LMFDB - Embedded newform 930.2.e.b.929.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(929,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("930.929");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.e (of order $2$, degree $1$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.19
Character	$\chi$	$=$	930.929
Dual form			930.2.e.b.929.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.522710 - 1.65129i) q^{3} +1.00000 q^{4} +(1.93647 - 1.11808i) q^{5} +(0.522710 - 1.65129i) q^{6} +3.41776i q^{7} +1.00000 q^{8} +(-2.45355 - 1.72630i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.522710 - 1.65129i) q^{3} +1.00000 q^{4} +(1.93647 - 1.11808i) q^{5} +(0.522710 - 1.65129i) q^{6} +3.41776i q^{7} +1.00000 q^{8} +(-2.45355 - 1.72630i) q^{9} +(1.93647 - 1.11808i) q^{10} -3.28772 q^{11} +(0.522710 - 1.65129i) q^{12} +4.68046 q^{13} +3.41776i q^{14} +(-0.834068 - 3.78211i) q^{15} +1.00000 q^{16} -5.44627i q^{17} +(-2.45355 - 1.72630i) q^{18} +6.86815 q^{19} +(1.93647 - 1.11808i) q^{20} +(5.64373 + 1.78650i) q^{21} -3.28772 q^{22} -3.10088i q^{23} +(0.522710 - 1.65129i) q^{24} +(2.49980 - 4.33024i) q^{25} +4.68046 q^{26} +(-4.13312 + 3.14918i) q^{27} +3.41776i q^{28} +6.42769 q^{29} +(-0.834068 - 3.78211i) q^{30} +(-5.16427 + 2.08095i) q^{31} +1.00000 q^{32} +(-1.71852 + 5.42899i) q^{33} -5.44627i q^{34} +(3.82133 + 6.61838i) q^{35} +(-2.45355 - 1.72630i) q^{36} -9.62056 q^{37} +6.86815 q^{38} +(2.44652 - 7.72882i) q^{39} +(1.93647 - 1.11808i) q^{40} +2.33381i q^{41} +(5.64373 + 1.78650i) q^{42} -3.46703 q^{43} -3.28772 q^{44} +(-6.68135 - 0.599654i) q^{45} -3.10088i q^{46} -8.08010 q^{47} +(0.522710 - 1.65129i) q^{48} -4.68110 q^{49} +(2.49980 - 4.33024i) q^{50} +(-8.99340 - 2.84682i) q^{51} +4.68046 q^{52} +6.10986i q^{53} +(-4.13312 + 3.14918i) q^{54} +(-6.36655 + 3.67593i) q^{55} +3.41776i q^{56} +(3.59005 - 11.3413i) q^{57} +6.42769 q^{58} +10.9268i q^{59} +(-0.834068 - 3.78211i) q^{60} +4.84643i q^{61} +(-5.16427 + 2.08095i) q^{62} +(5.90007 - 8.38564i) q^{63} +1.00000 q^{64} +(9.06355 - 5.23312i) q^{65} +(-1.71852 + 5.42899i) q^{66} -1.08830i q^{67} -5.44627i q^{68} +(-5.12047 - 1.62086i) q^{69} +(3.82133 + 6.61838i) q^{70} -1.09967i q^{71} +(-2.45355 - 1.72630i) q^{72} +2.96066 q^{73} -9.62056 q^{74} +(-5.84384 - 6.39137i) q^{75} +6.86815 q^{76} -11.2366i q^{77} +(2.44652 - 7.72882i) q^{78} +1.97839i q^{79} +(1.93647 - 1.11808i) q^{80} +(3.03980 + 8.47111i) q^{81} +2.33381i q^{82} +12.0282i q^{83} +(5.64373 + 1.78650i) q^{84} +(-6.08936 - 10.5465i) q^{85} -3.46703 q^{86} +(3.35982 - 10.6140i) q^{87} -3.28772 q^{88} -7.11220 q^{89} +(-6.68135 - 0.599654i) q^{90} +15.9967i q^{91} -3.10088i q^{92} +(0.736851 + 9.61546i) q^{93} -8.08010 q^{94} +(13.2999 - 7.67914i) q^{95} +(0.522710 - 1.65129i) q^{96} +14.3403i q^{97} -4.68110 q^{98} +(8.06657 + 5.67557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9	$ 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} + 4 q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{25} - 12 q^{31} + 32 q^{32} + 8 q^{33} - 16 q^{35} + 4 q^{36} + 8 q^{38} - 4 q^{39} - 2 q^{40} - 42 q^{45} + 4 q^{47} - 36 q^{49} + 10 q^{50} - 4 q^{51} - 12 q^{62} + 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} + 4 q^{72} + 8 q^{76} - 4 q^{78} - 2 q^{80} + 24 q^{81} + 4 q^{87} - 42 q^{90} - 24 q^{93} + 4 q^{94} + 26 q^{95} - 36 q^{98}+O(q^{100}) $ 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 + 4 * q^18 + 8 * q^19 - 2 * q^20 + 10 * q^25 - 12 * q^31 + 32 * q^32 + 8 * q^33 - 16 * q^35 + 4 * q^36 + 8 * q^38 - 4 * q^39 - 2 * q^40 - 42 * q^45 + 4 * q^47 - 36 * q^49 + 10 * q^50 - 4 * q^51 - 12 * q^62 + 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 + 4 * q^72 + 8 * q^76 - 4 * q^78 - 2 * q^80 + 24 * q^81 + 4 * q^87 - 42 * q^90 - 24 * q^93 + 4 * q^94 + 26 * q^95 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.522710	−	1.65129i	0.301787	−	0.953375i
$3$	0.522710	−	1.65129i	0.301787	−	0.953375i
$4$	1.00000			0.500000
$5$	1.93647	−	1.11808i	0.866014	−	0.500020i
$5$	1.93647	−	1.11808i	0.866014	−	0.500020i
$6$	0.522710	−	1.65129i	0.213395	−	0.674138i
$7$			3.41776i			1.29179i	0.763425	+	0.645896i	$0.223516\pi$
$7$			3.41776i			1.29179i	−0.763425	+	0.645896i	$0.776484\pi$
$8$	1.00000			0.353553
$9$	−2.45355	−	1.72630i	−0.817849	−	0.575432i
$10$	1.93647	−	1.11808i	0.612364	−	0.353568i
$11$	−3.28772			−0.991283			−0.495642	−	0.868527i	$-0.665067\pi$
$11$	−3.28772			−0.991283			−0.495642	+	0.868527i	$0.665067\pi$
$12$	0.522710	−	1.65129i	0.150893	−	0.476688i
$13$	4.68046			1.29813			0.649063	−	0.760735i	$-0.275161\pi$
$13$	4.68046			1.29813			0.649063	+	0.760735i	$0.275161\pi$
$14$			3.41776i			0.913435i
$15$	−0.834068	−	3.78211i	−0.215355	−	0.976536i
$16$	1.00000			0.250000
$17$		−	5.44627i		−	1.32091i	−0.750864	−	0.660457i	$-0.770362\pi$
$17$		−	5.44627i		−	1.32091i	0.750864	−	0.660457i	$-0.229638\pi$
$18$	−2.45355	−	1.72630i	−0.578307	−	0.406892i
$19$	6.86815			1.57566			0.787831	−	0.615891i	$-0.211204\pi$
$19$	6.86815			1.57566			0.787831	+	0.615891i	$0.211204\pi$
$20$	1.93647	−	1.11808i	0.433007	−	0.250010i
$21$	5.64373	+	1.78650i	1.23156	+	0.389846i
$22$	−3.28772			−0.700943
$23$		−	3.10088i		−	0.646578i	−0.946300	−	0.323289i	$-0.895211\pi$
$23$		−	3.10088i		−	0.646578i	0.946300	−	0.323289i	$-0.104789\pi$
$24$	0.522710	−	1.65129i	0.106698	−	0.337069i
$25$	2.49980	−	4.33024i	0.499960	−	0.866049i
$26$	4.68046			0.917913
$27$	−4.13312	+	3.14918i	−0.795419	+	0.606060i
$28$			3.41776i			0.645896i
$29$	6.42769			1.19359			0.596796	−	0.802393i	$-0.296440\pi$
$29$	6.42769			1.19359			0.596796	+	0.802393i	$0.296440\pi$
$30$	−0.834068	−	3.78211i	−0.152279	−	0.690515i
$31$	−5.16427	+	2.08095i	−0.927529	+	0.373750i
$31$	−5.16427	+	2.08095i	−0.927529	+	0.373750i
$32$	1.00000			0.176777
$33$	−1.71852	+	5.42899i	−0.299156	+	0.945065i
$34$		−	5.44627i		−	0.934028i
$35$	3.82133	+	6.61838i	0.645922	+	1.11871i
$36$	−2.45355	−	1.72630i	−0.408925	−	0.287716i
$37$	−9.62056			−1.58161			−0.790805	−	0.612068i	$-0.790338\pi$
$37$	−9.62056			−1.58161			−0.790805	+	0.612068i	$0.790338\pi$
$38$	6.86815			1.11416
$39$	2.44652	−	7.72882i	0.391757	−	1.23760i
$40$	1.93647	−	1.11808i	0.306182	−	0.176784i
$41$			2.33381i			0.364479i	0.983254	+	0.182240i	$0.0583346\pi$
$41$			2.33381i			0.364479i	−0.983254	+	0.182240i	$0.941665\pi$
$42$	5.64373	+	1.78650i	0.870847	+	0.275663i
$43$	−3.46703			−0.528717			−0.264358	−	0.964424i	$-0.585160\pi$
$43$	−3.46703			−0.528717			−0.264358	+	0.964424i	$0.585160\pi$
$44$	−3.28772			−0.495642
$45$	−6.68135	−	0.599654i	−0.995997	−	0.0893911i
$46$		−	3.10088i		−	0.457200i
$47$	−8.08010			−1.17860			−0.589302	−	0.807913i	$-0.700597\pi$
$47$	−8.08010			−1.17860			−0.589302	+	0.807913i	$0.700597\pi$
$48$	0.522710	−	1.65129i	0.0754467	−	0.238344i
$49$	−4.68110			−0.668728
$50$	2.49980	−	4.33024i	0.353525	−	0.612389i
$51$	−8.99340	−	2.84682i	−1.25933	−	0.398635i
$52$	4.68046			0.649063
$53$			6.10986i			0.839254i	0.907697	+	0.419627i	$0.137839\pi$
$53$			6.10986i			0.839254i	−0.907697	+	0.419627i	$0.862161\pi$
$54$	−4.13312	+	3.14918i	−0.562446	+	0.428549i
$55$	−6.36655	+	3.67593i	−0.858465	+	0.495662i
$56$			3.41776i			0.456718i
$57$	3.59005	−	11.3413i	0.475514	−	1.50220i
$58$	6.42769			0.843997
$59$			10.9268i			1.42255i	0.702912	+	0.711277i	$0.251883\pi$
$59$			10.9268i			1.42255i	−0.702912	+	0.711277i	$0.748117\pi$
$60$	−0.834068	−	3.78211i	−0.107678	−	0.488268i
$61$			4.84643i			0.620521i	0.950652	+	0.310261i	$0.100416\pi$
$61$			4.84643i			0.620521i	−0.950652	+	0.310261i	$0.899584\pi$
$62$	−5.16427	+	2.08095i	−0.655862	+	0.264281i
$63$	5.90007	−	8.38564i	0.743339	−	1.05649i
$64$	1.00000			0.125000
$65$	9.06355	−	5.23312i	1.12419	−	0.649089i
$66$	−1.71852	+	5.42899i	−0.211535	+	0.668262i
$67$		−	1.08830i		−	0.132957i	−0.997788	−	0.0664783i	$-0.978824\pi$
$67$		−	1.08830i		−	0.132957i	0.997788	−	0.0664783i	$-0.0211763\pi$
$68$		−	5.44627i		−	0.660457i
$69$	−5.12047	−	1.62086i	−0.616432	−	0.195129i
$70$	3.82133	+	6.61838i	0.456736	+	0.791048i
$71$		−	1.09967i		−	0.130506i	−0.997869	−	0.0652532i	$-0.979214\pi$
$71$		−	1.09967i		−	0.130506i	0.997869	−	0.0652532i	$-0.0207855\pi$
$72$	−2.45355	−	1.72630i	−0.289153	−	0.203446i
$73$	2.96066			0.346519			0.173260	−	0.984876i	$-0.444570\pi$
$73$	2.96066			0.346519			0.173260	+	0.984876i	$0.444570\pi$
$74$	−9.62056			−1.11837
$75$	−5.84384	−	6.39137i	−0.674788	−	0.738011i
$76$	6.86815			0.787831
$77$		−	11.2366i		−	1.28053i
$78$	2.44652	−	7.72882i	0.277014	−	0.875116i
$79$			1.97839i			0.222586i	0.993788	+	0.111293i	$0.0354992\pi$
$79$			1.97839i			0.222586i	−0.993788	+	0.111293i	$0.964501\pi$
$80$	1.93647	−	1.11808i	0.216503	−	0.125005i
$81$	3.03980	+	8.47111i	0.337755	+	0.941234i
$82$			2.33381i			0.257726i
$83$			12.0282i			1.32027i	0.751146	+	0.660136i	$0.229501\pi$
$83$			12.0282i			1.32027i	−0.751146	+	0.660136i	$0.770499\pi$
$84$	5.64373	+	1.78650i	0.615782	+	0.194923i
$85$	−6.08936	−	10.5465i	−0.660484	−	1.14393i
$86$	−3.46703			−0.373859
$87$	3.35982	−	10.6140i	0.360210	−	1.13794i
$88$	−3.28772			−0.350472
$89$	−7.11220			−0.753891			−0.376946	−	0.926235i	$-0.623026\pi$
$89$	−7.11220			−0.753891			−0.376946	+	0.926235i	$0.623026\pi$
$90$	−6.68135	−	0.599654i	−0.704276	−	0.0632090i
$91$			15.9967i			1.67691i
$92$		−	3.10088i		−	0.323289i
$93$	0.736851	+	9.61546i	0.0764079	+	0.997077i
$94$	−8.08010			−0.833399
$95$	13.2999	−	7.67914i	1.36455	−	0.787863i
$96$	0.522710	−	1.65129i	0.0533489	−	0.168535i
$97$			14.3403i			1.45603i	0.685560	+	0.728017i	$0.259558\pi$
$97$			14.3403i			1.45603i	−0.685560	+	0.728017i	$0.740442\pi$
$98$	−4.68110			−0.472862
$99$	8.06657	+	5.67557i	0.810721	+	0.570416i
$100$	2.49980	−	4.33024i	0.249980	−	0.433024i
$101$		−	3.54590i		−	0.352830i	−0.984316	−	0.176415i	$-0.943550\pi$
$101$		−	3.54590i		−	0.352830i	0.984316	−	0.176415i	$-0.0564501\pi$
$102$	−8.99340	−	2.84682i	−0.890479	−	0.281877i
$103$		−	17.4104i		−	1.71550i	−0.514066	−	0.857751i	$-0.671861\pi$
$103$		−	17.4104i		−	1.71550i	0.514066	−	0.857751i	$-0.328139\pi$
$104$	4.68046			0.458957
$105$	12.9263	−	2.85065i	1.26148	−	0.278194i
$106$			6.10986i			0.593442i
$107$	5.24571			0.507122			0.253561	−	0.967319i	$-0.418398\pi$
$107$	5.24571			0.507122			0.253561	+	0.967319i	$0.418398\pi$
$108$	−4.13312	+	3.14918i	−0.397710	+	0.303030i
$109$	8.34414			0.799224			0.399612	−	0.916684i	$-0.369145\pi$
$109$	8.34414			0.799224			0.399612	+	0.916684i	$0.369145\pi$
$110$	−6.36655	+	3.67593i	−0.607026	+	0.350486i
$111$	−5.02876	+	15.8864i	−0.477309	+	1.50787i
$112$			3.41776i			0.322948i
$113$	−4.96065			−0.466659			−0.233330	−	0.972398i	$-0.574962\pi$
$113$	−4.96065			−0.466659			−0.233330	+	0.972398i	$0.574962\pi$
$114$	3.59005	−	11.3413i	0.336239	−	1.06221i
$115$	−3.46703	−	6.00475i	−0.323302	−	0.559946i
$116$	6.42769			0.596796
$117$	−11.4837	−	8.07986i	−1.06167	−	0.746983i
$118$			10.9268i			1.00590i
$119$	18.6141			1.70635
$120$	−0.834068	−	3.78211i	−0.0761396	−	0.345258i
$121$	−0.190929			−0.0173572
$122$			4.84643i			0.438775i
$123$	3.85380	+	1.21990i	0.347485	+	0.109995i
$124$	−5.16427	+	2.08095i	−0.463765	+	0.186875i
$125$	−0.000779077	−	11.1803i	−6.96828e−5	−	1.00000i
$126$	5.90007	−	8.38564i	0.525620	−	0.747053i
$127$	0.0848877			0.00753257			0.00376628	−	0.999993i	$-0.498801\pi$
$127$	0.0848877			0.00753257			0.00376628	+	0.999993i	$0.498801\pi$
$128$	1.00000			0.0883883
$129$	−1.81225	+	5.72509i	−0.159560	+	0.504066i
$130$	9.06355	−	5.23312i	0.794926	−	0.458975i
$131$		−	1.14899i		−	0.100387i	−0.998740	−	0.0501937i	$-0.984016\pi$
$131$		−	1.14899i		−	0.100387i	0.998740	−	0.0501937i	$-0.0159839\pi$
$132$	−1.71852	+	5.42899i	−0.149578	+	0.472533i
$133$			23.4737i			2.03543i
$134$		−	1.08830i		−	0.0940145i
$135$	−4.48261	+	10.7194i	−0.385802	+	0.922582i
$136$		−	5.44627i		−	0.467014i
$137$			0.951653i			0.0813052i	0.999173	+	0.0406526i	$0.0129437\pi$
$137$			0.951653i			0.0813052i	−0.999173	+	0.0406526i	$0.987056\pi$
$138$	−5.12047	−	1.62086i	−0.435883	−	0.137977i
$139$			19.8731i			1.68562i	0.538212	+	0.842809i	$0.319100\pi$
$139$			19.8731i			1.68562i	−0.538212	+	0.842809i	$0.680900\pi$
$140$	3.82133	+	6.61838i	0.322961	+	0.559355i
$141$	−4.22355	+	13.3426i	−0.355687	+	1.12365i
$142$		−	1.09967i		−	0.0922820i
$143$	−15.3880			−1.28681
$144$	−2.45355	−	1.72630i	−0.204462	−	0.143858i
$145$	12.4470	−	7.18667i	1.03367	−	0.596820i
$146$	2.96066			0.245026
$147$	−2.44686	+	7.72987i	−0.201813	+	0.637549i
$148$	−9.62056			−0.790805
$149$		−	15.5439i		−	1.27341i	−0.771109	−	0.636703i	$-0.780298\pi$
$149$		−	15.5439i		−	1.27341i	0.771109	−	0.636703i	$-0.219702\pi$
$150$	−5.84384	−	6.39137i	−0.477147	−	0.521853i
$151$			19.8962i			1.61913i	0.587033	+	0.809563i	$0.300296\pi$
$151$			19.8962i			1.61913i	−0.587033	+	0.809563i	$0.699704\pi$
$152$	6.86815			0.557081
$153$	−9.40188	+	13.3627i	−0.760097	+	1.08031i
$154$		−	11.2366i		−	0.905473i
$155$	−7.67376	+	9.80375i	−0.616371	+	0.787456i
$156$	2.44652	−	7.72882i	0.195879	−	0.618801i
$157$		−	12.0529i		−	0.961929i	−0.876740	−	0.480965i	$-0.840287\pi$
$157$		−	12.0529i		−	0.961929i	0.876740	−	0.480965i	$-0.159713\pi$
$158$			1.97839i			0.157392i
$159$	10.0892	+	3.19369i	0.800124	+	0.253276i
$160$	1.93647	−	1.11808i	0.153091	−	0.0883919i
$161$	10.5981			0.835245
$162$	3.03980	+	8.47111i	0.238829	+	0.665553i
$163$		−	0.995539i		−	0.0779766i	−0.999240	−	0.0389883i	$-0.987586\pi$
$163$		−	0.995539i		−	0.0779766i	0.999240	−	0.0389883i	$-0.0124135\pi$
$164$			2.33381i			0.182240i
$165$	2.74218	+	12.4345i	0.213478	+	0.968024i
$166$			12.0282i			0.933573i
$167$		−	4.42181i		−	0.342170i	−0.985256	−	0.171085i	$-0.945273\pi$
$167$		−	4.42181i		−	0.342170i	0.985256	−	0.171085i	$-0.0547273\pi$
$168$	5.64373	+	1.78650i	0.435423	+	0.137831i
$169$	8.90669			0.685130
$170$	−6.08936	−	10.5465i	−0.467033	−	0.808881i
$171$	−16.8513	−	11.8565i	−1.28865	−	0.906687i
$172$	−3.46703			−0.264358
$173$	−12.7201			−0.967094			−0.483547	−	0.875318i	$-0.660652\pi$
$173$	−12.7201			−0.967094			−0.483547	+	0.875318i	$0.660652\pi$
$174$	3.35982	−	10.6140i	0.254707	−	0.804646i
$175$	14.7997	+	8.54372i	1.11876	+	0.645844i
$176$	−3.28772			−0.247821
$177$	18.0434	+	5.71157i	1.35623	+	0.429308i
$178$	−7.11220			−0.533082
$179$	−21.9549			−1.64098			−0.820492	−	0.571658i	$-0.806300\pi$
$179$	−21.9549			−1.64098			−0.820492	+	0.571658i	$0.806300\pi$
$180$	−6.68135	−	0.599654i	−0.497998	−	0.0446955i
$181$			0.359283i			0.0267053i	0.999911	+	0.0133527i	$0.00425041\pi$
$181$			0.359283i			0.0267053i	−0.999911	+	0.0133527i	$0.995750\pi$
$182$			15.9967i			1.18575i
$183$	8.00288	+	2.53328i	0.591590	+	0.187265i
$184$		−	3.10088i		−	0.228600i
$185$	−18.6299	+	10.7565i	−1.36970	+	0.790837i
$186$	0.736851	+	9.61546i	0.0540285	+	0.705040i
$187$			17.9058i			1.30940i
$188$	−8.08010			−0.589302
$189$	−10.7631	−	14.1260i	−0.782903	−	1.02752i
$190$	13.2999	−	7.67914i	0.964879	−	0.557103i
$191$		−	1.29019i		−	0.0933551i	−0.998910	−	0.0466776i	$-0.985137\pi$
$191$		−	1.29019i		−	0.0933551i	0.998910	−	0.0466776i	$-0.0148633\pi$
$192$	0.522710	−	1.65129i	0.0377233	−	0.119172i
$193$		−	19.2548i		−	1.38599i	−0.720943	−	0.692994i	$-0.756291\pi$
$193$		−	19.2548i		−	1.38599i	0.720943	−	0.692994i	$-0.243709\pi$
$194$			14.3403i			1.02957i
$195$	−3.90382	−	17.7020i	−0.279558	−	1.26767i
$196$	−4.68110			−0.334364
$197$			2.65138i			0.188903i	0.995529	+	0.0944514i	$0.0301097\pi$
$197$			2.65138i			0.188903i	−0.995529	+	0.0944514i	$0.969890\pi$
$198$	8.06657	+	5.67557i	0.573266	+	0.403345i
$199$		−	0.149907i		−	0.0106267i	−0.999986	−	0.00531333i	$-0.998309\pi$
$199$		−	0.149907i		−	0.0106267i	0.999986	−	0.00531333i	$-0.00169129\pi$
$200$	2.49980	−	4.33024i	0.176762	−	0.306194i
$201$	−1.79710	−	0.568863i	−0.126758	−	0.0401245i
$202$		−	3.54590i		−	0.249489i
$203$			21.9683i			1.54187i
$204$	−8.99340	−	2.84682i	−0.629664	−	0.199317i
$205$	2.60938	+	4.51933i	0.182247	+	0.315644i
$206$		−	17.4104i		−	1.21304i
$207$	−5.35304	+	7.60816i	−0.372062	+	0.528804i
$208$	4.68046			0.324531
$209$	−22.5805			−1.56193
$210$	12.9263	−	2.85065i	0.892002	−	0.196713i
$211$	18.9513			1.30466			0.652330	−	0.757935i	$-0.273791\pi$
$211$	18.9513			1.30466			0.652330	+	0.757935i	$0.273791\pi$
$212$			6.10986i			0.419627i
$213$	−1.81587	−	0.574807i	−0.124422	−	0.0393851i
$214$	5.24571			0.358589
$215$	−6.71378	+	3.87641i	−0.457876	+	0.264369i
$216$	−4.13312	+	3.14918i	−0.281223	+	0.214274i
$217$	−7.11220	−	17.6502i	−0.482807	−	1.19818i
$218$	8.34414			0.565136
$219$	1.54757	−	4.88893i	0.104575	−	0.330363i
$220$	−6.36655	+	3.67593i	−0.429233	+	0.247831i
$221$		−	25.4910i		−	1.71471i
$222$	−5.02876	+	15.8864i	−0.337508	+	1.06622i
$223$	−19.2236			−1.28731			−0.643655	−	0.765316i	$-0.722583\pi$
$223$	−19.2236			−1.28731			−0.643655	+	0.765316i	$0.722583\pi$
$224$			3.41776i			0.228359i
$225$	−13.6087	+	6.30907i	−0.907244	+	0.420604i
$226$	−4.96065			−0.329978
$227$	15.4034			1.02236			0.511178	−	0.859475i	$-0.329209\pi$
$227$	15.4034			1.02236			0.511178	+	0.859475i	$0.329209\pi$
$228$	3.59005	−	11.3413i	0.237757	−	0.751099i
$229$		−	30.1753i		−	1.99404i	−0.0771263	−	0.997021i	$-0.524574\pi$
$229$		−	30.1753i		−	1.99404i	0.0771263	−	0.997021i	$-0.475426\pi$
$230$	−3.46703	−	6.00475i	−0.228609	−	0.395941i
$231$	−18.5550	−	5.87350i	−1.22083	−	0.386448i
$232$	6.42769			0.421999
$233$	−1.91032			−0.125149			−0.0625745	−	0.998040i	$-0.519931\pi$
$233$	−1.91032			−0.125149			−0.0625745	+	0.998040i	$0.519931\pi$
$234$	−11.4837	−	8.07986i	−0.750715	−	0.528197i
$235$	−15.6468	+	9.03419i	−1.02069	+	0.589326i
$236$			10.9268i			0.711277i
$237$	3.26690	+	1.03412i	0.212208	+	0.0671734i
$238$	18.6141			1.20657
$239$	11.6740			0.755125			0.377563	−	0.925984i	$-0.376762\pi$
$239$	11.6740			0.755125			0.377563	+	0.925984i	$0.376762\pi$
$240$	−0.834068	−	3.78211i	−0.0538388	−	0.244134i
$241$			15.6943i			1.01096i	0.862839	+	0.505478i	$0.168684\pi$
$241$			15.6943i			1.01096i	−0.862839	+	0.505478i	$0.831316\pi$
$242$	−0.190929			−0.0122734
$243$	15.5772	−	0.591672i	0.999279	−	0.0379558i
$244$			4.84643i			0.310261i
$245$	−9.06478	+	5.23384i	−0.579128	+	0.334378i
$246$	3.85380	+	1.21990i	0.245709	+	0.0777782i
$247$	32.1461			2.04541
$248$	−5.16427	+	2.08095i	−0.327931	+	0.132141i
$249$	19.8622	+	6.28729i	1.25871	+	0.398441i
$250$	−0.000779077	−	11.1803i	−4.92732e−5	−	0.707107i
$251$	18.8620			1.19056			0.595280	−	0.803518i	$-0.297041\pi$
$251$	18.8620			1.19056			0.595280	+	0.803518i	$0.297041\pi$
$252$	5.90007	−	8.38564i	0.371670	−	0.528246i
$253$			10.1948i			0.640942i
$254$	0.0848877			0.00532633
$255$	−20.5984	+	4.54256i	−1.28992	+	0.284466i
$256$	1.00000			0.0625000
$257$	−1.65578			−0.103285			−0.0516423	−	0.998666i	$-0.516446\pi$
$257$	−1.65578			−0.103285			−0.0516423	+	0.998666i	$0.516446\pi$
$258$	−1.81225	+	5.72509i	−0.112826	+	0.356428i
$259$		−	32.8808i		−	2.04311i
$260$	9.06355	−	5.23312i	0.562097	−	0.324544i
$261$	−15.7707	−	11.0961i	−0.976179	−	0.686832i
$262$		−	1.14899i		−	0.0709846i
$263$		−	12.0854i		−	0.745220i	−0.927988	−	0.372610i	$-0.878463\pi$
$263$		−	12.0854i		−	0.745220i	0.927988	−	0.372610i	$-0.121537\pi$
$264$	−1.71852	+	5.42899i	−0.105768	+	0.334131i
$265$	6.83131	+	11.8315i	0.419644	+	0.726805i
$266$			23.4737i			1.43927i
$267$	−3.71762	+	11.7443i	−0.227514	+	0.718742i
$268$		−	1.08830i		−	0.0664783i
$269$	−8.92033			−0.543882			−0.271941	−	0.962314i	$-0.587666\pi$
$269$	−8.92033			−0.543882			−0.271941	+	0.962314i	$0.587666\pi$
$270$	−4.48261	+	10.7194i	−0.272803	+	0.652364i
$271$			6.61742i			0.401980i	0.979593	+	0.200990i	$0.0644158\pi$
$271$			6.61742i			0.401980i	−0.979593	+	0.200990i	$0.935584\pi$
$272$		−	5.44627i		−	0.330229i
$273$	26.4153	+	8.36163i	1.59872	+	0.506069i
$274$			0.951653i			0.0574915i
$275$	−8.21863	+	14.2366i	−0.495602	+	0.858500i
$276$	−5.12047	−	1.62086i	−0.308216	−	0.0975644i
$277$	9.77898			0.587562			0.293781	−	0.955873i	$-0.405086\pi$
$277$	9.77898			0.587562			0.293781	+	0.955873i	$0.405086\pi$
$278$			19.8731i			1.19191i
$279$	16.2631	+	3.80934i	0.973647	+	0.228059i
$280$	3.82133	+	6.61838i	0.228368	+	0.395524i
$281$			21.6030i			1.28873i	0.764719	+	0.644364i	$0.222878\pi$
$281$			21.6030i			1.28873i	−0.764719	+	0.644364i	$0.777122\pi$
$282$	−4.22355	+	13.3426i	−0.251509	+	0.794542i
$283$			9.80067i			0.582589i	0.956633	+	0.291295i	$0.0940860\pi$
$283$			9.80067i			0.582589i	−0.956633	+	0.291295i	$0.905914\pi$
$284$		−	1.09967i		−	0.0652532i
$285$	−5.72850	−	25.9761i	−0.339327	−	1.53869i
$286$	−15.3880			−0.909912
$287$	−7.97639			−0.470831
$288$	−2.45355	−	1.72630i	−0.144577	−	0.101723i
$289$	−12.6619			−0.744816
$290$	12.4470	−	7.18667i	0.730913	−	0.422016i
$291$	23.6800	+	7.49580i	1.38815	+	0.439412i
$292$	2.96066			0.173260
$293$	−19.1106			−1.11645			−0.558227	−	0.829688i	$-0.688518\pi$
$293$	−19.1106			−1.11645			−0.558227	+	0.829688i	$0.688518\pi$
$294$	−2.44686	+	7.72987i	−0.142704	+	0.450815i
$295$	12.2171	+	21.1595i	0.711305	+	1.23195i
$296$	−9.62056			−0.559183
$297$	13.5885	−	10.3536i	0.788486	−	0.600777i
$298$		−	15.5439i		−	0.900435i
$299$		−	14.5135i		−	0.839340i
$300$	−5.84384	−	6.39137i	−0.337394	−	0.369006i
$301$		−	11.8495i		−	0.682993i
$302$			19.8962i			1.14490i
$303$	−5.85533	−	1.85348i	−0.336380	−	0.106480i
$304$	6.86815			0.393916
$305$	5.41869	+	9.38494i	0.310273	+	0.537380i
$306$	−9.40188	+	13.3627i	−0.537470	+	0.763894i
$307$		−	25.7852i		−	1.47164i	−0.677177	−	0.735820i	$-0.736797\pi$
$307$		−	25.7852i		−	1.47164i	0.677177	−	0.735820i	$-0.263203\pi$
$308$		−	11.2366i		−	0.640266i
$309$	−28.7498	−	9.10061i	−1.63552	−	0.517716i
$310$	−7.67376	+	9.80375i	−0.435840	+	0.556815i
$311$			31.0081i			1.75831i	0.476538	+	0.879154i	$0.341892\pi$
$311$			31.0081i			1.75831i	−0.476538	+	0.879154i	$0.658108\pi$
$312$	2.44652	−	7.72882i	0.138507	−	0.437558i
$313$	31.8164			1.79837			0.899184	−	0.437570i	$-0.144161\pi$
$313$	31.8164			1.79837			0.899184	+	0.437570i	$0.144161\pi$
$314$		−	12.0529i		−	0.680187i
$315$	2.04947	−	22.8353i	0.115475	−	1.28662i
$316$			1.97839i			0.111293i
$317$	−34.6184			−1.94436			−0.972182	−	0.234226i	$-0.924745\pi$
$317$	−34.6184			−1.94436			−0.972182	+	0.234226i	$0.924745\pi$
$318$	10.0892	+	3.19369i	0.565773	+	0.179093i
$319$	−21.1324			−1.18319
$320$	1.93647	−	1.11808i	0.108252	−	0.0625025i
$321$	2.74199	−	8.66222i	0.153043	−	0.483478i
$322$	10.5981			0.590607
$323$		−	37.4058i		−	2.08132i
$324$	3.03980	+	8.47111i	0.168878	+	0.470617i
$325$	11.7002	−	20.2675i	0.649011	−	1.12424i
$326$		−	0.995539i		−	0.0551378i
$327$	4.36157	−	13.7786i	0.241195	−	0.761960i
$328$			2.33381i			0.128863i
$329$		−	27.6159i		−	1.52251i
$330$	2.74218	+	12.4345i	0.150952	+	0.684496i
$331$			10.3693i			0.569946i	0.958536	+	0.284973i	$0.0919846\pi$
$331$			10.3693i			0.569946i	−0.958536	+	0.284973i	$0.908015\pi$
$332$			12.0282i			0.660136i
$333$	23.6045	+	16.6079i	1.29352	+	0.910109i
$334$		−	4.42181i		−	0.241951i
$335$	−1.21680	−	2.10745i	−0.0664810	−	0.115142i
$336$	5.64373	+	1.78650i	0.307891	+	0.0974615i
$337$	−27.3911			−1.49209			−0.746045	−	0.665896i	$-0.768049\pi$
$337$	−27.3911			−1.49209			−0.746045	+	0.665896i	$0.768049\pi$
$338$	8.90669			0.484460
$339$	−2.59298	+	8.19150i	−0.140832	+	0.444901i
$340$	−6.08936	−	10.5465i	−0.330242	−	0.571965i
$341$	16.9786	−	6.84158i	0.919445	−	0.370492i
$342$	−16.8513	−	11.8565i	−0.911216	−	0.641124i
$343$			7.92546i			0.427935i
$344$	−3.46703			−0.186930
$345$	−11.7279	+	2.58634i	−0.631407	+	0.139244i
$346$	−12.7201			−0.683839
$347$		−	21.3382i		−	1.14549i	−0.819733	−	0.572746i	$-0.805878\pi$
$347$		−	21.3382i		−	1.14549i	0.819733	−	0.572746i	$-0.194122\pi$
$348$	3.35982	−	10.6140i	0.180105	−	0.568971i
$349$	−2.59544			−0.138931			−0.0694653	−	0.997584i	$-0.522129\pi$
$349$	−2.59544			−0.138931			−0.0694653	+	0.997584i	$0.522129\pi$
$350$	14.7997	+	8.54372i	0.791079	+	0.456681i
$351$	−19.3449	+	14.7396i	−1.03255	+	0.786742i
$352$	−3.28772			−0.175236
$353$		−	25.0194i		−	1.33165i	−0.746109	−	0.665824i	$-0.768080\pi$
$353$		−	25.0194i		−	1.33165i	0.746109	−	0.665824i	$-0.231920\pi$
$354$	18.0434	+	5.71157i	0.958998	+	0.303567i
$355$	−1.22951	−	2.12947i	−0.0652558	−	0.113020i
$356$	−7.11220			−0.376946
$357$	9.72975	−	30.7373i	0.514953	−	1.62679i
$358$	−21.9549			−1.16035
$359$		−	16.4820i		−	0.869888i	−0.900458	−	0.434944i	$-0.856768\pi$
$359$		−	16.4820i		−	0.869888i	0.900458	−	0.434944i	$-0.143232\pi$
$360$	−6.68135	−	0.599654i	−0.352138	−	0.0316045i
$361$	28.1715			1.48271
$362$			0.359283i			0.0188835i
$363$	−0.0998006	+	0.315280i	−0.00523817	+	0.0165479i
$364$			15.9967i			0.838455i
$365$	5.73322	−	3.31026i	0.300091	−	0.173267i
$366$	8.00288	+	2.53328i	0.418317	+	0.132416i
$367$	−23.0158			−1.20141			−0.600707	−	0.799470i	$-0.705114\pi$
$367$	−23.0158			−1.20141			−0.600707	+	0.799470i	$0.705114\pi$
$368$		−	3.10088i		−	0.161645i
$369$	4.02884	−	5.72610i	0.209733	−	0.298089i
$370$	−18.6299	+	10.7565i	−0.968521	+	0.559206i
$371$	−20.8820			−1.08414
$372$	0.736851	+	9.61546i	0.0382039	+	0.498538i
$373$		−	6.20223i		−	0.321139i	−0.987025	−	0.160570i	$-0.948667\pi$
$373$		−	6.20223i		−	0.321139i	0.987025	−	0.160570i	$-0.0513331\pi$
$374$			17.9058i			0.925886i
$375$	−18.4624	−	5.84279i	−0.953396	−	0.301720i
$376$	−8.08010			−0.416699
$377$	30.0845			1.54943
$378$	−10.7631	−	14.1260i	−0.553596	−	0.726564i
$379$	−19.4558			−0.999378			−0.499689	−	0.866205i	$-0.666552\pi$
$379$	−19.4558			−0.999378			−0.499689	+	0.866205i	$0.666552\pi$
$380$	13.2999	−	7.67914i	0.682273	−	0.393931i
$381$	0.0443717	−	0.140175i	0.00227323	−	0.00718136i
$382$		−	1.29019i		−	0.0660120i
$383$		−	20.6516i		−	1.05525i	−0.849477	−	0.527625i	$-0.823083\pi$
$383$		−	20.6516i		−	1.05525i	0.849477	−	0.527625i	$-0.176917\pi$
$384$	0.522710	−	1.65129i	0.0266744	−	0.0842673i
$385$	−12.5634	−	21.7593i	−0.640292	−	1.10896i
$386$		−	19.2548i		−	0.980042i
$387$	8.50652	+	5.98512i	0.432411	+	0.304241i
$388$			14.3403i			0.728017i
$389$	15.9392			0.808150			0.404075	−	0.914726i	$-0.367594\pi$
$389$	15.9392			0.808150			0.404075	+	0.914726i	$0.367594\pi$
$390$	−3.90382	−	17.7020i	−0.197678	−	0.896375i
$391$	−16.8882			−0.854075
$392$	−4.68110			−0.236431
$393$	−1.89731	−	0.600586i	−0.0957068	−	0.0302956i
$394$			2.65138i			0.133575i
$395$	2.21199	+	3.83108i	0.111297	+	0.192762i
$396$	8.06657	+	5.67557i	0.405360	+	0.285208i
$397$			34.3942i			1.72620i	0.505036	+	0.863098i	$0.331479\pi$
$397$			34.3942i			1.72620i	−0.505036	+	0.863098i	$0.668521\pi$
$398$		−	0.149907i		−	0.00751418i
$399$	38.7620	+	12.2699i	1.94053	+	0.614266i
$400$	2.49980	−	4.33024i	0.124990	−	0.216512i
$401$	12.7802			0.638214			0.319107	−	0.947719i	$-0.396617\pi$
$401$	12.7802			0.638214			0.319107	+	0.947719i	$0.396617\pi$
$402$	−1.79710	−	0.568863i	−0.0896311	−	0.0283723i
$403$	−24.1711	+	9.73981i	−1.20405	+	0.485174i
$404$		−	3.54590i		−	0.176415i
$405$	15.3578	+	13.0053i	0.763137	+	0.646237i
$406$			21.9683i			1.09027i
$407$	31.6296			1.56782
$408$	−8.99340	−	2.84682i	−0.445240	−	0.140939i
$409$			3.23048i			0.159737i	0.996805	+	0.0798686i	$0.0254501\pi$
$409$			3.23048i			0.159737i	−0.996805	+	0.0798686i	$0.974550\pi$
$410$	2.60938	+	4.51933i	0.128868	+	0.223194i
$411$	1.57146	+	0.497439i	0.0775144	+	0.0245368i
$412$		−	17.4104i		−	0.857751i
$413$	−37.3453			−1.83764
$414$	−5.35304	+	7.60816i	−0.263088	+	0.373921i
$415$	13.4485	+	23.2923i	0.660162	+	1.14337i
$416$	4.68046			0.229478
$417$	32.8164	+	10.3879i	1.60703	+	0.508697i
$418$	−22.5805			−1.10445
$419$			32.9933i			1.61183i	0.592033	+	0.805914i	$0.298325\pi$
$419$			32.9933i			1.61183i	−0.592033	+	0.805914i	$0.701675\pi$
$420$	12.9263	−	2.85065i	0.630741	−	0.139097i
$421$	16.6200			0.810007			0.405003	−	0.914315i	$-0.367270\pi$
$421$	16.6200			0.810007			0.405003	+	0.914315i	$0.367270\pi$
$422$	18.9513			0.922534
$423$	19.8249	+	13.9487i	0.963921	+	0.678207i
$424$			6.10986i			0.296721i
$425$	−23.5837	−	13.6146i	−1.14398	−	0.660404i
$426$	−1.81587	−	0.574807i	−0.0879794	−	0.0278495i
$427$	−16.5639			−0.801585
$428$	5.24571			0.253561
$429$	−8.04347	+	25.4101i	−0.388342	+	1.22681i
$430$	−6.71378	+	3.87641i	−0.323767	+	0.186937i
$431$			11.5566i			0.556661i	0.960485	+	0.278331i	$0.0897811\pi$
$431$			11.5566i			0.556661i	−0.960485	+	0.278331i	$0.910219\pi$
$432$	−4.13312	+	3.14918i	−0.198855	+	0.151515i
$433$	19.1307			0.919361			0.459681	−	0.888084i	$-0.347964\pi$
$433$	19.1307			0.919361			0.459681	+	0.888084i	$0.347964\pi$
$434$	−7.11220	−	17.6502i	−0.341396	−	0.847238i
$435$	−5.36113	−	24.3102i	−0.257047	−	1.16559i
$436$	8.34414			0.399612
$437$		−	21.2973i		−	1.01879i
$438$	1.54757	−	4.88893i	0.0739457	−	0.233602i
$439$	6.31038			0.301178			0.150589	−	0.988596i	$-0.451883\pi$
$439$	6.31038			0.301178			0.150589	+	0.988596i	$0.451883\pi$
$440$	−6.36655	+	3.67593i	−0.303513	+	0.175243i
$441$	11.4853	+	8.08096i	0.546919	+	0.384808i
$442$		−	25.4910i		−	1.21249i
$443$	−38.7666			−1.84185			−0.920927	−	0.389735i	$-0.872567\pi$
$443$	−38.7666			−1.84185			−0.920927	+	0.389735i	$0.872567\pi$
$444$	−5.02876	+	15.8864i	−0.238654	+	0.753934i
$445$	−13.7725	+	7.95200i	−0.652880	+	0.376961i
$446$	−19.2236			−0.910266
$447$	−25.6676	−	8.12496i	−1.21403	−	0.384297i
$448$			3.41776i			0.161474i
$449$	27.0762			1.27780			0.638902	−	0.769288i	$-0.279389\pi$
$449$	27.0762			1.27780			0.638902	+	0.769288i	$0.279389\pi$
$450$	−13.6087	+	6.30907i	−0.641518	+	0.297412i
$451$		−	7.67289i		−	0.361302i
$452$	−4.96065			−0.233330
$453$	32.8544	+	10.3999i	1.54364	+	0.488631i
$454$	15.4034			0.722915
$455$	17.8856	+	30.9770i	0.838488	+	1.45223i
$456$	3.59005	−	11.3413i	0.168120	−	0.531107i
$457$	24.5238			1.14718			0.573588	−	0.819144i	$-0.305551\pi$
$457$	24.5238			1.14718			0.573588	+	0.819144i	$0.305551\pi$
$458$		−	30.1753i		−	1.41000i
$459$	17.1513	+	22.5101i	0.800553	+	1.05068i
$460$	−3.46703	−	6.00475i	−0.161651	−	0.279973i
$461$	2.01028			0.0936283			0.0468141	−	0.998904i	$-0.485093\pi$
$461$	2.01028			0.0936283			0.0468141	+	0.998904i	$0.485093\pi$
$462$	−18.5550	−	5.87350i	−0.863256	−	0.273260i
$463$	−17.6292			−0.819298			−0.409649	−	0.912243i	$-0.634349\pi$
$463$	−17.6292			−0.819298			−0.409649	+	0.912243i	$0.634349\pi$
$464$	6.42769			0.298398
$465$	12.1777	+	17.7961i	0.564729	+	0.825277i
$466$	−1.91032			−0.0884938
$467$	−3.08510			−0.142761			−0.0713807	−	0.997449i	$-0.522741\pi$
$467$	−3.08510			−0.142761			−0.0713807	+	0.997449i	$0.522741\pi$
$468$	−11.4837	−	8.07986i	−0.530836	−	0.373492i
$469$	3.71954			0.171752
$470$	−15.6468	+	9.03419i	−0.721735	+	0.416716i
$471$	−19.9030	−	6.30019i	−0.917080	−	0.290298i
$472$			10.9268i			0.502949i
$473$	11.3986			0.524108
$474$	3.26690	+	1.03412i	0.150054	+	0.0474988i
$475$	17.1690	−	29.7408i	0.787768	−	1.36460i
$476$	18.6141			0.853174
$477$	10.5474	−	14.9908i	0.482934	−	0.686383i
$478$	11.6740			0.533954
$479$		−	4.14251i		−	0.189276i	−0.995512	−	0.0946380i	$-0.969831\pi$
$479$		−	4.14251i		−	0.189276i	0.995512	−	0.0946380i	$-0.0301693\pi$
$480$	−0.834068	−	3.78211i	−0.0380698	−	0.172629i
$481$	−45.0286			−2.05313
$482$			15.6943i			0.714854i
$483$	5.53972	−	17.5005i	0.252066	−	0.796302i
$484$	−0.190929			−0.00867860
$485$	16.0335	+	27.7694i	0.728046	+	1.26094i
$486$	15.5772	−	0.591672i	0.706597	−	0.0268388i
$487$	−21.6677			−0.981857			−0.490928	−	0.871200i	$-0.663342\pi$
$487$	−21.6677			−0.981857			−0.490928	+	0.871200i	$0.663342\pi$
$488$			4.84643i			0.219387i
$489$	−1.64393	−	0.520378i	−0.0743410	−	0.0235323i
$490$	−9.06478	+	5.23384i	−0.409505	+	0.236441i
$491$	−11.1308			−0.502328			−0.251164	−	0.967945i	$-0.580813\pi$
$491$	−11.1308			−0.502328			−0.251164	+	0.967945i	$0.580813\pi$
$492$	3.85380	+	1.21990i	0.173743	+	0.0549975i
$493$		−	35.0070i		−	1.57663i
$494$	32.1461			1.44632
$495$	21.9664	+	1.97149i	0.987315	+	0.0886119i
$496$	−5.16427	+	2.08095i	−0.231882	+	0.0934375i
$497$	3.75840			0.168587
$498$	19.8622	+	6.28729i	0.890046	+	0.281740i
$499$		−	41.0696i		−	1.83853i	−0.393639	−	0.919265i	$-0.628784\pi$
$499$		−	41.0696i		−	1.83853i	0.393639	−	0.919265i	$-0.371216\pi$
$500$	−0.000779077	−	11.1803i	−3.48414e−5	−	0.500000i
$501$	−7.30171	−	2.31133i	−0.326217	−	0.103262i
$502$	18.8620			0.841853
$503$	25.4390			1.13427			0.567135	−	0.823625i	$-0.308052\pi$
$503$	25.4390			1.13427			0.567135	+	0.823625i	$0.308052\pi$
$504$	5.90007	−	8.38564i	0.262810	−	0.373526i
$505$	−3.96460	−	6.86652i	−0.176422	−	0.305556i
$506$			10.1948i			0.453215i
$507$	4.65562	−	14.7076i	0.206763	−	0.653186i
$508$	0.0848877			0.00376628
$509$	20.5572			0.911182			0.455591	−	0.890189i	$-0.349428\pi$
$509$	20.5572			0.911182			0.455591	+	0.890189i	$0.349428\pi$
$510$	−20.5984	+	4.54256i	−0.912111	+	0.201148i
$511$			10.1188i			0.447631i
$512$	1.00000			0.0441942
$513$	−28.3869	+	21.6290i	−1.25331	+	0.954945i
$514$	−1.65578			−0.0730332
$515$	−19.4662	−	33.7147i	−0.857785	−	1.48565i
$516$	−1.81225	+	5.72509i	−0.0797799	+	0.252033i
$517$	26.5651			1.16833
$518$		−	32.8808i		−	1.44470i
$519$	−6.64895	+	21.0047i	−0.291856	+	0.922004i
$520$	9.06355	−	5.23312i	0.397463	−	0.229488i
$521$		−	28.7128i		−	1.25793i	−0.777434	−	0.628965i	$-0.783479\pi$
$521$		−	28.7128i		−	1.25793i	0.777434	−	0.628965i	$-0.216521\pi$
$522$	−15.7707	−	11.0961i	−0.690263	−	0.485663i
$523$	28.5390			1.24792			0.623962	−	0.781454i	$-0.285522\pi$
$523$	28.5390			1.24792			0.623962	+	0.781454i	$0.285522\pi$
$524$		−	1.14899i		−	0.0501937i
$525$	21.8442	−	19.9728i	0.953358	−	0.871686i
$526$		−	12.0854i		−	0.526950i
$527$	11.3334	+	28.1260i	0.493692	+	1.22519i
$528$	−1.71852	+	5.42899i	−0.0747891	+	0.236266i
$529$	13.3845			0.581937
$530$	6.83131	+	11.8315i	0.296733	+	0.513929i
$531$	18.8630	−	26.8095i	0.818583	−	1.16343i
$532$			23.4737i			1.01771i
$533$			10.9233i			0.473140i
$534$	−3.71762	+	11.7443i	−0.160877	+	0.508227i
$535$	10.1581	−	5.86512i	0.439175	−	0.253571i
$536$		−	1.08830i		−	0.0470072i
$537$	−11.4760	+	36.2540i	−0.495227	+	1.56447i
$538$	−8.92033			−0.384583
$539$	15.3901			0.662899
$540$	−4.48261	+	10.7194i	−0.192901	+	0.461291i
$541$	20.5791			0.884765			0.442383	−	0.896826i	$-0.354133\pi$
$541$	20.5791			0.884765			0.442383	+	0.896826i	$0.354133\pi$
$542$			6.61742i			0.284243i
$543$	0.593283	+	0.187801i	0.0254602	+	0.00805931i
$544$		−	5.44627i		−	0.233507i
$545$	16.1581	−	9.32941i	0.692139	−	0.399628i
$546$	26.4153	+	8.36163i	1.13047	+	0.357845i
$547$		−	13.6896i		−	0.585326i	−0.956216	−	0.292663i	$-0.905459\pi$
$547$		−	13.6896i		−	0.585326i	0.956216	−	0.292663i	$-0.0945414\pi$
$548$			0.951653i			0.0406526i
$549$	8.36637	−	11.8909i	0.357068	−	0.507493i
$550$	−8.21863	+	14.2366i	−0.350443	+	0.607051i
$551$	44.1464			1.88070
$552$	−5.12047	−	1.62086i	−0.217942	−	0.0689884i
$553$	−6.76165			−0.287535
$554$	9.77898			0.415469
$555$	8.02420	+	36.3860i	0.340608	+	1.54450i
$556$			19.8731i			0.842809i
$557$			17.0052i			0.720534i	0.932849	+	0.360267i	$0.117314\pi$
$557$			17.0052i			0.720534i	−0.932849	+	0.360267i	$0.882686\pi$
$558$	16.2631	+	3.80934i	0.688473	+	0.161262i
$559$	−16.2273			−0.686341
$560$	3.82133	+	6.61838i	0.161481	+	0.279678i
$561$	29.5677	+	9.35953i	1.24835	+	0.395160i
$562$			21.6030i			0.911268i
$563$	11.2291			0.473249			0.236624	−	0.971601i	$-0.423959\pi$
$563$	11.2291			0.473249			0.236624	+	0.971601i	$0.423959\pi$
$564$	−4.22355	+	13.3426i	−0.177844	+	0.561826i
$565$	−9.60613	+	5.54640i	−0.404133	+	0.233339i
$566$			9.80067i			0.411953i
$567$	−28.9522	+	10.3893i	−1.21588	+	0.436310i
$568$		−	1.09967i		−	0.0461410i
$569$	−24.8586			−1.04213			−0.521063	−	0.853518i	$-0.674464\pi$
$569$	−24.8586			−1.04213			−0.521063	+	0.853518i	$0.674464\pi$
$570$	−5.72850	−	25.9761i	−0.239941	−	1.08802i
$571$		−	42.3322i		−	1.77155i	−0.464117	−	0.885774i	$-0.653628\pi$
$571$		−	42.3322i		−	1.77155i	0.464117	−	0.885774i	$-0.346372\pi$
$572$	−15.3880			−0.643405
$573$	−2.13049	−	0.674397i	−0.0890025	−	0.0281733i
$574$	−7.97639			−0.332928
$575$	−13.4276	−	7.75158i	−0.559968	−	0.323263i
$576$	−2.45355	−	1.72630i	−0.102231	−	0.0719290i
$577$			2.86412i			0.119235i	0.998221	+	0.0596175i	$0.0189881\pi$
$577$			2.86412i			0.119235i	−0.998221	+	0.0596175i	$0.981012\pi$
$578$	−12.6619			−0.526664
$579$	−31.7953	−	10.0647i	−1.32137	−	0.418273i
$580$	12.4470	−	7.18667i	0.516834	−	0.298410i
$581$	−41.1097			−1.70552
$582$	23.6800	+	7.49580i	0.981568	+	0.310711i
$583$		−	20.0875i		−	0.831938i
$584$	2.96066			0.122513
$585$	−31.2718	−	2.80665i	−1.29293	−	0.116041i
$586$	−19.1106			−0.789452
$587$		−	44.7053i		−	1.84519i	−0.385775	−	0.922593i	$-0.626066\pi$
$587$		−	44.7053i		−	1.84519i	0.385775	−	0.922593i	$-0.373934\pi$
$588$	−2.44686	+	7.72987i	−0.100907	+	0.318774i
$589$	−35.4690	+	14.2923i	−1.46147	+	0.588904i
$590$	12.2171	+	21.1595i	0.502969	+	0.871121i
$591$	4.37821	+	1.38590i	0.180095	+	0.0570084i
$592$	−9.62056			−0.395402
$593$	−24.0845			−0.989034			−0.494517	−	0.869168i	$-0.664655\pi$
$593$	−24.0845			−0.989034			−0.494517	+	0.869168i	$0.664655\pi$
$594$	13.5885	−	10.3536i	0.557544	−	0.424813i
$595$	36.0455	−	20.8120i	1.47772	−	0.853208i
$596$		−	15.5439i		−	0.636703i
$597$	−0.247541	−	0.0783582i	−0.0101312	−	0.00320699i
$598$		−	14.5135i		−	0.593503i
$599$		−	18.8474i		−	0.770084i	−0.922899	−	0.385042i	$-0.874187\pi$
$599$		−	18.8474i		−	0.770084i	0.922899	−	0.385042i	$-0.125813\pi$
$600$	−5.84384	−	6.39137i	−0.238574	−	0.260926i
$601$		−	27.3129i		−	1.11412i	−0.830473	−	0.557058i	$-0.811930\pi$
$601$		−	27.3129i		−	1.11412i	0.830473	−	0.557058i	$-0.188070\pi$
$602$		−	11.8495i		−	0.482949i
$603$	−1.87872	+	2.67019i	−0.0765075	+	0.108738i
$604$			19.8962i			0.809563i
$605$	−0.369728	+	0.213474i	−0.0150316	+	0.00867895i
$606$	−5.85533	−	1.85348i	−0.237856	−	0.0752924i
$607$		−	38.6428i		−	1.56846i	−0.620469	−	0.784231i	$-0.713058\pi$
$607$		−	38.6428i		−	1.56846i	0.620469	−	0.784231i	$-0.286942\pi$
$608$	6.86815			0.278540
$609$	36.2762	+	11.4831i	1.46998	+	0.465317i
$610$	5.41869	+	9.38494i	0.219396	+	0.379985i
$611$	−37.8186			−1.52998
$612$	−9.40188	+	13.3627i	−0.380048	+	0.540155i
$613$	2.39370			0.0966807			0.0483404	−	0.998831i	$-0.484607\pi$
$613$	2.39370			0.0966807			0.0483404	+	0.998831i	$0.484607\pi$
$614$		−	25.7852i		−	1.04061i
$615$	8.82670	−	1.94655i	0.355927	−	0.0784925i
$616$		−	11.2366i		−	0.452737i
$617$	33.3480			1.34254			0.671271	−	0.741212i	$-0.265749\pi$
$617$	33.3480			1.34254			0.671271	+	0.741212i	$0.265749\pi$
$618$	−28.7498	−	9.10061i	−1.15649	−	0.366080i
$619$			12.9778i			0.521623i	0.965390	+	0.260812i	$0.0839901\pi$
$619$			12.9778i			0.521623i	−0.965390	+	0.260812i	$0.916010\pi$
$620$	−7.67376	+	9.80375i	−0.308185	+	0.393728i
$621$	9.76522	+	12.8163i	0.391865	+	0.514301i
$622$			31.0081i			1.24331i
$623$		−	24.3078i		−	0.973871i
$624$	2.44652	−	7.72882i	0.0979393	−	0.309400i
$625$	−12.5020	−	21.6495i	−0.500080	−	0.865979i
$626$	31.8164			1.27164
$627$	−11.8031	+	37.2871i	−0.471369	+	1.48910i
$628$		−	12.0529i		−	0.480965i
$629$			52.3962i			2.08917i
$630$	2.04947	−	22.8353i	0.0816530	−	0.909778i
$631$			11.2281i			0.446985i	0.974706	+	0.223492i	$0.0717458\pi$
$631$			11.2281i			0.446985i	−0.974706	+	0.223492i	$0.928254\pi$
$632$			1.97839i			0.0786959i
$633$	9.90603	−	31.2942i	0.393729	−	1.24383i
$634$	−34.6184			−1.37487
$635$	0.164382	−	0.0949112i	0.00652331	−	0.00376643i
$636$	10.0892	+	3.19369i	0.400062	+	0.126638i
$637$	−21.9097			−0.868093
$638$	−21.1324			−0.836641
$639$	−1.89835	+	2.69809i	−0.0750976	+	0.106735i
$640$	1.93647	−	1.11808i	0.0765455	−	0.0441960i
$641$	−32.7989			−1.29548			−0.647740	−	0.761862i	$-0.724286\pi$
$641$	−32.7989			−1.29548			−0.647740	+	0.761862i	$0.724286\pi$
$642$	2.74199	−	8.66222i	0.108218	−	0.341870i
$643$	20.1537			0.794784			0.397392	−	0.917649i	$-0.369915\pi$
$643$	20.1537			0.794784			0.397392	+	0.917649i	$0.369915\pi$
$644$	10.5981			0.417622
$645$	2.89174	+	13.1127i	0.113862	+	0.516311i
$646$		−	37.4058i		−	1.47171i
$647$		−	12.2378i		−	0.481116i	−0.970635	−	0.240558i	$-0.922669\pi$
$647$		−	12.2378i		−	0.481116i	0.970635	−	0.240558i	$-0.0773305\pi$
$648$	3.03980	+	8.47111i	0.119415	+	0.332776i
$649$		−	35.9243i		−	1.41015i
$650$	11.7002	−	20.2675i	0.458920	−	0.794958i
$651$	−32.8633	+	2.51838i	−1.28802	+	0.0987031i
$652$		−	0.995539i		−	0.0389883i
$653$	0.722505			0.0282738			0.0141369	−	0.999900i	$-0.495500\pi$
$653$	0.722505			0.0282738			0.0141369	+	0.999900i	$0.495500\pi$
$654$	4.36157	−	13.7786i	0.170551	−	0.538787i
$655$	−1.28466	−	2.22497i	−0.0501957	−	0.0869368i
$656$			2.33381i			0.0911198i
$657$	−7.26413	−	5.11098i	−0.283401	−	0.199398i
$658$		−	27.6159i		−	1.07658i
$659$		−	19.7963i		−	0.771154i	−0.922676	−	0.385577i	$-0.874002\pi$
$659$		−	19.7963i		−	0.771154i	0.922676	−	0.385577i	$-0.125998\pi$
$660$	2.74218	+	12.4345i	0.106739	+	0.484012i
$661$	−15.9633			−0.620899			−0.310449	−	0.950590i	$-0.600480\pi$
$661$	−15.9633			−0.620899			−0.310449	+	0.950590i	$0.600480\pi$
$662$			10.3693i			0.403012i
$663$	−42.0932	−	13.3244i	−1.63477	−	0.517478i
$664$			12.0282i			0.466787i
$665$	26.2455	+	45.4560i	1.01776	+	1.76271i
$666$	23.6045	+	16.6079i	0.914656	+	0.643544i
$667$		−	19.9315i		−	0.771751i
$668$		−	4.42181i		−	0.171085i
$669$	−10.0484	+	31.7439i	−0.388493	+	1.22729i
$670$	−1.21680	−	2.10745i	−0.0470091	−	0.0814178i
$671$		−	15.9337i		−	0.615112i
$672$	5.64373	+	1.78650i	0.217712	+	0.0689157i
$673$	42.7732			1.64879			0.824393	−	0.566018i	$-0.191517\pi$
$673$	42.7732			1.64879			0.824393	+	0.566018i	$0.191517\pi$
$674$	−27.3911			−1.05507
$675$	3.30474	+	25.7697i	0.127200	+	0.991877i
$676$	8.90669			0.342565
$677$		−	36.1383i		−	1.38891i	−0.719538	−	0.694453i	$-0.755646\pi$
$677$		−	36.1383i		−	1.38891i	0.719538	−	0.694453i	$-0.244354\pi$
$678$	−2.59298	+	8.19150i	−0.0995829	+	0.314593i
$679$	−49.0116			−1.88089
$680$	−6.08936	−	10.5465i	−0.233516	−	0.404440i
$681$	8.05149	−	25.4355i	0.308534	−	0.974689i
$682$	16.9786	−	6.84158i	0.650146	−	0.261978i
$683$	15.0101			0.574346			0.287173	−	0.957879i	$-0.407285\pi$
$683$	15.0101			0.574346			0.287173	+	0.957879i	$0.407285\pi$
$684$	−16.8513	−	11.8565i	−0.644327	−	0.453343i
$685$	1.06402	+	1.84284i	0.0406543	+	0.0704115i
$686$			7.92546i			0.302595i
$687$	−49.8284	−	15.7730i	−1.90107	−	0.601776i
$688$	−3.46703			−0.132179
$689$			28.5969i			1.08946i
$690$	−11.7279	+	2.58634i	−0.446472	+	0.0984604i
$691$	4.45097			0.169323			0.0846615	−	0.996410i	$-0.473019\pi$
$691$	4.45097			0.169323			0.0846615	+	0.996410i	$0.473019\pi$
$692$	−12.7201			−0.483547
$693$	−19.3978	+	27.5696i	−0.736860	+	1.04728i
$694$		−	21.3382i		−	0.809985i
$695$	22.2197	+	38.4837i	0.842843	+	1.45977i
$696$	3.35982	−	10.6140i	0.127354	−	0.402323i
$697$	12.7105			0.481446
$698$	−2.59544			−0.0982387
$699$	−0.998542	+	3.15450i	−0.0377683	+	0.119314i
$700$	14.7997	+	8.54372i	0.559378	+	0.322922i
$701$		−	19.7904i		−	0.747472i	−0.927535	−	0.373736i	$-0.878077\pi$
$701$		−	19.7904i		−	0.747472i	0.927535	−	0.373736i	$-0.121923\pi$
$702$	−19.3449	+	14.7396i	−0.730126	+	0.556310i
$703$	−66.0754			−2.49208
$704$	−3.28772			−0.123910
$705$	6.73935	+	30.5598i	0.253819	+	1.15095i
$706$		−	25.0194i		−	0.941618i
$707$	12.1190			0.455784
$708$	18.0434	+	5.71157i	0.678114	+	0.214654i
$709$			21.0629i			0.791035i	0.918458	+	0.395518i	$0.129435\pi$
$709$			21.0629i			0.791035i	−0.918458	+	0.395518i	$0.870565\pi$
$710$	−1.22951	−	2.12947i	−0.0461428	−	0.0799175i
$711$	3.41528	−	4.85406i	0.128083	−	0.182042i
$712$	−7.11220			−0.266541
$713$	6.45278	+	16.0138i	0.241659	+	0.599720i
$714$	9.72975	−	30.7373i	0.364127	−	1.15031i
$715$	−29.7984	+	17.2050i	−1.11440	+	0.643431i
$716$	−21.9549			−0.820492
$717$	6.10209	−	19.2771i	0.227887	−	0.719918i
$718$		−	16.4820i		−	0.615104i
$719$	−25.1433			−0.937687			−0.468843	−	0.883281i	$-0.655329\pi$
$719$	−25.1433			−0.937687			−0.468843	+	0.883281i	$0.655329\pi$
$720$	−6.68135	−	0.599654i	−0.248999	−	0.0223478i
$721$	59.5047			2.21607
$722$	28.1715			1.04844
$723$	25.9159	+	8.20355i	0.963821	+	0.305093i
$724$			0.359283i			0.0133527i
$725$	16.0679	−	27.8335i	0.596748	−	1.03371i
$726$	−0.0998006	+	0.315280i	−0.00370395	+	0.0117012i
$727$		−	2.99183i		−	0.110961i	−0.998460	−	0.0554804i	$-0.982331\pi$
$727$		−	2.99183i		−	0.110961i	0.998460	−	0.0554804i	$-0.0176690\pi$
$728$			15.9967i			0.592877i
$729$	7.16535	−	26.0319i	0.265383	−	0.964143i
$730$	5.73322	−	3.31026i	0.212196	−	0.122518i
$731$			18.8824i			0.698390i
$732$	8.00288	+	2.53328i	0.295795	+	0.0936326i
$733$		−	9.77710i		−	0.361126i	−0.983563	−	0.180563i	$-0.942208\pi$
$733$		−	9.77710i		−	0.361126i	0.983563	−	0.180563i	$-0.0577919\pi$
$734$	−23.0158			−0.849527
$735$	3.90435	+	17.7044i	0.144014	+	0.653037i
$736$		−	3.10088i		−	0.114300i
$737$			3.57801i			0.131798i
$738$	4.02884	−	5.72610i	0.148304	−	0.210781i
$739$			49.3086i			1.81385i	0.421296	+	0.906923i	$0.361575\pi$
$739$			49.3086i			1.81385i	−0.421296	+	0.906923i	$0.638425\pi$
$740$	−18.6299	+	10.7565i	−0.684848	+	0.395418i
$741$	16.8031	−	53.0827i	0.617277	−	1.95004i
$742$	−20.8820			−0.766604
$743$			34.1406i			1.25250i	0.779623	+	0.626249i	$0.215411\pi$
$743$			34.1406i			1.25250i	−0.779623	+	0.626249i	$0.784589\pi$
$744$	0.736851	+	9.61546i	0.0270143	+	0.352520i
$745$	−17.3793	−	30.1003i	−0.636729	−	1.10279i
$746$		−	6.20223i		−	0.227080i
$747$	20.7643	−	29.5119i	0.759727	−	1.07978i
$748$			17.9058i			0.654700i
$749$			17.9286i			0.655097i
$750$	−18.4624	−	5.84279i	−0.674153	−	0.213349i
$751$	−25.1022			−0.915991			−0.457996	−	0.888954i	$-0.651432\pi$
$751$	−25.1022			−0.915991			−0.457996	+	0.888954i	$0.651432\pi$
$752$	−8.08010			−0.294651
$753$	9.85937	−	31.1468i	0.359295	−	1.13505i
$754$	30.0845			1.09561
$755$	22.2455	+	38.5282i	0.809596	+	1.40219i
$756$	−10.7631	−	14.1260i	−0.391452	−	0.513758i
$757$	17.2025			0.625236			0.312618	−	0.949879i	$-0.398794\pi$
$757$	17.2025			0.625236			0.312618	+	0.949879i	$0.398794\pi$
$758$	−19.4558			−0.706667
$759$	16.8346	+	5.32893i	0.611059	+	0.193428i
$760$	13.2999	−	7.67914i	0.482440	−	0.278552i
$761$	40.4920			1.46783			0.733917	−	0.679239i	$-0.237690\pi$
$761$	40.4920			1.46783			0.733917	+	0.679239i	$0.237690\pi$
$762$	0.0443717	−	0.140175i	0.00160742	−	0.00507799i
$763$			28.5183i			1.03243i
$764$		−	1.29019i		−	0.0466776i
$765$	−3.26588	+	36.3884i	−0.118078	+	1.31563i
$766$		−	20.6516i		−	0.746174i
$767$			51.1426i			1.84665i
$768$	0.522710	−	1.65129i	0.0188617	−	0.0595860i
$769$	−21.5731			−0.777945			−0.388972	−	0.921249i	$-0.627170\pi$
$769$	−21.5731			−0.777945			−0.388972	+	0.921249i	$0.627170\pi$
$770$	−12.5634	−	21.7593i	−0.452755	−	0.784152i
$771$	−0.865492	+	2.73418i	−0.0311699	+	0.0984690i
$772$		−	19.2548i		−	0.692994i
$773$		−	15.5444i		−	0.559092i	−0.960132	−	0.279546i	$-0.909816\pi$
$773$		−	15.5444i		−	0.559092i	0.960132	−	0.279546i	$-0.0901840\pi$
$774$	8.50652	+	5.98512i	0.305761	+	0.215131i
$775$	−3.89860	+	27.5645i	−0.140042	+	0.990146i
$776$			14.3403i			0.514785i
$777$	−54.2958	−	17.1871i	−1.94785	−	0.616584i
$778$	15.9392			0.571448
$779$			16.0289i			0.574296i
$780$	−3.90382	−	17.7020i	−0.139779	−	0.633833i
$781$			3.61539i			0.129369i
$782$	−16.8882			−0.603922
$783$	−26.5664	+	20.2420i	−0.949406	+	0.723388i
$784$	−4.68110			−0.167182
$785$	−13.4761	−	23.3401i	−0.480984	−	0.833044i
$786$	−1.89731	−	0.600586i	−0.0676749	−	0.0214222i
$787$	0.181111			0.00645591			0.00322796	−	0.999995i	$-0.498973\pi$
$787$	0.181111			0.00645591			0.00322796	+	0.999995i	$0.498973\pi$
$788$			2.65138i			0.0944514i
$789$	−19.9566	−	6.31718i	−0.710475	−	0.224898i
$790$	2.21199	+	3.83108i	0.0786991	+	0.136304i
$791$		−	16.9543i		−	0.602827i
$792$	8.06657	+	5.67557i	0.286633	+	0.201673i
$793$			22.6835i			0.805515i
$794$			34.3942i			1.22061i
$795$	23.1081	−	5.09604i	0.819561	−	0.180738i
$796$		−	0.149907i		−	0.00531333i
$797$			9.04769i			0.320486i	0.987078	+	0.160243i	$0.0512277\pi$
$797$			9.04769i			0.320486i	−0.987078	+	0.160243i	$0.948772\pi$
$798$	38.7620	+	12.2699i	1.37216	+	0.434351i
$799$			44.0064i			1.55684i
$800$	2.49980	−	4.33024i	0.0883812	−	0.153097i
$801$	17.4501	+	12.2778i	0.616570	+	0.433813i
$802$	12.7802			0.451285
$803$	−9.73382			−0.343499
$804$	−1.79710	−	0.568863i	−0.0633788	−	0.0200623i
$805$	20.5228	−	11.8495i	0.723334	−	0.417639i
$806$	−24.1711	+	9.73981i	−0.851392	+	0.343070i
$807$	−4.66275	+	14.7301i	−0.164136	+	0.518524i
$808$		−	3.54590i		−	0.124744i
$809$	−46.4378			−1.63267			−0.816333	−	0.577582i	$-0.803996\pi$
$809$	−46.4378			−1.63267			−0.816333	+	0.577582i	$0.803996\pi$
$810$	15.3578	+	13.0053i	0.539619	+	0.456959i
$811$	28.7351			1.00902			0.504512	−	0.863404i	$-0.331672\pi$
$811$	28.7351			1.00902			0.504512	+	0.863404i	$0.331672\pi$
$812$			21.9683i			0.770937i
$813$	10.9273	+	3.45899i	0.383238	+	0.121312i
$814$	31.6296			1.10862
$815$	−1.11309	−	1.92783i	−0.0389899	−	0.0675288i
$816$	−8.99340	−	2.84682i	−0.314832	−	0.0996587i
$817$	−23.8121			−0.833079
$818$			3.23048i			0.112951i
$819$	27.6150	−	39.2487i	0.964948	−	1.37146i
$820$	2.60938	+	4.51933i	0.0911235	+	0.157822i
$821$	−14.7842			−0.515971			−0.257985	−	0.966149i	$-0.583059\pi$
$821$	−14.7842			−0.515971			−0.257985	+	0.966149i	$0.583059\pi$
$822$	1.57146	+	0.497439i	0.0548110	+	0.0173502i
$823$	37.1050			1.29340			0.646699	−	0.762745i	$-0.276149\pi$
$823$	37.1050			1.29340			0.646699	+	0.762745i	$0.276149\pi$
$824$		−	17.4104i		−	0.606521i
$825$	19.2129	+	21.0130i	0.668906	+	0.731578i
$826$	−37.3453			−1.29941
$827$			46.2613i			1.60866i	0.594181	+	0.804331i	$0.297476\pi$
$827$			46.2613i			1.60866i	−0.594181	+	0.804331i	$0.702524\pi$
$828$	−5.35304	+	7.60816i	−0.186031	+	0.264402i
$829$		−	26.7473i		−	0.928971i	−0.885581	−	0.464485i	$-0.846239\pi$
$829$		−	26.7473i		−	0.928971i	0.885581	−	0.464485i	$-0.153761\pi$
$830$	13.4485	+	23.2923i	0.466805	+	0.808487i
$831$	5.11157	−	16.1480i	0.177319	−	0.560167i
$832$	4.68046			0.162266
$833$			25.4945i			0.883333i
$834$	32.8164	+	10.3879i	1.13634	+	0.359703i
$835$	−4.94393	−	8.56269i	−0.171092	−	0.296324i
$836$	−22.5805			−0.780964
$837$	14.7912	−	24.8640i	0.511260	−	0.859426i
$838$			32.9933i			1.13973i
$839$		−	32.3153i		−	1.11565i	−0.829959	−	0.557825i	$-0.811636\pi$
$839$		−	32.3153i		−	1.11565i	0.829959	−	0.557825i	$-0.188364\pi$
$840$	12.9263	−	2.85065i	0.446001	−	0.0983566i
$841$	12.3152			0.424663
$842$	16.6200			0.572761
$843$	35.6729	+	11.2921i	1.22864	+	0.388921i
$844$	18.9513			0.652330
$845$	17.2475	−	9.95839i	0.593332	−	0.342579i
$846$	19.8249	+	13.9487i	0.681595	+	0.479565i
$847$		−	0.652550i		−	0.0224219i
$848$			6.10986i			0.209813i
$849$	16.1838	+	5.12291i	0.555426	+	0.175818i
$850$	−23.5837	−	13.6146i	−0.808913	−	0.466976i
$851$			29.8322i			1.02263i
$852$	−1.81587	−	0.574807i	−0.0622108	−	0.0196926i
$853$			47.3772i			1.62217i	0.584931	+	0.811083i	$0.301121\pi$
$853$			47.3772i			1.62217i	−0.584931	+	0.811083i	$0.698879\pi$
$854$	−16.5639			−0.566806
$855$	−45.8885	−	4.11851i	−1.56935	−	0.140850i
$856$	5.24571			0.179295
$857$	−27.1307			−0.926768			−0.463384	−	0.886158i	$-0.653365\pi$
$857$	−27.1307			−0.926768			−0.463384	+	0.886158i	$0.653365\pi$
$858$	−8.04347	+	25.4101i	−0.274600	+	0.867488i
$859$		−	12.7421i		−	0.434756i	−0.976087	−	0.217378i	$-0.930250\pi$
$859$		−	12.7421i		−	0.434756i	0.976087	−	0.217378i	$-0.0697504\pi$
$860$	−6.71378	+	3.87641i	−0.228938	+	0.132185i
$861$	−4.16934	+	13.1714i	−0.142091	+	0.448879i
$862$			11.5566i			0.393619i
$863$		−	32.7027i		−	1.11321i	−0.830776	−	0.556607i	$-0.812103\pi$
$863$		−	32.7027i		−	1.11321i	0.830776	−	0.556607i	$-0.187897\pi$
$864$	−4.13312	+	3.14918i	−0.140612	+	0.107137i
$865$	−24.6321	+	14.2221i	−0.837517	+	0.483567i
$866$	19.1307			0.650087
$867$	−6.61848	+	20.9085i	−0.224776	+	0.710089i
$868$	−7.11220	−	17.6502i	−0.241404	−	0.599088i
$869$		−	6.50437i		−	0.220646i
$870$	−5.36113	−	24.3102i	−0.181759	−	0.824194i
$871$		−	5.09373i		−	0.172594i
$872$	8.34414			0.282568
$873$	24.7556	−	35.1845i	0.837848	−	1.19082i
$874$		−	21.2973i		−	0.720392i
$875$	38.2117	−	0.00266270i	1.29179	−	9.00157e-5i
$876$	1.54757	−	4.88893i	0.0522875	−	0.165182i
$877$			32.8494i			1.10925i	0.832102	+	0.554623i	$0.187138\pi$
$877$			32.8494i			1.10925i	−0.832102	+	0.554623i	$0.812862\pi$
$878$	6.31038			0.212965
$879$	−9.98931	+	31.5573i	−0.336931	+	1.06440i
$880$	−6.36655	+	3.67593i	−0.214616	+	0.123915i
$881$	16.4527			0.554307			0.277154	−	0.960826i	$-0.410609\pi$
$881$	16.4527			0.554307			0.277154	+	0.960826i	$0.410609\pi$
$882$	11.4853	+	8.08096i	0.386730	+	0.272100i
$883$	−41.8226			−1.40744			−0.703721	−	0.710477i	$-0.748479\pi$
$883$	−41.8226			−1.40744			−0.703721	+	0.710477i	$0.748479\pi$
$884$		−	25.4910i		−	0.857357i
$885$	41.3265	−	9.11373i	1.38917	−	0.306355i
$886$	−38.7666			−1.30239
$887$	17.2847			0.580363			0.290182	−	0.956972i	$-0.406284\pi$
$887$	17.2847			0.580363			0.290182	+	0.956972i	$0.406284\pi$
$888$	−5.02876	+	15.8864i	−0.168754	+	0.533112i
$889$			0.290126i			0.00973051i
$890$	−13.7725	+	7.95200i	−0.461656	+	0.266552i
$891$	−9.99399	−	27.8506i	−0.334811	−	0.933030i
$892$	−19.2236			−0.643655
$893$	−55.4954			−1.85708
$894$	−25.6676	−	8.12496i	−0.858452	−	0.271739i
$895$	−42.5149	+	24.5473i	−1.42111	+	0.820525i
$896$			3.41776i			0.114179i
$897$	−23.9661	−	7.58637i	−0.800206	−	0.253302i
$898$	27.0762			0.903543
$899$	−33.1943	+	13.3757i	−1.10709	+	0.446105i
$900$	−13.6087	+	6.30907i	−0.453622	+	0.210302i
$901$	33.2759			1.10858
$902$		−	7.67289i		−	0.255479i
$903$	−19.5670	−	6.19384i	−0.651148	−	0.206118i
$904$	−4.96065			−0.164989
$905$	0.401707	+	0.695740i	0.0133532	+	0.0231272i
$906$	32.8544	+	10.3999i	1.09152	+	0.345514i
$907$			21.2955i			0.707105i	0.935415	+	0.353552i	$0.115026\pi$
$907$			21.2955i			0.707105i	−0.935415	+	0.353552i	$0.884974\pi$
$908$	15.4034			0.511178
$909$	−6.12128	+	8.70004i	−0.203030	+	0.288562i
$910$	17.8856	+	30.9770i	0.592901	+	1.02688i
$911$	7.23088			0.239570			0.119785	−	0.992800i	$-0.461780\pi$
$911$	7.23088			0.239570			0.119785	+	0.992800i	$0.461780\pi$
$912$	3.59005	−	11.3413i	0.118879	−	0.375549i
$913$		−	39.5455i		−	1.30876i
$914$	24.5238			0.811176
$915$	18.3297	−	4.04225i	0.605961	−	0.133633i
$916$		−	30.1753i		−	0.997021i
$917$	3.92696			0.129680
$918$	17.1513	+	22.5101i	0.566077	+	0.742944i
$919$	−12.7137			−0.419387			−0.209693	−	0.977767i	$-0.567247\pi$
$919$	−12.7137			−0.419387			−0.209693	+	0.977767i	$0.567247\pi$
$920$	−3.46703	−	6.00475i	−0.114305	−	0.197971i
$921$	−42.5790	−	13.4782i	−1.40303	−	0.444122i
$922$	2.01028			0.0662052
$923$		−	5.14694i		−	0.169414i
$924$	−18.5550	−	5.87350i	−0.610414	−	0.193224i
$925$	−24.0495	+	41.6593i	−0.790741	+	1.36975i
$926$	−17.6292			−0.579331
$927$	−30.0556	+	42.7174i	−0.987155	+	1.40302i
$928$	6.42769			0.210999
$929$	29.8417			0.979075			0.489538	−	0.871982i	$-0.337166\pi$
$929$	29.8417			0.979075			0.489538	+	0.871982i	$0.337166\pi$
$930$	12.1777	+	17.7961i	0.399323	+	0.583559i
$931$	−32.1505			−1.05369
$932$	−1.91032			−0.0625745
$933$	51.2035	+	16.2082i	1.67633	+	0.530634i
$934$	−3.08510			−0.100948
$935$	20.0201	+	34.6739i	0.654727	+	1.13396i
$936$	−11.4837	−	8.07986i	−0.375358	−	0.264099i
$937$		−	9.59077i		−	0.313317i	−0.987653	−	0.156658i	$-0.949928\pi$
$937$		−	9.59077i		−	0.313317i	0.987653	−	0.156658i	$-0.0500722\pi$
$938$	3.71954			0.121447
$939$	16.6307	−	52.5382i	0.542724	−	1.71452i
$940$	−15.6468	+	9.03419i	−0.510344	+	0.294663i
$941$	−16.6401			−0.542452			−0.271226	−	0.962516i	$-0.587429\pi$
$941$	−16.6401			−0.542452			−0.271226	+	0.962516i	$0.587429\pi$
$942$	−19.9030	−	6.30019i	−0.648473	−	0.205271i
$943$	7.23685			0.235664
$944$			10.9268i			0.355638i
$945$	−36.6365	−	15.3205i	−1.19178	−	0.498376i
$946$	11.3986			0.370601
$947$			2.95589i			0.0960534i	0.998846	+	0.0480267i	$0.0152933\pi$
$947$			2.95589i			0.0960534i	−0.998846	+	0.0480267i	$0.984707\pi$
$948$	3.26690	+	1.03412i	0.106104	+	0.0335867i
$949$	13.8573			0.449826
$950$	17.1690	−	29.7408i	0.557036	−	0.964918i
$951$	−18.0954	+	57.1652i	−0.586784	+	1.85371i
$952$	18.6141			0.603285
$953$			55.7228i			1.80504i	0.430648	+	0.902520i	$0.358285\pi$
$953$			55.7228i			1.80504i	−0.430648	+	0.902520i	$0.641715\pi$
$954$	10.5474	−	14.9908i	0.341486	−	0.485346i
$955$	−1.44254	−	2.49842i	−0.0466794	−	0.0808468i
$956$	11.6740			0.377563
$957$	−11.0461	+	34.8959i	−0.357071	+	1.12802i
$958$		−	4.14251i		−	0.133838i
$959$	−3.25252			−0.105030
$960$	−0.834068	−	3.78211i	−0.0269194	−	0.122067i
$961$	22.3393	−	21.4932i	0.720622	−	0.693328i
$962$	−45.0286			−1.45178
$963$	−12.8706	−	9.05566i	−0.414750	−	0.291814i
$964$			15.6943i			0.505478i
$965$	−21.5284	−	37.2862i	−0.693022	−	1.20029i
$966$	5.53972	−	17.5005i	0.178237	−	0.563071i
$967$	43.9466			1.41323			0.706614	−	0.707599i	$-0.250222\pi$
$967$	43.9466			1.41323			0.706614	+	0.707599i	$0.250222\pi$
$968$	−0.190929			−0.00613670
$969$	−61.7680	−	19.5524i	−1.98427	−	0.628113i
$970$	16.0335	+	27.7694i	0.514806	+	0.891623i
$971$			16.2976i			0.523016i	0.965201	+	0.261508i	$0.0842198\pi$
$971$			16.2976i			0.523016i	−0.965201	+	0.261508i	$0.915780\pi$
$972$	15.5772	−	0.591672i	0.499640	−	0.0189779i
$973$	−67.9217			−2.17747
$974$	−21.6677			−0.694278
$975$	−27.3518	−	29.9145i	−0.875960	−	0.958032i
$976$			4.84643i			0.155130i
$977$	−36.8820			−1.17996			−0.589979	−	0.807419i	$-0.700864\pi$
$977$	−36.8820			−1.17996			−0.589979	+	0.807419i	$0.700864\pi$
$978$	−1.64393	−	0.520378i	−0.0525670	−	0.0166399i
$979$	23.3829			0.747320
$980$	−9.06478	+	5.23384i	−0.289564	+	0.167189i
$981$	−20.4728	−	14.4045i	−0.653645	−	0.459899i
$982$	−11.1308			−0.355199
$983$			15.0465i			0.479909i	0.970784	+	0.239954i	$0.0771325\pi$
$983$			15.0465i			0.479909i	−0.970784	+	0.239954i	$0.922867\pi$
$984$	3.85380	+	1.21990i	0.122855	+	0.0388891i
$985$	2.96445	+	5.13430i	0.0944552	+	0.163593i
$986$		−	35.0070i		−	1.11485i
$987$	−45.6019	−	14.4351i	−1.45153	−	0.459474i
$988$	32.1461			1.02270
$989$			10.7508i			0.341857i
$990$	21.9664	+	1.97149i	0.698137	+	0.0626581i
$991$		−	13.1075i		−	0.416373i	−0.978089	−	0.208186i	$-0.933244\pi$
$991$		−	13.1075i		−	0.416373i	0.978089	−	0.208186i	$-0.0667561\pi$
$992$	−5.16427	+	2.08095i	−0.163966	+	0.0660703i
$993$	17.1227	+	5.42011i	0.543372	+	0.172002i
$994$	3.75840			0.119209
$995$	−0.167608	−	0.290291i	−0.00531354	−	0.00920283i
$996$	19.8622	+	6.28729i	0.629357	+	0.199220i
$997$			15.4902i			0.490579i	0.969450	+	0.245290i	$0.0788830\pi$
$997$			15.4902i			0.490579i	−0.969450	+	0.245290i	$0.921117\pi$
$998$		−	41.0696i		−	1.30004i
$999$	39.7629	−	30.2969i	1.25804	−	0.958550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.e.b.929.19	yes	32
3.2	odd	2		930.2.e.a.929.20	yes	32
5.4	even	2		930.2.e.a.929.14	yes	32
15.14	odd	2	inner	930.2.e.b.929.13	yes	32
31.30	odd	2	inner	930.2.e.b.929.14	yes	32
93.92	even	2		930.2.e.a.929.13	✓	32
155.154	odd	2		930.2.e.a.929.19	yes	32
465.464	even	2	inner	930.2.e.b.929.20	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.e.a.929.13	✓	32	93.92	even	2
930.2.e.a.929.14	yes	32	5.4	even	2
930.2.e.a.929.19	yes	32	155.154	odd	2
930.2.e.a.929.20	yes	32	3.2	odd	2
930.2.e.b.929.13	yes	32	15.14	odd	2	inner
930.2.e.b.929.14	yes	32	31.30	odd	2	inner
930.2.e.b.929.19	yes	32	1.1	even	1	trivial
930.2.e.b.929.20	yes	32	465.464	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.522710 - 1.65129i) q^{3} +1.00000 q^{4} +(1.93647 - 1.11808i) q^{5} +(0.522710 - 1.65129i) q^{6} +3.41776i q^{7} +1.00000 q^{8} +(-2.45355 - 1.72630i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.522710 - 1.65129i) q^{3} +1.00000 q^{4} +(1.93647 - 1.11808i) q^{5} +(0.522710 - 1.65129i) q^{6} +3.41776i q^{7} +1.00000 q^{8} +(-2.45355 - 1.72630i) q^{9} +(1.93647 - 1.11808i) q^{10} -3.28772 q^{11} +(0.522710 - 1.65129i) q^{12} +4.68046 q^{13} +3.41776i q^{14} +(-0.834068 - 3.78211i) q^{15} +1.00000 q^{16} -5.44627i q^{17} +(-2.45355 - 1.72630i) q^{18} +6.86815 q^{19} +(1.93647 - 1.11808i) q^{20} +(5.64373 + 1.78650i) q^{21} -3.28772 q^{22} -3.10088i q^{23} +(0.522710 - 1.65129i) q^{24} +(2.49980 - 4.33024i) q^{25} +4.68046 q^{26} +(-4.13312 + 3.14918i) q^{27} +3.41776i q^{28} +6.42769 q^{29} +(-0.834068 - 3.78211i) q^{30} +(-5.16427 + 2.08095i) q^{31} +1.00000 q^{32} +(-1.71852 + 5.42899i) q^{33} -5.44627i q^{34} +(3.82133 + 6.61838i) q^{35} +(-2.45355 - 1.72630i) q^{36} -9.62056 q^{37} +6.86815 q^{38} +(2.44652 - 7.72882i) q^{39} +(1.93647 - 1.11808i) q^{40} +2.33381i q^{41} +(5.64373 + 1.78650i) q^{42} -3.46703 q^{43} -3.28772 q^{44} +(-6.68135 - 0.599654i) q^{45} -3.10088i q^{46} -8.08010 q^{47} +(0.522710 - 1.65129i) q^{48} -4.68110 q^{49} +(2.49980 - 4.33024i) q^{50} +(-8.99340 - 2.84682i) q^{51} +4.68046 q^{52} +6.10986i q^{53} +(-4.13312 + 3.14918i) q^{54} +(-6.36655 + 3.67593i) q^{55} +3.41776i q^{56} +(3.59005 - 11.3413i) q^{57} +6.42769 q^{58} +10.9268i q^{59} +(-0.834068 - 3.78211i) q^{60} +4.84643i q^{61} +(-5.16427 + 2.08095i) q^{62} +(5.90007 - 8.38564i) q^{63} +1.00000 q^{64} +(9.06355 - 5.23312i) q^{65} +(-1.71852 + 5.42899i) q^{66} -1.08830i q^{67} -5.44627i q^{68} +(-5.12047 - 1.62086i) q^{69} +(3.82133 + 6.61838i) q^{70} -1.09967i q^{71} +(-2.45355 - 1.72630i) q^{72} +2.96066 q^{73} -9.62056 q^{74} +(-5.84384 - 6.39137i) q^{75} +6.86815 q^{76} -11.2366i q^{77} +(2.44652 - 7.72882i) q^{78} +1.97839i q^{79} +(1.93647 - 1.11808i) q^{80} +(3.03980 + 8.47111i) q^{81} +2.33381i q^{82} +12.0282i q^{83} +(5.64373 + 1.78650i) q^{84} +(-6.08936 - 10.5465i) q^{85} -3.46703 q^{86} +(3.35982 - 10.6140i) q^{87} -3.28772 q^{88} -7.11220 q^{89} +(-6.68135 - 0.599654i) q^{90} +15.9967i q^{91} -3.10088i q^{92} +(0.736851 + 9.61546i) q^{93} -8.08010 q^{94} +(13.2999 - 7.67914i) q^{95} +(0.522710 - 1.65129i) q^{96} +14.3403i q^{97} -4.68110 q^{98} +(8.06657 + 5.67557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9	\( 32 q + 32 q^{2} + 32 q^{4} - 2 q^{5} + 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} + 4 q^{18} + 8 q^{19} - 2 q^{20} + 10 q^{25} - 12 q^{31} + 32 q^{32} + 8 q^{33} - 16 q^{35} + 4 q^{36} + 8 q^{38} - 4 q^{39} - 2 q^{40} - 42 q^{45} + 4 q^{47} - 36 q^{49} + 10 q^{50} - 4 q^{51} - 12 q^{62} + 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} + 4 q^{72} + 8 q^{76} - 4 q^{78} - 2 q^{80} + 24 q^{81} + 4 q^{87} - 42 q^{90} - 24 q^{93} + 4 q^{94} + 26 q^{95} - 36 q^{98}+O(q^{100}) \) 32 * q + 32 * q^2 + 32 * q^4 - 2 * q^5 + 32 * q^8 + 4 * q^9 - 2 * q^10 + 32 * q^16 + 4 * q^18 + 8 * q^19 - 2 * q^20 + 10 * q^25 - 12 * q^31 + 32 * q^32 + 8 * q^33 - 16 * q^35 + 4 * q^36 + 8 * q^38 - 4 * q^39 - 2 * q^40 - 42 * q^45 + 4 * q^47 - 36 * q^49 + 10 * q^50 - 4 * q^51 - 12 * q^62 + 24 * q^63 + 32 * q^64 + 8 * q^66 - 8 * q^69 - 16 * q^70 + 4 * q^72 + 8 * q^76 - 4 * q^78 - 2 * q^80 + 24 * q^81 + 4 * q^87 - 42 * q^90 - 24 * q^93 + 4 * q^94 + 26 * q^95 - 36 * q^98

Introduction

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