LMFDB - Embedded newform 114.2.i.d.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	114.61
Dual form			114.2.i.d.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.907604 - 0.761570i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(1.11334 - 0.405223i) q^{10} +(-0.939693 - 1.62760i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.673648 + 3.82045i) q^{13} +(-0.407604 + 0.342020i) q^{14} +(-0.907604 - 0.761570i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.09240 - 0.397600i) q^{17} -1.00000 q^{18} +(-3.93969 + 1.86516i) q^{19} +1.18479 q^{20} +(0.500000 + 0.181985i) q^{21} +(-0.326352 - 1.85083i) q^{22} +(-5.13429 - 4.30818i) q^{23} +(0.766044 - 0.642788i) q^{24} +(-0.624485 + 3.54163i) q^{25} +(-1.93969 + 3.35965i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.500000 + 0.181985i) q^{28} +(3.77972 - 1.37570i) q^{29} +(-0.592396 - 1.02606i) q^{30} +(0.979055 - 1.69577i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.43969 + 1.20805i) q^{33} +(-0.890530 - 0.747243i) q^{34} +(0.109470 + 0.620838i) q^{35} +(-0.939693 - 0.342020i) q^{36} +6.88713 q^{37} +(-4.34002 + 0.405223i) q^{38} +3.87939 q^{39} +(1.11334 + 0.405223i) q^{40} +(-1.56031 - 8.84894i) q^{41} +(0.407604 + 0.342020i) q^{42} +(1.85844 - 1.55942i) q^{43} +(0.326352 - 1.85083i) q^{44} +(-0.592396 + 1.02606i) q^{45} +(-3.35117 - 5.80439i) q^{46} +(-1.91875 + 0.698367i) q^{47} +(0.939693 - 0.342020i) q^{48} +(3.35844 + 5.81699i) q^{49} +(-1.79813 + 3.11446i) q^{50} +(-0.201867 + 1.14484i) q^{51} +(-2.97178 + 2.49362i) q^{52} +(9.93629 + 8.33754i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-2.09240 - 0.761570i) q^{55} -0.532089 q^{56} +(2.52094 + 3.55596i) q^{57} +4.02229 q^{58} +(2.51842 + 0.916629i) q^{59} +(-0.205737 - 1.16679i) q^{60} +(-8.69253 - 7.29390i) q^{61} +(1.50000 - 1.25865i) q^{62} +(0.0923963 - 0.524005i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.29813 + 3.98048i) q^{65} +(-1.76604 + 0.642788i) q^{66} +(10.4966 - 3.82045i) q^{67} +(-0.581252 - 1.00676i) q^{68} +(-3.35117 + 5.80439i) q^{69} +(-0.109470 + 0.620838i) q^{70} +(4.65136 - 3.90295i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-0.0569038 - 0.322718i) q^{73} +(6.47178 + 2.35554i) q^{74} +3.59627 q^{75} +(-4.21688 - 1.10359i) q^{76} +1.00000 q^{77} +(3.64543 + 1.32683i) q^{78} +(-2.80154 - 15.8883i) q^{79} +(0.907604 + 0.761570i) q^{80} +(0.766044 - 0.642788i) q^{81} +(1.56031 - 8.84894i) q^{82} +(-5.78699 + 10.0234i) q^{83} +(0.266044 + 0.460802i) q^{84} +(-1.29426 + 0.471073i) q^{85} +(2.27972 - 0.829748i) q^{86} +(-2.01114 - 3.48340i) q^{87} +(0.939693 - 1.62760i) q^{88} +(-0.618089 + 3.50535i) q^{89} +(-0.907604 + 0.761570i) q^{90} +(-1.58125 - 1.32683i) q^{91} +(-1.16385 - 6.60051i) q^{92} +(-1.84002 - 0.669713i) q^{93} -2.04189 q^{94} +(-2.15523 + 4.69318i) q^{95} +1.00000 q^{96} +(-5.52481 - 2.01087i) q^{97} +(1.16637 + 6.61484i) q^{98} +(1.43969 + 1.20805i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} - 3 q^{17} - 6 q^{18} - 18 q^{19} + 3 q^{21} - 3 q^{22} - 21 q^{23} + 9 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 9 * q^15 - 3 * q^17 - 6 * q^18 - 18 * q^19 + 3 * q^21 - 3 * q^22 - 21 * q^23 + 9 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 - 3 * q^33 + 12 * q^34 + 18 * q^35 - 18 * q^37 - 6 * q^38 + 12 * q^39 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^46 - 9 * q^47 + 12 * q^49 + 3 * q^50 - 15 * q^51 - 3 * q^52 + 12 * q^53 - 9 * q^55 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 27 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 3 * q^63 - 3 * q^64 - 6 * q^66 + 21 * q^67 - 6 * q^68 + 6 * q^69 - 18 * q^70 + 39 * q^71 + 36 * q^73 + 24 * q^74 - 6 * q^75 - 9 * q^76 + 6 * q^77 + 6 * q^78 - 45 * q^79 + 9 * q^80 + 15 * q^82 - 27 * q^83 - 3 * q^84 - 18 * q^85 - 12 * q^86 - 6 * q^87 - 30 * q^89 - 9 * q^90 - 12 * q^91 - 3 * q^92 + 9 * q^93 - 6 * q^94 + 6 * q^96 - 6 * q^97 - 12 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.907604	−	0.761570i	0.405893	−	0.340584i	−0.416873	−	0.908965i	$-0.636874\pi$
$5$	0.907604	−	0.761570i	0.405893	−	0.340584i	0.822766	+	0.568380i	$0.192430\pi$
$6$	0.173648	−	0.984808i	0.0708916	−	0.402046i
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	−0.911914	−	0.410382i	$-0.865395\pi$
$7$	−0.266044	+	0.460802i	−0.100555	+	0.174167i	0.811358	+	0.584549i	$0.198729\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	1.11334	−	0.405223i	0.352069	−	0.128143i
$11$	−0.939693	−	1.62760i	−0.283328	−	0.490738i	0.688874	−	0.724881i	$-0.258105\pi$
$11$	−0.939693	−	1.62760i	−0.283328	−	0.490738i	−0.972202	+	0.234142i	$0.924772\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.673648	+	3.82045i	−0.186836	+	1.05960i	0.736737	+	0.676180i	$0.236366\pi$
$13$	−0.673648	+	3.82045i	−0.186836	+	1.05960i	−0.923573	+	0.383422i	$0.874745\pi$
$14$	−0.407604	+	0.342020i	−0.108937	+	0.0914087i
$15$	−0.907604	−	0.761570i	−0.234342	−	0.196637i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−1.09240	−	0.397600i	−0.264945	−	0.0964321i	0.206132	−	0.978524i	$-0.433912\pi$
$17$	−1.09240	−	0.397600i	−0.264945	−	0.0964321i	−0.471077	+	0.882092i	$0.656135\pi$
$18$	−1.00000			−0.235702
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$19$	−3.93969	+	1.86516i	−0.903827	+	0.427897i
$20$	1.18479			0.264928
$21$	0.500000	+	0.181985i	0.109109	+	0.0397124i
$22$	−0.326352	−	1.85083i	−0.0695784	−	0.394599i
$23$	−5.13429	−	4.30818i	−1.07057	−	0.898317i	−0.0754683	−	0.997148i	$-0.524045\pi$
$23$	−5.13429	−	4.30818i	−1.07057	−	0.898317i	−0.995104	+	0.0988312i	$0.968490\pi$
$24$	0.766044	−	0.642788i	0.156368	−	0.131208i
$25$	−0.624485	+	3.54163i	−0.124897	+	0.708326i
$26$	−1.93969	+	3.35965i	−0.380405	+	0.658881i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−0.500000	+	0.181985i	−0.0944911	+	0.0343920i
$29$	3.77972	−	1.37570i	0.701875	−	0.255462i	0.0336640	−	0.999433i	$-0.489282\pi$
$29$	3.77972	−	1.37570i	0.701875	−	0.255462i	0.668211	+	0.743971i	$0.267060\pi$
$30$	−0.592396	−	1.02606i	−0.108156	−	0.187332i
$31$	0.979055	−	1.69577i	0.175844	−	0.304570i	−0.764609	−	0.644494i	$-0.777068\pi$
$31$	0.979055	−	1.69577i	0.175844	−	0.304570i	0.940453	+	0.339924i	$0.110401\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−1.43969	+	1.20805i	−0.250618	+	0.210294i
$34$	−0.890530	−	0.747243i	−0.152725	−	0.128151i
$35$	0.109470	+	0.620838i	0.0185039	+	0.104941i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	6.88713			1.13224			0.566118	−	0.824324i	$-0.308445\pi$
$37$	6.88713			1.13224			0.566118	+	0.824324i	$0.308445\pi$
$38$	−4.34002	+	0.405223i	−0.704045	+	0.0657358i
$39$	3.87939			0.621199
$40$	1.11334	+	0.405223i	0.176035	+	0.0640714i
$41$	−1.56031	−	8.84894i	−0.243679	−	1.38197i	−0.823540	−	0.567258i	$-0.808004\pi$
$41$	−1.56031	−	8.84894i	−0.243679	−	1.38197i	0.579861	−	0.814715i	$-0.303107\pi$
$42$	0.407604	+	0.342020i	0.0628946	+	0.0527749i
$43$	1.85844	−	1.55942i	0.283410	−	0.237809i	−0.489989	−	0.871728i	$-0.662999\pi$
$43$	1.85844	−	1.55942i	0.283410	−	0.237809i	0.773399	+	0.633919i	$0.218555\pi$
$44$	0.326352	−	1.85083i	0.0491994	−	0.279024i
$45$	−0.592396	+	1.02606i	−0.0883092	+	0.152956i
$46$	−3.35117	−	5.80439i	−0.494103	−	0.855811i
$47$	−1.91875	+	0.698367i	−0.279878	+	0.101867i	−0.478145	−	0.878281i	$-0.658691\pi$
$47$	−1.91875	+	0.698367i	−0.279878	+	0.101867i	0.198267	+	0.980148i	$0.436469\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	3.35844	+	5.81699i	0.479777	+	0.830999i
$50$	−1.79813	+	3.11446i	−0.254294	+	0.440451i
$51$	−0.201867	+	1.14484i	−0.0282670	+	0.160310i
$52$	−2.97178	+	2.49362i	−0.412112	+	0.345803i
$53$	9.93629	+	8.33754i	1.36485	+	1.14525i	0.974450	+	0.224605i	$0.0721093\pi$
$53$	9.93629	+	8.33754i	1.36485	+	1.14525i	0.390404	+	0.920643i	$0.372335\pi$
$54$	0.173648	+	0.984808i	0.0236305	+	0.134015i
$55$	−2.09240	−	0.761570i	−0.282139	−	0.102690i
$56$	−0.532089			−0.0711034
$57$	2.52094	+	3.55596i	0.333907	+	0.470998i
$58$	4.02229			0.528152
$59$	2.51842	+	0.916629i	0.327870	+	0.119335i	0.500710	−	0.865615i	$-0.333072\pi$
$59$	2.51842	+	0.916629i	0.327870	+	0.119335i	−0.172840	+	0.984950i	$0.555294\pi$
$60$	−0.205737	−	1.16679i	−0.0265605	−	0.150632i
$61$	−8.69253	−	7.29390i	−1.11296	−	0.933888i	−0.114737	−	0.993396i	$-0.536603\pi$
$61$	−8.69253	−	7.29390i	−1.11296	−	0.933888i	−0.998228	+	0.0595075i	$0.981047\pi$
$62$	1.50000	−	1.25865i	0.190500	−	0.159849i
$63$	0.0923963	−	0.524005i	0.0116408	−	0.0660185i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.29813	+	3.98048i	0.285048	+	0.493718i
$66$	−1.76604	+	0.642788i	−0.217385	+	0.0791217i
$67$	10.4966	−	3.82045i	1.28236	−	0.466742i	0.391150	−	0.920327i	$-0.372077\pi$
$67$	10.4966	−	3.82045i	1.28236	−	0.466742i	0.891213	+	0.453585i	$0.149855\pi$
$68$	−0.581252	−	1.00676i	−0.0704871	−	0.122087i
$69$	−3.35117	+	5.80439i	−0.403433	+	0.698767i
$70$	−0.109470	+	0.620838i	−0.0130842	+	0.0742043i
$71$	4.65136	−	3.90295i	0.552015	−	0.463195i	−0.323608	−	0.946191i	$-0.604896\pi$
$71$	4.65136	−	3.90295i	0.552015	−	0.463195i	0.875623	+	0.482996i	$0.160451\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	−0.0569038	−	0.322718i	−0.00666009	−	0.0377712i	0.981297	−	0.192502i	$-0.0616601\pi$
$73$	−0.0569038	−	0.322718i	−0.00666009	−	0.0377712i	−0.987957	+	0.154731i	$0.950549\pi$
$74$	6.47178	+	2.35554i	0.752329	+	0.273825i
$75$	3.59627			0.415261
$76$	−4.21688	−	1.10359i	−0.483709	−	0.126590i
$77$	1.00000			0.113961
$78$	3.64543	+	1.32683i	0.412764	+	0.150234i
$79$	−2.80154	−	15.8883i	−0.315198	−	1.78757i	−0.571109	−	0.820874i	$-0.693487\pi$
$79$	−2.80154	−	15.8883i	−0.315198	−	1.78757i	0.255912	−	0.966700i	$-0.417624\pi$
$80$	0.907604	+	0.761570i	0.101473	+	0.0851461i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	1.56031	−	8.84894i	0.172307	−	0.977202i
$83$	−5.78699	+	10.0234i	−0.635205	+	1.10021i	0.351267	+	0.936275i	$0.385751\pi$
$83$	−5.78699	+	10.0234i	−0.635205	+	1.10021i	−0.986472	+	0.163931i	$0.947582\pi$
$84$	0.266044	+	0.460802i	0.0290278	+	0.0502777i
$85$	−1.29426	+	0.471073i	−0.140383	+	0.0510951i
$86$	2.27972	−	0.829748i	0.245828	−	0.0894741i
$87$	−2.01114	−	3.48340i	−0.215617	−	0.373460i
$88$	0.939693	−	1.62760i	0.100172	−	0.173502i
$89$	−0.618089	+	3.50535i	−0.0655173	+	0.371567i	0.934366	+	0.356314i	$0.115967\pi$
$89$	−0.618089	+	3.50535i	−0.0655173	+	0.371567i	−0.999884	+	0.0152532i	$0.995145\pi$
$90$	−0.907604	+	0.761570i	−0.0956698	+	0.0802765i
$91$	−1.58125	−	1.32683i	−0.165760	−	0.139089i
$92$	−1.16385	−	6.60051i	−0.121340	−	0.688151i
$93$	−1.84002	−	0.669713i	−0.190801	−	0.0694460i
$94$	−2.04189			−0.210605
$95$	−2.15523	+	4.69318i	−0.221122	+	0.481510i
$96$	1.00000			0.102062
$97$	−5.52481	−	2.01087i	−0.560960	−	0.204173i	0.0459494	−	0.998944i	$-0.485369\pi$
$97$	−5.52481	−	2.01087i	−0.560960	−	0.204173i	−0.606909	+	0.794771i	$0.707591\pi$
$98$	1.16637	+	6.61484i	0.117822	+	0.668199i
$99$	1.43969	+	1.20805i	0.144695	+	0.121413i
$100$	−2.75490	+	2.31164i	−0.275490	+	0.231164i
$101$	2.19594	−	12.4538i	0.218504	−	1.23920i	−0.656218	−	0.754572i	$-0.727845\pi$
$101$	2.19594	−	12.4538i	0.218504	−	1.23920i	0.874722	−	0.484626i	$-0.161044\pi$
$102$	−0.581252	+	1.00676i	−0.0575525	+	0.0996839i
$103$	−1.48158	−	2.56617i	−0.145985	−	0.252853i	0.783755	−	0.621070i	$-0.213302\pi$
$103$	−1.48158	−	2.56617i	−0.145985	−	0.252853i	−0.929740	+	0.368217i	$0.879968\pi$
$104$	−3.64543	+	1.32683i	−0.357464	+	0.130106i
$105$	0.592396	−	0.215615i	0.0578120	−	0.0210418i
$106$	6.48545	+	11.2331i	0.629923	+	1.09106i
$107$	−9.55690	+	16.5530i	−0.923901	+	1.60024i	−0.130581	+	0.991438i	$0.541684\pi$
$107$	−9.55690	+	16.5530i	−0.923901	+	1.60024i	−0.793320	+	0.608805i	$0.791649\pi$
$108$	−0.173648	+	0.984808i	−0.0167093	+	0.0947632i
$109$	−12.5719	+	10.5491i	−1.20417	+	1.01042i	−0.204670	+	0.978831i	$0.565612\pi$
$109$	−12.5719	+	10.5491i	−1.20417	+	1.01042i	−0.999501	+	0.0315888i	$0.989943\pi$
$110$	−1.70574	−	1.43128i	−0.162636	−	0.136468i
$111$	−1.19594	−	6.78250i	−0.113513	−	0.643766i
$112$	−0.500000	−	0.181985i	−0.0472456	−	0.0171960i
$113$	−5.73648			−0.539643			−0.269821	−	0.962910i	$-0.586965\pi$
$113$	−5.73648			−0.539643			−0.269821	+	0.962910i	$0.586965\pi$
$114$	1.15270	+	4.20372i	0.107961	+	0.393715i
$115$	−7.94087			−0.740490
$116$	3.77972	+	1.37570i	0.350938	+	0.127731i
$117$	−0.673648	−	3.82045i	−0.0622788	−	0.353201i
$118$	2.05303	+	1.72270i	0.188997	+	0.158587i
$119$	0.473841	−	0.397600i	0.0434369	−	0.0364479i
$120$	0.205737	−	1.16679i	0.0187811	−	0.106513i
$121$	3.73396	−	6.46740i	0.339451	−	0.587946i
$122$	−5.67365	−	9.82705i	−0.513668	−	0.889699i
$123$	−8.44356	+	3.07321i	−0.761330	+	0.277102i
$124$	1.84002	−	0.669713i	0.165239	−	0.0601420i
$125$	5.09240	+	8.82029i	0.455478	+	0.788911i
$126$	0.266044	−	0.460802i	0.0237011	−	0.0410515i
$127$	−0.327696	+	1.85846i	−0.0290783	+	0.164911i	−0.995889	−	0.0905828i	$-0.971127\pi$
$127$	−0.327696	+	1.85846i	−0.0290783	+	0.164911i	0.966811	+	0.255494i	$0.0822381\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−1.85844	−	1.55942i	−0.163627	−	0.137299i
$130$	0.798133	+	4.52644i	0.0700009	+	0.396995i
$131$	−10.0569	−	3.66041i	−0.878676	−	0.319812i	−0.137001	−	0.990571i	$-0.543746\pi$
$131$	−10.0569	−	3.66041i	−0.878676	−	0.319812i	−0.741675	+	0.670759i	$0.765968\pi$
$132$	−1.87939			−0.163579
$133$	0.188663	−	2.31164i	0.0163592	−	0.200444i
$134$	11.1702			0.964962
$135$	1.11334	+	0.405223i	0.0958211	+	0.0348760i
$136$	−0.201867	−	1.14484i	−0.0173099	−	0.0981695i
$137$	−8.62314	−	7.23567i	−0.736725	−	0.618185i	0.195231	−	0.980757i	$-0.437454\pi$
$137$	−8.62314	−	7.23567i	−0.736725	−	0.618185i	−0.931956	+	0.362572i	$0.881899\pi$
$138$	−5.13429	+	4.30818i	−0.437059	+	0.366736i
$139$	−2.11334	+	11.9854i	−0.179251	+	1.01658i	0.753870	+	0.657023i	$0.228185\pi$
$139$	−2.11334	+	11.9854i	−0.179251	+	1.01658i	−0.933122	+	0.359561i	$0.882926\pi$
$140$	−0.315207	+	0.545955i	−0.0266399	+	0.0461416i
$141$	1.02094	+	1.76833i	0.0859790	+	0.148920i
$142$	5.70574	−	2.07672i	0.478815	−	0.174274i
$143$	6.85117	−	2.49362i	0.572923	−	0.208527i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	2.38279	−	4.12711i	0.197880	−	0.342738i
$146$	0.0569038	−	0.322718i	0.00470939	−	0.0267083i
$147$	5.14543	−	4.31753i	0.424388	−	0.356104i
$148$	5.27584	+	4.42696i	0.433672	+	0.363894i
$149$	−2.84002	−	16.1066i	−0.232664	−	1.31950i	−0.847478	−	0.530830i	$-0.821880\pi$
$149$	−2.84002	−	16.1066i	−0.232664	−	1.31950i	0.614815	−	0.788672i	$-0.289231\pi$
$150$	3.37939	+	1.23000i	0.275926	+	0.100429i
$151$	20.5226			1.67010			0.835052	−	0.550170i	$-0.185437\pi$
$151$	20.5226			1.67010			0.835052	+	0.550170i	$0.185437\pi$
$152$	−3.58512	−	2.47929i	−0.290792	−	0.201097i
$153$	1.16250			0.0939829
$154$	0.939693	+	0.342020i	0.0757226	+	0.0275608i
$155$	−0.402856	−	2.28471i	−0.0323582	−	0.183512i
$156$	2.97178	+	2.49362i	0.237933	+	0.199649i
$157$	−2.45084	+	2.05650i	−0.195598	+	0.164126i	−0.735327	−	0.677713i	$-0.762971\pi$
$157$	−2.45084	+	2.05650i	−0.195598	+	0.164126i	0.539729	+	0.841839i	$0.318527\pi$
$158$	2.80154	−	15.8883i	0.222878	−	1.26401i
$159$	6.48545	−	11.2331i	0.514330	−	0.890845i
$160$	0.592396	+	1.02606i	0.0468330	+	0.0811172i
$161$	3.35117	−	1.21972i	0.264109	−	0.0961278i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	12.0039	+	20.7913i	0.940216	+	1.62850i	0.765058	+	0.643961i	$0.222710\pi$
$163$	12.0039	+	20.7913i	0.940216	+	1.62850i	0.175157	+	0.984540i	$0.443957\pi$
$164$	4.49273	−	7.78163i	0.350823	−	0.607643i
$165$	−0.386659	+	2.19285i	−0.0301014	+	0.170713i
$166$	−8.86618	+	7.43961i	−0.688149	+	0.577426i
$167$	2.80406	+	2.35289i	0.216985	+	0.182072i	0.744801	−	0.667287i	$-0.232544\pi$
$167$	2.80406	+	2.35289i	0.216985	+	0.182072i	−0.527816	+	0.849359i	$0.676989\pi$
$168$	0.0923963	+	0.524005i	0.00712853	+	0.0404279i
$169$	−1.92602	−	0.701015i	−0.148156	−	0.0539242i
$170$	−1.37733			−0.105636
$171$	3.06418	−	3.10013i	0.234324	−	0.237073i
$172$	2.42602			0.184982
$173$	5.01114	+	1.82391i	0.380990	+	0.138669i	0.525414	−	0.850847i	$-0.323911\pi$
$173$	5.01114	+	1.82391i	0.380990	+	0.138669i	−0.144424	+	0.989516i	$0.546133\pi$
$174$	−0.698463	−	3.96118i	−0.0529504	−	0.300296i
$175$	−1.46585	−	1.23000i	−0.110808	−	0.0929789i
$176$	1.43969	−	1.20805i	0.108521	−	0.0910599i
$177$	0.465385	−	2.63933i	0.0349805	−	0.198384i
$178$	−1.77972	+	3.08256i	−0.133395	+	0.231047i
$179$	12.6284	+	21.8730i	0.943888	+	1.63486i	0.757963	+	0.652297i	$0.226195\pi$
$179$	12.6284	+	21.8730i	0.943888	+	1.63486i	0.185924	+	0.982564i	$0.440472\pi$
$180$	−1.11334	+	0.405223i	−0.0829835	+	0.0302035i
$181$	16.2626	−	5.91912i	1.20879	−	0.439965i	0.342508	−	0.939515i	$-0.388724\pi$
$181$	16.2626	−	5.91912i	1.20879	−	0.439965i	0.866285	+	0.499550i	$0.166501\pi$
$182$	−1.03209	−	1.78763i	−0.0765035	−	0.132508i
$183$	−5.67365	+	9.82705i	−0.419408	+	0.726436i
$184$	1.16385	−	6.60051i	0.0858000	−	0.486596i
$185$	6.25078	−	5.24503i	0.459567	−	0.385622i
$186$	−1.50000	−	1.25865i	−0.109985	−	0.0922887i
$187$	0.379385	+	2.15160i	0.0277434	+	0.157341i
$188$	−1.91875	−	0.698367i	−0.139939	−	0.0509337i
$189$	−0.532089			−0.0387038
$190$	−3.63041	+	3.67301i	−0.263378	+	0.266468i
$191$	−15.1780			−1.09824			−0.549120	−	0.835743i	$-0.685037\pi$
$191$	−15.1780			−1.09824			−0.549120	+	0.835743i	$0.685037\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	2.25877	+	12.8101i	0.162590	+	0.922093i	0.951515	+	0.307603i	$0.0995269\pi$
$193$	2.25877	+	12.8101i	0.162590	+	0.922093i	−0.788925	+	0.614490i	$0.789362\pi$
$194$	−4.50387	−	3.77920i	−0.323359	−	0.271330i
$195$	3.52094	−	2.95442i	0.252140	−	0.211571i
$196$	−1.16637	+	6.61484i	−0.0833124	+	0.472488i
$197$	4.47431	−	7.74973i	0.318781	−	0.552145i	−0.661453	−	0.749987i	$-0.730060\pi$
$197$	4.47431	−	7.74973i	0.318781	−	0.552145i	0.980234	+	0.197842i	$0.0633931\pi$
$198$	0.939693	+	1.62760i	0.0667810	+	0.115668i
$199$	4.23308	−	1.54071i	0.300075	−	0.109218i	−0.187595	−	0.982246i	$-0.560069\pi$
$199$	4.23308	−	1.54071i	0.300075	−	0.109218i	0.487670	+	0.873028i	$0.337847\pi$
$200$	−3.37939	+	1.23000i	−0.238959	+	0.0869738i
$201$	−5.58512	−	9.67372i	−0.393944	−	0.682331i
$202$	6.32295	−	10.9517i	0.444881	−	0.770557i
$203$	−0.371644	+	2.10770i	−0.0260843	+	0.147932i
$204$	−0.890530	+	0.747243i	−0.0623495	+	0.0523175i
$205$	−8.15523	−	6.84305i	−0.569586	−	0.477939i
$206$	−0.514548	−	2.91815i	−0.0358503	−	0.203317i
$207$	6.29813	+	2.29233i	0.437751	+	0.159328i
$208$	−3.87939			−0.268987
$209$	6.73783	+	4.65955i	0.466065	+	0.322308i
$210$	0.630415			0.0435028
$211$	6.01754	+	2.19021i	0.414265	+	0.150780i	0.540740	−	0.841190i	$-0.318144\pi$
$211$	6.01754	+	2.19021i	0.414265	+	0.150780i	−0.126475	+	0.991970i	$0.540366\pi$
$212$	2.25237	+	12.7738i	0.154694	+	0.877311i
$213$	−4.65136	−	3.90295i	−0.318706	−	0.267426i
$214$	−14.6420	+	12.2861i	−1.00091	+	0.839862i
$215$	0.499123	−	2.83067i	0.0340399	−	0.193050i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	0.520945	+	0.902302i	0.0353640	+	0.0612523i
$218$	−15.4217	+	5.61305i	−1.04449	+	0.380164i
$219$	−0.307934	+	0.112079i	−0.0208082	+	0.00757357i
$220$	−1.11334	−	1.92836i	−0.0750614	−	0.130010i
$221$	2.25490	−	3.90560i	0.151681	−	0.262719i
$222$	1.19594	−	6.78250i	0.0802660	−	0.455211i
$223$	2.48886	−	2.08840i	0.166666	−	0.139849i	−0.555640	−	0.831423i	$-0.687527\pi$
$223$	2.48886	−	2.08840i	0.166666	−	0.139849i	0.722306	+	0.691574i	$0.243082\pi$
$224$	−0.407604	−	0.342020i	−0.0272342	−	0.0228522i
$225$	−0.624485	−	3.54163i	−0.0416323	−	0.236109i
$226$	−5.39053	−	1.96199i	−0.358573	−	0.130510i
$227$	−11.7023			−0.776711			−0.388356	−	0.921510i	$-0.626957\pi$
$227$	−11.7023			−0.776711			−0.388356	+	0.921510i	$0.626957\pi$
$228$	−0.354570	+	4.34445i	−0.0234820	+	0.287718i
$229$	−22.9067			−1.51372			−0.756860	−	0.653578i	$-0.773267\pi$
$229$	−22.9067			−1.51372			−0.756860	+	0.653578i	$0.773267\pi$
$230$	−7.46198	−	2.71594i	−0.492028	−	0.179084i
$231$	−0.173648	−	0.984808i	−0.0114252	−	0.0647956i
$232$	3.08125	+	2.58548i	0.202294	+	0.169745i
$233$	−2.45084	+	2.05650i	−0.160560	+	0.134726i	−0.719528	−	0.694463i	$-0.755642\pi$
$233$	−2.45084	+	2.05650i	−0.160560	+	0.134726i	0.558968	+	0.829189i	$0.311197\pi$
$234$	0.673648	−	3.82045i	0.0440378	−	0.249751i
$235$	−1.20961	+	2.09510i	−0.0789061	+	0.136669i
$236$	1.34002	+	2.32099i	0.0872280	+	0.151083i
$237$	−15.1604	+	5.51795i	−0.984777	+	0.358429i
$238$	0.581252	−	0.211558i	0.0376770	−	0.0137133i
$239$	−3.08647	−	5.34592i	−0.199647	−	0.345799i	0.748767	−	0.662833i	$-0.230646\pi$
$239$	−3.08647	−	5.34592i	−0.199647	−	0.345799i	−0.948414	+	0.317035i	$0.897313\pi$
$240$	0.592396	−	1.02606i	0.0382390	−	0.0662319i
$241$	0.266922	−	1.51379i	0.0171939	−	0.0975117i	−0.975003	−	0.222191i	$-0.928679\pi$
$241$	0.266922	−	1.51379i	0.0171939	−	0.0975117i	0.992197	+	0.124679i	$0.0397902\pi$
$242$	5.72075	−	4.80028i	0.367744	−	0.308574i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−1.97044	−	11.1749i	−0.126144	−	0.715400i
$245$	7.47818	+	2.72183i	0.477763	+	0.173892i
$246$	−8.98545			−0.572892
$247$	−4.47178	−	16.3079i	−0.284533	−	1.03764i
$248$	1.95811			0.124340
$249$	10.8760	+	3.95853i	0.689237	+	0.250862i
$250$	1.76857	+	10.0301i	0.111854	+	0.634357i
$251$	13.7456	+	11.5339i	0.867612	+	0.728013i	0.963594	−	0.267370i	$-0.0861545\pi$
$251$	13.7456	+	11.5339i	0.867612	+	0.728013i	−0.0959815	+	0.995383i	$0.530599\pi$
$252$	0.407604	−	0.342020i	0.0256766	−	0.0215452i
$253$	−2.18732	+	12.4049i	−0.137516	+	0.779889i
$254$	−0.943563	+	1.63430i	−0.0592044	+	0.102545i
$255$	0.688663	+	1.19280i	0.0431257	+	0.0746960i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−27.6386	+	10.0596i	−1.72405	+	0.627503i	−0.998179	−	0.0603277i	$-0.980785\pi$
$257$	−27.6386	+	10.0596i	−1.72405	+	0.627503i	−0.725871	+	0.687831i	$0.758563\pi$
$258$	−1.21301	−	2.10100i	−0.0755188	−	0.130802i
$259$	−1.83228	+	3.17360i	−0.113852	+	0.197198i
$260$	−0.798133	+	4.52644i	−0.0494981	+	0.280718i
$261$	−3.08125	+	2.58548i	−0.190725	+	0.160037i
$262$	−8.19846	−	6.87933i	−0.506503	−	0.425006i
$263$	1.85504	+	10.5204i	0.114386	+	0.648718i	0.987052	+	0.160400i	$0.0512783\pi$
$263$	1.85504	+	10.5204i	0.114386	+	0.648718i	−0.872666	+	0.488318i	$0.837611\pi$
$264$	−1.76604	−	0.642788i	−0.108693	−	0.0395608i
$265$	15.3678			0.944038
$266$	0.967911	−	2.10770i	0.0593464	−	0.129231i
$267$	3.55943			0.217834
$268$	10.4966	+	3.82045i	0.641182	+	0.233371i
$269$	−3.57310	−	20.2641i	−0.217856	−	1.23552i	−0.875882	−	0.482526i	$-0.839719\pi$
$269$	−3.57310	−	20.2641i	−0.217856	−	1.23552i	0.658026	−	0.752995i	$-0.271392\pi$
$270$	0.907604	+	0.761570i	0.0552350	+	0.0463477i
$271$	1.43763	−	1.20632i	0.0873300	−	0.0732786i	−0.598078	−	0.801438i	$-0.704069\pi$
$271$	1.43763	−	1.20632i	0.0873300	−	0.0732786i	0.685408	+	0.728160i	$0.259624\pi$
$272$	0.201867	−	1.14484i	0.0122400	−	0.0694163i
$273$	−1.03209	+	1.78763i	−0.0624649	+	0.108192i
$274$	−5.62836	−	9.74860i	−0.340021	−	0.588934i
$275$	6.35117	−	2.31164i	0.382990	−	0.139397i
$276$	−6.29813	+	2.29233i	−0.379103	+	0.137982i
$277$	−2.43629	−	4.21978i	−0.146382	−	0.253542i	0.783505	−	0.621385i	$-0.213430\pi$
$277$	−2.43629	−	4.21978i	−0.146382	−	0.253542i	−0.929888	+	0.367843i	$0.880096\pi$
$278$	−6.08512	+	10.5397i	−0.364961	+	0.632132i
$279$	−0.340022	+	1.92836i	−0.0203566	+	0.115448i
$280$	−0.482926	+	0.405223i	−0.0288603	+	0.0242167i
$281$	−0.309278	−	0.259515i	−0.0184500	−	0.0154814i	0.633516	−	0.773730i	$-0.281611\pi$
$281$	−0.309278	−	0.259515i	−0.0184500	−	0.0154814i	−0.651966	+	0.758248i	$0.726056\pi$
$282$	0.354570	+	2.01087i	0.0211144	+	0.119745i
$283$	−16.5287	−	6.01595i	−0.982528	−	0.357611i	−0.199706	−	0.979856i	$-0.563999\pi$
$283$	−16.5287	−	6.01595i	−0.982528	−	0.357611i	−0.782823	+	0.622245i	$0.786221\pi$
$284$	6.07192			0.360302
$285$	4.99613	+	1.30753i	0.295945	+	0.0774511i
$286$	7.29086			0.431118
$287$	4.49273	+	1.63522i	0.265197	+	0.0965239i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	−11.9875	−	10.0587i	−0.705148	−	0.591689i
$290$	3.65064	−	3.06325i	0.214373	−	0.179880i
$291$	−1.02094	+	5.79006i	−0.0598488	+	0.339420i
$292$	0.163848	−	0.283793i	0.00958848	−	0.0166077i
$293$	6.58765	+	11.4101i	0.384855	+	0.666588i	0.991749	−	0.128195i	$-0.0409183\pi$
$293$	6.58765	+	11.4101i	0.384855	+	0.666588i	−0.606894	+	0.794782i	$0.707585\pi$
$294$	6.31180	−	2.29731i	0.368112	−	0.133982i
$295$	2.98380	−	1.08602i	0.173724	−	0.0632303i
$296$	3.44356	+	5.96443i	0.200153	+	0.346675i
$297$	0.939693	−	1.62760i	0.0545265	−	0.0944427i
$298$	2.84002	−	16.1066i	0.164518	−	0.933028i
$299$	19.9179	−	16.7131i	1.15188	−	0.966542i
$300$	2.75490	+	2.31164i	0.159054	+	0.133462i
$301$	0.224155	+	1.27125i	0.0129201	+	0.0732735i
$302$	19.2849	+	7.01914i	1.10972	+	0.403906i
$303$	−12.6459			−0.726488
$304$	−2.52094	−	3.55596i	−0.144586	−	0.203948i
$305$	−13.4442			−0.769812
$306$	1.09240	+	0.397600i	0.0624481	+	0.0227293i
$307$	2.93494	+	16.6449i	0.167506	+	0.949975i	0.946443	+	0.322872i	$0.104648\pi$
$307$	2.93494	+	16.6449i	0.167506	+	0.949975i	−0.778937	+	0.627103i	$0.784241\pi$
$308$	0.766044	+	0.642788i	0.0436494	+	0.0366262i
$309$	−2.26991	+	1.90468i	−0.129131	+	0.108354i
$310$	0.402856	−	2.28471i	0.0228807	−	0.129763i
$311$	1.19072	−	2.06239i	0.0675197	−	0.116947i	−0.830289	−	0.557333i	$-0.811825\pi$
$311$	1.19072	−	2.06239i	0.0675197	−	0.116947i	0.897809	+	0.440385i	$0.145158\pi$
$312$	1.93969	+	3.35965i	0.109813	+	0.190203i
$313$	28.0621	−	10.2138i	1.58616	−	0.577317i	0.609632	−	0.792685i	$-0.291317\pi$
$313$	28.0621	−	10.2138i	1.58616	−	0.577317i	0.976533	+	0.215368i	$0.0690951\pi$
$314$	−3.00640	+	1.09424i	−0.169661	+	0.0617515i
$315$	−0.315207	−	0.545955i	−0.0177599	−	0.0307611i
$316$	8.06670	−	13.9719i	0.453788	−	0.785983i
$317$	−1.21941	+	6.91560i	−0.0684888	+	0.388419i	0.931224	+	0.364448i	$0.118742\pi$
$317$	−1.21941	+	6.91560i	−0.0684888	+	0.388419i	−0.999713	+	0.0239714i	$0.992369\pi$
$318$	9.93629	−	8.33754i	0.557199	−	0.467546i
$319$	−5.79086	−	4.85911i	−0.324226	−	0.272058i
$320$	0.205737	+	1.16679i	0.0115011	+	0.0652257i
$321$	17.9611	+	6.53731i	1.00249	+	0.364877i
$322$	3.56624			0.198739
$323$	5.04529	−	0.471073i	0.280728	−	0.0262112i
$324$	1.00000			0.0555556
$325$	−13.1099	−	4.77163i	−0.727208	−	0.264682i
$326$	4.16890	+	23.6430i	0.230894	+	1.30947i
$327$	12.5719	+	10.5491i	0.695229	+	0.583366i
$328$	6.88326	−	5.77574i	0.380064	−	0.318912i
$329$	0.188663	−	1.06996i	0.0104013	−	0.0589888i
$330$	−1.11334	+	1.92836i	−0.0612874	+	0.106153i
$331$	−13.5993	−	23.5546i	−0.747483	−	1.29468i	−0.949026	−	0.315199i	$-0.897929\pi$
$331$	−13.5993	−	23.5546i	−0.747483	−	1.29468i	0.201543	−	0.979480i	$-0.435404\pi$
$332$	−10.8760	+	3.95853i	−0.596897	+	0.217253i
$333$	−6.47178	+	2.35554i	−0.354651	+	0.129083i
$334$	1.83022	+	3.17004i	0.100145	+	0.173457i
$335$	6.61721	−	11.4613i	0.361537	−	0.626200i
$336$	−0.0923963	+	0.524005i	−0.00504063	+	0.0285868i
$337$	−8.59286	+	7.21027i	−0.468083	+	0.392768i	−0.846095	−	0.533032i	$-0.821052\pi$
$337$	−8.59286	+	7.21027i	−0.468083	+	0.392768i	0.378012	+	0.925801i	$0.376608\pi$
$338$	−1.57011	−	1.31748i	−0.0854026	−	0.0716613i
$339$	0.996130	+	5.64933i	0.0541023	+	0.306830i
$340$	−1.29426	−	0.471073i	−0.0701913	−	0.0255475i
$341$	−3.68004			−0.199286
$342$	3.93969	−	1.86516i	0.213034	−	0.100856i
$343$	−7.29860			−0.394087
$344$	2.27972	+	0.829748i	0.122914	+	0.0447370i
$345$	1.37892	+	7.82023i	0.0742385	+	0.421027i
$346$	4.08512	+	3.42782i	0.219618	+	0.184281i
$347$	1.48293	−	1.24432i	0.0796076	−	0.0667987i	−0.602115	−	0.798409i	$-0.705675\pi$
$347$	1.48293	−	1.24432i	0.0796076	−	0.0667987i	0.681723	+	0.731610i	$0.261231\pi$
$348$	0.698463	−	3.96118i	0.0374416	−	0.212342i
$349$	−7.19846	+	12.4681i	−0.385325	+	0.667402i	−0.991814	−	0.127689i	$-0.959244\pi$
$349$	−7.19846	+	12.4681i	−0.385325	+	0.667402i	0.606489	+	0.795092i	$0.292577\pi$
$350$	−0.956767	−	1.65717i	−0.0511413	−	0.0885794i
$351$	−3.64543	+	1.32683i	−0.194579	+	0.0708208i
$352$	1.76604	−	0.642788i	0.0941305	−	0.0342607i
$353$	−7.86184	−	13.6171i	−0.418444	−	0.724766i	0.577339	−	0.816504i	$-0.304091\pi$
$353$	−7.86184	−	13.6171i	−0.418444	−	0.724766i	−0.995783	+	0.0917384i	$0.970758\pi$
$354$	1.34002	−	2.32099i	0.0712214	−	0.123359i
$355$	1.24922	−	7.08467i	0.0663016	−	0.376015i
$356$	−2.72668	+	2.28796i	−0.144514	+	0.121262i
$357$	−0.473841	−	0.397600i	−0.0250783	−	0.0210432i
$358$	4.38578	+	24.8730i	0.231796	+	1.31458i
$359$	−14.5817	−	5.30731i	−0.769594	−	0.280109i	−0.0727672	−	0.997349i	$-0.523183\pi$
$359$	−14.5817	−	5.30731i	−0.769594	−	0.280109i	−0.696826	+	0.717240i	$0.745405\pi$
$360$	−1.18479			−0.0624440
$361$	12.0424	−	14.6963i	0.633808	−	0.773490i
$362$	17.3063			0.909601
$363$	−7.01754	−	2.55418i	−0.368325	−	0.134059i
$364$	−0.358441	−	2.03282i	−0.0187874	−	0.106549i
$365$	−0.297418	−	0.249563i	−0.0155676	−	0.0130627i
$366$	−8.69253	+	7.29390i	−0.454366	+	0.381258i
$367$	−2.73396	+	15.5050i	−0.142711	+	0.809356i	0.826465	+	0.562988i	$0.190348\pi$
$367$	−2.73396	+	15.5050i	−0.142711	+	0.809356i	−0.969176	+	0.246368i	$0.920763\pi$
$368$	3.35117	−	5.80439i	0.174692	−	0.302575i
$369$	4.49273	+	7.78163i	0.233882	+	0.405095i
$370$	7.66772	−	2.79082i	0.398626	−	0.145088i
$371$	−6.48545	+	2.36051i	−0.336708	+	0.122552i
$372$	−0.979055	−	1.69577i	−0.0507617	−	0.0879218i
$373$	14.8143	−	25.6592i	0.767057	−	1.32858i	−0.172095	−	0.985080i	$-0.555054\pi$
$373$	14.8143	−	25.6592i	0.767057	−	1.32858i	0.939152	−	0.343501i	$-0.111613\pi$
$374$	−0.379385	+	2.15160i	−0.0196175	+	0.111257i
$375$	7.80200	−	6.54666i	0.402894	−	0.338068i
$376$	−1.56418	−	1.31250i	−0.0806663	−	0.0676871i
$377$	2.70961	+	15.3669i	0.139552	+	0.791438i
$378$	−0.500000	−	0.181985i	−0.0257172	−	0.00936030i
$379$	4.72462			0.242688			0.121344	−	0.992611i	$-0.461280\pi$
$379$	4.72462			0.242688			0.121344	+	0.992611i	$0.461280\pi$
$380$	−4.66772	+	2.20983i	−0.239449	+	0.113362i
$381$	1.88713			0.0966804
$382$	−14.2626	−	5.19118i	−0.729740	−	0.265604i
$383$	−0.910130	−	5.16160i	−0.0465055	−	0.263746i	0.952686	−	0.303957i	$-0.0983079\pi$
$383$	−0.910130	−	5.16160i	−0.0465055	−	0.263746i	−0.999191	+	0.0402115i	$0.987197\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	0.907604	−	0.761570i	0.0462558	−	0.0388132i
$386$	−2.25877	+	12.8101i	−0.114968	+	0.652018i
$387$	−1.21301	+	2.10100i	−0.0616608	+	0.106800i
$388$	−2.93969	−	5.09170i	−0.149240	−	0.258492i
$389$	14.1677	−	5.15663i	0.718332	−	0.261451i	0.0431144	−	0.999070i	$-0.486272\pi$
$389$	14.1677	−	5.15663i	0.718332	−	0.261451i	0.675217	+	0.737619i	$0.264050\pi$
$390$	4.31908	−	1.57202i	0.218705	−	0.0796021i
$391$	3.89574	+	6.74763i	0.197016	+	0.341242i
$392$	−3.35844	+	5.81699i	−0.169627	+	0.293802i
$393$	−1.85844	+	10.5397i	−0.0937459	+	0.531660i
$394$	6.85504	−	5.75206i	0.345352	−	0.289785i
$395$	−14.6427	−	12.2867i	−0.736756	−	0.618212i
$396$	0.326352	+	1.85083i	0.0163998	+	0.0930079i
$397$	13.6677	+	4.97464i	0.685963	+	0.249670i	0.661406	−	0.750028i	$-0.269960\pi$
$397$	13.6677	+	4.97464i	0.685963	+	0.249670i	0.0245573	+	0.999698i	$0.492182\pi$
$398$	4.50475			0.225803
$399$	−2.30928	+	0.215615i	−0.115608	+	0.0107942i
$400$	−3.59627			−0.179813
$401$	−2.68257	−	0.976376i	−0.133961	−	0.0487579i	0.274170	−	0.961681i	$-0.411597\pi$
$401$	−2.68257	−	0.976376i	−0.133961	−	0.0487579i	−0.408131	+	0.912923i	$0.633819\pi$
$402$	−1.93969	−	11.0005i	−0.0967431	−	0.548657i
$403$	5.81908	+	4.88279i	0.289869	+	0.243229i
$404$	9.68732	−	8.12863i	0.481962	−	0.404414i
$405$	0.205737	−	1.16679i	0.0102232	−	0.0579784i
$406$	−1.07011	+	1.85348i	−0.0531085	+	0.0919867i
$407$	−6.47178	−	11.2095i	−0.320794	−	0.555632i
$408$	−1.09240	+	0.397600i	−0.0540817	+	0.0196841i
$409$	−32.1634	+	11.7065i	−1.59038	+	0.578851i	−0.977428	−	0.211269i	$-0.932240\pi$
$409$	−32.1634	+	11.7065i	−1.59038	+	0.578851i	−0.612952	+	0.790120i	$0.710018\pi$
$410$	−5.32295	−	9.21962i	−0.262882	−	0.455324i
$411$	−5.62836	+	9.74860i	−0.277626	+	0.480863i
$412$	0.514548	−	2.91815i	0.0253500	−	0.143767i
$413$	−1.09240	+	0.916629i	−0.0537533	+	0.0451044i
$414$	5.13429	+	4.30818i	0.252336	+	0.211735i
$415$	2.38120	+	13.5044i	0.116888	+	0.662907i
$416$	−3.64543	−	1.32683i	−0.178732	−	0.0650531i
$417$	12.1702			0.595979
$418$	4.73783	+	6.68302i	0.231735	+	0.326877i
$419$	−7.91891			−0.386864			−0.193432	−	0.981114i	$-0.561962\pi$
$419$	−7.91891			−0.386864			−0.193432	+	0.981114i	$0.561962\pi$
$420$	0.592396	+	0.215615i	0.0289060	+	0.0105209i
$421$	2.81480	+	15.9635i	0.137185	+	0.778014i	0.973313	+	0.229480i	$0.0737026\pi$
$421$	2.81480	+	15.9635i	0.137185	+	0.778014i	−0.836129	+	0.548534i	$0.815186\pi$
$422$	4.90554	+	4.11624i	0.238798	+	0.200375i
$423$	1.56418	−	1.31250i	0.0760529	−	0.0638160i
$424$	−2.25237	+	12.7738i	−0.109385	+	0.620353i
$425$	2.09034	−	3.62057i	0.101396	−	0.175623i
$426$	−3.03596	−	5.25844i	−0.147093	−	0.254772i
$427$	5.67365	−	2.06504i	0.274567	−	0.0999342i
$428$	−17.9611	+	6.53731i	−0.868183	+	0.315993i
$429$	−3.64543	−	6.31407i	−0.176003	−	0.304846i
$430$	1.43717	−	2.48925i	0.0693063	−	0.120042i
$431$	4.41622	−	25.0456i	0.212722	−	1.20641i	−0.672094	−	0.740466i	$-0.734605\pi$
$431$	4.41622	−	25.0456i	0.212722	−	1.20641i	0.884816	−	0.465940i	$-0.154284\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	9.07604	+	7.61570i	0.436167	+	0.365987i	0.834273	−	0.551352i	$-0.185888\pi$
$433$	9.07604	+	7.61570i	0.436167	+	0.365987i	−0.398106	+	0.917339i	$0.630332\pi$
$434$	0.180922	+	1.02606i	0.00868454	+	0.0492525i
$435$	−4.47818	−	1.62992i	−0.214712	−	0.0781489i
$436$	−16.4115			−0.785967
$437$	28.2629	+	7.39663i	1.35200	+	0.353829i
$438$	−0.327696			−0.0156579
$439$	−24.3002	−	8.84457i	−1.15979	−	0.422128i	−0.310766	−	0.950486i	$-0.600586\pi$
$439$	−24.3002	−	8.84457i	−1.15979	−	0.422128i	−0.849022	+	0.528358i	$0.822808\pi$
$440$	−0.386659	−	2.19285i	−0.0184333	−	0.104540i
$441$	−5.14543	−	4.31753i	−0.245020	−	0.205597i
$442$	3.45471	−	2.89884i	0.164324	−	0.137884i
$443$	0.160282	−	0.909006i	0.00761524	−	0.0431882i	−0.980763	−	0.195201i	$-0.937464\pi$
$443$	0.160282	−	0.909006i	0.00761524	−	0.0431882i	0.988379	+	0.152012i	$0.0485753\pi$
$444$	3.44356	−	5.96443i	0.163424	−	0.283059i
$445$	2.10859	+	3.65219i	0.0999569	+	0.173130i
$446$	3.05303	−	1.11121i	0.144565	−	0.0526175i
$447$	−15.3687	+	5.59375i	−0.726915	+	0.264575i
$448$	−0.266044	−	0.460802i	−0.0125694	−	0.0217709i
$449$	−4.67230	+	8.09267i	−0.220500	+	0.381917i	−0.954960	−	0.296735i	$-0.904102\pi$
$449$	−4.67230	+	8.09267i	−0.220500	+	0.381917i	0.734460	+	0.678652i	$0.237435\pi$
$450$	0.624485	−	3.54163i	0.0294385	−	0.166954i
$451$	−12.9363	+	10.8548i	−0.609146	+	0.511134i
$452$	−4.39440	−	3.68734i	−0.206695	−	0.173438i
$453$	−3.56371	−	20.2108i	−0.167438	−	0.949587i
$454$	−10.9966	−	4.00243i	−0.516096	−	0.187844i
$455$	−2.44562			−0.114653
$456$	−1.81908	+	3.96118i	−0.0851861	+	0.185499i
$457$	30.9009			1.44548			0.722740	−	0.691120i	$-0.242882\pi$
$457$	30.9009			1.44548			0.722740	+	0.691120i	$0.242882\pi$
$458$	−21.5253	−	7.83456i	−1.00581	−	0.366085i
$459$	−0.201867	−	1.14484i	−0.00942233	−	0.0534367i
$460$	−6.08306	−	5.10430i	−0.283624	−	0.237989i
$461$	−22.7422	+	19.0829i	−1.05921	+	0.888781i	−0.994032	−	0.109093i	$-0.965205\pi$
$461$	−22.7422	+	19.0829i	−1.05921	+	0.888781i	−0.0651765	+	0.997874i	$0.520761\pi$
$462$	0.173648	−	0.984808i	0.00807884	−	0.0458174i
$463$	5.91534	−	10.2457i	0.274909	−	0.476157i	−0.695203	−	0.718814i	$-0.744685\pi$
$463$	5.91534	−	10.2457i	0.274909	−	0.476157i	0.970112	+	0.242657i	$0.0780188\pi$
$464$	2.01114	+	3.48340i	0.0933650	+	0.161713i
$465$	−2.18004	+	0.793471i	−0.101097	+	0.0367964i
$466$	−3.00640	+	1.09424i	−0.139269	+	0.0506896i
$467$	−19.1591	−	33.1845i	−0.886577	−	1.53560i	−0.843895	−	0.536508i	$-0.819743\pi$
$467$	−19.1591	−	33.1845i	−0.886577	−	1.53560i	−0.0426825	−	0.999089i	$-0.513590\pi$
$468$	1.93969	−	3.35965i	0.0896623	−	0.155300i
$469$	−1.03209	+	5.85327i	−0.0476574	+	0.270279i
$470$	−1.85323	+	1.55504i	−0.0854829	+	0.0717287i
$471$	2.45084	+	2.05650i	0.112929	+	0.0947584i
$472$	0.465385	+	2.63933i	0.0214211	+	0.121485i
$473$	−4.28446	−	1.55942i	−0.197000	−	0.0717021i
$474$	−16.1334			−0.741032
$475$	−4.14543	−	15.1177i	−0.190205	−	0.693648i
$476$	0.618555			0.0283514
$477$	−12.1887	−	4.43631i	−0.558081	−	0.203125i
$478$	−1.07192	−	6.07915i	−0.0490284	−	0.278054i
$479$	28.5612	+	23.9657i	1.30500	+	1.09502i	0.989259	+	0.146176i	$0.0466964\pi$
$479$	28.5612	+	23.9657i	1.30500	+	1.09502i	0.315738	+	0.948846i	$0.397748\pi$
$480$	0.907604	−	0.761570i	0.0414263	−	0.0347608i
$481$	−4.63950	+	26.3119i	−0.211543	+	1.19972i
$482$	0.768571	−	1.33120i	0.0350074	−	0.0606347i
$483$	−1.78312	−	3.08845i	−0.0811347	−	0.140529i
$484$	7.01754	−	2.55418i	0.318979	−	0.116099i
$485$	−6.54576	+	2.38246i	−0.297228	+	0.108182i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−16.4893	+	28.5603i	−0.747203	+	1.29419i	0.201956	+	0.979395i	$0.435270\pi$
$487$	−16.4893	+	28.5603i	−0.747203	+	1.29419i	−0.949159	+	0.314798i	$0.898063\pi$
$488$	1.97044	−	11.1749i	0.0891975	−	0.505864i
$489$	18.3910	−	15.4319i	0.831670	−	0.697854i
$490$	6.09627	+	5.11538i	0.275401	+	0.231089i
$491$	3.07027	+	17.4124i	0.138559	+	0.785809i	0.972315	+	0.233675i	$0.0750752\pi$
$491$	3.07027	+	17.4124i	0.138559	+	0.785809i	−0.833755	+	0.552134i	$0.813814\pi$
$492$	−8.44356	−	3.07321i	−0.380665	−	0.138551i
$493$	−4.67593			−0.210593
$494$	1.37551	−	16.8538i	0.0618873	−	0.758289i
$495$	2.22668			0.100082
$496$	1.84002	+	0.669713i	0.0826194	+	0.0300710i
$497$	0.561023	+	3.18172i	0.0251653	+	0.142720i
$498$	8.86618	+	7.43961i	0.397303	+	0.333377i
$499$	20.7781	−	17.4349i	0.930157	−	0.780494i	−0.0456890	−	0.998956i	$-0.514548\pi$
$499$	20.7781	−	17.4349i	0.930157	−	0.780494i	0.975846	+	0.218462i	$0.0701039\pi$
$500$	−1.76857	+	10.0301i	−0.0790929	+	0.448558i
$501$	1.83022	−	3.17004i	0.0817683	−	0.141627i
$502$	8.97178	+	15.5396i	0.400430	+	0.693565i
$503$	−0.536837	+	0.195393i	−0.0239364	+	0.00871212i	−0.353961	−	0.935260i	$-0.615165\pi$
$503$	−0.536837	+	0.195393i	−0.0239364	+	0.00871212i	0.330024	+	0.943972i	$0.392943\pi$
$504$	0.500000	−	0.181985i	0.0222718	−	0.00810626i
$505$	−7.49138	−	12.9755i	−0.333362	−	0.577400i
$506$	−6.29813	+	10.9087i	−0.279986	+	0.484950i
$507$	−0.355914	+	2.01849i	−0.0158067	+	0.0896443i
$508$	−1.44562	+	1.21302i	−0.0641391	+	0.0538191i
$509$	31.0638	+	26.0656i	1.37688	+	1.15534i	0.970352	+	0.241698i	$0.0777043\pi$
$509$	31.0638	+	26.0656i	1.37688	+	1.15534i	0.406526	+	0.913639i	$0.366740\pi$
$510$	0.239170	+	1.35640i	0.0105906	+	0.0600625i
$511$	0.163848	+	0.0596358i	0.00724821	+	0.00263813i
$512$	−1.00000			−0.0441942
$513$	−3.58512	−	2.47929i	−0.158287	−	0.109463i
$514$	−29.4124			−1.29733
$515$	−3.29901	−	1.20074i	−0.145372	−	0.0529110i
$516$	−0.421274	−	2.38917i	−0.0185456	−	0.105177i
$517$	2.93969	+	2.46669i	0.129288	+	0.108485i
$518$	−2.80722	+	2.35554i	−0.123342	+	0.103496i
$519$	0.926022	−	5.25173i	0.0406479	−	0.230525i
$520$	−2.29813	+	3.98048i	−0.100780	+	0.174556i
$521$	−9.44996	−	16.3678i	−0.414010	−	0.717087i	0.581314	−	0.813680i	$-0.302539\pi$
$521$	−9.44996	−	16.3678i	−0.414010	−	0.717087i	−0.995324	+	0.0965927i	$0.969206\pi$
$522$	−3.77972	+	1.37570i	−0.165434	+	0.0602129i
$523$	4.45589	−	1.62181i	0.194842	−	0.0709168i	−0.242756	−	0.970087i	$-0.578051\pi$
$523$	4.45589	−	1.62181i	0.194842	−	0.0709168i	0.437598	+	0.899171i	$0.355829\pi$
$524$	−5.35117	−	9.26849i	−0.233767	−	0.404896i
$525$	−0.956767	+	1.65717i	−0.0417567	+	0.0723248i
$526$	−1.85504	+	10.5204i	−0.0808835	+	0.458713i
$527$	−1.74376	+	1.46318i	−0.0759592	+	0.0637373i
$528$	−1.43969	−	1.20805i	−0.0626546	−	0.0525734i
$529$	3.80659	+	21.5882i	0.165504	+	0.938619i
$530$	14.4410	+	5.25611i	0.627279	+	0.228311i
$531$	−2.68004			−0.116304
$532$	1.63041	−	1.64955i	0.0706875	−	0.0715169i
$533$	34.8580			1.50987
$534$	3.34477	+	1.21740i	0.144742	+	0.0526819i
$535$	3.93242	+	22.3019i	0.170013	+	0.964193i
$536$	8.55690	+	7.18009i	0.369602	+	0.310133i
$537$	19.3478	−	16.2347i	0.834918	−	0.700579i
$538$	3.57310	−	20.2641i	0.154047	−	0.873646i
$539$	6.31180	−	10.9324i	0.271869	−	0.470890i
$540$	0.592396	+	1.02606i	0.0254927	+	0.0441546i
$541$	26.6506	−	9.70004i	1.14580	−	0.417037i	0.301796	−	0.953373i	$-0.402414\pi$
$541$	26.6506	−	9.70004i	1.14580	−	0.417037i	0.844005	+	0.536335i	$0.180192\pi$
$542$	1.76352	−	0.641868i	0.0757496	−	0.0275706i
$543$	−8.65317	−	14.9877i	−0.371343	−	0.643185i
$544$	0.581252	−	1.00676i	0.0249210	−	0.0431644i
$545$	−3.37645	+	19.1488i	−0.144631	+	0.820244i
$546$	−1.58125	+	1.32683i	−0.0676713	+	0.0567830i
$547$	−5.27063	−	4.42258i	−0.225356	−	0.189096i	0.523118	−	0.852260i	$-0.324769\pi$
$547$	−5.27063	−	4.42258i	−0.225356	−	0.189096i	−0.748474	+	0.663164i	$0.769213\pi$
$548$	−1.95471	−	11.0857i	−0.0835010	−	0.473557i
$549$	10.6630	+	3.88100i	0.455084	+	0.165637i
$550$	6.75877			0.288195
$551$	−12.3250	+	12.4696i	−0.525063	+	0.531224i
$552$	−6.70233			−0.285270
$553$	8.06670	+	2.93604i	0.343031	+	0.124853i
$554$	−0.846114	−	4.79855i	−0.0359480	−	0.203871i
$555$	−6.25078	−	5.24503i	−0.265331	−	0.222639i
$556$	−9.32295	+	7.82288i	−0.395381	+	0.331764i
$557$	−2.45929	+	13.9473i	−0.104204	+	0.590968i	0.887332	+	0.461131i	$0.152556\pi$
$557$	−2.45929	+	13.9473i	−0.104204	+	0.590968i	−0.991535	+	0.129836i	$0.958555\pi$
$558$	−0.979055	+	1.69577i	−0.0414467	+	0.0717878i
$559$	4.70574	+	8.15058i	0.199031	+	0.344733i
$560$	−0.592396	+	0.215615i	−0.0250333	+	0.00911138i
$561$	2.05303	−	0.747243i	0.0866791	−	0.0315486i
$562$	−0.201867	−	0.349643i	−0.00851523	−	0.0147488i
$563$	18.1275	−	31.3977i	0.763982	−	1.32326i	−0.176801	−	0.984247i	$-0.556575\pi$
$563$	18.1275	−	31.3977i	0.763982	−	1.32326i	0.940783	−	0.339009i	$-0.110092\pi$
$564$	−0.354570	+	2.01087i	−0.0149301	+	0.0846728i
$565$	−5.20645	+	4.36873i	−0.219037	+	0.183794i
$566$	−13.4743	−	11.3063i	−0.566367	−	0.475239i
$567$	0.0923963	+	0.524005i	0.00388028	+	0.0220062i
$568$	5.70574	+	2.07672i	0.239407	+	0.0871372i
$569$	−30.2918			−1.26990			−0.634949	−	0.772554i	$-0.718979\pi$
$569$	−30.2918			−1.26990			−0.634949	+	0.772554i	$0.718979\pi$
$570$	4.24763	+	2.93745i	0.177913	+	0.123036i
$571$	3.39094			0.141906			0.0709532	−	0.997480i	$-0.477396\pi$
$571$	3.39094			0.141906			0.0709532	+	0.997480i	$0.477396\pi$
$572$	6.85117	+	2.49362i	0.286462	+	0.104264i
$573$	2.63563	+	14.9474i	0.110105	+	0.624436i
$574$	3.66250	+	3.07321i	0.152870	+	0.128273i
$575$	18.4643	−	15.4934i	0.770013	−	0.646117i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	11.1514	−	19.3147i	0.464237	−	0.804082i	−0.534930	−	0.844897i	$-0.679662\pi$
$577$	11.1514	−	19.3147i	0.464237	−	0.804082i	0.999167	+	0.0408143i	$0.0129952\pi$
$578$	−7.82429	−	13.5521i	−0.325448	−	0.563692i
$579$	12.2233	−	4.44891i	0.507982	−	0.184890i
$580$	4.47818	−	1.62992i	0.185946	−	0.0676789i
$581$	−3.07919	−	5.33332i	−0.127746	−	0.221263i
$582$	−2.93969	+	5.09170i	−0.121854	+	0.211058i
$583$	4.23308	−	24.0070i	0.175316	−	0.994268i
$584$	0.251030	−	0.210639i	0.0103877	−	0.00871630i
$585$	−3.52094	−	2.95442i	−0.145573	−	0.122150i
$586$	2.28787	+	12.9751i	0.0945109	+	0.535998i
$587$	27.0164	+	9.83315i	1.11508	+	0.405858i	0.832856	−	0.553490i	$-0.186704\pi$
$587$	27.0164	+	9.83315i	1.11508	+	0.405858i	0.282228	+	0.959347i	$0.408926\pi$
$588$	6.71688			0.277000
$589$	−0.694288	+	8.50692i	−0.0286076	+	0.350522i
$590$	3.17530			0.130725
$591$	−8.40895	−	3.06061i	−0.345898	−	0.125897i
$592$	1.19594	+	6.78250i	0.0491527	+	0.278759i
$593$	9.02094	+	7.56947i	0.370446	+	0.310841i	0.808938	−	0.587894i	$-0.200043\pi$
$593$	9.02094	+	7.56947i	0.370446	+	0.310841i	−0.438492	+	0.898735i	$0.644487\pi$
$594$	1.43969	−	1.20805i	0.0590713	−	0.0495667i
$595$	0.127260	−	0.721726i	0.00521714	−	0.0295879i
$596$	8.17752	−	14.1639i	0.334964	−	0.580175i
$597$	−2.25237	−	3.90123i	−0.0921835	−	0.159667i
$598$	24.4329	−	8.89284i	0.999135	−	0.363655i
$599$	20.3268	−	7.39836i	0.830531	−	0.302289i	0.108454	−	0.994101i	$-0.465410\pi$
$599$	20.3268	−	7.39836i	0.830531	−	0.302289i	0.722077	+	0.691813i	$0.243188\pi$
$600$	1.79813	+	3.11446i	0.0734085	+	0.127147i
$601$	13.0967	−	22.6842i	0.534227	−	0.925308i	−0.464973	−	0.885325i	$-0.653936\pi$
$601$	13.0967	−	22.6842i	0.534227	−	0.925308i	0.999200	−	0.0399835i	$-0.0127305\pi$
$602$	−0.224155	+	1.27125i	−0.00913589	+	0.0518122i
$603$	−8.55690	+	7.18009i	−0.348464	+	0.292396i
$604$	15.7212	+	13.1917i	0.639687	+	0.536761i
$605$	−1.53643	−	8.71351i	−0.0624646	−	0.354254i
$606$	−11.8833	−	4.32515i	−0.482724	−	0.175697i
$607$	−13.2249			−0.536783			−0.268392	−	0.963310i	$-0.586492\pi$
$607$	−13.2249			−0.536783			−0.268392	+	0.963310i	$0.586492\pi$
$608$	−1.15270	−	4.20372i	−0.0467483	−	0.170483i
$609$	2.14022			0.0867259
$610$	−12.6334	−	4.59818i	−0.511512	−	0.186175i
$611$	−1.37551	−	7.80093i	−0.0556474	−	0.315592i
$612$	0.890530	+	0.747243i	0.0359975	+	0.0302055i
$613$	−4.30722	+	3.61419i	−0.173967	+	0.145976i	−0.725614	−	0.688102i	$-0.758444\pi$
$613$	−4.30722	+	3.61419i	−0.173967	+	0.145976i	0.551647	+	0.834078i	$0.314000\pi$
$614$	−2.93494	+	16.6449i	−0.118445	+	0.671733i
$615$	−5.32295	+	9.21962i	−0.214642	+	0.371771i
$616$	0.500000	+	0.866025i	0.0201456	+	0.0348932i
$617$	−8.90673	+	3.24178i	−0.358571	+	0.130509i	−0.515023	−	0.857176i	$-0.672217\pi$
$617$	−8.90673	+	3.24178i	−0.358571	+	0.130509i	0.156452	+	0.987686i	$0.449994\pi$
$618$	−2.78446	+	1.01346i	−0.112008	+	0.0407674i
$619$	7.37464	+	12.7732i	0.296412	+	0.513400i	0.975312	−	0.220830i	$-0.0708766\pi$
$619$	7.37464	+	12.7732i	0.296412	+	0.513400i	−0.678901	+	0.734230i	$0.737543\pi$
$620$	1.15998	−	2.00914i	0.0465858	−	0.0806890i
$621$	1.16385	−	6.60051i	0.0467036	−	0.264869i
$622$	1.82429	−	1.53076i	0.0731475	−	0.0613780i
$623$	−1.45084	−	1.21740i	−0.0581266	−	0.0487740i
$624$	0.673648	+	3.82045i	0.0269675	+	0.152940i
$625$	−5.55778	−	2.02287i	−0.222311	−	0.0809147i
$626$	29.8631			1.19357
$627$	3.41875	−	7.44459i	0.136532	−	0.297308i
$628$	−3.19934			−0.127668
$629$	−7.52347	−	2.73832i	−0.299980	−	0.109184i
$630$	−0.109470	−	0.620838i	−0.00436141	−	0.0247348i
$631$	19.1518	+	16.0703i	0.762422	+	0.639748i	0.938756	−	0.344582i	$-0.111979\pi$
$631$	19.1518	+	16.0703i	0.762422	+	0.639748i	−0.176334	+	0.984330i	$0.556424\pi$
$632$	12.3589	−	10.3704i	0.491611	−	0.412511i
$633$	1.11200	−	6.30645i	0.0441979	−	0.250659i
$634$	−3.51114	+	6.08148i	−0.139445	+	0.241526i
$635$	1.11793	+	1.93631i	0.0443636	+	0.0768399i
$636$	12.1887	−	4.43631i	0.483312	−	0.175911i
$637$	−24.4859	+	8.91215i	−0.970167	+	0.353112i
$638$	−3.77972	−	6.54666i	−0.149640	−	0.259185i
$639$	−3.03596	+	5.25844i	−0.120101	+	0.208021i
$640$	−0.205737	+	1.16679i	−0.00813247	+	0.0461215i
$641$	−33.4996	+	28.1095i	−1.32315	+	1.11026i	−0.337528	+	0.941315i	$0.609591\pi$
$641$	−33.4996	+	28.1095i	−1.32315	+	1.11026i	−0.985626	+	0.168943i	$0.945965\pi$
$642$	14.6420	+	12.2861i	0.577875	+	0.484894i
$643$	−5.80912	−	32.9451i	−0.229089	−	1.29923i	−0.854712	−	0.519103i	$-0.826266\pi$
$643$	−5.80912	−	32.9451i	−0.229089	−	1.29923i	0.625622	−	0.780126i	$-0.284845\pi$
$644$	3.35117	+	1.21972i	0.132054	+	0.0480639i
$645$	−2.87433			−0.113177
$646$	4.90214	+	1.28293i	0.192872	+	0.0504761i
$647$	−32.1266			−1.26303			−0.631514	−	0.775365i	$-0.717566\pi$
$647$	−32.1266			−1.26303			−0.631514	+	0.775365i	$0.717566\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	−0.874638	−	4.96032i	−0.0343325	−	0.194709i
$650$	−10.6873	−	8.96773i	−0.419191	−	0.351743i
$651$	0.798133	−	0.669713i	0.0312813	−	0.0262481i
$652$	−4.16890	+	23.6430i	−0.163267	+	0.925932i
$653$	−1.44815	+	2.50827i	−0.0566704	+	0.0981561i	−0.892969	−	0.450118i	$-0.851382\pi$
$653$	−1.44815	+	2.50827i	−0.0566704	+	0.0981561i	0.836298	+	0.548275i	$0.184715\pi$
$654$	8.20574	+	14.2128i	0.320870	+	0.555763i
$655$	−11.9153	+	4.33683i	−0.465571	+	0.169454i
$656$	8.44356	−	3.07321i	0.329666	−	0.119989i
$657$	0.163848	+	0.283793i	0.00639232	+	0.0110718i
$658$	0.543233	−	0.940908i	0.0211774	−	0.0366804i
$659$	3.15926	−	17.9171i	0.123067	−	0.697950i	−0.859370	−	0.511355i	$-0.829144\pi$
$659$	3.15926	−	17.9171i	0.123067	−	0.697950i	0.982437	−	0.186595i	$-0.0597452\pi$
$660$	−1.70574	+	1.43128i	−0.0663957	+	0.0557126i
$661$	16.4081	+	13.7680i	0.638200	+	0.535513i	0.903465	−	0.428662i	$-0.141015\pi$
$661$	16.4081	+	13.7680i	0.638200	+	0.535513i	−0.265265	+	0.964176i	$0.585459\pi$
$662$	−4.72297	−	26.7853i	−0.183564	−	1.04104i
$663$	−4.23783	−	1.54244i	−0.164584	−	0.0599035i
$664$	−11.5740			−0.449157
$665$	−1.58924	−	2.24173i	−0.0616281	−	0.0869305i
$666$	−6.88713			−0.266871
$667$	−25.3329	−	9.22043i	−0.980894	−	0.357016i
$668$	0.635630	+	3.60483i	0.0245932	+	0.139475i
$669$	−2.48886	−	2.08840i	−0.0962247	−	0.0807421i
$670$	10.1382	−	8.50692i	0.391671	−	0.328651i
$671$	−3.70321	+	21.0020i	−0.142961	+	0.810771i
$672$	−0.266044	+	0.460802i	−0.0102629	+	0.0177758i
$673$	−20.3457	−	35.2398i	−0.784269	−	1.35839i	−0.929435	−	0.368987i	$-0.879705\pi$
$673$	−20.3457	−	35.2398i	−0.784269	−	1.35839i	0.145165	−	0.989407i	$-0.453629\pi$
$674$	−10.5407	+	3.83650i	−0.406013	+	0.147777i
$675$	−3.37939	+	1.23000i	−0.130073	+	0.0473426i
$676$	−1.02481	−	1.77503i	−0.0394160	−	0.0682704i
$677$	0.0680482	−	0.117863i	0.00261530	−	0.00452984i	−0.864715	−	0.502263i	$-0.832501\pi$
$677$	0.0680482	−	0.117863i	0.00261530	−	0.00452984i	0.867330	+	0.497733i	$0.165834\pi$
$678$	−0.996130	+	5.64933i	−0.0382561	+	0.216961i
$679$	2.39646	−	2.01087i	0.0919677	−	0.0771700i
$680$	−1.05509	−	0.885328i	−0.0404610	−	0.0339508i
$681$	2.03209	+	11.5245i	0.0778698	+	0.441622i
$682$	−3.45811	−	1.25865i	−0.132418	−	0.0481962i
$683$	−43.6459			−1.67006			−0.835032	−	0.550202i	$-0.814551\pi$
$683$	−43.6459			−1.67006			−0.835032	+	0.550202i	$0.814551\pi$
$684$	4.34002	−	0.405223i	0.165945	−	0.0154941i
$685$	−13.3369			−0.509576
$686$	−6.85844	−	2.49627i	−0.261856	−	0.0953080i
$687$	3.97771	+	22.5587i	0.151759	+	0.860669i
$688$	1.85844	+	1.55942i	0.0708524	+	0.0594522i
$689$	−38.5467	+	32.3445i	−1.46851	+	1.23223i
$690$	−1.37892	+	7.82023i	−0.0524945	+	0.297711i
$691$	−7.93376	+	13.7417i	−0.301815	+	0.522758i	−0.976547	−	0.215304i	$-0.930926\pi$
$691$	−7.93376	+	13.7417i	−0.301815	+	0.522758i	0.674732	+	0.738062i	$0.264259\pi$
$692$	2.66637	+	4.61830i	0.101360	+	0.175561i
$693$	−0.939693	+	0.342020i	−0.0356960	+	0.0129923i
$694$	1.81908	−	0.662090i	0.0690513	−	0.0251326i
$695$	7.20961	+	12.4874i	0.273476	+	0.473674i
$696$	2.01114	−	3.48340i	0.0762322	−	0.132038i
$697$	−1.81386	+	10.2869i	−0.0687050	+	0.389645i
$698$	−11.0287	+	9.25417i	−0.417442	+	0.350275i
$699$	2.45084	+	2.05650i	0.0926992	+	0.0777838i
$700$	−0.332282	−	1.88446i	−0.0125591	−	0.0712260i
$701$	−18.0513	−	6.57013i	−0.681787	−	0.248150i	−0.0221726	−	0.999754i	$-0.507058\pi$
$701$	−18.0513	−	6.57013i	−0.681787	−	0.248150i	−0.659615	+	0.751604i	$0.729281\pi$
$702$	−3.87939			−0.146418
$703$	−27.1332	+	12.8456i	−1.02335	+	0.484481i
$704$	1.87939			0.0708320
$705$	2.27332	+	0.827420i	0.0856181	+	0.0311624i
$706$	−2.73039	−	15.4848i	−0.102760	−	0.582779i
$707$	5.15451	+	4.32515i	0.193855	+	0.162664i
$708$	2.05303	−	1.72270i	0.0771577	−	0.0647430i
$709$	5.73489	−	32.5242i	0.215378	−	1.22147i	−0.664871	−	0.746959i	$-0.731513\pi$
$709$	5.73489	−	32.5242i	0.215378	−	1.22147i	0.880249	−	0.474512i	$-0.157376\pi$
$710$	3.59698	−	6.23016i	0.134992	−	0.233814i
$711$	8.06670	+	13.9719i	0.302525	+	0.523989i
$712$	−3.34477	+	1.21740i	−0.125351	+	0.0456239i
$713$	−12.3324	+	4.48864i	−0.461854	+	0.168101i
$714$	−0.309278	−	0.535685i	−0.0115744	−	0.0200475i
$715$	4.31908	−	7.48086i	0.161524	−	0.279768i
$716$	−4.38578	+	24.8730i	−0.163904	+	0.929548i
$717$	−4.72874	+	3.96788i	−0.176598	+	0.148183i
$718$	−11.8871	−	9.97448i	−0.443624	−	0.372244i
$719$	6.84952	+	38.8455i	0.255444	+	1.44869i	0.794931	+	0.606700i	$0.207507\pi$
$719$	6.84952	+	38.8455i	0.255444	+	1.44869i	−0.539487	+	0.841994i	$0.681382\pi$
$720$	−1.11334	−	0.405223i	−0.0414918	−	0.0151018i
$721$	1.57667			0.0587181
$722$	16.3425	−	9.69129i	0.608207	−	0.360672i
$723$	−1.53714			−0.0571669
$724$	16.2626	+	5.91912i	0.604396	+	0.219982i
$725$	2.51186	+	14.2455i	0.0932881	+	0.529063i
$726$	−5.72075	−	4.80028i	−0.212317	−	0.178155i
$727$	13.9816	−	11.7319i	0.518548	−	0.435114i	−0.345577	−	0.938390i	$-0.612317\pi$
$727$	13.9816	−	11.7319i	0.518548	−	0.435114i	0.864125	+	0.503277i	$0.167872\pi$
$728$	0.358441	−	2.03282i	0.0132847	−	0.0753413i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−0.194126	−	0.336236i	−0.00718492	−	0.0124446i
$731$	−2.65018	+	0.964586i	−0.0980204	+	0.0356765i
$732$	−10.6630	+	3.88100i	−0.394115	+	0.143446i
$733$	−7.69640	−	13.3306i	−0.284273	−	0.492376i	0.688160	−	0.725559i	$-0.258419\pi$
$733$	−7.69640	−	13.3306i	−0.284273	−	0.492376i	−0.972433	+	0.233184i	$0.925086\pi$
$734$	−7.87211	+	13.6349i	−0.290565	+	0.503273i
$735$	1.38191	−	7.83721i	0.0509726	−	0.289080i
$736$	5.13429	−	4.30818i	0.189252	−	0.158802i
$737$	−16.0817	−	13.4942i	−0.592378	−	0.497064i
$738$	1.56031	+	8.84894i	0.0574357	+	0.325734i
$739$	−14.2618	−	5.19086i	−0.524627	−	0.190949i	0.0661104	−	0.997812i	$-0.478941\pi$
$739$	−14.2618	−	5.19086i	−0.524627	−	0.190949i	−0.590738	+	0.806864i	$0.701163\pi$
$740$	8.15982			0.299961
$741$	−15.2836	+	7.23567i	−0.561457	+	0.265809i
$742$	−6.90167			−0.253368
$743$	9.27156	+	3.37457i	0.340141	+	0.123801i	0.506442	−	0.862274i	$-0.330960\pi$
$743$	9.27156	+	3.37457i	0.340141	+	0.123801i	−0.166302	+	0.986075i	$0.553183\pi$
$744$	−0.340022	−	1.92836i	−0.0124658	−	0.0706972i
$745$	−14.8439	−	12.4555i	−0.543838	−	0.456334i
$746$	22.6969	−	19.0449i	0.830991	−	0.697285i
$747$	2.00980	−	11.3981i	0.0735347	−	0.417036i
$748$	−1.09240	+	1.89209i	−0.0399420	+	0.0691815i
$749$	−5.08512	−	8.80769i	−0.185806	−	0.321826i
$750$	9.57057	−	3.48340i	0.349468	−	0.127196i
$751$	9.17024	−	3.33770i	0.334627	−	0.121794i	−0.169242	−	0.985575i	$-0.554132\pi$
$751$	9.17024	−	3.33770i	0.334627	−	0.121794i	0.503869	+	0.863780i	$0.331910\pi$
$752$	−1.02094	−	1.76833i	−0.0372300	−	0.0644843i
$753$	8.97178	−	15.5396i	0.326950	−	0.566294i
$754$	−2.70961	+	15.3669i	−0.0986781	+	0.559631i
$755$	18.6264	−	15.6294i	0.677883	−	0.568812i
$756$	−0.407604	−	0.342020i	−0.0148244	−	0.0124392i
$757$	−7.55438	−	42.8430i	−0.274569	−	1.55716i	−0.740329	−	0.672245i	$-0.765330\pi$
$757$	−7.55438	−	42.8430i	−0.274569	−	1.55716i	0.465761	−	0.884911i	$-0.345781\pi$
$758$	4.43969	+	1.61592i	0.161257	+	0.0586927i
$759$	12.5963			0.457216
$760$	−5.14203	+	0.480105i	−0.186521	+	0.0174152i
$761$	44.7137			1.62087			0.810435	−	0.585828i	$-0.199231\pi$
$761$	44.7137			1.62087			0.810435	+	0.585828i	$0.199231\pi$
$762$	1.77332	+	0.645435i	0.0642405	+	0.0233816i
$763$	−1.51636	−	8.59970i	−0.0548959	−	0.311330i
$764$	−11.6270	−	9.75622i	−0.420651	−	0.352968i
$765$	1.05509	−	0.885328i	0.0381470	−	0.0320091i
$766$	0.910130	−	5.16160i	0.0328843	−	0.186496i
$767$	−5.19846	+	9.00400i	−0.187706	+	0.325116i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−20.7690	+	7.55931i	−0.748951	+	0.272596i	−0.688164	−	0.725555i	$-0.741583\pi$
$769$	−20.7690	+	7.55931i	−0.748951	+	0.272596i	−0.0607865	+	0.998151i	$0.519361\pi$
$770$	1.11334	−	0.405223i	0.0401220	−	0.0146032i
$771$	14.7062	+	25.4719i	0.529631	+	0.917348i
$772$	−6.50387	+	11.2650i	−0.234079	+	0.405437i
$773$	7.32429	−	41.5381i	0.263436	−	1.49402i	−0.510014	−	0.860166i	$-0.670360\pi$
$773$	7.32429	−	41.5381i	0.263436	−	1.49402i	0.773451	−	0.633857i	$-0.218529\pi$
$774$	−1.85844	+	1.55942i	−0.0668003	+	0.0560521i
$775$	5.39440	+	4.52644i	0.193773	+	0.162594i
$776$	−1.02094	−	5.79006i	−0.0366498	−	0.207851i
$777$	3.44356	+	1.25335i	0.123537	+	0.0449638i
$778$	15.0770			0.540536
$779$	22.6518	+	31.9519i	0.811586	+	1.14480i
$780$	4.59627			0.164573
$781$	−10.7233	−	3.90295i	−0.383709	−	0.139659i
$782$	1.35298	+	7.67312i	0.0483824	+	0.274390i
$783$	3.08125	+	2.58548i	0.110115	+	0.0923974i
$784$	−5.14543	+	4.31753i	−0.183765	+	0.154197i
$785$	−0.658223	+	3.73297i	−0.0234930	+	0.133235i
$786$	−5.35117	+	9.26849i	−0.190870	+	0.330596i
$787$	14.2396	+	24.6638i	0.507588	+	0.879169i	0.999961	+	0.00878442i	$0.00279620\pi$
$787$	14.2396	+	24.6638i	0.507588	+	0.879169i	−0.492373	+	0.870384i	$0.663870\pi$
$788$	8.40895	−	3.06061i	0.299556	−	0.109030i
$789$	10.0385	−	3.65371i	0.357380	−	0.130076i
$790$	−9.55737	−	16.5539i	−0.340036	−	0.588960i
$791$	1.52616	−	2.64339i	0.0542640	−	0.0939880i
$792$	−0.326352	+	1.85083i	−0.0115964	+	0.0657665i
$793$	33.7217	−	28.2959i	1.19749	−	1.00482i
$794$	11.1420	+	9.34927i	0.395416	+	0.331793i
$795$	−2.66860	−	15.1344i	−0.0946453	−	0.536760i
$796$	4.23308	+	1.54071i	0.150037	+	0.0546092i
$797$	16.6081			0.588290			0.294145	−	0.955761i	$-0.404965\pi$
$797$	16.6081			0.588290			0.294145	+	0.955761i	$0.404965\pi$
$798$	−2.24376	−	0.587208i	−0.0794281	−	0.0207869i
$799$	2.37370			0.0839756
$800$	−3.37939	−	1.23000i	−0.119479	−	0.0434869i
$801$	−0.618089	−	3.50535i	−0.0218391	−	0.123856i
$802$	−2.18685	−	1.83499i	−0.0772204	−	0.0647956i
$803$	−0.471782	+	0.395872i	−0.0166488	+	0.0139700i
$804$	1.93969	−	11.0005i	0.0684077	−	0.387959i
$805$	2.11263	−	3.65917i	0.0744603	−	0.128969i
$806$	3.79813	+	6.57856i	0.133784	+	0.231720i
$807$	−19.3357	+	7.03763i	−0.680650	+	0.247736i
$808$	11.8833	−	4.32515i	0.418051	−	0.152158i
$809$	6.83915	+	11.8457i	0.240452	+	0.416474i	0.960843	−	0.277093i	$-0.0893712\pi$
$809$	6.83915	+	11.8457i	0.240452	+	0.416474i	−0.720391	+	0.693568i	$0.756038\pi$
$810$	0.592396	−	1.02606i	0.0208147	−	0.0360521i
$811$	−0.107355	+	0.608839i	−0.00376973	+	0.0213792i	−0.986635	−	0.162948i	$-0.947900\pi$
$811$	−0.107355	+	0.608839i	−0.00376973	+	0.0213792i	0.982865	+	0.184328i	$0.0590107\pi$
$812$	−1.63950	+	1.37570i	−0.0575352	+	0.0482777i
$813$	−1.43763	−	1.20632i	−0.0504200	−	0.0423074i
$814$	−2.24763	−	12.7469i	−0.0787793	−	0.446779i
$815$	26.7288	+	9.72849i	0.936269	+	0.340774i
$816$	−1.16250			−0.0406958
$817$	−4.41312	+	9.60991i	−0.154396	+	0.336208i
$818$	−34.2276			−1.19674
$819$	1.93969	+	0.705990i	0.0677783	+	0.0246693i
$820$	−1.84864	−	10.4842i	−0.0645573	−	0.366123i
$821$	4.68210	+	3.92875i	0.163407	+	0.137114i	0.720824	−	0.693118i	$-0.243763\pi$
$821$	4.68210	+	3.92875i	0.163407	+	0.137114i	−0.557418	+	0.830232i	$0.688208\pi$
$822$	−8.62314	+	7.23567i	−0.300767	+	0.252373i
$823$	5.32311	−	30.1889i	0.185552	−	1.05232i	−0.739692	−	0.672945i	$-0.765029\pi$
$823$	5.32311	−	30.1889i	0.185552	−	1.05232i	0.925244	−	0.379372i	$-0.123860\pi$
$824$	1.48158	−	2.56617i	0.0516133	−	0.0893969i
$825$	−3.37939	−	5.85327i	−0.117655	−	0.203785i
$826$	−1.34002	+	0.487728i	−0.0466253	+	0.0169702i
$827$	47.6550	−	17.3450i	1.65713	−	0.603145i	0.667219	−	0.744862i	$-0.267485\pi$
$827$	47.6550	−	17.3450i	1.65713	−	0.603145i	0.989907	+	0.141717i	$0.0452623\pi$
$828$	3.35117	+	5.80439i	0.116461	+	0.201717i
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	−0.730791	−	0.682601i	$-0.760849\pi$
$829$	6.50000	−	11.2583i	0.225754	−	0.391018i	0.956545	+	0.291583i	$0.0941820\pi$
$830$	−2.38120	+	13.5044i	−0.0826525	+	0.468746i
$831$	−3.73261	+	3.13203i	−0.129483	+	0.108649i
$832$	−2.97178	−	2.49362i	−0.103028	−	0.0864507i
$833$	−1.35591	−	7.68977i	−0.0469797	−	0.266435i
$834$	11.4363	+	4.16247i	0.396006	+	0.144135i
$835$	4.33687			0.150083
$836$	2.16637	+	7.90041i	0.0749256	+	0.273241i
$837$	1.95811			0.0676822
$838$	−7.44134	−	2.70843i	−0.257057	−	0.0935611i
$839$	−3.73308	−	21.1713i	−0.128880	−	0.730916i	−0.978927	−	0.204209i	$-0.934538\pi$
$839$	−3.73308	−	21.1713i	−0.128880	−	0.730916i	0.850047	−	0.526707i	$-0.176573\pi$
$840$	0.482926	+	0.405223i	0.0166625	+	0.0139815i
$841$	−9.82160	+	8.24130i	−0.338676	+	0.284183i
$842$	−2.81480	+	15.9635i	−0.0970043	+	0.550139i
$843$	−0.201867	+	0.349643i	−0.00695266	+	0.0120424i
$844$	3.20187	+	5.54580i	0.110213	+	0.190894i
$845$	−2.28194	+	0.830557i	−0.0785010	+	0.0285720i
$846$	1.91875	−	0.698367i	0.0659679	−	0.0240104i
$847$	1.98680	+	3.44123i	0.0682671	+	0.118242i
$848$	−6.48545	+	11.2331i	−0.222711	+	0.385747i
$849$	−3.05438	+	17.3222i	−0.104826	+	0.594498i
$850$	3.20258	−	2.68729i	0.109848	−	0.0921731i
$851$	−35.3605	−	29.6710i	−1.21214	−	1.01711i
$852$	−1.05438	−	5.97967i	−0.0361224	−	0.204860i
$853$	43.4397	+	15.8108i	1.48735	+	0.541351i	0.952750	−	0.303755i	$-0.0982406\pi$
$853$	43.4397	+	15.8108i	1.48735	+	0.541351i	0.534599	+	0.845106i	$0.320463\pi$
$854$	6.03777			0.206608
$855$	0.420092	−	5.14728i	0.0143669	−	0.176033i
$856$	−19.1138			−0.653296
$857$	41.0292	+	14.9334i	1.40153	+	0.510115i	0.928632	−	0.371003i	$-0.120986\pi$
$857$	41.0292	+	14.9334i	1.40153	+	0.510115i	0.472897	+	0.881118i	$0.343208\pi$
$858$	−1.26604	−	7.18009i	−0.0432220	−	0.245124i
$859$	15.4474	+	12.9619i	0.527060	+	0.442256i	0.867085	−	0.498161i	$-0.165991\pi$
$859$	15.4474	+	12.9619i	0.527060	+	0.442256i	−0.340025	+	0.940416i	$0.610436\pi$
$860$	2.20187	−	1.84759i	0.0750830	−	0.0630021i
$861$	0.830222	−	4.70842i	0.0282939	−	0.160463i
$862$	12.7160	−	22.0248i	0.433109	−	0.750166i
$863$	16.3466	+	28.3131i	0.556444	+	0.963789i	0.997790	+	0.0664522i	$0.0211680\pi$
$863$	16.3466	+	28.3131i	0.556444	+	0.963789i	−0.441346	+	0.897337i	$0.645499\pi$
$864$	−0.939693	+	0.342020i	−0.0319690	+	0.0116358i
$865$	5.93717	−	2.16095i	0.201870	−	0.0734746i
$866$	5.92396	+	10.2606i	0.201304	+	0.348670i
$867$	−7.82429	+	13.5521i	−0.265727	+	0.460252i
$868$	−0.180922	+	1.02606i	−0.00614090	+	0.0348268i
$869$	−23.2271	+	19.4899i	−0.787927	+	0.661149i
$870$	−3.65064	−	3.06325i	−0.123768	−	0.103854i
$871$	7.52481	+	42.6753i	0.254969	+	1.44600i
$872$	−15.4217	−	5.61305i	−0.522246	−	0.190082i
$873$	5.87939			0.198987
$874$	24.0287	+	16.6171i	0.812782	+	0.562080i
$875$	−5.41921			−0.183203
$876$	−0.307934	−	0.112079i	−0.0104041	−	0.00378679i
$877$	5.26099	+	29.8366i	0.177651	+	1.00751i	0.935039	+	0.354544i	$0.115364\pi$
$877$	5.26099	+	29.8366i	0.177651	+	1.00751i	−0.757388	+	0.652965i	$0.773525\pi$
$878$	−19.8097	−	16.6223i	−0.668546	−	0.560977i
$879$	10.0929	−	8.46892i	0.340424	−	0.285650i
$880$	0.386659	−	2.19285i	0.0130343	−	0.0739211i
$881$	−11.7788	+	20.4015i	−0.396839	+	0.687346i	−0.993334	−	0.115271i	$-0.963226\pi$
$881$	−11.7788	+	20.4015i	−0.396839	+	0.687346i	0.596495	+	0.802617i	$0.296560\pi$
$882$	−3.35844	−	5.81699i	−0.113085	−	0.195868i
$883$	−34.6079	+	12.5962i	−1.16465	+	0.423897i	−0.850756	−	0.525561i	$-0.823855\pi$
$883$	−34.6079	+	12.5962i	−1.16465	+	0.423897i	−0.313892	+	0.949459i	$0.601633\pi$
$884$	4.23783	−	1.54244i	0.142534	−	0.0518780i
$885$	−1.58765	−	2.74989i	−0.0533682	−	0.0924365i
$886$	0.461515	−	0.799367i	0.0155049	−	0.0268552i
$887$	0.748093	−	4.24265i	0.0251185	−	0.142454i	−0.969669	−	0.244420i	$-0.921402\pi$
$887$	0.748093	−	4.24265i	0.0251185	−	0.142454i	0.994788	+	0.101966i	$0.0325134\pi$
$888$	5.27584	−	4.42696i	0.177046	−	0.148559i
$889$	−0.769200	−	0.645435i	−0.0257981	−	0.0216472i
$890$	0.732307	+	4.15312i	0.0245470	+	0.139213i
$891$	−1.76604	−	0.642788i	−0.0591647	−	0.0215342i
$892$	3.24897			0.108784
$893$	6.25671	−	6.33012i	0.209373	−	0.211830i
$894$	−16.3550			−0.546994
$895$	28.1193	+	10.2346i	0.939925	+	0.342105i
$896$	−0.0923963	−	0.524005i	−0.00308674	−	0.0175058i
$897$	−19.9179	−	16.7131i	−0.665038	−	0.558033i
$898$	−7.15839	+	6.00660i	−0.238878	+	0.200443i
$899$	1.36767	−	7.75643i	0.0456143	−	0.258691i
$900$	1.79813	−	3.11446i	0.0599378	−	0.103815i
$901$	−7.53936	−	13.0586i	−0.251173	−	0.435044i
$902$	−15.8687	+	5.77574i	−0.528370	+	0.192311i
$903$	1.21301	−	0.441500i	0.0403665	−	0.0146922i
$904$	−2.86824	−	4.96794i	−0.0953963	−	0.165231i
$905$	10.2522	−	17.7574i	0.340795	−	0.590274i
$906$	3.56371	−	20.2108i	0.118396	−	0.671459i
$907$	17.8799	−	15.0030i	0.593691	−	0.498166i	−0.295720	−	0.955275i	$-0.595560\pi$
$907$	17.8799	−	15.0030i	0.593691	−	0.498166i	0.889411	+	0.457109i	$0.151115\pi$
$908$	−8.96451	−	7.52211i	−0.297498	−	0.249630i
$909$	2.19594	+	12.4538i	0.0728346	+	0.413066i
$910$	−2.29813	−	0.836452i	−0.0761824	−	0.0277281i
$911$	22.5631			0.747547			0.373774	−	0.927520i	$-0.378064\pi$
$911$	22.5631			0.747547			0.373774	+	0.927520i	$0.378064\pi$
$912$	−3.06418	+	3.10013i	−0.101465	+	0.102656i
$913$	21.7520			0.719885
$914$	29.0373	+	10.5687i	0.960469	+	0.349582i
$915$	2.33456	+	13.2399i	0.0771782	+	0.437699i
$916$	−17.5476	−	14.7242i	−0.579788	−	0.486500i
$917$	4.36231	−	3.66041i	0.144056	−	0.120878i
$918$	0.201867	−	1.14484i	0.00666259	−	0.0377854i
$919$	−2.12789	+	3.68561i	−0.0701926	+	0.121577i	−0.898986	−	0.437978i	$-0.855695\pi$
$919$	−2.12789	+	3.68561i	−0.0701926	+	0.121577i	0.828793	+	0.559555i	$0.189028\pi$
$920$	−3.97044	−	6.87700i	−0.130901	−	0.226728i
$921$	15.8824	−	5.78071i	0.523342	−	0.190481i
$922$	−27.8974	+	10.1538i	−0.918752	+	0.334398i
$923$	11.7777	+	20.3995i	0.387666	+	0.671458i
$924$	0.500000	−	0.866025i	0.0164488	−	0.0284901i
$925$	−4.30091	+	24.3917i	−0.141413	+	0.801993i
$926$	9.06283	−	7.60462i	0.297823	−	0.249903i
$927$	2.26991	+	1.90468i	0.0745538	+	0.0625581i
$928$	0.698463	+	3.96118i	0.0229282	+	0.130032i
$929$	−55.9347	−	20.3586i	−1.83516	−	0.667943i	−0.991341	−	0.131311i	$-0.958081\pi$
$929$	−55.9347	−	20.3586i	−1.83516	−	0.667943i	−0.843817	−	0.536632i	$-0.819697\pi$
$930$	−2.31996			−0.0760743
$931$	−24.0808	−	16.6531i	−0.789218	−	0.545784i
$932$	−3.19934			−0.104798
$933$	−2.23783	−	0.814502i	−0.0732631	−	0.0266656i
$934$	−6.65389	−	37.7361i	−0.217722	−	1.23476i
$935$	1.98293	+	1.66387i	0.0648486	+	0.0544144i
$936$	2.97178	−	2.49362i	0.0971357	−	0.0815065i
$937$	5.81877	−	32.9999i	0.190091	−	1.07806i	−0.729147	−	0.684357i	$-0.760083\pi$
$937$	5.81877	−	32.9999i	0.190091	−	1.07806i	0.919238	−	0.393703i	$-0.128806\pi$
$938$	−2.97178	+	5.14728i	−0.0970321	+	0.168065i
$939$	−14.9315	−	25.8622i	−0.487272	−	0.843981i
$940$	−2.27332	+	0.827420i	−0.0741475	+	0.0269875i
$941$	5.19119	−	1.88944i	0.169228	−	0.0615939i	−0.256017	−	0.966672i	$-0.582410\pi$
$941$	5.19119	−	1.88944i	0.169228	−	0.0615939i	0.425245	+	0.905078i	$0.360188\pi$
$942$	1.59967	+	2.77071i	0.0521201	+	0.0902746i
$943$	−30.1117	+	52.1551i	−0.980573	+	1.69840i
$944$	−0.465385	+	2.63933i	−0.0151470	+	0.0859028i
$945$	−0.482926	+	0.405223i	−0.0157096	+	0.0131819i
$946$	−3.49273	−	2.93075i	−0.113558	−	0.0952867i
$947$	−2.58822	−	14.6785i	−0.0841059	−	0.476988i	−0.997546	−	0.0700149i	$-0.977695\pi$
$947$	−2.58822	−	14.6785i	−0.0841059	−	0.476988i	0.913440	−	0.406973i	$-0.133416\pi$
$948$	−15.1604	−	5.51795i	−0.492388	−	0.179215i
$949$	1.27126			0.0412668
$950$	1.27513	−	15.6238i	0.0413707	−	0.506903i
$951$	7.02229			0.227713
$952$	0.581252	+	0.211558i	0.0188385	+	0.00685665i
$953$	−8.05138	−	45.6617i	−0.260810	−	1.47913i	−0.780707	−	0.624898i	$-0.785141\pi$
$953$	−8.05138	−	45.6617i	−0.260810	−	1.47913i	0.519897	−	0.854229i	$-0.325970\pi$
$954$	−9.93629	−	8.33754i	−0.321699	−	0.269938i
$955$	−13.7756	+	11.5591i	−0.445768	+	0.374044i
$956$	1.07192	−	6.07915i	0.0346683	−	0.196614i
$957$	−3.77972	+	6.54666i	−0.122181	+	0.211623i
$958$	18.6420	+	32.2889i	0.602297	+	1.04321i
$959$	5.62836	−	2.04855i	0.181749	−	0.0661513i
$960$	1.11334	−	0.405223i	0.0359329	−	0.0130785i
$961$	13.5829	+	23.5263i	0.438158	+	0.758912i
$962$	−13.3589	+	23.1383i	−0.430708	+	0.746009i
$963$	3.31908	−	18.8234i	0.106956	−	0.606576i
$964$	1.17752	−	0.988055i	0.0379253	−	0.0318231i
$965$	11.8059	+	9.90630i	0.380045	+	0.318895i
$966$	−0.619271	−	3.51206i	−0.0199247	−	0.112999i
$967$	21.8414	+	7.94961i	0.702371	+	0.255642i	0.668423	−	0.743781i	$-0.266970\pi$
$967$	21.8414	+	7.94961i	0.702371	+	0.255642i	0.0339481	+	0.999424i	$0.489192\pi$
$968$	7.46791			0.240028
$969$	−1.34002	−	4.88684i	−0.0430477	−	0.156988i
$970$	−6.96585			−0.223660
$971$	−4.63310	−	1.68631i	−0.148683	−	0.0541163i	0.266606	−	0.963805i	$-0.414098\pi$
$971$	−4.63310	−	1.68631i	−0.148683	−	0.0541163i	−0.415290	+	0.909689i	$0.636320\pi$
$972$	−0.173648	−	0.984808i	−0.00556977	−	0.0315877i
$973$	−4.96064	−	4.16247i	−0.159031	−	0.133443i
$974$	−25.2631	+	21.1983i	−0.809482	+	0.679236i
$975$	−2.42262	+	13.7394i	−0.0775859	+	0.440011i
$976$	5.67365	−	9.82705i	0.181609	−	0.314556i
$977$	−16.3721	−	28.3573i	−0.523790	−	0.907231i	−0.999617	−	0.0276920i	$-0.991184\pi$
$977$	−16.3721	−	28.3573i	−0.523790	−	0.907231i	0.475826	−	0.879539i	$-0.342149\pi$
$978$	22.5599	−	8.21113i	0.721386	−	0.262563i
$979$	6.28611	−	2.28796i	0.200905	−	0.0731234i
$980$	3.97906	+	6.89193i	0.127106	+	0.220155i
$981$	8.20574	−	14.2128i	0.261989	−	0.453778i
$982$	−3.07027	+	17.4124i	−0.0979762	+	0.555651i
$983$	−19.4886	+	16.3529i	−0.621590	+	0.521576i	−0.898303	−	0.439377i	$-0.855199\pi$
$983$	−19.4886	+	16.3529i	−0.621590	+	0.521576i	0.276713	+	0.960953i	$0.410755\pi$
$984$	−6.88326	−	5.77574i	−0.219430	−	0.184124i
$985$	−1.84106	−	10.4412i	−0.0586611	−	0.332684i
$986$	−4.39393	−	1.59926i	−0.139931	−	0.0509308i
$987$	−1.08647			−0.0345826
$988$	7.05690	−	15.3669i	0.224510	−	0.488888i
$989$	−16.2600			−0.517038
$990$	2.09240	+	0.761570i	0.0665007	+	0.0242043i
$991$	1.76311	+	9.99908i	0.0560070	+	0.317631i	0.999921	−	0.0125597i	$-0.00399797\pi$
$991$	1.76311	+	9.99908i	0.0560070	+	0.317631i	−0.943914	+	0.330191i	$0.892887\pi$
$992$	1.50000	+	1.25865i	0.0476250	+	0.0399622i
$993$	−20.8353	+	17.4829i	−0.661187	+	0.554802i
$994$	−0.561023	+	3.18172i	−0.0177946	+	0.100918i
$995$	2.66860	−	4.62214i	0.0846002	−	0.146532i
$996$	5.78699	+	10.0234i	0.183368	+	0.317602i
$997$	−52.4065	+	19.0744i	−1.65973	+	0.604092i	−0.990320	−	0.138801i	$-0.955675\pi$
$997$	−52.4065	+	19.0744i	−1.65973	+	0.604092i	−0.669410	+	0.742894i	$0.733453\pi$
$998$	25.4881	−	9.27692i	0.806813	−	0.293656i
$999$	3.44356	+	5.96443i	0.108950	+	0.188706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.d.61.1	yes	6
3.2	odd	2		342.2.u.a.289.1		6
4.3	odd	2		912.2.bo.f.289.1		6
19.5	even	9	inner	114.2.i.d.43.1	✓	6
19.9	even	9		2166.2.a.o.1.2		3
19.10	odd	18		2166.2.a.u.1.2		3
57.5	odd	18		342.2.u.a.271.1		6
57.29	even	18		6498.2.a.bn.1.2		3
57.47	odd	18		6498.2.a.bs.1.2		3
76.43	odd	18		912.2.bo.f.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.43.1	✓	6	19.5	even	9	inner
114.2.i.d.61.1	yes	6	1.1	even	1	trivial
342.2.u.a.271.1		6	57.5	odd	18
342.2.u.a.289.1		6	3.2	odd	2
912.2.bo.f.289.1		6	4.3	odd	2
912.2.bo.f.385.1		6	76.43	odd	18
2166.2.a.o.1.2		3	19.9	even	9
2166.2.a.u.1.2		3	19.10	odd	18
6498.2.a.bn.1.2		3	57.29	even	18
6498.2.a.bs.1.2		3	57.47	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.907604 - 0.761570i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-0.266044 + 0.460802i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(1.11334 - 0.405223i) q^{10} +(-0.939693 - 1.62760i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.673648 + 3.82045i) q^{13} +(-0.407604 + 0.342020i) q^{14} +(-0.907604 - 0.761570i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-1.09240 - 0.397600i) q^{17} -1.00000 q^{18} +(-3.93969 + 1.86516i) q^{19} +1.18479 q^{20} +(0.500000 + 0.181985i) q^{21} +(-0.326352 - 1.85083i) q^{22} +(-5.13429 - 4.30818i) q^{23} +(0.766044 - 0.642788i) q^{24} +(-0.624485 + 3.54163i) q^{25} +(-1.93969 + 3.35965i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.500000 + 0.181985i) q^{28} +(3.77972 - 1.37570i) q^{29} +(-0.592396 - 1.02606i) q^{30} +(0.979055 - 1.69577i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-1.43969 + 1.20805i) q^{33} +(-0.890530 - 0.747243i) q^{34} +(0.109470 + 0.620838i) q^{35} +(-0.939693 - 0.342020i) q^{36} +6.88713 q^{37} +(-4.34002 + 0.405223i) q^{38} +3.87939 q^{39} +(1.11334 + 0.405223i) q^{40} +(-1.56031 - 8.84894i) q^{41} +(0.407604 + 0.342020i) q^{42} +(1.85844 - 1.55942i) q^{43} +(0.326352 - 1.85083i) q^{44} +(-0.592396 + 1.02606i) q^{45} +(-3.35117 - 5.80439i) q^{46} +(-1.91875 + 0.698367i) q^{47} +(0.939693 - 0.342020i) q^{48} +(3.35844 + 5.81699i) q^{49} +(-1.79813 + 3.11446i) q^{50} +(-0.201867 + 1.14484i) q^{51} +(-2.97178 + 2.49362i) q^{52} +(9.93629 + 8.33754i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-2.09240 - 0.761570i) q^{55} -0.532089 q^{56} +(2.52094 + 3.55596i) q^{57} +4.02229 q^{58} +(2.51842 + 0.916629i) q^{59} +(-0.205737 - 1.16679i) q^{60} +(-8.69253 - 7.29390i) q^{61} +(1.50000 - 1.25865i) q^{62} +(0.0923963 - 0.524005i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.29813 + 3.98048i) q^{65} +(-1.76604 + 0.642788i) q^{66} +(10.4966 - 3.82045i) q^{67} +(-0.581252 - 1.00676i) q^{68} +(-3.35117 + 5.80439i) q^{69} +(-0.109470 + 0.620838i) q^{70} +(4.65136 - 3.90295i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(-0.0569038 - 0.322718i) q^{73} +(6.47178 + 2.35554i) q^{74} +3.59627 q^{75} +(-4.21688 - 1.10359i) q^{76} +1.00000 q^{77} +(3.64543 + 1.32683i) q^{78} +(-2.80154 - 15.8883i) q^{79} +(0.907604 + 0.761570i) q^{80} +(0.766044 - 0.642788i) q^{81} +(1.56031 - 8.84894i) q^{82} +(-5.78699 + 10.0234i) q^{83} +(0.266044 + 0.460802i) q^{84} +(-1.29426 + 0.471073i) q^{85} +(2.27972 - 0.829748i) q^{86} +(-2.01114 - 3.48340i) q^{87} +(0.939693 - 1.62760i) q^{88} +(-0.618089 + 3.50535i) q^{89} +(-0.907604 + 0.761570i) q^{90} +(-1.58125 - 1.32683i) q^{91} +(-1.16385 - 6.60051i) q^{92} +(-1.84002 - 0.669713i) q^{93} -2.04189 q^{94} +(-2.15523 + 4.69318i) q^{95} +1.00000 q^{96} +(-5.52481 - 2.01087i) q^{97} +(1.16637 + 6.61484i) q^{98} +(1.43969 + 1.20805i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} - 3 q^{17} - 6 q^{18} - 18 q^{19} + 3 q^{21} - 3 q^{22} - 21 q^{23} + 9 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 9 * q^15 - 3 * q^17 - 6 * q^18 - 18 * q^19 + 3 * q^21 - 3 * q^22 - 21 * q^23 + 9 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 - 3 * q^33 + 12 * q^34 + 18 * q^35 - 18 * q^37 - 6 * q^38 + 12 * q^39 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^46 - 9 * q^47 + 12 * q^49 + 3 * q^50 - 15 * q^51 - 3 * q^52 + 12 * q^53 - 9 * q^55 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 27 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 3 * q^63 - 3 * q^64 - 6 * q^66 + 21 * q^67 - 6 * q^68 + 6 * q^69 - 18 * q^70 + 39 * q^71 + 36 * q^73 + 24 * q^74 - 6 * q^75 - 9 * q^76 + 6 * q^77 + 6 * q^78 - 45 * q^79 + 9 * q^80 + 15 * q^82 - 27 * q^83 - 3 * q^84 - 18 * q^85 - 12 * q^86 - 6 * q^87 - 30 * q^89 - 9 * q^90 - 12 * q^91 - 3 * q^92 + 9 * q^93 - 6 * q^94 + 6 * q^96 - 6 * q^97 - 12 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

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Database

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