LMFDB - Embedded newform 210.2.u.a.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.4
Root			$-0.424637 - 3.22544i$ of defining polynomial
Character	$\chi$	$=$	210.103
Dual form			210.2.u.a.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.58356 - 1.57872i) q^{5} +1.00000i q^{6} +(2.22701 - 1.42843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.58356 - 1.57872i) q^{5} +1.00000i q^{6} +(2.22701 - 1.42843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.93478 + 1.12100i) q^{10} +(-0.230557 - 0.399337i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-4.00275 + 4.00275i) q^{13} +(1.95615 + 1.78142i) q^{14} +(1.93820 - 1.11507i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.424416 - 1.58394i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-2.91323 + 5.04586i) q^{19} +(-0.582041 + 2.15899i) q^{20} +(2.52083 - 0.803365i) q^{21} +(0.326057 - 0.326057i) q^{22} +(-4.26196 + 1.14199i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.0152997 - 4.99998i) q^{25} +(-4.90235 - 2.83037i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.21443 + 2.35056i) q^{28} -5.53773i q^{29} +(1.57872 + 1.58356i) q^{30} +(0.0280956 - 0.0162210i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.119345 - 0.445403i) q^{33} +1.63982 q^{34} +(1.27151 - 5.77782i) q^{35} -1.00000 q^{36} +(2.08723 + 7.78966i) q^{37} +(-5.62793 - 1.50800i) q^{38} +(-4.90235 + 2.83037i) q^{39} +(-2.23607 - 0.00342112i) q^{40} -10.9453i q^{41} +(1.42843 + 2.22701i) q^{42} +(4.75146 + 4.75146i) q^{43} +(0.399337 + 0.230557i) q^{44} +(2.16076 - 0.575432i) q^{45} +(-2.20615 - 3.82117i) q^{46} +(-8.73220 + 2.33979i) q^{47} +(0.707107 - 0.707107i) q^{48} +(2.91917 - 6.36227i) q^{49} +(4.83357 - 1.27931i) q^{50} +(0.819909 - 1.42012i) q^{51} +(1.46511 - 5.46786i) q^{52} +(0.710873 - 2.65301i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.995541 - 0.268388i) q^{55} +(-2.58479 - 0.564683i) q^{56} +(-4.11993 + 4.11993i) q^{57} +(5.34903 - 1.43327i) q^{58} +(0.958791 + 1.66067i) q^{59} +(-1.12100 + 1.93478i) q^{60} +(-11.7393 - 6.77768i) q^{61} +(0.0229400 + 0.0229400i) q^{62} +(2.64286 - 0.123551i) q^{63} +1.00000i q^{64} +(-0.0193661 + 12.6578i) q^{65} +(0.399337 - 0.230557i) q^{66} +(3.68040 + 0.986161i) q^{67} +(0.424416 + 1.58394i) q^{68} -4.41231 q^{69} +(5.91004 - 0.267226i) q^{70} +8.85877 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-3.91904 - 1.05010i) q^{73} +(-6.98401 + 4.03222i) q^{74} +(1.30887 - 4.82565i) q^{75} -5.82646i q^{76} +(-1.08388 - 0.559993i) q^{77} +(-4.00275 - 4.00275i) q^{78} +(-4.38319 - 2.53064i) q^{79} +(-0.575432 - 2.16076i) q^{80} +(0.500000 + 0.866025i) q^{81} +(10.5723 - 2.83285i) q^{82} +(1.08813 - 1.08813i) q^{83} +(-1.78142 + 1.95615i) q^{84} +(-1.82851 - 3.17829i) q^{85} +(-3.35979 + 5.81932i) q^{86} +(1.43327 - 5.34903i) q^{87} +(-0.119345 + 0.445403i) q^{88} +(-5.71423 + 9.89734i) q^{89} +(1.11507 + 1.93820i) q^{90} +(-3.19652 + 14.6318i) q^{91} +(3.11997 - 3.11997i) q^{92} +(0.0313366 - 0.00839662i) q^{93} +(-4.52012 - 7.82908i) q^{94} +(3.35273 + 12.5896i) q^{95} +(0.866025 + 0.500000i) q^{96} +(2.51799 + 2.51799i) q^{97} +(6.90101 + 1.17303i) q^{98} -0.461115i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 8 * q^7	$ 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 8 * q^7 + 8 * q^10 + 4 * q^11 - 16 * q^13 + 16 * q^14 + 4 * q^15 + 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^20 + 8 * q^21 + 4 * q^22 + 32 * q^23 - 8 * q^24 - 32 * q^25 - 12 * q^26 - 8 * q^28 - 4 * q^30 - 24 * q^31 + 8 * q^33 + 16 * q^34 + 4 * q^35 - 16 * q^36 - 8 * q^37 - 28 * q^38 - 12 * q^39 - 4 * q^42 - 24 * q^43 + 4 * q^45 - 4 * q^46 - 24 * q^47 + 52 * q^49 + 8 * q^51 - 8 * q^52 + 44 * q^53 - 8 * q^54 - 56 * q^55 + 8 * q^56 - 8 * q^57 + 48 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 16 * q^65 + 36 * q^67 - 12 * q^68 - 8 * q^69 + 32 * q^70 - 32 * q^71 - 40 * q^73 - 24 * q^74 - 24 * q^75 - 44 * q^77 - 16 * q^78 + 12 * q^79 + 12 * q^80 + 8 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^87 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 8 * q^92 + 40 * q^93 + 8 * q^94 - 48 * q^95 + 44 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.58356	−	1.57872i	0.708188	−	0.706024i
$5$	1.58356	−	1.57872i	0.708188	−	0.706024i
$6$			1.00000i			0.408248i
$7$	2.22701	−	1.42843i	0.841732	−	0.539896i
$7$	2.22701	−	1.42843i	0.841732	−	0.539896i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	1.93478	+	1.12100i	0.611831	+	0.354490i
$11$	−0.230557	−	0.399337i	−0.0695156	−	0.120405i	0.829173	−	0.558993i	$-0.188812\pi$
$11$	−0.230557	−	0.399337i	−0.0695156	−	0.120405i	−0.898688	+	0.438588i	$0.855479\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	−4.00275	+	4.00275i	−1.11016	+	1.11016i	−0.117035	+	0.993128i	$0.537339\pi$
$13$	−4.00275	+	4.00275i	−1.11016	+	1.11016i	−0.993128	+	0.117035i	$0.962661\pi$
$14$	1.95615	+	1.78142i	0.522803	+	0.476106i
$15$	1.93820	−	1.11507i	0.500441	−	0.287910i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.424416	−	1.58394i	0.102936	−	0.384162i	−0.895167	−	0.445731i	$-0.852944\pi$
$17$	0.424416	−	1.58394i	0.102936	−	0.384162i	0.998103	+	0.0615689i	$0.0196104\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	−2.91323	+	5.04586i	−0.668341	+	1.15760i	0.310027	+	0.950728i	$0.399662\pi$
$19$	−2.91323	+	5.04586i	−0.668341	+	1.15760i	−0.978368	+	0.206872i	$0.933672\pi$
$20$	−0.582041	+	2.15899i	−0.130148	+	0.482764i
$21$	2.52083	−	0.803365i	0.550091	−	0.175309i
$22$	0.326057	−	0.326057i	0.0695156	−	0.0695156i
$23$	−4.26196	+	1.14199i	−0.888680	+	0.238121i	−0.674149	−	0.738596i	$-0.735489\pi$
$23$	−4.26196	+	1.14199i	−0.888680	+	0.238121i	−0.214532	+	0.976717i	$0.568823\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	0.0152997	−	4.99998i	0.00305994	−	0.999995i
$26$	−4.90235	−	2.83037i	−0.961429	−	0.555081i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.21443	+	2.35056i	−0.229507	+	0.444215i
$29$		−	5.53773i		−	1.02833i	−0.857691	−	0.514165i	$-0.828102\pi$
$29$		−	5.53773i		−	1.02833i	0.857691	−	0.514165i	$-0.171898\pi$
$30$	1.57872	+	1.58356i	0.288233	+	0.289116i
$31$	0.0280956	−	0.0162210i	0.00504612	−	0.00291338i	−0.497475	−	0.867478i	$-0.665739\pi$
$31$	0.0280956	−	0.0162210i	0.00504612	−	0.00291338i	0.502521	+	0.864565i	$0.332406\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−0.119345	−	0.445403i	−0.0207753	−	0.0775346i
$34$	1.63982			0.281226
$35$	1.27151	−	5.77782i	0.214925	−	0.976631i
$36$	−1.00000			−0.166667
$37$	2.08723	+	7.78966i	0.343139	+	1.28061i	0.894772	+	0.446524i	$0.147338\pi$
$37$	2.08723	+	7.78966i	0.343139	+	1.28061i	−0.551633	+	0.834087i	$0.685995\pi$
$38$	−5.62793	−	1.50800i	−0.912970	−	0.244630i
$39$	−4.90235	+	2.83037i	−0.785003	+	0.453222i
$40$	−2.23607	−	0.00342112i	−0.353553	−	0.000540927i
$41$		−	10.9453i		−	1.70937i	−0.519149	−	0.854684i	$-0.673751\pi$
$41$		−	10.9453i		−	1.70937i	0.519149	−	0.854684i	$-0.326249\pi$
$42$	1.42843	+	2.22701i	0.220412	+	0.343636i
$43$	4.75146	+	4.75146i	0.724591	+	0.724591i	0.969537	−	0.244946i	$-0.0787703\pi$
$43$	4.75146	+	4.75146i	0.724591	+	0.724591i	−0.244946	+	0.969537i	$0.578770\pi$
$44$	0.399337	+	0.230557i	0.0602023	+	0.0347578i
$45$	2.16076	−	0.575432i	0.322107	−	0.0857803i
$46$	−2.20615	−	3.82117i	−0.325280	−	0.563401i
$47$	−8.73220	+	2.33979i	−1.27372	+	0.341293i	−0.831456	−	0.555591i	$-0.812492\pi$
$47$	−8.73220	+	2.33979i	−1.27372	+	0.341293i	−0.442266	+	0.896884i	$0.645825\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$	2.91917	−	6.36227i	0.417025	−	0.908895i
$50$	4.83357	−	1.27931i	0.683570	−	0.180922i
$51$	0.819909	−	1.42012i	0.114810	−	0.198857i
$52$	1.46511	−	5.46786i	0.203174	−	0.758255i
$53$	0.710873	−	2.65301i	0.0976459	−	0.364419i	−0.899761	−	0.436382i	$-0.856260\pi$
$53$	0.710873	−	2.65301i	0.0976459	−	0.364419i	0.997407	+	0.0719627i	$0.0229263\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−0.995541	−	0.268388i	−0.134239	−	0.0361894i
$56$	−2.58479	−	0.564683i	−0.345407	−	0.0754589i
$57$	−4.11993	+	4.11993i	−0.545698	+	0.545698i
$58$	5.34903	−	1.43327i	0.702362	−	0.188197i
$59$	0.958791	+	1.66067i	0.124824	+	0.216201i	0.921664	−	0.387989i	$-0.126830\pi$
$59$	0.958791	+	1.66067i	0.124824	+	0.216201i	−0.796840	+	0.604190i	$0.793497\pi$
$60$	−1.12100	+	1.93478i	−0.144720	+	0.249779i
$61$	−11.7393	−	6.77768i	−1.50306	−	0.867793i	−0.999994	−	0.00354661i	$-0.998871\pi$
$61$	−11.7393	−	6.77768i	−1.50306	−	0.867793i	−0.503068	−	0.864247i	$-0.667796\pi$
$62$	0.0229400	+	0.0229400i	0.00291338	+	0.00291338i
$63$	2.64286	−	0.123551i	0.332970	−	0.0155659i
$64$			1.00000i			0.125000i
$65$	−0.0193661	+	12.6578i	−0.00240207	+	1.57001i
$66$	0.399337	−	0.230557i	0.0491550	−	0.0283796i
$67$	3.68040	+	0.986161i	0.449633	+	0.120479i	0.476528	−	0.879160i	$-0.341895\pi$
$67$	3.68040	+	0.986161i	0.449633	+	0.120479i	−0.0268948	+	0.999638i	$0.508562\pi$
$68$	0.424416	+	1.58394i	0.0514680	+	0.192081i
$69$	−4.41231			−0.531179
$70$	5.91004	−	0.267226i	0.706385	−	0.0319396i
$71$	8.85877			1.05134			0.525671	−	0.850688i	$-0.323814\pi$
$71$	8.85877			1.05134			0.525671	+	0.850688i	$0.323814\pi$
$72$	−0.258819	−	0.965926i	−0.0305021	−	0.113835i
$73$	−3.91904	−	1.05010i	−0.458689	−	0.122905i	0.0220733	−	0.999756i	$-0.492973\pi$
$73$	−3.91904	−	1.05010i	−0.458689	−	0.122905i	−0.480762	+	0.876851i	$0.659640\pi$
$74$	−6.98401	+	4.03222i	−0.811875	+	0.468736i
$75$	1.30887	−	4.82565i	0.151135	−	0.557218i
$76$		−	5.82646i		−	0.668341i
$77$	−1.08388	−	0.559993i	−0.123519	−	0.0638172i
$78$	−4.00275	−	4.00275i	−0.453222	−	0.453222i
$79$	−4.38319	−	2.53064i	−0.493148	−	0.284719i	0.232732	−	0.972541i	$-0.425234\pi$
$79$	−4.38319	−	2.53064i	−0.493148	−	0.284719i	−0.725879	+	0.687822i	$0.758567\pi$
$80$	−0.575432	−	2.16076i	−0.0643352	−	0.241580i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	10.5723	−	2.83285i	1.16752	−	0.312836i
$83$	1.08813	−	1.08813i	0.119438	−	0.119438i	−0.644861	−	0.764299i	$-0.723085\pi$
$83$	1.08813	−	1.08813i	0.119438	−	0.119438i	0.764299	+	0.644861i	$0.223085\pi$
$84$	−1.78142	+	1.95615i	−0.194369	+	0.213434i
$85$	−1.82851	−	3.17829i	−0.198330	−	0.344734i
$86$	−3.35979	+	5.81932i	−0.362295	+	0.627514i
$87$	1.43327	−	5.34903i	0.153663	−	0.573476i
$88$	−0.119345	+	0.445403i	−0.0127222	+	0.0474801i
$89$	−5.71423	+	9.89734i	−0.605708	+	1.04912i	0.386232	+	0.922402i	$0.373777\pi$
$89$	−5.71423	+	9.89734i	−0.605708	+	1.04912i	−0.991939	+	0.126714i	$0.959557\pi$
$90$	1.11507	+	1.93820i	0.117539	+	0.204304i
$91$	−3.19652	+	14.6318i	−0.335087	+	1.53383i
$92$	3.11997	−	3.11997i	0.325280	−	0.325280i
$93$	0.0313366	−	0.00839662i	0.00324945	−	0.000870688i
$94$	−4.52012	−	7.82908i	−0.466215	−	0.807508i
$95$	3.35273	+	12.5896i	0.343983	+	1.29166i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	2.51799	+	2.51799i	0.255663	+	0.255663i	0.823288	−	0.567624i	$-0.192137\pi$
$97$	2.51799	+	2.51799i	0.255663	+	0.255663i	−0.567624	+	0.823288i	$0.692137\pi$
$98$	6.90101	+	1.17303i	0.697108	+	0.118494i
$99$		−	0.461115i		−	0.0463438i
$100$	2.48674	+	4.33776i	0.248674	+	0.433776i
$101$	3.90734	−	2.25590i	0.388795	−	0.224471i	−0.292843	−	0.956161i	$-0.594601\pi$
$101$	3.90734	−	2.25590i	0.388795	−	0.224471i	0.681638	+	0.731690i	$0.261268\pi$
$102$	1.58394	+	0.424416i	0.156834	+	0.0420234i
$103$	3.82414	+	14.2719i	0.376804	+	1.40625i	0.850692	+	0.525665i	$0.176183\pi$
$103$	3.82414	+	14.2719i	0.376804	+	1.40625i	−0.473888	+	0.880585i	$0.657150\pi$
$104$	5.66074			0.555081
$105$	2.72360	−	5.25186i	0.265796	−	0.512529i
$106$	2.74660			0.266773
$107$	1.52683	+	5.69821i	0.147604	+	0.550867i	0.999626	+	0.0273597i	$0.00870995\pi$
$107$	1.52683	+	5.69821i	0.147604	+	0.550867i	−0.852021	+	0.523507i	$0.824623\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	14.3923	−	8.30937i	1.37853	−	0.795893i	0.386546	−	0.922270i	$-0.373668\pi$
$109$	14.3923	−	8.30937i	1.37853	−	0.795893i	0.991982	+	0.126377i	$0.0403349\pi$
$110$	0.00157753	−	1.03108i	0.000150412	−	0.0983098i
$111$			8.06444i			0.765443i
$112$	−0.123551	−	2.64286i	−0.0116744	−	0.249727i
$113$	6.35390	+	6.35390i	0.597724	+	0.597724i	0.939706	−	0.341982i	$-0.111098\pi$
$113$	6.35390	+	6.35390i	0.597724	+	0.597724i	−0.341982	+	0.939706i	$0.611098\pi$
$114$	−5.04586	−	2.91323i	−0.472588	−	0.272849i
$115$	−4.94618	+	8.53684i	−0.461233	+	0.796064i
$116$	2.76886	+	4.79581i	0.257082	+	0.445280i
$117$	−5.46786	+	1.46511i	−0.505503	+	0.135449i
$118$	−1.35593	+	1.35593i	−0.124824	+	0.124824i
$119$	−1.31737	−	4.13371i	−0.120763	−	0.378936i
$120$	−2.15899	−	0.582041i	−0.197088	−	0.0531328i
$121$	5.39369	−	9.34214i	0.490335	−	0.849285i
$122$	3.50839	−	13.0935i	0.317634	−	1.18543i
$123$	2.83285	−	10.5723i	0.255430	−	0.953276i
$124$	−0.0162210	+	0.0280956i	−0.00145669	+	0.00252306i
$125$	−7.86932	−	7.94190i	−0.703854	−	0.710345i
$126$	0.803365	+	2.52083i	0.0715694	+	0.224574i
$127$	−11.7757	+	11.7757i	−1.04493	+	1.04493i	−0.0459856	+	0.998942i	$0.514643\pi$
$127$	−11.7757	+	11.7757i	−1.04493	+	1.04493i	−0.998942	+	0.0459856i	$0.985357\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	3.35979	+	5.81932i	0.295813	+	0.512363i
$130$	−12.2315	+	3.25737i	−1.07277	+	0.285690i
$131$	16.4341	+	9.48825i	1.43586	+	0.828992i	0.997558	−	0.0698379i	$-0.0222482\pi$
$131$	16.4341	+	9.48825i	1.43586	+	0.828992i	0.438298	+	0.898830i	$0.355582\pi$
$132$	0.326057	+	0.326057i	0.0283796	+	0.0283796i
$133$	0.719863	+	15.3985i	0.0624200	+	1.33522i
$134$			3.81023i			0.329154i
$135$	2.23607	+	0.00342112i	0.192450	+	0.000294443i
$136$	−1.42012	+	0.819909i	−0.121775	+	0.0703066i
$137$	4.27811	+	1.14632i	0.365503	+	0.0979364i	0.436896	−	0.899512i	$-0.356078\pi$
$137$	4.27811	+	1.14632i	0.365503	+	0.0979364i	−0.0713928	+	0.997448i	$0.522744\pi$
$138$	−1.14199	−	4.26196i	−0.0972126	−	0.362802i
$139$	−4.35020			−0.368979			−0.184489	−	0.982835i	$-0.559063\pi$
$139$	−4.35020			−0.368979			−0.184489	+	0.982835i	$0.559063\pi$
$140$	1.78775	+	5.63950i	0.151093	+	0.476625i
$141$	−9.04024			−0.761325
$142$	2.29282	+	8.55692i	0.192409	+	0.718080i
$143$	2.52131	+	0.675582i	0.210842	+	0.0564950i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−8.74251	−	8.76930i	−0.726026	−	0.728251i
$146$		−	4.05729i		−	0.335784i
$147$	4.46638	−	5.38994i	0.368381	−	0.444555i
$148$	−5.70242	−	5.70242i	−0.468736	−	0.468736i
$149$	3.75900	+	2.17026i	0.307949	+	0.177794i	0.646008	−	0.763330i	$-0.276437\pi$
$149$	3.75900	+	2.17026i	0.307949	+	0.177794i	−0.338059	+	0.941125i	$0.609770\pi$
$150$	4.99998	+	0.0152997i	0.408246	+	0.00124922i
$151$	−4.09257	−	7.08854i	−0.333049	−	0.576857i	0.650059	−	0.759884i	$-0.274744\pi$
$151$	−4.09257	−	7.08854i	−0.333049	−	0.576857i	−0.983108	+	0.183026i	$0.941411\pi$
$152$	5.62793	−	1.50800i	0.456485	−	0.122315i
$153$	1.15953	−	1.15953i	0.0937421	−	0.0937421i
$154$	0.260384	−	1.19188i	0.0209823	−	0.0960447i
$155$	0.0188826	−	0.0700419i	0.00151669	−	0.00562590i
$156$	2.83037	−	4.90235i	0.226611	−	0.392502i
$157$	5.63586	−	21.0333i	0.449790	−	1.67864i	−0.253178	−	0.967420i	$-0.581476\pi$
$157$	5.63586	−	21.0333i	0.449790	−	1.67864i	0.702969	−	0.711221i	$-0.251857\pi$
$158$	1.30995	−	4.88882i	0.104214	−	0.388933i
$159$	1.37330	−	2.37863i	0.108910	−	0.188637i
$160$	1.93820	−	1.11507i	0.153228	−	0.0881540i
$161$	−7.86019	+	8.63114i	−0.619470	+	0.680229i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	11.2769	−	3.02164i	0.883275	−	0.236673i	0.211456	−	0.977388i	$-0.432180\pi$
$163$	11.2769	−	3.02164i	0.883275	−	0.236673i	0.671820	+	0.740715i	$0.265513\pi$
$164$	5.47265	+	9.47890i	0.427342	+	0.740178i
$165$	−0.892155	−	0.516907i	−0.0694542	−	0.0402412i
$166$	1.33268	+	0.769426i	0.103436	+	0.0597190i
$167$	−15.5061	−	15.5061i	−1.19990	−	1.19990i	−0.974196	−	0.225703i	$-0.927532\pi$
$167$	−15.5061	−	15.5061i	−1.19990	−	1.19990i	−0.225703	−	0.974196i	$-0.572468\pi$
$168$	−2.35056	−	1.21443i	−0.181350	−	0.0936957i
$169$		−	19.0440i		−	1.46492i
$170$	2.59674	−	2.58881i	0.199161	−	0.198553i
$171$	−5.04586	+	2.91323i	−0.385867	+	0.222780i
$172$	−6.49061	−	1.73915i	−0.494905	−	0.132609i
$173$	−2.52204	−	9.41238i	−0.191747	−	0.715610i	−0.993085	−	0.117398i	$-0.962545\pi$
$173$	−2.52204	−	9.41238i	−0.191747	−	0.715610i	0.801338	−	0.598212i	$-0.204122\pi$
$174$	5.53773			0.419814
$175$	−7.10805	−	11.1569i	−0.537318	−	0.843380i
$176$	−0.461115			−0.0347578
$177$	0.496307	+	1.85224i	0.0373047	+	0.139223i
$178$	−11.0391	−	2.95790i	−0.827412	−	0.221704i
$179$	1.39876	−	0.807576i	0.104548	−	0.0603611i	−0.446814	−	0.894627i	$-0.647441\pi$
$179$	1.39876	−	0.807576i	0.104548	−	0.0603611i	0.551363	+	0.834266i	$0.314108\pi$
$180$	−1.58356	+	1.57872i	−0.118031	+	0.117671i
$181$			12.8519i			0.955277i	0.878556	+	0.477639i	$0.158507\pi$
$181$			12.8519i			0.955277i	−0.878556	+	0.477639i	$0.841493\pi$
$182$	−14.9606	+	0.699388i	−1.10895	+	0.0518421i
$183$	−9.58509	−	9.58509i	−0.708550	−	0.708550i
$184$	3.82117	+	2.20615i	0.281700	+	0.162640i
$185$	15.6029	+	9.04021i	1.14715	+	0.664649i
$186$	0.0162210	+	0.0280956i	0.00118938	+	0.00206007i
$187$	−0.730379	+	0.195704i	−0.0534106	+	0.0143113i
$188$	6.39241	−	6.39241i	0.466215	−	0.466215i
$189$	2.58479	+	0.564683i	0.188016	+	0.0410746i
$190$	−11.2928	+	6.49691i	−0.819269	+	0.471335i
$191$	5.30033	−	9.18043i	0.383518	−	0.664273i	−0.608044	−	0.793903i	$-0.708046\pi$
$191$	5.30033	−	9.18043i	0.383518	−	0.664273i	0.991562	+	0.129630i	$0.0413790\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	1.86766	−	6.97019i	0.134437	−	0.501726i	−0.865563	−	0.500801i	$-0.833039\pi$
$193$	1.86766	−	6.97019i	0.134437	−	0.501726i	1.00000		0.000924826i	$-0.000294381\pi$
$194$	−1.78049	+	3.08389i	−0.127832	+	0.221411i
$195$	−3.29478	+	12.2215i	−0.235944	+	0.875198i
$196$	0.653056	+	6.96947i	0.0466468	+	0.497819i
$197$	−9.72803	+	9.72803i	−0.693093	+	0.693093i	−0.962911	−	0.269818i	$-0.913036\pi$
$197$	−9.72803	+	9.72803i	−0.693093	+	0.693093i	0.269818	+	0.962911i	$0.413036\pi$
$198$	0.445403	−	0.119345i	0.0316534	−	0.00848150i
$199$	4.82648	+	8.35971i	0.342140	+	0.592604i	0.984830	−	0.173522i	$-0.0555149\pi$
$199$	4.82648	+	8.35971i	0.342140	+	0.592604i	−0.642690	+	0.766127i	$0.722182\pi$
$200$	−3.54634	+	3.52470i	−0.250764	+	0.249234i
$201$	3.29976	+	1.90512i	0.232747	+	0.134377i
$202$	3.19033	+	3.19033i	0.224471	+	0.224471i
$203$	−7.91026	−	12.3326i	−0.555191	−	0.865578i
$204$			1.63982i			0.114810i
$205$	−17.2795	−	17.3325i	−1.20686	−	1.21055i
$206$	−12.7958	+	7.38767i	−0.891527	+	0.514723i
$207$	−4.26196	−	1.14199i	−0.296227	−	0.0793737i
$208$	1.46511	+	5.46786i	0.101587	+	0.379128i
$209$	2.68667			0.185841
$210$	5.77782	+	1.27151i	0.398708	+	0.0877426i
$211$	1.33273			0.0917487			0.0458744	−	0.998947i	$-0.485393\pi$
$211$	1.33273			0.0917487			0.0458744	+	0.998947i	$0.485393\pi$
$212$	0.710873	+	2.65301i	0.0488229	+	0.182210i
$213$	8.55692	+	2.29282i	0.586310	+	0.157101i
$214$	−5.10888	+	2.94961i	−0.349236	+	0.201631i
$215$	15.0254	+	0.0229885i	1.02472	+	0.00156780i
$216$		−	1.00000i		−	0.0680414i
$217$	0.0393987	−	0.0762571i	0.00267456	−	0.00517667i
$218$	11.7512	+	11.7512i	0.795893	+	0.795893i
$219$	−3.51371	−	2.02864i	−0.237435	−	0.137083i
$220$	0.996357	−	0.265340i	0.0671744	−	0.0178892i
$221$	4.64129	+	8.03895i	0.312207	+	0.540758i
$222$	−7.78966	+	2.08723i	−0.522807	+	0.140086i
$223$	8.25284	−	8.25284i	0.552651	−	0.552651i	−0.374554	−	0.927205i	$-0.622204\pi$
$223$	8.25284	−	8.25284i	0.552651	−	0.552651i	0.927205	+	0.374554i	$0.122204\pi$
$224$	2.52083	−	0.803365i	0.168430	−	0.0536771i
$225$	2.51324	−	4.32246i	0.167549	−	0.288164i
$226$	−4.49288	+	7.78190i	−0.298862	+	0.517645i
$227$	−5.78787	+	21.6006i	−0.384154	+	1.43368i	0.455341	+	0.890317i	$0.349517\pi$
$227$	−5.78787	+	21.6006i	−0.384154	+	1.43368i	−0.839496	+	0.543367i	$0.817149\pi$
$228$	1.50800	−	5.62793i	0.0998696	−	0.372719i
$229$	2.48311	−	4.30087i	0.164088	−	0.284209i	−0.772243	−	0.635328i	$-0.780865\pi$
$229$	2.48311	−	4.30087i	0.164088	−	0.284209i	0.936331	+	0.351118i	$0.114198\pi$
$230$	−9.52612	−	2.56814i	−0.628134	−	0.169338i
$231$	−0.902010	−	0.821441i	−0.0593479	−	0.0540468i
$232$	−3.91576	+	3.91576i	−0.257082	+	0.257082i
$233$	−27.6582	+	7.41098i	−1.81195	+	0.485509i	−0.995736	−	0.0922466i	$-0.970595\pi$
$233$	−27.6582	+	7.41098i	−1.81195	+	0.485509i	−0.816210	+	0.577756i	$0.803929\pi$
$234$	−2.83037	−	4.90235i	−0.185027	−	0.320476i
$235$	−10.1341	+	17.4909i	−0.661074	+	1.14098i
$236$	−1.66067	−	0.958791i	−0.108101	−	0.0624120i
$237$	−3.57886	−	3.57886i	−0.232472	−	0.232472i
$238$	3.65189	−	2.34237i	0.236717	−	0.151833i
$239$		−	13.9230i		−	0.900603i	−0.892877	−	0.450302i	$-0.851316\pi$
$239$		−	13.9230i		−	0.900603i	0.892877	−	0.450302i	$-0.148684\pi$
$240$	0.00342112	−	2.23607i	0.000220833	−	0.144337i
$241$	0.915881	−	0.528784i	0.0589971	−	0.0340620i	−0.470211	−	0.882554i	$-0.655822\pi$
$241$	0.915881	−	0.528784i	0.0589971	−	0.0340620i	0.529208	+	0.848492i	$0.322489\pi$
$242$	10.4198	+	2.79198i	0.669810	+	0.179475i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	13.5554			0.867793
$245$	−5.42155	−	14.6836i	−0.346370	−	0.938098i
$246$	10.9453			0.697847
$247$	−8.53639	−	31.8582i	−0.543157	−	2.02709i
$248$	−0.0313366	−	0.00839662i	−0.00198988	−	0.000533186i
$249$	1.33268	−	0.769426i	0.0844554	−	0.0487604i
$250$	5.63455	−	9.65670i	0.356360	−	0.610743i
$251$			6.36260i			0.401604i	0.979632	+	0.200802i	$0.0643548\pi$
$251$			6.36260i			0.401604i	−0.979632	+	0.200802i	$0.935645\pi$
$252$	−2.22701	+	1.42843i	−0.140289	+	0.0899827i
$253$	1.43866	+	1.43866i	0.0904481	+	0.0904481i
$254$	−14.4223	−	8.32670i	−0.904934	−	0.522464i
$255$	−0.943603	−	3.54325i	−0.0590907	−	0.221887i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.0273	−	2.68681i	0.625488	−	0.167599i	0.0678664	−	0.997694i	$-0.478381\pi$
$257$	10.0273	−	2.68681i	0.625488	−	0.167599i	0.557621	+	0.830096i	$0.311714\pi$
$258$	−4.75146	+	4.75146i	−0.295813	+	0.295813i
$259$	15.7753	+	14.3662i	0.980228	+	0.892672i
$260$	−6.31212	−	10.9716i	−0.391461	−	0.680433i
$261$	2.76886	−	4.79581i	0.171388	−	0.296853i
$262$	−4.91148	+	18.3299i	−0.303432	+	1.13242i
$263$	6.15005	−	22.9523i	0.379228	−	1.41530i	−0.467839	−	0.883814i	$-0.654967\pi$
$263$	6.15005	−	22.9523i	0.379228	−	1.41530i	0.847067	−	0.531486i	$-0.178366\pi$
$264$	−0.230557	+	0.399337i	−0.0141898	+	0.0245775i
$265$	−3.06265	−	5.32346i	−0.188137	−	0.327018i
$266$	−14.6875	+	4.68077i	−0.900551	+	0.286996i
$267$	−8.08115	+	8.08115i	−0.494558	+	0.494558i
$268$	−3.68040	+	0.986161i	−0.224816	+	0.0602394i
$269$	−0.710036	−	1.22982i	−0.0432917	−	0.0749834i	0.843568	−	0.537023i	$-0.180451\pi$
$269$	−0.710036	−	1.22982i	−0.0432917	−	0.0749834i	−0.886859	+	0.462040i	$0.847118\pi$
$270$	0.575432	+	2.16076i	0.0350197	+	0.131500i
$271$	−0.306228	−	0.176801i	−0.0186020	−	0.0107399i	0.490670	−	0.871345i	$-0.336752\pi$
$271$	−0.306228	−	0.176801i	−0.0186020	−	0.0107399i	−0.509272	+	0.860606i	$0.670085\pi$
$272$	−1.15953	−	1.15953i	−0.0703066	−	0.0703066i
$273$	−6.87460	+	13.3059i	−0.416070	+	0.805312i
$274$			4.42902i			0.267567i
$275$	−2.00020	+	1.14667i	−0.120617	+	0.0691469i
$276$	3.82117	−	2.20615i	0.230007	−	0.132795i
$277$	22.7009	+	6.08269i	1.36397	+	0.365474i	0.865271	−	0.501304i	$-0.167146\pi$
$277$	22.7009	+	6.08269i	1.36397	+	0.365474i	0.498695	+	0.866778i	$0.333813\pi$
$278$	−1.12591	−	4.20197i	−0.0675278	−	0.252017i
$279$	0.0324420			0.00194225
$280$	−4.98463	+	3.18645i	−0.297889	+	0.190427i
$281$	28.4747			1.69866			0.849330	−	0.527862i	$-0.177006\pi$
$281$	28.4747			1.69866			0.849330	+	0.527862i	$0.177006\pi$
$282$	−2.33979	−	8.73220i	−0.139332	−	0.519995i
$283$	−3.62984	−	0.972612i	−0.215771	−	0.0578158i	0.149314	−	0.988790i	$-0.452294\pi$
$283$	−3.62984	−	0.972612i	−0.215771	−	0.0578158i	−0.365085	+	0.930974i	$0.618960\pi$
$284$	−7.67192	+	4.42939i	−0.455245	+	0.262836i
$285$	−0.0199330	+	13.0283i	−0.00118073	+	0.771732i
$286$			2.61025i			0.154347i
$287$	−15.6346	−	24.3753i	−0.922881	−	1.43883i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$	12.3937	+	7.15550i	0.729041	+	0.420912i
$290$	6.20776	−	10.7143i	0.364532	−	0.629164i
$291$	1.78049	+	3.08389i	0.104374	+	0.180781i
$292$	3.91904	−	1.05010i	0.229344	−	0.0614527i
$293$	4.18500	−	4.18500i	0.244490	−	0.244490i	−0.574215	−	0.818705i	$-0.694692\pi$
$293$	4.18500	−	4.18500i	0.244490	−	0.244490i	0.818705	+	0.574215i	$0.194692\pi$
$294$	6.36227	+	2.91917i	0.371055	+	0.170250i
$295$	4.14003	+	1.11611i	0.241042	+	0.0649825i
$296$	4.03222	−	6.98401i	0.234368	−	0.405938i
$297$	0.119345	−	0.445403i	0.00692511	−	0.0258449i
$298$	−1.12341	+	4.19262i	−0.0650773	+	0.242872i
$299$	12.4885	−	21.6307i	0.722226	−	1.25093i
$300$	1.27931	+	4.83357i	0.0738610	+	0.279066i
$301$	17.3687	+	3.79443i	1.00111	+	0.218707i
$302$	5.78777	−	5.78777i	0.333049	−	0.333049i
$303$	4.35807	−	1.16774i	0.250365	−	0.0670850i
$304$	2.91323	+	5.04586i	0.167085	+	0.289400i
$305$	−29.2899	+	7.80019i	−1.67713	+	0.446637i
$306$	1.42012	+	0.819909i	0.0811831	+	0.0468711i
$307$	18.0884	+	18.0884i	1.03236	+	1.03236i	0.999459	+	0.0329031i	$0.0104753\pi$
$307$	18.0884	+	18.0884i	1.03236	+	1.03236i	0.0329031	+	0.999459i	$0.489525\pi$
$308$	1.21866	−	0.0569710i	0.0694398	−	0.00324623i
$309$			14.7753i			0.840540i
$310$	0.0725425		0.000110988i	0.00412014		6.30370e-6i
$311$	−29.1137	+	16.8088i	−1.65089	+	0.953139i	−0.674177	+	0.738569i	$0.735502\pi$
$311$	−29.1137	+	16.8088i	−1.65089	+	0.953139i	−0.976709	+	0.214570i	$0.931165\pi$
$312$	5.46786	+	1.46511i	0.309556	+	0.0829454i
$313$	5.94363	+	22.1819i	0.335954	+	1.25380i	0.902831	+	0.429995i	$0.141485\pi$
$313$	5.94363	+	22.1819i	0.335954	+	1.25380i	−0.566877	+	0.823802i	$0.691849\pi$
$314$	21.7753			1.22885
$315$	3.99007	−	4.36799i	0.224815	−	0.246108i
$316$	5.06128			0.284719
$317$	6.63663	+	24.7683i	0.372751	+	1.39112i	0.856604	+	0.515975i	$0.172570\pi$
$317$	6.63663	+	24.7683i	0.372751	+	1.39112i	−0.483853	+	0.875149i	$0.660763\pi$
$318$	2.65301	+	0.710873i	0.148774	+	0.0398638i
$319$	−2.21142	+	1.27676i	−0.123816	+	0.0714850i
$320$	1.57872	+	1.58356i	0.0882530	+	0.0885235i
$321$			5.89922i			0.329262i
$322$	−10.3714	−	5.35846i	−0.577976	−	0.298615i
$323$	6.75593	+	6.75593i	0.375910	+	0.375910i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	19.9524	+	20.0749i	1.10676	+	1.11355i
$326$	5.83736	+	10.1106i	0.323301	+	0.559974i
$327$	16.0525	−	4.30125i	0.887704	−	0.237860i
$328$	−7.73949	+	7.73949i	−0.427342	+	0.427342i
$329$	−16.1045	+	17.6841i	−0.887870	+	0.974955i
$330$	0.268388	−	0.995541i	0.0147742	−	0.0548027i
$331$	5.93242	−	10.2753i	0.326076	−	0.564779i	−0.655654	−	0.755062i	$-0.727607\pi$
$331$	5.93242	−	10.2753i	0.326076	−	0.564779i	0.981729	+	0.190282i	$0.0609403\pi$
$332$	−0.398284	+	1.48642i	−0.0218587	+	0.0815777i
$333$	−2.08723	+	7.78966i	−0.114380	+	0.426870i
$334$	10.9645	−	18.9910i	0.599950	−	1.03914i
$335$	7.38499	−	4.24868i	0.403485	−	0.232130i
$336$	0.564683	−	2.58479i	0.0308060	−	0.141012i
$337$	−3.18746	+	3.18746i	−0.173632	+	0.173632i	−0.788573	−	0.614941i	$-0.789180\pi$
$337$	−3.18746	+	3.18746i	−0.173632	+	0.173632i	0.614941	+	0.788573i	$0.289180\pi$
$338$	18.3951	−	4.92895i	1.00056	−	0.268099i
$339$	4.49288	+	7.78190i	0.244020	+	0.422655i
$340$	3.17268	+	1.83823i	0.172063	+	0.0996919i
$341$	−0.0129553	−	0.00747975i	−0.000701569	−	0.000405051i
$342$	−4.11993	−	4.11993i	−0.222780	−	0.222780i
$343$	−2.58702	−	18.3387i	−0.139686	−	0.990196i
$344$		−	6.71958i		−	0.362295i
$345$	−6.98714	+	6.96579i	−0.376175	+	0.375025i
$346$	8.43891	−	4.87221i	0.453679	−	0.261931i
$347$	20.6922	+	5.54445i	1.11081	+	0.297642i	0.767161	−	0.641455i	$-0.221669\pi$
$347$	20.6922	+	5.54445i	1.11081	+	0.297642i	0.343653	+	0.939097i	$0.388336\pi$
$348$	1.43327	+	5.34903i	0.0768313	+	0.286738i
$349$	−16.0682			−0.860113			−0.430056	−	0.902802i	$-0.641506\pi$
$349$	−16.0682			−0.860113			−0.430056	+	0.902802i	$0.641506\pi$
$350$	8.93701	−	9.75346i	0.477703	−	0.521344i
$351$	−5.66074			−0.302148
$352$	−0.119345	−	0.445403i	−0.00636112	−	0.0237400i
$353$	−28.3943	−	7.60823i	−1.51128	−	0.404945i	−0.594418	−	0.804156i	$-0.702617\pi$
$353$	−28.3943	−	7.60823i	−1.51128	−	0.404945i	−0.916859	+	0.399211i	$0.869284\pi$
$354$	−1.66067	+	0.958791i	−0.0882638	+	0.0509592i
$355$	14.0284	−	13.9855i	0.744548	−	0.742273i
$356$		−	11.4285i		−	0.605708i
$357$	−0.202601	−	4.33382i	−0.0107228	−	0.229370i
$358$	1.14209	+	1.14209i	0.0603611	+	0.0603611i
$359$	−11.8017	−	6.81369i	−0.622868	−	0.359613i	0.155117	−	0.987896i	$-0.450425\pi$
$359$	−11.8017	−	6.81369i	−0.622868	−	0.359613i	−0.777985	+	0.628283i	$0.783758\pi$
$360$	−1.93478	−	1.12100i	−0.101972	−	0.0590816i
$361$	−7.47381	−	12.9450i	−0.393359	−	0.681317i
$362$	−12.4140	+	3.32633i	−0.652466	+	0.174828i
$363$	7.62782	−	7.62782i	0.400357	−	0.400357i
$364$	−4.54764	−	14.2698i	−0.238361	−	0.747940i
$365$	−7.86384	+	4.52416i	−0.411612	+	0.236805i
$366$	6.77768	−	11.7393i	0.354275	−	0.613622i
$367$	3.30230	−	12.3244i	0.172379	−	0.643326i	−0.824605	−	0.565709i	$-0.808602\pi$
$367$	3.30230	−	12.3244i	0.172379	−	0.643326i	0.996983	−	0.0776164i	$-0.0247309\pi$
$368$	−1.14199	+	4.26196i	−0.0595303	+	0.222170i
$369$	5.47265	−	9.47890i	0.284895	−	0.493452i
$370$	−4.69384	+	17.4110i	−0.244021	+	0.905157i
$371$	−2.20652	−	6.92373i	−0.114557	−	0.359462i
$372$	−0.0229400	+	0.0229400i	−0.00118938	+	0.00118938i
$373$	−3.86501	+	1.03563i	−0.200123	+	0.0536227i	−0.357488	−	0.933918i	$-0.616367\pi$
$373$	−3.86501	+	1.03563i	−0.200123	+	0.0536227i	0.157365	+	0.987540i	$0.449700\pi$
$374$	−0.378072	−	0.654840i	−0.0195496	−	0.0338610i
$375$	−5.54567	−	9.70801i	−0.286377	−	0.501320i
$376$	7.82908	+	4.52012i	0.403754	+	0.233107i
$377$	22.1661	+	22.1661i	1.14161	+	1.14161i
$378$	0.123551	+	2.64286i	0.00635476	+	0.135934i
$379$		−	1.00281i		−	0.0515109i	−0.999668	−	0.0257555i	$-0.991801\pi$
$379$		−	1.00281i		−	0.0515109i	0.999668	−	0.0257555i	$-0.00819912\pi$
$380$	−9.19833	−	9.22652i	−0.471865	−	0.473311i
$381$	−14.4223	+	8.32670i	−0.738875	+	0.426590i
$382$	10.2394	+	2.74365i	0.523895	+	0.140377i
$383$	−4.60780	−	17.1965i	−0.235447	−	0.878702i	−0.977947	−	0.208855i	$-0.933026\pi$
$383$	−4.60780	−	17.1965i	−0.235447	−	0.878702i	0.742499	−	0.669847i	$-0.233640\pi$
$384$	−1.00000			−0.0510310
$385$	−2.60046	+	0.824358i	−0.132531	+	0.0420132i
$386$	7.21608			0.367289
$387$	1.73915	+	6.49061i	0.0884062	+	0.329936i
$388$	−3.43964	−	0.921648i	−0.174621	−	0.0467896i
$389$	−9.75032	+	5.62935i	−0.494361	+	0.285419i	−0.726382	−	0.687291i	$-0.758800\pi$
$389$	−9.75032	+	5.62935i	−0.494361	+	0.285419i	0.232021	+	0.972711i	$0.425466\pi$
$390$	−12.6578	−	0.0193661i	−0.640952	−	0.000980640i
$391$			7.23538i			0.365909i
$392$	−6.56297	+	2.43463i	−0.331480	+	0.122968i
$393$	13.4184	+	13.4184i	0.676869	+	0.676869i
$394$	−11.9144	−	6.87875i	−0.600236	−	0.346547i
$395$	−10.9362	+	2.91242i	−0.550260	+	0.146540i
$396$	0.230557	+	0.399337i	0.0115859	+	0.0200674i
$397$	−3.70224	+	0.992011i	−0.185810	+	0.0497876i	−0.350524	−	0.936554i	$-0.613997\pi$
$397$	−3.70224	+	0.992011i	−0.185810	+	0.0497876i	0.164714	+	0.986341i	$0.447330\pi$
$398$	−6.82567	+	6.82567i	−0.342140	+	0.342140i
$399$	−3.29010	+	15.0602i	−0.164711	+	0.753951i
$400$	−4.32246	−	2.51324i	−0.216123	−	0.125662i
$401$	−0.450022	+	0.779461i	−0.0224730	+	0.0389244i	−0.877043	−	0.480412i	$-0.840487\pi$
$401$	−0.450022	+	0.779461i	−0.0224730	+	0.0389244i	0.854570	+	0.519336i	$0.173821\pi$
$402$	−0.986161	+	3.68040i	−0.0491852	+	0.183562i
$403$	−0.0475311	+	0.177388i	−0.00236769	+	0.00883634i
$404$	−2.25590	+	3.90734i	−0.112235	+	0.194397i
$405$	2.15899	+	0.582041i	0.107281	+	0.0289218i
$406$	9.86504	−	10.8326i	0.489594	−	0.537614i
$407$	2.62947	−	2.62947i	0.130338	−	0.130338i
$408$	−1.58394	+	0.424416i	−0.0784168	+	0.0210117i
$409$	6.44633	+	11.1654i	0.318751	+	0.552092i	0.980228	−	0.197873i	$-0.0634034\pi$
$409$	6.44633	+	11.1654i	0.318751	+	0.552092i	−0.661477	+	0.749965i	$0.730070\pi$
$410$	12.2696	−	21.1767i	0.605954	−	1.04584i
$411$	3.83565	+	2.21451i	0.189199	+	0.109234i
$412$	−10.4477	−	10.4477i	−0.514723	−	0.514723i
$413$	4.50740	+	2.32878i	0.221795	+	0.114592i
$414$		−	4.41231i		−	0.216853i
$415$	0.00526460	−	3.44097i	0.000258429	−	0.168911i
$416$	−4.90235	+	2.83037i	−0.240357	+	0.138770i
$417$	−4.20197	−	1.12591i	−0.205771	−	0.0551362i
$418$	0.695360	+	2.59512i	0.0340112	+	0.126931i
$419$	−19.8918			−0.971777			−0.485888	−	0.874021i	$-0.661504\pi$
$419$	−19.8918			−0.971777			−0.485888	+	0.874021i	$0.661504\pi$
$420$	0.267226	+	5.91004i	0.0130393	+	0.288380i
$421$	−12.6339			−0.615740			−0.307870	−	0.951428i	$-0.599616\pi$
$421$	−12.6339			−0.615740			−0.307870	+	0.951428i	$0.599616\pi$
$422$	0.344935	+	1.28732i	0.0167912	+	0.0626655i
$423$	−8.73220	−	2.33979i	−0.424574	−	0.113764i
$424$	−2.37863	+	1.37330i	−0.115516	+	0.0666934i
$425$	−7.91318	−	2.14630i	−0.383846	−	0.104111i
$426$			8.85877i			0.429209i
$427$	−35.8250	+	1.67477i	−1.73369	+	0.0810480i
$428$	−4.17138	−	4.17138i	−0.201631	−	0.201631i
$429$	2.26054	+	1.30513i	0.109140	+	0.0630120i
$430$	3.86666	+	14.5194i	0.186467	+	0.700187i
$431$	−15.3851	−	26.6477i	−0.741073	−	1.28358i	−0.952007	−	0.306075i	$-0.900984\pi$
$431$	−15.3851	−	26.6477i	−0.741073	−	1.28358i	0.210935	−	0.977500i	$-0.432349\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	3.04743	−	3.04743i	0.146450	−	0.146450i	−0.630080	−	0.776530i	$-0.716978\pi$
$433$	3.04743	−	3.04743i	0.146450	−	0.146450i	0.776530	+	0.630080i	$0.216978\pi$
$434$	0.0838558	+	0.0183195i	0.00402521	+	0.000879362i
$435$	−6.17495	−	10.7332i	−0.296066	−	0.514618i
$436$	−8.30937	+	14.3923i	−0.397947	+	0.689264i
$437$	6.65375	−	24.8321i	0.318292	−	1.18788i
$438$	1.05010	−	3.91904i	0.0501759	−	0.187259i
$439$	−18.4993	+	32.0418i	−0.882926	+	1.52927i	−0.0348530	+	0.999392i	$0.511096\pi$
$439$	−18.4993	+	32.0418i	−0.882926	+	1.52927i	−0.848073	+	0.529880i	$0.822237\pi$
$440$	0.514175	+	0.893732i	0.0245123	+	0.0426070i
$441$	5.70921	−	4.05030i	0.271867	−	0.192871i
$442$	−6.56378	+	6.56378i	−0.312207	+	0.312207i
$443$	17.1911	−	4.60633i	0.816773	−	0.218854i	0.173838	−	0.984774i	$-0.444383\pi$
$443$	17.1911	−	4.60633i	0.816773	−	0.218854i	0.642935	+	0.765921i	$0.277717\pi$
$444$	−4.03222	−	6.98401i	−0.191361	−	0.331447i
$445$	6.57630	+	24.6942i	0.311747	+	1.17062i
$446$	10.1076	+	5.83564i	0.478610	+	0.276326i
$447$	3.06921	+	3.06921i	0.145169	+	0.145169i
$448$	1.42843	+	2.22701i	0.0674870	+	0.105216i
$449$		−	2.41945i		−	0.114181i	−0.998369	−	0.0570904i	$-0.981818\pi$
$449$		−	2.41945i		−	0.114181i	0.998369	−	0.0570904i	$-0.0181823\pi$
$450$	4.82565	+	1.30887i	0.227483	+	0.0617006i
$451$	−4.37086	+	2.52352i	−0.205816	+	0.118828i
$452$	−8.67959	−	2.32569i	−0.408253	−	0.109391i
$453$	−2.11847	−	7.90624i	−0.0995345	−	0.371468i
$454$	−22.3626			−1.04953
$455$	18.0376	+	28.2167i	0.845618	+	1.32282i
$456$	5.82646			0.272849
$457$	−7.13275	−	26.6198i	−0.333656	−	1.24522i	−0.905319	−	0.424732i	$-0.860368\pi$
$457$	−7.13275	−	26.6198i	−0.333656	−	1.24522i	0.571663	−	0.820488i	$-0.306298\pi$
$458$	4.79700	+	1.28535i	0.224149	+	0.0600605i
$459$	1.42012	−	0.819909i	0.0662857	−	0.0382701i
$460$	0.0150950	−	9.86621i	0.000703810	−	0.460014i
$461$		−	1.02712i		−	0.0478378i	−0.999714	−	0.0239189i	$-0.992386\pi$
$461$		−	1.02712i		−	0.0478378i	0.999714	−	0.0239189i	$-0.00761434\pi$
$462$	0.559993	−	1.08388i	0.0260533	−	0.0504266i
$463$	−8.26507	−	8.26507i	−0.384111	−	0.384111i	0.488470	−	0.872581i	$-0.337555\pi$
$463$	−8.26507	−	8.26507i	−0.384111	−	0.384111i	−0.872581	+	0.488470i	$0.837555\pi$
$464$	−4.79581	−	2.76886i	−0.222640	−	0.128541i
$465$	0.0363674	−	0.0627682i	0.00168650	−	0.00291080i
$466$	−14.3169	−	24.7976i	−0.663218	−	1.14873i
$467$	−17.9129	+	4.79974i	−0.828910	+	0.222106i	−0.648238	−	0.761438i	$-0.724494\pi$
$467$	−17.9129	+	4.79974i	−0.828910	+	0.222106i	−0.180672	+	0.983543i	$0.557827\pi$
$468$	4.00275	−	4.00275i	0.185027	−	0.185027i
$469$	9.60497	−	3.06101i	0.443516	−	0.141344i
$470$	−19.5178	−	5.26179i	−0.900287	−	0.242708i
$471$	10.8876	−	18.8579i	0.501676	−	0.868928i
$472$	0.496307	−	1.85224i	0.0228444	−	0.0852563i
$473$	0.801949	−	2.99292i	0.0368737	−	0.137614i
$474$	2.53064	−	4.38319i	0.116236	−	0.201327i
$475$	25.1846	+	14.6433i	1.15555	+	0.671880i
$476$	3.20773	+	2.92121i	0.147026	+	0.133893i
$477$	1.94214	−	1.94214i	0.0889245	−	0.0889245i
$478$	13.4486	−	3.60353i	0.615123	−	0.164822i
$479$	4.23872	+	7.34168i	0.193672	+	0.335450i	0.946464	−	0.322808i	$-0.104627\pi$
$479$	4.23872	+	7.34168i	0.193672	+	0.335450i	−0.752792	+	0.658258i	$0.771294\pi$
$480$	2.16076	−	0.575432i	0.0986247	−	0.0262647i
$481$	−39.5347	−	22.8254i	−1.80263	−	1.04075i
$482$	0.747813	+	0.747813i	0.0340620	+	0.0340620i
$483$	−9.82626	+	6.30267i	−0.447110	+	0.286782i
$484$			10.7874i			0.490335i
$485$	7.96257	+	0.0121825i	0.361562	+	0.000553180i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	4.69084	+	1.25691i	0.212562	+	0.0569558i	0.363529	−	0.931583i	$-0.381572\pi$
$487$	4.69084	+	1.25691i	0.212562	+	0.0569558i	−0.150967	+	0.988539i	$0.548239\pi$
$488$	3.50839	+	13.0935i	0.158817	+	0.592714i
$489$	11.6747			0.527949
$490$	12.7800	−	9.03720i	0.577343	−	0.408259i
$491$	−37.8594			−1.70857			−0.854286	−	0.519803i	$-0.826005\pi$
$491$	−37.8594			−1.70857			−0.854286	+	0.519803i	$0.826005\pi$
$492$	2.83285	+	10.5723i	0.127715	+	0.476638i
$493$	−8.77144	−	2.35030i	−0.395046	−	0.105852i
$494$	28.5633	−	16.4910i	1.28512	−	0.741967i
$495$	−0.727970	−	0.730201i	−0.0327198	−	0.0328201i
$496$		−	0.0324420i		−	0.00145669i
$497$	19.7286	−	12.6541i	0.884949	−	0.567616i
$498$	1.08813	+	1.08813i	0.0487604	+	0.0487604i
$499$	−0.443575	−	0.256098i	−0.0198571	−	0.0114645i	0.490039	−	0.871701i	$-0.336983\pi$
$499$	−0.443575	−	0.256098i	−0.0198571	−	0.0114645i	−0.509896	+	0.860236i	$0.670316\pi$
$500$	10.7860	+	2.94322i	0.482364	+	0.131625i
$501$	−10.9645	−	18.9910i	−0.489857	−	0.848457i
$502$	−6.14580	+	1.64676i	−0.274301	+	0.0734986i
$503$	−8.58209	+	8.58209i	−0.382657	+	0.382657i	−0.872058	−	0.489402i	$-0.837215\pi$
$503$	−8.58209	+	8.58209i	−0.382657	+	0.382657i	0.489402	+	0.872058i	$0.337215\pi$
$504$	−1.95615	−	1.78142i	−0.0871339	−	0.0793509i
$505$	2.62606	−	9.74094i	0.116858	−	0.433466i
$506$	−1.01729	+	1.76200i	−0.0452240	+	0.0783303i
$507$	4.92895	−	18.3951i	0.218902	−	0.816954i
$508$	4.31022	−	16.0860i	0.191235	−	0.713699i
$509$	5.69382	−	9.86199i	0.252374	−	0.437125i	−0.711805	−	0.702377i	$-0.752122\pi$
$509$	5.69382	−	9.86199i	0.252374	−	0.437125i	0.964179	+	0.265252i	$0.0854553\pi$
$510$	3.17829	−	1.82851i	0.140737	−	0.0809678i
$511$	−10.2278	+	3.25948i	−0.452449	+	0.144191i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−5.62793	+	1.50800i	−0.248479	+	0.0665798i
$514$	5.19053	+	8.99026i	0.228944	+	0.396543i
$515$	28.5870	+	16.5631i	1.25969	+	0.729857i
$516$	−5.81932	−	3.35979i	−0.256181	−	0.147906i
$517$	2.94764	+	2.94764i	0.129637	+	0.129637i
$518$	−9.79374	+	18.9560i	−0.430312	+	0.832878i
$519$		−	9.74441i		−	0.427732i
$520$	8.96410	−	8.93671i	0.393102	−	0.391901i
$521$	16.8886	−	9.75063i	0.739902	−	0.427183i	−0.0821316	−	0.996621i	$-0.526173\pi$
$521$	16.8886	−	9.75063i	0.739902	−	0.427183i	0.822034	+	0.569439i	$0.192839\pi$
$522$	5.34903	+	1.43327i	0.234121	+	0.0627325i
$523$	−3.85439	−	14.3848i	−0.168541	−	0.629003i	−0.997562	−	0.0697859i	$-0.977768\pi$
$523$	−3.85439	−	14.3848i	−0.168541	−	0.629003i	0.829021	−	0.559217i	$-0.188898\pi$
$524$	−18.9765			−0.828992
$525$	−3.97824	−	12.6164i	−0.173624	−	0.550625i
$526$	23.7620			1.03607
$527$	−0.0137689	−	0.0513863i	−0.000599783	−	0.00223842i
$528$	−0.445403	−	0.119345i	−0.0193837	−	0.00519383i
$529$	−3.05841	+	1.76577i	−0.132974	+	0.0767728i
$530$	4.34940	−	4.33611i	0.188926	−	0.188349i
$531$			1.91758i			0.0832159i
$532$	−8.32269	−	12.9756i	−0.360834	−	0.562564i
$533$	43.8113	+	43.8113i	1.89768	+	1.89768i
$534$	−9.89734	−	5.71423i	−0.428300	−	0.247279i
$535$	11.4137	+	6.61300i	0.493457	+	0.285905i
$536$	−1.90512	−	3.29976i	−0.0822885	−	0.142528i
$537$	1.56012	−	0.418032i	0.0673241	−	0.0180394i
$538$	1.00414	−	1.00414i	0.0432917	−	0.0432917i
$539$	−3.21372	+	0.301133i	−0.138425	+	0.0129707i
$540$	−1.93820	+	1.11507i	−0.0834068	+	0.0479850i
$541$	−21.9060	+	37.9422i	−0.941810	+	1.63126i	−0.179796	+	0.983704i	$0.557544\pi$
$541$	−21.9060	+	37.9422i	−0.941810	+	1.63126i	−0.762015	+	0.647559i	$0.775790\pi$
$542$	0.0915187	−	0.341553i	0.00393107	−	0.0146709i
$543$	−3.32633	+	12.4140i	−0.142746	+	0.532737i
$544$	0.819909	−	1.42012i	0.0351533	−	0.0608873i
$545$	9.67279	−	35.8797i	0.414337	−	1.53692i
$546$	−14.6318	−	3.19652i	−0.626184	−	0.136799i
$547$	8.59346	−	8.59346i	0.367430	−	0.367430i	−0.499109	−	0.866539i	$-0.666339\pi$
$547$	8.59346	−	8.59346i	0.367430	−	0.367430i	0.866539	+	0.499109i	$0.166339\pi$
$548$	−4.27811	+	1.14632i	−0.182752	+	0.0489682i
$549$	−6.77768	−	11.7393i	−0.289264	−	0.501021i
$550$	−1.62529	−	1.63527i	−0.0693026	−	0.0697280i
$551$	27.9426	+	16.1327i	1.19039	+	0.687275i
$552$	3.11997	+	3.11997i	0.132795	+	0.132795i
$553$	−13.3763	+	0.625324i	−0.568817	+	0.0265915i
$554$			23.5017i			0.998492i
$555$	12.7315	+	12.7705i	0.540421	+	0.542078i
$556$	3.76738	−	2.17510i	0.159772	−	0.0922447i
$557$	−8.24166	−	2.20835i	−0.349210	−	0.0935706i	0.0799502	−	0.996799i	$-0.474524\pi$
$557$	−8.24166	−	2.20835i	−0.349210	−	0.0935706i	−0.429160	+	0.903228i	$0.641191\pi$
$558$	0.00839662	+	0.0313366i	0.000355457	+	0.00132658i
$559$	−38.0378			−1.60883
$560$	−4.36799	−	3.99007i	−0.184581	−	0.168611i
$561$	−0.756144			−0.0319244
$562$	7.36980	+	27.5045i	0.310876	+	1.16021i
$563$	−0.136431	−	0.0365566i	−0.00574988	−	0.00154068i	0.255943	−	0.966692i	$-0.417614\pi$
$563$	−0.136431	−	0.0365566i	−0.00574988	−	0.00154068i	−0.261693	+	0.965151i	$0.584281\pi$
$564$	7.82908	−	4.52012i	0.329664	−	0.190331i
$565$	20.0928	+	0.0307414i	0.845309	+	0.00129330i
$566$		−	3.75788i		−	0.157956i
$567$	2.35056	+	1.21443i	0.0987144	+	0.0510015i
$568$	−6.26410	−	6.26410i	−0.262836	−	0.262836i
$569$	3.62902	+	2.09521i	0.152136	+	0.0878359i	0.574136	−	0.818760i	$-0.305338\pi$
$569$	3.62902	+	2.09521i	0.152136	+	0.0878359i	−0.421999	+	0.906596i	$0.638672\pi$
$570$	−12.5896	+	3.35273i	−0.527319	+	0.140430i
$571$	4.89756	+	8.48282i	0.204957	+	0.354995i	0.950119	−	0.311888i	$-0.100961\pi$
$571$	4.89756	+	8.48282i	0.204957	+	0.354995i	−0.745162	+	0.666883i	$0.767628\pi$
$572$	−2.52131	+	0.675582i	−0.105421	+	0.0282475i
$573$	7.49579	−	7.49579i	0.313141	−	0.313141i
$574$	19.4982	−	21.4107i	0.813840	−	0.893663i
$575$	5.64471	+	21.3272i	0.235401	+	0.889405i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.10542	−	7.85753i	0.0876498	−	0.327113i	−0.908153	−	0.418638i	$-0.862507\pi$
$577$	2.10542	−	7.85753i	0.0876498	−	0.327113i	0.995803	+	0.0915250i	$0.0291741\pi$
$578$	−3.70396	+	13.8234i	−0.154064	+	0.574976i
$579$	3.60804	−	6.24930i	0.149945	−	0.259712i
$580$	11.9559	+	3.22318i	0.496441	+	0.133835i
$581$	0.868963	−	3.97761i	0.0360507	−	0.165019i
$582$	−2.51799	+	2.51799i	−0.104374	+	0.104374i
$583$	−1.22334	+	0.327794i	−0.0506657	+	0.0135758i
$584$	2.02864	+	3.51371i	0.0839459	+	0.145399i
$585$	−6.34566	+	10.9523i	−0.262361	+	0.452821i
$586$	5.12556	+	2.95924i	0.211735	+	0.122245i
$587$	20.3618	+	20.3618i	0.840423	+	0.840423i	0.988914	−	0.148491i	$-0.0474416\pi$
$587$	20.3618	+	20.3618i	0.840423	+	0.840423i	−0.148491	+	0.988914i	$0.547442\pi$
$588$	−1.17303	+	6.90101i	−0.0483749	+	0.284593i
$589$			0.189022i			0.00778852i
$590$	−0.00656028	+	4.28784i	−0.000270083	+	0.176527i
$591$	−11.9144	+	6.87875i	−0.490091	+	0.282954i
$592$	7.78966	+	2.08723i	0.320153	+	0.0857847i
$593$	4.85990	+	18.1374i	0.199572	+	0.744814i	0.991036	+	0.133597i	$0.0426529\pi$
$593$	4.85990	+	18.1374i	0.199572	+	0.744814i	−0.791463	+	0.611217i	$0.790680\pi$
$594$	0.461115			0.0189198
$595$	−8.61209	−	4.46620i	−0.353061	−	0.183096i
$596$	−4.34052			−0.177794
$597$	2.49837	+	9.32405i	0.102251	+	0.381608i
$598$	24.1259	+	6.46450i	0.986580	+	0.264353i
$599$	−21.0442	+	12.1499i	−0.859844	+	0.496431i	−0.863960	−	0.503561i	$-0.832023\pi$
$599$	−21.0442	+	12.1499i	−0.859844	+	0.496431i	0.00411624	+	0.999992i	$0.498690\pi$
$600$	−4.33776	+	2.48674i	−0.177088	+	0.101521i
$601$		−	21.1930i		−	0.864481i	−0.901758	−	0.432241i	$-0.857723\pi$
$601$		−	21.1930i		−	0.864481i	0.901758	−	0.432241i	$-0.142277\pi$
$602$	0.830208	+	17.7589i	0.0338368	+	0.723800i
$603$	2.69424	+	2.69424i	0.109718	+	0.109718i
$604$	7.08854	+	4.09257i	0.288429	+	0.166524i
$605$	−6.20740	−	23.3089i	−0.252367	−	0.947642i
$606$	2.25590	+	3.90734i	0.0916398	+	0.158725i
$607$	9.20949	−	2.46768i	0.373802	−	0.100160i	−0.0670268	−	0.997751i	$-0.521351\pi$
$607$	9.20949	−	2.46768i	0.373802	−	0.100160i	0.440829	+	0.897591i	$0.354685\pi$
$608$	−4.11993	+	4.11993i	−0.167085	+	0.167085i
$609$	−4.44881	−	13.9597i	−0.180275	−	0.565675i
$610$	−15.1152	−	26.2730i	−0.611996	−	1.06376i
$611$	25.5872	−	44.3184i	1.03515	−	1.79293i
$612$	−0.424416	+	1.58394i	−0.0171560	+	0.0640271i
$613$	−5.77664	+	21.5587i	−0.233316	+	0.870748i	0.745585	+	0.666411i	$0.232170\pi$
$613$	−5.77664	+	21.5587i	−0.233316	+	0.870748i	−0.978901	+	0.204337i	$0.934496\pi$
$614$	−12.7905	+	22.1537i	−0.516181	+	0.894051i
$615$	−12.2048	−	21.2142i	−0.492144	−	0.855438i
$616$	0.370443	+	1.16239i	0.0149256	+	0.0468342i
$617$	15.4571	−	15.4571i	0.622278	−	0.622278i	−0.323836	−	0.946113i	$-0.604973\pi$
$617$	15.4571	−	15.4571i	0.622278	−	0.622278i	0.946113	+	0.323836i	$0.104973\pi$
$618$	−14.2719	+	3.82414i	−0.574099	+	0.153829i
$619$	−12.3595	−	21.4073i	−0.496772	−	0.860434i	0.503221	−	0.864158i	$-0.332148\pi$
$619$	−12.3595	−	21.4073i	−0.496772	−	0.860434i	−0.999993	+	0.00372371i	$0.998815\pi$
$620$	0.0186682	+	0.0700994i	0.000749732	+	0.00281526i
$621$	−3.82117	−	2.20615i	−0.153338	−	0.0885299i
$622$	−23.7712	−	23.7712i	−0.953139	−	0.953139i
$623$	1.41200	+	30.2039i	0.0565704	+	1.21009i
$624$			5.66074i			0.226611i
$625$	−24.9995	−	0.152996i	−0.999981	−	0.00611986i
$626$	−19.8878	+	11.4822i	−0.794876	+	0.458922i
$627$	2.59512	+	0.695360i	0.103639	+	0.0277700i
$628$	5.63586	+	21.0333i	0.224895	+	0.839320i
$629$	13.2242			0.527284
$630$	5.25186	+	2.72360i	0.209239	+	0.108511i
$631$	34.7305			1.38260			0.691299	−	0.722569i	$-0.257039\pi$
$631$	34.7305			1.38260			0.691299	+	0.722569i	$0.257039\pi$
$632$	1.30995	+	4.88882i	0.0521072	+	0.194467i
$633$	1.28732	+	0.344935i	0.0511662	+	0.0137099i
$634$	−22.2066	+	12.8210i	−0.881937	+	0.509187i
$635$	−0.0569734	+	37.2381i	−0.00226092	+	1.47775i
$636$			2.74660i			0.108910i
$637$	13.7818	+	37.1513i	0.546056	+	1.47199i
$638$	−1.80562	−	1.80562i	−0.0714850	−	0.0714850i
$639$	7.67192	+	4.42939i	0.303497	+	0.175224i
$640$	−1.12100	+	1.93478i	−0.0443112	+	0.0764788i
$641$	−5.82603	−	10.0910i	−0.230115	−	0.398570i	0.727727	−	0.685867i	$-0.240577\pi$
$641$	−5.82603	−	10.0910i	−0.230115	−	0.398570i	−0.957842	+	0.287297i	$0.907243\pi$
$642$	−5.69821	+	1.52683i	−0.224890	+	0.0602592i
$643$	21.8198	−	21.8198i	0.860489	−	0.860489i	−0.130906	−	0.991395i	$-0.541789\pi$
$643$	21.8198	−	21.8198i	0.860489	−	0.860489i	0.991395	+	0.130906i	$0.0417886\pi$
$644$	2.49155	−	11.4049i	0.0981810	−	0.449415i
$645$	14.5075	+	3.91107i	0.571232	+	0.153998i
$646$	−4.77716	+	8.27429i	−0.187955	+	0.325548i
$647$	9.61474	−	35.8827i	0.377994	−	1.41069i	−0.470926	−	0.882173i	$-0.656080\pi$
$647$	9.61474	−	35.8827i	0.377994	−	1.41069i	0.848920	−	0.528521i	$-0.177253\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	0.442112	−	0.765761i	0.0173544	−	0.0300588i
$650$	−14.2268	+	24.4683i	−0.558021	+	0.959726i
$651$	0.0577930	−	0.0634615i	0.00226509	−	0.00248725i
$652$	−8.25527	+	8.25527i	−0.323301	+	0.323301i
$653$	−30.5404	+	8.18328i	−1.19514	+	0.320237i	−0.800915	−	0.598778i	$-0.795653\pi$
$653$	−30.5404	+	8.18328i	−1.19514	+	0.320237i	−0.394224	+	0.919014i	$0.628987\pi$
$654$	8.30937	+	14.3923i	0.324922	+	0.562782i
$655$	41.0036	−	10.9197i	1.60214	−	0.426667i
$656$	−9.47890	−	5.47265i	−0.370089	−	0.213671i
$657$	−2.86894	−	2.86894i	−0.111928	−	0.111928i
$658$	−21.2497	−	10.9788i	−0.828398	−	0.427997i
$659$		−	38.7284i		−	1.50864i	−0.656504	−	0.754322i	$-0.727966\pi$
$659$		−	38.7284i		−	1.50864i	0.656504	−	0.754322i	$-0.272034\pi$
$660$	1.03108	+	0.00157753i	0.0401348	+	6.14053e-5i
$661$	29.3286	−	16.9329i	1.14075	−	0.658613i	0.194135	−	0.980975i	$-0.437810\pi$
$661$	29.3286	−	16.9329i	1.14075	−	0.658613i	0.946617	+	0.322361i	$0.104477\pi$
$662$	11.4606	+	3.07085i	0.445427	+	0.119352i
$663$	2.40251	+	8.96628i	0.0933057	+	0.348222i
$664$	−1.53885			−0.0597190
$665$	25.4499	+	23.2480i	0.986905	+	0.901519i
$666$	−8.06444			−0.312491
$667$	6.32402	+	23.6016i	0.244867	+	0.913856i
$668$	21.1817	+	5.67563i	0.819546	+	0.219597i
$669$	10.1076	−	5.83564i	0.390784	−	0.225619i
$670$	6.01528	+	6.03372i	0.232391	+	0.233103i
$671$			6.25058i			0.241301i
$672$	2.64286	−	0.123551i	0.101951	−	0.00476607i
$673$	−24.7046	−	24.7046i	−0.952294	−	0.952294i	0.0466190	−	0.998913i	$-0.485155\pi$
$673$	−24.7046	−	24.7046i	−0.952294	−	0.952294i	−0.998913	+	0.0466190i	$0.985155\pi$
$674$	−3.90382	−	2.25387i	−0.150370	−	0.0868159i
$675$	3.54634	−	3.52470i	0.136499	−	0.135666i
$676$	9.52199	+	16.4926i	0.366230	+	0.634330i
$677$	−17.0046	+	4.55637i	−0.653540	+	0.175116i	−0.570329	−	0.821416i	$-0.693184\pi$
$677$	−17.0046	+	4.55637i	−0.653540	+	0.175116i	−0.0832112	+	0.996532i	$0.526518\pi$
$678$	−6.35390	+	6.35390i	−0.244020	+	0.244020i
$679$	9.20437	+	2.01082i	0.353231	+	0.0771683i
$680$	−0.954441	+	3.54035i	−0.0366011	+	0.135766i
$681$	−11.1813	+	19.3666i	−0.428469	+	0.742129i
$682$	0.00387180	−	0.0144498i	0.000148259	−	0.000553310i
$683$	−6.25658	+	23.3499i	−0.239401	+	0.893458i	0.736714	+	0.676205i	$0.236377\pi$
$683$	−6.25658	+	23.3499i	−0.239401	+	0.893458i	−0.976115	+	0.217254i	$0.930290\pi$
$684$	2.91323	−	5.04586i	0.111390	−	0.192933i
$685$	8.58433	−	4.93867i	0.327991	−	0.188697i
$686$	17.0442	−	7.24527i	0.650752	−	0.276626i
$687$	3.51165	−	3.51165i	0.133978	−	0.133978i
$688$	6.49061	−	1.73915i	0.247452	−	0.0663046i
$689$	7.77390	+	13.4648i	0.296162	+	0.512968i
$690$	−8.53684	−	4.94618i	−0.324992	−	0.188298i
$691$	−2.56844	−	1.48289i	−0.0977081	−	0.0564118i	0.450350	−	0.892852i	$-0.351299\pi$
$691$	−2.56844	−	1.48289i	−0.0977081	−	0.0564118i	−0.548058	+	0.836440i	$0.684633\pi$
$692$	6.89034	+	6.89034i	0.261931	+	0.261931i
$693$	−0.658670	−	1.02691i	−0.0250208	−	0.0390090i
$694$			21.4221i			0.813172i
$695$	−6.88878	+	6.86773i	−0.261306	+	0.260508i
$696$	−4.79581	+	2.76886i	−0.181785	+	0.104953i
$697$	−17.3367	−	4.64536i	−0.656675	−	0.175955i
$698$	−4.15876	−	15.5207i	−0.157412	−	0.587468i
$699$	−28.6338			−1.08303
$700$	11.7342	+	6.10811i	0.443510	+	0.230865i
$701$	−18.6815			−0.705591			−0.352795	−	0.935701i	$-0.614769\pi$
$701$	−18.6815			−0.705591			−0.352795	+	0.935701i	$0.614769\pi$
$702$	−1.46511	−	5.46786i	−0.0552969	−	0.206371i
$703$	−45.3861	−	12.1612i	−1.71177	−	0.458667i
$704$	0.399337	−	0.230557i	0.0150506	−	0.00868946i
$705$	−14.3157	+	14.2720i	−0.539161	+	0.537514i
$706$		−	29.3960i		−	1.10633i
$707$	5.47930	−	10.6053i	0.206070	−	0.398853i
$708$	−1.35593	−	1.35593i	−0.0509592	−	0.0509592i
$709$	18.3186	+	10.5763i	0.687971	+	0.397200i	0.802851	−	0.596179i	$-0.203315\pi$
$709$	18.3186	+	10.5763i	0.687971	+	0.397200i	−0.114880	+	0.993379i	$0.536649\pi$
$710$	17.1398	+	9.93064i	0.643244	+	0.372690i
$711$	−2.53064	−	4.38319i	−0.0949063	−	0.164383i
$712$	11.0391	−	2.95790i	0.413706	−	0.110852i
$713$	−0.101218	+	0.101218i	−0.00379065	+	0.00379065i
$714$	4.13371	−	1.31737i	0.154700	−	0.0493014i
$715$	5.05919	−	2.91061i	0.189203	−	0.108851i
$716$	−0.807576	+	1.39876i	−0.0301805	+	0.0522742i
$717$	3.60353	−	13.4486i	0.134576	−	0.502246i
$718$	3.52703	−	13.1630i	0.131628	−	0.491241i
$719$	4.30625	−	7.45864i	0.160596	−	0.278160i	−0.774487	−	0.632590i	$-0.781992\pi$
$719$	4.30625	−	7.45864i	0.160596	−	0.278160i	0.935083	+	0.354430i	$0.115325\pi$
$720$	0.582041	−	2.15899i	0.0216914	−	0.0804607i
$721$	28.9028	+	26.3211i	1.07640	+	0.980251i
$722$	10.5696	−	10.5696i	0.393359	−	0.393359i
$723$	1.02153	−	0.273719i	0.0379912	−	0.0101797i
$724$	−6.42597	−	11.1301i	−0.238819	−	0.413647i
$725$	−27.6885	−	0.0847256i	−1.02832	−	0.00314663i
$726$	9.34214	+	5.39369i	0.346719	+	0.200178i
$727$	12.8013	+	12.8013i	0.474774	+	0.474774i	0.903455	−	0.428682i	$-0.141022\pi$
$727$	12.8013	+	12.8013i	0.474774	+	0.474774i	−0.428682	+	0.903455i	$0.641022\pi$
$728$	12.6065	−	8.08597i	0.467230	−	0.299686i
$729$			1.00000i			0.0370370i
$730$	−6.40531	−	6.42494i	−0.237071	−	0.237798i
$731$	9.54263	−	5.50944i	0.352947	−	0.203774i
$732$	13.0935	+	3.50839i	0.483949	+	0.129674i
$733$	−8.56107	−	31.9503i	−0.316210	−	1.18011i	−0.922857	−	0.385142i	$-0.874153\pi$
$733$	−8.56107	−	31.9503i	−0.316210	−	1.18011i	0.606647	−	0.794971i	$-0.292514\pi$
$734$	12.7591			0.470947
$735$	−1.43643	−	15.5864i	−0.0529836	−	0.574914i
$736$	−4.41231			−0.162640
$737$	−0.454733	−	1.69709i	−0.0167503	−	0.0625130i
$738$	10.5723	+	2.83285i	0.389173	+	0.104279i
$739$	−40.9779	+	23.6586i	−1.50740	+	0.870296i	−0.507434	+	0.861690i	$0.669406\pi$
$739$	−40.9779	+	23.6586i	−1.50740	+	0.870296i	−0.999963	+	0.00860599i	$0.997261\pi$
$740$	−18.0326	−	0.0275895i	−0.662892	−	0.00101421i
$741$		−	32.9821i		−	1.21163i
$742$	6.11672	−	3.92333i	0.224552	−	0.144030i
$743$	−21.5587	−	21.5587i	−0.790914	−	0.790914i	0.190729	−	0.981643i	$-0.438915\pi$
$743$	−21.5587	−	21.5587i	−0.790914	−	0.790914i	−0.981643	+	0.190729i	$0.938915\pi$
$744$	−0.0280956	−	0.0162210i	−0.00103004	−	0.000594691i
$745$	9.37881	−	2.49767i	0.343613	−	0.0915076i
$746$	−2.00068	−	3.46527i	−0.0732500	−	0.126873i
$747$	1.48642	−	0.398284i	0.0543851	−	0.0145724i
$748$	0.534674	−	0.534674i	0.0195496	−	0.0195496i
$749$	11.5398	+	10.5090i	0.421654	+	0.383991i
$750$	7.94190	−	7.86932i	0.289997	−	0.287347i
$751$	−15.5069	+	26.8587i	−0.565854	+	0.980088i	0.431116	+	0.902297i	$0.358120\pi$
$751$	−15.5069	+	26.8587i	−0.565854	+	0.980088i	−0.996970	+	0.0777911i	$0.975213\pi$
$752$	−2.33979	+	8.73220i	−0.0853232	+	0.318431i
$753$	−1.64676	+	6.14580i	−0.0600114	+	0.223965i
$754$	−15.6738	+	27.1478i	−0.570807	+	0.988666i
$755$	−17.6716	−	4.76409i	−0.643136	−	0.173383i
$756$	−2.52083	+	0.803365i	−0.0916819	+	0.0292181i
$757$	−16.7486	+	16.7486i	−0.608738	+	0.608738i	−0.942616	−	0.333879i	$-0.891642\pi$
$757$	−16.7486	+	16.7486i	−0.608738	+	0.608738i	0.333879	+	0.942616i	$0.391642\pi$
$758$	0.968641	−	0.259546i	0.0351826	−	0.00942715i
$759$	1.01729	+	1.76200i	0.0369253	+	0.0639564i
$760$	6.53143	−	11.2729i	0.236920	−	0.408911i
$761$	−14.7359	−	8.50777i	−0.534175	−	0.308406i	0.208540	−	0.978014i	$-0.433129\pi$
$761$	−14.7359	−	8.50777i	−0.534175	−	0.308406i	−0.742715	+	0.669608i	$0.766462\pi$
$762$	−11.7757	−	11.7757i	−0.426590	−	0.426590i
$763$	20.1824	−	39.0634i	0.730651	−	1.41419i
$764$			10.6007i			0.383518i
$765$	0.00561002	−	3.66674i	0.000202831	−	0.132571i
$766$	15.4180	−	8.90158i	0.557075	−	0.321627i
$767$	−10.4851	−	2.80946i	−0.378593	−	0.101444i
$768$	−0.258819	−	0.965926i	−0.00933933	−	0.0348548i
$769$	7.70275			0.277768			0.138884	−	0.990309i	$-0.455648\pi$
$769$	7.70275			0.277768			0.138884	+	0.990309i	$0.455648\pi$
$770$	−1.46932	−	2.29849i	−0.0529505	−	0.0828317i
$771$	10.3811			0.373865
$772$	1.86766	+	6.97019i	0.0672185	+	0.250863i
$773$	2.92305	+	0.783229i	0.105135	+	0.0281708i	0.311003	−	0.950409i	$-0.399335\pi$
$773$	2.92305	+	0.783229i	0.105135	+	0.0281708i	−0.205868	+	0.978580i	$0.566002\pi$
$774$	−5.81932	+	3.35979i	−0.209171	+	0.120765i
$775$	−0.0806748	−	0.140726i	−0.00289793	−	0.00505501i
$776$		−	3.56097i		−	0.127832i
$777$	11.5195	+	17.9596i	0.413260	+	0.644298i
$778$	−7.96110	−	7.96110i	−0.285419	−	0.285419i
$779$	55.2284	+	31.8862i	1.97876	+	1.14244i
$780$	−3.25737	−	12.2315i	−0.116633	−	0.437958i
$781$	−2.04245	−	3.53763i	−0.0730848	−	0.126587i
$782$	−6.98884	+	1.87265i	−0.249920	+	0.0669660i
$783$	3.91576	−	3.91576i	0.139938	−	0.139938i
$784$	−4.05030	−	5.70921i	−0.144654	−	0.203900i
$785$	−24.2810	−	42.2048i	−0.866624	−	1.50636i
$786$	−9.48825	+	16.4341i	−0.338435	+	0.586186i
$787$	−5.80155	+	21.6517i	−0.206803	+	0.771799i	0.782089	+	0.623166i	$0.214154\pi$
$787$	−5.80155	+	21.6517i	−0.206803	+	0.771799i	−0.988892	+	0.148633i	$0.952513\pi$
$788$	3.56071	−	13.2887i	0.126845	−	0.473392i
$789$	11.8810	−	20.5785i	0.422974	−	0.732613i
$790$	−5.64368	−	9.80976i	−0.200793	−	0.349016i
$791$	23.2263	+	5.07411i	0.825833	+	0.180415i
$792$	−0.326057	+	0.326057i	−0.0115859	+	0.0115859i
$793$	74.1188	−	19.8601i	2.63203	−	0.705252i
$794$	−1.91642	−	3.31933i	−0.0680112	−	0.117799i
$795$	−1.58048	−	5.93474i	−0.0560539	−	0.210484i
$796$	−8.35971	−	4.82648i	−0.296302	−	0.171070i
$797$	−21.8939	−	21.8939i	−0.775520	−	0.775520i	0.203545	−	0.979066i	$-0.434754\pi$
$797$	−21.8939	−	21.8939i	−0.775520	−	0.775520i	−0.979066	+	0.203545i	$0.934754\pi$
$798$	−15.3985	+	0.719863i	−0.545103	+	0.0254829i
$799$			14.8243i			0.524447i
$800$	1.30887	−	4.82565i	0.0462755	−	0.170612i
$801$	−9.89734	+	5.71423i	−0.349705	+	0.201903i
$802$	−0.869376	−	0.232949i	−0.0306987	−	0.00822570i
$803$	0.484218	+	1.80713i	0.0170877	+	0.0637721i
$804$	−3.81023			−0.134377
$805$	1.17908	+	26.0769i	0.0415572	+	0.919091i
$806$	−0.183646			−0.00646865
$807$	−0.367542	−	1.37168i	−0.0129381	−	0.0482856i
$808$	−4.35807	−	1.16774i	−0.153316	−	0.0410810i
$809$	−0.938781	+	0.542005i	−0.0330058	+	0.0190559i	−0.516412	−	0.856340i	$-0.672733\pi$
$809$	−0.938781	+	0.542005i	−0.0330058	+	0.0190559i	0.483406	+	0.875396i	$0.339399\pi$
$810$	−0.00342112	+	2.23607i	−0.000120206	+	0.0785673i
$811$		−	33.8754i		−	1.18953i	−0.803901	−	0.594763i	$-0.797246\pi$
$811$		−	33.8754i		−	1.18953i	0.803901	−	0.594763i	$-0.202754\pi$
$812$	13.0168	+	6.72520i	0.456799	+	0.236008i
$813$	−0.250034	−	0.250034i	−0.00876907	−	0.00876907i
$814$	3.22043	+	1.85932i	0.112876	+	0.0651690i
$815$	13.0873	−	22.5880i	0.458428	−	0.791223i
$816$	−0.819909	−	1.42012i	−0.0287025	−	0.0497143i
$817$	−37.8173	+	10.1331i	−1.32306	+	0.354513i
$818$	−9.11649	+	9.11649i	−0.318751	+	0.318751i
$819$	−10.0842	+	11.0733i	−0.352370	+	0.386931i
$820$	23.6308	+	6.37061i	0.825222	+	0.222471i
$821$	−2.43319	+	4.21441i	−0.0849190	+	0.147084i	−0.905357	−	0.424652i	$-0.860396\pi$
$821$	−2.43319	+	4.21441i	−0.0849190	+	0.147084i	0.820438	+	0.571736i	$0.193730\pi$
$822$	−1.14632	+	4.27811i	−0.0399823	+	0.149216i
$823$	−8.98921	+	33.5482i	−0.313344	+	1.16942i	0.612177	+	0.790720i	$0.290294\pi$
$823$	−8.98921	+	33.5482i	−0.313344	+	1.16942i	−0.925521	+	0.378695i	$0.876373\pi$
$824$	7.38767	−	12.7958i	0.257362	−	0.445763i
$825$	−2.22883	+	0.589909i	−0.0775978	+	0.0205380i
$826$	−1.08283	+	4.95654i	−0.0376763	+	0.172460i
$827$	−38.4936	+	38.4936i	−1.33855	+	1.33855i	−0.441093	+	0.897461i	$0.645409\pi$
$827$	−38.4936	+	38.4936i	−1.33855	+	1.33855i	−0.897461	+	0.441093i	$0.854591\pi$
$828$	4.26196	−	1.14199i	0.148113	−	0.0396869i
$829$	−20.0652	−	34.7540i	−0.696895	−	1.20706i	−0.969538	−	0.244942i	$-0.921231\pi$
$829$	−20.0652	−	34.7540i	−0.696895	−	1.20706i	0.272643	−	0.962115i	$-0.412102\pi$
$830$	3.32509	−	0.885504i	0.115415	−	0.0307363i
$831$	20.3531	+	11.7509i	0.706041	+	0.407633i
$832$	−4.00275	−	4.00275i	−0.138770	−	0.138770i
$833$	−8.83852	−	7.32405i	−0.306236	−	0.253763i
$834$		−	4.35020i		−	0.150635i
$835$	−49.0346	−	0.0750217i	−1.69691	−	0.00259623i
$836$	−2.32672	+	1.34333i	−0.0804713	+	0.0464601i
$837$	0.0313366	+	0.00839662i	0.00108315	+	0.000290229i
$838$	−5.14837	−	19.2140i	−0.177848	−	0.663736i
$839$	27.8082			0.960044			0.480022	−	0.877256i	$-0.340629\pi$
$839$	27.8082			0.960044			0.480022	+	0.877256i	$0.340629\pi$
$840$	−5.63950	+	1.78775i	−0.194581	+	0.0616833i
$841$	−1.66640			−0.0574621
$842$	−3.26990	−	12.2034i	−0.112688	−	0.420558i
$843$	27.5045	+	7.36980i	0.947305	+	0.253830i
$844$	−1.15418	+	0.666364i	−0.0397284	+	0.0229372i
$845$	−30.0651	−	30.1572i	−1.03427	−	1.03744i
$846$		−	9.04024i		−	0.310810i
$847$	−1.33279	−	28.5096i	−0.0457951	−	0.979600i
$848$	−1.94214	−	1.94214i	−0.0666934	−	0.0666934i
$849$	−3.25442	−	1.87894i	−0.111691	−	0.0644851i
$850$	0.0250887	−	8.19905i	0.000860536	−	0.281225i
$851$	−17.7914	−	30.8156i	−0.609881	−	1.05635i
$852$	−8.55692	+	2.29282i	−0.293155	+	0.0785507i
$853$	−19.0929	+	19.0929i	−0.653729	+	0.653729i	−0.953889	−	0.300160i	$-0.902960\pi$
$853$	−19.0929	+	19.0929i	−0.653729	+	0.653729i	0.300160	+	0.953889i	$0.402960\pi$
$854$	−10.8899	−	34.1708i	−0.372645	−	1.16930i
$855$	−3.39124	+	12.5793i	−0.115978	+	0.430201i
$856$	2.94961	−	5.10888i	0.100816	−	0.174618i
$857$	−5.27688	+	19.6936i	−0.180255	+	0.672720i	0.815342	+	0.578980i	$0.196549\pi$
$857$	−5.27688	+	19.6936i	−0.180255	+	0.672720i	−0.995597	+	0.0937404i	$0.970118\pi$
$858$	−0.675582	+	2.52131i	−0.0230640	+	0.0860760i
$859$	2.24170	−	3.88275i	0.0764860	−	0.132478i	−0.825246	−	0.564774i	$-0.808963\pi$
$859$	2.24170	−	3.88275i	0.0764860	−	0.132478i	0.901732	+	0.432297i	$0.142297\pi$
$860$	−13.0239	+	7.49280i	−0.444111	+	0.255502i
$861$	−8.79306	−	27.5913i	−0.299667	−	0.940308i
$862$	21.7578	−	21.7578i	0.741073	−	0.741073i
$863$	18.9773	−	5.08496i	0.645996	−	0.173094i	0.0790782	−	0.996868i	$-0.474802\pi$
$863$	18.9773	−	5.08496i	0.645996	−	0.173094i	0.566918	+	0.823774i	$0.308136\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−18.8533	−	10.9234i	−0.641031	−	0.371408i
$866$	3.73232	+	2.15486i	0.126829	+	0.0732250i
$867$	10.1194	+	10.1194i	0.343673	+	0.343673i
$868$	0.00400824	+	0.0857399i	0.000136048	+	0.00291020i
$869$			2.33383i			0.0791697i
$870$	8.76930	−	8.74251i	0.297307	−	0.296399i
$871$	−18.6791	+	10.7844i	−0.632916	+	0.365414i
$872$	−16.0525	−	4.30125i	−0.543605	−	0.145659i
$873$	0.921648	+	3.43964i	0.0311931	+	0.116414i
$874$	25.7081			0.869590
$875$	−28.8695	−	6.44592i	−0.975968	−	0.217912i
$876$	4.05729			0.137083
$877$	3.48618	+	13.0106i	0.117720	+	0.439337i	0.999476	−	0.0323688i	$-0.0103051\pi$
$877$	3.48618	+	13.0106i	0.117720	+	0.439337i	−0.881756	+	0.471706i	$0.843638\pi$
$878$	−35.7380	−	9.57597i	−1.20610	−	0.323173i
$879$	5.12556	−	2.95924i	0.172881	−	0.0998127i
$880$	−0.730201	+	0.727970i	−0.0246151	+	0.0245399i
$881$			55.0357i			1.85420i	0.374813	+	0.927100i	$0.377707\pi$
$881$			55.0357i			1.85420i	−0.374813	+	0.927100i	$0.622293\pi$
$882$	5.38994	+	4.46638i	0.181489	+	0.150391i
$883$	3.82147	+	3.82147i	0.128603	+	0.128603i	0.768478	−	0.639876i	$-0.221014\pi$
$883$	3.82147	+	3.82147i	0.128603	+	0.128603i	−0.639876	+	0.768478i	$0.721014\pi$
$884$	−8.03895	−	4.64129i	−0.270379	−	0.156103i
$885$	3.71010	+	2.14960i	0.124714	+	0.0722580i
$886$	8.89875	+	15.4131i	0.298960	+	0.517813i
$887$	−22.1111	+	5.92466i	−0.742419	+	0.198931i	−0.610153	−	0.792284i	$-0.708892\pi$
$887$	−22.1111	+	5.92466i	−0.742419	+	0.198931i	−0.132266	+	0.991214i	$0.542225\pi$
$888$	5.70242	−	5.70242i	0.191361	−	0.191361i
$889$	−9.40390	+	43.0455i	−0.315397	+	1.44370i
$890$	−22.1507	+	12.7435i	−0.742492	+	0.427164i
$891$	0.230557	−	0.399337i	0.00772396	−	0.0133783i
$892$	−3.02075	+	11.2736i	−0.101142	+	0.377468i
$893$	13.6327	−	50.8778i	0.456200	−	1.70256i
$894$	−2.17026	+	3.75900i	−0.0725843	+	0.125720i
$895$	0.940085	−	3.48710i	0.0314236	−	0.116561i
$896$	−1.78142	+	1.95615i	−0.0595132	+	0.0653504i
$897$	17.6614	−	17.6614i	0.589695	−	0.589695i
$898$	2.33701	−	0.626200i	0.0779870	−	0.0208966i
$899$	−0.0898275	−	0.155586i	−0.00299592	−	0.00518908i
$900$	−0.0152997	+	4.99998i	−0.000509990	+	0.166666i
$901$	−3.90051	−	2.25196i	−0.129945	−	0.0750237i
$902$	−3.56879	−	3.56879i	−0.118828	−	0.118828i
$903$	15.7948	+	8.16049i	0.525618	+	0.271564i
$904$		−	8.98577i		−	0.298862i
$905$	20.2896	+	20.3518i	0.674449	+	0.676516i
$906$	7.08854	−	4.09257i	0.235501	−	0.135967i
$907$	−26.4300	−	7.08190i	−0.877595	−	0.235151i	−0.208226	−	0.978081i	$-0.566769\pi$
$907$	−26.4300	−	7.08190i	−0.877595	−	0.235151i	−0.669369	+	0.742930i	$0.733435\pi$
$908$	−5.78787	−	21.6006i	−0.192077	−	0.716842i
$909$	4.51181			0.149647
$910$	−22.5868	+	24.7260i	−0.748744	+	0.819660i
$911$	−55.5763			−1.84132			−0.920662	−	0.390360i	$-0.872350\pi$
$911$	−55.5763			−1.84132			−0.920662	+	0.390360i	$0.872350\pi$
$912$	1.50800	+	5.62793i	0.0499348	+	0.186359i
$913$	−0.685408	−	0.183655i	−0.0226837	−	0.00607808i
$914$	23.8666	−	13.7794i	0.789438	−	0.455782i
$915$	−30.3107	−	0.0463746i	−1.00204	−	0.00153310i
$916$			4.96622i			0.164088i
$917$	50.1523	−	2.34456i	1.65618	−	0.0774242i
$918$	1.15953	+	1.15953i	0.0382701	+	0.0382701i
$919$	17.4296	+	10.0630i	0.574948	+	0.331947i	0.759123	−	0.650947i	$-0.225628\pi$
$919$	17.4296	+	10.0630i	0.574948	+	0.331947i	−0.184175	+	0.982893i	$0.558961\pi$
$920$	9.53393	−	2.53898i	0.314324	−	0.0837077i
$921$	12.7905	+	22.1537i	0.421460	+	0.729990i
$922$	0.992122	−	0.265838i	0.0326738	−	0.00875492i
$923$	−35.4594	+	35.4594i	−1.16716	+	1.16716i
$924$	1.19188	+	0.260384i	0.0392101	+	0.00856599i
$925$	38.9800	−	10.3169i	1.28166	−	0.339219i
$926$	5.84429	−	10.1226i	0.192055	−	0.332650i
$927$	−3.82414	+	14.2719i	−0.125601	+	0.468750i
$928$	1.43327	−	5.34903i	0.0470494	−	0.175591i
$929$	13.0112	−	22.5360i	0.426883	−	0.739383i	−0.569711	−	0.821845i	$-0.692945\pi$
$929$	13.0112	−	22.5360i	0.426883	−	0.739383i	0.996594	+	0.0824618i	$0.0262782\pi$
$930$	0.0700419	+	0.0188826i	0.00229677	+	0.000619184i
$931$	23.5989	+	33.2645i	0.773423	+	1.09020i
$932$	20.2472	−	20.2472i	0.663218	−	0.663218i
$933$	−32.4721	+	8.70087i	−1.06309	+	0.284854i
$934$	−9.27239	−	16.0603i	−0.303402	−	0.525508i
$935$	−0.847634	+	1.46297i	−0.0277206	+	0.0478443i
$936$	4.90235	+	2.83037i	0.160238	+	0.0925135i
$937$	−17.1515	−	17.1515i	−0.560314	−	0.560314i	0.369082	−	0.929397i	$-0.379672\pi$
$937$	−17.1515	−	17.1515i	−0.560314	−	0.560314i	−0.929397	+	0.369082i	$0.879672\pi$
$938$	5.44265	+	8.48544i	0.177709	+	0.277059i
$939$			22.9644i			0.749416i
$940$	0.0309278	−	20.2146i	0.00100875	−	0.659326i
$941$	14.4025	−	8.31531i	0.469509	−	0.271071i	−0.246525	−	0.969136i	$-0.579289\pi$
$941$	14.4025	−	8.31531i	0.469509	−	0.271071i	0.716034	+	0.698065i	$0.245955\pi$
$942$	21.0333	+	5.63586i	0.685302	+	0.183626i
$943$	12.4994	+	46.6484i	0.407037	+	1.51908i
$944$	1.91758			0.0624120
$945$	4.98463	−	3.18645i	0.162150	−	0.103655i
$946$	3.09849			0.100741
$947$	−7.68510	−	28.6812i	−0.249732	−	0.932013i	−0.970946	−	0.239300i	$-0.923082\pi$
$947$	−7.68510	−	28.6812i	−0.249732	−	0.932013i	0.721213	−	0.692713i	$-0.243585\pi$
$948$	4.88882	+	1.30995i	0.158781	+	0.0425453i
$949$	19.8902	−	11.4836i	0.645664	−	0.372774i
$950$	−7.62606	+	28.1164i	−0.247422	+	0.912218i
$951$			25.6420i			0.831498i
$952$	−1.99145	+	3.85450i	−0.0645433	+	0.124925i
$953$	−30.9752	−	30.9752i	−1.00339	−	1.00339i	−0.999994	−	0.00339090i	$-0.998921\pi$
$953$	−30.9752	−	30.9752i	−1.00339	−	1.00339i	−0.00339090	−	0.999994i	$-0.501079\pi$
$954$	2.37863	+	1.37330i	0.0770109	+	0.0444622i
$955$	−6.09995	−	22.9055i	−0.197390	−	0.741203i
$956$	6.96149	+	12.0577i	0.225151	+	0.389973i
$957$	−2.46652	+	0.660901i	−0.0797312	+	0.0213639i
$958$	−5.99446	+	5.99446i	−0.193672	+	0.193672i
$959$	11.1648	−	3.55812i	0.360531	−	0.114898i
$960$	1.11507	+	1.93820i	0.0359887	+	0.0625551i
$961$	−15.4995	+	26.8459i	−0.499983	+	0.865996i
$962$	11.8153	−	44.0952i	0.380940	−	1.42169i
$963$	−1.52683	+	5.69821i	−0.0492014	+	0.183622i
$964$	−0.528784	+	0.915881i	−0.0170310	+	0.0294985i
$965$	−8.04643	−	13.9862i	−0.259024	−	0.450232i
$966$	−8.63114	−	7.86019i	−0.277702	−	0.252897i
$967$	−9.23140	+	9.23140i	−0.296862	+	0.296862i	−0.839783	−	0.542922i	$-0.817318\pi$
$967$	−9.23140	+	9.23140i	−0.296862	+	0.296862i	0.542922	+	0.839783i	$0.317318\pi$
$968$	−10.4198	+	2.79198i	−0.334905	+	0.0897376i
$969$	4.77716	+	8.27429i	0.153465	+	0.265809i
$970$	2.04910	+	7.69441i	0.0657926	+	0.247053i
$971$	21.1712	+	12.2232i	0.679416	+	0.392261i	0.799635	−	0.600486i	$-0.205026\pi$
$971$	21.1712	+	12.2232i	0.679416	+	0.392261i	−0.120219	+	0.992747i	$0.538360\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−9.68794	+	6.21395i	−0.310581	+	0.199210i
$974$			4.85631i			0.155606i
$975$	14.0768	+	24.5549i	0.450818	+	0.786387i
$976$	−11.7393	+	6.77768i	−0.375766	+	0.216948i
$977$	27.0527	+	7.24876i	0.865493	+	0.231908i	0.664138	−	0.747610i	$-0.268799\pi$
$977$	27.0527	+	7.24876i	0.865493	+	0.231908i	0.201355	+	0.979518i	$0.435465\pi$
$978$	3.02164	+	11.2769i	0.0966213	+	0.360596i
$979$	5.26983			0.168425
$980$	12.0370	+	10.0056i	0.384507	+	0.319616i
$981$	16.6187			0.530596
$982$	−9.79874	−	36.5694i	−0.312690	−	1.16698i
$983$	39.8535	+	10.6787i	1.27113	+	0.340598i	0.830463	−	0.557073i	$-0.188076\pi$
$983$	39.8535	+	10.6787i	1.27113	+	0.340598i	0.440666	+	0.897671i	$0.354742\pi$
$984$	−9.47890	+	5.47265i	−0.302176	+	0.174462i
$985$	−0.0470661	+	30.7627i	−0.00149965	+	0.980181i
$986$		−	9.08086i		−	0.289193i
$987$	−20.1327	+	12.9134i	−0.640832	+	0.411037i
$988$	23.3218	+	23.3218i	0.741967	+	0.741967i
$989$	−25.6766	−	14.8244i	−0.816470	−	0.471389i
$990$	0.516907	−	0.892155i	0.0164284	−	0.0283545i
$991$	18.1824	+	31.4928i	0.577582	+	1.00040i	0.995756	+	0.0920347i	$0.0293371\pi$
$991$	18.1824	+	31.4928i	0.577582	+	1.00040i	−0.418173	+	0.908367i	$0.637330\pi$
$992$	0.0313366	−	0.00839662i	0.000994938	−	0.000266593i
$993$	8.38971	−	8.38971i	0.266240	−	0.266240i
$994$	17.3291	+	15.7812i	0.549646	+	0.500550i
$995$	20.8406	+	5.61842i	0.660692	+	0.178116i
$996$	−0.769426	+	1.33268i	−0.0243802	+	0.0422277i
$997$	−4.64972	+	17.3530i	−0.147258	+	0.549575i	0.852386	+	0.522912i	$0.175155\pi$
$997$	−4.64972	+	17.3530i	−0.147258	+	0.549575i	−0.999644	+	0.0266623i	$0.991512\pi$
$998$	0.132566	−	0.494743i	0.00419631	−	0.0156608i
$999$	−4.03222	+	6.98401i	−0.127574	+	0.220964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.a.103.4	✓	16
3.2	odd	2		630.2.bv.a.523.1		16
5.2	odd	4		210.2.u.b.187.1	yes	16
5.3	odd	4		1050.2.bc.g.607.3		16
5.4	even	2		1050.2.bc.h.943.1		16
7.2	even	3		1470.2.m.d.1273.5		16
7.3	odd	6		210.2.u.b.73.1	yes	16
7.5	odd	6		1470.2.m.e.1273.8		16
15.2	even	4		630.2.bv.b.397.4		16
21.17	even	6		630.2.bv.b.73.4		16
35.2	odd	12		1470.2.m.e.97.8		16
35.3	even	12		1050.2.bc.h.157.1		16
35.12	even	12		1470.2.m.d.97.5		16
35.17	even	12	inner	210.2.u.a.157.4	yes	16
35.24	odd	6		1050.2.bc.g.493.3		16
105.17	odd	12		630.2.bv.a.577.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.4	✓	16	1.1	even	1	trivial
210.2.u.a.157.4	yes	16	35.17	even	12	inner
210.2.u.b.73.1	yes	16	7.3	odd	6
210.2.u.b.187.1	yes	16	5.2	odd	4
630.2.bv.a.523.1		16	3.2	odd	2
630.2.bv.a.577.1		16	105.17	odd	12
630.2.bv.b.73.4		16	21.17	even	6
630.2.bv.b.397.4		16	15.2	even	4
1050.2.bc.g.493.3		16	35.24	odd	6
1050.2.bc.g.607.3		16	5.3	odd	4
1050.2.bc.h.157.1		16	35.3	even	12
1050.2.bc.h.943.1		16	5.4	even	2
1470.2.m.d.97.5		16	35.12	even	12
1470.2.m.d.1273.5		16	7.2	even	3
1470.2.m.e.97.8		16	35.2	odd	12
1470.2.m.e.1273.8		16	7.5	odd	6

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.58356 - 1.57872i) q^{5} +1.00000i q^{6} +(2.22701 - 1.42843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.58356 - 1.57872i) q^{5} +1.00000i q^{6} +(2.22701 - 1.42843i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.93478 + 1.12100i) q^{10} +(-0.230557 - 0.399337i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-4.00275 + 4.00275i) q^{13} +(1.95615 + 1.78142i) q^{14} +(1.93820 - 1.11507i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.424416 - 1.58394i) q^{17} +(-0.258819 + 0.965926i) q^{18} +(-2.91323 + 5.04586i) q^{19} +(-0.582041 + 2.15899i) q^{20} +(2.52083 - 0.803365i) q^{21} +(0.326057 - 0.326057i) q^{22} +(-4.26196 + 1.14199i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.0152997 - 4.99998i) q^{25} +(-4.90235 - 2.83037i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.21443 + 2.35056i) q^{28} -5.53773i q^{29} +(1.57872 + 1.58356i) q^{30} +(0.0280956 - 0.0162210i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.119345 - 0.445403i) q^{33} +1.63982 q^{34} +(1.27151 - 5.77782i) q^{35} -1.00000 q^{36} +(2.08723 + 7.78966i) q^{37} +(-5.62793 - 1.50800i) q^{38} +(-4.90235 + 2.83037i) q^{39} +(-2.23607 - 0.00342112i) q^{40} -10.9453i q^{41} +(1.42843 + 2.22701i) q^{42} +(4.75146 + 4.75146i) q^{43} +(0.399337 + 0.230557i) q^{44} +(2.16076 - 0.575432i) q^{45} +(-2.20615 - 3.82117i) q^{46} +(-8.73220 + 2.33979i) q^{47} +(0.707107 - 0.707107i) q^{48} +(2.91917 - 6.36227i) q^{49} +(4.83357 - 1.27931i) q^{50} +(0.819909 - 1.42012i) q^{51} +(1.46511 - 5.46786i) q^{52} +(0.710873 - 2.65301i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-0.995541 - 0.268388i) q^{55} +(-2.58479 - 0.564683i) q^{56} +(-4.11993 + 4.11993i) q^{57} +(5.34903 - 1.43327i) q^{58} +(0.958791 + 1.66067i) q^{59} +(-1.12100 + 1.93478i) q^{60} +(-11.7393 - 6.77768i) q^{61} +(0.0229400 + 0.0229400i) q^{62} +(2.64286 - 0.123551i) q^{63} +1.00000i q^{64} +(-0.0193661 + 12.6578i) q^{65} +(0.399337 - 0.230557i) q^{66} +(3.68040 + 0.986161i) q^{67} +(0.424416 + 1.58394i) q^{68} -4.41231 q^{69} +(5.91004 - 0.267226i) q^{70} +8.85877 q^{71} +(-0.258819 - 0.965926i) q^{72} +(-3.91904 - 1.05010i) q^{73} +(-6.98401 + 4.03222i) q^{74} +(1.30887 - 4.82565i) q^{75} -5.82646i q^{76} +(-1.08388 - 0.559993i) q^{77} +(-4.00275 - 4.00275i) q^{78} +(-4.38319 - 2.53064i) q^{79} +(-0.575432 - 2.16076i) q^{80} +(0.500000 + 0.866025i) q^{81} +(10.5723 - 2.83285i) q^{82} +(1.08813 - 1.08813i) q^{83} +(-1.78142 + 1.95615i) q^{84} +(-1.82851 - 3.17829i) q^{85} +(-3.35979 + 5.81932i) q^{86} +(1.43327 - 5.34903i) q^{87} +(-0.119345 + 0.445403i) q^{88} +(-5.71423 + 9.89734i) q^{89} +(1.11507 + 1.93820i) q^{90} +(-3.19652 + 14.6318i) q^{91} +(3.11997 - 3.11997i) q^{92} +(0.0313366 - 0.00839662i) q^{93} +(-4.52012 - 7.82908i) q^{94} +(3.35273 + 12.5896i) q^{95} +(0.866025 + 0.500000i) q^{96} +(2.51799 + 2.51799i) q^{97} +(6.90101 + 1.17303i) q^{98} -0.461115i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 8 * q^7	\( 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 8 * q^7 + 8 * q^10 + 4 * q^11 - 16 * q^13 + 16 * q^14 + 4 * q^15 + 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^20 + 8 * q^21 + 4 * q^22 + 32 * q^23 - 8 * q^24 - 32 * q^25 - 12 * q^26 - 8 * q^28 - 4 * q^30 - 24 * q^31 + 8 * q^33 + 16 * q^34 + 4 * q^35 - 16 * q^36 - 8 * q^37 - 28 * q^38 - 12 * q^39 - 4 * q^42 - 24 * q^43 + 4 * q^45 - 4 * q^46 - 24 * q^47 + 52 * q^49 + 8 * q^51 - 8 * q^52 + 44 * q^53 - 8 * q^54 - 56 * q^55 + 8 * q^56 - 8 * q^57 + 48 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 16 * q^65 + 36 * q^67 - 12 * q^68 - 8 * q^69 + 32 * q^70 - 32 * q^71 - 40 * q^73 - 24 * q^74 - 24 * q^75 - 44 * q^77 - 16 * q^78 + 12 * q^79 + 12 * q^80 + 8 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^87 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 8 * q^92 + 40 * q^93 + 8 * q^94 - 48 * q^95 + 44 * q^97 - 8 * q^98

Introduction

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