LMFDB - Embedded newform 147.3.l.a.8.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,3,Mod(8,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 12]))

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

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

chi := DirichletCharacter("147.8");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	147.l (of order $14$, degree $6$, 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:	$4.00545988610$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			8.13
Character	$\chi$	$=$	147.8
Dual form			147.3.l.a.92.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07234 + 0.855164i) q^{2} +(1.25138 + 2.72655i) q^{3} +(-0.471473 + 2.06566i) q^{4} +(-3.74354 - 7.77355i) q^{5} +(-3.67355 - 1.85366i) q^{6} +(-2.26460 + 6.62356i) q^{7} +(-3.64131 - 7.56127i) q^{8} +(-5.86812 + 6.82387i) q^{9} +O(q^{10})$	\(q+(-1.07234 + 0.855164i) q^{2} +(1.25138 + 2.72655i) q^{3} +(-0.471473 + 2.06566i) q^{4} +(-3.74354 - 7.77355i) q^{5} +(-3.67355 - 1.85366i) q^{6} +(-2.26460 + 6.62356i) q^{7} +(-3.64131 - 7.56127i) q^{8} +(-5.86812 + 6.82387i) q^{9} +(10.6620 + 5.13455i) q^{10} +(-8.73343 + 6.96468i) q^{11} +(-6.22210 + 1.29942i) q^{12} +(-8.78888 - 11.0209i) q^{13} +(-3.23580 - 9.03933i) q^{14} +(16.5104 - 19.9346i) q^{15} +(2.73504 + 1.31712i) q^{16} +(4.67698 - 1.06749i) q^{17} +(0.457101 - 12.3357i) q^{18} +11.3836 q^{19} +(17.8225 - 4.06786i) q^{20} +(-20.8933 + 2.11401i) q^{21} +(3.40928 - 14.9370i) q^{22} +(-6.33144 - 1.44511i) q^{23} +(16.0595 - 19.3902i) q^{24} +(-30.8267 + 38.6554i) q^{25} +(18.8494 + 4.30224i) q^{26} +(-25.9488 - 7.46048i) q^{27} +(-12.6143 - 7.80072i) q^{28} +(-40.3007 + 9.19837i) q^{29} +(-0.657422 + 35.4957i) q^{30} -3.91043 q^{31} +(28.6686 - 6.54342i) q^{32} +(-29.9183 - 15.0967i) q^{33} +(-4.10244 + 5.14430i) q^{34} +(59.9662 - 7.19157i) q^{35} +(-11.3291 - 15.3388i) q^{36} +(7.51161 + 32.9105i) q^{37} +(-12.2071 + 9.73484i) q^{38} +(19.0508 - 37.7546i) q^{39} +(-45.1464 + 56.6118i) q^{40} +(30.7976 + 63.9518i) q^{41} +(20.5970 - 20.1342i) q^{42} +(47.3127 + 22.7846i) q^{43} +(-10.2691 - 21.3239i) q^{44} +(75.0132 + 20.0706i) q^{45} +(8.02527 - 3.86477i) q^{46} +(-48.5282 + 38.6999i) q^{47} +(-0.168643 + 9.10543i) q^{48} +(-38.7431 - 29.9995i) q^{49} -67.8137i q^{50} +(8.76322 + 11.4162i) q^{51} +(26.9091 - 12.9587i) q^{52} +(-13.9649 - 3.18739i) q^{53} +(34.2059 - 14.1903i) q^{54} +(86.8342 + 41.8171i) q^{55} +(58.3286 - 6.99518i) q^{56} +(14.2452 + 31.0379i) q^{57} +(35.3500 - 44.3275i) q^{58} +(-4.71955 + 9.80024i) q^{59} +(33.3938 + 43.5033i) q^{60} +(-21.2047 - 92.9037i) q^{61} +(4.19331 - 3.34406i) q^{62} +(-31.9093 - 54.3212i) q^{63} +(-32.7176 + 41.0266i) q^{64} +(-52.7700 + 109.578i) q^{65} +(44.9928 - 9.39627i) q^{66} +59.2372 q^{67} +10.1643i q^{68} +(-3.98285 - 19.0713i) q^{69} +(-58.1543 + 58.9928i) q^{70} +(-3.82646 - 0.873363i) q^{71} +(72.9647 + 19.5226i) q^{72} +(-79.7160 + 99.9607i) q^{73} +(-36.1989 - 28.8677i) q^{74} +(-143.972 - 35.6779i) q^{75} +(-5.36705 + 23.5146i) q^{76} +(-26.3532 - 73.6186i) q^{77} +(11.8574 + 56.7774i) q^{78} -54.5879 q^{79} -26.1917i q^{80} +(-12.1304 - 80.0865i) q^{81} +(-87.7147 - 42.2412i) q^{82} +(62.5660 + 49.8947i) q^{83} +(5.48381 - 44.1551i) q^{84} +(-25.8067 - 32.3605i) q^{85} +(-70.2200 + 16.0273i) q^{86} +(-75.5111 - 98.3712i) q^{87} +(84.4629 + 40.6752i) q^{88} +(19.8955 + 15.8662i) q^{89} +(-97.6035 + 42.6260i) q^{90} +(92.9010 - 33.2557i) q^{91} +(5.97020 - 12.3973i) q^{92} +(-4.89341 - 10.6620i) q^{93} +(18.9440 - 82.9991i) q^{94} +(-42.6150 - 88.4909i) q^{95} +(53.7161 + 69.9780i) q^{96} +113.967 q^{97} +(67.2004 - 0.962013i) q^{98} +(3.72275 - 100.465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 5 q^{3} + 62 q^{4} + 7 q^{6} - 14 q^{7} - 45 q^{9}+O(q^{10}) $ 216 * q - 5 * q^3 + 62 * q^4 + 7 * q^6 - 14 * q^7 - 45 * q^9	$ 216 q - 5 q^{3} + 62 q^{4} + 7 q^{6} - 14 q^{7} - 45 q^{9} - 42 q^{10} - 20 q^{12} + 22 q^{13} - 17 q^{15} - 170 q^{16} - 86 q^{18} - 40 q^{19} - 21 q^{21} - 118 q^{22} + 119 q^{24} + 174 q^{25} + 88 q^{27} - 168 q^{28} + 36 q^{30} - 164 q^{31} - 35 q^{33} - 294 q^{34} + 307 q^{36} + 8 q^{37} - 61 q^{39} - 42 q^{40} - 133 q^{42} + 138 q^{43} - 336 q^{45} - 46 q^{46} - 52 q^{48} - 14 q^{49} + 111 q^{51} + 550 q^{52} + 147 q^{54} + 126 q^{55} - 363 q^{57} + 630 q^{58} + 353 q^{60} + 86 q^{61} + 21 q^{63} + 146 q^{64} + 105 q^{66} + 100 q^{67} - 7 q^{69} - 532 q^{70} - 167 q^{72} + 18 q^{73} + 1107 q^{75} - 762 q^{76} - 699 q^{78} - 272 q^{79} - 265 q^{81} + 504 q^{82} - 1834 q^{84} - 650 q^{85} - 595 q^{87} - 242 q^{88} - 1323 q^{90} + 126 q^{91} + 233 q^{93} + 1358 q^{94} - 882 q^{96} - 20 q^{97} - 332 q^{99}+O(q^{100}) $ 216 * q - 5 * q^3 + 62 * q^4 + 7 * q^6 - 14 * q^7 - 45 * q^9 - 42 * q^10 - 20 * q^12 + 22 * q^13 - 17 * q^15 - 170 * q^16 - 86 * q^18 - 40 * q^19 - 21 * q^21 - 118 * q^22 + 119 * q^24 + 174 * q^25 + 88 * q^27 - 168 * q^28 + 36 * q^30 - 164 * q^31 - 35 * q^33 - 294 * q^34 + 307 * q^36 + 8 * q^37 - 61 * q^39 - 42 * q^40 - 133 * q^42 + 138 * q^43 - 336 * q^45 - 46 * q^46 - 52 * q^48 - 14 * q^49 + 111 * q^51 + 550 * q^52 + 147 * q^54 + 126 * q^55 - 363 * q^57 + 630 * q^58 + 353 * q^60 + 86 * q^61 + 21 * q^63 + 146 * q^64 + 105 * q^66 + 100 * q^67 - 7 * q^69 - 532 * q^70 - 167 * q^72 + 18 * q^73 + 1107 * q^75 - 762 * q^76 - 699 * q^78 - 272 * q^79 - 265 * q^81 + 504 * q^82 - 1834 * q^84 - 650 * q^85 - 595 * q^87 - 242 * q^88 - 1323 * q^90 + 126 * q^91 + 233 * q^93 + 1358 * q^94 - 882 * q^96 - 20 * q^97 - 332 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{6}{7}\right)$

Coefficient data

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

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

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

$2$	−1.07234	+	0.855164i	−0.536171	+	0.427582i	−0.853776	−	0.520641i	$-0.825693\pi$
$2$	−1.07234	+	0.855164i	−0.536171	+	0.427582i	0.317605	+	0.948223i	$0.397121\pi$
$3$	1.25138	+	2.72655i	0.417125	+	0.908849i
$3$	1.25138	+	2.72655i	0.417125	+	0.908849i
$4$	−0.471473	+	2.06566i	−0.117868	+	0.516414i
$5$	−3.74354	−	7.77355i	−0.748709	−	1.55471i	−0.829837	−	0.558006i	$-0.811567\pi$
$5$	−3.74354	−	7.77355i	−0.748709	−	1.55471i	0.0811286	−	0.996704i	$-0.474148\pi$
$6$	−3.67355	−	1.85366i	−0.612258	−	0.308943i
$7$	−2.26460	+	6.62356i	−0.323515	+	0.946223i
$7$	−2.26460	+	6.62356i	−0.323515	+	0.946223i
$8$	−3.64131	−	7.56127i	−0.455164	−	0.945158i
$9$	−5.86812	+	6.82387i	−0.652013	+	0.758208i
$10$	10.6620	+	5.13455i	1.06620	+	0.513455i
$11$	−8.73343	+	6.96468i	−0.793948	+	0.633152i	−0.934114	−	0.356976i	$-0.883808\pi$
$11$	−8.73343	+	6.96468i	−0.793948	+	0.633152i	0.140166	+	0.990128i	$0.455236\pi$
$12$	−6.22210	+	1.29942i	−0.518508	+	0.108285i
$13$	−8.78888	−	11.0209i	−0.676068	−	0.847762i	0.318918	−	0.947782i	$-0.396681\pi$
$13$	−8.78888	−	11.0209i	−0.676068	−	0.847762i	−0.994985	+	0.100020i	$0.968109\pi$
$14$	−3.23580	−	9.03933i	−0.231129	−	0.645666i
$15$	16.5104	−	19.9346i	1.10069	−	1.32897i
$16$	2.73504	+	1.31712i	0.170940	+	0.0823203i
$17$	4.67698	−	1.06749i	0.275117	−	0.0627935i	−0.0827366	−	0.996571i	$-0.526366\pi$
$17$	4.67698	−	1.06749i	0.275117	−	0.0627935i	0.357853	+	0.933778i	$0.383509\pi$
$18$	0.457101	−	12.3357i	0.0253945	−	0.685318i
$19$	11.3836			0.599137			0.299568	−	0.954075i	$-0.403157\pi$
$19$	11.3836			0.599137			0.299568	+	0.954075i	$0.403157\pi$
$20$	17.8225	−	4.06786i	0.891123	−	0.203393i
$21$	−20.8933	+	2.11401i	−0.994920	+	0.100667i
$22$	3.40928	−	14.9370i	0.154967	−	0.678956i
$23$	−6.33144	−	1.44511i	−0.275280	−	0.0628309i	0.0826521	−	0.996578i	$-0.473661\pi$
$23$	−6.33144	−	1.44511i	−0.275280	−	0.0628309i	−0.357932	+	0.933748i	$0.616518\pi$
$24$	16.0595	−	19.3902i	0.669146	−	0.807925i
$25$	−30.8267	+	38.6554i	−1.23307	+	1.54622i
$26$	18.8494	+	4.30224i	0.724975	+	0.165471i
$27$	−25.9488	−	7.46048i	−0.961067	−	0.276314i
$28$	−12.6143	−	7.80072i	−0.450511	−	0.278597i
$29$	−40.3007	+	9.19837i	−1.38968	+	0.317185i	−0.850929	−	0.525280i	$-0.823961\pi$
$29$	−40.3007	+	9.19837i	−1.38968	+	0.317185i	−0.538750	+	0.842466i	$0.681103\pi$
$30$	−0.657422	+	35.4957i	−0.0219141	+	1.18319i
$31$	−3.91043			−0.126143			−0.0630714	−	0.998009i	$-0.520090\pi$
$31$	−3.91043			−0.126143			−0.0630714	+	0.998009i	$0.520090\pi$
$32$	28.6686	−	6.54342i	0.895893	−	0.204482i
$33$	−29.9183	−	15.0967i	−0.906616	−	0.457475i
$34$	−4.10244	+	5.14430i	−0.120660	+	0.151303i
$35$	59.9662	−	7.19157i	1.71332	−	0.205473i
$36$	−11.3291	−	15.3388i	−0.314698	−	0.426077i
$37$	7.51161	+	32.9105i	0.203016	+	0.889473i	0.969087	+	0.246717i	$0.0793519\pi$
$37$	7.51161	+	32.9105i	0.203016	+	0.889473i	−0.766071	+	0.642756i	$0.777791\pi$
$38$	−12.2071	+	9.73484i	−0.321240	+	0.256180i
$39$	19.0508	−	37.7546i	0.488483	−	0.968066i
$40$	−45.1464	+	56.6118i	−1.12866	+	1.41530i
$41$	30.7976	+	63.9518i	0.751160	+	1.55980i	0.826691	+	0.562656i	$0.190220\pi$
$41$	30.7976	+	63.9518i	0.751160	+	1.55980i	−0.0755314	+	0.997143i	$0.524065\pi$
$42$	20.5970	−	20.1342i	0.490404	−	0.479385i
$43$	47.3127	+	22.7846i	1.10030	+	0.529875i	0.893752	−	0.448562i	$-0.148064\pi$
$43$	47.3127	+	22.7846i	1.10030	+	0.529875i	0.206545	+	0.978437i	$0.433778\pi$
$44$	−10.2691	−	21.3239i	−0.233388	−	0.484634i
$45$	75.0132	+	20.0706i	1.66696	+	0.446014i
$46$	8.02527	−	3.86477i	0.174462	−	0.0840167i
$47$	−48.5282	+	38.6999i	−1.03251	+	0.823403i	−0.984490	−	0.175443i	$-0.943864\pi$
$47$	−48.5282	+	38.6999i	−1.03251	+	0.823403i	−0.0480249	+	0.998846i	$0.515293\pi$
$48$	−0.168643	+	9.10543i	−0.00351340	+	0.189696i
$49$	−38.7431	−	29.9995i	−0.790676	−	0.612235i
$50$		−	67.8137i		−	1.35627i
$51$	8.76322	+	11.4162i	0.171828	+	0.223847i
$52$	26.9091	−	12.9587i	0.517483	−	0.249207i
$53$	−13.9649	−	3.18739i	−0.263488	−	0.0601394i	0.0887359	−	0.996055i	$-0.471717\pi$
$53$	−13.9649	−	3.18739i	−0.263488	−	0.0601394i	−0.352224	+	0.935916i	$0.614574\pi$
$54$	34.2059	−	14.1903i	0.633443	−	0.262784i
$55$	86.8342	+	41.8171i	1.57880	+	0.760312i
$56$	58.3286	−	6.99518i	1.04158	−	0.124914i
$57$	14.2452	+	31.0379i	0.249915	+	0.544525i
$58$	35.3500	−	44.3275i	0.609483	−	0.764267i
$59$	−4.71955	+	9.80024i	−0.0799923	+	0.166106i	−0.937129	−	0.348983i	$-0.886527\pi$
$59$	−4.71955	+	9.80024i	−0.0799923	+	0.166106i	0.857137	+	0.515089i	$0.172241\pi$
$60$	33.3938	+	43.5033i	0.556563	+	0.725056i
$61$	−21.2047	−	92.9037i	−0.347617	−	1.52301i	−0.782573	−	0.622559i	$-0.786093\pi$
$61$	−21.2047	−	92.9037i	−0.347617	−	1.52301i	0.434956	−	0.900452i	$-0.356764\pi$
$62$	4.19331	−	3.34406i	0.0676341	−	0.0539364i
$63$	−31.9093	−	54.3212i	−0.506498	−	0.862241i
$64$	−32.7176	+	41.0266i	−0.511213	+	0.641041i
$65$	−52.7700	+	109.578i	−0.811846	+	1.68582i
$66$	44.9928	−	9.39627i	0.681709	−	0.142368i
$67$	59.2372			0.884137			0.442069	−	0.896981i	$-0.354245\pi$
$67$	59.2372			0.884137			0.442069	+	0.896981i	$0.354245\pi$
$68$			10.1643i			0.149475i
$69$	−3.98285	−	19.0713i	−0.0577225	−	0.276396i
$70$	−58.1543	+	58.9928i	−0.830775	+	0.842754i
$71$	−3.82646	−	0.873363i	−0.0538937	−	0.0123009i	0.195489	−	0.980706i	$-0.437371\pi$
$71$	−3.82646	−	0.873363i	−0.0538937	−	0.0123009i	−0.249383	+	0.968405i	$0.580228\pi$
$72$	72.9647	+	19.5226i	1.01340	+	0.271147i
$73$	−79.7160	+	99.9607i	−1.09200	+	1.36932i	−0.168511	+	0.985700i	$0.553896\pi$
$73$	−79.7160	+	99.9607i	−1.09200	+	1.36932i	−0.923489	+	0.383625i	$0.874676\pi$
$74$	−36.1989	−	28.8677i	−0.489174	−	0.390103i
$75$	−143.972	−	35.6779i	−1.91962	−	0.475706i
$76$	−5.36705	+	23.5146i	−0.0706191	+	0.309403i
$77$	−26.3532	−	73.6186i	−0.342249	−	0.956086i
$78$	11.8574	+	56.7774i	0.152017	+	0.727915i
$79$	−54.5879			−0.690986			−0.345493	−	0.938421i	$-0.612288\pi$
$79$	−54.5879			−0.690986			−0.345493	+	0.938421i	$0.612288\pi$
$80$		−	26.1917i		−	0.327396i
$81$	−12.1304	−	80.0865i	−0.149758	−	0.988723i
$82$	−87.7147	−	42.2412i	−1.06969	−	0.515136i
$83$	62.5660	+	49.8947i	0.753807	+	0.601141i	0.923161	−	0.384414i	$-0.125597\pi$
$83$	62.5660	+	49.8947i	0.753807	+	0.601141i	−0.169354	+	0.985555i	$0.554168\pi$
$84$	5.48381	−	44.1551i	0.0652834	−	0.525656i
$85$	−25.8067	−	32.3605i	−0.303608	−	0.380712i
$86$	−70.2200	+	16.0273i	−0.816512	+	0.186363i
$87$	−75.5111	−	98.3712i	−0.867944	−	1.13070i
$88$	84.4629	+	40.6752i	0.959806	+	0.462218i
$89$	19.8955	+	15.8662i	0.223545	+	0.178271i	0.728858	−	0.684665i	$-0.240051\pi$
$89$	19.8955	+	15.8662i	0.223545	+	0.178271i	−0.505313	+	0.862936i	$0.668623\pi$
$90$	−97.6035	+	42.6260i	−1.08448	+	0.473622i
$91$	92.9010	−	33.2557i	1.02089	−	0.365447i
$92$	5.97020	−	12.3973i	0.0648935	−	0.134753i
$93$	−4.89341	−	10.6620i	−0.0526174	−	0.114645i
$94$	18.9440	−	82.9991i	0.201532	−	0.882969i
$95$	−42.6150	−	88.4909i	−0.448579	−	0.931483i
$96$	53.7161	+	69.9780i	0.559543	+	0.728937i
$97$	113.967			1.17491			0.587457	−	0.809255i	$-0.300129\pi$
$97$	113.967			1.17491			0.587457	+	0.809255i	$0.300129\pi$
$98$	67.2004	−	0.962013i	0.685718	−	0.00981646i
$99$	3.72275	−	100.465i	0.0376035	−	1.01480i
$100$	−65.3149	−	81.9023i	−0.653149	−	0.819023i
$101$	−24.2327	−	50.3198i	−0.239928	−	0.498216i	0.745882	−	0.666078i	$-0.232028\pi$
$101$	−24.2327	−	50.3198i	−0.239928	−	0.498216i	−0.985811	+	0.167862i	$0.946314\pi$
$102$	−19.1599	−	4.74805i	−0.187842	−	0.0465495i
$103$	59.9122	−	28.8522i	0.581671	−	0.280118i	−0.119821	−	0.992796i	$-0.538232\pi$
$103$	59.9122	−	28.8522i	0.581671	−	0.280118i	0.701492	+	0.712677i	$0.252518\pi$
$104$	−51.3289	+	106.586i	−0.493547	+	1.02486i
$105$	94.6484	+	154.501i	0.901413	+	1.47144i
$106$	17.7008	−	8.52428i	0.166989	−	0.0804177i
$107$	−58.2884	−	46.4834i	−0.544751	−	0.434425i	0.312054	−	0.950064i	$-0.398983\pi$
$107$	−58.2884	−	46.4834i	−0.544751	−	0.434425i	−0.856806	+	0.515640i	$0.827554\pi$
$108$	27.6449	−	50.0839i	0.255972	−	0.463740i
$109$	−81.9696	−	102.787i	−0.752015	−	0.942997i	0.247651	−	0.968849i	$-0.420341\pi$
$109$	−81.9696	−	102.787i	−0.752015	−	0.942997i	−0.999666	+	0.0258526i	$0.991770\pi$
$110$	−128.876	+	29.4152i	−1.17160	+	0.267411i
$111$	−80.3322	+	61.6642i	−0.723714	+	0.555533i
$112$	−14.9178	+	15.1329i	−0.133195	+	0.135115i
$113$	−68.4605	−	54.5954i	−0.605845	−	0.483145i	0.271866	−	0.962335i	$-0.412359\pi$
$113$	−68.4605	−	54.5954i	−0.605845	−	0.483145i	−0.877711	+	0.479190i	$0.840931\pi$
$114$	−41.8182	−	21.1013i	−0.366826	−	0.185099i
$115$	12.4684	+	54.6276i	0.108421	+	0.475022i
$116$		−	87.5842i		−	0.755036i
$117$	126.779	+	4.69782i	1.08358	+	0.0401523i
$118$	−3.31984	−	14.5452i	−0.0281343	−	0.123264i
$119$	−3.52093	+	33.3957i	−0.0295876	+	0.280636i
$120$	−210.850	−	52.2512i	−1.75708	−	0.435427i
$121$	0.841013	−	3.68472i	0.00695052	−	0.0304522i
$122$	102.186	+	81.4910i	0.837594	+	0.667959i
$123$	−135.828	+	163.999i	−1.10429	+	1.33332i
$124$	1.84366	−	8.07760i	0.0148682	−	0.0651419i
$125$	205.599	+	46.9266i	1.64479	+	0.375413i
$126$	80.6712	+	30.9632i	0.640248	+	0.245739i
$127$	9.15642	+	40.1169i	0.0720978	+	0.315881i	0.998098	−	0.0616411i	$-0.0196334\pi$
$127$	9.15642	+	40.1169i	0.0720978	+	0.315881i	−0.926001	+	0.377522i	$0.876776\pi$
$128$			45.6499i			0.356640i
$129$	−2.91732	+	157.513i	−0.0226149	+	1.22103i
$130$	−37.1197	−	162.632i	−0.285536	−	1.25102i
$131$	30.3950	−	63.1158i	0.232023	−	0.481800i	−0.752155	−	0.658987i	$-0.770985\pi$
$131$	30.3950	−	63.1158i	0.232023	−	0.481800i	0.984177	+	0.177187i	$0.0566996\pi$
$132$	45.2902	−	54.6833i	0.343108	−	0.414267i
$133$	−25.7794	+	75.4000i	−0.193830	+	0.566917i
$134$	−63.5225	+	50.6575i	−0.474048	+	0.378041i
$135$	39.1462	+	229.643i	0.289972	+	1.70106i
$136$	−25.1019	−	31.4768i	−0.184573	−	0.231447i
$137$	74.1947	−	154.067i	0.541567	−	1.12458i	−0.433189	−	0.901303i	$-0.642612\pi$
$137$	74.1947	−	154.067i	0.541567	−	1.12458i	0.974756	−	0.223273i	$-0.0716740\pi$
$138$	20.5801	+	17.0450i	0.149131	+	0.123515i
$139$	−34.5337	+	16.6306i	−0.248444	+	0.119644i	−0.553962	−	0.832542i	$-0.686885\pi$
$139$	−34.5337	+	16.6306i	−0.248444	+	0.119644i	0.305518	+	0.952186i	$0.401170\pi$
$140$	−13.4171	+	127.260i	−0.0958365	+	0.909001i
$141$	−166.244	−	83.8862i	−1.17904	−	0.594938i
$142$	4.85014	−	2.33570i	0.0341559	−	0.0164486i
$143$	153.514	+	35.0386i	1.07352	+	0.245025i
$144$	−25.0374	+	10.9345i	−0.173871	+	0.0759340i
$145$	222.371	+	278.845i	1.53360	+	1.92307i
$146$		−	175.362i		−	1.20111i
$147$	33.3128	−	143.176i	0.226618	−	0.973984i
$148$	−71.5233			−0.483266
$149$	−17.3226	+	13.8143i	−0.116259	+	0.0927137i	−0.679894	−	0.733311i	$-0.737974\pi$
$149$	−17.3226	+	13.8143i	−0.116259	+	0.0927137i	0.563634	+	0.826024i	$0.309403\pi$
$150$	184.897	−	84.8604i	1.23265	−	0.565736i
$151$	59.5629	−	260.962i	0.394456	−	1.72822i	−0.254208	−	0.967150i	$-0.581815\pi$
$151$	59.5629	−	260.962i	0.394456	−	1.72822i	0.648664	−	0.761075i	$-0.275328\pi$
$152$	−41.4512	−	86.0744i	−0.272706	−	0.566279i
$153$	−20.1607	+	38.1793i	−0.131769	+	0.249538i
$154$	91.2156	+	56.4080i	0.592309	+	0.366286i
$155$	14.6389	+	30.3979i	0.0944442	+	0.196115i
$156$	69.0060	+	57.1527i	0.442346	+	0.366364i
$157$	157.003	+	75.6084i	1.00002	+	0.481582i	0.860944	−	0.508700i	$-0.169874\pi$
$157$	157.003	+	75.6084i	1.00002	+	0.481582i	0.139072	+	0.990282i	$0.455588\pi$
$158$	58.5369	−	46.6816i	0.370487	−	0.295453i
$159$	−8.78473	−	42.0645i	−0.0552498	−	0.264557i
$160$	−158.188	−	198.361i	−0.988672	−	1.23976i
$161$	23.9100	−	38.6641i	0.148509	−	0.240150i
$162$	81.4950	+	75.5067i	0.503056	+	0.466090i
$163$	−110.996	−	53.4527i	−0.680956	−	0.327931i	0.0612315	−	0.998124i	$-0.480497\pi$
$163$	−110.996	−	53.4527i	−0.680956	−	0.327931i	−0.742187	+	0.670193i	$0.766211\pi$
$164$	−146.623	+	33.4656i	−0.894040	+	0.204059i
$165$	−5.35422	+	289.086i	−0.0324498	+	1.75204i
$166$	−109.760			−0.661206
$167$	−92.6645	+	21.1501i	−0.554877	+	0.126647i	−0.490759	−	0.871295i	$-0.663281\pi$
$167$	−92.6645	+	21.1501i	−0.554877	+	0.126647i	−0.0641181	+	0.997942i	$0.520423\pi$
$168$	92.0637	+	150.282i	0.547998	+	0.894537i
$169$	−6.60992	+	28.9600i	−0.0391120	+	0.171361i
$170$	55.3471	+	12.6326i	0.325571	+	0.0743095i
$171$	−66.8003	+	77.6802i	−0.390645	+	0.454270i
$172$	−69.3719	+	86.9896i	−0.403325	+	0.505753i
$173$	221.892	+	50.6455i	1.28262	+	0.292749i	0.808909	−	0.587934i	$-0.200059\pi$
$173$	221.892	+	50.6455i	1.28262	+	0.292749i	0.473706	+	0.880683i	$0.342916\pi$
$174$	165.097	+	40.9131i	0.948834	+	0.235133i
$175$	−186.226	−	291.722i	−1.06415	−	1.66698i
$176$	−33.0596	+	7.54564i	−0.187839	+	0.0428730i
$177$	−32.6267	−	0.604285i	−0.184332	−	0.00341404i
$178$	−34.9030			−0.196084
$179$	−210.447	+	48.0331i	−1.17568	+	0.268342i	−0.765362	−	0.643600i	$-0.777440\pi$
$179$	−210.447	+	48.0331i	−1.17568	+	0.268342i	−0.410319	+	0.911942i	$0.634583\pi$
$180$	−76.8257	+	145.489i	−0.426810	+	0.808271i
$181$	89.5942	−	112.348i	0.494996	−	0.620705i	−0.470097	−	0.882615i	$-0.655781\pi$
$181$	89.5942	−	112.348i	0.494996	−	0.620705i	0.965092	+	0.261910i	$0.0843524\pi$
$182$	−71.1825	+	115.107i	−0.391113	+	0.632456i
$183$	226.771	−	174.073i	1.23919	−	0.951218i
$184$	12.1279	+	53.1358i	0.0659125	+	0.288782i
$185$	227.711	−	181.594i	1.23087	−	0.981588i
$186$	14.3651	+	7.24860i	0.0772319	+	0.0389710i
$187$	−33.4113	+	41.8965i	−0.178670	+	0.224045i
$188$	−57.0610	−	118.488i	−0.303516	−	0.630258i
$189$	108.179	−	154.979i	0.572374	−	0.819992i
$190$	121.372	+	58.4497i	0.638800	+	0.307630i
$191$	117.423	+	243.832i	0.614780	+	1.27660i	0.943248	+	0.332089i	$0.107754\pi$
$191$	117.423	+	243.832i	0.614780	+	1.27660i	−0.328467	+	0.944515i	$0.606532\pi$
$192$	−152.803	−	37.8665i	−0.795849	−	0.197221i
$193$	−79.8866	+	38.4714i	−0.413920	+	0.199333i	−0.629242	−	0.777210i	$-0.716634\pi$
$193$	−79.8866	+	38.4714i	−0.413920	+	0.199333i	0.215321	+	0.976543i	$0.430920\pi$
$194$	−122.211	+	97.4602i	−0.629955	+	0.502372i
$195$	−364.805	−	6.75661i	−1.87079	−	0.0346493i
$196$	80.2350	−	65.8860i	0.409362	−	0.336153i
$197$			268.417i			1.36252i	0.732041	+	0.681261i	$0.238568\pi$
$197$			268.417i			1.36252i	−0.732041	+	0.681261i	$0.761432\pi$
$198$	81.9222	+	110.917i	0.413749	+	0.560185i
$199$	−130.478	+	62.8351i	−0.655670	+	0.315754i	−0.731976	−	0.681330i	$-0.761402\pi$
$199$	−130.478	+	62.8351i	−0.655670	+	0.315754i	0.0763059	+	0.997084i	$0.475687\pi$
$200$	404.533	+	92.3321i	2.02267	+	0.461661i
$201$	74.1280	+	161.513i	0.368796	+	0.803547i
$202$	69.0175	+	33.2371i	0.341671	+	0.164540i
$203$	30.3392	−	287.765i	0.149454	−	1.41756i
$204$	−27.7135	+	12.7194i	−0.135851	+	0.0623500i
$205$	381.840	−	478.812i	1.86263	−	2.33567i
$206$	−39.5730	+	82.1741i	−0.192102	+	0.398903i
$207$	47.0149	−	34.7248i	0.227125	−	0.167753i
$208$	−9.52201	−	41.7186i	−0.0457789	−	0.200570i
$209$	−99.4178	+	79.2831i	−0.475683	+	0.379345i
$210$	−233.619	−	84.7383i	−1.11247	−	0.403516i
$211$	−17.6765	+	22.1656i	−0.0837749	+	0.105050i	−0.821953	−	0.569556i	$-0.807115\pi$
$211$	−17.6765	+	22.1656i	−0.0837749	+	0.105050i	0.738178	+	0.674606i	$0.235687\pi$
$212$	13.1681	−	27.3438i	0.0621137	−	0.128980i
$213$	−2.40707	−	11.5259i	−0.0113008	−	0.0541123i
$214$	102.256			0.477832
$215$		−	453.083i		−	2.10736i
$216$	38.0771	+	223.372i	0.176283	+	1.03413i
$217$	8.85558	−	25.9010i	0.0408091	−	0.119359i
$218$	175.799	+	40.1249i	0.806417	+	0.184059i
$219$	−372.302	−	92.2610i	−1.70001	−	0.421283i
$220$	−127.320	+	159.654i	−0.578726	+	0.725700i
$221$	−52.8701	−	42.1625i	−0.239231	−	0.190781i
$222$	33.4106	−	134.822i	0.150498	−	0.607308i
$223$	−29.8239	+	130.667i	−0.133740	+	0.585952i	0.862996	+	0.505212i	$0.168586\pi$
$223$	−29.8239	+	130.667i	−0.133740	+	0.585952i	−0.996735	+	0.0807402i	$0.974272\pi$
$224$	−21.5823	+	204.706i	−0.0963495	+	0.913868i
$225$	−82.8850	−	437.192i	−0.368378	−	1.94307i
$226$	120.101			0.531421
$227$		−	70.5857i		−	0.310950i	−0.987840	−	0.155475i	$-0.950309\pi$
$227$		−	70.5857i		−	0.310950i	0.987840	−	0.155475i	$-0.0496908\pi$
$228$	−70.8299	+	14.7921i	−0.310657	+	0.0648775i
$229$	−278.547	−	134.141i	−1.21636	−	0.585769i	−0.288065	−	0.957611i	$-0.593012\pi$
$229$	−278.547	−	134.141i	−1.21636	−	0.585769i	−0.928296	+	0.371842i	$0.878726\pi$
$230$	−60.0859	−	47.9169i	−0.261243	−	0.208334i
$231$	167.747	−	163.978i	0.726177	−	0.709861i
$232$	216.299	+	271.230i	0.932323	+	1.16910i
$233$	−88.8384	+	20.2768i	−0.381281	+	0.0870248i	−0.408865	−	0.912595i	$-0.634075\pi$
$233$	−88.8384	+	20.2768i	−0.381281	+	0.0870248i	0.0275849	+	0.999619i	$0.491218\pi$
$234$	−139.968	+	103.379i	−0.598155	+	0.441793i
$235$	482.503	+	232.361i	2.05320	+	0.988771i
$236$	−18.0188	−	14.3695i	−0.0763508	−	0.0608877i
$237$	−68.3100	−	148.837i	−0.288228	−	0.628002i
$238$	−24.7832	−	38.8226i	−0.104131	−	0.163120i
$239$	−85.4926	+	177.527i	−0.357709	+	0.742791i	−0.999714	−	0.0239094i	$-0.992389\pi$
$239$	−85.4926	+	177.527i	−0.357709	+	0.742791i	0.642005	+	0.766701i	$0.278103\pi$
$240$	71.4128	−	32.7756i	0.297553	−	0.136565i
$241$	−81.6080	+	357.548i	−0.338623	+	1.48360i	0.463315	+	0.886194i	$0.346660\pi$
$241$	−81.6080	+	357.548i	−0.338623	+	1.48360i	−0.801937	+	0.597408i	$0.796197\pi$
$242$	2.24918	+	4.67048i	0.00929415	+	0.0192995i
$243$	203.180	−	133.292i	0.836132	−	0.548528i
$244$	201.904			0.827477
$245$	−88.1660	+	413.476i	−0.359861	+	1.68766i
$246$	5.40851	−	292.018i	0.0219858	−	1.18706i
$247$	−100.049	−	125.458i	−0.405057	−	0.507925i
$248$	14.2391	+	29.5678i	0.0574157	+	0.119225i
$249$	−57.7467	+	233.026i	−0.231914	+	0.935848i
$250$	−260.602	+	125.499i	−1.04241	+	0.501998i
$251$	−3.91946	+	8.13885i	−0.0156154	+	0.0324257i	−0.908631	−	0.417601i	$-0.862871\pi$
$251$	−3.91946	+	8.13885i	−0.0156154	+	0.0324257i	0.893015	+	0.450026i	$0.148585\pi$
$252$	127.253	−	40.3028i	0.504974	−	0.159932i
$253$	65.3599	−	31.4757i	0.258340	−	0.124410i
$254$	−44.1253	−	35.1888i	−0.173722	−	0.138538i
$255$	55.9387	−	110.858i	0.219367	−	0.434738i
$256$	−169.909	−	213.059i	−0.663706	−	0.832261i
$257$	8.57413	−	1.95699i	0.0333624	−	0.00761474i	−0.205807	−	0.978593i	$-0.565982\pi$
$257$	8.57413	−	1.95699i	0.0333624	−	0.00761474i	0.239170	+	0.970978i	$0.423125\pi$
$258$	−131.571	−	171.402i	−0.509964	−	0.664349i
$259$	−234.996	−	24.7757i	−0.907319	−	0.0956591i
$260$	−201.471	−	160.668i	−0.774888	−	0.617952i
$261$	173.721	−	328.984i	0.665597	−	1.26047i
$262$	21.3806	+	93.6744i	0.0816052	+	0.357536i
$263$			21.9820i			0.0835818i	0.999126	+	0.0417909i	$0.0133063\pi$
$263$			21.9820i			0.0835818i	−0.999126	+	0.0417909i	$0.986694\pi$
$264$	−5.20801	+	281.192i	−0.0197273	+	1.06512i
$265$	27.5008	+	120.489i	0.103776	+	0.454674i
$266$	−36.8350	−	102.900i	−0.138478	−	0.386842i
$267$	−18.3630	+	74.1006i	−0.0687754	+	0.277530i
$268$	−27.9287	+	122.364i	−0.104212	+	0.456581i
$269$	−241.622	−	192.687i	−0.898221	−	0.716308i	0.0612474	−	0.998123i	$-0.480492\pi$
$269$	−241.622	−	192.687i	−0.898221	−	0.716308i	−0.959469	+	0.281815i	$0.909064\pi$
$270$	−238.360	−	212.779i	−0.882816	−	0.788072i
$271$	−96.9818	+	424.905i	−0.357866	+	1.56791i	0.400632	+	0.916239i	$0.368791\pi$
$271$	−96.9818	+	424.905i	−0.357866	+	1.56791i	−0.758498	+	0.651675i	$0.774066\pi$
$272$	14.1977	+	3.24054i	0.0521976	+	0.0119138i
$273$	206.927	+	211.684i	0.757975	+	0.775398i
$274$	52.1904	+	228.661i	0.190476	+	0.834529i
$275$		−	552.292i		−	2.00833i
$276$	41.2727	+	0.764418i	0.149539	+	0.00276963i
$277$	77.3637	+	338.953i	0.279291	+	1.22366i	0.898692	+	0.438581i	$0.144519\pi$
$277$	77.3637	+	338.953i	0.279291	+	1.22366i	−0.619400	+	0.785075i	$0.712624\pi$
$278$	22.8101	−	47.3657i	0.0820507	−	0.170380i
$279$	22.9469	−	26.6842i	0.0822468	−	0.0956425i
$280$	−272.733	−	427.234i	−0.974047	−	1.52583i
$281$	32.3904	−	25.8305i	0.115268	−	0.0919235i	−0.564159	−	0.825666i	$-0.690800\pi$
$281$	32.3904	−	25.8305i	0.115268	−	0.0919235i	0.679428	+	0.733743i	$0.262228\pi$
$282$	250.007	−	52.2113i	0.886550	−	0.185147i
$283$	−274.069	−	343.672i	−0.968441	−	1.21439i	−0.976741	−	0.214421i	$-0.931213\pi$
$283$	−274.069	−	343.672i	−0.968441	−	1.21439i	0.00829996	−	0.999966i	$-0.497358\pi$
$284$	3.60814	−	7.49237i	0.0127047	−	0.0263816i
$285$	187.947	−	226.927i	0.659464	−	0.796236i
$286$	−194.583	+	93.7063i	−0.680361	+	0.327645i
$287$	−493.333	+	59.1640i	−1.71893	+	0.206146i
$288$	−123.579	+	234.028i	−0.429094	+	0.812598i
$289$	−239.645	+	115.407i	−0.829223	+	0.399333i
$290$	−476.916	−	108.853i	−1.64454	−	0.375355i
$291$	142.615	+	310.735i	0.490086	+	1.06782i
$292$	−168.901	−	211.795i	−0.578427	−	0.725324i
$293$		−	15.1561i		−	0.0517273i	−0.999665	−	0.0258637i	$-0.991766\pi$
$293$		−	15.1561i		−	0.0517273i	0.999665	−	0.0258637i	$-0.00823357\pi$
$294$	86.7159	+	182.021i	0.294952	+	0.619119i
$295$	93.8504			0.318137
$296$	221.493	−	176.635i	0.748287	−	0.596739i
$297$	278.582	−	115.570i	0.937986	−	0.389123i
$298$	6.76226	−	29.6274i	0.0226921	−	0.0994208i
$299$	39.7198	+	82.4791i	0.132842	+	0.275850i
$300$	141.577	−	280.575i	0.471923	−	0.935249i
$301$	−258.060	+	261.781i	−0.857342	+	0.869703i
$302$	159.293	+	330.776i	0.527462	+	1.09529i
$303$	106.875	−	129.041i	0.352723	−	0.425877i
$304$	31.1346	+	14.9936i	0.102416	+	0.0493211i
$305$	−642.810	+	512.624i	−2.10758	+	1.68074i
$306$	−11.0304	−	58.1819i	−0.0360471	−	0.190137i
$307$	153.418	+	192.380i	0.499732	+	0.626644i	0.966169	−	0.257910i	$-0.0830340\pi$
$307$	153.418	+	192.380i	0.499732	+	0.626644i	−0.466437	+	0.884554i	$0.654463\pi$
$308$	164.496	−	19.7275i	0.534077	−	0.0640503i
$309$	153.639	+	127.248i	0.497215	+	0.411807i
$310$	−41.6930	−	20.0783i	−0.134494	−	0.0647687i
$311$	−27.4317	+	6.26110i	−0.0882048	+	0.0201322i	−0.266396	−	0.963864i	$-0.585833\pi$
$311$	−27.4317	+	6.26110i	−0.0882048	+	0.0201322i	0.178191	+	0.983996i	$0.442976\pi$
$312$	−354.842	−	6.57210i	−1.13732	−	0.0210644i
$313$	27.8954			0.0891227			0.0445614	−	0.999007i	$-0.485811\pi$
$313$	27.8954			0.0891227			0.0445614	+	0.999007i	$0.485811\pi$
$314$	−233.018	+	53.1848i	−0.742095	+	0.169378i
$315$	−302.814	+	451.403i	−0.961316	+	1.43302i
$316$	25.7367	−	112.760i	0.0814453	−	0.356835i
$317$	457.231	+	104.360i	1.44237	+	0.329211i	0.870919	−	0.491426i	$-0.163524\pi$
$317$	457.231	+	104.360i	1.44237	+	0.329211i	0.571449	+	0.820637i	$0.306381\pi$
$318$	45.3923	+	37.5951i	0.142743	+	0.118224i
$319$	287.900	−	361.015i	0.902507	−	1.13171i
$320$	441.402	+	100.747i	1.37938	+	0.314835i
$321$	53.7986	−	217.094i	0.167597	−	0.676306i
$322$	7.42445	+	61.9081i	0.0230573	+	0.192261i
$323$	53.2409	−	12.1519i	0.164832	−	0.0376219i
$324$	171.150	+	12.7014i	0.528242	+	0.0392019i
$325$	696.950			2.14446
$326$	164.736	−	37.6000i	0.505326	−	0.115337i
$327$	177.678	−	352.119i	0.543357	−	1.07682i
$328$	371.413	−	465.737i	1.13236	−	1.41993i
$329$	−146.434	−	409.069i	−0.445089	−	1.24337i
$330$	−241.475	−	314.578i	−0.731742	−	0.953267i
$331$	112.149	+	491.359i	0.338820	+	1.48447i	0.801528	+	0.597957i	$0.204021\pi$
$331$	112.149	+	491.359i	0.338820	+	1.48447i	−0.462708	+	0.886511i	$0.653122\pi$
$332$	−132.563	+	105.716i	−0.399287	+	0.318421i
$333$	−268.656	−	141.865i	−0.806775	−	0.426020i
$334$	81.2813	−	101.923i	0.243357	−	0.305160i
$335$	−221.757	−	460.483i	−0.661961	−	1.37458i
$336$	−59.9285	−	21.7372i	−0.178358	−	0.0646941i
$337$	−6.61362	−	3.18495i	−0.0196250	−	0.00945089i	0.424046	−	0.905641i	$-0.360610\pi$
$337$	−6.61362	−	3.18495i	−0.0196250	−	0.00945089i	−0.443670	+	0.896190i	$0.646324\pi$
$338$	−17.6774	−	36.7075i	−0.0523001	−	0.108602i
$339$	63.1872	−	254.980i	0.186393	−	0.752154i
$340$	79.0129	−	38.0506i	0.232391	−	0.111914i
$341$	34.1514	−	27.2349i	0.100151	−	0.0798676i
$342$	5.20345	−	140.425i	0.0152148	−	0.410599i
$343$	286.441	−	188.680i	0.835106	−	0.550089i
$344$		−	440.710i		−	1.28113i
$345$	−133.342	+	102.355i	−0.386499	+	0.296682i
$346$	−281.255	+	135.445i	−0.812875	+	0.391460i
$347$	213.022	+	48.6209i	0.613897	+	0.140118i	0.518153	−	0.855288i	$-0.326620\pi$
$347$	213.022	+	48.6209i	0.613897	+	0.140118i	0.0957440	+	0.995406i	$0.469477\pi$
$348$	238.802	−	109.601i	0.686214	−	0.314945i
$349$	83.5712	+	40.2458i	0.239459	+	0.115317i	0.549765	−	0.835319i	$-0.314717\pi$
$349$	83.5712	+	40.2458i	0.239459	+	0.115317i	−0.310306	+	0.950637i	$0.600432\pi$
$350$	449.168	+	153.571i	1.28334	+	0.438775i
$351$	145.840	+	351.549i	0.415498	+	1.00156i
$352$	−204.802	+	256.814i	−0.581824	+	0.729585i
$353$	−19.3851	+	40.2536i	−0.0549153	+	0.114033i	−0.926621	−	0.375998i	$-0.877300\pi$
$353$	−19.3851	+	40.2536i	−0.0549153	+	0.114033i	0.871705	+	0.490030i	$0.163014\pi$
$354$	35.5038	−	27.2532i	0.100293	−	0.0769865i
$355$	7.53537	+	33.0146i	0.0212264	+	0.0929989i
$356$	−42.1542	+	33.6169i	−0.118411	+	0.0944294i
$357$	−95.4610	+	32.1906i	−0.267398	+	0.0901698i
$358$	184.595	−	231.475i	0.515628	−	0.646577i
$359$	−114.456	+	237.670i	−0.318818	+	0.662033i	−0.997367	−	0.0725224i	$-0.976895\pi$
$359$	−114.456	+	237.670i	−0.318818	+	0.662033i	0.678548	+	0.734556i	$0.262609\pi$
$360$	−121.387	−	640.278i	−0.337187	−	1.77855i
$361$	−231.414			−0.641035
$362$			197.093i			0.544455i
$363$	11.0990	−	2.31791i	0.0305757	−	0.00638541i
$364$	24.8945	+	207.581i	0.0683916	+	0.570276i
$365$	1075.47	+	245.469i	2.94649	+	0.672518i
$366$	−94.3154	+	380.592i	−0.257692	+	1.03987i
$367$	161.345	−	202.320i	0.439631	−	0.551280i	−0.511815	−	0.859096i	$-0.671027\pi$
$367$	161.345	−	202.320i	0.439631	−	0.551280i	0.951446	+	0.307816i	$0.0995981\pi$
$368$	−15.4133	−	12.2917i	−0.0418841	−	0.0334014i
$369$	−617.122	−	165.118i	−1.67242	−	0.447475i
$370$	−88.8920	+	389.461i	−0.240249	+	1.05260i
$371$	52.7368	−	85.2790i	0.142148	−	0.229862i
$372$	24.3311	−	5.08129i	0.0654061	−	0.0136594i
$373$	−666.348			−1.78645			−0.893227	−	0.449605i	$-0.851565\pi$
$373$	−666.348			−1.78645			−0.893227	+	0.449605i	$0.851565\pi$
$374$		−	73.4995i		−	0.196523i
$375$	129.334	+	619.298i	0.344891	+	1.65146i
$376$	469.327	+	226.016i	1.24821	+	0.601106i
$377$	455.572	+	363.307i	1.20841	+	0.963679i
$378$	16.5275	+	258.701i	0.0437235	+	0.684393i
$379$	43.8258	+	54.9558i	0.115635	+	0.145002i	0.836280	−	0.548302i	$-0.184726\pi$
$379$	43.8258	+	54.9558i	0.115635	+	0.145002i	−0.720645	+	0.693304i	$0.756154\pi$
$380$	202.884	−	46.3069i	0.533904	−	0.121860i
$381$	−97.9224	+	75.1667i	−0.257014	+	0.197288i
$382$	−334.434	−	161.055i	−0.875480	−	0.421609i
$383$	255.407	+	203.680i	0.666859	+	0.531803i	0.897376	−	0.441266i	$-0.145470\pi$
$383$	255.407	+	203.680i	0.666859	+	0.531803i	−0.230517	+	0.973068i	$0.574042\pi$
$384$	−124.467	+	57.1252i	−0.324132	+	0.148763i
$385$	−473.624	+	480.452i	−1.23019	+	1.24793i
$386$	52.7664	−	109.571i	0.136701	−	0.283862i
$387$	−433.116	+	189.153i	−1.11916	+	0.488768i
$388$	−53.7322	+	235.416i	−0.138485	+	0.606742i
$389$	160.733	+	333.765i	0.413194	+	0.858007i	0.998873	+	0.0474637i	$0.0151138\pi$
$389$	160.733	+	333.765i	0.413194	+	0.858007i	−0.585678	+	0.810543i	$0.699172\pi$
$390$	396.973	−	304.722i	1.01788	−	0.781339i
$391$	−31.1547			−0.0796795
$392$	−85.7583	+	402.185i	−0.218771	+	1.02598i
$393$	210.124	+	3.89174i	0.534666	+	0.00990264i
$394$	−229.540	−	287.834i	−0.582590	−	0.730544i
$395$	204.352	+	424.342i	0.517347	+	1.07428i
$396$	205.772	+	55.0566i	0.519625	+	0.139032i
$397$	−260.812	+	125.601i	−0.656958	+	0.316374i	−0.732499	−	0.680769i	$-0.761646\pi$
$397$	−260.812	+	125.601i	−0.656958	+	0.316374i	0.0755409	+	0.997143i	$0.475932\pi$
$398$	86.1831	−	178.961i	0.216540	−	0.449651i
$399$	−237.841	+	24.0651i	−0.596093	+	0.0603134i
$400$	−135.226	+	65.1215i	−0.338065	+	0.162804i
$401$	−441.550	−	352.124i	−1.10112	−	0.878116i	−0.107879	−	0.994164i	$-0.534406\pi$
$401$	−441.550	−	352.124i	−1.10112	−	0.878116i	−0.993244	+	0.116048i	$0.962977\pi$
$402$	−217.611	−	109.806i	−0.541320	−	0.273148i
$403$	34.3683	+	43.0965i	0.0852811	+	0.106939i
$404$	115.369	−	26.3321i	0.285566	−	0.0651785i
$405$	−577.146	+	394.103i	−1.42505	+	0.973095i
$406$	213.552	+	334.527i	0.525991	+	0.823959i
$407$	−294.813	−	235.106i	−0.724357	−	0.577655i
$408$	54.4111	−	107.831i	0.133361	−	0.264291i
$409$	−74.7673	−	327.577i	−0.182805	−	0.800922i	−0.980287	−	0.197579i	$-0.936692\pi$
$409$	−74.7673	−	327.577i	−0.182805	−	0.800922i	0.797482	−	0.603343i	$-0.206165\pi$
$410$			839.986i			2.04875i
$411$	512.916	+	9.49981i	1.24797	+	0.0231139i
$412$	31.3517	+	137.361i	0.0760965	+	0.333400i
$413$	−54.2246	−	53.4539i	−0.131294	−	0.129428i
$414$	−20.7206	+	77.4423i	−0.0500497	+	0.187059i
$415$	153.640	−	673.142i	0.370218	−	1.62203i
$416$	−324.079	−	258.444i	−0.779036	−	0.621260i
$417$	−88.5587	−	73.3468i	−0.212371	−	0.175892i
$418$	38.8099	−	170.037i	0.0928465	−	0.406787i
$419$	−29.0364	−	6.62738i	−0.0692994	−	0.0158171i	0.187731	−	0.982221i	$-0.439887\pi$
$419$	−29.0364	−	6.62738i	−0.0692994	−	0.0158171i	−0.257030	+	0.966403i	$0.582744\pi$
$420$	−363.771	+	122.668i	−0.866121	+	0.292067i
$421$	0.155465	+	0.681137i	0.000369276	+	0.00161790i	0.975112	−	0.221712i	$-0.0711645\pi$
$421$	0.155465	+	0.681137i	0.000369276	+	0.00161790i	−0.974743	+	0.223330i	$0.928307\pi$
$422$		−	38.8854i		−	0.0921456i
$423$	20.6858	−	558.246i	0.0489026	−	1.31973i
$424$	26.7498	+	117.198i	0.0630891	+	0.276411i
$425$	−102.911	+	213.698i	−0.242145	+	0.502818i
$426$	12.4377	+	10.3013i	0.0291966	+	0.0241814i
$427$	663.373	+	69.9398i	1.55357	+	0.163793i
$428$	123.500	−	98.4881i	0.288552	−	0.230112i
$429$	96.5694	+	462.410i	0.225104	+	1.07788i
$430$	387.460	+	485.860i	0.901070	+	1.12991i
$431$	159.637	−	331.490i	0.370387	−	0.769117i	−0.629582	−	0.776934i	$-0.716774\pi$
$431$	159.637	−	331.490i	0.370387	−	0.769117i	0.999969	+	0.00781670i	$0.00248816\pi$
$432$	−61.1446	−	54.5825i	−0.141539	−	0.126348i
$433$	607.703	−	292.654i	1.40347	−	0.675876i	0.429608	−	0.903015i	$-0.358652\pi$
$433$	607.703	−	292.654i	1.40347	−	0.675876i	0.973862	+	0.227139i	$0.0729373\pi$
$434$	12.6534	+	35.3476i	0.0291552	+	0.0814462i
$435$	−482.014	+	955.246i	−1.10808	+	2.19597i
$436$	250.968	−	120.860i	0.575615	−	0.277202i
$437$	−72.0746	−	16.4506i	−0.164930	−	0.0376443i
$438$	478.133	−	219.444i	1.09163	−	0.501014i
$439$	−373.842	−	468.782i	−0.851575	−	1.06784i	−0.996917	−	0.0784602i	$-0.975000\pi$
$439$	−373.842	−	468.782i	−0.851575	−	1.06784i	0.145342	−	0.989381i	$-0.453572\pi$
$440$		−	808.846i		−	1.83829i
$441$	432.062	−	88.3374i	0.979732	−	0.200312i
$442$	92.7507			0.209843
$443$	57.7179	−	46.0285i	0.130289	−	0.103902i	−0.556177	−	0.831064i	$-0.687732\pi$
$443$	57.7179	−	46.0285i	0.130289	−	0.103902i	0.686466	+	0.727162i	$0.259161\pi$
$444$	−89.5026	−	195.012i	−0.201582	−	0.439216i
$445$	48.8565	−	214.055i	0.109790	−	0.481021i
$446$	−79.7604	−	165.624i	−0.178835	−	0.371355i
$447$	−59.3426	−	29.9441i	−0.132758	−	0.0669890i
$448$	−197.650	−	309.616i	−0.441183	−	0.691108i
$449$	−89.7058	−	186.276i	−0.199790	−	0.414869i	0.776869	−	0.629662i	$-0.216807\pi$
$449$	−89.7058	−	186.276i	−0.199790	−	0.414869i	−0.976660	+	0.214793i	$0.931092\pi$
$450$	462.752	+	397.939i	1.02834	+	0.884308i
$451$	−714.372	−	344.023i	−1.58397	−	0.762801i
$452$	145.053	−	115.676i	0.320913	−	0.255919i
$453$	786.061	−	164.160i	1.73523	−	0.362385i
$454$	60.3623	+	75.6919i	0.132957	+	0.166722i
$455$	−606.293	−	597.676i	−1.33251	−	1.31357i
$456$	182.815	−	220.730i	0.400910	−	0.484057i
$457$	−137.451	−	66.1929i	−0.300768	−	0.144842i	0.277413	−	0.960751i	$-0.410523\pi$
$457$	−137.451	−	66.1929i	−0.300768	−	0.144842i	−0.578181	+	0.815909i	$0.696237\pi$
$458$	413.410	−	94.3581i	0.902641	−	0.206022i
$459$	−129.326	−	7.19239i	−0.281756	−	0.0156697i
$460$	−118.720			−0.258088
$461$	533.050	−	121.665i	1.15629	−	0.263916i	0.398973	−	0.916963i	$-0.369367\pi$
$461$	533.050	−	121.665i	1.15629	−	0.263916i	0.757317	+	0.653047i	$0.226510\pi$
$462$	−39.6541	+	319.291i	−0.0858314	+	0.691107i
$463$	−55.9105	+	244.960i	−0.120757	+	0.529071i	0.877974	+	0.478708i	$0.158895\pi$
$463$	−55.9105	+	244.960i	−0.120757	+	0.529071i	−0.998731	+	0.0503625i	$0.983962\pi$
$464$	−122.339	−	27.9232i	−0.263662	−	0.0601792i
$465$	−64.5626	+	77.9527i	−0.138844	+	0.167640i
$466$	77.9251	−	97.7150i	0.167221	−	0.209689i
$467$	494.787	+	112.932i	1.05950	+	0.241824i	0.716555	−	0.697530i	$-0.245718\pi$
$467$	494.787	+	112.932i	1.05950	+	0.241824i	0.342947	+	0.939355i	$0.388575\pi$
$468$	−69.4771	+	259.668i	−0.148455	+	0.554846i
$469$	−134.149	+	392.361i	−0.286032	+	0.836591i
$470$	−716.115	+	163.449i	−1.52365	+	0.347763i
$471$	−9.68082	+	522.689i	−0.0205538	+	1.10974i
$472$	91.2876			0.193406
$473$	−571.890	+	130.530i	−1.20907	+	0.275962i
$474$	200.531	+	101.187i	0.423062	+	0.213475i
$475$	−350.918	+	440.038i	−0.738776	+	0.926395i
$476$	−67.3240	−	23.0182i	−0.141437	−	0.0483575i
$477$	103.698	−	76.5904i	0.217396	−	0.160567i
$478$	−60.1376	−	263.480i	−0.125811	−	0.551213i
$479$	−326.302	+	260.217i	−0.681214	+	0.543250i	−0.901820	−	0.432113i	$-0.857768\pi$
$479$	−326.302	+	260.217i	−0.681214	+	0.543250i	0.220605	+	0.975363i	$0.429197\pi$
$480$	342.888	−	679.530i	0.714351	−	1.41569i
$481$	296.685	−	372.031i	0.616809	−	0.773454i
$482$	−218.251	−	453.202i	−0.452802	−	0.940253i
$483$	135.340	+	16.8084i	0.280207	+	0.0348000i
$484$	7.21485	+	3.47449i	0.0149067	+	0.00717869i
$485$	−426.639	−	885.925i	−0.879668	−	1.82665i
$486$	−103.892	+	316.687i	−0.213769	+	0.651620i
$487$	646.356	−	311.268i	1.32722	−	0.639155i	0.370138	−	0.928977i	$-0.379310\pi$
$487$	646.356	−	311.268i	1.32722	−	0.639155i	0.957081	+	0.289822i	$0.0935960\pi$
$488$	−625.256	+	498.625i	−1.28126	+	1.02177i
$489$	6.84403	−	369.525i	0.0139960	−	0.755674i
$490$	−259.046	−	518.784i	−0.528665	−	1.05874i
$491$			368.111i			0.749717i	0.927082	+	0.374858i	$0.122309\pi$
$491$			368.111i			0.749717i	−0.927082	+	0.374858i	$0.877691\pi$
$492$	−274.726	−	357.895i	−0.558385	−	0.727429i
$493$	−178.666	+	86.0412i	−0.362407	+	0.174526i
$494$	214.574	+	48.9750i	0.434359	+	0.0991397i
$495$	−794.908	+	347.157i	−1.60587	+	0.701328i
$496$	−10.6952	−	5.15052i	−0.0215628	−	0.0103841i
$497$	14.4502	−	23.3669i	0.0290748	−	0.0470160i
$498$	−137.351	−	299.266i	−0.275806	−	0.600936i
$499$	105.599	−	132.417i	0.211622	−	0.265365i	−0.664680	−	0.747128i	$-0.731432\pi$
$499$	105.599	−	132.417i	0.211622	−	0.265365i	0.876301	+	0.481763i	$0.160003\pi$
$500$	−193.869	+	402.572i	−0.387737	+	0.805145i
$501$	−173.625	−	226.188i	−0.346557	−	0.451472i
$502$	−2.75705	−	12.0794i	−0.00549212	−	0.0240626i
$503$	−663.787	+	529.353i	−1.31966	+	1.05239i	−0.325377	+	0.945584i	$0.605491\pi$
$503$	−663.787	+	529.353i	−1.31966	+	1.05239i	−0.994280	+	0.106806i	$0.965937\pi$
$504$	−294.545	+	439.076i	−0.584415	+	0.871182i
$505$	−300.447	+	376.749i	−0.594945	+	0.746037i
$506$	−43.1713	+	89.6461i	−0.0853187	+	0.177166i
$507$	−87.2322	+	18.2175i	−0.172056	+	0.0359320i
$508$	−87.1847			−0.171623
$509$		−	160.168i		−	0.314672i	−0.987545	−	0.157336i	$-0.949709\pi$
$509$		−	160.168i		−	0.314672i	0.987545	−	0.157336i	$-0.0502905\pi$
$510$	34.8166	+	166.715i	0.0682678	+	0.326891i
$511$	−481.571	−	754.375i	−0.942408	−	1.47627i
$512$	186.379	+	42.5397i	0.364021	+	0.0830854i
$513$	−295.391	−	84.9271i	−0.575811	−	0.165550i
$514$	−7.52084	+	9.43084i	−0.0146320	+	0.0183479i
$515$	−448.567	−	357.721i	−0.871005	−	0.694603i
$516$	−323.991	−	80.2890i	−0.627890	−	0.155599i
$517$	154.285	−	675.966i	0.298423	−	1.30748i
$518$	273.183	−	174.392i	0.527380	−	0.336664i
$519$	139.583	+	668.377i	0.268947	+	1.28782i
$520$	1020.70			1.96289
$521$			99.9073i			0.191761i	0.995393	+	0.0958803i	$0.0305666\pi$
$521$			99.9073i			0.191761i	−0.995393	+	0.0958803i	$0.969433\pi$
$522$	95.0471	+	501.343i	0.182083	+	0.960427i
$523$	−1.81207	−	0.872649i	−0.00346477	−	0.00166854i	0.432151	−	0.901801i	$-0.357755\pi$
$523$	−1.81207	−	0.872649i	−0.00346477	−	0.00166854i	−0.435615	+	0.900133i	$0.643469\pi$
$524$	116.045	+	92.5429i	0.221460	+	0.176609i
$525$	562.354	−	872.808i	1.07115	−	1.66249i
$526$	−18.7982	−	23.5722i	−0.0357381	−	0.0448141i
$527$	−18.2890	+	4.17434i	−0.0347040	+	0.00792096i
$528$	−61.9435	−	80.6961i	−0.117317	−	0.152834i
$529$	−438.614	−	211.225i	−0.829137	−	0.399292i
$530$	−132.528	−	105.687i	−0.250052	−	0.199410i
$531$	−39.1807	−	89.7145i	−0.0737866	−	0.168954i
$532$	−143.596	−	88.8003i	−0.269918	−	0.166918i
$533$	434.130	−	901.481i	0.814504	−	1.69133i
$534$	−43.6767	−	95.1646i	−0.0817916	−	0.178211i
$535$	−143.136	+	627.120i	−0.267544	+	1.17219i
$536$	−215.701	−	447.908i	−0.402428	−	0.835649i
$537$	−394.313	−	513.686i	−0.734288	−	0.956585i
$538$	423.880			0.787880
$539$	547.297	−	7.83488i	1.01539	−	0.0145360i
$540$	−492.820	−	27.4079i	−0.912629	−	0.0507553i
$541$	102.849	+	128.968i	0.190108	+	0.238388i	0.867746	−	0.497007i	$-0.165568\pi$
$541$	102.849	+	128.968i	0.190108	+	0.238388i	−0.677638	+	0.735396i	$0.736996\pi$
$542$	−259.366	−	538.578i	−0.478534	−	0.993687i
$543$	418.437	+	103.694i	0.770602	+	0.190965i
$544$	127.097	−	61.2069i	0.233635	−	0.112513i
$545$	−492.160	+	1021.98i	−0.903046	+	1.87519i
$546$	−402.921	−	50.0404i	−0.737950	−	0.0916491i
$547$	−437.994	+	210.927i	−0.800720	+	0.385606i	−0.789053	−	0.614326i	$-0.789428\pi$
$547$	−437.994	+	210.927i	−0.800720	+	0.385606i	−0.0116671	+	0.999932i	$0.503714\pi$
$548$	283.268	+	225.899i	0.516913	+	0.412225i
$549$	758.394	+	400.472i	1.38141	+	0.729457i
$550$	472.300	+	592.246i	0.858728	+	1.07681i
$551$	−458.767	+	104.711i	−0.832608	+	0.190037i
$552$	−129.701	+	99.5601i	−0.234965	+	0.180363i
$553$	123.620	−	361.566i	0.223544	−	0.653827i
$554$	−372.820	−	297.314i	−0.672961	−	0.536669i
$555$	780.076	+	393.624i	1.40554	+	0.709232i
$556$	−18.0713	−	79.1757i	−0.0325024	−	0.142402i
$557$			890.518i			1.59877i	0.600816	+	0.799387i	$0.294842\pi$
$557$			890.518i			1.59877i	−0.600816	+	0.799387i	$0.705158\pi$
$558$	−1.78746	+	48.2379i	−0.00320333	+	0.0864479i
$559$	−164.719	−	721.681i	−0.294667	−	1.29102i
$560$	173.482	+	59.3138i	0.309789	+	0.105917i
$561$	−156.043	−	38.6693i	−0.278151	−	0.0689293i
$562$	−12.6443	+	55.3983i	−0.0224987	+	0.0985734i
$563$	845.485	+	674.252i	1.50175	+	1.19761i	0.924584	+	0.380978i	$0.124413\pi$
$563$	845.485	+	674.252i	1.50175	+	1.19761i	0.577165	+	0.816627i	$0.304159\pi$
$564$	251.660	−	303.853i	0.446205	−	0.538747i
$565$	−168.115	+	736.561i	−0.297549	+	1.30365i
$566$	587.791	+	134.159i	1.03850	+	0.237031i
$567$	557.929	+	101.018i	0.984001	+	0.178162i
$568$	7.32959	+	32.1130i	0.0129042	+	0.0565370i
$569$			865.670i			1.52139i	0.649110	+	0.760694i	$0.275141\pi$
$569$			865.670i			1.52139i	−0.649110	+	0.760694i	$0.724859\pi$
$570$	−7.48383	+	404.069i	−0.0131295	+	0.708893i
$571$	−70.4818	−	308.801i	−0.123436	−	0.540807i	−0.998396	−	0.0566129i	$-0.981970\pi$
$571$	−70.4818	−	308.801i	−0.123436	−	0.540807i	0.874960	−	0.484194i	$-0.160887\pi$
$572$	−144.755	+	300.588i	−0.253069	+	0.525503i
$573$	−517.878	+	625.284i	−0.903801	+	1.09125i
$574$	478.426	−	485.324i	0.833495	−	0.845513i
$575$	251.039	−	200.197i	0.436589	−	0.348168i
$576$	−87.9693	−	464.010i	−0.152724	−	0.805573i
$577$	−122.170	−	153.197i	−0.211733	−	0.265505i	0.664612	−	0.747189i	$-0.268597\pi$
$577$	−122.170	−	153.197i	−0.211733	−	0.265505i	−0.876345	+	0.481683i	$0.840025\pi$
$578$	158.290	−	328.692i	0.273858	−	0.568671i
$579$	−204.862	−	169.672i	−0.353821	−	0.293044i
$580$	−680.840	+	327.875i	−1.17386	+	0.565302i
$581$	−472.168	+	301.418i	−0.812681	+	0.518791i
$582$	−418.662	−	211.255i	−0.719350	−	0.362982i
$583$	144.160	−	69.4239i	0.247273	−	0.119081i
$584$	1046.10	+	238.766i	1.79127	+	0.408845i
$585$	−438.085	−	1003.11i	−0.748864	−	1.71472i
$586$	12.9609	+	16.2525i	0.0221177	+	0.0277347i
$587$		−	734.814i		−	1.25181i	−0.779898	−	0.625906i	$-0.784729\pi$
$587$		−	734.814i		−	1.25181i	0.779898	−	0.625906i	$-0.215271\pi$
$588$	280.046	+	136.316i	0.476268	+	0.231830i
$589$	−44.5147			−0.0755768
$590$	−100.640	+	80.2575i	−0.170576	+	0.136030i
$591$	−731.851	+	335.890i	−1.23833	+	0.568342i
$592$	−22.8027	+	99.9052i	−0.0385181	+	0.168759i
$593$	−270.841	−	562.406i	−0.456730	−	0.948409i	−0.994443	−	0.105281i	$-0.966426\pi$
$593$	−270.841	−	562.406i	−0.456730	−	0.948409i	0.537713	−	0.843128i	$-0.319288\pi$
$594$	−199.904	+	362.163i	−0.336539	+	0.609703i
$595$	272.784	−	97.6482i	0.458460	−	0.164115i
$596$	−20.3685	−	42.2957i	−0.0341754	−	0.0709660i
$597$	−334.600	−	277.125i	−0.560469	−	0.464196i
$598$	−113.126	−	54.4788i	−0.189175	−	0.0911017i
$599$	−226.583	+	180.694i	−0.378269	+	0.301660i	−0.794106	−	0.607780i	$-0.792060\pi$
$599$	−226.583	+	180.694i	−0.378269	+	0.301660i	0.415836	+	0.909440i	$0.363489\pi$
$600$	254.475	+	1218.52i	0.424126	+	2.03087i
$601$	263.984	+	331.025i	0.439241	+	0.550791i	0.951343	−	0.308134i	$-0.0997044\pi$
$601$	263.984	+	331.025i	0.439241	+	0.550791i	−0.512102	+	0.858925i	$0.671133\pi$
$602$	52.8630	−	501.402i	0.0878124	−	0.832894i
$603$	−347.611	+	404.227i	−0.576469	+	0.670360i
$604$	510.975	+	246.073i	0.845986	+	0.407405i
$605$	−31.7917	+	7.25625i	−0.0525483	+	0.0119938i
$606$	−4.25564	+	229.771i	−0.00702250	+	0.379161i
$607$	−485.893			−0.800482			−0.400241	−	0.916410i	$-0.631074\pi$
$607$	−485.893			−0.800482			−0.400241	+	0.916410i	$0.631074\pi$
$608$	326.352	−	74.4876i	0.536762	−	0.122513i
$609$	822.570	−	277.381i	1.35069	−	0.455469i
$610$	250.935	−	1099.42i	0.411368	−	1.80232i
$611$	853.016	+	194.695i	1.39610	+	0.318650i
$612$	−69.3600	−	59.6455i	−0.113333	−	0.0974599i
$613$	−349.339	+	438.057i	−0.569883	+	0.714611i	−0.980350	−	0.197264i	$-0.936794\pi$
$613$	−349.339	+	438.057i	−0.569883	+	0.714611i	0.410467	+	0.911876i	$0.365366\pi$
$614$	−329.032	−	75.0995i	−0.535883	−	0.122312i
$615$	1783.33	+	441.931i	2.89972	+	0.718587i
$616$	−460.690	+	467.332i	−0.747873	+	0.758656i
$617$	−451.907	+	103.145i	−0.732426	+	0.167171i	−0.572439	−	0.819948i	$-0.694003\pi$
$617$	−451.907	+	103.145i	−0.732426	+	0.167171i	−0.159988	+	0.987119i	$0.551145\pi$
$618$	−273.572	−	5.06688i	−0.442673	−	0.00819883i
$619$	778.474			1.25763			0.628816	−	0.777554i	$-0.283540\pi$
$619$	778.474			1.25763			0.628816	+	0.777554i	$0.283540\pi$
$620$	−69.6934	+	15.9071i	−0.112409	+	0.0256566i
$621$	153.512	+	84.7345i	0.247202	+	0.136448i
$622$	24.0619	−	30.1726i	0.0386847	−	0.0485090i
$623$	−150.146	+	95.8487i	−0.241005	+	0.153850i
$624$	101.832	−	78.1679i	0.163193	−	0.125269i
$625$	−129.835	−	568.843i	−0.207735	−	0.910148i
$626$	−29.9134	+	23.8552i	−0.0477850	+	0.0381073i
$627$	−340.578	−	171.854i	−0.543187	−	0.274090i
$628$	−230.203	+	288.666i	−0.366566	+	0.459659i
$629$	70.2633	+	145.903i	0.111706	+	0.231961i
$630$	−61.3026	−	743.014i	−0.0973058	−	1.17939i
$631$	722.366	+	347.873i	1.14480	+	0.551304i	0.907466	−	0.420125i	$-0.138014\pi$
$631$	722.366	+	347.873i	1.14480	+	0.551304i	0.237329	+	0.971429i	$0.423728\pi$
$632$	198.772	+	412.754i	0.314512	+	0.653091i
$633$	−82.5556	−	20.4583i	−0.130420	−	0.0323196i
$634$	−579.552	+	279.098i	−0.914120	+	0.440217i
$635$	277.573	−	221.357i	0.437123	−	0.348594i
$636$	91.0325	+	1.68603i	0.143133	+	0.00265099i
$637$	9.88701	+	690.646i	0.0155212	+	1.08422i
$638$			633.332i			0.992684i
$639$	28.4138	−	20.9862i	0.0444661	−	0.0328423i
$640$	354.862	−	170.892i	0.554471	−	0.267019i
$641$	1169.33	+	266.892i	1.82423	+	0.416369i	0.990695	−	0.136098i	$-0.0434563\pi$
$641$	1169.33	+	266.892i	1.82423	+	0.416369i	0.833535	+	0.552467i	$0.186313\pi$
$642$	127.961	+	278.806i	0.199316	+	0.434277i
$643$	−223.366	−	107.568i	−0.347382	−	0.167290i	0.252054	−	0.967713i	$-0.418894\pi$
$643$	−223.366	−	107.568i	−0.347382	−	0.167290i	−0.599436	+	0.800423i	$0.704608\pi$
$644$	68.5938	+	67.6189i	0.106512	+	0.104998i
$645$	1235.35	−	566.977i	1.91527	−	0.879034i
$646$	−46.7005	+	58.5606i	−0.0722919	+	0.0906511i
$647$	438.998	−	911.589i	0.678513	−	1.40895i	−0.222403	−	0.974955i	$-0.571390\pi$
$647$	438.998	−	911.589i	0.678513	−	1.40895i	0.900916	−	0.433993i	$-0.142896\pi$
$648$	−561.385	+	383.341i	−0.866335	+	0.591576i
$649$	−27.0377	−	118.460i	−0.0416605	−	0.182527i
$650$	−747.368	+	596.006i	−1.14980	+	0.916932i
$651$	81.7018	−	8.26669i	0.125502	−	0.0126984i
$652$	162.746	−	204.078i	0.249611	−	0.313002i
$653$	−40.1422	+	83.3560i	−0.0614734	+	0.127651i	−0.929442	−	0.368968i	$-0.879711\pi$
$653$	−40.1422	+	83.3560i	−0.0614734	+	0.127651i	0.867969	+	0.496619i	$0.165425\pi$
$654$	110.588	+	529.535i	0.169095	+	0.809687i
$655$	−604.419			−0.922776
$656$			215.475i			0.328468i
$657$	−214.336	−	1130.55i	−0.326234	−	1.72078i
$658$	506.849	+	313.437i	0.770287	+	0.476348i
$659$	−201.846	−	46.0700i	−0.306291	−	0.0699090i	0.0666128	−	0.997779i	$-0.478781\pi$
$659$	−201.846	−	46.0700i	−0.306291	−	0.0699090i	−0.372904	+	0.927870i	$0.621638\pi$
$660$	−594.629	−	147.356i	−0.900953	−	0.223267i
$661$	159.613	−	200.149i	0.241472	−	0.302797i	−0.646296	−	0.763086i	$-0.723683\pi$
$661$	159.613	−	200.149i	0.241472	−	0.302797i	0.887769	+	0.460290i	$0.152254\pi$
$662$	−540.455	−	430.998i	−0.816397	−	0.651055i
$663$	48.7977	−	196.914i	0.0736014	−	0.297005i
$664$	149.445	−	654.760i	0.225067	−	0.986084i
$665$	682.631	−	81.8660i	1.02651	−	0.123107i
$666$	409.408	−	77.6177i	0.614727	−	0.116543i
$667$	268.454			0.402480
$668$		−	201.385i		−	0.301474i
$669$	−393.591	+	82.1974i	−0.588328	+	0.122866i
$670$	631.588	+	304.157i	0.942668	+	0.453965i
$671$	832.233	+	663.684i	1.24029	+	0.989097i
$672$	−585.149	+	197.319i	−0.870757	+	0.293630i
$673$	−424.092	−	531.795i	−0.630152	−	0.790185i	0.359581	−	0.933114i	$-0.382920\pi$
$673$	−424.092	−	531.795i	−0.630152	−	0.790185i	−0.989733	+	0.142929i	$0.954348\pi$
$674$	9.81571	−	2.24037i	0.0145634	−	0.00332399i
$675$	1088.30	−	773.081i	1.61230	−	1.14531i
$676$	−56.7049	−	27.3077i	−0.0838830	−	0.0403959i
$677$	−418.056	−	333.389i	−0.617513	−	0.492450i	0.264055	−	0.964508i	$-0.414940\pi$
$677$	−418.056	−	333.389i	−0.617513	−	0.492450i	−0.881568	+	0.472058i	$0.843511\pi$
$678$	150.292	+	327.461i	0.221669	+	0.482981i
$679$	−258.089	+	754.865i	−0.380102	+	1.11173i
$680$	−150.716	+	312.966i	−0.221642	+	0.460244i
$681$	192.455	−	88.3292i	0.282607	−	0.129705i
$682$	−13.3317	+	58.4102i	−0.0195480	+	0.0856454i
$683$	−83.0513	−	172.458i	−0.121598	−	0.252501i	0.831281	−	0.555853i	$-0.187608\pi$
$683$	−83.0513	−	172.458i	−0.121598	−	0.252501i	−0.952878	+	0.303353i	$0.901894\pi$
$684$	−128.966	−	174.611i	−0.188547	−	0.255279i
$685$	−1475.40			−2.15386
$686$	−145.810	+	447.284i	−0.212551	+	0.652018i
$687$	17.1753	−	927.332i	0.0250004	−	1.34983i
$688$	99.3920	+	124.634i	0.144465	+	0.181153i
$689$	87.6076	+	181.919i	0.127152	+	0.264033i
$690$	55.4577	−	223.789i	0.0803734	−	0.324332i
$691$	1005.47	−	484.210i	1.45510	−	0.700738i	0.471626	−	0.881799i	$-0.343667\pi$
$691$	1005.47	−	484.210i	1.45510	−	0.700738i	0.983472	+	0.181060i	$0.0579529\pi$
$692$	−209.232	+	434.476i	−0.302359	+	0.627855i
$693$	657.008	+	252.172i	0.948063	+	0.363885i
$694$	−270.011	+	130.031i	−0.389065	+	0.187364i
$695$	258.557	+	206.192i	0.372025	+	0.296680i
$696$	−468.851	+	929.160i	−0.673636	+	1.33500i
$697$	212.307	+	266.225i	0.304602	+	0.381959i
$698$	−124.034	+	28.3099i	−0.177699	+	0.0405585i
$699$	−166.456	−	216.848i	−0.238134	−	0.310226i
$700$	690.397	−	247.141i	0.986282	−	0.353058i
$701$	−717.614	−	572.278i	−1.02370	−	0.816374i	−0.0405516	−	0.999177i	$-0.512912\pi$
$701$	−717.614	−	572.278i	−1.02370	−	0.816374i	−0.983150	+	0.182803i	$0.941483\pi$
$702$	−457.022	−	252.263i	−0.651028	−	0.359349i
$703$	85.5092	+	374.640i	0.121635	+	0.532916i
$704$		−	586.171i		−	0.832629i
$705$	−29.7513	+	1606.34i	−0.0422004	+	2.27849i
$706$	−13.6360	−	59.7430i	−0.0193144	−	0.0846219i
$707$	388.174	−	46.5526i	0.549044	−	0.0658452i
$708$	16.6309	−	67.1107i	0.0234899	−	0.0947892i
$709$	−78.9109	+	345.731i	−0.111299	+	0.487632i	0.888299	+	0.459266i	$0.151888\pi$
$709$	−78.9109	+	345.731i	−0.111299	+	0.487632i	−0.999598	+	0.0283660i	$0.990970\pi$
$710$	−36.3134	−	28.9590i	−0.0511456	−	0.0407873i
$711$	320.328	−	372.501i	0.450532	−	0.523911i
$712$	47.5224	−	208.209i	0.0667449	−	0.292428i
$713$	24.7586	+	5.65100i	0.0347246	+	0.00792566i
$714$	74.8385	−	116.154i	0.104816	−	0.162681i
$715$	−302.312	−	1324.52i	−0.422815	−	1.85247i
$716$		−	457.357i		−	0.638767i
$717$	−591.019	−	10.9464i	−0.824295	−	0.0152669i
$718$	−80.5110	−	352.742i	−0.112132	−	0.491284i
$719$	−173.247	+	359.752i	−0.240956	+	0.500350i	−0.986017	−	0.166646i	$-0.946706\pi$
$719$	−173.247	+	359.752i	−0.240956	+	0.500350i	0.745061	+	0.666997i	$0.232420\pi$
$720$	178.728	+	153.696i	0.248234	+	0.213466i
$721$	55.4268	+	462.171i	0.0768749	+	0.641013i
$722$	248.155	−	197.897i	0.343704	−	0.274095i
$723$	−1076.99	+	224.919i	−1.48962	+	0.311091i
$724$	189.830	+	238.040i	0.262197	+	0.328784i
$725$	886.770	−	1841.40i	1.22313	−	2.53986i
$726$	−9.91971	+	11.9770i	−0.0136635	+	0.0164973i
$727$	359.268	−	173.014i	0.494179	−	0.237984i	−0.170159	−	0.985417i	$-0.554428\pi$
$727$	359.268	−	173.014i	0.494179	−	0.237984i	0.664337	+	0.747433i	$0.268714\pi$
$728$	−589.737	−	581.355i	−0.810078	−	0.798564i
$729$	617.683	+	387.181i	0.847301	+	0.531113i
$730$	−1363.19	+	656.476i	−1.86738	+	0.899282i
$731$	245.603	+	56.0573i	0.335982	+	0.0766858i
$732$	252.658	+	550.502i	0.345162	+	0.752052i
$733$	429.625	+	538.733i	0.586119	+	0.734970i	0.983143	−	0.182839i	$-0.0585286\pi$
$733$	429.625	+	538.733i	0.586119	+	0.734970i	−0.397024	+	0.917808i	$0.629957\pi$
$734$			354.932i			0.483558i
$735$	−1237.69	+	277.025i	−1.68393	+	0.376905i
$736$	−190.969			−0.259469
$737$	−517.344	+	412.568i	−0.701959	+	0.559794i
$738$	802.969	−	350.678i	1.08803	−	0.475173i
$739$	55.3106	−	242.332i	0.0748452	−	0.327918i	−0.923619	−	0.383311i	$-0.874784\pi$
$739$	55.3106	−	242.332i	0.0748452	−	0.327918i	0.998465	+	0.0553925i	$0.0176410\pi$
$740$	267.751	+	555.990i	0.361825	+	0.751338i
$741$	216.867	−	429.783i	0.292668	−	0.580004i
$742$	16.3757	+	136.547i	0.0220696	+	0.184025i
$743$	596.579	+	1238.81i	0.802933	+	1.66731i	0.743177	+	0.669094i	$0.233318\pi$
$743$	596.579	+	1238.81i	0.802933	+	1.66731i	0.0597554	+	0.998213i	$0.480968\pi$
$744$	−62.7995	+	75.8240i	−0.0844079	+	0.101914i
$745$	172.235	+	82.9438i	0.231187	+	0.111334i
$746$	714.552	−	569.836i	0.957845	−	0.763856i
$747$	−707.619	+	134.154i	−0.947281	+	0.179590i
$748$	−70.7912	−	88.7694i	−0.0946407	−	0.118676i
$749$	439.886	−	280.810i	0.587298	−	0.374913i
$750$	−668.292	−	553.498i	−0.891056	−	0.737997i
$751$	−58.8314	−	28.3317i	−0.0783374	−	0.0377253i	0.394305	−	0.918980i	$-0.370985\pi$
$751$	−58.8314	−	28.3317i	−0.0783374	−	0.0377253i	−0.472642	+	0.881254i	$0.656700\pi$
$752$	−183.699	+	41.9281i	−0.244281	+	0.0557555i
$753$	−27.0957	−	0.501844i	−0.0359836	−	0.000666459i
$754$	−799.216			−1.05997
$755$	−2251.58	+	513.908i	−2.98222	+	0.680672i
$756$	269.129	+	296.528i	0.355991	+	0.392233i
$757$	−225.975	+	990.063i	−0.298514	+	1.30788i	0.573826	+	0.818977i	$0.305459\pi$
$757$	−225.975	+	990.063i	−0.298514	+	1.30788i	−0.872340	+	0.488899i	$0.837399\pi$
$758$	−93.9924	−	21.4532i	−0.124001	−	0.0283023i
$759$	167.610	+	138.819i	0.220830	+	0.182897i
$760$	−513.929	+	644.446i	−0.676222	+	0.847956i
$761$	−849.666	−	193.931i	−1.11651	−	0.254837i	−0.375828	−	0.926689i	$-0.622642\pi$
$761$	−849.666	−	193.931i	−1.11651	−	0.254837i	−0.740685	+	0.671853i	$0.765499\pi$
$762$	40.7265	−	164.344i	0.0534468	−	0.215675i
$763$	866.442	−	310.160i	1.13557	−	0.406500i
$764$	−559.034	+	127.596i	−0.731720	+	0.167010i
$765$	372.261	+	13.7941i	0.486615	+	0.0180315i
$766$	−448.064			−0.584940
$767$	149.487	−	34.1194i	0.194898	−	0.0444843i
$768$	368.295	−	729.880i	0.479551	−	0.950365i
$769$	−694.758	+	871.199i	−0.903457	+	1.13290i	0.0871554	+	0.996195i	$0.472222\pi$
$769$	−694.758	+	871.199i	−0.903457	+	1.13290i	−0.990612	+	0.136704i	$0.956349\pi$
$770$	97.0208	−	920.235i	0.126001	−	1.19511i
$771$	16.0653	+	20.9288i	0.0208369	+	0.0271450i
$772$	−41.8043	−	183.156i	−0.0541506	−	0.237249i
$773$	295.119	−	235.350i	0.381784	−	0.304463i	−0.413728	−	0.910401i	$-0.635773\pi$
$773$	295.119	−	235.350i	0.381784	−	0.304463i	0.795512	+	0.605938i	$0.207202\pi$
$774$	302.691	−	573.222i	0.391074	−	0.740597i
$775$	120.545	−	151.159i	0.155543	−	0.195044i
$776$	−414.988	−	861.732i	−0.534779	−	1.11048i
$777$	−226.516	−	671.730i	−0.291526	−	0.864518i
$778$	−457.784	−	220.457i	−0.588411	−	0.283364i
$779$	350.587	+	728.001i	0.450047	+	0.934533i
$780$	185.952	−	750.375i	0.238400	−	0.962020i
$781$	39.5008	−	19.0226i	0.0505772	−	0.0243567i
$782$	33.4084	−	26.6423i	0.0427218	−	0.0340695i
$783$	1114.38	+	61.9756i	1.42322	+	0.0791514i
$784$	−66.4508	−	133.079i	−0.0847587	−	0.169744i
$785$		−	1503.51i		−	1.91530i
$786$	−228.652	+	175.517i	−0.290906	+	0.223304i
$787$	−14.5840	+	7.02327i	−0.0185311	+	0.00892410i	−0.443126	−	0.896459i	$-0.646131\pi$
$787$	−14.5840	+	7.02327i	−0.0185311	+	0.00892410i	0.424595	+	0.905383i	$0.360416\pi$
$788$	−554.457	−	126.551i	−0.703625	−	0.160598i
$789$	−59.9350	+	27.5077i	−0.0759632	+	0.0348641i
$790$	−582.017	−	280.285i	−0.736731	−	0.354791i
$791$	516.652	−	329.815i	0.653163	−	0.416960i
$792$	−773.201	+	337.677i	−0.976263	+	0.426360i
$793$	−837.517	+	1050.21i	−1.05614	+	1.32435i
$794$	172.271	−	357.724i	0.216966	−	0.450534i
$795$	−294.104	+	225.759i	−0.369942	+	0.283973i
$796$	−68.2787	−	299.148i	−0.0857772	−	0.375815i
$797$	644.630	−	514.075i	0.808820	−	0.645013i	−0.129190	−	0.991620i	$-0.541238\pi$
$797$	644.630	−	514.075i	0.808820	−	0.645013i	0.938010	+	0.346607i	$0.112666\pi$
$798$	234.467	−	229.199i	0.293819	−	0.287217i
$799$	−185.654	+	232.802i	−0.232357	+	0.291367i
$800$	−630.818	+	1309.91i	−0.788523	+	1.63738i
$801$	−225.018	+	42.6600i	−0.280921	+	0.0532585i
$802$	774.617			0.965856
$803$		−	1428.20i		−	1.77858i
$804$	−368.580	+	76.9740i	−0.458432	+	0.0957388i
$805$	−390.065	−	41.1248i	−0.484553	−	0.0510867i
$806$	−73.7091	−	16.8236i	−0.0914504	−	0.0208730i
$807$	223.010	−	899.916i	0.276345	−	1.11514i
$808$	−292.242	+	366.460i	−0.361686	+	0.453540i
$809$	−704.917	−	562.152i	−0.871343	−	0.694873i	0.0820420	−	0.996629i	$-0.473856\pi$
$809$	−704.917	−	562.152i	−0.871343	−	0.694873i	−0.953385	+	0.301756i	$0.902427\pi$
$810$	281.874	−	916.168i	0.347993	−	1.13107i
$811$	−185.985	+	814.854i	−0.229328	+	1.00475i	0.720862	+	0.693079i	$0.243746\pi$
$811$	−185.985	+	814.854i	−0.229328	+	1.00475i	−0.950190	+	0.311673i	$0.899111\pi$
$812$	580.119	+	198.344i	0.714433	+	0.244266i
$813$	−1279.88	+	267.290i	−1.57427	+	0.328770i
$814$	517.194			0.635374
$815$			1062.93i			1.30421i
$816$	8.93122	+	42.7659i	0.0109451	+	0.0524092i
$817$	538.589	+	259.371i	0.659228	+	0.317467i
$818$	360.308	+	287.336i	0.440475	+	0.351267i
$819$	−318.222	+	829.092i	−0.388549	+	1.01232i
$820$	809.035	+	1014.50i	0.986628	+	1.23719i
$821$	275.172	−	62.8061i	0.335166	−	0.0764995i	−0.0516257	−	0.998667i	$-0.516440\pi$
$821$	275.172	−	62.8061i	0.335166	−	0.0764995i	0.386792	+	0.922167i	$0.373583\pi$
$822$	−558.145	+	428.440i	−0.679009	+	0.521217i
$823$	910.360	+	438.406i	1.10615	+	0.532693i	0.895586	−	0.444888i	$-0.146756\pi$
$823$	910.360	+	438.406i	1.10615	+	0.532693i	0.210562	+	0.977581i	$0.432471\pi$
$824$	−436.318	−	347.952i	−0.529512	−	0.422272i
$825$	1505.85	−	691.125i	1.82527	−	0.837727i
$826$	103.859	+	10.9499i	0.125737	+	0.0132566i
$827$	−266.040	+	552.437i	−0.321693	+	0.668002i	−0.997619	−	0.0689675i	$-0.978030\pi$
$827$	−266.040	+	552.437i	−0.321693	+	0.668002i	0.675926	+	0.736969i	$0.263744\pi$
$828$	49.5634	+	113.488i	0.0598591	+	0.137063i
$829$	362.833	−	1589.67i	0.437675	−	1.91758i	0.0421858	−	0.999110i	$-0.486568\pi$
$829$	362.833	−	1589.67i	0.437675	−	1.91758i	0.395489	−	0.918471i	$-0.370575\pi$
$830$	410.892	+	853.226i	0.495051	+	1.02798i
$831$	−827.359	+	635.093i	−0.995619	+	0.764252i
$832$	739.702			0.889065
$833$	−213.225	−	98.9492i	−0.255972	−	0.118787i
$834$	157.689	+	2.92058i	0.189075	+	0.00350189i
$835$	511.305	+	641.156i	0.612341	+	0.767851i
$836$	−116.899	−	242.743i	−0.139831	−	0.290362i
$837$	101.471	+	29.1737i	0.121232	+	0.0348550i
$838$	36.8045	−	17.7241i	0.0439194	−	0.0211505i
$839$	107.861	−	223.975i	0.128558	−	0.266954i	−0.826748	−	0.562573i	$-0.809812\pi$
$839$	107.861	−	223.975i	0.128558	−	0.266954i	0.955306	+	0.295619i	$0.0955258\pi$
$840$	823.581	−	1278.25i	0.980454	−	1.52173i
$841$	781.822	−	376.506i	0.929634	−	0.447688i
$842$	−0.749195	−	0.597463i	−0.000889780	−	0.000709576i
$843$	110.961	+	55.9904i	0.131626	+	0.0664180i
$844$	−37.4526	−	46.9641i	−0.0443751	−	0.0556446i
$845$	249.866	−	57.0303i	0.295700	−	0.0674915i
$846$	455.209	+	616.320i	0.538072	+	0.728510i
$847$	22.5014	+	13.9149i	0.0265660	+	0.0164285i
$848$	−33.9963	−	27.1111i	−0.0400899	−	0.0319706i
$849$	594.073	−	1177.32i	0.699733	−	1.38672i
$850$	−72.3904	−	317.163i	−0.0851652	−	0.373133i
$851$		−	219.226i		−	0.257610i
$852$	24.9434	+	0.461982i	0.0292763	+	0.000542232i
$853$	279.740	+	1225.62i	0.327949	+	1.43684i	0.823034	+	0.567992i	$0.192280\pi$
$853$	279.740	+	1225.62i	0.327949	+	1.43684i	−0.495085	+	0.868844i	$0.664863\pi$
$854$	−771.173	+	492.293i	−0.903012	+	0.576456i
$855$	853.920	+	228.476i	0.998737	+	0.267224i
$856$	−139.227	+	609.995i	−0.162649	+	0.712610i
$857$	−192.540	−	153.546i	−0.224668	−	0.179166i	0.504687	−	0.863303i	$-0.331608\pi$
$857$	−192.540	−	153.546i	−0.224668	−	0.179166i	−0.729354	+	0.684136i	$0.760179\pi$
$858$	−498.991	−	413.279i	−0.581575	−	0.481677i
$859$	167.006	−	731.702i	0.194419	−	0.851806i	−0.779769	−	0.626068i	$-0.784663\pi$
$859$	167.006	−	731.702i	0.194419	−	0.851806i	0.974188	−	0.225739i	$-0.0724795\pi$
$860$	935.914	+	213.616i	1.08827	+	0.248391i
$861$	−778.658	−	1271.06i	−0.904365	−	1.47626i
$862$	112.293	+	491.986i	0.130270	+	0.570749i
$863$		−	189.791i		−	0.219920i	−0.993936	−	0.109960i	$-0.964928\pi$
$863$		−	189.791i		−	0.219920i	0.993936	−	0.109960i	$-0.0350722\pi$
$864$	−792.733	−	44.0873i	−0.917515	−	0.0510270i
$865$	−436.969	−	1914.48i	−0.505166	−	2.21328i
$866$	−401.398	+	833.511i	−0.463508	+	0.962483i
$867$	−614.549	−	508.987i	−0.708823	−	0.587067i
$868$	49.3273	+	30.5042i	0.0568287	+	0.0351431i
$869$	476.740	−	380.187i	0.548607	−	0.437500i
$870$	−300.008	−	1436.55i	−0.344837	−	1.65121i
$871$	−520.628	−	652.847i	−0.597736	−	0.749538i
$872$	−478.720	+	994.072i	−0.548991	+	1.13999i
$873$	−668.770	+	777.694i	−0.766059	+	0.890829i
$874$	91.3565	−	43.9950i	0.104527	−	0.0503375i
$875$	−776.422	+	1255.53i	−0.887340	+	1.43489i
$876$	366.110	−	725.550i	0.417934	−	0.828253i
$877$	404.515	−	194.804i	0.461249	−	0.222126i	−0.188804	−	0.982015i	$-0.560461\pi$
$877$	404.515	−	194.804i	0.461249	−	0.222126i	0.650053	+	0.759889i	$0.274747\pi$
$878$	801.772	+	182.999i	0.913180	+	0.208427i
$879$	41.3238	−	18.9660i	0.0470123	−	0.0215768i
$880$	182.416	+	228.743i	0.207291	+	0.259935i
$881$		−	283.293i		−	0.321558i	−0.986990	−	0.160779i	$-0.948599\pi$
$881$		−	283.293i		−	0.321558i	0.986990	−	0.160779i	$-0.0514006\pi$
$882$	−387.775	+	464.212i	−0.439654	+	0.526317i
$883$	−901.124			−1.02053			−0.510263	−	0.860018i	$-0.670452\pi$
$883$	−901.124			−1.02053			−0.510263	+	0.860018i	$0.670452\pi$
$884$	112.020	−	89.3330i	0.126720	−	0.101055i
$885$	117.442	+	255.888i	0.132703	+	0.289139i
$886$	−22.5314	+	98.7165i	−0.0254305	+	0.111418i
$887$	85.8970	+	178.367i	0.0968399	+	0.201090i	0.943761	−	0.330629i	$-0.107261\pi$
$887$	85.8970	+	178.367i	0.0968399	+	0.201090i	−0.846921	+	0.531719i	$0.821546\pi$
$888$	758.774	+	382.875i	0.854475	+	0.431165i
$889$	−286.452	−	30.2008i	−0.322219	−	0.0339717i
$890$	130.661	+	271.320i	0.146810	+	0.304854i
$891$	663.717	+	614.946i	0.744912	+	0.690175i
$892$	−255.852	−	123.212i	−0.286830	−	0.138130i
$893$	−552.425	+	440.544i	−0.618617	+	0.493331i
$894$	89.2426	−	18.6374i	0.0998240	−	0.0208472i
$895$	1161.21	+	1456.11i	1.29744	+	1.62693i
$896$	−302.365	−	103.379i	−0.337461	−	0.115378i
$897$	−175.179	+	211.510i	−0.195294	+	0.235798i
$898$	255.492	+	123.038i	0.284512	+	0.137014i
$899$	157.593	−	35.9696i	0.175298	−	0.0400107i
$900$	942.166	+	34.9120i	1.04685	+	0.0387911i
$901$	−68.7159			−0.0762663
$902$	1060.25	−	241.994i	1.17544	−	0.268286i
$903$	−1036.69	−	376.027i	−1.14805	−	0.416419i
$904$	−163.524	+	716.447i	−0.180890	+	0.792530i
$905$	−1208.74	−	275.887i	−1.33562	−	0.304847i
$906$	−702.541	+	848.247i	−0.775432	+	0.936255i
$907$	−989.387	+	1240.65i	−1.09083	+	1.36786i	−0.166606	+	0.986024i	$0.553281\pi$
$907$	−989.387	+	1240.65i	−1.09083	+	1.36786i	−0.924229	+	0.381840i	$0.875291\pi$
$908$	145.806	+	33.2792i	0.160579	+	0.0366511i
$909$	485.577	+	129.922i	0.534188	+	0.142928i
$910$	1161.26	+	122.433i	1.27611	+	0.134541i
$911$	−1165.64	+	266.051i	−1.27952	+	0.292043i	−0.807670	−	0.589635i	$-0.799272\pi$
$911$	−1165.64	+	266.051i	−1.27952	+	0.292043i	−0.471852	+	0.881678i	$0.656414\pi$
$912$	−1.91977	+	103.653i	−0.00210501	+	0.113654i
$913$	−893.916			−0.979097
$914$	204.000	−	46.5617i	0.223195	−	0.0509428i
$915$	−2202.09	−	1111.17i	−2.40666	−	1.21439i
$916$	408.416	−	512.138i	0.445869	−	0.559103i
$917$	349.219	+	344.255i	0.380827	+	0.375415i
$918$	144.832	−	102.882i	0.157770	−	0.112072i
$919$	−185.989	−	814.873i	−0.202382	−	0.886695i	−0.969481	−	0.245166i	$-0.921158\pi$
$919$	−185.989	−	814.873i	−0.202382	−	0.886695i	0.767099	−	0.641529i	$-0.221700\pi$
$920$	367.652	−	293.193i	0.399622	−	0.318688i
$921$	−332.549	+	659.040i	−0.361074	+	0.715570i
$922$	−467.568	+	586.311i	−0.507123	+	0.635912i
$923$	24.0050	+	49.8469i	0.0260076	+	0.0540053i
$924$	259.634	+	423.819i	0.280989	+	0.458678i
$925$	−1503.73	−	724.157i	−1.62565	−	0.782873i
$926$	−149.526	−	310.493i	−0.161475	−	0.335306i
$927$	−154.688	+	578.141i	−0.166870	+	0.623668i
$928$	−1095.18	+	527.409i	−1.18015	+	0.568328i
$929$	1083.40	−	863.979i	1.16620	−	0.930010i	0.167754	−	0.985829i	$-0.446348\pi$
$929$	1083.40	−	863.979i	1.16620	−	0.930010i	0.998441	+	0.0558193i	$0.0177771\pi$
$930$	2.57080	−	138.804i	0.00276430	−	0.149251i
$931$	−441.036	−	341.502i	−0.473723	−	0.366812i
$932$		−	193.069i		−	0.207156i
$933$	−51.3985	−	66.9588i	−0.0550895	−	0.0717672i
$934$	−627.157	+	302.023i	−0.671474	+	0.323365i
$935$	450.761	+	102.883i	0.482098	+	0.110036i
$936$	−426.122	−	975.719i	−0.455259	−	1.04243i
$937$	−652.214	−	314.090i	−0.696066	−	0.335208i	0.0521718	−	0.998638i	$-0.483386\pi$
$937$	−652.214	−	314.090i	−0.696066	−	0.335208i	−0.748238	+	0.663430i	$0.769100\pi$
$938$	−191.680	−	535.464i	−0.204349	−	0.570858i
$939$	34.9076	+	76.0582i	0.0371753	+	0.0809991i
$940$	−707.465	+	887.133i	−0.752623	+	0.943759i
$941$	193.938	−	402.717i	0.206098	−	0.427967i	−0.772140	−	0.635452i	$-0.780814\pi$
$941$	193.938	−	402.717i	0.206098	−	0.427967i	0.978238	+	0.207486i	$0.0665280\pi$
$942$	−436.604	−	568.780i	−0.463486	−	0.603801i
$943$	−102.576	−	449.413i	−0.108776	−	0.476578i
$944$	−25.8163	+	20.5878i	−0.0273478	+	0.0218091i
$945$	−1609.70	−	260.764i	−1.70339	−	0.275940i
$946$	501.637	−	629.033i	0.530271	−	0.664939i
$947$	325.575	−	676.063i	0.343796	−	0.713899i	−0.655346	−	0.755329i	$-0.727477\pi$
$947$	325.575	−	676.063i	0.343796	−	0.713899i	0.999141	+	0.0414299i	$0.0131913\pi$
$948$	339.651	−	70.9326i	0.358282	−	0.0748234i
$949$	1802.27			1.89913
$950$		−	771.964i		−	0.812593i
$951$	287.625	+	1377.25i	0.302445	+	1.44822i
$952$	265.335	−	94.9816i	0.278713	−	0.0997706i
$953$	−252.026	−	57.5234i	−0.264456	−	0.0603603i	0.0882368	−	0.996100i	$-0.471877\pi$
$953$	−252.026	−	57.5234i	−0.264456	−	0.0603603i	−0.352693	+	0.935739i	$0.614734\pi$
$954$	−45.7021	+	170.810i	−0.0479058	+	0.179046i
$955$	1455.86	−	1825.59i	1.52446	−	1.91161i
$956$	−326.403	−	260.297i	−0.341425	−	0.272278i
$957$	1344.59	+	333.207i	1.40501	+	0.348179i
$958$	127.379	−	558.083i	0.132963	−	0.582550i
$959$	852.450	+	840.334i	0.888895	+	0.876261i
$960$	277.668	+	1329.58i	0.289238	+	1.38498i
$961$	−945.709			−0.984088
$962$			652.659i			0.678440i
$963$	659.240	−	124.982i	0.684569	−	0.129784i
$964$	−700.096	−	337.148i	−0.726240	−	0.349739i
$965$	598.118	+	476.983i	0.619811	+	0.494283i
$966$	−159.504	+	97.7134i	−0.165118	+	0.101153i
$967$	135.451	+	169.850i	0.140073	+	0.175646i	0.846920	−	0.531721i	$-0.178454\pi$
$967$	135.451	+	169.850i	0.140073	+	0.175646i	−0.706847	+	0.707367i	$0.749883\pi$
$968$	−30.9235	+	7.05809i	−0.0319458	+	0.00729142i
$969$	99.7570	+	129.957i	0.102948	+	0.134115i
$970$	1215.11	+	585.168i	1.25269	+	0.603266i
$971$	674.768	+	538.110i	0.694921	+	0.554181i	0.905995	−	0.423289i	$-0.139125\pi$
$971$	674.768	+	538.110i	0.694921	+	0.554181i	−0.211074	+	0.977470i	$0.567696\pi$
$972$	179.542	+	482.544i	0.184714	+	0.496444i
$973$	−31.9483	−	266.398i	−0.0328349	−	0.273790i
$974$	−426.928	+	886.526i	−0.438325	+	0.910191i
$975$	872.146	+	1900.27i	0.894508	+	1.94899i
$976$	64.3702	−	282.024i	0.0659531	−	0.288959i
$977$	72.5418	+	150.635i	0.0742495	+	0.154181i	0.934789	−	0.355202i	$-0.115588\pi$
$977$	72.5418	+	150.635i	0.0742495	+	0.154181i	−0.860540	+	0.509383i	$0.829874\pi$
$978$	308.665	+	402.109i	0.315608	+	0.411155i
$979$	−284.259			−0.290356
$980$	−812.531	−	377.063i	−0.829114	−	0.384758i
$981$	1182.41	+	43.8143i	1.20531	+	0.0446628i
$982$	−314.795	−	394.741i	−0.320565	−	0.401976i
$983$	502.457	+	1043.36i	0.511147	+	1.06141i	0.983652	+	0.180079i	$0.0576355\pi$
$983$	502.457	+	1043.36i	0.511147	+	1.06141i	−0.472505	+	0.881328i	$0.656650\pi$
$984$	1734.63	+	429.863i	1.76284	+	0.436852i
$985$	2086.55	−	1004.83i	2.11833	−	1.02013i
$986$	118.012	−	245.055i	0.119688	−	0.248534i
$987$	932.103	−	911.159i	0.944380	−	0.923160i
$988$	306.323	−	147.517i	0.310043	−	0.149309i
$989$	−266.632	−	212.632i	−0.269597	−	0.214997i
$990$	555.537	−	1052.05i	0.561148	−	1.06267i
$991$	105.240	+	131.967i	0.106196	+	0.133165i	0.832089	−	0.554642i	$-0.187145\pi$
$991$	105.240	+	131.967i	0.106196	+	0.133165i	−0.725893	+	0.687807i	$0.758573\pi$
$992$	−112.106	+	25.5876i	−0.113010	+	0.0257939i
$993$	−1199.37	+	920.656i	−1.20783	+	0.927146i
$994$	4.48703	+	37.4146i	0.00451411	+	0.0376405i
$995$	976.903	+	779.054i	0.981812	+	0.782969i
$996$	−454.126	−	229.150i	−0.455950	−	0.230071i
$997$	33.9438	+	148.718i	0.0340460	+	0.149165i	0.989094	−	0.147286i	$-0.0470539\pi$
$997$	33.9438	+	148.718i	0.0340460	+	0.149165i	−0.955048	+	0.296451i	$0.904197\pi$
$998$			232.301i			0.232767i
$999$	50.6107	−	910.029i	0.0506614	−	0.910940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.3.l.a.8.13	✓	216
3.2	odd	2	inner	147.3.l.a.8.24	yes	216
49.43	even	7	inner	147.3.l.a.92.24	yes	216
147.92	odd	14	inner	147.3.l.a.92.13	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.3.l.a.8.13	✓	216	1.1	even	1	trivial
147.3.l.a.8.24	yes	216	3.2	odd	2	inner
147.3.l.a.92.13	yes	216	147.92	odd	14	inner
147.3.l.a.92.24	yes	216	49.43	even	7	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	147.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07234 + 0.855164i) q^{2} +(1.25138 + 2.72655i) q^{3} +(-0.471473 + 2.06566i) q^{4} +(-3.74354 - 7.77355i) q^{5} +(-3.67355 - 1.85366i) q^{6} +(-2.26460 + 6.62356i) q^{7} +(-3.64131 - 7.56127i) q^{8} +(-5.86812 + 6.82387i) q^{9} +O(q^{10})\)	\(q+(-1.07234 + 0.855164i) q^{2} +(1.25138 + 2.72655i) q^{3} +(-0.471473 + 2.06566i) q^{4} +(-3.74354 - 7.77355i) q^{5} +(-3.67355 - 1.85366i) q^{6} +(-2.26460 + 6.62356i) q^{7} +(-3.64131 - 7.56127i) q^{8} +(-5.86812 + 6.82387i) q^{9} +(10.6620 + 5.13455i) q^{10} +(-8.73343 + 6.96468i) q^{11} +(-6.22210 + 1.29942i) q^{12} +(-8.78888 - 11.0209i) q^{13} +(-3.23580 - 9.03933i) q^{14} +(16.5104 - 19.9346i) q^{15} +(2.73504 + 1.31712i) q^{16} +(4.67698 - 1.06749i) q^{17} +(0.457101 - 12.3357i) q^{18} +11.3836 q^{19} +(17.8225 - 4.06786i) q^{20} +(-20.8933 + 2.11401i) q^{21} +(3.40928 - 14.9370i) q^{22} +(-6.33144 - 1.44511i) q^{23} +(16.0595 - 19.3902i) q^{24} +(-30.8267 + 38.6554i) q^{25} +(18.8494 + 4.30224i) q^{26} +(-25.9488 - 7.46048i) q^{27} +(-12.6143 - 7.80072i) q^{28} +(-40.3007 + 9.19837i) q^{29} +(-0.657422 + 35.4957i) q^{30} -3.91043 q^{31} +(28.6686 - 6.54342i) q^{32} +(-29.9183 - 15.0967i) q^{33} +(-4.10244 + 5.14430i) q^{34} +(59.9662 - 7.19157i) q^{35} +(-11.3291 - 15.3388i) q^{36} +(7.51161 + 32.9105i) q^{37} +(-12.2071 + 9.73484i) q^{38} +(19.0508 - 37.7546i) q^{39} +(-45.1464 + 56.6118i) q^{40} +(30.7976 + 63.9518i) q^{41} +(20.5970 - 20.1342i) q^{42} +(47.3127 + 22.7846i) q^{43} +(-10.2691 - 21.3239i) q^{44} +(75.0132 + 20.0706i) q^{45} +(8.02527 - 3.86477i) q^{46} +(-48.5282 + 38.6999i) q^{47} +(-0.168643 + 9.10543i) q^{48} +(-38.7431 - 29.9995i) q^{49} -67.8137i q^{50} +(8.76322 + 11.4162i) q^{51} +(26.9091 - 12.9587i) q^{52} +(-13.9649 - 3.18739i) q^{53} +(34.2059 - 14.1903i) q^{54} +(86.8342 + 41.8171i) q^{55} +(58.3286 - 6.99518i) q^{56} +(14.2452 + 31.0379i) q^{57} +(35.3500 - 44.3275i) q^{58} +(-4.71955 + 9.80024i) q^{59} +(33.3938 + 43.5033i) q^{60} +(-21.2047 - 92.9037i) q^{61} +(4.19331 - 3.34406i) q^{62} +(-31.9093 - 54.3212i) q^{63} +(-32.7176 + 41.0266i) q^{64} +(-52.7700 + 109.578i) q^{65} +(44.9928 - 9.39627i) q^{66} +59.2372 q^{67} +10.1643i q^{68} +(-3.98285 - 19.0713i) q^{69} +(-58.1543 + 58.9928i) q^{70} +(-3.82646 - 0.873363i) q^{71} +(72.9647 + 19.5226i) q^{72} +(-79.7160 + 99.9607i) q^{73} +(-36.1989 - 28.8677i) q^{74} +(-143.972 - 35.6779i) q^{75} +(-5.36705 + 23.5146i) q^{76} +(-26.3532 - 73.6186i) q^{77} +(11.8574 + 56.7774i) q^{78} -54.5879 q^{79} -26.1917i q^{80} +(-12.1304 - 80.0865i) q^{81} +(-87.7147 - 42.2412i) q^{82} +(62.5660 + 49.8947i) q^{83} +(5.48381 - 44.1551i) q^{84} +(-25.8067 - 32.3605i) q^{85} +(-70.2200 + 16.0273i) q^{86} +(-75.5111 - 98.3712i) q^{87} +(84.4629 + 40.6752i) q^{88} +(19.8955 + 15.8662i) q^{89} +(-97.6035 + 42.6260i) q^{90} +(92.9010 - 33.2557i) q^{91} +(5.97020 - 12.3973i) q^{92} +(-4.89341 - 10.6620i) q^{93} +(18.9440 - 82.9991i) q^{94} +(-42.6150 - 88.4909i) q^{95} +(53.7161 + 69.9780i) q^{96} +113.967 q^{97} +(67.2004 - 0.962013i) q^{98} +(3.72275 - 100.465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 5 q^{3} + 62 q^{4} + 7 q^{6} - 14 q^{7} - 45 q^{9}+O(q^{10}) \) 216 * q - 5 * q^3 + 62 * q^4 + 7 * q^6 - 14 * q^7 - 45 * q^9	\( 216 q - 5 q^{3} + 62 q^{4} + 7 q^{6} - 14 q^{7} - 45 q^{9} - 42 q^{10} - 20 q^{12} + 22 q^{13} - 17 q^{15} - 170 q^{16} - 86 q^{18} - 40 q^{19} - 21 q^{21} - 118 q^{22} + 119 q^{24} + 174 q^{25} + 88 q^{27} - 168 q^{28} + 36 q^{30} - 164 q^{31} - 35 q^{33} - 294 q^{34} + 307 q^{36} + 8 q^{37} - 61 q^{39} - 42 q^{40} - 133 q^{42} + 138 q^{43} - 336 q^{45} - 46 q^{46} - 52 q^{48} - 14 q^{49} + 111 q^{51} + 550 q^{52} + 147 q^{54} + 126 q^{55} - 363 q^{57} + 630 q^{58} + 353 q^{60} + 86 q^{61} + 21 q^{63} + 146 q^{64} + 105 q^{66} + 100 q^{67} - 7 q^{69} - 532 q^{70} - 167 q^{72} + 18 q^{73} + 1107 q^{75} - 762 q^{76} - 699 q^{78} - 272 q^{79} - 265 q^{81} + 504 q^{82} - 1834 q^{84} - 650 q^{85} - 595 q^{87} - 242 q^{88} - 1323 q^{90} + 126 q^{91} + 233 q^{93} + 1358 q^{94} - 882 q^{96} - 20 q^{97} - 332 q^{99}+O(q^{100}) \) 216 * q - 5 * q^3 + 62 * q^4 + 7 * q^6 - 14 * q^7 - 45 * q^9 - 42 * q^10 - 20 * q^12 + 22 * q^13 - 17 * q^15 - 170 * q^16 - 86 * q^18 - 40 * q^19 - 21 * q^21 - 118 * q^22 + 119 * q^24 + 174 * q^25 + 88 * q^27 - 168 * q^28 + 36 * q^30 - 164 * q^31 - 35 * q^33 - 294 * q^34 + 307 * q^36 + 8 * q^37 - 61 * q^39 - 42 * q^40 - 133 * q^42 + 138 * q^43 - 336 * q^45 - 46 * q^46 - 52 * q^48 - 14 * q^49 + 111 * q^51 + 550 * q^52 + 147 * q^54 + 126 * q^55 - 363 * q^57 + 630 * q^58 + 353 * q^60 + 86 * q^61 + 21 * q^63 + 146 * q^64 + 105 * q^66 + 100 * q^67 - 7 * q^69 - 532 * q^70 - 167 * q^72 + 18 * q^73 + 1107 * q^75 - 762 * q^76 - 699 * q^78 - 272 * q^79 - 265 * q^81 + 504 * q^82 - 1834 * q^84 - 650 * q^85 - 595 * q^87 - 242 * q^88 - 1323 * q^90 + 126 * q^91 + 233 * q^93 + 1358 * q^94 - 882 * q^96 - 20 * q^97 - 332 * q^99

Introduction

L-functions

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