LMFDB - Embedded newform 273.3.bo.c.160.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,3,Mod(160,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("273.160");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	273.bo (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:	$7.43871121704$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			160.5
Character	$\chi$	$=$	273.160
Dual form			273.3.bo.c.244.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23101 - 1.28808i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.31828 + 2.28333i) q^{4} +8.28362 q^{5} +(2.23101 + 3.86423i) q^{6} +(-1.15847 + 6.90347i) q^{7} +3.51244i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-2.23101 - 1.28808i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.31828 + 2.28333i) q^{4} +8.28362 q^{5} +(2.23101 + 3.86423i) q^{6} +(-1.15847 + 6.90347i) q^{7} +3.51244i q^{8} +(1.50000 + 2.59808i) q^{9} +(-18.4809 - 10.6699i) q^{10} +(-6.63313 - 3.82964i) q^{11} -4.56665i q^{12} +(-12.6362 + 3.05381i) q^{13} +(11.4768 - 13.9095i) q^{14} +(-12.4254 - 7.17383i) q^{15} +(9.79740 - 16.9696i) q^{16} +(-22.5309 + 13.0082i) q^{17} -7.72845i q^{18} +(-11.1976 - 19.3948i) q^{19} +(10.9201 + 18.9142i) q^{20} +(7.71629 - 9.35194i) q^{21} +(9.86573 + 17.0879i) q^{22} +(-16.6714 + 28.8758i) q^{23} +(3.04186 - 5.26865i) q^{24} +43.6184 q^{25} +(32.1251 + 9.46332i) q^{26} -5.19615i q^{27} +(-17.2901 + 6.45553i) q^{28} +(-11.2274 + 19.4464i) q^{29} +(18.4809 + 32.0098i) q^{30} -39.3539 q^{31} +(-31.5488 + 18.2147i) q^{32} +(6.63313 + 11.4889i) q^{33} +67.0223 q^{34} +(-9.59634 + 57.1858i) q^{35} +(-3.95484 + 6.84998i) q^{36} +(7.35303 + 4.24527i) q^{37} +57.6934i q^{38} +(21.5990 + 6.36257i) q^{39} +29.0957i q^{40} +(-16.0214 + 27.7499i) q^{41} +(-29.2612 + 10.9251i) q^{42} +(-15.6700 - 27.1412i) q^{43} -20.1941i q^{44} +(12.4254 + 21.5215i) q^{45} +(74.3883 - 42.9481i) q^{46} +31.6325 q^{47} +(-29.3922 + 16.9696i) q^{48} +(-46.3159 - 15.9950i) q^{49} +(-97.3132 - 56.1838i) q^{50} +45.0618 q^{51} +(-23.6309 - 24.8268i) q^{52} +93.4856 q^{53} +(-6.69304 + 11.5927i) q^{54} +(-54.9463 - 31.7233i) q^{55} +(-24.2480 - 4.06906i) q^{56} +38.7896i q^{57} +(50.0970 - 28.9235i) q^{58} +(-4.85138 - 8.40284i) q^{59} -37.8284i q^{60} +(11.6324 - 6.71600i) q^{61} +(87.7990 + 50.6908i) q^{62} +(-19.6735 + 7.34541i) q^{63} +15.4685 q^{64} +(-104.674 + 25.2966i) q^{65} -34.1759i q^{66} +(49.5118 + 28.5857i) q^{67} +(-59.4040 - 34.2969i) q^{68} +(50.0143 - 28.8758i) q^{69} +(95.0692 - 115.221i) q^{70} +(-30.2202 + 17.4476i) q^{71} +(-9.12557 + 5.26865i) q^{72} +57.2114 q^{73} +(-10.9365 - 18.9425i) q^{74} +(-65.4276 - 37.7746i) q^{75} +(29.5231 - 51.1355i) q^{76} +(34.1221 - 41.3551i) q^{77} +(-39.9922 - 42.0162i) q^{78} -59.4292 q^{79} +(81.1579 - 140.570i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(71.4880 - 41.2736i) q^{82} -128.485 q^{83} +(31.5258 + 5.29033i) q^{84} +(-186.637 + 107.755i) q^{85} +80.7364i q^{86} +(33.6822 - 19.4464i) q^{87} +(13.4514 - 23.2984i) q^{88} +(-25.4040 + 44.0010i) q^{89} -64.0196i q^{90} +(-6.44321 - 90.7716i) q^{91} -87.9103 q^{92} +(59.0308 + 34.0814i) q^{93} +(-70.5726 - 40.7451i) q^{94} +(-92.7567 - 160.659i) q^{95} +63.0976 q^{96} +(-29.7641 - 51.5529i) q^{97} +(82.7286 + 95.3433i) q^{98} -22.9778i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	$ 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) $ 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−2.23101	−	1.28808i	−1.11551	−	0.644038i	−0.175256	−	0.984523i	$-0.556075\pi$
$2$	−2.23101	−	1.28808i	−1.11551	−	0.644038i	−0.940250	+	0.340485i	$0.889409\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i
$4$	1.31828	+	2.28333i	0.329570	+	0.570831i
$5$	8.28362			1.65672			0.828362	−	0.560193i	$-0.189273\pi$
$5$	8.28362			1.65672			0.828362	+	0.560193i	$0.189273\pi$
$6$	2.23101	+	3.86423i	0.371835	+	0.644038i
$7$	−1.15847	+	6.90347i	−0.165496	+	0.986210i
$7$	−1.15847	+	6.90347i	−0.165496	+	0.986210i
$8$			3.51244i			0.439054i
$9$	1.50000	+	2.59808i	0.166667	+	0.288675i
$10$	−18.4809	−	10.6699i	−1.84809	−	1.06699i
$11$	−6.63313	−	3.82964i	−0.603011	−	0.348149i	0.167214	−	0.985921i	$-0.446523\pi$
$11$	−6.63313	−	3.82964i	−0.603011	−	0.348149i	−0.770225	+	0.637772i	$0.779856\pi$
$12$		−	4.56665i		−	0.380554i
$13$	−12.6362	+	3.05381i	−0.972017	+	0.234909i
$13$	−12.6362	+	3.05381i	−0.972017	+	0.234909i
$14$	11.4768	−	13.9095i	0.819769	−	0.993538i
$15$	−12.4254	−	7.17383i	−0.828362	−	0.478255i
$16$	9.79740	−	16.9696i	0.612337	−	1.06060i
$17$	−22.5309	+	13.0082i	−1.32535	+	0.765189i	−0.984576	−	0.174958i	$-0.944021\pi$
$17$	−22.5309	+	13.0082i	−1.32535	+	0.765189i	−0.340770	+	0.940147i	$0.610688\pi$
$18$		−	7.72845i		−	0.429359i
$19$	−11.1976	−	19.3948i	−0.589347	−	1.02078i	−0.994318	−	0.106450i	$-0.966052\pi$
$19$	−11.1976	−	19.3948i	−0.589347	−	1.02078i	0.404971	−	0.914330i	$-0.367282\pi$
$20$	10.9201	+	18.9142i	0.546006	+	0.945710i
$21$	7.71629	−	9.35194i	0.367442	−	0.445331i
$22$	9.86573	+	17.0879i	0.448442	+	0.776725i
$23$	−16.6714	+	28.8758i	−0.724845	+	1.25547i	0.234193	+	0.972190i	$0.424755\pi$
$23$	−16.6714	+	28.8758i	−0.724845	+	1.25547i	−0.959038	+	0.283278i	$0.908578\pi$
$24$	3.04186	−	5.26865i	0.126744	−	0.219527i
$25$	43.6184			1.74474
$26$	32.1251	+	9.46332i	1.23558	+	0.363974i
$27$		−	5.19615i		−	0.192450i
$28$	−17.2901	+	6.45553i	−0.617502	+	0.230555i
$29$	−11.2274	+	19.4464i	−0.387152	+	0.670567i	−0.992065	−	0.125724i	$-0.959875\pi$
$29$	−11.2274	+	19.4464i	−0.387152	+	0.670567i	0.604913	+	0.796292i	$0.293208\pi$
$30$	18.4809	+	32.0098i	0.616029	+	1.06699i
$31$	−39.3539			−1.26948			−0.634740	−	0.772726i	$-0.718893\pi$
$31$	−39.3539			−1.26948			−0.634740	+	0.772726i	$0.718893\pi$
$32$	−31.5488	+	18.2147i	−0.985900	+	0.569210i
$33$	6.63313	+	11.4889i	0.201004	+	0.348149i
$34$	67.0223			1.97124
$35$	−9.59634	+	57.1858i	−0.274181	+	1.63388i
$36$	−3.95484	+	6.84998i	−0.109857	+	0.190277i
$37$	7.35303	+	4.24527i	0.198731	+	0.114737i	0.596063	−	0.802937i	$-0.296731\pi$
$37$	7.35303	+	4.24527i	0.198731	+	0.114737i	−0.397333	+	0.917675i	$0.630064\pi$
$38$			57.6934i			1.51825i
$39$	21.5990	+	6.36257i	0.553821	+	0.163143i
$40$			29.0957i			0.727392i
$41$	−16.0214	+	27.7499i	−0.390767	+	0.676828i	−0.992551	−	0.121831i	$-0.961123\pi$
$41$	−16.0214	+	27.7499i	−0.390767	+	0.676828i	0.601784	+	0.798659i	$0.294457\pi$
$42$	−29.2612	+	10.9251i	−0.696694	+	0.260122i
$43$	−15.6700	−	27.1412i	−0.364418	−	0.631190i	0.624265	−	0.781213i	$-0.285399\pi$
$43$	−15.6700	−	27.1412i	−0.364418	−	0.631190i	−0.988683	+	0.150023i	$0.952065\pi$
$44$		−	20.1941i		−	0.458957i
$45$	12.4254	+	21.5215i	0.276121	+	0.478255i
$46$	74.3883	−	42.9481i	1.61714	−	0.933655i
$47$	31.6325			0.673033			0.336516	−	0.941678i	$-0.390751\pi$
$47$	31.6325			0.673033			0.336516	+	0.941678i	$0.390751\pi$
$48$	−29.3922	+	16.9696i	−0.612337	+	0.353533i
$49$	−46.3159	−	15.9950i	−0.945222	−	0.326428i
$50$	−97.3132	−	56.1838i	−1.94626	−	1.12368i
$51$	45.0618			0.883564
$52$	−23.6309	−	24.8268i	−0.454441	−	0.477439i
$53$	93.4856			1.76388			0.881939	−	0.471363i	$-0.156238\pi$
$53$	93.4856			1.76388			0.881939	+	0.471363i	$0.156238\pi$
$54$	−6.69304	+	11.5927i	−0.123945	+	0.214679i
$55$	−54.9463	−	31.7233i	−0.999024	−	0.576787i
$56$	−24.2480	−	4.06906i	−0.433000	−	0.0726617i
$57$			38.7896i			0.680520i
$58$	50.0970	−	28.9235i	0.863741	−	0.498681i
$59$	−4.85138	−	8.40284i	−0.0822269	−	0.142421i	0.821979	−	0.569517i	$-0.192870\pi$
$59$	−4.85138	−	8.40284i	−0.0822269	−	0.142421i	−0.904206	+	0.427096i	$0.859537\pi$
$60$		−	37.8284i		−	0.630474i
$61$	11.6324	−	6.71600i	0.190696	−	0.110098i	−0.401612	−	0.915810i	$-0.631550\pi$
$61$	11.6324	−	6.71600i	0.190696	−	0.110098i	0.592308	+	0.805711i	$0.298217\pi$
$62$	87.7990	+	50.6908i	1.41611	+	0.817593i
$63$	−19.6735	+	7.34541i	−0.312277	+	0.116594i
$64$	15.4685			0.241696
$65$	−104.674	+	25.2966i	−1.61036	+	0.389179i
$66$		−	34.1759i		−	0.517816i
$67$	49.5118	+	28.5857i	0.738983	+	0.426652i	0.821699	−	0.569921i	$-0.193026\pi$
$67$	49.5118	+	28.5857i	0.738983	+	0.426652i	−0.0827167	+	0.996573i	$0.526360\pi$
$68$	−59.4040	−	34.2969i	−0.873588	−	0.504366i
$69$	50.0143	−	28.8758i	0.724845	−	0.418489i
$70$	95.0692	−	115.221i	1.35813	−	1.64602i
$71$	−30.2202	+	17.4476i	−0.425636	+	0.245741i	−0.697486	−	0.716599i	$-0.745698\pi$
$71$	−30.2202	+	17.4476i	−0.425636	+	0.245741i	0.271850	+	0.962340i	$0.412365\pi$
$72$	−9.12557	+	5.26865i	−0.126744	+	0.0731757i
$73$	57.2114			0.783718			0.391859	−	0.920025i	$-0.371832\pi$
$73$	57.2114			0.783718			0.391859	+	0.920025i	$0.371832\pi$
$74$	−10.9365	−	18.9425i	−0.147790	−	0.255980i
$75$	−65.4276	−	37.7746i	−0.872368	−	0.503662i
$76$	29.5231	−	51.1355i	0.388462	−	0.672836i
$77$	34.1221	−	41.3551i	0.443144	−	0.537079i
$78$	−39.9922	−	42.0162i	−0.512721	−	0.538669i
$79$	−59.4292			−0.752268			−0.376134	−	0.926565i	$-0.622747\pi$
$79$	−59.4292			−0.752268			−0.376134	+	0.926565i	$0.622747\pi$
$80$	81.1579	−	140.570i	1.01447	−	1.75712i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	71.4880	−	41.2736i	0.871805	−	0.503337i
$83$	−128.485			−1.54802			−0.774008	−	0.633176i	$-0.781751\pi$
$83$	−128.485			−1.54802			−0.774008	+	0.633176i	$0.781751\pi$
$84$	31.5258	+	5.29033i	0.375307	+	0.0629802i
$85$	−186.637	+	107.755i	−2.19573	+	1.26771i
$86$			80.7364i			0.938795i
$87$	33.6822	−	19.4464i	0.387152	−	0.223522i
$88$	13.4514	−	23.2984i	0.152856	−	0.264755i
$89$	−25.4040	+	44.0010i	−0.285438	+	0.494394i	−0.972715	−	0.232002i	$-0.925472\pi$
$89$	−25.4040	+	44.0010i	−0.285438	+	0.494394i	0.687277	+	0.726395i	$0.258806\pi$
$90$		−	64.0196i		−	0.711329i
$91$	−6.44321	−	90.7716i	−0.0708045	−	0.997490i
$92$	−87.9103			−0.955547
$93$	59.0308	+	34.0814i	0.634740	+	0.366467i
$94$	−70.5726	−	40.7451i	−0.750772	−	0.433458i
$95$	−92.7567	−	160.659i	−0.976386	−	1.69115i
$96$	63.0976			0.657267
$97$	−29.7641	−	51.5529i	−0.306846	−	0.531474i	0.670824	−	0.741616i	$-0.265940\pi$
$97$	−29.7641	−	51.5529i	−0.306846	−	0.531474i	−0.977671	+	0.210143i	$0.932607\pi$
$98$	82.7286	+	95.3433i	0.844170	+	0.972891i
$99$		−	22.9778i		−	0.232099i
$100$	57.5012	+	99.5950i	0.575012	+	0.995950i
$101$	75.6269	+	43.6632i	0.748781	+	0.432309i	0.825253	−	0.564763i	$-0.191032\pi$
$101$	75.6269	+	43.6632i	0.748781	+	0.432309i	−0.0764723	+	0.997072i	$0.524366\pi$
$102$	−100.533	−	58.0430i	−0.985621	−	0.569049i
$103$		−	25.4004i		−	0.246606i	−0.992369	−	0.123303i	$-0.960651\pi$
$103$		−	25.4004i		−	0.246606i	0.992369	−	0.123303i	$-0.0393487\pi$
$104$	−10.7263	−	44.3839i	−0.103138	−	0.426769i
$105$	63.9188	−	77.4680i	0.608751	−	0.737790i
$106$	−208.568	−	120.417i	−1.96762	−	1.13600i
$107$	38.9234	−	67.4174i	0.363770	−	0.630069i	−0.624808	−	0.780779i	$-0.714823\pi$
$107$	38.9234	−	67.4174i	0.363770	−	0.630069i	0.988578	+	0.150710i	$0.0481560\pi$
$108$	11.8645	−	6.84998i	0.109857	−	0.0634257i
$109$			206.192i			1.89167i	0.324646	+	0.945835i	$0.394755\pi$
$109$			206.192i			1.89167i	−0.324646	+	0.945835i	$0.605245\pi$
$110$	81.7239	+	141.550i	0.742945	+	1.28682i
$111$	−7.35303	−	12.7358i	−0.0662435	−	0.114737i
$112$	105.799	+	87.2949i	0.944635	+	0.779418i
$113$	94.1495	+	163.072i	0.833181	+	1.44311i	0.895503	+	0.445056i	$0.146816\pi$
$113$	94.1495	+	163.072i	0.833181	+	1.44311i	−0.0623219	+	0.998056i	$0.519851\pi$
$114$	49.9640	−	86.5401i	0.438280	−	0.759124i
$115$	−138.100	+	239.196i	−1.20087	+	2.07996i
$116$	−59.2034			−0.510374
$117$	−26.8884	−	28.2492i	−0.229815	−	0.241446i
$118$			24.9958i			0.211829i
$119$	−63.7005	−	170.611i	−0.535298	−	1.43371i
$120$	25.1976	−	43.6435i	0.209980	−	0.363696i
$121$	−31.1678	−	53.9841i	−0.257585	−	0.446150i
$122$	−34.6029			−0.283630
$123$	48.0643	−	27.7499i	0.390767	−	0.225609i
$124$	−51.8794	−	89.8577i	−0.418382	−	0.724659i
$125$	154.228			1.23382
$126$	53.3532	+	8.95319i	0.423438	+	0.0710571i
$127$	9.39640	−	16.2750i	0.0739874	−	0.128150i	−0.826658	−	0.562705i	$-0.809761\pi$
$127$	9.39640	−	16.2750i	0.0739874	−	0.128150i	0.900645	+	0.434555i	$0.143094\pi$
$128$	91.6847	+	52.9342i	0.716287	+	0.413548i
$129$			54.2823i			0.420793i
$130$	266.112	+	78.3906i	2.04702	+	0.603004i
$131$		−	148.964i		−	1.13713i	−0.822639	−	0.568564i	$-0.807499\pi$
$131$		−	148.964i		−	1.13713i	0.822639	−	0.568564i	$-0.192501\pi$
$132$	−17.4886	+	30.2912i	−0.132490	+	0.229479i
$133$	146.864	−	54.8340i	1.10424	−	0.412286i
$134$	−73.6410	−	127.550i	−0.549560	−	0.951866i
$135$		−	43.0430i		−	0.318837i
$136$	−45.6905	−	79.1383i	−0.335960	−	0.581899i
$137$	45.8847	−	26.4915i	0.334925	−	0.193369i	−0.323101	−	0.946365i	$-0.604725\pi$
$137$	45.8847	−	26.4915i	0.334925	−	0.193369i	0.658025	+	0.752996i	$0.271392\pi$
$138$	−148.777			−1.07809
$139$	−1.95128	+	1.12657i	−0.0140380	+	0.00810482i	−0.507003	−	0.861945i	$-0.669247\pi$
$139$	−1.95128	+	1.12657i	−0.0140380	+	0.00810482i	0.492965	+	0.870049i	$0.335913\pi$
$140$	−143.224	+	53.4752i	−1.02303	+	0.381966i
$141$	−47.4488	−	27.3946i	−0.336516	−	0.194288i
$142$	89.8954			0.633066
$143$	95.5127	+	28.1358i	0.667921	+	0.196754i
$144$	58.7844			0.408225
$145$	−93.0036	+	161.087i	−0.641404	+	1.11094i
$146$	−127.639	−	73.6926i	−0.874242	−	0.504744i
$147$	55.6218	+	64.1032i	0.378380	+	0.436076i
$148$			22.3858i			0.151256i
$149$	151.125	−	87.2523i	1.01426	−	0.585586i	0.101827	−	0.994802i	$-0.467531\pi$
$149$	151.125	−	87.2523i	1.01426	−	0.585586i	0.912437	+	0.409216i	$0.134198\pi$
$150$	97.3132	+	168.551i	0.648755	+	1.12368i
$151$			181.423i			1.20148i	0.799445	+	0.600740i	$0.205127\pi$
$151$			181.423i			1.20148i	−0.799445	+	0.600740i	$0.794873\pi$
$152$	68.1230	−	39.3308i	0.448178	−	0.258755i
$153$	−67.5927	−	39.0246i	−0.441782	−	0.255063i
$154$	−129.395	+	48.3119i	−0.840229	+	0.313714i
$155$	−325.992			−2.10318
$156$	13.9457	+	57.7052i	0.0893955	+	0.369905i
$157$		−	8.01044i		−	0.0510219i	−0.999675	−	0.0255110i	$-0.991879\pi$
$157$		−	8.01044i		−	0.0510219i	0.999675	−	0.0255110i	$-0.00812127\pi$
$158$	132.587	+	76.5493i	0.839160	+	0.484489i
$159$	−140.228	−	80.9609i	−0.881939	−	0.509188i
$160$	−261.338	+	150.884i	−1.63336	+	0.943024i
$161$	−180.030	−	148.542i	−1.11820	−	0.922624i
$162$	20.0791	−	11.5927i	0.123945	−	0.0715598i
$163$	70.4503	−	40.6745i	0.432210	−	0.249537i	−0.268078	−	0.963397i	$-0.586388\pi$
$163$	70.4503	−	40.6745i	0.432210	−	0.249537i	0.700288	+	0.713861i	$0.253055\pi$
$164$	−84.4828			−0.515139
$165$	54.9463	+	95.1698i	0.333008	+	0.576787i
$166$	286.652	+	165.499i	1.72682	+	0.996981i
$167$	−148.794	+	257.720i	−0.890985	+	1.54323i	−0.0522882	+	0.998632i	$0.516651\pi$
$167$	−148.794	+	257.720i	−0.890985	+	1.54323i	−0.838697	+	0.544599i	$0.816682\pi$
$168$	32.8481	+	27.1030i	0.195524	+	0.161327i
$169$	150.348	−	77.1773i	0.889636	−	0.456671i
$170$	555.187			3.26581
$171$	33.5928	−	58.1844i	0.196449	−	0.340260i
$172$	41.3147	−	71.5592i	0.240202	−	0.416042i
$173$	−90.8869	+	52.4736i	−0.525358	+	0.303316i	−0.739124	−	0.673569i	$-0.764760\pi$
$173$	−90.8869	+	52.4736i	−0.525358	+	0.303316i	0.213766	+	0.976885i	$0.431427\pi$
$174$	−100.194			−0.575828
$175$	−50.5307	+	301.118i	−0.288747	+	1.72068i
$176$	−129.975	+	75.0410i	−0.738493	+	0.426369i
$177$			16.8057i			0.0949474i
$178$	113.353	−	65.4446i	0.636816	−	0.367666i
$179$	−50.2388	+	87.0162i	−0.280664	+	0.486124i	−0.971548	−	0.236841i	$-0.923888\pi$
$179$	−50.2388	+	87.0162i	−0.280664	+	0.486124i	0.690884	+	0.722965i	$0.257221\pi$
$180$	−32.7604	+	56.7426i	−0.182002	+	0.315237i
$181$		−	156.777i		−	0.866169i	−0.901353	−	0.433085i	$-0.857425\pi$
$181$		−	156.777i		−	0.866169i	0.901353	−	0.433085i	$-0.142575\pi$
$182$	−102.546	+	210.812i	−0.563439	+	1.15831i
$183$	−23.2649			−0.127131
$184$	−101.424	−	58.5573i	−0.551219	−	0.318246i
$185$	60.9097	+	35.1662i	0.329242	+	0.190088i
$186$	−87.7990	−	152.072i	−0.472037	−	0.817593i
$187$	199.267			1.06560
$188$	41.7005	+	72.2274i	0.221811	+	0.384188i
$189$	35.8715	+	6.01959i	0.189796	+	0.0318497i
$190$			477.910i			2.51532i
$191$	96.2326	+	166.680i	0.503835	+	0.872669i	0.999990	+	0.00443441i	$0.00141152\pi$
$191$	96.2326	+	166.680i	0.503835	+	0.872669i	−0.496155	+	0.868234i	$0.665255\pi$
$192$	−23.2028	−	13.3961i	−0.120848	−	0.0697716i
$193$	−292.674	−	168.975i	−1.51644	−	0.875520i	−0.999814	−	0.0193112i	$-0.993853\pi$
$193$	−292.674	−	168.975i	−1.51644	−	0.875520i	−0.516631	−	0.856208i	$-0.672814\pi$
$194$			153.354i			0.790483i
$195$	178.918	+	52.7052i	0.917529	+	0.270283i
$196$	−24.5356	−	126.840i	−0.125181	−	0.647143i
$197$	44.1470	+	25.4883i	0.224096	+	0.129382i	0.607846	−	0.794055i	$-0.292034\pi$
$197$	44.1470	+	25.4883i	0.224096	+	0.129382i	−0.383749	+	0.923437i	$0.625367\pi$
$198$	−29.5972	+	51.2638i	−0.149481	+	0.258908i
$199$	75.3360	−	43.4953i	0.378573	−	0.218569i	−0.298624	−	0.954371i	$-0.596528\pi$
$199$	75.3360	−	43.4953i	0.378573	−	0.218569i	0.677197	+	0.735802i	$0.263194\pi$
$200$			153.207i			0.766034i
$201$	−49.5118	−	85.7570i	−0.246328	−	0.426652i
$202$	−112.483	−	194.826i	−0.556847	−	0.964487i
$203$	−121.241	−	100.036i	−0.597248	−	0.492790i
$204$	59.4040	+	102.891i	0.291196	+	0.504366i
$205$	−132.715	+	229.870i	−0.647393	+	1.12132i
$206$	−32.7176	+	56.6686i	−0.158823	+	0.275090i
$207$	−100.029			−0.483230
$208$	−71.9802	+	244.351i	−0.346059	+	1.17476i
$209$			171.531i			0.820722i
$210$	−242.388	+	90.4997i	−1.15423	+	0.430951i
$211$	147.886	−	256.145i	0.700879	−	1.21396i	−0.267279	−	0.963619i	$-0.586124\pi$
$211$	147.886	−	256.145i	0.700879	−	1.21396i	0.968158	−	0.250340i	$-0.0805423\pi$
$212$	123.240	+	213.458i	0.581321	+	1.00688i
$213$	60.4403			0.283757
$214$	−173.677	+	100.273i	−0.811576	+	0.468564i
$215$	−129.804	−	224.827i	−0.603740	−	1.04571i
$216$	18.2511			0.0844961
$217$	45.5903	−	271.678i	0.210094	−	1.25197i
$218$	265.591	−	460.017i	1.21831	−	2.11017i
$219$	−85.8171	−	49.5465i	−0.391859	−	0.226240i
$220$		−	167.280i		−	0.760366i
$221$	244.981	−	233.180i	1.10851	−	1.05511i
$222$			37.8850i			0.170653i
$223$	−142.987	+	247.660i	−0.641195	+	1.11058i	0.343971	+	0.938980i	$0.388228\pi$
$223$	−142.987	+	247.660i	−0.641195	+	1.11058i	−0.985166	+	0.171603i	$0.945105\pi$
$224$	−89.1964	−	238.898i	−0.398198	−	1.06651i
$225$	65.4276	+	113.324i	0.290789	+	0.503662i
$226$		−	485.087i		−	2.14640i
$227$	−113.416	−	196.443i	−0.499632	−	0.865387i	0.500368	−	0.865813i	$-0.333198\pi$
$227$	−113.416	−	196.443i	−0.499632	−	0.865387i	−1.00000		0.000425321i	$0.999865\pi$
$228$	−88.5693	+	51.1355i	−0.388462	+	0.224279i
$229$	71.0201			0.310132			0.155066	−	0.987904i	$-0.450441\pi$
$229$	71.0201			0.310132			0.155066	+	0.987904i	$0.450441\pi$
$230$	616.205	−	355.766i	2.67915	−	1.54681i
$231$	−86.9977	+	32.4820i	−0.376613	+	0.140615i
$232$	−68.3044	−	39.4356i	−0.294415	−	0.169981i
$233$	242.401			1.04035			0.520175	−	0.854060i	$-0.325867\pi$
$233$	242.401			1.04035			0.520175	+	0.854060i	$0.325867\pi$
$234$	23.6013	+	97.6585i	0.100860	+	0.417344i
$235$	262.032			1.11503
$236$	12.7910	−	22.1546i	0.0541990	−	0.0938753i
$237$	89.1437	+	51.4672i	0.376134	+	0.217161i
$238$	−77.6434	+	462.686i	−0.326233	+	1.94406i
$239$			424.333i			1.77545i	0.460374	+	0.887725i	$0.347715\pi$
$239$			424.333i			1.77545i	−0.460374	+	0.887725i	$0.652285\pi$
$240$	−243.474	+	140.570i	−1.01447	+	0.585707i
$241$	−125.182	−	216.821i	−0.519427	−	0.899674i	−0.999745	−	0.0225796i	$-0.992812\pi$
$241$	−125.182	−	216.821i	−0.519427	−	0.899674i	0.480318	−	0.877094i	$-0.340521\pi$
$242$			160.586i			0.663577i
$243$	13.5000	−	7.79423i	0.0555556	−	0.0320750i
$244$	30.6696	+	17.7071i	0.125695	+	0.0725701i
$245$	−383.663	−	132.496i	−1.56597	−	0.540801i
$246$	−142.976			−0.581204
$247$	200.723	+	210.882i	0.812646	+	0.853772i
$248$		−	138.228i		−	0.557370i
$249$	192.728	+	111.272i	0.774008	+	0.446874i
$250$	−344.084	−	198.657i	−1.37634	−	0.794628i
$251$	269.763	−	155.748i	1.07475	−	0.620510i	0.145278	−	0.989391i	$-0.453592\pi$
$251$	269.763	−	155.748i	1.07475	−	0.620510i	0.929477	+	0.368881i	$0.120259\pi$
$252$	−42.7071	−	35.2376i	−0.169472	−	0.139832i
$253$	221.167	−	127.691i	0.874179	−	0.504708i
$254$	−41.9270	+	24.2066i	−0.165067	+	0.0953014i
$255$	373.275			1.46382
$256$	−167.304	−	289.778i	−0.653530	−	1.13195i
$257$	−279.168	−	161.178i	−1.08626	−	0.627150i	−0.153679	−	0.988121i	$-0.549112\pi$
$257$	−279.168	−	161.178i	−1.08626	−	0.627150i	−0.932577	+	0.360971i	$0.882445\pi$
$258$	69.9198	−	121.105i	0.271007	−	0.469398i
$259$	−37.8254	+	45.8434i	−0.146044	+	0.177002i
$260$	−195.750	−	205.656i	−0.752883	−	0.790985i
$261$	−67.3645			−0.258101
$262$	−191.877	+	332.340i	−0.732353	+	1.26847i
$263$	−47.5391	+	82.3401i	−0.180757	+	0.313080i	−0.942139	−	0.335224i	$-0.891188\pi$
$263$	−47.5391	+	82.3401i	−0.180757	+	0.313080i	0.761382	+	0.648304i	$0.224521\pi$
$264$	−40.3541	+	23.2984i	−0.152856	+	0.0882516i
$265$	774.399			2.92226
$266$	−398.285	−	66.8362i	−1.49731	−	0.251264i
$267$	76.2120	−	44.0010i	0.285438	−	0.164798i
$268$			150.736i			0.562446i
$269$	16.7376	−	9.66348i	0.0622217	−	0.0359237i	−0.468566	−	0.883428i	$-0.655229\pi$
$269$	16.7376	−	9.66348i	0.0622217	−	0.0359237i	0.530788	+	0.847505i	$0.321896\pi$
$270$	−55.4426	+	96.0294i	−0.205343	+	0.355664i
$271$	188.759	−	326.940i	0.696527	−	1.20642i	−0.273137	−	0.961975i	$-0.588061\pi$
$271$	188.759	−	326.940i	0.696527	−	1.20642i	0.969663	−	0.244444i	$-0.0786055\pi$
$272$			509.787i			1.87422i
$273$	−68.9457	+	141.737i	−0.252548	+	0.519185i
$274$	−136.492			−0.498148
$275$	−289.326	−	167.043i	−1.05210	−	0.607428i
$276$	131.866	+	76.1326i	0.477774	+	0.275843i
$277$	−28.1823	−	48.8132i	−0.101741	−	0.176221i	0.810661	−	0.585516i	$-0.199108\pi$
$277$	−28.1823	−	48.8132i	−0.101741	−	0.176221i	−0.912402	+	0.409295i	$0.865775\pi$
$278$	5.80443			0.0208792
$279$	−59.0308	−	102.244i	−0.211580	−	0.366467i
$280$	−200.861	−	33.7065i	−0.717362	−	0.120380i
$281$		−	279.332i		−	0.994063i	−0.867732	−	0.497032i	$-0.834423\pi$
$281$		−	279.332i		−	0.994063i	0.867732	−	0.497032i	$-0.165577\pi$
$282$	70.5726	+	122.235i	0.250257	+	0.433458i
$283$	−220.541	−	127.329i	−0.779295	−	0.449926i	0.0568851	−	0.998381i	$-0.481883\pi$
$283$	−220.541	−	127.329i	−0.779295	−	0.449926i	−0.836181	+	0.548454i	$0.815216\pi$
$284$	−79.6772	−	46.0016i	−0.280553	−	0.161978i
$285$			321.318i			1.12743i
$286$	−176.849	−	185.799i	−0.618353	−	0.649647i
$287$	−173.011	−	142.751i	−0.602824	−	0.497390i
$288$	−94.6464	−	54.6441i	−0.328633	−	0.189737i
$289$	193.927	−	335.892i	0.671028	−	1.16226i
$290$	414.985	−	239.591i	1.43098	−	0.826177i
$291$			103.106i			0.354316i
$292$	75.4206	+	130.632i	0.258290	+	0.447371i
$293$	83.3787	+	144.416i	0.284569	+	0.492888i	0.972505	−	0.232884i	$-0.0748162\pi$
$293$	83.3787	+	144.416i	0.284569	+	0.492888i	−0.687936	+	0.725772i	$0.741483\pi$
$294$	−41.5232	−	214.660i	−0.141235	−	0.730136i
$295$	−40.1870	−	69.6060i	−0.136227	−	0.235952i
$296$	−14.9113	+	25.8270i	−0.0503758	+	0.0872535i
$297$	−19.8994	+	34.4667i	−0.0670013	+	0.116050i
$298$	−449.550			−1.50856
$299$	122.483	−	415.792i	0.409641	−	1.39061i
$300$		−	199.190i		−	0.663967i
$301$	205.521	−	76.7349i	0.682796	−	0.254933i
$302$	233.687	−	404.758i	0.773798	−	1.34026i
$303$	−75.6269	−	130.990i	−0.249594	−	0.432309i
$304$	−438.829			−1.44352
$305$	96.3588	−	55.6328i	0.315930	−	0.182403i
$306$	100.533	+	174.129i	0.328540	+	0.569049i
$307$	−540.118			−1.75934			−0.879671	−	0.475584i	$-0.842237\pi$
$307$	−540.118			−1.75934			−0.879671	+	0.475584i	$0.842237\pi$
$308$	139.410	+	23.3943i	0.452628	+	0.0759555i
$309$	−21.9974	+	38.1006i	−0.0711889	+	0.123303i
$310$	727.293	+	419.903i	2.34611	+	1.35453i
$311$		−	3.65376i		−	0.0117484i	−0.999983	−	0.00587421i	$-0.998130\pi$
$311$		−	3.65376i		−	0.0117484i	0.999983	−	0.00587421i	$-0.00186983\pi$
$312$	−22.3481	+	75.8652i	−0.0716286	+	0.243158i
$313$			272.425i			0.870367i	0.900342	+	0.435183i	$0.143316\pi$
$313$			272.425i			0.870367i	−0.900342	+	0.435183i	$0.856684\pi$
$314$	−10.3181	+	17.8714i	−0.0328600	+	0.0569153i
$315$	−162.967	+	60.8466i	−0.517357	+	0.193164i
$316$	−78.3442	−	135.696i	−0.247925	−	0.429418i
$317$		−	331.095i		−	1.04446i	−0.852804	−	0.522232i	$-0.825100\pi$
$317$		−	331.095i		−	1.04446i	0.852804	−	0.522232i	$-0.174900\pi$
$318$	208.568	+	361.250i	0.655873	+	1.13600i
$319$	148.946	−	85.9938i	0.466914	−	0.269573i
$320$	128.136			0.400424
$321$	−116.770	+	67.4174i	−0.363770	+	0.210023i
$322$	210.314	+	563.292i	0.653150	+	1.74935i
$323$	504.584	+	291.321i	1.56218	+	0.901924i
$324$	−23.7290			−0.0732377
$325$	−551.172	+	133.202i	−1.69591	+	0.409854i
$326$	−209.567			−0.642844
$327$	178.568	−	309.288i	0.546078	−	0.945835i
$328$	−97.4698	−	56.2742i	−0.297164	−	0.171568i
$329$	−36.6454	+	218.374i	−0.111384	+	0.663752i
$330$		−	283.100i		−	0.857879i
$331$	−243.471	+	140.568i	−0.735562	+	0.424677i	−0.820453	−	0.571713i	$-0.806279\pi$
$331$	−243.471	+	140.568i	−0.735562	+	0.424677i	0.0848917	+	0.996390i	$0.472946\pi$
$332$	−169.379	−	293.374i	−0.510179	−	0.883656i
$333$			25.4716i			0.0764914i
$334$	663.925	−	383.317i	1.98780	−	1.14766i
$335$	410.137	+	236.793i	1.22429	+	0.706844i
$336$	−83.0991	−	222.567i	−0.247319	−	0.662402i
$337$	−267.433			−0.793569			−0.396784	−	0.917912i	$-0.629874\pi$
$337$	−267.433			−0.793569			−0.396784	+	0.917912i	$0.629874\pi$
$338$	−434.840	−	21.4766i	−1.28651	−	0.0635401i
$339$		−	326.143i		−	0.962075i
$340$	−492.080	−	284.103i	−1.44729	−	0.835596i
$341$	261.039	+	150.711i	0.765511	+	0.441968i
$342$	−149.892	+	86.5401i	−0.438280	+	0.253041i
$343$	164.076	−	301.211i	0.478357	−	0.878166i
$344$	95.3316	−	55.0397i	0.277127	−	0.159999i
$345$	414.299	−	239.196i	1.20087	−	0.693321i
$346$	270.360			0.781387
$347$	−34.4272	−	59.6296i	−0.0992138	−	0.171843i	0.812146	−	0.583455i	$-0.198299\pi$
$347$	−34.4272	−	59.6296i	−0.0992138	−	0.171843i	−0.911359	+	0.411611i	$0.864966\pi$
$348$	88.8051	+	51.2717i	0.255187	+	0.147332i
$349$	−199.564	+	345.654i	−0.571816	+	0.990414i	0.424564	+	0.905398i	$0.360427\pi$
$349$	−199.564	+	345.654i	−0.571816	+	0.990414i	−0.996380	+	0.0850160i	$0.972906\pi$
$350$	500.598	−	606.712i	1.43028	−	1.73346i
$351$	15.8681	+	65.6598i	0.0452082	+	0.187065i
$352$	279.023			0.792679
$353$	−312.767	+	541.728i	−0.886024	+	1.53464i	−0.0414892	+	0.999139i	$0.513210\pi$
$353$	−312.767	+	541.728i	−0.886024	+	1.53464i	−0.844535	+	0.535500i	$0.820123\pi$
$354$	21.6470	−	37.4937i	0.0611497	−	0.105914i
$355$	−250.332	+	144.529i	−0.705162	+	0.407125i
$356$	−133.958			−0.376287
$357$	−52.2028	+	311.083i	−0.146226	+	0.871380i
$358$	224.167	−	129.423i	0.626165	−	0.361516i
$359$			105.936i			0.295085i	0.989056	+	0.147542i	$0.0471363\pi$
$359$			105.936i			0.295085i	−0.989056	+	0.147542i	$0.952864\pi$
$360$	−75.5928	+	43.6435i	−0.209980	+	0.121232i
$361$	−70.2723	+	121.715i	−0.194660	+	0.337161i
$362$	−201.940	+	349.771i	−0.557846	+	0.966217i
$363$			107.968i			0.297433i
$364$	198.767	−	134.374i	0.546064	−	0.369160i
$365$	473.918			1.29840
$366$	51.9043	+	29.9670i	0.141815	+	0.0818769i
$367$	188.508	+	108.835i	0.513646	+	0.296554i	0.734331	−	0.678791i	$-0.237496\pi$
$367$	188.508	+	108.835i	0.513646	+	0.296554i	−0.220685	+	0.975345i	$0.570829\pi$
$368$	326.673	+	565.815i	0.887699	+	1.53754i
$369$	−96.1286			−0.260511
$370$	−90.5936	−	156.913i	−0.244848	−	0.424088i
$371$	−108.300	+	645.375i	−0.291915	+	1.73956i
$372$			179.715i			0.483106i
$373$	298.940	+	517.779i	0.801447	+	1.38815i	0.918664	+	0.395040i	$0.129269\pi$
$373$	298.940	+	517.779i	0.801447	+	1.38815i	−0.117217	+	0.993106i	$0.537397\pi$
$374$	−444.567	−	256.671i	−1.18868	−	0.686286i
$375$	−231.342	−	133.565i	−0.616911	−	0.356174i
$376$			111.107i			0.295498i
$377$	82.4863	−	280.016i	0.218797	−	0.742748i
$378$	−72.2761	−	59.6350i	−0.191207	−	0.157765i
$379$	209.269	+	120.822i	0.552162	+	0.318791i	0.749994	−	0.661445i	$-0.230057\pi$
$379$	209.269	+	120.822i	0.552162	+	0.318791i	−0.197831	+	0.980236i	$0.563390\pi$
$380$	244.558	−	423.587i	0.643574	−	1.11470i
$381$	−28.1892	+	16.2750i	−0.0739874	+	0.0427167i
$382$		−	495.819i		−	1.29796i
$383$	269.168	+	466.213i	0.702789	+	1.21727i	0.967483	+	0.252934i	$0.0813956\pi$
$383$	269.168	+	466.213i	0.702789	+	1.21727i	−0.264694	+	0.964332i	$0.585271\pi$
$384$	−91.6847	−	158.803i	−0.238762	−	0.413548i
$385$	282.654	−	342.570i	0.734167	−	0.889792i
$386$	435.306	+	753.972i	1.12774	+	1.95330i
$387$	47.0099	−	81.4235i	0.121473	−	0.210397i
$388$	78.4748	−	135.922i	0.202255	−	0.350315i
$389$	−291.577			−0.749556			−0.374778	−	0.927115i	$-0.622281\pi$
$389$	−291.577			−0.749556			−0.374778	+	0.927115i	$0.622281\pi$
$390$	−331.280	−	348.046i	−0.849437	−	0.892426i
$391$		−	867.462i		−	2.21857i
$392$	56.1812	−	162.682i	0.143319	−	0.415004i
$393$	−129.006	+	223.446i	−0.328260	+	0.568564i
$394$	−65.6616	−	113.729i	−0.166654	−	0.288653i
$395$	−492.289			−1.24630
$396$	52.4659	−	30.2912i	0.132490	−	0.0764929i
$397$	4.48257	+	7.76403i	0.0112911	+	0.0195568i	0.871616	−	0.490190i	$-0.163073\pi$
$397$	4.48257	+	7.76403i	0.0112911	+	0.0195568i	−0.860325	+	0.509747i	$0.829739\pi$
$398$	−224.101			−0.563067
$399$	−267.783	−	44.9367i	−0.671135	−	0.112623i
$400$	427.347	−	740.186i	1.06837	−	1.85047i
$401$	−580.368	−	335.076i	−1.44730	−	0.835601i	−0.448983	−	0.893541i	$-0.648213\pi$
$401$	−580.368	−	335.076i	−1.44730	−	0.835601i	−0.998320	+	0.0579399i	$0.981547\pi$
$402$			255.100i			0.634577i
$403$	497.284	−	120.179i	1.23396	−	0.298212i
$404$			230.241i			0.569904i
$405$	−37.2763	+	64.5644i	−0.0920402	+	0.159418i
$406$	141.637	+	379.350i	0.348859	+	0.934361i
$407$	−32.5157	−	56.3189i	−0.0798912	−	0.138376i
$408$			158.277i			0.387933i
$409$	50.6646	+	87.7536i	0.123874	+	0.214556i	0.921292	−	0.388871i	$-0.127135\pi$
$409$	50.6646	+	87.7536i	0.123874	+	0.214556i	−0.797418	+	0.603427i	$0.793801\pi$
$410$	592.180	−	341.895i	1.44434	−	0.833891i
$411$	−91.7694			−0.223283
$412$	57.9973	−	33.4848i	0.140770	−	0.0812737i
$413$	63.6290	−	23.7569i	0.154065	−	0.0575229i
$414$	223.165	+	128.844i	0.539046	+	0.311218i
$415$	−1064.32			−2.56464
$416$	343.034	−	326.509i	0.824600	−	0.784878i
$417$	3.90255			0.00935864
$418$	220.945	−	382.688i	0.528576	−	0.915521i
$419$	264.864	+	152.919i	0.632133	+	0.364962i	0.781578	−	0.623808i	$-0.214415\pi$
$419$	264.864	+	152.919i	0.632133	+	0.364962i	−0.149445	+	0.988770i	$0.547749\pi$
$420$	261.147	+	43.8231i	0.621780	+	0.104341i
$421$			29.7414i			0.0706446i	0.999376	+	0.0353223i	$0.0112458\pi$
$421$			29.7414i			0.0706446i	−0.999376	+	0.0353223i	$0.988754\pi$
$422$	−659.869	+	380.976i	−1.56367	+	0.902786i
$423$	47.4488	+	82.1837i	0.112172	+	0.194288i
$424$			328.362i			0.774439i
$425$	−982.761	+	567.397i	−2.31238	+	1.33505i
$426$	−134.843	−	77.8517i	−0.316533	−	0.182751i
$427$	32.8878	+	88.0846i	0.0770207	+	0.206287i
$428$	205.248			0.479551
$429$	−118.903	−	124.920i	−0.277162	−	0.291189i
$430$			668.790i			1.55532i
$431$	−259.911	−	150.060i	−0.603042	−	0.348167i	0.167195	−	0.985924i	$-0.446529\pi$
$431$	−259.911	−	150.060i	−0.603042	−	0.348167i	−0.770238	+	0.637757i	$0.779862\pi$
$432$	−88.1766	−	50.9088i	−0.204112	−	0.117844i
$433$	132.723	−	76.6275i	0.306519	−	0.176969i	−0.338849	−	0.940841i	$-0.610038\pi$
$433$	132.723	−	76.6275i	0.306519	−	0.176969i	0.645368	+	0.763872i	$0.276704\pi$
$434$	−451.655	+	547.394i	−1.04068	+	1.26128i
$435$	279.011	−	161.087i	0.641404	−	0.370315i
$436$	−470.804	+	271.819i	−1.07983	+	0.623437i
$437$	746.720			1.70874
$438$	127.639	+	221.078i	0.291414	+	0.504744i
$439$	516.473	+	298.186i	1.17648	+	0.679239i	0.955197	−	0.295972i	$-0.0956435\pi$
$439$	516.473	+	298.186i	1.17648	+	0.679239i	0.221279	+	0.975211i	$0.428977\pi$
$440$	111.426	−	192.995i	0.253241	−	0.438626i
$441$	−27.9177	−	144.325i	−0.0633055	−	0.327267i
$442$	−846.908	+	204.673i	−1.91608	+	0.463062i
$443$	−305.596			−0.689834			−0.344917	−	0.938633i	$-0.612093\pi$
$443$	−305.596			−0.689834			−0.344917	+	0.938633i	$0.612093\pi$
$444$	19.3867	−	33.5787i	0.0436637	−	0.0756278i
$445$	−210.437	+	364.488i	−0.472893	+	0.819074i
$446$	638.010	−	368.355i	1.43052	−	0.825908i
$447$	−302.251			−0.676176
$448$	−17.9199	+	106.787i	−0.0399997	+	0.238363i
$449$	−57.0904	+	32.9611i	−0.127150	+	0.0734101i	−0.562226	−	0.826984i	$-0.690055\pi$
$449$	−57.0904	+	32.9611i	−0.127150	+	0.0734101i	0.435076	+	0.900394i	$0.356722\pi$
$450$		−	337.103i		−	0.749117i
$451$	212.544	−	122.713i	0.471274	−	0.272090i
$452$	−248.230	+	429.948i	−0.549182	+	0.951212i
$453$	157.117	−	272.135i	0.346837	−	0.600740i
$454$			584.356i			1.28713i
$455$	−53.3731	−	751.918i	−0.117304	−	1.65257i
$456$	−136.246			−0.298785
$457$	710.831	+	410.399i	1.55543	+	0.898027i	0.997684	+	0.0680150i	$0.0216666\pi$
$457$	710.831	+	410.399i	1.55543	+	0.898027i	0.557745	+	0.830012i	$0.311667\pi$
$458$	−158.447	−	91.4793i	−0.345954	−	0.199737i
$459$	67.5927	+	117.074i	0.147261	+	0.255063i
$460$	−728.216			−1.58308
$461$	−130.344	−	225.763i	−0.282743	−	0.489724i	0.689317	−	0.724460i	$-0.257911\pi$
$461$	−130.344	−	225.763i	−0.282743	−	0.489724i	−0.972059	+	0.234736i	$0.924578\pi$
$462$	235.932	+	39.5918i	0.510676	+	0.0856965i
$463$			569.493i			1.23001i	0.788525	+	0.615003i	$0.210845\pi$
$463$			569.493i			1.23001i	−0.788525	+	0.615003i	$0.789155\pi$
$464$	219.999	+	381.049i	0.474135	+	0.821227i
$465$	488.989	+	282.318i	1.05159	+	0.607135i
$466$	−540.801	−	312.231i	−1.16052	−	0.670024i
$467$		−	365.466i		−	0.782583i	−0.920267	−	0.391292i	$-0.872028\pi$
$467$		−	365.466i		−	0.782583i	0.920267	−	0.391292i	$-0.127972\pi$
$468$	29.0557	−	98.6352i	0.0620847	−	0.210759i
$469$	−254.698	+	308.688i	−0.543067	+	0.658183i
$470$	−584.597	−	337.517i	−1.24382	−	0.718121i
$471$	−6.93725	+	12.0157i	−0.0147288	+	0.0255110i
$472$	29.5144	−	17.0402i	0.0625306	−	0.0361021i
$473$			240.041i			0.507486i
$474$	−132.587	−	229.648i	−0.279720	−	0.484489i
$475$	−488.421	−	845.970i	−1.02826	−	1.78099i
$476$	305.586	−	370.362i	0.641986	−	0.778071i
$477$	140.228	+	242.883i	0.293980	+	0.509188i
$478$	546.573	−	946.692i	1.14346	−	1.98053i
$479$	29.2498	−	50.6621i	0.0610642	−	0.105766i	−0.833877	−	0.551950i	$-0.813884\pi$
$479$	29.2498	−	50.6621i	0.0610642	−	0.105766i	0.894941	+	0.446184i	$0.147217\pi$
$480$	522.677			1.08891
$481$	−105.879	−	31.1895i	−0.220122	−	0.0648430i
$482$			644.975i			1.33812i
$483$	141.403	+	378.724i	0.292760	+	0.784108i
$484$	82.1756	−	142.332i	0.169784	−	0.294075i
$485$	−246.555	−	427.045i	−0.508360	−	0.880505i
$486$	−40.1582			−0.0826301
$487$	−506.512	+	292.435i	−1.04007	+	0.600483i	−0.919852	−	0.392265i	$-0.871691\pi$
$487$	−506.512	+	292.435i	−1.04007	+	0.600483i	−0.120214	+	0.992748i	$0.538358\pi$
$488$	23.5895	+	40.8582i	0.0483391	+	0.0837259i
$489$	−140.901			−0.288140
$490$	685.293	+	789.788i	1.39856	+	1.61181i
$491$	75.1148	−	130.103i	0.152983	−	0.264975i	−0.779340	−	0.626602i	$-0.784445\pi$
$491$	75.1148	−	130.103i	0.152983	−	0.264975i	0.932323	+	0.361627i	$0.117779\pi$
$492$	126.724	+	73.1643i	0.257570	+	0.148708i
$493$		−	584.194i		−	1.18498i
$494$	−176.185	−	729.027i	−0.356650	−	1.47576i
$495$		−	190.340i		−	0.384524i
$496$	−385.565	+	667.819i	−0.777350	+	1.34641i
$497$	−85.4400	−	228.837i	−0.171911	−	0.460436i
$498$	−286.652	−	496.496i	−0.575607	−	0.996981i
$499$			426.915i			0.855542i	0.903887	+	0.427771i	$0.140701\pi$
$499$			426.915i			0.855542i	−0.903887	+	0.427771i	$0.859299\pi$
$500$	203.315	+	352.152i	0.406630	+	0.704304i
$501$	446.383	−	257.720i	0.890985	−	0.514410i
$502$	−802.461			−1.59853
$503$	−12.9927	+	7.50131i	−0.0258303	+	0.0149132i	−0.512860	−	0.858473i	$-0.671414\pi$
$503$	−12.9927	+	7.50131i	−0.0258303	+	0.0149132i	0.487029	+	0.873386i	$0.338081\pi$
$504$	−25.8003	−	69.1017i	−0.0511910	−	0.137107i
$505$	626.464	+	361.689i	1.24052	+	0.716217i
$506$	−657.903			−1.30020
$507$	−292.360	−	14.4396i	−0.576647	−	0.0284804i
$508$	49.5483			0.0975361
$509$	−281.347	+	487.307i	−0.552744	+	0.957380i	0.445332	+	0.895366i	$0.353086\pi$
$509$	−281.347	+	487.307i	−0.552744	+	0.957380i	−0.998075	+	0.0620144i	$0.980248\pi$
$510$	−832.781	−	480.806i	−1.63290	−	0.942757i
$511$	−66.2778	+	394.957i	−0.129702	+	0.772911i
$512$			438.525i			0.856495i
$513$	−100.778	+	58.1844i	−0.196449	+	0.113420i
$514$	415.218	+	719.179i	0.807817	+	1.39918i
$515$		−	210.407i		−	0.408558i
$516$	−123.944	+	71.5592i	−0.240202	+	0.138681i
$517$	−209.823	−	121.141i	−0.405846	−	0.234315i
$518$	143.439	−	53.5553i	0.276909	−	0.103389i
$519$	181.774			0.350239
$520$	−88.8528	−	367.660i	−0.170871	−	0.707038i
$521$		−	648.325i		−	1.24439i	−0.782864	−	0.622193i	$-0.786242\pi$
$521$		−	648.325i		−	1.24439i	0.782864	−	0.622193i	$-0.213758\pi$
$522$	150.291	+	86.7705i	0.287914	+	0.166227i
$523$	248.995	+	143.757i	0.476090	+	0.274871i	0.718786	−	0.695232i	$-0.244698\pi$
$523$	248.995	+	143.757i	0.476090	+	0.274871i	−0.242695	+	0.970103i	$0.578032\pi$
$524$	340.133	−	196.376i	0.649108	−	0.374763i
$525$	336.572	−	407.917i	0.641090	−	0.776984i
$526$	212.121	−	122.468i	0.403271	−	0.232829i
$527$	886.677	−	511.923i	1.68250	−	0.971392i
$528$	259.949			0.492329
$529$	−291.373	−	504.673i	−0.550799	−	0.954012i
$530$	−1727.69	−	997.485i	−3.25980	−	1.88205i
$531$	14.5542	−	25.2085i	0.0274090	−	0.0474737i
$532$	318.811	+	263.051i	0.599269	+	0.494457i
$533$	117.707	−	399.581i	0.220839	−	0.749683i
$534$	−226.707			−0.424544
$535$	322.427	−	558.460i	0.602667	−	1.04385i
$536$	−100.405	+	173.907i	−0.187323	+	0.324454i
$537$	150.717	−	87.0162i	0.280664	−	0.162041i
$538$	−49.7892			−0.0925450
$539$	245.964	+	283.470i	0.456334	+	0.525918i
$540$	98.2811	−	56.7426i	0.182002	−	0.105079i
$541$		−	224.331i		−	0.414660i	−0.978271	−	0.207330i	$-0.933523\pi$
$541$		−	224.331i		−	0.414660i	0.978271	−	0.207330i	$-0.0664775\pi$
$542$	−842.246	+	486.271i	−1.55396	+	0.897179i
$543$	−135.773	+	235.165i	−0.250041	+	0.433085i
$544$	473.882	−	820.787i	0.871106	−	1.50880i
$545$			1708.02i			3.13398i
$546$	336.387	−	227.411i	0.616094	−	0.416503i
$547$	−262.218			−0.479376			−0.239688	−	0.970850i	$-0.577045\pi$
$547$	−262.218			−0.479376			−0.239688	+	0.970850i	$0.577045\pi$
$548$	120.978	+	69.8465i	0.220762	+	0.127457i
$549$	34.8973	+	20.1480i	0.0635653	+	0.0366994i
$550$	430.327	+	745.348i	0.782413	+	1.35518i
$551$	502.880			0.912668
$552$	101.424	+	175.672i	0.183740	+	0.318246i
$553$	68.8470	−	410.268i	0.124497	−	0.741894i
$554$			145.204i			0.262101i
$555$	−60.9097	−	105.499i	−0.109747	−	0.190088i
$556$	−5.14465	−	2.97027i	−0.00925297	−	0.00534221i
$557$	390.019	+	225.177i	0.700213	+	0.404268i	0.807427	−	0.589968i	$-0.200860\pi$
$557$	390.019	+	225.177i	0.700213	+	0.404268i	−0.107214	+	0.994236i	$0.534193\pi$
$558$			304.145i			0.545062i
$559$	280.893	+	295.109i	0.502492	+	0.527923i
$560$	876.400	+	723.118i	1.56500	+	1.29128i
$561$	−298.900	−	172.570i	−0.532799	−	0.307612i
$562$	−359.801	+	623.193i	−0.640214	+	1.10888i
$563$	−587.923	+	339.438i	−1.04427	+	0.602909i	−0.921039	−	0.389469i	$-0.872658\pi$
$563$	−587.923	+	339.438i	−1.04427	+	0.602909i	−0.123229	+	0.992378i	$0.539325\pi$
$564$		−	144.455i		−	0.256125i
$565$	779.898	+	1350.82i	1.38035	+	2.39084i
$566$	328.019	+	568.146i	0.579539	+	1.00379i
$567$	−48.5941	−	40.0950i	−0.0857039	−	0.0707143i
$568$	−61.2836	−	106.146i	−0.107894	−	0.186877i
$569$	−124.052	+	214.864i	−0.218017	+	0.377616i	−0.954202	−	0.299164i	$-0.903292\pi$
$569$	−124.052	+	214.864i	−0.218017	+	0.377616i	0.736185	+	0.676781i	$0.236625\pi$
$570$	413.883	−	716.866i	0.726110	−	1.25766i
$571$	910.138			1.59394			0.796968	−	0.604021i	$-0.206436\pi$
$571$	910.138			1.59394			0.796968	+	0.604021i	$0.206436\pi$
$572$	61.6691	+	255.177i	0.107813	+	0.446114i
$573$		−	333.359i		−	0.581779i
$574$	202.115	+	541.330i	0.352116	+	0.943084i
$575$	−727.181	+	1259.51i	−1.26466	+	2.19046i
$576$	23.2028	+	40.1884i	0.0402827	+	0.0697716i
$577$	368.799			0.639166			0.319583	−	0.947558i	$-0.396457\pi$
$577$	368.799			0.639166			0.319583	+	0.947558i	$0.396457\pi$
$578$	−865.308	+	499.586i	−1.49707	+	0.864336i
$579$	292.674	+	506.926i	0.505481	+	0.875520i
$580$	−490.419			−0.845550
$581$	148.847	−	886.995i	0.256190	−	1.52667i
$582$	132.808	−	230.031i	0.228193	−	0.395241i
$583$	−620.102	−	358.016i	−1.06364	−	0.614092i
$584$			200.951i			0.344095i
$585$	−222.733	−	234.005i	−0.380740	−	0.400009i
$586$		−	429.592i		−	0.733092i
$587$	178.775	−	309.647i	0.304557	−	0.527508i	−0.672606	−	0.740001i	$-0.734825\pi$
$587$	178.775	−	309.647i	0.304557	−	0.527508i	0.977163	+	0.212493i	$0.0681582\pi$
$588$	−73.0434	+	211.509i	−0.124223	+	0.359708i
$589$	440.669	+	763.260i	0.748164	+	1.29586i
$590$			207.056i			0.350942i
$591$	−44.1470	−	76.4648i	−0.0746988	−	0.129382i
$592$	144.081	−	83.1853i	0.243380	−	0.140516i
$593$	323.881			0.546174			0.273087	−	0.961989i	$-0.411955\pi$
$593$	323.881			0.546174			0.273087	+	0.961989i	$0.411955\pi$
$594$	88.7915	−	51.2638i	0.149481	−	0.0863027i
$595$	−527.671	−	1413.28i	−0.886841	−	2.37526i
$596$	398.451	+	230.046i	0.668542	+	0.385983i
$597$	−150.672			−0.252382
$598$	−808.832	+	769.870i	−1.35256	+	1.28741i
$599$	−34.4618			−0.0575323			−0.0287661	−	0.999586i	$-0.509158\pi$
$599$	−34.4618			−0.0575323			−0.0287661	+	0.999586i	$0.509158\pi$
$600$	132.681	−	229.810i	0.221135	−	0.383017i
$601$	−159.132	−	91.8748i	−0.264778	−	0.152870i	0.361734	−	0.932281i	$-0.382185\pi$
$601$	−159.132	−	91.8748i	−0.264778	−	0.152870i	−0.626512	+	0.779412i	$0.715518\pi$
$602$	−557.361	−	93.5308i	−0.925850	−	0.155367i
$603$			171.514i			0.284435i
$604$	−414.249	+	239.167i	−0.685842	+	0.395971i
$605$	−258.182	−	447.184i	−0.426747	−	0.739147i
$606$			389.653i			0.642991i
$607$	235.626	−	136.039i	0.388182	−	0.224117i	−0.293190	−	0.956054i	$-0.594717\pi$
$607$	235.626	−	136.039i	0.388182	−	0.224117i	0.681372	+	0.731937i	$0.261384\pi$
$608$	706.542	+	407.922i	1.16207	+	0.670924i
$609$	95.2281	+	255.053i	0.156368	+	0.418806i
$610$	−286.637			−0.469897
$611$	−399.716	+	96.5998i	−0.654199	+	0.158101i
$612$		−	205.781i		−	0.336244i
$613$	490.051	+	282.931i	0.799431	+	0.461551i	0.843272	−	0.537487i	$-0.180626\pi$
$613$	490.051	+	282.931i	0.799431	+	0.461551i	−0.0438415	+	0.999039i	$0.513960\pi$
$614$	1205.01	+	695.713i	1.96256	+	1.13308i
$615$	398.146	−	229.870i	0.647393	−	0.373772i
$616$	145.257	+	119.852i	0.235807	+	0.194564i
$617$	−349.335	+	201.689i	−0.566183	+	0.326886i	−0.755623	−	0.655006i	$-0.772666\pi$
$617$	−349.335	+	201.689i	−0.566183	+	0.326886i	0.189440	+	0.981892i	$0.439333\pi$
$618$	98.1529	−	56.6686i	0.158823	−	0.0916967i
$619$	−254.973			−0.411911			−0.205956	−	0.978561i	$-0.566030\pi$
$619$	−254.973			−0.411911			−0.205956	+	0.978561i	$0.566030\pi$
$620$	−429.749	−	744.347i	−0.693143	−	1.20056i
$621$	150.043	+	86.6273i	0.241615	+	0.139496i
$622$	−4.70632	+	8.15158i	−0.00756643	+	0.0131054i
$623$	−274.330	−	226.350i	−0.440337	−	0.363322i
$624$	319.584	−	304.190i	0.512155	−	0.487484i
$625$	187.104			0.299367
$626$	350.904	−	607.783i	0.560549	−	0.970900i
$627$	148.550	−	257.296i	0.236922	−	0.410361i
$628$	18.2904	−	10.5600i	0.0291249	−	0.0168153i
$629$	−220.894			−0.351182
$630$	441.958	+	74.1649i	0.701520	+	0.117722i
$631$	−437.346	+	252.502i	−0.693100	+	0.400162i	−0.804772	−	0.593583i	$-0.797713\pi$
$631$	−437.346	+	252.502i	−0.693100	+	0.400162i	0.111672	+	0.993745i	$0.464379\pi$
$632$		−	208.741i		−	0.330286i
$633$	−443.657	+	256.145i	−0.700879	+	0.404653i
$634$	−426.475	+	738.677i	−0.672674	+	1.16511i
$635$	77.8363	−	134.816i	0.122577	−	0.212309i
$636$		−	426.916i		−	0.671252i
$637$	634.104	+	60.6758i	0.995453	+	0.0952524i
$638$	−443.066			−0.694461
$639$	−90.6605	−	52.3429i	−0.141879	−	0.0819137i
$640$	759.481	+	438.487i	1.18669	+	0.685136i
$641$	101.776	+	176.281i	0.158777	+	0.275009i	0.934428	−	0.356153i	$-0.115912\pi$
$641$	101.776	+	176.281i	0.158777	+	0.275009i	−0.775651	+	0.631162i	$0.782578\pi$
$642$	347.355			0.541051
$643$	−416.989	−	722.246i	−0.648506	−	1.12324i	−0.983480	−	0.181017i	$-0.942061\pi$
$643$	−416.989	−	722.246i	−0.648506	−	1.12324i	0.334974	−	0.942227i	$-0.391272\pi$
$644$	101.842	−	606.887i	0.158139	−	0.942371i
$645$			449.654i			0.697138i
$646$	−750.488	−	1299.88i	−1.16175	−	2.01220i
$647$	−376.292	−	217.252i	−0.581595	−	0.335784i	0.180172	−	0.983635i	$-0.442335\pi$
$647$	−376.292	−	217.252i	−0.581595	−	0.335784i	−0.761767	+	0.647851i	$0.775668\pi$
$648$	−27.3767	−	15.8060i	−0.0422480	−	0.0243919i
$649$			74.3162i			0.114509i
$650$	1401.25	+	412.775i	2.15576	+	0.635038i
$651$	−303.666	+	368.035i	−0.466460	+	0.565338i
$652$	185.746	+	107.241i	0.284887	+	0.164479i
$653$	−444.288	+	769.529i	−0.680379	+	1.17845i	0.294486	+	0.955656i	$0.404851\pi$
$653$	−444.288	+	769.529i	−0.680379	+	1.17845i	−0.974865	+	0.222795i	$0.928482\pi$
$654$	−796.773	+	460.017i	−1.21831	+	0.703390i
$655$		−	1233.96i		−	1.88391i
$656$	313.937	+	543.754i	0.478562	+	0.828894i
$657$	85.8171	+	148.640i	0.130620	+	0.226240i
$658$	363.039	−	439.994i	0.551731	−	0.668684i
$659$	−375.272	−	649.990i	−0.569457	−	0.986328i	−0.996620	−	0.0821531i	$-0.973820\pi$
$659$	−375.272	−	649.990i	−0.569457	−	0.986328i	0.427163	−	0.904175i	$-0.359513\pi$
$660$	−144.869	+	250.921i	−0.219499	+	0.380183i
$661$	−305.791	+	529.646i	−0.462619	+	0.801280i	−0.999091	−	0.0426386i	$-0.986424\pi$
$661$	−305.791	+	529.646i	−0.462619	+	0.801280i	0.536471	+	0.843918i	$0.319757\pi$
$662$	724.249			1.09403
$663$	−569.411	+	137.610i	−0.858840	+	0.207557i
$664$		−	451.296i		−	0.679663i
$665$	1216.56	−	454.224i	1.82942	−	0.683044i
$666$	32.8094	−	56.8276i	0.0492634	−	0.0853267i
$667$	−374.354	−	648.400i	−0.561250	−	0.972114i
$668$	−784.610			−1.17457
$669$	428.960	−	247.660i	0.641195	−	0.370194i
$670$	−610.014	−	1056.58i	−0.910469	−	1.57698i
$671$	−102.879			−0.153322
$672$	−73.0968	+	435.593i	−0.108775	+	0.648203i
$673$	167.433	−	290.003i	0.248786	−	0.430911i	−0.714403	−	0.699735i	$-0.753302\pi$
$673$	167.433	−	290.003i	0.248786	−	0.430911i	0.963189	+	0.268824i	$0.0866349\pi$
$674$	596.646	+	344.474i	0.885231	+	0.511089i
$675$		−	226.648i		−	0.335775i
$676$	374.422	+	241.553i	0.553879	+	0.357327i
$677$			459.067i			0.678090i	0.940770	+	0.339045i	$0.110104\pi$
$677$			459.067i			0.678090i	−0.940770	+	0.339045i	$0.889896\pi$
$678$	−420.097	+	727.630i	−0.619612	+	1.07320i
$679$	390.375	−	145.753i	0.574927	−	0.214658i
$680$	−378.483	−	655.552i	−0.556592	−	0.964046i
$681$			392.886i			0.576925i
$682$	−388.254	−	672.476i	−0.569288	−	0.986036i
$683$	−41.5563	+	23.9925i	−0.0608438	+	0.0351282i	−0.530113	−	0.847927i	$-0.677851\pi$
$683$	−41.5563	+	23.9925i	−0.0608438	+	0.0351282i	0.469270	+	0.883055i	$0.344517\pi$
$684$	177.139			0.258975
$685$	380.091	−	219.446i	0.554878	−	0.320359i
$686$	−754.039	+	460.662i	−1.09918	+	0.671520i
$687$	−106.530	−	61.5052i	−0.155066	−	0.0895273i
$688$	−614.099			−0.892586
$689$	−1181.31	+	285.487i	−1.71452	+	0.414350i
$690$	−1232.41			−1.78610
$691$	565.724	−	979.863i	0.818704	−	1.41804i	−0.0879342	−	0.996126i	$-0.528027\pi$
$691$	565.724	−	979.863i	0.818704	−	1.41804i	0.906638	−	0.421910i	$-0.138640\pi$
$692$	−239.629	−	138.350i	−0.346284	−	0.199927i
$693$	158.627	+	26.6191i	0.228899	+	0.0384115i
$694$			177.379i			0.255590i
$695$	−16.1636	+	9.33208i	−0.0232570	+	0.0134275i
$696$	68.3044	+	118.307i	0.0981385	+	0.169981i
$697$		−	833.641i		−	1.19604i
$698$	890.458	−	514.106i	1.27573	−	0.736542i
$699$	−363.602	−	209.926i	−0.520175	−	0.300323i
$700$	−754.165	+	281.580i	−1.07738	+	0.402257i
$701$	−464.399			−0.662480			−0.331240	−	0.943547i	$-0.607467\pi$
$701$	−464.399			−0.662480			−0.331240	+	0.943547i	$0.607467\pi$
$702$	49.1729	−	166.927i	0.0700468	−	0.237788i
$703$		−	190.147i		−	0.270480i
$704$	−102.605	−	59.2389i	−0.145745	−	0.0841462i
$705$	−393.048	−	226.926i	−0.557515	−	0.321881i
$706$	1395.57	−	805.734i	1.97673	−	1.14127i
$707$	−389.039	+	471.506i	−0.550268	+	0.666910i
$708$	−38.3729	+	22.1546i	−0.0541990	+	0.0312918i
$709$	−700.552	+	404.464i	−0.988084	+	0.570471i	−0.904701	−	0.426047i	$-0.859906\pi$
$709$	−700.552	+	404.464i	−0.988084	+	0.570471i	−0.0833833	+	0.996518i	$0.526573\pi$
$710$	744.660			1.04882
$711$	−89.1437	−	154.401i	−0.125378	−	0.217161i
$712$	−154.551	−	89.2299i	−0.217066	−	0.125323i
$713$	656.085	−	1136.37i	0.920175	−	1.59379i
$714$	517.163	−	626.788i	0.724318	−	0.877855i
$715$	791.191	+	233.067i	1.10656	+	0.325967i
$716$	−264.915			−0.369993
$717$	367.483	−	636.499i	0.512528	−	0.887725i
$718$	136.453	−	236.343i	0.190046	−	0.329169i
$719$	639.856	−	369.421i	0.889925	−	0.513799i	0.0160073	−	0.999872i	$-0.494904\pi$
$719$	639.856	−	369.421i	0.889925	−	0.513799i	0.873918	+	0.486073i	$0.161571\pi$
$720$	486.948			0.676316
$721$	175.351	+	29.4256i	0.243205	+	0.0408122i
$722$	313.557	−	181.032i	0.434289	−	0.250737i
$723$			433.643i			0.599783i
$724$	357.972	−	206.675i	0.494437	−	0.285463i
$725$	−489.722	+	848.223i	−0.675478	+	1.16996i
$726$	139.071	−	240.879i	0.191558	−	0.331789i
$727$			149.435i			0.205550i	0.994705	+	0.102775i	$0.0327722\pi$
$727$			149.435i			0.205550i	−0.994705	+	0.102775i	$0.967228\pi$
$728$	318.829	−	22.6314i	0.437952	−	0.0310870i
$729$	−27.0000			−0.0370370
$730$	−1057.32	−	610.442i	−1.44838	−	0.836222i
$731$	706.116	+	407.676i	0.965959	+	0.557697i
$732$	−30.6696	−	53.1213i	−0.0418984	−	0.0725701i
$733$	−427.405			−0.583090			−0.291545	−	0.956557i	$-0.594169\pi$
$733$	−427.405			−0.583090			−0.291545	+	0.956557i	$0.594169\pi$
$734$	−280.376	−	485.626i	−0.381984	−	0.661616i
$735$	460.750	+	531.006i	0.626871	+	0.722458i
$736$		−	1214.66i		−	1.65035i
$737$	−218.945	−	379.225i	−0.297077	−	0.514552i
$738$	214.464	+	123.821i	0.290602	+	0.167779i
$739$	379.729	+	219.237i	0.513842	+	0.296667i	0.734411	−	0.678705i	$-0.237458\pi$
$739$	379.729	+	219.237i	0.513842	+	0.296667i	−0.220570	+	0.975371i	$0.570792\pi$
$740$			185.436i			0.250589i
$741$	−118.456	−	490.154i	−0.159860	−	0.661477i
$742$	1072.91	−	1300.34i	1.44597	−	1.75248i
$743$	−493.634	−	285.000i	−0.664379	−	0.383580i	0.129564	−	0.991571i	$-0.458642\pi$
$743$	−493.634	−	285.000i	−0.664379	−	0.383580i	−0.793944	+	0.607991i	$0.791975\pi$
$744$	−119.709	+	207.342i	−0.160899	+	0.278685i
$745$	1251.87	−	722.765i	1.68036	−	0.970154i
$746$		−	1540.23i		−	2.06465i
$747$	−192.728	−	333.815i	−0.258003	−	0.446874i
$748$	262.689	+	454.991i	0.351189	+	0.608277i
$749$	420.322	+	346.808i	0.561178	+	0.463028i
$750$	344.084	+	595.971i	0.458779	+	0.794628i
$751$	518.196	−	897.542i	0.690009	−	1.19513i	−0.281826	−	0.959466i	$-0.590940\pi$
$751$	518.196	−	897.542i	0.690009	−	1.19513i	0.971835	−	0.235664i	$-0.0757266\pi$
$752$	309.916	−	536.791i	0.412123	−	0.713818i
$753$	−539.527			−0.716503
$754$	−544.710	+	518.471i	−0.722427	+	0.687627i
$755$			1502.84i			1.99052i
$756$	33.5439	+	89.8418i	0.0443703	+	0.118838i
$757$	137.510	−	238.175i	0.181652	−	0.314630i	−0.760791	−	0.648996i	$-0.775189\pi$
$757$	137.510	−	238.175i	0.181652	−	0.314630i	0.942443	+	0.334366i	$0.108522\pi$
$758$	−311.255	−	539.110i	−0.410627	−	0.711227i
$759$	−442.335			−0.582786
$760$	564.305	−	325.802i	0.742507	−	0.428686i
$761$	−673.816	−	1167.08i	−0.885435	−	1.53362i	−0.845214	−	0.534428i	$-0.820527\pi$
$761$	−673.816	−	1167.08i	−0.885435	−	1.53362i	−0.0402216	−	0.999191i	$-0.512806\pi$
$762$	83.8540			0.110045
$763$	−1423.44	−	238.868i	−1.86559	−	0.313064i
$764$	−253.723	+	439.461i	−0.332098	+	0.575210i
$765$	−559.912	−	323.265i	−0.731911	−	0.422569i
$766$		−	1386.84i		−	1.81049i
$767$	86.9639	+	91.3650i	0.113382	+	0.119120i
$768$			579.557i			0.754631i
$769$	9.94312	−	17.2220i	0.0129299	−	0.0223953i	−0.859488	−	0.511156i	$-0.829217\pi$
$769$	9.94312	−	17.2220i	0.0129299	−	0.0223953i	0.872418	+	0.488761i	$0.162551\pi$
$770$	−1071.86	+	400.197i	−1.39203	+	0.519737i
$771$	279.168	+	483.533i	0.362085	+	0.627150i
$772$		−	891.026i		−	1.15418i
$773$	−112.434	−	194.742i	−0.145452	−	0.251930i	0.784090	−	0.620648i	$-0.213130\pi$
$773$	−112.434	−	194.742i	−0.145452	−	0.251930i	−0.929541	+	0.368718i	$0.879797\pi$
$774$	−209.759	+	121.105i	−0.271007	+	0.156466i
$775$	−1716.55			−2.21491
$776$	181.076	−	104.544i	0.233346	−	0.134722i
$777$	96.4397	−	36.0074i	0.124118	−	0.0463415i
$778$	650.513	+	375.574i	0.836135	+	0.482743i
$779$	717.606			0.921189
$780$	115.521	+	478.008i	0.148104	+	0.612831i
$781$	267.272			0.342218
$782$	−1117.36	+	1935.32i	−1.42884	+	2.47483i
$783$	101.047	+	58.3393i	0.129051	+	0.0745075i
$784$	−725.203	+	629.253i	−0.925004	+	0.802618i
$785$		−	66.3555i		−	0.0845292i
$786$	575.630	−	332.340i	0.732353	−	0.422824i
$787$	539.605	+	934.622i	0.685647	+	1.18758i	0.973233	+	0.229821i	$0.0738141\pi$
$787$	539.605	+	934.622i	0.685647	+	1.18758i	−0.287585	+	0.957755i	$0.592853\pi$
$788$			134.403i			0.170562i
$789$	142.617	−	82.3401i	0.180757	−	0.104360i
$790$	1098.30	+	634.105i	1.39026	+	0.802665i
$791$	−1234.83	+	461.044i	−1.56110	+	0.582863i
$792$	80.7081			0.101904
$793$	−126.481	+	120.388i	−0.159497	+	0.151814i
$794$		−	23.0955i		−	0.0290876i
$795$	−1161.60	−	670.649i	−1.46113	−	0.843584i
$796$	198.628	+	114.678i	0.249532	+	0.144068i
$797$	−700.195	+	404.258i	−0.878539	+	0.507224i	−0.870176	−	0.492741i	$-0.835995\pi$
$797$	−700.195	+	404.258i	−0.878539	+	0.507224i	−0.00836226	+	0.999965i	$0.502662\pi$
$798$	539.546	+	445.179i	0.676122	+	0.557869i
$799$	−712.709	+	411.483i	−0.892001	+	0.514997i
$800$	−1376.11	+	794.496i	−1.72014	+	0.993120i
$801$	−152.424			−0.190292
$802$	863.206	+	1495.12i	1.07632	+	1.86424i
$803$	−379.491	−	219.099i	−0.472591	−	0.272851i
$804$	130.541	−	226.103i	0.162364	−	0.281223i
$805$	−1491.30	−	1230.47i	−1.85254	−	1.52853i
$806$	−1264.25	−	372.418i	−1.56855	−	0.462057i
$807$	−33.4753			−0.0414812
$808$	−153.364	+	265.634i	−0.189807	+	0.328756i
$809$	566.917	−	981.929i	0.700763	−	1.21376i	−0.267437	−	0.963575i	$-0.586177\pi$
$809$	566.917	−	981.929i	0.700763	−	1.21376i	0.968199	−	0.250181i	$-0.0804901\pi$
$810$	166.328	−	96.0294i	0.205343	−	0.118555i
$811$	935.504			1.15352			0.576759	−	0.816914i	$-0.304317\pi$
$811$	935.504			1.15352			0.576759	+	0.816914i	$0.304317\pi$
$812$	68.5855	−	408.709i	0.0844649	−	0.503337i
$813$	−566.276	+	326.940i	−0.696527	+	0.402140i
$814$			167.531i			0.205812i
$815$	583.583	−	336.932i	0.716053	−	0.413414i
$816$	441.488	−	764.680i	0.541039	−	0.937108i
$817$	−350.932	+	607.832i	−0.429537	+	0.743980i
$818$		−	261.039i		−	0.319119i
$819$	226.167	−	152.897i	0.276150	−	0.186688i
$820$	−699.824			−0.853444
$821$	151.705	+	87.5868i	0.184780	+	0.106683i	0.589537	−	0.807742i	$-0.299310\pi$
$821$	151.705	+	87.5868i	0.184780	+	0.106683i	−0.404756	+	0.914425i	$0.632644\pi$
$822$	204.739	+	118.206i	0.249074	+	0.143803i
$823$	−142.238	−	246.363i	−0.172828	−	0.299348i	0.766579	−	0.642150i	$-0.221957\pi$
$823$	−142.238	−	246.363i	−0.172828	−	0.299348i	−0.939408	+	0.342802i	$0.888624\pi$
$824$	89.2172			0.108273
$825$	289.326	+	501.128i	0.350699	+	0.607428i
$826$	−172.558	−	28.9569i	−0.208908	−	0.0350568i
$827$			1288.31i			1.55781i	0.627143	+	0.778904i	$0.284224\pi$
$827$			1288.31i			1.55781i	−0.627143	+	0.778904i	$0.715776\pi$
$828$	−131.866	−	228.398i	−0.159258	−	0.275843i
$829$	881.709	+	509.055i	1.06358	+	0.614059i	0.926421	−	0.376490i	$-0.122869\pi$
$829$	881.709	+	509.055i	1.06358	+	0.614059i	0.137161	+	0.990549i	$0.456202\pi$
$830$	2374.52	+	1370.93i	2.86087	+	1.65172i
$831$			97.6264i			0.117481i
$832$	−195.464	+	47.2380i	−0.234933	+	0.0567765i
$833$	1251.60	−	242.107i	1.50253	−	0.290644i
$834$	−8.70665	−	5.02679i	−0.0104396	−	0.00602732i
$835$	−1232.56	+	2134.85i	−1.47612	+	2.55671i
$836$	−391.661	+	226.126i	−0.468494	+	0.270485i
$837$			204.489i			0.244311i
$838$	−393.943	−	682.329i	−0.470099	−	0.814235i
$839$	−143.632	−	248.778i	−0.171195	−	0.296518i	0.767643	−	0.640877i	$-0.221429\pi$
$839$	−143.632	−	248.778i	−0.171195	−	0.296518i	−0.938838	+	0.344360i	$0.888096\pi$
$840$	272.101	+	224.511i	0.323930	+	0.267275i
$841$	168.390	+	291.661i	0.200226	+	0.346802i
$842$	38.3091	−	66.3534i	0.0454978	−	0.0788045i
$843$	−241.908	+	418.998i	−0.286961	+	0.497032i
$844$	779.818			0.923954
$845$	1245.43	−	639.308i	1.47388	−	0.756577i
$846$		−	244.471i		−	0.288972i
$847$	408.785	−	152.627i	0.482627	−	0.180197i
$848$	915.915	−	1586.41i	1.08009	−	1.87077i
$849$	220.541	+	381.988i	0.259765	+	0.449926i
$850$	2923.40			3.43930
$851$	−245.171	+	141.550i	−0.288098	+	0.166333i
$852$	79.6772	+	138.005i	0.0935178	+	0.161978i
$853$	−1667.60			−1.95498			−0.977492	−	0.210974i	$-0.932336\pi$
$853$	−1667.60			−1.95498			−0.977492	+	0.210974i	$0.932336\pi$
$854$	40.0864	−	238.880i	0.0469396	−	0.279719i
$855$	278.270	−	481.978i	0.325462	−	0.563717i
$856$	236.799	+	136.716i	0.276634	+	0.159715i
$857$			423.912i			0.494646i	0.968933	+	0.247323i	$0.0795509\pi$
$857$			423.912i			0.494646i	−0.968933	+	0.247323i	$0.920449\pi$
$858$	104.367	+	431.854i	0.121640	+	0.503327i
$859$			716.858i			0.834526i	0.908786	+	0.417263i	$0.137011\pi$
$859$			716.858i			0.834526i	−0.908786	+	0.417263i	$0.862989\pi$
$860$	342.236	−	592.770i	0.397948	−	0.689267i
$861$	135.890	+	363.958i	0.157828	+	0.422716i
$862$	386.577	+	669.571i	0.448465	+	0.776764i
$863$			1270.55i			1.47224i	0.676848	+	0.736122i	$0.263345\pi$
$863$			1270.55i			1.47224i	−0.676848	+	0.736122i	$0.736655\pi$
$864$	94.6464	+	163.932i	0.109544	+	0.189737i
$865$	−752.873	+	434.671i	−0.870373	+	0.502510i
$866$	−394.808			−0.455898
$867$	−581.782	+	335.892i	−0.671028	+	0.387418i
$868$	680.431	−	254.050i	0.783906	−	0.292685i
$869$	394.201	+	227.592i	0.453626	+	0.261901i
$870$	−829.969			−0.953988
$871$	−712.938	−	210.015i	−0.818528	−	0.241120i
$872$	−724.236			−0.830546
$873$	89.2923	−	154.659i	0.102282	−	0.177158i
$874$	−1665.94	−	961.831i	−1.90611	−	1.10049i
$875$	−178.668	+	1064.71i	−0.204192	+	1.21681i
$876$		−	261.265i		−	0.298247i
$877$	1367.90	−	789.756i	1.55975	−	0.900520i	0.562466	−	0.826820i	$-0.309853\pi$
$877$	1367.90	−	789.756i	1.55975	−	0.900520i	0.997280	−	0.0737001i	$-0.0234808\pi$
$878$	−768.172	−	1330.51i	−0.874911	−	1.51539i
$879$		−	288.832i		−	0.328592i
$880$	−1076.66	+	621.611i	−1.22348	+	0.706376i
$881$	1419.87	+	819.762i	1.61166	+	0.930490i	0.988987	+	0.148005i	$0.0472851\pi$
$881$	1419.87	+	819.762i	1.61166	+	0.930490i	0.622669	+	0.782485i	$0.286048\pi$
$882$	−123.616	+	357.950i	−0.140154	+	0.405839i
$883$	55.1278			0.0624324			0.0312162	−	0.999513i	$-0.490062\pi$
$883$	55.1278			0.0624324			0.0312162	+	0.999513i	$0.490062\pi$
$884$	855.378	+	251.975i	0.967623	+	0.285039i
$885$			139.212i			0.157302i
$886$	681.790	+	393.631i	0.769514	+	0.444279i
$887$	729.647	+	421.262i	0.822601	+	0.474929i	0.851313	−	0.524659i	$-0.175807\pi$
$887$	729.647	+	421.262i	0.822601	+	0.474929i	−0.0287115	+	0.999588i	$0.509140\pi$
$888$	44.7338	−	25.8270i	0.0503758	−	0.0290845i
$889$	101.469	+	83.7220i	0.114138	+	0.0941755i
$890$	938.976	−	542.118i	1.05503	−	0.609121i
$891$	59.6981	−	34.4667i	0.0670013	−	0.0386832i
$892$	−753.985			−0.845274
$893$	−354.208	−	613.507i	−0.396650	−	0.687018i
$894$	674.325	+	389.322i	0.754279	+	0.435483i
$895$	−416.160	+	720.810i	−0.464983	+	0.805374i
$896$	−471.644	+	571.620i	−0.526388	+	0.637969i
$897$	−543.811	+	517.615i	−0.606255	+	0.577051i
$898$	169.826			0.189116
$899$	441.842	−	765.293i	0.491482	−	0.851271i
$900$	−172.504	+	298.785i	−0.191671	+	0.331983i
$901$	−2106.31	+	1216.08i	−2.33775	+	1.34970i
$902$	−632.252			−0.700945
$903$	−374.737	−	62.8845i	−0.414991	−	0.0696396i
$904$	−572.779	+	330.694i	−0.633605	+	0.365812i
$905$		−	1298.68i		−	1.43500i
$906$	−701.061	+	404.758i	−0.773798	+	0.446753i
$907$	−684.644	+	1185.84i	−0.754845	+	1.30743i	0.190607	+	0.981666i	$0.438954\pi$
$907$	−684.644	+	1185.84i	−0.754845	+	1.30743i	−0.945451	+	0.325763i	$0.894379\pi$
$908$	299.029	−	517.933i	0.329327	−	0.570411i
$909$			261.979i			0.288206i
$910$	−849.451	+	1746.29i	−0.933462	+	1.91900i
$911$	1323.66			1.45297			0.726485	−	0.687182i	$-0.241152\pi$
$911$	1323.66			1.45297			0.726485	+	0.687182i	$0.241152\pi$
$912$	658.244	+	380.037i	0.721759	+	0.416707i
$913$	852.259	+	492.052i	0.933471	+	0.538940i
$914$	−1057.25	−	1831.21i	−1.15673	−	2.00351i
$915$	−192.718			−0.210620
$916$	93.6243	+	162.162i	0.102210	+	0.177033i
$917$	1028.37	+	172.570i	1.12145	+	0.188190i
$918$		−	348.258i		−	0.379366i
$919$	411.008	+	711.887i	0.447234	+	0.774632i	0.998205	−	0.0598924i	$-0.0190758\pi$
$919$	411.008	+	711.887i	0.447234	+	0.774632i	−0.550971	+	0.834525i	$0.685742\pi$
$920$	−840.160	−	485.067i	−0.913217	−	0.527246i
$921$	810.177	+	467.756i	0.879671	+	0.507878i
$922$			671.573i			0.728388i
$923$	328.587	−	312.759i	0.355999	−	0.338850i
$924$	−188.854	−	155.824i	−0.204388	−	0.168640i
$925$	320.727	+	185.172i	0.346732	+	0.200186i
$926$	733.550	−	1270.55i	0.792171	−	1.37208i
$927$	65.9921	−	38.1006i	0.0711889	−	0.0411009i
$928$		−	818.016i		−	0.881483i
$929$	−594.395	−	1029.52i	−0.639822	−	1.10820i	−0.985472	−	0.169841i	$-0.945675\pi$
$929$	−594.395	−	1029.52i	−0.639822	−	1.10820i	0.345649	−	0.938364i	$-0.387659\pi$
$930$	−727.293	−	1259.71i	−0.782036	−	1.35453i
$931$	208.408	+	1077.39i	0.223854	+	1.15724i
$932$	319.553	+	553.481i	0.342868	+	0.593864i
$933$	−3.16425	+	5.48064i	−0.00339148	+	0.00587421i
$934$	−470.748	+	815.360i	−0.504013	+	0.872977i
$935$	1650.65			1.76540
$936$	99.2233	−	94.4437i	0.106008	−	0.100901i
$937$			945.481i			1.00905i	0.863397	+	0.504526i	$0.168333\pi$
$937$			945.481i			1.00905i	−0.863397	+	0.504526i	$0.831667\pi$
$938$	965.849	−	360.616i	1.02969	−	0.384452i
$939$	235.927	−	408.637i	0.251253	−	0.435183i
$940$	345.431	+	598.304i	0.367480	+	0.636494i
$941$	−1622.42			−1.72415			−0.862074	−	0.506782i	$-0.830835\pi$
$941$	−1622.42			−1.72415			−0.862074	+	0.506782i	$0.830835\pi$
$942$	30.9542	−	17.8714i	0.0328600	−	0.0189718i
$943$	−534.200	−	925.262i	−0.566490	−	0.981190i
$944$	−190.124			−0.201402
$945$	297.146	+	49.8640i	0.314440	+	0.0527662i
$946$	309.191	−	535.535i	0.326840	−	0.566104i
$947$	−187.150	−	108.051i	−0.197624	−	0.114098i	0.397923	−	0.917419i	$-0.369731\pi$
$947$	−187.150	−	108.051i	−0.197624	−	0.114098i	−0.595547	+	0.803321i	$0.703064\pi$
$948$			271.392i			0.286279i
$949$	−722.936	+	174.713i	−0.761788	+	0.184102i
$950$			2516.49i			2.64894i
$951$	−286.737	+	496.642i	−0.301511	+	0.522232i
$952$	599.260	−	223.744i	0.629475	−	0.235025i
$953$	489.726	+	848.230i	0.513878	+	0.890063i	0.999870	+	0.0160998i	$0.00512495\pi$
$953$	489.726	+	848.230i	0.513878	+	0.890063i	−0.485992	+	0.873963i	$0.661542\pi$
$954$		−	722.499i		−	0.757337i
$955$	797.154	+	1380.71i	0.834716	+	1.44577i
$956$	−968.890	+	559.389i	−1.01348	+	0.585135i
$957$	−297.891			−0.311276
$958$	−130.513	+	75.3518i	−0.136235	+	0.0786553i
$959$	129.728	+	347.453i	0.135274	+	0.362308i
$960$	−192.203	−	110.969i	−0.200212	−	0.115592i
$961$	587.726			0.611578
$962$	196.043	+	205.964i	0.203787	+	0.214100i
$963$	233.541			0.242514
$964$	330.049	−	571.662i	0.342375	−	0.593010i
$965$	−2424.40	−	1399.73i	−2.51233	−	1.45049i
$966$	172.353	−	1027.08i	0.178420	−	1.06323i
$967$		−	938.652i		−	0.970684i	−0.874324	−	0.485342i	$-0.838695\pi$
$967$		−	938.652i		−	0.970684i	0.874324	−	0.485342i	$-0.161305\pi$
$968$	189.616	−	109.475i	0.195884	−	0.113094i
$969$	−504.584	−	873.964i	−0.520726	−	0.901924i
$970$			1270.32i			1.30961i
$971$	−493.556	+	284.955i	−0.508297	+	0.293465i	−0.732133	−	0.681161i	$-0.761475\pi$
$971$	−493.556	+	284.955i	−0.508297	+	0.293465i	0.223836	+	0.974627i	$0.428142\pi$
$972$	35.5935	+	20.5499i	0.0366189	+	0.0211419i
$973$	−5.51675	−	14.7757i	−0.00566983	−	0.0151857i
$974$	1506.71			1.54693
$975$	942.114	+	277.525i	0.966271	+	0.284641i
$976$		−	263.197i		−	0.269669i
$977$	−870.399	−	502.525i	−0.890890	−	0.514355i	−0.0166562	−	0.999861i	$-0.505302\pi$
$977$	−870.399	−	502.525i	−0.890890	−	0.514355i	−0.874233	+	0.485506i	$0.838635\pi$
$978$	314.351	+	181.491i	0.321422	+	0.185573i
$979$	337.016	−	194.576i	0.344245	−	0.198750i
$980$	−203.243	−	1050.70i	−0.207391	−	1.07214i
$981$	−535.703	+	309.288i	−0.546078	+	0.315278i
$982$	−335.164	+	193.507i	−0.341308	+	0.197054i
$983$	557.100			0.566734			0.283367	−	0.959012i	$-0.408549\pi$
$983$	557.100			0.566734			0.283367	+	0.959012i	$0.408549\pi$
$984$	97.4698	+	168.823i	0.0990547	+	0.171568i
$985$	365.697	+	211.135i	0.371266	+	0.214350i
$986$	−752.487	+	1303.34i	−0.763171	+	1.32185i
$987$	244.086	−	295.826i	0.247301	−	0.299722i
$988$	−216.902	+	736.318i	−0.219537	+	0.745261i
$989$	1044.96			1.05658
$990$	−245.172	+	424.650i	−0.247648	+	0.428939i
$991$	812.915	−	1408.01i	0.820297	−	1.42080i	−0.0851637	−	0.996367i	$-0.527141\pi$
$991$	812.915	−	1408.01i	0.820297	−	1.42080i	0.905461	−	0.424430i	$-0.139525\pi$
$992$	1241.57	−	716.819i	1.25158	−	0.722600i
$993$	486.942			0.490374
$994$	−104.141	+	620.591i	−0.104770	+	0.624337i
$995$	624.055	−	360.298i	0.627191	−	0.362109i
$996$			586.748i			0.589104i
$997$	−699.947	+	404.115i	−0.702054	+	0.405331i	−0.808112	−	0.589029i	$-0.799510\pi$
$997$	−699.947	+	404.115i	−0.702054	+	0.405331i	0.106058	+	0.994360i	$0.466177\pi$
$998$	549.900	−	952.454i	0.551002	−	0.954363i
$999$	22.0591	−	38.2075i	0.0220812	−	0.0382457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.3.bo.c.160.5	✓	36
7.6	odd	2		273.3.bo.d.160.5	yes	36
13.10	even	6		273.3.bo.d.244.5	yes	36
91.62	odd	6	inner	273.3.bo.c.244.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.3.bo.c.160.5	✓	36	1.1	even	1	trivial
273.3.bo.c.244.5	yes	36	91.62	odd	6	inner
273.3.bo.d.160.5	yes	36	7.6	odd	2
273.3.bo.d.244.5	yes	36	13.10	even	6

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	273.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23101 - 1.28808i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.31828 + 2.28333i) q^{4} +8.28362 q^{5} +(2.23101 + 3.86423i) q^{6} +(-1.15847 + 6.90347i) q^{7} +3.51244i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-2.23101 - 1.28808i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(1.31828 + 2.28333i) q^{4} +8.28362 q^{5} +(2.23101 + 3.86423i) q^{6} +(-1.15847 + 6.90347i) q^{7} +3.51244i q^{8} +(1.50000 + 2.59808i) q^{9} +(-18.4809 - 10.6699i) q^{10} +(-6.63313 - 3.82964i) q^{11} -4.56665i q^{12} +(-12.6362 + 3.05381i) q^{13} +(11.4768 - 13.9095i) q^{14} +(-12.4254 - 7.17383i) q^{15} +(9.79740 - 16.9696i) q^{16} +(-22.5309 + 13.0082i) q^{17} -7.72845i q^{18} +(-11.1976 - 19.3948i) q^{19} +(10.9201 + 18.9142i) q^{20} +(7.71629 - 9.35194i) q^{21} +(9.86573 + 17.0879i) q^{22} +(-16.6714 + 28.8758i) q^{23} +(3.04186 - 5.26865i) q^{24} +43.6184 q^{25} +(32.1251 + 9.46332i) q^{26} -5.19615i q^{27} +(-17.2901 + 6.45553i) q^{28} +(-11.2274 + 19.4464i) q^{29} +(18.4809 + 32.0098i) q^{30} -39.3539 q^{31} +(-31.5488 + 18.2147i) q^{32} +(6.63313 + 11.4889i) q^{33} +67.0223 q^{34} +(-9.59634 + 57.1858i) q^{35} +(-3.95484 + 6.84998i) q^{36} +(7.35303 + 4.24527i) q^{37} +57.6934i q^{38} +(21.5990 + 6.36257i) q^{39} +29.0957i q^{40} +(-16.0214 + 27.7499i) q^{41} +(-29.2612 + 10.9251i) q^{42} +(-15.6700 - 27.1412i) q^{43} -20.1941i q^{44} +(12.4254 + 21.5215i) q^{45} +(74.3883 - 42.9481i) q^{46} +31.6325 q^{47} +(-29.3922 + 16.9696i) q^{48} +(-46.3159 - 15.9950i) q^{49} +(-97.3132 - 56.1838i) q^{50} +45.0618 q^{51} +(-23.6309 - 24.8268i) q^{52} +93.4856 q^{53} +(-6.69304 + 11.5927i) q^{54} +(-54.9463 - 31.7233i) q^{55} +(-24.2480 - 4.06906i) q^{56} +38.7896i q^{57} +(50.0970 - 28.9235i) q^{58} +(-4.85138 - 8.40284i) q^{59} -37.8284i q^{60} +(11.6324 - 6.71600i) q^{61} +(87.7990 + 50.6908i) q^{62} +(-19.6735 + 7.34541i) q^{63} +15.4685 q^{64} +(-104.674 + 25.2966i) q^{65} -34.1759i q^{66} +(49.5118 + 28.5857i) q^{67} +(-59.4040 - 34.2969i) q^{68} +(50.0143 - 28.8758i) q^{69} +(95.0692 - 115.221i) q^{70} +(-30.2202 + 17.4476i) q^{71} +(-9.12557 + 5.26865i) q^{72} +57.2114 q^{73} +(-10.9365 - 18.9425i) q^{74} +(-65.4276 - 37.7746i) q^{75} +(29.5231 - 51.1355i) q^{76} +(34.1221 - 41.3551i) q^{77} +(-39.9922 - 42.0162i) q^{78} -59.4292 q^{79} +(81.1579 - 140.570i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(71.4880 - 41.2736i) q^{82} -128.485 q^{83} +(31.5258 + 5.29033i) q^{84} +(-186.637 + 107.755i) q^{85} +80.7364i q^{86} +(33.6822 - 19.4464i) q^{87} +(13.4514 - 23.2984i) q^{88} +(-25.4040 + 44.0010i) q^{89} -64.0196i q^{90} +(-6.44321 - 90.7716i) q^{91} -87.9103 q^{92} +(59.0308 + 34.0814i) q^{93} +(-70.5726 - 40.7451i) q^{94} +(-92.7567 - 160.659i) q^{95} +63.0976 q^{96} +(-29.7641 - 51.5529i) q^{97} +(82.7286 + 95.3433i) q^{98} -22.9778i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9}+O(q^{10}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9	\( 36 q - 54 q^{3} + 44 q^{4} - 4 q^{5} + 10 q^{7} + 54 q^{9} + 42 q^{11} - 36 q^{13} + 16 q^{14} + 6 q^{15} - 96 q^{16} - 12 q^{17} + 12 q^{19} - 10 q^{20} - 18 q^{22} + 24 q^{23} + 264 q^{25} + 114 q^{26} - 104 q^{28} + 76 q^{29} - 160 q^{31} - 42 q^{33} - 192 q^{34} - 100 q^{35} - 132 q^{36} + 6 q^{37} + 60 q^{39} + 200 q^{41} + 18 q^{42} + 48 q^{43} - 6 q^{45} + 396 q^{46} + 56 q^{47} + 288 q^{48} - 154 q^{49} - 102 q^{50} + 24 q^{51} - 360 q^{52} + 76 q^{53} + 192 q^{55} - 132 q^{56} - 162 q^{58} + 128 q^{59} - 120 q^{61} + 24 q^{62} - 30 q^{63} - 484 q^{64} - 284 q^{65} - 144 q^{67} + 234 q^{68} - 72 q^{69} + 300 q^{70} - 96 q^{71} + 728 q^{73} - 144 q^{74} - 396 q^{75} - 516 q^{76} - 160 q^{77} - 144 q^{78} + 68 q^{79} - 58 q^{80} - 162 q^{81} + 72 q^{82} + 368 q^{83} + 108 q^{84} - 324 q^{85} - 228 q^{87} + 186 q^{88} + 92 q^{89} + 176 q^{91} - 1044 q^{92} + 240 q^{93} - 336 q^{94} - 2 q^{95} - 72 q^{97} + 234 q^{98}+O(q^{100}) \) 36 * q - 54 * q^3 + 44 * q^4 - 4 * q^5 + 10 * q^7 + 54 * q^9 + 42 * q^11 - 36 * q^13 + 16 * q^14 + 6 * q^15 - 96 * q^16 - 12 * q^17 + 12 * q^19 - 10 * q^20 - 18 * q^22 + 24 * q^23 + 264 * q^25 + 114 * q^26 - 104 * q^28 + 76 * q^29 - 160 * q^31 - 42 * q^33 - 192 * q^34 - 100 * q^35 - 132 * q^36 + 6 * q^37 + 60 * q^39 + 200 * q^41 + 18 * q^42 + 48 * q^43 - 6 * q^45 + 396 * q^46 + 56 * q^47 + 288 * q^48 - 154 * q^49 - 102 * q^50 + 24 * q^51 - 360 * q^52 + 76 * q^53 + 192 * q^55 - 132 * q^56 - 162 * q^58 + 128 * q^59 - 120 * q^61 + 24 * q^62 - 30 * q^63 - 484 * q^64 - 284 * q^65 - 144 * q^67 + 234 * q^68 - 72 * q^69 + 300 * q^70 - 96 * q^71 + 728 * q^73 - 144 * q^74 - 396 * q^75 - 516 * q^76 - 160 * q^77 - 144 * q^78 + 68 * q^79 - 58 * q^80 - 162 * q^81 + 72 * q^82 + 368 * q^83 + 108 * q^84 - 324 * q^85 - 228 * q^87 + 186 * q^88 + 92 * q^89 + 176 * q^91 - 1044 * q^92 + 240 * q^93 - 336 * q^94 - 2 * q^95 - 72 * q^97 + 234 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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