LMFDB - Embedded newform 66.3.c.a.23.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [66,3,Mod(23,66)] 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("66.23"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(66, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	66.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.79836974478$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 5x^{6} - 50x^{5} - 34x^{4} + 586x^{3} - 431x^{2} - 1830x + 3051 $ x^8 - 2x^7 + 5x^6 - 50x^5 - 34x^4 + 586x^3 - 431x^2 - 1830*x + 3051
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.4
Root			$-2.28135 + 0.533982i$ of defining polynomial
Character	$\chi$	$=$	66.23
Dual form			66.3.c.a.23.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +(2.28135 + 1.94820i) q^{3} -2.00000 q^{4} -5.56529i q^{5} +(2.75516 - 3.22631i) q^{6} +9.94529 q^{7} +2.82843i q^{8} +(1.40907 + 8.88901i) q^{9} -7.87050 q^{10} -3.31662i q^{11} +(-4.56269 - 3.89639i) q^{12} -18.1460 q^{13} -14.0648i q^{14} +(10.8423 - 12.6963i) q^{15} +4.00000 q^{16} +18.4880i q^{17} +(12.5710 - 1.99273i) q^{18} -29.8323 q^{19} +11.1306i q^{20} +(22.6886 + 19.3754i) q^{21} -4.69042 q^{22} +13.1449i q^{23} +(-5.51033 + 6.45262i) q^{24} -5.97241 q^{25} +25.6624i q^{26} +(-14.1030 + 23.0240i) q^{27} -19.8906 q^{28} -15.8427i q^{29} +(-17.9553 - 15.3333i) q^{30} +22.6040 q^{31} -5.65685i q^{32} +(6.46143 - 7.56637i) q^{33} +26.1460 q^{34} -55.3484i q^{35} +(-2.81814 - 17.7780i) q^{36} +21.8376 q^{37} +42.1893i q^{38} +(-41.3974 - 35.3520i) q^{39} +15.7410 q^{40} -9.61310i q^{41} +(27.4009 - 32.0866i) q^{42} -44.2559 q^{43} +6.63325i q^{44} +(49.4699 - 7.84188i) q^{45} +18.5897 q^{46} -52.9352i q^{47} +(9.12538 + 7.79278i) q^{48} +49.9088 q^{49} +8.44626i q^{50} +(-36.0183 + 42.1776i) q^{51} +36.2921 q^{52} +51.1232i q^{53} +(32.5609 + 19.9446i) q^{54} -18.4580 q^{55} +28.1295i q^{56} +(-68.0579 - 58.1192i) q^{57} -22.4050 q^{58} -54.9673i q^{59} +(-21.6845 + 25.3927i) q^{60} +24.0552 q^{61} -31.9669i q^{62} +(14.0136 + 88.4038i) q^{63} -8.00000 q^{64} +100.988i q^{65} +(-10.7005 - 9.13785i) q^{66} +107.181 q^{67} -36.9761i q^{68} +(-25.6088 + 29.9881i) q^{69} -78.2745 q^{70} -46.5360i q^{71} +(-25.1419 + 3.98545i) q^{72} +6.88285 q^{73} -30.8831i q^{74} +(-13.6251 - 11.6354i) q^{75} +59.6647 q^{76} -32.9848i q^{77} +(-49.9953 + 58.5447i) q^{78} -63.7079 q^{79} -22.2611i q^{80} +(-77.0290 + 25.0505i) q^{81} -13.5950 q^{82} -57.4231i q^{83} +(-45.3773 - 38.7507i) q^{84} +102.891 q^{85} +62.5873i q^{86} +(30.8648 - 36.1428i) q^{87} +9.38083 q^{88} +108.987i q^{89} +(-11.0901 - 69.9610i) q^{90} -180.468 q^{91} -26.2898i q^{92} +(51.5675 + 44.0370i) q^{93} -74.8617 q^{94} +166.025i q^{95} +(11.0207 - 12.9052i) q^{96} -87.7799 q^{97} -70.5818i q^{98} +(29.4815 - 4.67336i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} - 16 q^{4} + 8 q^{6} + 8 q^{7} - 6 q^{9} - 16 q^{10} + 4 q^{12} - 8 q^{13} - 18 q^{15} + 32 q^{16} - 32 q^{18} + 64 q^{19} + 100 q^{21} - 16 q^{24} - 132 q^{25} - 44 q^{27} - 16 q^{28} - 24 q^{30}+ \cdots + 110 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 - 16 * q^4 + 8 * q^6 + 8 * q^7 - 6 * q^9 - 16 * q^10 + 4 * q^12 - 8 * q^13 - 18 * q^15 + 32 * q^16 - 32 * q^18 + 64 * q^19 + 100 * q^21 - 16 * q^24 - 132 * q^25 - 44 * q^27 - 16 * q^28 - 24 * q^30 + 28 * q^31 + 22 * q^33 + 72 * q^34 + 12 * q^36 + 4 * q^37 - 72 * q^39 + 32 * q^40 + 48 * q^42 - 120 * q^43 + 130 * q^45 - 16 * q^46 - 8 * q^48 + 192 * q^49 - 148 * q^51 + 16 * q^52 + 176 * q^54 - 132 * q^55 - 248 * q^57 - 136 * q^58 + 36 * q^60 + 24 * q^61 - 196 * q^63 - 64 * q^64 - 20 * q^67 + 374 * q^69 + 240 * q^70 + 64 * q^72 + 392 * q^73 + 340 * q^75 - 128 * q^76 - 232 * q^78 - 40 * q^79 - 222 * q^81 - 152 * q^82 - 200 * q^84 + 24 * q^85 + 232 * q^87 - 224 * q^90 - 576 * q^91 - 54 * q^93 - 256 * q^94 + 32 * q^96 - 132 * q^97 + 110 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	2.28135	+	1.94820i	0.760448	+	0.649398i
$3$	2.28135	+	1.94820i	0.760448	+	0.649398i
$4$	−2.00000			−0.500000
$5$		−	5.56529i		−	1.11306i	−0.830828	−	0.556529i	$-0.812133\pi$
$5$		−	5.56529i		−	1.11306i	0.830828	−	0.556529i	$-0.187867\pi$
$6$	2.75516	−	3.22631i	0.459194	−	0.537718i
$7$	9.94529			1.42076			0.710378	−	0.703820i	$-0.248524\pi$
$7$	9.94529			1.42076			0.710378	+	0.703820i	$0.248524\pi$
$8$			2.82843i			0.353553i
$9$	1.40907	+	8.88901i	0.156563	+	0.987668i
$10$	−7.87050			−0.787050
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	−4.56269	−	3.89639i	−0.380224	−	0.324699i
$13$	−18.1460			−1.39585			−0.697924	−	0.716171i	$-0.745893\pi$
$13$	−18.1460			−1.39585			−0.697924	+	0.716171i	$0.745893\pi$
$14$		−	14.0648i		−	1.00463i
$15$	10.8423	−	12.6963i	0.722818	−	0.846423i
$16$	4.00000			0.250000
$17$			18.4880i			1.08753i	0.839237	+	0.543766i	$0.183002\pi$
$17$			18.4880i			1.08753i	−0.839237	+	0.543766i	$0.816998\pi$
$18$	12.5710	−	1.99273i	0.698387	−	0.110707i
$19$	−29.8323			−1.57012			−0.785061	−	0.619418i	$-0.787369\pi$
$19$	−29.8323			−1.57012			−0.785061	+	0.619418i	$0.787369\pi$
$20$			11.1306i			0.556529i
$21$	22.6886	+	19.3754i	1.08041	+	0.922637i
$22$	−4.69042			−0.213201
$23$			13.1449i			0.571518i	0.958302	+	0.285759i	$0.0922456\pi$
$23$			13.1449i			0.571518i	−0.958302	+	0.285759i	$0.907754\pi$
$24$	−5.51033	+	6.45262i	−0.229597	+	0.268859i
$25$	−5.97241			−0.238896
$26$			25.6624i			0.987014i
$27$	−14.1030	+	23.0240i	−0.522332	+	0.852742i
$28$	−19.8906			−0.710378
$29$		−	15.8427i		−	0.546302i	−0.961971	−	0.273151i	$-0.911934\pi$
$29$		−	15.8427i		−	0.546302i	0.961971	−	0.273151i	$-0.0880658\pi$
$30$	−17.9553	−	15.3333i	−0.598511	−	0.511109i
$31$	22.6040			0.729161			0.364581	−	0.931172i	$-0.381212\pi$
$31$	22.6040			0.729161			0.364581	+	0.931172i	$0.381212\pi$
$32$		−	5.65685i		−	0.176777i
$33$	6.46143	−	7.56637i	0.195801	−	0.229284i
$34$	26.1460			0.769001
$35$		−	55.3484i		−	1.58138i
$36$	−2.81814	−	17.7780i	−0.0782817	−	0.493834i
$37$	21.8376			0.590207			0.295103	−	0.955465i	$-0.404646\pi$
$37$	21.8376			0.590207			0.295103	+	0.955465i	$0.404646\pi$
$38$			42.1893i			1.11024i
$39$	−41.3974	−	35.3520i	−1.06147	−	0.906462i
$40$	15.7410			0.393525
$41$		−	9.61310i		−	0.234466i	−0.993104	−	0.117233i	$-0.962598\pi$
$41$		−	9.61310i		−	0.234466i	0.993104	−	0.117233i	$-0.0374024\pi$
$42$	27.4009	−	32.0866i	0.652403	−	0.763966i
$43$	−44.2559			−1.02921			−0.514604	−	0.857428i	$-0.672061\pi$
$43$	−44.2559			−1.02921			−0.514604	+	0.857428i	$0.672061\pi$
$44$			6.63325i			0.150756i
$45$	49.4699	−	7.84188i	1.09933	−	0.174264i
$46$	18.5897			0.404124
$47$		−	52.9352i		−	1.12628i	−0.826361	−	0.563141i	$-0.809593\pi$
$47$		−	52.9352i		−	1.12628i	0.826361	−	0.563141i	$-0.190407\pi$
$48$	9.12538	+	7.79278i	0.190112	+	0.162350i
$49$	49.9088			1.01855
$50$			8.44626i			0.168925i
$51$	−36.0183	+	42.1776i	−0.706241	+	0.827012i
$52$	36.2921			0.697924
$53$			51.1232i			0.964589i	0.876009	+	0.482295i	$0.160197\pi$
$53$			51.1232i			0.964589i	−0.876009	+	0.482295i	$0.839803\pi$
$54$	32.5609	+	19.9446i	0.602980	+	0.369344i
$55$	−18.4580			−0.335599
$56$			28.1295i			0.502313i
$57$	−68.0579	−	58.1192i	−1.19400	−	1.01964i
$58$	−22.4050			−0.386294
$59$		−	54.9673i		−	0.931649i	−0.884877	−	0.465824i	$-0.845758\pi$
$59$		−	54.9673i		−	0.931649i	0.884877	−	0.465824i	$-0.154242\pi$
$60$	−21.6845	+	25.3927i	−0.361409	+	0.423211i
$61$	24.0552			0.394347			0.197174	−	0.980369i	$-0.436824\pi$
$61$	24.0552			0.394347			0.197174	+	0.980369i	$0.436824\pi$
$62$		−	31.9669i		−	0.515595i
$63$	14.0136	+	88.4038i	0.222438	+	1.40324i
$64$	−8.00000			−0.125000
$65$			100.988i			1.55366i
$66$	−10.7005	−	9.13785i	−0.162128	−	0.138452i
$67$	107.181			1.59972			0.799859	−	0.600188i	$-0.204908\pi$
$67$	107.181			1.59972			0.799859	+	0.600188i	$0.204908\pi$
$68$		−	36.9761i		−	0.543766i
$69$	−25.6088	+	29.9881i	−0.371143	+	0.434610i
$70$	−78.2745			−1.11821
$71$		−	46.5360i		−	0.655436i	−0.944776	−	0.327718i	$-0.893720\pi$
$71$		−	46.5360i		−	0.655436i	0.944776	−	0.327718i	$-0.106280\pi$
$72$	−25.1419	+	3.98545i	−0.349193	+	0.0553535i
$73$	6.88285			0.0942857			0.0471428	−	0.998888i	$-0.484988\pi$
$73$	6.88285			0.0942857			0.0471428	+	0.998888i	$0.484988\pi$
$74$		−	30.8831i		−	0.417339i
$75$	−13.6251	−	11.6354i	−0.181668	−	0.155139i
$76$	59.6647			0.785061
$77$		−	32.9848i		−	0.428374i
$78$	−49.9953	+	58.5447i	−0.640966	+	0.750573i
$79$	−63.7079			−0.806429			−0.403215	−	0.915105i	$-0.632107\pi$
$79$	−63.7079			−0.806429			−0.403215	+	0.915105i	$0.632107\pi$
$80$		−	22.2611i		−	0.278264i
$81$	−77.0290	+	25.0505i	−0.950976	+	0.309265i
$82$	−13.5950			−0.165792
$83$		−	57.4231i		−	0.691844i	−0.938263	−	0.345922i	$-0.887566\pi$
$83$		−	57.4231i		−	0.691844i	0.938263	−	0.345922i	$-0.112434\pi$
$84$	−45.3773	−	38.7507i	−0.540206	−	0.461318i
$85$	102.891			1.21049
$86$			62.5873i			0.727760i
$87$	30.8648	−	36.1428i	0.354767	−	0.415434i
$88$	9.38083			0.106600
$89$			108.987i			1.22457i	0.790636	+	0.612286i	$0.209750\pi$
$89$			108.987i			1.22457i	−0.790636	+	0.612286i	$0.790250\pi$
$90$	−11.0901	−	69.9610i	−0.123223	−	0.777344i
$91$	−180.468			−1.98316
$92$		−	26.2898i		−	0.285759i
$93$	51.5675	+	44.0370i	0.554490	+	0.473516i
$94$	−74.8617			−0.796401
$95$			166.025i			1.74764i
$96$	11.0207	−	12.9052i	0.114799	−	0.134430i
$97$	−87.7799			−0.904947			−0.452474	−	0.891778i	$-0.649458\pi$
$97$	−87.7799			−0.904947			−0.452474	+	0.891778i	$0.649458\pi$
$98$		−	70.5818i		−	0.720222i
$99$	29.4815	−	4.67336i	0.297793	−	0.0472056i
$100$	11.9448			0.119448
$101$			176.529i			1.74781i	0.486093	+	0.873907i	$0.338422\pi$
$101$			176.529i			1.74781i	−0.486093	+	0.873907i	$0.661578\pi$
$102$	59.6481	+	50.9376i	0.584786	+	0.499388i
$103$	125.829			1.22164			0.610822	−	0.791768i	$-0.290839\pi$
$103$	125.829			1.22164			0.610822	+	0.791768i	$0.290839\pi$
$104$		−	51.3247i		−	0.493507i
$105$	107.829	−	126.269i	1.02695	−	1.20256i
$106$	72.2992			0.682068
$107$		−	112.226i		−	1.04884i	−0.851458	−	0.524422i	$-0.824281\pi$
$107$		−	112.226i		−	1.04884i	0.851458	−	0.524422i	$-0.175719\pi$
$108$	28.2059	−	46.0481i	0.261166	−	0.426371i
$109$	77.2632			0.708837			0.354418	−	0.935087i	$-0.384679\pi$
$109$	77.2632			0.708837			0.354418	+	0.935087i	$0.384679\pi$
$110$			26.1035i			0.237305i
$111$	49.8192	+	42.5440i	0.448822	+	0.383279i
$112$	39.7812			0.355189
$113$		−	207.293i		−	1.83445i	−0.398370	−	0.917225i	$-0.630424\pi$
$113$		−	207.293i		−	1.83445i	0.398370	−	0.917225i	$-0.369576\pi$
$114$	−82.1930	+	96.2483i	−0.720991	+	0.844284i
$115$	73.1552			0.636132
$116$			31.6855i			0.273151i
$117$	−25.5690	−	161.300i	−0.218539	−	1.37864i
$118$	−77.7354			−0.658775
$119$			183.869i			1.54512i
$120$	35.9107	+	30.6666i	0.299256	+	0.255555i
$121$	−11.0000			−0.0909091
$122$		−	34.0192i		−	0.278846i
$123$	18.7282	−	21.9308i	0.152262	−	0.178299i
$124$	−45.2080			−0.364581
$125$		−	105.894i		−	0.847152i
$126$	125.022	−	19.8183i	0.992237	−	0.157288i
$127$	77.1097			0.607163			0.303581	−	0.952805i	$-0.401818\pi$
$127$	77.1097			0.607163			0.303581	+	0.952805i	$0.401818\pi$
$128$			11.3137i			0.0883883i
$129$	−100.963	−	86.2192i	−0.782659	−	0.668366i
$130$	142.818			1.09860
$131$		−	67.8077i		−	0.517616i	−0.965929	−	0.258808i	$-0.916670\pi$
$131$		−	67.8077i		−	0.517616i	0.965929	−	0.258808i	$-0.0833297\pi$
$132$	−12.9229	+	15.1327i	−0.0979005	+	0.114642i
$133$	−296.691			−2.23076
$134$		−	151.577i		−	1.13117i
$135$	128.135	+	78.4870i	0.949151	+	0.581385i
$136$	−52.2921			−0.384501
$137$			12.2030i			0.0890729i	0.999008	+	0.0445364i	$0.0141811\pi$
$137$			12.2030i			0.0890729i	−0.999008	+	0.0445364i	$0.985819\pi$
$138$	42.4095	+	36.2164i	0.307315	+	0.262437i
$139$	−100.084			−0.720031			−0.360016	−	0.932946i	$-0.617229\pi$
$139$	−100.084			−0.720031			−0.360016	+	0.932946i	$0.617229\pi$
$140$			110.697i			0.790691i
$141$	103.128	−	120.763i	0.731405	−	0.856479i
$142$	−65.8118			−0.463463
$143$			60.1836i			0.420864i
$144$	5.63628	+	35.5560i	0.0391409	+	0.246917i
$145$	−88.1694			−0.608065
$146$		−	9.73382i		−	0.0666700i
$147$	113.859	+	97.2322i	0.774553	+	0.661443i
$148$	−43.6753			−0.295103
$149$			172.468i			1.15750i	0.815504	+	0.578752i	$0.196460\pi$
$149$			172.468i			1.15750i	−0.815504	+	0.578752i	$0.803540\pi$
$150$	−16.4550	+	19.2688i	−0.109700	+	0.128459i
$151$	6.75844			0.0447579			0.0223790	−	0.999750i	$-0.492876\pi$
$151$	6.75844			0.0447579			0.0223790	+	0.999750i	$0.492876\pi$
$152$		−	84.3786i		−	0.555122i
$153$	−164.340	+	26.0510i	−1.07412	+	0.170268i
$154$	−46.6476			−0.302906
$155$		−	125.798i		−	0.811598i
$156$	82.7947	+	70.7040i	0.530736	+	0.453231i
$157$	−28.6116			−0.182239			−0.0911197	−	0.995840i	$-0.529045\pi$
$157$	−28.6116			−0.182239			−0.0911197	+	0.995840i	$0.529045\pi$
$158$			90.0966i			0.570232i
$159$	−99.5980	+	116.630i	−0.626403	+	0.733520i
$160$	−31.4820			−0.196763
$161$			130.730i			0.811987i
$162$	35.4267	+	108.936i	0.218684	+	0.672441i
$163$	−38.2298			−0.234539			−0.117269	−	0.993100i	$-0.537414\pi$
$163$	−38.2298			−0.234539			−0.117269	+	0.993100i	$0.537414\pi$
$164$			19.2262i			0.117233i
$165$	−42.1090	−	35.9597i	−0.255206	−	0.217938i
$166$	−81.2085			−0.489208
$167$		−	7.40637i		−	0.0443495i	−0.999754	−	0.0221747i	$-0.992941\pi$
$167$		−	7.40637i		−	0.0443495i	0.999754	−	0.0221747i	$-0.00705902\pi$
$168$	−54.8018	+	64.1732i	−0.326201	+	0.381983i
$169$	160.279			0.948394
$170$		−	145.510i		−	0.855942i
$171$	−42.0359	−	265.180i	−0.245824	−	1.55076i
$172$	88.5118			0.514604
$173$		−	171.502i		−	0.991341i	−0.868511	−	0.495670i	$-0.834922\pi$
$173$		−	171.502i		−	0.991341i	0.868511	−	0.495670i	$-0.165078\pi$
$174$	−51.1136	−	43.6494i	−0.293756	−	0.250858i
$175$	−59.3974			−0.339414
$176$		−	13.2665i		−	0.0753778i
$177$	107.087	−	125.399i	0.605011	−	0.708471i
$178$	154.131			0.865903
$179$			274.694i			1.53460i	0.641288	+	0.767301i	$0.278401\pi$
$179$			274.694i			1.53460i	−0.641288	+	0.767301i	$0.721599\pi$
$180$	−98.9398	+	15.6838i	−0.549665	+	0.0871320i
$181$	−303.937			−1.67921			−0.839606	−	0.543196i	$-0.817214\pi$
$181$	−303.937			−1.67921			−0.839606	+	0.543196i	$0.817214\pi$
$182$			255.220i			1.40231i
$183$	54.8782	+	46.8642i	0.299881	+	0.256088i
$184$	−37.1794			−0.202062
$185$		−	121.533i		−	0.656934i
$186$	62.2777	−	72.9275i	0.334827	−	0.392083i
$187$	61.3179			0.327903
$188$			105.870i			0.563141i
$189$	−140.258	+	228.981i	−0.742106	+	1.21154i
$190$	234.795			1.23577
$191$		−	222.456i		−	1.16469i	−0.812941	−	0.582346i	$-0.802135\pi$
$191$		−	222.456i		−	1.16469i	0.812941	−	0.582346i	$-0.197865\pi$
$192$	−18.2508	−	15.5856i	−0.0950560	−	0.0811748i
$193$	143.274			0.742353			0.371177	−	0.928562i	$-0.378954\pi$
$193$	143.274			0.742353			0.371177	+	0.928562i	$0.378954\pi$
$194$			124.139i			0.639894i
$195$	−196.744	+	230.388i	−1.00894	+	1.18148i
$196$	−99.8177			−0.509274
$197$			6.60585i			0.0335322i	0.999859	+	0.0167661i	$0.00533707\pi$
$197$			6.60585i			0.0335322i	−0.999859	+	0.0167661i	$0.994663\pi$
$198$	−6.60913	−	41.6932i	−0.0333794	−	0.210572i
$199$	−10.1627			−0.0510689			−0.0255344	−	0.999674i	$-0.508129\pi$
$199$	−10.1627			−0.0510689			−0.0255344	+	0.999674i	$0.508129\pi$
$200$		−	16.8925i		−	0.0844626i
$201$	244.517	+	208.810i	1.21650	+	1.03885i
$202$	249.650			1.23589
$203$		−	157.561i		−	0.776161i
$204$	72.0366	−	84.3552i	0.353121	−	0.413506i
$205$	−53.4996			−0.260974
$206$		−	177.949i		−	0.863832i
$207$	−116.845	+	18.5221i	−0.564470	+	0.0894788i
$208$	−72.5841			−0.348962
$209$			98.9427i			0.473410i
$210$	−178.571	−	152.494i	−0.850338	−	0.726162i
$211$	196.251			0.930101			0.465051	−	0.885284i	$-0.346036\pi$
$211$	196.251			0.930101			0.465051	+	0.885284i	$0.346036\pi$
$212$		−	102.246i		−	0.482295i
$213$	90.6611	−	106.165i	0.425639	−	0.498425i
$214$	−158.712			−0.741645
$215$			246.297i			1.14557i
$216$	−65.1218	−	39.8892i	−0.301490	−	0.184672i
$217$	224.803			1.03596
$218$		−	109.267i		−	0.501223i
$219$	15.7022	+	13.4091i	0.0716994	+	0.0612290i
$220$	36.9159			0.167800
$221$		−	335.485i		−	1.51803i
$222$	60.1663	−	70.4550i	0.271019	−	0.317365i
$223$	344.258			1.54376			0.771880	−	0.635768i	$-0.219317\pi$
$223$	344.258			1.54376			0.771880	+	0.635768i	$0.219317\pi$
$224$		−	56.2591i		−	0.251157i
$225$	−8.41555	−	53.0888i	−0.0374024	−	0.235950i
$226$	−293.156			−1.29715
$227$		−	376.155i		−	1.65707i	−0.559937	−	0.828535i	$-0.689175\pi$
$227$		−	376.155i		−	1.65707i	0.559937	−	0.828535i	$-0.310825\pi$
$228$	136.116	+	116.238i	0.596999	+	0.509818i
$229$	28.1230			0.122808			0.0614040	−	0.998113i	$-0.480442\pi$
$229$	28.1230			0.122808			0.0614040	+	0.998113i	$0.480442\pi$
$230$		−	103.457i		−	0.449813i
$231$	64.2608	−	75.2497i	0.278185	−	0.325756i
$232$	44.8101			0.193147
$233$			307.576i			1.32007i	0.751236	+	0.660034i	$0.229458\pi$
$233$			307.576i			1.32007i	−0.751236	+	0.660034i	$0.770542\pi$
$234$	−228.113	+	36.1601i	−0.974842	+	0.154530i
$235$	−294.600			−1.25362
$236$			109.935i			0.465824i
$237$	−145.340	−	124.115i	−0.613248	−	0.523694i
$238$	260.030			1.09256
$239$			195.774i			0.819137i	0.912279	+	0.409569i	$0.134321\pi$
$239$			195.774i			0.819137i	−0.912279	+	0.409569i	$0.865679\pi$
$240$	43.3691	−	50.7854i	0.180704	−	0.211606i
$241$	−94.8734			−0.393666			−0.196833	−	0.980437i	$-0.563066\pi$
$241$	−94.8734			−0.393666			−0.196833	+	0.980437i	$0.563066\pi$
$242$			15.5563i			0.0642824i
$243$	−224.533	−	92.9188i	−0.924004	−	0.382382i
$244$	−48.1104			−0.197174
$245$		−	277.757i		−	1.13370i
$246$	−31.0148	−	26.4857i	−0.126076	−	0.107665i
$247$	541.339			2.19165
$248$			63.9338i			0.257797i
$249$	111.871	−	131.002i	0.449282	−	0.526112i
$250$	−149.757			−0.599027
$251$			297.104i			1.18368i	0.806055	+	0.591840i	$0.201598\pi$
$251$			297.104i			1.18368i	−0.806055	+	0.591840i	$0.798402\pi$
$252$	−28.0272	−	176.808i	−0.111219	−	0.701618i
$253$	43.5967			0.172319
$254$		−	109.050i		−	0.429329i
$255$	234.730	+	200.452i	0.920511	+	0.786087i
$256$	16.0000			0.0625000
$257$			375.940i			1.46280i	0.681948	+	0.731401i	$0.261133\pi$
$257$			375.940i			1.46280i	−0.681948	+	0.731401i	$0.738867\pi$
$258$	−121.932	+	142.783i	−0.472606	+	0.553424i
$259$	217.182			0.838540
$260$		−	201.976i		−	0.776830i
$261$	140.826	−	22.3236i	0.539565	−	0.0855309i
$262$	−95.8946			−0.366010
$263$		−	138.319i		−	0.525927i	−0.964806	−	0.262963i	$-0.915300\pi$
$263$		−	138.319i		−	0.525927i	0.964806	−	0.262963i	$-0.0846998\pi$
$264$	21.4009	+	18.2757i	0.0810641	+	0.0692261i
$265$	284.515			1.07364
$266$			419.585i			1.57739i
$267$	−212.328	+	248.637i	−0.795235	+	0.931224i
$268$	−214.362			−0.799859
$269$			25.8825i			0.0962173i	0.998842	+	0.0481087i	$0.0153194\pi$
$269$			25.8825i			0.0962173i	−0.998842	+	0.0481087i	$0.984681\pi$
$270$	110.997	−	181.211i	0.411101	−	0.671151i
$271$	−250.001			−0.922512			−0.461256	−	0.887267i	$-0.652601\pi$
$271$	−250.001			−0.922512			−0.461256	+	0.887267i	$0.652601\pi$
$272$			73.9522i			0.271883i
$273$	−411.709	−	351.586i	−1.50809	−	1.28786i
$274$	17.2576			0.0629840
$275$			19.8082i			0.0720300i
$276$	51.2177	−	59.9761i	0.185571	−	0.217305i
$277$	256.366			0.925511			0.462755	−	0.886486i	$-0.346861\pi$
$277$	256.366			0.925511			0.462755	+	0.886486i	$0.346861\pi$
$278$			141.541i			0.509139i
$279$	31.8506	+	200.927i	0.114160	+	0.720169i
$280$	156.549			0.559103
$281$			132.023i			0.469834i	0.972015	+	0.234917i	$0.0754818\pi$
$281$			132.023i			0.469834i	−0.972015	+	0.234917i	$0.924518\pi$
$282$	−170.785	−	145.845i	−0.605622	−	0.517182i
$283$	−282.713			−0.998984			−0.499492	−	0.866318i	$-0.666480\pi$
$283$	−282.713			−0.998984			−0.499492	+	0.866318i	$0.666480\pi$
$284$			93.0719i			0.327718i
$285$	−323.450	+	378.761i	−1.13491	+	1.32899i
$286$	85.1125			0.297596
$287$		−	95.6050i		−	0.333119i
$288$	50.2838	−	7.97091i	0.174597	−	0.0276768i
$289$	−52.8076			−0.182725
$290$			124.690i			0.429967i
$291$	−200.256	−	171.012i	−0.688166	−	0.587671i
$292$	−13.7657			−0.0471428
$293$			307.689i			1.05013i	0.851061	+	0.525066i	$0.175959\pi$
$293$			307.689i			1.05013i	−0.851061	+	0.525066i	$0.824041\pi$
$294$	137.507	−	161.021i	0.467711	−	0.547692i
$295$	−305.909			−1.03698
$296$			61.7662i			0.208670i
$297$	76.3621	+	46.7742i	0.257112	+	0.157489i
$298$	243.907			0.818478
$299$		−	238.528i		−	0.797752i
$300$	27.2503	+	23.2708i	0.0908342	+	0.0775695i
$301$	−440.138			−1.46225
$302$		−	9.55788i		−	0.0316486i
$303$	−343.913	+	402.724i	−1.13503	+	1.32912i
$304$	−119.329			−0.392531
$305$		−	133.874i		−	0.438931i
$306$	36.8416	+	232.412i	0.120397	+	0.759518i
$307$	−24.7602			−0.0806521			−0.0403260	−	0.999187i	$-0.512840\pi$
$307$	−24.7602			−0.0806521			−0.0403260	+	0.999187i	$0.512840\pi$
$308$			65.9696i			0.214187i
$309$	287.060	+	245.140i	0.928997	+	0.793333i
$310$	−177.905			−0.573887
$311$		−	227.492i		−	0.731486i	−0.930716	−	0.365743i	$-0.880815\pi$
$311$		−	227.492i		−	0.731486i	0.930716	−	0.365743i	$-0.119185\pi$
$312$	99.9906	−	117.089i	0.320483	−	0.375287i
$313$	−491.341			−1.56978			−0.784889	−	0.619636i	$-0.787280\pi$
$313$	−491.341			−1.56978			−0.784889	+	0.619636i	$0.787280\pi$
$314$			40.4629i			0.128863i
$315$	491.993	−	77.9898i	1.56188	−	0.247587i
$316$	127.416			0.403215
$317$		−	69.5592i		−	0.219430i	−0.993963	−	0.109715i	$-0.965006\pi$
$317$		−	69.5592i		−	0.219430i	0.993963	−	0.109715i	$-0.0349938\pi$
$318$	164.939	+	140.853i	0.518677	+	0.442934i
$319$	−52.5445			−0.164716
$320$			44.5223i			0.139132i
$321$	218.639	−	256.027i	0.681118	−	0.797592i
$322$	184.880			0.574162
$323$		−	551.541i		−	1.70756i
$324$	154.058	−	50.1010i	0.475488	−	0.154633i
$325$	108.376			0.333463
$326$			54.0651i			0.165844i
$327$	176.264	+	150.524i	0.539034	+	0.460317i
$328$	27.1899			0.0828962
$329$		−	526.456i		−	1.60017i
$330$	−50.8547	+	59.5511i	−0.154105	+	0.180458i
$331$	−480.359			−1.45124			−0.725618	−	0.688098i	$-0.758446\pi$
$331$	−480.359			−1.45124			−0.725618	+	0.688098i	$0.758446\pi$
$332$			114.846i			0.345922i
$333$	30.7708	+	194.115i	0.0924048	+	0.582928i
$334$	−10.4742			−0.0313598
$335$		−	596.493i		−	1.78058i
$336$	90.7546	+	77.5015i	0.270103	+	0.230659i
$337$	−168.133			−0.498911			−0.249456	−	0.968386i	$-0.580252\pi$
$337$	−168.133			−0.498911			−0.249456	+	0.968386i	$0.580252\pi$
$338$		−	226.668i		−	0.670616i
$339$	403.847	−	472.906i	1.19129	−	1.39500i
$340$	−205.782			−0.605243
$341$		−	74.9690i		−	0.219850i
$342$	−375.021	+	59.4477i	−1.09655	+	0.173824i
$343$	9.03876			0.0263521
$344$		−	125.175i		−	0.363880i
$345$	166.892	+	142.521i	0.483745	+	0.413103i
$346$	−242.540			−0.700984
$347$			253.016i			0.729152i	0.931174	+	0.364576i	$0.118786\pi$
$347$			253.016i			0.729152i	−0.931174	+	0.364576i	$0.881214\pi$
$348$	−61.7295	+	72.2856i	−0.177384	+	0.207717i
$349$	266.422			0.763385			0.381693	−	0.924289i	$-0.375341\pi$
$349$	266.422			0.763385			0.381693	+	0.924289i	$0.375341\pi$
$350$			84.0006i			0.240002i
$351$	255.913	−	417.795i	0.729096	−	1.19030i
$352$	−18.7617			−0.0533002
$353$			224.309i			0.635436i	0.948185	+	0.317718i	$0.102917\pi$
$353$			224.309i			0.635436i	−0.948185	+	0.317718i	$0.897083\pi$
$354$	−177.341	−	151.444i	−0.500964	−	0.427807i
$355$	−258.986			−0.729538
$356$		−	217.974i		−	0.612286i
$357$	−358.213	+	419.469i	−1.00340	+	1.17498i
$358$	388.475			1.08513
$359$			243.464i			0.678172i	0.940755	+	0.339086i	$0.110118\pi$
$359$			243.464i			0.678172i	−0.940755	+	0.339086i	$0.889882\pi$
$360$	22.1802	+	139.922i	0.0616116	+	0.388672i
$361$	528.968			1.46529
$362$			429.832i			1.18738i
$363$	−25.0948	−	21.4301i	−0.0691317	−	0.0590362i
$364$	360.935			0.991580
$365$		−	38.3050i		−	0.104945i
$366$	66.2760	−	77.6094i	0.181082	−	0.212048i
$367$	287.112			0.782322			0.391161	−	0.920322i	$-0.372074\pi$
$367$	287.112			0.782322			0.391161	+	0.920322i	$0.372074\pi$
$368$			52.5796i			0.142879i
$369$	85.4509	−	13.5455i	0.231574	−	0.0367088i
$370$	−171.873			−0.464522
$371$			508.435i			1.37045i
$372$	−103.135	−	88.0740i	−0.277245	−	0.236758i
$373$	509.085			1.36484			0.682419	−	0.730961i	$-0.260928\pi$
$373$	509.085			1.36484			0.682419	+	0.730961i	$0.260928\pi$
$374$		−	86.7166i		−	0.231863i
$375$	206.302	−	241.581i	0.550139	−	0.644215i
$376$	149.723			0.398201
$377$			287.483i			0.762555i
$378$	323.828	+	198.355i	0.856687	+	0.524748i
$379$	330.575			0.872229			0.436115	−	0.899891i	$-0.356354\pi$
$379$	330.575			0.872229			0.436115	+	0.899891i	$0.356354\pi$
$380$		−	332.051i		−	0.873818i
$381$	175.914	+	150.225i	0.461716	+	0.394291i
$382$	−314.601			−0.823562
$383$			9.41868i			0.0245918i	0.999924	+	0.0122959i	$0.00391401\pi$
$383$			9.41868i			0.0245918i	−0.999924	+	0.0122959i	$0.996086\pi$
$384$	−22.0413	+	25.8105i	−0.0573993	+	0.0672148i
$385$	−183.570			−0.476805
$386$		−	202.620i		−	0.524923i
$387$	−62.3597	−	393.391i	−0.161136	−	1.01652i
$388$	175.560			0.452474
$389$		−	118.462i		−	0.304531i	−0.988340	−	0.152265i	$-0.951343\pi$
$389$		−	118.462i		−	0.304531i	0.988340	−	0.152265i	$-0.0486568\pi$
$390$	325.818	+	278.238i	0.835431	+	0.713431i
$391$	−243.024			−0.621544
$392$			141.164i			0.360111i
$393$	132.103	−	154.693i	0.336139	−	0.393620i
$394$	9.34208			0.0237109
$395$			354.553i			0.897602i
$396$	−58.9630	+	9.34672i	−0.148897	+	0.0236028i
$397$	−503.584			−1.26847			−0.634237	−	0.773139i	$-0.718685\pi$
$397$	−503.584			−1.26847			−0.634237	+	0.773139i	$0.718685\pi$
$398$			14.3722i			0.0361112i
$399$	−676.855	−	578.013i	−1.69638	−	1.44865i
$400$	−23.8896			−0.0597241
$401$			261.527i			0.652187i	0.945338	+	0.326093i	$0.105732\pi$
$401$			261.527i			0.652187i	−0.945338	+	0.326093i	$0.894268\pi$
$402$	295.301	−	345.799i	0.734581	−	0.860197i
$403$	−410.173			−1.01780
$404$		−	353.058i		−	0.873907i
$405$	139.413	+	428.689i	0.344230	+	1.05849i
$406$	−222.825			−0.548829
$407$		−	72.4273i		−	0.177954i
$408$	−119.296	−	101.875i	−0.292393	−	0.249694i
$409$	−602.515			−1.47314			−0.736571	−	0.676360i	$-0.763556\pi$
$409$	−602.515			−1.47314			−0.736571	+	0.676360i	$0.763556\pi$
$410$			75.6599i			0.184536i
$411$	−23.7738	+	27.8392i	−0.0578438	+	0.0677353i
$412$	−251.659			−0.610822
$413$		−	546.666i		−	1.32365i
$414$	26.1942	+	165.244i	0.0632710	+	0.399140i
$415$	−319.576			−0.770062
$416$			102.649i			0.246754i
$417$	−228.327	−	194.984i	−0.547547	−	0.467587i
$418$	139.926			0.334751
$419$			388.828i			0.927991i	0.885837	+	0.463996i	$0.153585\pi$
$419$			388.828i			0.927991i	−0.885837	+	0.463996i	$0.846415\pi$
$420$	−215.659	+	252.538i	−0.513474	+	0.601280i
$421$	659.919			1.56750			0.783751	−	0.621075i	$-0.213304\pi$
$421$	659.919			1.56750			0.783751	+	0.621075i	$0.213304\pi$
$422$		−	277.541i		−	0.657681i
$423$	470.542	−	74.5895i	1.11239	−	0.176334i
$424$	−144.598			−0.341034
$425$		−	110.418i		−	0.259807i
$426$	−150.139	−	128.214i	−0.352440	−	0.300972i
$427$	239.236			0.560271
$428$			224.453i			0.524422i
$429$	−117.249	+	137.300i	−0.273309	+	0.320046i
$430$	348.316			0.810038
$431$		−	263.846i		−	0.612171i	−0.952004	−	0.306086i	$-0.900981\pi$
$431$		−	263.846i		−	0.612171i	0.952004	−	0.306086i	$-0.0990194\pi$
$432$	−56.4118	+	92.0962i	−0.130583	+	0.213186i
$433$	−118.654			−0.274028			−0.137014	−	0.990569i	$-0.543751\pi$
$433$	−118.654			−0.274028			−0.137014	+	0.990569i	$0.543751\pi$
$434$		−	317.920i		−	0.732535i
$435$	−201.145	−	171.771i	−0.462402	−	0.394876i
$436$	−154.526			−0.354418
$437$		−	392.143i		−	0.897353i
$438$	18.9634	−	22.2062i	0.0432954	−	0.0506991i
$439$	339.275			0.772837			0.386419	−	0.922324i	$-0.373712\pi$
$439$	339.275			0.772837			0.386419	+	0.922324i	$0.373712\pi$
$440$		−	52.2070i		−	0.118652i
$441$	70.3251	+	443.640i	0.159467	+	1.00599i
$442$	−474.447			−1.07341
$443$			399.434i			0.901658i	0.892610	+	0.450829i	$0.148872\pi$
$443$			399.434i			0.901658i	−0.892610	+	0.450829i	$0.851128\pi$
$444$	−99.6384	−	85.0880i	−0.224411	−	0.191640i
$445$	606.543			1.36302
$446$		−	486.855i		−	1.09160i
$447$	−336.001	+	393.459i	−0.751681	+	0.880221i
$448$	−79.5623			−0.177595
$449$			508.464i			1.13244i	0.824255	+	0.566218i	$0.191594\pi$
$449$			508.464i			1.13244i	−0.824255	+	0.566218i	$0.808406\pi$
$450$	−75.0789	+	11.9014i	−0.166842	+	0.0264475i
$451$	−31.8830			−0.0706941
$452$			414.586i			0.917225i
$453$	15.4183	+	13.1668i	0.0340361	+	0.0290657i
$454$	−531.963			−1.17173
$455$			1004.35i			2.20737i
$456$	164.386	−	192.497i	0.360496	−	0.422142i
$457$	−214.301			−0.468929			−0.234465	−	0.972125i	$-0.575334\pi$
$457$	−214.301			−0.468929			−0.234465	+	0.972125i	$0.575334\pi$
$458$		−	39.7720i		−	0.0868384i
$459$	−425.669	−	260.736i	−0.927385	−	0.568052i
$460$	−146.310			−0.318066
$461$			235.232i			0.510265i	0.966906	+	0.255133i	$0.0821192\pi$
$461$			235.232i			0.510265i	−0.966906	+	0.255133i	$0.917881\pi$
$462$	−106.419	−	90.8785i	−0.230345	−	0.196707i
$463$	−554.128			−1.19682			−0.598410	−	0.801190i	$-0.704201\pi$
$463$	−554.128			−1.19682			−0.598410	+	0.801190i	$0.704201\pi$
$464$		−	63.3710i		−	0.136575i
$465$	245.079	−	286.988i	0.527051	−	0.617179i
$466$	434.978			0.933428
$467$			598.471i			1.28152i	0.767740	+	0.640761i	$0.221381\pi$
$467$			598.471i			1.28152i	−0.767740	+	0.640761i	$0.778619\pi$
$468$	51.1381	+	322.601i	0.109269	+	0.689318i
$469$	1065.95			2.27281
$470$			416.627i			0.886440i
$471$	−65.2729	−	55.7409i	−0.138584	−	0.118346i
$472$	155.471			0.329387
$473$			146.780i			0.310318i
$474$	−175.526	+	205.541i	−0.370307	+	0.433632i
$475$	178.171			0.375097
$476$		−	367.738i		−	0.772559i
$477$	−454.435	+	72.0362i	−0.952694	+	0.151019i
$478$	276.866			0.579218
$479$		−	24.3883i		−	0.0509151i	−0.999676	−	0.0254575i	$-0.991896\pi$
$479$		−	24.3883i		−	0.0509151i	0.999676	−	0.0254575i	$-0.00810426\pi$
$480$	−71.8213	−	61.3331i	−0.149628	−	0.127777i
$481$	−396.267			−0.823839
$482$			134.171i			0.278364i
$483$	−254.687	+	298.240i	−0.527303	+	0.617474i
$484$	22.0000			0.0454545
$485$			488.520i			1.00726i
$486$	−131.407	+	317.538i	−0.270385	+	0.653370i
$487$	−335.376			−0.688658			−0.344329	−	0.938849i	$-0.611894\pi$
$487$	−335.376			−0.688658			−0.344329	+	0.938849i	$0.611894\pi$
$488$			68.0383i			0.139423i
$489$	−87.2154	−	74.4791i	−0.178355	−	0.152309i
$490$	−392.808			−0.801648
$491$		−	476.704i		−	0.970884i	−0.874269	−	0.485442i	$-0.838659\pi$
$491$		−	476.704i		−	0.970884i	0.874269	−	0.485442i	$-0.161341\pi$
$492$	−37.4564	+	43.8616i	−0.0761308	+	0.0891495i
$493$	292.901			0.594120
$494$		−	765.568i		−	1.54973i
$495$	−26.0086	−	164.073i	−0.0525426	−	0.331461i
$496$	90.4160			0.182290
$497$		−	462.814i		−	0.931215i
$498$	−185.265	−	158.210i	−0.372017	−	0.317691i
$499$	353.684			0.708785			0.354393	−	0.935097i	$-0.384688\pi$
$499$	353.684			0.708785			0.354393	+	0.935097i	$0.384688\pi$
$500$			211.788i			0.423576i
$501$	14.4290	−	16.8965i	0.0288005	−	0.0337255i
$502$	420.168			0.836989
$503$		−	250.745i		−	0.498500i	−0.968439	−	0.249250i	$-0.919816\pi$
$503$		−	250.745i		−	0.498500i	0.968439	−	0.249250i	$-0.0801840\pi$
$504$	−250.044	+	39.6365i	−0.496119	+	0.0786439i
$505$	982.436			1.94542
$506$		−	61.6551i		−	0.121848i
$507$	365.651	+	312.254i	0.721205	+	0.615886i
$508$	−154.219			−0.303581
$509$		−	677.779i		−	1.33159i	−0.746135	−	0.665795i	$-0.768093\pi$
$509$		−	677.779i		−	1.33159i	0.746135	−	0.665795i	$-0.231907\pi$
$510$	283.482	−	331.959i	0.555848	−	0.650900i
$511$	68.4520			0.133957
$512$		−	22.6274i		−	0.0441942i
$513$	420.724	−	686.861i	0.820125	−	1.33891i
$514$	531.659			1.03436
$515$		−	700.276i		−	1.35976i
$516$	201.926	+	172.438i	0.391330	+	0.334183i
$517$	−175.566			−0.339587
$518$		−	307.141i		−	0.592937i
$519$	334.119	−	391.255i	0.643775	−	0.753864i
$520$	−285.637			−0.549302
$521$			570.949i			1.09587i	0.836520	+	0.547936i	$0.184586\pi$
$521$			570.949i			1.09587i	−0.836520	+	0.547936i	$0.815414\pi$
$522$	−31.5703	−	199.159i	−0.0604794	−	0.381530i
$523$	512.547			0.980013			0.490006	−	0.871719i	$-0.336994\pi$
$523$	512.547			0.980013			0.490006	+	0.871719i	$0.336994\pi$
$524$			135.615i			0.258808i
$525$	−135.506	−	115.718i	−0.258106	−	0.220415i
$526$	−195.612			−0.371886
$527$			417.904i			0.792986i
$528$	25.8457	−	30.2655i	0.0489502	−	0.0573210i
$529$	356.211			0.673368
$530$		−	402.366i		−	0.759180i
$531$	488.605	−	77.4528i	0.920159	−	0.145862i
$532$	593.383			1.11538
$533$			174.440i			0.327279i
$534$	351.626	+	300.277i	0.658475	+	0.562316i
$535$	−624.572			−1.16742
$536$			303.154i			0.565586i
$537$	−535.157	+	626.671i	−0.996568	+	1.16698i
$538$	36.6033			0.0680359
$539$		−	165.529i		−	0.307104i
$540$	−256.271	−	156.974i	−0.474576	−	0.290692i
$541$	−706.578			−1.30606			−0.653030	−	0.757332i	$-0.726502\pi$
$541$	−706.578			−1.30606			−0.653030	+	0.757332i	$0.726502\pi$
$542$			353.555i			0.652315i
$543$	−693.386	−	592.129i	−1.27695	−	1.09048i
$544$	104.584			0.192250
$545$		−	429.992i		−	0.788976i
$546$	−497.218	+	582.244i	−0.910656	+	1.06638i
$547$	769.246			1.40630			0.703150	−	0.711042i	$-0.251776\pi$
$547$	769.246			1.40630			0.703150	+	0.711042i	$0.251776\pi$
$548$		−	24.4060i		−	0.0445364i
$549$	33.8954	+	213.827i	0.0617403	+	0.389484i
$550$	28.0131			0.0509329
$551$			472.626i			0.857761i
$552$	−84.8191	−	72.4327i	−0.153658	−	0.131219i
$553$	−633.594			−1.14574
$554$		−	362.557i		−	0.654435i
$555$	236.770	−	277.258i	0.426612	−	0.499564i
$556$	200.169			0.360016
$557$		−	913.366i		−	1.63980i	−0.572510	−	0.819898i	$-0.694030\pi$
$557$		−	913.366i		−	1.63980i	0.572510	−	0.819898i	$-0.305970\pi$
$558$	284.154	−	45.0436i	0.509237	−	0.0807233i
$559$	803.070			1.43662
$560$		−	221.394i		−	0.395346i
$561$	139.887	+	119.459i	0.249353	+	0.212940i
$562$	186.709			0.332223
$563$		−	734.690i		−	1.30496i	−0.757808	−	0.652478i	$-0.773730\pi$
$563$		−	734.690i		−	1.30496i	0.757808	−	0.652478i	$-0.226270\pi$
$564$	−206.256	+	241.527i	−0.365703	+	0.428239i
$565$	−1153.64			−2.04185
$566$			399.816i			0.706389i
$567$	−766.076	+	249.134i	−1.35110	+	0.439391i
$568$	131.624			0.231732
$569$			325.569i			0.572177i	0.958203	+	0.286089i	$0.0923552\pi$
$569$			325.569i			0.572177i	−0.958203	+	0.286089i	$0.907645\pi$
$570$	535.650	+	457.427i	0.939736	+	0.802504i
$571$	110.422			0.193383			0.0966915	−	0.995314i	$-0.469174\pi$
$571$	110.422			0.193383			0.0966915	+	0.995314i	$0.469174\pi$
$572$		−	120.367i		−	0.210432i
$573$	433.388	−	507.499i	0.756349	−	0.885688i
$574$	−135.206			−0.235550
$575$		−	78.5068i		−	0.136534i
$576$	−11.2726	−	71.1121i	−0.0195704	−	0.123458i
$577$	−860.135			−1.49070			−0.745351	−	0.666672i	$-0.767718\pi$
$577$	−860.135			−1.49070			−0.745351	+	0.666672i	$0.767718\pi$
$578$			74.6813i			0.129206i
$579$	326.858	+	279.126i	0.564521	+	0.482083i
$580$	176.339			0.304033
$581$		−	571.089i		−	0.982942i
$582$	−241.848	+	283.205i	−0.415546	+	0.486607i
$583$	169.557			0.290835
$584$			19.4676i			0.0333350i
$585$	−897.682	+	142.299i	−1.53450	+	0.243246i
$586$	435.138			0.742556
$587$			167.636i			0.285581i	0.989753	+	0.142791i	$0.0456076\pi$
$587$			167.636i			0.285581i	−0.989753	+	0.142791i	$0.954392\pi$
$588$	−227.719	−	194.464i	−0.387277	−	0.330722i
$589$	−674.330			−1.14487
$590$			432.620i			0.733254i
$591$	−12.8695	+	15.0702i	−0.0217758	+	0.0254995i
$592$	87.3506			0.147552
$593$		−	560.335i		−	0.944915i	−0.881353	−	0.472458i	$-0.843367\pi$
$593$		−	560.335i		−	0.944915i	0.881353	−	0.472458i	$-0.156633\pi$
$594$	66.1487	−	107.992i	0.111361	−	0.181805i
$595$	1023.28			1.71980
$596$		−	344.936i		−	0.578752i
$597$	−23.1846	−	19.7989i	−0.0388353	−	0.0331641i
$598$	−337.329			−0.564096
$599$			202.084i			0.337368i	0.985670	+	0.168684i	$0.0539518\pi$
$599$			202.084i			0.337368i	−0.985670	+	0.168684i	$0.946048\pi$
$600$	32.9099	−	38.5377i	0.0548499	−	0.0642295i
$601$	−302.803			−0.503831			−0.251916	−	0.967749i	$-0.581061\pi$
$601$	−302.803			−0.503831			−0.251916	+	0.967749i	$0.581061\pi$
$602$			622.449i			1.03397i
$603$	151.026	+	952.734i	0.250457	+	1.57999i
$604$	−13.5169			−0.0223790
$605$			61.2181i			0.101187i
$606$	569.538	+	486.367i	0.939831	+	0.802586i
$607$	639.850			1.05412			0.527059	−	0.849829i	$-0.323295\pi$
$607$	639.850			1.05412			0.527059	+	0.849829i	$0.323295\pi$
$608$			168.757i			0.277561i
$609$	306.959	−	359.450i	0.504038	−	0.590231i
$610$	−189.326			−0.310371
$611$			960.564i			1.57212i
$612$	328.681	−	52.1019i	0.537060	−	0.0851338i
$613$	618.980			1.00975			0.504877	−	0.863191i	$-0.331538\pi$
$613$	618.980			1.00975			0.504877	+	0.863191i	$0.331538\pi$
$614$			35.0162i			0.0570296i
$615$	−122.051	−	104.228i	−0.198457	−	0.169476i
$616$	93.2951			0.151453
$617$		−	426.575i		−	0.691370i	−0.938351	−	0.345685i	$-0.887647\pi$
$617$		−	426.575i		−	0.691370i	0.938351	−	0.345685i	$-0.112353\pi$
$618$	346.680	−	405.964i	0.560971	−	0.656900i
$619$	−799.993			−1.29240			−0.646198	−	0.763170i	$-0.723642\pi$
$619$	−799.993			−1.29240			−0.646198	+	0.763170i	$0.723642\pi$
$620$			251.595i			0.405799i
$621$	−302.649	−	185.382i	−0.487357	−	0.298522i
$622$	−321.723			−0.517239
$623$			1083.91i			1.73982i
$624$	−165.589	−	141.408i	−0.265368	−	0.226616i
$625$	−738.641			−1.18182
$626$			694.860i			1.11000i
$627$	−192.760	+	225.722i	−0.307432	+	0.360004i
$628$	57.2232			0.0911197
$629$			403.735i			0.641869i
$630$	−110.294	−	695.783i	−0.175070	−	1.10442i
$631$	108.289			0.171614			0.0858072	−	0.996312i	$-0.472653\pi$
$631$	108.289			0.171614			0.0858072	+	0.996312i	$0.472653\pi$
$632$		−	180.193i		−	0.285116i
$633$	447.717	+	382.336i	0.707294	+	0.604006i
$634$	−98.3716			−0.155160
$635$		−	429.137i		−	0.675807i
$636$	199.196	−	233.259i	0.313201	−	0.366760i
$637$	−905.648			−1.42174
$638$			74.3091i			0.116472i
$639$	413.659	−	65.5725i	0.647353	−	0.102617i
$640$	62.9640			0.0983813
$641$		−	593.109i		−	0.925286i	−0.886545	−	0.462643i	$-0.846901\pi$
$641$		−	593.109i		−	0.925286i	0.886545	−	0.462643i	$-0.153099\pi$
$642$	−362.077	−	309.202i	−0.563983	−	0.481623i
$643$	−55.2692			−0.0859551			−0.0429776	−	0.999076i	$-0.513684\pi$
$643$	−55.2692			−0.0859551			−0.0429776	+	0.999076i	$0.513684\pi$
$644$		−	261.460i		−	0.405994i
$645$	−479.834	+	561.888i	−0.743929	+	0.871144i
$646$	−779.997			−1.20743
$647$		−	1178.46i		−	1.82142i	−0.413046	−	0.910710i	$-0.635535\pi$
$647$		−	1178.46i		−	1.82142i	0.413046	−	0.910710i	$-0.364465\pi$
$648$	−70.8535	−	217.871i	−0.109342	−	0.336221i
$649$	−182.306			−0.280903
$650$		−	153.266i		−	0.235794i
$651$	512.854	+	437.961i	0.787794	+	0.672751i
$652$	76.4596			0.117269
$653$			14.0119i			0.0214577i	0.999942	+	0.0107289i	$0.00341517\pi$
$653$			14.0119i			0.0214577i	−0.999942	+	0.0107289i	$0.996585\pi$
$654$	212.873	−	249.275i	0.325494	−	0.381154i
$655$	−377.369			−0.576136
$656$		−	38.4524i		−	0.0586164i
$657$	9.69843	+	61.1818i	0.0147617	+	0.0931229i
$658$	−744.521			−1.13149
$659$			1184.59i			1.79755i	0.438408	+	0.898776i	$0.355542\pi$
$659$			1184.59i			1.79755i	−0.438408	+	0.898776i	$0.644458\pi$
$660$	84.2180	+	71.9194i	0.127603	+	0.108969i
$661$	−259.706			−0.392898			−0.196449	−	0.980514i	$-0.562941\pi$
$661$	−259.706			−0.392898			−0.196449	+	0.980514i	$0.562941\pi$
$662$			679.330i			1.02618i
$663$	653.590	−	765.356i	0.985806	−	1.15438i
$664$	162.417			0.244604
$665$			1651.17i			2.48297i
$666$	274.520	−	43.5165i	0.412193	−	0.0653400i
$667$	208.251			0.312221
$668$			14.8127i			0.0221747i
$669$	785.372	+	670.683i	1.17395	+	1.00252i
$670$	−843.569			−1.25906
$671$		−	79.7820i		−	0.118900i
$672$	109.604	−	128.346i	0.163101	−	0.190992i
$673$	982.316			1.45961			0.729804	−	0.683657i	$-0.239611\pi$
$673$	982.316			1.45961			0.729804	+	0.683657i	$0.239611\pi$
$674$			237.776i			0.352784i
$675$	84.2286	−	137.509i	0.124783	−	0.203717i
$676$	−320.557			−0.474197
$677$		−	1348.52i		−	1.99190i	−0.0899183	−	0.995949i	$-0.528661\pi$
$677$		−	1348.52i		−	1.99190i	0.0899183	−	0.995949i	$-0.471339\pi$
$678$	−668.791	−	571.126i	−0.986417	−	0.842368i
$679$	−872.997			−1.28571
$680$			291.020i			0.427971i
$681$	732.823	−	858.139i	1.07610	−	1.26012i
$682$	−106.022			−0.155458
$683$		−	122.188i		−	0.178899i	−0.995991	−	0.0894495i	$-0.971489\pi$
$683$		−	122.188i		−	0.178899i	0.995991	−	0.0894495i	$-0.0285108\pi$
$684$	84.0717	+	530.360i	0.122912	+	0.775380i
$685$	67.9131			0.0991432
$686$		−	12.7827i		−	0.0186337i
$687$	64.1583	+	54.7892i	0.0933891	+	0.0797513i
$688$	−177.024			−0.257302
$689$		−	927.684i		−	1.34642i
$690$	201.554	−	236.021i	0.292108	−	0.342060i
$691$	−351.379			−0.508508			−0.254254	−	0.967138i	$-0.581830\pi$
$691$	−351.379			−0.508508			−0.254254	+	0.967138i	$0.581830\pi$
$692$			343.004i			0.495670i
$693$	293.202	−	46.4779i	0.423091	−	0.0670677i
$694$	357.818			0.515588
$695$			556.998i			0.801436i
$696$	102.227	+	87.2987i	0.146878	+	0.125429i
$697$	177.727			0.254989
$698$		−	376.777i		−	0.539795i
$699$	−599.217	+	701.686i	−0.857249	+	1.00384i
$700$	118.795			0.169707
$701$			285.995i			0.407982i	0.978973	+	0.203991i	$0.0653913\pi$
$701$			285.995i			0.407982i	−0.978973	+	0.203991i	$0.934609\pi$
$702$	−590.852	−	361.915i	−0.841669	−	0.515549i
$703$	−651.468			−0.926697
$704$			26.5330i			0.0376889i
$705$	−672.083	−	573.938i	−0.953310	−	0.814096i
$706$	317.221			0.449321
$707$			1755.63i			2.48322i
$708$	−214.174	+	250.799i	−0.302506	+	0.354235i
$709$	447.807			0.631603			0.315801	−	0.948825i	$-0.397727\pi$
$709$	447.807			0.631603			0.315801	+	0.948825i	$0.397727\pi$
$710$			366.261i			0.515861i
$711$	−89.7689	−	566.300i	−0.126257	−	0.796484i
$712$	−308.262			−0.432952
$713$			297.128i			0.416729i
$714$	593.218	+	506.589i	0.830838	+	0.709509i
$715$	334.939			0.468446
$716$		−	549.387i		−	0.767301i
$717$	−381.406	+	446.628i	−0.531947	+	0.622912i
$718$	344.310			0.479540
$719$		−	845.198i		−	1.17552i	−0.809036	−	0.587760i	$-0.800010\pi$
$719$		−	845.198i		−	1.17552i	0.809036	−	0.587760i	$-0.199990\pi$
$720$	197.880	−	31.3675i	0.274833	−	0.0435660i
$721$	1251.41			1.73566
$722$		−	748.074i		−	1.03611i
$723$	−216.439	−	184.832i	−0.299362	−	0.255646i
$724$	607.875			0.839606
$725$			94.6194i			0.130510i
$726$	−30.3068	+	35.4894i	−0.0417449	+	0.0488835i
$727$	−354.124			−0.487103			−0.243551	−	0.969888i	$-0.578312\pi$
$727$	−354.124			−0.487103			−0.243551	+	0.969888i	$0.578312\pi$
$728$		−	510.440i		−	0.701153i
$729$	−331.213	−	649.414i	−0.454339	−	0.890829i
$730$	−54.1715			−0.0742076
$731$		−	818.205i		−	1.11930i
$732$	−109.756	−	93.7284i	−0.149940	−	0.128044i
$733$	646.262			0.881667			0.440834	−	0.897589i	$-0.354683\pi$
$733$	646.262			0.881667			0.440834	+	0.897589i	$0.354683\pi$
$734$		−	406.038i		−	0.553185i
$735$	541.125	−	633.660i	0.736224	−	0.862122i
$736$	74.3588			0.101031
$737$		−	355.479i		−	0.482333i
$738$	−19.1563	−	120.846i	−0.0259570	−	0.163748i
$739$	−102.126			−0.138195			−0.0690975	−	0.997610i	$-0.522012\pi$
$739$	−102.126			−0.138195			−0.0690975	+	0.997610i	$0.522012\pi$
$740$			243.066i			0.328467i
$741$	1234.98	+	1054.63i	1.66664	+	1.42326i
$742$	719.036			0.969052
$743$		−	874.107i		−	1.17646i	−0.808695	−	0.588228i	$-0.799826\pi$
$743$		−	874.107i		−	1.17646i	0.808695	−	0.588228i	$-0.200174\pi$
$744$	−124.555	+	145.855i	−0.167413	+	0.196042i
$745$	959.834			1.28837
$746$		−	719.954i		−	0.965086i
$747$	510.434	−	80.9131i	0.683312	−	0.108317i
$748$	−122.636			−0.163952
$749$		−	1116.12i		−	1.49015i
$750$	−341.647	−	291.755i	−0.455529	−	0.389007i
$751$	−40.8837			−0.0544390			−0.0272195	−	0.999629i	$-0.508665\pi$
$751$	−40.8837			−0.0544390			−0.0272195	+	0.999629i	$0.508665\pi$
$752$		−	211.741i		−	0.281570i
$753$	−578.816	+	677.796i	−0.768680	+	0.900128i
$754$	406.563			0.539208
$755$		−	37.6127i		−	0.0498181i
$756$	280.516	−	457.962i	0.371053	−	0.605770i
$757$	−956.794			−1.26393			−0.631965	−	0.774997i	$-0.717751\pi$
$757$	−956.794			−1.26393			−0.631965	+	0.774997i	$0.717751\pi$
$758$		−	467.504i		−	0.616759i
$759$	99.4592	+	84.9349i	0.131040	+	0.111904i
$760$	−469.591			−0.617883
$761$		−	362.644i		−	0.476536i	−0.971199	−	0.238268i	$-0.923420\pi$
$761$		−	362.644i		−	0.476536i	0.971199	−	0.238268i	$-0.0765797\pi$
$762$	212.450	−	248.780i	0.278806	−	0.326483i
$763$	768.405			1.00708
$764$			444.912i			0.582346i
$765$	144.981	+	914.601i	0.189518	+	1.19556i
$766$	13.3200			0.0173891
$767$			997.438i			1.30044i
$768$	36.5015	+	31.1711i	0.0475280	+	0.0405874i
$769$	−495.032			−0.643735			−0.321867	−	0.946785i	$-0.604311\pi$
$769$	−495.032			−0.643735			−0.321867	+	0.946785i	$0.604311\pi$
$770$			259.607i			0.337152i
$771$	−732.404	+	857.649i	−0.949941	+	1.11239i
$772$	−286.548			−0.371177
$773$			992.365i			1.28378i	0.766795	+	0.641892i	$0.221850\pi$
$773$			992.365i			1.28378i	−0.766795	+	0.641892i	$0.778150\pi$
$774$	−556.339	+	88.1900i	−0.718785	+	0.113941i
$775$	−135.000			−0.174194
$776$		−	248.279i		−	0.319947i
$777$	495.467	+	423.113i	0.637666	+	0.544546i
$778$	−167.531			−0.215336
$779$			286.781i			0.368140i
$780$	393.488	−	460.776i	0.504472	−	0.590739i
$781$	−154.342			−0.197621
$782$			343.687i			0.439498i
$783$	364.764	+	223.430i	0.465855	+	0.285351i
$784$	199.635			0.254637
$785$			159.232i			0.202843i
$786$	−218.769	−	186.821i	−0.278332	−	0.237686i
$787$	−783.433			−0.995468			−0.497734	−	0.867330i	$-0.665834\pi$
$787$	−783.433			−0.995468			−0.497734	+	0.867330i	$0.665834\pi$
$788$		−	13.2117i		−	0.0167661i
$789$	269.472	−	315.553i	0.341536	−	0.399940i
$790$	501.413			0.634700
$791$		−	2061.59i		−	2.60630i
$792$	13.2183	+	83.3863i	0.0166897	+	0.105286i
$793$	−436.506			−0.550449
$794$			712.175i			0.896946i
$795$	649.078	+	554.292i	0.816450	+	0.697222i
$796$	20.3254			0.0255344
$797$		−	1017.08i		−	1.27613i	−0.769983	−	0.638065i	$-0.779735\pi$
$797$		−	1017.08i		−	1.27613i	0.769983	−	0.638065i	$-0.220265\pi$
$798$	−817.433	+	957.218i	−1.02435	+	1.19952i
$799$	978.668			1.22487
$800$			33.7851i			0.0422313i
$801$	−968.786	+	153.570i	−1.20947	+	0.191723i
$802$	369.855			0.461166
$803$		−	22.8278i		−	0.0284282i
$804$	−489.034	−	417.619i	−0.608251	−	0.519427i
$805$	727.550			0.903788
$806$			580.072i			0.719693i
$807$	−50.4241	+	59.0468i	−0.0624834	+	0.0731683i
$808$	−499.300			−0.617946
$809$			631.715i			0.780859i	0.920633	+	0.390429i	$0.127673\pi$
$809$			631.715i			0.780859i	−0.920633	+	0.390429i	$0.872327\pi$
$810$	606.257	−	197.160i	0.748466	−	0.243407i
$811$	−187.481			−0.231173			−0.115586	−	0.993297i	$-0.536875\pi$
$811$	−187.481			−0.231173			−0.115586	+	0.993297i	$0.536875\pi$
$812$			315.122i			0.388081i
$813$	−570.338	−	487.050i	−0.701523	−	0.599078i
$814$	−102.428			−0.125832
$815$			212.760i			0.261055i
$816$	−144.073	+	168.710i	−0.176560	+	0.206753i
$817$	1320.26			1.61598
$818$			852.085i			1.04167i
$819$	−254.292	−	1604.18i	−0.310490	−	1.95870i
$820$	106.999			0.130487
$821$			552.000i			0.672351i	0.941799	+	0.336176i	$0.109134\pi$
$821$			552.000i			0.672351i	−0.941799	+	0.336176i	$0.890866\pi$
$822$	39.3706	+	33.6212i	0.0478961	+	0.0409017i
$823$	−625.501			−0.760026			−0.380013	−	0.924981i	$-0.624080\pi$
$823$	−625.501			−0.760026			−0.380013	+	0.924981i	$0.624080\pi$
$824$			355.899i			0.431916i
$825$	−38.5903	+	45.1894i	−0.0467762	+	0.0547751i
$826$	−773.102			−0.935959
$827$			785.480i			0.949795i	0.880041	+	0.474897i	$0.157515\pi$
$827$			785.480i			0.949795i	−0.880041	+	0.474897i	$0.842485\pi$
$828$	233.690	−	37.0442i	0.282235	−	0.0447394i
$829$	−766.063			−0.924081			−0.462040	−	0.886859i	$-0.652882\pi$
$829$	−766.063			−0.924081			−0.462040	+	0.886859i	$0.652882\pi$
$830$			451.948i			0.544516i
$831$	584.860	+	499.452i	0.703803	+	0.601025i
$832$	145.168			0.174481
$833$			922.717i			1.10770i
$834$	−275.749	+	322.903i	−0.330634	+	0.387174i
$835$	−41.2185			−0.0493635
$836$		−	197.885i		−	0.236705i
$837$	−318.783	+	520.436i	−0.380864	+	0.621787i
$838$	549.886			0.656189
$839$			46.5567i			0.0554907i	0.999615	+	0.0277454i	$0.00883276\pi$
$839$			46.5567i			0.0554907i	−0.999615	+	0.0277454i	$0.991167\pi$
$840$	357.142	+	304.988i	0.425169	+	0.363081i
$841$	590.007			0.701554
$842$		−	933.266i		−	1.10839i
$843$	−257.207	+	301.191i	−0.305109	+	0.357284i
$844$	−392.503			−0.465051
$845$		−	891.997i		−	1.05562i
$846$	−105.485	−	665.446i	−0.124687	−	0.786580i
$847$	−109.398			−0.129160
$848$			204.493i			0.241147i
$849$	−644.965	−	550.779i	−0.759676	−	0.648739i
$850$	−156.155			−0.183712
$851$			287.054i			0.337314i
$852$	−181.322	+	212.329i	−0.212820	+	0.249213i
$853$	761.049			0.892203			0.446102	−	0.894982i	$-0.352812\pi$
$853$	761.049			0.892203			0.446102	+	0.894982i	$0.352812\pi$
$854$		−	338.330i		−	0.396172i
$855$	−1475.80	+	233.942i	−1.72608	+	0.273616i
$856$	317.424			0.370823
$857$			571.655i			0.667042i	0.942743	+	0.333521i	$0.108237\pi$
$857$			571.655i			0.667042i	−0.942743	+	0.333521i	$0.891763\pi$
$858$	194.171	+	165.816i	0.226306	+	0.193258i
$859$	−390.487			−0.454584			−0.227292	−	0.973827i	$-0.572987\pi$
$859$	−390.487			−0.454584			−0.227292	+	0.973827i	$0.572987\pi$
$860$		−	492.594i		−	0.572783i
$861$	186.257	−	218.108i	0.216327	−	0.253320i
$862$	−373.134			−0.432871
$863$		−	1182.37i		−	1.37007i	−0.728512	−	0.685033i	$-0.759788\pi$
$863$		−	1182.37i		−	1.37007i	0.728512	−	0.685033i	$-0.240212\pi$
$864$	130.244	+	79.7783i	0.150745	+	0.0923361i
$865$	−954.458			−1.10342
$866$			167.802i			0.193767i
$867$	−120.472	−	102.880i	−0.138953	−	0.118662i
$868$	−449.607			−0.517980
$869$			211.295i			0.243148i
$870$	−242.921	+	284.462i	−0.279220	+	0.326968i
$871$	−1944.91			−2.23296
$872$			218.533i			0.250612i
$873$	−123.688	−	780.276i	−0.141682	−	0.893787i
$874$	−554.574			−0.634524
$875$		−	1053.15i		−	1.20360i
$876$	−31.4043	−	26.8183i	−0.0358497	−	0.0306145i
$877$	94.2282			0.107444			0.0537219	−	0.998556i	$-0.482892\pi$
$877$	94.2282			0.107444			0.0537219	+	0.998556i	$0.482892\pi$
$878$		−	479.808i		−	0.546478i
$879$	−599.438	+	701.944i	−0.681954	+	0.798572i
$880$	−73.8319			−0.0838998
$881$		−	783.438i		−	0.889260i	−0.895714	−	0.444630i	$-0.853335\pi$
$881$		−	783.438i		−	0.889260i	0.895714	−	0.444630i	$-0.146665\pi$
$882$	627.402	−	99.4547i	0.711340	−	0.112760i
$883$	220.393			0.249596			0.124798	−	0.992182i	$-0.460172\pi$
$883$	220.393			0.249596			0.124798	+	0.992182i	$0.460172\pi$
$884$			670.969i			0.759015i
$885$	−697.883	−	595.970i	−0.788568	−	0.673412i
$886$	564.886			0.637568
$887$		−	122.340i		−	0.137925i	−0.997619	−	0.0689626i	$-0.978031\pi$
$887$		−	122.340i		−	0.137925i	0.997619	−	0.0689626i	$-0.0219689\pi$
$888$	−120.333	+	140.910i	−0.135510	+	0.158682i
$889$	766.878			0.862630
$890$		−	857.782i		−	0.963800i
$891$	83.0831	+	255.476i	0.0932470	+	0.286730i
$892$	−688.517			−0.771880
$893$			1579.18i			1.76840i
$894$	556.435	+	475.178i	0.622410	+	0.531519i
$895$	1528.75			1.70810
$896$			112.518i			0.125578i
$897$	464.699	−	544.165i	0.518059	−	0.606649i
$898$	719.077			0.800754
$899$		−	358.110i		−	0.398342i
$900$	16.8311	+	106.178i	0.0187012	+	0.117975i
$901$	−945.168			−1.04902
$902$			45.0894i			0.0499883i
$903$	−1004.11	−	857.475i	−1.11197	−	0.949585i
$904$	586.312			0.648576
$905$			1691.50i			1.86906i
$906$	18.6206	−	21.8048i	0.0205526	−	0.0240671i
$907$	1341.47			1.47902			0.739508	−	0.673148i	$-0.235058\pi$
$907$	1341.47			1.47902			0.739508	+	0.673148i	$0.235058\pi$
$908$			752.310i			0.828535i
$909$	−1569.17	+	248.742i	−1.72626	+	0.273644i
$910$	1420.37			1.56085
$911$		−	838.576i		−	0.920500i	−0.887789	−	0.460250i	$-0.847760\pi$
$911$		−	838.576i		−	0.920500i	0.887789	−	0.460250i	$-0.152240\pi$
$912$	−272.231	−	232.477i	−0.298499	−	0.254909i
$913$	−190.451			−0.208599
$914$			303.067i			0.331583i
$915$	260.813	−	305.413i	0.285041	−	0.333784i
$916$	−56.2461			−0.0614040
$917$		−	674.368i		−	0.735406i
$918$	−368.736	+	601.988i	−0.401674	+	0.655760i
$919$	1542.64			1.67861			0.839304	−	0.543662i	$-0.182963\pi$
$919$	1542.64			1.67861			0.839304	+	0.543662i	$0.182963\pi$
$920$			206.914i			0.224907i
$921$	−56.4865	−	48.2377i	−0.0613318	−	0.0523753i
$922$	332.669			0.360812
$923$			844.443i			0.914890i
$924$	−128.522	+	150.499i	−0.139093	+	0.162878i
$925$	−130.423			−0.140998
$926$			783.655i			0.846280i
$927$	177.302	+	1118.50i	0.191265	+	1.20658i
$928$	−89.6201			−0.0965734
$929$			316.465i			0.340651i	0.985388	+	0.170326i	$0.0544819\pi$
$929$			316.465i			0.340651i	−0.985388	+	0.170326i	$0.945518\pi$
$930$	−405.862	−	346.593i	−0.436411	−	0.372681i
$931$	−1488.90			−1.59925
$932$		−	615.151i		−	0.660034i
$933$	443.199	−	518.988i	0.475026	−	0.556258i
$934$	846.365			0.906173
$935$		−	341.252i		−	0.364975i
$936$	456.226	−	72.3202i	0.487421	−	0.0772652i
$937$	1744.49			1.86178			0.930891	−	0.365298i	$-0.119033\pi$
$937$	1744.49			1.86178			0.930891	+	0.365298i	$0.119033\pi$
$938$		−	1507.48i		−	1.60712i
$939$	−1120.92	−	957.227i	−1.19374	−	1.01941i
$940$	589.199			0.626808
$941$			867.051i			0.921415i	0.887552	+	0.460707i	$0.152404\pi$
$941$			867.051i			0.921415i	−0.887552	+	0.460707i	$0.847596\pi$
$942$	−78.8296	+	92.3098i	−0.0836832	+	0.0979934i
$943$	126.363			0.134001
$944$		−	219.869i		−	0.232912i
$945$	1274.34	+	780.576i	1.34851	+	0.826006i
$946$	207.579			0.219428
$947$		−	957.148i		−	1.01072i	−0.862910	−	0.505358i	$-0.831360\pi$
$947$		−	957.148i		−	1.01072i	0.862910	−	0.505358i	$-0.168640\pi$
$948$	290.679	+	248.231i	0.306624	+	0.261847i
$949$	−124.896			−0.131609
$950$		−	251.972i		−	0.265233i
$951$	135.515	−	158.689i	0.142497	−	0.166865i
$952$	−520.060			−0.546281
$953$			1044.56i			1.09607i	0.836455	+	0.548036i	$0.184624\pi$
$953$			1044.56i			1.09607i	−0.836455	+	0.548036i	$0.815376\pi$
$954$	101.875	+	642.668i	0.106787	+	0.673656i
$955$	−1238.03			−1.29637
$956$		−	391.548i		−	0.409569i
$957$	−119.872	−	102.367i	−0.125258	−	0.106966i
$958$	−34.4903			−0.0360024
$959$			121.362i			0.126551i
$960$	−86.7381	+	101.571i	−0.0903522	+	0.105803i
$961$	−450.059			−0.468324
$962$			560.406i			0.582542i
$963$	997.582	−	158.135i	1.03591	−	0.164211i
$964$	189.747			0.196833
$965$		−	797.362i		−	0.826282i
$966$	421.775	+	360.182i	0.436620	+	0.372860i
$967$	62.2081			0.0643310			0.0321655	−	0.999483i	$-0.489760\pi$
$967$	62.2081			0.0643310			0.0321655	+	0.999483i	$0.489760\pi$
$968$		−	31.1127i		−	0.0321412i
$969$	1074.51	−	1258.26i	1.10889	−	1.29851i
$970$	690.872			0.712239
$971$		−	774.251i		−	0.797375i	−0.917087	−	0.398688i	$-0.869466\pi$
$971$		−	774.251i		−	0.797375i	0.917087	−	0.398688i	$-0.130534\pi$
$972$	449.066	+	185.838i	0.462002	+	0.191191i
$973$	−995.368			−1.02299
$974$			474.294i			0.486955i
$975$	247.242	+	211.137i	0.253582	+	0.216551i
$976$	96.2207			0.0985868
$977$			735.185i			0.752492i	0.926520	+	0.376246i	$0.122785\pi$
$977$			735.185i			0.752492i	−0.926520	+	0.376246i	$0.877215\pi$
$978$	−105.329	+	123.341i	−0.107699	+	0.126116i
$979$	361.469			0.369222
$980$			555.514i			0.566851i
$981$	108.869	+	686.793i	0.110978	+	0.700095i
$982$	−674.161			−0.686519
$983$			1151.37i			1.17128i	0.810572	+	0.585638i	$0.199156\pi$
$983$			1151.37i			1.17128i	−0.810572	+	0.585638i	$0.800844\pi$
$984$	62.0296	+	52.9713i	0.0630382	+	0.0538326i
$985$	36.7634			0.0373233
$986$		−	414.225i		−	0.420107i
$987$	1025.64	−	1201.03i	1.03915	−	1.21685i
$988$	−1082.68			−1.09583
$989$		−	581.740i		−	0.588210i
$990$	−232.034	+	36.7817i	−0.234378	+	0.0371532i
$991$	775.178			0.782218			0.391109	−	0.920344i	$-0.372091\pi$
$991$	775.178			0.782218			0.391109	+	0.920344i	$0.372091\pi$
$992$		−	127.868i		−	0.128899i
$993$	−1095.86	−	935.833i	−1.10359	−	0.942430i
$994$	−654.517			−0.658468
$995$			56.5584i			0.0568426i
$996$	−223.743	+	262.004i	−0.224641	+	0.263056i
$997$	−13.1448			−0.0131844			−0.00659219	−	0.999978i	$-0.502098\pi$
$997$	−13.1448			−0.0131844			−0.00659219	+	0.999978i	$0.502098\pi$
$998$		−	500.184i		−	0.501187i
$999$	−307.975	+	502.791i	−0.308284	+	0.503294i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.3.c.a.23.4	✓	8
3.2	odd	2	inner	66.3.c.a.23.8	yes	8
4.3	odd	2		528.3.i.e.353.1		8
11.10	odd	2		726.3.c.e.485.8		8
12.11	even	2		528.3.i.e.353.2		8
33.32	even	2		726.3.c.e.485.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.3.c.a.23.4	✓	8	1.1	even	1	trivial
66.3.c.a.23.8	yes	8	3.2	odd	2	inner
528.3.i.e.353.1		8	4.3	odd	2
528.3.i.e.353.2		8	12.11	even	2
726.3.c.e.485.4		8	33.32	even	2
726.3.c.e.485.8		8	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	66.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(2.28135 + 1.94820i) q^{3} -2.00000 q^{4} -5.56529i q^{5} +(2.75516 - 3.22631i) q^{6} +9.94529 q^{7} +2.82843i q^{8} +(1.40907 + 8.88901i) q^{9} -7.87050 q^{10} -3.31662i q^{11} +(-4.56269 - 3.89639i) q^{12} -18.1460 q^{13} -14.0648i q^{14} +(10.8423 - 12.6963i) q^{15} +4.00000 q^{16} +18.4880i q^{17} +(12.5710 - 1.99273i) q^{18} -29.8323 q^{19} +11.1306i q^{20} +(22.6886 + 19.3754i) q^{21} -4.69042 q^{22} +13.1449i q^{23} +(-5.51033 + 6.45262i) q^{24} -5.97241 q^{25} +25.6624i q^{26} +(-14.1030 + 23.0240i) q^{27} -19.8906 q^{28} -15.8427i q^{29} +(-17.9553 - 15.3333i) q^{30} +22.6040 q^{31} -5.65685i q^{32} +(6.46143 - 7.56637i) q^{33} +26.1460 q^{34} -55.3484i q^{35} +(-2.81814 - 17.7780i) q^{36} +21.8376 q^{37} +42.1893i q^{38} +(-41.3974 - 35.3520i) q^{39} +15.7410 q^{40} -9.61310i q^{41} +(27.4009 - 32.0866i) q^{42} -44.2559 q^{43} +6.63325i q^{44} +(49.4699 - 7.84188i) q^{45} +18.5897 q^{46} -52.9352i q^{47} +(9.12538 + 7.79278i) q^{48} +49.9088 q^{49} +8.44626i q^{50} +(-36.0183 + 42.1776i) q^{51} +36.2921 q^{52} +51.1232i q^{53} +(32.5609 + 19.9446i) q^{54} -18.4580 q^{55} +28.1295i q^{56} +(-68.0579 - 58.1192i) q^{57} -22.4050 q^{58} -54.9673i q^{59} +(-21.6845 + 25.3927i) q^{60} +24.0552 q^{61} -31.9669i q^{62} +(14.0136 + 88.4038i) q^{63} -8.00000 q^{64} +100.988i q^{65} +(-10.7005 - 9.13785i) q^{66} +107.181 q^{67} -36.9761i q^{68} +(-25.6088 + 29.9881i) q^{69} -78.2745 q^{70} -46.5360i q^{71} +(-25.1419 + 3.98545i) q^{72} +6.88285 q^{73} -30.8831i q^{74} +(-13.6251 - 11.6354i) q^{75} +59.6647 q^{76} -32.9848i q^{77} +(-49.9953 + 58.5447i) q^{78} -63.7079 q^{79} -22.2611i q^{80} +(-77.0290 + 25.0505i) q^{81} -13.5950 q^{82} -57.4231i q^{83} +(-45.3773 - 38.7507i) q^{84} +102.891 q^{85} +62.5873i q^{86} +(30.8648 - 36.1428i) q^{87} +9.38083 q^{88} +108.987i q^{89} +(-11.0901 - 69.9610i) q^{90} -180.468 q^{91} -26.2898i q^{92} +(51.5675 + 44.0370i) q^{93} -74.8617 q^{94} +166.025i q^{95} +(11.0207 - 12.9052i) q^{96} -87.7799 q^{97} -70.5818i q^{98} +(29.4815 - 4.67336i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} - 16 q^{4} + 8 q^{6} + 8 q^{7} - 6 q^{9} - 16 q^{10} + 4 q^{12} - 8 q^{13} - 18 q^{15} + 32 q^{16} - 32 q^{18} + 64 q^{19} + 100 q^{21} - 16 q^{24} - 132 q^{25} - 44 q^{27} - 16 q^{28} - 24 q^{30}+ \cdots + 110 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 - 16 * q^4 + 8 * q^6 + 8 * q^7 - 6 * q^9 - 16 * q^10 + 4 * q^12 - 8 * q^13 - 18 * q^15 + 32 * q^16 - 32 * q^18 + 64 * q^19 + 100 * q^21 - 16 * q^24 - 132 * q^25 - 44 * q^27 - 16 * q^28 - 24 * q^30 + 28 * q^31 + 22 * q^33 + 72 * q^34 + 12 * q^36 + 4 * q^37 - 72 * q^39 + 32 * q^40 + 48 * q^42 - 120 * q^43 + 130 * q^45 - 16 * q^46 - 8 * q^48 + 192 * q^49 - 148 * q^51 + 16 * q^52 + 176 * q^54 - 132 * q^55 - 248 * q^57 - 136 * q^58 + 36 * q^60 + 24 * q^61 - 196 * q^63 - 64 * q^64 - 20 * q^67 + 374 * q^69 + 240 * q^70 + 64 * q^72 + 392 * q^73 + 340 * q^75 - 128 * q^76 - 232 * q^78 - 40 * q^79 - 222 * q^81 - 152 * q^82 - 200 * q^84 + 24 * q^85 + 232 * q^87 - 224 * q^90 - 576 * q^91 - 54 * q^93 - 256 * q^94 + 32 * q^96 - 132 * q^97 + 110 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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