LMFDB - Embedded newform 946.2.f.h.861.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(345,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			861.8
Character	$\chi$	$=$	946.861
Dual form			946.2.f.h.345.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.716858 + 2.20626i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.37704 - 1.72702i) q^{5} +(1.87676 + 1.36355i) q^{6} +(-0.0358425 + 0.110312i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.92666 + 1.39980i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.716858 + 2.20626i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.37704 - 1.72702i) q^{5} +(1.87676 + 1.36355i) q^{6} +(-0.0358425 + 0.110312i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.92666 + 1.39980i) q^{9} -2.93818 q^{10} +(2.20089 - 2.48115i) q^{11} +2.31980 q^{12} +(1.90025 - 1.38061i) q^{13} +(0.0358425 + 0.110312i) q^{14} +(2.10626 - 6.48240i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.75557 + 4.18166i) q^{17} +(-0.735918 + 2.26492i) q^{18} +(-1.19852 - 3.68865i) q^{19} +(-2.37704 + 1.72702i) q^{20} -0.269071 q^{21} +(0.322175 - 3.30094i) q^{22} +4.60534 q^{23} +(1.87676 - 1.36355i) q^{24} +(1.12263 + 3.45511i) q^{25} +(0.725832 - 2.23388i) q^{26} +(1.16081 + 0.843379i) q^{27} +(0.0938370 + 0.0681766i) q^{28} +(0.507151 - 1.56085i) q^{29} +(-2.10626 - 6.48240i) q^{30} +(3.65873 - 2.65822i) q^{31} -1.00000 q^{32} +(7.05179 + 3.07711i) q^{33} +7.11427 q^{34} +(0.275710 - 0.200315i) q^{35} +(0.735918 + 2.26492i) q^{36} +(-1.31806 + 4.05656i) q^{37} +(-3.13776 - 2.27971i) q^{38} +(4.40821 + 3.20275i) q^{39} +(-0.907948 + 2.79438i) q^{40} +(-1.73496 - 5.33967i) q^{41} +(-0.217683 + 0.158156i) q^{42} -1.00000 q^{43} +(-1.67960 - 2.85989i) q^{44} +6.99723 q^{45} +(3.72580 - 2.70695i) q^{46} +(-2.22202 - 6.83868i) q^{47} +(0.716858 - 2.20626i) q^{48} +(5.65223 + 4.10659i) q^{49} +(2.93909 + 2.13538i) q^{50} +(-5.09992 + 15.6960i) q^{51} +(-0.725832 - 2.23388i) q^{52} +(0.572722 - 0.416107i) q^{53} +1.43484 q^{54} +(-9.51659 + 2.09680i) q^{55} +0.115989 q^{56} +(7.27897 - 5.28848i) q^{57} +(-0.507151 - 1.56085i) q^{58} +(-3.37276 + 10.3803i) q^{59} +(-5.51426 - 4.00635i) q^{60} +(-5.15951 - 3.74860i) q^{61} +(1.39751 - 4.30110i) q^{62} +(-0.0853583 - 0.262706i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.90132 q^{65} +(7.51369 - 1.65550i) q^{66} -7.69907 q^{67} +(5.75557 - 4.18166i) q^{68} +(3.30138 + 10.1606i) q^{69} +(0.105312 - 0.324117i) q^{70} +(-5.68659 - 4.13155i) q^{71} +(1.92666 + 1.39980i) q^{72} +(2.73278 - 8.41064i) q^{73} +(1.31806 + 4.05656i) q^{74} +(-6.81811 + 4.95365i) q^{75} -3.87848 q^{76} +(0.194815 + 0.331715i) q^{77} +5.44885 q^{78} +(-5.68812 + 4.13266i) q^{79} +(0.907948 + 2.79438i) q^{80} +(-3.23633 + 9.96041i) q^{81} +(-4.54219 - 3.30010i) q^{82} +(9.85152 + 7.15755i) q^{83} +(-0.0831476 + 0.255902i) q^{84} +(-6.45939 - 19.8800i) q^{85} +(-0.809017 + 0.587785i) q^{86} +3.80720 q^{87} +(-3.03982 - 1.32645i) q^{88} -3.01884 q^{89} +(5.66087 - 4.11287i) q^{90} +(0.0841884 + 0.259105i) q^{91} +(1.42313 - 4.37994i) q^{92} +(8.48753 + 6.16655i) q^{93} +(-5.81733 - 4.22654i) q^{94} +(-3.52146 + 10.8379i) q^{95} +(-0.716858 - 2.20626i) q^{96} +(14.0633 - 10.2176i) q^{97} +6.98655 q^{98} +(-0.767254 + 7.86112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} + q^{6} + q^{7} + 10 q^{8} - 11 q^{9}+O(q^{10}) $ 40 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 + q^6 + q^7 + 10 * q^8 - 11 * q^9	\( 40 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} + q^{6} + q^{7} + 10 q^{8} - 11 q^{9} - 5 q^{11} + 4 q^{12} + 5 q^{13} - q^{14} - 11 q^{15} - 10 q^{16} + 3 q^{17} + 11 q^{18} + 3 q^{19} - 5 q^{20} - 44 q^{21} + 22 q^{23} + q^{24} - 9 q^{25} - 20 q^{26} - 16 q^{27} + 11 q^{28} - 5 q^{29} + 11 q^{30} - 17 q^{31} - 40 q^{32} + 56 q^{33} + 42 q^{34} + 12 q^{35} - 11 q^{36} + 29 q^{37} - 13 q^{38} - 34 q^{39} - 5 q^{40} - 12 q^{41} - 26 q^{42} - 40 q^{43} + 10 q^{44} - 8 q^{45} - 2 q^{46} - 23 q^{47} - q^{48} - 3 q^{49} + 19 q^{50} - 51 q^{51} + 20 q^{52} - 8 q^{53} - 64 q^{54} + 11 q^{55} + 24 q^{56} + 30 q^{57} + 5 q^{58} + 26 q^{59} + 4 q^{60} - 19 q^{61} - 23 q^{62} + 13 q^{63} - 10 q^{64} - 12 q^{65} - 6 q^{66} + 10 q^{67} + 3 q^{68} + 87 q^{69} + 8 q^{70} + 23 q^{71} + 11 q^{72} - 56 q^{73} - 29 q^{74} - 90 q^{75} - 32 q^{76} + 13 q^{77} + 94 q^{78} + 47 q^{79} + 5 q^{80} - 66 q^{81} + 2 q^{82} - 34 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{86} + 24 q^{87} + 5 q^{88} + 60 q^{89} - 77 q^{90} - 28 q^{91} - 13 q^{92} + 12 q^{93} - 17 q^{94} - 34 q^{95} + q^{96} + q^{97} - 12 q^{98} + 144 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 + q^6 + q^7 + 10 * q^8 - 11 * q^9 - 5 * q^11 + 4 * q^12 + 5 * q^13 - q^14 - 11 * q^15 - 10 * q^16 + 3 * q^17 + 11 * q^18 + 3 * q^19 - 5 * q^20 - 44 * q^21 + 22 * q^23 + q^24 - 9 * q^25 - 20 * q^26 - 16 * q^27 + 11 * q^28 - 5 * q^29 + 11 * q^30 - 17 * q^31 - 40 * q^32 + 56 * q^33 + 42 * q^34 + 12 * q^35 - 11 * q^36 + 29 * q^37 - 13 * q^38 - 34 * q^39 - 5 * q^40 - 12 * q^41 - 26 * q^42 - 40 * q^43 + 10 * q^44 - 8 * q^45 - 2 * q^46 - 23 * q^47 - q^48 - 3 * q^49 + 19 * q^50 - 51 * q^51 + 20 * q^52 - 8 * q^53 - 64 * q^54 + 11 * q^55 + 24 * q^56 + 30 * q^57 + 5 * q^58 + 26 * q^59 + 4 * q^60 - 19 * q^61 - 23 * q^62 + 13 * q^63 - 10 * q^64 - 12 * q^65 - 6 * q^66 + 10 * q^67 + 3 * q^68 + 87 * q^69 + 8 * q^70 + 23 * q^71 + 11 * q^72 - 56 * q^73 - 29 * q^74 - 90 * q^75 - 32 * q^76 + 13 * q^77 + 94 * q^78 + 47 * q^79 + 5 * q^80 - 66 * q^81 + 2 * q^82 - 34 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^86 + 24 * q^87 + 5 * q^88 + 60 * q^89 - 77 * q^90 - 28 * q^91 - 13 * q^92 + 12 * q^93 - 17 * q^94 - 34 * q^95 + q^96 + q^97 - 12 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.716858	+	2.20626i	0.413878	+	1.27379i	0.913250	+	0.407399i	$0.133564\pi$
$3$	0.716858	+	2.20626i	0.413878	+	1.27379i	−0.499372	+	0.866388i	$0.666436\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−2.37704	−	1.72702i	−1.06304	−	0.772347i	−0.0883953	−	0.996085i	$-0.528174\pi$
$5$	−2.37704	−	1.72702i	−1.06304	−	0.772347i	−0.974649	+	0.223738i	$0.928174\pi$
$6$	1.87676	+	1.36355i	0.766184	+	0.556665i
$7$	−0.0358425	+	0.110312i	−0.0135472	+	0.0416940i	−0.957602	−	0.288096i	$-0.906978\pi$
$7$	−0.0358425	+	0.110312i	−0.0135472	+	0.0416940i	0.944054	+	0.329790i	$0.106978\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−1.92666	+	1.39980i	−0.642219	+	0.466600i
$10$	−2.93818			−0.929135
$11$	2.20089	−	2.48115i	0.663593	−	0.748094i
$11$	2.20089	−	2.48115i	0.663593	−	0.748094i
$12$	2.31980			0.669669
$13$	1.90025	−	1.38061i	0.527035	−	0.382913i	−0.292212	−	0.956353i	$-0.594391\pi$
$13$	1.90025	−	1.38061i	0.527035	−	0.382913i	0.819248	+	0.573440i	$0.194391\pi$
$14$	0.0358425	+	0.110312i	0.00957932	+	0.0294821i
$15$	2.10626	−	6.48240i	0.543834	−	1.67375i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.75557	+	4.18166i	1.39593	+	1.01420i	0.995185	+	0.0980130i	$0.0312487\pi$
$17$	5.75557	+	4.18166i	1.39593	+	1.01420i	0.400745	+	0.916190i	$0.368751\pi$
$18$	−0.735918	+	2.26492i	−0.173458	+	0.533847i
$19$	−1.19852	−	3.68865i	−0.274959	−	0.846235i	−0.989230	−	0.146367i	$-0.953242\pi$
$19$	−1.19852	−	3.68865i	−0.274959	−	0.846235i	0.714272	−	0.699868i	$-0.246758\pi$
$20$	−2.37704	+	1.72702i	−0.531522	+	0.386174i
$21$	−0.269071			−0.0587162
$22$	0.322175	−	3.30094i	0.0686880	−	0.703763i
$23$	4.60534			0.960280			0.480140	−	0.877192i	$-0.340586\pi$
$23$	4.60534			0.960280			0.480140	+	0.877192i	$0.340586\pi$
$24$	1.87676	−	1.36355i	0.383092	−	0.278333i
$25$	1.12263	+	3.45511i	0.224527	+	0.691022i
$26$	0.725832	−	2.23388i	0.142347	−	0.438100i
$27$	1.16081	+	0.843379i	0.223398	+	0.162308i
$28$	0.0938370	+	0.0681766i	0.0177335	+	0.0128842i
$29$	0.507151	−	1.56085i	0.0941756	−	0.289843i	−0.892862	−	0.450330i	$-0.851306\pi$
$29$	0.507151	−	1.56085i	0.0941756	−	0.289843i	0.987038	+	0.160487i	$0.0513065\pi$
$30$	−2.10626	−	6.48240i	−0.384549	−	1.18352i
$31$	3.65873	−	2.65822i	0.657127	−	0.477431i	−0.208564	−	0.978009i	$-0.566879\pi$
$31$	3.65873	−	2.65822i	0.657127	−	0.477431i	0.865692	+	0.500578i	$0.166879\pi$
$32$	−1.00000			−0.176777
$33$	7.05179	+	3.07711i	1.22756	+	0.535656i
$34$	7.11427			1.22009
$35$	0.275710	−	0.200315i	0.0466035	−	0.0338595i
$36$	0.735918	+	2.26492i	0.122653	+	0.377487i
$37$	−1.31806	+	4.05656i	−0.216687	+	0.666894i	0.782342	+	0.622849i	$0.214025\pi$
$37$	−1.31806	+	4.05656i	−0.216687	+	0.666894i	−0.999030	+	0.0440458i	$0.985975\pi$
$38$	−3.13776	−	2.27971i	−0.509011	−	0.369818i
$39$	4.40821	+	3.20275i	0.705878	+	0.512851i
$40$	−0.907948	+	2.79438i	−0.143559	+	0.441830i
$41$	−1.73496	−	5.33967i	−0.270956	−	0.833916i	−0.990261	−	0.139222i	$-0.955540\pi$
$41$	−1.73496	−	5.33967i	−0.270956	−	0.833916i	0.719305	−	0.694694i	$-0.244460\pi$
$42$	−0.217683	+	0.158156i	−0.0335893	+	0.0244040i
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$	−1.67960	−	2.85989i	−0.253209	−	0.431144i
$45$	6.99723			1.04308
$46$	3.72580	−	2.70695i	0.549339	−	0.399118i
$47$	−2.22202	−	6.83868i	−0.324115	−	0.997524i	−0.971838	−	0.235648i	$-0.924279\pi$
$47$	−2.22202	−	6.83868i	−0.324115	−	0.997524i	0.647723	−	0.761876i	$-0.275721\pi$
$48$	0.716858	−	2.20626i	0.103470	−	0.318447i
$49$	5.65223	+	4.10659i	0.807462	+	0.586656i
$50$	2.93909	+	2.13538i	0.415651	+	0.301988i
$51$	−5.09992	+	15.6960i	−0.714132	+	2.19787i
$52$	−0.725832	−	2.23388i	−0.100655	−	0.309784i
$53$	0.572722	−	0.416107i	0.0786694	−	0.0571567i	−0.547755	−	0.836639i	$-0.684518\pi$
$53$	0.572722	−	0.416107i	0.0786694	−	0.0571567i	0.626425	+	0.779482i	$0.284518\pi$
$54$	1.43484			0.195257
$55$	−9.51659	+	2.09680i	−1.28322	+	0.282733i
$56$	0.115989			0.0154997
$57$	7.27897	−	5.28848i	0.964124	−	0.700477i
$58$	−0.507151	−	1.56085i	−0.0665922	−	0.204950i
$59$	−3.37276	+	10.3803i	−0.439096	+	1.35140i	0.449735	+	0.893162i	$0.351519\pi$
$59$	−3.37276	+	10.3803i	−0.439096	+	1.35140i	−0.888831	+	0.458236i	$0.848481\pi$
$60$	−5.51426	−	4.00635i	−0.711888	−	0.517217i
$61$	−5.15951	−	3.74860i	−0.660607	−	0.479959i	0.206261	−	0.978497i	$-0.433870\pi$
$61$	−5.15951	−	3.74860i	−0.660607	−	0.479959i	−0.866868	+	0.498538i	$0.833870\pi$
$62$	1.39751	−	4.30110i	0.177484	−	0.546240i
$63$	−0.0853583	−	0.262706i	−0.0107541	−	0.0330978i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−6.90132			−0.856004
$66$	7.51369	−	1.65550i	0.924872	−	0.203778i
$67$	−7.69907			−0.940591			−0.470295	−	0.882509i	$-0.655853\pi$
$67$	−7.69907			−0.940591			−0.470295	+	0.882509i	$0.655853\pi$
$68$	5.75557	−	4.18166i	0.697965	−	0.507101i
$69$	3.30138	+	10.1606i	0.397439	+	1.22319i
$70$	0.105312	−	0.324117i	0.0125872	−	0.0387394i
$71$	−5.68659	−	4.13155i	−0.674875	−	0.490325i	0.196779	−	0.980448i	$-0.436952\pi$
$71$	−5.68659	−	4.13155i	−0.674875	−	0.490325i	−0.871653	+	0.490123i	$0.836952\pi$
$72$	1.92666	+	1.39980i	0.227059	+	0.164968i
$73$	2.73278	−	8.41064i	0.319848	−	0.984391i	−0.653865	−	0.756611i	$-0.726853\pi$
$73$	2.73278	−	8.41064i	0.319848	−	0.984391i	0.973713	−	0.227779i	$-0.0731465\pi$
$74$	1.31806	+	4.05656i	0.153221	+	0.471566i
$75$	−6.81811	+	4.95365i	−0.787288	+	0.571998i
$76$	−3.87848			−0.444892
$77$	0.194815	+	0.331715i	0.0222012	+	0.0378024i
$78$	5.44885			0.616960
$79$	−5.68812	+	4.13266i	−0.639963	+	0.464960i	−0.859837	−	0.510568i	$-0.829435\pi$
$79$	−5.68812	+	4.13266i	−0.639963	+	0.464960i	0.219874	+	0.975528i	$0.429435\pi$
$80$	0.907948	+	2.79438i	0.101512	+	0.312421i
$81$	−3.23633	+	9.96041i	−0.359592	+	1.10671i
$82$	−4.54219	−	3.30010i	−0.501601	−	0.364435i
$83$	9.85152	+	7.15755i	1.08134	+	0.785643i	0.977917	−	0.208994i	$-0.0670190\pi$
$83$	9.85152	+	7.15755i	1.08134	+	0.785643i	0.103428	+	0.994637i	$0.467019\pi$
$84$	−0.0831476	+	0.255902i	−0.00907215	+	0.0279212i
$85$	−6.45939	−	19.8800i	−0.700620	−	2.15629i
$86$	−0.809017	+	0.587785i	−0.0872385	+	0.0633825i
$87$	3.80720			0.408175
$88$	−3.03982	−	1.32645i	−0.324046	−	0.141400i
$89$	−3.01884			−0.319996			−0.159998	−	0.987117i	$-0.551149\pi$
$89$	−3.01884			−0.319996			−0.159998	+	0.987117i	$0.551149\pi$
$90$	5.66087	−	4.11287i	0.596709	−	0.433534i
$91$	0.0841884	+	0.259105i	0.00882535	+	0.0271616i
$92$	1.42313	−	4.37994i	0.148371	−	0.456640i
$93$	8.48753	+	6.16655i	0.880116	+	0.639442i
$94$	−5.81733	−	4.22654i	−0.600012	−	0.435934i
$95$	−3.52146	+	10.8379i	−0.361294	+	1.11195i
$96$	−0.716858	−	2.20626i	−0.0731640	−	0.225176i
$97$	14.0633	−	10.2176i	1.42791	−	1.03744i	0.437509	−	0.899214i	$-0.355861\pi$
$97$	14.0633	−	10.2176i	1.42791	−	1.03744i	0.990401	−	0.138223i	$-0.0441390\pi$
$98$	6.98655			0.705748
$99$	−0.767254	+	7.86112i	−0.0771120	+	0.790073i
$100$	3.63292			0.363292
$101$	−2.53807	+	1.84402i	−0.252548	+	0.183487i	−0.706855	−	0.707358i	$-0.749887\pi$
$101$	−2.53807	+	1.84402i	−0.252548	+	0.183487i	0.454307	+	0.890845i	$0.349887\pi$
$102$	5.09992	+	15.6960i	0.504968	+	1.55413i
$103$	0.142128	−	0.437426i	0.0140043	−	0.0431009i	−0.943810	−	0.330488i	$-0.892787\pi$
$103$	0.142128	−	0.437426i	0.0140043	−	0.0431009i	0.957814	+	0.287387i	$0.0927867\pi$
$104$	−1.90025	−	1.38061i	−0.186335	−	0.135380i
$105$	0.639593	+	0.464692i	0.0624179	+	0.0453493i
$106$	0.218760	−	0.673275i	0.0212479	−	0.0653943i
$107$	4.62775	+	14.2427i	0.447381	+	1.37690i	0.879851	+	0.475250i	$0.157642\pi$
$107$	4.62775	+	14.2427i	0.447381	+	1.37690i	−0.432470	+	0.901648i	$0.642358\pi$
$108$	1.16081	−	0.843379i	0.111699	−	0.0811542i
$109$	6.45526			0.618302			0.309151	−	0.951013i	$-0.399955\pi$
$109$	6.45526			0.618302			0.309151	+	0.951013i	$0.399955\pi$
$110$	−6.46661	+	7.29006i	−0.616568	+	0.695080i
$111$	−9.89470			−0.939163
$112$	0.0938370	−	0.0681766i	0.00886676	−	0.00644208i
$113$	4.10327	+	12.6286i	0.386004	+	1.18800i	0.935750	+	0.352665i	$0.114725\pi$
$113$	4.10327	+	12.6286i	0.386004	+	1.18800i	−0.549746	+	0.835332i	$0.685275\pi$
$114$	2.78032	−	8.55695i	0.260401	−	0.801432i
$115$	−10.9471	−	7.95352i	−1.02082	−	0.741669i
$116$	−1.32774	−	0.964659i	−0.123277	−	0.0895663i
$117$	−1.72855	+	5.31994i	−0.159805	+	0.491829i
$118$	3.37276	+	10.3803i	0.310488	+	0.955583i
$119$	−0.667582	+	0.485027i	−0.0611971	+	0.0444623i
$120$	−6.81600			−0.622213
$121$	−1.31217	−	10.9215i	−0.119289	−	0.992860i
$122$	−6.37750			−0.577392
$123$	10.5370	−	7.65557i	0.950088	−	0.690280i
$124$	−1.39751	−	4.30110i	−0.125500	−	0.386250i
$125$	−1.24124	+	3.82014i	−0.111020	+	0.341684i
$126$	−0.223471	−	0.162361i	−0.0199084	−	0.0144643i
$127$	−13.6381	−	9.90869i	−1.21019	−	0.879254i	−0.214941	−	0.976627i	$-0.568956\pi$
$127$	−13.6381	−	9.90869i	−1.21019	−	0.879254i	−0.995248	+	0.0973732i	$0.968956\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−0.716858	−	2.20626i	−0.0631158	−	0.194251i
$130$	−5.58329	+	4.05650i	−0.489687	+	0.355778i
$131$	−18.6457			−1.62908			−0.814542	−	0.580104i	$-0.803012\pi$
$131$	−18.6457			−1.62908			−0.814542	+	0.580104i	$0.803012\pi$
$132$	5.10563	−	5.75577i	0.444388	−	0.500975i
$133$	0.449861			0.0390079
$134$	−6.22868	+	4.52540i	−0.538076	+	0.390935i
$135$	−1.30276	−	4.00949i	−0.112124	−	0.345082i
$136$	2.19843	−	6.76608i	0.188514	−	0.580186i
$137$	−6.95846	−	5.05562i	−0.594501	−	0.431930i	0.249422	−	0.968395i	$-0.419759\pi$
$137$	−6.95846	−	5.05562i	−0.594501	−	0.431930i	−0.843923	+	0.536465i	$0.819759\pi$
$138$	8.64312	+	6.27959i	0.735751	+	0.534554i
$139$	−0.206669	+	0.636062i	−0.0175295	+	0.0539501i	−0.959439	−	0.281918i	$-0.909030\pi$
$139$	−0.206669	+	0.636062i	−0.0175295	+	0.0539501i	0.941909	+	0.335868i	$0.109030\pi$
$140$	−0.105312	−	0.324117i	−0.00890048	−	0.0273929i
$141$	13.4951	−	9.80473i	1.13649	−	0.825707i
$142$	−7.02902			−0.589862
$143$	0.756739	−	7.75338i	0.0632817	−	0.648370i
$144$	2.38148			0.198457
$145$	−3.90114	+	2.83434i	−0.323972	+	0.235379i
$146$	−2.73278	−	8.41064i	−0.226167	−	0.696070i
$147$	−5.00836	+	15.4142i	−0.413083	+	1.27134i
$148$	3.45072	+	2.50709i	0.283647	+	0.206082i
$149$	7.19843	+	5.22997i	0.589719	+	0.428456i	0.842215	−	0.539142i	$-0.181251\pi$
$149$	7.19843	+	5.22997i	0.589719	+	0.428456i	−0.252496	+	0.967598i	$0.581251\pi$
$150$	−2.60429	+	8.01517i	−0.212639	+	0.654436i
$151$	1.22918	+	3.78304i	0.100030	+	0.307860i	0.988532	−	0.151013i	$-0.0482535\pi$
$151$	1.22918	+	3.78304i	0.100030	+	0.307860i	−0.888502	+	0.458872i	$0.848253\pi$
$152$	−3.13776	+	2.27971i	−0.254506	+	0.184909i
$153$	−16.9425			−1.36972
$154$	0.352586	+	0.153854i	0.0284122	+	0.0123979i
$155$	−13.2878			−1.06730
$156$	4.40821	−	3.20275i	0.352939	−	0.256425i
$157$	−6.03392	−	18.5705i	−0.481559	−	1.48209i	−0.836903	−	0.547352i	$-0.815636\pi$
$157$	−6.03392	−	18.5705i	−0.481559	−	1.48209i	0.355343	−	0.934736i	$-0.384364\pi$
$158$	−2.17267	+	6.68678i	−0.172848	+	0.531972i
$159$	1.32860	+	0.965286i	0.105365	+	0.0765521i
$160$	2.37704	+	1.72702i	0.187922	+	0.136533i
$161$	−0.165067	+	0.508024i	−0.0130091	+	0.0400379i
$162$	3.23633	+	9.96041i	0.254270	+	0.782563i
$163$	−13.6420	+	9.91147i	−1.06852	+	0.776326i	−0.975646	−	0.219352i	$-0.929606\pi$
$163$	−13.6420	+	9.91147i	−1.06852	+	0.776326i	−0.0928754	+	0.995678i	$0.529606\pi$
$164$	−5.61446			−0.438416
$165$	−11.4481	−	19.4930i	−0.891237	−	1.51753i
$166$	12.1771			0.945130
$167$	11.8513	−	8.61048i	0.917082	−	0.666299i	−0.0257141	−	0.999669i	$-0.508186\pi$
$167$	11.8513	−	8.61048i	0.917082	−	0.666299i	0.942796	+	0.333370i	$0.108186\pi$
$168$	0.0831476	+	0.255902i	0.00641498	+	0.0197433i
$169$	−2.31236	+	7.11670i	−0.177874	+	0.547439i
$170$	−16.9109	−	12.2865i	−1.29701	−	0.942331i
$171$	7.47251	+	5.42909i	0.571437	+	0.415173i
$172$	−0.309017	+	0.951057i	−0.0235623	+	0.0725174i
$173$	2.09585	+	6.45037i	0.159345	+	0.490413i	0.998575	−	0.0533632i	$-0.0169941\pi$
$173$	2.09585	+	6.45037i	0.159345	+	0.490413i	−0.839230	+	0.543776i	$0.816994\pi$
$174$	3.08009	−	2.23782i	0.233501	−	0.169648i
$175$	−0.421378			−0.0318532
$176$	−3.23894	+	0.713639i	−0.244144	+	0.0537926i
$177$	−25.3194			−1.90312
$178$	−2.44229	+	1.77443i	−0.183057	+	0.132999i
$179$	1.55629	+	4.78978i	0.116323	+	0.358005i	0.992221	−	0.124492i	$-0.0397300\pi$
$179$	1.55629	+	4.78978i	0.116323	+	0.358005i	−0.875898	+	0.482497i	$0.839730\pi$
$180$	2.16226	−	6.65476i	0.161165	−	0.496016i
$181$	−20.9186	−	15.1983i	−1.55487	−	1.12968i	−0.940064	−	0.340997i	$-0.889235\pi$
$181$	−20.9186	−	15.1983i	−1.55487	−	1.12968i	−0.614803	−	0.788681i	$-0.710765\pi$
$182$	0.220408	+	0.160136i	0.0163377	+	0.0118701i
$183$	4.57176	−	14.0704i	0.337955	−	1.04012i
$184$	−1.42313	−	4.37994i	−0.104914	−	0.322893i
$185$	10.1388	−	7.36630i	0.745422	−	0.541581i
$186$	10.4912			0.769249
$187$	23.0427	−	5.07703i	1.68505	−	0.371269i
$188$	−7.19061			−0.524429
$189$	−0.134641	+	0.0978226i	−0.00979371	+	0.00711555i
$190$	3.52146	+	10.8379i	0.255474	+	0.786267i
$191$	−2.87204	+	8.83924i	−0.207814	+	0.639585i	0.791772	+	0.610816i	$0.209159\pi$
$191$	−2.87204	+	8.83924i	−0.207814	+	0.639585i	−0.999586	+	0.0287688i	$0.990841\pi$
$192$	−1.87676	−	1.36355i	−0.135443	−	0.0984054i
$193$	4.42662	+	3.21612i	0.318635	+	0.231502i	0.735593	−	0.677424i	$-0.236904\pi$
$193$	4.42662	+	3.21612i	0.318635	+	0.231502i	−0.416958	+	0.908926i	$0.636904\pi$
$194$	5.37169	−	16.5324i	0.385665	−	1.18696i
$195$	−4.94727	−	15.2261i	−0.354281	−	1.09037i
$196$	5.65223	−	4.10659i	0.403731	−	0.293328i
$197$	1.10657			0.0788399			0.0394199	−	0.999223i	$-0.487449\pi$
$197$	1.10657			0.0788399			0.0394199	+	0.999223i	$0.487449\pi$
$198$	3.99993	+	6.81076i	0.284263	+	0.484020i
$199$	3.99691			0.283333			0.141667	−	0.989914i	$-0.454754\pi$
$199$	3.99691			0.283333			0.141667	+	0.989914i	$0.454754\pi$
$200$	2.93909	−	2.13538i	0.207825	−	0.150994i
$201$	−5.51914	−	16.9862i	−0.389290	−	1.19811i
$202$	−0.969458	+	2.98368i	−0.0682108	+	0.209931i
$203$	0.154003	+	0.111890i	0.0108089	+	0.00785312i
$204$	13.3518	+	9.70063i	0.934811	+	0.679180i
$205$	−5.09764	+	15.6889i	−0.356035	+	1.09576i
$206$	−0.142128	−	0.437426i	−0.00990255	−	0.0304769i
$207$	−8.87292	+	6.44655i	−0.616710	+	0.448066i
$208$	−2.34884			−0.162863
$209$	−11.7899	−	5.14462i	−0.815524	−	0.355861i
$210$	0.790581			0.0545552
$211$	14.7463	−	10.7138i	1.01518	−	0.737569i	0.0498885	−	0.998755i	$-0.484113\pi$
$211$	14.7463	−	10.7138i	1.01518	−	0.737569i	0.965289	+	0.261185i	$0.0841134\pi$
$212$	−0.218760	−	0.673275i	−0.0150245	−	0.0462407i
$213$	5.03881	−	15.5079i	0.345254	−	1.06258i
$214$	12.1156	+	8.80250i	0.828205	+	0.601726i
$215$	2.37704	+	1.72702i	0.162113	+	0.117782i
$216$	0.443391	−	1.36462i	0.0301689	−	0.0928504i
$217$	0.162096	+	0.498879i	0.0110038	+	0.0338661i
$218$	5.22242	−	3.79431i	0.353707	−	0.256983i
$219$	20.5151			1.38628
$220$	−0.946610	+	9.69876i	−0.0638205	+	0.653891i
$221$	16.7103			1.12406
$222$	−8.00498	+	5.81596i	−0.537259	+	0.390342i
$223$	5.97424	+	18.3868i	0.400065	+	1.23127i	0.924946	+	0.380097i	$0.124110\pi$
$223$	5.97424	+	18.3868i	0.400065	+	1.23127i	−0.524882	+	0.851175i	$0.675890\pi$
$224$	0.0358425	−	0.110312i	0.00239483	−	0.00737053i
$225$	−6.99939	−	5.08536i	−0.466626	−	0.339024i
$226$	10.7425	+	7.80489i	0.714581	+	0.519174i
$227$	−6.38111	+	19.6390i	−0.423529	+	1.30349i	0.480866	+	0.876794i	$0.340322\pi$
$227$	−6.38111	+	19.6390i	−0.423529	+	1.30349i	−0.904396	+	0.426695i	$0.859678\pi$
$228$	−2.78032	−	8.55695i	−0.184131	−	0.566698i
$229$	7.73867	−	5.62247i	0.511386	−	0.371543i	−0.301963	−	0.953320i	$-0.597642\pi$
$229$	7.73867	−	5.62247i	0.511386	−	0.371543i	0.813349	+	0.581776i	$0.197642\pi$
$230$	−13.5313			−0.892230
$231$	−0.592196	+	0.667605i	−0.0389636	+	0.0439252i
$232$	−1.64118			−0.107748
$233$	−8.74481	+	6.35347i	−0.572891	+	0.416230i	−0.836154	−	0.548494i	$-0.815201\pi$
$233$	−8.74481	+	6.35347i	−0.572891	+	0.416230i	0.263263	+	0.964724i	$0.415201\pi$
$234$	1.72855	+	5.31994i	0.112999	+	0.347776i
$235$	−6.52871	+	20.0933i	−0.425886	+	1.31074i
$236$	8.83000	+	6.41537i	0.574784	+	0.417605i
$237$	−13.1953	−	9.58695i	−0.857127	−	0.622739i
$238$	−0.254994	+	0.784790i	−0.0165288	+	0.0508704i
$239$	6.15412	+	18.9404i	0.398077	+	1.22515i	0.926539	+	0.376198i	$0.122769\pi$
$239$	6.15412	+	18.9404i	0.398077	+	1.22515i	−0.528462	+	0.848957i	$0.677231\pi$
$240$	−5.51426	+	4.00635i	−0.355944	+	0.258608i
$241$	3.23715			0.208523			0.104262	−	0.994550i	$-0.466752\pi$
$241$	3.23715			0.208523			0.104262	+	0.994550i	$0.466752\pi$
$242$	−7.48104	−	8.06437i	−0.480900	−	0.518397i
$243$	−19.9907			−1.28241
$244$	−5.15951	+	3.74860i	−0.330304	+	0.239980i
$245$	−6.34342	−	19.5231i	−0.405267	−	1.24728i
$246$	4.02477	−	12.3870i	0.256610	−	0.789765i
$247$	−7.37009	−	5.35469i	−0.468948	−	0.340710i
$248$	−3.65873	−	2.65822i	−0.232330	−	0.168797i
$249$	−8.72929	+	26.8660i	−0.553196	+	1.70256i
$250$	1.24124	+	3.82014i	0.0785029	+	0.241607i
$251$	−0.893681	+	0.649297i	−0.0564086	+	0.0409833i	−0.615632	−	0.788034i	$-0.711099\pi$
$251$	−0.893681	+	0.649297i	−0.0564086	+	0.0409833i	0.559224	+	0.829017i	$0.311099\pi$
$252$	−0.276225			−0.0174006
$253$	10.1358	−	11.4265i	0.637235	−	0.718379i
$254$	−16.8577			−1.05774
$255$	39.2300	−	28.5022i	2.45668	−	1.78488i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−1.52418	+	4.69094i	−0.0950756	+	0.292613i	−0.987273	−	0.159032i	$-0.949163\pi$
$257$	−1.52418	+	4.69094i	−0.0950756	+	0.292613i	0.892198	+	0.451645i	$0.149163\pi$
$258$	−1.87676	−	1.36355i	−0.116842	−	0.0848906i
$259$	−0.400245	−	0.290795i	−0.0248700	−	0.0180691i
$260$	−2.13263	+	6.56355i	−0.132260	+	0.407054i
$261$	1.20777	+	3.71713i	0.0747591	+	0.230085i
$262$	−15.0847	+	10.9597i	−0.931937	+	0.677092i
$263$	6.60005			0.406977			0.203488	−	0.979077i	$-0.434772\pi$
$263$	6.60005			0.406977			0.203488	+	0.979077i	$0.434772\pi$
$264$	0.747383	−	7.65753i	0.0459983	−	0.471288i
$265$	−2.08001			−0.127774
$266$	0.363945	−	0.264422i	0.0223149	−	0.0162127i
$267$	−2.16408	−	6.66035i	−0.132439	−	0.407607i
$268$	−2.37914	+	7.32225i	−0.145329	+	0.447277i
$269$	−12.4934	−	9.07702i	−0.761739	−	0.553436i	0.137704	−	0.990473i	$-0.456028\pi$
$269$	−12.4934	−	9.07702i	−0.761739	−	0.553436i	−0.899443	+	0.437038i	$0.856028\pi$
$270$	−3.41068	−	2.47800i	−0.207567	−	0.150806i
$271$	−4.79896	+	14.7697i	−0.291516	+	0.897194i	0.692853	+	0.721079i	$0.256353\pi$
$271$	−4.79896	+	14.7697i	−0.291516	+	0.897194i	−0.984369	+	0.176116i	$0.943647\pi$
$272$	−2.19843	−	6.76608i	−0.133299	−	0.410254i
$273$	−0.511303	+	0.371484i	−0.0309455	+	0.0224832i
$274$	−8.60113			−0.519613
$275$	11.0434	+	4.81890i	0.665944	+	0.290590i
$276$	10.6835			0.643070
$277$	−5.87707	+	4.26994i	−0.353119	+	0.256556i	−0.750176	−	0.661238i	$-0.770031\pi$
$277$	−5.87707	+	4.26994i	−0.353119	+	0.256556i	0.397057	+	0.917794i	$0.370031\pi$
$278$	0.206669	+	0.636062i	0.0123952	+	0.0381485i
$279$	−3.32814	+	10.2430i	−0.199251	+	0.613231i
$280$	−0.275710	−	0.200315i	−0.0164768	−	0.0119711i
$281$	3.72342	+	2.70522i	0.222121	+	0.161380i	0.693281	−	0.720668i	$-0.256165\pi$
$281$	3.72342	+	2.70522i	0.222121	+	0.161380i	−0.471160	+	0.882048i	$0.656165\pi$
$282$	5.15465	−	15.8644i	0.306955	−	0.944710i
$283$	−2.36996	−	7.29399i	−0.140879	−	0.433583i	0.855579	−	0.517673i	$-0.173202\pi$
$283$	−2.36996	−	7.29399i	−0.140879	−	0.433583i	−0.996458	+	0.0840904i	$0.973202\pi$
$284$	−5.68659	+	4.13155i	−0.337437	+	0.245163i
$285$	−26.4357			−1.56592
$286$	−3.94511	−	6.71742i	−0.233279	−	0.397209i
$287$	0.651215			0.0384400
$288$	1.92666	−	1.39980i	0.113529	−	0.0824840i
$289$	10.3870	+	31.9677i	0.610997	+	1.88046i
$290$	−1.49010	+	4.58606i	−0.0875018	+	0.269303i
$291$	32.6240	+	23.7027i	1.91245	+	1.38948i
$292$	−7.15452	−	5.19806i	−0.418686	−	0.304194i
$293$	−5.91172	+	18.1944i	−0.345366	+	1.06293i	0.616021	+	0.787730i	$0.288744\pi$
$293$	−5.91172	+	18.1944i	−0.345366	+	1.06293i	−0.961387	+	0.275199i	$0.911256\pi$
$294$	5.00836	+	15.4142i	0.292094	+	0.898972i
$295$	25.9441	−	18.8495i	1.51053	−	1.09746i
$296$	4.26532			0.247917
$297$	4.64737	−	1.02396i	0.269667	−	0.0594162i
$298$	8.89775			0.515433
$299$	8.75131	−	6.35820i	0.506101	−	0.367704i
$300$	2.60429	+	8.01517i	0.150359	+	0.462756i
$301$	0.0358425	−	0.110312i	0.00206593	−	0.00635828i
$302$	3.21805	+	2.33805i	0.185178	+	0.134540i
$303$	−5.88783	−	4.27776i	−0.338247	−	0.245751i
$304$	−1.19852	+	3.68865i	−0.0687396	+	0.211559i
$305$	5.79044	+	17.8212i	0.331560	+	1.02044i
$306$	−13.7068	+	9.95855i	−0.783564	+	0.569293i
$307$	3.88159			0.221534			0.110767	−	0.993846i	$-0.464669\pi$
$307$	3.88159			0.221534			0.110767	+	0.993846i	$0.464669\pi$
$308$	0.375681	−	0.0827743i	0.0214064	−	0.00471650i
$309$	1.06696			0.0606974
$310$	−10.7500	+	7.81035i	−0.610560	+	0.443598i
$311$	7.60880	+	23.4175i	0.431456	+	1.32788i	0.896675	+	0.442689i	$0.145975\pi$
$311$	7.60880	+	23.4175i	0.431456	+	1.32788i	−0.465220	+	0.885195i	$0.654025\pi$
$312$	1.68379	−	5.18216i	0.0953256	−	0.293382i
$313$	4.50726	+	3.27472i	0.254765	+	0.185098i	0.707836	−	0.706377i	$-0.249672\pi$
$313$	4.50726	+	3.27472i	0.254765	+	0.185098i	−0.453071	+	0.891475i	$0.649672\pi$
$314$	−15.7970	−	11.4772i	−0.891477	−	0.647696i
$315$	−0.250798	+	0.771878i	−0.0141309	+	0.0434904i
$316$	2.17267	+	6.68678i	0.122222	+	0.376161i
$317$	−21.2985	+	15.4743i	−1.19624	+	0.869123i	−0.993910	−	0.110194i	$-0.964853\pi$
$317$	−21.2985	+	15.4743i	−1.19624	+	0.869123i	−0.202335	+	0.979316i	$0.564853\pi$
$318$	1.64224			0.0920924
$319$	−2.75651	−	4.69357i	−0.154335	−	0.262790i
$320$	2.93818			0.164249
$321$	−28.1058	+	20.4201i	−1.56871	+	1.13974i
$322$	0.165067	+	0.508024i	0.00919883	+	0.0283111i
$323$	8.52657	−	26.2421i	0.474431	−	1.46015i
$324$	8.47283	+	6.15587i	0.470713	+	0.341993i
$325$	6.90346	+	5.01566i	0.382935	+	0.278219i
$326$	−5.21077	+	16.0371i	−0.288598	+	0.888212i
$327$	4.62751	+	14.2420i	0.255902	+	0.787585i
$328$	−4.54219	+	3.30010i	−0.250801	+	0.182217i
$329$	0.834032			0.0459816
$330$	−20.7194	−	9.04111i	−1.14057	−	0.497697i
$331$	−26.7247			−1.46892			−0.734460	−	0.678651i	$-0.762565\pi$
$331$	−26.7247			−1.46892			−0.734460	+	0.678651i	$0.762565\pi$
$332$	9.85152	−	7.15755i	0.540672	−	0.392821i
$333$	−3.13893	−	9.66062i	−0.172012	−	0.529399i
$334$	4.52680	−	13.9320i	0.247695	−	0.762328i
$335$	18.3010	+	13.2964i	0.999890	+	0.726463i
$336$	0.217683	+	0.158156i	0.0118756	+	0.00862812i
$337$	−9.43872	+	29.0494i	−0.514160	+	1.58242i	0.270645	+	0.962679i	$0.412763\pi$
$337$	−9.43872	+	29.0494i	−0.514160	+	1.58242i	−0.784805	+	0.619743i	$0.787237\pi$
$338$	2.31236	+	7.11670i	0.125776	+	0.387098i
$339$	−24.9205	+	18.1058i	−1.35350	+	0.983372i
$340$	−20.9030			−1.13363
$341$	1.45702	−	14.9283i	0.0789020	−	0.808413i
$342$	9.23653			0.499454
$343$	−1.31246	+	0.953555i	−0.0708659	+	0.0514871i
$344$	0.309017	+	0.951057i	0.0166611	+	0.0512775i
$345$	9.70005	−	29.8537i	0.522233	−	1.60727i
$346$	5.48702	+	3.98655i	0.294984	+	0.214318i
$347$	21.3112	+	15.4835i	1.14405	+	0.831199i	0.987678	−	0.156500i	$-0.0500210\pi$
$347$	21.3112	+	15.4835i	1.14405	+	0.831199i	0.156369	+	0.987699i	$0.450021\pi$
$348$	1.17649	−	3.62086i	0.0630665	−	0.194099i
$349$	1.46262	+	4.50149i	0.0782924	+	0.240959i	0.982541	−	0.186048i	$-0.0595679\pi$
$349$	1.46262	+	4.50149i	0.0782924	+	0.240959i	−0.904248	+	0.427007i	$0.859568\pi$
$350$	−0.340902	+	0.247680i	−0.0182220	+	0.0132390i
$351$	3.37022			0.179889
$352$	−2.20089	+	2.48115i	−0.117308	+	0.132246i
$353$	15.1089			0.804168			0.402084	−	0.915603i	$-0.368286\pi$
$353$	15.1089			0.804168			0.402084	+	0.915603i	$0.368286\pi$
$354$	−20.4838	+	14.8824i	−1.08870	+	0.790990i
$355$	6.38199	+	19.6417i	0.338721	+	1.04247i
$356$	−0.932872	+	2.87108i	−0.0494421	+	0.152167i
$357$	−1.54866	−	1.12517i	−0.0819637	−	0.0595501i
$358$	4.07443	+	2.96025i	0.215340	+	0.156454i
$359$	−3.12137	+	9.60658i	−0.164740	+	0.507016i	−0.999017	−	0.0443287i	$-0.985885\pi$
$359$	−3.12137	+	9.60658i	−0.164740	+	0.507016i	0.834277	+	0.551345i	$0.185885\pi$
$360$	−2.16226	−	6.65476i	−0.113961	−	0.350736i
$361$	3.20159	−	2.32609i	0.168505	−	0.122426i
$362$	−25.8568			−1.35900
$363$	23.1550	−	10.7241i	1.21532	−	0.562871i
$364$	0.272440			0.0142797
$365$	−21.0213	+	15.2729i	−1.10030	+	0.799418i
$366$	−4.57176	−	14.0704i	−0.238970	−	0.735474i
$367$	10.3146	−	31.7452i	0.538419	−	1.65708i	−0.197724	−	0.980258i	$-0.563355\pi$
$367$	10.3146	−	31.7452i	0.538419	−	1.65708i	0.736143	−	0.676826i	$-0.236645\pi$
$368$	−3.72580	−	2.70695i	−0.194221	−	0.141110i
$369$	10.8171	+	7.85912i	0.563118	+	0.409129i
$370$	3.87269	−	11.9189i	0.201332	−	0.619635i
$371$	0.0253738	+	0.0780925i	0.00131734	+	0.00405436i
$372$	8.48753	−	6.16655i	0.440058	−	0.319721i
$373$	37.6263			1.94821			0.974107	−	0.226087i	$-0.0725933\pi$
$373$	37.6263			1.94821			0.974107	+	0.226087i	$0.0725933\pi$
$374$	15.6577	−	17.6516i	0.809642	−	0.912740i
$375$	−9.31803			−0.481181
$376$	−5.81733	+	4.22654i	−0.300006	+	0.217967i
$377$	−1.19122	−	3.66619i	−0.0613508	−	0.188818i
$378$	−0.0514284	+	0.158280i	−0.00264519	+	0.00814106i
$379$	−19.2424	−	13.9804i	−0.988416	−	0.718126i	−0.0288421	−	0.999584i	$-0.509182\pi$
$379$	−19.2424	−	13.9804i	−0.988416	−	0.718126i	−0.959574	+	0.281458i	$0.909182\pi$
$380$	9.21930	+	6.69822i	0.472940	+	0.343611i
$381$	12.0846	−	37.1924i	0.619111	−	1.90543i
$382$	2.87204	+	8.83924i	0.146947	+	0.452255i
$383$	10.8420	−	7.87718i	0.554001	−	0.402505i	−0.275257	−	0.961371i	$-0.588763\pi$
$383$	10.8420	−	7.87718i	0.554001	−	0.402505i	0.829259	+	0.558865i	$0.188763\pi$
$384$	−2.31980			−0.118382
$385$	0.109796	−	1.12495i	0.00559574	−	0.0573327i
$386$	5.47160			0.278497
$387$	1.92666	−	1.39980i	0.0979375	−	0.0711558i
$388$	−5.37169	−	16.5324i	−0.272706	−	0.839304i
$389$	0.695515	−	2.14057i	0.0352640	−	0.108531i	−0.931875	−	0.362779i	$-0.881828\pi$
$389$	0.695515	−	2.14057i	0.0352640	−	0.108531i	0.967139	+	0.254248i	$0.0818279\pi$
$390$	−12.9521	−	9.41027i	−0.655856	−	0.476508i
$391$	26.5064	+	19.2580i	1.34048	+	0.973918i
$392$	2.15896	−	6.64460i	0.109044	−	0.335603i
$393$	−13.3663	−	41.1374i	−0.674243	−	2.07511i
$394$	0.895234	−	0.650426i	0.0451013	−	0.0327680i
$395$	20.6581			1.03942
$396$	7.23928	+	3.15892i	0.363787	+	0.158742i
$397$	−12.1701			−0.610800			−0.305400	−	0.952224i	$-0.598790\pi$
$397$	−12.1701			−0.610800			−0.305400	+	0.952224i	$0.598790\pi$
$398$	3.23357	−	2.34933i	0.162084	−	0.117761i
$399$	0.322486	+	0.992511i	0.0161445	+	0.0496877i
$400$	1.12263	−	3.45511i	0.0561317	−	0.172756i
$401$	−6.45290	−	4.68831i	−0.322243	−	0.234123i	0.414889	−	0.909872i	$-0.363820\pi$
$401$	−6.45290	−	4.68831i	−0.322243	−	0.234123i	−0.737132	+	0.675749i	$0.763820\pi$
$402$	−14.4493	−	10.4980i	−0.720665	−	0.523594i
$403$	3.28253	−	10.1026i	0.163514	−	0.503246i
$404$	0.969458	+	2.98368i	0.0482323	+	0.148444i
$405$	24.8947	−	18.0871i	1.23703	−	0.898754i
$406$	0.190358			0.00944731
$407$	7.16402	+	12.1983i	0.355108	+	0.604649i
$408$	16.5037			0.817055
$409$	27.4750	−	19.9617i	1.35855	−	0.987044i	0.360014	−	0.932947i	$-0.382772\pi$
$409$	27.4750	−	19.9617i	1.35855	−	0.987044i	0.998536	−	0.0540971i	$-0.0172280\pi$
$410$	5.09764	+	15.6889i	0.251755	+	0.774821i
$411$	6.16579	−	18.9763i	0.304136	−	0.936034i
$412$	−0.372097	−	0.270344i	−0.0183319	−	0.0133189i
$413$	−1.02418	−	0.744112i	−0.0503967	−	0.0366153i
$414$	−3.38915	+	10.4307i	−0.166568	+	0.512643i
$415$	−11.0562	−	34.0275i	−0.542729	−	1.67035i
$416$	−1.90025	+	1.38061i	−0.0931675	+	0.0676902i
$417$	−1.55147			−0.0759760
$418$	−12.5622	+	2.76784i	−0.614435	+	0.135379i
$419$	−22.8886			−1.11818			−0.559092	−	0.829106i	$-0.688850\pi$
$419$	−22.8886			−1.11818			−0.559092	+	0.829106i	$0.688850\pi$
$420$	0.639593	−	0.464692i	0.0312090	−	0.0226746i
$421$	−3.47755	−	10.7028i	−0.169485	−	0.521622i	0.829854	−	0.557981i	$-0.188424\pi$
$421$	−3.47755	−	10.7028i	−0.169485	−	0.521622i	−0.999339	+	0.0363594i	$0.988424\pi$
$422$	5.63259	−	17.3353i	0.274190	−	0.843870i
$423$	13.8539	+	10.0654i	0.673598	+	0.489397i
$424$	−0.572722	−	0.416107i	−0.0278138	−	0.0202079i
$425$	−7.98672	+	24.5806i	−0.387413	+	1.19233i
$426$	−5.03881	−	15.5079i	−0.244131	−	0.751358i
$427$	0.598446	−	0.434796i	0.0289608	−	0.0210413i
$428$	14.9757			0.723878
$429$	17.6485	−	3.88851i	0.852076	−	0.187739i
$430$	2.93818			0.141692
$431$	21.3911	−	15.5416i	1.03037	−	0.748611i	0.0619910	−	0.998077i	$-0.480255\pi$
$431$	21.3911	−	15.5416i	1.03037	−	0.748611i	0.968384	+	0.249466i	$0.0802550\pi$
$432$	−0.443391	−	1.36462i	−0.0213326	−	0.0656551i
$433$	−6.13032	+	18.8672i	−0.294604	+	0.906699i	0.688750	+	0.724999i	$0.258160\pi$
$433$	−6.13032	+	18.8672i	−0.294604	+	0.906699i	−0.983354	+	0.181700i	$0.941840\pi$
$434$	0.424372	+	0.308324i	0.0203705	+	0.0148000i
$435$	−9.04987	−	6.57511i	−0.433908	−	0.315253i
$436$	1.99479	−	6.13932i	0.0955329	−	0.294020i
$437$	−5.51958	−	16.9875i	−0.264037	−	0.812623i
$438$	16.5971	−	12.0585i	0.793038	−	0.576176i
$439$	7.31769			0.349254			0.174627	−	0.984635i	$-0.444128\pi$
$439$	7.31769			0.349254			0.174627	+	0.984635i	$0.444128\pi$
$440$	4.93497	+	8.40287i	0.235265	+	0.400591i
$441$	−16.6383			−0.792301
$442$	13.5189	−	9.82207i	0.643029	−	0.467188i
$443$	−5.17162	−	15.9166i	−0.245711	−	0.756222i	−0.995519	−	0.0945654i	$-0.969854\pi$
$443$	−5.17162	−	15.9166i	−0.245711	−	0.756222i	0.749807	−	0.661656i	$-0.230146\pi$
$444$	−3.05763	+	9.41042i	−0.145109	+	0.446599i
$445$	7.17589	+	5.21359i	0.340170	+	0.247148i
$446$	15.6408	+	11.3637i	0.740612	+	0.538086i
$447$	−6.37843	+	19.6308i	−0.301689	+	0.928504i
$448$	−0.0358425	−	0.110312i	−0.00169340	−	0.00521175i
$449$	13.8759	−	10.0814i	0.654844	−	0.475772i	−0.210074	−	0.977686i	$-0.567370\pi$
$449$	13.8759	−	10.0814i	0.654844	−	0.475772i	0.864918	+	0.501913i	$0.167370\pi$
$450$	−8.65173			−0.407846
$451$	−17.0670	−	7.44732i	−0.803652	−	0.350681i
$452$	13.2785			0.624567
$453$	−7.46523	+	5.42381i	−0.350747	+	0.254833i
$454$	6.38111	+	19.6390i	0.299480	+	0.921706i
$455$	0.247361	−	0.761299i	0.0115965	−	0.0356902i
$456$	−7.27897	−	5.28848i	−0.340869	−	0.247656i
$457$	−20.3432	−	14.7802i	−0.951613	−	0.691388i	−0.000425515	−	1.00000i	$-0.500135\pi$
$457$	−20.3432	−	14.7802i	−0.951613	−	0.691388i	−0.951188	+	0.308612i	$0.900135\pi$
$458$	2.95591	−	9.09735i	0.138121	−	0.425091i
$459$	3.15440	+	9.70825i	0.147235	+	0.453142i
$460$	−10.9471	+	7.95352i	−0.510410	+	0.370835i
$461$	25.8044			1.20183			0.600916	−	0.799312i	$-0.294803\pi$
$461$	25.8044			1.20183			0.600916	+	0.799312i	$0.294803\pi$
$462$	−0.0866882	+	0.888188i	−0.00403310	+	0.0413223i
$463$	−8.10195			−0.376529			−0.188265	−	0.982118i	$-0.560286\pi$
$463$	−8.10195			−0.376529			−0.188265	+	0.982118i	$0.560286\pi$
$464$	−1.32774	+	0.964659i	−0.0616387	+	0.0447831i
$465$	−9.52544	−	29.3163i	−0.441731	−	1.35951i
$466$	−3.34022	+	10.2801i	−0.154733	+	0.476218i
$467$	−27.1405	−	19.7188i	−1.25591	−	0.912475i	−0.257365	−	0.966314i	$-0.582854\pi$
$467$	−27.1405	−	19.7188i	−1.25591	−	0.912475i	−0.998550	+	0.0538393i	$0.982854\pi$
$468$	4.52541	+	3.28791i	0.209187	+	0.151984i
$469$	0.275954	−	0.849300i	0.0127424	−	0.0392170i
$470$	6.52871	+	20.0933i	0.301147	+	0.926835i
$471$	36.6459	−	26.6248i	1.68856	−	1.22681i
$472$	10.9145			0.502380
$473$	−2.20089	+	2.48115i	−0.101197	+	0.114083i
$474$	−16.3103			−0.749156
$475$	11.3992	−	8.28201i	0.523032	−	0.380005i
$476$	0.254994	+	0.784790i	0.0116876	+	0.0359708i
$477$	−0.520974	+	1.60339i	−0.0238537	+	0.0734143i
$478$	16.1117	+	11.7058i	0.736932	+	0.535412i
$479$	−10.4654	−	7.60354i	−0.478175	−	0.347414i	0.322444	−	0.946589i	$-0.395496\pi$
$479$	−10.4654	−	7.60354i	−0.478175	−	0.347414i	−0.800619	+	0.599174i	$0.795496\pi$
$480$	−2.10626	+	6.48240i	−0.0961372	+	0.295880i
$481$	3.09591	+	9.52822i	0.141161	+	0.434449i
$482$	2.61891	−	1.90275i	0.119288	−	0.0866680i
$483$	−1.23917			−0.0563840
$484$	−10.7924	−	2.12696i	−0.490564	−	0.0966801i
$485$	−51.0749			−2.31919
$486$	−16.1728	+	11.7503i	−0.733615	+	0.533003i
$487$	−6.76088	−	20.8078i	−0.306365	−	0.942893i	−0.979164	−	0.203069i	$-0.934909\pi$
$487$	−6.76088	−	20.8078i	−0.306365	−	0.942893i	0.672800	−	0.739825i	$-0.265091\pi$
$488$	−1.97076	+	6.06536i	−0.0892120	+	0.274566i
$489$	−31.6467	−	22.9926i	−1.43111	−	1.03976i
$490$	−16.6073	−	12.0659i	−0.750241	−	0.545082i
$491$	−6.24128	+	19.2087i	−0.281665	+	0.866875i	0.705714	+	0.708497i	$0.250627\pi$
$491$	−6.24128	+	19.2087i	−0.281665	+	0.866875i	−0.987379	+	0.158378i	$0.949373\pi$
$492$	−4.02477	−	12.3870i	−0.181451	−	0.558448i
$493$	9.44589	−	6.86284i	0.425422	−	0.309087i
$494$	−9.10993			−0.409875
$495$	15.4001	−	17.3611i	0.692184	−	0.780325i
$496$	−4.52244			−0.203064
$497$	0.659582	−	0.479214i	0.0295863	−	0.0214957i
$498$	8.72929	+	26.8660i	0.391169	+	1.20389i
$499$	−3.74363	+	11.5217i	−0.167588	+	0.515782i	−0.999218	−	0.0395481i	$-0.987408\pi$
$499$	−3.74363	+	11.5217i	−0.167588	+	0.515782i	0.831630	+	0.555330i	$0.187408\pi$
$500$	3.24961	+	2.36098i	0.145327	+	0.105586i
$501$	27.4927	+	19.9746i	1.22828	+	0.892400i
$502$	−0.341356	+	1.05059i	−0.0152355	+	0.0468899i
$503$	1.57072	+	4.83418i	0.0700349	+	0.215545i	0.979948	−	0.199254i	$-0.0638518\pi$
$503$	1.57072	+	4.83418i	0.0700349	+	0.215545i	−0.909913	+	0.414799i	$0.863852\pi$
$504$	−0.223471	+	0.162361i	−0.00995419	+	0.00723214i
$505$	9.21776			0.410185
$506$	1.48373	−	15.2020i	0.0659597	−	0.675809i
$507$	−17.3590			−0.770938
$508$	−13.6381	+	9.90869i	−0.605095	+	0.439627i
$509$	−5.14150	−	15.8239i	−0.227893	−	0.701382i	−0.997985	−	0.0634494i	$-0.979790\pi$
$509$	−5.14150	−	15.8239i	−0.227893	−	0.701382i	0.770092	−	0.637933i	$-0.220210\pi$
$510$	14.9845	−	46.1176i	0.663525	−	2.04212i
$511$	0.829845	+	0.602917i	0.0367102	+	0.0266715i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	1.71968	−	5.29264i	0.0759258	−	0.233676i
$514$	1.52418	+	4.69094i	0.0672286	+	0.206908i
$515$	−1.09329	+	0.794320i	−0.0481760	+	0.0350019i
$516$	−2.31980			−0.102124
$517$	−21.8582	−	9.53802i	−0.961322	−	0.419481i
$518$	−0.494730			−0.0217372
$519$	−12.7288	+	9.24801i	−0.558732	+	0.405942i
$520$	2.13263	+	6.56355i	0.0935219	+	0.287831i
$521$	8.84336	−	27.2171i	0.387435	−	1.19240i	−0.547264	−	0.836960i	$-0.684331\pi$
$521$	8.84336	−	27.2171i	0.387435	−	1.19240i	0.934699	−	0.355441i	$-0.115669\pi$
$522$	3.16198	+	2.29732i	0.138396	+	0.100551i
$523$	−0.777749	−	0.565068i	−0.0340086	−	0.0247087i	0.570651	−	0.821193i	$-0.306691\pi$
$523$	−0.777749	−	0.565068i	−0.0340086	−	0.0247087i	−0.604660	+	0.796484i	$0.706691\pi$
$524$	−5.76185	+	17.7331i	−0.251707	+	0.774676i
$525$	−0.302068	−	0.929671i	−0.0131833	−	0.0405742i
$526$	5.33955	−	3.87941i	0.232816	−	0.169150i
$527$	32.1739			1.40152
$528$	−3.89634	−	6.63437i	−0.169566	−	0.288724i
$529$	−1.79084			−0.0778624
$530$	−1.68276	+	1.22260i	−0.0730945	+	0.0531063i
$531$	−8.03216	−	24.7204i	−0.348566	−	1.07278i
$532$	0.139015	−	0.427843i	0.00602705	−	0.0185493i
$533$	−10.6689	−	7.75140i	−0.462121	−	0.335751i
$534$	−5.66563	−	4.11632i	−0.245176	−	0.178131i
$535$	13.5972	−	41.8478i	0.587857	−	1.80924i
$536$	2.37914	+	7.32225i	0.102763	+	0.316273i
$537$	−9.45188	+	6.86719i	−0.407879	+	0.296341i
$538$	−15.4427			−0.665784
$539$	22.6290	−	4.98588i	0.974700	−	0.214757i
$540$	−4.21583			−0.181420
$541$	−34.2201	+	24.8623i	−1.47124	+	1.06892i	−0.490983	+	0.871169i	$0.663362\pi$
$541$	−34.2201	+	24.8623i	−1.47124	+	1.06892i	−0.980253	+	0.197746i	$0.936638\pi$
$542$	4.79896	+	14.7697i	0.206133	+	0.634412i
$543$	18.5357	−	57.0469i	0.795442	−	2.44812i
$544$	−5.75557	−	4.18166i	−0.246768	−	0.179287i
$545$	−15.3444	−	11.1484i	−0.657283	−	0.477544i
$546$	−0.195301	+	0.601073i	−0.00835809	+	0.0257236i
$547$	13.9976	+	43.0803i	0.598495	+	1.84198i	0.536495	+	0.843904i	$0.319748\pi$
$547$	13.9976	+	43.0803i	0.598495	+	1.84198i	0.0620007	+	0.998076i	$0.480252\pi$
$548$	−6.95846	+	5.05562i	−0.297251	+	0.215965i
$549$	15.1879			0.648204
$550$	11.7668	−	2.59259i	0.501738	−	0.110549i
$551$	−6.36527			−0.271169
$552$	8.64312	−	6.27959i	0.367875	−	0.267277i
$553$	−0.252005	−	0.775592i	−0.0107164	−	0.0329815i
$554$	−2.24484	+	6.90891i	−0.0953741	+	0.293531i
$555$	23.5201	+	17.0883i	0.998372	+	0.725360i
$556$	0.541067	+	0.393108i	0.0229464	+	0.0166715i
$557$	0.0914132	−	0.281341i	0.00387330	−	0.0119208i	−0.949101	−	0.314971i	$-0.898005\pi$
$557$	0.0914132	−	0.281341i	0.00387330	−	0.0119208i	0.952974	+	0.303051i	$0.0980051\pi$
$558$	3.32814	+	10.2430i	0.140892	+	0.433620i
$559$	−1.90025	+	1.38061i	−0.0803721	+	0.0583938i
$560$	−0.340797			−0.0144013
$561$	27.7196	+	47.1987i	1.17032	+	1.99273i
$562$	4.60240			0.194141
$563$	0.540063	−	0.392379i	0.0227609	−	0.0165368i	−0.576347	−	0.817205i	$-0.695522\pi$
$563$	0.540063	−	0.392379i	0.0227609	−	0.0165368i	0.599108	+	0.800669i	$0.295522\pi$
$564$	−5.15465	−	15.8644i	−0.217050	−	0.668011i
$565$	12.0562	−	37.1051i	0.507207	−	1.56102i
$566$	−6.20464	−	4.50793i	−0.260800	−	0.189483i
$567$	−0.982754	−	0.714013i	−0.0412718	−	0.0299857i
$568$	−2.17209	+	6.68499i	−0.0911387	+	0.280496i
$569$	7.78185	+	23.9501i	0.326232	+	1.00404i	0.970881	+	0.239561i	$0.0770033\pi$
$569$	7.78185	+	23.9501i	0.326232	+	1.00404i	−0.644649	+	0.764478i	$0.722997\pi$
$570$	−21.3870	+	15.5385i	−0.895801	+	0.650838i
$571$	−21.7387			−0.909736			−0.454868	−	0.890559i	$-0.650313\pi$
$571$	−21.7387			−0.909736			−0.454868	+	0.890559i	$0.650313\pi$
$572$	−7.14006	−	3.11563i	−0.298541	−	0.130271i
$573$	−21.5605			−0.900704
$574$	0.526844	−	0.382775i	0.0219900	−	0.0159767i
$575$	5.17011	+	15.9120i	0.215609	+	0.663575i
$576$	0.735918	−	2.26492i	0.0306632	−	0.0943718i
$577$	0.993141	+	0.721559i	0.0413450	+	0.0300389i	0.608266	−	0.793733i	$-0.291865\pi$
$577$	0.993141	+	0.721559i	0.0413450	+	0.0300389i	−0.566921	+	0.823772i	$0.691865\pi$
$578$	27.1934	+	19.7572i	1.13110	+	0.821789i
$579$	−3.92236	+	12.0718i	−0.163008	+	0.501686i
$580$	1.49010	+	4.58606i	0.0618731	+	0.190426i
$581$	−1.14267	+	0.830196i	−0.0474058	+	0.0344423i
$582$	40.3255			1.67155
$583$	0.228076	−	2.33681i	0.00944592	−	0.0967809i
$584$	−8.84347			−0.365945
$585$	13.2965	−	9.66047i	0.549742	−	0.399411i
$586$	5.91172	+	18.1944i	0.244211	+	0.751604i
$587$	−6.51448	+	20.0495i	−0.268881	+	0.827531i	0.721893	+	0.692005i	$0.243272\pi$
$587$	−6.51448	+	20.0495i	−0.268881	+	0.827531i	−0.990774	+	0.135526i	$0.956728\pi$
$588$	13.1121	+	9.52647i	0.540732	+	0.392865i
$589$	−14.1903	−	10.3099i	−0.584702	−	0.424811i
$590$	9.90978	−	30.4992i	0.407979	−	1.25563i
$591$	0.793254	+	2.44139i	0.0326301	+	0.100425i
$592$	3.45072	−	2.50709i	0.141824	−	0.103041i
$593$	15.1295			0.621293			0.310646	−	0.950526i	$-0.399455\pi$
$593$	15.1295			0.621293			0.310646	+	0.950526i	$0.399455\pi$
$594$	3.15793	−	3.56005i	0.129571	−	0.146071i
$595$	2.42452			0.0993956
$596$	7.19843	−	5.22997i	0.294859	−	0.214228i
$597$	2.86522	+	8.81824i	0.117266	+	0.360906i
$598$	3.34270	−	10.2878i	0.136693	−	0.420699i
$599$	9.39589	+	6.82651i	0.383906	+	0.278924i	0.762954	−	0.646453i	$-0.223748\pi$
$599$	9.39589	+	6.82651i	0.383906	+	0.278924i	−0.379048	+	0.925377i	$0.623748\pi$
$600$	6.81811	+	4.95365i	0.278348	+	0.202232i
$601$	6.59113	−	20.2854i	0.268858	−	0.827460i	−0.721922	−	0.691975i	$-0.756741\pi$
$601$	6.59113	−	20.2854i	0.268858	−	0.827460i	0.990779	−	0.135485i	$-0.0432591\pi$
$602$	−0.0358425	−	0.110312i	−0.00146083	−	0.00449598i
$603$	14.8335	−	10.7771i	0.604066	−	0.438879i
$604$	3.97773			0.161851
$605$	−15.7425	+	28.2269i	−0.640023	+	1.14759i
$606$	−7.27776			−0.295639
$607$	−22.1769	+	16.1124i	−0.900132	+	0.653984i	−0.938500	−	0.345280i	$-0.887784\pi$
$607$	−22.1769	+	16.1124i	−0.900132	+	0.653984i	0.0383682	+	0.999264i	$0.487784\pi$
$608$	1.19852	+	3.68865i	0.0486063	+	0.149595i
$609$	−0.136460	+	0.419980i	−0.00552963	+	0.0170184i
$610$	15.1596	+	11.0141i	0.613793	+	0.445947i
$611$	−13.6640	−	9.92746i	−0.552786	−	0.401622i
$612$	−5.23552	+	16.1133i	−0.211633	+	0.651341i
$613$	−6.52273	−	20.0749i	−0.263451	−	0.810818i	−0.992046	−	0.125874i	$-0.959827\pi$
$613$	−6.52273	−	20.0749i	−0.263451	−	0.810818i	0.728596	−	0.684944i	$-0.240173\pi$
$614$	3.14027	−	2.28154i	0.126731	−	0.0920755i
$615$	−38.2682			−1.54312
$616$	0.255279	−	0.287785i	0.0102855	−	0.0115952i
$617$	−12.3935			−0.498942			−0.249471	−	0.968382i	$-0.580257\pi$
$617$	−12.3935			−0.498942			−0.249471	+	0.968382i	$0.580257\pi$
$618$	0.863191	−	0.627145i	0.0347226	−	0.0252275i
$619$	−4.66236	−	14.3493i	−0.187396	−	0.576746i	0.812585	−	0.582842i	$-0.198060\pi$
$619$	−4.66236	−	14.3493i	−0.187396	−	0.576746i	−0.999981	+	0.00609620i	$0.998060\pi$
$620$	−4.10614	+	12.6374i	−0.164907	+	0.507530i
$621$	5.34593	+	3.88405i	0.214525	+	0.155862i
$622$	19.9201	+	14.4728i	0.798723	+	0.580307i
$623$	0.108203	−	0.333014i	0.00433505	−	0.0133419i
$624$	−1.68379	−	5.18216i	−0.0674054	−	0.207452i
$625$	24.2434	−	17.6139i	0.969736	−	0.704555i
$626$	5.57128			0.222673
$627$	2.89871	−	29.6996i	0.115763	−	1.18609i
$628$	−19.5262			−0.779179
$629$	−24.5493	+	17.8361i	−0.978846	+	0.711173i
$630$	0.250798	+	0.771878i	0.00999205	+	0.0307524i
$631$	13.7309	−	42.2595i	0.546620	−	1.68232i	−0.170485	−	0.985360i	$-0.554534\pi$
$631$	13.7309	−	42.2595i	0.546620	−	1.68232i	0.717106	−	0.696964i	$-0.245466\pi$
$632$	5.68812	+	4.13266i	0.226261	+	0.164388i
$633$	34.2085	+	24.8539i	1.35967	+	0.987855i
$634$	−8.13532	+	25.0379i	−0.323095	+	0.994383i
$635$	15.3059	+	47.1067i	0.607396	+	1.86937i
$636$	1.32860	−	0.965286i	0.0526825	−	0.0382761i
$637$	16.4103			0.650199
$638$	−4.98888	−	2.17694i	−0.197512	−	0.0861860i
$639$	16.7395			0.662203
$640$	2.37704	−	1.72702i	0.0939608	−	0.0682665i
$641$	0.955836	+	2.94176i	0.0377533	+	0.116193i	0.968157	−	0.250344i	$-0.0805436\pi$
$641$	0.955836	+	2.94176i	0.0377533	+	0.116193i	−0.930404	+	0.366536i	$0.880544\pi$
$642$	−10.7355	+	33.0403i	−0.423695	+	1.30400i
$643$	10.0748	+	7.31975i	0.397310	+	0.288663i	0.768445	−	0.639916i	$-0.221031\pi$
$643$	10.0748	+	7.31975i	0.397310	+	0.288663i	−0.371134	+	0.928579i	$0.621031\pi$
$644$	0.432151	+	0.313976i	0.0170291	+	0.0123724i
$645$	−2.10626	+	6.48240i	−0.0829339	+	0.255244i
$646$	−8.52657	−	26.2421i	−0.335474	−	1.03248i
$647$	−6.39869	+	4.64892i	−0.251558	+	0.182768i	−0.706417	−	0.707796i	$-0.749690\pi$
$647$	−6.39869	+	4.64892i	−0.251558	+	0.182768i	0.454859	+	0.890564i	$0.349690\pi$
$648$	10.4730			0.411418
$649$	18.3319	+	31.2142i	0.719592	+	1.22526i
$650$	8.53315			0.334698
$651$	−0.984459	+	0.715252i	−0.0385840	+	0.0280329i
$652$	5.21077	+	16.0371i	0.204069	+	0.628061i
$653$	12.7753	−	39.3184i	0.499937	−	1.53865i	−0.309181	−	0.951003i	$-0.600055\pi$
$653$	12.7753	−	39.3184i	0.499937	−	1.53865i	0.809118	−	0.587646i	$-0.199945\pi$
$654$	12.1150	+	8.80205i	0.473733	+	0.344187i
$655$	44.3216	+	32.2016i	1.73179	+	1.25822i
$656$	−1.73496	+	5.33967i	−0.0677389	+	0.208479i
$657$	6.50807	+	20.0298i	0.253904	+	0.781436i
$658$	0.674746	−	0.490231i	0.0263043	−	0.0191112i
$659$	18.4684			0.719428			0.359714	−	0.933063i	$-0.382874\pi$
$659$	18.4684			0.719428			0.359714	+	0.933063i	$0.382874\pi$
$660$	−22.0766	+	4.86417i	−0.859331	+	0.189337i
$661$	−10.7091			−0.416536			−0.208268	−	0.978072i	$-0.566783\pi$
$661$	−10.7091			−0.416536			−0.208268	+	0.978072i	$0.566783\pi$
$662$	−21.6207	+	15.7084i	−0.840313	+	0.610523i
$663$	11.9789	+	36.8673i	0.465222	+	1.43181i
$664$	3.76295	−	11.5812i	0.146031	−	0.449436i
$665$	−1.06934	−	0.776919i	−0.0414671	−	0.0301276i
$666$	−8.21781	−	5.97059i	−0.318434	−	0.231356i
$667$	2.33560	−	7.18825i	0.0904349	−	0.278330i
$668$	−4.52680	−	13.9320i	−0.175147	−	0.539047i
$669$	−36.2835	+	26.3615i	−1.40280	+	1.01919i
$670$	22.6213			0.873936
$671$	−20.6563	+	4.55124i	−0.797429	+	0.175699i
$672$	0.269071			0.0103797
$673$	−9.38664	+	6.81979i	−0.361828	+	0.262884i	−0.753814	−	0.657087i	$-0.771788\pi$
$673$	−9.38664	+	6.81979i	−0.361828	+	0.262884i	0.391986	+	0.919971i	$0.371788\pi$
$674$	9.43872	+	29.0494i	0.363566	+	1.11894i
$675$	−1.61080	+	4.95754i	−0.0619998	+	0.190816i
$676$	6.05383	+	4.39836i	0.232840	+	0.169168i
$677$	17.3830	+	12.6295i	0.668084	+	0.485392i	0.869383	−	0.494138i	$-0.164516\pi$
$677$	17.3830	+	12.6295i	0.668084	+	0.485392i	−0.201299	+	0.979530i	$0.564516\pi$
$678$	−9.51878	+	29.2958i	−0.365567	+	1.12510i
$679$	0.623057	+	1.91757i	0.0239107	+	0.0735897i
$680$	−16.9109	+	12.2865i	−0.648504	+	0.471166i
$681$	−47.9032			−1.83566
$682$	−7.59588	−	12.9337i	−0.290861	−	0.495256i
$683$	5.74851			0.219961			0.109980	−	0.993934i	$-0.464921\pi$
$683$	5.74851			0.219961			0.109980	+	0.993934i	$0.464921\pi$
$684$	7.47251	−	5.42909i	0.285718	−	0.207587i
$685$	7.80938	+	24.0348i	0.298381	+	0.918323i
$686$	−0.501313	+	1.54288i	−0.0191402	+	0.0589076i
$687$	17.9522	+	13.0430i	0.684918	+	0.497622i
$688$	0.809017	+	0.587785i	0.0308435	+	0.0224091i
$689$	0.513833	−	1.58142i	0.0195755	−	0.0602472i
$690$	−9.70005	−	29.8537i	−0.369275	−	1.13651i
$691$	−21.3879	+	15.5392i	−0.813632	+	0.591138i	−0.914881	−	0.403723i	$-0.867716\pi$
$691$	−21.3879	+	15.5392i	−0.813632	+	0.591138i	0.101249	+	0.994861i	$0.467716\pi$
$692$	6.78232			0.257825
$693$	−0.839676	−	0.366400i	−0.0318967	−	0.0139184i
$694$	26.3421			0.999934
$695$	1.58975	−	1.15502i	0.0603028	−	0.0438126i
$696$	−1.17649	−	3.62086i	−0.0445947	−	0.137248i
$697$	12.3430	−	37.9879i	0.467525	−	1.43889i
$698$	3.82920	+	2.78207i	0.144937	+	0.105303i
$699$	−20.2862	−	14.7388i	−0.767295	−	0.557473i
$700$	−0.130213	+	0.400755i	−0.00492159	+	0.0151471i
$701$	−13.3791	−	41.1765i	−0.505320	−	1.55522i	−0.800231	−	0.599691i	$-0.795290\pi$
$701$	−13.3791	−	41.1765i	−0.505320	−	1.55522i	0.294911	−	0.955525i	$-0.404710\pi$
$702$	2.72656	−	1.98096i	0.102907	−	0.0747667i
$703$	16.5430			0.623930
$704$	−0.322175	+	3.30094i	−0.0121424	+	0.124409i
$705$	−49.0112			−1.84587
$706$	12.2234	−	8.88082i	0.460034	−	0.334234i
$707$	−0.112446	−	0.346074i	−0.00422898	−	0.0130155i
$708$	−7.82413	+	24.0802i	−0.294049	+	0.904990i
$709$	31.6814	+	23.0179i	1.18982	+	0.864455i	0.993245	−	0.116034i	$-0.0370182\pi$
$709$	31.6814	+	23.0179i	1.18982	+	0.864455i	0.196575	+	0.980489i	$0.437018\pi$
$710$	16.7083	+	12.1393i	0.627050	+	0.455578i
$711$	5.17416	−	15.9244i	0.194046	−	0.597213i
$712$	0.932872	+	2.87108i	0.0349608	+	0.107598i
$713$	16.8497	−	12.2420i	0.631026	−	0.458467i
$714$	−1.91425			−0.0716389
$715$	−15.1891	+	17.1232i	−0.568038	+	0.640371i
$716$	5.03627			0.188214
$717$	−37.3759	+	27.1552i	−1.39583	+	1.01413i
$718$	3.12137	+	9.60658i	0.116488	+	0.358514i
$719$	−6.27224	+	19.3040i	−0.233915	+	0.719917i	0.763348	+	0.645987i	$0.223554\pi$
$719$	−6.27224	+	19.3040i	−0.233915	+	0.719917i	−0.997263	+	0.0739298i	$0.976446\pi$
$720$	−5.66087	−	4.11287i	−0.210968	−	0.153277i
$721$	0.0431591	+	0.0313569i	0.00160733	+	0.00116779i
$722$	1.22290	−	3.76370i	0.0455116	−	0.140070i
$723$	2.32058	+	7.14201i	0.0863033	+	0.265614i
$724$	−20.9186	+	15.1983i	−0.777434	+	0.564839i
$725$	5.96226			0.221433
$726$	12.4293	−	22.2862i	0.461293	−	0.827117i
$727$	−7.87752			−0.292161			−0.146081	−	0.989273i	$-0.546666\pi$
$727$	−7.87752			−0.292161			−0.146081	+	0.989273i	$0.546666\pi$
$728$	0.220408	−	0.160136i	0.00816887	−	0.00593503i
$729$	−4.62153	−	14.2236i	−0.171168	−	0.526800i
$730$	−8.02942	+	24.7120i	−0.297182	+	0.914632i
$731$	−5.75557	−	4.18166i	−0.212877	−	0.154664i
$732$	−11.9690	−	8.69601i	−0.442388	−	0.321414i
$733$	14.1517	−	43.5546i	0.522706	−	1.60872i	−0.246101	−	0.969244i	$-0.579150\pi$
$733$	14.1517	−	43.5546i	0.522706	−	1.60872i	0.768807	−	0.639480i	$-0.220850\pi$
$734$	−10.3146	−	31.7452i	−0.380720	−	1.17174i
$735$	38.5256	−	27.9905i	1.42104	−	1.03245i
$736$	−4.60534			−0.169755
$737$	−16.9448	+	19.1025i	−0.624169	+	0.703650i
$738$	13.3707			0.492183
$739$	10.6353	−	7.72698i	0.391225	−	0.284242i	−0.374732	−	0.927133i	$-0.622265\pi$
$739$	10.6353	−	7.72698i	0.391225	−	0.284242i	0.765957	+	0.642891i	$0.222265\pi$
$740$	−3.87269	−	11.9189i	−0.142363	−	0.438148i
$741$	6.53053	−	20.0989i	0.239905	−	0.738352i
$742$	0.0664294	+	0.0482638i	0.00243870	+	0.00177182i
$743$	−24.2589	−	17.6251i	−0.889971	−	0.646602i	0.0458994	−	0.998946i	$-0.485385\pi$
$743$	−24.2589	−	17.6251i	−0.889971	−	0.646602i	−0.935870	+	0.352344i	$0.885385\pi$
$744$	3.24195	−	9.97769i	0.118856	−	0.365800i
$745$	−8.07870	−	24.8637i	−0.295981	−	0.910935i
$746$	30.4403	−	22.1162i	1.11450	−	0.809730i
$747$	−28.9996			−1.06104
$748$	2.29204	−	23.4838i	0.0838054	−	0.858652i
$749$	−1.73702			−0.0634692
$750$	−7.53844	+	5.47700i	−0.275265	+	0.199992i
$751$	14.7873	+	45.5107i	0.539597	+	1.66071i	0.733502	+	0.679687i	$0.237884\pi$
$751$	14.7873	+	45.5107i	0.539597	+	1.66071i	−0.193906	+	0.981020i	$0.562116\pi$
$752$	−2.22202	+	6.83868i	−0.0810288	+	0.249381i
$753$	−2.07316	−	1.50624i	−0.0755503	−	0.0548905i
$754$	−3.11865	−	2.26583i	−0.113574	−	0.0825166i
$755$	3.61157	−	11.1153i	0.131438	−	0.404526i
$756$	0.0514284	+	0.158280i	0.00187043	+	0.00575660i
$757$	34.3807	−	24.9790i	1.24959	−	0.907878i	0.251389	−	0.967886i	$-0.419113\pi$
$757$	34.3807	−	24.9790i	1.24959	−	0.907878i	0.998198	+	0.0600085i	$0.0191128\pi$
$758$	−23.7849			−0.863907
$759$	32.4759	+	14.1711i	1.17880	+	0.514380i
$760$	11.3957			0.413365
$761$	−21.9633	+	15.9573i	−0.796168	+	0.578450i	−0.909787	−	0.415074i	$-0.863756\pi$
$761$	−21.9633	+	15.9573i	−0.796168	+	0.578450i	0.113619	+	0.993524i	$0.463756\pi$
$762$	−12.0846	−	37.1924i	−0.437777	−	1.34734i
$763$	−0.231373	+	0.712093i	−0.00837627	+	0.0257795i
$764$	7.51911	+	5.46295i	0.272032	+	0.197643i
$765$	40.2730	+	29.2601i	1.45607	+	1.05790i
$766$	4.14128	−	12.7456i	0.149631	−	0.460516i
$767$	7.92208	+	24.3816i	0.286050	+	0.880370i
$768$	−1.87676	+	1.36355i	−0.0677217	+	0.0492027i
$769$	43.0596			1.55277			0.776384	−	0.630260i	$-0.217052\pi$
$769$	43.0596			1.55277			0.776384	+	0.630260i	$0.217052\pi$
$770$	−0.572401	−	0.974640i	−0.0206279	−	0.0351236i
$771$	−11.4421			−0.412076
$772$	4.42662	−	3.21612i	0.159317	−	0.115751i
$773$	−13.3468	−	41.0771i	−0.480049	−	1.47744i	−0.839025	−	0.544093i	$-0.816874\pi$
$773$	−13.3468	−	41.0771i	−0.480049	−	1.47744i	0.358976	−	0.933347i	$-0.383126\pi$
$774$	0.735918	−	2.26492i	0.0264520	−	0.0814110i
$775$	13.2919	+	9.65711i	0.477458	+	0.346894i
$776$	−14.0633	−	10.2176i	−0.504842	−	0.366789i
$777$	0.354651	−	1.09150i	0.0127230	−	0.0391575i
$778$	−0.695515	−	2.14057i	−0.0249354	−	0.0767433i
$779$	−17.6168	+	12.7994i	−0.631188	+	0.458585i
$780$	−16.0097			−0.573239
$781$	−22.7666	+	5.01618i	−0.814651	+	0.179493i
$782$	32.7637			1.17163
$783$	1.90510	−	1.38413i	0.0680826	−	0.0494649i
$784$	−2.15896	−	6.64460i	−0.0771058	−	0.237307i
$785$	−17.7288	+	54.5635i	−0.632767	+	1.94746i
$786$	−34.9935	−	25.4243i	−1.24818	−	0.906855i
$787$	35.1900	+	25.5670i	1.25439	+	0.911367i	0.998468	−	0.0553311i	$-0.0176214\pi$
$787$	35.1900	+	25.5670i	1.25439	+	0.911367i	0.255921	+	0.966698i	$0.417621\pi$
$788$	0.341949	−	1.05241i	0.0121814	−	0.0374906i
$789$	4.73130	+	14.5614i	0.168439	+	0.518401i
$790$	16.7127	−	12.1425i	0.594612	−	0.432011i
$791$	−1.54016			−0.0547616
$792$	7.71347	−	1.69952i	0.274086	−	0.0603898i
$793$	−14.9797			−0.531946
$794$	−9.84582	+	7.15340i	−0.349415	+	0.253865i
$795$	−1.49107	−	4.58905i	−0.0528828	−	0.162757i
$796$	1.23511	−	3.80129i	0.0437774	−	0.134733i
$797$	−36.9007	−	26.8099i	−1.30709	−	0.949656i	−0.307091	−	0.951680i	$-0.599356\pi$
$797$	−36.9007	−	26.8099i	−1.30709	−	0.949656i	−0.999998	+	0.00202459i	$0.999356\pi$
$798$	0.844280	+	0.613406i	0.0298872	+	0.0217143i
$799$	15.8081	−	48.6522i	0.559249	−	1.72119i
$800$	−1.12263	−	3.45511i	−0.0396911	−	0.122157i
$801$	5.81627	−	4.22576i	0.205508	−	0.149310i
$802$	−7.97623			−0.281650
$803$	−14.8535	−	25.2913i	−0.524168	−	0.892511i
$804$	−17.8603			−0.629885
$805$	1.26974	−	0.922520i	0.0447524	−	0.0325146i
$806$	−3.28253	−	10.1026i	−0.115622	−	0.355849i
$807$	11.0703	−	34.0708i	0.389692	−	1.19935i
$808$	2.53807	+	1.84402i	0.0892891	+	0.0648723i
$809$	−8.80998	−	6.40082i	−0.309742	−	0.225041i	0.422044	−	0.906576i	$-0.361313\pi$
$809$	−8.80998	−	6.40082i	−0.309742	−	0.225041i	−0.731786	+	0.681535i	$0.761313\pi$
$810$	9.50894	−	29.2655i	0.334110	−	1.02828i
$811$	−3.18406	−	9.79952i	−0.111807	−	0.344108i	0.879460	−	0.475972i	$-0.157904\pi$
$811$	−3.18406	−	9.79952i	−0.111807	−	0.344108i	−0.991268	+	0.131864i	$0.957904\pi$
$812$	0.154003	−	0.111890i	0.00540444	−	0.00392656i
$813$	−36.0260			−1.26349
$814$	12.9658	+	5.65775i	0.454452	+	0.198304i
$815$	49.5448			1.73548
$816$	13.3518	−	9.70063i	0.467406	−	0.339590i
$817$	1.19852	+	3.68865i	0.0419308	+	0.129050i
$818$	10.4945	−	32.2988i	0.366932	−	1.12930i
$819$	−0.524898	−	0.381361i	−0.0183414	−	0.0133258i
$820$	13.3458	+	9.69629i	0.466055	+	0.338609i
$821$	−10.9872	+	33.8152i	−0.383457	+	1.18016i	0.554137	+	0.832426i	$0.313048\pi$
$821$	−10.9872	+	33.8152i	−0.383457	+	1.18016i	−0.937594	+	0.347733i	$0.886952\pi$
$822$	−6.16579	−	18.9763i	−0.215057	−	0.661876i
$823$	−30.1743	+	21.9229i	−1.05181	+	0.764184i	−0.972556	−	0.232670i	$-0.925254\pi$
$823$	−30.1743	+	21.9229i	−1.05181	+	0.764184i	−0.0792537	+	0.996854i	$0.525254\pi$
$824$	−0.459937			−0.0160227
$825$	−2.71518	+	27.8192i	−0.0945305	+	0.968539i
$826$	−1.26596			−0.0440483
$827$	−20.2456	+	14.7093i	−0.704008	+	0.511492i	−0.881235	−	0.472678i	$-0.843287\pi$
$827$	−20.2456	+	14.7093i	−0.704008	+	0.511492i	0.177227	+	0.984170i	$0.443287\pi$
$828$	3.38915	+	10.4307i	0.117781	+	0.362493i
$829$	−5.47316	+	16.8446i	−0.190091	+	0.585039i	−0.999999	−	0.00151798i	$-0.999517\pi$
$829$	−5.47316	+	16.8446i	−0.190091	+	0.585039i	0.809908	+	0.586557i	$0.199517\pi$
$830$	−28.9456	−	21.0302i	−1.00472	−	0.729968i
$831$	−13.6336	−	9.90541i	−0.472946	−	0.343615i
$832$	−0.725832	+	2.23388i	−0.0251637	+	0.0774459i
$833$	15.3594	+	47.2715i	0.532173	+	1.63786i
$834$	−1.25517	+	0.911933i	−0.0434629	+	0.0315777i
$835$	−43.0415			−1.48951
$836$	−8.53611	+	9.62308i	−0.295227	+	0.332821i
$837$	6.48899			0.224292
$838$	−18.5173	+	13.4536i	−0.639670	+	0.464747i
$839$	15.1468	+	46.6169i	0.522924	+	1.60940i	0.768384	+	0.639989i	$0.221061\pi$
$839$	15.1468	+	46.6169i	0.522924	+	1.60940i	−0.245460	+	0.969407i	$0.578939\pi$
$840$	0.244303	−	0.751887i	0.00842925	−	0.0259426i
$841$	21.2824	+	15.4626i	0.733877	+	0.533193i
$842$	−9.10433	−	6.61469i	−0.313756	−	0.227957i
$843$	−3.29927	+	10.1541i	−0.113633	+	0.349726i
$844$	−5.63259	−	17.3353i	−0.193882	−	0.596706i
$845$	17.7873	−	12.9232i	0.611900	−	0.444572i
$846$	17.1243			0.588746
$847$	1.25180	+	0.246704i	0.0430123	+	0.00847685i
$848$	−0.707924			−0.0243102
$849$	14.3935	−	10.4575i	0.493985	−	0.358901i
$850$	7.98672	+	24.5806i	0.273942	+	0.843108i
$851$	−6.07010	+	18.6818i	−0.208080	+	0.640405i
$852$	−13.1918	−	9.58438i	−0.451943	−	0.328356i
$853$	−0.263599	−	0.191516i	−0.00902546	−	0.00655738i	0.583263	−	0.812283i	$-0.301776\pi$
$853$	−0.263599	−	0.191516i	−0.00902546	−	0.00655738i	−0.592289	+	0.805726i	$0.701776\pi$
$854$	0.228586	−	0.703515i	0.00782205	−	0.0240738i
$855$	−8.38629	−	25.8103i	−0.286805	−	0.882695i
$856$	12.1156	−	8.80250i	0.414103	−	0.300863i
$857$	−28.1608			−0.961956			−0.480978	−	0.876733i	$-0.659718\pi$
$857$	−28.1608			−0.961956			−0.480978	+	0.876733i	$0.659718\pi$
$858$	11.9923	−	13.5194i	0.409411	−	0.461544i
$859$	−46.4200			−1.58383			−0.791915	−	0.610631i	$-0.790916\pi$
$859$	−46.4200			−1.58383			−0.791915	+	0.610631i	$0.790916\pi$
$860$	2.37704	−	1.72702i	0.0810564	−	0.0588909i
$861$	0.466829	+	1.43675i	0.0159095	+	0.0489644i
$862$	8.17069	−	25.1468i	0.278295	−	0.856503i
$863$	24.1367	+	17.5364i	0.821624	+	0.596945i	0.917177	−	0.398479i	$-0.130462\pi$
$863$	24.1367	+	17.5364i	0.821624	+	0.596945i	−0.0955529	+	0.995424i	$0.530462\pi$
$864$	−1.16081	−	0.843379i	−0.0394916	−	0.0286923i
$865$	6.15800	−	18.9524i	0.209378	−	0.644400i
$866$	6.13032	+	18.8672i	0.208317	+	0.641133i
$867$	−63.0833	+	45.8327i	−2.14242	+	1.55656i
$868$	0.524553			0.0178045
$869$	−2.26518	+	23.2086i	−0.0768410	+	0.787297i
$870$	−11.1863			−0.379249
$871$	−14.6302	+	10.6294i	−0.495724	+	0.360165i
$872$	−1.99479	−	6.13932i	−0.0675520	−	0.207904i
$873$	−12.7926	+	39.3715i	−0.432963	+	1.33252i
$874$	−14.4504	−	10.4989i	−0.488793	−	0.355129i
$875$	−0.376918	−	0.273847i	−0.0127422	−	0.00925773i
$876$	6.33951	−	19.5110i	0.214192	−	0.659216i
$877$	−17.9713	−	55.3100i	−0.606848	−	1.86768i	−0.483554	−	0.875314i	$-0.660654\pi$
$877$	−17.9713	−	55.3100i	−0.606848	−	1.86768i	−0.123293	−	0.992370i	$-0.539346\pi$
$878$	5.92013	−	4.30123i	0.199795	−	0.145159i
$879$	−44.3795			−1.49688
$880$	8.93155	+	3.89736i	0.301083	+	0.131380i
$881$	12.2658			0.413245			0.206623	−	0.978421i	$-0.433753\pi$
$881$	12.2658			0.413245			0.206623	+	0.978421i	$0.433753\pi$
$882$	−13.4607	+	9.77976i	−0.453245	+	0.329302i
$883$	4.93995	+	15.2036i	0.166242	+	0.511642i	0.999126	−	0.0418070i	$-0.0133115\pi$
$883$	4.93995	+	15.2036i	0.166242	+	0.511642i	−0.832883	+	0.553449i	$0.813311\pi$
$884$	5.16377	−	15.8924i	0.173676	−	0.534520i
$885$	60.1853	+	43.7272i	2.02311	+	1.46987i
$886$	−13.5395	−	9.83701i	−0.454868	−	0.330481i
$887$	5.08439	−	15.6482i	0.170717	−	0.525414i	−0.828695	−	0.559701i	$-0.810916\pi$
$887$	5.08439	−	15.6482i	0.170717	−	0.525414i	0.999412	+	0.0342872i	$0.0109161\pi$
$888$	3.05763	+	9.41042i	0.102607	+	0.315793i
$889$	1.58187	−	1.14930i	0.0530543	−	0.0385462i
$890$	8.86989			0.297319
$891$	17.5904	+	29.9516i	0.589301	+	1.00342i
$892$	19.3330			0.647318
$893$	−22.5624	+	16.3925i	−0.755022	+	0.548556i
$894$	6.37843	+	19.6308i	0.213327	+	0.656552i
$895$	4.57268	−	14.0733i	0.152848	−	0.470417i
$896$	−0.0938370	−	0.0681766i	−0.00313487	−	0.00227762i
$897$	20.3013	+	14.7498i	0.677841	+	0.492480i
$898$	5.30012	−	16.3121i	0.176867	−	0.544342i
$899$	−2.29356	−	7.05885i	−0.0764945	−	0.235426i
$900$	−6.99939	+	5.08536i	−0.233313	+	0.169512i
$901$	5.03636			0.167786
$902$	−18.1849	+	4.00670i	−0.605491	+	0.133409i
$903$	0.269071			0.00895413
$904$	10.7425	−	7.80489i	0.357291	−	0.259587i
$905$	23.4767	+	72.2537i	0.780390	+	2.40179i
$906$	−2.85147	+	8.77591i	−0.0947336	+	0.291560i
$907$	2.44255	+	1.77462i	0.0811035	+	0.0589251i	0.627598	−	0.778537i	$-0.284038\pi$
$907$	2.44255	+	1.77462i	0.0811035	+	0.0589251i	−0.546495	+	0.837463i	$0.684038\pi$
$908$	16.7060	+	12.1376i	0.554407	+	0.402800i
$909$	2.30875	−	7.10559i	0.0765762	−	0.235677i
$910$	−0.247361	−	0.761299i	−0.00819994	−	0.0252368i
$911$	−31.6212	+	22.9741i	−1.04766	+	0.761167i	−0.971765	−	0.235949i	$-0.924180\pi$
$911$	−31.6212	+	22.9741i	−1.04766	+	0.761167i	−0.0758909	+	0.997116i	$0.524180\pi$
$912$	−8.99731			−0.297931
$913$	39.4410	−	8.69009i	1.30531	−	0.287600i
$914$	−25.1455			−0.831741
$915$	−35.1672	+	25.5505i	−1.16259	+	0.844673i
$916$	−2.95591	−	9.09735i	−0.0976660	−	0.300585i
$917$	0.668310	−	2.05685i	0.0220696	−	0.0679231i
$918$	8.25833	+	6.00003i	0.272566	+	0.198030i
$919$	−22.3486	−	16.2372i	−0.737212	−	0.535616i	0.154625	−	0.987973i	$-0.450583\pi$
$919$	−22.3486	−	16.2372i	−0.737212	−	0.535616i	−0.891837	+	0.452357i	$0.850583\pi$
$920$	−4.18141	+	12.8691i	−0.137857	+	0.424280i
$921$	2.78255	+	8.56380i	0.0916881	+	0.282187i
$922$	20.8762	−	15.1675i	0.687522	−	0.499514i
$923$	−16.5100			−0.543435
$924$	0.451932	+	0.769513i	0.0148675	+	0.0253151i
$925$	−15.4956			−0.509491
$926$	−6.55461	+	4.76220i	−0.215398	+	0.156496i
$927$	0.338476	+	1.04172i	0.0111170	+	0.0342146i
$928$	−0.507151	+	1.56085i	−0.0166480	+	0.0512374i
$929$	1.01912	+	0.740431i	0.0334361	+	0.0242927i	0.604378	−	0.796698i	$-0.293422\pi$
$929$	1.01912	+	0.740431i	0.0334361	+	0.0242927i	−0.570942	+	0.820991i	$0.693422\pi$
$930$	−24.9379	−	18.1185i	−0.817746	−	0.594128i
$931$	8.37349	−	25.7710i	0.274430	−	0.844609i
$932$	3.34022	+	10.2801i	0.109413	+	0.336737i
$933$	−46.2107	+	33.5740i	−1.51287	+	1.09916i
$934$	−33.5475			−1.09771
$935$	−63.5415	−	27.7269i	−2.07803	−	0.906767i
$936$	5.59372			0.182836
$937$	25.8271	−	18.7645i	0.843735	−	0.613009i	−0.0796765	−	0.996821i	$-0.525389\pi$
$937$	25.8271	−	18.7645i	0.843735	−	0.613009i	0.923412	+	0.383811i	$0.125389\pi$
$938$	−0.275954	−	0.849300i	−0.00901022	−	0.0277306i
$939$	−3.99382	+	12.2917i	−0.130333	+	0.401125i
$940$	17.0924	+	12.4183i	0.557492	+	0.405042i
$941$	4.15447	+	3.01840i	0.135432	+	0.0983969i	0.653439	−	0.756980i	$-0.273326\pi$
$941$	4.15447	+	3.01840i	0.135432	+	0.0983969i	−0.518007	+	0.855377i	$0.673326\pi$
$942$	13.9975	−	43.0799i	0.456063	−	1.40362i
$943$	−7.99010	−	24.5910i	−0.260193	−	0.800793i
$944$	8.83000	−	6.41537i	0.287392	−	0.208802i
$945$	0.488989			0.0159068
$946$	−0.322175	+	3.30094i	−0.0104748	+	0.107323i
$947$	58.1054			1.88817			0.944086	−	0.329700i	$-0.106948\pi$
$947$	58.1054			1.88817			0.944086	+	0.329700i	$0.106948\pi$
$948$	−13.1953	+	9.58695i	−0.428563	+	0.311370i
$949$	−6.41887	−	19.7553i	−0.208365	−	0.641283i
$950$	4.35411	−	13.4006i	0.141266	−	0.434772i
$951$	−49.4084	−	35.8973i	−1.60218	−	1.16405i
$952$	0.667582	+	0.485027i	0.0216365	+	0.0157198i
$953$	−8.86705	+	27.2900i	−0.287232	+	0.884009i	0.698489	+	0.715621i	$0.253856\pi$
$953$	−8.86705	+	27.2900i	−0.287232	+	0.884009i	−0.985721	+	0.168388i	$0.946144\pi$
$954$	0.520974	+	1.60339i	0.0168671	+	0.0519117i
$955$	22.0925	−	16.0512i	0.714897	−	0.519403i
$956$	19.9151			0.644102
$957$	8.37923	−	9.44622i	0.270862	−	0.305353i
$958$	−12.9359			−0.417940
$959$	0.807104	−	0.586395i	0.0260627	−	0.0189357i
$960$	2.10626	+	6.48240i	0.0679793	+	0.209219i
$961$	−3.25937	+	10.0313i	−0.105141	+	0.323591i
$962$	8.10518	+	5.88876i	0.261322	+	0.189861i
$963$	−28.8531	−	20.9630i	−0.929777	−	0.675523i
$964$	1.00034	−	3.07872i	0.0322186	−	0.0991588i
$965$	−4.96793	−	15.2897i	−0.159923	−	0.492193i
$966$	−1.00251	+	0.728363i	−0.0322551	+	0.0234347i
$967$	−58.6585			−1.88633			−0.943166	−	0.332322i	$-0.892168\pi$
$967$	−58.6585			−1.88633			−0.943166	+	0.332322i	$0.892168\pi$
$968$	−9.98144	+	4.62287i	−0.320816	+	0.148585i
$969$	64.0093			2.05627
$970$	−41.3205	+	30.0211i	−1.32672	+	0.963919i
$971$	−16.2925	−	50.1430i	−0.522850	−	1.60917i	−0.768529	−	0.639815i	$-0.779011\pi$
$971$	−16.2925	−	50.1430i	−0.522850	−	1.60917i	0.245679	−	0.969351i	$-0.420989\pi$
$972$	−6.17748	+	19.0123i	−0.198143	+	0.609821i
$973$	−0.0627578	−	0.0455962i	−0.00201192	−	0.00146175i
$974$	−17.7002	−	12.8600i	−0.567151	−	0.412059i
$975$	−6.11706	+	18.8264i	−0.195903	+	0.602926i
$976$	1.97076	+	6.06536i	0.0630824	+	0.194148i
$977$	23.0742	−	16.7644i	0.738210	−	0.536341i	−0.153940	−	0.988080i	$-0.549196\pi$
$977$	23.0742	−	16.7644i	0.738210	−	0.536341i	0.892150	+	0.451739i	$0.149196\pi$
$978$	−39.1174			−1.25084
$979$	−6.64412	+	7.49017i	−0.212347	+	0.239387i
$980$	−20.5278			−0.655735
$981$	−12.4371	+	9.03607i	−0.397086	+	0.288500i
$982$	6.24128	+	19.2087i	0.199167	+	0.612974i
$983$	5.82141	−	17.9164i	0.185674	−	0.571446i	−0.814285	−	0.580465i	$-0.802871\pi$
$983$	5.82141	−	17.9164i	0.185674	−	0.571446i	0.999959	+	0.00901891i	$0.00287085\pi$
$984$	−10.5370	−	7.65557i	−0.335907	−	0.244051i
$985$	−2.63036	−	1.91107i	−0.0838103	−	0.0608918i
$986$	3.60801	−	11.1043i	0.114902	−	0.353633i
$987$	0.597882	+	1.84009i	0.0190308	+	0.0585708i
$988$	−7.37009	+	5.35469i	−0.234474	+	0.170355i
$989$	−4.60534			−0.146441
$990$	2.25433	−	23.0974i	0.0716474	−	0.734084i
$991$	−41.4428			−1.31647			−0.658237	−	0.752811i	$-0.728698\pi$
$991$	−41.4428			−1.31647			−0.658237	+	0.752811i	$0.728698\pi$
$992$	−3.65873	+	2.65822i	−0.116165	+	0.0843987i
$993$	−19.1578	−	58.9617i	−0.607954	−	1.87109i
$994$	0.251938	−	0.775385i	0.00799098	−	0.0245937i
$995$	−9.50082	−	6.90275i	−0.301196	−	0.218832i
$996$	22.8536	+	16.6041i	0.724143	+	0.526121i
$997$	12.6114	−	38.8138i	0.399407	−	1.22925i	−0.526070	−	0.850441i	$-0.676335\pi$
$997$	12.6114	−	38.8138i	0.399407	−	1.22925i	0.925476	−	0.378805i	$-0.123665\pi$
$998$	3.74363	+	11.5217i	0.118502	+	0.364713i
$999$	−4.95123	+	3.59728i	−0.156650	+	0.113813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.h.861.8	yes	40
11.4	even	5	inner	946.2.f.h.345.8	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.h.345.8	✓	40	11.4	even	5	inner
946.2.f.h.861.8	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.716858 + 2.20626i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.37704 - 1.72702i) q^{5} +(1.87676 + 1.36355i) q^{6} +(-0.0358425 + 0.110312i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.92666 + 1.39980i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.716858 + 2.20626i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-2.37704 - 1.72702i) q^{5} +(1.87676 + 1.36355i) q^{6} +(-0.0358425 + 0.110312i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.92666 + 1.39980i) q^{9} -2.93818 q^{10} +(2.20089 - 2.48115i) q^{11} +2.31980 q^{12} +(1.90025 - 1.38061i) q^{13} +(0.0358425 + 0.110312i) q^{14} +(2.10626 - 6.48240i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.75557 + 4.18166i) q^{17} +(-0.735918 + 2.26492i) q^{18} +(-1.19852 - 3.68865i) q^{19} +(-2.37704 + 1.72702i) q^{20} -0.269071 q^{21} +(0.322175 - 3.30094i) q^{22} +4.60534 q^{23} +(1.87676 - 1.36355i) q^{24} +(1.12263 + 3.45511i) q^{25} +(0.725832 - 2.23388i) q^{26} +(1.16081 + 0.843379i) q^{27} +(0.0938370 + 0.0681766i) q^{28} +(0.507151 - 1.56085i) q^{29} +(-2.10626 - 6.48240i) q^{30} +(3.65873 - 2.65822i) q^{31} -1.00000 q^{32} +(7.05179 + 3.07711i) q^{33} +7.11427 q^{34} +(0.275710 - 0.200315i) q^{35} +(0.735918 + 2.26492i) q^{36} +(-1.31806 + 4.05656i) q^{37} +(-3.13776 - 2.27971i) q^{38} +(4.40821 + 3.20275i) q^{39} +(-0.907948 + 2.79438i) q^{40} +(-1.73496 - 5.33967i) q^{41} +(-0.217683 + 0.158156i) q^{42} -1.00000 q^{43} +(-1.67960 - 2.85989i) q^{44} +6.99723 q^{45} +(3.72580 - 2.70695i) q^{46} +(-2.22202 - 6.83868i) q^{47} +(0.716858 - 2.20626i) q^{48} +(5.65223 + 4.10659i) q^{49} +(2.93909 + 2.13538i) q^{50} +(-5.09992 + 15.6960i) q^{51} +(-0.725832 - 2.23388i) q^{52} +(0.572722 - 0.416107i) q^{53} +1.43484 q^{54} +(-9.51659 + 2.09680i) q^{55} +0.115989 q^{56} +(7.27897 - 5.28848i) q^{57} +(-0.507151 - 1.56085i) q^{58} +(-3.37276 + 10.3803i) q^{59} +(-5.51426 - 4.00635i) q^{60} +(-5.15951 - 3.74860i) q^{61} +(1.39751 - 4.30110i) q^{62} +(-0.0853583 - 0.262706i) q^{63} +(-0.809017 + 0.587785i) q^{64} -6.90132 q^{65} +(7.51369 - 1.65550i) q^{66} -7.69907 q^{67} +(5.75557 - 4.18166i) q^{68} +(3.30138 + 10.1606i) q^{69} +(0.105312 - 0.324117i) q^{70} +(-5.68659 - 4.13155i) q^{71} +(1.92666 + 1.39980i) q^{72} +(2.73278 - 8.41064i) q^{73} +(1.31806 + 4.05656i) q^{74} +(-6.81811 + 4.95365i) q^{75} -3.87848 q^{76} +(0.194815 + 0.331715i) q^{77} +5.44885 q^{78} +(-5.68812 + 4.13266i) q^{79} +(0.907948 + 2.79438i) q^{80} +(-3.23633 + 9.96041i) q^{81} +(-4.54219 - 3.30010i) q^{82} +(9.85152 + 7.15755i) q^{83} +(-0.0831476 + 0.255902i) q^{84} +(-6.45939 - 19.8800i) q^{85} +(-0.809017 + 0.587785i) q^{86} +3.80720 q^{87} +(-3.03982 - 1.32645i) q^{88} -3.01884 q^{89} +(5.66087 - 4.11287i) q^{90} +(0.0841884 + 0.259105i) q^{91} +(1.42313 - 4.37994i) q^{92} +(8.48753 + 6.16655i) q^{93} +(-5.81733 - 4.22654i) q^{94} +(-3.52146 + 10.8379i) q^{95} +(-0.716858 - 2.20626i) q^{96} +(14.0633 - 10.2176i) q^{97} +6.98655 q^{98} +(-0.767254 + 7.86112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} + q^{6} + q^{7} + 10 q^{8} - 11 q^{9}+O(q^{10}) \) 40 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 + q^6 + q^7 + 10 * q^8 - 11 * q^9	\( 40 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} + q^{6} + q^{7} + 10 q^{8} - 11 q^{9} - 5 q^{11} + 4 q^{12} + 5 q^{13} - q^{14} - 11 q^{15} - 10 q^{16} + 3 q^{17} + 11 q^{18} + 3 q^{19} - 5 q^{20} - 44 q^{21} + 22 q^{23} + q^{24} - 9 q^{25} - 20 q^{26} - 16 q^{27} + 11 q^{28} - 5 q^{29} + 11 q^{30} - 17 q^{31} - 40 q^{32} + 56 q^{33} + 42 q^{34} + 12 q^{35} - 11 q^{36} + 29 q^{37} - 13 q^{38} - 34 q^{39} - 5 q^{40} - 12 q^{41} - 26 q^{42} - 40 q^{43} + 10 q^{44} - 8 q^{45} - 2 q^{46} - 23 q^{47} - q^{48} - 3 q^{49} + 19 q^{50} - 51 q^{51} + 20 q^{52} - 8 q^{53} - 64 q^{54} + 11 q^{55} + 24 q^{56} + 30 q^{57} + 5 q^{58} + 26 q^{59} + 4 q^{60} - 19 q^{61} - 23 q^{62} + 13 q^{63} - 10 q^{64} - 12 q^{65} - 6 q^{66} + 10 q^{67} + 3 q^{68} + 87 q^{69} + 8 q^{70} + 23 q^{71} + 11 q^{72} - 56 q^{73} - 29 q^{74} - 90 q^{75} - 32 q^{76} + 13 q^{77} + 94 q^{78} + 47 q^{79} + 5 q^{80} - 66 q^{81} + 2 q^{82} - 34 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{86} + 24 q^{87} + 5 q^{88} + 60 q^{89} - 77 q^{90} - 28 q^{91} - 13 q^{92} + 12 q^{93} - 17 q^{94} - 34 q^{95} + q^{96} + q^{97} - 12 q^{98} + 144 q^{99}+O(q^{100}) \) 40 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 + q^6 + q^7 + 10 * q^8 - 11 * q^9 - 5 * q^11 + 4 * q^12 + 5 * q^13 - q^14 - 11 * q^15 - 10 * q^16 + 3 * q^17 + 11 * q^18 + 3 * q^19 - 5 * q^20 - 44 * q^21 + 22 * q^23 + q^24 - 9 * q^25 - 20 * q^26 - 16 * q^27 + 11 * q^28 - 5 * q^29 + 11 * q^30 - 17 * q^31 - 40 * q^32 + 56 * q^33 + 42 * q^34 + 12 * q^35 - 11 * q^36 + 29 * q^37 - 13 * q^38 - 34 * q^39 - 5 * q^40 - 12 * q^41 - 26 * q^42 - 40 * q^43 + 10 * q^44 - 8 * q^45 - 2 * q^46 - 23 * q^47 - q^48 - 3 * q^49 + 19 * q^50 - 51 * q^51 + 20 * q^52 - 8 * q^53 - 64 * q^54 + 11 * q^55 + 24 * q^56 + 30 * q^57 + 5 * q^58 + 26 * q^59 + 4 * q^60 - 19 * q^61 - 23 * q^62 + 13 * q^63 - 10 * q^64 - 12 * q^65 - 6 * q^66 + 10 * q^67 + 3 * q^68 + 87 * q^69 + 8 * q^70 + 23 * q^71 + 11 * q^72 - 56 * q^73 - 29 * q^74 - 90 * q^75 - 32 * q^76 + 13 * q^77 + 94 * q^78 + 47 * q^79 + 5 * q^80 - 66 * q^81 + 2 * q^82 - 34 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^86 + 24 * q^87 + 5 * q^88 + 60 * q^89 - 77 * q^90 - 28 * q^91 - 13 * q^92 + 12 * q^93 - 17 * q^94 - 34 * q^95 + q^96 + q^97 - 12 * q^98 + 144 * q^99

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