LMFDB - Embedded newform 650.2.w.e.293.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(193,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.193"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,6,0,-6,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.3
Root			$-1.62980i$ of defining polynomial
Character	$\chi$	$=$	650.293
Dual form			650.2.w.e.457.3

$q$-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} +(0.814901 - 3.04125i) q^{6} +(-0.696972 + 0.402397i) q^{7} -1.00000 q^{8} +(5.98707 - 3.45663i) q^{9} +(-0.778529 - 2.90551i) q^{11} +(-2.22635 - 2.22635i) q^{12} +(3.59966 - 0.206024i) q^{13} +0.804795i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.87508 + 6.99788i) q^{17} -6.91327i q^{18} +(-4.51652 - 1.21020i) q^{19} +(-1.79175 + 1.79175i) q^{21} +(-2.90551 - 0.778529i) q^{22} +(-0.113254 - 0.422668i) q^{23} +(-3.04125 + 0.814901i) q^{24} +(1.62141 - 3.22041i) q^{26} +(8.71230 - 8.71230i) q^{27} +(0.696972 + 0.402397i) q^{28} +(3.58287 + 2.06857i) q^{29} +(-0.536500 - 0.536500i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.73540 - 8.20196i) q^{33} +(5.12281 + 5.12281i) q^{34} +(-5.98707 - 3.45663i) q^{36} +(-0.835172 - 0.482187i) q^{37} +(-3.30632 + 3.30632i) q^{38} +(10.7796 - 3.55994i) q^{39} +(1.63091 - 0.437002i) q^{41} +(0.655828 + 2.44758i) q^{42} +(-6.14091 - 1.64545i) q^{43} +(-2.12698 + 2.12698i) q^{44} +(-0.422668 - 0.113254i) q^{46} +1.72276i q^{47} +(-0.814901 + 3.04125i) q^{48} +(-3.17615 + 5.50126i) q^{49} +22.8103i q^{51} +(-1.97825 - 3.01438i) q^{52} +(5.01074 + 5.01074i) q^{53} +(-3.18892 - 11.9012i) q^{54} +(0.696972 - 0.402397i) q^{56} -14.7221 q^{57} +(3.58287 - 2.06857i) q^{58} +(0.0422769 - 0.157780i) q^{59} +(1.11898 + 1.93813i) q^{61} +(-0.732873 + 0.196373i) q^{62} +(-2.78188 + 4.81836i) q^{63} +1.00000 q^{64} -9.47080 q^{66} +(-2.20825 + 3.82479i) q^{67} +(6.99788 - 1.87508i) q^{68} +(-0.688865 - 1.19315i) q^{69} +(2.63643 - 9.83928i) q^{71} +(-5.98707 + 3.45663i) q^{72} +1.73949 q^{73} +(-0.835172 + 0.482187i) q^{74} +(1.21020 + 4.51652i) q^{76} +(1.71178 + 1.71178i) q^{77} +(2.30679 - 11.1154i) q^{78} +7.75722i q^{79} +(9.02673 - 15.6348i) q^{81} +(0.437002 - 1.63091i) q^{82} +15.6444i q^{83} +(2.44758 + 0.655828i) q^{84} +(-4.49546 + 4.49546i) q^{86} +(12.5821 + 3.37136i) q^{87} +(0.778529 + 2.90551i) q^{88} +(-5.91063 + 1.58375i) q^{89} +(-2.42596 + 1.59209i) q^{91} +(-0.309415 + 0.309415i) q^{92} +(-2.06883 - 1.19444i) q^{93} +(1.49195 + 0.861379i) q^{94} +(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^{16} - 36 q^{19} - 24 q^{21} - 6 q^{23} + 6 q^{26} + 12 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{31} + 6 q^{32} - 18 q^{33}+ \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^16 - 36 * q^19 - 24 * q^21 - 6 * q^23 + 6 * q^26 + 12 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^31 + 6 * q^32 - 18 * q^33 + 12 * q^34 - 24 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 18 * q^41 - 18 * q^42 - 6 * q^44 - 6 * q^46 - 18 * q^53 + 6 * q^54 + 6 * q^56 - 6 * q^58 - 18 * q^59 + 18 * q^61 - 36 * q^62 + 12 * q^64 - 36 * q^66 - 24 * q^67 + 12 * q^68 + 42 * q^69 + 18 * q^71 - 24 * q^72 + 12 * q^73 - 6 * q^74 + 30 * q^76 + 30 * q^77 - 30 * q^78 + 30 * q^81 + 18 * q^82 + 6 * q^84 + 60 * q^87 - 6 * q^88 - 6 * q^89 - 6 * q^91 + 30 * q^93 - 24 * q^94 - 6 * q^97 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{11}{12}\right)$

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	$-0.220254\pi$
$3$	3.04125	−	0.814901i	1.75587	−	0.470483i	0.985863	+	0.167556i	$0.0535874\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.814901	−	3.04125i	0.332682	−	1.24159i
$7$	−0.696972	+	0.402397i	−0.263431	+	0.152092i	−0.625899	−	0.779904i	$-0.715268\pi$
$7$	−0.696972	+	0.402397i	−0.263431	+	0.152092i	0.362468	+	0.931996i	$0.381934\pi$
$8$	−1.00000			−0.353553
$9$	5.98707	−	3.45663i	1.99569	−	1.15221i
$10$		0			0
$11$	−0.778529	−	2.90551i	−0.234735	−	0.876044i	−0.978268	−	0.207344i	$-0.933518\pi$
$11$	−0.778529	−	2.90551i	−0.234735	−	0.876044i	0.743533	−	0.668700i	$-0.233149\pi$
$12$	−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
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.87508	+	6.99788i	−0.454773	+	1.69724i	0.233981	+	0.972241i	$0.424825\pi$
$17$	−1.87508	+	6.99788i	−0.454773	+	1.69724i	−0.688754	+	0.724995i	$0.741842\pi$
$18$		−	6.91327i		−	1.62947i
$19$	−4.51652	−	1.21020i	−1.03616	−	0.277638i	−0.299639	−	0.954053i	$-0.596866\pi$
$19$	−4.51652	−	1.21020i	−1.03616	−	0.277638i	−0.736521	+	0.676414i	$0.763533\pi$
$20$		0			0
$21$	−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	$-0.0978599\pi$
$23$	−0.113254	−	0.422668i	−0.0236150	−	0.0881324i	−0.976728	+	0.214483i	$0.931193\pi$
$24$	−3.04125	+	0.814901i	−0.620793	+	0.166341i
$25$		0			0
$26$	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	0.794302	−	0.607523i	$-0.207837\pi$
$29$	3.58287	+	2.06857i	0.665322	+	0.384124i	−0.128980	+	0.991647i	$0.541170\pi$
$30$		0			0
$31$	−0.536500	−	0.536500i	−0.0963583	−	0.0963583i	0.657284	−	0.753643i	$-0.271705\pi$
$31$	−0.536500	−	0.536500i	−0.0963583	−	0.0963583i	−0.753643	+	0.657284i	$0.771705\pi$
$32$	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			0
$36$	−5.98707	−	3.45663i	−0.997844	−	0.576106i
$37$	−0.835172	−	0.482187i	−0.137301	−	0.0792710i	0.429776	−	0.902936i	$-0.358593\pi$
$37$	−0.835172	−	0.482187i	−0.137301	−	0.0792710i	−0.567077	+	0.823665i	$0.691926\pi$
$38$	−3.30632	+	3.30632i	−0.536356	+	0.536356i
$39$	10.7796	−	3.55994i	1.72611	−	0.570046i
$40$		0			0
$41$	1.63091	−	0.437002i	0.254706	−	0.0682483i	−0.129207	−	0.991618i	$-0.541243\pi$
$41$	1.63091	−	0.437002i	0.254706	−	0.0682483i	0.383913	+	0.923369i	$0.374576\pi$
$42$	0.655828	+	2.44758i	0.101196	+	0.377670i
$43$	−6.14091	−	1.64545i	−0.936480	−	0.250929i	−0.241864	−	0.970310i	$-0.577759\pi$
$43$	−6.14091	−	1.64545i	−0.936480	−	0.250929i	−0.694616	+	0.719381i	$0.744426\pi$
$44$	−2.12698	+	2.12698i	−0.320654	+	0.320654i
$45$		0			0
$46$	−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
$50$		0			0
$51$			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	$-0.0882055\pi$
$53$	5.01074	+	5.01074i	0.688278	+	0.688278i	−0.273573	+	0.961851i	$0.588206\pi$
$54$	−3.18892	−	11.9012i	−0.433958	−	1.61955i
$55$		0			0
$56$	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	−0.963119	−	0.269075i	$-0.913282\pi$
$59$	0.0422769	−	0.157780i	0.00550398	−	0.0205411i	0.968623	+	0.248534i	$0.0799487\pi$
$60$		0			0
$61$	1.11898	+	1.93813i	0.143271	+	0.248153i	0.928727	−	0.370765i	$-0.120905\pi$
$61$	1.11898	+	1.93813i	0.143271	+	0.248153i	−0.785456	+	0.618918i	$0.787571\pi$
$62$	−0.732873	+	0.196373i	−0.0930750	+	0.0249394i
$63$	−2.78188	+	4.81836i	−0.350484	+	0.607056i
$64$	1.00000			0.125000
$65$		0			0
$66$	−9.47080			−1.16578
$67$	−2.20825	+	3.82479i	−0.269780	+	0.467273i	−0.968805	−	0.247824i	$-0.920284\pi$
$67$	−2.20825	+	3.82479i	−0.269780	+	0.467273i	0.699025	+	0.715097i	$0.253618\pi$
$68$	6.99788	−	1.87508i	0.848618	−	0.227387i
$69$	−0.688865	−	1.19315i	−0.0829296	−	0.143638i
$70$		0			0
$71$	2.63643	−	9.83928i	0.312886	−	1.16771i	−0.613055	−	0.790040i	$-0.710060\pi$
$71$	2.63643	−	9.83928i	0.312886	−	1.16771i	0.925941	−	0.377668i	$-0.123274\pi$
$72$	−5.98707	+	3.45663i	−0.705582	+	0.407368i
$73$	1.73949			0.203592			0.101796	−	0.994805i	$-0.467541\pi$
$73$	1.73949			0.203592			0.101796	+	0.994805i	$0.467541\pi$
$74$	−0.835172	+	0.482187i	−0.0970867	+	0.0560530i
$75$		0			0
$76$	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	$0.143739\pi$
$79$			7.75722i			0.872756i	−0.899763	+	0.436378i	$0.856261\pi$
$80$		0			0
$81$	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
$85$		0			0
$86$	−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	−0.558092	−	0.829779i	$-0.688467\pi$
$89$	−5.91063	+	1.58375i	−0.626525	+	0.167877i	−0.0684328	+	0.997656i	$0.521800\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	2.22635	+	2.22635i	0.227226	+	0.227226i
$97$	−6.70520	−	11.6138i	−0.680810	−	1.17920i	−0.974734	−	0.223369i	$-0.928294\pi$
$97$	−6.70520	−	11.6138i	−0.680810	−	1.17920i	0.293924	−	0.955829i	$-0.405039\pi$
$98$	3.17615	+	5.50126i	0.320840	+	0.555711i
$99$	−14.7044	−	14.7044i	−1.47785	−	1.47785i
$100$		0			0
$101$	9.02570	+	5.21099i	0.898091	+	0.518513i	0.876580	−	0.481256i	$-0.159819\pi$
$101$	9.02570	+	5.21099i	0.898091	+	0.518513i	0.0215104	+	0.999769i	$0.493153\pi$
$102$	19.7543	+	11.4052i	1.95597	+	1.12928i
$103$	−11.9307	+	11.9307i	−1.17557	+	1.17557i	−0.194709	+	0.980861i	$0.562376\pi$
$103$	−11.9307	+	11.9307i	−1.17557	+	1.17557i	−0.980861	+	0.194709i	$0.937624\pi$
$104$	−3.59966	+	0.206024i	−0.352976	+	0.0202024i
$105$		0			0
$106$	6.84480	−	1.83406i	0.664826	−	0.178140i
$107$	−2.91943	−	10.8955i	−0.282232	−	1.05330i	−0.950839	−	0.309687i	$-0.899776\pi$
$107$	−2.91943	−	10.8955i	−0.282232	−	1.05330i	0.668607	−	0.743616i	$-0.266891\pi$
$108$	−11.9012	−	3.18892i	−1.14520	−	0.306854i
$109$	5.74393	−	5.74393i	0.550169	−	0.550169i	−0.376321	−	0.926489i	$-0.622811\pi$
$109$	5.74393	−	5.74393i	0.550169	−	0.550169i	0.926489	+	0.376321i	$0.122811\pi$
$110$		0			0
$111$	−2.93290	−	0.785868i	−0.278379	−	0.0745913i
$112$		−	0.804795i		−	0.0760459i
$113$	4.47593	−	16.7044i	0.421060	−	1.57142i	−0.351320	−	0.936255i	$-0.614267\pi$
$113$	4.47593	−	16.7044i	0.421060	−	1.57142i	0.772380	−	0.635161i	$-0.219066\pi$
$114$	−7.36103	+	12.7497i	−0.689424	+	1.19412i
$115$		0			0
$116$		−	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
$120$		0			0
$121$	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
$125$		0			0
$126$	2.78188	+	4.81836i	0.247830	+	0.429253i
$127$	3.97326	−	1.06463i	0.352570	−	0.0944707i	−0.0781875	−	0.996939i	$-0.524913\pi$
$127$	3.97326	−	1.06463i	0.352570	−	0.0944707i	0.430757	+	0.902468i	$0.358247\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−20.0169			−1.76239
$130$		0			0
$131$	−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
$135$		0			0
$136$	1.87508	−	6.99788i	0.160787	−	0.600064i
$137$	−6.99324	+	4.03755i	−0.597473	+	0.344951i	−0.768047	−	0.640394i	$-0.778771\pi$
$137$	−6.99324	+	4.03755i	−0.597473	+	0.344951i	0.170574	+	0.985345i	$0.445438\pi$
$138$	−1.37773			−0.117280
$139$	−13.2173	+	7.63102i	−1.12108	+	0.647254i	−0.941676	−	0.336521i	$-0.890750\pi$
$139$	−13.2173	+	7.63102i	−1.12108	+	0.647254i	−0.179402	+	0.983776i	$0.557416\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	0.669386	−	0.742915i	$-0.266557\pi$
$149$	10.7129	+	2.87051i	0.877634	+	0.235161i	0.208248	+	0.978076i	$0.433224\pi$
$150$		0			0
$151$	11.2046	−	11.2046i	0.911815	−	0.911815i	−0.0845999	−	0.996415i	$-0.526961\pi$
$151$	11.2046	−	11.2046i	0.911815	−	0.911815i	0.996415	+	0.0845999i	$0.0269612\pi$
$152$	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
$155$		0			0
$156$	−8.47279	−	7.55542i	−0.678366	−	0.604918i
$157$	−2.13077	+	2.13077i	−0.170054	+	0.170054i	−0.787003	−	0.616949i	$-0.788368\pi$
$157$	−2.13077	+	2.13077i	−0.170054	+	0.170054i	0.616949	+	0.787003i	$0.288368\pi$
$158$	6.71795	+	3.87861i	0.534452	+	0.308566i
$159$	19.3222	+	11.1557i	1.53235	+	0.884702i
$160$		0			0
$161$	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	$-0.250216\pi$
$163$	−3.31273	−	5.73782i	−0.259473	−	0.449421i	−0.966101	+	0.258165i	$0.916882\pi$
$164$	−1.19391	−	1.19391i	−0.0932289	−	0.0932289i
$165$		0			0
$166$	13.5485	+	7.82220i	1.05156	+	0.607121i
$167$	7.39866	+	4.27162i	0.572526	+	0.330548i	0.758158	−	0.652071i	$-0.226100\pi$
$167$	7.39866	+	4.27162i	0.572526	+	0.330548i	−0.185632	+	0.982619i	$0.559433\pi$
$168$	1.79175	−	1.79175i	0.138237	−	0.138237i
$169$	12.9151	−	1.48324i	0.993470	−	0.114095i
$170$		0			0
$171$	−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	$-0.460290\pi$
$173$	−3.47144	−	0.930169i	−0.263929	−	0.0707195i	−0.388357	+	0.921509i	$0.626957\pi$
$174$	9.21072	−	9.21072i	0.698263	−	0.698263i
$175$		0			0
$176$	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	−0.710383	−	0.703816i	$-0.751478\pi$
$179$	3.40272	−	5.89368i	0.254331	−	0.440514i	0.964714	+	0.263302i	$0.0848114\pi$
$180$		0			0
$181$		−	11.5815i		−	0.860846i	−0.902627	−	0.430423i	$-0.858364\pi$
$181$		−	11.5815i		−	0.860846i	0.902627	−	0.430423i	$-0.141636\pi$
$182$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$	2.32947	+	4.03477i	0.168555	+	0.291946i	0.937912	−	0.346873i	$-0.112757\pi$
$191$	2.32947	+	4.03477i	0.168555	+	0.291946i	−0.769357	+	0.638819i	$0.779423\pi$
$192$	3.04125	−	0.814901i	0.219483	−	0.0588104i
$193$	−6.69708	+	11.5997i	−0.482066	+	0.834963i	−0.999788	−	0.0205858i	$-0.993447\pi$
$193$	−6.69708	+	11.5997i	−0.482066	+	0.834963i	0.517722	+	0.855549i	$0.326780\pi$
$194$	−13.4104			−0.962811
$195$		0			0
$196$	6.35231			0.453736
$197$	−11.0122	+	19.0737i	−0.784586	+	1.35894i	0.144661	+	0.989481i	$0.453791\pi$
$197$	−11.0122	+	19.0737i	−0.784586	+	1.35894i	−0.929246	+	0.369461i	$0.879542\pi$
$198$	−20.0866	+	5.38218i	−1.42749	+	0.382495i
$199$	−5.69362	−	9.86164i	−0.403610	−	0.699073i	0.590549	−	0.807002i	$-0.298911\pi$
$199$	−5.69362	−	9.86164i	−0.403610	−	0.699073i	−0.994159	+	0.107929i	$0.965578\pi$
$200$		0			0
$201$	−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			0
$206$	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
$210$		0			0
$211$	1.35943	−	2.35460i	0.0935868	−	0.162097i	−0.815431	−	0.578854i	$-0.803500\pi$
$211$	1.35943	−	2.35460i	0.0935868	−	0.162097i	0.909018	+	0.416757i	$0.136833\pi$
$212$	1.83406	−	6.84480i	0.125964	−	0.470103i
$213$		−	32.0721i		−	2.19755i
$214$	−10.8955	−	2.91943i	−0.744798	−	0.199568i
$215$		0			0
$216$	−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
$220$		0			0
$221$	−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	−0.990834	−	0.135085i	$-0.956869\pi$
$223$	−23.9414	−	13.8226i	−1.60324	−	0.925630i	−0.612404	−	0.790545i	$-0.709797\pi$
$224$	−0.696972	−	0.402397i	−0.0465684	−	0.0268863i
$225$		0			0
$226$	−12.2285	−	12.2285i	−0.813425	−	0.813425i
$227$	1.72981	+	2.99612i	0.114812	+	0.198859i	0.917704	−	0.397264i	$-0.130040\pi$
$227$	1.72981	+	2.99612i	0.114812	+	0.198859i	−0.802893	+	0.596123i	$0.796707\pi$
$228$	7.36103	+	12.7497i	0.487496	+	0.844368i
$229$	−8.92266	−	8.92266i	−0.589626	−	0.589626i	0.347904	−	0.937530i	$-0.386893\pi$
$229$	−8.92266	−	8.92266i	−0.589626	−	0.589626i	−0.937530	+	0.347904i	$0.886893\pi$
$230$		0			0
$231$	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	$-0.732070\pi$
$233$	1.21530	−	1.21530i	0.0796169	−	0.0796169i	0.745794	+	0.666177i	$0.232070\pi$
$234$	−1.42430	−	24.8854i	−0.0931096	−	1.62681i
$235$		0			0
$236$	−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	−0.276400	−	0.961043i	$-0.589141\pi$
$239$	10.5843	−	10.5843i	0.684643	−	0.684643i	0.961043	+	0.276400i	$0.0891415\pi$
$240$		0			0
$241$	−26.2460	−	7.03259i	−1.69065	−	0.453009i	−0.720094	−	0.693877i	$-0.755901\pi$
$241$	−26.2460	−	7.03259i	−1.69065	−	0.453009i	−0.970558	+	0.240868i	$0.922568\pi$
$242$		−	1.95191i		−	0.125474i
$243$	5.14501	−	19.2014i	0.330052	−	1.23177i
$244$	1.11898	−	1.93813i	0.0716355	−	0.124076i
$245$		0			0
$246$		−	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
$250$		0			0
$251$	22.8576	−	13.1969i	1.44276	−	0.832979i	0.444728	−	0.895666i	$-0.353300\pi$
$251$	22.8576	−	13.1969i	1.44276	−	0.832979i	0.998033	+	0.0626870i	$0.0199670\pi$
$252$	5.56376			0.350484
$253$	−1.13990	+	0.658119i	−0.0716646	+	0.0413756i
$254$	1.06463	−	3.97326i	0.0668009	−	0.249304i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.96070	−	0.525368i	0.122305	−	0.0327715i	−0.197147	−	0.980374i	$-0.563168\pi$
$257$	1.96070	−	0.525368i	0.122305	−	0.0327715i	0.319452	+	0.947602i	$0.396501\pi$
$258$	−10.0085	+	17.3352i	−0.623100	+	1.07924i
$259$	0.776122			0.0482259
$260$		0			0
$261$	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	$-0.244734\pi$
$263$	27.3875	−	7.33845i	1.68878	−	0.452508i	0.970075	+	0.242804i	$0.0780671\pi$
$264$	4.73540	+	8.20196i	0.291444	+	0.504796i
$265$		0			0
$266$	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	−0.411307	−	0.911497i	$-0.634927\pi$
$269$	2.82789	−	1.63268i	0.172420	−	0.0995465i	0.583726	+	0.811951i	$0.301594\pi$
$270$		0			0
$271$	1.42316	+	5.31129i	0.0864505	+	0.322638i	0.995585	−	0.0938651i	$-0.0299222\pi$
$271$	1.42316	+	5.31129i	0.0864505	+	0.322638i	−0.909134	+	0.416503i	$0.863256\pi$
$272$	−5.12281	−	5.12281i	−0.310616	−	0.310616i
$273$	−6.08056	+	6.81885i	−0.368012	+	0.412696i
$274$			8.07510i			0.487835i
$275$		0			0
$276$	−0.688865	+	1.19315i	−0.0414648	+	0.0718192i
$277$	5.54414	−	20.6910i	0.333115	−	1.24320i	−0.572783	−	0.819707i	$-0.694136\pi$
$277$	5.54414	−	20.6910i	0.333115	−	1.24320i	0.905898	−	0.423496i	$-0.139197\pi$
$278$			15.2620i			0.915356i
$279$	−5.06655	−	1.35758i	−0.303326	−	0.0812760i
$280$		0			0
$281$	−15.6657	+	15.6657i	−0.934539	+	0.934539i	−0.997985	−	0.0634460i	$-0.979791\pi$
$281$	−15.6657	+	15.6657i	−0.934539	+	0.934539i	0.0634460	+	0.997985i	$0.479791\pi$
$282$	5.23934	+	1.40388i	0.311998	+	0.0835996i
$283$	−2.33476	−	8.71344i	−0.138787	−	0.517960i	−0.999954	−	0.00963733i	$-0.996932\pi$
$283$	−2.33476	−	8.71344i	−0.138787	−	0.517960i	0.861167	−	0.508323i	$-0.169734\pi$
$284$	−9.83928	+	2.63643i	−0.583854	+	0.156443i
$285$		0			0
$286$	−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
$290$		0			0
$291$	−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	$-0.267828\pi$
$293$	−5.34888	−	9.26452i	−0.312485	−	0.541239i	−0.978900	+	0.204342i	$0.934495\pi$
$294$	14.1425	+	14.1425i	0.824805	+	0.824805i
$295$		0			0
$296$	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
$300$		0			0
$301$	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
$305$		0			0
$306$	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			0
$311$		−	10.1340i		−	0.574646i	−0.957834	−	0.287323i	$-0.907235\pi$
$311$		−	10.1340i		−	0.574646i	0.957834	−	0.287323i	$-0.0927654\pi$
$312$	−10.7796	+	3.55994i	−0.610273	+	0.201542i
$313$	−10.4449	−	10.4449i	−0.590383	−	0.590383i	0.347352	−	0.937735i	$-0.387081\pi$
$313$	−10.4449	−	10.4449i	−0.590383	−	0.590383i	−0.937735	+	0.347352i	$0.887081\pi$
$314$	0.779916	+	2.91069i	0.0440132	+	0.164260i
$315$		0			0
$316$	6.71795	−	3.87861i	0.377914	−	0.218189i
$317$	24.4508			1.37329			0.686646	−	0.726992i	$-0.259082\pi$
$317$	24.4508			1.37329			0.686646	+	0.726992i	$0.259082\pi$
$318$	19.3222	−	11.1557i	1.08353	−	0.625579i
$319$	3.22088	−	12.0205i	0.180335	−	0.673019i
$320$		0			0
$321$	−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
$325$		0			0
$326$	−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
$330$		0			0
$331$	−0.310163	+	1.15754i	−0.0170481	+	0.0636243i	−0.973926	−	0.226866i	$-0.927152\pi$
$331$	−0.310163	+	1.15754i	−0.0170481	+	0.0636243i	0.956878	+	0.290491i	$0.0938186\pi$
$332$	13.5485	−	7.82220i	0.743568	−	0.429299i
$333$	−6.66697			−0.365348
$334$	7.39866	−	4.27162i	0.404837	−	0.233733i
$335$		0			0
$336$	−0.655828	−	2.44758i	−0.0357783	−	0.133527i
$337$	0.358931	+	0.358931i	0.0195522	+	0.0195522i	0.716815	−	0.697263i	$-0.245599\pi$
$337$	0.358931	+	0.358931i	0.0195522	+	0.0195522i	−0.697263	+	0.716815i	$0.745599\pi$
$338$	5.17303	−	11.9264i	0.281376	−	0.648712i
$339$		−	54.4496i		−	2.95730i
$340$		0			0
$341$	−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
$345$		0			0
$346$	−2.54127	+	2.54127i	−0.136619	+	0.136619i
$347$	−12.6705	−	3.39505i	−0.680187	−	0.182256i	−0.0978479	−	0.995201i	$-0.531196\pi$
$347$	−12.6705	−	3.39505i	−0.680187	−	0.182256i	−0.582339	+	0.812946i	$0.697863\pi$
$348$	−3.37136	−	12.5821i	−0.180724	−	0.674470i
$349$	22.5950	−	6.05431i	1.20948	−	0.324080i	0.402924	−	0.915234i	$-0.367994\pi$
$349$	22.5950	−	6.05431i	1.20948	−	0.324080i	0.806559	+	0.591154i	$0.201327\pi$
$350$		0			0
$351$	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	$-0.117114\pi$
$353$	20.4439	+	11.8033i	1.08812	+	0.628227i	0.155045	+	0.987907i	$0.450448\pi$
$354$	−0.445396	−	0.257149i	−0.0236725	−	0.0136673i
$355$		0			0
$356$	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	0.425666	−	0.904880i	$-0.360040\pi$
$359$	−9.07981	−	9.07981i	−0.479214	−	0.479214i	−0.904880	+	0.425666i	$0.860040\pi$
$360$		0			0
$361$	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			0
$366$	6.80621	−	1.82372i	0.355766	−	0.0953273i
$367$	−8.65453	−	32.2992i	−0.451763	−	1.68600i	−0.697434	−	0.716649i	$-0.745675\pi$
$367$	−8.65453	−	32.2992i	−0.451763	−	1.68600i	0.245671	−	0.969353i	$-0.420992\pi$
$368$	0.422668	+	0.113254i	0.0220331	+	0.00590375i
$369$	8.25383	−	8.25383i	0.429677	−	0.429677i
$370$		0			0
$371$	−5.50866	−	1.47604i	−0.285995	−	0.0766322i
$372$			2.38888i			0.123857i
$373$	−6.19820	+	23.1320i	−0.320931	+	1.19773i	0.597409	+	0.801937i	$0.296197\pi$
$373$	−6.19820	+	23.1320i	−0.320931	+	1.19773i	−0.918340	+	0.395793i	$0.870470\pi$
$374$	10.8961	−	18.8726i	0.563424	−	0.975880i
$375$		0			0
$376$		−	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	0.934169	−	0.356830i	$-0.116142\pi$
$379$	−1.03686	−	3.86961i	−0.0532599	−	0.198769i	−0.987429	+	0.158061i	$0.949476\pi$
$380$		0			0
$381$	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	$-0.897829\pi$
$383$	−22.5091	+	12.9957i	−1.15016	+	0.664047i	−0.201236	+	0.979543i	$0.564496\pi$
$384$	0.814901	−	3.04125i	0.0415852	−	0.155198i
$385$		0			0
$386$	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	$0.411044\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−5.38218	+	20.0866i	−0.270465	+	1.00939i
$397$	−24.0126	+	13.8637i	−1.20516	+	0.695799i	−0.961698	−	0.274112i	$-0.911616\pi$
$397$	−24.0126	+	13.8637i	−1.20516	+	0.695799i	−0.243461	+	0.969911i	$0.578283\pi$
$398$	−11.3872			−0.570791
$399$	10.2609	−	5.92412i	0.513686	−	0.296577i
$400$		0			0
$401$	−7.44840	−	27.7978i	−0.371955	−	1.38816i	−0.857743	−	0.514079i	$-0.828134\pi$
$401$	−7.44840	−	27.7978i	−0.371955	−	1.38816i	0.485787	−	0.874077i	$-0.338533\pi$
$402$	9.83266	+	9.83266i	0.490408	+	0.490408i
$403$	−2.04175	−	1.82069i	−0.101707	−	0.0906949i
$404$		−	10.4220i		−	0.518513i
$405$		0			0
$406$	−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	−0.358779	−	0.933423i	$-0.616807\pi$
$409$	−22.9783	−	6.15701i	−1.13620	−	0.304444i	−0.777423	+	0.628978i	$0.783473\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	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	0.997066	+	0.0765449i	$0.0243888\pi$
$419$	31.9711	+	18.4585i	1.56189	+	0.901757i	0.564823	+	0.825212i	$0.308944\pi$
$420$		0			0
$421$	10.2278	+	10.2278i	0.498473	+	0.498473i	0.910962	−	0.412489i	$-0.135341\pi$
$421$	10.2278	+	10.2278i	0.498473	+	0.498473i	−0.412489	+	0.910962i	$0.635341\pi$
$422$	−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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−13.9188	+	3.72952i	−0.670444	+	0.179645i	−0.577955	−	0.816069i	$-0.696149\pi$
$431$	−13.9188	+	3.72952i	−0.670444	+	0.179645i	−0.0924890	+	0.995714i	$0.529482\pi$
$432$	3.18892	+	11.9012i	0.153427	+	0.572598i
$433$	10.7032	+	2.86792i	0.514364	+	0.137823i	0.506658	−	0.862147i	$-0.330881\pi$
$433$	10.7032	+	2.86792i	0.514364	+	0.137823i	0.00770546	+	0.999970i	$0.497547\pi$
$434$	0.431773	−	0.431773i	0.0207257	−	0.0207257i
$435$		0			0
$436$	−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	−0.913995	−	0.405727i	$-0.867019\pi$
$439$	−2.21315	+	3.83328i	−0.105628	+	0.182953i	0.808367	+	0.588679i	$0.200352\pi$
$440$		0			0
$441$			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	$-0.344400\pi$
$443$	−8.69869	−	8.69869i	−0.413287	−	0.413287i	−0.882882	+	0.469595i	$0.844400\pi$
$444$	0.785868	+	2.93290i	0.0372957	+	0.139189i
$445$		0			0
$446$	−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	0.684114	+	0.729376i	$0.260189\pi$
$449$	−5.78549	+	21.5917i	−0.273034	+	1.01898i	−0.957147	+	0.289601i	$0.906477\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	14.7221			0.689424
$457$	0.643128	−	1.11393i	0.0300843	−	0.0521075i	−0.850591	−	0.525827i	$-0.823756\pi$
$457$	0.643128	−	1.11393i	0.0300843	−	0.0521075i	0.880676	+	0.473720i	$0.157089\pi$
$458$	−12.1886	+	3.26592i	−0.569535	+	0.152606i
$459$	44.6314	+	77.3039i	2.08322	+	3.60824i
$460$		0			0
$461$	−2.59056	+	9.66810i	−0.120654	+	0.450288i	−0.999648	−	0.0265460i	$-0.991549\pi$
$461$	−2.59056	+	9.66810i	−0.120654	+	0.450288i	0.878993	+	0.476834i	$0.158216\pi$
$462$	6.60089	−	3.81103i	0.307101	−	0.177305i
$463$	−9.95491			−0.462644			−0.231322	−	0.972877i	$-0.574305\pi$
$463$	−9.95491			−0.462644			−0.231322	+	0.972877i	$0.574305\pi$
$464$	−3.58287	+	2.06857i	−0.166331	+	0.0960310i
$465$		0			0
$466$	−0.444830	−	1.66013i	−0.0206064	−	0.0769040i
$467$	3.56456	+	3.56456i	0.164948	+	0.164948i	0.784755	−	0.619807i	$-0.212789\pi$
$467$	3.56456	+	3.56456i	0.164948	+	0.164948i	−0.619807	+	0.784755i	$0.712789\pi$
$468$	−22.2636	−	11.2092i	−1.02913	−	0.518147i
$469$		−	3.55437i		−	0.164125i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−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	−0.502812	−	0.864396i	$-0.667701\pi$
$479$	−11.0757	+	2.96772i	−0.506061	+	0.135599i	−0.00324963	+	0.999995i	$0.501034\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	−14.0564	−	14.0564i	−0.637612	−	0.637612i
$487$	−0.122308	−	0.211843i	−0.00554230	−	0.00959954i	0.863241	−	0.504792i	$-0.168431\pi$
$487$	−0.122308	−	0.211843i	−0.00554230	−	0.00959954i	−0.868783	+	0.495193i	$0.835098\pi$
$488$	−1.11898	−	1.93813i	−0.0506539	−	0.0877352i
$489$	−14.7506	−	14.7506i	−0.667046	−	0.667046i
$490$		0			0
$491$	−17.4955	−	10.1011i	−0.789563	−	0.455854i	0.0502457	−	0.998737i	$-0.484000\pi$
$491$	−17.4955	−	10.1011i	−0.789563	−	0.455854i	−0.839809	+	0.542882i	$0.817333\pi$
$492$	−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
$495$		0			0
$496$	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	−0.644155	−	0.764895i	$-0.722791\pi$
$499$	2.69714	−	2.69714i	0.120740	−	0.120740i	0.764895	+	0.644155i	$0.222791\pi$
$500$		0			0
$501$	25.9821	+	6.96189i	1.16080	+	0.311034i
$502$		−	26.3937i		−	1.17801i
$503$	−3.06353	+	11.4333i	−0.136596	+	0.509784i	0.863390	+	0.504537i	$0.168337\pi$
$503$	−3.06353	+	11.4333i	−0.136596	+	0.509784i	−0.999986	+	0.00524701i	$0.998330\pi$
$504$	2.78188	−	4.81836i	0.123915	−	0.214627i
$505$		0			0
$506$			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	−0.999423	−	0.0339709i	$-0.989185\pi$
$509$	−3.40407	−	12.7042i	−0.150883	−	0.563102i	0.848540	−	0.529131i	$-0.177482\pi$
$510$		0			0
$511$	−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
$515$		0			0
$516$	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			0
$521$	−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	$-0.487293\pi$
$523$	13.1286	−	3.51781i	0.574075	−	0.153823i	0.534165	+	0.845380i	$0.320626\pi$
$524$	2.95421	+	5.11684i	0.129055	+	0.223530i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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
$540$		0			0
$541$	9.16253	−	9.16253i	0.393928	−	0.393928i	−0.482157	−	0.876085i	$-0.660147\pi$
$541$	9.16253	−	9.16253i	0.393928	−	0.393928i	0.876085	+	0.482157i	$0.160147\pi$
$542$	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
$545$		0			0
$546$	2.86502	+	8.67535i	0.122611	+	0.371271i
$547$	22.6416	−	22.6416i	0.968085	−	0.968085i	−0.0314209	−	0.999506i	$-0.510003\pi$
$547$	22.6416	−	22.6416i	0.968085	−	0.968085i	0.999506	+	0.0314209i	$0.0100032\pi$
$548$	6.99324	+	4.03755i	0.298737	+	0.172476i
$549$	13.3988	+	7.73582i	0.571849	+	0.330157i
$550$		0			0
$551$	−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
$555$		0			0
$556$	13.2173	+	7.63102i	0.560539	+	0.323627i
$557$	26.0519	+	15.0411i	1.10386	+	0.637311i	0.937231	−	0.348709i	$-0.113380\pi$
$557$	26.0519	+	15.0411i	1.10386	+	0.637311i	0.166624	+	0.986020i	$0.446713\pi$
$558$	−3.70897	+	3.70897i	−0.157013	+	0.157013i
$559$	−22.4442	−	4.65789i	−0.949288	−	0.197008i
$560$		0			0
$561$	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	$-0.588983\pi$
$563$	−23.6201	−	6.32898i	−0.995468	−	0.266735i	−0.719546	+	0.694445i	$0.755650\pi$
$564$	3.83546	−	3.83546i	0.161502	−	0.161502i
$565$		0			0
$566$	−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	−0.550438	−	0.834876i	$-0.685539\pi$
$569$	10.6818	−	18.5014i	0.447805	−	0.775621i	0.998243	+	0.0592553i	$0.0188726\pi$
$570$		0			0
$571$			21.6572i			0.906327i	0.891427	+	0.453163i	$0.149705\pi$
$571$			21.6572i			0.906327i	−0.891427	+	0.453163i	$0.850295\pi$
$572$	−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			0
$576$	5.98707	−	3.45663i	0.249461	−	0.144026i
$577$	−10.9211			−0.454650			−0.227325	−	0.973819i	$-0.572998\pi$
$577$	−10.9211			−0.454650			−0.227325	+	0.973819i	$0.572998\pi$
$578$	−30.7320	+	17.7431i	−1.27828	+	0.738018i
$579$	−10.9149	+	40.7350i	−0.453608	+	1.69289i
$580$		0			0
$581$	−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
$585$		0			0
$586$	−10.6978			−0.441920
$587$	−14.1110	+	24.4409i	−0.582423	+	1.00879i	0.412769	+	0.910836i	$0.364562\pi$
$587$	−14.1110	+	24.4409i	−0.582423	+	1.00879i	−0.995191	+	0.0979498i	$0.968772\pi$
$588$	19.3190	−	5.17650i	0.796700	−	0.213475i
$589$	1.77384	+	3.07239i	0.0730899	+	0.126595i
$590$		0			0
$591$	−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	$-0.298928\pi$
$593$	28.7595			1.18101			0.590506	+	0.807033i	$0.298928\pi$
$594$	−32.0964	+	18.5309i	−1.31693	+	0.760332i
$595$		0			0
$596$	−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	$-0.950227\pi$
$599$		−	7.62284i		−	0.311461i	0.987800	−	0.155730i	$-0.0497731\pi$
$600$		0			0
$601$	−8.07815	+	13.9918i	−0.329515	+	0.570736i	−0.982416	−	0.186707i	$-0.940218\pi$
$601$	−8.07815	+	13.9918i	−0.329515	+	0.570736i	0.652901	+	0.757443i	$0.273552\pi$
$602$	1.32425	−	4.94217i	0.0539724	−	0.201428i
$603$			30.5324i			1.24337i
$604$	−15.3057	−	4.10116i	−0.622781	−	0.166874i
$605$		0			0
$606$	23.2030	−	23.2030i	0.942556	−	0.942556i
$607$	−32.1964	−	8.62700i	−1.30681	−	0.350159i	−0.462790	−	0.886468i	$-0.653151\pi$
$607$	−32.1964	−	8.62700i	−1.30681	−	0.350159i	−0.844022	+	0.536309i	$0.819818\pi$
$608$	−1.21020	−	4.51652i	−0.0490800	−	0.183169i
$609$	−10.1260	+	2.71325i	−0.410326	+	0.109946i
$610$		0			0
$611$	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	$-0.00983592\pi$
$613$	36.4581	+	21.0491i	1.47253	+	0.850164i	0.473005	+	0.881060i	$0.343169\pi$
$614$	−11.1833	−	6.45668i	−0.451321	−	0.260570i
$615$		0			0
$616$	−1.71178	−	1.71178i	−0.0689697	−	0.0689697i
$617$	6.28781	+	10.8908i	0.253138	+	0.438447i	0.964388	−	0.264491i	$-0.0852041\pi$
$617$	6.28781	+	10.8908i	0.253138	+	0.438447i	−0.711250	+	0.702939i	$0.751871\pi$
$618$	26.5620	+	46.0067i	1.06848	+	1.85066i
$619$	8.75232	+	8.75232i	0.351786	+	0.351786i	0.860774	−	0.508988i	$-0.169980\pi$
$619$	8.75232	+	8.75232i	0.351786	+	0.351786i	−0.508988	+	0.860774i	$0.669980\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	−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
$630$		0			0
$631$	26.6071	+	7.12936i	1.05921	+	0.283815i	0.746054	−	0.665886i	$-0.231946\pi$
$631$	26.6071	+	7.12936i	1.05921	+	0.283815i	0.313159	+	0.949701i	$0.398613\pi$
$632$		−	7.75722i		−	0.308566i
$633$	2.21560	−	8.26871i	0.0880620	−	0.328652i
$634$	12.2254	−	21.1750i	0.485532	−	0.840966i
$635$		0			0
$636$		−	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
$640$		0			0
$641$	25.0061	−	14.4373i	0.987680	−	0.570237i	0.0830998	−	0.996541i	$-0.473518\pi$
$641$	25.0061	−	14.4373i	0.987680	−	0.570237i	0.904580	+	0.426304i	$0.140185\pi$
$642$	−35.5148			−1.40166
$643$	9.27773	−	5.35650i	0.365878	−	0.211240i	−0.305778	−	0.952103i	$-0.598917\pi$
$643$	9.27773	−	5.35650i	0.365878	−	0.211240i	0.671656	+	0.740863i	$0.265583\pi$
$644$	0.0911459	−	0.340161i	0.00359165	−	0.0134042i
$645$		0			0
$646$	−16.9376	−	29.3369i	−0.666403	−	1.15424i
$647$	38.4306	−	10.2974i	1.51086	−	0.404834i	0.594140	−	0.804362i	$-0.297492\pi$
$647$	38.4306	−	10.2974i	1.51086	−	0.404834i	0.916721	+	0.399527i	$0.130826\pi$
$648$	−9.02673	+	15.6348i	−0.354604	+	0.614191i
$649$	−0.491344			−0.0192869
$650$		0			0
$651$	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	$-0.954161\pi$
$653$	−45.3569	+	12.1534i	−1.77495	+	0.475598i	−0.785306	+	0.619108i	$0.787494\pi$
$654$	−12.7880	−	22.1495i	−0.500050	−	0.866113i
$655$		0			0
$656$	−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	−0.929248	−	0.369457i	$-0.879544\pi$
$659$	−27.5684	+	15.9166i	−1.07391	+	0.620024i	−0.144665	+	0.989481i	$0.546210\pi$
$660$		0			0
$661$	−1.26555	−	4.72310i	−0.0492243	−	0.183707i	0.936936	−	0.349500i	$-0.113648\pi$
$661$	−1.26555	−	4.72310i	−0.0492243	−	0.183707i	−0.986161	+	0.165792i	$0.946982\pi$
$662$	0.847381	+	0.847381i	0.0329344	+	0.0329344i
$663$	4.69948	+	82.1094i	0.182513	+	3.18886i
$664$		−	15.6444i		−	0.607121i
$665$		0			0
$666$	−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
$670$		0			0
$671$	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	$-0.0138643\pi$
$673$	2.90751	+	10.8510i	0.112076	+	0.418275i	−0.886975	+	0.461817i	$0.847198\pi$
$674$	0.490309	−	0.131378i	0.0188860	−	0.00506048i
$675$		0			0
$676$	−7.74207	−	10.4432i	−0.297772	−	0.401661i
$677$	−12.8047	+	12.8047i	−0.492125	+	0.492125i	−0.908975	−	0.416850i	$-0.863134\pi$
$677$	−12.8047	+	12.8047i	−0.492125	+	0.492125i	0.416850	+	0.908975i	$0.363134\pi$
$678$	−47.1548	−	27.2248i	−1.81097	−	1.04556i
$679$	9.34669	+	5.39631i	0.358693	+	0.207091i
$680$		0			0
$681$	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	0.922161	+	0.386806i	$0.126422\pi$
$683$	20.8046	+	36.0346i	0.796064	+	1.37882i	−0.126097	+	0.992018i	$0.540245\pi$
$684$	22.8575	+	22.8575i	0.873978	+	0.873978i
$685$		0			0
$686$	−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			0
$691$	−17.8985	+	4.79589i	−0.680891	+	0.182444i	−0.582656	−	0.812719i	$-0.697986\pi$
$691$	−17.8985	+	4.79589i	−0.680891	+	0.182444i	−0.0982353	+	0.995163i	$0.531320\pi$
$692$	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
$695$		0			0
$696$	−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
$700$		0			0
$701$			8.16233i			0.308287i	0.988048	+	0.154143i	$0.0492618\pi$
$701$			8.16233i			0.308287i	−0.988048	+	0.154143i	$0.950738\pi$
$702$	−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
$705$		0			0
$706$	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	0.839237	+	0.543766i	$0.183002\pi$
$709$	−4.24559	+	15.8447i	−0.159446	+	0.595062i	−0.998683	+	0.0512963i	$0.983665\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	−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	0.847280	−	0.531147i	$-0.178239\pi$
$719$	−0.974618	−	1.68809i	−0.0363471	−	0.0629550i	−0.883627	+	0.468192i	$0.844906\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−1.59061	−	5.93625i	−0.0590332	−	0.220315i
$727$	−27.9848	−	27.9848i	−1.03790	−	1.03790i	−0.999253	−	0.0386462i	$-0.987695\pi$
$727$	−27.9848	−	27.9848i	−1.03790	−	1.03790i	−0.0386462	−	0.999253i	$-0.512305\pi$
$728$	2.42596	−	1.59209i	0.0899121	−	0.0590067i
$729$		−	8.42862i		−	0.312171i
$730$		0			0
$731$	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
$735$		0			0
$736$	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	−0.0146022	−	0.999893i	$-0.504648\pi$
$739$	12.8501	−	3.44317i	0.472699	−	0.126659i	0.487301	+	0.873234i	$0.337982\pi$
$740$		0			0
$741$	−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	$-0.263597\pi$
$743$	10.2608	+	5.92409i	0.376433	+	0.217334i	−0.299832	+	0.953992i	$0.596931\pi$
$744$	2.06883	+	1.19444i	0.0758469	+	0.0437902i
$745$		0			0
$746$	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
$750$		0			0
$751$	33.0412	+	19.0764i	1.20569	+	0.696106i	0.961815	−	0.273700i	$-0.0882476\pi$
$751$	33.0412	+	19.0764i	1.20569	+	0.696106i	0.243876	+	0.969806i	$0.421581\pi$
$752$	−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
$755$		0			0
$756$	9.57804	−	2.56643i	0.348350	−	0.0933401i
$757$	3.87261	+	14.4528i	0.140752	+	0.525295i	0.999908	+	0.0135805i	$0.00432294\pi$
$757$	3.87261	+	14.4528i	0.140752	+	0.525295i	−0.859155	+	0.511715i	$0.829010\pi$
$758$	−3.86961	−	1.03686i	−0.140551	−	0.0376604i
$759$	−2.93040	+	2.93040i	−0.106367	+	0.106367i
$760$		0			0
$761$	25.4496	+	6.81919i	0.922546	+	0.247195i	0.688673	−	0.725072i	$-0.258193\pi$
$761$	25.4496	+	6.81919i	0.922546	+	0.247195i	0.233873	+	0.972267i	$0.424860\pi$
$762$		−	12.9512i		−	0.469174i
$763$	−1.69202	+	6.31470i	−0.0612552	+	0.228608i
$764$	2.32947	−	4.03477i	0.0842774	−	0.145973i
$765$		0			0
$766$			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	0.847422	+	0.530920i	$0.178153\pi$
$769$	10.5098	+	39.2231i	0.378993	+	1.41442i	−0.468429	+	0.883501i	$0.655180\pi$
$770$		0			0
$771$	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	$-0.801649\pi$
$773$	−19.8145	+	11.4399i	−0.712677	+	0.411464i	0.0993742	+	0.995050i	$0.468316\pi$
$774$	−11.3754	+	42.4538i	−0.408882	+	1.52597i
$775$		0			0
$776$	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
$780$		0			0
$781$	−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
$785$		0			0
$786$	−4.81477	+	17.9690i	−0.171737	+	0.640932i
$787$	23.9422	−	13.8230i	0.853447	−	0.492738i	−0.00836529	−	0.999965i	$-0.502663\pi$
$787$	23.9422	−	13.8230i	0.853447	−	0.492738i	0.861812	+	0.507227i	$0.169329\pi$
$788$	22.0244			0.784586
$789$	77.3120	−	44.6361i	2.75238	−	1.58909i
$790$		0			0
$791$	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
$795$		0			0
$796$	−5.69362	+	9.86164i	−0.201805	+	0.349537i
$797$	3.73648	−	13.9447i	0.132353	−	0.493948i	−0.867642	−	0.497190i	$-0.834365\pi$
$797$	3.73648	−	13.9447i	0.132353	−	0.493948i	0.999995	+	0.00324171i	$0.00103187\pi$
$798$		−	11.8482i		−	0.419423i
$799$	−12.0557	−	3.23030i	−0.426498	−	0.114280i
$800$		0			0
$801$	−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			0
$806$	−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	0.990179	+	0.139806i	$0.0446480\pi$
$809$	45.6891	+	26.3786i	1.60634	+	0.927423i	0.616165	+	0.787617i	$0.288685\pi$
$810$		0			0
$811$	31.7531	+	31.7531i	1.11500	+	1.11500i	0.992464	+	0.122540i	$0.0391038\pi$
$811$	31.7531	+	31.7531i	1.11500	+	1.11500i	0.122540	+	0.992464i	$0.460896\pi$
$812$	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
$815$		0			0
$816$	−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
$820$		0			0
$821$	−51.2844	+	13.7416i	−1.78984	+	0.479586i	−0.992319	−	0.123707i	$-0.960522\pi$
$821$	−51.2844	+	13.7416i	−1.78984	+	0.479586i	−0.797520	+	0.603293i	$0.793855\pi$
$822$	6.58040	+	24.5584i	0.229518	+	0.856573i
$823$	37.1169	+	9.94545i	1.29381	+	0.346677i	0.839108	−	0.543965i	$-0.183077\pi$
$823$	37.1169	+	9.94545i	1.29381	+	0.346677i	0.454707	+	0.890641i	$0.349744\pi$
$824$	11.9307	−	11.9307i	0.415627	−	0.415627i
$825$		0			0
$826$	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	−0.953416	−	0.301658i	$-0.902460\pi$
$829$	−6.20374	+	10.7452i	−0.215465	+	0.373196i	0.737951	+	0.674854i	$0.235793\pi$
$830$		0			0
$831$		−	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
$835$		0			0
$836$	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	−0.996286	−	0.0861070i	$-0.972557\pi$
$839$	−2.61916	+	9.77485i	−0.0904235	+	0.337465i	0.905862	+	0.423572i	$0.139224\pi$
$840$		0			0
$841$	−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			0
$846$	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
$850$		0			0
$851$	−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	$-0.590959\pi$
$853$	−16.4655			−0.563769			−0.281884	+	0.959448i	$0.590959\pi$
$854$	−1.55980	+	0.900551i	−0.0533752	+	0.0308162i
$855$		0			0
$856$	2.91943	+	10.8955i	0.0997840	+	0.372399i
$857$	−26.1677	−	26.1677i	−0.893870	−	0.893870i	0.101015	−	0.994885i	$-0.467791\pi$
$857$	−26.1677	−	26.1677i	−0.893870	−	0.893870i	−0.994885	+	0.101015i	$0.967791\pi$
$858$	−34.0917	+	1.95122i	−1.16387	+	0.0666135i
$859$			3.70443i			0.126394i	0.998001	+	0.0631968i	$0.0201296\pi$
$859$			3.70443i			0.126394i	−0.998001	+	0.0631968i	$0.979870\pi$
$860$		0			0
$861$	−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
$865$		0			0
$866$	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
$870$		0			0
$871$	−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
$875$		0			0
$876$	−3.87271	−	3.87271i	−0.130847	−	0.130847i
$877$	−1.65175	−	2.86091i	−0.0557755	−	0.0966060i	0.836790	−	0.547525i	$-0.184430\pi$
$877$	−1.65175	−	2.86091i	−0.0557755	−	0.0966060i	−0.892565	+	0.450919i	$0.851096\pi$
$878$	2.21315	+	3.83328i	0.0746901	+	0.129367i
$879$	−23.8169	−	23.8169i	−0.803325	−	0.803325i
$880$		0			0
$881$	6.11016	+	3.52770i	0.205857	+	0.118851i	0.599384	−	0.800461i	$-0.295412\pi$
$881$	6.11016	+	3.52770i	0.205857	+	0.118851i	−0.393528	+	0.919313i	$0.628745\pi$
$882$	38.0317	+	21.9576i	1.28059	+	0.739351i
$883$	−22.1294	+	22.1294i	−0.744714	+	0.744714i	−0.973481	−	0.228767i	$-0.926531\pi$
$883$	−22.1294	+	22.1294i	−0.744714	+	0.744714i	0.228767	+	0.973481i	$0.426531\pi$
$884$	24.8037	−	8.19138i	0.834238	−	0.275506i
$885$		0			0
$886$	−11.8826	+	3.18394i	−0.399205	+	0.106967i
$887$	9.59340	+	35.8031i	0.322115	+	1.20215i	0.917180	+	0.398472i	$0.130459\pi$
$887$	9.59340	+	35.8031i	0.322115	+	1.20215i	−0.595066	+	0.803677i	$0.702874\pi$
$888$	2.93290	+	0.785868i	0.0984217	+	0.0263720i
$889$	−2.34085	+	2.34085i	−0.0785095	+	0.0785095i
$890$		0			0
$891$	−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
$895$		0			0
$896$			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
$900$		0			0
$901$	−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
$905$		0			0
$906$	−24.9453	−	43.2065i	−0.828752	−	1.43544i
$907$	34.0294	−	9.11815i	1.12993	−	0.302763i	0.355033	−	0.934854i	$-0.384470\pi$
$907$	34.0294	−	9.11815i	1.12993	−	0.302763i	0.774895	+	0.632090i	$0.217803\pi$
$908$	1.72981	−	2.99612i	0.0574058	−	0.0994297i
$909$	72.0499			2.38975
$910$		0			0
$911$	−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
$915$		0			0
$916$	−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	−0.773929	−	0.633272i	$-0.781711\pi$
$919$	−18.5669	+	10.7196i	−0.612464	+	0.353606i	0.161465	+	0.986878i	$0.448378\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	−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	0.150472	−	0.988614i	$-0.451921\pi$
$929$	−6.50804	−	1.74382i	−0.213522	−	0.0572130i	−0.363994	+	0.931401i	$0.618587\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	−20.8392	+	13.6762i	−0.681152	+	0.447020i
$937$	18.4026	−	18.4026i	0.601188	−	0.601188i	−0.339440	−	0.940628i	$-0.610237\pi$
$937$	18.4026	−	18.4026i	0.601188	−	0.601188i	0.940628	+	0.339440i	$0.110237\pi$
$938$	−3.07817	−	1.77718i	−0.100506	−	0.0580271i
$939$	−40.2772	−	23.2541i	−1.31440	−	0.758868i
$940$		0			0
$941$	32.3684	+	32.3684i	1.05518	+	1.05518i	0.998386	+	0.0567952i	$0.0180882\pi$
$941$	32.3684	+	32.3684i	1.05518	+	1.05518i	0.0567952	+	0.998386i	$0.481912\pi$
$942$	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
$945$		0			0
$946$	16.5614	+	9.56175i	0.538459	+	0.310879i
$947$	−25.0053	−	14.4368i	−0.812562	−	0.469133i	0.0352831	−	0.999377i	$-0.488767\pi$
$947$	−25.0053	−	14.4368i	−0.812562	−	0.469133i	−0.847845	+	0.530245i	$0.822100\pi$
$948$	17.2703	−	17.2703i	0.560913	−	0.560913i
$949$	6.26157	−	0.358377i	0.203259	−	0.0116334i
$950$		0			0
$951$	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	$-0.324179\pi$
$953$	17.0854	+	4.57801i	0.553449	+	0.148296i	0.0287541	+	0.999587i	$0.490846\pi$
$954$	34.6406	−	34.6406i	1.12153	−	1.12153i
$955$		0			0
$956$	−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
$960$		0			0
$961$		−	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
$965$		0			0
$966$	0.960240	−	0.554395i	0.0308952	−	0.0178374i
$967$	−0.721666			−0.0232072			−0.0116036	−	0.999933i	$-0.503694\pi$
$967$	−0.721666			−0.0232072			−0.0116036	+	0.999933i	$0.503694\pi$
$968$	−1.69040	+	0.975956i	−0.0543317	+	0.0313684i
$969$	27.6050	−	103.023i	0.886800	−	3.30958i
$970$		0			0
$971$	15.4150	+	26.6996i	0.494691	+	0.856830i	0.999981	−	0.00611936i	$-0.00194787\pi$
$971$	15.4150	+	26.6996i	0.494691	+	0.856830i	−0.505290	+	0.862950i	$0.668615\pi$
$972$	−19.2014	+	5.14501i	−0.615886	+	0.165026i
$973$	6.14140	−	10.6372i	0.196884	−	0.341014i
$974$	−0.244616			−0.00783799
$975$		0			0
$976$	−2.23796			−0.0716355
$977$	−9.26370	+	16.0452i	−0.296372	+	0.513331i	−0.975303	−	0.220871i	$-0.929110\pi$
$977$	−9.26370	+	16.0452i	−0.296372	+	0.513331i	0.678931	+	0.734202i	$0.262443\pi$
$978$	−20.1497	+	5.39910i	−0.644317	+	0.172644i
$979$	9.20319	+	15.9404i	0.294135	+	0.509457i
$980$		0			0
$981$	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	$-0.485240\pi$
$983$	2.90661			0.0927066			0.0463533	+	0.998925i	$0.485240\pi$
$984$	−4.60390	+	2.65807i	−0.146767	+	0.0847360i
$985$		0			0
$986$	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
$990$		0			0
$991$	25.5607	−	44.2724i	0.811961	−	1.40636i	−0.0995281	−	0.995035i	$-0.531733\pi$
$991$	25.5607	−	44.2724i	0.811961	−	1.40636i	0.911489	−	0.411323i	$-0.134933\pi$
$992$	0.196373	−	0.732873i	0.00623484	−	0.0232687i
$993$			3.77313i			0.119737i
$994$	7.91860	+	2.12178i	0.251163	+	0.0672989i
$995$		0			0
$996$	34.8299	−	34.8299i	1.10363	−	1.10363i
$997$	−3.73922	−	1.00192i	−0.118422	−	0.0317312i	0.199121	−	0.979975i	$-0.436191\pi$
$997$	−3.73922	−	1.00192i	−0.118422	−	0.0317312i	−0.317543	+	0.948244i	$0.602858\pi$
$998$	−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	650.2.w.e.293.3		12
5.2	odd	4		650.2.t.e.7.1		12
5.3	odd	4		130.2.p.a.7.3	✓	12
5.4	even	2		130.2.s.a.33.1	yes	12
13.2	odd	12		650.2.t.e.93.1		12
65.2	even	12	inner	650.2.w.e.457.3		12
65.28	even	12		130.2.s.a.67.1	yes	12
65.54	odd	12		130.2.p.a.93.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.a.7.3	✓	12	5.3	odd	4
130.2.p.a.93.3	yes	12	65.54	odd	12
130.2.s.a.33.1	yes	12	5.4	even	2
130.2.s.a.67.1	yes	12	65.28	even	12
650.2.t.e.7.1		12	5.2	odd	4
650.2.t.e.93.1		12	13.2	odd	12
650.2.w.e.293.3		12	1.1	even	1	trivial
650.2.w.e.457.3		12	65.2	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (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} +(0.814901 - 3.04125i) q^{6} +(-0.696972 + 0.402397i) q^{7} -1.00000 q^{8} +(5.98707 - 3.45663i) q^{9} +(-0.778529 - 2.90551i) q^{11} +(-2.22635 - 2.22635i) q^{12} +(3.59966 - 0.206024i) q^{13} +0.804795i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.87508 + 6.99788i) q^{17} -6.91327i q^{18} +(-4.51652 - 1.21020i) q^{19} +(-1.79175 + 1.79175i) q^{21} +(-2.90551 - 0.778529i) q^{22} +(-0.113254 - 0.422668i) q^{23} +(-3.04125 + 0.814901i) q^{24} +(1.62141 - 3.22041i) q^{26} +(8.71230 - 8.71230i) q^{27} +(0.696972 + 0.402397i) q^{28} +(3.58287 + 2.06857i) q^{29} +(-0.536500 - 0.536500i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-4.73540 - 8.20196i) q^{33} +(5.12281 + 5.12281i) q^{34} +(-5.98707 - 3.45663i) q^{36} +(-0.835172 - 0.482187i) q^{37} +(-3.30632 + 3.30632i) q^{38} +(10.7796 - 3.55994i) q^{39} +(1.63091 - 0.437002i) q^{41} +(0.655828 + 2.44758i) q^{42} +(-6.14091 - 1.64545i) q^{43} +(-2.12698 + 2.12698i) q^{44} +(-0.422668 - 0.113254i) q^{46} +1.72276i q^{47} +(-0.814901 + 3.04125i) q^{48} +(-3.17615 + 5.50126i) q^{49} +22.8103i q^{51} +(-1.97825 - 3.01438i) q^{52} +(5.01074 + 5.01074i) q^{53} +(-3.18892 - 11.9012i) q^{54} +(0.696972 - 0.402397i) q^{56} -14.7221 q^{57} +(3.58287 - 2.06857i) q^{58} +(0.0422769 - 0.157780i) q^{59} +(1.11898 + 1.93813i) q^{61} +(-0.732873 + 0.196373i) q^{62} +(-2.78188 + 4.81836i) q^{63} +1.00000 q^{64} -9.47080 q^{66} +(-2.20825 + 3.82479i) q^{67} +(6.99788 - 1.87508i) q^{68} +(-0.688865 - 1.19315i) q^{69} +(2.63643 - 9.83928i) q^{71} +(-5.98707 + 3.45663i) q^{72} +1.73949 q^{73} +(-0.835172 + 0.482187i) q^{74} +(1.21020 + 4.51652i) q^{76} +(1.71178 + 1.71178i) q^{77} +(2.30679 - 11.1154i) q^{78} +7.75722i q^{79} +(9.02673 - 15.6348i) q^{81} +(0.437002 - 1.63091i) q^{82} +15.6444i q^{83} +(2.44758 + 0.655828i) q^{84} +(-4.49546 + 4.49546i) q^{86} +(12.5821 + 3.37136i) q^{87} +(0.778529 + 2.90551i) q^{88} +(-5.91063 + 1.58375i) q^{89} +(-2.42596 + 1.59209i) q^{91} +(-0.309415 + 0.309415i) q^{92} +(-2.06883 - 1.19444i) q^{93} +(1.49195 + 0.861379i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 6 q^{7} - 12 q^{8} + 24 q^{9} + 6 q^{11} + 6 q^{13} - 6 q^{16} - 36 q^{19} - 24 q^{21} - 6 q^{23} + 6 q^{26} + 12 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{31} + 6 q^{32} - 18 q^{33}+ \cdots - 54 q^{99}+O(q^{100}) \) 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^16 - 36 * q^19 - 24 * q^21 - 6 * q^23 + 6 * q^26 + 12 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^31 + 6 * q^32 - 18 * q^33 + 12 * q^34 - 24 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^39 + 18 * q^41 - 18 * q^42 - 6 * q^44 - 6 * q^46 - 18 * q^53 + 6 * q^54 + 6 * q^56 - 6 * q^58 - 18 * q^59 + 18 * q^61 - 36 * q^62 + 12 * q^64 - 36 * q^66 - 24 * q^67 + 12 * q^68 + 42 * q^69 + 18 * q^71 - 24 * q^72 + 12 * q^73 - 6 * q^74 + 30 * q^76 + 30 * q^77 - 30 * q^78 + 30 * q^81 + 18 * q^82 + 6 * q^84 + 60 * q^87 - 6 * q^88 - 6 * q^89 - 6 * q^91 + 30 * q^93 - 24 * q^94 - 6 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more