LMFDB - Embedded newform 130.2.s.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(33,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.33"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.s (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 192x^{8} + 680x^{6} + 1104x^{4} + 672x^{2} + 4 $ x^12 + 24x^10 + 192x^8 + 680x^6 + 1104x^4 + 672*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.1
Root			$-1.62980i$ of defining polynomial
Character	$\chi$	$=$	130.67
Dual form			130.2.s.a.33.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-3.04125 - 0.814901i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.208246 + 2.22635i) q^{5} +(0.814901 + 3.04125i) q^{6} +(0.696972 + 0.402397i) q^{7} +1.00000 q^{8} +(5.98707 + 3.45663i) q^{9} +(1.82395 - 1.29352i) q^{10} +(-0.778529 + 2.90551i) q^{11} +(2.22635 - 2.22635i) q^{12} +(-3.59966 - 0.206024i) q^{13} -0.804795i q^{14} +(1.18093 - 6.94059i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87508 + 6.99788i) q^{17} -6.91327i q^{18} +(-4.51652 + 1.21020i) q^{19} +(-2.03220 - 0.932829i) q^{20} +(-1.79175 - 1.79175i) q^{21} +(2.90551 - 0.778529i) q^{22} +(0.113254 - 0.422668i) q^{23} +(-3.04125 - 0.814901i) q^{24} +(-4.91327 + 0.927256i) q^{25} +(1.62141 + 3.22041i) q^{26} +(-8.71230 - 8.71230i) q^{27} +(-0.696972 + 0.402397i) q^{28} +(3.58287 - 2.06857i) q^{29} +(-6.60119 + 2.44758i) q^{30} +(-0.536500 + 0.536500i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.73540 - 8.20196i) q^{33} +(5.12281 - 5.12281i) q^{34} +(-0.750735 + 1.63550i) q^{35} +(-5.98707 + 3.45663i) q^{36} +(0.835172 - 0.482187i) q^{37} +(3.30632 + 3.30632i) q^{38} +(10.7796 + 3.55994i) q^{39} +(0.208246 + 2.22635i) q^{40} +(1.63091 + 0.437002i) q^{41} +(-0.655828 + 2.44758i) q^{42} +(6.14091 - 1.64545i) q^{43} +(-2.12698 - 2.12698i) q^{44} +(-6.44889 + 14.0491i) q^{45} +(-0.422668 + 0.113254i) q^{46} +1.72276i q^{47} +(0.814901 + 3.04125i) q^{48} +(-3.17615 - 5.50126i) q^{49} +(3.25966 + 3.79139i) q^{50} -22.8103i q^{51} +(1.97825 - 3.01438i) q^{52} +(-5.01074 + 5.01074i) q^{53} +(-3.18892 + 11.9012i) q^{54} +(-6.63080 - 1.12822i) q^{55} +(0.696972 + 0.402397i) q^{56} +14.7221 q^{57} +(-3.58287 - 2.06857i) q^{58} +(0.0422769 + 0.157780i) q^{59} +(5.42026 + 4.49301i) q^{60} +(1.11898 - 1.93813i) q^{61} +(0.732873 + 0.196373i) q^{62} +(2.78188 + 4.81836i) q^{63} +1.00000 q^{64} +(-0.290932 - 8.05701i) q^{65} -9.47080 q^{66} +(2.20825 + 3.82479i) q^{67} +(-6.99788 - 1.87508i) q^{68} +(-0.688865 + 1.19315i) q^{69} +(1.79175 - 0.167595i) q^{70} +(2.63643 + 9.83928i) q^{71} +(5.98707 + 3.45663i) q^{72} -1.73949 q^{73} +(-0.835172 - 0.482187i) q^{74} +(15.6981 + 1.18381i) q^{75} +(1.21020 - 4.51652i) q^{76} +(-1.71178 + 1.71178i) q^{77} +(-2.30679 - 11.1154i) q^{78} -7.75722i q^{79} +(1.82395 - 1.29352i) q^{80} +(9.02673 + 15.6348i) q^{81} +(-0.437002 - 1.63091i) q^{82} +15.6444i q^{83} +(2.44758 - 0.655828i) q^{84} +(-15.1893 + 5.63186i) q^{85} +(-4.49546 - 4.49546i) q^{86} +(-12.5821 + 3.37136i) q^{87} +(-0.778529 + 2.90551i) q^{88} +(-5.91063 - 1.58375i) q^{89} +(15.3914 - 1.43966i) q^{90} +(-2.42596 - 1.59209i) q^{91} +(0.309415 + 0.309415i) q^{92} +(2.06883 - 1.19444i) q^{93} +(1.49195 - 0.861379i) q^{94} +(-3.63487 - 9.80333i) q^{95} +(2.22635 - 2.22635i) q^{96} +(6.70520 - 11.6138i) q^{97} +(-3.17615 + 5.50126i) q^{98} +(-14.7044 + 14.7044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 6 q^{7} + 12 q^{8} + 24 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} - 6 q^{16} - 36 q^{19} - 24 q^{21} + 6 q^{23} + 12 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} - 18 q^{30}+ \cdots - 54 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 6 * q^7 + 12 * q^8 + 24 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 - 6 * q^16 - 36 * q^19 - 24 * q^21 + 6 * q^23 + 12 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 - 18 * q^30 - 24 * q^31 - 6 * q^32 + 18 * q^33 + 12 * q^34 - 12 * q^35 - 24 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^39 + 18 * q^41 + 18 * q^42 - 6 * q^44 - 18 * q^45 - 6 * q^46 + 6 * q^50 + 18 * q^53 + 6 * q^54 - 6 * q^55 + 6 * q^56 + 6 * q^58 - 18 * q^59 + 24 * q^60 + 18 * q^61 + 36 * q^62 + 12 * q^64 + 42 * q^65 - 36 * q^66 + 24 * q^67 - 12 * q^68 + 42 * q^69 + 24 * q^70 + 18 * q^71 + 24 * q^72 - 12 * q^73 - 6 * q^74 + 24 * q^75 + 30 * q^76 - 30 * q^77 + 30 * q^78 + 30 * q^81 - 18 * q^82 + 6 * q^84 - 42 * q^85 - 60 * q^87 + 6 * q^88 - 6 * q^89 + 12 * q^90 - 6 * q^91 - 30 * q^93 - 24 * q^94 - 24 * q^95 + 6 * q^97 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−3.04125	−	0.814901i	−1.75587	−	0.470483i	−0.770004	−	0.638039i	$-0.779746\pi$
$3$	−3.04125	−	0.814901i	−1.75587	−	0.470483i	−0.985863	+	0.167556i	$0.946413\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.208246	+	2.22635i	0.0931304	+	0.995654i
$5$	0.208246	+	2.22635i	0.0931304	+	0.995654i
$6$	0.814901	+	3.04125i	0.332682	+	1.24159i
$7$	0.696972	+	0.402397i	0.263431	+	0.152092i	0.625899	−	0.779904i	$-0.284732\pi$
$7$	0.696972	+	0.402397i	0.263431	+	0.152092i	−0.362468	+	0.931996i	$0.618066\pi$
$8$	1.00000			0.353553
$9$	5.98707	+	3.45663i	1.99569	+	1.15221i
$10$	1.82395	−	1.29352i	0.576784	−	0.409047i
$11$	−0.778529	+	2.90551i	−0.234735	+	0.876044i	0.743533	+	0.668700i	$0.233149\pi$
$11$	−0.778529	+	2.90551i	−0.234735	+	0.876044i	−0.978268	+	0.207344i	$0.933518\pi$
$12$	2.22635	−	2.22635i	0.642692	−	0.642692i
$13$	−3.59966	−	0.206024i	−0.998366	−	0.0571409i
$13$	−3.59966	−	0.206024i	−0.998366	−	0.0571409i
$14$		−	0.804795i		−	0.215090i
$15$	1.18093	−	6.94059i	0.304914	−	1.79205i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.87508	+	6.99788i	0.454773	+	1.69724i	0.688754	+	0.724995i	$0.258158\pi$
$17$	1.87508	+	6.99788i	0.454773	+	1.69724i	−0.233981	+	0.972241i	$0.575175\pi$
$18$		−	6.91327i		−	1.62947i
$19$	−4.51652	+	1.21020i	−1.03616	+	0.277638i	−0.736521	−	0.676414i	$-0.763533\pi$
$19$	−4.51652	+	1.21020i	−1.03616	+	0.277638i	−0.299639	+	0.954053i	$0.596866\pi$
$20$	−2.03220	−	0.932829i	−0.454413	−	0.208587i
$21$	−1.79175	−	1.79175i	−0.390993	−	0.390993i
$22$	2.90551	−	0.778529i	0.619457	−	0.165983i
$23$	0.113254	−	0.422668i	0.0236150	−	0.0881324i	−0.953113	−	0.302616i	$-0.902140\pi$
$23$	0.113254	−	0.422668i	0.0236150	−	0.0881324i	0.976728	+	0.214483i	$0.0688068\pi$
$24$	−3.04125	−	0.814901i	−0.620793	−	0.166341i
$25$	−4.91327	+	0.927256i	−0.982653	+	0.185451i
$26$	1.62141	+	3.22041i	0.317984	+	0.631574i
$27$	−8.71230	−	8.71230i	−1.67668	−	1.67668i
$28$	−0.696972	+	0.402397i	−0.131715	+	0.0760459i
$29$	3.58287	−	2.06857i	0.665322	−	0.384124i	−0.128980	−	0.991647i	$-0.541170\pi$
$29$	3.58287	−	2.06857i	0.665322	−	0.384124i	0.794302	+	0.607523i	$0.207837\pi$
$30$	−6.60119	+	2.44758i	−1.20521	+	0.446865i
$31$	−0.536500	+	0.536500i	−0.0963583	+	0.0963583i	−0.753643	−	0.657284i	$-0.771705\pi$
$31$	−0.536500	+	0.536500i	−0.0963583	+	0.0963583i	0.657284	+	0.753643i	$0.271705\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.73540	−	8.20196i	0.824328	−	1.42778i
$34$	5.12281	−	5.12281i	0.878554	−	0.878554i
$35$	−0.750735	+	1.63550i	−0.126897	+	0.276450i
$36$	−5.98707	+	3.45663i	−0.997844	+	0.576106i
$37$	0.835172	−	0.482187i	0.137301	−	0.0792710i	−0.429776	−	0.902936i	$-0.641407\pi$
$37$	0.835172	−	0.482187i	0.137301	−	0.0792710i	0.567077	+	0.823665i	$0.308074\pi$
$38$	3.30632	+	3.30632i	0.536356	+	0.536356i
$39$	10.7796	+	3.55994i	1.72611	+	0.570046i
$40$	0.208246	+	2.22635i	0.0329266	+	0.352017i
$41$	1.63091	+	0.437002i	0.254706	+	0.0682483i	0.383913	−	0.923369i	$-0.374576\pi$
$41$	1.63091	+	0.437002i	0.254706	+	0.0682483i	−0.129207	+	0.991618i	$0.541243\pi$
$42$	−0.655828	+	2.44758i	−0.101196	+	0.377670i
$43$	6.14091	−	1.64545i	0.936480	−	0.250929i	0.241864	−	0.970310i	$-0.422241\pi$
$43$	6.14091	−	1.64545i	0.936480	−	0.250929i	0.694616	+	0.719381i	$0.255574\pi$
$44$	−2.12698	−	2.12698i	−0.320654	−	0.320654i
$45$	−6.44889	+	14.0491i	−0.961344	+	2.09432i
$46$	−0.422668	+	0.113254i	−0.0623190	+	0.0166983i
$47$			1.72276i			0.251290i	0.992075	+	0.125645i	$0.0401000\pi$
$47$			1.72276i			0.251290i	−0.992075	+	0.125645i	$0.959900\pi$
$48$	0.814901	+	3.04125i	0.117621	+	0.438967i
$49$	−3.17615	−	5.50126i	−0.453736	−	0.785894i
$50$	3.25966	+	3.79139i	0.460986	+	0.536183i
$51$		−	22.8103i		−	3.19408i
$52$	1.97825	−	3.01438i	0.274334	−	0.418020i
$53$	−5.01074	+	5.01074i	−0.688278	+	0.688278i	−0.961851	−	0.273573i	$-0.911794\pi$
$53$	−5.01074	+	5.01074i	−0.688278	+	0.688278i	0.273573	+	0.961851i	$0.411794\pi$
$54$	−3.18892	+	11.9012i	−0.433958	+	1.61955i
$55$	−6.63080	−	1.12822i	−0.894098	−	0.152129i
$56$	0.696972	+	0.402397i	0.0931369	+	0.0537726i
$57$	14.7221			1.94998
$58$	−3.58287	−	2.06857i	−0.470454	−	0.271617i
$59$	0.0422769	+	0.157780i	0.00550398	+	0.0205411i	0.968623	−	0.248534i	$-0.0799487\pi$
$59$	0.0422769	+	0.157780i	0.00550398	+	0.0205411i	−0.963119	+	0.269075i	$0.913282\pi$
$60$	5.42026	+	4.49301i	0.699753	+	0.580045i
$61$	1.11898	−	1.93813i	0.143271	−	0.248153i	−0.785456	−	0.618918i	$-0.787571\pi$
$61$	1.11898	−	1.93813i	0.143271	−	0.248153i	0.928727	+	0.370765i	$0.120905\pi$
$62$	0.732873	+	0.196373i	0.0930750	+	0.0249394i
$63$	2.78188	+	4.81836i	0.350484	+	0.607056i
$64$	1.00000			0.125000
$65$	−0.290932	−	8.05701i	−0.0360856	−	0.999349i
$66$	−9.47080			−1.16578
$67$	2.20825	+	3.82479i	0.269780	+	0.467273i	0.968805	−	0.247824i	$-0.0797156\pi$
$67$	2.20825	+	3.82479i	0.269780	+	0.467273i	−0.699025	+	0.715097i	$0.746382\pi$
$68$	−6.99788	−	1.87508i	−0.848618	−	0.227387i
$69$	−0.688865	+	1.19315i	−0.0829296	+	0.143638i
$70$	1.79175	−	0.167595i	0.214156	−	0.0200314i
$71$	2.63643	+	9.83928i	0.312886	+	1.16771i	0.925941	+	0.377668i	$0.123274\pi$
$71$	2.63643	+	9.83928i	0.312886	+	1.16771i	−0.613055	+	0.790040i	$0.710060\pi$
$72$	5.98707	+	3.45663i	0.705582	+	0.407368i
$73$	−1.73949			−0.203592			−0.101796	−	0.994805i	$-0.532459\pi$
$73$	−1.73949			−0.203592			−0.101796	+	0.994805i	$0.532459\pi$
$74$	−0.835172	−	0.482187i	−0.0970867	−	0.0560530i
$75$	15.6981	+	1.18381i	1.81266	+	0.136694i
$76$	1.21020	−	4.51652i	0.138819	−	0.518080i
$77$	−1.71178	+	1.71178i	−0.195076	+	0.195076i
$78$	−2.30679	−	11.1154i	−0.261193	−	1.25857i
$79$		−	7.75722i		−	0.872756i	−0.899763	−	0.436378i	$-0.856261\pi$
$79$		−	7.75722i		−	0.872756i	0.899763	−	0.436378i	$-0.143739\pi$
$80$	1.82395	−	1.29352i	0.203924	−	0.144620i
$81$	9.02673	+	15.6348i	1.00297	+	1.73720i
$82$	−0.437002	−	1.63091i	−0.0482588	−	0.180104i
$83$			15.6444i			1.71720i	0.512649	+	0.858599i	$0.328664\pi$
$83$			15.6444i			1.71720i	−0.512649	+	0.858599i	$0.671336\pi$
$84$	2.44758	−	0.655828i	0.267053	−	0.0715567i
$85$	−15.1893	+	5.63186i	−1.64751	+	0.610861i
$86$	−4.49546	−	4.49546i	−0.484758	−	0.484758i
$87$	−12.5821	+	3.37136i	−1.34894	+	0.361448i
$88$	−0.778529	+	2.90551i	−0.0829914	+	0.309728i
$89$	−5.91063	−	1.58375i	−0.626525	−	0.167877i	−0.0684328	−	0.997656i	$-0.521800\pi$
$89$	−5.91063	−	1.58375i	−0.626525	−	0.167877i	−0.558092	+	0.829779i	$0.688467\pi$
$90$	15.3914	−	1.43966i	1.62239	−	0.151753i
$91$	−2.42596	−	1.59209i	−0.254310	−	0.166896i
$92$	0.309415	+	0.309415i	0.0322587	+	0.0322587i
$93$	2.06883	−	1.19444i	0.214527	−	0.123857i
$94$	1.49195	−	0.861379i	0.153883	−	0.0888444i
$95$	−3.63487	−	9.80333i	−0.372930	−	1.00580i
$96$	2.22635	−	2.22635i	0.227226	−	0.227226i
$97$	6.70520	−	11.6138i	0.680810	−	1.17920i	−0.293924	−	0.955829i	$-0.594961\pi$
$97$	6.70520	−	11.6138i	0.680810	−	1.17920i	0.974734	−	0.223369i	$-0.0717056\pi$
$98$	−3.17615	+	5.50126i	−0.320840	+	0.555711i
$99$	−14.7044	+	14.7044i	−1.47785	+	1.47785i
$100$	1.65361	−	4.71864i	0.165361	−	0.471864i
$101$	9.02570	−	5.21099i	0.898091	−	0.518513i	0.0215104	−	0.999769i	$-0.493153\pi$
$101$	9.02570	−	5.21099i	0.898091	−	0.518513i	0.876580	+	0.481256i	$0.159819\pi$
$102$	−19.7543	+	11.4052i	−1.95597	+	1.12928i
$103$	11.9307	+	11.9307i	1.17557	+	1.17557i	0.980861	+	0.194709i	$0.0623762\pi$
$103$	11.9307	+	11.9307i	1.17557	+	1.17557i	0.194709	+	0.980861i	$0.437624\pi$
$104$	−3.59966	−	0.206024i	−0.352976	−	0.0202024i
$105$	3.61595	−	4.36220i	0.352880	−	0.425707i
$106$	6.84480	+	1.83406i	0.664826	+	0.178140i
$107$	2.91943	−	10.8955i	0.282232	−	1.05330i	−0.668607	−	0.743616i	$-0.733109\pi$
$107$	2.91943	−	10.8955i	0.282232	−	1.05330i	0.950839	−	0.309687i	$-0.100224\pi$
$108$	11.9012	−	3.18892i	1.14520	−	0.306854i
$109$	5.74393	+	5.74393i	0.550169	+	0.550169i	0.926489	−	0.376321i	$-0.122811\pi$
$109$	5.74393	+	5.74393i	0.550169	+	0.550169i	−0.376321	+	0.926489i	$0.622811\pi$
$110$	2.33834	+	6.30655i	0.222952	+	0.601306i
$111$	−2.93290	+	0.785868i	−0.278379	+	0.0745913i
$112$		−	0.804795i		−	0.0760459i
$113$	−4.47593	−	16.7044i	−0.421060	−	1.57142i	−0.772380	−	0.635161i	$-0.780934\pi$
$113$	−4.47593	−	16.7044i	−0.421060	−	1.57142i	0.351320	−	0.936255i	$-0.385733\pi$
$114$	−7.36103	−	12.7497i	−0.689424	−	1.19412i
$115$	0.964592	+	0.164123i	0.0899487	+	0.0153046i
$116$			4.13714i			0.384124i
$117$	−20.8392	−	13.6762i	−1.92659	−	1.26436i
$118$	0.115503	−	0.115503i	0.0106329	−	0.0106329i
$119$	−1.50905	+	5.63186i	−0.138335	+	0.516272i
$120$	1.18093	−	6.94059i	0.107803	−	0.633586i
$121$	1.69040	+	0.975956i	0.153673	+	0.0887232i
$122$	−2.23796			−0.202616
$123$	−4.60390	−	2.65807i	−0.415120	−	0.239670i
$124$	−0.196373	−	0.732873i	−0.0176348	−	0.0658140i
$125$	−3.08756	−	10.7456i	−0.276160	−	0.961112i
$126$	2.78188	−	4.81836i	0.247830	−	0.429253i
$127$	−3.97326	−	1.06463i	−0.352570	−	0.0944707i	0.0781875	−	0.996939i	$-0.475087\pi$
$127$	−3.97326	−	1.06463i	−0.352570	−	0.0944707i	−0.430757	+	0.902468i	$0.641753\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−20.0169			−1.76239
$130$	−6.83211	+	4.28046i	−0.599215	+	0.375421i
$131$	−5.90842			−0.516221			−0.258110	−	0.966115i	$-0.583100\pi$
$131$	−5.90842			−0.516221			−0.258110	+	0.966115i	$0.583100\pi$
$132$	4.73540	+	8.20196i	0.412164	+	0.713889i
$133$	−3.63487	−	0.973961i	−0.315183	−	0.0844531i
$134$	2.20825	−	3.82479i	0.190763	−	0.330412i
$135$	17.5823	−	21.2109i	1.51325	−	1.82555i
$136$	1.87508	+	6.99788i	0.160787	+	0.600064i
$137$	6.99324	+	4.03755i	0.597473	+	0.344951i	0.768047	−	0.640394i	$-0.221229\pi$
$137$	6.99324	+	4.03755i	0.597473	+	0.344951i	−0.170574	+	0.985345i	$0.554562\pi$
$138$	1.37773			0.117280
$139$	−13.2173	−	7.63102i	−1.12108	−	0.647254i	−0.179402	−	0.983776i	$-0.557416\pi$
$139$	−13.2173	−	7.63102i	−1.12108	−	0.647254i	−0.941676	+	0.336521i	$0.890750\pi$
$140$	−1.04102	−	1.46791i	−0.0879821	−	0.124061i
$141$	1.40388	−	5.23934i	0.118228	−	0.441232i
$142$	7.20285	−	7.20285i	0.604450	−	0.604450i
$143$	3.40104	−	10.2984i	0.284410	−	0.861200i
$144$		−	6.91327i		−	0.576106i
$145$	5.35148	+	7.54595i	0.444416	+	0.626657i
$146$	0.869744	+	1.50644i	0.0719806	+	0.124674i
$147$	5.17650	+	19.3190i	0.426950	+	1.59340i
$148$			0.964373i			0.0792710i
$149$	10.7129	−	2.87051i	0.877634	−	0.235161i	0.208248	−	0.978076i	$-0.433224\pi$
$149$	10.7129	−	2.87051i	0.877634	−	0.235161i	0.669386	+	0.742915i	$0.266557\pi$
$150$	−6.82384	−	14.1869i	−0.557164	−	1.15835i
$151$	11.2046	+	11.2046i	0.911815	+	0.911815i	0.996415	−	0.0845999i	$-0.0269612\pi$
$151$	11.2046	+	11.2046i	0.911815	+	0.911815i	−0.0845999	+	0.996415i	$0.526961\pi$
$152$	−4.51652	+	1.21020i	−0.366338	+	0.0981600i
$153$	−12.9629	+	48.3782i	−1.04799	+	3.91115i
$154$	2.33834	+	0.626556i	0.188429	+	0.0504893i
$155$	−1.30616	−	1.08271i	−0.104913	−	0.0869656i
$156$	−8.47279	+	7.55542i	−0.678366	+	0.604918i
$157$	2.13077	+	2.13077i	0.170054	+	0.170054i	0.787003	−	0.616949i	$-0.211632\pi$
$157$	2.13077	+	2.13077i	0.170054	+	0.170054i	−0.616949	+	0.787003i	$0.711632\pi$
$158$	−6.71795	+	3.87861i	−0.534452	+	0.308566i
$159$	19.3222	−	11.1557i	1.53235	−	0.884702i
$160$	−2.03220	−	0.932829i	−0.160659	−	0.0737466i
$161$	0.249015	−	0.249015i	0.0196251	−	0.0196251i
$162$	9.02673	−	15.6348i	0.709207	−	1.22838i
$163$	3.31273	−	5.73782i	0.259473	−	0.449421i	−0.706628	−	0.707586i	$-0.749784\pi$
$163$	3.31273	−	5.73782i	0.259473	−	0.449421i	0.966101	+	0.258165i	$0.0831177\pi$
$164$	−1.19391	+	1.19391i	−0.0932289	+	0.0932289i
$165$	19.2466	+	8.83464i	1.49834	+	0.687776i
$166$	13.5485	−	7.82220i	1.05156	−	0.607121i
$167$	−7.39866	+	4.27162i	−0.572526	+	0.330548i	−0.758158	−	0.652071i	$-0.773900\pi$
$167$	−7.39866	+	4.27162i	−0.572526	+	0.330548i	0.185632	+	0.982619i	$0.440567\pi$
$168$	−1.79175	−	1.79175i	−0.138237	−	0.138237i
$169$	12.9151	+	1.48324i	0.993470	+	0.114095i
$170$	12.4720	+	10.3384i	0.956556	+	0.792916i
$171$	−31.2239	−	8.36642i	−2.38775	−	0.639796i
$172$	−1.64545	+	6.14091i	−0.125465	+	0.468240i
$173$	3.47144	−	0.930169i	0.263929	−	0.0707195i	−0.124428	−	0.992229i	$-0.539710\pi$
$173$	3.47144	−	0.930169i	0.263929	−	0.0707195i	0.388357	+	0.921509i	$0.373043\pi$
$174$	9.21072	+	9.21072i	0.698263	+	0.698263i
$175$	−3.79754	−	1.33081i	−0.287067	−	0.100600i
$176$	2.90551	−	0.778529i	0.219011	−	0.0586838i
$177$		−	0.514299i		−	0.0386570i
$178$	1.58375	+	5.91063i	0.118707	+	0.443020i
$179$	3.40272	+	5.89368i	0.254331	+	0.440514i	0.964714	−	0.263302i	$-0.0848114\pi$
$179$	3.40272	+	5.89368i	0.254331	+	0.440514i	−0.710383	+	0.703816i	$0.751478\pi$
$180$	−8.94246	−	12.6095i	−0.666531	−	0.939855i
$181$			11.5815i			0.860846i	0.902627	+	0.430423i	$0.141636\pi$
$181$			11.5815i			0.860846i	−0.902627	+	0.430423i	$0.858364\pi$
$182$	−0.165807	+	2.89699i	−0.0122905	+	0.214739i
$183$	−4.98249	+	4.98249i	−0.368316	+	0.368316i
$184$	0.113254	−	0.422668i	0.00834917	−	0.0311595i
$185$	1.24744	+	1.75897i	0.0917134	+	0.129322i
$186$	−2.06883	−	1.19444i	−0.151694	−	0.0875804i
$187$	−21.7922			−1.59360
$188$	−1.49195	−	0.861379i	−0.108812	−	0.0628225i
$189$	−2.56643	−	9.57804i	−0.186680	−	0.696700i
$190$	−6.67250	+	8.04956i	−0.484074	+	0.583976i
$191$	2.32947	−	4.03477i	0.168555	−	0.291946i	−0.769357	−	0.638819i	$-0.779423\pi$
$191$	2.32947	−	4.03477i	0.168555	−	0.291946i	0.937912	+	0.346873i	$0.112757\pi$
$192$	−3.04125	−	0.814901i	−0.219483	−	0.0588104i
$193$	6.69708	+	11.5997i	0.482066	+	0.834963i	0.999788	−	0.0205858i	$-0.00655313\pi$
$193$	6.69708	+	11.5997i	0.482066	+	0.834963i	−0.517722	+	0.855549i	$0.673220\pi$
$194$	−13.4104			−0.962811
$195$	−5.68086	+	24.7405i	−0.406815	+	1.77170i
$196$	6.35231			0.453736
$197$	11.0122	+	19.0737i	0.784586	+	1.35894i	0.929246	+	0.369461i	$0.120458\pi$
$197$	11.0122	+	19.0737i	0.784586	+	1.35894i	−0.144661	+	0.989481i	$0.546209\pi$
$198$	20.0866	+	5.38218i	1.42749	+	0.382495i
$199$	−5.69362	+	9.86164i	−0.403610	+	0.699073i	−0.994159	−	0.107929i	$-0.965578\pi$
$199$	−5.69362	+	9.86164i	−0.403610	+	0.699073i	0.590549	+	0.807002i	$0.298911\pi$
$200$	−4.91327	+	0.927256i	−0.347420	+	0.0655669i
$201$	−3.59900	−	13.4317i	−0.253854	−	0.947396i
$202$	−9.02570	−	5.21099i	−0.635046	−	0.366644i
$203$	3.32955			0.233688
$204$	19.7543	+	11.4052i	1.38308	+	0.798521i
$205$	−0.633288	+	3.72199i	−0.0442308	+	0.259955i
$206$	4.36695	−	16.2977i	0.304260	−	1.13551i
$207$	2.13907	−	2.13907i	0.148675	−	0.148675i
$208$	1.62141	+	3.22041i	0.112424	+	0.223295i
$209$		−	14.0650i		−	0.972894i
$210$	−5.58575	−	0.950403i	−0.385453	−	0.0655840i
$211$	1.35943	+	2.35460i	0.0935868	+	0.162097i	0.909018	−	0.416757i	$-0.136833\pi$
$211$	1.35943	+	2.35460i	0.0935868	+	0.162097i	−0.815431	+	0.578854i	$0.803500\pi$
$212$	−1.83406	−	6.84480i	−0.125964	−	0.470103i
$213$		−	32.0721i		−	2.19755i
$214$	−10.8955	+	2.91943i	−0.744798	+	0.199568i
$215$	4.94217	+	13.3292i	0.337053	+	0.909041i
$216$	−8.71230	−	8.71230i	−0.592797	−	0.592797i
$217$	−0.589812	+	0.158040i	−0.0400391	+	0.0107284i
$218$	2.10242	−	7.84636i	0.142394	−	0.531422i
$219$	5.29022	+	1.41751i	0.357480	+	0.0957865i
$220$	4.29247	−	5.17834i	0.289398	−	0.349123i
$221$	−5.30791	−	25.5763i	−0.357048	−	1.72045i
$222$	2.14703	+	2.14703i	0.144099	+	0.144099i
$223$	23.9414	−	13.8226i	1.60324	−	0.925630i	0.612404	−	0.790545i	$-0.290203\pi$
$223$	23.9414	−	13.8226i	1.60324	−	0.925630i	0.990834	−	0.135085i	$-0.0431306\pi$
$224$	−0.696972	+	0.402397i	−0.0465684	+	0.0268863i
$225$	−32.6212	−	11.4318i	−2.17475	−	0.762121i
$226$	−12.2285	+	12.2285i	−0.813425	+	0.813425i
$227$	−1.72981	+	2.99612i	−0.114812	+	0.198859i	−0.917704	−	0.397264i	$-0.869960\pi$
$227$	−1.72981	+	2.99612i	−0.114812	+	0.198859i	0.802893	+	0.596123i	$0.203293\pi$
$228$	−7.36103	+	12.7497i	−0.487496	+	0.844368i
$229$	−8.92266	+	8.92266i	−0.589626	+	0.589626i	−0.937530	−	0.347904i	$-0.886893\pi$
$229$	−8.92266	+	8.92266i	−0.589626	+	0.589626i	0.347904	+	0.937530i	$0.386893\pi$
$230$	−0.340161	−	0.917423i	−0.0224296	−	0.0604931i
$231$	6.60089	−	3.81103i	0.434307	−	0.250747i
$232$	3.58287	−	2.06857i	0.235227	−	0.135808i
$233$	−1.21530	−	1.21530i	−0.0796169	−	0.0796169i	0.666177	−	0.745794i	$-0.267930\pi$
$233$	−1.21530	−	1.21530i	−0.0796169	−	0.0796169i	−0.745794	+	0.666177i	$0.767930\pi$
$234$	−1.42430	+	24.8854i	−0.0931096	+	1.62681i
$235$	−3.83546	+	0.358757i	−0.250198	+	0.0234027i
$236$	−0.157780	−	0.0422769i	−0.0102706	−	0.00275199i
$237$	−6.32137	+	23.5917i	−0.410617	+	1.53244i
$238$	5.63186	−	1.50905i	0.365059	−	0.0978173i
$239$	10.5843	+	10.5843i	0.684643	+	0.684643i	0.961043	−	0.276400i	$-0.0891415\pi$
$239$	10.5843	+	10.5843i	0.684643	+	0.684643i	−0.276400	+	0.961043i	$0.589141\pi$
$240$	−6.60119	+	2.44758i	−0.426105	+	0.157991i
$241$	−26.2460	+	7.03259i	−1.69065	+	0.453009i	−0.970558	−	0.240868i	$-0.922568\pi$
$241$	−26.2460	+	7.03259i	−1.69065	+	0.453009i	−0.720094	+	0.693877i	$0.755901\pi$
$242$		−	1.95191i		−	0.125474i
$243$	−5.14501	−	19.2014i	−0.330052	−	1.23177i
$244$	1.11898	+	1.93813i	0.0716355	+	0.124076i
$245$	11.5863	−	8.21684i	0.740222	−	0.524955i
$246$			5.31613i			0.338944i
$247$	16.5073	−	3.42579i	1.05033	−	0.217978i
$248$	−0.536500	+	0.536500i	−0.0340678	+	0.0340678i
$249$	12.7486	−	47.5786i	0.807912	−	3.01517i
$250$	−7.76214	+	8.04669i	−0.490921	+	0.508917i
$251$	22.8576	+	13.1969i	1.44276	+	0.832979i	0.998033	−	0.0626870i	$-0.0199670\pi$
$251$	22.8576	+	13.1969i	1.44276	+	0.832979i	0.444728	+	0.895666i	$0.353300\pi$
$252$	−5.56376			−0.350484
$253$	1.13990	+	0.658119i	0.0716646	+	0.0413756i
$254$	1.06463	+	3.97326i	0.0668009	+	0.249304i
$255$	50.7838	−	4.75015i	3.18020	−	0.297466i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.96070	−	0.525368i	−0.122305	−	0.0327715i	0.197147	−	0.980374i	$-0.436832\pi$
$257$	−1.96070	−	0.525368i	−0.122305	−	0.0327715i	−0.319452	+	0.947602i	$0.603499\pi$
$258$	10.0085	+	17.3352i	0.623100	+	1.07924i
$259$	0.776122			0.0482259
$260$	7.12304	+	3.77655i	0.441752	+	0.234212i
$261$	28.6012			1.77037
$262$	2.95421	+	5.11684i	0.182512	+	0.316119i
$263$	−27.3875	−	7.33845i	−1.68878	−	0.452508i	−0.718708	−	0.695312i	$-0.755266\pi$
$263$	−27.3875	−	7.33845i	−1.68878	−	0.452508i	−0.970075	+	0.242804i	$0.921933\pi$
$264$	4.73540	−	8.20196i	0.291444	−	0.504796i
$265$	−12.1991	−	10.1122i	−0.749387	−	0.621187i
$266$	0.973961	+	3.63487i	0.0597174	+	0.222868i
$267$	16.6851	+	9.63315i	1.02111	+	0.589539i
$268$	−4.41649			−0.269780
$269$	2.82789	+	1.63268i	0.172420	+	0.0995465i	0.583726	−	0.811951i	$-0.301594\pi$
$269$	2.82789	+	1.63268i	0.172420	+	0.0995465i	−0.411307	+	0.911497i	$0.634927\pi$
$270$	−27.1604	−	4.62128i	−1.65293	−	0.281242i
$271$	1.42316	−	5.31129i	0.0864505	−	0.322638i	−0.909134	−	0.416503i	$-0.863256\pi$
$271$	1.42316	−	5.31129i	0.0864505	−	0.322638i	0.995585	+	0.0938651i	$0.0299222\pi$
$272$	5.12281	−	5.12281i	0.310616	−	0.310616i
$273$	6.08056	+	6.81885i	0.368012	+	0.412696i
$274$		−	8.07510i		−	0.487835i
$275$	1.13097	−	14.9974i	0.0682000	−	0.904380i
$276$	−0.688865	−	1.19315i	−0.0414648	−	0.0718192i
$277$	−5.54414	−	20.6910i	−0.333115	−	1.24320i	−0.905898	−	0.423496i	$-0.860803\pi$
$277$	−5.54414	−	20.6910i	−0.333115	−	1.24320i	0.572783	−	0.819707i	$-0.305864\pi$
$278$			15.2620i			0.915356i
$279$	−5.06655	+	1.35758i	−0.303326	+	0.0812760i
$280$	−0.750735	+	1.63550i	−0.0448650	+	0.0977399i
$281$	−15.6657	−	15.6657i	−0.934539	−	0.934539i	0.0634460	−	0.997985i	$-0.479791\pi$
$281$	−15.6657	−	15.6657i	−0.934539	−	0.934539i	−0.997985	+	0.0634460i	$0.979791\pi$
$282$	−5.23934	+	1.40388i	−0.311998	+	0.0835996i
$283$	2.33476	−	8.71344i	0.138787	−	0.517960i	−0.861167	−	0.508323i	$-0.830266\pi$
$283$	2.33476	−	8.71344i	0.138787	−	0.517960i	0.999954	−	0.00963733i	$-0.00306771\pi$
$284$	−9.83928	−	2.63643i	−0.583854	−	0.156443i
$285$	3.06581	+	32.7765i	0.181603	+	1.94151i
$286$	−10.6192	+	2.20383i	−0.627929	+	0.130315i
$287$	0.960854	+	0.960854i	0.0567174	+	0.0567174i
$288$	−5.98707	+	3.45663i	−0.352791	+	0.203684i
$289$	−30.7320	+	17.7431i	−1.80777	+	1.04371i
$290$	3.85924	−	8.40749i	0.226623	−	0.493705i
$291$	−29.8563	+	29.8563i	−1.75021	+	1.75021i
$292$	0.869744	−	1.50644i	0.0508979	−	0.0881578i
$293$	5.34888	−	9.26452i	0.312485	−	0.541239i	−0.666415	−	0.745581i	$-0.732172\pi$
$293$	5.34888	−	9.26452i	0.312485	−	0.541239i	0.978900	+	0.204342i	$0.0655054\pi$
$294$	14.1425	−	14.1425i	0.824805	−	0.824805i
$295$	−0.342468	+	0.126980i	−0.0199393	+	0.00739307i
$296$	0.835172	−	0.482187i	0.0485434	−	0.0280265i
$297$	32.0964	−	18.5309i	1.86242	−	1.07527i
$298$	−7.84237	−	7.84237i	−0.454297	−	0.454297i
$299$	−0.494754	+	1.49813i	−0.0286124	+	0.0866390i
$300$	−8.87426	+	13.0030i	−0.512355	+	0.750731i
$301$	4.94217	+	1.32425i	0.284862	+	0.0763285i
$302$	4.10116	−	15.3057i	0.235995	−	0.880746i
$303$	−31.6958	+	8.49288i	−1.82088	+	0.487903i
$304$	3.30632	+	3.30632i	0.189631	+	0.189631i
$305$	4.54799	+	2.08764i	0.260417	+	0.119538i
$306$	48.3782	−	12.9629i	2.76560	−	0.741040i
$307$		−	12.9134i		−	0.737005i	−0.929627	−	0.368502i	$-0.879871\pi$
$307$		−	12.9134i		−	0.737005i	0.929627	−	0.368502i	$-0.120129\pi$
$308$	−0.626556	−	2.33834i	−0.0357013	−	0.133239i
$309$	−26.5620	−	46.0067i	−1.51106	−	2.61723i
$310$	−0.284577	+	1.67253i	−0.0161629	+	0.0949931i
$311$			10.1340i			0.574646i	0.957834	+	0.287323i	$0.0927654\pi$
$311$			10.1340i			0.574646i	−0.957834	+	0.287323i	$0.907235\pi$
$312$	10.7796	+	3.55994i	0.610273	+	0.201542i
$313$	10.4449	−	10.4449i	0.590383	−	0.590383i	−0.347352	−	0.937735i	$-0.612919\pi$
$313$	10.4449	−	10.4449i	0.590383	−	0.590383i	0.937735	+	0.347352i	$0.112919\pi$
$314$	0.779916	−	2.91069i	0.0440132	−	0.164260i
$315$	−10.1480	+	7.19684i	−0.571777	+	0.405496i
$316$	6.71795	+	3.87861i	0.377914	+	0.218189i
$317$	−24.4508			−1.37329			−0.686646	−	0.726992i	$-0.740918\pi$
$317$	−24.4508			−1.37329			−0.686646	+	0.726992i	$0.740918\pi$
$318$	−19.3222	−	11.1557i	−1.08353	−	0.625579i
$319$	3.22088	+	12.0205i	0.180335	+	0.673019i
$320$	0.208246	+	2.22635i	0.0116413	+	0.124457i
$321$	−17.7574	+	30.7568i	−0.991123	+	1.71667i
$322$	−0.340161	−	0.0911459i	−0.0189564	−	0.00507936i
$323$	−16.9376	−	29.3369i	−0.942436	−	1.63235i
$324$	−18.0535			−1.00297
$325$	17.8771	−	2.32555i	0.991645	−	0.128999i
$326$	−6.62547			−0.366951
$327$	−12.7880	−	22.1495i	−0.707178	−	1.22487i
$328$	1.63091	+	0.437002i	0.0900522	+	0.0241294i
$329$	−0.693233	+	1.20071i	−0.0382192	+	0.0661975i
$330$	−1.97226	−	21.0853i	−0.108569	−	1.16071i
$331$	−0.310163	−	1.15754i	−0.0170481	−	0.0636243i	0.956878	−	0.290491i	$-0.0938186\pi$
$331$	−0.310163	−	1.15754i	−0.0170481	−	0.0636243i	−0.973926	+	0.226866i	$0.927152\pi$
$332$	−13.5485	−	7.82220i	−0.743568	−	0.429299i
$333$	6.66697			0.365348
$334$	7.39866	+	4.27162i	0.404837	+	0.233733i
$335$	−8.05547	+	5.71283i	−0.440117	+	0.312125i
$336$	−0.655828	+	2.44758i	−0.0357783	+	0.133527i
$337$	−0.358931	+	0.358931i	−0.0195522	+	0.0195522i	−0.716815	−	0.697263i	$-0.754401\pi$
$337$	−0.358931	+	0.358931i	−0.0195522	+	0.0195522i	0.697263	+	0.716815i	$0.254401\pi$
$338$	−5.17303	−	11.9264i	−0.281376	−	0.648712i
$339$			54.4496i			2.95730i
$340$	2.71730	−	15.9702i	0.147366	−	0.866107i
$341$	−1.14113	−	1.97649i	−0.0617954	−	0.107033i
$342$	8.36642	+	31.2239i	0.452404	+	1.68840i
$343$		−	10.7459i		−	0.580222i
$344$	6.14091	−	1.64545i	0.331096	−	0.0887168i
$345$	−2.79982	−	1.28519i	−0.150737	−	0.0691921i
$346$	−2.54127	−	2.54127i	−0.136619	−	0.136619i
$347$	12.6705	−	3.39505i	0.680187	−	0.182256i	0.0978479	−	0.995201i	$-0.468804\pi$
$347$	12.6705	−	3.39505i	0.680187	−	0.182256i	0.582339	+	0.812946i	$0.302137\pi$
$348$	3.37136	−	12.5821i	0.180724	−	0.674470i
$349$	22.5950	+	6.05431i	1.20948	+	0.324080i	0.806559	−	0.591154i	$-0.201327\pi$
$349$	22.5950	+	6.05431i	1.20948	+	0.324080i	0.402924	+	0.915234i	$0.367994\pi$
$350$	0.746251	+	3.95417i	0.0398888	+	0.211359i
$351$	29.5664	+	33.1563i	1.57814	+	1.76975i
$352$	−2.12698	−	2.12698i	−0.113368	−	0.113368i
$353$	−20.4439	+	11.8033i	−1.08812	+	0.628227i	−0.933076	−	0.359680i	$-0.882886\pi$
$353$	−20.4439	+	11.8033i	−1.08812	+	0.628227i	−0.155045	+	0.987907i	$0.549552\pi$
$354$	−0.445396	+	0.257149i	−0.0236725	+	0.0136673i
$355$	−21.3567	+	7.91860i	−1.13349	+	0.420276i
$356$	4.32688	−	4.32688i	0.229324	−	0.229324i
$357$	9.17881	−	15.8982i	0.485794	−	0.841420i
$358$	3.40272	−	5.89368i	0.179839	−	0.311490i
$359$	−9.07981	+	9.07981i	−0.479214	+	0.479214i	−0.904880	−	0.425666i	$-0.860040\pi$
$359$	−9.07981	+	9.07981i	−0.479214	+	0.479214i	0.425666	+	0.904880i	$0.360040\pi$
$360$	−6.44889	+	14.0491i	−0.339887	+	0.740454i
$361$	2.47989	−	1.43177i	0.130521	−	0.0753561i
$362$	10.0299	−	5.79075i	0.527159	−	0.304355i
$363$	−4.34564	−	4.34564i	−0.228087	−	0.228087i
$364$	2.59177	−	1.30490i	0.135846	−	0.0683953i
$365$	−0.362241	−	3.87271i	−0.0189606	−	0.202707i
$366$	6.80621	+	1.82372i	0.355766	+	0.0953273i
$367$	8.65453	−	32.2992i	0.451763	−	1.68600i	−0.245671	−	0.969353i	$-0.579008\pi$
$367$	8.65453	−	32.2992i	0.451763	−	1.68600i	0.697434	−	0.716649i	$-0.254325\pi$
$368$	−0.422668	+	0.113254i	−0.0220331	+	0.00590375i
$369$	8.25383	+	8.25383i	0.429677	+	0.429677i
$370$	0.899595	−	1.95980i	0.0467677	−	0.101885i
$371$	−5.50866	+	1.47604i	−0.285995	+	0.0766322i
$372$			2.38888i			0.123857i
$373$	6.19820	+	23.1320i	0.320931	+	1.19773i	0.918340	+	0.395793i	$0.129530\pi$
$373$	6.19820	+	23.1320i	0.320931	+	1.19773i	−0.597409	+	0.801937i	$0.703803\pi$
$374$	10.8961	+	18.8726i	0.563424	+	0.975880i
$375$	0.633498	+	35.1960i	0.0327137	+	1.81751i
$376$			1.72276i			0.0888444i
$377$	−13.3233	+	6.70799i	−0.686184	+	0.345479i
$378$	−7.01161	+	7.01161i	−0.360638	+	0.360638i
$379$	−1.03686	+	3.86961i	−0.0532599	+	0.198769i	−0.987429	−	0.158061i	$-0.949476\pi$
$379$	−1.03686	+	3.86961i	−0.0532599	+	0.198769i	0.934169	+	0.356830i	$0.116142\pi$
$380$	10.3074	+	1.75378i	0.528757	+	0.0899669i
$381$	11.2161	+	6.47562i	0.574618	+	0.331756i
$382$	−4.65895			−0.238373
$383$	22.5091	+	12.9957i	1.15016	+	0.664047i	0.948927	−	0.315495i	$-0.102171\pi$
$383$	22.5091	+	12.9957i	1.15016	+	0.664047i	0.201236	+	0.979543i	$0.435504\pi$
$384$	0.814901	+	3.04125i	0.0415852	+	0.155198i
$385$	−4.16750	−	3.45455i	−0.212395	−	0.176060i
$386$	6.69708	−	11.5997i	0.340872	−	0.590408i
$387$	42.4538	+	11.3754i	2.15805	+	0.578247i
$388$	6.70520	+	11.6138i	0.340405	+	0.589599i
$389$	10.8809			0.551682			0.275841	−	0.961203i	$-0.411044\pi$
$389$	10.8809			0.551682			0.275841	+	0.961203i	$0.411044\pi$
$390$	24.2663	−	7.45046i	1.22877	−	0.377269i
$391$	3.17014			0.160321
$392$	−3.17615	−	5.50126i	−0.160420	−	0.277855i
$393$	17.9690	+	4.81477i	0.906415	+	0.242873i
$394$	11.0122	−	19.0737i	0.554786	−	0.960917i
$395$	17.2703	−	1.61541i	0.868963	−	0.0812801i
$396$	−5.38218	−	20.0866i	−0.270465	−	1.00939i
$397$	24.0126	+	13.8637i	1.20516	+	0.695799i	0.961698	−	0.274112i	$-0.0883838\pi$
$397$	24.0126	+	13.8637i	1.20516	+	0.695799i	0.243461	+	0.969911i	$0.421717\pi$
$398$	11.3872			0.570791
$399$	10.2609	+	5.92412i	0.513686	+	0.296577i
$400$	3.25966	+	3.79139i	0.162983	+	0.189569i
$401$	−7.44840	+	27.7978i	−0.371955	+	1.38816i	0.485787	+	0.874077i	$0.338533\pi$
$401$	−7.44840	+	27.7978i	−0.371955	+	1.38816i	−0.857743	+	0.514079i	$0.828134\pi$
$402$	−9.83266	+	9.83266i	−0.490408	+	0.490408i
$403$	2.04175	−	1.82069i	0.101707	−	0.0906949i
$404$			10.4220i			0.518513i
$405$	−32.9287	+	23.3525i	−1.63624	+	1.16040i
$406$	−1.66477	−	2.88347i	−0.0826213	−	0.143104i
$407$	0.750792	+	2.80199i	0.0372154	+	0.138890i
$408$		−	22.8103i		−	1.12928i
$409$	−22.9783	+	6.15701i	−1.13620	+	0.304444i	−0.777423	−	0.628978i	$-0.783473\pi$
$409$	−22.9783	+	6.15701i	−1.13620	+	0.304444i	−0.358779	+	0.933423i	$0.616807\pi$
$410$	3.53998	−	1.31255i	0.174827	−	0.0648223i
$411$	−17.9780	−	17.9780i	−0.886789	−	0.886789i
$412$	−16.2977	+	4.36695i	−0.802929	+	0.215144i
$413$	−0.0340242	+	0.126980i	−0.00167422	+	0.00624828i
$414$	−2.92202	−	0.782952i	−0.143609	−	0.0384800i
$415$	−34.8299	+	3.25788i	−1.70973	+	0.159923i
$416$	1.97825	−	3.01438i	0.0969918	−	0.147792i
$417$	33.9786	+	33.9786i	1.66394	+	1.66394i
$418$	−12.1806	+	7.03248i	−0.595773	+	0.343970i
$419$	31.9711	−	18.4585i	1.56189	−	0.901757i	0.564823	−	0.825212i	$-0.308944\pi$
$419$	31.9711	−	18.4585i	1.56189	−	0.901757i	0.997066	−	0.0765449i	$-0.0243888\pi$
$420$	1.96980	+	5.31260i	0.0961164	+	0.259228i
$421$	10.2278	−	10.2278i	0.498473	−	0.498473i	−0.412489	−	0.910962i	$-0.635341\pi$
$421$	10.2278	−	10.2278i	0.498473	−	0.498473i	0.910962	+	0.412489i	$0.135341\pi$
$422$	1.35943	−	2.35460i	0.0661758	−	0.114620i
$423$	−5.95494	+	10.3143i	−0.289539	+	0.501496i
$424$	−5.01074	+	5.01074i	−0.243343	+	0.243343i
$425$	−15.7016	−	32.6438i	−0.761639	−	1.58346i
$426$	−27.7753	+	16.0361i	−1.34572	+	0.776950i
$427$	1.55980	−	0.900551i	0.0754840	−	0.0435807i
$428$	7.97603	+	7.97603i	0.385536	+	0.385536i
$429$	−18.7356	+	28.5486i	−0.904565	+	1.37834i
$430$	9.07230	−	10.9446i	0.437505	−	0.527797i
$431$	−13.9188	−	3.72952i	−0.670444	−	0.179645i	−0.0924890	−	0.995714i	$-0.529482\pi$
$431$	−13.9188	−	3.72952i	−0.670444	−	0.179645i	−0.577955	+	0.816069i	$0.696149\pi$
$432$	−3.18892	+	11.9012i	−0.153427	+	0.572598i
$433$	−10.7032	+	2.86792i	−0.514364	+	0.137823i	−0.506658	−	0.862147i	$-0.669119\pi$
$433$	−10.7032	+	2.86792i	−0.514364	+	0.137823i	−0.00770546	+	0.999970i	$0.502453\pi$
$434$	0.431773	+	0.431773i	0.0207257	+	0.0207257i
$435$	−10.1260	−	27.3100i	−0.485504	−	1.30942i
$436$	−7.84636	+	2.10242i	−0.375772	+	0.100688i
$437$			2.04605i			0.0978758i
$438$	−1.41751	−	5.29022i	−0.0677313	−	0.252777i
$439$	−2.21315	−	3.83328i	−0.105628	−	0.182953i	0.808367	−	0.588679i	$-0.200352\pi$
$439$	−2.21315	−	3.83328i	−0.105628	−	0.182953i	−0.913995	+	0.405727i	$0.867019\pi$
$440$	−6.63080	−	1.12822i	−0.316111	−	0.0537856i
$441$		−	43.9152i		−	2.09120i
$442$	−19.4958	+	17.3849i	−0.927320	+	0.826917i
$443$	8.69869	−	8.69869i	0.413287	−	0.413287i	−0.469595	−	0.882882i	$-0.655600\pi$
$443$	8.69869	−	8.69869i	0.413287	−	0.413287i	0.882882	+	0.469595i	$0.155600\pi$
$444$	0.785868	−	2.93290i	0.0372957	−	0.139189i
$445$	2.29511	−	13.4889i	0.108799	−	0.639437i
$446$	−23.9414	−	13.8226i	−1.13366	−	0.654519i
$447$	−34.9197			−1.65165
$448$	0.696972	+	0.402397i	0.0329289	+	0.0190115i
$449$	−5.78549	−	21.5917i	−0.273034	−	1.01898i	−0.957147	−	0.289601i	$-0.906477\pi$
$449$	−5.78549	−	21.5917i	−0.273034	−	1.01898i	0.684114	−	0.729376i	$-0.260189\pi$
$450$	6.41037	+	33.9667i	0.302188	+	1.60121i
$451$	−2.53943	+	4.39842i	−0.119577	+	0.207113i
$452$	16.7044	+	4.47593i	0.785708	+	0.210530i
$453$	−24.9453	−	43.2065i	−1.17203	−	2.03002i
$454$	3.45962			0.162368
$455$	3.03935	−	5.73258i	0.142487	−	0.268748i
$456$	14.7221			0.689424
$457$	−0.643128	−	1.11393i	−0.0300843	−	0.0521075i	0.850591	−	0.525827i	$-0.176244\pi$
$457$	−0.643128	−	1.11393i	−0.0300843	−	0.0521075i	−0.880676	+	0.473720i	$0.842911\pi$
$458$	12.1886	+	3.26592i	0.569535	+	0.152606i
$459$	44.6314	−	77.3039i	2.08322	−	3.60824i
$460$	−0.624431	+	0.753299i	−0.0291142	+	0.0351228i
$461$	−2.59056	−	9.66810i	−0.120654	−	0.450288i	0.878993	−	0.476834i	$-0.158216\pi$
$461$	−2.59056	−	9.66810i	−0.120654	−	0.450288i	−0.999648	+	0.0265460i	$0.991549\pi$
$462$	−6.60089	−	3.81103i	−0.307101	−	0.177305i
$463$	9.95491			0.462644			0.231322	−	0.972877i	$-0.425695\pi$
$463$	9.95491			0.462644			0.231322	+	0.972877i	$0.425695\pi$
$464$	−3.58287	−	2.06857i	−0.166331	−	0.0960310i
$465$	3.09006	+	4.35719i	0.143298	+	0.202060i
$466$	−0.444830	+	1.66013i	−0.0206064	+	0.0769040i
$467$	−3.56456	+	3.56456i	−0.164948	+	0.164948i	−0.784755	−	0.619807i	$-0.787211\pi$
$467$	−3.56456	+	3.56456i	−0.164948	+	0.164948i	0.619807	+	0.784755i	$0.287211\pi$
$468$	22.2636	−	11.2092i	1.02913	−	0.518147i
$469$			3.55437i			0.164125i
$470$	2.22842	+	3.14223i	0.102789	+	0.144940i
$471$	−4.74384	−	8.21658i	−0.218585	−	0.378600i
$472$	0.0422769	+	0.157780i	0.00194595	+	0.00726239i
$473$			19.1235i			0.879300i
$474$	23.5917	−	6.32137i	1.08360	−	0.290350i
$475$	21.0687	−	10.1340i	0.966699	−	0.464980i
$476$	−4.12281	−	4.12281i	−0.188969	−	0.188969i
$477$	−47.3199	+	12.6793i	−2.16663	+	0.580547i
$478$	3.87413	−	14.4584i	0.177199	−	0.661314i
$479$	−11.0757	−	2.96772i	−0.506061	−	0.135599i	−0.00324963	−	0.999995i	$-0.501034\pi$
$479$	−11.0757	−	2.96772i	−0.506061	−	0.135599i	−0.502812	+	0.864396i	$0.667701\pi$
$480$	5.42026	+	4.49301i	0.247400	+	0.205077i
$481$	−3.10568	+	1.56364i	−0.141607	+	0.0712959i
$482$	19.2134	+	19.2134i	0.875146	+	0.875146i
$483$	−0.960240	+	0.554395i	−0.0436924	+	0.0252258i
$484$	−1.69040	+	0.975956i	−0.0768366	+	0.0443616i
$485$	27.2526	+	12.5096i	1.23748	+	0.568032i
$486$	−14.0564	+	14.0564i	−0.637612	+	0.637612i
$487$	0.122308	−	0.211843i	0.00554230	−	0.00959954i	−0.863241	−	0.504792i	$-0.831569\pi$
$487$	0.122308	−	0.211843i	0.00554230	−	0.00959954i	0.868783	+	0.495193i	$0.164902\pi$
$488$	1.11898	−	1.93813i	0.0506539	−	0.0877352i
$489$	−14.7506	+	14.7506i	−0.667046	+	0.667046i
$490$	−12.9091	−	5.92561i	−0.583176	−	0.267692i
$491$	−17.4955	+	10.1011i	−0.789563	+	0.455854i	−0.839809	−	0.542882i	$-0.817333\pi$
$491$	−17.4955	+	10.1011i	−0.789563	+	0.455854i	0.0502457	+	0.998737i	$0.484000\pi$
$492$	4.60390	−	2.65807i	0.207560	−	0.119835i
$493$	21.1938	+	21.1938i	0.954519	+	0.954519i
$494$	−11.2205	−	12.5828i	−0.504832	−	0.566128i
$495$	−35.7992	−	29.6750i	−1.60906	−	1.33379i
$496$	0.732873	+	0.196373i	0.0329070	+	0.00881740i
$497$	−2.12178	+	7.91860i	−0.0951750	+	0.355198i
$498$	−47.5786	+	12.7486i	−2.13205	+	0.571280i
$499$	2.69714	+	2.69714i	0.120740	+	0.120740i	0.764895	−	0.644155i	$-0.222791\pi$
$499$	2.69714	+	2.69714i	0.120740	+	0.120740i	−0.644155	+	0.764895i	$0.722791\pi$
$500$	10.8497	+	2.69887i	0.485214	+	0.120697i
$501$	25.9821	−	6.96189i	1.16080	−	0.311034i
$502$		−	26.3937i		−	1.17801i
$503$	3.06353	+	11.4333i	0.136596	+	0.509784i	0.999986	+	0.00524701i	$0.00167018\pi$
$503$	3.06353	+	11.4333i	0.136596	+	0.509784i	−0.863390	+	0.504537i	$0.831663\pi$
$504$	2.78188	+	4.81836i	0.123915	+	0.214627i
$505$	13.4811	+	19.0092i	0.599899	+	0.845898i
$506$		−	1.31624i		−	0.0585139i
$507$	−38.0694	−	15.0354i	−1.69072	−	0.667747i
$508$	2.90863	−	2.90863i	0.129049	−	0.129049i
$509$	−3.40407	+	12.7042i	−0.150883	+	0.563102i	0.848540	+	0.529131i	$0.177482\pi$
$509$	−3.40407	+	12.7042i	−0.150883	+	0.563102i	−0.999423	+	0.0339709i	$0.989185\pi$
$510$	−29.5056	−	41.6049i	−1.30653	−	1.84230i
$511$	−1.21238	−	0.699966i	−0.0536324	−	0.0309647i
$512$	1.00000			0.0441942
$513$	49.8929	+	28.8057i	2.20283	+	1.27180i
$514$	0.525368	+	1.96070i	0.0231730	+	0.0864827i
$515$	−24.0775	+	29.0465i	−1.06098	+	1.27994i
$516$	10.0085	−	17.3352i	0.440598	−	0.763138i
$517$	−5.00549	−	1.34122i	−0.220141	−	0.0589866i
$518$	−0.388061	−	0.672141i	−0.0170504	−	0.0295322i
$519$	−11.3155			−0.496696
$520$	−0.290932	−	8.05701i	−0.0127582	−	0.353323i
$521$	−2.54807			−0.111633			−0.0558165	−	0.998441i	$-0.517776\pi$
$521$	−2.54807			−0.111633			−0.0558165	+	0.998441i	$0.517776\pi$
$522$	−14.3006	−	24.7693i	−0.625919	−	1.08412i
$523$	−13.1286	−	3.51781i	−0.574075	−	0.153823i	−0.0399102	−	0.999203i	$-0.512707\pi$
$523$	−13.1286	−	3.51781i	−0.574075	−	0.153823i	−0.534165	+	0.845380i	$0.679374\pi$
$524$	2.95421	−	5.11684i	0.129055	−	0.223530i
$525$	10.4648	+	7.14195i	0.456721	+	0.311700i
$526$	7.33845	+	27.3875i	0.319972	+	1.19415i
$527$	−4.76035	−	2.74839i	−0.207364	−	0.119722i
$528$	−9.47080			−0.412164
$529$	19.7528	+	11.4043i	0.858816	+	0.495838i
$530$	−2.65785	+	15.6209i	−0.115450	+	0.678527i
$531$	−0.292272	+	1.09077i	−0.0126835	+	0.0473355i
$532$	2.66091	−	2.66091i	0.115365	−	0.115365i
$533$	−5.78070	−	1.90907i	−0.250390	−	0.0826909i
$534$		−	19.2663i		−	0.833734i
$535$	24.8651	+	4.23074i	1.07501	+	0.182911i
$536$	2.20825	+	3.82479i	0.0953817	+	0.165206i
$537$	−5.54575	−	20.6970i	−0.239317	−	0.893142i
$538$		−	3.26537i		−	0.140780i
$539$	18.4567	−	4.94545i	0.794986	−	0.213016i
$540$	9.57804	+	25.8322i	0.412173	+	1.11164i
$541$	9.16253	+	9.16253i	0.393928	+	0.393928i	0.876085	−	0.482157i	$-0.160147\pi$
$541$	9.16253	+	9.16253i	0.393928	+	0.393928i	−0.482157	+	0.876085i	$0.660147\pi$
$542$	−5.31129	+	1.42316i	−0.228139	+	0.0611298i
$543$	9.43777	−	35.2222i	0.405014	−	1.51153i
$544$	−6.99788	−	1.87508i	−0.300032	−	0.0803933i
$545$	−11.5919	+	13.9842i	−0.496540	+	0.599015i
$546$	2.86502	−	8.67535i	0.122611	−	0.371271i
$547$	−22.6416	−	22.6416i	−0.968085	−	0.968085i	0.0314209	−	0.999506i	$-0.489997\pi$
$547$	−22.6416	−	22.6416i	−0.968085	−	0.968085i	−0.999506	+	0.0314209i	$0.989997\pi$
$548$	−6.99324	+	4.03755i	−0.298737	+	0.172476i
$549$	13.3988	−	7.73582i	0.571849	−	0.330157i
$550$	−13.5536	+	6.51927i	−0.577929	+	0.277983i
$551$	−13.6787	+	13.6787i	−0.582733	+	0.582733i
$552$	−0.688865	+	1.19315i	−0.0293200	+	0.0507838i
$553$	3.12149	−	5.40657i	0.132739	−	0.229911i
$554$	−15.1469	+	15.1469i	−0.643529	+	0.643529i
$555$	−2.36038	−	6.36601i	−0.100193	−	0.270222i
$556$	13.2173	−	7.63102i	0.560539	−	0.323627i
$557$	−26.0519	+	15.0411i	−1.10386	+	0.637311i	−0.937231	−	0.348709i	$-0.886620\pi$
$557$	−26.0519	+	15.0411i	−1.10386	+	0.637311i	−0.166624	+	0.986020i	$0.553287\pi$
$558$	3.70897	+	3.70897i	0.157013	+	0.157013i
$559$	−22.4442	+	4.65789i	−0.949288	+	0.197008i
$560$	1.79175	−	0.167595i	0.0757154	−	0.00708219i
$561$	66.2756	+	17.7585i	2.79816	+	0.749764i
$562$	−5.73406	+	21.3998i	−0.241877	+	0.902696i
$563$	23.6201	−	6.32898i	0.995468	−	0.266735i	0.275922	−	0.961180i	$-0.411017\pi$
$563$	23.6201	−	6.32898i	0.995468	−	0.266735i	0.719546	+	0.694445i	$0.244350\pi$
$564$	3.83546	+	3.83546i	0.161502	+	0.161502i
$565$	36.2577	−	13.4436i	1.52537	−	0.565576i
$566$	−8.71344	+	2.33476i	−0.366253	+	0.0981373i
$567$			14.5293i			0.610174i
$568$	2.63643	+	9.83928i	0.110622	+	0.412847i
$569$	10.6818	+	18.5014i	0.447805	+	0.775621i	0.998243	−	0.0592553i	$-0.0188726\pi$
$569$	10.6818	+	18.5014i	0.447805	+	0.775621i	−0.550438	+	0.834876i	$0.685539\pi$
$570$	26.8523	−	19.0433i	1.12472	−	0.797636i
$571$		−	21.6572i		−	0.906327i	−0.891427	−	0.453163i	$-0.850295\pi$
$571$		−	21.6572i		−	0.906327i	0.891427	−	0.453163i	$-0.149705\pi$
$572$	7.21820	+	8.09462i	0.301808	+	0.338453i
$573$	−10.3724	+	10.3724i	−0.433315	+	0.433315i
$574$	0.351697	−	1.31255i	0.0146795	−	0.0547848i
$575$	−0.164523	+	2.18170i	−0.00686110	+	0.0909831i
$576$	5.98707	+	3.45663i	0.249461	+	0.144026i
$577$	10.9211			0.454650			0.227325	−	0.973819i	$-0.427002\pi$
$577$	10.9211			0.454650			0.227325	+	0.973819i	$0.427002\pi$
$578$	30.7320	+	17.7431i	1.27828	+	0.738018i
$579$	−10.9149	−	40.7350i	−0.453608	−	1.69289i
$580$	−9.21072	+	0.861542i	−0.382454	+	0.0357736i
$581$	−6.29527	+	10.9037i	−0.261172	+	0.452363i
$582$	40.7844	+	10.9282i	1.69057	+	0.452986i
$583$	−10.6577	−	18.4598i	−0.441399	−	0.764525i
$584$	−1.73949			−0.0719806
$585$	26.1083	−	49.2435i	1.07945	−	2.03597i
$586$	−10.6978			−0.441920
$587$	14.1110	+	24.4409i	0.582423	+	1.00879i	0.995191	+	0.0979498i	$0.0312285\pi$
$587$	14.1110	+	24.4409i	0.582423	+	1.00879i	−0.412769	+	0.910836i	$0.635438\pi$
$588$	−19.3190	−	5.17650i	−0.796700	−	0.213475i
$589$	1.77384	−	3.07239i	0.0730899	−	0.126595i
$590$	0.281202	+	0.233096i	0.0115769	+	0.00959642i
$591$	−17.9477	−	66.9816i	−0.738268	−	2.75526i
$592$	−0.835172	−	0.482187i	−0.0343253	−	0.0198177i
$593$	−28.7595			−1.18101			−0.590506	−	0.807033i	$-0.701072\pi$
$593$	−28.7595			−1.18101			−0.590506	+	0.807033i	$0.701072\pi$
$594$	−32.0964	−	18.5309i	−1.31693	−	0.760332i
$595$	−12.8527	−	2.18687i	−0.526911	−	0.0896528i
$596$	−2.87051	+	10.7129i	−0.117581	+	0.438817i
$597$	25.3520	−	25.3520i	1.03759	−	1.03759i
$598$	1.54479	−	0.320594i	0.0631714	−	0.0131101i
$599$			7.62284i			0.311461i	0.987800	+	0.155730i	$0.0497731\pi$
$599$			7.62284i			0.311461i	−0.987800	+	0.155730i	$0.950227\pi$
$600$	15.6981	+	1.18381i	0.640872	+	0.0483287i
$601$	−8.07815	−	13.9918i	−0.329515	−	0.570736i	0.652901	−	0.757443i	$-0.273552\pi$
$601$	−8.07815	−	13.9918i	−0.329515	−	0.570736i	−0.982416	+	0.186707i	$0.940218\pi$
$602$	−1.32425	−	4.94217i	−0.0539724	−	0.201428i
$603$			30.5324i			1.24337i
$604$	−15.3057	+	4.10116i	−0.622781	+	0.166874i
$605$	−1.82080	+	3.96667i	−0.0740260	+	0.161268i
$606$	23.2030	+	23.2030i	0.942556	+	0.942556i
$607$	32.1964	−	8.62700i	1.30681	−	0.350159i	0.462790	−	0.886468i	$-0.346849\pi$
$607$	32.1964	−	8.62700i	1.30681	−	0.350159i	0.844022	+	0.536309i	$0.180182\pi$
$608$	1.21020	−	4.51652i	0.0490800	−	0.183169i
$609$	−10.1260	−	2.71325i	−0.410326	−	0.109946i
$610$	−0.466047	−	4.98249i	−0.0188697	−	0.201735i
$611$	0.354930	−	6.20134i	0.0143589	−	0.250879i
$612$	−35.4153	−	35.4153i	−1.43158	−	1.43158i
$613$	−36.4581	+	21.0491i	−1.47253	+	0.850164i	−0.999523	−	0.0308956i	$-0.990164\pi$
$613$	−36.4581	+	21.0491i	−1.47253	+	0.850164i	−0.473005	+	0.881060i	$0.656831\pi$
$614$	−11.1833	+	6.45668i	−0.451321	+	0.260570i
$615$	4.95904	−	10.8034i	0.199968	−	0.435637i
$616$	−1.71178	+	1.71178i	−0.0689697	+	0.0689697i
$617$	−6.28781	+	10.8908i	−0.253138	+	0.438447i	−0.964388	−	0.264491i	$-0.914796\pi$
$617$	−6.28781	+	10.8908i	−0.253138	+	0.438447i	0.711250	+	0.702939i	$0.248129\pi$
$618$	−26.5620	+	46.0067i	−1.06848	+	1.85066i
$619$	8.75232	−	8.75232i	0.351786	−	0.351786i	−0.508988	−	0.860774i	$-0.669980\pi$
$619$	8.75232	−	8.75232i	0.351786	−	0.351786i	0.860774	+	0.508988i	$0.169980\pi$
$620$	1.59074	−	0.589812i	0.0638856	−	0.0236874i
$621$	−4.66911	+	2.69571i	−0.187365	+	0.108175i
$622$	8.77630	−	5.06700i	0.351898	−	0.203168i
$623$	−3.48225	−	3.48225i	−0.139513	−	0.139513i
$624$	−2.30679	−	11.1154i	−0.0923456	−	0.444970i
$625$	23.2804	−	9.11172i	0.931216	−	0.364469i
$626$	−14.2680	−	3.82311i	−0.570266	−	0.152802i
$627$	−11.4615	+	42.7751i	−0.457730	+	1.70827i
$628$	−2.91069	+	0.779916i	−0.116149	+	0.0311221i
$629$	4.94030	+	4.94030i	0.196983	+	0.196983i
$630$	11.3067	+	5.19003i	0.450468	+	0.206776i
$631$	26.6071	−	7.12936i	1.05921	−	0.283815i	0.313159	−	0.949701i	$-0.398613\pi$
$631$	26.6071	−	7.12936i	1.05921	−	0.283815i	0.746054	+	0.665886i	$0.231946\pi$
$632$		−	7.75722i		−	0.308566i
$633$	−2.21560	−	8.26871i	−0.0880620	−	0.328652i
$634$	12.2254	+	21.1750i	0.485532	+	0.840966i
$635$	1.54283	−	9.06756i	0.0612252	−	0.359835i
$636$			22.3113i			0.884702i
$637$	10.2997	+	20.4570i	0.408088	+	0.810537i
$638$	8.79962	−	8.79962i	0.348380	−	0.348380i
$639$	−18.2263	+	68.0216i	−0.721022	+	2.69089i
$640$	1.82395	−	1.29352i	0.0720981	−	0.0511309i
$641$	25.0061	+	14.4373i	0.987680	+	0.570237i	0.904580	−	0.426304i	$-0.140185\pi$
$641$	25.0061	+	14.4373i	0.987680	+	0.570237i	0.0830998	+	0.996541i	$0.473518\pi$
$642$	35.5148			1.40166
$643$	−9.27773	−	5.35650i	−0.365878	−	0.211240i	0.305778	−	0.952103i	$-0.401083\pi$
$643$	−9.27773	−	5.35650i	−0.365878	−	0.211240i	−0.671656	+	0.740863i	$0.734417\pi$
$644$	0.0911459	+	0.340161i	0.00359165	+	0.0134042i
$645$	−4.16844	−	44.5647i	−0.164132	−	1.75473i
$646$	−16.9376	+	29.3369i	−0.666403	+	1.15424i
$647$	−38.4306	−	10.2974i	−1.51086	−	0.404834i	−0.594140	−	0.804362i	$-0.702508\pi$
$647$	−38.4306	−	10.2974i	−1.51086	−	0.404834i	−0.916721	+	0.399527i	$0.869174\pi$
$648$	9.02673	+	15.6348i	0.354604	+	0.614191i
$649$	−0.491344			−0.0192869
$650$	−10.9526	−	14.3193i	−0.429595	−	0.561648i
$651$	1.92255			0.0753508
$652$	3.31273	+	5.73782i	0.129737	+	0.224710i
$653$	45.3569	+	12.1534i	1.77495	+	0.475598i	0.989649	−	0.143511i	$-0.0458391\pi$
$653$	45.3569	+	12.1534i	1.77495	+	0.475598i	0.785306	+	0.619108i	$0.212506\pi$
$654$	−12.7880	+	22.1495i	−0.500050	+	0.866113i
$655$	−1.23040	−	13.1542i	−0.0480758	−	0.513977i
$656$	−0.437002	−	1.63091i	−0.0170621	−	0.0636765i
$657$	−10.4144	−	6.01278i	−0.406306	−	0.234581i
$658$	1.38647			0.0540501
$659$	−27.5684	−	15.9166i	−1.07391	−	0.620024i	−0.144665	−	0.989481i	$-0.546210\pi$
$659$	−27.5684	−	15.9166i	−1.07391	−	0.620024i	−0.929248	+	0.369457i	$0.879544\pi$
$660$	−17.2743	+	12.2507i	−0.672401	+	0.476857i
$661$	−1.26555	+	4.72310i	−0.0492243	+	0.183707i	−0.986161	−	0.165792i	$-0.946982\pi$
$661$	−1.26555	+	4.72310i	−0.0492243	+	0.183707i	0.936936	+	0.349500i	$0.113648\pi$
$662$	−0.847381	+	0.847381i	−0.0329344	+	0.0329344i
$663$	−4.69948	+	82.1094i	−0.182513	+	3.18886i
$664$			15.6444i			0.607121i
$665$	1.41143	−	8.29532i	0.0547329	−	0.321679i
$666$	−3.33348	−	5.77376i	−0.129170	−	0.223729i
$667$	−0.468546	−	1.74864i	−0.0181422	−	0.0677075i
$668$		−	8.54324i		−	0.330548i
$669$	−84.0760	+	22.5281i	−3.25057	+	0.870986i
$670$	8.97519	+	4.11983i	0.346742	+	0.159163i
$671$	4.76011	+	4.76011i	0.183762	+	0.183762i
$672$	2.44758	−	0.655828i	0.0944175	−	0.0252991i
$673$	−2.90751	+	10.8510i	−0.112076	+	0.418275i	−0.999052	−	0.0435423i	$-0.986136\pi$
$673$	−2.90751	+	10.8510i	−0.112076	+	0.418275i	0.886975	+	0.461817i	$0.152802\pi$
$674$	0.490309	+	0.131378i	0.0188860	+	0.00506048i
$675$	50.8844	+	34.7273i	1.95854	+	1.33666i
$676$	−7.74207	+	10.4432i	−0.297772	+	0.401661i
$677$	12.8047	+	12.8047i	0.492125	+	0.492125i	0.908975	−	0.416850i	$-0.136866\pi$
$677$	12.8047	+	12.8047i	0.492125	+	0.492125i	−0.416850	+	0.908975i	$0.636866\pi$
$678$	47.1548	−	27.2248i	1.81097	−	1.04556i
$679$	9.34669	−	5.39631i	0.358693	−	0.207091i
$680$	−15.1893	+	5.63186i	−0.582482	+	0.215972i
$681$	7.70233	−	7.70233i	0.295154	−	0.295154i
$682$	−1.14113	+	1.97649i	−0.0436960	+	0.0756836i
$683$	−20.8046	+	36.0346i	−0.796064	+	1.37882i	0.126097	+	0.992018i	$0.459755\pi$
$683$	−20.8046	+	36.0346i	−0.796064	+	1.37882i	−0.922161	+	0.386806i	$0.873578\pi$
$684$	22.8575	−	22.8575i	0.873978	−	0.873978i
$685$	−7.53269	+	16.4102i	−0.287809	+	0.627002i
$686$	−9.30619	+	5.37293i	−0.355312	+	0.205139i
$687$	34.4071	−	19.8650i	1.31271	−	0.757895i
$688$	−4.49546	−	4.49546i	−0.171388	−	0.171388i
$689$	19.0693	−	17.0046i	0.726483	−	0.647825i
$690$	0.286907	+	3.06731i	0.0109223	+	0.116770i
$691$	−17.8985	−	4.79589i	−0.680891	−	0.182444i	−0.0982353	−	0.995163i	$-0.531320\pi$
$691$	−17.8985	−	4.79589i	−0.680891	−	0.182444i	−0.582656	+	0.812719i	$0.697986\pi$
$692$	−0.930169	+	3.47144i	−0.0353597	+	0.131964i
$693$	−16.1656	+	4.33155i	−0.614079	+	0.164542i
$694$	−9.27544	−	9.27544i	−0.352091	−	0.352091i
$695$	14.2369	−	31.0155i	0.540035	−	1.17648i
$696$	−12.5821	+	3.37136i	−0.476923	+	0.127791i
$697$			12.2324i			0.463334i
$698$	−6.05431	−	22.5950i	−0.229159	−	0.855233i
$699$	2.70568	+	4.68638i	0.102338	+	0.177255i
$700$	3.05129	−	2.62336i	0.115328	−	0.0991536i
$701$		−	8.16233i		−	0.308287i	−0.988048	−	0.154143i	$-0.950738\pi$
$701$		−	8.16233i		−	0.308287i	0.988048	−	0.154143i	$-0.0492618\pi$
$702$	13.9310	−	42.1834i	0.525791	−	1.59211i
$703$	−3.18853	+	3.18853i	−0.120258	+	0.120258i
$704$	−0.778529	+	2.90551i	−0.0293419	+	0.109505i
$705$	11.9569	+	2.03445i	0.450325	+	0.0766218i
$706$	20.4439	+	11.8033i	0.769418	+	0.444223i
$707$	8.38755			0.315446
$708$	0.445396	+	0.257149i	0.0167390	+	0.00966426i
$709$	−4.24559	−	15.8447i	−0.159446	−	0.595062i	−0.998683	−	0.0512963i	$-0.983665\pi$
$709$	−4.24559	−	15.8447i	−0.159446	−	0.595062i	0.839237	−	0.543766i	$-0.183002\pi$
$710$	17.5360	+	14.5361i	0.658116	+	0.545530i
$711$	26.8139	−	46.4430i	1.00560	−	1.74175i
$712$	−5.91063	−	1.58375i	−0.221510	−	0.0593535i
$713$	0.166001	+	0.287522i	0.00621679	+	0.0107678i
$714$	−18.3576			−0.687017
$715$	23.6362	+	5.42731i	0.883944	+	0.202970i
$716$	−6.80543			−0.254331
$717$	−23.5644	−	40.8147i	−0.880028	−	1.52425i
$718$	12.4033	+	3.32344i	0.462885	+	0.124030i
$719$	−0.974618	+	1.68809i	−0.0363471	+	0.0629550i	−0.883627	−	0.468192i	$-0.844906\pi$
$719$	−0.974618	+	1.68809i	−0.0363471	+	0.0629550i	0.847280	+	0.531147i	$0.178239\pi$
$720$	15.3914	−	1.43966i	0.573602	−	0.0536529i
$721$	3.51450	+	13.1163i	0.130887	+	0.488476i
$722$	−2.47989	−	1.43177i	−0.0922920	−	0.0532848i
$723$	85.5514			3.18169
$724$	−10.0299	−	5.79075i	−0.372757	−	0.215212i
$725$	−15.6855	+	13.4857i	−0.582545	+	0.500845i
$726$	−1.59061	+	5.93625i	−0.0590332	+	0.220315i
$727$	27.9848	−	27.9848i	1.03790	−	1.03790i	0.0386462	−	0.999253i	$-0.487695\pi$
$727$	27.9848	−	27.9848i	1.03790	−	1.03790i	0.999253	−	0.0386462i	$-0.0123045\pi$
$728$	−2.42596	−	1.59209i	−0.0899121	−	0.0590067i
$729$			8.42862i			0.312171i
$730$	−3.17275	+	2.25007i	−0.117429	+	0.0832787i
$731$	23.0294	+	39.8880i	0.851772	+	1.47531i
$732$	−1.82372	−	6.80621i	−0.0674066	−	0.251565i
$733$		−	31.6699i		−	1.16975i	−0.811122	−	0.584877i	$-0.801143\pi$
$733$		−	31.6699i		−	1.16975i	0.811122	−	0.584877i	$-0.198857\pi$
$734$	−32.2992	+	8.65453i	−1.19218	+	0.319445i
$735$	−41.9328	+	15.5478i	−1.54671	+	0.573489i
$736$	0.309415	+	0.309415i	0.0114052	+	0.0114052i
$737$	−12.8322	+	3.43837i	−0.472679	+	0.126654i
$738$	3.02111	−	11.2749i	0.111209	−	0.415036i
$739$	12.8501	+	3.44317i	0.472699	+	0.126659i	0.487301	−	0.873234i	$-0.337982\pi$
$739$	12.8501	+	3.44317i	0.472699	+	0.126659i	−0.0146022	+	0.999893i	$0.504648\pi$
$740$	−2.14703	+	0.200827i	−0.0789265	+	0.00738254i
$741$	−52.9944	−	3.03310i	−1.94680	−	0.111424i
$742$	4.03262	+	4.03262i	0.148042	+	0.148042i
$743$	−10.2608	+	5.92409i	−0.376433	+	0.217334i	−0.676265	−	0.736658i	$-0.736403\pi$
$743$	−10.2608	+	5.92409i	−0.376433	+	0.217334i	0.299832	+	0.953992i	$0.403069\pi$
$744$	2.06883	−	1.19444i	0.0758469	−	0.0437902i
$745$	8.62167	+	23.2529i	0.315874	+	0.851919i
$746$	16.9338	−	16.9338i	0.619991	−	0.619991i
$747$	−54.0770	+	93.6641i	−1.97857	+	3.42699i
$748$	10.8961	−	18.8726i	0.398401	−	0.690051i
$749$	6.41906	−	6.41906i	0.234547	−	0.234547i
$750$	30.1639	−	18.1466i	1.10143	−	0.662621i
$751$	33.0412	−	19.0764i	1.20569	−	0.696106i	0.243876	−	0.969806i	$-0.421581\pi$
$751$	33.0412	−	19.0764i	1.20569	−	0.696106i	0.961815	+	0.273700i	$0.0882476\pi$
$752$	1.49195	−	0.861379i	0.0544059	−	0.0314112i
$753$	−58.7617	−	58.7617i	−2.14139	−	2.14139i
$754$	12.4709	+	8.18431i	0.454165	+	0.298055i
$755$	−22.6120	+	27.2786i	−0.822935	+	0.992770i
$756$	9.57804	+	2.56643i	0.348350	+	0.0933401i
$757$	−3.87261	+	14.4528i	−0.140752	+	0.525295i	0.859155	+	0.511715i	$0.170990\pi$
$757$	−3.87261	+	14.4528i	−0.140752	+	0.525295i	−0.999908	+	0.0135805i	$0.995677\pi$
$758$	3.86961	−	1.03686i	0.140551	−	0.0376604i
$759$	−2.93040	−	2.93040i	−0.106367	−	0.106367i
$760$	−3.63487	−	9.80333i	−0.131851	−	0.355604i
$761$	25.4496	−	6.81919i	0.922546	−	0.247195i	0.233873	−	0.972267i	$-0.424860\pi$
$761$	25.4496	−	6.81919i	0.922546	−	0.247195i	0.688673	+	0.725072i	$0.258193\pi$
$762$		−	12.9512i		−	0.469174i
$763$	1.69202	+	6.31470i	0.0612552	+	0.228608i
$764$	2.32947	+	4.03477i	0.0842774	+	0.145973i
$765$	−110.406	−	18.7854i	−3.99175	−	0.679188i
$766$		−	25.9913i		−	0.939105i
$767$	−0.119676	−	0.576663i	−0.00432125	−	0.0208221i
$768$	2.22635	−	2.22635i	0.0803365	−	0.0803365i
$769$	10.5098	−	39.2231i	0.378993	−	1.41442i	−0.468429	−	0.883501i	$-0.655180\pi$
$769$	10.5098	−	39.2231i	0.378993	−	1.41442i	0.847422	−	0.530920i	$-0.178153\pi$
$770$	−0.907983	+	5.33644i	−0.0327214	+	0.192312i
$771$	5.53486	+	3.19555i	0.199333	+	0.115085i
$772$	−13.3942			−0.482066
$773$	19.8145	+	11.4399i	0.712677	+	0.411464i	0.812052	−	0.583586i	$-0.198351\pi$
$773$	19.8145	+	11.4399i	0.712677	+	0.411464i	−0.0993742	+	0.995050i	$0.531684\pi$
$774$	−11.3754	−	42.4538i	−0.408882	−	1.52597i
$775$	2.13850	−	3.13344i	0.0768171	−	0.112557i
$776$	6.70520	−	11.6138i	0.240703	−	0.416909i
$777$	−2.36038	−	0.632462i	−0.0846782	−	0.0226895i
$778$	−5.44043	−	9.42310i	−0.195049	−	0.337835i
$779$	−7.89491			−0.282865
$780$	−18.5854	−	17.2900i	−0.665465	−	0.619081i
$781$	−30.6407			−1.09641
$782$	−1.58507	−	2.74542i	−0.0566820	−	0.0981762i
$783$	−49.2370	−	13.1930i	−1.75959	−	0.471480i
$784$	−3.17615	+	5.50126i	−0.113434	+	0.196474i
$785$	−4.30012	+	5.18757i	−0.153478	+	0.185152i
$786$	−4.81477	−	17.9690i	−0.171737	−	0.640932i
$787$	−23.9422	−	13.8230i	−0.853447	−	0.492738i	0.00836529	−	0.999965i	$-0.497337\pi$
$787$	−23.9422	−	13.8230i	−0.853447	−	0.492738i	−0.861812	+	0.507227i	$0.830671\pi$
$788$	−22.0244			−0.784586
$789$	77.3120	+	44.6361i	2.75238	+	1.58909i
$790$	−10.0341	−	14.1488i	−0.356998	−	0.503392i
$791$	3.60220	−	13.4436i	0.128080	−	0.477999i
$792$	−14.7044	+	14.7044i	−0.522497	+	0.522497i
$793$	−4.42726	+	6.74609i	−0.157217	+	0.239561i
$794$		−	27.7274i		−	0.984008i
$795$	28.8602	+	40.6948i	1.02356	+	1.44330i
$796$	−5.69362	−	9.86164i	−0.201805	−	0.349537i
$797$	−3.73648	−	13.9447i	−0.132353	−	0.493948i	0.867642	−	0.497190i	$-0.165635\pi$
$797$	−3.73648	−	13.9447i	−0.132353	−	0.493948i	−0.999995	+	0.00324171i	$0.998968\pi$
$798$		−	11.8482i		−	0.419423i
$799$	−12.0557	+	3.23030i	−0.426498	+	0.114280i
$800$	1.65361	−	4.71864i	0.0584638	−	0.166829i
$801$	−29.9129	−	29.9129i	−1.05692	−	1.05692i
$802$	27.7978	−	7.44840i	0.981575	−	0.263012i
$803$	1.35424	−	5.05410i	0.0477902	−	0.178355i
$804$	13.4317	+	3.59900i	0.473698	+	0.126927i
$805$	0.606251	+	0.502539i	0.0213675	+	0.0177122i
$806$	−2.59764	−	0.857865i	−0.0914979	−	0.0302170i
$807$	−7.26985	−	7.26985i	−0.255911	−	0.255911i
$808$	9.02570	−	5.21099i	0.317523	−	0.183322i
$809$	45.6891	−	26.3786i	1.60634	−	0.927423i	0.616165	−	0.787617i	$-0.288685\pi$
$809$	45.6891	−	26.3786i	1.60634	−	0.927423i	0.990179	−	0.139806i	$-0.0446480\pi$
$810$	36.6882	+	16.8408i	1.28909	+	0.591725i
$811$	31.7531	−	31.7531i	1.11500	−	1.11500i	0.122540	−	0.992464i	$-0.460896\pi$
$811$	31.7531	−	31.7531i	1.11500	−	1.11500i	0.992464	−	0.122540i	$-0.0391038\pi$
$812$	−1.66477	+	2.88347i	−0.0584221	+	0.101190i
$813$	−8.65635	+	14.9932i	−0.303591	+	0.525836i
$814$	2.05120	−	2.05120i	0.0718946	−	0.0718946i
$815$	13.4643	+	6.18043i	0.471633	+	0.216491i
$816$	−19.7543	+	11.4052i	−0.691539	+	0.399260i
$817$	−25.7442	+	14.8634i	−0.900676	+	0.520006i
$818$	16.8213	+	16.8213i	0.588141	+	0.588141i
$819$	−9.02112	−	17.9176i	−0.315224	−	0.626091i
$820$	−2.90669	−	2.40944i	−0.101506	−	0.0841412i
$821$	−51.2844	−	13.7416i	−1.78984	−	0.479586i	−0.797520	−	0.603293i	$-0.793855\pi$
$821$	−51.2844	−	13.7416i	−1.78984	−	0.479586i	−0.992319	+	0.123707i	$0.960522\pi$
$822$	−6.58040	+	24.5584i	−0.229518	+	0.856573i
$823$	−37.1169	+	9.94545i	−1.29381	+	0.346677i	−0.839108	−	0.543965i	$-0.816923\pi$
$823$	−37.1169	+	9.94545i	−1.29381	+	0.346677i	−0.454707	+	0.890641i	$0.650256\pi$
$824$	11.9307	+	11.9307i	0.415627	+	0.415627i
$825$	−15.6610	+	44.6893i	−0.545245	+	1.55588i
$826$	0.126980	−	0.0340242i	0.00441820	−	0.00118385i
$827$		−	51.3144i		−	1.78438i	−0.451664	−	0.892188i	$-0.649169\pi$
$827$		−	51.3144i		−	1.78438i	0.451664	−	0.892188i	$-0.350831\pi$
$828$	0.782952	+	2.92202i	0.0272095	+	0.101547i
$829$	−6.20374	−	10.7452i	−0.215465	−	0.373196i	0.737951	−	0.674854i	$-0.235793\pi$
$829$	−6.20374	−	10.7452i	−0.215465	−	0.373196i	−0.953416	+	0.301658i	$0.902460\pi$
$830$	20.2364	+	28.5347i	0.702415	+	0.990453i
$831$			67.4445i			2.33962i
$832$	−3.59966	−	0.206024i	−0.124796	−	0.00714261i
$833$	32.5416	−	32.5416i	1.12750	−	1.12750i
$834$	12.4370	−	46.4157i	0.430660	−	1.60724i
$835$	−11.0509	−	15.5825i	−0.382431	−	0.539254i
$836$	12.1806	+	7.03248i	0.421275	+	0.243223i
$837$	9.34831			0.323125
$838$	−31.9711	−	18.4585i	−1.10442	−	0.637639i
$839$	−2.61916	−	9.77485i	−0.0904235	−	0.337465i	0.905862	−	0.423572i	$-0.139224\pi$
$839$	−2.61916	−	9.77485i	−0.0904235	−	0.337465i	−0.996286	+	0.0861070i	$0.972557\pi$
$840$	3.61595	−	4.36220i	0.124762	−	0.150510i
$841$	−5.94203	+	10.2919i	−0.204898	+	0.354893i
$842$	−13.9715	−	3.74364i	−0.481488	−	0.129014i
$843$	34.8774	+	60.4094i	1.20124	+	2.08061i
$844$	−2.71885			−0.0935868
$845$	−0.612685	+	29.0624i	−0.0210770	+	0.999778i
$846$	11.9099			0.409470
$847$	0.785444	+	1.36043i	0.0269882	+	0.0467449i
$848$	6.84480	+	1.83406i	0.235051	+	0.0629818i
$849$	−14.2012	+	24.5972i	−0.487383	+	0.844172i
$850$	−20.4196	+	29.9199i	−0.700385	+	1.02624i
$851$	−0.109219	−	0.407610i	−0.00374397	−	0.0139727i
$852$	27.7753	+	16.0361i	0.951566	+	0.549387i
$853$	16.4655			0.563769			0.281884	−	0.959448i	$-0.409041\pi$
$853$	16.4655			0.563769			0.281884	+	0.959448i	$0.409041\pi$
$854$	−1.55980	−	0.900551i	−0.0533752	−	0.0308162i
$855$	12.1243	−	71.2576i	0.414643	−	2.43696i
$856$	2.91943	−	10.8955i	0.0997840	−	0.372399i
$857$	26.1677	−	26.1677i	0.893870	−	0.893870i	−0.101015	−	0.994885i	$-0.532209\pi$
$857$	26.1677	−	26.1677i	0.893870	−	0.893870i	0.994885	+	0.101015i	$0.0322089\pi$
$858$	34.0917	+	1.95122i	1.16387	+	0.0666135i
$859$		−	3.70443i		−	0.126394i	−0.998001	−	0.0631968i	$-0.979870\pi$
$859$		−	3.70443i		−	0.126394i	0.998001	−	0.0631968i	$-0.0201296\pi$
$860$	−14.0145	−	2.38453i	−0.477890	−	0.0813119i
$861$	−2.13920	−	3.70520i	−0.0729036	−	0.126273i
$862$	3.72952	+	13.9188i	0.127028	+	0.474075i
$863$			9.65640i			0.328708i	0.986401	+	0.164354i	$0.0525539\pi$
$863$			9.65640i			0.328708i	−0.986401	+	0.164354i	$0.947446\pi$
$864$	11.9012	−	3.18892i	0.404888	−	0.108489i
$865$	2.79379	+	7.53493i	0.0949919	+	0.256195i
$866$	7.83530	+	7.83530i	0.266254	+	0.266254i
$867$	107.923	−	28.9178i	3.66525	−	0.982100i
$868$	0.158040	−	0.589812i	0.00536422	−	0.0200195i
$869$	22.5387	+	6.03922i	0.764572	+	0.204867i
$870$	−18.5882	+	22.4244i	−0.630199	+	0.760258i
$871$	−7.16093	−	14.2229i	−0.242639	−	0.481925i
$872$	5.74393	+	5.74393i	0.194514	+	0.194514i
$873$	80.2890	−	46.3549i	2.71737	−	1.56887i
$874$	1.77193	−	1.02302i	0.0599364	−	0.0346043i
$875$	2.17203	−	8.73178i	0.0734282	−	0.295188i
$876$	−3.87271	+	3.87271i	−0.130847	+	0.130847i
$877$	1.65175	−	2.86091i	0.0557755	−	0.0966060i	−0.836790	−	0.547525i	$-0.815570\pi$
$877$	1.65175	−	2.86091i	0.0557755	−	0.0966060i	0.892565	+	0.450919i	$0.148904\pi$
$878$	−2.21315	+	3.83328i	−0.0746901	+	0.129367i
$879$	−23.8169	+	23.8169i	−0.803325	+	0.803325i
$880$	2.33834	+	6.30655i	0.0788253	+	0.212594i
$881$	6.11016	−	3.52770i	0.205857	−	0.118851i	−0.393528	−	0.919313i	$-0.628745\pi$
$881$	6.11016	−	3.52770i	0.205857	−	0.118851i	0.599384	+	0.800461i	$0.295412\pi$
$882$	−38.0317	+	21.9576i	−1.28059	+	0.739351i
$883$	22.1294	+	22.1294i	0.744714	+	0.744714i	0.973481	−	0.228767i	$-0.0734694\pi$
$883$	22.1294	+	22.1294i	0.744714	+	0.744714i	−0.228767	+	0.973481i	$0.573469\pi$
$884$	24.8037	+	8.19138i	0.834238	+	0.275506i
$885$	1.14501	−	0.107101i	0.0384890	−	0.00360015i
$886$	−11.8826	−	3.18394i	−0.399205	−	0.106967i
$887$	−9.59340	+	35.8031i	−0.322115	+	1.20215i	0.595066	+	0.803677i	$0.297126\pi$
$887$	−9.59340	+	35.8031i	−0.322115	+	1.20215i	−0.917180	+	0.398472i	$0.869541\pi$
$888$	−2.93290	+	0.785868i	−0.0984217	+	0.0263720i
$889$	−2.34085	−	2.34085i	−0.0785095	−	0.0785095i
$890$	−12.8293	+	4.75684i	−0.430040	+	0.159450i
$891$	−52.4545	+	14.0551i	−1.75729	+	0.470865i
$892$			27.6452i			0.925630i
$893$	−2.08488	−	7.78087i	−0.0697677	−	0.260377i
$894$	17.4599	+	30.2414i	0.583945	+	1.01142i
$895$	−12.4128	+	8.80297i	−0.414914	+	0.294251i
$896$		−	0.804795i		−	0.0268863i
$897$	2.72550	−	4.15301i	0.0910017	−	0.138665i
$898$	−15.8062	+	15.8062i	−0.527461	+	0.527461i
$899$	−0.812422	+	3.03200i	−0.0270958	+	0.101123i
$900$	26.2109	−	22.5349i	0.873696	−	0.751164i
$901$	−44.4601	−	25.6691i	−1.48118	−	0.855160i
$902$	5.07885			0.169107
$903$	−13.9512	−	8.05476i	−0.464268	−	0.268046i
$904$	−4.47593	−	16.7044i	−0.148867	−	0.555579i
$905$	−25.7845	+	2.41180i	−0.857105	+	0.0801709i
$906$	−24.9453	+	43.2065i	−0.828752	+	1.43544i
$907$	−34.0294	−	9.11815i	−1.12993	−	0.302763i	−0.355033	−	0.934854i	$-0.615530\pi$
$907$	−34.0294	−	9.11815i	−1.12993	−	0.302763i	−0.774895	+	0.632090i	$0.782197\pi$
$908$	−1.72981	−	2.99612i	−0.0574058	−	0.0994297i
$909$	72.0499			2.38975
$910$	−6.48423	+	0.234140i	−0.214950	+	0.00776168i
$911$	−45.7346			−1.51525			−0.757627	−	0.652687i	$-0.773642\pi$
$911$	−45.7346			−1.51525			−0.757627	+	0.652687i	$0.773642\pi$
$912$	−7.36103	−	12.7497i	−0.243748	−	0.422184i
$913$	−45.4550	−	12.1796i	−1.50434	−	0.403087i
$914$	−0.643128	+	1.11393i	−0.0212728	+	0.0368456i
$915$	−12.1304	−	10.0552i	−0.401017	−	0.332414i
$916$	−3.26592	−	12.1886i	−0.107909	−	0.402722i
$917$	−4.11800	−	2.37753i	−0.135988	−	0.0785130i
$918$	−89.2629			−2.94611
$919$	−18.5669	−	10.7196i	−0.612464	−	0.353606i	0.161465	−	0.986878i	$-0.448378\pi$
$919$	−18.5669	−	10.7196i	−0.612464	−	0.353606i	−0.773929	+	0.633272i	$0.781711\pi$
$920$	0.964592	+	0.164123i	0.0318017	+	0.00541098i
$921$	−10.5231	+	39.2728i	−0.346748	+	1.29408i
$922$	−7.07754	+	7.07754i	−0.233086	+	0.233086i
$923$	−7.46311	−	35.9612i	−0.245651	−	1.18368i
$924$			7.62205i			0.250747i
$925$	−3.65631	+	3.14353i	−0.120219	+	0.103359i
$926$	−4.97746	−	8.62121i	−0.163569	−	0.283310i
$927$	30.1899	+	112.670i	0.991566	+	3.70058i
$928$			4.13714i			0.135808i
$929$	−6.50804	+	1.74382i	−0.213522	+	0.0572130i	−0.363994	−	0.931401i	$-0.618587\pi$
$929$	−6.50804	+	1.74382i	−0.213522	+	0.0572130i	0.150472	+	0.988614i	$0.451921\pi$
$930$	2.22841	−	4.85467i	0.0730725	−	0.159191i
$931$	21.0028	+	21.0028i	0.688338	+	0.688338i
$932$	1.66013	−	0.444830i	0.0543793	−	0.0145709i
$933$	8.25820	−	30.8200i	0.270361	−	1.00900i
$934$	4.86928	+	1.30472i	0.159328	+	0.0426917i
$935$	−4.53814	−	48.5171i	−0.148413	−	1.58668i
$936$	−20.8392	−	13.6762i	−0.681152	−	0.447020i
$937$	−18.4026	−	18.4026i	−0.601188	−	0.601188i	0.339440	−	0.940628i	$-0.389763\pi$
$937$	−18.4026	−	18.4026i	−0.601188	−	0.601188i	−0.940628	+	0.339440i	$0.889763\pi$
$938$	3.07817	−	1.77718i	0.100506	−	0.0580271i
$939$	−40.2772	+	23.2541i	−1.31440	+	0.758868i
$940$	1.60704	−	3.50098i	0.0524158	−	0.114190i
$941$	32.3684	−	32.3684i	1.05518	−	1.05518i	0.0567952	−	0.998386i	$-0.481912\pi$
$941$	32.3684	−	32.3684i	1.05518	−	1.05518i	0.998386	−	0.0567952i	$-0.0180882\pi$
$942$	−4.74384	+	8.21658i	−0.154563	+	0.267710i
$943$	0.369414	−	0.639843i	0.0120298	−	0.0208362i
$944$	0.115503	−	0.115503i	0.00375929	−	0.00375929i
$945$	20.7896	−	7.70836i	0.676286	−	0.250753i
$946$	16.5614	−	9.56175i	0.538459	−	0.310879i
$947$	25.0053	−	14.4368i	0.812562	−	0.469133i	−0.0352831	−	0.999377i	$-0.511233\pi$
$947$	25.0053	−	14.4368i	0.812562	−	0.469133i	0.847845	+	0.530245i	$0.177900\pi$
$948$	−17.2703	−	17.2703i	−0.560913	−	0.560913i
$949$	6.26157	+	0.358377i	0.203259	+	0.0116334i
$950$	−19.3107	−	13.1790i	−0.626520	−	0.427584i
$951$	74.3609	+	19.9249i	2.41132	+	0.646111i
$952$	−1.50905	+	5.63186i	−0.0489087	+	0.182530i
$953$	−17.0854	+	4.57801i	−0.553449	+	0.148296i	−0.524695	−	0.851290i	$-0.675821\pi$
$953$	−17.0854	+	4.57801i	−0.553449	+	0.148296i	−0.0287541	+	0.999587i	$0.509154\pi$
$954$	34.6406	+	34.6406i	1.12153	+	1.12153i
$955$	9.46791	+	4.34600i	0.306374	+	0.140633i
$956$	−14.4584	+	3.87413i	−0.467620	+	0.125298i
$957$		−	39.1820i		−	1.26658i
$958$	2.96772	+	11.0757i	0.0958828	+	0.357839i
$959$	3.24940	+	5.62812i	0.104929	+	0.181742i
$960$	1.18093	−	6.94059i	0.0381142	−	0.224006i
$961$			30.4243i			0.981430i
$962$	2.90699	+	1.90777i	0.0937252	+	0.0615091i
$963$	55.1404	−	55.1404i	1.77687	−	1.77687i
$964$	7.03259	−	26.2460i	0.226504	−	0.845326i
$965$	−24.4303	+	17.3256i	−0.786439	+	0.557732i
$966$	0.960240	+	0.554395i	0.0308952	+	0.0178374i
$967$	0.721666			0.0232072			0.0116036	−	0.999933i	$-0.496306\pi$
$967$	0.721666			0.0232072			0.0116036	+	0.999933i	$0.496306\pi$
$968$	1.69040	+	0.975956i	0.0543317	+	0.0313684i
$969$	27.6050	+	103.023i	0.886800	+	3.30958i
$970$	−2.79266	−	29.8563i	−0.0896670	−	0.958627i
$971$	15.4150	−	26.6996i	0.494691	−	0.856830i	−0.505290	−	0.862950i	$-0.668615\pi$
$971$	15.4150	−	26.6996i	0.494691	−	0.856830i	0.999981	+	0.00611936i	$0.00194787\pi$
$972$	19.2014	+	5.14501i	0.615886	+	0.165026i
$973$	−6.14140	−	10.6372i	−0.196884	−	0.341014i
$974$	−0.244616			−0.00783799
$975$	−56.2639	−	7.49549i	−1.80189	−	0.240048i
$976$	−2.23796			−0.0716355
$977$	9.26370	+	16.0452i	0.296372	+	0.513331i	0.975303	−	0.220871i	$-0.0708899\pi$
$977$	9.26370	+	16.0452i	0.296372	+	0.513331i	−0.678931	+	0.734202i	$0.737557\pi$
$978$	20.1497	+	5.39910i	0.644317	+	0.172644i
$979$	9.20319	−	15.9404i	0.294135	−	0.509457i
$980$	1.32284	+	14.1425i	0.0422566	+	0.451764i
$981$	14.5346	+	54.2440i	0.464055	+	1.73188i
$982$	17.4955	+	10.1011i	0.558305	+	0.322338i
$983$	−2.90661			−0.0927066			−0.0463533	−	0.998925i	$-0.514760\pi$
$983$	−2.90661			−0.0927066			−0.0463533	+	0.998925i	$0.514760\pi$
$984$	−4.60390	−	2.65807i	−0.146767	−	0.0847360i
$985$	−40.1714	+	28.4890i	−1.27997	+	0.907734i
$986$	7.75746	−	28.9512i	0.247048	−	0.921995i
$987$	3.08676	−	3.08676i	0.0982526	−	0.0982526i
$988$	−5.28681	+	16.0086i	−0.168196	+	0.509302i
$989$		−	2.78192i		−	0.0884599i
$990$	−7.79967	+	45.8405i	−0.247890	+	1.45691i
$991$	25.5607	+	44.2724i	0.811961	+	1.40636i	0.911489	+	0.411323i	$0.134933\pi$
$991$	25.5607	+	44.2724i	0.811961	+	1.40636i	−0.0995281	+	0.995035i	$0.531733\pi$
$992$	−0.196373	−	0.732873i	−0.00623484	−	0.0232687i
$993$			3.77313i			0.119737i
$994$	7.91860	−	2.12178i	0.251163	−	0.0672989i
$995$	−23.1411	−	10.6223i	−0.733623	−	0.336751i
$996$	34.8299	+	34.8299i	1.10363	+	1.10363i
$997$	3.73922	−	1.00192i	0.118422	−	0.0317312i	−0.199121	−	0.979975i	$-0.563809\pi$
$997$	3.73922	−	1.00192i	0.118422	−	0.0317312i	0.317543	+	0.948244i	$0.397142\pi$
$998$	0.987220	−	3.68436i	0.0312499	−	0.116626i
$999$	−11.4772	−	3.07531i	−0.363123	−	0.0972986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.s.a.67.1	yes	12
5.2	odd	4		650.2.t.e.93.1		12
5.3	odd	4		130.2.p.a.93.3	yes	12
5.4	even	2		650.2.w.e.457.3		12
13.7	odd	12		130.2.p.a.7.3	✓	12
65.7	even	12		650.2.w.e.293.3		12
65.33	even	12	inner	130.2.s.a.33.1	yes	12
65.59	odd	12		650.2.t.e.7.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.a.7.3	✓	12	13.7	odd	12
130.2.p.a.93.3	yes	12	5.3	odd	4
130.2.s.a.33.1	yes	12	65.33	even	12	inner
130.2.s.a.67.1	yes	12	1.1	even	1	trivial
650.2.t.e.7.1		12	65.59	odd	12
650.2.t.e.93.1		12	5.2	odd	4
650.2.w.e.293.3		12	65.7	even	12
650.2.w.e.457.3		12	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.s (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-3.04125 - 0.814901i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.208246 + 2.22635i) q^{5} +(0.814901 + 3.04125i) q^{6} +(0.696972 + 0.402397i) q^{7} +1.00000 q^{8} +(5.98707 + 3.45663i) q^{9} +(1.82395 - 1.29352i) q^{10} +(-0.778529 + 2.90551i) q^{11} +(2.22635 - 2.22635i) q^{12} +(-3.59966 - 0.206024i) q^{13} -0.804795i q^{14} +(1.18093 - 6.94059i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87508 + 6.99788i) q^{17} -6.91327i q^{18} +(-4.51652 + 1.21020i) q^{19} +(-2.03220 - 0.932829i) q^{20} +(-1.79175 - 1.79175i) q^{21} +(2.90551 - 0.778529i) q^{22} +(0.113254 - 0.422668i) q^{23} +(-3.04125 - 0.814901i) q^{24} +(-4.91327 + 0.927256i) q^{25} +(1.62141 + 3.22041i) q^{26} +(-8.71230 - 8.71230i) q^{27} +(-0.696972 + 0.402397i) q^{28} +(3.58287 - 2.06857i) q^{29} +(-6.60119 + 2.44758i) q^{30} +(-0.536500 + 0.536500i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(4.73540 - 8.20196i) q^{33} +(5.12281 - 5.12281i) q^{34} +(-0.750735 + 1.63550i) q^{35} +(-5.98707 + 3.45663i) q^{36} +(0.835172 - 0.482187i) q^{37} +(3.30632 + 3.30632i) q^{38} +(10.7796 + 3.55994i) q^{39} +(0.208246 + 2.22635i) q^{40} +(1.63091 + 0.437002i) q^{41} +(-0.655828 + 2.44758i) q^{42} +(6.14091 - 1.64545i) q^{43} +(-2.12698 - 2.12698i) q^{44} +(-6.44889 + 14.0491i) q^{45} +(-0.422668 + 0.113254i) q^{46} +1.72276i q^{47} +(0.814901 + 3.04125i) q^{48} +(-3.17615 - 5.50126i) q^{49} +(3.25966 + 3.79139i) q^{50} -22.8103i q^{51} +(1.97825 - 3.01438i) q^{52} +(-5.01074 + 5.01074i) q^{53} +(-3.18892 + 11.9012i) q^{54} +(-6.63080 - 1.12822i) q^{55} +(0.696972 + 0.402397i) q^{56} +14.7221 q^{57} +(-3.58287 - 2.06857i) q^{58} +(0.0422769 + 0.157780i) q^{59} +(5.42026 + 4.49301i) q^{60} +(1.11898 - 1.93813i) q^{61} +(0.732873 + 0.196373i) q^{62} +(2.78188 + 4.81836i) q^{63} +1.00000 q^{64} +(-0.290932 - 8.05701i) q^{65} -9.47080 q^{66} +(2.20825 + 3.82479i) q^{67} +(-6.99788 - 1.87508i) q^{68} +(-0.688865 + 1.19315i) q^{69} +(1.79175 - 0.167595i) q^{70} +(2.63643 + 9.83928i) q^{71} +(5.98707 + 3.45663i) q^{72} -1.73949 q^{73} +(-0.835172 - 0.482187i) q^{74} +(15.6981 + 1.18381i) q^{75} +(1.21020 - 4.51652i) q^{76} +(-1.71178 + 1.71178i) q^{77} +(-2.30679 - 11.1154i) q^{78} -7.75722i q^{79} +(1.82395 - 1.29352i) q^{80} +(9.02673 + 15.6348i) q^{81} +(-0.437002 - 1.63091i) q^{82} +15.6444i q^{83} +(2.44758 - 0.655828i) q^{84} +(-15.1893 + 5.63186i) q^{85} +(-4.49546 - 4.49546i) q^{86} +(-12.5821 + 3.37136i) q^{87} +(-0.778529 + 2.90551i) q^{88} +(-5.91063 - 1.58375i) q^{89} +(15.3914 - 1.43966i) q^{90} +(-2.42596 - 1.59209i) q^{91} +(0.309415 + 0.309415i) q^{92} +(2.06883 - 1.19444i) q^{93} +(1.49195 - 0.861379i) q^{94} +(-3.63487 - 9.80333i) q^{95} +(2.22635 - 2.22635i) q^{96} +(6.70520 - 11.6138i) q^{97} +(-3.17615 + 5.50126i) q^{98} +(-14.7044 + 14.7044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 6 q^{7} + 12 q^{8} + 24 q^{9} + 6 q^{11} - 6 q^{13} - 6 q^{15} - 6 q^{16} - 36 q^{19} - 24 q^{21} + 6 q^{23} + 12 q^{25} + 6 q^{26} - 12 q^{27} - 6 q^{28} - 6 q^{29} - 18 q^{30}+ \cdots - 54 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 6 * q^7 + 12 * q^8 + 24 * q^9 + 6 * q^11 - 6 * q^13 - 6 * q^15 - 6 * q^16 - 36 * q^19 - 24 * q^21 + 6 * q^23 + 12 * q^25 + 6 * q^26 - 12 * q^27 - 6 * q^28 - 6 * q^29 - 18 * q^30 - 24 * q^31 - 6 * q^32 + 18 * q^33 + 12 * q^34 - 12 * q^35 - 24 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^39 + 18 * q^41 + 18 * q^42 - 6 * q^44 - 18 * q^45 - 6 * q^46 + 6 * q^50 + 18 * q^53 + 6 * q^54 - 6 * q^55 + 6 * q^56 + 6 * q^58 - 18 * q^59 + 24 * q^60 + 18 * q^61 + 36 * q^62 + 12 * q^64 + 42 * q^65 - 36 * q^66 + 24 * q^67 - 12 * q^68 + 42 * q^69 + 24 * q^70 + 18 * q^71 + 24 * q^72 - 12 * q^73 - 6 * q^74 + 24 * q^75 + 30 * q^76 - 30 * q^77 + 30 * q^78 + 30 * q^81 - 18 * q^82 + 6 * q^84 - 42 * q^85 - 60 * q^87 + 6 * q^88 - 6 * q^89 + 12 * q^90 - 6 * q^91 - 30 * q^93 - 24 * q^94 - 24 * q^95 + 6 * q^97 - 54 * q^99

Introduction

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