LMFDB - Embedded newform 930.2.e.a.929.13

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			929.13
Character	$\chi$	$=$	930.929
Dual form			930.2.e.a.929.14

$q$-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} +(2.85849 + 2.61324i) 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} +(-2.85849 - 2.61324i) 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} +(2.82108 - 6.08618i) 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} +(2.85849 + 2.61324i) 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} +(-8.45718 - 1.86444i) 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} +(-2.82108 + 6.08618i) 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} + 10 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} - 10 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 + 10 * 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 - 10 * 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	$-0.724839\pi$
$13$	−4.68046			−1.29813			−0.649063	+	0.760735i	$0.724839\pi$
$14$		−	3.41776i		−	0.913435i
$15$	2.85849	+	2.61324i	0.738058	+	0.674737i
$16$	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	$0.296440\pi$
$30$	−2.85849	−	2.61324i	−0.521886	−	0.477111i
$31$	−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	$-0.209662\pi$
$37$	9.62056			1.58161			0.790805	+	0.612068i	$0.209662\pi$
$38$	−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	$-0.941665\pi$
$41$		−	2.33381i		−	0.364479i	0.983254	−	0.182240i	$-0.0583346\pi$
$42$	−5.64373	+	1.78650i	−0.870847	+	0.275663i
$43$	3.46703			0.528717			0.264358	−	0.964424i	$-0.414840\pi$
$43$	3.46703			0.528717			0.264358	+	0.964424i	$0.414840\pi$
$44$	−3.28772			−0.495642
$45$	2.82108	−	6.08618i	0.420541	−	0.907273i
$46$			3.10088i			0.457200i
$47$	8.08010			1.17860			0.589302	−	0.807913i	$-0.299403\pi$
$47$	8.08010			1.17860			0.589302	+	0.807913i	$0.299403\pi$
$48$	−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	$-0.748117\pi$
$59$		−	10.9268i		−	1.42255i	0.702912	−	0.711277i	$-0.251883\pi$
$60$	2.85849	+	2.61324i	0.369029	+	0.337368i
$61$		−	4.84643i		−	0.620521i	−0.950652	−	0.310261i	$-0.899584\pi$
$61$		−	4.84643i		−	0.620521i	0.950652	−	0.310261i	$-0.100416\pi$
$62$	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	$0.0207855\pi$
$71$			1.09967i			0.130506i	−0.997869	+	0.0652532i	$0.979214\pi$
$72$	2.45355	−	1.72630i	0.289153	−	0.203446i
$73$	−2.96066			−0.346519			−0.173260	−	0.984876i	$-0.555430\pi$
$73$	−2.96066			−0.346519			−0.173260	+	0.984876i	$0.555430\pi$
$74$	−9.62056			−1.11837
$75$	−8.45718	−	1.86444i	−0.976551	−	0.215287i
$76$	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	$-0.964501\pi$
$79$		−	1.97839i		−	0.222586i	0.993788	−	0.111293i	$-0.0354992\pi$
$80$	−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	$0.623026\pi$
$90$	−2.82108	+	6.08618i	−0.297368	+	0.641539i
$91$		−	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	$0.0564501\pi$
$101$			3.54590i			0.352830i	−0.984316	+	0.176415i	$0.943550\pi$
$102$	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
$105$	−8.93145	+	9.76963i	−0.871620	+	0.953418i
$106$		−	6.10986i		−	0.593442i
$107$	−5.24571			−0.507122			−0.253561	−	0.967319i	$-0.581602\pi$
$107$	−5.24571			−0.507122			−0.253561	+	0.967319i	$0.581602\pi$
$108$	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	$-0.425038\pi$
$113$	4.96065			0.466659			0.233330	+	0.972398i	$0.425038\pi$
$114$	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
$120$	−2.85849	−	2.61324i	−0.260943	−	0.238555i
$121$	−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	$-0.501199\pi$
$127$	−0.0848877			−0.00753257			−0.00376628	+	0.999993i	$0.501199\pi$
$128$	−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	$0.0159839\pi$
$131$			1.14899i			0.100387i	−0.998740	+	0.0501937i	$0.984016\pi$
$132$	1.71852	+	5.42899i	0.149578	+	0.472533i
$133$			23.4737i			2.03543i
$134$			1.08830i			0.0940145i
$135$	−11.5247	−	1.47712i	−0.991886	−	0.127131i
$136$			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	$-0.680900\pi$
$139$		−	19.8731i		−	1.68562i	0.538212	−	0.842809i	$-0.319100\pi$
$140$	−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	$0.219702\pi$
$149$			15.5439i			1.27341i	−0.771109	+	0.636703i	$0.780298\pi$
$150$	8.45718	+	1.86444i	0.690526	+	0.152231i
$151$		−	19.8962i		−	1.61913i	−0.587033	−	0.809563i	$-0.699704\pi$
$151$		−	19.8962i		−	1.61913i	0.587033	−	0.809563i	$-0.300296\pi$
$152$	−6.86815			−0.557081
$153$	9.40188	+	13.3627i	0.760097	+	1.08031i
$154$			11.2366i			0.905473i
$155$	12.3271	−	1.74437i	0.990136	−	0.140111i
$156$	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
$165$	−9.39789	−	8.59160i	−0.731625	−	0.668855i
$166$		−	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	$-0.339348\pi$
$173$	12.7201			0.967094			0.483547	+	0.875318i	$0.339348\pi$
$174$	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	$0.806300\pi$
$180$	2.82108	−	6.08618i	0.210271	−	0.453637i
$181$		−	0.359283i		−	0.0267053i	−0.999911	−	0.0133527i	$-0.995750\pi$
$181$		−	0.359283i		−	0.0267053i	0.999911	−	0.0133527i	$-0.00425041\pi$
$182$			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	$0.0148633\pi$
$191$			1.29019i			0.0933551i	−0.998910	+	0.0466776i	$0.985137\pi$
$192$	−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
$195$	−13.3790	−	12.2312i	−0.958093	−	0.875893i
$196$	−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	$0.00169129\pi$
$199$			0.149907i			0.0106267i	−0.999986	+	0.00531333i	$0.998309\pi$
$200$	−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
$210$	8.93145	−	9.76963i	0.616328	−	0.674169i
$211$	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	$-0.277417\pi$
$223$	19.2236			1.28731			0.643655	+	0.765316i	$0.277417\pi$
$224$		−	3.41776i		−	0.228359i
$225$	1.34191	+	14.9399i	0.0894605	+	0.995990i
$226$	−4.96065			−0.329978
$227$	−15.4034			−1.02236			−0.511178	−	0.859475i	$-0.670791\pi$
$227$	−15.4034			−1.02236			−0.511178	+	0.859475i	$0.670791\pi$
$228$	−3.59005	−	11.3413i	−0.237757	−	0.751099i
$229$			30.1753i			1.99404i	0.0771263	+	0.997021i	$0.475426\pi$
$229$			30.1753i			1.99404i	−0.0771263	+	0.997021i	$0.524574\pi$
$230$	−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	$-0.480069\pi$
$233$	1.91032			0.125149			0.0625745	+	0.998040i	$0.480069\pi$
$234$	−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	$0.376762\pi$
$240$	2.85849	+	2.61324i	0.184515	+	0.168684i
$241$		−	15.6943i		−	1.01096i	−0.862839	−	0.505478i	$-0.831316\pi$
$241$		−	15.6943i		−	1.01096i	0.862839	−	0.505478i	$-0.168684\pi$
$242$	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
$255$	14.2324	−	15.5681i	0.891270	−	0.974912i
$256$	1.00000			0.0625000
$257$	1.65578			0.103285			0.0516423	−	0.998666i	$-0.483554\pi$
$257$	1.65578			0.103285			0.0516423	+	0.998666i	$0.483554\pi$
$258$	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	$0.587666\pi$
$270$	11.5247	+	1.47712i	0.701369	+	0.0898948i
$271$		−	6.61742i		−	0.401980i	−0.979593	−	0.200990i	$-0.935584\pi$
$271$		−	6.61742i		−	0.401980i	0.979593	−	0.200990i	$-0.0644158\pi$
$272$		−	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	$-0.594914\pi$
$277$	−9.77898			−0.587562			−0.293781	+	0.955873i	$0.594914\pi$
$278$			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	$-0.777122\pi$
$281$		−	21.6030i		−	1.28873i	0.764719	−	0.644364i	$-0.222878\pi$
$282$	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
$285$	19.6325	+	17.9482i	1.16293	+	1.06316i
$286$	−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	$-0.311482\pi$
$293$	19.1106			1.11645			0.558227	+	0.829688i	$0.311482\pi$
$294$	−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
$300$	−8.45718	−	1.86444i	−0.488275	−	0.107644i
$301$			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
$310$	−12.3271	+	1.74437i	−0.700132	+	0.0990733i
$311$		−	31.0081i		−	1.75831i	−0.476538	−	0.879154i	$-0.658108\pi$
$311$		−	31.0081i		−	1.75831i	0.476538	−	0.879154i	$-0.341892\pi$
$312$	−2.44652	−	7.72882i	−0.138507	−	0.437558i
$313$	−31.8164			−1.79837			−0.899184	−	0.437570i	$-0.855839\pi$
$313$	−31.8164			−1.79837			−0.899184	+	0.437570i	$0.855839\pi$
$314$			12.0529i			0.680187i
$315$	20.8011	+	9.64177i	1.17201	+	0.543252i
$316$		−	1.97839i		−	0.111293i
$317$	34.6184			1.94436			0.972182	−	0.234226i	$-0.0752554\pi$
$317$	34.6184			1.94436			0.972182	+	0.234226i	$0.0752554\pi$
$318$	−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
$330$	9.39789	+	8.59160i	0.517337	+	0.472952i
$331$		−	10.3693i		−	0.569946i	−0.958536	−	0.284973i	$-0.908015\pi$
$331$		−	10.3693i		−	0.569946i	0.958536	−	0.284973i	$-0.0919846\pi$
$332$			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	$-0.231951\pi$
$337$	27.3911			1.49209			0.746045	+	0.665896i	$0.231951\pi$
$338$	−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
$345$	8.10336	−	8.86383i	0.436270	−	0.477212i
$346$	−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	$0.143232\pi$
$359$			16.4820i			0.869888i	−0.900458	+	0.434944i	$0.856768\pi$
$360$	−2.82108	+	6.08618i	−0.148684	+	0.320770i
$361$	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	$-0.294886\pi$
$367$	23.0158			1.20141			0.600707	+	0.799470i	$0.294886\pi$
$368$		−	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
$375$	18.4616	−	5.84536i	0.953354	−	0.301853i
$376$	−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	$0.367594\pi$
$390$	13.3790	+	12.2312i	0.677474	+	0.619350i
$391$	−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
$405$	3.58490	+	19.8027i	0.178135	+	0.984006i
$406$		−	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	$-0.974550\pi$
$409$		−	3.23048i		−	0.159737i	0.996805	−	0.0798686i	$-0.0254501\pi$
$410$	−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	$-0.701675\pi$
$419$		−	32.9933i		−	1.61183i	0.592033	−	0.805914i	$-0.298325\pi$
$420$	−8.93145	+	9.76963i	−0.435810	+	0.476709i
$421$	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	$-0.910219\pi$
$431$		−	11.5566i		−	0.556661i	0.960485	−	0.278331i	$-0.0897811\pi$
$432$	4.13312	+	3.14918i	0.198855	+	0.151515i
$433$	−19.1307			−0.919361			−0.459681	−	0.888084i	$-0.652036\pi$
$433$	−19.1307			−0.919361			−0.459681	+	0.888084i	$0.652036\pi$
$434$	−7.11220	+	17.6502i	−0.341396	+	0.847238i
$435$	18.3735	+	16.7971i	0.880941	+	0.805361i
$436$	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	$-0.127433\pi$
$443$	38.7666			1.84185			0.920927	+	0.389735i	$0.127433\pi$
$444$	−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	$0.279389\pi$
$450$	−1.34191	−	14.9399i	−0.0632581	−	0.704272i
$451$			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	$-0.694449\pi$
$457$	−24.5238			−1.14718			−0.573588	+	0.819144i	$0.694449\pi$
$458$		−	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	$-0.365651\pi$
$463$	17.6292			0.819298			0.409649	+	0.912243i	$0.365651\pi$
$464$	6.42769			0.298398
$465$	−9.32396	−	19.4439i	−0.432388	−	0.901688i
$466$	−1.91032			−0.0884938
$467$	3.08510			0.142761			0.0713807	−	0.997449i	$-0.477259\pi$
$467$	3.08510			0.142761			0.0713807	+	0.997449i	$0.477259\pi$
$468$	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	$0.0301693\pi$
$479$			4.14251i			0.189276i	−0.995512	+	0.0946380i	$0.969831\pi$
$480$	−2.85849	−	2.61324i	−0.130472	−	0.119278i
$481$	−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	$-0.336658\pi$
$487$	21.6677			0.981857			0.490928	+	0.871200i	$0.336658\pi$
$488$			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
$495$	−9.27489	+	20.0096i	−0.416876	+	0.899365i
$496$	−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	$0.371216\pi$
$499$			41.0696i			1.83853i	−0.393639	+	0.919265i	$0.628784\pi$
$500$	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	$-0.691948\pi$
$503$	−25.4390			−1.13427			−0.567135	+	0.823625i	$0.691948\pi$
$504$	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	$0.349428\pi$
$510$	−14.2324	+	15.5681i	−0.630223	+	0.689367i
$511$		−	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	$0.216521\pi$
$521$			28.7128i			1.25793i	−0.777434	+	0.628965i	$0.783479\pi$
$522$	15.7707	−	11.0961i	0.690263	−	0.485663i
$523$	−28.5390			−1.24792			−0.623962	−	0.781454i	$-0.714478\pi$
$523$	−28.5390			−1.24792			−0.623962	+	0.781454i	$0.714478\pi$
$524$			1.14899i			0.0501937i
$525$	6.37222	−	28.9046i	0.278107	−	1.26150i
$526$			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
$540$	−11.5247	−	1.47712i	−0.495943	−	0.0635653i
$541$	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
$555$	27.5002	+	25.1409i	1.16732	+	1.06717i
$556$		−	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	$-0.576041\pi$
$563$	−11.2291			−0.473249			−0.236624	+	0.971601i	$0.576041\pi$
$564$	−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	$0.674464\pi$
$570$	−19.6325	−	17.9482i	−0.822316	−	0.751766i
$571$			42.3322i			1.77155i	0.464117	+	0.885774i	$0.346372\pi$
$571$			42.3322i			1.77155i	−0.464117	+	0.885774i	$0.653628\pi$
$572$	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
$585$	−13.2039	+	28.4861i	−0.545915	+	1.17775i
$586$	−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	$-0.335345\pi$
$593$	24.0845			0.989034			0.494517	+	0.869168i	$0.335345\pi$
$594$	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	$0.125813\pi$
$599$			18.8474i			0.770084i	−0.922899	+	0.385042i	$0.874187\pi$
$600$	8.45718	+	1.86444i	0.345263	+	0.0761156i
$601$			27.3129i			1.11412i	0.830473	+	0.557058i	$0.188070\pi$
$601$			27.3129i			1.11412i	−0.830473	+	0.557058i	$0.811930\pi$
$602$		−	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	$-0.515393\pi$
$613$	−2.39370			−0.0966807			−0.0483404	+	0.998831i	$0.515393\pi$
$614$			25.7852i			1.04061i
$615$	6.09880	−	6.67115i	0.245928	−	0.269007i
$616$			11.2366i			0.452737i
$617$	−33.3480			−1.34254			−0.671271	−	0.741212i	$-0.734251\pi$
$617$	−33.3480			−1.34254			−0.671271	+	0.741212i	$0.734251\pi$
$618$	28.7498	−	9.10061i	1.15649	−	0.366080i
$619$		−	12.9778i		−	0.521623i	−0.965390	−	0.260812i	$-0.916010\pi$
$619$		−	12.9778i		−	0.521623i	0.965390	−	0.260812i	$-0.0839901\pi$
$620$	12.3271	−	1.74437i	0.495068	−	0.0700554i
$621$	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
$630$	−20.8011	−	9.64177i	−0.828736	−	0.384137i
$631$		−	11.2281i		−	0.446985i	−0.974706	−	0.223492i	$-0.928254\pi$
$631$		−	11.2281i		−	0.446985i	0.974706	−	0.223492i	$-0.0717458\pi$
$632$			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	$-0.630085\pi$
$643$	−20.1537			−0.794784			−0.397392	+	0.917649i	$0.630085\pi$
$644$	10.5981			0.417622
$645$	9.91046	+	9.06019i	0.390224	+	0.356745i
$646$			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	$-0.504500\pi$
$653$	−0.722505			−0.0282738			−0.0141369	+	0.999900i	$0.504500\pi$
$654$	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	$0.125998\pi$
$659$			19.7963i			0.771154i	−0.922676	+	0.385577i	$0.874002\pi$
$660$	−9.39789	−	8.59160i	−0.365813	−	0.334428i
$661$	−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	$-0.808483\pi$
$673$	−42.7732			−1.64879			−0.824393	+	0.566018i	$0.808483\pi$
$674$	−27.3911			−1.05507
$675$	23.9687	−	10.0251i	0.922555	−	0.385866i
$676$	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	$-0.592715\pi$
$683$	−15.0101			−0.574346			−0.287173	+	0.957879i	$0.592715\pi$
$684$	−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
$690$	−8.10336	+	8.86383i	−0.308490	+	0.337440i
$691$	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	$0.121923\pi$
$701$			19.7904i			0.747472i	−0.927535	+	0.373736i	$0.878077\pi$
$702$	19.3449	+	14.7396i	0.730126	+	0.556310i
$703$	66.0754			2.49208
$704$	−3.28772			−0.123910
$705$	23.0969	+	21.1153i	0.869879	+	0.795247i
$706$			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	$-0.870565\pi$
$709$		−	21.0629i		−	0.791035i	0.918458	−	0.395518i	$-0.129435\pi$
$710$	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	$0.655329\pi$
$720$	2.82108	−	6.08618i	0.105135	−	0.226818i
$721$	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
$735$	−13.3809	−	12.2328i	−0.493560	−	0.451215i
$736$			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	$-0.638425\pi$
$739$		−	49.3086i		−	1.81385i	0.421296	−	0.906923i	$-0.361575\pi$
$740$	−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
$750$	−18.4616	+	5.84536i	−0.674123	+	0.213442i
$751$	−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	$-0.601206\pi$
$757$	−17.2025			−0.625236			−0.312618	+	0.949879i	$0.601206\pi$
$758$	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
$765$	−33.1470	−	15.3643i	−1.19843	−	0.555499i
$766$			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
$775$	−21.9207	+	17.1606i	−0.787413	+	0.616426i
$776$		−	14.3403i		−	0.514785i
$777$	54.2958	−	17.1871i	1.94785	−	0.616584i
$778$	−15.9392			−0.571448
$779$		−	16.0289i		−	0.574296i
$780$	−13.3790	−	12.2312i	−0.479046	−	0.437947i
$781$		−	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	$-0.501027\pi$
$787$	−0.181111			−0.00645591			−0.00322796	+	0.999995i	$0.501027\pi$
$788$			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
$795$	−15.9666	+	17.4650i	−0.566275	+	0.619418i
$796$			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	$0.803996\pi$
$810$	−3.58490	−	19.8027i	−0.125960	−	0.695797i
$811$	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	$-0.723851\pi$
$823$	−37.1050			−1.29340			−0.646699	+	0.762745i	$0.723851\pi$
$824$			17.4104i			0.606521i
$825$	27.8048	+	6.12976i	0.968039	+	0.213411i
$826$	−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	$0.153761\pi$
$829$			26.7473i			0.928971i	−0.885581	+	0.464485i	$0.846239\pi$
$830$	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	$0.188364\pi$
$839$			32.3153i			1.11565i	−0.829959	+	0.557825i	$0.811636\pi$
$840$	8.93145	−	9.76963i	0.308164	−	0.337084i
$841$	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
$855$	19.3756	−	41.8008i	0.662631	−	1.42956i
$856$	5.24571			0.179295
$857$	27.1307			0.926768			0.463384	−	0.886158i	$-0.346635\pi$
$857$	27.1307			0.926768			0.463384	+	0.886158i	$0.346635\pi$
$858$	8.04347	+	25.4101i	0.274600	+	0.867488i
$859$			12.7421i			0.434756i	0.976087	+	0.217378i	$0.0697504\pi$
$859$			12.7421i			0.434756i	−0.976087	+	0.217378i	$0.930250\pi$
$860$	−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
$870$	−18.3735	−	16.7971i	−0.622919	−	0.569476i
$871$			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	$-0.251521\pi$
$883$	41.8226			1.40744			0.703721	+	0.710477i	$0.251521\pi$
$884$			25.4910i			0.857357i
$885$	28.5545	−	31.2342i	0.959849	−	1.04993i
$886$	−38.7666			−1.30239
$887$	−17.2847			−0.580363			−0.290182	−	0.956972i	$-0.593716\pi$
$887$	−17.2847			−0.580363			−0.290182	+	0.956972i	$0.593716\pi$
$888$	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
$900$	1.34191	+	14.9399i	0.0447302	+	0.497995i
$901$	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
$915$	12.6649	−	13.8535i	0.418689	−	0.457981i
$916$			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	$0.337166\pi$
$930$	9.32396	+	19.4439i	0.305745	+	0.637589i
$931$	−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
$945$	5.04845	−	39.3886i	0.164226	−	1.28131i
$946$	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
$960$	2.85849	+	2.61324i	0.0922573	+	0.0843421i
$961$	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	$-0.749778\pi$
$967$	−43.9466			−1.41323			−0.706614	+	0.707599i	$0.749778\pi$
$968$	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	$-0.915780\pi$
$971$		−	16.2976i		−	0.523016i	0.965201	−	0.261508i	$-0.0842198\pi$
$972$	−15.5772	−	0.591672i	−0.499640	−	0.0189779i
$973$	67.9217			2.17747
$974$	−21.6677			−0.694278
$975$	39.5835	+	8.72645i	1.26769	+	0.279470i
$976$		−	4.84643i		−	0.155130i
$977$	36.8820			1.17996			0.589979	−	0.807419i	$-0.299136\pi$
$977$	36.8820			1.17996			0.589979	+	0.807419i	$0.299136\pi$
$978$	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
$990$	9.27489	−	20.0096i	0.294776	−	0.635947i
$991$			13.1075i			0.416373i	0.978089	+	0.208186i	$0.0667561\pi$
$991$			13.1075i			0.416373i	−0.978089	+	0.208186i	$0.933244\pi$
$992$	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.a.929.13	✓	32
3.2	odd	2		930.2.e.b.929.14	yes	32
5.4	even	2		930.2.e.b.929.20	yes	32
15.14	odd	2	inner	930.2.e.a.929.19	yes	32
31.30	odd	2	inner	930.2.e.a.929.20	yes	32
93.92	even	2		930.2.e.b.929.19	yes	32
155.154	odd	2		930.2.e.b.929.13	yes	32
465.464	even	2	inner	930.2.e.a.929.14	yes	32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
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} +(2.85849 + 2.61324i) 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} +(-2.85849 - 2.61324i) 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} +(2.82108 - 6.08618i) 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} +(2.85849 + 2.61324i) 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} +(-8.45718 - 1.86444i) 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} +(-2.82108 + 6.08618i) 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	\( 32 q - 32 q^{2} + 32 q^{4} + 2 q^{5} - 32 q^{8} + 4 q^{9} - 2 q^{10} + 32 q^{16} - 4 q^{18} + 8 q^{19} + 2 q^{20} + 10 q^{25} - 12 q^{31} - 32 q^{32} - 8 q^{33} + 16 q^{35} + 4 q^{36} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 10 q^{45} - 4 q^{47} - 36 q^{49} - 10 q^{50} - 4 q^{51} + 12 q^{62} - 24 q^{63} + 32 q^{64} + 8 q^{66} - 8 q^{69} - 16 q^{70} - 4 q^{72} + 8 q^{76} + 4 q^{78} + 2 q^{80} + 24 q^{81} - 4 q^{87} - 10 q^{90} + 24 q^{93} + 4 q^{94} - 26 q^{95} + 36 q^{98}+O(q^{100}) \) 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 + 10 * 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 - 10 * q^90 + 24 * q^93 + 4 * q^94 - 26 * q^95 + 36 * q^98

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