LMFDB - Embedded newform 68.2.i.b.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [68,2,Mod(3,68)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(68, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 1]))

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

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

chi := DirichletCharacter("68.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 68 = 2^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	68.i (of order $16$, degree $8$, 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:	$0.542982733745$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	68.7
Dual form			68.2.i.b.39.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.827293 - 1.14699i) q^{2} +(-1.80045 - 1.20302i) q^{3} +(-0.631174 - 1.89779i) q^{4} +(0.177432 + 0.892011i) q^{5} +(-2.86936 + 1.06985i) q^{6} +(3.16204 + 0.628968i) q^{7} +(-2.69892 - 0.846081i) q^{8} +(0.646311 + 1.56033i) q^{9} +O(q^{10})$	\(q+(0.827293 - 1.14699i) q^{2} +(-1.80045 - 1.20302i) q^{3} +(-0.631174 - 1.89779i) q^{4} +(0.177432 + 0.892011i) q^{5} +(-2.86936 + 1.06985i) q^{6} +(3.16204 + 0.628968i) q^{7} +(-2.69892 - 0.846081i) q^{8} +(0.646311 + 1.56033i) q^{9} +(1.16992 + 0.534441i) q^{10} +(2.03611 + 3.04725i) q^{11} +(-1.14669 + 4.17620i) q^{12} +(0.674154 - 0.674154i) q^{13} +(3.33735 - 3.10649i) q^{14} +(0.753652 - 1.81948i) q^{15} +(-3.20324 + 2.39567i) q^{16} +(-0.463051 + 4.09702i) q^{17} +(2.32437 + 0.549539i) q^{18} +(-6.92889 - 2.87004i) q^{19} +(1.58086 - 0.899743i) q^{20} +(-4.93643 - 4.93643i) q^{21} +(5.17962 + 0.185572i) q^{22} +(1.74858 - 1.16837i) q^{23} +(3.84141 + 4.77019i) q^{24} +(3.85520 - 1.59687i) q^{25} +(-0.215525 - 1.33097i) q^{26} +(-0.553872 + 2.78450i) q^{27} +(-0.802143 - 6.39788i) q^{28} +(-7.94007 + 1.57938i) q^{29} +(-1.46343 - 2.36967i) q^{30} +(-1.92916 + 2.88719i) q^{31} +(0.0977985 + 5.65601i) q^{32} -7.93591i q^{33} +(4.31617 + 3.92055i) q^{34} +2.93217i q^{35} +(2.55325 - 2.21140i) q^{36} +(3.94344 - 5.90177i) q^{37} +(-9.02413 + 5.57301i) q^{38} +(-2.02480 + 0.402758i) q^{39} +(0.275839 - 2.55758i) q^{40} +(-0.0665472 + 0.334555i) q^{41} +(-9.74591 + 1.57817i) q^{42} +(7.55666 - 3.13007i) q^{43} +(4.49791 - 5.78746i) q^{44} +(-1.27716 + 0.853369i) q^{45} +(0.106486 - 2.97219i) q^{46} +(-4.03395 - 4.03395i) q^{47} +(8.64933 - 0.459724i) q^{48} +(3.13572 + 1.29886i) q^{49} +(1.35778 - 5.74296i) q^{50} +(5.76251 - 6.81943i) q^{51} +(-1.70491 - 0.853896i) q^{52} +(-1.49660 + 3.61311i) q^{53} +(2.73558 + 2.93889i) q^{54} +(-2.35691 + 2.35691i) q^{55} +(-8.00192 - 4.37287i) q^{56} +(9.02240 + 13.5030i) q^{57} +(-4.75723 + 10.4138i) q^{58} +(2.57178 + 6.20882i) q^{59} +(-3.92868 - 0.281870i) q^{60} +(-5.23170 - 1.04065i) q^{61} +(1.71560 + 4.60128i) q^{62} +(1.06226 + 5.34034i) q^{63} +(6.56830 + 4.56700i) q^{64} +(0.720969 + 0.481736i) q^{65} +(-9.10242 - 6.56532i) q^{66} +0.313037 q^{67} +(8.06757 - 1.70716i) q^{68} -4.55381 q^{69} +(3.36317 + 2.42576i) q^{70} +(-5.04978 - 3.37416i) q^{71} +(-0.424172 - 4.75803i) q^{72} +(1.46898 + 7.38509i) q^{73} +(-3.50690 - 9.40557i) q^{74} +(-8.86217 - 1.76280i) q^{75} +(-1.07341 + 14.9611i) q^{76} +(4.52163 + 10.9162i) q^{77} +(-1.21314 + 2.65563i) q^{78} +(-1.91258 - 2.86238i) q^{79} +(-2.70532 - 2.43226i) q^{80} +(7.92972 - 7.92972i) q^{81} +(0.328678 + 0.353104i) q^{82} +(1.34592 - 3.24933i) q^{83} +(-6.25258 + 12.4841i) q^{84} +(-3.73675 + 0.313896i) q^{85} +(2.66141 - 11.2569i) q^{86} +(16.1957 + 6.70849i) q^{87} +(-2.91706 - 9.94699i) q^{88} +(-2.89855 - 2.89855i) q^{89} +(-0.0777766 + 2.17087i) q^{90} +(2.55572 - 1.70768i) q^{91} +(-3.32098 - 2.58101i) q^{92} +(6.94672 - 2.87743i) q^{93} +(-7.96417 + 1.28965i) q^{94} +(1.33070 - 6.68988i) q^{95} +(6.62823 - 10.3010i) q^{96} +(-3.78697 + 0.753275i) q^{97} +(4.08394 - 2.52211i) q^{98} +(-3.43876 + 5.14647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) $ 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/68\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.827293	−	1.14699i	0.584984	−	0.811045i
$2$	0.827293	−	1.14699i	0.584984	−	0.811045i
$3$	−1.80045	−	1.20302i	−1.03949	−	0.694566i	−0.0860950	−	0.996287i	$-0.527439\pi$
$3$	−1.80045	−	1.20302i	−1.03949	−	0.694566i	−0.953396	+	0.301721i	$0.902439\pi$
$4$	−0.631174	−	1.89779i	−0.315587	−	0.948897i
$5$	0.177432	+	0.892011i	0.0793500	+	0.398919i	0.999964	+	0.00844627i	$0.00268856\pi$
$5$	0.177432	+	0.892011i	0.0793500	+	0.398919i	−0.920614	+	0.390473i	$0.872311\pi$
$6$	−2.86936	+	1.06985i	−1.17141	+	0.436764i
$7$	3.16204	+	0.628968i	1.19514	+	0.237728i	0.752267	−	0.658858i	$-0.228960\pi$
$7$	3.16204	+	0.628968i	1.19514	+	0.237728i	0.442870	+	0.896586i	$0.353960\pi$
$8$	−2.69892	−	0.846081i	−0.954211	−	0.299135i
$9$	0.646311	+	1.56033i	0.215437	+	0.520111i
$10$	1.16992	+	0.534441i	0.369960	+	0.169005i
$11$	2.03611	+	3.04725i	0.613910	+	0.918781i	0.999993	−	0.00368310i	$-0.00117237\pi$
$11$	2.03611	+	3.04725i	0.613910	+	0.918781i	−0.386084	+	0.922464i	$0.626172\pi$
$12$	−1.14669	+	4.17620i	−0.331021	+	1.20557i
$13$	0.674154	−	0.674154i	0.186977	−	0.186977i	−0.607411	−	0.794388i	$-0.707792\pi$
$13$	0.674154	−	0.674154i	0.186977	−	0.186977i	0.794388	+	0.607411i	$0.207792\pi$
$14$	3.33735	−	3.10649i	0.891945	−	0.830243i
$15$	0.753652	−	1.81948i	0.194592	−	0.469787i
$16$	−3.20324	+	2.39567i	−0.800810	+	0.598919i
$17$	−0.463051	+	4.09702i	−0.112306	+	0.993674i
$17$	−0.463051	+	4.09702i	−0.112306	+	0.993674i
$18$	2.32437	+	0.549539i	0.547860	+	0.129528i
$19$	−6.92889	−	2.87004i	−1.58960	−	0.658432i	−0.599700	−	0.800225i	$-0.704713\pi$
$19$	−6.92889	−	2.87004i	−1.58960	−	0.658432i	−0.989896	+	0.141793i	$0.954713\pi$
$20$	1.58086	−	0.899743i	0.353491	−	0.201189i
$21$	−4.93643	−	4.93643i	−1.07722	−	1.07722i
$22$	5.17962	+	0.185572i	1.10430	+	0.0395641i
$23$	1.74858	−	1.16837i	0.364605	−	0.243621i	−0.359750	−	0.933049i	$-0.617138\pi$
$23$	1.74858	−	1.16837i	0.364605	−	0.243621i	0.724355	+	0.689428i	$0.242138\pi$
$24$	3.84141	+	4.77019i	0.784125	+	0.973710i
$25$	3.85520	−	1.59687i	0.771039	−	0.319375i
$26$	−0.215525	−	1.33097i	−0.0422680	−	0.261025i
$27$	−0.553872	+	2.78450i	−0.106593	+	0.535878i
$28$	−0.802143	−	6.39788i	−0.151591	−	1.20909i
$29$	−7.94007	+	1.57938i	−1.47443	+	0.293283i	−0.865889	−	0.500237i	$-0.833246\pi$
$29$	−7.94007	+	1.57938i	−1.47443	+	0.293283i	−0.608545	+	0.793520i	$0.708246\pi$
$30$	−1.46343	−	2.36967i	−0.267185	−	0.432641i
$31$	−1.92916	+	2.88719i	−0.346487	+	0.518555i	−0.963254	−	0.268591i	$-0.913442\pi$
$31$	−1.92916	+	2.88719i	−0.346487	+	0.518555i	0.616767	+	0.787146i	$0.288442\pi$
$32$	0.0977985	+	5.65601i	0.0172885	+	0.999851i
$33$		−	7.93591i		−	1.38147i
$34$	4.31617	+	3.92055i	0.740216	+	0.672369i
$35$			2.93217i			0.495627i
$36$	2.55325	−	2.21140i	0.425542	−	0.368567i
$37$	3.94344	−	5.90177i	0.648297	−	0.970245i	−0.351128	−	0.936328i	$-0.614202\pi$
$37$	3.94344	−	5.90177i	0.648297	−	0.970245i	0.999425	−	0.0339172i	$-0.0107983\pi$
$38$	−9.02413	+	5.57301i	−1.46391	+	0.904061i
$39$	−2.02480	+	0.402758i	−0.324228	+	0.0644930i
$40$	0.275839	−	2.55758i	0.0436140	−	0.404390i
$41$	−0.0665472	+	0.334555i	−0.0103929	+	0.0522488i	−0.985634	−	0.168897i	$-0.945980\pi$
$41$	−0.0665472	+	0.334555i	−0.0103929	+	0.0522488i	0.975241	+	0.221145i	$0.0709796\pi$
$42$	−9.74591	+	1.57817i	−1.50383	+	0.243516i
$43$	7.55666	−	3.13007i	1.15238	−	0.477331i	0.277049	−	0.960856i	$-0.410644\pi$
$43$	7.55666	−	3.13007i	1.15238	−	0.477331i	0.875331	+	0.483525i	$0.160644\pi$
$44$	4.49791	−	5.78746i	0.678086	−	0.872492i
$45$	−1.27716	+	0.853369i	−0.190387	+	0.127213i
$46$	0.106486	−	2.97219i	0.0157005	−	0.438225i
$47$	−4.03395	−	4.03395i	−0.588413	−	0.588413i	0.348789	−	0.937201i	$-0.386593\pi$
$47$	−4.03395	−	4.03395i	−0.588413	−	0.588413i	−0.937201	+	0.348789i	$0.886593\pi$
$48$	8.64933	−	0.459724i	1.24842	−	0.0663554i
$49$	3.13572	+	1.29886i	0.447961	+	0.185551i
$50$	1.35778	−	5.74296i	0.192019	−	0.812177i
$51$	5.76251	−	6.81943i	0.806913	−	0.954911i
$52$	−1.70491	−	0.853896i	−0.236429	−	0.118414i
$53$	−1.49660	+	3.61311i	−0.205574	+	0.496299i	−0.992717	−	0.120471i	$-0.961559\pi$
$53$	−1.49660	+	3.61311i	−0.205574	+	0.496299i	0.787143	+	0.616771i	$0.211559\pi$
$54$	2.73558	+	2.93889i	0.372266	+	0.399932i
$55$	−2.35691	+	2.35691i	−0.317806	+	0.317806i
$56$	−8.00192	−	4.37287i	−1.06930	−	0.584350i
$57$	9.02240	+	13.5030i	1.19505	+	1.78851i
$58$	−4.75723	+	10.4138i	−0.624655	+	1.36740i
$59$	2.57178	+	6.20882i	0.334817	+	0.808319i	0.998196	+	0.0600358i	$0.0191215\pi$
$59$	2.57178	+	6.20882i	0.334817	+	0.808319i	−0.663380	+	0.748283i	$0.730879\pi$
$60$	−3.92868	−	0.281870i	−0.507190	−	0.0363893i
$61$	−5.23170	−	1.04065i	−0.669851	−	0.133242i	−0.151563	−	0.988448i	$-0.548431\pi$
$61$	−5.23170	−	1.04065i	−0.669851	−	0.133242i	−0.518288	+	0.855206i	$0.673431\pi$
$62$	1.71560	+	4.60128i	0.217882	+	0.584363i
$63$	1.06226	+	5.34034i	0.133832	+	0.672819i
$64$	6.56830	+	4.56700i	0.821037	+	0.570875i
$65$	0.720969	+	0.481736i	0.0894252	+	0.0597520i
$66$	−9.10242	−	6.56532i	−1.12043	−	0.808135i
$67$	0.313037			0.0382436			0.0191218	−	0.999817i	$-0.493913\pi$
$67$	0.313037			0.0382436			0.0191218	+	0.999817i	$0.493913\pi$
$68$	8.06757	−	1.70716i	0.978336	−	0.207023i
$69$	−4.55381			−0.548215
$70$	3.36317	+	2.42576i	0.401976	+	0.289934i
$71$	−5.04978	−	3.37416i	−0.599299	−	0.400439i	0.218588	−	0.975817i	$-0.429855\pi$
$71$	−5.04978	−	3.37416i	−0.599299	−	0.400439i	−0.817887	+	0.575378i	$0.804855\pi$
$72$	−0.424172	−	4.75803i	−0.0499891	−	0.560740i
$73$	1.46898	+	7.38509i	0.171932	+	0.864359i	0.966398	+	0.257051i	$0.0827507\pi$
$73$	1.46898	+	7.38509i	0.171932	+	0.864359i	−0.794466	+	0.607308i	$0.792249\pi$
$74$	−3.50690	−	9.40557i	−0.407668	−	1.09338i
$75$	−8.86217	−	1.76280i	−1.02332	−	0.203550i
$76$	−1.07341	+	14.9611i	−0.123129	+	1.71616i
$77$	4.52163	+	10.9162i	0.515287	+	1.24401i
$78$	−1.21314	+	2.65563i	−0.137362	+	0.300691i
$79$	−1.91258	−	2.86238i	−0.215182	−	0.322042i	0.708138	−	0.706074i	$-0.249535\pi$
$79$	−1.91258	−	2.86238i	−0.215182	−	0.322042i	−0.923320	+	0.384032i	$0.874535\pi$
$80$	−2.70532	−	2.43226i	−0.302464	−	0.271934i
$81$	7.92972	−	7.92972i	0.881080	−	0.881080i
$82$	0.328678	+	0.353104i	0.0362964	+	0.0389938i
$83$	1.34592	−	3.24933i	0.147734	−	0.356660i	−0.832638	−	0.553817i	$-0.813171\pi$
$83$	1.34592	−	3.24933i	0.147734	−	0.356660i	0.980372	+	0.197157i	$0.0631707\pi$
$84$	−6.25258	+	12.4841i	−0.682213	+	1.36212i
$85$	−3.73675	+	0.313896i	−0.405307	+	0.0340468i
$86$	2.66141	−	11.2569i	0.286987	−	1.21386i
$87$	16.1957	+	6.70849i	1.73636	+	0.719226i
$88$	−2.91706	−	9.94699i	−0.310960	−	1.06035i
$89$	−2.89855	−	2.89855i	−0.307245	−	0.307245i	0.536595	−	0.843840i	$-0.319710\pi$
$89$	−2.89855	−	2.89855i	−0.307245	−	0.307245i	−0.843840	+	0.536595i	$0.819710\pi$
$90$	−0.0777766	+	2.17087i	−0.00819837	+	0.228830i
$91$	2.55572	−	1.70768i	0.267912	−	0.179013i
$92$	−3.32098	−	2.58101i	−0.346236	−	0.269089i
$93$	6.94672	−	2.87743i	0.720341	−	0.298375i
$94$	−7.96417	+	1.28965i	−0.821441	+	0.133017i
$95$	1.33070	−	6.68988i	0.136527	−	0.686367i
$96$	6.62823	−	10.3010i	0.676491	−	1.05134i
$97$	−3.78697	+	0.753275i	−0.384508	+	0.0764835i	−0.383560	−	0.923516i	$-0.625302\pi$
$97$	−3.78697	+	0.753275i	−0.384508	+	0.0764835i	−0.000948610		1.00000i	$0.500302\pi$
$98$	4.08394	−	2.52211i	0.412540	−	0.254771i
$99$	−3.43876	+	5.14647i	−0.345609	+	0.517240i
$100$	−5.46384	−	6.30846i	−0.546384	−	0.630846i
$101$		−	13.4322i		−	1.33655i	−0.743912	−	0.668277i	$-0.767032\pi$
$101$		−	13.4322i		−	1.33655i	0.743912	−	0.668277i	$-0.232968\pi$
$102$	−3.05453	−	12.2512i	−0.302444	−	1.21305i
$103$		−	4.14324i		−	0.408246i	−0.978945	−	0.204123i	$-0.934566\pi$
$103$		−	4.14324i		−	0.408246i	0.978945	−	0.204123i	$-0.0654342\pi$
$104$	−2.38987	+	1.24910i	−0.234346	+	0.122484i
$105$	3.52747	−	5.27923i	0.344246	−	0.515200i
$106$	2.90608	+	4.70569i	0.282263	+	0.457057i
$107$	5.43508	−	1.08111i	0.525429	−	0.104514i	0.0747535	−	0.997202i	$-0.476183\pi$
$107$	5.43508	−	1.08111i	0.525429	−	0.104514i	0.450676	+	0.892688i	$0.351183\pi$
$108$	5.63400	−	0.706370i	0.542132	−	0.0679705i
$109$	1.89505	−	9.52706i	0.181513	−	0.912526i	−0.777439	−	0.628958i	$-0.783482\pi$
$109$	1.89505	−	9.52706i	0.181513	−	0.912526i	0.958952	−	0.283568i	$-0.0915183\pi$
$110$	0.753499	+	4.65321i	0.0718433	+	0.443666i
$111$	−14.1999	+	5.88180i	−1.34780	+	0.558276i
$112$	−11.6356	+	5.56048i	−1.09946	+	0.525416i
$113$	−6.31407	+	4.21893i	−0.593978	+	0.396883i	−0.815910	−	0.578179i	$-0.803764\pi$
$113$	−6.31407	+	4.21893i	−0.593978	+	0.396883i	0.221932	+	0.975062i	$0.428764\pi$
$114$	22.9520	+	0.822308i	2.14965	+	0.0770162i
$115$	1.35245	+	1.35245i	0.126117	+	0.126117i
$116$	8.00889	+	14.0717i	0.743607	+	1.30653i
$117$	1.48762	+	0.616191i	0.137530	+	0.0569668i
$118$	9.24906	+	2.18671i	0.851445	+	0.201303i
$119$	−4.04108	+	12.6637i	−0.370445	+	1.16088i
$120$	−3.57347	+	4.27297i	−0.326212	+	0.390067i
$121$	−0.930485	+	2.24639i	−0.0845895	+	0.204217i
$122$	−5.52176	+	5.13979i	−0.499917	+	0.465335i
$123$	0.522293	−	0.522293i	0.0470936	−	0.0470936i
$124$	6.69693	+	1.83883i	0.601402	+	0.165132i
$125$	4.63488	+	6.93659i	0.414556	+	0.620428i
$126$	7.00411	+	3.19962i	0.623976	+	0.285045i
$127$	−6.09317	−	14.7102i	−0.540681	−	1.30532i	−0.924243	−	0.381805i	$-0.875303\pi$
$127$	−6.09317	−	14.7102i	−0.540681	−	1.30532i	0.383562	−	0.923515i	$-0.374697\pi$
$128$	10.6722	−	3.75552i	0.943299	−	0.331945i
$129$	−17.3709	−	3.45530i	−1.52943	−	0.304222i
$130$	1.14900	−	0.428408i	0.100774	−	0.0375738i
$131$	−0.461932	−	2.32229i	−0.0403592	−	0.202899i	0.955345	−	0.295493i	$-0.0954841\pi$
$131$	−0.461932	−	2.32229i	−0.0403592	−	0.202899i	−0.995704	+	0.0925942i	$0.970484\pi$
$132$	−15.0607	+	5.00894i	−1.31087	+	0.435972i
$133$	−20.1042	−	13.4332i	−1.74326	−	1.16481i
$134$	0.258974	−	0.359051i	0.0223719	−	0.0310173i
$135$	−2.58208			−0.222230
$136$	4.71615	−	10.6657i	0.404406	−	0.914580i
$137$	0.977887			0.0835466			0.0417733	−	0.999127i	$-0.486699\pi$
$137$	0.977887			0.0835466			0.0417733	+	0.999127i	$0.486699\pi$
$138$	−3.76734	+	5.22318i	−0.320697	+	0.444627i
$139$	7.34411	+	4.90718i	0.622919	+	0.416221i	0.826579	−	0.562820i	$-0.190284\pi$
$139$	7.34411	+	4.90718i	0.622919	+	0.416221i	−0.203660	+	0.979042i	$0.565284\pi$
$140$	5.56465	−	1.85071i	0.470299	−	0.156413i
$141$	2.41000	+	12.1159i	0.202958	+	1.02034i
$142$	−8.04777	+	3.00064i	−0.675354	+	0.251808i
$143$	3.42696	+	0.681666i	0.286577	+	0.0570037i
$144$	−5.80833	−	3.44977i	−0.484028	−	0.287481i
$145$	−2.81764	−	6.80239i	−0.233993	−	0.564908i
$146$	9.68590	+	4.42472i	0.801611	+	0.366192i
$147$	−4.08316	−	6.11088i	−0.336773	−	0.504017i
$148$	−13.6893	−	3.75879i	−1.12526	−	0.308970i
$149$	−0.904368	+	0.904368i	−0.0740887	+	0.0740887i	−0.743180	−	0.669091i	$-0.766683\pi$
$149$	−0.904368	+	0.904368i	−0.0740887	+	0.0740887i	0.669091	+	0.743180i	$0.266683\pi$
$150$	−9.35352	+	8.70648i	−0.763712	+	0.710881i
$151$	−7.18716	+	17.3513i	−0.584883	+	1.41203i	0.303457	+	0.952845i	$0.401859\pi$
$151$	−7.18716	+	17.3513i	−0.584883	+	1.41203i	−0.888340	+	0.459187i	$0.848141\pi$
$152$	16.2722	+	13.6084i	1.31985	+	1.10379i
$153$	−6.69199	+	1.92544i	−0.541015	+	0.155662i
$154$	16.2614	+	3.84461i	1.31038	+	0.309807i
$155$	−2.91770	−	1.20855i	−0.234355	−	0.0970732i
$156$	2.04235	+	3.58845i	0.163519	+	0.287306i
$157$	12.2168	+	12.2168i	0.975006	+	0.975006i	0.999695	−	0.0246888i	$-0.00785948\pi$
$157$	12.2168	+	12.2168i	0.975006	+	0.975006i	−0.0246888	+	0.999695i	$0.507859\pi$
$158$	−4.86538	−	0.174314i	−0.387069	−	0.0138676i
$159$	7.04121	−	4.70479i	0.558405	−	0.373114i
$160$	−5.02787	+	1.09079i	−0.397488	+	0.0862349i
$161$	6.26395	−	2.59461i	0.493669	−	0.204484i
$162$	−2.53511	−	15.6555i	−0.199177	−	1.23001i
$163$	−4.44421	+	22.3426i	−0.348098	+	1.75000i	0.269021	+	0.963134i	$0.413300\pi$
$163$	−4.44421	+	22.3426i	−0.348098	+	1.75000i	−0.617118	+	0.786870i	$0.711700\pi$
$164$	0.676920	−	0.0848697i	0.0528585	−	0.00662721i
$165$	7.07892	−	1.40808i	0.551093	−	0.109619i
$166$	−2.61348	−	4.23190i	−0.202846	−	0.328459i
$167$	13.1080	−	19.6176i	1.01433	−	1.51805i	0.167725	−	0.985834i	$-0.446358\pi$
$167$	13.1080	−	19.6176i	1.01433	−	1.51805i	0.846606	−	0.532220i	$-0.178642\pi$
$168$	9.14640	+	17.4996i	0.705660	+	1.35013i
$169$			12.0910i			0.930080i
$170$	−2.73135	+	4.54570i	−0.209485	+	0.348639i
$171$		−	12.6663i		−	0.968616i
$172$	−10.7098	−	12.3654i	−0.816614	−	0.942850i
$173$	1.26877	−	1.89885i	0.0964631	−	0.144367i	−0.780099	−	0.625656i	$-0.784831\pi$
$173$	1.26877	−	1.89885i	0.0964631	−	0.144367i	0.876562	+	0.481289i	$0.159831\pi$
$174$	21.0932	−	13.0265i	1.59907	−	0.987533i
$175$	13.1947	−	2.62458i	0.997423	−	0.198400i
$176$	−13.8224	−	4.88322i	−1.04190	−	0.368087i
$177$	2.83899	−	14.2726i	0.213392	−	1.07279i
$178$	−5.72255	+	0.926659i	−0.428923	+	0.0694560i
$179$	11.0542	−	4.57880i	0.826230	−	0.342236i	0.0708211	−	0.997489i	$-0.477438\pi$
$179$	11.0542	−	4.57880i	0.826230	−	0.342236i	0.755409	+	0.655253i	$0.227438\pi$
$180$	2.42563	+	1.88516i	0.180795	+	0.140511i
$181$	−0.942575	+	0.629809i	−0.0700611	+	0.0468133i	−0.590107	−	0.807325i	$-0.700915\pi$
$181$	−0.942575	+	0.629809i	−0.0700611	+	0.0468133i	0.520046	+	0.854138i	$0.325915\pi$
$182$	0.155639	−	4.34414i	0.0115367	−	0.322009i
$183$	8.16750	+	8.16750i	0.603759	+	0.603759i
$184$	−5.70781	+	1.67388i	−0.420786	+	0.123400i
$185$	5.96413	+	2.47042i	0.438492	+	0.181629i
$186$	2.44659	−	10.3483i	0.179393	−	0.758774i
$187$	−13.4275	+	6.93095i	−0.981914	+	0.506841i
$188$	−5.10949	+	10.2017i	−0.372647	+	0.744038i
$189$	−3.50273	+	8.45634i	−0.254786	+	0.615108i
$190$	−6.57235	−	7.06079i	−0.476808	−	0.512244i
$191$	−2.66246	+	2.66246i	−0.192649	+	0.192649i	−0.796840	−	0.604191i	$-0.793496\pi$
$191$	−2.66246	+	2.66246i	−0.192649	+	0.192649i	0.604191	+	0.796840i	$0.293496\pi$
$192$	−6.33169	−	16.1245i	−0.456950	−	1.16368i
$193$	0.294920	+	0.441379i	0.0212288	+	0.0317712i	0.841932	−	0.539583i	$-0.181418\pi$
$193$	0.294920	+	0.441379i	0.0212288	+	0.0317712i	−0.820703	+	0.571354i	$0.806418\pi$
$194$	−2.26893	+	4.96679i	−0.162900	+	0.356595i
$195$	−0.718530	−	1.73468i	−0.0514550	−	0.124223i
$196$	0.485781	−	6.77076i	0.0346986	−	0.483626i
$197$	21.1565	+	4.20829i	1.50734	+	0.299828i	0.878513	−	0.477719i	$-0.158536\pi$
$197$	21.1565	+	4.20829i	1.50734	+	0.299828i	0.628825	+	0.777547i	$0.283536\pi$
$198$	3.05809	+	8.20187i	0.217329	+	0.582881i
$199$	−1.65726	−	8.33159i	−0.117480	−	0.590611i	−0.994012	−	0.109268i	$-0.965149\pi$
$199$	−1.65726	−	8.33159i	−0.117480	−	0.590611i	0.876533	−	0.481343i	$-0.159851\pi$
$200$	−11.7559	+	1.04802i	−0.831270	+	0.0741065i
$201$	−0.563609	−	0.376591i	−0.0397539	−	0.0265627i
$202$	−15.4066	−	11.1124i	−1.08401	−	0.781864i
$203$	−26.1002			−1.83187
$204$	−16.5790	−	6.63182i	−1.16076	−	0.464320i
$205$	−0.310235			−0.0216677
$206$	−4.75226	−	3.42767i	−0.331105	−	0.238817i
$207$	2.95317	+	1.97324i	0.205259	+	0.137150i
$208$	−0.544423	+	3.77453i	−0.0377489	+	0.261716i
$209$	−5.36223	−	26.9578i	−0.370914	−	1.86471i
$210$	−3.13698	−	8.41344i	−0.216472	−	0.580583i
$211$	0.782326	+	0.155614i	0.0538575	+	0.0107129i	0.221946	−	0.975059i	$-0.428759\pi$
$211$	0.782326	+	0.155614i	0.0538575	+	0.0107129i	−0.168088	+	0.985772i	$0.553759\pi$
$212$	7.80155	+	0.559737i	0.535813	+	0.0384429i
$213$	5.03270	+	12.1500i	0.344835	+	0.832505i
$214$	3.25639	−	7.12838i	0.222602	−	0.487286i
$215$	4.13285	+	6.18525i	0.281858	+	0.421830i
$216$	3.85077	−	7.04652i	0.262012	−	0.479455i
$217$	−7.91603	+	7.91603i	−0.537375	+	0.537375i
$218$	−9.35968	−	10.0553i	−0.633918	−	0.681029i
$219$	6.23959	−	15.0637i	0.421633	−	1.01791i
$220$	5.96055	+	2.98531i	0.401860	+	0.201269i
$221$	2.44985	+	3.07419i	0.164795	+	0.206792i
$222$	−5.00113	+	21.1532i	−0.335654	+	1.41971i
$223$	0.247116	+	0.102359i	0.0165481	+	0.00685446i	0.390942	−	0.920415i	$-0.372149\pi$
$223$	0.247116	+	0.102359i	0.0165481	+	0.00685446i	−0.374394	+	0.927270i	$0.622149\pi$
$224$	−3.24821	+	17.9460i	−0.217030	+	1.19907i
$225$	4.98331	+	4.98331i	0.332221	+	0.332221i
$226$	−0.384516	+	10.7325i	−0.0255776	+	0.713913i
$227$	−15.1875	+	10.1480i	−1.00803	+	0.673545i	−0.945878	−	0.324522i	$-0.894797\pi$
$227$	−15.1875	+	10.1480i	−1.00803	+	0.673545i	−0.0621526	+	0.998067i	$0.519797\pi$
$228$	19.9312	−	25.6454i	1.31997	−	1.69841i
$229$	16.4229	−	6.80260i	1.08526	−	0.449528i	0.232907	−	0.972499i	$-0.425176\pi$
$229$	16.4229	−	6.80260i	1.08526	−	0.449528i	0.852351	+	0.522971i	$0.175176\pi$
$230$	2.67012	−	0.432375i	0.176062	−	0.0285100i
$231$	4.99144	−	25.0937i	0.328413	−	1.65104i
$232$	22.7659	+	2.45533i	1.49465	+	0.161200i
$233$	−6.37670	+	1.26840i	−0.417751	+	0.0830959i	−0.399490	−	0.916737i	$-0.630813\pi$
$233$	−6.37670	+	1.26840i	−0.417751	+	0.0830959i	−0.0182608	+	0.999833i	$0.505813\pi$
$234$	1.93746	−	1.19651i	0.126656	−	0.0782184i
$235$	2.88258	−	4.31408i	0.188039	−	0.281420i
$236$	10.1598	−	8.79954i	0.661347	−	0.572801i
$237$			7.45444i			0.484218i
$238$	11.1820	+	15.1117i	0.724820	+	0.979543i
$239$			27.0202i			1.74779i	0.486113	+	0.873896i	$0.338414\pi$
$239$			27.0202i			1.74779i	−0.486113	+	0.873896i	$0.661586\pi$
$240$	1.94475	+	7.63373i	0.125533	+	0.492755i
$241$	−14.0631	+	21.0470i	−0.905886	+	1.35575i	0.0285392	+	0.999593i	$0.490914\pi$
$241$	−14.0631	+	21.0470i	−0.905886	+	1.35575i	−0.934425	+	0.356161i	$0.884086\pi$
$242$	1.80680	+	2.92568i	0.116146	+	0.188070i
$243$	−15.4632	+	3.07582i	−0.991965	+	0.197314i
$244$	1.32717	+	10.5855i	0.0849635	+	0.677668i
$245$	−0.602219	+	3.02756i	−0.0384744	+	0.193424i
$246$	−0.166976	−	1.03115i	−0.0106460	−	0.0657440i
$247$	−6.60598	+	2.73629i	−0.420329	+	0.174106i
$248$	7.64944	−	6.16006i	0.485740	−	0.391165i
$249$	−6.33228	+	4.23109i	−0.401292	+	0.268135i
$250$	11.7906	+	0.422426i	0.745704	+	0.0267166i
$251$	5.16682	+	5.16682i	0.326127	+	0.326127i	0.851112	−	0.524985i	$-0.175929\pi$
$251$	5.16682	+	5.16682i	0.326127	+	0.326127i	−0.524985	+	0.851112i	$0.675929\pi$
$252$	9.46439	−	5.38663i	0.596200	−	0.339326i
$253$	7.12061	+	2.94945i	0.447669	+	0.185431i
$254$	−21.9133	−	5.18084i	−1.37496	−	0.325075i
$255$	7.10546	+	3.93024i	0.444961	+	0.246121i
$256$	4.52149	−	15.3478i	0.282593	−	0.959240i
$257$	8.65012	−	20.8832i	0.539580	−	1.30266i	−0.385437	−	0.922734i	$-0.625949\pi$
$257$	8.65012	−	20.8832i	0.539580	−	1.30266i	0.925017	−	0.379926i	$-0.124051\pi$
$258$	−18.3340	+	17.0658i	−1.14143	+	1.06247i
$259$	16.1813	−	16.1813i	1.00546	−	1.00546i
$260$	0.459179	−	1.67231i	0.0284771	−	0.103712i
$261$	−7.59610	−	11.3684i	−0.470187	−	0.703684i
$262$	−3.04580	−	1.39138i	−0.188170	−	0.0859598i
$263$	−6.76487	−	16.3318i	−0.417140	−	1.00706i	−0.983172	−	0.182681i	$-0.941522\pi$
$263$	−6.76487	−	16.3318i	−0.417140	−	1.00706i	0.566032	−	0.824383i	$-0.308478\pi$
$264$	−6.71442	+	21.4184i	−0.413244	+	1.31821i
$265$	−3.48848	−	0.693902i	−0.214296	−	0.0426260i
$266$	−32.0399	+	11.9462i	−1.96449	+	0.732466i
$267$	1.73167	+	8.70571i	0.105977	+	0.532781i
$268$	−0.197581	−	0.594080i	−0.0120692	−	0.0362892i
$269$	1.69975	+	1.13574i	0.103636	+	0.0692471i	0.606308	−	0.795230i	$-0.292650\pi$
$269$	1.69975	+	1.13574i	0.103636	+	0.0692471i	−0.502672	+	0.864477i	$0.667650\pi$
$270$	−2.13614	+	2.96162i	−0.130001	+	0.180239i
$271$	24.8630			1.51032			0.755160	−	0.655541i	$-0.227559\pi$
$271$	24.8630			1.51032			0.755160	+	0.655541i	$0.227559\pi$
$272$	−8.33187	−	14.2331i	−0.505194	−	0.863006i
$273$	−6.65583			−0.402829
$274$	0.808999	−	1.12163i	0.0488734	−	0.0677600i
$275$	12.7157	+	8.49634i	0.766784	+	0.512349i
$276$	2.87425	+	8.64220i	0.173009	+	0.520199i
$277$	−0.798040	−	4.01202i	−0.0479495	−	0.241059i	0.949376	−	0.314141i	$-0.101716\pi$
$277$	−0.798040	−	4.01202i	−0.0479495	−	0.241059i	−0.997326	+	0.0730823i	$0.976716\pi$
$278$	11.7042	−	4.36395i	0.701972	−	0.261732i
$279$	−5.75181	−	1.14411i	−0.344352	−	0.0684959i
$280$	2.48085	−	7.91368i	0.148259	−	0.472933i
$281$	−3.84373	−	9.27959i	−0.229298	−	0.553574i	0.766794	−	0.641893i	$-0.221851\pi$
$281$	−3.84373	−	9.27959i	−0.229298	−	0.553574i	−0.996092	+	0.0883187i	$0.971851\pi$
$282$	15.8906	+	7.25913i	0.946270	+	0.432275i
$283$	1.63507	+	2.44705i	0.0971947	+	0.145462i	0.876880	−	0.480710i	$-0.159621\pi$
$283$	1.63507	+	2.44705i	0.0971947	+	0.145462i	−0.779685	+	0.626172i	$0.784621\pi$
$284$	−3.21616	+	11.7131i	−0.190844	+	0.695046i
$285$	−10.4439	+	10.4439i	−0.618646	+	0.618646i
$286$	3.61697	−	3.36676i	0.213876	−	0.199081i
$287$	−0.420849	+	1.01602i	−0.0248420	+	0.0599738i
$288$	−8.76204	+	3.80814i	−0.516308	+	0.224397i
$289$	−16.5712	−	3.79426i	−0.974775	−	0.223192i
$290$	−10.1333	−	2.39576i	−0.595048	−	0.140684i
$291$	7.72446	+	3.19958i	0.452816	+	0.187562i
$292$	13.0882	−	7.44910i	0.765928	−	0.435926i
$293$	−16.0913	−	16.0913i	−0.940066	−	0.940066i	0.0582371	−	0.998303i	$-0.481452\pi$
$293$	−16.0913	−	16.0913i	−0.940066	−	0.940066i	−0.998303	+	0.0582371i	$0.981452\pi$
$294$	−10.3871	−	0.372142i	−0.605788	−	0.0217038i
$295$	−5.08202	+	3.39569i	−0.295886	+	0.197705i
$296$	−15.6364	+	12.5919i	−0.908846	+	0.731890i
$297$	−9.61283	+	3.98176i	−0.557793	+	0.231045i
$298$	0.289124	+	1.78548i	0.0167485	+	0.103430i
$299$	0.391156	−	1.96647i	0.0226211	−	0.113724i
$300$	2.24815	+	17.9312i	0.129797	+	1.03526i
$301$	25.8632	−	5.14450i	1.49073	−	0.296524i
$302$	13.9559	+	22.5982i	0.803074	+	1.30038i
$303$	−16.1593	+	24.1840i	−0.928325	+	1.38934i
$304$	29.0706	−	7.40594i	1.66731	−	0.424760i
$305$		−	4.85138i		−	0.277789i
$306$	−3.32778	+	9.26854i	−0.190236	+	0.529847i
$307$			2.57929i			0.147208i	0.997288	+	0.0736038i	$0.0234500\pi$
$307$			2.57929i			0.147208i	−0.997288	+	0.0736038i	$0.976550\pi$
$308$	17.8627	−	15.4711i	1.01782	−	0.881548i
$309$	−4.98441	+	7.45970i	−0.283553	+	0.424368i
$310$	−3.79999	+	2.34675i	−0.215825	+	0.133286i
$311$	−18.2953	+	3.63916i	−1.03743	+	0.206358i	−0.684288	−	0.729212i	$-0.739887\pi$
$311$	−18.2953	+	3.63916i	−1.03743	+	0.206358i	−0.353142	+	0.935570i	$0.614887\pi$
$312$	5.80554	+	0.626136i	0.328674	+	0.0354479i
$313$	1.04254	−	5.24122i	0.0589280	−	0.296251i	−0.940071	−	0.340978i	$-0.889242\pi$
$313$	1.04254	−	5.24122i	0.0589280	−	0.296251i	0.998999	+	0.0447269i	$0.0142418\pi$
$314$	24.1194	−	3.90568i	1.36114	−	0.220410i
$315$	−4.57516	+	1.89509i	−0.257781	+	0.106776i
$316$	−4.22503	+	5.43633i	−0.237676	+	0.305818i
$317$	5.61492	−	3.75177i	0.315365	−	0.210720i	−0.387806	−	0.921741i	$-0.626767\pi$
$317$	5.61492	−	3.75177i	0.315365	−	0.210720i	0.703171	+	0.711021i	$0.251767\pi$
$318$	0.428798	−	11.9684i	0.0240458	−	0.671157i
$319$	−20.9796	−	20.9796i	−1.17463	−	1.17463i
$320$	−2.90839	+	6.66932i	−0.162584	+	0.372826i
$321$	−11.0862	−	4.59205i	−0.618771	−	0.256303i
$322$	2.20613	−	9.33120i	0.122943	−	0.520007i
$323$	14.9670	−	27.0588i	0.832789	−	1.50559i
$324$	−20.0540	−	10.0439i	−1.11411	−	0.557997i
$325$	1.52246	−	3.67553i	0.0844506	−	0.203882i
$326$	21.9500	+	23.5813i	1.21570	+	1.30605i
$327$	−14.8732	+	14.8732i	−0.822491	+	0.822491i
$328$	0.462666	−	0.846632i	0.0255465	−	0.0467475i
$329$	−10.2183	−	15.2927i	−0.563352	−	0.843116i
$330$	4.24128	−	9.28435i	0.233475	−	0.511087i
$331$	3.39280	+	8.19093i	0.186485	+	0.450214i	0.989278	−	0.146043i	$-0.0466538\pi$
$331$	3.39280	+	8.19093i	0.186485	+	0.450214i	−0.802793	+	0.596257i	$0.796654\pi$
$332$	−7.01607	−	0.503380i	−0.385057	−	0.0276266i
$333$	11.7574	+	2.33869i	0.644302	+	0.128160i
$334$	−11.6570	−	31.2643i	−0.637842	−	1.71071i
$335$	0.0555429	+	0.279233i	0.00303463	+	0.0152561i
$336$	27.6387	+	3.98649i	1.50781	+	0.217481i
$337$	16.8871	+	11.2836i	0.919900	+	0.614658i	0.922775	−	0.385338i	$-0.125915\pi$
$337$	16.8871	+	11.2836i	0.919900	+	0.614658i	−0.00287518	+	0.999996i	$0.500915\pi$
$338$	13.8683	+	10.0028i	0.754336	+	0.544082i
$339$	16.4436			0.893096
$340$	2.95425	+	6.89345i	0.160217	+	0.373850i
$341$	−12.7260			−0.689150
$342$	−14.5281	−	10.4787i	−0.785591	−	0.566625i
$343$	−9.66619	−	6.45874i	−0.521925	−	0.348739i
$344$	−23.0431	+	2.05426i	−1.24240	+	0.110758i
$345$	−0.807992	−	4.06205i	−0.0435008	−	0.218693i
$346$	−1.12832	−	3.02618i	−0.0606589	−	0.162688i
$347$	−0.849345	−	0.168945i	−0.0455952	−	0.00906946i	0.172240	−	0.985055i	$-0.444900\pi$
$347$	−0.849345	−	0.168945i	−0.0455952	−	0.00906946i	−0.217835	+	0.975986i	$0.569900\pi$
$348$	2.50901	−	34.9704i	0.134497	−	1.87461i
$349$	−3.80159	−	9.17784i	−0.203494	−	0.491278i	0.788879	−	0.614549i	$-0.210662\pi$
$349$	−3.80159	−	9.17784i	−0.203494	−	0.491278i	−0.992373	+	0.123270i	$0.960662\pi$
$350$	7.90548	−	17.3054i	0.422565	−	0.925015i
$351$	1.50379	+	2.25058i	0.0802663	+	0.120127i
$352$	−17.0361	+	11.8143i	−0.908030	+	0.629702i
$353$	8.42296	−	8.42296i	0.448309	−	0.448309i	−0.446483	−	0.894792i	$-0.647324\pi$
$353$	8.42296	−	8.42296i	0.448309	−	0.448309i	0.894792	+	0.446483i	$0.147324\pi$
$354$	−14.0218	−	15.0639i	−0.745252	−	0.800637i
$355$	2.11379	−	5.10314i	0.112188	−	0.270847i
$356$	−3.67136	+	7.33033i	−0.194582	+	0.388507i
$357$	22.5105	−	17.9388i	1.19138	−	0.949425i
$358$	3.89322	−	16.4671i	0.205763	−	0.870312i
$359$	−27.8384	−	11.5310i	−1.46926	−	0.608585i	−0.502566	−	0.864539i	$-0.667611\pi$
$359$	−27.8384	−	11.5310i	−1.46926	−	0.608585i	−0.966689	+	0.255953i	$0.917611\pi$
$360$	4.16896	−	1.22259i	0.219723	−	0.0644363i
$361$	26.3373	+	26.3373i	1.38618	+	1.38618i
$362$	−0.0574012	+	1.60216i	−0.00301694	+	0.0842077i
$363$	4.37775	−	2.92512i	0.229772	−	0.153529i
$364$	−4.85392	−	3.77239i	−0.254415	−	0.197727i
$365$	−6.32693	+	2.62070i	−0.331167	+	0.137174i
$366$	16.1250	−	2.61113i	0.842865	−	0.136486i
$367$	2.95037	−	14.8325i	0.154008	−	0.774251i	−0.824147	−	0.566376i	$-0.808345\pi$
$367$	2.95037	−	14.8325i	0.154008	−	0.774251i	0.978155	−	0.207876i	$-0.0666549\pi$
$368$	−2.80211	+	7.93159i	−0.146070	+	0.413463i
$369$	−0.565027	+	0.112391i	−0.0294142	+	0.00585084i
$370$	7.76764	−	4.79704i	0.403820	−	0.249386i
$371$	−7.00484	+	10.4835i	−0.363673	+	0.544275i
$372$	−9.84534	−	11.3673i	−0.510457	−	0.589366i
$373$			12.4137i			0.642757i	0.946951	+	0.321379i	$0.104146\pi$
$373$			12.4137i			0.642757i	−0.946951	+	0.321379i	$0.895854\pi$
$374$	−3.15872	+	21.1351i	−0.163334	+	1.09287i
$375$		−	18.0649i		−	0.932866i
$376$	7.47425	+	14.3004i	0.385455	+	0.737484i
$377$	−4.28808	+	6.41757i	−0.220847	+	0.330521i
$378$	6.80156	+	11.0135i	0.349834	+	0.566471i
$379$	7.83466	−	1.55841i	0.402439	−	0.0800501i	0.0102792	−	0.999947i	$-0.496728\pi$
$379$	7.83466	−	1.55841i	0.402439	−	0.0800501i	0.392160	+	0.919897i	$0.371728\pi$
$380$	−13.5359	+	1.69708i	−0.694378	+	0.0870585i
$381$	−6.72627	+	33.8152i	−0.344597	+	1.73241i
$382$	0.851182	+	5.25645i	0.0435503	+	0.268943i
$383$	17.5469	−	7.26818i	0.896607	−	0.371387i	0.113692	−	0.993516i	$-0.463732\pi$
$383$	17.5469	−	7.26818i	0.896607	−	0.371387i	0.782915	+	0.622129i	$0.213732\pi$
$384$	−23.7328	−	6.07727i	−1.21111	−	0.310130i
$385$	−8.93506	+	5.97022i	−0.455373	+	0.304270i
$386$	0.750243	+	0.0268792i	0.0381863	+	0.00136812i
$387$	9.76789	+	9.76789i	0.496530	+	0.496530i
$388$	3.81979	+	6.71143i	0.193921	+	0.340721i
$389$	4.51548	+	1.87037i	0.228944	+	0.0948317i	0.494207	−	0.869344i	$-0.335459\pi$
$389$	4.51548	+	1.87037i	0.228944	+	0.0948317i	−0.265263	+	0.964176i	$0.585459\pi$
$390$	−2.58410	−	0.610945i	−0.130851	−	0.0309364i
$391$	3.97714	+	7.70500i	0.201133	+	0.389659i
$392$	−7.36412	−	6.15859i	−0.371944	−	0.311056i
$393$	−1.96208	+	4.73688i	−0.0989739	+	0.238944i
$394$	22.3295	−	20.7848i	1.12494	−	1.04712i
$395$	2.21392	−	2.21392i	0.111394	−	0.111394i
$396$	11.9374	+	3.27775i	0.599877	+	0.164713i
$397$	−16.4323	−	24.5926i	−0.824712	−	1.23427i	−0.969570	−	0.244816i	$-0.921273\pi$
$397$	−16.4323	−	24.5926i	−0.824712	−	1.23427i	0.144858	−	0.989452i	$-0.453727\pi$
$398$	−10.9273	−	4.99181i	−0.547736	−	0.250217i
$399$	20.0362	+	48.3717i	1.00307	+	2.42162i
$400$	−8.52353	+	14.3510i	−0.426176	+	0.717548i
$401$	17.2362	+	3.42850i	0.860737	+	0.171211i	0.605674	−	0.795713i	$-0.292904\pi$
$401$	17.2362	+	3.42850i	0.860737	+	0.171211i	0.255063	+	0.966924i	$0.417904\pi$
$402$	−0.898216	+	0.334903i	−0.0447989	+	0.0167034i
$403$	0.645861	+	3.24696i	0.0321726	+	0.161743i
$404$	−25.4916	+	8.47806i	−1.26825	+	0.421799i
$405$	8.48038	+	5.66641i	0.421394	+	0.281566i
$406$	−21.5925	+	29.9366i	−1.07162	+	1.48573i
$407$	26.0134			1.28944
$408$	−21.3223	+	13.5295i	−1.05561	+	0.669811i
$409$	37.2165			1.84024			0.920118	−	0.391640i	$-0.128092\pi$
$409$	37.2165			1.84024			0.920118	+	0.391640i	$0.128092\pi$
$410$	−0.256655	+	0.355836i	−0.0126753	+	0.0175735i
$411$	−1.76064	−	1.17642i	−0.0868459	−	0.0580286i
$412$	−7.86301	+	2.61510i	−0.387383	+	0.128837i
$413$	4.22690	+	21.2501i	0.207992	+	1.04565i
$414$	4.70642	−	1.75480i	0.231308	−	0.0862439i
$415$	3.13725	+	0.624037i	0.154001	+	0.0306328i
$416$	3.87895	+	3.74709i	0.190181	+	0.183716i
$417$	−7.31926	−	17.6703i	−0.358426	−	0.865316i
$418$	−35.3564	−	16.1515i	−1.72934	−	0.789998i
$419$	0.719401	+	1.07666i	0.0351450	+	0.0525982i	0.848626	−	0.528993i	$-0.177430\pi$
$419$	0.719401	+	1.07666i	0.0351450	+	0.0525982i	−0.813481	+	0.581591i	$0.802430\pi$
$420$	−12.2453	−	3.36230i	−0.597511	−	0.164063i
$421$	−20.3767	+	20.3767i	−0.993098	+	0.993098i	−0.999976	−	0.00687860i	$-0.997810\pi$
$421$	−20.3767	+	20.3767i	−0.993098	+	0.993098i	0.00687860	+	0.999976i	$0.497810\pi$
$422$	0.825701	−	0.768582i	0.0401945	−	0.0374140i
$423$	3.68712	−	8.90149i	0.179274	−	0.432805i
$424$	7.09618	−	8.48524i	0.344621	−	0.412080i
$425$	4.75728	+	16.5343i	0.230762	+	0.802029i
$426$	18.0995	+	4.27916i	0.876922	+	0.207326i
$427$	−15.8883	−	6.58115i	−0.768889	−	0.318484i
$428$	−5.48220	−	9.63230i	−0.264992	−	0.465595i
$429$	−5.35002	−	5.35002i	−0.258302	−	0.258302i
$430$	10.5135	+	0.376671i	0.507006	+	0.0181647i
$431$	0.221345	−	0.147898i	0.0106618	−	0.00712400i	−0.550228	−	0.835015i	$-0.685459\pi$
$431$	0.221345	−	0.147898i	0.0106618	−	0.00712400i	0.560890	+	0.827891i	$0.310459\pi$
$432$	−4.89658	−	10.2463i	−0.235587	−	0.492977i
$433$	−15.4713	+	6.40841i	−0.743502	+	0.307969i	−0.722087	−	0.691802i	$-0.756817\pi$
$433$	−15.4713	+	6.40841i	−0.743502	+	0.307969i	−0.0214147	+	0.999771i	$0.506817\pi$
$434$	2.53074	+	15.6285i	0.121479	+	0.750191i
$435$	−3.11041	+	15.6371i	−0.149133	+	0.749740i
$436$	−19.2765	+	2.41681i	−0.923176	+	0.115744i
$437$	−15.4690	+	3.07698i	−0.739983	+	0.147192i
$438$	−12.1160	−	19.6189i	−0.578923	−	0.937425i
$439$	−7.74857	+	11.5966i	−0.369819	+	0.553474i	−0.968975	−	0.247159i	$-0.920503\pi$
$439$	−7.74857	+	11.5966i	−0.369819	+	0.553474i	0.599156	+	0.800633i	$0.295503\pi$
$440$	8.35524	−	4.36697i	0.398320	−	0.208187i
$441$			5.73224i			0.272964i
$442$	5.55281	−	0.266705i	0.264120	−	0.0126859i
$443$		−	16.5985i		−	0.788617i	−0.918978	−	0.394309i	$-0.870984\pi$
$443$		−	16.5985i		−	0.788617i	0.918978	−	0.394309i	$-0.129016\pi$
$444$	20.1251	+	23.2361i	0.955094	+	1.10274i
$445$	2.07124	−	3.09983i	0.0981862	−	0.146946i
$446$	0.321842	−	0.198759i	0.0152397	−	0.00941153i
$447$	2.71625	−	0.540295i	0.128474	−	0.0255551i
$448$	17.8967	+	18.5723i	0.845540	+	0.877458i
$449$	−5.30857	+	26.6880i	−0.250527	+	1.25948i	0.626644	+	0.779306i	$0.284428\pi$
$449$	−5.30857	+	26.6880i	−0.250527	+	1.25948i	−0.877171	+	0.480179i	$0.840572\pi$
$450$	9.83846	−	1.59315i	0.463789	−	0.0751019i
$451$	−1.15497	+	0.478405i	−0.0543855	+	0.0225272i
$452$	11.9919	+	9.31992i	0.564053	+	0.438372i
$453$	33.8142	−	22.5939i	1.58873	−	1.06156i
$454$	−0.924893	+	25.8153i	−0.0434074	+	1.21157i
$455$	1.97673	+	1.97673i	0.0926707	+	0.0926707i
$456$	−12.9261	−	44.0771i	−0.605320	−	2.06410i
$457$	−24.0766	−	9.97285i	−1.12626	−	0.466510i	−0.259749	−	0.965676i	$-0.583640\pi$
$457$	−24.0766	−	9.97285i	−1.12626	−	0.466510i	−0.866506	+	0.499166i	$0.833640\pi$
$458$	5.78405	−	24.4647i	0.270271	−	1.14316i
$459$	−11.1517	−	3.55859i	−0.520517	−	0.166101i
$460$	1.71304	−	3.42030i	0.0798709	−	0.159472i
$461$	3.80040	−	9.17497i	0.177002	−	0.427321i	−0.810333	−	0.585970i	$-0.800714\pi$
$461$	3.80040	−	9.17497i	0.177002	−	0.427321i	0.987335	+	0.158649i	$0.0507137\pi$
$462$	−24.6528	−	26.4849i	−1.14695	−	1.23219i
$463$	19.5614	−	19.5614i	0.909097	−	0.909097i	−0.0871028	−	0.996199i	$-0.527761\pi$
$463$	19.5614	−	19.5614i	0.909097	−	0.909097i	0.996199	+	0.0871028i	$0.0277609\pi$
$464$	21.6503	−	24.0809i	1.00509	−	1.11793i
$465$	3.79926	+	5.68600i	0.176187	+	0.263682i
$466$	−3.82055	+	8.36335i	−0.176983	+	0.387425i
$467$	−2.74887	−	6.63636i	−0.127203	−	0.307094i	0.847429	−	0.530908i	$-0.178149\pi$
$467$	−2.74887	−	6.63636i	−0.127203	−	0.307094i	−0.974632	+	0.223814i	$0.928149\pi$
$468$	0.230459	−	3.21211i	0.0106530	−	0.148480i
$469$	0.989836	+	0.196891i	0.0457064	+	0.00909157i
$470$	−2.56348	−	6.87530i	−0.118244	−	0.317134i
$471$	−7.29866	−	36.6928i	−0.336304	−	1.69072i
$472$	−1.68785	−	18.9330i	−0.0776895	−	0.871462i
$473$	24.9243	+	16.6539i	1.14602	+	0.765746i
$474$	8.55017	+	6.16701i	0.392723	+	0.283260i
$475$	−31.2953			−1.43593
$476$	26.5837	−	0.323850i	1.21846	−	0.0148437i
$477$	−6.60492			−0.302419
$478$	30.9919	+	22.3536i	1.41754	+	1.02243i
$479$	−16.0213	−	10.7051i	−0.732030	−	0.489127i	0.132830	−	0.991139i	$-0.457593\pi$
$479$	−16.0213	−	10.7051i	−0.732030	−	0.489127i	−0.864861	+	0.502012i	$0.832593\pi$
$480$	10.3647	+	4.08472i	0.473081	+	0.186441i
$481$	−1.32022	−	6.63718i	−0.0601967	−	0.302629i
$482$	12.5063	+	33.5423i	0.569648	+	1.52781i
$483$	−14.3993	−	2.86420i	−0.655192	−	0.130326i
$484$	4.85048	+	0.348006i	0.220476	+	0.0158185i
$485$	−1.34386	−	3.24436i	−0.0610215	−	0.147319i
$486$	−9.26466	+	20.2808i	−0.420253	+	0.919954i
$487$	7.29819	+	10.9225i	0.330712	+	0.494946i	0.959144	−	0.282919i	$-0.0913027\pi$
$487$	7.29819	+	10.9225i	0.330712	+	0.494946i	−0.628431	+	0.777865i	$0.716303\pi$
$488$	13.2394	+	7.23507i	0.599322	+	0.327516i
$489$	34.8802	−	34.8802i	1.57734	−	1.57734i
$490$	2.97437	+	3.19542i	0.134368	+	0.144354i
$491$	−2.59251	+	6.25888i	−0.116999	+	0.282459i	−0.971520	−	0.236956i	$-0.923850\pi$
$491$	−2.59251	+	6.25888i	−0.116999	+	0.282459i	0.854522	+	0.519415i	$0.173850\pi$
$492$	−1.32086	−	0.661546i	−0.0595490	−	0.0298248i
$493$	−2.79409	−	33.2620i	−0.125839	−	1.49804i
$494$	−2.32659	+	9.84071i	−0.104678	+	0.442754i
$495$	−5.20086	−	2.15427i	−0.233761	−	0.0968270i
$496$	−0.737210	−	13.8700i	−0.0331017	−	0.622782i
$497$	−13.8454	−	13.8454i	−0.621050	−	0.621050i
$498$	−0.385625	+	10.7634i	−0.0172803	+	0.482320i
$499$	−7.35051	+	4.91145i	−0.329054	+	0.219867i	−0.709112	−	0.705096i	$-0.750904\pi$
$499$	−7.35051	+	4.91145i	−0.329054	+	0.219867i	0.380058	+	0.924963i	$0.375904\pi$
$500$	10.2388	−	13.1742i	0.457893	−	0.589170i
$501$	−47.2008	+	19.5512i	−2.10878	+	0.873484i
$502$	10.2008	−	1.65182i	0.455283	−	0.0737244i
$503$	−7.56240	+	38.0188i	−0.337191	+	1.69517i	0.324900	+	0.945748i	$0.394669\pi$
$503$	−7.56240	+	38.0188i	−0.337191	+	1.69517i	−0.662091	+	0.749424i	$0.730331\pi$
$504$	1.65141	−	15.3119i	0.0735595	−	0.682045i
$505$	11.9817	−	2.38330i	0.533178	−	0.106056i
$506$	9.27382	−	5.72721i	0.412272	−	0.254606i
$507$	14.5458	−	21.7693i	0.646001	−	0.966809i
$508$	−24.0711	+	20.8483i	−1.06798	+	0.924993i
$509$			6.10259i			0.270493i	0.990812	+	0.135246i	$0.0431826\pi$
$509$			6.10259i			0.270493i	−0.990812	+	0.135246i	$0.956817\pi$
$510$	10.3862	−	4.89843i	0.459910	−	0.216906i
$511$			24.2759i			1.07390i
$512$	−13.8632	−	17.8833i	−0.612674	−	0.790336i
$513$	11.8294	−	17.7039i	0.522279	−	0.781646i
$514$	−16.7967	−	27.1981i	−0.740870	−	1.19966i
$515$	3.69581	−	0.735143i	0.162857	−	0.0323943i
$516$	4.40664	+	35.1474i	0.193992	+	1.54728i
$517$	4.07890	−	20.5060i	0.179390	−	0.901854i
$518$	−5.17313	−	31.9465i	−0.227294	−	1.40365i
$519$	−4.56873	+	1.89243i	−0.200545	+	0.0830685i
$520$	−1.53825	−	1.91016i	−0.0674566	−	0.0837662i
$521$	15.5811	−	10.4110i	0.682621	−	0.456113i	−0.165294	−	0.986244i	$-0.552857\pi$
$521$	15.5811	−	10.4110i	0.682621	−	0.456113i	0.847915	+	0.530132i	$0.177857\pi$
$522$	−19.3236	−	0.692314i	−0.845771	−	0.0303017i
$523$	20.7839	+	20.7839i	0.908818	+	0.908818i	0.996177	−	0.0873586i	$-0.0278426\pi$
$523$	20.7839	+	20.7839i	0.908818	+	0.908818i	−0.0873586	+	0.996177i	$0.527843\pi$
$524$	−4.11566	+	2.34242i	−0.179794	+	0.102329i
$525$	−26.9138	−	11.1481i	−1.17461	−	0.486541i
$526$	−24.3290	−	5.75197i	−1.06079	−	0.250798i
$527$	−10.9356	−	9.24073i	−0.476362	−	0.402532i
$528$	19.0119	+	25.4206i	0.827385	+	1.10629i
$529$	−7.10925	+	17.1633i	−0.309098	+	0.746229i
$530$	−3.68189	+	3.42719i	−0.159931	+	0.148868i
$531$	−8.02565	+	8.02565i	−0.348283	+	0.348283i
$532$	−12.8042	+	46.6324i	−0.555133	+	2.02177i
$533$	0.180679	+	0.270405i	0.00782606	+	0.0117125i
$534$	11.4180	+	5.21596i	0.494104	+	0.225717i
$535$	1.92872	+	4.65633i	0.0833856	+	0.201311i
$536$	−0.844862	−	0.264855i	−0.0364925	−	0.0114400i
$537$	−25.4110	−	5.05456i	−1.09656	−	0.218120i
$538$	2.70887	−	1.01001i	0.116788	−	0.0435446i
$539$	2.42672	+	12.2000i	0.104526	+	0.525489i
$540$	1.62974	+	4.90026i	0.0701329	+	0.210874i
$541$	−29.8086	−	19.9175i	−1.28157	−	0.856320i	−0.286757	−	0.958003i	$-0.592577\pi$
$541$	−29.8086	−	19.9175i	−1.28157	−	0.856320i	−0.994817	+	0.101683i	$0.967577\pi$
$542$	20.5690	−	28.5176i	0.883513	−	1.22494i
$543$	2.45474			0.105343
$544$	−23.2181	−	2.21834i	−0.995467	−	0.0951104i
$545$	8.83448			0.378428
$546$	−5.50632	+	7.63417i	−0.235649	+	0.326712i
$547$	−12.9489	−	8.65220i	−0.553657	−	0.369942i	0.247046	−	0.969004i	$-0.420540\pi$
$547$	−12.9489	−	8.65220i	−0.553657	−	0.369942i	−0.800702	+	0.599062i	$0.795540\pi$
$548$	−0.617217	−	1.85583i	−0.0263662	−	0.0792771i
$549$	−1.75754	−	8.83577i	−0.0750102	−	0.377102i
$550$	20.2648	−	7.55579i	0.864094	−	0.322180i
$551$	59.5487	+	11.8450i	2.53686	+	0.504613i
$552$	12.2904	+	3.85289i	0.523112	+	0.163990i
$553$	−4.24730	−	10.2539i	−0.180614	−	0.436040i
$554$	−5.26196	−	2.40377i	−0.223559	−	0.102126i
$555$	−7.76615	−	11.6229i	−0.329655	−	0.493363i
$556$	4.67740	−	17.0349i	0.198366	−	0.722440i
$557$	−19.1649	+	19.1649i	−0.812042	+	0.812042i	−0.984940	−	0.172898i	$-0.944687\pi$
$557$	−19.1649	+	19.1649i	−0.812042	+	0.812042i	0.172898	+	0.984940i	$0.444687\pi$
$558$	−6.07071	+	5.65076i	−0.256994	+	0.239216i
$559$	2.98420	−	7.20450i	0.126218	−	0.304718i
$560$	−7.02453	−	9.39245i	−0.296840	−	0.396903i
$561$	32.5136	+	3.67473i	1.37273	+	0.155147i
$562$	−13.8235	−	3.26821i	−0.583109	−	0.137861i
$563$	18.1553	+	7.52019i	0.765156	+	0.316938i	0.730909	−	0.682475i	$-0.239097\pi$
$563$	18.1553	+	7.52019i	0.765156	+	0.316938i	0.0342476	+	0.999413i	$0.489097\pi$
$564$	21.4723	−	12.2209i	0.904147	−	0.514593i
$565$	−4.88365	−	4.88365i	−0.205457	−	0.205457i
$566$	4.15943	+	0.149021i	0.174834	+	0.00626383i
$567$	30.0616	−	20.0865i	1.26247	−	0.843555i
$568$	10.7741	+	13.3791i	0.452073	+	0.561374i
$569$	−39.0628	+	16.1803i	−1.63760	+	0.678315i	−0.996052	−	0.0887705i	$-0.971706\pi$
$569$	−39.0628	+	16.1803i	−1.63760	+	0.678315i	−0.641545	+	0.767085i	$0.721706\pi$
$570$	3.33890	+	20.6193i	0.139851	+	0.863647i
$571$	1.26728	−	6.37102i	0.0530338	−	0.266619i	−0.945166	−	0.326589i	$-0.894101\pi$
$571$	1.26728	−	6.37102i	0.0530338	−	0.266619i	0.998200	+	0.0599703i	$0.0191006\pi$
$572$	−0.869349	−	6.93392i	−0.0363493	−	0.289922i
$573$	7.99663	−	1.59063i	0.334064	−	0.0664495i
$574$	0.817200	+	1.32326i	0.0341093	+	0.0552317i
$575$	4.87540	−	7.29655i	0.203318	−	0.304287i
$576$	−2.88088	+	13.2004i	−0.120037	+	0.550017i
$577$			32.6020i			1.35724i	0.734489	+	0.678621i	$0.237422\pi$
$577$			32.6020i			1.35724i	−0.734489	+	0.678621i	$0.762578\pi$
$578$	−18.0612	+	15.8680i	−0.751246	+	0.660022i
$579$		−	1.14948i		−	0.0477706i
$580$	−11.1311	+	9.64080i	−0.462194	+	0.400312i
$581$	6.29957	−	9.42797i	0.261350	−	0.391138i
$582$	10.0603	−	6.21289i	0.417012	−	0.257533i
$583$	−14.0573	+	2.79617i	−0.582194	+	0.115806i
$584$	2.28371	−	21.1746i	0.0945006	−	0.876211i
$585$	−0.285698	+	1.43630i	−0.0118122	+	0.0593837i
$586$	−31.7688	+	5.14436i	−1.31236	+	0.212512i
$587$	−30.5185	+	12.6412i	−1.25963	+	0.521758i	−0.909797	−	0.415053i	$-0.863763\pi$
$587$	−30.5185	+	12.6412i	−1.25963	+	0.521758i	−0.349837	+	0.936810i	$0.613763\pi$
$588$	−9.02001	+	11.6060i	−0.371979	+	0.478624i
$589$	21.6533	−	14.4683i	0.892208	−	0.596155i
$590$	−0.309486	+	8.63826i	−0.0127413	+	0.355631i
$591$	−33.0286	−	33.0286i	−1.35861	−	1.35861i
$592$	1.50695	+	28.3520i	0.0619351	+	1.16526i
$593$	9.65090	+	3.99753i	0.396315	+	0.164159i	0.571935	−	0.820299i	$-0.306193\pi$
$593$	9.65090	+	3.99753i	0.396315	+	0.164159i	−0.175620	+	0.984458i	$0.556193\pi$
$594$	−3.38558	+	14.3199i	−0.138912	+	0.587553i
$595$	−12.0132	−	1.35774i	−0.492492	−	0.0556621i
$596$	2.28712	+	1.14549i	0.0936839	+	0.0469211i
$597$	−7.03929	+	16.9943i	−0.288099	+	0.695532i
$598$	−1.93192	−	2.07550i	−0.0790023	−	0.0848735i
$599$	−9.81208	+	9.81208i	−0.400911	+	0.400911i	−0.878554	−	0.477643i	$-0.841491\pi$
$599$	−9.81208	+	9.81208i	−0.400911	+	0.400911i	0.477643	+	0.878554i	$0.341491\pi$
$600$	22.4268	+	12.2557i	0.915570	+	0.500339i
$601$	−2.80282	−	4.19471i	−0.114329	−	0.171106i	0.769892	−	0.638174i	$-0.220310\pi$
$601$	−2.80282	−	4.19471i	−0.114329	−	0.171106i	−0.884221	+	0.467069i	$0.845310\pi$
$602$	15.4957	−	33.9208i	0.631558	−	1.38251i
$603$	0.202319	+	0.488442i	0.00823908	+	0.0198909i
$604$	37.4656	+	2.68804i	1.52445	+	0.109375i
$605$	−2.16890	−	0.431421i	−0.0881783	−	0.0175398i
$606$	14.3704	+	38.5418i	0.583759	+	1.56565i
$607$	2.03087	+	10.2099i	0.0824306	+	0.414407i	0.999864	+	0.0165164i	$0.00525757\pi$
$607$	2.03087	+	10.2099i	0.0824306	+	0.414407i	−0.917433	+	0.397890i	$0.869742\pi$
$608$	15.5553	−	39.4705i	0.630852	−	1.60074i
$609$	46.9921	+	31.3991i	1.90422	+	1.27236i
$610$	−5.56448	−	4.01351i	−0.225299	−	0.162502i
$611$	−5.43901			−0.220039
$612$	7.87788	+	11.4847i	0.318445	+	0.464242i
$613$	−19.6934			−0.795409			−0.397705	−	0.917514i	$-0.630193\pi$
$613$	−19.6934			−0.795409			−0.397705	+	0.917514i	$0.630193\pi$
$614$	2.95842	+	2.13382i	0.119392	+	0.0861141i
$615$	0.558562	+	0.373219i	0.0225234	+	0.0150497i
$616$	−2.96753	−	33.2875i	−0.119565	−	1.34119i
$617$	−0.214653	−	1.07913i	−0.00864159	−	0.0434442i	0.976224	−	0.216765i	$-0.0695504\pi$
$617$	−0.214653	−	1.07913i	−0.00864159	−	0.0434442i	−0.984865	+	0.173320i	$0.944550\pi$
$618$	4.43264	+	11.8884i	0.178307	+	0.478223i
$619$	12.7222	+	2.53060i	0.511348	+	0.101714i	0.444019	−	0.896017i	$-0.353552\pi$
$619$	12.7222	+	2.53060i	0.511348	+	0.101714i	0.0673293	+	0.997731i	$0.478552\pi$
$620$	−0.452005	+	6.30000i	−0.0181530	+	0.253014i
$621$	2.28483	+	5.51606i	0.0916870	+	0.221352i
$622$	−10.9615	+	23.9952i	−0.439515	+	0.962118i
$623$	−7.34222	−	10.9884i	−0.294160	−	0.440241i
$624$	5.52105	−	6.14090i	0.221019	−	0.245833i
$625$	9.38806	−	9.38806i	0.375522	−	0.375522i
$626$	−5.14914	−	5.53181i	−0.205801	−	0.221096i
$627$	−22.7764	+	54.9871i	−0.909601	+	2.19597i
$628$	15.4740	−	30.8959i	0.617481	−	1.23288i
$629$	22.3537	+	18.8892i	0.891299	+	0.753160i
$630$	−1.61134	+	6.81546i	−0.0641974	+	0.271534i
$631$	33.9275	+	14.0532i	1.35063	+	0.559450i	0.936468	−	0.350753i	$-0.114074\pi$
$631$	33.9275	+	14.0532i	1.35063	+	0.559450i	0.414163	+	0.910203i	$0.364074\pi$
$632$	2.74009	+	9.34351i	0.108995	+	0.371665i
$633$	−1.22133	−	1.22133i	−0.0485436	−	0.0485436i
$634$	0.341939	−	9.54407i	0.0135801	−	0.379044i
$635$	12.0405	−	8.04524i	0.477814	−	0.319265i
$636$	−13.3729	−	10.3932i	−0.530272	−	0.412118i
$637$	2.98959	−	1.23833i	0.118452	−	0.0490644i
$638$	−41.4196	+	6.70713i	−1.63982	+	0.265538i
$639$	2.00108	−	10.0601i	0.0791614	−	0.397971i
$640$	5.24356	+	8.85338i	0.207270	+	0.349960i
$641$	−6.11736	+	1.21682i	−0.241621	+	0.0480614i	−0.314415	−	0.949286i	$-0.601808\pi$
$641$	−6.11736	+	1.21682i	−0.241621	+	0.0480614i	0.0727941	+	0.997347i	$0.476808\pi$
$642$	−14.4386	+	8.91679i	−0.569845	+	0.351918i
$643$	22.7889	−	34.1060i	0.898707	−	1.34501i	−0.0396037	−	0.999215i	$-0.512610\pi$
$643$	22.7889	−	34.1060i	0.898707	−	1.34501i	0.938310	−	0.345794i	$-0.112390\pi$
$644$	−8.87768	−	10.2500i	−0.349830	−	0.403908i
$645$		−	16.1081i		−	0.634258i
$646$	−18.6541	−	39.5526i	−0.733935	−	1.55618i
$647$			4.47277i			0.175843i	0.996127	+	0.0879213i	$0.0280224\pi$
$647$			4.47277i			0.175843i	−0.996127	+	0.0879213i	$0.971978\pi$
$648$	−28.1108	+	14.6925i	−1.10430	+	0.577175i
$649$	−13.6834	+	20.4787i	−0.537121	+	0.803858i
$650$	−2.95628	−	4.78698i	−0.115955	−	0.187761i
$651$	23.7756	−	4.72926i	0.931839	−	0.185354i
$652$	45.2066	−	5.66784i	1.77043	−	0.221970i
$653$	−8.62585	+	43.3651i	−0.337556	+	1.69701i	0.323138	+	0.946352i	$0.395262\pi$
$653$	−8.62585	+	43.3651i	−0.337556	+	1.69701i	−0.660694	+	0.750656i	$0.729738\pi$
$654$	4.75493	+	29.3639i	0.185933	+	1.14822i
$655$	1.98954	−	0.824096i	0.0777380	−	0.0322001i
$656$	−0.588319	−	1.23109i	−0.0229700	−	0.0480658i
$657$	−10.5738	+	7.06516i	−0.412522	+	0.275638i
$658$	−25.9941	−	0.931301i	−1.01336	−	0.0363059i
$659$	−25.4492	−	25.4492i	−0.991361	−	0.991361i	0.00860248	−	0.999963i	$-0.497262\pi$
$659$	−25.4492	−	25.4492i	−0.991361	−	0.991361i	−0.999963	+	0.00860248i	$0.997262\pi$
$660$	−7.14028	−	12.5456i	−0.277935	−	0.488336i
$661$	1.16785	+	0.483738i	0.0454239	+	0.0188152i	0.405280	−	0.914193i	$-0.367174\pi$
$661$	1.16785	+	0.483738i	0.0454239	+	0.0188152i	−0.359856	+	0.933008i	$0.617174\pi$
$662$	12.2018	+	2.88480i	0.474235	+	0.112121i
$663$	−0.712523	−	8.48216i	−0.0276721	−	0.329420i
$664$	−6.38171	+	7.63092i	−0.247658	+	0.296137i
$665$	8.41545	−	20.3167i	0.326337	−	0.787847i
$666$	12.4093	−	11.5508i	0.480849	−	0.447586i
$667$	−12.0386	+	12.0386i	−0.466136	+	0.466136i
$668$	−45.5036	−	12.4943i	−1.76059	−	0.483418i
$669$	−0.321781	−	0.481579i	−0.0124408	−	0.0186189i
$670$	0.366228	+	0.167300i	0.0141486	+	0.00646337i
$671$	−7.48119	−	18.0612i	−0.288808	−	0.697244i
$672$	27.4377	−	28.4033i	1.05843	−	1.09568i
$673$	13.4959	+	2.68450i	0.520229	+	0.103480i	0.448219	−	0.893924i	$-0.352059\pi$
$673$	13.4959	+	2.68450i	0.520229	+	0.103480i	0.0720101	+	0.997404i	$0.477059\pi$
$674$	26.9128	−	10.0345i	1.03664	−	0.386515i
$675$	2.31122	+	11.6193i	0.0889588	+	0.447226i
$676$	22.9463	−	7.63154i	0.882549	−	0.293521i
$677$	6.33204	+	4.23093i	0.243360	+	0.162608i	0.671269	−	0.741214i	$-0.265750\pi$
$677$	6.33204	+	4.23093i	0.243360	+	0.162608i	−0.427909	+	0.903822i	$0.640750\pi$
$678$	13.6037	−	18.8607i	0.522447	−	0.724341i
$679$	−12.4483			−0.477723
$680$	10.3507	+	2.31441i	0.396933	+	0.0887536i
$681$	39.5526			1.51566
$682$	−10.5281	+	14.5966i	−0.403142	+	0.558932i
$683$	31.9188	+	21.3275i	1.22134	+	0.816073i	0.987717	−	0.156255i	$-0.0499422\pi$
$683$	31.9188	+	21.3275i	1.22134	+	0.816073i	0.233622	+	0.972327i	$0.424942\pi$
$684$	−24.0380	+	7.99464i	−0.919117	+	0.305683i
$685$	0.173509	+	0.872286i	0.00662942	+	0.0333283i
$686$	−15.4049	+	5.74375i	−0.588161	+	0.219298i
$687$	−37.7524	−	7.50941i	−1.44034	−	0.286502i
$688$	−16.7072	+	28.1297i	−0.636954	+	1.07243i
$689$	1.42685	+	3.44473i	0.0543588	+	0.131234i
$690$	−5.32758	−	2.43375i	−0.202817	−	0.0926511i
$691$	−8.33971	−	12.4813i	−0.317257	−	0.474809i	0.638228	−	0.769847i	$-0.279668\pi$
$691$	−8.33971	−	12.4813i	−0.317257	−	0.474809i	−0.955486	+	0.295038i	$0.904668\pi$
$692$	−4.40445	−	1.20936i	−0.167432	−	0.0459731i
$693$	−14.1105	+	14.1105i	−0.536012	+	0.536012i
$694$	−0.896436	+	0.834423i	−0.0340282	+	0.0316743i
$695$	−3.07417	+	7.42171i	−0.116610	+	0.281522i
$696$	−38.0350	−	31.8085i	−1.44171	−	1.20570i
$697$	−1.33987	−	0.427561i	−0.0507510	−	0.0161950i
$698$	−13.6719	−	3.23238i	−0.517490	−	0.122347i
$699$	13.0069	+	5.38761i	0.491964	+	0.203778i
$700$	−13.3090	−	23.3842i	−0.503034	−	0.883839i
$701$	−32.1698	−	32.1698i	−1.21504	−	1.21504i	−0.969349	−	0.245689i	$-0.920986\pi$
$701$	−32.1698	−	32.1698i	−1.21504	−	1.21504i	−0.245689	−	0.969349i	$-0.579014\pi$
$702$	3.82546	+	0.137056i	0.144383	+	0.00517286i
$703$	−44.2619	+	29.5749i	−1.66937	+	1.11544i
$704$	−0.543039	+	29.3142i	−0.0204665	+	1.10482i
$705$	−10.3799	+	4.29949i	−0.390929	+	0.161928i
$706$	−2.69280	−	16.6293i	−0.101345	−	0.625852i
$707$	8.44844	−	42.4732i	0.317736	−	1.59737i
$708$	−28.8783	+	3.62065i	−1.08531	+	0.136072i
$709$	33.4960	−	6.66277i	1.25797	−	0.250226i	0.479295	−	0.877654i	$-0.340893\pi$
$709$	33.4960	−	6.66277i	1.25797	−	0.250226i	0.778674	+	0.627429i	$0.215893\pi$
$710$	−4.10453	−	6.64629i	−0.154040	−	0.249431i
$711$	3.23014	−	4.83424i	0.121140	−	0.181298i
$712$	5.37053	+	10.2753i	0.201269	+	0.385085i
$713$			7.30246i			0.273479i
$714$	−1.95292	−	40.6600i	−0.0730864	−	1.52166i
$715$			3.17784i			0.118844i
$716$	−15.6668	−	18.0886i	−0.585494	−	0.676002i
$717$	32.5059	−	48.6486i	1.21396	−	1.81681i
$718$	−36.2565	+	22.3908i	−1.35308	+	0.835619i
$719$	10.5030	−	2.08917i	0.391695	−	0.0779129i	0.00468600	−	0.999989i	$-0.498508\pi$
$719$	10.5030	−	2.08917i	0.391695	−	0.0779129i	0.387009	+	0.922076i	$0.373508\pi$
$720$	2.04665	−	5.79320i	0.0762740	−	0.215900i
$721$	2.60597	−	13.1011i	0.0970513	−	0.487910i
$722$	51.9974	−	8.41999i	1.93514	−	0.313359i
$723$	50.6400	−	20.9758i	1.88332	−	0.780097i
$724$	1.79018	+	1.39129i	0.0665313	+	0.0517070i
$725$	−28.0884	+	18.7681i	−1.04318	+	0.697030i
$726$	0.266597	−	7.44117i	0.00989435	−	0.276168i
$727$	33.0560	+	33.0560i	1.22598	+	1.22598i	0.965472	+	0.260508i	$0.0838900\pi$
$727$	33.0560	+	33.0560i	1.22598	+	1.22598i	0.260508	+	0.965472i	$0.416110\pi$
$728$	−8.34251	+	2.44653i	−0.309194	+	0.0906746i
$729$	0.459001	+	0.190125i	0.0170000	+	0.00704165i
$730$	−2.22831	+	9.42502i	−0.0824733	+	0.348835i
$731$	9.32485	+	32.4092i	0.344892	+	1.19870i
$732$	10.3451	−	20.6553i	0.382366	−	0.763443i
$733$	2.10804	−	5.08927i	0.0778623	−	0.187976i	−0.880155	−	0.474686i	$-0.842562\pi$
$733$	2.10804	−	5.08927i	0.0778623	−	0.187976i	0.958017	+	0.286710i	$0.0925616\pi$
$734$	−14.5719	−	15.6549i	−0.537860	−	0.577832i
$735$	4.72649	−	4.72649i	0.174339	−	0.174339i
$736$	6.77930	+	9.77574i	0.249888	+	0.360339i
$737$	0.637378	+	0.953904i	0.0234781	+	0.0351375i
$738$	−0.338532	+	0.741061i	−0.0124615	+	0.0272788i
$739$	−7.02636	−	16.9631i	−0.258469	−	0.623999i	0.740369	−	0.672201i	$-0.234651\pi$
$739$	−7.02636	−	16.9631i	−0.258469	−	0.623999i	−0.998838	+	0.0482019i	$0.984651\pi$
$740$	0.923952	−	12.8780i	0.0339652	−	0.473403i
$741$	15.1856	+	3.02060i	0.557856	+	0.110964i
$742$	6.22940	+	16.7074i	0.228688	+	0.613348i
$743$	3.45503	+	17.3696i	0.126753	+	0.637229i	0.990967	+	0.134105i	$0.0428160\pi$
$743$	3.45503	+	17.3696i	0.126753	+	0.637229i	−0.864214	+	0.503124i	$0.832184\pi$
$744$	−21.1831	+	1.88845i	−0.776612	+	0.0692338i
$745$	−0.967169	−	0.646242i	−0.0354343	−	0.0236765i
$746$	14.2384	+	10.2698i	0.521305	+	0.376003i
$747$	5.93991			0.217330
$748$	21.6286	+	21.1079i	0.790819	+	0.771783i
$749$	17.8659			0.652806
$750$	−20.7202	−	14.9449i	−0.756596	−	0.545712i
$751$	2.37357	+	1.58597i	0.0866129	+	0.0578729i	0.598123	−	0.801405i	$-0.295914\pi$
$751$	2.37357	+	1.58597i	0.0866129	+	0.0578729i	−0.511510	+	0.859278i	$0.670914\pi$
$752$	22.5858	+	3.25768i	0.823618	+	0.118795i
$753$	−3.08681	−	15.5184i	−0.112490	−	0.565523i
$754$	3.81339	+	10.2276i	0.138875	+	0.372467i
$755$	−16.7528	−	3.33234i	−0.609697	−	0.121276i
$756$	18.2592	+	1.31004i	0.664081	+	0.0476457i
$757$	4.01632	+	9.69626i	0.145976	+	0.352416i	0.979908	−	0.199450i	$-0.0639157\pi$
$757$	4.01632	+	9.69626i	0.145976	+	0.352416i	−0.833932	+	0.551867i	$0.813916\pi$
$758$	4.69407	−	10.2755i	0.170496	−	0.373224i
$759$	−9.27205	−	13.8766i	−0.336554	−	0.503689i
$760$	−9.25163	+	16.9295i	−0.335592	+	0.614099i
$761$	17.9565	−	17.9565i	0.650922	−	0.650922i	−0.302293	−	0.953215i	$-0.597752\pi$
$761$	17.9565	−	17.9565i	0.650922	−	0.650922i	0.953215	+	0.302293i	$0.0977520\pi$
$762$	33.2212	+	35.6901i	1.20348	+	1.29292i
$763$	11.9844	−	28.9330i	0.433866	−	1.04744i
$764$	6.73327	+	3.37232i	0.243601	+	0.122006i
$765$	−2.90488	−	5.62769i	−0.105026	−	0.203470i
$766$	6.17992	−	26.1391i	0.223290	−	0.944444i
$767$	5.91947	+	2.45192i	0.213740	+	0.0885338i
$768$	−26.6045	+	22.1936i	−0.960008	+	0.800842i
$769$	32.2353	+	32.2353i	1.16244	+	1.16244i	0.983941	+	0.178495i	$0.0571229\pi$
$769$	32.2353	+	32.2353i	1.16244	+	1.16244i	0.178495	+	0.983941i	$0.442877\pi$
$770$	−0.544130	+	15.1875i	−0.0196091	+	0.547321i
$771$	−40.6971	+	27.1930i	−1.46567	+	0.979330i
$772$	0.651500	−	0.838284i	0.0234480	−	0.0301705i
$773$	14.4854	−	6.00007i	0.521005	−	0.215807i	−0.106653	−	0.994296i	$-0.534013\pi$
$773$	14.4854	−	6.00007i	0.521005	−	0.215807i	0.627658	+	0.778489i	$0.284013\pi$
$774$	19.2846	−	3.12277i	0.693170	−	0.112246i
$775$	−2.82681	+	14.2113i	−0.101542	+	0.510486i
$776$	10.8580	+	1.17105i	0.389781	+	0.0420384i
$777$	−48.6002	+	9.66718i	−1.74352	+	0.346808i
$778$	5.88093	−	3.63187i	0.210841	−	0.130209i
$779$	1.42129	−	2.12710i	0.0509228	−	0.0762114i
$780$	−2.83856	+	2.45851i	−0.101637	+	0.0880287i
$781$		−	22.2581i		−	0.796458i
$782$	12.1278	+	1.81255i	0.433690	+	0.0648166i
$783$		−	22.9839i		−	0.821378i
$784$	−13.1561	+	3.35162i	−0.469861	+	0.119701i
$785$	−8.72986	+	13.0652i	−0.311582	+	0.466316i
$786$	3.80994	+	6.16928i	0.135896	+	0.220051i
$787$	−1.62538	+	0.323309i	−0.0579387	+	0.0115247i	−0.223975	−	0.974595i	$-0.571903\pi$
$787$	−1.62538	+	0.323309i	−0.0579387	+	0.0115247i	0.166036	+	0.986120i	$0.446903\pi$
$788$	−5.36696	−	42.8068i	−0.191190	−	1.52493i
$789$	−7.46776	+	37.5430i	−0.265859	+	1.33657i
$790$	−0.707784	−	4.37090i	−0.0251818	−	0.155510i
$791$	−22.6189	+	9.36905i	−0.804235	+	0.333125i
$792$	13.6353	−	10.9804i	0.484508	−	0.390173i
$793$	−4.22853	+	2.82541i	−0.150159	+	0.100333i
$794$	−41.8018	−	1.49765i	−1.48349	−	0.0531495i
$795$	5.44606	+	5.44606i	0.193152	+	0.193152i
$796$	−14.7656	+	8.40381i	−0.523354	+	0.297865i
$797$	−9.22061	−	3.81930i	−0.326611	−	0.135287i	0.213352	−	0.976975i	$-0.431562\pi$
$797$	−9.22061	−	3.81930i	−0.326611	−	0.135287i	−0.539963	+	0.841689i	$0.681562\pi$
$798$	72.0578	+	17.0362i	2.55082	+	0.603076i
$799$	18.3951	−	14.6593i	0.650773	−	0.518608i
$800$	9.40897	+	21.6489i	0.332657	+	0.765403i
$801$	2.64933	−	6.39606i	0.0936096	−	0.225994i
$802$	18.1919	−	16.9334i	0.642377	−	0.597940i
$803$	−19.5132	+	19.5132i	−0.688606	+	0.688606i
$804$	−0.358958	+	1.30731i	−0.0126595	+	0.0461052i
$805$	3.42585	+	5.12715i	0.120745	+	0.180708i
$806$	4.25855	+	1.94539i	0.150001	+	0.0685235i
$807$	−1.69400	−	4.08968i	−0.0596316	−	0.143964i
$808$	−11.3647	+	36.2524i	−0.399810	+	1.27536i
$809$	−41.1019	−	8.17568i	−1.44507	−	0.287442i	−0.590607	−	0.806960i	$-0.701112\pi$
$809$	−41.1019	−	8.17568i	−1.44507	−	0.287442i	−0.854459	+	0.519518i	$0.826112\pi$
$810$	13.5151	−	5.03914i	0.474871	−	0.177057i
$811$	−6.56370	−	32.9979i	−0.230483	−	1.15871i	−0.906623	−	0.421941i	$-0.861349\pi$
$811$	−6.56370	−	32.9979i	−0.230483	−	1.15871i	0.676141	−	0.736773i	$-0.263651\pi$
$812$	16.4737	+	49.5327i	0.578115	+	1.73826i
$813$	−44.7646	−	29.9108i	−1.56996	−	1.04902i
$814$	21.5207	−	29.8372i	0.754301	−	1.04579i
$815$	−20.7184			−0.725732
$816$	−2.12158	+	35.6494i	−0.0742702	+	1.24798i
$817$	−61.3427			−2.14611
$818$	30.7889	−	42.6869i	1.07651	−	1.49251i
$819$	4.31633	+	2.88408i	0.150825	+	0.100778i
$820$	0.195812	+	0.588761i	0.00683805	+	0.0205604i
$821$	5.73735	+	28.8436i	0.200235	+	1.00665i	0.941904	+	0.335883i	$0.109035\pi$
$821$	5.73735	+	28.8436i	0.200235	+	1.00665i	−0.741669	+	0.670766i	$0.765965\pi$
$822$	−2.80591	+	1.04619i	−0.0978673	+	0.0364901i
$823$	−31.3802	−	6.24191i	−1.09384	−	0.217579i	−0.384981	−	0.922925i	$-0.625792\pi$
$823$	−31.3802	−	6.24191i	−1.09384	−	0.217579i	−0.708864	+	0.705345i	$0.750792\pi$
$824$	−3.50551	+	11.1823i	−0.122120	+	0.389552i
$825$	−12.6727	−	30.5945i	−0.441205	−	1.06516i
$826$	27.8705	+	12.7318i	0.969739	+	0.442996i
$827$	−9.31474	−	13.9405i	−0.323905	−	0.484759i	0.633405	−	0.773820i	$-0.281657\pi$
$827$	−9.31474	−	13.9405i	−0.323905	−	0.484759i	−0.957310	+	0.289062i	$0.906657\pi$
$828$	1.88085	−	6.84996i	0.0653639	−	0.238053i
$829$	−1.59951	+	1.59951i	−0.0555532	+	0.0555532i	−0.734338	−	0.678784i	$-0.762507\pi$
$829$	−1.59951	+	1.59951i	−0.0555532	+	0.0555532i	0.678784	+	0.734338i	$0.262507\pi$
$830$	3.31119	−	3.08213i	0.114933	−	0.106982i
$831$	−3.38972	+	8.18350i	−0.117588	+	0.283882i
$832$	7.50690	−	1.34918i	0.260255	−	0.0467744i
$833$	−6.77345	+	12.2457i	−0.234686	+	0.424288i
$834$	−26.3228	−	6.22336i	−0.911484	−	0.215497i
$835$	19.8249	+	8.21173i	0.686068	+	0.284179i
$836$	−47.7758	+	27.1914i	−1.65236	+	0.940436i
$837$	−6.97089	−	6.97089i	−0.240949	−	0.240949i
$838$	1.83007	+	0.0655666i	0.0632188	+	0.00226496i
$839$	15.4658	−	10.3339i	0.533940	−	0.356767i	−0.259184	−	0.965828i	$-0.583453\pi$
$839$	15.4658	−	10.3339i	0.533940	−	0.356767i	0.793123	+	0.609061i	$0.208453\pi$
$840$	−13.9870	+	11.2637i	−0.482597	+	0.388634i
$841$	33.7577	−	13.9829i	1.16406	−	0.482169i
$842$	6.51437	+	40.2293i	0.224500	+	1.38639i
$843$	−4.24311	+	21.3316i	−0.146141	+	0.734698i
$844$	−0.198460	−	1.58291i	−0.00683127	−	0.0544861i
$845$	−10.7853	+	2.14534i	−0.371027	+	0.0738018i
$846$	−7.15960	−	11.5932i	−0.246152	−	0.398583i
$847$	−4.35513	+	6.51792i	−0.149644	+	0.223958i
$848$	−3.86187	−	15.1590i	−0.132617	−	0.520563i
$849$		−	6.37283i		−	0.218715i
$850$	22.9003	+	8.22212i	0.785474	+	0.282016i
$851$		−	14.9271i		−	0.511695i
$852$	19.8817	−	17.2198i	0.681136	−	0.589940i
$853$	−20.2830	+	30.3557i	−0.694478	+	1.03936i	0.301817	+	0.953366i	$0.402407\pi$
$853$	−20.2830	+	30.3557i	−0.694478	+	1.03936i	−0.996296	+	0.0859945i	$0.972593\pi$
$854$	−20.6928	+	12.7792i	−0.708093	+	0.437295i
$855$	11.2985	−	2.24741i	0.386400	−	0.0768597i
$856$	−15.5835	−	1.68071i	−0.532634	−	0.0574453i
$857$	3.35894	−	16.8865i	0.114739	−	0.576834i	−0.880050	−	0.474881i	$-0.842491\pi$
$857$	3.35894	−	16.8865i	0.114739	−	0.576834i	0.994789	−	0.101952i	$-0.0325089\pi$
$858$	−10.5625	+	1.71039i	−0.360596	+	0.0583918i
$859$	−39.4842	+	16.3549i	−1.34718	+	0.558022i	−0.935507	−	0.353308i	$-0.885057\pi$
$859$	−39.4842	+	16.3549i	−1.34718	+	0.558022i	−0.411677	+	0.911330i	$0.635057\pi$
$860$	9.12977	−	11.7473i	0.311323	−	0.400578i
$861$	1.98002	−	1.32300i	0.0674787	−	0.0450878i
$862$	0.0134795	−	0.376236i	0.000459115	−	0.0128146i
$863$	26.0030	+	26.0030i	0.885154	+	0.885154i	0.994053	−	0.108899i	$-0.0347324\pi$
$863$	26.0030	+	26.0030i	0.885154	+	0.885154i	−0.108899	+	0.994053i	$0.534732\pi$
$864$	−15.8033	−	2.86039i	−0.537641	−	0.0973123i
$865$	1.91892	+	0.794843i	0.0652452	+	0.0270255i
$866$	−5.44888	+	23.0470i	−0.185161	+	0.783170i
$867$	25.2710	+	26.7669i	0.858248	+	0.909051i
$868$	20.0194	+	10.0266i	0.679502	+	0.340325i
$869$	4.82816	−	11.6562i	0.163784	−	0.395410i
$870$	15.3624	+	16.5040i	0.520832	+	0.559539i
$871$	0.211035	−	0.211035i	0.00715066	−	0.00715066i
$872$	−13.1752	+	24.1094i	−0.446170	+	0.816446i
$873$	−3.62292	−	5.42208i	−0.122617	−	0.183509i
$874$	−9.26813	+	20.2884i	−0.313499	+	0.686264i
$875$	10.2928	+	24.8490i	0.347959	+	0.840048i
$876$	−32.5261	−	2.33364i	−1.09895	−	0.0788465i
$877$	28.6706	+	5.70293i	0.968136	+	0.192574i	0.653741	−	0.756718i	$-0.273198\pi$
$877$	28.6706	+	5.70293i	0.968136	+	0.192574i	0.314395	+	0.949292i	$0.398198\pi$
$878$	6.89080	+	18.4813i	0.232553	+	0.623713i
$879$	9.61342	+	48.3299i	0.324253	+	1.63013i
$880$	1.90336	−	13.1961i	0.0641622	−	0.444842i
$881$	5.34841	+	3.57369i	0.180192	+	0.120401i	0.642395	−	0.766374i	$-0.277941\pi$
$881$	5.34841	+	3.57369i	0.180192	+	0.120401i	−0.462203	+	0.886774i	$0.652941\pi$
$882$	6.57482	+	4.74224i	0.221386	+	0.159679i
$883$	4.81922			0.162180			0.0810898	−	0.996707i	$-0.474160\pi$
$883$	4.81922			0.162180			0.0810898	+	0.996707i	$0.474160\pi$
$884$	4.28789	−	6.58966i	0.144217	−	0.221634i
$885$	13.2350			0.444890
$886$	−19.0383	−	13.7318i	−0.639604	−	0.461329i
$887$	−2.76219	−	1.84563i	−0.0927451	−	0.0619703i	0.508333	−	0.861161i	$-0.330262\pi$
$887$	−2.76219	−	1.84563i	−0.0927451	−	0.0619703i	−0.601078	+	0.799190i	$0.705262\pi$
$888$	43.3009	−	3.86021i	1.45308	−	0.129540i
$889$	−10.0146	−	50.3467i	−0.335878	−	1.68857i
$890$	−1.84195	−	4.94016i	−0.0617424	−	0.165595i
$891$	40.3096	+	8.01808i	1.35042	+	0.268616i
$892$	0.0382828	−	0.533582i	0.00128180	−	0.0178657i
$893$	16.3732	+	39.5284i	0.547909	+	1.32277i
$894$	1.62742	−	3.56249i	0.0544290	−	0.119147i
$895$	6.04571	+	9.04805i	0.202086	+	0.302443i
$896$	36.1080	−	5.16263i	1.20628	−	0.172471i
$897$	−3.06997	+	3.06997i	−0.102503	+	0.102503i
$898$	26.2191	+	28.1677i	0.874944	+	0.939968i
$899$	10.7577	−	25.9714i	0.358789	−	0.866194i
$900$	6.31196	−	12.6026i	0.210399	−	0.420087i
$901$	−14.1100	−	7.80466i	−0.470072	−	0.260011i
$902$	−0.406774	+	1.72052i	−0.0135441	+	0.0572871i
$903$	−52.7543	−	21.8515i	−1.75555	−	0.727174i
$904$	20.6107	−	6.04432i	0.685502	−	0.201031i
$905$	−0.729039	−	0.729039i	−0.0242341	−	0.0242341i
$906$	2.05923	−	57.4764i	0.0684132	−	1.90952i
$907$	45.6516	−	30.5034i	1.51584	−	1.01285i	0.529463	−	0.848333i	$-0.322393\pi$
$907$	45.6516	−	30.5034i	1.51584	−	1.01285i	0.986374	−	0.164517i	$-0.0526067\pi$
$908$	28.8447	+	22.4176i	0.957245	+	0.743955i
$909$	20.9587	−	8.68138i	0.695156	−	0.287943i
$910$	3.90263	−	0.631957i	0.129371	−	0.0209492i
$911$	6.45377	−	32.4453i	0.213823	−	1.07496i	−0.713488	−	0.700668i	$-0.752885\pi$
$911$	6.45377	−	32.4453i	0.213823	−	1.07496i	0.927311	−	0.374293i	$-0.122115\pi$
$912$	−61.2497	−	21.6385i	−2.02818	−	0.716524i
$913$	12.6420	−	2.51464i	0.418388	−	0.0832225i
$914$	−31.3571	+	19.3651i	−1.03720	+	0.640542i
$915$	−5.83632	+	8.73467i	−0.192943	+	0.288759i
$916$	−23.2756	−	26.8737i	−0.769049	−	0.887932i
$917$		−	7.63370i		−	0.252087i
$918$	−13.3074	+	9.84690i	−0.439209	+	0.324996i
$919$		−	40.9992i		−	1.35244i	−0.736701	−	0.676219i	$-0.763617\pi$
$919$		−	40.9992i		−	1.35244i	0.736701	−	0.676219i	$-0.236383\pi$
$920$	−2.50587	−	4.79443i	−0.0826160	−	0.158068i
$921$	3.10294	−	4.64388i	0.102245	−	0.153021i
$922$	−7.37956	−	11.9494i	−0.243033	−	0.393533i
$923$	−5.67903	+	1.12963i	−0.186928	+	0.0371822i
$924$	−50.7730	+	6.36573i	−1.67031	+	0.209417i
$925$	5.77833	−	29.0496i	0.189990	−	0.955147i
$926$	−6.25374	−	38.6198i	−0.205511	−	1.26913i
$927$	6.46483	−	2.67782i	0.212333	−	0.0879511i
$928$	−9.70950	−	44.7546i	−0.318730	−	1.46914i
$929$	4.64762	−	3.10544i	0.152484	−	0.101886i	−0.476988	−	0.878910i	$-0.658271\pi$
$929$	4.64762	−	3.10544i	0.152484	−	0.101886i	0.629471	+	0.777024i	$0.283271\pi$
$930$	9.66489	+	0.346268i	0.316924	+	0.0113546i
$931$	−17.9993	−	17.9993i	−0.589903	−	0.589903i
$932$	6.43197	+	11.3011i	0.210686	+	0.370179i
$933$	37.3178	+	15.4575i	1.22173	+	0.506057i
$934$	−9.88597	−	2.33729i	−0.323479	−	0.0764783i
$935$	−8.56494	−	10.7477i	−0.280104	−	0.351487i
$936$	−3.49360	−	2.92169i	−0.114192	−	0.0954984i
$937$	14.5036	−	35.0149i	0.473813	−	1.14389i	−0.488651	−	0.872479i	$-0.662511\pi$
$937$	14.5036	−	35.0149i	0.473813	−	1.14389i	0.962465	−	0.271407i	$-0.0874890\pi$
$938$	1.04472	−	0.972446i	0.0341112	−	0.0317515i
$939$	−8.18236	+	8.18236i	−0.267021	+	0.267021i
$940$	−10.0066	−	2.74760i	−0.326381	−	0.0896169i
$941$	−20.3402	−	30.4413i	−0.663072	−	0.992357i	−0.998730	−	0.0503737i	$-0.983959\pi$
$941$	−20.3402	−	30.4413i	−0.663072	−	0.992357i	0.335658	−	0.941984i	$-0.391041\pi$
$942$	−48.1245	−	21.9842i	−1.56798	−	0.716285i
$943$	0.274520	+	0.662749i	0.00893960	+	0.0215821i
$944$	−23.1123	−	13.7272i	−0.752242	−	0.446782i
$945$	−8.16464	−	1.62405i	−0.265596	−	0.0528303i
$946$	39.7215	−	14.8103i	1.29146	−	0.481524i
$947$	2.83798	+	14.2675i	0.0922218	+	0.463630i	0.999107	+	0.0422526i	$0.0134534\pi$
$947$	2.83798	+	14.2675i	0.0922218	+	0.463630i	−0.906885	+	0.421378i	$0.861547\pi$
$948$	14.1470	−	4.70505i	0.459473	−	0.152813i
$949$	5.96900	+	3.98836i	0.193762	+	0.129468i
$950$	−25.8904	+	35.8954i	−0.839995	+	1.16460i
$951$	−14.6229			−0.474179
$952$	21.6210	−	30.7592i	0.700742	−	0.996910i
$953$	−11.7945			−0.382062			−0.191031	−	0.981584i	$-0.561183\pi$
$953$	−11.7945			−0.382062			−0.191031	+	0.981584i	$0.561183\pi$
$954$	−5.46420	+	7.57578i	−0.176910	+	0.245275i
$955$	−2.84735	−	1.90254i	−0.0921380	−	0.0615647i
$956$	51.2788	−	17.0544i	1.65847	−	0.551580i
$957$	12.5338	+	63.0117i	0.405160	+	2.03688i
$958$	−25.5329	+	9.52001i	−0.824930	+	0.307578i
$959$	3.09212	+	0.615060i	0.0998497	+	0.0198613i
$960$	13.2598	−	8.50893i	0.427957	−	0.274625i
$961$	7.24897	+	17.5006i	0.233838	+	0.564534i
$962$	−8.70499	−	3.97661i	−0.280660	−	0.128211i
$963$	5.19963	+	7.78180i	0.167556	+	0.250765i
$964$	48.8190	+	13.4046i	1.57236	+	0.431734i
$965$	−0.341387	+	0.341387i	−0.0109896	+	0.0109896i
$966$	−15.1977	+	14.1464i	−0.488977	+	0.455151i
$967$	6.09348	−	14.7110i	0.195953	−	0.473073i	−0.795110	−	0.606465i	$-0.792587\pi$
$967$	6.09348	−	14.7110i	0.195953	−	0.473073i	0.991063	+	0.133392i	$0.0425870\pi$
$968$	4.41193	−	5.27555i	0.141805	−	0.169563i
$969$	−59.4998	+	30.7124i	−1.91141	+	0.986625i
$970$	−4.83301	−	1.14264i	−0.155179	−	0.0366881i
$971$	−38.6001	−	15.9887i	−1.23874	−	0.513102i	−0.335417	−	0.942070i	$-0.608877\pi$
$971$	−38.6001	−	15.9887i	−1.23874	−	0.513102i	−0.903320	+	0.428968i	$0.858877\pi$
$972$	15.5972	+	27.4046i	0.500282	+	0.879003i
$973$	20.1359	+	20.1359i	0.645527	+	0.645527i
$974$	18.5657	+	0.665162i	0.594885	+	0.0213132i
$975$	−7.16286	+	4.78607i	−0.229395	+	0.153277i
$976$	19.2515	−	9.20000i	0.616224	−	0.294485i
$977$	23.2591	−	9.63422i	0.744123	−	0.308226i	0.0217820	−	0.999763i	$-0.493066\pi$
$977$	23.2591	−	9.63422i	0.744123	−	0.308226i	0.722341	+	0.691537i	$0.243066\pi$
$978$	−11.1511	−	68.8634i	−0.356574	−	2.20201i
$979$	2.93085	−	14.7344i	0.0936702	−	0.470912i
$980$	6.12579	−	0.768028i	0.195681	−	0.0245338i
$981$	16.0902	−	3.20053i	0.513719	−	0.102185i
$982$	5.03411	+	8.15152i	0.160645	+	0.260125i
$983$	−5.26747	+	7.88333i	−0.168006	+	0.251439i	−0.905913	−	0.423463i	$-0.860814\pi$
$983$	−5.26747	+	7.88333i	−0.168006	+	0.251439i	0.737907	+	0.674902i	$0.235814\pi$
$984$	−1.85153	+	0.967723i	−0.0590245	+	0.0308499i
$985$			19.6185i			0.625098i
$986$	−40.4627	−	24.3126i	−1.28859	−	0.774270i
$987$			39.8267i			1.26770i
$988$	9.36243	+	10.8097i	0.297859	+	0.343903i
$989$	9.55638	−	14.3021i	0.303875	−	0.454781i
$990$	−6.77355	+	4.18312i	−0.215278	+	0.132948i
$991$	−29.9616	+	5.95972i	−0.951760	+	0.189317i	−0.646467	−	0.762942i	$-0.723754\pi$
$991$	−29.9616	+	5.95972i	−0.951760	+	0.189317i	−0.305293	+	0.952259i	$0.598754\pi$
$992$	−16.5187	−	10.6290i	−0.524468	−	0.337471i
$993$	3.74532	−	18.8290i	0.118854	−	0.597520i
$994$	−27.3347	+	4.42633i	−0.867003	+	0.140395i
$995$	7.13782	−	2.95658i	0.226284	−	0.0937299i
$996$	12.0265	+	9.34680i	0.381075	+	0.296165i
$997$	−25.7083	+	17.1777i	−0.814189	+	0.544024i	−0.891520	−	0.452982i	$-0.850360\pi$
$997$	−25.7083	+	17.1777i	−0.814189	+	0.544024i	0.0773308	+	0.997005i	$0.475360\pi$
$998$	−0.447633	+	12.4942i	−0.0141696	+	0.395496i
$999$	14.2493	+	14.2493i	0.450829	+	0.450829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	68.2.i.b.7.5	yes	48
3.2	odd	2		612.2.bd.d.415.2		48
4.3	odd	2	inner	68.2.i.b.7.3	✓	48
12.11	even	2		612.2.bd.d.415.4		48
17.5	odd	16	inner	68.2.i.b.39.3	yes	48
51.5	even	16		612.2.bd.d.379.4		48
68.39	even	16	inner	68.2.i.b.39.5	yes	48
204.107	odd	16		612.2.bd.d.379.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.i.b.7.3	✓	48	4.3	odd	2	inner
68.2.i.b.7.5	yes	48	1.1	even	1	trivial
68.2.i.b.39.3	yes	48	17.5	odd	16	inner
68.2.i.b.39.5	yes	48	68.39	even	16	inner
612.2.bd.d.379.2		48	204.107	odd	16
612.2.bd.d.379.4		48	51.5	even	16
612.2.bd.d.415.2		48	3.2	odd	2
612.2.bd.d.415.4		48	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	68.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.827293 - 1.14699i) q^{2} +(-1.80045 - 1.20302i) q^{3} +(-0.631174 - 1.89779i) q^{4} +(0.177432 + 0.892011i) q^{5} +(-2.86936 + 1.06985i) q^{6} +(3.16204 + 0.628968i) q^{7} +(-2.69892 - 0.846081i) q^{8} +(0.646311 + 1.56033i) q^{9} +O(q^{10})\)	\(q+(0.827293 - 1.14699i) q^{2} +(-1.80045 - 1.20302i) q^{3} +(-0.631174 - 1.89779i) q^{4} +(0.177432 + 0.892011i) q^{5} +(-2.86936 + 1.06985i) q^{6} +(3.16204 + 0.628968i) q^{7} +(-2.69892 - 0.846081i) q^{8} +(0.646311 + 1.56033i) q^{9} +(1.16992 + 0.534441i) q^{10} +(2.03611 + 3.04725i) q^{11} +(-1.14669 + 4.17620i) q^{12} +(0.674154 - 0.674154i) q^{13} +(3.33735 - 3.10649i) q^{14} +(0.753652 - 1.81948i) q^{15} +(-3.20324 + 2.39567i) q^{16} +(-0.463051 + 4.09702i) q^{17} +(2.32437 + 0.549539i) q^{18} +(-6.92889 - 2.87004i) q^{19} +(1.58086 - 0.899743i) q^{20} +(-4.93643 - 4.93643i) q^{21} +(5.17962 + 0.185572i) q^{22} +(1.74858 - 1.16837i) q^{23} +(3.84141 + 4.77019i) q^{24} +(3.85520 - 1.59687i) q^{25} +(-0.215525 - 1.33097i) q^{26} +(-0.553872 + 2.78450i) q^{27} +(-0.802143 - 6.39788i) q^{28} +(-7.94007 + 1.57938i) q^{29} +(-1.46343 - 2.36967i) q^{30} +(-1.92916 + 2.88719i) q^{31} +(0.0977985 + 5.65601i) q^{32} -7.93591i q^{33} +(4.31617 + 3.92055i) q^{34} +2.93217i q^{35} +(2.55325 - 2.21140i) q^{36} +(3.94344 - 5.90177i) q^{37} +(-9.02413 + 5.57301i) q^{38} +(-2.02480 + 0.402758i) q^{39} +(0.275839 - 2.55758i) q^{40} +(-0.0665472 + 0.334555i) q^{41} +(-9.74591 + 1.57817i) q^{42} +(7.55666 - 3.13007i) q^{43} +(4.49791 - 5.78746i) q^{44} +(-1.27716 + 0.853369i) q^{45} +(0.106486 - 2.97219i) q^{46} +(-4.03395 - 4.03395i) q^{47} +(8.64933 - 0.459724i) q^{48} +(3.13572 + 1.29886i) q^{49} +(1.35778 - 5.74296i) q^{50} +(5.76251 - 6.81943i) q^{51} +(-1.70491 - 0.853896i) q^{52} +(-1.49660 + 3.61311i) q^{53} +(2.73558 + 2.93889i) q^{54} +(-2.35691 + 2.35691i) q^{55} +(-8.00192 - 4.37287i) q^{56} +(9.02240 + 13.5030i) q^{57} +(-4.75723 + 10.4138i) q^{58} +(2.57178 + 6.20882i) q^{59} +(-3.92868 - 0.281870i) q^{60} +(-5.23170 - 1.04065i) q^{61} +(1.71560 + 4.60128i) q^{62} +(1.06226 + 5.34034i) q^{63} +(6.56830 + 4.56700i) q^{64} +(0.720969 + 0.481736i) q^{65} +(-9.10242 - 6.56532i) q^{66} +0.313037 q^{67} +(8.06757 - 1.70716i) q^{68} -4.55381 q^{69} +(3.36317 + 2.42576i) q^{70} +(-5.04978 - 3.37416i) q^{71} +(-0.424172 - 4.75803i) q^{72} +(1.46898 + 7.38509i) q^{73} +(-3.50690 - 9.40557i) q^{74} +(-8.86217 - 1.76280i) q^{75} +(-1.07341 + 14.9611i) q^{76} +(4.52163 + 10.9162i) q^{77} +(-1.21314 + 2.65563i) q^{78} +(-1.91258 - 2.86238i) q^{79} +(-2.70532 - 2.43226i) q^{80} +(7.92972 - 7.92972i) q^{81} +(0.328678 + 0.353104i) q^{82} +(1.34592 - 3.24933i) q^{83} +(-6.25258 + 12.4841i) q^{84} +(-3.73675 + 0.313896i) q^{85} +(2.66141 - 11.2569i) q^{86} +(16.1957 + 6.70849i) q^{87} +(-2.91706 - 9.94699i) q^{88} +(-2.89855 - 2.89855i) q^{89} +(-0.0777766 + 2.17087i) q^{90} +(2.55572 - 1.70768i) q^{91} +(-3.32098 - 2.58101i) q^{92} +(6.94672 - 2.87743i) q^{93} +(-7.96417 + 1.28965i) q^{94} +(1.33070 - 6.68988i) q^{95} +(6.62823 - 10.3010i) q^{96} +(-3.78697 + 0.753275i) q^{97} +(4.08394 - 2.52211i) q^{98} +(-3.43876 + 5.14647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 48 q - 8 q^{2} - 8 q^{4} - 16 q^{5} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 24 q^{20} - 16 q^{21} - 8 q^{22} + 8 q^{24} + 16 q^{25} - 16 q^{26} + 40 q^{28} + 56 q^{30} + 32 q^{32} + 56 q^{34} + 56 q^{36} - 16 q^{37} + 32 q^{38} + 56 q^{40} - 48 q^{41} + 40 q^{42} + 24 q^{44} - 64 q^{45} + 8 q^{46} - 32 q^{48} - 16 q^{49} - 16 q^{52} + 48 q^{53} - 24 q^{54} - 48 q^{56} + 64 q^{57} - 64 q^{58} - 112 q^{60} + 16 q^{61} - 64 q^{62} - 56 q^{64} + 96 q^{65} - 96 q^{66} - 32 q^{68} + 32 q^{69} - 80 q^{70} - 64 q^{72} + 64 q^{73} - 16 q^{74} - 64 q^{76} + 16 q^{77} - 112 q^{78} - 24 q^{80} + 64 q^{81} - 40 q^{82} - 80 q^{85} + 64 q^{86} + 56 q^{88} - 16 q^{89} + 48 q^{90} + 104 q^{92} - 16 q^{93} + 88 q^{94} + 144 q^{96} - 16 q^{97} + 72 q^{98}+O(q^{100}) \) 48 * q - 8 * q^2 - 8 * q^4 - 16 * q^5 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 24 * q^20 - 16 * q^21 - 8 * q^22 + 8 * q^24 + 16 * q^25 - 16 * q^26 + 40 * q^28 + 56 * q^30 + 32 * q^32 + 56 * q^34 + 56 * q^36 - 16 * q^37 + 32 * q^38 + 56 * q^40 - 48 * q^41 + 40 * q^42 + 24 * q^44 - 64 * q^45 + 8 * q^46 - 32 * q^48 - 16 * q^49 - 16 * q^52 + 48 * q^53 - 24 * q^54 - 48 * q^56 + 64 * q^57 - 64 * q^58 - 112 * q^60 + 16 * q^61 - 64 * q^62 - 56 * q^64 + 96 * q^65 - 96 * q^66 - 32 * q^68 + 32 * q^69 - 80 * q^70 - 64 * q^72 + 64 * q^73 - 16 * q^74 - 64 * q^76 + 16 * q^77 - 112 * q^78 - 24 * q^80 + 64 * q^81 - 40 * q^82 - 80 * q^85 + 64 * q^86 + 56 * q^88 - 16 * q^89 + 48 * q^90 + 104 * q^92 - 16 * q^93 + 88 * q^94 + 144 * q^96 - 16 * q^97 + 72 * q^98

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