LMFDB - Embedded newform 138.3.c.a.47.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,3,Mod(47,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("138.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	138.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.76022764817$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 10 x^{14} + 8 x^{13} - 119 x^{12} + 416 x^{11} - 774 x^{10} - 1284 x^{9} + \cdots + 43046721 $ x^16 - 4x^15 + 10x^14 + 8x^13 - 119x^12 + 416x^11 - 774x^10 - 1284x^9 + 7956x^8 - 11556x^7 - 62694x^6 + 303264x^5 - 780759x^4 + 472392x^3 + 5314410x^2 - 19131876*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{8}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.16
Root			$2.97243 - 0.405752i$ of defining polynomial
Character	$\chi$	$=$	138.47
Dual form			138.3.c.a.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} +(2.97243 - 0.405752i) q^{3} -2.00000 q^{4} -6.32168i q^{5} +(0.573819 + 4.20366i) q^{6} +5.04690 q^{7} -2.82843i q^{8} +(8.67073 - 2.41214i) q^{9} +O(q^{10})$	\(q+1.41421i q^{2} +(2.97243 - 0.405752i) q^{3} -2.00000 q^{4} -6.32168i q^{5} +(0.573819 + 4.20366i) q^{6} +5.04690 q^{7} -2.82843i q^{8} +(8.67073 - 2.41214i) q^{9} +8.94020 q^{10} +0.319973i q^{11} +(-5.94487 + 0.811503i) q^{12} +8.36075 q^{13} +7.13740i q^{14} +(-2.56503 - 18.7908i) q^{15} +4.00000 q^{16} +14.8242i q^{17} +(3.41128 + 12.2623i) q^{18} -29.3358 q^{19} +12.6434i q^{20} +(15.0016 - 2.04779i) q^{21} -0.452510 q^{22} +4.79583i q^{23} +(-1.14764 - 8.40731i) q^{24} -14.9636 q^{25} +11.8239i q^{26} +(24.7944 - 10.6881i) q^{27} -10.0938 q^{28} +27.3404i q^{29} +(26.5742 - 3.62750i) q^{30} -1.04203 q^{31} +5.65685i q^{32} +(0.129829 + 0.951098i) q^{33} -20.9646 q^{34} -31.9049i q^{35} +(-17.3415 + 4.82428i) q^{36} +10.7173 q^{37} -41.4871i q^{38} +(24.8518 - 3.39239i) q^{39} -17.8804 q^{40} -44.8026i q^{41} +(2.89601 + 21.2154i) q^{42} -70.4263 q^{43} -0.639945i q^{44} +(-15.2488 - 54.8136i) q^{45} -6.78233 q^{46} +76.8257i q^{47} +(11.8897 - 1.62301i) q^{48} -23.5288 q^{49} -21.1617i q^{50} +(6.01495 + 44.0640i) q^{51} -16.7215 q^{52} -16.5226i q^{53} +(15.1152 + 35.0646i) q^{54} +2.02276 q^{55} -14.2748i q^{56} +(-87.1988 + 11.9030i) q^{57} -38.6652 q^{58} -80.1894i q^{59} +(5.13006 + 37.5815i) q^{60} -92.6464 q^{61} -1.47365i q^{62} +(43.7603 - 12.1738i) q^{63} -8.00000 q^{64} -52.8540i q^{65} +(-1.34506 + 0.183606i) q^{66} +44.6725 q^{67} -29.6485i q^{68} +(1.94592 + 14.2553i) q^{69} +45.1203 q^{70} +71.8139i q^{71} +(-6.82256 - 24.5245i) q^{72} +128.345 q^{73} +15.1565i q^{74} +(-44.4783 + 6.07150i) q^{75} +58.6716 q^{76} +1.61487i q^{77} +(4.79756 + 35.1457i) q^{78} -19.3035 q^{79} -25.2867i q^{80} +(69.3632 - 41.8300i) q^{81} +63.3605 q^{82} +132.324i q^{83} +(-30.0032 + 4.09558i) q^{84} +93.7140 q^{85} -99.5978i q^{86} +(11.0934 + 81.2676i) q^{87} +0.905019 q^{88} +56.6074i q^{89} +(77.5181 - 21.5650i) q^{90} +42.1959 q^{91} -9.59166i q^{92} +(-3.09735 + 0.422803i) q^{93} -108.648 q^{94} +185.451i q^{95} +(2.29528 + 16.8146i) q^{96} +58.7167 q^{97} -33.2747i q^{98} +(0.771819 + 2.77440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9} - 8 q^{12} - 8 q^{13} + 28 q^{15} + 64 q^{16} + 16 q^{18} + 40 q^{19} + 4 q^{21} + 16 q^{22} + 16 q^{24} - 192 q^{25} - 80 q^{27} - 24 q^{30} + 136 q^{31} - 84 q^{33} - 16 q^{34} + 8 q^{36} - 136 q^{37} + 156 q^{39} + 128 q^{42} + 72 q^{43} + 4 q^{45} + 16 q^{48} + 224 q^{49} - 4 q^{51} + 16 q^{52} - 176 q^{54} - 96 q^{55} - 160 q^{57} - 56 q^{60} + 48 q^{61} + 204 q^{63} - 128 q^{64} - 144 q^{66} - 304 q^{67} - 176 q^{70} - 32 q^{72} + 408 q^{73} + 68 q^{75} - 80 q^{76} + 328 q^{78} + 312 q^{79} + 164 q^{81} + 160 q^{82} - 8 q^{84} - 464 q^{85} - 268 q^{87} - 32 q^{88} + 32 q^{90} - 72 q^{91} - 108 q^{93} - 32 q^{96} + 168 q^{97} - 60 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9 - 8 * q^12 - 8 * q^13 + 28 * q^15 + 64 * q^16 + 16 * q^18 + 40 * q^19 + 4 * q^21 + 16 * q^22 + 16 * q^24 - 192 * q^25 - 80 * q^27 - 24 * q^30 + 136 * q^31 - 84 * q^33 - 16 * q^34 + 8 * q^36 - 136 * q^37 + 156 * q^39 + 128 * q^42 + 72 * q^43 + 4 * q^45 + 16 * q^48 + 224 * q^49 - 4 * q^51 + 16 * q^52 - 176 * q^54 - 96 * q^55 - 160 * q^57 - 56 * q^60 + 48 * q^61 + 204 * q^63 - 128 * q^64 - 144 * q^66 - 304 * q^67 - 176 * q^70 - 32 * q^72 + 408 * q^73 + 68 * q^75 - 80 * q^76 + 328 * q^78 + 312 * q^79 + 164 * q^81 + 160 * q^82 - 8 * q^84 - 464 * q^85 - 268 * q^87 - 32 * q^88 + 32 * q^90 - 72 * q^91 - 108 * q^93 - 32 * q^96 + 168 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$1$

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
$3$	2.97243	−	0.405752i	0.990811	−	0.135251i
$3$	2.97243	−	0.405752i	0.990811	−	0.135251i
$4$	−2.00000			−0.500000
$5$		−	6.32168i		−	1.26434i	−0.774832	−	0.632168i	$-0.782165\pi$
$5$		−	6.32168i		−	1.26434i	0.774832	−	0.632168i	$-0.217835\pi$
$6$	0.573819	+	4.20366i	0.0956366	+	0.700609i
$7$	5.04690			0.720986			0.360493	−	0.932762i	$-0.382608\pi$
$7$	5.04690			0.720986			0.360493	+	0.932762i	$0.382608\pi$
$8$		−	2.82843i		−	0.353553i
$9$	8.67073	−	2.41214i	0.963415	−	0.268016i
$10$	8.94020			0.894020
$11$			0.319973i			0.0290884i	0.999894	+	0.0145442i	$0.00462973\pi$
$11$			0.319973i			0.0290884i	−0.999894	+	0.0145442i	$0.995370\pi$
$12$	−5.94487	+	0.811503i	−0.495406	+	0.0676253i
$13$	8.36075			0.643135			0.321567	−	0.946887i	$-0.395790\pi$
$13$	8.36075			0.643135			0.321567	+	0.946887i	$0.395790\pi$
$14$			7.13740i			0.509814i
$15$	−2.56503	−	18.7908i	−0.171002	−	1.25272i
$16$	4.00000			0.250000
$17$			14.8242i			0.872013i	0.899943	+	0.436007i	$0.143608\pi$
$17$			14.8242i			0.872013i	−0.899943	+	0.436007i	$0.856392\pi$
$18$	3.41128	+	12.2623i	0.189516	+	0.681237i
$19$	−29.3358			−1.54399			−0.771995	−	0.635629i	$-0.780741\pi$
$19$	−29.3358			−1.54399			−0.771995	+	0.635629i	$0.780741\pi$
$20$			12.6434i			0.632168i
$21$	15.0016	−	2.04779i	0.714361	−	0.0975137i
$22$	−0.452510			−0.0205686
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	−1.14764	−	8.40731i	−0.0478183	−	0.350305i
$25$	−14.9636			−0.598544
$26$			11.8239i			0.454765i
$27$	24.7944	−	10.6881i	0.918313	−	0.395855i
$28$	−10.0938			−0.360493
$29$			27.3404i			0.942773i	0.881927	+	0.471386i	$0.156246\pi$
$29$			27.3404i			0.942773i	−0.881927	+	0.471386i	$0.843754\pi$
$30$	26.5742	−	3.62750i	0.885805	−	0.120917i
$31$	−1.04203			−0.0336137			−0.0168069	−	0.999859i	$-0.505350\pi$
$31$	−1.04203			−0.0336137			−0.0168069	+	0.999859i	$0.505350\pi$
$32$			5.65685i			0.176777i
$33$	0.129829	+	0.951098i	0.00393422	+	0.0288211i
$34$	−20.9646			−0.616607
$35$		−	31.9049i		−	0.911568i
$36$	−17.3415	+	4.82428i	−0.481707	+	0.134008i
$37$	10.7173			0.289656			0.144828	−	0.989457i	$-0.453737\pi$
$37$	10.7173			0.289656			0.144828	+	0.989457i	$0.453737\pi$
$38$		−	41.4871i		−	1.09177i
$39$	24.8518	−	3.39239i	0.637225	−	0.0869843i
$40$	−17.8804			−0.447010
$41$		−	44.8026i		−	1.09275i	−0.837542	−	0.546374i	$-0.816008\pi$
$41$		−	44.8026i		−	1.09275i	0.837542	−	0.546374i	$-0.183992\pi$
$42$	2.89601	+	21.2154i	0.0689526	+	0.505130i
$43$	−70.4263			−1.63782			−0.818910	−	0.573922i	$-0.805421\pi$
$43$	−70.4263			−1.63782			−0.818910	+	0.573922i	$0.805421\pi$
$44$		−	0.639945i		−	0.0145442i
$45$	−15.2488	−	54.8136i	−0.338862	−	1.21808i
$46$	−6.78233			−0.147442
$47$			76.8257i			1.63459i	0.576219	+	0.817295i	$0.304527\pi$
$47$			76.8257i			1.63459i	−0.576219	+	0.817295i	$0.695473\pi$
$48$	11.8897	−	1.62301i	0.247703	−	0.0338126i
$49$	−23.5288			−0.480179
$50$		−	21.1617i		−	0.423234i
$51$	6.01495	+	44.0640i	0.117940	+	0.864001i
$52$	−16.7215			−0.321567
$53$		−	16.5226i		−	0.311747i	−0.987777	−	0.155873i	$-0.950181\pi$
$53$		−	16.5226i		−	0.311747i	0.987777	−	0.155873i	$-0.0498192\pi$
$54$	15.1152	+	35.0646i	0.279912	+	0.649345i
$55$	2.02276			0.0367775
$56$		−	14.2748i		−	0.254907i
$57$	−87.1988	+	11.9030i	−1.52980	+	0.208825i
$58$	−38.6652			−0.666641
$59$		−	80.1894i		−	1.35914i	−0.733610	−	0.679571i	$-0.762166\pi$
$59$		−	80.1894i		−	1.35914i	0.733610	−	0.679571i	$-0.237834\pi$
$60$	5.13006	+	37.5815i	0.0855010	+	0.626359i
$61$	−92.6464			−1.51879			−0.759396	−	0.650628i	$-0.774506\pi$
$61$	−92.6464			−1.51879			−0.759396	+	0.650628i	$0.774506\pi$
$62$		−	1.47365i		−	0.0237685i
$63$	43.7603	−	12.1738i	0.694608	−	0.193235i
$64$	−8.00000			−0.125000
$65$		−	52.8540i		−	0.813138i
$66$	−1.34506	+	0.183606i	−0.0203796	+	0.00278192i
$67$	44.6725			0.666754			0.333377	−	0.942794i	$-0.391812\pi$
$67$	44.6725			0.666754			0.333377	+	0.942794i	$0.391812\pi$
$68$		−	29.6485i		−	0.436007i
$69$	1.94592	+	14.2553i	0.0282017	+	0.206598i
$70$	45.1203			0.644576
$71$			71.8139i			1.01146i	0.862691	+	0.505732i	$0.168778\pi$
$71$			71.8139i			1.01146i	−0.862691	+	0.505732i	$0.831222\pi$
$72$	−6.82256	−	24.5245i	−0.0947578	−	0.340618i
$73$	128.345			1.75815			0.879073	−	0.476687i	$-0.158162\pi$
$73$	128.345			1.75815			0.879073	+	0.476687i	$0.158162\pi$
$74$			15.1565i			0.204818i
$75$	−44.4783	+	6.07150i	−0.593044	+	0.0809534i
$76$	58.6716			0.771995
$77$			1.61487i			0.0209723i
$78$	4.79756	+	35.1457i	0.0615072	+	0.450586i
$79$	−19.3035			−0.244348			−0.122174	−	0.992509i	$-0.538987\pi$
$79$	−19.3035			−0.244348			−0.122174	+	0.992509i	$0.538987\pi$
$80$		−	25.2867i		−	0.316084i
$81$	69.3632	−	41.8300i	0.856335	−	0.516420i
$82$	63.3605			0.772689
$83$			132.324i			1.59426i	0.603808	+	0.797130i	$0.293649\pi$
$83$			132.324i			1.59426i	−0.603808	+	0.797130i	$0.706351\pi$
$84$	−30.0032	+	4.09558i	−0.357181	+	0.0487569i
$85$	93.7140			1.10252
$86$		−	99.5978i		−	1.15811i
$87$	11.0934	+	81.2676i	0.127511	+	0.934110i
$88$	0.905019			0.0102843
$89$			56.6074i			0.636038i	0.948084	+	0.318019i	$0.103018\pi$
$89$			56.6074i			0.636038i	−0.948084	+	0.318019i	$0.896982\pi$
$90$	77.5181	−	21.5650i	0.861312	−	0.239611i
$91$	42.1959			0.463691
$92$		−	9.59166i		−	0.104257i
$93$	−3.09735	+	0.422803i	−0.0333049	+	0.00454627i
$94$	−108.648			−1.15583
$95$			185.451i			1.95212i
$96$	2.29528	+	16.8146i	0.0239091	+	0.175152i
$97$	58.7167			0.605327			0.302664	−	0.953097i	$-0.402124\pi$
$97$	58.7167			0.605327			0.302664	+	0.953097i	$0.402124\pi$
$98$		−	33.2747i		−	0.339538i
$99$	0.771819	+	2.77440i	0.00779615	+	0.0280242i
$100$	29.9272			0.299272
$101$			87.2915i			0.864272i	0.901808	+	0.432136i	$0.142240\pi$
$101$			87.2915i			0.864272i	−0.901808	+	0.432136i	$0.857760\pi$
$102$	−62.3160	+	8.50643i	−0.610941	+	0.0833964i
$103$	51.8313			0.503217			0.251608	−	0.967829i	$-0.419040\pi$
$103$	51.8313			0.503217			0.251608	+	0.967829i	$0.419040\pi$
$104$		−	23.6478i		−	0.227383i
$105$	−12.9455	−	94.8352i	−0.123290	−	0.903192i
$106$	23.3665			0.220438
$107$			45.1231i			0.421711i	0.977517	+	0.210856i	$0.0676250\pi$
$107$			45.1231i			0.421711i	−0.977517	+	0.210856i	$0.932375\pi$
$108$	−49.5889	+	21.3762i	−0.459156	+	0.197928i
$109$	−131.231			−1.20395			−0.601976	−	0.798514i	$-0.705620\pi$
$109$	−131.231			−1.20395			−0.601976	+	0.798514i	$0.705620\pi$
$110$			2.86062i			0.0260056i
$111$	31.8564	−	4.34855i	0.286994	−	0.0391761i
$112$	20.1876			0.180247
$113$		−	220.246i		−	1.94908i	−0.224213	−	0.974540i	$-0.571981\pi$
$113$		−	220.246i		−	1.94908i	0.224213	−	0.974540i	$-0.428019\pi$
$114$	−16.8335	−	123.318i	−0.147662	−	1.08173i
$115$	30.3177			0.263632
$116$		−	54.6808i		−	0.471386i
$117$	72.4939	−	20.1673i	0.619606	−	0.172370i
$118$	113.405			0.961059
$119$			74.8164i			0.628710i
$120$	−53.1483	+	7.25500i	−0.442903	+	0.0604583i
$121$	120.898			0.999154
$122$		−	131.022i		−	1.07395i
$123$	−18.1787	−	133.173i	−0.147795	−	1.08271i
$124$	2.08405			0.0168069
$125$		−	63.4469i		−	0.507575i
$126$	17.2164	+	61.8865i	0.136638	+	0.491162i
$127$	−136.775			−1.07697			−0.538486	−	0.842634i	$-0.681004\pi$
$127$	−136.775			−1.07697			−0.538486	+	0.842634i	$0.681004\pi$
$128$		−	11.3137i		−	0.0883883i
$129$	−209.337	+	28.5756i	−1.62277	+	0.221516i
$130$	74.7468			0.574976
$131$			106.277i			0.811277i	0.914034	+	0.405638i	$0.132951\pi$
$131$			106.277i			0.811277i	−0.914034	+	0.405638i	$0.867049\pi$
$132$	−0.259659	−	1.90220i	−0.00196711	−	0.0144106i
$133$	−148.055			−1.11320
$134$			63.1765i			0.471467i
$135$	−67.5666	−	156.742i	−0.500494	−	1.16106i
$136$	41.9292			0.308303
$137$		−	142.094i		−	1.03718i	−0.855022	−	0.518592i	$-0.826456\pi$
$137$		−	142.094i		−	1.03718i	0.855022	−	0.518592i	$-0.173544\pi$
$138$	−20.1600	+	2.75194i	−0.146087	+	0.0199416i
$139$	−176.774			−1.27175			−0.635876	−	0.771791i	$-0.719361\pi$
$139$	−176.774			−1.27175			−0.635876	+	0.771791i	$0.719361\pi$
$140$			63.8098i			0.455784i
$141$	31.1722	+	228.359i	0.221079	+	1.61957i
$142$	−101.560			−0.715213
$143$			2.67521i			0.0187078i
$144$	34.6829	−	9.64856i	0.240854	−	0.0670039i
$145$	172.837			1.19198
$146$			181.507i			1.24320i
$147$	−69.9377	+	9.54684i	−0.475767	+	0.0649445i
$148$	−21.4345			−0.144828
$149$		−	151.335i		−	1.01567i	−0.861454	−	0.507835i	$-0.830446\pi$
$149$		−	151.335i		−	1.01567i	0.861454	−	0.507835i	$-0.169554\pi$
$150$	−8.58640	−	62.9018i	−0.0572427	−	0.419346i
$151$	282.413			1.87028			0.935142	−	0.354274i	$-0.115272\pi$
$151$	282.413			1.87028			0.935142	+	0.354274i	$0.115272\pi$
$152$			82.9742i			0.545883i
$153$	35.7581	+	128.537i	0.233713	+	0.840110i
$154$	−2.28377			−0.0148297
$155$			6.58735i			0.0424990i
$156$	−49.7036	+	6.78478i	−0.318613	+	0.0434922i
$157$	81.1583			0.516932			0.258466	−	0.966020i	$-0.416783\pi$
$157$	81.1583			0.516932			0.258466	+	0.966020i	$0.416783\pi$
$158$		−	27.2992i		−	0.172780i
$159$	−6.70406	−	49.1123i	−0.0421639	−	0.308882i
$160$	35.7608			0.223505
$161$			24.2041i			0.150336i
$162$	59.1566	+	98.0943i	0.365164	+	0.605521i
$163$	−16.1658			−0.0991768			−0.0495884	−	0.998770i	$-0.515791\pi$
$163$	−16.1658			−0.0991768			−0.0495884	+	0.998770i	$0.515791\pi$
$164$			89.6053i			0.546374i
$165$	6.01253	−	0.820739i	0.0364396	−	0.00497418i
$166$	−187.134			−1.12731
$167$			198.586i			1.18914i	0.804044	+	0.594570i	$0.202678\pi$
$167$			198.586i			1.18914i	−0.804044	+	0.594570i	$0.797322\pi$
$168$	−5.79202	−	42.4309i	−0.0344763	−	0.252565i
$169$	−99.0978			−0.586377
$170$			132.532i			0.779598i
$171$	−254.363	+	70.7621i	−1.48750	+	0.413813i
$172$	140.853			0.818910
$173$		−	190.662i		−	1.10209i	−0.834474	−	0.551047i	$-0.814229\pi$
$173$		−	190.662i		−	1.10209i	0.834474	−	0.551047i	$-0.185771\pi$
$174$	−114.930	+	15.6885i	−0.660516	+	0.0901636i
$175$	−75.5198			−0.431542
$176$			1.27989i			0.00727211i
$177$	−32.5370	−	238.358i	−0.183825	−	1.34665i
$178$	−80.0549			−0.449747
$179$		−	137.546i		−	0.768415i	−0.923247	−	0.384207i	$-0.874475\pi$
$179$		−	137.546i		−	0.768415i	0.923247	−	0.384207i	$-0.125525\pi$
$180$	30.4975	+	109.627i	0.169431	+	0.609040i
$181$	229.352			1.26714			0.633570	−	0.773685i	$-0.281589\pi$
$181$	229.352			1.26714			0.633570	+	0.773685i	$0.281589\pi$
$182$			59.6740i			0.327879i
$183$	−275.385	+	37.5914i	−1.50484	+	0.205418i
$184$	13.5647			0.0737210
$185$		−	67.7511i		−	0.366222i
$186$	−0.597934	−	4.38032i	−0.00321470	−	0.0235501i
$187$	−4.74335			−0.0253655
$188$		−	153.651i		−	0.817295i
$189$	125.135	−	53.9417i	0.662091	−	0.285406i
$190$	−262.268			−1.38036
$191$		−	197.681i		−	1.03498i	−0.855689	−	0.517490i	$-0.826866\pi$
$191$		−	197.681i		−	1.03498i	0.855689	−	0.517490i	$-0.173134\pi$
$192$	−23.7795	+	3.24601i	−0.123851	+	0.0169063i
$193$	−170.763			−0.884783			−0.442392	−	0.896822i	$-0.645870\pi$
$193$	−170.763			−0.884783			−0.442392	+	0.896822i	$0.645870\pi$
$194$			83.0380i			0.428031i
$195$	−21.4456	−	157.105i	−0.109977	−	0.805667i
$196$	47.0576			0.240090
$197$		−	40.5838i		−	0.206009i	−0.994681	−	0.103005i	$-0.967154\pi$
$197$		−	40.5838i		−	0.206009i	0.994681	−	0.103005i	$-0.0328457\pi$
$198$	−3.92359	+	1.09152i	−0.0198161	+	0.00551271i
$199$	168.032			0.844381			0.422191	−	0.906507i	$-0.361261\pi$
$199$	168.032			0.844381			0.422191	+	0.906507i	$0.361261\pi$
$200$			42.3234i			0.211617i
$201$	132.786	−	18.1260i	0.660628	−	0.0901789i
$202$	−123.449			−0.611133
$203$			137.984i			0.679726i
$204$	−12.0299	−	88.1281i	−0.0589701	−	0.432000i
$205$	−283.228			−1.38160
$206$			73.3006i			0.355828i
$207$	11.5682	+	41.5834i	0.0558851	+	0.200886i
$208$	33.4430			0.160784
$209$		−	9.38666i		−	0.0449122i
$210$	134.117	−	18.3076i	0.638653	−	0.0871792i
$211$	37.8276			0.179278			0.0896388	−	0.995974i	$-0.471429\pi$
$211$	37.8276			0.179278			0.0896388	+	0.995974i	$0.471429\pi$
$212$			33.0452i			0.155873i
$213$	29.1386	+	213.462i	0.136801	+	1.00217i
$214$	−63.8137			−0.298195
$215$			445.212i			2.07075i
$216$	−30.2305	−	70.1293i	−0.139956	−	0.324673i
$217$	−5.25900			−0.0242350
$218$		−	185.588i		−	0.851323i
$219$	381.496	−	52.0761i	1.74199	−	0.237790i
$220$	−4.04553			−0.0183888
$221$			123.942i			0.560822i
$222$	6.14978	+	45.0517i	0.0277017	+	0.202936i
$223$	−87.9056			−0.394196			−0.197098	−	0.980384i	$-0.563152\pi$
$223$	−87.9056			−0.394196			−0.197098	+	0.980384i	$0.563152\pi$
$224$			28.5496i			0.127454i
$225$	−129.745	+	36.0943i	−0.576646	+	0.160419i
$226$	311.475			1.37821
$227$		−	426.088i		−	1.87704i	−0.345224	−	0.938520i	$-0.612197\pi$
$227$		−	426.088i		−	1.87704i	0.345224	−	0.938520i	$-0.387803\pi$
$228$	174.398	−	23.8061i	0.764901	−	0.104413i
$229$	26.2544			0.114648			0.0573240	−	0.998356i	$-0.481743\pi$
$229$	26.2544			0.114648			0.0573240	+	0.998356i	$0.481743\pi$
$230$			42.8757i			0.186416i
$231$	0.655236	+	4.80010i	0.00283652	+	0.0207796i
$232$	77.3304			0.333321
$233$		−	16.3398i		−	0.0701279i	−0.999385	−	0.0350639i	$-0.988837\pi$
$233$		−	16.3398i		−	0.0701279i	0.999385	−	0.0350639i	$-0.0111635\pi$
$234$	28.5209	+	102.522i	0.121884	+	0.438127i
$235$	485.667			2.06667
$236$			160.379i			0.679571i
$237$	−57.3783	+	7.83241i	−0.242102	+	0.0330481i
$238$	−105.806			−0.444565
$239$		−	354.989i		−	1.48531i	−0.669674	−	0.742655i	$-0.733566\pi$
$239$		−	354.989i		−	1.48531i	0.669674	−	0.742655i	$-0.266434\pi$
$240$	−10.2601	−	75.1631i	−0.0427505	−	0.313179i
$241$	34.3200			0.142406			0.0712032	−	0.997462i	$-0.477316\pi$
$241$	34.3200			0.142406			0.0712032	+	0.997462i	$0.477316\pi$
$242$			170.975i			0.706508i
$243$	189.205	−	152.481i	0.778621	−	0.627495i
$244$	185.293			0.759396
$245$			148.741i			0.607107i
$246$	188.335	−	25.7086i	0.765589	−	0.104507i
$247$	−245.269			−0.992994
$248$			2.94729i			0.0118842i
$249$	53.6905	+	393.323i	0.215624	+	1.57961i
$250$	89.7275			0.358910
$251$		−	254.329i		−	1.01326i	−0.862163	−	0.506631i	$-0.830891\pi$
$251$		−	254.329i		−	1.01326i	0.862163	−	0.506631i	$-0.169109\pi$
$252$	−87.5207	+	24.3477i	−0.347304	+	0.0966177i
$253$	−1.53453			−0.00606536
$254$		−	193.430i		−	0.761534i
$255$	278.559	−	38.0246i	1.09239	−	0.149116i
$256$	16.0000			0.0625000
$257$		−	333.530i		−	1.29778i	−0.760881	−	0.648892i	$-0.775233\pi$
$257$		−	333.530i		−	1.29778i	0.760881	−	0.648892i	$-0.224767\pi$
$258$	−40.4120	−	296.048i	−0.156635	−	1.14747i
$259$	54.0890			0.208838
$260$			105.708i			0.406569i
$261$	65.9489	+	237.061i	0.252678	+	0.908281i
$262$	−150.299			−0.573659
$263$			88.6394i			0.337032i	0.985699	+	0.168516i	$0.0538975\pi$
$263$			88.6394i			0.337032i	−0.985699	+	0.168516i	$0.946103\pi$
$264$	2.69011	−	0.367213i	0.0101898	−	0.00139096i
$265$	−104.450			−0.394153
$266$		−	209.381i		−	0.787148i
$267$	22.9685	+	168.262i	0.0860245	+	0.630194i
$268$	−89.3451			−0.333377
$269$			336.165i			1.24969i	0.780751	+	0.624843i	$0.214837\pi$
$269$			336.165i			1.24969i	−0.780751	+	0.624843i	$0.785163\pi$
$270$	221.667	−	95.5537i	0.820990	−	0.353902i
$271$	170.056			0.627514			0.313757	−	0.949503i	$-0.398412\pi$
$271$	170.056			0.627514			0.313757	+	0.949503i	$0.398412\pi$
$272$			59.2969i			0.218003i
$273$	125.425	−	17.1211i	0.459431	−	0.0627145i
$274$	200.951			0.733400
$275$		−	4.78794i		−	0.0174107i
$276$	−3.89183	−	28.5106i	−0.0141008	−	0.103299i
$277$	−198.801			−0.717693			−0.358846	−	0.933397i	$-0.616830\pi$
$277$	−198.801			−0.717693			−0.358846	+	0.933397i	$0.616830\pi$
$278$		−	249.996i		−	0.899265i
$279$	−9.03512	+	2.51351i	−0.0323839	+	0.00900900i
$280$	−90.2406			−0.322288
$281$		−	340.700i		−	1.21246i	−0.795291	−	0.606228i	$-0.792682\pi$
$281$		−	340.700i		−	1.21246i	0.795291	−	0.606228i	$-0.207318\pi$
$282$	−322.949	+	44.0841i	−1.14521	+	0.156327i
$283$	41.4310			0.146399			0.0731996	−	0.997317i	$-0.476679\pi$
$283$	41.4310			0.146399			0.0731996	+	0.997317i	$0.476679\pi$
$284$		−	143.628i		−	0.505732i
$285$	75.2472	+	551.242i	0.264025	+	1.93418i
$286$	−3.78332			−0.0132284
$287$		−	226.115i		−	0.787856i
$288$	13.6451	+	49.0491i	0.0473789	+	0.170309i
$289$	69.2423			0.239593
$290$			244.429i			0.842858i
$291$	174.532	−	23.8244i	0.599765	−	0.0818708i
$292$	−256.689			−0.879073
$293$			31.4719i			0.107413i	0.998557	+	0.0537063i	$0.0171035\pi$
$293$			31.4719i			0.107413i	−0.998557	+	0.0537063i	$0.982897\pi$
$294$	−13.5013	−	98.9069i	−0.0459227	−	0.336418i
$295$	−506.931			−1.71841
$296$		−	30.3130i		−	0.102409i
$297$	3.41990	+	7.93355i	0.0115148	+	0.0267123i
$298$	214.020			0.718187
$299$			40.0968i			0.134103i
$300$	88.9566	−	12.1430i	0.296522	−	0.0404767i
$301$	−355.434			−1.18085
$302$			399.392i			1.32249i
$303$	35.4187	+	259.468i	0.116893	+	0.856331i
$304$	−117.343			−0.385997
$305$			585.680i			1.92026i
$306$	−181.779	+	50.5696i	−0.594048	+	0.165260i
$307$	−16.8237			−0.0548005			−0.0274002	−	0.999625i	$-0.508723\pi$
$307$	−16.8237			−0.0548005			−0.0274002	+	0.999625i	$0.508723\pi$
$308$		−	3.22974i		−	0.0104862i
$309$	154.065	−	21.0306i	0.498593	−	0.0680603i
$310$	−9.31592			−0.0300513
$311$			461.168i			1.48285i	0.671033	+	0.741427i	$0.265851\pi$
$311$			461.168i			1.48285i	−0.671033	+	0.741427i	$0.734149\pi$
$312$	−9.59513	−	70.2915i	−0.0307536	−	0.225293i
$313$	−137.459			−0.439168			−0.219584	−	0.975594i	$-0.570470\pi$
$313$	−137.459			−0.439168			−0.219584	+	0.975594i	$0.570470\pi$
$314$			114.775i			0.365526i
$315$	−76.9590	−	276.639i	−0.244314	−	0.878218i
$316$	38.6069			0.122174
$317$		−	350.996i		−	1.10724i	−0.832769	−	0.553621i	$-0.813246\pi$
$317$		−	350.996i		−	1.10724i	0.832769	−	0.553621i	$-0.186754\pi$
$318$	69.4553	−	9.48098i	0.218413	−	0.0298144i
$319$	−8.74818			−0.0274238
$320$			50.5734i			0.158042i
$321$	18.3088	+	134.125i	0.0570367	+	0.417836i
$322$	−34.2298			−0.106304
$323$		−	434.881i		−	1.34638i
$324$	−138.726	+	83.6601i	−0.428168	+	0.258210i
$325$	−125.107			−0.384944
$326$		−	22.8619i		−	0.0701286i
$327$	−390.075	+	53.2471i	−1.19289	+	0.162835i
$328$	−126.721			−0.386345
$329$			387.732i			1.17852i
$330$	1.16070	+	8.50300i	0.00351728	+	0.0257667i
$331$	114.103			0.344721			0.172361	−	0.985034i	$-0.444861\pi$
$331$	114.103			0.344721			0.172361	+	0.985034i	$0.444861\pi$
$332$		−	264.647i		−	0.797130i
$333$	92.9265	−	25.8515i	0.279059	−	0.0776323i
$334$	−280.844			−0.840849
$335$		−	282.405i		−	0.843001i
$336$	60.0063	−	8.19115i	0.178590	−	0.0243784i
$337$	−442.698			−1.31364			−0.656822	−	0.754046i	$-0.728100\pi$
$337$	−442.698			−1.31364			−0.656822	+	0.754046i	$0.728100\pi$
$338$		−	140.145i		−	0.414631i
$339$	−89.3652	−	654.667i	−0.263614	−	1.93117i
$340$	−187.428			−0.551259
$341$		−	0.333420i		−	0.000977770i
$342$	−100.073	−	359.723i	−0.292610	−	1.05182i
$343$	−366.046			−1.06719
$344$			199.196i			0.579057i
$345$	90.1174	−	12.3015i	0.261210	−	0.0356564i
$346$	269.637			0.779298
$347$		−	103.932i		−	0.299517i	−0.988723	−	0.149758i	$-0.952150\pi$
$347$		−	103.932i		−	0.299517i	0.988723	−	0.149758i	$-0.0478496\pi$
$348$	−22.1868	−	162.535i	−0.0637553	−	0.467055i
$349$	−163.937			−0.469735			−0.234867	−	0.972027i	$-0.575466\pi$
$349$	−163.937			−0.469735			−0.234867	+	0.972027i	$0.575466\pi$
$350$		−	106.801i		−	0.305146i
$351$	207.300	−	89.3605i	0.590599	−	0.254588i
$352$	−1.81004			−0.00514216
$353$			615.778i			1.74441i	0.489137	+	0.872207i	$0.337312\pi$
$353$			615.778i			1.74441i	−0.489137	+	0.872207i	$0.662688\pi$
$354$	337.089	−	46.0142i	0.952228	−	0.129984i
$355$	453.984			1.27883
$356$		−	113.215i		−	0.318019i
$357$	30.3569	+	222.387i	0.0850333	+	0.622933i
$358$	194.520			0.543351
$359$			556.874i			1.55118i	0.631236	+	0.775591i	$0.282548\pi$
$359$			556.874i			1.55118i	−0.631236	+	0.775591i	$0.717452\pi$
$360$	−155.036	+	43.1300i	−0.430656	+	0.119806i
$361$	499.590			1.38390
$362$			324.353i			0.896003i
$363$	359.360	−	49.0544i	0.989973	−	0.135136i
$364$	−84.3918			−0.231846
$365$		−	811.354i		−	2.22289i
$366$	−53.1623	−	389.454i	−0.145252	−	1.06408i
$367$	−407.330			−1.10989			−0.554945	−	0.831887i	$-0.687261\pi$
$367$	−407.330			−1.10989			−0.554945	+	0.831887i	$0.687261\pi$
$368$			19.1833i			0.0521286i
$369$	−108.070	−	388.472i	−0.292873	−	1.05277i
$370$	95.8145			0.258958
$371$		−	83.3879i		−	0.224765i
$372$	6.19470	−	0.845607i	0.0166524	−	0.00227314i
$373$	52.1858			0.139908			0.0699542	−	0.997550i	$-0.477715\pi$
$373$	52.1858			0.139908			0.0699542	+	0.997550i	$0.477715\pi$
$374$		−	6.70811i		−	0.0179361i
$375$	−25.7437	−	188.592i	−0.0686498	−	0.502911i
$376$	217.296			0.577915
$377$			228.586i			0.606330i
$378$	76.2851	+	176.968i	0.201813	+	0.468169i
$379$	−467.409			−1.23327			−0.616635	−	0.787250i	$-0.711504\pi$
$379$	−467.409			−1.23327			−0.616635	+	0.787250i	$0.711504\pi$
$380$		−	370.903i		−	0.976060i
$381$	−406.556	+	55.4968i	−1.06708	+	0.145661i
$382$	279.564			0.731842
$383$			311.616i			0.813619i	0.913513	+	0.406810i	$0.133359\pi$
$383$			311.616i			0.813619i	−0.913513	+	0.406810i	$0.866641\pi$
$384$	−4.59055	−	33.6293i	−0.0119546	−	0.0875762i
$385$	10.2087			0.0265161
$386$		−	241.496i		−	0.625636i
$387$	−610.647	+	169.878i	−1.57790	+	0.438961i
$388$	−117.433			−0.302664
$389$		−	37.6791i		−	0.0968614i	−0.998827	−	0.0484307i	$-0.984578\pi$
$389$		−	37.6791i		−	0.0968614i	0.998827	−	0.0484307i	$-0.0154220\pi$
$390$	222.180	−	30.3286i	0.569692	−	0.0777657i
$391$	−71.0945			−0.181827
$392$			66.5494i			0.169769i
$393$	43.1222	+	315.902i	0.109726	+	0.803822i
$394$	57.3942			0.145671
$395$			122.030i			0.308937i
$396$	−1.54364	−	5.54879i	−0.00389807	−	0.0140121i
$397$	302.716			0.762508			0.381254	−	0.924470i	$-0.375492\pi$
$397$	302.716			0.762508			0.381254	+	0.924470i	$0.375492\pi$
$398$			237.633i			0.597068i
$399$	−440.084	+	60.0735i	−1.10297	+	0.150560i
$400$	−59.8544			−0.149636
$401$			734.641i			1.83202i	0.401154	+	0.916011i	$0.368609\pi$
$401$			734.641i			1.83202i	−0.401154	+	0.916011i	$0.631391\pi$
$402$	25.6340	+	187.788i	0.0637661	+	0.467134i
$403$	−8.71212			−0.0216182
$404$		−	174.583i		−	0.432136i
$405$	−264.436	−	438.491i	−0.652928	−	1.08270i
$406$	−195.139			−0.480639
$407$			3.42923i			0.00842563i
$408$	124.632	−	17.0129i	0.305470	−	0.0416982i
$409$	620.780			1.51780			0.758900	−	0.651207i	$-0.225737\pi$
$409$	620.780			1.51780			0.758900	+	0.651207i	$0.225737\pi$
$410$		−	400.545i		−	0.976938i
$411$	−57.6549	−	422.366i	−0.140280	−	1.02765i
$412$	−103.663			−0.251608
$413$		−	404.708i		−	0.979923i
$414$	−58.8078	+	16.3599i	−0.142048	+	0.0395167i
$415$	836.506			2.01568
$416$			47.2956i			0.113691i
$417$	−525.448	+	71.7261i	−1.26007	+	0.172005i
$418$	13.2747			0.0317577
$419$			220.886i			0.527173i	0.964636	+	0.263587i	$0.0849055\pi$
$419$			220.886i			0.527173i	−0.964636	+	0.263587i	$0.915094\pi$
$420$	25.8909	+	189.670i	0.0616450	+	0.451596i
$421$	568.704			1.35084			0.675421	−	0.737432i	$-0.263962\pi$
$421$	568.704			1.35084			0.675421	+	0.737432i	$0.263962\pi$
$422$			53.4963i			0.126768i
$423$	185.314	+	666.135i	0.438096	+	1.57479i
$424$	−46.7329			−0.110219
$425$		−	221.824i		−	0.521938i
$426$	−301.881	+	41.2082i	−0.708641	+	0.0967329i
$427$	−467.577			−1.09503
$428$		−	90.2462i		−	0.210856i
$429$	1.08547	+	7.95189i	0.00253024	+	0.0185359i
$430$	−629.625			−1.46424
$431$			398.633i			0.924903i	0.886645	+	0.462451i	$0.153030\pi$
$431$			398.633i			0.924903i	−0.886645	+	0.462451i	$0.846970\pi$
$432$	99.1778	−	42.7524i	0.229578	−	0.0989638i
$433$	−172.140			−0.397553			−0.198776	−	0.980045i	$-0.563697\pi$
$433$	−172.140			−0.397553			−0.198776	+	0.980045i	$0.563697\pi$
$434$		−	7.43735i		−	0.0171367i
$435$	513.747	−	70.1290i	1.18103	−	0.161216i
$436$	262.462			0.601976
$437$		−	140.690i		−	0.321944i
$438$	73.6467	+	539.517i	0.168143	+	1.23177i
$439$	219.158			0.499221			0.249611	−	0.968346i	$-0.419697\pi$
$439$	219.158			0.499221			0.249611	+	0.968346i	$0.419697\pi$
$440$		−	5.72124i		−	0.0130028i
$441$	−204.012	+	56.7547i	−0.462612	+	0.128695i
$442$	−175.280			−0.396561
$443$		−	226.183i		−	0.510571i	−0.966866	−	0.255285i	$-0.917831\pi$
$443$		−	226.183i		−	0.510571i	0.966866	−	0.255285i	$-0.0821694\pi$
$444$	−63.7127	+	8.69710i	−0.143497	+	0.0195881i
$445$	357.853			0.804165
$446$		−	124.317i		−	0.278738i
$447$	−61.4043	−	449.833i	−0.137370	−	1.00634i
$448$	−40.3752			−0.0901233
$449$		−	304.088i		−	0.677257i	−0.940920	−	0.338628i	$-0.890037\pi$
$449$		−	304.088i		−	0.677257i	0.940920	−	0.338628i	$-0.109963\pi$
$450$	−51.0450	−	183.488i	−0.113433	−	0.407750i
$451$	14.3356			0.0317863
$452$			440.492i			0.974540i
$453$	839.454	−	114.589i	1.85310	−	0.252957i
$454$	602.580			1.32727
$455$		−	266.749i		−	0.586261i
$456$	33.6669	+	246.635i	0.0738309	+	0.540867i
$457$	234.476			0.513076			0.256538	−	0.966534i	$-0.417418\pi$
$457$	234.476			0.513076			0.256538	+	0.966534i	$0.417418\pi$
$458$			37.1293i			0.0810684i
$459$	158.443	+	367.559i	0.345191	+	0.800781i
$460$	−60.6354			−0.131816
$461$		−	462.739i		−	1.00377i	−0.864934	−	0.501886i	$-0.832640\pi$
$461$		−	462.739i		−	1.00377i	0.864934	−	0.501886i	$-0.167360\pi$
$462$	−6.78836	+	0.926644i	−0.0146934	+	0.00200572i
$463$	−681.249			−1.47138			−0.735690	−	0.677318i	$-0.763142\pi$
$463$	−681.249			−1.47138			−0.735690	+	0.677318i	$0.763142\pi$
$464$			109.362i			0.235693i
$465$	2.67283	+	19.5805i	0.00574801	+	0.0421085i
$466$	23.1080			0.0495879
$467$		−	706.963i		−	1.51384i	−0.653508	−	0.756919i	$-0.726704\pi$
$467$		−	706.963i		−	1.51384i	0.653508	−	0.756919i	$-0.273296\pi$
$468$	−144.988	+	40.3346i	−0.309803	+	0.0861851i
$469$	225.458			0.480721
$470$			686.837i			1.46136i
$471$	241.238	−	32.9301i	0.512182	−	0.0699153i
$472$	−226.810			−0.480529
$473$		−	22.5345i		−	0.0476416i
$474$	−11.0767	−	81.1451i	−0.0233686	−	0.171192i
$475$	438.969			0.924146
$476$		−	149.633i		−	0.314355i
$477$	−39.8548	−	143.263i	−0.0835530	−	0.300341i
$478$	502.031			1.05027
$479$			717.077i			1.49703i	0.663118	+	0.748515i	$0.269233\pi$
$479$			717.077i			1.49703i	−0.663118	+	0.748515i	$0.730767\pi$
$480$	106.297	−	14.5100i	0.221451	−	0.0302292i
$481$	89.6044			0.186288
$482$			48.5357i			0.100697i
$483$	9.82085	+	71.9451i	0.0203330	+	0.148955i
$484$	−241.795			−0.499577
$485$		−	371.188i		−	0.765336i
$486$	215.641	+	267.576i	0.443706	+	0.550568i
$487$	582.452			1.19600			0.598000	−	0.801496i	$-0.295962\pi$
$487$	582.452			1.19600			0.598000	+	0.801496i	$0.295962\pi$
$488$			262.044i			0.536974i
$489$	−48.0518	+	6.55931i	−0.0982655	+	0.0134137i
$490$	−210.352			−0.429290
$491$		−	297.747i		−	0.606410i	−0.952925	−	0.303205i	$-0.901943\pi$
$491$		−	297.747i		−	0.606410i	0.952925	−	0.303205i	$-0.0980567\pi$
$492$	36.3575	+	266.346i	0.0738973	+	0.541353i
$493$	−405.301			−0.822111
$494$		−	346.863i		−	0.702153i
$495$	17.5388	−	4.87919i	0.0354320	−	0.00985695i
$496$	−4.16810			−0.00840343
$497$			362.438i			0.729251i
$498$	−556.243	+	75.9298i	−1.11695	+	0.152469i
$499$	−508.035			−1.01811			−0.509053	−	0.860735i	$-0.670004\pi$
$499$	−508.035			−1.01811			−0.509053	+	0.860735i	$0.670004\pi$
$500$			126.894i			0.253788i
$501$	80.5767	+	590.285i	0.160832	+	1.17821i
$502$	359.675			0.716484
$503$			612.718i			1.21813i	0.793121	+	0.609064i	$0.208455\pi$
$503$			612.718i			1.21813i	−0.793121	+	0.609064i	$0.791545\pi$
$504$	−34.4328	−	123.773i	−0.0683191	−	0.245581i
$505$	551.829			1.09273
$506$		−	2.17016i		−	0.00428885i
$507$	−294.562	+	40.2091i	−0.580990	+	0.0793079i
$508$	273.551			0.538486
$509$			562.892i			1.10588i	0.833222	+	0.552939i	$0.186494\pi$
$509$			562.892i			1.10588i	−0.833222	+	0.552939i	$0.813506\pi$
$510$	53.7749	+	393.941i	0.105441	+	0.772434i
$511$	647.743			1.26760
$512$			22.6274i			0.0441942i
$513$	−727.365	+	313.544i	−1.41787	+	0.611196i
$514$	471.683			0.917672
$515$		−	327.661i		−	0.636235i
$516$	418.675	−	57.1511i	0.811385	−	0.110758i
$517$	−24.5821			−0.0475476
$518$			76.4934i			0.147671i
$519$	−77.3615	−	566.731i	−0.149059	−	1.09197i
$520$	−149.494			−0.287488
$521$		−	684.396i		−	1.31362i	−0.754056	−	0.656810i	$-0.771905\pi$
$521$		−	684.396i		−	1.31362i	0.754056	−	0.656810i	$-0.228095\pi$
$522$	−335.255	+	93.2658i	−0.642252	+	0.178670i
$523$	−131.392			−0.251227			−0.125614	−	0.992079i	$-0.540090\pi$
$523$	−131.392			−0.251227			−0.125614	+	0.992079i	$0.540090\pi$
$524$		−	212.554i		−	0.405638i
$525$	−224.478	+	30.6423i	−0.427577	+	0.0583663i
$526$	−125.355			−0.238318
$527$		−	15.4472i		−	0.0293116i
$528$	0.519318	+	3.80439i	0.000983556	+	0.00720529i
$529$	−23.0000			−0.0434783
$530$		−	147.715i		−	0.278708i
$531$	−193.428	−	695.301i	−0.364271	−	1.30942i
$532$	296.110			0.556598
$533$		−	374.584i		−	0.702784i
$534$	−237.958	+	32.4824i	−0.445614	+	0.0608285i
$535$	285.254			0.533184
$536$		−	126.353i		−	0.235733i
$537$	−55.8096	−	408.847i	−0.103929	−	0.761354i
$538$	−475.410			−0.883661
$539$		−	7.52856i		−	0.0139677i
$540$	135.133	+	313.485i	0.250247	+	0.580528i
$541$	976.445			1.80489			0.902445	−	0.430805i	$-0.141770\pi$
$541$	976.445			1.80489			0.902445	+	0.430805i	$0.141770\pi$
$542$			240.496i			0.443720i
$543$	681.735	−	93.0601i	1.25550	−	0.171381i
$544$	−83.8585			−0.154152
$545$			829.598i			1.52220i
$546$	24.2128	+	177.377i	0.0443458	+	0.324867i
$547$	498.193			0.910773			0.455386	−	0.890294i	$-0.349501\pi$
$547$	498.193			0.910773			0.455386	+	0.890294i	$0.349501\pi$
$548$			284.188i			0.518592i
$549$	−803.312	+	223.476i	−1.46323	+	0.407060i
$550$	6.77117			0.0123112
$551$		−	802.053i		−	1.45563i
$552$	40.3201	−	5.50388i	0.0730436	−	0.00997080i
$553$	−97.4227			−0.176171
$554$		−	281.147i		−	0.507485i
$555$	−27.4901	−	201.386i	−0.0495317	−	0.362857i
$556$	353.547			0.635876
$557$		−	160.207i		−	0.287626i	−0.989605	−	0.143813i	$-0.954064\pi$
$557$		−	160.207i		−	0.287626i	0.989605	−	0.143813i	$-0.0459363\pi$
$558$	−3.55464	−	12.7776i	−0.00637032	−	0.0228989i
$559$	−588.817			−1.05334
$560$		−	127.620i		−	0.227892i
$561$	−14.0993	+	1.92462i	−0.0251324	+	0.00343070i
$562$	481.823			0.857335
$563$		−	96.9209i		−	0.172151i	−0.996289	−	0.0860754i	$-0.972567\pi$
$563$		−	96.9209i		−	0.172151i	0.996289	−	0.0860754i	$-0.0274326\pi$
$564$	−62.3443	−	456.719i	−0.110540	−	0.809785i
$565$	−1392.32			−2.46429
$566$			58.5923i			0.103520i
$567$	350.069	−	211.112i	0.617406	−	0.372332i
$568$	203.120			0.357606
$569$		−	186.466i		−	0.327708i	−0.986485	−	0.163854i	$-0.947607\pi$
$569$		−	186.466i		−	0.327708i	0.986485	−	0.163854i	$-0.0523926\pi$
$570$	−779.574	+	106.416i	−1.36767	+	0.186694i
$571$	−10.0343			−0.0175732			−0.00878660	−	0.999961i	$-0.502797\pi$
$571$	−10.0343			−0.0175732			−0.00878660	+	0.999961i	$0.502797\pi$
$572$		−	5.35042i		−	0.00935389i
$573$	−80.2095	−	587.595i	−0.139982	−	1.02547i
$574$	319.774			0.557098
$575$		−	71.7629i		−	0.124805i
$576$	−69.3659	+	19.2971i	−0.120427	+	0.0335019i
$577$	−563.352			−0.976347			−0.488173	−	0.872747i	$-0.662337\pi$
$577$	−563.352			−0.976347			−0.488173	+	0.872747i	$0.662337\pi$
$578$			97.9233i			0.169418i
$579$	−507.582	+	69.2874i	−0.876653	+	0.119667i
$580$	−345.675			−0.595991
$581$			667.824i			1.14944i
$582$	33.6928	+	246.825i	0.0578914	+	0.424098i
$583$	5.28677			0.00906822
$584$		−	363.014i		−	0.621599i
$585$	−127.491	−	458.283i	−0.217934	−	0.783389i
$586$	−44.5079			−0.0759521
$587$			220.947i			0.376400i	0.982131	+	0.188200i	$0.0602653\pi$
$587$			220.947i			0.376400i	−0.982131	+	0.188200i	$0.939735\pi$
$588$	139.875	−	19.0937i	0.237883	−	0.0324722i
$589$	30.5687			0.0518992
$590$		−	716.909i		−	1.21510i
$591$	−16.4670	−	120.633i	−0.0278629	−	0.204116i
$592$	42.8691			0.0724140
$593$			250.637i			0.422659i	0.977415	+	0.211329i	$0.0677793\pi$
$593$			250.637i			0.422659i	−0.977415	+	0.211329i	$0.932221\pi$
$594$	−11.2197	+	4.83646i	−0.0188884	+	0.00814219i
$595$	472.965			0.794900
$596$			302.670i			0.507835i
$597$	499.464	−	68.1792i	0.836623	−	0.114203i
$598$	−56.7054			−0.0948251
$599$			511.586i			0.854067i	0.904236	+	0.427033i	$0.140441\pi$
$599$			511.586i			0.854067i	−0.904236	+	0.427033i	$0.859559\pi$
$600$	17.1728	+	125.804i	0.0286213	+	0.209673i
$601$	−1015.45			−1.68960			−0.844801	−	0.535080i	$-0.820281\pi$
$601$	−1015.45			−1.68960			−0.844801	+	0.535080i	$0.820281\pi$
$602$		−	502.660i		−	0.834984i
$603$	387.344	−	107.756i	0.642361	−	0.178701i
$604$	−564.826			−0.935142
$605$		−	764.276i		−	1.26327i
$606$	−366.944	+	50.0896i	−0.605517	+	0.0826560i
$607$	−303.401			−0.499837			−0.249919	−	0.968267i	$-0.580404\pi$
$607$	−303.401			−0.499837			−0.249919	+	0.968267i	$0.580404\pi$
$608$		−	165.948i		−	0.272941i
$609$	55.9874	+	410.150i	0.0919333	+	0.673480i
$610$	−828.277			−1.35783
$611$			642.321i			1.05126i
$612$	−71.5162	−	257.074i	−0.116857	−	0.420055i
$613$	484.158			0.789818			0.394909	−	0.918720i	$-0.370776\pi$
$613$	484.158			0.789818			0.394909	+	0.918720i	$0.370776\pi$
$614$		−	23.7924i		−	0.0387498i
$615$	−841.876	+	114.920i	−1.36890	+	0.186862i
$616$	4.56754			0.00741484
$617$		−	961.403i		−	1.55819i	−0.626906	−	0.779095i	$-0.715679\pi$
$617$		−	961.403i		−	1.55819i	0.626906	−	0.779095i	$-0.284321\pi$
$618$	29.7418	+	217.881i	0.0481259	+	0.352559i
$619$	−294.258			−0.475377			−0.237688	−	0.971341i	$-0.576390\pi$
$619$	−294.258			−0.475377			−0.237688	+	0.971341i	$0.576390\pi$
$620$		−	13.1747i		−	0.0212495i
$621$	51.2583	+	118.910i	0.0825415	+	0.191481i
$622$	−652.190			−1.04854
$623$			285.692i			0.458574i
$624$	99.4072	−	13.5696i	0.159306	−	0.0217461i
$625$	−775.181			−1.24029
$626$		−	194.397i		−	0.310538i
$627$	−3.80865	−	27.9012i	−0.00607440	−	0.0444995i
$628$	−162.317			−0.258466
$629$			158.875i			0.252584i
$630$	391.226	−	108.837i	0.620994	−	0.172756i
$631$	168.568			0.267144			0.133572	−	0.991039i	$-0.457355\pi$
$631$	168.568			0.267144			0.133572	+	0.991039i	$0.457355\pi$
$632$			54.5984i			0.0863899i
$633$	112.440	−	15.3486i	0.177630	−	0.0242474i
$634$	496.383			0.782938
$635$			864.650i			1.36165i
$636$	13.4081	+	98.2246i	0.0210820	+	0.154441i
$637$	−196.718			−0.308820
$638$		−	12.3718i		−	0.0193915i
$639$	173.225	+	622.679i	0.271088	+	0.974459i
$640$	−71.5216			−0.111753
$641$			906.697i			1.41450i	0.706961	+	0.707252i	$0.250065\pi$
$641$			906.697i			1.41450i	−0.706961	+	0.707252i	$0.749935\pi$
$642$	−189.682	+	25.8925i	−0.295455	+	0.0403310i
$643$	−1215.31			−1.89006			−0.945030	−	0.326983i	$-0.893968\pi$
$643$	−1215.31			−1.89006			−0.945030	+	0.326983i	$0.893968\pi$
$644$		−	48.4082i		−	0.0751680i
$645$	180.646	+	1323.36i	0.280071	+	2.05173i
$646$	615.014			0.952034
$647$		−	483.987i		−	0.748048i	−0.927419	−	0.374024i	$-0.877978\pi$
$647$		−	483.987i		−	0.748048i	0.927419	−	0.374024i	$-0.122022\pi$
$648$	−118.313	−	196.189i	−0.182582	−	0.302760i
$649$	25.6584			0.0395353
$650$		−	176.928i		−	0.272197i
$651$	−15.6320	+	2.13385i	−0.0240123	+	0.00327780i
$652$	32.3316			0.0495884
$653$		−	227.515i		−	0.348415i	−0.984709	−	0.174207i	$-0.944264\pi$
$653$		−	227.515i		−	0.348415i	0.984709	−	0.174207i	$-0.0557363\pi$
$654$	−75.3028	−	551.649i	−0.115142	−	0.843500i
$655$	671.850			1.02573
$656$		−	179.211i		−	0.273187i
$657$	1112.84	−	309.585i	1.69382	−	0.471211i
$658$	−548.336			−0.833337
$659$			689.384i			1.04611i	0.852300	+	0.523053i	$0.175207\pi$
$659$			689.384i			1.04611i	−0.852300	+	0.523053i	$0.824793\pi$
$660$	−12.0251	+	1.64148i	−0.0182198	+	0.00248709i
$661$	92.8476			0.140465			0.0702327	−	0.997531i	$-0.477626\pi$
$661$	92.8476			0.140465			0.0702327	+	0.997531i	$0.477626\pi$
$662$			161.366i			0.243755i
$663$	50.2895	+	368.409i	0.0758515	+	0.555669i
$664$	374.267			0.563656
$665$			935.956i			1.40745i
$666$	36.5596	+	131.418i	0.0548943	+	0.197324i
$667$	−131.120			−0.196582
$668$		−	397.173i		−	0.594570i
$669$	−261.294	+	35.6678i	−0.390574	+	0.0533152i
$670$	399.382			0.596092
$671$		−	29.6443i		−	0.0441793i
$672$	11.5840	+	84.8618i	0.0172382	+	0.126282i
$673$	486.070			0.722244			0.361122	−	0.932519i	$-0.382394\pi$
$673$	486.070			0.722244			0.361122	+	0.932519i	$0.382394\pi$
$674$		−	626.069i		−	0.928886i
$675$	−371.014	+	159.932i	−0.549651	+	0.236937i
$676$	198.196			0.293189
$677$			73.2436i			0.108188i	0.998536	+	0.0540942i	$0.0172271\pi$
$677$			73.2436i			0.108188i	−0.998536	+	0.0540942i	$0.982773\pi$
$678$	925.839	−	126.381i	1.36554	−	0.186403i
$679$	296.338			0.436432
$680$		−	265.063i		−	0.389799i
$681$	−172.886	−	1266.52i	−0.253871	−	1.85979i
$682$	0.471527			0.000691388
$683$			452.614i			0.662686i	0.943510	+	0.331343i	$0.107502\pi$
$683$			452.614i			0.662686i	−0.943510	+	0.331343i	$0.892498\pi$
$684$	508.726	−	141.524i	0.743751	−	0.206907i
$685$	−898.273			−1.31135
$686$		−	517.667i		−	0.754616i
$687$	78.0394	−	10.6528i	0.113595	−	0.0155062i
$688$	−281.705			−0.409455
$689$		−	138.141i		−	0.200495i
$690$	17.3969	+	127.445i	0.0252129	+	0.184703i
$691$	−765.658			−1.10804			−0.554022	−	0.832502i	$-0.686908\pi$
$691$	−765.658			−1.10804			−0.554022	+	0.832502i	$0.686908\pi$
$692$			381.324i			0.551047i
$693$	3.89529	+	14.0021i	0.00562091	+	0.0202051i
$694$	146.982			0.211790
$695$			1117.51i			1.60792i
$696$	229.859	−	31.3769i	0.330258	−	0.0450818i
$697$	664.165			0.952890
$698$		−	231.843i		−	0.332153i
$699$	−6.62990	−	48.5690i	−0.00948483	−	0.0694835i
$700$	151.040			0.215771
$701$			90.8198i			0.129558i	0.997900	+	0.0647788i	$0.0206342\pi$
$701$			90.8198i			0.129558i	−0.997900	+	0.0647788i	$0.979366\pi$
$702$	126.375	+	293.167i	0.180021	+	0.417617i
$703$	−314.400			−0.447226
$704$		−	2.55978i		−	0.00363605i
$705$	1443.61	−	197.060i	2.04768	−	0.279518i
$706$	−870.842			−1.23349
$707$			440.552i			0.623128i
$708$	65.0740	+	476.715i	0.0919124	+	0.673327i
$709$	539.411			0.760806			0.380403	−	0.924821i	$-0.375785\pi$
$709$	539.411			0.760806			0.380403	+	0.924821i	$0.375785\pi$
$710$			642.031i			0.904269i
$711$	−167.375	+	46.5626i	−0.235408	+	0.0654889i
$712$	160.110			0.224873
$713$		−	4.99738i		−	0.00700895i
$714$	−314.503	+	42.9311i	−0.440480	+	0.0601276i
$715$	16.9118			0.0236529
$716$			275.093i			0.384207i
$717$	−144.037	−	1055.18i	−0.200889	−	1.47166i
$718$	−787.539			−1.09685
$719$		−	922.285i		−	1.28273i	−0.767235	−	0.641367i	$-0.778368\pi$
$719$		−	922.285i		−	1.28273i	0.767235	−	0.641367i	$-0.221632\pi$
$720$	−60.9951	−	219.254i	−0.0847154	−	0.304520i
$721$	261.588			0.362812
$722$			706.526i			0.978568i
$723$	102.014	−	13.9254i	0.141098	−	0.0192605i
$724$	−458.705			−0.633570
$725$		−	409.111i		−	0.564291i
$726$	69.3734	+	508.212i	0.0955556	+	0.700017i
$727$	109.039			0.149984			0.0749922	−	0.997184i	$-0.476107\pi$
$727$	109.039			0.149984			0.0749922	+	0.997184i	$0.476107\pi$
$728$		−	119.348i		−	0.163940i
$729$	500.529	−	530.011i	0.686597	−	0.727038i
$730$	1147.43			1.57182
$731$		−	1044.02i		−	1.42820i
$732$	550.771	−	75.1828i	0.752419	−	0.102709i
$733$	1006.54			1.37318			0.686589	−	0.727046i	$-0.259107\pi$
$733$	1006.54			1.37318			0.686589	+	0.727046i	$0.259107\pi$
$734$		−	576.051i		−	0.784811i
$735$	60.3520	+	442.124i	0.0821116	+	0.601529i
$736$	−27.1293			−0.0368605
$737$			14.2940i			0.0193948i
$738$	549.382	−	152.834i	0.744420	−	0.207093i
$739$	1275.23			1.72562			0.862811	−	0.505527i	$-0.168702\pi$
$739$	1275.23			1.72562			0.862811	+	0.505527i	$0.168702\pi$
$740$			135.502i			0.183111i
$741$	−729.047	+	99.5185i	−0.983870	+	0.134303i
$742$	117.928			0.158933
$743$			885.606i			1.19193i	0.803009	+	0.595967i	$0.203231\pi$
$743$			885.606i			1.19193i	−0.803009	+	0.595967i	$0.796769\pi$
$744$	1.19587	+	8.76063i	0.00160735	+	0.0117750i
$745$	−956.690			−1.28415
$746$			73.8019i			0.0989302i
$747$	319.183	+	1147.34i	0.427286	+	1.53593i
$748$	9.48669			0.0126827
$749$			227.732i			0.304048i
$750$	266.709	−	36.4071i	0.355612	−	0.0485427i
$751$	287.477			0.382792			0.191396	−	0.981513i	$-0.438698\pi$
$751$	287.477			0.382792			0.191396	+	0.981513i	$0.438698\pi$
$752$			307.303i			0.408648i
$753$	−103.194	−	755.975i	−0.137044	−	1.00395i
$754$	−323.270			−0.428740
$755$		−	1785.32i		−	2.36467i
$756$	−250.270	+	107.883i	−0.331045	+	0.142703i
$757$	−325.129			−0.429497			−0.214749	−	0.976669i	$-0.568893\pi$
$757$	−325.129			−0.429497			−0.214749	+	0.976669i	$0.568893\pi$
$758$		−	661.016i		−	0.872053i
$759$	−4.56130	+	0.622640i	−0.00600962	+	0.000820342i
$760$	524.536			0.690179
$761$			1170.46i			1.53806i	0.639215	+	0.769028i	$0.279259\pi$
$761$			1170.46i			1.53806i	−0.639215	+	0.769028i	$0.720741\pi$
$762$	−78.4844	−	574.957i	−0.102998	−	0.754537i
$763$	−662.309			−0.868033
$764$			395.363i			0.517490i
$765$	812.569	−	226.051i	1.06218	−	0.295492i
$766$	−440.692			−0.575316
$767$		−	670.444i		−	0.874112i
$768$	47.5589	−	6.49203i	0.0619257	−	0.00845316i
$769$	−277.812			−0.361264			−0.180632	−	0.983551i	$-0.557814\pi$
$769$	−277.812			−0.361264			−0.180632	+	0.983551i	$0.557814\pi$
$770$			14.4373i			0.0187497i
$771$	−135.331	−	991.397i	−0.175526	−	1.28586i
$772$	341.526			0.442392
$773$		−	255.927i		−	0.331083i	−0.986203	−	0.165542i	$-0.947063\pi$
$773$		−	255.927i		−	0.331083i	0.986203	−	0.165542i	$-0.0529372\pi$
$774$	−240.244	−	863.586i	−0.310392	−	1.11574i
$775$	15.5924			0.0201193
$776$		−	166.076i		−	0.214015i
$777$	160.776	−	21.9467i	0.206919	−	0.0282454i
$778$	53.2863			0.0684913
$779$			1314.32i			1.68719i
$780$	42.8912	+	314.210i	0.0549887	+	0.402833i
$781$	−22.9785			−0.0294219
$782$		−	100.543i		−	0.128571i
$783$	292.217	+	677.891i	0.373202	+	0.865761i
$784$	−94.1151			−0.120045
$785$		−	513.056i		−	0.653575i
$786$	−446.753	+	60.9839i	−0.568388	+	0.0775877i
$787$	760.871			0.966800			0.483400	−	0.875400i	$-0.339402\pi$
$787$	760.871			0.966800			0.483400	+	0.875400i	$0.339402\pi$
$788$			81.1677i			0.103005i
$789$	35.9656	+	263.475i	0.0455838	+	0.333935i
$790$	−172.577			−0.218452
$791$		−	1111.56i		−	1.40526i
$792$	7.84718	−	2.18303i	0.00990805	−	0.00275635i
$793$	−774.594			−0.976789
$794$			428.105i			0.539175i
$795$	−310.472	+	42.3809i	−0.390531	+	0.0533093i
$796$	−336.064			−0.422191
$797$			693.646i			0.870322i	0.900353	+	0.435161i	$0.143309\pi$
$797$			693.646i			0.870322i	−0.900353	+	0.435161i	$0.856691\pi$
$798$	−84.9568	−	622.372i	−0.106462	−	0.779915i
$799$	−1138.88			−1.42538
$800$		−	84.6469i		−	0.105809i
$801$	136.545	+	490.827i	0.170468	+	0.612768i
$802$	−1038.94			−1.29543
$803$			41.0668i			0.0511417i
$804$	−265.572	+	36.2519i	−0.330314	+	0.0450894i
$805$	153.010			0.190075
$806$		−	12.3208i		−	0.0152863i
$807$	136.400	+	999.230i	0.169021	+	1.23820i
$808$	246.898			0.305566
$809$			382.730i			0.473090i	0.971620	+	0.236545i	$0.0760151\pi$
$809$			382.730i			0.473090i	−0.971620	+	0.236545i	$0.923985\pi$
$810$	620.121	−	373.969i	0.765581	−	0.461690i
$811$	−1153.93			−1.42284			−0.711422	−	0.702765i	$-0.751948\pi$
$811$	−1153.93			−1.42284			−0.711422	+	0.702765i	$0.751948\pi$
$812$		−	275.969i		−	0.339863i
$813$	505.481	−	69.0007i	0.621748	−	0.0848717i
$814$	−4.84967			−0.00595782
$815$			102.195i			0.125393i
$816$	24.0598	+	176.256i	0.0294851	+	0.216000i
$817$	2066.01			2.52878
$818$			877.916i			1.07325i
$819$	365.869	−	101.782i	0.446727	−	0.124276i
$820$	566.456			0.690800
$821$		−	670.688i		−	0.816916i	−0.912777	−	0.408458i	$-0.866067\pi$
$821$		−	670.688i		−	0.816916i	0.912777	−	0.408458i	$-0.133933\pi$
$822$	597.315	−	81.5364i	0.726661	−	0.0991927i
$823$	−52.2109			−0.0634397			−0.0317199	−	0.999497i	$-0.510098\pi$
$823$	−52.2109			−0.0634397			−0.0317199	+	0.999497i	$0.510098\pi$
$824$		−	146.601i		−	0.177914i
$825$	−1.94271	−	14.2318i	−0.00235481	−	0.0172507i
$826$	572.344			0.692910
$827$			251.359i			0.303941i	0.988385	+	0.151970i	$0.0485618\pi$
$827$			251.359i			0.303941i	−0.988385	+	0.151970i	$0.951438\pi$
$828$	−23.1364	−	83.1667i	−0.0279426	−	0.100443i
$829$	139.265			0.167992			0.0839959	−	0.996466i	$-0.473232\pi$
$829$	139.265			0.167992			0.0839959	+	0.996466i	$0.473232\pi$
$830$			1183.00i			1.42530i
$831$	−590.922	+	80.6638i	−0.711098	+	0.0970683i
$832$	−66.8860			−0.0803919
$833$		−	348.796i		−	0.418723i
$834$	−101.436	−	743.095i	−0.121626	−	0.891002i
$835$	1255.40			1.50347
$836$			18.7733i			0.0224561i
$837$	−25.8364	+	11.1373i	−0.0308679	+	0.0133062i
$838$	−312.379			−0.372768
$839$		−	13.9621i		−	0.0166413i	−0.999965	−	0.00832067i	$-0.997351\pi$
$839$		−	13.9621i		−	0.0166413i	0.999965	−	0.00832067i	$-0.00264858\pi$
$840$	−268.234	+	36.6153i	−0.319327	+	0.0435896i
$841$	93.5017			0.111179
$842$			804.270i			0.955189i
$843$	−138.240	−	1012.71i	−0.163985	−	1.20131i
$844$	−75.6551			−0.0896388
$845$			626.464i			0.741378i
$846$	−942.058	+	262.074i	−1.11354	+	0.309780i
$847$	610.158			0.720376
$848$		−	66.0903i		−	0.0779367i
$849$	123.151	−	16.8107i	0.145054	−	0.0198006i
$850$	313.706			0.369066
$851$			51.3982i			0.0603974i
$852$	−58.2772	−	426.924i	−0.0684005	−	0.501085i
$853$	−650.580			−0.762696			−0.381348	−	0.924432i	$-0.624540\pi$
$853$	−650.580			−0.762696			−0.381348	+	0.924432i	$0.624540\pi$
$854$		−	661.254i		−	0.774302i
$855$	447.335	+	1608.00i	0.523199	+	1.88070i
$856$	127.627			0.149097
$857$		−	1384.33i		−	1.61532i	−0.589651	−	0.807658i	$-0.700735\pi$
$857$		−	1384.33i		−	1.61532i	0.589651	−	0.807658i	$-0.299265\pi$
$858$	−11.2457	+	1.53509i	−0.0131068	+	0.00178915i
$859$	−146.175			−0.170168			−0.0850842	−	0.996374i	$-0.527116\pi$
$859$	−146.175			−0.170168			−0.0850842	+	0.996374i	$0.527116\pi$
$860$		−	890.424i		−	1.03538i
$861$	−91.7463	−	672.111i	−0.106558	−	0.780616i
$862$	−563.752			−0.654005
$863$			482.460i			0.559050i	0.960138	+	0.279525i	$0.0901771\pi$
$863$			482.460i			0.559050i	−0.960138	+	0.279525i	$0.909823\pi$
$864$	60.4610	+	140.259i	0.0699780	+	0.162336i
$865$	−1205.30			−1.39342
$866$		−	243.443i		−	0.281112i
$867$	205.818	−	28.0952i	0.237391	−	0.0324050i
$868$	10.5180			0.0121175
$869$		−	6.17658i		−	0.00710769i
$870$	99.1774	+	726.549i	0.113997	+	0.835113i
$871$	373.496			0.428813
$872$			371.177i			0.425661i
$873$	509.117	−	141.633i	0.583181	−	0.162237i
$874$	198.965			0.227649
$875$		−	320.210i		−	0.365955i
$876$	−762.992	+	104.152i	−0.870996	+	0.118895i
$877$	−126.903			−0.144701			−0.0723505	−	0.997379i	$-0.523050\pi$
$877$	−126.903			−0.144701			−0.0723505	+	0.997379i	$0.523050\pi$
$878$			309.936i			0.353003i
$879$	12.7698	+	93.5481i	0.0145276	+	0.106426i
$880$	8.09105			0.00919438
$881$			1232.23i			1.39867i	0.714795	+	0.699334i	$0.246520\pi$
$881$			1232.23i			1.39867i	−0.714795	+	0.699334i	$0.753480\pi$
$882$	−80.2633	−	288.516i	−0.0910014	−	0.327116i
$883$	476.337			0.539453			0.269726	−	0.962937i	$-0.413067\pi$
$883$	476.337			0.539453			0.269726	+	0.962937i	$0.413067\pi$
$884$		−	247.883i		−	0.280411i
$885$	−1506.82	+	205.688i	−1.70262	+	0.232416i
$886$	319.871			0.361028
$887$		−	13.0701i		−	0.0147352i	−0.999973	−	0.00736761i	$-0.997655\pi$
$887$		−	13.0701i		−	0.0147352i	0.999973	−	0.00736761i	$-0.00234520\pi$
$888$	−12.2996	−	90.1034i	−0.0138508	−	0.101468i
$889$	−690.292			−0.776482
$890$			506.081i			0.568631i
$891$	13.3845	+	22.1943i	0.0150218	+	0.0249094i
$892$	175.811			0.197098
$893$		−	2253.74i		−	2.52379i
$894$	636.159	−	86.8388i	0.711588	−	0.0971352i
$895$	−869.523			−0.971534
$896$		−	57.0992i		−	0.0637268i
$897$	16.2693	+	119.185i	0.0181375	+	0.132871i
$898$	430.046			0.478893
$899$		−	28.4894i		−	0.0316901i
$900$	259.491	−	72.1886i	0.288323	−	0.0802095i
$901$	244.935			0.271847
$902$			20.2736i			0.0224763i
$903$	−1056.51	+	144.218i	−1.17000	+	0.159710i
$904$	−622.950			−0.689104
$905$		−	1449.89i		−	1.60209i
$906$	162.054	+	1187.17i	0.178867	+	1.31034i
$907$	−11.9995			−0.0132298			−0.00661492	−	0.999978i	$-0.502106\pi$
$907$	−11.9995			−0.0132298			−0.00661492	+	0.999978i	$0.502106\pi$
$908$			852.177i			0.938520i
$909$	210.559	+	756.881i	0.231638	+	0.832653i
$910$	377.240			0.414549
$911$		−	243.002i		−	0.266742i	−0.991066	−	0.133371i	$-0.957420\pi$
$911$		−	243.002i		−	0.266742i	0.991066	−	0.133371i	$-0.0425801\pi$
$912$	−348.795	+	47.6122i	−0.382451	+	0.0522064i
$913$	−42.3399			−0.0463745
$914$			331.599i			0.362799i
$915$	237.641	+	1740.90i	0.259717	+	1.90262i
$916$	−52.5088			−0.0573240
$917$			536.371i			0.584919i
$918$	−519.806	+	224.072i	−0.566238	+	0.244087i
$919$	−1539.65			−1.67536			−0.837679	−	0.546163i	$-0.816088\pi$
$919$	−1539.65			−1.67536			−0.837679	+	0.546163i	$0.816088\pi$
$920$		−	85.7514i		−	0.0932080i
$921$	−50.0075	+	6.82626i	−0.0542969	+	0.00741179i
$922$	654.412			0.709774
$923$			600.419i			0.650508i
$924$	−1.31047	−	9.60019i	−0.00141826	−	0.0103898i
$925$	−160.369			−0.173372
$926$		−	963.432i		−	1.04042i
$927$	449.416	−	125.024i	0.484806	−	0.134870i
$928$	−154.661			−0.166660
$929$		−	1484.86i		−	1.59835i	−0.601101	−	0.799173i	$-0.705271\pi$
$929$		−	1484.86i		−	1.59835i	0.601101	−	0.799173i	$-0.294729\pi$
$930$	−27.6909	+	3.77995i	−0.0297752	+	0.00406446i
$931$	690.236			0.741392
$932$			32.6796i			0.0350639i
$933$	187.119	+	1370.79i	0.200557	+	1.46923i
$934$	999.796			1.07045
$935$			29.9859i			0.0320705i
$936$	−57.0418	−	205.044i	−0.0609420	−	0.219064i
$937$	−701.970			−0.749167			−0.374584	−	0.927193i	$-0.622214\pi$
$937$	−701.970			−0.749167			−0.374584	+	0.927193i	$0.622214\pi$
$938$			318.846i			0.339921i
$939$	−408.589	+	55.7744i	−0.435132	+	0.0593977i
$940$	−971.335			−1.03333
$941$			430.721i			0.457727i	0.973459	+	0.228863i	$0.0735009\pi$
$941$			430.721i			0.457727i	−0.973459	+	0.228863i	$0.926499\pi$
$942$	46.5702	+	341.161i	0.0494376	+	0.362167i
$943$	214.866			0.227854
$944$		−	320.758i		−	0.339786i
$945$	−341.002	−	791.064i	−0.360849	−	0.837105i
$946$	31.8686			0.0336877
$947$		−	831.353i		−	0.877881i	−0.898516	−	0.438940i	$-0.855354\pi$
$947$		−	831.353i		−	0.877881i	0.898516	−	0.438940i	$-0.144646\pi$
$948$	114.757	−	15.6648i	0.121051	−	0.0165241i
$949$	1073.06			1.13073
$950$			620.796i			0.653470i
$951$	−142.417	−	1043.31i	−0.149755	−	1.09707i
$952$	211.613			0.222282
$953$		−	277.997i		−	0.291707i	−0.989306	−	0.145853i	$-0.953407\pi$
$953$		−	277.997i		−	0.291707i	0.989306	−	0.145853i	$-0.0465928\pi$
$954$	202.604	−	56.3632i	0.212373	−	0.0590809i
$955$	−1249.68			−1.30856
$956$			709.979i			0.742655i
$957$	−26.0034	+	3.54959i	−0.0271718	+	0.00370908i
$958$	−1014.10			−1.05856
$959$		−	717.135i		−	0.747795i
$960$	20.5202	+	150.326i	0.0213753	+	0.156590i
$961$	−959.914			−0.998870
$962$			126.720i			0.131725i
$963$	108.843	+	391.250i	0.113025	+	0.406283i
$964$	−68.6399			−0.0712032
$965$			1079.51i			1.11866i
$966$	−101.746	+	13.8888i	−0.105327	+	0.0143776i
$967$	63.8059			0.0659834			0.0329917	−	0.999456i	$-0.489497\pi$
$967$	63.8059			0.0659834			0.0329917	+	0.999456i	$0.489497\pi$
$968$		−	341.950i		−	0.353254i
$969$	−176.454	−	1292.65i	−0.182099	−	1.33401i
$970$	524.939			0.541175
$971$			235.862i			0.242906i	0.992597	+	0.121453i	$0.0387554\pi$
$971$			235.862i			0.242906i	−0.992597	+	0.121453i	$0.961245\pi$
$972$	−378.410	+	304.962i	−0.389310	+	0.313747i
$973$	−892.159			−0.916916
$974$			823.711i			0.845699i
$975$	−371.872	+	50.7623i	−0.381407	+	0.0520639i
$976$	−370.585			−0.379698
$977$		−	609.277i		−	0.623620i	−0.950144	−	0.311810i	$-0.899065\pi$
$977$		−	609.277i		−	0.623620i	0.950144	−	0.311810i	$-0.100935\pi$
$978$	−9.27626	−	67.9556i	−0.00948493	−	0.0694842i
$979$	−18.1128			−0.0185013
$980$		−	297.483i		−	0.303554i
$981$	−1137.87	+	316.547i	−1.15990	+	0.322678i
$982$	421.078			0.428797
$983$		−	493.432i		−	0.501965i	−0.967992	−	0.250983i	$-0.919246\pi$
$983$		−	493.432i		−	0.501965i	0.967992	−	0.250983i	$-0.0807537\pi$
$984$	−376.670	+	51.4172i	−0.382795	+	0.0522533i
$985$	−256.558			−0.260465
$986$		−	573.182i		−	0.581320i
$987$	157.323	+	1152.51i	0.159395	+	1.16769i
$988$	490.539			0.496497
$989$		−	337.753i		−	0.341509i
$990$	6.90021	+	24.8037i	0.00696991	+	0.0250542i
$991$	−1179.25			−1.18996			−0.594980	−	0.803741i	$-0.702840\pi$
$991$	−1179.25			−1.18996			−0.594980	+	0.803741i	$0.702840\pi$
$992$		−	5.89459i		−	0.00594212i
$993$	339.163	−	46.2974i	0.341554	−	0.0466237i
$994$	−512.565			−0.515659
$995$		−	1062.24i		−	1.06758i
$996$	−107.381	−	786.646i	−0.107812	−	0.789805i
$997$	1313.36			1.31732			0.658658	−	0.752442i	$-0.271124\pi$
$997$	1313.36			1.31732			0.658658	+	0.752442i	$0.271124\pi$
$998$		−	718.470i		−	0.719910i
$999$	265.729	−	114.547i	0.265995	−	0.114662i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.3.c.a.47.16	yes	16
3.2	odd	2	inner	138.3.c.a.47.8	✓	16
4.3	odd	2		1104.3.g.c.737.2		16
12.11	even	2		1104.3.g.c.737.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.c.a.47.8	✓	16	3.2	odd	2	inner
138.3.c.a.47.16	yes	16	1.1	even	1	trivial
1104.3.g.c.737.1		16	12.11	even	2
1104.3.g.c.737.2		16	4.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	138.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} +(2.97243 - 0.405752i) q^{3} -2.00000 q^{4} -6.32168i q^{5} +(0.573819 + 4.20366i) q^{6} +5.04690 q^{7} -2.82843i q^{8} +(8.67073 - 2.41214i) q^{9} +O(q^{10})\)	\(q+1.41421i q^{2} +(2.97243 - 0.405752i) q^{3} -2.00000 q^{4} -6.32168i q^{5} +(0.573819 + 4.20366i) q^{6} +5.04690 q^{7} -2.82843i q^{8} +(8.67073 - 2.41214i) q^{9} +8.94020 q^{10} +0.319973i q^{11} +(-5.94487 + 0.811503i) q^{12} +8.36075 q^{13} +7.13740i q^{14} +(-2.56503 - 18.7908i) q^{15} +4.00000 q^{16} +14.8242i q^{17} +(3.41128 + 12.2623i) q^{18} -29.3358 q^{19} +12.6434i q^{20} +(15.0016 - 2.04779i) q^{21} -0.452510 q^{22} +4.79583i q^{23} +(-1.14764 - 8.40731i) q^{24} -14.9636 q^{25} +11.8239i q^{26} +(24.7944 - 10.6881i) q^{27} -10.0938 q^{28} +27.3404i q^{29} +(26.5742 - 3.62750i) q^{30} -1.04203 q^{31} +5.65685i q^{32} +(0.129829 + 0.951098i) q^{33} -20.9646 q^{34} -31.9049i q^{35} +(-17.3415 + 4.82428i) q^{36} +10.7173 q^{37} -41.4871i q^{38} +(24.8518 - 3.39239i) q^{39} -17.8804 q^{40} -44.8026i q^{41} +(2.89601 + 21.2154i) q^{42} -70.4263 q^{43} -0.639945i q^{44} +(-15.2488 - 54.8136i) q^{45} -6.78233 q^{46} +76.8257i q^{47} +(11.8897 - 1.62301i) q^{48} -23.5288 q^{49} -21.1617i q^{50} +(6.01495 + 44.0640i) q^{51} -16.7215 q^{52} -16.5226i q^{53} +(15.1152 + 35.0646i) q^{54} +2.02276 q^{55} -14.2748i q^{56} +(-87.1988 + 11.9030i) q^{57} -38.6652 q^{58} -80.1894i q^{59} +(5.13006 + 37.5815i) q^{60} -92.6464 q^{61} -1.47365i q^{62} +(43.7603 - 12.1738i) q^{63} -8.00000 q^{64} -52.8540i q^{65} +(-1.34506 + 0.183606i) q^{66} +44.6725 q^{67} -29.6485i q^{68} +(1.94592 + 14.2553i) q^{69} +45.1203 q^{70} +71.8139i q^{71} +(-6.82256 - 24.5245i) q^{72} +128.345 q^{73} +15.1565i q^{74} +(-44.4783 + 6.07150i) q^{75} +58.6716 q^{76} +1.61487i q^{77} +(4.79756 + 35.1457i) q^{78} -19.3035 q^{79} -25.2867i q^{80} +(69.3632 - 41.8300i) q^{81} +63.3605 q^{82} +132.324i q^{83} +(-30.0032 + 4.09558i) q^{84} +93.7140 q^{85} -99.5978i q^{86} +(11.0934 + 81.2676i) q^{87} +0.905019 q^{88} +56.6074i q^{89} +(77.5181 - 21.5650i) q^{90} +42.1959 q^{91} -9.59166i q^{92} +(-3.09735 + 0.422803i) q^{93} -108.648 q^{94} +185.451i q^{95} +(2.29528 + 16.8146i) q^{96} +58.7167 q^{97} -33.2747i q^{98} +(0.771819 + 2.77440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} - 4 q^{9} - 8 q^{12} - 8 q^{13} + 28 q^{15} + 64 q^{16} + 16 q^{18} + 40 q^{19} + 4 q^{21} + 16 q^{22} + 16 q^{24} - 192 q^{25} - 80 q^{27} - 24 q^{30} + 136 q^{31} - 84 q^{33} - 16 q^{34} + 8 q^{36} - 136 q^{37} + 156 q^{39} + 128 q^{42} + 72 q^{43} + 4 q^{45} + 16 q^{48} + 224 q^{49} - 4 q^{51} + 16 q^{52} - 176 q^{54} - 96 q^{55} - 160 q^{57} - 56 q^{60} + 48 q^{61} + 204 q^{63} - 128 q^{64} - 144 q^{66} - 304 q^{67} - 176 q^{70} - 32 q^{72} + 408 q^{73} + 68 q^{75} - 80 q^{76} + 328 q^{78} + 312 q^{79} + 164 q^{81} + 160 q^{82} - 8 q^{84} - 464 q^{85} - 268 q^{87} - 32 q^{88} + 32 q^{90} - 72 q^{91} - 108 q^{93} - 32 q^{96} + 168 q^{97} - 60 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 - 4 * q^9 - 8 * q^12 - 8 * q^13 + 28 * q^15 + 64 * q^16 + 16 * q^18 + 40 * q^19 + 4 * q^21 + 16 * q^22 + 16 * q^24 - 192 * q^25 - 80 * q^27 - 24 * q^30 + 136 * q^31 - 84 * q^33 - 16 * q^34 + 8 * q^36 - 136 * q^37 + 156 * q^39 + 128 * q^42 + 72 * q^43 + 4 * q^45 + 16 * q^48 + 224 * q^49 - 4 * q^51 + 16 * q^52 - 176 * q^54 - 96 * q^55 - 160 * q^57 - 56 * q^60 + 48 * q^61 + 204 * q^63 - 128 * q^64 - 144 * q^66 - 304 * q^67 - 176 * q^70 - 32 * q^72 + 408 * q^73 + 68 * q^75 - 80 * q^76 + 328 * q^78 + 312 * q^79 + 164 * q^81 + 160 * q^82 - 8 * q^84 - 464 * q^85 - 268 * q^87 - 32 * q^88 + 32 * q^90 - 72 * q^91 - 108 * q^93 - 32 * q^96 + 168 * q^97 - 60 * q^99

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