LMFDB - Embedded newform 55.2.l.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [55,2,Mod(2,55)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(55, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("55.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	55.l (of order $20$, 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:	$0.439177211117$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	55.2
Dual form			55.2.l.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15100 - 2.25897i) q^{2} +(0.313634 - 1.98021i) q^{3} +(-2.60258 + 3.58214i) q^{4} +(1.91314 + 1.15755i) q^{5} +(-4.83422 + 1.57073i) q^{6} +(-1.78576 + 0.282837i) q^{7} +(6.07934 + 0.962874i) q^{8} +(-0.969677 - 0.315067i) q^{9} +O(q^{10})$	\(q+(-1.15100 - 2.25897i) q^{2} +(0.313634 - 1.98021i) q^{3} +(-2.60258 + 3.58214i) q^{4} +(1.91314 + 1.15755i) q^{5} +(-4.83422 + 1.57073i) q^{6} +(-1.78576 + 0.282837i) q^{7} +(6.07934 + 0.962874i) q^{8} +(-0.969677 - 0.315067i) q^{9} +(0.412838 - 5.65406i) q^{10} +(1.72268 - 2.83415i) q^{11} +(6.27711 + 6.27711i) q^{12} +(-2.00993 + 1.02411i) q^{13} +(2.69434 + 3.70844i) q^{14} +(2.89220 - 3.42536i) q^{15} +(-2.08573 - 6.41923i) q^{16} +(2.99738 + 1.52724i) q^{17} +(0.404374 + 2.55312i) q^{18} +(-1.05647 + 0.767569i) q^{19} +(-9.12557 + 3.84051i) q^{20} +3.62488i q^{21} +(-8.38507 - 0.629367i) q^{22} +(-3.16488 + 3.16488i) q^{23} +(3.81337 - 11.7364i) q^{24} +(2.32018 + 4.42908i) q^{25} +(4.62687 + 3.36162i) q^{26} +(1.80258 - 3.53776i) q^{27} +(3.63442 - 7.13295i) q^{28} +(-2.37569 - 1.72604i) q^{29} +(-11.0667 - 2.59081i) q^{30} +(-1.23925 + 3.81401i) q^{31} +(-3.39552 + 3.39552i) q^{32} +(-5.07190 - 4.30014i) q^{33} -8.52886i q^{34} +(-3.74380 - 1.52600i) q^{35} +(3.65227 - 2.65353i) q^{36} +(0.501987 + 3.16942i) q^{37} +(2.94992 + 1.50306i) q^{38} +(1.39757 + 4.30127i) q^{39} +(10.5160 + 8.87923i) q^{40} +(0.766287 + 1.05470i) q^{41} +(8.18851 - 4.17225i) q^{42} +(4.55431 + 4.55431i) q^{43} +(5.66890 + 13.5469i) q^{44} +(-1.49042 - 1.72521i) q^{45} +(10.7922 + 3.50658i) q^{46} +(-7.62854 - 1.20824i) q^{47} +(-13.3656 + 2.11690i) q^{48} +(-3.54845 + 1.15296i) q^{49} +(7.33465 - 10.3391i) q^{50} +(3.96433 - 5.45644i) q^{51} +(1.56249 - 9.86517i) q^{52} +(-2.89146 - 5.67482i) q^{53} -10.0665 q^{54} +(6.57637 - 3.42803i) q^{55} -11.1286 q^{56} +(1.18860 + 2.33276i) q^{57} +(-1.16465 + 7.35329i) q^{58} +(7.28135 - 10.0219i) q^{59} +(4.74292 + 19.2750i) q^{60} +(-8.85435 + 2.87695i) q^{61} +(10.0421 - 1.59052i) q^{62} +(1.82072 + 0.288374i) q^{63} +(-1.25983 - 0.409344i) q^{64} +(-5.03072 - 0.367324i) q^{65} +(-3.87611 + 16.4068i) q^{66} +(-2.46236 - 2.46236i) q^{67} +(-13.2717 + 6.76227i) q^{68} +(5.27449 + 7.25972i) q^{69} +(0.861947 + 10.2136i) q^{70} +(-2.09243 - 6.43984i) q^{71} +(-5.59163 - 2.84908i) q^{72} +(-1.47735 - 9.32763i) q^{73} +(6.58185 - 4.78199i) q^{74} +(9.49818 - 3.20531i) q^{75} -5.78207i q^{76} +(-2.27469 + 5.54835i) q^{77} +(8.10784 - 8.10784i) q^{78} +(0.353860 - 1.08907i) q^{79} +(3.44026 - 14.6952i) q^{80} +(-8.91472 - 6.47692i) q^{81} +(1.50055 - 2.94499i) q^{82} +(-4.75092 + 9.32422i) q^{83} +(-12.9848 - 9.43403i) q^{84} +(3.96654 + 6.39143i) q^{85} +(5.04603 - 15.5301i) q^{86} +(-4.16301 + 4.16301i) q^{87} +(13.2017 - 15.5710i) q^{88} +3.85743i q^{89} +(-2.18173 + 5.35254i) q^{90} +(3.29960 - 2.39730i) q^{91} +(-3.10019 - 19.5739i) q^{92} +(7.16385 + 3.65016i) q^{93} +(6.05109 + 18.6233i) q^{94} +(-2.90966 + 0.245553i) q^{95} +(5.65887 + 7.78877i) q^{96} +(-0.693249 + 0.353228i) q^{97} +(6.68878 + 6.68878i) q^{98} +(-2.56339 + 2.20545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8}+O(q^{10}) $ 32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8	$ 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8} - 24 q^{11} + 12 q^{12} - 10 q^{13} + 14 q^{15} - 8 q^{16} - 10 q^{18} + 16 q^{20} + 10 q^{22} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 50 q^{28} + 30 q^{30} - 28 q^{31} + 66 q^{33} - 10 q^{35} + 24 q^{36} - 8 q^{37} + 10 q^{38} - 50 q^{40} + 40 q^{41} - 10 q^{42} - 28 q^{45} + 60 q^{46} - 28 q^{47} - 54 q^{48} - 50 q^{50} + 20 q^{51} - 50 q^{52} - 24 q^{53} - 64 q^{55} - 80 q^{56} + 30 q^{57} - 50 q^{58} + 34 q^{60} - 60 q^{61} + 100 q^{62} - 30 q^{63} - 100 q^{66} - 8 q^{67} - 30 q^{68} + 30 q^{70} + 24 q^{71} + 80 q^{72} + 50 q^{73} + 34 q^{75} + 70 q^{77} + 60 q^{78} + 98 q^{80} - 12 q^{81} - 10 q^{82} + 90 q^{83} + 30 q^{85} + 100 q^{86} + 170 q^{88} - 20 q^{90} + 20 q^{91} - 68 q^{92} - 8 q^{93} - 40 q^{95} - 8 q^{97}+O(q^{100}) $ 32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8 - 24 * q^11 + 12 * q^12 - 10 * q^13 + 14 * q^15 - 8 * q^16 - 10 * q^18 + 16 * q^20 + 10 * q^22 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 50 * q^28 + 30 * q^30 - 28 * q^31 + 66 * q^33 - 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 + 40 * q^41 - 10 * q^42 - 28 * q^45 + 60 * q^46 - 28 * q^47 - 54 * q^48 - 50 * q^50 + 20 * q^51 - 50 * q^52 - 24 * q^53 - 64 * q^55 - 80 * q^56 + 30 * q^57 - 50 * q^58 + 34 * q^60 - 60 * q^61 + 100 * q^62 - 30 * q^63 - 100 * q^66 - 8 * q^67 - 30 * q^68 + 30 * q^70 + 24 * q^71 + 80 * q^72 + 50 * q^73 + 34 * q^75 + 70 * q^77 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 + 90 * q^83 + 30 * q^85 + 100 * q^86 + 170 * q^88 - 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 - 40 * q^95 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.15100	−	2.25897i	−0.813883	−	1.59733i	−0.801939	−	0.597406i	$-0.796198\pi$
$2$	−1.15100	−	2.25897i	−0.813883	−	1.59733i	−0.0119437	−	0.999929i	$-0.503802\pi$
$3$	0.313634	−	1.98021i	0.181076	−	1.14327i	−0.714918	−	0.699208i	$-0.753536\pi$
$3$	0.313634	−	1.98021i	0.181076	−	1.14327i	0.895995	−	0.444064i	$-0.146464\pi$
$4$	−2.60258	+	3.58214i	−1.30129	+	1.79107i
$5$	1.91314	+	1.15755i	0.855580	+	0.517670i
$5$	1.91314	+	1.15755i	0.855580	+	0.517670i
$6$	−4.83422	+	1.57073i	−1.97356	+	0.641249i
$7$	−1.78576	+	0.282837i	−0.674955	+	0.106902i	−0.484497	−	0.874793i	$-0.660997\pi$
$7$	−1.78576	+	0.282837i	−0.674955	+	0.106902i	−0.190458	+	0.981695i	$0.560997\pi$
$8$	6.07934	+	0.962874i	2.14937	+	0.340427i
$9$	−0.969677	−	0.315067i	−0.323226	−	0.105022i
$10$	0.412838	−	5.65406i	0.130551	−	1.78797i
$11$	1.72268	−	2.83415i	0.519407	−	0.854527i
$11$	1.72268	−	2.83415i	0.519407	−	0.854527i
$12$	6.27711	+	6.27711i	1.81205	+	1.81205i
$13$	−2.00993	+	1.02411i	−0.557454	+	0.284037i	−0.709933	−	0.704270i	$-0.751275\pi$
$13$	−2.00993	+	1.02411i	−0.557454	+	0.284037i	0.152478	+	0.988307i	$0.451275\pi$
$14$	2.69434	+	3.70844i	0.720093	+	0.991122i
$15$	2.89220	−	3.42536i	0.746763	−	0.884423i
$16$	−2.08573	−	6.41923i	−0.521434	−	1.60481i
$17$	2.99738	+	1.52724i	0.726972	+	0.370411i	0.777981	−	0.628288i	$-0.216244\pi$
$17$	2.99738	+	1.52724i	0.726972	+	0.370411i	−0.0510094	+	0.998698i	$0.516244\pi$
$18$	0.404374	+	2.55312i	0.0953119	+	0.601775i
$19$	−1.05647	+	0.767569i	−0.242370	+	0.176092i	−0.702339	−	0.711843i	$-0.747861\pi$
$19$	−1.05647	+	0.767569i	−0.242370	+	0.176092i	0.459968	+	0.887935i	$0.347861\pi$
$20$	−9.12557	+	3.84051i	−2.04054	+	0.858765i
$21$			3.62488i			0.791014i
$22$	−8.38507	−	0.629367i	−1.78770	−	0.134181i
$23$	−3.16488	+	3.16488i	−0.659922	+	0.659922i	−0.955362	−	0.295439i	$-0.904534\pi$
$23$	−3.16488	+	3.16488i	−0.659922	+	0.659922i	0.295439	+	0.955362i	$0.404534\pi$
$24$	3.81337	−	11.7364i	0.778402	−	2.39567i
$25$	2.32018	+	4.42908i	0.464035	+	0.885817i
$26$	4.62687	+	3.36162i	0.907405	+	0.659268i
$27$	1.80258	−	3.53776i	0.346907	−	0.680843i
$28$	3.63442	−	7.13295i	0.686841	−	1.34800i
$29$	−2.37569	−	1.72604i	−0.441154	−	0.320517i	0.344939	−	0.938625i	$-0.387900\pi$
$29$	−2.37569	−	1.72604i	−0.441154	−	0.320517i	−0.786093	+	0.618108i	$0.787900\pi$
$30$	−11.0667	−	2.59081i	−2.02050	−	0.473014i
$31$	−1.23925	+	3.81401i	−0.222575	+	0.685016i	0.775953	+	0.630790i	$0.217269\pi$
$31$	−1.23925	+	3.81401i	−0.222575	+	0.685016i	−0.998529	+	0.0542261i	$0.982731\pi$
$32$	−3.39552	+	3.39552i	−0.600248	+	0.600248i
$33$	−5.07190	−	4.30014i	−0.882905	−	0.748558i
$34$		−	8.52886i		−	1.46269i
$35$	−3.74380	−	1.52600i	−0.632818	−	0.257940i
$36$	3.65227	−	2.65353i	0.608712	−	0.442255i
$37$	0.501987	+	3.16942i	0.0825262	+	0.521050i	0.993972	+	0.109631i	$0.0349668\pi$
$37$	0.501987	+	3.16942i	0.0825262	+	0.521050i	−0.911446	+	0.411419i	$0.865033\pi$
$38$	2.94992	+	1.50306i	0.478539	+	0.243828i
$39$	1.39757	+	4.30127i	0.223790	+	0.688754i
$40$	10.5160	+	8.87923i	1.66273	+	1.40393i
$41$	0.766287	+	1.05470i	0.119674	+	0.164717i	0.864651	−	0.502373i	$-0.167540\pi$
$41$	0.766287	+	1.05470i	0.119674	+	0.164717i	−0.744977	+	0.667090i	$0.767540\pi$
$42$	8.18851	−	4.17225i	1.26351	−	0.643793i
$43$	4.55431	+	4.55431i	0.694526	+	0.694526i	0.963224	−	0.268698i	$-0.0865935\pi$
$43$	4.55431	+	4.55431i	0.694526	+	0.694526i	−0.268698	+	0.963224i	$0.586593\pi$
$44$	5.66890	+	13.5469i	0.854620	+	2.04228i
$45$	−1.49042	−	1.72521i	−0.222178	−	0.257179i
$46$	10.7922	+	3.50658i	1.59122	+	0.517017i
$47$	−7.62854	−	1.20824i	−1.11274	−	0.176240i	−0.427114	−	0.904198i	$-0.640470\pi$
$47$	−7.62854	−	1.20824i	−1.11274	−	0.176240i	−0.685622	+	0.727957i	$0.740470\pi$
$48$	−13.3656	+	2.11690i	−1.92915	+	0.305548i
$49$	−3.54845	+	1.15296i	−0.506921	+	0.164709i
$50$	7.33465	−	10.3391i	1.03728	−	1.46217i
$51$	3.96433	−	5.45644i	0.555118	−	0.764054i
$52$	1.56249	−	9.86517i	0.216678	−	1.36805i
$53$	−2.89146	−	5.67482i	−0.397173	−	0.779496i	0.602656	−	0.798001i	$-0.294109\pi$
$53$	−2.89146	−	5.67482i	−0.397173	−	0.779496i	−0.999829	+	0.0185052i	$0.994109\pi$
$54$	−10.0665			−1.36988
$55$	6.57637	−	3.42803i	0.886757	−	0.462235i
$56$	−11.1286			−1.48712
$57$	1.18860	+	2.33276i	0.157434	+	0.308981i
$58$	−1.16465	+	7.35329i	−0.152926	+	0.965535i
$59$	7.28135	−	10.0219i	0.947952	−	1.30474i	−0.00447977	−	0.999990i	$-0.501426\pi$
$59$	7.28135	−	10.0219i	0.947952	−	1.30474i	0.952431	−	0.304753i	$-0.0985740\pi$
$60$	4.74292	+	19.2750i	0.612308	+	2.48839i
$61$	−8.85435	+	2.87695i	−1.13368	+	0.368356i	−0.814975	−	0.579496i	$-0.803249\pi$
$61$	−8.85435	+	2.87695i	−1.13368	+	0.368356i	−0.318709	+	0.947853i	$0.603249\pi$
$62$	10.0421	−	1.59052i	1.27535	−	0.201996i
$63$	1.82072	+	0.288374i	0.229390	+	0.0363318i
$64$	−1.25983	−	0.409344i	−0.157479	−	0.0511679i
$65$	−5.03072	−	0.367324i	−0.623984	−	0.0455609i
$66$	−3.87611	+	16.4068i	−0.477117	+	2.01953i
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	0.540512	−	0.841336i	$-0.318231\pi$
$67$	−2.46236	−	2.46236i	−0.300825	−	0.300825i	−0.841336	+	0.540512i	$0.818231\pi$
$68$	−13.2717	+	6.76227i	−1.60943	+	0.820046i
$69$	5.27449	+	7.25972i	0.634974	+	0.873967i
$70$	0.861947	+	10.2136i	0.103022	+	1.22076i
$71$	−2.09243	−	6.43984i	−0.248326	−	0.764268i	−0.995072	−	0.0991588i	$-0.968385\pi$
$71$	−2.09243	−	6.43984i	−0.248326	−	0.764268i	0.746746	−	0.665110i	$-0.231615\pi$
$72$	−5.59163	−	2.84908i	−0.658980	−	0.335767i
$73$	−1.47735	−	9.32763i	−0.172911	−	1.09172i	−0.909600	−	0.415485i	$-0.863612\pi$
$73$	−1.47735	−	9.32763i	−0.172911	−	1.09172i	0.736689	−	0.676232i	$-0.236388\pi$
$74$	6.58185	−	4.78199i	0.765125	−	0.555896i
$75$	9.49818	−	3.20531i	1.09676	−	0.370118i
$76$		−	5.78207i		−	0.663249i
$77$	−2.27469	+	5.54835i	−0.259225	+	0.632293i
$78$	8.10784	−	8.10784i	0.918032	−	0.918032i
$79$	0.353860	−	1.08907i	0.0398123	−	0.122530i	−0.929175	−	0.369640i	$-0.879481\pi$
$79$	0.353860	−	1.08907i	0.0398123	−	0.122530i	0.968987	+	0.247110i	$0.0794810\pi$
$80$	3.44026	−	14.6952i	0.384633	−	1.64297i
$81$	−8.91472	−	6.47692i	−0.990524	−	0.719658i
$82$	1.50055	−	2.94499i	0.165708	−	0.325220i
$83$	−4.75092	+	9.32422i	−0.521482	+	1.02347i	0.468658	+	0.883380i	$0.344738\pi$
$83$	−4.75092	+	9.32422i	−0.521482	+	1.02347i	−0.990139	+	0.140086i	$0.955262\pi$
$84$	−12.9848	−	9.43403i	−1.41676	−	1.02934i
$85$	3.96654	+	6.39143i	0.430232	+	0.693248i
$86$	5.04603	−	15.5301i	0.544128	−	1.67465i
$87$	−4.16301	+	4.16301i	−0.446321	+	0.446321i
$88$	13.2017	−	15.5710i	1.40730	−	1.65988i
$89$			3.85743i			0.408887i	0.978878	+	0.204443i	$0.0655384\pi$
$89$			3.85743i			0.408887i	−0.978878	+	0.204443i	$0.934462\pi$
$90$	−2.18173	+	5.35254i	−0.229974	+	0.564207i
$91$	3.29960	−	2.39730i	0.345892	−	0.251305i
$92$	−3.10019	−	19.5739i	−0.323218	−	2.04072i
$93$	7.16385	+	3.65016i	0.742857	+	0.378504i
$94$	6.05109	+	18.6233i	0.624123	+	1.92085i
$95$	−2.90966	+	0.245553i	−0.298525	+	0.0251932i
$96$	5.65887	+	7.78877i	0.577556	+	0.794938i
$97$	−0.693249	+	0.353228i	−0.0703888	+	0.0358649i	−0.488831	−	0.872379i	$-0.662576\pi$
$97$	−0.693249	+	0.353228i	−0.0703888	+	0.0358649i	0.418442	+	0.908244i	$0.362576\pi$
$98$	6.68878	+	6.68878i	0.675669	+	0.675669i
$99$	−2.56339	+	2.20545i	−0.257630	+	0.221656i
$100$	−21.9040	−	3.21584i	−2.19040	−	0.321584i
$101$	9.28960	+	3.01837i	0.924350	+	0.300339i	0.732250	−	0.681036i	$-0.238470\pi$
$101$	9.28960	+	3.01837i	0.924350	+	0.300339i	0.192100	+	0.981375i	$0.438470\pi$
$102$	−16.8889	−	2.67494i	−1.67225	−	0.264858i
$103$	4.61435	−	0.730841i	0.454665	−	0.0720119i	0.0750982	−	0.997176i	$-0.476073\pi$
$103$	4.61435	−	0.730841i	0.454665	−	0.0720119i	0.379567	+	0.925164i	$0.376073\pi$
$104$	−13.2051	+	4.29061i	−1.29487	+	0.420729i
$105$	−4.19597	+	6.93489i	−0.409485	+	0.676776i
$106$	−9.49117	+	13.0635i	−0.921864	+	1.26884i
$107$	−2.39372	+	15.1133i	−0.231410	+	1.46106i	0.549015	+	0.835813i	$0.315003\pi$
$107$	−2.39372	+	15.1133i	−0.231410	+	1.46106i	−0.780424	+	0.625250i	$0.784997\pi$
$108$	7.98140	+	15.6644i	0.768011	+	1.50731i
$109$	17.8837			1.71295			0.856476	−	0.516187i	$-0.172649\pi$
$109$	17.8837			1.71295			0.856476	+	0.516187i	$0.172649\pi$
$110$	−15.3132	−	10.9102i	−1.46006	−	1.04024i
$111$	6.43355			0.610646
$112$	5.54022	+	10.8733i	0.523502	+	1.02743i
$113$	1.16850	−	7.37759i	0.109923	−	0.694025i	−0.869760	−	0.493474i	$-0.835727\pi$
$113$	1.16850	−	7.37759i	0.109923	−	0.694025i	0.979683	−	0.200551i	$-0.0642733\pi$
$114$	3.90155	−	5.37003i	0.365414	−	0.502949i
$115$	−9.71833	+	2.39135i	−0.906239	+	0.222994i
$116$	12.3658	−	4.01790i	1.14814	−	0.373053i
$117$	2.27165	−	0.359793i	0.210014	−	0.0332629i
$118$	−31.0201	−	4.91310i	−2.85563	−	0.452288i
$119$	−5.78457	−	1.87952i	−0.530271	−	0.172295i
$120$	20.8809	−	18.0391i	1.90615	−	1.64674i
$121$	−5.06477	−	9.76464i	−0.460433	−	0.887694i
$122$	16.6904	+	16.6904i	1.51107	+	1.51107i
$123$	2.32886	−	1.18662i	0.209987	−	0.106994i
$124$	−10.4371	−	14.3654i	−0.937277	−	1.29005i
$125$	−0.688059	+	11.1591i	−0.0615419	+	0.998105i
$126$	−1.44423	−	4.44489i	−0.128662	−	0.395982i
$127$	−0.183716	−	0.0936079i	−0.0163021	−	0.00830635i	0.445820	−	0.895122i	$-0.352912\pi$
$127$	−0.183716	−	0.0936079i	−0.0163021	−	0.00830635i	−0.462123	+	0.886816i	$0.652912\pi$
$128$	2.02777	+	12.8028i	0.179231	+	1.13162i
$129$	10.4469	−	7.59009i	0.919794	−	0.668270i
$130$	4.96061	+	11.7871i	0.435074	+	1.03379i
$131$			0.551708i			0.0482029i	0.999710	+	0.0241015i	$0.00767248\pi$
$131$			0.551708i			0.0482029i	−0.999710	+	0.0241015i	$0.992328\pi$
$132$	28.6037	−	6.97682i	2.48963	−	0.607254i
$133$	1.66950	−	1.66950i	0.144764	−	0.144764i
$134$	−2.72821	+	8.39658i	−0.235682	+	0.725354i
$135$	7.54370	−	4.68165i	0.649259	−	0.402932i
$136$	16.7516	+	12.1707i	1.43644	+	1.04363i
$137$	7.02615	−	13.7896i	0.600284	−	1.17812i	−0.368362	−	0.929682i	$-0.620081\pi$
$137$	7.02615	−	13.7896i	0.600284	−	1.17812i	0.968647	−	0.248442i	$-0.0799186\pi$
$138$	10.3285	−	20.2709i	0.879223	−	1.72557i
$139$	1.15101	+	0.836256i	0.0976272	+	0.0709303i	0.635528	−	0.772078i	$-0.280782\pi$
$139$	1.15101	+	0.836256i	0.0976272	+	0.0709303i	−0.537901	+	0.843008i	$0.680782\pi$
$140$	15.2099	−	9.43929i	1.28547	−	0.797766i
$141$	−4.78513	+	14.7271i	−0.402981	+	1.24025i
$142$	−12.1390	+	12.1390i	−1.01868	+	1.01868i
$143$	−0.559982	+	7.46065i	−0.0468280	+	0.623891i
$144$			6.88173i			0.573477i
$145$	−2.54705	−	6.05212i	−0.211521	−	0.502601i
$146$	−19.3704	+	14.0734i	−1.60311	+	1.16473i
$147$	1.17019	+	7.38826i	0.0965153	+	0.609373i
$148$	−12.6598	−	6.45048i	−1.04063	−	0.530226i
$149$	−7.35615	−	22.6399i	−0.602639	−	1.85473i	−0.512269	−	0.858825i	$-0.671195\pi$
$149$	−7.35615	−	22.6399i	−0.602639	−	1.85473i	−0.0903702	−	0.995908i	$-0.528805\pi$
$150$	−18.1732	−	17.7668i	−1.48383	−	1.45065i
$151$	−8.45592	−	11.6386i	−0.688133	−	0.947134i	0.311862	−	0.950127i	$-0.399047\pi$
$151$	−8.45592	−	11.6386i	−0.688133	−	0.947134i	−0.999996	+	0.00299311i	$0.999047\pi$
$152$	−7.16170	+	3.64907i	−0.580891	+	0.295979i
$153$	−2.42531	−	2.42531i	−0.196075	−	0.196075i
$154$	15.1517	−	1.24771i	1.22096	−	0.100543i
$155$	−6.78574	+	5.86223i	−0.545044	+	0.470866i
$156$	−19.0450	−	6.18810i	−1.52482	−	0.495445i
$157$	13.3277	+	2.11091i	1.06367	+	0.168469i	0.663654	−	0.748040i	$-0.269005\pi$
$157$	13.3277	+	2.11091i	1.06367	+	0.168469i	0.400016	+	0.916508i	$0.369005\pi$
$158$	−2.86747	+	0.454163i	−0.228124	+	0.0361312i
$159$	−12.1442	+	3.94588i	−0.963095	+	0.312928i
$160$	−10.4266	+	2.56562i	−0.824291	+	0.202830i
$161$	4.75657	−	6.54686i	0.374870	−	0.515965i
$162$	−4.37031	+	27.5931i	−0.343364	+	2.16792i
$163$	−0.487228	−	0.956239i	−0.0381626	−	0.0748984i	0.871138	−	0.491039i	$-0.163383\pi$
$163$	−0.487228	−	0.956239i	−0.0381626	−	0.0748984i	−0.909300	+	0.416140i	$0.863383\pi$
$164$	−5.77242			−0.450750
$165$	−4.72563	−	14.0977i	−0.367890	−	1.09750i
$166$	26.5315			2.05924
$167$	−0.858874	−	1.68563i	−0.0664616	−	0.130438i	0.855386	−	0.517992i	$-0.173320\pi$
$167$	−0.858874	−	1.68563i	−0.0664616	−	0.130438i	−0.921847	+	0.387554i	$0.873320\pi$
$168$	−3.49030	+	22.0369i	−0.269283	+	1.70018i
$169$	−4.65019	+	6.40044i	−0.357707	+	0.492342i
$170$	9.87255	−	16.3169i	0.757190	−	1.25145i
$171$	1.26627	−	0.411435i	0.0968339	−	0.0314633i
$172$	−28.1671	+	4.46123i	−2.14772	+	0.340166i
$173$	18.7140	+	2.96401i	1.42280	+	0.225350i	0.819919	−	0.572480i	$-0.194019\pi$
$173$	18.7140	+	2.96401i	1.42280	+	0.225350i	0.602883	+	0.797830i	$0.294019\pi$
$174$	14.1958	+	4.61248i	1.07618	+	0.349671i
$175$	−5.39599	−	7.25306i	−0.407898	−	0.548280i
$176$	−21.7861	−	5.14699i	−1.64219	−	0.387969i
$177$	−17.5618	−	17.5618i	−1.32002	−	1.32002i
$178$	8.71383	−	4.43992i	0.653129	−	0.332786i
$179$	−9.62961	−	13.2540i	−0.719751	−	0.990652i	−0.999532	−	0.0305880i	$-0.990262\pi$
$179$	−9.62961	−	13.2540i	−0.719751	−	0.990652i	0.279781	−	0.960064i	$-0.409738\pi$
$180$	10.0589	−	0.848892i	0.749744	−	0.0632726i
$181$	4.59306	+	14.1360i	0.341400	+	1.05072i	0.963483	+	0.267769i	$0.0862864\pi$
$181$	4.59306	+	14.1360i	0.341400	+	1.05072i	−0.622084	+	0.782951i	$0.713714\pi$
$182$	−9.21329	−	4.69440i	−0.682934	−	0.347972i
$183$	2.91994	+	18.4357i	0.215848	+	1.36281i
$184$	−22.2878	+	16.1930i	−1.64307	+	1.19376i
$185$	−2.70838	+	6.64461i	−0.199124	+	0.488522i
$186$		−	20.3843i		−	1.49465i
$187$	9.49195	−	5.86407i	0.694120	−	0.428823i
$188$	24.1819	−	24.1819i	1.76365	−	1.76365i
$189$	−2.21837	+	6.82744i	−0.161363	+	0.496623i
$190$	3.90373	+	6.29021i	0.283206	+	0.456340i
$191$	1.54488	+	1.12242i	0.111784	+	0.0812156i	0.642273	−	0.766476i	$-0.277992\pi$
$191$	1.54488	+	1.12242i	0.111784	+	0.0812156i	−0.530489	+	0.847692i	$0.677992\pi$
$192$	−1.20571	+	2.36634i	−0.0870146	+	0.170776i
$193$	5.16774	−	10.1423i	0.371982	−	0.730056i	−0.626811	−	0.779171i	$-0.715640\pi$
$193$	5.16774	−	10.1423i	0.371982	−	0.730056i	0.998793	+	0.0491153i	$0.0156402\pi$
$194$	1.59586	+	1.15946i	0.114576	+	0.0832446i
$195$	−2.30518	+	9.84666i	−0.165077	+	0.705134i
$196$	5.10504	−	15.7117i	0.364646	−	1.12226i
$197$	13.8092	−	13.8092i	0.983863	−	0.983863i	−0.0160086	−	0.999872i	$-0.505096\pi$
$197$	13.8092	−	13.8092i	0.983863	−	0.983863i	0.999872	+	0.0160086i	$0.00509592\pi$
$198$	7.93251	+	3.25214i	0.563739	+	0.231120i
$199$			22.3508i			1.58441i	0.610258	+	0.792203i	$0.291066\pi$
$199$			22.3508i			1.58441i	−0.610258	+	0.792203i	$0.708934\pi$
$200$	9.84050	+	29.1600i	0.695828	+	2.06192i
$201$	−5.64825	+	4.10369i	−0.398397	+	0.289452i
$202$	−3.87394	−	24.4591i	−0.272570	−	1.72094i
$203$	4.73060	+	2.41036i	0.332023	+	0.169174i
$204$	9.22823	+	28.4016i	0.646105	+	1.98851i
$205$	0.245143	+	2.90480i	0.0171215	+	0.202880i
$206$	−6.96208	−	9.58248i	−0.485071	−	0.667643i
$207$	4.06606	−	2.07176i	0.282610	−	0.143997i
$208$	10.7662	+	10.7662i	0.746501	+	0.746501i
$209$	0.355449	+	4.31646i	0.0245869	+	0.298576i
$210$	20.4953	+	1.49649i	1.41431	+	0.103267i
$211$	−0.358113	−	0.116358i	−0.0246535	−	0.00801042i	0.296664	−	0.954982i	$-0.404126\pi$
$211$	−0.358113	−	0.116358i	−0.0246535	−	0.00801042i	−0.321318	+	0.946971i	$0.604126\pi$
$212$	27.8532	+	4.41152i	1.91297	+	0.302984i
$213$	−13.4085	+	2.12369i	−0.918733	+	0.145513i
$214$	36.8958	−	11.9882i	2.52215	−	0.819495i
$215$	3.44119	+	13.9848i	0.234687	+	0.953758i
$216$	14.3649	−	19.7716i	0.977409	−	1.34529i
$217$	1.13426	−	7.16142i	0.0769984	−	0.486149i
$218$	−20.5843	−	40.3989i	−1.39414	−	2.73616i
$219$	−18.9340			−1.27944
$220$	−4.83583	+	32.4792i	−0.326032	+	2.18974i
$221$	−7.58859			−0.510464
$222$	−7.40504	−	14.5332i	−0.496994	−	0.975405i
$223$	1.19037	−	7.51570i	0.0797131	−	0.503289i	−0.915237	−	0.402916i	$-0.867997\pi$
$223$	1.19037	−	7.51570i	0.0797131	−	0.503289i	0.994950	−	0.100372i	$-0.0320034\pi$
$224$	5.10321	−	7.02396i	0.340972	−	0.469308i
$225$	−0.854361	−	5.02579i	−0.0569574	−	0.335053i
$226$	−18.0107	+	5.85204i	−1.19806	+	0.389272i
$227$	−8.10167	+	1.28318i	−0.537727	+	0.0851676i	−0.419390	−	0.907806i	$-0.637756\pi$
$227$	−8.10167	+	1.28318i	−0.537727	+	0.0851676i	−0.118336	+	0.992974i	$0.537756\pi$
$228$	−11.4497	−	1.81345i	−0.758274	−	0.120099i
$229$	7.21772	+	2.34518i	0.476960	+	0.154974i	0.537624	−	0.843184i	$-0.319322\pi$
$229$	7.21772	+	2.34518i	0.476960	+	0.154974i	−0.0606641	+	0.998158i	$0.519322\pi$
$230$	16.5878	+	19.2010i	1.09377	+	1.26608i
$231$	10.2734	+	6.24450i	0.675943	+	0.410858i
$232$	−12.7807	−	12.7807i	−0.839092	−	0.839092i
$233$	−23.3597	+	11.9023i	−1.53034	+	0.779749i	−0.997777	−	0.0666396i	$-0.978772\pi$
$233$	−23.3597	+	11.9023i	−1.53034	+	0.779749i	−0.532566	+	0.846388i	$0.678772\pi$
$234$	−3.42744	−	4.71746i	−0.224059	−	0.308390i
$235$	−13.1958	−	11.1419i	−0.860801	−	0.726818i
$236$	16.9496	+	52.1656i	1.10333	+	3.39569i
$237$	−2.04560	−	1.04228i	−0.132876	−	0.0677036i
$238$	2.41228	+	15.2305i	0.156365	+	0.987248i
$239$	−1.84133	+	1.33781i	−0.119106	+	0.0865356i	−0.645744	−	0.763554i	$-0.723452\pi$
$239$	−1.84133	+	1.33781i	−0.119106	+	0.0865356i	0.526638	+	0.850090i	$0.323452\pi$
$240$	−28.0205	−	11.4213i	−1.80872	−	0.737244i
$241$		−	6.29531i		−	0.405517i	−0.979229	−	0.202758i	$-0.935009\pi$
$241$		−	6.29531i		−	0.405517i	0.979229	−	0.202758i	$-0.0649906\pi$
$242$	−16.2285	+	22.6803i	−1.04321	+	1.45795i
$243$	−7.19883	+	7.19883i	−0.461805	+	0.461805i
$244$	12.7385	−	39.2050i	0.815498	−	2.50984i
$245$	−8.12326	−	1.90172i	−0.518976	−	0.121496i
$246$	−5.36106	−	3.89504i	−0.341809	−	0.248339i
$247$	1.33735	−	2.62470i	0.0850936	−	0.167006i
$248$	−11.2062	+	21.9934i	−0.711596	+	1.39658i
$249$	16.9738	+	12.3322i	1.07567	+	0.781521i
$250$	26.0002	−	11.2899i	1.64439	−	0.714037i
$251$	−8.21826	+	25.2932i	−0.518732	+	1.59649i	0.257655	+	0.966237i	$0.417050\pi$
$251$	−8.21826	+	25.2932i	−0.518732	+	1.59649i	−0.776387	+	0.630256i	$0.782950\pi$
$252$	−5.77157	+	5.77157i	−0.363575	+	0.363575i
$253$	3.51766	+	14.4218i	0.221153	+	0.906690i
$254$			0.522752i			0.0328004i
$255$	13.9004	−	5.85000i	0.870476	−	0.366341i
$256$	24.4439	−	17.7595i	1.52774	−	1.10997i
$257$	3.09337	+	19.5307i	0.192959	+	1.21829i	0.873955	+	0.486007i	$0.161547\pi$
$257$	3.09337	+	19.5307i	0.192959	+	1.21829i	−0.680996	+	0.732287i	$0.738453\pi$
$258$	−29.1702	−	14.8629i	−1.81606	−	0.925326i
$259$	−1.79286	−	5.51786i	−0.111403	−	0.342863i
$260$	14.4086	−	17.0648i	0.893586	−	1.05831i
$261$	1.75983	+	2.42220i	0.108931	+	0.149931i
$262$	1.24629	−	0.635018i	0.0769962	−	0.0392315i
$263$	−5.91748	−	5.91748i	−0.364888	−	0.364888i	0.500721	−	0.865609i	$-0.333068\pi$
$263$	−5.91748	−	5.91748i	−0.364888	−	0.364888i	−0.865609	+	0.500721i	$0.833068\pi$
$264$	−26.6933	−	31.0256i	−1.64286	−	1.90949i
$265$	1.03710	−	14.2037i	0.0637085	−	0.872526i
$266$	−5.69297	−	1.84976i	−0.349058	−	0.113416i
$267$	7.63850	+	1.20982i	0.467469	+	0.0740398i
$268$	15.2290	−	2.41203i	0.930258	−	0.147338i
$269$	−9.23539	+	3.00076i	−0.563092	+	0.182960i	−0.576712	−	0.816948i	$-0.695664\pi$
$269$	−9.23539	+	3.00076i	−0.563092	+	0.182960i	0.0136201	+	0.999907i	$0.495664\pi$
$270$	−19.2586	−	11.6524i	−1.17204	−	0.709144i
$271$	1.79360	−	2.46868i	0.108954	−	0.149962i	−0.751058	−	0.660236i	$-0.770456\pi$
$271$	1.79360	−	2.46868i	0.108954	−	0.149962i	0.860012	+	0.510274i	$0.170456\pi$
$272$	3.55198	−	22.4263i	0.215370	−	1.35979i
$273$	−3.71228	−	7.28576i	−0.224677	−	0.440954i
$274$	−39.2374			−2.37042
$275$	16.5496	+	1.05417i	0.997977	+	0.0635687i
$276$	−39.7326			−2.39162
$277$	−1.08057	−	2.12073i	−0.0649249	−	0.127422i	0.856263	−	0.516540i	$-0.172780\pi$
$277$	−1.08057	−	2.12073i	−0.0649249	−	0.127422i	−0.921188	+	0.389117i	$0.872780\pi$
$278$	0.564265	−	3.56263i	0.0338424	−	0.213672i
$279$	2.40334	−	3.30791i	0.143884	−	0.198039i
$280$	−21.2905	−	12.8819i	−1.27235	−	0.769839i
$281$	26.8503	−	8.72419i	1.60175	−	0.520442i	0.634214	−	0.773157i	$-0.281324\pi$
$281$	26.8503	−	8.72419i	1.60175	−	0.520442i	0.967541	+	0.252716i	$0.0813238\pi$
$282$	38.7759	−	6.14150i	2.30907	−	0.365721i
$283$	16.8040	+	2.66149i	0.998893	+	0.158209i	0.634406	−	0.773000i	$-0.281245\pi$
$283$	16.8040	+	2.66149i	0.998893	+	0.158209i	0.364486	+	0.931209i	$0.381245\pi$
$284$	28.5141	+	9.26479i	1.69200	+	0.549764i
$285$	−0.426322	+	5.83874i	−0.0252532	+	0.345857i
$286$	17.4979	−	7.32225i	1.03467	−	0.432974i
$287$	−1.66672	−	1.66672i	−0.0983831	−	0.0983831i
$288$	4.36237	−	2.22274i	0.257055	−	0.130976i
$289$	−3.34052	−	4.59783i	−0.196501	−	0.270461i
$290$	−10.7399	+	12.7197i	−0.630669	+	0.746927i
$291$	0.482038	+	1.48356i	0.0282576	+	0.0869678i
$292$	37.2578	+	18.9838i	2.18035	+	1.11094i
$293$	−1.67148	−	10.5533i	−0.0976492	−	0.616533i	−0.987174	−	0.159646i	$-0.948965\pi$
$293$	−1.67148	−	10.5533i	−0.0976492	−	0.616533i	0.889525	−	0.456886i	$-0.151035\pi$
$294$	15.3430	−	11.1473i	0.894821	−	0.650126i
$295$	25.5311	−	10.7448i	1.48648	−	0.625586i
$296$			19.7514i			1.14803i
$297$	−6.92127	−	11.2032i	−0.401613	−	0.650076i
$298$	−42.6760	+	42.6760i	−2.47215	+	2.47215i
$299$	3.12000	−	9.60236i	0.180434	−	0.555319i
$300$	−13.2379	+	42.3659i	−0.764288	+	2.44599i
$301$	−9.42104	−	6.84479i	−0.543020	−	0.394527i
$302$	−16.5584	+	32.4977i	−0.952831	+	1.87004i
$303$	8.89053	−	17.4487i	0.510748	−	1.00240i
$304$	7.13071	+	5.18077i	0.408975	+	0.297137i
$305$	−20.2698	−	4.74532i	−1.16064	−	0.271716i
$306$	−2.68716	+	8.27024i	−0.153615	+	0.472778i
$307$	−22.9923	+	22.9923i	−1.31224	+	1.31224i	−0.392474	+	0.919763i	$0.628381\pi$
$307$	−22.9923	+	22.9923i	−1.31224	+	1.31224i	−0.919763	+	0.392474i	$0.871619\pi$
$308$	−13.9549	−	22.5882i	−0.795154	−	1.28708i
$309$		−	9.36657i		−	0.532846i
$310$	21.0530	+	8.58134i	1.19573	+	0.487388i
$311$	−11.2361	+	8.16354i	−0.637143	+	0.462912i	−0.858868	−	0.512198i	$-0.828832\pi$
$311$	−11.2361	+	8.16354i	−0.637143	+	0.462912i	0.221724	+	0.975109i	$0.428832\pi$
$312$	4.35471	+	27.4946i	0.246537	+	1.55657i
$313$	−15.4928	−	7.89399i	−0.875707	−	0.446195i	−0.0424612	−	0.999098i	$-0.513520\pi$
$313$	−15.4928	−	7.89399i	−0.875707	−	0.446195i	−0.833245	+	0.552903i	$0.813520\pi$
$314$	−10.5718	−	32.5367i	−0.596601	−	1.83615i
$315$	3.14949	+	2.65927i	0.177453	+	0.149833i
$316$	2.98025	+	4.10196i	0.167652	+	0.230753i
$317$	14.3960	−	7.33513i	0.808560	−	0.411982i	−0.000287853	−	1.00000i	$-0.500092\pi$
$317$	14.3960	−	7.33513i	0.808560	−	0.411982i	0.808848	+	0.588018i	$0.200092\pi$
$318$	22.8916	+	22.8916i	1.28370	+	1.28370i
$319$	−8.98439	+	3.75964i	−0.503029	+	0.210500i
$320$	−1.93639	−	2.24144i	−0.108248	−	0.125300i
$321$	29.1768	+	9.48011i	1.62849	+	0.529128i
$322$	−20.2640	−	3.20950i	−1.12927	−	0.178859i
$323$	−4.33890	+	0.687214i	−0.241423	+	0.0382376i
$324$	46.4024	−	15.0771i	2.57791	−	0.837615i
$325$	−9.19926	−	6.52603i	−0.510283	−	0.361999i
$326$	−1.59932	+	2.20127i	−0.0885779	+	0.121917i
$327$	5.60894	−	35.4135i	0.310175	−	1.95837i
$328$	3.64298	+	7.14975i	0.201150	+	0.394779i
$329$	13.9645			0.769887
$330$	−26.4071	+	26.9016i	−1.45366	+	1.48088i
$331$	14.6837			0.807090			0.403545	−	0.914960i	$-0.367778\pi$
$331$	14.6837			0.807090			0.403545	+	0.914960i	$0.367778\pi$
$332$	−21.0360	−	41.2854i	−1.15450	−	2.26583i
$333$	0.511816	−	3.23148i	0.0280473	−	0.177084i
$334$	−2.81924	+	3.88034i	−0.154262	+	0.212323i
$335$	−1.86053	−	7.56111i	−0.101652	−	0.413108i
$336$	23.2690	−	7.56054i	1.26943	−	0.412461i
$337$	−13.3250	+	2.11047i	−0.725859	+	0.114965i	−0.508420	−	0.861109i	$-0.669770\pi$
$337$	−13.3250	+	2.11047i	−0.725859	+	0.114965i	−0.217439	+	0.976074i	$0.569770\pi$
$338$	19.8108	+	3.13772i	1.07757	+	0.170670i
$339$	−14.2427	−	4.62772i	−0.773555	−	0.251343i
$340$	−33.2182	−	2.42547i	−1.80151	−	0.131539i
$341$	8.67464	+	10.0825i	0.469758	+	0.545999i
$342$	−2.38690	−	2.38690i	−0.129069	−	0.129069i
$343$	17.2873	−	8.80832i	0.933426	−	0.475604i
$344$	23.3020	+	32.0725i	1.25636	+	1.72923i
$345$	1.68736	+	19.9943i	0.0908446	+	1.07646i
$346$	−14.8443	−	45.6861i	−0.798035	−	2.45610i
$347$	10.9022	+	5.55495i	0.585261	+	0.298205i	0.721438	−	0.692479i	$-0.243482\pi$
$347$	10.9022	+	5.55495i	0.585261	+	0.298205i	−0.136177	+	0.990685i	$0.543482\pi$
$348$	−4.07793	−	25.7470i	−0.218600	−	1.38018i
$349$	−16.4807	+	11.9739i	−0.882193	+	0.640951i	−0.933831	−	0.357715i	$-0.883556\pi$
$349$	−16.4807	+	11.9739i	−0.882193	+	0.640951i	0.0516378	+	0.998666i	$0.483556\pi$
$350$	−10.1737	+	20.5377i	−0.543805	+	1.09779i
$351$			8.95670i			0.478073i
$352$	3.77401	+	15.4728i	0.201156	+	0.824702i
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	−0.237495	−	0.971389i	$-0.576326\pi$
$353$	13.7886	−	13.7886i	0.733893	−	0.733893i	0.971389	+	0.237495i	$0.0763264\pi$
$354$	−19.4579	+	59.8853i	−1.03418	+	3.18287i
$355$	3.45131	−	14.7424i	0.183176	−	0.782444i
$356$	−13.8179	−	10.0393i	−0.732345	−	0.532079i
$357$	−5.53607	+	10.8652i	−0.293000	+	0.575045i
$358$	−18.8567	+	37.0084i	−0.996610	+	1.95596i
$359$	13.3648	+	9.71011i	0.705368	+	0.512480i	0.881676	−	0.471855i	$-0.156415\pi$
$359$	13.3648	+	9.71011i	0.705368	+	0.512480i	−0.176308	+	0.984335i	$0.556415\pi$
$360$	−7.39961	−	11.9232i	−0.389994	−	0.628410i
$361$	−5.34436	+	16.4483i	−0.281282	+	0.865697i
$362$	26.6462	−	26.6462i	1.40049	−	1.40049i
$363$	−20.9245	+	6.96676i	−1.09825	+	0.365660i
$364$			18.0588i			0.946537i
$365$	7.97079	−	19.5551i	0.417210	−	1.02356i
$366$	38.2850	−	27.8157i	2.00119	−	1.45395i
$367$	−1.00765	−	6.36207i	−0.0525990	−	0.332097i	−0.999930	−	0.0118406i	$-0.996231\pi$
$367$	−1.00765	−	6.36207i	−0.0525990	−	0.332097i	0.947331	−	0.320256i	$-0.103769\pi$
$368$	26.9172	+	13.7150i	1.40315	+	0.714943i
$369$	−0.410749	−	1.26415i	−0.0213827	−	0.0658092i
$370$	18.1274	−	1.52981i	0.942396	−	0.0795310i
$371$	6.76851	+	9.31606i	0.351404	+	0.483666i
$372$	−31.7199	+	16.1621i	−1.64460	+	0.837965i
$373$	9.69631	+	9.69631i	0.502056	+	0.502056i	0.912076	−	0.410021i	$-0.134478\pi$
$373$	9.69631	+	9.69631i	0.502056	+	0.502056i	−0.410021	+	0.912076i	$0.634478\pi$
$374$	−24.1720	−	14.6925i	−1.24991	−	0.759730i
$375$	21.8816	+	4.86238i	1.12996	+	0.251092i
$376$	−45.2131	−	14.6906i	−2.33169	−	0.757612i
$377$	6.54262	+	1.03625i	0.336962	+	0.0533696i
$378$	17.9763	−	2.84717i	0.924604	−	0.146443i
$379$	20.4487	−	6.64419i	1.05038	−	0.341289i	0.267563	−	0.963540i	$-0.413782\pi$
$379$	20.4487	−	6.64419i	1.05038	−	0.341289i	0.782818	+	0.622251i	$0.213782\pi$
$380$	6.69301	−	11.0619i	0.343344	−	0.567463i
$381$	−0.242982	+	0.334436i	−0.0124484	+	0.0171337i
$382$	0.757356	−	4.78176i	0.0387497	−	0.244656i
$383$	−0.137756	−	0.270362i	−0.00703902	−	0.0138148i	0.887460	−	0.460884i	$-0.152468\pi$
$383$	−0.137756	−	0.270362i	−0.00703902	−	0.0138148i	−0.894499	+	0.447069i	$0.852468\pi$
$384$	25.9882			1.32620
$385$	−10.7743	+	7.98168i	−0.549107	+	0.406784i
$386$	−28.8592			−1.46889
$387$	−2.98130	−	5.85112i	−0.151548	−	0.297429i
$388$	0.538921	−	3.40262i	0.0273596	−	0.172742i
$389$	2.11680	−	2.91353i	0.107326	−	0.147722i	−0.751975	−	0.659191i	$-0.770899\pi$
$389$	2.11680	−	2.91353i	0.107326	−	0.147722i	0.859301	+	0.511470i	$0.170899\pi$
$390$	24.8966	−	6.12620i	1.26069	−	0.310212i
$391$	−14.3199	+	4.65281i	−0.724187	+	0.235303i
$392$	−22.6824	+	3.59254i	−1.14563	+	0.181451i
$393$	1.09249	+	0.173034i	0.0551091	+	0.00872842i
$394$	−47.0890	−	15.3001i	−2.37231	−	0.770810i
$395$	1.93763	−	1.67393i	0.0974927	−	0.0842244i
$396$	−1.22881	−	14.9222i	−0.0617500	−	0.749871i
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.992731	+	0.120357i	$0.0384039\pi$
$397$	22.1781	+	22.1781i	1.11309	+	1.11309i	0.120357	+	0.992731i	$0.461596\pi$
$398$	50.4898	−	25.7259i	2.53083	−	1.28952i
$399$	−2.78235	−	3.82957i	−0.139292	−	0.191718i
$400$	23.5920	−	24.1316i	1.17960	−	1.20658i
$401$	−3.08934	−	9.50802i	−0.154274	−	0.474808i	0.843812	−	0.536639i	$-0.180306\pi$
$401$	−3.08934	−	9.50802i	−0.154274	−	0.474808i	−0.998087	+	0.0618306i	$0.980306\pi$
$402$	15.7713	+	8.03587i	0.786600	+	0.400793i
$403$	−1.41517	−	8.93502i	−0.0704945	−	0.445085i
$404$	−34.9891	+	25.4211i	−1.74077	+	1.26475i
$405$	−9.55773	−	22.7104i	−0.474927	−	1.12849i
$406$		−	13.4606i		−	0.668040i
$407$	9.84737	+	4.03719i	0.488116	+	0.200116i
$408$	29.3544	−	29.3544i	1.45326	−	1.45326i
$409$	−9.39140	+	28.9037i	−0.464375	+	1.42920i	0.395393	+	0.918512i	$0.370609\pi$
$409$	−9.39140	+	28.9037i	−0.464375	+	1.42920i	−0.859767	+	0.510686i	$0.829391\pi$
$410$	6.27971	−	3.89721i	0.310133	−	0.192470i
$411$	−25.1026	−	18.2381i	−1.23822	−	0.899619i
$412$	−9.39122	+	18.4313i	−0.462672	+	0.908045i
$413$	−10.1682	+	19.9562i	−0.500344	+	0.981981i
$414$	−9.36009	−	6.80051i	−0.460023	−	0.334227i
$415$	−19.8824	+	12.3391i	−0.975987	+	0.605701i
$416$	3.34737	−	10.3021i	0.164118	−	0.505104i
$417$	2.01695	−	2.01695i	0.0987706	−	0.0987706i
$418$	9.34163	−	5.77121i	0.456914	−	0.282279i
$419$		−	7.48185i		−	0.365512i	−0.983158	−	0.182756i	$-0.941498\pi$
$419$		−	7.48185i		−	0.365512i	0.983158	−	0.182756i	$-0.0585019\pi$
$420$	−13.9214	−	33.0791i	−0.679295	−	1.61410i
$421$	−16.5226	+	12.0043i	−0.805260	+	0.585056i	−0.912453	−	0.409182i	$-0.865814\pi$
$421$	−16.5226	+	12.0043i	−0.805260	+	0.585056i	0.107192	+	0.994238i	$0.465814\pi$
$422$	0.149340	+	0.942896i	0.00726976	+	0.0458995i
$423$	7.01654	+	3.57511i	0.341156	+	0.173828i
$424$	−12.1141	−	37.2833i	−0.588311	−	1.81064i
$425$	0.190165	+	16.8191i	0.00922437	+	0.815847i
$426$	20.2305	+	27.8450i	0.980173	+	1.34909i
$427$	14.9981	−	7.64189i	0.725807	−	0.369817i
$428$	−47.9083	−	47.9083i	−2.31573	−	2.31573i
$429$	14.5980	+	3.44879i	0.704797	+	0.166509i
$430$	27.6305	−	23.8702i	1.33246	−	1.15112i
$431$	−32.0182	−	10.4034i	−1.54226	−	0.501112i	−0.590264	−	0.807210i	$-0.700976\pi$
$431$	−32.0182	−	10.4034i	−1.54226	−	0.501112i	−0.952000	+	0.306098i	$0.900976\pi$
$432$	−26.4694	−	4.19235i	−1.27351	−	0.201704i
$433$	11.4564	−	1.81451i	0.550557	−	0.0871997i	0.125043	−	0.992151i	$-0.460093\pi$
$433$	11.4564	−	1.81451i	0.550557	−	0.0871997i	0.425514	+	0.904952i	$0.360093\pi$
$434$	−17.4830	+	5.68056i	−0.839210	+	0.272676i
$435$	−12.7833	+	3.14553i	−0.612911	+	0.150816i
$436$	−46.5438	+	64.0620i	−2.22904	+	3.06801i
$437$	0.914330	−	5.77285i	0.0437383	−	0.276153i
$438$	21.7931	+	42.7713i	1.04131	+	2.04369i
$439$	−10.7242			−0.511837			−0.255918	−	0.966698i	$-0.582378\pi$
$439$	−10.7242			−0.511837			−0.255918	+	0.966698i	$0.582378\pi$
$440$	43.2808	−	14.5079i	2.06333	−	0.691639i
$441$	3.80411			0.181148
$442$	8.73450	+	17.1424i	0.415458	+	0.815382i
$443$	−6.30958	+	39.8371i	−0.299777	+	1.89272i	0.132835	+	0.991138i	$0.457592\pi$
$443$	−6.30958	+	39.8371i	−0.299777	+	1.89272i	−0.432612	+	0.901580i	$0.642408\pi$
$444$	−16.7438	+	23.0459i	−0.794626	+	1.09371i
$445$	−4.46515	+	7.37979i	−0.211669	+	0.349836i
$446$	−18.3479	+	5.96159i	−0.868797	+	0.282289i
$447$	−47.1388	+	7.46605i	−2.22959	+	0.353132i
$448$	2.36553	+	0.374664i	0.111761	+	0.0177012i
$449$	3.46337	+	1.12532i	0.163447	+	0.0531070i	0.389597	−	0.920985i	$-0.372614\pi$
$449$	3.46337	+	1.12532i	0.163447	+	0.0531070i	−0.226151	+	0.974092i	$0.572614\pi$
$450$	−10.3698	+	7.71468i	−0.488835	+	0.363674i
$451$	4.30925	−	0.354856i	0.202915	−	0.0167095i
$452$	23.3865	+	23.3865i	1.10001	+	1.10001i
$453$	−25.6988	+	13.0942i	−1.20744	+	0.615220i
$454$	12.2237	+	16.8245i	0.573688	+	0.789613i
$455$	9.08757	−	0.766921i	0.426032	−	0.0359538i
$456$	4.97976	+	15.3261i	0.233198	+	0.717711i
$457$	−16.1207	−	8.21391i	−0.754094	−	0.384230i	0.0342910	−	0.999412i	$-0.489083\pi$
$457$	−16.1207	−	8.21391i	−0.754094	−	0.384230i	−0.788385	+	0.615182i	$0.789083\pi$
$458$	−3.00993	−	19.0039i	−0.140645	−	0.887996i
$459$	10.8060	−	7.85105i	0.504383	−	0.366456i
$460$	16.7265	−	41.0361i	0.779879	−	1.91332i
$461$		−	35.5884i		−	1.65751i	−0.559608	−	0.828757i	$-0.689048\pi$
$461$		−	35.5884i		−	1.65751i	0.559608	−	0.828757i	$-0.310952\pi$
$462$	2.28138	−	30.3949i	0.106139	−	1.41410i
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	−0.803266	−	0.595620i	$-0.796907\pi$
$463$	−4.46802	+	4.46802i	−0.207647	+	0.207647i	0.595620	+	0.803266i	$0.296907\pi$
$464$	−6.12479	+	18.8502i	−0.284336	+	0.875097i
$465$	9.48019	+	15.2757i	0.439633	+	0.708396i
$466$	53.7742	+	39.0692i	2.49104	+	1.80985i
$467$	3.92827	−	7.70967i	0.181779	−	0.356761i	−0.782079	−	0.623180i	$-0.785840\pi$
$467$	3.92827	−	7.70967i	0.181779	−	0.356761i	0.963857	+	0.266419i	$0.0858404\pi$
$468$	−4.62330	+	9.07374i	−0.213712	+	0.419434i
$469$	5.09363	+	3.70074i	0.235202	+	0.170884i
$470$	−9.98082	+	42.6334i	−0.460381	+	1.96653i
$471$	8.36006	−	25.7296i	0.385211	−	1.18556i
$472$	53.9157	−	53.9157i	2.48167	−	2.48167i
$473$	20.7532	−	5.06198i	0.954233	−	0.232750i
$474$			5.82062i			0.267350i
$475$	−5.85082	−	2.89829i	−0.268454	−	0.132983i
$476$	21.7875	−	15.8295i	0.998628	−	0.725545i
$477$	1.01584	+	6.41374i	0.0465120	+	0.293665i
$478$	5.14145	+	2.61970i	0.235165	+	0.119822i
$479$	4.75378	+	14.6306i	0.217206	+	0.668490i	0.998990	+	0.0449410i	$0.0143100\pi$
$479$	4.75378	+	14.6306i	0.217206	+	0.668490i	−0.781784	+	0.623549i	$0.785690\pi$
$480$	1.81033	+	21.4514i	0.0826300	+	0.979117i
$481$	−4.25480	−	5.85623i	−0.194002	−	0.267021i
$482$	−14.2209	+	7.24593i	−0.647746	+	0.330043i
$483$	−11.4723	−	11.4723i	−0.522008	−	0.522008i
$484$	48.1597	+	7.27051i	2.18908	+	0.330478i
$485$	−1.73516	−	0.126694i	−0.0787894	−	0.00575290i
$486$	24.5478	+	7.97608i	1.11351	+	0.361802i
$487$	−5.87316	−	0.930218i	−0.266138	−	0.0421522i	0.0219390	−	0.999759i	$-0.493016\pi$
$487$	−5.87316	−	0.930218i	−0.266138	−	0.0421522i	−0.288077	+	0.957607i	$0.593016\pi$
$488$	−56.5988	+	8.96437i	−2.56211	+	0.405798i
$489$	−2.04636	+	0.664903i	−0.0925396	+	0.0300679i
$490$	5.05397	+	20.5391i	0.228315	+	0.927863i
$491$	24.0702	−	33.1298i	1.08627	−	1.49513i	0.233851	−	0.972272i	$-0.424867\pi$
$491$	24.0702	−	33.1298i	1.08627	−	1.49513i	0.852422	−	0.522855i	$-0.175133\pi$
$492$	−1.81042	+	11.4306i	−0.0816202	+	0.515330i
$493$	−4.48477	−	8.80185i	−0.201984	−	0.396415i
$494$	−7.46842			−0.336020
$495$	−7.45701	+	1.25208i	−0.335168	+	0.0562769i
$496$	27.0678			1.21538
$497$	5.55801	+	10.9082i	0.249311	+	0.489300i
$498$	8.32117	−	52.5378i	0.372880	−	2.35427i
$499$	13.6289	−	18.7585i	0.610111	−	0.839746i	−0.386475	−	0.922300i	$-0.626308\pi$
$499$	13.6289	−	18.7585i	0.610111	−	0.839746i	0.996587	+	0.0825534i	$0.0263075\pi$
$500$	−38.1829	−	31.5072i	−1.70759	−	1.40905i
$501$	−3.60727	+	1.17207i	−0.161161	+	0.0523644i
$502$	66.5959	−	10.5478i	2.97232	−	0.470769i
$503$	−3.30226	−	0.523026i	−0.147240	−	0.0233206i	0.0823791	−	0.996601i	$-0.473748\pi$
$503$	−3.30226	−	0.523026i	−0.147240	−	0.0233206i	−0.229619	+	0.973280i	$0.573748\pi$
$504$	10.7911	+	3.50626i	0.480676	+	0.156181i
$505$	14.2784	+	16.5277i	0.635379	+	0.735473i
$506$	28.5296	−	24.5458i	1.26829	−	1.09120i
$507$	11.2157	+	11.2157i	0.498108	+	0.498108i
$508$	0.813450	−	0.414474i	0.0360910	−	0.0183893i
$509$	−13.0172	−	17.9166i	−0.576977	−	0.794141i	0.416383	−	0.909189i	$-0.363298\pi$
$509$	−13.0172	−	17.9166i	−0.576977	−	0.794141i	−0.993360	+	0.115049i	$0.963298\pi$
$510$	−29.2144	−	24.6672i	−1.29363	−	1.09228i
$511$	5.27640	+	16.2391i	0.233414	+	0.718375i
$512$	−45.1541	−	23.0072i	−1.99555	−	1.01678i
$513$	0.811108	+	5.12114i	0.0358113	+	0.226104i
$514$	40.5589	−	29.4678i	1.78898	−	1.29977i
$515$	9.67385	+	3.94312i	0.426281	+	0.173755i
$516$			57.1759i			2.51703i
$517$	−16.5658	+	19.5390i	−0.728565	+	0.859323i
$518$	−10.4011	+	10.4011i	−0.456998	+	0.456998i
$519$	11.7387	−	36.1280i	0.515272	−	1.58584i
$520$	−30.2298	−	7.07704i	−1.32567	−	0.310349i
$521$	8.59679	+	6.24594i	0.376632	+	0.273639i	0.759956	−	0.649975i	$-0.225221\pi$
$521$	8.59679	+	6.24594i	0.376632	+	0.273639i	−0.383323	+	0.923614i	$0.625221\pi$
$522$	3.44611	−	6.76338i	0.150832	−	0.296025i
$523$	19.6244	−	38.5151i	0.858116	−	1.68415i	0.137847	−	0.990454i	$-0.455982\pi$
$523$	19.6244	−	38.5151i	0.858116	−	1.68415i	0.720269	−	0.693694i	$-0.244018\pi$
$524$	−1.97629	−	1.43586i	−0.0863348	−	0.0627259i
$525$	−16.0549	+	8.41036i	−0.700694	+	0.367058i
$526$	−6.55638	+	20.1785i	−0.285872	+	0.879823i
$527$	−9.53941	+	9.53941i	−0.415543	+	0.415543i
$528$	−17.0249	+	41.5267i	−0.740915	+	1.80722i
$529$			2.96712i			0.129005i
$530$	−33.2795	+	14.0057i	−1.44557	+	0.608370i
$531$	−10.2181	+	7.42391i	−0.443429	+	0.322170i
$532$	1.63538	+	10.3254i	0.0709028	+	0.447663i
$533$	−2.62032	−	1.33512i	−0.113499	−	0.0578304i
$534$	−6.05900	−	18.6477i	−0.262198	−	0.806964i
$535$	−22.0739	+	26.1430i	−0.954338	+	1.13026i
$536$	−12.5986	−	17.3405i	−0.544176	−	0.748994i
$537$	−29.2658	+	14.9117i	−1.26291	+	0.643487i
$538$	17.4086	+	17.4086i	0.750538	+	0.750538i
$539$	−2.84517	+	12.0430i	−0.122550	+	0.518728i
$540$	−2.86274	+	39.2069i	−0.123193	+	1.68720i
$541$	−20.0780	−	6.52373i	−0.863220	−	0.280477i	−0.156247	−	0.987718i	$-0.549940\pi$
$541$	−20.0780	−	6.52373i	−0.863220	−	0.280477i	−0.706973	+	0.707241i	$0.749940\pi$
$542$	−7.64114	−	1.21024i	−0.328215	−	0.0519841i
$543$	29.4327	−	4.66168i	1.26308	−	0.200052i
$544$	−15.3634	+	4.99188i	−0.658702	+	0.214025i
$545$	34.2140	+	20.7012i	1.46557	+	0.886744i
$546$	−12.1855	+	16.7719i	−0.521490	+	0.717770i
$547$	0.218056	−	1.37675i	0.00932342	−	0.0588658i	−0.982588	−	0.185798i	$-0.940513\pi$
$547$	0.218056	−	1.37675i	0.00932342	−	0.0588658i	0.991911	+	0.126932i	$0.0405130\pi$
$548$	31.1101	+	61.0571i	1.32896	+	2.60823i
$549$	9.49230			0.405121
$550$	−16.6673	−	38.5984i	−0.710696	−	1.64584i
$551$	3.83469			0.163363
$552$	25.0753	+	49.2130i	1.06727	+	2.09464i
$553$	−0.323881	+	2.04490i	−0.0137728	+	0.0869581i
$554$	−3.54693	+	4.88193i	−0.150695	+	0.207414i
$555$	12.3083	+	7.44713i	0.522456	+	0.316113i
$556$	−5.99117	+	1.94665i	−0.254082	+	0.0825563i
$557$	−3.78516	+	0.599510i	−0.160382	+	0.0254021i	−0.236109	−	0.971727i	$-0.575872\pi$
$557$	−3.78516	+	0.599510i	−0.160382	+	0.0254021i	0.0757269	+	0.997129i	$0.475872\pi$
$558$	−10.2387	−	1.62166i	−0.433440	−	0.0686502i
$559$	−13.8180	−	4.48973i	−0.584438	−	0.189895i
$560$	−1.98715	+	27.2152i	−0.0839722	+	1.15005i
$561$	−8.63507	−	20.6352i	−0.364573	−	0.871218i
$562$	−50.6125	−	50.6125i	−2.13496	−	2.13496i
$563$	−2.17596	+	1.10871i	−0.0917058	+	0.0467264i	−0.499242	−	0.866463i	$-0.666388\pi$
$563$	−2.17596	+	1.10871i	−0.0917058	+	0.0467264i	0.407536	+	0.913189i	$0.366388\pi$
$564$	−40.3009	−	55.4695i	−1.69698	−	2.33569i
$565$	10.7754	−	12.7617i	0.453324	−	0.536891i
$566$	−13.3292	−	41.0231i	−0.560269	−	1.72433i
$567$	17.7515	+	9.04483i	0.745492	+	0.379847i
$568$	−6.51986	−	41.1648i	−0.273567	−	1.72723i
$569$	−5.21403	+	3.78822i	−0.218584	+	0.158810i	−0.691689	−	0.722196i	$-0.743133\pi$
$569$	−5.21403	+	3.78822i	−0.218584	+	0.158810i	0.473105	+	0.881006i	$0.343133\pi$
$570$	13.6803	−	5.75736i	0.573003	−	0.241149i
$571$		−	13.2864i		−	0.556019i	−0.960578	−	0.278009i	$-0.910325\pi$
$571$		−	13.2864i		−	0.556019i	0.960578	−	0.278009i	$-0.0896747\pi$
$572$	−25.2677	−	21.4228i	−1.05649	−	0.895733i
$573$	2.70715	−	2.70715i	0.113093	−	0.113093i
$574$	−1.84667	+	5.68346i	−0.0770785	+	0.237223i
$575$	−21.3606	−	6.67444i	−0.890797	−	0.278343i
$576$	1.09266	+	0.793862i	0.0455274	+	0.0330776i
$577$	−8.50263	+	16.6874i	−0.353969	+	0.694704i	−0.997496	−	0.0707197i	$-0.977470\pi$
$577$	−8.50263	+	16.6874i	−0.353969	+	0.694704i	0.643527	+	0.765423i	$0.277470\pi$
$578$	−6.54143	+	12.8383i	−0.272088	+	0.534002i
$579$	−18.4630	−	13.4141i	−0.767295	−	0.557473i
$580$	28.3084	+	6.62722i	1.17544	+	0.275180i
$581$	5.84679	−	17.9946i	0.242566	−	0.746540i
$582$	2.79649	−	2.79649i	0.115918	−	0.115918i
$583$	−21.0643	−	1.58105i	−0.872395	−	0.0654803i
$584$		−	58.1284i		−	2.40537i
$585$	4.76244	+	1.94120i	0.196903	+	0.0802588i
$586$	−21.9158	+	15.9228i	−0.905334	+	0.657764i
$587$	−1.31860	−	8.32531i	−0.0544244	−	0.343622i	−0.999842	−	0.0177617i	$-0.994346\pi$
$587$	−1.31860	−	8.32531i	−0.0544244	−	0.343622i	0.945418	−	0.325861i	$-0.105654\pi$
$588$	−29.5113	−	15.0367i	−1.21702	−	0.620105i
$589$	−1.61829	−	4.98059i	−0.0666805	−	0.205221i
$590$	−53.6585	−	45.3066i	−2.20909	−	1.86524i
$591$	−23.0140	−	31.6760i	−0.946669	−	1.30298i
$592$	19.2983	−	9.83295i	0.793153	−	0.404132i
$593$	4.37233	+	4.37233i	0.179550	+	0.179550i	0.791160	−	0.611610i	$-0.209478\pi$
$593$	4.37233	+	4.37233i	0.179550	+	0.179550i	−0.611610	+	0.791160i	$0.709478\pi$
$594$	−17.3413	+	28.5299i	−0.711522	+	1.17060i
$595$	−8.89103	−	10.2917i	−0.364497	−	0.421918i
$596$	100.244	+	32.5713i	4.10616	+	1.33417i
$597$	44.2592	+	7.00996i	1.81141	+	0.286899i
$598$	−25.2826	+	4.00437i	−1.03388	+	0.163751i
$599$	34.7989	−	11.3068i	1.42184	−	0.461985i	0.505656	−	0.862735i	$-0.331250\pi$
$599$	34.7989	−	11.3068i	1.42184	−	0.461985i	0.916187	+	0.400750i	$0.131250\pi$
$600$	60.8290	−	10.3407i	2.48333	−	0.422155i
$601$	6.33088	−	8.71371i	0.258242	−	0.355440i	−0.660134	−	0.751147i	$-0.729501\pi$
$601$	6.33088	−	8.71371i	0.258242	−	0.355440i	0.918376	+	0.395708i	$0.129501\pi$
$602$	−4.61853	+	29.1603i	−0.188237	+	1.18848i
$603$	1.61188	+	3.16350i	0.0656410	+	0.128828i
$604$	63.6982			2.59184
$605$	1.61343	−	24.5438i	0.0655952	−	0.997846i
$606$	−49.6491			−2.01686
$607$	15.0249	+	29.4880i	0.609842	+	1.19688i	0.965043	+	0.262092i	$0.0844124\pi$
$607$	15.0249	+	29.4880i	0.609842	+	1.19688i	−0.355201	+	0.934790i	$0.615588\pi$
$608$	0.980962	−	6.19355i	0.0397833	−	0.251182i
$609$	6.25669	−	8.61159i	0.253534	−	0.348959i
$610$	12.6111	+	51.2508i	0.510607	+	2.07508i
$611$	16.5702	−	5.38398i	0.670359	−	0.217813i
$612$	14.9998	−	2.37574i	0.606332	−	0.0960336i
$613$	−21.3721	−	3.38501i	−0.863213	−	0.136719i	−0.290898	−	0.956754i	$-0.593954\pi$
$613$	−21.3721	−	3.38501i	−0.863213	−	0.136719i	−0.572314	+	0.820034i	$0.693954\pi$
$614$	78.4030	+	25.4747i	3.16409	+	1.02807i
$615$	5.82899	+	0.425611i	0.235048	+	0.0171623i
$616$	−19.1710	+	31.5401i	−0.772421	+	1.27079i
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	0.0616431	−	0.998098i	$-0.480366\pi$
$617$	−23.2611	−	23.2611i	−0.936455	−	0.936455i	−0.998098	+	0.0616431i	$0.980366\pi$
$618$	−21.1588	+	10.7810i	−0.851133	+	0.433674i
$619$	24.3484	+	33.5126i	0.978643	+	1.34699i	0.937557	+	0.347831i	$0.113082\pi$
$619$	24.3484	+	33.5126i	0.978643	+	1.34699i	0.0410856	+	0.999156i	$0.486918\pi$
$620$	−3.33893	−	39.5644i	−0.134095	−	1.58894i
$621$	5.49164	+	16.9015i	0.220372	+	0.678235i
$622$	31.3741	+	15.9859i	1.25798	+	0.640975i
$623$	−1.09102	−	6.88845i	−0.0437109	−	0.275980i
$624$	24.6959	−	17.9426i	0.988627	−	0.718279i
$625$	−14.2336	+	20.5525i	−0.569343	+	0.822100i
$626$			44.0839i			1.76195i
$627$	8.65895	+	0.649924i	0.345805	+	0.0259555i
$628$	−42.2480	+	42.2480i	−1.68588	+	1.68588i
$629$	−3.33583	+	10.2666i	−0.133008	+	0.409357i
$630$	2.38215	−	10.1754i	0.0949071	−	0.405399i
$631$	25.4513	+	18.4915i	1.01320	+	0.736134i	0.964878	−	0.262697i	$-0.0846121\pi$
$631$	25.4513	+	18.4915i	1.01320	+	0.736134i	0.0483238	+	0.998832i	$0.484612\pi$
$632$	3.19987	−	6.28010i	0.127284	−	0.249809i
$633$	−0.342729	+	0.672644i	−0.0136223	+	0.0267352i
$634$	−33.1397	−	24.0774i	−1.31615	−	0.956236i
$635$	−0.243118	−	0.391744i	−0.00964783	−	0.0155459i
$636$	17.4714	−	53.7715i	0.692787	−	2.13218i
$637$	5.95137	−	5.95137i	0.235802	−	0.235802i
$638$	18.8340	+	15.9681i	0.745645	+	0.632184i
$639$			6.90382i			0.273111i
$640$	−10.9404	+	26.8407i	−0.432459	+	1.06097i
$641$	−16.6022	+	12.0622i	−0.655749	+	0.476430i	−0.865225	−	0.501384i	$-0.832824\pi$
$641$	−16.6022	+	12.0622i	−0.655749	+	0.476430i	0.209476	+	0.977814i	$0.432824\pi$
$642$	−12.1673	−	76.8212i	−0.480204	−	3.03189i
$643$	15.7020	+	8.00058i	0.619228	+	0.315512i	0.735314	−	0.677727i	$-0.237035\pi$
$643$	15.7020	+	8.00058i	0.619228	+	0.315512i	−0.116086	+	0.993239i	$0.537035\pi$
$644$	11.0724	+	34.0774i	0.436314	+	1.34284i
$645$	28.7721	−	2.42815i	1.13290	−	0.0956082i
$646$	6.54649	+	9.01047i	0.257568	+	0.354512i
$647$	5.13354	−	2.61567i	0.201820	−	0.102833i	−0.350159	−	0.936690i	$-0.613873\pi$
$647$	5.13354	−	2.61567i	0.201820	−	0.102833i	0.551980	+	0.833857i	$0.313873\pi$
$648$	−47.9592	−	47.9592i	−1.88401	−	1.88401i
$649$	−15.8602	−	37.9010i	−0.622566	−	1.48774i
$650$	−4.15374	+	28.2924i	−0.162923	+	1.10972i
$651$	−13.8253	−	4.49212i	−0.541858	−	0.176060i
$652$	4.69343	+	0.743366i	0.183809	+	0.0291125i
$653$	5.76236	−	0.912669i	0.225499	−	0.0357155i	−0.0426625	−	0.999090i	$-0.513584\pi$
$653$	5.76236	−	0.912669i	0.225499	−	0.0357155i	0.268161	+	0.963374i	$0.413584\pi$
$654$	−86.4540	+	28.0906i	−3.38062	+	1.09843i
$655$	−0.638627	+	1.05549i	−0.0249532	+	0.0412415i
$656$	5.17212	−	7.11881i	0.201937	−	0.277943i
$657$	−1.50628	+	9.51025i	−0.0587654	+	0.371030i
$658$	−16.0732	−	31.5454i	−0.626598	−	1.22977i
$659$	−5.21347			−0.203088			−0.101544	−	0.994831i	$-0.532378\pi$
$659$	−5.21347			−0.203088			−0.101544	+	0.994831i	$0.532378\pi$
$660$	62.7987	+	19.7625i	2.44444	+	0.769254i
$661$	4.56016			0.177369			0.0886847	−	0.996060i	$-0.471734\pi$
$661$	4.56016			0.177369			0.0886847	+	0.996060i	$0.471734\pi$
$662$	−16.9010	−	33.1701i	−0.656877	−	1.28919i
$663$	−2.38004	+	15.0270i	−0.0924330	+	0.583599i
$664$	−37.8606	+	52.1106i	−1.46927	+	2.02228i
$665$	5.12651	−	1.26146i	0.198798	−	0.0489173i
$666$	−7.88892	+	2.56327i	−0.305689	+	0.0993245i
$667$	12.9815	−	2.05606i	0.502644	−	0.0796110i
$668$	8.27346	+	1.31039i	0.320110	+	0.0507004i
$669$	−14.5093	−	4.71435i	−0.560962	−	0.182267i
$670$	−14.9389	+	12.9058i	−0.577139	+	0.498593i
$671$	−7.09949	+	30.0506i	−0.274073	+	1.16009i
$672$	−12.3084	−	12.3084i	−0.474805	−	0.474805i
$673$	−0.498417	+	0.253956i	−0.0192126	+	0.00978930i	−0.463570	−	0.886060i	$-0.653432\pi$
$673$	−0.498417	+	0.253956i	−0.0192126	+	0.00978930i	0.444358	+	0.895849i	$0.353432\pi$
$674$	20.1046	+	27.6716i	0.774401	+	1.06587i
$675$	19.8514	−	0.224449i	0.764079	−	0.00863905i
$676$	−10.8248	−	33.3153i	−0.416338	−	1.28136i
$677$	−25.9390	−	13.2166i	−0.996918	−	0.507955i	−0.122157	−	0.992511i	$-0.538981\pi$
$677$	−25.9390	−	13.2166i	−0.996918	−	0.507955i	−0.874760	+	0.484556i	$0.838981\pi$
$678$	5.93947	+	37.5003i	0.228104	+	1.44019i
$679$	1.13807	−	0.826858i	0.0436752	−	0.0317319i
$680$	17.9599	+	42.6750i	0.688729	+	1.63651i
$681$			16.4454i			0.630190i
$682$	12.7916	−	31.2008i	0.489815	−	1.19474i
$683$	5.43554	−	5.43554i	0.207985	−	0.207985i	−0.595425	−	0.803411i	$-0.703016\pi$
$683$	5.43554	−	5.43554i	0.207985	−	0.207985i	0.803411	+	0.595425i	$0.203016\pi$
$684$	−1.82174	+	5.60674i	−0.0696560	+	0.214379i
$685$	29.4041	−	18.2483i	1.12347	−	0.697231i
$686$	−39.7955	−	28.9131i	−1.51940	−	1.10391i
$687$	6.90765	−	13.5570i	0.263543	−	0.517233i
$688$	19.7361	−	38.7343i	0.752432	−	1.47673i
$689$	11.6233	+	8.44481i	0.442812	+	0.321722i
$690$	43.2244	−	26.8252i	1.64552	−	1.02122i
$691$	−2.91716	+	8.97809i	−0.110974	+	0.341542i	−0.991086	−	0.133223i	$-0.957467\pi$
$691$	−2.91716	+	8.97809i	−0.110974	+	0.341542i	0.880112	+	0.474766i	$0.157467\pi$
$692$	−59.3222	+	59.3222i	−2.25509	+	2.25509i
$693$	3.95382	−	4.66342i	0.150193	−	0.177149i
$694$		−	31.0215i		−	1.17756i
$695$	1.23403	+	2.93222i	0.0468094	+	0.111225i
$696$	−29.3168	+	21.2999i	−1.11125	+	0.807371i
$697$	0.686067	+	4.33166i	0.0259866	+	0.164073i
$698$	46.0182	+	23.4474i	1.74181	+	0.887499i
$699$	16.2427	+	49.9899i	0.614356	+	1.89079i
$700$	40.0249	−	0.452542i	1.51280	−	0.0171045i
$701$	−11.5843	−	15.9445i	−0.437535	−	0.602215i	0.532127	−	0.846664i	$-0.321393\pi$
$701$	−11.5843	−	15.9445i	−0.437535	−	0.602215i	−0.969662	+	0.244449i	$0.921393\pi$
$702$	20.2329	−	10.3092i	0.763643	−	0.389095i
$703$	−2.96308	−	2.96308i	−0.111755	−	0.111755i
$704$	−3.33042	+	2.86537i	−0.125520	+	0.107993i
$705$	−26.2019	+	22.6360i	−0.986822	+	0.852520i
$706$	−47.0188	−	15.2773i	−1.76958	−	0.574970i
$707$	−17.4427	−	2.76266i	−0.656001	−	0.103900i
$708$	108.615	−	17.2029i	4.08199	−	0.646523i
$709$	−42.2836	+	13.7388i	−1.58799	+	0.515970i	−0.964100	−	0.265540i	$-0.914450\pi$
$709$	−42.2836	+	13.7388i	−1.58799	+	0.515970i	−0.623893	+	0.781510i	$0.714450\pi$
$710$	−37.2751	+	9.17212i	−1.39891	+	0.344224i
$711$	−0.686259	+	0.944555i	−0.0257367	+	0.0354236i
$712$	−3.71422	+	23.4507i	−0.139196	+	0.878850i
$713$	−8.14881	−	15.9929i	−0.305175	−	0.598940i
$714$	30.9161			1.15701
$715$	−9.70736	+	13.6250i	−0.363035	+	0.509547i
$716$	72.5395			2.71093
$717$	2.07163	+	4.06580i	0.0773664	+	0.151840i
$718$	6.55191	−	41.3671i	0.244515	−	1.54381i
$719$	−14.1002	+	19.4073i	−0.525850	+	0.723770i	−0.986491	−	0.163816i	$-0.947620\pi$
$719$	−14.1002	+	19.4073i	−0.525850	+	0.723770i	0.460641	+	0.887587i	$0.347620\pi$
$720$	−7.96592	+	13.1657i	−0.296872	+	0.490656i
$721$	−8.03342	+	2.61022i	−0.299180	+	0.0972095i
$722$	43.3075	−	6.85924i	1.61174	−	0.255274i
$723$	−12.4660	−	1.97442i	−0.463616	−	0.0734296i
$724$	−62.5908	−	20.3370i	−2.32617	−	0.755819i
$725$	2.13276	−	14.5268i	0.0792087	−	0.539513i
$726$	39.8219	+	39.2490i	1.47793	+	1.45667i
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	0.300379	−	0.953820i	$-0.402887\pi$
$727$	−17.6187	−	17.6187i	−0.653441	−	0.653441i	−0.953820	+	0.300379i	$0.902887\pi$
$728$	22.3677	−	11.3969i	0.829002	−	0.422398i
$729$	−7.43339	−	10.2312i	−0.275311	−	0.378933i
$730$	−53.3489	+	4.50224i	−1.97453	+	0.166635i
$731$	6.69547	+	20.6065i	0.247641	+	0.762161i
$732$	−73.6387	−	37.5208i	−2.72177	−	1.38681i
$733$	−0.00846331	−	0.0534353i	−0.000312600	−	0.00197368i	0.987532	−	0.157421i	$-0.0503180\pi$
$733$	−0.00846331	−	0.0534353i	−0.000312600	−	0.00197368i	−0.987844	+	0.155448i	$0.950318\pi$
$734$	−13.2119	+	9.59902i	−0.487661	+	0.354306i
$735$	−6.31353	+	15.4893i	−0.232878	+	0.571331i
$736$		−	21.4928i		−	0.792235i
$737$	−11.2205	+	2.73683i	−0.413313	+	0.100813i
$738$	−2.38292	+	2.38292i	−0.0877163	+	0.0877163i
$739$	−5.95011	+	18.3126i	−0.218878	+	0.673638i	0.779977	+	0.625808i	$0.215231\pi$
$739$	−5.95011	+	18.3126i	−0.218878	+	0.673638i	−0.998855	+	0.0478303i	$0.984769\pi$
$740$	−16.7531	−	26.9949i	−0.615858	−	0.992352i
$741$	−4.77800	−	3.47142i	−0.175524	−	0.127526i
$742$	13.2541	−	26.0127i	0.486575	−	0.954957i
$743$	−3.38155	+	6.63666i	−0.124057	+	0.243475i	−0.944679	−	0.327995i	$-0.893627\pi$
$743$	−3.38155	+	6.63666i	−0.124057	+	0.243475i	0.820622	+	0.571471i	$0.193627\pi$
$744$	40.0369	+	29.0885i	1.46782	+	1.06644i
$745$	12.1334	−	51.8283i	0.444534	−	1.89884i
$746$	10.7432	−	33.0642i	0.393337	−	1.21057i
$747$	7.54462	−	7.54462i	0.276043	−	0.276043i
$748$	−3.69760	+	49.2632i	−0.135198	+	1.80124i
$749$		−	27.6659i		−	1.01089i
$750$	−14.2018	−	55.0266i	−0.518577	−	2.00929i
$751$	24.3907	−	17.7209i	0.890031	−	0.646645i	−0.0458552	−	0.998948i	$-0.514601\pi$
$751$	24.3907	−	17.7209i	0.890031	−	0.646645i	0.935886	+	0.352303i	$0.114601\pi$
$752$	8.15512	+	51.4894i	0.297387	+	1.87763i
$753$	47.5082	+	24.2066i	1.73130	+	0.882139i
$754$	−5.18973	−	15.9723i	−0.188999	−	0.581678i
$755$	−2.70514	−	32.0543i	−0.0984500	−	1.16658i
$756$	−18.6834	−	25.7154i	−0.679507	−	0.935261i
$757$	39.6521	−	20.2037i	1.44118	−	0.734318i	0.453566	−	0.891223i	$-0.350152\pi$
$757$	39.6521	−	20.2037i	1.44118	−	0.734318i	0.987614	+	0.156905i	$0.0501516\pi$
$758$	−38.5456	−	38.5456i	−1.40004	−	1.40004i
$759$	29.6613	−	2.44254i	1.07664	−	0.0886584i
$760$	−17.9253	−	1.30883i	−0.650218	−	0.0474764i
$761$	44.8060	+	14.5584i	1.62422	+	0.527740i	0.972932	−	0.231093i	$-0.0742301\pi$
$761$	44.8060	+	14.5584i	1.62422	+	0.527740i	0.651285	+	0.758833i	$0.274230\pi$
$762$	1.03516	+	0.163953i	0.0374997	+	0.00593938i
$763$	−31.9361	+	5.05818i	−1.15616	+	0.183118i
$764$	−8.04134	+	2.61279i	−0.290926	+	0.0945274i
$765$	−1.83254	−	7.44735i	−0.0662555	−	0.269259i
$766$	−0.452182	+	0.622375i	−0.0163380	+	0.0224873i
$767$	−4.37145	+	27.6003i	−0.157844	+	0.996588i
$768$	−27.5011	−	53.9739i	−0.992359	−	1.94761i
$769$	29.7849			1.07407			0.537036	−	0.843559i	$-0.319544\pi$
$769$	29.7849			1.07407			0.537036	+	0.843559i	$0.319544\pi$
$770$	30.4316	+	15.1518i	1.09668	+	0.546033i
$771$	39.6451			1.42778
$772$	22.8815	+	44.9076i	0.823525	+	1.61626i
$773$	−1.11434	+	7.03566i	−0.0400800	+	0.253055i	−0.999590	−	0.0286180i	$-0.990889\pi$
$773$	−1.11434	+	7.03566i	−0.0400800	+	0.253055i	0.959510	+	0.281673i	$0.0908894\pi$
$774$	−9.78604	+	13.4693i	−0.351752	+	0.484145i
$775$	−19.7678	+	3.36044i	−0.710082	+	0.120711i
$776$	−4.55461	+	1.47988i	−0.163501	+	0.0531247i
$777$	−11.4888	+	1.81965i	−0.412158	+	0.0652794i
$778$	−9.01803	−	1.42832i	−0.323312	−	0.0512076i
$779$	−1.61912	−	0.526083i	−0.0580108	−	0.0188489i
$780$	−29.2727	−	33.8842i	−1.04813	−	1.21325i
$781$	−21.8560	−	5.16351i	−0.782070	−	0.184765i
$782$	26.9928	+	26.9928i	0.965260	+	0.965260i
$783$	−10.3887	+	5.29330i	−0.371261	+	0.189167i
$784$	14.8022	+	20.3735i	0.528651	+	0.727626i
$785$	23.0543	+	19.4659i	0.822844	+	0.694769i
$786$	−0.866586	−	2.66708i	−0.0309101	−	0.0951316i
$787$	−25.7117	−	13.1008i	−0.916524	−	0.466992i	−0.0689202	−	0.997622i	$-0.521955\pi$
$787$	−25.7117	−	13.1008i	−0.916524	−	0.466992i	−0.847604	+	0.530630i	$0.821955\pi$
$788$	13.5270	+	85.4058i	0.481878	+	3.04246i
$789$	−13.5737	+	9.86191i	−0.483238	+	0.351093i
$790$	−6.01157	−	2.45035i	−0.213882	−	0.0871796i
$791$			13.5051i			0.480187i
$792$	−17.7073	+	10.9395i	−0.629201	+	0.388717i
$793$	14.8503	−	14.8503i	0.527350	−	0.527350i
$794$	24.5726	−	75.6268i	0.872051	−	2.68390i
$795$	−27.8010	−	6.50843i	−0.985999	−	0.230830i
$796$	−80.0636	−	58.1696i	−2.83778	−	2.06177i
$797$	14.0459	−	27.5666i	0.497531	−	0.976460i	−0.496569	−	0.867997i	$-0.665407\pi$
$797$	14.0459	−	27.5666i	0.497531	−	0.976460i	0.994100	−	0.108463i	$-0.0345930\pi$
$798$	−5.44840	+	10.6931i	−0.192871	+	0.378531i
$799$	−21.0204	−	15.2722i	−0.743647	−	0.540291i
$800$	−22.9172	−	7.16084i	−0.810246	−	0.253174i
$801$	1.21535	−	3.74046i	0.0429423	−	0.132163i
$802$	−17.9225	+	17.9225i	−0.632866	+	0.632866i
$803$	−28.9809	−	11.8815i	−1.02271	−	0.419288i
$804$		−	30.9130i		−	1.09022i
$805$	16.6783	−	7.01908i	0.587831	−	0.247390i
$806$	−18.5551	+	13.4811i	−0.653575	+	0.474850i
$807$	3.04559	+	19.2291i	0.107210	+	0.676897i
$808$	53.5684	+	27.2945i	1.88453	+	0.960215i
$809$	6.07857	+	18.7079i	0.213711	+	0.657735i	0.999243	+	0.0389136i	$0.0123897\pi$
$809$	6.07857	+	18.7079i	0.213711	+	0.657735i	−0.785531	+	0.618822i	$0.787610\pi$
$810$	−40.3012	+	47.7304i	−1.41604	+	1.67708i
$811$	24.8398	+	34.1891i	0.872243	+	1.20054i	0.978509	+	0.206202i	$0.0661105\pi$
$811$	24.8398	+	34.1891i	0.872243	+	1.20054i	−0.106266	+	0.994338i	$0.533890\pi$
$812$	−20.9460	+	10.6725i	−0.735061	+	0.374532i
$813$	−4.32597	−	4.32597i	−0.151718	−	0.151718i
$814$	−2.21447	−	26.8918i	−0.0776170	−	0.942556i
$815$	0.174757	−	2.39340i	0.00612147	−	0.0838373i
$816$	−43.2947	−	14.0673i	−1.51562	−	0.492454i
$817$	−8.30723	−	1.31574i	−0.290633	−	0.0460318i
$818$	76.1023	−	12.0534i	2.66085	−	0.421438i
$819$	−3.95486	+	1.28501i	−0.138194	+	0.0449019i
$820$	−11.0434	−	6.68184i	−0.385653	−	0.233340i
$821$	−31.2544	+	43.0180i	−1.09079	+	1.50134i	−0.243726	+	0.969844i	$0.578370\pi$
$821$	−31.2544	+	43.0180i	−1.09079	+	1.50134i	−0.847061	+	0.531496i	$0.821630\pi$
$822$	−12.3062	+	77.6982i	−0.429227	+	2.71004i
$823$	0.635792	+	1.24781i	0.0221623	+	0.0434960i	0.901822	−	0.432107i	$-0.142230\pi$
$823$	0.635792	+	1.24781i	0.0221623	+	0.0434960i	−0.879660	+	0.475603i	$0.842230\pi$
$824$	28.7559			1.00176
$825$	7.27797	−	32.4409i	0.253387	−	1.12945i
$826$	56.7841			1.97577
$827$	−7.84783	−	15.4022i	−0.272896	−	0.535588i	0.713363	−	0.700794i	$-0.247171\pi$
$827$	−7.84783	−	15.4022i	−0.272896	−	0.535588i	−0.986259	+	0.165206i	$0.947171\pi$
$828$	−3.16089	+	19.9571i	−0.109849	+	0.693557i
$829$	21.0969	−	29.0374i	0.732727	−	1.00851i	−0.266277	−	0.963897i	$-0.585794\pi$
$829$	21.0969	−	29.0374i	0.732727	−	1.00851i	0.999004	−	0.0446158i	$-0.0142064\pi$
$830$	50.7583	+	30.7114i	1.76185	+	1.06601i
$831$	−4.53838	+	1.47461i	−0.157435	+	0.0511536i
$832$	2.95138	−	0.467453i	0.102321	−	0.0162060i
$833$	−12.3969	−	1.96348i	−0.429527	−	0.0680304i
$834$	−6.87776	−	2.23472i	−0.238157	−	0.0773820i
$835$	0.308058	−	4.21903i	0.0106608	−	0.146006i
$836$	−16.3872	−	9.96064i	−0.566764	−	0.344496i
$837$	11.2592	+	11.2592i	0.389176	+	0.389176i
$838$	−16.9013	+	8.61164i	−0.583845	+	0.297484i
$839$	2.91587	+	4.01335i	0.100667	+	0.138556i	0.856379	−	0.516348i	$-0.172709\pi$
$839$	2.91587	+	4.01335i	0.100667	+	0.138556i	−0.755712	+	0.654904i	$0.772709\pi$
$840$	−32.1862	+	38.1194i	−1.11053	+	1.31524i
$841$	−6.29681	−	19.3796i	−0.217131	−	0.668261i
$842$	46.1350	+	23.5070i	1.58992	+	0.810103i
$843$	−8.85453	−	55.9053i	−0.304966	−	1.92548i
$844$	1.34883	−	0.979980i	0.0464285	−	0.0337323i
$845$	−16.3053	+	6.86210i	−0.560918	+	0.236063i
$846$		−	19.9651i		−	0.686415i
$847$	11.8063	+	16.0048i	0.405668	+	0.549932i
$848$	−30.3971	+	30.3971i	−1.04384	+	1.04384i
$849$	10.5406	−	32.4406i	0.361752	−	1.11336i
$850$	37.7751	−	19.7885i	1.29567	−	0.678738i
$851$	−11.6196	−	8.44211i	−0.398313	−	0.289392i
$852$	27.2892	−	53.5580i	0.934912	−	1.83487i
$853$	−12.0658	+	23.6804i	−0.413125	+	0.810803i	0.586875	+	0.809678i	$0.300358\pi$
$853$	−12.0658	+	23.6804i	−0.413125	+	0.810803i	−0.999999	+	0.00112492i	$0.999642\pi$
$854$	−34.5257	−	25.0844i	−1.18144	−	0.858369i
$855$	2.89880	+	0.678632i	0.0991368	+	0.0232087i
$856$	−29.1045	+	89.5744i	−0.994771	+	3.06159i
$857$	−1.04396	+	1.04396i	−0.0356609	+	0.0356609i	−0.724712	−	0.689051i	$-0.758027\pi$
$857$	−1.04396	+	1.04396i	−0.0356609	+	0.0356609i	0.689051	+	0.724712i	$0.258027\pi$
$858$	−9.01162	−	36.9460i	−0.307651	−	1.26132i
$859$			13.9402i			0.475633i	0.971310	+	0.237816i	$0.0764316\pi$
$859$			13.9402i			0.475633i	−0.971310	+	0.237816i	$0.923568\pi$
$860$	−59.0516	−	24.0698i	−2.01364	−	0.820773i
$861$	−3.82318	+	2.77770i	−0.130294	+	0.0946638i
$862$	13.3522	+	84.3026i	0.454778	+	2.87136i
$863$	−45.7166	−	23.2938i	−1.55621	−	0.792929i	−0.556919	−	0.830567i	$-0.688017\pi$
$863$	−45.7166	−	23.2938i	−1.55621	−	0.792929i	−0.999291	+	0.0376382i	$0.988017\pi$
$864$	5.89184	+	18.1332i	0.200445	+	0.616905i
$865$	32.3715	+	27.3329i	1.10066	+	0.929347i
$866$	−17.2852	−	23.7911i	−0.587376	−	0.808454i
$867$	−10.1524	+	5.17288i	−0.344792	+	0.175680i
$868$	22.7012	+	22.7012i	0.770529	+	0.770529i
$869$	−2.47699	−	2.87900i	−0.0840262	−	0.0976635i
$870$	21.8192	+	25.2565i	0.739742	+	0.856277i
$871$	7.47089	+	2.42744i	0.253141	+	0.0822507i
$872$	108.721	+	17.2198i	3.68177	+	0.583135i
$873$	0.783518	−	0.124097i	0.0265181	−	0.00420005i
$874$	−14.0931	+	4.57913i	−0.476706	+	0.154891i
$875$	−1.92751	−	20.1222i	−0.0651617	−	0.680254i
$876$	49.2771	−	67.8241i	1.66492	−	2.29156i
$877$	1.04392	−	6.59105i	0.0352507	−	0.222564i	−0.963774	−	0.266720i	$-0.914060\pi$
$877$	1.04392	−	6.59105i	0.0352507	−	0.222564i	0.999025	+	0.0441563i	$0.0140600\pi$
$878$	12.3436	+	24.2256i	0.416575	+	0.817574i
$879$	−21.4220			−0.722546
$880$	−35.7219	−	35.0653i	−1.20418	−	1.18205i
$881$	−14.4573			−0.487080			−0.243540	−	0.969891i	$-0.578309\pi$
$881$	−14.4573			−0.487080			−0.243540	+	0.969891i	$0.578309\pi$
$882$	−4.37854	−	8.59337i	−0.147433	−	0.289354i
$883$	−1.63650	+	10.3324i	−0.0550725	+	0.347714i	0.944730	+	0.327849i	$0.106324\pi$
$883$	−1.63650	+	10.3324i	−0.0550725	+	0.347714i	−0.999803	+	0.0198651i	$0.993676\pi$
$884$	19.7499	−	27.1834i	0.664260	−	0.914276i
$885$	−13.2695	−	53.9267i	−0.446050	−	1.81272i
$886$	97.2533	−	31.5995i	3.26729	−	1.06161i
$887$	9.76140	−	1.54605i	0.327756	−	0.0519114i	0.00961170	−	0.999954i	$-0.496940\pi$
$887$	9.76140	−	1.54605i	0.327756	−	0.0519114i	0.318144	+	0.948042i	$0.396940\pi$
$888$	39.1118	+	6.19470i	1.31250	+	0.207880i
$889$	0.354548	+	0.115200i	0.0118912	+	0.00386368i
$890$	21.8101	+	1.59249i	0.731078	+	0.0533805i
$891$	−33.7137	+	14.1080i	−1.12945	+	0.472635i
$892$	23.8243	+	23.8243i	0.797695	+	0.797695i
$893$	8.98671	−	4.57896i	0.300729	−	0.153229i
$894$	71.1225	+	97.8918i	2.37869	+	3.27399i
$895$	−3.08061	−	36.5034i	−0.102973	−	1.22018i
$896$	−7.24221	−	22.2892i	−0.241945	−	0.744631i
$897$	−18.0361	−	9.18986i	−0.602208	−	0.306840i
$898$	−1.44429	−	9.11891i	−0.0481967	−	0.304302i
$899$	9.52719	−	6.92191i	0.317750	−	0.230859i
$900$	20.2266	+	10.0196i	0.674221	+	0.333985i
$901$		−	21.4256i		−	0.713789i
$902$	−5.76157	−	9.32604i	−0.191839	−	0.310523i
$903$	−16.5088	+	16.5088i	−0.549380	+	0.549380i
$904$	14.2074	−	43.7258i	0.472530	−	1.45430i
$905$	−7.57591	+	32.3607i	−0.251832	+	1.07571i
$906$	59.1589	+	42.9815i	1.96542	+	1.42796i
$907$	5.25319	−	10.3100i	0.174429	−	0.342337i	−0.787196	−	0.616703i	$-0.788468\pi$
$907$	5.25319	−	10.3100i	0.174429	−	0.342337i	0.961625	+	0.274366i	$0.0884680\pi$
$908$	16.4887	−	32.3609i	0.547196	−	1.07393i
$909$	−8.05692	−	5.85370i	−0.267231	−	0.194155i
$910$	−12.1923	−	19.6458i	−0.404170	−	0.651253i
$911$	−2.69510	+	8.29465i	−0.0892925	+	0.274814i	−0.985724	−	0.168368i	$-0.946150\pi$
$911$	−2.69510	+	8.29465i	−0.0892925	+	0.274814i	0.896432	+	0.443182i	$0.146150\pi$
$912$	12.4954	−	12.4954i	0.413765	−	0.413765i
$913$	18.2419	+	29.5274i	0.603718	+	0.977215i
$914$			45.8704i			1.51726i
$915$	−15.7540	+	38.6500i	−0.520811	+	1.27773i
$916$	−27.1854	+	19.7514i	−0.898231	+	0.652603i
$917$	−0.156043	−	0.985219i	−0.00515301	−	0.0325348i
$918$	−30.1731	−	15.3740i	−0.995861	−	0.507416i
$919$	1.78507	+	5.49388i	0.0588840	+	0.181226i	0.976172	−	0.216998i	$-0.0696265\pi$
$919$	1.78507	+	5.49388i	0.0588840	+	0.181226i	−0.917288	+	0.398224i	$0.869627\pi$
$920$	−61.3836	+	5.18031i	−2.02376	+	0.170790i
$921$	38.3182	+	52.7405i	1.26263	+	1.73786i
$922$	−80.3931	+	40.9623i	−2.64761	+	1.34902i
$923$	10.8007	+	10.8007i	0.355511	+	0.355511i
$924$	−49.1061	+	20.5491i	−1.61547	+	0.676016i
$925$	−12.8729	+	9.57696i	−0.423260	+	0.314889i
$926$	15.2359	+	4.95043i	0.500681	+	0.162681i
$927$	−4.70469	−	0.745150i	−0.154522	−	0.0244739i
$928$	13.9275	−	2.20590i	0.457192	−	0.0724121i
$929$	−17.2514	+	5.60532i	−0.566000	+	0.183905i	−0.578019	−	0.816023i	$-0.696174\pi$
$929$	−17.2514	+	5.60532i	−0.566000	+	0.183905i	0.0120191	+	0.999928i	$0.496174\pi$
$930$	23.5958	−	38.9979i	0.773735	−	1.27879i
$931$	2.86384	−	3.94174i	0.0938587	−	0.129185i
$932$	18.1595	−	114.654i	0.594833	−	3.75563i
$933$	12.6414	+	24.8102i	0.413862	+	0.812251i
$934$	−21.9374			−0.717813
$935$	24.9473	−	0.231399i	0.815864	−	0.00756755i
$936$	14.1566			0.462722
$937$	−14.5907	−	28.6359i	−0.476659	−	0.935496i	−0.996686	−	0.0813459i	$-0.974078\pi$
$937$	−14.5907	−	28.6359i	−0.476659	−	0.935496i	0.520027	−	0.854150i	$-0.325922\pi$
$938$	2.49708	−	15.7659i	0.0815325	−	0.514776i
$939$	−20.4908	+	28.2032i	−0.668692	+	0.920376i
$940$	74.2550	−	18.2716i	2.42193	−	0.595955i
$941$	−4.95612	+	1.61034i	−0.161565	+	0.0524956i	−0.388683	−	0.921372i	$-0.627070\pi$
$941$	−4.95612	+	1.61034i	−0.161565	+	0.0524956i	0.227118	+	0.973867i	$0.427070\pi$
$942$	−67.7450	+	10.7297i	−2.20725	+	0.349594i
$943$	−5.76321	−	0.912803i	−0.187676	−	0.0297250i
$944$	−79.5200	−	25.8376i	−2.58816	−	0.840943i
$945$	−12.1471	+	10.4940i	−0.395146	+	0.341368i
$946$	−35.3219	−	41.0545i	−1.14841	−	1.33480i
$947$	−0.545091	−	0.545091i	−0.0177131	−	0.0177131i	0.698195	−	0.715908i	$-0.253987\pi$
$947$	−0.545091	−	0.545091i	−0.0177131	−	0.0177131i	−0.715908	+	0.698195i	$0.753987\pi$
$948$	9.05742	−	4.61499i	0.294171	−	0.149888i
$949$	12.5219	+	17.2349i	0.406478	+	0.559469i
$950$	0.187154	+	16.5528i	0.00607207	+	0.537043i
$951$	−10.0100	−	30.8076i	−0.324596	−	0.999004i
$952$	−33.3567	−	16.9961i	−1.08110	−	0.550846i
$953$	2.12456	+	13.4139i	0.0688211	+	0.434519i	0.997908	+	0.0646568i	$0.0205953\pi$
$953$	2.12456	+	13.4139i	0.0688211	+	0.434519i	−0.929086	+	0.369863i	$0.879405\pi$
$954$	13.3192	−	9.67699i	0.431226	−	0.313304i
$955$	1.65631	+	3.93562i	0.0535970	+	0.127354i
$956$		−	10.0777i		−	0.325935i
$957$	4.62705	+	18.9701i	0.149571	+	0.613216i
$958$	27.5786	−	27.5786i	0.891023	−	0.891023i
$959$	−8.64682	+	26.6122i	−0.279221	+	0.859352i
$960$	−5.04583	+	3.13146i	−0.162853	+	0.101067i
$961$	12.0686	+	8.76834i	0.389309	+	0.282850i
$962$	−8.33177	+	16.3520i	−0.268627	+	0.527210i
$963$	7.08285	−	13.9009i	0.228242	−	0.447950i
$964$	22.5507	+	16.3840i	0.726309	+	0.527694i
$965$	21.6267	−	13.4216i	0.696189	−	0.432057i
$966$	−12.7110	+	39.1203i	−0.408968	+	1.25867i
$967$	28.7882	−	28.7882i	0.925767	−	0.925767i	−0.0716619	−	0.997429i	$-0.522830\pi$
$967$	28.7882	−	28.7882i	0.925767	−	0.925767i	0.997429	+	0.0716619i	$0.0228303\pi$
$968$	−21.3884	−	64.2393i	−0.687448	−	2.06473i
$969$			8.80745i			0.282936i
$970$	1.71097	+	4.06550i	0.0549360	+	0.130535i
$971$	23.7651	−	17.2663i	0.762657	−	0.554103i	−0.137067	−	0.990562i	$-0.543768\pi$
$971$	23.7651	−	17.2663i	0.762657	−	0.554103i	0.899724	+	0.436459i	$0.143768\pi$
$972$	−7.05171	−	44.5227i	−0.226184	−	1.42807i
$973$	−2.29195	−	1.16781i	−0.0734765	−	0.0374382i
$974$	4.65870	+	14.3380i	0.149274	+	0.459419i
$975$	−15.8081	+	16.1696i	−0.506264	+	0.517843i
$976$	36.9357	+	50.8376i	1.18228	+	1.62727i
$977$	−20.8453	+	10.6212i	−0.666901	+	0.339803i	−0.754450	−	0.656357i	$-0.772096\pi$
$977$	−20.8453	+	10.6212i	−0.666901	+	0.339803i	0.0875496	+	0.996160i	$0.472096\pi$
$978$	3.85737	+	3.85737i	0.123345	+	0.123345i
$979$	10.9325	+	6.64511i	0.349405	+	0.212379i
$980$	27.9536	−	24.1493i	0.892946	−	0.771420i
$981$	−17.3414	−	5.63458i	−0.553670	−	0.179898i
$982$	−102.544	−	16.2414i	−3.27232	−	0.518284i
$983$	−20.6008	+	3.26285i	−0.657064	+	0.104069i	−0.476059	−	0.879413i	$-0.657935\pi$
$983$	−20.6008	+	3.26285i	−0.657064	+	0.104069i	−0.181005	+	0.983482i	$0.557935\pi$
$984$	15.3005	−	4.97144i	0.487763	−	0.158484i
$985$	42.4036	−	10.4341i	1.35109	−	0.332457i
$986$	−14.7212	+	20.2619i	−0.468817	+	0.645271i
$987$	4.37973	−	27.6526i	0.139408	−	0.880190i
$988$	5.92148	+	11.6216i	0.188387	+	0.369731i
$989$	−28.8277			−0.916666
$990$	11.4115	+	15.4040i	0.362680	+	0.489572i
$991$	−6.50787			−0.206729			−0.103365	−	0.994644i	$-0.532961\pi$
$991$	−6.50787			−0.206729			−0.103365	+	0.994644i	$0.532961\pi$
$992$	−8.74265	−	17.1584i	−0.277579	−	0.544780i
$993$	4.60531	−	29.0768i	0.146145	−	0.922724i
$994$	18.2440	−	25.1108i	0.578666	−	0.796465i
$995$	−25.8721	+	42.7601i	−0.820200	+	1.35559i
$996$	−88.3512	+	28.7071i	−2.79952	+	0.909618i
$997$	26.0805	−	4.13075i	0.825978	−	0.130822i	0.270886	−	0.962611i	$-0.412683\pi$
$997$	26.0805	−	4.13075i	0.825978	−	0.130822i	0.555092	+	0.831789i	$0.312683\pi$
$998$	−58.0618	−	9.19609i	−1.83792	−	0.291097i
$999$	12.1175	+	3.93723i	0.383382	+	0.124568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.2.l.a.2.1	✓	32
3.2	odd	2		495.2.bj.a.442.4		32
4.3	odd	2		880.2.cm.a.497.1		32
5.2	odd	4		275.2.bm.b.68.4		32
5.3	odd	4	inner	55.2.l.a.13.1	yes	32
5.4	even	2		275.2.bm.b.57.4		32
11.2	odd	10		605.2.m.d.602.4		32
11.3	even	5		605.2.m.d.282.1		32
11.4	even	5		605.2.e.b.362.16		32
11.5	even	5		605.2.m.e.457.4		32
11.6	odd	10	inner	55.2.l.a.17.1	yes	32
11.7	odd	10		605.2.e.b.362.1		32
11.8	odd	10		605.2.m.c.282.4		32
11.9	even	5		605.2.m.c.602.1		32
11.10	odd	2		605.2.m.e.112.4		32
15.8	even	4		495.2.bj.a.343.4		32
20.3	even	4		880.2.cm.a.673.1		32
33.17	even	10		495.2.bj.a.127.4		32
44.39	even	10		880.2.cm.a.17.1		32
55.3	odd	20		605.2.m.d.403.4		32
55.8	even	20		605.2.m.c.403.1		32
55.13	even	20		605.2.m.d.118.1		32
55.17	even	20		275.2.bm.b.193.4		32
55.18	even	20		605.2.e.b.483.16		32
55.28	even	20	inner	55.2.l.a.28.1	yes	32
55.38	odd	20		605.2.m.e.578.4		32
55.39	odd	10		275.2.bm.b.182.4		32
55.43	even	4		605.2.m.e.233.4		32
55.48	odd	20		605.2.e.b.483.1		32
55.53	odd	20		605.2.m.c.118.4		32
165.83	odd	20		495.2.bj.a.28.4		32
220.83	odd	20		880.2.cm.a.193.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.1	✓	32	1.1	even	1	trivial
55.2.l.a.13.1	yes	32	5.3	odd	4	inner
55.2.l.a.17.1	yes	32	11.6	odd	10	inner
55.2.l.a.28.1	yes	32	55.28	even	20	inner
275.2.bm.b.57.4		32	5.4	even	2
275.2.bm.b.68.4		32	5.2	odd	4
275.2.bm.b.182.4		32	55.39	odd	10
275.2.bm.b.193.4		32	55.17	even	20
495.2.bj.a.28.4		32	165.83	odd	20
495.2.bj.a.127.4		32	33.17	even	10
495.2.bj.a.343.4		32	15.8	even	4
495.2.bj.a.442.4		32	3.2	odd	2
605.2.e.b.362.1		32	11.7	odd	10
605.2.e.b.362.16		32	11.4	even	5
605.2.e.b.483.1		32	55.48	odd	20
605.2.e.b.483.16		32	55.18	even	20
605.2.m.c.118.4		32	55.53	odd	20
605.2.m.c.282.4		32	11.8	odd	10
605.2.m.c.403.1		32	55.8	even	20
605.2.m.c.602.1		32	11.9	even	5
605.2.m.d.118.1		32	55.13	even	20
605.2.m.d.282.1		32	11.3	even	5
605.2.m.d.403.4		32	55.3	odd	20
605.2.m.d.602.4		32	11.2	odd	10
605.2.m.e.112.4		32	11.10	odd	2
605.2.m.e.233.4		32	55.43	even	4
605.2.m.e.457.4		32	11.5	even	5
605.2.m.e.578.4		32	55.38	odd	20
880.2.cm.a.17.1		32	44.39	even	10
880.2.cm.a.193.1		32	220.83	odd	20
880.2.cm.a.497.1		32	4.3	odd	2
880.2.cm.a.673.1		32	20.3	even	4

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15100 - 2.25897i) q^{2} +(0.313634 - 1.98021i) q^{3} +(-2.60258 + 3.58214i) q^{4} +(1.91314 + 1.15755i) q^{5} +(-4.83422 + 1.57073i) q^{6} +(-1.78576 + 0.282837i) q^{7} +(6.07934 + 0.962874i) q^{8} +(-0.969677 - 0.315067i) q^{9} +O(q^{10})\)	\(q+(-1.15100 - 2.25897i) q^{2} +(0.313634 - 1.98021i) q^{3} +(-2.60258 + 3.58214i) q^{4} +(1.91314 + 1.15755i) q^{5} +(-4.83422 + 1.57073i) q^{6} +(-1.78576 + 0.282837i) q^{7} +(6.07934 + 0.962874i) q^{8} +(-0.969677 - 0.315067i) q^{9} +(0.412838 - 5.65406i) q^{10} +(1.72268 - 2.83415i) q^{11} +(6.27711 + 6.27711i) q^{12} +(-2.00993 + 1.02411i) q^{13} +(2.69434 + 3.70844i) q^{14} +(2.89220 - 3.42536i) q^{15} +(-2.08573 - 6.41923i) q^{16} +(2.99738 + 1.52724i) q^{17} +(0.404374 + 2.55312i) q^{18} +(-1.05647 + 0.767569i) q^{19} +(-9.12557 + 3.84051i) q^{20} +3.62488i q^{21} +(-8.38507 - 0.629367i) q^{22} +(-3.16488 + 3.16488i) q^{23} +(3.81337 - 11.7364i) q^{24} +(2.32018 + 4.42908i) q^{25} +(4.62687 + 3.36162i) q^{26} +(1.80258 - 3.53776i) q^{27} +(3.63442 - 7.13295i) q^{28} +(-2.37569 - 1.72604i) q^{29} +(-11.0667 - 2.59081i) q^{30} +(-1.23925 + 3.81401i) q^{31} +(-3.39552 + 3.39552i) q^{32} +(-5.07190 - 4.30014i) q^{33} -8.52886i q^{34} +(-3.74380 - 1.52600i) q^{35} +(3.65227 - 2.65353i) q^{36} +(0.501987 + 3.16942i) q^{37} +(2.94992 + 1.50306i) q^{38} +(1.39757 + 4.30127i) q^{39} +(10.5160 + 8.87923i) q^{40} +(0.766287 + 1.05470i) q^{41} +(8.18851 - 4.17225i) q^{42} +(4.55431 + 4.55431i) q^{43} +(5.66890 + 13.5469i) q^{44} +(-1.49042 - 1.72521i) q^{45} +(10.7922 + 3.50658i) q^{46} +(-7.62854 - 1.20824i) q^{47} +(-13.3656 + 2.11690i) q^{48} +(-3.54845 + 1.15296i) q^{49} +(7.33465 - 10.3391i) q^{50} +(3.96433 - 5.45644i) q^{51} +(1.56249 - 9.86517i) q^{52} +(-2.89146 - 5.67482i) q^{53} -10.0665 q^{54} +(6.57637 - 3.42803i) q^{55} -11.1286 q^{56} +(1.18860 + 2.33276i) q^{57} +(-1.16465 + 7.35329i) q^{58} +(7.28135 - 10.0219i) q^{59} +(4.74292 + 19.2750i) q^{60} +(-8.85435 + 2.87695i) q^{61} +(10.0421 - 1.59052i) q^{62} +(1.82072 + 0.288374i) q^{63} +(-1.25983 - 0.409344i) q^{64} +(-5.03072 - 0.367324i) q^{65} +(-3.87611 + 16.4068i) q^{66} +(-2.46236 - 2.46236i) q^{67} +(-13.2717 + 6.76227i) q^{68} +(5.27449 + 7.25972i) q^{69} +(0.861947 + 10.2136i) q^{70} +(-2.09243 - 6.43984i) q^{71} +(-5.59163 - 2.84908i) q^{72} +(-1.47735 - 9.32763i) q^{73} +(6.58185 - 4.78199i) q^{74} +(9.49818 - 3.20531i) q^{75} -5.78207i q^{76} +(-2.27469 + 5.54835i) q^{77} +(8.10784 - 8.10784i) q^{78} +(0.353860 - 1.08907i) q^{79} +(3.44026 - 14.6952i) q^{80} +(-8.91472 - 6.47692i) q^{81} +(1.50055 - 2.94499i) q^{82} +(-4.75092 + 9.32422i) q^{83} +(-12.9848 - 9.43403i) q^{84} +(3.96654 + 6.39143i) q^{85} +(5.04603 - 15.5301i) q^{86} +(-4.16301 + 4.16301i) q^{87} +(13.2017 - 15.5710i) q^{88} +3.85743i q^{89} +(-2.18173 + 5.35254i) q^{90} +(3.29960 - 2.39730i) q^{91} +(-3.10019 - 19.5739i) q^{92} +(7.16385 + 3.65016i) q^{93} +(6.05109 + 18.6233i) q^{94} +(-2.90966 + 0.245553i) q^{95} +(5.65887 + 7.78877i) q^{96} +(-0.693249 + 0.353228i) q^{97} +(6.68878 + 6.68878i) q^{98} +(-2.56339 + 2.20545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8}+O(q^{10}) \) 32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8	\( 32 q - 10 q^{2} - 4 q^{3} - 2 q^{5} - 20 q^{6} - 10 q^{8} - 24 q^{11} + 12 q^{12} - 10 q^{13} + 14 q^{15} - 8 q^{16} - 10 q^{18} + 16 q^{20} + 10 q^{22} - 24 q^{23} + 16 q^{25} + 20 q^{26} - 16 q^{27} + 50 q^{28} + 30 q^{30} - 28 q^{31} + 66 q^{33} - 10 q^{35} + 24 q^{36} - 8 q^{37} + 10 q^{38} - 50 q^{40} + 40 q^{41} - 10 q^{42} - 28 q^{45} + 60 q^{46} - 28 q^{47} - 54 q^{48} - 50 q^{50} + 20 q^{51} - 50 q^{52} - 24 q^{53} - 64 q^{55} - 80 q^{56} + 30 q^{57} - 50 q^{58} + 34 q^{60} - 60 q^{61} + 100 q^{62} - 30 q^{63} - 100 q^{66} - 8 q^{67} - 30 q^{68} + 30 q^{70} + 24 q^{71} + 80 q^{72} + 50 q^{73} + 34 q^{75} + 70 q^{77} + 60 q^{78} + 98 q^{80} - 12 q^{81} - 10 q^{82} + 90 q^{83} + 30 q^{85} + 100 q^{86} + 170 q^{88} - 20 q^{90} + 20 q^{91} - 68 q^{92} - 8 q^{93} - 40 q^{95} - 8 q^{97}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8 - 24 * q^11 + 12 * q^12 - 10 * q^13 + 14 * q^15 - 8 * q^16 - 10 * q^18 + 16 * q^20 + 10 * q^22 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 50 * q^28 + 30 * q^30 - 28 * q^31 + 66 * q^33 - 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 + 40 * q^41 - 10 * q^42 - 28 * q^45 + 60 * q^46 - 28 * q^47 - 54 * q^48 - 50 * q^50 + 20 * q^51 - 50 * q^52 - 24 * q^53 - 64 * q^55 - 80 * q^56 + 30 * q^57 - 50 * q^58 + 34 * q^60 - 60 * q^61 + 100 * q^62 - 30 * q^63 - 100 * q^66 - 8 * q^67 - 30 * q^68 + 30 * q^70 + 24 * q^71 + 80 * q^72 + 50 * q^73 + 34 * q^75 + 70 * q^77 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 + 90 * q^83 + 30 * q^85 + 100 * q^86 + 170 * q^88 - 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 - 40 * q^95 - 8 * q^97

Introduction

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