LMFDB - Embedded newform 39.3.i.b.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,3,Mod(29,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("39.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	39.i (of order $6$, degree $2$, 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:	$1.06267303101$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 5 x^{10} - 2 x^{9} - 11 x^{8} + 25 x^{7} - 50 x^{6} + 75 x^{5} - 99 x^{4} + \cdots + 729 $ x^12 - 3x^11 + 5x^10 - 2x^9 - 11x^8 + 25x^7 - 50x^6 + 75x^5 - 99x^4 - 54x^3 + 405x^2 - 729*x + 729
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.1
Root			$-0.822039 + 1.52455i$ of defining polynomial
Character	$\chi$	$=$	39.35
Dual form			39.3.i.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55336 - 1.47418i) q^{2} +(2.99371 - 0.194134i) q^{3} +(2.34642 + 4.06412i) q^{4} -5.36177i q^{5} +(-7.93021 - 3.91758i) q^{6} +(-4.07426 - 7.05683i) q^{7} -2.04276i q^{8} +(8.92462 - 1.16237i) q^{9} +O(q^{10})$	\(q+(-2.55336 - 1.47418i) q^{2} +(2.99371 - 0.194134i) q^{3} +(2.34642 + 4.06412i) q^{4} -5.36177i q^{5} +(-7.93021 - 3.91758i) q^{6} +(-4.07426 - 7.05683i) q^{7} -2.04276i q^{8} +(8.92462 - 1.16237i) q^{9} +(-7.90422 + 13.6905i) q^{10} +(7.19679 + 4.15507i) q^{11} +(7.81350 + 11.7113i) q^{12} +(3.05780 + 12.6353i) q^{13} +24.0248i q^{14} +(-1.04090 - 16.0516i) q^{15} +(6.37429 - 11.0406i) q^{16} +(-13.8098 + 7.97312i) q^{17} +(-24.5013 - 10.1886i) q^{18} +(11.9485 + 20.6955i) q^{19} +(21.7909 - 12.5810i) q^{20} +(-13.5671 - 20.3352i) q^{21} +(-12.2506 - 21.2187i) q^{22} +(-3.37402 - 1.94799i) q^{23} +(-0.396571 - 6.11545i) q^{24} -3.74858 q^{25} +(10.8190 - 36.7701i) q^{26} +(26.4921 - 5.21236i) q^{27} +(19.1199 - 33.1166i) q^{28} +(10.6509 + 6.14930i) q^{29} +(-21.0052 + 42.5199i) q^{30} -40.4440 q^{31} +(-39.6280 + 22.8792i) q^{32} +(22.3517 + 11.0419i) q^{33} +47.0153 q^{34} +(-37.8371 + 21.8452i) q^{35} +(25.6649 + 33.5434i) q^{36} +(1.16926 - 2.02522i) q^{37} -70.4573i q^{38} +(11.6071 + 37.2327i) q^{39} -10.9528 q^{40} +(41.9371 + 24.2124i) q^{41} +(4.66404 + 71.9233i) q^{42} +(-27.6034 - 47.8105i) q^{43} +38.9982i q^{44} +(-6.23233 - 47.8518i) q^{45} +(5.74338 + 9.94783i) q^{46} -71.2193i q^{47} +(16.9394 - 34.2898i) q^{48} +(-8.69920 + 15.0674i) q^{49} +(9.57146 + 5.52608i) q^{50} +(-39.7948 + 26.5502i) q^{51} +(-44.1764 + 42.0750i) q^{52} +19.9225i q^{53} +(-75.3278 - 25.7451i) q^{54} +(22.2785 - 38.5875i) q^{55} +(-14.4154 + 8.32275i) q^{56} +(39.7882 + 59.6367i) q^{57} +(-18.1304 - 31.4027i) q^{58} +(-55.0792 + 31.8000i) q^{59} +(62.7933 - 41.8942i) q^{60} +(25.9498 + 44.9464i) q^{61} +(103.268 + 59.6218i) q^{62} +(-44.5638 - 58.2437i) q^{63} +83.9184 q^{64} +(67.7474 - 16.3952i) q^{65} +(-40.7942 - 61.1445i) q^{66} +(-16.1943 + 28.0493i) q^{67} +(-64.8075 - 37.4166i) q^{68} +(-10.4790 - 5.17671i) q^{69} +128.815 q^{70} +(-29.1922 + 16.8541i) q^{71} +(-2.37444 - 18.2309i) q^{72} -50.2185 q^{73} +(-5.97108 + 3.44741i) q^{74} +(-11.2222 + 0.727728i) q^{75} +(-56.0727 + 97.1208i) q^{76} -67.7153i q^{77} +(25.2507 - 112.179i) q^{78} -89.8735 q^{79} +(-59.1971 - 34.1775i) q^{80} +(78.2978 - 20.7473i) q^{81} +(-71.3870 - 123.646i) q^{82} -12.8679i q^{83} +(50.8103 - 102.853i) q^{84} +(42.7500 + 74.0452i) q^{85} +162.770i q^{86} +(33.0795 + 16.3415i) q^{87} +(8.48782 - 14.7013i) q^{88} +(29.3126 + 16.9237i) q^{89} +(-54.6288 + 131.370i) q^{90} +(76.7066 - 73.0577i) q^{91} -18.2832i q^{92} +(-121.078 + 7.85157i) q^{93} +(-104.990 + 181.848i) q^{94} +(110.964 - 64.0654i) q^{95} +(-114.193 + 76.1870i) q^{96} +(47.3560 + 82.0230i) q^{97} +(44.4243 - 25.6484i) q^{98} +(69.0583 + 28.7171i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} + 10 q^{4} - 12 q^{6} - 16 q^{7} + 6 q^{9}+O(q^{10}) $ 12 * q - 4 * q^3 + 10 * q^4 - 12 * q^6 - 16 * q^7 + 6 * q^9	$ 12 q - 4 q^{3} + 10 q^{4} - 12 q^{6} - 16 q^{7} + 6 q^{9} - 6 q^{10} - 34 q^{13} + 2 q^{15} + 50 q^{16} - 80 q^{18} + 84 q^{19} - 100 q^{21} - 40 q^{22} + 48 q^{24} + 8 q^{25} + 128 q^{27} + 12 q^{28} + 142 q^{30} + 32 q^{31} + 14 q^{33} - 124 q^{34} + 74 q^{36} - 90 q^{37} + 138 q^{39} + 4 q^{40} - 78 q^{42} - 76 q^{43} - 152 q^{45} - 100 q^{46} + 56 q^{48} + 62 q^{49} - 368 q^{51} - 456 q^{52} - 144 q^{54} + 152 q^{55} - 36 q^{57} + 238 q^{58} + 324 q^{60} + 38 q^{61} + 220 q^{63} + 476 q^{64} - 252 q^{66} + 24 q^{67} + 242 q^{69} + 896 q^{70} + 12 q^{72} - 580 q^{73} + 20 q^{75} - 320 q^{76} + 464 q^{78} + 80 q^{79} - 102 q^{81} - 570 q^{82} - 250 q^{84} + 278 q^{85} + 70 q^{87} - 12 q^{88} - 852 q^{90} - 124 q^{91} - 300 q^{93} - 184 q^{94} - 928 q^{96} + 120 q^{97} + 384 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 + 10 * q^4 - 12 * q^6 - 16 * q^7 + 6 * q^9 - 6 * q^10 - 34 * q^13 + 2 * q^15 + 50 * q^16 - 80 * q^18 + 84 * q^19 - 100 * q^21 - 40 * q^22 + 48 * q^24 + 8 * q^25 + 128 * q^27 + 12 * q^28 + 142 * q^30 + 32 * q^31 + 14 * q^33 - 124 * q^34 + 74 * q^36 - 90 * q^37 + 138 * q^39 + 4 * q^40 - 78 * q^42 - 76 * q^43 - 152 * q^45 - 100 * q^46 + 56 * q^48 + 62 * q^49 - 368 * q^51 - 456 * q^52 - 144 * q^54 + 152 * q^55 - 36 * q^57 + 238 * q^58 + 324 * q^60 + 38 * q^61 + 220 * q^63 + 476 * q^64 - 252 * q^66 + 24 * q^67 + 242 * q^69 + 896 * q^70 + 12 * q^72 - 580 * q^73 + 20 * q^75 - 320 * q^76 + 464 * q^78 + 80 * q^79 - 102 * q^81 - 570 * q^82 - 250 * q^84 + 278 * q^85 + 70 * q^87 - 12 * q^88 - 852 * q^90 - 124 * q^91 - 300 * q^93 - 184 * q^94 - 928 * q^96 + 120 * q^97 + 384 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.55336	−	1.47418i	−1.27668	−	0.737091i	−0.300443	−	0.953800i	$-0.597134\pi$
$2$	−2.55336	−	1.47418i	−1.27668	−	0.737091i	−0.976236	+	0.216709i	$0.930468\pi$
$3$	2.99371	−	0.194134i	0.997904	−	0.0647115i
$3$	2.99371	−	0.194134i	0.997904	−	0.0647115i
$4$	2.34642	+	4.06412i	0.586606	+	1.01603i
$5$		−	5.36177i		−	1.07235i	−0.844106	−	0.536177i	$-0.819868\pi$
$5$		−	5.36177i		−	1.07235i	0.844106	−	0.536177i	$-0.180132\pi$
$6$	−7.93021	−	3.91758i	−1.32170	−	0.652930i
$7$	−4.07426	−	7.05683i	−0.582037	−	1.00812i	−0.995238	−	0.0974779i	$-0.968922\pi$
$7$	−4.07426	−	7.05683i	−0.582037	−	1.00812i	0.413200	−	0.910640i	$-0.364411\pi$
$8$		−	2.04276i		−	0.255345i
$9$	8.92462	−	1.16237i	0.991625	−	0.129152i
$10$	−7.90422	+	13.6905i	−0.790422	+	1.36905i
$11$	7.19679	+	4.15507i	0.654253	+	0.377733i	0.790084	−	0.612999i	$-0.210037\pi$
$11$	7.19679	+	4.15507i	0.654253	+	0.377733i	−0.135831	+	0.990732i	$0.543370\pi$
$12$	7.81350	+	11.7113i	0.651125	+	0.975941i
$13$	3.05780	+	12.6353i	0.235215	+	0.971943i
$13$	3.05780	+	12.6353i	0.235215	+	0.971943i
$14$			24.0248i			1.71606i
$15$	−1.04090	−	16.0516i	−0.0693936	−	1.07011i
$16$	6.37429	−	11.0406i	0.398393	−	0.690037i
$17$	−13.8098	+	7.97312i	−0.812344	+	0.469007i	−0.847769	−	0.530366i	$-0.822055\pi$
$17$	−13.8098	+	7.97312i	−0.812344	+	0.469007i	0.0354255	+	0.999372i	$0.488721\pi$
$18$	−24.5013	−	10.1886i	−1.36118	−	0.566032i
$19$	11.9485	+	20.6955i	0.628871	+	1.08924i	0.987779	+	0.155863i	$0.0498160\pi$
$19$	11.9485	+	20.6955i	0.628871	+	1.08924i	−0.358908	+	0.933373i	$0.616851\pi$
$20$	21.7909	−	12.5810i	1.08955	−	0.629049i
$21$	−13.5671	−	20.3352i	−0.646054	−	0.968341i
$22$	−12.2506	−	21.2187i	−0.556848	−	0.964488i
$23$	−3.37402	−	1.94799i	−0.146696	−	0.0846952i	0.424855	−	0.905261i	$-0.360325\pi$
$23$	−3.37402	−	1.94799i	−0.146696	−	0.0846952i	−0.571552	+	0.820566i	$0.693658\pi$
$24$	−0.396571	−	6.11545i	−0.0165238	−	0.254810i
$25$	−3.74858			−0.149943
$26$	10.8190	−	36.7701i	0.416116	−	1.41423i
$27$	26.4921	−	5.21236i	0.981189	−	0.193050i
$28$	19.1199	−	33.1166i	0.682853	−	1.18274i
$29$	10.6509	+	6.14930i	0.367272	+	0.212045i	0.672266	−	0.740310i	$-0.265321\pi$
$29$	10.6509	+	6.14930i	0.367272	+	0.212045i	−0.304994	+	0.952354i	$0.598654\pi$
$30$	−21.0052	+	42.5199i	−0.700172	+	1.41733i
$31$	−40.4440			−1.30465			−0.652323	−	0.757941i	$-0.726205\pi$
$31$	−40.4440			−1.30465			−0.652323	+	0.757941i	$0.726205\pi$
$32$	−39.6280	+	22.8792i	−1.23838	+	0.714976i
$33$	22.3517	+	11.0419i	0.677326	+	0.334604i
$34$	47.0153			1.38280
$35$	−37.8371	+	21.8452i	−1.08106	+	0.624150i
$36$	25.6649	+	33.5434i	0.712915	+	0.931761i
$37$	1.16926	−	2.02522i	0.0316016	−	0.0547357i	−0.849792	−	0.527118i	$-0.823273\pi$
$37$	1.16926	−	2.02522i	0.0316016	−	0.0547357i	0.881394	+	0.472382i	$0.156606\pi$
$38$		−	70.4573i		−	1.85414i
$39$	11.6071	+	37.2327i	0.297618	+	0.954685i
$40$	−10.9528			−0.273821
$41$	41.9371	+	24.2124i	1.02286	+	0.590547i	0.914930	−	0.403612i	$-0.132246\pi$
$41$	41.9371	+	24.2124i	1.02286	+	0.590547i	0.107927	+	0.994159i	$0.465579\pi$
$42$	4.66404	+	71.9233i	0.111049	+	1.71246i
$43$	−27.6034	−	47.8105i	−0.641940	−	1.11187i	−0.984999	−	0.172559i	$-0.944796\pi$
$43$	−27.6034	−	47.8105i	−0.641940	−	1.11187i	0.343059	−	0.939314i	$-0.388537\pi$
$44$			38.9982i			0.886322i
$45$	−6.23233	−	47.8518i	−0.138496	−	1.06337i
$46$	5.74338	+	9.94783i	0.124856	+	0.216257i
$47$		−	71.2193i		−	1.51530i	−0.652659	−	0.757652i	$-0.726347\pi$
$47$		−	71.2193i		−	1.51530i	0.652659	−	0.757652i	$-0.273653\pi$
$48$	16.9394	−	34.2898i	0.352905	−	0.714371i
$49$	−8.69920	+	15.0674i	−0.177535	+	0.307499i
$50$	9.57146	+	5.52608i	0.191429	+	0.110522i
$51$	−39.7948	+	26.5502i	−0.780291	+	0.520592i
$52$	−44.1764	+	42.0750i	−0.849546	+	0.809134i
$53$			19.9225i			0.375896i	0.982179	+	0.187948i	$0.0601837\pi$
$53$			19.9225i			0.375896i	−0.982179	+	0.187948i	$0.939816\pi$
$54$	−75.3278	−	25.7451i	−1.39496	−	0.476762i
$55$	22.2785	−	38.5875i	0.405064	−	0.701591i
$56$	−14.4154	+	8.32275i	−0.257418	+	0.148621i
$57$	39.7882	+	59.6367i	0.698039	+	1.04626i
$58$	−18.1304	−	31.4027i	−0.312593	−	0.541426i
$59$	−55.0792	+	31.8000i	−0.933545	+	0.538983i	−0.887931	−	0.459976i	$-0.847858\pi$
$59$	−55.0792	+	31.8000i	−0.933545	+	0.538983i	−0.0456142	+	0.998959i	$0.514525\pi$
$60$	62.7933	−	41.8942i	1.04655	−	0.698237i
$61$	25.9498	+	44.9464i	0.425407	+	0.736827i	0.996458	−	0.0840875i	$-0.0267975\pi$
$61$	25.9498	+	44.9464i	0.425407	+	0.736827i	−0.571051	+	0.820914i	$0.693464\pi$
$62$	103.268	+	59.6218i	1.66561	+	0.961642i
$63$	−44.5638	−	58.2437i	−0.707363	−	0.924504i
$64$	83.9184			1.31122
$65$	67.7474	−	16.3952i	1.04227	−	0.252234i
$66$	−40.7942	−	61.1445i	−0.618094	−	0.926432i
$67$	−16.1943	+	28.0493i	−0.241706	+	0.418647i	−0.961200	−	0.275852i	$-0.911040\pi$
$67$	−16.1943	+	28.0493i	−0.241706	+	0.418647i	0.719495	+	0.694498i	$0.244374\pi$
$68$	−64.8075	−	37.4166i	−0.953051	−	0.550244i
$69$	−10.4790	−	5.17671i	−0.151870	−	0.0750247i
$70$	128.815			1.84022
$71$	−29.1922	+	16.8541i	−0.411158	+	0.237382i	−0.691287	−	0.722580i	$-0.742956\pi$
$71$	−29.1922	+	16.8541i	−0.411158	+	0.237382i	0.280129	+	0.959962i	$0.409623\pi$
$72$	−2.37444	−	18.2309i	−0.0329783	−	0.253207i
$73$	−50.2185			−0.687925			−0.343962	−	0.938983i	$-0.611769\pi$
$73$	−50.2185			−0.687925			−0.343962	+	0.938983i	$0.611769\pi$
$74$	−5.97108	+	3.44741i	−0.0806903	+	0.0465866i
$75$	−11.2222	+	0.727728i	−0.149629	+	0.00970304i
$76$	−56.0727	+	97.1208i	−0.737799	+	1.27790i
$77$		−	67.7153i		−	0.879419i
$78$	25.2507	−	112.179i	0.323727	−	1.43820i
$79$	−89.8735			−1.13764			−0.568820	−	0.822462i	$-0.692600\pi$
$79$	−89.8735			−1.13764			−0.568820	+	0.822462i	$0.692600\pi$
$80$	−59.1971	−	34.1775i	−0.739964	−	0.427218i
$81$	78.2978	−	20.7473i	0.966640	−	0.256140i
$82$	−71.3870	−	123.646i	−0.870573	−	1.50788i
$83$		−	12.8679i		−	0.155035i	−0.996991	−	0.0775177i	$-0.975301\pi$
$83$		−	12.8679i		−	0.155035i	0.996991	−	0.0775177i	$-0.0246994\pi$
$84$	50.8103	−	102.853i	0.604885	−	1.22445i
$85$	42.7500	+	74.0452i	0.502941	+	0.871120i
$86$			162.770i			1.89267i
$87$	33.0795	+	16.3415i	0.380224	+	0.187834i
$88$	8.48782	−	14.7013i	0.0964525	−	0.167061i
$89$	29.3126	+	16.9237i	0.329355	+	0.190153i	0.655555	−	0.755147i	$-0.272435\pi$
$89$	29.3126	+	16.9237i	0.329355	+	0.190153i	−0.326199	+	0.945301i	$0.605768\pi$
$90$	−54.6288	+	131.370i	−0.606987	+	1.45967i
$91$	76.7066	−	73.0577i	0.842929	−	0.802832i
$92$		−	18.2832i		−	0.198731i
$93$	−121.078	+	7.85157i	−1.30191	+	0.0844255i
$94$	−104.990	+	181.848i	−1.11692	+	1.93456i
$95$	110.964	−	64.0654i	1.16805	−	0.674372i
$96$	−114.193	+	76.1870i	−1.18951	+	0.793615i
$97$	47.3560	+	82.0230i	0.488206	+	0.845598i	0.999908	−	0.0135653i	$-0.00431810\pi$
$97$	47.3560	+	82.0230i	0.488206	+	0.845598i	−0.511702	+	0.859163i	$0.670985\pi$
$98$	44.4243	−	25.6484i	0.453309	−	0.261718i
$99$	69.0583	+	28.7171i	0.697559	+	0.290072i
$100$	−8.79575	−	15.2347i	−0.0879575	−	0.152347i
$101$	−23.2609	−	13.4297i	−0.230305	−	0.132967i	0.380408	−	0.924819i	$-0.375784\pi$
$101$	−23.2609	−	13.4297i	−0.230305	−	0.132967i	−0.610713	+	0.791852i	$0.709117\pi$
$102$	140.750	−	9.12728i	1.37990	−	0.0894832i
$103$	36.0959			0.350446			0.175223	−	0.984529i	$-0.443935\pi$
$103$	36.0959			0.350446			0.175223	+	0.984529i	$0.443935\pi$
$104$	25.8109	−	6.24636i	0.248181	−	0.0600612i
$105$	−109.032	+	72.7439i	−1.03840	+	0.692799i
$106$	29.3694	−	50.8692i	0.277070	−	0.479899i
$107$	−112.771	−	65.1082i	−1.05393	−	0.608488i	−0.130184	−	0.991490i	$-0.541557\pi$
$107$	−112.771	−	65.1082i	−1.05393	−	0.608488i	−0.923747	+	0.383002i	$0.874890\pi$
$108$	83.3454	+	95.4368i	0.771716	+	0.883674i
$109$	67.1597			0.616144			0.308072	−	0.951363i	$-0.400316\pi$
$109$	67.1597			0.616144			0.308072	+	0.951363i	$0.400316\pi$
$110$	−113.770	+	65.6851i	−1.03427	+	0.597138i
$111$	3.10727	−	6.28992i	0.0279934	−	0.0566659i
$112$	−103.882			−0.927518
$113$	−37.1150	+	21.4284i	−0.328451	+	0.189632i	−0.655153	−	0.755496i	$-0.727396\pi$
$113$	−37.1150	+	21.4284i	−0.328451	+	0.189632i	0.326702	+	0.945127i	$0.394063\pi$
$114$	−13.6782	−	210.929i	−0.119984	−	1.85025i
$115$	−10.4447	+	18.0907i	−0.0908232	+	0.157310i
$116$			57.7154i			0.497547i
$117$	41.9765	+	109.211i	0.358774	+	0.933425i
$118$	187.516			1.58912
$119$	112.530	+	64.9691i	0.945628	+	0.545959i
$120$	−32.7896	+	2.12632i	−0.273247	+	0.0177193i
$121$	−25.9708	−	44.9828i	−0.214635	−	0.371759i
$122$		−	153.019i		−	1.25426i
$123$	130.248	+	64.3435i	1.05893	+	0.523118i
$124$	−94.8988	−	164.369i	−0.765313	−	1.32556i
$125$		−	113.945i		−	0.911562i
$126$	27.9256	+	214.412i	0.221632	+	1.70168i
$127$	−25.4151	+	44.0203i	−0.200119	+	0.346616i	−0.948567	−	0.316578i	$-0.897466\pi$
$127$	−25.4151	+	44.0203i	−0.200119	+	0.346616i	0.748448	+	0.663194i	$0.230800\pi$
$128$	−55.7615	−	32.1939i	−0.435637	−	0.251515i
$129$	−91.9184	−	137.772i	−0.712545	−	1.06800i
$130$	−197.153	−	58.0091i	−1.51656	−	0.446224i
$131$			56.1068i			0.428296i	0.976801	+	0.214148i	$0.0686975\pi$
$131$			56.1068i			0.428296i	−0.976801	+	0.214148i	$0.931302\pi$
$132$	7.57089	+	116.749i	0.0573552	+	0.884465i
$133$	97.3630	−	168.638i	0.732053	−	1.26795i
$134$	82.6996	−	47.7466i	0.617161	−	0.356318i
$135$	−27.9475	−	142.045i	−0.207018	−	1.05218i
$136$	16.2872	+	28.2102i	0.119759	+	0.207428i
$137$	−56.6511	+	32.7075i	−0.413512	+	0.238741i	−0.692297	−	0.721612i	$-0.743401\pi$
$137$	−56.6511	+	32.7075i	−0.413512	+	0.238741i	0.278786	+	0.960353i	$0.410068\pi$
$138$	19.1252	+	28.6659i	0.138589	+	0.207724i
$139$	−101.238	−	175.350i	−0.728332	−	1.26151i	−0.957588	−	0.288142i	$-0.906962\pi$
$139$	−101.238	−	175.350i	−0.728332	−	1.26151i	0.229255	−	0.973366i	$-0.426371\pi$
$140$	−177.564	−	102.516i	−1.26831	−	0.732260i
$141$	−13.8261	−	213.210i	−0.0980575	−	1.51213i
$142$	99.3841			0.699888
$143$	−30.4940	+	103.639i	−0.213245	+	0.724746i
$144$	44.0549	−	105.942i	0.305937	−	0.735711i
$145$	32.9711	−	57.1077i	0.227387	−	0.393846i
$146$	128.226	+	74.0312i	0.878259	+	0.507063i
$147$	−23.1178	+	46.7964i	−0.157264	+	0.318343i
$148$	10.9743			0.0741508
$149$	113.486	−	65.5209i	0.761648	−	0.439738i	−0.0682392	−	0.997669i	$-0.521738\pi$
$149$	113.486	−	65.5209i	0.761648	−	0.439738i	0.829887	+	0.557931i	$0.188405\pi$
$150$	29.7270	+	14.6854i	0.198180	+	0.0979024i
$151$	−13.7507			−0.0910642			−0.0455321	−	0.998963i	$-0.514498\pi$
$151$	−13.7507			−0.0910642			−0.0455321	+	0.998963i	$0.514498\pi$
$152$	42.2760	−	24.4081i	0.278132	−	0.160579i
$153$	−113.980	+	87.2091i	−0.744967	+	0.569994i
$154$	−99.8246	+	172.901i	−0.648212	+	1.12274i
$155$			216.851i			1.39904i
$156$	−124.083	+	134.536i	−0.795405	+	0.862413i
$157$	229.038			1.45884			0.729420	−	0.684066i	$-0.239790\pi$
$157$	229.038			1.45884			0.729420	+	0.684066i	$0.239790\pi$
$158$	229.479	+	132.490i	1.45240	+	0.838543i
$159$	3.86764	+	59.6422i	0.0243248	+	0.375108i
$160$	122.673	+	212.476i	0.766708	+	1.32798i
$161$			31.7465i			0.197183i
$162$	−230.508	−	62.4498i	−1.42289	−	0.385493i
$163$	39.0554	+	67.6460i	0.239604	+	0.415006i	0.960601	−	0.277932i	$-0.0896491\pi$
$163$	39.0554	+	67.6460i	0.239604	+	0.415006i	−0.720997	+	0.692938i	$0.756316\pi$
$164$			227.250i			1.38567i
$165$	59.2043	−	119.845i	0.358814	−	0.726333i
$166$	−18.9697	+	32.8565i	−0.114275	+	0.197931i
$167$	50.5270	+	29.1718i	0.302557	+	0.174681i	0.643591	−	0.765370i	$-0.277444\pi$
$167$	50.5270	+	29.1718i	0.302557	+	0.174681i	−0.341034	+	0.940051i	$0.610777\pi$
$168$	−41.5399	+	27.7144i	−0.247261	+	0.164967i
$169$	−150.300	+	77.2722i	−0.889347	+	0.457232i
$170$		−	252.085i		−	1.48285i
$171$	130.692	+	170.811i	0.764281	+	0.998894i
$172$	129.539	−	224.367i	0.753131	−	1.30446i
$173$	−229.629	+	132.577i	−1.32734	+	0.766339i	−0.984887	−	0.173197i	$-0.944590\pi$
$173$	−229.629	+	132.577i	−1.32734	+	0.766339i	−0.342450	+	0.939536i	$0.611257\pi$
$174$	−60.3734	−	90.4910i	−0.346974	−	0.520063i
$175$	15.2727	+	26.4531i	0.0872725	+	0.151160i
$176$	91.7488	−	52.9712i	0.521300	−	0.300973i
$177$	−158.718	+	105.893i	−0.896710	+	0.598264i
$178$	−49.8971	−	86.4243i	−0.280321	−	0.485530i
$179$	−79.4334	−	45.8609i	−0.443762	−	0.256206i	0.261430	−	0.965222i	$-0.415806\pi$
$179$	−79.4334	−	45.8609i	−0.443762	−	0.256206i	−0.705192	+	0.709016i	$0.749139\pi$
$180$	179.852	−	137.610i	0.999177	−	0.764497i
$181$	−114.099			−0.630380			−0.315190	−	0.949029i	$-0.602068\pi$
$181$	−114.099			−0.630380			−0.315190	+	0.949029i	$0.602068\pi$
$182$	−303.560	+	73.4630i	−1.66791	+	0.403643i
$183$	86.4120	+	129.519i	0.472197	+	0.707754i
$184$	−3.97928	+	6.89232i	−0.0216265	+	0.0374582i
$185$	−10.8588	−	6.26931i	−0.0586960	−	0.0338881i
$186$	320.729	+	158.443i	1.72435	+	0.851842i
$187$	−132.515			−0.708638
$188$	289.444	−	167.111i	1.53960	−	0.888886i
$189$	−144.718	−	165.714i	−0.765706	−	0.876792i
$190$	−377.776			−1.98829
$191$	182.239	−	105.216i	0.954133	−	0.550869i	0.0597708	−	0.998212i	$-0.480963\pi$
$191$	182.239	−	105.216i	0.954133	−	0.550869i	0.894362	+	0.447343i	$0.147630\pi$
$192$	251.227	−	16.2914i	1.30848	−	0.0848513i
$193$	−48.6254	+	84.2217i	−0.251945	+	0.436382i	−0.964061	−	0.265680i	$-0.914404\pi$
$193$	−48.6254	+	84.2217i	−0.251945	+	0.436382i	0.712116	+	0.702062i	$0.247737\pi$
$194$		−	279.245i		−	1.43941i
$195$	199.633	−	62.2347i	1.02376	−	0.319152i
$196$	−81.6480			−0.416571
$197$	−235.347	−	135.878i	−1.19465	−	0.689734i	−0.235296	−	0.971924i	$-0.575606\pi$
$197$	−235.347	−	135.878i	−1.19465	−	0.689734i	−0.959359	+	0.282190i	$0.908939\pi$
$198$	−133.996	−	175.130i	−0.676749	−	0.884493i
$199$	58.6089	+	101.514i	0.294517	+	0.510118i	0.974872	−	0.222764i	$-0.0715079\pi$
$199$	58.6089	+	101.514i	0.294517	+	0.510118i	−0.680355	+	0.732882i	$0.738175\pi$
$200$			7.65746i			0.0382873i
$201$	−43.0357	+	87.1154i	−0.214108	+	0.433410i
$202$	39.5955	+	68.5814i	0.196017	+	0.339512i
$203$		−	100.215i		−	0.493672i
$204$	−201.279	−	99.4332i	−0.986660	−	0.487418i
$205$	129.821	−	224.857i	0.633275	−	1.09686i
$206$	−92.1657	−	53.2119i	−0.447406	−	0.258310i
$207$	−32.3761	−	13.4632i	−0.156406	−	0.0650398i
$208$	158.992	+	46.7809i	0.764385	+	0.224908i
$209$			198.588i			0.950182i
$210$	385.636	−	25.0075i	1.83636	−	0.119083i
$211$	28.6549	−	49.6317i	0.135805	−	0.235221i	−0.790100	−	0.612978i	$-0.789971\pi$
$211$	28.6549	−	49.6317i	0.135805	−	0.235221i	0.925905	+	0.377757i	$0.123305\pi$
$212$	−80.9675	+	46.7466i	−0.381922	+	0.220503i
$213$	−84.1211	+	56.1236i	−0.394935	+	0.263491i
$214$	191.963	+	332.489i	0.897021	+	1.55369i
$215$	−256.349	+	148.003i	−1.19232	+	0.688387i
$216$	−10.6476	−	54.1171i	−0.0492946	−	0.250542i
$217$	164.779	+	285.406i	0.759352	+	1.31524i
$218$	−171.483	−	99.0055i	−0.786618	−	0.454154i
$219$	−150.340	+	9.74914i	−0.686483	+	0.0445166i
$220$	209.099			0.950451
$221$	−142.970	−	150.111i	−0.646924	−	0.679234i
$222$	−17.2064	+	11.4797i	−0.0775065	+	0.0517105i
$223$	13.7806	−	23.8687i	0.0617963	−	0.107034i	−0.833472	−	0.552562i	$-0.813650\pi$
$223$	13.7806	−	23.8687i	0.0617963	−	0.107034i	0.895268	+	0.445527i	$0.146984\pi$
$224$	322.910	+	186.432i	1.44156	+	0.832286i
$225$	−33.4546	+	4.35722i	−0.148687	+	0.0193654i
$226$	126.357			0.559103
$227$	337.392	−	194.793i	1.48631	−	0.858120i	0.486430	−	0.873720i	$-0.338299\pi$
$227$	337.392	−	194.793i	1.48631	−	0.858120i	0.999878	+	0.0155994i	$0.00496563\pi$
$228$	−149.011	+	301.637i	−0.653557	+	1.32297i
$229$	364.212			1.59045			0.795223	−	0.606316i	$-0.207354\pi$
$229$	364.212			1.59045			0.795223	+	0.606316i	$0.207354\pi$
$230$	53.3380	−	30.7947i	0.231904	−	0.133890i
$231$	−13.1459	−	202.720i	−0.0569085	−	0.877576i
$232$	12.5616	−	21.7573i	0.0541447	−	0.0937813i
$233$			309.679i			1.32909i	0.747246	+	0.664547i	$0.231376\pi$
$233$			309.679i			1.32909i	−0.747246	+	0.664547i	$0.768624\pi$
$234$	53.8154	−	340.735i	0.229980	−	1.45613i
$235$	−381.861			−1.62494
$236$	−258.478	−	149.232i	−1.09525	−	0.632341i
$237$	−269.055	+	17.4475i	−1.13525	+	0.0736183i
$238$	−191.553	−	331.779i	−0.804842	−	1.39403i
$239$		−	16.1075i		−	0.0673954i	−0.999432	−	0.0336977i	$-0.989272\pi$
$239$		−	16.1075i		−	0.0673954i	0.999432	−	0.0336977i	$-0.0107283\pi$
$240$	−183.854	−	90.8253i	−0.766059	−	0.378439i
$241$	−143.814	−	249.094i	−0.596740	−	1.03358i	−0.993299	−	0.115574i	$-0.963129\pi$
$241$	−143.814	−	249.094i	−0.596740	−	1.03358i	0.396559	−	0.918009i	$-0.370204\pi$
$242$			153.143i			0.632822i
$243$	230.373	−	77.3119i	0.948038	−	0.318156i
$244$	−121.779	+	210.927i	−0.499093	+	0.864454i
$245$	80.7882	+	46.6431i	0.329748	+	0.190380i
$246$	−237.716	−	356.302i	−0.966325	−	1.44838i
$247$	−224.957	+	214.256i	−0.910756	+	0.867432i
$248$			82.6175i			0.333135i
$249$	−2.49811	−	38.5229i	−0.0100326	−	0.154711i
$250$	−167.976	+	290.943i	−0.671904	+	1.16377i
$251$	423.327	−	244.408i	1.68656	−	0.973737i	0.729444	−	0.684041i	$-0.239779\pi$
$251$	423.327	−	244.408i	1.68656	−	0.973737i	0.957118	−	0.289697i	$-0.0935545\pi$
$252$	132.144	−	317.777i	0.524382	−	1.26102i
$253$	−16.1881	−	28.0385i	−0.0639844	−	0.110824i
$254$	129.788	−	74.9330i	0.510975	−	0.295012i
$255$	142.356	+	213.371i	0.558259	+	0.836748i
$256$	−72.9173	−	126.297i	−0.284833	−	0.493346i
$257$	313.426	+	180.957i	1.21956	+	0.704112i	0.964823	−	0.262899i	$-0.0846787\pi$
$257$	313.426	+	180.957i	1.21956	+	0.704112i	0.254734	+	0.967011i	$0.418012\pi$
$258$	31.5992	+	487.286i	0.122478	+	1.88871i
$259$	−19.0555			−0.0735733
$260$	225.596	+	236.864i	0.867678	+	0.911014i
$261$	102.203	+	42.4999i	0.391582	+	0.162835i
$262$	82.7116	−	143.261i	0.315693	−	0.546797i
$263$	−78.4373	−	45.2858i	−0.298241	−	0.172189i	0.343412	−	0.939185i	$-0.388417\pi$
$263$	−78.4373	−	45.2858i	−0.298241	−	0.172189i	−0.641652	+	0.766996i	$0.721751\pi$
$264$	22.5561	−	45.6593i	0.0854396	−	0.172952i
$265$	106.820			0.403094
$266$	−497.205	+	287.062i	−1.86919	+	1.07918i
$267$	91.0391	+	44.9740i	0.340970	+	0.168442i
$268$	−151.995			−0.567144
$269$	−207.395	+	119.739i	−0.770983	+	0.445127i	−0.833225	−	0.552934i	$-0.813508\pi$
$269$	−207.395	+	119.739i	−0.770983	+	0.445127i	0.0622419	+	0.998061i	$0.480175\pi$
$270$	−138.040	+	403.890i	−0.511257	+	1.49589i
$271$	128.354	−	222.316i	0.473632	−	0.820355i	−0.525912	−	0.850539i	$-0.676276\pi$
$271$	128.354	−	222.316i	0.473632	−	0.820355i	0.999544	+	0.0301841i	$0.00960935\pi$
$272$			203.292i			0.747396i
$273$	215.454	−	233.605i	0.789210	−	0.855696i
$274$	192.867			0.703895
$275$	−26.9777	−	15.5756i	−0.0981008	−	0.0566385i
$276$	−3.54940	−	54.7347i	−0.0128602	−	0.198314i
$277$	−119.879	−	207.636i	−0.432775	−	0.749587i	0.564337	−	0.825545i	$-0.309132\pi$
$277$	−119.879	−	207.636i	−0.432775	−	0.749587i	−0.997111	+	0.0759574i	$0.975799\pi$
$278$			596.974i			2.14739i
$279$	−360.948	+	47.0107i	−1.29372	+	0.168497i
$280$	44.6247	+	77.2922i	0.159374	+	0.276044i
$281$		−	345.747i		−	1.23041i	−0.788365	−	0.615207i	$-0.789072\pi$
$281$		−	345.747i		−	1.23041i	0.788365	−	0.615207i	$-0.210928\pi$
$282$	−279.007	+	564.784i	−0.989387	+	2.00278i
$283$	40.4767	−	70.1077i	0.143027	−	0.247730i	−0.785608	−	0.618725i	$-0.787650\pi$
$283$	40.4767	−	70.1077i	0.143027	−	0.247730i	0.928635	+	0.370994i	$0.120983\pi$
$284$	−136.994	−	79.0938i	−0.482375	−	0.278499i
$285$	319.758	−	213.335i	1.12196	−	0.748545i
$286$	230.644	−	219.673i	0.806449	−	0.768087i
$287$		−	394.591i		−	1.37488i
$288$	−327.071	+	250.251i	−1.13566	+	0.868927i
$289$	−17.3589	+	30.0664i	−0.0600653	+	0.104036i
$290$	−168.374	+	97.2109i	−0.580600	+	0.335210i
$291$	157.694	+	236.360i	0.541903	+	0.812233i
$292$	−117.834	−	204.094i	−0.403541	−	0.698953i
$293$	306.470	−	176.941i	1.04597	−	0.603893i	0.124454	−	0.992225i	$-0.460282\pi$
$293$	306.470	−	176.941i	1.04597	−	0.603893i	0.921520	+	0.388332i	$0.126949\pi$
$294$	128.014	−	85.4082i	0.435423	−	0.290504i
$295$	170.504	+	295.322i	0.577980	+	1.00109i
$296$	−4.13704	−	2.38852i	−0.0139765	−	0.00806934i
$297$	212.316	+	72.5642i	0.714868	+	0.244324i
$298$	−386.359			−1.29651
$299$	14.2963	−	48.5881i	0.0478137	−	0.162502i
$300$	−29.2895	−	43.9007i	−0.0976317	−	0.146336i
$301$	−224.927	+	389.585i	−0.747266	+	1.29430i
$302$	35.1104	+	20.2710i	0.116260	+	0.0671226i
$303$	−72.2435	−	35.6888i	−0.238427	−	0.117785i
$304$	304.654			1.00215
$305$	240.992	−	139.137i	0.790139	−	0.456187i
$306$	419.594	−	54.6489i	1.37122	−	0.178591i
$307$	243.598			0.793478			0.396739	−	0.917931i	$-0.370142\pi$
$307$	243.598			0.793478			0.396739	+	0.917931i	$0.370142\pi$
$308$	275.203	−	158.889i	0.893517	−	0.515873i
$309$	108.061	−	7.00746i	0.349711	−	0.0226778i
$310$	319.678	−	553.699i	1.03122	−	1.78613i
$311$			326.177i			1.04880i	0.851472	+	0.524400i	$0.175710\pi$
$311$			326.177i			1.04880i	−0.851472	+	0.524400i	$0.824290\pi$
$312$	76.0576	−	23.7106i	0.243774	−	0.0759955i
$313$	−253.830			−0.810958			−0.405479	−	0.914104i	$-0.632895\pi$
$313$	−253.830			−0.810958			−0.405479	+	0.914104i	$0.632895\pi$
$314$	−584.816	−	337.643i	−1.86247	−	1.07530i
$315$	−312.290	+	238.941i	−0.991395	+	0.758543i
$316$	−210.881	−	365.257i	−0.667346	−	1.15588i
$317$		−	393.046i		−	1.23989i	−0.784644	−	0.619947i	$-0.787154\pi$
$317$		−	393.046i		−	1.23989i	0.784644	−	0.619947i	$-0.212846\pi$
$318$	78.0480	−	157.989i	0.245434	−	0.496822i
$319$	51.1015	+	88.5104i	0.160193	+	0.277462i
$320$		−	449.951i		−	1.40610i
$321$	−350.243	−	173.022i	−1.09110	−	0.539011i
$322$	46.8001	−	81.0601i	0.145342	−	0.251739i
$323$	−330.015	−	190.534i	−1.02172	−	0.589890i
$324$	268.040	+	269.530i	0.827283	+	0.831883i
$325$	−11.4624	−	47.3643i	−0.0352689	−	0.145736i
$326$		−	230.299i		−	0.706440i
$327$	201.057	−	13.0380i	0.614852	−	0.0398716i
$328$	49.4602	−	85.6676i	0.150793	−	0.261182i
$329$	−502.582	+	290.166i	−1.52760	+	0.881963i
$330$	−327.843	+	218.729i	−0.993463	+	0.662815i
$331$	−165.970	−	287.468i	−0.501420	−	0.868484i	−0.999999	−	0.00164002i	$-0.999478\pi$
$331$	−165.970	−	287.468i	−0.501420	−	0.868484i	0.498579	−	0.866844i	$-0.333855\pi$
$332$	52.2969	−	30.1936i	0.157521	−	0.0909447i
$333$	8.08117	−	19.4334i	0.0242678	−	0.0583586i
$334$	−86.0090	−	148.972i	−0.257512	−	0.446024i
$335$	150.394	+	86.8300i	0.448937	+	0.259194i
$336$	−310.993	+	20.1671i	−0.925574	+	0.0600211i
$337$	489.287			1.45189			0.725945	−	0.687753i	$-0.241403\pi$
$337$	489.287			1.45189			0.725945	+	0.687753i	$0.241403\pi$
$338$	497.682	+	24.2655i	1.47243	+	0.0717915i
$339$	−106.952	+	71.3556i	−0.315492	+	0.210489i
$340$	−200.619	+	347.483i	−0.590057	+	1.02201i
$341$	−291.067	−	168.048i	−0.853569	−	0.492808i
$342$	−81.8971	−	628.805i	−0.239465	−	1.83861i
$343$	−257.506			−0.750747
$344$	−97.6656	+	56.3873i	−0.283912	+	0.163916i
$345$	−27.7563	+	56.1860i	−0.0804531	+	0.162858i
$346$	781.768			2.25944
$347$	−342.520	+	197.754i	−0.987089	+	0.569896i	−0.904403	−	0.426680i	$-0.859683\pi$
$347$	−342.520	+	197.754i	−0.987089	+	0.569896i	−0.0826859	+	0.996576i	$0.526350\pi$
$348$	11.2046	+	172.783i	0.0321970	+	0.496504i
$349$	−341.007	+	590.641i	−0.977097	+	1.69238i	−0.304261	+	0.952589i	$0.598410\pi$
$349$	−341.007	+	590.641i	−0.977097	+	1.69238i	−0.672835	+	0.739792i	$0.734924\pi$
$350$		−	90.0588i		−	0.257311i
$351$	146.867	+	318.796i	0.418425	+	0.908251i
$352$	−380.259			−1.08028
$353$	172.994	+	99.8782i	0.490068	+	0.282941i	0.724603	−	0.689167i	$-0.242023\pi$
$353$	172.994	+	99.8782i	0.490068	+	0.282941i	−0.234534	+	0.972108i	$0.575357\pi$
$354$	561.368	−	36.4033i	1.58579	−	0.102834i
$355$	90.3679	+	156.522i	0.254558	+	0.440907i
$356$			158.840i			0.446181i
$357$	349.494	+	172.653i	0.978976	+	0.483621i
$358$	135.215	+	234.199i	0.377694	+	0.654186i
$359$			286.250i			0.797354i	0.917091	+	0.398677i	$0.130531\pi$
$359$			286.250i			0.797354i	−0.917091	+	0.398677i	$0.869469\pi$
$360$	−97.7499	+	12.7312i	−0.271527	+	0.0353644i
$361$	−105.036	+	181.927i	−0.290957	+	0.503953i
$362$	291.335	+	168.202i	0.804792	+	0.464647i
$363$	−86.4819	−	129.624i	−0.238242	−	0.357090i
$364$	476.902	+	140.321i	1.31017	+	0.385497i
$365$			269.260i			0.737699i
$366$	−29.7063	−	458.095i	−0.0811647	−	1.25163i
$367$	−63.4015	+	109.815i	−0.172756	+	0.299222i	−0.939382	−	0.342871i	$-0.888601\pi$
$367$	−63.4015	+	109.815i	−0.172756	+	0.299222i	0.766626	+	0.642094i	$0.221934\pi$
$368$	−43.0139	+	24.8341i	−0.116886	+	0.0674839i
$369$	402.417	+	167.340i	1.09056	+	0.453497i
$370$	18.4842	+	32.0156i	0.0499573	+	0.0865286i
$371$	140.590	−	81.1694i	0.378948	−	0.218786i
$372$	−316.009	−	473.652i	−0.849488	−	1.27326i
$373$	−160.623	−	278.206i	−0.430623	−	0.745862i	0.566304	−	0.824197i	$-0.308373\pi$
$373$	−160.623	−	278.206i	−0.430623	−	0.745862i	−0.996927	+	0.0783351i	$0.975040\pi$
$374$	338.359	+	195.352i	0.904703	+	0.522331i
$375$	−22.1207	−	341.119i	−0.0589885	−	0.909651i
$376$	−145.484			−0.386926
$377$	−45.1297	+	153.380i	−0.119707	+	0.406844i
$378$	125.226	+	636.467i	0.331286	+	1.68378i
$379$	194.589	−	337.037i	0.513426	−	0.889280i	−0.486453	−	0.873707i	$-0.661709\pi$
$379$	194.589	−	337.037i	0.513426	−	0.889280i	0.999879	−	0.0155732i	$-0.00495730\pi$
$380$	520.739	+	300.649i	1.37037	+	0.791181i
$381$	−67.5397	+	136.718i	−0.177269	+	0.358840i
$382$	−620.430			−1.62416
$383$	−348.764	+	201.359i	−0.910612	+	0.525742i	−0.880628	−	0.473808i	$-0.842879\pi$
$383$	−348.764	+	201.359i	−0.910612	+	0.525742i	−0.0299840	+	0.999550i	$0.509546\pi$
$384$	−173.184	−	85.5541i	−0.451000	−	0.222797i
$385$	−363.074			−0.943049
$386$	248.316	−	143.365i	0.643306	−	0.371413i
$387$	−301.923	−	394.606i	−0.780164	−	1.01965i
$388$	−222.234	+	384.921i	−0.572769	+	0.992065i
$389$		−	408.894i		−	1.05114i	−0.850750	−	0.525571i	$-0.823852\pi$
$389$		−	408.894i		−	1.05114i	0.850750	−	0.525571i	$-0.176148\pi$
$390$	−601.480	−	135.388i	−1.54226	−	0.347150i
$391$	62.1262			0.158890
$392$	30.7792	+	17.7704i	0.0785185	+	0.0453327i
$393$	10.8923	+	167.968i	0.0277157	+	0.427399i
$394$	400.617	+	693.888i	1.01679	+	1.76114i
$395$			481.881i			1.21995i
$396$	45.3301	+	348.044i	0.114470	+	0.878899i
$397$	−42.0863	−	72.8956i	−0.106011	−	0.183616i	0.808140	−	0.588991i	$-0.200474\pi$
$397$	−42.0863	−	72.8956i	−0.106011	−	0.183616i	−0.914151	+	0.405374i	$0.867141\pi$
$398$		−	345.601i		−	0.868343i
$399$	258.738	−	523.754i	0.648467	−	1.31267i
$400$	−23.8945	+	41.3865i	−0.0597363	+	0.103466i
$401$	436.240	+	251.863i	1.08788	+	0.628088i	0.933011	−	0.359847i	$-0.117171\pi$
$401$	436.240	+	251.863i	1.08788	+	0.628088i	0.154869	+	0.987935i	$0.450505\pi$
$402$	238.309	−	158.994i	0.592810	−	0.395509i
$403$	−123.670	−	511.021i	−0.306873	−	1.26804i
$404$		−	126.047i		−	0.311997i
$405$	−111.242	−	419.815i	−0.274673	−	1.03658i
$406$	−147.736	+	255.886i	−0.363881	+	0.630260i
$407$	16.8298	−	9.71671i	0.0413510	−	0.0238740i
$408$	54.2357	+	81.2914i	0.132931	+	0.199244i
$409$	−33.3284	−	57.7266i	−0.0814876	−	0.141141i	0.822401	−	0.568908i	$-0.192634\pi$
$409$	−33.3284	−	57.7266i	−0.0814876	−	0.141141i	−0.903889	+	0.427767i	$0.859300\pi$
$410$	−662.961	+	382.761i	−1.61698	+	0.933562i
$411$	−163.247	+	108.915i	−0.397196	+	0.265000i
$412$	84.6963	+	146.698i	0.205573	+	0.356064i
$413$	448.814	+	259.123i	1.08672	+	0.627416i
$414$	62.8205	+	82.1047i	0.151740	+	0.198321i
$415$	−68.9950			−0.166253
$416$	−410.260	−	430.750i	−0.986201	−	1.03546i
$417$	−337.119	−	505.293i	−0.808440	−	1.21173i
$418$	292.755	−	507.066i	0.700371	−	1.21308i
$419$	96.6062	+	55.7756i	0.230564	+	0.133116i	0.610832	−	0.791760i	$-0.290835\pi$
$419$	96.6062	+	55.7756i	0.230564	+	0.133116i	−0.380268	+	0.924876i	$0.624168\pi$
$420$	−551.476	−	272.433i	−1.31304	−	0.648651i
$421$	−248.461			−0.590170			−0.295085	−	0.955471i	$-0.595348\pi$
$421$	−248.461			−0.590170			−0.295085	+	0.955471i	$0.595348\pi$
$422$	−146.332	+	84.4850i	−0.346759	+	0.200201i
$423$	−82.7828	−	635.605i	−0.195704	−	1.50261i
$424$	40.6969			0.0959834
$425$	51.7673	−	29.8878i	0.121805	−	0.0703243i
$426$	297.527	−	19.2939i	0.698421	−	0.0452908i
$427$	211.453	−	366.247i	0.495206	−	0.857721i
$428$		−	611.085i		−	1.42777i
$429$	−71.1705	+	316.184i	−0.165899	+	0.737026i
$430$	872.734			2.02961
$431$	82.9457	+	47.8887i	0.192450	+	0.111111i	0.593129	−	0.805108i	$-0.297892\pi$
$431$	82.9457	+	47.8887i	0.192450	+	0.111111i	−0.400679	+	0.916218i	$0.631226\pi$
$432$	111.321	−	325.714i	0.257687	−	0.753967i
$433$	357.961	+	620.007i	0.826700	+	1.43189i	0.900613	+	0.434622i	$0.143118\pi$
$433$	357.961	+	620.007i	0.826700	+	1.43189i	−0.0739125	+	0.997265i	$0.523549\pi$
$434$		−	971.659i		−	2.23885i
$435$	87.6195	−	177.365i	0.201424	−	0.407735i
$436$	157.585	+	272.945i	0.361433	+	0.626021i
$437$		−	93.1026i		−	0.213049i
$438$	398.243	+	196.735i	0.909231	+	0.449167i
$439$	−235.861	+	408.523i	−0.537269	+	0.930577i	0.461781	+	0.886994i	$0.347211\pi$
$439$	−235.861	+	408.523i	−0.537269	+	0.930577i	−0.999050	+	0.0435827i	$0.986123\pi$
$440$	−78.8252	−	45.5097i	−0.179148	−	0.103431i
$441$	−60.1232	+	144.583i	−0.136334	+	0.327852i
$442$	143.763	+	594.050i	0.325256	+	1.34401i
$443$			678.551i			1.53172i	0.643008	+	0.765859i	$0.277686\pi$
$443$			678.551i			1.53172i	−0.643008	+	0.765859i	$0.722314\pi$
$444$	32.8540	−	2.13049i	0.0739954	−	0.00479841i
$445$	90.7408	−	157.168i	0.203912	−	0.353186i
$446$	−70.3735	+	40.6302i	−0.157788	+	0.0910990i
$447$	327.023	−	218.182i	0.731595	−	0.488103i
$448$	−341.905	−	592.197i	−0.763181	−	1.32187i
$449$	12.3192	−	7.11251i	0.0274370	−	0.0158408i	−0.486219	−	0.873837i	$-0.661624\pi$
$449$	12.3192	−	7.11251i	0.0274370	−	0.0158408i	0.513656	+	0.857996i	$0.328291\pi$
$450$	91.8450	+	38.1927i	0.204100	+	0.0848726i
$451$	201.208	+	348.503i	0.446138	+	0.772734i
$452$	−174.175	−	100.560i	−0.385343	−	0.222478i
$453$	−41.1656	+	2.66948i	−0.0908733	+	0.00589290i
$454$	−1148.64			−2.53005
$455$	−391.719	−	411.283i	−0.860920	−	0.903919i
$456$	121.824	−	81.2779i	0.267157	−	0.178241i
$457$	302.258	−	523.526i	0.661396	−	1.14557i	−0.318853	−	0.947804i	$-0.603298\pi$
$457$	302.258	−	523.526i	0.661396	−	1.14557i	0.980249	−	0.197767i	$-0.0633691\pi$
$458$	−929.964	−	536.915i	−2.03049	−	1.17230i
$459$	−324.293	+	283.206i	−0.706520	+	0.617008i
$460$	−98.0305			−0.213110
$461$	−418.860	+	241.829i	−0.908590	+	0.524574i	−0.879977	−	0.475016i	$-0.842442\pi$
$461$	−418.860	+	241.829i	−0.908590	+	0.524574i	−0.0286125	+	0.999591i	$0.509109\pi$
$462$	−265.280	+	536.996i	−0.574199	+	1.16233i
$463$	392.769			0.848312			0.424156	−	0.905589i	$-0.360571\pi$
$463$	392.769			0.848312			0.424156	+	0.905589i	$0.360571\pi$
$464$	135.784	−	78.3948i	0.292637	−	0.168954i
$465$	42.0983	+	649.191i	0.0905341	+	1.39611i
$466$	456.523	−	790.721i	0.979663	−	1.69683i
$467$		−	112.871i		−	0.241693i	−0.992671	−	0.120847i	$-0.961439\pi$
$467$		−	112.871i		−	0.241693i	0.992671	−	0.120847i	$-0.0385609\pi$
$468$	−345.351	+	426.852i	−0.737930	+	0.912077i
$469$	263.919			0.562727
$470$	975.029	+	562.933i	2.07453	+	1.19773i
$471$	685.673	−	44.4641i	1.45578	−	0.0944037i
$472$	64.9598	+	112.514i	0.137627	+	0.238377i
$473$		−	458.776i		−	0.969928i
$474$	712.715	+	352.087i	1.50362	+	0.742799i
$475$	−44.7901	−	77.5787i	−0.0942949	−	0.163323i
$476$			609.780i			1.28105i
$477$	23.1572	+	177.801i	0.0485476	+	0.372748i
$478$	−23.7454	+	41.1282i	−0.0496765	+	0.0860423i
$479$	−586.570	−	338.656i	−1.22457	−	0.707007i	−0.258683	−	0.965962i	$-0.583288\pi$
$479$	−586.570	−	338.656i	−1.22457	−	0.707007i	−0.965889	+	0.258955i	$0.916622\pi$
$480$	408.497	+	612.278i	0.851036	+	1.27558i
$481$	29.1645	+	8.58120i	0.0606331	+	0.0178403i
$482$			848.033i			1.75941i
$483$	6.16308	+	95.0398i	0.0127600	+	0.196770i
$484$	121.877	−	211.097i	0.251812	−	0.436152i
$485$	439.788	−	253.912i	0.906780	−	0.523530i
$486$	−702.197	−	142.207i	−1.44485	−	0.292608i
$487$	−156.257	−	270.645i	−0.320856	−	0.555738i	0.659809	−	0.751433i	$-0.270637\pi$
$487$	−156.257	−	270.645i	−0.320856	−	0.555738i	−0.980665	+	0.195695i	$0.937304\pi$
$488$	91.8150	−	53.0094i	0.188145	−	0.108626i
$489$	130.053	+	194.931i	0.265957	+	0.398631i
$490$	−137.521	−	238.193i	−0.280655	−	0.486108i
$491$	−594.240	−	343.085i	−1.21027	−	0.698747i	−0.247448	−	0.968901i	$-0.579592\pi$
$491$	−594.240	−	343.085i	−1.21027	−	0.698747i	−0.962817	+	0.270154i	$0.912925\pi$
$492$	44.1171	+	680.322i	0.0896689	+	1.38277i
$493$	−196.116			−0.397802
$494$	890.247	−	215.444i	1.80212	−	0.436122i
$495$	153.975	−	370.275i	0.311060	−	0.748030i
$496$	−257.802	+	446.526i	−0.519762	+	0.900254i
$497$	237.873	+	137.336i	0.478618	+	0.276330i
$498$	−50.4112	+	102.045i	−0.101227	+	0.204911i
$499$	−334.798			−0.670937			−0.335469	−	0.942051i	$-0.608895\pi$
$499$	−334.798			−0.670937			−0.335469	+	0.942051i	$0.608895\pi$
$500$	463.088	−	267.364i	0.926175	−	0.534728i
$501$	156.927	+	77.5229i	0.313227	+	0.154736i
$502$	−1441.21			−2.87093
$503$	−299.985	+	173.196i	−0.596391	+	0.344327i	−0.767621	−	0.640904i	$-0.778559\pi$
$503$	−299.985	+	173.196i	−0.596391	+	0.344327i	0.171229	+	0.985231i	$0.445226\pi$
$504$	−118.978	+	91.0334i	−0.236068	+	0.180622i
$505$	−72.0067	+	124.719i	−0.142588	+	0.246969i
$506$			95.4565i			0.188649i
$507$	−434.953	+	260.509i	−0.857895	+	0.513825i
$508$	−238.538			−0.469564
$509$	461.694	+	266.559i	0.907062	+	0.523692i	0.879485	−	0.475927i	$-0.157888\pi$
$509$	461.694	+	266.559i	0.907062	+	0.523692i	0.0275770	+	0.999620i	$0.491221\pi$
$510$	−48.9384	−	754.670i	−0.0959576	−	1.47975i
$511$	204.603	+	354.383i	0.400398	+	0.693509i
$512$			687.525i			1.34282i
$513$	424.415	+	485.987i	0.827319	+	0.947343i
$514$	−533.526	−	924.095i	−1.03799	−	1.79785i
$515$		−	193.538i		−	0.375802i
$516$	344.244	−	696.839i	0.667139	−	1.35046i
$517$	295.921	−	512.550i	0.572381	−	0.991392i
$518$	48.6555	+	28.0913i	0.0939295	+	0.0542302i
$519$	−661.707	+	441.475i	−1.27496	+	0.850626i
$520$	−33.4916	−	138.392i	−0.0644068	−	0.266138i
$521$		−	863.482i		−	1.65736i	−0.559726	−	0.828678i	$-0.689093\pi$
$521$		−	863.482i		−	1.65736i	0.559726	−	0.828678i	$-0.310907\pi$
$522$	−198.308	−	259.183i	−0.379901	−	0.496520i
$523$	−93.0580	+	161.181i	−0.177931	+	0.308186i	−0.941172	−	0.337929i	$-0.890274\pi$
$523$	−93.0580	+	161.181i	−0.177931	+	0.308186i	0.763241	+	0.646114i	$0.223607\pi$
$524$	−228.025	+	131.650i	−0.435162	+	0.251241i
$525$	50.8575	+	76.2279i	0.0968713	+	0.145196i
$526$	133.519	+	231.262i	0.253838	+	0.439661i
$527$	558.525	−	322.465i	1.05982	−	0.611888i
$528$	264.386	−	176.392i	0.500731	−	0.334076i
$529$	−256.911	−	444.982i	−0.485653	−	0.841176i
$530$	−272.749	−	157.472i	−0.514621	−	0.297117i
$531$	−454.598	+	347.825i	−0.856116	+	0.655038i
$532$	913.819			1.71771
$533$	−177.695	+	603.923i	−0.333386	+	1.13306i
$534$	−166.155	−	249.043i	−0.311153	−	0.466372i
$535$	−349.095	+	604.650i	−0.652514	+	1.13019i
$536$	57.2981	+	33.0811i	0.106899	+	0.0617184i
$537$	−246.704	−	121.874i	−0.459411	−	0.226953i
$538$	706.070			1.31240
$539$	−125.213	+	72.2915i	−0.232305	+	0.134121i
$540$	511.710	−	446.879i	0.947611	−	0.827553i
$541$	125.473			0.231928			0.115964	−	0.993253i	$-0.463004\pi$
$541$	125.473			0.231928			0.115964	+	0.993253i	$0.463004\pi$
$542$	−655.469	+	378.435i	−1.20935	+	0.698220i
$543$	−341.579	+	22.1505i	−0.629058	+	0.0407928i
$544$	364.838	−	631.918i	0.670658	−	1.16161i
$545$		−	360.095i		−	0.660724i
$546$	−894.509	+	278.859i	−1.63829	+	0.510730i
$547$	635.286			1.16140			0.580700	−	0.814117i	$-0.302779\pi$
$547$	635.286			1.16140			0.580700	+	0.814117i	$0.302779\pi$
$548$	−265.855	−	153.491i	−0.485137	−	0.280094i
$549$	283.837	+	370.967i	0.517007	+	0.675714i
$550$	45.9225	+	79.5401i	0.0834954	+	0.144618i
$551$			293.901i			0.533395i
$552$	−10.5748	+	21.4061i	−0.0191572	+	0.0387792i
$553$	366.168	+	634.222i	0.662148	+	1.14687i
$554$			706.891i			1.27598i
$555$	−33.7251	−	16.6604i	−0.0607659	−	0.0300188i
$556$	475.095	−	822.889i	0.854488	−	1.48002i
$557$	739.120	+	426.731i	1.32697	+	0.766124i	0.984829	−	0.173527i	$-0.0555163\pi$
$557$	739.120	+	426.731i	1.32697	+	0.766124i	0.342136	+	0.939650i	$0.388850\pi$
$558$	990.931	+	412.067i	1.77586	+	0.738472i
$559$	519.693	−	494.971i	0.929683	−	0.885459i
$560$			556.992i			0.994628i
$561$	−396.713	+	25.7258i	−0.707153	+	0.0458570i
$562$	−509.693	+	882.815i	−0.906927	+	1.57084i
$563$	549.994	−	317.539i	0.976899	−	0.564013i	0.0755662	−	0.997141i	$-0.475924\pi$
$563$	549.994	−	317.539i	0.976899	−	0.564013i	0.901332	+	0.433128i	$0.142590\pi$
$564$	834.070	−	556.472i	1.47885	−	0.986652i
$565$	114.894	+	199.002i	0.203352	+	0.352216i
$566$	−206.703	+	119.340i	−0.365200	+	0.210848i
$567$	−465.416	−	468.004i	−0.820840	−	0.825404i
$568$	34.4290	+	59.6327i	0.0606144	+	0.104987i
$569$	−646.707	−	373.376i	−1.13657	−	0.656197i	−0.190989	−	0.981592i	$-0.561169\pi$
$569$	−646.707	−	373.376i	−1.13657	−	0.656197i	−0.945578	+	0.325395i	$0.894503\pi$
$570$	−1130.95	+	73.3393i	−1.98413	+	0.128665i
$571$	525.192			0.919775			0.459888	−	0.887977i	$-0.347890\pi$
$571$	525.192			0.919775			0.459888	+	0.887977i	$0.347890\pi$
$572$	−492.752	+	119.249i	−0.861455	+	0.208477i
$573$	525.146	−	350.365i	0.916486	−	0.611458i
$574$	−581.698	+	1007.53i	−1.01341	+	1.75528i
$575$	12.6478	+	7.30219i	0.0219961	+	0.0126995i
$576$	748.940	−	97.5438i	1.30024	−	0.169347i
$577$	−429.935			−0.745122			−0.372561	−	0.928008i	$-0.621520\pi$
$577$	−429.935			−0.745122			−0.372561	+	0.928008i	$0.621520\pi$
$578$	88.6468	−	51.1802i	0.153368	−	0.0885471i
$579$	−129.220	+	261.575i	−0.223178	+	0.451771i
$580$	309.457			0.533546
$581$	−90.8069	+	52.4274i	−0.156294	+	0.0902364i
$582$	−54.2111	−	835.980i	−0.0931463	−	1.43639i
$583$	−82.7793	+	143.378i	−0.141988	+	0.245931i
$584$			102.585i			0.175658i
$585$	585.563	−	225.068i	1.00096	−	0.384732i
$586$	−1043.37			−1.78050
$587$	68.6735	+	39.6486i	0.116991	+	0.0675445i	0.557353	−	0.830275i	$-0.311817\pi$
$587$	68.6735	+	39.6486i	0.116991	+	0.0675445i	−0.440363	+	0.897820i	$0.645150\pi$
$588$	−244.431	+	15.8507i	−0.415698	+	0.0269569i
$589$	−483.247	−	837.009i	−0.820454	−	1.42107i
$590$		−	1005.42i		−	1.70410i
$591$	−730.940	−	361.090i	−1.23678	−	0.610981i
$592$	−14.9064	−	25.8187i	−0.0251797	−	0.0436126i
$593$			553.253i			0.932973i	0.884528	+	0.466487i	$0.154480\pi$
$593$			553.253i			0.932973i	−0.884528	+	0.466487i	$0.845520\pi$
$594$	−435.145	−	498.274i	−0.732568	−	0.838845i
$595$	348.349	−	603.359i	0.585461	−	1.01405i
$596$	532.570	+	307.480i	0.893574	+	0.515905i
$597$	195.165	+	292.524i	0.326910	+	0.489990i
$598$	−108.131	+	102.988i	−0.180822	+	0.172220i
$599$		−	811.166i		−	1.35420i	−0.735891	−	0.677100i	$-0.763236\pi$
$599$		−	811.166i		−	1.35420i	0.735891	−	0.677100i	$-0.236764\pi$
$600$	1.48658	+	22.9242i	0.00247763	+	0.0382070i
$601$	278.602	−	482.553i	0.463565	−	0.802918i	−0.535571	−	0.844490i	$-0.679903\pi$
$601$	278.602	−	482.553i	0.463565	−	0.802918i	0.999135	+	0.0415727i	$0.0132368\pi$
$602$	1148.64	−	663.167i	1.90804	−	1.10161i
$603$	−111.924	+	269.153i	−0.185612	+	0.446357i
$604$	−32.2649	−	55.8845i	−0.0534188	−	0.0925241i
$605$	−241.188	+	139.250i	−0.398657	+	0.230165i
$606$	131.852	+	197.626i	0.217577	+	0.326116i
$607$	473.214	+	819.631i	0.779595	+	1.35030i	0.932175	+	0.362007i	$0.117908\pi$
$607$	473.214	+	819.631i	0.779595	+	1.35030i	−0.152580	+	0.988291i	$0.548758\pi$
$608$	−946.995	−	546.748i	−1.55756	−	0.899256i
$609$	−19.4553	−	300.016i	−0.0319462	−	0.492637i
$610$	−820.453			−1.34501
$611$	899.874	−	217.774i	1.47279	−	0.356423i
$612$	−621.874	−	258.599i	−1.01613	−	0.422548i
$613$	146.884	−	254.411i	0.239616	−	0.415026i	−0.720988	−	0.692947i	$-0.756312\pi$
$613$	146.884	−	254.411i	0.239616	−	0.415026i	0.960604	+	0.277921i	$0.0896453\pi$
$614$	−621.993	−	359.108i	−1.01302	−	0.584866i
$615$	344.995	−	698.361i	0.560968	−	1.13555i
$616$	−138.326			−0.224556
$617$	287.782	−	166.151i	0.466421	−	0.269288i	−0.248320	−	0.968678i	$-0.579878\pi$
$617$	287.782	−	166.151i	0.466421	−	0.269288i	0.714740	+	0.699390i	$0.246545\pi$
$618$	−286.248	−	141.409i	−0.463184	−	0.228816i
$619$	−240.740			−0.388918			−0.194459	−	0.980911i	$-0.562295\pi$
$619$	−240.740			−0.388918			−0.194459	+	0.980911i	$0.562295\pi$
$620$	−881.311	+	508.825i	−1.42147	+	0.820686i
$621$	−99.5384	−	34.0197i	−0.160287	−	0.0547822i
$622$	480.844	−	832.847i	0.773061	−	1.33898i
$623$		−	275.806i		−	0.442706i
$624$	485.058	+	109.183i	0.777337	+	0.174972i
$625$	−704.663			−1.12746
$626$	648.118	+	374.191i	1.03533	+	0.597750i
$627$	38.5528	+	594.515i	0.0614877	+	0.948191i
$628$	537.420	+	930.838i	0.855764	+	1.48223i
$629$			37.2906i			0.0592855i
$630$	1149.63	−	149.731i	1.82481	−	0.237668i
$631$	110.704	+	191.745i	0.175443	+	0.303875i	0.940314	−	0.340307i	$-0.110531\pi$
$631$	110.704	+	191.745i	0.175443	+	0.303875i	−0.764872	+	0.644183i	$0.777198\pi$
$632$			183.590i			0.290491i
$633$	76.1492	−	154.146i	0.120299	−	0.243516i
$634$	−579.422	+	1003.59i	−0.913914	+	1.58295i
$635$	236.027	+	136.270i	0.371695	+	0.214598i
$636$	−233.318	+	155.664i	−0.366853	+	0.244755i
$637$	−216.982	−	63.8434i	−0.340630	−	0.100225i
$638$		−	301.332i		−	0.472306i
$639$	−240.939	+	184.349i	−0.377056	+	0.288496i
$640$	−172.616	+	298.980i	−0.269713	+	0.467157i
$641$	−653.795	+	377.469i	−1.01996	+	0.588875i	−0.914093	−	0.405505i	$-0.867096\pi$
$641$	−653.795	+	377.469i	−1.01996	+	0.588875i	−0.105869	+	0.994380i	$0.533762\pi$
$642$	639.228	+	958.110i	0.995683	+	1.49238i
$643$	−149.181	−	258.388i	−0.232007	−	0.401848i	0.726392	−	0.687281i	$-0.241196\pi$
$643$	−149.181	−	258.388i	−0.232007	−	0.401848i	−0.958399	+	0.285433i	$0.907863\pi$
$644$	−129.022	+	74.4906i	−0.200344	+	0.115669i
$645$	−738.703	+	492.845i	−1.14528	+	0.764101i
$646$	561.764	+	973.005i	0.869604	+	1.50620i
$647$	861.729	+	497.519i	1.33188	+	0.768963i	0.985588	−	0.169162i	$-0.0541062\pi$
$647$	861.729	+	497.519i	1.33188	+	0.768963i	0.346295	+	0.938126i	$0.387439\pi$
$648$	−42.3819	−	159.944i	−0.0654042	−	0.246827i
$649$	−528.524			−0.814367
$650$	−40.5559	+	137.836i	−0.0623937	+	0.212055i
$651$	548.709	+	822.435i	0.842871	+	1.26334i
$652$	−183.281	+	317.452i	−0.281106	+	0.486890i
$653$	−372.508	−	215.068i	−0.570456	−	0.329353i	0.186875	−	0.982384i	$-0.440164\pi$
$653$	−372.508	−	215.068i	−0.570456	−	0.329353i	−0.757331	+	0.653031i	$0.773497\pi$
$654$	−532.590	−	263.103i	−0.814358	−	0.402299i
$655$	300.832			0.459285
$656$	534.639	−	308.674i	0.814998	−	0.470539i
$657$	−448.181	+	58.3722i	−0.682163	+	0.0888466i
$658$	1711.03			2.60035
$659$	320.410	−	184.989i	0.486206	−	0.280711i	−0.236793	−	0.971560i	$-0.576096\pi$
$659$	320.410	−	184.989i	0.486206	−	0.280711i	0.722999	+	0.690849i	$0.242763\pi$
$660$	625.983	−	40.5934i	0.948459	−	0.0615051i
$661$	−612.685	+	1061.20i	−0.926907	+	1.60545i	−0.138441	+	0.990371i	$0.544209\pi$
$661$	−612.685	+	1061.20i	−0.926907	+	1.60545i	−0.788466	+	0.615079i	$0.789124\pi$
$662$			978.679i			1.47837i
$663$	−457.153	−	421.633i	−0.689522	−	0.635947i
$664$	−26.2862			−0.0395876
$665$	−904.196	−	522.038i	−1.35969	−	0.785020i
$666$	−49.2825	+	37.7074i	−0.0739978	+	0.0566177i
$667$	−23.9575	−	41.4957i	−0.0359183	−	0.0622124i
$668$			273.797i			0.409876i
$669$	36.6214	−	74.1312i	0.0547405	−	0.110809i
$670$	−256.006	−	443.416i	−0.382099	−	0.661815i
$671$			431.293i			0.642762i
$672$	1002.89	+	495.436i	1.49240	+	0.737256i
$673$	391.959	−	678.893i	0.582406	−	1.00876i	−0.412787	−	0.910827i	$-0.635445\pi$
$673$	391.959	−	678.893i	0.582406	−	1.00876i	0.995193	−	0.0979293i	$-0.0312219\pi$
$674$	−1249.32	−	721.298i	−1.85360	−	1.07017i
$675$	−99.3077	+	19.5389i	−0.147122	+	0.0289466i
$676$	−666.711	−	429.523i	−0.986258	−	0.635390i
$677$			401.094i			0.592458i	0.955117	+	0.296229i	$0.0957292\pi$
$677$			401.094i			0.592458i	−0.955117	+	0.296229i	$0.904271\pi$
$678$	378.277	−	24.5303i	0.557931	−	0.0361804i
$679$	385.881	−	668.366i	0.568308	−	0.984339i
$680$	151.257	−	87.3282i	0.222436	−	0.128424i
$681$	972.238	−	648.654i	1.42766	−	0.952503i
$682$	495.465	+	858.171i	0.726489	+	1.25832i
$683$	−845.291	+	488.029i	−1.23762	+	0.714538i	−0.968606	−	0.248600i	$-0.920030\pi$
$683$	−845.291	+	488.029i	−1.23762	+	0.714538i	−0.269009	+	0.963138i	$0.586696\pi$
$684$	−387.538	+	931.943i	−0.566576	+	1.36249i
$685$	175.370	+	303.750i	0.256015	+	0.443431i
$686$	657.506	+	379.611i	0.958463	+	0.553369i
$687$	1090.35	−	70.7061i	1.58711	−	0.102920i
$688$	−703.809			−1.02298
$689$	−251.726	+	60.9190i	−0.365350	+	0.0884165i
$690$	153.700	−	102.545i	0.222754	−	0.148616i
$691$	−426.020	+	737.889i	−0.616527	+	1.06786i	0.373587	+	0.927595i	$0.378128\pi$
$691$	−426.020	+	737.889i	−0.616527	+	1.06786i	−0.990114	+	0.140262i	$0.955206\pi$
$692$	−1077.62	−	622.162i	−1.55725	−	0.899077i
$693$	−78.7099	−	604.334i	−0.113578	−	0.872054i
$694$	1166.10			1.68026
$695$	−940.185	+	542.816i	−1.35278	+	0.781030i
$696$	33.3819	−	67.5736i	0.0479625	−	0.0970885i
$697$	−772.193			−1.10788
$698$	1741.42	−	1005.41i	2.49488	−	1.44042i
$699$	60.1193	+	927.090i	0.0860076	+	1.32631i
$700$	−71.6723	+	124.140i	−0.102389	+	0.177343i
$701$		−	858.485i		−	1.22466i	−0.790603	−	0.612329i	$-0.790233\pi$
$701$		−	858.485i		−	1.22466i	0.790603	−	0.612329i	$-0.209767\pi$
$702$	94.9594	−	1030.51i	0.135270	−	1.46796i
$703$	55.8839			0.0794934
$704$	603.942	+	348.686i	0.857873	+	0.495293i
$705$	−1143.18	+	74.1324i	−1.62154	+	0.105152i
$706$	−294.477	−	510.050i	−0.417107	−	0.722450i
$707$			218.864i			0.309567i
$708$	−802.780	−	396.579i	−1.13387	−	0.560140i
$709$	341.120	+	590.837i	0.481128	+	0.833339i	0.999765	−	0.0216558i	$-0.00689381\pi$
$709$	341.120	+	590.837i	0.481128	+	0.833339i	−0.518637	+	0.854994i	$0.673560\pi$
$710$		−	532.875i		−	0.750528i
$711$	−802.087	+	104.466i	−1.12811	+	0.146928i
$712$	34.5710	−	59.8788i	0.0485548	−	0.0840994i
$713$	136.459	+	78.7845i	0.191387	+	0.110497i
$714$	−637.863	−	956.063i	−0.893365	−	1.33902i
$715$	555.687	+	163.502i	0.777184	+	0.228674i
$716$		−	430.436i		−	0.601168i
$717$	−3.12702	−	48.2212i	−0.00436126	−	0.0672541i
$718$	421.985	−	730.899i	0.587722	−	1.01797i
$719$	1160.57	−	670.057i	1.61415	−	0.931928i	0.625752	−	0.780022i	$-0.284792\pi$
$719$	1160.57	−	670.057i	1.61415	−	0.931928i	0.988395	−	0.151907i	$-0.0485413\pi$
$720$	−568.039	−	236.212i	−0.788943	−	0.328073i
$721$	−147.064	−	254.722i	−0.203972	−	0.353291i
$722$	536.387	−	309.683i	0.742918	−	0.428924i
$723$	−478.896	−	717.795i	−0.662374	−	0.992801i
$724$	−267.724	−	463.711i	−0.369784	−	0.640485i
$725$	−39.9257	−	23.0511i	−0.0550699	−	0.0317946i
$726$	29.7303	+	458.466i	0.0409509	+	0.631496i
$727$	−433.440			−0.596203			−0.298101	−	0.954534i	$-0.596353\pi$
$727$	−433.440			−0.596203			−0.298101	+	0.954534i	$0.596353\pi$
$728$	−149.240	−	156.693i	−0.204999	−	0.215238i
$729$	674.663	−	276.173i	0.925463	−	0.378838i
$730$	396.938	−	687.517i	0.543751	−	0.941804i
$731$	762.398	+	440.170i	1.04295	+	0.602148i
$732$	−323.622	+	655.095i	−0.442107	+	0.894939i
$733$	150.667			0.205549			0.102774	−	0.994705i	$-0.467228\pi$
$733$	150.667			0.205549			0.102774	+	0.994705i	$0.467228\pi$
$734$	323.773	−	186.931i	0.441108	−	0.254674i
$735$	250.912	+	123.952i	0.341376	+	0.168642i
$736$	178.274			0.242220
$737$	−233.094	+	134.577i	−0.316273	+	0.182601i
$738$	−780.824	−	1020.52i	−1.05803	−	1.38281i
$739$	270.056	−	467.750i	0.365434	−	0.632950i	−0.623412	−	0.781894i	$-0.714254\pi$
$739$	270.056	−	467.750i	0.365434	−	0.632950i	0.988846	+	0.148944i	$0.0475873\pi$
$740$		−	58.8418i		−	0.0795159i
$741$	−631.861	+	685.092i	−0.852714	+	0.924550i
$742$	−478.634			−0.645059
$743$	−283.786	−	163.844i	−0.381947	−	0.220517i	0.296718	−	0.954965i	$-0.404108\pi$
$743$	−283.786	−	163.844i	−0.381947	−	0.220517i	−0.678665	+	0.734448i	$0.737441\pi$
$744$	16.0389	+	247.333i	0.0215577	+	0.332437i
$745$	−351.308	−	608.483i	−0.471554	−	0.816756i
$746$			947.147i			1.26963i
$747$	−14.9573	−	114.842i	−0.0200231	−	0.153737i
$748$	−310.937	−	538.559i	−0.415691	−	0.719998i
$749$			1061.07i			1.41665i
$750$	−446.390	+	903.609i	−0.595186	+	1.20481i
$751$	−536.134	+	928.612i	−0.713894	+	1.23650i	0.249490	+	0.968377i	$0.419737\pi$
$751$	−536.134	+	928.612i	−0.713894	+	1.23650i	−0.963385	+	0.268124i	$0.913596\pi$
$752$	−786.303	−	453.972i	−1.04562	−	0.603686i
$753$	1219.87	−	813.870i	1.62002	−	1.08084i
$754$	341.343	−	325.105i	0.452709	−	0.431174i
$755$			73.7281i			0.0976531i
$756$	333.910	−	976.988i	0.441680	−	1.29231i
$757$	−99.6433	+	172.587i	−0.131629	+	0.227988i	−0.924305	−	0.381655i	$-0.875354\pi$
$757$	−99.6433	+	172.587i	−0.131629	+	0.227988i	0.792676	+	0.609644i	$0.208687\pi$
$758$	−993.708	+	573.718i	−1.31096	+	0.756883i
$759$	−53.9056	−	80.7966i	−0.0710219	−	0.106451i
$760$	−130.870	−	226.674i	−0.172198	−	0.298256i
$761$	−602.260	+	347.715i	−0.791406	+	0.456918i	−0.840457	−	0.541878i	$-0.817714\pi$
$761$	−602.260	+	347.715i	−0.791406	+	0.456918i	0.0490513	+	0.998796i	$0.484380\pi$
$762$	374.000	−	249.524i	0.490814	−	0.327459i
$763$	−273.626	−	473.934i	−0.358619	−	0.621146i
$764$	855.222	+	493.763i	1.11940	+	0.646286i
$765$	467.595	+	611.134i	0.611236	+	0.798868i
$766$	1187.36			1.55008
$767$	−570.222	−	598.702i	−0.743445	−	0.780576i
$768$	−242.812	−	363.940i	−0.316162	−	0.473880i
$769$	517.491	−	896.321i	0.672940	−	1.16557i	−0.304126	−	0.952632i	$-0.598364\pi$
$769$	517.491	−	896.321i	0.672940	−	1.16557i	0.977066	−	0.212935i	$-0.0683022\pi$
$770$	927.057	+	535.237i	1.20397	+	0.695113i
$771$	973.438	+	480.886i	1.26257	+	0.623717i
$772$	−456.383			−0.591170
$773$	−119.204	+	68.8223i	−0.154209	+	0.0890327i	−0.575119	−	0.818070i	$-0.695044\pi$
$773$	−119.204	+	68.8223i	−0.154209	+	0.0890327i	0.420910	+	0.907103i	$0.361711\pi$
$774$	189.198	+	1452.66i	0.244442	+	1.87682i
$775$	151.607			0.195623
$776$	167.554	−	96.7371i	0.215920	−	0.124661i
$777$	−57.0467	+	3.69933i	−0.0734191	+	0.00476104i
$778$	−602.784	+	1044.05i	−0.774787	+	1.34197i
$779$			1157.21i			1.48551i
$780$	721.354	+	665.305i	0.924812	+	0.852956i
$781$	−280.120			−0.358668
$782$	−158.630	−	91.5853i	−0.202852	−	0.117117i
$783$	314.217	+	107.391i	0.401299	+	0.137154i
$784$	110.902	+	192.089i	0.141457	+	0.245011i
$785$		−	1228.05i		−	1.56439i
$786$	219.803	−	444.939i	0.279648	−	0.566080i
$787$	92.4090	+	160.057i	0.117419	+	0.203376i	0.918744	−	0.394853i	$-0.129204\pi$
$787$	92.4090	+	160.057i	0.117419	+	0.203376i	−0.801325	+	0.598229i	$0.795871\pi$
$788$		−	1275.31i		−	1.61841i
$789$	−243.610	−	120.345i	−0.308758	−	0.152529i
$790$	710.380	−	1230.41i	0.899215	−	1.55749i
$791$	302.432	+	174.609i	0.382342	+	0.220745i
$792$	58.6623	−	141.070i	0.0740685	−	0.178118i
$793$	−488.561	+	465.320i	−0.616092	+	0.586785i
$794$			248.171i			0.312558i
$795$	319.788	−	20.7374i	0.402249	−	0.0260848i
$796$	−275.042	+	476.387i	−0.345531	+	0.598477i
$797$	−781.310	+	451.090i	−0.980314	+	0.565985i	−0.902365	−	0.430973i	$-0.858171\pi$
$797$	−781.310	+	451.090i	−0.980314	+	0.565985i	−0.0779492	+	0.996957i	$0.524837\pi$
$798$	−1432.76	+	955.904i	−1.79544	+	1.19787i
$799$	567.839	+	983.527i	0.710688	+	1.23095i
$800$	148.549	−	85.7646i	0.185686	−	0.107206i
$801$	281.276	+	116.965i	0.351156	+	0.146024i
$802$	−742.584	−	1286.19i	−0.925915	−	1.60373i
$803$	−361.412	−	208.661i	−0.450077	−	0.259852i
$804$	−455.028	+	29.5074i	−0.565955	+	0.0367007i
$805$	170.217			0.211450
$806$	−437.564	+	1487.13i	−0.542884	+	1.84507i
$807$	−597.634	+	398.727i	−0.740563	+	0.494086i
$808$	−27.4336	+	47.5164i	−0.0339525	+	0.0588075i
$809$	1244.85	+	718.713i	1.53875	+	0.888397i	0.998912	+	0.0466267i	$0.0148471\pi$
$809$	1244.85	+	718.713i	1.53875	+	0.888397i	0.539836	+	0.841770i	$0.318486\pi$
$810$	−334.842	+	1235.93i	−0.413385	+	1.52584i
$811$	−1064.77			−1.31292			−0.656458	−	0.754363i	$-0.727946\pi$
$811$	−1064.77			−1.31292			−0.656458	+	0.754363i	$0.727946\pi$
$812$	407.288	−	235.148i	0.501586	−	0.289591i
$813$	341.097	−	690.468i	0.419553	−	0.849285i
$814$	−57.2968			−0.0703892
$815$	362.702	−	209.406i	0.445034	−	0.256940i
$816$	39.4659	+	608.597i	0.0483651	+	0.745830i
$817$	659.642	−	1142.53i	0.807395	−	1.39845i
$818$			196.529i			0.240255i
$819$	599.658	−	741.174i	0.732183	−	0.904974i
$820$	1218.46			1.48593
$821$	−87.3580	−	50.4362i	−0.106404	−	0.0614326i	0.445853	−	0.895106i	$-0.352900\pi$
$821$	−87.3580	−	50.4362i	−0.106404	−	0.0614326i	−0.552258	+	0.833673i	$0.686234\pi$
$822$	577.389	−	37.4422i	0.702420	−	0.0455501i
$823$	576.812	+	999.068i	0.700866	+	1.21393i	0.968163	+	0.250321i	$0.0805361\pi$
$823$	576.812	+	999.068i	0.700866	+	1.21393i	−0.267297	+	0.963614i	$0.586131\pi$
$824$		−	73.7354i		−	0.0894847i
$825$	−83.7873	−	41.3915i	−0.101560	−	0.0501715i
$826$	−763.988	−	1323.27i	−0.924925	−	1.60202i
$827$		−	1537.83i		−	1.85953i	−0.368159	−	0.929763i	$-0.620012\pi$
$827$		−	1537.83i		−	1.85953i	0.368159	−	0.929763i	$-0.379988\pi$
$828$	−21.2518	−	163.171i	−0.0256664	−	0.197066i
$829$	−370.373	+	641.506i	−0.446771	+	0.773831i	−0.998174	−	0.0604088i	$-0.980760\pi$
$829$	−370.373	+	641.506i	−0.446771	+	0.773831i	0.551402	+	0.834239i	$0.314093\pi$
$830$	176.169	+	101.711i	0.212252	+	0.122544i
$831$	−399.191	−	598.329i	−0.480374	−	0.720011i
$832$	256.606	+	1060.33i	0.308420	+	1.27444i
$833$		−	277.439i		−	0.333060i
$834$	115.893	+	1787.17i	0.138961	+	2.14289i
$835$	156.412	−	270.914i	0.187320	−	0.324448i
$836$	−807.087	+	465.972i	−0.965415	+	0.557382i
$837$	−1071.45	+	210.809i	−1.28010	+	0.251862i
$838$	−164.447	−	284.830i	−0.196237	−	0.339893i
$839$	661.700	−	382.033i	0.788677	−	0.455343i	−0.0508197	−	0.998708i	$-0.516183\pi$
$839$	661.700	−	382.033i	0.788677	−	0.455343i	0.839497	+	0.543365i	$0.182850\pi$
$840$	148.599	+	222.727i	0.176903	+	0.265152i
$841$	−344.872	−	597.336i	−0.410074	−	0.710269i
$842$	634.411	+	366.277i	0.753457	+	0.435009i
$843$	−67.1213	−	1035.07i	−0.0796219	−	1.22784i
$844$	268.946			0.318656
$845$	414.316	+	805.873i	0.490315	+	0.953695i
$846$	−725.623	+	1744.96i	−0.857711	+	2.06261i
$847$	−211.624	+	366.543i	−0.249851	+	0.432755i
$848$	219.956	+	126.992i	0.259382	+	0.149754i
$849$	107.565	−	217.740i	0.126696	−	0.256467i
$850$	−176.240			−0.207342
$851$	−7.89021	+	4.55542i	−0.00927169	+	0.00535301i
$852$	−425.477	−	210.189i	−0.499386	−	0.246700i
$853$	−442.013			−0.518186			−0.259093	−	0.965852i	$-0.583424\pi$
$853$	−442.013			−0.518186			−0.259093	+	0.965852i	$0.583424\pi$
$854$	−1079.83	+	623.440i	−1.26444	+	0.730023i
$855$	915.849	−	700.741i	1.07117	−	0.819580i
$856$	−133.001	+	230.364i	−0.155375	+	0.269117i
$857$		−	404.037i		−	0.471455i	−0.971819	−	0.235727i	$-0.924253\pi$
$857$		−	404.037i		−	0.471455i	0.971819	−	0.235727i	$-0.0757473\pi$
$858$	647.837	−	702.413i	0.755054	−	0.818663i
$859$	445.806			0.518982			0.259491	−	0.965746i	$-0.416445\pi$
$859$	445.806			0.518982			0.259491	+	0.965746i	$0.416445\pi$
$860$	−1203.01	−	694.556i	−1.39884	−	0.807624i
$861$	−76.6036	−	1181.29i	−0.0889705	−	1.37200i
$862$	−141.193	−	244.554i	−0.163797	−	0.283706i
$863$			933.098i			1.08123i	0.841271	+	0.540613i	$0.181808\pi$
$863$			933.098i			1.08123i	−0.841271	+	0.540613i	$0.818192\pi$
$864$	−930.574	+	812.675i	−1.07705	+	0.940596i
$865$	710.845	+	1231.22i	0.821786	+	1.42338i
$866$		−	2110.80i		−	2.43741i
$867$	−46.1305	+	93.3802i	−0.0532070	+	0.107705i
$868$	−773.285	+	1339.37i	−0.890881	+	1.54305i
$869$	−646.800	−	373.430i	−0.744304	−	0.429724i
$870$	−485.192	+	323.709i	−0.557692	+	0.372079i
$871$	−403.929	−	118.850i	−0.463754	−	0.136452i
$872$		−	137.191i		−	0.157329i
$873$	517.975	+	676.979i	0.593328	+	0.775463i
$874$	−137.250	+	237.724i	−0.157037	+	0.271996i
$875$	−804.092	+	464.243i	−0.918962	+	0.530563i
$876$	−392.382	−	588.124i	−0.447925	−	0.671374i
$877$	−587.553	−	1017.67i	−0.669957	−	1.16040i	−0.977916	−	0.209000i	$-0.932979\pi$
$877$	−587.553	−	1017.67i	−0.669957	−	1.16040i	0.307958	−	0.951400i	$-0.400354\pi$
$878$	1204.47	−	695.404i	1.37184	−	0.792032i
$879$	883.134	−	589.206i	1.00470	−	0.670314i
$880$	−284.019	−	491.936i	−0.322749	−	0.559018i
$881$	−813.901	−	469.906i	−0.923838	−	0.533378i	−0.0389805	−	0.999240i	$-0.512411\pi$
$881$	−813.901	−	469.906i	−0.923838	−	0.533378i	−0.884857	+	0.465862i	$0.845744\pi$
$882$	366.657	−	280.539i	0.415711	−	0.318072i
$883$	70.9369			0.0803362			0.0401681	−	0.999193i	$-0.487211\pi$
$883$	70.9369			0.0803362			0.0401681	+	0.999193i	$0.487211\pi$
$884$	274.600	−	933.272i	0.310634	−	1.05574i
$885$	567.772	+	851.008i	0.641551	+	0.961591i
$886$	1000.31	−	1732.58i	1.12902	−	1.95551i
$887$	461.041	+	266.182i	0.519775	+	0.300092i	0.736843	−	0.676064i	$-0.236316\pi$
$887$	461.041	+	266.182i	0.519775	+	0.300092i	−0.217067	+	0.976157i	$0.569649\pi$
$888$	−12.8488	−	6.34741i	−0.0144694	−	0.00714798i
$889$	414.191			0.465907
$890$	−463.387	+	267.537i	−0.520660	+	0.300603i
$891$	649.699	+	176.018i	0.729180	+	0.197552i
$892$	129.340			0.145000
$893$	1473.92	−	850.967i	1.65052	−	0.952931i
$894$	−1156.65	+	75.0055i	−1.29379	+	0.0838988i
$895$	−245.896	+	425.904i	−0.274744	+	0.475870i
$896$			524.666i			0.585564i
$897$	33.3663	−	148.234i	0.0371977	−	0.165256i
$898$	−41.9405			−0.0467044
$899$	−430.765	−	248.702i	−0.479160	−	0.276643i
$900$	−96.2070	−	125.740i	−0.106897	−	0.139711i
$901$	−158.844	−	275.126i	−0.176298	−	0.305357i
$902$		−	1186.47i		−	1.31538i
$903$	−597.735	+	1209.97i	−0.661943	+	1.33995i
$904$	43.7731	+	75.8172i	0.0484215	+	0.0838686i
$905$			611.771i			0.675990i
$906$	109.046	+	53.8695i	0.120360	+	0.0594586i
$907$	−70.8388	+	122.696i	−0.0781023	+	0.135277i	−0.902431	−	0.430834i	$-0.858219\pi$
$907$	−70.8388	+	122.696i	−0.0781023	+	0.135277i	0.824329	+	0.566111i	$0.191553\pi$
$908$	1583.33	+	914.135i	1.74375	+	1.00676i
$909$	−223.205	−	92.8171i	−0.245550	−	0.102109i
$910$	393.892	+	1627.62i	0.432848	+	1.78859i
$911$		−	416.850i		−	0.457574i	−0.973476	−	0.228787i	$-0.926524\pi$
$911$		−	416.850i		−	0.457574i	0.973476	−	0.228787i	$-0.0734760\pi$
$912$	912.046	−	59.1438i	1.00005	−	0.0648507i
$913$	53.4672	−	92.6079i	0.0585621	−	0.101432i
$914$	−1543.55	+	891.166i	−1.68878	+	0.975018i
$915$	694.451	−	463.321i	0.758963	−	0.506362i
$916$	854.596	+	1480.20i	0.932965	+	1.61594i
$917$	395.936	−	228.594i	0.431773	−	0.249284i
$918$	1245.53	−	245.061i	1.35679	−	0.266951i
$919$	−131.990	−	228.614i	−0.143624	−	0.248764i	0.785235	−	0.619198i	$-0.212542\pi$
$919$	−131.990	−	228.614i	−0.143624	−	0.248764i	−0.928859	+	0.370434i	$0.879209\pi$
$920$	36.9550	+	21.3360i	0.0401685	+	0.0231913i
$921$	729.262	−	47.2907i	0.791815	−	0.0513472i
$922$	1426.00			1.54664
$923$	−302.220	−	317.314i	−0.327432	−	0.343786i
$924$	793.034	−	529.094i	0.858262	−	0.572612i
$925$	−4.38306	+	7.59169i	−0.00473845	+	0.00820723i
$926$	−1002.88	−	579.012i	−1.08302	−	0.625283i
$927$	322.142	−	41.9566i	0.347511	−	0.0452606i
$928$	−562.765			−0.606428
$929$	316.090	−	182.494i	0.340247	−	0.196442i	−0.320134	−	0.947372i	$-0.603728\pi$
$929$	316.090	−	182.494i	0.340247	−	0.196442i	0.660381	+	0.750930i	$0.270395\pi$
$930$	849.533	−	1719.68i	0.913477	−	1.84912i
$931$	−415.771			−0.446585
$932$	−1258.57	+	726.638i	−1.35040	+	0.779654i
$933$	63.3222	+	976.480i	0.0678694	+	1.04660i
$934$	−166.392	+	288.199i	−0.178150	+	0.308565i
$935$			710.517i			0.759911i
$936$	223.092	−	85.7481i	0.238346	−	0.0916112i
$937$	1721.58			1.83734			0.918668	−	0.395031i	$-0.129266\pi$
$937$	1721.58			1.83734			0.918668	+	0.395031i	$0.129266\pi$
$938$	−673.879	−	389.064i	−0.718421	−	0.414781i
$939$	−759.893	+	49.2771i	−0.809258	+	0.0524783i
$940$	−896.008	−	1551.93i	−0.953200	−	1.65099i
$941$			421.408i			0.447830i	0.974609	+	0.223915i	$0.0718837\pi$
$941$			421.408i			0.447830i	−0.974609	+	0.223915i	$0.928116\pi$
$942$	−1816.32	−	897.274i	−1.92815	−	0.952521i
$943$	−94.3310	−	163.386i	−0.100033	−	0.173262i
$944$			810.809i			0.858908i
$945$	−888.518	+	775.947i	−0.940231	+	0.821108i
$946$	−676.319	+	1171.42i	−0.714925	+	1.23829i
$947$	−974.052	−	562.369i	−1.02857	−	0.593843i	−0.111992	−	0.993709i	$-0.535723\pi$
$947$	−974.052	−	562.369i	−1.02857	−	0.593843i	−0.916573	+	0.399866i	$0.869057\pi$
$948$	−702.227	−	1052.54i	−0.740745	−	1.11027i
$949$	−153.558	−	634.524i	−0.161810	−	0.668624i
$950$			264.115i			0.278016i
$951$	−76.3038	−	1176.67i	−0.0802353	−	1.23729i
$952$	132.717	−	229.872i	0.139408	−	0.241462i
$953$	293.234	−	169.299i	0.307696	−	0.177648i	−0.338199	−	0.941075i	$-0.609818\pi$
$953$	293.234	−	169.299i	0.307696	−	0.177648i	0.645895	+	0.763426i	$0.276484\pi$
$954$	202.982	−	488.127i	0.212769	−	0.511663i
$955$	−564.144	−	977.126i	−0.590727	−	1.02317i
$956$	65.4629	−	37.7950i	0.0684758	−	0.0395345i
$957$	170.166	+	255.054i	0.177812	+	0.266514i
$958$	998.482	+	1729.42i	1.04226	+	1.80524i
$959$	461.622	+	266.518i	0.481358	+	0.277912i
$960$	−87.3510	−	1347.02i	−0.0909906	−	1.40315i
$961$	674.718			0.702100
$962$	−61.8173	−	64.9047i	−0.0642591	−	0.0674685i
$963$	−1082.12	−	449.985i	−1.12369	−	0.467274i
$964$	674.898	−	1168.96i	0.700102	−	1.21261i
$965$	451.577	+	260.718i	0.467956	+	0.270174i
$966$	124.369	−	251.756i	0.128747	−	0.260617i
$967$	−914.569			−0.945780			−0.472890	−	0.881122i	$-0.656789\pi$
$967$	−914.569			−0.945780			−0.472890	+	0.881122i	$0.656789\pi$
$968$	−91.8893	+	53.0523i	−0.0949269	+	0.0548061i
$969$	−1024.96	−	506.338i	−1.05775	−	0.522536i
$970$	−1497.25			−1.54356
$971$	973.021	−	561.774i	1.00208	−	0.578552i	0.0932178	−	0.995646i	$-0.470285\pi$
$971$	973.021	−	561.774i	1.00208	−	0.578552i	0.908863	+	0.417094i	$0.136951\pi$
$972$	854.758	+	754.860i	0.879381	+	0.776604i
$973$	−824.942	+	1428.84i	−0.847833	+	1.46849i
$974$			921.403i			0.945999i
$975$	−43.5102	−	139.570i	−0.0446258	−	0.143148i
$976$	661.647			0.677917
$977$	−348.149	−	201.004i	−0.356345	−	0.205736i	0.311131	−	0.950367i	$-0.399292\pi$
$977$	−348.149	−	201.004i	−0.356345	−	0.205736i	−0.667476	+	0.744631i	$0.732625\pi$
$978$	−44.7090	−	689.450i	−0.0457147	−	0.704959i
$979$	140.638	+	243.592i	0.143655	+	0.248817i
$980$			437.778i			0.446712i
$981$	599.375	−	78.0640i	0.610983	−	0.0795760i
$982$	1011.54	+	1752.04i	1.03008	+	1.78415i
$983$			537.168i			0.546458i	0.961949	+	0.273229i	$0.0880916\pi$
$983$			537.168i			0.546458i	−0.961949	+	0.273229i	$0.911908\pi$
$984$	131.439	−	266.066i	0.133576	−	0.270392i
$985$	−728.545	+	1261.88i	−0.739639	+	1.28109i
$986$	500.755	+	289.111i	0.507865	+	0.293216i
$987$	−1448.25	+	966.241i	−1.46733	+	0.978968i
$988$	−1398.61	−	411.517i	−1.41559	−	0.416516i
$989$			215.085i			0.217477i
$990$	−939.004	+	718.458i	−0.948489	+	0.725715i
$991$	−441.811	+	765.239i	−0.445823	+	0.772189i	−0.998109	−	0.0614662i	$-0.980422\pi$
$991$	−441.811	+	765.239i	−0.445823	+	0.772189i	0.552286	+	0.833655i	$0.313756\pi$
$992$	1602.72	−	925.328i	1.61564	−	0.932791i
$993$	−552.674	−	828.377i	−0.556570	−	0.834216i
$994$	−404.917	−	701.337i	−0.407361	−	0.705570i
$995$	544.292	−	314.247i	0.547027	−	0.315826i
$996$	150.700	−	100.544i	0.151306	−	0.100948i
$997$	692.084	+	1198.73i	0.694167	+	1.20233i	0.970461	+	0.241259i	$0.0775603\pi$
$997$	692.084	+	1198.73i	0.694167	+	1.20233i	−0.276294	+	0.961073i	$0.589106\pi$
$998$	854.858	+	493.552i	0.856571	+	0.494542i
$999$	20.4200	−	59.7469i	0.0204404	−	0.0598067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.3.i.b.35.1	yes	12
3.2	odd	2	inner	39.3.i.b.35.6	yes	12
13.3	even	3	inner	39.3.i.b.29.6	yes	12
13.4	even	6		507.3.c.g.170.1		6
13.6	odd	12		507.3.d.d.506.11		12
13.7	odd	12		507.3.d.d.506.1		12
13.9	even	3		507.3.c.h.170.6		6
39.17	odd	6		507.3.c.g.170.6		6
39.20	even	12		507.3.d.d.506.12		12
39.29	odd	6	inner	39.3.i.b.29.1	✓	12
39.32	even	12		507.3.d.d.506.2		12
39.35	odd	6		507.3.c.h.170.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.i.b.29.1	✓	12	39.29	odd	6	inner
39.3.i.b.29.6	yes	12	13.3	even	3	inner
39.3.i.b.35.1	yes	12	1.1	even	1	trivial
39.3.i.b.35.6	yes	12	3.2	odd	2	inner
507.3.c.g.170.1		6	13.4	even	6
507.3.c.g.170.6		6	39.17	odd	6
507.3.c.h.170.1		6	39.35	odd	6
507.3.c.h.170.6		6	13.9	even	3
507.3.d.d.506.1		12	13.7	odd	12
507.3.d.d.506.2		12	39.32	even	12
507.3.d.d.506.11		12	13.6	odd	12
507.3.d.d.506.12		12	39.20	even	12

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	39.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.55336 - 1.47418i) q^{2} +(2.99371 - 0.194134i) q^{3} +(2.34642 + 4.06412i) q^{4} -5.36177i q^{5} +(-7.93021 - 3.91758i) q^{6} +(-4.07426 - 7.05683i) q^{7} -2.04276i q^{8} +(8.92462 - 1.16237i) q^{9} +O(q^{10})\)	\(q+(-2.55336 - 1.47418i) q^{2} +(2.99371 - 0.194134i) q^{3} +(2.34642 + 4.06412i) q^{4} -5.36177i q^{5} +(-7.93021 - 3.91758i) q^{6} +(-4.07426 - 7.05683i) q^{7} -2.04276i q^{8} +(8.92462 - 1.16237i) q^{9} +(-7.90422 + 13.6905i) q^{10} +(7.19679 + 4.15507i) q^{11} +(7.81350 + 11.7113i) q^{12} +(3.05780 + 12.6353i) q^{13} +24.0248i q^{14} +(-1.04090 - 16.0516i) q^{15} +(6.37429 - 11.0406i) q^{16} +(-13.8098 + 7.97312i) q^{17} +(-24.5013 - 10.1886i) q^{18} +(11.9485 + 20.6955i) q^{19} +(21.7909 - 12.5810i) q^{20} +(-13.5671 - 20.3352i) q^{21} +(-12.2506 - 21.2187i) q^{22} +(-3.37402 - 1.94799i) q^{23} +(-0.396571 - 6.11545i) q^{24} -3.74858 q^{25} +(10.8190 - 36.7701i) q^{26} +(26.4921 - 5.21236i) q^{27} +(19.1199 - 33.1166i) q^{28} +(10.6509 + 6.14930i) q^{29} +(-21.0052 + 42.5199i) q^{30} -40.4440 q^{31} +(-39.6280 + 22.8792i) q^{32} +(22.3517 + 11.0419i) q^{33} +47.0153 q^{34} +(-37.8371 + 21.8452i) q^{35} +(25.6649 + 33.5434i) q^{36} +(1.16926 - 2.02522i) q^{37} -70.4573i q^{38} +(11.6071 + 37.2327i) q^{39} -10.9528 q^{40} +(41.9371 + 24.2124i) q^{41} +(4.66404 + 71.9233i) q^{42} +(-27.6034 - 47.8105i) q^{43} +38.9982i q^{44} +(-6.23233 - 47.8518i) q^{45} +(5.74338 + 9.94783i) q^{46} -71.2193i q^{47} +(16.9394 - 34.2898i) q^{48} +(-8.69920 + 15.0674i) q^{49} +(9.57146 + 5.52608i) q^{50} +(-39.7948 + 26.5502i) q^{51} +(-44.1764 + 42.0750i) q^{52} +19.9225i q^{53} +(-75.3278 - 25.7451i) q^{54} +(22.2785 - 38.5875i) q^{55} +(-14.4154 + 8.32275i) q^{56} +(39.7882 + 59.6367i) q^{57} +(-18.1304 - 31.4027i) q^{58} +(-55.0792 + 31.8000i) q^{59} +(62.7933 - 41.8942i) q^{60} +(25.9498 + 44.9464i) q^{61} +(103.268 + 59.6218i) q^{62} +(-44.5638 - 58.2437i) q^{63} +83.9184 q^{64} +(67.7474 - 16.3952i) q^{65} +(-40.7942 - 61.1445i) q^{66} +(-16.1943 + 28.0493i) q^{67} +(-64.8075 - 37.4166i) q^{68} +(-10.4790 - 5.17671i) q^{69} +128.815 q^{70} +(-29.1922 + 16.8541i) q^{71} +(-2.37444 - 18.2309i) q^{72} -50.2185 q^{73} +(-5.97108 + 3.44741i) q^{74} +(-11.2222 + 0.727728i) q^{75} +(-56.0727 + 97.1208i) q^{76} -67.7153i q^{77} +(25.2507 - 112.179i) q^{78} -89.8735 q^{79} +(-59.1971 - 34.1775i) q^{80} +(78.2978 - 20.7473i) q^{81} +(-71.3870 - 123.646i) q^{82} -12.8679i q^{83} +(50.8103 - 102.853i) q^{84} +(42.7500 + 74.0452i) q^{85} +162.770i q^{86} +(33.0795 + 16.3415i) q^{87} +(8.48782 - 14.7013i) q^{88} +(29.3126 + 16.9237i) q^{89} +(-54.6288 + 131.370i) q^{90} +(76.7066 - 73.0577i) q^{91} -18.2832i q^{92} +(-121.078 + 7.85157i) q^{93} +(-104.990 + 181.848i) q^{94} +(110.964 - 64.0654i) q^{95} +(-114.193 + 76.1870i) q^{96} +(47.3560 + 82.0230i) q^{97} +(44.4243 - 25.6484i) q^{98} +(69.0583 + 28.7171i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} + 10 q^{4} - 12 q^{6} - 16 q^{7} + 6 q^{9}+O(q^{10}) \) 12 * q - 4 * q^3 + 10 * q^4 - 12 * q^6 - 16 * q^7 + 6 * q^9	\( 12 q - 4 q^{3} + 10 q^{4} - 12 q^{6} - 16 q^{7} + 6 q^{9} - 6 q^{10} - 34 q^{13} + 2 q^{15} + 50 q^{16} - 80 q^{18} + 84 q^{19} - 100 q^{21} - 40 q^{22} + 48 q^{24} + 8 q^{25} + 128 q^{27} + 12 q^{28} + 142 q^{30} + 32 q^{31} + 14 q^{33} - 124 q^{34} + 74 q^{36} - 90 q^{37} + 138 q^{39} + 4 q^{40} - 78 q^{42} - 76 q^{43} - 152 q^{45} - 100 q^{46} + 56 q^{48} + 62 q^{49} - 368 q^{51} - 456 q^{52} - 144 q^{54} + 152 q^{55} - 36 q^{57} + 238 q^{58} + 324 q^{60} + 38 q^{61} + 220 q^{63} + 476 q^{64} - 252 q^{66} + 24 q^{67} + 242 q^{69} + 896 q^{70} + 12 q^{72} - 580 q^{73} + 20 q^{75} - 320 q^{76} + 464 q^{78} + 80 q^{79} - 102 q^{81} - 570 q^{82} - 250 q^{84} + 278 q^{85} + 70 q^{87} - 12 q^{88} - 852 q^{90} - 124 q^{91} - 300 q^{93} - 184 q^{94} - 928 q^{96} + 120 q^{97} + 384 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 + 10 * q^4 - 12 * q^6 - 16 * q^7 + 6 * q^9 - 6 * q^10 - 34 * q^13 + 2 * q^15 + 50 * q^16 - 80 * q^18 + 84 * q^19 - 100 * q^21 - 40 * q^22 + 48 * q^24 + 8 * q^25 + 128 * q^27 + 12 * q^28 + 142 * q^30 + 32 * q^31 + 14 * q^33 - 124 * q^34 + 74 * q^36 - 90 * q^37 + 138 * q^39 + 4 * q^40 - 78 * q^42 - 76 * q^43 - 152 * q^45 - 100 * q^46 + 56 * q^48 + 62 * q^49 - 368 * q^51 - 456 * q^52 - 144 * q^54 + 152 * q^55 - 36 * q^57 + 238 * q^58 + 324 * q^60 + 38 * q^61 + 220 * q^63 + 476 * q^64 - 252 * q^66 + 24 * q^67 + 242 * q^69 + 896 * q^70 + 12 * q^72 - 580 * q^73 + 20 * q^75 - 320 * q^76 + 464 * q^78 + 80 * q^79 - 102 * q^81 - 570 * q^82 - 250 * q^84 + 278 * q^85 + 70 * q^87 - 12 * q^88 - 852 * q^90 - 124 * q^91 - 300 * q^93 - 184 * q^94 - 928 * q^96 + 120 * q^97 + 384 * q^99

Introduction

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