LMFDB - Embedded newform 210.3.o.a.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(31,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("210.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.o (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:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.3
Root			$-1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	210.61
Dual form			210.3.o.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-6.16205 - 10.6730i) q^{11} +(-3.00000 - 1.73205i) q^{12} -7.26007i q^{13} +(-7.73861 + 6.17364i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(8.04643 - 4.64561i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(5.26235 + 3.03822i) q^{19} +4.47214i q^{20} +(-11.9886 + 1.80922i) q^{21} -17.4289 q^{22} +(1.12514 - 1.94880i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-8.89173 - 5.13364i) q^{26} -5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} +42.2122 q^{29} +(-2.73861 + 4.74342i) q^{30} +(-1.05527 + 0.609262i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-18.4862 - 10.6730i) q^{33} -13.1398i q^{34} +(9.76139 + 12.2358i) q^{35} -6.00000 q^{36} +(-17.5296 + 30.3622i) q^{37} +(7.44209 - 4.29669i) q^{38} +(-6.28740 - 10.8901i) q^{39} +(5.47723 + 3.16228i) q^{40} -57.8811i q^{41} +(-6.26139 + 15.9623i) q^{42} -34.0190 q^{43} +(-12.3241 + 21.3460i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(-1.59119 - 2.75603i) q^{46} +(49.4411 + 28.5448i) q^{47} +6.92820i q^{48} +(35.9317 + 33.3154i) q^{49} +7.07107 q^{50} +(8.04643 - 13.9368i) q^{51} +(-12.5748 + 7.26007i) q^{52} +(-7.27009 - 12.5922i) q^{53} +(-6.36396 - 3.67423i) q^{54} +27.5575i q^{55} +(18.4317 + 7.23003i) q^{56} +10.5247 q^{57} +(29.8485 - 51.6992i) q^{58} +(50.1067 - 28.9291i) q^{59} +(3.87298 + 6.70820i) q^{60} +(-5.07658 - 2.93096i) q^{61} +1.72325i q^{62} +(-16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(-8.11700 + 14.0591i) q^{65} +(-26.1434 + 15.0939i) q^{66} +(-24.7355 - 42.8431i) q^{67} +(-16.0929 - 9.29122i) q^{68} -3.89761i q^{69} +(21.8881 - 3.30318i) q^{70} +101.986 q^{71} +(-4.24264 + 7.34847i) q^{72} +(71.2783 - 41.1525i) q^{73} +(24.7906 + 42.9387i) q^{74} +(7.50000 + 4.33013i) q^{75} -12.1529i q^{76} +(12.8732 + 85.3029i) q^{77} -17.7835 q^{78} +(-55.8530 + 96.7403i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-70.8895 - 40.9281i) q^{82} -91.6237i q^{83} +(15.1223 + 18.9557i) q^{84} -20.7758 q^{85} +(-24.0551 + 41.6646i) q^{86} +(63.3183 - 36.5568i) q^{87} +(17.4289 + 30.1878i) q^{88} +(110.673 + 63.8973i) q^{89} +9.48683i q^{90} +(-18.5582 + 47.3108i) q^{91} -4.50057 q^{92} +(-1.05527 + 1.82779i) q^{93} +(69.9203 - 40.3685i) q^{94} +(-6.79367 - 11.7670i) q^{95} +(8.48528 + 4.89898i) q^{96} -61.4455i q^{97} +(66.2104 - 20.4496i) q^{98} -36.9723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9	$ 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 40 q^{14} - 16 q^{16} + 84 q^{17} + 108 q^{19} - 48 q^{22} + 12 q^{23} + 20 q^{25} - 96 q^{26} + 72 q^{29} - 132 q^{31} - 12 q^{33} + 100 q^{35} - 48 q^{36} - 96 q^{37} - 168 q^{38} + 24 q^{39} - 72 q^{42} - 112 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} + 156 q^{49} + 84 q^{51} + 48 q^{52} + 32 q^{53} + 16 q^{56} + 216 q^{57} + 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} + 20 q^{65} - 72 q^{66} - 120 q^{67} - 168 q^{68} + 8 q^{71} + 24 q^{73} - 16 q^{74} + 60 q^{75} - 216 q^{77} - 192 q^{78} + 12 q^{79} - 36 q^{81} + 24 q^{82} + 120 q^{85} - 40 q^{86} + 108 q^{87} + 48 q^{88} + 492 q^{89} - 308 q^{91} - 48 q^{92} - 132 q^{93} + 480 q^{94} - 40 q^{95} - 24 q^{99}+O(q^{100}) $ 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 40 * q^14 - 16 * q^16 + 84 * q^17 + 108 * q^19 - 48 * q^22 + 12 * q^23 + 20 * q^25 - 96 * q^26 + 72 * q^29 - 132 * q^31 - 12 * q^33 + 100 * q^35 - 48 * q^36 - 96 * q^37 - 168 * q^38 + 24 * q^39 - 72 * q^42 - 112 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 + 156 * q^49 + 84 * q^51 + 48 * q^52 + 32 * q^53 + 16 * q^56 + 216 * q^57 + 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 + 20 * q^65 - 72 * q^66 - 120 * q^67 - 168 * q^68 + 8 * q^71 + 24 * q^73 - 16 * q^74 + 60 * q^75 - 216 * q^77 - 192 * q^78 + 12 * q^79 - 36 * q^81 + 24 * q^82 + 120 * q^85 - 40 * q^86 + 108 * q^87 + 48 * q^88 + 492 * q^89 - 308 * q^91 - 48 * q^92 - 132 * q^93 + 480 * q^94 - 40 * q^95 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$3$	1.50000	−	0.866025i	0.500000	−	0.288675i
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$5$	−1.93649	−	1.11803i	−0.387298	−	0.223607i
$6$		−	2.44949i		−	0.408248i
$7$	−6.51658	−	2.55620i	−0.930940	−	0.365172i
$7$	−6.51658	−	2.55620i	−0.930940	−	0.365172i
$8$	−2.82843			−0.353553
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−2.73861	+	1.58114i	−0.273861	+	0.158114i
$11$	−6.16205	−	10.6730i	−0.560187	−	0.970272i	−0.997480	−	0.0709528i	$-0.977396\pi$
$11$	−6.16205	−	10.6730i	−0.560187	−	0.970272i	0.437293	−	0.899319i	$-0.355937\pi$
$12$	−3.00000	−	1.73205i	−0.250000	−	0.144338i
$13$		−	7.26007i		−	0.558467i	−0.960223	−	0.279233i	$-0.909920\pi$
$13$		−	7.26007i		−	0.558467i	0.960223	−	0.279233i	$-0.0900803\pi$
$14$	−7.73861	+	6.17364i	−0.552758	+	0.440975i
$15$	−3.87298			−0.258199
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	8.04643	−	4.64561i	0.473319	−	0.273271i	−0.244309	−	0.969697i	$-0.578561\pi$
$17$	8.04643	−	4.64561i	0.473319	−	0.273271i	0.717628	+	0.696426i	$0.245228\pi$
$18$	−2.12132	−	3.67423i	−0.117851	−	0.204124i
$19$	5.26235	+	3.03822i	0.276966	+	0.159906i	0.632049	−	0.774928i	$-0.282214\pi$
$19$	5.26235	+	3.03822i	0.276966	+	0.159906i	−0.355083	+	0.934835i	$0.615547\pi$
$20$			4.47214i			0.223607i
$21$	−11.9886	+	1.80922i	−0.570886	+	0.0861535i
$22$	−17.4289			−0.792224
$23$	1.12514	−	1.94880i	0.0489192	−	0.0847306i	−0.840529	−	0.541767i	$-0.817756\pi$
$23$	1.12514	−	1.94880i	0.0489192	−	0.0847306i	0.889448	+	0.457036i	$0.151089\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$	2.50000	+	4.33013i	0.100000	+	0.173205i
$26$	−8.89173	−	5.13364i	−0.341990	−	0.197448i
$27$		−	5.19615i		−	0.192450i
$28$	2.08911	+	13.8433i	0.0746112	+	0.494402i
$29$	42.2122			1.45559			0.727797	−	0.685793i	$-0.240544\pi$
$29$	42.2122			1.45559			0.727797	+	0.685793i	$0.240544\pi$
$30$	−2.73861	+	4.74342i	−0.0912871	+	0.158114i
$31$	−1.05527	+	0.609262i	−0.0340411	+	0.0196536i	−0.516924	−	0.856031i	$-0.672923\pi$
$31$	−1.05527	+	0.609262i	−0.0340411	+	0.0196536i	0.482883	+	0.875685i	$0.339590\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$	−18.4862	−	10.6730i	−0.560187	−	0.323424i
$34$		−	13.1398i		−	0.386464i
$35$	9.76139	+	12.2358i	0.278897	+	0.349595i
$36$	−6.00000			−0.166667
$37$	−17.5296	+	30.3622i	−0.473774	+	0.820600i	−0.999549	−	0.0300231i	$-0.990442\pi$
$37$	−17.5296	+	30.3622i	−0.473774	+	0.820600i	0.525775	+	0.850623i	$0.323775\pi$
$38$	7.44209	−	4.29669i	0.195845	−	0.113071i
$39$	−6.28740	−	10.8901i	−0.161215	−	0.279233i
$40$	5.47723	+	3.16228i	0.136931	+	0.0790569i
$41$		−	57.8811i		−	1.41173i	−0.708345	−	0.705867i	$-0.750558\pi$
$41$		−	57.8811i		−	1.41173i	0.708345	−	0.705867i	$-0.249442\pi$
$42$	−6.26139	+	15.9623i	−0.149081	+	0.380055i
$43$	−34.0190			−0.791140			−0.395570	−	0.918436i	$-0.629453\pi$
$43$	−34.0190			−0.791140			−0.395570	+	0.918436i	$0.629453\pi$
$44$	−12.3241	+	21.3460i	−0.280093	+	0.485136i
$45$	−5.80948	+	3.35410i	−0.129099	+	0.0745356i
$46$	−1.59119	−	2.75603i	−0.0345911	−	0.0599136i
$47$	49.4411	+	28.5448i	1.05194	+	0.607337i	0.923191	−	0.384340i	$-0.125571\pi$
$47$	49.4411	+	28.5448i	1.05194	+	0.607337i	0.128747	+	0.991677i	$0.458904\pi$
$48$			6.92820i			0.144338i
$49$	35.9317	+	33.3154i	0.733300	+	0.679906i
$50$	7.07107			0.141421
$51$	8.04643	−	13.9368i	0.157773	−	0.273271i
$52$	−12.5748	+	7.26007i	−0.241823	+	0.139617i
$53$	−7.27009	−	12.5922i	−0.137172	−	0.237588i	0.789253	−	0.614068i	$-0.210468\pi$
$53$	−7.27009	−	12.5922i	−0.137172	−	0.237588i	−0.926425	+	0.376480i	$0.877134\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$			27.5575i			0.501046i
$56$	18.4317	+	7.23003i	0.329137	+	0.129108i
$57$	10.5247			0.184644
$58$	29.8485	−	51.6992i	0.514630	−	0.891365i
$59$	50.1067	−	28.9291i	0.849266	−	0.490324i	−0.0111375	−	0.999938i	$-0.503545\pi$
$59$	50.1067	−	28.9291i	0.849266	−	0.490324i	0.860403	+	0.509614i	$0.170212\pi$
$60$	3.87298	+	6.70820i	0.0645497	+	0.111803i
$61$	−5.07658	−	2.93096i	−0.0832226	−	0.0480486i	0.457811	−	0.889049i	$-0.348634\pi$
$61$	−5.07658	−	2.93096i	−0.0832226	−	0.0480486i	−0.541034	+	0.841001i	$0.681967\pi$
$62$			1.72325i			0.0277944i
$63$	−16.4161	+	13.0963i	−0.260573	+	0.207877i
$64$	8.00000			0.125000
$65$	−8.11700	+	14.0591i	−0.124877	+	0.216293i
$66$	−26.1434	+	15.0939i	−0.396112	+	0.228695i
$67$	−24.7355	−	42.8431i	−0.369186	−	0.639449i	0.620252	−	0.784402i	$-0.287030\pi$
$67$	−24.7355	−	42.8431i	−0.369186	−	0.639449i	−0.989439	+	0.144953i	$0.953697\pi$
$68$	−16.0929	−	9.29122i	−0.236660	−	0.136636i
$69$		−	3.89761i		−	0.0564871i
$70$	21.8881	−	3.30318i	0.312687	−	0.0471882i
$71$	101.986			1.43643			0.718214	−	0.695822i	$-0.244960\pi$
$71$	101.986			1.43643			0.718214	+	0.695822i	$0.244960\pi$
$72$	−4.24264	+	7.34847i	−0.0589256	+	0.102062i
$73$	71.2783	−	41.1525i	0.976415	−	0.563733i	0.0752290	−	0.997166i	$-0.476031\pi$
$73$	71.2783	−	41.1525i	0.976415	−	0.563733i	0.901186	+	0.433433i	$0.142698\pi$
$74$	24.7906	+	42.9387i	0.335009	+	0.580252i
$75$	7.50000	+	4.33013i	0.100000	+	0.0577350i
$76$		−	12.1529i		−	0.159906i
$77$	12.8732	+	85.3029i	0.167185	+	1.10783i
$78$	−17.7835			−0.227993
$79$	−55.8530	+	96.7403i	−0.707001	+	1.22456i	0.258964	+	0.965887i	$0.416619\pi$
$79$	−55.8530	+	96.7403i	−0.707001	+	1.22456i	−0.965965	+	0.258674i	$0.916714\pi$
$80$	7.74597	−	4.47214i	0.0968246	−	0.0559017i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−70.8895	−	40.9281i	−0.864507	−	0.499123i
$83$		−	91.6237i		−	1.10390i	−0.833877	−	0.551950i	$-0.813884\pi$
$83$		−	91.6237i		−	1.10390i	0.833877	−	0.551950i	$-0.186116\pi$
$84$	15.1223	+	18.9557i	0.180027	+	0.225663i
$85$	−20.7758			−0.244421
$86$	−24.0551	+	41.6646i	−0.279710	+	0.484472i
$87$	63.3183	−	36.5568i	0.727797	−	0.420194i
$88$	17.4289	+	30.1878i	0.198056	+	0.343043i
$89$	110.673	+	63.8973i	1.24352	+	0.717947i	0.969809	−	0.243864i	$-0.0784151\pi$
$89$	110.673	+	63.8973i	1.24352	+	0.717947i	0.273712	+	0.961812i	$0.411748\pi$
$90$			9.48683i			0.105409i
$91$	−18.5582	+	47.3108i	−0.203936	+	0.519899i
$92$	−4.50057			−0.0489192
$93$	−1.05527	+	1.82779i	−0.0113470	+	0.0196536i
$94$	69.9203	−	40.3685i	0.743833	−	0.429452i
$95$	−6.79367	−	11.7670i	−0.0715123	−	0.123863i
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$		−	61.4455i		−	0.633459i	−0.948516	−	0.316729i	$-0.897415\pi$
$97$		−	61.4455i		−	0.633459i	0.948516	−	0.316729i	$-0.102585\pi$
$98$	66.2104	−	20.4496i	0.675616	−	0.208669i
$99$	−36.9723			−0.373458
$100$	5.00000	−	8.66025i	0.0500000	−	0.0866025i
$101$	53.8141	−	31.0696i	0.532813	−	0.307620i	−0.209348	−	0.977841i	$-0.567134\pi$
$101$	53.8141	−	31.0696i	0.532813	−	0.307620i	0.742161	+	0.670221i	$0.233801\pi$
$102$	−11.3794	−	19.7096i	−0.111562	−	0.193232i
$103$	−154.102	−	88.9709i	−1.49614	−	0.863795i	−0.496147	−	0.868238i	$-0.665252\pi$
$103$	−154.102	−	88.9709i	−1.49614	−	0.863795i	−0.999990	+	0.00444312i	$0.998586\pi$
$104$			20.5346i			0.197448i
$105$	25.2386	+	9.90012i	0.240368	+	0.0942869i
$106$	−20.5629			−0.193990
$107$	−42.4855	+	73.5871i	−0.397061	+	0.687730i	−0.993362	−	0.115031i	$-0.963303\pi$
$107$	−42.4855	+	73.5871i	−0.397061	+	0.687730i	0.596301	+	0.802761i	$0.296637\pi$
$108$	−9.00000	+	5.19615i	−0.0833333	+	0.0481125i
$109$	86.4291	+	149.700i	0.792928	+	1.37339i	0.924147	+	0.382037i	$0.124777\pi$
$109$	86.4291	+	149.700i	0.792928	+	1.37339i	−0.131219	+	0.991353i	$0.541889\pi$
$110$	33.7510	+	19.4861i	0.306827	+	0.177147i
$111$			60.7244i			0.547067i
$112$	21.8881	−	17.4617i	0.195429	−	0.155908i
$113$	−82.0616			−0.726209			−0.363105	−	0.931748i	$-0.618283\pi$
$113$	−82.0616			−0.726209			−0.363105	+	0.931748i	$0.618283\pi$
$114$	7.44209	−	12.8901i	0.0652815	−	0.113071i
$115$	−4.35766	+	2.51590i	−0.0378927	+	0.0218774i
$116$	−42.2122	−	73.1137i	−0.363898	−	0.630290i
$117$	−18.8622	−	10.8901i	−0.161215	−	0.0930778i
$118$		−	81.8238i		−	0.693422i
$119$	−64.3103	+	9.70520i	−0.540423	+	0.0815563i
$120$	10.9545			0.0912871
$121$	−15.4418	+	26.7460i	−0.127618	+	0.221042i
$122$	−7.17937	+	4.14501i	−0.0588473	+	0.0339755i
$123$	−50.1265	−	86.8216i	−0.407532	−	0.705867i
$124$	2.11055	+	1.21852i	0.0170205	+	0.00982681i
$125$		−	11.1803i		−	0.0894427i
$126$	4.43168	+	29.3660i	0.0351720	+	0.233063i
$127$	−193.480			−1.52346			−0.761732	−	0.647892i	$-0.775651\pi$
$127$	−193.480			−1.52346			−0.761732	+	0.647892i	$0.775651\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$	−51.0285	+	29.4613i	−0.395570	+	0.228382i
$130$	11.4792	+	19.8825i	0.0883013	+	0.152942i
$131$	−156.850	−	90.5572i	−1.19733	−	0.691276i	−0.237368	−	0.971420i	$-0.576285\pi$
$131$	−156.850	−	90.5572i	−1.19733	−	0.691276i	−0.959958	+	0.280143i	$0.909618\pi$
$132$			42.6920i			0.323424i
$133$	−26.5263	−	33.2504i	−0.199446	−	0.250003i
$134$	−69.9625			−0.522108
$135$	−5.80948	+	10.0623i	−0.0430331	+	0.0745356i
$136$	−22.7587	+	13.1398i	−0.167344	+	0.0966159i
$137$	−0.631666	−	1.09408i	−0.00461070	−	0.00798597i	0.863711	−	0.503988i	$-0.168134\pi$
$137$	−0.631666	−	1.09408i	−0.00461070	−	0.00798597i	−0.868322	+	0.496002i	$0.834801\pi$
$138$	−4.77358	−	2.75603i	−0.0345911	−	0.0199712i
$139$		−	12.1327i		−	0.0872857i	−0.999047	−	0.0436428i	$-0.986104\pi$
$139$		−	12.1327i		−	0.0872857i	0.999047	−	0.0436428i	$-0.0138964\pi$
$140$	11.4317	−	29.1430i	0.0816548	−	0.208165i
$141$	98.8822			0.701292
$142$	72.1153	−	124.907i	0.507854	−	0.879629i
$143$	−77.4866	+	44.7369i	−0.541865	+	0.312846i
$144$	6.00000	+	10.3923i	0.0416667	+	0.0721688i
$145$	−81.7436	−	47.1947i	−0.563749	−	0.325481i
$146$		−	116.397i		−	0.797239i
$147$	82.7495	+	18.8553i	0.562922	+	0.128268i
$148$	70.1185			0.473774
$149$	−144.863	+	250.910i	−0.972233	+	1.68396i	−0.283453	+	0.958986i	$0.591480\pi$
$149$	−144.863	+	250.910i	−0.972233	+	1.68396i	−0.688780	+	0.724971i	$0.741853\pi$
$150$	10.6066	−	6.12372i	0.0707107	−	0.0408248i
$151$	−58.6516	−	101.588i	−0.388421	−	0.672765i	0.603816	−	0.797124i	$-0.293646\pi$
$151$	−58.6516	−	101.588i	−0.388421	−	0.672765i	−0.992237	+	0.124358i	$0.960313\pi$
$152$	−14.8842	−	8.59339i	−0.0979223	−	0.0565354i
$153$		−	27.8737i		−	0.182181i
$154$	113.577	+	44.5518i	0.737513	+	0.289298i
$155$	2.72470			0.0175787
$156$	−12.5748	+	21.7802i	−0.0806077	+	0.139617i
$157$	159.121	−	91.8687i	1.01351	−	0.585151i	0.101294	−	0.994857i	$-0.467702\pi$
$157$	159.121	−	91.8687i	1.01351	−	0.585151i	0.912218	+	0.409705i	$0.134368\pi$
$158$	78.9881	+	136.811i	0.499925	+	0.865895i
$159$	−21.8103	−	12.5922i	−0.137172	−	0.0791960i
$160$		−	12.6491i		−	0.0790569i
$161$	−12.3136	+	9.82345i	−0.0764821	+	0.0610152i
$162$	−12.7279			−0.0785674
$163$	−60.7854	+	105.283i	−0.372917	+	0.645911i	−0.990013	−	0.140977i	$-0.954976\pi$
$163$	−60.7854	+	105.283i	−0.372917	+	0.645911i	0.617096	+	0.786888i	$0.288309\pi$
$164$	−100.253	+	57.8811i	−0.611298	+	0.352933i
$165$	23.8655	+	41.3363i	0.144640	+	0.250523i
$166$	−112.216	−	64.7878i	−0.675998	−	0.390288i
$167$		−	94.6539i		−	0.566790i	−0.959003	−	0.283395i	$-0.908539\pi$
$167$		−	94.6539i		−	0.566790i	0.959003	−	0.283395i	$-0.0914608\pi$
$168$	33.9089	−	5.11726i	0.201839	−	0.0304599i
$169$	116.291			0.688115
$170$	−14.6907	+	25.4450i	−0.0864159	+	0.149677i
$171$	15.7871	−	9.11466i	0.0923220	−	0.0533021i
$172$	34.0190	+	58.9227i	0.197785	+	0.342574i
$173$	−225.766	−	130.346i	−1.30501	−	0.753445i	−0.323747	−	0.946144i	$-0.604943\pi$
$173$	−225.766	−	130.346i	−1.30501	−	0.753445i	−0.981258	+	0.192699i	$0.938276\pi$
$174$		−	103.398i		−	0.594244i
$175$	−5.22278	−	34.6081i	−0.0298445	−	0.197761i
$176$	49.2964			0.280093
$177$	50.1067	−	86.7873i	0.283089	−	0.490324i
$178$	156.516	−	90.3645i	0.879302	−	0.507666i
$179$	−153.264	−	265.462i	−0.856225	−	1.48303i	−0.875504	−	0.483212i	$-0.839470\pi$
$179$	−153.264	−	265.462i	−0.856225	−	1.48303i	0.0192782	−	0.999814i	$-0.493863\pi$
$180$	11.6190	+	6.70820i	0.0645497	+	0.0372678i
$181$			314.885i			1.73970i	0.493318	+	0.869849i	$0.335784\pi$
$181$			314.885i			1.73970i	−0.493318	+	0.869849i	$0.664216\pi$
$182$	44.8211	+	56.1828i	0.246270	+	0.308697i
$183$	−10.1532			−0.0554817
$184$	−3.18238	+	5.51205i	−0.0172956	+	0.0299568i
$185$	67.8920	−	39.1974i	0.366984	−	0.211878i
$186$	1.49238	+	2.58488i	0.00802356	+	0.0138972i
$187$	−99.1651	−	57.2530i	−0.530295	−	0.306166i
$188$		−	114.179i		−	0.607337i
$189$	−13.2824	+	33.8612i	−0.0702773	+	0.179160i
$190$	−19.2154			−0.101134
$191$	45.3946	−	78.6257i	0.237668	−	0.411653i	−0.722377	−	0.691500i	$-0.756950\pi$
$191$	45.3946	−	78.6257i	0.237668	−	0.411653i	0.960045	+	0.279847i	$0.0902837\pi$
$192$	12.0000	−	6.92820i	0.0625000	−	0.0360844i
$193$	114.828	+	198.887i	0.594961	+	1.03050i	0.993552	+	0.113374i	$0.0361659\pi$
$193$	114.828	+	198.887i	0.594961	+	1.03050i	−0.398591	+	0.917129i	$0.630501\pi$
$194$	−75.2551	−	43.4485i	−0.387913	−	0.223962i
$195$			28.1181i			0.144195i
$196$	21.7723	−	95.5509i	0.111083	−	0.487504i
$197$	227.989			1.15730			0.578652	−	0.815574i	$-0.303579\pi$
$197$	227.989			1.15730			0.578652	+	0.815574i	$0.303579\pi$
$198$	−26.1434	+	45.2817i	−0.132037	+	0.228695i
$199$	9.56623	−	5.52307i	0.0480715	−	0.0277541i	−0.475772	−	0.879569i	$-0.657831\pi$
$199$	9.56623	−	5.52307i	0.0480715	−	0.0277541i	0.523843	+	0.851815i	$0.324498\pi$
$200$	−7.07107	−	12.2474i	−0.0353553	−	0.0612372i
$201$	−74.2064	−	42.8431i	−0.369186	−	0.213150i
$202$		−	87.8781i		−	0.435040i
$203$	−275.079	−	107.903i	−1.35507	−	0.531541i
$204$	−32.1857			−0.157773
$205$	−64.7130	+	112.086i	−0.315673	+	0.546762i
$206$	−217.933	+	125.824i	−1.05793	+	0.610796i
$207$	−3.37543	−	5.84641i	−0.0163064	−	0.0282435i
$208$	25.1496	+	14.5201i	0.120912	+	0.0698083i
$209$		−	74.8867i		−	0.358310i
$210$	29.9715	−	23.9104i	0.142722	−	0.113859i
$211$	151.187			0.716526			0.358263	−	0.933621i	$-0.383369\pi$
$211$	151.187			0.716526			0.358263	+	0.933621i	$0.383369\pi$
$212$	−14.5402	+	25.1843i	−0.0685858	+	0.118794i
$213$	152.980	−	88.3228i	0.718214	−	0.414661i
$214$	60.0836	+	104.068i	0.280765	+	0.486298i
$215$	65.8775	+	38.0344i	0.306407	+	0.176904i
$216$			14.6969i			0.0680414i
$217$	8.43417	−	1.27282i	0.0388671	−	0.00586552i
$218$	244.458			1.12137
$219$	71.2783	−	123.458i	0.325472	−	0.563733i
$220$	47.7311	−	27.5575i	0.216959	−	0.125262i
$221$	−33.7274	−	58.4176i	−0.152613	−	0.264333i
$222$	74.3719	+	42.9387i	0.335009	+	0.193417i
$223$			308.586i			1.38379i	0.721997	+	0.691896i	$0.243224\pi$
$223$			308.586i			1.38379i	−0.721997	+	0.691896i	$0.756776\pi$
$224$	−5.90890	−	39.1546i	−0.0263790	−	0.174797i
$225$	15.0000			0.0666667
$226$	−58.0263	+	100.505i	−0.256754	+	0.444710i
$227$	86.9683	−	50.2112i	0.383120	−	0.221195i	−0.296055	−	0.955171i	$-0.595671\pi$
$227$	86.9683	−	50.2112i	0.383120	−	0.221195i	0.679175	+	0.733976i	$0.262338\pi$
$228$	−10.5247	−	18.2293i	−0.0461610	−	0.0799532i
$229$	277.125	+	159.998i	1.21015	+	0.698682i	0.962793	−	0.270241i	$-0.0871034\pi$
$229$	277.125	+	159.998i	1.21015	+	0.698682i	0.247361	+	0.968923i	$0.420437\pi$
$230$			7.11603i			0.0309392i
$231$	93.1843	+	116.806i	0.403395	+	0.505653i
$232$	−119.394			−0.514630
$233$	−155.395	+	269.151i	−0.666929	+	1.15516i	0.311829	+	0.950138i	$0.399058\pi$
$233$	−155.395	+	269.151i	−0.666929	+	1.15516i	−0.978758	+	0.205017i	$0.934275\pi$
$234$	−26.6752	+	15.4009i	−0.113997	+	0.0658159i
$235$	−63.8282	−	110.554i	−0.271609	−	0.470441i
$236$	−100.213	−	57.8582i	−0.424633	−	0.245162i
$237$			193.481i			0.816374i
$238$	−33.5879	+	85.6264i	−0.141126	+	0.359775i
$239$	136.263			0.570139			0.285069	−	0.958507i	$-0.407983\pi$
$239$	136.263			0.570139			0.285069	+	0.958507i	$0.407983\pi$
$240$	7.74597	−	13.4164i	0.0322749	−	0.0559017i
$241$	334.441	−	193.090i	1.38772	−	0.801202i	0.394665	−	0.918825i	$-0.370861\pi$
$241$	334.441	−	193.090i	1.38772	−	0.801202i	0.993058	+	0.117623i	$0.0375274\pi$
$242$	21.8380	+	37.8246i	0.0902398	+	0.156300i
$243$	−13.5000	−	7.79423i	−0.0555556	−	0.0320750i
$244$			11.7239i			0.0480486i
$245$	−32.3337	−	104.688i	−0.131974	−	0.427297i
$246$	−141.779			−0.576338
$247$	22.0577	−	38.2050i	0.0893024	−	0.154676i
$248$	2.98476	−	1.72325i	0.0120353	−	0.00694860i
$249$	−79.3485	−	137.436i	−0.318669	−	0.551950i
$250$	−13.6931	−	7.90569i	−0.0547723	−	0.0316228i
$251$			99.3717i			0.395903i	0.980212	+	0.197952i	$0.0634289\pi$
$251$			99.3717i			0.395903i	−0.980212	+	0.197952i	$0.936571\pi$
$252$	39.0995	+	15.3372i	0.155157	+	0.0608619i
$253$	−27.7328			−0.109616
$254$	−136.811	+	236.964i	−0.538626	+	0.932928i
$255$	−31.1637	+	17.9924i	−0.122211	+	0.0705583i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	18.2886	+	10.5589i	0.0711617	+	0.0410852i	0.535159	−	0.844752i	$-0.320252\pi$
$257$	18.2886	+	10.5589i	0.0711617	+	0.0410852i	−0.463997	+	0.885837i	$0.653585\pi$
$258$			83.3292i			0.322982i
$259$	191.845	−	153.049i	0.740715	−	0.590921i
$260$	32.4680			0.124877
$261$	63.3183	−	109.671i	0.242599	−	0.420194i
$262$	−221.819	+	128.067i	−0.846637	+	0.488806i
$263$	190.259	+	329.538i	0.723417	+	1.25299i	0.959622	+	0.281292i	$0.0907629\pi$
$263$	190.259	+	329.538i	0.723417	+	1.25299i	−0.236205	+	0.971703i	$0.575904\pi$
$264$	52.2868	+	30.1878i	0.198056	+	0.114348i
$265$			32.5128i			0.122690i
$266$	−59.4802	+	8.97628i	−0.223610	+	0.0337454i
$267$	221.347			0.829014
$268$	−49.4709	+	85.6862i	−0.184593	+	0.319725i
$269$	14.5415	−	8.39551i	0.0540574	−	0.0312101i	−0.472728	−	0.881209i	$-0.656731\pi$
$269$	14.5415	−	8.39551i	0.0540574	−	0.0312101i	0.526785	+	0.849998i	$0.323397\pi$
$270$	8.21584	+	14.2302i	0.0304290	+	0.0527046i
$271$	320.146	+	184.836i	1.18135	+	0.682052i	0.956326	−	0.292301i	$-0.0944209\pi$
$271$	320.146	+	184.836i	1.18135	+	0.682052i	0.225023	+	0.974353i	$0.427754\pi$
$272$			37.1649i			0.136636i
$273$	13.1351	+	87.0381i	0.0481139	+	0.318821i
$274$	−1.78662			−0.00652051
$275$	30.8103	−	53.3650i	0.112037	−	0.194054i
$276$	−6.75086	+	3.89761i	−0.0244596	+	0.0141218i
$277$	−242.912	−	420.736i	−0.876940	−	1.51890i	−0.854682	−	0.519152i	$-0.826248\pi$
$277$	−242.912	−	420.736i	−0.876940	−	1.51890i	−0.0222577	−	0.999752i	$-0.507085\pi$
$278$	−14.8595	−	8.57912i	−0.0534513	−	0.0308601i
$279$			3.65557i			0.0131024i
$280$	−27.6094	−	34.6081i	−0.0986049	−	0.123600i
$281$	360.234			1.28197			0.640986	−	0.767553i	$-0.278526\pi$
$281$	360.234			1.28197			0.640986	+	0.767553i	$0.278526\pi$
$282$	69.9203	−	121.106i	0.247944	−	0.429452i
$283$	234.261	−	135.251i	0.827778	−	0.477918i	−0.0253131	−	0.999680i	$-0.508058\pi$
$283$	234.261	−	135.251i	0.827778	−	0.477918i	0.853091	+	0.521762i	$0.174725\pi$
$284$	−101.986	−	176.646i	−0.359107	−	0.621992i
$285$	−20.3810	−	11.7670i	−0.0715123	−	0.0412877i
$286$			126.535i			0.442431i
$287$	−147.956	+	377.187i	−0.515525	+	1.31424i
$288$	16.9706			0.0589256
$289$	−101.337	+	175.520i	−0.350646	+	0.607336i
$290$	−115.603	+	66.7434i	−0.398631	+	0.230150i
$291$	−53.2134	−	92.1683i	−0.182864	−	0.316729i
$292$	−142.557	−	82.3051i	−0.488207	−	0.281867i
$293$			9.63230i			0.0328747i	0.999865	+	0.0164374i	$0.00523241\pi$
$293$			9.63230i			0.0328747i	−0.999865	+	0.0164374i	$0.994768\pi$
$294$	81.6057	−	88.0143i	0.277570	−	0.299368i
$295$	−129.375			−0.438559
$296$	49.5813	−	85.8773i	0.167504	−	0.290126i
$297$	−55.4585	+	32.0190i	−0.186729	+	0.107808i
$298$	204.867	+	354.840i	0.687472	+	1.19074i
$299$	−14.1484	−	8.16861i	−0.0473192	−	0.0273198i
$300$		−	17.3205i		−	0.0577350i
$301$	221.688	+	86.9594i	0.736504	+	0.288902i
$302$	−165.892			−0.549310
$303$	53.8141	−	93.2088i	0.177604	−	0.307620i
$304$	−21.0494	+	12.1529i	−0.0692415	+	0.0399766i
$305$	6.55383	+	11.3516i	0.0214880	+	0.0372183i
$306$	−34.1381	−	19.7096i	−0.111562	−	0.0644106i
$307$			46.0412i			0.149971i	0.997185	+	0.0749857i	$0.0238911\pi$
$307$			46.0412i			0.149971i	−0.997185	+	0.0749857i	$0.976109\pi$
$308$	134.876	−	107.600i	0.437908	−	0.349350i
$309$	−308.204			−0.997425
$310$	1.92666	−	3.33707i	0.00621502	−	0.0107647i
$311$	−378.160	+	218.331i	−1.21595	+	0.702029i	−0.964049	−	0.265724i	$-0.914389\pi$
$311$	−378.160	+	218.331i	−1.21595	+	0.702029i	−0.251901	+	0.967753i	$0.581056\pi$
$312$	17.7835	+	30.8019i	0.0569983	+	0.0987239i
$313$	248.135	+	143.261i	0.792764	+	0.457703i	0.840935	−	0.541137i	$-0.182006\pi$
$313$	248.135	+	143.261i	0.792764	+	0.457703i	−0.0481706	+	0.998839i	$0.515339\pi$
$314$		−	259.844i		−	0.827529i
$315$	46.4317	−	7.00710i	0.147402	−	0.0222447i
$316$	223.412			0.707001
$317$	0.684418	−	1.18545i	0.00215905	−	0.00373958i	−0.864944	−	0.501869i	$-0.832646\pi$
$317$	0.684418	−	1.18545i	0.00215905	−	0.00373958i	0.867103	+	0.498129i	$0.165979\pi$
$318$	−30.8444	+	17.8080i	−0.0969949	+	0.0560001i
$319$	−260.114	−	450.531i	−0.815404	−	1.41232i
$320$	−15.4919	−	8.94427i	−0.0484123	−	0.0279508i
$321$			147.174i			0.458487i
$322$	3.32418	+	22.0273i	0.0103235	+	0.0684077i
$323$	56.4575			0.174791
$324$	−9.00000	+	15.5885i	−0.0277778	+	0.0481125i
$325$	31.4370	−	18.1502i	0.0967293	−	0.0558467i
$326$	85.9636	+	148.893i	0.263692	+	0.456728i
$327$	259.287	+	149.700i	0.792928	+	0.457797i
$328$			163.712i			0.499123i
$329$	−249.221	−	312.396i	−0.757510	−	0.949533i
$330$	67.5019			0.204551
$331$	192.017	−	332.583i	0.580111	−	1.00478i	−0.415354	−	0.909660i	$-0.636342\pi$
$331$	192.017	−	332.583i	0.580111	−	1.00478i	0.995466	−	0.0951223i	$-0.0303242\pi$
$332$	−158.697	+	91.6237i	−0.478003	+	0.275975i
$333$	52.5889	+	91.0866i	0.157925	+	0.273533i
$334$	−115.927	−	66.9304i	−0.347087	−	0.200391i
$335$			110.620i			0.330210i
$336$	17.7099	−	45.1482i	0.0527080	−	0.134370i
$337$	−141.948			−0.421211			−0.210606	−	0.977571i	$-0.567544\pi$
$337$	−141.948			−0.421211			−0.210606	+	0.977571i	$0.567544\pi$
$338$	82.2305	−	142.427i	0.243285	−	0.421383i
$339$	−123.092	+	71.0675i	−0.363105	+	0.209639i
$340$	20.7758	+	35.9847i	0.0611053	+	0.105837i
$341$	13.0053	+	7.50861i	0.0381387	+	0.0220194i
$342$		−	25.7802i		−	0.0753806i
$343$	−148.991	−	308.951i	−0.434376	−	0.900732i
$344$	96.2203			0.279710
$345$	−4.35766	+	7.54769i	−0.0126309	+	0.0218774i
$346$	−319.281	+	184.337i	−0.922778	+	0.532766i
$347$	125.176	+	216.811i	0.360737	+	0.624815i	0.988082	−	0.153926i	$-0.0491918\pi$
$347$	125.176	+	216.811i	0.360737	+	0.624815i	−0.627345	+	0.778741i	$0.715858\pi$
$348$	−126.637	−	73.1137i	−0.363898	−	0.210097i
$349$		−	195.188i		−	0.559277i	−0.960105	−	0.279639i	$-0.909785\pi$
$349$		−	195.188i		−	0.559277i	0.960105	−	0.279639i	$-0.0902147\pi$
$350$	−46.0792	−	18.0751i	−0.131655	−	0.0516431i
$351$	−37.7244			−0.107477
$352$	34.8578	−	60.3756i	0.0990280	−	0.171521i
$353$	123.148	−	71.0997i	0.348862	−	0.201416i	−0.315322	−	0.948985i	$-0.602113\pi$
$353$	123.148	−	71.0997i	0.348862	−	0.201416i	0.664184	+	0.747569i	$0.268779\pi$
$354$	−70.8615	−	122.736i	−0.200174	−	0.346711i
$355$	−197.496	−	114.024i	−0.556326	−	0.321195i
$356$		−	255.589i		−	0.717947i
$357$	−88.0605	+	70.2522i	−0.246668	+	0.196785i
$358$	−433.497			−1.21089
$359$	328.443	−	568.880i	0.914884	−	1.58462i	0.107812	−	0.994171i	$-0.465616\pi$
$359$	328.443	−	568.880i	0.914884	−	1.58462i	0.807072	−	0.590453i	$-0.201051\pi$
$360$	16.4317	−	9.48683i	0.0456435	−	0.0263523i
$361$	−162.038	−	280.659i	−0.448860	−	0.777448i
$362$	385.654	+	222.658i	1.06534	+	0.615076i
$363$			53.4921i			0.147361i
$364$	100.503	−	15.1671i	0.276107	−	0.0416678i
$365$	−184.040			−0.504218
$366$	−7.17937	+	12.4350i	−0.0196158	+	0.0339755i
$367$	−444.403	+	256.576i	−1.21091	+	0.699117i	−0.962957	−	0.269655i	$-0.913090\pi$
$367$	−444.403	+	256.576i	−1.21091	+	0.699117i	−0.247950	+	0.968773i	$0.579757\pi$
$368$	4.50057	+	7.79522i	0.0122298	+	0.0211827i
$369$	−150.379	−	86.8216i	−0.407532	−	0.235289i
$370$		−	110.867i		−	0.299641i
$371$	15.1880	+	100.642i	0.0409381	+	0.271271i
$372$	4.22109			0.0113470
$373$	316.262	−	547.782i	0.847887	−	1.46858i	−0.0352027	−	0.999380i	$-0.511208\pi$
$373$	316.262	−	547.782i	0.847887	−	1.46858i	0.883090	−	0.469204i	$-0.155459\pi$
$374$	−140.241	+	80.9679i	−0.374975	+	0.216492i
$375$	−9.68246	−	16.7705i	−0.0258199	−	0.0447214i
$376$	−139.841	−	80.7370i	−0.371916	−	0.214726i
$377$		−	306.463i		−	0.812900i
$378$	32.0792	+	40.2110i	0.0848656	+	0.106378i
$379$	−617.180			−1.62844			−0.814222	−	0.580553i	$-0.802836\pi$
$379$	−617.180			−1.62844			−0.814222	+	0.580553i	$0.802836\pi$
$380$	−13.5873	+	23.5340i	−0.0357562	+	0.0619315i
$381$	−290.220	+	167.559i	−0.761732	+	0.439786i
$382$	−64.1976	−	111.193i	−0.168057	−	0.291082i
$383$	150.642	+	86.9735i	0.393322	+	0.227085i	0.683599	−	0.729858i	$-0.260414\pi$
$383$	150.642	+	86.9735i	0.393322	+	0.227085i	−0.290276	+	0.956943i	$0.593747\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	70.4426	−	179.581i	0.182968	−	0.466444i
$386$	324.781			0.841402
$387$	−51.0285	+	88.3840i	−0.131857	+	0.228382i
$388$	−106.427	+	61.4455i	−0.274296	+	0.158365i
$389$	−98.0961	−	169.907i	−0.252175	−	0.436780i	0.711949	−	0.702231i	$-0.247813\pi$
$389$	−98.0961	−	169.907i	−0.252175	−	0.436780i	−0.964124	+	0.265451i	$0.914479\pi$
$390$	34.4375	+	19.8825i	0.0883013	+	0.0509808i
$391$		−	20.9079i		−	0.0534729i
$392$	−101.630	−	94.2301i	−0.259261	−	0.240383i
$393$	−313.699			−0.798217
$394$	161.213	−	279.228i	0.409169	−	0.708702i
$395$	216.318	−	124.891i	0.547640	−	0.316180i
$396$	36.9723	+	64.0379i	0.0933645	+	0.161712i
$397$	−345.285	−	199.350i	−0.869736	−	0.502142i	−0.00247542	−	0.999997i	$-0.500788\pi$
$397$	−345.285	−	199.350i	−0.869736	−	0.502142i	−0.867260	+	0.497855i	$0.834121\pi$
$398$		−	15.6216i		−	0.0392502i
$399$	−68.5851	−	26.9033i	−0.171893	−	0.0674267i
$400$	−20.0000			−0.0500000
$401$	−173.599	+	300.683i	−0.432916	+	0.749833i	−0.997123	−	0.0758008i	$-0.975849\pi$
$401$	−173.599	+	300.683i	−0.432916	+	0.749833i	0.564207	+	0.825633i	$0.309182\pi$
$402$	−104.944	+	60.5893i	−0.261054	+	0.150720i
$403$	4.42328	+	7.66135i	0.0109759	+	0.0190108i
$404$	−107.628	−	62.1392i	−0.266407	−	0.153810i
$405$			20.1246i			0.0496904i
$406$	−326.664	+	260.603i	−0.804591	+	0.641880i
$407$	432.074			1.06161
$408$	−22.7587	+	39.4193i	−0.0557812	+	0.0966159i
$409$	293.397	−	169.393i	0.717352	−	0.414163i	−0.0964252	−	0.995340i	$-0.530741\pi$
$409$	293.397	−	169.393i	0.717352	−	0.414163i	0.813777	+	0.581177i	$0.197408\pi$
$410$	91.5180	+	158.514i	0.223215	+	0.386619i
$411$	−1.89500	−	1.09408i	−0.00461070	−	0.00266199i
$412$			355.884i			0.863795i
$413$	−400.473	+	60.4361i	−0.969668	+	0.146334i
$414$	−9.54715			−0.0230608
$415$	−102.438	+	177.429i	−0.246840	+	0.427539i
$416$	35.5669	−	20.5346i	0.0854974	−	0.0493619i
$417$	−10.5072	−	18.1991i	−0.0251972	−	0.0436428i
$418$	−91.7171	−	52.9529i	−0.219419	−	0.126682i
$419$		−	369.514i		−	0.881894i	−0.897533	−	0.440947i	$-0.854643\pi$
$419$		−	369.514i		−	0.881894i	0.897533	−	0.440947i	$-0.145357\pi$
$420$	−8.09110	−	53.6147i	−0.0192645	−	0.127654i
$421$	−217.571			−0.516797			−0.258398	−	0.966038i	$-0.583195\pi$
$421$	−217.571			−0.516797			−0.258398	+	0.966038i	$0.583195\pi$
$422$	106.905	−	185.166i	0.253330	−	0.438781i
$423$	148.323	−	85.6345i	0.350646	−	0.202446i
$424$	20.5629	+	35.6160i	0.0484975	+	0.0840001i
$425$	40.2322	+	23.2280i	0.0946639	+	0.0546542i
$426$		−	249.815i		−	0.586420i
$427$	25.5898	+	32.0766i	0.0599293	+	0.0751209i
$428$	169.942			0.397061
$429$	−77.4866	+	134.211i	−0.180622	+	0.312846i
$430$	93.1649	−	53.7888i	0.216663	−	0.125090i
$431$	142.916	+	247.537i	0.331591	+	0.574332i	0.982824	−	0.184546i	$-0.0590814\pi$
$431$	142.916	+	247.537i	0.331591	+	0.574332i	−0.651233	+	0.758878i	$0.725748\pi$
$432$	18.0000	+	10.3923i	0.0416667	+	0.0240563i
$433$			643.490i			1.48612i	0.669224	+	0.743060i	$0.266626\pi$
$433$			643.490i			1.48612i	−0.669224	+	0.743060i	$0.733374\pi$
$434$	4.40498	−	11.2297i	0.0101497	−	0.0258749i
$435$	−163.487			−0.375833
$436$	172.858	−	299.399i	0.396464	−	0.686695i
$437$	11.8418	−	6.83686i	0.0270979	−	0.0156450i
$438$	−100.803	−	174.595i	−0.230143	−	0.398620i
$439$	494.013	+	285.218i	1.12531	+	0.649700i	0.942752	−	0.333494i	$-0.108228\pi$
$439$	494.013	+	285.218i	1.12531	+	0.649700i	0.182562	+	0.983194i	$0.441561\pi$
$440$		−	77.9445i		−	0.177147i
$441$	140.453	−	43.3802i	0.318488	−	0.0983677i
$442$	−95.3956			−0.215827
$443$	33.0074	−	57.1705i	0.0745089	−	0.129053i	−0.826364	−	0.563137i	$-0.809594\pi$
$443$	33.0074	−	57.1705i	0.0745089	−	0.129053i	0.900873	+	0.434084i	$0.142928\pi$
$444$	105.178	−	60.7244i	0.236887	−	0.136767i
$445$	−142.879	−	247.473i	−0.321076	−	0.556120i
$446$	377.939	+	218.203i	0.847396	+	0.489244i
$447$			501.819i			1.12264i
$448$	−52.1327	−	20.4496i	−0.116368	−	0.0456464i
$449$	515.072			1.14715			0.573577	−	0.819152i	$-0.305555\pi$
$449$	515.072			1.14715			0.573577	+	0.819152i	$0.305555\pi$
$450$	10.6066	−	18.3712i	0.0235702	−	0.0408248i
$451$	−617.764	+	356.666i	−1.36977	+	0.790834i
$452$	82.0616	+	142.135i	0.181552	+	0.314458i
$453$	−175.955	−	101.588i	−0.388421	−	0.224255i
$454$		−	142.019i		−	0.312816i
$455$	88.8329	−	70.8683i	0.195237	−	0.155755i
$456$	−29.7684			−0.0652815
$457$	−39.5136	+	68.4395i	−0.0864629	+	0.149758i	−0.906014	−	0.423248i	$-0.860890\pi$
$457$	−39.5136	+	68.4395i	−0.0864629	+	0.149758i	0.819551	+	0.573007i	$0.194223\pi$
$458$	391.914	−	226.272i	0.855708	−	0.494043i
$459$	−24.1393	−	41.8105i	−0.0525910	−	0.0910904i
$460$	8.71532	+	5.03179i	0.0189463	+	0.0109387i
$461$			9.58316i			0.0207878i	0.999946	+	0.0103939i	$0.00330854\pi$
$461$			9.58316i			0.0207878i	−0.999946	+	0.0103939i	$0.996691\pi$
$462$	208.948	−	31.5328i	0.452269	−	0.0682529i
$463$	−232.103			−0.501303			−0.250652	−	0.968077i	$-0.580645\pi$
$463$	−232.103			−0.501303			−0.250652	+	0.968077i	$0.580645\pi$
$464$	−84.4244	+	146.227i	−0.181949	+	0.315145i
$465$	4.08705	−	2.35966i	0.00878937	−	0.00507454i
$466$	219.761	+	380.637i	0.471590	+	0.816818i
$467$	593.692	+	342.768i	1.27129	+	0.733979i	0.975230	−	0.221191i	$-0.0709944\pi$
$467$	593.692	+	342.768i	1.27129	+	0.733979i	0.296058	+	0.955170i	$0.404328\pi$
$468$			43.5604i			0.0930778i
$469$	51.6752	+	342.419i	0.110182	+	0.730105i
$470$	−180.533			−0.384114
$471$	159.121	−	275.606i	0.337837	−	0.585151i
$472$	−141.723	+	81.8238i	−0.300261	+	0.173356i
$473$	209.627	+	363.085i	0.443186	+	0.767621i
$474$	236.964	+	136.811i	0.499925	+	0.288632i
$475$			30.3822i			0.0639626i
$476$	81.1202	+	101.684i	0.170421	+	0.213621i
$477$	−43.6206			−0.0914477
$478$	96.3526	−	166.888i	0.201575	−	0.349137i
$479$	−544.818	+	314.551i	−1.13741	+	0.656682i	−0.945787	−	0.324787i	$-0.894707\pi$
$479$	−544.818	+	314.551i	−1.13741	+	0.656682i	−0.191619	+	0.981469i	$0.561374\pi$
$480$	−10.9545	−	18.9737i	−0.0228218	−	0.0395285i
$481$	220.432	+	127.266i	0.458278	+	0.264587i
$482$		−	546.140i		−	1.13307i
$483$	−9.96307	+	25.3991i	−0.0206275	+	0.0525861i
$484$	61.7673			0.127618
$485$	−68.6982	+	118.989i	−0.141646	+	0.245338i
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	249.384	+	431.946i	0.512083	+	0.886953i	0.999902	+	0.0140085i	$0.00445918\pi$
$487$	249.384	+	431.946i	0.512083	+	0.886953i	−0.487819	+	0.872945i	$0.662207\pi$
$488$	14.3587	+	8.29002i	0.0294236	+	0.0169877i
$489$			210.567i			0.430607i
$490$	−151.079	−	34.4250i	−0.308325	−	0.0702550i
$491$	166.583			0.339274			0.169637	−	0.985507i	$-0.445741\pi$
$491$	166.583			0.339274			0.169637	+	0.985507i	$0.445741\pi$
$492$	−100.253	+	173.643i	−0.203766	+	0.352933i
$493$	339.658	−	196.101i	0.688961	−	0.397772i
$494$	−31.1943	−	54.0301i	−0.0631463	−	0.109373i
$495$	71.5966	+	41.3363i	0.144640	+	0.0835077i
$496$		−	4.87410i		−	0.00982681i
$497$	−664.603	−	260.698i	−1.33723	−	0.524543i
$498$	−224.431			−0.450665
$499$	−18.1531	+	31.4421i	−0.0363790	+	0.0630102i	−0.883642	−	0.468164i	$-0.844916\pi$
$499$	−18.1531	+	31.4421i	−0.0363790	+	0.0630102i	0.847263	+	0.531174i	$0.178249\pi$
$500$	−19.3649	+	11.1803i	−0.0387298	+	0.0223607i
$501$	−81.9727	−	141.981i	−0.163618	−	0.283395i
$502$	121.705	+	70.2664i	0.242440	+	0.139973i
$503$			634.940i			1.26231i	0.775658	+	0.631153i	$0.217418\pi$
$503$			634.940i			1.26231i	−0.775658	+	0.631153i	$0.782582\pi$
$504$	46.4317	−	37.0419i	0.0921263	−	0.0734958i
$505$	−138.947			−0.275143
$506$	−19.6100	+	33.9656i	−0.0387550	+	0.0671256i
$507$	174.437	−	100.711i	0.344057	−	0.198642i
$508$	193.480	+	335.117i	0.380866	+	0.659680i
$509$	500.864	+	289.174i	0.984015	+	0.568121i	0.903480	−	0.428631i	$-0.141004\pi$
$509$	500.864	+	289.174i	0.984015	+	0.568121i	0.0805350	+	0.996752i	$0.474337\pi$
$510$			50.8901i			0.0997845i
$511$	−569.685	+	85.9723i	−1.11484	+	0.168243i
$512$	−22.6274			−0.0441942
$513$	15.7871	−	27.3440i	0.0307740	−	0.0533021i
$514$	25.8639	−	14.9325i	0.0503189	−	0.0290516i
$515$	198.945	+	344.583i	0.386301	+	0.669093i
$516$	102.057	+	58.9227i	0.197785	+	0.114191i
$517$		−	703.579i		−	1.36089i
$518$	−51.7904	−	343.183i	−0.0999815	−	0.662516i
$519$	−451.532			−0.870003
$520$	22.9583	−	39.7650i	0.0441507	−	0.0764712i
$521$	−550.974	+	318.105i	−1.05753	+	0.610566i	−0.924748	−	0.380579i	$-0.875725\pi$
$521$	−550.974	+	318.105i	−1.05753	+	0.610566i	−0.132783	+	0.991145i	$0.542391\pi$
$522$	−89.5456	−	155.098i	−0.171543	−	0.297122i
$523$	392.868	+	226.823i	0.751182	+	0.433695i	0.826121	−	0.563493i	$-0.190543\pi$
$523$	392.868	+	226.823i	0.751182	+	0.433695i	−0.0749389	+	0.997188i	$0.523876\pi$
$524$			362.229i			0.691276i
$525$	−37.8057	−	47.3891i	−0.0720108	−	0.0902650i
$526$	538.133			1.02307
$527$	−5.66079	+	9.80477i	−0.0107415	+	0.0186049i
$528$	73.9447	−	42.6920i	0.140047	−	0.0808560i
$529$	261.968	+	453.742i	0.495214	+	0.857735i
$530$	39.8199	+	22.9901i	0.0751320	+	0.0433775i
$531$		−	173.575i		−	0.326882i
$532$	−31.0652	+	79.1953i	−0.0583933	+	0.148863i
$533$	−420.220			−0.788406
$534$	156.516	−	271.093i	0.293101	−	0.507666i
$535$	164.546	−	95.0005i	0.307562	−	0.177571i
$536$	69.9625	+	121.179i	0.130527	+	0.226079i
$537$	−459.793	−	265.462i	−0.856225	−	0.494342i
$538$		−	23.7461i		−	0.0441377i
$539$	134.162	−	588.790i	0.248909	−	1.09237i
$540$	23.2379			0.0430331
$541$	288.159	−	499.106i	0.532641	−	0.922562i	−0.466632	−	0.884451i	$-0.654533\pi$
$541$	288.159	−	499.106i	0.532641	−	0.922562i	0.999274	−	0.0381102i	$-0.0121338\pi$
$542$	452.754	−	261.398i	0.835340	−	0.482284i
$543$	272.699	+	472.328i	0.502208	+	0.869849i
$544$	45.5175	+	26.2795i	0.0836718	+	0.0483080i
$545$		−	386.523i		−	0.709216i
$546$	115.887	+	45.4581i	0.212248	+	0.0832566i
$547$	481.306			0.879901			0.439950	−	0.898022i	$-0.354996\pi$
$547$	481.306			0.879901			0.439950	+	0.898022i	$0.354996\pi$
$548$	−1.26333	+	2.18815i	−0.00230535	+	0.00399298i
$549$	−15.2297	+	8.79289i	−0.0277409	+	0.0160162i
$550$	−43.5723	−	75.4694i	−0.0792224	−	0.137217i
$551$	222.136	+	128.250i	0.403150	+	0.232759i
$552$			11.0241i			0.0199712i
$553$	611.259	−	487.645i	1.10535	−	0.881817i
$554$	−687.060			−1.24018
$555$	67.8920	−	117.592i	0.122328	−	0.211878i
$556$	−21.0145	+	12.1327i	−0.0377958	+	0.0218214i
$557$	−54.4056	−	94.2333i	−0.0976762	−	0.169180i	0.813046	−	0.582199i	$-0.197808\pi$
$557$	−54.4056	−	94.2333i	−0.0976762	−	0.169180i	−0.910722	+	0.413019i	$0.864474\pi$
$558$	4.47714	+	2.58488i	0.00802356	+	0.00463240i
$559$			246.980i			0.441825i
$560$	−61.9089	+	9.34279i	−0.110552	+	0.0166836i
$561$	−198.330			−0.353530
$562$	254.724	−	441.195i	0.453245	−	0.785044i
$563$	521.516	−	301.097i	0.926316	−	0.534809i	0.0406717	−	0.999173i	$-0.487050\pi$
$563$	521.516	−	301.097i	0.926316	−	0.534809i	0.885645	+	0.464364i	$0.153717\pi$
$564$	−98.8822	−	171.269i	−0.175323	−	0.303669i
$565$	158.912	+	91.7477i	0.281260	+	0.162385i
$566$		−	382.547i		−	0.675878i
$567$	9.40101	+	62.2946i	0.0165803	+	0.109867i
$568$	−288.461			−0.507854
$569$	4.76685	−	8.25642i	0.00837759	−	0.0145104i	−0.861806	−	0.507238i	$-0.830667\pi$
$569$	4.76685	−	8.25642i	0.00837759	−	0.0145104i	0.870184	+	0.492727i	$0.164000\pi$
$570$	−28.8231	+	16.6410i	−0.0505668	+	0.0291948i
$571$	−491.103	−	850.615i	−0.860075	−	1.48969i	−0.871856	−	0.489762i	$-0.837084\pi$
$571$	−491.103	−	850.615i	−0.860075	−	1.48969i	0.0117813	−	0.999931i	$-0.496250\pi$
$572$	154.973	+	89.4739i	0.270932	+	0.156423i
$573$		−	157.251i		−	0.274435i
$574$	357.337	+	447.919i	0.622538	+	0.780347i
$575$	11.2514			0.0195677
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	−454.001	+	262.117i	−0.786830	+	0.454276i	−0.838845	−	0.544370i	$-0.816769\pi$
$577$	−454.001	+	262.117i	−0.786830	+	0.454276i	0.0520155	+	0.998646i	$0.483435\pi$
$578$	143.312	+	248.223i	0.247944	+	0.429452i
$579$	344.483	+	198.887i	0.594961	+	0.343501i
$580$			188.779i			0.325481i
$581$	−234.209	+	597.073i	−0.403113	+	1.02767i
$582$	−150.510			−0.258608
$583$	−89.5974	+	155.187i	−0.153683	+	0.266187i
$584$	−201.605	+	116.397i	−0.345215	+	0.199310i
$585$	24.3510	+	42.1772i	0.0416256	+	0.0720977i
$586$	11.7971	+	6.81106i	0.0201316	+	0.0116230i
$587$		−	651.322i		−	1.10958i	−0.831991	−	0.554789i	$-0.812799\pi$
$587$		−	651.322i		−	1.10958i	0.831991	−	0.554789i	$-0.187201\pi$
$588$	−50.0911	−	162.182i	−0.0851889	−	0.275819i
$589$	−7.40429			−0.0125710
$590$	−91.4818	+	158.451i	−0.155054	+	0.268561i
$591$	341.984	−	197.444i	0.578652	−	0.334085i
$592$	−70.1185	−	121.449i	−0.118443	−	0.205150i
$593$	−610.904	−	352.706i	−1.03019	−	0.594782i	−0.113152	−	0.993578i	$-0.536095\pi$
$593$	−610.904	−	352.706i	−1.03019	−	0.594782i	−0.917040	+	0.398796i	$0.869428\pi$
$594$			90.5633i			0.152464i
$595$	135.387	+	53.1071i	0.227541	+	0.0892556i
$596$	579.451			0.972233
$597$	9.56623	−	16.5692i	0.0160238	−	0.0277541i
$598$	−20.0089	+	11.5522i	−0.0334597	+	0.0193180i
$599$	296.910	+	514.263i	0.495676	+	0.858535i	0.999988	−	0.00498610i	$-0.00158713\pi$
$599$	296.910	+	514.263i	0.495676	+	0.858535i	−0.504312	+	0.863522i	$0.668254\pi$
$600$	−21.2132	−	12.2474i	−0.0353553	−	0.0204124i
$601$		−	12.1644i		−	0.0202403i	−0.999949	−	0.0101202i	$-0.996779\pi$
$601$		−	12.1644i		−	0.0202403i	0.999949	−	0.0101202i	$-0.00322140\pi$
$602$	263.260	−	210.021i	0.437309	−	0.348873i
$603$	−148.413			−0.246124
$604$	−117.303	+	203.175i	−0.194211	+	0.336383i
$605$	59.8059	−	34.5290i	0.0988528	−	0.0570727i
$606$	−76.1047	−	131.817i	−0.125585	−	0.217520i
$607$	698.521	+	403.291i	1.15078	+	0.664401i	0.949076	−	0.315047i	$-0.102020\pi$
$607$	698.521	+	403.291i	1.15078	+	0.664401i	0.201700	+	0.979447i	$0.435353\pi$
$608$			34.3736i			0.0565354i
$609$	−506.066	+	76.3714i	−0.830978	+	0.125405i
$610$	18.5370			0.0303886
$611$	207.237	−	358.946i	0.339178	−	0.587473i
$612$	−48.2786	+	27.8737i	−0.0788866	+	0.0455452i
$613$	397.237	+	688.035i	0.648021	+	1.12241i	0.983595	+	0.180392i	$0.0577365\pi$
$613$	397.237	+	688.035i	0.648021	+	1.12241i	−0.335574	+	0.942014i	$0.608930\pi$
$614$	56.3887	+	32.5560i	0.0918383	+	0.0530229i
$615$			224.172i			0.364508i
$616$	−36.4110	−	241.273i	−0.0591087	−	0.391677i
$617$	108.982			0.176633			0.0883164	−	0.996092i	$-0.471851\pi$
$617$	108.982			0.176633			0.0883164	+	0.996092i	$0.471851\pi$
$618$	−217.933	+	377.472i	−0.352643	+	0.610796i
$619$	−310.725	+	179.397i	−0.501979	+	0.289818i	−0.729531	−	0.683948i	$-0.760261\pi$
$619$	−310.725	+	179.397i	−0.501979	+	0.289818i	0.227551	+	0.973766i	$0.426928\pi$
$620$	−2.72470	−	4.71932i	−0.00439468	−	0.00761181i
$621$	−10.1263	−	5.84641i	−0.0163064	−	0.00941451i
$622$			617.533i			0.992819i
$623$	−557.878	−	699.296i	−0.895470	−	1.12246i
$624$	50.2992			0.0806077
$625$	−12.5000	+	21.6506i	−0.0200000	+	0.0346410i
$626$	350.916	−	202.602i	0.560569	−	0.323645i
$627$	−64.8538	−	112.330i	−0.103435	−	0.179155i
$628$	−318.243	−	183.737i	−0.506756	−	0.292576i
$629$			325.743i			0.517875i
$630$	24.2502	−	61.8217i	0.0384925	−	0.0981297i
$631$	−612.351			−0.970446			−0.485223	−	0.874391i	$-0.661262\pi$
$631$	−612.351			−0.970446			−0.485223	+	0.874391i	$0.661262\pi$
$632$	157.976	−	273.623i	0.249962	−	0.432948i
$633$	226.781	−	130.932i	0.358263	−	0.206843i
$634$	−0.967913	−	1.67647i	−0.00152668	−	0.00264428i
$635$	374.672	+	216.317i	0.590035	+	0.340657i
$636$			50.3687i			0.0791960i
$637$	241.872	−	260.866i	0.379705	−	0.409523i
$638$	−735.713			−1.15316
$639$	152.980	−	264.969i	0.239405	−	0.414661i
$640$	−21.9089	+	12.6491i	−0.0342327	+	0.0197642i
$641$	−459.706	−	796.233i	−0.717169	−	1.24217i	−0.962117	−	0.272637i	$-0.912104\pi$
$641$	−459.706	−	796.233i	−0.717169	−	1.24217i	0.244947	−	0.969536i	$-0.421229\pi$
$642$	180.251	+	104.068i	0.280765	+	0.162099i
$643$		−	835.879i		−	1.29997i	−0.759948	−	0.649984i	$-0.774776\pi$
$643$		−	835.879i		−	1.29997i	0.759948	−	0.649984i	$-0.225224\pi$
$644$	29.3283	+	11.5044i	0.0455409	+	0.0178639i
$645$	131.755			0.204271
$646$	39.9215	−	69.1461i	0.0617980	−	0.107037i
$647$	−492.933	+	284.595i	−0.761876	+	0.439869i	−0.829969	−	0.557810i	$-0.811642\pi$
$647$	−492.933	+	284.595i	−0.761876	+	0.439869i	0.0680932	+	0.997679i	$0.478308\pi$
$648$	12.7279	+	22.0454i	0.0196419	+	0.0340207i
$649$	−617.520	−	356.525i	−0.951495	−	0.549346i
$650$		−	51.3364i		−	0.0789791i
$651$	11.5490	−	9.21343i	0.0177403	−	0.0141527i
$652$	243.142			0.372917
$653$	−196.162	+	339.763i	−0.300402	+	0.520311i	−0.976227	−	0.216751i	$-0.930454\pi$
$653$	−196.162	+	339.763i	−0.300402	+	0.520311i	0.675825	+	0.737062i	$0.263787\pi$
$654$	366.688	−	211.707i	0.560684	−	0.323711i
$655$	202.492	+	350.727i	0.309148	+	0.535460i
$656$	200.506	+	115.762i	0.305649	+	0.176467i
$657$		−	246.915i		−	0.375822i
$658$	−558.831	+	84.3343i	−0.849288	+	0.128168i
$659$	505.063			0.766408			0.383204	−	0.923664i	$-0.374821\pi$
$659$	505.063			0.766408			0.383204	+	0.923664i	$0.374821\pi$
$660$	47.7311	−	82.6726i	0.0723198	−	0.125262i
$661$	−255.815	+	147.695i	−0.387013	+	0.223442i	−0.680865	−	0.732409i	$-0.738396\pi$
$661$	−255.815	+	147.695i	−0.387013	+	0.223442i	0.293852	+	0.955851i	$0.405063\pi$
$662$	−271.553	−	470.343i	−0.410201	−	0.710488i
$663$	−101.182	−	58.4176i	−0.152613	−	0.0881110i
$664$			259.151i			0.390288i
$665$	14.1927	+	94.0465i	0.0213425	+	0.141423i
$666$	148.744			0.223339
$667$	47.4948	−	82.2633i	0.0712065	−	0.123333i
$668$	−163.945	+	94.6539i	−0.245427	+	0.141698i
$669$	267.243	+	462.878i	0.399466	+	0.691896i
$670$	135.482	+	78.2204i	0.202212	+	0.116747i
$671$			72.2430i			0.107665i
$672$	−42.7723	−	53.6147i	−0.0636492	−	0.0797838i
$673$	−624.569			−0.928038			−0.464019	−	0.885825i	$-0.653593\pi$
$673$	−624.569			−0.928038			−0.464019	+	0.885825i	$0.653593\pi$
$674$	−100.373	+	173.850i	−0.148921	+	0.257938i
$675$	22.5000	−	12.9904i	0.0333333	−	0.0192450i
$676$	−116.291	−	201.423i	−0.172029	−	0.297963i
$677$	−676.847	−	390.778i	−0.999774	−	0.577220i	−0.0915926	−	0.995797i	$-0.529196\pi$
$677$	−676.847	−	390.778i	−0.999774	−	0.577220i	−0.908181	+	0.418577i	$0.862529\pi$
$678$			201.009i			0.296474i
$679$	−157.067	+	400.415i	−0.231321	+	0.589712i
$680$	58.7628			0.0864159
$681$	86.9683	−	150.634i	0.127707	−	0.221195i
$682$	18.3923	−	10.6188i	0.0269681	−	0.0155701i
$683$	−50.8525	−	88.0791i	−0.0744546	−	0.128959i	0.826394	−	0.563092i	$-0.190388\pi$
$683$	−50.8525	−	88.0791i	−0.0744546	−	0.128959i	−0.900849	+	0.434133i	$0.857055\pi$
$684$	−31.5741	−	18.2293i	−0.0461610	−	0.0266511i
$685$			2.82490i			0.00412393i
$686$	−483.739	−	35.9855i	−0.705158	−	0.0524570i
$687$	554.250			0.806769
$688$	68.0380	−	117.845i	0.0988925	−	0.171287i
$689$	−91.4200	+	52.7814i	−0.132685	+	0.0766057i
$690$	6.16266	+	10.6740i	0.00893139	+	0.0154696i
$691$	634.684	+	366.435i	0.918501	+	0.530297i	0.883157	−	0.469078i	$-0.155414\pi$
$691$	634.684	+	366.435i	0.918501	+	0.530297i	0.0353446	+	0.999375i	$0.488747\pi$
$692$			521.384i			0.753445i
$693$	240.933	+	94.5087i	0.347667	+	0.136376i
$694$	354.051			0.510160
$695$	−13.5648	+	23.4949i	−0.0195177	+	0.0338056i
$696$	−179.091	+	103.398i	−0.257315	+	0.148561i
$697$	−268.893	−	465.736i	−0.385786	−	0.668201i
$698$	−239.055	−	138.019i	−0.342486	−	0.197734i
$699$			538.303i			0.770104i
$700$	−54.7203	+	43.6543i	−0.0781718	+	0.0623632i
$701$	−795.928			−1.13542			−0.567709	−	0.823229i	$-0.692170\pi$
$701$	−795.928			−1.13542			−0.567709	+	0.823229i	$0.692170\pi$
$702$	−26.6752	+	46.2028i	−0.0379988	+	0.0658159i
$703$	−184.494	+	106.518i	−0.262438	+	0.151519i
$704$	−49.2964	−	85.3839i	−0.0700233	−	0.121284i
$705$	−191.485	−	110.554i	−0.271609	−	0.156814i
$706$		−	201.100i		−	0.284845i
$707$	−430.104	+	64.9079i	−0.608351	+	0.0918075i
$708$	−200.427			−0.283089
$709$	−514.532	+	891.196i	−0.725715	+	1.25698i	0.232964	+	0.972485i	$0.425158\pi$
$709$	−514.532	+	891.196i	−0.725715	+	1.25698i	−0.958679	+	0.284490i	$0.908176\pi$
$710$	−279.301	+	161.255i	−0.393382	+	0.227119i
$711$	167.559	+	290.221i	0.235667	+	0.408187i
$712$	−313.032	−	180.729i	−0.439651	−	0.253833i
$713$			2.74203i			0.00384576i
$714$	23.7728	+	157.527i	0.0332952	+	0.220627i
$715$	200.070			0.279818
$716$	−306.529	+	530.923i	−0.428113	+	0.741513i
$717$	204.395	−	118.007i	0.285069	−	0.164585i
$718$	−464.489	−	804.518i	−0.646920	−	1.12050i
$719$	−136.549	−	78.8367i	−0.189915	−	0.109648i	0.402028	−	0.915628i	$-0.368306\pi$
$719$	−136.549	−	78.8367i	−0.189915	−	0.109648i	−0.591943	+	0.805980i	$0.701639\pi$
$720$		−	26.8328i		−	0.0372678i
$721$	776.792	+	973.702i	1.07738	+	1.35049i
$722$	−458.314			−0.634784
$723$	334.441	−	579.269i	0.462574	−	0.801202i
$724$	545.397	−	314.885i	0.753311	−	0.434925i
$725$	105.531	+	182.784i	0.145559	+	0.252116i
$726$	65.5141	+	37.8246i	0.0902398	+	0.0521000i
$727$			13.5224i			0.0186003i	0.999957	+	0.00930013i	$0.00296037\pi$
$727$			13.5224i			0.0186003i	−0.999957	+	0.00930013i	$0.997040\pi$
$728$	52.4905	−	133.815i	0.0721023	−	0.183812i
$729$	−27.0000			−0.0370370
$730$	−130.136	+	225.402i	−0.178268	+	0.308769i
$731$	−273.732	+	158.039i	−0.374462	+	0.216196i
$732$	10.1532	+	17.5858i	0.0138704	+	0.0240243i
$733$	341.622	+	197.235i	0.466060	+	0.269080i	0.714589	−	0.699545i	$-0.246614\pi$
$733$	341.622	+	197.235i	0.466060	+	0.269080i	−0.248529	+	0.968624i	$0.579947\pi$
$734$			725.707i			0.988701i
$735$	−139.163	−	129.030i	−0.189337	−	0.175551i
$736$	12.7295			0.0172956
$737$	−304.843	+	528.003i	−0.413626	+	0.716422i
$738$	−212.669	+	122.784i	−0.288169	+	0.166374i
$739$	−475.080	−	822.863i	−0.642869	−	1.11348i	−0.984789	−	0.173753i	$-0.944411\pi$
$739$	−475.080	−	822.863i	−0.642869	−	1.11348i	0.341920	−	0.939729i	$-0.388923\pi$
$740$	−135.784	−	78.3949i	−0.183492	−	0.105939i
$741$		−	76.4101i		−	0.103118i
$742$	134.000	+	52.5630i	0.180593	+	0.0708396i
$743$	425.883			0.573194			0.286597	−	0.958051i	$-0.407476\pi$
$743$	425.883			0.573194			0.286597	+	0.958051i	$0.407476\pi$
$744$	2.98476	−	5.16976i	0.00401178	−	0.00694860i
$745$	561.051	−	323.923i	0.753088	−	0.434796i
$746$	−447.262	−	774.680i	−0.599547	−	1.03845i
$747$	−238.045	−	137.436i	−0.318669	−	0.183983i
$748$			229.012i			0.306166i
$749$	464.964	−	370.935i	0.620779	−	0.495240i
$750$	−27.3861			−0.0365148
$751$	315.874	−	547.109i	0.420604	−	0.728508i	−0.575395	−	0.817876i	$-0.695151\pi$
$751$	315.874	−	547.109i	0.420604	−	0.728508i	0.995999	+	0.0893683i	$0.0284848\pi$
$752$	−197.764	+	114.179i	−0.262985	+	0.151834i
$753$	86.0584	+	149.058i	0.114287	+	0.197952i
$754$	−375.340	−	216.702i	−0.497798	−	0.287404i
$755$			262.298i			0.347414i
$756$	71.9316	−	10.8553i	0.0951477	−	0.0143589i
$757$	882.903			1.16632			0.583159	−	0.812358i	$-0.301816\pi$
$757$	882.903			1.16632			0.583159	+	0.812358i	$0.301816\pi$
$758$	−436.412	+	755.889i	−0.575742	+	0.997214i
$759$	−41.5991	+	24.0173i	−0.0548078	+	0.0316433i
$760$	19.2154	+	33.2820i	0.0252834	+	0.0437922i
$761$	−981.049	−	566.409i	−1.28916	−	0.744295i	−0.310653	−	0.950523i	$-0.600548\pi$
$761$	−981.049	−	566.409i	−1.28916	−	0.744295i	−0.978504	+	0.206228i	$0.933881\pi$
$762$			473.927i			0.621952i
$763$	−180.560	−	1196.46i	−0.236645	−	1.56810i
$764$	−181.578			−0.237668
$765$	−31.1637	+	53.9771i	−0.0407368	+	0.0705583i
$766$	213.041	−	122.999i	0.278121	−	0.160573i
$767$	−210.027	−	363.778i	−0.273829	−	0.474287i
$768$	−24.0000	−	13.8564i	−0.0312500	−	0.0180422i
$769$			41.6421i			0.0541510i	0.999633	+	0.0270755i	$0.00861944\pi$
$769$			41.6421i			0.0541510i	−0.999633	+	0.0270755i	$0.991381\pi$
$770$	−170.130	−	213.257i	−0.220949	−	0.276957i
$771$	36.5771			0.0474411
$772$	229.655	−	397.774i	0.297481	−	0.515252i
$773$	1114.00	−	643.167i	1.44114	−	0.832041i	0.443211	−	0.896417i	$-0.353839\pi$
$773$	1114.00	−	643.167i	1.44114	−	0.832041i	0.997926	+	0.0643767i	$0.0205059\pi$
$774$	72.1652	+	124.994i	0.0932367	+	0.161491i
$775$	−5.27637	−	3.04631i	−0.00680821	−	0.00393072i
$776$			173.794i			0.223962i
$777$	155.224	−	395.716i	0.199773	−	0.509287i
$778$	−277.458			−0.356629
$779$	175.855	−	304.591i	0.225745	−	0.391002i
$780$	48.7020	−	28.1181i	0.0624385	−	0.0360489i
$781$	−628.446	−	1088.50i	−0.804668	−	1.39373i
$782$	−25.6068	−	14.7841i	−0.0327453	−	0.0189055i
$783$		−	219.341i		−	0.280129i
$784$	−187.271	+	57.8402i	−0.238866	+	0.0737758i
$785$	−410.850			−0.523375
$786$	−221.819	+	384.202i	−0.282212	+	0.488806i
$787$	−863.836	+	498.736i	−1.09763	+	0.633718i	−0.935598	−	0.353067i	$-0.885139\pi$
$787$	−863.836	+	498.736i	−1.09763	+	0.633718i	−0.162034	+	0.986785i	$0.551805\pi$
$788$	−227.989	−	394.889i	−0.289326	−	0.501128i
$789$	570.776	+	329.538i	0.723417	+	0.417665i
$790$		−	353.246i		−	0.447146i
$791$	534.761	+	209.766i	0.676057	+	0.265191i
$792$	104.574			0.132037
$793$	−21.2790	+	36.8563i	−0.0268335	+	0.0464770i
$794$	−488.307	+	281.924i	−0.614996	+	0.355068i
$795$	28.1569	+	48.7693i	0.0354175	+	0.0613450i
$796$	−19.1325	−	11.0461i	−0.0240358	−	0.0138771i
$797$		−	971.547i		−	1.21901i	−0.792784	−	0.609503i	$-0.791369\pi$
$797$		−	971.547i		−	1.21901i	0.792784	−	0.609503i	$-0.208631\pi$
$798$	−81.4466	+	64.9758i	−0.102063	+	0.0814233i
$799$	530.433			0.663871
$800$	−14.1421	+	24.4949i	−0.0176777	+	0.0306186i
$801$	332.020	−	191.692i	0.414507	−	0.239316i
$802$	245.507	+	425.230i	0.306118	+	0.530212i
$803$	−878.441	−	507.168i	−1.09395	−	0.631592i
$804$			171.372i			0.213150i
$805$	34.8282	−	5.25599i	0.0432648	−	0.00652918i
$806$	12.5109			0.0155223
$807$	14.5415	−	25.1865i	0.0180191	−	0.0312101i
$808$	−152.209	+	87.8781i	−0.188378	+	0.108760i
$809$	652.112	+	1129.49i	0.806072	+	1.39616i	0.915565	+	0.402170i	$0.131744\pi$
$809$	652.112	+	1129.49i	0.806072	+	1.39616i	−0.109493	+	0.993988i	$0.534923\pi$
$810$	24.6475	+	14.2302i	0.0304290	+	0.0175682i
$811$			210.763i			0.259880i	0.991522	+	0.129940i	$0.0414785\pi$
$811$			210.763i			0.259880i	−0.991522	+	0.129940i	$0.958521\pi$
$812$	88.1861	+	584.354i	0.108604	+	0.719648i
$813$	640.291			0.787566
$814$	305.523	−	529.181i	0.375335	−	0.650099i
$815$	235.421	−	135.920i	0.288860	−	0.166773i
$816$	32.1857	+	55.7473i	0.0394433	+	0.0683178i
$817$	−179.020	−	103.357i	−0.219119	−	0.126508i
$818$		−	479.115i		−	0.585716i
$819$	95.0798	+	119.182i	0.116093	+	0.145521i
$820$	258.852			0.315673
$821$	362.253	−	627.440i	0.441234	−	0.764239i	−0.556548	−	0.830816i	$-0.687874\pi$
$821$	362.253	−	627.440i	0.441234	−	0.764239i	0.997781	+	0.0665766i	$0.0212077\pi$
$822$	−2.67993	+	1.54726i	−0.00326026	+	0.00188231i
$823$	223.018	+	386.279i	0.270982	+	0.469355i	0.969114	−	0.246615i	$-0.0793182\pi$
$823$	223.018	+	386.279i	0.270982	+	0.469355i	−0.698131	+	0.715970i	$0.745985\pi$
$824$	435.867	+	251.648i	0.528964	+	0.305398i
$825$		−	106.730i		−	0.129370i
$826$	−209.158	+	533.212i	−0.253218	+	0.645535i
$827$	−702.737			−0.849743			−0.424871	−	0.905254i	$-0.639681\pi$
$827$	−702.737			−0.849743			−0.424871	+	0.905254i	$0.639681\pi$
$828$	−6.75086	+	11.6928i	−0.00815321	+	0.0141218i
$829$	−361.023	+	208.437i	−0.435492	+	0.251431i	−0.701683	−	0.712489i	$-0.747568\pi$
$829$	−361.023	+	208.437i	−0.435492	+	0.251431i	0.266192	+	0.963920i	$0.414235\pi$
$830$	144.870	+	250.922i	0.174542	+	0.302316i
$831$	−728.737	−	420.736i	−0.876940	−	0.506301i
$832$		−	58.0805i		−	0.0698083i
$833$	443.892	+	101.145i	0.532883	+	0.121423i
$834$	−29.7189			−0.0356342
$835$	−105.826	+	183.297i	−0.126738	+	0.219517i
$836$	−129.708	+	74.8867i	−0.155153	+	0.0895774i
$837$	3.16582	+	5.48336i	0.00378234	+	0.00655121i
$838$	−452.560	−	261.286i	−0.540047	−	0.311797i
$839$			359.231i			0.428166i	0.976815	+	0.214083i	$0.0686763\pi$
$839$			359.231i			0.428166i	−0.976815	+	0.214083i	$0.931324\pi$
$840$	−71.3856	−	28.0018i	−0.0849828	−	0.0333354i
$841$	940.871			1.11875
$842$	−153.846	+	266.469i	−0.182715	+	0.316472i
$843$	540.351	−	311.972i	0.640986	−	0.370073i
$844$	−151.187	−	261.864i	−0.179132	−	0.310265i
$845$	−225.197	−	130.018i	−0.266506	−	0.153867i
$846$		−	242.211i		−	0.286301i
$847$	168.996	−	134.820i	0.199523	−	0.159174i
$848$	58.1607			0.0685858
$849$	234.261	−	405.752i	0.275926	−	0.477918i
$850$	56.8969	−	32.8494i	0.0669375	−	0.0386464i
$851$	39.4467	+	68.3236i	0.0463533	+	0.0802863i
$852$	−305.959	−	176.646i	−0.359107	−	0.207331i
$853$		−	988.948i		−	1.15938i	−0.814838	−	0.579688i	$-0.803174\pi$
$853$		−	988.948i		−	1.15938i	0.814838	−	0.579688i	$-0.196826\pi$
$854$	57.3804	−	8.65939i	0.0671902	−	0.0101398i
$855$	−40.7620			−0.0476749
$856$	120.167	−	208.136i	0.140382	−	0.243149i
$857$	312.893	−	180.649i	0.365103	−	0.210792i	−0.306214	−	0.951963i	$-0.599062\pi$
$857$	312.893	−	180.649i	0.365103	−	0.210792i	0.671317	+	0.741170i	$0.265729\pi$
$858$	109.583	+	189.803i	0.127719	+	0.221215i
$859$	−608.464	−	351.297i	−0.708339	−	0.408960i	0.102106	−	0.994773i	$-0.467442\pi$
$859$	−608.464	−	351.297i	−0.708339	−	0.408960i	−0.810446	+	0.585814i	$0.800775\pi$
$860$		−	152.138i		−	0.176904i
$861$	104.720	+	693.913i	0.121626	+	0.805939i
$862$	404.226			0.468940
$863$	−551.208	+	954.720i	−0.638711	+	1.10628i	0.347005	+	0.937863i	$0.387199\pi$
$863$	−551.208	+	954.720i	−0.638711	+	1.10628i	−0.985716	+	0.168417i	$0.946135\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$	291.462	+	504.828i	0.336951	+	0.583616i
$866$	788.111	+	455.016i	0.910059	+	0.525423i
$867$			351.040i			0.404891i
$868$	−10.6388	−	13.3356i	−0.0122566	−	0.0153636i
$869$	1376.68			1.58421
$870$	−115.603	+	200.230i	−0.132877	+	0.230150i
$871$	−311.044	+	179.581i	−0.357111	+	0.206178i
$872$	−244.458	−	423.414i	−0.280342	−	0.485567i
$873$	−159.640	−	92.1683i	−0.182864	−	0.105576i
$874$		−	19.3376i		−	0.0221254i
$875$	−28.5792	+	72.8576i	−0.0326619	+	0.0832658i
$876$	−285.113			−0.325472
$877$	−334.061	+	578.610i	−0.380913	+	0.659761i	−0.991193	−	0.132425i	$-0.957724\pi$
$877$	−334.061	+	578.610i	−0.380913	+	0.659761i	0.610280	+	0.792186i	$0.291057\pi$
$878$	698.640	−	403.360i	0.795717	−	0.459408i
$879$	8.34182	+	14.4484i	0.00949012	+	0.0164374i
$880$	−95.4621	−	55.1151i	−0.108480	−	0.0626308i
$881$		−	15.3854i		−	0.0174636i	−0.999962	−	0.00873178i	$-0.997221\pi$
$881$		−	15.3854i		−	0.0174636i	0.999962	−	0.00873178i	$-0.00277945\pi$
$882$	46.1859	−	202.694i	0.0523650	−	0.229812i
$883$	51.0884			0.0578577			0.0289289	−	0.999581i	$-0.490790\pi$
$883$	51.0884			0.0578577			0.0289289	+	0.999581i	$0.490790\pi$
$884$	−67.4549	+	116.835i	−0.0763064	+	0.132167i
$885$	−194.062	+	112.042i	−0.219279	+	0.126601i
$886$	−46.6796	−	80.8514i	−0.0526857	−	0.0912543i
$887$	26.3653	+	15.2220i	0.0297241	+	0.0171612i	0.514788	−	0.857317i	$-0.327870\pi$
$887$	26.3653	+	15.2220i	0.0297241	+	0.0171612i	−0.485064	+	0.874478i	$0.661204\pi$
$888$		−	171.755i		−	0.193417i
$889$	1260.83	+	494.574i	1.41825	+	0.556326i
$890$	−404.122			−0.454070
$891$	−55.4585	+	96.0569i	−0.0622430	+	0.107808i
$892$	534.486	−	308.586i	0.599200	−	0.345948i
$893$	173.451	+	300.426i	0.194234	+	0.336423i
$894$	614.600	+	354.840i	0.687472	+	0.396912i
$895$			685.419i			0.765831i
$896$	−61.9089	+	49.3891i	−0.0690948	+	0.0551218i
$897$	−28.2969			−0.0315462
$898$	364.211	−	630.832i	0.405580	−	0.702485i
$899$	−44.5454	+	25.7183i	−0.0495500	+	0.0286077i
$900$	−15.0000	−	25.9808i	−0.0166667	−	0.0288675i
$901$	−116.997	−	67.5480i	−0.129852	−	0.0749700i
$902$			1008.80i			1.11841i
$903$	407.841	−	61.5480i	0.451651	−	0.0681595i
$904$	232.105			0.256754
$905$	352.053	−	609.773i	0.389008	−	0.673782i
$906$	−248.838	+	143.666i	−0.274655	+	0.158572i
$907$	345.008	+	597.571i	0.380384	+	0.658844i	0.991117	−	0.132993i	$-0.0424586\pi$
$907$	345.008	+	597.571i	0.380384	+	0.658844i	−0.610733	+	0.791836i	$0.709125\pi$
$908$	−173.937	−	100.422i	−0.191560	−	0.110597i
$909$		−	186.418i		−	0.205080i
$910$	−23.9813	−	158.909i	−0.0263531	−	0.174625i
$911$	−264.542			−0.290386			−0.145193	−	0.989403i	$-0.546380\pi$
$911$	−264.542			−0.290386			−0.145193	+	0.989403i	$0.546380\pi$
$912$	−21.0494	+	36.4587i	−0.0230805	+	0.0399766i
$913$	−977.899	+	564.590i	−1.07108	+	0.618390i
$914$	55.8806	+	96.7881i	0.0611385	+	0.105895i
$915$	19.6615	+	11.3516i	0.0214880	+	0.0124061i
$916$		−	639.993i		−	0.698682i
$917$	790.641	+	991.063i	0.862204	+	1.08077i
$918$	−68.2762			−0.0743750
$919$	−269.068	+	466.039i	−0.292783	+	0.507115i	−0.974467	−	0.224532i	$-0.927915\pi$
$919$	−269.068	+	466.039i	−0.292783	+	0.507115i	0.681684	+	0.731647i	$0.261248\pi$
$920$	12.3253	−	7.11603i	0.0133971	−	0.00773481i
$921$	39.8729	+	69.0618i	0.0432930	+	0.0749857i
$922$	11.7369	+	6.77632i	0.0127299	+	0.00734959i
$923$		−	740.428i		−	0.802198i
$924$	109.129	−	278.206i	0.118105	−	0.301088i
$925$	−175.296			−0.189510
$926$	−164.122	+	284.267i	−0.177237	+	0.306984i
$927$	−462.306	+	266.913i	−0.498712	+	0.287932i
$928$	119.394	+	206.797i	0.128658	+	0.222841i
$929$	−770.069	−	444.600i	−0.828922	−	0.478579i	0.0245611	−	0.999698i	$-0.492181\pi$
$929$	−770.069	−	444.600i	−0.828922	−	0.478579i	−0.853484	+	0.521120i	$0.825515\pi$
$930$		−	6.67413i		−	0.00717649i
$931$	87.8657	+	284.486i	0.0943778	+	0.305570i
$932$	621.578			0.666929
$933$	−378.160	+	654.993i	−0.405317	+	0.702029i
$934$	839.607	−	484.747i	0.898937	−	0.519001i
$935$	128.022	+	221.740i	0.136921	+	0.237155i
$936$	53.3504	+	30.8019i	0.0569983	+	0.0329080i
$937$			997.355i			1.06441i	0.846615	+	0.532206i	$0.178637\pi$
$937$			997.355i			1.06441i	−0.846615	+	0.532206i	$0.821363\pi$
$938$	455.916	+	178.838i	0.486051	+	0.190659i
$939$	496.270			0.528509
$940$	−127.656	+	221.107i	−0.135805	+	0.235221i
$941$	−959.098	+	553.735i	−1.01923	+	0.588454i	−0.913882	−	0.405981i	$-0.866930\pi$
$941$	−959.098	+	553.735i	−1.01923	+	0.588454i	−0.105351	+	0.994435i	$0.533597\pi$
$942$	−225.032	−	389.766i	−0.238887	−	0.413764i
$943$	−112.799	−	65.1245i	−0.119617	−	0.0690609i
$944$			231.433i			0.245162i
$945$	63.5792	−	50.7217i	0.0672796	−	0.0536737i
$946$	592.915			0.626760
$947$	−293.801	+	508.878i	−0.310244	+	0.537358i	−0.978415	−	0.206650i	$-0.933744\pi$
$947$	−293.801	+	508.878i	−0.310244	+	0.537358i	0.668171	+	0.744008i	$0.267077\pi$
$948$	335.118	−	193.481i	0.353500	−	0.204093i
$949$	−298.770	−	517.485i	−0.314826	−	0.545295i
$950$	37.2105	+	21.4835i	0.0391689	+	0.0226142i
$951$		−	2.37089i		−	0.00249305i
$952$	181.897	−	27.4504i	0.191068	−	0.0288345i
$953$	441.771			0.463558			0.231779	−	0.972768i	$-0.425545\pi$
$953$	441.771			0.463558			0.231779	+	0.972768i	$0.425545\pi$
$954$	−30.8444	+	53.4241i	−0.0323316	+	0.0560001i
$955$	−175.812	+	101.505i	−0.184097	+	0.106288i
$956$	−136.263	−	236.015i	−0.142535	−	0.246877i
$957$	−780.342	−	450.531i	−0.815404	−	0.470774i
$958$			889.684i			0.928688i
$959$	1.31962	+	8.74431i	0.00137604	+	0.00911815i
$960$	−30.9839			−0.0322749
$961$	−479.758	+	830.965i	−0.499227	+	0.864687i
$962$	311.738	−	179.982i	0.324051	−	0.187091i
$963$	127.457	+	220.761i	0.132354	+	0.229243i
$964$	−668.883	−	386.179i	−0.693862	−	0.400601i
$965$		−	513.524i		−	0.532150i
$966$	24.0624	+	30.1621i	0.0249094	+	0.0312237i
$967$	1581.63			1.63561			0.817804	−	0.575497i	$-0.195191\pi$
$967$	1581.63			1.63561			0.817804	+	0.575497i	$0.195191\pi$
$968$	43.6761	−	75.6492i	0.0451199	−	0.0781500i
$969$	84.6863	−	48.8937i	0.0873956	−	0.0504579i
$970$	97.1539	+	168.275i	0.100159	+	0.173480i
$971$	517.033	+	298.509i	0.532475	+	0.307425i	0.742024	−	0.670374i	$-0.233866\pi$
$971$	517.033	+	298.509i	0.532475	+	0.307425i	−0.209549	+	0.977798i	$0.567199\pi$
$972$			31.1769i			0.0320750i
$973$	−31.0136	+	79.0638i	−0.0318742	+	0.0812577i
$974$	705.365			0.724194
$975$	31.4370	−	54.4505i	0.0322431	−	0.0558467i
$976$	20.3063	−	11.7239i	0.0208056	−	0.0120121i
$977$	105.721	+	183.114i	0.108210	+	0.187425i	0.915045	−	0.403351i	$-0.132155\pi$
$977$	105.721	+	183.114i	0.108210	+	0.187425i	−0.806835	+	0.590777i	$0.798821\pi$
$978$	257.891	+	148.893i	0.263692	+	0.152243i
$979$		−	1574.96i		−	1.60874i
$980$	−148.991	+	160.691i	−0.152032	+	0.163971i
$981$	518.575			0.528618
$982$	117.792	−	204.022i	0.119951	−	0.207762i
$983$	−513.418	+	296.422i	−0.522297	+	0.301548i	−0.737874	−	0.674939i	$-0.764170\pi$
$983$	−513.418	+	296.422i	−0.522297	+	0.301548i	0.215577	+	0.976487i	$0.430837\pi$
$984$	141.779	+	245.569i	0.144084	+	0.249562i
$985$	−441.499	−	254.899i	−0.448222	−	0.258781i
$986$		−	554.659i		−	0.562534i
$987$	−644.374	−	252.763i	−0.652861	−	0.256092i
$988$	−88.2308			−0.0893024
$989$	−38.2762	+	66.2964i	−0.0387020	+	0.0670338i
$990$	101.253	−	58.4584i	0.102276	−	0.0590489i
$991$	189.970	+	329.038i	0.191696	+	0.332027i	0.945812	−	0.324714i	$-0.105268\pi$
$991$	189.970	+	329.038i	0.191696	+	0.332027i	−0.754117	+	0.656740i	$0.771935\pi$
$992$	−5.96953	−	3.44651i	−0.00601767	−	0.00347430i
$993$		−	665.166i		−	0.669855i
$994$	−789.233	+	629.628i	−0.793997	+	0.633428i
$995$	−24.6999			−0.0248240
$996$	−158.697	+	274.871i	−0.159334	+	0.275975i
$997$	178.950	−	103.317i	0.179489	−	0.103628i	−0.407564	−	0.913177i	$-0.633622\pi$
$997$	178.950	−	103.317i	0.179489	−	0.103628i	0.587052	+	0.809549i	$0.300288\pi$
$998$	25.6724	+	44.4658i	0.0257238	+	0.0445550i
$999$	157.767	+	91.0866i	0.157925	+	0.0911778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.o.a.61.3	yes	8
3.2	odd	2		630.3.v.b.271.2		8
5.2	odd	4		1050.3.q.c.649.5		16
5.3	odd	4		1050.3.q.c.649.4		16
5.4	even	2		1050.3.p.b.901.2		8
7.2	even	3		1470.3.f.a.391.4		8
7.3	odd	6	inner	210.3.o.a.31.3	✓	8
7.5	odd	6		1470.3.f.a.391.1		8
21.17	even	6		630.3.v.b.451.2		8
35.3	even	12		1050.3.q.c.199.5		16
35.17	even	12		1050.3.q.c.199.4		16
35.24	odd	6		1050.3.p.b.451.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.3	✓	8	7.3	odd	6	inner
210.3.o.a.61.3	yes	8	1.1	even	1	trivial
630.3.v.b.271.2		8	3.2	odd	2
630.3.v.b.451.2		8	21.17	even	6
1050.3.p.b.451.2		8	35.24	odd	6
1050.3.p.b.901.2		8	5.4	even	2
1050.3.q.c.199.4		16	35.17	even	12
1050.3.q.c.199.5		16	35.3	even	12
1050.3.q.c.649.4		16	5.3	odd	4
1050.3.q.c.649.5		16	5.2	odd	4
1470.3.f.a.391.1		8	7.5	odd	6
1470.3.f.a.391.4		8	7.2	even	3

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} -2.44949i q^{6} +(-6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.73861 + 1.58114i) q^{10} +(-6.16205 - 10.6730i) q^{11} +(-3.00000 - 1.73205i) q^{12} -7.26007i q^{13} +(-7.73861 + 6.17364i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(8.04643 - 4.64561i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(5.26235 + 3.03822i) q^{19} +4.47214i q^{20} +(-11.9886 + 1.80922i) q^{21} -17.4289 q^{22} +(1.12514 - 1.94880i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-8.89173 - 5.13364i) q^{26} -5.19615i q^{27} +(2.08911 + 13.8433i) q^{28} +42.2122 q^{29} +(-2.73861 + 4.74342i) q^{30} +(-1.05527 + 0.609262i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-18.4862 - 10.6730i) q^{33} -13.1398i q^{34} +(9.76139 + 12.2358i) q^{35} -6.00000 q^{36} +(-17.5296 + 30.3622i) q^{37} +(7.44209 - 4.29669i) q^{38} +(-6.28740 - 10.8901i) q^{39} +(5.47723 + 3.16228i) q^{40} -57.8811i q^{41} +(-6.26139 + 15.9623i) q^{42} -34.0190 q^{43} +(-12.3241 + 21.3460i) q^{44} +(-5.80948 + 3.35410i) q^{45} +(-1.59119 - 2.75603i) q^{46} +(49.4411 + 28.5448i) q^{47} +6.92820i q^{48} +(35.9317 + 33.3154i) q^{49} +7.07107 q^{50} +(8.04643 - 13.9368i) q^{51} +(-12.5748 + 7.26007i) q^{52} +(-7.27009 - 12.5922i) q^{53} +(-6.36396 - 3.67423i) q^{54} +27.5575i q^{55} +(18.4317 + 7.23003i) q^{56} +10.5247 q^{57} +(29.8485 - 51.6992i) q^{58} +(50.1067 - 28.9291i) q^{59} +(3.87298 + 6.70820i) q^{60} +(-5.07658 - 2.93096i) q^{61} +1.72325i q^{62} +(-16.4161 + 13.0963i) q^{63} +8.00000 q^{64} +(-8.11700 + 14.0591i) q^{65} +(-26.1434 + 15.0939i) q^{66} +(-24.7355 - 42.8431i) q^{67} +(-16.0929 - 9.29122i) q^{68} -3.89761i q^{69} +(21.8881 - 3.30318i) q^{70} +101.986 q^{71} +(-4.24264 + 7.34847i) q^{72} +(71.2783 - 41.1525i) q^{73} +(24.7906 + 42.9387i) q^{74} +(7.50000 + 4.33013i) q^{75} -12.1529i q^{76} +(12.8732 + 85.3029i) q^{77} -17.7835 q^{78} +(-55.8530 + 96.7403i) q^{79} +(7.74597 - 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-70.8895 - 40.9281i) q^{82} -91.6237i q^{83} +(15.1223 + 18.9557i) q^{84} -20.7758 q^{85} +(-24.0551 + 41.6646i) q^{86} +(63.3183 - 36.5568i) q^{87} +(17.4289 + 30.1878i) q^{88} +(110.673 + 63.8973i) q^{89} +9.48683i q^{90} +(-18.5582 + 47.3108i) q^{91} -4.50057 q^{92} +(-1.05527 + 1.82779i) q^{93} +(69.9203 - 40.3685i) q^{94} +(-6.79367 - 11.7670i) q^{95} +(8.48528 + 4.89898i) q^{96} -61.4455i q^{97} +(66.2104 - 20.4496i) q^{98} -36.9723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9}+O(q^{10}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9	\( 8 q + 12 q^{3} - 8 q^{4} + 12 q^{9} - 4 q^{11} - 24 q^{12} - 40 q^{14} - 16 q^{16} + 84 q^{17} + 108 q^{19} - 48 q^{22} + 12 q^{23} + 20 q^{25} - 96 q^{26} + 72 q^{29} - 132 q^{31} - 12 q^{33} + 100 q^{35} - 48 q^{36} - 96 q^{37} - 168 q^{38} + 24 q^{39} - 72 q^{42} - 112 q^{43} - 8 q^{44} + 8 q^{46} - 24 q^{47} + 156 q^{49} + 84 q^{51} + 48 q^{52} + 32 q^{53} + 16 q^{56} + 216 q^{57} + 104 q^{58} + 132 q^{59} + 96 q^{61} + 64 q^{64} + 20 q^{65} - 72 q^{66} - 120 q^{67} - 168 q^{68} + 8 q^{71} + 24 q^{73} - 16 q^{74} + 60 q^{75} - 216 q^{77} - 192 q^{78} + 12 q^{79} - 36 q^{81} + 24 q^{82} + 120 q^{85} - 40 q^{86} + 108 q^{87} + 48 q^{88} + 492 q^{89} - 308 q^{91} - 48 q^{92} - 132 q^{93} + 480 q^{94} - 40 q^{95} - 24 q^{99}+O(q^{100}) \) 8 * q + 12 * q^3 - 8 * q^4 + 12 * q^9 - 4 * q^11 - 24 * q^12 - 40 * q^14 - 16 * q^16 + 84 * q^17 + 108 * q^19 - 48 * q^22 + 12 * q^23 + 20 * q^25 - 96 * q^26 + 72 * q^29 - 132 * q^31 - 12 * q^33 + 100 * q^35 - 48 * q^36 - 96 * q^37 - 168 * q^38 + 24 * q^39 - 72 * q^42 - 112 * q^43 - 8 * q^44 + 8 * q^46 - 24 * q^47 + 156 * q^49 + 84 * q^51 + 48 * q^52 + 32 * q^53 + 16 * q^56 + 216 * q^57 + 104 * q^58 + 132 * q^59 + 96 * q^61 + 64 * q^64 + 20 * q^65 - 72 * q^66 - 120 * q^67 - 168 * q^68 + 8 * q^71 + 24 * q^73 - 16 * q^74 + 60 * q^75 - 216 * q^77 - 192 * q^78 + 12 * q^79 - 36 * q^81 + 24 * q^82 + 120 * q^85 - 40 * q^86 + 108 * q^87 + 48 * q^88 + 492 * q^89 - 308 * q^91 - 48 * q^92 - 132 * q^93 + 480 * q^94 - 40 * q^95 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more