LMFDB - Embedded newform 138.3.c.a.47.6

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			47.6
Root			$1.62763 - 2.52009i$ of defining polynomial
Character	$\chi$	$=$	138.47
Dual form			138.3.c.a.47.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(1.62763 - 2.52009i) q^{3} -2.00000 q^{4} -1.81026i q^{5} +(-3.56394 - 2.30181i) q^{6} +9.47484 q^{7} +2.82843i q^{8} +(-3.70167 - 8.20351i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(1.62763 - 2.52009i) q^{3} -2.00000 q^{4} -1.81026i q^{5} +(-3.56394 - 2.30181i) q^{6} +9.47484 q^{7} +2.82843i q^{8} +(-3.70167 - 8.20351i) q^{9} -2.56010 q^{10} -11.4637i q^{11} +(-3.25525 + 5.04017i) q^{12} -20.7422 q^{13} -13.3995i q^{14} +(-4.56202 - 2.94643i) q^{15} +4.00000 q^{16} +27.7399i q^{17} +(-11.6015 + 5.23495i) q^{18} +10.5192 q^{19} +3.62053i q^{20} +(15.4215 - 23.8774i) q^{21} -16.2121 q^{22} +4.79583i q^{23} +(7.12788 + 4.60362i) q^{24} +21.7229 q^{25} +29.3339i q^{26} +(-26.6985 - 4.02373i) q^{27} -18.9497 q^{28} -20.5838i q^{29} +(-4.16689 + 6.45167i) q^{30} +13.1567 q^{31} -5.65685i q^{32} +(-28.8895 - 18.6586i) q^{33} +39.2302 q^{34} -17.1520i q^{35} +(7.40334 + 16.4070i) q^{36} +63.2079 q^{37} -14.8764i q^{38} +(-33.7606 + 52.2722i) q^{39} +5.12020 q^{40} +1.80432i q^{41} +(-33.7678 - 21.8093i) q^{42} +47.2905 q^{43} +22.9274i q^{44} +(-14.8505 + 6.70100i) q^{45} +6.78233 q^{46} +48.8498i q^{47} +(6.51050 - 10.0803i) q^{48} +40.7727 q^{49} -30.7209i q^{50} +(69.9071 + 45.1503i) q^{51} +41.4844 q^{52} -19.1831i q^{53} +(-5.69041 + 37.7574i) q^{54} -20.7523 q^{55} +26.7989i q^{56} +(17.1213 - 26.5093i) q^{57} -29.1099 q^{58} +117.009i q^{59} +(9.12404 + 5.89287i) q^{60} -63.4305 q^{61} -18.6063i q^{62} +(-35.0727 - 77.7270i) q^{63} -8.00000 q^{64} +37.5489i q^{65} +(-26.3873 + 40.8559i) q^{66} -87.8883 q^{67} -55.4799i q^{68} +(12.0859 + 7.80582i) q^{69} -24.2566 q^{70} -6.81275i q^{71} +(23.2030 - 10.4699i) q^{72} +74.4816 q^{73} -89.3894i q^{74} +(35.3568 - 54.7437i) q^{75} -21.0384 q^{76} -108.617i q^{77} +(73.9240 + 47.7447i) q^{78} -28.6865 q^{79} -7.24106i q^{80} +(-53.5953 + 60.7334i) q^{81} +2.55169 q^{82} +20.7975i q^{83} +(-30.8430 + 47.7548i) q^{84} +50.2166 q^{85} -66.8788i q^{86} +(-51.8730 - 33.5027i) q^{87} +32.4242 q^{88} +23.5142i q^{89} +(9.47664 + 21.0018i) q^{90} -196.529 q^{91} -9.59166i q^{92} +(21.4141 - 33.1559i) q^{93} +69.0841 q^{94} -19.0425i q^{95} +(-14.2558 - 9.20724i) q^{96} +24.5487 q^{97} -57.6613i q^{98} +(-94.0426 + 42.4348i) 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
$3$	1.62763	−	2.52009i	0.542542	−	0.840029i
$3$	1.62763	−	2.52009i	0.542542	−	0.840029i
$4$	−2.00000			−0.500000
$5$		−	1.81026i		−	0.362053i	−0.983478	−	0.181026i	$-0.942058\pi$
$5$		−	1.81026i		−	0.362053i	0.983478	−	0.181026i	$-0.0579420\pi$
$6$	−3.56394	−	2.30181i	−0.593990	−	0.383635i
$7$	9.47484			1.35355			0.676775	−	0.736190i	$-0.263377\pi$
$7$	9.47484			1.35355			0.676775	+	0.736190i	$0.263377\pi$
$8$			2.82843i			0.353553i
$9$	−3.70167	−	8.20351i	−0.411296	−	0.911502i
$10$	−2.56010			−0.256010
$11$		−	11.4637i		−	1.04215i	−0.853510	−	0.521077i	$-0.825530\pi$
$11$		−	11.4637i		−	1.04215i	0.853510	−	0.521077i	$-0.174470\pi$
$12$	−3.25525	+	5.04017i	−0.271271	+	0.420014i
$13$	−20.7422			−1.59556			−0.797778	−	0.602952i	$-0.793991\pi$
$13$	−20.7422			−1.59556			−0.797778	+	0.602952i	$0.793991\pi$
$14$		−	13.3995i		−	0.957104i
$15$	−4.56202	−	2.94643i	−0.304135	−	0.196429i
$16$	4.00000			0.250000
$17$			27.7399i			1.63176i	0.578220	+	0.815881i	$0.303748\pi$
$17$			27.7399i			1.63176i	−0.578220	+	0.815881i	$0.696252\pi$
$18$	−11.6015	+	5.23495i	−0.644529	+	0.290831i
$19$	10.5192			0.553642			0.276821	−	0.960921i	$-0.410719\pi$
$19$	10.5192			0.553642			0.276821	+	0.960921i	$0.410719\pi$
$20$			3.62053i			0.181026i
$21$	15.4215	−	23.8774i	0.734357	−	1.13702i
$22$	−16.2121			−0.736914
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	7.12788	+	4.60362i	0.296995	+	0.191818i
$25$	21.7229			0.868918
$26$			29.3339i			1.12823i
$27$	−26.6985	−	4.02373i	−0.988833	−	0.149027i
$28$	−18.9497			−0.676775
$29$		−	20.5838i		−	0.709786i	−0.934907	−	0.354893i	$-0.884517\pi$
$29$		−	20.5838i		−	0.709786i	0.934907	−	0.354893i	$-0.115483\pi$
$30$	−4.16689	+	6.45167i	−0.138896	+	0.215056i
$31$	13.1567			0.424409			0.212204	−	0.977225i	$-0.431936\pi$
$31$	13.1567			0.424409			0.212204	+	0.977225i	$0.431936\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−28.8895	−	18.6586i	−0.875440	−	0.565412i
$34$	39.2302			1.15383
$35$		−	17.1520i		−	0.490056i
$36$	7.40334	+	16.4070i	0.205648	+	0.455751i
$37$	63.2079			1.70832			0.854160	−	0.520009i	$-0.174072\pi$
$37$	63.2079			1.70832			0.854160	+	0.520009i	$0.174072\pi$
$38$		−	14.8764i		−	0.391484i
$39$	−33.7606	+	52.2722i	−0.865656	+	1.34031i
$40$	5.12020			0.128005
$41$			1.80432i			0.0440078i	0.999758	+	0.0220039i	$0.00700462\pi$
$41$			1.80432i			0.0440078i	−0.999758	+	0.0220039i	$0.992995\pi$
$42$	−33.7678	−	21.8093i	−0.803995	−	0.519269i
$43$	47.2905			1.09978			0.549889	−	0.835238i	$-0.314670\pi$
$43$	47.2905			1.09978			0.549889	+	0.835238i	$0.314670\pi$
$44$			22.9274i			0.521077i
$45$	−14.8505	+	6.70100i	−0.330012	+	0.148911i
$46$	6.78233			0.147442
$47$			48.8498i			1.03936i	0.854362	+	0.519679i	$0.173948\pi$
$47$			48.8498i			1.03936i	−0.854362	+	0.519679i	$0.826052\pi$
$48$	6.51050	−	10.0803i	0.135635	−	0.210007i
$49$	40.7727			0.832095
$50$		−	30.7209i		−	0.614418i
$51$	69.9071	+	45.1503i	1.37073	+	0.885299i
$52$	41.4844			0.797778
$53$		−	19.1831i		−	0.361945i	−0.983488	−	0.180972i	$-0.942076\pi$
$53$		−	19.1831i		−	0.361945i	0.983488	−	0.180972i	$-0.0579244\pi$
$54$	−5.69041	+	37.7574i	−0.105378	+	0.699211i
$55$	−20.7523			−0.377315
$56$			26.7989i			0.478552i
$57$	17.1213	−	26.5093i	0.300374	−	0.465075i
$58$	−29.1099			−0.501895
$59$			117.009i			1.98321i	0.129301	+	0.991605i	$0.458727\pi$
$59$			117.009i			1.98321i	−0.129301	+	0.991605i	$0.541273\pi$
$60$	9.12404	+	5.89287i	0.152067	+	0.0982144i
$61$	−63.4305			−1.03984			−0.519922	−	0.854214i	$-0.674039\pi$
$61$	−63.4305			−1.03984			−0.519922	+	0.854214i	$0.674039\pi$
$62$		−	18.6063i		−	0.300102i
$63$	−35.0727	−	77.7270i	−0.556710	−	1.23376i
$64$	−8.00000			−0.125000
$65$			37.5489i			0.577675i
$66$	−26.3873	+	40.8559i	−0.399807	+	0.619029i
$67$	−87.8883			−1.31177			−0.655883	−	0.754863i	$-0.727704\pi$
$67$	−87.8883			−1.31177			−0.655883	+	0.754863i	$0.727704\pi$
$68$		−	55.4799i		−	0.815881i
$69$	12.0859	+	7.80582i	0.175158	+	0.113128i
$70$	−24.2566			−0.346522
$71$		−	6.81275i		−	0.0959542i	−0.998848	−	0.0479771i	$-0.984723\pi$
$71$		−	6.81275i		−	0.0959542i	0.998848	−	0.0479771i	$-0.0152775\pi$
$72$	23.2030	−	10.4699i	0.322264	−	0.145415i
$73$	74.4816			1.02030			0.510148	−	0.860087i	$-0.329591\pi$
$73$	74.4816			1.02030			0.510148	+	0.860087i	$0.329591\pi$
$74$		−	89.3894i		−	1.20797i
$75$	35.3568	−	54.7437i	0.471424	−	0.729916i
$76$	−21.0384			−0.276821
$77$		−	108.617i		−	1.41061i
$78$	73.9240	+	47.7447i	0.947744	+	0.612111i
$79$	−28.6865			−0.363120			−0.181560	−	0.983380i	$-0.558115\pi$
$79$	−28.6865			−0.363120			−0.181560	+	0.983380i	$0.558115\pi$
$80$		−	7.24106i		−	0.0905132i
$81$	−53.5953	+	60.7334i	−0.661670	+	0.749795i
$82$	2.55169			0.0311182
$83$			20.7975i			0.250572i	0.992121	+	0.125286i	$0.0399849\pi$
$83$			20.7975i			0.250572i	−0.992121	+	0.125286i	$0.960015\pi$
$84$	−30.8430	+	47.7548i	−0.367179	+	0.568510i
$85$	50.2166			0.590784
$86$		−	66.8788i		−	0.777661i
$87$	−51.8730	−	33.5027i	−0.596241	−	0.385089i
$88$	32.4242			0.368457
$89$			23.5142i			0.264204i	0.991236	+	0.132102i	$0.0421727\pi$
$89$			23.5142i			0.264204i	−0.991236	+	0.132102i	$0.957827\pi$
$90$	9.47664	+	21.0018i	0.105296	+	0.233354i
$91$	−196.529			−2.15966
$92$		−	9.59166i		−	0.104257i
$93$	21.4141	−	33.1559i	0.230259	−	0.356515i
$94$	69.0841			0.734937
$95$		−	19.0425i		−	0.200448i
$96$	−14.2558	−	9.20724i	−0.148497	−	0.0959088i
$97$	24.5487			0.253079			0.126540	−	0.991962i	$-0.459613\pi$
$97$	24.5487			0.253079			0.126540	+	0.991962i	$0.459613\pi$
$98$		−	57.6613i		−	0.588380i
$99$	−94.0426	+	42.4348i	−0.949925	+	0.428634i
$100$	−43.4459			−0.434459
$101$		−	92.0421i		−	0.911308i	−0.890157	−	0.455654i	$-0.849405\pi$
$101$		−	92.0421i		−	0.911308i	0.890157	−	0.455654i	$-0.150595\pi$
$102$	63.8521	−	98.8635i	0.626001	−	0.969250i
$103$	−117.916			−1.14482			−0.572409	−	0.819968i	$-0.693991\pi$
$103$	−117.916			−1.14482			−0.572409	+	0.819968i	$0.693991\pi$
$104$		−	58.6678i		−	0.564114i
$105$	−43.2244	−	27.9170i	−0.411661	−	0.265876i
$106$	−27.1289			−0.255933
$107$		−	40.1896i		−	0.375604i	−0.982207	−	0.187802i	$-0.939864\pi$
$107$		−	40.1896i		−	0.375604i	0.982207	−	0.187802i	$-0.0601363\pi$
$108$	53.3970	+	8.04746i	0.494417	+	0.0745135i
$109$	−113.768			−1.04374			−0.521870	−	0.853025i	$-0.674765\pi$
$109$	−113.768			−1.04374			−0.521870	+	0.853025i	$0.674765\pi$
$110$			29.3482i			0.266802i
$111$	102.879	−	159.289i	0.926836	−	1.43504i
$112$	37.8994			0.338387
$113$			129.039i			1.14194i	0.820971	+	0.570969i	$0.193433\pi$
$113$			129.039i			1.14194i	−0.820971	+	0.570969i	$0.806567\pi$
$114$	−37.4898	−	24.2132i	−0.328858	−	0.212397i
$115$	8.68172			0.0754932
$116$			41.1676i			0.354893i
$117$	76.7808	+	170.159i	0.656246	+	1.45435i
$118$	165.476			1.40234
$119$			262.832i			2.20867i
$120$	8.33377	−	12.9033i	0.0694481	−	0.107528i
$121$	−10.4164			−0.0860858
$122$			89.7042i			0.735281i
$123$	4.54704	+	2.93676i	0.0369678	+	0.0238761i
$124$	−26.3133			−0.212204
$125$		−	84.5809i		−	0.676647i
$126$	−109.923	+	49.6003i	−0.872402	+	0.393653i
$127$	−68.5824			−0.540019			−0.270009	−	0.962858i	$-0.587027\pi$
$127$	−68.5824			−0.540019			−0.270009	+	0.962858i	$0.587027\pi$
$128$			11.3137i			0.0883883i
$129$	76.9712	−	119.176i	0.596676	−	0.923845i
$130$	53.1022			0.408478
$131$		−	186.736i		−	1.42547i	−0.701434	−	0.712734i	$-0.747456\pi$
$131$		−	186.736i		−	1.42547i	0.701434	−	0.712734i	$-0.252544\pi$
$132$	57.7790	+	37.3172i	0.437720	+	0.282706i
$133$	99.6678			0.749382
$134$			124.293i			0.927559i
$135$	−7.28401	+	48.3313i	−0.0539557	+	0.358010i
$136$	−78.4604			−0.576915
$137$		−	167.406i		−	1.22194i	−0.791652	−	0.610972i	$-0.790779\pi$
$137$		−	167.406i		−	1.22194i	0.791652	−	0.610972i	$-0.209221\pi$
$138$	11.0391	−	17.0921i	0.0799934	−	0.123855i
$139$	197.172			1.41850			0.709251	−	0.704956i	$-0.249033\pi$
$139$	197.172			1.41850			0.709251	+	0.704956i	$0.249033\pi$
$140$			34.3039i			0.245028i
$141$	123.106	+	79.5092i	0.873090	+	0.563895i
$142$	−9.63468			−0.0678499
$143$			237.783i			1.66281i
$144$	−14.8067	−	32.8141i	−0.102824	−	0.227875i
$145$	−37.2621			−0.256980
$146$		−	105.333i		−	0.721459i
$147$	66.3626	−	102.751i	0.451447	−	0.698984i
$148$	−126.416			−0.854160
$149$			106.490i			0.714695i	0.933971	+	0.357348i	$0.116319\pi$
$149$			106.490i			0.714695i	−0.933971	+	0.357348i	$0.883681\pi$
$150$	−77.4193	−	50.0021i	−0.516128	−	0.333347i
$151$	−83.3947			−0.552283			−0.276141	−	0.961117i	$-0.589056\pi$
$151$	−83.3947			−0.552283			−0.276141	+	0.961117i	$0.589056\pi$
$152$			29.7528i			0.195742i
$153$	227.565	−	102.684i	1.48735	−	0.671138i
$154$	−153.607			−0.997450
$155$		−	23.8170i		−	0.153658i
$156$	67.5211	−	104.544i	0.432828	−	0.670156i
$157$	−34.5546			−0.220093			−0.110046	−	0.993926i	$-0.535100\pi$
$157$	−34.5546			−0.220093			−0.110046	+	0.993926i	$0.535100\pi$
$158$			40.5688i			0.256764i
$159$	−48.3430	−	31.2228i	−0.304044	−	0.196370i
$160$	−10.2404			−0.0640025
$161$			45.4398i			0.282234i
$162$	85.8900	+	75.7952i	0.530185	+	0.467872i
$163$	−297.844			−1.82726			−0.913630	−	0.406546i	$-0.866733\pi$
$163$	−297.844			−1.82726			−0.913630	+	0.406546i	$0.866733\pi$
$164$		−	3.60864i		−	0.0220039i
$165$	−33.7770	+	52.2976i	−0.204709	+	0.316955i
$166$	29.4121			0.177181
$167$			104.050i			0.623052i	0.950238	+	0.311526i	$0.100840\pi$
$167$			104.050i			0.623052i	−0.950238	+	0.311526i	$0.899160\pi$
$168$	67.5355	+	43.6186i	0.401997	+	0.259634i
$169$	261.240			1.54580
$170$		−	71.0171i		−	0.417747i
$171$	−38.9386	−	86.2944i	−0.227711	−	0.504646i
$172$	−94.5809			−0.549889
$173$		−	12.5888i		−	0.0727676i	−0.999338	−	0.0363838i	$-0.988416\pi$
$173$		−	12.5888i		−	0.0727676i	0.999338	−	0.0363838i	$-0.0115839\pi$
$174$	−47.3800	+	73.3594i	−0.272299	+	0.421606i
$175$	205.821			1.17612
$176$		−	45.8548i		−	0.260539i
$177$	294.874	+	190.448i	1.66595	+	1.07598i
$178$	33.2541			0.186821
$179$			123.876i			0.692046i	0.938226	+	0.346023i	$0.112468\pi$
$179$			123.876i			0.692046i	−0.938226	+	0.346023i	$0.887532\pi$
$180$	29.7011	−	13.4020i	0.165006	−	0.0744555i
$181$	−315.353			−1.74228			−0.871140	−	0.491035i	$-0.836619\pi$
$181$	−315.353			−1.74228			−0.871140	+	0.491035i	$0.836619\pi$
$182$			277.934i			1.52711i
$183$	−103.241	+	159.850i	−0.564159	+	0.873499i
$184$	−13.5647			−0.0737210
$185$		−	114.423i		−	0.618502i
$186$	−46.8896	−	30.2841i	−0.252094	−	0.162818i
$187$	318.002			1.70055
$188$		−	97.6996i		−	0.519679i
$189$	−252.964	−	38.1242i	−1.33843	−	0.201715i
$190$	−26.9302			−0.141738
$191$			140.909i			0.737745i	0.929480	+	0.368873i	$0.120256\pi$
$191$			140.909i			0.737745i	−0.929480	+	0.368873i	$0.879744\pi$
$192$	−13.0210	+	20.1607i	−0.0678177	+	0.105004i
$193$	226.542			1.17379			0.586897	−	0.809662i	$-0.300349\pi$
$193$	226.542			1.17379			0.586897	+	0.809662i	$0.300349\pi$
$194$		−	34.7171i		−	0.178954i
$195$	94.6264	+	61.1155i	0.485264	+	0.313413i
$196$	−81.5453			−0.416048
$197$			150.595i			0.764441i	0.924071	+	0.382221i	$0.124841\pi$
$197$			150.595i			0.764441i	−0.924071	+	0.382221i	$0.875159\pi$
$198$	60.0119	+	132.996i	0.303090	+	0.671699i
$199$	−8.00643			−0.0402333			−0.0201167	−	0.999798i	$-0.506404\pi$
$199$	−8.00643			−0.0402333			−0.0201167	+	0.999798i	$0.506404\pi$
$200$			61.4418i			0.307209i
$201$	−143.049	+	221.486i	−0.711688	+	1.10192i
$202$	−130.167			−0.644392
$203$		−	195.028i		−	0.960731i
$204$	−139.814	−	90.3005i	−0.685363	−	0.442650i
$205$	3.26630			0.0159332
$206$			166.759i			0.809509i
$207$	39.3427	−	17.7526i	0.190061	−	0.0857612i
$208$	−82.9689			−0.398889
$209$		−	120.589i		−	0.576981i
$210$	−39.4806	+	61.1286i	−0.188003	+	0.291089i
$211$	−87.8983			−0.416580			−0.208290	−	0.978067i	$-0.566790\pi$
$211$	−87.8983			−0.416580			−0.208290	+	0.978067i	$0.566790\pi$
$212$			38.3661i			0.180972i
$213$	−17.1687	−	11.0886i	−0.0806043	−	0.0520592i
$214$	−56.8367			−0.265592
$215$		−	85.6082i		−	0.398178i
$216$	11.3808	−	75.5147i	0.0526890	−	0.349605i
$217$	124.657			0.574458
$218$			160.892i			0.738036i
$219$	121.228	−	187.700i	0.553554	−	0.857078i
$220$	41.5046			0.188657
$221$		−	575.388i		−	2.60357i
$222$	−225.269	−	145.493i	−1.01473	−	0.655372i
$223$	−50.4601			−0.226279			−0.113139	−	0.993579i	$-0.536091\pi$
$223$	−50.4601			−0.226279			−0.113139	+	0.993579i	$0.536091\pi$
$224$		−	53.5978i		−	0.239276i
$225$	−80.4111	−	178.204i	−0.357383	−	0.792020i
$226$	182.489			0.807473
$227$		−	44.4987i		−	0.196030i	−0.995185	−	0.0980148i	$-0.968751\pi$
$227$		−	44.4987i		−	0.196030i	0.995185	−	0.0980148i	$-0.0312492\pi$
$228$	−34.2427	+	53.0186i	−0.150187	+	0.232538i
$229$	95.4401			0.416769			0.208385	−	0.978047i	$-0.433179\pi$
$229$	95.4401			0.416769			0.208385	+	0.978047i	$0.433179\pi$
$230$		−	12.2778i		−	0.0533818i
$231$	−273.724	−	176.787i	−1.18495	−	0.765314i
$232$	58.2198			0.250947
$233$		−	389.122i		−	1.67005i	−0.550210	−	0.835026i	$-0.685452\pi$
$233$		−	389.122i		−	1.67005i	0.550210	−	0.835026i	$-0.314548\pi$
$234$	240.641	−	108.584i	1.02838	−	0.464036i
$235$	88.4311			0.376302
$236$		−	234.019i		−	0.991605i
$237$	−46.6908	+	72.2923i	−0.197008	+	0.305031i
$238$	371.700			1.56177
$239$			48.4876i			0.202877i	0.994842	+	0.101438i	$0.0323445\pi$
$239$			48.4876i			0.202877i	−0.994842	+	0.101438i	$0.967656\pi$
$240$	−18.2481	−	11.7857i	−0.0760337	−	0.0491072i
$241$	−406.475			−1.68662			−0.843309	−	0.537428i	$-0.819396\pi$
$241$	−406.475			−1.68662			−0.843309	+	0.537428i	$0.819396\pi$
$242$			14.7310i			0.0608718i
$243$	65.8202	+	233.916i	0.270865	+	0.962617i
$244$	126.861			0.519922
$245$		−	73.8093i		−	0.301262i
$246$	4.15320	−	6.43049i	0.0168829	−	0.0261402i
$247$	−218.192			−0.883367
$248$			37.2127i			0.150051i
$249$	52.4115	+	33.8506i	0.210488	+	0.135946i
$250$	−119.615			−0.478462
$251$		−	110.128i		−	0.438758i	−0.975640	−	0.219379i	$-0.929597\pi$
$251$		−	110.128i		−	0.438758i	0.975640	−	0.219379i	$-0.0704032\pi$
$252$	70.1455	+	155.454i	0.278355	+	0.616881i
$253$	54.9780			0.217304
$254$			96.9902i			0.381851i
$255$	81.7339	−	126.550i	0.320525	−	0.496276i
$256$	16.0000			0.0625000
$257$		−	30.6830i		−	0.119389i	−0.998217	−	0.0596945i	$-0.980987\pi$
$257$		−	30.6830i		−	0.119389i	0.998217	−	0.0596945i	$-0.0190127\pi$
$258$	−168.540	−	108.854i	−0.653257	−	0.421913i
$259$	598.885			2.31230
$260$		−	75.0978i		−	0.288838i
$261$	−168.860	+	76.1944i	−0.646971	+	0.291933i
$262$	−264.085			−1.00796
$263$		−	168.890i		−	0.642166i	−0.947051	−	0.321083i	$-0.895953\pi$
$263$		−	168.890i		−	0.642166i	0.947051	−	0.321083i	$-0.104047\pi$
$264$	52.7745	−	81.7119i	0.199903	−	0.309515i
$265$	−34.7264			−0.131043
$266$		−	140.952i		−	0.529893i
$267$	59.2577	+	38.2723i	0.221939	+	0.143342i
$268$	175.777			0.655883
$269$			465.034i			1.72875i	0.502847	+	0.864375i	$0.332286\pi$
$269$			465.034i			1.72875i	−0.502847	+	0.864375i	$0.667714\pi$
$270$	68.3508	+	10.3012i	0.253151	+	0.0381524i
$271$	−165.783			−0.611744			−0.305872	−	0.952073i	$-0.598948\pi$
$271$	−165.783			−0.611744			−0.305872	+	0.952073i	$0.598948\pi$
$272$			110.960i			0.407940i
$273$	−319.876	+	495.271i	−1.17171	+	1.81418i
$274$	−236.748			−0.864045
$275$		−	249.025i		−	0.905546i
$276$	−24.1718	−	15.6116i	−0.0875790	−	0.0565639i
$277$	−468.797			−1.69241			−0.846205	−	0.532858i	$-0.821118\pi$
$277$	−468.797			−1.69241			−0.846205	+	0.532858i	$0.821118\pi$
$278$		−	278.843i		−	1.00303i
$279$	−48.7016	−	107.931i	−0.174558	−	0.386849i
$280$	48.5131			0.173261
$281$		−	6.19405i		−	0.0220429i	−0.999939	−	0.0110214i	$-0.996492\pi$
$281$		−	6.19405i		−	0.0220429i	0.999939	−	0.0110214i	$-0.00350830\pi$
$282$	112.443	−	174.098i	0.398734	−	0.617368i
$283$	392.632			1.38739			0.693696	−	0.720268i	$-0.255981\pi$
$283$	392.632			1.38739			0.693696	+	0.720268i	$0.255981\pi$
$284$			13.6255i			0.0479771i
$285$	−47.9888	−	30.9941i	−0.168382	−	0.108751i
$286$	336.275			1.17579
$287$			17.0956i			0.0595667i
$288$	−46.4061	+	20.9398i	−0.161132	+	0.0727076i
$289$	−480.505			−1.66265
$290$			52.6966i			0.181712i
$291$	39.9561	−	61.8649i	0.137306	−	0.212594i
$292$	−148.963			−0.510148
$293$		−	312.715i		−	1.06729i	−0.845710	−	0.533643i	$-0.820823\pi$
$293$		−	312.715i		−	1.06729i	0.845710	−	0.533643i	$-0.179177\pi$
$294$	−145.311	−	93.8509i	−0.494256	−	0.319221i
$295$	211.818			0.718027
$296$			178.779i			0.603983i
$297$	−46.1268	+	306.063i	−0.155309	+	1.03052i
$298$	150.599			0.505366
$299$		−	99.4762i		−	0.332696i
$300$	−70.7136	+	109.487i	−0.235712	+	0.364958i
$301$	448.070			1.48860
$302$			117.938i			0.390523i
$303$	−231.954	−	149.810i	−0.765525	−	0.494423i
$304$	42.0768			0.138411
$305$			114.826i			0.376478i
$306$	−145.217	−	321.826i	−0.474566	−	1.05172i
$307$	453.834			1.47829			0.739143	−	0.673548i	$-0.235231\pi$
$307$	453.834			1.47829			0.739143	+	0.673548i	$0.235231\pi$
$308$			217.233i			0.705304i
$309$	−191.924	+	297.159i	−0.621112	+	0.961681i
$310$	−33.6824			−0.108653
$311$			479.647i			1.54227i	0.636670	+	0.771137i	$0.280311\pi$
$311$			479.647i			1.54227i	−0.636670	+	0.771137i	$0.719689\pi$
$312$	−147.848	−	95.4893i	−0.473872	−	0.306055i
$313$	49.9052			0.159441			0.0797207	−	0.996817i	$-0.474597\pi$
$313$	49.9052			0.159441			0.0797207	+	0.996817i	$0.474597\pi$
$314$			48.8676i			0.155629i
$315$	−140.706	+	63.4909i	−0.446687	+	0.201558i
$316$	57.3729			0.181560
$317$			287.874i			0.908119i	0.890971	+	0.454060i	$0.150025\pi$
$317$			287.874i			0.908119i	−0.890971	+	0.454060i	$0.849975\pi$
$318$	−44.1558	+	68.3673i	−0.138855	+	0.214991i
$319$	−235.966			−0.739707
$320$			14.4821i			0.0452566i
$321$	−101.281	−	65.4136i	−0.315518	−	0.203781i
$322$	64.2615			0.199570
$323$			291.802i			0.903412i
$324$	107.191	−	121.467i	0.330835	−	0.374897i
$325$	−450.582			−1.38641
$326$			421.214i			1.29207i
$327$	−185.171	+	286.704i	−0.566273	+	0.876772i
$328$	−5.10339			−0.0155591
$329$			462.844i			1.40682i
$330$	73.9600	+	47.7679i	0.224121	+	0.144751i
$331$	188.084			0.568230			0.284115	−	0.958790i	$-0.408300\pi$
$331$	188.084			0.568230			0.284115	+	0.958790i	$0.408300\pi$
$332$		−	41.5950i		−	0.125286i
$333$	−233.975	−	518.527i	−0.702626	−	1.55714i
$334$	147.148			0.440564
$335$			159.101i			0.474929i
$336$	61.6860	−	95.5097i	0.183589	−	0.284255i
$337$	393.531			1.16775			0.583874	−	0.811844i	$-0.301536\pi$
$337$	393.531			1.16775			0.583874	+	0.811844i	$0.301536\pi$
$338$		−	369.448i		−	1.09304i
$339$	325.190	+	210.027i	0.959261	+	0.619550i
$340$	−100.433			−0.295392
$341$		−	150.824i		−	0.442299i
$342$	−122.039	+	55.0675i	−0.356838	+	0.161016i
$343$	−77.9527			−0.227267
$344$			133.758i			0.388830i
$345$	14.1306	−	21.8787i	0.0409582	−	0.0634165i
$346$	−17.8032			−0.0514545
$347$			352.445i			1.01569i	0.861448	+	0.507845i	$0.169558\pi$
$347$			352.445i			1.01569i	−0.861448	+	0.507845i	$0.830442\pi$
$348$	103.746	+	67.0055i	0.298120	+	0.192544i
$349$	229.293			0.656999			0.328500	−	0.944504i	$-0.393457\pi$
$349$	229.293			0.656999			0.328500	+	0.944504i	$0.393457\pi$
$350$		−	291.076i		−	0.831644i
$351$	553.786	+	83.4611i	1.57774	+	0.237781i
$352$	−64.8485			−0.184229
$353$		−	477.331i		−	1.35221i	−0.736804	−	0.676107i	$-0.763666\pi$
$353$		−	477.331i		−	1.35221i	0.736804	−	0.676107i	$-0.236334\pi$
$354$	269.334	−	417.015i	0.760829	−	1.17801i
$355$	−12.3329			−0.0347405
$356$		−	47.0283i		−	0.132102i
$357$	662.358	+	427.792i	1.85535	+	1.19830i
$358$	175.187			0.489351
$359$		−	478.214i		−	1.33207i	−0.745920	−	0.666036i	$-0.767990\pi$
$359$		−	478.214i		−	1.33207i	0.745920	−	0.666036i	$-0.232010\pi$
$360$	−18.9533	−	42.0036i	−0.0526480	−	0.116677i
$361$	−250.346			−0.693480
$362$			445.976i			1.23198i
$363$	−16.9540	+	26.2502i	−0.0467051	+	0.0723145i
$364$	393.059			1.07983
$365$		−	134.831i		−	0.369401i
$366$	226.062	+	146.005i	0.617657	+	0.398921i
$367$	−3.02332			−0.00823793			−0.00411897	−	0.999992i	$-0.501311\pi$
$367$	−3.02332			−0.00823793			−0.00411897	+	0.999992i	$0.501311\pi$
$368$			19.1833i			0.0521286i
$369$	14.8018	−	6.67899i	0.0401132	−	0.0181003i
$370$	−161.819			−0.437347
$371$		−	181.756i		−	0.489910i
$372$	−42.8283	+	66.3119i	−0.115130	+	0.178258i
$373$	−68.8547			−0.184597			−0.0922985	−	0.995731i	$-0.529421\pi$
$373$	−68.8547			−0.184597			−0.0922985	+	0.995731i	$0.529421\pi$
$374$		−	449.723i		−	1.20247i
$375$	−213.151	−	137.666i	−0.568403	−	0.367109i
$376$	−138.168			−0.367468
$377$			426.954i			1.13250i
$378$	−53.9158	+	357.745i	−0.142634	+	0.946416i
$379$	−38.1826			−0.100746			−0.0503728	−	0.998730i	$-0.516041\pi$
$379$	−38.1826			−0.100746			−0.0503728	+	0.998730i	$0.516041\pi$
$380$			38.0851i			0.100224i
$381$	−111.627	+	172.834i	−0.292983	+	0.453631i
$382$	199.276			0.521665
$383$			483.396i			1.26213i	0.775730	+	0.631065i	$0.217382\pi$
$383$			483.396i			1.26213i	−0.775730	+	0.631065i	$0.782618\pi$
$384$	28.5115	+	18.4145i	0.0742487	+	0.0479544i
$385$	−196.625			−0.510714
$386$		−	320.379i		−	0.829998i
$387$	−175.054	−	387.948i	−0.452335	−	1.00245i
$388$	−49.0974			−0.126540
$389$		−	683.943i		−	1.75821i	−0.476630	−	0.879104i	$-0.658142\pi$
$389$		−	683.943i		−	1.75821i	0.476630	−	0.879104i	$-0.341858\pi$
$390$	86.4304	−	133.822i	0.221617	−	0.343133i
$391$	−133.036			−0.340246
$392$			115.323i			0.294190i
$393$	−470.592	−	303.937i	−1.19743	−	0.773377i
$394$	212.973			0.540542
$395$			51.9301i			0.131469i
$396$	188.085	−	84.8696i	0.474963	−	0.214317i
$397$	440.292			1.10905			0.554525	−	0.832167i	$-0.312900\pi$
$397$	440.292			1.10905			0.554525	+	0.832167i	$0.312900\pi$
$398$			11.3228i			0.0284493i
$399$	162.222	−	251.171i	0.406571	−	0.629502i
$400$	86.8918			0.217229
$401$			324.249i			0.808600i	0.914626	+	0.404300i	$0.132485\pi$
$401$			324.249i			0.808600i	−0.914626	+	0.404300i	$0.867515\pi$
$402$	313.229	+	202.302i	0.779176	+	0.503239i
$403$	−272.898			−0.677167
$404$			184.084i			0.455654i
$405$	109.943	+	97.0217i	0.271465	+	0.239560i
$406$	−275.812			−0.679339
$407$		−	724.596i		−	1.78033i
$408$	−127.704	+	197.727i	−0.313001	+	0.484625i
$409$	−300.680			−0.735160			−0.367580	−	0.929992i	$-0.619814\pi$
$409$	−300.680			−0.735160			−0.367580	+	0.929992i	$0.619814\pi$
$410$		−	4.61924i		−	0.0112664i
$411$	−421.878	−	272.475i	−1.02647	−	0.662956i
$412$	235.833			0.572409
$413$			1108.65i			2.68437i
$414$	−25.1059	−	55.6389i	−0.0606424	−	0.134394i
$415$	37.6490			0.0907205
$416$			117.336i			0.282057i
$417$	320.922	−	496.890i	0.769597	−	1.19158i
$418$	−170.539			−0.407987
$419$			354.350i			0.845705i	0.906198	+	0.422853i	$0.138971\pi$
$419$			354.350i			0.845705i	−0.906198	+	0.422853i	$0.861029\pi$
$420$	86.4489	+	55.8340i	0.205831	+	0.132938i
$421$	513.552			1.21984			0.609919	−	0.792463i	$-0.291202\pi$
$421$	513.552			1.21984			0.609919	+	0.792463i	$0.291202\pi$
$422$			124.307i			0.294566i
$423$	400.740	−	180.826i	0.947376	−	0.427484i
$424$	54.2579			0.127967
$425$			602.593i			1.41787i
$426$	−15.6817	+	24.2802i	−0.0368114	+	0.0569959i
$427$	−600.994			−1.40748
$428$			80.3792i			0.187802i
$429$	599.232	+	387.021i	1.39681	+	0.902147i
$430$	−121.068			−0.281554
$431$		−	428.880i		−	0.995081i	−0.867441	−	0.497540i	$-0.834237\pi$
$431$		−	428.880i		−	0.995081i	0.867441	−	0.497540i	$-0.165763\pi$
$432$	−106.794	−	16.0949i	−0.247208	−	0.0372568i
$433$	425.420			0.982495			0.491247	−	0.871020i	$-0.336541\pi$
$433$	425.420			0.982495			0.491247	+	0.871020i	$0.336541\pi$
$434$		−	176.292i		−	0.406203i
$435$	−60.6488	+	93.9038i	−0.139423	+	0.215871i
$436$	227.535			0.521870
$437$			50.4483i			0.115442i
$438$	−265.448	−	171.443i	−0.606046	−	0.391422i
$439$	−854.325			−1.94607			−0.973036	−	0.230654i	$-0.925913\pi$
$439$	−854.325			−1.94607			−0.973036	+	0.230654i	$0.925913\pi$
$440$		−	58.6964i		−	0.133401i
$441$	−150.927	−	334.479i	−0.342238	−	0.758456i
$442$	−813.722			−1.84100
$443$		−	713.189i		−	1.60991i	−0.593338	−	0.804954i	$-0.702190\pi$
$443$		−	713.189i		−	1.60991i	0.593338	−	0.804954i	$-0.297810\pi$
$444$	−205.758	+	318.579i	−0.463418	+	0.717519i
$445$	42.5669			0.0956559
$446$			71.3614i			0.160003i
$447$	268.363	+	173.325i	0.600365	+	0.387752i
$448$	−75.7987			−0.169194
$449$		−	157.299i		−	0.350333i	−0.984539	−	0.175166i	$-0.943954\pi$
$449$		−	157.299i		−	0.350333i	0.984539	−	0.175166i	$-0.0560463\pi$
$450$	−252.019	+	113.719i	−0.560043	+	0.252708i
$451$	20.6842			0.0458629
$452$		−	258.078i		−	0.570969i
$453$	−135.735	+	210.162i	−0.299637	+	0.463933i
$454$	−62.9307			−0.138614
$455$			355.770i			0.781912i
$456$	74.9796	+	48.4264i	0.164429	+	0.106198i
$457$	254.902			0.557773			0.278887	−	0.960324i	$-0.410035\pi$
$457$	254.902			0.557773			0.278887	+	0.960324i	$0.410035\pi$
$458$		−	134.973i		−	0.294700i
$459$	111.618	−	740.615i	0.243177	−	1.61354i
$460$	−17.3634			−0.0377466
$461$		−	312.999i		−	0.678958i	−0.940614	−	0.339479i	$-0.889749\pi$
$461$		−	312.999i		−	0.678958i	0.940614	−	0.339479i	$-0.110251\pi$
$462$	−250.015	+	387.104i	−0.541158	+	0.837887i
$463$	77.6665			0.167746			0.0838731	−	0.996476i	$-0.473271\pi$
$463$	77.6665			0.167746			0.0838731	+	0.996476i	$0.473271\pi$
$464$		−	82.3352i		−	0.177447i
$465$	−60.0210	−	38.7652i	−0.129077	−	0.0833661i
$466$	−550.302			−1.18091
$467$		−	286.398i		−	0.613271i	−0.951827	−	0.306635i	$-0.900797\pi$
$467$		−	286.398i		−	0.613271i	0.951827	−	0.306635i	$-0.0992032\pi$
$468$	−153.562	−	340.318i	−0.328123	−	0.727176i
$469$	−832.728			−1.77554
$470$		−	125.060i		−	0.266086i
$471$	−56.2420	+	87.0806i	−0.119410	+	0.184884i
$472$	−330.953			−0.701171
$473$		−	542.124i		−	1.14614i
$474$	102.237	+	66.0308i	0.215689	+	0.139305i
$475$	228.508			0.481070
$476$		−	525.663i		−	1.10433i
$477$	−157.369	+	71.0093i	−0.329913	+	0.148867i
$478$	68.5718			0.143456
$479$			83.7687i			0.174882i	0.996170	+	0.0874412i	$0.0278690\pi$
$479$			83.7687i			0.174882i	−0.996170	+	0.0874412i	$0.972131\pi$
$480$	−16.6675	+	25.8067i	−0.0347240	+	0.0537639i
$481$	−1311.07			−2.72572
$482$			574.843i			1.19262i
$483$	114.512	+	73.9589i	0.237085	+	0.153124i
$484$	20.8328			0.0430429
$485$		−	44.4396i		−	0.0916281i
$486$	330.807	−	93.0839i	0.680673	−	0.191531i
$487$	−107.309			−0.220346			−0.110173	−	0.993912i	$-0.535141\pi$
$487$	−107.309			−0.220346			−0.110173	+	0.993912i	$0.535141\pi$
$488$		−	179.408i		−	0.367640i
$489$	−484.778	+	750.591i	−0.991366	+	1.53495i
$490$	−104.382			−0.213025
$491$			18.6421i			0.0379676i	0.999820	+	0.0189838i	$0.00604310\pi$
$491$			18.6421i			0.0379676i	−0.999820	+	0.0189838i	$0.993957\pi$
$492$	−9.09408	−	5.87352i	−0.0184839	−	0.0119380i
$493$	570.994			1.15820
$494$			308.569i			0.624635i
$495$	76.8182	+	170.242i	0.155188	+	0.343923i
$496$	52.6267			0.106102
$497$		−	64.5497i		−	0.129879i
$498$	47.8719	−	74.1211i	0.0961284	−	0.148838i
$499$	762.051			1.52716			0.763578	−	0.645716i	$-0.223441\pi$
$499$	762.051			1.52716			0.763578	+	0.645716i	$0.223441\pi$
$500$			169.162i			0.338323i
$501$	262.214	+	169.354i	0.523382	+	0.338032i
$502$	−155.745			−0.310249
$503$			281.325i			0.559294i	0.960103	+	0.279647i	$0.0902175\pi$
$503$			281.325i			0.559294i	−0.960103	+	0.279647i	$0.909783\pi$
$504$	219.845	−	99.2007i	0.436201	−	0.196827i
$505$	−166.621			−0.329942
$506$		−	77.7506i		−	0.153657i
$507$	425.200	−	658.346i	0.838659	−	1.29851i
$508$	137.165			0.270009
$509$		−	641.974i		−	1.26125i	−0.776089	−	0.630623i	$-0.782799\pi$
$509$		−	641.974i		−	1.26125i	0.776089	−	0.630623i	$-0.217201\pi$
$510$	−178.969	−	115.589i	−0.350920	−	0.226645i
$511$	705.702			1.38102
$512$		−	22.6274i		−	0.0441942i
$513$	−280.847	−	42.3264i	−0.547460	−	0.0825077i
$514$	−43.3923			−0.0844208
$515$			213.460i			0.414485i
$516$	−153.942	+	238.352i	−0.298338	+	0.461923i
$517$	559.999			1.08317
$518$		−	846.951i		−	1.63504i
$519$	−31.7249	−	20.4899i	−0.0611269	−	0.0394795i
$520$	−106.204			−0.204239
$521$		−	617.002i		−	1.18427i	−0.805840	−	0.592133i	$-0.798286\pi$
$521$		−	617.002i		−	1.18427i	0.805840	−	0.592133i	$-0.201714\pi$
$522$	107.755	+	238.803i	0.206428	+	0.457478i
$523$	−67.0565			−0.128215			−0.0641076	−	0.997943i	$-0.520420\pi$
$523$	−67.0565			−0.128215			−0.0641076	+	0.997943i	$0.520420\pi$
$524$			373.473i			0.712734i
$525$	335.000	−	518.688i	0.638096	−	0.987977i
$526$	−238.846			−0.454080
$527$			364.965i			0.692534i
$528$	−115.558	−	74.6344i	−0.218860	−	0.141353i
$529$	−23.0000			−0.0434783
$530$			49.1106i			0.0926614i
$531$	959.889	−	433.130i	1.80770	−	0.815688i
$532$	−199.336			−0.374691
$533$		−	37.4256i		−	0.0702169i
$534$	54.1252	−	83.8031i	0.101358	−	0.156935i
$535$	−72.7538			−0.135988
$536$		−	248.586i		−	0.463779i
$537$	312.179	+	201.624i	0.581339	+	0.375464i
$538$	657.657			1.22241
$539$		−	467.406i		−	0.867172i
$540$	14.5680	−	96.6627i	0.0269778	−	0.179005i
$541$	−83.5420			−0.154422			−0.0772108	−	0.997015i	$-0.524601\pi$
$541$	−83.5420			−0.154422			−0.0772108	+	0.997015i	$0.524601\pi$
$542$			234.452i			0.432568i
$543$	−513.276	+	794.716i	−0.945260	+	1.46357i
$544$	156.921			0.288457
$545$			205.950i			0.377889i
$546$	700.418	+	452.373i	1.28282	+	0.828522i
$547$	853.768			1.56082			0.780410	−	0.625269i	$-0.215011\pi$
$547$	853.768			1.56082			0.780410	+	0.625269i	$0.215011\pi$
$548$			334.813i			0.610972i
$549$	234.799	+	520.353i	0.427684	+	0.947819i
$550$	−352.175			−0.640318
$551$		−	216.525i		−	0.392968i
$552$	−22.0782	+	34.1841i	−0.0399967	+	0.0619277i
$553$	−271.800			−0.491500
$554$			662.980i			1.19671i
$555$	−288.356	−	186.238i	−0.519560	−	0.335564i
$556$	−394.344			−0.709251
$557$		−	676.505i		−	1.21455i	−0.794491	−	0.607275i	$-0.792263\pi$
$557$		−	676.505i		−	1.21455i	0.794491	−	0.607275i	$-0.207737\pi$
$558$	−152.637	+	68.8745i	−0.273544	+	0.123431i
$559$	−980.909			−1.75476
$560$		−	68.6079i		−	0.122514i
$561$	517.589	−	801.393i	0.922618	−	1.42851i
$562$	−8.75970			−0.0155867
$563$			757.449i			1.34538i	0.739924	+	0.672690i	$0.234861\pi$
$563$			757.449i			1.34538i	−0.739924	+	0.672690i	$0.765139\pi$
$564$	−246.211	−	159.018i	−0.436545	−	0.281948i
$565$	233.595			0.413442
$566$		−	555.265i		−	0.981034i
$567$	−507.807	+	575.439i	−0.895603	+	1.01488i
$568$	19.2694			0.0339249
$569$		−	431.316i		−	0.758025i	−0.925392	−	0.379012i	$-0.876264\pi$
$569$		−	431.316i		−	0.758025i	0.925392	−	0.379012i	$-0.123736\pi$
$570$	−43.8323	+	67.8665i	−0.0768988	+	0.119064i
$571$	−415.206			−0.727157			−0.363578	−	0.931564i	$-0.618445\pi$
$571$	−415.206			−0.727157			−0.363578	+	0.931564i	$0.618445\pi$
$572$		−	475.565i		−	0.831407i
$573$	355.104	+	229.348i	0.619727	+	0.400258i
$574$	24.1769			0.0421200
$575$			104.180i			0.181182i
$576$	29.6133	+	65.6281i	0.0514121	+	0.113938i
$577$	−474.524			−0.822399			−0.411200	−	0.911545i	$-0.634890\pi$
$577$	−474.524			−0.822399			−0.411200	+	0.911545i	$0.634890\pi$
$578$			679.536i			1.17567i
$579$	368.726	−	570.906i	0.636833	−	0.986021i
$580$	74.5242			0.128490
$581$			197.053i			0.339162i
$582$	−87.4901	−	56.5065i	−0.150327	−	0.0970902i
$583$	−219.909			−0.377202
$584$			210.666i			0.360729i
$585$	308.033	−	138.994i	0.526552	−	0.237596i
$586$	−442.245			−0.754685
$587$			1004.18i			1.71070i	0.518054	+	0.855348i	$0.326657\pi$
$587$			1004.18i			1.71070i	−0.518054	+	0.855348i	$0.673343\pi$
$588$	−132.725	+	205.501i	−0.225723	+	0.349492i
$589$	138.398			0.234970
$590$		−	299.556i		−	0.507722i
$591$	379.512	+	245.112i	0.642152	+	0.414741i
$592$	252.832			0.427080
$593$			422.527i			0.712524i	0.934386	+	0.356262i	$0.115949\pi$
$593$			422.527i			0.712524i	−0.934386	+	0.356262i	$0.884051\pi$
$594$	432.839	+	65.2332i	0.728685	+	0.109820i
$595$	475.795			0.799655
$596$		−	212.979i		−	0.357348i
$597$	−13.0315	+	20.1769i	−0.0218283	+	0.0337971i
$598$	−140.681			−0.235252
$599$			1076.12i			1.79653i	0.439450	+	0.898267i	$0.355173\pi$
$599$			1076.12i			1.79653i	−0.439450	+	0.898267i	$0.644827\pi$
$600$	154.839	+	100.004i	0.258064	+	0.166674i
$601$	213.229			0.354791			0.177395	−	0.984140i	$-0.443233\pi$
$601$	213.229			0.354791			0.177395	+	0.984140i	$0.443233\pi$
$602$		−	633.666i		−	1.05260i
$603$	325.333	+	720.993i	0.539525	+	1.19568i
$604$	166.789			0.276141
$605$			18.8564i			0.0311676i
$606$	−211.864	+	328.033i	−0.349610	+	0.541308i
$607$	456.744			0.752461			0.376230	−	0.926526i	$-0.377220\pi$
$607$	456.744			0.752461			0.376230	+	0.926526i	$0.377220\pi$
$608$		−	59.5056i		−	0.0978710i
$609$	−491.488	−	317.433i	−0.807041	−	0.521237i
$610$	162.388			0.266210
$611$		−	1013.25i		−	1.65835i
$612$	−455.130	+	205.368i	−0.743677	+	0.335569i
$613$	−709.339			−1.15716			−0.578580	−	0.815625i	$-0.696393\pi$
$613$	−709.339			−1.15716			−0.578580	+	0.815625i	$0.696393\pi$
$614$		−	641.818i		−	1.04531i
$615$	5.31631	−	8.23135i	0.00864440	−	0.0133843i
$616$	307.215			0.498725
$617$			719.037i			1.16538i	0.812696	+	0.582688i	$0.197999\pi$
$617$			719.037i			1.16538i	−0.812696	+	0.582688i	$0.802001\pi$
$618$	420.247	+	271.421i	0.680011	+	0.439193i
$619$	−614.921			−0.993410			−0.496705	−	0.867920i	$-0.665457\pi$
$619$	−614.921			−0.993410			−0.496705	+	0.867920i	$0.665457\pi$
$620$			47.6341i			0.0768292i
$621$	19.2971	−	128.041i	0.0310743	−	0.206186i
$622$	678.323			1.09055
$623$			222.793i			0.357613i
$624$	−135.042	+	209.089i	−0.216414	+	0.335078i
$625$	389.960			0.623936
$626$		−	70.5766i		−	0.112742i
$627$	−303.895	−	196.274i	−0.484680	−	0.313036i
$628$	69.1092			0.110046
$629$			1753.38i			2.78757i
$630$	89.7897	+	198.989i	0.142523	+	0.315855i
$631$	−459.838			−0.728744			−0.364372	−	0.931253i	$-0.618716\pi$
$631$	−459.838			−0.728744			−0.364372	+	0.931253i	$0.618716\pi$
$632$		−	81.1376i		−	0.128382i
$633$	−143.066	+	221.511i	−0.226012	+	0.349939i
$634$	407.115			0.642137
$635$			124.152i			0.195515i
$636$	96.6859	+	62.4457i	0.152022	+	0.0981850i
$637$	−845.715			−1.32765
$638$			333.707i			0.523052i
$639$	−55.8885	+	25.2185i	−0.0874624	+	0.0394656i
$640$	20.4808			0.0320013
$641$			474.470i			0.740203i	0.928991	+	0.370102i	$0.120677\pi$
$641$			474.470i			0.740203i	−0.928991	+	0.370102i	$0.879323\pi$
$642$	−92.5089	+	143.233i	−0.144095	+	0.223105i
$643$	−8.99877			−0.0139950			−0.00699749	−	0.999976i	$-0.502227\pi$
$643$	−8.99877			−0.0139950			−0.00699749	+	0.999976i	$0.502227\pi$
$644$		−	90.8795i		−	0.141117i
$645$	−215.740	−	139.338i	−0.334481	−	0.216028i
$646$	412.671			0.638809
$647$		−	411.244i		−	0.635616i	−0.948155	−	0.317808i	$-0.897053\pi$
$647$		−	411.244i		−	0.635616i	0.948155	−	0.317808i	$-0.102947\pi$
$648$	−171.780	−	151.590i	−0.265092	−	0.233936i
$649$	1341.36			2.06681
$650$			637.219i			0.980337i
$651$	202.896	−	314.147i	0.311667	−	0.482561i
$652$	595.687			0.913630
$653$		−	262.756i		−	0.402382i	−0.979552	−	0.201191i	$-0.935519\pi$
$653$		−	262.756i		−	0.402382i	0.979552	−	0.201191i	$-0.0644813\pi$
$654$	405.461	+	261.872i	0.619971	+	0.400415i
$655$	−338.042			−0.516095
$656$			7.21728i			0.0110020i
$657$	−275.706	−	611.011i	−0.419644	−	0.930002i
$658$	654.561			0.994773
$659$			594.754i			0.902509i	0.892395	+	0.451255i	$0.149023\pi$
$659$			594.754i			0.902509i	−0.892395	+	0.451255i	$0.850977\pi$
$660$	67.5540	−	104.595i	0.102355	−	0.158478i
$661$	463.099			0.700604			0.350302	−	0.936637i	$-0.386079\pi$
$661$	463.099			0.700604			0.350302	+	0.936637i	$0.386079\pi$
$662$		−	265.991i		−	0.401800i
$663$	−1450.03	−	936.516i	−2.18707	−	1.41254i
$664$	−58.8242			−0.0885907
$665$		−	180.425i		−	0.271316i
$666$	−733.308	+	330.890i	−1.10106	+	0.496832i
$667$	98.7164			0.148001
$668$		−	208.099i		−	0.311526i
$669$	−82.1302	+	127.164i	−0.122766	+	0.190080i
$670$	225.003			0.335825
$671$			727.148i			1.08368i
$672$	−135.071	−	87.2372i	−0.200999	−	0.129817i
$673$	823.303			1.22333			0.611666	−	0.791116i	$-0.290500\pi$
$673$	823.303			1.22333			0.611666	+	0.791116i	$0.290500\pi$
$674$		−	556.537i		−	0.825722i
$675$	−579.970	−	87.4073i	−0.859215	−	0.129492i
$676$	−522.479			−0.772898
$677$		−	1288.94i		−	1.90391i	−0.306243	−	0.951953i	$-0.599072\pi$
$677$		−	1288.94i		−	1.90391i	0.306243	−	0.951953i	$-0.400928\pi$
$678$	297.024	−	459.888i	0.438088	−	0.678300i
$679$	232.595			0.342555
$680$			142.034i			0.208874i
$681$	−112.141	−	72.4272i	−0.164670	−	0.106354i
$682$	−213.297			−0.312753
$683$			529.807i			0.775706i	0.921721	+	0.387853i	$0.126783\pi$
$683$			529.807i			0.775706i	−0.921721	+	0.387853i	$0.873217\pi$
$684$	77.8772	+	172.589i	0.113856	+	0.252323i
$685$	−303.050			−0.442408
$686$			110.242i			0.160702i
$687$	155.341	−	240.517i	0.226115	−	0.350098i
$688$	189.162			0.274945
$689$			397.899i			0.577502i
$690$	−30.9411	−	19.9837i	−0.0448422	−	0.0289619i
$691$	365.200			0.528510			0.264255	−	0.964453i	$-0.414874\pi$
$691$	365.200			0.528510			0.264255	+	0.964453i	$0.414874\pi$
$692$			25.1776i			0.0363838i
$693$	−891.039	+	402.063i	−1.28577	+	0.580178i
$694$	498.432			0.718202
$695$		−	356.933i		−	0.513573i
$696$	94.7600	−	146.719i	0.136149	−	0.210803i
$697$	−50.0517			−0.0718102
$698$		−	324.269i		−	0.464569i
$699$	−980.622	−	633.345i	−1.40289	−	0.906074i
$700$	−411.643			−0.588061
$701$		−	779.111i		−	1.11143i	−0.831374	−	0.555714i	$-0.812445\pi$
$701$		−	779.111i		−	1.11143i	0.831374	−	0.555714i	$-0.187555\pi$
$702$	118.032	−	783.172i	0.168136	−	1.11563i
$703$	664.896			0.945799
$704$			91.7096i			0.130269i
$705$	143.933	−	222.854i	0.204160	−	0.316105i
$706$	−675.049			−0.956160
$707$		−	872.085i		−	1.23350i
$708$	−589.748	−	380.895i	−0.832977	−	0.537988i
$709$	−849.950			−1.19880			−0.599401	−	0.800449i	$-0.704594\pi$
$709$	−849.950			−1.19880			−0.599401	+	0.800449i	$0.704594\pi$
$710$			17.4413i			0.0245652i
$711$	106.188	+	235.330i	0.149350	+	0.330984i
$712$	−66.5081			−0.0934103
$713$			63.0971i			0.0884953i
$714$	604.989	−	936.716i	0.847323	−	1.31193i
$715$	430.449			0.602027
$716$		−	247.753i		−	0.346023i
$717$	122.193	+	78.9196i	0.170422	+	0.110069i
$718$	−676.297			−0.941917
$719$			1317.97i			1.83305i	0.399974	+	0.916527i	$0.369019\pi$
$719$			1317.97i			1.83305i	−0.399974	+	0.916527i	$0.630981\pi$
$720$	−59.4021	+	26.8040i	−0.0825029	+	0.0372278i
$721$	−1117.24			−1.54957
$722$			354.043i			0.490365i
$723$	−661.589	+	1024.35i	−0.915061	+	1.41681i
$724$	630.705			0.871140
$725$		−	447.141i		−	0.616746i
$726$	37.1233	+	23.9765i	0.0511341	+	0.0330255i
$727$	184.059			0.253176			0.126588	−	0.991955i	$-0.459597\pi$
$727$	184.059			0.253176			0.126588	+	0.991955i	$0.459597\pi$
$728$		−	555.869i		−	0.763556i
$729$	696.619	+	214.855i	0.955582	+	0.294726i
$730$	−190.680			−0.261206
$731$			1311.83i			1.79458i
$732$	206.482	−	319.700i	0.282079	−	0.436749i
$733$	878.627			1.19867			0.599336	−	0.800498i	$-0.295431\pi$
$733$	878.627			1.19867			0.599336	+	0.800498i	$0.295431\pi$
$734$			4.27562i			0.00582510i
$735$	−186.006	−	120.134i	−0.253069	−	0.163448i
$736$	27.1293			0.0368605
$737$			1007.53i			1.36706i
$738$	−9.44552	−	20.9329i	−0.0127988	−	0.0283643i
$739$	163.651			0.221450			0.110725	−	0.993851i	$-0.464683\pi$
$739$	163.651			0.221450			0.110725	+	0.993851i	$0.464683\pi$
$740$			228.846i			0.309251i
$741$	−355.134	+	549.862i	−0.479263	+	0.742053i
$742$	−257.042			−0.346418
$743$		−	855.253i		−	1.15108i	−0.817773	−	0.575540i	$-0.804792\pi$
$743$		−	855.253i		−	1.15108i	0.817773	−	0.575540i	$-0.195208\pi$
$744$	93.7791	+	60.5683i	0.126047	+	0.0814090i
$745$	192.774			0.258757
$746$			97.3752i			0.130530i
$747$	170.613	−	76.9855i	0.228397	−	0.103060i
$748$	−636.005			−0.850274
$749$		−	380.790i		−	0.508398i
$750$	−194.689	+	301.441i	−0.259586	+	0.401922i
$751$	−327.080			−0.435525			−0.217763	−	0.976002i	$-0.569876\pi$
$751$	−327.080			−0.435525			−0.217763	+	0.976002i	$0.569876\pi$
$752$			195.399i			0.259839i
$753$	−277.533	−	179.248i	−0.368570	−	0.238045i
$754$	603.804			0.800801
$755$			150.966i			0.199956i
$756$	505.928	+	76.2484i	0.669217	+	0.100858i
$757$	1122.84			1.48328			0.741638	−	0.670800i	$-0.234049\pi$
$757$	1122.84			1.48328			0.741638	+	0.670800i	$0.234049\pi$
$758$			53.9983i			0.0712379i
$759$	89.4836	−	138.549i	0.117897	−	0.182542i
$760$	53.8604			0.0708690
$761$		−	1177.71i		−	1.54759i	−0.633439	−	0.773793i	$-0.718357\pi$
$761$		−	1177.71i		−	1.54759i	0.633439	−	0.773793i	$-0.281643\pi$
$762$	244.424	+	157.864i	0.320766	+	0.207170i
$763$	−1077.93			−1.41275
$764$		−	281.819i		−	0.368873i
$765$	−185.885	−	411.953i	−0.242987	−	0.538501i
$766$	683.625			0.892460
$767$		−	2427.04i		−	3.16432i
$768$	26.0420	−	40.3214i	0.0339089	−	0.0525018i
$769$	87.7176			0.114067			0.0570335	−	0.998372i	$-0.481836\pi$
$769$	87.7176			0.114067			0.0570335	+	0.998372i	$0.481836\pi$
$770$			278.070i			0.361130i
$771$	−77.3238	−	49.9404i	−0.100290	−	0.0647736i
$772$	−453.085			−0.586897
$773$		−	566.538i		−	0.732908i	−0.930436	−	0.366454i	$-0.880572\pi$
$773$		−	566.538i		−	0.732908i	0.930436	−	0.366454i	$-0.119428\pi$
$774$	−548.641	+	247.563i	−0.708839	+	0.319849i
$775$	285.801			0.368776
$776$			69.4342i			0.0894771i
$777$	974.760	−	1509.24i	1.25452	−	1.94240i
$778$	−967.242			−1.24324
$779$			18.9800i			0.0243646i
$780$	−189.253	−	122.231i	−0.242632	−	0.156707i
$781$	−78.0993			−0.0999991
$782$			188.141i			0.240590i
$783$	−82.8237	+	549.556i	−0.105777	+	0.701860i
$784$	163.091			0.208024
$785$			62.5529i			0.0796853i
$786$	−429.832	+	665.517i	−0.546860	+	0.846714i
$787$	−809.810			−1.02898			−0.514492	−	0.857495i	$-0.672019\pi$
$787$	−809.810			−1.02898			−0.514492	+	0.857495i	$0.672019\pi$
$788$		−	301.190i		−	0.382221i
$789$	−425.616	−	274.889i	−0.539438	−	0.348402i
$790$	73.4402			0.0929623
$791$			1222.63i			1.54567i
$792$	−120.024	−	265.993i	−0.151545	−	0.335849i
$793$	1315.69			1.65913
$794$		−	622.668i		−	0.784216i
$795$	−56.5216	+	87.5135i	−0.0710964	+	0.110080i
$796$	16.0129			0.0201167
$797$			982.528i			1.23278i	0.787440	+	0.616392i	$0.211406\pi$
$797$			982.528i			1.23278i	−0.787440	+	0.616392i	$0.788594\pi$
$798$	−355.210	−	229.416i	−0.445125	−	0.287489i
$799$	−1355.09			−1.69598
$800$		−	122.884i		−	0.153604i
$801$	192.899	−	87.0417i	0.240823	−	0.108666i
$802$	458.557			0.571767
$803$		−	853.835i		−	1.06331i
$804$	286.099	−	442.972i	0.355844	−	0.550961i
$805$	82.2580			0.102184
$806$			385.937i			0.478830i
$807$	1171.93	+	756.901i	1.45220	+	0.937920i
$808$	260.334			0.322196
$809$		−	676.055i		−	0.835668i	−0.908523	−	0.417834i	$-0.862789\pi$
$809$		−	676.055i		−	0.835668i	0.908523	−	0.417834i	$-0.137211\pi$
$810$	137.209	−	155.484i	0.169394	−	0.191955i
$811$	−987.522			−1.21766			−0.608830	−	0.793301i	$-0.708361\pi$
$811$	−987.522			−1.21766			−0.608830	+	0.793301i	$0.708361\pi$
$812$			390.057i			0.480365i
$813$	−269.832	+	417.786i	−0.331897	+	0.513882i
$814$	−1024.73			−1.25889
$815$			539.176i			0.661565i
$816$	279.628	+	180.601i	0.342682	+	0.221325i
$817$	497.458			0.608884
$818$			425.226i			0.519837i
$819$	727.486	+	1612.23i	0.888261	+	1.96854i
$820$	−6.53259			−0.00796658
$821$		−	69.6109i		−	0.0847879i	−0.999101	−	0.0423940i	$-0.986502\pi$
$821$		−	69.6109i		−	0.0847879i	0.999101	−	0.0423940i	$-0.0134985\pi$
$822$	−385.338	+	596.626i	−0.468781	+	0.725823i
$823$	197.240			0.239660			0.119830	−	0.992794i	$-0.461765\pi$
$823$	197.240			0.239660			0.119830	+	0.992794i	$0.461765\pi$
$824$		−	333.518i		−	0.404755i
$825$	−627.565	−	405.320i	−0.760685	−	0.491297i
$826$	1567.86			1.89814
$827$		−	1453.99i		−	1.75815i	−0.476687	−	0.879073i	$-0.658162\pi$
$827$		−	1453.99i		−	1.75815i	0.476687	−	0.879073i	$-0.341838\pi$
$828$	−78.6853	+	35.5052i	−0.0950306	+	0.0428806i
$829$	282.757			0.341082			0.170541	−	0.985351i	$-0.445448\pi$
$829$	282.757			0.341082			0.170541	+	0.985351i	$0.445448\pi$
$830$		−	53.2437i		−	0.0641490i
$831$	−763.027	+	1181.41i	−0.918203	+	1.42167i
$832$	165.938			0.199444
$833$			1131.03i			1.35778i
$834$	−702.709	−	453.852i	−0.842576	−	0.544187i
$835$	188.357			0.225578
$836$			241.178i			0.288490i
$837$	−351.263	−	52.9389i	−0.419669	−	0.0632483i
$838$	501.127			0.598004
$839$		−	615.413i		−	0.733507i	−0.930318	−	0.366754i	$-0.880469\pi$
$839$		−	615.413i		−	0.733507i	0.930318	−	0.366754i	$-0.119531\pi$
$840$	78.9612	−	122.257i	0.0940014	−	0.145544i
$841$	417.307			0.496203
$842$		−	726.272i		−	0.862556i
$843$	−15.6095	−	10.0816i	−0.0185166	−	0.0119592i
$844$	175.797			0.208290
$845$		−	472.913i		−	0.559660i
$846$	−255.726	−	566.732i	−0.302277	−	0.669896i
$847$	−98.6935			−0.116521
$848$		−	76.7322i		−	0.0904861i
$849$	639.058	−	989.466i	0.752718	−	1.16545i
$850$	852.196			1.00258
$851$			303.134i			0.356210i
$852$	34.3374	+	22.1772i	0.0403022	+	0.0260296i
$853$	46.2353			0.0542032			0.0271016	−	0.999633i	$-0.491372\pi$
$853$	46.2353			0.0542032			0.0271016	+	0.999633i	$0.491372\pi$
$854$			849.934i			0.995238i
$855$	−156.216	+	70.4892i	−0.182708	+	0.0824435i
$856$	113.673			0.132796
$857$			760.430i			0.887316i	0.896196	+	0.443658i	$0.146319\pi$
$857$			760.430i			0.887316i	−0.896196	+	0.443658i	$0.853681\pi$
$858$	547.330	−	847.443i	0.637914	−	0.987695i
$859$	−136.881			−0.159349			−0.0796746	−	0.996821i	$-0.525388\pi$
$859$	−136.881			−0.159349			−0.0796746	+	0.996821i	$0.525388\pi$
$860$			171.216i			0.199089i
$861$	43.0825	+	27.8253i	0.0500378	+	0.0323174i
$862$	−606.528			−0.703628
$863$		−	1465.61i		−	1.69827i	−0.528177	−	0.849134i	$-0.677124\pi$
$863$		−	1465.61i		−	1.69827i	0.528177	−	0.849134i	$-0.322876\pi$
$864$	−22.7617	+	151.029i	−0.0263445	+	0.174803i
$865$	−22.7890			−0.0263457
$866$		−	601.635i		−	0.694729i
$867$	−782.082	+	1210.91i	−0.902055	+	1.39667i
$868$	−249.315			−0.287229
$869$			328.853i			0.378427i
$870$	132.800	+	85.7703i	0.152644	+	0.0985866i
$871$	1823.00			2.09299
$872$		−	321.784i		−	0.369018i
$873$	−90.8712	−	201.386i	−0.104091	−	0.230682i
$874$	71.3447			0.0816301
$875$		−	801.391i		−	0.915875i
$876$	−242.456	+	375.400i	−0.276777	+	0.428539i
$877$	−1504.98			−1.71605			−0.858026	−	0.513607i	$-0.828309\pi$
$877$	−1504.98			−1.71605			−0.858026	+	0.513607i	$0.828309\pi$
$878$			1208.20i			1.37608i
$879$	−788.068	−	508.982i	−0.896550	−	0.579047i
$880$	−83.0093			−0.0943287
$881$			1519.48i			1.72473i	0.506291	+	0.862363i	$0.331016\pi$
$881$			1519.48i			1.72473i	−0.506291	+	0.862363i	$0.668984\pi$
$882$	−473.025	+	213.443i	−0.536309	+	0.241999i
$883$	−156.578			−0.177325			−0.0886625	−	0.996062i	$-0.528259\pi$
$883$	−156.578			−0.177325			−0.0886625	+	0.996062i	$0.528259\pi$
$884$			1150.78i			1.30178i
$885$	344.760	−	533.800i	0.389560	−	0.603163i
$886$	−1008.60			−1.13838
$887$		−	231.562i		−	0.261062i	−0.991444	−	0.130531i	$-0.958332\pi$
$887$		−	231.562i		−	0.261062i	0.991444	−	0.130531i	$-0.0416681\pi$
$888$	450.538	+	290.985i	0.507363	+	0.327686i
$889$	−649.808			−0.730942
$890$		−	60.1986i		−	0.0676389i
$891$	696.229	+	614.400i	0.781402	+	0.689563i
$892$	100.920			0.113139
$893$			513.861i			0.575432i
$894$	245.119	−	379.523i	0.274182	−	0.424522i
$895$	224.249			0.250557
$896$			107.196i			0.119638i
$897$	−250.689	−	161.910i	−0.279474	−	0.180502i
$898$	−222.455			−0.247723
$899$		−	270.814i		−	0.301239i
$900$	160.822	+	356.409i	0.178691	+	0.396010i
$901$	532.137			0.590607
$902$		−	29.2518i		−	0.0324300i
$903$	729.290	−	1129.17i	0.807630	−	1.25047i
$904$	−364.978			−0.403736
$905$			570.872i			0.630797i
$906$	297.214	+	191.959i	0.328050	+	0.211875i
$907$	−542.846			−0.598507			−0.299253	−	0.954174i	$-0.596738\pi$
$907$	−542.846			−0.598507			−0.299253	+	0.954174i	$0.596738\pi$
$908$			88.9974i			0.0980148i
$909$	−755.069	+	340.709i	−0.830659	+	0.374818i
$910$	503.135			0.552895
$911$			450.832i			0.494876i	0.968904	+	0.247438i	$0.0795887\pi$
$911$			450.832i			0.494876i	−0.968904	+	0.247438i	$0.920411\pi$
$912$	68.4853	−	106.037i	0.0750935	−	0.116269i
$913$	238.416			0.261135
$914$		−	360.486i		−	0.394405i
$915$	289.371	+	186.894i	0.316253	+	0.204255i
$916$	−190.880			−0.208385
$917$		−	1769.30i		−	1.92944i
$918$	−1047.39	−	157.852i	−1.14095	−	0.171952i
$919$	−508.727			−0.553566			−0.276783	−	0.960932i	$-0.589268\pi$
$919$	−508.727			−0.553566			−0.276783	+	0.960932i	$0.589268\pi$
$920$			24.5556i			0.0266909i
$921$	738.672	−	1143.70i	0.802033	−	1.24180i
$922$	−442.648			−0.480096
$923$			141.312i			0.153100i
$924$	547.447	+	353.575i	0.592475	+	0.382657i
$925$	1373.06			1.48439
$926$		−	109.837i		−	0.118614i
$927$	436.487	+	967.328i	0.470860	+	1.04350i
$928$	−116.440			−0.125474
$929$			1052.86i			1.13332i	0.823950	+	0.566662i	$0.191766\pi$
$929$			1052.86i			1.13332i	−0.823950	+	0.566662i	$0.808234\pi$
$930$	−54.8223	+	84.8825i	−0.0589487	+	0.0912715i
$931$	428.896			0.460683
$932$			778.245i			0.835026i
$933$	1208.75	+	780.686i	1.29555	+	0.836748i
$934$	−405.027			−0.433648
$935$		−	575.668i		−	0.615688i
$936$	−481.283	+	217.169i	−0.514191	+	0.232018i
$937$	928.931			0.991389			0.495694	−	0.868497i	$-0.334914\pi$
$937$	928.931			0.991389			0.495694	+	0.868497i	$0.334914\pi$
$938$			1177.66i			1.25550i
$939$	81.2269	−	125.765i	0.0865037	−	0.133935i
$940$	−176.862			−0.188151
$941$			242.488i			0.257692i	0.991665	+	0.128846i	$0.0411273\pi$
$941$			242.488i			0.257692i	−0.991665	+	0.128846i	$0.958873\pi$
$942$	123.151	+	79.5381i	0.130733	+	0.0844354i
$943$	−8.65321			−0.00917626
$944$			468.038i			0.495803i
$945$	−69.0149	+	457.932i	−0.0730316	+	0.484584i
$946$	−766.678			−0.810442
$947$		−	58.4123i		−	0.0616814i	−0.999524	−	0.0308407i	$-0.990182\pi$
$947$		−	58.4123i		−	0.0616814i	0.999524	−	0.0308407i	$-0.00981846\pi$
$948$	93.3816	−	144.585i	0.0985038	−	0.152515i
$949$	−1544.91			−1.62794
$950$		−	323.159i		−	0.340168i
$951$	725.467	+	468.551i	0.762846	+	0.492693i
$952$	−743.400			−0.780883
$953$		−	604.191i		−	0.633988i	−0.948428	−	0.316994i	$-0.897326\pi$
$953$		−	604.191i		−	0.633988i	0.948428	−	0.316994i	$-0.102674\pi$
$954$	100.422	+	222.553i	0.105265	+	0.233284i
$955$	255.083			0.267103
$956$		−	96.9751i		−	0.101438i
$957$	−384.065	+	594.656i	−0.401322	+	0.621375i
$958$	118.467			0.123661
$959$		−	1586.15i		−	1.65396i
$960$	36.4962	+	23.5715i	0.0380168	+	0.0245536i
$961$	−787.902			−0.819877
$962$			1854.14i			1.92738i
$963$	−329.696	+	148.769i	−0.342363	+	0.154485i
$964$	812.950			0.843309
$965$		−	410.101i		−	0.424976i
$966$	104.594	−	161.945i	0.108275	−	0.167644i
$967$	283.232			0.292898			0.146449	−	0.989218i	$-0.453216\pi$
$967$	283.232			0.292898			0.146449	+	0.989218i	$0.453216\pi$
$968$		−	29.4620i		−	0.0304359i
$969$	735.367	+	474.945i	0.758892	+	0.490139i
$970$	−62.8472			−0.0647909
$971$			445.086i			0.458379i	0.973382	+	0.229189i	$0.0736075\pi$
$971$			445.086i			0.458379i	−0.973382	+	0.229189i	$0.926393\pi$
$972$	−131.640	−	467.832i	−0.135433	−	0.481309i
$973$	1868.17			1.92001
$974$			151.757i			0.155808i
$975$	−733.379	+	1135.51i	−0.752183	+	1.16462i
$976$	−253.722			−0.259961
$977$			42.5379i			0.0435393i	0.999763	+	0.0217697i	$0.00693004\pi$
$977$			42.5379i			0.0435393i	−0.999763	+	0.0217697i	$0.993070\pi$
$978$	1061.50	+	685.579i	1.08537	+	0.701001i
$979$	269.559			0.275342
$980$			147.619i			0.150631i
$981$	421.130	+	933.295i	0.429287	+	0.951371i
$982$	26.3639			0.0268472
$983$		−	1590.83i		−	1.61835i	−0.587570	−	0.809173i	$-0.699915\pi$
$983$		−	1590.83i		−	1.61835i	0.587570	−	0.809173i	$-0.300085\pi$
$984$	−8.30641	+	12.8610i	−0.00844147	+	0.0130701i
$985$	272.617			0.276768
$986$		−	807.507i		−	0.818972i
$987$	1166.41	+	753.337i	1.18177	+	0.763260i
$988$	436.383			0.441683
$989$			226.797i			0.229320i
$990$	240.759	−	108.637i	0.243190	−	0.109735i
$991$	1527.16			1.54103			0.770514	−	0.637423i	$-0.220000\pi$
$991$	1527.16			1.54103			0.770514	+	0.637423i	$0.220000\pi$
$992$		−	74.4253i		−	0.0750255i
$993$	306.131	−	473.988i	0.308289	−	0.477330i
$994$	−91.2871			−0.0918382
$995$			14.4938i			0.0145666i
$996$	−104.823	−	67.7011i	−0.105244	−	0.0679730i
$997$	−604.514			−0.606333			−0.303167	−	0.952938i	$-0.598044\pi$
$997$	−604.514			−0.606333			−0.303167	+	0.952938i	$0.598044\pi$
$998$		−	1077.70i		−	1.07986i
$999$	−1687.56	−	254.331i	−1.68924	−	0.254586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.3.c.a.47.6	✓	16
3.2	odd	2	inner	138.3.c.a.47.14	yes	16
4.3	odd	2		1104.3.g.c.737.6		16
12.11	even	2		1104.3.g.c.737.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.3.c.a.47.6	✓	16	1.1	even	1	trivial
138.3.c.a.47.14	yes	16	3.2	odd	2	inner
1104.3.g.c.737.5		16	12.11	even	2
1104.3.g.c.737.6		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)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(1.62763 - 2.52009i) q^{3} -2.00000 q^{4} -1.81026i q^{5} +(-3.56394 - 2.30181i) q^{6} +9.47484 q^{7} +2.82843i q^{8} +(-3.70167 - 8.20351i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(1.62763 - 2.52009i) q^{3} -2.00000 q^{4} -1.81026i q^{5} +(-3.56394 - 2.30181i) q^{6} +9.47484 q^{7} +2.82843i q^{8} +(-3.70167 - 8.20351i) q^{9} -2.56010 q^{10} -11.4637i q^{11} +(-3.25525 + 5.04017i) q^{12} -20.7422 q^{13} -13.3995i q^{14} +(-4.56202 - 2.94643i) q^{15} +4.00000 q^{16} +27.7399i q^{17} +(-11.6015 + 5.23495i) q^{18} +10.5192 q^{19} +3.62053i q^{20} +(15.4215 - 23.8774i) q^{21} -16.2121 q^{22} +4.79583i q^{23} +(7.12788 + 4.60362i) q^{24} +21.7229 q^{25} +29.3339i q^{26} +(-26.6985 - 4.02373i) q^{27} -18.9497 q^{28} -20.5838i q^{29} +(-4.16689 + 6.45167i) q^{30} +13.1567 q^{31} -5.65685i q^{32} +(-28.8895 - 18.6586i) q^{33} +39.2302 q^{34} -17.1520i q^{35} +(7.40334 + 16.4070i) q^{36} +63.2079 q^{37} -14.8764i q^{38} +(-33.7606 + 52.2722i) q^{39} +5.12020 q^{40} +1.80432i q^{41} +(-33.7678 - 21.8093i) q^{42} +47.2905 q^{43} +22.9274i q^{44} +(-14.8505 + 6.70100i) q^{45} +6.78233 q^{46} +48.8498i q^{47} +(6.51050 - 10.0803i) q^{48} +40.7727 q^{49} -30.7209i q^{50} +(69.9071 + 45.1503i) q^{51} +41.4844 q^{52} -19.1831i q^{53} +(-5.69041 + 37.7574i) q^{54} -20.7523 q^{55} +26.7989i q^{56} +(17.1213 - 26.5093i) q^{57} -29.1099 q^{58} +117.009i q^{59} +(9.12404 + 5.89287i) q^{60} -63.4305 q^{61} -18.6063i q^{62} +(-35.0727 - 77.7270i) q^{63} -8.00000 q^{64} +37.5489i q^{65} +(-26.3873 + 40.8559i) q^{66} -87.8883 q^{67} -55.4799i q^{68} +(12.0859 + 7.80582i) q^{69} -24.2566 q^{70} -6.81275i q^{71} +(23.2030 - 10.4699i) q^{72} +74.4816 q^{73} -89.3894i q^{74} +(35.3568 - 54.7437i) q^{75} -21.0384 q^{76} -108.617i q^{77} +(73.9240 + 47.7447i) q^{78} -28.6865 q^{79} -7.24106i q^{80} +(-53.5953 + 60.7334i) q^{81} +2.55169 q^{82} +20.7975i q^{83} +(-30.8430 + 47.7548i) q^{84} +50.2166 q^{85} -66.8788i q^{86} +(-51.8730 - 33.5027i) q^{87} +32.4242 q^{88} +23.5142i q^{89} +(9.47664 + 21.0018i) q^{90} -196.529 q^{91} -9.59166i q^{92} +(21.4141 - 33.1559i) q^{93} +69.0841 q^{94} -19.0425i q^{95} +(-14.2558 - 9.20724i) q^{96} +24.5487 q^{97} -57.6613i q^{98} +(-94.0426 + 42.4348i) 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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