LMFDB - Embedded newform 63.3.r.a.29.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(29,63)]

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([1, 0]))

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

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

chi := DirichletCharacter("63.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.r (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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	63.29
Dual form			63.3.r.a.50.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50746 - 1.44768i) q^{2} +(2.16846 + 2.07310i) q^{3} +(2.19156 + 3.79590i) q^{4} +(-6.82498 + 3.94040i) q^{5} +(-2.43614 - 8.33747i) q^{6} +(-1.32288 + 2.29129i) q^{7} -1.10929i q^{8} +(0.404480 + 8.99091i) q^{9} +O(q^{10})$	\(q+(-2.50746 - 1.44768i) q^{2} +(2.16846 + 2.07310i) q^{3} +(2.19156 + 3.79590i) q^{4} +(-6.82498 + 3.94040i) q^{5} +(-2.43614 - 8.33747i) q^{6} +(-1.32288 + 2.29129i) q^{7} -1.10929i q^{8} +(0.404480 + 8.99091i) q^{9} +22.8178 q^{10} +(1.97436 + 1.13990i) q^{11} +(-3.11696 + 12.7746i) q^{12} +(7.03250 + 12.1806i) q^{13} +(6.63411 - 3.83020i) q^{14} +(-22.9686 - 5.60426i) q^{15} +(7.16036 - 12.4021i) q^{16} -5.53839i q^{17} +(12.0017 - 23.1299i) q^{18} -33.1571 q^{19} +(-29.9147 - 17.2713i) q^{20} +(-7.61869 + 2.22612i) q^{21} +(-3.30042 - 5.71649i) q^{22} +(21.8623 - 12.6222i) q^{23} +(2.29967 - 2.40545i) q^{24} +(18.5535 - 32.1357i) q^{25} -40.7233i q^{26} +(-17.7620 + 20.3350i) q^{27} -11.5967 q^{28} +(9.48807 + 5.47794i) q^{29} +(49.4796 + 47.3036i) q^{30} +(13.5915 + 23.5412i) q^{31} +(-39.7513 + 22.9504i) q^{32} +(1.91821 + 6.56488i) q^{33} +(-8.01782 + 13.8873i) q^{34} -20.8506i q^{35} +(-33.2421 + 21.2395i) q^{36} -0.870105 q^{37} +(83.1401 + 48.0010i) q^{38} +(-10.0020 + 40.9924i) q^{39} +(4.37103 + 7.57085i) q^{40} +(3.05234 - 1.76227i) q^{41} +(22.3262 + 5.44753i) q^{42} +(31.7481 - 54.9893i) q^{43} +9.99263i q^{44} +(-38.1884 - 59.7689i) q^{45} -73.0916 q^{46} +(72.7692 + 42.0133i) q^{47} +(41.2378 - 12.0494i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-93.0444 + 53.7192i) q^{50} +(11.4817 - 12.0098i) q^{51} +(-30.8243 + 53.3893i) q^{52} +33.8390i q^{53} +(73.9760 - 25.2754i) q^{54} -17.9666 q^{55} +(2.54169 + 1.46745i) q^{56} +(-71.9001 - 68.7382i) q^{57} +(-15.8606 - 27.4714i) q^{58} +(2.45665 - 1.41835i) q^{59} +(-29.0639 - 99.4685i) q^{60} +(-33.3549 + 57.7724i) q^{61} -78.7049i q^{62} +(-21.1358 - 10.9671i) q^{63} +75.6166 q^{64} +(-95.9933 - 55.4217i) q^{65} +(4.69404 - 19.2381i) q^{66} +(26.6661 + 46.1871i) q^{67} +(21.0232 - 12.1377i) q^{68} +(73.5746 + 17.9520i) q^{69} +(-30.1851 + 52.2821i) q^{70} +73.1679i q^{71} +(9.97349 - 0.448685i) q^{72} +97.8302 q^{73} +(2.18175 + 1.25963i) q^{74} +(106.853 - 31.2217i) q^{75} +(-72.6659 - 125.861i) q^{76} +(-5.22367 + 3.01589i) q^{77} +(84.4236 - 88.3070i) q^{78} +(0.527503 - 0.913661i) q^{79} +112.859i q^{80} +(-80.6728 + 7.27329i) q^{81} -10.2048 q^{82} +(34.2831 + 19.7934i) q^{83} +(-25.1469 - 24.0411i) q^{84} +(21.8235 + 37.7994i) q^{85} +(-159.214 + 91.9223i) q^{86} +(9.21821 + 31.5485i) q^{87} +(1.26447 - 2.19013i) q^{88} -124.332i q^{89} +(9.22935 + 205.153i) q^{90} -37.2125 q^{91} +(95.8250 + 55.3246i) q^{92} +(-19.3307 + 79.2250i) q^{93} +(-121.644 - 210.693i) q^{94} +(226.297 - 130.652i) q^{95} +(-133.778 - 32.6414i) q^{96} +(-0.919837 + 1.59320i) q^{97} +20.2675i q^{98} +(-9.45013 + 18.2124i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	$ 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.50746	−	1.44768i	−1.25373	−	0.723841i	−0.281881	−	0.959449i	$-0.590958\pi$
$2$	−2.50746	−	1.44768i	−1.25373	−	0.723841i	−0.971848	+	0.235609i	$0.924292\pi$
$3$	2.16846	+	2.07310i	0.722822	+	0.691035i
$3$	2.16846	+	2.07310i	0.722822	+	0.691035i
$4$	2.19156	+	3.79590i	0.547891	+	0.948974i
$5$	−6.82498	+	3.94040i	−1.36500	+	0.788080i	−0.990284	−	0.139061i	$-0.955592\pi$
$5$	−6.82498	+	3.94040i	−1.36500	+	0.788080i	−0.374712	+	0.927141i	$0.622258\pi$
$6$	−2.43614	−	8.33747i	−0.406023	−	1.38958i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$		−	1.10929i		−	0.138661i
$9$	0.404480	+	8.99091i	0.0449423	+	0.998990i
$10$	22.8178			2.28178
$11$	1.97436	+	1.13990i	0.179487	+	0.103627i	0.587052	−	0.809549i	$-0.300288\pi$
$11$	1.97436	+	1.13990i	0.179487	+	0.103627i	−0.407564	+	0.913176i	$0.633622\pi$
$12$	−3.11696	+	12.7746i	−0.259747	+	1.06455i
$13$	7.03250	+	12.1806i	0.540961	+	0.936973i	0.998849	+	0.0479625i	$0.0152728\pi$
$13$	7.03250	+	12.1806i	0.540961	+	0.936973i	−0.457888	+	0.889010i	$0.651394\pi$
$14$	6.63411	−	3.83020i	0.473865	−	0.273586i
$15$	−22.9686	−	5.60426i	−1.53124	−	0.373617i
$16$	7.16036	−	12.4021i	0.447522	−	0.775131i
$17$		−	5.53839i		−	0.325788i	−0.986644	−	0.162894i	$-0.947917\pi$
$17$		−	5.53839i		−	0.325788i	0.986644	−	0.162894i	$-0.0520828\pi$
$18$	12.0017	−	23.1299i	0.666764	−	1.28499i
$19$	−33.1571			−1.74511			−0.872556	−	0.488514i	$-0.837539\pi$
$19$	−33.1571			−1.74511			−0.872556	+	0.488514i	$0.837539\pi$
$20$	−29.9147	−	17.2713i	−1.49574	−	0.863564i
$21$	−7.61869	+	2.22612i	−0.362795	+	0.106006i
$22$	−3.30042	−	5.71649i	−0.150019	−	0.259841i
$23$	21.8623	−	12.6222i	0.950533	−	0.548790i	0.0572863	−	0.998358i	$-0.481755\pi$
$23$	21.8623	−	12.6222i	0.950533	−	0.548790i	0.893246	+	0.449567i	$0.148422\pi$
$24$	2.29967	−	2.40545i	0.0958194	−	0.100227i
$25$	18.5535	−	32.1357i	0.742141	−	1.28543i
$26$		−	40.7233i		−	1.56628i
$27$	−17.7620	+	20.3350i	−0.657851	+	0.753148i
$28$	−11.5967			−0.414166
$29$	9.48807	+	5.47794i	0.327175	+	0.188894i	0.654586	−	0.755987i	$-0.272843\pi$
$29$	9.48807	+	5.47794i	0.327175	+	0.188894i	−0.327411	+	0.944882i	$0.606176\pi$
$30$	49.4796	+	47.3036i	1.64932	+	1.57679i
$31$	13.5915	+	23.5412i	0.438437	+	0.759395i	0.997569	−	0.0696836i	$-0.0221990\pi$
$31$	13.5915	+	23.5412i	0.438437	+	0.759395i	−0.559132	+	0.829078i	$0.688866\pi$
$32$	−39.7513	+	22.9504i	−1.24223	+	0.717200i
$33$	1.91821	+	6.56488i	0.0581275	+	0.198936i
$34$	−8.01782	+	13.8873i	−0.235818	+	0.408449i
$35$		−	20.8506i		−	0.595733i
$36$	−33.2421	+	21.2395i	−0.923392	+	0.589986i
$37$	−0.870105			−0.0235164			−0.0117582	−	0.999931i	$-0.503743\pi$
$37$	−0.870105			−0.0235164			−0.0117582	+	0.999931i	$0.503743\pi$
$38$	83.1401	+	48.0010i	2.18790	+	1.26318i
$39$	−10.0020	+	40.9924i	−0.256462	+	1.05109i
$40$	4.37103	+	7.57085i	0.109276	+	0.189271i
$41$	3.05234	−	1.76227i	0.0744474	−	0.0429822i	−0.462314	−	0.886716i	$-0.652981\pi$
$41$	3.05234	−	1.76227i	0.0744474	−	0.0429822i	0.536762	+	0.843734i	$0.319647\pi$
$42$	22.3262	+	5.44753i	0.531577	+	0.129703i
$43$	31.7481	−	54.9893i	0.738328	−	1.27882i	−0.214920	−	0.976632i	$-0.568949\pi$
$43$	31.7481	−	54.9893i	0.738328	−	1.27882i	0.953248	−	0.302190i	$-0.0977177\pi$
$44$			9.99263i			0.227105i
$45$	−38.1884	−	59.7689i	−0.848630	−	1.32820i
$46$	−73.0916			−1.58895
$47$	72.7692	+	42.0133i	1.54828	+	0.893900i	0.998273	+	0.0587395i	$0.0187081\pi$
$47$	72.7692	+	42.0133i	1.54828	+	0.893900i	0.550007	+	0.835160i	$0.314625\pi$
$48$	41.2378	−	12.0494i	0.859121	−	0.251028i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	−93.0444	+	53.7192i	−1.86089	+	1.07438i
$51$	11.4817	−	12.0098i	0.225130	−	0.235486i
$52$	−30.8243	+	53.3893i	−0.592775	+	1.02672i
$53$			33.8390i			0.638472i	0.947675	+	0.319236i	$0.103426\pi$
$53$			33.8390i			0.638472i	−0.947675	+	0.319236i	$0.896574\pi$
$54$	73.9760	−	25.2754i	1.36993	−	0.468064i
$55$	−17.9666			−0.326666
$56$	2.54169	+	1.46745i	0.0453874	+	0.0262044i
$57$	−71.9001	−	68.7382i	−1.26141	−	1.20593i
$58$	−15.8606	−	27.4714i	−0.273459	−	0.473645i
$59$	2.45665	−	1.41835i	0.0416382	−	0.0240398i	−0.479036	−	0.877795i	$-0.659014\pi$
$59$	2.45665	−	1.41835i	0.0416382	−	0.0240398i	0.520675	+	0.853755i	$0.325680\pi$
$60$	−29.0639	−	99.4685i	−0.484398	−	1.65781i
$61$	−33.3549	+	57.7724i	−0.546802	+	0.947088i	0.451689	+	0.892175i	$0.350821\pi$
$61$	−33.3549	+	57.7724i	−0.546802	+	0.947088i	−0.998491	+	0.0549130i	$0.982512\pi$
$62$		−	78.7049i		−	1.26943i
$63$	−21.1358	−	10.9671i	−0.335489	−	0.174080i
$64$	75.6166			1.18151
$65$	−95.9933	−	55.4217i	−1.47682	−	0.852642i
$66$	4.69404	−	19.2381i	0.0711218	−	0.291487i
$67$	26.6661	+	46.1871i	0.398002	+	0.689359i	0.993479	−	0.114013i	$-0.0363704\pi$
$67$	26.6661	+	46.1871i	0.398002	+	0.689359i	−0.595477	+	0.803372i	$0.703037\pi$
$68$	21.0232	−	12.1377i	0.309164	−	0.178496i
$69$	73.5746	+	17.9520i	1.06630	+	0.260174i
$70$	−30.1851	+	52.2821i	−0.431216	+	0.746887i
$71$			73.1679i			1.03053i	0.857030	+	0.515267i	$0.172307\pi$
$71$			73.1679i			1.03053i	−0.857030	+	0.515267i	$0.827693\pi$
$72$	9.97349	−	0.448685i	0.138521	−	0.00623173i
$73$	97.8302			1.34014			0.670070	−	0.742298i	$-0.266264\pi$
$73$	97.8302			1.34014			0.670070	+	0.742298i	$0.266264\pi$
$74$	2.18175	+	1.25963i	0.0294831	+	0.0170221i
$75$	106.853	−	31.2217i	1.42471	−	0.416289i
$76$	−72.6659	−	125.861i	−0.956131	−	1.65607i
$77$	−5.22367	+	3.01589i	−0.0678399	+	0.0391674i
$78$	84.4236	−	88.3070i	1.08235	−	1.13214i
$79$	0.527503	−	0.913661i	0.00667725	−	0.0115653i	−0.862667	−	0.505772i	$-0.831208\pi$
$79$	0.527503	−	0.913661i	0.00667725	−	0.0115653i	0.869345	+	0.494206i	$0.164541\pi$
$80$			112.859i			1.41073i
$81$	−80.6728	+	7.27329i	−0.995960	+	0.0897937i
$82$	−10.2048			−0.124449
$83$	34.2831	+	19.7934i	0.413049	+	0.238474i	0.692099	−	0.721802i	$-0.256686\pi$
$83$	34.2831	+	19.7934i	0.413049	+	0.238474i	−0.279050	+	0.960277i	$0.590019\pi$
$84$	−25.1469	−	24.0411i	−0.299368	−	0.286203i
$85$	21.8235	+	37.7994i	0.256747	+	0.444698i
$86$	−159.214	+	91.9223i	−1.85133	+	1.06886i
$87$	9.21821	+	31.5485i	0.105956	+	0.362626i
$88$	1.26447	−	2.19013i	0.0143690	−	0.0248879i
$89$		−	124.332i		−	1.39699i	−0.715617	−	0.698493i	$-0.753854\pi$
$89$		−	124.332i		−	1.39699i	0.715617	−	0.698493i	$-0.246146\pi$
$90$	9.22935	+	205.153i	0.102548	+	2.27947i
$91$	−37.2125			−0.408928
$92$	95.8250	+	55.3246i	1.04158	+	0.601354i
$93$	−19.3307	+	79.2250i	−0.207857	+	0.851882i
$94$	−121.644	−	210.693i	−1.29408	−	2.24142i
$95$	226.297	−	130.652i	2.38207	−	1.37529i
$96$	−133.778	−	32.6414i	−1.39352	−	0.340014i
$97$	−0.919837	+	1.59320i	−0.00948286	+	0.0164248i	−0.870728	−	0.491765i	$-0.836352\pi$
$97$	−0.919837	+	1.59320i	−0.00948286	+	0.0164248i	0.861245	+	0.508190i	$0.169685\pi$
$98$			20.2675i			0.206812i
$99$	−9.45013	+	18.2124i	−0.0954558	+	0.183963i
$100$	162.645			1.62645
$101$	−124.594	−	71.9344i	−1.23360	−	0.712221i	−0.265825	−	0.964021i	$-0.585644\pi$
$101$	−124.594	−	71.9344i	−1.23360	−	0.712221i	−0.967779	+	0.251800i	$0.918978\pi$
$102$	−46.1761	+	13.4923i	−0.452707	+	0.132277i
$103$	35.4547	+	61.4093i	0.344220	+	0.596207i	0.985212	−	0.171341i	$-0.0548100\pi$
$103$	35.4547	+	61.4093i	0.344220	+	0.596207i	−0.640992	+	0.767548i	$0.721477\pi$
$104$	13.5118	−	7.80105i	0.129921	−	0.0750101i
$105$	43.2256	−	45.2139i	0.411672	−	0.430609i
$106$	48.9881	−	84.8499i	0.462152	−	0.800471i
$107$		−	127.998i		−	1.19624i	−0.801405	−	0.598122i	$-0.795914\pi$
$107$		−	127.998i		−	1.19624i	0.801405	−	0.598122i	$-0.204086\pi$
$108$	−116.116	−	22.8573i	−1.07515	−	0.211641i
$109$	−114.310			−1.04871			−0.524357	−	0.851499i	$-0.675694\pi$
$109$	−114.310			−1.04871			−0.524357	+	0.851499i	$0.675694\pi$
$110$	45.0506	+	26.0099i	0.409550	+	0.236454i
$111$	−1.88679	−	1.80382i	−0.0169981	−	0.0162506i
$112$	18.9445	+	32.8129i	0.169148	+	0.292972i
$113$	−38.7606	+	22.3784i	−0.343014	+	0.198039i	−0.661604	−	0.749853i	$-0.730124\pi$
$113$	−38.7606	+	22.3784i	−0.343014	+	0.198039i	0.318590	+	0.947893i	$0.396791\pi$
$114$	80.7754	+	276.447i	0.708556	+	2.42497i
$115$	−99.4729	+	172.292i	−0.864982	+	1.49819i
$116$			48.0210i			0.413974i
$117$	−106.671	+	68.1554i	−0.911714	+	0.582524i
$118$	−8.21327			−0.0696040
$119$	12.6900	+	7.32660i	0.106639	+	0.0615681i
$120$	−6.21673	+	25.4787i	−0.0518061	+	0.212323i
$121$	−57.9013	−	100.288i	−0.478523	−	0.828826i
$122$	167.272	−	96.5745i	1.37108	−	0.791595i
$123$	10.2723	+	2.50640i	0.0835144	+	0.0203772i
$124$	−59.5734	+	103.184i	−0.480431	+	0.832131i
$125$			95.4135i			0.763308i
$126$	37.1204	+	58.0974i	0.294606	+	0.461091i
$127$	86.6595			0.682358			0.341179	−	0.939998i	$-0.389174\pi$
$127$	86.6595			0.682358			0.341179	+	0.939998i	$0.389174\pi$
$128$	−30.6004	−	17.6672i	−0.239066	−	0.138025i
$129$	182.843	−	53.4253i	1.41739	−	0.414150i
$130$	160.466	+	277.935i	1.23435	+	2.13796i
$131$	−34.2488	+	19.7736i	−0.261441	+	0.150943i	−0.624992	−	0.780631i	$-0.714898\pi$
$131$	−34.2488	+	19.7736i	−0.261441	+	0.150943i	0.363551	+	0.931574i	$0.381564\pi$
$132$	−20.7158	+	21.6687i	−0.156938	+	0.164157i
$133$	43.8628	−	75.9725i	0.329795	−	0.571222i
$134$		−	154.416i		−	1.15236i
$135$	41.0971	−	208.775i	0.304423	−	1.54648i
$136$	−6.14366			−0.0451740
$137$	−14.5489	−	8.39981i	−0.106196	−	0.0613125i	0.445961	−	0.895052i	$-0.352862\pi$
$137$	−14.5489	−	8.39981i	−0.106196	−	0.0613125i	−0.552157	+	0.833740i	$0.686195\pi$
$138$	−158.496	−	151.526i	−1.14853	−	1.09802i
$139$	64.2398	+	111.267i	0.462157	+	0.800479i	0.999068	−	0.0431596i	$-0.0137424\pi$
$139$	64.2398	+	111.267i	0.462157	+	0.800479i	−0.536911	+	0.843639i	$0.680409\pi$
$140$	79.1469	−	45.6955i	0.565335	−	0.326396i
$141$	70.6994	+	241.962i	0.501414	+	1.71605i
$142$	105.924	−	183.466i	0.745943	−	1.29201i
$143$			32.0653i			0.224233i
$144$	114.402	+	59.3617i	0.794461	+	0.412234i
$145$	−86.3411			−0.595456
$146$	−245.305	−	141.627i	−1.68017	−	0.970048i
$147$	4.97790	−	20.4015i	0.0338632	−	0.138786i
$148$	−1.90689	−	3.30283i	−0.0128844	−	0.0223164i
$149$	−75.6300	+	43.6650i	−0.507584	+	0.293054i	−0.731840	−	0.681476i	$-0.761338\pi$
$149$	−75.6300	+	43.6650i	−0.507584	+	0.293054i	0.224256	+	0.974530i	$0.428005\pi$
$150$	−313.129	−	76.4025i	−2.08753	−	0.509350i
$151$	65.7695	−	113.916i	0.435560	−	0.754412i	−0.561781	−	0.827286i	$-0.689884\pi$
$151$	65.7695	−	113.916i	0.435560	−	0.754412i	0.997341	+	0.0728740i	$0.0232171\pi$
$152$			36.7808i			0.241979i
$153$	49.7951	−	2.24017i	0.325458	−	0.0146416i
$154$	17.4642			0.113404
$155$	−185.524	−	107.112i	−1.19693	−	0.691047i
$156$	−177.523	+	51.8708i	−1.13797	+	0.332505i
$157$	13.8263	+	23.9478i	0.0880655	+	0.152534i	0.906693	−	0.421790i	$-0.138598\pi$
$157$	13.8263	+	23.9478i	0.0880655	+	0.152534i	−0.818628	+	0.574324i	$0.805265\pi$
$158$	−2.64538	+	1.52731i	−0.0167429	+	0.00966653i
$159$	−70.1518	+	73.3787i	−0.441206	+	0.461502i
$160$	180.868	−	313.272i	1.13042	−	1.95795i
$161$			66.7903i			0.414846i
$162$	212.813	+	98.5510i	1.31366	+	0.608340i
$163$	16.9528			0.104005			0.0520024	−	0.998647i	$-0.483440\pi$
$163$	16.9528			0.104005			0.0520024	+	0.998647i	$0.483440\pi$
$164$	13.3788	+	7.72425i	0.0815781	+	0.0470991i
$165$	−38.9600	−	37.2467i	−0.236121	−	0.225737i
$166$	−57.3090	−	99.2620i	−0.345235	−	0.597964i
$167$	−146.216	+	84.4180i	−0.875546	+	0.505497i	−0.869187	−	0.494483i	$-0.835357\pi$
$167$	−146.216	+	84.4180i	−0.875546	+	0.505497i	−0.00635903	+	0.999980i	$0.502024\pi$
$168$	2.46940	+	8.45131i	0.0146988	+	0.0503054i
$169$	−14.4120	+	24.9624i	−0.0852783	+	0.147706i
$170$		−	126.374i		−	0.743375i
$171$	−13.4114	−	298.113i	−0.0784293	−	1.74335i
$172$	278.312			1.61809
$173$	32.9137	+	19.0027i	0.190252	+	0.109842i	0.592101	−	0.805864i	$-0.298299\pi$
$173$	32.9137	+	19.0027i	0.190252	+	0.109842i	−0.401848	+	0.915706i	$0.631632\pi$
$174$	22.5579	−	92.4515i	0.129643	−	0.531330i
$175$	49.0880	+	85.0230i	0.280503	+	0.485846i
$176$	28.2743	−	16.3242i	0.160649	−	0.0927509i
$177$	8.26755	+	2.01726i	0.0467093	+	0.0113969i
$178$	−179.993	+	311.757i	−1.01120	+	1.75144i
$179$			42.3732i			0.236722i	0.992971	+	0.118361i	$0.0377640\pi$
$179$			42.3732i			0.236722i	−0.992971	+	0.118361i	$0.962236\pi$
$180$	143.185	−	275.946i	0.795469	−	1.53304i
$181$	244.184			1.34908			0.674540	−	0.738238i	$-0.264342\pi$
$181$	244.184			1.34908			0.674540	+	0.738238i	$0.264342\pi$
$182$	93.3087	+	53.8718i	0.512685	+	0.295999i
$183$	−192.097	+	56.1292i	−1.04971	+	0.306717i
$184$	−14.0016	−	24.2515i	−0.0760957	−	0.131802i
$185$	5.93845	−	3.42856i	0.0320997	−	0.0185328i
$186$	163.163	−	170.669i	0.877223	−	0.917574i
$187$	6.31320	−	10.9348i	0.0337604	−	0.0584748i
$188$			368.299i			1.95904i
$189$	−23.0964	−	67.5985i	−0.122203	−	0.357664i
$190$	−756.572			−3.98196
$191$	132.215	+	76.3342i	0.692224	+	0.399656i	0.804445	−	0.594028i	$-0.202463\pi$
$191$	132.215	+	76.3342i	0.692224	+	0.399656i	−0.112221	+	0.993683i	$0.535796\pi$
$192$	163.972	+	156.761i	0.854021	+	0.816464i
$193$	−137.840	−	238.745i	−0.714195	−	1.23702i	−0.963269	−	0.268537i	$-0.913460\pi$
$193$	−137.840	−	238.745i	−0.714195	−	1.23702i	0.249075	−	0.968484i	$-0.419874\pi$
$194$	4.61290	−	2.66326i	0.0237779	−	0.0137282i
$195$	−93.2630	−	319.184i	−0.478272	−	1.63684i
$196$	15.3409	−	26.5713i	0.0782701	−	0.135568i
$197$		−	143.269i		−	0.727254i	−0.931545	−	0.363627i	$-0.881538\pi$
$197$		−	143.269i		−	0.727254i	0.931545	−	0.363627i	$-0.118462\pi$
$198$	50.0615	−	31.9860i	0.252836	−	0.161545i
$199$	−133.941			−0.673072			−0.336536	−	0.941671i	$-0.609255\pi$
$199$	−133.941			−0.673072			−0.336536	+	0.941671i	$0.609255\pi$
$200$	−35.6477	−	20.5812i	−0.178238	−	0.102906i
$201$	−37.9261	+	155.437i	−0.188687	+	0.773317i
$202$	208.276	+	360.745i	1.03107	+	1.78587i
$203$	−25.1031	+	14.4933i	−0.123660	+	0.0713954i
$204$	70.7507	+	17.2630i	0.346817	+	0.0846223i
$205$	−13.8881	+	24.0549i	−0.0677469	+	0.117341i
$206$		−	205.308i		−	0.996642i
$207$	122.328	+	191.456i	0.590955	+	0.924908i
$208$	201.421			0.968369
$209$	−65.4642	−	37.7958i	−0.313226	−	0.180841i
$210$	−173.842	+	50.7951i	−0.827817	+	0.241881i
$211$	138.956	+	240.678i	0.658558	+	1.14066i	0.980989	+	0.194063i	$0.0621666\pi$
$211$	138.956	+	240.678i	0.658558	+	1.14066i	−0.322431	+	0.946593i	$0.604500\pi$
$212$	−128.449	+	74.1603i	−0.605894	+	0.349813i
$213$	−151.685	+	158.662i	−0.712135	+	0.744893i
$214$	−185.301	+	320.950i	−0.865890	+	1.49977i
$215$			500.401i			2.32745i
$216$	22.5573	+	19.7031i	0.104432	+	0.0912182i
$217$	−71.9197			−0.331427
$218$	286.627	+	165.484i	1.31480	+	0.759101i
$219$	212.141	+	202.812i	0.968682	+	0.926083i
$220$	−39.3750	−	68.1995i	−0.178977	−	0.309998i
$221$	67.4611	−	38.9487i	0.305254	−	0.176238i
$222$	2.11970	+	7.25447i	0.00954819	+	0.0326778i
$223$	−18.0999	+	31.3499i	−0.0811654	+	0.140583i	−0.903751	−	0.428059i	$-0.859198\pi$
$223$	−18.0999	+	31.3499i	−0.0811654	+	0.140583i	0.822585	+	0.568642i	$0.192531\pi$
$224$		−	121.442i		−	0.542152i
$225$	296.433	+	153.815i	1.31748	+	0.683622i
$226$	129.587			0.573395
$227$	−55.3087	−	31.9325i	−0.243650	−	0.140672i	0.373203	−	0.927750i	$-0.378260\pi$
$227$	−55.3087	−	31.9325i	−0.243650	−	0.140672i	−0.616853	+	0.787078i	$0.711593\pi$
$228$	103.350	−	423.569i	0.453288	−	1.85776i
$229$	−113.951	−	197.369i	−0.497602	−	0.861872i	0.502394	−	0.864639i	$-0.332453\pi$
$229$	−113.951	−	197.369i	−0.497602	−	0.861872i	−0.999996	+	0.00276684i	$0.999119\pi$
$230$	498.848	−	288.010i	2.16891	−	1.25222i
$231$	−17.5796	−	4.28936i	−0.0761021	−	0.0185687i
$232$	6.07660	−	10.5250i	0.0261923	−	0.0453663i
$233$			410.821i			1.76318i	0.472018	+	0.881589i	$0.343526\pi$
$233$			410.821i			1.76318i	−0.472018	+	0.881589i	$0.656474\pi$
$234$	366.139	−	16.4718i	1.56470	−	0.0703921i
$235$	−662.197			−2.81786
$236$	10.7678	+	6.21680i	0.0456264	+	0.0263424i
$237$	3.03799	−	0.887675i	0.0128185	−	0.00374546i
$238$	−21.2132	−	36.7423i	−0.0891309	−	0.154379i
$239$	364.478	−	210.431i	1.52501	−	0.880466i	0.525451	−	0.850824i	$-0.323897\pi$
$239$	364.478	−	210.431i	1.52501	−	0.880466i	0.999561	−	0.0296419i	$-0.00943669\pi$
$240$	−233.968	+	244.730i	−0.974866	+	1.01971i
$241$	174.583	−	302.386i	0.724410	−	1.25472i	−0.234806	−	0.972042i	$-0.575445\pi$
$241$	174.583	−	302.386i	0.724410	−	1.25472i	0.959216	−	0.282673i	$-0.0912212\pi$
$242$			335.290i			1.38550i
$243$	−190.014	−	151.471i	−0.781952	−	0.623338i
$244$	−292.397			−1.19835
$245$	47.7748	+	27.5828i	0.194999	+	0.112583i
$246$	−22.1288	−	21.1557i	−0.0899545	−	0.0859986i
$247$	−233.177	−	403.875i	−0.944038	−	1.63512i
$248$	26.1140	−	15.0769i	0.105298	−	0.0607940i
$249$	33.3080	+	113.994i	0.133767	+	0.457806i
$250$	138.128	−	239.245i	0.552513	−	0.956981i
$251$			275.387i			1.09716i	0.836099	+	0.548579i	$0.184831\pi$
$251$			275.387i			1.09716i	−0.836099	+	0.548579i	$0.815169\pi$
$252$	−4.69062	−	104.264i	−0.0186136	−	0.413748i
$253$	57.5520			0.227478
$254$	−217.295	−	125.455i	−0.855492	−	0.493919i
$255$	−31.0386	+	127.209i	−0.121720	+	0.498859i
$256$	−100.080	−	173.344i	−0.390939	−	0.677126i
$257$	99.8851	−	57.6687i	0.388658	−	0.224392i	−0.292921	−	0.956137i	$-0.594627\pi$
$257$	99.8851	−	57.6687i	0.388658	−	0.224392i	0.681578	+	0.731745i	$0.261294\pi$
$258$	−535.815	−	130.737i	−2.07680	−	0.506733i
$259$	1.15104	−	1.99366i	0.00444417	−	0.00769753i
$260$		−	485.841i		−	1.86862i
$261$	−45.4139	+	87.5220i	−0.174000	+	0.335334i
$262$	114.503			0.437036
$263$	−188.211	−	108.664i	−0.715630	−	0.413169i	0.0975121	−	0.995234i	$-0.468912\pi$
$263$	−188.211	−	108.664i	−0.715630	−	0.413169i	−0.813142	+	0.582065i	$0.802245\pi$
$264$	7.28234	−	2.12784i	0.0275846	−	0.00806000i
$265$	−133.339	−	230.951i	−0.503167	−	0.871512i
$266$	−219.968	+	126.999i	−0.826948	+	0.477438i
$267$	257.753	−	269.609i	0.965366	−	1.00977i
$268$	−116.881	+	202.444i	−0.436123	+	0.755387i
$269$		−	85.7347i		−	0.318716i	−0.987221	−	0.159358i	$-0.949058\pi$
$269$		−	85.7347i		−	0.318716i	0.987221	−	0.159358i	$-0.0509424\pi$
$270$	−405.289	+	464.000i	−1.50107	+	1.71852i
$271$	288.827			1.06578			0.532891	−	0.846184i	$-0.321105\pi$
$271$	288.827			1.06578			0.532891	+	0.846184i	$0.321105\pi$
$272$	−68.6877	−	39.6568i	−0.252528	−	0.145797i
$273$	−80.6940	−	77.1453i	−0.295582	−	0.282584i
$274$	24.3205	+	42.1243i	0.0887609	+	0.153738i
$275$	73.2628	−	42.2983i	0.266410	−	0.153812i
$276$	93.0995	+	318.625i	0.337317	+	1.15444i
$277$	176.245	−	305.266i	0.636265	−	1.10204i	−0.349981	−	0.936757i	$-0.613812\pi$
$277$	176.245	−	305.266i	0.636265	−	1.10204i	0.986246	−	0.165286i	$-0.0528547\pi$
$278$		−	371.995i		−	1.33811i
$279$	−206.160	+	131.722i	−0.738923	+	0.472123i
$280$	−23.1293			−0.0826048
$281$	−261.845	−	151.176i	−0.931832	−	0.537994i	−0.0444416	−	0.999012i	$-0.514151\pi$
$281$	−261.845	−	151.176i	−0.931832	−	0.537994i	−0.887391	+	0.461018i	$0.847484\pi$
$282$	173.009	−	709.061i	0.613506	−	2.51440i
$283$	67.9930	+	117.767i	0.240258	+	0.416139i	0.960788	−	0.277285i	$-0.0894346\pi$
$283$	67.9930	+	117.767i	0.240258	+	0.416139i	−0.720530	+	0.693424i	$0.756101\pi$
$284$	−277.738	+	160.352i	−0.977951	+	0.564620i
$285$	761.573	+	185.821i	2.67218	+	0.652004i
$286$	46.4204	−	80.4024i	0.162309	−	0.281127i
$287$			9.32506i			0.0324915i
$288$	−222.424	−	348.117i	−0.772304	−	1.20874i
$289$	258.326			0.893862
$290$	216.497	+	124.994i	0.746540	+	0.431015i
$291$	−5.29751	+	1.54789i	−0.0182045	+	0.00531921i
$292$	214.401	+	371.353i	0.734250	+	1.27176i
$293$	0.576708	−	0.332963i	0.00196829	−	0.00113639i	−0.499016	−	0.866593i	$-0.666305\pi$
$293$	0.576708	−	0.332963i	0.00196829	−	0.00113639i	0.500984	+	0.865457i	$0.332972\pi$
$294$	−42.0167	+	43.9494i	−0.142914	+	0.149488i
$295$	−11.1777	+	19.3604i	−0.0378906	+	0.0656285i
$296$			0.965196i			0.00326080i
$297$	−58.2484	+	19.9018i	−0.196123	+	0.0670094i
$298$	252.852			0.848497
$299$	307.492	+	177.531i	1.02840	+	0.593749i
$300$	352.690	+	337.180i	1.17563	+	1.12393i
$301$	83.9976	+	145.488i	0.279062	+	0.483349i
$302$	−329.829	+	190.427i	−1.09215	+	0.630552i
$303$	−121.050	−	414.283i	−0.399506	−	1.36727i
$304$	−237.417	+	411.218i	−0.780977	+	1.35269i
$305$		−	525.727i		−	1.72369i
$306$	−128.102	−	66.4704i	−0.418635	−	0.217223i
$307$	−260.484			−0.848482			−0.424241	−	0.905549i	$-0.639459\pi$
$307$	−260.484			−0.848482			−0.424241	+	0.905549i	$0.639459\pi$
$308$	−22.8960	−	13.2190i	−0.0743376	−	0.0429189i
$309$	−50.4256	+	206.665i	−0.163190	+	0.668819i
$310$	310.129	+	537.159i	1.00042	+	1.73277i
$311$	29.5765	−	17.0760i	0.0951012	−	0.0549067i	−0.451695	−	0.892172i	$-0.649181\pi$
$311$	29.5765	−	17.0760i	0.0951012	−	0.0549067i	0.546796	+	0.837266i	$0.315847\pi$
$312$	45.4723	+	11.0951i	0.145745	+	0.0355612i
$313$	−146.877	+	254.399i	−0.469256	+	0.812775i	−0.999382	−	0.0351436i	$-0.988811\pi$
$313$	−146.877	+	254.399i	−0.469256	+	0.812775i	0.530126	+	0.847919i	$0.322144\pi$
$314$		−	80.0642i		−	0.254982i
$315$	187.466	−	8.43368i	0.595131	−	0.0267736i
$316$	4.62422			0.0146336
$317$	352.994	+	203.801i	1.11355	+	0.642907i	0.939746	−	0.341874i	$-0.111062\pi$
$317$	352.994	+	203.801i	1.11355	+	0.642907i	0.173801	+	0.984781i	$0.444395\pi$
$318$	282.132	−	82.4366i	0.887207	−	0.259235i
$319$	12.4886	+	21.6309i	0.0391492	+	0.0678083i
$320$	−516.082	+	297.960i	−1.61276	+	0.931125i
$321$	265.353	−	277.559i	0.826646	−	0.864671i
$322$	96.6910	−	167.474i	0.300283	−	0.520105i
$323$			183.637i			0.568536i
$324$	−204.408	−	290.286i	−0.630889	−	0.895944i
$325$	521.911			1.60588
$326$	−42.5083	−	24.5422i	−0.130394	−	0.0752828i
$327$	−247.877	−	236.976i	−0.758033	−	0.724697i
$328$	−1.95486	−	3.38592i	−0.00595995	−	0.0103229i
$329$	−192.529	+	111.157i	−0.585195	+	0.337862i
$330$	43.7692	+	149.796i	0.132634	+	0.453928i
$331$	−162.294	+	281.102i	−0.490316	+	0.849252i	−0.999938	−	0.0111467i	$-0.996452\pi$
$331$	−162.294	+	281.102i	−0.490316	+	0.849252i	0.509622	+	0.860398i	$0.329785\pi$
$332$			173.514i			0.522631i
$333$	−0.351940	−	7.82303i	−0.00105688	−	0.0234926i
$334$	488.841			1.46360
$335$	−363.991	−	210.150i	−1.08654	−	0.627315i
$336$	−26.9440	+	110.428i	−0.0801904	+	0.328653i
$337$	−12.2780	−	21.2661i	−0.0364332	−	0.0631041i	0.847234	−	0.531220i	$-0.178266\pi$
$337$	−12.2780	−	21.2661i	−0.0364332	−	0.0631041i	−0.883667	+	0.468116i	$0.844933\pi$
$338$	72.2752	−	41.7281i	0.213832	−	0.123456i
$339$	−130.444	−	31.8279i	−0.384790	−	0.0938875i
$340$	−95.6550	+	165.679i	−0.281338	+	0.487292i
$341$			61.9719i			0.181736i
$342$	−397.944	+	766.920i	−1.16358	+	2.24246i
$343$	18.5203			0.0539949
$344$	−60.9989	−	35.2177i	−0.177322	−	0.102377i
$345$	−572.883	+	167.392i	−1.66053	+	0.485194i
$346$	−55.0198	−	95.2970i	−0.159017	−	0.275425i
$347$	76.0638	−	43.9154i	0.219204	−	0.126557i	−0.386378	−	0.922341i	$-0.626274\pi$
$347$	76.0638	−	43.9154i	0.219204	−	0.126557i	0.605582	+	0.795783i	$0.292941\pi$
$348$	−99.5525	+	104.132i	−0.286070	+	0.299229i
$349$	19.8106	−	34.3129i	0.0567638	−	0.0983178i	−0.836247	−	0.548353i	$-0.815255\pi$
$349$	19.8106	−	34.3129i	0.0567638	−	0.0983178i	0.893011	+	0.450035i	$0.148588\pi$
$350$		−	284.255i		−	0.812158i
$351$	−372.604	−	73.3466i	−1.06155	−	0.208965i
$352$	−104.644			−0.297285
$353$	103.562	+	59.7915i	0.293376	+	0.169381i	0.639463	−	0.768821i	$-0.279157\pi$
$353$	103.562	+	59.7915i	0.293376	+	0.169381i	−0.346087	+	0.938202i	$0.612490\pi$
$354$	−17.8102	−	17.0270i	−0.0503113	−	0.0480988i
$355$	−288.311	−	499.369i	−0.812144	−	1.40667i
$356$	471.951	−	272.481i	1.32570	−	0.765396i
$357$	12.3291	+	42.1952i	0.0345353	+	0.118194i
$358$	61.3429	−	106.249i	0.171349	−	0.296785i
$359$		−	697.731i		−	1.94354i	−0.235930	−	0.971770i	$-0.575814\pi$
$359$		−	697.731i		−	1.94354i	0.235930	−	0.971770i	$-0.424186\pi$
$360$	−66.3008	+	42.3618i	−0.184169	+	0.117672i
$361$	738.396			2.04542
$362$	−612.280	−	353.500i	−1.69138	−	0.976520i
$363$	82.3504	−	337.506i	0.226861	−	0.929769i
$364$	−81.5535	−	141.255i	−0.224048	−	0.388063i
$365$	−667.689	+	385.490i	−1.82928	+	1.05614i
$366$	562.933	+	137.354i	1.53807	+	0.375283i
$367$	159.043	−	275.470i	0.433358	−	0.750599i	−0.563802	−	0.825910i	$-0.690662\pi$
$367$	159.043	−	275.470i	0.433358	−	0.750599i	0.997160	+	0.0753115i	$0.0239951\pi$
$368$		−	361.517i		−	0.982384i
$369$	17.0790	+	26.7305i	0.0462846	+	0.0724404i
$370$	−19.8539			−0.0536591
$371$	−77.5349	−	44.7648i	−0.208989	−	0.120660i
$372$	−343.094	+	100.249i	−0.922297	+	0.269488i
$373$	194.442	+	336.783i	0.521292	+	0.902903i	0.999693	+	0.0247624i	$0.00788292\pi$
$373$	194.442	+	336.783i	0.521292	+	0.902903i	−0.478402	+	0.878141i	$0.658784\pi$
$374$	−31.6602	+	18.2790i	−0.0846528	+	0.0488743i
$375$	−197.802	+	206.901i	−0.527472	+	0.551735i
$376$	46.6048	−	80.7218i	0.123949	−	0.214686i
$377$			154.094i			0.408738i
$378$	−39.9477	+	202.937i	−0.105682	+	0.536869i
$379$	430.954			1.13708			0.568541	−	0.822655i	$-0.307508\pi$
$379$	430.954			1.13708			0.568541	+	0.822655i	$0.307508\pi$
$380$	991.887	+	572.666i	2.61023	+	1.50702i
$381$	187.918	+	179.654i	0.493223	+	0.471533i
$382$	−221.015	−	382.810i	−0.578574	−	1.00212i
$383$	194.962	−	112.561i	0.509038	−	0.293893i	−0.223400	−	0.974727i	$-0.571716\pi$
$383$	194.962	−	112.561i	0.509038	−	0.293893i	0.732438	+	0.680833i	$0.238382\pi$
$384$	−29.7301	−	101.749i	−0.0774221	−	0.264970i
$385$	23.7676	−	41.1667i	0.0617341	−	0.106927i
$386$			798.191i			2.06785i
$387$	507.245	+	263.202i	1.31071	+	0.680109i
$388$	−8.06352			−0.0207823
$389$	299.597	+	172.973i	0.770173	+	0.444659i	0.832936	−	0.553369i	$-0.186658\pi$
$389$	299.597	+	172.973i	0.770173	+	0.444659i	−0.0627635	+	0.998028i	$0.519991\pi$
$390$	−228.224	+	935.356i	−0.585189	+	2.39835i
$391$	−69.9065	−	121.082i	−0.178789	−	0.309672i
$392$	−6.72469	+	3.88250i	−0.0171548	+	0.00990434i
$393$	−115.260	−	28.1231i	−0.293283	−	0.0715600i
$394$	−207.408	+	359.241i	−0.526416	+	0.911779i
$395$			8.31429i			0.0210488i
$396$	−89.8428	+	4.04182i	−0.226876	+	0.0102066i
$397$	−663.550			−1.67141			−0.835705	−	0.549178i	$-0.814941\pi$
$397$	−663.550			−1.67141			−0.835705	+	0.549178i	$0.814941\pi$
$398$	335.852	+	193.904i	0.843850	+	0.487197i
$399$	252.614	−	73.8117i	0.633117	−	0.184992i
$400$	−265.700	−	460.206i	−0.664250	−	1.15051i
$401$	−191.553	+	110.593i	−0.477689	+	0.275794i	−0.719453	−	0.694541i	$-0.755607\pi$
$401$	−191.553	+	110.593i	−0.477689	+	0.275794i	0.241764	+	0.970335i	$0.422274\pi$
$402$	320.121	−	334.846i	0.796320	−	0.832951i
$403$	−191.165	+	331.107i	−0.474355	+	0.821606i
$404$		−	630.595i		−	1.56088i
$405$	521.930	−	367.523i	1.28872	−	0.907465i
$406$	83.9265			0.206716
$407$	−1.71790	−	0.991831i	−0.00422089	−	0.00243693i
$408$	−13.3223	−	12.7364i	−0.0326527	−	0.0312168i
$409$	−128.610	−	222.758i	−0.314449	−	0.544641i	0.664871	−	0.746958i	$-0.268486\pi$
$409$	−128.610	−	222.758i	−0.314449	−	0.544641i	−0.979320	+	0.202317i	$0.935153\pi$
$410$	69.6477	−	40.2111i	0.169872	−	0.0980759i
$411$	−14.1351	−	48.3761i	−0.0343920	−	0.117703i
$412$	−155.402	+	269.165i	−0.377190	+	0.653312i
$413$			7.50520i			0.0181724i
$414$	−29.5641	−	657.159i	−0.0714109	−	1.58734i
$415$	−311.975			−0.751747
$416$	−559.101	−	322.797i	−1.34399	−	0.775955i
$417$	−91.3654	+	374.453i	−0.219102	+	0.897970i
$418$	109.432	+	189.542i	0.261800	+	0.453451i
$419$	312.350	−	180.335i	0.745465	−	0.430394i	−0.0785879	−	0.996907i	$-0.525041\pi$
$419$	312.350	−	180.335i	0.745465	−	0.430394i	0.824053	+	0.566513i	$0.191708\pi$
$420$	266.359	+	64.9907i	0.634188	+	0.154740i
$421$	−207.240	+	358.951i	−0.492257	+	0.852615i	−0.999960	−	0.00891739i	$-0.997161\pi$
$421$	−207.240	+	358.951i	−0.492257	+	0.852615i	0.507703	+	0.861532i	$0.330495\pi$
$422$		−	804.655i		−	1.90676i
$423$	−348.304	+	671.254i	−0.823413	+	1.58689i
$424$	37.5372			0.0885311
$425$	−177.980	−	102.757i	−0.418776	−	0.241780i
$426$	610.035	−	178.247i	1.43201	−	0.418421i
$427$	−88.2488	−	152.851i	−0.206672	−	0.357966i
$428$	485.868	−	280.516i	1.13521	−	0.655411i
$429$	−66.4747	+	69.5325i	−0.154953	+	0.162080i
$430$	724.421	−	1254.73i	1.68470	−	2.91799i
$431$			228.418i			0.529972i	0.964252	+	0.264986i	$0.0853673\pi$
$431$			228.418i			0.529972i	−0.964252	+	0.264986i	$0.914633\pi$
$432$	125.015	+	365.892i	0.289386	+	0.846972i
$433$	−419.884			−0.969708			−0.484854	−	0.874595i	$-0.661127\pi$
$433$	−419.884			−0.969708			−0.484854	+	0.874595i	$0.661127\pi$
$434$	180.336	+	104.117i	0.415520	+	0.239900i
$435$	−187.228	−	178.994i	−0.430408	−	0.411481i
$436$	−250.517	−	433.908i	−0.574580	−	0.995202i
$437$	−724.890	+	418.515i	−1.65879	+	0.957701i
$438$	−238.328	−	815.656i	−0.544128	−	1.86223i
$439$	−132.842	+	230.089i	−0.302601	+	0.524121i	−0.976724	−	0.214498i	$-0.931188\pi$
$439$	−132.842	+	230.089i	−0.302601	+	0.524121i	0.674123	+	0.738619i	$0.264522\pi$
$440$			19.9301i			0.0452958i
$441$	53.0888	−	33.9202i	0.120383	−	0.0769166i
$442$	−225.541			−0.510274
$443$	556.867	+	321.507i	1.25704	+	0.725750i	0.972497	−	0.232915i	$-0.0748264\pi$
$443$	556.867	+	321.507i	1.25704	+	0.725750i	0.284538	+	0.958665i	$0.408160\pi$
$444$	2.71209	−	11.1153i	0.00610830	−	0.0250344i
$445$	489.917	+	848.561i	1.10094	+	1.90688i
$446$	90.7693	−	52.4057i	0.203519	−	0.117502i
$447$	−254.523	−	62.1029i	−0.569403	−	0.138933i
$448$	−100.031	+	173.259i	−0.223284	+	0.386740i
$449$		−	514.030i		−	1.14483i	−0.819963	−	0.572416i	$-0.806006\pi$
$449$		−	514.030i		−	1.14483i	0.819963	−	0.572416i	$-0.193994\pi$
$450$	−520.619	−	814.825i	−1.15693	−	1.81072i
$451$	8.03524			0.0178165
$452$	−169.892	−	98.0874i	−0.375868	−	0.217008i
$453$	378.779	−	110.676i	0.836157	−	0.244318i
$454$	92.4561	+	160.139i	0.203648	+	0.352728i
$455$	253.974	−	146.632i	0.558185	−	0.322268i
$456$	−76.2503	+	79.7578i	−0.167216	+	0.174907i
$457$	20.0379	−	34.7067i	0.0438466	−	0.0759446i	−0.843269	−	0.537491i	$-0.819372\pi$
$457$	20.0379	−	34.7067i	0.0438466	−	0.0759446i	0.887116	+	0.461547i	$0.152705\pi$
$458$			659.858i			1.44074i
$459$	112.623	+	98.3727i	0.245366	+	0.214320i
$460$	−872.004			−1.89566
$461$	−321.793	−	185.787i	−0.698032	−	0.403009i	0.108582	−	0.994087i	$-0.465369\pi$
$461$	−321.793	−	185.787i	−0.698032	−	0.403009i	−0.806614	+	0.591078i	$0.798702\pi$
$462$	37.8704	+	36.2050i	0.0819707	+	0.0783659i
$463$	82.9153	+	143.613i	0.179083	+	0.310180i	0.941567	−	0.336827i	$-0.109354\pi$
$463$	82.9153	+	143.613i	0.179083	+	0.310180i	−0.762484	+	0.647007i	$0.776020\pi$
$464$	135.876	−	78.4480i	0.292836	−	0.169069i
$465$	−180.247	−	616.880i	−0.387628	−	1.32662i
$466$	594.737	−	1030.12i	1.27626	−	2.21055i
$467$		−	162.544i		−	0.348060i	−0.984740	−	0.174030i	$-0.944321\pi$
$467$		−	162.544i		−	0.348060i	0.984740	−	0.174030i	$-0.0556789\pi$
$468$	−492.486	−	255.544i	−1.05232	−	0.546033i
$469$	−141.104			−0.300861
$470$	1660.43	+	958.650i	3.53283	+	2.03968i
$471$	−19.6645	+	80.5934i	−0.0417506	+	0.171111i
$472$	−1.57336	−	2.72513i	−0.00333338	−	0.00577359i
$473$	125.364	−	72.3792i	0.265041	−	0.153022i
$474$	−8.90269	−	2.17223i	−0.0187821	−	0.00458276i
$475$	−615.182	+	1065.53i	−1.29512	+	2.24321i
$476$			64.2268i			0.134930i
$477$	−304.244	+	13.6872i	−0.637827	+	0.0286944i
$478$	−1218.55			−2.54927
$479$	−200.025	−	115.485i	−0.417589	−	0.241095i	0.276456	−	0.961027i	$-0.410840\pi$
$479$	−200.025	−	115.485i	−0.417589	−	0.241095i	−0.694045	+	0.719931i	$0.744173\pi$
$480$	1041.65	−	304.362i	2.17011	−	0.634087i
$481$	−6.11901	−	10.5984i	−0.0127214	−	0.0220342i
$482$	−875.518	+	505.481i	−1.81643	+	1.04872i
$483$	−138.463	+	144.832i	−0.286673	+	0.299860i
$484$	253.788	−	439.575i	0.524356	−	0.908212i
$485$		−	14.4981i		−	0.0298930i
$486$	257.171	+	654.888i	0.529159	+	1.34751i
$487$	−361.340			−0.741971			−0.370985	−	0.928639i	$-0.620980\pi$
$487$	−361.340			−0.741971			−0.370985	+	0.928639i	$0.620980\pi$
$488$	64.0861	+	37.0001i	0.131324	+	0.0758200i
$489$	36.7615	+	35.1448i	0.0751769	+	0.0718709i
$490$	−79.8623	−	138.325i	−0.162984	−	0.282297i
$491$	6.98433	−	4.03241i	0.0142247	−	0.00821264i	−0.492871	−	0.870103i	$-0.664052\pi$
$491$	6.98433	−	4.03241i	0.0142247	−	0.00821264i	0.507095	+	0.861890i	$0.330719\pi$
$492$	12.9983	+	44.4854i	0.0264193	+	0.0904175i
$493$	30.3390	−	52.5486i	0.0615395	−	0.106589i
$494$			1350.27i			2.73333i
$495$	−7.26715	−	161.536i	−0.0146811	−	0.326336i
$496$	389.281			0.784841
$497$	−167.649	−	96.7921i	−0.337322	−	0.194753i
$498$	81.5080	−	334.054i	0.163671	−	0.670790i
$499$	48.5938	+	84.1670i	0.0973824	+	0.168671i	0.910600	−	0.413288i	$-0.135620\pi$
$499$	48.5938	+	84.1670i	0.0973824	+	0.168671i	−0.813218	+	0.581959i	$0.802286\pi$
$500$	−362.180	+	209.105i	−0.724360	+	0.418209i
$501$	−492.072	−	120.064i	−0.982180	−	0.239649i
$502$	398.672	−	690.520i	0.794167	−	1.37554i
$503$			306.769i			0.609880i	0.952372	+	0.304940i	$0.0986363\pi$
$503$			306.769i			0.609880i	−0.952372	+	0.304940i	$0.901364\pi$
$504$	−12.1656	+	23.4457i	−0.0241381	+	0.0465192i
$505$	1133.80			2.24515
$506$	−144.309	−	83.3169i	−0.285196	−	0.164658i
$507$	−83.0016	+	24.2524i	−0.163711	+	0.0478351i
$508$	189.920	+	328.951i	0.373858	+	0.647541i
$509$	85.0056	−	49.0780i	0.167005	−	0.0964205i	−0.414168	−	0.910201i	$-0.635927\pi$
$509$	85.0056	−	49.0780i	0.167005	−	0.0964205i	0.581173	+	0.813780i	$0.302594\pi$
$510$	261.986	−	274.037i	0.513698	−	0.537328i
$511$	−129.417	+	224.157i	−0.253263	+	0.438664i
$512$			720.875i			1.40796i
$513$	588.936	−	674.250i	1.14802	−	1.31433i
$514$	−333.944			−0.649696
$515$	−483.955	−	279.411i	−0.939718	−	0.542546i
$516$	603.509	+	576.969i	1.16959	+	1.11816i
$517$	95.7817	+	165.899i	0.185264	+	0.320887i
$518$	−5.77237	+	3.33268i	−0.0111436	+	0.00643375i
$519$	31.9775	+	109.440i	0.0616138	+	0.210867i
$520$	−61.4786	+	106.484i	−0.118228	+	0.204777i
$521$		−	144.455i		−	0.277264i	−0.990344	−	0.138632i	$-0.955729\pi$
$521$		−	144.455i		−	0.277264i	0.990344	−	0.138632i	$-0.0442705\pi$
$522$	240.577	−	153.713i	0.460876	−	0.294469i
$523$	377.311			0.721437			0.360718	−	0.932675i	$-0.382532\pi$
$523$	377.311			0.721437			0.360718	+	0.932675i	$0.382532\pi$
$524$	−150.117	−	86.6700i	−0.286483	−	0.165401i
$525$	−69.8158	+	286.134i	−0.132982	+	0.545017i
$526$	314.620	+	544.938i	0.598137	+	1.03600i
$527$	130.381	−	75.2752i	0.247401	−	0.142837i
$528$	95.1534	+	23.2171i	0.180215	+	0.0439718i
$529$	54.1387	−	93.7710i	0.102342	−	0.177261i
$530$			772.132i			1.45685i
$531$	13.7459	+	21.5138i	0.0258868	+	0.0405157i
$532$	384.512			0.722767
$533$	42.9312	+	24.7863i	0.0805463	+	0.0465034i
$534$	−1036.61	+	302.890i	−1.94122	+	0.567209i
$535$	504.364	+	873.584i	0.942737	+	1.63287i
$536$	51.2347	−	29.5804i	0.0955871	−	0.0551873i
$537$	−87.8440	+	91.8848i	−0.163583	+	0.171108i
$538$	−124.116	+	214.976i	−0.230700	+	0.399584i
$539$		−	15.9586i		−	0.0296077i
$540$	882.556	−	301.544i	1.63436	−	0.558414i
$541$	−968.183			−1.78962			−0.894809	−	0.446449i	$-0.852688\pi$
$541$	−968.183			−1.78962			−0.894809	+	0.446449i	$0.852688\pi$
$542$	−724.222	−	418.130i	−1.33620	−	0.771457i
$543$	529.504	+	506.218i	0.975145	+	0.932262i
$544$	127.108	+	220.158i	0.233655	+	0.404702i
$545$	780.161	−	450.426i	1.43149	−	0.826470i
$546$	90.6548	+	310.258i	0.166034	+	0.568238i
$547$	372.444	−	645.092i	0.680885	−	1.17933i	−0.293826	−	0.955859i	$-0.594929\pi$
$547$	372.444	−	645.092i	0.680885	−	1.17933i	0.974711	−	0.223468i	$-0.0717379\pi$
$548$		−	73.6348i		−	0.134370i
$549$	−532.917	−	276.523i	−0.970706	−	0.503685i
$550$	−244.938			−0.445341
$551$	−314.597	−	181.633i	−0.570957	−	0.329642i
$552$	19.9139	−	81.6153i	0.0360759	−	0.147854i
$553$	1.39564	+	2.41732i	0.00252376	+	0.00437129i
$554$	−883.855	+	510.294i	−1.59541	+	0.921108i
$555$	19.9851	+	4.87630i	0.0360092	+	0.00878612i
$556$	−281.571	+	487.695i	−0.506423	+	0.877150i
$557$			303.912i			0.545623i	0.962067	+	0.272812i	$0.0879536\pi$
$557$			303.912i			0.545623i	−0.962067	+	0.272812i	$0.912046\pi$
$558$	707.628	−	31.8346i	1.26815	−	0.0570512i
$559$	893.074			1.59763
$560$	−258.592	−	149.298i	−0.461771	−	0.266604i
$561$	36.3589	−	10.6238i	0.0648108	−	0.0189372i
$562$	437.710	+	758.136i	0.778843	+	1.34900i
$563$	523.390	−	302.179i	0.929644	−	0.536730i	0.0429450	−	0.999077i	$-0.486326\pi$
$563$	523.390	−	302.179i	0.929644	−	0.536730i	0.886699	+	0.462347i	$0.152993\pi$
$564$	−763.522	+	798.644i	−1.35376	+	1.41603i
$565$	176.360	−	305.464i	0.312142	−	0.540645i
$566$		−	393.729i		−	0.695634i
$567$	90.0549	−	194.466i	0.158827	−	0.342974i
$568$	81.1642			0.142895
$569$	−442.648	−	255.563i	−0.777939	−	0.449144i	0.0577601	−	0.998330i	$-0.481604\pi$
$569$	−442.648	−	255.563i	−0.777939	−	0.449144i	−0.835700	+	0.549187i	$0.814937\pi$
$570$	−1640.60	−	1568.45i	−2.87825	−	2.75167i
$571$	−241.544	−	418.367i	−0.423020	−	0.732692i	0.573213	−	0.819406i	$-0.305697\pi$
$571$	−241.544	−	418.367i	−0.423020	−	0.732692i	−0.996233	+	0.0867141i	$0.972363\pi$
$572$	−121.717	+	70.2732i	−0.212791	+	0.122855i
$573$	128.454	+	439.623i	0.224178	+	0.767230i
$574$	13.4997	−	23.3822i	0.0235187	−	0.0407355i
$575$		−	936.744i		−	1.62912i
$576$	30.5854	+	679.862i	0.0530997	+	1.18032i
$577$	−835.397			−1.44783			−0.723914	−	0.689890i	$-0.757659\pi$
$577$	−835.397			−1.44783			−0.723914	+	0.689890i	$0.757659\pi$
$578$	−647.742	−	373.974i	−1.12066	−	0.647014i
$579$	196.043	−	803.466i	0.338589	−	1.38768i
$580$	−189.222	−	327.742i	−0.326245	−	0.565073i
$581$	−90.7046	+	52.3683i	−0.156118	+	0.0901348i
$582$	15.5241	+	3.78784i	0.0266738	+	0.00650832i
$583$	−38.5730	+	66.8105i	−0.0661630	+	0.114598i
$584$		−	108.522i		−	0.185825i
$585$	459.464	−	885.483i	0.785409	−	1.51365i
$586$	−1.92810			−0.00329027
$587$	874.239	+	504.742i	1.48933	+	0.859868i	0.999926	−	0.0121870i	$-0.00387933\pi$
$587$	874.239	+	504.742i	1.48933	+	0.859868i	0.489409	+	0.872055i	$0.337213\pi$
$588$	88.3513	−	25.8155i	0.150257	−	0.0439040i
$589$	−450.657	−	780.560i	−0.765121	−	1.32523i
$590$	56.0554	−	32.3636i	0.0950092	−	0.0548536i
$591$	297.012	−	310.674i	0.502558	−	0.525675i
$592$	−6.23026	+	10.7911i	−0.0105241	+	0.0182283i
$593$		−	1127.85i		−	1.90193i	−0.309291	−	0.950967i	$-0.600092\pi$
$593$		−	1127.85i		−	1.90193i	0.309291	−	0.950967i	$-0.399908\pi$
$594$	174.867	+	34.4222i	0.294389	+	0.0579499i
$595$	−115.479			−0.194082
$596$	−331.496	−	191.389i	−0.556201	−	0.321123i
$597$	−290.447	−	277.674i	−0.486511	−	0.465116i
$598$	−514.016	−	890.302i	−0.859559	−	1.48880i
$599$	−715.944	+	413.350i	−1.19523	+	0.690067i	−0.959488	−	0.281748i	$-0.909086\pi$
$599$	−715.944	+	413.350i	−1.19523	+	0.690067i	−0.235743	+	0.971815i	$0.575752\pi$
$600$	−34.6338	−	118.531i	−0.0577229	−	0.197551i
$601$	273.249	−	473.280i	0.454657	−	0.787488i	−0.544012	−	0.839078i	$-0.683095\pi$
$601$	273.249	−	473.280i	0.454657	−	0.787488i	0.998668	+	0.0515892i	$0.0164287\pi$
$602$		−	486.407i		−	0.807985i
$603$	−404.478	+	258.434i	−0.670776	+	0.428581i
$604$	576.552			0.954557
$605$	790.350	+	456.309i	1.30636	+	0.754229i
$606$	−296.222	+	1214.04i	−0.488815	+	2.00337i
$607$	−242.893	−	420.704i	−0.400154	−	0.693087i	0.593590	−	0.804767i	$-0.297710\pi$
$607$	−242.893	−	420.704i	−0.400154	−	0.693087i	−0.993744	+	0.111681i	$0.964377\pi$
$608$	1318.04	−	760.970i	2.16783	−	1.25159i
$609$	−84.4812	−	20.6131i	−0.138721	−	0.0338475i
$610$	−761.085	+	1318.24i	−1.24768	+	2.16105i
$611$			1181.83i			1.93426i
$612$	117.633	+	184.108i	0.192210	+	0.300830i
$613$	365.664			0.596516			0.298258	−	0.954485i	$-0.403594\pi$
$613$	365.664			0.596516			0.298258	+	0.954485i	$0.403594\pi$
$614$	653.153	+	377.098i	1.06377	+	0.614166i
$615$	−79.9842	+	23.3707i	−0.130056	+	0.0380012i
$616$	3.34548	+	5.79454i	0.00543098	+	0.00940673i
$617$	515.476	−	297.610i	0.835455	−	0.482350i	−0.0202619	−	0.999795i	$-0.506450\pi$
$617$	515.476	−	297.610i	0.835455	−	0.482350i	0.855717	+	0.517445i	$0.173117\pi$
$618$	425.625	−	445.204i	0.688714	−	0.720394i
$619$	79.0373	−	136.897i	0.127685	−	0.221158i	−0.795094	−	0.606486i	$-0.792579\pi$
$619$	79.0373	−	136.897i	0.127685	−	0.221158i	0.922779	+	0.385329i	$0.125912\pi$
$620$		−	938.973i		−	1.51447i
$621$	−131.645	+	668.764i	−0.211989	+	1.07691i
$622$	−98.8823			−0.158975
$623$	284.880	+	164.475i	0.457271	+	0.264006i
$624$	436.774	+	417.566i	0.699958	+	0.669177i
$625$	87.8709	+	152.197i	0.140593	+	0.243515i
$626$	736.576	−	425.262i	1.17664	−	0.679333i
$627$	−63.6022	−	217.673i	−0.101439	−	0.347166i
$628$	−60.6023	+	104.966i	−0.0965006	+	0.167144i
$629$			4.81898i			0.00766134i
$630$	−482.273	−	250.244i	−0.765513	−	0.397213i
$631$	711.074			1.12690			0.563450	−	0.826150i	$-0.309474\pi$
$631$	711.074			1.12690			0.563450	+	0.826150i	$0.309474\pi$
$632$	−1.01351	−	0.585152i	−0.00160366	−	0.000925873i
$633$	−197.631	+	809.972i	−0.312213	+	1.27958i
$634$	−590.079	−	1022.05i	−0.930724	−	1.61206i
$635$	−591.449	+	341.473i	−0.931416	+	0.537753i
$636$	−432.280	−	105.475i	−0.679686	−	0.165841i
$637$	49.2275	−	85.2645i	0.0772802	−	0.133853i
$638$		−	72.3179i		−	0.113351i
$639$	−657.846	+	29.5950i	−1.02949	+	0.0463145i
$640$	278.463			0.435098
$641$	566.142	+	326.862i	0.883217	+	0.509925i	0.871718	−	0.490008i	$-0.163006\pi$
$641$	566.142	+	326.862i	0.883217	+	0.509925i	0.0114991	+	0.999934i	$0.496340\pi$
$642$	−1067.18	+	311.821i	−1.66227	+	0.485703i
$643$	−195.263	−	338.205i	−0.303675	−	0.525980i	0.673291	−	0.739378i	$-0.264880\pi$
$643$	−195.263	−	338.205i	−0.303675	−	0.525980i	−0.976965	+	0.213398i	$0.931547\pi$
$644$	−253.529	+	146.375i	−0.393679	+	0.227291i
$645$	−1037.38	+	1085.10i	−1.60835	+	1.68233i
$646$	265.848	−	460.462i	0.411529	−	0.712790i
$647$		−	1020.72i		−	1.57761i	−0.614642	−	0.788806i	$-0.710700\pi$
$647$		−	1020.72i		−	1.57761i	0.614642	−	0.788806i	$-0.289300\pi$
$648$	8.06816	+	89.4892i	0.0124509	+	0.138101i
$649$	6.46710			0.00996471
$650$	−1308.67	−	755.561i	−2.01334	−	1.16240i
$651$	−155.955	−	149.097i	−0.239563	−	0.229028i
$652$	37.1531	+	64.3510i	0.0569832	+	0.0986978i
$653$	181.851	−	104.992i	0.278486	−	0.160784i	−0.354252	−	0.935150i	$-0.615264\pi$
$653$	181.851	−	104.992i	0.278486	−	0.160784i	0.632738	+	0.774366i	$0.281931\pi$
$654$	278.475	+	953.053i	0.425802	+	1.45727i
$655$	155.832	−	269.908i	0.237911	−	0.412074i
$656$		−	50.4740i		−	0.0769420i
$657$	39.5704	+	879.582i	0.0602289	+	1.33879i
$658$	643.678			0.978234
$659$	44.1708	+	25.5020i	0.0670270	+	0.0386980i	0.533139	−	0.846028i	$-0.321012\pi$
$659$	44.1708	+	25.5020i	0.0670270	+	0.0386980i	−0.466112	+	0.884726i	$0.654346\pi$
$660$	56.0013	−	229.517i	0.0848505	−	0.347752i
$661$	359.117	+	622.008i	0.543293	+	0.941011i	0.998712	+	0.0507337i	$0.0161560\pi$
$661$	359.117	+	622.008i	0.543293	+	0.941011i	−0.455419	+	0.890277i	$0.650511\pi$
$662$	813.893	−	469.901i	1.22945	−	0.709821i
$663$	227.032	+	55.3950i	0.342431	+	0.0835521i
$664$	21.9565	−	38.0298i	0.0330670	−	0.0572738i
$665$			691.348i			1.03962i
$666$	−10.4428	+	20.1254i	−0.0156799	+	0.0302184i
$667$	276.574			0.414654
$668$	−640.884	−	370.015i	−0.959407	−	0.553914i
$669$	−104.241	+	30.4582i	−0.155815	+	0.0455280i
$670$	608.462	+	1053.89i	0.908152	+	1.57297i
$671$	−131.709	+	76.0424i	−0.196288	+	0.113327i
$672$	251.762	−	263.343i	0.374646	−	0.391879i
$673$	−428.262	+	741.772i	−0.636348	+	1.10219i	0.349880	+	0.936795i	$0.386222\pi$
$673$	−428.262	+	741.772i	−0.636348	+	1.10219i	−0.986228	+	0.165392i	$0.947111\pi$
$674$			71.0984i			0.105487i
$675$	323.931	+	948.079i	0.479898	+	1.40456i
$676$	−126.340			−0.186893
$677$	402.265	+	232.248i	0.594188	+	0.343054i	0.766752	−	0.641944i	$-0.221872\pi$
$677$	402.265	+	232.248i	0.594188	+	0.343054i	−0.172564	+	0.984998i	$0.555205\pi$
$678$	281.006	+	268.648i	0.414462	+	0.396236i
$679$	−2.43366	−	4.21522i	−0.00358418	−	0.00620799i
$680$	41.9303	−	24.2085i	0.0616622	−	0.0356007i
$681$	−53.7356	−	183.905i	−0.0789068	−	0.270051i
$682$	89.7155	−	155.392i	0.131548	−	0.227847i
$683$			713.026i			1.04396i	0.852957	+	0.521981i	$0.174807\pi$
$683$			713.026i			1.04396i	−0.852957	+	0.521981i	$0.825193\pi$
$684$	1102.21	−	704.241i	1.61142	−	1.02959i
$685$	132.394			0.193277
$686$	−46.4388	−	26.8114i	−0.0676950	−	0.0390837i
$687$	162.067	−	664.219i	0.235906	−	0.966840i
$688$	−454.656	−	787.486i	−0.660837	−	1.14460i
$689$	−412.181	+	237.973i	−0.598231	+	0.345389i
$690$	1678.81	+	409.624i	2.43306	+	0.593658i
$691$	270.538	−	468.586i	0.391517	−	0.678127i	−0.601133	−	0.799149i	$-0.705284\pi$
$691$	270.538	−	468.586i	0.391517	−	0.678127i	0.992650	+	0.121022i	$0.0386171\pi$
$692$			166.583i			0.240726i
$693$	−29.2284	−	45.7456i	−0.0421767	−	0.0660110i
$694$	−254.302			−0.366430
$695$	−876.870	−	506.261i	−1.26168	−	0.728433i
$696$	34.9963	−	10.2256i	0.0502820	−	0.0146920i
$697$	−9.76014	−	16.9051i	−0.0140031	−	0.0242540i
$698$	−99.3483	+	57.3588i	−0.142333	+	0.0821759i
$699$	−851.674	+	890.850i	−1.21842	+	1.27446i
$700$	−215.159	+	372.666i	−0.307370	+	0.532381i
$701$		−	708.853i		−	1.01120i	−0.862767	−	0.505602i	$-0.831271\pi$
$701$		−	708.853i		−	1.01120i	0.862767	−	0.505602i	$-0.168729\pi$
$702$	828.107	+	723.326i	1.17964	+	1.03038i
$703$	28.8502			0.0410387
$704$	149.295	+	86.1952i	0.212066	+	0.122436i
$705$	−1435.95	−	1372.80i	−2.03681	−	1.94724i
$706$	−173.118	−	299.849i	−0.245210	−	0.424715i
$707$	329.645	−	190.320i	0.466258	−	0.269194i
$708$	10.4616	+	35.8037i	0.0147762	+	0.0505702i
$709$	253.472	−	439.027i	0.357507	−	0.619220i	−0.630037	−	0.776565i	$-0.716960\pi$
$709$	253.472	−	439.027i	0.357507	−	0.619220i	0.987544	+	0.157345i	$0.0502936\pi$
$710$			1669.53i			2.35145i
$711$	8.42801	+	4.37317i	0.0118537	+	0.00615073i
$712$	−137.920			−0.193707
$713$	594.283	+	343.110i	0.833497	+	0.481220i
$714$	30.1706	−	123.651i	0.0422557	−	0.173181i
$715$	−126.350	−	218.845i	−0.176714	−	0.306077i
$716$	−160.844	+	92.8635i	−0.224643	+	0.129698i
$717$	1226.60	+	299.287i	1.71074	+	0.417416i
$718$	−1010.09	+	1749.53i	−1.40681	+	2.43667i
$719$			644.811i			0.896817i	0.893829	+	0.448409i	$0.148009\pi$
$719$			644.811i			0.896817i	−0.893829	+	0.448409i	$0.851991\pi$
$720$	−1014.70	+	45.6491i	−1.40931	+	0.0634016i
$721$	−187.608			−0.260206
$722$	−1851.50	−	1068.96i	−2.56440	−	1.48056i
$723$	1005.46	−	293.786i	1.39067	−	0.406343i
$724$	535.144	+	926.896i	0.739149	+	1.28024i
$725$	352.074	−	203.270i	0.485620	−	0.280373i
$726$	−695.092	+	727.065i	−0.957427	+	1.00147i
$727$	−158.880	+	275.188i	−0.218542	+	0.378525i	−0.954362	−	0.298651i	$-0.903463\pi$
$727$	−158.880	+	275.188i	−0.218542	+	0.378525i	0.735821	+	0.677177i	$0.236797\pi$
$728$			41.2793i			0.0567023i
$729$	−98.0240	−	722.380i	−0.134464	−	0.990919i
$730$	2232.27			3.05790
$731$	−304.552	−	175.833i	−0.416624	−	0.240538i
$732$	−634.054	−	606.170i	−0.866193	−	0.828101i
$733$	219.361	+	379.945i	0.299265	+	0.518342i	0.975968	−	0.217914i	$-0.0699251\pi$
$733$	219.361	+	379.945i	0.299265	+	0.518342i	−0.676703	+	0.736256i	$0.736592\pi$
$734$	−797.585	+	460.486i	−1.08663	+	0.627365i
$735$	46.4160	+	158.855i	0.0631510	+	0.216129i
$736$	−579.368	+	1003.50i	−0.787185	+	1.36344i
$737$			121.587i			0.164975i
$738$	−4.12765	−	91.7506i	−0.00559303	−	0.124323i
$739$	107.875			0.145974			0.0729869	−	0.997333i	$-0.476747\pi$
$739$	107.875			0.145974			0.0729869	+	0.997333i	$0.476747\pi$
$740$	26.0290	+	15.0278i	0.0351743	+	0.0203079i
$741$	331.638	−	1359.19i	0.447555	−	1.83427i
$742$	129.610	+	224.492i	0.174677	+	0.302550i
$743$	180.989	−	104.494i	0.243593	−	0.140638i	−0.373234	−	0.927737i	$-0.621751\pi$
$743$	180.989	−	104.494i	0.243593	−	0.140638i	0.616827	+	0.787099i	$0.288418\pi$
$744$	87.8832	+	21.4432i	0.118123	+	0.0288215i
$745$	344.116	−	596.026i	0.461900	−	0.800034i
$746$		−	1125.96i		−	1.50933i
$747$	−164.093	+	316.242i	−0.219670	+	0.423350i
$748$	55.3431			0.0739881
$749$	293.281	+	169.326i	0.391563	+	0.226069i
$750$	795.507	−	232.441i	1.06068	−	0.309921i
$751$	559.605	+	969.264i	0.745146	+	1.29063i	0.950126	+	0.311865i	$0.100954\pi$
$751$	559.605	+	969.264i	0.745146	+	1.29063i	−0.204980	+	0.978766i	$0.565713\pi$
$752$	1042.11	−	601.660i	1.38578	−	0.800080i
$753$	−570.905	+	597.166i	−0.758174	+	0.793049i
$754$	223.080	−	386.385i	0.295861	−	0.512447i
$755$			1036.63i			1.37302i
$756$	205.980	−	235.818i	0.272460	−	0.311929i
$757$	−1313.80			−1.73553			−0.867766	−	0.496972i	$-0.834445\pi$
$757$	−1313.80			−1.73553			−0.867766	+	0.496972i	$0.834445\pi$
$758$	−1080.60	−	623.884i	−1.42559	−	0.823066i
$759$	124.799	+	119.311i	0.164426	+	0.157195i
$760$	−144.931	−	251.028i	−0.190699	−	0.330300i
$761$	−1030.97	+	595.228i	−1.35475	+	0.782166i	−0.988911	−	0.148511i	$-0.952552\pi$
$761$	−1030.97	+	595.228i	−1.35475	+	0.782166i	−0.365841	+	0.930677i	$0.619219\pi$
$762$	−211.115	−	722.521i	−0.277053	−	0.948190i
$763$	151.218	−	261.916i	0.198188	−	0.343272i
$764$			669.165i			0.875870i
$765$	−331.023	+	211.502i	−0.432710	+	0.276473i
$766$	−651.811			−0.850928
$767$	34.5528	+	19.9491i	0.0450493	+	0.0260092i
$768$	142.340	−	583.368i	0.185339	−	0.759594i
$769$	−506.113	−	876.613i	−0.658144	−	1.13994i	−0.981096	−	0.193523i	$-0.938008\pi$
$769$	−506.113	−	876.613i	−0.658144	−	1.13994i	0.322952	−	0.946415i	$-0.395325\pi$
$770$	−119.193	+	68.8159i	−0.154796	+	0.0893712i
$771$	336.151	+	82.0197i	0.435993	+	0.106381i
$772$	604.168	−	1046.45i	0.782601	−	1.35551i
$773$		−	829.031i		−	1.07248i	−0.844064	−	0.536242i	$-0.819843\pi$
$773$		−	829.031i		−	1.07248i	0.844064	−	0.536242i	$-0.180157\pi$
$774$	−890.864	−	1394.30i	−1.15099	−	1.80142i
$775$	1008.68			1.30153
$776$	1.76732	+	1.02036i	0.00227747	+	0.00131490i
$777$	6.62906	−	1.93696i	0.00853161	−	0.00249287i
$778$	−500.818	−	867.443i	−0.643725	−	1.11496i
$779$	−101.207	+	58.4319i	−0.129919	+	0.0750088i
$780$	1007.20	−	1053.53i	1.29128	−	1.35068i
$781$	−83.4040	+	144.460i	−0.106791	+	0.184968i
$782$			404.809i			0.517659i
$783$	−279.921	+	95.6408i	−0.357498	+	0.122147i
$784$	−100.245			−0.127864
$785$	−188.728	−	108.962i	−0.240418	−	0.138805i
$786$	248.296	+	237.377i	0.315899	+	0.302007i
$787$	79.3434	+	137.427i	0.100818	+	0.174621i	0.912022	−	0.410142i	$-0.134521\pi$
$787$	79.3434	+	137.427i	0.100818	+	0.174621i	−0.811204	+	0.584763i	$0.801187\pi$
$788$	543.835	−	313.983i	0.690145	−	0.398456i
$789$	−182.858	−	625.813i	−0.231759	−	0.793173i
$790$	12.0364	−	20.8477i	0.0152360	−	0.0263895i
$791$		−	118.415i		−	0.149704i
$792$	20.2027	+	10.4829i	0.0255085	+	0.0132360i
$793$	−938.273			−1.18319
$794$	1663.82	+	960.609i	2.09550	+	1.20983i
$795$	189.643	−	777.235i	0.238544	−	0.977654i
$796$	−293.541	−	508.428i	−0.368770	−	0.638728i
$797$	−521.363	+	301.009i	−0.654157	+	0.377678i	−0.790047	−	0.613046i	$-0.789944\pi$
$797$	−521.363	+	301.009i	−0.654157	+	0.377678i	0.135890	+	0.990724i	$0.456611\pi$
$798$	−740.274	−	180.625i	−0.927662	−	0.226347i
$799$	232.686	−	403.024i	0.291221	−	0.504410i
$800$			1703.24i			2.12906i
$801$	1117.86	−	50.2898i	1.39557	−	0.0627837i
$802$	640.416			0.798524
$803$	193.152	+	111.516i	0.240538	+	0.138875i
$804$	−673.139	+	196.686i	−0.837238	+	0.244634i
$805$	−263.181	−	455.842i	−0.326932	−	0.566264i
$806$	958.676	−	553.492i	1.18942	−	0.686714i
$807$	177.737	−	185.913i	0.220244	−	0.230375i
$808$	−79.7958	+	138.210i	−0.0987572	+	0.171052i
$809$			41.1554i			0.0508719i	0.999676	+	0.0254360i	$0.00809739\pi$
$809$			41.1554i			0.0508719i	−0.999676	+	0.0254360i	$0.991903\pi$
$810$	−1840.77	+	165.960i	−2.27256	+	0.204889i
$811$	−825.208			−1.01752			−0.508759	−	0.860909i	$-0.669896\pi$
$811$	−825.208			−1.01752			−0.508759	+	0.860909i	$0.669896\pi$
$812$	−110.030	−	63.5258i	−0.135505	−	0.0782337i
$813$	626.312	+	598.769i	0.770371	+	0.736493i
$814$	2.87171	+	4.97395i	0.00352790	+	0.00611050i
$815$	−115.702	+	66.8007i	−0.141966	+	0.0819641i
$816$	−66.7340	−	228.391i	−0.0817819	−	0.279891i
$817$	−1052.68	+	1823.29i	−1.28847	+	2.23169i
$818$			744.743i			0.910443i
$819$	−15.0517	−	334.574i	−0.0183782	−	0.408515i
$820$	−121.747			−0.148472
$821$	628.152	+	362.664i	0.765106	+	0.441734i	0.831126	−	0.556084i	$-0.187697\pi$
$821$	628.152	+	362.664i	0.765106	+	0.441734i	−0.0660199	+	0.997818i	$0.521030\pi$
$822$	−34.5900	+	141.764i	−0.0420803	+	0.172462i
$823$	702.615	+	1216.96i	0.853724	+	1.47869i	0.877824	+	0.478984i	$0.158995\pi$
$823$	702.615	+	1216.96i	0.853724	+	1.47869i	−0.0240994	+	0.999710i	$0.507672\pi$
$824$	68.1205	−	39.3294i	0.0826705	−	0.0477298i
$825$	246.556	+	60.1590i	0.298856	+	0.0729200i
$826$	10.8651	−	18.8190i	0.0131539	−	0.0227833i
$827$			304.535i			0.368241i	0.982904	+	0.184120i	$0.0589436\pi$
$827$			304.535i			0.368241i	−0.982904	+	0.184120i	$0.941056\pi$
$828$	−458.659	+	883.931i	−0.553936	+	1.06755i
$829$	−1072.42			−1.29363			−0.646813	−	0.762649i	$-0.723898\pi$
$829$	−1072.42			−1.29363			−0.646813	+	0.762649i	$0.723898\pi$
$830$	782.265	+	451.641i	0.942487	+	0.544145i
$831$	1015.03	−	296.583i	1.22146	−	0.356899i
$832$	531.774	+	921.059i	0.639151	+	1.10704i
$833$	−33.5747	+	19.3844i	−0.0403058	+	0.0232705i
$834$	771.184	−	806.658i	0.924681	−	0.967216i
$835$	665.282	−	1152.30i	0.796745	−	1.38000i
$836$		−	331.327i		−	0.396324i
$837$	−720.124	−	141.755i	−0.860363	−	0.169361i
$838$	−1044.27			−1.24615
$839$	−855.402	−	493.866i	−1.01955	−	0.588637i	−0.105576	−	0.994411i	$-0.533669\pi$
$839$	−855.402	−	493.866i	−1.01955	−	0.588637i	−0.913973	+	0.405774i	$0.867002\pi$
$840$	−50.1552	−	47.9495i	−0.0597085	−	0.0570828i
$841$	−360.484	−	624.377i	−0.428638	−	0.742422i
$842$	1039.29	−	600.036i	1.23431	−	0.712632i
$843$	−254.397	−	870.652i	−0.301776	−	1.03280i
$844$	−609.060	+	1054.92i	−0.721636	+	1.24991i
$845$		−	227.157i		−	0.268825i
$846$	1845.12	−	1178.91i	2.18099	−	1.39351i
$847$	306.385			0.361729
$848$	419.675	+	242.300i	0.494900	+	0.285731i
$849$	−96.7035	+	396.331i	−0.113903	+	0.466821i
$850$	297.518	+	515.316i	0.350021	+	0.606254i
$851$	−19.0225	+	10.9826i	−0.0223531	+	0.0129055i
$852$	−934.692	−	228.062i	−1.09706	−	0.267678i
$853$	845.062	−	1463.69i	0.990694	−	1.71593i	0.377475	−	0.926020i	$-0.376792\pi$
$853$	845.062	−	1463.69i	0.990694	−	1.71593i	0.613219	−	0.789913i	$-0.289874\pi$
$854$			511.024i			0.598389i
$855$	1266.22	+	1981.77i	1.48095	+	2.31785i
$856$	−141.987			−0.165872
$857$	847.547	+	489.332i	0.988970	+	0.570982i	0.904966	−	0.425483i	$-0.139896\pi$
$857$	847.547	+	489.332i	0.988970	+	0.570982i	0.0840036	+	0.996465i	$0.473229\pi$
$858$	267.344	−	78.1156i	0.311589	−	0.0910438i
$859$	−733.574	−	1270.59i	−0.853986	−	1.47915i	−0.877583	−	0.479425i	$-0.840845\pi$
$859$	−733.574	−	1270.59i	−0.853986	−	1.47915i	0.0235970	−	0.999722i	$-0.492488\pi$
$860$	−1899.47	+	1096.66i	−2.20869	+	1.27519i
$861$	−19.3318	+	20.2211i	−0.0224528	+	0.0234856i
$862$	330.676	−	572.748i	0.383615	−	0.664441i
$863$		−	609.830i		−	0.706640i	−0.935503	−	0.353320i	$-0.885053\pi$
$863$		−	609.830i		−	0.706640i	0.935503	−	0.353320i	$-0.114947\pi$
$864$	239.365	−	1215.99i	0.277043	−	1.40739i
$865$	−299.513			−0.346258
$866$	1052.84	+	607.858i	1.21575	+	0.701914i
$867$	560.171	+	535.537i	0.646103	+	0.617690i
$868$	−157.616	−	273.000i	−0.181586	−	0.314516i
$869$	2.08296	−	1.20260i	0.00239696	−	0.00138389i
$870$	210.339	+	719.866i	0.241769	+	0.827432i
$871$	−375.059	+	649.621i	−0.430607	+	0.745834i
$872$			126.802i			0.145415i
$873$	−14.6964	−	7.62575i	−0.0168344	−	0.00873511i
$874$	2423.51			2.77289
$875$	−218.620	−	126.220i	−0.249851	−	0.144252i
$876$	−304.933	+	1249.74i	−0.348097	+	1.42665i
$877$	173.512	+	300.532i	0.197847	+	0.342682i	0.947830	−	0.318776i	$-0.103272\pi$
$877$	173.512	+	300.532i	0.197847	+	0.342682i	−0.749983	+	0.661457i	$0.769938\pi$
$878$	666.191	−	384.626i	0.758760	−	0.438070i
$879$	1.94084	+	0.473558i	0.00220801	+	0.000538747i
$880$	−128.647	+	222.824i	−0.146190	+	0.253209i
$881$		−	1350.00i		−	1.53235i	−0.642629	−	0.766177i	$-0.722156\pi$
$881$		−	1350.00i		−	1.53235i	0.642629	−	0.766177i	$-0.277844\pi$
$882$	−182.224	+	8.19782i	−0.206603	+	0.00929458i
$883$	−1409.36			−1.59610			−0.798050	−	0.602591i	$-0.794135\pi$
$883$	−1409.36			−1.59610			−0.798050	+	0.602591i	$0.794135\pi$
$884$	295.691	+	170.717i	0.334492	+	0.193119i
$885$	−64.3747	+	18.8098i	−0.0727397	+	0.0212540i
$886$	−930.880	−	1612.33i	−1.05065	−	1.81979i
$887$	531.379	−	306.792i	0.599075	−	0.345876i	−0.169603	−	0.985512i	$-0.554248\pi$
$887$	531.379	−	306.792i	0.599075	−	0.345876i	0.768677	+	0.639637i	$0.220915\pi$
$888$	−2.00095	+	2.09299i	−0.00225332	+	0.00235697i
$889$	−114.640	+	198.562i	−0.128954	+	0.223354i
$890$		−	2836.98i		−	3.18761i
$891$	−167.568	−	77.5986i	−0.188067	−	0.0870916i
$892$	−158.668			−0.177879
$893$	−2412.82	−	1393.04i	−2.70192	−	1.55996i
$894$	548.301	+	524.189i	0.613312	+	0.586341i
$895$	−166.967	−	289.196i	−0.186556	−	0.323124i
$896$	80.9611	−	46.7429i	0.0903584	−	0.0521685i
$897$	298.747	+	1022.43i	0.333051	+	1.13984i
$898$	−744.151	+	1288.91i	−0.828677	+	1.43531i
$899$			297.814i			0.331273i
$900$	65.7867	+	1462.33i	0.0730963	+	1.62481i
$901$	187.414			0.208006
$902$	−20.1480	−	11.6325i	−0.0223370	−	0.0128963i
$903$	−119.466	+	489.622i	−0.132299	+	0.542217i
$904$	24.8241	+	42.9966i	0.0274603	+	0.0475626i
$905$	−1666.55	+	962.182i	−1.84149	+	1.06318i
$906$	−1110.00	−	270.836i	−1.22516	−	0.298935i
$907$	349.937	−	606.108i	0.385818	−	0.668256i	−0.606065	−	0.795415i	$-0.707253\pi$
$907$	349.937	−	606.108i	0.385818	−	0.668256i	0.991882	+	0.127160i	$0.0405861\pi$
$908$		−	279.928i		−	0.308291i
$909$	596.359	−	1149.31i	0.656061	−	1.26437i
$910$	−849.106			−0.933084
$911$	−624.833	−	360.747i	−0.685875	−	0.395990i	0.116190	−	0.993227i	$-0.462932\pi$
$911$	−624.833	−	360.747i	−0.685875	−	0.395990i	−0.802065	+	0.597237i	$0.796265\pi$
$912$	−1367.33	+	399.522i	−1.49926	+	0.438073i
$913$	45.1248	+	78.1585i	0.0494248	+	0.0856062i
$914$	−100.488	+	58.0170i	−0.109944	+	0.0634759i
$915$	1089.89	−	1140.02i	1.19113	−	1.24592i
$916$	499.461	−	865.092i	0.545263	−	0.944423i
$917$		−	104.632i		−	0.114102i
$918$	−139.985	−	409.708i	−0.152489	−	0.446305i
$919$	307.815			0.334946			0.167473	−	0.985877i	$-0.446439\pi$
$919$	307.815			0.334946			0.167473	+	0.985877i	$0.446439\pi$
$920$	191.121	+	110.344i	0.207741	+	0.119939i
$921$	−564.851	−	540.011i	−0.613301	−	0.586331i
$922$	537.921	+	931.707i	0.583429	+	1.01053i
$923$	−891.233	+	514.553i	−0.965582	+	0.557479i
$924$	−22.2448	−	76.1307i	−0.0240744	−	0.0823926i
$925$	−16.1435	+	27.9614i	−0.0174525	+	0.0302286i
$926$		−	480.139i		−	0.518509i
$927$	−537.784	+	343.608i	−0.580134	+	0.370667i
$928$	−502.884			−0.541900
$929$	1381.60	+	797.666i	1.48719	+	0.858628i	0.999893	−	0.0146091i	$-0.00465039\pi$
$929$	1381.60	+	797.666i	1.48719	+	0.858628i	0.487295	+	0.873238i	$0.337984\pi$
$930$	−441.083	+	1807.74i	−0.474283	+	1.94381i
$931$	116.050	+	201.004i	0.124651	+	0.215902i
$932$	−1559.43	+	900.339i	−1.67321	+	0.966029i
$933$	99.5358	+	24.2864i	0.106684	+	0.0260305i
$934$	−235.312	+	407.572i	−0.251940	+	0.436373i
$935$			99.5061i			0.106424i
$936$	75.6038	+	118.328i	0.0807733	+	0.126419i
$937$	−837.751			−0.894078			−0.447039	−	0.894515i	$-0.647521\pi$
$937$	−837.751			−0.894078			−0.447039	+	0.894515i	$0.647521\pi$
$938$	353.812	+	204.273i	0.377198	+	0.217776i
$939$	−845.893	+	247.163i	−0.900844	+	0.263219i
$940$	−1451.25	−	2513.63i	−1.54388	−	2.67408i
$941$	−321.187	+	185.438i	−0.341326	+	0.197064i	−0.660858	−	0.750511i	$-0.729807\pi$
$941$	−321.187	+	185.438i	−0.341326	+	0.197064i	0.319532	+	0.947575i	$0.396474\pi$
$942$	165.981	−	173.616i	0.176201	−	0.184306i
$943$	44.4874	−	77.0544i	0.0471765	−	0.0817120i
$944$		−	40.6236i		−	0.0430334i
$945$	423.998	+	370.349i	0.448675	+	0.391904i
$946$	−419.128			−0.443053
$947$	746.149	+	430.789i	0.787908	+	0.454899i	0.839225	−	0.543784i	$-0.183009\pi$
$947$	746.149	+	430.789i	0.787908	+	0.454899i	−0.0513178	+	0.998682i	$0.516342\pi$
$948$	10.0275	+	9.58649i	0.0105775	+	0.0101123i
$949$	687.991	+	1191.63i	0.724964	+	1.25567i
$950$	3085.09	−	1781.18i	3.24746	−	1.87492i
$951$	342.954	+	1173.73i	0.360625	+	1.23421i
$952$	8.12730	−	14.0769i	0.00853708	−	0.0147867i
$953$			1636.29i			1.71698i	0.512826	+	0.858492i	$0.328598\pi$
$953$			1636.29i			1.71698i	−0.512826	+	0.858492i	$0.671402\pi$
$954$	782.692	+	406.128i	0.820432	+	0.425710i
$955$	−1203.15			−1.25984
$956$	1597.55	+	922.347i	1.67108	+	0.964798i
$957$	−17.7620	+	72.7959i	−0.0185600	+	0.0760668i
$958$	334.370	+	579.145i	0.349029	+	0.604536i
$959$	38.4928	−	22.2238i	0.0401384	−	0.0231739i
$960$	−1736.81	−	423.775i	−1.80917	−	0.441433i
$961$	111.040	−	192.327i	0.115546	−	0.200132i
$962$			35.4335i			0.0368332i
$963$	1150.82	−	51.7727i	1.19504	−	0.0537619i
$964$	1530.44			1.58759
$965$	1881.50	+	1086.29i	1.94974	+	1.12569i
$966$	556.862	−	162.710i	0.576461	−	0.168437i
$967$	580.799	+	1005.97i	0.600620	+	1.04030i	0.992727	+	0.120385i	$0.0384128\pi$
$967$	580.799	+	1005.97i	0.600620	+	1.04030i	−0.392107	+	0.919919i	$0.628254\pi$
$968$	−111.248	+	64.2291i	−0.114926	+	0.0663524i
$969$	−380.699	+	398.211i	−0.392878	+	0.410950i
$970$	−20.9886	+	36.3534i	−0.0216378	+	0.0374777i
$971$			1020.48i			1.05096i	0.850806	+	0.525480i	$0.176114\pi$
$971$			1020.48i			1.05096i	−0.850806	+	0.525480i	$0.823886\pi$
$972$	158.541	−	1053.23i	0.163108	−	1.08357i
$973$	−339.925			−0.349358
$974$	906.044	+	523.105i	0.930230	+	0.537068i
$975$	1131.75	+	1081.98i	1.16076	+	1.10972i
$976$	477.666	+	827.342i	0.489412	+	0.847686i
$977$	229.807	−	132.679i	0.235217	−	0.135803i	−0.377760	−	0.925904i	$-0.623305\pi$
$977$	229.807	−	132.679i	0.235217	−	0.135803i	0.612976	+	0.790101i	$0.289972\pi$
$978$	−41.2993	−	141.343i	−0.0422283	−	0.144523i
$979$	141.726	−	245.476i	0.144766	−	0.250741i
$980$			241.798i			0.246733i
$981$	−46.2360	−	1027.75i	−0.0471315	−	1.04765i
$982$	−23.3506			−0.0237786
$983$	−256.189	−	147.911i	−0.260620	−	0.150469i	0.363998	−	0.931400i	$-0.381412\pi$
$983$	−256.189	−	147.911i	−0.260620	−	0.150469i	−0.624617	+	0.780931i	$0.714745\pi$
$984$	2.78032	−	11.3949i	0.00282553	−	0.0115802i
$985$	564.538	+	977.808i	0.573135	+	0.992698i
$986$	−152.147	+	87.8423i	−0.154308	+	0.0890895i
$987$	−647.932	−	158.093i	−0.656466	−	0.160176i
$988$	1022.05	−	1770.24i	1.03446	−	1.79174i
$989$		−	1602.92i		−	1.62075i
$990$	−215.631	+	415.566i	−0.217809	+	0.419763i
$991$	1102.54			1.11255			0.556274	−	0.830999i	$-0.312230\pi$
$991$	1102.54			1.11255			0.556274	+	0.830999i	$0.312230\pi$
$992$	−1080.56	−	623.863i	−1.08928	−	0.628894i
$993$	−934.684	+	273.107i	−0.941273	+	0.275032i
$994$	280.248	+	485.404i	0.281940	+	0.488334i
$995$	914.147	−	527.783i	0.918740	−	0.530435i
$996$	−359.712	+	376.258i	−0.361156	+	0.377769i
$997$	−330.852	+	573.053i	−0.331848	+	0.574778i	−0.982874	−	0.184278i	$-0.941005\pi$
$997$	−330.852	+	573.053i	−0.331848	+	0.574778i	0.651026	+	0.759055i	$0.274339\pi$
$998$		−	281.394i		−	0.281957i
$999$	15.4548	−	17.6936i	0.0154703	−	0.0177113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.r.a.29.3	✓	24
3.2	odd	2		189.3.r.a.8.10		24
7.2	even	3		441.3.j.h.263.10		24
7.3	odd	6		441.3.n.h.128.10		24
7.4	even	3		441.3.n.g.128.10		24
7.5	odd	6		441.3.j.g.263.10		24
7.6	odd	2		441.3.r.h.344.3		24
9.2	odd	6		567.3.b.a.323.5		24
9.4	even	3		189.3.r.a.71.10		24
9.5	odd	6	inner	63.3.r.a.50.3	yes	24
9.7	even	3		567.3.b.a.323.20		24
63.5	even	6		441.3.n.h.410.10		24
63.23	odd	6		441.3.n.g.410.10		24
63.32	odd	6		441.3.j.h.275.3		24
63.41	even	6		441.3.r.h.50.3		24
63.59	even	6		441.3.j.g.275.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.3	✓	24	1.1	even	1	trivial
63.3.r.a.50.3	yes	24	9.5	odd	6	inner
189.3.r.a.8.10		24	3.2	odd	2
189.3.r.a.71.10		24	9.4	even	3
441.3.j.g.263.10		24	7.5	odd	6
441.3.j.g.275.3		24	63.59	even	6
441.3.j.h.263.10		24	7.2	even	3
441.3.j.h.275.3		24	63.32	odd	6
441.3.n.g.128.10		24	7.4	even	3
441.3.n.g.410.10		24	63.23	odd	6
441.3.n.h.128.10		24	7.3	odd	6
441.3.n.h.410.10		24	63.5	even	6
441.3.r.h.50.3		24	63.41	even	6
441.3.r.h.344.3		24	7.6	odd	2
567.3.b.a.323.5		24	9.2	odd	6
567.3.b.a.323.20		24	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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50746 - 1.44768i) q^{2} +(2.16846 + 2.07310i) q^{3} +(2.19156 + 3.79590i) q^{4} +(-6.82498 + 3.94040i) q^{5} +(-2.43614 - 8.33747i) q^{6} +(-1.32288 + 2.29129i) q^{7} -1.10929i q^{8} +(0.404480 + 8.99091i) q^{9} +O(q^{10})\)	\(q+(-2.50746 - 1.44768i) q^{2} +(2.16846 + 2.07310i) q^{3} +(2.19156 + 3.79590i) q^{4} +(-6.82498 + 3.94040i) q^{5} +(-2.43614 - 8.33747i) q^{6} +(-1.32288 + 2.29129i) q^{7} -1.10929i q^{8} +(0.404480 + 8.99091i) q^{9} +22.8178 q^{10} +(1.97436 + 1.13990i) q^{11} +(-3.11696 + 12.7746i) q^{12} +(7.03250 + 12.1806i) q^{13} +(6.63411 - 3.83020i) q^{14} +(-22.9686 - 5.60426i) q^{15} +(7.16036 - 12.4021i) q^{16} -5.53839i q^{17} +(12.0017 - 23.1299i) q^{18} -33.1571 q^{19} +(-29.9147 - 17.2713i) q^{20} +(-7.61869 + 2.22612i) q^{21} +(-3.30042 - 5.71649i) q^{22} +(21.8623 - 12.6222i) q^{23} +(2.29967 - 2.40545i) q^{24} +(18.5535 - 32.1357i) q^{25} -40.7233i q^{26} +(-17.7620 + 20.3350i) q^{27} -11.5967 q^{28} +(9.48807 + 5.47794i) q^{29} +(49.4796 + 47.3036i) q^{30} +(13.5915 + 23.5412i) q^{31} +(-39.7513 + 22.9504i) q^{32} +(1.91821 + 6.56488i) q^{33} +(-8.01782 + 13.8873i) q^{34} -20.8506i q^{35} +(-33.2421 + 21.2395i) q^{36} -0.870105 q^{37} +(83.1401 + 48.0010i) q^{38} +(-10.0020 + 40.9924i) q^{39} +(4.37103 + 7.57085i) q^{40} +(3.05234 - 1.76227i) q^{41} +(22.3262 + 5.44753i) q^{42} +(31.7481 - 54.9893i) q^{43} +9.99263i q^{44} +(-38.1884 - 59.7689i) q^{45} -73.0916 q^{46} +(72.7692 + 42.0133i) q^{47} +(41.2378 - 12.0494i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-93.0444 + 53.7192i) q^{50} +(11.4817 - 12.0098i) q^{51} +(-30.8243 + 53.3893i) q^{52} +33.8390i q^{53} +(73.9760 - 25.2754i) q^{54} -17.9666 q^{55} +(2.54169 + 1.46745i) q^{56} +(-71.9001 - 68.7382i) q^{57} +(-15.8606 - 27.4714i) q^{58} +(2.45665 - 1.41835i) q^{59} +(-29.0639 - 99.4685i) q^{60} +(-33.3549 + 57.7724i) q^{61} -78.7049i q^{62} +(-21.1358 - 10.9671i) q^{63} +75.6166 q^{64} +(-95.9933 - 55.4217i) q^{65} +(4.69404 - 19.2381i) q^{66} +(26.6661 + 46.1871i) q^{67} +(21.0232 - 12.1377i) q^{68} +(73.5746 + 17.9520i) q^{69} +(-30.1851 + 52.2821i) q^{70} +73.1679i q^{71} +(9.97349 - 0.448685i) q^{72} +97.8302 q^{73} +(2.18175 + 1.25963i) q^{74} +(106.853 - 31.2217i) q^{75} +(-72.6659 - 125.861i) q^{76} +(-5.22367 + 3.01589i) q^{77} +(84.4236 - 88.3070i) q^{78} +(0.527503 - 0.913661i) q^{79} +112.859i q^{80} +(-80.6728 + 7.27329i) q^{81} -10.2048 q^{82} +(34.2831 + 19.7934i) q^{83} +(-25.1469 - 24.0411i) q^{84} +(21.8235 + 37.7994i) q^{85} +(-159.214 + 91.9223i) q^{86} +(9.21821 + 31.5485i) q^{87} +(1.26447 - 2.19013i) q^{88} -124.332i q^{89} +(9.22935 + 205.153i) q^{90} -37.2125 q^{91} +(95.8250 + 55.3246i) q^{92} +(-19.3307 + 79.2250i) q^{93} +(-121.644 - 210.693i) q^{94} +(226.297 - 130.652i) q^{95} +(-133.778 - 32.6414i) q^{96} +(-0.919837 + 1.59320i) q^{97} +20.2675i q^{98} +(-9.45013 + 18.2124i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9}+O(q^{10}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9	\( 24 q + 2 q^{3} + 24 q^{4} - 18 q^{5} - 14 q^{6} + 26 q^{9} - 18 q^{11} + 4 q^{12} - 10 q^{15} - 48 q^{16} - 62 q^{18} - 24 q^{19} - 18 q^{20} - 14 q^{21} - 24 q^{22} + 72 q^{23} + 54 q^{24} + 54 q^{25} - 124 q^{27} + 54 q^{29} - 212 q^{30} + 30 q^{31} + 126 q^{32} - 178 q^{33} + 60 q^{34} + 124 q^{36} + 84 q^{37} - 144 q^{38} + 92 q^{39} - 60 q^{40} + 180 q^{41} + 140 q^{42} - 60 q^{43} - 118 q^{45} - 168 q^{46} + 378 q^{47} + 436 q^{48} - 84 q^{49} - 378 q^{50} + 168 q^{51} - 18 q^{52} + 514 q^{54} - 132 q^{55} - 232 q^{57} + 90 q^{58} - 90 q^{59} + 76 q^{60} + 28 q^{63} + 324 q^{64} + 126 q^{65} + 202 q^{66} + 6 q^{67} - 738 q^{68} - 432 q^{69} - 246 q^{72} - 72 q^{73} - 792 q^{74} + 40 q^{75} + 84 q^{76} + 28 q^{78} - 6 q^{79} - 34 q^{81} - 108 q^{82} - 558 q^{83} - 322 q^{84} + 126 q^{85} + 90 q^{86} + 428 q^{87} + 168 q^{88} - 488 q^{90} + 84 q^{91} + 774 q^{92} - 738 q^{93} - 354 q^{94} + 648 q^{95} - 280 q^{96} - 270 q^{97} + 296 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 + 24 * q^4 - 18 * q^5 - 14 * q^6 + 26 * q^9 - 18 * q^11 + 4 * q^12 - 10 * q^15 - 48 * q^16 - 62 * q^18 - 24 * q^19 - 18 * q^20 - 14 * q^21 - 24 * q^22 + 72 * q^23 + 54 * q^24 + 54 * q^25 - 124 * q^27 + 54 * q^29 - 212 * q^30 + 30 * q^31 + 126 * q^32 - 178 * q^33 + 60 * q^34 + 124 * q^36 + 84 * q^37 - 144 * q^38 + 92 * q^39 - 60 * q^40 + 180 * q^41 + 140 * q^42 - 60 * q^43 - 118 * q^45 - 168 * q^46 + 378 * q^47 + 436 * q^48 - 84 * q^49 - 378 * q^50 + 168 * q^51 - 18 * q^52 + 514 * q^54 - 132 * q^55 - 232 * q^57 + 90 * q^58 - 90 * q^59 + 76 * q^60 + 28 * q^63 + 324 * q^64 + 126 * q^65 + 202 * q^66 + 6 * q^67 - 738 * q^68 - 432 * q^69 - 246 * q^72 - 72 * q^73 - 792 * q^74 + 40 * q^75 + 84 * q^76 + 28 * q^78 - 6 * q^79 - 34 * q^81 - 108 * q^82 - 558 * q^83 - 322 * q^84 + 126 * q^85 + 90 * q^86 + 428 * q^87 + 168 * q^88 - 488 * q^90 + 84 * q^91 + 774 * q^92 - 738 * q^93 - 354 * q^94 + 648 * q^95 - 280 * q^96 - 270 * q^97 + 296 * q^99

Introduction

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