LMFDB - Embedded newform 494.2.h.d.315.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [494,2,Mod(315,494)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("494.315"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(494, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 494 = 2 \cdot 13 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	494.h (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22,22,0,22,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$3.94460985985$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.8
Character	$\chi$	$=$	494.315
Dual form			494.2.h.d.425.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.40196 q^{3} +1.00000 q^{4} +(2.07009 - 3.58550i) q^{5} +1.40196 q^{6} +(-1.49255 + 2.58517i) q^{7} +1.00000 q^{8} -1.03450 q^{9} +(2.07009 - 3.58550i) q^{10} +(0.870115 + 1.50708i) q^{11} +1.40196 q^{12} +(1.77099 + 3.14064i) q^{13} +(-1.49255 + 2.58517i) q^{14} +(2.90218 - 5.02673i) q^{15} +1.00000 q^{16} +(-0.958786 - 1.66067i) q^{17} -1.03450 q^{18} +(1.52372 - 4.08390i) q^{19} +(2.07009 - 3.58550i) q^{20} +(-2.09250 + 3.62431i) q^{21} +(0.870115 + 1.50708i) q^{22} +(0.667216 - 1.15565i) q^{23} +1.40196 q^{24} +(-6.07052 - 10.5144i) q^{25} +(1.77099 + 3.14064i) q^{26} -5.65622 q^{27} +(-1.49255 + 2.58517i) q^{28} +(-4.25646 + 7.37240i) q^{29} +(2.90218 - 5.02673i) q^{30} -2.21976 q^{31} +1.00000 q^{32} +(1.21987 + 2.11287i) q^{33} +(-0.958786 - 1.66067i) q^{34} +(6.17941 + 10.7030i) q^{35} -1.03450 q^{36} +(-5.50065 - 9.52741i) q^{37} +(1.52372 - 4.08390i) q^{38} +(2.48286 + 4.40306i) q^{39} +(2.07009 - 3.58550i) q^{40} -1.82630 q^{41} +(-2.09250 + 3.62431i) q^{42} +(2.91447 + 5.04801i) q^{43} +(0.870115 + 1.50708i) q^{44} +(-2.14151 + 3.70920i) q^{45} +(0.667216 - 1.15565i) q^{46} +(4.55241 + 7.88500i) q^{47} +1.40196 q^{48} +(-0.955401 - 1.65480i) q^{49} +(-6.07052 - 10.5144i) q^{50} +(-1.34418 - 2.32819i) q^{51} +(1.77099 + 3.14064i) q^{52} +(-0.629479 - 1.09029i) q^{53} -5.65622 q^{54} +7.20485 q^{55} +(-1.49255 + 2.58517i) q^{56} +(2.13620 - 5.72548i) q^{57} +(-4.25646 + 7.37240i) q^{58} +(1.32913 + 2.30212i) q^{59} +(2.90218 - 5.02673i) q^{60} -2.34851 q^{61} -2.21976 q^{62} +(1.54404 - 2.67436i) q^{63} +1.00000 q^{64} +(14.9268 + 0.151530i) q^{65} +(1.21987 + 2.11287i) q^{66} +(-5.92238 + 10.2579i) q^{67} +(-0.958786 - 1.66067i) q^{68} +(0.935412 - 1.62018i) q^{69} +(6.17941 + 10.7030i) q^{70} +(4.22117 + 7.31128i) q^{71} -1.03450 q^{72} +(-5.78569 + 10.0211i) q^{73} +(-5.50065 - 9.52741i) q^{74} +(-8.51064 - 14.7409i) q^{75} +(1.52372 - 4.08390i) q^{76} -5.19475 q^{77} +(2.48286 + 4.40306i) q^{78} +(7.59090 - 13.1478i) q^{79} +(2.07009 - 3.58550i) q^{80} -4.82630 q^{81} -1.82630 q^{82} +5.33295 q^{83} +(-2.09250 + 3.62431i) q^{84} -7.93908 q^{85} +(2.91447 + 5.04801i) q^{86} +(-5.96739 + 10.3358i) q^{87} +(0.870115 + 1.50708i) q^{88} +(-4.67331 + 8.09441i) q^{89} +(-2.14151 + 3.70920i) q^{90} +(-10.7624 - 0.109255i) q^{91} +(0.667216 - 1.15565i) q^{92} -3.11201 q^{93} +(4.55241 + 7.88500i) q^{94} +(-11.4886 - 13.9173i) q^{95} +1.40196 q^{96} +(-3.10147 - 5.37191i) q^{97} +(-0.955401 - 1.65480i) q^{98} +(-0.900135 - 1.55908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 22 q^{4} - 2 q^{5} - 5 q^{7} + 22 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{13} - 5 q^{14} - 3 q^{15} + 22 q^{16} + q^{17} + 10 q^{18} + 12 q^{19} - 2 q^{20} + q^{21} - 2 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) $ 22 * q + 22 * q^2 + 22 * q^4 - 2 * q^5 - 5 * q^7 + 22 * q^8 + 10 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^13 - 5 * q^14 - 3 * q^15 + 22 * q^16 + q^17 + 10 * q^18 + 12 * q^19 - 2 * q^20 + q^21 - 2 * q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 6 * q^27 - 5 * q^28 - 7 * q^29 - 3 * q^30 + 6 * q^31 + 22 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 10 * q^36 - 9 * q^37 + 12 * q^38 + 13 * q^39 - 2 * q^40 - 24 * q^41 + q^42 - 10 * q^43 - 2 * q^44 - 15 * q^45 + 4 * q^46 + 19 * q^47 - 14 * q^49 - 9 * q^50 - 22 * q^51 + 2 * q^52 - 9 * q^53 - 6 * q^54 + 48 * q^55 - 5 * q^56 + 13 * q^57 - 7 * q^58 - 12 * q^59 - 3 * q^60 - 22 * q^61 + 6 * q^62 - 23 * q^63 + 22 * q^64 + 13 * q^65 - 4 * q^66 + 3 * q^67 + q^68 - 20 * q^69 - 3 * q^70 + 4 * q^71 + 10 * q^72 - 38 * q^73 - 9 * q^74 - 20 * q^75 + 12 * q^76 - 76 * q^77 + 13 * q^78 - 5 * q^79 - 2 * q^80 - 90 * q^81 - 24 * q^82 - 10 * q^83 + q^84 + 24 * q^85 - 10 * q^86 + 4 * q^87 - 2 * q^88 + 3 * q^89 - 15 * q^90 + 34 * q^91 + 4 * q^92 + 22 * q^93 + 19 * q^94 - 33 * q^95 - 31 * q^97 - 14 * q^98 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/494\mathbb{Z}\right)^\times$.

$n$	$287$	$457$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.40196			0.809423			0.404712	−	0.914444i	$-0.367372\pi$
$3$	1.40196			0.809423			0.404712	+	0.914444i	$0.367372\pi$
$4$	1.00000			0.500000
$5$	2.07009	−	3.58550i	0.925771	−	1.60348i	0.135454	−	0.990784i	$-0.456751\pi$
$5$	2.07009	−	3.58550i	0.925771	−	1.60348i	0.790317	−	0.612698i	$-0.209916\pi$
$6$	1.40196			0.572349
$7$	−1.49255	+	2.58517i	−0.564130	+	0.977102i	0.433000	+	0.901394i	$0.357455\pi$
$7$	−1.49255	+	2.58517i	−0.564130	+	0.977102i	−0.997130	+	0.0757082i	$0.975878\pi$
$8$	1.00000			0.353553
$9$	−1.03450			−0.344834
$10$	2.07009	−	3.58550i	0.654619	−	1.13383i
$11$	0.870115	+	1.50708i	0.262350	+	0.454403i	0.966866	−	0.255285i	$-0.0821693\pi$
$11$	0.870115	+	1.50708i	0.262350	+	0.454403i	−0.704516	+	0.709688i	$0.748836\pi$
$12$	1.40196			0.404712
$13$	1.77099	+	3.14064i	0.491183	+	0.871056i
$13$	1.77099	+	3.14064i	0.491183	+	0.871056i
$14$	−1.49255	+	2.58517i	−0.398900	+	0.690916i
$15$	2.90218	−	5.02673i	0.749341	−	1.29790i
$16$	1.00000			0.250000
$17$	−0.958786	−	1.66067i	−0.232540	−	0.402771i	0.726015	−	0.687679i	$-0.241370\pi$
$17$	−0.958786	−	1.66067i	−0.232540	−	0.402771i	−0.958555	+	0.284908i	$0.908037\pi$
$18$	−1.03450			−0.243834
$19$	1.52372	−	4.08390i	0.349565	−	0.936912i
$19$	1.52372	−	4.08390i	0.349565	−	0.936912i
$20$	2.07009	−	3.58550i	0.462885	−	0.801741i
$21$	−2.09250	+	3.62431i	−0.456620	+	0.790889i
$22$	0.870115	+	1.50708i	0.185509	+	0.321311i
$23$	0.667216	−	1.15565i	0.139124	−	0.240970i	−0.788041	−	0.615623i	$-0.788905\pi$
$23$	0.667216	−	1.15565i	0.139124	−	0.240970i	0.927165	+	0.374652i	$0.122238\pi$
$24$	1.40196			0.286174
$25$	−6.07052	−	10.5144i	−1.21410	−	2.10289i
$26$	1.77099	+	3.14064i	0.347319	+	0.615930i
$27$	−5.65622			−1.08854
$28$	−1.49255	+	2.58517i	−0.282065	+	0.488551i
$29$	−4.25646	+	7.37240i	−0.790404	+	1.36902i	0.135312	+	0.990803i	$0.456796\pi$
$29$	−4.25646	+	7.37240i	−0.790404	+	1.36902i	−0.925717	+	0.378217i	$0.876537\pi$
$30$	2.90218	−	5.02673i	0.529864	−	0.917751i
$31$	−2.21976			−0.398680			−0.199340	−	0.979930i	$-0.563880\pi$
$31$	−2.21976			−0.398680			−0.199340	+	0.979930i	$0.563880\pi$
$32$	1.00000			0.176777
$33$	1.21987	+	2.11287i	0.212352	+	0.367804i
$34$	−0.958786	−	1.66067i	−0.164430	−	0.284802i
$35$	6.17941	+	10.7030i	1.04451	+	1.80915i
$36$	−1.03450			−0.172417
$37$	−5.50065	−	9.52741i	−0.904302	−	1.56630i	−0.821852	−	0.569702i	$-0.807059\pi$
$37$	−5.50065	−	9.52741i	−0.904302	−	1.56630i	−0.0824503	−	0.996595i	$-0.526275\pi$
$38$	1.52372	−	4.08390i	0.247180	−	0.662497i
$39$	2.48286	+	4.40306i	0.397575	+	0.705053i
$40$	2.07009	−	3.58550i	0.327309	−	0.566917i
$41$	−1.82630			−0.285221			−0.142610	−	0.989779i	$-0.545550\pi$
$41$	−1.82630			−0.285221			−0.142610	+	0.989779i	$0.545550\pi$
$42$	−2.09250	+	3.62431i	−0.322879	+	0.559243i
$43$	2.91447	+	5.04801i	0.444453	+	0.769815i	0.998014	−	0.0629939i	$-0.0200649\pi$
$43$	2.91447	+	5.04801i	0.444453	+	0.769815i	−0.553561	+	0.832808i	$0.686732\pi$
$44$	0.870115	+	1.50708i	0.131175	+	0.227201i
$45$	−2.14151	+	3.70920i	−0.319237	+	0.552935i
$46$	0.667216	−	1.15565i	0.0983757	−	0.170392i
$47$	4.55241	+	7.88500i	0.664037	+	1.15015i	0.979546	+	0.201223i	$0.0644915\pi$
$47$	4.55241	+	7.88500i	0.664037	+	1.15015i	−0.315509	+	0.948923i	$0.602175\pi$
$48$	1.40196			0.202356
$49$	−0.955401	−	1.65480i	−0.136486	−	0.236400i
$50$	−6.07052	−	10.5144i	−0.858501	−	1.48697i
$51$	−1.34418	−	2.32819i	−0.188223	−	0.326012i
$52$	1.77099	+	3.14064i	0.245592	+	0.435528i
$53$	−0.629479	−	1.09029i	−0.0864656	−	0.149763i	0.819549	−	0.573009i	$-0.194224\pi$
$53$	−0.629479	−	1.09029i	−0.0864656	−	0.149763i	−0.906015	+	0.423246i	$0.860891\pi$
$54$	−5.65622			−0.769714
$55$	7.20485			0.971502
$56$	−1.49255	+	2.58517i	−0.199450	+	0.345458i
$57$	2.13620	−	5.72548i	0.282946	−	0.758358i
$58$	−4.25646	+	7.37240i	−0.558900	+	0.968044i
$59$	1.32913	+	2.30212i	0.173038	+	0.299711i	0.939481	−	0.342602i	$-0.111308\pi$
$59$	1.32913	+	2.30212i	0.173038	+	0.299711i	−0.766443	+	0.642313i	$0.777975\pi$
$60$	2.90218	−	5.02673i	0.374670	−	0.648948i
$61$	−2.34851			−0.300696			−0.150348	−	0.988633i	$-0.548039\pi$
$61$	−2.34851			−0.300696			−0.150348	+	0.988633i	$0.548039\pi$
$62$	−2.21976			−0.281909
$63$	1.54404	−	2.67436i	0.194531	−	0.336938i
$64$	1.00000			0.125000
$65$	14.9268	+	0.151530i	1.85145	+	0.0187950i
$66$	1.21987	+	2.11287i	0.150155	+	0.260077i
$67$	−5.92238	+	10.2579i	−0.723534	+	1.25320i	0.236041	+	0.971743i	$0.424150\pi$
$67$	−5.92238	+	10.2579i	−0.723534	+	1.25320i	−0.959575	+	0.281455i	$0.909183\pi$
$68$	−0.958786	−	1.66067i	−0.116270	−	0.201385i
$69$	0.935412	−	1.62018i	0.112610	−	0.195047i
$70$	6.17941	+	10.7030i	0.738581	+	1.27926i
$71$	4.22117	+	7.31128i	0.500961	+	0.867689i	0.999999	+	0.00110950i	$0.000353164\pi$
$71$	4.22117	+	7.31128i	0.500961	+	0.867689i	−0.499039	+	0.866580i	$0.666314\pi$
$72$	−1.03450			−0.121917
$73$	−5.78569	+	10.0211i	−0.677163	+	1.17288i	0.298668	+	0.954357i	$0.403458\pi$
$73$	−5.78569	+	10.0211i	−0.677163	+	1.17288i	−0.975831	+	0.218524i	$0.929876\pi$
$74$	−5.50065	−	9.52741i	−0.639438	−	1.10754i
$75$	−8.51064	−	14.7409i	−0.982724	−	1.70213i
$76$	1.52372	−	4.08390i	0.174783	−	0.468456i
$77$	−5.19475			−0.591997
$78$	2.48286	+	4.40306i	0.281128	+	0.498548i
$79$	7.59090	−	13.1478i	0.854043	−	1.47925i	−0.0234871	−	0.999724i	$-0.507477\pi$
$79$	7.59090	−	13.1478i	0.854043	−	1.47925i	0.877530	−	0.479522i	$-0.159190\pi$
$80$	2.07009	−	3.58550i	0.231443	−	0.400871i
$81$	−4.82630			−0.536256
$82$	−1.82630			−0.201682
$83$	5.33295			0.585368			0.292684	−	0.956209i	$-0.405452\pi$
$83$	5.33295			0.585368			0.292684	+	0.956209i	$0.405452\pi$
$84$	−2.09250	+	3.62431i	−0.228310	+	0.395445i
$85$	−7.93908			−0.861114
$86$	2.91447	+	5.04801i	0.314275	+	0.544341i
$87$	−5.96739	+	10.3358i	−0.639772	+	1.10812i
$88$	0.870115	+	1.50708i	0.0927546	+	0.160656i
$89$	−4.67331	+	8.09441i	−0.495370	+	0.858005i	−0.999986	−	0.00533854i	$-0.998301\pi$
$89$	−4.67331	+	8.09441i	−0.495370	+	0.858005i	0.504616	+	0.863344i	$0.331634\pi$
$90$	−2.14151	+	3.70920i	−0.225735	+	0.390984i
$91$	−10.7624	−	0.109255i	−1.12820	−	0.0114530i
$92$	0.667216	−	1.15565i	0.0695621	−	0.120485i
$93$	−3.11201			−0.322701
$94$	4.55241	+	7.88500i	0.469545	+	0.813276i
$95$	−11.4886	−	13.9173i	−1.17870	−	1.42789i
$96$	1.40196			0.143087
$97$	−3.10147	−	5.37191i	−0.314907	−	0.545435i	0.664511	−	0.747279i	$-0.268640\pi$
$97$	−3.10147	−	5.37191i	−0.314907	−	0.545435i	−0.979418	+	0.201844i	$0.935307\pi$
$98$	−0.955401	−	1.65480i	−0.0965101	−	0.167160i
$99$	−0.900135	−	1.55908i	−0.0904670	−	0.156693i
$100$	−6.07052	−	10.5144i	−0.607052	−	1.05144i
$101$	−1.34774	+	2.33435i	−0.134105	+	0.232276i	−0.925255	−	0.379345i	$-0.876149\pi$
$101$	−1.34774	+	2.33435i	−0.134105	+	0.232276i	0.791150	+	0.611622i	$0.209483\pi$
$102$	−1.34418	−	2.32819i	−0.133094	−	0.230525i
$103$	0.671870			0.0662014			0.0331007	−	0.999452i	$-0.489462\pi$
$103$	0.671870			0.0662014			0.0331007	+	0.999452i	$0.489462\pi$
$104$	1.77099	+	3.14064i	0.173659	+	0.307965i
$105$	8.66330	+	15.0053i	0.845451	+	1.46436i
$106$	−0.629479	−	1.09029i	−0.0611404	−	0.105898i
$107$	−6.20149	−	10.7413i	−0.599521	−	1.03840i	−0.992892	−	0.119021i	$-0.962024\pi$
$107$	−6.20149	−	10.7413i	−0.599521	−	1.03840i	0.393371	−	0.919380i	$-0.371309\pi$
$108$	−5.65622			−0.544270
$109$	9.33720	−	16.1725i	0.894341	−	1.54904i	0.0597233	−	0.998215i	$-0.480978\pi$
$109$	9.33720	−	16.1725i	0.894341	−	1.54904i	0.834618	−	0.550829i	$-0.185688\pi$
$110$	7.20485			0.686956
$111$	−7.71171	−	13.3571i	−0.731963	−	1.26780i
$112$	−1.49255	+	2.58517i	−0.141033	+	0.244276i
$113$	−4.55539	+	7.89018i	−0.428536	+	0.742245i	−0.996743	−	0.0806398i	$-0.974304\pi$
$113$	−4.55539	+	7.89018i	−0.428536	+	0.742245i	0.568208	+	0.822885i	$0.307637\pi$
$114$	2.13620	−	5.72548i	0.200073	−	0.536240i
$115$	−2.76239	−	4.78460i	−0.257594	−	0.446166i
$116$	−4.25646	+	7.37240i	−0.395202	+	0.684510i
$117$	−1.83209	−	3.24899i	−0.169377	−	0.300370i
$118$	1.32913	+	2.30212i	0.122356	+	0.211927i
$119$	5.72414			0.524731
$120$	2.90218	−	5.02673i	0.264932	−	0.458876i
$121$	3.98580	−	6.90361i	0.362345	−	0.627601i
$122$	−2.34851			−0.212624
$123$	−2.56041			−0.230864
$124$	−2.21976			−0.199340
$125$	−29.5651			−2.64438
$126$	1.54404	−	2.67436i	0.137554	−	0.238251i
$127$	2.04690	−	3.54534i	0.181633	−	0.314598i	−0.760804	−	0.648982i	$-0.775195\pi$
$127$	2.04690	−	3.54534i	0.181633	−	0.314598i	0.942437	+	0.334384i	$0.108528\pi$
$128$	1.00000			0.0883883
$129$	4.08598	+	7.07712i	0.359750	+	0.623106i
$130$	14.9268	+	0.151530i	1.30917	+	0.0132901i
$131$	4.87502	−	8.44378i	0.425932	−	0.737737i	−0.570575	−	0.821246i	$-0.693279\pi$
$131$	4.87502	−	8.44378i	0.425932	−	0.737737i	0.996507	+	0.0835092i	$0.0266128\pi$
$132$	1.21987	+	2.11287i	0.106176	+	0.183902i
$133$	8.28336	+	10.0345i	0.718258	+	0.870102i
$134$	−5.92238	+	10.2579i	−0.511616	+	0.886145i
$135$	−11.7089	+	20.2803i	−1.00774	+	1.74545i
$136$	−0.958786	−	1.66067i	−0.0822152	−	0.142401i
$137$	11.8362			1.01123			0.505617	−	0.862758i	$-0.331265\pi$
$137$	11.8362			1.01123			0.505617	+	0.862758i	$0.331265\pi$
$138$	0.935412	−	1.62018i	0.0796276	−	0.137919i
$139$	5.37935			0.456271			0.228135	−	0.973629i	$-0.426737\pi$
$139$	5.37935			0.456271			0.228135	+	0.973629i	$0.426737\pi$
$140$	6.17941	+	10.7030i	0.522255	+	0.904573i
$141$	6.38230	+	11.0545i	0.537487	+	0.930955i
$142$	4.22117	+	7.31128i	0.354233	+	0.613549i
$143$	−3.19224	+	5.40174i	−0.266949	+	0.451716i
$144$	−1.03450			−0.0862084
$145$	17.6225	+	30.5230i	1.46347	+	2.53480i
$146$	−5.78569	+	10.0211i	−0.478827	+	0.829353i
$147$	−1.33944	−	2.31997i	−0.110475	−	0.191348i
$148$	−5.50065	−	9.52741i	−0.452151	−	0.783148i
$149$	0.801263	+	1.38783i	0.0656420	+	0.113695i	0.896979	−	0.442074i	$-0.145757\pi$
$149$	0.801263	+	1.38783i	0.0656420	+	0.113695i	−0.831337	+	0.555769i	$0.812424\pi$
$150$	−8.51064	−	14.7409i	−0.694891	−	1.20359i
$151$	7.39245			0.601589			0.300795	−	0.953689i	$-0.402748\pi$
$151$	7.39245			0.601589			0.300795	+	0.953689i	$0.402748\pi$
$152$	1.52372	−	4.08390i	0.123590	−	0.331248i
$153$	0.991865	+	1.71796i	0.0801875	+	0.138889i
$154$	−5.19475			−0.418605
$155$	−4.59509	+	7.95892i	−0.369086	+	0.639276i
$156$	2.48286	+	4.40306i	0.198788	+	0.352527i
$157$	9.83272	−	17.0308i	0.784737	−	1.35920i	−0.144420	−	0.989517i	$-0.546131\pi$
$157$	9.83272	−	17.0308i	0.784737	−	1.35920i	0.929156	−	0.369687i	$-0.120535\pi$
$158$	7.59090	−	13.1478i	0.603900	−	1.04598i
$159$	−0.882506	−	1.52855i	−0.0699873	−	0.121222i
$160$	2.07009	−	3.58550i	0.163655	−	0.283458i
$161$	1.99170	+	3.44973i	0.156968	+	0.271877i
$162$	−4.82630			−0.379190
$163$	−4.52736	+	7.84161i	−0.354610	+	0.614202i	−0.987051	−	0.160406i	$-0.948720\pi$
$163$	−4.52736	+	7.84161i	−0.354610	+	0.614202i	0.632441	+	0.774608i	$0.282053\pi$
$164$	−1.82630			−0.142610
$165$	10.1009			0.786357
$166$	5.33295			0.413917
$167$	4.57067	−	7.91664i	0.353689	−	0.612608i	−0.633203	−	0.773985i	$-0.718260\pi$
$167$	4.57067	−	7.91664i	0.353689	−	0.612608i	0.986893	+	0.161378i	$0.0515937\pi$
$168$	−2.09250	+	3.62431i	−0.161440	+	0.279622i
$169$	−6.72722	+	11.1241i	−0.517478	+	0.855696i
$170$	−7.93908			−0.608900
$171$	−1.57629	+	4.22480i	−0.120542	+	0.323079i
$172$	2.91447	+	5.04801i	0.222226	+	0.384907i
$173$	0.0296150	+	0.0512947i	0.00225159	+	0.00389986i	0.867149	−	0.498049i	$-0.165950\pi$
$173$	0.0296150	+	0.0512947i	0.00225159	+	0.00389986i	−0.864897	+	0.501949i	$0.832617\pi$
$174$	−5.96739	+	10.3358i	−0.452387	+	0.783557i
$175$	36.2422			2.73965
$176$	0.870115	+	1.50708i	0.0655874	+	0.113601i
$177$	1.86339	+	3.22749i	0.140061	+	0.242593i
$178$	−4.67331	+	8.09441i	−0.350279	+	0.606701i
$179$	−10.3608	−	17.9455i	−0.774404	−	1.34131i	−0.935129	−	0.354308i	$-0.884716\pi$
$179$	−10.3608	−	17.9455i	−0.774404	−	1.34131i	0.160724	−	0.986999i	$-0.448617\pi$
$180$	−2.14151	+	3.70920i	−0.159619	+	0.276467i
$181$	−9.60677	−	16.6394i	−0.714066	−	1.23680i	−0.963319	−	0.268359i	$-0.913518\pi$
$181$	−9.60677	−	16.6394i	−0.714066	−	1.23680i	0.249253	−	0.968438i	$-0.419815\pi$
$182$	−10.7624	−	0.109255i	−0.797760	−	0.00809849i
$183$	−3.29252			−0.243390
$184$	0.667216	−	1.15565i	0.0491878	−	0.0851958i
$185$	−45.5473			−3.34871
$186$	−3.11201			−0.228184
$187$	1.66851	−	2.88994i	0.122013	−	0.211333i
$188$	4.55241	+	7.88500i	0.332018	+	0.575073i
$189$	8.44218	−	14.6223i	0.614078	−	1.06361i
$190$	−11.4886	−	13.9173i	−0.833470	−	1.00967i
$191$	13.6378	−	23.6214i	0.986799	−	1.70919i	0.353148	−	0.935567i	$-0.385111\pi$
$191$	13.6378	−	23.6214i	0.986799	−	1.70919i	0.633651	−	0.773619i	$-0.281555\pi$
$192$	1.40196			0.101178
$193$	0.620649			0.0446753			0.0223376	−	0.999750i	$-0.492889\pi$
$193$	0.620649			0.0446753			0.0223376	+	0.999750i	$0.492889\pi$
$194$	−3.10147	−	5.37191i	−0.222673	−	0.385681i
$195$	20.9269	+	0.212440i	1.49860	+	0.0152131i
$196$	−0.955401	−	1.65480i	−0.0682429	−	0.118200i
$197$	−2.37109	−	4.10684i	−0.168933	−	0.292600i	0.769112	−	0.639114i	$-0.220699\pi$
$197$	−2.37109	−	4.10684i	−0.168933	−	0.292600i	−0.938045	+	0.346514i	$0.887365\pi$
$198$	−0.900135	−	1.55908i	−0.0639698	−	0.110799i
$199$	2.73492			0.193874			0.0969368	−	0.995291i	$-0.469096\pi$
$199$	2.73492			0.193874			0.0969368	+	0.995291i	$0.469096\pi$
$200$	−6.07052	−	10.5144i	−0.429250	−	0.743483i
$201$	−8.30296	+	14.3811i	−0.585645	+	1.01437i
$202$	−1.34774	+	2.33435i	−0.0948264	+	0.164244i
$203$	−12.7059	−	22.0073i	−0.891782	−	1.54461i
$204$	−1.34418	−	2.32819i	−0.0941116	−	0.163006i
$205$	−3.78061	+	6.54820i	−0.264049	+	0.457346i
$206$	0.671870			0.0468114
$207$	−0.690236	+	1.19552i	−0.0479747	+	0.0830946i
$208$	1.77099	+	3.14064i	0.122796	+	0.217764i
$209$	7.48060	−	1.25709i	0.517444	−	0.0869549i
$210$	8.66330	+	15.0053i	0.597824	+	1.03546i
$211$	−10.6505			−0.733212			−0.366606	−	0.930376i	$-0.619480\pi$
$211$	−10.6505			−0.733212			−0.366606	+	0.930376i	$0.619480\pi$
$212$	−0.629479	−	1.09029i	−0.0432328	−	0.0748814i
$213$	5.91792	+	10.2501i	0.405489	+	0.702328i
$214$	−6.20149	−	10.7413i	−0.423925	−	0.734260i
$215$	24.1328			1.64585
$216$	−5.65622			−0.384857
$217$	3.31309	−	5.73844i	0.224907	−	0.389551i
$218$	9.33720	−	16.1725i	0.632395	−	1.09534i
$219$	−8.11132	+	14.0492i	−0.548112	+	0.949358i
$220$	7.20485			0.485751
$221$	3.51755	−	5.95222i	0.236616	−	0.400389i
$222$	−7.71171	−	13.3571i	−0.517576	−	0.896468i
$223$	1.86129			0.124641			0.0623207	−	0.998056i	$-0.480150\pi$
$223$	1.86129			0.124641			0.0623207	+	0.998056i	$0.480150\pi$
$224$	−1.49255	+	2.58517i	−0.0997251	+	0.172729i
$225$	6.27996	+	10.8772i	0.418664	+	0.725147i
$226$	−4.55539	+	7.89018i	−0.303020	+	0.524847i
$227$	−9.97749	+	17.2815i	−0.662230	+	1.14702i	0.317799	+	0.948158i	$0.397056\pi$
$227$	−9.97749	+	17.2815i	−0.662230	+	1.14702i	−0.980029	+	0.198857i	$0.936277\pi$
$228$	2.13620	−	5.72548i	0.141473	−	0.379179i
$229$	−19.9778			−1.32017			−0.660085	−	0.751191i	$-0.729480\pi$
$229$	−19.9778			−1.32017			−0.660085	+	0.751191i	$0.729480\pi$
$230$	−2.76239	−	4.78460i	−0.182147	−	0.315487i
$231$	−7.28285			−0.479176
$232$	−4.25646	+	7.37240i	−0.279450	+	0.484022i
$233$	7.13929	−	12.3656i	0.467710	−	0.810098i	−0.531609	−	0.846990i	$-0.678412\pi$
$233$	7.13929	−	12.3656i	0.467710	−	0.810098i	0.999319	+	0.0368918i	$0.0117457\pi$
$234$	−1.83209	−	3.24899i	−0.119767	−	0.212393i
$235$	37.6955			2.45898
$236$	1.32913	+	2.30212i	0.0865190	+	0.149855i
$237$	10.6422	−	18.4328i	0.691282	−	1.19734i
$238$	5.72414			0.371041
$239$	−7.45761			−0.482392			−0.241196	−	0.970476i	$-0.577540\pi$
$239$	−7.45761			−0.482392			−0.241196	+	0.970476i	$0.577540\pi$
$240$	2.90218	−	5.02673i	0.187335	−	0.324474i
$241$	25.1117			1.61759			0.808795	−	0.588091i	$-0.200120\pi$
$241$	25.1117			1.61759			0.808795	+	0.588091i	$0.200120\pi$
$242$	3.98580	−	6.90361i	0.256217	−	0.443781i
$243$	10.2024			0.654482
$244$	−2.34851			−0.150348
$245$	−7.91105			−0.505418
$246$	−2.56041			−0.163246
$247$	15.5246	−	2.44708i	0.987804	−	0.155704i
$248$	−2.21976			−0.140955
$249$	7.47660			0.473810
$250$	−29.5651			−1.86986
$251$	−30.8107			−1.94475			−0.972377	−	0.233415i	$-0.925010\pi$
$251$	−30.8107			−1.94475			−0.972377	+	0.233415i	$0.925010\pi$
$252$	1.54404	−	2.67436i	0.0972656	−	0.168469i
$253$	2.32222			0.145997
$254$	2.04690	−	3.54534i	0.128434	−	0.222454i
$255$	−11.1303			−0.697006
$256$	1.00000			0.0625000
$257$	−9.41325	+	16.3042i	−0.587182	+	1.01703i	0.407417	+	0.913242i	$0.366430\pi$
$257$	−9.41325	+	16.3042i	−0.587182	+	1.01703i	−0.994599	+	0.103788i	$0.966904\pi$
$258$	4.08598	+	7.07712i	0.254382	+	0.440602i
$259$	32.8400			2.04058
$260$	14.9268	+	0.151530i	0.925723	+	0.00939751i
$261$	4.40331	−	7.62676i	0.272558	−	0.472084i
$262$	4.87502	−	8.44378i	0.301180	−	0.521658i
$263$	20.1704			1.24376			0.621879	−	0.783113i	$-0.286370\pi$
$263$	20.1704			1.24376			0.621879	+	0.783113i	$0.286370\pi$
$264$	1.21987	+	2.11287i	0.0750777	+	0.130038i
$265$	−5.21231			−0.320189
$266$	8.28336	+	10.0345i	0.507885	+	0.615255i
$267$	−6.55180	+	11.3481i	−0.400964	+	0.694490i
$268$	−5.92238	+	10.2579i	−0.361767	+	0.626599i
$269$	11.2931	+	19.5602i	0.688553	+	1.19261i	0.972306	+	0.233712i	$0.0750872\pi$
$269$	11.2931	+	19.5602i	0.688553	+	1.19261i	−0.283753	+	0.958897i	$0.591579\pi$
$270$	−11.7089	+	20.2803i	−0.712579	+	1.23422i
$271$	3.80977			0.231427			0.115714	−	0.993283i	$-0.463085\pi$
$271$	3.80977			0.231427			0.115714	+	0.993283i	$0.463085\pi$
$272$	−0.958786	−	1.66067i	−0.0581349	−	0.100693i
$273$	−15.0884	−	0.153171i	−0.913193	−	0.00927032i
$274$	11.8362			0.715051
$275$	10.5641	−	18.2975i	0.637039	−	1.10338i
$276$	0.935412	−	1.62018i	0.0563052	−	0.0975235i
$277$	0.340617	−	0.589967i	0.0204657	−	0.0354477i	−0.855611	−	0.517619i	$-0.826818\pi$
$277$	0.340617	−	0.589967i	0.0204657	−	0.0354477i	0.876077	+	0.482171i	$0.160152\pi$
$278$	5.37935			0.322632
$279$	2.29634			0.137478
$280$	6.17941	+	10.7030i	0.369290	+	0.639630i
$281$	−0.975740	−	1.69003i	−0.0582078	−	0.100819i	0.835453	−	0.549562i	$-0.185205\pi$
$281$	−0.975740	−	1.69003i	−0.0582078	−	0.100819i	−0.893661	+	0.448743i	$0.851872\pi$
$282$	6.38230	+	11.0545i	0.380061	+	0.658284i
$283$	28.7409			1.70847			0.854233	−	0.519890i	$-0.174027\pi$
$283$	28.7409			1.70847			0.854233	+	0.519890i	$0.174027\pi$
$284$	4.22117	+	7.31128i	0.250480	+	0.433845i
$285$	−16.1066	−	19.5116i	−0.954071	−	1.15577i
$286$	−3.19224	+	5.40174i	−0.188761	+	0.319412i
$287$	2.72585	−	4.72130i	0.160902	−	0.278690i
$288$	−1.03450			−0.0609586
$289$	6.66146	−	11.5380i	0.391851	−	0.678705i
$290$	17.6225	+	30.5230i	1.03483	+	1.79237i
$291$	−4.34815	−	7.53121i	−0.254893	−	0.441488i
$292$	−5.78569	+	10.0211i	−0.338582	+	0.586441i
$293$	5.32861	−	9.22943i	0.311301	−	0.539189i	−0.667343	−	0.744750i	$-0.732569\pi$
$293$	5.32861	−	9.22943i	0.311301	−	0.539189i	0.978644	+	0.205561i	$0.0659020\pi$
$294$	−1.33944	−	2.31997i	−0.0781175	−	0.135303i
$295$	11.0057			0.640774
$296$	−5.50065	−	9.52741i	−0.319719	−	0.553770i
$297$	−4.92156	−	8.52439i	−0.285578	−	0.494635i
$298$	0.801263	+	1.38783i	0.0464159	+	0.0803947i
$299$	4.81112	+	0.0488402i	0.278234	+	0.00282450i
$300$	−8.51064	−	14.7409i	−0.491362	−	0.851064i
$301$	−17.4000			−1.00292
$302$	7.39245			0.425388
$303$	−1.88948	+	3.27267i	−0.108548	+	0.188010i
$304$	1.52372	−	4.08390i	0.0873914	−	0.234228i
$305$	−4.86162	+	8.42057i	−0.278375	+	0.482160i
$306$	0.991865	+	1.71796i	0.0567012	+	0.0982093i
$307$	−12.6954	+	21.9890i	−0.724563	+	1.25498i	0.234591	+	0.972094i	$0.424625\pi$
$307$	−12.6954	+	21.9890i	−0.724563	+	1.25498i	−0.959154	+	0.282885i	$0.908708\pi$
$308$	−5.19475			−0.295999
$309$	0.941937			0.0535849
$310$	−4.59509	+	7.95892i	−0.260983	+	0.452036i
$311$	15.9363			0.903663			0.451832	−	0.892103i	$-0.350771\pi$
$311$	15.9363			0.903663			0.451832	+	0.892103i	$0.350771\pi$
$312$	2.48286	+	4.40306i	0.140564	+	0.249274i
$313$	−14.4014	−	24.9439i	−0.814013	−	1.40991i	−0.910035	−	0.414532i	$-0.863945\pi$
$313$	−14.4014	−	24.9439i	−0.814013	−	1.40991i	0.0960218	−	0.995379i	$-0.469388\pi$
$314$	9.83272	−	17.0308i	0.554893	−	0.961102i
$315$	−6.39261	−	11.0723i	−0.360182	−	0.623854i
$316$	7.59090	−	13.1478i	0.427021	−	0.739623i
$317$	5.30895	+	9.19537i	0.298180	+	0.516464i	0.975720	−	0.219023i	$-0.0702870\pi$
$317$	5.30895	+	9.19537i	0.298180	+	0.516464i	−0.677539	+	0.735487i	$0.736954\pi$
$318$	−0.882506	−	1.52855i	−0.0494885	−	0.0857166i
$319$	−14.8144			−0.829449
$320$	2.07009	−	3.58550i	0.115721	−	0.200435i
$321$	−8.69426	−	15.0589i	−0.485266	−	0.840506i
$322$	1.99170	+	3.44973i	0.110993	+	0.192246i
$323$	−8.24292	+	1.38520i	−0.458648	+	0.0770746i
$324$	−4.82630			−0.268128
$325$	22.2713	−	37.6862i	1.23539	−	2.09046i
$326$	−4.52736	+	7.84161i	−0.250747	+	0.434307i
$327$	13.0904	−	22.6732i	0.723901	−	1.25383i
$328$	−1.82630			−0.100841
$329$	−27.1787			−1.49841
$330$	10.1009			0.556038
$331$	2.77655	−	4.80913i	0.152613	−	0.264334i	−0.779574	−	0.626310i	$-0.784565\pi$
$331$	2.77655	−	4.80913i	0.152613	−	0.264334i	0.932187	+	0.361976i	$0.117898\pi$
$332$	5.33295			0.292684
$333$	5.69043	+	9.85612i	0.311834	+	0.540112i
$334$	4.57067	−	7.91664i	0.250096	−	0.433179i
$335$	24.5197	+	42.4693i	1.33965	+	2.32035i
$336$	−2.09250	+	3.62431i	−0.114155	+	0.197722i
$337$	−10.8372	+	18.7705i	−0.590338	+	1.02250i	0.403848	+	0.914826i	$0.367672\pi$
$337$	−10.8372	+	18.7705i	−0.590338	+	1.02250i	−0.994187	+	0.107670i	$0.965661\pi$
$338$	−6.72722	+	11.1241i	−0.365912	+	0.605069i
$339$	−6.38649	+	11.0617i	−0.346867	+	0.600791i
$340$	−7.93908			−0.430557
$341$	−1.93144	−	3.34536i	−0.104593	−	0.181161i
$342$	−1.57629	+	4.22480i	−0.0852360	+	0.228451i
$343$	−15.1917			−0.820277
$344$	2.91447	+	5.04801i	0.157138	+	0.272171i
$345$	−3.87277	−	6.70783i	−0.208503	−	0.361137i
$346$	0.0296150	+	0.0512947i	0.00159211	+	0.00275762i
$347$	−0.0148911	−	0.0257921i	−0.000799396	−	0.00138459i	0.865625	−	0.500692i	$-0.166921\pi$
$347$	−0.0148911	−	0.0257921i	−0.000799396	−	0.00138459i	−0.866425	+	0.499308i	$0.833588\pi$
$348$	−5.96739	+	10.3358i	−0.319886	+	0.554059i
$349$	16.1290	+	27.9362i	0.863365	+	1.49539i	0.868661	+	0.495407i	$0.164981\pi$
$349$	16.1290	+	27.9362i	0.863365	+	1.49539i	−0.00529553	+	0.999986i	$0.501686\pi$
$350$	36.2422			1.93722
$351$	−10.0171	−	17.7641i	−0.534673	−	0.948180i
$352$	0.870115	+	1.50708i	0.0463773	+	0.0803278i
$353$	−0.652406	−	1.13000i	−0.0347241	−	0.0601438i	0.848141	−	0.529770i	$-0.177722\pi$
$353$	−0.652406	−	1.13000i	−0.0347241	−	0.0601438i	−0.882865	+	0.469627i	$0.844389\pi$
$354$	1.86339	+	3.22749i	0.0990381	+	0.171539i
$355$	34.9527			1.85510
$356$	−4.67331	+	8.09441i	−0.247685	+	0.429003i
$357$	8.02503			0.424729
$358$	−10.3608	−	17.9455i	−0.547587	−	0.948448i
$359$	1.40739	−	2.43768i	0.0742794	−	0.128656i	−0.826493	−	0.562947i	$-0.809668\pi$
$359$	1.40739	−	2.43768i	0.0742794	−	0.128656i	0.900773	+	0.434291i	$0.143001\pi$
$360$	−2.14151	+	3.70920i	−0.112867	+	0.195492i
$361$	−14.3566	−	12.4455i	−0.755608	−	0.655024i
$362$	−9.60677	−	16.6394i	−0.504921	−	0.874548i
$363$	5.58794	−	9.67860i	0.293291	−	0.507995i
$364$	−10.7624	−	0.109255i	−0.564101	−	0.00572649i
$365$	23.9537	+	41.4891i	1.25380	+	2.17164i
$366$	−3.29252			−0.172103
$367$	−2.79428	+	4.83983i	−0.145860	+	0.252637i	−0.929694	−	0.368334i	$-0.879928\pi$
$367$	−2.79428	+	4.83983i	−0.145860	+	0.252637i	0.783833	+	0.620971i	$0.213262\pi$
$368$	0.667216	−	1.15565i	0.0347810	−	0.0602425i
$369$	1.88931			0.0983537
$370$	−45.5473			−2.36789
$371$	3.75811			0.195112
$372$	−3.11201			−0.161350
$373$	−0.762985	+	1.32153i	−0.0395059	+	0.0684261i	−0.885102	−	0.465397i	$-0.845912\pi$
$373$	−0.762985	+	1.32153i	−0.0395059	+	0.0684261i	0.845596	+	0.533823i	$0.179245\pi$
$374$	1.66851	−	2.88994i	0.0862765	−	0.149435i
$375$	−41.4492			−2.14043
$376$	4.55241	+	7.88500i	0.234772	+	0.406638i
$377$	−30.6922	−	0.311573i	−1.58073	−	0.0160468i
$378$	8.44218	−	14.6223i	0.434219	−	0.752089i
$379$	4.27509	+	7.40467i	0.219596	+	0.380352i	0.954685	−	0.297619i	$-0.0961926\pi$
$379$	4.27509	+	7.40467i	0.219596	+	0.380352i	−0.735088	+	0.677972i	$0.762859\pi$
$380$	−11.4886	−	13.9173i	−0.589352	−	0.713944i
$381$	2.86968	−	4.97043i	0.147018	−	0.254643i
$382$	13.6378	−	23.6214i	0.697772	−	1.20858i
$383$	3.09591	+	5.36228i	0.158194	+	0.274000i	0.934217	−	0.356704i	$-0.116100\pi$
$383$	3.09591	+	5.36228i	0.158194	+	0.274000i	−0.776024	+	0.630704i	$0.782766\pi$
$384$	1.40196			0.0715436
$385$	−10.7536	+	18.6258i	−0.548054	+	0.949257i
$386$	0.620649			0.0315902
$387$	−3.01502	−	5.22217i	−0.153262	−	0.265458i
$388$	−3.10147	−	5.37191i	−0.157453	−	0.272717i
$389$	6.19495	+	10.7300i	0.314096	+	0.544031i	0.979245	−	0.202680i	$-0.0649652\pi$
$389$	6.19495	+	10.7300i	0.314096	+	0.544031i	−0.665149	+	0.746711i	$0.731632\pi$
$390$	20.9269	+	0.212440i	1.05967	+	0.0107573i
$391$	−2.55887			−0.129408
$392$	−0.955401	−	1.65480i	−0.0482550	−	0.0835802i
$393$	6.83459	−	11.8379i	0.344760	−	0.597141i
$394$	−2.37109	−	4.10684i	−0.119454	−	0.206900i
$395$	−31.4276	−	54.4343i	−1.58130	−	2.73889i
$396$	−0.900135	−	1.55908i	−0.0452335	−	0.0783467i
$397$	−15.2433	−	26.4022i	−0.765040	−	1.32509i	−0.940225	−	0.340553i	$-0.889386\pi$
$397$	−15.2433	−	26.4022i	−0.765040	−	1.32509i	0.175185	−	0.984536i	$-0.443948\pi$
$398$	2.73492			0.137089
$399$	11.6130	+	14.0680i	0.581375	+	0.704281i
$400$	−6.07052	−	10.5144i	−0.303526	−	0.525722i
$401$	−22.0341			−1.10033			−0.550165	−	0.835056i	$-0.685435\pi$
$401$	−22.0341			−1.10033			−0.550165	+	0.835056i	$0.685435\pi$
$402$	−8.30296	+	14.3811i	−0.414114	+	0.717266i
$403$	−3.93116	−	6.97145i	−0.195825	−	0.347273i
$404$	−1.34774	+	2.33435i	−0.0670524	+	0.116138i
$405$	−9.99087	+	17.3047i	−0.496450	+	0.859877i
$406$	−12.7059	−	22.0073i	−0.630585	−	1.09221i
$407$	9.57240	−	16.5799i	0.474486	−	0.821834i
$408$	−1.34418	−	2.32819i	−0.0665469	−	0.115263i
$409$	2.55199			0.126188			0.0630939	−	0.998008i	$-0.479903\pi$
$409$	2.55199			0.126188			0.0630939	+	0.998008i	$0.479903\pi$
$410$	−3.78061	+	6.54820i	−0.186711	+	0.323393i
$411$	16.5939			0.818517
$412$	0.671870			0.0331007
$413$	−7.93516			−0.390464
$414$	−0.690236	+	1.19552i	−0.0339232	+	0.0587568i
$415$	11.0397	−	19.1213i	0.541916	−	0.938627i
$416$	1.77099	+	3.14064i	0.0868297	+	0.153982i
$417$	7.54165			0.369316
$418$	7.48060	−	1.25709i	0.365888	−	0.0614864i
$419$	6.03069	+	10.4455i	0.294619	+	0.510295i	0.974896	−	0.222660i	$-0.0714740\pi$
$419$	6.03069	+	10.4455i	0.294619	+	0.510295i	−0.680277	+	0.732955i	$0.738141\pi$
$420$	8.66330	+	15.0053i	0.422726	+	0.732182i
$421$	−9.00322	+	15.5940i	−0.438790	+	0.760007i	−0.997596	−	0.0692914i	$-0.977926\pi$
$421$	−9.00322	+	15.5940i	−0.438790	+	0.760007i	0.558806	+	0.829298i	$0.311260\pi$
$422$	−10.6505			−0.518459
$423$	−4.70947	−	8.15704i	−0.228982	−	0.396609i
$424$	−0.629479	−	1.09029i	−0.0305702	−	0.0529492i
$425$	−11.6407	+	20.1622i	−0.564654	+	0.978010i
$426$	5.91792	+	10.2501i	0.286724	+	0.496621i
$427$	3.50526	−	6.07129i	0.169632	−	0.293810i
$428$	−6.20149	−	10.7413i	−0.299760	−	0.519200i
$429$	−4.47540	+	7.57304i	−0.216074	+	0.365630i
$430$	24.1328			1.16379
$431$	−16.4452	+	28.4839i	−0.792137	+	1.37202i	0.132504	+	0.991182i	$0.457698\pi$
$431$	−16.4452	+	28.4839i	−0.792137	+	1.37202i	−0.924641	+	0.380839i	$0.875635\pi$
$432$	−5.65622			−0.272135
$433$	−3.19546			−0.153564			−0.0767821	−	0.997048i	$-0.524465\pi$
$433$	−3.19546			−0.153564			−0.0767821	+	0.997048i	$0.524465\pi$
$434$	3.31309	−	5.73844i	0.159034	−	0.275454i
$435$	24.7060	+	42.7921i	1.18456	+	2.05173i
$436$	9.33720	−	16.1725i	0.447171	−	0.774522i
$437$	−3.70292	−	4.48574i	−0.177135	−	0.214582i
$438$	−8.11132	+	14.0492i	−0.387574	+	0.671297i
$439$	−7.53259			−0.359511			−0.179755	−	0.983711i	$-0.557531\pi$
$439$	−7.53259			−0.359511			−0.179755	+	0.983711i	$0.557531\pi$
$440$	7.20485			0.343478
$441$	0.988363	+	1.71190i	0.0470649	+	0.0815188i
$442$	3.51755	−	5.95222i	0.167313	−	0.283118i
$443$	15.7496	+	27.2792i	0.748287	+	1.29607i	0.948643	+	0.316349i	$0.102457\pi$
$443$	15.7496	+	27.2792i	0.748287	+	1.29607i	−0.200356	+	0.979723i	$0.564210\pi$
$444$	−7.71171	−	13.3571i	−0.365982	−	0.633899i
$445$	19.3483	+	33.5122i	0.917197	+	1.58863i
$446$	1.86129			0.0881348
$447$	1.12334	+	1.94568i	0.0531322	+	0.0920276i
$448$	−1.49255	+	2.58517i	−0.0705163	+	0.122138i
$449$	12.7687	−	22.1160i	0.602591	−	1.04372i	−0.389836	−	0.920884i	$-0.627468\pi$
$449$	12.7687	−	22.1160i	0.602591	−	1.04372i	0.992427	−	0.122835i	$-0.0391984\pi$
$450$	6.27996	+	10.8772i	0.296040	+	0.512756i
$451$	−1.58909	−	2.75239i	−0.0748275	−	0.129605i
$452$	−4.55539	+	7.89018i	−0.214268	+	0.371123i
$453$	10.3639			0.486940
$454$	−9.97749	+	17.2815i	−0.468267	+	0.811062i
$455$	−22.6708	+	38.3622i	−1.06282	+	1.79845i
$456$	2.13620	−	5.72548i	0.100037	−	0.268120i
$457$	−7.33436	−	12.7035i	−0.343087	−	0.594244i	0.641917	−	0.766774i	$-0.278139\pi$
$457$	−7.33436	−	12.7035i	−0.343087	−	0.594244i	−0.985004	+	0.172530i	$0.944806\pi$
$458$	−19.9778			−0.933501
$459$	5.42310	+	9.39309i	0.253129	+	0.438432i
$460$	−2.76239	−	4.78460i	−0.128797	−	0.223083i
$461$	2.17357	+	3.76473i	0.101233	+	0.175341i	0.912193	−	0.409761i	$-0.134388\pi$
$461$	2.17357	+	3.76473i	0.101233	+	0.175341i	−0.810960	+	0.585102i	$0.801055\pi$
$462$	−7.28285			−0.338829
$463$	30.6651			1.42513			0.712563	−	0.701608i	$-0.247534\pi$
$463$	30.6651			1.42513			0.712563	+	0.701608i	$0.247534\pi$
$464$	−4.25646	+	7.37240i	−0.197601	+	0.342255i
$465$	−6.44214	+	11.1581i	−0.298747	+	0.517445i
$466$	7.13929	−	12.3656i	0.330721	−	0.572826i
$467$	21.3706			0.988912			0.494456	−	0.869203i	$-0.335367\pi$
$467$	21.3706			0.988912			0.494456	+	0.869203i	$0.335367\pi$
$468$	−1.83209	−	3.24899i	−0.0846883	−	0.150185i
$469$	−17.6789	−	30.6207i	−0.816335	−	1.41393i
$470$	37.6955			1.73876
$471$	13.7851	−	23.8765i	0.635184	−	1.10017i
$472$	1.32913	+	2.30212i	0.0611782	+	0.105964i
$473$	−5.07185	+	8.78470i	−0.233204	+	0.403921i
$474$	10.6422	−	18.4328i	0.488810	−	0.846645i
$475$	−52.1897	+	8.77034i	−2.39463	+	0.402411i
$476$	5.72414			0.262365
$477$	0.651197	+	1.12791i	0.0298163	+	0.0516433i
$478$	−7.45761			−0.341103
$479$	−6.46369	+	11.1954i	−0.295333	+	0.511533i	−0.975062	−	0.221931i	$-0.928764\pi$
$479$	−6.46369	+	11.1954i	−0.295333	+	0.511533i	0.679729	+	0.733463i	$0.262097\pi$
$480$	2.90218	−	5.02673i	0.132466	−	0.229438i
$481$	20.1806	−	34.1485i	0.920155	−	1.55704i
$482$	25.1117			1.14381
$483$	2.79230	+	4.83640i	0.127054	+	0.220064i
$484$	3.98580	−	6.90361i	0.181173	−	0.313800i
$485$	−25.6813			−1.16613
$486$	10.2024			0.462788
$487$	−11.6976	+	20.2608i	−0.530067	+	0.918103i	0.469318	+	0.883029i	$0.344500\pi$
$487$	−11.6976	+	20.2608i	−0.530067	+	0.918103i	−0.999385	+	0.0350738i	$0.988833\pi$
$488$	−2.34851			−0.106312
$489$	−6.34718	+	10.9936i	−0.287030	+	0.497150i
$490$	−7.91105			−0.357385
$491$	−15.6809			−0.707668			−0.353834	−	0.935308i	$-0.615122\pi$
$491$	−15.6809			−0.707668			−0.353834	+	0.935308i	$0.615122\pi$
$492$	−2.56041			−0.115432
$493$	16.3241			0.735202
$494$	15.5246	−	2.44708i	0.698483	−	0.110100i
$495$	−7.45343			−0.335007
$496$	−2.21976			−0.0996700
$497$	−25.2012			−1.13043
$498$	7.47660			0.335034
$499$	−12.1504	+	21.0451i	−0.543927	+	0.942110i	0.454746	+	0.890621i	$0.349730\pi$
$499$	−12.1504	+	21.0451i	−0.543927	+	0.942110i	−0.998674	+	0.0514888i	$0.983603\pi$
$500$	−29.5651			−1.32219
$501$	6.40791	−	11.0988i	0.286284	−	0.495859i
$502$	−30.8107			−1.37515
$503$	−25.2343			−1.12514			−0.562572	−	0.826749i	$-0.690188\pi$
$503$	−25.2343			−1.12514			−0.562572	+	0.826749i	$0.690188\pi$
$504$	1.54404	−	2.67436i	0.0687771	−	0.119126i
$505$	5.57986	+	9.66461i	0.248301	+	0.430069i
$506$	2.32222			0.103235
$507$	−9.43130	+	15.5955i	−0.418859	+	0.692621i
$508$	2.04690	−	3.54534i	0.0908167	−	0.157299i
$509$	−5.68406	+	9.84509i	−0.251942	+	0.436376i	−0.964060	−	0.265683i	$-0.914402\pi$
$509$	−5.68406	+	9.84509i	−0.251942	+	0.436376i	0.712119	+	0.702059i	$0.247736\pi$
$510$	−11.1303			−0.492858
$511$	−17.2708	−	29.9140i	−0.764017	−	1.32332i
$512$	1.00000			0.0441942
$513$	−8.61850	+	23.0995i	−0.380516	+	1.01987i
$514$	−9.41325	+	16.3042i	−0.415201	+	0.719149i
$515$	1.39083	−	2.40899i	0.0612873	−	0.106153i
$516$	4.08598	+	7.07712i	0.179875	+	0.311553i
$517$	−7.92223	+	13.7217i	−0.348419	+	0.603480i
$518$	32.8400			1.44291
$519$	0.0415191	+	0.0719132i	0.00182249	+	0.00315664i
$520$	14.9268	+	0.151530i	0.654585	+	0.00664505i
$521$	−31.5409			−1.38183			−0.690916	−	0.722935i	$-0.742793\pi$
$521$	−31.5409			−1.38183			−0.690916	+	0.722935i	$0.742793\pi$
$522$	4.40331	−	7.62676i	0.192728	−	0.333814i
$523$	2.06036	−	3.56864i	0.0900931	−	0.156046i	−0.817457	−	0.575990i	$-0.804617\pi$
$523$	2.06036	−	3.56864i	0.0900931	−	0.156046i	0.907550	+	0.419944i	$0.137950\pi$
$524$	4.87502	−	8.44378i	0.212966	−	0.368868i
$525$	50.8101			2.21754
$526$	20.1704			0.879470
$527$	2.12827	+	3.68627i	0.0927089	+	0.160577i
$528$	1.21987	+	2.11287i	0.0530880	+	0.0919510i
$529$	10.6096	+	18.3764i	0.461289	+	0.798976i
$530$	−5.21231			−0.226408
$531$	−1.37499	−	2.38155i	−0.0596693	−	0.103350i
$532$	8.28336	+	10.0345i	0.359129	+	0.435051i
$533$	−3.23436	−	5.73576i	−0.140096	−	0.248443i
$534$	−6.55180	+	11.3481i	−0.283524	+	0.491078i
$535$	−51.3505			−2.22008
$536$	−5.92238	+	10.2579i	−0.255808	+	0.443072i
$537$	−14.5255	−	25.1589i	−0.626821	−	1.08569i
$538$	11.2931	+	19.5602i	0.486881	+	0.843302i
$539$	1.66262	−	2.87974i	0.0716140	−	0.124039i
$540$	−11.7089	+	20.2803i	−0.503869	+	0.872727i
$541$	−12.2194	−	21.1647i	−0.525355	−	0.909941i	−0.999564	−	0.0295292i	$-0.990599\pi$
$541$	−12.2194	−	21.1647i	−0.525355	−	0.909941i	0.474209	−	0.880412i	$-0.342734\pi$
$542$	3.80977			0.163644
$543$	−13.4683	−	23.3278i	−0.577981	−	1.00109i
$544$	−0.958786	−	1.66067i	−0.0411076	−	0.0712005i
$545$	−38.6576	−	66.9569i	−1.65591	−	2.86812i
$546$	−15.0884	−	0.153171i	−0.645725	−	0.00655510i
$547$	6.19370	+	10.7278i	0.264823	+	0.458688i	0.967517	−	0.252805i	$-0.0813530\pi$
$547$	6.19370	+	10.7278i	0.264823	+	0.458688i	−0.702694	+	0.711492i	$0.748020\pi$
$548$	11.8362			0.505617
$549$	2.42953			0.103690
$550$	10.5641	−	18.2975i	0.450454	−	0.780210i
$551$	23.6225	+	28.6164i	1.00635	+	1.21910i
$552$	0.935412	−	1.62018i	0.0398138	−	0.0689595i
$553$	22.6596	+	39.2475i	0.963583	+	1.66897i
$554$	0.340617	−	0.589967i	0.0144714	−	0.0250653i
$555$	−63.8556			−2.71052
$556$	5.37935			0.228135
$557$	18.0492	−	31.2622i	0.764770	−	1.32462i	−0.175598	−	0.984462i	$-0.556186\pi$
$557$	18.0492	−	31.2622i	0.764770	−	1.32462i	0.940368	−	0.340159i	$-0.110481\pi$
$558$	2.29634			0.0972118
$559$	−10.6925	+	18.0933i	−0.452244	+	0.765263i
$560$	6.17941	+	10.7030i	0.261128	+	0.452286i
$561$	2.33919	−	4.05159i	0.0987605	−	0.171058i
$562$	−0.975740	−	1.69003i	−0.0411591	−	0.0712897i
$563$	4.03136	−	6.98252i	0.169901	−	0.294278i	−0.768484	−	0.639870i	$-0.778988\pi$
$563$	4.03136	−	6.98252i	0.169901	−	0.294278i	0.938385	+	0.345592i	$0.112322\pi$
$564$	6.38230	+	11.0545i	0.268743	+	0.465477i
$565$	18.8601	+	32.6667i	0.793451	+	1.37430i
$566$	28.7409			1.20807
$567$	7.20349	−	12.4768i	0.302518	−	0.523977i
$568$	4.22117	+	7.31128i	0.177116	+	0.306774i
$569$	−0.265229	−	0.459389i	−0.0111190	−	0.0192586i	0.860412	−	0.509598i	$-0.170206\pi$
$569$	−0.265229	−	0.459389i	−0.0111190	−	0.0192586i	−0.871531	+	0.490340i	$0.836873\pi$
$570$	−16.1066	−	19.5116i	−0.674630	−	0.817250i
$571$	−23.9639			−1.00286			−0.501429	−	0.865199i	$-0.667192\pi$
$571$	−23.9639			−1.00286			−0.501429	+	0.865199i	$0.667192\pi$
$572$	−3.19224	+	5.40174i	−0.133474	+	0.225858i
$573$	19.1197	−	33.1164i	0.798738	−	1.38346i
$574$	2.72585	−	4.72130i	0.113775	−	0.197063i
$575$	−16.2014			−0.675645
$576$	−1.03450			−0.0431042
$577$	0.847646			0.0352880			0.0176440	−	0.999844i	$-0.494383\pi$
$577$	0.847646			0.0352880			0.0176440	+	0.999844i	$0.494383\pi$
$578$	6.66146	−	11.5380i	0.277080	−	0.479917i
$579$	0.870127			0.0361612
$580$	17.6225	+	30.5230i	0.731733	+	1.26740i
$581$	−7.95969	+	13.7866i	−0.330224	+	0.571964i
$582$	−4.34815	−	7.53121i	−0.180237	−	0.312179i
$583$	1.09544	−	1.89736i	0.0453684	−	0.0785804i
$584$	−5.78569	+	10.0211i	−0.239413	+	0.414676i
$585$	−15.4418	−	0.156758i	−0.638441	−	0.00648116i
$586$	5.32861	−	9.22943i	0.220123	−	0.381264i
$587$	−32.1179			−1.32565			−0.662824	−	0.748775i	$-0.730642\pi$
$587$	−32.1179			−1.32565			−0.662824	+	0.748775i	$0.730642\pi$
$588$	−1.33944	−	2.31997i	−0.0552374	−	0.0956740i
$589$	−3.38229	+	9.06527i	−0.139365	+	0.373528i
$590$	11.0057			0.453096
$591$	−3.32417	−	5.75764i	−0.136738	−	0.236838i
$592$	−5.50065	−	9.52741i	−0.226075	−	0.391574i
$593$	21.7518	+	37.6753i	0.893241	+	1.54714i	0.835967	+	0.548780i	$0.184908\pi$
$593$	21.7518	+	37.6753i	0.893241	+	1.54714i	0.0572741	+	0.998358i	$0.481759\pi$
$594$	−4.92156	−	8.52439i	−0.201934	−	0.349760i
$595$	11.8495	−	20.5239i	0.485780	−	0.841396i
$596$	0.801263	+	1.38783i	0.0328210	+	0.0568476i
$597$	3.83426			0.156926
$598$	4.81112	+	0.0488402i	0.196741	+	0.00199723i
$599$	9.39079	+	16.2653i	0.383697	+	0.664583i	0.991588	−	0.129438i	$-0.0413173\pi$
$599$	9.39079	+	16.2653i	0.383697	+	0.664583i	−0.607890	+	0.794021i	$0.707984\pi$
$600$	−8.51064	−	14.7409i	−0.347445	−	0.601793i
$601$	−9.72504	−	16.8443i	−0.396693	−	0.687092i	0.596623	−	0.802522i	$-0.296509\pi$
$601$	−9.72504	−	16.8443i	−0.396693	−	0.687092i	−0.993316	+	0.115430i	$0.963175\pi$
$602$	−17.4000			−0.709169
$603$	6.12671	−	10.6118i	0.249499	−	0.432145i
$604$	7.39245			0.300795
$605$	−16.5019	−	28.5821i	−0.670898	−	1.16203i
$606$	−1.88948	+	3.27267i	−0.0767547	+	0.132943i
$607$	10.0568	−	17.4189i	0.408194	−	0.707012i	−0.586494	−	0.809954i	$-0.699492\pi$
$607$	10.0568	−	17.4189i	0.408194	−	0.707012i	0.994687	+	0.102941i	$0.0328254\pi$
$608$	1.52372	−	4.08390i	0.0617950	−	0.165624i
$609$	−17.8132	−	30.8534i	−0.721829	−	1.25024i
$610$	−4.86162	+	8.42057i	−0.196841	+	0.340939i
$611$	−16.7017	+	28.2617i	−0.675678	+	1.14335i
$612$	0.991865	+	1.71796i	0.0400938	+	0.0694444i
$613$	20.3939			0.823702			0.411851	−	0.911251i	$-0.364882\pi$
$613$	20.3939			0.823702			0.411851	+	0.911251i	$0.364882\pi$
$614$	−12.6954	+	21.9890i	−0.512343	+	0.887405i
$615$	−5.30027	+	9.18034i	−0.213727	+	0.370187i
$616$	−5.19475			−0.209303
$617$	42.6367			1.71649			0.858244	−	0.513242i	$-0.171556\pi$
$617$	42.6367			1.71649			0.858244	+	0.513242i	$0.171556\pi$
$618$	0.941937			0.0378903
$619$	19.3446			0.777527			0.388763	−	0.921338i	$-0.372902\pi$
$619$	19.3446			0.777527			0.388763	+	0.921338i	$0.372902\pi$
$620$	−4.59509	+	7.95892i	−0.184543	+	0.319638i
$621$	−3.77392	+	6.53662i	−0.151442	+	0.262306i
$622$	15.9363			0.638986
$623$	−13.9503	−	24.1626i	−0.558906	−	0.968053i
$624$	2.48286	+	4.40306i	0.0993938	+	0.176263i
$625$	−30.8498	+	53.4333i	−1.23399	+	2.13733i
$626$	−14.4014	−	24.9439i	−0.575594	−	0.996958i
$627$	10.4875	−	1.76240i	0.418831	−	0.0703834i
$628$	9.83272	−	17.0308i	0.392368	−	0.679602i
$629$	−10.5479	+	18.2695i	−0.420572	+	0.728452i
$630$	−6.39261	−	11.0723i	−0.254687	−	0.441132i
$631$	−5.07636			−0.202087			−0.101043	−	0.994882i	$-0.532218\pi$
$631$	−5.07636			−0.202087			−0.101043	+	0.994882i	$0.532218\pi$
$632$	7.59090	−	13.1478i	0.301950	−	0.522992i
$633$	−14.9316			−0.593479
$634$	5.30895	+	9.19537i	0.210845	+	0.365195i
$635$	−8.47453	−	14.6783i	−0.336302	−	0.582492i
$636$	−0.882506	−	1.52855i	−0.0349937	−	0.0606108i
$637$	3.50514	−	5.93120i	0.138879	−	0.235003i
$638$	−14.8144			−0.586509
$639$	−4.36680	−	7.56353i	−0.172748	−	0.299208i
$640$	2.07009	−	3.58550i	0.0818274	−	0.141729i
$641$	−1.52697	−	2.64478i	−0.0603116	−	0.104463i	0.834293	−	0.551321i	$-0.185876\pi$
$641$	−1.52697	−	2.64478i	−0.0603116	−	0.104463i	−0.894605	+	0.446858i	$0.852543\pi$
$642$	−8.69426	−	15.0589i	−0.343135	−	0.594327i
$643$	−7.31125	−	12.6635i	−0.288328	−	0.499398i	0.685083	−	0.728465i	$-0.259766\pi$
$643$	−7.31125	−	12.6635i	−0.288328	−	0.499398i	−0.973411	+	0.229067i	$0.926433\pi$
$644$	1.99170	+	3.44973i	0.0784842	+	0.135939i
$645$	33.8333			1.33219
$646$	−8.24292	+	1.38520i	−0.324313	+	0.0545000i
$647$	−7.91168	−	13.7034i	−0.311040	−	0.538737i	0.667548	−	0.744567i	$-0.267344\pi$
$647$	−7.91168	−	13.7034i	−0.311040	−	0.538737i	−0.978588	+	0.205830i	$0.934011\pi$
$648$	−4.82630			−0.189595
$649$	−2.31299	+	4.00622i	−0.0907929	+	0.157258i
$650$	22.2713	−	37.6862i	0.873551	−	1.47818i
$651$	4.64483	−	8.04508i	0.182045	−	0.315312i
$652$	−4.52736	+	7.84161i	−0.177305	+	0.307101i
$653$	18.5732	+	32.1698i	0.726827	+	1.25890i	0.958218	+	0.286040i	$0.0923390\pi$
$653$	18.5732	+	32.1698i	0.726827	+	1.25890i	−0.231391	+	0.972861i	$0.574328\pi$
$654$	13.0904	−	22.6732i	0.511875	−	0.886594i
$655$	−20.1834	−	34.9587i	−0.788632	−	1.36595i
$656$	−1.82630			−0.0713052
$657$	5.98530	−	10.3668i	0.233509	−	0.404449i
$658$	−27.1787			−1.05954
$659$	12.3156			0.479747			0.239873	−	0.970804i	$-0.422894\pi$
$659$	12.3156			0.479747			0.239873	+	0.970804i	$0.422894\pi$
$660$	10.1009			0.393178
$661$	18.5854	−	32.1909i	0.722889	−	1.25208i	−0.236948	−	0.971522i	$-0.576147\pi$
$661$	18.5854	−	32.1909i	0.722889	−	1.25208i	0.959837	−	0.280558i	$-0.0905194\pi$
$662$	2.77655	−	4.80913i	0.107914	−	0.186912i
$663$	4.93148	−	8.34478i	0.191523	−	0.324085i
$664$	5.33295			0.206959
$665$	53.1259	−	8.92766i	2.06013	−	0.346200i
$666$	5.69043	+	9.85612i	0.220500	+	0.381917i
$667$	5.67995	+	9.83797i	0.219929	+	0.380928i
$668$	4.57067	−	7.91664i	0.176845	−	0.306304i
$669$	2.60946			0.100888
$670$	24.5197	+	42.4693i	0.947278	+	1.64073i
$671$	−2.04347	−	3.53940i	−0.0788874	−	0.136637i
$672$	−2.09250	+	3.62431i	−0.0807198	+	0.139811i
$673$	17.1089	+	29.6335i	0.659500	+	1.14229i	0.980745	+	0.195292i	$0.0625654\pi$
$673$	17.1089	+	29.6335i	0.659500	+	1.14229i	−0.321245	+	0.946996i	$0.604101\pi$
$674$	−10.8372	+	18.7705i	−0.417432	+	0.723014i
$675$	34.3362	+	59.4720i	1.32160	+	2.28908i
$676$	−6.72722	+	11.1241i	−0.258739	+	0.427848i
$677$	1.00065			0.0384582			0.0192291	−	0.999815i	$-0.493879\pi$
$677$	1.00065			0.0384582			0.0192291	+	0.999815i	$0.493879\pi$
$678$	−6.38649	+	11.0617i	−0.245272	+	0.424823i
$679$	18.5164			0.710594
$680$	−7.93908			−0.304450
$681$	−13.9881	+	24.2281i	−0.536024	+	0.928421i
$682$	−1.93144	−	3.34536i	−0.0739588	−	0.128100i
$683$	−17.0539	+	29.5383i	−0.652550	+	1.13025i	0.329952	+	0.943998i	$0.392967\pi$
$683$	−17.0539	+	29.5383i	−0.652550	+	1.13025i	−0.982502	+	0.186252i	$0.940366\pi$
$684$	−1.57629	+	4.22480i	−0.0602710	+	0.161539i
$685$	24.5020	−	42.4386i	0.936172	−	1.62150i
$686$	−15.1917			−0.580024
$687$	−28.0081			−1.06858
$688$	2.91447	+	5.04801i	0.111113	+	0.192454i
$689$	2.30941	−	3.90786i	0.0879814	−	0.148877i
$690$	−3.87277	−	6.70783i	−0.147434	−	0.255363i
$691$	−9.24779	−	16.0176i	−0.351803	−	0.609340i	0.634763	−	0.772707i	$-0.281098\pi$
$691$	−9.24779	−	16.0176i	−0.351803	−	0.609340i	−0.986565	+	0.163367i	$0.947765\pi$
$692$	0.0296150	+	0.0512947i	0.00112579	+	0.00194993i
$693$	5.37398			0.204141
$694$	−0.0148911	−	0.0257921i	−0.000565258	−	0.000979056i
$695$	11.1357	−	19.2876i	0.422402	−	0.731622i
$696$	−5.96739	+	10.3358i	−0.226193	+	0.391779i
$697$	1.75103	+	3.03288i	0.0663252	+	0.114879i
$698$	16.1290	+	27.9362i	0.610492	+	1.05740i
$699$	10.0090	−	17.3361i	0.378576	−	0.655712i
$700$	36.2422			1.36982
$701$	11.0332	−	19.1101i	0.416718	−	0.721777i	−0.578889	−	0.815406i	$-0.696514\pi$
$701$	11.0332	−	19.1101i	0.416718	−	0.721777i	0.995607	+	0.0936294i	$0.0298469\pi$
$702$	−10.0171	−	17.7641i	−0.378071	−	0.670464i
$703$	−47.2905	+	7.94703i	−1.78359	+	0.299728i
$704$	0.870115	+	1.50708i	0.0327937	+	0.0568003i
$705$	52.8477			1.99036
$706$	−0.652406	−	1.13000i	−0.0245536	−	0.0425281i
$707$	−4.02312	−	6.96826i	−0.151305	−	0.262068i
$708$	1.86339	+	3.22749i	0.0700305	+	0.121296i
$709$	21.6742			0.813992			0.406996	−	0.913430i	$-0.366576\pi$
$709$	21.6742			0.813992			0.406996	+	0.913430i	$0.366576\pi$
$710$	34.9527			1.31175
$711$	−7.85279	+	13.6014i	−0.294503	+	0.510094i
$712$	−4.67331	+	8.09441i	−0.175140	+	0.303351i
$713$	−1.48106	+	2.56527i	−0.0554660	+	0.0960700i
$714$	8.02503			0.300329
$715$	12.7597	+	22.6278i	0.477186	+	0.846233i
$716$	−10.3608	−	17.9455i	−0.387202	−	0.670654i
$717$	−10.4553			−0.390460
$718$	1.40739	−	2.43768i	0.0525235	−	0.0909733i
$719$	−10.2162	−	17.6949i	−0.380999	−	0.659910i	0.610206	−	0.792243i	$-0.291087\pi$
$719$	−10.2162	−	17.6949i	−0.380999	−	0.659910i	−0.991205	+	0.132333i	$0.957753\pi$
$720$	−2.14151	+	3.70920i	−0.0798093	+	0.138234i
$721$	−1.00280	+	1.73690i	−0.0373462	+	0.0646855i
$722$	−14.3566	−	12.4455i	−0.534296	−	0.463172i
$723$	35.2057			1.30932
$724$	−9.60677	−	16.6394i	−0.357033	−	0.618399i
$725$	103.356			3.83853
$726$	5.58794	−	9.67860i	0.207388	−	0.359207i
$727$	2.35066	−	4.07146i	0.0871811	−	0.151002i	−0.819137	−	0.573597i	$-0.805547\pi$
$727$	2.35066	−	4.07146i	0.0871811	−	0.151002i	0.906319	+	0.422595i	$0.138881\pi$
$728$	−10.7624	−	0.109255i	−0.398880	−	0.00404924i
$729$	28.7822			1.06601
$730$	23.9537	+	41.4891i	0.886568	+	1.53558i
$731$	5.58871	−	9.67992i	0.206706	−	0.358025i
$732$	−3.29252			−0.121695
$733$	8.08978			0.298803			0.149401	−	0.988777i	$-0.452265\pi$
$733$	8.08978			0.298803			0.149401	+	0.988777i	$0.452265\pi$
$734$	−2.79428	+	4.83983i	−0.103139	+	0.178641i
$735$	−11.0910			−0.409098
$736$	0.667216	−	1.15565i	0.0245939	−	0.0425979i
$737$	−20.6126			−0.759275
$738$	1.88931			0.0695466
$739$	−6.72527			−0.247393			−0.123697	−	0.992320i	$-0.539475\pi$
$739$	−6.72527			−0.247393			−0.123697	+	0.992320i	$0.539475\pi$
$740$	−45.5473			−1.67435
$741$	21.7648	−	3.43072i	0.799551	−	0.126031i
$742$	3.75811			0.137965
$743$	10.2746			0.376938			0.188469	−	0.982079i	$-0.439648\pi$
$743$	10.2746			0.376938			0.188469	+	0.982079i	$0.439648\pi$
$744$	−3.11201			−0.114092
$745$	6.63473			0.243078
$746$	−0.762985	+	1.32153i	−0.0279349	+	0.0483846i
$747$	−5.51695			−0.201854
$748$	1.66851	−	2.88994i	0.0610067	−	0.105667i
$749$	37.0241			1.35283
$750$	−41.4492			−1.51351
$751$	−7.82655	+	13.5560i	−0.285595	+	0.494665i	−0.972753	−	0.231843i	$-0.925525\pi$
$751$	−7.82655	+	13.5560i	−0.285595	+	0.494665i	0.687158	+	0.726508i	$0.258858\pi$
$752$	4.55241	+	7.88500i	0.166009	+	0.287536i
$753$	−43.1955			−1.57413
$754$	−30.6922	−	0.311573i	−1.11774	−	0.0113468i
$755$	15.3030	−	26.5056i	0.556934	−	0.964637i
$756$	8.44218	−	14.6223i	0.307039	−	0.531807i
$757$	−21.0388			−0.764667			−0.382333	−	0.924024i	$-0.624879\pi$
$757$	−21.0388			−0.764667			−0.382333	+	0.924024i	$0.624879\pi$
$758$	4.27509	+	7.40467i	0.155278	+	0.268950i
$759$	3.25566			0.118173
$760$	−11.4886	−	13.9173i	−0.416735	−	0.504835i
$761$	−18.6760	+	32.3477i	−0.677003	+	1.17260i	0.298876	+	0.954292i	$0.403388\pi$
$761$	−18.6760	+	32.3477i	−0.677003	+	1.17260i	−0.975879	+	0.218311i	$0.929945\pi$
$762$	2.86968	−	4.97043i	0.103958	−	0.180060i
$763$	27.8724	+	48.2765i	1.00905	+	1.74773i
$764$	13.6378	−	23.6214i	0.493400	−	0.854593i
$765$	8.21299			0.296941
$766$	3.09591	+	5.36228i	0.111860	+	0.193747i
$767$	−4.87626	+	8.25134i	−0.176071	+	0.297939i
$768$	1.40196			0.0505890
$769$	11.3108	−	19.5908i	0.407877	−	0.706463i	−0.586775	−	0.809750i	$-0.699603\pi$
$769$	11.3108	−	19.5908i	0.407877	−	0.706463i	0.994652	+	0.103287i	$0.0329360\pi$
$770$	−10.7536	+	18.6258i	−0.387532	+	0.671226i
$771$	−13.1970	+	22.8579i	−0.475279	+	0.823208i
$772$	0.620649			0.0223376
$773$	−3.41682			−0.122895			−0.0614473	−	0.998110i	$-0.519572\pi$
$773$	−3.41682			−0.122895			−0.0614473	+	0.998110i	$0.519572\pi$
$774$	−3.01502	−	5.22217i	−0.108373	−	0.187707i
$775$	13.4751	+	23.3395i	0.484039	+	0.838379i
$776$	−3.10147	−	5.37191i	−0.111336	−	0.192840i
$777$	46.0404			1.65169
$778$	6.19495	+	10.7300i	0.222100	+	0.384688i
$779$	−2.78278	+	7.45845i	−0.0997033	+	0.267227i
$780$	20.9269	+	0.212440i	0.749302	+	0.00760657i
$781$	−7.34580	+	12.7233i	−0.262854	+	0.455276i
$782$	−2.55887			−0.0915050
$783$	24.0755	−	41.6999i	0.860387	−	1.49023i
$784$	−0.955401	−	1.65480i	−0.0341215	−	0.0591001i
$785$	−40.7092	−	70.5104i	−1.45297	−	2.51662i
$786$	6.83459	−	11.8379i	0.243782	−	0.422243i
$787$	−9.90324	+	17.1529i	−0.353012	+	0.611435i	−0.986776	−	0.162092i	$-0.948176\pi$
$787$	−9.90324	+	17.1529i	−0.353012	+	0.611435i	0.633763	+	0.773527i	$0.281509\pi$
$788$	−2.37109	−	4.10684i	−0.0844664	−	0.146300i
$789$	28.2781			1.00673
$790$	−31.4276	−	54.4343i	−1.11815	−	1.93668i
$791$	−13.5983	−	23.5529i	−0.483500	−	0.837446i
$792$	−0.900135	−	1.55908i	−0.0319849	−	0.0553995i
$793$	−4.15918	−	7.37582i	−0.147697	−	0.261923i
$794$	−15.2433	−	26.4022i	−0.540965	−	0.936979i
$795$	−7.30746			−0.259169
$796$	2.73492			0.0969368
$797$	−16.2726	+	28.1850i	−0.576405	+	0.998362i	0.419483	+	0.907763i	$0.362212\pi$
$797$	−16.2726	+	28.1850i	−0.576405	+	0.998362i	−0.995887	+	0.0905991i	$0.971122\pi$
$798$	11.6130	+	14.0680i	0.411094	+	0.498002i
$799$	8.72957	−	15.1201i	0.308830	−	0.534909i
$800$	−6.07052	−	10.5144i	−0.214625	−	0.371742i
$801$	4.83454	−	8.37367i	0.170820	−	0.295869i
$802$	−22.0341			−0.778051
$803$	−20.1369			−0.710614
$804$	−8.30296	+	14.3811i	−0.292823	+	0.507184i
$805$	16.4920			0.581267
$806$	−3.93116	−	6.97145i	−0.138469	−	0.245559i
$807$	15.8325	+	27.4227i	0.557331	+	0.965326i
$808$	−1.34774	+	2.33435i	−0.0474132	+	0.0821221i
$809$	−18.5635	−	32.1529i	−0.652657	−	1.13044i	−0.982476	−	0.186391i	$-0.940321\pi$
$809$	−18.5635	−	32.1529i	−0.652657	−	1.13044i	0.329819	−	0.944044i	$-0.393012\pi$
$810$	−9.99087	+	17.3047i	−0.351043	+	0.608025i
$811$	16.3475	+	28.3147i	0.574039	+	0.994265i	0.996145	+	0.0877185i	$0.0279576\pi$
$811$	16.3475	+	28.3147i	0.574039	+	0.994265i	−0.422106	+	0.906546i	$0.638709\pi$
$812$	−12.7059	−	22.0073i	−0.445891	−	0.772306i
$813$	5.34116			0.187323
$814$	9.57240	−	16.5799i	0.335512	−	0.581125i
$815$	18.7440	+	32.4656i	0.656575	+	1.13722i
$816$	−1.34418	−	2.32819i	−0.0470558	−	0.0815030i
$817$	25.0564	−	4.21066i	0.876614	−	0.147312i
$818$	2.55199			0.0892283
$819$	11.1337	+	0.113024i	0.389042	+	0.00394938i
$820$	−3.78061	+	6.54820i	−0.132025	+	0.228673i
$821$	−5.49280	+	9.51381i	−0.191700	+	0.332034i	−0.945814	−	0.324710i	$-0.894733\pi$
$821$	−5.49280	+	9.51381i	−0.191700	+	0.332034i	0.754114	+	0.656744i	$0.228067\pi$
$822$	16.5939			0.578779
$823$	55.3116			1.92804			0.964020	−	0.265830i	$-0.0856460\pi$
$823$	55.3116			1.92804			0.964020	+	0.265830i	$0.0856460\pi$
$824$	0.671870			0.0234057
$825$	14.8105	−	25.6525i	0.515634	−	0.893104i
$826$	−7.93516			−0.276100
$827$	14.0756	+	24.3797i	0.489458	+	0.847766i	0.999926	−	0.0121307i	$-0.00386141\pi$
$827$	14.0756	+	24.3797i	0.489458	+	0.847766i	−0.510469	+	0.859896i	$0.670528\pi$
$828$	−0.690236	+	1.19552i	−0.0239874	+	0.0415473i
$829$	−20.5548	−	35.6020i	−0.713899	−	1.23651i	−0.963383	−	0.268130i	$-0.913594\pi$
$829$	−20.5548	−	35.6020i	−0.713899	−	1.23651i	0.249484	−	0.968379i	$-0.419739\pi$
$830$	11.0397	−	19.1213i	0.383193	−	0.663709i
$831$	0.477533	−	0.827111i	0.0165654	−	0.0286922i
$832$	1.77099	+	3.14064i	0.0613979	+	0.108882i
$833$	−1.83205	+	3.17320i	−0.0634768	+	0.109945i
$834$	7.54165			0.261146
$835$	−18.9234	−	32.7762i	−0.654870	−	1.13427i
$836$	7.48060	−	1.25709i	0.258722	−	0.0434775i
$837$	12.5554			0.433979
$838$	6.03069	+	10.4455i	0.208327	+	0.360833i
$839$	−11.2081	−	19.4131i	−0.386948	−	0.670214i	0.605089	−	0.796158i	$-0.293137\pi$
$839$	−11.2081	−	19.4131i	−0.386948	−	0.670214i	−0.992037	+	0.125944i	$0.959804\pi$
$840$	8.66330	+	15.0053i	0.298912	+	0.517731i
$841$	−21.7349	−	37.6459i	−0.749478	−	1.29813i
$842$	−9.00322	+	15.5940i	−0.310271	+	0.537406i
$843$	−1.36795	−	2.36936i	−0.0471147	−	0.0816051i
$844$	−10.6505			−0.366606
$845$	25.9593	+	47.1482i	0.893028	+	1.62195i
$846$	−4.70947	−	8.15704i	−0.161915	−	0.280445i
$847$	11.8980	+	20.6079i	0.408820	+	0.708097i
$848$	−0.629479	−	1.09029i	−0.0216164	−	0.0374407i
$849$	40.2936			1.38287
$850$	−11.6407	+	20.1622i	−0.399271	+	0.691558i
$851$	−14.6805			−0.503241
$852$	5.91792	+	10.2501i	0.202745	+	0.351164i
$853$	19.1222	−	33.1205i	0.654730	−	1.13403i	−0.327231	−	0.944944i	$-0.606116\pi$
$853$	19.1222	−	33.1205i	0.654730	−	1.13403i	0.981961	−	0.189081i	$-0.0605510\pi$
$854$	3.50526	−	6.07129i	0.119948	−	0.207755i
$855$	11.8850	+	14.3975i	0.406457	+	0.492384i
$856$	−6.20149	−	10.7413i	−0.211963	−	0.367130i
$857$	5.48232	−	9.49566i	0.187272	−	0.324365i	−0.757067	−	0.653337i	$-0.773369\pi$
$857$	5.48232	−	9.49566i	0.187272	−	0.324365i	0.944340	+	0.328971i	$0.106702\pi$
$858$	−4.47540	+	7.57304i	−0.152788	+	0.258539i
$859$	−28.0250	−	48.5408i	−0.956202	−	1.65619i	−0.731593	−	0.681742i	$-0.761223\pi$
$859$	−28.0250	−	48.5408i	−0.956202	−	1.65619i	−0.224609	−	0.974449i	$-0.572110\pi$
$860$	24.1328			0.822923
$861$	3.82153	−	6.61909i	0.130238	−	0.225578i
$862$	−16.4452	+	28.4839i	−0.560125	+	0.970166i
$863$	18.0956			0.615981			0.307990	−	0.951390i	$-0.400344\pi$
$863$	18.0956			0.615981			0.307990	+	0.951390i	$0.400344\pi$
$864$	−5.65622			−0.192428
$865$	0.245222			0.00833781
$866$	−3.19546			−0.108586
$867$	9.33912	−	16.1758i	0.317173	−	0.549360i
$868$	3.31309	−	5.73844i	0.112454	−	0.194776i
$869$	26.4198			0.896231
$870$	24.7060	+	42.7921i	0.837613	+	1.45079i
$871$	−42.7047	−	0.433518i	−1.44699	−	0.0146892i
$872$	9.33720	−	16.1725i	0.316197	−	0.547670i
$873$	3.20848	+	5.55725i	0.108590	+	0.188084i
$874$	−3.70292	−	4.48574i	−0.125253	−	0.151732i
$875$	44.1274	−	76.4308i	1.49178	−	2.58383i
$876$	−8.11132	+	14.0492i	−0.274056	+	0.474679i
$877$	5.46988	+	9.47411i	0.184705	+	0.319918i	0.943477	−	0.331438i	$-0.107534\pi$
$877$	5.46988	+	9.47411i	0.184705	+	0.319918i	−0.758772	+	0.651356i	$0.774200\pi$
$878$	−7.53259			−0.254213
$879$	7.47051	−	12.9393i	0.251974	−	0.436432i
$880$	7.20485			0.242876
$881$	−10.5224	−	18.2254i	−0.354510	−	0.614029i	0.632524	−	0.774541i	$-0.282019\pi$
$881$	−10.5224	−	18.2254i	−0.354510	−	0.614029i	−0.987034	+	0.160512i	$0.948686\pi$
$882$	0.988363	+	1.71190i	0.0332799	+	0.0576425i
$883$	4.60709	+	7.97972i	0.155041	+	0.268539i	0.933074	−	0.359685i	$-0.117116\pi$
$883$	4.60709	+	7.97972i	0.155041	+	0.268539i	−0.778033	+	0.628223i	$0.783782\pi$
$884$	3.51755	−	5.95222i	0.118308	−	0.200195i
$885$	15.4295			0.518658
$886$	15.7496	+	27.2792i	0.529119	+	0.916461i
$887$	−11.9141	+	20.6359i	−0.400038	+	0.692886i	−0.993730	−	0.111807i	$-0.964336\pi$
$887$	−11.9141	+	20.6359i	−0.400038	+	0.692886i	0.593692	+	0.804692i	$0.297670\pi$
$888$	−7.71171	−	13.3571i	−0.258788	−	0.448234i
$889$	6.11020	+	10.5832i	0.204930	+	0.354949i
$890$	19.3483	+	33.5122i	0.648556	+	1.12333i
$891$	−4.19944	−	7.27364i	−0.140686	−	0.243676i
$892$	1.86129			0.0623207
$893$	39.1382	−	6.57706i	1.30971	−	0.220093i
$894$	1.12334	+	1.94568i	0.0375701	+	0.0650734i
$895$	−85.7912			−2.86768
$896$	−1.49255	+	2.58517i	−0.0498625	+	0.0863645i
$897$	6.74501	+	0.0684722i	0.225209	+	0.00228622i
$898$	12.7687	−	22.1160i	0.426096	−	0.738021i
$899$	9.44830	−	16.3649i	0.315118	−	0.545801i
$900$	6.27996	+	10.8772i	0.209332	+	0.362573i
$901$	−1.20707	+	2.09071i	−0.0402134	+	0.0696516i
$902$	−1.58909	−	2.75239i	−0.0529110	−	0.0916446i
$903$	−24.3941			−0.811784
$904$	−4.55539	+	7.89018i	−0.151510	+	0.262423i
$905$	−79.5474			−2.64424
$906$	10.3639			0.344319
$907$	−51.6075			−1.71360			−0.856799	−	0.515650i	$-0.827550\pi$
$907$	−51.6075			−1.71360			−0.856799	+	0.515650i	$0.827550\pi$
$908$	−9.97749	+	17.2815i	−0.331115	+	0.573508i
$909$	1.39424	−	2.41489i	0.0462439	−	0.0800967i
$910$	−22.6708	+	38.3622i	−0.751528	+	1.27170i
$911$	22.3225			0.739577			0.369789	−	0.929116i	$-0.379430\pi$
$911$	22.3225			0.739577			0.369789	+	0.929116i	$0.379430\pi$
$912$	2.13620	−	5.72548i	0.0707366	−	0.189590i
$913$	4.64028	+	8.03720i	0.153571	+	0.265993i
$914$	−7.33436	−	12.7035i	−0.242599	−	0.420194i
$915$	−6.81580	+	11.8053i	−0.225323	+	0.390272i
$916$	−19.9778			−0.660085
$917$	14.5524	+	25.2055i	0.480563	+	0.832359i
$918$	5.42310	+	9.39309i	0.178989	+	0.310018i
$919$	−6.19416	+	10.7286i	−0.204326	+	0.353904i	−0.949918	−	0.312500i	$-0.898834\pi$
$919$	−6.19416	+	10.7286i	−0.204326	+	0.353904i	0.745591	+	0.666403i	$0.232167\pi$
$920$	−2.76239	−	4.78460i	−0.0910733	−	0.157744i
$921$	−17.7984	+	30.8278i	−0.586478	+	1.01581i
$922$	2.17357	+	3.76473i	0.0715827	+	0.123985i
$923$	−15.4864	+	26.2053i	−0.509743	+	0.862559i
$924$	−7.28285			−0.239588
$925$	−66.7836	+	115.673i	−2.19583	+	3.80329i
$926$	30.6651			1.00772
$927$	−0.695051			−0.0228285
$928$	−4.25646	+	7.37240i	−0.139725	+	0.242011i
$929$	−16.4723	−	28.5309i	−0.540439	−	0.936068i	−0.998879	−	0.0473427i	$-0.984925\pi$
$929$	−16.4723	−	28.5309i	−0.540439	−	0.936068i	0.458439	−	0.888726i	$-0.348409\pi$
$930$	−6.44214	+	11.1581i	−0.211246	+	0.365889i
$931$	−8.21382	+	1.38031i	−0.269197	+	0.0452378i
$932$	7.13929	−	12.3656i	0.233855	−	0.405049i
$933$	22.3421			0.731446
$934$	21.3706			0.699267
$935$	−6.90791	−	11.9649i	−0.225913	−	0.391293i
$936$	−1.83209	−	3.24899i	−0.0598836	−	0.106197i
$937$	12.0700	+	20.9058i	0.394309	+	0.682964i	0.993013	−	0.118007i	$-0.0376506\pi$
$937$	12.0700	+	20.9058i	0.394309	+	0.682964i	−0.598704	+	0.800971i	$0.704317\pi$
$938$	−17.6789	−	30.6207i	−0.577236	−	0.999802i
$939$	−20.1902	−	34.9704i	−0.658881	−	1.14122i
$940$	37.6955			1.22949
$941$	−7.89245	−	13.6701i	−0.257286	−	0.445633i	0.708228	−	0.705984i	$-0.249495\pi$
$941$	−7.89245	−	13.6701i	−0.257286	−	0.445633i	−0.965514	+	0.260351i	$0.916162\pi$
$942$	13.7851	−	23.8765i	0.449143	−	0.777939i
$943$	−1.21854	+	2.11057i	−0.0396811	+	0.0687297i
$944$	1.32913	+	2.30212i	0.0432595	+	0.0749277i
$945$	−34.9521	−	60.5388i	−1.13699	−	1.96933i
$946$	−5.07185	+	8.78470i	−0.164900	+	0.285615i
$947$	45.2122			1.46920			0.734599	−	0.678502i	$-0.237370\pi$
$947$	45.2122			1.46920			0.734599	+	0.678502i	$0.237370\pi$
$948$	10.6422	−	18.4328i	0.345641	−	0.598668i
$949$	−41.7190	−	0.423512i	−1.35426	−	0.0137478i
$950$	−52.1897	+	8.77034i	−1.69326	+	0.284547i
$951$	7.44295	+	12.8916i	0.241354	+	0.418038i
$952$	5.72414			0.185520
$953$	22.4202	+	38.8330i	0.726263	+	1.25792i	0.958452	+	0.285253i	$0.0920778\pi$
$953$	22.4202	+	38.8330i	0.726263	+	1.25792i	−0.232189	+	0.972671i	$0.574589\pi$
$954$	0.651197	+	1.12791i	0.0210833	+	0.0365173i
$955$	−56.4630	−	97.7968i	−1.82710	−	3.16463i
$956$	−7.45761			−0.241196
$957$	−20.7693			−0.671375
$958$	−6.46369	+	11.1954i	−0.208832	+	0.361708i
$959$	−17.6661	+	30.5986i	−0.570468	+	0.988080i
$960$	2.90218	−	5.02673i	0.0936676	−	0.162237i
$961$	−26.0727			−0.841054
$962$	20.1806	−	34.1485i	0.650648	−	1.10099i
$963$	6.41545	+	11.1119i	0.206735	+	0.358076i
$964$	25.1117			0.808795
$965$	1.28480	−	2.22533i	0.0413591	−	0.0716360i
$966$	2.79230	+	4.83640i	0.0898406	+	0.155609i
$967$	3.41949	−	5.92272i	0.109963	−	0.190462i	−0.805792	−	0.592199i	$-0.798260\pi$
$967$	3.41949	−	5.92272i	0.109963	−	0.190462i	0.915755	+	0.401737i	$0.131593\pi$
$968$	3.98580	−	6.90361i	0.128108	−	0.221890i
$969$	−11.5563	+	1.94200i	−0.371241	+	0.0623860i
$970$	−25.6813			−0.824576
$971$	5.46921	+	9.47295i	0.175515	+	0.304001i	0.940339	−	0.340238i	$-0.110508\pi$
$971$	5.46921	+	9.47295i	0.175515	+	0.304001i	−0.764824	+	0.644239i	$0.777174\pi$
$972$	10.2024			0.327241
$973$	−8.02894	+	13.9065i	−0.257396	+	0.445823i
$974$	−11.6976	+	20.2608i	−0.374814	+	0.649197i
$975$	31.2235	−	52.8347i	0.999951	−	1.69206i
$976$	−2.34851			−0.0751739
$977$	−6.92471	−	11.9940i	−0.221541	−	0.383721i	0.733735	−	0.679436i	$-0.237775\pi$
$977$	−6.92471	−	11.9940i	−0.221541	−	0.383721i	−0.955276	+	0.295715i	$0.904442\pi$
$978$	−6.34718	+	10.9936i	−0.202961	+	0.351538i
$979$	−16.2653			−0.519840
$980$	−7.91105			−0.252709
$981$	−9.65934	+	16.7305i	−0.308399	+	0.534163i
$982$	−15.6809			−0.500397
$983$	−17.9144	+	31.0286i	−0.571380	+	0.989659i	0.425045	+	0.905172i	$0.360258\pi$
$983$	−17.9144	+	31.0286i	−0.571380	+	0.989659i	−0.996425	+	0.0844865i	$0.973075\pi$
$984$	−2.56041			−0.0816229
$985$	−19.6334			−0.625572
$986$	16.3241			0.519866
$987$	−38.1036			−1.21285
$988$	15.5246	−	2.44708i	0.493902	−	0.0778521i
$989$	7.77833			0.247336
$990$	−7.45343			−0.236885
$991$	21.3029			0.676709			0.338355	−	0.941019i	$-0.390130\pi$
$991$	21.3029			0.676709			0.338355	+	0.941019i	$0.390130\pi$
$992$	−2.21976			−0.0704773
$993$	3.89262	−	6.74222i	0.123529	−	0.213958i
$994$	−25.2012			−0.799333
$995$	5.66153	−	9.80605i	0.179482	−	0.310873i
$996$	7.47660			0.236905
$997$	−0.315137			−0.00998050			−0.00499025	−	0.999988i	$-0.501588\pi$
$997$	−0.315137			−0.00998050			−0.00499025	+	0.999988i	$0.501588\pi$
$998$	−12.1504	+	21.0451i	−0.384615	+	0.666172i
$999$	31.1129	+	53.8891i	0.984369	+	1.70498i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	494.2.h.d.315.8	yes	22
13.9	even	3		494.2.e.d.87.4	✓	22
19.7	even	3		494.2.e.d.159.4	yes	22
247.178	even	3	inner	494.2.h.d.425.8	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.e.d.87.4	✓	22	13.9	even	3
494.2.e.d.159.4	yes	22	19.7	even	3
494.2.h.d.315.8	yes	22	1.1	even	1	trivial
494.2.h.d.425.8	yes	22	247.178	even	3	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:	\( N \)	\(=\)	\( 494 = 2 \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	494.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.40196 q^{3} +1.00000 q^{4} +(2.07009 - 3.58550i) q^{5} +1.40196 q^{6} +(-1.49255 + 2.58517i) q^{7} +1.00000 q^{8} -1.03450 q^{9} +(2.07009 - 3.58550i) q^{10} +(0.870115 + 1.50708i) q^{11} +1.40196 q^{12} +(1.77099 + 3.14064i) q^{13} +(-1.49255 + 2.58517i) q^{14} +(2.90218 - 5.02673i) q^{15} +1.00000 q^{16} +(-0.958786 - 1.66067i) q^{17} -1.03450 q^{18} +(1.52372 - 4.08390i) q^{19} +(2.07009 - 3.58550i) q^{20} +(-2.09250 + 3.62431i) q^{21} +(0.870115 + 1.50708i) q^{22} +(0.667216 - 1.15565i) q^{23} +1.40196 q^{24} +(-6.07052 - 10.5144i) q^{25} +(1.77099 + 3.14064i) q^{26} -5.65622 q^{27} +(-1.49255 + 2.58517i) q^{28} +(-4.25646 + 7.37240i) q^{29} +(2.90218 - 5.02673i) q^{30} -2.21976 q^{31} +1.00000 q^{32} +(1.21987 + 2.11287i) q^{33} +(-0.958786 - 1.66067i) q^{34} +(6.17941 + 10.7030i) q^{35} -1.03450 q^{36} +(-5.50065 - 9.52741i) q^{37} +(1.52372 - 4.08390i) q^{38} +(2.48286 + 4.40306i) q^{39} +(2.07009 - 3.58550i) q^{40} -1.82630 q^{41} +(-2.09250 + 3.62431i) q^{42} +(2.91447 + 5.04801i) q^{43} +(0.870115 + 1.50708i) q^{44} +(-2.14151 + 3.70920i) q^{45} +(0.667216 - 1.15565i) q^{46} +(4.55241 + 7.88500i) q^{47} +1.40196 q^{48} +(-0.955401 - 1.65480i) q^{49} +(-6.07052 - 10.5144i) q^{50} +(-1.34418 - 2.32819i) q^{51} +(1.77099 + 3.14064i) q^{52} +(-0.629479 - 1.09029i) q^{53} -5.65622 q^{54} +7.20485 q^{55} +(-1.49255 + 2.58517i) q^{56} +(2.13620 - 5.72548i) q^{57} +(-4.25646 + 7.37240i) q^{58} +(1.32913 + 2.30212i) q^{59} +(2.90218 - 5.02673i) q^{60} -2.34851 q^{61} -2.21976 q^{62} +(1.54404 - 2.67436i) q^{63} +1.00000 q^{64} +(14.9268 + 0.151530i) q^{65} +(1.21987 + 2.11287i) q^{66} +(-5.92238 + 10.2579i) q^{67} +(-0.958786 - 1.66067i) q^{68} +(0.935412 - 1.62018i) q^{69} +(6.17941 + 10.7030i) q^{70} +(4.22117 + 7.31128i) q^{71} -1.03450 q^{72} +(-5.78569 + 10.0211i) q^{73} +(-5.50065 - 9.52741i) q^{74} +(-8.51064 - 14.7409i) q^{75} +(1.52372 - 4.08390i) q^{76} -5.19475 q^{77} +(2.48286 + 4.40306i) q^{78} +(7.59090 - 13.1478i) q^{79} +(2.07009 - 3.58550i) q^{80} -4.82630 q^{81} -1.82630 q^{82} +5.33295 q^{83} +(-2.09250 + 3.62431i) q^{84} -7.93908 q^{85} +(2.91447 + 5.04801i) q^{86} +(-5.96739 + 10.3358i) q^{87} +(0.870115 + 1.50708i) q^{88} +(-4.67331 + 8.09441i) q^{89} +(-2.14151 + 3.70920i) q^{90} +(-10.7624 - 0.109255i) q^{91} +(0.667216 - 1.15565i) q^{92} -3.11201 q^{93} +(4.55241 + 7.88500i) q^{94} +(-11.4886 - 13.9173i) q^{95} +1.40196 q^{96} +(-3.10147 - 5.37191i) q^{97} +(-0.955401 - 1.65480i) q^{98} +(-0.900135 - 1.55908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 22 q^{4} - 2 q^{5} - 5 q^{7} + 22 q^{8} + 10 q^{9} - 2 q^{10} - 2 q^{11} + 2 q^{13} - 5 q^{14} - 3 q^{15} + 22 q^{16} + q^{17} + 10 q^{18} + 12 q^{19} - 2 q^{20} + q^{21} - 2 q^{22}+ \cdots - 2 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 22 * q^4 - 2 * q^5 - 5 * q^7 + 22 * q^8 + 10 * q^9 - 2 * q^10 - 2 * q^11 + 2 * q^13 - 5 * q^14 - 3 * q^15 + 22 * q^16 + q^17 + 10 * q^18 + 12 * q^19 - 2 * q^20 + q^21 - 2 * q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 6 * q^27 - 5 * q^28 - 7 * q^29 - 3 * q^30 + 6 * q^31 + 22 * q^32 - 4 * q^33 + q^34 - 3 * q^35 + 10 * q^36 - 9 * q^37 + 12 * q^38 + 13 * q^39 - 2 * q^40 - 24 * q^41 + q^42 - 10 * q^43 - 2 * q^44 - 15 * q^45 + 4 * q^46 + 19 * q^47 - 14 * q^49 - 9 * q^50 - 22 * q^51 + 2 * q^52 - 9 * q^53 - 6 * q^54 + 48 * q^55 - 5 * q^56 + 13 * q^57 - 7 * q^58 - 12 * q^59 - 3 * q^60 - 22 * q^61 + 6 * q^62 - 23 * q^63 + 22 * q^64 + 13 * q^65 - 4 * q^66 + 3 * q^67 + q^68 - 20 * q^69 - 3 * q^70 + 4 * q^71 + 10 * q^72 - 38 * q^73 - 9 * q^74 - 20 * q^75 + 12 * q^76 - 76 * q^77 + 13 * q^78 - 5 * q^79 - 2 * q^80 - 90 * q^81 - 24 * q^82 - 10 * q^83 + q^84 + 24 * q^85 - 10 * q^86 + 4 * q^87 - 2 * q^88 + 3 * q^89 - 15 * q^90 + 34 * q^91 + 4 * q^92 + 22 * q^93 + 19 * q^94 - 33 * q^95 - 31 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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