{22} +(-3.64146 + 3.12086i) q^{23} -3.07060 q^{24} +(-0.643127 + 0.742208i) q^{25} +(5.10888 - 3.28328i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.324040 + 0.709548i) q^{28} +(1.01549 - 7.06290i) q^{29} +(2.59204 - 0.761090i) q^{30} +(-0.120549 - 0.0774724i) q^{31} +(1.71081 - 3.74616i) q^{32} +(-5.59524 - 1.64291i) q^{33} +(-2.16138 - 2.49437i) q^{34} +(-1.60168 - 1.84843i) q^{35} +(0.748442 + 0.219762i) q^{36} +(-1.71500 + 3.75533i) q^{37} +(-0.186552 - 0.119890i) q^{38} +(-5.27555 + 1.54904i) q^{39} +(-1.06881 + 7.43373i) q^{40} +(0.593129 + 1.29877i) q^{41} +(0.157189 + 1.09328i) q^{42} +(1.66555 - 1.07038i) q^{43} +(2.97881 - 3.43773i) q^{44} -2.44583 q^{45} +(0.0287839 - 5.29701i) q^{46} +10.6698 q^{47} +(1.19935 - 1.38413i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.154373 - 1.07369i) q^{50} +(1.24134 + 2.71816i) q^{51} +(0.610369 - 4.24521i) q^{52} +(9.05999 - 2.66025i) q^{53} +(0.929180 + 0.597148i) q^{54} +(-5.92496 + 12.9739i) q^{55} +(-2.94622 - 0.865089i) q^{56} +(0.131477 + 0.151732i) q^{57} +(5.16117 + 5.95631i) q^{58} +(-13.5935 - 3.99142i) q^{59} +(0.792546 - 1.73543i) q^{60} +(-2.72926 - 1.75399i) q^{61} +(0.151863 - 0.0445911i) q^{62} +(0.142315 - 0.989821i) q^{63} +(3.41126 + 7.46962i) q^{64} +(1.91383 + 13.3110i) q^{65} +(5.41847 - 3.48224i) q^{66} +(5.37406 - 6.20200i) q^{67} -2.33091 q^{68} +(-1.37613 + 4.59416i) q^{69} +2.70146 q^{70} +(6.41785 - 7.40659i) q^{71} +(-2.58316 + 1.66009i) q^{72} +(-1.64590 - 11.4475i) q^{73} +(-1.89425 - 4.14783i) q^{74} +(-0.139765 + 0.972086i) q^{75} +(-0.150265 + 0.0441218i) q^{76} +(-4.90573 - 3.15272i) q^{77} +(2.52279 - 5.52414i) q^{78} +(10.0097 + 2.93910i) q^{79} +(-2.93341 - 3.38534i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.51315 - 0.444301i) q^{82} +(-2.76414 + 6.05262i) q^{83} +(0.656210 + 0.421721i) q^{84} +(7.01257 - 2.05908i) q^{85} +(-0.311210 + 2.16452i) q^{86} +(-2.96421 - 6.49071i) q^{87} +(2.54830 + 17.7238i) q^{88} +(-10.2432 + 6.58292i) q^{89} +(1.76908 - 2.04163i) q^{90} -5.49827 q^{91} +(-2.81386 - 2.46512i) q^{92} -0.143297 q^{93} +(-7.71754 + 8.90652i) q^{94} +(0.413098 - 0.265482i) q^{95} +(-0.586099 - 4.07641i) q^{96} +(3.49448 + 7.65184i) q^{97} +(-0.157189 + 1.09328i) q^{98} +(-5.59524 + 1.64291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	−0.723306	+	0.834739i	−0.511454	+	0.590250i	−0.951470	−	0.307740i	$-0.900427\pi$
$2$	−0.723306	+	0.834739i	−0.511454	+	0.590250i	0.440016	+	0.897990i	$0.354973\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	0.111011	+	0.772099i	0.0555055	+	0.386050i
$5$	−1.01603	−	2.22480i	−0.454384	−	0.994963i	−0.988732	−	0.149698i	$-0.952170\pi$
$5$	−1.01603	−	2.22480i	−0.454384	−	0.994963i	0.534347	−	0.845265i	$-0.320557\pi$
$6$	−0.157189	+	1.09328i	−0.0641723	+	0.446328i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	−2.58316	−	1.66009i	−0.913284	−	0.586932i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	2.59204	+	0.761090i	0.819674	+	0.240678i
$11$	−3.81879	−	4.40712i	−1.15141	−	1.32880i	−0.935888	−	0.352298i	$-0.885400\pi$
$11$	−3.81879	−	4.40712i	−1.15141	−	1.32880i	−0.215521	−	0.976499i	$-0.569145\pi$
$12$	0.510817	+	0.589514i	0.147460	+	0.170178i
$13$	−5.27555	−	1.54904i	−1.46318	−	0.429627i	−0.549301	−	0.835625i	$-0.685106\pi$
$13$	−5.27555	−	1.54904i	−1.46318	−	0.429627i	−0.913874	+	0.405998i	$0.866924\pi$
$14$	−0.458834	+	1.00471i	−0.122628	+	0.268519i
$15$	−2.05756	−	1.32232i	−0.531260	−	0.341420i
$16$	1.75727	−	0.515982i	0.439319	−	0.128996i
$17$	−0.425265	+	2.95778i	−0.103142	+	0.717368i	0.870976	+	0.491326i	$0.163488\pi$
$17$	−0.425265	+	2.95778i	−0.103142	+	0.717368i	−0.974118	+	0.226042i	$0.927421\pi$
$18$	0.458834	+	1.00471i	0.108148	+	0.236811i
$19$	0.0285726	+	0.198727i	0.00655501	+	0.0455911i	0.992836	−	0.119482i	$-0.0381232\pi$
$19$	0.0285726	+	0.198727i	0.00655501	+	0.0455911i	−0.986281	+	0.165073i	$0.947214\pi$
$20$	1.60498	−	1.03146i	0.358884	−	0.230641i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	6.44095			1.37322
$23$	−3.64146	+	3.12086i	−0.759297	+	0.650744i
$23$	−3.64146	+	3.12086i	−0.759297	+	0.650744i
$24$	−3.07060			−0.626784
$25$	−0.643127	+	0.742208i	−0.128625	+	0.148442i
$26$	5.10888	−	3.28328i	1.00193	−	0.643904i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	0.324040	+	0.709548i	0.0612378	+	0.134092i
$29$	1.01549	−	7.06290i	0.188572	−	1.31155i	−0.647136	−	0.762374i	$-0.724034\pi$
$29$	1.01549	−	7.06290i	0.188572	−	1.31155i	0.835708	−	0.549173i	$-0.185057\pi$
$30$	2.59204	−	0.761090i	0.473239	−	0.138955i
$31$	−0.120549	−	0.0774724i	−0.0216513	−	0.0139145i	0.529770	−	0.848141i	$-0.322278\pi$
$31$	−0.120549	−	0.0774724i	−0.0216513	−	0.0139145i	−0.551422	+	0.834227i	$0.685914\pi$
$32$	1.71081	−	3.74616i	0.302432	−	0.662234i
$33$	−5.59524	−	1.64291i	−0.974006	−	0.285994i
$34$	−2.16138	−	2.49437i	−0.370674	−	0.427780i
$35$	−1.60168	−	1.84843i	−0.270733	−	0.312442i
$36$	0.748442	+	0.219762i	0.124740	+	0.0366271i
$37$	−1.71500	+	3.75533i	−0.281945	+	0.617373i	−0.996626	−	0.0820775i	$-0.973845\pi$
$37$	−1.71500	+	3.75533i	−0.281945	+	0.617373i	0.714681	+	0.699450i	$0.246572\pi$
$38$	−0.186552	−	0.119890i	−0.0302628	−	0.0194487i
$39$	−5.27555	+	1.54904i	−0.844765	+	0.248045i
$40$	−1.06881	+	7.43373i	−0.168994	+	1.17538i
$41$	0.593129	+	1.29877i	0.0926312	+	0.202834i	0.950276	−	0.311408i	$-0.100801\pi$
$41$	0.593129	+	1.29877i	0.0926312	+	0.202834i	−0.857645	+	0.514242i	$0.828073\pi$
$42$	0.157189	+	1.09328i	0.0242548	+	0.168696i
$43$	1.66555	−	1.07038i	0.253994	−	0.163232i	−0.407448	−	0.913228i	$-0.633581\pi$
$43$	1.66555	−	1.07038i	0.253994	−	0.163232i	0.661442	+	0.749996i	$0.269945\pi$
$44$	2.97881	−	3.43773i	0.449072	−	0.518257i
$45$	−2.44583			−0.364603
$46$	0.0287839	−	5.29701i	0.00424395	−	0.781001i
$47$	10.6698			1.55635			0.778177	−	0.628046i	$-0.216145\pi$
$47$	10.6698			1.55635			0.778177	+	0.628046i	$0.216145\pi$
$48$	1.19935	−	1.38413i	0.173112	−	0.199781i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.154373	−	1.07369i	−0.0218316	−	0.151842i
$51$	1.24134	+	2.71816i	0.173823	+	0.380619i
$52$	0.610369	−	4.24521i	0.0846430	−	0.588705i
$53$	9.05999	−	2.66025i	1.24448	−	0.365414i	0.407786	−	0.913077i	$-0.366301\pi$
$53$	9.05999	−	2.66025i	1.24448	−	0.365414i	0.836699	+	0.547664i	$0.184483\pi$
$54$	0.929180	+	0.597148i	0.126445	+	0.0812615i
$55$	−5.92496	+	12.9739i	−0.798921	+	1.74939i
$56$	−2.94622	−	0.865089i	−0.393706	−	0.115602i
$57$	0.131477	+	0.151732i	0.0174145	+	0.0200974i
$58$	5.16117	+	5.95631i	0.677695	+	0.782101i
$59$	−13.5935	−	3.99142i	−1.76973	−	0.519638i	−0.775926	−	0.630824i	$-0.782717\pi$
$59$	−13.5935	−	3.99142i	−1.76973	−	0.519638i	−0.993800	+	0.111186i	$0.964535\pi$
$60$	0.792546	−	1.73543i	0.102317	−	0.224044i
$61$	−2.72926	−	1.75399i	−0.349445	−	0.224575i	0.354129	−	0.935197i	$-0.384777\pi$
$61$	−2.72926	−	1.75399i	−0.349445	−	0.224575i	−0.703574	+	0.710622i	$0.748414\pi$
$62$	0.151863	−	0.0445911i	0.0192867	−	0.00566307i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	3.41126	+	7.46962i	0.426407	+	0.933702i
$65$	1.91383	+	13.3110i	0.237381	+	1.65102i
$66$	5.41847	−	3.48224i	0.666968	−	0.428634i
$67$	5.37406	−	6.20200i	0.656546	−	0.757694i	−0.325663	−	0.945486i	$-0.605587\pi$
$67$	5.37406	−	6.20200i	0.656546	−	0.757694i	0.982209	+	0.187792i	$0.0601329\pi$
$68$	−2.33091			−0.282664
$69$	−1.37613	+	4.59416i	−0.165666	+	0.553071i
$70$	2.70146			0.322887
$71$	6.41785	−	7.40659i	0.761659	−	0.879001i	−0.233985	−	0.972240i	$-0.575177\pi$
$71$	6.41785	−	7.40659i	0.761659	−	0.879001i	0.995644	+	0.0932392i	$0.0297221\pi$
$72$	−2.58316	+	1.66009i	−0.304428	+	0.195644i
$73$	−1.64590	−	11.4475i	−0.192638	−	1.33982i	−0.824992	−	0.565145i	$-0.808820\pi$
$73$	−1.64590	−	11.4475i	−0.192638	−	1.33982i	0.632354	−	0.774680i	$-0.282089\pi$
$74$	−1.89425	−	4.14783i	−0.220202	−	0.482176i
$75$	−0.139765	+	0.972086i	−0.0161387	+	0.112247i
$76$	−0.150265	+	0.0441218i	−0.0172366	+	0.00506112i
$77$	−4.90573	−	3.15272i	−0.559060	−	0.359286i
$78$	2.52279	−	5.52414i	0.285650	−	0.625486i
$79$	10.0097	+	2.93910i	1.12617	+	0.330674i	0.791203	−	0.611554i	$-0.209455\pi$
$79$	10.0097	+	2.93910i	1.12617	+	0.330674i	0.334971	+	0.942228i	$0.391273\pi$
$80$	−2.93341	−	3.38534i	−0.327965	−	0.378492i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−1.51315	−	0.444301i	−0.167099	−	0.0490648i
$83$	−2.76414	+	6.05262i	−0.303404	+	0.664361i	−0.998511	−	0.0545444i	$-0.982629\pi$
$83$	−2.76414	+	6.05262i	−0.303404	+	0.664361i	0.695108	+	0.718906i	$0.255357\pi$
$84$	0.656210	+	0.421721i	0.0715984	+	0.0460135i
$85$	7.01257	−	2.05908i	0.760620	−	0.223338i
$86$	−0.311210	+	2.16452i	−0.0335587	+	0.233406i
$87$	−2.96421	−	6.49071i	−0.317796	−	0.695877i
$88$	2.54830	+	17.7238i	0.271650	+	1.88937i
$89$	−10.2432	+	6.58292i	−1.08578	+	0.697789i	−0.955886	−	0.293739i	$-0.905100\pi$
$89$	−10.2432	+	6.58292i	−1.08578	+	0.697789i	−0.129895	+	0.991528i	$0.541464\pi$
$90$	1.76908	−	2.04163i	0.186478	−	0.215207i
$91$	−5.49827			−0.576376
$92$	−2.81386	−	2.46512i	−0.293365	−	0.257006i
$93$	−0.143297			−0.0148592
$94$	−7.71754	+	8.90652i	−0.796004	+	0.918637i
$95$	0.413098	−	0.265482i	0.0423830	−	0.0272379i
$96$	−0.586099	−	4.07641i	−0.0598185	−	0.416047i
$97$	3.49448	+	7.65184i	0.354811	+	0.776927i	0.999918	+	0.0128348i	$0.00408556\pi$
$97$	3.49448	+	7.65184i	0.354811	+	0.776927i	−0.645107	+	0.764092i	$0.723187\pi$
$98$	−0.157189	+	1.09328i	−0.0158785	+	0.110438i
$99$	−5.59524	+	1.64291i	−0.562343	+	0.165119i
$100$	−0.644453	−	0.414165i	−0.0644453	−	0.0414165i
$101$	1.01418	−	2.22074i	0.100914	−	0.220971i	−0.852440	−	0.522825i	$-0.824878\pi$
$101$	1.01418	−	2.22074i	0.100914	−	0.220971i	0.953354	+	0.301854i	$0.0976054\pi$
$102$	−3.16683	−	0.929864i	−0.313563	−	0.0920703i
$103$	5.18064	+	5.97877i	0.510463	+	0.589106i	0.951217	−	0.308522i	$-0.0998343\pi$
$103$	5.18064	+	5.97877i	0.510463	+	0.589106i	−0.440754	+	0.897628i	$0.645289\pi$
$104$	11.0560	+	12.7593i	1.08413	+	1.25116i
$105$	−2.34676	−	0.689070i	−0.229020	−	0.0672463i
$106$	−4.33252	+	9.48690i	−0.420812	+	0.921450i
$107$	5.40913	+	3.47624i	0.522921	+	0.336061i	0.775326	−	0.631561i	$-0.217585\pi$
$107$	5.40913	+	3.47624i	0.522921	+	0.336061i	−0.252406	+	0.967621i	$0.581222\pi$
$108$	0.748442	−	0.219762i	0.0720188	−	0.0211466i
$109$	0.496251	−	3.45150i	0.0475322	−	0.330594i	−0.952156	−	0.305613i	$-0.901138\pi$
$109$	0.496251	−	3.45150i	0.0475322	−	0.330594i	0.999688	−	0.0249806i	$-0.00795241\pi$
$110$	−6.54423	−	14.3299i	−0.623968	−	1.36630i
$111$	0.587534	+	4.08639i	0.0557662	+	0.387863i
$112$	1.54072	−	0.990163i	0.145585	−	0.0935616i
$113$	−8.93615	+	10.3129i	−0.840642	+	0.970152i	−0.999854	−	0.0170920i	$-0.994559\pi$
$113$	−8.93615	+	10.3129i	−0.840642	+	0.970152i	0.159212	+	0.987244i	$0.449105\pi$
$114$	−0.221755			−0.0207693
$115$	10.6432	+	4.93064i	0.992479	+	0.459784i
$116$	5.56599			0.516789
$117$	−3.60060	+	4.15532i	−0.332876	+	0.384159i
$118$	13.1641	−	8.46003i	1.21185	−	0.778809i
$119$	0.425265	+	2.95778i	0.0389840	+	0.271140i
$120$	3.11984	+	6.83150i	0.284801	+	0.623627i
$121$	−3.27408	+	22.7717i	−0.297643	+	2.07016i
$122$	3.43821	−	1.00955i	0.311281	−	0.0914003i
$123$	1.20114	+	0.771926i	0.108303	+	0.0696022i
$124$	0.0464340	−	0.101676i	0.00416990	−	0.00913081i
$125$	−9.42907	−	2.76863i	−0.843362	−	0.247633i
$126$	0.723306	+	0.834739i	0.0644372	+	0.0743645i
$127$	−10.5875	−	12.2186i	−0.939489	−	1.08423i	−0.996309	−	0.0858432i	$-0.972642\pi$
$127$	−10.5875	−	12.2186i	−0.939489	−	1.08423i	0.0568200	−	0.998384i	$-0.481904\pi$
$128$	−0.799558	−	0.234772i	−0.0706716	−	0.0207511i
$129$	0.822457	−	1.80093i	0.0724133	−	0.158563i
$130$	−12.4955	−	8.03035i	−1.09592	−	0.704308i
$131$	−16.4460	+	4.82898i	−1.43689	+	0.421910i	−0.905186	−	0.425017i	$-0.860268\pi$
$131$	−16.4460	+	4.82898i	−1.43689	+	0.421910i	−0.531709	+	0.846927i	$0.678450\pi$
$132$	0.647356	−	4.50246i	0.0563451	−	0.391889i
$133$	0.0834032	+	0.182627i	0.00723197	+	0.0158358i
$134$	1.28996	+	8.97188i	0.111436	+	0.775052i
$135$	−2.05756	+	1.32232i	−0.177087	+	0.113807i
$136$	6.00872	−	6.93444i	0.515244	−	0.594623i
$137$	9.64019			0.823617			0.411808	−	0.911270i	$-0.364897\pi$
$137$	9.64019			0.823617			0.411808	+	0.911270i	$0.364897\pi$
$138$	−2.83956	−	4.47169i	−0.241720	−	0.380655i
$139$	8.14753			0.691065			0.345532	−	0.938407i	$-0.387698\pi$
$139$	8.14753			0.691065			0.345532	+	0.938407i	$0.387698\pi$
$140$	1.24937	−	1.44185i	0.105591	−	0.121859i
$141$	8.97602	−	5.76854i	0.755917	−	0.485799i
$142$	1.54051	+	10.7145i	0.129277	+	0.899138i
$143$	13.3194	+	29.1655i	1.11383	+	2.43894i
$144$	0.260644	−	1.81282i	0.0217203	−	0.151068i
$145$	−16.7453	+	4.91688i	−1.39063	+	0.408324i
$146$	10.7461	+	6.90612i	0.889357	+	0.571555i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	−3.08987	−	0.907269i	−0.253986	−	0.0745770i
$149$	1.65757	+	1.91294i	0.135794	+	0.156714i	0.819573	−	0.572974i	$-0.194211\pi$
$149$	1.65757	+	1.91294i	0.135794	+	0.156714i	−0.683780	+	0.729689i	$0.739665\pi$
$150$	−0.710346	−	0.819783i	−0.0579995	−	0.0669350i
$151$	−16.1426	−	4.73988i	−1.31366	−	0.385726i	−0.451461	−	0.892291i	$-0.649097\pi$
$151$	−16.1426	−	4.73988i	−1.31366	−	0.385726i	−0.862202	+	0.506565i	$0.830915\pi$
$152$	0.256098	−	0.560777i	0.0207723	−	0.0454850i
$153$	2.51383	+	1.61554i	0.203231	+	0.130609i
$154$	6.18005	−	1.81463i	0.498002	−	0.146227i
$155$	−0.0498786	+	0.346913i	−0.00400635	+	0.0278648i
$156$	−1.78166	−	3.90129i	−0.142647	−	0.312353i
$157$	−1.77851	−	12.3698i	−0.141941	−	0.987218i	−0.928931	−	0.370253i	$-0.879271\pi$
$157$	−1.77851	−	12.3698i	−0.141941	−	0.987218i	0.786990	−	0.616965i	$-0.211638\pi$
$158$	−9.69342	+	6.22958i	−0.771167	+	0.495599i
$159$	6.18351	−	7.13615i	0.490384	−	0.565933i
$160$	−10.0727			−0.796319
$161$	−2.61471	+	4.02036i	−0.206068	+	0.316849i
$162$	1.10452			0.0867792
$163$	5.07031	−	5.85145i	0.397137	−	0.458321i	−0.521600	−	0.853190i	$-0.674665\pi$
$163$	5.07031	−	5.85145i	0.397137	−	0.458321i	0.918737	+	0.394869i	$0.129210\pi$
$164$	−0.936936	+	0.602132i	−0.0731624	+	0.0470186i
$165$	2.02980	+	14.1176i	0.158020	+	1.09905i
$166$	−3.05304	−	6.68523i	−0.236962	−	0.518874i
$167$	1.99690	−	13.8888i	0.154525	−	1.07474i	−0.753988	−	0.656888i	$-0.771873\pi$
$167$	1.99690	−	13.8888i	0.154525	−	1.07474i	0.908513	−	0.417856i	$-0.137218\pi$
$168$	−2.94622	+	0.865089i	−0.227306	+	0.0667431i
$169$	14.4956	+	9.31578i	1.11505	+	0.716598i
$170$	−3.35344	+	7.34301i	−0.257197	+	0.563184i
$171$	0.192638	+	0.0565636i	0.0147314	+	0.00432553i
$172$	1.01134	+	1.16715i	0.0771138	+	0.0889940i
$173$	5.67797	+	6.55272i	0.431688	+	0.498194i	0.929362	−	0.369170i	$-0.120358\pi$
$173$	5.67797	+	6.55272i	0.431688	+	0.498194i	−0.497674	+	0.867364i	$0.665812\pi$
$174$	7.56207	+	2.22043i	0.573279	+	0.168330i
$175$	−0.407972	+	0.893334i	−0.0308398	+	0.0675297i
$176$	−8.98466	−	5.77409i	−0.677244	−	0.435239i
$177$	−13.5935	+	3.99142i	−1.02175	+	0.300013i
$178$	1.91396	−	13.3119i	0.143458	−	0.997769i
$179$	−2.74721	−	6.01555i	−0.205336	−	0.449623i	0.778746	−	0.627340i	$-0.215856\pi$
$179$	−2.74721	−	6.01555i	−0.205336	−	0.449623i	−0.984082	+	0.177716i	$0.943129\pi$
$180$	−0.271514	−	1.88842i	−0.0202375	−	0.140755i
$181$	−4.26654	+	2.74194i	−0.317129	+	0.203807i	−0.689515	−	0.724271i	$-0.742176\pi$
$181$	−4.26654	+	2.74194i	−0.317129	+	0.203807i	0.372386	+	0.928078i	$0.378540\pi$
$182$	3.97693	−	4.58962i	0.294790	−	0.340206i
$183$	−3.24427			−0.239824
$184$	14.5874	−	2.01651i	1.07540	−	0.148659i
$185$	10.0974			0.742374
$186$	0.103648	−	0.119616i	0.00759982	−	0.00877067i
$187$	14.6593	−	9.42096i	1.07199	−	0.688929i
$188$	1.18447	+	8.23816i	0.0863862	+	0.600829i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	−0.0771880	+	0.536854i	−0.00559980	+	0.0389475i
$191$	−19.6812	+	5.77891i	−1.42408	+	0.418147i	−0.900882	−	0.434064i	$-0.857079\pi$
$191$	−19.6812	+	5.77891i	−1.42408	+	0.418147i	−0.523197	+	0.852212i	$0.675261\pi$
$192$	6.90811	+	4.43957i	0.498550	+	0.320399i
$193$	1.24909	−	2.73512i	0.0899112	−	0.196878i	−0.859334	−	0.511414i	$-0.829122\pi$
$193$	1.24909	−	2.73512i	0.0899112	−	0.196878i	0.949245	+	0.314536i	$0.101849\pi$
$194$	−8.91487	−	2.61764i	−0.640051	−	0.187936i
$195$	8.80646	+	10.1632i	0.630644	+	0.727802i
$196$	0.510817	+	0.589514i	0.0364869	+	0.0421081i
$197$	−3.27837	−	0.962615i	−0.233574	−	0.0685835i	0.162851	−	0.986651i	$-0.447931\pi$
$197$	−3.27837	−	0.962615i	−0.233574	−	0.0685835i	−0.396425	+	0.918067i	$0.629749\pi$
$198$	2.67567	−	5.85890i	0.190151	−	0.416374i
$199$	−13.8826	−	8.92180i	−0.984111	−	0.632450i	−0.0535418	−	0.998566i	$-0.517051\pi$
$199$	−13.8826	−	8.92180i	−0.984111	−	0.632450i	−0.930569	+	0.366116i	$0.880687\pi$
$200$	2.89343	−	0.849589i	0.204597	−	0.0600750i
$201$	1.16789	−	8.12289i	0.0823770	−	0.572944i
$202$	1.12018	+	2.45284i	0.0788153	+	0.172581i
$203$	−1.01549	−	7.06290i	−0.0712735	−	0.495718i
$204$	−1.96089	+	1.26019i	−0.137290	+	0.0882306i
$205$	2.28687	−	2.63919i	0.159722	−	0.184329i
$206$	−8.73790			−0.608799
$207$	1.32612	+	4.60884i	0.0921715	+	0.320337i
$208$	−10.0699			−0.698220
$209$	0.766701	−	0.884821i	0.0530338	−	0.0612043i
$210$	2.27262	−	1.46052i	0.156825	−	0.100786i
$211$	−2.31249	−	16.0837i	−0.159198	−	1.10725i	−0.900115	−	0.435652i	$-0.856518\pi$
$211$	−2.31249	−	16.0837i	−0.159198	−	1.10725i	0.740917	−	0.671597i	$-0.234391\pi$
$212$	3.05974	+	6.69989i	0.210144	+	0.460150i
$213$	1.39473	−	9.70057i	0.0955655	−	0.664672i
$214$	−6.81421	+	2.00083i	−0.465810	+	0.136774i
$215$	−4.07365	−	2.61798i	−0.277821	−	0.178545i
$216$	−1.27558	+	2.79312i	−0.0867919	+	0.190048i
$217$	−0.137493	−	0.0403715i	−0.00933362	−	0.00274060i
$218$	2.52216	+	2.91073i	0.170823	+	0.197140i
$219$	−7.57359	−	8.74038i	−0.511775	−	0.590620i
$220$	−10.6748	−	3.13441i	−0.719697	−	0.211322i
$221$	6.82524	−	14.9452i	0.459115	−	1.00532i
$222$	−3.83604	−	2.46527i	−0.257458	−	0.165458i
$223$	13.2555	−	3.89216i	0.887653	−	0.260638i	0.194046	−	0.980992i	$-0.437839\pi$
$223$	13.2555	−	3.89216i	0.887653	−	0.260638i	0.693607	+	0.720354i	$0.256021\pi$
$224$	0.586099	−	4.07641i	0.0391604	−	0.272366i
$225$	0.407972	+	0.893334i	0.0271981	+	0.0595556i
$226$	−2.14499	−	14.9187i	−0.142682	−	0.992378i
$227$	9.31919	−	5.98908i	0.618536	−	0.397509i	−0.193513	−	0.981098i	$-0.561988\pi$
$227$	9.31919	−	5.98908i	0.618536	−	0.397509i	0.812050	+	0.583588i	$0.198352\pi$
$228$	−0.102557	+	0.118357i	−0.00679201	+	0.00783839i
$229$	26.9585			1.78147			0.890733	−	0.454527i	$-0.150192\pi$
$229$	26.9585			1.78147			0.890733	+	0.454527i	$0.150192\pi$
$230$	−11.8141	+	5.31790i	−0.778995	+	0.350652i
$231$	−5.83146			−0.383682
$232$	−14.3483	+	16.5588i	−0.942009	+	1.08714i
$233$	9.84225	−	6.32523i	0.644787	−	0.414379i	−0.176971	−	0.984216i	$-0.556630\pi$
$233$	9.84225	−	6.32523i	0.644787	−	0.414379i	0.821758	+	0.569837i	$0.192994\pi$
$234$	−0.864270	−	6.01113i	−0.0564991	−	0.392960i
$235$	−10.8409	−	23.7383i	−0.707182	−	1.54851i
$236$	1.57274	−	10.9386i	0.102377	−	0.712045i
$237$	10.0097	−	2.93910i	0.650197	−	0.190915i
$238$	−2.77657	−	1.78440i	−0.179979	−	0.115665i
$239$	8.99998	−	19.7072i	0.582161	−	1.27475i	−0.357904	−	0.933758i	$-0.616509\pi$
$239$	8.99998	−	19.7072i	0.582161	−	1.27475i	0.940065	−	0.340996i	$-0.110764\pi$
$240$	−4.29799	−	1.26201i	−0.277434	−	0.0814621i
$241$	−11.0460	−	12.7478i	−0.711538	−	0.821159i	0.278724	−	0.960371i	$-0.410088\pi$
$241$	−11.0460	−	12.7478i	−0.711538	−	0.821159i	−0.990263	+	0.139212i	$0.955543\pi$
$242$	−16.6403	−	19.2039i	−1.06968	−	1.23447i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	1.05127	−	2.30197i	0.0673009	−	0.147368i
$245$	−2.05756	−	1.32232i	−0.131453	−	0.0844796i
$246$	−1.51315	+	0.444301i	−0.0964749	+	0.0283276i
$247$	0.157100	−	1.09266i	0.00999605	−	0.0695240i
$248$	0.182787	+	0.400247i	0.0116070	+	0.0254157i
$249$	0.946952	+	6.58619i	0.0600106	+	0.417383i
$250$	9.13118	−	5.86826i	0.577507	−	0.371141i
$251$	6.77404	−	7.81765i	0.427573	−	0.493446i	−0.500556	−	0.865704i	$-0.666871\pi$
$251$	6.77404	−	7.81765i	0.427573	−	0.493446i	0.928129	+	0.372258i	$0.121416\pi$
$252$	0.780039			0.0491378
$253$	27.6600	+	4.13044i	1.73897	+	0.259678i
$254$	17.8574			1.12047
$255$	4.78613	−	5.52349i	0.299719	−	0.345894i
$256$	−13.0419	+	8.38154i	−0.815121	+	0.523846i
$257$	2.14011	+	14.8848i	0.133496	+	0.928487i	0.940947	+	0.338553i	$0.109937\pi$
$257$	2.14011	+	14.8848i	0.133496	+	0.928487i	−0.807451	+	0.589935i	$0.799154\pi$
$258$	0.908419	+	1.98916i	0.0565557	+	0.123840i
$259$	−0.587534	+	4.08639i	−0.0365076	+	0.253916i
$260$	−10.0649	+	2.95533i	−0.624200	+	0.183282i
$261$	−6.00279	−	3.85776i	−0.371563	−	0.238789i
$262$	7.86455	−	17.2210i	0.485874	−	1.06391i
$263$	15.6827	+	4.60486i	0.967037	+	0.283948i	0.726863	−	0.686782i	$-0.240977\pi$
$263$	15.6827	+	4.60486i	0.967037	+	0.283948i	0.240174	+	0.970730i	$0.422796\pi$
$264$	11.7260	+	13.5325i	0.721685	+	0.832869i
$265$	−15.1238	−	17.4538i	−0.929048	−	1.07218i
$266$	−0.212772	−	0.0624756i	−0.0130459	−	0.00383062i
$267$	−5.05816	+	11.0758i	−0.309554	+	0.677829i
$268$	5.38514	+	3.46082i	0.328950	+	0.211403i
$269$	−7.06487	+	2.07443i	−0.430753	+	0.126480i	−0.489920	−	0.871768i	$-0.662974\pi$
$269$	−7.06487	+	2.07443i	−0.430753	+	0.126480i	0.0591667	+	0.998248i	$0.481156\pi$
$270$	0.384458	−	2.67397i	0.0233974	−	0.162732i
$271$	−7.33481	−	16.0610i	−0.445558	−	0.975635i	−0.990545	−	0.137191i	$-0.956193\pi$
$271$	−7.33481	−	16.0610i	−0.445558	−	0.975635i	0.544987	−	0.838445i	$-0.316535\pi$
$272$	0.778857	+	5.41707i	0.0472251	+	0.328458i
$273$	−4.62544	+	2.97259i	−0.279944	+	0.179909i
$274$	−6.97280	+	8.04704i	−0.421242	+	0.486140i
$275$	5.72697			0.345349
$276$	−3.69991	−	0.552504i	−0.222708	−	0.0332568i
$277$	29.9958			1.80227			0.901137	−	0.433534i	$-0.142734\pi$
$277$	29.9958			1.80227			0.901137	+	0.433534i	$0.142734\pi$
$278$	−5.89316	+	6.80107i	−0.353448	+	0.407901i
$279$	−0.120549	+	0.0774724i	−0.00721710	+	0.00463815i
$280$	1.06881	+	7.43373i	0.0638736	+	0.444250i
$281$	3.28906	+	7.20204i	0.196209	+	0.429638i	0.982007	−	0.188846i	$-0.0604746\pi$
$281$	3.28906	+	7.20204i	0.196209	+	0.429638i	−0.785798	+	0.618483i	$0.787747\pi$
$282$	−1.67718	+	11.6651i	−0.0998747	+	0.694644i
$283$	−30.4935	+	8.95370i	−1.81265	+	0.532242i	−0.998806	−	0.0488426i	$-0.984447\pi$
$283$	−30.4935	+	8.95370i	−1.81265	+	0.532242i	−0.813843	+	0.581085i	$0.802629\pi$
$284$	6.43108	+	4.13300i	0.381614	+	0.245249i
$285$	0.203990	−	0.446676i	0.0120833	−	0.0264588i
$286$	−33.9796	−	9.97731i	−2.00925	−	0.589970i
$287$	0.935009	+	1.07906i	0.0551919	+	0.0636948i
$288$	−2.69693	−	3.11242i	−0.158918	−	0.183401i
$289$	7.74375	+	2.27377i	0.455515	+	0.133751i
$290$	8.00770	−	17.5344i	0.470228	−	1.02966i
$291$	7.07664	+	4.54788i	0.414840	+	0.266602i
$292$	8.65587	−	2.54159i	0.506546	−	0.148735i
$293$	1.19056	−	8.28049i	0.0695530	−	0.483752i	−0.925037	−	0.379876i	$-0.875967\pi$
$293$	1.19056	−	8.28049i	0.0695530	−	0.483752i	0.994590	−	0.103875i	$-0.0331243\pi$
$294$	0.458834	+	1.00471i	0.0267597	+	0.0585956i
$295$	4.93136	+	34.2983i	0.287115	+	1.99693i
$296$	10.6643	−	6.85355i	0.619851	−	0.398354i
$297$	−3.81879	+	4.40712i	−0.221589	+	0.255727i
$298$	−2.79574			−0.161953
$299$	24.0451	−	10.8235i	1.39056	−	0.625939i
$300$	−0.766062			−0.0442286
$301$	1.29652	−	1.49627i	0.0747303	−	0.0862434i
$302$	15.6326	−	10.0464i	0.899553	−	0.578108i
$303$	−0.347441	−	2.41651i	−0.0199600	−	0.138825i
$304$	0.152750	+	0.334475i	0.00876080	+	0.0191835i
$305$	−1.12926	+	7.85417i	−0.0646612	+	0.449729i
$306$	−3.16683	+	0.929864i	−0.181035	+	0.0531568i
$307$	−22.9930	−	14.7767i	−1.31228	−	0.843352i	−0.317789	−	0.948161i	$-0.602940\pi$
$307$	−22.9930	−	14.7767i	−1.31228	−	0.843352i	−0.994492	+	0.104809i	$0.966577\pi$
$308$	1.88962	−	4.13770i	0.107671	−	0.235767i
$309$	7.59060	+	2.22880i	0.431814	+	0.126792i
$310$	−0.253505	−	0.292560i	−0.0143981	−	0.0166163i
$311$	8.48831	+	9.79603i	0.481328	+	0.555482i	0.943528	−	0.331294i	$-0.107485\pi$
$311$	8.48831	+	9.79603i	0.481328	+	0.555482i	−0.462200	+	0.886776i	$0.652940\pi$
$312$	16.1991	+	4.75650i	0.917096	+	0.269284i
$313$	2.75518	−	6.03301i	0.155732	−	0.341006i	−0.815643	−	0.578555i	$-0.803617\pi$
$313$	2.75518	−	6.03301i	0.155732	−	0.341006i	0.971375	+	0.237549i	$0.0763441\pi$
$314$	11.6120	+	7.46256i	0.655302	+	0.421137i
$315$	−2.34676	+	0.689070i	−0.132225	+	0.0388247i
$316$	−1.15809	+	8.05471i	−0.0651478	+	0.453113i
$317$	−1.76242	−	3.85916i	−0.0989874	−	0.216752i	0.853659	−	0.520832i	$-0.174378\pi$
$317$	−1.76242	−	3.85916i	−0.0989874	−	0.216752i	−0.952647	+	0.304080i	$0.901651\pi$
$318$	1.48426	+	10.3232i	0.0832330	+	0.578898i
$319$	−35.0050	+	22.4963i	−1.95990	+	1.25955i
$320$	13.1525	−	15.1788i	0.735246	−	0.848519i
$321$	6.42985			0.358879
$322$	−1.46472	−	5.09055i	−0.0816257	−	0.283685i
$323$	−0.599943			−0.0333817
$324$	0.510817	−	0.589514i	0.0283787	−	0.0327508i
$325$	4.54256	−	2.91933i	0.251976	−	0.161935i
$326$	1.21705	+	8.46478i	0.0674062	+	0.468821i
$327$	−1.44855	−	3.17188i	−0.0801050	−	0.175406i
$328$	0.623937	−	4.33958i	0.0344512	−	0.239613i
$329$	10.2376	−	3.00604i	0.564418	−	0.165728i
$330$	−13.2527	−	8.51697i	−0.729535	−	0.468844i
$331$	4.96411	−	10.8699i	0.272852	−	0.597463i	−0.722753	−	0.691106i	$-0.757124\pi$
$331$	4.96411	−	10.8699i	0.272852	−	0.597463i	0.995606	+	0.0936425i	$0.0298511\pi$
$332$	−4.98007	−	1.46228i	−0.273317	−	0.0802531i
$333$	2.70353	+	3.12004i	0.148153	+	0.170977i
$334$	10.1491	+	11.7127i	0.555335	+	0.640891i
$335$	−19.2585	−	5.65479i	−1.05220	−	0.308954i
$336$	0.760817	−	1.66596i	0.0415060	−	0.0908854i
$337$	−3.55207	−	2.28277i	−0.193493	−	0.124351i	0.440307	−	0.897847i	$-0.354870\pi$
$337$	−3.55207	−	2.28277i	−0.193493	−	0.124351i	−0.633800	+	0.773497i	$0.718506\pi$
$338$	−18.2610	+	5.36192i	−0.993269	+	0.291650i
$339$	−1.94201	+	13.5070i	−0.105476	+	0.733598i
$340$	2.36829	+	5.18582i	0.128438	+	0.281241i
$341$	0.118923	+	0.827127i	0.00644003	+	0.0447914i
$342$	−0.186552	+	0.119890i	−0.0100876	+	0.00648290i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	−6.07932			−0.327775
$345$	11.6193	−	1.60621i	0.625562	−	0.0864753i
$346$	−9.57672			−0.514848
$347$	−21.7130	+	25.0582i	−1.16562	+	1.34519i	−0.238178	+	0.971222i	$0.576550\pi$
$347$	−21.7130	+	25.0582i	−1.16562	+	1.34519i	−0.927440	+	0.373973i	$0.877995\pi$
$348$	4.68241	−	3.00920i	0.251003	−	0.161310i
$349$	−0.448561	−	3.11981i	−0.0240109	−	0.167000i	0.974288	−	0.225307i	$-0.0723386\pi$
$349$	−0.448561	−	3.11981i	−0.0240109	−	0.167000i	−0.998299	+	0.0583078i	$0.981430\pi$
$350$	−0.450612	−	0.986704i	−0.0240862	−	0.0527415i
$351$	−0.782486	+	5.44231i	−0.0417660	+	0.290489i
$352$	−23.0430	+	6.76604i	−1.22820	+	0.360631i
$353$	2.47065	+	1.58779i	0.131499	+	0.0845095i	0.604737	−	0.796425i	$-0.293278\pi$
$353$	2.47065	+	1.58779i	0.131499	+	0.0845095i	−0.473237	+	0.880935i	$0.656915\pi$
$354$	6.50048	−	14.2341i	0.345497	−	0.756532i
$355$	−22.9990	−	6.75311i	−1.22066	−	0.358418i
$356$	−6.21978	−	7.17801i	−0.329648	−	0.380434i
$357$	1.95685	+	2.25833i	0.103568	+	0.119523i
$358$	7.00849	+	2.05788i	0.370410	+	0.108762i
$359$	4.12084	−	9.02339i	0.217490	−	0.476236i	−0.769167	−	0.639047i	$-0.779329\pi$
$359$	4.12084	−	9.02339i	0.217490	−	0.476236i	0.986657	+	0.162811i	$0.0520561\pi$
$360$	6.31796	+	4.06031i	0.332986	+	0.213997i
$361$	18.1917	−	5.34156i	0.957457	−	0.281135i
$362$	0.797208	−	5.54471i	0.0419003	−	0.291423i
$363$	9.55699	+	20.9269i	0.501612	+	1.09838i
$364$	−0.610369	−	4.24521i	−0.0319920	−	0.222510i
$365$	−23.7961	+	15.2928i	−1.24554	+	0.800463i
$366$	2.34660	−	2.70812i	0.122659	−	0.141556i
$367$	−10.7769			−0.562551			−0.281275	−	0.959627i	$-0.590757\pi$
$367$	−10.7769			−0.562551			−0.281275	+	0.959627i	$0.590757\pi$
$368$	−4.78874	+	7.36314i	−0.249630	+	0.383830i
$369$	1.42780			0.0743282
$370$	−7.30350	+	8.42868i	−0.379691	+	0.438186i
$371$	7.94351	−	5.10499i	0.412407	−	0.265038i
$372$	−0.0159076	−	0.110640i	−0.000824770	−	0.00573640i
$373$	5.90359	+	12.9271i	0.305676	+	0.669338i	0.998667	−	0.0516085i	$-0.0164348\pi$
$373$	5.90359	+	12.9271i	0.305676	+	0.669338i	−0.692991	+	0.720946i	$0.743708\pi$
$374$	−2.73911	+	19.0509i	−0.141636	+	0.985100i
$375$	−9.42907	+	2.76863i	−0.486915	+	0.142971i
$376$	−27.5618	−	17.7129i	−1.42139	−	0.913473i
$377$	−16.2980	+	35.6877i	−0.839390	+	1.83801i
$378$	1.05978	+	0.311179i	0.0545091	+	0.0160053i
$379$	−11.9320	−	13.7703i	−0.612906	−	0.707332i	0.361438	−	0.932396i	$-0.382286\pi$
$379$	−11.9320	−	13.7703i	−0.612906	−	0.707332i	−0.974344	+	0.225065i	$0.927741\pi$
$380$	0.250837	+	0.289481i	0.0128677	+	0.0148501i
$381$	−15.5127	−	4.55493i	−0.794738	−	0.233356i
$382$	9.41161	−	20.6086i	0.481540	−	1.05443i
$383$	−6.99010	−	4.49226i	−0.357177	−	0.229544i	0.349729	−	0.936851i	$-0.386274\pi$
$383$	−6.99010	−	4.49226i	−0.357177	−	0.229544i	−0.706907	+	0.707307i	$0.749910\pi$
$384$	−0.799558	+	0.234772i	−0.0408023	+	0.0119806i
$385$	−2.02980	+	14.1176i	−0.103448	+	0.719498i
$386$	1.37964	+	3.02099i	0.0702217	+	0.153764i
$387$	−0.281761	−	1.95969i	−0.0143227	−	0.0996167i
$388$	−5.52006	+	3.54753i	−0.280238	+	0.180098i
$389$	−16.8102	+	19.4000i	−0.852310	+	0.983618i	−0.999985	−	0.00541795i	$-0.998275\pi$
$389$	−16.8102	+	19.4000i	−0.852310	+	0.983618i	0.147676	+	0.989036i	$0.452821\pi$
$390$	−14.8534			−0.752130
$391$	−7.68224	−	12.0978i	−0.388508	−	0.611814i
$392$	−3.07060			−0.155089
$393$	−11.2245	+	12.9538i	−0.566202	+	0.653432i
$394$	3.17480	−	2.04032i	0.159944	−	0.102790i
$395$	−3.63123	−	25.2557i	−0.182707	−	1.27075i
$396$	−1.88962	−	4.13770i	−0.0949572	−	0.207927i
$397$	−2.65020	+	18.4326i	−0.133010	+	0.925105i	0.808590	+	0.588372i	$0.200231\pi$
$397$	−2.65020	+	18.4326i	−0.133010	+	0.925105i	−0.941600	+	0.336733i	$0.890678\pi$
$398$	17.4887	−	5.13516i	0.876631	−	0.257402i
$399$	0.168899	+	0.108545i	0.00845553	+	0.00543404i
$400$	−0.747185	+	1.63611i	−0.0373592	+	0.0818053i
$401$	−12.0976	−	3.55219i	−0.604127	−	0.177388i	−0.0346562	−	0.999399i	$-0.511034\pi$
$401$	−12.0976	−	3.55219i	−0.604127	−	0.177388i	−0.569471	+	0.822012i	$0.692852\pi$
$402$	5.93575	+	6.85022i	0.296048	+	0.341658i
$403$	0.515957	+	0.595446i	0.0257016	+	0.0296613i
$404$	1.82721	+	0.536518i	0.0909072	+	0.0266928i
$405$	−1.01603	+	2.22480i	−0.0504872	+	0.110551i
$406$	6.63019	+	4.26097i	0.329051	+	0.211468i
$407$	23.0994	−	6.78261i	1.14500	−	0.336201i
$408$	1.30582	−	9.08218i	0.0646478	−	0.449635i
$409$	13.7771	+	30.1676i	0.681233	+	1.49169i	0.861331	+	0.508043i	$0.169631\pi$
$409$	13.7771	+	30.1676i	0.681233	+	1.49169i	−0.180099	+	0.983649i	$0.557642\pi$
$410$	0.548929	+	3.81789i	0.0271097	+	0.188552i
$411$	8.10984	−	5.21188i	0.400029	−	0.257083i
$412$	−4.04110	+	4.66368i	−0.199091	+	0.229763i
$413$	−14.1674			−0.697132
$414$	−4.80637	−	2.22664i	−0.236220	−	0.109433i
$415$	16.2744			0.798877
$416$	−14.8285	+	17.1129i	−0.727025	+	0.839031i
$417$	6.85414	−	4.40489i	0.335649	−	0.215708i
$418$	0.184035	+	1.27999i	0.00900145	+	0.0626064i
$419$	−2.04930	−	4.48733i	−0.100115	−	0.219221i	0.852946	−	0.521998i	$-0.174813\pi$
$419$	−2.04930	−	4.48733i	−0.100115	−	0.219221i	−0.953061	+	0.302778i	$0.902086\pi$
$420$	0.271514	−	1.88842i	0.0132485	−	0.0921456i
$421$	31.3898	−	9.21689i	1.52985	−	0.449204i	0.594843	−	0.803842i	$-0.297214\pi$
$421$	31.3898	−	9.21689i	1.52985	−	0.449204i	0.935004	+	0.354638i	$0.115396\pi$
$422$	15.0984	+	9.70312i	0.734976	+	0.472341i
$423$	4.43240	−	9.70561i	0.215511	−	0.471903i
$424$	−27.8196	−	8.16858i	−1.35104	−	0.396701i
$425$	−1.92179	−	2.21787i	−0.0932206	−	0.107582i
$426$	7.08863	+	8.18072i	0.343445	+	0.396357i
$427$	−3.11286	−	0.914017i	−0.150642	−	0.0442324i
$428$	−2.08353	+	4.56229i	−0.100711	+	0.220527i
$429$	26.9731	+	17.3345i	1.30227	+	0.836919i
$430$	5.13183	−	1.50684i	0.247479	−	0.0726663i
$431$	3.19777	−	22.2410i	0.154031	−	1.07131i	−0.755342	−	0.655331i	$-0.772529\pi$
$431$	3.19777	−	22.2410i	0.154031	−	1.07131i	0.909373	−	0.415981i	$-0.136562\pi$
$432$	−0.760817	−	1.66596i	−0.0366048	−	0.0801534i
$433$	2.83802	+	19.7388i	0.136386	+	0.948588i	0.936981	+	0.349381i	$0.113608\pi$
$433$	2.83802	+	19.7388i	0.136386	+	0.948588i	−0.800594	+	0.599207i	$0.795483\pi$
$434$	0.133149	−	0.0855697i	0.00639136	−	0.00410748i
$435$	−11.4288	+	13.1896i	−0.547970	+	0.632391i
$436$	2.71999			0.130264
$437$	−0.724246	−	0.634486i	−0.0346454	−	0.0303516i
$438$	12.7740			0.610363
$439$	7.81878	−	9.02335i	0.373170	−	0.430661i	−0.537839	−	0.843048i	$-0.680759\pi$
$439$	7.81878	−	9.02335i	0.373170	−	0.430661i	0.911009	+	0.412387i	$0.135305\pi$
$440$	36.8429	−	23.6775i	1.75642	−	1.12878i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	7.53860	+	16.5072i	0.358575	+	0.785169i
$443$	−3.61529	+	25.1449i	−0.171768	+	1.19467i	0.703380	+	0.710814i	$0.251673\pi$
$443$	−3.61529	+	25.1449i	−0.171768	+	1.19467i	−0.875148	+	0.483856i	$0.839236\pi$
$444$	−3.08987	+	0.907269i	−0.146639	+	0.0430571i
$445$	25.0532	+	16.1007i	1.18764	+	0.763247i
$446$	−6.33883	+	13.8801i	−0.300152	+	0.657242i
$447$	2.42865	+	0.713117i	0.114871	+	0.0337293i
$448$	5.37751	+	6.20598i	0.254064	+	0.293205i
$449$	2.40476	+	2.77524i	0.113488	+	0.130972i	0.809651	−	0.586912i	$-0.199656\pi$
$449$	2.40476	+	2.77524i	0.113488	+	0.130972i	−0.696163	+	0.717884i	$0.745111\pi$
$450$	−1.04079	−	0.305603i	−0.0490633	−	0.0144063i
$451$	3.45881	−	7.57373i	0.162869	−	0.356633i
$452$	−8.95456	−	5.75475i	−0.421187	−	0.270681i
$453$	−16.1426	+	4.73988i	−0.758443	+	0.222699i
$454$	−1.74130	+	12.1110i	−0.0817234	+	0.568399i
$455$	5.58643	+	12.2326i	0.261896	+	0.573472i
$456$	−0.0877353	−	0.610212i	−0.00410858	−	0.0285758i
$457$	−5.87256	+	3.77407i	−0.274707	+	0.176543i	−0.670739	−	0.741693i	$-0.734023\pi$
$457$	−5.87256	+	3.77407i	−0.274707	+	0.176543i	0.396033	+	0.918236i	$0.370387\pi$
$458$	−19.4992	+	22.5033i	−0.911139	+	1.05151i
$459$	2.98820			0.139477
$460$	−2.62543	+	8.76493i	−0.122411	+	0.408667i
$461$	12.5251			0.583354			0.291677	−	0.956517i	$-0.405787\pi$
$461$	12.5251			0.583354			0.291677	+	0.956517i	$0.405787\pi$
$462$	4.21793	−	4.86775i	0.196236	−	0.226468i
$463$	27.3983	−	17.6078i	1.27331	−	0.818305i	0.283260	−	0.959043i	$-0.408584\pi$
$463$	27.3983	−	17.6078i	1.27331	−	0.818305i	0.990047	+	0.140738i	$0.0449477\pi$
$464$	−1.85983	−	12.9354i	−0.0863406	−	0.600512i
$465$	0.145595	+	0.318809i	0.00675181	+	0.0147844i
$466$	−1.83904	+	12.7908i	−0.0851917	+	0.592522i
$467$	23.8965	−	7.01664i	1.10580	−	0.324691i	0.322644	−	0.946520i	$-0.395428\pi$
$467$	23.8965	−	7.01664i	1.10580	−	0.324691i	0.783153	+	0.621829i	$0.213610\pi$
$468$	−3.60802	−	2.31874i	−0.166781	−	0.107184i
$469$	3.40907	−	7.46482i	0.157416	−	0.344693i
$470$	27.6566	+	8.12070i	1.27570	+	0.374580i
$471$	−8.18380	−	9.44461i	−0.377090	−	0.435185i
$472$	28.4881	+	32.8770i	1.31127	+	1.51329i
$473$	−11.0777	−	3.25271i	−0.509353	−	0.149560i
$474$	−4.78666	+	10.4813i	−0.219858	+	0.481423i
$475$	−0.165873	−	0.106600i	−0.00761077	−	0.00489114i
$476$	−2.23649	+	0.656694i	−0.102509	+	0.0300995i
$477$	1.34380	−	9.34636i	0.0615286	−	0.427941i
$478$	9.94065	+	21.7670i	0.454675	+	0.995599i
$479$	−0.811181	−	5.64189i	−0.0370638	−	0.257784i	0.962862	−	0.269995i	$-0.0870221\pi$
$479$	−0.811181	−	5.64189i	−0.0370638	−	0.257784i	−0.999925	+	0.0122109i	$0.996113\pi$
$480$	−8.47371	+	5.44572i	−0.386770	+	0.248562i
$481$	14.8648	−	17.1548i	0.677775	−	0.782194i
$482$	18.6308			0.848608
$483$	−0.0260601	+	4.79576i	−0.00118578	+	0.218215i
$484$	−17.9455			−0.815704
$485$	13.4733	−	15.5491i	0.611793	−	0.706047i
$486$	0.929180	−	0.597148i	0.0421485	−	0.0270872i
$487$	−1.63857	−	11.3965i	−0.0742506	−	0.516424i	−0.992674	−	0.120825i	$-0.961446\pi$
$487$	−1.63857	−	11.3965i	−0.0742506	−	0.516424i	0.918423	−	0.395599i	$-0.129463\pi$
$488$	4.13831	+	9.06165i	0.187333	+	0.410201i
$489$	1.10188	−	7.66377i	0.0498289	−	0.346568i
$490$	2.59204	−	0.761090i	0.117096	−	0.0343826i
$491$	−33.3191	−	21.4129i	−1.50367	−	0.966349i	−0.994393	−	0.105744i	$-0.966277\pi$
$491$	−33.3191	−	21.4129i	−1.50367	−	0.966349i	−0.509274	−	0.860604i	$-0.670086\pi$
$492$	−0.462664	+	1.01309i	−0.0208585	+	0.0456737i
$493$	20.4587	+	6.00721i	0.921412	+	0.270551i
$494$	0.798451	+	0.921462i	0.0359240	+	0.0414585i
$495$	9.34011	+	10.7791i	0.419807	+	0.484483i
$496$	−0.251813	−	0.0739389i	−0.0113067	−	0.00331995i
$497$	4.07120	−	8.91469i	0.182618	−	0.399879i
$498$	−6.18269	−	3.97337i	−0.277053	−	0.178051i
$499$	3.86944	−	1.13617i	0.173220	−	0.0508619i	−0.193972	−	0.981007i	$-0.562137\pi$
$499$	3.86944	−	1.13617i	0.173220	−	0.0508619i	0.367192	+	0.930145i	$0.380319\pi$
$500$	1.09092	−	7.58753i	0.0487875	−	0.339325i
$501$	−5.82893	−	12.7636i	−0.260417	−	0.570234i
$502$	1.62600	+	11.3091i	0.0725721	+	0.504750i
$503$	23.0998	−	14.8453i	1.02997	−	0.661920i	0.0874815	−	0.996166i	$-0.472118\pi$
$503$	23.0998	−	14.8453i	1.02997	−	0.661920i	0.942486	+	0.334246i	$0.108482\pi$
$504$	−2.01082	+	2.32061i	−0.0895690	+	0.103368i
$505$	−5.97114			−0.265712
$506$	−23.4545	+	20.1013i	−1.04268	+	0.893612i
$507$	17.2310			0.765255
$508$	8.25866	−	9.53100i	0.366419	−	0.422870i
$509$	−36.7706	+	23.6310i	−1.62983	+	1.04743i	−0.680688	+	0.732573i	$0.738319\pi$
$509$	−36.7706	+	23.6310i	−1.62983	+	1.04743i	−0.949140	+	0.314854i	$0.898045\pi$
$510$	1.14884	+	7.99034i	0.0508714	+	0.353818i
$511$	−4.80435	−	10.5201i	−0.212532	−	0.465380i
$512$	2.67409	−	18.5987i	0.118179	−	0.821954i
$513$	0.192638	−	0.0565636i	0.00850518	−	0.00249735i
$514$	−13.9729	−	8.97982i	−0.616317	−	0.396083i
$515$	8.03790	−	17.6005i	0.354192	−	0.775573i
$516$	1.48180	+	0.435095i	0.0652325	+	0.0191540i
$517$	−40.7458	−	47.0232i	−1.79200	−	2.06808i
$518$	−2.98610	−	3.44615i	−0.131202	−	0.151415i
$519$	8.31928	+	2.44276i	0.365176	+	0.107225i
$520$	17.1537	−	37.5614i	0.752241	−	1.64718i
$521$	23.5032	+	15.1046i	1.02970	+	0.661745i	0.942417	−	0.334439i	$-0.108547\pi$
$521$	23.5032	+	15.1046i	1.02970	+	0.661745i	0.0872781	+	0.996184i	$0.472183\pi$
$522$	7.56207	−	2.22043i	0.330983	−	0.0971854i
$523$	−2.91454	+	20.2711i	−0.127444	+	0.886393i	0.821333	+	0.570448i	$0.193231\pi$
$523$	−2.91454	+	20.2711i	−0.127444	+	0.886393i	−0.948778	+	0.315945i	$0.897679\pi$
$524$	−5.55414	−	12.1619i	−0.242634	−	0.531294i
$525$	0.139765	+	0.972086i	0.00609984	+	0.0424253i
$526$	−15.1872	+	9.76025i	−0.662195	+	0.425567i
$527$	0.280412	−	0.323613i	0.0122149	−	0.0140968i
$528$	−10.6801			−0.464791
$529$	3.52046	−	22.7290i	0.153063	−	0.988216i
$530$	25.5085			1.10802
$531$	−9.27767	+	10.7070i	−0.402617	+	0.464644i
$532$	−0.131748	+	0.0846692i	−0.00571199	+	0.00367087i
$533$	−1.11723	−	7.77052i	−0.0483927	−	0.336579i
$534$	−5.58683	−	12.2334i	−0.241766	−	0.529393i
$535$	2.23809	−	15.5662i	0.0967610	−	0.672987i
$536$	−24.1779	+	7.09928i	−1.04433	+	0.306642i
$537$	−5.56335	−	3.57535i	−0.240076	−	0.154288i
$538$	3.37845	−	7.39778i	0.145655	−	0.318941i
$539$	−5.59524	−	1.64291i	−0.241004	−	0.0707652i
$540$	−1.24937	−	1.44185i	−0.0537644	−	0.0620474i
$541$	−8.89131	−	10.2611i	−0.382267	−	0.441160i	0.531709	−	0.846927i	$-0.321550\pi$
$541$	−8.89131	−	10.2611i	−0.382267	−	0.441160i	−0.913977	+	0.405767i	$0.867004\pi$
$542$	18.7120	+	5.49435i	0.803751	+	0.236003i
$543$	−2.10684	+	4.61333i	−0.0904130	+	0.197977i
$544$	10.3528	+	6.65333i	0.443872	+	0.285259i
$545$	−8.18313	+	2.40278i	−0.350527	+	0.102924i
$546$	0.864270	−	6.01113i	0.0369873	−	0.257253i
$547$	14.3430	+	31.4068i	0.613262	+	1.34286i	0.920320	+	0.391166i	$0.127928\pi$
$547$	14.3430	+	31.4068i	0.613262	+	1.34286i	−0.307058	+	0.951691i	$0.599345\pi$
$548$	1.07017	+	7.44318i	0.0457153	+	0.317957i
$549$	−2.72926	+	1.75399i	−0.116482	+	0.0748583i
$550$	−4.14235	+	4.78053i	−0.176630	+	0.203842i
$551$	1.43260			0.0610310
$552$	11.1815	−	9.58293i	0.475916	−	0.407876i
$553$	10.4322			0.443623
$554$	−21.6961	+	25.0387i	−0.921781	+	1.06379i
$555$	8.49446	−	5.45906i	0.360570	−	0.231724i
$556$	0.904466	+	6.29070i	0.0383579	+	0.266785i
$557$	17.9386	+	39.2801i	0.760084	+	1.66435i	0.747348	+	0.664433i	$0.231327\pi$
$557$	17.9386	+	39.2801i	0.760084	+	1.66435i	0.0127363	+	0.999919i	$0.495946\pi$
$558$	0.0225248	−	0.156664i	0.000953552	−	0.00663210i
$559$	−10.4448	+	3.06686i	−0.441767	+	0.129714i
$560$	−3.76835	−	2.42177i	−0.159242	−	0.102338i
$561$	7.23883	−	15.8508i	0.305624	−	0.669223i
$562$	−8.39082	−	2.46377i	−0.353946	−	0.103928i
$563$	7.90114	+	9.11841i	0.332994	+	0.384295i	0.897412	−	0.441194i	$-0.145445\pi$
$563$	7.90114	+	9.11841i	0.332994	+	0.384295i	−0.564418	+	0.825489i	$0.690899\pi$
$564$	5.45032	+	6.29001i	0.229500	+	0.264857i
$565$	32.0235	+	9.40296i	1.34724	+	0.395585i
$566$	14.5821	−	31.9304i	0.612932	−	1.34213i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	−28.8740	+	8.47816i	−1.21152	+	0.355736i
$569$	4.69069	−	32.6245i	0.196644	−	1.36769i	−0.617292	−	0.786734i	$-0.711770\pi$
$569$	4.69069	−	32.6245i	0.196644	−	1.36769i	0.813936	−	0.580955i	$-0.197321\pi$
$570$	0.225311	+	0.493361i	0.00943722	+	0.0206646i
$571$	−4.41460	−	30.7042i	−0.184745	−	1.28493i	−0.845356	−	0.534204i	$-0.820612\pi$
$571$	−4.41460	−	30.7042i	−0.184745	−	1.28493i	0.660610	−	0.750729i	$-0.270298\pi$
$572$	−21.0400	+	13.5216i	−0.879728	+	0.565367i
$573$	−13.4325	+	15.5020i	−0.561152	+	0.647604i
$574$	−1.57703			−0.0658240
$575$	0.0255932	−	4.70983i	0.00106731	−	0.196414i
$576$	8.21169			0.342154
$577$	−23.6241	+	27.2637i	−0.983486	+	1.13500i	0.00735600	+	0.999973i	$0.497658\pi$
$577$	−23.6241	+	27.2637i	−0.983486	+	1.13500i	−0.990842	+	0.135030i	$0.956887\pi$
$578$	−7.49910	+	4.81938i	−0.311922	+	0.200460i
$579$	−0.427918	−	2.97623i	−0.0177837	−	0.123688i
$580$	−5.65524	−	12.3832i	−0.234821	−	0.514186i
$581$	−0.946952	+	6.58619i	−0.0392862	+	0.273241i
$582$	−8.91487	+	2.61764i	−0.369533	+	0.108505i
$583$	−46.3223	−	29.7695i	−1.91847	−	1.23293i
$584$	−14.7523	+	32.3029i	−0.610453	+	1.33671i
$585$	12.9031	+	3.78869i	0.533478	+	0.156643i
$586$	6.05092	+	6.98313i	0.249961	+	0.288471i
$587$	24.2854	+	28.0269i	1.00237	+	1.15679i	0.987614	+	0.156901i	$0.0501503\pi$
$587$	24.2854	+	28.0269i	1.00237	+	1.15679i	0.0147517	+	0.999891i	$0.495304\pi$
$588$	0.748442	+	0.219762i	0.0308652	+	0.00906285i
$589$	0.0119514	−	0.0261700i	0.000492451	−	0.00107832i
$590$	−32.1971	−	20.6918i	−1.32553	−	0.851868i
$591$	−3.27837	+	0.962615i	−0.134854	+	0.0395967i
$592$	−1.07605	+	7.48406i	−0.0442252	+	0.307593i
$593$	−9.68781	−	21.2134i	−0.397831	−	0.871128i	−0.997486	−	0.0708692i	$-0.977423\pi$
$593$	−9.68781	−	21.2134i	−0.397831	−	0.871128i	0.599655	−	0.800259i	$-0.295305\pi$
$594$	−0.916643	−	6.37539i	−0.0376103	−	0.261585i
$595$	6.14841	−	3.95134i	0.252060	−	0.161989i
$596$	−1.29297	+	1.49217i	−0.0529622	+	0.0611216i
$597$	−16.5023			−0.675393
$598$	−8.35714	+	27.9001i	−0.341749	+	1.14092i
$599$	12.1056			0.494623			0.247311	−	0.968936i	$-0.420453\pi$
$599$	12.1056			0.494623			0.247311	+	0.968936i	$0.420453\pi$
$600$	1.97479	−	2.27903i	0.0806204	−	0.0930409i
$601$	6.54838	−	4.20839i	0.267114	−	0.171664i	−0.400227	−	0.916416i	$-0.631069\pi$
$601$	6.54838	−	4.20839i	0.267114	−	0.171664i	0.667341	+	0.744752i	$0.267432\pi$
$602$	0.311210	+	2.16452i	0.0126840	+	0.0882191i
$603$	−3.40907	−	7.46482i	−0.138828	−	0.303991i
$604$	1.86766	−	12.9898i	0.0759938	−	0.528549i
$605$	53.9892	−	15.8527i	2.19497	−	0.644502i
$606$	2.26846	+	1.45785i	0.0921499	+	0.0592211i
$607$	9.81290	−	21.4872i	0.398293	−	0.872140i	−0.599147	−	0.800639i	$-0.704494\pi$
$607$	9.81290	−	21.4872i	0.398293	−	0.872140i	0.997440	−	0.0715016i	$-0.0227791\pi$
$608$	0.793346	+	0.232947i	0.0321744	+	0.00944727i
$609$	−4.67278	−	5.39267i	−0.189351	−	0.218522i
$610$	−5.73939	−	6.62361i	−0.232381	−	0.268182i
$611$	−56.2892	−	16.5280i	−2.27722	−	0.668651i
$612$	−0.968295	+	2.12027i	−0.0391410	+	0.0857069i
$613$	16.7998	+	10.7966i	0.678536	+	0.436069i	0.833994	−	0.551774i	$-0.186049\pi$
$613$	16.7998	+	10.7966i	0.678536	+	0.436069i	−0.155458	+	0.987843i	$0.549685\pi$
$614$	28.9657	−	8.50510i	1.16896	−	0.343238i
$615$	0.496985	−	3.45661i	0.0200404	−	0.139384i
$616$	7.43846	+	16.2880i	0.299704	+	0.656260i
$617$	5.35903	+	37.2729i	0.215747	+	1.50055i	0.753500	+	0.657448i	$0.228364\pi$
$617$	5.35903	+	37.2729i	0.215747	+	1.50055i	−0.537753	+	0.843102i	$0.680727\pi$
$618$	−7.35079	+	4.72407i	−0.295692	+	0.190030i
$619$	18.1341	−	20.9279i	0.728872	−	0.841163i	−0.263472	−	0.964667i	$-0.584868\pi$
$619$	18.1341	−	20.9279i	0.728872	−	0.841163i	0.992344	+	0.123504i	$0.0394133\pi$
$620$	−0.273389			−0.0109796
$621$	3.60733	+	3.16025i	0.144757	+	0.126816i
$622$	−14.3168			−0.574050
$623$	−7.97368	+	9.20212i	−0.319459	+	0.368675i
$624$	−8.47132	+	5.44419i	−0.339124	+	0.217942i
$625$	4.11943	+	28.6513i	0.164777	+	1.14605i
$626$	3.04315	+	6.66357i	0.121629	+	0.266330i
$627$	0.166620	−	1.15887i	0.00665417	−	0.0462807i
$628$	9.35329	−	2.74637i	0.373237	−	0.109592i
$629$	−10.3781	−	6.66962i	−0.413803	−	0.265935i
$630$	1.12223	−	2.45734i	0.0447107	−	0.0979027i
$631$	−13.1988	−	3.87553i	−0.525437	−	0.154282i	0.00824707	−	0.999966i	$-0.497375\pi$
$631$	−13.1988	−	3.87553i	−0.525437	−	0.154282i	−0.533685	+	0.845684i	$0.679193\pi$
$632$	−20.9773	−	24.2091i	−0.834433	−	0.962987i
$633$	−10.6409	−	12.2803i	−0.422938	−	0.488096i
$634$	4.49616	+	1.32019i	0.178566	+	0.0524316i
$635$	−16.4268	+	35.9697i	−0.651877	+	1.42741i
$636$	6.19625	+	3.98209i	0.245697	+	0.157900i
$637$	−5.27555	+	1.54904i	−0.209025	+	0.0613753i
$638$	6.54073	−	45.4918i	0.258950	−	1.80104i
$639$	−4.07120	−	8.91469i	−0.161054	−	0.352660i
$640$	0.290058	+	2.01740i	0.0114655	+	0.0797446i
$641$	16.2902	−	10.4691i	0.643424	−	0.413503i	−0.177834	−	0.984060i	$-0.556909\pi$
$641$	16.2902	−	10.4691i	0.643424	−	0.413503i	0.821258	+	0.570557i	$0.193273\pi$
$642$	−4.65075	+	5.36725i	−0.183550	+	0.211828i
$643$	−25.0782			−0.988988			−0.494494	−	0.869181i	$-0.664647\pi$
$643$	−25.0782			−0.988988			−0.494494	+	0.869181i	$0.664647\pi$
$644$	−3.39438	−	1.57251i	−0.133757	−	0.0619655i
$645$	−4.84236			−0.190668
$646$	0.433942	−	0.500796i	0.0170732	−	0.0197035i
$647$	−12.5919	+	8.09235i	−0.495040	+	0.318143i	−0.764230	−	0.644944i	$-0.776881\pi$
$647$	−12.5919	+	8.09235i	−0.495040	+	0.318143i	0.269189	+	0.963087i	$0.413244\pi$
$648$	0.436993	+	3.03935i	0.0171667	+	0.119397i
$649$	34.3202	+	75.1507i	1.34718	+	2.94992i
$650$	−0.848784	+	5.90342i	−0.0332921	+	0.231551i
$651$	−0.137493	+	0.0403715i	−0.00538877	+	0.00158228i
$652$	5.08076	+	3.26521i	0.198978	+	0.127875i
$653$	6.34073	−	13.8843i	0.248132	−	0.543333i	−0.744051	−	0.668123i	$-0.767098\pi$
$653$	6.34073	−	13.8843i	0.248132	−	0.543333i	0.992183	+	0.124789i	$0.0398255\pi$
$654$	3.69544	+	1.08508i	0.144503	+	0.0424300i
$655$	27.4533	+	31.6828i	1.07269	+	1.23795i
$656$	1.71243	+	1.97625i	0.0668593	+	0.0771598i
$657$	−11.0967	−	3.25829i	−0.432924	−	0.127118i
$658$	−4.89567	+	10.7200i	−0.190853	+	0.417910i
$659$	−21.2578	−	13.6616i	−0.828086	−	0.532178i	0.0565833	−	0.998398i	$-0.481979\pi$
$659$	−21.2578	−	13.6616i	−0.828086	−	0.532178i	−0.884669	+	0.466219i	$0.845616\pi$
$660$	−10.6748	+	3.13441i	−0.415517	+	0.122007i
$661$	−2.14439	+	14.9146i	−0.0834073	+	0.580110i	0.904665	+	0.426122i	$0.140121\pi$
$661$	−2.14439	+	14.9146i	−0.0834073	+	0.580110i	−0.988073	+	0.153988i	$0.950788\pi$
$662$	5.48296	+	12.0060i	0.213101	+	0.466626i
$663$	−2.33822	−	16.2627i	−0.0908090	−	0.631591i
$664$	17.1881	−	11.0461i	0.667028	−	0.428673i
$665$	0.321570	−	0.371111i	0.0124699	−	0.0143911i
$666$	−4.55990			−0.176693
$667$	18.3445	+	28.8885i	0.710300	+	1.11857i
$668$	10.9452			0.423481
$669$	9.04696	−	10.4407i	0.349776	−	0.403663i
$670$	18.6500	−	11.9857i	0.720514	−	0.463046i
$671$	2.69243	+	18.7263i	0.103940	+	0.722920i
$672$	−1.71081	−	3.74616i	−0.0659961	−	0.144511i
$673$	2.44858	−	17.0302i	0.0943858	−	0.656468i	−0.886621	−	0.462496i	$-0.846954\pi$
$673$	2.44858	−	17.0302i	0.0943858	−	0.656468i	0.981007	−	0.193972i	$-0.0621370\pi$
$674$	4.47475	−	1.31391i	0.172361	−	0.0506098i
$675$	0.826180	+	0.530954i	0.0317997	+	0.0204364i
$676$	−5.58353	+	12.2262i	−0.214751	+	0.470239i
$677$	−36.1295	−	10.6086i	−1.38857	−	0.407720i	−0.499825	−	0.866126i	$-0.666602\pi$
$677$	−36.1295	−	10.6086i	−1.38857	−	0.407720i	−0.888743	+	0.458406i	$0.848421\pi$
$678$	−9.87014	−	11.3907i	−0.379060	−	0.437459i
$679$	5.50870	+	6.35738i	0.211405	+	0.243974i
$680$	−21.5328	−	6.32261i	−0.825747	−	0.242461i
$681$	4.60186	−	10.0767i	0.176344	−	0.386139i
$682$	−0.776453	−	0.498996i	−0.0297319	−	0.0191075i
$683$	21.7341	−	6.38169i	0.831630	−	0.244189i	0.161913	−	0.986805i	$-0.448234\pi$
$683$	21.7341	−	6.38169i	0.831630	−	0.244189i	0.669717	+	0.742616i	$0.266415\pi$
$684$	−0.0222878	+	0.155015i	−0.000852194	+	0.00592714i
$685$	−9.79476	−	21.4475i	−0.374239	−	0.819468i
$686$	0.157189	+	1.09328i	0.00600152	+	0.0417415i
$687$	22.6789	−	14.5748i	0.865254	−	0.556065i
$688$	2.37453	−	2.74035i	0.0905281	−	0.104475i
$689$	−51.9173			−1.97789
$690$	−7.06354	+	10.8609i	−0.268904	+	0.413466i
$691$	−13.7911			−0.524639			−0.262320	−	0.964981i	$-0.584487\pi$
$691$	−13.7911			−0.524639			−0.262320	+	0.964981i	$0.584487\pi$
$692$	−4.42903	+	5.11138i	−0.168367	+	0.194305i
$693$	−4.90573	+	3.15272i	−0.186353	+	0.119762i
$694$	−5.21189	−	36.2495i	−0.197841	−	1.37601i
$695$	−8.27817	−	18.1267i	−0.314009	−	0.687584i
$696$	−3.11817	+	21.6874i	−0.118194	+	0.822058i
$697$	−4.09372	+	1.20202i	−0.155061	+	0.0455299i
$698$	2.92867	+	1.88214i	0.110852	+	0.0712402i
$699$	4.86015	−	10.6422i	0.183828	−	0.402526i
$700$	−0.735032	−	0.215825i	−0.0277816	−	0.00815741i
$701$	−12.2051	−	14.0854i	−0.460980	−	0.532000i	0.476900	−	0.878957i	$-0.341760\pi$
$701$	−12.2051	−	14.0854i	−0.460980	−	0.532000i	−0.937881	+	0.346958i	$0.887215\pi$
$702$	−3.97693	−	4.58962i	−0.150100	−	0.173224i
$703$	−0.795289	−	0.233518i	−0.0299949	−	0.00880729i
$704$	19.8926	−	43.5587i	0.749731	−	1.64168i
$705$	−21.9538	−	14.1089i	−0.826829	−	0.531371i
$706$	−3.11242	+	0.913890i	−0.117138	+	0.0343947i
$707$	0.347441	−	2.41651i	0.0130669	−	0.0908821i
$708$	−4.59080	−	10.0525i	−0.172533	−	0.377794i
$709$	1.33280	+	9.26986i	0.0500545	+	0.348137i	0.999423	+	0.0339715i	$0.0108156\pi$
$709$	1.33280	+	9.26986i	0.0500545	+	0.348137i	−0.949368	+	0.314165i	$0.898275\pi$
$710$	22.2724	−	14.3136i	0.835868	−	0.537180i
$711$	6.83166	−	7.88415i	0.256207	−	0.295679i
$712$	37.3881			1.40118
$713$	0.680756	−	0.0941052i	0.0254945	−	0.00352427i
$714$	−3.30052			−0.123519
$715$	51.3545	−	59.2662i	1.92055	−	2.21643i
$716$	4.33963	−	2.78891i	0.162180	−	0.104227i
$717$	−3.08326	−	21.4445i	−0.115146	−	0.800860i
$718$	4.55155	+	9.96650i	0.169862	+	0.371947i
$719$	−0.0733463	+	0.510135i	−0.00273536	+	0.0190248i	−0.991143	−	0.132796i	$-0.957605\pi$
$719$	−0.0733463	+	0.510135i	−0.00273536	+	0.0190248i	0.988408	+	0.151821i	$0.0485136\pi$
$720$	−4.29799	+	1.26201i	−0.160177	+	0.0470322i
$721$	6.65520	+	4.27704i	0.247853	+	0.159285i
$722$	−8.69934	+	19.0489i	−0.323756	+	0.708927i
$723$	−16.1845	−	4.75220i	−0.601909	−	0.176736i
$724$	−2.59068	−	2.98980i	−0.0962819	−	0.111115i
$725$	4.58905	+	5.29605i	0.170433	+	0.196690i
$726$	−24.3811	−	7.15894i	−0.904868	−	0.265693i
$727$	7.10116	−	15.5494i	0.263367	−	0.576694i	−0.731037	−	0.682338i	$-0.760963\pi$
$727$	7.10116	−	15.5494i	0.263367	−	0.576694i	0.994404	+	0.105644i	$0.0336904\pi$
$728$	14.2029	+	9.12765i	0.526394	+	0.338293i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	4.44633	−	30.9249i	0.164566	−	1.14458i
$731$	2.45766	+	5.38153i	0.0909000	+	0.199043i
$732$	−0.360150	−	2.50490i	−0.0133115	−	0.0925838i
$733$	−41.4363	+	26.6295i	−1.53048	+	0.983583i	−0.540668	+	0.841236i	$0.681828\pi$
$733$	−41.4363	+	26.6295i	−1.53048	+	0.983583i	−0.989817	+	0.142346i	$0.954535\pi$
$734$	7.79501	−	8.99592i	0.287719	−	0.332046i
$735$	−2.44583			−0.0902158
$736$	5.46138	+	18.9807i	0.201309	+	0.699638i
$737$	−47.8554			−1.76277
$738$	−1.03274	+	1.19184i	−0.0380155	+	0.0438722i
$739$	−29.9109	+	19.2226i	−1.10029	+	0.707114i	−0.959156	−	0.282877i	$-0.908711\pi$
$739$	−29.9109	+	19.2226i	−1.10029	+	0.707114i	−0.141134	+	0.989990i	$0.545075\pi$
$740$	1.12092	+	7.79618i	0.0412059	+	0.286593i
$741$	−0.458573	−	1.00414i	−0.0168461	−	0.0368878i
$742$	−1.48426	+	10.3232i	−0.0544888	+	0.378978i
$743$	43.6117	−	12.8056i	1.59996	−	0.469790i	0.644424	−	0.764669i	$-0.277097\pi$
$743$	43.6117	−	12.8056i	1.59996	−	0.469790i	0.955535	+	0.294879i	$0.0952792\pi$
$744$	0.370159	+	0.237887i	0.0135707	+	0.00872136i
$745$	2.57177	−	5.63139i	0.0942224	−	0.206318i
$746$	−15.0608	−	4.42226i	−0.551416	−	0.161910i
$747$	4.35739	+	5.02870i	0.159429	+	0.183990i
$748$	8.90126	+	10.2726i	0.325462	+	0.375604i
$749$	6.16939	+	1.81150i	0.225425	+	0.0661907i
$750$	4.50902	−	9.87338i	0.164646	−	0.360525i
$751$	25.6531	+	16.4863i	0.936096	+	0.601593i	0.917285	−	0.398230i	$-0.130376\pi$
$751$	25.6531	+	16.4863i	0.936096	+	0.601593i	0.0188110	+	0.999823i	$0.494012\pi$
$752$	18.7498	−	5.50544i	0.683735	−	0.200763i
$753$	1.47214	−	10.2389i	0.0536477	−	0.373128i
$754$	−18.0015	−	39.4177i	−0.655574	−	1.43551i
$755$	5.85608	+	40.7299i	0.213124	+	1.48231i
$756$	0.656210	−	0.421721i	0.0238661	−	0.0153378i
$757$	−1.77388	+	2.04716i	−0.0644727	+	0.0744055i	−0.787070	−	0.616864i	$-0.788403\pi$
$757$	−1.77388	+	2.04716i	−0.0644727	+	0.0744055i	0.722597	+	0.691270i	$0.242948\pi$
$758$	20.1251			0.730976
$759$	25.5021	−	11.4794i	0.925669	−	0.416675i
$760$	−1.50782			−0.0546945
$761$	−12.4965	+	14.4218i	−0.452999	+	0.522788i	−0.935605	−	0.353049i	$-0.885145\pi$
$761$	−12.4965	+	14.4218i	−0.452999	+	0.522788i	0.482606	+	0.875838i	$0.339690\pi$
$762$	15.0226	−	9.65442i	0.544210	−	0.349743i
$763$	−0.496251	−	3.45150i	−0.0179655	−	0.124953i
$764$	−6.64672	−	14.5543i	−0.240470	−	0.526556i
$765$	1.04013	−	7.23423i	0.0376058	−	0.261554i
$766$	8.80584	−	2.58563i	0.318168	−	0.0934226i
$767$	65.5305	+	42.1139i	2.36617	+	1.52064i
$768$	−6.44017	+	14.1020i	−0.232389	+	0.508862i
$769$	−16.4066	−	4.81740i	−0.591636	−	0.173720i	−0.0278094	−	0.999613i	$-0.508853\pi$
$769$	−16.4066	−	4.81740i	−0.591636	−	0.173720i	−0.563827	+	0.825893i	$0.690671\pi$
$770$	−10.3163	−	11.9057i	−0.371775	−	0.429051i
$771$	9.84770	+	11.3648i	0.354656	+	0.409295i
$772$	2.25044	+	0.660790i	0.0809952	+	0.0237823i
$773$	9.59806	−	21.0168i	0.345218	−	0.755923i	−0.654782	−	0.755818i	$-0.727239\pi$
$773$	9.59806	−	21.0168i	0.345218	−	0.755923i	1.00000		0.000104692i	$-3.33244e-5\pi$
$774$	1.83963	+	1.18226i	0.0661242	+	0.0424954i
$775$	0.135029	−	0.0396482i	0.00485039	−	0.00142420i
$776$	3.67599	−	25.5671i	0.131960	−	0.917805i
$777$	1.71500	+	3.75533i	0.0615254	+	0.134722i
$778$	−4.03503	−	28.0642i	−0.144663	−	1.00615i
$779$	−0.241154	+	0.154980i	−0.00864023	+	0.00555274i
$780$	−6.86938	+	7.92769i	−0.245963	+	0.283857i
$781$	−57.1502			−2.04499
$782$	15.6552	+	2.33777i	0.559827	+	0.0835984i
$783$	−7.13553			−0.255003
$784$	1.19935	−	1.38413i	0.0428340	−	0.0494331i
$785$	−25.7134	+	16.5250i	−0.917750	+	0.589802i
$786$	−2.69428	−	18.7391i	−0.0961016	−	0.668401i
$787$	−9.31296	−	20.3925i	−0.331971	−	0.726915i	0.667878	−	0.744270i	$-0.267203\pi$
$787$	−9.31296	−	20.3925i	−0.331971	−	0.726915i	−0.999849	+	0.0173553i	$0.994475\pi$
$788$	0.379299	−	2.63809i	0.0135120	−	0.0939779i
$789$	15.6827	−	4.60486i	0.558319	−	0.163937i
$790$	23.7085	+	15.2365i	0.843509	+	0.542090i
$791$	−5.66870	+	12.4127i	−0.201556	+	0.441346i
$792$	17.1808	+	5.04473i	0.610492	+	0.179257i
$793$	11.6813	+	13.4810i	0.414817	+	0.478724i
$794$	−13.4695	−	15.5446i	−0.478014	−	0.551658i
$795$	−22.1592	−	6.50652i	−0.785905	−	0.230763i
$796$	5.34739	−	11.7092i	0.189533	−	0.415020i
$797$	−5.44465	−	3.49907i	−0.192859	−	0.123943i	0.440648	−	0.897680i	$-0.354749\pi$
$797$	−5.44465	−	3.49907i	−0.192859	−	0.123943i	−0.633507	+	0.773737i	$0.718385\pi$
$798$	−0.212772	+	0.0624756i	−0.00753206	+	0.00221161i
$799$	−4.53750	+	31.5590i	−0.160525	+	1.11648i
$800$	1.68016	+	3.67904i	0.0594026	+	0.130074i
$801$	1.73285	+	12.0522i	0.0612271	+	0.425844i
$802$	11.7154	−	7.52905i	0.413686	−	0.265860i
$803$	−44.1650	+	50.9692i	−1.55855	+	1.79866i
$804$	6.40132			0.225757
$805$	11.6012	+	1.73239i	0.408887	+	0.0610587i
$806$	−0.870237			−0.0306528
$807$	−4.82183	+	5.56468i	−0.169736	+	0.195886i
$808$	−6.30640	+	4.05288i	−0.221859	+	0.142580i
$809$	4.61540	+	32.1008i	0.162269	+	1.12860i	0.894344	+	0.447380i	$0.147643\pi$
$809$	4.61540	+	32.1008i	0.162269	+	1.12860i	−0.732075	+	0.681224i	$0.761448\pi$
$810$	−1.12223	−	2.45734i	−0.0394311	−	0.0863421i
$811$	−3.31207	+	23.0360i	−0.116303	+	0.808902i	0.845268	+	0.534343i	$0.179441\pi$
$811$	−3.31207	+	23.0360i	−0.116303	+	0.808902i	−0.961570	+	0.274559i	$0.911468\pi$
$812$	5.34053	−	1.56812i	0.187416	−	0.0550302i
$813$	−14.8537	−	9.54586i	−0.520940	−	0.334788i
$814$	−11.0463	+	24.1879i	−0.387171	+	0.847786i
$815$	−18.1699	−	5.33518i	−0.636465	−	0.186883i
$816$	3.58390	+	4.13604i	0.125462	+	0.144791i
$817$	0.260304	+	0.300406i	0.00910687	+	0.0105099i
$818$	−35.1471	−	10.3201i	−1.22889	−	0.360835i
$819$	−2.28406	+	5.00140i	−0.0798117	+	0.174763i
$820$	2.29159	+	1.47271i	0.0800257	+	0.0514294i
$821$	45.8765	−	13.4705i	1.60110	−	0.470125i	0.645248	−	0.763973i	$-0.276754\pi$
$821$	45.8765	−	13.4705i	1.60110	−	0.470125i	0.955852	+	0.293848i	$0.0949359\pi$
$822$	−1.51533	+	10.5394i	−0.0528534	+	0.367603i
$823$	−15.3251	−	33.5572i	−0.534198	−	1.16973i	−0.963779	−	0.266702i	$-0.914066\pi$
$823$	−15.3251	−	33.5572i	−0.534198	−	1.16973i	0.429581	−	0.903028i	$-0.358661\pi$
$824$	−3.45707	−	24.0445i	−0.120433	−	0.837628i
$825$	4.81783	−	3.09623i	0.167735	−	0.107797i
$826$	10.2474	−	11.8261i	0.356551	−	0.411482i
$827$	45.1400			1.56967			0.784836	−	0.619703i	$-0.212747\pi$
$827$	45.1400			1.56967			0.784836	+	0.619703i	$0.212747\pi$
$828$	−3.41127	+	1.53553i	−0.118550	+	0.0533632i
$829$	12.6167			0.438195			0.219098	−	0.975703i	$-0.429689\pi$
$829$	12.6167			0.438195			0.219098	+	0.975703i	$0.429689\pi$
$830$	−11.7713	+	13.5848i	−0.408589	+	0.471537i
$831$	25.2341	−	16.2170i	0.875361	−	0.562560i
$832$	−6.42553	−	44.6905i	−0.222765	−	1.54937i
$833$	1.24134	+	2.71816i	0.0430100	+	0.0941787i
$834$	−1.28071	+	8.90750i	−0.0443472	+	0.308442i
$835$	−32.9287	+	9.66873i	−1.13954	+	0.334600i
$836$	0.768282	+	0.493745i	0.0265716	+	0.0170765i
$837$	−0.0595279	+	0.130348i	−0.00205758	+	0.00450548i
$838$	5.22802	+	1.53509i	0.180599	+	0.0530287i
$839$	11.9616	+	13.8044i	0.412959	+	0.476580i	0.923679	−	0.383167i	$-0.125167\pi$
$839$	11.9616	+	13.8044i	0.412959	+	0.476580i	−0.510720	+	0.859747i	$0.670621\pi$
$840$	4.91812	+	5.67581i	0.169691	+	0.195834i
$841$	−21.0280	−	6.17439i	−0.725104	−	0.212910i
$842$	−15.0107	+	32.8690i	−0.517305	+	1.13274i
$843$	6.66065	+	4.28054i	0.229405	+	0.147430i
$844$	12.1615	−	3.57094i	0.418617	−	0.122917i
$845$	5.99773	−	41.7151i	0.206328	−	1.43504i
$846$	4.89567	+	10.7200i	0.168317	+	0.368562i
$847$	3.27408	+	22.7717i	0.112499	+	0.782445i
$848$	14.5482	−	9.34959i	0.499589	−	0.321066i
$849$	−20.8120	+	24.0184i	−0.714267	+	0.824308i
$850$	3.24138			0.111179
$851$	−5.47475	−	19.0272i	−0.187672	−	0.652243i
$852$	7.64464			0.261901
$853$	26.3294	−	30.3858i	0.901502	−	1.04039i	−0.0974782	−	0.995238i	$-0.531078\pi$
$853$	26.3294	−	30.3858i	0.901502	−	1.04039i	0.998980	−	0.0451511i	$-0.0143769\pi$
$854$	3.01451	−	1.93731i	0.103155	−	0.0662934i
$855$	−0.0698838	−	0.486053i	−0.00238998	−	0.0166227i
$856$	−8.20176	−	17.9593i	−0.280330	−	0.613838i
$857$	3.54662	−	24.6673i	0.121150	−	0.842619i	−0.835106	−	0.550089i	$-0.814594\pi$
$857$	3.54662	−	24.6673i	0.121150	−	0.842619i	0.956256	−	0.292530i	$-0.0944970\pi$
$858$	−33.9796	+	9.97731i	−1.16004	+	0.340620i
$859$	10.4652	+	6.72560i	0.357069	+	0.229475i	0.706860	−	0.707353i	$-0.250111\pi$
$859$	10.4652	+	6.72560i	0.357069	+	0.229475i	−0.349791	+	0.936828i	$0.613747\pi$
$860$	1.56912	−	3.43589i	0.0535065	−	0.117163i
$861$	1.36996	+	0.402257i	0.0466882	+	0.0137089i
$862$	16.2525	+	18.7564i	0.553562	+	0.638844i
$863$	−29.1782	−	33.6734i	−0.993236	−	1.14626i	−0.989246	−	0.146264i	$-0.953275\pi$
$863$	−29.1782	−	33.6734i	−0.993236	−	1.14626i	−0.00399074	−	0.999992i	$-0.501270\pi$
$864$	−3.95150	−	1.16027i	−0.134433	−	0.0394731i
$865$	8.80952	−	19.2902i	0.299533	−	0.655885i
$866$	−18.5295	−	11.9082i	−0.629659	−	0.404658i
$867$	7.74375	−	2.27377i	0.262992	−	0.0772213i
$868$	0.0159076	−	0.110640i	0.000539939	−	0.00375536i
$869$	−25.2718	−	55.3375i	−0.857287	−	1.87720i
$870$	−2.74331	−	19.0802i	−0.0930071	−	0.646878i
$871$	−37.9583	+	24.3943i	−1.28617	+	0.826570i
$872$	−7.01171	+	8.09195i	−0.237447	+	0.274028i
$873$	8.41202			0.284704
$874$	1.05348	−	0.145629i	0.0356345	−	0.00492599i
$875$	−9.82714			−0.332218
$876$	5.90769	−	6.81784i	0.199602	−	0.230353i
$877$	−10.5855	+	6.80291i	−0.357448	+	0.229718i	−0.707023	−	0.707190i	$-0.749962\pi$
$877$	−10.5855	+	6.80291i	−0.357448	+	0.229718i	0.349575	+	0.936908i	$0.386326\pi$
$878$	1.87678	+	13.0533i	0.0633382	+	0.440527i
$879$	−3.47521	−	7.60966i	−0.117216	−	0.256667i
$880$	−3.71750	+	25.8558i	−0.125317	+	0.871599i
$881$	−2.94364	+	0.864331i	−0.0991738	+	0.0291201i	−0.330943	−	0.943651i	$-0.607367\pi$
$881$	−2.94364	+	0.864331i	−0.0991738	+	0.0291201i	0.231769	+	0.972771i	$0.425549\pi$
$882$	0.929180	+	0.597148i	0.0312871	+	0.0201070i
$883$	2.14217	−	4.69070i	0.0720897	−	0.157854i	−0.870156	−	0.492776i	$-0.835982\pi$
$883$	2.14217	−	4.69070i	0.0720897	−	0.157854i	0.942246	+	0.334921i	$0.108710\pi$
$884$	12.2968	+	3.61068i	0.413588	+	0.121440i
$885$	22.6916	+	26.1875i	0.762770	+	0.880284i
$886$	−18.3745	−	21.2053i	−0.617303	−	0.712405i
$887$	−15.8029	−	4.64015i	−0.530609	−	0.155801i	0.00544383	−	0.999985i	$-0.498267\pi$
$887$	−15.8029	−	4.64015i	−0.530609	−	0.155801i	−0.536053	+	0.844184i	$0.680085\pi$
$888$	5.26610	−	11.5311i	0.176719	−	0.386960i
$889$	−13.6010	−	8.74084i	−0.456163	−	0.293158i
$890$	−31.5610	+	9.26715i	−1.05793	+	0.310636i
$891$	−0.829903	+	5.77210i	−0.0278028	+	0.193373i
$892$	4.47664	+	9.80247i	0.149889	+	0.328211i
$893$	0.304865	+	2.12038i	0.0102019	+	0.0709559i
$894$	−2.35193	+	1.51149i	−0.0786602	+	0.0505518i
$895$	−10.5922	+	12.2240i	−0.354057	+	0.408604i
$896$	−0.833313			−0.0278390
$897$	14.3764	−	22.1050i	0.480013	−	0.738066i
$898$	−4.05598			−0.135350
$899$	−0.669597	+	0.772756i	−0.0223323	+	0.0257728i
$900$	−0.644453	+	0.414165i	−0.0214818	+	0.0138055i
$901$	4.01555	+	27.9288i	0.133777	+	0.930443i
$902$	3.82032	+	8.36532i	0.127203	+	0.278535i
$903$	0.281761	−	1.95969i	0.00937642	−	0.0652145i
$904$	40.2038	−	11.8049i	1.33716	−	0.392625i
$905$	10.4352	+	6.70631i	0.346879	+	0.222925i
$906$	7.71944	−	16.9032i	0.256461	−	0.561571i
$907$	1.99700	+	0.586371i	0.0663092	+	0.0194701i	0.314719	−	0.949185i	$-0.398090\pi$
$907$	1.99700	+	0.586371i	0.0663092	+	0.0194701i	−0.248410	+	0.968655i	$0.579908\pi$
$908$	5.65870	+	6.53049i	0.187790	+	0.216722i
$909$	−1.59875	−	1.84505i	−0.0530271	−	0.0611966i
$910$	−14.2517	−	4.18468i	−0.472440	−	0.138721i
$911$	−6.91149	+	15.1341i	−0.228988	+	0.501414i	−0.988895	−	0.148618i	$-0.952517\pi$
$911$	−6.91149	+	15.1341i	−0.228988	+	0.501414i	0.759907	+	0.650032i	$0.225245\pi$
$912$	0.309332	+	0.198796i	0.0102430	+	0.00658278i
$913$	37.2303	−	10.9318i	1.23214	−	0.361790i
$914$	1.09730	−	7.63186i	0.0362953	−	0.252440i
$915$	3.29629	+	7.21788i	0.108972	+	0.238616i
$916$	2.99269	+	20.8146i	0.0988812	+	0.687734i
$917$	−14.4193	+	9.26675i	−0.476169	+	0.306015i
$918$	−2.16138	+	2.49437i	−0.0713362	+	0.0823264i
$919$	19.5352			0.644407			0.322204	−	0.946670i	$-0.395576\pi$
$919$	19.5352			0.644407			0.322204	+	0.946670i	$0.395576\pi$
$920$	−19.3076	−	30.4052i	−0.636553	−	1.00243i
$921$	−27.3319			−0.900616
$922$	−9.05951	+	10.4552i	−0.298359	+	0.344325i
$923$	−45.3308	+	29.1324i	−1.49208	+	0.958903i
$924$	−0.647356	−	4.50246i	−0.0212965	−	0.148120i
$925$	−1.68427	−	3.68805i	−0.0553786	−	0.121262i
$926$	−5.11941	+	35.6063i	−0.168234	+	1.17009i
$927$	7.59060	−	2.22880i	0.249308	−	0.0732034i
$928$	−24.7214	−	15.8875i	−0.811521	−	0.521533i
$929$	−0.667160	+	1.46088i	−0.0218888	+	0.0479298i	−0.920261	−	0.391306i	$-0.872023\pi$
$929$	−0.667160	+	1.46088i	−0.0218888	+	0.0479298i	0.898372	+	0.439236i	$0.144751\pi$
$930$	−0.371432	−	0.109062i	−0.0121797	−	0.00357629i
$931$	0.131477	+	0.151732i	0.00430898	+	0.00497283i
$932$	5.97630	+	6.89702i	0.195760	+	0.225919i
$933$	12.4369	+	3.65182i	0.407167	+	0.119555i
$934$	−11.4274	+	25.0225i	−0.373916	+	0.818762i
$935$	−35.8542	−	23.0421i	−1.17256	−	0.753556i
$936$	16.1991	−	4.75650i	0.529485	−	0.155471i
$937$	−3.79781	+	26.4143i	−0.124069	+	0.862919i	0.828802	+	0.559542i	$0.189023\pi$
$937$	−3.79781	+	26.4143i	−0.124069	+	0.862919i	−0.952871	+	0.303376i	$0.901886\pi$
$938$	3.76538	+	8.24503i	0.122944	+	0.269210i
$939$	−0.943883	−	6.56485i	−0.0308025	−	0.214236i
$940$	17.1248	−	11.0055i	0.558550	−	0.358959i
$941$	38.4950	−	44.4256i	1.25490	−	1.44823i	0.411092	−	0.911594i	$-0.365148\pi$
$941$	38.4950	−	44.4256i	1.25490	−	1.44823i	0.843811	−	0.536641i	$-0.180307\pi$
$942$	13.8032			0.449732
$943$	−6.21314	−	2.87835i	−0.202328	−	0.0937320i
$944$	−25.9470			−0.844504
$945$	−1.60168	+	1.84843i	−0.0521026	+	0.0601296i
$946$	10.7277	−	6.89429i	0.348789	−	0.224153i
$947$	−8.33188	−	57.9495i	−0.270750	−	1.88311i	−0.440703	−	0.897653i	$-0.645271\pi$
$947$	−8.33188	−	57.9495i	−0.270750	−	1.88311i	0.169953	−	0.985452i	$-0.445638\pi$
$948$	3.38046	+	7.40217i	0.109792	+	0.240411i
$949$	−9.04959	+	62.9413i	−0.293762	+	2.04316i
$950$	0.208960	−	0.0613562i	0.00677956	−	0.00199066i
$951$	−3.56906	−	2.29370i	−0.115735	−	0.0743783i
$952$	3.81167	−	8.34640i	0.123537	−	0.270508i
$953$	−16.0948	−	4.72586i	−0.521361	−	0.153085i	0.0104548	−	0.999945i	$-0.496672\pi$
$953$	−16.0948	−	4.72586i	−0.521361	−	0.153085i	−0.531816	+	0.846860i	$0.678490\pi$
$954$	6.82980	+	7.88200i	0.221123	+	0.255189i
$955$	32.8537	+	37.9152i	1.06312	+	1.22691i
$956$	16.2150	+	4.76116i	0.524431	+	0.153987i
$957$	−17.2856	+	37.8503i	−0.558765	+	1.22353i
$958$	5.29624	+	3.40368i	0.171114	+	0.109968i
$959$	9.24969	−	2.71595i	0.298688	−	0.0877027i
$960$	2.85831	−	19.8800i	0.0922515	−	0.641623i
$961$	−12.8693	−	28.1799i	−0.415140	−	0.909029i
$962$	3.56806	+	24.8164i	0.115039	+	0.800113i
$963$	5.40913	−	3.47624i	0.174307	−	0.112020i
$964$	8.61634	−	9.94379i	0.277514	−	0.320268i
$965$	−7.35421			−0.236741
$966$	−3.98436	−	3.49056i	−0.128195	−	0.112307i
$967$	52.8417			1.69928			0.849638	−	0.527366i	$-0.176820\pi$
$967$	52.8417			1.69928			0.849638	+	0.527366i	$0.176820\pi$
$968$	46.2606	−	53.3876i	1.48687	−	1.71594i
$969$	−0.504704	+	0.324353i	−0.0162134	+	0.0104197i
$970$	3.23407	+	22.4935i	0.103840	+	0.722222i
$971$	−2.96367	−	6.48954i	−0.0951088	−	0.208259i	0.856098	−	0.516814i	$-0.172882\pi$
$971$	−2.96367	−	6.48954i	−0.0951088	−	0.208259i	−0.951207	+	0.308555i	$0.900155\pi$
$972$	0.111011	−	0.772099i	0.00356068	−	0.0247651i
$973$	7.81750	−	2.29543i	0.250618	−	0.0735879i
$974$	10.6983	+	6.87537i	0.342795	+	0.220301i
$975$	2.24314	−	4.91179i	0.0718380	−	0.157303i
$976$	−5.70108	−	1.67399i	−0.182487	−	0.0535831i
$977$	−10.4869	−	12.1026i	−0.335507	−	0.387196i	0.562779	−	0.826608i	$-0.309732\pi$
$977$	−10.4869	−	12.1026i	−0.335507	−	0.387196i	−0.898286	+	0.439412i	$0.855187\pi$
$978$	5.60025	+	6.46304i	0.179076	+	0.206665i
$979$	68.1285	+	20.0043i	2.17740	+	0.639341i
$980$	0.792546	−	1.73543i	0.0253170	−	0.0554364i
$981$	−2.93345	−	1.88521i	−0.0936578	−	0.0601902i
$982$	41.9740	−	12.3247i	1.33944	−	0.393296i
$983$	−2.83539	+	19.7205i	−0.0904348	+	0.628988i	0.893313	+	0.449434i	$0.148374\pi$
$983$	−2.83539	+	19.7205i	−0.0904348	+	0.628988i	−0.983748	+	0.179553i	$0.942535\pi$
$984$	−1.82126	−	3.98801i	−0.0580598	−	0.127133i
$985$	1.18930	+	8.27178i	0.0378943	+	0.263561i
$986$	−19.8123	+	12.7326i	−0.630953	+	0.405489i
$987$	6.98725	−	8.06371i	0.222406	−	0.256671i
$988$	0.861078			0.0273946
$989$	−2.72452	+	9.09571i	−0.0866346	+	0.289227i
$990$	−15.7535			−0.500678
$991$	24.0888	−	27.7999i	0.765205	−	0.883094i	−0.230744	−	0.973015i	$-0.574116\pi$
$991$	24.0888	−	27.7999i	0.765205	−	0.883094i	0.995949	+	0.0899208i	$0.0286614\pi$
$992$	−0.496462	+	0.319056i	−0.0157627	+	0.0101301i
$993$	−1.70063	−	11.8281i	−0.0539679	−	0.375355i
$994$	4.49672	+	9.84644i	0.142627	+	0.312310i
$995$	−5.74408	+	39.9509i	−0.182099	+	1.26653i
$996$	−4.98007	+	1.46228i	−0.157800	+	0.0463341i
$997$	4.00477	+	2.57371i	0.126832	+	0.0815103i	0.602519	−	0.798105i	$-0.294164\pi$
$997$	4.00477	+	2.57371i	0.126832	+	0.0815103i	−0.475686	+	0.879615i	$0.657800\pi$
$998$	−1.85038	+	4.05177i	−0.0585728	+	0.128257i
$999$	3.96118	+	1.16311i	0.125326	+	0.0367991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.85.3	✓	80
23.13	even	11	inner	483.2.q.f.358.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.85.3	✓	80	1.1	even	1	trivial
483.2.q.f.358.3	yes	80	23.13	even	11	inner

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.723306 + 0.834739i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.111011 + 0.772099i) q^{4} +(-1.01603 - 2.22480i) q^{5} +(-0.157189 + 1.09328i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-2.58316 - 1.66009i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.723306 + 0.834739i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.111011 + 0.772099i) q^{4} +(-1.01603 - 2.22480i) q^{5} +(-0.157189 + 1.09328i) q^{6} +(0.959493 - 0.281733i) q^{7} +(-2.58316 - 1.66009i) q^{8} +(0.415415 - 0.909632i) q^{9} +(2.59204 + 0.761090i) q^{10} +(-3.81879 - 4.40712i) q^{11} +(0.510817 + 0.589514i) q^{12} +(-5.27555 - 1.54904i) q^{13} +(-0.458834 + 1.00471i) q^{14} +(-2.05756 - 1.32232i) q^{15} +(1.75727 - 0.515982i) q^{16} +(-0.425265 + 2.95778i) q^{17} +(0.458834 + 1.00471i) q^{18} +(0.0285726 + 0.198727i) q^{19} +(1.60498 - 1.03146i) q^{20} +(0.654861 - 0.755750i) q^{21} +6.44095 q^{22} +(-3.64146 + 3.12086i) q^{23} -3.07060 q^{24} +(-0.643127 + 0.742208i) q^{25} +(5.10888 - 3.28328i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.324040 + 0.709548i) q^{28} +(1.01549 - 7.06290i) q^{29} +(2.59204 - 0.761090i) q^{30} +(-0.120549 - 0.0774724i) q^{31} +(1.71081 - 3.74616i) q^{32} +(-5.59524 - 1.64291i) q^{33} +(-2.16138 - 2.49437i) q^{34} +(-1.60168 - 1.84843i) q^{35} +(0.748442 + 0.219762i) q^{36} +(-1.71500 + 3.75533i) q^{37} +(-0.186552 - 0.119890i) q^{38} +(-5.27555 + 1.54904i) q^{39} +(-1.06881 + 7.43373i) q^{40} +(0.593129 + 1.29877i) q^{41} +(0.157189 + 1.09328i) q^{42} +(1.66555 - 1.07038i) q^{43} +(2.97881 - 3.43773i) q^{44} -2.44583 q^{45} +(0.0287839 - 5.29701i) q^{46} +10.6698 q^{47} +(1.19935 - 1.38413i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.154373 - 1.07369i) q^{50} +(1.24134 + 2.71816i) q^{51} +(0.610369 - 4.24521i) q^{52} +(9.05999 - 2.66025i) q^{53} +(0.929180 + 0.597148i) q^{54} +(-5.92496 + 12.9739i) q^{55} +(-2.94622 - 0.865089i) q^{56} +(0.131477 + 0.151732i) q^{57} +(5.16117 + 5.95631i) q^{58} +(-13.5935 - 3.99142i) q^{59} +(0.792546 - 1.73543i) q^{60} +(-2.72926 - 1.75399i) q^{61} +(0.151863 - 0.0445911i) q^{62} +(0.142315 - 0.989821i) q^{63} +(3.41126 + 7.46962i) q^{64} +(1.91383 + 13.3110i) q^{65} +(5.41847 - 3.48224i) q^{66} +(5.37406 - 6.20200i) q^{67} -2.33091 q^{68} +(-1.37613 + 4.59416i) q^{69} +2.70146 q^{70} +(6.41785 - 7.40659i) q^{71} +(-2.58316 + 1.66009i) q^{72} +(-1.64590 - 11.4475i) q^{73} +(-1.89425 - 4.14783i) q^{74} +(-0.139765 + 0.972086i) q^{75} +(-0.150265 + 0.0441218i) q^{76} +(-4.90573 - 3.15272i) q^{77} +(2.52279 - 5.52414i) q^{78} +(10.0097 + 2.93910i) q^{79} +(-2.93341 - 3.38534i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.51315 - 0.444301i) q^{82} +(-2.76414 + 6.05262i) q^{83} +(0.656210 + 0.421721i) q^{84} +(7.01257 - 2.05908i) q^{85} +(-0.311210 + 2.16452i) q^{86} +(-2.96421 - 6.49071i) q^{87} +(2.54830 + 17.7238i) q^{88} +(-10.2432 + 6.58292i) q^{89} +(1.76908 - 2.04163i) q^{90} -5.49827 q^{91} +(-2.81386 - 2.46512i) q^{92} -0.143297 q^{93} +(-7.71754 + 8.90652i) q^{94} +(0.413098 - 0.265482i) q^{95} +(-0.586099 - 4.07641i) q^{96} +(3.49448 + 7.65184i) q^{97} +(-0.157189 + 1.09328i) q^{98} +(-5.59524 + 1.64291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

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