LMFDB - Embedded newform 961.2.g.o.338.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(235,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.235"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,4,-2,-4,-8,-24,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	16.0.26873856000000000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 8x^{10} - 16x^{8} + 32x^{6} - 128x^{2} + 256 $ x^16 - 2x^14 + 8x^10 - 16x^8 + 32x^6 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			338.2
Root			$-1.38331 + 0.294032i$ of defining polynomial
Character	$\chi$	$=$	961.338
Dual form			961.2.g.o.816.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.95314 - 1.41904i) q^{2} +(0.252354 - 2.40099i) q^{3} +(1.18305 - 3.64105i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.91421 - 5.04757i) q^{6} +(-2.36146 + 0.501943i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-2.76662 - 0.588063i) q^{9} +(0.252354 + 2.40099i) q^{10} +(-3.50801 - 3.89604i) q^{11} +(-8.44357 - 3.75932i) q^{12} +(1.67035 - 0.743688i) q^{13} +(-3.89998 + 4.33137i) q^{14} +(1.95314 + 1.41904i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(-0.114805 + 0.127503i) q^{17} +(-6.23808 + 2.77737i) q^{18} +(1.44869 + 0.644997i) q^{19} +(2.56172 + 2.84508i) q^{20} +(0.609237 + 5.79650i) q^{21} +(-12.3803 - 2.63151i) q^{22} +(-1.23607 - 3.80423i) q^{23} +(-10.4240 + 2.21568i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.20711 - 3.82282i) q^{26} +(0.127999 - 0.393941i) q^{27} +(-0.966119 + 9.19201i) q^{28} +(0.947822 - 0.688633i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(-10.2396 + 7.43951i) q^{33} +(-0.0432971 + 0.411944i) q^{34} +(0.746033 - 2.29605i) q^{35} +(-5.41421 + 9.37769i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(3.74477 - 0.795975i) q^{38} +(-1.36407 - 4.19817i) q^{39} +(4.31775 + 0.917767i) q^{40} +(-0.991482 - 9.43332i) q^{41} +(9.41538 + 10.4568i) q^{42} +(8.13009 + 3.61975i) q^{43} +(-18.3358 + 8.16364i) q^{44} +(1.89259 - 2.10193i) q^{45} +(-7.81256 - 5.67616i) q^{46} +(1.34042 + 0.973874i) q^{47} +(-4.84627 + 5.38233i) q^{48} +(-1.07029 + 0.476522i) q^{49} +(8.82198 + 3.92780i) q^{50} +(0.277163 + 0.307821i) q^{51} +(-0.731699 - 6.96165i) q^{52} +(-0.167824 - 0.0356720i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(5.12808 - 1.09001i) q^{55} +(5.32843 + 9.22911i) q^{56} +(1.91421 - 3.31552i) q^{57} +(0.874032 - 2.68999i) q^{58} +(1.05271 - 10.0159i) q^{59} +(7.47745 - 5.43269i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(7.95136 - 5.77700i) q^{64} +(-0.191123 + 1.81841i) q^{65} +(-9.44243 + 29.0608i) q^{66} +(2.62132 - 4.54026i) q^{67} +(0.328427 + 0.568852i) q^{68} +(-9.44583 + 2.00777i) q^{69} +(-1.80108 - 5.54316i) q^{70} +(13.7636 + 2.92554i) q^{71} +(1.30507 + 12.4169i) q^{72} +(2.56172 + 2.84508i) q^{73} +(-2.20549 - 0.981949i) q^{74} +(8.82198 - 3.92780i) q^{75} +(4.06234 - 4.51168i) q^{76} +(10.2396 + 7.43951i) q^{77} +(-8.62158 - 6.26394i) q^{78} +(-10.1993 + 11.3275i) q^{79} +(2.74064 - 1.22021i) q^{80} +(-8.66524 - 3.85801i) q^{81} +(-15.3228 - 17.0176i) q^{82} +(-0.425542 - 4.04877i) q^{83} +(21.8261 + 4.63928i) q^{84} +(-0.0530189 - 0.163176i) q^{85} +(21.0158 - 4.46704i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-11.5711 + 20.0417i) q^{88} +(-3.85816 + 11.8742i) q^{89} +(0.713765 - 6.79102i) q^{90} +(-3.57117 + 2.59461i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(-1.28293 + 0.932102i) q^{95} +(0.400180 - 3.80745i) q^{96} +(3.34617 - 10.2984i) q^{97} +(-1.41421 + 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

Coefficient data

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

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

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

$2$	1.95314	−	1.41904i	1.38108	−	1.00341i	0.384300	−	0.923208i	$-0.374443\pi$
$2$	1.95314	−	1.41904i	1.38108	−	1.00341i	0.996778	−	0.0802039i	$-0.0255571\pi$
$3$	0.252354	−	2.40099i	0.145697	−	1.38621i	−0.640369	−	0.768068i	$-0.721218\pi$
$3$	0.252354	−	2.40099i	0.145697	−	1.38621i	0.786065	−	0.618143i	$-0.212115\pi$
$4$	1.18305	−	3.64105i	0.591525	−	1.82053i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	−2.91421	−	5.04757i	−1.18972	−	2.06066i
$7$	−2.36146	+	0.501943i	−0.892547	+	0.189717i	−0.631285	−	0.775551i	$-0.717472\pi$
$7$	−2.36146	+	0.501943i	−0.892547	+	0.189717i	−0.261262	+	0.965268i	$0.584139\pi$
$8$	−1.36407	−	4.19817i	−0.482271	−	1.48428i
$9$	−2.76662	−	0.588063i	−0.922206	−	0.196021i
$10$	0.252354	+	2.40099i	0.0798014	+	0.759259i
$11$	−3.50801	−	3.89604i	−1.05771	−	1.17470i	−0.984137	−	0.177410i	$-0.943228\pi$
$11$	−3.50801	−	3.89604i	−1.05771	−	1.17470i	−0.0735683	−	0.997290i	$-0.523439\pi$
$12$	−8.44357	−	3.75932i	−2.43745	−	1.08522i
$13$	1.67035	−	0.743688i	0.463272	−	0.206262i	−0.161809	−	0.986822i	$-0.551733\pi$
$13$	1.67035	−	0.743688i	0.463272	−	0.206262i	0.625081	+	0.780560i	$0.285066\pi$
$14$	−3.89998	+	4.33137i	−1.04231	+	1.15761i
$15$	1.95314	+	1.41904i	0.504299	+	0.366394i
$16$	−2.42705	−	1.76336i	−0.606763	−	0.440839i
$17$	−0.114805	+	0.127503i	−0.0278442	+	0.0309241i	−0.756906	−	0.653524i	$-0.773290\pi$
$17$	−0.114805	+	0.127503i	−0.0278442	+	0.0309241i	0.729062	+	0.684448i	$0.239957\pi$
$18$	−6.23808	+	2.77737i	−1.47033	+	0.654633i
$19$	1.44869	+	0.644997i	0.332352	+	0.147973i	0.566127	−	0.824318i	$-0.308441\pi$
$19$	1.44869	+	0.644997i	0.332352	+	0.147973i	−0.233775	+	0.972291i	$0.575108\pi$
$20$	2.56172	+	2.84508i	0.572818	+	0.636178i
$21$	0.609237	+	5.79650i	0.132946	+	1.26490i
$22$	−12.3803	−	2.63151i	−2.63948	−	0.561039i
$23$	−1.23607	−	3.80423i	−0.257738	−	0.793236i	−0.993278	−	0.115755i	$-0.963071\pi$
$23$	−1.23607	−	3.80423i	−0.257738	−	0.793236i	0.735540	−	0.677481i	$-0.236929\pi$
$24$	−10.4240	+	2.21568i	−2.12779	+	0.452275i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.20711	−	3.82282i	0.432849	−	0.749717i
$27$	0.127999	−	0.393941i	0.0246334	−	0.0758139i
$28$	−0.966119	+	9.19201i	−0.182579	+	1.73713i
$29$	0.947822	−	0.688633i	0.176006	−	0.127876i	−0.496294	−	0.868154i	$-0.665306\pi$
$29$	0.947822	−	0.688633i	0.176006	−	0.127876i	0.672300	+	0.740278i	$0.265306\pi$
$30$	5.82843			1.06412
$31$		0			0
$31$		0			0
$32$	1.58579			0.280330
$33$	−10.2396	+	7.43951i	−1.78249	+	1.29505i
$34$	−0.0432971	+	0.411944i	−0.00742539	+	0.0706479i
$35$	0.746033	−	2.29605i	0.126103	−	0.388104i
$36$	−5.41421	+	9.37769i	−0.902369	+	1.56295i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	3.74477	−	0.795975i	0.607481	−	0.129124i
$39$	−1.36407	−	4.19817i	−0.218426	−	0.672245i
$40$	4.31775	+	0.917767i	0.682697	+	0.145112i
$41$	−0.991482	−	9.43332i	−0.154843	−	1.47324i	−0.745604	−	0.666390i	$-0.767839\pi$
$41$	−0.991482	−	9.43332i	−0.154843	−	1.47324i	0.590760	−	0.806847i	$-0.298828\pi$
$42$	9.41538	+	10.4568i	1.45283	+	1.61353i
$43$	8.13009	+	3.61975i	1.23983	+	0.552007i	0.918673	−	0.395020i	$-0.129262\pi$
$43$	8.13009	+	3.61975i	1.23983	+	0.552007i	0.321155	+	0.947027i	$0.395929\pi$
$44$	−18.3358	+	8.16364i	−2.76423	+	1.23071i
$45$	1.89259	−	2.10193i	0.282130	−	0.313337i
$46$	−7.81256	−	5.67616i	−1.15190	−	0.836904i
$47$	1.34042	+	0.973874i	0.195521	+	0.142054i	0.681238	−	0.732062i	$-0.261442\pi$
$47$	1.34042	+	0.973874i	0.195521	+	0.142054i	−0.485718	+	0.874116i	$0.661442\pi$
$48$	−4.84627	+	5.38233i	−0.699499	+	0.776873i
$49$	−1.07029	+	0.476522i	−0.152898	+	0.0680745i
$50$	8.82198	+	3.92780i	1.24762	+	0.555474i
$51$	0.277163	+	0.307821i	0.0388106	+	0.0431035i
$52$	−0.731699	−	6.96165i	−0.101468	−	0.965408i
$53$	−0.167824	−	0.0356720i	−0.0230523	−	0.00489993i	0.196371	−	0.980530i	$-0.437084\pi$
$53$	−0.167824	−	0.0356720i	−0.0230523	−	0.00489993i	−0.219423	+	0.975630i	$0.570418\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	5.12808	−	1.09001i	0.691470	−	0.146976i
$56$	5.32843	+	9.22911i	0.712041	+	1.23329i
$57$	1.91421	−	3.31552i	0.253544	−	0.439151i
$58$	0.874032	−	2.68999i	0.114766	−	0.353214i
$59$	1.05271	−	10.0159i	0.137052	−	1.30396i	−0.682471	−	0.730912i	$-0.739095\pi$
$59$	1.05271	−	10.0159i	0.137052	−	1.30396i	0.819523	−	0.573046i	$-0.194239\pi$
$60$	7.47745	−	5.43269i	0.965335	−	0.701357i
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$		0			0
$63$	6.82843			0.860301
$64$	7.95136	−	5.77700i	0.993921	−	0.722126i
$65$	−0.191123	+	1.81841i	−0.0237059	+	0.225546i
$66$	−9.44243	+	29.0608i	−1.16228	+	3.57714i
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	−0.660293	−	0.751008i	$-0.729568\pi$
$67$	2.62132	−	4.54026i	0.320245	−	0.554681i	0.980539	+	0.196327i	$0.0629013\pi$
$68$	0.328427	+	0.568852i	0.0398276	+	0.0689835i
$69$	−9.44583	+	2.00777i	−1.13714	+	0.241707i
$70$	−1.80108	−	5.54316i	−0.215271	−	0.662535i
$71$	13.7636	+	2.92554i	1.63344	+	0.347198i	0.931133	−	0.364680i	$-0.118822\pi$
$71$	13.7636	+	2.92554i	1.63344	+	0.347198i	0.702304	+	0.711878i	$0.252155\pi$
$72$	1.30507	+	12.4169i	0.153804	+	1.46334i
$73$	2.56172	+	2.84508i	0.299826	+	0.332991i	0.874167	−	0.485626i	$-0.161408\pi$
$73$	2.56172	+	2.84508i	0.299826	+	0.332991i	−0.574341	+	0.818616i	$0.694741\pi$
$74$	−2.20549	−	0.981949i	−0.256383	−	0.114149i
$75$	8.82198	−	3.92780i	1.01867	−	0.453543i
$76$	4.06234	−	4.51168i	0.465982	−	0.517525i
$77$	10.2396	+	7.43951i	1.16691	+	0.847811i
$78$	−8.62158	−	6.26394i	−0.976201	−	0.709252i
$79$	−10.1993	+	11.3275i	−1.14751	+	1.27444i	−0.191378	+	0.981516i	$0.561296\pi$
$79$	−10.1993	+	11.3275i	−1.14751	+	1.27444i	−0.956135	+	0.292926i	$0.905371\pi$
$80$	2.74064	−	1.22021i	0.306412	−	0.136424i
$81$	−8.66524	−	3.85801i	−0.962804	−	0.428668i
$82$	−15.3228	−	17.0176i	−1.69211	−	1.87928i
$83$	−0.425542	−	4.04877i	−0.0467094	−	0.444410i	−0.992735	−	0.120319i	$-0.961608\pi$
$83$	−0.425542	−	4.04877i	−0.0467094	−	0.444410i	0.946026	−	0.324091i	$-0.105058\pi$
$84$	21.8261	+	4.63928i	2.38142	+	0.506187i
$85$	−0.0530189	−	0.163176i	−0.00575071	−	0.0176989i
$86$	21.0158	−	4.46704i	2.26619	−	0.481693i
$87$	−1.41421	−	2.44949i	−0.151620	−	0.262613i
$88$	−11.5711	+	20.0417i	−1.23348	+	2.13645i
$89$	−3.85816	+	11.8742i	−0.408965	+	1.25866i	0.508575	+	0.861018i	$0.330173\pi$
$89$	−3.85816	+	11.8742i	−0.408965	+	1.25866i	−0.917539	+	0.397646i	$0.869827\pi$
$90$	0.713765	−	6.79102i	0.0752374	−	0.715836i
$91$	−3.57117	+	2.59461i	−0.374361	+	0.271989i
$92$	−15.3137			−1.59656
$93$		0			0
$94$	4.00000			0.412568
$95$	−1.28293	+	0.932102i	−0.131626	+	0.0956316i
$96$	0.400180	−	3.80745i	0.0408432	−	0.388597i
$97$	3.34617	−	10.2984i	0.339752	−	1.04565i	−0.624582	−	0.780959i	$-0.714731\pi$
$97$	3.34617	−	10.2984i	0.339752	−	1.04565i	0.964334	−	0.264689i	$-0.0852694\pi$
$98$	−1.41421	+	2.44949i	−0.142857	+	0.247436i
$99$	7.41421	+	12.8418i	0.745157	+	1.29065i
$100$	14.9791	−	3.18390i	1.49791	−	0.318390i
$101$	2.62210	+	8.06998i	0.260908	+	0.802993i	0.992608	+	0.121366i	$0.0387274\pi$
$101$	2.62210	+	8.06998i	0.260908	+	0.802993i	−0.731700	+	0.681627i	$0.761273\pi$
$102$	0.978148	+	0.207912i	0.0968510	+	0.0205863i
$103$	1.26177	+	12.0049i	0.124326	+	1.18288i	0.861707	+	0.507405i	$0.169395\pi$
$103$	1.26177	+	12.0049i	0.124326	+	1.18288i	−0.737382	+	0.675477i	$0.763938\pi$
$104$	−5.40060	−	5.99797i	−0.529572	−	0.588150i
$105$	−5.32453	−	2.37063i	−0.519621	−	0.231350i
$106$	−0.378403	+	0.168476i	−0.0367537	+	0.0163638i
$107$	6.41414	−	7.12363i	0.620079	−	0.688667i	−0.348519	−	0.937302i	$-0.613315\pi$
$107$	6.41414	−	7.12363i	0.620079	−	0.688667i	0.968597	+	0.248635i	$0.0799819\pi$
$108$	−1.28293	−	0.932102i	−0.123450	−	0.0896915i
$109$	4.18389	+	3.03977i	0.400744	+	0.291158i	0.769844	−	0.638232i	$-0.220334\pi$
$109$	4.18389	+	3.03977i	0.400744	+	0.291158i	−0.369100	+	0.929390i	$0.620334\pi$
$110$	8.46909	−	9.40588i	0.807496	−	0.896815i
$111$	−2.20549	+	0.981949i	−0.209336	+	0.0932025i
$112$	6.61648	+	2.94585i	0.625199	+	0.278356i
$113$	3.57526	+	3.97073i	0.336332	+	0.373535i	0.887459	−	0.460887i	$-0.152469\pi$
$113$	3.57526	+	3.97073i	0.336332	+	0.373535i	−0.551127	+	0.834422i	$0.685802\pi$
$114$	−0.966119	−	9.19201i	−0.0904853	−	0.860910i
$115$	3.91259	+	0.831647i	0.364851	+	0.0775515i
$116$	−1.38603	−	4.26576i	−0.128689	−	0.396066i
$117$	−5.05856	+	1.07523i	−0.467664	+	0.0994051i
$118$	−12.1569	−	21.0563i	−1.11913	−	1.93839i
$119$	0.207107	−	0.358719i	0.0189854	−	0.0328838i
$120$	3.29315	−	10.1353i	0.300622	−	0.925219i
$121$	−1.72318	+	16.3950i	−0.156653	+	1.49045i
$122$	5.52431	−	4.01365i	0.500148	−	0.363379i
$123$	−22.8995			−2.06478
$124$		0			0
$125$	−9.00000			−0.804984
$126$	13.3369	−	9.68981i	1.18814	−	0.863236i
$127$	1.13931	−	10.8398i	0.101097	−	0.961875i	−0.819953	−	0.572431i	$-0.806000\pi$
$127$	1.13931	−	10.8398i	0.101097	−	0.961875i	0.921050	−	0.389444i	$-0.127333\pi$
$128$	6.35226	−	19.5502i	0.561466	−	1.72801i
$129$	10.7426	−	18.6068i	0.945837	−	1.63824i
$130$	2.20711	+	3.82282i	0.193576	+	0.335284i
$131$	4.65340	−	0.989111i	0.406569	−	0.0864190i	−8.73932e−5	−	1.00000i	$-0.500028\pi$
$131$	4.65340	−	0.989111i	0.406569	−	0.0864190i	0.406657	+	0.913581i	$0.366694\pi$
$132$	14.9737	+	46.0842i	1.30329	+	4.01112i
$133$	−3.74477	−	0.795975i	−0.324712	−	0.0690198i
$134$	−1.32300	−	12.5875i	−0.114290	−	1.08740i
$135$	0.277163	+	0.307821i	0.0238544	+	0.0264930i
$136$	0.691882	+	0.308046i	0.0593284	+	0.0264147i
$137$	−6.83814	+	3.04454i	−0.584222	+	0.260112i	−0.677494	−	0.735528i	$-0.736934\pi$
$137$	−6.83814	+	3.04454i	−0.584222	+	0.260112i	0.0932720	+	0.995641i	$0.470267\pi$
$138$	−15.5999	+	17.3255i	−1.32795	+	1.47484i
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$	−7.47745	−	5.43269i	−0.631960	−	0.459146i
$141$	2.67652	−	2.97258i	0.225404	−	0.250336i
$142$	31.0337	−	13.8171i	2.60429	−	1.15950i
$143$	−8.75705	−	3.89889i	−0.732301	−	0.326042i
$144$	5.67776	+	6.30579i	0.473147	+	0.525483i
$145$	0.122463	+	1.16515i	0.0101700	+	0.0967608i
$146$	9.04067	+	1.92165i	0.748211	+	0.159037i
$147$	0.874032	+	2.68999i	0.0720889	+	0.221867i
$148$	−3.74477	+	0.795975i	−0.307818	+	0.0654287i
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	0.844818	−	0.535054i	$-0.179709\pi$
$149$	−0.500000	−	0.866025i	−0.0409616	−	0.0709476i	−0.885779	+	0.464107i	$0.846375\pi$
$150$	11.6569	−	20.1903i	0.951778	−	1.64853i
$151$	−5.35023	+	16.4663i	−0.435396	+	1.34001i	0.457285	+	0.889320i	$0.348822\pi$
$151$	−5.35023	+	16.4663i	−0.435396	+	1.34001i	−0.892681	+	0.450690i	$0.851178\pi$
$152$	0.731699	−	6.96165i	0.0593486	−	0.564665i
$153$	0.392601	−	0.285241i	0.0317399	−	0.0230604i
$154$	30.5563			2.46230
$155$		0			0
$156$	−16.8995			−1.35304
$157$	−11.9964	+	8.71593i	−0.957421	+	0.695607i	−0.952550	−	0.304381i	$-0.901550\pi$
$157$	−11.9964	+	8.71593i	−0.957421	+	0.695607i	−0.00487058	+	0.999988i	$0.501550\pi$
$158$	−3.84654	+	36.5974i	−0.306014	+	2.91153i
$159$	−0.127999	+	0.393941i	−0.0101510	+	0.0312415i
$160$	−0.792893	+	1.37333i	−0.0626837	+	0.108571i
$161$	4.82843	+	8.36308i	0.380533	+	0.659103i
$162$	−22.3991	+	4.76107i	−1.75984	+	0.374065i
$163$	−4.00812	−	12.3357i	−0.313941	−	0.966210i	−0.976188	−	0.216925i	$-0.930397\pi$
$163$	−4.00812	−	12.3357i	−0.313941	−	0.966210i	0.662248	−	0.749285i	$-0.269603\pi$
$164$	−35.5202	−	7.55004i	−2.77366	−	0.589559i
$165$	−1.32300	−	12.5875i	−0.102996	−	0.979937i
$166$	−6.57650	−	7.30394i	−0.510436	−	0.566896i
$167$	−7.81661	−	3.48018i	−0.604868	−	0.269304i	0.0813675	−	0.996684i	$-0.474071\pi$
$167$	−7.81661	−	3.48018i	−0.604868	−	0.269304i	−0.686235	+	0.727380i	$0.740738\pi$
$168$	23.5036	−	10.4645i	1.81334	−	0.807353i
$169$	−6.46170	+	7.17644i	−0.497054	+	0.552034i
$170$	−0.335106	−	0.243469i	−0.0257014	−	0.0186732i
$171$	−3.62867	−	2.63638i	−0.277491	−	0.201609i
$172$	22.7980	−	25.3197i	1.73833	−	1.93061i
$173$	−13.0762	+	5.82191i	−0.994167	+	0.442632i	−0.838337	−	0.545152i	$-0.816472\pi$
$173$	−13.0762	+	5.82191i	−0.994167	+	0.442632i	−0.155830	+	0.987784i	$0.549805\pi$
$174$	−6.23808	−	2.77737i	−0.472908	−	0.210552i
$175$	−6.46170	−	7.17644i	−0.488458	−	0.542488i
$176$	1.64402	+	15.6418i	0.123922	+	1.17904i
$177$	−23.7824	−	5.05510i	−1.78759	−	0.379965i
$178$	9.31443	+	28.6669i	0.698146	+	2.14867i
$179$	6.60969	−	1.40493i	0.494032	−	0.105010i	0.0458431	−	0.998949i	$-0.485403\pi$
$179$	6.60969	−	1.40493i	0.494032	−	0.105010i	0.448189	+	0.893939i	$0.352069\pi$
$180$	−5.41421	−	9.37769i	−0.403552	−	0.698972i
$181$	5.15685	−	8.93193i	0.383306	−	0.663905i	−0.608227	−	0.793763i	$-0.708119\pi$
$181$	5.15685	−	8.93193i	0.383306	−	0.663905i	0.991533	+	0.129858i	$0.0414522\pi$
$182$	−3.29315	+	10.1353i	−0.244104	+	0.751276i
$183$	0.713765	−	6.79102i	0.0527630	−	0.502007i
$184$	−14.2847	+	10.3784i	−1.05308	+	0.765109i
$185$	1.00000			0.0735215
$186$		0			0
$187$	0.899495			0.0657776
$188$	5.13171	−	3.72841i	0.374269	−	0.271922i
$189$	−0.104528	+	0.994522i	−0.00760333	+	0.0723408i
$190$	−1.18305	+	3.64105i	−0.0858274	+	0.264150i
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	−0.845431	−	0.534084i	$-0.820657\pi$
$191$	0.550253	−	0.953065i	0.0398149	−	0.0689614i	0.885246	+	0.465123i	$0.153990\pi$
$192$	−11.8640	−	20.5490i	−0.856208	−	1.48300i
$193$	20.6801	−	4.39570i	1.48859	−	0.316409i	0.609392	−	0.792869i	$-0.291414\pi$
$193$	20.6801	−	4.39570i	1.48859	−	0.316409i	0.879196	+	0.476460i	$0.158080\pi$
$194$	−8.07836	−	24.8626i	−0.579993	−	1.78503i
$195$	4.31775	+	0.917767i	0.309201	+	0.0657226i
$196$	0.468840	+	4.46071i	0.0334885	+	0.318622i
$197$	2.33211	+	2.59007i	0.166156	+	0.184535i	0.820473	−	0.571686i	$-0.193710\pi$
$197$	2.33211	+	2.59007i	0.166156	+	0.184535i	−0.654317	+	0.756221i	$0.727044\pi$
$198$	32.7040	+	14.5608i	2.32417	+	1.03479i
$199$	14.2383	−	6.33931i	1.00933	−	0.449382i	0.165623	−	0.986189i	$-0.447036\pi$
$199$	14.2383	−	6.33931i	1.00933	−	0.449382i	0.843705	+	0.536807i	$0.180370\pi$
$200$	11.8147	−	13.1216i	0.835428	−	0.927837i
$201$	−10.2396	−	7.43951i	−0.722246	−	0.524743i
$202$	16.5729	+	12.0409i	1.16607	+	0.847198i
$203$	−1.89259	+	2.10193i	−0.132834	+	0.147527i
$204$	1.44869	−	0.644997i	0.101428	−	0.0451589i
$205$	8.66524	+	3.85801i	0.605206	+	0.269455i
$206$	19.4999	+	21.6568i	1.35862	+	1.50890i
$207$	1.18260	+	11.2517i	0.0821967	+	0.782049i
$208$	−5.36541	−	1.14045i	−0.372025	−	0.0790763i
$209$	−2.56908	−	7.90681i	−0.177707	−	0.546925i
$210$	−13.7636	+	2.92554i	−0.949777	+	0.201881i
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	0.705425	−	0.708785i	$-0.250756\pi$
$211$	−3.79289	−	6.56948i	−0.261114	−	0.452262i	−0.966538	+	0.256523i	$0.917423\pi$
$212$	−0.328427	+	0.568852i	−0.0225565	+	0.0390689i
$213$	10.4975	−	32.3079i	0.719276	−	2.21370i
$214$	2.41901	−	23.0154i	0.165360	−	1.57330i
$215$	−7.19984	+	5.23099i	−0.491025	+	0.356751i
$216$	−1.82843			−0.124409
$217$		0			0
$218$	12.4853			0.845610
$219$	7.47745	−	5.43269i	0.505279	−	0.367107i
$220$	2.09800	−	19.9611i	0.141447	−	1.34578i
$221$	−0.0969413	+	0.298355i	−0.00652097	+	0.0200695i
$222$	−2.91421	+	5.04757i	−0.195589	+	0.338770i
$223$	−0.863961	−	1.49642i	−0.0578551	−	0.100208i	0.835647	−	0.549266i	$-0.185093\pi$
$223$	−0.863961	−	1.49642i	−0.0578551	−	0.100208i	−0.893502	+	0.449059i	$0.851759\pi$
$224$	−3.74477	+	0.795975i	−0.250208	+	0.0531833i
$225$	−3.49613	−	10.7600i	−0.233075	−	0.717332i
$226$	12.6176	+	2.68196i	0.839311	+	0.178401i
$227$	1.62916	+	15.5004i	0.108131	+	1.02880i	0.905222	+	0.424939i	$0.139704\pi$
$227$	1.62916	+	15.5004i	0.108131	+	1.02880i	−0.797091	+	0.603859i	$0.793629\pi$
$228$	−9.80735	−	10.8922i	−0.649508	−	0.721351i
$229$	10.4923	+	4.67148i	0.693352	+	0.308700i	0.722988	−	0.690860i	$-0.242768\pi$
$229$	10.4923	+	4.67148i	0.693352	+	0.308700i	−0.0296358	+	0.999561i	$0.509435\pi$
$230$	8.82198	−	3.92780i	0.581704	−	0.258991i
$231$	20.4462	−	22.7078i	1.34526	−	1.49406i
$232$	−4.18389	−	3.03977i	−0.274686	−	0.199571i
$233$	11.9964	+	8.71593i	0.785914	+	0.571000i	0.906748	−	0.421673i	$-0.138557\pi$
$233$	11.9964	+	8.71593i	0.785914	+	0.571000i	−0.120834	+	0.992673i	$0.538557\pi$
$234$	−8.35428	+	9.27837i	−0.546137	+	0.606546i
$235$	−1.51361	+	0.673903i	−0.0987371	+	0.0439606i
$236$	−35.2230	−	15.6823i	−2.29282	−	1.02083i
$237$	24.6233	+	27.3470i	1.59946	+	1.77638i
$238$	−0.104528	−	0.994522i	−0.00677557	−	0.0644653i
$239$	12.4786	+	2.65240i	0.807172	+	0.171570i	0.592975	−	0.805221i	$-0.297953\pi$
$239$	12.4786	+	2.65240i	0.807172	+	0.171570i	0.214197	+	0.976790i	$0.431287\pi$
$240$	−2.23810	−	6.88816i	−0.144469	−	0.444629i
$241$	−24.1180	+	5.12645i	−1.55358	+	0.330224i	−0.903144	−	0.429338i	$-0.858747\pi$
$241$	−24.1180	+	5.12645i	−1.55358	+	0.330224i	−0.650436	+	0.759561i	$0.725414\pi$
$242$	19.8995	+	34.4669i	1.27919	+	2.21562i
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$	3.34617	−	10.2984i	0.214216	−	0.659290i
$245$	0.122463	−	1.16515i	0.00782386	−	0.0744390i
$246$	−44.7259	+	32.4953i	−2.85162	+	2.07182i
$247$	2.89949			0.184490
$248$		0			0
$249$	−9.82843			−0.622851
$250$	−17.5783	+	12.7714i	−1.11175	+	0.807731i
$251$	−0.374817	+	3.56614i	−0.0236582	+	0.225093i	0.976304	+	0.216403i	$0.0694327\pi$
$251$	−0.374817	+	3.56614i	−0.0236582	+	0.225093i	−0.999962	+	0.00868950i	$0.997234\pi$
$252$	8.07836	−	24.8626i	0.508889	−	1.56620i
$253$	−10.4853	+	18.1610i	−0.659204	+	1.14177i
$254$	−13.1569	−	22.7883i	−0.825534	−	1.42987i
$255$	−0.405162	+	0.0861198i	−0.0253722	+	0.00539303i
$256$	−9.26141	−	28.5037i	−0.578838	−	1.78148i
$257$	0.306853	+	0.0652237i	0.0191410	+	0.00406854i	0.217472	−	0.976067i	$-0.430219\pi$
$257$	0.306853	+	0.0652237i	0.0191410	+	0.00406854i	−0.198331	+	0.980135i	$0.563552\pi$
$258$	−5.42190	−	51.5859i	−0.337553	−	3.21160i
$259$	1.61542	+	1.79411i	0.100378	+	0.111481i
$260$	6.39482	+	2.84716i	0.396590	+	0.176573i
$261$	−3.02722	+	1.34781i	−0.187380	+	0.0834271i
$262$	7.68515	−	8.53523i	0.474790	−	0.527308i
$263$	0.555221	+	0.403392i	0.0342364	+	0.0248742i	0.604772	−	0.796399i	$-0.293264\pi$
$263$	0.555221	+	0.403392i	0.0342364	+	0.0248742i	−0.570535	+	0.821273i	$0.693264\pi$
$264$	45.1998	+	32.8396i	2.78186	+	2.02114i
$265$	0.114805	−	0.127503i	0.00705239	−	0.00783248i
$266$	−8.44357	+	3.75932i	−0.517709	+	0.230499i
$267$	27.5362	+	12.2599i	1.68519	+	0.750294i
$268$	−13.4302	−	14.9157i	−0.820378	−	0.911122i
$269$	3.32698	+	31.6541i	0.202849	+	1.92998i	0.341977	+	0.939708i	$0.388903\pi$
$269$	3.32698	+	31.6541i	0.202849	+	1.92998i	−0.139128	+	0.990274i	$0.544430\pi$
$270$	0.978148	+	0.207912i	0.0595282	+	0.0126531i
$271$	−7.20433	−	22.1727i	−0.437632	−	1.34689i	−0.890365	−	0.455247i	$-0.849551\pi$
$271$	−7.20433	−	22.1727i	−0.437632	−	1.34689i	0.452733	−	0.891646i	$-0.350449\pi$
$272$	0.503471	−	0.107016i	0.0305274	−	0.00648880i
$273$	5.32843	+	9.22911i	0.322491	+	0.558571i
$274$	−9.03553	+	15.6500i	−0.545857	+	0.945451i
$275$	6.48026	−	19.9442i	0.390774	−	1.20268i
$276$	−3.86448	+	36.7680i	−0.232614	+	2.21318i
$277$	11.4412	−	8.31254i	0.687437	−	0.499452i	−0.188380	−	0.982096i	$-0.560324\pi$
$277$	11.4412	−	8.31254i	0.687437	−	0.499452i	0.875817	+	0.482644i	$0.160324\pi$
$278$		0			0
$279$		0			0
$280$	−10.6569			−0.636869
$281$	−1.61803	+	1.17557i	−0.0965238	+	0.0701287i	−0.635000	−	0.772512i	$-0.719000\pi$
$281$	−1.61803	+	1.17557i	−0.0965238	+	0.0701287i	0.538477	+	0.842641i	$0.319000\pi$
$282$	1.00942	−	9.60395i	0.0601099	−	0.571907i
$283$	−0.724072	+	2.22846i	−0.0430416	+	0.132468i	−0.970268	−	0.242032i	$-0.922186\pi$
$283$	−0.724072	+	2.22846i	−0.0430416	+	0.132468i	0.927227	+	0.374501i	$0.122186\pi$
$284$	26.9350	−	46.6528i	1.59830	−	2.76834i
$285$	1.91421	+	3.31552i	0.113388	+	0.196394i
$286$	−22.6364	+	4.81152i	−1.33852	+	0.284511i
$287$	7.07633	+	21.7787i	0.417703	+	1.28556i
$288$	−4.38727	−	0.932542i	−0.258522	−	0.0549506i
$289$	1.77391	+	16.8776i	0.104347	+	0.992800i
$290$	1.89259	+	2.10193i	0.111137	+	0.123430i
$291$	−23.8820	−	10.6330i	−1.39999	−	0.623315i
$292$	13.3897	−	5.96148i	0.783573	−	0.348869i
$293$	−16.5938	+	18.4292i	−0.969418	+	1.07665i	0.0276109	+	0.999619i	$0.491210\pi$
$293$	−16.5938	+	18.4292i	−0.969418	+	1.07665i	−0.997029	+	0.0770290i	$0.975457\pi$
$294$	5.52431	+	4.01365i	0.322185	+	0.234081i
$295$	8.14767	+	5.91963i	0.474375	+	0.344654i
$296$	−2.95369	+	3.28040i	−0.171679	+	0.190669i
$297$	−1.98383	+	0.883258i	−0.115114	+	0.0512518i
$298$	−2.20549	−	0.981949i	−0.127761	−	0.0568828i
$299$	−4.89383	−	5.43514i	−0.283017	−	0.314323i
$300$	−3.86448	−	36.7680i	−0.223116	−	2.12280i
$301$	−21.0158	−	4.46704i	−1.21133	−	0.257476i
$302$	12.9166	+	39.7532i	0.743267	+	2.28754i
$303$	20.0376	−	4.25913i	1.15113	−	0.244681i
$304$	−2.37868	−	4.11999i	−0.136427	−	0.236298i
$305$	−1.41421	+	2.44949i	−0.0809776	+	0.140257i
$306$	0.362036	−	1.11423i	0.0206962	−	0.0636964i
$307$	0.288223	−	2.74225i	0.0164497	−	0.156509i	−0.983214	−	0.182459i	$-0.941594\pi$
$307$	0.288223	−	2.74225i	0.0164497	−	0.156509i	0.999663	+	0.0259500i	$0.00826107\pi$
$308$	39.2016	−	28.4816i	2.23372	−	1.62289i
$309$	29.1421			1.65784
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$	−15.7639	+	11.4532i	−0.892456	+	0.648408i
$313$	−0.400180	+	3.80745i	−0.0226195	+	0.215210i	0.977374	+	0.211520i	$0.0678413\pi$
$313$	−0.400180	+	3.80745i	−0.0226195	+	0.215210i	−0.999993	+	0.00369021i	$0.998825\pi$
$314$	−11.0625	+	34.0469i	−0.624293	+	1.92138i
$315$	−3.41421	+	5.91359i	−0.192369	+	0.333193i
$316$	29.1777	+	50.5372i	1.64137	+	2.84294i
$317$	2.12412	−	0.451495i	0.119302	−	0.0253585i	−0.147874	−	0.989006i	$-0.547243\pi$
$317$	2.12412	−	0.451495i	0.119302	−	0.0253585i	0.267176	+	0.963648i	$0.413910\pi$
$318$	0.309017	+	0.951057i	0.0173288	+	0.0533326i
$319$	−6.00792	−	1.27702i	−0.336379	−	0.0714995i
$320$	1.02735	+	9.77459i	0.0574306	+	0.546416i
$321$	−15.4851	−	17.1980i	−0.864295	−	0.959896i
$322$	21.2981	+	9.48254i	1.18690	+	0.528441i
$323$	−0.248556	+	0.110664i	−0.0138300	+	0.00615751i
$324$	−24.2986	+	26.9863i	−1.34992	+	1.49924i
$325$	5.91691	+	4.29889i	0.328211	+	0.238460i
$326$	−25.3333	−	18.4057i	−1.40308	−	1.01940i
$327$	8.35428	−	9.27837i	0.461993	−	0.513095i
$328$	−38.2502	+	17.0301i	−2.11201	+	0.940329i
$329$	−3.65418	−	1.62695i	−0.201462	−	0.0896965i
$330$	−20.4462	−	22.7078i	−1.12553	−	1.25002i
$331$	−0.0791656	−	0.753210i	−0.00435134	−	0.0414002i	0.992131	−	0.125206i	$-0.0399592\pi$
$331$	−0.0791656	−	0.753210i	−0.00435134	−	0.0414002i	−0.996482	+	0.0838057i	$0.973292\pi$
$332$	−15.2452	−	3.24047i	−0.836689	−	0.177844i
$333$	0.874032	+	2.68999i	0.0478967	+	0.147411i
$334$	−20.2055	+	4.29480i	−1.10559	+	0.235001i
$335$	2.62132	+	4.54026i	0.143218	+	0.248061i
$336$	8.74264	−	15.1427i	0.476950	−	0.826102i
$337$	−4.11416	+	12.6621i	−0.224113	+	0.689748i	0.774268	+	0.632858i	$0.218118\pi$
$337$	−4.11416	+	12.6621i	−0.224113	+	0.689748i	−0.998380	+	0.0568898i	$0.981882\pi$
$338$	−2.43695	+	23.1860i	−0.132552	+	1.26115i
$339$	10.4359	−	7.58213i	0.566801	−	0.411805i
$340$	−0.656854			−0.0356229
$341$		0			0
$342$	−10.8284			−0.585534
$343$	15.9602	−	11.5958i	0.861771	−	0.626113i
$344$	4.10632	−	39.0691i	0.221398	−	2.10646i
$345$	2.98413	−	9.18421i	0.160660	−	0.494461i
$346$	−17.2782	+	29.9267i	−0.928880	+	1.60887i
$347$	−11.2782	−	19.5344i	−0.605444	−	1.04866i	−0.991981	−	0.126386i	$-0.959662\pi$
$347$	−11.2782	−	19.5344i	−0.605444	−	1.04866i	0.386537	−	0.922274i	$-0.373671\pi$
$348$	−10.5918	+	2.25136i	−0.567780	+	0.120685i
$349$	10.8504	+	33.3942i	0.580810	+	1.78755i	0.615484	+	0.788150i	$0.288961\pi$
$349$	10.8504	+	33.3942i	0.580810	+	1.78755i	−0.0346738	+	0.999399i	$0.511039\pi$
$350$	−22.8042	−	4.84719i	−1.21894	−	0.259093i
$351$	−0.0791656	−	0.753210i	−0.00422555	−	0.0402034i
$352$	−5.56296	−	6.17829i	−0.296507	−	0.329304i
$353$	2.74064	+	1.22021i	0.145869	+	0.0649452i	0.478373	−	0.878157i	$-0.341227\pi$
$353$	2.74064	+	1.22021i	0.145869	+	0.0649452i	−0.332504	+	0.943102i	$0.607893\pi$
$354$	−53.6237	+	23.8748i	−2.85007	+	1.26893i
$355$	−9.41538	+	10.4568i	−0.499717	+	0.554992i
$356$	38.6702	+	28.0955i	2.04952	+	1.48906i
$357$	−0.809017	−	0.587785i	−0.0428177	−	0.0311089i
$358$	10.9160	−	12.1234i	0.576929	−	0.640744i
$359$	24.5739	−	10.9410i	1.29696	−	0.577444i	0.361995	−	0.932180i	$-0.382096\pi$
$359$	24.5739	−	10.9410i	1.29696	−	0.577444i	0.934967	+	0.354736i	$0.115429\pi$
$360$	−11.4059	−	5.07822i	−0.601142	−	0.267646i
$361$	−11.0308	−	12.2510i	−0.580569	−	0.644787i
$362$	−2.60271	−	24.7631i	−0.136795	−	1.30152i
$363$	38.9293	+	8.27468i	2.04326	+	0.434308i
$364$	5.22223	+	16.0724i	0.273719	+	0.842421i
$365$	−3.74477	+	0.795975i	−0.196010	+	0.0416632i
$366$	−8.24264	−	14.2767i	−0.430850	−	0.746254i
$367$	−9.10660	+	15.7731i	−0.475361	+	0.823349i	−0.999602	−	0.0282210i	$-0.991016\pi$
$367$	−9.10660	+	15.7731i	−0.475361	+	0.823349i	0.524241	+	0.851570i	$0.324349\pi$
$368$	−3.70820	+	11.4127i	−0.193303	+	0.594927i
$369$	−2.80433	+	26.6815i	−0.145988	+	1.38898i
$370$	1.95314	−	1.41904i	0.101539	−	0.0737723i
$371$	0.414214			0.0215049
$372$		0			0
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	1.75684	−	1.27642i	0.0908440	−	0.0660020i
$375$	−2.27119	+	21.6089i	−0.117284	+	1.11588i
$376$	2.26006	−	6.95575i	0.116554	−	0.358715i
$377$	1.07107	−	1.85514i	0.0551628	−	0.0955448i
$378$	1.20711	+	2.09077i	0.0620869	+	0.107538i
$379$	28.7426	−	6.10944i	1.47641	−	0.313821i	0.601800	−	0.798647i	$-0.294450\pi$
$379$	28.7426	−	6.10944i	1.47641	−	0.313821i	0.874611	+	0.484826i	$0.161117\pi$
$380$	1.87606	+	5.77393i	0.0962400	+	0.296196i
$381$	−25.7387	−	5.47093i	−1.31863	−	0.280284i
$382$	−0.277717	−	2.64230i	−0.0142092	−	0.135192i
$383$	16.6610	+	18.5039i	0.851338	+	0.945507i	0.999052	−	0.0435234i	$-0.0138583\pi$
$383$	16.6610	+	18.5039i	0.851338	+	0.945507i	−0.147714	+	0.989030i	$0.547192\pi$
$384$	−45.3369	−	20.1853i	−2.31359	−	1.03008i
$385$	−11.5626	+	5.14801i	−0.589285	+	0.262367i
$386$	34.1535	−	37.9313i	1.73837	−	1.93065i
$387$	−20.3642	−	14.7955i	−1.03517	−	0.752096i
$388$	−33.5385	−	24.3671i	−1.70266	−	1.23705i
$389$	11.4703	−	12.7391i	0.581569	−	0.645897i	−0.378520	−	0.925593i	$-0.623567\pi$
$389$	11.4703	−	12.7391i	0.581569	−	0.645897i	0.960089	+	0.279696i	$0.0902336\pi$
$390$	9.73552	−	4.33453i	0.492977	−	0.219488i
$391$	0.626958	+	0.279140i	0.0317067	+	0.0141167i
$392$	3.46046	+	3.84323i	0.174780	+	0.194112i
$393$	−1.20054	−	11.4224i	−0.0605592	−	0.576182i
$394$	8.23034	+	1.74941i	0.414639	+	0.0881342i
$395$	−4.71024	−	14.4966i	−0.236998	−	0.729404i
$396$	55.5290	−	11.8031i	2.79044	−	0.593126i
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	0.995368	−	0.0961392i	$-0.0306494\pi$
$397$	8.25736	+	14.3022i	0.414425	+	0.717805i	−0.580943	+	0.813944i	$0.697316\pi$
$398$	18.8137	−	32.5863i	0.943046	−	1.63340i
$399$	−2.85613	+	8.79027i	−0.142985	+	0.440064i
$400$	1.25434	−	11.9343i	0.0627171	−	0.596713i
$401$	17.1282	−	12.4443i	0.855340	−	0.621441i	−0.0712735	−	0.997457i	$-0.522706\pi$
$401$	17.1282	−	12.4443i	0.855340	−	0.621441i	0.926613	+	0.376016i	$0.122706\pi$
$402$	−30.5563			−1.52401
$403$		0			0
$404$	32.4853			1.61620
$405$	7.67375	−	5.57531i	0.381312	−	0.277039i
$406$	−0.713765	+	6.79102i	−0.0354236	+	0.337033i
$407$	−1.62007	+	4.98605i	−0.0803036	+	0.247149i
$408$	0.914214	−	1.58346i	0.0452603	−	0.0783932i
$409$	−4.67157	−	8.09140i	−0.230994	−	0.400094i	0.727107	−	0.686525i	$-0.240865\pi$
$409$	−4.67157	−	8.09140i	−0.230994	−	0.400094i	−0.958101	+	0.286431i	$0.907531\pi$
$410$	22.3991	−	4.76107i	1.10621	−	0.235133i
$411$	5.58427	+	17.1866i	0.275452	+	0.847753i
$412$	45.2033	+	9.60827i	2.22701	+	0.473365i
$413$	2.54147	+	24.1805i	0.125058	+	1.18985i
$414$	18.2764	+	20.2980i	0.898238	+	0.997594i
$415$	3.71911	+	1.65585i	0.182564	+	0.0812826i
$416$	2.64882	−	1.17933i	0.129869	−	0.0578215i
$417$		0			0
$418$	−16.2378	−	11.7975i	−0.794218	−	0.577033i
$419$	−22.6525	−	16.4580i	−1.10665	−	0.804025i	−0.124514	−	0.992218i	$-0.539737\pi$
$419$	−22.6525	−	16.4580i	−1.10665	−	0.804025i	−0.982132	+	0.188193i	$0.939737\pi$
$420$	−14.9308	+	16.5823i	−0.728548	+	0.809134i
$421$	−2.61079	+	1.16240i	−0.127242	+	0.0566518i	−0.469370	−	0.883002i	$-0.655519\pi$
$421$	−2.61079	+	1.16240i	−0.127242	+	0.0566518i	0.342128	+	0.939653i	$0.388852\pi$
$422$	−16.7304	−	7.44886i	−0.814423	−	0.362605i
$423$	−3.13574	−	3.48259i	−0.152465	−	0.169329i
$424$	0.0791656	+	0.753210i	0.00384462	+	0.0365791i
$425$	−0.671294	−	0.142688i	−0.0325626	−	0.00692139i
$426$	−25.3432	−	77.9982i	−1.22788	−	3.77903i
$427$	−6.67921	+	1.41971i	−0.323230	+	0.0687046i
$428$	−18.3492	−	31.7818i	−0.886944	−	1.53623i
$429$	−11.5711	+	20.0417i	−0.558656	+	0.967621i
$430$	−6.63932	+	20.4337i	−0.320176	+	0.985401i
$431$	2.63857	−	25.1044i	0.127096	−	1.20923i	−0.726080	−	0.687610i	$-0.758660\pi$
$431$	2.63857	−	25.1044i	0.127096	−	1.20923i	0.853175	−	0.521624i	$-0.174674\pi$
$432$	−1.00532	+	0.730406i	−0.0483684	+	0.0351417i
$433$	−35.1127			−1.68741			−0.843704	−	0.536808i	$-0.819630\pi$
$433$	−35.1127			−1.68741			−0.843704	+	0.536808i	$0.819630\pi$
$434$		0			0
$435$	2.82843			0.135613
$436$	16.0177	−	11.6376i	0.767110	−	0.557338i
$437$	0.663039	−	6.30840i	0.0317175	−	0.301772i
$438$	6.89532	−	21.2216i	0.329471	−	1.01401i
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	−0.685286	−	0.728274i	$-0.740323\pi$
$439$	6.03553	−	10.4539i	0.288060	−	0.498935i	0.973347	+	0.229339i	$0.0736563\pi$
$440$	−11.5711	−	20.0417i	−0.551629	−	0.955449i
$441$	3.24130	−	0.688959i	0.154347	−	0.0328076i
$442$	0.234037	+	0.720292i	0.0111320	+	0.0342608i
$443$	12.9533	+	2.75330i	0.615428	+	0.130813i	0.505070	−	0.863079i	$-0.331467\pi$
$443$	12.9533	+	2.75330i	0.615428	+	0.130813i	0.110358	+	0.993892i	$0.464800\pi$
$444$	0.966119	+	9.19201i	0.0458500	+	0.436233i
$445$	−8.35428	−	9.27837i	−0.396031	−	0.439837i
$446$	−3.81092	−	1.69673i	−0.180452	−	0.0803426i
$447$	−2.20549	+	0.981949i	−0.104316	+	0.0464446i
$448$	−15.8771	+	17.6333i	−0.750121	+	0.833094i
$449$	−3.74366	−	2.71993i	−0.176674	−	0.128361i	0.495934	−	0.868360i	$-0.334826\pi$
$449$	−3.74366	−	2.71993i	−0.176674	−	0.128361i	−0.672608	+	0.739999i	$0.734826\pi$
$450$	−22.0973	−	16.0546i	−1.04167	−	0.756821i
$451$	−33.2745	+	36.9550i	−1.56683	+	1.74015i
$452$	18.6873	−	8.32014i	0.878979	−	0.391347i
$453$	38.1853	+	17.0012i	1.79410	+	0.798785i
$454$	25.1777	+	27.9626i	1.18165	+	1.31235i
$455$	−0.461411	−	4.39003i	−0.0216313	−	0.205808i
$456$	−16.5302	−	3.51360i	−0.774098	−	0.164540i
$457$	9.61435	+	29.5899i	0.449740	+	1.38416i	0.877200	+	0.480124i	$0.159409\pi$
$457$	9.61435	+	29.5899i	0.449740	+	1.38416i	−0.427460	+	0.904034i	$0.640591\pi$
$458$	27.1220	−	5.76496i	1.26733	−	0.269379i
$459$	0.0355339	+	0.0615465i	0.00165858	+	0.00287275i
$460$	7.65685	−	13.2621i	0.357003	−	0.618347i
$461$	8.07836	−	24.8626i	0.376247	−	1.15797i	−0.566387	−	0.824140i	$-0.691659\pi$
$461$	8.07836	−	24.8626i	0.376247	−	1.15797i	0.942634	−	0.333829i	$-0.108341\pi$
$462$	7.71102	−	73.3654i	0.358749	−	3.41327i
$463$	−20.2016	+	14.6773i	−0.938848	+	0.682113i	−0.948143	−	0.317843i	$-0.897041\pi$
$463$	−20.2016	+	14.6773i	−0.938848	+	0.682113i	0.00929477	+	0.999957i	$0.497041\pi$
$464$	−3.51472			−0.163167
$465$		0			0
$466$	35.7990			1.65836
$467$	6.47214	−	4.70228i	0.299495	−	0.217596i	−0.427881	−	0.903835i	$-0.640740\pi$
$467$	6.47214	−	4.70228i	0.299495	−	0.217596i	0.727376	+	0.686239i	$0.240740\pi$
$468$	−2.06956	+	19.6905i	−0.0956654	+	0.910195i
$469$	−3.91118	+	12.0374i	−0.180602	+	0.555835i
$470$	−2.00000	+	3.46410i	−0.0922531	+	0.159787i
$471$	17.8995	+	31.0028i	0.824765	+	1.42854i
$472$	−43.4844	+	9.24289i	−2.00153	+	0.425438i
$473$	−14.4178	−	44.3733i	−0.662929	−	2.04029i
$474$	86.8992	+	18.4710i	3.99141	+	0.848401i
$475$	0.663039	+	6.30840i	0.0304223	+	0.289449i
$476$	−1.06110	−	1.17847i	−0.0486354	−	0.0540150i
$477$	0.443327	+	0.197382i	0.0202985	+	0.00903749i
$478$	28.1363	−	12.5271i	1.28692	−	0.572975i
$479$	6.50925	−	7.22925i	0.297415	−	0.330313i	−0.575853	−	0.817554i	$-0.695330\pi$
$479$	6.50925	−	7.22925i	0.297415	−	0.330313i	0.873268	+	0.487240i	$0.161996\pi$
$480$	3.09726	+	2.25029i	0.141370	+	0.102711i
$481$	−1.47923	−	1.07472i	−0.0674470	−	0.0490031i
$482$	−39.8313	+	44.2371i	−1.81427	+	2.01495i
$483$	21.2981	−	9.48254i	0.969099	−	0.431470i
$484$	57.6563	+	25.6702i	2.62074	+	1.16683i
$485$	7.24563	+	8.04709i	0.329007	+	0.365400i
$486$	5.46519	+	51.9979i	0.247906	+	2.35867i
$487$	17.0049	+	3.61450i	0.770565	+	0.163789i	0.576386	−	0.817178i	$-0.304463\pi$
$487$	17.0049	+	3.61450i	0.770565	+	0.163789i	0.194179	+	0.980966i	$0.437796\pi$
$488$	−3.85816	−	11.8742i	−0.174651	−	0.537520i
$489$	−30.6294	+	6.51049i	−1.38511	+	0.294414i
$490$	−1.41421	−	2.44949i	−0.0638877	−	0.110657i
$491$	−2.20711	+	3.82282i	−0.0996053	+	0.172522i	−0.911521	−	0.411253i	$-0.865091\pi$
$491$	−2.20711	+	3.82282i	−0.0996053	+	0.172522i	0.811916	+	0.583774i	$0.198425\pi$
$492$	−27.0912	+	83.3782i	−1.22137	+	3.75898i
$493$	−0.0210113	+	0.199909i	−0.000946300	+	0.00900345i
$494$	5.66312	−	4.11450i	0.254796	−	0.185120i
$495$	−14.8284			−0.666488
$496$		0			0
$497$	−33.9706			−1.52379
$498$	−19.1963	+	13.9469i	−0.860206	+	0.624977i
$499$	−4.20342	+	39.9929i	−0.188171	+	1.79033i	0.339221	+	0.940707i	$0.389837\pi$
$499$	−4.20342	+	39.9929i	−0.188171	+	1.79033i	−0.527392	+	0.849622i	$0.676830\pi$
$500$	−10.6474	+	32.7695i	−0.476168	+	1.46549i
$501$	−10.3284	+	17.8894i	−0.461440	+	0.799238i
$502$	4.32843	+	7.49706i	0.193187	+	0.334610i
$503$	−22.8738	+	4.86197i	−1.01989	+	0.216784i	−0.687367	−	0.726310i	$-0.741234\pi$
$503$	−22.8738	+	4.86197i	−1.01989	+	0.216784i	−0.332524	+	0.943095i	$0.607900\pi$
$504$	−9.31443	−	28.6669i	−0.414898	−	1.27692i
$505$	−8.29986	−	1.76419i	−0.369339	−	0.0785054i
$506$	5.29201	+	50.3501i	0.235258	+	2.23833i
$507$	15.5999	+	17.3255i	0.692817	+	0.769451i
$508$	−38.1204	−	16.9723i	−1.69132	−	0.753023i
$509$	6.21119	−	2.76540i	0.275306	−	0.122574i	−0.264440	−	0.964402i	$-0.585187\pi$
$509$	6.21119	−	2.76540i	0.275306	−	0.122574i	0.539746	+	0.841828i	$0.318520\pi$
$510$	−0.669131	+	0.743145i	−0.0296296	+	0.0329070i
$511$	−7.47745	−	5.43269i	−0.330783	−	0.240328i
$512$	−25.2758	−	18.3640i	−1.11704	−	0.811580i
$513$	0.439521	−	0.488138i	0.0194053	−	0.0215518i
$514$	0.691882	−	0.308046i	0.0305176	−	0.0135873i
$515$	−11.0275	−	4.90975i	−0.485928	−	0.216349i
$516$	−55.0392	−	61.1273i	−2.42297	−	2.69098i
$517$	−0.907965	−	8.63871i	−0.0399322	−	0.379930i
$518$	5.70106	+	1.21180i	0.250490	+	0.0532434i
$519$	10.6785	+	32.8650i	0.468734	+	1.44262i
$520$	7.89470	−	1.67807i	0.346205	−	0.0735882i
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	−0.978698	−	0.205304i	$-0.934182\pi$
$521$	−15.2279	−	26.3755i	−0.667147	−	1.15553i	0.311551	−	0.950229i	$-0.399152\pi$
$522$	−4.00000	+	6.92820i	−0.175075	+	0.303239i
$523$	−2.47214	+	7.60845i	−0.108099	+	0.332694i	−0.990445	−	0.137906i	$-0.955963\pi$
$523$	−2.47214	+	7.60845i	−0.108099	+	0.332694i	0.882346	+	0.470601i	$0.155963\pi$
$524$	1.90380	−	18.1134i	0.0831678	−	0.791289i
$525$	−18.8612	+	13.7035i	−0.823170	+	0.598068i
$526$	1.65685			0.0722423
$527$		0			0
$528$	37.9706			1.65246
$529$	5.66312	−	4.11450i	0.246223	−	0.178891i
$530$	0.0432971	−	0.411944i	0.00188071	−	0.0178937i
$531$	−8.80244	+	27.0911i	−0.381993	+	1.17565i
$532$	−7.32843	+	12.6932i	−0.317728	+	0.550320i
$533$	−8.67157	−	15.0196i	−0.375608	−	0.650571i
$534$	71.1794	−	15.1296i	3.08023	−	0.654724i
$535$	2.96217	+	9.11662i	0.128066	+	0.394146i
$536$	−22.6364	−	4.81152i	−0.977745	−	0.207826i
$537$	−1.70525	−	16.2243i	−0.0735868	−	0.700132i
$538$	51.4164	+	57.1037i	2.21672	+	2.46192i
$539$	5.61112	+	2.49823i	0.241688	+	0.107606i
$540$	1.44869	−	0.644997i	0.0623416	−	0.0277563i
$541$	16.9185	−	18.7899i	0.727382	−	0.807840i	−0.260098	−	0.965582i	$-0.583755\pi$
$541$	16.9185	−	18.7899i	0.727382	−	0.807840i	0.987480	+	0.157742i	$0.0504216\pi$
$542$	−45.5349	−	33.0831i	−1.95589	−	1.42104i
$543$	−20.1441	−	14.6356i	−0.864467	−	0.628072i
$544$	−0.182056	+	0.202193i	−0.00780557	+	0.00866897i
$545$	−4.72447	+	2.10347i	−0.202374	+	0.0901027i
$546$	23.5036	+	10.4645i	1.00586	+	0.447839i
$547$	3.83273	+	4.25668i	0.163876	+	0.182002i	0.819490	−	0.573094i	$-0.194257\pi$
$547$	3.83273	+	4.25668i	0.163876	+	0.182002i	−0.655614	+	0.755096i	$0.727590\pi$
$548$	2.99546	+	28.4999i	0.127960	+	1.21745i
$549$	−7.82518	−	1.66329i	−0.333971	−	0.0709876i
$550$	−15.6447	−	48.1495i	−0.667094	−	2.05310i
$551$	1.81727	−	0.386272i	0.0774181	−	0.0164557i
$552$	21.3137	+	36.9164i	0.907172	+	1.57127i
$553$	18.3995	−	31.8689i	0.782426	−	1.35520i
$554$	10.5505	−	32.4711i	0.448248	−	1.37956i
$555$	0.252354	−	2.40099i	0.0107118	−	0.101916i
$556$		0			0
$557$	44.4853			1.88490			0.942451	−	0.334344i	$-0.108515\pi$
$557$	44.4853			1.88490			0.942451	+	0.334344i	$0.108515\pi$
$558$		0			0
$559$	16.2721			0.688236
$560$	−5.85942	+	4.25712i	−0.247606	+	0.179896i
$561$	0.226991	−	2.15968i	0.00958357	−	0.0911816i
$562$	−1.49207	+	4.59211i	−0.0629390	+	0.193706i
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	−0.911787	−	0.410663i	$-0.865297\pi$
$563$	−2.37868	+	4.11999i	−0.100249	+	0.173637i	0.811538	+	0.584300i	$0.198631\pi$
$564$	−7.65685	−	13.2621i	−0.322412	−	0.558433i
$565$	−5.22639	+	1.11090i	−0.219876	+	0.0467360i
$566$	1.74806	+	5.37999i	0.0734766	+	0.226138i
$567$	22.3991	+	4.76107i	0.940673	+	0.199946i
$568$	−6.49254	−	61.7724i	−0.272421	−	2.59191i
$569$	10.1321	+	11.2528i	0.424758	+	0.471742i	0.917098	−	0.398661i	$-0.130525\pi$
$569$	10.1321	+	11.2528i	0.424758	+	0.471742i	−0.492340	+	0.870403i	$0.663858\pi$
$570$	8.44357	+	3.75932i	0.353662	+	0.157461i
$571$	−37.3635	+	16.6353i	−1.56362	+	0.696167i	−0.992219	−	0.124507i	$-0.960265\pi$
$571$	−37.3635	+	16.6353i	−1.56362	+	0.696167i	−0.571397	+	0.820674i	$0.693598\pi$
$572$	−24.5561	+	27.2723i	−1.02674	+	1.14031i
$573$	−2.14944	−	1.56166i	−0.0897942	−	0.0652393i
$574$	44.7259	+	32.4953i	1.86682	+	1.35633i
$575$	10.7061	−	11.8903i	0.446475	−	0.495861i
$576$	−25.3956	+	11.3069i	−1.05815	+	0.471119i
$577$	−31.0337	−	13.8171i	−1.29195	−	0.575212i	−0.358368	−	0.933581i	$-0.616667\pi$
$577$	−31.0337	−	13.8171i	−1.29195	−	0.575212i	−0.933580	+	0.358368i	$0.883333\pi$
$578$	27.4147	+	30.4471i	1.14030	+	1.26643i
$579$	−5.33530	−	50.7620i	−0.221728	−	2.10960i
$580$	4.38727	+	0.932542i	0.182171	+	0.0387217i
$581$	3.03715	+	9.34739i	0.126002	+	0.387795i
$582$	−61.7335	+	13.1219i	−2.55894	+	0.543919i
$583$	0.449747	+	0.778985i	0.0186266	+	0.0322623i
$584$	8.44975	−	14.6354i	0.349653	−	0.605617i
$585$	1.59810	−	4.91846i	0.0660735	−	0.203353i
$586$	−6.25813	+	59.5421i	−0.258521	+	2.45966i
$587$	16.4580	−	11.9574i	0.679292	−	0.493535i	−0.193831	−	0.981035i	$-0.562091\pi$
$587$	16.4580	−	11.9574i	0.679292	−	0.493535i	0.873123	+	0.487500i	$0.162091\pi$
$588$	10.8284			0.446557
$589$		0			0
$590$	24.3137			1.00098
$591$	6.80724	−	4.94575i	0.280013	−	0.203441i
$592$	−0.313585	+	2.98357i	−0.0128883	+	0.122624i
$593$	6.58630	−	20.2705i	0.270467	−	0.832411i	−0.719916	−	0.694061i	$-0.755820\pi$
$593$	6.58630	−	20.2705i	0.270467	−	0.832411i	0.990383	−	0.138351i	$-0.0441801\pi$
$594$	−2.62132	+	4.54026i	−0.107554	+	0.186289i
$595$	0.207107	+	0.358719i	0.00849055	+	0.0147061i
$596$	−3.74477	+	0.795975i	−0.153392	+	0.0326044i
$597$	−11.6275	−	35.7858i	−0.475882	−	1.46462i
$598$	−17.2710	−	3.67107i	−0.706264	−	0.150121i
$599$	−3.64799	−	34.7083i	−0.149053	−	1.41814i	−0.771872	−	0.635778i	$-0.780680\pi$
$599$	−3.64799	−	34.7083i	−0.149053	−	1.41814i	0.622819	−	0.782366i	$-0.285987\pi$
$600$	−28.5233	−	31.6783i	−1.16446	−	1.29326i
$601$	−21.4549	−	9.55232i	−0.875162	−	0.389647i	−0.0805401	−	0.996751i	$-0.525664\pi$
$601$	−21.4549	−	9.55232i	−0.875162	−	0.389647i	−0.794622	+	0.607104i	$0.792331\pi$
$602$	−47.3857	+	21.0975i	−1.93130	+	0.859868i
$603$	−9.92215	+	11.0197i	−0.404061	+	0.448756i
$604$	53.6251	+	38.9609i	2.18197	+	1.58530i
$605$	−13.3369	−	9.68981i	−0.542221	−	0.393947i
$606$	33.0924	−	36.7529i	1.34429	−	1.49298i
$607$	−4.03258	+	1.79542i	−0.163678	+	0.0728739i	−0.486940	−	0.873435i	$-0.661887\pi$
$607$	−4.03258	+	1.79542i	−0.163678	+	0.0728739i	0.323262	+	0.946309i	$0.395220\pi$
$608$	2.29731	+	1.02283i	0.0931682	+	0.0414812i
$609$	4.56911	+	5.07451i	0.185150	+	0.205630i
$610$	0.713765	+	6.79102i	0.0288995	+	0.274960i
$611$	2.96324	+	0.629855i	0.119880	+	0.0254812i
$612$	−0.574112	−	1.76693i	−0.0232071	−	0.0714241i
$613$	10.0883	−	2.14434i	0.407464	−	0.0866091i	0.000380010	−	1.00000i	$-0.499879\pi$
$613$	10.0883	−	2.14434i	0.407464	−	0.0866091i	0.407084	+	0.913391i	$0.366546\pi$
$614$	−3.32843	−	5.76500i	−0.134324	−	0.232657i
$615$	11.4497	−	19.8315i	0.461698	−	0.799685i
$616$	17.2648	−	53.1356i	0.695619	−	2.14089i
$617$	−2.43387	+	23.1567i	−0.0979839	+	0.932254i	0.829529	+	0.558463i	$0.188609\pi$
$617$	−2.43387	+	23.1567i	−0.0979839	+	0.932254i	−0.927513	+	0.373791i	$0.878058\pi$
$618$	56.9187	−	41.3538i	2.28960	−	1.66350i
$619$	−31.6569			−1.27240			−0.636198	−	0.771526i	$-0.719494\pi$
$619$	−31.6569			−1.27240			−0.636198	+	0.771526i	$0.719494\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$	−22.0973	+	16.0546i	−0.886019	+	0.643731i
$623$	3.15071	−	29.9770i	0.126231	−	1.20100i
$624$	−4.09220	+	12.5945i	−0.163819	+	0.504183i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	4.62132	+	8.00436i	0.184705	+	0.319919i
$627$	−19.6325	+	4.17301i	−0.784045	+	0.166654i
$628$	17.5428	+	53.9911i	0.700032	+	2.15448i
$629$	0.167824	+	0.0356720i	0.00669156	+	0.00142234i
$630$	1.72318	+	16.3950i	0.0686532	+	0.653191i
$631$	−21.4203	−	23.7897i	−0.852730	−	0.947053i	0.146380	−	0.989228i	$-0.453238\pi$
$631$	−21.4203	−	23.7897i	−0.852730	−	0.947053i	−0.999110	+	0.0421756i	$0.986571\pi$
$632$	61.4672	+	27.3670i	2.44504	+	1.08860i
$633$	−16.7304	+	7.44886i	−0.664974	+	0.296065i
$634$	3.50801	−	3.89604i	0.139321	−	0.154732i
$635$	8.81788	+	6.40656i	0.349927	+	0.254237i
$636$	1.28293	+	0.932102i	0.0508714	+	0.0369602i
$637$	−1.43337	+	1.59192i	−0.0567921	+	0.0630740i
$638$	−13.5464	+	6.03126i	−0.536309	+	0.238780i
$639$	−36.3582	−	16.1877i	−1.43831	−	0.640376i
$640$	13.7549	+	15.2763i	0.543709	+	0.603851i
$641$	−2.08749	−	19.8612i	−0.0824510	−	0.784469i	−0.955132	−	0.296179i	$-0.904288\pi$
$641$	−2.08749	−	19.8612i	−0.0824510	−	0.784469i	0.872682	−	0.488290i	$-0.162379\pi$
$642$	−54.6492	−	11.6160i	−2.15683	−	0.458448i
$643$	3.92028	+	12.0654i	0.154601	+	0.475812i	0.998120	−	0.0612864i	$-0.0195203\pi$
$643$	3.92028	+	12.0654i	0.154601	+	0.475812i	−0.843519	+	0.537099i	$0.819520\pi$
$644$	36.1627	−	7.68661i	1.42501	−	0.302895i
$645$	10.7426	+	18.6068i	0.422991	+	0.732642i
$646$	−0.328427	+	0.568852i	−0.0129218	+	0.0223812i
$647$	−7.01045	+	21.5759i	−0.275609	+	0.848238i	0.713448	+	0.700708i	$0.247132\pi$
$647$	−7.01045	+	21.5759i	−0.275609	+	0.848238i	−0.989058	+	0.147530i	$0.952868\pi$
$648$	−4.37661	+	41.6407i	−0.171930	+	1.63580i
$649$	−42.7153	+	31.0345i	−1.67672	+	1.21821i
$650$	17.6569			0.692559
$651$		0			0
$652$	−49.6569			−1.94471
$653$	−17.9134	+	13.0148i	−0.701004	+	0.509309i	−0.880259	−	0.474493i	$-0.842631\pi$
$653$	−17.9134	+	13.0148i	−0.701004	+	0.509309i	0.179255	+	0.983803i	$0.442631\pi$
$654$	3.15071	−	29.9770i	0.123203	−	1.17219i
$655$	−1.47010	+	4.52452i	−0.0574418	+	0.176788i
$656$	−14.2279	+	24.6435i	−0.555507	+	0.962166i
$657$	−5.41421	−	9.37769i	−0.211229	−	0.365859i
$658$	−9.44583	+	2.00777i	−0.368237	+	0.0782711i
$659$	2.98413	+	9.18421i	0.116245	+	0.357766i	0.992205	−	0.124619i	$-0.0397707\pi$
$659$	2.98413	+	9.18421i	0.116245	+	0.357766i	−0.875959	+	0.482385i	$0.839771\pi$
$660$	−47.3970	−	10.0745i	−1.84492	−	0.392151i
$661$	−3.46430	−	32.9606i	−0.134746	−	1.28202i	−0.827755	−	0.561090i	$-0.810382\pi$
$661$	−3.46430	−	32.9606i	−0.134746	−	1.28202i	0.693010	−	0.720928i	$-0.256284\pi$
$662$	−1.22346	−	1.35879i	−0.0475510	−	0.0528107i
$663$	0.691882	+	0.308046i	0.0268705	+	0.0119635i
$664$	−16.4169	+	7.30929i	−0.637100	+	0.283655i
$665$	2.56172	−	2.84508i	0.0993392	−	0.110327i
$666$	5.52431	+	4.01365i	0.214063	+	0.155526i
$667$	−3.79129	−	2.75453i	−0.146799	−	0.106656i
$668$	−21.9190	+	24.3435i	−0.848070	+	0.941877i
$669$	−3.81092	+	1.69673i	−0.147339	+	0.0655994i
$670$	11.5626	+	5.14801i	0.446703	+	0.198885i
$671$	−9.92215	−	11.0197i	−0.383041	−	0.425410i
$672$	0.966119	+	9.19201i	0.0372689	+	0.354589i
$673$	−20.2055	−	4.29480i	−0.778863	−	0.165552i	−0.198708	−	0.980059i	$-0.563675\pi$
$673$	−20.2055	−	4.29480i	−0.778863	−	0.165552i	−0.580155	+	0.814506i	$0.697008\pi$
$674$	9.93247	+	30.5690i	0.382584	+	1.17747i
$675$	1.62065	−	0.344479i	0.0623788	−	0.0132590i
$676$	18.4853	+	32.0174i	0.710972	+	1.23144i
$677$	−20.2990	+	35.1589i	−0.780154	+	1.35127i	0.151698	+	0.988427i	$0.451526\pi$
$677$	−20.2990	+	35.1589i	−0.780154	+	1.35127i	−0.931852	+	0.362839i	$0.881808\pi$
$678$	9.62345	−	29.6179i	0.369586	−	1.13747i
$679$	−2.73260	+	25.9989i	−0.104867	+	0.997747i
$680$	−0.612717	+	0.445165i	−0.0234966	+	0.0170713i
$681$	37.6274			1.44189
$682$		0			0
$683$	−46.6274			−1.78415			−0.892074	−	0.451889i	$-0.850750\pi$
$683$	−46.6274			−1.78415			−0.892074	+	0.451889i	$0.850750\pi$
$684$	−13.8921	+	10.0932i	−0.531178	+	0.385923i
$685$	0.782425	−	7.44428i	0.0298949	−	0.284431i
$686$	14.7177	−	45.2964i	0.561924	−	1.72942i
$687$	13.8640	−	24.0131i	0.528943	−	0.916156i
$688$	−13.3492	−	23.1216i	−0.508935	−	0.881501i
$689$	−0.306853	+	0.0652237i	−0.0116902	+	0.00248482i
$690$	−7.20433	−	22.1727i	−0.274264	−	0.844099i
$691$	−13.7636	−	2.92554i	−0.523591	−	0.111293i	−0.0614690	−	0.998109i	$-0.519579\pi$
$691$	−13.7636	−	2.92554i	−0.523591	−	0.111293i	−0.462122	+	0.886816i	$0.652912\pi$
$692$	5.72805	+	54.4988i	0.217748	+	2.07173i
$693$	−23.9542	−	26.6038i	−0.909945	−	1.01060i
$694$	−49.7479	−	22.1492i	−1.88840	−	0.840772i
$695$		0			0
$696$	−8.35428	+	9.27837i	−0.316668	+	0.351696i
$697$	1.31661	+	0.956572i	0.0498701	+	0.0362327i
$698$	68.5800	+	49.8263i	2.59579	+	1.88595i
$699$	23.9542	−	26.6038i	0.906031	−	1.00625i
$700$	−33.7743	+	15.0373i	−1.27655	+	0.568356i
$701$	3.18396	+	1.41759i	0.120257	+	0.0535417i	0.465983	−	0.884794i	$-0.345701\pi$
$701$	3.18396	+	1.41759i	0.120257	+	0.0535417i	−0.345726	+	0.938335i	$0.612367\pi$
$702$	−1.22346	−	1.35879i	−0.0461764	−	0.0512841i
$703$	−0.165760	−	1.57710i	−0.00625175	−	0.0594814i
$704$	−50.4009	−	10.7130i	−1.89956	−	0.403763i
$705$	1.23607	+	3.80423i	0.0465530	+	0.143275i
$706$	7.08437	−	1.50583i	0.266624	−	0.0566726i
$707$	−10.2426	−	17.7408i	−0.385214	−	0.667210i
$708$	−46.5416	+	80.6125i	−1.74914	+	3.02960i
$709$	−1.64203	+	5.05364i	−0.0616676	+	0.189793i	−0.977144	−	0.212578i	$-0.931814\pi$
$709$	−1.64203	+	5.05364i	−0.0616676	+	0.189793i	0.915476	+	0.402372i	$0.131814\pi$
$710$	−3.55089	+	33.7845i	−0.133263	+	1.26791i
$711$	34.8789	−	25.3410i	1.30806	−	0.950362i
$712$	55.1127			2.06544
$713$		0			0
$714$	−2.41421			−0.0903497
$715$	7.75506	−	5.63438i	0.290023	−	0.210714i
$716$	2.70416	−	25.7283i	0.101059	−	0.961513i
$717$	9.51741	−	29.2916i	0.355434	−	1.09391i
$718$	32.4706	−	56.2407i	1.21179	−	2.09888i
$719$	−3.03553	−	5.25770i	−0.113206	−	0.196079i	0.803855	−	0.594825i	$-0.202779\pi$
$719$	−3.03553	−	5.25770i	−0.113206	−	0.196079i	−0.917061	+	0.398746i	$0.869445\pi$
$720$	−8.29986	+	1.76419i	−0.309317	+	0.0657474i
$721$	−9.00542	−	27.7158i	−0.335379	−	1.03219i
$722$	−38.9293	−	8.27468i	−1.44880	−	0.307952i
$723$	6.22226	+	59.2008i	0.231408	+	2.20170i
$724$	−26.4208	−	29.3433i	−0.981922	−	1.09053i
$725$	4.28114	+	1.90609i	0.158998	+	0.0707903i
$726$	87.7764	−	39.0806i	3.25769	−	1.45042i
$727$	−31.3425	+	34.8094i	−1.16243	+	1.29101i	−0.212990	+	0.977054i	$0.568320\pi$
$727$	−31.3425	+	34.8094i	−1.16243	+	1.29101i	−0.949438	+	0.313954i	$0.898346\pi$
$728$	15.7639	+	11.4532i	0.584250	+	0.424482i
$729$	19.2776	+	14.0060i	0.713985	+	0.518741i
$730$	−6.18453	+	6.86862i	−0.228900	+	0.254219i
$731$	−1.39490	+	0.621051i	−0.0515924	+	0.0229704i
$732$	−23.8820	−	10.6330i	−0.882705	−	0.393006i
$733$	−19.8246	−	22.0175i	−0.732239	−	0.813234i	0.255915	−	0.966699i	$-0.417623\pi$
$733$	−19.8246	−	22.0175i	−0.732239	−	0.813234i	−0.988154	+	0.153466i	$0.950957\pi$
$734$	4.59618	+	43.7297i	0.169648	+	1.61409i
$735$	−2.76662	−	0.588063i	−0.102048	−	0.0216910i
$736$	−1.96014	−	6.03269i	−0.0722517	−	0.222368i
$737$	−26.8847	+	5.71451i	−0.990309	+	0.210497i
$738$	32.3848	+	56.0921i	1.19210	+	2.06478i
$739$	3.93503	−	6.81567i	0.144752	−	0.250718i	−0.784528	−	0.620093i	$-0.787095\pi$
$739$	3.93503	−	6.81567i	0.144752	−	0.250718i	0.929281	+	0.369375i	$0.120428\pi$
$740$	1.18305	−	3.64105i	0.0434897	−	0.133848i
$741$	0.731699	−	6.96165i	0.0268796	−	0.255743i
$742$	0.809017	−	0.587785i	0.0296999	−	0.0215783i
$743$	−5.65685			−0.207530			−0.103765	−	0.994602i	$-0.533089\pi$
$743$	−5.65685			−0.207530			−0.103765	+	0.994602i	$0.533089\pi$
$744$		0			0
$745$	1.00000			0.0366372
$746$	19.5314	−	14.1904i	0.715095	−	0.519547i
$747$	−1.20362	+	11.4516i	−0.0440380	+	0.418994i
$748$	1.06415	−	3.27511i	0.0389091	−	0.119750i
$749$	−11.5711	+	20.0417i	−0.422798	+	0.732307i
$750$	26.2279	+	45.4281i	0.957708	+	1.65880i
$751$	1.21549	−	0.258360i	0.0443537	−	0.00942767i	−0.185681	−	0.982610i	$-0.559449\pi$
$751$	1.21549	−	0.258360i	0.0443537	−	0.00942767i	0.230035	+	0.973182i	$0.426116\pi$
$752$	−1.53599	−	4.72729i	−0.0560117	−	0.172386i
$753$	8.46768	+	1.79986i	0.308579	+	0.0655906i
$754$	−0.540577	−	5.14324i	−0.0196866	−	0.187306i
$755$	−11.5851	−	12.8666i	−0.421626	−	0.468263i
$756$	3.49744	+	1.55716i	0.127201	+	0.0566334i
$757$	31.6606	−	14.0962i	1.15072	−	0.512336i	0.259431	−	0.965762i	$-0.416465\pi$
$757$	31.6606	−	14.0962i	1.15072	−	0.512336i	0.891294	+	0.453426i	$0.149798\pi$
$758$	47.4689	−	52.7195i	1.72415	−	1.91486i
$759$	40.9584	+	29.7580i	1.48670	+	1.08015i
$760$	5.66312	+	4.11450i	0.205423	+	0.149248i
$761$	−13.6876	+	15.2017i	−0.496176	+	0.551060i	−0.938268	−	0.345911i	$-0.887570\pi$
$761$	−13.6876	+	15.2017i	−0.496176	+	0.551060i	0.442091	+	0.896970i	$0.354237\pi$
$762$	−58.0347	+	25.8387i	−2.10238	+	0.936038i
$763$	−11.4059	−	5.07822i	−0.412920	−	0.183844i
$764$	−2.81918	−	3.13102i	−0.101994	−	0.113276i
$765$	0.0507257	+	0.482623i	0.00183399	+	0.0174493i
$766$	58.7991	+	12.4981i	2.12450	+	0.451576i
$767$	−5.69030	−	17.5130i	−0.205465	−	0.632356i
$768$	−70.7742	+	15.0435i	−2.55384	+	0.542836i
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	0.999443	−	0.0333680i	$-0.0106233\pi$
$769$	13.0563	+	22.6143i	0.470824	+	0.815491i	−0.528619	+	0.848859i	$0.677290\pi$
$770$	−15.2782	+	26.4626i	−0.550587	+	0.953645i
$771$	0.234037	−	0.720292i	0.00842863	−	0.0259407i
$772$	8.46065	−	80.4977i	0.304506	−	2.89718i
$773$	−14.5623	+	10.5801i	−0.523770	+	0.380541i	−0.818022	−	0.575187i	$-0.804929\pi$
$773$	−14.5623	+	10.5801i	−0.523770	+	0.380541i	0.294252	+	0.955728i	$0.404929\pi$
$774$	−60.7696			−2.18432
$775$		0			0
$776$	−47.7990			−1.71588
$777$	4.71530	−	3.42586i	0.169160	−	0.122902i
$778$	4.32589	−	41.1581i	0.155091	−	1.47559i
$779$	4.64812	−	14.3054i	0.166536	−	0.512546i
$780$	8.44975	−	14.6354i	0.302549	−	0.524031i
$781$	−36.8848	−	63.8863i	−1.31984	−	2.28603i
$782$	1.62065	−	0.344479i	0.0579543	−	0.0123186i
$783$	−0.149960	−	0.461530i	−0.00535914	−	0.0164937i
$784$	3.43791	+	0.730751i	0.122783	+	0.0260983i
$785$	−1.54999	−	14.7472i	−0.0553216	−	0.526350i
$786$	−18.5536	−	20.6059i	−0.661785	−	0.734987i
$787$	36.1634	+	16.1010i	1.28909	+	0.573938i	0.932785	−	0.360433i	$-0.117371\pi$
$787$	36.1634	+	16.1010i	1.28909	+	0.573938i	0.356301	+	0.934371i	$0.384038\pi$
$788$	12.1896	−	5.42715i	0.434235	−	0.193334i
$789$	1.10865	−	1.23128i	0.0394691	−	0.0438348i
$790$	−29.7710	−	21.6299i	−1.05920	−	0.769557i
$791$	−10.4359	−	7.58213i	−0.371058	−	0.269590i
$792$	43.7985	−	48.6432i	1.55631	−	1.72846i
$793$	4.72447	−	2.10347i	0.167771	−	0.0746963i
$794$	36.4231	+	16.2166i	1.29261	+	0.575506i
$795$	−0.277163	−	0.307821i	−0.00982996	−	0.0109173i
$796$	−6.23711	−	59.3422i	−0.221069	−	2.10333i
$797$	21.9651	+	4.66883i	0.778045	+	0.165379i	0.579783	−	0.814771i	$-0.303137\pi$
$797$	21.9651	+	4.66883i	0.778045	+	0.165379i	0.198261	+	0.980149i	$0.436471\pi$
$798$	6.89532	+	21.2216i	0.244092	+	0.751236i
$799$	−0.278059	+	0.0591033i	−0.00983703	+	0.00209093i
$800$	3.17157	+	5.49333i	0.112132	+	0.194218i
$801$	17.6569	−	30.5826i	0.623874	−	1.08058i
$802$	15.7947	−	48.6111i	0.557730	−	1.71652i
$803$	2.09800	−	19.9611i	0.0740367	−	0.704413i
$804$	−39.2016	+	28.4816i	−1.38253	+	1.00447i
$805$	−9.65685			−0.340359
$806$		0			0
$807$	76.8406			2.70492
$808$	30.3024	−	22.0160i	1.06604	−	0.774520i
$809$	4.80523	−	45.7187i	0.168943	−	1.60738i	−0.501320	−	0.865262i	$-0.667152\pi$
$809$	4.80523	−	45.7187i	0.168943	−	1.60738i	0.670263	−	0.742123i	$-0.266181\pi$
$810$	7.07633	−	21.7787i	0.248637	−	0.765226i
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	−0.950423	−	0.310961i	$-0.899349\pi$
$811$	−5.86396	+	10.1567i	−0.205912	+	0.356649i	0.744511	+	0.667610i	$0.232683\pi$
$812$	5.41421	+	9.37769i	0.190002	+	0.329093i
$813$	−55.0543	+	11.7022i	−1.93084	+	0.410413i
$814$	3.91118	+	12.0374i	0.137087	+	0.421910i
$815$	12.6871	+	2.69673i	0.444411	+	0.0944624i
$816$	−0.129891	−	1.23583i	−0.00454711	−	0.0432628i
$817$	9.44324	+	10.4878i	0.330377	+	0.366921i
$818$	−20.6063	−	9.17449i	−0.720481	−	0.320779i
$819$	11.4059	−	5.07822i	0.398553	−	0.177447i
$820$	24.2986	−	26.9863i	0.848544	−	0.942404i
$821$	6.86474	+	4.98752i	0.239581	+	0.174066i	0.701097	−	0.713066i	$-0.252694\pi$
$821$	6.86474	+	4.98752i	0.239581	+	0.174066i	−0.461516	+	0.887132i	$0.652694\pi$
$822$	35.2953	+	25.6436i	1.23107	+	0.894422i
$823$	−4.15744	+	4.61731i	−0.144919	+	0.160949i	−0.811234	−	0.584721i	$-0.801204\pi$
$823$	−4.15744	+	4.61731i	−0.144919	+	0.160949i	0.666315	+	0.745670i	$0.267871\pi$
$824$	48.6776	−	21.6727i	1.69576	−	0.755003i
$825$	−46.2504	−	20.5920i	−1.61023	−	0.716922i
$826$	39.2770	+	43.6215i	1.36662	+	1.51779i
$827$	−1.78749	−	17.0068i	−0.0621571	−	0.591385i	−0.980626	−	0.195891i	$-0.937240\pi$
$827$	−1.78749	−	17.0068i	−0.0621571	−	0.591385i	0.918469	−	0.395494i	$-0.129427\pi$
$828$	42.3672	+	9.00543i	1.47236	+	0.312960i
$829$	−14.3465	−	44.1541i	−0.498276	−	1.53354i	−0.811788	−	0.583952i	$-0.801506\pi$
$829$	−14.3465	−	44.1541i	−0.498276	−	1.53354i	0.313512	−	0.949584i	$-0.398494\pi$
$830$	9.61365	−	2.04344i	0.333695	−	0.0709290i
$831$	−17.0711	−	29.5680i	−0.592189	−	1.02570i
$832$	8.98528	−	15.5630i	0.311509	−	0.539549i
$833$	0.0621155	−	0.191172i	0.00215218	−	0.00662372i
$834$		0			0
$835$	6.92223	−	5.02930i	0.239554	−	0.174046i
$836$	−31.8284			−1.10081
$837$		0			0
$838$	−67.5980			−2.33513
$839$	−24.7781	+	18.0023i	−0.855435	+	0.621510i	−0.926639	−	0.375952i	$-0.877316\pi$
$839$	−24.7781	+	18.0023i	−0.855435	+	0.621510i	0.0712042	+	0.997462i	$0.477316\pi$
$840$	−2.68930	+	25.5870i	−0.0927897	+	0.882835i
$841$	−8.53734	+	26.2752i	−0.294391	+	0.906043i
$842$	−3.44975	+	5.97514i	−0.118886	+	0.205917i
$843$	2.41421	+	4.18154i	0.0831499	+	0.144020i
$844$	−28.4070	+	6.03809i	−0.977809	+	0.207840i
$845$	−2.98413	−	9.18421i	−0.102657	−	0.315947i
$846$	−11.0665	−	2.35225i	−0.380473	−	0.0808721i
$847$	−4.16013	−	39.5810i	−0.142944	−	1.36002i
$848$	0.344414	+	0.382510i	0.0118272	+	0.0131355i
$849$	5.16779	+	2.30085i	0.177358	+	0.0789650i
$850$	−1.51361	+	0.673903i	−0.0519165	+	0.0231147i
$851$	−2.67652	+	2.97258i	−0.0917500	+	0.101899i
$852$	−105.216	−	76.4437i	−3.60463	−	2.61892i
$853$	26.2811	+	19.0944i	0.899849	+	0.653779i	0.938427	−	0.345477i	$-0.112283\pi$
$853$	26.2811	+	19.0944i	0.899849	+	0.653779i	−0.0385780	+	0.999256i	$0.512283\pi$
$854$	−11.0308	+	12.2510i	−0.377466	+	0.419219i
$855$	4.09751	−	1.82433i	0.140132	−	0.0623907i
$856$	−38.6555	−	17.2105i	−1.32122	−	0.588244i
$857$	−1.68268	−	1.86880i	−0.0574791	−	0.0638370i	0.713720	−	0.700432i	$-0.247009\pi$
$857$	−1.68268	−	1.86880i	−0.0574791	−	0.0638370i	−0.771199	+	0.636595i	$0.780342\pi$
$858$	5.84001	+	55.5640i	0.199375	+	1.89692i
$859$	12.3396	+	2.62285i	0.421020	+	0.0894906i	0.413550	−	0.910482i	$-0.364289\pi$
$859$	12.3396	+	2.62285i	0.421020	+	0.0894906i	0.00747029	+	0.999972i	$0.497622\pi$
$860$	10.5285	+	32.4035i	0.359020	+	1.10495i
$861$	54.0762	−	11.4942i	1.84291	−	0.391723i
$862$	−30.4706	−	52.7766i	−1.03783	−	1.79758i
$863$	19.6924	−	34.1082i	0.670337	−	1.16106i	−0.307472	−	0.951557i	$-0.599483\pi$
$863$	19.6924	−	34.1082i	0.670337	−	1.16106i	0.977809	−	0.209500i	$-0.0671836\pi$
$864$	0.202979	−	0.624706i	0.00690549	−	0.0212529i
$865$	1.49619	−	14.2353i	0.0508720	−	0.484015i
$866$	−68.5800	+	49.8263i	−2.33044	+	1.69317i
$867$	40.9706			1.39143
$868$		0			0
$869$	79.9117			2.71082
$870$	5.52431	−	4.01365i	0.187292	−	0.136075i
$871$	1.00199	−	9.53327i	0.0339511	−	0.323023i
$872$	7.05437	−	21.7111i	0.238891	−	0.735231i
$873$	−15.3137	+	26.5241i	−0.518291	+	0.897705i
$874$	−7.65685	−	13.2621i	−0.258997	−	0.448596i
$875$	21.2531	−	4.51749i	0.718486	−	0.152719i
$876$	−10.9345	−	33.6529i	−0.369442	−	1.13703i
$877$	−47.1189	−	10.0154i	−1.59109	−	0.338197i	−0.674580	−	0.738202i	$-0.735675\pi$
$877$	−47.1189	−	10.0154i	−1.59109	−	0.338197i	−0.916513	+	0.400005i	$0.869008\pi$
$878$	−3.04618	−	28.9825i	−0.102804	−	0.978112i
$879$	40.0609	+	44.4921i	1.35122	+	1.50068i
$880$	−14.3682	−	6.39712i	−0.484351	−	0.215647i
$881$	31.3471	−	13.9566i	1.05611	−	0.470211i	0.196152	−	0.980573i	$-0.437155\pi$
$881$	31.3471	−	13.9566i	1.05611	−	0.470211i	0.859960	+	0.510362i	$0.170489\pi$
$882$	5.35304	−	5.94516i	0.180246	−	0.200184i
$883$	−21.2644	−	15.4495i	−0.715605	−	0.519917i	0.169372	−	0.985552i	$-0.445826\pi$
$883$	−21.2644	−	15.4495i	−0.715605	−	0.519917i	−0.884977	+	0.465635i	$0.845826\pi$
$884$	0.971638	+	0.705936i	0.0326797	+	0.0237432i
$885$	16.2690	−	18.0686i	0.546878	−	0.607370i
$886$	29.2066	−	13.0036i	0.981214	−	0.436864i
$887$	48.7156	+	21.6896i	1.63571	+	0.728265i	0.999079	−	0.0429026i	$-0.0136605\pi$
$887$	48.7156	+	21.6896i	1.63571	+	0.728265i	0.636632	+	0.771168i	$0.280327\pi$
$888$	7.13083	+	7.91959i	0.239295	+	0.265764i
$889$	2.75053	+	26.1696i	0.0922499	+	0.877699i
$890$	−29.4835	−	6.26690i	−0.988288	−	0.210067i
$891$	15.3668	+	47.2941i	0.514806	+	1.58441i
$892$	−6.47067	+	1.37538i	−0.216654	+	0.0460512i
$893$	1.31371	+	2.27541i	0.0439616	+	0.0761437i
$894$	−2.91421	+	5.04757i	−0.0974659	+	0.168816i
$895$	−2.08814	+	6.42663i	−0.0697988	+	0.214819i
$896$	−5.18748	+	49.3556i	−0.173301	+	1.64885i
$897$	−14.2847	+	10.3784i	−0.476952	+	0.346526i
$898$	−11.1716			−0.372800
$899$		0			0
$900$	−43.3137			−1.44379
$901$	0.0238152	−	0.0173028i	0.000793401	−	0.000576439i
$902$	−12.5490	+	119.396i	−0.417837	+	3.97546i
$903$	−16.0287	+	49.3314i	−0.533403	+	1.64164i
$904$	11.7929	−	20.4259i	0.392226	−	0.679355i
$905$	5.15685	+	8.93193i	0.171420	+	0.296908i
$906$	98.7065	−	20.9807i	3.27930	−	0.697038i
$907$	17.0929	+	52.6065i	0.567560	+	1.74677i	0.660221	+	0.751071i	$0.270463\pi$
$907$	17.0929	+	52.6065i	0.567560	+	1.74677i	−0.0926615	+	0.995698i	$0.529537\pi$
$908$	58.3651	+	12.4059i	1.93692	+	0.411704i
$909$	−2.50868	−	23.8685i	−0.0832078	−	0.791669i
$910$	−7.13083	−	7.91959i	−0.236385	−	0.262532i
$911$	44.8018	+	19.9470i	1.48435	+	0.660875i	0.979336	−	0.202238i	$-0.0648214\pi$
$911$	44.8018	+	19.9470i	1.48435	+	0.660875i	0.505012	+	0.863112i	$0.331488\pi$
$912$	−10.4923	+	4.67148i	−0.347436	+	0.154688i
$913$	−14.2814	+	15.8610i	−0.472644	+	0.524924i
$914$	60.7674	+	44.1501i	2.01001	+	1.46036i
$915$	5.52431	+	4.01365i	0.182628	+	0.132687i
$916$	29.4220	−	32.6765i	0.972132	−	1.07966i
$917$	−10.4923	+	4.67148i	−0.346487	+	0.154266i
$918$	0.156740	+	0.0697850i	0.00517318	+	0.00230325i
$919$	−10.1042	−	11.2219i	−0.333307	−	0.370175i	0.553073	−	0.833133i	$-0.313455\pi$
$919$	−10.1042	−	11.2219i	−0.333307	−	0.370175i	−0.886380	+	0.462957i	$0.846788\pi$
$920$	−1.84564	−	17.5601i	−0.0608491	−	0.578940i
$921$	−6.51139	−	1.38404i	−0.214557	−	0.0456056i
$922$	−19.5029	−	60.0237i	−0.642294	−	1.97678i
$923$	25.1657	−	5.34914i	0.828339	−	0.176069i
$924$	−58.4914	−	101.310i	−1.92423	−	3.33286i
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	−18.6289	+	57.3337i	−0.612182	+	1.88410i
$927$	3.56882	−	33.9551i	0.117216	−	1.11523i
$928$	1.50304	−	1.09203i	0.0493398	−	0.0358475i
$929$	24.4853			0.803336			0.401668	−	0.915785i	$-0.368431\pi$
$929$	24.4853			0.803336			0.401668	+	0.915785i	$0.368431\pi$
$930$		0			0
$931$	−1.85786			−0.0608890
$932$	45.9275	−	33.3683i	1.50441	−	1.09302i
$933$	−2.85506	+	27.1641i	−0.0934705	+	0.889312i
$934$	5.96826	−	18.3684i	0.195288	−	0.601033i
$935$	−0.449747	+	0.778985i	−0.0147083	+	0.0254755i
$936$	11.4142	+	19.7700i	0.373085	+	0.646203i
$937$	−37.4765	+	7.96587i	−1.22430	+	0.260234i	−0.774314	−	0.632801i	$-0.781905\pi$
$937$	−37.4765	+	7.96587i	−1.22430	+	0.260234i	−0.449988	+	0.893035i	$0.648572\pi$
$938$	9.44243	+	29.0608i	0.308306	+	0.948869i
$939$	9.04067	+	1.92165i	0.295031	+	0.0627108i
$940$	0.663039	+	6.30840i	0.0216260	+	0.205757i
$941$	−23.4196	−	26.0101i	−0.763456	−	0.847904i	0.228623	−	0.973515i	$-0.426578\pi$
$941$	−23.4196	−	26.0101i	−0.763456	−	0.847904i	−0.992080	+	0.125611i	$0.959911\pi$
$942$	78.9545	+	35.1528i	2.57248	+	1.14534i
$943$	−34.6609	+	15.4320i	−1.12872	+	0.502537i
$944$	−20.2166	+	22.4528i	−0.657994	+	0.730776i
$945$	−0.809017	−	0.587785i	−0.0263173	−	0.0191207i
$946$	−91.1274	−	66.2079i	−2.96281	−	2.15260i
$947$	26.0288	−	28.9080i	0.845824	−	0.939382i	−0.152983	−	0.988229i	$-0.548888\pi$
$947$	26.0288	−	28.9080i	0.845824	−	0.939382i	0.998806	+	0.0488465i	$0.0155545\pi$
$948$	128.702	−	57.3020i	4.18006	−	1.86108i
$949$	6.39482	+	2.84716i	0.207585	+	0.0924226i
$950$	10.2469	+	11.3803i	0.332452	+	0.369226i
$951$	−0.548005	−	5.21392i	−0.0177703	−	0.169073i
$952$	−1.78847	−	0.380151i	−0.0579647	−	0.0123208i
$953$	6.33030	+	19.4827i	0.205059	+	0.631105i	0.999711	+	0.0240406i	$0.00765311\pi$
$953$	6.33030	+	19.4827i	0.205059	+	0.631105i	−0.794652	+	0.607065i	$0.792347\pi$
$954$	1.14597	−	0.243584i	0.0371022	−	0.00788631i
$955$	0.550253	+	0.953065i	0.0178058	+	0.0308405i
$956$	24.4203	−	42.2972i	0.789809	−	1.36799i
$957$	−4.58224	+	14.1027i	−0.148123	+	0.455875i
$958$	2.45488	−	23.3566i	0.0793136	−	0.754618i
$959$	14.6198	−	10.6219i	0.472098	−	0.342999i
$960$	23.7279			0.765815
$961$		0			0
$962$	−4.41421			−0.142320
$963$	−21.9346	+	15.9364i	−0.706834	+	0.513545i
$964$	−9.86717	+	93.8799i	−0.317800	+	3.02367i
$965$	−6.53328	+	20.1074i	−0.210314	+	0.647279i
$966$	28.1421	−	48.7436i	0.905458	−	1.56830i
$967$	23.2782	+	40.3190i	0.748576	+	1.29657i	0.948505	+	0.316761i	$0.102595\pi$
$967$	23.2782	+	40.3190i	0.748576	+	1.29657i	−0.199930	+	0.979810i	$0.564071\pi$
$968$	71.1794	−	15.1296i	2.28779	−	0.486285i
$969$	0.202979	+	0.624706i	0.00652063	+	0.0200684i
$970$	25.5709	+	5.43526i	0.821031	+	0.174516i
$971$	−6.13566	−	58.3769i	−0.196903	−	1.87340i	−0.432611	−	0.901581i	$-0.642408\pi$
$971$	−6.13566	−	58.3769i	−0.196903	−	1.87340i	0.235708	−	0.971824i	$-0.424259\pi$
$972$	55.4787	+	61.6154i	1.77948	+	1.97631i
$973$		0			0
$974$	38.3420	−	17.0710i	1.22856	−	0.546989i
$975$	11.8147	−	13.1216i	0.378375	−	0.420228i
$976$	−6.86474	−	4.98752i	−0.219735	−	0.159647i
$977$	−13.3369	−	9.68981i	−0.426684	−	0.310004i	0.353637	−	0.935383i	$-0.384945\pi$
$977$	−13.3369	−	9.68981i	−0.426684	−	0.310004i	−0.780322	+	0.625378i	$0.784945\pi$
$978$	−50.5849	+	56.1802i	−1.61753	+	1.79645i
$979$	59.7969	−	26.6233i	1.91112	−	0.850884i
$980$	−4.09751	−	1.82433i	−0.130890	−	0.0582760i
$981$	−9.78765	−	10.8703i	−0.312496	−	0.347062i
$982$	1.11394	+	10.5985i	0.0355474	+	0.338211i
$983$	−47.7733	−	10.1545i	−1.52373	−	0.323879i	−0.631472	−	0.775399i	$-0.717549\pi$
$983$	−47.7733	−	10.1545i	−1.52373	−	0.323879i	−0.892261	+	0.451520i	$0.850882\pi$
$984$	31.2364	+	96.1359i	0.995782	+	3.06470i
$985$	−3.40912	+	0.724631i	−0.108624	+	0.0230887i
$986$	0.242641	+	0.420266i	0.00772725	+	0.0133840i
$987$	−4.82843	+	8.36308i	−0.153691	+	0.266200i
$988$	3.43024	−	10.5572i	0.109131	−	0.335870i
$989$	3.72100	−	35.4030i	0.118321	−	1.12575i
$990$	−28.9620	+	21.0421i	−0.920473	+	0.668762i
$991$	−19.9411			−0.633451			−0.316725	−	0.948517i	$-0.602583\pi$
$991$	−19.9411			−0.633451			−0.316725	+	0.948517i	$0.602583\pi$
$992$		0			0
$993$	−1.82843			−0.0580234
$994$	−66.3493	+	48.2056i	−2.10447	+	1.52899i
$995$	−1.62916	+	15.5004i	−0.0516478	+	0.491396i
$996$	−11.6275	+	35.7858i	−0.368432	+	1.13392i
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	−0.215559	−	0.976491i	$-0.569157\pi$
$997$	23.2990	−	40.3550i	0.737886	−	1.27806i	0.953445	−	0.301566i	$-0.0975093\pi$
$998$	48.5416	+	84.0766i	1.53656	+	2.66140i
$999$	−0.405162	+	0.0861198i	−0.0128188	+	0.00272471i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.o.338.2		16
31.2	even	5	inner	961.2.g.o.732.2		16
31.3	odd	30		961.2.d.i.531.1		8
31.4	even	5	inner	961.2.g.o.448.1		16
31.5	even	3	inner	961.2.g.o.235.2		16
31.6	odd	6		961.2.d.i.388.2		8
31.7	even	15		961.2.d.l.628.1		8
31.8	even	5		31.2.c.a.25.1	yes	4
31.9	even	15		31.2.c.a.5.1	✓	4
31.10	even	15	inner	961.2.g.o.816.2		16
31.11	odd	30		961.2.g.r.846.1		16
31.12	odd	30		961.2.d.i.374.2		8
31.13	odd	30		961.2.g.r.547.1		16
31.14	even	15		961.2.a.a.1.1		2
31.15	odd	10		961.2.g.r.844.1		16
31.16	even	5	inner	961.2.g.o.844.1		16
31.17	odd	30		961.2.a.c.1.1		2
31.18	even	15	inner	961.2.g.o.547.1		16
31.19	even	15		961.2.d.l.374.2		8
31.20	even	15	inner	961.2.g.o.846.1		16
31.21	odd	30		961.2.g.r.816.2		16
31.22	odd	30		961.2.c.a.439.1		4
31.23	odd	10		961.2.c.a.521.1		4
31.24	odd	30		961.2.d.i.628.1		8
31.25	even	3		961.2.d.l.388.2		8
31.26	odd	6		961.2.g.r.235.2		16
31.27	odd	10		961.2.g.r.448.1		16
31.28	even	15		961.2.d.l.531.1		8
31.29	odd	10		961.2.g.r.732.2		16
31.30	odd	2		961.2.g.r.338.2		16
93.8	odd	10		279.2.h.c.118.2		4
93.14	odd	30		8649.2.a.l.1.2		2
93.17	even	30		8649.2.a.k.1.2		2
93.71	odd	30		279.2.h.c.253.2		4
124.39	odd	10		496.2.i.h.273.1		4
124.71	odd	30		496.2.i.h.129.1		4
155.8	odd	20		775.2.o.d.149.4		8
155.9	even	30		775.2.e.e.501.2		4
155.39	even	10		775.2.e.e.676.2		4
155.102	odd	60		775.2.o.d.749.1		8
155.132	odd	20		775.2.o.d.149.1		8
155.133	odd	60		775.2.o.d.749.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	31.9	even	15
31.2.c.a.25.1	yes	4	31.8	even	5
279.2.h.c.118.2		4	93.8	odd	10
279.2.h.c.253.2		4	93.71	odd	30
496.2.i.h.129.1		4	124.71	odd	30
496.2.i.h.273.1		4	124.39	odd	10
775.2.e.e.501.2		4	155.9	even	30
775.2.e.e.676.2		4	155.39	even	10
775.2.o.d.149.1		8	155.132	odd	20
775.2.o.d.149.4		8	155.8	odd	20
775.2.o.d.749.1		8	155.102	odd	60
775.2.o.d.749.4		8	155.133	odd	60
961.2.a.a.1.1		2	31.14	even	15
961.2.a.c.1.1		2	31.17	odd	30
961.2.c.a.439.1		4	31.22	odd	30
961.2.c.a.521.1		4	31.23	odd	10
961.2.d.i.374.2		8	31.12	odd	30
961.2.d.i.388.2		8	31.6	odd	6
961.2.d.i.531.1		8	31.3	odd	30
961.2.d.i.628.1		8	31.24	odd	30
961.2.d.l.374.2		8	31.19	even	15
961.2.d.l.388.2		8	31.25	even	3
961.2.d.l.531.1		8	31.28	even	15
961.2.d.l.628.1		8	31.7	even	15
961.2.g.o.235.2		16	31.5	even	3	inner
961.2.g.o.338.2		16	1.1	even	1	trivial
961.2.g.o.448.1		16	31.4	even	5	inner
961.2.g.o.547.1		16	31.18	even	15	inner
961.2.g.o.732.2		16	31.2	even	5	inner
961.2.g.o.816.2		16	31.10	even	15	inner
961.2.g.o.844.1		16	31.16	even	5	inner
961.2.g.o.846.1		16	31.20	even	15	inner
961.2.g.r.235.2		16	31.26	odd	6
961.2.g.r.338.2		16	31.30	odd	2
961.2.g.r.448.1		16	31.27	odd	10
961.2.g.r.547.1		16	31.13	odd	30
961.2.g.r.732.2		16	31.29	odd	10
961.2.g.r.816.2		16	31.21	odd	30
961.2.g.r.844.1		16	31.15	odd	10
961.2.g.r.846.1		16	31.11	odd	30
8649.2.a.k.1.2		2	93.17	even	30
8649.2.a.l.1.2		2	93.14	odd	30

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.95314 - 1.41904i) q^{2} +(0.252354 - 2.40099i) q^{3} +(1.18305 - 3.64105i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.91421 - 5.04757i) q^{6} +(-2.36146 + 0.501943i) q^{7} +(-1.36407 - 4.19817i) q^{8} +(-2.76662 - 0.588063i) q^{9} +(0.252354 + 2.40099i) q^{10} +(-3.50801 - 3.89604i) q^{11} +(-8.44357 - 3.75932i) q^{12} +(1.67035 - 0.743688i) q^{13} +(-3.89998 + 4.33137i) q^{14} +(1.95314 + 1.41904i) q^{15} +(-2.42705 - 1.76336i) q^{16} +(-0.114805 + 0.127503i) q^{17} +(-6.23808 + 2.77737i) q^{18} +(1.44869 + 0.644997i) q^{19} +(2.56172 + 2.84508i) q^{20} +(0.609237 + 5.79650i) q^{21} +(-12.3803 - 2.63151i) q^{22} +(-1.23607 - 3.80423i) q^{23} +(-10.4240 + 2.21568i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.20711 - 3.82282i) q^{26} +(0.127999 - 0.393941i) q^{27} +(-0.966119 + 9.19201i) q^{28} +(0.947822 - 0.688633i) q^{29} +5.82843 q^{30} +1.58579 q^{32} +(-10.2396 + 7.43951i) q^{33} +(-0.0432971 + 0.411944i) q^{34} +(0.746033 - 2.29605i) q^{35} +(-5.41421 + 9.37769i) q^{36} +(-0.500000 - 0.866025i) q^{37} +(3.74477 - 0.795975i) q^{38} +(-1.36407 - 4.19817i) q^{39} +(4.31775 + 0.917767i) q^{40} +(-0.991482 - 9.43332i) q^{41} +(9.41538 + 10.4568i) q^{42} +(8.13009 + 3.61975i) q^{43} +(-18.3358 + 8.16364i) q^{44} +(1.89259 - 2.10193i) q^{45} +(-7.81256 - 5.67616i) q^{46} +(1.34042 + 0.973874i) q^{47} +(-4.84627 + 5.38233i) q^{48} +(-1.07029 + 0.476522i) q^{49} +(8.82198 + 3.92780i) q^{50} +(0.277163 + 0.307821i) q^{51} +(-0.731699 - 6.96165i) q^{52} +(-0.167824 - 0.0356720i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(5.12808 - 1.09001i) q^{55} +(5.32843 + 9.22911i) q^{56} +(1.91421 - 3.31552i) q^{57} +(0.874032 - 2.68999i) q^{58} +(1.05271 - 10.0159i) q^{59} +(7.47745 - 5.43269i) q^{60} +2.82843 q^{61} +6.82843 q^{63} +(7.95136 - 5.77700i) q^{64} +(-0.191123 + 1.81841i) q^{65} +(-9.44243 + 29.0608i) q^{66} +(2.62132 - 4.54026i) q^{67} +(0.328427 + 0.568852i) q^{68} +(-9.44583 + 2.00777i) q^{69} +(-1.80108 - 5.54316i) q^{70} +(13.7636 + 2.92554i) q^{71} +(1.30507 + 12.4169i) q^{72} +(2.56172 + 2.84508i) q^{73} +(-2.20549 - 0.981949i) q^{74} +(8.82198 - 3.92780i) q^{75} +(4.06234 - 4.51168i) q^{76} +(10.2396 + 7.43951i) q^{77} +(-8.62158 - 6.26394i) q^{78} +(-10.1993 + 11.3275i) q^{79} +(2.74064 - 1.22021i) q^{80} +(-8.66524 - 3.85801i) q^{81} +(-15.3228 - 17.0176i) q^{82} +(-0.425542 - 4.04877i) q^{83} +(21.8261 + 4.63928i) q^{84} +(-0.0530189 - 0.163176i) q^{85} +(21.0158 - 4.46704i) q^{86} +(-1.41421 - 2.44949i) q^{87} +(-11.5711 + 20.0417i) q^{88} +(-3.85816 + 11.8742i) q^{89} +(0.713765 - 6.79102i) q^{90} +(-3.57117 + 2.59461i) q^{91} -15.3137 q^{92} +4.00000 q^{94} +(-1.28293 + 0.932102i) q^{95} +(0.400180 - 3.80745i) q^{96} +(3.34617 - 10.2984i) q^{97} +(-1.41421 + 2.44949i) q^{98} +(7.41421 + 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 8 q^{5} - 24 q^{6} + 2 q^{7} + 12 q^{8} - 2 q^{10} - 2 q^{11} - 10 q^{12} - 2 q^{13} - 6 q^{14} + 4 q^{15} - 12 q^{16} - 6 q^{17} - 8 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 8 * q^5 - 24 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 2 * q^11 - 10 * q^12 - 2 * q^13 - 6 * q^14 + 4 * q^15 - 12 * q^16 - 6 * q^17 - 8 * q^18 + 6 * q^19 + 2 * q^20 - 6 * q^21 + 14 * q^22 + 16 * q^23 + 10 * q^24 + 32 * q^25 + 24 * q^26 + 4 * q^27 + 10 * q^28 + 16 * q^29 + 48 * q^30 + 48 * q^32 - 28 * q^33 - 2 * q^34 - 4 * q^35 - 64 * q^36 - 8 * q^37 - 2 * q^38 + 12 * q^39 - 6 * q^40 + 2 * q^41 + 14 * q^42 - 2 * q^43 - 26 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 8 * q^49 + 8 * q^50 - 2 * q^51 + 14 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 + 40 * q^56 + 8 * q^57 - 6 * q^59 + 20 * q^60 + 64 * q^63 + 28 * q^64 - 2 * q^65 + 60 * q^66 + 8 * q^67 - 40 * q^68 + 8 * q^69 + 12 * q^70 - 14 * q^71 - 8 * q^72 + 2 * q^73 - 2 * q^74 + 8 * q^75 - 2 * q^76 + 28 * q^77 - 20 * q^78 - 22 * q^79 + 6 * q^80 - 2 * q^81 - 26 * q^82 - 6 * q^83 - 22 * q^84 + 12 * q^85 - 26 * q^86 - 72 * q^88 + 16 * q^89 - 8 * q^90 - 12 * q^91 - 64 * q^92 + 64 * q^94 - 12 * q^95 - 2 * q^96 - 32 * q^97 + 96 * q^99

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