LMFDB - Embedded newform 1170.2.bj.b.199.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(199,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1170.199");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bj (of order $6$, degree $2$, 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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.1
Root			$2.40987i$ of defining polynomial
Character	$\chi$	$=$	1170.199
Dual form			1170.2.bj.b.829.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10653 + 0.750022i) q^{5} +(-0.702803 - 1.21729i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10653 + 0.750022i) q^{5} +(-0.702803 - 1.21729i) q^{7} -1.00000 q^{8} +(-0.403726 + 2.19932i) q^{10} +(4.59726 + 2.65423i) q^{11} +(-1.58700 + 3.23750i) q^{13} -1.40561 q^{14} +(-0.500000 + 0.866025i) q^{16} +(6.09726 - 3.52026i) q^{17} +(2.28793 - 1.32094i) q^{19} +(1.70280 + 1.44930i) q^{20} +(4.59726 - 2.65423i) q^{22} +(-2.30933 - 1.33329i) q^{23} +(3.87493 - 3.15989i) q^{25} +(2.01026 + 2.99314i) q^{26} +(-0.702803 + 1.21729i) q^{28} +(2.10653 - 3.64862i) q^{29} -5.07645i q^{31} +(0.500000 + 0.866025i) q^{32} -7.04051i q^{34} +(2.39347 + 2.03714i) q^{35} +(0.412995 - 0.715328i) q^{37} -2.64187i q^{38} +(2.10653 - 0.750022i) q^{40} +(-2.43440 - 1.40550i) q^{41} +(4.57586 - 2.64187i) q^{43} -5.30846i q^{44} +(-2.30933 + 1.33329i) q^{46} -1.79070 q^{47} +(2.51214 - 4.35115i) q^{49} +(-0.799077 - 4.93573i) q^{50} +(3.59726 - 0.244364i) q^{52} -7.93952i q^{53} +(-11.6750 - 2.14317i) q^{55} +(0.702803 + 1.21729i) q^{56} +(-2.10653 - 3.64862i) q^{58} +(-5.59815 + 3.23210i) q^{59} +(7.36754 + 12.7610i) q^{61} +(-4.39634 - 2.53823i) q^{62} +1.00000 q^{64} +(0.914875 - 8.01018i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-6.09726 - 3.52026i) q^{68} +(2.96095 - 1.05424i) q^{70} +(8.34802 - 4.81973i) q^{71} +7.04281 q^{73} +(-0.412995 - 0.715328i) q^{74} +(-2.28793 - 1.32094i) q^{76} -7.46160i q^{77} +4.05956 q^{79} +(0.403726 - 2.19932i) q^{80} +(-2.43440 + 1.40550i) q^{82} +8.55910 q^{83} +(-10.2038 + 11.9886i) q^{85} -5.28374i q^{86} +(-4.59726 - 2.65423i) q^{88} +(13.1289 + 7.57999i) q^{89} +(5.05633 - 0.343480i) q^{91} +2.66659i q^{92} +(-0.895350 + 1.55079i) q^{94} +(-3.82886 + 4.49859i) q^{95} +(-2.18328 - 3.78155i) q^{97} +(-2.51214 - 4.35115i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} + 5 q^{7} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 + 5 * q^7 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} + 5 q^{7} - 8 q^{8} + 3 q^{11} + 4 q^{13} + 10 q^{14} - 4 q^{16} + 15 q^{17} + 9 q^{19} + 3 q^{20} + 3 q^{22} + 6 q^{23} + 5 q^{25} - q^{26} + 5 q^{28} + 3 q^{29} + 4 q^{32} + 33 q^{35} + 20 q^{37} + 3 q^{40} - 21 q^{41} + 18 q^{43} + 6 q^{46} - 6 q^{47} - 15 q^{49} + q^{50} - 5 q^{52} - 23 q^{55} - 5 q^{56} - 3 q^{58} - 30 q^{59} - 5 q^{61} + 6 q^{62} + 8 q^{64} + 6 q^{65} - 16 q^{67} - 15 q^{68} + 18 q^{70} + 26 q^{73} - 20 q^{74} - 9 q^{76} + 4 q^{79} - 21 q^{82} + 48 q^{83} - 34 q^{85} - 3 q^{88} + 39 q^{89} + 19 q^{91} - 3 q^{94} - 9 q^{95} - 4 q^{97} + 15 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 + 5 * q^7 - 8 * q^8 + 3 * q^11 + 4 * q^13 + 10 * q^14 - 4 * q^16 + 15 * q^17 + 9 * q^19 + 3 * q^20 + 3 * q^22 + 6 * q^23 + 5 * q^25 - q^26 + 5 * q^28 + 3 * q^29 + 4 * q^32 + 33 * q^35 + 20 * q^37 + 3 * q^40 - 21 * q^41 + 18 * q^43 + 6 * q^46 - 6 * q^47 - 15 * q^49 + q^50 - 5 * q^52 - 23 * q^55 - 5 * q^56 - 3 * q^58 - 30 * q^59 - 5 * q^61 + 6 * q^62 + 8 * q^64 + 6 * q^65 - 16 * q^67 - 15 * q^68 + 18 * q^70 + 26 * q^73 - 20 * q^74 - 9 * q^76 + 4 * q^79 - 21 * q^82 + 48 * q^83 - 34 * q^85 - 3 * q^88 + 39 * q^89 + 19 * q^91 - 3 * q^94 - 9 * q^95 - 4 * q^97 + 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.10653	+	0.750022i	−0.942069	+	0.335420i
$5$	−2.10653	+	0.750022i	−0.942069	+	0.335420i
$6$		0			0
$7$	−0.702803	−	1.21729i	−0.265635	−	0.460093i	0.702095	−	0.712083i	$-0.252248\pi$
$7$	−0.702803	−	1.21729i	−0.265635	−	0.460093i	−0.967730	+	0.251991i	$0.918915\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.403726	+	2.19932i	−0.127670	+	0.695486i
$11$	4.59726	+	2.65423i	1.38613	+	0.800280i	0.992876	−	0.119151i	$-0.0380173\pi$
$11$	4.59726	+	2.65423i	1.38613	+	0.800280i	0.393250	+	0.919432i	$0.371351\pi$
$12$		0			0
$13$	−1.58700	+	3.23750i	−0.440156	+	0.897921i
$13$	−1.58700	+	3.23750i	−0.440156	+	0.897921i
$14$	−1.40561			−0.375664
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.09726	−	3.52026i	1.47880	−	0.853787i	0.479091	−	0.877766i	$-0.340967\pi$
$17$	6.09726	−	3.52026i	1.47880	−	0.853787i	0.999712	+	0.0239782i	$0.00763323\pi$
$18$		0			0
$19$	2.28793	−	1.32094i	0.524887	−	0.303044i	−0.214045	−	0.976824i	$-0.568664\pi$
$19$	2.28793	−	1.32094i	0.524887	−	0.303044i	0.738932	+	0.673780i	$0.235331\pi$
$20$	1.70280	+	1.44930i	0.380758	+	0.324073i
$21$		0			0
$22$	4.59726	−	2.65423i	0.980139	−	0.565884i
$23$	−2.30933	−	1.33329i	−0.481529	−	0.278011i	0.239524	−	0.970890i	$-0.423008\pi$
$23$	−2.30933	−	1.33329i	−0.481529	−	0.278011i	−0.721054	+	0.692879i	$0.756342\pi$
$24$		0			0
$25$	3.87493	−	3.15989i	0.774987	−	0.631978i
$26$	2.01026	+	2.99314i	0.394244	+	0.587003i
$27$		0			0
$28$	−0.702803	+	1.21729i	−0.132817	+	0.230046i
$29$	2.10653	−	3.64862i	0.391173	−	0.677531i	−0.601432	−	0.798924i	$-0.705403\pi$
$29$	2.10653	−	3.64862i	0.391173	−	0.677531i	0.992605	+	0.121393i	$0.0387362\pi$
$30$		0			0
$31$		−	5.07645i		−	0.911758i	−0.890042	−	0.455879i	$-0.849325\pi$
$31$		−	5.07645i		−	0.911758i	0.890042	−	0.455879i	$-0.150675\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	7.04051i		−	1.20744i
$35$	2.39347	+	2.03714i	0.404570	+	0.344340i
$36$		0			0
$37$	0.412995	−	0.715328i	0.0678960	−	0.117599i	−0.830079	−	0.557646i	$-0.811705\pi$
$37$	0.412995	−	0.715328i	0.0678960	−	0.117599i	0.897975	+	0.440047i	$0.145038\pi$
$38$		−	2.64187i		−	0.428568i
$39$		0			0
$40$	2.10653	−	0.750022i	0.333072	−	0.118589i
$41$	−2.43440	−	1.40550i	−0.380189	−	0.219502i	0.297711	−	0.954656i	$-0.403777\pi$
$41$	−2.43440	−	1.40550i	−0.380189	−	0.219502i	−0.677901	+	0.735154i	$0.737110\pi$
$42$		0			0
$43$	4.57586	−	2.64187i	0.697812	−	0.402882i	−0.108720	−	0.994072i	$-0.534675\pi$
$43$	4.57586	−	2.64187i	0.697812	−	0.402882i	0.806532	+	0.591191i	$0.201342\pi$
$44$		−	5.30846i		−	0.800280i
$45$		0			0
$46$	−2.30933	+	1.33329i	−0.340493	+	0.196583i
$47$	−1.79070			−0.261200			−0.130600	−	0.991435i	$-0.541690\pi$
$47$	−1.79070			−0.261200			−0.130600	+	0.991435i	$0.541690\pi$
$48$		0			0
$49$	2.51214	−	4.35115i	0.358877	−	0.621592i
$50$	−0.799077	−	4.93573i	−0.113007	−	0.698018i
$51$		0			0
$52$	3.59726	−	0.244364i	0.498850	−	0.0338872i
$53$		−	7.93952i		−	1.09058i	−0.838248	−	0.545288i	$-0.816420\pi$
$53$		−	7.93952i		−	1.09058i	0.838248	−	0.545288i	$-0.183580\pi$
$54$		0			0
$55$	−11.6750	−	2.14317i	−1.57426	−	0.288984i
$56$	0.702803	+	1.21729i	0.0939160	+	0.162667i
$57$		0			0
$58$	−2.10653	−	3.64862i	−0.276601	−	0.479087i
$59$	−5.59815	+	3.23210i	−0.728817	+	0.420783i	−0.817989	−	0.575233i	$-0.804911\pi$
$59$	−5.59815	+	3.23210i	−0.728817	+	0.420783i	0.0891719	+	0.996016i	$0.471578\pi$
$60$		0			0
$61$	7.36754	+	12.7610i	0.943317	+	1.63387i	0.759086	+	0.650991i	$0.225646\pi$
$61$	7.36754	+	12.7610i	0.943317	+	1.63387i	0.184232	+	0.982883i	$0.441020\pi$
$62$	−4.39634	−	2.53823i	−0.558335	−	0.322355i
$63$		0			0
$64$	1.00000			0.125000
$65$	0.914875	−	8.01018i	0.113476	−	0.993541i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	−6.09726	−	3.52026i	−0.739401	−	0.426894i
$69$		0			0
$70$	2.96095	−	1.05424i	0.353901	−	0.126005i
$71$	8.34802	−	4.81973i	0.990728	−	0.571997i	0.0852359	−	0.996361i	$-0.472836\pi$
$71$	8.34802	−	4.81973i	0.990728	−	0.571997i	0.905492	+	0.424364i	$0.139502\pi$
$72$		0			0
$73$	7.04281			0.824298			0.412149	−	0.911116i	$-0.364778\pi$
$73$	7.04281			0.824298			0.412149	+	0.911116i	$0.364778\pi$
$74$	−0.412995	−	0.715328i	−0.0480097	−	0.0831552i
$75$		0			0
$76$	−2.28793	−	1.32094i	−0.262443	−	0.151522i
$77$		−	7.46160i		−	0.850329i
$78$		0			0
$79$	4.05956			0.456736			0.228368	−	0.973575i	$-0.426661\pi$
$79$	4.05956			0.456736			0.228368	+	0.973575i	$0.426661\pi$
$80$	0.403726	−	2.19932i	0.0451380	−	0.245891i
$81$		0			0
$82$	−2.43440	+	1.40550i	−0.268834	+	0.155212i
$83$	8.55910			0.939484			0.469742	−	0.882804i	$-0.344347\pi$
$83$	8.55910			0.939484			0.469742	+	0.882804i	$0.344347\pi$
$84$		0			0
$85$	−10.2038	+	11.9886i	−1.10676	+	1.30035i
$86$		−	5.28374i		−	0.569761i
$87$		0			0
$88$	−4.59726	−	2.65423i	−0.490070	−	0.282942i
$89$	13.1289	+	7.57999i	1.39166	+	0.803477i	0.993499	−	0.113838i	$-0.0363143\pi$
$89$	13.1289	+	7.57999i	1.39166	+	0.803477i	0.398163	+	0.917314i	$0.369648\pi$
$90$		0			0
$91$	5.05633	−	0.343480i	0.530048	−	0.0360065i
$92$			2.66659i			0.278011i
$93$		0			0
$94$	−0.895350	+	1.55079i	−0.0923483	+	0.159952i
$95$	−3.82886	+	4.49859i	−0.392832	+	0.461545i
$96$		0			0
$97$	−2.18328	−	3.78155i	−0.221678	−	0.383958i	0.733639	−	0.679539i	$-0.237820\pi$
$97$	−2.18328	−	3.78155i	−0.221678	−	0.383958i	−0.955318	+	0.295581i	$0.904487\pi$
$98$	−2.51214	−	4.35115i	−0.253764	−	0.439532i
$99$		0			0
$100$	−4.67401	−	1.77585i	−0.467401	−	0.177585i
$101$	−4.19353	+	7.26341i	−0.417272	+	0.722737i	−0.995664	−	0.0930224i	$-0.970347\pi$
$101$	−4.19353	+	7.26341i	−0.417272	+	0.722737i	0.578392	+	0.815759i	$0.303681\pi$
$102$		0			0
$103$			5.56518i			0.548354i	0.961679	+	0.274177i	$0.0884054\pi$
$103$			5.56518i			0.548354i	−0.961679	+	0.274177i	$0.911595\pi$
$104$	1.58700	−	3.23750i	0.155619	−	0.317463i
$105$		0			0
$106$	−6.87583	−	3.96976i	−0.667839	−	0.385577i
$107$	13.1503	+	7.59234i	1.27129	+	0.733980i	0.975231	−	0.221190i	$-0.0709941\pi$
$107$	13.1503	+	7.59234i	1.27129	+	0.733980i	0.296059	+	0.955170i	$0.404327\pi$
$108$		0			0
$109$			0.667003i			0.0638873i	0.999490	+	0.0319436i	$0.0101697\pi$
$109$			0.667003i			0.0638873i	−0.999490	+	0.0319436i	$0.989830\pi$
$110$	−7.69353	+	9.03926i	−0.733550	+	0.861860i
$111$		0			0
$112$	1.40561			0.132817
$113$	2.91774	−	1.68456i	0.274478	−	0.158470i	−0.356443	−	0.934317i	$-0.616011\pi$
$113$	2.91774	−	1.68456i	0.274478	−	0.158470i	0.630921	+	0.775847i	$0.282677\pi$
$114$		0			0
$115$	5.86468	+	1.07657i	0.546884	+	0.100391i
$116$	−4.21306			−0.391173
$117$		0			0
$118$			6.46419i			0.595077i
$119$	−8.57035	−	4.94809i	−0.785642	−	0.453591i
$120$		0			0
$121$	8.58987	+	14.8781i	0.780897	+	1.35255i
$122$	14.7351			1.33405
$123$		0			0
$124$	−4.39634	+	2.53823i	−0.394803	+	0.227939i
$125$	−5.79268	+	9.56268i	−0.518113	+	0.855312i
$126$		0			0
$127$	−9.39545	−	5.42446i	−0.833711	−	0.481343i	0.0214106	−	0.999771i	$-0.493184\pi$
$127$	−9.39545	−	5.42446i	−0.833711	−	0.481343i	−0.855122	+	0.518428i	$0.826518\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−6.47958	−	4.79740i	−0.568297	−	0.420759i
$131$	−15.3500			−1.34114			−0.670568	−	0.741848i	$-0.733949\pi$
$131$	−15.3500			−1.34114			−0.670568	+	0.741848i	$0.733949\pi$
$132$		0			0
$133$	−3.21593	−	1.85672i	−0.278856	−	0.160998i
$134$	2.00000	+	3.46410i	0.172774	+	0.299253i
$135$		0			0
$136$	−6.09726	+	3.52026i	−0.522836	+	0.301859i
$137$	−5.69541	−	9.86475i	−0.486592	−	0.842802i	0.513289	−	0.858216i	$-0.328427\pi$
$137$	−5.69541	−	9.86475i	−0.486592	−	0.842802i	−0.999881	+	0.0154136i	$0.995094\pi$
$138$		0			0
$139$	−5.67500	−	9.82938i	−0.481347	−	0.833717i	0.518424	−	0.855124i	$-0.326519\pi$
$139$	−5.67500	−	9.82938i	−0.481347	−	0.833717i	−0.999771	+	0.0214063i	$0.993186\pi$
$140$	0.567480	−	3.09138i	0.0479608	−	0.261269i
$141$		0			0
$142$		−	9.63946i		−	0.808926i
$143$	−15.8889	+	10.6714i	−1.32870	+	0.892384i
$144$		0			0
$145$	−1.70092	+	9.26586i	−0.141254	+	0.769488i
$146$	3.52140	−	6.09925i	0.291433	−	0.504778i
$147$		0			0
$148$	−0.825990			−0.0678960
$149$	−1.70092	+	0.982029i	−0.139345	+	0.0804509i	−0.568052	−	0.822993i	$-0.692303\pi$
$149$	−1.70092	+	0.982029i	−0.139345	+	0.0804509i	0.428707	+	0.903444i	$0.358969\pi$
$150$		0			0
$151$			10.3602i			0.843101i	0.906805	+	0.421550i	$0.138514\pi$
$151$			10.3602i			0.843101i	−0.906805	+	0.421550i	$0.861486\pi$
$152$	−2.28793	+	1.32094i	−0.185575	+	0.107142i
$153$		0			0
$154$	−6.46194	−	3.73080i	−0.520718	−	0.300637i
$155$	3.80745	+	10.6937i	0.305822	+	0.858939i
$156$		0			0
$157$		−	5.83105i		−	0.465368i	−0.972552	−	0.232684i	$-0.925249\pi$
$157$		−	5.83105i		−	0.465368i	0.972552	−	0.232684i	$-0.0747508\pi$
$158$	2.02978	−	3.51568i	0.161481	−	0.279693i
$159$		0			0
$160$	−1.70280	−	1.44930i	−0.134618	−	0.114577i
$161$			3.74817i			0.295397i
$162$		0			0
$163$	5.87592	+	10.1774i	0.460238	+	0.797155i	0.998973	−	0.0453204i	$-0.0144309\pi$
$163$	5.87592	+	10.1774i	0.460238	+	0.797155i	−0.538735	+	0.842475i	$0.681098\pi$
$164$			2.81100i			0.219502i
$165$		0			0
$166$	4.27955	−	7.41240i	0.332158	−	0.575314i
$167$	5.58799	−	9.67869i	0.432412	−	0.748959i	−0.564669	−	0.825318i	$-0.690996\pi$
$167$	5.58799	−	9.67869i	0.432412	−	0.748959i	0.997080	+	0.0763585i	$0.0243293\pi$
$168$		0			0
$169$	−7.96283	−	10.2759i	−0.612525	−	0.790451i
$170$	5.28054	+	14.8310i	0.404999	+	1.13749i
$171$		0			0
$172$	−4.57586	−	2.64187i	−0.348906	−	0.201441i
$173$	0.461938	−	0.266700i	0.0351205	−	0.0202768i	−0.482337	−	0.875986i	$-0.660212\pi$
$173$	0.461938	−	0.266700i	0.0351205	−	0.0202768i	0.517457	+	0.855709i	$0.326879\pi$
$174$		0			0
$175$	−6.56982	−	2.49614i	−0.496631	−	0.188691i
$176$	−4.59726	+	2.65423i	−0.346532	+	0.200070i
$177$		0			0
$178$	13.1289	−	7.57999i	0.984054	−	0.568144i
$179$	4.61867	−	7.99976i	0.345215	−	0.597930i	−0.640178	−	0.768227i	$-0.721139\pi$
$179$	4.61867	−	7.99976i	0.345215	−	0.597930i	0.985393	+	0.170297i	$0.0544726\pi$
$180$		0			0
$181$	−4.76464			−0.354153			−0.177077	−	0.984197i	$-0.556664\pi$
$181$	−4.76464			−0.354153			−0.177077	+	0.984197i	$0.556664\pi$
$182$	2.23070	−	4.55065i	0.165351	−	0.337317i
$183$		0			0
$184$	2.30933	+	1.33329i	0.170246	+	0.0982917i
$185$	−0.333474	+	1.81662i	−0.0245175	+	0.133560i
$186$		0			0
$187$	37.3743			2.73308
$188$	0.895350	+	1.55079i	0.0653001	+	0.113103i
$189$		0			0
$190$	1.98146	+	5.56518i	0.143750	+	0.403741i
$191$	−8.97219	−	15.5403i	−0.649205	−	1.12446i	−0.983313	−	0.181922i	$-0.941768\pi$
$191$	−8.97219	−	15.5403i	−0.649205	−	1.12446i	0.334108	−	0.942535i	$-0.391565\pi$
$192$		0			0
$193$	−10.4731	+	18.1399i	−0.753869	+	1.30574i	0.192065	+	0.981382i	$0.438481\pi$
$193$	−10.4731	+	18.1399i	−0.753869	+	1.30574i	−0.945934	+	0.324358i	$0.894852\pi$
$194$	−4.36656			−0.313501
$195$		0			0
$196$	−5.02427			−0.358877
$197$	−13.3862	+	23.1855i	−0.953726	+	1.65190i	−0.216468	+	0.976290i	$0.569454\pi$
$197$	−13.3862	+	23.1855i	−0.953726	+	1.65190i	−0.737258	+	0.675611i	$0.763880\pi$
$198$		0			0
$199$	−7.19452	−	12.4613i	−0.510006	−	0.883357i	−0.999933	−	0.0115929i	$-0.996310\pi$
$199$	−7.19452	−	12.4613i	−0.510006	−	0.883357i	0.489927	−	0.871764i	$-0.337024\pi$
$200$	−3.87493	+	3.15989i	−0.273999	+	0.223438i
$201$		0			0
$202$	4.19353	+	7.26341i	0.295056	+	0.511052i
$203$	−5.92190			−0.415636
$204$		0			0
$205$	6.18229	+	1.13488i	0.431790	+	0.0792632i
$206$	4.81959	+	2.78259i	0.335797	+	0.193872i
$207$		0			0
$208$	−2.01026	−	2.99314i	−0.139386	−	0.207537i
$209$	14.0243			0.970079
$210$		0			0
$211$	12.1954	−	21.1231i	0.839567	−	1.45417i	−0.0506903	−	0.998714i	$-0.516142\pi$
$211$	12.1954	−	21.1231i	0.839567	−	1.45417i	0.890257	−	0.455458i	$-0.150525\pi$
$212$	−6.87583	+	3.96976i	−0.472234	+	0.272644i
$213$		0			0
$214$	13.1503	−	7.59234i	0.898938	−	0.519002i
$215$	−7.65771	+	8.99718i	−0.522252	+	0.613602i
$216$		0			0
$217$	−6.17952	+	3.56775i	−0.419493	+	0.242194i
$218$	0.577641	+	0.333501i	0.0391228	+	0.0225876i
$219$		0			0
$220$	3.98146	+	11.1824i	0.268430	+	0.753919i
$221$	1.72045	+	25.3266i	0.115730	+	1.70365i
$222$		0			0
$223$	1.48974	−	2.58031i	0.0997606	−	0.172790i	−0.811825	−	0.583901i	$-0.801526\pi$
$223$	1.48974	−	2.58031i	0.0997606	−	0.172790i	0.911586	+	0.411110i	$0.134859\pi$
$224$	0.702803	−	1.21729i	0.0469580	−	0.0813337i
$225$		0			0
$226$		−	3.36912i		−	0.224110i
$227$	1.98146	+	3.43199i	0.131514	+	0.227789i	0.924260	−	0.381762i	$-0.124683\pi$
$227$	1.98146	+	3.43199i	0.131514	+	0.227789i	−0.792746	+	0.609552i	$0.791349\pi$
$228$		0			0
$229$			9.85151i			0.651006i	0.945541	+	0.325503i	$0.105534\pi$
$229$			9.85151i			0.651006i	−0.945541	+	0.325503i	$0.894466\pi$
$230$	3.86468	−	4.54067i	0.254829	−	0.299403i
$231$		0			0
$232$	−2.10653	+	3.64862i	−0.138300	+	0.239543i
$233$			19.3821i			1.26976i	0.772610	+	0.634881i	$0.218951\pi$
$233$			19.3821i			1.26976i	−0.772610	+	0.634881i	$0.781049\pi$
$234$		0			0
$235$	3.77216	−	1.34307i	0.246069	−	0.0876119i
$236$	5.59815	+	3.23210i	0.364409	+	0.210391i
$237$		0			0
$238$	−8.57035	+	4.94809i	−0.555533	+	0.320737i
$239$		−	30.0138i		−	1.94143i	−0.240232	−	0.970715i	$-0.577224\pi$
$239$		−	30.0138i		−	1.94143i	0.240232	−	0.970715i	$-0.422776\pi$
$240$		0			0
$241$	−16.5815	+	9.57333i	−1.06811	+	0.616672i	−0.927664	−	0.373416i	$-0.878186\pi$
$241$	−16.5815	+	9.57333i	−1.06811	+	0.616672i	−0.140444	+	0.990089i	$0.544853\pi$
$242$	17.1797			1.10436
$243$		0			0
$244$	7.36754	−	12.7610i	0.471659	−	0.816937i
$245$	−2.02843	+	11.0500i	−0.129592	+	0.705957i
$246$		0			0
$247$	0.645579	+	9.50350i	0.0410772	+	0.604693i
$248$			5.07645i			0.322355i
$249$		0			0
$250$	5.38519	+	9.79795i	0.340589	+	0.619676i
$251$	8.52150	+	14.7597i	0.537872	+	0.931622i	0.999018	+	0.0442979i	$0.0141051\pi$
$251$	8.52150	+	14.7597i	0.537872	+	0.931622i	−0.461146	+	0.887324i	$0.652562\pi$
$252$		0			0
$253$	−7.07774	−	12.2590i	−0.444973	−	0.770717i
$254$	−9.39545	+	5.42446i	−0.589523	+	0.340361i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.12328	−	4.11263i	−0.444338	−	0.256539i	0.261098	−	0.965312i	$-0.415915\pi$
$257$	−7.12328	−	4.11263i	−0.444338	−	0.256539i	−0.705436	+	0.708774i	$0.749249\pi$
$258$		0			0
$259$	−1.16102			−0.0721421
$260$	−7.39446	+	3.21279i	−0.458585	+	0.199249i
$261$		0			0
$262$	−7.67500	+	13.2935i	−0.474163	+	0.821274i
$263$	9.03229	+	5.21479i	0.556955	+	0.321558i	0.751922	−	0.659252i	$-0.229127\pi$
$263$	9.03229	+	5.21479i	0.556955	+	0.321558i	−0.194968	+	0.980810i	$0.562460\pi$
$264$		0			0
$265$	5.95482	+	16.7248i	0.365801	+	1.02740i
$266$	−3.21593	+	1.85672i	−0.197181	+	0.113843i
$267$		0			0
$268$	4.00000			0.244339
$269$	−11.3206	−	19.6078i	−0.690228	−	1.19551i	−0.971763	−	0.235959i	$-0.924177\pi$
$269$	−11.3206	−	19.6078i	−0.690228	−	1.19551i	0.281535	−	0.959551i	$-0.409156\pi$
$270$		0			0
$271$	0.218603	+	0.126211i	0.0132792	+	0.00766675i	0.506625	−	0.862167i	$-0.330893\pi$
$271$	0.218603	+	0.126211i	0.0132792	+	0.00766675i	−0.493346	+	0.869833i	$0.664226\pi$
$272$			7.04051i			0.426894i
$273$		0			0
$274$	−11.3908			−0.688145
$275$	26.2011	−	4.24187i	1.57999	−	0.255794i
$276$		0			0
$277$	−4.03166	+	2.32768i	−0.242239	+	0.139857i	−0.616205	−	0.787586i	$-0.711331\pi$
$277$	−4.03166	+	2.32768i	−0.242239	+	0.139857i	0.373966	+	0.927442i	$0.377998\pi$
$278$	−11.3500			−0.680727
$279$		0			0
$280$	−2.39347	−	2.03714i	−0.143037	−	0.121742i
$281$		−	3.70262i		−	0.220880i	−0.993883	−	0.110440i	$-0.964774\pi$
$281$		−	3.70262i		−	0.220880i	0.993883	−	0.110440i	$-0.0352260\pi$
$282$		0			0
$283$	−4.63147	−	2.67398i	−0.275312	−	0.158952i	0.355987	−	0.934491i	$-0.384145\pi$
$283$	−4.63147	−	2.67398i	−0.275312	−	0.158952i	−0.631299	+	0.775539i	$0.717478\pi$
$284$	−8.34802	−	4.81973i	−0.495364	−	0.285998i
$285$		0			0
$286$	1.29720	+	19.0959i	0.0767049	+	1.12917i
$287$			3.95116i			0.233230i
$288$		0			0
$289$	16.2844	−	28.2054i	0.957906	−	1.65914i
$290$	7.17401	+	6.10597i	0.421272	+	0.358555i
$291$		0			0
$292$	−3.52140	−	6.09925i	−0.206075	−	0.356932i
$293$	12.0871	+	20.9355i	0.706136	+	1.22306i	0.966280	+	0.257493i	$0.0828966\pi$
$293$	12.0871	+	20.9355i	0.706136	+	1.22306i	−0.260144	+	0.965570i	$0.583770\pi$
$294$		0			0
$295$	9.36853	−	11.0072i	0.545457	−	0.640866i
$296$	−0.412995	+	0.715328i	−0.0240048	+	0.0415776i
$297$		0			0
$298$			1.96406i			0.113775i
$299$	7.98146	−	5.36052i	0.461580	−	0.310007i
$300$		0			0
$301$	−6.43185	−	3.71343i	−0.370726	−	0.214039i
$302$	8.97219	+	5.18010i	0.516292	+	0.298081i
$303$		0			0
$304$			2.64187i			0.151522i
$305$	−25.0910	−	21.3555i	−1.43670	−	1.22281i
$306$		0			0
$307$	−27.5443			−1.57204			−0.786019	−	0.618203i	$-0.787861\pi$
$307$	−27.5443			−1.57204			−0.786019	+	0.618203i	$0.787861\pi$
$308$	−6.46194	+	3.73080i	−0.368203	+	0.212582i
$309$		0			0
$310$	11.1647	+	2.04950i	0.634115	+	0.116404i
$311$	−12.8262			−0.727306			−0.363653	−	0.931534i	$-0.618471\pi$
$311$	−12.8262			−0.727306			−0.363653	+	0.931534i	$0.618471\pi$
$312$		0			0
$313$			2.72604i			0.154085i	0.997028	+	0.0770425i	$0.0245477\pi$
$313$			2.72604i			0.154085i	−0.997028	+	0.0770425i	$0.975452\pi$
$314$	−5.04984	−	2.91552i	−0.284979	−	0.164533i
$315$		0			0
$316$	−2.02978	−	3.51568i	−0.114184	−	0.197773i
$317$	−1.89961			−0.106692			−0.0533462	−	0.998576i	$-0.516989\pi$
$317$	−1.89961			−0.106692			−0.0533462	+	0.998576i	$0.516989\pi$
$318$		0			0
$319$	19.3685	−	11.1824i	1.08443	−	0.626096i
$320$	−2.10653	+	0.750022i	−0.117759	+	0.0419275i
$321$		0			0
$322$	3.24601	+	1.87409i	0.180893	+	0.104439i
$323$	9.30006	−	16.1082i	0.517469	−	0.896283i
$324$		0			0
$325$	4.08060	+	17.5599i	0.226351	+	0.974046i
$326$	11.7518			0.650874
$327$		0			0
$328$	2.43440	+	1.40550i	0.134417	+	0.0776058i
$329$	1.25851	+	2.17980i	0.0693839	+	0.120176i
$330$		0			0
$331$	7.78318	−	4.49362i	0.427802	−	0.246992i	−0.270608	−	0.962690i	$-0.587225\pi$
$331$	7.78318	−	4.49362i	0.427802	−	0.246992i	0.698410	+	0.715698i	$0.253891\pi$
$332$	−4.27955	−	7.41240i	−0.234871	−	0.406808i
$333$		0			0
$334$	−5.58799	−	9.67869i	−0.305761	−	0.529594i
$335$	1.61491	−	8.79728i	0.0882317	−	0.480647i
$336$		0			0
$337$		−	1.37859i		−	0.0750967i	−0.999295	−	0.0375484i	$-0.988045\pi$
$337$		−	1.37859i		−	0.0750967i	0.999295	−	0.0375484i	$-0.0119548\pi$
$338$	−12.8806	+	1.75808i	−0.700611	+	0.0956271i
$339$		0			0
$340$	15.4843	+	2.84244i	0.839756	+	0.154153i
$341$	13.4741	−	23.3378i	0.729662	−	1.26381i
$342$		0			0
$343$	−16.9014			−0.912589
$344$	−4.57586	+	2.64187i	−0.246714	+	0.142440i
$345$		0			0
$346$		−	0.533400i		−	0.0286758i
$347$	−10.3020	+	5.94788i	−0.553042	+	0.319299i	−0.750348	−	0.661043i	$-0.770114\pi$
$347$	−10.3020	+	5.94788i	−0.553042	+	0.319299i	0.197306	+	0.980342i	$0.436781\pi$
$348$		0			0
$349$	3.95580	+	2.28388i	0.211749	+	0.122254i	0.602124	−	0.798403i	$-0.294321\pi$
$349$	3.95580	+	2.28388i	0.211749	+	0.122254i	−0.390375	+	0.920656i	$0.627655\pi$
$350$	−5.44663	+	4.44156i	−0.291135	+	0.237411i
$351$		0			0
$352$			5.30846i			0.282942i
$353$	0.421009	−	0.729210i	0.0224081	−	0.0388119i	−0.854604	−	0.519280i	$-0.826200\pi$
$353$	0.421009	−	0.729210i	0.0224081	−	0.0388119i	0.877012	+	0.480468i	$0.159533\pi$
$354$		0			0
$355$	−13.9704	+	16.4141i	−0.741474	+	0.871170i
$356$		−	15.1600i		−	0.803477i
$357$		0			0
$358$	−4.61867	−	7.99976i	−0.244104	−	0.422801i
$359$			8.05922i			0.425349i	0.977123	+	0.212675i	$0.0682174\pi$
$359$			8.05922i			0.425349i	−0.977123	+	0.212675i	$0.931783\pi$
$360$		0			0
$361$	−6.01026	+	10.4101i	−0.316329	+	0.547898i
$362$	−2.38232	+	4.12630i	−0.125212	+	0.216874i
$363$		0			0
$364$	−2.82563	−	4.20717i	−0.148103	−	0.220516i
$365$	−14.8359	+	5.28226i	−0.776546	+	0.276486i
$366$		0			0
$367$	14.3052	+	8.25912i	0.746726	+	0.431122i	0.824510	−	0.565848i	$-0.191451\pi$
$367$	14.3052	+	8.25912i	0.746726	+	0.431122i	−0.0777837	+	0.996970i	$0.524784\pi$
$368$	2.30933	−	1.33329i	0.120382	−	0.0695027i
$369$		0			0
$370$	1.40650	+	1.19710i	0.0731204	+	0.0622345i
$371$	−9.66470	+	5.57992i	−0.501766	+	0.289695i
$372$		0			0
$373$	22.9969	−	13.2773i	1.19073	−	0.687471i	0.232261	−	0.972653i	$-0.425388\pi$
$373$	22.9969	−	13.2773i	1.19073	−	0.687471i	0.958473	+	0.285183i	$0.0920543\pi$
$374$	18.6871	−	32.3671i	0.966289	−	1.67366i
$375$		0			0
$376$	1.79070			0.0923483
$377$	8.46933	+	12.6103i	0.436193	+	0.649462i
$378$		0			0
$379$	−1.00089	−	0.577865i	−0.0514124	−	0.0296830i	0.474073	−	0.880485i	$-0.342783\pi$
$379$	−1.00089	−	0.577865i	−0.0514124	−	0.0296830i	−0.525486	+	0.850802i	$0.676116\pi$
$380$	5.81032	+	1.06659i	0.298063	+	0.0547151i
$381$		0			0
$382$	−17.9444			−0.918115
$383$	17.5039	+	30.3176i	0.894405	+	1.54916i	0.834539	+	0.550949i	$0.185734\pi$
$383$	17.5039	+	30.3176i	0.894405	+	1.54916i	0.0598661	+	0.998206i	$0.480933\pi$
$384$		0			0
$385$	5.59637	+	15.7181i	0.285217	+	0.801068i
$386$	10.4731	+	18.1399i	0.533066	+	0.923298i
$387$		0			0
$388$	−2.18328	+	3.78155i	−0.110839	+	0.191979i
$389$	−11.3135			−0.573615			−0.286807	−	0.957988i	$-0.592594\pi$
$389$	−11.3135			−0.573615			−0.286807	+	0.957988i	$0.592594\pi$
$390$		0			0
$391$	−18.7741			−0.949449
$392$	−2.51214	+	4.35115i	−0.126882	+	0.219766i
$393$		0			0
$394$	13.3862	+	23.1855i	0.674386	+	1.16807i
$395$	−8.55159	+	3.04476i	−0.430277	+	0.153199i
$396$		0			0
$397$	9.00287	+	15.5934i	0.451841	+	0.782611i	0.998500	−	0.0547435i	$-0.0174341\pi$
$397$	9.00287	+	15.5934i	0.451841	+	0.782611i	−0.546660	+	0.837355i	$0.684101\pi$
$398$	−14.3890			−0.721258
$399$		0			0
$400$	0.799077	+	4.93573i	0.0399538	+	0.246787i
$401$	−3.97385	−	2.29430i	−0.198445	−	0.114572i	0.397485	−	0.917609i	$-0.369883\pi$
$401$	−3.97385	−	2.29430i	−0.198445	−	0.114572i	−0.595930	+	0.803037i	$0.703216\pi$
$402$		0			0
$403$	16.4350	+	8.05636i	0.818687	+	0.401316i
$404$	8.38707			0.417272
$405$		0			0
$406$	−2.96095	+	5.12852i	−0.146950	+	0.254524i
$407$	3.79729	−	2.19237i	0.188225	−	0.108672i
$408$		0			0
$409$	−22.7332	+	13.1250i	−1.12408	+	0.648991i	−0.942441	−	0.334374i	$-0.891475\pi$
$409$	−22.7332	+	13.1250i	−1.12408	+	0.648991i	−0.181644	+	0.983364i	$0.558142\pi$
$410$	4.07398	−	4.78658i	0.201199	−	0.236392i
$411$		0			0
$412$	4.81959	−	2.78259i	0.237444	−	0.137088i
$413$	7.86880	+	4.54305i	0.387198	+	0.223549i
$414$		0			0
$415$	−18.0300	+	6.41952i	−0.885058	+	0.315122i
$416$	−3.59726	+	0.244364i	−0.176370	+	0.0119809i
$417$		0			0
$418$	7.01214	−	12.1454i	0.342975	−	0.594050i
$419$	−6.03869	+	10.4593i	−0.295009	+	0.510971i	−0.974987	−	0.222262i	$-0.928656\pi$
$419$	−6.03869	+	10.4593i	−0.295009	+	0.510971i	0.679978	+	0.733233i	$0.261989\pi$
$420$		0			0
$421$		−	3.11716i		−	0.151921i	−0.997111	−	0.0759604i	$-0.975798\pi$
$421$		−	3.11716i		−	0.151921i	0.997111	−	0.0759604i	$-0.0242023\pi$
$422$	−12.1954	−	21.1231i	−0.593663	−	1.02826i
$423$		0			0
$424$			7.93952i			0.385577i
$425$	12.5029	−	32.9074i	0.606478	−	1.59624i
$426$		0			0
$427$	10.3559	−	17.9369i	0.501155	−	0.868027i
$428$		−	15.1847i		−	0.733980i
$429$		0			0
$430$	3.96293	+	11.1304i	0.191109	+	0.536754i
$431$	−4.52932	−	2.61501i	−0.218170	−	0.125960i	0.386933	−	0.922108i	$-0.373535\pi$
$431$	−4.52932	−	2.61501i	−0.218170	−	0.125960i	−0.605103	+	0.796148i	$0.706868\pi$
$432$		0			0
$433$	−19.3178	+	11.1531i	−0.928354	+	0.535986i	−0.886291	−	0.463129i	$-0.846727\pi$
$433$	−19.3178	+	11.1531i	−0.928354	+	0.535986i	−0.0420637	+	0.999115i	$0.513393\pi$
$434$			7.13549i			0.342515i
$435$		0			0
$436$	0.577641	−	0.333501i	0.0276640	−	0.0159718i
$437$	−7.04478			−0.336998
$438$		0			0
$439$	2.62417	−	4.54520i	0.125245	−	0.216931i	−0.796584	−	0.604528i	$-0.793362\pi$
$439$	2.62417	−	4.54520i	0.125245	−	0.216931i	0.921829	+	0.387598i	$0.126695\pi$
$440$	11.6750	+	2.14317i	0.556584	+	0.102171i
$441$		0			0
$442$	22.7937	+	11.1733i	1.08418	+	0.531461i
$443$			1.11623i			0.0530338i	0.999648	+	0.0265169i	$0.00844158\pi$
$443$			1.11623i			0.0530338i	−0.999648	+	0.0265169i	$0.991558\pi$
$444$		0			0
$445$	−33.3416	−	6.12048i	−1.58054	−	0.290139i
$446$	−1.48974	−	2.58031i	−0.0705414	−	0.122181i
$447$		0			0
$448$	−0.702803	−	1.21729i	−0.0332043	−	0.0575116i
$449$	−29.8678	+	17.2442i	−1.40955	+	0.813802i	−0.995344	−	0.0963822i	$-0.969273\pi$
$449$	−29.8678	+	17.2442i	−1.40955	+	0.813802i	−0.414203	+	0.910185i	$0.635940\pi$
$450$		0			0
$451$	−7.46105	−	12.9229i	−0.351327	−	0.608516i
$452$	−2.91774	−	1.68456i	−0.137239	−	0.0792350i
$453$		0			0
$454$	3.96293			0.185989
$455$	−10.3937	+	4.51591i	−0.487264	+	0.211709i
$456$		0			0
$457$	2.03770	−	3.52940i	0.0953196	−	0.165098i	−0.814422	−	0.580273i	$-0.802946\pi$
$457$	2.03770	−	3.52940i	0.0953196	−	0.165098i	0.909742	+	0.415174i	$0.136279\pi$
$458$	8.53166	+	4.92576i	0.398658	+	0.230165i
$459$		0			0
$460$	−2.00000	−	5.61725i	−0.0932505	−	0.261905i
$461$	−26.2766	+	15.1708i	−1.22383	+	0.706576i	−0.965731	−	0.259544i	$-0.916428\pi$
$461$	−26.2766	+	15.1708i	−1.22383	+	0.706576i	−0.258094	+	0.966120i	$0.583094\pi$
$462$		0			0
$463$	25.2291			1.17250			0.586248	−	0.810132i	$-0.300605\pi$
$463$	25.2291			1.17250			0.586248	+	0.810132i	$0.300605\pi$
$464$	2.10653	+	3.64862i	0.0977932	+	0.169383i
$465$		0			0
$466$	16.7854	+	9.69104i	0.777568	+	0.448929i
$467$		−	21.9997i		−	1.01802i	−0.860759	−	0.509012i	$-0.830011\pi$
$467$		−	21.9997i		−	1.01802i	0.860759	−	0.509012i	$-0.169989\pi$
$468$		0			0
$469$	5.62242			0.259619
$470$	0.722953	−	3.93832i	0.0333473	−	0.181661i
$471$		0			0
$472$	5.59815	−	3.23210i	0.257676	−	0.148769i
$473$	28.0485			1.28967
$474$		0			0
$475$	4.69156	−	12.3481i	0.215264	−	0.566571i
$476$			9.89618i			0.453591i
$477$		0			0
$478$	−25.9927	−	15.0069i	−1.18888	−	0.686399i
$479$	19.1462	+	11.0541i	0.874812	+	0.505073i	0.868944	−	0.494910i	$-0.164799\pi$
$479$	19.1462	+	11.0541i	0.874812	+	0.505073i	0.00586793	+	0.999983i	$0.498132\pi$
$480$		0			0
$481$	1.66045	+	2.47230i	0.0757101	+	0.112727i
$482$			19.1467i			0.872107i
$483$		0			0
$484$	8.58987	−	14.8781i	0.390449	−	0.676277i
$485$	7.43539	+	6.32844i	0.337624	+	0.287360i
$486$		0			0
$487$	−1.83437	−	3.17722i	−0.0831231	−	0.143973i	0.821467	−	0.570256i	$-0.193156\pi$
$487$	−1.83437	−	3.17722i	−0.0831231	−	0.143973i	−0.904590	+	0.426283i	$0.859823\pi$
$488$	−7.36754	−	12.7610i	−0.333513	−	0.577662i
$489$		0			0
$490$	8.55534	+	7.28166i	0.386491	+	0.328952i
$491$	13.2345	−	22.9228i	0.597263	−	1.03449i	−0.395960	−	0.918268i	$-0.629588\pi$
$491$	13.2345	−	22.9228i	0.597263	−	1.03449i	0.993223	−	0.116222i	$-0.0370785\pi$
$492$		0			0
$493$		−	29.6621i		−	1.33591i
$494$	8.55306	+	4.19266i	0.384821	+	0.188637i
$495$		0			0
$496$	4.39634	+	2.53823i	0.197401	+	0.113970i
$497$	−11.7340	−	6.77464i	−0.526343	−	0.303884i
$498$		0			0
$499$		−	37.0404i		−	1.65816i	−0.559133	−	0.829078i	$-0.688866\pi$
$499$		−	37.0404i		−	1.65816i	0.559133	−	0.829078i	$-0.311134\pi$
$500$	11.1779	+	0.235262i	0.499889	+	0.0105212i
$501$		0			0
$502$	17.0430			0.760666
$503$	29.4618	−	17.0098i	1.31364	−	0.758429i	0.330940	−	0.943652i	$-0.392634\pi$
$503$	29.4618	−	17.0098i	1.31364	−	0.758429i	0.982696	+	0.185223i	$0.0593008\pi$
$504$		0			0
$505$	3.38608	−	18.4458i	0.150679	−	0.820829i
$506$	−14.1555			−0.629288
$507$		0			0
$508$			10.8489i			0.481343i
$509$	13.9811	+	8.07197i	0.619700	+	0.357784i	0.776752	−	0.629806i	$-0.216866\pi$
$509$	13.9811	+	8.07197i	0.619700	+	0.357784i	−0.157052	+	0.987590i	$0.550199\pi$
$510$		0			0
$511$	−4.94971	−	8.57314i	−0.218962	−	0.379254i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−7.12328	+	4.11263i	−0.314195	+	0.181400i
$515$	−4.17401	−	11.7232i	−0.183929	−	0.516587i
$516$		0			0
$517$	−8.23232	−	4.75293i	−0.362057	−	0.209034i
$518$	−0.580508	+	1.00547i	−0.0255061	+	0.0441778i
$519$		0			0
$520$	−0.914875	+	8.01018i	−0.0401199	+	0.351270i
$521$	36.5483			1.60121			0.800605	−	0.599193i	$-0.204512\pi$
$521$	36.5483			1.60121			0.800605	+	0.599193i	$0.204512\pi$
$522$		0			0
$523$	0.577641	+	0.333501i	0.0252585	+	0.0145830i	0.512576	−	0.858642i	$-0.328691\pi$
$523$	0.577641	+	0.333501i	0.0252585	+	0.0145830i	−0.487318	+	0.873225i	$0.662025\pi$
$524$	7.67500	+	13.2935i	0.335284	+	0.580729i
$525$		0			0
$526$	9.03229	−	5.21479i	0.393826	−	0.227376i
$527$	−17.8704	−	30.9525i	−0.778447	−	1.34831i
$528$		0			0
$529$	−7.94466	−	13.7605i	−0.345420	−	0.598285i
$530$	17.4615	+	3.20539i	0.758481	+	0.139233i
$531$		0			0
$532$			3.71343i			0.160998i
$533$	8.41372	−	5.65083i	0.364438	−	0.244765i
$534$		0			0
$535$	−33.3960	−	6.13046i	−1.44383	−	0.265043i
$536$	2.00000	−	3.46410i	0.0863868	−	0.149626i
$537$		0			0
$538$	−22.6412			−0.976129
$539$	23.0979	−	13.3356i	0.994896	−	0.574404i
$540$		0			0
$541$		−	7.70275i		−	0.331167i	−0.986196	−	0.165584i	$-0.947049\pi$
$541$		−	7.70275i		−	0.331167i	0.986196	−	0.165584i	$-0.0529508\pi$
$542$	0.218603	−	0.126211i	0.00938981	−	0.00542121i
$543$		0			0
$544$	6.09726	+	3.52026i	0.261418	+	0.150930i
$545$	−0.500267	−	1.40506i	−0.0214291	−	0.0601862i
$546$		0			0
$547$		−	27.5445i		−	1.17772i	−0.808236	−	0.588858i	$-0.799578\pi$
$547$		−	27.5445i		−	1.17772i	0.808236	−	0.588858i	$-0.200422\pi$
$548$	−5.69541	+	9.86475i	−0.243296	+	0.421401i
$549$		0			0
$550$	9.42701	−	24.8118i	0.401969	−	1.05798i
$551$		−	11.1304i		−	0.474169i
$552$		0			0
$553$	−2.85307	−	4.94167i	−0.121325	−	0.210141i
$554$			4.65536i			0.197787i
$555$		0			0
$556$	−5.67500	+	9.82938i	−0.240673	+	0.416859i
$557$	2.08137	−	3.60503i	0.0881903	−	0.152750i	−0.818556	−	0.574427i	$-0.805225\pi$
$557$	2.08137	−	3.60503i	0.0881903	−	0.152750i	0.906746	+	0.421677i	$0.138558\pi$
$558$		0			0
$559$	1.29116	+	19.0070i	0.0546101	+	0.803911i
$560$	−2.96095	+	1.05424i	−0.125123	+	0.0445496i
$561$		0			0
$562$	−3.20656	−	1.85131i	−0.135261	−	0.0780928i
$563$	−27.3575	+	15.7949i	−1.15298	+	0.665674i	−0.949612	−	0.313428i	$-0.898523\pi$
$563$	−27.3575	+	15.7949i	−1.15298	+	0.665674i	−0.203370	+	0.979102i	$0.565189\pi$
$564$		0			0
$565$	−4.88285	+	5.73694i	−0.205423	+	0.241355i
$566$	−4.63147	+	2.67398i	−0.194675	+	0.112396i
$567$		0			0
$568$	−8.34802	+	4.81973i	−0.350275	+	0.202231i
$569$	−11.9583	+	20.7124i	−0.501318	+	0.868309i	0.498680	+	0.866786i	$0.333818\pi$
$569$	−11.9583	+	20.7124i	−0.501318	+	0.868309i	−0.999999	+	0.00152301i	$0.999515\pi$
$570$		0			0
$571$	0.653231			0.0273369			0.0136684	−	0.999907i	$-0.495649\pi$
$571$	0.653231			0.0273369			0.0136684	+	0.999907i	$0.495649\pi$
$572$	17.1861	+	8.42455i	0.718589	+	0.352248i
$573$		0			0
$574$	3.42181	+	1.97558i	0.142823	+	0.0824592i
$575$	−13.1616	+	2.13081i	−0.548875	+	0.0888608i
$576$		0			0
$577$	−21.3167			−0.887425			−0.443712	−	0.896169i	$-0.646339\pi$
$577$	−21.3167			−0.887425			−0.443712	+	0.896169i	$0.646339\pi$
$578$	−16.2844	−	28.2054i	−0.677341	−	1.17319i
$579$		0			0
$580$	8.87493	−	3.15989i	0.368512	−	0.131207i
$581$	−6.01536	−	10.4189i	−0.249559	−	0.432250i
$582$		0			0
$583$	21.0733	−	36.5000i	0.872767	−	1.51168i
$584$	−7.04281			−0.291433
$585$		0			0
$586$	24.1742			0.998627
$587$	7.61491	−	13.1894i	0.314301	−	0.544385i	−0.664988	−	0.746854i	$-0.731563\pi$
$587$	7.61491	−	13.1894i	0.314301	−	0.544385i	0.979289	+	0.202469i	$0.0648966\pi$
$588$		0			0
$589$	−6.70567	−	11.6146i	−0.276302	−	0.478570i
$590$	−4.84829	−	13.6170i	−0.199601	−	0.560603i
$591$		0			0
$592$	0.412995	+	0.715328i	0.0169740	+	0.0293998i
$593$	9.70527			0.398548			0.199274	−	0.979944i	$-0.436142\pi$
$593$	9.70527			0.398548			0.199274	+	0.979944i	$0.436142\pi$
$594$		0			0
$595$	21.7649	+	3.99535i	0.892273	+	0.163793i
$596$	1.70092	+	0.982029i	0.0696725	+	0.0402255i
$597$		0			0
$598$	−0.651618	−	9.59241i	−0.0266467	−	0.392263i
$599$	1.20026			0.0490411			0.0245206	−	0.999699i	$-0.492194\pi$
$599$	1.20026			0.0490411			0.0245206	+	0.999699i	$0.492194\pi$
$600$		0			0
$601$	−7.03681	+	12.1881i	−0.287037	+	0.497163i	−0.973101	−	0.230378i	$-0.926004\pi$
$601$	−7.03681	+	12.1881i	−0.287037	+	0.497163i	0.686064	+	0.727541i	$0.259337\pi$
$602$	−6.43185	+	3.71343i	−0.262143	+	0.151348i
$603$		0			0
$604$	8.97219	−	5.18010i	0.365073	−	0.210775i
$605$	−29.2537	−	24.8986i	−1.18933	−	1.01227i
$606$		0			0
$607$	−27.3053	+	15.7647i	−1.10829	+	0.639870i	−0.938385	−	0.345591i	$-0.887678\pi$
$607$	−27.3053	+	15.7647i	−1.10829	+	0.639870i	−0.169902	+	0.985461i	$0.554345\pi$
$608$	2.28793	+	1.32094i	0.0927877	+	0.0535710i
$609$		0			0
$610$	−31.0399	+	11.0516i	−1.25677	+	0.447468i
$611$	2.84185	−	5.79739i	0.114969	−	0.234537i
$612$		0			0
$613$	−1.41675	+	2.45389i	−0.0572222	+	0.0991117i	−0.893217	−	0.449625i	$-0.851558\pi$
$613$	−1.41675	+	2.45389i	−0.0572222	+	0.0991117i	0.835995	+	0.548737i	$0.184891\pi$
$614$	−13.7722	+	23.8541i	−0.555799	+	0.962673i
$615$		0			0
$616$			7.46160i			0.300637i
$617$	1.12704	+	1.95209i	0.0453730	+	0.0785883i	0.887820	−	0.460191i	$-0.152219\pi$
$617$	1.12704	+	1.95209i	0.0453730	+	0.0785883i	−0.842447	+	0.538779i	$0.818886\pi$
$618$		0			0
$619$			6.37526i			0.256243i	0.991758	+	0.128122i	$0.0408948\pi$
$619$			6.37526i			0.256243i	−0.991758	+	0.128122i	$0.959105\pi$
$620$	7.35729	−	8.64420i	0.295476	−	0.347159i
$621$		0			0
$622$	−6.41309	+	11.1078i	−0.257141	+	0.445382i
$623$		−	21.3090i		−	0.853725i
$624$		0			0
$625$	5.03022	−	24.4887i	0.201209	−	0.979548i
$626$	2.36082	+	1.36302i	0.0943575	+	0.0544773i
$627$		0			0
$628$	−5.04984	+	2.91552i	−0.201510	+	0.116342i
$629$		−	5.81539i		−	0.231875i
$630$		0			0
$631$	−26.7025	+	15.4167i	−1.06301	+	0.613729i	−0.926263	−	0.376877i	$-0.876998\pi$
$631$	−26.7025	+	15.4167i	−1.06301	+	0.613729i	−0.136746	+	0.990606i	$0.543665\pi$
$632$	−4.05956			−0.161481
$633$		0			0
$634$	−0.949803	+	1.64511i	−0.0377215	+	0.0653355i
$635$	23.8603	+	4.38000i	0.946865	+	0.173815i
$636$		0			0
$637$	10.1001	+	15.0383i	0.400179	+	0.595840i
$638$		−	22.3649i		−	0.885433i
$639$		0			0
$640$	−0.403726	+	2.19932i	−0.0159587	+	0.0869357i
$641$	−9.59449	−	16.6181i	−0.378960	−	0.656377i	0.611952	−	0.790895i	$-0.290385\pi$
$641$	−9.59449	−	16.6181i	−0.378960	−	0.656377i	−0.990911	+	0.134518i	$0.957051\pi$
$642$		0			0
$643$	12.2778	+	21.2657i	0.484188	+	0.838638i	0.999835	−	0.0181630i	$-0.00578179\pi$
$643$	12.2778	+	21.2657i	0.484188	+	0.838638i	−0.515647	+	0.856801i	$0.672448\pi$
$644$	3.24601	−	1.87409i	0.127911	−	0.0738493i
$645$		0			0
$646$	−9.30006	−	16.1082i	−0.365906	−	0.633768i
$647$	−25.4323	−	14.6834i	−0.999849	−	0.577263i	−0.0916452	−	0.995792i	$-0.529213\pi$
$647$	−25.4323	−	14.6834i	−0.999849	−	0.577263i	−0.908204	+	0.418529i	$0.862546\pi$
$648$		0			0
$649$	−34.3149			−1.34698
$650$	17.2476	+	5.24602i	0.676506	+	0.205766i
$651$		0			0
$652$	5.87592	−	10.1774i	0.230119	−	0.398577i
$653$	−21.6951	−	12.5257i	−0.848997	−	0.490168i	0.0113155	−	0.999936i	$-0.496398\pi$
$653$	−21.6951	−	12.5257i	−0.848997	−	0.490168i	−0.860312	+	0.509767i	$0.829731\pi$
$654$		0			0
$655$	32.3352	−	11.5128i	1.26344	−	0.449844i
$656$	2.43440	−	1.40550i	0.0950473	−	0.0548756i
$657$		0			0
$658$	2.51702			0.0981236
$659$	−17.5467	−	30.3917i	−0.683521	−	1.18389i	−0.973899	−	0.226981i	$-0.927114\pi$
$659$	−17.5467	−	30.3917i	−0.683521	−	1.18389i	0.290378	−	0.956912i	$-0.406219\pi$
$660$		0			0
$661$	26.9586	+	15.5646i	1.04857	+	0.605392i	0.922248	−	0.386598i	$-0.126350\pi$
$661$	26.9586	+	15.5646i	1.04857	+	0.605392i	0.126321	+	0.991989i	$0.459683\pi$
$662$		−	8.98724i		−	0.349299i
$663$		0			0
$664$	−8.55910			−0.332158
$665$	8.16702	+	1.49921i	0.316704	+	0.0581369i
$666$		0			0
$667$	−9.72935	+	5.61725i	−0.376722	+	0.217501i
$668$	−11.1760			−0.432412
$669$		0			0
$670$	−6.81121	−	5.79719i	−0.263140	−	0.223965i
$671$			78.2206i			3.01967i
$672$		0			0
$673$	−0.167875	−	0.0969228i	−0.00647112	−	0.00373610i	0.496761	−	0.867887i	$-0.334523\pi$
$673$	−0.167875	−	0.0969228i	−0.00647112	−	0.00373610i	−0.503232	+	0.864151i	$0.667856\pi$
$674$	−1.19390	−	0.689296i	−0.0459872	−	0.0265507i
$675$		0			0
$676$	−4.91774	+	12.0339i	−0.189144	+	0.462844i
$677$			21.9008i			0.841718i	0.907126	+	0.420859i	$0.138271\pi$
$677$			21.9008i			0.841718i	−0.907126	+	0.420859i	$0.861729\pi$
$678$		0			0
$679$	−3.06883	+	5.31537i	−0.117771	+	0.203985i
$680$	10.2038	−	11.9886i	0.391298	−	0.459742i
$681$		0			0
$682$	−13.4741	−	23.3378i	−0.515949	−	0.893650i
$683$	−2.55910	−	4.43250i	−0.0979214	−	0.169605i	0.812903	−	0.582399i	$-0.197886\pi$
$683$	−2.55910	−	4.43250i	−0.0979214	−	0.169605i	−0.910824	+	0.412795i	$0.864553\pi$
$684$		0			0
$685$	19.3963	+	16.5087i	0.741096	+	0.630765i
$686$	−8.45069	+	14.6370i	−0.322649	+	0.558845i
$687$		0			0
$688$			5.28374i			0.201441i
$689$	25.7042	+	12.6001i	0.979252	+	0.480024i
$690$		0			0
$691$	−1.66003	−	0.958418i	−0.0631505	−	0.0364600i	0.468092	−	0.883680i	$-0.344941\pi$
$691$	−1.66003	−	0.958418i	−0.0631505	−	0.0364600i	−0.531243	+	0.847220i	$0.678275\pi$
$692$	−0.461938	−	0.266700i	−0.0175603	−	0.0101384i
$693$		0			0
$694$			11.8958i			0.451557i
$695$	19.3268	+	16.4495i	0.733108	+	0.623966i
$696$		0			0
$697$	−19.7909			−0.749633
$698$	3.95580	−	2.28388i	0.149729	−	0.0864463i
$699$		0			0
$700$	1.12319	+	6.93770i	0.0424525	+	0.262220i
$701$	23.4448			0.885500			0.442750	−	0.896645i	$-0.354003\pi$
$701$	23.4448			0.885500			0.442750	+	0.896645i	$0.354003\pi$
$702$		0			0
$703$		−	2.18216i		−	0.0823017i
$704$	4.59726	+	2.65423i	0.173266	+	0.100035i
$705$		0			0
$706$	−0.421009	−	0.729210i	−0.0158449	−	0.0274442i
$707$	11.7889			0.443368
$708$		0			0
$709$	−4.33100	+	2.50051i	−0.162654	+	0.0939085i	−0.579118	−	0.815244i	$-0.696603\pi$
$709$	−4.33100	+	2.50051i	−0.162654	+	0.0939085i	0.416463	+	0.909153i	$0.363269\pi$
$710$	7.22981	+	20.3058i	0.271330	+	0.762064i
$711$		0			0
$712$	−13.1289	−	7.57999i	−0.492027	−	0.284072i
$713$	−6.76840	+	11.7232i	−0.253479	+	0.439038i
$714$		0			0
$715$	25.4668	−	34.3966i	0.952404	−	1.28636i
$716$	−9.23733			−0.345215
$717$		0			0
$718$	6.97949	+	4.02961i	0.260472	+	0.150384i
$719$	−22.7388	−	39.3848i	−0.848016	−	1.46881i	−0.882976	−	0.469418i	$-0.844464\pi$
$719$	−22.7388	−	39.3848i	−0.848016	−	1.46881i	0.0349601	−	0.999389i	$-0.488870\pi$
$720$		0			0
$721$	6.77444	−	3.91123i	0.252293	−	0.145662i
$722$	6.01026	+	10.4101i	0.223679	+	0.387423i
$723$		0			0
$724$	2.38232	+	4.12630i	0.0885383	+	0.153353i
$725$	−3.36656	−	20.7945i	−0.125031	−	0.772290i
$726$		0			0
$727$			6.38432i			0.236781i	0.992967	+	0.118391i	$0.0377735\pi$
$727$			6.38432i			0.236781i	−0.992967	+	0.118391i	$0.962226\pi$
$728$	−5.05633	+	0.343480i	−0.187400	+	0.0127302i
$729$		0			0
$730$	−2.84337	+	15.4894i	−0.105238	+	0.573288i
$731$	18.6001	−	32.2164i	0.687951	−	1.19157i
$732$		0			0
$733$	46.0006			1.69907			0.849536	−	0.527530i	$-0.176882\pi$
$733$	46.0006			1.69907			0.849536	+	0.527530i	$0.176882\pi$
$734$	14.3052	−	8.25912i	0.528015	−	0.304850i
$735$		0			0
$736$		−	2.66659i		−	0.0982917i
$737$	−18.3890	+	10.6169i	−0.677369	+	0.391079i
$738$		0			0
$739$	−4.14392	−	2.39250i	−0.152437	−	0.0880094i	0.421841	−	0.906670i	$-0.361384\pi$
$739$	−4.14392	−	2.39250i	−0.152437	−	0.0880094i	−0.574278	+	0.818660i	$0.694717\pi$
$740$	1.73997	−	0.619511i	0.0639627	−	0.0227737i
$741$		0			0
$742$			11.1598i			0.409691i
$743$	7.90749	−	13.6962i	0.290098	−	0.502464i	−0.683735	−	0.729730i	$-0.739646\pi$
$743$	7.90749	−	13.6962i	0.290098	−	0.502464i	0.973833	+	0.227267i	$0.0729789\pi$
$744$		0			0
$745$	2.84650	−	3.34440i	0.104288	−	0.122529i
$746$		−	26.5545i		−	0.972231i
$747$		0			0
$748$	−18.6871	−	32.3671i	−0.683269	−	1.18346i
$749$		−	21.3437i		−	0.779881i
$750$		0			0
$751$	−4.94420	+	8.56360i	−0.180416	+	0.312490i	−0.942022	−	0.335550i	$-0.891078\pi$
$751$	−4.94420	+	8.56360i	−0.180416	+	0.312490i	0.761606	+	0.648040i	$0.224411\pi$
$752$	0.895350	−	1.55079i	0.0326501	−	0.0565516i
$753$		0			0
$754$	15.1555	−	1.02952i	0.551930	−	0.0374929i
$755$	−7.77038	−	21.8241i	−0.282793	−	0.794259i
$756$		0			0
$757$	7.56985	+	4.37046i	0.275131	+	0.158847i	0.631217	−	0.775606i	$-0.282556\pi$
$757$	7.56985	+	4.37046i	0.275131	+	0.158847i	−0.356086	+	0.934453i	$0.615889\pi$
$758$	−1.00089	+	0.577865i	−0.0363540	+	0.0209890i
$759$		0			0
$760$	3.82886	−	4.49859i	0.138887	−	0.163181i
$761$	−42.8460	+	24.7372i	−1.55317	+	0.896721i	−0.555286	+	0.831659i	$0.687391\pi$
$761$	−42.8460	+	24.7372i	−1.55317	+	0.896721i	−0.997881	+	0.0650620i	$0.979275\pi$
$762$		0			0
$763$	0.811936	−	0.468772i	0.0293941	−	0.0169707i
$764$	−8.97219	+	15.5403i	−0.324603	+	0.562228i
$765$		0			0
$766$	35.0077			1.26488
$767$	−1.57962	−	23.2534i	−0.0570366	−	0.839631i
$768$		0			0
$769$	20.2409	+	11.6861i	0.729906	+	0.421412i	0.818388	−	0.574666i	$-0.194868\pi$
$769$	20.2409	+	11.6861i	0.729906	+	0.421412i	−0.0884817	+	0.996078i	$0.528201\pi$
$770$	16.4104	+	3.01245i	0.591391	+	0.108561i
$771$		0			0
$772$	20.9462			0.753869
$773$	−0.828857	−	1.43562i	−0.0298119	−	0.0516358i	0.850735	−	0.525596i	$-0.176158\pi$
$773$	−0.828857	−	1.43562i	−0.0298119	−	0.0516358i	−0.880546	+	0.473960i	$0.842824\pi$
$774$		0			0
$775$	−16.0410	−	19.6709i	−0.576211	−	0.706600i
$776$	2.18328	+	3.78155i	0.0783751	+	0.135750i
$777$		0			0
$778$	−5.65673	+	9.79774i	−0.202803	+	0.351266i
$779$	−7.42631			−0.266075
$780$		0			0
$781$	51.1707			1.83103
$782$	−9.38707	+	16.2589i	−0.335681	+	0.581416i
$783$		0			0
$784$	2.51214	+	4.35115i	0.0897191	+	0.155398i
$785$	4.37342	+	12.2833i	0.156094	+	0.438409i
$786$		0			0
$787$	−21.6724	−	37.5376i	−0.772536	−	1.33807i	−0.936169	−	0.351550i	$-0.885655\pi$
$787$	−21.6724	−	37.5376i	−0.772536	−	1.33807i	0.163633	−	0.986521i	$-0.447679\pi$
$788$	26.7724			0.953726
$789$		0			0
$790$	−1.63895	+	8.92827i	−0.0583113	+	0.317654i
$791$	−4.10120	−	2.36783i	−0.145822	−	0.0841902i
$792$		0			0
$793$	−53.0060	+	3.60073i	−1.88230	+	0.127866i
$794$	18.0057			0.639000
$795$		0			0
$796$	−7.19452	+	12.4613i	−0.255003	+	0.441678i
$797$	−17.6871	+	10.2117i	−0.626509	+	0.361715i	−0.779399	−	0.626528i	$-0.784475\pi$
$797$	−17.6871	+	10.2117i	−0.626509	+	0.361715i	0.152890	+	0.988243i	$0.451142\pi$
$798$		0			0
$799$	−10.9184	+	6.30372i	−0.386264	+	0.223010i
$800$	4.67401	+	1.77585i	0.165251	+	0.0627857i
$801$		0			0
$802$	−3.97385	+	2.29430i	−0.140321	+	0.0810146i
$803$	32.3776	+	18.6932i	1.14258	+	0.659670i
$804$		0			0
$805$	−2.81121	−	7.89563i	−0.0990822	−	0.278285i
$806$	15.1945	−	10.2050i	0.535204	−	0.359455i
$807$		0			0
$808$	4.19353	−	7.26341i	0.147528	−	0.255526i
$809$	−11.5118	+	19.9390i	−0.404732	+	0.701017i	−0.994290	−	0.106709i	$-0.965969\pi$
$809$	−11.5118	+	19.9390i	−0.404732	+	0.701017i	0.589558	+	0.807726i	$0.299302\pi$
$810$		0			0
$811$			5.67837i			0.199395i	0.995018	+	0.0996973i	$0.0317874\pi$
$811$			5.67837i			0.199395i	−0.995018	+	0.0996973i	$0.968213\pi$
$812$	2.96095	+	5.12852i	0.103909	+	0.179976i
$813$		0			0
$814$		−	4.38474i		−	0.153685i
$815$	−20.0111	−	17.0319i	−0.700957	−	0.596602i
$816$		0			0
$817$	6.97949	−	12.0888i	0.244181	−	0.422935i
$818$			26.2500i			0.917811i
$819$		0			0
$820$	−2.10831	−	5.92146i	−0.0736255	−	0.206786i
$821$	11.2259	+	6.48129i	0.391787	+	0.226198i	0.682934	−	0.730480i	$-0.260704\pi$
$821$	11.2259	+	6.48129i	0.391787	+	0.226198i	−0.291147	+	0.956678i	$0.594037\pi$
$822$		0			0
$823$	−7.09023	+	4.09355i	−0.247150	+	0.142692i	−0.618459	−	0.785817i	$-0.712243\pi$
$823$	−7.09023	+	4.09355i	−0.247150	+	0.142692i	0.371309	+	0.928510i	$0.378909\pi$
$824$		−	5.56518i		−	0.193872i
$825$		0			0
$826$	7.86880	−	4.54305i	0.273791	−	0.158073i
$827$	−9.13747			−0.317741			−0.158870	−	0.987299i	$-0.550785\pi$
$827$	−9.13747			−0.317741			−0.158870	+	0.987299i	$0.550785\pi$
$828$		0			0
$829$	2.45257	−	4.24798i	0.0851814	−	0.147539i	−0.820287	−	0.571952i	$-0.806186\pi$
$829$	2.45257	−	4.24798i	0.0851814	−	0.147539i	0.905469	+	0.424413i	$0.139520\pi$
$830$	−3.45554	+	18.8242i	−0.119943	+	0.653398i
$831$		0			0
$832$	−1.58700	+	3.23750i	−0.0550195	+	0.112240i
$833$		−	35.3734i		−	1.22562i
$834$		0			0
$835$	−4.51204	+	24.5796i	−0.156146	+	0.850611i
$836$	−7.01214	−	12.1454i	−0.242520	−	0.420057i
$837$		0			0
$838$	6.03869	+	10.4593i	0.208603	+	0.361311i
$839$	1.95525	−	1.12887i	0.0675028	−	0.0389727i	−0.465869	−	0.884854i	$-0.654258\pi$
$839$	1.95525	−	1.12887i	0.0675028	−	0.0389727i	0.533372	+	0.845881i	$0.320925\pi$
$840$		0			0
$841$	5.62507	+	9.74290i	0.193968	+	0.335962i
$842$	−2.69954	−	1.55858i	−0.0930321	−	0.0537121i
$843$		0			0
$844$	−24.3908			−0.839567
$845$	24.4811	+	15.6741i	0.842174	+	0.539206i
$846$		0			0
$847$	12.0740	−	20.9127i	0.414867	−	0.718570i
$848$	6.87583	+	3.96976i	0.236117	+	0.136322i
$849$		0			0
$850$	−22.2472	−	27.2815i	−0.763074	−	0.935748i
$851$	−1.90749	+	1.10129i	−0.0653878	+	0.0377516i
$852$		0			0
$853$	14.7832			0.506166			0.253083	−	0.967445i	$-0.418555\pi$
$853$	14.7832			0.506166			0.253083	+	0.967445i	$0.418555\pi$
$854$	−10.3559	−	17.9369i	−0.354370	−	0.613788i
$855$		0			0
$856$	−13.1503	−	7.59234i	−0.449469	−	0.259501i
$857$			19.3235i			0.660079i	0.943967	+	0.330039i	$0.107062\pi$
$857$			19.3235i			0.660079i	−0.943967	+	0.330039i	$0.892938\pi$
$858$		0			0
$859$	48.8245			1.66587			0.832935	−	0.553371i	$-0.186659\pi$
$859$	48.8245			1.66587			0.832935	+	0.553371i	$0.186659\pi$
$860$	11.6206	+	2.13319i	0.396261	+	0.0727411i
$861$		0			0
$862$	−4.52932	+	2.61501i	−0.154269	+	0.0890675i
$863$	15.2366			0.518660			0.259330	−	0.965789i	$-0.416498\pi$
$863$	15.2366			0.518660			0.259330	+	0.965789i	$0.416498\pi$
$864$		0			0
$865$	−0.773055	+	0.908276i	−0.0262847	+	0.0308823i
$866$			22.3063i			0.757998i
$867$		0			0
$868$	6.17952	+	3.56775i	0.209747	+	0.121097i
$869$	18.6629	+	10.7750i	0.633094	+	0.365517i
$870$		0			0
$871$	−8.04102	−	11.9725i	−0.272460	−	0.405674i
$872$		−	0.667003i		−	0.0225876i
$873$		0			0
$874$	−3.52239	+	6.10096i	−0.119147	+	0.206368i
$875$	15.7117	+	0.330686i	0.531152	+	0.0111792i
$876$		0			0
$877$	0.222953	+	0.386166i	0.00752859	+	0.0130399i	0.869765	−	0.493466i	$-0.164270\pi$
$877$	0.222953	+	0.386166i	0.00752859	+	0.0130399i	−0.862237	+	0.506506i	$0.830937\pi$
$878$	−2.62417	−	4.54520i	−0.0885616	−	0.153393i
$879$		0			0
$880$	7.69353	−	9.03926i	0.259349	−	0.304713i
$881$	19.4053	−	33.6110i	0.653782	−	1.13238i	−0.328415	−	0.944534i	$-0.606514\pi$
$881$	19.4053	−	33.6110i	0.653782	−	1.13238i	0.982198	−	0.187851i	$-0.0601522\pi$
$882$		0			0
$883$			25.2239i			0.848853i	0.905462	+	0.424427i	$0.139524\pi$
$883$			25.2239i			0.848853i	−0.905462	+	0.424427i	$0.860476\pi$
$884$	21.0732	−	14.1532i	0.708769	−	0.476025i
$885$		0			0
$886$	0.966685	+	0.558116i	0.0324764	+	0.0187503i
$887$	−0.226808	−	0.130947i	−0.00761545	−	0.00439678i	0.496187	−	0.868215i	$-0.334733\pi$
$887$	−0.226808	−	0.130947i	−0.00761545	−	0.00439678i	−0.503803	+	0.863819i	$0.668066\pi$
$888$		0			0
$889$			15.2493i			0.511446i
$890$	−21.9713	+	25.8144i	−0.736480	+	0.865302i
$891$		0			0
$892$	−2.97949			−0.0997606
$893$	−4.09699	+	2.36540i	−0.137101	+	0.0791551i
$894$		0			0
$895$	−3.72935	+	20.3158i	−0.124659	+	0.679084i
$896$	−1.40561			−0.0469580
$897$		0			0
$898$			34.4883i			1.15089i
$899$	−18.5220	−	10.6937i	−0.617744	−	0.356655i
$900$		0			0
$901$	−27.9491	−	48.4093i	−0.931121	−	1.61275i
$902$	−14.9221			−0.496851
$903$		0			0
$904$	−2.91774	+	1.68456i	−0.0970426	+	0.0560276i
$905$	10.0369	−	3.57359i	0.333637	−	0.118790i
$906$		0			0
$907$	32.9635	+	19.0315i	1.09454	+	0.631930i	0.934780	−	0.355226i	$-0.115596\pi$
$907$	32.9635	+	19.0315i	1.09454	+	0.631930i	0.159755	+	0.987157i	$0.448930\pi$
$908$	1.98146	−	3.43199i	0.0657572	−	0.113895i
$909$		0			0
$910$	−1.28595	+	11.2592i	−0.0426289	+	0.373238i
$911$	50.4261			1.67069			0.835346	−	0.549725i	$-0.185267\pi$
$911$	50.4261			1.67069			0.835346	+	0.549725i	$0.185267\pi$
$912$		0			0
$913$	39.3484	+	22.7178i	1.30224	+	0.751850i
$914$	−2.03770	−	3.52940i	−0.0674011	−	0.116742i
$915$		0			0
$916$	8.53166	−	4.92576i	0.281894	−	0.162752i
$917$	10.7880	+	18.6854i	0.356252	+	0.617046i
$918$		0			0
$919$	−3.36458	−	5.82763i	−0.110987	−	0.192236i	0.805181	−	0.593029i	$-0.202068\pi$
$919$	−3.36458	−	5.82763i	−0.110987	−	0.192236i	−0.916169	+	0.400793i	$0.868735\pi$
$920$	−5.86468	−	1.07657i	−0.193353	−	0.0354935i
$921$		0			0
$922$			30.3417i			0.999249i
$923$	2.35554	+	34.6757i	0.0775335	+	1.14136i
$924$		0			0
$925$	−0.660029	−	4.07687i	−0.0217016	−	0.134047i
$926$	12.6145	−	21.8490i	0.414540	−	0.718004i
$927$		0			0
$928$	4.21306			0.138300
$929$	−13.8526	+	7.99782i	−0.454490	+	0.262400i	−0.709725	−	0.704479i	$-0.751181\pi$
$929$	−13.8526	+	7.99782i	−0.454490	+	0.262400i	0.255234	+	0.966879i	$0.417847\pi$
$930$		0			0
$931$		−	13.2735i		−	0.435021i
$932$	16.7854	−	9.69104i	0.549823	−	0.317441i
$933$		0			0
$934$	−19.0523	−	10.9999i	−0.623410	−	0.359926i
$935$	−78.7300	+	28.0315i	−2.57475	+	0.916729i
$936$		0			0
$937$			32.2129i			1.05235i	0.850376	+	0.526176i	$0.176375\pi$
$937$			32.2129i			1.05235i	−0.850376	+	0.526176i	$0.823625\pi$
$938$	2.81121	−	4.86916i	0.0917893	−	0.158984i
$939$		0			0
$940$	−3.04921	−	2.59526i	−0.0994543	−	0.0846479i
$941$			14.9874i			0.488576i	0.969703	+	0.244288i	$0.0785542\pi$
$941$			14.9874i			0.488576i	−0.969703	+	0.244288i	$0.921446\pi$
$942$		0			0
$943$	3.74789	+	6.49154i	0.122048	+	0.211394i
$944$		−	6.46419i		−	0.210391i
$945$		0			0
$946$	14.0243	−	24.2908i	0.455968	−	0.789760i
$947$	−7.43878	+	12.8844i	−0.241728	+	0.418685i	−0.961207	−	0.275829i	$-0.911048\pi$
$947$	−7.43878	+	12.8844i	−0.241728	+	0.418685i	0.719479	+	0.694515i	$0.244381\pi$
$948$		0			0
$949$	−11.1770	+	22.8011i	−0.362820	+	0.740155i
$950$	−8.34802	−	10.2371i	−0.270846	−	0.332135i
$951$		0			0
$952$	8.57035	+	4.94809i	0.277767	+	0.160369i
$953$	−5.73486	+	3.31103i	−0.185770	+	0.107255i	−0.590001	−	0.807402i	$-0.700873\pi$
$953$	−5.73486	+	3.31103i	−0.185770	+	0.107255i	0.404231	+	0.914657i	$0.367539\pi$
$954$		0			0
$955$	30.5558	+	26.0067i	0.988761	+	0.841559i
$956$	−25.9927	+	15.0069i	−0.840664	+	0.485358i
$957$		0			0
$958$	19.1462	−	11.0541i	0.618586	−	0.357141i
$959$	−8.00551	+	13.8659i	−0.258511	+	0.447755i
$960$		0			0
$961$	5.22962			0.168697
$962$	2.97130	−	0.201842i	0.0957986	−	0.00650766i
$963$		0			0
$964$	16.5815	+	9.57333i	0.534054	+	0.308336i
$965$	8.45652	−	46.0673i	0.272225	−	1.48296i
$966$		0			0
$967$	24.8355			0.798655			0.399328	−	0.916808i	$-0.369244\pi$
$967$	24.8355			0.798655			0.399328	+	0.916808i	$0.369244\pi$
$968$	−8.58987	−	14.8781i	−0.276089	−	0.478200i
$969$		0			0
$970$	9.19828	−	3.27501i	0.295339	−	0.105154i
$971$	−11.5415	−	19.9904i	−0.370383	−	0.641522i	0.619241	−	0.785201i	$-0.287440\pi$
$971$	−11.5415	−	19.9904i	−0.370383	−	0.641522i	−0.989624	+	0.143678i	$0.954107\pi$
$972$		0			0
$973$	−7.97681	+	13.8162i	−0.255725	+	0.442928i
$974$	−3.66873			−0.117554
$975$		0			0
$976$	−14.7351			−0.471659
$977$	−4.00989	+	6.94534i	−0.128288	+	0.222201i	−0.923013	−	0.384768i	$-0.874281\pi$
$977$	−4.00989	+	6.94534i	−0.128288	+	0.222201i	0.794725	+	0.606969i	$0.207615\pi$
$978$		0			0
$979$	40.2381	+	69.6943i	1.28601	+	2.22744i
$980$	10.5838	−	3.76832i	0.338086	−	0.120374i
$981$		0			0
$982$	−13.2345	−	22.9228i	−0.422329	−	0.731495i
$983$	−16.0606			−0.512254			−0.256127	−	0.966643i	$-0.582447\pi$
$983$	−16.0606			−0.512254			−0.256127	+	0.966643i	$0.582447\pi$
$984$		0			0
$985$	10.8087	−	58.8810i	0.344394	−	1.87610i
$986$	−25.6881	−	14.8310i	−0.818076	−	0.472317i
$987$		0			0
$988$	7.90749	−	5.31084i	0.251571	−	0.168960i
$989$	−14.0896			−0.448022
$990$		0			0
$991$	17.2373	−	29.8559i	0.547562	−	0.948405i	−0.450879	−	0.892585i	$-0.648889\pi$
$991$	17.2373	−	29.8559i	0.547562	−	0.948405i	0.998441	−	0.0558199i	$-0.0177773\pi$
$992$	4.39634	−	2.53823i	0.139584	−	0.0805888i
$993$		0			0
$994$	−11.7340	+	6.77464i	−0.372181	+	0.214879i
$995$	24.5017	+	20.8540i	0.776756	+	0.661116i
$996$		0			0
$997$	−38.3187	+	22.1233i	−1.21357	+	0.700652i	−0.963534	−	0.267586i	$-0.913774\pi$
$997$	−38.3187	+	22.1233i	−1.21357	+	0.700652i	−0.250031	+	0.968238i	$0.580441\pi$
$998$	−32.0779	−	18.5202i	−1.01541	−	0.586247i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bj.b.199.1		8
3.2	odd	2		130.2.m.a.69.4	yes	8
5.4	even	2		1170.2.bj.a.199.4		8
12.11	even	2		1040.2.df.c.849.1		8
13.10	even	6		1170.2.bj.a.829.4		8
15.2	even	4		650.2.m.e.251.4		16
15.8	even	4		650.2.m.e.251.5		16
15.14	odd	2		130.2.m.b.69.1	yes	8
39.17	odd	6		1690.2.c.e.1689.2		8
39.20	even	12		1690.2.b.e.339.10		16
39.23	odd	6		130.2.m.b.49.1	yes	8
39.32	even	12		1690.2.b.e.339.2		16
39.35	odd	6		1690.2.c.f.1689.2		8
60.59	even	2		1040.2.df.a.849.4		8
65.49	even	6	inner	1170.2.bj.b.829.1		8
156.23	even	6		1040.2.df.a.49.4		8
195.23	even	12		650.2.m.e.101.5		16
195.32	odd	12		8450.2.a.cs.1.2		8
195.59	even	12		1690.2.b.e.339.7		16
195.62	even	12		650.2.m.e.101.4		16
195.74	odd	6		1690.2.c.e.1689.7		8
195.98	odd	12		8450.2.a.cs.1.7		8
195.134	odd	6		1690.2.c.f.1689.7		8
195.137	odd	12		8450.2.a.cr.1.2		8
195.149	even	12		1690.2.b.e.339.15		16
195.179	odd	6		130.2.m.a.49.4	✓	8
195.188	odd	12		8450.2.a.cr.1.7		8
780.179	even	6		1040.2.df.c.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.4	✓	8	195.179	odd	6
130.2.m.a.69.4	yes	8	3.2	odd	2
130.2.m.b.49.1	yes	8	39.23	odd	6
130.2.m.b.69.1	yes	8	15.14	odd	2
650.2.m.e.101.4		16	195.62	even	12
650.2.m.e.101.5		16	195.23	even	12
650.2.m.e.251.4		16	15.2	even	4
650.2.m.e.251.5		16	15.8	even	4
1040.2.df.a.49.4		8	156.23	even	6
1040.2.df.a.849.4		8	60.59	even	2
1040.2.df.c.49.1		8	780.179	even	6
1040.2.df.c.849.1		8	12.11	even	2
1170.2.bj.a.199.4		8	5.4	even	2
1170.2.bj.a.829.4		8	13.10	even	6
1170.2.bj.b.199.1		8	1.1	even	1	trivial
1170.2.bj.b.829.1		8	65.49	even	6	inner
1690.2.b.e.339.2		16	39.32	even	12
1690.2.b.e.339.7		16	195.59	even	12
1690.2.b.e.339.10		16	39.20	even	12
1690.2.b.e.339.15		16	195.149	even	12
1690.2.c.e.1689.2		8	39.17	odd	6
1690.2.c.e.1689.7		8	195.74	odd	6
1690.2.c.f.1689.2		8	39.35	odd	6
1690.2.c.f.1689.7		8	195.134	odd	6
8450.2.a.cr.1.2		8	195.137	odd	12
8450.2.a.cr.1.7		8	195.188	odd	12
8450.2.a.cs.1.2		8	195.32	odd	12
8450.2.a.cs.1.7		8	195.98	odd	12

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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10653 + 0.750022i) q^{5} +(-0.702803 - 1.21729i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.10653 + 0.750022i) q^{5} +(-0.702803 - 1.21729i) q^{7} -1.00000 q^{8} +(-0.403726 + 2.19932i) q^{10} +(4.59726 + 2.65423i) q^{11} +(-1.58700 + 3.23750i) q^{13} -1.40561 q^{14} +(-0.500000 + 0.866025i) q^{16} +(6.09726 - 3.52026i) q^{17} +(2.28793 - 1.32094i) q^{19} +(1.70280 + 1.44930i) q^{20} +(4.59726 - 2.65423i) q^{22} +(-2.30933 - 1.33329i) q^{23} +(3.87493 - 3.15989i) q^{25} +(2.01026 + 2.99314i) q^{26} +(-0.702803 + 1.21729i) q^{28} +(2.10653 - 3.64862i) q^{29} -5.07645i q^{31} +(0.500000 + 0.866025i) q^{32} -7.04051i q^{34} +(2.39347 + 2.03714i) q^{35} +(0.412995 - 0.715328i) q^{37} -2.64187i q^{38} +(2.10653 - 0.750022i) q^{40} +(-2.43440 - 1.40550i) q^{41} +(4.57586 - 2.64187i) q^{43} -5.30846i q^{44} +(-2.30933 + 1.33329i) q^{46} -1.79070 q^{47} +(2.51214 - 4.35115i) q^{49} +(-0.799077 - 4.93573i) q^{50} +(3.59726 - 0.244364i) q^{52} -7.93952i q^{53} +(-11.6750 - 2.14317i) q^{55} +(0.702803 + 1.21729i) q^{56} +(-2.10653 - 3.64862i) q^{58} +(-5.59815 + 3.23210i) q^{59} +(7.36754 + 12.7610i) q^{61} +(-4.39634 - 2.53823i) q^{62} +1.00000 q^{64} +(0.914875 - 8.01018i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-6.09726 - 3.52026i) q^{68} +(2.96095 - 1.05424i) q^{70} +(8.34802 - 4.81973i) q^{71} +7.04281 q^{73} +(-0.412995 - 0.715328i) q^{74} +(-2.28793 - 1.32094i) q^{76} -7.46160i q^{77} +4.05956 q^{79} +(0.403726 - 2.19932i) q^{80} +(-2.43440 + 1.40550i) q^{82} +8.55910 q^{83} +(-10.2038 + 11.9886i) q^{85} -5.28374i q^{86} +(-4.59726 - 2.65423i) q^{88} +(13.1289 + 7.57999i) q^{89} +(5.05633 - 0.343480i) q^{91} +2.66659i q^{92} +(-0.895350 + 1.55079i) q^{94} +(-3.82886 + 4.49859i) q^{95} +(-2.18328 - 3.78155i) q^{97} +(-2.51214 - 4.35115i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} + 5 q^{7} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 + 5 * q^7 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 3 q^{5} + 5 q^{7} - 8 q^{8} + 3 q^{11} + 4 q^{13} + 10 q^{14} - 4 q^{16} + 15 q^{17} + 9 q^{19} + 3 q^{20} + 3 q^{22} + 6 q^{23} + 5 q^{25} - q^{26} + 5 q^{28} + 3 q^{29} + 4 q^{32} + 33 q^{35} + 20 q^{37} + 3 q^{40} - 21 q^{41} + 18 q^{43} + 6 q^{46} - 6 q^{47} - 15 q^{49} + q^{50} - 5 q^{52} - 23 q^{55} - 5 q^{56} - 3 q^{58} - 30 q^{59} - 5 q^{61} + 6 q^{62} + 8 q^{64} + 6 q^{65} - 16 q^{67} - 15 q^{68} + 18 q^{70} + 26 q^{73} - 20 q^{74} - 9 q^{76} + 4 q^{79} - 21 q^{82} + 48 q^{83} - 34 q^{85} - 3 q^{88} + 39 q^{89} + 19 q^{91} - 3 q^{94} - 9 q^{95} - 4 q^{97} + 15 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 3 * q^5 + 5 * q^7 - 8 * q^8 + 3 * q^11 + 4 * q^13 + 10 * q^14 - 4 * q^16 + 15 * q^17 + 9 * q^19 + 3 * q^20 + 3 * q^22 + 6 * q^23 + 5 * q^25 - q^26 + 5 * q^28 + 3 * q^29 + 4 * q^32 + 33 * q^35 + 20 * q^37 + 3 * q^40 - 21 * q^41 + 18 * q^43 + 6 * q^46 - 6 * q^47 - 15 * q^49 + q^50 - 5 * q^52 - 23 * q^55 - 5 * q^56 - 3 * q^58 - 30 * q^59 - 5 * q^61 + 6 * q^62 + 8 * q^64 + 6 * q^65 - 16 * q^67 - 15 * q^68 + 18 * q^70 + 26 * q^73 - 20 * q^74 - 9 * q^76 + 4 * q^79 - 21 * q^82 + 48 * q^83 - 34 * q^85 - 3 * q^88 + 39 * q^89 + 19 * q^91 - 3 * q^94 - 9 * q^95 - 4 * q^97 + 15 * q^98

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