LMFDB - Embedded newform 63.3.l.a.34.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(13,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("63.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.l (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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			34.12
Character	$\chi$	$=$	63.34
Dual form			63.3.l.a.13.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30753 - 2.26471i) q^{2} +(0.512678 + 2.95587i) q^{3} +(-1.41927 - 2.45825i) q^{4} +(3.19140 - 1.84256i) q^{5} +(7.36452 + 2.70382i) q^{6} +(-0.808038 - 6.95321i) q^{7} +3.03728 q^{8} +(-8.47432 + 3.03082i) q^{9} +O(q^{10})$	\(q+(1.30753 - 2.26471i) q^{2} +(0.512678 + 2.95587i) q^{3} +(-1.41927 - 2.45825i) q^{4} +(3.19140 - 1.84256i) q^{5} +(7.36452 + 2.70382i) q^{6} +(-0.808038 - 6.95321i) q^{7} +3.03728 q^{8} +(-8.47432 + 3.03082i) q^{9} -9.63680i q^{10} +(-6.63066 + 11.4846i) q^{11} +(6.53863 - 5.45547i) q^{12} +(-16.2463 + 9.37981i) q^{13} +(-16.8035 - 7.26156i) q^{14} +(7.08252 + 8.48873i) q^{15} +(9.64842 - 16.7116i) q^{16} +8.23398i q^{17} +(-4.21651 + 23.1548i) q^{18} -22.6432i q^{19} +(-9.05893 - 5.23018i) q^{20} +(20.1385 - 5.95321i) q^{21} +(17.3396 + 30.0330i) q^{22} +(0.369057 + 0.639226i) q^{23} +(1.55715 + 8.97781i) q^{24} +(-5.70996 + 9.88995i) q^{25} +49.0575i q^{26} +(-13.3033 - 23.4952i) q^{27} +(-15.9459 + 11.8548i) q^{28} +(-6.13829 + 10.6318i) q^{29} +(28.4851 - 4.94058i) q^{30} +(28.6323 - 16.5308i) q^{31} +(-19.1566 - 33.1803i) q^{32} +(-37.3465 - 13.7114i) q^{33} +(18.6476 + 10.7662i) q^{34} +(-15.3905 - 20.7016i) q^{35} +(19.4779 + 16.5304i) q^{36} -9.96860 q^{37} +(-51.2802 - 29.6066i) q^{38} +(-36.0546 - 43.2131i) q^{39} +(9.69320 - 5.59637i) q^{40} +(23.3769 - 13.4966i) q^{41} +(12.8494 - 53.3918i) q^{42} +(10.1549 - 17.5888i) q^{43} +37.6428 q^{44} +(-21.4605 + 25.2870i) q^{45} +1.93021 q^{46} +(69.3523 + 40.0406i) q^{47} +(54.3437 + 19.9518i) q^{48} +(-47.6941 + 11.2369i) q^{49} +(14.9319 + 25.8628i) q^{50} +(-24.3386 + 4.22138i) q^{51} +(46.1158 + 26.6250i) q^{52} +39.0420 q^{53} +(-70.6041 - 0.592511i) q^{54} +48.8695i q^{55} +(-2.45424 - 21.1189i) q^{56} +(66.9302 - 11.6087i) q^{57} +(16.0520 + 27.8029i) q^{58} +(40.3543 - 23.2986i) q^{59} +(10.8154 - 29.4584i) q^{60} +(-34.7549 - 20.0658i) q^{61} -86.4583i q^{62} +(27.9215 + 56.4747i) q^{63} -23.0042 q^{64} +(-34.5657 + 59.8695i) q^{65} +(-79.8840 + 66.6508i) q^{66} +(-54.5167 - 94.4257i) q^{67} +(20.2412 - 11.6862i) q^{68} +(-1.70026 + 1.41860i) q^{69} +(-67.0067 + 7.78690i) q^{70} +83.8258 q^{71} +(-25.7389 + 9.20546i) q^{72} +37.3200i q^{73} +(-13.0342 + 22.5760i) q^{74} +(-32.1608 - 11.8075i) q^{75} +(-55.6625 + 32.1368i) q^{76} +(85.2129 + 36.8243i) q^{77} +(-145.008 + 25.1507i) q^{78} +(-49.4165 + 85.5918i) q^{79} -71.1111i q^{80} +(62.6283 - 51.3683i) q^{81} -70.5890i q^{82} +(-124.459 - 71.8564i) q^{83} +(-43.2165 - 41.0562i) q^{84} +(15.1716 + 26.2779i) q^{85} +(-26.5557 - 45.9958i) q^{86} +(-34.5732 - 12.6933i) q^{87} +(-20.1392 + 34.8821i) q^{88} +133.114i q^{89} +(29.2074 + 81.6653i) q^{90} +(78.3474 + 105.385i) q^{91} +(1.04758 - 1.81447i) q^{92} +(63.5421 + 76.1582i) q^{93} +(181.360 - 104.708i) q^{94} +(-41.7213 - 72.2635i) q^{95} +(88.2554 - 73.6353i) q^{96} +(58.0415 + 33.5103i) q^{97} +(-36.9132 + 122.706i) q^{98} +(21.3825 - 117.421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 24 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 24 * q^9	$ 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 24 q^{9} + 4 q^{11} + 34 q^{14} - 54 q^{15} - 42 q^{16} + 54 q^{18} + 18 q^{21} + 14 q^{22} + 4 q^{23} + 28 q^{25} + 20 q^{28} - 38 q^{29} + 168 q^{30} - 168 q^{32} - 264 q^{35} + 234 q^{36} + 36 q^{37} - 228 q^{39} - 192 q^{42} - 66 q^{43} + 108 q^{44} - 40 q^{46} - 38 q^{49} + 196 q^{50} + 246 q^{51} + 520 q^{53} + 332 q^{56} - 198 q^{57} - 34 q^{58} + 96 q^{60} + 48 q^{63} + 72 q^{64} - 102 q^{65} + 68 q^{67} + 102 q^{70} - 332 q^{71} - 1308 q^{72} - 616 q^{74} + 334 q^{77} - 168 q^{78} + 146 q^{79} + 276 q^{81} + 498 q^{84} + 78 q^{85} - 340 q^{86} - 74 q^{88} - 384 q^{91} + 606 q^{92} + 534 q^{93} - 360 q^{95} - 1076 q^{98} + 900 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 24 * q^9 + 4 * q^11 + 34 * q^14 - 54 * q^15 - 42 * q^16 + 54 * q^18 + 18 * q^21 + 14 * q^22 + 4 * q^23 + 28 * q^25 + 20 * q^28 - 38 * q^29 + 168 * q^30 - 168 * q^32 - 264 * q^35 + 234 * q^36 + 36 * q^37 - 228 * q^39 - 192 * q^42 - 66 * q^43 + 108 * q^44 - 40 * q^46 - 38 * q^49 + 196 * q^50 + 246 * q^51 + 520 * q^53 + 332 * q^56 - 198 * q^57 - 34 * q^58 + 96 * q^60 + 48 * q^63 + 72 * q^64 - 102 * q^65 + 68 * q^67 + 102 * q^70 - 332 * q^71 - 1308 * q^72 - 616 * q^74 + 334 * q^77 - 168 * q^78 + 146 * q^79 + 276 * q^81 + 498 * q^84 + 78 * q^85 - 340 * q^86 - 74 * q^88 - 384 * q^91 + 606 * q^92 + 534 * q^93 - 360 * q^95 - 1076 * q^98 + 900 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.30753	−	2.26471i	0.653765	−	1.13235i	−0.328437	−	0.944526i	$-0.606522\pi$
$2$	1.30753	−	2.26471i	0.653765	−	1.13235i	0.982202	−	0.187828i	$-0.0601449\pi$
$3$	0.512678	+	2.95587i	0.170893	+	0.985290i
$3$	0.512678	+	2.95587i	0.170893	+	0.985290i
$4$	−1.41927	−	2.45825i	−0.354818	−	0.614562i
$5$	3.19140	−	1.84256i	0.638281	−	0.368512i	−0.145671	−	0.989333i	$-0.546534\pi$
$5$	3.19140	−	1.84256i	0.638281	−	0.368512i	0.783952	+	0.620822i	$0.213201\pi$
$6$	7.36452	+	2.70382i	1.22742	+	0.450637i
$7$	−0.808038	−	6.95321i	−0.115434	−	0.993315i
$7$	−0.808038	−	6.95321i	−0.115434	−	0.993315i
$8$	3.03728			0.379661
$9$	−8.47432	+	3.03082i	−0.941591	+	0.336758i
$10$		−	9.63680i		−	0.963680i
$11$	−6.63066	+	11.4846i	−0.602787	+	1.04406i	0.389610	+	0.920980i	$0.372610\pi$
$11$	−6.63066	+	11.4846i	−0.602787	+	1.04406i	−0.992397	+	0.123078i	$0.960724\pi$
$12$	6.53863	−	5.45547i	0.544886	−	0.454622i
$13$	−16.2463	+	9.37981i	−1.24972	+	0.721524i	−0.971053	−	0.238865i	$-0.923225\pi$
$13$	−16.2463	+	9.37981i	−1.24972	+	0.721524i	−0.278663	+	0.960389i	$0.589891\pi$
$14$	−16.8035	−	7.26156i	−1.20025	−	0.518683i
$15$	7.08252	+	8.48873i	0.472168	+	0.565915i
$16$	9.64842	−	16.7116i	0.603027	−	1.04447i
$17$			8.23398i			0.484352i	0.970232	+	0.242176i	$0.0778611\pi$
$17$			8.23398i			0.484352i	−0.970232	+	0.242176i	$0.922139\pi$
$18$	−4.21651	+	23.1548i	−0.234251	+	1.28638i
$19$		−	22.6432i		−	1.19175i	−0.803079	−	0.595873i	$-0.796806\pi$
$19$		−	22.6432i		−	1.19175i	0.803079	−	0.595873i	$-0.203194\pi$
$20$	−9.05893	−	5.23018i	−0.452947	−	0.261509i
$21$	20.1385	−	5.95321i	0.958976	−	0.283486i
$22$	17.3396	+	30.0330i	0.788162	+	1.36514i
$23$	0.369057	+	0.639226i	0.0160460	+	0.0277924i	0.873937	−	0.486039i	$-0.161559\pi$
$23$	0.369057	+	0.639226i	0.0160460	+	0.0277924i	−0.857891	+	0.513832i	$0.828226\pi$
$24$	1.55715	+	8.97781i	0.0648812	+	0.374076i
$25$	−5.70996	+	9.88995i	−0.228399	+	0.395598i
$26$			49.0575i			1.88683i
$27$	−13.3033	−	23.4952i	−0.492715	−	0.870191i
$28$	−15.9459	+	11.8548i	−0.569496	+	0.423387i
$29$	−6.13829	+	10.6318i	−0.211665	+	0.366615i	−0.952236	−	0.305364i	$-0.901222\pi$
$29$	−6.13829	+	10.6318i	−0.211665	+	0.366615i	0.740571	+	0.671978i	$0.234555\pi$
$30$	28.4851	−	4.94058i	0.949504	−	0.164686i
$31$	28.6323	−	16.5308i	0.923621	−	0.533253i	0.0388326	−	0.999246i	$-0.487636\pi$
$31$	28.6323	−	16.5308i	0.923621	−	0.533253i	0.884788	+	0.465993i	$0.154303\pi$
$32$	−19.1566	−	33.1803i	−0.598645	−	1.03688i
$33$	−37.3465	−	13.7114i	−1.13171	−	0.415498i
$34$	18.6476	+	10.7662i	0.548458	+	0.316652i
$35$	−15.3905	−	20.7016i	−0.439727	−	0.591475i
$36$	19.4779	+	16.5304i	0.541052	+	0.459179i
$37$	−9.96860			−0.269422			−0.134711	−	0.990885i	$-0.543011\pi$
$37$	−9.96860			−0.269422			−0.134711	+	0.990885i	$0.543011\pi$
$38$	−51.2802	−	29.6066i	−1.34948	−	0.779122i
$39$	−36.0546	−	43.2131i	−0.924477	−	1.10803i
$40$	9.69320	−	5.59637i	0.242330	−	0.139909i
$41$	23.3769	−	13.4966i	0.570167	−	0.329186i	−0.187049	−	0.982351i	$-0.559892\pi$
$41$	23.3769	−	13.4966i	0.570167	−	0.329186i	0.757216	+	0.653164i	$0.226559\pi$
$42$	12.8494	−	53.3918i	0.305938	−	1.27123i
$43$	10.1549	−	17.5888i	0.236160	−	0.409042i	−0.723449	−	0.690378i	$-0.757444\pi$
$43$	10.1549	−	17.5888i	0.236160	−	0.409042i	0.959609	+	0.281336i	$0.0907776\pi$
$44$	37.6428			0.855518
$45$	−21.4605	+	25.2870i	−0.476900	+	0.561933i
$46$	1.93021			0.0419612
$47$	69.3523	+	40.0406i	1.47558	+	0.851927i	0.999621	−	0.0275406i	$-0.00876755\pi$
$47$	69.3523	+	40.0406i	1.47558	+	0.851927i	0.475959	+	0.879467i	$0.342101\pi$
$48$	54.3437	+	19.9518i	1.13216	+	0.415663i
$49$	−47.6941	+	11.2369i	−0.973350	+	0.229325i
$50$	14.9319	+	25.8628i	0.298638	+	0.517256i
$51$	−24.3386	+	4.22138i	−0.477227	+	0.0827722i
$52$	46.1158	+	26.6250i	0.886842	+	0.512019i
$53$	39.0420			0.736641			0.368320	−	0.929699i	$-0.379933\pi$
$53$	39.0420			0.736641			0.368320	+	0.929699i	$0.379933\pi$
$54$	−70.6041	−	0.592511i	−1.30748	−	0.0109724i
$55$			48.8695i			0.888536i
$56$	−2.45424	−	21.1189i	−0.0438258	−	0.377123i
$57$	66.9302	−	11.6087i	1.17421	−	0.203661i
$58$	16.0520	+	27.8029i	0.276758	+	0.479360i
$59$	40.3543	−	23.2986i	0.683971	−	0.394891i	−0.117378	−	0.993087i	$-0.537449\pi$
$59$	40.3543	−	23.2986i	0.683971	−	0.394891i	0.801350	+	0.598196i	$0.204116\pi$
$60$	10.8154	−	29.4584i	0.180257	−	0.490973i
$61$	−34.7549	−	20.0658i	−0.569753	−	0.328947i	0.187298	−	0.982303i	$-0.440027\pi$
$61$	−34.7549	−	20.0658i	−0.569753	−	0.328947i	−0.757051	+	0.653356i	$0.773360\pi$
$62$		−	86.4583i		−	1.39449i
$63$	27.9215	+	56.4747i	0.443198	+	0.896424i
$64$	−23.0042			−0.359440
$65$	−34.5657	+	59.8695i	−0.531779	+	0.921069i
$66$	−79.8840	+	66.6508i	−1.21036	+	1.00986i
$67$	−54.5167	−	94.4257i	−0.813682	−	1.40934i	−0.910270	−	0.414014i	$-0.864126\pi$
$67$	−54.5167	−	94.4257i	−0.813682	−	1.40934i	0.0965884	−	0.995324i	$-0.469207\pi$
$68$	20.2412	−	11.6862i	0.297664	−	0.171857i
$69$	−1.70026	+	1.41860i	−0.0246415	+	0.0205595i
$70$	−67.0067	+	7.78690i	−0.957238	+	0.111241i
$71$	83.8258			1.18064			0.590322	−	0.807168i	$-0.299001\pi$
$71$	83.8258			1.18064			0.590322	+	0.807168i	$0.299001\pi$
$72$	−25.7389	+	9.20546i	−0.357485	+	0.127854i
$73$			37.3200i			0.511233i	0.966778	+	0.255617i	$0.0822785\pi$
$73$			37.3200i			0.511233i	−0.966778	+	0.255617i	$0.917722\pi$
$74$	−13.0342	+	22.5760i	−0.176138	+	0.305081i
$75$	−32.1608	−	11.8075i	−0.428810	−	0.157434i
$76$	−55.6625	+	32.1368i	−0.732402	+	0.422852i
$77$	85.2129	+	36.8243i	1.10666	+	0.478238i
$78$	−145.008	+	25.1507i	−1.85907	+	0.322445i
$79$	−49.4165	+	85.5918i	−0.625525	+	1.08344i	0.362914	+	0.931823i	$0.381782\pi$
$79$	−49.4165	+	85.5918i	−0.625525	+	1.08344i	−0.988439	+	0.151618i	$0.951552\pi$
$80$		−	71.1111i		−	0.888889i
$81$	62.6283	−	51.3683i	0.773189	−	0.634176i
$82$		−	70.5890i		−	0.860842i
$83$	−124.459	−	71.8564i	−1.49951	−	0.865740i	−0.499506	−	0.866310i	$-0.666485\pi$
$83$	−124.459	−	71.8564i	−1.49951	−	0.865740i	−1.00000		0.000570370i	$0.999818\pi$
$84$	−43.2165	−	41.0562i	−0.514482	−	0.488765i
$85$	15.1716	+	26.2779i	0.178489	+	0.309152i
$86$	−26.5557	−	45.9958i	−0.308787	−	0.534834i
$87$	−34.5732	−	12.6933i	−0.397394	−	0.145900i
$88$	−20.1392	+	34.8821i	−0.228854	+	0.396388i
$89$			133.114i			1.49566i	0.663887	+	0.747832i	$0.268905\pi$
$89$			133.114i			1.49566i	−0.663887	+	0.747832i	$0.731095\pi$
$90$	29.2074	+	81.6653i	0.324527	+	0.907393i
$91$	78.3474	+	105.385i	0.860960	+	1.15807i
$92$	1.04758	−	1.81447i	0.0113868	−	0.0197225i
$93$	63.5421	+	76.1582i	0.683249	+	0.818905i
$94$	181.360	−	104.708i	1.92937	−	1.11392i
$95$	−41.7213	−	72.2635i	−0.439172	−	0.760668i
$96$	88.2554	−	73.6353i	0.919327	−	0.767035i
$97$	58.0415	+	33.5103i	0.598366	+	0.345467i	0.768399	−	0.639972i	$-0.221054\pi$
$97$	58.0415	+	33.5103i	0.598366	+	0.345467i	−0.170032	+	0.985438i	$0.554387\pi$
$98$	−36.9132	+	122.706i	−0.376665	+	1.25210i
$99$	21.3825	−	117.421i	0.215985	−	1.18607i
$100$	32.4159			0.324159
$101$	−18.6008	−	10.7392i	−0.184166	−	0.106328i	0.405082	−	0.914280i	$-0.367243\pi$
$101$	−18.6008	−	10.7392i	−0.184166	−	0.106328i	−0.589249	+	0.807952i	$0.700576\pi$
$102$	−22.2632	+	60.6393i	−0.218267	+	0.594503i
$103$	12.9916	−	7.50068i	0.126132	−	0.0728222i	−0.435607	−	0.900137i	$-0.643466\pi$
$103$	12.9916	−	7.50068i	0.126132	−	0.0728222i	0.561738	+	0.827315i	$0.310133\pi$
$104$	−49.3446	+	28.4891i	−0.474468	+	0.273934i
$105$	53.3009	−	56.1055i	0.507628	−	0.534338i
$106$	51.0485	−	88.4187i	0.481590	−	0.834138i
$107$	−51.7878			−0.483998			−0.241999	−	0.970276i	$-0.577803\pi$
$107$	−51.7878			−0.483998			−0.241999	+	0.970276i	$0.577803\pi$
$108$	−38.8759	+	66.0488i	−0.359962	+	0.611563i
$109$	141.473			1.29792			0.648960	−	0.760823i	$-0.275204\pi$
$109$	141.473			1.29792			0.648960	+	0.760823i	$0.275204\pi$
$110$	110.675	+	63.8983i	1.00614	+	0.580894i
$111$	−5.11068	−	29.4659i	−0.0460422	−	0.265458i
$112$	−123.995	−	53.5839i	−1.10710	−	0.478428i
$113$	−53.4919	−	92.6507i	−0.473380	−	0.819918i	0.526156	−	0.850388i	$-0.323633\pi$
$113$	−53.4919	−	92.6507i	−0.473380	−	0.819918i	−0.999536	+	0.0304701i	$0.990300\pi$
$114$	61.2231	−	166.756i	0.537044	−	1.46277i
$115$	2.35562	+	1.36002i	0.0204837	+	0.0118263i
$116$	34.8476			0.300410
$117$	109.248	−	128.727i	0.933743	−	1.10023i
$118$		−	121.854i		−	1.03266i
$119$	57.2525	−	6.65337i	0.481114	−	0.0559107i
$120$	21.5116	+	25.7827i	0.179264	+	0.214856i
$121$	−27.4312	−	47.5123i	−0.226704	−	0.392663i
$122$	−90.8862	+	52.4732i	−0.744969	+	0.430108i
$123$	51.8791	+	62.1795i	0.421781	+	0.505524i
$124$	−81.2738	−	46.9235i	−0.655434	−	0.378415i
$125$			134.212i			1.07369i
$126$	164.407	+	10.6083i	1.30482	+	0.0841931i
$127$	−179.059			−1.40991			−0.704956	−	0.709251i	$-0.749033\pi$
$127$	−179.059			−1.40991			−0.704956	+	0.709251i	$0.749033\pi$
$128$	46.5479	−	80.6234i	0.363656	−	0.629870i
$129$	57.1964	+	20.9991i	0.443383	+	0.162784i
$130$	90.3913	+	156.562i	0.695318	+	1.20433i
$131$	−101.017	+	58.3219i	−0.771119	+	0.445206i	−0.833274	−	0.552861i	$-0.813536\pi$
$131$	−101.017	+	58.3219i	−0.771119	+	0.445206i	0.0621549	+	0.998067i	$0.480203\pi$
$132$	19.2986	+	111.267i	0.146202	+	0.842933i
$133$	−157.443	+	18.2965i	−1.18378	+	0.137568i
$134$	−285.129			−2.12783
$135$	−85.7474	−	50.4704i	−0.635166	−	0.373855i
$136$			25.0089i			0.183889i
$137$	−35.8160	+	62.0351i	−0.261430	+	0.452811i	−0.966622	−	0.256206i	$-0.917528\pi$
$137$	−35.8160	+	62.0351i	−0.261430	+	0.452811i	0.705192	+	0.709017i	$0.250861\pi$
$138$	0.989579	+	5.70546i	0.00717086	+	0.0413439i
$139$	188.775	−	108.989i	1.35809	−	0.784094i	0.368724	−	0.929539i	$-0.379795\pi$
$139$	188.775	−	108.989i	1.35809	−	0.784094i	0.989366	+	0.145445i	$0.0464612\pi$
$140$	−29.0465	+	67.2148i	−0.207475	+	0.480106i
$141$	−82.7992	+	225.524i	−0.587229	+	1.59946i
$142$	109.605	−	189.841i	0.771864	−	1.33691i
$143$		−	248.777i		−	1.73970i
$144$	−31.1141	+	170.862i	−0.216070	+	1.18654i
$145$			45.2406i			0.312004i
$146$	84.5190	+	48.7971i	0.578897	+	0.334226i
$147$	−57.6666	−	135.217i	−0.392290	−	0.919842i
$148$	14.1481	+	24.5053i	0.0955955	+	0.165576i
$149$	−13.2091	−	22.8789i	−0.0886520	−	0.153550i	0.818290	−	0.574806i	$-0.194923\pi$
$149$	−13.2091	−	22.8789i	−0.0886520	−	0.153550i	−0.906942	+	0.421256i	$0.861589\pi$
$150$	−68.7918	+	57.3960i	−0.458612	+	0.382640i
$151$	−41.6516	+	72.1427i	−0.275838	+	0.477766i	−0.970346	−	0.241719i	$-0.922289\pi$
$151$	−41.6516	+	72.1427i	−0.275838	+	0.477766i	0.694508	+	0.719485i	$0.255622\pi$
$152$		−	68.7737i		−	0.452459i
$153$	−24.9557	−	69.7774i	−0.163109	−	0.456061i
$154$	194.815	−	144.833i	1.26503	−	0.940477i
$155$	60.9180	−	105.513i	0.393020	−	0.680730i
$156$	−55.0574	+	149.962i	−0.352932	+	0.961297i
$157$	−128.067	+	73.9397i	−0.815715	+	0.470953i	−0.848937	−	0.528495i	$-0.822757\pi$
$157$	−128.067	+	73.9397i	−0.815715	+	0.470953i	0.0332215	+	0.999448i	$0.489423\pi$
$158$	129.227	+	223.828i	0.817893	+	1.41663i
$159$	20.0160	+	115.403i	0.125887	+	0.725804i
$160$	−122.273	−	70.5944i	−0.764207	−	0.441215i
$161$	4.14646	−	3.08265i	0.0257544	−	0.0191469i
$162$	−34.4458	−	209.000i	−0.212629	−	1.29013i
$163$	−80.9615			−0.496696			−0.248348	−	0.968671i	$-0.579888\pi$
$163$	−80.9615			−0.496696			−0.248348	+	0.968671i	$0.579888\pi$
$164$	−66.3562	−	38.3108i	−0.404611	−	0.233602i
$165$	−144.452	+	25.0543i	−0.875465	+	0.151844i
$166$	−325.468	+	187.909i	−1.96065	+	1.13198i
$167$	1.93139	−	1.11509i	0.0115652	−	0.00667716i	−0.494206	−	0.869345i	$-0.664541\pi$
$167$	1.93139	−	1.11509i	0.0115652	−	0.00667716i	0.505771	+	0.862668i	$0.331208\pi$
$168$	61.1664	−	18.0816i	0.364085	−	0.107629i
$169$	91.4615	−	158.416i	0.541192	−	0.937373i
$170$	79.3492			0.466760
$171$	68.6273	+	191.885i	0.401329	+	1.12214i
$172$	−57.6502			−0.335175
$173$	−146.304	−	84.4688i	−0.845690	−	0.488259i	0.0135045	−	0.999909i	$-0.495701\pi$
$173$	−146.304	−	84.4688i	−0.845690	−	0.488259i	−0.859194	+	0.511650i	$0.829035\pi$
$174$	−73.9521	+	61.7015i	−0.425012	+	0.354606i
$175$	73.3807	+	31.7111i	0.419318	+	0.181206i
$176$	127.951	+	221.617i	0.726993	+	1.25919i
$177$	89.5563	+	107.337i	0.505968	+	0.606426i
$178$	301.465	+	174.051i	1.69362	+	0.977814i
$179$	74.8944			0.418405			0.209202	−	0.977872i	$-0.432913\pi$
$179$	74.8944			0.418405			0.209202	+	0.977872i	$0.432913\pi$
$180$	92.6200	+	16.8662i	0.514556	+	0.0937012i
$181$			1.66857i			0.00921864i	0.999989	+	0.00460932i	$0.00146720\pi$
$181$			1.66857i			0.00921864i	−0.999989	+	0.00460932i	$0.998533\pi$
$182$	341.107	−	39.6404i	1.87421	−	0.217804i
$183$	41.4937	−	113.018i	0.226741	−	0.617586i
$184$	1.12093	+	1.94151i	0.00609202	+	0.0105517i
$185$	−31.8138	+	18.3677i	−0.171967	+	0.0992849i
$186$	255.559	−	44.3253i	1.37398	−	0.238308i
$187$	−94.5642	−	54.5967i	−0.505691	−	0.291961i
$188$		−	227.314i		−	1.20911i
$189$	−152.617	+	111.486i	−0.807498	+	0.589871i
$190$	−218.208			−1.14846
$191$	−60.4724	+	104.741i	−0.316609	+	0.548383i	−0.979778	−	0.200086i	$-0.935878\pi$
$191$	−60.4724	+	104.741i	−0.316609	+	0.548383i	0.663169	+	0.748470i	$0.269211\pi$
$192$	−11.7937	−	67.9973i	−0.0614257	−	0.354153i
$193$	−101.401	−	175.631i	−0.525393	−	0.910007i	−0.999563	−	0.0295736i	$-0.990585\pi$
$193$	−101.401	−	175.631i	−0.525393	−	0.910007i	0.474170	−	0.880433i	$-0.342748\pi$
$194$	151.782	−	87.6315i	0.782382	−	0.451709i
$195$	−194.687	−	71.4778i	−0.998397	−	0.366553i
$196$	95.3140	+	101.296i	0.486296	+	0.516816i
$197$	−213.013			−1.08129			−0.540643	−	0.841252i	$-0.681819\pi$
$197$	−213.013			−1.08129			−0.540643	+	0.841252i	$0.681819\pi$
$198$	−237.966	−	201.956i	−1.20185	−	1.01998i
$199$		−	200.308i		−	1.00657i	−0.864119	−	0.503287i	$-0.832124\pi$
$199$		−	200.308i		−	1.00657i	0.864119	−	0.503287i	$-0.167876\pi$
$200$	−17.3428	+	30.0386i	−0.0867139	+	0.150193i
$201$	251.160	−	209.554i	1.24955	−	1.04256i
$202$	−48.6422	+	28.0836i	−0.240803	+	0.139028i
$203$	78.8852	+	34.0899i	0.388597	+	0.167930i
$204$	44.9202	+	53.8390i	0.220197	+	0.263916i
$205$	49.7366	−	86.1464i	0.242618	−	0.420226i
$206$		−	39.2295i		−	0.190434i
$207$	−5.06489	−	4.29846i	−0.0244681	−	0.0207655i
$208$			362.001i			1.74039i
$209$	260.048	+	150.139i	1.24425	+	0.718369i
$210$	−57.3699	−	194.071i	−0.273190	−	0.924146i
$211$	142.883	+	247.481i	0.677173	+	1.17290i	0.975829	+	0.218537i	$0.0701284\pi$
$211$	142.883	+	247.481i	0.677173	+	1.17290i	−0.298656	+	0.954361i	$0.596538\pi$
$212$	−55.4111	−	95.9749i	−0.261373	−	0.452712i
$213$	42.9757	+	247.778i	0.201764	+	1.16328i
$214$	−67.7141	+	117.284i	−0.316421	+	0.548058i
$215$		−	74.8439i		−	0.348111i
$216$	−40.4059	−	71.3615i	−0.187064	−	0.330377i
$217$	−138.078	−	185.728i	−0.636306	−	0.855891i
$218$	184.981	−	320.396i	0.848535	−	1.46970i
$219$	−110.313	+	19.1332i	−0.503713	+	0.0873660i
$220$	120.133	−	69.3590i	0.546061	−	0.315268i
$221$	−77.2331	−	133.772i	−0.349471	−	0.605302i
$222$	−73.4140	−	26.9533i	−0.330694	−	0.121411i
$223$	326.190	+	188.326i	1.46273	+	0.844510i	0.999137	−	0.0415367i	$-0.0132254\pi$
$223$	326.190	+	188.326i	1.46273	+	0.844510i	0.463597	+	0.886046i	$0.346559\pi$
$224$	−215.230	+	160.011i	−0.960848	+	0.714335i
$225$	18.4134	−	101.116i	0.0818375	−	0.449406i
$226$	−279.769			−1.23792
$227$	−191.360	−	110.482i	−0.842997	−	0.486704i	0.0152850	−	0.999883i	$-0.495134\pi$
$227$	−191.360	−	110.482i	−0.842997	−	0.486704i	−0.858282	+	0.513179i	$0.828468\pi$
$228$	−123.529	−	148.055i	−0.541794	−	0.649365i
$229$	−24.9109	+	14.3823i	−0.108781	+	0.0628049i	−0.553404	−	0.832913i	$-0.686671\pi$
$229$	−24.9109	+	14.3823i	−0.108781	+	0.0628049i	0.444622	+	0.895718i	$0.353338\pi$
$230$	6.16009	−	3.55653i	0.0267830	−	0.0154632i
$231$	−65.1610	+	270.757i	−0.282082	+	1.17211i
$232$	−18.6437	+	32.2919i	−0.0803609	+	0.139189i
$233$	405.664			1.74105			0.870524	−	0.492126i	$-0.163780\pi$
$233$	405.664			1.74105			0.870524	+	0.492126i	$0.163780\pi$
$234$	−148.684	−	415.729i	−0.635404	−	1.77662i
$235$	295.108			1.25578
$236$	−114.547	−	66.1340i	−0.485370	−	0.280229i
$237$	−278.333	−	102.188i	−1.17440	−	0.431171i
$238$	59.7915	−	138.360i	0.251225	−	0.581344i
$239$	66.2069	+	114.674i	0.277016	+	0.479807i	0.970642	−	0.240529i	$-0.0773210\pi$
$239$	66.2069	+	114.674i	0.277016	+	0.479807i	−0.693625	+	0.720336i	$0.743988\pi$
$240$	210.195	−	36.4571i	0.875813	−	0.151905i
$241$	−71.7575	−	41.4292i	−0.297749	−	0.171905i	0.343682	−	0.939086i	$-0.388326\pi$
$241$	−71.7575	−	41.4292i	−0.297749	−	0.171905i	−0.641431	+	0.767181i	$0.721659\pi$
$242$	−143.469			−0.592846
$243$	183.946	+	158.786i	0.756980	+	0.653439i
$244$			113.915i			0.466865i
$245$	−131.507	+	123.741i	−0.536762	+	0.505064i
$246$	208.652	−	36.1895i	0.848178	−	0.147112i
$247$	212.388	+	367.868i	0.859872	+	1.48934i
$248$	86.9643	−	50.2089i	0.350662	−	0.202455i
$249$	148.591	−	404.724i	0.596750	−	1.62540i
$250$	303.950	+	175.486i	1.21580	+	0.701943i
$251$			182.888i			0.728636i	0.931275	+	0.364318i	$0.118698\pi$
$251$			182.888i			0.728636i	−0.931275	+	0.364318i	$0.881302\pi$
$252$	99.2007	−	148.791i	0.393654	−	0.590440i
$253$	−9.78837			−0.0386892
$254$	−234.125	+	405.516i	−0.921752	+	1.59652i
$255$	−69.8960	+	58.3173i	−0.274102	+	0.228695i
$256$	−167.734	−	290.524i	−0.655211	−	1.13486i
$257$	−41.1681	+	23.7684i	−0.160187	+	0.0924842i	−0.577951	−	0.816072i	$-0.696147\pi$
$257$	−41.1681	+	23.7684i	−0.160187	+	0.0924842i	0.417763	+	0.908556i	$0.362814\pi$
$258$	122.343	−	102.076i	0.474197	−	0.395644i
$259$	8.05501	+	69.3137i	0.0311004	+	0.267620i
$260$	196.232			0.754739
$261$	19.7947	−	108.702i	0.0758417	−	0.416481i
$262$			305.031i			1.16424i
$263$	204.796	−	354.717i	0.778693	−	1.34874i	−0.154003	−	0.988070i	$-0.549217\pi$
$263$	204.796	−	354.717i	0.778693	−	1.34874i	0.932696	−	0.360665i	$-0.117450\pi$
$264$	−113.432	−	41.6455i	−0.429666	−	0.157748i
$265$	124.599	−	71.9371i	0.470184	−	0.271461i
$266$	−164.425	+	380.485i	−0.618138	+	1.43039i
$267$	−393.468	+	68.2447i	−1.47366	+	0.255598i
$268$	−154.748	+	268.031i	−0.577418	+	1.00012i
$269$			154.435i			0.574108i	0.957914	+	0.287054i	$0.0926759\pi$
$269$			154.435i			0.574108i	−0.957914	+	0.287054i	$0.907324\pi$
$270$	−226.418	+	128.201i	−0.838585	+	0.474820i
$271$		−	62.1999i		−	0.229520i	−0.993393	−	0.114760i	$-0.963390\pi$
$271$		−	62.1999i		−	0.229520i	0.993393	−	0.114760i	$-0.0366099\pi$
$272$	137.603	+	79.4449i	0.505892	+	0.292077i
$273$	−271.336	+	285.613i	−0.993905	+	1.04620i
$274$	93.6609	+	162.226i	0.341828	+	0.592064i
$275$	−75.7216	−	131.154i	−0.275351	−	0.476922i
$276$	5.90041	+	2.16628i	0.0213783	+	0.00784885i
$277$	2.87637	−	4.98202i	0.0103840	−	0.0179856i	−0.860787	−	0.508966i	$-0.830028\pi$
$277$	2.87637	−	4.98202i	0.0103840	−	0.0179856i	0.871171	+	0.490980i	$0.163361\pi$
$278$		−	570.026i		−	2.05045i
$279$	−192.537	+	226.867i	−0.690097	+	0.813143i
$280$	−46.7452	−	62.8767i	−0.166947	−	0.224560i
$281$	−126.093	+	218.400i	−0.448731	+	0.777225i	−0.998304	−	0.0582207i	$-0.981457\pi$
$281$	−126.093	+	218.400i	−0.448731	+	0.777225i	0.549573	+	0.835446i	$0.314791\pi$
$282$	402.484	+	482.396i	1.42725	+	1.71062i
$283$	−117.523	+	67.8520i	−0.415276	+	0.239760i	−0.693054	−	0.720886i	$-0.743735\pi$
$283$	−117.523	+	67.8520i	−0.415276	+	0.239760i	0.277778	+	0.960645i	$0.410402\pi$
$284$	−118.971	−	206.065i	−0.418914	−	0.725580i
$285$	192.212	−	160.371i	0.674427	−	0.562704i
$286$	−563.408	−	325.284i	−1.96996	−	1.13736i
$287$	−112.734	−	151.638i	−0.392802	−	0.528356i
$288$	262.903	+	223.120i	0.912858	+	0.774722i
$289$	221.202			0.765404
$290$	102.457	+	59.1534i	0.353299	+	0.203977i
$291$	−69.2954	+	188.743i	−0.238129	+	0.648602i
$292$	91.7419	−	52.9672i	0.314185	−	0.181395i
$293$	−72.9007	+	42.0892i	−0.248808	+	0.143649i	−0.619218	−	0.785219i	$-0.712550\pi$
$293$	−72.9007	+	42.0892i	−0.248808	+	0.143649i	0.370410	+	0.928868i	$0.379217\pi$
$294$	−381.627	−	46.2019i	−1.29805	−	0.157149i
$295$	85.8579	−	148.710i	0.291044	−	0.504103i
$296$	−30.2775			−0.102289
$297$	358.043	+	3.00470i	1.20553	+	0.0101168i
$298$	−69.0854			−0.231830
$299$	−11.9916	−	6.92337i	−0.0401058	−	0.0231551i
$300$	16.6189	+	95.8172i	0.0553965	+	0.319391i
$301$	−130.504	−	56.3967i	−0.433568	−	0.187364i
$302$	108.921	+	188.658i	0.360667	+	0.624694i
$303$	22.2073	−	60.4872i	0.0732916	−	0.199628i
$304$	−378.403	−	218.471i	−1.24475	−	0.718654i
$305$	−147.889			−0.484883
$306$	−190.656	−	34.7186i	−0.623058	−	0.113460i
$307$		−	155.490i		−	0.506483i	−0.967403	−	0.253242i	$-0.918503\pi$
$307$		−	155.490i		−	0.506483i	0.967403	−	0.253242i	$-0.0814968\pi$
$308$	−30.4168	−	261.738i	−0.0987559	−	0.849799i
$309$	28.8315	+	34.5559i	0.0933059	+	0.111831i
$310$	−159.304	−	275.923i	−0.513885	−	0.890075i
$311$	168.154	−	97.0835i	0.540687	−	0.312166i	−0.204670	−	0.978831i	$-0.565612\pi$
$311$	168.154	−	97.0835i	0.540687	−	0.312166i	0.745357	+	0.666665i	$0.232279\pi$
$312$	−109.508	−	131.251i	−0.350987	−	0.420675i
$313$	−300.308	−	173.383i	−0.959450	−	0.553939i	−0.0634463	−	0.997985i	$-0.520209\pi$
$313$	−300.308	−	173.383i	−0.959450	−	0.553939i	−0.896004	+	0.444047i	$0.853542\pi$
$314$			386.713i			1.23157i
$315$	193.167	+	128.787i	0.613227	+	0.408846i
$316$	280.541			0.887789
$317$	−34.5304	+	59.8083i	−0.108929	+	0.188670i	−0.915336	−	0.402690i	$-0.868075\pi$
$317$	−34.5304	+	59.8083i	−0.108929	+	0.188670i	0.806408	+	0.591360i	$0.201409\pi$
$318$	287.525	+	105.562i	0.904168	+	0.331957i
$319$	−81.4018	−	140.992i	−0.255178	−	0.441981i
$320$	−73.4156	+	42.3865i	−0.229424	+	0.132458i
$321$	−26.5505	−	153.078i	−0.0827118	−	0.476878i
$322$	−1.55969	−	13.4212i	−0.00484375	−	0.0416807i
$323$	186.443			0.577224
$324$	−215.162	−	81.0504i	−0.664082	−	0.250156i
$325$		−	214.233i		−	0.659180i
$326$	−105.860	+	183.354i	−0.324723	+	0.562436i
$327$	72.5302	+	418.176i	0.221805	+	1.27883i
$328$	71.0022	−	40.9931i	0.216470	−	0.124979i
$329$	222.371	−	514.575i	0.675899	−	1.56406i
$330$	−132.134	+	359.900i	−0.400407	+	1.09061i
$331$	125.821	−	217.928i	0.380123	−	0.658393i	−0.610956	−	0.791664i	$-0.709215\pi$
$331$	125.821	−	217.928i	0.380123	−	0.658393i	0.991080	+	0.133272i	$0.0425483\pi$
$332$			407.935i			1.22872i
$333$	84.4771	−	30.2130i	0.253685	−	0.0907298i
$334$		−	5.83203i		−	0.0174612i
$335$	−347.970	−	200.900i	−1.03872	−	0.599702i
$336$	94.8173	−	393.985i	0.282194	−	1.17257i
$337$	−140.785	−	243.846i	−0.417759	−	0.723580i	0.577955	−	0.816069i	$-0.303851\pi$
$337$	−140.785	−	243.846i	−0.417759	−	0.723580i	−0.995714	+	0.0924890i	$0.970518\pi$
$338$	−239.177	−	414.267i	−0.707625	−	1.22564i
$339$	246.439	−	205.615i	0.726960	−	0.606534i
$340$	43.0652	−	74.5910i	0.126662	−	0.219385i
$341$			438.441i			1.28575i
$342$	524.297	+	95.4751i	1.53303	+	0.279167i
$343$	116.671	+	322.547i	0.340150	+	0.940371i
$344$	30.8433	−	53.4222i	0.0896608	−	0.155297i
$345$	−2.81236	+	7.66016i	−0.00815177	+	0.0222034i
$346$	−382.595	+	220.891i	−1.10576	+	0.638414i
$347$	105.071	+	181.988i	0.302798	+	0.524462i	0.976769	−	0.214296i	$-0.0687459\pi$
$347$	105.071	+	181.988i	0.302798	+	0.524462i	−0.673971	+	0.738758i	$0.735413\pi$
$348$	17.8656	+	103.005i	0.0513379	+	0.295991i
$349$	64.0467	+	36.9774i	0.183515	+	0.105952i	0.588943	−	0.808175i	$-0.299544\pi$
$349$	64.0467	+	36.9774i	0.183515	+	0.105952i	−0.405428	+	0.914127i	$0.632878\pi$
$350$	167.764	−	124.723i	0.479325	−	0.356351i
$351$	436.509	+	256.927i	1.24362	+	0.731985i
$352$	508.085			1.44342
$353$	281.010	+	162.241i	0.796061	+	0.459606i	0.842092	−	0.539334i	$-0.181324\pi$
$353$	281.010	+	162.241i	0.796061	+	0.459606i	−0.0460309	+	0.998940i	$0.514657\pi$
$354$	360.186	−	62.4721i	1.01747	−	0.176475i
$355$	267.522	−	154.454i	0.753583	−	0.435081i
$356$	327.228	−	188.925i	0.919179	−	0.530688i
$357$	49.0186	+	165.820i	0.137307	+	0.464482i
$358$	97.9267	−	169.614i	0.273538	−	0.473782i
$359$	261.171			0.727495			0.363748	−	0.931498i	$-0.381497\pi$
$359$	261.171			0.727495			0.363748	+	0.931498i	$0.381497\pi$
$360$	−65.1817	+	76.8038i	−0.181060	+	0.213344i
$361$	−151.713			−0.420257
$362$	3.77883	+	2.18171i	0.0104388	+	0.00602683i
$363$	126.377	−	105.442i	0.348145	−	0.290473i
$364$	147.866	−	342.167i	0.406224	−	0.940018i
$365$	68.7643	+	119.103i	0.188395	+	0.326310i
$366$	−201.699	−	241.746i	−0.551091	−	0.660508i
$367$	−97.1508	−	56.0900i	−0.264716	−	0.152834i	0.361768	−	0.932268i	$-0.382173\pi$
$367$	−97.1508	−	56.0900i	−0.264716	−	0.152834i	−0.626484	+	0.779434i	$0.715507\pi$
$368$	14.2433			0.0387046
$369$	−157.197	+	185.226i	−0.426008	+	0.501967i
$370$			96.0654i			0.259636i
$371$	−31.5474	−	271.467i	−0.0850334	−	0.731716i
$372$	97.0323	−	264.291i	0.260840	−	0.710461i
$373$	7.84680	+	13.5911i	0.0210370	+	0.0364371i	0.876352	−	0.481671i	$-0.159970\pi$
$373$	7.84680	+	13.5911i	0.0210370	+	0.0364371i	−0.855315	+	0.518108i	$0.826637\pi$
$374$	−247.291	+	142.774i	−0.661206	+	0.381748i
$375$	−396.712	+	68.8074i	−1.05790	+	0.183486i
$376$	210.643	+	121.615i	0.560220	+	0.323443i
$377$		−	230.304i		−	0.610885i
$378$	52.9310	+	491.404i	0.140029	+	1.30001i
$379$	197.268			0.520496			0.260248	−	0.965542i	$-0.416196\pi$
$379$	197.268			0.520496			0.260248	+	0.965542i	$0.416196\pi$
$380$	−118.428	+	205.123i	−0.311652	+	0.539797i
$381$	−91.7996	−	529.275i	−0.240944	−	1.38917i
$382$	158.139	+	273.905i	0.413976	+	0.717028i
$383$	−474.698	+	274.067i	−1.23942	+	0.715580i	−0.968976	−	0.247155i	$-0.920504\pi$
$383$	−474.698	+	274.067i	−1.23942	+	0.715580i	−0.270446	+	0.962735i	$0.587171\pi$
$384$	262.176	+	96.2557i	0.682751	+	0.250666i
$385$	339.800	−	39.4884i	0.882596	−	0.102567i
$386$	−530.339			−1.37393
$387$	−32.7474	+	179.831i	−0.0846186	+	0.464679i
$388$		−	190.241i		−	0.490311i
$389$	−152.755	+	264.579i	−0.392686	+	0.680152i	−0.992803	−	0.119760i	$-0.961787\pi$
$389$	−152.755	+	264.579i	−0.392686	+	0.680152i	0.600117	+	0.799912i	$0.295121\pi$
$390$	−416.436	+	347.451i	−1.06778	+	0.890900i
$391$	−5.26337	+	3.03881i	−0.0134613	+	0.00777189i
$392$	−144.861	+	34.1297i	−0.369543	+	0.0870656i
$393$	−224.181	−	268.691i	−0.570435	−	0.683693i
$394$	−278.522	+	482.413i	−0.706907	+	1.22440i
$395$			364.211i			0.922052i
$396$	−318.997	+	114.088i	−0.805548	+	0.288102i
$397$		−	472.112i		−	1.18920i	−0.804022	−	0.594599i	$-0.797311\pi$
$397$		−	472.112i		−	1.18920i	0.804022	−	0.594599i	$-0.202689\pi$
$398$	−453.640	−	261.909i	−1.13980	−	0.658063i
$399$	−134.800	−	455.999i	−0.337844	−	1.14286i
$400$	110.184	+	190.845i	0.275461	+	0.477112i
$401$	−347.256	−	601.466i	−0.865976	−	1.49991i	−0.866075	−	0.499915i	$-0.833365\pi$
$401$	−347.256	−	601.466i	−0.865976	−	1.49991i	9.86522e−5	−	1.00000i	$-0.499969\pi$
$402$	−146.179	−	842.804i	−0.363630	−	2.09653i
$403$	−310.112	+	537.130i	−0.769509	+	1.33283i
$404$			60.9671i			0.150909i
$405$	105.223	−	279.333i	0.259810	−	0.689711i
$406$	180.348	−	134.079i	0.444208	−	0.330243i
$407$	66.0983	−	114.486i	0.162404	−	0.281292i
$408$	−73.9231	+	12.8215i	−0.181184	+	0.0314253i
$409$	−256.107	+	147.864i	−0.626180	+	0.361525i	−0.779271	−	0.626687i	$-0.784410\pi$
$409$	−256.107	+	147.864i	−0.626180	+	0.361525i	0.153091	+	0.988212i	$0.451077\pi$
$410$	−130.064	−	225.278i	−0.317230	−	0.549459i
$411$	−201.730	−	74.0633i	−0.490826	−	0.180203i
$412$	−36.8771	−	21.2910i	−0.0895075	−	0.0516772i
$413$	−194.608	−	261.766i	−0.471205	−	0.633815i
$414$	−16.3573	+	5.85013i	−0.0395103	+	0.0141308i
$415$	−529.598			−1.27614
$416$	622.449	+	359.371i	1.49627	+	0.863873i
$417$	418.938	+	502.117i	1.00465	+	1.20412i
$418$	680.042	−	392.623i	1.62690	−	0.939289i
$419$	−191.051	+	110.304i	−0.455970	+	0.263254i	−0.710348	−	0.703850i	$-0.751463\pi$
$419$	−191.051	+	110.304i	−0.455970	+	0.263254i	0.254378	+	0.967105i	$0.418129\pi$
$420$	−213.570	−	51.3982i	−0.508499	−	0.122377i
$421$	−355.146	+	615.130i	−0.843576	+	1.46112i	0.0432759	+	0.999063i	$0.486221\pi$
$421$	−355.146	+	615.130i	−0.843576	+	1.46112i	−0.886852	+	0.462054i	$0.847113\pi$
$422$	747.298			1.77085
$423$	−709.069	−	129.122i	−1.67629	−	0.305254i
$424$	118.582			0.279673
$425$	−81.4336	−	47.0157i	−0.191608	−	0.110625i
$426$	617.337	+	226.650i	1.44915	+	0.532042i
$427$	−111.438	+	257.872i	−0.260979	+	0.603916i
$428$	73.5009	+	127.307i	0.171731	+	0.297447i
$429$	735.353	−	127.543i	1.71411	−	0.297302i
$430$	−169.500	−	97.8607i	−0.394185	−	0.227583i
$431$	72.6197			0.168491			0.0842456	−	0.996445i	$-0.473152\pi$
$431$	72.6197			0.168491			0.0842456	+	0.996445i	$0.473152\pi$
$432$	−520.997	−	4.37221i	−1.20601	−	0.0101209i
$433$			572.654i			1.32253i	0.750154	+	0.661264i	$0.229980\pi$
$433$			572.654i			1.32253i	−0.750154	+	0.661264i	$0.770020\pi$
$434$	−601.162	+	69.8616i	−1.38517	+	0.160971i
$435$	−133.725	+	23.1939i	−0.307414	+	0.0533192i
$436$	−200.789	−	347.776i	−0.460525	−	0.797652i
$437$	14.4741	−	8.35663i	0.0331215	−	0.0191227i
$438$	−100.907	+	274.844i	−0.230381	+	0.627498i
$439$	386.765	+	223.299i	0.881013	+	0.508653i	0.870992	−	0.491297i	$-0.163477\pi$
$439$	386.765	+	223.299i	0.881013	+	0.508653i	0.0100205	+	0.999950i	$0.496810\pi$
$440$			148.430i			0.337342i
$441$	370.119	−	239.778i	0.839271	−	0.543713i
$442$	−403.939			−0.913888
$443$	−301.249	+	521.778i	−0.680020	+	1.17783i	0.294955	+	0.955511i	$0.404695\pi$
$443$	−301.249	+	521.778i	−0.680020	+	1.17783i	−0.974974	+	0.222317i	$0.928638\pi$
$444$	−65.1810	+	54.3834i	−0.146804	+	0.122485i
$445$	245.271	+	424.821i	0.551170	+	0.954654i
$446$	853.006	−	492.483i	1.91257	−	1.10422i
$447$	60.8550	−	50.7740i	0.136141	−	0.113588i
$448$	18.5883	+	159.953i	0.0414916	+	0.357037i
$449$	−59.7471			−0.133067			−0.0665335	−	0.997784i	$-0.521194\pi$
$449$	−59.7471			−0.133067			−0.0665335	+	0.997784i	$0.521194\pi$
$450$	−204.923	−	173.914i	−0.455385	−	0.386475i
$451$			357.966i			0.793717i
$452$	−151.839	+	262.993i	−0.335927	+	0.581843i
$453$	−234.598	−	86.1307i	−0.517877	−	0.190134i
$454$	−500.419	+	288.917i	−1.10224	+	0.636381i
$455$	444.215	+	191.965i	0.976297	+	0.421902i
$456$	203.286	−	35.2588i	0.445803	−	0.0773219i
$457$	355.662	−	616.024i	0.778253	−	1.34797i	−0.154695	−	0.987962i	$-0.549439\pi$
$457$	355.662	−	616.024i	0.778253	−	1.34797i	0.932948	−	0.360012i	$-0.117227\pi$
$458$			75.2213i			0.164239i
$459$	193.459	−	109.539i	0.421478	−	0.238647i
$460$		−	7.72094i		−	0.0167847i
$461$	1.39410	+	0.804886i	0.00302409	+	0.00174596i	0.501511	−	0.865151i	$-0.332778\pi$
$461$	1.39410	+	0.804886i	0.00302409	+	0.00174596i	−0.498487	+	0.866897i	$0.666111\pi$
$462$	527.986	+	501.594i	1.14283	+	1.08570i
$463$	21.4251	+	37.1094i	0.0462745	+	0.0801499i	0.888235	−	0.459389i	$-0.151932\pi$
$463$	21.4251	+	37.1094i	0.0462745	+	0.0801499i	−0.841960	+	0.539539i	$0.818598\pi$
$464$	118.450	+	205.161i	0.255279	+	0.442157i
$465$	343.114	+	125.971i	0.737880	+	0.270906i
$466$	530.418	−	918.711i	1.13824	−	1.97148i
$467$			231.151i			0.494969i	0.968892	+	0.247485i	$0.0796040\pi$
$467$			231.151i			0.494969i	−0.968892	+	0.247485i	$0.920396\pi$
$468$	−471.496	−	85.8599i	−1.00747	−	0.183461i
$469$	−612.510	+	455.365i	−1.30599	+	0.970928i
$470$	385.863	−	668.334i	0.820985	−	1.42199i
$471$	−284.213	−	340.643i	−0.603425	−	0.723233i
$472$	122.568	−	70.7644i	0.259677	−	0.149925i
$473$	134.667	+	233.251i	0.284709	+	0.493130i
$474$	−595.354	+	496.730i	−1.25602	+	1.04795i
$475$	223.940	+	129.292i	0.471452	+	0.272193i
$476$	−97.6125	−	131.298i	−0.205068	−	0.275836i
$477$	−330.854	+	118.329i	−0.693615	+	0.248069i
$478$	346.270			0.724415
$479$	213.744	+	123.405i	0.446229	+	0.257631i	0.706236	−	0.707976i	$-0.250392\pi$
$479$	213.744	+	123.405i	0.446229	+	0.257631i	−0.260007	+	0.965607i	$0.583725\pi$
$480$	145.981	−	397.616i	0.304127	−	0.828366i
$481$	161.953	−	93.5035i	0.336700	−	0.194394i
$482$	−187.650	+	108.340i	−0.389316	+	0.224771i
$483$	11.2377	+	10.6760i	0.0232665	+	0.0221035i
$484$	−77.8647	+	134.866i	−0.160877	+	0.278648i
$485$	246.979			0.509234
$486$	600.118	−	208.967i	1.23481	−	0.429974i
$487$	−618.473			−1.26996			−0.634982	−	0.772527i	$-0.718993\pi$
$487$	−618.473			−1.26996			−0.634982	+	0.772527i	$0.718993\pi$
$488$	−105.561	−	60.9454i	−0.216313	−	0.124888i
$489$	−41.5072	−	239.311i	−0.0848818	−	0.489390i
$490$	108.288	+	459.619i	0.220996	+	0.937998i
$491$	−160.661	−	278.274i	−0.327212	−	0.566749i	0.654745	−	0.755850i	$-0.272776\pi$
$491$	−160.661	−	278.274i	−0.327212	−	0.566749i	−0.981958	+	0.189101i	$0.939443\pi$
$492$	79.2222	−	215.781i	0.161021	−	0.438580i
$493$	−87.5422	−	50.5425i	−0.177570	−	0.102520i
$494$	1110.82			2.24862
$495$	−148.115	−	414.136i	−0.299221	−	0.836638i
$496$		−	637.986i		−	1.28626i
$497$	−67.7345	−	582.858i	−0.136287	−	1.17275i
$498$	−722.294	−	865.703i	−1.45039	−	1.73836i
$499$	−80.4854	−	139.405i	−0.161293	−	0.279368i	0.774039	−	0.633137i	$-0.218233\pi$
$499$	−80.4854	−	139.405i	−0.161293	−	0.279368i	−0.935333	+	0.353769i	$0.884900\pi$
$500$	329.926	−	190.483i	0.659851	−	0.380965i
$501$	4.28623	+	5.13724i	0.00855534	+	0.0102540i
$502$	414.187	+	239.131i	0.825074	+	0.476357i
$503$		−	941.248i		−	1.87127i	−0.352971	−	0.935634i	$-0.614829\pi$
$503$		−	941.248i		−	1.87127i	0.352971	−	0.935634i	$-0.385171\pi$
$504$	84.8055	+	171.530i	0.168265	+	0.340337i
$505$	−79.1501			−0.156733
$506$	−12.7986	+	22.1678i	−0.0252937	+	0.0438099i
$507$	515.147	+	189.132i	1.01607	+	0.373041i
$508$	254.133	+	440.171i	0.500262	+	0.866479i
$509$	410.539	−	237.025i	0.806560	−	0.465667i	−0.0392001	−	0.999231i	$-0.512481\pi$
$509$	410.539	−	237.025i	0.806560	−	0.465667i	0.845760	+	0.533564i	$0.179148\pi$
$510$	40.6806	+	234.546i	0.0797659	+	0.459894i
$511$	259.494	−	30.1560i	0.507816	−	0.0590137i
$512$	−504.886			−0.986105
$513$	−532.005	+	301.229i	−1.03705	+	0.587191i
$514$			124.312i			0.241852i
$515$	27.6409	−	47.8754i	0.0536716	−	0.0929620i
$516$	−29.5560	−	170.406i	−0.0572791	−	0.330245i
$517$	−919.702	+	530.990i	−1.77892	+	1.02706i
$518$	167.508	+	72.3875i	0.323374	+	0.139744i
$519$	174.672	−	475.762i	0.336554	−	0.916689i
$520$	−104.986	+	181.841i	−0.201896	+	0.349694i
$521$			179.082i			0.343728i	0.985121	+	0.171864i	$0.0549790\pi$
$521$			179.082i			0.343728i	−0.985121	+	0.171864i	$0.945021\pi$
$522$	−220.295	−	186.960i	−0.422021	−	0.358160i
$523$		−	742.307i		−	1.41932i	−0.704542	−	0.709662i	$-0.748848\pi$
$523$		−	742.307i		−	1.41932i	0.704542	−	0.709662i	$-0.251152\pi$
$524$	286.740	+	165.549i	0.547213	+	0.315934i
$525$	−56.1131	+	233.161i	−0.106882	+	0.444117i
$526$	−535.554	−	927.607i	−1.01816	−	1.76351i
$527$	136.115	+	235.757i	0.258282	+	0.447357i
$528$	−589.474	+	491.824i	−1.11643	+	0.931485i
$529$	264.228	−	457.656i	0.499485	−	0.865133i
$530$		−	376.240i		−	0.709886i
$531$	−271.362	+	319.746i	−0.511039	+	0.602159i
$532$	268.431	+	361.065i	0.504570	+	0.678694i
$533$	−253.192	+	438.541i	−0.475031	+	0.822778i
$534$	−359.917	+	980.323i	−0.674002	+	1.83581i
$535$	−165.276	+	95.4220i	−0.308927	+	0.178359i
$536$	−165.583	−	286.798i	−0.308923	−	0.535070i
$537$	38.3967	+	221.378i	0.0715023	+	0.412250i
$538$	349.751	+	201.929i	0.650094	+	0.375332i
$539$	187.192	−	622.258i	0.347294	−	1.15447i
$540$	−2.37007	+	282.420i	−0.00438902	+	0.522999i
$541$	−546.499			−1.01016			−0.505082	−	0.863071i	$-0.668538\pi$
$541$	−546.499			−1.01016			−0.505082	+	0.863071i	$0.668538\pi$
$542$	−140.865	−	81.3283i	−0.259898	−	0.150052i
$543$	−4.93209	+	0.855441i	−0.00908303	+	0.00157540i
$544$	273.206	−	157.735i	0.502216	−	0.289955i
$545$	451.498	−	260.673i	0.828437	−	0.478298i
$546$	292.050	+	987.945i	0.534890	+	1.80942i
$547$	192.148	−	332.810i	0.351276	−	0.608429i	−0.635197	−	0.772350i	$-0.719081\pi$
$547$	192.148	−	332.810i	0.351276	−	0.608429i	0.986473	+	0.163922i	$0.0524144\pi$
$548$	203.330			0.371041
$549$	355.340	+	64.7079i	0.647250	+	0.117865i
$550$	−396.033			−0.720060
$551$	240.738	+	138.990i	0.436911	+	0.252251i
$552$	−5.16418	+	4.30870i	−0.00935539	+	0.00780561i
$553$	635.068	+	274.441i	1.14841	+	0.496277i
$554$	−7.52189	−	13.0283i	−0.0135774	−	0.0235168i
$555$	−70.6028	−	84.6207i	−0.127212	−	0.152470i
$556$	−535.845	−	309.370i	−0.963749	−	0.556421i
$557$	−314.249			−0.564182			−0.282091	−	0.959388i	$-0.591028\pi$
$557$	−314.249			−0.564182			−0.282091	+	0.959388i	$0.591028\pi$
$558$	262.039	+	732.675i	0.469605	+	1.31304i
$559$			381.004i			0.681581i
$560$	−494.450	+	57.4605i	−0.882947	+	0.102608i
$561$	112.900	−	307.510i	0.201247	−	0.548146i
$562$	329.742	+	571.130i	0.586730	+	1.01625i
$563$	98.8474	−	57.0696i	0.175573	−	0.101367i	−0.409638	−	0.912248i	$-0.634345\pi$
$563$	98.8474	−	57.0696i	0.175573	−	0.101367i	0.585211	+	0.810881i	$0.301012\pi$
$564$	671.909	−	116.539i	1.19133	−	0.206629i
$565$	−341.429	−	197.124i	−0.604299	−	0.348892i
$566$			354.874i			0.626986i
$567$	−407.780	−	393.960i	−0.719189	−	0.694814i
$568$	254.603			0.448244
$569$	178.041	−	308.376i	0.312901	−	0.541961i	−0.666088	−	0.745873i	$-0.732032\pi$
$569$	178.041	−	308.376i	0.312901	−	0.541961i	0.978989	+	0.203912i	$0.0653657\pi$
$570$	−111.870	−	644.993i	−0.196264	−	1.13157i
$571$	−170.256	−	294.892i	−0.298171	−	0.516448i	0.677546	−	0.735480i	$-0.263043\pi$
$571$	−170.256	−	294.892i	−0.298171	−	0.516448i	−0.975718	+	0.219032i	$0.929710\pi$
$572$	−611.556	+	353.082i	−1.06915	+	0.617276i
$573$	−340.604	−	125.050i	−0.594423	−	0.218237i
$574$	−490.820	+	57.0386i	−0.855087	+	0.0993705i
$575$	−8.42921			−0.0146595
$576$	194.945	−	69.7215i	0.338446	−	0.121044i
$577$		−	390.835i		−	0.677356i	−0.940902	−	0.338678i	$-0.890020\pi$
$577$		−	390.835i		−	0.677356i	0.940902	−	0.338678i	$-0.109980\pi$
$578$	289.228	−	500.957i	0.500394	−	0.866708i
$579$	467.157	−	389.770i	0.806835	−	0.673178i
$580$	111.213	−	64.2086i	0.191746	−	0.110705i
$581$	−399.065	+	923.452i	−0.686859	+	1.58942i
$582$	336.842	+	403.721i	0.578767	+	0.693679i
$583$	−258.874	+	448.383i	−0.444037	+	0.769095i
$584$			113.352i			0.194095i
$585$	111.467	−	612.116i	0.190542	−	1.04635i
$586$			220.132i			0.375652i
$587$	878.394	+	507.141i	1.49641	+	0.863954i	0.999991	−	0.00412823i	$-0.00131406\pi$
$587$	878.394	+	507.141i	1.49641	+	0.863954i	0.496421	+	0.868082i	$0.334647\pi$
$588$	−250.552	+	333.668i	−0.426109	+	0.567463i
$589$	−374.311	−	648.325i	−0.635502	−	1.10072i
$590$	−224.524	−	388.886i	−0.380549	−	0.659130i
$591$	−109.207	−	629.640i	−0.184784	−	1.06538i
$592$	−96.1812	+	166.591i	−0.162468	+	0.281403i
$593$			769.152i			1.29705i	0.761193	+	0.648526i	$0.224614\pi$
$593$			769.152i			1.29705i	−0.761193	+	0.648526i	$0.775386\pi$
$594$	474.957	−	806.934i	0.799590	−	1.35847i
$595$	170.457	−	126.725i	0.286482	−	0.212983i
$596$	−37.4947	+	64.9427i	−0.0629106	+	0.108964i
$597$	592.085	−	102.694i	0.991767	−	0.172016i
$598$	−31.3588	+	18.1050i	−0.0524395	+	0.0302760i
$599$	263.413	+	456.244i	0.439754	+	0.761677i	0.997670	−	0.0682206i	$-0.0217322\pi$
$599$	263.413	+	456.244i	0.439754	+	0.761677i	−0.557916	+	0.829897i	$0.688399\pi$
$600$	−97.6814	−	35.8629i	−0.162802	−	0.0597714i
$601$	−35.7573	−	20.6445i	−0.0594963	−	0.0343502i	0.469957	−	0.882689i	$-0.344269\pi$
$601$	−35.7573	−	20.6445i	−0.0594963	−	0.0343502i	−0.529453	+	0.848339i	$0.677603\pi$
$602$	−298.360	+	221.813i	−0.495615	+	0.368461i
$603$	748.179	+	634.963i	1.24076	+	1.05301i
$604$	236.460			0.391489
$605$	−175.088	−	101.087i	−0.289402	−	0.167086i
$606$	−107.949	−	129.382i	−0.178134	−	0.213502i
$607$	−388.261	+	224.163i	−0.639640	+	0.369296i	−0.784476	−	0.620159i	$-0.787068\pi$
$607$	−388.261	+	224.163i	−0.639640	+	0.369296i	0.144836	+	0.989456i	$0.453735\pi$
$608$	−751.307	+	433.767i	−1.23570	+	0.713433i
$609$	−60.3224	+	250.652i	−0.0990515	+	0.411579i
$610$	−193.370	+	334.926i	−0.317000	+	0.549059i
$611$	−1502.29			−2.45874
$612$	−136.111	+	160.380i	−0.222404	+	0.262059i
$613$	1000.80			1.63262			0.816309	−	0.577615i	$-0.196016\pi$
$613$	1000.80			1.63262			0.816309	+	0.577615i	$0.196016\pi$
$614$	−352.140	−	203.308i	−0.573518	−	0.331121i
$615$	280.136	+	102.850i	0.455506	+	0.167235i
$616$	258.816	+	111.846i	0.420155	+	0.181568i
$617$	−88.6179	−	153.491i	−0.143627	−	0.248769i	0.785233	−	0.619201i	$-0.212543\pi$
$617$	−88.6179	−	153.491i	−0.143627	−	0.248769i	−0.928860	+	0.370431i	$0.879210\pi$
$618$	115.957	−	20.1121i	0.187633	−	0.0325439i
$619$	−290.267	−	167.586i	−0.468928	−	0.270736i	0.246863	−	0.969050i	$-0.420600\pi$
$619$	−290.267	−	167.586i	−0.468928	−	0.270736i	−0.715791	+	0.698315i	$0.753934\pi$
$620$	−345.837			−0.557801
$621$	10.1090	−	17.1749i	0.0162786	−	0.0276568i
$622$		−	507.759i		−	0.816332i
$623$	925.570	−	107.561i	1.48567	−	0.172651i
$624$	−1070.03	+	185.590i	−1.71479	+	0.297420i
$625$	104.544	+	181.075i	0.167270	+	0.289720i
$626$	−785.323	+	453.407i	−1.25451	+	0.724292i
$627$	−310.470	+	845.642i	−0.495168	+	1.34871i
$628$	363.524	+	209.881i	0.578860	+	0.334205i
$629$		−	82.0812i		−	0.130495i
$630$	544.235	−	269.074i	0.863865	−	0.427101i
$631$	1077.15			1.70705			0.853524	−	0.521053i	$-0.174461\pi$
$631$	1077.15			1.70705			0.853524	+	0.521053i	$0.174461\pi$
$632$	−150.092	+	259.967i	−0.237487	+	0.411340i
$633$	−658.269	+	549.223i	−1.03992	+	0.867651i
$634$	90.2990	+	156.402i	0.142427	+	0.246691i
$635$	−571.449	+	329.926i	−0.899920	+	0.519569i
$636$	255.281	−	212.992i	0.401385	−	0.334893i
$637$	669.453	−	629.920i	1.05095	−	0.988886i
$638$	−425.741			−0.667306
$639$	−710.367	+	254.061i	−1.11169	+	0.397591i
$640$		−	343.069i		−	0.536045i
$641$	−102.765	+	177.995i	−0.160320	+	0.277683i	−0.934984	−	0.354691i	$-0.884586\pi$
$641$	−102.765	+	177.995i	−0.160320	+	0.277683i	0.774663	+	0.632374i	$0.217919\pi$
$642$	−381.393	−	140.025i	−0.594069	−	0.218107i
$643$	413.913	−	238.973i	0.643721	−	0.371653i	−0.142325	−	0.989820i	$-0.545458\pi$
$643$	413.913	−	238.973i	0.643721	−	0.371653i	0.786047	+	0.618167i	$0.212125\pi$
$644$	−13.4629	−	5.81791i	−0.0209051	−	0.00903402i
$645$	221.229	−	38.3708i	0.342990	−	0.0594897i
$646$	243.780	−	422.240i	0.377369	−	0.653622i
$647$			308.180i			0.476322i	0.971226	+	0.238161i	$0.0765446\pi$
$647$			308.180i			0.476322i	−0.971226	+	0.238161i	$0.923455\pi$
$648$	190.220	−	156.020i	0.293549	−	0.240772i
$649$			617.939i			0.952141i
$650$	−485.176	−	280.117i	−0.746425	−	0.430949i
$651$	478.199	−	503.360i	0.734561	−	0.773211i
$652$	114.906	+	199.023i	0.176237	+	0.305251i
$653$	350.775	+	607.559i	0.537174	+	0.930413i	0.999055	+	0.0434705i	$0.0138415\pi$
$653$	350.775	+	607.559i	0.537174	+	0.930413i	−0.461881	+	0.886942i	$0.652825\pi$
$654$	1041.88	+	382.518i	1.59309	+	0.584890i
$655$	−214.923	+	372.258i	−0.328127	+	0.568332i
$656$		−	520.885i		−	0.794032i
$657$	−113.110	−	316.262i	−0.172162	−	0.481373i
$658$	−874.606	−	1176.43i	−1.32919	−	1.78788i
$659$	362.623	−	628.082i	0.550263	−	0.953084i	−0.447992	−	0.894038i	$-0.647861\pi$
$659$	362.623	−	628.082i	0.550263	−	0.953084i	0.998255	−	0.0590463i	$-0.0188060\pi$
$660$	266.606	+	319.540i	0.403948	+	0.484151i
$661$	716.938	−	413.924i	1.08463	−	0.626210i	0.152486	−	0.988306i	$-0.451272\pi$
$661$	716.938	−	413.924i	1.08463	−	0.626210i	0.932141	+	0.362096i	$0.117939\pi$
$662$	−329.029	−	569.895i	−0.497023	−	0.860868i
$663$	355.816	−	296.873i	0.536675	−	0.447772i
$664$	−378.017	−	218.248i	−0.569303	−	0.328687i
$665$	−468.750	+	348.489i	−0.704888	+	0.524043i
$666$	42.0327	−	230.820i	0.0631121	−	0.346577i
$667$	−9.06152			−0.0135855
$668$	−5.48232	−	3.16522i	−0.00820706	−	0.00473835i
$669$	−389.436	+	1060.72i	−0.582116	+	1.58554i
$670$	−909.961	+	525.366i	−1.35815	+	0.784129i
$671$	460.896	−	266.098i	0.686879	−	0.396570i
$672$	−583.315	−	554.158i	−0.868029	−	0.824639i
$673$	−582.601	+	1009.10i	−0.865678	+	1.49940i	0.000694329		1.00000i	$0.499779\pi$
$673$	−582.601	+	1009.10i	−0.865678	+	1.49940i	−0.866372	+	0.499399i	$0.833554\pi$
$674$	−736.321			−1.09247
$675$	308.327	+	2.58748i	0.456781	+	0.00383331i
$676$	−519.235			−0.768099
$677$	255.760	+	147.663i	0.377785	+	0.218114i	0.676854	−	0.736117i	$-0.263343\pi$
$677$	255.760	+	147.663i	0.377785	+	0.218114i	−0.299069	+	0.954231i	$0.596676\pi$
$678$	−143.432	−	826.961i	−0.211551	−	1.21971i
$679$	186.104	−	430.652i	0.274086	−	0.634245i
$680$	46.0804	+	79.8136i	0.0677653	+	0.117373i
$681$	228.464	−	622.278i	0.335483	−	0.913770i
$682$	992.942	+	573.275i	1.45593	+	0.840580i
$683$	−637.558			−0.933467			−0.466734	−	0.884398i	$-0.654569\pi$
$683$	−637.558			−0.933467			−0.466734	+	0.884398i	$0.654569\pi$
$684$	374.301	−	441.040i	0.547224	−	0.644796i
$685$			263.972i			0.385361i
$686$	883.027	+	157.514i	1.28721	+	0.229612i
$687$	−55.2836	−	66.2599i	−0.0804710	−	0.0964482i
$688$	−195.957	−	339.408i	−0.284822	−	0.493326i
$689$	−634.287	+	366.206i	−0.920591	+	0.531504i
$690$	13.6708	+	16.3851i	0.0198127	+	0.0237465i
$691$	−635.956	−	367.169i	−0.920342	−	0.531360i	−0.0365976	−	0.999330i	$-0.511652\pi$
$691$	−635.956	−	367.169i	−0.920342	−	0.531360i	−0.883744	+	0.467971i	$0.844985\pi$
$692$			479.537i			0.692972i
$693$	−833.729	−	53.7962i	−1.20307	−	0.0776280i
$694$	549.534			0.791835
$695$	401.637	−	695.656i	0.577895	−	1.00094i
$696$	−105.009	−	38.5531i	−0.150875	−	0.0553923i
$697$	111.131	+	192.484i	0.159442	+	0.276161i
$698$	167.486	−	96.6981i	0.239951	−	0.138536i
$699$	207.975	+	1199.09i	0.297532	+	1.71544i
$700$	−26.1933	−	225.395i	−0.0374190	−	0.321992i
$701$	1045.20			1.49101			0.745507	−	0.666498i	$-0.232208\pi$
$701$	1045.20			1.49101			0.745507	+	0.666498i	$0.232208\pi$
$702$	1152.61	−	652.627i	1.64190	−	0.929668i
$703$			225.721i			0.321082i
$704$	152.533	−	264.195i	0.216666	−	0.375276i
$705$	151.295	+	872.301i	0.214604	+	1.23731i
$706$	734.857	−	424.270i	1.04087	−	0.600949i
$707$	−59.6415	+	138.013i	−0.0843585	+	0.195209i
$708$	136.757	−	372.493i	0.193160	−	0.526119i
$709$	−25.0780	+	43.4364i	−0.0353710	+	0.0612644i	−0.883169	−	0.469055i	$-0.844595\pi$
$709$	−25.0780	+	43.4364i	−0.0353710	+	0.0612644i	0.847798	+	0.530319i	$0.177928\pi$
$710$		−	807.812i		−	1.13776i
$711$	159.358	−	875.105i	0.224132	−	1.23081i
$712$			404.306i			0.567845i
$713$	21.1339	+	12.2017i	0.0296408	+	0.0171131i
$714$	439.627	+	105.802i	0.615724	+	0.148182i
$715$	−458.386	−	793.948i	−0.641100	−	1.11042i
$716$	−106.295	−	184.109i	−0.148457	−	0.257136i
$717$	−305.018	+	254.490i	−0.425408	+	0.354937i
$718$	341.489	−	591.476i	0.475611	−	0.823782i
$719$		−	1315.02i		−	1.82896i	−0.404629	−	0.914481i	$-0.632599\pi$
$719$		−	1315.02i		−	1.82896i	0.404629	−	0.914481i	$-0.367401\pi$
$720$	215.525	+	602.618i	0.299340	+	0.836970i
$721$	−62.6515	−	84.2722i	−0.0868953	−	0.116882i
$722$	−198.369	+	343.585i	−0.274750	+	0.475880i
$723$	85.6708	−	233.346i	0.118493	−	0.322746i
$724$	4.10177	−	2.36816i	0.00566543	−	0.00327094i
$725$	−70.0988	−	121.415i	−0.0966880	−	0.167468i
$726$	−73.5532	−	424.074i	−0.101313	−	0.584125i
$727$	−701.577	−	405.056i	−0.965030	−	0.557160i	−0.0673125	−	0.997732i	$-0.521442\pi$
$727$	−701.577	−	405.056i	−0.965030	−	0.557160i	−0.897717	+	0.440572i	$0.854776\pi$
$728$	237.963	+	320.083i	0.326873	+	0.439675i
$729$	−375.044	+	625.126i	−0.514464	+	0.857512i
$730$	359.646			0.492665
$731$	144.826	+	83.6152i	0.198120	+	0.114385i
$732$	−336.718	+	58.4017i	−0.459997	+	0.0797838i
$733$	87.1731	−	50.3294i	0.118926	−	0.0686622i	−0.439357	−	0.898313i	$-0.644794\pi$
$733$	87.1731	−	50.3294i	0.118926	−	0.0686622i	0.558283	+	0.829650i	$0.311460\pi$
$734$	−254.055	+	146.679i	−0.346124	+	0.199835i
$735$	−433.182	−	325.277i	−0.589363	−	0.442554i
$736$	14.1398	−	24.4909i	0.0192117	−	0.0332756i
$737$	1445.93			1.96191
$738$	213.943	+	598.194i	0.289895	+	0.810561i
$739$	422.292			0.571437			0.285719	−	0.958314i	$-0.407768\pi$
$739$	422.292			0.571437			0.285719	+	0.958314i	$0.407768\pi$
$740$	90.3048	+	52.1375i	0.122034	+	0.0704561i
$741$	−978.482	+	816.390i	−1.32049	+	1.10174i
$742$	−656.042	−	283.505i	−0.884154	−	0.382083i
$743$	405.350	+	702.087i	0.545559	+	0.944936i	0.998572	+	0.0534316i	$0.0170159\pi$
$743$	405.350	+	702.087i	0.545559	+	0.944936i	−0.453013	+	0.891504i	$0.649651\pi$
$744$	192.996	+	231.314i	0.259403	+	0.310906i
$745$	−84.3114	−	48.6772i	−0.113170	−	0.0653386i
$746$	41.0397			0.0550130
$747$	1272.49	+	231.722i	1.70347	+	0.310203i
$748$			309.950i			0.414372i
$749$	41.8465	+	360.091i	0.0558699	+	0.480763i
$750$	−362.884	+	988.405i	−0.483846	+	1.31787i
$751$	−199.187	−	345.003i	−0.265230	−	0.459391i	0.702394	−	0.711788i	$-0.252114\pi$
$751$	−199.187	−	345.003i	−0.265230	−	0.459391i	−0.967624	+	0.252397i	$0.918781\pi$
$752$	1338.28	−	772.656i	1.77963	−	1.02747i
$753$	−540.592	+	93.7625i	−0.717918	+	0.124519i
$754$	−521.571	−	301.129i	−0.691739	−	0.399376i
$755$			306.982i			0.406599i
$756$	490.664	+	216.942i	0.649027	+	0.286961i
$757$	730.998			0.965652			0.482826	−	0.875716i	$-0.339610\pi$
$757$	730.998			0.965652			0.482826	+	0.875716i	$0.339610\pi$
$758$	257.934	−	446.754i	0.340282	−	0.589385i
$759$	−5.01828	−	28.9331i	−0.00661170	−	0.0381201i
$760$	−126.720	−	219.485i	−0.166736	−	0.288796i
$761$	−79.2466	+	45.7530i	−0.104135	+	0.0601222i	−0.551163	−	0.834398i	$-0.685816\pi$
$761$	−79.2466	+	45.7530i	−0.104135	+	0.0601222i	0.447028	+	0.894520i	$0.352482\pi$
$762$	−1318.68	−	484.143i	−1.73056	−	0.635358i
$763$	−114.316	−	983.693i	−0.149824	−	1.28924i
$764$	343.307			0.449354
$765$	−208.213	−	176.705i	−0.272173	−	0.230988i
$766$			1433.40i			1.87129i
$767$	−437.072	+	757.031i	−0.569846	+	0.987003i
$768$	772.757	−	644.745i	1.00619	−	0.839512i
$769$	391.783	−	226.196i	0.509470	−	0.294143i	−0.223146	−	0.974785i	$-0.571633\pi$
$769$	391.783	−	226.196i	0.509470	−	0.294143i	0.732616	+	0.680642i	$0.238299\pi$
$770$	354.868	−	821.179i	0.460868	−	1.06647i
$771$	−91.3624	−	109.502i	−0.118499	−	0.142026i
$772$	−287.830	+	498.537i	−0.372837	+	0.645773i
$773$		−	1138.79i		−	1.47321i	−0.676321	−	0.736607i	$-0.736427\pi$
$773$		−	1138.79i		−	1.47321i	0.676321	−	0.736607i	$-0.263573\pi$
$774$	364.446	+	309.298i	0.470861	+	0.399609i
$775$			377.562i			0.487177i
$776$	176.289	+	101.780i	0.227176	+	0.131160i
$777$	−200.753	+	59.3452i	−0.258369	+	0.0763773i
$778$	399.463	+	691.890i	0.513449	+	0.889319i
$779$	−305.606	−	529.326i	−0.392306	−	0.679494i
$780$	100.604	+	580.037i	0.128979	+	0.743637i
$781$	−555.820	+	962.709i	−0.711677	+	1.23266i
$782$			15.8933i			0.0203240i
$783$	331.456	+	2.78158i	0.423315	+	0.00355247i
$784$	−272.387	+	905.462i	−0.347432	+	1.15493i
$785$	−272.476	+	471.943i	−0.347103	+	0.601201i
$786$	−901.631	+	156.383i	−1.14711	+	0.198960i
$787$	−252.358	+	145.699i	−0.320659	+	0.185132i	−0.651686	−	0.758489i	$-0.725938\pi$
$787$	−252.358	+	145.699i	−0.320659	+	0.185132i	0.331028	+	0.943621i	$0.392605\pi$
$788$	302.324	+	523.640i	0.383660	+	0.664518i
$789$	1153.49	+	423.495i	1.46197	+	0.536749i
$790$	824.831	+	476.217i	1.04409	+	0.602806i
$791$	−600.996	+	446.806i	−0.759793	+	0.564862i
$792$	64.9447	−	356.640i	0.0820008	−	0.450304i
$793$	752.852			0.949372
$794$	−1069.20	−	617.300i	−1.34659	−	0.777457i
$795$	276.516	+	331.417i	0.347818	+	0.416876i
$796$	−492.407	+	284.292i	−0.618602	+	0.357150i
$797$	833.171	−	481.032i	1.04538	−	0.603553i	0.124031	−	0.992278i	$-0.460418\pi$
$797$	833.171	−	481.032i	1.04538	−	0.603553i	0.921354	+	0.388725i	$0.127085\pi$
$798$	−1208.96	−	290.951i	−1.51499	−	0.364601i
$799$	−329.693	+	571.045i	−0.412632	+	0.714700i
$800$	437.535			0.546919
$801$	−403.445	−	1128.05i	−0.503677	−	1.40831i
$802$	−1816.19			−2.26458
$803$	−428.607	−	247.456i	−0.533757	−	0.308165i
$804$	−871.601	−	320.001i	−1.08408	−	0.398011i
$805$	7.55306	−	17.4781i	0.00938268	−	0.0217119i
$806$	810.962	+	1404.63i	1.00616	+	1.74271i
$807$	−456.490	+	79.1755i	−0.565663	+	0.0981109i
$808$	−56.4959	−	32.6179i	−0.0699206	−	0.0403687i
$809$	681.749			0.842706			0.421353	−	0.906897i	$-0.361555\pi$
$809$	681.749			0.842706			0.421353	+	0.906897i	$0.361555\pi$
$810$	−495.026	−	603.536i	−0.611143	−	0.745106i
$811$		−	1531.25i		−	1.88810i	−0.329801	−	0.944050i	$-0.606982\pi$
$811$		−	1531.25i		−	1.88810i	0.329801	−	0.944050i	$-0.393018\pi$
$812$	−28.1582	−	242.302i	−0.0346776	−	0.298402i
$813$	183.855	−	31.8886i	0.226144	−	0.0392233i
$814$	−172.851	−	299.387i	−0.212348	−	0.367797i
$815$	−258.381	+	149.176i	−0.317032	+	0.183038i
$816$	−164.283	+	447.465i	−0.201327	+	0.548364i
$817$	−398.266	−	229.939i	−0.487474	−	0.281443i
$818$			773.345i			0.945410i
$819$	−983.343	−	655.607i	−1.20066	−	0.800497i
$820$	−282.359			−0.344340
$821$	−46.3290	+	80.2441i	−0.0564299	+	0.0977395i	−0.892860	−	0.450334i	$-0.851305\pi$
$821$	−46.3290	+	80.2441i	−0.0564299	+	0.0977395i	0.836430	+	0.548073i	$0.184638\pi$
$822$	−431.499	+	360.019i	−0.524938	+	0.437979i
$823$	−253.184	−	438.528i	−0.307636	−	0.532841i	0.670209	−	0.742172i	$-0.266204\pi$
$823$	−253.184	−	438.528i	−0.307636	−	0.532841i	−0.977845	+	0.209332i	$0.932871\pi$
$824$	39.4591	−	22.7817i	0.0478872	−	0.0276477i
$825$	348.852	−	291.063i	0.422851	−	0.352803i
$826$	−847.278	+	98.4630i	−1.02576	+	0.119205i
$827$	−909.882			−1.10022			−0.550110	−	0.835092i	$-0.685414\pi$
$827$	−909.882			−1.10022			−0.550110	+	0.835092i	$0.685414\pi$
$828$	−3.37824	+	18.5514i	−0.00408000	+	0.0224051i
$829$		−	162.129i		−	0.195572i	−0.995207	−	0.0977862i	$-0.968824\pi$
$829$		−	162.129i		−	0.195572i	0.995207	−	0.0977862i	$-0.0311761\pi$
$830$	−692.466	+	1199.39i	−0.834296	+	1.44504i
$831$	16.2009	+	5.94800i	0.0194956	+	0.00715765i
$832$	373.733	−	215.775i	0.449198	−	0.259345i
$833$	−92.5245	−	392.713i	−0.111074	−	0.471444i
$834$	1684.92	−	292.240i	2.02029	−	0.350408i
$835$	4.10922	−	7.11738i	0.00492122	−	0.00852380i
$836$		−	852.352i		−	1.01956i
$837$	−769.298	−	452.804i	−0.919114	−	0.540985i
$838$			576.901i			0.688426i
$839$	−640.732	−	369.927i	−0.763686	−	0.440914i	0.0669319	−	0.997758i	$-0.478679\pi$
$839$	−640.732	−	369.927i	−0.763686	−	0.440914i	−0.830617	+	0.556843i	$0.812012\pi$
$840$	161.890	−	170.408i	0.192726	−	0.202867i
$841$	345.143	+	597.805i	0.410396	+	0.710826i
$842$	928.727	+	1608.60i	1.10300	+	1.91045i
$843$	−710.208	−	260.747i	−0.842477	−	0.309308i
$844$	405.581	−	702.486i	0.480546	−	0.832330i
$845$		−	674.092i		−	0.797743i
$846$	−1219.55	+	1437.00i	−1.44155	+	1.69859i
$847$	−308.197	+	229.127i	−0.363869	+	0.270516i
$848$	376.693	−	652.452i	0.444214	−	0.769401i
$849$	−260.813	−	312.596i	−0.307200	−	0.368194i
$850$	−212.954	+	122.949i	−0.250534	+	0.144646i
$851$	−3.67898	−	6.37219i	−0.00432313	−	0.00748788i
$852$	548.106	−	457.309i	0.643317	−	0.536748i
$853$	824.037	+	475.758i	0.966045	+	0.557747i	0.898028	−	0.439938i	$-0.144999\pi$
$853$	824.037	+	475.758i	0.966045	+	0.557747i	0.0680170	+	0.997684i	$0.478333\pi$
$854$	438.296	+	589.550i	0.513228	+	0.690340i
$855$	572.578	+	485.934i	0.669681	+	0.568344i
$856$	−157.294			−0.183755
$857$	−1109.18	−	640.387i	−1.29426	−	0.747243i	−0.314856	−	0.949139i	$-0.601956\pi$
$857$	−1109.18	−	640.387i	−1.29426	−	0.747243i	−0.979407	+	0.201896i	$0.935290\pi$
$858$	672.649	−	1832.13i	0.783973	−	2.13534i
$859$	−656.241	+	378.881i	−0.763959	+	0.441072i	−0.830715	−	0.556697i	$-0.812068\pi$
$859$	−656.241	+	378.881i	−0.763959	+	0.441072i	0.0667562	+	0.997769i	$0.478735\pi$
$860$	−183.985	+	106.224i	−0.213936	+	0.123516i
$861$	390.426	−	410.969i	0.453457	−	0.477316i
$862$	94.9525	−	164.462i	0.110154	−	0.190792i
$863$	−1321.75			−1.53158			−0.765790	−	0.643091i	$-0.777652\pi$
$863$	−1321.75			−1.53158			−0.765790	+	0.643091i	$0.777652\pi$
$864$	−524.729	+	891.496i	−0.607325	+	1.03182i
$865$	−622.555			−0.719716
$866$	1296.90	+	748.763i	1.49757	+	0.864622i
$867$	113.405	+	653.843i	0.130802	+	0.754144i
$868$	−260.596	+	603.030i	−0.300226	+	0.694735i
$869$	−655.327	−	1135.06i	−0.754117	−	1.30617i
$870$	−122.322	+	333.175i	−0.140601	+	0.382960i
$871$	1771.39	+	1022.71i	2.03374	+	1.17418i
$872$	429.694			0.492769
$873$	−593.426	−	108.064i	−0.679755	−	0.123784i
$874$		−	43.7062i		−	0.0500071i
$875$	933.201	−	108.448i	1.06652	−	0.123941i
$876$	203.598	+	244.022i	0.232418	+	0.278564i
$877$	241.743	+	418.711i	0.275648	+	0.477436i	0.970298	−	0.241911i	$-0.0777743\pi$
$877$	241.743	+	418.711i	0.275648	+	0.477436i	−0.694651	+	0.719347i	$0.744441\pi$
$878$	1011.41	−	583.939i	1.15195	−	0.665079i
$879$	−161.785	−	193.907i	−0.184056	−	0.220599i
$880$	816.685	+	471.513i	0.928051	+	0.535811i
$881$		−	379.667i		−	0.430950i	−0.976509	−	0.215475i	$-0.930870\pi$
$881$		−	379.667i		−	0.430950i	0.976509	−	0.215475i	$-0.0691299\pi$
$882$	−59.0852	−	1151.73i	−0.0669901	−	1.30581i
$883$	−754.801			−0.854814			−0.427407	−	0.904059i	$-0.640573\pi$
$883$	−754.801			−0.854814			−0.427407	+	0.904059i	$0.640573\pi$
$884$	−219.229	+	379.716i	−0.247997	+	0.429543i
$885$	483.586	+	177.544i	0.546424	+	0.200615i
$886$	787.784	+	1364.48i	0.889146	+	1.54005i
$887$	−181.405	+	104.734i	−0.204516	+	0.118077i	−0.598760	−	0.800929i	$-0.704340\pi$
$887$	−181.405	+	104.734i	−0.204516	+	0.118077i	0.394244	+	0.919006i	$0.371006\pi$
$888$	−15.5226	−	89.4962i	−0.0174804	−	0.100784i
$889$	144.686	+	1245.03i	0.162752	+	1.40049i
$890$	1282.79			1.44134
$891$	174.679	+	1059.87i	0.196049	+	1.18953i
$892$		−	1069.14i		−	1.19859i
$893$	906.645	−	1570.35i	1.01528	−	1.75852i
$894$	−35.4186	−	204.207i	−0.0396181	−	0.228420i
$895$	239.018	−	137.997i	0.267060	−	0.154187i
$896$	−598.203	−	258.511i	−0.667638	−	0.288516i
$897$	14.3167	−	38.9952i	0.0159607	−	0.0434729i
$898$	−78.1211	+	135.310i	−0.0869945	+	0.150679i
$899$			405.884i			0.451484i
$900$	−274.703	+	98.2468i	−0.305226	+	0.109163i
$901$			321.471i			0.356793i
$902$	810.689	+	468.052i	0.898768	+	0.518904i
$903$	99.7945	−	414.666i	0.110514	−	0.459210i
$904$	−162.470	−	281.407i	−0.179724	−	0.311291i
$905$	3.07444	+	5.32509i	0.00339718	+	0.00588408i
$906$	−501.805	+	418.678i	−0.553869	+	0.462117i
$907$	464.373	−	804.318i	0.511988	−	0.886790i	−0.487915	−	0.872891i	$-0.662242\pi$
$907$	464.373	−	804.318i	0.511988	−	0.886790i	0.999903	−	0.0138986i	$-0.00442420\pi$
$908$			627.215i			0.690765i
$909$	190.177	+	34.6315i	0.209216	+	0.0380985i
$910$	1015.57	−	755.018i	1.11601	−	0.829690i
$911$	−157.855	+	273.414i	−0.173277	+	0.300125i	−0.939564	−	0.342374i	$-0.888769\pi$
$911$	−157.855	+	273.414i	−0.173277	+	0.300125i	0.766287	+	0.642499i	$0.222102\pi$
$912$	451.772	−	1230.51i	0.495365	−	1.34925i
$913$	1650.49	−	952.911i	1.80777	−	1.04371i
$914$	−930.077	−	1610.94i	−1.01759	−	1.76252i
$915$	−75.8196	−	437.141i	−0.0828630	−	0.477750i
$916$	70.7107	+	40.8248i	0.0771951	+	0.0445686i
$917$	487.150	+	655.262i	0.531243	+	0.714572i
$918$	4.87872	−	581.353i	0.00531451	−	0.633282i
$919$	−374.838			−0.407876			−0.203938	−	0.978984i	$-0.565374\pi$
$919$	−374.838			−0.407876			−0.203938	+	0.978984i	$0.565374\pi$
$920$	7.15469	+	4.13076i	0.00777684	+	0.00448996i
$921$	459.609	−	79.7165i	0.499033	−	0.0865543i
$922$	3.64566	−	2.10483i	0.00395408	−	0.00228289i
$923$	−1361.86	+	786.270i	−1.47547	+	0.851863i
$924$	758.069	−	224.096i	0.820421	−	0.242528i
$925$	56.9203	−	98.5889i	0.0615355	−	0.106583i
$926$	112.056			0.121011
$927$	−87.3615	+	102.938i	−0.0942411	+	0.111045i
$928$	470.356			0.506849
$929$	−838.196	−	483.932i	−0.902256	−	0.520918i	−0.0243244	−	0.999704i	$-0.507743\pi$
$929$	−838.196	−	483.932i	−0.902256	−	0.520918i	−0.877931	+	0.478787i	$0.841077\pi$
$930$	733.921	−	612.343i	0.789163	−	0.658433i
$931$	254.439	+	1079.95i	0.273297	+	1.15999i
$932$	−575.747	−	997.223i	−0.617754	−	1.06998i
$933$	373.175	+	447.267i	0.399973	+	0.479386i
$934$	523.489	+	302.236i	0.560481	+	0.323594i
$935$	−402.390			−0.430364
$936$	331.817	−	390.981i	0.354505	−	0.417715i
$937$			184.891i			0.197322i	0.995121	+	0.0986610i	$0.0314559\pi$
$937$			184.891i			0.197322i	−0.995121	+	0.0986610i	$0.968544\pi$
$938$	230.395	+	1982.56i	0.245624	+	2.11360i
$939$	358.536	−	976.560i	0.381827	−	1.04000i
$940$	−418.838	−	725.449i	−0.445573	−	0.771754i
$941$	−1091.52	+	630.188i	−1.15995	+	0.669700i	−0.951293	−	0.308288i	$-0.900244\pi$
$941$	−1091.52	+	630.188i	−1.15995	+	0.669700i	−0.208661	+	0.977988i	$0.566911\pi$
$942$	−1143.07	+	198.260i	−1.21345	+	0.210467i
$943$	17.2548	+	9.96206i	0.0182978	+	0.0105642i
$944$		−	899.178i		−	0.952519i
$945$	−281.644	+	637.001i	−0.298036	+	0.674075i
$946$	704.326			0.744531
$947$	229.847	−	398.107i	0.242711	−	0.420387i	−0.718775	−	0.695243i	$-0.755297\pi$
$947$	229.847	−	398.107i	0.242711	−	0.420387i	0.961485	+	0.274856i	$0.0886301\pi$
$948$	143.827	+	829.243i	0.151717	+	0.874729i
$949$	−350.055	−	606.312i	−0.368867	−	0.638896i
$950$	585.616	−	338.105i	0.616438	−	0.355900i
$951$	−194.489	−	71.4048i	−0.204510	−	0.0750839i
$952$	173.892	−	20.2082i	0.182660	−	0.0212271i
$953$	−278.059			−0.291772			−0.145886	−	0.989301i	$-0.546603\pi$
$953$	−278.059			−0.291772			−0.145886	+	0.989301i	$0.546603\pi$
$954$	−164.621	+	904.007i	−0.172558	+	0.947597i
$955$			445.695i			0.466697i
$956$	187.931	−	325.506i	0.196581	−	0.340488i
$957$	375.021	−	312.896i	0.391871	−	0.326956i
$958$	558.953	−	322.712i	0.583459	−	0.336860i
$959$	460.283	+	198.909i	0.479962	+	0.207413i
$960$	−162.928	−	195.276i	−0.169716	−	0.203413i
$961$	66.0373	−	114.380i	0.0687173	−	0.119022i
$962$		−	489.035i		−	0.508352i
$963$	438.867	−	156.959i	0.455729	−	0.162990i
$964$			235.197i			0.243980i
$965$	−647.222	−	373.674i	−0.670696	−	0.387227i
$966$	38.8716	−	11.4910i	0.0402398	−	0.0118954i
$967$	239.574	+	414.955i	0.247750	+	0.429116i	0.962901	−	0.269854i	$-0.0869755\pi$
$967$	239.574	+	414.955i	0.247750	+	0.429116i	−0.715151	+	0.698970i	$0.753642\pi$
$968$	−83.3164	−	144.308i	−0.0860707	−	0.149079i
$969$	95.5854	+	551.102i	0.0986434	+	0.568733i
$970$	322.932	−	559.335i	0.332920	−	0.576634i
$971$			1621.52i			1.66995i	0.550291	+	0.834973i	$0.314517\pi$
$971$			1621.52i			1.66995i	−0.550291	+	0.834973i	$0.685483\pi$
$972$	129.265	−	677.545i	0.132989	−	0.697063i
$973$	−910.361	−	1224.52i	−0.935623	−	1.25850i
$974$	−808.672	+	1400.66i	−0.830258	+	1.43805i
$975$	633.246	−	109.833i	0.649483	−	0.112649i
$976$	−670.660	+	387.206i	−0.687152	+	0.396727i
$977$	211.767	+	366.791i	0.216752	+	0.375425i	0.953813	−	0.300401i	$-0.0971204\pi$
$977$	211.767	+	366.791i	0.216752	+	0.375425i	−0.737061	+	0.675826i	$0.763787\pi$
$978$	−596.243	−	218.905i	−0.609655	−	0.223830i
$979$	−1528.77	−	882.634i	−1.56156	−	0.901567i
$980$	490.829	+	147.654i	0.500846	+	0.150668i
$981$	−1198.89	+	428.780i	−1.22211	+	0.437084i
$982$	−840.278			−0.855680
$983$	1363.91	+	787.455i	1.38750	+	0.801073i	0.993033	−	0.117837i	$-0.0375961\pi$
$983$	1363.91	+	787.455i	1.38750	+	0.801073i	0.394466	+	0.918910i	$0.370929\pi$
$984$	157.572	+	188.857i	0.160134	+	0.191928i
$985$	−679.812	+	392.490i	−0.690164	+	0.398467i
$986$	−228.928	+	132.172i	−0.232179	+	0.134048i
$987$	1635.02	+	393.488i	1.65656	+	0.398671i
$988$	602.874	−	1044.21i	0.610196	−	1.05689i
$989$	14.9910			0.0151577
$990$	−1131.56	−	206.059i	−1.14299	−	0.208140i
$991$	640.630			0.646448			0.323224	−	0.946322i	$-0.395233\pi$
$991$	640.630			0.646448			0.323224	+	0.946322i	$0.395233\pi$
$992$	−1097.00	−	633.351i	−1.10584	−	0.638458i
$993$	708.672	+	260.183i	0.713668	+	0.262017i
$994$	−1408.57	−	608.706i	−1.41707	−	0.612380i
$995$	−369.079	−	639.264i	−0.370934	−	0.642477i
$996$	−1205.80	+	209.139i	−1.21064	+	0.209979i
$997$	264.891	+	152.935i	0.265688	+	0.153395i	0.626926	−	0.779078i	$-0.284313\pi$
$997$	264.891	+	152.935i	0.265688	+	0.153395i	−0.361239	+	0.932473i	$0.617646\pi$
$998$	−420.948			−0.421792
$999$	132.615	+	234.214i	0.132748	+	0.234448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.l.a.34.12	yes	28
3.2	odd	2		189.3.l.a.181.3		28
7.2	even	3		441.3.t.b.178.3		28
7.3	odd	6		441.3.k.a.313.11		28
7.4	even	3		441.3.k.a.313.12		28
7.5	odd	6		441.3.t.b.178.4		28
7.6	odd	2	inner	63.3.l.a.34.11	yes	28
9.2	odd	6		567.3.d.g.244.11		14
9.4	even	3	inner	63.3.l.a.13.11	✓	28
9.5	odd	6		189.3.l.a.118.4		28
9.7	even	3		567.3.d.h.244.4		14
21.20	even	2		189.3.l.a.181.4		28
63.4	even	3		441.3.t.b.166.4		28
63.13	odd	6	inner	63.3.l.a.13.12	yes	28
63.20	even	6		567.3.d.g.244.12		14
63.31	odd	6		441.3.t.b.166.3		28
63.34	odd	6		567.3.d.h.244.3		14
63.40	odd	6		441.3.k.a.31.12		28
63.41	even	6		189.3.l.a.118.3		28
63.58	even	3		441.3.k.a.31.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.l.a.13.11	✓	28	9.4	even	3	inner
63.3.l.a.13.12	yes	28	63.13	odd	6	inner
63.3.l.a.34.11	yes	28	7.6	odd	2	inner
63.3.l.a.34.12	yes	28	1.1	even	1	trivial
189.3.l.a.118.3		28	63.41	even	6
189.3.l.a.118.4		28	9.5	odd	6
189.3.l.a.181.3		28	3.2	odd	2
189.3.l.a.181.4		28	21.20	even	2
441.3.k.a.31.11		28	63.58	even	3
441.3.k.a.31.12		28	63.40	odd	6
441.3.k.a.313.11		28	7.3	odd	6
441.3.k.a.313.12		28	7.4	even	3
441.3.t.b.166.3		28	63.31	odd	6
441.3.t.b.166.4		28	63.4	even	3
441.3.t.b.178.3		28	7.2	even	3
441.3.t.b.178.4		28	7.5	odd	6
567.3.d.g.244.11		14	9.2	odd	6
567.3.d.g.244.12		14	63.20	even	6
567.3.d.h.244.3		14	63.34	odd	6
567.3.d.h.244.4		14	9.7	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:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30753 - 2.26471i) q^{2} +(0.512678 + 2.95587i) q^{3} +(-1.41927 - 2.45825i) q^{4} +(3.19140 - 1.84256i) q^{5} +(7.36452 + 2.70382i) q^{6} +(-0.808038 - 6.95321i) q^{7} +3.03728 q^{8} +(-8.47432 + 3.03082i) q^{9} +O(q^{10})\)	\(q+(1.30753 - 2.26471i) q^{2} +(0.512678 + 2.95587i) q^{3} +(-1.41927 - 2.45825i) q^{4} +(3.19140 - 1.84256i) q^{5} +(7.36452 + 2.70382i) q^{6} +(-0.808038 - 6.95321i) q^{7} +3.03728 q^{8} +(-8.47432 + 3.03082i) q^{9} -9.63680i q^{10} +(-6.63066 + 11.4846i) q^{11} +(6.53863 - 5.45547i) q^{12} +(-16.2463 + 9.37981i) q^{13} +(-16.8035 - 7.26156i) q^{14} +(7.08252 + 8.48873i) q^{15} +(9.64842 - 16.7116i) q^{16} +8.23398i q^{17} +(-4.21651 + 23.1548i) q^{18} -22.6432i q^{19} +(-9.05893 - 5.23018i) q^{20} +(20.1385 - 5.95321i) q^{21} +(17.3396 + 30.0330i) q^{22} +(0.369057 + 0.639226i) q^{23} +(1.55715 + 8.97781i) q^{24} +(-5.70996 + 9.88995i) q^{25} +49.0575i q^{26} +(-13.3033 - 23.4952i) q^{27} +(-15.9459 + 11.8548i) q^{28} +(-6.13829 + 10.6318i) q^{29} +(28.4851 - 4.94058i) q^{30} +(28.6323 - 16.5308i) q^{31} +(-19.1566 - 33.1803i) q^{32} +(-37.3465 - 13.7114i) q^{33} +(18.6476 + 10.7662i) q^{34} +(-15.3905 - 20.7016i) q^{35} +(19.4779 + 16.5304i) q^{36} -9.96860 q^{37} +(-51.2802 - 29.6066i) q^{38} +(-36.0546 - 43.2131i) q^{39} +(9.69320 - 5.59637i) q^{40} +(23.3769 - 13.4966i) q^{41} +(12.8494 - 53.3918i) q^{42} +(10.1549 - 17.5888i) q^{43} +37.6428 q^{44} +(-21.4605 + 25.2870i) q^{45} +1.93021 q^{46} +(69.3523 + 40.0406i) q^{47} +(54.3437 + 19.9518i) q^{48} +(-47.6941 + 11.2369i) q^{49} +(14.9319 + 25.8628i) q^{50} +(-24.3386 + 4.22138i) q^{51} +(46.1158 + 26.6250i) q^{52} +39.0420 q^{53} +(-70.6041 - 0.592511i) q^{54} +48.8695i q^{55} +(-2.45424 - 21.1189i) q^{56} +(66.9302 - 11.6087i) q^{57} +(16.0520 + 27.8029i) q^{58} +(40.3543 - 23.2986i) q^{59} +(10.8154 - 29.4584i) q^{60} +(-34.7549 - 20.0658i) q^{61} -86.4583i q^{62} +(27.9215 + 56.4747i) q^{63} -23.0042 q^{64} +(-34.5657 + 59.8695i) q^{65} +(-79.8840 + 66.6508i) q^{66} +(-54.5167 - 94.4257i) q^{67} +(20.2412 - 11.6862i) q^{68} +(-1.70026 + 1.41860i) q^{69} +(-67.0067 + 7.78690i) q^{70} +83.8258 q^{71} +(-25.7389 + 9.20546i) q^{72} +37.3200i q^{73} +(-13.0342 + 22.5760i) q^{74} +(-32.1608 - 11.8075i) q^{75} +(-55.6625 + 32.1368i) q^{76} +(85.2129 + 36.8243i) q^{77} +(-145.008 + 25.1507i) q^{78} +(-49.4165 + 85.5918i) q^{79} -71.1111i q^{80} +(62.6283 - 51.3683i) q^{81} -70.5890i q^{82} +(-124.459 - 71.8564i) q^{83} +(-43.2165 - 41.0562i) q^{84} +(15.1716 + 26.2779i) q^{85} +(-26.5557 - 45.9958i) q^{86} +(-34.5732 - 12.6933i) q^{87} +(-20.1392 + 34.8821i) q^{88} +133.114i q^{89} +(29.2074 + 81.6653i) q^{90} +(78.3474 + 105.385i) q^{91} +(1.04758 - 1.81447i) q^{92} +(63.5421 + 76.1582i) q^{93} +(181.360 - 104.708i) q^{94} +(-41.7213 - 72.2635i) q^{95} +(88.2554 - 73.6353i) q^{96} +(58.0415 + 33.5103i) q^{97} +(-36.9132 + 122.706i) q^{98} +(21.3825 - 117.421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 24 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 24 * q^9	\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 24 q^{9} + 4 q^{11} + 34 q^{14} - 54 q^{15} - 42 q^{16} + 54 q^{18} + 18 q^{21} + 14 q^{22} + 4 q^{23} + 28 q^{25} + 20 q^{28} - 38 q^{29} + 168 q^{30} - 168 q^{32} - 264 q^{35} + 234 q^{36} + 36 q^{37} - 228 q^{39} - 192 q^{42} - 66 q^{43} + 108 q^{44} - 40 q^{46} - 38 q^{49} + 196 q^{50} + 246 q^{51} + 520 q^{53} + 332 q^{56} - 198 q^{57} - 34 q^{58} + 96 q^{60} + 48 q^{63} + 72 q^{64} - 102 q^{65} + 68 q^{67} + 102 q^{70} - 332 q^{71} - 1308 q^{72} - 616 q^{74} + 334 q^{77} - 168 q^{78} + 146 q^{79} + 276 q^{81} + 498 q^{84} + 78 q^{85} - 340 q^{86} - 74 q^{88} - 384 q^{91} + 606 q^{92} + 534 q^{93} - 360 q^{95} - 1076 q^{98} + 900 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 26 * q^4 + 8 * q^8 - 24 * q^9 + 4 * q^11 + 34 * q^14 - 54 * q^15 - 42 * q^16 + 54 * q^18 + 18 * q^21 + 14 * q^22 + 4 * q^23 + 28 * q^25 + 20 * q^28 - 38 * q^29 + 168 * q^30 - 168 * q^32 - 264 * q^35 + 234 * q^36 + 36 * q^37 - 228 * q^39 - 192 * q^42 - 66 * q^43 + 108 * q^44 - 40 * q^46 - 38 * q^49 + 196 * q^50 + 246 * q^51 + 520 * q^53 + 332 * q^56 - 198 * q^57 - 34 * q^58 + 96 * q^60 + 48 * q^63 + 72 * q^64 - 102 * q^65 + 68 * q^67 + 102 * q^70 - 332 * q^71 - 1308 * q^72 - 616 * q^74 + 334 * q^77 - 168 * q^78 + 146 * q^79 + 276 * q^81 + 498 * q^84 + 78 * q^85 - 340 * q^86 - 74 * q^88 - 384 * q^91 + 606 * q^92 + 534 * q^93 - 360 * q^95 - 1076 * q^98 + 900 * q^99

Introduction

L-functions

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