LMFDB - Embedded newform 363.2.e.l.130.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,2,Mod(124,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.124"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,5,-1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.l.148.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.690983 - 2.12663i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(0.618034 + 1.90211i) q^{5} +(0.690983 + 2.12663i) q^{6} +(3.61803 + 2.62866i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +4.47214 q^{10} +3.00000 q^{12} +(8.09017 - 5.87785i) q^{14} +(-1.61803 - 1.17557i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.38197 + 4.25325i) q^{17} +(-1.80902 - 1.31433i) q^{18} +(3.61803 - 2.62866i) q^{19} +(1.85410 - 5.70634i) q^{20} -4.47214 q^{21} -4.00000 q^{23} +(0.690983 - 2.12663i) q^{24} +(0.809017 - 0.587785i) q^{25} +(0.309017 + 0.951057i) q^{27} +(-4.14590 - 12.7598i) q^{28} +(-3.61803 - 2.62866i) q^{29} +(-3.61803 + 2.62866i) q^{30} -6.70820 q^{32} +10.0000 q^{34} +(-2.76393 + 8.50651i) q^{35} +(-2.42705 + 1.76336i) q^{36} +(-1.61803 - 1.17557i) q^{37} +(-3.09017 - 9.51057i) q^{38} +(-3.61803 - 2.62866i) q^{40} +(3.61803 - 2.62866i) q^{41} +(-3.09017 + 9.51057i) q^{42} +4.47214 q^{43} +2.00000 q^{45} +(-2.76393 + 8.50651i) q^{46} +(-6.47214 + 4.70228i) q^{47} +(0.809017 + 0.587785i) q^{48} +(4.01722 + 12.3637i) q^{49} +(-0.690983 - 2.12663i) q^{50} +(-3.61803 - 2.62866i) q^{51} +(1.85410 - 5.70634i) q^{53} +2.23607 q^{54} -10.0000 q^{56} +(-1.38197 + 4.25325i) q^{57} +(-8.09017 + 5.87785i) q^{58} +(1.85410 + 5.70634i) q^{60} +(2.76393 + 8.50651i) q^{61} +(3.61803 - 2.62866i) q^{63} +(-4.01722 + 12.3637i) q^{64} -12.0000 q^{67} +(4.14590 - 12.7598i) q^{68} +(3.23607 - 2.35114i) q^{69} +(16.1803 + 11.7557i) q^{70} +(-2.47214 - 7.60845i) q^{71} +(0.690983 + 2.12663i) q^{72} +(7.23607 + 5.25731i) q^{73} +(-3.61803 + 2.62866i) q^{74} +(-0.309017 + 0.951057i) q^{75} -13.4164 q^{76} +(4.14590 - 12.7598i) q^{79} +(1.61803 - 1.17557i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.09017 - 9.51057i) q^{82} +(-2.76393 - 8.50651i) q^{83} +(10.8541 + 7.88597i) q^{84} +(-7.23607 + 5.25731i) q^{85} +(3.09017 - 9.51057i) q^{86} +4.47214 q^{87} -14.0000 q^{89} +(1.38197 - 4.25325i) q^{90} +(9.70820 + 7.05342i) q^{92} +(5.52786 + 17.0130i) q^{94} +(7.23607 + 5.25731i) q^{95} +(5.42705 - 3.94298i) q^{96} +(0.618034 - 1.90211i) q^{97} +29.0689 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} + 5 q^{6} + 10 q^{7} - 5 q^{8} - q^{9} + 12 q^{12} + 10 q^{14} - 2 q^{15} + q^{16} + 10 q^{17} - 5 q^{18} + 10 q^{19} - 6 q^{20} - 16 q^{23} + 5 q^{24} + q^{25}+ \cdots - 2 q^{97}+O(q^{100}) $ 4 * q + 5 * q^2 - q^3 - 3 * q^4 - 2 * q^5 + 5 * q^6 + 10 * q^7 - 5 * q^8 - q^9 + 12 * q^12 + 10 * q^14 - 2 * q^15 + q^16 + 10 * q^17 - 5 * q^18 + 10 * q^19 - 6 * q^20 - 16 * q^23 + 5 * q^24 + q^25 - q^27 - 30 * q^28 - 10 * q^29 - 10 * q^30 + 40 * q^34 - 20 * q^35 - 3 * q^36 - 2 * q^37 + 10 * q^38 - 10 * q^40 + 10 * q^41 + 10 * q^42 + 8 * q^45 - 20 * q^46 - 8 * q^47 + q^48 - 13 * q^49 - 5 * q^50 - 10 * q^51 - 6 * q^53 - 40 * q^56 - 10 * q^57 - 10 * q^58 - 6 * q^60 + 20 * q^61 + 10 * q^63 + 13 * q^64 - 48 * q^67 + 30 * q^68 + 4 * q^69 + 20 * q^70 + 8 * q^71 + 5 * q^72 + 20 * q^73 - 10 * q^74 + q^75 + 30 * q^79 + 2 * q^80 - q^81 + 10 * q^82 - 20 * q^83 + 30 * q^84 - 20 * q^85 - 10 * q^86 - 56 * q^89 + 10 * q^90 + 12 * q^92 + 40 * q^94 + 20 * q^95 + 15 * q^96 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.690983	−	2.12663i	0.488599	−	1.50375i	−0.338101	−	0.941110i	$-0.609785\pi$
$2$	0.690983	−	2.12663i	0.488599	−	1.50375i	0.826700	−	0.562643i	$-0.190215\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−2.42705	−	1.76336i	−1.21353	−	0.881678i
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	0.988847	+	0.148932i	$0.0475836\pi$
$5$	0.618034	+	1.90211i	0.276393	+	0.850651i	−0.712454	+	0.701719i	$0.752416\pi$
$6$	0.690983	+	2.12663i	0.282093	+	0.868192i
$7$	3.61803	+	2.62866i	1.36749	+	0.993538i	0.997929	+	0.0643314i	$0.0204915\pi$
$7$	3.61803	+	2.62866i	1.36749	+	0.993538i	0.369560	+	0.929207i	$0.379509\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	4.47214			1.41421
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$	8.09017	−	5.87785i	2.16219	−	1.57092i
$15$	−1.61803	−	1.17557i	−0.417775	−	0.303531i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	1.38197	+	4.25325i	0.335176	+	1.03157i	0.966635	+	0.256157i	$0.0824563\pi$
$17$	1.38197	+	4.25325i	0.335176	+	1.03157i	−0.631459	+	0.775409i	$0.717544\pi$
$18$	−1.80902	−	1.31433i	−0.426389	−	0.309790i
$19$	3.61803	−	2.62866i	0.830034	−	0.603055i	−0.0895350	−	0.995984i	$-0.528538\pi$
$19$	3.61803	−	2.62866i	0.830034	−	0.603055i	0.919569	+	0.392929i	$0.128538\pi$
$20$	1.85410	−	5.70634i	0.414590	−	1.27598i
$21$	−4.47214			−0.975900
$22$		0			0
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	0.690983	−	2.12663i	0.141046	−	0.434096i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−4.14590	−	12.7598i	−0.783501	−	2.41137i
$29$	−3.61803	−	2.62866i	−0.671852	−	0.488129i	0.198793	−	0.980042i	$-0.436298\pi$
$29$	−3.61803	−	2.62866i	−0.671852	−	0.488129i	−0.870645	+	0.491912i	$0.836298\pi$
$30$	−3.61803	+	2.62866i	−0.660560	+	0.479925i
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$	−6.70820			−1.18585
$33$		0			0
$34$	10.0000			1.71499
$35$	−2.76393	+	8.50651i	−0.467190	+	1.43786i
$36$	−2.42705	+	1.76336i	−0.404508	+	0.293893i
$37$	−1.61803	−	1.17557i	−0.266003	−	0.193263i	0.446786	−	0.894641i	$-0.352568\pi$
$37$	−1.61803	−	1.17557i	−0.266003	−	0.193263i	−0.712789	+	0.701378i	$0.752568\pi$
$38$	−3.09017	−	9.51057i	−0.501292	−	1.54282i
$39$		0			0
$40$	−3.61803	−	2.62866i	−0.572061	−	0.415627i
$41$	3.61803	−	2.62866i	0.565042	−	0.410527i	−0.268259	−	0.963347i	$-0.586448\pi$
$41$	3.61803	−	2.62866i	0.565042	−	0.410527i	0.833301	+	0.552820i	$0.186448\pi$
$42$	−3.09017	+	9.51057i	−0.476824	+	1.46751i
$43$	4.47214			0.681994			0.340997	−	0.940064i	$-0.389235\pi$
$43$	4.47214			0.681994			0.340997	+	0.940064i	$0.389235\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$	−2.76393	+	8.50651i	−0.407520	+	1.25422i
$47$	−6.47214	+	4.70228i	−0.944058	+	0.685898i	−0.949394	−	0.314087i	$-0.898301\pi$
$47$	−6.47214	+	4.70228i	−0.944058	+	0.685898i	0.00533600	+	0.999986i	$0.498301\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	4.01722	+	12.3637i	0.573889	+	1.76625i
$50$	−0.690983	−	2.12663i	−0.0977198	−	0.300750i
$51$	−3.61803	−	2.62866i	−0.506626	−	0.368085i
$52$		0			0
$53$	1.85410	−	5.70634i	0.254680	−	0.783826i	−0.739212	−	0.673473i	$-0.764802\pi$
$53$	1.85410	−	5.70634i	0.254680	−	0.783826i	0.993892	−	0.110353i	$-0.0351982\pi$
$54$	2.23607			0.304290
$55$		0			0
$56$	−10.0000			−1.33631
$57$	−1.38197	+	4.25325i	−0.183046	+	0.563357i
$58$	−8.09017	+	5.87785i	−1.06229	+	0.771800i
$59$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$59$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$60$	1.85410	+	5.70634i	0.239364	+	0.736685i
$61$	2.76393	+	8.50651i	0.353885	+	1.08915i	0.956653	+	0.291230i	$0.0940645\pi$
$61$	2.76393	+	8.50651i	0.353885	+	1.08915i	−0.602768	+	0.797917i	$0.705935\pi$
$62$		0			0
$63$	3.61803	−	2.62866i	0.455829	−	0.331179i
$64$	−4.01722	+	12.3637i	−0.502153	+	1.54547i
$65$		0			0
$66$		0			0
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	4.14590	−	12.7598i	0.502764	−	1.54735i
$69$	3.23607	−	2.35114i	0.389577	−	0.283044i
$70$	16.1803	+	11.7557i	1.93392	+	1.40508i
$71$	−2.47214	−	7.60845i	−0.293389	−	0.902957i	−0.983758	−	0.179500i	$-0.942552\pi$
$71$	−2.47214	−	7.60845i	−0.293389	−	0.902957i	0.690369	−	0.723457i	$-0.257448\pi$
$72$	0.690983	+	2.12663i	0.0814331	+	0.250625i
$73$	7.23607	+	5.25731i	0.846918	+	0.615322i	0.924294	−	0.381680i	$-0.124654\pi$
$73$	7.23607	+	5.25731i	0.846918	+	0.615322i	−0.0773767	+	0.997002i	$0.524654\pi$
$74$	−3.61803	+	2.62866i	−0.420588	+	0.305575i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	−13.4164			−1.53897
$77$		0			0
$78$		0			0
$79$	4.14590	−	12.7598i	0.466450	−	1.43559i	−0.390700	−	0.920518i	$-0.627767\pi$
$79$	4.14590	−	12.7598i	0.466450	−	1.43559i	0.857150	−	0.515067i	$-0.172233\pi$
$80$	1.61803	−	1.17557i	0.180902	−	0.131433i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−3.09017	−	9.51057i	−0.341252	−	1.05027i
$83$	−2.76393	−	8.50651i	−0.303381	−	0.933711i	−0.980276	−	0.197631i	$-0.936675\pi$
$83$	−2.76393	−	8.50651i	−0.303381	−	0.933711i	0.676895	−	0.736079i	$-0.263325\pi$
$84$	10.8541	+	7.88597i	1.18428	+	0.860430i
$85$	−7.23607	+	5.25731i	−0.784862	+	0.570235i
$86$	3.09017	−	9.51057i	0.333222	−	1.02555i
$87$	4.47214			0.479463
$88$		0			0
$89$	−14.0000			−1.48400			−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000			−1.48400			−0.741999	+	0.670402i	$0.766122\pi$
$90$	1.38197	−	4.25325i	0.145672	−	0.448332i
$91$		0			0
$92$	9.70820	+	7.05342i	1.01215	+	0.735370i
$93$		0			0
$94$	5.52786	+	17.0130i	0.570156	+	1.75476i
$95$	7.23607	+	5.25731i	0.742405	+	0.539389i
$96$	5.42705	−	3.94298i	0.553896	−	0.402429i
$97$	0.618034	−	1.90211i	0.0627518	−	0.193130i	−0.914766	−	0.403985i	$-0.867625\pi$
$97$	0.618034	−	1.90211i	0.0627518	−	0.193130i	0.977517	+	0.210855i	$0.0676247\pi$
$98$	29.0689			2.93640
$99$		0			0
$100$	−3.00000			−0.300000
$101$	1.38197	−	4.25325i	0.137511	−	0.423215i	−0.858461	−	0.512878i	$-0.828579\pi$
$101$	1.38197	−	4.25325i	0.137511	−	0.423215i	0.995972	+	0.0896637i	$0.0285792\pi$
$102$	−8.09017	+	5.87785i	−0.801046	+	0.581994i
$103$	−12.9443	−	9.40456i	−1.27544	−	0.926659i	−0.276032	−	0.961148i	$-0.589020\pi$
$103$	−12.9443	−	9.40456i	−1.27544	−	0.926659i	−0.999405	+	0.0344892i	$0.989020\pi$
$104$		0			0
$105$	−2.76393	−	8.50651i	−0.269732	−	0.830150i
$106$	−10.8541	−	7.88597i	−1.05424	−	0.765953i
$107$	−7.23607	+	5.25731i	−0.699537	+	0.508243i	−0.879781	−	0.475378i	$-0.842311\pi$
$107$	−7.23607	+	5.25731i	−0.699537	+	0.508243i	0.180244	+	0.983622i	$0.442311\pi$
$108$	0.927051	−	2.85317i	0.0892055	−	0.274546i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	2.00000			0.189832
$112$	1.38197	−	4.25325i	0.130584	−	0.401895i
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	−0.792210	−	0.610249i	$-0.791070\pi$
$113$	−4.85410	+	3.52671i	−0.456636	+	0.331765i	0.335575	+	0.942014i	$0.391070\pi$
$114$	8.09017	+	5.87785i	0.757714	+	0.550511i
$115$	−2.47214	−	7.60845i	−0.230528	−	0.709492i
$116$	4.14590	+	12.7598i	0.384937	+	1.18471i
$117$		0			0
$118$		0			0
$119$	−6.18034	+	19.0211i	−0.566551	+	1.74366i
$120$	4.47214			0.408248
$121$		0			0
$122$	20.0000			1.81071
$123$	−1.38197	+	4.25325i	−0.124608	+	0.383503i
$124$		0			0
$125$	9.70820	+	7.05342i	0.868328	+	0.630877i
$126$	−3.09017	−	9.51057i	−0.275294	−	0.847268i
$127$	4.14590	+	12.7598i	0.367889	+	1.13225i	0.948152	+	0.317817i	$0.102950\pi$
$127$	4.14590	+	12.7598i	0.367889	+	1.13225i	−0.580263	+	0.814429i	$0.697050\pi$
$128$	12.6631	+	9.20029i	1.11927	+	0.813199i
$129$	−3.61803	+	2.62866i	−0.318550	+	0.231440i
$130$		0			0
$131$	−17.8885			−1.56293			−0.781465	−	0.623949i	$-0.785527\pi$
$131$	−17.8885			−1.56293			−0.781465	+	0.623949i	$0.785527\pi$
$132$		0			0
$133$	20.0000			1.73422
$134$	−8.29180	+	25.5195i	−0.716302	+	2.20455i
$135$	−1.61803	+	1.17557i	−0.139258	+	0.101177i
$136$	−8.09017	−	5.87785i	−0.693726	−	0.504022i
$137$	6.79837	+	20.9232i	0.580824	+	1.78759i	0.615429	+	0.788192i	$0.288983\pi$
$137$	6.79837	+	20.9232i	0.580824	+	1.78759i	−0.0346048	+	0.999401i	$0.511017\pi$
$138$	−2.76393	−	8.50651i	−0.235282	−	0.724122i
$139$	−10.8541	−	7.88597i	−0.920633	−	0.668879i	0.0230486	−	0.999734i	$-0.492663\pi$
$139$	−10.8541	−	7.88597i	−0.920633	−	0.668879i	−0.943681	+	0.330855i	$0.892663\pi$
$140$	21.7082	−	15.7719i	1.83468	−	1.33297i
$141$	2.47214	−	7.60845i	0.208191	−	0.640747i
$142$	−17.8885			−1.50117
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	2.76393	−	8.50651i	0.229532	−	0.706427i
$146$	16.1803	−	11.7557i	1.33909	−	0.972909i
$147$	−10.5172	−	7.64121i	−0.867446	−	0.630236i
$148$	1.85410	+	5.70634i	0.152406	+	0.469058i
$149$	−6.90983	−	21.2663i	−0.566075	−	1.74220i	−0.664735	−	0.747079i	$-0.731455\pi$
$149$	−6.90983	−	21.2663i	−0.566075	−	1.74220i	0.0986594	−	0.995121i	$-0.468545\pi$
$150$	1.80902	+	1.31433i	0.147706	+	0.107314i
$151$	−10.8541	+	7.88597i	−0.883294	+	0.641751i	−0.934121	−	0.356957i	$-0.883814\pi$
$151$	−10.8541	+	7.88597i	−0.883294	+	0.641751i	0.0508267	+	0.998707i	$0.483814\pi$
$152$	−3.09017	+	9.51057i	−0.250646	+	0.771409i
$153$	4.47214			0.361551
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.61803	+	1.17557i	−0.129133	+	0.0938207i	−0.650477	−	0.759526i	$-0.725431\pi$
$157$	−1.61803	+	1.17557i	−0.129133	+	0.0938207i	0.521344	+	0.853347i	$0.325431\pi$
$158$	−24.2705	−	17.6336i	−1.93086	−	1.40285i
$159$	1.85410	+	5.70634i	0.147040	+	0.452542i
$160$	−4.14590	−	12.7598i	−0.327762	−	1.00875i
$161$	−14.4721	−	10.5146i	−1.14056	−	0.828668i
$162$	−1.80902	+	1.31433i	−0.142130	+	0.103263i
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	−0.890906	−	0.454187i	$-0.849930\pi$
$163$	1.23607	−	3.80423i	0.0968163	−	0.297970i	0.987723	+	0.156217i	$0.0499299\pi$
$164$	−13.4164			−1.04765
$165$		0			0
$166$	−20.0000			−1.55230
$167$	2.76393	−	8.50651i	0.213879	−	0.658253i	−0.785352	−	0.619050i	$-0.787518\pi$
$167$	2.76393	−	8.50651i	0.213879	−	0.658253i	0.999231	−	0.0392036i	$-0.0124821\pi$
$168$	8.09017	−	5.87785i	0.624170	−	0.453486i
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$	6.18034	+	19.0211i	0.474010	+	1.45885i
$171$	−1.38197	−	4.25325i	−0.105682	−	0.325254i
$172$	−10.8541	−	7.88597i	−0.827618	−	0.601299i
$173$	10.8541	−	7.88597i	0.825222	−	0.599559i	−0.0929814	−	0.995668i	$-0.529640\pi$
$173$	10.8541	−	7.88597i	0.825222	−	0.599559i	0.918204	+	0.396109i	$0.129640\pi$
$174$	3.09017	−	9.51057i	0.234265	−	0.720994i
$175$	4.47214			0.338062
$176$		0			0
$177$		0			0
$178$	−9.67376	+	29.7728i	−0.725079	+	2.23156i
$179$	3.23607	−	2.35114i	0.241875	−	0.175733i	−0.460243	−	0.887793i	$-0.652238\pi$
$179$	3.23607	−	2.35114i	0.241875	−	0.175733i	0.702118	+	0.712060i	$0.252238\pi$
$180$	−4.85410	−	3.52671i	−0.361803	−	0.262866i
$181$	−3.09017	−	9.51057i	−0.229691	−	0.706915i	−0.997781	−	0.0665740i	$-0.978793\pi$
$181$	−3.09017	−	9.51057i	−0.229691	−	0.706915i	0.768091	−	0.640341i	$-0.221207\pi$
$182$		0			0
$183$	−7.23607	−	5.25731i	−0.534906	−	0.388632i
$184$	7.23607	−	5.25731i	0.533450	−	0.387574i
$185$	1.23607	−	3.80423i	0.0908775	−	0.279692i
$186$		0			0
$187$		0			0
$188$	24.0000			1.75038
$189$	−1.38197	+	4.25325i	−0.100523	+	0.309379i
$190$	16.1803	−	11.7557i	1.17385	−	0.852848i
$191$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$191$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$192$	−4.01722	−	12.3637i	−0.289918	−	0.892276i
$193$	−5.52786	−	17.0130i	−0.397904	−	1.22462i	−0.926677	−	0.375860i	$-0.877347\pi$
$193$	−5.52786	−	17.0130i	−0.397904	−	1.22462i	0.528772	−	0.848764i	$-0.322653\pi$
$194$	−3.61803	−	2.62866i	−0.259760	−	0.188726i
$195$		0			0
$196$	12.0517	−	37.0912i	0.860833	−	2.64937i
$197$	22.3607			1.59313			0.796566	−	0.604551i	$-0.206648\pi$
$197$	22.3607			1.59313			0.796566	+	0.604551i	$0.206648\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−0.690983	+	2.12663i	−0.0488599	+	0.150375i
$201$	9.70820	−	7.05342i	0.684764	−	0.497510i
$202$	−8.09017	−	5.87785i	−0.569222	−	0.413564i
$203$	−6.18034	−	19.0211i	−0.433775	−	1.33502i
$204$	4.14590	+	12.7598i	0.290271	+	0.893362i
$205$	7.23607	+	5.25731i	0.505389	+	0.367187i
$206$	−28.9443	+	21.0292i	−2.01664	+	1.46518i
$207$	−1.23607	+	3.80423i	−0.0859127	+	0.264412i
$208$		0			0
$209$		0			0
$210$	−20.0000			−1.38013
$211$	−1.38197	+	4.25325i	−0.0951385	+	0.292806i	−0.987290	−	0.158931i	$-0.949195\pi$
$211$	−1.38197	+	4.25325i	−0.0951385	+	0.292806i	0.892151	+	0.451737i	$0.149195\pi$
$212$	−14.5623	+	10.5801i	−1.00014	+	0.726647i
$213$	6.47214	+	4.70228i	0.443463	+	0.322195i
$214$	6.18034	+	19.0211i	0.422479	+	1.30026i
$215$	2.76393	+	8.50651i	0.188499	+	0.580139i
$216$	−1.80902	−	1.31433i	−0.123088	−	0.0894287i
$217$		0			0
$218$		0			0
$219$	−8.94427			−0.604398
$220$		0			0
$221$		0			0
$222$	1.38197	−	4.25325i	0.0927515	−	0.285460i
$223$	12.9443	−	9.40456i	0.866813	−	0.629776i	−0.0629172	−	0.998019i	$-0.520040\pi$
$223$	12.9443	−	9.40456i	0.866813	−	0.629776i	0.929730	+	0.368243i	$0.120040\pi$
$224$	−24.2705	−	17.6336i	−1.62164	−	1.17819i
$225$	−0.309017	−	0.951057i	−0.0206011	−	0.0634038i
$226$	4.14590	+	12.7598i	0.275781	+	0.848767i
$227$	−7.23607	−	5.25731i	−0.480275	−	0.348940i	0.321157	−	0.947026i	$-0.395928\pi$
$227$	−7.23607	−	5.25731i	−0.480275	−	0.348940i	−0.801432	+	0.598086i	$0.795928\pi$
$228$	10.8541	−	7.88597i	0.718830	−	0.522261i
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	−0.795541	−	0.605900i	$-0.792813\pi$
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	0.999745	−	0.0225760i	$-0.00718678\pi$
$230$	−17.8885			−1.17954
$231$		0			0
$232$	10.0000			0.656532
$233$	−1.38197	+	4.25325i	−0.0905356	+	0.278640i	−0.986065	−	0.166363i	$-0.946798\pi$
$233$	−1.38197	+	4.25325i	−0.0905356	+	0.278640i	0.895529	+	0.445003i	$0.146798\pi$
$234$		0			0
$235$	−12.9443	−	9.40456i	−0.844391	−	0.613486i
$236$		0			0
$237$	4.14590	+	12.7598i	0.269305	+	0.828836i
$238$	36.1803	+	26.2866i	2.34522	+	1.70390i
$239$	−7.23607	+	5.25731i	−0.468062	+	0.340067i	−0.796686	−	0.604394i	$-0.793415\pi$
$239$	−7.23607	+	5.25731i	−0.468062	+	0.340067i	0.328623	+	0.944461i	$0.393415\pi$
$240$	−0.618034	+	1.90211i	−0.0398939	+	0.122781i
$241$	8.94427			0.576151			0.288076	−	0.957608i	$-0.406985\pi$
$241$	8.94427			0.576151			0.288076	+	0.957608i	$0.406985\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	8.29180	−	25.5195i	0.530828	−	1.63372i
$245$	−21.0344	+	15.2824i	−1.34384	+	0.976358i
$246$	8.09017	+	5.87785i	0.515810	+	0.374758i
$247$		0			0
$248$		0			0
$249$	7.23607	+	5.25731i	0.458567	+	0.333169i
$250$	21.7082	−	15.7719i	1.37295	−	0.997505i
$251$	−3.70820	+	11.4127i	−0.234060	+	0.720362i	0.763185	+	0.646180i	$0.223635\pi$
$251$	−3.70820	+	11.4127i	−0.234060	+	0.720362i	−0.997245	+	0.0741818i	$0.976365\pi$
$252$	−13.4164			−0.845154
$253$		0			0
$254$	30.0000			1.88237
$255$	2.76393	−	8.50651i	0.173084	−	0.532698i
$256$	7.28115	−	5.29007i	0.455072	−	0.330629i
$257$	17.7984	+	12.9313i	1.11023	+	0.806631i	0.982700	−	0.185204i	$-0.0592945\pi$
$257$	17.7984	+	12.9313i	1.11023	+	0.806631i	0.127532	+	0.991834i	$0.459294\pi$
$258$	3.09017	+	9.51057i	0.192386	+	0.592102i
$259$	−2.76393	−	8.50651i	−0.171742	−	0.528569i
$260$		0			0
$261$	−3.61803	+	2.62866i	−0.223951	+	0.162710i
$262$	−12.3607	+	38.0423i	−0.763645	+	2.35026i
$263$	8.94427			0.551527			0.275764	−	0.961225i	$-0.411069\pi$
$263$	8.94427			0.551527			0.275764	+	0.961225i	$0.411069\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$	13.8197	−	42.5325i	0.847338	−	2.60784i
$267$	11.3262	−	8.22899i	0.693155	−	0.503606i
$268$	29.1246	+	21.1603i	1.77907	+	1.29257i
$269$	−3.09017	−	9.51057i	−0.188411	−	0.579869i	0.811579	−	0.584242i	$-0.198608\pi$
$269$	−3.09017	−	9.51057i	−0.188411	−	0.579869i	−0.999990	+	0.00437267i	$0.998608\pi$
$270$	1.38197	+	4.25325i	0.0841038	+	0.258845i
$271$	10.8541	+	7.88597i	0.659340	+	0.479038i	0.866440	−	0.499281i	$-0.166403\pi$
$271$	10.8541	+	7.88597i	0.659340	+	0.479038i	−0.207100	+	0.978320i	$0.566403\pi$
$272$	3.61803	−	2.62866i	0.219376	−	0.159386i
$273$		0			0
$274$	49.1935			2.97189
$275$		0			0
$276$	−12.0000			−0.722315
$277$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$277$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$278$	−24.2705	+	17.6336i	−1.45565	+	1.05759i
$279$		0			0
$280$	−6.18034	−	19.0211i	−0.369346	−	1.13673i
$281$	9.67376	+	29.7728i	0.577088	+	1.77610i	0.628956	+	0.777441i	$0.283483\pi$
$281$	9.67376	+	29.7728i	0.577088	+	1.77610i	−0.0518675	+	0.998654i	$0.516517\pi$
$282$	−14.4721	−	10.5146i	−0.861803	−	0.626137i
$283$	10.8541	−	7.88597i	0.645209	−	0.468772i	−0.216427	−	0.976299i	$-0.569440\pi$
$283$	10.8541	−	7.88597i	0.645209	−	0.468772i	0.861636	+	0.507527i	$0.169440\pi$
$284$	−7.41641	+	22.8254i	−0.440083	+	1.35444i
$285$	−8.94427			−0.529813
$286$		0			0
$287$	20.0000			1.18056
$288$	−2.07295	+	6.37988i	−0.122150	+	0.375938i
$289$	−2.42705	+	1.76336i	−0.142768	+	0.103727i
$290$	−16.1803	−	11.7557i	−0.950142	−	0.690319i
$291$	0.618034	+	1.90211i	0.0362298	+	0.111504i
$292$	−8.29180	−	25.5195i	−0.485241	−	1.49342i
$293$	18.0902	+	13.1433i	1.05684	+	0.767838i	0.973501	−	0.228683i	$-0.0734419\pi$
$293$	18.0902	+	13.1433i	1.05684	+	0.767838i	0.0833380	+	0.996521i	$0.473442\pi$
$294$	−23.5172	+	17.0863i	−1.37155	+	0.996491i
$295$		0			0
$296$	4.47214			0.259938
$297$		0			0
$298$	−50.0000			−2.89642
$299$		0			0
$300$	2.42705	−	1.76336i	0.140126	−	0.101807i
$301$	16.1803	+	11.7557i	0.932619	+	0.677588i
$302$	9.27051	+	28.5317i	0.533458	+	1.64181i
$303$	1.38197	+	4.25325i	0.0793919	+	0.244343i
$304$	−3.61803	−	2.62866i	−0.207508	−	0.150764i
$305$	−14.4721	+	10.5146i	−0.828672	+	0.602066i
$306$	3.09017	−	9.51057i	0.176653	−	0.543683i
$307$	−4.47214			−0.255238			−0.127619	−	0.991823i	$-0.540734\pi$
$307$	−4.47214			−0.255238			−0.127619	+	0.991823i	$0.540734\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$		0			0
$311$	9.70820	−	7.05342i	0.550502	−	0.399963i	−0.277469	−	0.960735i	$-0.589495\pi$
$311$	9.70820	−	7.05342i	0.550502	−	0.399963i	0.827970	+	0.560772i	$0.189495\pi$
$312$		0			0
$313$	4.32624	+	13.3148i	0.244533	+	0.752596i	0.995713	+	0.0924984i	$0.0294853\pi$
$313$	4.32624	+	13.3148i	0.244533	+	0.752596i	−0.751179	+	0.660098i	$0.770515\pi$
$314$	1.38197	+	4.25325i	0.0779889	+	0.240025i
$315$	7.23607	+	5.25731i	0.407706	+	0.296216i
$316$	−32.5623	+	23.6579i	−1.83177	+	1.33086i
$317$	5.56231	−	17.1190i	0.312410	−	0.961500i	−0.664397	−	0.747380i	$-0.731312\pi$
$317$	5.56231	−	17.1190i	0.312410	−	0.961500i	0.976807	−	0.214120i	$-0.0686884\pi$
$318$	13.4164			0.752355
$319$		0			0
$320$	−26.0000			−1.45344
$321$	2.76393	−	8.50651i	0.154268	−	0.474787i
$322$	−32.3607	+	23.5114i	−1.80339	+	1.31024i
$323$	16.1803	+	11.7557i	0.900298	+	0.654105i
$324$	0.927051	+	2.85317i	0.0515028	+	0.158509i
$325$		0			0
$326$	−7.23607	−	5.25731i	−0.400769	−	0.291176i
$327$		0			0
$328$	−3.09017	+	9.51057i	−0.170626	+	0.525133i
$329$	−35.7771			−1.97245
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	−8.29180	+	25.5195i	−0.455071	+	1.40057i
$333$	−1.61803	+	1.17557i	−0.0886677	+	0.0644209i
$334$	−16.1803	−	11.7557i	−0.885349	−	0.643244i
$335$	−7.41641	−	22.8254i	−0.405202	−	1.24708i
$336$	1.38197	+	4.25325i	0.0753924	+	0.232034i
$337$	−7.23607	−	5.25731i	−0.394174	−	0.286384i	0.372990	−	0.927835i	$-0.378333\pi$
$337$	−7.23607	−	5.25731i	−0.394174	−	0.286384i	−0.767164	+	0.641451i	$0.778333\pi$
$338$	23.5172	−	17.0863i	1.27917	−	0.929370i
$339$	1.85410	−	5.70634i	0.100701	−	0.309926i
$340$	26.8328			1.45521
$341$		0			0
$342$	−10.0000			−0.540738
$343$	−8.29180	+	25.5195i	−0.447715	+	1.37792i
$344$	−8.09017	+	5.87785i	−0.436193	+	0.316913i
$345$	6.47214	+	4.70228i	0.348448	+	0.253162i
$346$	−9.27051	−	28.5317i	−0.498386	−	1.53387i
$347$	2.76393	+	8.50651i	0.148376	+	0.456653i	0.997430	−	0.0716528i	$-0.0228274\pi$
$347$	2.76393	+	8.50651i	0.148376	+	0.456653i	−0.849054	+	0.528306i	$0.822827\pi$
$348$	−10.8541	−	7.88597i	−0.581841	−	0.422732i
$349$	21.7082	−	15.7719i	1.16201	−	0.844252i	0.171982	−	0.985100i	$-0.444983\pi$
$349$	21.7082	−	15.7719i	1.16201	−	0.844252i	0.990031	+	0.140848i	$0.0449828\pi$
$350$	3.09017	−	9.51057i	0.165177	−	0.508361i
$351$		0			0
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$		0			0
$355$	12.9443	−	9.40456i	0.687011	−	0.499142i
$356$	33.9787	+	24.6870i	1.80087	+	1.30841i
$357$	−6.18034	−	19.0211i	−0.327098	−	1.00670i
$358$	−2.76393	−	8.50651i	−0.146078	−	0.449583i
$359$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$359$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$360$	−3.61803	+	2.62866i	−0.190687	+	0.138542i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	−22.3607			−1.17525
$363$		0			0
$364$		0			0
$365$	−5.52786	+	17.0130i	−0.289342	+	0.890502i
$366$	−16.1803	+	11.7557i	−0.845760	+	0.614481i
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	0.405908	−	0.913914i	$-0.366955\pi$
$367$	−6.47214	−	4.70228i	−0.337843	−	0.245457i	−0.743751	+	0.668457i	$0.766955\pi$
$368$	1.23607	+	3.80423i	0.0644345	+	0.198309i
$369$	−1.38197	−	4.25325i	−0.0719423	−	0.221416i
$370$	−7.23607	−	5.25731i	−0.376185	−	0.273315i
$371$	21.7082	−	15.7719i	1.12703	−	0.818838i
$372$		0			0
$373$	−26.8328			−1.38935			−0.694675	−	0.719323i	$-0.744452\pi$
$373$	−26.8328			−1.38935			−0.694675	+	0.719323i	$0.744452\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$	5.52786	−	17.0130i	0.285078	−	0.877379i
$377$		0			0
$378$	8.09017	+	5.87785i	0.416113	+	0.302324i
$379$	−6.18034	−	19.0211i	−0.317463	−	0.977050i	−0.974729	−	0.223391i	$-0.928287\pi$
$379$	−6.18034	−	19.0211i	−0.317463	−	0.977050i	0.657266	−	0.753659i	$-0.271713\pi$
$380$	−8.29180	−	25.5195i	−0.425360	−	1.30912i
$381$	−10.8541	−	7.88597i	−0.556072	−	0.404010i
$382$		0			0
$383$	−11.1246	+	34.2380i	−0.568441	+	1.74948i	0.0890579	+	0.996026i	$0.471614\pi$
$383$	−11.1246	+	34.2380i	−0.568441	+	1.74948i	−0.657499	+	0.753455i	$0.728386\pi$
$384$	−15.6525			−0.798762
$385$		0			0
$386$	−40.0000			−2.03595
$387$	1.38197	−	4.25325i	0.0702493	−	0.216205i
$388$	−4.85410	+	3.52671i	−0.246430	+	0.179042i
$389$	−8.09017	−	5.87785i	−0.410188	−	0.298019i	0.363490	−	0.931598i	$-0.381585\pi$
$389$	−8.09017	−	5.87785i	−0.410188	−	0.298019i	−0.773678	+	0.633579i	$0.781585\pi$
$390$		0			0
$391$	−5.52786	−	17.0130i	−0.279556	−	0.860385i
$392$	−23.5172	−	17.0863i	−1.18780	−	0.862987i
$393$	14.4721	−	10.5146i	0.730023	−	0.530393i
$394$	15.4508	−	47.5528i	0.778403	−	2.39568i
$395$	26.8328			1.35011
$396$		0			0
$397$	22.0000			1.10415			0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000			1.10415			0.552074	+	0.833795i	$0.313837\pi$
$398$		0			0
$399$	−16.1803	+	11.7557i	−0.810030	+	0.588521i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	9.27051	+	28.5317i	0.462947	+	1.42480i	0.861546	+	0.507679i	$0.169497\pi$
$401$	9.27051	+	28.5317i	0.462947	+	1.42480i	−0.398599	+	0.917125i	$0.630503\pi$
$402$	−8.29180	−	25.5195i	−0.413557	−	1.27280i
$403$		0			0
$404$	−10.8541	+	7.88597i	−0.540012	+	0.392342i
$405$	0.618034	−	1.90211i	0.0307104	−	0.0945168i
$406$	−44.7214			−2.21948
$407$		0			0
$408$	10.0000			0.495074
$409$	−8.29180	+	25.5195i	−0.410003	+	1.26186i	0.506642	+	0.862157i	$0.330887\pi$
$409$	−8.29180	+	25.5195i	−0.410003	+	1.26186i	−0.916645	+	0.399703i	$0.869113\pi$
$410$	16.1803	−	11.7557i	0.799090	−	0.580573i
$411$	−17.7984	−	12.9313i	−0.877929	−	0.637853i
$412$	14.8328	+	45.6507i	0.730760	+	2.24905i
$413$		0			0
$414$	7.23607	+	5.25731i	0.355633	+	0.258383i
$415$	14.4721	−	10.5146i	0.710409	−	0.516143i
$416$		0			0
$417$	13.4164			0.657004
$418$		0			0
$419$	4.00000			0.195413			0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000			0.195413			0.0977064	+	0.995215i	$0.468849\pi$
$420$	−8.29180	+	25.5195i	−0.404598	+	1.24523i
$421$	−8.09017	+	5.87785i	−0.394291	+	0.286469i	−0.767211	−	0.641394i	$-0.778356\pi$
$421$	−8.09017	+	5.87785i	−0.394291	+	0.286469i	0.372921	+	0.927863i	$0.378356\pi$
$422$	8.09017	+	5.87785i	0.393823	+	0.286129i
$423$	2.47214	+	7.60845i	0.120199	+	0.369936i
$424$	4.14590	+	12.7598i	0.201343	+	0.619669i
$425$	3.61803	+	2.62866i	0.175500	+	0.127509i
$426$	14.4721	−	10.5146i	0.701177	−	0.509435i
$427$	−12.3607	+	38.0423i	−0.598175	+	1.84099i
$428$	26.8328			1.29701
$429$		0			0
$430$	20.0000			0.964486
$431$	−2.76393	+	8.50651i	−0.133134	+	0.409744i	−0.995295	−	0.0968900i	$-0.969110\pi$
$431$	−2.76393	+	8.50651i	−0.133134	+	0.409744i	0.862161	+	0.506634i	$0.169110\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	0.698281	−	0.715824i	$-0.253949\pi$
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	−0.465008	+	0.885307i	$0.653949\pi$
$434$		0			0
$435$	2.76393	+	8.50651i	0.132520	+	0.407856i
$436$		0			0
$437$	−14.4721	+	10.5146i	−0.692296	+	0.502983i
$438$	−6.18034	+	19.0211i	−0.295308	+	0.908865i
$439$	−13.4164			−0.640330			−0.320165	−	0.947362i	$-0.603738\pi$
$439$	−13.4164			−0.640330			−0.320165	+	0.947362i	$0.603738\pi$
$440$		0			0
$441$	13.0000			0.619048
$442$		0			0
$443$	19.4164	−	14.1068i	0.922501	−	0.670236i	−0.0216440	−	0.999766i	$-0.506890\pi$
$443$	19.4164	−	14.1068i	0.922501	−	0.670236i	0.944145	+	0.329529i	$0.106890\pi$
$444$	−4.85410	−	3.52671i	−0.230365	−	0.167370i
$445$	−8.65248	−	26.6296i	−0.410167	−	1.26236i
$446$	−11.0557	−	34.0260i	−0.523504	−	1.61118i
$447$	18.0902	+	13.1433i	0.855636	+	0.621656i
$448$	−47.0344	+	34.1725i	−2.22217	+	1.61450i
$449$	−1.85410	+	5.70634i	−0.0875005	+	0.269299i	−0.985227	−	0.171255i	$-0.945218\pi$
$449$	−1.85410	+	5.70634i	−0.0875005	+	0.269299i	0.897726	+	0.440554i	$0.145218\pi$
$450$	−2.23607			−0.105409
$451$		0			0
$452$	18.0000			0.846649
$453$	4.14590	−	12.7598i	0.194791	−	0.599506i
$454$	−16.1803	+	11.7557i	−0.759381	+	0.551723i
$455$		0			0
$456$	−3.09017	−	9.51057i	−0.144710	−	0.445373i
$457$	8.29180	+	25.5195i	0.387874	+	1.19375i	0.934374	+	0.356294i	$0.115960\pi$
$457$	8.29180	+	25.5195i	0.387874	+	1.19375i	−0.546500	+	0.837459i	$0.684040\pi$
$458$	−18.0902	−	13.1433i	−0.845298	−	0.614145i
$459$	−3.61803	+	2.62866i	−0.168875	+	0.122695i
$460$	−7.41641	+	22.8254i	−0.345792	+	1.06424i
$461$	13.4164			0.624864			0.312432	−	0.949940i	$-0.398856\pi$
$461$	13.4164			0.624864			0.312432	+	0.949940i	$0.398856\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	−1.38197	+	4.25325i	−0.0641562	+	0.197452i
$465$		0			0
$466$	8.09017	+	5.87785i	0.374770	+	0.272286i
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	0.877424	−	0.479716i	$-0.159260\pi$
$467$	−2.47214	−	7.60845i	−0.114397	−	0.352077i	−0.991821	+	0.127639i	$0.959260\pi$
$468$		0			0
$469$	−43.4164	−	31.5439i	−2.00478	−	1.45656i
$470$	−28.9443	+	21.0292i	−1.33510	+	0.970007i
$471$	0.618034	−	1.90211i	0.0284775	−	0.0876447i
$472$		0			0
$473$		0			0
$474$	30.0000			1.37795
$475$	1.38197	−	4.25325i	0.0634089	−	0.195153i
$476$	48.5410	−	35.2671i	2.22487	−	1.61647i
$477$	−4.85410	−	3.52671i	−0.222254	−	0.161477i
$478$	6.18034	+	19.0211i	0.282682	+	0.870006i
$479$	−2.76393	−	8.50651i	−0.126287	−	0.388672i	0.867846	−	0.496833i	$-0.165504\pi$
$479$	−2.76393	−	8.50651i	−0.126287	−	0.388672i	−0.994133	+	0.108161i	$0.965504\pi$
$480$	10.8541	+	7.88597i	0.495420	+	0.359943i
$481$		0			0
$482$	6.18034	−	19.0211i	0.281507	−	0.866389i
$483$	17.8885			0.813957
$484$		0			0
$485$	4.00000			0.181631
$486$	0.690983	−	2.12663i	0.0313436	−	0.0964658i
$487$	−6.47214	+	4.70228i	−0.293280	+	0.213081i	−0.724689	−	0.689076i	$-0.758017\pi$
$487$	−6.47214	+	4.70228i	−0.293280	+	0.213081i	0.431409	+	0.902157i	$0.358017\pi$
$488$	−16.1803	−	11.7557i	−0.732450	−	0.532156i
$489$	1.23607	+	3.80423i	0.0558969	+	0.172033i
$490$	17.9656	+	55.2923i	0.811601	+	2.49785i
$491$	21.7082	+	15.7719i	0.979678	+	0.711777i	0.957637	−	0.287980i	$-0.0929836\pi$
$491$	21.7082	+	15.7719i	0.979678	+	0.711777i	0.0220410	+	0.999757i	$0.492984\pi$
$492$	10.8541	−	7.88597i	0.489341	−	0.355527i
$493$	6.18034	−	19.0211i	0.278349	−	0.856669i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.0557	−	34.0260i	0.495917	−	1.52628i
$498$	16.1803	−	11.7557i	0.725058	−	0.526786i
$499$	16.1803	+	11.7557i	0.724331	+	0.526258i	0.887765	−	0.460297i	$-0.152257\pi$
$499$	16.1803	+	11.7557i	0.724331	+	0.526258i	−0.163434	+	0.986554i	$0.552257\pi$
$500$	−11.1246	−	34.2380i	−0.497508	−	1.53117i
$501$	2.76393	+	8.50651i	0.123483	+	0.380043i
$502$	21.7082	+	15.7719i	0.968885	+	0.703936i
$503$	21.7082	−	15.7719i	0.967921	−	0.703236i	0.0129442	−	0.999916i	$-0.495880\pi$
$503$	21.7082	−	15.7719i	0.967921	−	0.703236i	0.954977	+	0.296680i	$0.0958796\pi$
$504$	−3.09017	+	9.51057i	−0.137647	+	0.423634i
$505$	8.94427			0.398015
$506$		0			0
$507$	−13.0000			−0.577350
$508$	12.4377	−	38.2793i	0.551833	−	1.69837i
$509$	−24.2705	+	17.6336i	−1.07577	+	0.781594i	−0.976941	−	0.213511i	$-0.931510\pi$
$509$	−24.2705	+	17.6336i	−1.07577	+	0.781594i	−0.0988307	+	0.995104i	$0.531510\pi$
$510$	−16.1803	−	11.7557i	−0.716477	−	0.520551i
$511$	12.3607	+	38.0423i	0.546804	+	1.68289i
$512$	3.45492	+	10.6331i	0.152687	+	0.469923i
$513$	3.61803	+	2.62866i	0.159740	+	0.116058i
$514$	39.7984	−	28.9152i	1.75543	−	1.27540i
$515$	9.88854	−	30.4338i	0.435741	−	1.34107i
$516$	13.4164			0.590624
$517$		0			0
$518$	−20.0000			−0.878750
$519$	−4.14590	+	12.7598i	−0.181985	+	0.560091i
$520$		0			0
$521$	−24.2705	−	17.6336i	−1.06331	−	0.772540i	−0.0886124	−	0.996066i	$-0.528243\pi$
$521$	−24.2705	−	17.6336i	−1.06331	−	0.772540i	−0.974698	+	0.223526i	$0.928243\pi$
$522$	3.09017	+	9.51057i	0.135253	+	0.416266i
$523$	1.38197	+	4.25325i	0.0604292	+	0.185982i	0.976714	−	0.214545i	$-0.0688270\pi$
$523$	1.38197	+	4.25325i	0.0604292	+	0.185982i	−0.916285	+	0.400527i	$0.868827\pi$
$524$	43.4164	+	31.5439i	1.89665	+	1.37800i
$525$	−3.61803	+	2.62866i	−0.157904	+	0.114724i
$526$	6.18034	−	19.0211i	0.269476	−	0.829361i
$527$		0			0
$528$		0			0
$529$	−7.00000			−0.304348
$530$	8.29180	−	25.5195i	0.360173	−	1.10850i
$531$		0			0
$532$	−48.5410	−	35.2671i	−2.10452	−	1.52902i
$533$		0			0
$534$	−9.67376	−	29.7728i	−0.418625	−	1.28839i
$535$	−14.4721	−	10.5146i	−0.625685	−	0.454587i
$536$	21.7082	−	15.7719i	0.937652	−	0.681244i
$537$	−1.23607	+	3.80423i	−0.0533403	+	0.164164i
$538$	−22.3607			−0.964037
$539$		0			0
$540$	6.00000			0.258199
$541$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$541$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$542$	24.2705	−	17.6336i	1.04251	−	0.757426i
$543$	8.09017	+	5.87785i	0.347182	+	0.252243i
$544$	−9.27051	−	28.5317i	−0.397470	−	1.22329i
$545$		0			0
$546$		0			0
$547$	−32.5623	+	23.6579i	−1.39226	+	1.01154i	−0.396651	+	0.917970i	$0.629828\pi$
$547$	−32.5623	+	23.6579i	−1.39226	+	1.01154i	−0.995613	+	0.0935692i	$0.970172\pi$
$548$	20.3951	−	62.7697i	0.871236	−	2.68139i
$549$	8.94427			0.381732
$550$		0			0
$551$	−20.0000			−0.852029
$552$	−2.76393	+	8.50651i	−0.117641	+	0.362061i
$553$	48.5410	−	35.2671i	2.06417	−	1.49971i
$554$		0			0
$555$	1.23607	+	3.80423i	0.0524682	+	0.161480i
$556$	12.4377	+	38.2793i	0.527476	+	1.62340i
$557$	32.5623	+	23.6579i	1.37971	+	1.00242i	0.996907	+	0.0785870i	$0.0250408\pi$
$557$	32.5623	+	23.6579i	1.37971	+	1.00242i	0.382802	+	0.923830i	$0.374959\pi$
$558$		0			0
$559$		0			0
$560$	8.94427			0.377964
$561$		0			0
$562$	70.0000			2.95277
$563$	5.52786	−	17.0130i	0.232972	−	0.717013i	−0.764412	−	0.644728i	$-0.776971\pi$
$563$	5.52786	−	17.0130i	0.232972	−	0.717013i	0.997384	−	0.0722854i	$-0.0230292\pi$
$564$	−19.4164	+	14.1068i	−0.817578	+	0.594005i
$565$	−9.70820	−	7.05342i	−0.408427	−	0.296740i
$566$	−9.27051	−	28.5317i	−0.389669	−	1.19928i
$567$	−1.38197	−	4.25325i	−0.0580371	−	0.178620i
$568$	14.4721	+	10.5146i	0.607237	+	0.441184i
$569$	−3.61803	+	2.62866i	−0.151676	+	0.110199i	−0.661035	−	0.750355i	$-0.729883\pi$
$569$	−3.61803	+	2.62866i	−0.151676	+	0.110199i	0.509359	+	0.860554i	$0.329883\pi$
$570$	−6.18034	+	19.0211i	−0.258866	+	0.796707i
$571$	−13.4164			−0.561459			−0.280730	−	0.959787i	$-0.590576\pi$
$571$	−13.4164			−0.561459			−0.280730	+	0.959787i	$0.590576\pi$
$572$		0			0
$573$		0			0
$574$	13.8197	−	42.5325i	0.576821	−	1.77527i
$575$	−3.23607	+	2.35114i	−0.134953	+	0.0980494i
$576$	10.5172	+	7.64121i	0.438218	+	0.318384i
$577$	−0.618034	−	1.90211i	−0.0257291	−	0.0791860i	0.937367	−	0.348342i	$-0.113255\pi$
$577$	−0.618034	−	1.90211i	−0.0257291	−	0.0791860i	−0.963097	+	0.269156i	$0.913255\pi$
$578$	2.07295	+	6.37988i	0.0862233	+	0.265368i
$579$	14.4721	+	10.5146i	0.601441	+	0.436973i
$580$	−21.7082	+	15.7719i	−0.901384	+	0.654894i
$581$	12.3607	−	38.0423i	0.512807	−	1.57826i
$582$	4.47214			0.185376
$583$		0			0
$584$	−20.0000			−0.827606
$585$		0			0
$586$	40.4508	−	29.3893i	1.67101	−	1.21406i
$587$	6.47214	+	4.70228i	0.267134	+	0.194084i	0.713286	−	0.700873i	$-0.247206\pi$
$587$	6.47214	+	4.70228i	0.267134	+	0.194084i	−0.446152	+	0.894957i	$0.647206\pi$
$588$	12.0517	+	37.0912i	0.497002	+	1.52962i
$589$		0			0
$590$		0			0
$591$	−18.0902	+	13.1433i	−0.744130	+	0.540642i
$592$	−0.618034	+	1.90211i	−0.0254010	+	0.0781764i
$593$	−22.3607			−0.918243			−0.459122	−	0.888373i	$-0.651836\pi$
$593$	−22.3607			−0.918243			−0.459122	+	0.888373i	$0.651836\pi$
$594$		0			0
$595$	−40.0000			−1.63984
$596$	−20.7295	+	63.7988i	−0.849113	+	2.61330i
$597$		0			0
$598$		0			0
$599$	−11.1246	−	34.2380i	−0.454539	−	1.39893i	−0.871675	−	0.490084i	$-0.836966\pi$
$599$	−11.1246	−	34.2380i	−0.454539	−	1.39893i	0.417136	−	0.908844i	$-0.363034\pi$
$600$	−0.690983	−	2.12663i	−0.0282093	−	0.0868192i
$601$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$601$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$602$	36.1803	−	26.2866i	1.47460	−	1.07136i
$603$	−3.70820	+	11.4127i	−0.151010	+	0.464760i
$604$	40.2492			1.63772
$605$		0			0
$606$	10.0000			0.406222
$607$	−1.38197	+	4.25325i	−0.0560923	+	0.172634i	−0.975178	−	0.221425i	$-0.928929\pi$
$607$	−1.38197	+	4.25325i	−0.0560923	+	0.172634i	0.919085	+	0.394059i	$0.128929\pi$
$608$	−24.2705	+	17.6336i	−0.984299	+	0.715135i
$609$	16.1803	+	11.7557i	0.655660	+	0.476365i
$610$	12.3607	+	38.0423i	0.500469	+	1.54029i
$611$		0			0
$612$	−10.8541	−	7.88597i	−0.438751	−	0.318771i
$613$	−36.1803	+	26.2866i	−1.46131	+	1.06170i	−0.478291	+	0.878201i	$0.658744\pi$
$613$	−36.1803	+	26.2866i	−1.46131	+	1.06170i	−0.983019	+	0.183503i	$0.941256\pi$
$614$	−3.09017	+	9.51057i	−0.124709	+	0.383815i
$615$	−8.94427			−0.360668
$616$		0			0
$617$	−2.00000			−0.0805170			−0.0402585	−	0.999189i	$-0.512818\pi$
$617$	−2.00000			−0.0805170			−0.0402585	+	0.999189i	$0.512818\pi$
$618$	11.0557	−	34.0260i	0.444727	−	1.36873i
$619$	−35.5967	+	25.8626i	−1.43075	+	1.03950i	−0.440878	+	0.897567i	$0.645333\pi$
$619$	−35.5967	+	25.8626i	−1.43075	+	1.03950i	−0.989876	+	0.141937i	$0.954667\pi$
$620$		0			0
$621$	−1.23607	−	3.80423i	−0.0496017	−	0.152658i
$622$	−8.29180	−	25.5195i	−0.332471	−	1.02324i
$623$	−50.6525	−	36.8012i	−2.02935	−	1.47441i
$624$		0			0
$625$	−5.87132	+	18.0701i	−0.234853	+	0.722803i
$626$	31.3050			1.25120
$627$		0			0
$628$	6.00000			0.239426
$629$	2.76393	−	8.50651i	0.110205	−	0.339177i
$630$	16.1803	−	11.7557i	0.644640	−	0.468358i
$631$	−25.8885	−	18.8091i	−1.03061	−	0.748780i	−0.0621766	−	0.998065i	$-0.519804\pi$
$631$	−25.8885	−	18.8091i	−1.03061	−	0.748780i	−0.968430	+	0.249286i	$0.919804\pi$
$632$	9.27051	+	28.5317i	0.368761	+	1.13493i
$633$	−1.38197	−	4.25325i	−0.0549282	−	0.169052i
$634$	−32.5623	−	23.6579i	−1.29321	−	0.939575i
$635$	−21.7082	+	15.7719i	−0.861464	+	0.625890i
$636$	5.56231	−	17.1190i	0.220560	−	0.678813i
$637$		0			0
$638$		0			0
$639$	−8.00000			−0.316475
$640$	−9.67376	+	29.7728i	−0.382389	+	1.17687i
$641$	24.2705	−	17.6336i	0.958628	−	0.696484i	0.00579592	−	0.999983i	$-0.498155\pi$
$641$	24.2705	−	17.6336i	0.958628	−	0.696484i	0.952832	+	0.303500i	$0.0981551\pi$
$642$	−16.1803	−	11.7557i	−0.638587	−	0.463961i
$643$	11.1246	+	34.2380i	0.438712	+	1.35022i	0.889235	+	0.457451i	$0.151238\pi$
$643$	11.1246	+	34.2380i	0.438712	+	1.35022i	−0.450523	+	0.892765i	$0.648762\pi$
$644$	16.5836	+	51.0390i	0.653485	+	2.01122i
$645$	−7.23607	−	5.25731i	−0.284920	−	0.207006i
$646$	36.1803	−	26.2866i	1.42350	−	1.03423i
$647$	−3.70820	+	11.4127i	−0.145785	+	0.448679i	−0.997111	−	0.0759575i	$-0.975799\pi$
$647$	−3.70820	+	11.4127i	−0.145785	+	0.448679i	0.851327	+	0.524636i	$0.175799\pi$
$648$	2.23607			0.0878410
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−9.70820	+	7.05342i	−0.380203	+	0.276233i
$653$	−37.2148	−	27.0381i	−1.45633	−	1.05808i	−0.984301	−	0.176499i	$-0.943523\pi$
$653$	−37.2148	−	27.0381i	−1.45633	−	1.05808i	−0.472026	−	0.881585i	$-0.656477\pi$
$654$		0			0
$655$	−11.0557	−	34.0260i	−0.431983	−	1.32951i
$656$	−3.61803	−	2.62866i	−0.141260	−	0.102632i
$657$	7.23607	−	5.25731i	0.282306	−	0.205107i
$658$	−24.7214	+	76.0845i	−0.963739	+	2.96608i
$659$	17.8885			0.696839			0.348419	−	0.937339i	$-0.386719\pi$
$659$	17.8885			0.696839			0.348419	+	0.937339i	$0.386719\pi$
$660$		0			0
$661$	−22.0000			−0.855701			−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000			−0.855701			−0.427850	+	0.903850i	$0.640729\pi$
$662$	−13.8197	+	42.5325i	−0.537116	+	1.65307i
$663$		0			0
$664$	16.1803	+	11.7557i	0.627919	+	0.456210i
$665$	12.3607	+	38.0423i	0.479327	+	1.47522i
$666$	1.38197	+	4.25325i	0.0535501	+	0.164810i
$667$	14.4721	+	10.5146i	0.560363	+	0.407128i
$668$	−21.7082	+	15.7719i	−0.839916	+	0.610234i
$669$	−4.94427	+	15.2169i	−0.191157	+	0.588320i
$670$	−53.6656			−2.07328
$671$		0			0
$672$	30.0000			1.15728
$673$	−5.52786	+	17.0130i	−0.213083	+	0.655804i	0.786201	+	0.617971i	$0.212045\pi$
$673$	−5.52786	+	17.0130i	−0.213083	+	0.655804i	−0.999284	+	0.0378322i	$0.987955\pi$
$674$	−16.1803	+	11.7557i	−0.623243	+	0.452813i
$675$	0.809017	+	0.587785i	0.0311391	+	0.0226239i
$676$	−12.0517	−	37.0912i	−0.463525	−	1.42658i
$677$	−9.67376	−	29.7728i	−0.371793	−	1.14426i	−0.945617	−	0.325282i	$-0.894541\pi$
$677$	−9.67376	−	29.7728i	−0.371793	−	1.14426i	0.573824	−	0.818979i	$-0.305459\pi$
$678$	−10.8541	−	7.88597i	−0.416849	−	0.302859i
$679$	7.23607	−	5.25731i	0.277695	−	0.201757i
$680$	6.18034	−	19.0211i	0.237005	−	0.729427i
$681$	8.94427			0.342745
$682$		0			0
$683$	44.0000			1.68361			0.841807	−	0.539779i	$-0.181492\pi$
$683$	44.0000			1.68361			0.841807	+	0.539779i	$0.181492\pi$
$684$	−4.14590	+	12.7598i	−0.158522	+	0.487882i
$685$	−35.5967	+	25.8626i	−1.36008	+	0.988157i
$686$	48.5410	+	35.2671i	1.85330	+	1.34650i
$687$	3.09017	+	9.51057i	0.117897	+	0.362851i
$688$	−1.38197	−	4.25325i	−0.0526870	−	0.162154i
$689$		0			0
$690$	14.4721	−	10.5146i	0.550945	−	0.400285i
$691$	3.70820	−	11.4127i	0.141067	−	0.434159i	−0.855418	−	0.517939i	$-0.826699\pi$
$691$	3.70820	−	11.4127i	0.141067	−	0.434159i	0.996484	+	0.0837803i	$0.0266994\pi$
$692$	−40.2492			−1.53005
$693$		0			0
$694$	20.0000			0.759190
$695$	8.29180	−	25.5195i	0.314526	−	0.968011i
$696$	−8.09017	+	5.87785i	−0.306657	+	0.222799i
$697$	16.1803	+	11.7557i	0.612874	+	0.445279i
$698$	−18.5410	−	57.0634i	−0.701788	−	2.15988i
$699$	−1.38197	−	4.25325i	−0.0522708	−	0.160873i
$700$	−10.8541	−	7.88597i	−0.410246	−	0.298062i
$701$	18.0902	−	13.1433i	0.683256	−	0.496415i	−0.191180	−	0.981555i	$-0.561231\pi$
$701$	18.0902	−	13.1433i	0.683256	−	0.496415i	0.874436	+	0.485140i	$0.161231\pi$
$702$		0			0
$703$	−8.94427			−0.337340
$704$		0			0
$705$	16.0000			0.602595
$706$	−9.67376	+	29.7728i	−0.364077	+	1.12051i
$707$	16.1803	−	11.7557i	0.608524	−	0.442119i
$708$		0			0
$709$	−1.85410	−	5.70634i	−0.0696323	−	0.214306i	0.910185	−	0.414202i	$-0.135939\pi$
$709$	−1.85410	−	5.70634i	−0.0696323	−	0.214306i	−0.979817	+	0.199896i	$0.935939\pi$
$710$	−11.0557	−	34.0260i	−0.414914	−	1.27697i
$711$	−10.8541	−	7.88597i	−0.407061	−	0.295747i
$712$	25.3262	−	18.4006i	0.949141	−	0.689591i
$713$		0			0
$714$	−44.7214			−1.67365
$715$		0			0
$716$	−12.0000			−0.448461
$717$	2.76393	−	8.50651i	0.103221	−	0.317681i
$718$		0			0
$719$	19.4164	+	14.1068i	0.724110	+	0.526097i	0.887695	−	0.460433i	$-0.152306\pi$
$719$	19.4164	+	14.1068i	0.724110	+	0.526097i	−0.163585	+	0.986529i	$0.552306\pi$
$720$	−0.618034	−	1.90211i	−0.0230328	−	0.0708876i
$721$	−22.1115	−	68.0521i	−0.823474	−	2.53439i
$722$	−1.80902	−	1.31433i	−0.0673246	−	0.0489142i
$723$	−7.23607	+	5.25731i	−0.269112	+	0.195522i
$724$	−9.27051	+	28.5317i	−0.344536	+	1.06037i
$725$	−4.47214			−0.166091
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	32.3607	+	23.5114i	1.19772	+	0.870196i
$731$	6.18034	+	19.0211i	0.228588	+	0.703522i
$732$	8.29180	+	25.5195i	0.306474	+	0.943229i
$733$	14.4721	+	10.5146i	0.534541	+	0.388366i	0.822053	−	0.569410i	$-0.192828\pi$
$733$	14.4721	+	10.5146i	0.534541	+	0.388366i	−0.287513	+	0.957777i	$0.592828\pi$
$734$	−14.4721	+	10.5146i	−0.534176	+	0.388102i
$735$	8.03444	−	24.7275i	0.296355	−	0.912086i
$736$	26.8328			0.989071
$737$		0			0
$738$	−10.0000			−0.368105
$739$	1.38197	−	4.25325i	0.0508364	−	0.156458i	−0.922415	−	0.386199i	$-0.873788\pi$
$739$	1.38197	−	4.25325i	0.0508364	−	0.156458i	0.973252	+	0.229741i	$0.0737878\pi$
$740$	−9.70820	+	7.05342i	−0.356881	+	0.259289i
$741$		0			0
$742$	−18.5410	−	57.0634i	−0.680662	−	2.09486i
$743$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$743$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$744$		0			0
$745$	36.1803	−	26.2866i	1.32555	−	0.963065i
$746$	−18.5410	+	57.0634i	−0.678835	+	2.08924i
$747$	−8.94427			−0.327254
$748$		0			0
$749$	−40.0000			−1.46157
$750$	−8.29180	+	25.5195i	−0.302774	+	0.931841i
$751$	−25.8885	+	18.8091i	−0.944686	+	0.686355i	−0.949544	−	0.313633i	$-0.898454\pi$
$751$	−25.8885	+	18.8091i	−0.944686	+	0.686355i	0.00485778	+	0.999988i	$0.498454\pi$
$752$	6.47214	+	4.70228i	0.236015	+	0.171475i
$753$	−3.70820	−	11.4127i	−0.135134	−	0.415901i
$754$		0			0
$755$	−21.7082	−	15.7719i	−0.790042	−	0.573999i
$756$	10.8541	−	7.88597i	0.394760	−	0.286810i
$757$	12.9787	−	39.9444i	0.471719	−	1.45180i	−0.378612	−	0.925555i	$-0.623599\pi$
$757$	12.9787	−	39.9444i	0.471719	−	1.45180i	0.850331	−	0.526248i	$-0.176401\pi$
$758$	−44.7214			−1.62435
$759$		0			0
$760$	−20.0000			−0.725476
$761$	−9.67376	+	29.7728i	−0.350674	+	1.07926i	0.607802	+	0.794088i	$0.292051\pi$
$761$	−9.67376	+	29.7728i	−0.350674	+	1.07926i	−0.958476	+	0.285174i	$0.907949\pi$
$762$	−24.2705	+	17.6336i	−0.879228	+	0.638796i
$763$		0			0
$764$		0			0
$765$	2.76393	+	8.50651i	0.0999302	+	0.307553i
$766$	65.1246	+	47.3158i	2.35305	+	1.70959i
$767$		0			0
$768$	−2.78115	+	8.55951i	−0.100356	+	0.308865i
$769$	35.7771			1.29015			0.645077	−	0.764117i	$-0.276825\pi$
$769$	35.7771			1.29015			0.645077	+	0.764117i	$0.276825\pi$
$770$		0			0
$771$	−22.0000			−0.792311
$772$	−16.5836	+	51.0390i	−0.596857	+	1.83694i
$773$	−11.3262	+	8.22899i	−0.407376	+	0.295976i	−0.772539	−	0.634968i	$-0.781013\pi$
$773$	−11.3262	+	8.22899i	−0.407376	+	0.295976i	0.365162	+	0.930944i	$0.381013\pi$
$774$	−8.09017	−	5.87785i	−0.290795	−	0.211275i
$775$		0			0
$776$	1.38197	+	4.25325i	0.0496097	+	0.152683i
$777$	7.23607	+	5.25731i	0.259592	+	0.188605i
$778$	−18.0902	+	13.1433i	−0.648564	+	0.471209i
$779$	6.18034	−	19.0211i	0.221434	−	0.681503i
$780$		0			0
$781$		0			0
$782$	−40.0000			−1.43040
$783$	1.38197	−	4.25325i	0.0493874	−	0.151999i
$784$	10.5172	−	7.64121i	0.375615	−	0.272900i
$785$	−3.23607	−	2.35114i	−0.115500	−	0.0839158i
$786$	−12.3607	−	38.0423i	−0.440891	−	1.35692i
$787$	12.4377	+	38.2793i	0.443356	+	1.36451i	0.884277	+	0.466963i	$0.154652\pi$
$787$	12.4377	+	38.2793i	0.443356	+	1.36451i	−0.440921	+	0.897546i	$0.645348\pi$
$788$	−54.2705	−	39.4298i	−1.93331	−	1.40463i
$789$	−7.23607	+	5.25731i	−0.257611	+	0.187165i
$790$	18.5410	−	57.0634i	0.659660	−	2.03022i
$791$	−26.8328			−0.954065
$792$		0			0
$793$		0			0
$794$	15.2016	−	46.7858i	0.539486	−	1.66037i
$795$	−9.70820	+	7.05342i	−0.344315	+	0.250159i
$796$		0			0
$797$	12.9787	+	39.9444i	0.459730	+	1.41490i	0.865492	+	0.500924i	$0.167006\pi$
$797$	12.9787	+	39.9444i	0.459730	+	1.41490i	−0.405762	+	0.913979i	$0.632994\pi$
$798$	13.8197	+	42.5325i	0.489211	+	1.50564i
$799$	−28.9443	−	21.0292i	−1.02397	−	0.743961i
$800$	−5.42705	+	3.94298i	−0.191875	+	0.139406i
$801$	−4.32624	+	13.3148i	−0.152860	+	0.470455i
$802$	67.0820			2.36875
$803$		0			0
$804$	−36.0000			−1.26962
$805$	11.0557	−	34.0260i	0.389663	−	1.19926i
$806$		0			0
$807$	8.09017	+	5.87785i	0.284787	+	0.206910i
$808$	3.09017	+	9.51057i	0.108712	+	0.334581i
$809$	−4.14590	−	12.7598i	−0.145762	−	0.448609i	0.851346	−	0.524604i	$-0.175787\pi$
$809$	−4.14590	−	12.7598i	−0.145762	−	0.448609i	−0.997108	+	0.0759949i	$0.975787\pi$
$810$	−3.61803	−	2.62866i	−0.127125	−	0.0923615i
$811$	3.61803	−	2.62866i	0.127046	−	0.0923046i	−0.522447	−	0.852672i	$-0.674981\pi$
$811$	3.61803	−	2.62866i	0.127046	−	0.0923046i	0.649494	+	0.760367i	$0.274981\pi$
$812$	−18.5410	+	57.0634i	−0.650662	+	2.00253i
$813$	−13.4164			−0.470534
$814$		0			0
$815$	8.00000			0.280228
$816$	−1.38197	+	4.25325i	−0.0483785	+	0.148894i
$817$	16.1803	−	11.7557i	0.566078	−	0.411280i
$818$	48.5410	+	35.2671i	1.69720	+	1.23309i
$819$		0			0
$820$	−8.29180	−	25.5195i	−0.289562	−	0.891180i
$821$	−18.0902	−	13.1433i	−0.631351	−	0.458704i	0.225517	−	0.974239i	$-0.427593\pi$
$821$	−18.0902	−	13.1433i	−0.631351	−	0.458704i	−0.856868	+	0.515536i	$0.827593\pi$
$822$	−39.7984	+	28.9152i	−1.38813	+	1.00853i
$823$	4.94427	−	15.2169i	0.172346	−	0.530428i	−0.827156	−	0.561973i	$-0.810043\pi$
$823$	4.94427	−	15.2169i	0.172346	−	0.530428i	0.999502	+	0.0315446i	$0.0100426\pi$
$824$	35.7771			1.24635
$825$		0			0
$826$		0			0
$827$	13.8197	−	42.5325i	0.480557	−	1.47900i	−0.357758	−	0.933814i	$-0.616459\pi$
$827$	13.8197	−	42.5325i	0.480557	−	1.47900i	0.838314	−	0.545187i	$-0.183541\pi$
$828$	9.70820	−	7.05342i	0.337383	−	0.245123i
$829$	−11.3262	−	8.22899i	−0.393377	−	0.285805i	0.373461	−	0.927646i	$-0.378171\pi$
$829$	−11.3262	−	8.22899i	−0.393377	−	0.285805i	−0.766838	+	0.641841i	$0.778171\pi$
$830$	−12.3607	−	38.0423i	−0.429045	−	1.32047i
$831$		0			0
$832$		0			0
$833$	−47.0344	+	34.1725i	−1.62965	+	1.18401i
$834$	9.27051	−	28.5317i	0.321012	−	0.987972i
$835$	17.8885			0.619059
$836$		0			0
$837$		0			0
$838$	2.76393	−	8.50651i	0.0954784	−	0.293852i
$839$	16.1803	−	11.7557i	0.558607	−	0.405852i	−0.272342	−	0.962201i	$-0.587798\pi$
$839$	16.1803	−	11.7557i	0.558607	−	0.405852i	0.830949	+	0.556349i	$0.187798\pi$
$840$	16.1803	+	11.7557i	0.558275	+	0.405610i
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$	6.90983	+	21.2663i	0.238128	+	0.732884i
$843$	−25.3262	−	18.4006i	−0.872282	−	0.633750i
$844$	10.8541	−	7.88597i	0.373614	−	0.271446i
$845$	−8.03444	+	24.7275i	−0.276393	+	0.850651i
$846$	17.8885			0.615021
$847$		0			0
$848$	−6.00000			−0.206041
$849$	−4.14590	+	12.7598i	−0.142287	+	0.437914i
$850$	8.09017	−	5.87785i	0.277491	−	0.201609i
$851$	6.47214	+	4.70228i	0.221862	+	0.161192i
$852$	−7.41641	−	22.8254i	−0.254082	−	0.781984i
$853$	2.76393	+	8.50651i	0.0946352	+	0.291257i	0.987158	−	0.159744i	$-0.0510669\pi$
$853$	2.76393	+	8.50651i	0.0946352	+	0.291257i	−0.892523	+	0.451001i	$0.851067\pi$
$854$	72.3607	+	52.5731i	2.47613	+	1.79901i
$855$	7.23607	−	5.25731i	0.247468	−	0.179796i
$856$	6.18034	−	19.0211i	0.211240	−	0.650129i
$857$	40.2492			1.37489			0.687444	−	0.726238i	$-0.258733\pi$
$857$	40.2492			1.37489			0.687444	+	0.726238i	$0.258733\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	8.29180	−	25.5195i	0.282748	−	0.870209i
$861$	−16.1803	+	11.7557i	−0.551425	+	0.400633i
$862$	16.1803	+	11.7557i	0.551105	+	0.400401i
$863$	1.23607	+	3.80423i	0.0420762	+	0.129497i	0.969888	−	0.243551i	$-0.0783124\pi$
$863$	1.23607	+	3.80423i	0.0420762	+	0.129497i	−0.927812	+	0.373049i	$0.878312\pi$
$864$	−2.07295	−	6.37988i	−0.0705232	−	0.217048i
$865$	21.7082	+	15.7719i	0.738101	+	0.536262i
$866$	10.8541	−	7.88597i	0.368837	−	0.267976i
$867$	0.927051	−	2.85317i	0.0314843	−	0.0968987i
$868$		0			0
$869$		0			0
$870$	20.0000			0.678064
$871$		0			0
$872$		0			0
$873$	−1.61803	−	1.17557i	−0.0547622	−	0.0397870i
$874$	12.3607	+	38.0423i	0.418106	+	1.28680i
$875$	16.5836	+	51.0390i	0.560628	+	1.72543i
$876$	21.7082	+	15.7719i	0.733452	+	0.532884i
$877$	7.23607	−	5.25731i	0.244345	−	0.177527i	−0.458872	−	0.888502i	$-0.651746\pi$
$877$	7.23607	−	5.25731i	0.244345	−	0.177527i	0.703217	+	0.710976i	$0.251746\pi$
$878$	−9.27051	+	28.5317i	−0.312865	+	0.962898i
$879$	−22.3607			−0.754207
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$	8.98278	−	27.6462i	0.302466	−	0.930894i
$883$	−35.5967	+	25.8626i	−1.19793	+	0.870344i	−0.994079	−	0.108659i	$-0.965344\pi$
$883$	−35.5967	+	25.8626i	−1.19793	+	0.870344i	−0.203847	+	0.979003i	$0.565344\pi$
$884$		0			0
$885$		0			0
$886$	−16.5836	−	51.0390i	−0.557137	−	1.71469i
$887$	43.4164	+	31.5439i	1.45778	+	1.05914i	0.983934	+	0.178532i	$0.0571347\pi$
$887$	43.4164	+	31.5439i	1.45778	+	1.05914i	0.473846	+	0.880608i	$0.342865\pi$
$888$	−3.61803	+	2.62866i	−0.121413	+	0.0882119i
$889$	−18.5410	+	57.0634i	−0.621846	+	1.91384i
$890$	−62.6099			−2.09869
$891$		0			0
$892$	−48.0000			−1.60716
$893$	−11.0557	+	34.0260i	−0.369966	+	1.13864i
$894$	40.4508	−	29.3893i	1.35288	−	0.982924i
$895$	6.47214	+	4.70228i	0.216340	+	0.157180i
$896$	21.6312	+	66.5740i	0.722647	+	2.22408i
$897$		0			0
$898$	10.8541	+	7.88597i	0.362206	+	0.263158i
$899$		0			0
$900$	−0.927051	+	2.85317i	−0.0309017	+	0.0951057i
$901$	26.8328			0.893931
$902$		0			0
$903$	−20.0000			−0.665558
$904$	4.14590	−	12.7598i	0.137891	−	0.424383i
$905$	16.1803	−	11.7557i	0.537853	−	0.390773i
$906$	−24.2705	−	17.6336i	−0.806334	−	0.585836i
$907$	−3.70820	−	11.4127i	−0.123129	−	0.378952i	0.870427	−	0.492298i	$-0.163843\pi$
$907$	−3.70820	−	11.4127i	−0.123129	−	0.378952i	−0.993556	+	0.113346i	$0.963843\pi$
$908$	8.29180	+	25.5195i	0.275173	+	0.846895i
$909$	−3.61803	−	2.62866i	−0.120003	−	0.0871870i
$910$		0			0
$911$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$911$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$912$	4.47214			0.148087
$913$		0			0
$914$	60.0000			1.98462
$915$	5.52786	−	17.0130i	0.182746	−	0.562433i
$916$	−24.2705	+	17.6336i	−0.801920	+	0.582629i
$917$	−64.7214	−	47.0228i	−2.13729	−	1.55283i
$918$	3.09017	+	9.51057i	0.101991	+	0.313895i
$919$	6.90983	+	21.2663i	0.227934	+	0.701510i	0.997980	+	0.0635214i	$0.0202331\pi$
$919$	6.90983	+	21.2663i	0.227934	+	0.701510i	−0.770046	+	0.637988i	$0.779767\pi$
$920$	14.4721	+	10.5146i	0.477132	+	0.346657i
$921$	3.61803	−	2.62866i	0.119218	−	0.0866171i
$922$	9.27051	−	28.5317i	0.305308	−	0.939641i
$923$		0			0
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	16.5836	−	51.0390i	0.544971	−	1.67725i
$927$	−12.9443	+	9.40456i	−0.425146	+	0.308886i
$928$	24.2705	+	17.6336i	0.796719	+	0.578850i
$929$	9.27051	+	28.5317i	0.304156	+	0.936095i	0.979991	+	0.199042i	$0.0637830\pi$
$929$	9.27051	+	28.5317i	0.304156	+	0.936095i	−0.675835	+	0.737053i	$0.736217\pi$
$930$		0			0
$931$	47.0344	+	34.1725i	1.54149	+	1.11996i
$932$	10.8541	−	7.88597i	0.355538	−	0.258313i
$933$	−3.70820	+	11.4127i	−0.121401	+	0.373634i
$934$	−17.8885			−0.585331
$935$		0			0
$936$		0			0
$937$	16.5836	−	51.0390i	0.541762	−	1.66737i	−0.186804	−	0.982397i	$-0.559813\pi$
$937$	16.5836	−	51.0390i	0.541762	−	1.66737i	0.728566	−	0.684976i	$-0.240187\pi$
$938$	−97.0820	+	70.5342i	−3.16984	+	2.30302i
$939$	−11.3262	−	8.22899i	−0.369618	−	0.268543i
$940$	14.8328	+	45.6507i	0.483793	+	1.48896i
$941$	6.90983	+	21.2663i	0.225254	+	0.693261i	0.998266	+	0.0588688i	$0.0187494\pi$
$941$	6.90983	+	21.2663i	0.225254	+	0.693261i	−0.773012	+	0.634392i	$0.781251\pi$
$942$	−3.61803	−	2.62866i	−0.117882	−	0.0856462i
$943$	−14.4721	+	10.5146i	−0.471278	+	0.342403i
$944$		0			0
$945$	−8.94427			−0.290957
$946$		0			0
$947$	52.0000			1.68977			0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000			1.68977			0.844886	+	0.534946i	$0.179668\pi$
$948$	12.4377	−	38.2793i	0.403958	−	1.24325i
$949$		0			0
$950$	−8.09017	−	5.87785i	−0.262480	−	0.190703i
$951$	5.56231	+	17.1190i	0.180370	+	0.555122i
$952$	−13.8197	−	42.5325i	−0.447898	−	1.37849i
$953$	−18.0902	−	13.1433i	−0.585998	−	0.425753i	0.254883	−	0.966972i	$-0.417963\pi$
$953$	−18.0902	−	13.1433i	−0.585998	−	0.425753i	−0.840882	+	0.541219i	$0.817963\pi$
$954$	−10.8541	+	7.88597i	−0.351415	+	0.255318i
$955$		0			0
$956$	26.8328			0.867835
$957$		0			0
$958$	−20.0000			−0.646171
$959$	−30.4033	+	93.5716i	−0.981772	+	3.02158i
$960$	21.0344	−	15.2824i	0.678884	−	0.493238i
$961$	25.0795	+	18.2213i	0.809017	+	0.587785i
$962$		0			0
$963$	2.76393	+	8.50651i	0.0890665	+	0.274118i
$964$	−21.7082	−	15.7719i	−0.699174	−	0.507980i
$965$	28.9443	−	21.0292i	0.931749	−	0.676955i
$966$	12.3607	−	38.0423i	0.397698	−	1.22399i
$967$	13.4164			0.431443			0.215721	−	0.976455i	$-0.430790\pi$
$967$	13.4164			0.431443			0.215721	+	0.976455i	$0.430790\pi$
$968$		0			0
$969$	−20.0000			−0.642493
$970$	2.76393	−	8.50651i	0.0887445	−	0.273128i
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	−2.42705	−	1.76336i	−0.0778477	−	0.0565597i
$973$	−18.5410	−	57.0634i	−0.594398	−	1.82937i
$974$	5.52786	+	17.0130i	0.177124	+	0.545132i
$975$		0			0
$976$	7.23607	−	5.25731i	0.231621	−	0.168282i
$977$	−12.9787	+	39.9444i	−0.415226	+	1.27793i	0.496823	+	0.867852i	$0.334500\pi$
$977$	−12.9787	+	39.9444i	−0.415226	+	1.27793i	−0.912049	+	0.410082i	$0.865500\pi$
$978$	8.94427			0.286006
$979$		0			0
$980$	78.0000			2.49162
$981$		0			0
$982$	48.5410	−	35.2671i	1.54901	−	1.12542i
$983$	−29.1246	−	21.1603i	−0.928931	−	0.674908i	0.0168000	−	0.999859i	$-0.494652\pi$
$983$	−29.1246	−	21.1603i	−0.928931	−	0.674908i	−0.945731	+	0.324951i	$0.894652\pi$
$984$	−3.09017	−	9.51057i	−0.0985110	−	0.303186i
$985$	13.8197	+	42.5325i	0.440331	+	1.35520i
$986$	−36.1803	−	26.2866i	−1.15222	−	0.837134i
$987$	28.9443	−	21.0292i	0.921306	−	0.669368i
$988$		0			0
$989$	−17.8885			−0.568823
$990$		0			0
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$		0			0
$993$	16.1803	−	11.7557i	0.513468	−	0.373056i
$994$	−64.7214	−	47.0228i	−2.05284	−	1.49147i
$995$		0			0
$996$	−8.29180	−	25.5195i	−0.262736	−	0.808617i
$997$	21.7082	+	15.7719i	0.687506	+	0.499502i	0.875839	−	0.482603i	$-0.160309\pi$
$997$	21.7082	+	15.7719i	0.687506	+	0.499502i	−0.188334	+	0.982105i	$0.560309\pi$
$998$	36.1803	−	26.2866i	1.14527	−	0.832086i
$999$	0.618034	−	1.90211i	0.0195537	−	0.0601802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.l.130.1		4
11.2	odd	10	inner	363.2.e.l.124.1		4
11.3	even	5		363.2.e.a.202.1		4
11.4	even	5		363.2.a.g.1.2	yes	2
11.5	even	5	inner	363.2.e.l.148.1		4
11.6	odd	10		363.2.e.a.148.1		4
11.7	odd	10		363.2.a.g.1.1	✓	2
11.8	odd	10	inner	363.2.e.l.202.1		4
11.9	even	5		363.2.e.a.124.1		4
11.10	odd	2		363.2.e.a.130.1		4
33.26	odd	10		1089.2.a.p.1.1		2
33.29	even	10		1089.2.a.p.1.2		2
44.7	even	10		5808.2.a.bx.1.1		2
44.15	odd	10		5808.2.a.bx.1.2		2
55.4	even	10		9075.2.a.bi.1.1		2
55.29	odd	10		9075.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.a.g.1.1	✓	2	11.7	odd	10
363.2.a.g.1.2	yes	2	11.4	even	5
363.2.e.a.124.1		4	11.9	even	5
363.2.e.a.130.1		4	11.10	odd	2
363.2.e.a.148.1		4	11.6	odd	10
363.2.e.a.202.1		4	11.3	even	5
363.2.e.l.124.1		4	11.2	odd	10	inner
363.2.e.l.130.1		4	1.1	even	1	trivial
363.2.e.l.148.1		4	11.5	even	5	inner
363.2.e.l.202.1		4	11.8	odd	10	inner
1089.2.a.p.1.1		2	33.26	odd	10
1089.2.a.p.1.2		2	33.29	even	10
5808.2.a.bx.1.1		2	44.7	even	10
5808.2.a.bx.1.2		2	44.15	odd	10
9075.2.a.bi.1.1		2	55.4	even	10
9075.2.a.bi.1.2		2	55.29	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.690983 - 2.12663i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.42705 - 1.76336i) q^{4} +(0.618034 + 1.90211i) q^{5} +(0.690983 + 2.12663i) q^{6} +(3.61803 + 2.62866i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +4.47214 q^{10} +3.00000 q^{12} +(8.09017 - 5.87785i) q^{14} +(-1.61803 - 1.17557i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(1.38197 + 4.25325i) q^{17} +(-1.80902 - 1.31433i) q^{18} +(3.61803 - 2.62866i) q^{19} +(1.85410 - 5.70634i) q^{20} -4.47214 q^{21} -4.00000 q^{23} +(0.690983 - 2.12663i) q^{24} +(0.809017 - 0.587785i) q^{25} +(0.309017 + 0.951057i) q^{27} +(-4.14590 - 12.7598i) q^{28} +(-3.61803 - 2.62866i) q^{29} +(-3.61803 + 2.62866i) q^{30} -6.70820 q^{32} +10.0000 q^{34} +(-2.76393 + 8.50651i) q^{35} +(-2.42705 + 1.76336i) q^{36} +(-1.61803 - 1.17557i) q^{37} +(-3.09017 - 9.51057i) q^{38} +(-3.61803 - 2.62866i) q^{40} +(3.61803 - 2.62866i) q^{41} +(-3.09017 + 9.51057i) q^{42} +4.47214 q^{43} +2.00000 q^{45} +(-2.76393 + 8.50651i) q^{46} +(-6.47214 + 4.70228i) q^{47} +(0.809017 + 0.587785i) q^{48} +(4.01722 + 12.3637i) q^{49} +(-0.690983 - 2.12663i) q^{50} +(-3.61803 - 2.62866i) q^{51} +(1.85410 - 5.70634i) q^{53} +2.23607 q^{54} -10.0000 q^{56} +(-1.38197 + 4.25325i) q^{57} +(-8.09017 + 5.87785i) q^{58} +(1.85410 + 5.70634i) q^{60} +(2.76393 + 8.50651i) q^{61} +(3.61803 - 2.62866i) q^{63} +(-4.01722 + 12.3637i) q^{64} -12.0000 q^{67} +(4.14590 - 12.7598i) q^{68} +(3.23607 - 2.35114i) q^{69} +(16.1803 + 11.7557i) q^{70} +(-2.47214 - 7.60845i) q^{71} +(0.690983 + 2.12663i) q^{72} +(7.23607 + 5.25731i) q^{73} +(-3.61803 + 2.62866i) q^{74} +(-0.309017 + 0.951057i) q^{75} -13.4164 q^{76} +(4.14590 - 12.7598i) q^{79} +(1.61803 - 1.17557i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-3.09017 - 9.51057i) q^{82} +(-2.76393 - 8.50651i) q^{83} +(10.8541 + 7.88597i) q^{84} +(-7.23607 + 5.25731i) q^{85} +(3.09017 - 9.51057i) q^{86} +4.47214 q^{87} -14.0000 q^{89} +(1.38197 - 4.25325i) q^{90} +(9.70820 + 7.05342i) q^{92} +(5.52786 + 17.0130i) q^{94} +(7.23607 + 5.25731i) q^{95} +(5.42705 - 3.94298i) q^{96} +(0.618034 - 1.90211i) q^{97} +29.0689 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} + 5 q^{6} + 10 q^{7} - 5 q^{8} - q^{9} + 12 q^{12} + 10 q^{14} - 2 q^{15} + q^{16} + 10 q^{17} - 5 q^{18} + 10 q^{19} - 6 q^{20} - 16 q^{23} + 5 q^{24} + q^{25}+ \cdots - 2 q^{97}+O(q^{100}) \) 4 * q + 5 * q^2 - q^3 - 3 * q^4 - 2 * q^5 + 5 * q^6 + 10 * q^7 - 5 * q^8 - q^9 + 12 * q^12 + 10 * q^14 - 2 * q^15 + q^16 + 10 * q^17 - 5 * q^18 + 10 * q^19 - 6 * q^20 - 16 * q^23 + 5 * q^24 + q^25 - q^27 - 30 * q^28 - 10 * q^29 - 10 * q^30 + 40 * q^34 - 20 * q^35 - 3 * q^36 - 2 * q^37 + 10 * q^38 - 10 * q^40 + 10 * q^41 + 10 * q^42 + 8 * q^45 - 20 * q^46 - 8 * q^47 + q^48 - 13 * q^49 - 5 * q^50 - 10 * q^51 - 6 * q^53 - 40 * q^56 - 10 * q^57 - 10 * q^58 - 6 * q^60 + 20 * q^61 + 10 * q^63 + 13 * q^64 - 48 * q^67 + 30 * q^68 + 4 * q^69 + 20 * q^70 + 8 * q^71 + 5 * q^72 + 20 * q^73 - 10 * q^74 + q^75 + 30 * q^79 + 2 * q^80 - q^81 + 10 * q^82 - 20 * q^83 + 30 * q^84 - 20 * q^85 - 10 * q^86 - 56 * q^89 + 10 * q^90 + 12 * q^92 + 40 * q^94 + 20 * q^95 + 15 * q^96 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more