LMFDB - Embedded newform 43.3.d.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,3,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.17166513675$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 37x^{10} + 483x^{8} + 2718x^{6} + 6923x^{4} + 7253x^{2} + 1849 $ x^12 + 37x^10 + 483x^8 + 2718x^6 + 6923x^4 + 7253*x^2 + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.3
Root			$-0.604188i$ of defining polynomial
Character	$\chi$	$=$	43.7
Dual form			43.3.d.a.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.604188i q^{2} +(-1.35447 + 0.782004i) q^{3} +3.63496 q^{4} +(4.60389 - 2.65806i) q^{5} +(0.472478 + 0.818356i) q^{6} +(-0.191259 - 0.110424i) q^{7} -4.61295i q^{8} +(-3.27694 + 5.67582i) q^{9} +O(q^{10})$	\(q-0.604188i q^{2} +(-1.35447 + 0.782004i) q^{3} +3.63496 q^{4} +(4.60389 - 2.65806i) q^{5} +(0.472478 + 0.818356i) q^{6} +(-0.191259 - 0.110424i) q^{7} -4.61295i q^{8} +(-3.27694 + 5.67582i) q^{9} +(-1.60597 - 2.78161i) q^{10} -12.5758 q^{11} +(-4.92344 + 2.84255i) q^{12} +(-3.33345 + 5.77371i) q^{13} +(-0.0667167 + 0.115557i) q^{14} +(-4.15722 + 7.20052i) q^{15} +11.7527 q^{16} +(4.41963 - 7.65503i) q^{17} +(3.42927 + 1.97989i) q^{18} +(-20.3963 + 11.7758i) q^{19} +(16.7349 - 9.66192i) q^{20} +0.345407 q^{21} +7.59812i q^{22} +(-14.5361 - 25.1773i) q^{23} +(3.60735 + 6.24811i) q^{24} +(1.63052 - 2.82414i) q^{25} +(3.48841 + 2.01403i) q^{26} -24.3264i q^{27} +(-0.695220 - 0.401385i) q^{28} +(26.9000 + 15.5307i) q^{29} +(4.35047 + 2.51174i) q^{30} +(17.3121 + 29.9855i) q^{31} -25.5527i q^{32} +(17.0335 - 9.83430i) q^{33} +(-4.62508 - 2.67029i) q^{34} -1.17405 q^{35} +(-11.9115 + 20.6314i) q^{36} +(35.4962 - 20.4937i) q^{37} +(7.11480 + 12.3232i) q^{38} -10.4271i q^{39} +(-12.2615 - 21.2375i) q^{40} -18.0428 q^{41} -0.208691i q^{42} +(-16.4775 + 39.7176i) q^{43} -45.7123 q^{44} +34.8411i q^{45} +(-15.2118 + 8.78254i) q^{46} +35.2170 q^{47} +(-15.9187 + 9.19069i) q^{48} +(-24.4756 - 42.3930i) q^{49} +(-1.70631 - 0.985141i) q^{50} +13.8247i q^{51} +(-12.1170 + 20.9872i) q^{52} +(-35.9119 - 62.2013i) q^{53} -14.6977 q^{54} +(-57.8974 + 33.4271i) q^{55} +(-0.509379 + 0.882270i) q^{56} +(18.4175 - 31.9000i) q^{57} +(9.38347 - 16.2526i) q^{58} +22.2615 q^{59} +(-15.1113 + 26.1736i) q^{60} +(65.8081 + 37.9943i) q^{61} +(18.1169 - 10.4598i) q^{62} +(1.25349 - 0.723703i) q^{63} +31.5723 q^{64} +35.4420i q^{65} +(-5.94176 - 10.2914i) q^{66} +(-34.2118 - 59.2566i) q^{67} +(16.0652 - 27.8257i) q^{68} +(39.3775 + 22.7346i) q^{69} +0.709347i q^{70} +(12.9209 + 7.45986i) q^{71} +(26.1823 + 15.1164i) q^{72} +(40.2453 + 23.2357i) q^{73} +(-12.3821 - 21.4464i) q^{74} +5.10029i q^{75} +(-74.1396 + 42.8045i) q^{76} +(2.40523 + 1.38866i) q^{77} -6.29993 q^{78} +(40.1769 - 69.5884i) q^{79} +(54.1083 - 31.2394i) q^{80} +(-10.4691 - 18.1330i) q^{81} +10.9013i q^{82} +(22.6967 + 39.3118i) q^{83} +1.25554 q^{84} -46.9905i q^{85} +(23.9969 + 9.95554i) q^{86} -48.5803 q^{87} +58.0113i q^{88} +(93.4602 - 53.9593i) q^{89} +21.0506 q^{90} +(1.27511 - 0.736184i) q^{91} +(-52.8381 - 91.5183i) q^{92} +(-46.8976 - 27.0763i) q^{93} -21.2777i q^{94} +(-62.6015 + 108.429i) q^{95} +(19.9823 + 34.6104i) q^{96} +99.3401 q^{97} +(-25.6134 + 14.7879i) q^{98} +(41.2100 - 71.3778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9}+O(q^{10}) $ 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9	$ 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9} - q^{10} + 28 q^{11} - 6 q^{12} + 24 q^{13} - 18 q^{14} - 13 q^{15} + 110 q^{16} - 7 q^{17} + 33 q^{18} + 66 q^{19} - 99 q^{20} - 80 q^{21} - 16 q^{23} - 2 q^{24} - 21 q^{25} + 9 q^{26} - 192 q^{28} - 111 q^{29} + 99 q^{30} - 29 q^{31} - 114 q^{33} + 213 q^{34} + 38 q^{35} + 152 q^{36} + 120 q^{37} + 172 q^{38} - 29 q^{40} + 94 q^{41} + 5 q^{43} - 174 q^{44} + 156 q^{46} - 18 q^{47} - 213 q^{48} - 99 q^{49} - 198 q^{50} - 234 q^{52} - 58 q^{53} + 128 q^{54} - 258 q^{55} + 315 q^{56} + 51 q^{57} - 196 q^{58} + 336 q^{59} - 5 q^{60} + 204 q^{61} + 261 q^{62} - 153 q^{63} - 604 q^{64} - 201 q^{66} + 115 q^{67} - 106 q^{68} + 423 q^{69} - 66 q^{71} + 294 q^{72} + 249 q^{73} - 214 q^{74} - 438 q^{76} + 117 q^{77} + 136 q^{78} + 236 q^{79} + 681 q^{80} + 110 q^{81} - 4 q^{83} + 248 q^{84} + 102 q^{86} - 408 q^{87} - 45 q^{89} - 44 q^{90} - 156 q^{91} - 483 q^{92} - 567 q^{93} - 389 q^{95} - 278 q^{96} - 370 q^{97} - 879 q^{98} + 157 q^{99}+O(q^{100}) $ 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9 - q^10 + 28 * q^11 - 6 * q^12 + 24 * q^13 - 18 * q^14 - 13 * q^15 + 110 * q^16 - 7 * q^17 + 33 * q^18 + 66 * q^19 - 99 * q^20 - 80 * q^21 - 16 * q^23 - 2 * q^24 - 21 * q^25 + 9 * q^26 - 192 * q^28 - 111 * q^29 + 99 * q^30 - 29 * q^31 - 114 * q^33 + 213 * q^34 + 38 * q^35 + 152 * q^36 + 120 * q^37 + 172 * q^38 - 29 * q^40 + 94 * q^41 + 5 * q^43 - 174 * q^44 + 156 * q^46 - 18 * q^47 - 213 * q^48 - 99 * q^49 - 198 * q^50 - 234 * q^52 - 58 * q^53 + 128 * q^54 - 258 * q^55 + 315 * q^56 + 51 * q^57 - 196 * q^58 + 336 * q^59 - 5 * q^60 + 204 * q^61 + 261 * q^62 - 153 * q^63 - 604 * q^64 - 201 * q^66 + 115 * q^67 - 106 * q^68 + 423 * q^69 - 66 * q^71 + 294 * q^72 + 249 * q^73 - 214 * q^74 - 438 * q^76 + 117 * q^77 + 136 * q^78 + 236 * q^79 + 681 * q^80 + 110 * q^81 - 4 * q^83 + 248 * q^84 + 102 * q^86 - 408 * q^87 - 45 * q^89 - 44 * q^90 - 156 * q^91 - 483 * q^92 - 567 * q^93 - 389 * q^95 - 278 * q^96 - 370 * q^97 - 879 * q^98 + 157 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	0.604188i		−	0.302094i	−0.988527	−	0.151047i	$-0.951736\pi$
$2$		−	0.604188i		−	0.302094i	0.988527	−	0.151047i	$-0.0482645\pi$
$3$	−1.35447	+	0.782004i	−0.451490	+	0.260668i	−0.708459	−	0.705752i	$-0.750609\pi$
$3$	−1.35447	+	0.782004i	−0.451490	+	0.260668i	0.256969	+	0.966420i	$0.417276\pi$
$4$	3.63496			0.908739
$5$	4.60389	−	2.65806i	0.920777	−	0.531611i	0.0368945	−	0.999319i	$-0.488253\pi$
$5$	4.60389	−	2.65806i	0.920777	−	0.531611i	0.883883	+	0.467708i	$0.154920\pi$
$6$	0.472478	+	0.818356i	0.0787463	+	0.136393i
$7$	−0.191259	−	0.110424i	−0.0273228	−	0.0157748i	0.486276	−	0.873805i	$-0.338355\pi$
$7$	−0.191259	−	0.110424i	−0.0273228	−	0.0157748i	−0.513599	+	0.858030i	$0.671688\pi$
$8$		−	4.61295i		−	0.576619i
$9$	−3.27694	+	5.67582i	−0.364104	+	0.630647i
$10$	−1.60597	−	2.78161i	−0.160597	−	0.278161i
$11$	−12.5758			−1.14325			−0.571625	−	0.820515i	$-0.693687\pi$
$11$	−12.5758			−1.14325			−0.571625	+	0.820515i	$0.693687\pi$
$12$	−4.92344	+	2.84255i	−0.410287	+	0.236879i
$13$	−3.33345	+	5.77371i	−0.256419	+	0.444131i	−0.965280	−	0.261217i	$-0.915876\pi$
$13$	−3.33345	+	5.77371i	−0.256419	+	0.444131i	0.708861	+	0.705348i	$0.249209\pi$
$14$	−0.0667167	+	0.115557i	−0.00476548	+	0.00825405i
$15$	−4.15722	+	7.20052i	−0.277148	+	0.480035i
$16$	11.7527			0.734546
$17$	4.41963	−	7.65503i	0.259979	−	0.450296i	−0.706257	−	0.707955i	$-0.749618\pi$
$17$	4.41963	−	7.65503i	0.259979	−	0.450296i	0.966236	+	0.257659i	$0.0829512\pi$
$18$	3.42927	+	1.97989i	0.190515	+	0.109994i
$19$	−20.3963	+	11.7758i	−1.07349	+	0.619779i	−0.929133	−	0.369746i	$-0.879445\pi$
$19$	−20.3963	+	11.7758i	−1.07349	+	0.619779i	−0.144357	+	0.989526i	$0.546111\pi$
$20$	16.7349	−	9.66192i	0.836747	−	0.483096i
$21$	0.345407			0.0164480
$22$			7.59812i			0.345369i
$23$	−14.5361	−	25.1773i	−0.632004	−	1.09466i	−0.987141	−	0.159849i	$-0.948899\pi$
$23$	−14.5361	−	25.1773i	−0.632004	−	1.09466i	0.355137	−	0.934814i	$-0.384434\pi$
$24$	3.60735	+	6.24811i	0.150306	+	0.260338i
$25$	1.63052	−	2.82414i	0.0652208	−	0.112966i
$26$	3.48841	+	2.01403i	0.134169	+	0.0774628i
$27$		−	24.3264i		−	0.900978i
$28$	−0.695220	−	0.401385i	−0.0248293	−	0.0143352i
$29$	26.9000	+	15.5307i	0.927585	+	0.535542i	0.886047	−	0.463595i	$-0.153441\pi$
$29$	26.9000	+	15.5307i	0.927585	+	0.535542i	0.0415382	+	0.999137i	$0.486774\pi$
$30$	4.35047	+	2.51174i	0.145016	+	0.0837248i
$31$	17.3121	+	29.9855i	0.558456	+	0.967274i	0.997626	+	0.0688700i	$0.0219394\pi$
$31$	17.3121	+	29.9855i	0.558456	+	0.967274i	−0.439170	+	0.898404i	$0.644727\pi$
$32$		−	25.5527i		−	0.798521i
$33$	17.0335	−	9.83430i	0.516167	−	0.298009i
$34$	−4.62508	−	2.67029i	−0.136032	−	0.0785380i
$35$	−1.17405			−0.0335443
$36$	−11.9115	+	20.6314i	−0.330876	+	0.573094i
$37$	35.4962	−	20.4937i	0.959356	−	0.553885i	0.0633814	−	0.997989i	$-0.479812\pi$
$37$	35.4962	−	20.4937i	0.959356	−	0.553885i	0.895975	+	0.444105i	$0.146478\pi$
$38$	7.11480	+	12.3232i	0.187232	+	0.324295i
$39$		−	10.4271i		−	0.267361i
$40$	−12.2615	−	21.2375i	−0.306537	−	0.530938i
$41$	−18.0428			−0.440068			−0.220034	−	0.975492i	$-0.570617\pi$
$41$	−18.0428			−0.440068			−0.220034	+	0.975492i	$0.570617\pi$
$42$		−	0.208691i		−	0.00496883i
$43$	−16.4775	+	39.7176i	−0.383199	+	0.923666i
$43$	−16.4775	+	39.7176i	−0.383199	+	0.923666i
$44$	−45.7123			−1.03892
$45$			34.8411i			0.774248i
$46$	−15.2118	+	8.78254i	−0.330691	+	0.190925i
$47$	35.2170			0.749299			0.374649	−	0.927167i	$-0.377763\pi$
$47$	35.2170			0.749299			0.374649	+	0.927167i	$0.377763\pi$
$48$	−15.9187	+	9.19069i	−0.331640	+	0.191473i
$49$	−24.4756	−	42.3930i	−0.499502	−	0.865163i
$50$	−1.70631	−	0.985141i	−0.0341263	−	0.0197028i
$51$			13.8247i			0.271072i
$52$	−12.1170	+	20.9872i	−0.233018	+	0.403600i
$53$	−35.9119	−	62.2013i	−0.677584	−	1.17361i	−0.975707	−	0.219082i	$-0.929694\pi$
$53$	−35.9119	−	62.2013i	−0.677584	−	1.17361i	0.298123	−	0.954527i	$-0.403639\pi$
$54$	−14.6977			−0.272180
$55$	−57.8974	+	33.4271i	−1.05268	+	0.607765i
$56$	−0.509379	+	0.882270i	−0.00909605	+	0.0157548i
$57$	18.4175	−	31.9000i	0.323113	−	0.559649i
$58$	9.38347	−	16.2526i	0.161784	−	0.280218i
$59$	22.2615			0.377313			0.188656	−	0.982043i	$-0.439587\pi$
$59$	22.2615			0.377313			0.188656	+	0.982043i	$0.439587\pi$
$60$	−15.1113	+	26.1736i	−0.251855	+	0.436226i
$61$	65.8081	+	37.9943i	1.07882	+	0.622857i	0.930578	−	0.366094i	$-0.119305\pi$
$61$	65.8081	+	37.9943i	1.07882	+	0.622857i	0.148243	+	0.988951i	$0.452638\pi$
$62$	18.1169	−	10.4598i	0.292208	−	0.168706i
$63$	1.25349	−	0.723703i	0.0198967	−	0.0114874i
$64$	31.5723			0.493318
$65$			35.4420i			0.545262i
$66$	−5.94176	−	10.2914i	−0.0900267	−	0.155931i
$67$	−34.2118	−	59.2566i	−0.510624	−	0.884426i	−0.999924	−	0.0123111i	$-0.996081\pi$
$67$	−34.2118	−	59.2566i	−0.510624	−	0.884426i	0.489300	−	0.872115i	$-0.337252\pi$
$68$	16.0652	−	27.8257i	0.236253	−	0.409202i
$69$	39.3775	+	22.7346i	0.570688	+	0.329487i
$70$			0.709347i			0.0101335i
$71$	12.9209	+	7.45986i	0.181984	+	0.105068i	0.588224	−	0.808698i	$-0.299827\pi$
$71$	12.9209	+	7.45986i	0.181984	+	0.105068i	−0.406241	+	0.913766i	$0.633161\pi$
$72$	26.1823	+	15.1164i	0.363643	+	0.209949i
$73$	40.2453	+	23.2357i	0.551306	+	0.318297i	0.749649	−	0.661836i	$-0.230223\pi$
$73$	40.2453	+	23.2357i	0.551306	+	0.318297i	−0.198343	+	0.980133i	$0.563556\pi$
$74$	−12.3821	−	21.4464i	−0.167325	−	0.289816i
$75$			5.10029i			0.0680039i
$76$	−74.1396	+	42.8045i	−0.975522	+	0.563218i
$77$	2.40523	+	1.38866i	0.0312368	+	0.0180346i
$78$	−6.29993			−0.0807683
$79$	40.1769	−	69.5884i	0.508568	−	0.880866i	−0.491382	−	0.870944i	$-0.663508\pi$
$79$	40.1769	−	69.5884i	0.508568	−	0.880866i	0.999951	−	0.00992224i	$-0.00315840\pi$
$80$	54.1083	−	31.2394i	0.676353	−	0.390493i
$81$	−10.4691	−	18.1330i	−0.129248	−	0.223864i
$82$			10.9013i			0.132942i
$83$	22.6967	+	39.3118i	0.273454	+	0.473637i	0.969744	−	0.244124i	$-0.0785005\pi$
$83$	22.6967	+	39.3118i	0.273454	+	0.473637i	−0.696290	+	0.717761i	$0.745167\pi$
$84$	1.25554			0.0149469
$85$		−	46.9905i		−	0.552830i
$86$	23.9969	+	9.95554i	0.279034	+	0.115762i
$87$	−48.5803			−0.558394
$88$			58.0113i			0.659220i
$89$	93.4602	−	53.9593i	1.05012	−	0.606284i	0.127434	−	0.991847i	$-0.459326\pi$
$89$	93.4602	−	53.9593i	1.05012	−	0.606284i	0.922682	+	0.385563i	$0.125993\pi$
$90$	21.0506			0.233896
$91$	1.27511	−	0.736184i	0.0140122	−	0.00808993i
$92$	−52.8381	−	91.5183i	−0.574327	−	0.994764i
$93$	−46.8976	−	27.0763i	−0.504275	−	0.291143i
$94$		−	21.2777i		−	0.226359i
$95$	−62.6015	+	108.429i	−0.658963	+	1.14136i
$96$	19.9823	+	34.6104i	0.208149	+	0.360524i
$97$	99.3401			1.02412			0.512062	−	0.858948i	$-0.328882\pi$
$97$	99.3401			1.02412			0.512062	+	0.858948i	$0.328882\pi$
$98$	−25.6134	+	14.7879i	−0.261361	+	0.150897i
$99$	41.2100	−	71.3778i	0.416262	−	0.720988i
$100$	5.92687	−	10.2656i	0.0592687	−	0.102656i
$101$	−90.1301	+	156.110i	−0.892377	+	1.54564i	−0.0553593	+	0.998467i	$0.517630\pi$
$101$	−90.1301	+	156.110i	−0.892377	+	1.54564i	−0.837018	+	0.547176i	$0.815703\pi$
$102$	8.35272			0.0818894
$103$	−27.7762	+	48.1099i	−0.269672	+	0.467086i	−0.968777	−	0.247933i	$-0.920249\pi$
$103$	−27.7762	+	48.1099i	−0.269672	+	0.467086i	0.699105	+	0.715019i	$0.253582\pi$
$104$	26.6338	+	15.3770i	0.256094	+	0.147856i
$105$	1.59022	−	0.918111i	0.0151449	−	0.00874392i
$106$	−37.5813	+	21.6976i	−0.354540	+	0.204694i
$107$	−209.487			−1.95782			−0.978910	−	0.204290i	$-0.934512\pi$
$107$	−209.487			−1.95782			−0.978910	+	0.204290i	$0.934512\pi$
$108$		−	88.4254i		−	0.818754i
$109$	−92.5158	−	160.242i	−0.848769	−	1.47011i	−0.882308	−	0.470673i	$-0.844011\pi$
$109$	−92.5158	−	160.242i	−0.848769	−	1.47011i	0.0335389	−	0.999437i	$-0.489322\pi$
$110$	20.1962	+	34.9809i	0.183602	+	0.318008i
$111$	−32.0524	+	55.5163i	−0.288760	+	0.500147i
$112$	−2.24782	−	1.29778i	−0.0200698	−	0.0115873i
$113$			130.147i			1.15174i	0.817540	+	0.575872i	$0.195337\pi$
$113$			130.147i			1.15174i	−0.817540	+	0.575872i	$0.804663\pi$
$114$	−19.2736	−	11.1276i	−0.169067	−	0.0976106i
$115$	−133.845	−	77.2755i	−1.16387	−	0.671961i
$116$	97.7802	+	56.4534i	0.842933	+	0.486668i
$117$	−21.8470	−	37.8402i	−0.186727	−	0.323420i
$118$		−	13.4501i		−	0.113984i
$119$	−1.69059	+	0.976065i	−0.0142067	+	0.00820222i
$120$	33.2156	+	19.1771i	0.276797	+	0.159809i
$121$	37.1496			0.307022
$122$	22.9557	−	39.7605i	0.188162	−	0.325905i
$123$	24.4385	−	14.1096i	0.198687	−	0.114712i
$124$	62.9289	+	108.996i	0.507491	+	0.879000i
$125$			115.567i			0.924534i
$126$	−0.437253	−	0.757344i	−0.00347026	−	0.00601067i
$127$	173.151			1.36339			0.681697	−	0.731634i	$-0.261242\pi$
$127$	173.151			1.36339			0.681697	+	0.731634i	$0.261242\pi$
$128$		−	121.286i		−	0.947549i
$129$	−8.74100	−	66.6819i	−0.0677597	−	0.516914i
$130$	21.4136			0.164720
$131$			170.198i			1.29922i	0.760268	+	0.649609i	$0.225067\pi$
$131$			170.198i			1.29922i	−0.760268	+	0.649609i	$0.774933\pi$
$132$	61.9160	−	35.7472i	0.469061	−	0.270812i
$133$	5.20131			0.0391076
$134$	−35.8021	+	20.6704i	−0.267180	+	0.154256i
$135$	−64.6609	−	111.996i	−0.478970	−	0.829600i
$136$	−35.3123	−	20.3876i	−0.259649	−	0.149909i
$137$		−	74.1386i		−	0.541158i	−0.962698	−	0.270579i	$-0.912785\pi$
$137$		−	74.1386i		−	0.541158i	0.962698	−	0.270579i	$-0.0872151\pi$
$138$	13.7360	−	23.7914i	0.0995360	−	0.172401i
$139$	−14.1932	−	24.5833i	−0.102109	−	0.176858i	0.810444	−	0.585816i	$-0.199226\pi$
$139$	−14.1932	−	24.5833i	−0.102109	−	0.176858i	−0.912553	+	0.408957i	$0.865892\pi$
$140$	−4.26762			−0.0304830
$141$	−47.7005	+	27.5399i	−0.338301	+	0.195318i
$142$	4.50716	−	7.80663i	0.0317406	−	0.0549763i
$143$	41.9207	−	72.6087i	0.293152	−	0.507753i
$144$	−38.5130	+	66.7065i	−0.267451	+	0.463239i
$145$	165.126			1.13880
$146$	14.0387	−	24.3158i	0.0961555	−	0.166546i
$147$	66.3030	+	38.2801i	0.451041	+	0.260409i
$148$	129.027	−	74.4938i	0.871805	−	0.503337i
$149$	−124.500	+	71.8803i	−0.835572	+	0.482418i	−0.855757	−	0.517378i	$-0.826908\pi$
$149$	−124.500	+	71.8803i	−0.835572	+	0.482418i	0.0201845	+	0.999796i	$0.493575\pi$
$150$	3.08154			0.0205436
$151$		−	153.685i		−	1.01778i	−0.860832	−	0.508890i	$-0.830056\pi$
$151$		−	153.685i		−	1.01778i	0.860832	−	0.508890i	$-0.169944\pi$
$152$	54.3212	+	94.0871i	0.357376	+	0.618994i
$153$	28.9657	+	50.1701i	0.189319	+	0.327909i
$154$	0.839013	−	1.45321i	0.00544813	−	0.00943644i
$155$	159.406	+	92.0332i	1.02843	+	0.593763i
$156$		−	37.9020i		−	0.242962i
$157$	−223.673	−	129.138i	−1.42467	−	0.822535i	−0.427978	−	0.903789i	$-0.640774\pi$
$157$	−223.673	−	129.138i	−1.42467	−	0.822535i	−0.996693	+	0.0812543i	$0.974107\pi$
$158$	−42.0445	−	24.2744i	−0.266104	−	0.153635i
$159$	97.2834	+	56.1666i	0.611845	+	0.353249i
$160$	−67.9204	−	117.642i	−0.424503	−	0.735260i
$161$			6.42052i			0.0398790i
$162$	−10.9558	+	6.32531i	−0.0676281	+	0.0390451i
$163$	231.318	+	133.551i	1.41913	+	0.819334i	0.996222	−	0.0868403i	$-0.0276770\pi$
$163$	231.318	+	133.551i	1.41913	+	0.819334i	0.422905	+	0.906174i	$0.361010\pi$
$164$	−65.5848			−0.399907
$165$	52.2802	−	90.5520i	0.316850	−	0.548800i
$166$	23.7517	−	13.7131i	0.143083	−	0.0826089i
$167$	1.27559	+	2.20938i	0.00763825	+	0.0132298i	0.869819	−	0.493370i	$-0.164235\pi$
$167$	1.27559	+	2.20938i	0.00763825	+	0.0132298i	−0.862181	+	0.506600i	$0.830902\pi$
$168$		−	1.59335i		−	0.00948420i
$169$	62.2762	+	107.866i	0.368498	+	0.638258i
$170$	−28.3911			−0.167007
$171$		−	154.354i		−	0.902657i
$172$	−59.8952	+	144.372i	−0.348228	+	0.839371i
$173$	−130.931			−0.756829			−0.378414	−	0.925636i	$-0.623531\pi$
$173$	−130.931			−0.756829			−0.378414	+	0.925636i	$0.623531\pi$
$174$			29.3517i			0.168688i
$175$	−0.623704	+	0.360096i	−0.00356403	+	0.00205769i
$176$	−147.800			−0.839770
$177$	−30.1525	+	17.4086i	−0.170353	+	0.0983534i
$178$	−32.6016	−	56.4676i	−0.183155	−	0.317234i
$179$	−103.357	−	59.6733i	−0.577415	−	0.333371i	0.182690	−	0.983170i	$-0.441519\pi$
$179$	−103.357	−	59.6733i	−0.577415	−	0.333371i	−0.760105	+	0.649800i	$0.774853\pi$
$180$			126.646i			0.703589i
$181$	−163.797	+	283.705i	−0.904956	+	1.56743i	−0.0839794	+	0.996467i	$0.526763\pi$
$181$	−163.797	+	283.705i	−0.904956	+	1.56743i	−0.820976	+	0.570962i	$0.806570\pi$
$182$	−0.444794	−	0.770405i	−0.00244392	−	0.00423299i
$183$	−118.847			−0.649436
$184$	−116.141	+	67.0543i	−0.631204	+	0.364426i
$185$	108.947	−	188.702i	0.588902	−	1.02001i
$186$	−16.3592	+	28.3350i	−0.0879527	+	0.152339i
$187$	−55.5802	+	96.2678i	−0.297221	+	0.514801i
$188$	128.012			0.680917
$189$	−2.68621	+	4.65265i	−0.0142128	+	0.0246172i
$190$	65.5115	+	37.8231i	0.344797	+	0.199069i
$191$	134.939	−	77.9071i	0.706487	−	0.407891i	−0.103272	−	0.994653i	$-0.532931\pi$
$191$	134.939	−	77.9071i	0.706487	−	0.407891i	0.809759	+	0.586762i	$0.199598\pi$
$192$	−42.7638	+	24.6897i	−0.222728	+	0.128592i
$193$	−166.694			−0.863699			−0.431849	−	0.901946i	$-0.642139\pi$
$193$	−166.694			−0.863699			−0.431849	+	0.901946i	$0.642139\pi$
$194$		−	60.0201i		−	0.309382i
$195$	−27.7158	−	48.0052i	−0.142132	−	0.246180i
$196$	−88.9678	−	154.097i	−0.453917	−	0.786208i
$197$	15.9193	−	27.5731i	0.0808088	−	0.139965i	−0.822789	−	0.568347i	$-0.807583\pi$
$197$	15.9193	−	27.5731i	0.0808088	−	0.139965i	0.903598	+	0.428382i	$0.140916\pi$
$198$	−43.1256	−	24.8986i	−0.217806	−	0.125750i
$199$			66.8113i			0.335735i	0.985810	+	0.167868i	$0.0536881\pi$
$199$			66.8113i			0.335735i	−0.985810	+	0.167868i	$0.946312\pi$
$200$	−13.0276	−	7.52151i	−0.0651382	−	0.0376075i
$201$	92.6778	+	53.5075i	0.461083	+	0.266207i
$202$	94.3197	+	54.4555i	0.466929	+	0.269582i
$203$	−3.42991	−	5.94079i	−0.0168961	−	0.0292650i
$204$			50.2522i			0.246334i
$205$	−83.0671	+	47.9588i	−0.405205	+	0.233945i
$206$	29.0674	+	16.7821i	0.141104	+	0.0814664i
$207$	190.536			0.920462
$208$	−39.1772	+	67.8569i	−0.188352	+	0.326235i
$209$	256.499	−	148.090i	1.22727	−	0.708563i
$210$	−0.554712	−	0.960789i	−0.00264149	−	0.00457519i
$211$		−	250.280i		−	1.18616i	−0.805143	−	0.593080i	$-0.797912\pi$
$211$		−	250.280i		−	1.18616i	0.805143	−	0.593080i	$-0.202088\pi$
$212$	−130.538	−	226.099i	−0.615747	−	1.06650i
$213$	−23.3346			−0.109552
$214$			126.569i			0.591446i
$215$	29.7109	+	226.654i	0.138190	+	1.05420i
$216$	−112.216			−0.519521
$217$		−	7.64668i		−	0.0352381i
$218$	−96.8164	+	55.8969i	−0.444112	+	0.256408i
$219$	−72.6815			−0.331879
$220$	−210.454	+	121.506i	−0.956611	+	0.552300i
$221$	29.4653	+	51.0354i	0.133327	+	0.230929i
$222$	33.5423	+	19.3657i	0.151091	+	0.0872327i
$223$		−	239.280i		−	1.07301i	−0.843899	−	0.536503i	$-0.819745\pi$
$223$		−	239.280i		−	1.07301i	0.843899	−	0.536503i	$-0.180255\pi$
$224$	−2.82162	+	4.88719i	−0.0125965	+	0.0218178i
$225$	10.6862	+	18.5091i	0.0474943	+	0.0822626i
$226$	78.6333			0.347935
$227$	68.0829	−	39.3077i	0.299925	−	0.173162i	−0.342484	−	0.939524i	$-0.611268\pi$
$227$	68.0829	−	39.3077i	0.299925	−	0.173162i	0.642409	+	0.766362i	$0.277935\pi$
$228$	66.9467	−	115.955i	0.293626	−	0.508575i
$229$	77.3291	−	133.938i	0.337682	−	0.584882i	−0.646315	−	0.763071i	$-0.723691\pi$
$229$	77.3291	−	133.938i	0.337682	−	0.584882i	0.983996	+	0.178189i	$0.0570239\pi$
$230$	−46.6890	+	80.8677i	−0.202996	+	0.351599i
$231$	−4.34376			−0.0188041
$232$	71.6424	−	124.088i	0.308803	−	0.534863i
$233$	95.9135	+	55.3757i	0.411646	+	0.237664i	0.691497	−	0.722380i	$-0.256952\pi$
$233$	95.9135	+	55.3757i	0.411646	+	0.237664i	−0.279851	+	0.960043i	$0.590285\pi$
$234$	−22.8626	+	13.1997i	−0.0977033	+	0.0564091i
$235$	162.135	−	93.6088i	0.689937	−	0.398335i
$236$	80.9194			0.342879
$237$			125.674i			0.530270i
$238$	0.589727	+	1.02144i	0.00247784	+	0.00429175i
$239$	117.275	+	203.126i	0.490689	+	0.849899i	0.999943	−	0.0107180i	$-0.00341172\pi$
$239$	117.275	+	203.126i	0.490689	+	0.849899i	−0.509253	+	0.860617i	$0.670078\pi$
$240$	−48.8587	+	84.6258i	−0.203578	+	0.352608i
$241$	105.088	+	60.6724i	0.436049	+	0.251753i	0.701920	−	0.712256i	$-0.252326\pi$
$241$	105.088	+	60.6724i	0.436049	+	0.251753i	−0.265872	+	0.964008i	$0.585660\pi$
$242$		−	22.4454i		−	0.0927494i
$243$	217.966	+	125.843i	0.896978	+	0.517871i
$244$	239.209	+	138.108i	0.980367	+	0.566015i
$245$	−225.366	−	130.115i	−0.919861	−	0.531082i
$246$	−8.52483	−	14.7654i	−0.0346538	−	0.0600221i
$247$		−	157.016i		−	0.635694i
$248$	138.322	−	79.8600i	0.557748	−	0.322016i
$249$	−61.4841	−	35.4978i	−0.246924	−	0.142562i
$250$	69.8241			0.279296
$251$	181.439	−	314.262i	0.722865	−	1.25204i	−0.236982	−	0.971514i	$-0.576158\pi$
$251$	181.439	−	314.262i	0.722865	−	1.25204i	0.959847	−	0.280525i	$-0.0905086\pi$
$252$	4.55638	−	2.63063i	0.0180809	−	0.0104390i
$253$	182.802	+	316.623i	0.722539	+	1.25147i
$254$		−	104.616i		−	0.411874i
$255$	36.7468	+	63.6473i	0.144105	+	0.249597i
$256$	53.0096			0.207069
$257$		−	174.265i		−	0.678075i	−0.940773	−	0.339037i	$-0.889899\pi$
$257$		−	174.265i		−	0.678075i	0.940773	−	0.339037i	$-0.110101\pi$
$258$	−40.2884	+	5.28121i	−0.156157	+	0.0204698i
$259$	−9.05197			−0.0349497
$260$			128.830i			0.495500i
$261$	−176.299	+	101.786i	−0.675475	+	0.389986i
$262$	102.831			0.392486
$263$	−141.628	+	81.7690i	−0.538510	+	0.310909i	−0.744475	−	0.667650i	$-0.767300\pi$
$263$	−141.628	+	81.7690i	−0.538510	+	0.310909i	0.205965	+	0.978559i	$0.433967\pi$
$264$	−45.3651	−	78.5747i	−0.171838	−	0.297631i
$265$	−330.669	−	190.912i	−1.24781	−	0.720422i
$266$		−	3.14257i		−	0.0118142i
$267$	−84.3928	+	146.173i	−0.316078	+	0.547463i
$268$	−124.358	−	215.395i	−0.464024	−	0.803713i
$269$	−274.403			−1.02009			−0.510043	−	0.860149i	$-0.670370\pi$
$269$	−274.403			−1.02009			−0.510043	+	0.860149i	$0.670370\pi$
$270$	−67.6667	+	39.0674i	−0.250617	+	0.144694i
$271$	−47.6589	+	82.5476i	−0.175863	+	0.304604i	−0.940460	−	0.339905i	$-0.889605\pi$
$271$	−47.6589	+	82.5476i	−0.175863	+	0.304604i	0.764597	+	0.644509i	$0.222938\pi$
$272$	51.9428	−	89.9676i	0.190966	−	0.330763i
$273$	−1.15140	+	1.99428i	−0.00421757	+	0.00730505i
$274$	−44.7937			−0.163481
$275$	−20.5050	+	35.5157i	−0.0745637	+	0.129148i
$276$	143.135	+	82.6392i	0.518606	+	0.299418i
$277$	−388.285	+	224.177i	−1.40175	+	0.809302i	−0.994572	−	0.104046i	$-0.966821\pi$
$277$	−388.285	+	224.177i	−1.40175	+	0.809302i	−0.407180	+	0.913348i	$0.633488\pi$
$278$	−14.8530	+	8.57536i	−0.0534279	+	0.0308466i
$279$	−226.923			−0.813345
$280$			5.41583i			0.0193422i
$281$	−125.621	−	217.581i	−0.447048	−	0.774311i	0.551144	−	0.834410i	$-0.314191\pi$
$281$	−125.621	−	217.581i	−0.447048	−	0.774311i	−0.998192	+	0.0600996i	$0.980858\pi$
$282$	16.6393	+	28.8201i	0.0590045	+	0.102199i
$283$	−30.7044	+	53.1815i	−0.108496	+	0.187921i	−0.915161	−	0.403088i	$-0.867937\pi$
$283$	−30.7044	+	53.1815i	−0.108496	+	0.187921i	0.806665	+	0.591009i	$0.201270\pi$
$284$	46.9667	+	27.1163i	0.165376	+	0.0954798i
$285$		−	195.819i		−	0.687083i
$286$	−43.8693	−	25.3280i	−0.153389	−	0.0885594i
$287$	3.45086	+	1.99235i	0.0120239	+	0.00694200i
$288$	145.032	+	83.7345i	0.503585	+	0.290745i
$289$	105.434	+	182.616i	0.364822	+	0.631891i
$290$		−	99.7671i		−	0.344025i
$291$	−134.553	+	77.6844i	−0.462382	+	0.266957i
$292$	146.290	+	84.4606i	0.500993	+	0.289249i
$293$	−201.977			−0.689341			−0.344670	−	0.938724i	$-0.612009\pi$
$293$	−201.977			−0.689341			−0.344670	+	0.938724i	$0.612009\pi$
$294$	23.1284	−	40.0595i	0.0786679	−	0.136257i
$295$	102.489	−	59.1722i	0.347421	−	0.200584i
$296$	−94.5366	−	163.742i	−0.319380	−	0.553183i
$297$			305.923i			1.03004i
$298$	43.4292	+	75.2216i	0.145736	+	0.252421i
$299$	193.822			0.648233
$300$			18.5393i			0.0617978i
$301$	7.53725	−	5.77686i	0.0250407	−	0.0191922i
$302$	−92.8545			−0.307465
$303$		−	281.928i		−	0.930457i
$304$	−239.712	+	138.398i	−0.788527	+	0.455256i
$305$	403.964			1.32447
$306$	30.3122	−	17.5008i	0.0990595	−	0.0571920i
$307$	191.916	+	332.408i	0.625133	+	1.08276i	0.988515	+	0.151122i	$0.0482887\pi$
$307$	191.916	+	332.408i	0.625133	+	1.08276i	−0.363382	+	0.931640i	$0.618378\pi$
$308$	8.74291	+	5.04772i	0.0283861	+	0.0163887i
$309$		−	86.8845i		−	0.281180i
$310$	55.6054	−	96.3114i	0.179372	−	0.310682i
$311$	−17.6458	−	30.5634i	−0.0567389	−	0.0982747i	0.836261	−	0.548332i	$-0.184737\pi$
$311$	−17.6458	−	30.5634i	−0.0567389	−	0.0982747i	−0.893000	+	0.450057i	$0.851404\pi$
$312$	−48.0997			−0.154166
$313$	−406.270	+	234.560i	−1.29799	+	0.749392i	−0.980056	−	0.198722i	$-0.936321\pi$
$313$	−406.270	+	234.560i	−1.29799	+	0.749392i	−0.317930	+	0.948114i	$0.602988\pi$
$314$	−78.0236	+	135.141i	−0.248483	+	0.430385i
$315$	3.84729	−	6.66370i	0.0122136	−	0.0211546i
$316$	146.041	−	252.951i	0.462156	−	0.800478i
$317$	−100.114			−0.315817			−0.157909	−	0.987454i	$-0.550475\pi$
$317$	−100.114			−0.315817			−0.157909	+	0.987454i	$0.550475\pi$
$318$	33.9352	−	58.7775i	0.106714	−	0.184835i
$319$	−338.287	−	195.310i	−1.06046	−	0.612258i
$320$	145.355	−	83.9210i	0.454236	−	0.262253i
$321$	283.744	−	163.820i	0.883937	−	0.510341i
$322$	3.87920			0.0120472
$323$			208.179i			0.644517i
$324$	−38.0547	−	65.9127i	−0.117453	−	0.203434i
$325$	10.8705	+	18.8283i	0.0334477	+	0.0579332i
$326$	80.6902	−	139.759i	0.247516	−	0.428710i
$327$	250.620	+	144.696i	0.766422	+	0.442494i
$328$			83.2306i			0.253752i
$329$	−6.73559	−	3.88879i	−0.0204729	−	0.0118200i
$330$	−54.7104	−	31.5871i	−0.165789	−	0.0957184i
$331$	172.239	+	99.4425i	0.520361	+	0.300430i	0.737082	−	0.675803i	$-0.236203\pi$
$331$	172.239	+	99.4425i	0.520361	+	0.300430i	−0.216722	+	0.976233i	$0.569536\pi$
$332$	82.5015	+	142.897i	0.248499	+	0.430412i
$333$			268.627i			0.806687i
$334$	1.33488	−	0.770695i	0.00399666	−	0.00230747i
$335$	−315.014	−	181.874i	−0.940342	−	0.542907i
$336$	4.05948			0.0120818
$337$	−145.866	+	252.647i	−0.432836	+	0.749694i	−0.997116	−	0.0758894i	$-0.975820\pi$
$337$	−145.866	+	252.647i	−0.432836	+	0.749694i	0.564280	+	0.825583i	$0.309154\pi$
$338$	65.1711	−	37.6265i	0.192814	−	0.111321i
$339$	−101.776	−	176.280i	−0.300223	−	0.520001i
$340$		−	170.809i		−	0.502378i
$341$	−217.713	−	377.090i	−0.638455	−	1.10584i
$342$	−93.2591			−0.272687
$343$			21.6323i			0.0630678i
$344$	183.215	+	76.0101i	0.532603	+	0.220960i
$345$	241.719			0.700635
$346$			79.1072i			0.228633i
$347$	145.932	−	84.2539i	0.420553	−	0.242807i	−0.274761	−	0.961513i	$-0.588599\pi$
$347$	145.932	−	84.2539i	0.420553	−	0.242807i	0.695314	+	0.718706i	$0.255265\pi$
$348$	−176.587			−0.507435
$349$	546.683	−	315.628i	1.56643	−	0.904377i	0.569847	−	0.821751i	$-0.307003\pi$
$349$	546.683	−	315.628i	1.56643	−	0.904377i	0.996581	−	0.0826262i	$-0.0263308\pi$
$350$	0.217566	+	0.376835i	0.000621616	+	0.00107667i
$351$	140.454	+	81.0909i	0.400152	+	0.231028i
$352$			321.344i			0.912909i
$353$	126.748	−	219.535i	0.359061	−	0.621912i	−0.628743	−	0.777613i	$-0.716430\pi$
$353$	126.748	−	219.535i	0.359061	−	0.621912i	0.987804	+	0.155701i	$0.0497637\pi$
$354$	10.5180	+	18.2178i	0.0297120	+	0.0514627i
$355$	79.3149			0.223422
$356$	339.724	−	196.140i	0.954281	−	0.550954i
$357$	1.52657	−	2.64410i	0.00427612	−	0.00740645i
$358$	−36.0539	+	62.4472i	−0.100709	+	0.174434i
$359$	−108.184	+	187.379i	−0.301347	+	0.521948i	−0.976441	−	0.215783i	$-0.930770\pi$
$359$	−108.184	+	187.379i	−0.301347	+	0.521948i	0.675094	+	0.737731i	$0.264103\pi$
$360$	160.720			0.446446
$361$	96.8392	−	167.730i	0.268253	−	0.464627i
$362$	171.411	+	98.9642i	0.473511	+	0.273382i
$363$	−50.3181	+	29.0512i	−0.138617	+	0.0800308i
$364$	4.63496	−	2.67600i	0.0127334	−	0.00735164i
$365$	247.047			0.676840
$366$			71.8058i			0.196191i
$367$	−69.7081	−	120.738i	−0.189940	−	0.328986i	0.755290	−	0.655391i	$-0.227496\pi$
$367$	−69.7081	−	120.738i	−0.189940	−	0.328986i	−0.945230	+	0.326405i	$0.894163\pi$
$368$	−170.839	−	295.902i	−0.464236	−	0.804081i
$369$	59.1252	−	102.408i	0.160231	−	0.277528i
$370$	−114.011	−	65.8245i	−0.308139	−	0.177904i
$371$			15.8621i			0.0427550i
$372$	−170.471	−	98.4213i	−0.458254	−	0.264573i
$373$	108.896	+	62.8712i	0.291947	+	0.168556i	0.638819	−	0.769357i	$-0.279423\pi$
$373$	108.896	+	62.8712i	0.291947	+	0.168556i	−0.346873	+	0.937912i	$0.612756\pi$
$374$	58.1639	+	33.5809i	0.155518	+	0.0897886i
$375$	−90.3737	−	156.532i	−0.240996	−	0.417418i
$376$		−	162.454i		−	0.432060i
$377$	−179.339	+	103.542i	−0.475702	+	0.274646i
$378$	2.81108	+	1.62298i	0.00743671	+	0.00429359i
$379$	89.6485			0.236540			0.118270	−	0.992981i	$-0.462265\pi$
$379$	89.6485			0.236540			0.118270	+	0.992981i	$0.462265\pi$
$380$	−227.554	+	394.135i	−0.598826	+	1.03720i
$381$	−234.528	+	135.405i	−0.615560	+	0.355394i
$382$	−47.0706	−	81.5286i	−0.123221	−	0.213426i
$383$			340.606i			0.889310i	0.895702	+	0.444655i	$0.146674\pi$
$383$			340.606i			0.889310i	−0.895702	+	0.444655i	$0.853326\pi$
$384$	94.8464	+	164.279i	0.246996	+	0.427809i
$385$	14.7646			0.0383495
$386$			100.714i			0.260918i
$387$	−171.434	−	223.676i	−0.442983	−	0.577974i
$388$	361.097			0.930662
$389$			172.745i			0.444076i	0.975038	+	0.222038i	$0.0712709\pi$
$389$			172.745i			0.444076i	−0.975038	+	0.222038i	$0.928729\pi$
$390$	−29.0042	+	16.7456i	−0.0743696	+	0.0429373i
$391$	−256.977			−0.657230
$392$	−195.557	+	112.905i	−0.498869	+	0.288022i
$393$	−133.095	−	230.528i	−0.338665	−	0.586585i
$394$	−16.6593	−	9.61827i	−0.0422826	−	0.0244119i
$395$		−	427.170i		−	1.08144i
$396$	149.796	−	259.455i	0.378274	−	0.655190i
$397$	102.480	+	177.501i	0.258137	+	0.447106i	0.965743	−	0.259501i	$-0.0835582\pi$
$397$	102.480	+	177.501i	0.258137	+	0.447106i	−0.707606	+	0.706607i	$0.750225\pi$
$398$	40.3666			0.101424
$399$	−7.04503	+	4.06745i	−0.0176567	+	0.0101941i
$400$	19.1631	−	33.1914i	0.0479077	−	0.0829785i
$401$	−123.010	+	213.059i	−0.306758	+	0.531320i	−0.977651	−	0.210234i	$-0.932578\pi$
$401$	−123.010	+	213.059i	−0.306758	+	0.531320i	0.670893	+	0.741554i	$0.265911\pi$
$402$	32.3286	−	55.9948i	0.0804195	−	0.139291i
$403$	−230.837			−0.572796
$404$	−327.619	+	567.453i	−0.810938	+	1.40459i
$405$	−96.3971	−	55.6549i	−0.238018	−	0.137419i
$406$	−3.58935	+	2.07231i	−0.00884077	+	0.00510422i
$407$	−446.391	+	257.724i	−1.09678	+	0.633229i
$408$	63.7726			0.156305
$409$		−	85.8861i		−	0.209990i	−0.994473	−	0.104995i	$-0.966517\pi$
$409$		−	85.8861i		−	0.209990i	0.994473	−	0.104995i	$-0.0334827\pi$
$410$	28.9761	+	50.1881i	0.0706735	+	0.122410i
$411$	57.9767	+	100.419i	0.141063	+	0.244328i
$412$	−100.965	+	174.877i	−0.245062	+	0.424459i
$413$	−4.25771	−	2.45819i	−0.0103092	−	0.00595204i
$414$		−	115.119i		−	0.278066i
$415$	208.986	+	120.658i	0.503581	+	0.290743i
$416$	147.534	+	85.1786i	0.354648	+	0.204756i
$417$	38.4485	+	22.1983i	0.0922027	+	0.0532333i
$418$	−89.4740	−	154.974i	−0.214053	−	0.370750i
$419$		−	36.2090i		−	0.0864177i	−0.999066	−	0.0432088i	$-0.986242\pi$
$419$		−	36.2090i		−	0.0864177i	0.999066	−	0.0432088i	$-0.0137581\pi$
$420$	5.78036	−	3.33729i	0.0137628	−	0.00794594i
$421$	−355.920	−	205.491i	−0.845416	−	0.488101i	0.0136856	−	0.999906i	$-0.495644\pi$
$421$	−355.920	−	205.491i	−0.845416	−	0.488101i	−0.859102	+	0.511805i	$0.828977\pi$
$422$	−151.216			−0.358332
$423$	−115.404	+	199.886i	−0.272823	+	0.472543i
$424$	−286.931	+	165.660i	−0.676725	+	0.390707i
$425$	−14.4126	−	24.9634i	−0.0339120	−	0.0587373i
$426$			14.0985i			0.0330950i
$427$	−8.39094	−	14.5335i	−0.0196509	−	0.0340364i
$428$	−761.476			−1.77915
$429$			131.129i			0.305661i
$430$	136.942	−	17.9510i	0.318469	−	0.0417465i
$431$	134.704			0.312537			0.156269	−	0.987715i	$-0.450053\pi$
$431$	134.704			0.312537			0.156269	+	0.987715i	$0.450053\pi$
$432$		−	285.902i		−	0.661810i
$433$	539.347	−	311.392i	1.24561	−	0.719151i	0.275376	−	0.961337i	$-0.411198\pi$
$433$	539.347	−	311.392i	1.24561	−	0.719151i	0.970230	+	0.242186i	$0.0778643\pi$
$434$	−4.62003			−0.0106452
$435$	−223.658	+	129.129i	−0.514157	+	0.296849i
$436$	−336.291	−	582.473i	−0.771309	−	1.33595i
$437$	592.965	+	342.349i	1.35690	+	0.783406i
$438$			43.9133i			0.100259i
$439$	216.760	−	375.440i	0.493759	−	0.855215i	−0.506215	−	0.862407i	$-0.668956\pi$
$439$	216.760	−	375.440i	0.493759	−	0.855215i	0.999974	+	0.00719174i	$0.00228922\pi$
$440$	154.197	+	267.078i	0.350449	+	0.606995i
$441$	320.820			0.727484
$442$	30.8350	−	17.8026i	0.0697624	−	0.0402773i
$443$	−230.405	+	399.073i	−0.520101	+	0.900842i	0.479626	+	0.877473i	$0.340772\pi$
$443$	−230.405	+	399.073i	−0.520101	+	0.900842i	−0.999727	+	0.0233686i	$0.992561\pi$
$444$	−116.509	+	201.799i	−0.262408	+	0.454503i
$445$	286.854	−	496.845i	0.644615	−	1.11651i
$446$	−144.570			−0.324149
$447$	112.421	−	194.719i	0.251502	−	0.435614i
$448$	−6.03850	−	3.48633i	−0.0134788	−	0.00778199i
$449$	612.829	−	353.817i	1.36487	−	0.788011i	0.374606	−	0.927184i	$-0.377778\pi$
$449$	612.829	−	353.817i	1.36487	−	0.788011i	0.990268	+	0.139173i	$0.0444445\pi$
$450$	11.1830	−	6.45649i	0.0248510	−	0.0143478i
$451$	226.902			0.503109
$452$			473.079i			1.04663i
$453$	120.182	+	208.162i	0.265303	+	0.459518i
$454$	−23.7492	−	41.1349i	−0.0523111	−	0.0906055i
$455$	3.91364	−	6.77862i	0.00860140	−	0.0148981i
$456$	−147.153	−	84.9588i	−0.322704	−	0.186313i
$457$			124.213i			0.271801i	0.990723	+	0.135900i	$0.0433927\pi$
$457$			124.213i			0.271801i	−0.990723	+	0.135900i	$0.956607\pi$
$458$	−80.9237	−	46.7213i	−0.176689	−	0.102012i
$459$	−186.219	−	107.514i	−0.405707	−	0.234235i
$460$	−486.521	−	280.893i	−1.05766	−	0.610637i
$461$	98.9152	+	171.326i	0.214566	+	0.371640i	0.953138	−	0.302535i	$-0.0978328\pi$
$461$	98.9152	+	171.326i	0.214566	+	0.371640i	−0.738572	+	0.674175i	$0.764499\pi$
$462$			2.62445i			0.00568062i
$463$	213.347	−	123.176i	0.460792	−	0.266038i	−0.251585	−	0.967835i	$-0.580952\pi$
$463$	213.347	−	123.176i	0.460792	−	0.266038i	0.712377	+	0.701797i	$0.247619\pi$
$464$	316.148	+	182.528i	0.681354	+	0.393380i
$465$	−287.882			−0.619100
$466$	33.4573	−	57.9498i	0.0717968	−	0.124356i
$467$	−489.217	+	282.450i	−1.04757	+	0.604817i	−0.921969	−	0.387263i	$-0.873421\pi$
$467$	−489.217	+	282.450i	−1.04757	+	0.604817i	−0.125605	+	0.992080i	$0.540087\pi$
$468$	−79.4130	−	137.547i	−0.169686	−	0.293905i
$469$			15.1112i			0.0322200i
$470$	−56.5573	−	97.9602i	−0.120335	−	0.208426i
$471$	403.946			0.857634
$472$		−	102.691i		−	0.217566i
$473$	207.218	−	499.479i	0.438092	−	1.05598i
$474$	75.9308			0.160191
$475$			76.8027i			0.161690i
$476$	−6.14523	+	3.54795i	−0.0129102	+	0.00745368i
$477$	470.725			0.986844
$478$	122.726	−	70.8560i	0.256749	−	0.148234i
$479$	384.645	+	666.225i	0.803018	+	1.39087i	0.917621	+	0.397456i	$0.130107\pi$
$479$	384.645	+	666.225i	0.803018	+	1.39087i	−0.114604	+	0.993411i	$0.536560\pi$
$480$	183.992	+	106.228i	0.383318	+	0.221309i
$481$			273.259i			0.568107i
$482$	36.6576	−	63.4927i	0.0760530	−	0.131728i
$483$	−5.02087	−	8.69641i	−0.0103952	−	0.0180050i
$484$	135.037			0.279003
$485$	457.351	−	264.051i	0.942991	−	0.544436i
$486$	76.0326	−	131.692i	0.156446	−	0.270972i
$487$	−29.3289	+	50.7991i	−0.0602236	+	0.104310i	−0.894565	−	0.446937i	$-0.852515\pi$
$487$	−29.3289	+	50.7991i	−0.0602236	+	0.104310i	0.834342	+	0.551248i	$0.185848\pi$
$488$	175.266	−	303.569i	0.359151	−	0.622068i
$489$	−417.751			−0.854297
$490$	−78.6140	+	136.163i	−0.160437	+	0.277885i
$491$	−616.298	−	355.820i	−1.25519	−	0.724684i	−0.283055	−	0.959104i	$-0.591348\pi$
$491$	−616.298	−	355.820i	−1.25519	−	0.724684i	−0.972136	+	0.234419i	$0.924681\pi$
$492$	88.8328	−	51.2876i	0.180554	−	0.104243i
$493$	237.776	−	137.280i	0.482304	−	0.278459i
$494$	−94.8674			−0.192039
$495$		−	438.154i		−	0.885159i
$496$	203.465	+	352.412i	0.410212	+	0.710507i
$497$	−1.64749	−	2.85354i	−0.00331487	−	0.00574152i
$498$	−21.4474	+	37.1479i	−0.0430670	+	0.0745943i
$499$	−604.469	−	348.990i	−1.21136	−	0.699379i	−0.248305	−	0.968682i	$-0.579873\pi$
$499$	−604.469	−	348.990i	−1.21136	−	0.699379i	−0.963056	+	0.269303i	$0.913207\pi$
$500$			420.080i			0.840160i
$501$	−3.45549	−	1.99503i	−0.00689719	−	0.00398210i
$502$	−189.873	−	109.623i	−0.378234	−	0.218373i
$503$	−343.462	−	198.298i	−0.682827	−	0.394231i	0.118092	−	0.993003i	$-0.462322\pi$
$503$	−343.462	−	198.298i	−0.682827	−	0.394231i	−0.800919	+	0.598772i	$0.795656\pi$
$504$	−3.33841	−	5.78229i	−0.00662382	−	0.0114728i
$505$			958.283i			1.89759i
$506$	191.300	−	110.447i	0.378063	−	0.218275i
$507$	−168.703	−	97.4005i	−0.332747	−	0.192111i
$508$	629.397			1.23897
$509$	153.474	−	265.824i	0.301520	−	0.522248i	−0.674960	−	0.737854i	$-0.735839\pi$
$509$	153.474	−	265.824i	0.301520	−	0.522248i	0.976480	+	0.215606i	$0.0691727\pi$
$510$	38.4550	−	22.2020i	0.0754019	−	0.0435333i
$511$	−5.13153	−	8.88807i	−0.0100421	−	0.0173935i
$512$		−	517.173i		−	1.01010i
$513$	286.463	+	496.168i	0.558407	+	0.967190i
$514$	−105.289			−0.204842
$515$			295.323i			0.573443i
$516$	−31.7732	−	242.386i	−0.0615759	−	0.469740i
$517$	−442.881			−0.856636
$518$			5.46909i			0.0105581i
$519$	177.343	−	102.389i	0.341701	−	0.197281i
$520$	163.492			0.314408
$521$	752.575	−	434.499i	1.44448	−	0.833971i	0.446337	−	0.894865i	$-0.352728\pi$
$521$	752.575	−	434.499i	1.44448	−	0.833971i	0.998144	+	0.0608936i	$0.0193950\pi$
$522$	61.4981	+	106.518i	0.117812	+	0.204057i
$523$	−109.513	−	63.2275i	−0.209394	−	0.120894i	0.391635	−	0.920120i	$-0.371909\pi$
$523$	−109.513	−	63.2275i	−0.209394	−	0.120894i	−0.601030	+	0.799227i	$0.705243\pi$
$524$			618.661i			1.18065i
$525$	0.563193	−	0.975479i	0.00107275	−	0.00185806i
$526$	49.4039	+	85.5700i	0.0939237	+	0.162681i
$527$	306.053			0.580746
$528$	200.190	−	115.580i	0.379148	−	0.218901i
$529$	−158.097	+	273.831i	−0.298859	+	0.517639i
$530$	−115.347	+	199.786i	−0.217635	+	0.376955i
$531$	−72.9494	+	126.352i	−0.137381	+	0.237951i
$532$	18.9065			0.0355386
$533$	60.1448	−	104.174i	0.112842	−	0.195448i
$534$	88.3158	+	50.9891i	0.165385	+	0.0954853i
$535$	−964.454	+	556.828i	−1.80272	+	1.04080i
$536$	−273.348	+	157.817i	−0.509977	+	0.294435i
$537$	186.659			0.347596
$538$			165.791i			0.308162i
$539$	307.799	+	533.124i	0.571056	+	0.989098i
$540$	−235.040	−	407.101i	−0.435259	−	0.753890i
$541$	41.5175	−	71.9104i	0.0767421	−	0.132921i	−0.825100	−	0.564986i	$-0.808882\pi$
$541$	41.5175	−	71.9104i	0.0767421	−	0.132921i	0.901843	+	0.432065i	$0.142215\pi$
$542$	49.8743	+	28.7949i	0.0920190	+	0.0531272i
$543$		−	512.360i		−	0.943573i
$544$	−195.606	−	112.933i	−0.359571	−	0.207598i
$545$	−851.865	−	491.824i	−1.56305	−	0.902430i
$546$	1.20492	+	0.695661i	0.00220681	+	0.00127410i
$547$	−64.9429	−	112.484i	−0.118726	−	0.205639i	0.800537	−	0.599283i	$-0.204548\pi$
$547$	−64.9429	−	112.484i	−0.118726	−	0.205639i	−0.919263	+	0.393644i	$0.871214\pi$
$548$		−	269.491i		−	0.491771i
$549$	−431.298	+	249.010i	−0.785606	+	0.453570i
$550$	21.4582	+	12.3889i	0.0390149	+	0.0225253i
$551$	−731.546			−1.32767
$552$	104.874	−	181.646i	0.189988	−	0.329069i
$553$	−15.3684	+	8.87296i	−0.0277910	+	0.0160451i
$554$	135.445	+	234.597i	0.244485	+	0.423461i
$555$			340.788i			0.614032i
$556$	−51.5916	−	89.3593i	−0.0927907	−	0.160718i
$557$	−172.643			−0.309952			−0.154976	−	0.987918i	$-0.549530\pi$
$557$	−172.643			−0.309952			−0.154976	+	0.987918i	$0.549530\pi$
$558$			137.104i			0.245707i
$559$	−174.391	−	227.533i	−0.311969	−	0.407036i
$560$	−13.7983			−0.0246398
$561$		−	173.856i		−	0.309904i
$562$	−131.460	+	75.8985i	−0.233915	+	0.135051i
$563$	−658.660			−1.16991			−0.584956	−	0.811065i	$-0.698888\pi$
$563$	−658.660			−1.16991			−0.584956	+	0.811065i	$0.698888\pi$
$564$	−173.389	+	100.106i	−0.307427	+	0.177493i
$565$	345.938	+	599.182i	0.612280	+	1.06050i
$566$	32.1316	+	18.5512i	0.0567697	+	0.0327760i
$567$			4.62414i			0.00815546i
$568$	34.4120	−	59.6033i	0.0605844	−	0.104935i
$569$	−265.701	−	460.208i	−0.466962	−	0.808802i	0.532326	−	0.846540i	$-0.321318\pi$
$569$	−265.701	−	460.208i	−0.466962	−	0.808802i	−0.999288	+	0.0377376i	$0.987985\pi$
$570$	−118.311			−0.207564
$571$	474.814	−	274.134i	0.831548	−	0.480094i	−0.0228344	−	0.999739i	$-0.507269\pi$
$571$	474.814	−	274.134i	0.831548	−	0.480094i	0.854382	+	0.519645i	$0.173936\pi$
$572$	152.380	−	263.930i	0.266398	−	0.461415i
$573$	−121.847	+	211.046i	−0.212648	+	0.368317i
$574$	1.20376	−	2.08497i	0.00209714	−	0.00363235i
$575$	−94.8056			−0.164879
$576$	−103.461	+	179.199i	−0.179619	+	0.311109i
$577$	−804.072	−	464.231i	−1.39354	−	0.804560i	−0.399834	−	0.916588i	$-0.630932\pi$
$577$	−804.072	−	464.231i	−1.39354	−	0.804560i	−0.993705	+	0.112027i	$0.964266\pi$
$578$	110.335	−	63.7018i	0.190890	−	0.110211i
$579$	225.782	−	130.355i	0.389952	−	0.225139i
$580$	600.226			1.03487
$581$		−	10.0250i		−	0.0172548i
$582$	46.9360	+	81.2955i	0.0806460	+	0.139683i
$583$	451.620	+	782.228i	0.774648	+	1.34173i
$584$	107.185	−	185.650i	0.183536	−	0.317893i
$585$	−201.163	−	116.141i	−0.343868	−	0.198532i
$586$			122.032i			0.208246i
$587$	846.271	+	488.595i	1.44169	+	0.832359i	0.997962	−	0.0638034i	$-0.0203231\pi$
$587$	846.271	+	488.595i	1.44169	+	0.832359i	0.443726	+	0.896163i	$0.353656\pi$
$588$	241.009	+	139.146i	0.409879	+	0.236644i
$589$	−706.207	−	407.729i	−1.19899	−	0.692239i
$590$	−35.7511	−	61.9228i	−0.0605952	−	0.104954i
$591$			49.7959i			0.0842571i
$592$	417.177	−	240.857i	0.704691	−	0.406854i
$593$	−688.730	−	397.638i	−1.16143	−	0.670554i	−0.209786	−	0.977747i	$-0.567277\pi$
$593$	−688.730	−	397.638i	−1.16143	−	0.670554i	−0.951647	+	0.307194i	$0.900610\pi$
$594$	184.835			0.311170
$595$	−5.18887	+	8.98738i	−0.00872079	+	0.0151048i
$596$	−452.553	+	261.282i	−0.759317	+	0.438392i
$597$	−52.2467	−	90.4939i	−0.0875154	−	0.151581i
$598$		−	117.105i		−	0.195827i
$599$	227.549	+	394.126i	0.379881	+	0.657973i	0.991045	−	0.133531i	$-0.0426316\pi$
$599$	227.549	+	394.126i	0.379881	+	0.657973i	−0.611164	+	0.791504i	$0.709298\pi$
$600$	23.5274			0.0392123
$601$			878.971i			1.46251i	0.682102	+	0.731257i	$0.261066\pi$
$601$			878.971i			1.46251i	−0.682102	+	0.731257i	$0.738934\pi$
$602$	−3.49031	−	4.55392i	−0.00579786	−	0.00756465i
$603$	448.440			0.743681
$604$		−	558.637i		−	0.924896i
$605$	171.033	−	98.7458i	0.282699	−	0.163216i
$606$	−170.338			−0.281086
$607$	353.277	−	203.964i	0.582004	−	0.336020i	−0.179925	−	0.983680i	$-0.557586\pi$
$607$	353.277	−	203.964i	0.582004	−	0.336020i	0.761930	+	0.647660i	$0.224252\pi$
$608$	300.903	+	521.180i	0.494907	+	0.857203i
$609$	9.29144	+	5.36442i	0.0152569	+	0.00880857i
$610$		−	244.070i		−	0.400115i
$611$	−117.394	+	203.333i	−0.192135	+	0.332787i
$612$	105.289	+	182.366i	0.172041	+	0.297984i
$613$	−65.8730			−0.107460			−0.0537300	−	0.998555i	$-0.517111\pi$
$613$	−65.8730			−0.107460			−0.0537300	+	0.998555i	$0.517111\pi$
$614$	200.837	−	115.953i	0.327096	−	0.188849i
$615$	75.0080	−	129.918i	0.121964	−	0.211248i
$616$	6.40582	−	11.0952i	0.0103991	−	0.0180117i
$617$	368.298	−	637.911i	0.596917	−	1.03389i	−0.396356	−	0.918097i	$-0.629725\pi$
$617$	368.298	−	637.911i	0.596917	−	1.03389i	0.993273	−	0.115794i	$-0.0369412\pi$
$618$	−52.4946			−0.0849427
$619$	450.893	−	780.969i	0.728421	−	1.26166i	−0.229129	−	0.973396i	$-0.573588\pi$
$619$	450.893	−	780.969i	0.728421	−	1.26166i	0.957550	−	0.288267i	$-0.0930789\pi$
$620$	579.435	+	334.537i	0.934572	+	0.539576i
$621$	−612.472	+	353.611i	−0.986268	+	0.569422i
$622$	−18.4661	+	10.6614i	−0.0296882	+	0.0171405i
$623$	−23.8335			−0.0382561
$624$		−	122.547i		−	0.196389i
$625$	347.946	+	602.660i	0.556713	+	0.964256i
$626$	141.718	+	245.463i	0.226387	+	0.392114i
$627$	−231.614	+	401.166i	−0.369400	+	0.639819i
$628$	−813.043	−	469.411i	−1.29466	−	0.747469i
$629$		−	362.299i		−	0.575992i
$630$	−4.02613	−	2.32448i	−0.00639068	−	0.00368966i
$631$	223.405	+	128.983i	0.354049	+	0.204410i	0.666467	−	0.745534i	$-0.267806\pi$
$631$	223.405	+	128.983i	0.354049	+	0.204410i	−0.312418	+	0.949945i	$0.601139\pi$
$632$	−321.008	−	185.334i	−0.507924	−	0.293250i
$633$	195.720	+	338.997i	0.309194	+	0.535540i
$634$			60.4877i			0.0954065i
$635$	797.168	−	460.245i	1.25538	−	0.724796i
$636$	353.621	+	204.163i	0.556008	+	0.321011i
$637$	326.353			0.512328
$638$	−118.004	+	204.389i	−0.184960	+	0.320359i
$639$	−84.6817	+	48.8910i	−0.132522	+	0.0765117i
$640$	−322.386	−	558.388i	−0.503728	−	0.872482i
$641$			347.860i			0.542683i	0.962483	+	0.271342i	$0.0874673\pi$
$641$			347.860i			0.542683i	−0.962483	+	0.271342i	$0.912533\pi$
$642$	−98.9779	−	171.435i	−0.154171	−	0.267032i
$643$	−116.326			−0.180911			−0.0904556	−	0.995900i	$-0.528832\pi$
$643$	−116.326			−0.180911			−0.0904556	+	0.995900i	$0.528832\pi$
$644$			23.3383i			0.0362396i
$645$	−217.487	−	283.762i	−0.337189	−	0.439941i
$646$	125.779			0.194705
$647$		−	737.443i		−	1.13979i	−0.821718	−	0.569894i	$-0.806984\pi$
$647$		−	737.443i		−	1.13979i	0.821718	−	0.569894i	$-0.193016\pi$
$648$	−83.6467	+	48.2934i	−0.129084	+	0.0745269i
$649$	−279.955			−0.431363
$650$	11.3758	−	6.56784i	0.0175013	−	0.0101044i
$651$	5.97973	+	10.3572i	0.00918546	+	0.0159097i
$652$	840.830	+	485.453i	1.28962	+	0.744561i
$653$			104.276i			0.159688i	0.996807	+	0.0798440i	$0.0254422\pi$
$653$			104.276i			0.159688i	−0.996807	+	0.0798440i	$0.974558\pi$
$654$	87.4233	−	151.422i	0.133675	−	0.231532i
$655$	452.395	+	783.571i	0.690679	+	1.19629i
$656$	−212.052			−0.323251
$657$	−263.763	+	152.284i	−0.401466	+	0.231786i
$658$	−2.34956	+	4.06956i	−0.00357076	+	0.00618475i
$659$	133.718	−	231.606i	0.202910	−	0.351450i	−0.746555	−	0.665324i	$-0.768293\pi$
$659$	133.718	−	231.606i	0.202910	−	0.351450i	0.949465	+	0.313874i	$0.101627\pi$
$660$	190.036	−	329.153i	0.287934	−	0.498716i
$661$	594.889			0.899983			0.449991	−	0.893033i	$-0.351427\pi$
$661$	594.889			0.899983			0.449991	+	0.893033i	$0.351427\pi$
$662$	60.0820	−	104.065i	0.0907582	−	0.157198i
$663$	−79.8197	−	46.0839i	−0.120392	−	0.0695082i
$664$	181.344	−	104.699i	0.273108	−	0.157679i
$665$	23.9462	−	13.8254i	0.0360094	−	0.0207900i
$666$	162.301			0.243695
$667$		−	903.024i		−	1.35386i
$668$	4.63671	+	8.03101i	0.00694118	+	0.0120225i
$669$	187.118	+	324.098i	0.279698	+	0.484452i
$670$	−109.886	+	190.328i	−0.164009	+	0.284072i
$671$	−827.586	−	477.807i	−1.23336	−	0.712082i
$672$		−	8.82607i		−	0.0131340i
$673$	437.353	+	252.506i	0.649856	+	0.375194i	0.788401	−	0.615162i	$-0.210909\pi$
$673$	437.353	+	252.506i	0.649856	+	0.375194i	−0.138545	+	0.990356i	$0.544243\pi$
$674$	152.646	+	88.1303i	0.226478	+	0.130757i
$675$	−68.7012	−	39.6647i	−0.101780	−	0.0587625i
$676$	226.371	+	392.087i	0.334869	+	0.580010i
$677$		−	1280.47i		−	1.89139i	−0.325055	−	0.945695i	$-0.605383\pi$
$677$		−	1280.47i		−	1.89139i	0.325055	−	0.945695i	$-0.394617\pi$
$678$	−106.507	+	61.4916i	−0.157089	+	0.0906955i
$679$	−18.9997	−	10.9695i	−0.0279819	−	0.0161554i
$680$	−216.765			−0.318772
$681$	−61.4776	+	106.482i	−0.0902754	+	0.156362i
$682$	−227.833	+	131.540i	−0.334067	+	0.192874i
$683$	250.489	+	433.859i	0.366748	+	0.635226i	0.989055	−	0.147547i	$-0.0471379\pi$
$683$	250.489	+	433.859i	0.366748	+	0.635226i	−0.622307	+	0.782773i	$0.713805\pi$
$684$		−	561.071i		−	0.820280i
$685$	−197.065	−	341.326i	−0.287686	−	0.498286i
$686$	13.0700			0.0190524
$687$			241.887i			0.352091i
$688$	−193.656	+	466.791i	−0.281477	+	0.678475i
$689$	478.843			0.694982
$690$		−	146.044i		−	0.211658i
$691$	−954.473	+	551.065i	−1.38129	+	0.797490i	−0.992313	−	0.123756i	$-0.960506\pi$
$691$	−954.473	+	551.065i	−1.38129	+	0.797490i	−0.388980	+	0.921246i	$0.627173\pi$
$692$	−475.930			−0.687760
$693$	−15.7636	+	9.10111i	−0.0227469	+	0.0131329i
$694$	−50.9052	−	88.1704i	−0.0733504	−	0.127047i
$695$	−130.688	−	75.4526i	−0.188040	−	0.108565i
$696$			224.099i			0.321981i
$697$	−79.7426	+	138.118i	−0.114408	+	0.198161i
$698$	−190.699	−	330.299i	−0.273207	−	0.473208i
$699$	−173.216			−0.247805
$700$	−2.26714	+	1.30893i	−0.00323877	+	0.00186990i
$701$	−655.951	+	1136.14i	−0.935737	+	1.62074i	−0.162421	+	0.986721i	$0.551930\pi$
$701$	−655.951	+	1136.14i	−0.935737	+	1.62074i	−0.773315	+	0.634022i	$0.781403\pi$
$702$	48.9941	−	84.8603i	0.0697922	−	0.120884i
$703$	−482.660	+	835.992i	−0.686572	+	1.18918i
$704$	−397.046			−0.563986
$705$	−146.405	+	253.581i	−0.207667	+	0.359689i
$706$	−132.640	−	76.5799i	−0.187876	−	0.108470i
$707$	34.4764	−	19.9050i	0.0487644	−	0.0281542i
$708$	−109.603	+	63.2793i	−0.154807	+	0.0893776i
$709$	446.548			0.629828			0.314914	−	0.949120i	$-0.398024\pi$
$709$	446.548			0.629828			0.314914	+	0.949120i	$0.398024\pi$
$710$		−	47.9211i		−	0.0674945i
$711$	263.314	+	456.074i	0.370344	+	0.641454i
$712$	−248.912	−	431.127i	−0.349595	−	0.605516i
$713$	503.302	−	871.744i	0.705893	−	1.22264i
$714$	−1.59754	−	0.922338i	−0.00223744	−	0.00129179i
$715$		−	445.710i		−	0.623371i
$716$	−375.699	−	216.910i	−0.524720	−	0.302947i
$717$	−317.690	−	183.419i	−0.443083	−	0.255814i
$718$	113.212	+	65.3632i	0.157677	+	0.0910351i
$719$	−4.76359	−	8.25079i	−0.00662530	−	0.0114754i	0.862694	−	0.505727i	$-0.168776\pi$
$719$	−4.76359	−	8.25079i	−0.00662530	−	0.0114754i	−0.869319	+	0.494251i	$0.835442\pi$
$720$			409.479i			0.568720i
$721$	10.6249	−	6.13431i	0.0147364	−	0.00850805i
$722$	−101.341	−	58.5091i	−0.140361	−	0.0810376i
$723$	−189.784			−0.262496
$724$	−595.395	+	1031.25i	−0.822369	+	1.42438i
$725$	87.7219	−	50.6462i	0.120996	−	0.0698569i
$726$	17.5524	+	30.4016i	0.0241768	+	0.0418755i
$727$		−	592.651i		−	0.815201i	−0.913160	−	0.407600i	$-0.866366\pi$
$727$		−	592.651i		−	0.815201i	0.913160	−	0.407600i	$-0.133634\pi$
$728$	−3.39598	−	5.88201i	−0.00466481	−	0.00807968i
$729$	−205.194			−0.281473
$730$		−	149.263i		−	0.204469i
$731$	231.215	+	301.674i	0.316300	+	0.412686i
$732$	−432.003			−0.590168
$733$		−	533.855i		−	0.728315i	−0.931337	−	0.364158i	$-0.881357\pi$
$733$		−	533.855i		−	0.728315i	0.931337	−	0.364158i	$-0.118643\pi$
$734$	−72.9484	+	42.1168i	−0.0993848	+	0.0573798i
$735$	407.002			0.553745
$736$	−643.346	+	371.436i	−0.874112	+	0.504669i
$737$	430.239	+	745.196i	0.583771	+	1.01112i
$738$	−61.8736	−	35.7227i	−0.0838395	−	0.0484048i
$739$			46.7872i			0.0633115i	0.999499	+	0.0316558i	$0.0100780\pi$
$739$			46.7872i			0.0633115i	−0.999499	+	0.0316558i	$0.989922\pi$
$740$	396.017	−	685.922i	0.535159	−	0.926922i
$741$	122.787	+	212.674i	0.165705	+	0.287010i
$742$	9.58370			0.0129160
$743$	899.231	−	519.171i	1.21027	−	0.698750i	0.247452	−	0.968900i	$-0.420407\pi$
$743$	899.231	−	519.171i	1.21027	−	0.698750i	0.962818	+	0.270150i	$0.0870734\pi$
$744$	−124.902	+	216.336i	−0.167879	+	0.290774i
$745$	−382.123	+	661.857i	−0.512917	+	0.888399i
$746$	37.9860	−	65.7938i	0.0509196	−	0.0881954i
$747$	−297.503			−0.398263
$748$	−202.032	+	349.929i	−0.270096	+	0.467820i
$749$	40.0663	+	23.1323i	0.0534931	+	0.0308843i
$750$	−94.5747	+	54.6027i	−0.126100	+	0.0728036i
$751$	470.731	−	271.777i	0.626806	−	0.361887i	−0.152708	−	0.988271i	$-0.548799\pi$
$751$	470.731	−	271.777i	0.626806	−	0.361887i	0.779514	+	0.626385i	$0.215466\pi$
$752$	413.896			0.550394
$753$			567.545i			0.753712i
$754$	62.5587	+	108.355i	0.0829691	+	0.143707i
$755$	−408.503	−	707.547i	−0.541063	−	0.937149i
$756$	−9.76426	+	16.9122i	−0.0129157	+	0.0223706i
$757$	954.009	+	550.797i	1.26025	+	0.727605i	0.973123	−	0.230287i	$-0.0739666\pi$
$757$	954.009	+	550.797i	1.26025	+	0.727605i	0.287127	+	0.957893i	$0.407300\pi$
$758$		−	54.1646i		−	0.0714572i
$759$	−495.201	−	285.905i	−0.652439	−	0.376686i
$760$	500.177	+	288.778i	0.658128	+	0.379971i
$761$	1.19512	+	0.690001i	0.00157046	+	0.000906703i	0.500785	−	0.865572i	$-0.333045\pi$
$761$	1.19512	+	0.690001i	0.00157046	+	0.000906703i	−0.499215	+	0.866478i	$0.666378\pi$
$762$	81.8101	+	141.699i	0.107362	+	0.185957i
$763$			40.8637i			0.0535567i
$764$	490.498	−	283.189i	0.642013	−	0.370666i
$765$	266.710	+	153.985i	0.348641	+	0.201288i
$766$	205.790			0.268655
$767$	−74.2075	+	128.531i	−0.0967503	+	0.167576i
$768$	−71.7999	+	41.4537i	−0.0934895	+	0.0539762i
$769$	−379.114	−	656.644i	−0.492996	−	0.853894i	0.506972	−	0.861963i	$-0.330765\pi$
$769$	−379.114	−	656.644i	−0.492996	−	0.853894i	−0.999967	+	0.00806904i	$0.997432\pi$
$770$		−	8.92057i		−	0.0115852i
$771$	136.276	+	236.037i	0.176752	+	0.306144i
$772$	−605.925			−0.784877
$773$		−	70.0326i		−	0.0905984i	−0.998973	−	0.0452992i	$-0.985576\pi$
$773$		−	70.0326i		−	0.0905984i	0.998973	−	0.0452992i	$-0.0144241\pi$
$774$	−135.142	+	103.579i	−0.174603	+	0.133823i
$775$	112.911			0.145692
$776$		−	458.251i		−	0.590529i
$777$	12.2606	−	7.07868i	0.0157795	−	0.00911027i
$778$	104.371			0.134153
$779$	368.006	−	212.469i	0.472409	−	0.272745i
$780$	−100.746	−	174.497i	−0.129161	−	0.223714i
$781$	−162.490	−	93.8134i	−0.208053	−	0.120120i
$782$			155.262i			0.198545i
$783$	377.806	−	654.379i	0.482511	−	0.835734i
$784$	−287.655	−	498.234i	−0.366907	−	0.635502i
$785$	−1373.02			−1.74907
$786$	−139.282	+	80.4146i	−0.177204	+	0.102309i
$787$	−47.3875	+	82.0775i	−0.0602128	+	0.104292i	−0.894560	−	0.446947i	$-0.852511\pi$
$787$	−47.3875	+	82.0775i	−0.0602128	+	0.104292i	0.834348	+	0.551239i	$0.185845\pi$
$788$	57.8661	−	100.227i	0.0734341	−	0.127192i
$789$	127.887	−	221.508i	0.162088	−	0.280745i
$790$	−258.091			−0.326697
$791$	14.3713	−	24.8918i	0.0181685	−	0.0314688i
$792$	−329.262	−	190.100i	−0.415735	−	0.240025i
$793$	−438.736	+	253.304i	−0.553261	+	0.319425i
$794$	107.244	−	61.9174i	0.135068	−	0.0779816i
$795$	597.175			0.751164
$796$			242.856i			0.305096i
$797$	−301.208	−	521.708i	−0.377928	−	0.654590i	0.612833	−	0.790213i	$-0.290030\pi$
$797$	−301.208	−	521.708i	−0.377928	−	0.654590i	−0.990761	+	0.135623i	$0.956697\pi$
$798$	2.45750	+	4.25652i	0.00307958	+	0.00533399i
$799$	155.646	−	269.588i	0.194802	−	0.337406i
$800$	−72.1644	−	41.6641i	−0.0902055	−	0.0520802i
$801$			707.285i			0.883003i
$802$	128.728	+	74.3211i	0.160509	+	0.0926697i
$803$	−506.116	−	292.206i	−0.630281	−	0.363893i
$804$	336.880	+	194.498i	0.419005	+	0.241912i
$805$	17.0661	+	29.5593i	0.0212001	+	0.0367197i
$806$			139.469i			0.173038i
$807$	371.671	−	214.584i	0.460559	−	0.265904i
$808$	720.127	+	415.766i	0.891246	+	0.514561i
$809$	137.445			0.169895			0.0849475	−	0.996385i	$-0.472928\pi$
$809$	137.445			0.169895			0.0849475	+	0.996385i	$0.472928\pi$
$810$	−33.6260	+	58.2420i	−0.0415136	+	0.0719037i
$811$	48.0563	−	27.7453i	0.0592556	−	0.0342112i	−0.470080	−	0.882624i	$-0.655775\pi$
$811$	48.0563	−	27.7453i	0.0592556	−	0.0342112i	0.529335	+	0.848413i	$0.322441\pi$
$812$	−12.4676	−	21.5945i	−0.0153542	−	0.0265942i
$813$		−	149.078i		−	0.183368i
$814$	155.714	+	269.704i	0.191295	+	0.331332i
$815$	1419.95			1.74227
$816$			162.478i			0.199115i
$817$	−131.626	−	1004.13i	−0.161109	−	1.22904i
$818$	−51.8914			−0.0634369
$819$			9.64972i			0.0117823i
$820$	−301.945	+	174.328i	−0.368226	+	0.212595i
$821$	607.734			0.740236			0.370118	−	0.928985i	$-0.379317\pi$
$821$	607.734			0.740236			0.370118	+	0.928985i	$0.379317\pi$
$822$	60.6718	−	35.0289i	0.0738099	−	0.0426142i
$823$	168.012	+	291.005i	0.204146	+	0.353591i	0.949860	−	0.312675i	$-0.101225\pi$
$823$	168.012	+	291.005i	0.204146	+	0.353591i	−0.745714	+	0.666266i	$0.767892\pi$
$824$	221.928	+	128.130i	0.269331	+	0.155498i
$825$		−	64.1401i		−	0.0777455i
$826$	−1.48521	+	2.57246i	−0.00179808	+	0.00311436i
$827$	503.149	+	871.480i	0.608403	+	1.05379i	0.991504	+	0.130078i	$0.0415229\pi$
$827$	503.149	+	871.480i	0.608403	+	1.05379i	−0.383101	+	0.923707i	$0.625144\pi$
$828$	692.589			0.836460
$829$	377.835	−	218.143i	0.455773	−	0.263140i	−0.254493	−	0.967075i	$-0.581908\pi$
$829$	377.835	−	218.143i	0.455773	−	0.263140i	0.710265	+	0.703934i	$0.248575\pi$
$830$	72.9002	−	126.267i	0.0878316	−	0.152129i
$831$	350.614	−	607.282i	0.421918	−	0.730784i
$832$	−105.245	+	182.289i	−0.126496	+	0.219098i
$833$	−432.693			−0.519439
$834$	13.4119	−	23.2301i	0.0160815	−	0.0278539i
$835$	11.7453	+	6.78117i	0.0140663	+	0.00812116i
$836$	932.362	−	538.299i	1.11527	−	0.643899i
$837$	729.439	−	421.142i	0.871492	−	0.503156i
$838$	−21.8771			−0.0261063
$839$			1182.78i			1.40974i	0.709334	+	0.704872i	$0.248996\pi$
$839$			1182.78i			1.40974i	−0.709334	+	0.704872i	$0.751004\pi$
$840$	−4.23520	−	7.33559i	−0.00504191	−	0.00873284i
$841$	61.9056	+	107.224i	0.0736095	+	0.127495i
$842$	−124.155	+	215.043i	−0.147452	+	0.255395i
$843$	340.299	+	196.472i	0.403676	+	0.233063i
$844$		−	909.756i		−	1.07791i
$845$	573.425	+	331.067i	0.678610	+	0.391796i
$846$	120.769	+	69.7258i	0.142752	+	0.0824182i
$847$	−7.10521	−	4.10220i	−0.00838868	−	0.00484321i
$848$	−422.063	−	731.035i	−0.497716	−	0.862070i
$849$		−	96.0438i		−	0.113126i
$850$	−15.0826	+	8.70793i	−0.0177442	+	0.0102446i
$851$	−1031.95	−	595.798i	−1.21263	−	0.700115i
$852$	−84.8201			−0.0995542
$853$	283.643	−	491.284i	0.332524	−	0.575948i	−0.650482	−	0.759522i	$-0.725433\pi$
$853$	283.643	−	491.284i	0.332524	−	0.575948i	0.983006	+	0.183573i	$0.0587665\pi$
$854$	−8.78099	+	5.06971i	−0.0102822	+	0.00593642i
$855$	−410.283	−	710.630i	−0.479863	−	0.831146i
$856$			966.352i			1.12892i
$857$	−126.426	−	218.976i	−0.147521	−	0.255514i	0.782790	−	0.622287i	$-0.213796\pi$
$857$	−126.426	−	218.976i	−0.147521	−	0.255514i	−0.930311	+	0.366772i	$0.880463\pi$
$858$	79.2263			0.0923384
$859$			270.788i			0.315236i	0.987500	+	0.157618i	$0.0503815\pi$
$859$			270.788i			0.315236i	−0.987500	+	0.157618i	$0.949619\pi$
$860$	107.998	+	823.877i	0.125579	+	0.957996i
$861$	−6.23211			−0.00723823
$862$		−	81.3863i		−	0.0944156i
$863$	171.077	−	98.7715i	0.198236	−	0.114451i	−0.397597	−	0.917560i	$-0.630156\pi$
$863$	171.077	−	98.7715i	0.198236	−	0.114451i	0.595832	+	0.803109i	$0.296822\pi$
$864$	−621.604			−0.719449
$865$	−602.793	+	348.023i	−0.696871	+	0.402338i
$866$	−188.140	−	325.867i	−0.217251	−	0.376290i
$867$	−285.614	−	164.899i	−0.329428	−	0.190195i
$868$		−	27.7953i		−	0.0320223i
$869$	−505.255	+	875.127i	−0.581421	+	1.00705i
$870$	78.0183	+	135.132i	0.0896762	+	0.155324i
$871$	456.173			0.523735
$872$	−739.189	+	426.771i	−0.847693	+	0.489416i
$873$	−325.531	+	563.837i	−0.372888	+	0.645861i
$874$	206.843	−	358.263i	0.236662	−	0.409911i
$875$	12.7613	−	22.1032i	0.0145843	−	0.0252608i
$876$	−264.194			−0.301592
$877$	90.7021	−	157.101i	0.103423	−	0.179134i	−0.809670	−	0.586886i	$-0.800354\pi$
$877$	90.7021	−	157.101i	0.103423	−	0.179134i	0.913093	+	0.407752i	$0.133687\pi$
$878$	−226.836	−	130.964i	−0.258356	−	0.149162i
$879$	273.572	−	157.947i	0.311231	−	0.179689i
$880$	−680.452	+	392.859i	−0.773241	+	0.446431i
$881$	−1021.60			−1.15959			−0.579793	−	0.814763i	$-0.696867\pi$
$881$	−1021.60			−1.15959			−0.579793	+	0.814763i	$0.696867\pi$
$882$		−	193.836i		−	0.219769i
$883$	−572.475	−	991.556i	−0.648329	−	1.12294i	−0.983522	−	0.180790i	$-0.942135\pi$
$883$	−572.475	−	991.556i	−0.648329	−	1.12294i	0.335192	−	0.942150i	$-0.391199\pi$
$884$	107.105	+	185.511i	0.121160	+	0.209854i
$885$	−92.5458	+	160.294i	−0.104572	+	0.181123i
$886$	241.115	+	139.208i	0.272139	+	0.157120i
$887$			1356.57i			1.52940i	0.644388	+	0.764698i	$0.277112\pi$
$887$			1356.57i			1.52940i	−0.644388	+	0.764698i	$0.722888\pi$
$888$	256.094	+	147.856i	0.288394	+	0.166505i
$889$	−33.1168	−	19.1200i	−0.0372517	−	0.0215073i
$890$	−300.188	−	173.314i	−0.337290	−	0.194734i
$891$	131.657	+	228.036i	0.147763	+	0.255933i
$892$		−	869.773i		−	0.975082i
$893$	−718.297	+	414.709i	−0.804364	+	0.464400i
$894$	−117.647	−	67.9236i	−0.131596	−	0.0759772i
$895$	−634.460			−0.708894
$896$	−13.3929	+	23.1971i	−0.0149474	+	0.0258897i
$897$	−262.526	+	151.569i	−0.292671	+	0.168974i
$898$	−213.772	−	370.264i	−0.238053	−	0.412321i
$899$			1075.48i			1.19631i
$900$	38.8440	+	67.2797i	0.0431600	+	0.0747553i
$901$	−634.871			−0.704629
$902$		−	137.091i		−	0.151986i
$903$	−5.69146	+	13.7188i	−0.00630284	+	0.0151924i
$904$	600.362			0.664117
$905$			1741.53i			1.92434i
$906$	125.769	−	72.6126i	0.138818	−	0.0801464i
$907$	1080.78			1.19160			0.595800	−	0.803133i	$-0.296835\pi$
$907$	1080.78			1.19160			0.595800	+	0.803133i	$0.296835\pi$
$908$	247.478	−	142.882i	0.272553	−	0.157359i
$909$	−590.701	−	1023.12i	−0.649837	−	1.12555i
$910$	−4.09556	−	2.36457i	−0.00450061	−	0.00259843i
$911$		−	883.627i		−	0.969952i	−0.874527	−	0.484976i	$-0.838828\pi$
$911$		−	883.627i		−	0.969952i	0.874527	−	0.484976i	$-0.161172\pi$
$912$	216.456	−	374.912i	0.237342	−	0.411088i
$913$	−285.428	−	494.376i	−0.312627	−	0.541485i
$914$	75.0480			0.0821094
$915$	−547.157	+	315.901i	−0.597986	+	0.345248i
$916$	281.088	−	486.859i	0.306865	−	0.531505i
$917$	18.7938	−	32.5519i	0.0204949	−	0.0354982i
$918$	−64.9586	+	112.512i	−0.0707610	+	0.122562i
$919$	−856.536			−0.932030			−0.466015	−	0.884777i	$-0.654311\pi$
$919$	−856.536			−0.932030			−0.466015	+	0.884777i	$0.654311\pi$
$920$	−356.468	+	617.421i	−0.387465	+	0.671110i
$921$	−519.889	−	300.158i	−0.564483	−	0.325905i
$922$	103.513	−	59.7634i	0.112270	−	0.0648193i
$923$	−86.1421	+	49.7342i	−0.0933284	+	0.0538832i
$924$	−15.7894			−0.0170881
$925$		−	133.662i		−	0.144499i
$926$	−74.4213	−	128.902i	−0.0803686	−	0.139203i
$927$	−182.042	−	315.306i	−0.196378	−	0.340136i
$928$	396.851	−	687.366i	0.427641	−	0.740696i
$929$	192.760	+	111.290i	0.207492	+	0.119795i	0.600145	−	0.799891i	$-0.295109\pi$
$929$	192.760	+	111.290i	0.207492	+	0.119795i	−0.392653	+	0.919686i	$0.628443\pi$
$930$			173.935i			0.187026i
$931$	998.424	+	576.440i	1.07242	+	0.619162i
$932$	348.641	+	201.288i	0.374079	+	0.215974i
$933$	47.8015	+	27.5982i	0.0512342	+	0.0295801i
$934$	170.653	+	295.579i	0.182712	+	0.316466i
$935$			590.942i			0.632023i
$936$	−174.555	+	100.779i	−0.186490	+	0.107670i
$937$	−491.839	−	283.963i	−0.524908	−	0.303056i	0.214033	−	0.976827i	$-0.431340\pi$
$937$	−491.839	−	283.963i	−0.524908	−	0.303056i	−0.738940	+	0.673771i	$0.764673\pi$
$938$	9.12999			0.00973346
$939$	366.854	−	635.409i	0.390685	−	0.676687i
$940$	589.355	−	340.264i	0.626973	−	0.361983i
$941$	405.967	+	703.155i	0.431421	+	0.747242i	0.996996	−	0.0774542i	$-0.0246792\pi$
$941$	405.967	+	703.155i	0.431421	+	0.747242i	−0.565575	+	0.824697i	$0.691346\pi$
$942$		−	244.059i		−	0.259086i
$943$	262.272	+	454.269i	0.278125	+	0.481727i
$944$	261.633			0.277154
$945$			28.5604i			0.0302226i
$946$	−301.779	−	125.198i	−0.319006	−	0.132345i
$947$	463.600			0.489545			0.244773	−	0.969580i	$-0.421287\pi$
$947$	463.600			0.489545			0.244773	+	0.969580i	$0.421287\pi$
$948$			456.820i			0.481877i
$949$	−268.312	+	154.910i	−0.282731	+	0.163235i
$950$	46.4033			0.0488456
$951$	135.602	−	78.2896i	0.142588	−	0.0823235i
$952$	4.50254	+	7.79862i	0.00472956	+	0.00819183i
$953$	−990.680	−	571.969i	−1.03954	−	0.600178i	−0.119836	−	0.992794i	$-0.538237\pi$
$953$	−990.680	−	571.969i	−1.03954	−	0.600178i	−0.919702	+	0.392616i	$0.871570\pi$
$954$		−	284.406i		−	0.298120i
$955$	414.163	−	717.351i	0.433678	−	0.751153i
$956$	426.289	+	738.353i	0.445908	+	0.772336i
$957$	610.934			0.638385
$958$	402.525	−	232.398i	0.420173	−	0.242587i
$959$	−8.18666	+	14.1797i	−0.00853666	+	0.0147859i
$960$	−131.253	+	227.337i	−0.136722	+	0.236810i
$961$	−118.920	+	205.976i	−0.123746	+	0.214335i
$962$	165.100			0.171622
$963$	686.475	−	1189.01i	0.712851	−	1.23469i
$964$	381.989	+	220.542i	0.396254	+	0.228778i
$965$	−767.440	+	443.082i	−0.795274	+	0.459152i
$966$	−5.25427	+	3.03355i	−0.00543920	+	0.00314032i
$967$	−1758.30			−1.81831			−0.909153	−	0.416463i	$-0.863270\pi$
$967$	−1758.30			−1.81831			−0.909153	+	0.416463i	$0.863270\pi$
$968$		−	171.369i		−	0.177034i
$969$	−162.797	−	281.973i	−0.168005	−	0.290993i
$970$	−159.537	−	276.326i	−0.164471	−	0.284872i
$971$	−442.048	+	765.650i	−0.455251	+	0.788517i	−0.998703	−	0.0509230i	$-0.983784\pi$
$971$	−442.048	+	765.650i	−0.455251	+	0.788517i	0.543452	+	0.839440i	$0.317117\pi$
$972$	792.296	+	457.432i	0.815119	+	0.470609i
$973$			6.26906i			0.00644302i
$974$	30.6922	+	17.7202i	0.0315115	+	0.0181932i
$975$	−29.4476	−	17.0016i	−0.0302027	−	0.0174375i
$976$	773.425	+	446.537i	0.792443	+	0.457517i
$977$	−729.706	−	1263.89i	−0.746884	−	1.29364i	−0.949309	−	0.314344i	$-0.898216\pi$
$977$	−729.706	−	1263.89i	−0.746884	−	1.29364i	0.202425	−	0.979298i	$-0.435118\pi$
$978$			252.400i			0.258078i
$979$	−1175.33	+	678.579i	−1.20054	+	0.693135i
$980$	−819.195	−	472.963i	−0.835914	−	0.482615i
$981$	1212.67			1.23616
$982$	−214.982	+	372.360i	−0.218923	+	0.379186i
$983$	−866.749	+	500.418i	−0.881739	+	0.509072i	−0.871231	−	0.490873i	$-0.836678\pi$
$983$	−866.749	+	500.418i	−0.881739	+	0.509072i	−0.0105076	+	0.999945i	$0.503345\pi$
$984$	−65.0867	−	112.733i	−0.0661450	−	0.114566i
$985$		−	169.258i		−	0.171835i
$986$	−82.9430	−	143.662i	−0.0841207	−	0.145701i
$987$	12.1642			0.0123244
$988$		−	570.748i		−	0.577680i
$989$	1239.50	−	162.480i	1.25329	−	0.164287i
$990$	−264.727			−0.267401
$991$		−	175.518i		−	0.177112i	−0.996071	−	0.0885558i	$-0.971775\pi$
$991$		−	175.518i		−	0.177112i	0.996071	−	0.0885558i	$-0.0282252\pi$
$992$	766.209	−	442.371i	0.772389	−	0.445939i
$993$	−311.058			−0.313250
$994$	−1.72407	+	0.995394i	−0.00173448	+	0.00100140i
$995$	177.588	+	307.592i	0.178480	+	0.309137i
$996$	−223.492	−	129.033i	−0.224389	−	0.129551i
$997$			212.707i			0.213347i	0.994294	+	0.106673i	$0.0340199\pi$
$997$			212.707i			0.213347i	−0.994294	+	0.106673i	$0.965980\pi$
$998$	−210.856	+	365.213i	−0.211278	+	0.365945i
$999$	−498.539	−	863.494i	−0.499038	−	0.864359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.3.d.a.7.3	✓	12
3.2	odd	2		387.3.j.c.136.4		12
4.3	odd	2		688.3.t.c.609.5		12
43.37	odd	6	inner	43.3.d.a.37.4	yes	12
129.80	even	6		387.3.j.c.37.3		12
172.123	even	6		688.3.t.c.209.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.3.d.a.7.3	✓	12	1.1	even	1	trivial
43.3.d.a.37.4	yes	12	43.37	odd	6	inner
387.3.j.c.37.3		12	129.80	even	6
387.3.j.c.136.4		12	3.2	odd	2
688.3.t.c.209.5		12	172.123	even	6
688.3.t.c.609.5		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.604188i q^{2} +(-1.35447 + 0.782004i) q^{3} +3.63496 q^{4} +(4.60389 - 2.65806i) q^{5} +(0.472478 + 0.818356i) q^{6} +(-0.191259 - 0.110424i) q^{7} -4.61295i q^{8} +(-3.27694 + 5.67582i) q^{9} +O(q^{10})\)	\(q-0.604188i q^{2} +(-1.35447 + 0.782004i) q^{3} +3.63496 q^{4} +(4.60389 - 2.65806i) q^{5} +(0.472478 + 0.818356i) q^{6} +(-0.191259 - 0.110424i) q^{7} -4.61295i q^{8} +(-3.27694 + 5.67582i) q^{9} +(-1.60597 - 2.78161i) q^{10} -12.5758 q^{11} +(-4.92344 + 2.84255i) q^{12} +(-3.33345 + 5.77371i) q^{13} +(-0.0667167 + 0.115557i) q^{14} +(-4.15722 + 7.20052i) q^{15} +11.7527 q^{16} +(4.41963 - 7.65503i) q^{17} +(3.42927 + 1.97989i) q^{18} +(-20.3963 + 11.7758i) q^{19} +(16.7349 - 9.66192i) q^{20} +0.345407 q^{21} +7.59812i q^{22} +(-14.5361 - 25.1773i) q^{23} +(3.60735 + 6.24811i) q^{24} +(1.63052 - 2.82414i) q^{25} +(3.48841 + 2.01403i) q^{26} -24.3264i q^{27} +(-0.695220 - 0.401385i) q^{28} +(26.9000 + 15.5307i) q^{29} +(4.35047 + 2.51174i) q^{30} +(17.3121 + 29.9855i) q^{31} -25.5527i q^{32} +(17.0335 - 9.83430i) q^{33} +(-4.62508 - 2.67029i) q^{34} -1.17405 q^{35} +(-11.9115 + 20.6314i) q^{36} +(35.4962 - 20.4937i) q^{37} +(7.11480 + 12.3232i) q^{38} -10.4271i q^{39} +(-12.2615 - 21.2375i) q^{40} -18.0428 q^{41} -0.208691i q^{42} +(-16.4775 + 39.7176i) q^{43} -45.7123 q^{44} +34.8411i q^{45} +(-15.2118 + 8.78254i) q^{46} +35.2170 q^{47} +(-15.9187 + 9.19069i) q^{48} +(-24.4756 - 42.3930i) q^{49} +(-1.70631 - 0.985141i) q^{50} +13.8247i q^{51} +(-12.1170 + 20.9872i) q^{52} +(-35.9119 - 62.2013i) q^{53} -14.6977 q^{54} +(-57.8974 + 33.4271i) q^{55} +(-0.509379 + 0.882270i) q^{56} +(18.4175 - 31.9000i) q^{57} +(9.38347 - 16.2526i) q^{58} +22.2615 q^{59} +(-15.1113 + 26.1736i) q^{60} +(65.8081 + 37.9943i) q^{61} +(18.1169 - 10.4598i) q^{62} +(1.25349 - 0.723703i) q^{63} +31.5723 q^{64} +35.4420i q^{65} +(-5.94176 - 10.2914i) q^{66} +(-34.2118 - 59.2566i) q^{67} +(16.0652 - 27.8257i) q^{68} +(39.3775 + 22.7346i) q^{69} +0.709347i q^{70} +(12.9209 + 7.45986i) q^{71} +(26.1823 + 15.1164i) q^{72} +(40.2453 + 23.2357i) q^{73} +(-12.3821 - 21.4464i) q^{74} +5.10029i q^{75} +(-74.1396 + 42.8045i) q^{76} +(2.40523 + 1.38866i) q^{77} -6.29993 q^{78} +(40.1769 - 69.5884i) q^{79} +(54.1083 - 31.2394i) q^{80} +(-10.4691 - 18.1330i) q^{81} +10.9013i q^{82} +(22.6967 + 39.3118i) q^{83} +1.25554 q^{84} -46.9905i q^{85} +(23.9969 + 9.95554i) q^{86} -48.5803 q^{87} +58.0113i q^{88} +(93.4602 - 53.9593i) q^{89} +21.0506 q^{90} +(1.27511 - 0.736184i) q^{91} +(-52.8381 - 91.5183i) q^{92} +(-46.8976 - 27.0763i) q^{93} -21.2777i q^{94} +(-62.6015 + 108.429i) q^{95} +(19.9823 + 34.6104i) q^{96} +99.3401 q^{97} +(-25.6134 + 14.7879i) q^{98} +(41.2100 - 71.3778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9}+O(q^{10}) \) 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9	\( 12 q - 26 q^{4} - 3 q^{5} - 9 q^{6} + 9 q^{7} - 12 q^{9} - q^{10} + 28 q^{11} - 6 q^{12} + 24 q^{13} - 18 q^{14} - 13 q^{15} + 110 q^{16} - 7 q^{17} + 33 q^{18} + 66 q^{19} - 99 q^{20} - 80 q^{21} - 16 q^{23} - 2 q^{24} - 21 q^{25} + 9 q^{26} - 192 q^{28} - 111 q^{29} + 99 q^{30} - 29 q^{31} - 114 q^{33} + 213 q^{34} + 38 q^{35} + 152 q^{36} + 120 q^{37} + 172 q^{38} - 29 q^{40} + 94 q^{41} + 5 q^{43} - 174 q^{44} + 156 q^{46} - 18 q^{47} - 213 q^{48} - 99 q^{49} - 198 q^{50} - 234 q^{52} - 58 q^{53} + 128 q^{54} - 258 q^{55} + 315 q^{56} + 51 q^{57} - 196 q^{58} + 336 q^{59} - 5 q^{60} + 204 q^{61} + 261 q^{62} - 153 q^{63} - 604 q^{64} - 201 q^{66} + 115 q^{67} - 106 q^{68} + 423 q^{69} - 66 q^{71} + 294 q^{72} + 249 q^{73} - 214 q^{74} - 438 q^{76} + 117 q^{77} + 136 q^{78} + 236 q^{79} + 681 q^{80} + 110 q^{81} - 4 q^{83} + 248 q^{84} + 102 q^{86} - 408 q^{87} - 45 q^{89} - 44 q^{90} - 156 q^{91} - 483 q^{92} - 567 q^{93} - 389 q^{95} - 278 q^{96} - 370 q^{97} - 879 q^{98} + 157 q^{99}+O(q^{100}) \) 12 * q - 26 * q^4 - 3 * q^5 - 9 * q^6 + 9 * q^7 - 12 * q^9 - q^10 + 28 * q^11 - 6 * q^12 + 24 * q^13 - 18 * q^14 - 13 * q^15 + 110 * q^16 - 7 * q^17 + 33 * q^18 + 66 * q^19 - 99 * q^20 - 80 * q^21 - 16 * q^23 - 2 * q^24 - 21 * q^25 + 9 * q^26 - 192 * q^28 - 111 * q^29 + 99 * q^30 - 29 * q^31 - 114 * q^33 + 213 * q^34 + 38 * q^35 + 152 * q^36 + 120 * q^37 + 172 * q^38 - 29 * q^40 + 94 * q^41 + 5 * q^43 - 174 * q^44 + 156 * q^46 - 18 * q^47 - 213 * q^48 - 99 * q^49 - 198 * q^50 - 234 * q^52 - 58 * q^53 + 128 * q^54 - 258 * q^55 + 315 * q^56 + 51 * q^57 - 196 * q^58 + 336 * q^59 - 5 * q^60 + 204 * q^61 + 261 * q^62 - 153 * q^63 - 604 * q^64 - 201 * q^66 + 115 * q^67 - 106 * q^68 + 423 * q^69 - 66 * q^71 + 294 * q^72 + 249 * q^73 - 214 * q^74 - 438 * q^76 + 117 * q^77 + 136 * q^78 + 236 * q^79 + 681 * q^80 + 110 * q^81 - 4 * q^83 + 248 * q^84 + 102 * q^86 - 408 * q^87 - 45 * q^89 - 44 * q^90 - 156 * q^91 - 483 * q^92 - 567 * q^93 - 389 * q^95 - 278 * q^96 - 370 * q^97 - 879 * q^98 + 157 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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