LMFDB - Embedded newform 138.3.c.a.47.7

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			47.7
Root			$2.42141 - 1.77110i$ of defining polynomial
Character	$\chi$	$=$	138.47
Dual form			138.3.c.a.47.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(2.42141 - 1.77110i) q^{3} -2.00000 q^{4} -4.98213i q^{5} +(-2.50471 - 3.42438i) q^{6} -12.5950 q^{7} +2.82843i q^{8} +(2.72641 - 8.57710i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(2.42141 - 1.77110i) q^{3} -2.00000 q^{4} -4.98213i q^{5} +(-2.50471 - 3.42438i) q^{6} -12.5950 q^{7} +2.82843i q^{8} +(2.72641 - 8.57710i) q^{9} -7.04580 q^{10} +3.76623i q^{11} +(-4.84281 + 3.54220i) q^{12} +21.0705 q^{13} +17.8120i q^{14} +(-8.82385 - 12.0638i) q^{15} +4.00000 q^{16} -18.3546i q^{17} +(-12.1299 - 3.85573i) q^{18} +1.71289 q^{19} +9.96426i q^{20} +(-30.4975 + 22.3069i) q^{21} +5.32625 q^{22} +4.79583i q^{23} +(5.00943 + 6.84877i) q^{24} +0.178363 q^{25} -29.7983i q^{26} +(-8.58916 - 25.5974i) q^{27} +25.1899 q^{28} +6.94964i q^{29} +(-17.0607 + 12.4788i) q^{30} +18.4158 q^{31} -5.65685i q^{32} +(6.67036 + 9.11956i) q^{33} -25.9573 q^{34} +62.7498i q^{35} +(-5.45282 + 17.1542i) q^{36} -20.5418 q^{37} -2.42240i q^{38} +(51.0203 - 37.3180i) q^{39} +14.0916 q^{40} -44.5482i q^{41} +(31.5468 + 43.1300i) q^{42} +72.9831 q^{43} -7.53245i q^{44} +(-42.7323 - 13.5833i) q^{45} +6.78233 q^{46} -12.3762i q^{47} +(9.68562 - 7.08440i) q^{48} +109.633 q^{49} -0.252244i q^{50} +(-32.5078 - 44.4438i) q^{51} -42.1411 q^{52} +86.0772i q^{53} +(-36.2002 + 12.1469i) q^{54} +18.7638 q^{55} -35.6239i q^{56} +(4.14761 - 3.03370i) q^{57} +9.82827 q^{58} +63.1522i q^{59} +(17.6477 + 24.1275i) q^{60} +18.8964 q^{61} -26.0439i q^{62} +(-34.3390 + 108.028i) q^{63} -8.00000 q^{64} -104.976i q^{65} +(12.8970 - 9.43332i) q^{66} -34.1330 q^{67} +36.7091i q^{68} +(8.49390 + 11.6127i) q^{69} +88.7416 q^{70} +132.300i q^{71} +(24.2597 + 7.71145i) q^{72} -42.0960 q^{73} +29.0505i q^{74} +(0.431890 - 0.315900i) q^{75} -3.42578 q^{76} -47.4355i q^{77} +(-52.7757 - 72.1537i) q^{78} -63.7892 q^{79} -19.9285i q^{80} +(-66.1334 - 46.7694i) q^{81} -63.0007 q^{82} -163.569i q^{83} +(60.9950 - 44.6139i) q^{84} -91.4448 q^{85} -103.214i q^{86} +(12.3085 + 16.8279i) q^{87} -10.6525 q^{88} -5.63612i q^{89} +(-19.2097 + 60.4325i) q^{90} -265.383 q^{91} -9.59166i q^{92} +(44.5922 - 32.6163i) q^{93} -17.5026 q^{94} -8.53385i q^{95} +(-10.0189 - 13.6975i) q^{96} +123.776 q^{97} -155.045i q^{98} +(32.3033 + 10.2683i) 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
$3$	2.42141	−	1.77110i	0.807135	−	0.590367i
$3$	2.42141	−	1.77110i	0.807135	−	0.590367i
$4$	−2.00000			−0.500000
$5$		−	4.98213i		−	0.996426i	−0.867055	−	0.498213i	$-0.833990\pi$
$5$		−	4.98213i		−	0.996426i	0.867055	−	0.498213i	$-0.166010\pi$
$6$	−2.50471	−	3.42438i	−0.417452	−	0.570731i
$7$	−12.5950			−1.79928			−0.899640	−	0.436632i	$-0.856171\pi$
$7$	−12.5950			−1.79928			−0.899640	+	0.436632i	$0.856171\pi$
$8$			2.82843i			0.353553i
$9$	2.72641	−	8.57710i	0.302934	−	0.953011i
$10$	−7.04580			−0.704580
$11$			3.76623i			0.342384i	0.985238	+	0.171192i	$0.0547619\pi$
$11$			3.76623i			0.342384i	−0.985238	+	0.171192i	$0.945238\pi$
$12$	−4.84281	+	3.54220i	−0.403568	+	0.295183i
$13$	21.0705			1.62081			0.810406	−	0.585869i	$-0.199247\pi$
$13$	21.0705			1.62081			0.810406	+	0.585869i	$0.199247\pi$
$14$			17.8120i			1.27228i
$15$	−8.82385	−	12.0638i	−0.588257	−	0.804251i
$16$	4.00000			0.250000
$17$		−	18.3546i		−	1.07968i	−0.841768	−	0.539840i	$-0.818485\pi$
$17$		−	18.3546i		−	1.07968i	0.841768	−	0.539840i	$-0.181515\pi$
$18$	−12.1299	−	3.85573i	−0.673881	−	0.214207i
$19$	1.71289			0.0901522			0.0450761	−	0.998984i	$-0.485647\pi$
$19$	1.71289			0.0901522			0.0450761	+	0.998984i	$0.485647\pi$
$20$			9.96426i			0.498213i
$21$	−30.4975	+	22.3069i	−1.45226	+	1.06224i
$22$	5.32625			0.242102
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	5.00943	+	6.84877i	0.208726	+	0.285365i
$25$	0.178363			0.00713454
$26$		−	29.7983i		−	1.14609i
$27$	−8.58916	−	25.5974i	−0.318117	−	0.948051i
$28$	25.1899			0.899640
$29$			6.94964i			0.239643i	0.992795	+	0.119821i	$0.0382322\pi$
$29$			6.94964i			0.239643i	−0.992795	+	0.119821i	$0.961768\pi$
$30$	−17.0607	+	12.4788i	−0.568691	+	0.415960i
$31$	18.4158			0.594059			0.297030	−	0.954868i	$-0.404004\pi$
$31$	18.4158			0.594059			0.297030	+	0.954868i	$0.404004\pi$
$32$		−	5.65685i		−	0.176777i
$33$	6.67036	+	9.11956i	0.202132	+	0.276350i
$34$	−25.9573			−0.763449
$35$			62.7498i			1.79285i
$36$	−5.45282	+	17.1542i	−0.151467	+	0.476506i
$37$	−20.5418			−0.555184			−0.277592	−	0.960699i	$-0.589536\pi$
$37$	−20.5418			−0.555184			−0.277592	+	0.960699i	$0.589536\pi$
$38$		−	2.42240i		−	0.0637472i
$39$	51.0203	−	37.3180i	1.30821	−	0.956873i
$40$	14.0916			0.352290
$41$		−	44.5482i		−	1.08654i	−0.839557	−	0.543271i	$-0.817186\pi$
$41$		−	44.5482i		−	1.08654i	0.839557	−	0.543271i	$-0.182814\pi$
$42$	31.5468	+	43.1300i	0.751114	+	1.02690i
$43$	72.9831			1.69728			0.848641	−	0.528969i	$-0.177421\pi$
$43$	72.9831			1.69728			0.848641	+	0.528969i	$0.177421\pi$
$44$		−	7.53245i		−	0.171192i
$45$	−42.7323	−	13.5833i	−0.949606	−	0.301852i
$46$	6.78233			0.147442
$47$		−	12.3762i		−	0.263323i	−0.991295	−	0.131662i	$-0.957969\pi$
$47$		−	12.3762i		−	0.263323i	0.991295	−	0.131662i	$-0.0420312\pi$
$48$	9.68562	−	7.08440i	0.201784	−	0.147592i
$49$	109.633			2.23741
$50$		−	0.252244i		−	0.00504488i
$51$	−32.5078	−	44.4438i	−0.637407	−	0.871448i
$52$	−42.1411			−0.810406
$53$			86.0772i			1.62410i	0.583590	+	0.812049i	$0.301648\pi$
$53$			86.0772i			1.62410i	−0.583590	+	0.812049i	$0.698352\pi$
$54$	−36.2002	+	12.1469i	−0.670374	+	0.224943i
$55$	18.7638			0.341161
$56$		−	35.6239i		−	0.636142i
$57$	4.14761	−	3.03370i	0.0727650	−	0.0532229i
$58$	9.82827			0.169453
$59$			63.1522i			1.07038i	0.844733	+	0.535188i	$0.179759\pi$
$59$			63.1522i			1.07038i	−0.844733	+	0.535188i	$0.820241\pi$
$60$	17.6477	+	24.1275i	0.294128	+	0.402125i
$61$	18.8964			0.309777			0.154889	−	0.987932i	$-0.450498\pi$
$61$	18.8964			0.309777			0.154889	+	0.987932i	$0.450498\pi$
$62$		−	26.0439i		−	0.420063i
$63$	−34.3390	+	108.028i	−0.545064	+	1.71473i
$64$	−8.00000			−0.125000
$65$		−	104.976i		−	1.61502i
$66$	12.8970	−	9.43332i	0.195409	−	0.142929i
$67$	−34.1330			−0.509447			−0.254724	−	0.967014i	$-0.581985\pi$
$67$	−34.1330			−0.509447			−0.254724	+	0.967014i	$0.581985\pi$
$68$			36.7091i			0.539840i
$69$	8.49390	+	11.6127i	0.123100	+	0.168299i
$70$	88.7416			1.26774
$71$			132.300i			1.86338i	0.363251	+	0.931691i	$0.381667\pi$
$71$			132.300i			1.86338i	−0.363251	+	0.931691i	$0.618333\pi$
$72$	24.2597	+	7.71145i	0.336940	+	0.107104i
$73$	−42.0960			−0.576658			−0.288329	−	0.957531i	$-0.593100\pi$
$73$	−42.0960			−0.576658			−0.288329	+	0.957531i	$0.593100\pi$
$74$			29.0505i			0.392574i
$75$	0.431890	−	0.315900i	0.00575854	−	0.00421199i
$76$	−3.42578			−0.0450761
$77$		−	47.4355i		−	0.616045i
$78$	−52.7757	−	72.1537i	−0.676611	−	0.925047i
$79$	−63.7892			−0.807458			−0.403729	−	0.914879i	$-0.632286\pi$
$79$	−63.7892			−0.807458			−0.403729	+	0.914879i	$0.632286\pi$
$80$		−	19.9285i		−	0.249107i
$81$	−66.1334	−	46.7694i	−0.816461	−	0.577400i
$82$	−63.0007			−0.768302
$83$		−	163.569i		−	1.97071i	−0.170526	−	0.985353i	$-0.554547\pi$
$83$		−	163.569i		−	1.97071i	0.170526	−	0.985353i	$-0.445453\pi$
$84$	60.9950	−	44.6139i	0.726131	−	0.531118i
$85$	−91.4448			−1.07582
$86$		−	103.214i		−	1.20016i
$87$	12.3085	+	16.8279i	0.141477	+	0.193424i
$88$	−10.6525			−0.121051
$89$		−	5.63612i		−	0.0633272i	−0.999499	−	0.0316636i	$-0.989919\pi$
$89$		−	5.63612i		−	0.0633272i	0.999499	−	0.0316636i	$-0.0100805\pi$
$90$	−19.2097	+	60.4325i	−0.213442	+	0.671473i
$91$	−265.383			−2.91629
$92$		−	9.59166i		−	0.104257i
$93$	44.5922	−	32.6163i	0.479486	−	0.350713i
$94$	−17.5026			−0.186198
$95$		−	8.53385i		−	0.0898300i
$96$	−10.0189	−	13.6975i	−0.104363	−	0.142683i
$97$	123.776			1.27604			0.638021	−	0.770019i	$-0.279753\pi$
$97$	123.776			1.27604			0.638021	+	0.770019i	$0.279753\pi$
$98$		−	155.045i		−	1.58209i
$99$	32.3033	+	10.2683i	0.326296	+	0.103720i
$100$	−0.356727			−0.00356727
$101$			46.8126i			0.463491i	0.972776	+	0.231746i	$0.0744437\pi$
$101$			46.8126i			0.463491i	−0.972776	+	0.231746i	$0.925556\pi$
$102$	−62.8531	+	45.9729i	−0.616207	+	0.450715i
$103$	−17.8343			−0.173148			−0.0865742	−	0.996245i	$-0.527592\pi$
$103$	−17.8343			−0.173148			−0.0865742	+	0.996245i	$0.527592\pi$
$104$			59.5965i			0.573043i
$105$	111.136	+	151.943i	1.05844	+	1.44707i
$106$	121.731			1.14841
$107$			131.182i			1.22600i	0.790081	+	0.613002i	$0.210038\pi$
$107$			131.182i			1.22600i	−0.790081	+	0.613002i	$0.789962\pi$
$108$	17.1783	+	51.1948i	0.159059	+	0.474026i
$109$	−127.495			−1.16968			−0.584841	−	0.811148i	$-0.698843\pi$
$109$	−127.495			−1.16968			−0.584841	+	0.811148i	$0.698843\pi$
$110$		−	26.5361i		−	0.241237i
$111$	−49.7400	+	36.3816i	−0.448108	+	0.327762i
$112$	−50.3798			−0.449820
$113$		−	92.2362i		−	0.816250i	−0.912926	−	0.408125i	$-0.866183\pi$
$113$		−	92.2362i		−	0.816250i	0.912926	−	0.408125i	$-0.133817\pi$
$114$	−4.29030	−	5.86560i	−0.0376342	−	0.0514526i
$115$	23.8935			0.207769
$116$		−	13.8993i		−	0.119821i
$117$	57.4469	−	180.724i	0.491000	−	1.54465i
$118$	89.3107			0.756870
$119$			231.175i			1.94265i
$120$	34.1215	−	24.9576i	0.284346	−	0.207980i
$121$	106.816			0.882773
$122$		−	26.7235i		−	0.219045i
$123$	−78.8994	−	107.869i	−0.641459	−	0.876987i
$124$	−36.8317			−0.297030
$125$		−	125.442i		−	1.00354i
$126$	152.775	+	48.5627i	1.21250	+	0.385418i
$127$	−88.5664			−0.697373			−0.348687	−	0.937239i	$-0.613372\pi$
$127$	−88.5664			−0.697373			−0.348687	+	0.937239i	$0.613372\pi$
$128$			11.3137i			0.0883883i
$129$	176.722	−	129.260i	1.36994	−	1.00202i
$130$	−148.459			−1.14199
$131$			127.489i			0.973197i	0.873626	+	0.486599i	$0.161763\pi$
$131$			127.489i			0.973197i	−0.873626	+	0.486599i	$0.838237\pi$
$132$	−13.3407	−	18.2391i	−0.101066	−	0.138175i
$133$	−21.5738			−0.162209
$134$			48.2713i			0.360234i
$135$	−127.530	+	42.7923i	−0.944663	+	0.316980i
$136$	51.9145			0.381725
$137$			109.803i			0.801479i	0.916192	+	0.400740i	$0.131247\pi$
$137$			109.803i			0.801479i	−0.916192	+	0.400740i	$0.868753\pi$
$138$	16.4228	−	12.0122i	0.119006	−	0.0870448i
$139$	−141.609			−1.01877			−0.509383	−	0.860540i	$-0.670126\pi$
$139$	−141.609			−1.01877			−0.509383	+	0.860540i	$0.670126\pi$
$140$		−	125.500i		−	0.896425i
$141$	−21.9195	−	29.9678i	−0.155457	−	0.212537i
$142$	187.101			1.31761
$143$			79.3564i			0.554940i
$144$	10.9056	−	34.3084i	0.0757336	−	0.238253i
$145$	34.6240			0.238786
$146$			59.5327i			0.407758i
$147$	265.466	−	194.171i	1.80589	−	1.32089i
$148$	41.0836			0.277592
$149$			105.232i			0.706256i	0.935575	+	0.353128i	$0.114882\pi$
$149$			105.232i			0.706256i	−0.935575	+	0.353128i	$0.885118\pi$
$150$	−0.446749	−	0.610785i	−0.00297833	−	0.00407190i
$151$	−147.486			−0.976726			−0.488363	−	0.872641i	$-0.662406\pi$
$151$	−147.486			−0.976726			−0.488363	+	0.872641i	$0.662406\pi$
$152$			4.84479i			0.0318736i
$153$	−157.429	−	50.0421i	−1.02895	−	0.327072i
$154$	−67.0839			−0.435610
$155$		−	91.7501i		−	0.591936i
$156$	−102.041	+	74.6361i	−0.654107	+	0.478436i
$157$	184.120			1.17274			0.586370	−	0.810043i	$-0.300556\pi$
$157$	184.120			1.17274			0.586370	+	0.810043i	$0.300556\pi$
$158$			90.2115i			0.570959i
$159$	152.451	+	208.428i	0.958813	+	1.31087i
$160$	−28.1832			−0.176145
$161$		−	60.4033i		−	0.375176i
$162$	−66.1419	+	93.5267i	−0.408283	+	0.577325i
$163$	316.417			1.94121			0.970604	−	0.240683i	$-0.0773713\pi$
$163$	316.417			1.94121			0.970604	+	0.240683i	$0.0773713\pi$
$164$			89.0965i			0.543271i
$165$	45.4349	−	33.2326i	0.275363	−	0.201410i
$166$	−231.321			−1.39350
$167$		−	261.268i		−	1.56448i	−0.622979	−	0.782238i	$-0.714078\pi$
$167$		−	261.268i		−	1.56448i	0.622979	−	0.782238i	$-0.285922\pi$
$168$	−63.0935	−	86.2600i	−0.375557	−	0.513452i
$169$	274.968			1.62703
$170$			129.323i			0.760721i
$171$	4.67005	−	14.6917i	0.0273102	−	0.0859161i
$172$	−145.966			−0.848641
$173$		−	155.410i		−	0.898323i	−0.893451	−	0.449161i	$-0.851723\pi$
$173$		−	155.410i		−	0.898323i	0.893451	−	0.449161i	$-0.148277\pi$
$174$	23.7982	−	17.4069i	0.136771	−	0.100039i
$175$	−2.24648			−0.0128370
$176$			15.0649i			0.0855960i
$177$	111.849	+	152.917i	0.631915	+	0.863939i
$178$	−7.97067			−0.0447791
$179$			100.472i			0.561297i	0.959811	+	0.280649i	$0.0905495\pi$
$179$			100.472i			0.561297i	−0.959811	+	0.280649i	$0.909450\pi$
$180$	85.4645	+	27.1667i	0.474803	+	0.150926i
$181$	−64.8588			−0.358336			−0.179168	−	0.983818i	$-0.557341\pi$
$181$	−64.8588			−0.358336			−0.179168	+	0.983818i	$0.557341\pi$
$182$			375.308i			2.06213i
$183$	45.7558	−	33.4674i	0.250032	−	0.182882i
$184$	−13.5647			−0.0737210
$185$			102.342i			0.553199i
$186$	−46.1264	−	63.0629i	−0.247991	−	0.339048i
$187$	69.1274			0.369665
$188$			24.7524i			0.131662i
$189$	108.180	+	322.398i	0.572382	+	1.70581i
$190$	−12.0687			−0.0635194
$191$			98.7641i			0.517089i	0.965999	+	0.258545i	$0.0832429\pi$
$191$			98.7641i			0.517089i	−0.965999	+	0.258545i	$0.916757\pi$
$192$	−19.3712	+	14.1688i	−0.100892	+	0.0737958i
$193$	−261.023			−1.35245			−0.676226	−	0.736695i	$-0.736386\pi$
$193$	−261.023			−1.35245			−0.676226	+	0.736695i	$0.736386\pi$
$194$		−	175.046i		−	0.902298i
$195$	−185.923	−	254.190i	−0.953453	−	1.30354i
$196$	−219.266			−1.11870
$197$			166.972i			0.847572i	0.905762	+	0.423786i	$0.139299\pi$
$197$			166.972i			0.847572i	−0.905762	+	0.423786i	$0.860701\pi$
$198$	14.5215	−	45.6838i	0.0733411	−	0.230726i
$199$	9.68481			0.0486674			0.0243337	−	0.999704i	$-0.492254\pi$
$199$	9.68481			0.0486674			0.0243337	+	0.999704i	$0.492254\pi$
$200$			0.504488i			0.00252244i
$201$	−82.6498	+	60.4529i	−0.411193	+	0.300761i
$202$	66.2030			0.327738
$203$		−	87.5304i		−	0.431184i
$204$	65.0155	+	88.8877i	0.318704	+	0.435724i
$205$	−221.945			−1.08266
$206$			25.2215i			0.122434i
$207$	41.1343	+	13.0754i	0.198717	+	0.0631662i
$208$	84.2822			0.405203
$209$			6.45114i			0.0308667i
$210$	214.879	−	157.170i	1.02323	−	0.748429i
$211$	258.231			1.22385			0.611923	−	0.790918i	$-0.290396\pi$
$211$	258.231			1.22385			0.611923	+	0.790918i	$0.290396\pi$
$212$		−	172.154i		−	0.812049i
$213$	234.317	+	320.352i	1.10008	+	1.50400i
$214$	185.520			0.866916
$215$		−	363.611i		−	1.69122i
$216$	72.4003	−	24.2938i	0.335187	−	0.112471i
$217$	−231.947			−1.06888
$218$			180.306i			0.827090i
$219$	−101.931	+	74.5562i	−0.465441	+	0.340439i
$220$	−37.5277			−0.170580
$221$		−	386.741i		−	1.74996i
$222$	51.4513	+	70.3430i	0.231763	+	0.316860i
$223$	203.350			0.911882			0.455941	−	0.890010i	$-0.349303\pi$
$223$	203.350			0.911882			0.455941	+	0.890010i	$0.349303\pi$
$224$			71.2479i			0.318071i
$225$	0.486292	−	1.52984i	0.00216130	−	0.00679930i
$226$	−130.442			−0.577176
$227$			92.2538i			0.406405i	0.979137	+	0.203202i	$0.0651349\pi$
$227$			92.2538i			0.406405i	−0.979137	+	0.203202i	$0.934865\pi$
$228$	−8.29521	+	6.06741i	−0.0363825	+	0.0266114i
$229$	25.4853			0.111289			0.0556447	−	0.998451i	$-0.482279\pi$
$229$	25.4853			0.111289			0.0556447	+	0.998451i	$0.482279\pi$
$230$		−	33.7905i		−	0.146915i
$231$	−84.0130	−	114.861i	−0.363692	−	0.497232i
$232$	−19.6565			−0.0847265
$233$		−	271.700i		−	1.16609i	−0.812438	−	0.583047i	$-0.801860\pi$
$233$		−	271.700i		−	1.16609i	0.812438	−	0.583047i	$-0.198140\pi$
$234$	−255.583	−	81.2423i	−1.09223	−	0.347189i
$235$	−61.6598			−0.262382
$236$		−	126.304i		−	0.535188i
$237$	−154.459	+	112.977i	−0.651728	+	0.476696i
$238$	326.931			1.37366
$239$		−	269.373i		−	1.12709i	−0.826087	−	0.563543i	$-0.809438\pi$
$239$		−	269.373i		−	1.12709i	0.826087	−	0.563543i	$-0.190562\pi$
$240$	−35.2954	−	48.2550i	−0.147064	−	0.201063i
$241$	−301.722			−1.25196			−0.625979	−	0.779840i	$-0.715300\pi$
$241$	−301.722			−1.25196			−0.625979	+	0.779840i	$0.715300\pi$
$242$		−	151.060i		−	0.624215i
$243$	−242.969	+	3.88113i	−0.999872	+	0.0159717i
$244$	−37.7928			−0.154889
$245$		−	546.206i		−	2.22941i
$246$	−152.550	+	111.581i	−0.620123	+	0.453580i
$247$	36.0916			0.146120
$248$			52.0878i			0.210032i
$249$	−289.696	−	396.066i	−1.16344	−	1.59063i
$250$	−177.402			−0.709607
$251$			43.2337i			0.172246i	0.996285	+	0.0861229i	$0.0274478\pi$
$251$			43.2337i			0.172246i	−0.996285	+	0.0861229i	$0.972552\pi$
$252$	68.6781	−	216.057i	0.272532	−	0.857367i
$253$	−18.0622			−0.0713920
$254$			125.252i			0.493117i
$255$	−221.425	+	161.958i	−0.868333	+	0.635129i
$256$	16.0000			0.0625000
$257$			222.792i			0.866894i	0.901179	+	0.433447i	$0.142703\pi$
$257$			222.792i			0.866894i	−0.901179	+	0.433447i	$0.857297\pi$
$258$	−182.802	−	249.922i	−0.708534	−	0.968691i
$259$	258.723			0.998931
$260$			209.952i			0.807509i
$261$	59.6078	+	18.9476i	0.228382	+	0.0725960i
$262$	180.296			0.688154
$263$			101.986i			0.387781i	0.981023	+	0.193891i	$0.0621107\pi$
$263$			101.986i			0.387781i	−0.981023	+	0.193891i	$0.937889\pi$
$264$	−25.7940	+	18.8666i	−0.0977046	+	0.0714645i
$265$	428.848			1.61829
$266$			30.5100i			0.114699i
$267$	−9.98213	−	13.6473i	−0.0373862	−	0.0511136i
$268$	68.2659			0.254724
$269$		−	366.148i		−	1.36115i	−0.732680	−	0.680573i	$-0.761731\pi$
$269$		−	366.148i		−	1.36115i	0.732680	−	0.680573i	$-0.238269\pi$
$270$	60.5175	+	180.354i	0.224139	+	0.667978i
$271$	−186.460			−0.688043			−0.344022	−	0.938962i	$-0.611789\pi$
$271$	−186.460			−0.688043			−0.344022	+	0.938962i	$0.611789\pi$
$272$		−	73.4182i		−	0.269920i
$273$	−642.599	+	470.019i	−2.35384	+	1.72168i
$274$	155.284			0.566731
$275$			0.671757i			0.00244275i
$276$	−16.9878	−	23.2253i	−0.0615500	−	0.0841497i
$277$	189.083			0.682609			0.341305	−	0.939953i	$-0.389131\pi$
$277$	189.083			0.682609			0.341305	+	0.939953i	$0.389131\pi$
$278$			200.265i			0.720377i
$279$	50.2091	−	157.954i	0.179961	−	0.566145i
$280$	−177.483			−0.633868
$281$			242.155i			0.861763i	0.902409	+	0.430881i	$0.141797\pi$
$281$			242.155i			0.861763i	−0.902409	+	0.430881i	$0.858203\pi$
$282$	−42.3808	+	30.9988i	−0.150287	+	0.109925i
$283$	165.120			0.583462			0.291731	−	0.956500i	$-0.405769\pi$
$283$	165.120			0.583462			0.291731	+	0.956500i	$0.405769\pi$
$284$		−	264.600i		−	0.931691i
$285$	−15.1143	−	20.6639i	−0.0530327	−	0.0725050i
$286$	112.227			0.392402
$287$			561.083i			1.95499i
$288$	−48.5194	−	15.4229i	−0.168470	−	0.0535518i
$289$	−47.8898			−0.165709
$290$		−	48.9658i		−	0.168847i
$291$	299.712	−	219.220i	1.02994	−	0.753333i
$292$	84.1920			0.288329
$293$			304.873i			1.04052i	0.854007	+	0.520261i	$0.174165\pi$
$293$			304.873i			1.04052i	−0.854007	+	0.520261i	$0.825835\pi$
$294$	−274.599	−	375.426i	−0.934012	−	1.27696i
$295$	314.633			1.06655
$296$		−	58.1010i		−	0.196287i
$297$	96.4056	−	32.3487i	0.324598	−	0.108918i
$298$	148.821			0.499399
$299$			101.051i			0.337962i
$300$	−0.863781	+	0.631799i	−0.00287927	+	0.00210600i
$301$	−919.220			−3.05389
$302$			208.576i			0.690650i
$303$	82.9098	+	113.352i	0.273630	+	0.374100i
$304$	6.85157			0.0225381
$305$		−	94.1443i		−	0.308670i
$306$	−70.7702	+	222.638i	−0.231275	+	0.727576i
$307$	74.0000			0.241042			0.120521	−	0.992711i	$-0.461543\pi$
$307$	74.0000			0.241042			0.120521	+	0.992711i	$0.461543\pi$
$308$			94.8709i			0.308023i
$309$	−43.1840	+	31.5863i	−0.139754	+	0.102221i
$310$	−129.754			−0.418562
$311$			138.111i			0.444088i	0.975037	+	0.222044i	$0.0712728\pi$
$311$			138.111i			0.444088i	−0.975037	+	0.222044i	$0.928727\pi$
$312$	105.551	+	144.307i	0.338306	+	0.462523i
$313$	159.737			0.510343			0.255171	−	0.966896i	$-0.417868\pi$
$313$	159.737			0.510343			0.255171	+	0.966896i	$0.417868\pi$
$314$		−	260.385i		−	0.829253i
$315$	538.211	+	171.082i	1.70861	+	0.543116i
$316$	127.578			0.403729
$317$			57.7496i			0.182176i	0.995843	+	0.0910878i	$0.0290344\pi$
$317$			57.7496i			0.182176i	−0.995843	+	0.0910878i	$0.970966\pi$
$318$	294.761	−	215.599i	0.926922	−	0.677983i
$319$	−26.1739			−0.0820499
$320$			39.8571i			0.124553i
$321$	232.337	+	317.646i	0.723792	+	0.989551i
$322$	−85.4232			−0.265289
$323$		−	31.4394i		−	0.0973355i
$324$	132.267	+	93.5388i	0.408231	+	0.288700i
$325$	3.75822			0.0115637
$326$		−	447.481i		−	1.37264i
$327$	−308.718	+	225.807i	−0.944091	+	0.690541i
$328$	126.001			0.384151
$329$			155.878i			0.473792i
$330$	−46.9980	−	64.2546i	−0.142418	−	0.194711i
$331$	33.3867			0.100866			0.0504331	−	0.998727i	$-0.483940\pi$
$331$	33.3867			0.100866			0.0504331	+	0.998727i	$0.483940\pi$
$332$			327.137i			0.985353i
$333$	−56.0053	+	176.189i	−0.168184	+	0.529096i
$334$	−369.488			−1.10625
$335$			170.055i			0.507627i
$336$	−121.990	+	89.2277i	−0.363066	+	0.265559i
$337$	631.696			1.87447			0.937234	−	0.348701i	$-0.113377\pi$
$337$	631.696			1.87447			0.937234	+	0.348701i	$0.113377\pi$
$338$		−	388.863i		−	1.15048i
$339$	−163.360	−	223.341i	−0.481887	−	0.658824i
$340$	182.890			0.537911
$341$			69.3582i			0.203396i
$342$	−20.7771	−	6.60444i	−0.0607519	−	0.0193112i
$343$	−763.671			−2.22645
$344$			206.427i			0.600080i
$345$	57.8558	−	42.3177i	0.167698	−	0.122660i
$346$	−219.783			−0.635210
$347$		−	56.2743i		−	0.162174i	−0.996707	−	0.0810870i	$-0.974161\pi$
$347$		−	56.2743i		−	0.162174i	0.996707	−	0.0810870i	$-0.0258391\pi$
$348$	−24.6170	−	33.6558i	−0.0707385	−	0.0967120i
$349$	−3.27247			−0.00937671			−0.00468836	−	0.999989i	$-0.501492\pi$
$349$	−3.27247			−0.00937671			−0.00468836	+	0.999989i	$0.501492\pi$
$350$			3.17700i			0.00907716i
$351$	−180.978	−	539.351i	−0.515608	−	1.53661i
$352$	21.3050			0.0605255
$353$			164.815i			0.466897i	0.972369	+	0.233449i	$0.0750011\pi$
$353$			164.815i			0.466897i	−0.972369	+	0.233449i	$0.924999\pi$
$354$	216.257	−	158.178i	0.610897	−	0.446831i
$355$	659.137			1.85672
$356$			11.2722i			0.0316636i
$357$	409.434	+	559.768i	1.14687	+	1.56798i
$358$	142.089			0.396897
$359$			265.797i			0.740383i	0.928955	+	0.370191i	$0.120708\pi$
$359$			265.797i			0.740383i	−0.928955	+	0.370191i	$0.879292\pi$
$360$	38.4195	−	120.865i	0.106721	−	0.335736i
$361$	−358.066			−0.991873
$362$			91.7243i			0.253382i
$363$	258.644	−	189.181i	0.712517	−	0.521160i
$364$	530.765			1.45815
$365$			209.728i			0.574597i
$366$	−47.3301	−	64.7085i	−0.129317	−	0.176799i
$367$	71.9707			0.196106			0.0980528	−	0.995181i	$-0.468739\pi$
$367$	71.9707			0.196106			0.0980528	+	0.995181i	$0.468739\pi$
$368$			19.1833i			0.0521286i
$369$	−382.095	−	121.457i	−1.03549	−	0.329151i
$370$	144.733			0.391171
$371$		−	1084.14i		−	2.92221i
$372$	−89.1844	+	65.2326i	−0.239743	+	0.175356i
$373$	576.310			1.54507			0.772533	−	0.634974i	$-0.218989\pi$
$373$	576.310			1.54507			0.772533	+	0.634974i	$0.218989\pi$
$374$		−	97.7609i		−	0.261393i
$375$	−222.170	−	303.746i	−0.592454	−	0.809989i
$376$	35.0051			0.0930988
$377$			146.433i			0.388416i
$378$	455.940	−	152.990i	1.20619	−	0.404735i
$379$	−108.830			−0.287149			−0.143575	−	0.989639i	$-0.545860\pi$
$379$	−108.830			−0.287149			−0.143575	+	0.989639i	$0.545860\pi$
$380$			17.0677i			0.0449150i
$381$	−214.455	+	156.860i	−0.562874	+	0.411706i
$382$	139.673			0.365637
$383$			134.013i			0.349905i	0.984577	+	0.174952i	$0.0559771\pi$
$383$			134.013i			0.349905i	−0.984577	+	0.174952i	$0.944023\pi$
$384$	20.0377	+	27.3951i	0.0521815	+	0.0713413i
$385$	−236.330			−0.613844
$386$			369.142i			0.956327i
$387$	198.982	−	625.984i	0.514165	−	1.61753i
$388$	−247.552			−0.638021
$389$			184.114i			0.473300i	0.971595	+	0.236650i	$0.0760494\pi$
$389$			184.114i			0.473300i	−0.971595	+	0.236650i	$0.923951\pi$
$390$	−359.479	+	262.935i	−0.921741	+	0.674193i
$391$	88.0254			0.225129
$392$			310.089i			0.791044i
$393$	225.795	+	308.702i	0.574543	+	0.785502i
$394$	236.134			0.599324
$395$			317.806i			0.804572i
$396$	−64.6066	−	20.5366i	−0.163148	−	0.0518600i
$397$	187.813			0.473080			0.236540	−	0.971622i	$-0.423986\pi$
$397$	187.813			0.473080			0.236540	+	0.971622i	$0.423986\pi$
$398$		−	13.6964i		−	0.0344130i
$399$	−52.2390	+	38.2094i	−0.130925	+	0.0957629i
$400$	0.713454			0.00178363
$401$		−	477.140i		−	1.18988i	−0.803772	−	0.594938i	$-0.797177\pi$
$401$		−	477.140i		−	1.18988i	0.803772	−	0.594938i	$-0.202823\pi$
$402$	85.4933	+	116.884i	0.212670	+	0.290757i
$403$	388.032			0.962858
$404$		−	93.6252i		−	0.231746i
$405$	−233.011	+	329.485i	−0.575337	+	0.813544i
$406$	−123.787			−0.304893
$407$		−	77.3650i		−	0.190086i
$408$	125.706	−	91.9458i	0.308103	−	0.225357i
$409$	−67.9295			−0.166087			−0.0830434	−	0.996546i	$-0.526464\pi$
$409$	−67.9295			−0.166087			−0.0830434	+	0.996546i	$0.526464\pi$
$410$			313.878i			0.765556i
$411$	194.471	+	265.877i	0.473166	+	0.646902i
$412$	35.6686			0.0865742
$413$		−	795.400i		−	1.92591i
$414$	18.4914	−	58.1727i	0.0446652	−	0.140514i
$415$	−814.920			−1.96366
$416$		−	119.193i		−	0.286522i
$417$	−342.892	+	250.803i	−0.822282	+	0.601446i
$418$	9.12329			0.0218260
$419$			13.3283i			0.0318099i	0.999874	+	0.0159049i	$0.00506292\pi$
$419$			13.3283i			0.0318099i	−0.999874	+	0.0159049i	$0.994937\pi$
$420$	−222.272	−	303.885i	−0.529219	−	0.723536i
$421$	−118.742			−0.282047			−0.141024	−	0.990006i	$-0.545039\pi$
$421$	−118.742			−0.282047			−0.141024	+	0.990006i	$0.545039\pi$
$422$		−	365.194i		−	0.865389i
$423$	−106.152	−	33.7426i	−0.250950	−	0.0797696i
$424$	−243.463			−0.574205
$425$		−	3.27378i		−	0.00770302i
$426$	453.047	−	331.374i	1.06349	−	0.777873i
$427$	−237.999			−0.557376
$428$		−	262.365i		−	0.613002i
$429$	140.548	+	192.154i	0.327618	+	0.447912i
$430$	−514.224			−1.19587
$431$		−	583.544i		−	1.35393i	−0.736015	−	0.676966i	$-0.763295\pi$
$431$		−	583.544i		−	1.35393i	0.736015	−	0.676966i	$-0.236705\pi$
$432$	−34.3566	−	102.390i	−0.0795293	−	0.237013i
$433$	−85.4225			−0.197281			−0.0986403	−	0.995123i	$-0.531449\pi$
$433$	−85.4225			−0.197281			−0.0986403	+	0.995123i	$0.531449\pi$
$434$			328.022i			0.755812i
$435$	83.8388	−	61.3226i	0.192733	−	0.140971i
$436$	254.991			0.584841
$437$			8.21474i			0.0187980i
$438$	105.438	+	144.153i	0.240727	+	0.329116i
$439$	100.765			0.229534			0.114767	−	0.993392i	$-0.463388\pi$
$439$	100.765			0.229534			0.114767	+	0.993392i	$0.463388\pi$
$440$			53.0721i			0.120618i
$441$	298.905	−	940.334i	0.677788	−	2.13228i
$442$	−546.934			−1.23741
$443$		−	167.058i		−	0.377105i	−0.982063	−	0.188553i	$-0.939620\pi$
$443$		−	167.058i		−	0.377105i	0.982063	−	0.188553i	$-0.0603796\pi$
$444$	99.4800	−	72.7631i	0.224054	−	0.163881i
$445$	−28.0799			−0.0631009
$446$		−	287.580i		−	0.644798i
$447$	186.377	+	254.810i	0.416950	+	0.570044i
$448$	100.760			0.224910
$449$			754.733i			1.68092i	0.541874	+	0.840460i	$0.317715\pi$
$449$			754.733i			1.68092i	−0.541874	+	0.840460i	$0.682285\pi$
$450$	−2.16352	−	0.687721i	−0.00480783	−	0.00152827i
$451$	167.779			0.372015
$452$			184.472i			0.408125i
$453$	−357.123	+	261.212i	−0.788350	+	0.576627i
$454$	130.467			0.287371
$455$			1322.17i			2.90587i
$456$	8.58061	+	11.7312i	0.0188171	+	0.0257263i
$457$	−267.179			−0.584638			−0.292319	−	0.956321i	$-0.594427\pi$
$457$	−267.179			−0.584638			−0.292319	+	0.956321i	$0.594427\pi$
$458$		−	36.0416i		−	0.0786934i
$459$	−469.829	+	157.650i	−1.02359	+	0.343465i
$460$	−47.7869			−0.103885
$461$			807.083i			1.75072i	0.483469	+	0.875362i	$0.339377\pi$
$461$			807.083i			1.75072i	−0.483469	+	0.875362i	$0.660623\pi$
$462$	−162.437	+	118.812i	−0.351596	+	0.257169i
$463$	−247.242			−0.533999			−0.267000	−	0.963697i	$-0.586032\pi$
$463$	−247.242			−0.533999			−0.267000	+	0.963697i	$0.586032\pi$
$464$			27.7986i			0.0599107i
$465$	−162.499	−	222.164i	−0.349459	−	0.477773i
$466$	−384.242			−0.824553
$467$		−	304.740i		−	0.652548i	−0.945275	−	0.326274i	$-0.894207\pi$
$467$		−	304.740i		−	0.652548i	0.945275	−	0.326274i	$-0.105793\pi$
$468$	−114.894	+	361.448i	−0.245500	+	0.772326i
$469$	429.903			0.916638
$470$			87.2001i			0.185532i
$471$	445.830	−	326.095i	0.946560	−	0.692347i
$472$	−178.621			−0.378435
$473$			274.871i			0.581122i
$474$	159.774	+	218.439i	0.337075	+	0.460841i
$475$	0.305517			0.000643195
$476$		−	462.350i		−	0.971323i
$477$	738.293	+	234.682i	1.54778	+	0.491995i
$478$	−380.952			−0.796970
$479$			610.112i			1.27372i	0.770979	+	0.636861i	$0.219767\pi$
$479$			610.112i			1.27372i	−0.770979	+	0.636861i	$0.780233\pi$
$480$	−68.2429	+	49.9153i	−0.142173	+	0.103990i
$481$	−432.827			−0.899848
$482$			426.699i			0.885268i
$483$	−106.980	−	146.261i	−0.221491	−	0.302818i
$484$	−213.631			−0.441387
$485$		−	616.669i		−	1.27148i
$486$	5.48875	+	343.610i	0.0112937	+	0.707017i
$487$	−933.394			−1.91662			−0.958310	−	0.285731i	$-0.907763\pi$
$487$	−933.394			−1.91662			−0.958310	+	0.285731i	$0.907763\pi$
$488$			53.4471i			0.109523i
$489$	766.174	−	560.406i	1.56682	−	1.14602i
$490$	−772.452			−1.57643
$491$		−	900.662i		−	1.83434i	−0.398494	−	0.917171i	$-0.630467\pi$
$491$		−	900.662i		−	1.83434i	0.398494	−	0.917171i	$-0.369533\pi$
$492$	157.799	+	215.739i	0.320729	+	0.438493i
$493$	127.558			0.258737
$494$		−	51.0412i		−	0.103322i
$495$	51.1579	−	160.939i	0.103349	−	0.325130i
$496$	73.6633			0.148515
$497$		−	1666.32i		−	3.35275i
$498$	−560.122	+	409.693i	−1.12474	+	0.822676i
$499$	−917.754			−1.83919			−0.919593	−	0.392872i	$-0.871481\pi$
$499$	−917.754			−1.83919			−0.919593	+	0.392872i	$0.871481\pi$
$500$			250.884i			0.501768i
$501$	−462.731	−	632.635i	−0.923615	−	1.26274i
$502$	61.1417			0.121796
$503$		−	16.9170i		−	0.0336321i	−0.999859	−	0.0168161i	$-0.994647\pi$
$503$		−	16.9170i		−	0.0336321i	0.999859	−	0.0168161i	$-0.00535297\pi$
$504$	−305.550	−	97.1255i	−0.606250	−	0.192709i
$505$	233.227			0.461835
$506$			25.5438i			0.0504818i
$507$	665.809	−	486.996i	1.31323	−	0.960544i
$508$	177.133			0.348687
$509$		−	321.466i		−	0.631563i	−0.948832	−	0.315782i	$-0.897733\pi$
$509$		−	321.466i		−	0.631563i	0.948832	−	0.315782i	$-0.102267\pi$
$510$	229.043	+	313.142i	0.449104	+	0.614004i
$511$	530.198			1.03757
$512$		−	22.6274i		−	0.0441942i
$513$	−14.7123	−	43.8456i	−0.0286790	−	0.0854689i
$514$	315.075			0.612987
$515$			88.8528i			0.172530i
$516$	−353.443	+	258.521i	−0.684968	+	0.501009i
$517$	46.6115			0.0901577
$518$		−	365.890i		−	0.706351i
$519$	−275.246	−	376.310i	−0.530340	−	0.725068i
$520$	296.918			0.570995
$521$			689.701i			1.32380i	0.749591	+	0.661901i	$0.230250\pi$
$521$			689.701i			1.32380i	−0.749591	+	0.661901i	$0.769750\pi$
$522$	26.7959	−	84.2981i	0.0513332	−	0.161491i
$523$	−722.920			−1.38226			−0.691129	−	0.722732i	$-0.742886\pi$
$523$	−722.920			−1.38226			−0.691129	+	0.722732i	$0.742886\pi$
$524$		−	254.978i		−	0.486599i
$525$	−5.43964	+	3.97874i	−0.0103612	+	0.00757856i
$526$	144.231			0.274203
$527$		−	338.015i		−	0.641394i
$528$	26.6815	+	36.4782i	0.0505331	+	0.0690876i
$529$	−23.0000			−0.0434783
$530$		−	606.482i		−	1.14431i
$531$	541.663	+	172.179i	1.02008	+	0.324254i
$532$	43.1476			0.0811046
$533$		−	938.656i		−	1.76108i
$534$	−19.3002	+	14.1169i	−0.0361428	+	0.0264361i
$535$	653.568			1.22162
$536$		−	96.5426i		−	0.180117i
$537$	177.946	+	243.284i	0.331371	+	0.453043i
$538$	−517.812			−0.962476
$539$			412.903i			0.766054i
$540$	255.059	−	85.5847i	0.472332	−	0.158490i
$541$	−255.799			−0.472826			−0.236413	−	0.971653i	$-0.575972\pi$
$541$	−255.799			−0.472826			−0.236413	+	0.971653i	$0.575972\pi$
$542$			263.694i			0.486520i
$543$	−157.050	+	114.871i	−0.289226	+	0.211550i
$544$	−103.829			−0.190862
$545$			635.198i			1.16550i
$546$	664.708	+	908.772i	1.21741	+	1.66442i
$547$	122.812			0.224520			0.112260	−	0.993679i	$-0.464191\pi$
$547$	122.812			0.224520			0.112260	+	0.993679i	$0.464191\pi$
$548$		−	219.605i		−	0.400740i
$549$	51.5193	−	162.076i	0.0938421	−	0.295221i
$550$	0.950008			0.00172729
$551$			11.9040i			0.0216043i
$552$	−32.8455	+	24.0244i	−0.0595028	+	0.0435224i
$553$	803.422			1.45284
$554$		−	267.403i		−	0.482678i
$555$	181.258	+	247.811i	0.326591	+	0.446507i
$556$	283.217			0.509383
$557$		−	566.898i		−	1.01777i	−0.860835	−	0.508885i	$-0.830058\pi$
$557$		−	566.898i		−	1.01777i	0.860835	−	0.508885i	$-0.169942\pi$
$558$	−223.381	−	71.0064i	−0.400325	−	0.127252i
$559$	1537.79			2.75097
$560$			250.999i			0.448213i
$561$	167.386	−	122.432i	0.298370	−	0.218238i
$562$	342.459			0.609358
$563$			242.696i			0.431077i	0.976495	+	0.215538i	$0.0691506\pi$
$563$			242.696i			0.431077i	−0.976495	+	0.215538i	$0.930849\pi$
$564$	43.8389	+	59.9355i	0.0777286	+	0.106269i
$565$	−459.533			−0.813333
$566$		−	233.515i		−	0.412570i
$567$	832.947	+	589.059i	1.46904	+	1.03890i
$568$	−374.201			−0.658805
$569$		−	572.573i		−	1.00628i	−0.864205	−	0.503140i	$-0.832178\pi$
$569$		−	572.573i		−	1.00628i	0.864205	−	0.503140i	$-0.167822\pi$
$570$	−29.2232	+	21.3749i	−0.0512688	+	0.0374998i
$571$	−742.383			−1.30015			−0.650073	−	0.759872i	$-0.725262\pi$
$571$	−742.383			−1.30015			−0.650073	+	0.759872i	$0.725262\pi$
$572$		−	158.713i		−	0.277470i
$573$	174.921	+	239.148i	0.305272	+	0.417361i
$574$	793.492			1.38239
$575$			0.855401i			0.00148765i
$576$	−21.8113	+	68.6168i	−0.0378668	+	0.119126i
$577$	−291.577			−0.505332			−0.252666	−	0.967554i	$-0.581307\pi$
$577$	−291.577			−0.505332			−0.252666	+	0.967554i	$0.581307\pi$
$578$			67.7265i			0.117174i
$579$	−632.043	+	462.298i	−1.09161	+	0.798442i
$580$	−69.2480			−0.119393
$581$			2060.14i			3.54585i
$582$	−310.024	−	423.857i	−0.532687	−	0.728277i
$583$	−324.186			−0.556065
$584$		−	119.065i		−	0.203879i
$585$	−900.392	−	286.208i	−1.53913	−	0.489245i
$586$	431.156			0.735760
$587$		−	419.335i		−	0.714370i	−0.934034	−	0.357185i	$-0.883737\pi$
$587$		−	419.335i		−	0.714370i	0.934034	−	0.357185i	$-0.116263\pi$
$588$	−530.932	+	388.342i	−0.902946	+	0.660446i
$589$	31.5443			0.0535558
$590$		−	444.958i		−	0.754166i
$591$	295.723	+	404.306i	0.500378	+	0.684105i
$592$	−82.1672			−0.138796
$593$			1111.57i			1.87448i	0.348682	+	0.937241i	$0.386629\pi$
$593$			1111.57i			1.87448i	−0.348682	+	0.937241i	$0.613371\pi$
$594$	−45.7480	−	136.338i	−0.0770168	−	0.229525i
$595$	1151.74			1.93570
$596$		−	210.464i		−	0.353128i
$597$	23.4509	−	17.1528i	0.0392812	−	0.0287316i
$598$	142.907			0.238976
$599$			295.057i			0.492583i	0.969196	+	0.246291i	$0.0792120\pi$
$599$			295.057i			0.492583i	−0.969196	+	0.246291i	$0.920788\pi$
$600$	0.893499	+	1.22157i	0.00148916	+	0.00203595i
$601$	−641.405			−1.06723			−0.533614	−	0.845728i	$-0.679167\pi$
$601$	−641.405			−1.06723			−0.533614	+	0.845728i	$0.679167\pi$
$602$			1299.97i			2.15942i
$603$	−93.0605	+	292.762i	−0.154329	+	0.485509i
$604$	294.971			0.488363
$605$		−	532.169i		−	0.879618i
$606$	160.304	−	117.252i	0.264529	−	0.193485i
$607$	88.1255			0.145182			0.0725910	−	0.997362i	$-0.476873\pi$
$607$	88.1255			0.145182			0.0725910	+	0.997362i	$0.476873\pi$
$608$		−	9.68958i		−	0.0159368i
$609$	−155.025	−	211.947i	−0.254557	−	0.348024i
$610$	−133.140			−0.218263
$611$		−	260.773i		−	0.426797i
$612$	314.858	+	100.084i	0.514474	+	0.163536i
$613$	−504.648			−0.823243			−0.411621	−	0.911355i	$-0.635037\pi$
$613$	−504.648			−0.823243			−0.411621	+	0.911355i	$0.635037\pi$
$614$		−	104.652i		−	0.170443i
$615$	−537.419	+	393.087i	−0.873853	+	0.639166i
$616$	134.168			0.217805
$617$		−	127.347i		−	0.206397i	−0.994661	−	0.103199i	$-0.967092\pi$
$617$		−	127.347i		−	0.206397i	0.994661	−	0.103199i	$-0.0329077\pi$
$618$	44.6698	+	61.0715i	0.0722812	+	0.0988211i
$619$	−264.710			−0.427641			−0.213821	−	0.976873i	$-0.568591\pi$
$619$	−264.710			−0.427641			−0.213821	+	0.976873i	$0.568591\pi$
$620$			183.500i			0.295968i
$621$	122.761	−	41.1922i	0.197682	−	0.0663320i
$622$	195.319			0.314017
$623$			70.9867i			0.113943i
$624$	204.081	−	149.272i	0.327053	−	0.239218i
$625$	−620.509			−0.992815
$626$		−	225.903i		−	0.360867i
$627$	11.4256	+	15.6208i	0.0182227	+	0.0249136i
$628$	−368.240			−0.586370
$629$			377.036i			0.599421i
$630$	241.946	−	761.145i	0.384041	−	1.20817i
$631$	441.449			0.699603			0.349801	−	0.936824i	$-0.386249\pi$
$631$	441.449			0.699603			0.349801	+	0.936824i	$0.386249\pi$
$632$		−	180.423i		−	0.285480i
$633$	625.283	−	457.354i	0.987809	−	0.722517i
$634$	81.6703			0.128818
$635$			441.249i			0.694881i
$636$	−304.903	−	416.855i	−0.479406	−	0.655433i
$637$	2310.03			3.62642
$638$			37.0155i			0.0580180i
$639$	1134.75	+	360.705i	1.77582	+	0.564483i
$640$	56.3664			0.0880725
$641$		−	237.963i		−	0.371238i	−0.982622	−	0.185619i	$-0.940571\pi$
$641$		−	237.963i		−	0.371238i	0.982622	−	0.185619i	$-0.0594289\pi$
$642$	449.219	−	328.574i	0.699718	−	0.511798i
$643$	−478.906			−0.744800			−0.372400	−	0.928072i	$-0.621465\pi$
$643$	−478.906			−0.744800			−0.372400	+	0.928072i	$0.621465\pi$
$644$			120.807i			0.187588i
$645$	−643.992	−	880.451i	−0.998438	−	1.36504i
$646$	−44.4620			−0.0688266
$647$			369.380i			0.570912i	0.958392	+	0.285456i	$0.0921450\pi$
$647$			369.380i			0.570912i	−0.958392	+	0.285456i	$0.907855\pi$
$648$	132.284	−	187.053i	0.204142	−	0.288663i
$649$	−237.846			−0.366480
$650$		−	5.31492i		−	0.00817680i
$651$	−561.637	+	410.801i	−0.862730	+	0.631030i
$652$	−632.834			−0.970604
$653$			649.219i			0.994210i	0.867690	+	0.497105i	$0.165604\pi$
$653$			649.219i			0.994210i	−0.867690	+	0.497105i	$0.834396\pi$
$654$	319.339	+	436.593i	0.488286	+	0.667573i
$655$	635.166			0.969719
$656$		−	178.193i		−	0.271636i
$657$	−114.771	+	361.062i	−0.174689	+	0.549561i
$658$	220.444			0.335022
$659$			450.517i			0.683637i	0.939766	+	0.341819i	$0.111043\pi$
$659$			450.517i			0.683637i	−0.939766	+	0.341819i	$0.888957\pi$
$660$	−90.8697	+	66.4653i	−0.137681	+	0.100705i
$661$	−7.88122			−0.0119232			−0.00596159	−	0.999982i	$-0.501898\pi$
$661$	−7.88122			−0.0119232			−0.00596159	+	0.999982i	$0.501898\pi$
$662$		−	47.2160i		−	0.0713232i
$663$	−684.956	−	936.456i	−1.03312	−	1.41245i
$664$	462.642			0.696750
$665$			107.484i			0.161629i
$666$	249.169	+	79.2035i	0.374128	+	0.118924i
$667$	−33.3293			−0.0499690
$668$			522.535i			0.782238i
$669$	492.392	−	360.153i	0.736012	−	0.538345i
$670$	240.494			0.358946
$671$			71.1681i			0.106063i
$672$	126.187	+	172.520i	0.187778	+	0.256726i
$673$	−320.905			−0.476828			−0.238414	−	0.971164i	$-0.576628\pi$
$673$	−320.905			−0.476828			−0.238414	+	0.971164i	$0.576628\pi$
$674$		−	893.353i		−	1.32545i
$675$	−1.53199	−	4.56564i	−0.00226962	−	0.00676391i
$676$	−549.936			−0.813514
$677$		−	314.230i		−	0.464150i	−0.972698	−	0.232075i	$-0.925449\pi$
$677$		−	314.230i		−	0.464150i	0.972698	−	0.232075i	$-0.0745515\pi$
$678$	−315.852	+	231.025i	−0.465859	+	0.340745i
$679$	−1558.96			−2.29596
$680$		−	258.645i		−	0.380360i
$681$	163.391	+	223.384i	0.239928	+	0.328023i
$682$	98.0873			0.143823
$683$		−	1068.64i		−	1.56463i	−0.622881	−	0.782316i	$-0.714038\pi$
$683$		−	1068.64i		−	1.56463i	0.622881	−	0.782316i	$-0.285962\pi$
$684$	−9.34009	+	29.3833i	−0.0136551	+	0.0429580i
$685$	547.051			0.798615
$686$			1079.99i			1.57434i
$687$	61.7101	−	45.1369i	0.0898255	−	0.0657015i
$688$	291.932			0.424320
$689$			1813.69i			2.63236i
$690$	−59.8463	−	81.8204i	−0.0867337	−	0.118580i
$691$	374.425			0.541859			0.270929	−	0.962599i	$-0.412669\pi$
$691$	374.425			0.541859			0.270929	+	0.962599i	$0.412669\pi$
$692$			310.820i			0.449161i
$693$	−406.859	−	129.329i	−0.587098	−	0.186621i
$694$	−79.5839			−0.114674
$695$			705.512i			1.01513i
$696$	−47.5965	+	34.8137i	−0.0683857	+	0.0500197i
$697$	−817.663			−1.17312
$698$			4.62797i			0.00663034i
$699$	−481.208	−	657.896i	−0.688423	−	0.941196i
$700$	4.49296			0.00641852
$701$		−	131.881i		−	0.188132i	−0.995566	−	0.0940660i	$-0.970014\pi$
$701$		−	131.881i		−	0.188132i	0.995566	−	0.0940660i	$-0.0299865\pi$
$702$	−762.757	+	255.942i	−1.08655	+	0.364590i
$703$	−35.1859			−0.0500510
$704$		−	30.1298i		−	0.0427980i
$705$	−149.303	+	109.206i	−0.211778	+	0.154902i
$706$	233.083			0.330146
$707$		−	589.603i		−	0.833950i
$708$	−223.698	−	305.834i	−0.315957	−	0.431969i
$709$	−467.982			−0.660060			−0.330030	−	0.943970i	$-0.607059\pi$
$709$	−467.982			−0.660060			−0.330030	+	0.943970i	$0.607059\pi$
$710$		−	932.160i		−	1.31290i
$711$	−173.915	+	547.126i	−0.244607	+	0.769517i
$712$	15.9413			0.0223895
$713$			88.3192i			0.123870i
$714$	791.632	−	579.027i	1.10873	−	0.810962i
$715$	395.364			0.552957
$716$		−	200.944i		−	0.280649i
$717$	−477.087	−	652.262i	−0.665394	−	0.909711i
$718$	375.894			0.523530
$719$		−	569.565i		−	0.792163i	−0.918215	−	0.396082i	$-0.870370\pi$
$719$		−	569.565i		−	0.792163i	0.918215	−	0.396082i	$-0.129630\pi$
$720$	−170.929	−	54.3333i	−0.237401	−	0.0754630i
$721$	224.622			0.311543
$722$			506.382i			0.701360i
$723$	−730.591	+	534.379i	−1.01050	+	0.739114i
$724$	129.718			0.179168
$725$			1.23956i			0.00170974i
$726$	−267.542	−	365.777i	−0.368516	−	0.503826i
$727$	75.3699			0.103672			0.0518362	−	0.998656i	$-0.483493\pi$
$727$	75.3699			0.103672			0.0518362	+	0.998656i	$0.483493\pi$
$728$		−	750.616i		−	1.03107i
$729$	−581.453	+	439.720i	−0.797603	+	0.603183i
$730$	296.600			0.406301
$731$		−	1339.57i		−	1.83252i
$732$	−91.5117	+	66.9348i	−0.125016	+	0.0914410i
$733$	863.972			1.17868			0.589339	−	0.807886i	$-0.299388\pi$
$733$	863.972			1.17868			0.589339	+	0.807886i	$0.299388\pi$
$734$		−	101.782i		−	0.138668i
$735$	−967.386	−	1322.59i	−1.31617	−	1.79944i
$736$	27.1293			0.0368605
$737$		−	128.552i		−	0.174427i
$738$	−171.766	+	540.364i	−0.232745	+	0.732200i
$739$	−288.087			−0.389834			−0.194917	−	0.980820i	$-0.562444\pi$
$739$	−288.087			−0.389834			−0.194917	+	0.980820i	$0.562444\pi$
$740$		−	204.684i		−	0.276600i
$741$	87.3923	−	63.9218i	0.117938	−	0.0862642i
$742$	−1533.20			−2.06631
$743$			1299.94i			1.74958i	0.484501	+	0.874791i	$0.339001\pi$
$743$			1299.94i			1.74958i	−0.484501	+	0.874791i	$0.660999\pi$
$744$	92.2528	+	126.126i	0.123996	+	0.169524i
$745$	524.281			0.703733
$746$		−	815.025i		−	1.09253i
$747$	−1402.94	−	445.955i	−1.87811	−	0.596995i
$748$	−138.255			−0.184833
$749$		−	1652.24i		−	2.20592i
$750$	−429.561	+	314.196i	−0.572749	+	0.418928i
$751$	−1236.53			−1.64652			−0.823258	−	0.567667i	$-0.807846\pi$
$751$	−1236.53			−1.64652			−0.823258	+	0.567667i	$0.807846\pi$
$752$		−	49.5047i		−	0.0658308i
$753$	76.5712	+	104.686i	0.101688	+	0.139026i
$754$	207.087			0.274651
$755$			734.793i			0.973236i
$756$	−216.360	−	644.796i	−0.286191	−	0.852905i
$757$	705.351			0.931771			0.465886	−	0.884845i	$-0.345736\pi$
$757$	705.351			0.931771			0.465886	+	0.884845i	$0.345736\pi$
$758$			153.908i			0.203045i
$759$	−43.7359	+	31.9899i	−0.0576230	+	0.0421475i
$760$	24.1374			0.0317597
$761$			56.6243i			0.0744078i	0.999308	+	0.0372039i	$0.0118451\pi$
$761$			56.6243i			0.0744078i	−0.999308	+	0.0372039i	$0.988155\pi$
$762$	221.833	+	303.285i	0.291120	+	0.398012i
$763$	1605.80			2.10459
$764$		−	197.528i		−	0.258545i
$765$	−249.316	+	784.332i	−0.325903	+	1.02527i
$766$	189.524			0.247420
$767$			1330.65i			1.73488i
$768$	38.7425	−	28.3376i	0.0504460	−	0.0368979i
$769$	−18.3140			−0.0238154			−0.0119077	−	0.999929i	$-0.503790\pi$
$769$	−18.3140			−0.0238154			−0.0119077	+	0.999929i	$0.503790\pi$
$770$			334.221i			0.434053i
$771$	394.587	+	539.469i	0.511785	+	0.699701i
$772$	522.046			0.676226
$773$			685.118i			0.886311i	0.896445	+	0.443155i	$0.146141\pi$
$773$			685.118i			0.886311i	−0.896445	+	0.443155i	$0.853859\pi$
$774$	−885.275	−	281.403i	−1.14377	−	0.363570i
$775$	3.28471			0.00423834
$776$			350.092i			0.451149i
$777$	626.473	−	458.224i	0.806272	−	0.589735i
$778$	260.376			0.334673
$779$		−	76.3063i		−	0.0979542i
$780$	371.847	+	508.380i	0.476727	+	0.651769i
$781$	−498.272			−0.637993
$782$		−	124.487i		−	0.159190i
$783$	177.893	−	59.6916i	0.227194	−	0.0762344i
$784$	438.532			0.559352
$785$		−	917.311i		−	1.16855i
$786$	436.571	−	319.323i	0.555434	−	0.406263i
$787$	793.897			1.00876			0.504382	−	0.863481i	$-0.331720\pi$
$787$	793.897			1.00876			0.504382	+	0.863481i	$0.331720\pi$
$788$		−	333.943i		−	0.423786i
$789$	180.628	+	246.951i	0.228933	+	0.312992i
$790$	449.446			0.568919
$791$			1161.71i			1.46866i
$792$	−29.0431	+	91.3676i	−0.0366705	+	0.115363i
$793$	398.157			0.502090
$794$		−	265.608i		−	0.334518i
$795$	1038.41	−	759.532i	1.30618	−	0.955386i
$796$	−19.3696			−0.0243337
$797$		−	955.266i		−	1.19858i	−0.800533	−	0.599288i	$-0.795450\pi$
$797$		−	955.266i		−	1.19858i	0.800533	−	0.599288i	$-0.204550\pi$
$798$	54.0362	+	73.8770i	0.0677146	+	0.0925777i
$799$	−227.159			−0.284305
$800$		−	1.00898i		−	0.00126122i
$801$	−48.3416	−	15.3664i	−0.0603515	−	0.0191840i
$802$	−674.778			−0.841369
$803$		−	158.543i		−	0.197438i
$804$	165.300	−	120.906i	0.205596	−	0.150380i
$805$	−300.937			−0.373835
$806$		−	548.760i		−	0.680843i
$807$	−648.485	−	886.594i	−0.803575	−	1.09863i
$808$	−132.406			−0.163869
$809$			605.897i			0.748946i	0.927238	+	0.374473i	$0.122176\pi$
$809$			605.897i			0.748946i	−0.927238	+	0.374473i	$0.877824\pi$
$810$	465.962	+	329.528i	0.575262	+	0.406824i
$811$	747.889			0.922182			0.461091	−	0.887353i	$-0.347458\pi$
$811$	747.889			0.922182			0.461091	+	0.887353i	$0.347458\pi$
$812$			175.061i			0.215592i
$813$	−451.494	+	330.239i	−0.555344	+	0.406198i
$814$	−109.411			−0.134411
$815$		−	1576.43i		−	1.93427i
$816$	−130.031	−	177.775i	−0.159352	−	0.217862i
$817$	125.012			0.153014
$818$			96.0668i			0.117441i
$819$	−723.542	+	2276.21i	−0.883446	+	2.77926i
$820$	443.890			0.541330
$821$			57.3762i			0.0698858i	0.999389	+	0.0349429i	$0.0111249\pi$
$821$			57.3762i			0.0698858i	−0.999389	+	0.0349429i	$0.988875\pi$
$822$	376.006	−	275.024i	0.457429	−	0.334579i
$823$	1484.50			1.80377			0.901883	−	0.431980i	$-0.142185\pi$
$823$	1484.50			1.80377			0.901883	+	0.431980i	$0.142185\pi$
$824$		−	50.4430i		−	0.0612172i
$825$	1.18975	+	1.62660i	0.00144212	+	0.00197163i
$826$	−1124.87			−1.36182
$827$		−	836.449i		−	1.01143i	−0.862702	−	0.505713i	$-0.831230\pi$
$827$		−	836.449i		−	1.01143i	0.862702	−	0.505713i	$-0.168770\pi$
$828$	−82.2687	−	26.1508i	−0.0993583	−	0.0315831i
$829$	−342.477			−0.413121			−0.206560	−	0.978434i	$-0.566227\pi$
$829$	−342.477			−0.413121			−0.206560	+	0.978434i	$0.566227\pi$
$830$			1152.47i			1.38852i
$831$	457.846	−	334.884i	0.550958	−	0.402990i
$832$	−168.564			−0.202601
$833$		−	2012.27i		−	2.41569i
$834$	354.689	+	484.922i	0.425286	+	0.581441i
$835$	−1301.67			−1.55889
$836$		−	12.9023i		−	0.0154333i
$837$	−158.177	−	471.397i	−0.188980	−	0.563199i
$838$	18.8491			0.0224930
$839$			708.411i			0.844352i	0.906514	+	0.422176i	$0.138734\pi$
$839$			708.411i			0.844352i	−0.906514	+	0.422176i	$0.861266\pi$
$840$	−429.759	+	314.340i	−0.511617	+	0.374215i
$841$	792.703			0.942571
$842$			167.926i			0.199438i
$843$	428.881	+	586.356i	0.508756	+	0.695559i
$844$	−516.463			−0.611923
$845$		−	1369.93i		−	1.62121i
$846$	−47.7192	+	150.121i	−0.0564057	+	0.177448i
$847$	−1345.34			−1.58836
$848$			344.309i			0.406024i
$849$	399.822	−	292.443i	0.470933	−	0.344456i
$850$	−4.62983			−0.00544686
$851$		−	98.5150i		−	0.115764i
$852$	−468.634	−	640.705i	−0.550039	−	0.752001i
$853$	−1622.71			−1.90236			−0.951178	−	0.308644i	$-0.900125\pi$
$853$	−1622.71			−1.90236			−0.951178	+	0.308644i	$0.900125\pi$
$854$			336.582i			0.394124i
$855$	−73.1957	−	23.2668i	−0.0856091	−	0.0272126i
$856$	−371.040			−0.433458
$857$		−	154.383i		−	0.180143i	−0.995935	−	0.0900715i	$-0.971290\pi$
$857$		−	154.383i		−	0.180143i	0.995935	−	0.0900715i	$-0.0287096\pi$
$858$	271.747	−	198.765i	0.316721	−	0.231661i
$859$	−171.369			−0.199499			−0.0997494	−	0.995013i	$-0.531804\pi$
$859$	−171.369			−0.199499			−0.0997494	+	0.995013i	$0.531804\pi$
$860$			727.223i			0.845608i
$861$	993.735	+	1358.61i	1.15416	+	1.57795i
$862$	−825.256			−0.957374
$863$			490.441i			0.568298i	0.958780	+	0.284149i	$0.0917110\pi$
$863$			490.441i			0.568298i	−0.958780	+	0.284149i	$0.908289\pi$
$864$	−144.801	+	48.5876i	−0.167593	+	0.0562357i
$865$	−774.272			−0.895112
$866$			120.806i			0.139498i
$867$	−115.961	+	84.8177i	−0.133749	+	0.0978290i
$868$	463.893			0.534439
$869$		−	240.245i		−	0.276461i
$870$	−86.7232	−	118.566i	−0.0996819	−	0.136283i
$871$	−719.200			−0.825718
$872$		−	360.611i		−	0.413545i
$873$	337.464	−	1061.64i	0.386557	−	1.21608i
$874$	11.6174			0.0132922
$875$			1579.94i			1.80564i
$876$	203.863	−	149.112i	0.232720	−	0.170220i
$877$	111.509			0.127148			0.0635742	−	0.997977i	$-0.479750\pi$
$877$	111.509			0.127148			0.0635742	+	0.997977i	$0.479750\pi$
$878$		−	142.504i		−	0.162305i
$879$	539.961	+	738.221i	0.614290	+	0.839842i
$880$	75.0553			0.0852902
$881$			1693.76i			1.92254i	0.275601	+	0.961272i	$0.411123\pi$
$881$			1693.76i			1.92254i	−0.275601	+	0.961272i	$0.588877\pi$
$882$	−1329.83	−	422.715i	−1.50775	−	0.479269i
$883$	−313.231			−0.354735			−0.177368	−	0.984145i	$-0.556758\pi$
$883$	−313.231			−0.354735			−0.177368	+	0.984145i	$0.556758\pi$
$884$			773.481i			0.874979i
$885$	761.853	−	557.246i	0.860851	−	0.629656i
$886$	−236.255			−0.266654
$887$		−	1460.04i		−	1.64605i	−0.568009	−	0.823023i	$-0.692286\pi$
$887$		−	1460.04i		−	1.64605i	0.568009	−	0.823023i	$-0.307714\pi$
$888$	−102.903	−	140.686i	−0.115881	−	0.158430i
$889$	1115.49			1.25477
$890$			39.7109i			0.0446190i
$891$	176.144	−	249.073i	0.197693	−	0.279543i
$892$	−406.700			−0.455941
$893$		−	21.1991i		−	0.0237392i
$894$	360.356	−	263.577i	0.403082	−	0.294828i
$895$	500.566			0.559291
$896$		−	142.496i		−	0.159035i
$897$	178.971	+	244.685i	0.199522	+	0.272781i
$898$	1067.35			1.18859
$899$			127.983i			0.142362i
$900$	−0.972584	+	3.05968i	−0.00108065	+	0.00339965i
$901$	1579.91			1.75351
$902$		−	237.275i		−	0.263054i
$903$	−2225.80	+	1628.03i	−2.46490	+	1.80291i
$904$	260.884			0.288588
$905$			323.135i			0.357056i
$906$	369.409	+	505.048i	0.407737	+	0.557448i
$907$	−956.585			−1.05467			−0.527335	−	0.849658i	$-0.676809\pi$
$907$	−956.585			−1.05467			−0.527335	+	0.849658i	$0.676809\pi$
$908$		−	184.508i		−	0.203202i
$909$	401.516	+	127.630i	0.441712	+	0.140407i
$910$	1869.83			2.05476
$911$		−	957.270i		−	1.05079i	−0.850858	−	0.525395i	$-0.823918\pi$
$911$		−	957.270i		−	1.05079i	0.850858	−	0.525395i	$-0.176082\pi$
$912$	16.5904	−	12.1348i	0.0181913	−	0.0133057i
$913$	616.036			0.674739
$914$			377.849i			0.413401i
$915$	−166.739	−	227.962i	−0.182228	−	0.249138i
$916$	−50.9705			−0.0556447
$917$		−	1605.72i		−	1.75105i
$918$	222.951	+	664.438i	0.242866	+	0.723789i
$919$	−1044.24			−1.13628			−0.568140	−	0.822932i	$-0.692337\pi$
$919$	−1044.24			−1.13628			−0.568140	+	0.822932i	$0.692337\pi$
$920$			67.5809i			0.0734575i
$921$	179.184	−	131.061i	0.194554	−	0.142303i
$922$	1141.39			1.23795
$923$			2787.64i			3.02019i
$924$	168.026	+	229.721i	0.181846	+	0.248616i
$925$	−3.66391			−0.00396098
$926$			349.652i			0.377594i
$927$	−48.6236	+	152.967i	−0.0524526	+	0.165012i
$928$	39.3131			0.0423632
$929$			398.105i			0.428530i	0.976776	+	0.214265i	$0.0687357\pi$
$929$			398.105i			0.428530i	−0.976776	+	0.214265i	$0.931264\pi$
$930$	−314.188	+	229.808i	−0.337836	+	0.247105i
$931$	187.790			0.201707
$932$			543.400i			0.583047i
$933$	244.609	+	334.423i	0.262175	+	0.358439i
$934$	−430.967			−0.461421
$935$		−	344.402i		−	0.368344i
$936$	511.165	+	162.485i	0.546117	+	0.173595i
$937$	−507.700			−0.541836			−0.270918	−	0.962602i	$-0.587327\pi$
$937$	−507.700			−0.541836			−0.270918	+	0.962602i	$0.587327\pi$
$938$		−	607.975i		−	0.648161i
$939$	386.789	−	282.911i	0.411915	−	0.301289i
$940$	123.320			0.131191
$941$		−	1276.30i		−	1.35632i	−0.734913	−	0.678162i	$-0.762777\pi$
$941$		−	1276.30i		−	1.35632i	0.734913	−	0.678162i	$-0.237223\pi$
$942$	−461.168	−	630.499i	−0.489563	−	0.669319i
$943$	213.646			0.226560
$944$			252.609i			0.267594i
$945$	1606.23	−	538.968i	1.69971	−	0.570336i
$946$	388.726			0.410916
$947$			342.978i			0.362173i	0.983467	+	0.181087i	$0.0579614\pi$
$947$			342.978i			0.362173i	−0.983467	+	0.181087i	$0.942039\pi$
$948$	308.919	−	225.954i	0.325864	−	0.238348i
$949$	−886.986			−0.934653
$950$		−	0.432067i		−	0.000454807i
$951$	102.280	+	139.835i	0.107550	+	0.147040i
$952$	−653.862			−0.686829
$953$		−	89.4655i		−	0.0938778i	−0.998898	−	0.0469389i	$-0.985053\pi$
$953$		−	89.4655i		−	0.0938778i	0.998898	−	0.0469389i	$-0.0149466\pi$
$954$	331.890	−	1044.10i	0.347893	−	1.09445i
$955$	492.056			0.515242
$956$			538.747i			0.563543i
$957$	−63.3777	+	46.3566i	−0.0662253	+	0.0484395i
$958$	862.829			0.900657
$959$		−	1382.96i		−	1.44209i
$960$	70.5908	+	96.5101i	0.0735321	+	0.100531i
$961$	−621.857			−0.647094
$962$			612.109i			0.636288i
$963$	1125.16	+	357.657i	1.16840	+	0.371399i
$964$	603.444			0.625979
$965$			1300.45i			1.34762i
$966$	−206.844	+	151.293i	−0.214124	+	0.156618i
$967$	1047.87			1.08363			0.541816	−	0.840497i	$-0.317737\pi$
$967$	1047.87			1.08363			0.541816	+	0.840497i	$0.317737\pi$
$968$			302.120i			0.312107i
$969$	−55.6823	−	76.1275i	−0.0574637	−	0.0785629i
$970$	−872.101			−0.899074
$971$			423.388i			0.436033i	0.975945	+	0.218016i	$0.0699586\pi$
$971$			423.388i			0.436033i	−0.975945	+	0.218016i	$0.930041\pi$
$972$	485.938	−	7.76226i	0.499936	−	0.00798587i
$973$	1783.55			1.83305
$974$			1320.02i			1.35525i
$975$	9.10017	−	6.65618i	0.00933350	−	0.00682685i
$976$	75.5856			0.0774443
$977$		−	507.287i		−	0.519229i	−0.965712	−	0.259614i	$-0.916405\pi$
$977$		−	507.287i		−	0.519229i	0.965712	−	0.259614i	$-0.0835955\pi$
$978$	−792.534	−	1083.53i	−0.810362	−	1.10791i
$979$	21.2269			0.0216822
$980$			1092.41i			1.11471i
$981$	−347.605	+	1093.54i	−0.354337	+	1.11472i
$982$	−1273.73			−1.29708
$983$		−	609.939i		−	0.620488i	−0.950657	−	0.310244i	$-0.899589\pi$
$983$		−	609.939i		−	0.620488i	0.950657	−	0.310244i	$-0.100411\pi$
$984$	305.101	−	223.161i	0.310062	−	0.226790i
$985$	831.875			0.844543
$986$		−	180.394i		−	0.182955i
$987$	276.075	+	377.443i	0.279711	+	0.382414i
$988$	−72.1831			−0.0730599
$989$			350.015i			0.353908i
$990$	−227.603	−	72.3482i	−0.229902	−	0.0730790i
$991$	945.221			0.953805			0.476903	−	0.878956i	$-0.341759\pi$
$991$	945.221			0.953805			0.476903	+	0.878956i	$0.341759\pi$
$992$		−	104.176i		−	0.105016i
$993$	80.8428	−	59.1312i	0.0814127	−	0.0595481i
$994$	−2356.53			−2.37075
$995$		−	48.2510i		−	0.0484935i
$996$	579.393	+	792.132i	0.581720	+	0.795313i
$997$	−1498.51			−1.50302			−0.751509	−	0.659723i	$-0.770673\pi$
$997$	−1498.51			−1.50302			−0.751509	+	0.659723i	$0.770673\pi$
$998$			1297.90i			1.30050i
$999$	176.437	+	525.816i	0.176613	+	0.526343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.3.c.a.47.7	✓	16
3.2	odd	2	inner	138.3.c.a.47.15	yes	16
4.3	odd	2		1104.3.g.c.737.4		16
12.11	even	2		1104.3.g.c.737.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.c.a.47.7	✓	16	1.1	even	1	trivial
138.3.c.a.47.15	yes	16	3.2	odd	2	inner
1104.3.g.c.737.3		16	12.11	even	2
1104.3.g.c.737.4		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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(2.42141 - 1.77110i) q^{3} -2.00000 q^{4} -4.98213i q^{5} +(-2.50471 - 3.42438i) q^{6} -12.5950 q^{7} +2.82843i q^{8} +(2.72641 - 8.57710i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(2.42141 - 1.77110i) q^{3} -2.00000 q^{4} -4.98213i q^{5} +(-2.50471 - 3.42438i) q^{6} -12.5950 q^{7} +2.82843i q^{8} +(2.72641 - 8.57710i) q^{9} -7.04580 q^{10} +3.76623i q^{11} +(-4.84281 + 3.54220i) q^{12} +21.0705 q^{13} +17.8120i q^{14} +(-8.82385 - 12.0638i) q^{15} +4.00000 q^{16} -18.3546i q^{17} +(-12.1299 - 3.85573i) q^{18} +1.71289 q^{19} +9.96426i q^{20} +(-30.4975 + 22.3069i) q^{21} +5.32625 q^{22} +4.79583i q^{23} +(5.00943 + 6.84877i) q^{24} +0.178363 q^{25} -29.7983i q^{26} +(-8.58916 - 25.5974i) q^{27} +25.1899 q^{28} +6.94964i q^{29} +(-17.0607 + 12.4788i) q^{30} +18.4158 q^{31} -5.65685i q^{32} +(6.67036 + 9.11956i) q^{33} -25.9573 q^{34} +62.7498i q^{35} +(-5.45282 + 17.1542i) q^{36} -20.5418 q^{37} -2.42240i q^{38} +(51.0203 - 37.3180i) q^{39} +14.0916 q^{40} -44.5482i q^{41} +(31.5468 + 43.1300i) q^{42} +72.9831 q^{43} -7.53245i q^{44} +(-42.7323 - 13.5833i) q^{45} +6.78233 q^{46} -12.3762i q^{47} +(9.68562 - 7.08440i) q^{48} +109.633 q^{49} -0.252244i q^{50} +(-32.5078 - 44.4438i) q^{51} -42.1411 q^{52} +86.0772i q^{53} +(-36.2002 + 12.1469i) q^{54} +18.7638 q^{55} -35.6239i q^{56} +(4.14761 - 3.03370i) q^{57} +9.82827 q^{58} +63.1522i q^{59} +(17.6477 + 24.1275i) q^{60} +18.8964 q^{61} -26.0439i q^{62} +(-34.3390 + 108.028i) q^{63} -8.00000 q^{64} -104.976i q^{65} +(12.8970 - 9.43332i) q^{66} -34.1330 q^{67} +36.7091i q^{68} +(8.49390 + 11.6127i) q^{69} +88.7416 q^{70} +132.300i q^{71} +(24.2597 + 7.71145i) q^{72} -42.0960 q^{73} +29.0505i q^{74} +(0.431890 - 0.315900i) q^{75} -3.42578 q^{76} -47.4355i q^{77} +(-52.7757 - 72.1537i) q^{78} -63.7892 q^{79} -19.9285i q^{80} +(-66.1334 - 46.7694i) q^{81} -63.0007 q^{82} -163.569i q^{83} +(60.9950 - 44.6139i) q^{84} -91.4448 q^{85} -103.214i q^{86} +(12.3085 + 16.8279i) q^{87} -10.6525 q^{88} -5.63612i q^{89} +(-19.2097 + 60.4325i) q^{90} -265.383 q^{91} -9.59166i q^{92} +(44.5922 - 32.6163i) q^{93} -17.5026 q^{94} -8.53385i q^{95} +(-10.0189 - 13.6975i) q^{96} +123.776 q^{97} -155.045i q^{98} +(32.3033 + 10.2683i) 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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