LMFDB - Embedded newform 669.2.i.b.4.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [720] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$20$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.5
Character	$\chi$	$=$	669.4
Dual form			669.2.i.b.502.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.72125 + 0.608157i) q^{2} +(0.372856 - 0.927889i) q^{3} +(1.03678 - 0.837141i) q^{4} +(1.37137 + 2.22725i) q^{5} +(-0.0774777 + 1.82389i) q^{6} +(-0.171615 + 1.34017i) q^{7} +(0.638833 - 1.03753i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-3.71499 - 2.99965i) q^{10} +(0.139415 - 3.28193i) q^{11} +(-0.390204 - 1.27415i) q^{12} +(1.70082 + 4.23265i) q^{13} +(-0.519640 - 2.41114i) q^{14} +(2.57797 - 0.442037i) q^{15} +(-1.03010 + 4.77966i) q^{16} +(-0.311137 + 7.32441i) q^{17} +(1.66348 + 0.751938i) q^{18} +(4.78945 - 1.24708i) q^{19} +(3.28633 + 1.16113i) q^{20} +(1.17954 + 0.658931i) q^{21} +(1.75596 + 5.73381i) q^{22} +(-3.65546 - 5.93684i) q^{23} +(-0.724520 - 0.979616i) q^{24} +(-0.828960 + 1.64414i) q^{25} +(-5.50165 - 6.25109i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(0.943983 + 1.53313i) q^{28} +(0.796933 - 3.69778i) q^{29} +(-4.16850 + 2.32866i) q^{30} +(-0.596749 + 0.0507908i) q^{31} +(-0.824205 - 6.43633i) q^{32} +(-2.99329 - 1.35305i) q^{33} +(-3.91884 - 12.7964i) q^{34} +(-3.22024 + 1.45564i) q^{35} +(-1.32776 - 0.113009i) q^{36} +(0.436620 + 10.2784i) q^{37} +(-7.48543 + 5.05927i) q^{38} +4.56159 q^{39} +3.18692 q^{40} +(-6.94351 + 4.69299i) q^{41} +(-2.43102 - 0.416840i) q^{42} +(-0.0862527 - 0.171072i) q^{43} +(-2.60290 - 3.51935i) q^{44} +(0.551050 - 2.55688i) q^{45} +(9.90248 + 7.99570i) q^{46} +(6.69992 + 1.74452i) q^{47} +(4.05092 + 2.73794i) q^{48} +(5.00753 + 1.30386i) q^{49} +(0.426951 - 3.33412i) q^{50} +(6.68023 + 3.01965i) q^{51} +(5.30670 + 2.96450i) q^{52} +(0.174098 - 0.197814i) q^{53} +(1.31795 - 1.26316i) q^{54} +(7.50087 - 4.19024i) q^{55} +(1.28083 + 1.03420i) q^{56} +(0.628629 - 4.90906i) q^{57} +(0.877109 + 6.84947i) q^{58} +(-2.71391 + 8.86185i) q^{59} +(2.30273 - 2.61641i) q^{60} +(4.09580 + 10.1928i) q^{61} +(0.996266 - 0.450341i) q^{62} +(1.05121 - 0.848796i) q^{63} +(0.930507 + 1.84555i) q^{64} +(-7.09471 + 9.59269i) q^{65} +(5.97506 + 0.508553i) q^{66} +(-8.10612 + 6.54523i) q^{67} +(5.80898 + 7.85426i) q^{68} +(-6.87169 + 1.17827i) q^{69} +(4.65758 - 4.46393i) q^{70} +(-0.285807 + 0.933257i) q^{71} +(-1.17912 + 0.307018i) q^{72} +(12.9958 + 7.25987i) q^{73} +(-7.00240 - 17.4261i) q^{74} +(1.21650 + 1.38221i) q^{75} +(3.92162 - 5.30239i) q^{76} +(4.37442 + 0.750069i) q^{77} +(-7.85164 + 2.77416i) q^{78} +(-1.37665 + 0.930456i) q^{79} +(-12.0581 + 4.26041i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(9.09745 - 12.3006i) q^{82} +(2.42114 - 4.80205i) q^{83} +(1.77454 - 0.304276i) q^{84} +(-16.7400 + 9.35151i) q^{85} +(0.252501 + 0.242003i) q^{86} +(-3.13399 - 2.11821i) q^{87} +(-3.31604 - 2.24125i) q^{88} +(-2.53675 + 4.11994i) q^{89} +(0.606489 + 4.73616i) q^{90} +(-5.96435 + 1.55300i) q^{91} +(-8.75987 - 3.09506i) q^{92} +(-0.175374 + 0.572655i) q^{93} +(-12.5932 + 1.07184i) q^{94} +(9.34566 + 8.95709i) q^{95} +(-6.27951 - 1.63506i) q^{96} +(3.14412 - 5.10638i) q^{97} +(-9.41217 + 0.801093i) q^{98} +(-2.37155 + 2.27294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) $ 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

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 $

$2$	−1.72125	+	0.608157i	−1.21711	+	0.430032i	−0.863015	−	0.505178i	$-0.831427\pi$
$2$	−1.72125	+	0.608157i	−1.21711	+	0.430032i	−0.354093	+	0.935210i	$0.615210\pi$
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$4$	1.03678	−	0.837141i	0.518390	−	0.418570i
$5$	1.37137	+	2.22725i	0.613296	+	0.996056i	0.997351	+	0.0727457i	$0.0231762\pi$
$5$	1.37137	+	2.22725i	0.613296	+	0.996056i	−0.384054	+	0.923310i	$0.625472\pi$
$6$	−0.0774777	+	1.82389i	−0.0316301	+	0.744598i
$7$	−0.171615	+	1.34017i	−0.0648645	+	0.506536i	0.926589	+	0.376076i	$0.122727\pi$
$7$	−0.171615	+	1.34017i	−0.0648645	+	0.506536i	−0.991453	+	0.130461i	$0.958354\pi$
$8$	0.638833	−	1.03753i	0.225861	−	0.366822i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	−3.71499	−	2.99965i	−1.17478	−	0.948572i
$11$	0.139415	−	3.28193i	0.0420351	−	0.989539i	−0.846970	−	0.531641i	$-0.821575\pi$
$11$	0.139415	−	3.28193i	0.0420351	−	0.989539i	0.889005	−	0.457898i	$-0.151398\pi$
$12$	−0.390204	−	1.27415i	−0.112642	−	0.367815i
$13$	1.70082	+	4.23265i	0.471722	+	1.17393i	0.954507	+	0.298187i	$0.0963820\pi$
$13$	1.70082	+	4.23265i	0.471722	+	1.17393i	−0.482785	+	0.875739i	$0.660375\pi$
$14$	−0.519640	−	2.41114i	−0.138880	−	0.644403i
$15$	2.57797	−	0.442037i	0.665628	−	0.114133i
$16$	−1.03010	+	4.77966i	−0.257524	+	1.19492i
$17$	−0.311137	+	7.32441i	−0.0754618	+	1.77643i	0.419733	+	0.907648i	$0.362124\pi$
$17$	−0.311137	+	7.32441i	−0.0754618	+	1.77643i	−0.495195	+	0.868782i	$0.664903\pi$
$18$	1.66348	+	0.751938i	0.392085	+	0.177234i
$19$	4.78945	−	1.24708i	1.09877	−	0.286099i	0.341951	−	0.939718i	$-0.388912\pi$
$19$	4.78945	−	1.24708i	1.09877	−	0.286099i	0.756824	+	0.653619i	$0.226750\pi$
$20$	3.28633	+	1.16113i	0.734846	+	0.259638i
$21$	1.17954	+	0.658931i	0.257397	+	0.143790i
$22$	1.75596	+	5.73381i	0.374372	+	1.22245i
$23$	−3.65546	−	5.93684i	−0.762215	−	1.23792i	−0.965909	−	0.258881i	$-0.916646\pi$
$23$	−3.65546	−	5.93684i	−0.762215	−	1.23792i	0.203694	−	0.979035i	$-0.434705\pi$
$24$	−0.724520	−	0.979616i	−0.147892	−	0.199963i
$25$	−0.828960	+	1.64414i	−0.165792	+	0.328829i
$26$	−5.50165	−	6.25109i	−1.07896	−	1.22594i
$27$	−0.911228	+	0.411901i	−0.175366	+	0.0792704i
$28$	0.943983	+	1.53313i	0.178396	+	0.289734i
$29$	0.796933	−	3.69778i	0.147987	−	0.686661i	−0.841287	−	0.540588i	$-0.818202\pi$
$29$	0.796933	−	3.69778i	0.147987	−	0.686661i	0.989274	−	0.146072i	$-0.0466632\pi$
$30$	−4.16850	+	2.32866i	−0.761060	+	0.425154i
$31$	−0.596749	+	0.0507908i	−0.107179	+	0.00912230i	−0.138273	−	0.990394i	$-0.544155\pi$
$31$	−0.596749	+	0.0507908i	−0.107179	+	0.00912230i	0.0310935	+	0.999516i	$0.490101\pi$
$32$	−0.824205	−	6.43633i	−0.145700	−	1.13779i
$33$	−2.99329	−	1.35305i	−0.521064	−	0.235536i
$34$	−3.91884	−	12.7964i	−0.672076	−	2.19456i
$35$	−3.22024	+	1.45564i	−0.544320	+	0.246048i
$36$	−1.32776	−	0.113009i	−0.221293	−	0.0188348i
$37$	0.436620	+	10.2784i	0.0717799	+	1.68975i	0.569164	+	0.822224i	$0.307267\pi$
$37$	0.436620	+	10.2784i	0.0717799	+	1.68975i	−0.497384	+	0.867530i	$0.665706\pi$
$38$	−7.48543	+	5.05927i	−1.21430	+	0.820721i
$39$	4.56159			0.730439
$40$	3.18692			0.503896
$41$	−6.94351	+	4.69299i	−1.08439	+	0.732922i	−0.965609	−	0.259998i	$-0.916278\pi$
$41$	−6.94351	+	4.69299i	−1.08439	+	0.732922i	−0.118785	+	0.992920i	$0.537900\pi$
$42$	−2.43102	−	0.416840i	−0.375114	−	0.0643198i
$43$	−0.0862527	−	0.171072i	−0.0131534	−	0.0260882i	0.886254	−	0.463200i	$-0.153299\pi$
$43$	−0.0862527	−	0.171072i	−0.0131534	−	0.0260882i	−0.899407	+	0.437112i	$0.856001\pi$
$44$	−2.60290	−	3.51935i	−0.392401	−	0.530562i
$45$	0.551050	−	2.55688i	0.0821457	−	0.381157i
$46$	9.90248	+	7.99570i	1.46004	+	1.17890i
$47$	6.69992	+	1.74452i	0.977284	+	0.254465i	0.706139	−	0.708074i	$-0.250435\pi$
$47$	6.69992	+	1.74452i	0.977284	+	0.254465i	0.271145	+	0.962538i	$0.412598\pi$
$48$	4.05092	+	2.73794i	0.584700	+	0.395188i
$49$	5.00753	+	1.30386i	0.715361	+	0.186266i
$50$	0.426951	−	3.33412i	0.0603800	−	0.471516i
$51$	6.68023	+	3.01965i	0.935419	+	0.422836i
$52$	5.30670	+	2.96450i	0.735907	+	0.411102i
$53$	0.174098	−	0.197814i	0.0239142	−	0.0271718i	−0.738592	−	0.674152i	$-0.764509\pi$
$53$	0.174098	−	0.197814i	0.0239142	−	0.0271718i	0.762506	+	0.646981i	$0.223969\pi$
$54$	1.31795	−	1.26316i	0.179351	−	0.171894i
$55$	7.50087	−	4.19024i	1.01142	−	0.565011i
$56$	1.28083	+	1.03420i	0.171158	+	0.138201i
$57$	0.628629	−	4.90906i	0.0832640	−	0.650220i
$58$	0.877109	+	6.84947i	0.115170	+	0.899380i
$59$	−2.71391	+	8.86185i	−0.353321	+	1.15371i	0.585895	+	0.810387i	$0.300743\pi$
$59$	−2.71391	+	8.86185i	−0.353321	+	1.15371i	−0.939216	+	0.343328i	$0.888446\pi$
$60$	2.30273	−	2.61641i	0.297282	−	0.337778i
$61$	4.09580	+	10.1928i	0.524414	+	1.30505i	0.921894	+	0.387443i	$0.126642\pi$
$61$	4.09580	+	10.1928i	0.524414	+	1.30505i	−0.397480	+	0.917611i	$0.630115\pi$
$62$	0.996266	−	0.450341i	0.126526	−	0.0571933i
$63$	1.05121	−	0.848796i	0.132440	−	0.106938i
$64$	0.930507	+	1.84555i	0.116313	+	0.230694i
$65$	−7.09471	+	9.59269i	−0.879991	+	1.18983i
$66$	5.97506	+	0.508553i	0.735479	+	0.0625985i
$67$	−8.10612	+	6.54523i	−0.990320	+	0.799627i	−0.979731	−	0.200317i	$-0.935803\pi$
$67$	−8.10612	+	6.54523i	−0.990320	+	0.799627i	−0.0105884	+	0.999944i	$0.503370\pi$
$68$	5.80898	+	7.85426i	0.704442	+	0.952469i
$69$	−6.87169	+	1.17827i	−0.827254	+	0.141847i
$70$	4.65758	−	4.46393i	0.556688	−	0.533542i
$71$	−0.285807	+	0.933257i	−0.0339190	+	0.110757i	−0.971521	−	0.236953i	$-0.923851\pi$
$71$	−0.285807	+	0.933257i	−0.0339190	+	0.110757i	0.937602	+	0.347710i	$0.113041\pi$
$72$	−1.17912	+	0.307018i	−0.138960	+	0.0361824i
$73$	12.9958	+	7.25987i	1.52104	+	0.849704i	0.999993	−	0.00382434i	$-0.00121733\pi$
$73$	12.9958	+	7.25987i	1.52104	+	0.849704i	0.521047	+	0.853528i	$0.325542\pi$
$74$	−7.00240	−	17.4261i	−0.814012	−	2.02575i
$75$	1.21650	+	1.38221i	0.140469	+	0.159604i
$76$	3.92162	−	5.30239i	0.449841	−	0.608225i
$77$	4.37442	+	0.750069i	0.498511	+	0.0854783i
$78$	−7.85164	+	2.77416i	−0.889024	+	0.314112i
$79$	−1.37665	+	0.930456i	−0.154886	+	0.104685i	−0.634966	−	0.772540i	$-0.718986\pi$
$79$	−1.37665	+	0.930456i	−0.154886	+	0.104685i	0.480080	+	0.877225i	$0.340608\pi$
$80$	−12.0581	+	4.26041i	−1.34814	+	0.476329i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	9.09745	−	12.3006i	1.00464	−	1.35837i
$83$	2.42114	−	4.80205i	0.265755	−	0.527093i	−0.720270	−	0.693694i	$-0.755982\pi$
$83$	2.42114	−	4.80205i	0.265755	−	0.527093i	0.986024	+	0.166601i	$0.0532792\pi$
$84$	1.77454	−	0.304276i	0.193618	−	0.0331992i
$85$	−16.7400	+	9.35151i	−1.81570	+	1.01431i
$86$	0.252501	+	0.242003i	0.0272279	+	0.0260958i
$87$	−3.13399	−	2.11821i	−0.335999	−	0.227096i
$88$	−3.31604	−	2.24125i	−0.353491	−	0.238918i
$89$	−2.53675	+	4.11994i	−0.268895	+	0.436713i	−0.957504	−	0.288420i	$-0.906870\pi$
$89$	−2.53675	+	4.11994i	−0.268895	+	0.436713i	0.688609	+	0.725133i	$0.258222\pi$
$90$	0.606489	+	4.73616i	0.0639296	+	0.499235i
$91$	−5.96435	+	1.55300i	−0.625234	+	0.162798i
$92$	−8.75987	−	3.09506i	−0.913280	−	0.322682i
$93$	−0.175374	+	0.572655i	−0.0181854	+	0.0593815i
$94$	−12.5932	+	1.07184i	−1.29889	+	0.110552i
$95$	9.34566	+	8.95709i	0.958845	+	0.918978i
$96$	−6.27951	−	1.63506i	−0.640900	−	0.166877i
$97$	3.14412	−	5.10638i	0.319238	−	0.518475i	−0.651490	−	0.758657i	$-0.725856\pi$
$97$	3.14412	−	5.10638i	0.319238	−	0.518475i	0.970728	+	0.240182i	$0.0772072\pi$
$98$	−9.41217	+	0.801093i	−0.950772	+	0.0809227i
$99$	−2.37155	+	2.27294i	−0.238349	+	0.228439i
$100$	0.516932	+	2.39857i	0.0516932	+	0.239857i
$101$	−8.96945	−	10.1913i	−0.892494	−	1.01407i	−0.999803	−	0.0198440i	$-0.993683\pi$
$101$	−8.96945	−	10.1913i	−0.892494	−	1.01407i	0.107310	−	0.994226i	$-0.465776\pi$
$102$	−13.3348	−	1.13496i	−1.32034	−	0.112377i
$103$	2.53042	−	6.29720i	0.249330	−	0.620481i	−0.749823	−	0.661639i	$-0.769861\pi$
$103$	2.53042	−	6.29720i	0.249330	−	0.620481i	0.999153	+	0.0411574i	$0.0131045\pi$
$104$	5.47804	+	0.939304i	0.537166	+	0.0921064i
$105$	0.149985	+	3.53077i	0.0146371	+	0.344568i
$106$	−0.179365	+	0.446367i	−0.0174215	+	0.0433550i
$107$	7.76627	+	15.4035i	0.750793	+	1.48911i	0.868301	+	0.496038i	$0.165212\pi$
$107$	7.76627	+	15.4035i	0.750793	+	1.48911i	−0.117508	+	0.993072i	$0.537491\pi$
$108$	−0.599924	+	1.18988i	−0.0577277	+	0.114496i
$109$	−2.78214	−	12.9092i	−0.266480	−	1.23647i	−0.890470	−	0.455041i	$-0.849624\pi$
$109$	−2.78214	−	12.9092i	−0.266480	−	1.23647i	0.623990	−	0.781432i	$-0.285511\pi$
$110$	−10.3626	+	11.7742i	−0.988031	+	1.12262i
$111$	9.69999	+	3.42722i	0.920682	+	0.325298i
$112$	−6.22878	−	2.20077i	−0.588564	−	0.207953i
$113$	6.56056	−	7.45424i	0.617165	−	0.701236i	−0.355176	−	0.934799i	$-0.615579\pi$
$113$	6.56056	−	7.45424i	0.617165	−	0.701236i	0.972342	+	0.233563i	$0.0750386\pi$
$114$	1.90345	+	8.83202i	0.178274	+	0.827195i
$115$	8.20983	−	16.2832i	0.765570	−	1.51842i
$116$	−2.26932	−	4.50093i	−0.210701	−	0.417901i
$117$	1.70082	−	4.23265i	0.157241	−	0.391309i
$118$	−0.718071	−	16.9040i	−0.0661038	−	1.55614i
$119$	−9.76255	−	1.67396i	−0.894931	−	0.153451i
$120$	1.18826	−	2.95710i	0.108473	−	0.269945i
$121$	0.208739	+	0.0177663i	0.0189763	+	0.00161512i
$122$	−13.2487	−	15.0535i	−1.19948	−	1.36288i
$123$	1.76564	+	8.19262i	0.159203	+	0.738703i
$124$	−0.576178	+	0.552222i	−0.0517423	+	0.0495910i
$125$	8.23209	−	0.700654i	0.736301	−	0.0626684i
$126$	−1.29320	+	2.10029i	−0.115208	+	0.187109i
$127$	−3.42571	−	0.891987i	−0.303983	−	0.0791510i	0.0968593	−	0.995298i	$-0.469120\pi$
$127$	−3.42571	−	0.891987i	−0.303983	−	0.0791510i	−0.400842	+	0.916147i	$0.631282\pi$
$128$	6.64537	+	6.36907i	0.587373	+	0.562952i
$129$	−0.190896	+	0.0162476i	−0.0168074	+	0.00143052i
$130$	6.37793	−	20.8261i	0.559381	−	1.82657i
$131$	1.83261	+	0.647501i	0.160116	+	0.0565724i	0.411995	−	0.911186i	$-0.364832\pi$
$131$	1.83261	+	0.647501i	0.160116	+	0.0565724i	−0.251879	+	0.967759i	$0.581048\pi$
$132$	−4.23607	+	1.10299i	−0.368703	+	0.0960027i
$133$	0.849349	+	6.63269i	0.0736479	+	0.575127i
$134$	9.97213	−	16.1958i	0.861461	−	1.39910i
$135$	−2.16704	−	1.46466i	−0.186509	−	0.126058i
$136$	7.40053	+	5.00188i	0.634590	+	0.428908i
$137$	−7.85540	−	7.52879i	−0.671132	−	0.643228i	0.277087	−	0.960845i	$-0.410631\pi$
$137$	−7.85540	−	7.52879i	−0.671132	−	0.643228i	−0.948219	+	0.317617i	$0.897118\pi$
$138$	11.1113	−	6.20716i	0.945859	−	0.528388i
$139$	−6.36276	+	1.09101i	−0.539683	+	0.0925379i	−0.432385	−	0.901689i	$-0.642328\pi$
$139$	−6.36276	+	1.09101i	−0.539683	+	0.0925379i	−0.107298	+	0.994227i	$0.534220\pi$
$140$	−2.12010	+	4.20497i	−0.179181	+	0.355385i
$141$	4.11683	−	5.56633i	0.346700	−	0.468769i
$142$	−0.0756213	−	1.78018i	−0.00634600	−	0.149390i
$143$	14.1284	−	4.99188i	1.18147	−	0.417442i
$144$	4.05092	−	2.73794i	0.337577	−	0.228162i
$145$	9.32877	−	3.29607i	0.774712	−	0.273723i
$146$	−26.7841	−	4.59260i	−2.21667	−	0.380086i
$147$	3.07693	−	4.16028i	0.253781	−	0.343134i
$148$	9.05713	+	10.2909i	0.744491	+	0.845906i
$149$	2.02555	+	5.04076i	0.165939	+	0.412955i	0.987594	−	0.157030i	$-0.0501920\pi$
$149$	2.02555	+	5.04076i	0.165939	+	0.412955i	−0.821655	+	0.569986i	$0.806949\pi$
$150$	−2.93451	−	1.63931i	−0.239601	−	0.133849i
$151$	−10.5386	+	2.74403i	−0.857617	+	0.223306i	−0.654699	−	0.755889i	$-0.727205\pi$
$151$	−10.5386	+	2.74403i	−0.857617	+	0.223306i	−0.202918	+	0.979196i	$0.565043\pi$
$152$	1.76578	−	5.76587i	0.143223	−	0.467674i
$153$	5.29267	−	5.07261i	0.427887	−	0.410096i
$154$	−7.98563	+	1.36927i	−0.643500	+	0.110339i
$155$	−0.931489	−	1.25946i	−0.0748190	−	0.101162i
$156$	4.72936	−	3.81869i	0.378652	−	0.305740i
$157$	−19.6444	−	1.67198i	−1.56779	−	0.133439i	−0.731546	−	0.681792i	$-0.761201\pi$
$157$	−19.6444	−	1.67198i	−1.56779	−	0.133439i	−0.836247	+	0.548353i	$0.815255\pi$
$158$	1.80371	−	2.43877i	0.143495	−	0.194018i
$159$	−0.118636	−	0.235300i	−0.00940843	−	0.0186605i
$160$	13.2050	−	10.6623i	1.04395	−	0.842930i
$161$	8.58370	−	3.88008i	0.676490	−	0.305793i
$162$	−0.680661	−	1.69389i	−0.0534778	−	0.133085i
$163$	−8.73191	+	9.92138i	−0.683936	+	0.777102i	−0.984258	−	0.176736i	$-0.943446\pi$
$163$	−8.73191	+	9.92138i	−0.683936	+	0.777102i	0.300323	+	0.953838i	$0.402906\pi$
$164$	−3.27019	+	10.6783i	−0.255359	+	0.833835i
$165$	−1.09133	−	8.52233i	−0.0849597	−	0.663462i
$166$	−1.24699	+	9.73796i	−0.0967855	+	0.755812i
$167$	13.1363	+	10.6068i	1.01652	+	0.820782i	0.983906	−	0.178686i	$-0.0571846\pi$
$167$	13.1363	+	10.6068i	1.01652	+	0.820782i	0.0326134	+	0.999468i	$0.489617\pi$
$168$	1.43719	−	0.802862i	0.110882	−	0.0619422i
$169$	−5.63712	+	5.40274i	−0.433624	+	0.415595i
$170$	23.1265	−	26.2768i	1.77372	−	2.01534i
$171$	−4.32067	−	2.41367i	−0.330410	−	0.184578i
$172$	−0.232636	−	0.105158i	−0.0177383	−	0.00801824i
$173$	2.31297	−	18.0623i	0.175852	−	1.37325i	−0.627902	−	0.778293i	$-0.716086\pi$
$173$	2.31297	−	18.0623i	0.175852	−	1.37325i	0.803754	−	0.594962i	$-0.202833\pi$
$174$	6.68258	+	1.74001i	0.506605	+	0.131910i
$175$	−2.06117	−	1.39311i	−0.155810	−	0.105309i
$176$	15.5429	+	4.04706i	1.17159	+	0.305059i
$177$	7.21092	+	5.82241i	0.542006	+	0.437639i
$178$	1.86081	−	8.63419i	0.139474	−	0.647160i
$179$	−6.57989	−	8.89659i	−0.491804	−	0.664963i	0.486128	−	0.873888i	$-0.338409\pi$
$179$	−6.57989	−	8.89659i	−0.491804	−	0.664963i	−0.977932	+	0.208925i	$0.933004\pi$
$180$	−1.56915	−	3.11223i	−0.116958	−	0.231972i
$181$	4.61974	+	0.792133i	0.343382	+	0.0588788i	0.338108	−	0.941107i	$-0.390213\pi$
$181$	4.61974	+	0.792133i	0.343382	+	0.0588788i	0.00527423	+	0.999986i	$0.498321\pi$
$182$	9.32169	−	6.30036i	0.690969	−	0.467014i
$183$	10.9849			0.812029
$184$	−8.49487			−0.626250
$185$	−22.2937	+	15.0679i	−1.63907	+	1.10782i
$186$	−0.0464019	−	1.09234i	−0.00340235	−	0.0800940i
$187$	23.9948	+	2.04226i	1.75467	+	0.149345i
$188$	8.40675	−	3.80009i	0.613125	−	0.277150i
$189$	−0.395636	−	1.29189i	−0.0287783	−	0.0939711i
$190$	−21.5335	−	9.73378i	−1.56221	−	0.706162i
$191$	−2.82838	−	22.0872i	−0.204655	−	1.59818i	−0.689970	−	0.723838i	$-0.742376\pi$
$191$	−2.82838	−	22.0872i	−0.204655	−	1.59818i	0.485315	−	0.874339i	$-0.338705\pi$
$192$	2.05941	−	0.175282i	0.148625	−	0.0126499i
$193$	16.2756	−	9.09210i	1.17154	−	0.654464i	0.224157	−	0.974553i	$-0.428037\pi$
$193$	16.2756	−	9.09210i	1.17154	−	0.654464i	0.947387	+	0.320090i	$0.103713\pi$
$194$	−2.30635	+	10.7015i	−0.165586	+	0.768322i
$195$	6.25564	+	10.1598i	0.447976	+	0.727559i
$196$	6.28322	−	2.84019i	0.448801	−	0.202871i
$197$	−13.8806	−	15.7714i	−0.988949	−	1.12366i	−0.992323	−	0.123670i	$-0.960534\pi$
$197$	−13.8806	−	15.7714i	−0.988949	−	1.12366i	0.00337488	−	0.999994i	$-0.498926\pi$
$198$	2.69972	−	5.35458i	0.191861	−	0.380533i
$199$	−10.5871	−	14.3147i	−0.750500	−	1.01474i	−0.998937	−	0.0460955i	$-0.985322\pi$
$199$	−10.5871	−	14.3147i	−0.750500	−	1.01474i	0.248437	−	0.968648i	$-0.420083\pi$
$200$	1.17628	+	1.91040i	0.0831758	+	0.135086i
$201$	3.05083	+	9.96201i	0.215189	+	0.702666i
$202$	21.6366	+	12.0869i	1.52234	+	0.850432i
$203$	4.81889	+	1.70262i	0.338220	+	0.119501i
$204$	9.45380	−	2.46158i	0.661898	−	0.172345i
$205$	−19.9746	−	9.02909i	−1.39509	−	0.630619i
$206$	−0.525809	+	12.3780i	−0.0366348	+	0.862413i
$207$	−1.46885	+	6.81549i	−0.102092	+	0.473709i
$208$	−21.9826	+	3.76930i	−1.52422	+	0.261354i
$209$	−3.42510	−	15.8925i	−0.236919	−	1.09931i
$210$	−2.40542	−	5.98613i	−0.165990	−	0.413082i
$211$	−4.88842	−	15.9624i	−0.336533	−	1.09889i	−0.950802	−	0.309798i	$-0.899738\pi$
$211$	−4.88842	−	15.9624i	−0.336533	−	1.09889i	0.614270	−	0.789096i	$-0.289451\pi$
$212$	0.0149033	−	0.350834i	0.00102356	−	0.0240954i
$213$	0.759394	+	0.613168i	0.0520328	+	0.0420135i
$214$	−22.7354	−	21.7901i	−1.55416	−	1.48954i
$215$	0.262735	−	0.426709i	0.0179184	−	0.0291013i
$216$	−0.154763	+	1.20856i	−0.0105303	+	0.0822323i
$217$	0.0343430	−	0.808461i	0.00233136	−	0.0548819i
$218$	12.6396	+	20.5279i	0.856059	+	1.39033i
$219$	11.5819	−	9.35174i	0.782633	−	0.631932i
$220$	4.26893	−	10.6236i	0.287811	−	0.716245i
$221$	−31.5308	+	11.1406i	−2.12099	+	0.749395i
$222$	−18.7804			−1.26046
$223$	12.7615	−	7.75520i	0.854576	−	0.519327i
$223$	12.7615	−	7.75520i	0.854576	−	0.519327i
$224$	8.76722			0.585785
$225$	1.73612	−	0.613411i	0.115741	−	0.0408940i
$226$	−6.75902	+	16.8205i	−0.449603	+	1.11888i
$227$	11.1743	−	9.02264i	0.741667	−	0.598854i	−0.181438	−	0.983402i	$-0.558075\pi$
$227$	11.1743	−	9.02264i	0.741667	−	0.598854i	0.923105	+	0.384548i	$0.125643\pi$
$228$	−3.45782	−	5.61586i	−0.229000	−	0.371919i
$229$	0.0360710	−	0.849140i	0.00238364	−	0.0561127i	−0.997513	−	0.0704808i	$-0.977547\pi$
$229$	0.0360710	−	0.849140i	0.00238364	−	0.0561127i	0.999897	+	0.0143681i	$0.00457366\pi$
$230$	−4.22842	+	33.0204i	−0.278814	+	2.17730i
$231$	2.32701	−	3.77930i	0.153106	−	0.248660i
$232$	−3.32745	−	3.18911i	−0.218458	−	0.209375i
$233$	−1.09160	−	0.881406i	−0.0715131	−	0.0577428i	0.591800	−	0.806085i	$-0.298418\pi$
$233$	−1.09160	−	0.881406i	−0.0715131	−	0.0577428i	−0.663313	+	0.748342i	$0.730850\pi$
$234$	−0.353422	+	8.31982i	−0.0231039	+	0.543884i
$235$	5.30259	+	17.3148i	0.345903	+	1.12949i
$236$	4.60489	+	11.4597i	0.299753	+	0.745964i
$237$	0.350065	+	1.62431i	0.0227392	+	0.105510i
$238$	17.8218	−	3.05586i	1.15522	−	0.198082i
$239$	3.20310	−	14.8625i	0.207192	−	0.961373i	−0.747612	−	0.664136i	$-0.768800\pi$
$239$	3.20310	−	14.8625i	0.207192	−	0.961373i	0.954804	−	0.297237i	$-0.0960651\pi$
$240$	−0.542766	+	12.7771i	−0.0350354	+	0.824761i
$241$	25.3049	+	11.4385i	1.63003	+	0.736820i	0.999234	−	0.0391278i	$-0.0124579\pi$
$241$	25.3049	+	11.4385i	1.63003	+	0.736820i	0.630797	+	0.775948i	$0.282728\pi$
$242$	−0.370097	+	0.0963657i	−0.0237907	+	0.00619463i
$243$	0.942877	+	0.333140i	0.0604856	+	0.0213709i
$244$	12.7793	+	7.13892i	0.818108	+	0.457022i
$245$	3.96317	+	12.9411i	0.253197	+	0.826776i
$246$	−8.02151	−	13.0278i	−0.511433	−	0.830620i
$247$	13.4244	+	18.1510i	0.854175	+	1.15492i
$248$	−0.328526	+	0.651592i	−0.0208614	+	0.0413761i
$249$	−3.55303	−	4.03702i	−0.225164	−	0.255836i
$250$	−13.7434	+	6.21240i	−0.869208	+	0.392907i
$251$	6.00694	+	9.75589i	0.379154	+	0.615786i	0.983494	−	0.180941i	$-0.0579143\pi$
$251$	6.00694	+	9.75589i	0.379154	+	0.615786i	−0.604339	+	0.796727i	$0.706563\pi$
$252$	0.379315	−	1.76003i	0.0238946	−	0.110871i
$253$	−19.9939	+	11.1693i	−1.25701	+	0.702206i
$254$	6.43898	−	0.548038i	0.404018	−	0.0343870i
$255$	2.43555	+	19.0196i	0.152520	+	1.19105i
$256$	−19.0785	−	8.62403i	−1.19241	−	0.539002i
$257$	4.50252	+	14.7023i	0.280859	+	0.917102i	0.979468	+	0.201598i	$0.0646135\pi$
$257$	4.50252	+	14.7023i	0.280859	+	0.917102i	−0.698609	+	0.715504i	$0.746197\pi$
$258$	0.318698	−	0.144061i	0.0198413	−	0.00896883i
$259$	−13.8497	−	1.17878i	−0.860578	−	0.0732460i
$260$	0.674777	+	15.8848i	0.0418479	+	0.985132i
$261$	−3.13399	+	2.11821i	−0.193989	+	0.131114i
$262$	−3.54816			−0.219206
$263$	−8.39161			−0.517449			−0.258724	−	0.965951i	$-0.583302\pi$
$263$	−8.39161			−0.517449			−0.258724	+	0.965951i	$0.583302\pi$
$264$	−3.31604	+	2.24125i	−0.204088	+	0.137939i
$265$	0.679335	+	0.116484i	0.0417312	+	0.00715553i
$266$	−5.49566	−	10.9000i	−0.336960	−	0.668321i
$267$	2.87701	+	3.88997i	0.176070	+	0.238062i
$268$	−2.92497	+	13.5719i	−0.178671	+	0.829037i
$269$	5.07541	+	4.09811i	0.309453	+	0.249866i	0.770399	−	0.637562i	$-0.220057\pi$
$269$	5.07541	+	4.09811i	0.309453	+	0.249866i	−0.460945	+	0.887428i	$0.652490\pi$
$270$	4.62076	+	1.20315i	0.281211	+	0.0732216i
$271$	−19.2442	−	13.0068i	−1.16900	−	0.790107i	−0.187633	−	0.982239i	$-0.560082\pi$
$271$	−19.2442	−	13.0068i	−1.16900	−	0.790107i	−0.981369	+	0.192132i	$0.938460\pi$
$272$	−34.6877	−	9.03197i	−2.10325	−	0.547644i
$273$	−0.782839	+	6.11330i	−0.0473796	+	0.369994i
$274$	18.0998	+	8.18163i	1.09345	+	0.494270i
$275$	5.28040	+	2.94981i	0.318420	+	0.177880i
$276$	−6.13805	+	6.97417i	−0.369467	+	0.419796i
$277$	23.2565	−	22.2895i	1.39735	−	1.33925i	0.524365	−	0.851494i	$-0.324303\pi$
$277$	23.2565	−	22.2895i	1.39735	−	1.33925i	0.872981	−	0.487754i	$-0.162184\pi$
$278$	10.2884	−	5.74745i	0.617058	−	0.344709i
$279$	0.465971	+	0.376245i	0.0278969	+	0.0225252i
$280$	−0.546924	+	4.27101i	−0.0326849	+	0.255241i
$281$	−1.43459	−	11.2029i	−0.0855805	−	0.668310i	−0.976710	−	0.214562i	$-0.931168\pi$
$281$	−1.43459	−	11.2029i	−0.0855805	−	0.668310i	0.891130	−	0.453748i	$-0.149913\pi$
$282$	−3.70091	+	12.0847i	−0.220386	+	0.719635i
$283$	−1.03421	+	1.17509i	−0.0614776	+	0.0698521i	−0.780598	−	0.625033i	$-0.785085\pi$
$283$	−1.03421	+	1.17509i	−0.0614776	+	0.0698521i	0.719121	+	0.694885i	$0.244545\pi$
$284$	0.484949	+	1.20684i	0.0287764	+	0.0716129i
$285$	11.7958	−	5.33203i	0.698722	−	0.315842i
$286$	−21.2827	+	17.1845i	−1.25847	+	1.01614i
$287$	−5.09779	−	10.1109i	−0.300913	−	0.596825i
$288$	−3.85851	+	5.21705i	−0.227365	+	0.307418i
$289$	−36.6114	−	3.11609i	−2.15361	−	0.183299i
$290$	−14.0526	+	11.3467i	−0.825199	+	0.666302i
$291$	−3.56585	−	4.82135i	−0.209034	−	0.282632i
$292$	19.5513	−	3.35240i	1.14415	−	0.196185i
$293$	4.31679	−	4.13731i	0.252190	−	0.241704i	−0.555209	−	0.831711i	$-0.687362\pi$
$293$	4.31679	−	4.13731i	0.252190	−	0.241704i	0.807398	+	0.590007i	$0.200875\pi$
$294$	−2.76606	+	9.03214i	−0.161320	+	0.526765i
$295$	−23.4593	+	6.10834i	−1.36586	+	0.355641i
$296$	10.9431	+	6.11315i	0.636052	+	0.355320i
$297$	1.22479	+	3.04801i	0.0710697	+	0.176864i
$298$	−6.55205	−	7.44457i	−0.379550	−	0.431252i
$299$	18.9113	−	25.5698i	1.09367	−	1.47874i
$300$	2.41835	+	0.414668i	0.139624	+	0.0239409i
$301$	0.244068	−	0.0862346i	0.0140678	−	0.00497048i
$302$	16.4707	−	11.1323i	0.947785	−	0.640591i
$303$	−12.8007	+	4.52277i	−0.735380	+	0.259826i
$304$	1.02701	+	24.1766i	0.0589029	+	1.38662i
$305$	−17.0850	+	23.1005i	−0.978286	+	1.32273i
$306$	−6.02507	+	11.9500i	−0.344430	+	0.683137i
$307$	16.5230	−	2.83315i	0.943015	−	0.161696i	0.323100	−	0.946365i	$-0.395275\pi$
$307$	16.5230	−	2.83315i	0.943015	−	0.161696i	0.619915	+	0.784669i	$0.287167\pi$
$308$	5.16322	−	2.88435i	0.294202	−	0.164351i
$309$	−4.89962	−	4.69590i	−0.278729	−	0.267141i
$310$	2.36927	+	1.60135i	0.134566	+	0.0909505i
$311$	24.7053	+	16.6979i	1.40091	+	0.946851i	0.999521	+	0.0309439i	$0.00985131\pi$
$311$	24.7053	+	16.6979i	1.40091	+	0.946851i	0.401390	+	0.915907i	$0.368527\pi$
$312$	2.91409	−	4.73279i	0.164978	−	0.267941i
$313$	0.583636	+	4.55770i	0.0329891	+	0.257616i	0.999996	+	0.00286588i	$0.000912240\pi$
$313$	0.583636	+	4.55770i	0.0329891	+	0.257616i	−0.967007	+	0.254750i	$0.918007\pi$
$314$	34.8298	−	9.06896i	1.96556	−	0.511791i
$315$	3.33209	+	1.17730i	0.187742	+	0.0663334i
$316$	−0.648364	+	2.11713i	−0.0364733	+	0.119098i
$317$	10.4695	−	0.891088i	0.588027	−	0.0500485i	0.212984	−	0.977056i	$-0.431682\pi$
$317$	10.4695	−	0.891088i	0.588027	−	0.0500485i	0.375043	+	0.927007i	$0.377628\pi$
$318$	0.347301	+	0.332861i	0.0194757	+	0.0186659i
$319$	−12.0248	−	3.13100i	−0.673257	−	0.175303i
$320$	−2.83443	+	4.60341i	−0.158449	+	0.257338i
$321$	17.1884	−	1.46295i	0.959364	−	0.0816539i
$322$	−12.4150	+	11.8988i	−0.691861	+	0.663095i
$323$	7.64391	+	35.4679i	0.425319	+	1.97349i
$324$	0.880389	+	1.00032i	0.0489105	+	0.0555731i
$325$	−8.36900	−	0.712307i	−0.464229	−	0.0395117i
$326$	8.99606	−	22.3875i	0.498245	−	1.23993i
$327$	−13.0156	−	2.23175i	−0.719765	−	0.123416i
$328$	0.433381	+	10.2021i	0.0239295	+	0.563319i
$329$	−3.48777	+	8.67964i	−0.192287	+	0.478524i
$330$	7.06136	+	14.0054i	0.388715	+	0.770970i
$331$	10.0043	−	19.8423i	0.549883	−	1.09063i	−0.432129	−	0.901812i	$-0.642237\pi$
$331$	10.0043	−	19.8423i	0.549883	−	1.09063i	0.982012	−	0.188817i	$-0.0604653\pi$
$332$	−1.50980	−	7.00550i	−0.0828610	−	0.384477i
$333$	6.79679	−	7.72265i	0.372462	−	0.423199i
$334$	−29.0615	−	10.2681i	−1.59018	−	0.561845i
$335$	−25.6944	−	9.07839i	−1.40383	−	0.496006i
$336$	−4.36451	+	4.95904i	−0.238103	+	0.270538i
$337$	0.948904	+	4.40293i	0.0516901	+	0.239843i	0.996017	−	0.0891666i	$-0.0284203\pi$
$337$	0.948904	+	4.40293i	0.0516901	+	0.239843i	−0.944327	+	0.329009i	$0.893285\pi$
$338$	6.41718	−	12.7277i	0.349049	−	0.692297i
$339$	−4.47056	−	8.86683i	−0.242808	−	0.481580i
$340$	−9.52712	+	23.7092i	−0.516681	+	1.28581i
$341$	0.0834964	+	1.96557i	0.00452158	+	0.106442i
$342$	8.90485	+	1.52689i	0.481519	+	0.0825648i
$343$	−6.13316	+	15.2630i	−0.331159	+	0.824122i
$344$	−0.232593	−	0.0197966i	−0.0125406	−	0.00106736i
$345$	−12.0479	−	13.6891i	−0.648639	−	0.736997i
$346$	7.00353	+	32.4965i	0.376512	+	1.74702i
$347$	−14.7258	+	14.1136i	−0.790525	+	0.757657i	−0.974286	−	0.225314i	$-0.927659\pi$
$347$	−14.7258	+	14.1136i	−0.790525	+	0.757657i	0.183761	+	0.982971i	$0.441173\pi$
$348$	−5.02249	+	0.427477i	−0.269234	+	0.0229152i
$349$	10.9731	−	17.8215i	0.587377	−	0.953961i	−0.411713	−	0.911313i	$-0.635069\pi$
$349$	10.9731	−	17.8215i	0.587377	−	0.953961i	0.999090	−	0.0426474i	$-0.0135792\pi$
$350$	4.39502	+	1.14437i	0.234924	+	0.0611694i
$351$	−3.29327	−	3.15634i	−0.175782	−	0.168473i
$352$	−21.2385	+	1.80766i	−1.13202	+	0.0963488i
$353$	−5.94809	+	19.4225i	−0.316585	+	1.03376i	0.646127	+	0.763230i	$0.276387\pi$
$353$	−5.94809	+	19.4225i	−0.316585	+	1.03376i	−0.962712	+	0.270528i	$0.912802\pi$
$354$	−15.9527	−	5.63646i	−0.847878	−	0.299574i
$355$	−2.47054	+	0.643279i	−0.131123	+	0.0341417i
$356$	0.818923	+	6.39509i	0.0434028	+	0.338939i
$357$	−5.19328	+	8.43441i	−0.274857	+	0.446397i
$358$	16.7362	+	11.3117i	0.884534	+	0.597840i
$359$	−23.1439	−	15.6426i	−1.22149	−	0.825583i	−0.232361	−	0.972630i	$-0.574645\pi$
$359$	−23.1439	−	15.6426i	−1.22149	−	0.825583i	−0.989130	+	0.147046i	$0.953023\pi$
$360$	−2.30081	−	2.20515i	−0.121263	−	0.116222i
$361$	4.79635	−	2.67940i	0.252440	−	0.141021i
$362$	−8.43347	+	1.44606i	−0.443253	+	0.0760034i
$363$	0.0943149	−	0.187062i	0.00495025	−	0.00981823i
$364$	−4.88364	+	6.60312i	−0.255972	+	0.346098i
$365$	1.65249	+	38.9008i	0.0864951	+	2.03616i
$366$	−18.9078	+	6.68056i	−0.988328	+	0.349198i
$367$	−11.5244	+	7.78916i	−0.601571	+	0.406591i	−0.822554	−	0.568687i	$-0.807452\pi$
$367$	−11.5244	+	7.78916i	−0.601571	+	0.406591i	0.220983	+	0.975278i	$0.429073\pi$
$368$	32.1415	−	11.3563i	1.67549	−	0.591990i
$369$	8.26017	+	1.41635i	0.430007	+	0.0737322i
$370$	29.2095	−	39.4938i	1.51853	−	2.05318i
$371$	0.235226	+	0.267269i	0.0122123	+	0.0138759i
$372$	0.297569	+	0.740529i	0.0154282	+	0.0383946i
$373$	11.5036	+	6.42631i	0.595635	+	0.332742i	0.756257	−	0.654274i	$-0.227026\pi$
$373$	11.5036	+	6.42631i	0.595635	+	0.332742i	−0.160622	+	0.987016i	$0.551350\pi$
$374$	−42.5431	+	11.0774i	−2.19985	+	0.572797i
$375$	2.41926	−	7.89971i	0.124930	−	0.407939i
$376$	6.09012	−	5.83691i	0.314074	−	0.301016i
$377$	17.0069	−	2.91612i	0.875898	−	0.150188i
$378$	1.46666	+	1.98306i	0.0754369	+	0.101997i
$379$	8.16898	−	6.59599i	0.419612	−	0.338813i	−0.395142	−	0.918620i	$-0.629305\pi$
$379$	8.16898	−	6.59599i	0.419612	−	0.338813i	0.814754	+	0.579807i	$0.196872\pi$
$380$	17.1877	+	1.46289i	0.881712	+	0.0750448i
$381$	−2.10496	+	2.84610i	−0.107841	+	0.145810i
$382$	18.3009	+	36.2976i	0.936354	+	1.85715i
$383$	13.6468	−	11.0190i	0.697319	−	0.563046i	−0.212950	−	0.977063i	$-0.568307\pi$
$383$	13.6468	−	11.0190i	0.697319	−	0.563046i	0.910269	+	0.414017i	$0.135875\pi$
$384$	8.38756	−	3.79142i	0.428026	−	0.193480i
$385$	4.32836	+	10.7715i	0.220594	+	0.548968i
$386$	−22.4850	+	25.5479i	−1.14446	+	1.30035i
$387$	−0.0561007	+	0.183188i	−0.00285176	+	0.00931197i
$388$	−1.01500	−	7.92627i	−0.0515287	−	0.402395i
$389$	−1.95983	+	15.3046i	−0.0993676	+	0.775976i	0.863186	+	0.504885i	$0.168465\pi$
$389$	−1.95983	+	15.3046i	−0.0993676	+	0.775976i	−0.962554	+	0.271090i	$0.912616\pi$
$390$	−16.9463	−	13.6832i	−0.858108	−	0.692874i
$391$	44.6212	−	24.9269i	2.25659	−	1.26061i
$392$	4.55177	−	4.36251i	0.229899	−	0.220340i
$393$	1.28411	−	1.45903i	0.0647747	−	0.0735984i
$394$	33.4834	+	18.7049i	1.68687	+	0.942341i
$395$	−3.96026	−	1.79015i	−0.199262	−	0.0900723i
$396$	−0.555997	+	4.34186i	−0.0279399	+	0.218187i
$397$	−27.3379	−	7.11823i	−1.37205	−	0.357254i	−0.508302	−	0.861179i	$-0.669727\pi$
$397$	−27.3379	−	7.11823i	−1.37205	−	0.357254i	−0.863747	+	0.503925i	$0.831889\pi$
$398$	26.9287	+	18.2006i	1.34981	+	0.912314i
$399$	6.47108	+	1.68494i	0.323959	+	0.0843525i
$400$	−7.00455	−	5.65578i	−0.350227	−	0.282789i
$401$	−5.72067	+	26.5440i	−0.285676	+	1.32554i	0.575735	+	0.817636i	$0.304716\pi$
$401$	−5.72067	+	26.5440i	−0.285676	+	1.32554i	−0.861412	+	0.507907i	$0.830419\pi$
$402$	−11.3097	−	15.2917i	−0.564077	−	0.762682i
$403$	−1.22994	−	2.43944i	−0.0612678	−	0.121517i
$404$	−17.8309	−	3.05741i	−0.887119	−	0.152112i
$405$	−2.16704	+	1.46466i	−0.107681	+	0.0727797i
$406$	−9.32997			−0.463039
$407$	33.7938			1.67510
$408$	7.40053	−	5.00188i	0.366381	−	0.247630i
$409$	0.0278014	+	0.654466i	0.00137469	+	0.0323613i	0.999655	−	0.0262550i	$-0.00835819\pi$
$409$	0.0278014	+	0.654466i	0.00137469	+	0.0323613i	−0.998281	+	0.0586163i	$0.981331\pi$
$410$	39.8724	+	3.39364i	1.96916	+	0.167600i
$411$	−9.91482	+	4.48178i	−0.489062	+	0.221070i
$412$	−2.64815	−	8.64712i	−0.130465	−	0.426013i
$413$	−11.4106	−	5.15793i	−0.561480	−	0.253805i
$414$	−1.61662	−	12.6245i	−0.0794528	−	0.620458i
$415$	14.0156	−	1.19291i	0.688001	−	0.0585575i
$416$	25.8409	−	14.4356i	1.26696	−	0.707764i
$417$	−1.36007	+	6.31073i	−0.0666027	+	0.309038i
$418$	15.5606	+	25.2720i	0.761093	+	1.23609i
$419$	0.588185	−	0.265876i	0.0287347	−	0.0129889i	−0.397483	−	0.917610i	$-0.630116\pi$
$419$	0.588185	−	0.265876i	0.0287347	−	0.0129889i	0.426217	+	0.904621i	$0.359846\pi$
$420$	3.11125	+	3.53507i	0.151814	+	0.172494i
$421$	4.56206	−	9.04831i	0.222341	−	0.440987i	−0.754103	−	0.656756i	$-0.771928\pi$
$421$	4.56206	−	9.04831i	0.222341	−	0.440987i	0.976445	+	0.215768i	$0.0692256\pi$
$422$	18.1218	+	24.5023i	0.882156	+	1.19275i
$423$	−3.62994	−	5.89541i	−0.176494	−	0.286644i
$424$	−0.0940184	−	0.307002i	−0.00456594	−	0.0149093i
$425$	−11.7845	−	6.58320i	−0.571631	−	0.319332i
$426$	−1.68001	−	0.593585i	−0.0813967	−	0.0287593i
$427$	−14.3630	+	3.73983i	−0.695073	+	0.180983i
$428$	20.9468	+	9.46854i	1.01250	+	0.457679i
$429$	0.635953	−	14.9708i	0.0307041	−	0.722798i
$430$	−0.192727	+	0.894258i	−0.00929414	+	0.0431250i
$431$	−31.1578	+	5.34255i	−1.50082	+	0.257342i	−0.859978	−	0.510331i	$-0.829523\pi$
$431$	−31.1578	+	5.34255i	−1.50082	+	0.257342i	−0.640842	+	0.767672i	$0.721415\pi$
$432$	−1.03010	−	4.77966i	−0.0495605	−	0.229962i
$433$	−2.85908	−	7.11508i	−0.137398	−	0.341929i	0.843304	−	0.537437i	$-0.180608\pi$
$433$	−2.85908	−	7.11508i	−0.137398	−	0.341929i	−0.980702	+	0.195508i	$0.937364\pi$
$434$	0.432558	+	1.41245i	0.0207635	+	0.0677998i
$435$	0.419911	−	9.88503i	0.0201332	−	0.473951i
$436$	−13.6913	−	11.0549i	−0.655692	−	0.529434i
$437$	−24.9113	−	23.8755i	−1.19167	−	1.14212i
$438$	−14.2481	+	23.1403i	−0.680798	+	1.10569i
$439$	3.75461	−	29.3203i	0.179198	−	1.39938i	−0.613465	−	0.789722i	$-0.710225\pi$
$439$	3.75461	−	29.3203i	0.179198	−	1.39938i	0.792663	−	0.609661i	$-0.208694\pi$
$440$	0.444303	−	10.4592i	0.0211813	−	0.498624i
$441$	−2.71303	−	4.40623i	−0.129192	−	0.209821i
$442$	47.4973	−	38.3514i	2.25922	−	1.82419i
$443$	−13.1660	+	32.7649i	−0.625537	+	1.55671i	0.192347	+	0.981327i	$0.438390\pi$
$443$	−13.1660	+	32.7649i	−0.625537	+	1.55671i	−0.817885	+	0.575382i	$0.804853\pi$
$444$	12.9258	−	4.56698i	0.613432	−	0.216739i
$445$	−12.6550			−0.599903
$446$	−17.2494	+	21.1097i	−0.816784	+	0.999571i
$447$	5.43251			0.256949
$448$	−2.63304	+	0.930312i	−0.124399	+	0.0439531i
$449$	−6.89768	+	17.1655i	−0.325522	+	0.810092i	0.672054	+	0.740502i	$0.265412\pi$
$449$	−6.89768	+	17.1655i	−0.325522	+	0.810092i	−0.997576	+	0.0695900i	$0.977831\pi$
$450$	−2.61525	+	2.11167i	−0.123284	+	0.0995449i
$451$	14.4340	+	23.4424i	0.679673	+	1.10386i
$452$	0.561600	−	13.2205i	0.0264155	−	0.621841i
$453$	−1.38322	+	10.8018i	−0.0649893	+	0.507511i
$454$	−13.7467	+	22.3260i	−0.645162	+	1.04781i
$455$	−11.6383	−	11.1544i	−0.545610	−	0.522925i
$456$	−4.69171	−	3.78829i	−0.219709	−	0.177403i
$457$	1.51028	−	35.5531i	0.0706478	−	1.66310i	−0.518499	−	0.855078i	$-0.673509\pi$
$457$	1.51028	−	35.5531i	0.0706478	−	1.66310i	0.589147	−	0.808026i	$-0.299464\pi$
$458$	0.454323	+	1.48352i	0.0212291	+	0.0693203i
$459$	−2.73342	−	6.80237i	−0.127585	−	0.317507i
$460$	−5.11957	−	23.7549i	−0.238701	−	1.10758i
$461$	6.16617	−	1.05730i	0.287187	−	0.0492432i	−0.0236042	−	0.999721i	$-0.507514\pi$
$461$	6.16617	−	1.05730i	0.287187	−	0.0492432i	0.310791	+	0.950478i	$0.399406\pi$
$462$	−1.70696	+	7.92032i	−0.0794149	+	0.368487i
$463$	0.703519	−	16.5614i	0.0326953	−	0.769673i	−0.905661	−	0.424003i	$-0.860625\pi$
$463$	0.703519	−	16.5614i	0.0326953	−	0.769673i	0.938356	−	0.345670i	$-0.112348\pi$
$464$	16.8532	+	7.61814i	0.782392	+	0.353663i
$465$	−1.51595	+	0.394722i	−0.0703004	+	0.0183048i
$466$	2.41495	+	0.853257i	0.111870	+	0.0395264i
$467$	9.45401	+	5.28133i	0.437479	+	0.244391i	0.690878	−	0.722971i	$-0.257224\pi$
$467$	9.45401	+	5.28133i	0.437479	+	0.244391i	−0.253399	+	0.967362i	$0.581548\pi$
$468$	−1.77995	−	5.81215i	−0.0822783	−	0.268667i
$469$	−7.38058	−	11.9868i	−0.340804	−	0.553500i
$470$	−19.6572	−	26.5783i	−0.906719	−	1.22596i
$471$	−8.87595	+	17.6044i	−0.408982	+	0.811168i
$472$	7.46070	+	8.47700i	0.343407	+	0.390186i
$473$	−0.573471	+	0.259225i	−0.0263682	+	0.0119192i
$474$	−1.59039	−	2.58295i	−0.0730488	−	0.118639i
$475$	−1.91989	+	8.90832i	−0.0880906	+	0.408742i
$476$	−11.5229	+	6.43710i	−0.528153	+	0.295044i
$477$	−0.262567	+	0.0223477i	−0.0120221	+	0.00102323i
$478$	3.52536	+	27.5300i	0.161246	+	1.25919i
$479$	8.73718	+	3.94945i	0.399212	+	0.180455i	0.601503	−	0.798870i	$-0.294569\pi$
$479$	8.73718	+	3.94945i	0.399212	+	0.180455i	−0.202292	+	0.979325i	$0.564839\pi$
$480$	−4.96987	−	16.2283i	−0.226842	−	0.740718i
$481$	−42.7622	+	19.3297i	−1.94979	+	0.881359i
$482$	−50.5125	−	4.29925i	−2.30078	−	0.195825i
$483$	−0.399793	−	9.41143i	−0.0181912	−	0.428235i
$484$	0.231289	−	0.156324i	0.0105131	−	0.00710565i
$485$	15.6850			0.712217
$486$	−1.82553			−0.0828077
$487$	13.2027	−	8.92348i	0.598272	−	0.404361i	−0.223066	−	0.974803i	$-0.571606\pi$
$487$	13.2027	−	8.92348i	0.598272	−	0.404361i	0.821338	+	0.570442i	$0.193228\pi$
$488$	13.1919	+	2.26197i	0.597168	+	0.102395i
$489$	5.95019	+	11.8015i	0.269077	+	0.533682i
$490$	−14.6918	−	19.8646i	−0.663709	−	0.897393i
$491$	−1.08226	+	5.02171i	−0.0488418	+	0.226627i	−0.995387	−	0.0959457i	$-0.969412\pi$
$491$	−1.08226	+	5.02171i	−0.0488418	+	0.226627i	0.946545	+	0.322572i	$0.104548\pi$
$492$	8.68896	+	7.01584i	0.391729	+	0.316299i
$493$	26.8361	+	6.98758i	1.20864	+	0.314705i
$494$	−34.1455	−	23.0783i	−1.53628	−	1.03834i
$495$	−8.31468	−	2.16498i	−0.373717	−	0.0973084i
$496$	0.371946	−	2.90458i	0.0167009	−	0.130419i
$497$	−1.20167	−	0.543190i	−0.0539024	−	0.0243654i
$498$	8.57080	+	4.78793i	0.384067	+	0.214552i
$499$	−6.27255	+	7.12700i	−0.280798	+	0.319048i	−0.873925	−	0.486060i	$-0.838434\pi$
$499$	−6.27255	+	7.12700i	−0.280798	+	0.319048i	0.593127	+	0.805109i	$0.297893\pi$
$500$	7.94832	−	7.61785i	0.355460	−	0.340680i
$501$	14.7399	−	8.23422i	0.658532	−	0.367878i
$502$	−16.2726	−	13.1392i	−0.726280	−	0.586430i
$503$	0.777077	−	6.06831i	0.0346481	−	0.270572i	−0.965307	−	0.261117i	$-0.915909\pi$
$503$	0.777077	−	6.06831i	0.0346481	−	0.270572i	0.999955	−	0.00945534i	$-0.00300977\pi$
$504$	−0.209102	−	1.63290i	−0.00931413	−	0.0727353i
$505$	10.3981	−	33.9532i	0.462708	−	1.51090i
$506$	27.6219	−	31.3846i	1.22794	−	1.39521i
$507$	2.91131	+	7.24507i	0.129296	+	0.321765i
$508$	−4.29843	+	1.94301i	−0.190712	+	0.0862072i
$509$	21.3500	−	17.2389i	0.946321	−	0.764101i	−0.0255359	−	0.999674i	$-0.508129\pi$
$509$	21.3500	−	17.2389i	0.946321	−	0.764101i	0.971857	+	0.235573i	$0.0756968\pi$
$510$	−15.7591	−	31.2563i	−0.697825	−	1.38405i
$511$	−11.9597	+	16.1706i	−0.529067	+	0.715346i
$512$	19.7406	+	1.68017i	0.872421	+	0.0742539i
$513$	−3.85061	+	3.10915i	−0.170009	+	0.137272i
$514$	−16.6912	−	22.5680i	−0.736219	−	0.995434i
$515$	17.4956	−	2.99992i	0.770947	−	0.132192i
$516$	−0.184315	+	0.176652i	−0.00811402	+	0.00777666i
$517$	6.65947	−	21.7455i	0.292883	−	0.956364i
$518$	24.5557	−	6.39380i	1.07891	−	0.280928i
$519$	−15.8974	−	8.88084i	−0.697820	−	0.389826i
$520$	5.42037	+	13.4891i	0.237699	+	0.591536i
$521$	−23.9609	−	27.2249i	−1.04975	−	1.19274i	−0.980778	−	0.195126i	$-0.937488\pi$
$521$	−23.9609	−	27.2249i	−1.04975	−	1.19274i	−0.0689691	−	0.997619i	$-0.521971\pi$
$522$	4.10618	−	5.55192i	0.179723	−	0.243001i
$523$	22.2465	+	3.81455i	0.972773	+	0.166799i	0.633376	−	0.773844i	$-0.281669\pi$
$523$	22.2465	+	3.81455i	0.972773	+	0.166799i	0.339397	+	0.940643i	$0.389777\pi$
$524$	2.44206	−	0.862834i	0.106682	−	0.0376931i
$525$	−2.06117	+	1.39311i	−0.0899568	+	0.0608002i
$526$	14.4441	−	5.10341i	0.629791	−	0.222519i
$527$	−0.186342	−	4.38664i	−0.00811719	−	0.191085i
$528$	9.55050	−	12.9131i	0.415632	−	0.561972i
$529$	−11.5290	+	22.8664i	−0.501261	+	0.994191i
$530$	−1.24015	+	0.212644i	−0.0538685	+	0.00923668i
$531$	8.09118	−	4.52001i	0.351128	−	0.196152i
$532$	6.43308	+	6.16561i	0.278909	+	0.267313i
$533$	−31.6734	−	21.4075i	−1.37193	−	0.927262i
$534$	−7.31776	−	4.94594i	−0.316670	−	0.214032i
$535$	−23.6569	+	38.4213i	−1.02278	+	1.66110i
$536$	1.61242	+	12.5916i	0.0696461	+	0.543876i
$537$	−10.7084	+	2.78825i	−0.462102	+	0.120322i
$538$	−11.2283	−	3.96723i	−0.484088	−	0.171039i
$539$	4.97730	−	16.2526i	0.214387	−	0.700049i
$540$	−3.47287	+	0.295585i	−0.149449	+	0.0127200i
$541$	−29.2848	−	28.0672i	−1.25905	−	1.20670i	−0.968268	−	0.249913i	$-0.919598\pi$
$541$	−29.2848	−	28.0672i	−1.25905	−	1.20670i	−0.290782	−	0.956789i	$-0.593915\pi$
$542$	41.0343	+	10.6845i	1.76257	+	0.458938i
$543$	2.45751	−	3.99125i	0.105462	−	0.171281i
$544$	47.3988	−	4.03423i	2.03221	−	0.172966i
$545$	24.9366	−	23.8998i	1.06817	−	1.02375i
$546$	−2.37038	−	10.9986i	−0.101443	−	0.470697i
$547$	20.2143	+	22.9679i	0.864302	+	0.982038i	0.999962	−	0.00871744i	$-0.00277488\pi$
$547$	20.2143	+	22.9679i	0.864302	+	0.982038i	−0.135660	+	0.990755i	$0.543315\pi$
$548$	−14.4470	−	1.22962i	−0.617144	−	0.0525267i
$549$	4.09580	−	10.1928i	0.174805	−	0.435018i
$550$	−10.8828	−	1.86605i	−0.464046	−	0.0795687i
$551$	−0.794543	−	18.7042i	−0.0338487	−	0.796824i
$552$	−3.16737	+	7.88230i	−0.134812	+	0.335493i
$553$	−1.01071	−	2.00463i	−0.0429799	−	0.0852456i
$554$	−26.4747	+	52.5094i	−1.12480	+	2.23091i
$555$	5.66901	+	26.3043i	0.240636	+	1.11655i
$556$	−5.68346	+	6.45766i	−0.241032	+	0.273866i
$557$	−5.42758	−	1.91769i	−0.229974	−	0.0812550i	0.215666	−	0.976467i	$-0.430808\pi$
$557$	−5.42758	−	1.91769i	−0.229974	−	0.0812550i	−0.445640	+	0.895212i	$0.647024\pi$
$558$	−1.03087	−	0.364229i	−0.0436402	−	0.0154190i
$559$	0.577388	−	0.656040i	0.0244209	−	0.0277475i
$560$	−3.64031	−	16.8911i	−0.153831	−	0.713779i
$561$	10.8416	−	21.5031i	0.457733	−	0.907860i
$562$	9.28242	+	18.4106i	0.391555	+	0.776604i
$563$	8.58207	−	21.3573i	0.361691	−	0.900103i	−0.630593	−	0.776114i	$-0.717188\pi$
$563$	8.58207	−	21.3573i	0.361691	−	0.900103i	0.992284	−	0.123989i	$-0.0395686\pi$
$564$	−0.391551	−	9.21742i	−0.0164873	−	0.388123i
$565$	25.5994	+	4.38946i	1.07698	+	0.184666i
$566$	1.06550	−	2.65160i	0.0447863	−	0.111455i
$567$	−1.34625	−	0.114582i	−0.0565370	−	0.00481201i
$568$	0.785699	+	0.892728i	0.0329672	+	0.0374580i
$569$	−5.45348	−	25.3042i	−0.228622	−	1.06081i	−0.935460	−	0.353433i	$-0.885014\pi$
$569$	−5.45348	−	25.3042i	−0.228622	−	1.06081i	0.706838	−	0.707375i	$-0.250121\pi$
$570$	−17.0608	+	16.3514i	−0.714598	+	0.684887i
$571$	31.7350	−	2.70105i	1.32807	−	0.113035i	0.600807	−	0.799394i	$-0.294846\pi$
$571$	31.7350	−	2.70105i	1.32807	−	0.113035i	0.727263	+	0.686359i	$0.240792\pi$
$572$	10.4691	−	17.0029i	0.437736	−	0.710928i
$573$	−21.5491	−	5.61095i	−0.900226	−	0.234401i
$574$	14.9236	+	14.3031i	0.622898	+	0.596999i
$575$	12.7912	−	1.08870i	0.533432	−	0.0454018i
$576$	0.605223	−	1.97626i	0.0252176	−	0.0823442i
$577$	−15.9888	−	5.64919i	−0.665621	−	0.235179i	−0.0211140	−	0.999777i	$-0.506721\pi$
$577$	−15.9888	−	5.64919i	−0.665621	−	0.235179i	−0.644507	+	0.764598i	$0.722938\pi$
$578$	64.9124	−	16.9019i	2.70000	−	0.703026i
$579$	−2.36799	−	18.4920i	−0.0984105	−	0.768502i
$580$	6.91261	−	11.2268i	0.287030	−	0.466167i
$581$	6.02005	+	4.06884i	0.249754	+	0.168804i
$582$	9.06986	+	6.13015i	0.375958	+	0.254103i
$583$	−0.624940	−	0.598957i	−0.0258824	−	0.0248062i
$584$	15.8345	−	8.84566i	0.655234	−	0.366036i
$585$	11.7596	−	2.01639i	0.486201	−	0.0833675i
$586$	−4.91415	+	9.74663i	−0.203002	+	0.402630i
$587$	−26.1042	+	35.2952i	−1.07743	+	1.45679i	−0.198345	+	0.980132i	$0.563556\pi$
$587$	−26.1042	+	35.2952i	−1.07743	+	1.45679i	−0.879090	+	0.476656i	$0.841849\pi$
$588$	−0.292646	−	6.88911i	−0.0120685	−	0.284102i
$589$	−2.79476	+	0.987451i	−0.115156	+	0.0406872i
$590$	36.6646	−	24.7809i	1.50946	−	1.02021i
$591$	−19.8095	+	6.99916i	−0.814856	+	0.287907i
$592$	−49.5769	−	8.50082i	−2.03760	−	0.349381i
$593$	−1.52972	+	2.06832i	−0.0628180	+	0.0849355i	−0.834284	−	0.551335i	$-0.814119\pi$
$593$	−1.52972	+	2.06832i	−0.0628180	+	0.0849355i	0.771466	+	0.636271i	$0.219524\pi$
$594$	−3.96185	−	4.50153i	−0.162557	−	0.184700i
$595$	−9.65976	−	24.0392i	−0.396012	−	0.985513i
$596$	6.31987	+	3.53049i	0.258872	+	0.144615i
$597$	−17.2299	+	4.48633i	−0.705175	+	0.183613i
$598$	−17.0007	+	55.5130i	−0.695209	+	2.27010i
$599$	1.68836	−	1.61816i	0.0689843	−	0.0661161i	−0.656657	−	0.754190i	$-0.728030\pi$
$599$	1.68836	−	1.61816i	0.0689843	−	0.0661161i	0.725641	+	0.688074i	$0.241543\pi$
$600$	2.21123	−	0.379153i	0.0902730	−	0.0154789i
$601$	6.32517	+	8.55219i	0.258009	+	0.348851i	0.913853	−	0.406045i	$-0.133092\pi$
$601$	6.32517	+	8.55219i	0.258009	+	0.348851i	−0.655844	+	0.754896i	$0.727687\pi$
$602$	−0.367657	+	0.296863i	−0.0149846	+	0.0120992i
$603$	10.3812	+	0.883567i	0.422753	+	0.0359816i
$604$	−8.62904	+	11.6672i	−0.351111	+	0.474733i
$605$	0.246689	+	0.489278i	0.0100293	+	0.0198920i
$606$	19.2826	−	15.5696i	0.783304	−	0.632474i
$607$	−0.330283	+	0.149298i	−0.0134058	+	0.00605980i	−0.418593	−	0.908174i	$-0.637477\pi$
$607$	−0.330283	+	0.149298i	−0.0134058	+	0.00605980i	0.405187	+	0.914234i	$0.367206\pi$
$608$	−11.9741	−	29.7986i	−0.485613	−	1.20849i
$609$	3.37660	−	3.83656i	0.136827	−	0.155465i
$610$	15.3589	−	50.1521i	0.621864	−	2.03060i
$611$	4.01139	+	31.3255i	0.162284	+	1.26730i
$612$	1.24084	−	9.68989i	0.0501579	−	0.391691i
$613$	7.29569	+	5.89085i	0.294670	+	0.237929i	0.764188	−	0.644993i	$-0.223140\pi$
$613$	7.29569	+	5.89085i	0.294670	+	0.237929i	−0.469518	+	0.882923i	$0.655572\pi$
$614$	−26.7172	+	14.9251i	−1.07822	+	0.602328i
$615$	−15.8256	+	15.1677i	−0.638152	+	0.611619i
$616$	3.57274	−	4.05942i	0.143950	−	0.163559i
$617$	2.54226	+	1.42019i	0.102347	+	0.0571747i	0.538030	−	0.842926i	$-0.319169\pi$
$617$	2.54226	+	1.42019i	0.102347	+	0.0571747i	−0.435683	+	0.900100i	$0.643493\pi$
$618$	11.2893	+	5.10309i	0.454123	+	0.205276i
$619$	−0.624440	+	4.87634i	−0.0250984	+	0.195997i	−0.999597	−	0.0283981i	$-0.990959\pi$
$619$	−0.624440	+	4.87634i	−0.0250984	+	0.195997i	0.974498	+	0.224395i	$0.0720405\pi$
$620$	−2.02009	−	0.525991i	−0.0811288	−	0.0211243i
$621$	5.77635	+	3.90413i	0.231797	+	0.156667i
$622$	−52.6790	−	13.7166i	−2.11224	−	0.549984i
$623$	−5.08607	−	4.10672i	−0.203769	−	0.164532i
$624$	−4.69888	+	21.8029i	−0.188106	+	0.872813i
$625$	18.3243	+	24.7761i	0.732971	+	0.991043i
$626$	−3.77638	−	7.49000i	−0.150934	−	0.299361i
$627$	−16.0235	−	2.74751i	−0.639919	−	0.109725i
$628$	−21.7666	+	14.7116i	−0.868581	+	0.587059i
$629$	−75.4188			−3.00715
$630$	−6.45134			−0.257027
$631$	4.38591	−	2.96436i	0.174600	−	0.118009i	−0.469557	−	0.882902i	$-0.655586\pi$
$631$	4.38591	−	2.96436i	0.174600	−	0.118009i	0.644158	+	0.764893i	$0.277208\pi$
$632$	0.0859244	+	2.02273i	0.00341789	+	0.0804597i
$633$	−16.6340	−	1.41576i	−0.661142	−	0.0562714i
$634$	−17.4788	+	7.90090i	−0.694170	+	0.313785i
$635$	−2.71125	−	8.85316i	−0.107593	−	0.351327i
$636$	−0.319978	−	0.144639i	−0.0126880	−	0.00573533i
$637$	2.99812	+	23.4128i	0.118790	+	0.927647i
$638$	22.6018	−	1.92369i	0.894813	−	0.0761598i
$639$	0.852096	−	0.476010i	0.0337084	−	0.0188306i
$640$	−5.07224	+	23.5353i	−0.200498	+	0.930313i
$641$	−4.25001	−	6.90246i	−0.167865	−	0.272631i	0.756615	−	0.653861i	$-0.226852\pi$
$641$	−4.25001	−	6.90246i	−0.167865	−	0.272631i	−0.924480	+	0.381230i	$0.875501\pi$
$642$	−28.6959	+	12.9714i	−1.13254	+	0.511938i
$643$	−6.53460	−	7.42474i	−0.257699	−	0.292803i	0.607408	−	0.794390i	$-0.292209\pi$
$643$	−6.53460	−	7.42474i	−0.257699	−	0.292803i	−0.865107	+	0.501587i	$0.832750\pi$
$644$	5.65123	−	11.2085i	0.222690	−	0.441679i
$645$	−0.297976	−	0.402891i	−0.0117328	−	0.0158638i
$646$	−34.7271	−	56.4004i	−1.36632	−	2.21905i
$647$	12.8745	+	42.0395i	0.506147	+	1.65274i	0.734077	+	0.679066i	$0.237615\pi$
$647$	12.8745	+	42.0395i	0.506147	+	1.65274i	−0.227930	+	0.973677i	$0.573196\pi$
$648$	1.06371	+	0.594223i	0.0417864	+	0.0233433i
$649$	28.7056	+	10.1423i	1.12679	+	0.398122i
$650$	14.8384	−	3.86361i	0.582008	−	0.151543i
$651$	−0.737357	−	0.333307i	−0.0288993	−	0.0130633i
$652$	−0.747474	+	17.5961i	−0.0292733	+	0.689117i
$653$	0.534176	−	2.47859i	0.0209039	−	0.0969946i	−0.965900	−	0.258917i	$-0.916634\pi$
$653$	0.534176	−	2.47859i	0.0209039	−	0.0969946i	0.986803	+	0.161923i	$0.0517695\pi$
$654$	23.7604	−	4.07413i	0.929105	−	0.159311i
$655$	1.07104	+	4.96964i	0.0418489	+	0.194180i
$656$	−15.2784	−	38.0219i	−0.596523	−	1.48450i
$657$	−4.35899	−	14.2336i	−0.170060	−	0.555305i
$658$	0.724740	−	17.0609i	0.0282533	−	0.665105i
$659$	1.97567	+	1.59525i	0.0769614	+	0.0621420i	0.665932	−	0.746013i	$-0.268034\pi$
$659$	1.97567	+	1.59525i	0.0769614	+	0.0621420i	−0.588970	+	0.808155i	$0.700467\pi$
$660$	−8.26586	−	7.92218i	−0.321748	−	0.308370i
$661$	−10.8036	+	17.5462i	−0.420212	+	0.682467i	−0.990273	−	0.139135i	$-0.955568\pi$
$661$	−10.8036	+	17.5462i	−0.420212	+	0.682467i	0.570062	+	0.821602i	$0.306919\pi$
$662$	−5.15263	+	40.2377i	−0.200263	+	1.56388i
$663$	−1.41928	+	33.4110i	−0.0551203	+	1.29757i
$664$	−3.43556	−	5.57971i	−0.133326	−	0.216535i
$665$	−13.6079	+	10.9876i	−0.527691	+	0.426081i
$666$	−7.00240	+	17.4261i	−0.271337	+	0.675249i
$667$	−24.8663	+	8.78582i	−0.962826	+	0.340188i
$668$	22.4989			0.870508
$669$	−2.43774	−	14.7329i	−0.0942486	−	0.569606i
$670$	49.7475			1.92191
$671$	34.0231	−	12.0211i	1.31345	−	0.464070i
$672$	3.26891	−	8.13501i	0.126101	−	0.313815i
$673$	−9.35679	+	7.55508i	−0.360678	+	0.291227i	−0.791450	−	0.611234i	$-0.790674\pi$
$673$	−9.35679	+	7.55508i	−0.360678	+	0.291227i	0.430772	+	0.902461i	$0.358241\pi$
$674$	−4.31097	−	7.00147i	−0.166052	−	0.269686i
$675$	0.0781470	−	1.83964i	0.00300788	−	0.0708078i
$676$	−1.32159	+	10.3205i	−0.0508305	+	0.396943i
$677$	−7.29672	+	11.8506i	−0.280436	+	0.455456i	−0.960731	−	0.277482i	$-0.910500\pi$
$677$	−7.29672	+	11.8506i	−0.280436	+	0.455456i	0.680295	+	0.732938i	$0.261852\pi$
$678$	13.0874	+	12.5432i	0.502618	+	0.481720i
$679$	6.30384	+	5.08999i	0.241919	+	0.195336i
$680$	−0.991567	+	23.3423i	−0.0380249	+	0.895135i
$681$	−4.20559	−	13.7327i	−0.161159	−	0.526238i
$682$	−1.33909	−	3.33246i	−0.0512765	−	0.127607i
$683$	−6.54442	−	30.3662i	−0.250415	−	1.16193i	−0.911397	−	0.411529i	$-0.864995\pi$
$683$	−6.54442	−	30.3662i	−0.250415	−	1.16193i	0.660981	−	0.750403i	$-0.270140\pi$
$684$	−6.50017	+	1.11457i	−0.248540	+	0.0426165i
$685$	5.99582	−	27.8207i	0.229089	−	1.06297i
$686$	1.27444	−	30.0013i	0.0486583	−	1.14545i
$687$	−0.774458	−	0.350077i	−0.0295474	−	0.0133563i
$688$	0.906515	−	0.236038i	0.0345605	−	0.00899887i
$689$	1.13339	+	0.400451i	0.0431786	+	0.0152560i
$690$	29.0626	+	16.2354i	1.10640	+	0.618070i
$691$	4.43483	+	14.4812i	0.168709	+	0.550892i	0.999988	−	0.00496353i	$-0.00157995\pi$
$691$	4.43483	+	14.4812i	0.168709	+	0.550892i	−0.831279	+	0.555856i	$0.812391\pi$
$692$	−12.7227	−	20.6629i	−0.483644	−	0.785487i
$693$	−2.63913	−	3.56835i	−0.100252	−	0.135550i
$694$	16.7636	−	33.2486i	0.636338	−	1.26210i
$695$	−11.1557	−	12.6753i	−0.423158	−	0.480801i
$696$	−4.19980	+	1.89843i	−0.159193	+	0.0719598i
$697$	−32.2130	−	52.3172i	−1.22015	−	1.98166i
$698$	−8.04923	+	37.3486i	−0.304668	+	1.41366i
$699$	−1.22486	+	0.684246i	−0.0463284	+	0.0258806i
$700$	−3.30321	+	0.281144i	−0.124849	+	0.0106263i
$701$	−4.03769	−	31.5309i	−0.152501	−	1.19091i	−0.869537	−	0.493869i	$-0.835582\pi$
$701$	−4.03769	−	31.5309i	−0.152501	−	1.19091i	0.717035	−	0.697037i	$-0.245499\pi$
$702$	7.58809	+	3.43003i	0.286394	+	0.129458i
$703$	14.9091	+	48.6833i	0.562307	+	1.83612i
$704$	6.18669	−	2.79656i	0.233170	−	0.105399i
$705$	18.0433	+	1.53571i	0.679550	+	0.0578382i
$706$	−1.57380	−	37.0484i	−0.0592307	−	1.39434i
$707$	15.1973	−	10.2716i	0.571554	−	0.386303i
$708$	12.3503			0.464153
$709$	12.2633			0.460558			0.230279	−	0.973125i	$-0.426036\pi$
$709$	12.2633			0.460558			0.230279	+	0.973125i	$0.426036\pi$
$710$	3.86121	−	2.60972i	0.144909	−	0.0979411i
$711$	1.63770	+	0.280812i	0.0614187	+	0.0105313i
$712$	2.65401	+	5.26391i	0.0994631	+	0.197273i
$713$	2.48293	+	3.35714i	0.0929863	+	0.125726i
$714$	3.80948	−	17.6761i	0.142566	−	0.661510i
$715$	30.4934	+	24.6217i	1.14039	+	0.920800i
$716$	−14.2696	−	3.71551i	−0.533280	−	0.138855i
$717$	−12.5964	−	8.51369i	−0.470422	−	0.317950i
$718$	49.3497	+	12.8497i	1.84171	+	0.479545i
$719$	−6.34976	+	49.5862i	−0.236806	+	1.84925i	0.240670	+	0.970607i	$0.422633\pi$
$719$	−6.34976	+	49.5862i	−0.236806	+	1.84925i	−0.477476	+	0.878645i	$0.658448\pi$
$720$	11.6534	+	5.26767i	0.434296	+	0.196314i
$721$	8.00505	+	4.47189i	0.298124	+	0.166542i
$722$	−6.62623	+	7.52886i	−0.246603	+	0.280195i
$723$	20.0488	−	19.2152i	0.745622	−	0.714621i
$724$	5.45278	−	3.04610i	0.202651	−	0.113208i
$725$	5.41906	+	4.37559i	0.201259	+	0.162505i
$726$	−0.0485763	+	0.379339i	−0.00180284	+	0.0140786i
$727$	−3.43887	−	26.8547i	−0.127541	−	0.995984i	−0.921599	−	0.388143i	$-0.873117\pi$
$727$	−3.43887	−	26.8547i	−0.127541	−	0.995984i	0.794058	−	0.607841i	$-0.207964\pi$
$728$	−2.19894	+	7.18030i	−0.0814982	+	0.266120i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	−26.5021	−	65.9531i	−0.980888	−	2.44103i
$731$	1.27984	−	0.578523i	0.0473365	−	0.0213974i
$732$	11.3889	−	9.19593i	0.420948	−	0.339892i
$733$	14.1165	+	27.9984i	0.521404	+	1.03414i	0.988681	+	0.150032i	$0.0479377\pi$
$733$	14.1165	+	27.9984i	0.521404	+	1.03414i	−0.467277	+	0.884111i	$0.654765\pi$
$734$	15.0994	−	20.4158i	0.557330	−	0.753560i
$735$	13.4856	+	1.14779i	0.497423	+	0.0423370i
$736$	−35.1986	+	28.4209i	−1.29744	+	1.04761i
$737$	20.3509	+	27.5162i	0.749634	+	1.01357i
$738$	−15.0792	+	2.58559i	−0.555073	+	0.0951768i
$739$	−2.25957	+	2.16563i	−0.0831198	+	0.0796639i	−0.732351	−	0.680927i	$-0.761577\pi$
$739$	−2.25957	+	2.16563i	−0.0831198	+	0.0796639i	0.649232	+	0.760591i	$0.275091\pi$
$740$	−10.4997	+	34.2851i	−0.385977	+	1.26035i
$741$	21.8475	−	5.68865i	0.802588	−	0.208978i
$742$	−0.567425	−	0.316983i	−0.0208308	−	0.0116368i
$743$	0.127435	+	0.317134i	0.00467513	+	0.0116345i	0.930208	−	0.367032i	$-0.119626\pi$
$743$	0.127435	+	0.317134i	0.00467513	+	0.0116345i	−0.925533	+	0.378666i	$0.876383\pi$
$744$	0.482112	+	0.547786i	0.0176751	+	0.0200828i
$745$	−8.44926	+	11.4242i	−0.309557	+	0.418549i
$746$	−23.7088	−	4.06529i	−0.868042	−	0.148841i
$747$	−5.07068	+	1.79158i	−0.185526	+	0.0655507i
$748$	26.5870	−	17.9697i	0.972117	−	0.657036i
$749$	−21.9761	+	7.76464i	−0.802988	+	0.283714i
$750$	0.640110	+	15.0687i	0.0233735	+	0.550230i
$751$	20.5458	−	27.7798i	0.749727	−	1.01370i	−0.249248	−	0.968440i	$-0.580183\pi$
$751$	20.5458	−	27.7798i	0.749727	−	1.01370i	0.998975	−	0.0452587i	$-0.0144112\pi$
$752$	−15.2398	+	30.2263i	−0.555738	+	1.10224i
$753$	11.2921	−	1.93623i	0.411507	−	0.0705600i
$754$	−27.4996	+	15.3622i	−1.00148	+	0.559459i
$755$	−20.5640	−	19.7090i	−0.748399	−	0.717282i
$756$	−1.49168	−	1.00820i	−0.0542519	−	0.0366679i
$757$	15.1959	+	10.2707i	0.552305	+	0.373293i	0.804106	−	0.594486i	$-0.202644\pi$
$757$	15.1959	+	10.2707i	0.552305	+	0.373293i	−0.251801	+	0.967779i	$0.581023\pi$
$758$	−10.0495	+	16.3214i	−0.365013	+	0.592819i
$759$	2.90898	+	22.7167i	0.105589	+	0.824563i
$760$	15.2636	−	3.97432i	0.553668	−	0.144164i
$761$	31.3806	+	11.0875i	1.13755	+	0.401921i	0.834474	−	0.551047i	$-0.185771\pi$
$761$	31.3806	+	11.0875i	1.13755	+	0.401921i	0.303072	+	0.952968i	$0.401988\pi$
$762$	1.89230	−	6.17900i	0.0685507	−	0.223842i
$763$	17.7779	−	1.51312i	0.643604	−	0.0547788i
$764$	−21.4225	−	20.5318i	−0.775040	−	0.742816i
$765$	18.5562	+	4.83166i	0.670900	+	0.174689i
$766$	−16.7883	+	27.2659i	−0.606586	+	0.985158i
$767$	−42.1250	+	3.58537i	−1.52105	+	0.129460i
$768$	−15.1157	+	14.4872i	−0.545440	+	0.522762i
$769$	−2.58862	−	12.0112i	−0.0933481	−	0.433137i	−0.999938	−	0.0111242i	$-0.996459\pi$
$769$	−2.58862	−	12.0112i	−0.0933481	−	0.433137i	0.906590	−	0.422012i	$-0.138676\pi$
$770$	−14.0010	−	15.9082i	−0.504560	−	0.573292i
$771$	15.3209	+	1.30400i	0.551767	+	0.0469623i
$772$	9.26285	−	23.0515i	0.333377	−	0.829641i
$773$	8.02080	+	1.37530i	0.288488	+	0.0494663i	0.311425	−	0.950271i	$-0.399194\pi$
$773$	8.02080	+	1.37530i	0.288488	+	0.0494663i	−0.0229371	+	0.999737i	$0.507302\pi$
$774$	−0.0148436	−	0.349431i	−0.000533543	−	0.0125600i
$775$	0.411174	−	1.02325i	0.0147698	−	0.0367561i
$776$	−3.28946	−	6.52425i	−0.118085	−	0.234207i
$777$	−6.25773	+	12.4115i	−0.224495	+	0.445259i
$778$	−5.93425	−	27.5350i	−0.212753	−	0.987178i
$779$	−27.4031	+	31.1359i	−0.981817	+	1.11556i
$780$	14.9909	+	5.29662i	0.536760	+	0.189650i
$781$	3.02304	+	1.06811i	0.108173	+	0.0382199i
$782$	−61.6448	+	70.0421i	−2.20441	+	2.50470i
$783$	0.796933	+	3.69778i	0.0284801	+	0.132148i
$784$	−11.3902	+	22.5912i	−0.406794	+	0.806829i
$785$	−23.2158	−	46.0459i	−0.828609	−	1.64345i
$786$	−1.32295	+	3.29230i	−0.0471882	+	0.117432i
$787$	−0.328301	−	7.72846i	−0.0117027	−	0.275490i	−0.995409	−	0.0957090i	$-0.969488\pi$
$787$	−0.328301	−	7.72846i	−0.0117027	−	0.275490i	0.983707	−	0.179781i	$-0.0575388\pi$
$788$	−27.5939	−	4.73146i	−0.982993	−	0.168551i
$789$	−3.12887	+	7.78648i	−0.111391	+	0.277206i
$790$	7.90530	+	0.672840i	0.281258	+	0.0239386i
$791$	8.86405	+	10.0715i	0.315169	+	0.358102i
$792$	0.843226	+	3.91258i	0.0299627	+	0.139028i
$793$	−36.1763	+	34.6722i	−1.28466	+	1.23125i
$794$	51.3844	−	4.37346i	1.82356	−	0.155208i
$795$	0.361378	−	0.586915i	0.0128168	−	0.0208157i
$796$	−22.9599	−	5.97830i	−0.813793	−	0.211895i
$797$	0.281641	+	0.269931i	0.00997623	+	0.00956144i	0.696910	−	0.717158i	$-0.254557\pi$
$797$	0.281641	+	0.269931i	0.00997623	+	0.00956144i	−0.686934	+	0.726720i	$0.741044\pi$
$798$	−12.1631	+	1.03523i	−0.430568	+	0.0366467i
$799$	−14.8622	+	48.5302i	−0.525787	+	1.71687i
$800$	11.2655	+	3.98035i	0.398296	+	0.140727i
$801$	4.68217	−	1.21914i	0.165436	−	0.0430763i
$802$	−6.29620	−	49.1679i	−0.222327	−	1.73618i
$803$	25.6382	−	41.6391i	0.904752	−	1.46941i
$804$	11.5026	+	7.77443i	0.405667	+	0.274183i
$805$	20.4133	+	13.7970i	0.719476	+	0.486281i
$806$	3.60060	+	3.45090i	0.126826	+	0.121553i
$807$	5.69499	−	3.18141i	0.200473	−	0.111991i
$808$	−16.3037	+	2.79556i	−0.573563	+	0.0983473i
$809$	−0.945702	+	1.87569i	−0.0332491	+	0.0659457i	−0.908941	−	0.416924i	$-0.863108\pi$
$809$	−0.945702	+	1.87569i	−0.0332491	+	0.0659457i	0.875692	+	0.482870i	$0.160405\pi$
$810$	2.83928	−	3.83895i	0.0997620	−	0.134887i
$811$	0.339546	+	7.99318i	0.0119231	+	0.280678i	0.995155	+	0.0983187i	$0.0313465\pi$
$811$	0.339546	+	7.99318i	0.0119231	+	0.280678i	−0.983232	+	0.182360i	$0.941627\pi$
$812$	6.42146	−	2.26884i	0.225349	−	0.0796208i
$813$	−19.2442	+	13.0068i	−0.674924	+	0.456169i
$814$	−58.1676	+	20.5519i	−2.03877	+	0.720344i
$815$	−34.0721	−	5.84224i	−1.19349	−	0.204645i
$816$	−21.3142	+	28.8187i	−0.746146	+	1.00886i
$817$	−0.626442	−	0.711777i	−0.0219164	−	0.0249019i
$818$	−0.445871	−	1.10959i	−0.0155895	−	0.0387960i
$819$	5.38058	+	3.00577i	0.188013	+	0.105030i
$820$	−28.2679	+	7.36038i	−0.987157	+	0.257036i
$821$	8.48909	−	27.7198i	0.296271	−	0.967428i	−0.676653	−	0.736302i	$-0.736570\pi$
$821$	8.48909	−	27.7198i	0.296271	−	0.967428i	0.972924	−	0.231125i	$-0.0742408\pi$
$822$	14.3403	−	13.7440i	0.500175	−	0.479378i
$823$	35.6911	−	6.11985i	1.24411	−	0.213325i	0.490967	−	0.871178i	$-0.336644\pi$
$823$	35.6911	−	6.11985i	1.24411	−	0.213325i	0.753146	+	0.657854i	$0.228535\pi$
$824$	−4.91702	−	6.64824i	−0.171292	−	0.231603i
$825$	4.70593	−	3.79977i	0.163839	−	0.132291i
$826$	22.7774	+	1.93864i	0.792527	+	0.0674540i
$827$	30.0817	−	40.6731i	1.04604	−	1.41434i	0.140503	−	0.990080i	$-0.455128\pi$
$827$	30.0817	−	40.6731i	1.04604	−	1.41434i	0.905539	−	0.424262i	$-0.139467\pi$
$828$	4.18265	+	8.29579i	0.145357	+	0.288299i
$829$	14.2354	−	11.4943i	0.494416	−	0.399213i	−0.348458	−	0.937325i	$-0.613294\pi$
$829$	14.2354	−	11.4943i	0.494416	−	0.399213i	0.842874	+	0.538111i	$0.180862\pi$
$830$	−23.3990	+	10.5770i	−0.812190	+	0.367133i
$831$	−12.0109	−	29.8902i	−0.416653	−	1.03688i
$832$	−6.22894	+	7.07746i	−0.215950	+	0.245367i
$833$	−11.1080	+	36.2715i	−0.384870	+	1.25673i
$834$	−1.49690	−	11.6895i	−0.0518333	−	0.404774i
$835$	−5.60930	+	43.8038i	−0.194118	+	1.51589i
$836$	−16.8553	−	13.6097i	−0.582954	−	0.470702i
$837$	0.522854	−	0.292084i	0.0180725	−	0.0100959i
$838$	−0.850719	+	0.815348i	−0.0293876	+	0.0281657i
$839$	−10.4441	+	11.8668i	−0.360570	+	0.409687i	−0.902468	−	0.430757i	$-0.858246\pi$
$839$	−10.4441	+	11.8668i	−0.360570	+	0.409687i	0.541898	+	0.840444i	$0.317706\pi$
$840$	3.75909	+	2.09996i	0.129701	+	0.0724554i
$841$	13.3871	+	6.05137i	0.461625	+	0.208668i
$842$	−2.34966	+	18.3489i	−0.0809747	+	0.632343i
$843$	−10.9300	−	2.84594i	−0.376448	−	0.0980194i
$844$	−18.4310	−	12.4572i	−0.634420	−	0.428793i
$845$	−19.7638	−	5.14610i	−0.679897	−	0.177031i
$846$	9.83338	+	7.93990i	0.338078	+	0.272979i
$847$	−0.0596327	+	0.276697i	−0.00204900	+	0.00950741i
$848$	0.766146	+	1.03590i	0.0263096	+	0.0355729i
$849$	0.704744	+	1.39778i	0.0241868	+	0.0479716i
$850$	24.2876	+	4.16453i	0.833059	+	0.142842i
$851$	59.4250	−	40.1643i	2.03706	−	1.37681i
$852$	1.30063			0.0445589
$853$	−36.6407			−1.25455			−0.627277	−	0.778797i	$-0.715830\pi$
$853$	−36.6407			−1.25455			−0.627277	+	0.778797i	$0.715830\pi$
$854$	22.4479	−	15.1721i	0.768151	−	0.519179i
$855$	−0.549398	−	12.9333i	−0.0187890	−	0.442308i
$856$	20.9429	+	1.78250i	0.715814	+	0.0609247i
$857$	−24.5368	+	11.0913i	−0.838162	+	0.378873i	−0.784836	−	0.619704i	$-0.787253\pi$
$857$	−24.5368	+	11.0913i	−0.838162	+	0.378873i	−0.0533263	+	0.998577i	$0.516982\pi$
$858$	8.00997	+	26.1553i	0.273456	+	0.892928i
$859$	−2.54981	−	1.15259i	−0.0869985	−	0.0393258i	0.367932	−	0.929853i	$-0.380066\pi$
$859$	−2.54981	−	1.15259i	−0.0869985	−	0.0393258i	−0.454931	+	0.890527i	$0.650336\pi$
$860$	−0.0848172	−	0.662350i	−0.00289224	−	0.0225859i
$861$	−11.2825	+	0.960283i	−0.384507	+	0.0327263i
$862$	50.3814	−	28.1447i	1.71600	−	0.958613i
$863$	−2.47883	+	11.5018i	−0.0843802	+	0.391525i	−0.999943	−	0.0106489i	$-0.996610\pi$
$863$	−2.47883	+	11.5018i	−0.0843802	+	0.391525i	0.915563	+	0.402174i	$0.131745\pi$
$864$	3.40217	+	5.52548i	0.115744	+	0.187981i
$865$	43.4013	−	19.6186i	1.47569	−	0.667053i
$866$	9.24827	+	10.5081i	0.314269	+	0.357079i
$867$	−16.5422	+	32.8094i	−0.561802	+	1.11427i
$868$	−0.641190	−	0.866946i	−0.0217634	−	0.0294261i
$869$	2.86177	+	4.64780i	0.0970788	+	0.157666i
$870$	5.28887	+	17.2700i	0.179310	+	0.585507i
$871$	−41.4907	−	23.1781i	−1.40586	−	0.785360i
$872$	−15.1710	−	5.36024i	−0.513754	−	0.181521i
$873$	−5.80323	+	1.51104i	−0.196409	+	0.0511410i
$874$	57.3987	+	25.9458i	1.94154	+	0.877631i
$875$	−0.473758	+	11.1526i	−0.0160160	+	0.377028i
$876$	4.17916	−	19.3914i	0.141201	−	0.655174i
$877$	−5.33291	+	0.914419i	−0.180080	+	0.0308777i	−0.258334	−	0.966056i	$-0.583173\pi$
$877$	−5.33291	+	0.914419i	−0.180080	+	0.0308777i	0.0782543	+	0.996933i	$0.475065\pi$
$878$	11.3687	+	52.7510i	0.383676	+	1.78026i
$879$	−2.22942	−	5.54812i	−0.0751965	−	0.187134i
$880$	12.3013	+	40.1680i	0.414677	+	1.35406i
$881$	0.478491	−	11.2641i	0.0161208	−	0.379496i	−0.972855	−	0.231417i	$-0.925664\pi$
$881$	0.478491	−	11.2641i	0.0161208	−	0.379496i	0.988976	−	0.148079i	$-0.0473090\pi$
$882$	7.34948	+	5.93429i	0.247470	+	0.199818i
$883$	−24.4535	−	23.4368i	−0.822927	−	0.788712i	0.157098	−	0.987583i	$-0.449786\pi$
$883$	−24.4535	−	23.4368i	−0.822927	−	0.788712i	−0.980026	+	0.198871i	$0.936272\pi$
$884$	−23.3643	+	37.9461i	−0.785827	+	1.27626i
$885$	−3.07911	+	24.0452i	−0.103503	+	0.808270i
$886$	2.73584	−	64.4037i	0.0919122	−	2.16368i
$887$	−11.4170	−	18.5423i	−0.383344	−	0.622591i	0.600917	−	0.799312i	$-0.294802\pi$
$887$	−11.4170	−	18.5423i	−0.383344	−	0.622591i	−0.984261	+	0.176721i	$0.943451\pi$
$888$	9.75252	−	7.87461i	0.327273	−	0.264255i
$889$	1.78332	−	4.43796i	0.0598106	−	0.148844i
$890$	21.7824	−	7.69620i	0.730147	−	0.257977i
$891$	3.28489			0.110048
$892$	6.73871	−	18.7236i	0.225629	−	0.626914i
$893$	34.2645			1.14662
$894$	−9.35071	+	3.30382i	−0.312735	+	0.110496i
$895$	10.7915	−	26.8556i	0.360719	−	0.897683i
$896$	−9.67608	+	7.81289i	−0.323255	+	0.261010i
$897$	−16.6747	−	27.0814i	−0.556752	−	0.904222i
$898$	1.43330	−	33.7411i	0.0478300	−	1.12595i
$899$	−0.287756	+	2.24713i	−0.00959719	+	0.0749458i
$900$	1.28646	−	2.08935i	0.0428821	−	0.0696450i
$901$	1.39470	+	1.33671i	0.0464643	+	0.0445324i
$902$	−39.1013	−	31.5721i	−1.30193	−	1.05123i
$903$	0.0109861	−	0.258621i	0.000365594	−	0.00860636i
$904$	−3.54290	−	11.5688i	−0.117835	−	0.384772i
$905$	4.57110	+	11.3756i	0.151948	+	0.378138i
$906$	−4.18830	−	19.4338i	−0.139147	−	0.645643i
$907$	−8.90671	+	1.52721i	−0.295742	+	0.0507101i	−0.314959	−	0.949105i	$-0.601991\pi$
$907$	−8.90671	+	1.52721i	−0.295742	+	0.0507101i	0.0192168	+	0.999815i	$0.493883\pi$
$908$	4.03209	−	18.7090i	0.133810	−	0.620879i
$909$	−0.576190	+	13.5640i	−0.0191110	+	0.449888i
$910$	26.8160	+	12.1216i	0.888941	+	0.401827i
$911$	−32.2634	+	8.40074i	−1.06893	+	0.278329i	−0.744529	−	0.667590i	$-0.767326\pi$
$911$	−32.2634	+	8.40074i	−1.06893	+	0.278329i	−0.324405	+	0.945918i	$0.605164\pi$
$912$	22.8161	+	8.06144i	0.755516	+	0.266941i
$913$	−15.4224	−	8.61549i	−0.510408	−	0.285131i
$914$	19.0223	+	62.1143i	0.629201	+	2.05456i
$915$	15.0644	+	24.4662i	0.498015	+	0.808827i
$916$	−0.673452	−	0.910567i	−0.0222515	−	0.0300860i
$917$	−1.18226	+	2.34488i	−0.0390418	+	0.0774348i
$918$	8.84180	+	10.0462i	0.291823	+	0.331575i
$919$	−16.3579	+	7.39423i	−0.539597	+	0.243913i	−0.663231	−	0.748415i	$-0.730815\pi$
$919$	−16.3579	+	7.39423i	−0.539597	+	0.243913i	0.123634	+	0.992328i	$0.460545\pi$
$920$	−11.6496	−	18.9202i	−0.384077	−	0.623780i
$921$	3.53185	−	16.3878i	0.116378	−	0.539997i
$922$	−9.97052	+	5.56987i	−0.328362	+	0.183434i
$923$	−4.43625	+	0.377581i	−0.146021	+	0.0124282i
$924$	−0.751214	−	5.86634i	−0.0247131	−	0.192988i
$925$	−17.2611	−	7.80250i	−0.567541	−	0.256545i
$926$	8.86099	+	28.9342i	0.291190	+	0.950836i
$927$	−6.18413	+	2.79540i	−0.203113	+	0.0918131i
$928$	−24.4570	−	2.08160i	−0.802840	−	0.0683318i
$929$	−1.17578	−	27.6787i	−0.0385760	−	0.908110i	−0.909250	−	0.416250i	$-0.863344\pi$
$929$	−1.17578	−	27.6787i	−0.0385760	−	0.908110i	0.870674	−	0.491860i	$-0.163683\pi$
$930$	2.36927	−	1.60135i	0.0776915	−	0.0525103i
$931$	25.6093			0.839311
$932$	−1.86961			−0.0612411
$933$	24.7053	−	16.6979i	0.808817	−	0.546665i
$934$	−19.4846	−	3.34097i	−0.637555	−	0.109320i
$935$	28.3572	+	56.2431i	0.927379	+	1.83935i
$936$	−3.30496	−	4.46861i	−0.108026	−	0.146061i
$937$	3.63676	−	16.8746i	0.118808	−	0.551270i	−0.878487	−	0.477766i	$-0.841447\pi$
$937$	3.63676	−	16.8746i	0.118808	−	0.551270i	0.997295	−	0.0735041i	$-0.0234182\pi$
$938$	19.9937	+	16.1438i	0.652818	+	0.527113i
$939$	4.44665	+	1.15782i	0.145111	+	0.0377840i
$940$	19.9925	+	13.5126i	0.652085	+	0.440732i
$941$	−5.57279	−	1.45104i	−0.181668	−	0.0473026i	0.160032	−	0.987112i	$-0.448840\pi$
$941$	−5.57279	−	1.45104i	−0.181668	−	0.0473026i	−0.341699	+	0.939809i	$0.611002\pi$
$942$	4.57151	−	35.6996i	0.148948	−	1.16316i
$943$	53.2432	+	24.0675i	1.73384	+	0.783744i
$944$	−39.5611	−	22.1001i	−1.28760	−	0.719298i
$945$	2.33479	−	2.65284i	0.0759508	−	0.0862969i
$946$	0.829438	−	0.794952i	0.0269674	−	0.0258461i
$947$	19.1783	−	10.7136i	0.623211	−	0.348146i	−0.143966	−	0.989583i	$-0.545985\pi$
$947$	19.1783	−	10.7136i	0.623211	−	0.348146i	0.767176	+	0.641436i	$0.221661\pi$
$948$	1.72272	+	1.39100i	0.0559512	+	0.0451775i
$949$	−8.62505	+	67.3543i	−0.279981	+	2.18641i
$950$	−2.11304	−	16.5011i	−0.0685562	−	0.535365i
$951$	3.07680	−	10.0468i	0.0997721	−	0.325790i
$952$	−7.97341	+	9.05956i	−0.258420	+	0.293622i
$953$	17.0321	+	42.3860i	0.551723	+	1.37302i	0.900109	+	0.435665i	$0.143487\pi$
$953$	17.0321	+	42.3860i	0.551723	+	1.37302i	−0.348385	+	0.937351i	$0.613270\pi$
$954$	0.438352	−	0.198148i	0.0141922	−	0.00641527i
$955$	45.3150	−	36.5893i	1.46636	−	1.18400i
$956$	−9.12106	−	18.0905i	−0.294996	−	0.585090i
$957$	−7.38873	+	9.99023i	−0.238844	+	0.322938i
$958$	−17.4408	−	1.48443i	−0.563486	−	0.0479597i
$959$	11.4380	−	9.23551i	0.369351	−	0.298230i
$960$	3.21461	+	4.34645i	0.103751	+	0.140281i
$961$	−30.2006	+	5.17841i	−0.974212	+	0.167045i
$962$	61.8489	−	59.2774i	1.99409	−	1.91118i
$963$	5.05136	−	16.4944i	0.162778	−	0.531525i
$964$	35.8112	−	9.32452i	1.15340	−	0.300323i
$965$	42.5703	+	23.7812i	1.37039	+	0.765543i
$966$	6.41177	+	15.9563i	0.206295	+	0.513385i
$967$	−11.8689	−	13.4857i	−0.381677	−	0.433669i	0.527835	−	0.849347i	$-0.323004\pi$
$967$	−11.8689	−	13.4857i	−0.381677	−	0.433669i	−0.909512	+	0.415678i	$0.863544\pi$
$968$	0.151782	−	0.205223i	0.00487847	−	0.00659613i
$969$	35.7603	+	6.13173i	1.14879	+	0.196979i
$970$	−26.9977	+	9.53891i	−0.866845	+	0.306276i
$971$	−20.0905	+	13.5788i	−0.644734	+	0.435764i	−0.838215	−	0.545340i	$-0.816401\pi$
$971$	−20.0905	+	13.5788i	−0.644734	+	0.435764i	0.193481	+	0.981104i	$0.438022\pi$
$972$	1.25644	−	0.443929i	0.0403004	−	0.0142390i
$973$	−0.370184	−	8.71441i	−0.0118675	−	0.279371i
$974$	−17.2983	+	23.3889i	−0.554274	+	0.749428i
$975$	−3.78138	+	7.49992i	−0.121101	+	0.240190i
$976$	−52.9372	+	9.07699i	−1.69448	+	0.290547i
$977$	46.9240	−	26.2133i	1.50123	−	0.838638i	0.501581	−	0.865111i	$-0.332752\pi$
$977$	46.9240	−	26.2133i	1.50123	−	0.838638i	0.999650	+	0.0264729i	$0.00842756\pi$
$978$	−17.4189	−	16.6947i	−0.556996	−	0.533837i
$979$	13.1677	+	8.89981i	0.420842	+	0.284439i
$980$	14.9424	+	10.0993i	0.477319	+	0.322611i
$981$	−6.92377	+	11.2449i	−0.221059	+	0.359023i
$982$	−1.19114	−	9.30181i	−0.0380109	−	0.296833i
$983$	15.0117	−	3.90875i	0.478799	−	0.124670i	−0.00474638	−	0.999989i	$-0.501511\pi$
$983$	15.0117	−	3.90875i	0.478799	−	0.124670i	0.483546	+	0.875319i	$0.339349\pi$
$984$	9.62804	+	3.40180i	0.306931	+	0.108446i
$985$	16.0914	−	52.5439i	0.512714	−	1.67419i
$986$	−50.4412	+	4.29318i	−1.60638	+	0.136723i
$987$	6.75331	+	6.47252i	0.214960	+	0.206023i
$988$	29.1131	+	7.58047i	0.926212	+	0.241167i
$989$	−0.700333	+	1.13741i	−0.0222693	+	0.0361677i
$990$	15.6283	−	1.33016i	0.496700	−	0.0422754i
$991$	−14.9322	+	14.3114i	−0.474338	+	0.454616i	−0.890706	−	0.454580i	$-0.849789\pi$
$991$	−14.9322	+	14.3114i	−0.474338	+	0.454616i	0.416368	+	0.909196i	$0.363303\pi$
$992$	0.818750	+	3.79901i	0.0259953	+	0.120619i
$993$	−14.6813	−	16.6811i	−0.465896	−	0.529360i
$994$	2.39873	+	0.204162i	0.0760829	+	0.00647561i
$995$	17.3636	−	43.2109i	0.550463	−	1.36988i
$996$	−7.06326	−	1.21112i	−0.223808	−	0.0383757i
$997$	−1.62011	−	38.1386i	−0.0513093	−	1.20786i	−0.821560	−	0.570121i	$-0.806896\pi$
$997$	−1.62011	−	38.1386i	−0.0513093	−	1.20786i	0.770251	−	0.637741i	$-0.220131\pi$
$998$	6.46230	−	16.0820i	0.204560	−	0.509068i
$999$	−4.63154	−	9.18610i	−0.146535	−	0.290635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.b.4.5	✓	720
223.56	even	37	inner	669.2.i.b.502.5	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.b.4.5	✓	720	1.1	even	1	trivial
669.2.i.b.502.5	yes	720	223.56	even	37	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72125 + 0.608157i) q^{2} +(0.372856 - 0.927889i) q^{3} +(1.03678 - 0.837141i) q^{4} +(1.37137 + 2.22725i) q^{5} +(-0.0774777 + 1.82389i) q^{6} +(-0.171615 + 1.34017i) q^{7} +(0.638833 - 1.03753i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-3.71499 - 2.99965i) q^{10} +(0.139415 - 3.28193i) q^{11} +(-0.390204 - 1.27415i) q^{12} +(1.70082 + 4.23265i) q^{13} +(-0.519640 - 2.41114i) q^{14} +(2.57797 - 0.442037i) q^{15} +(-1.03010 + 4.77966i) q^{16} +(-0.311137 + 7.32441i) q^{17} +(1.66348 + 0.751938i) q^{18} +(4.78945 - 1.24708i) q^{19} +(3.28633 + 1.16113i) q^{20} +(1.17954 + 0.658931i) q^{21} +(1.75596 + 5.73381i) q^{22} +(-3.65546 - 5.93684i) q^{23} +(-0.724520 - 0.979616i) q^{24} +(-0.828960 + 1.64414i) q^{25} +(-5.50165 - 6.25109i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(0.943983 + 1.53313i) q^{28} +(0.796933 - 3.69778i) q^{29} +(-4.16850 + 2.32866i) q^{30} +(-0.596749 + 0.0507908i) q^{31} +(-0.824205 - 6.43633i) q^{32} +(-2.99329 - 1.35305i) q^{33} +(-3.91884 - 12.7964i) q^{34} +(-3.22024 + 1.45564i) q^{35} +(-1.32776 - 0.113009i) q^{36} +(0.436620 + 10.2784i) q^{37} +(-7.48543 + 5.05927i) q^{38} +4.56159 q^{39} +3.18692 q^{40} +(-6.94351 + 4.69299i) q^{41} +(-2.43102 - 0.416840i) q^{42} +(-0.0862527 - 0.171072i) q^{43} +(-2.60290 - 3.51935i) q^{44} +(0.551050 - 2.55688i) q^{45} +(9.90248 + 7.99570i) q^{46} +(6.69992 + 1.74452i) q^{47} +(4.05092 + 2.73794i) q^{48} +(5.00753 + 1.30386i) q^{49} +(0.426951 - 3.33412i) q^{50} +(6.68023 + 3.01965i) q^{51} +(5.30670 + 2.96450i) q^{52} +(0.174098 - 0.197814i) q^{53} +(1.31795 - 1.26316i) q^{54} +(7.50087 - 4.19024i) q^{55} +(1.28083 + 1.03420i) q^{56} +(0.628629 - 4.90906i) q^{57} +(0.877109 + 6.84947i) q^{58} +(-2.71391 + 8.86185i) q^{59} +(2.30273 - 2.61641i) q^{60} +(4.09580 + 10.1928i) q^{61} +(0.996266 - 0.450341i) q^{62} +(1.05121 - 0.848796i) q^{63} +(0.930507 + 1.84555i) q^{64} +(-7.09471 + 9.59269i) q^{65} +(5.97506 + 0.508553i) q^{66} +(-8.10612 + 6.54523i) q^{67} +(5.80898 + 7.85426i) q^{68} +(-6.87169 + 1.17827i) q^{69} +(4.65758 - 4.46393i) q^{70} +(-0.285807 + 0.933257i) q^{71} +(-1.17912 + 0.307018i) q^{72} +(12.9958 + 7.25987i) q^{73} +(-7.00240 - 17.4261i) q^{74} +(1.21650 + 1.38221i) q^{75} +(3.92162 - 5.30239i) q^{76} +(4.37442 + 0.750069i) q^{77} +(-7.85164 + 2.77416i) q^{78} +(-1.37665 + 0.930456i) q^{79} +(-12.0581 + 4.26041i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(9.09745 - 12.3006i) q^{82} +(2.42114 - 4.80205i) q^{83} +(1.77454 - 0.304276i) q^{84} +(-16.7400 + 9.35151i) q^{85} +(0.252501 + 0.242003i) q^{86} +(-3.13399 - 2.11821i) q^{87} +(-3.31604 - 2.24125i) q^{88} +(-2.53675 + 4.11994i) q^{89} +(0.606489 + 4.73616i) q^{90} +(-5.96435 + 1.55300i) q^{91} +(-8.75987 - 3.09506i) q^{92} +(-0.175374 + 0.572655i) q^{93} +(-12.5932 + 1.07184i) q^{94} +(9.34566 + 8.95709i) q^{95} +(-6.27951 - 1.63506i) q^{96} +(3.14412 - 5.10638i) q^{97} +(-9.41217 + 0.801093i) q^{98} +(-2.37155 + 2.27294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) \) 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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