LMFDB - Embedded newform 63.3.r.a.29.7

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			29.7
Character	$\chi$	$=$	63.29
Dual form			63.3.r.a.50.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.526549 + 0.304003i) q^{2} +(1.22623 - 2.73795i) q^{3} +(-1.81516 - 3.14396i) q^{4} +(0.914466 - 0.527967i) q^{5} +(1.47801 - 1.06889i) q^{6} +(-1.32288 + 2.29129i) q^{7} -4.63929i q^{8} +(-5.99274 - 6.71469i) q^{9} +O(q^{10})$	\(q+(0.526549 + 0.304003i) q^{2} +(1.22623 - 2.73795i) q^{3} +(-1.81516 - 3.14396i) q^{4} +(0.914466 - 0.527967i) q^{5} +(1.47801 - 1.06889i) q^{6} +(-1.32288 + 2.29129i) q^{7} -4.63929i q^{8} +(-5.99274 - 6.71469i) q^{9} +0.642015 q^{10} +(18.9272 + 10.9276i) q^{11} +(-10.8338 + 1.11463i) q^{12} +(8.12859 + 14.0791i) q^{13} +(-1.39312 + 0.804317i) q^{14} +(-0.324207 - 3.15117i) q^{15} +(-5.85030 + 10.1330i) q^{16} -14.1018i q^{17} +(-1.11419 - 5.35742i) q^{18} -20.3958 q^{19} +(-3.31981 - 1.91669i) q^{20} +(4.65129 + 6.43160i) q^{21} +(6.64405 + 11.5078i) q^{22} +(4.32361 - 2.49624i) q^{23} +(-12.7021 - 5.68881i) q^{24} +(-11.9425 + 20.6850i) q^{25} +9.88447i q^{26} +(-25.7329 + 8.17411i) q^{27} +9.60495 q^{28} +(26.0574 + 15.0442i) q^{29} +(0.787255 - 1.75780i) q^{30} +(-20.6710 - 35.8032i) q^{31} +(-22.2319 + 12.8356i) q^{32} +(53.1282 - 38.4219i) q^{33} +(4.28699 - 7.42528i) q^{34} +2.79374i q^{35} +(-10.2329 + 31.0292i) q^{36} +19.9781 q^{37} +(-10.7394 - 6.20039i) q^{38} +(48.5155 - 4.99149i) q^{39} +(-2.44939 - 4.24247i) q^{40} +(13.3140 - 7.68686i) q^{41} +(0.493903 + 4.80056i) q^{42} +(0.851359 - 1.47460i) q^{43} -79.3416i q^{44} +(-9.02530 - 2.97638i) q^{45} +3.03545 q^{46} +(-18.6613 - 10.7741i) q^{47} +(20.5699 + 28.4432i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-12.5766 + 7.26112i) q^{50} +(-38.6100 - 17.2920i) q^{51} +(29.5095 - 51.1119i) q^{52} +36.3418i q^{53} +(-16.0346 - 3.51882i) q^{54} +23.0777 q^{55} +(10.6299 + 6.13720i) q^{56} +(-25.0099 + 55.8427i) q^{57} +(9.14700 + 15.8431i) q^{58} +(-67.7180 + 39.0970i) q^{59} +(-9.31865 + 6.73918i) q^{60} +(23.0131 - 39.8599i) q^{61} -25.1362i q^{62} +(23.3129 - 4.84840i) q^{63} +31.1941 q^{64} +(14.8667 + 8.58326i) q^{65} +(39.6550 - 4.07988i) q^{66} +(-20.9530 - 36.2917i) q^{67} +(-44.3354 + 25.5971i) q^{68} +(-1.53285 - 14.8988i) q^{69} +(-0.849306 + 1.47104i) q^{70} +2.65470i q^{71} +(-31.1514 + 27.8021i) q^{72} -82.5384 q^{73} +(10.5194 + 6.07339i) q^{74} +(41.9904 + 58.0625i) q^{75} +(37.0217 + 64.1235i) q^{76} +(-50.0766 + 28.9117i) q^{77} +(27.0632 + 12.1206i) q^{78} +(-19.4593 + 33.7045i) q^{79} +12.3551i q^{80} +(-9.17407 + 80.4788i) q^{81} +9.34731 q^{82} +(-33.1355 - 19.1308i) q^{83} +(11.7778 - 26.2979i) q^{84} +(-7.44529 - 12.8956i) q^{85} +(0.896565 - 0.517632i) q^{86} +(73.1426 - 52.8962i) q^{87} +(50.6963 - 87.8086i) q^{88} +58.2883i q^{89} +(-3.84743 - 4.31093i) q^{90} -43.0125 q^{91} +(-15.6961 - 9.06216i) q^{92} +(-123.375 + 12.6934i) q^{93} +(-6.55071 - 11.3462i) q^{94} +(-18.6513 + 10.7683i) q^{95} +(7.88190 + 76.6092i) q^{96} +(-42.7655 + 74.0720i) q^{97} -4.25604i q^{98} +(-40.0502 - 192.576i) 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 $

$2$	0.526549	+	0.304003i	0.263274	+	0.152002i	0.625827	−	0.779962i	$-0.284761\pi$
$2$	0.526549	+	0.304003i	0.263274	+	0.152002i	−0.362553	+	0.931963i	$0.618095\pi$
$3$	1.22623	−	2.73795i	0.408742	−	0.912650i
$3$	1.22623	−	2.73795i	0.408742	−	0.912650i
$4$	−1.81516	−	3.14396i	−0.453791	−	0.785989i
$5$	0.914466	−	0.527967i	0.182893	−	0.105593i	−0.405758	−	0.913981i	$-0.632992\pi$
$5$	0.914466	−	0.527967i	0.182893	−	0.105593i	0.588651	+	0.808387i	$0.299659\pi$
$6$	1.47801	−	1.06889i	0.246336	−	0.178148i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$7$	−1.32288	+	2.29129i	−0.188982	+	0.327327i
$8$		−	4.63929i		−	0.579911i
$9$	−5.99274	−	6.71469i	−0.665860	−	0.746076i
$10$	0.642015			0.0642015
$11$	18.9272	+	10.9276i	1.72065	+	0.993418i	0.917596	+	0.397513i	$0.130127\pi$
$11$	18.9272	+	10.9276i	1.72065	+	0.993418i	0.803055	+	0.595905i	$0.203207\pi$
$12$	−10.8338	+	1.11463i	−0.902816	+	0.0928858i
$13$	8.12859	+	14.0791i	0.625276	+	1.08301i	0.988487	+	0.151304i	$0.0483471\pi$
$13$	8.12859	+	14.0791i	0.625276	+	1.08301i	−0.363211	+	0.931707i	$0.618320\pi$
$14$	−1.39312	+	0.804317i	−0.0995084	+	0.0574512i
$15$	−0.324207	−	3.15117i	−0.0216138	−	0.210078i
$16$	−5.85030	+	10.1330i	−0.365644	+	0.633313i
$17$		−	14.1018i		−	0.829517i	−0.909931	−	0.414759i	$-0.863866\pi$
$17$		−	14.1018i		−	0.829517i	0.909931	−	0.414759i	$-0.136134\pi$
$18$	−1.11419	−	5.35742i	−0.0618992	−	0.297635i
$19$	−20.3958			−1.07346			−0.536732	−	0.843753i	$-0.680341\pi$
$19$	−20.3958			−1.07346			−0.536732	+	0.843753i	$0.680341\pi$
$20$	−3.31981	−	1.91669i	−0.165991	−	0.0958347i
$21$	4.65129	+	6.43160i	0.221490	+	0.306267i
$22$	6.64405	+	11.5078i	0.302002	+	0.523083i
$23$	4.32361	−	2.49624i	0.187983	−	0.108532i	−0.403055	−	0.915176i	$-0.632052\pi$
$23$	4.32361	−	2.49624i	0.187983	−	0.108532i	0.591038	+	0.806644i	$0.298718\pi$
$24$	−12.7021	−	5.68881i	−0.529256	−	0.237034i
$25$	−11.9425	+	20.6850i	−0.477700	+	0.827401i
$26$			9.88447i			0.380172i
$27$	−25.7329	+	8.17411i	−0.953072	+	0.302745i
$28$	9.60495			0.343034
$29$	26.0574	+	15.0442i	0.898531	+	0.518767i	0.876723	−	0.480995i	$-0.159725\pi$
$29$	26.0574	+	15.0442i	0.898531	+	0.518767i	0.0218077	+	0.999762i	$0.493058\pi$
$30$	0.787255	−	1.75780i	0.0262418	−	0.0585935i
$31$	−20.6710	−	35.8032i	−0.666807	−	1.15494i	−0.978792	−	0.204856i	$-0.934327\pi$
$31$	−20.6710	−	35.8032i	−0.666807	−	1.15494i	0.311985	−	0.950087i	$-0.399006\pi$
$32$	−22.2319	+	12.8356i	−0.694747	+	0.401112i
$33$	53.1282	−	38.4219i	1.60995	−	1.16430i
$34$	4.28699	−	7.42528i	0.126088	−	0.218391i
$35$			2.79374i			0.0798212i
$36$	−10.2329	+	31.0292i	−0.284247	+	0.861922i
$37$	19.9781			0.539947			0.269974	−	0.962868i	$-0.412985\pi$
$37$	19.9781			0.539947			0.269974	+	0.962868i	$0.412985\pi$
$38$	−10.7394	−	6.20039i	−0.282616	−	0.163168i
$39$	48.5155	−	4.99149i	1.24399	−	0.127987i
$40$	−2.44939	−	4.24247i	−0.0612348	−	0.106062i
$41$	13.3140	−	7.68686i	0.324732	−	0.187484i	−0.328768	−	0.944411i	$-0.606633\pi$
$41$	13.3140	−	7.68686i	0.324732	−	0.187484i	0.653500	+	0.756927i	$0.273300\pi$
$42$	0.493903	+	4.80056i	0.0117596	+	0.114299i
$43$	0.851359	−	1.47460i	0.0197991	−	0.0342930i	−0.855956	−	0.517048i	$-0.827031\pi$
$43$	0.851359	−	1.47460i	0.0197991	−	0.0342930i	0.875755	+	0.482756i	$0.160364\pi$
$44$		−	79.3416i		−	1.80322i
$45$	−9.02530	−	2.97638i	−0.200562	−	0.0661418i
$46$	3.03545			0.0659881
$47$	−18.6613	−	10.7741i	−0.397048	−	0.229236i	0.288162	−	0.957582i	$-0.406956\pi$
$47$	−18.6613	−	10.7741i	−0.397048	−	0.229236i	−0.685209	+	0.728346i	$0.740289\pi$
$48$	20.5699	+	28.4432i	0.428540	+	0.592566i
$49$	−3.50000	−	6.06218i	−0.0714286	−	0.123718i
$50$	−12.5766	+	7.26112i	−0.251532	+	0.145222i
$51$	−38.6100	−	17.2920i	−0.757059	−	0.339058i
$52$	29.5095	−	51.1119i	0.567490	−	0.982921i
$53$			36.3418i			0.685694i	0.939391	+	0.342847i	$0.111391\pi$
$53$			36.3418i			0.685694i	−0.939391	+	0.342847i	$0.888609\pi$
$54$	−16.0346	−	3.51882i	−0.296937	−	0.0651634i
$55$	23.0777			0.419594
$56$	10.6299	+	6.13720i	0.189820	+	0.109593i
$57$	−25.0099	+	55.8427i	−0.438769	+	0.979697i
$58$	9.14700	+	15.8431i	0.157707	+	0.273156i
$59$	−67.7180	+	39.0970i	−1.14776	+	0.662661i	−0.948341	−	0.317252i	$-0.897240\pi$
$59$	−67.7180	+	39.0970i	−1.14776	+	0.662661i	−0.199422	+	0.979914i	$0.563906\pi$
$60$	−9.31865	+	6.73918i	−0.155311	+	0.112320i
$61$	23.0131	−	39.8599i	0.377264	−	0.653440i	−0.613399	−	0.789773i	$-0.710198\pi$
$61$	23.0131	−	39.8599i	0.377264	−	0.653440i	0.990663	+	0.136333i	$0.0435316\pi$
$62$		−	25.1362i		−	0.405423i
$63$	23.3129	−	4.84840i	0.370047	−	0.0769588i
$64$	31.1941			0.487409
$65$	14.8667	+	8.58326i	0.228718	+	0.132050i
$66$	39.6550	−	4.07988i	0.600833	−	0.0618164i
$67$	−20.9530	−	36.2917i	−0.312731	−	0.541666i	0.666221	−	0.745754i	$-0.267911\pi$
$67$	−20.9530	−	36.2917i	−0.312731	−	0.541666i	−0.978953	+	0.204088i	$0.934577\pi$
$68$	−44.3354	+	25.5971i	−0.651991	+	0.376427i
$69$	−1.53285	−	14.8988i	−0.0222153	−	0.215924i
$70$	−0.849306	+	1.47104i	−0.0121329	+	0.0210149i
$71$			2.65470i			0.0373901i	0.999825	+	0.0186951i	$0.00595117\pi$
$71$			2.65470i			0.0373901i	−0.999825	+	0.0186951i	$0.994049\pi$
$72$	−31.1514	+	27.8021i	−0.432658	+	0.386140i
$73$	−82.5384			−1.13066			−0.565331	−	0.824864i	$-0.691252\pi$
$73$	−82.5384			−1.13066			−0.565331	+	0.824864i	$0.691252\pi$
$74$	10.5194	+	6.07339i	0.142154	+	0.0820729i
$75$	41.9904	+	58.0625i	0.559871	+	0.774166i
$76$	37.0217	+	64.1235i	0.487128	+	0.843731i
$77$	−50.0766	+	28.9117i	−0.650345	+	0.375477i
$78$	27.0632	+	12.1206i	0.346964	+	0.155392i
$79$	−19.4593	+	33.7045i	−0.246320	+	0.426639i	−0.962502	−	0.271275i	$-0.912555\pi$
$79$	−19.4593	+	33.7045i	−0.246320	+	0.426639i	0.716182	+	0.697914i	$0.245888\pi$
$80$			12.3551i			0.154438i
$81$	−9.17407	+	80.4788i	−0.113260	+	0.993565i
$82$	9.34731			0.113992
$83$	−33.1355	−	19.1308i	−0.399223	−	0.230492i	0.286925	−	0.957953i	$-0.407367\pi$
$83$	−33.1355	−	19.1308i	−0.399223	−	0.230492i	−0.686149	+	0.727461i	$0.740700\pi$
$84$	11.7778	−	26.2979i	0.140212	−	0.313070i
$85$	−7.44529	−	12.8956i	−0.0875916	−	0.151713i
$86$	0.896565	−	0.517632i	0.0104252	−	0.00601897i
$87$	73.1426	−	52.8962i	0.840720	−	0.608003i
$88$	50.6963	−	87.8086i	0.576094	−	0.997824i
$89$			58.2883i			0.654925i	0.944864	+	0.327463i	$0.106194\pi$
$89$			58.2883i			0.654925i	−0.944864	+	0.327463i	$0.893806\pi$
$90$	−3.84743	−	4.31093i	−0.0427492	−	0.0478992i
$91$	−43.0125			−0.472665
$92$	−15.6961	−	9.06216i	−0.170610	−	0.0985017i
$93$	−123.375	+	12.6934i	−1.32661	+	0.136488i
$94$	−6.55071	−	11.3462i	−0.0696884	−	0.120704i
$95$	−18.6513	+	10.7683i	−0.196329	+	0.113351i
$96$	7.88190	+	76.6092i	0.0821031	+	0.798012i
$97$	−42.7655	+	74.0720i	−0.440881	+	0.763629i	−0.997755	−	0.0669683i	$-0.978667\pi$
$97$	−42.7655	+	74.0720i	−0.440881	+	0.763629i	0.556874	+	0.830597i	$0.312001\pi$
$98$		−	4.25604i		−	0.0434290i
$99$	−40.0502	−	192.576i	−0.404547	−	1.94522i
$100$	86.7104			0.867104
$101$	93.7358	+	54.1184i	0.928077	+	0.535826i	0.886203	−	0.463297i	$-0.153334\pi$
$101$	93.7358	+	54.1184i	0.928077	+	0.535826i	0.0418744	+	0.999123i	$0.486667\pi$
$102$	−15.0732	−	20.8426i	−0.147777	−	0.204340i
$103$	−53.7784	−	93.1468i	−0.522120	−	0.904338i	−0.999669	−	0.0257331i	$-0.991808\pi$
$103$	−53.7784	−	93.1468i	−0.522120	−	0.904338i	0.477549	−	0.878605i	$-0.341525\pi$
$104$	65.3172	−	37.7109i	0.628050	−	0.362605i
$105$	7.64912	+	3.42576i	0.0728488	+	0.0326262i
$106$	−11.0480	+	19.1357i	−0.104227	+	0.180526i
$107$		−	183.691i		−	1.71674i	−0.513031	−	0.858370i	$-0.671477\pi$
$107$		−	183.691i		−	1.71674i	0.513031	−	0.858370i	$-0.328523\pi$
$108$	72.4086	+	66.0659i	0.670450	+	0.611721i
$109$	−21.4645			−0.196922			−0.0984610	−	0.995141i	$-0.531392\pi$
$109$	−21.4645			−0.196922			−0.0984610	+	0.995141i	$0.531392\pi$
$110$	12.1515	+	7.01568i	0.110468	+	0.0637789i
$111$	24.4976	−	54.6989i	0.220699	−	0.492783i
$112$	−15.4784	−	26.8094i	−0.138200	−	0.239370i
$113$	141.157	−	81.4968i	1.24917	−	0.721211i	0.278229	−	0.960515i	$-0.410252\pi$
$113$	141.157	−	81.4968i	1.24917	−	0.721211i	0.970945	+	0.239304i	$0.0769192\pi$
$114$	−30.1453	+	21.8008i	−0.264432	+	0.191235i
$115$	2.63586	−	4.56545i	0.0229205	−	0.0396995i
$116$		−	109.231i		−	0.941647i
$117$	45.8244	−	138.954i	0.391662	−	1.18764i
$118$	−47.5425			−0.402902
$119$	32.3113	+	18.6549i	0.271523	+	0.156764i
$120$	−14.6192	+	1.50409i	−0.121827	+	0.0125341i
$121$	178.325	+	308.868i	1.47376	+	2.55263i
$122$	24.2350	−	13.9921i	0.198648	−	0.114689i
$123$	−4.72023	−	45.8790i	−0.0383759	−	0.373000i
$124$	−75.0425	+	129.977i	−0.605182	+	1.04821i
$125$			51.6194i			0.412955i
$126$	13.7493	+	4.53429i	0.109122	+	0.0359864i
$127$	−7.50601			−0.0591024			−0.0295512	−	0.999563i	$-0.509408\pi$
$127$	−7.50601			−0.0591024			−0.0295512	+	0.999563i	$0.509408\pi$
$128$	105.353	+	60.8255i	0.823069	+	0.475199i
$129$	−2.99342	−	4.13917i	−0.0232048	−	0.0320866i
$130$	5.21868	+	9.03902i	0.0401437	+	0.0695309i
$131$	12.1947	−	7.04061i	0.0930893	−	0.0537451i	−0.452733	−	0.891646i	$-0.649551\pi$
$131$	12.1947	−	7.04061i	0.0930893	−	0.0537451i	0.545822	+	0.837901i	$0.316217\pi$
$132$	−217.233	−	97.2906i	−1.64571	−	0.737050i
$133$	26.9811	−	46.7327i	0.202866	−	0.351373i
$134$		−	25.4791i		−	0.190143i
$135$	−19.2162	+	21.0611i	−0.142342	+	0.156008i
$136$	−65.4223			−0.481046
$137$	−135.772	−	78.3878i	−0.991034	−	0.572174i	−0.0854509	−	0.996342i	$-0.527233\pi$
$137$	−135.772	−	78.3878i	−0.991034	−	0.572174i	−0.905583	+	0.424169i	$0.860566\pi$
$138$	3.72215	−	8.31092i	0.0269721	−	0.0602241i
$139$	−55.2338	−	95.6677i	−0.397365	−	0.688257i	0.596035	−	0.802959i	$-0.296742\pi$
$139$	−55.2338	−	95.6677i	−0.397365	−	0.688257i	−0.993400	+	0.114702i	$0.963409\pi$
$140$	8.78340	−	5.07110i	0.0627386	−	0.0362221i
$141$	−52.3818	+	37.8821i	−0.371502	+	0.268668i
$142$	−0.807037	+	1.39783i	−0.00568336	+	0.00984387i
$143$			355.304i			2.48464i
$144$	103.099	−	21.4416i	0.715968	−	0.148900i
$145$	31.7715			0.219114
$146$	−43.4605	−	25.0919i	−0.297675	−	0.171863i
$147$	−20.8897	+	2.14923i	−0.142107	+	0.0146206i
$148$	−36.2634	−	62.8101i	−0.245023	−	0.424393i
$149$	101.687	−	58.7090i	0.682463	−	0.394020i	−0.118319	−	0.992976i	$-0.537751\pi$
$149$	101.687	−	58.7090i	0.682463	−	0.394020i	0.800783	+	0.598955i	$0.204417\pi$
$150$	4.45880	+	43.3379i	0.0297253	+	0.288920i
$151$	−51.1797	+	88.6459i	−0.338939	+	0.587059i	−0.984233	−	0.176875i	$-0.943401\pi$
$151$	−51.1797	+	88.6459i	−0.338939	+	0.587059i	0.645295	+	0.763934i	$0.276735\pi$
$152$			94.6220i			0.622513i
$153$	−94.6891	+	84.5084i	−0.618883	+	0.552343i
$154$	−35.1570			−0.228292
$155$	−37.8059	−	21.8272i	−0.243909	−	0.140821i
$156$	−103.757	−	143.470i	−0.665106	−	0.919680i
$157$	41.7307	+	72.2797i	0.265801	+	0.460380i	0.967773	−	0.251824i	$-0.0810304\pi$
$157$	41.7307	+	72.2797i	0.265801	+	0.460380i	−0.701972	+	0.712204i	$0.747697\pi$
$158$	−20.4925	+	11.8314i	−0.129700	+	0.0748821i
$159$	99.5020	+	44.5632i	0.625799	+	0.280272i
$160$	−13.5535	+	23.4754i	−0.0847097	+	0.146721i
$161$			13.2088i			0.0820425i
$162$	−29.2964	+	39.5871i	−0.180842	+	0.244365i
$163$	−77.3382			−0.474468			−0.237234	−	0.971453i	$-0.576241\pi$
$163$	−77.3382			−0.474468			−0.237234	+	0.971453i	$0.576241\pi$
$164$	−48.3343	−	27.9058i	−0.294721	−	0.170157i
$165$	28.2984	−	63.1855i	0.171506	−	0.382942i
$166$	−11.6317	−	20.1466i	−0.0700702	−	0.121365i
$167$	276.594	−	159.692i	1.65625	−	0.956238i	0.681831	−	0.731510i	$-0.261184\pi$
$167$	276.594	−	159.692i	1.65625	−	0.956238i	0.974422	−	0.224728i	$-0.0721493\pi$
$168$	29.8381	−	21.5787i	0.177607	−	0.128444i
$169$	−47.6481	+	82.5289i	−0.281941	+	0.488337i
$170$		−	9.05356i		−	0.0532562i
$171$	122.227	+	136.951i	0.714777	+	0.800886i
$172$	−6.18143			−0.0359385
$173$	−58.1895	−	33.5957i	−0.336356	−	0.194195i	0.322304	−	0.946636i	$-0.395543\pi$
$173$	−58.1895	−	33.5957i	−0.336356	−	0.194195i	−0.658659	+	0.752441i	$0.728876\pi$
$174$	54.5938	−	5.61686i	0.313757	−	0.0322808i
$175$	−31.5969	−	54.7274i	−0.180554	−	0.312728i
$176$	−221.459	+	127.859i	−1.25829	+	0.726474i
$177$	24.0081	+	233.350i	0.135639	+	1.31836i
$178$	−17.7198	+	30.6917i	−0.0995496	+	0.172425i
$179$			275.869i			1.54117i	0.637337	+	0.770585i	$0.280036\pi$
$179$			275.869i			1.54117i	−0.637337	+	0.770585i	$0.719964\pi$
$180$	7.02478	+	33.7778i	0.0390265	+	0.187654i
$181$	274.461			1.51636			0.758181	−	0.652044i	$-0.226088\pi$
$181$	274.461			1.51636			0.758181	+	0.652044i	$0.226088\pi$
$182$	−22.6482	−	13.0759i	−0.124441	−	0.0718458i
$183$	−80.9151	−	111.886i	−0.442159	−	0.611398i
$184$	−11.5808	−	20.0585i	−0.0629389	−	0.109013i
$185$	18.2693	−	10.5478i	0.0987527	−	0.0570149i
$186$	−68.8217	−	30.8226i	−0.370009	−	0.165713i
$187$	154.099	−	266.907i	0.824058	−	1.42731i
$188$			78.2269i			0.416100i
$189$	15.3122	−	69.7749i	0.0810171	−	0.369179i
$190$	−13.0944			−0.0689180
$191$	−47.6864	−	27.5317i	−0.249667	−	0.144145i	0.369945	−	0.929054i	$-0.379377\pi$
$191$	−47.6864	−	27.5317i	−0.249667	−	0.144145i	−0.619612	+	0.784908i	$0.712710\pi$
$192$	38.2511	−	85.4080i	0.199224	−	0.444833i
$193$	−114.576	−	198.452i	−0.593660	−	1.02825i	−0.993734	−	0.111767i	$-0.964349\pi$
$193$	−114.576	−	198.452i	−0.593660	−	1.02825i	0.400074	−	0.916483i	$-0.368984\pi$
$194$	−45.0362	+	26.0017i	−0.232146	+	0.134029i
$195$	41.7304	−	30.1791i	0.214002	−	0.154765i
$196$	−12.7061	+	22.0077i	−0.0648273	+	0.112284i
$197$		−	276.616i		−	1.40414i	−0.712106	−	0.702072i	$-0.752258\pi$
$197$		−	276.616i		−	1.40414i	0.712106	−	0.702072i	$-0.247742\pi$
$198$	37.4554	−	113.576i	0.189169	−	0.573617i
$199$	137.830			0.692612			0.346306	−	0.938122i	$-0.387436\pi$
$199$	137.830			0.692612			0.346306	+	0.938122i	$0.387436\pi$
$200$	95.9637	+	55.4047i	0.479819	+	0.277023i
$201$	−125.058	+	12.8665i	−0.622178	+	0.0640125i
$202$	32.9043	+	56.9920i	0.162893	+	0.282138i
$203$	−68.9414	+	39.8033i	−0.339613	+	0.196076i
$204$	15.7183	+	152.776i	0.0770504	+	0.748902i
$205$	8.11682	−	14.0587i	0.0395942	−	0.0685792i
$206$		−	65.3951i		−	0.317452i
$207$	−42.6717	−	14.0724i	−0.206144	−	0.0679825i
$208$	−190.219			−0.914514
$209$	−386.035	−	222.877i	−1.84706	−	1.06640i
$210$	2.98620	+	4.12918i	0.0142200	+	0.0196628i
$211$	112.988	+	195.700i	0.535487	+	0.927490i	0.999140	+	0.0414730i	$0.0132051\pi$
$211$	112.988	+	195.700i	0.535487	+	0.927490i	−0.463653	+	0.886017i	$0.653462\pi$
$212$	114.257	−	65.9663i	0.538948	−	0.311162i
$213$	7.26844	+	3.25526i	0.0341241	+	0.0152829i
$214$	55.8427	−	96.7224i	0.260947	−	0.451974i
$215$		−	1.79796i		−	0.00836260i
$216$	37.9220	+	119.382i	0.175565	+	0.552697i
$217$	109.381			0.504058
$218$	−11.3021	−	6.52527i	−0.0518445	−	0.0299325i
$219$	−101.211	+	225.986i	−0.462149	+	1.03190i
$220$	−41.8898	−	72.5552i	−0.190408	−	0.329796i
$221$	198.541	−	114.628i	0.898376	−	0.518678i
$222$	29.5278	−	21.3543i	0.133008	−	0.0961906i
$223$	85.6801	−	148.402i	0.384215	−	0.665481i	−0.607445	−	0.794362i	$-0.707805\pi$
$223$	85.6801	−	148.402i	0.384215	−	0.665481i	0.991660	+	0.128881i	$0.0411386\pi$
$224$		−	67.9196i		−	0.303212i
$225$	210.462	−	43.7698i	0.935386	−	0.194533i
$226$	99.1012			0.438501
$227$	−256.120	−	147.871i	−1.12828	−	0.651414i	−0.184780	−	0.982780i	$-0.559157\pi$
$227$	−256.120	−	147.871i	−1.12828	−	0.651414i	−0.943503	+	0.331365i	$0.892491\pi$
$228$	220.964	−	22.7338i	0.969141	−	0.0997096i
$229$	3.87680	+	6.71481i	0.0169292	+	0.0293223i	0.874366	−	0.485267i	$-0.161278\pi$
$229$	3.87680	+	6.71481i	0.0169292	+	0.0293223i	−0.857437	+	0.514590i	$0.827944\pi$
$230$	2.77582	−	1.60262i	0.0120688	−	0.00696792i
$231$	17.7537	+	172.559i	0.0768558	+	0.747011i
$232$	69.7946	−	120.888i	0.300839	−	0.521068i
$233$			1.76156i			0.00756033i	0.999993	+	0.00378016i	$0.00120327\pi$
$233$			1.76156i			0.00756033i	−0.999993	+	0.00378016i	$0.998797\pi$
$234$	66.3711	−	59.2351i	0.283637	−	0.253141i
$235$	−22.7534			−0.0968232
$236$	245.839	+	141.935i	1.04169	+	0.601420i
$237$	68.4197	+	94.6079i	0.288691	+	0.399189i
$238$	11.3423	+	19.6455i	0.0476567	+	0.0825439i
$239$	−82.1746	+	47.4435i	−0.343827	+	0.198508i	−0.661963	−	0.749537i	$-0.730276\pi$
$239$	−82.1746	+	47.4435i	−0.343827	+	0.198508i	0.318136	+	0.948045i	$0.396943\pi$
$240$	33.8276	+	15.1501i	0.140948	+	0.0631254i
$241$	42.3051	−	73.2746i	0.175540	−	0.304044i	−0.764808	−	0.644258i	$-0.777166\pi$
$241$	42.3051	−	73.2746i	0.175540	−	0.304044i	0.940348	+	0.340214i	$0.110500\pi$
$242$			216.845i			0.896056i
$243$	209.097	+	123.803i	0.860483	+	0.509479i
$244$	−167.090			−0.684796
$245$	−6.40126	−	3.69577i	−0.0261276	−	0.0150848i
$246$	11.4619	−	25.5925i	0.0465931	−	0.104034i
$247$	−165.789	−	287.155i	−0.671212	−	1.16257i
$248$	−166.101	+	95.8987i	−0.669764	+	0.386688i
$249$	−93.0109	+	67.2648i	−0.373538	+	0.270140i
$250$	−15.6924	+	27.1801i	−0.0627698	+	0.108720i
$251$			308.555i			1.22930i	0.788799	+	0.614651i	$0.210703\pi$
$251$			308.555i			1.22930i	−0.788799	+	0.614651i	$0.789297\pi$
$252$	−57.5600	−	64.4942i	−0.228413	−	0.255929i
$253$	109.111			0.431271
$254$	−3.95228	−	2.28185i	−0.0155602	−	0.00898366i
$255$	−44.4371	+	4.57189i	−0.174263	+	0.0179290i
$256$	−25.4060	−	44.0045i	−0.0992423	−	0.171893i
$257$	−119.136	+	68.7833i	−0.463565	+	0.267639i	−0.713542	−	0.700613i	$-0.752910\pi$
$257$	−119.136	+	68.7833i	−0.463565	+	0.267639i	0.249977	+	0.968252i	$0.419577\pi$
$258$	−0.317860	−	3.08948i	−0.00123202	−	0.0119747i
$259$	−26.4285	+	45.7755i	−0.102040	+	0.176739i
$260$		−	62.3201i		−	0.239693i
$261$	−55.1379	−	265.124i	−0.211256	−	1.01580i
$262$	8.56147			0.0326774
$263$	−252.981	−	146.059i	−0.961905	−	0.555356i	−0.0651459	−	0.997876i	$-0.520751\pi$
$263$	−252.981	−	146.059i	−0.961905	−	0.555356i	−0.896759	+	0.442520i	$0.854085\pi$
$264$	−178.250	−	246.477i	−0.675191	−	0.933625i
$265$	19.1873	+	33.2333i	0.0724048	+	0.125409i
$266$	28.4138	−	16.4047i	0.106819	−	0.0616718i
$267$	159.591	+	71.4746i	0.597717	+	0.267695i
$268$	−76.0663	+	131.751i	−0.283829	+	0.491607i
$269$		−	406.452i		−	1.51097i	−0.655164	−	0.755487i	$-0.727400\pi$
$269$		−	406.452i		−	1.51097i	0.655164	−	0.755487i	$-0.272600\pi$
$270$	−16.5209	+	5.24790i	−0.0611886	+	0.0194367i
$271$	−164.831			−0.608233			−0.304116	−	0.952635i	$-0.598361\pi$
$271$	−164.831			−0.608233			−0.304116	+	0.952635i	$0.598361\pi$
$272$	142.894	+	82.4997i	0.525344	+	0.303308i
$273$	−52.7430	+	117.766i	−0.193198	+	0.431377i
$274$	−47.6603	−	82.5500i	−0.173943	−	0.301277i
$275$	−452.075	+	261.006i	−1.64391	+	0.949112i
$276$	−44.0587	+	31.8629i	−0.159633	+	0.115445i
$277$	−172.178	+	298.221i	−0.621582	+	1.07661i	0.367609	+	0.929980i	$0.380176\pi$
$277$	−172.178	+	298.221i	−0.621582	+	1.07661i	−0.989191	+	0.146631i	$0.953157\pi$
$278$		−	67.1650i		−	0.241601i
$279$	−116.532	+	353.359i	−0.417676	+	1.26652i
$280$	12.9610			0.0462892
$281$	369.989	+	213.613i	1.31669	+	0.760189i	0.983194	−	0.182565i	$-0.0584399\pi$
$281$	369.989	+	213.613i	1.31669	+	0.760189i	0.333491	+	0.942753i	$0.391773\pi$
$282$	−39.0979	+	4.02256i	−0.138645	+	0.0142644i
$283$	−27.7732	−	48.1045i	−0.0981384	−	0.169981i	0.812776	−	0.582577i	$-0.197955\pi$
$283$	−27.7732	−	48.1045i	−0.0981384	−	0.169981i	−0.910914	+	0.412596i	$0.864622\pi$
$284$	8.34626	−	4.81872i	0.0293883	−	0.0169673i
$285$	6.61246	+	64.2707i	0.0232016	+	0.225511i
$286$	−108.014	+	187.085i	−0.377670	+	0.654143i
$287$			40.6750i			0.141725i
$288$	219.417	+	72.3599i	0.761865	+	0.251250i
$289$	90.1395			0.311901
$290$	16.7292	+	9.65863i	0.0576870	+	0.0333056i
$291$	150.365	+	207.919i	0.516719	+	0.714497i
$292$	149.821	+	259.497i	0.513085	+	0.888689i
$293$	61.2947	−	35.3885i	0.209197	−	0.120780i	−0.391741	−	0.920075i	$-0.628127\pi$
$293$	61.2947	−	35.3885i	0.209197	−	0.120780i	0.600938	+	0.799296i	$0.294794\pi$
$294$	−11.6528	−	5.21887i	−0.0396355	−	0.0177513i
$295$	−41.2839	+	71.5058i	−0.139945	+	0.242393i
$296$		−	92.6839i		−	0.313121i
$297$	−576.375	−	126.487i	−1.94066	−	0.425881i
$298$	71.3909			0.239567
$299$	70.2897	+	40.5818i	0.235083	+	0.135725i
$300$	106.326	−	237.409i	0.354422	−	0.791363i
$301$	2.25249	+	3.90142i	0.00748334	+	0.0129615i
$302$	−53.8973	+	31.1176i	−0.178468	+	0.103038i
$303$	263.115	−	190.283i	0.868365	−	0.627996i
$304$	119.322	−	206.671i	0.392505	−	0.679839i
$305$		−	48.6007i		−	0.159346i
$306$	−75.5493	+	15.7120i	−0.246893	+	0.0513465i
$307$	−56.5282			−0.184131			−0.0920655	−	0.995753i	$-0.529347\pi$
$307$	−56.5282			−0.184131			−0.0920655	+	0.995753i	$0.529347\pi$
$308$	181.794	+	104.959i	0.590242	+	0.340776i
$309$	−320.976	+	33.0234i	−1.03876	+	0.106872i
$310$	−13.2711	−	22.9862i	−0.0428100	−	0.0741491i
$311$	489.541	−	282.637i	1.57409	−	0.908800i	0.578428	−	0.815733i	$-0.303666\pi$
$311$	489.541	−	282.637i	1.57409	−	0.908800i	0.995660	−	0.0930665i	$-0.0296669\pi$
$312$	−23.1570	−	225.077i	−0.0742210	−	0.721401i
$313$	−7.29712	+	12.6390i	−0.0233135	+	0.0403801i	−0.877447	−	0.479674i	$-0.840755\pi$
$313$	−7.29712	+	12.6390i	−0.0233135	+	0.0403801i	0.854133	+	0.520054i	$0.174088\pi$
$314$			50.7450i			0.161608i
$315$	18.7591	−	16.7422i	0.0595527	−	0.0531497i
$316$	141.287			0.447112
$317$	210.858	+	121.739i	0.665167	+	0.384034i	0.794243	−	0.607600i	$-0.207868\pi$
$317$	210.858	+	121.739i	0.665167	+	0.384034i	−0.129076	+	0.991635i	$0.541201\pi$
$318$	38.8453	+	53.7136i	0.122155	+	0.168911i
$319$	328.795	+	569.490i	1.03071	+	1.78523i
$320$	28.5260	−	16.4695i	0.0891437	−	0.0514672i
$321$	−502.937	−	225.247i	−1.56678	−	0.701703i
$322$	−4.01553	+	6.95510i	−0.0124706	+	0.0215997i
$323$			287.617i			0.890456i
$324$	269.674	−	117.239i	0.832328	−	0.361850i
$325$	−388.303			−1.19478
$326$	−40.7224	−	23.5111i	−0.124915	−	0.0721198i
$327$	−26.3203	+	58.7687i	−0.0804903	+	0.179721i
$328$	−35.6615	−	61.7676i	−0.108724	−	0.188316i
$329$	49.3730	−	28.5055i	0.150070	−	0.0866430i
$330$	34.1091	−	24.6674i	0.103361	−	0.0747498i
$331$	154.134	−	266.968i	0.465661	−	0.806549i	−0.533570	−	0.845756i	$-0.679150\pi$
$331$	154.134	−	266.968i	0.465661	−	0.806549i	0.999231	+	0.0392068i	$0.0124831\pi$
$332$			138.902i			0.418380i
$333$	−119.723	−	134.146i	−0.359530	−	0.402842i
$334$	194.187			0.581399
$335$	−38.3216	−	22.1250i	−0.114393	−	0.0660448i
$336$	−92.3830	+	9.50478i	−0.274949	+	0.0282880i
$337$	66.3297	+	114.886i	0.196824	+	0.340909i	0.947497	−	0.319765i	$-0.103604\pi$
$337$	66.3297	+	114.886i	0.196824	+	0.340909i	−0.750673	+	0.660674i	$0.770271\pi$
$338$	−50.1781	+	28.9703i	−0.148456	+	0.0857111i
$339$	−50.0444	−	486.413i	−0.147624	−	1.43485i
$340$	−27.0288	+	46.8153i	−0.0794966	+	0.137692i
$341$		−	903.538i		−	2.64967i
$342$	22.7247	+	109.269i	0.0664465	+	0.319500i
$343$	18.5203			0.0539949
$344$	−6.84108	−	3.94970i	−0.0198869	−	0.0114817i
$345$	−9.26780	−	12.8151i	−0.0268632	−	0.0371453i
$346$	−20.4264	−	35.3796i	−0.0590359	−	0.102253i
$347$	359.479	−	207.545i	1.03596	−	0.598113i	0.117276	−	0.993099i	$-0.462584\pi$
$347$	359.479	−	207.545i	1.03596	−	0.598113i	0.918687	+	0.394986i	$0.129251\pi$
$348$	−299.069	−	133.942i	−0.859395	−	0.384891i
$349$	147.383	−	255.275i	0.422302	−	0.731448i	−0.573862	−	0.818952i	$-0.694556\pi$
$349$	147.383	−	255.275i	0.422302	−	0.731448i	0.996164	+	0.0875035i	$0.0278889\pi$
$350$		−	38.4222i		−	0.109778i
$351$	−324.257	−	295.854i	−0.923809	−	0.842887i
$352$	−561.049			−1.59389
$353$	−8.00809	−	4.62348i	−0.0226858	−	0.0130977i	0.488614	−	0.872500i	$-0.337503\pi$
$353$	−8.00809	−	4.62348i	−0.0226858	−	0.0130977i	−0.511300	+	0.859402i	$0.670836\pi$
$354$	−58.2978	+	130.169i	−0.164683	+	0.367709i
$355$	1.40160	+	2.42763i	0.00394816	+	0.00683841i
$356$	183.256	−	105.803i	0.514764	−	0.297199i
$357$	90.6971	−	65.5915i	0.254054	−	0.183730i
$358$	−83.8652	+	145.259i	−0.234260	+	0.405751i
$359$			102.869i			0.286544i	0.989683	+	0.143272i	$0.0457624\pi$
$359$			102.869i			0.286544i	−0.989683	+	0.143272i	$0.954238\pi$
$360$	−13.8083	+	41.8709i	−0.0383564	+	0.116308i
$361$	54.9890			0.152324
$362$	144.517	+	83.4371i	0.399219	+	0.230489i
$363$	1064.33	−	109.503i	2.93204	−	0.301662i
$364$	78.0747	+	135.229i	0.214491	+	0.371509i
$365$	−75.4786	+	43.5776i	−0.206791	+	0.119391i
$366$	−8.59207	−	83.5118i	−0.0234756	−	0.228174i
$367$	−272.194	+	471.455i	−0.741674	+	1.28462i	0.210058	+	0.977689i	$0.432635\pi$
$367$	−272.194	+	471.455i	−0.741674	+	1.28462i	−0.951733	+	0.306929i	$0.900699\pi$
$368$			58.4149i			0.158736i
$369$	−131.402	−	43.3342i	−0.356104	−	0.117437i
$370$	12.8262			0.0346654
$371$	−83.2695	−	48.0757i	−0.224446	−	0.129584i
$372$	263.853	+	364.844i	0.709282	+	0.980765i
$373$	−214.715	−	371.897i	−0.575643	−	0.997042i	−0.995971	−	0.0896706i	$-0.971419\pi$
$373$	−214.715	−	371.897i	−0.575643	−	0.997042i	0.420329	−	0.907372i	$-0.361915\pi$
$374$	162.281	−	93.6930i	0.433907	−	0.250516i
$375$	141.331	+	63.2970i	0.376883	+	0.168792i
$376$	−49.9840	+	86.5749i	−0.132936	+	0.230252i
$377$			489.154i			1.29749i
$378$	29.2744	−	32.0849i	0.0774456	−	0.0848808i
$379$	−449.221			−1.18528			−0.592639	−	0.805468i	$-0.701914\pi$
$379$	−449.221			−1.18528			−0.592639	+	0.805468i	$0.701914\pi$
$380$	67.7103	+	39.0925i	0.178185	+	0.102875i
$381$	−9.20406	+	20.5511i	−0.0241576	+	0.0539398i
$382$	−16.7395	−	28.9936i	−0.0438206	−	0.0758995i
$383$	−359.903	+	207.790i	−0.939694	+	0.542533i	−0.889864	−	0.456225i	$-0.849201\pi$
$383$	−359.903	+	207.790i	−0.939694	+	0.542533i	−0.0498296	+	0.998758i	$0.515868\pi$
$384$	295.723	−	213.865i	0.770113	−	0.556940i
$385$	−30.5289	+	52.8776i	−0.0792958	+	0.137344i
$386$		−	139.326i		−	0.360949i
$387$	−15.0034	+	3.12027i	−0.0387686	+	0.00806272i
$388$	310.506			0.800272
$389$	183.406	+	105.890i	0.471482	+	0.272210i	0.716860	−	0.697217i	$-0.245579\pi$
$389$	183.406	+	105.890i	0.471482	+	0.272210i	−0.245378	+	0.969427i	$0.578912\pi$
$390$	31.1477	−	3.20461i	0.0798658	−	0.00821695i
$391$	−35.2014	−	60.9706i	−0.0900291	−	0.155935i
$392$	−28.1242	+	16.2375i	−0.0717454	+	0.0414222i
$393$	−4.32340	−	42.0219i	−0.0110010	−	0.106926i
$394$	84.0922	−	145.652i	0.213432	−	0.369675i
$395$			41.0955i			0.104039i
$396$	−532.754	+	475.474i	−1.34534	+	1.20069i
$397$	602.802			1.51839			0.759196	−	0.650862i	$-0.225592\pi$
$397$	602.802			1.51839			0.759196	+	0.650862i	$0.225592\pi$
$398$	72.5741	+	41.9007i	0.182347	+	0.105278i
$399$	−94.8668	−	131.178i	−0.237761	−	0.328766i
$400$	−139.734	−	242.027i	−0.349336	−	0.605068i
$401$	−431.917	+	249.368i	−1.07710	+	0.621864i	−0.930113	−	0.367274i	$-0.880291\pi$
$401$	−431.917	+	249.368i	−1.07710	+	0.621864i	−0.146988	+	0.989138i	$0.546958\pi$
$402$	−69.7605	−	31.2431i	−0.173534	−	0.0777192i
$403$	336.052	−	582.060i	0.833877	−	1.44432i
$404$		−	392.935i		−	0.972612i
$405$	34.1008	+	78.4387i	0.0841995	+	0.193676i
$406$	−48.4014			−0.119215
$407$	378.128	+	218.312i	0.929061	+	0.536394i
$408$	−80.2224	+	179.123i	−0.196624	+	0.439027i
$409$	265.579	+	459.996i	0.649338	+	1.12469i	0.983281	+	0.182093i	$0.0582871\pi$
$409$	265.579	+	459.996i	0.649338	+	1.12469i	−0.333944	+	0.942593i	$0.608380\pi$
$410$	8.54780	−	4.93508i	0.0208483	−	0.0120368i
$411$	−381.109	+	275.615i	−0.927272	+	0.670596i
$412$	−195.233	+	338.154i	−0.473867	+	0.820761i
$413$		−	206.882i		−	0.500925i
$414$	−18.1907	−	20.3821i	−0.0439389	−	0.0492322i
$415$	−40.4018			−0.0973537
$416$	−361.428	−	208.671i	−0.868818	−	0.501612i
$417$	−329.663	+	33.9172i	−0.790558	+	0.0813361i
$418$	−135.511	−	234.712i	−0.324189	−	0.561511i
$419$	−256.304	+	147.977i	−0.611704	+	0.353168i	−0.773632	−	0.633635i	$-0.781562\pi$
$419$	−256.304	+	147.977i	−0.611704	+	0.353168i	0.161928	+	0.986803i	$0.448229\pi$
$420$	−3.11399	−	30.2668i	−0.00741425	−	0.0720639i
$421$	−164.115	+	284.256i	−0.389822	+	0.675192i	−0.992425	−	0.122849i	$-0.960797\pi$
$421$	−164.115	+	284.256i	−0.389822	+	0.675192i	0.602603	+	0.798041i	$0.294130\pi$
$422$			137.394i			0.325579i
$423$	39.4875	+	189.871i	0.0933511	+	0.448867i
$424$	168.600			0.397642
$425$	291.696	+	168.411i	0.686343	+	0.396260i
$426$	2.83758	+	3.92368i	0.00666098	+	0.00921052i
$427$	60.8869	+	105.459i	0.142592	+	0.246977i
$428$	−577.517	+	333.430i	−1.34934	+	0.779041i
$429$	972.805	+	435.683i	2.26761	+	1.01558i
$430$	0.546585	−	0.946714i	0.00127113	−	0.00220166i
$431$		−	344.723i		−	0.799820i	−0.916554	−	0.399910i	$-0.869041\pi$
$431$		−	344.723i		−	0.799820i	0.916554	−	0.399910i	$-0.130959\pi$
$432$	67.7170	−	308.573i	0.156752	−	0.714290i
$433$	−668.552			−1.54400			−0.772000	−	0.635622i	$-0.780744\pi$
$433$	−668.552			−1.54400			−0.772000	+	0.635622i	$0.780744\pi$
$434$	57.5943	+	33.2521i	0.132706	+	0.0766177i
$435$	38.9590	−	86.9887i	0.0895609	−	0.199974i
$436$	38.9616	+	67.4835i	0.0893614	+	0.154779i
$437$	−88.1835	+	50.9127i	−0.201793	+	0.116505i
$438$	−121.993	+	88.2243i	−0.278522	+	0.201425i
$439$	−266.985	+	462.431i	−0.608165	+	1.05337i	0.383377	+	0.923592i	$0.374761\pi$
$439$	−266.985	+	462.431i	−0.608165	+	1.05337i	−0.991543	+	0.129782i	$0.958572\pi$
$440$		−	107.064i		−	0.243327i
$441$	−19.7310	+	59.8305i	−0.0447416	+	0.135670i
$442$	139.389			0.315359
$443$	146.716	+	84.7067i	0.331188	+	0.191211i	0.656368	−	0.754441i	$-0.272092\pi$
$443$	146.716	+	84.7067i	0.331188	+	0.191211i	−0.325181	+	0.945652i	$0.605425\pi$
$444$	−216.438	+	22.2681i	−0.487473	+	0.0501535i
$445$	30.7743	+	53.3027i	0.0691558	+	0.119781i
$446$	90.2295	−	52.0940i	0.202308	−	0.116803i
$447$	−36.0512	−	350.405i	−0.0806515	−	0.783903i
$448$	−41.2660	+	71.4748i	−0.0921116	+	0.159542i
$449$		−	253.851i		−	0.565370i	−0.959213	−	0.282685i	$-0.908775\pi$
$449$		−	253.851i		−	0.565370i	0.959213	−	0.282685i	$-0.0912251\pi$
$450$	124.125	+	40.9341i	0.275832	+	0.0909646i
$451$	335.996			0.745001
$452$	−512.445	−	295.860i	−1.13373	−	0.654558i
$453$	179.950	+	248.827i	0.397241	+	0.549288i
$454$	−89.9065	−	155.723i	−0.198032	−	0.343002i
$455$	−39.3335	+	22.7092i	−0.0864472	+	0.0499103i
$456$	259.070	+	116.028i	0.568137	+	0.254447i
$457$	118.649	−	205.507i	0.259626	−	0.449686i	−0.706515	−	0.707698i	$-0.749734\pi$
$457$	118.649	−	205.507i	0.259626	−	0.449686i	0.966142	+	0.258012i	$0.0830673\pi$
$458$			4.71423i			0.0102931i
$459$	115.270	+	362.880i	0.251132	+	0.790589i
$460$	−19.1381			−0.0416045
$461$	−629.107	−	363.215i	−1.36466	−	0.787886i	−0.374418	−	0.927260i	$-0.622158\pi$
$461$	−629.107	−	363.215i	−1.36466	−	0.787886i	−0.990240	+	0.139374i	$0.955491\pi$
$462$	−43.1104	+	96.2582i	−0.0933126	+	0.208351i
$463$	−327.616	−	567.448i	−0.707594	−	1.22559i	−0.965747	−	0.259485i	$-0.916447\pi$
$463$	−327.616	−	567.448i	−0.707594	−	1.22559i	0.258153	−	0.966104i	$-0.416886\pi$
$464$	−304.887	+	176.027i	−0.657084	+	0.379368i
$465$	−106.120	+	76.7455i	−0.228216	+	0.165044i
$466$	−0.535519	+	0.927546i	−0.00114918	+	0.00199044i
$467$			171.238i			0.366677i	0.983050	+	0.183339i	$0.0586905\pi$
$467$			171.238i			0.366677i	−0.983050	+	0.183339i	$0.941309\pi$
$468$	−520.043	+	108.154i	−1.11120	+	0.231097i
$469$	110.873			0.236403
$470$	−11.9808	−	6.91712i	−0.0254911	−	0.0147173i
$471$	249.069	−	25.6254i	0.528810	−	0.0544063i
$472$	181.382	+	314.163i	0.384285	+	0.665600i
$473$	32.2276	−	18.6066i	0.0681345	−	0.0393375i
$474$	7.26524	+	70.6155i	0.0153275	+	0.148978i
$475$	243.577	−	421.888i	0.512794	−	0.888185i
$476$		−	135.447i		−	0.284552i
$477$	244.024	−	217.787i	0.511580	−	0.456576i
$478$	−57.6919			−0.120694
$479$	733.604	+	423.546i	1.53153	+	0.884230i	0.999291	+	0.0376370i	$0.0119830\pi$
$479$	733.604	+	423.546i	1.53153	+	0.884230i	0.532240	+	0.846593i	$0.321350\pi$
$480$	47.6549	+	65.8951i	0.0992810	+	0.137281i
$481$	162.394	+	281.274i	0.337616	+	0.584769i
$482$	44.5514	−	25.7218i	0.0924303	−	0.0533647i
$483$	36.1651	+	16.1970i	0.0748761	+	0.0335342i
$484$	647.378	−	1121.29i	1.33756	−	2.31672i
$485$			90.3151i			0.186217i
$486$	72.4634	+	128.755i	0.149102	+	0.264927i
$487$	69.7703			0.143266			0.0716328	−	0.997431i	$-0.477179\pi$
$487$	69.7703			0.143266			0.0716328	+	0.997431i	$0.477179\pi$
$488$	−184.921	−	106.764i	−0.378937	−	0.218779i
$489$	−94.8341	+	211.748i	−0.193935	+	0.433023i
$490$	−2.24705	−	3.89201i	−0.00458582	−	0.00794287i
$491$	211.867	−	122.322i	0.431501	−	0.249127i	−0.268485	−	0.963284i	$-0.586523\pi$
$491$	211.867	−	122.322i	0.431501	−	0.249127i	0.699986	+	0.714157i	$0.253190\pi$
$492$	−135.673	+	98.1180i	−0.275759	+	0.199427i
$493$	212.151	−	367.456i	0.430326	−	0.745347i
$494$		−	201.602i		−	0.408101i
$495$	−138.299	−	154.959i	−0.279391	−	0.313049i
$496$	483.726			0.975255
$497$	−6.08268	−	3.51184i	−0.0122388	−	0.00706607i
$498$	−69.4235	+	7.14260i	−0.139405	+	0.0143426i
$499$	−208.497	−	361.127i	−0.417829	−	0.723701i	0.577892	−	0.816113i	$-0.303875\pi$
$499$	−208.497	−	361.127i	−0.417829	−	0.723701i	−0.995721	+	0.0924125i	$0.970542\pi$
$500$	162.289	−	93.6976i	0.324578	−	0.187395i
$501$	−98.0612	−	953.119i	−0.195731	−	1.90243i
$502$	−93.8016	+	162.469i	−0.186856	+	0.323644i
$503$			691.668i			1.37509i	0.726144	+	0.687543i	$0.241311\pi$
$503$			691.668i			1.37509i	−0.726144	+	0.687543i	$0.758689\pi$
$504$	−22.4931	−	108.155i	−0.0446292	−	0.214594i
$505$	114.291			0.226319
$506$	57.4525	+	33.1702i	0.113543	+	0.0655538i
$507$	167.533	+	231.657i	0.330439	+	0.456917i
$508$	13.6246	+	23.5986i	0.0268202	+	0.0464539i
$509$	−202.028	+	116.641i	−0.396912	+	0.229157i	−0.685151	−	0.728401i	$-0.740264\pi$
$509$	−202.028	+	116.641i	−0.396912	+	0.229157i	0.288239	+	0.957559i	$0.406930\pi$
$510$	−24.7882	−	11.1017i	−0.0486043	−	0.0217680i
$511$	109.188	−	189.119i	0.213675	−	0.370096i
$512$		−	517.498i		−	1.01074i
$513$	524.844	−	166.718i	1.02309	−	0.324986i
$514$	−83.6413			−0.162726
$515$	−98.3570	−	56.7864i	−0.190984	−	0.110265i
$516$	−7.57982	+	16.9244i	−0.0146896	+	0.0327993i
$517$	−235.470	−	407.845i	−0.455454	−	0.788869i
$518$	−27.8318	+	16.0687i	−0.0537293	+	0.0310206i
$519$	−163.337	+	118.124i	−0.314715	+	0.227599i
$520$	39.8202	−	68.9707i	0.0765774	−	0.132636i
$521$		−	256.233i		−	0.491809i	−0.969294	−	0.245905i	$-0.920915\pi$
$521$		−	256.233i		−	0.491809i	0.969294	−	0.245905i	$-0.0790850\pi$
$522$	51.5656	−	156.363i	0.0987847	−	0.299545i
$523$	235.246			0.449802			0.224901	−	0.974382i	$-0.427794\pi$
$523$	235.246			0.449802			0.224901	+	0.974382i	$0.427794\pi$
$524$	−44.2708	−	25.5597i	−0.0844862	−	0.0487781i
$525$	−188.586	+	19.4026i	−0.359211	+	0.0369573i
$526$	−88.8045	−	153.814i	−0.168830	−	0.292422i
$527$	−504.890	+	291.498i	−0.958045	+	0.553128i
$528$	78.5141	+	763.129i	0.148701	+	1.44532i
$529$	−252.038	+	436.542i	−0.476442	+	0.825221i
$530$			23.3320i			0.0440226i
$531$	668.341	+	220.407i	1.25865	+	0.415079i
$532$	−195.901			−0.368234
$533$	216.449	+	124.967i	0.406095	+	0.234459i
$534$	62.3037	+	86.1509i	0.116674	+	0.161331i
$535$	−96.9830	−	167.979i	−0.181277	−	0.313980i
$536$	−168.367	+	97.2070i	−0.314118	+	0.181356i
$537$	755.317	+	338.278i	1.40655	+	0.629940i
$538$	123.563	−	214.017i	0.229670	−	0.397801i
$539$		−	152.986i		−	0.283834i
$540$	101.096	+	22.1857i	0.187214	+	0.0410846i
$541$	−175.154			−0.323760			−0.161880	−	0.986810i	$-0.551756\pi$
$541$	−175.154			−0.323760			−0.161880	+	0.986810i	$0.551756\pi$
$542$	−86.7916	−	50.1092i	−0.160132	−	0.0924524i
$543$	336.552	−	751.462i	0.619800	−	1.38391i
$544$	181.005	+	313.510i	0.332730	+	0.576304i
$545$	−19.6286	+	11.3326i	−0.0360157	+	0.0207937i
$546$	−63.5730	+	45.9755i	−0.116434	+	0.0842043i
$547$	−153.703	+	266.221i	−0.280992	+	0.486692i	−0.971629	−	0.236509i	$-0.923997\pi$
$547$	−153.703	+	266.221i	−0.280992	+	0.486692i	0.690637	+	0.723201i	$0.257330\pi$
$548$			569.147i			1.03859i
$549$	−405.558	+	84.3441i	−0.738722	+	0.153632i
$550$	−317.386			−0.577066
$551$	−531.462	−	306.840i	−0.964540	−	0.556878i
$552$	−69.1197	+	7.11134i	−0.125217	+	0.0128829i
$553$	−51.4844	−	89.1737i	−0.0931003	−	0.161254i
$554$	−181.320	+	104.685i	−0.327293	+	0.188963i
$555$	−6.47702	−	62.9542i	−0.0116703	−	0.113431i
$556$	−200.517	+	347.305i	−0.360642	+	0.624650i
$557$			353.461i			0.634579i	0.948329	+	0.317290i	$0.102773\pi$
$557$			353.461i			0.634579i	−0.948329	+	0.317290i	$0.897227\pi$
$558$	−168.782	+	150.635i	−0.302476	+	0.269955i
$559$	27.6814			0.0495195
$560$	−28.3090	−	16.3442i	−0.0505518	−	0.0291861i
$561$	−541.818	−	749.203i	−0.965808	−	1.33548i
$562$	129.878	+	224.955i	0.231100	+	0.400276i
$563$	175.929	−	101.573i	0.312485	−	0.180413i	−0.335553	−	0.942021i	$-0.608923\pi$
$563$	175.929	−	101.573i	0.312485	−	0.180413i	0.648038	+	0.761608i	$0.275590\pi$
$564$	214.181	+	95.9238i	0.379754	+	0.170078i
$565$	86.0553	−	149.052i	0.152310	−	0.263809i
$566$		−	33.7725i		−	0.0596687i
$567$	−172.264	−	127.484i	−0.303816	−	0.224839i
$568$	12.3159			0.0216830
$569$	188.506	+	108.834i	0.331294	+	0.191273i	0.656415	−	0.754400i	$-0.272072\pi$
$569$	188.506	+	108.834i	0.331294	+	0.191273i	−0.325122	+	0.945672i	$0.605405\pi$
$570$	−16.0567	+	35.8519i	−0.0281697	+	0.0628980i
$571$	−324.722	−	562.435i	−0.568690	−	0.985000i	−0.996696	−	0.0812239i	$-0.974117\pi$
$571$	−324.722	−	562.435i	−0.568690	−	0.985000i	0.428006	−	0.903776i	$-0.359216\pi$
$572$	1117.06	−	644.935i	1.95290	−	1.12751i
$573$	−133.855	+	96.8028i	−0.233604	+	0.168940i
$574$	−12.3653	+	21.4174i	−0.0215424	+	0.0373125i
$575$			119.245i			0.207383i
$576$	−186.939	−	209.459i	−0.324546	−	0.363644i
$577$	621.590			1.07728			0.538640	−	0.842536i	$-0.318938\pi$
$577$	621.590			1.07728			0.538640	+	0.842536i	$0.318938\pi$
$578$	47.4628	+	27.4027i	0.0821156	+	0.0474095i
$579$	−683.849	+	70.3574i	−1.18109	+	0.121515i
$580$	−57.6705	−	99.8882i	−0.0994318	−	0.172221i
$581$	87.6684	−	50.6154i	0.150892	−	0.0871177i
$582$	15.9667	+	155.191i	0.0274343	+	0.266651i
$583$	−397.129	+	687.847i	−0.681181	+	1.17984i
$584$			382.919i			0.655684i
$585$	−31.4581	−	151.262i	−0.0537745	−	0.258568i
$586$	43.0328			0.0734349
$587$	−297.051	−	171.502i	−0.506049	−	0.292168i	0.225159	−	0.974322i	$-0.427710\pi$
$587$	−297.051	−	171.502i	−0.506049	−	0.292168i	−0.731208	+	0.682154i	$0.761043\pi$
$588$	44.6754	+	61.7752i	0.0759785	+	0.105060i
$589$	421.602	+	730.236i	0.715793	+	1.23979i
$590$	−43.4760	+	25.1009i	−0.0736881	+	0.0425438i
$591$	−757.362	−	339.194i	−1.28149	−	0.573932i
$592$	−116.878	+	202.438i	−0.197428	+	0.341956i
$593$			755.991i			1.27486i	0.770509	+	0.637429i	$0.220002\pi$
$593$			755.991i			1.27486i	−0.770509	+	0.637429i	$0.779998\pi$
$594$	−265.037	−	241.821i	−0.446191	−	0.407106i
$595$	39.3967			0.0662130
$596$	−369.157	−	213.133i	−0.619391	−	0.357606i
$597$	169.010	−	377.371i	0.283099	−	0.632112i
$598$	24.6740	+	42.7366i	0.0412608	+	0.0714658i
$599$	594.729	−	343.367i	0.992870	−	0.573234i	0.0867391	−	0.996231i	$-0.472355\pi$
$599$	594.729	−	343.367i	0.992870	−	0.573234i	0.906131	+	0.422997i	$0.139022\pi$
$600$	269.368	−	194.805i	0.448947	−	0.324676i
$601$	−203.146	+	351.860i	−0.338014	+	0.585458i	−0.984059	−	0.177842i	$-0.943088\pi$
$601$	−203.146	+	351.860i	−0.338014	+	0.585458i	0.646045	+	0.763299i	$0.276422\pi$
$602$			2.73905i			0.00454992i
$603$	−118.121	+	358.179i	−0.195889	+	0.593996i
$604$	371.598			0.615229
$605$	326.144	+	188.300i	0.539082	+	0.311239i
$606$	196.389	−	20.2054i	0.324075	−	0.0333423i
$607$	121.884	+	211.109i	0.200797	+	0.347791i	0.948786	−	0.315921i	$-0.102313\pi$
$607$	121.884	+	211.109i	0.200797	+	0.347791i	−0.747988	+	0.663712i	$0.768980\pi$
$608$	453.438	−	261.792i	0.745785	−	0.430579i
$609$	24.4419	+	237.566i	0.0401344	+	0.390092i
$610$	14.7748	−	25.5906i	0.0242209	−	0.0419518i
$611$		−	350.312i		−	0.573343i
$612$	437.567	+	144.302i	0.714979	+	0.235787i
$613$	−437.440			−0.713605			−0.356802	−	0.934180i	$-0.616133\pi$
$613$	−437.440			−0.713605			−0.356802	+	0.934180i	$0.616133\pi$
$614$	−29.7649	−	17.1847i	−0.0484770	−	0.0279882i
$615$	−28.5391	−	39.4626i	−0.0464050	−	0.0641669i
$616$	134.130	+	232.320i	0.217743	+	0.377142i
$617$	252.875	−	145.998i	0.409846	−	0.236625i	−0.280877	−	0.959744i	$-0.590625\pi$
$617$	252.875	−	145.998i	0.409846	−	0.236625i	0.690724	+	0.723119i	$0.257292\pi$
$618$	−179.049	−	80.1892i	−0.289723	−	0.129756i
$619$	−481.483	+	833.953i	−0.777840	+	1.34726i	0.155344	+	0.987860i	$0.450351\pi$
$619$	−481.483	+	833.953i	−0.777840	+	1.34726i	−0.933184	+	0.359399i	$0.882982\pi$
$620$			158.480i			0.255613i
$621$	−90.8546	+	99.5771i	−0.146304	+	0.160350i
$622$	343.690			0.552556
$623$	−133.555	−	77.1082i	−0.214375	−	0.123769i
$624$	−233.251	+	520.810i	−0.373800	+	0.834631i
$625$	−271.309	−	469.921i	−0.434095	−	0.751874i
$626$	−7.68458	+	4.43669i	−0.0122757	+	0.00708737i
$627$	−1083.59	+	783.646i	−1.72822	+	1.24983i
$628$	151.496	−	262.399i	0.241236	−	0.417833i
$629$		−	281.726i		−	0.447896i
$630$	14.9673	−	3.11275i	0.0237575	−	0.00494087i
$631$	−1093.87			−1.73355			−0.866777	−	0.498695i	$-0.833813\pi$
$631$	−1093.87			−1.73355			−0.866777	+	0.498695i	$0.833813\pi$
$632$	156.365	+	90.2773i	0.247413	+	0.142844i
$633$	674.366	−	69.3818i	1.06535	−	0.109608i
$634$	74.0180	+	128.203i	0.116748	+	0.202213i
$635$	−6.86399	+	3.96293i	−0.0108094	+	0.00624083i
$636$	−40.5076	−	393.720i	−0.0636913	−	0.619056i
$637$	56.9002	−	98.5540i	0.0893252	−	0.154716i
$638$			399.819i			0.626675i
$639$	17.8255	−	15.9089i	0.0278959	−	0.0248966i
$640$	128.455			0.200712
$641$	528.459	+	305.106i	0.824430	+	0.475985i	0.851942	−	0.523637i	$-0.175425\pi$
$641$	528.459	+	305.106i	0.824430	+	0.475985i	−0.0275120	+	0.999621i	$0.508758\pi$
$642$	−196.345	−	271.498i	−0.305834	−	0.422894i
$643$	490.571	+	849.694i	0.762941	+	1.32145i	0.941328	+	0.337493i	$0.109579\pi$
$643$	490.571	+	849.694i	0.762941	+	1.32145i	−0.178387	+	0.983960i	$0.557088\pi$
$644$	41.5280	−	23.9762i	0.0644845	−	0.0372301i
$645$	−4.92272	−	2.20470i	−0.00763213	−	0.00341815i
$646$	−87.4366	+	151.445i	−0.135351	+	0.234434i
$647$		−	353.250i		−	0.545981i	−0.962017	−	0.272990i	$-0.911987\pi$
$647$		−	353.250i		−	0.545981i	0.962017	−	0.272990i	$-0.0880127\pi$
$648$	373.364	+	42.5611i	0.576179	+	0.0656808i
$649$	−1708.95			−2.63320
$650$	−204.460	−	118.045i	−0.314555	−	0.181608i
$651$	134.125	−	299.479i	0.206030	−	0.460029i
$652$	140.382	+	243.148i	0.215309	+	0.372926i
$653$	504.313	−	291.165i	0.772302	−	0.445889i	−0.0613935	−	0.998114i	$-0.519554\pi$
$653$	504.313	−	291.165i	0.772302	−	0.445889i	0.833695	+	0.552225i	$0.186221\pi$
$654$	−31.7248	+	22.9431i	−0.0485089	+	0.0350813i
$655$	7.43443	−	12.8768i	0.0113503	−	0.0196592i
$656$			179.882i			0.274210i
$657$	494.631	+	554.219i	0.752863	+	0.843561i
$658$	34.6631			0.0526795
$659$	−531.436	−	306.824i	−0.806427	−	0.465591i	0.0392864	−	0.999228i	$-0.487492\pi$
$659$	−531.436	−	306.824i	−0.806427	−	0.465591i	−0.845714	+	0.533637i	$0.820825\pi$
$660$	−250.019	+	25.7231i	−0.378816	+	0.0389743i
$661$	222.908	+	386.088i	0.337228	+	0.584097i	0.983910	−	0.178663i	$-0.0571772\pi$
$661$	222.908	+	386.088i	0.337228	+	0.584097i	−0.646682	+	0.762760i	$0.723844\pi$
$662$	162.318	−	93.7144i	0.245194	−	0.141563i
$663$	−70.3890	−	684.155i	−0.106167	−	1.03191i
$664$	−88.7533	+	153.725i	−0.133665	+	0.231514i
$665$		−	56.9806i		−	0.0856851i
$666$	−22.2593	−	107.031i	−0.0334223	−	0.160707i
$667$	150.216			0.225211
$668$	−1004.13	−	579.733i	−1.50318	−	0.867864i
$669$	−301.255	−	416.562i	−0.450306	−	0.622664i
$670$	−13.4521	−	23.2998i	−0.0200778	−	0.0347758i
$671$	871.145	−	502.956i	1.29828	−	0.749562i
$672$	−185.960	−	83.2847i	−0.276727	−	0.123936i
$673$	−50.0003	+	86.6031i	−0.0742947	+	0.128682i	−0.900779	−	0.434277i	$-0.857004\pi$
$673$	−50.0003	+	86.6031i	−0.0742947	+	0.128682i	0.826485	+	0.562959i	$0.190337\pi$
$674$			80.6577i			0.119670i
$675$	138.234	−	629.906i	0.204791	−	0.933193i
$676$	345.956			0.511770
$677$	739.773	+	427.108i	1.09272	+	0.630884i	0.934300	−	0.356488i	$-0.116026\pi$
$677$	739.773	+	427.108i	1.09272	+	0.630884i	0.158422	+	0.987371i	$0.449359\pi$
$678$	121.520	−	271.334i	0.179234	−	0.400198i
$679$	−113.147	−	195.976i	−0.166637	−	0.288625i
$680$	−59.8265	+	34.5408i	−0.0879801	+	0.0507953i
$681$	−718.925	+	519.921i	−1.05569	+	0.763467i
$682$	274.678	−	475.757i	0.402754	−	0.697591i
$683$			268.139i			0.392589i	0.980545	+	0.196295i	$0.0628909\pi$
$683$			268.139i			0.392589i	−0.980545	+	0.196295i	$0.937109\pi$
$684$	208.708	−	632.865i	0.305128	−	0.925242i
$685$	−165.545			−0.241671
$686$	9.75182	+	5.63022i	0.0142155	+	0.00820731i
$687$	23.1386	−	2.38061i	0.0336807	−	0.00346522i
$688$	9.96141	+	17.2537i	0.0144788	+	0.0250780i
$689$	−511.661	+	295.408i	−0.742614	+	0.428748i
$690$	−0.984114	−	9.56523i	−0.00142625	−	0.0138627i
$691$	396.988	−	687.604i	0.574513	−	0.995086i	−0.421581	−	0.906791i	$-0.638525\pi$
$691$	396.988	−	687.604i	0.574513	−	0.995086i	0.996094	−	0.0882951i	$-0.0281419\pi$
$692$			243.927i			0.352496i
$693$	494.229	+	162.988i	0.713173	+	0.235192i
$694$	252.378			0.363657
$695$	−101.019	−	58.3233i	−0.145351	−	0.0839184i
$696$	−245.401	−	339.330i	−0.352587	−	0.487543i
$697$	−108.398	−	187.752i	−0.155521	−	0.269371i
$698$	155.209	−	89.6100i	0.222363	−	0.128381i
$699$	4.82305	+	2.16007i	0.00689994	+	0.00309022i
$700$	−114.707	+	198.678i	−0.163867	+	0.283826i
$701$			608.220i			0.867647i	0.900998	+	0.433823i	$0.142836\pi$
$701$			608.220i			0.867647i	−0.900998	+	0.433823i	$0.857164\pi$
$702$	−80.7968	−	254.356i	−0.115095	−	0.362331i
$703$	−407.469			−0.579614
$704$	590.417	+	340.877i	0.838660	+	0.484201i
$705$	−27.9009	+	62.2978i	−0.0395757	+	0.0883657i
$706$	−2.81110	−	4.86897i	−0.00398173	−	0.00689656i
$707$	−248.002	+	143.184i	−0.350780	+	0.202523i
$708$	690.065	−	499.050i	0.974668	−	0.704873i
$709$	423.910	−	734.234i	0.597899	−	1.03559i	−0.395232	−	0.918581i	$-0.629336\pi$
$709$	423.910	−	734.234i	0.597899	−	1.03559i	0.993131	−	0.117010i	$-0.0373309\pi$
$710$			1.70436i			0.00240050i
$711$	342.930	−	71.3192i	0.482320	−	0.100308i
$712$	270.416			0.379798
$713$	−178.747	−	103.199i	−0.250697	−	0.144740i
$714$	67.6965	−	6.96492i	0.0948130	−	0.00975479i
$715$	187.589	+	324.914i	0.262362	+	0.454425i
$716$	867.321	−	500.748i	1.21134	−	0.699369i
$717$	29.1334	+	283.166i	0.0406324	+	0.394932i
$718$	−31.2726	+	54.1657i	−0.0435551	+	0.0754397i
$719$			42.1298i			0.0585950i	0.999571	+	0.0292975i	$0.00932702\pi$
$719$			42.1298i			0.0585950i	−0.999571	+	0.0292975i	$0.990673\pi$
$720$	82.9604	−	74.0407i	0.115223	−	0.102834i
$721$	284.568			0.394686
$722$	28.9544	+	16.7168i	0.0401031	+	0.0231535i
$723$	−148.747	−	205.680i	−0.205735	−	0.284482i
$724$	−498.193	−	862.895i	−0.688111	−	1.19184i
$725$	−622.381	+	359.332i	−0.858457	+	0.495630i
$726$	593.712	+	265.901i	0.817785	+	0.366255i
$727$	180.096	−	311.935i	0.247725	−	0.429072i	−0.715169	−	0.698951i	$-0.753651\pi$
$727$	180.096	−	311.935i	0.247725	−	0.429072i	0.962894	+	0.269879i	$0.0869838\pi$
$728$			199.547i			0.274103i
$729$	595.368	−	420.688i	0.816691	−	0.577075i
$730$	−52.9909			−0.0725902
$731$	−20.7945	−	12.0057i	−0.0284466	−	0.0164237i
$732$	−204.890	+	457.485i	−0.279905	+	0.624979i
$733$	−183.938	−	318.590i	−0.250938	−	0.434638i	0.712846	−	0.701321i	$-0.247406\pi$
$733$	−183.938	−	318.590i	−0.250938	−	0.434638i	−0.963784	+	0.266682i	$0.914072\pi$
$734$	−286.647	+	165.496i	−0.390528	+	0.225471i
$735$	−17.9682	+	12.9945i	−0.0244466	+	0.0176796i
$736$	−64.0813	+	110.992i	−0.0870670	+	0.150805i
$737$		−	915.864i		−	1.24269i
$738$	−56.0160	−	62.7643i	−0.0759025	−	0.0850465i
$739$	650.912			0.880801			0.440401	−	0.897801i	$-0.354836\pi$
$739$	650.912			0.880801			0.440401	+	0.897801i	$0.354836\pi$
$740$	−66.3234	−	38.2918i	−0.0896262	−	0.0517457i
$741$	−989.512	+	101.805i	−1.33537	+	0.137389i
$742$	−29.2303	−	50.6284i	−0.0393939	−	0.0682323i
$743$	845.004	−	487.864i	1.13729	−	0.656613i	0.191530	−	0.981487i	$-0.438655\pi$
$743$	845.004	−	487.864i	1.13729	−	0.656613i	0.945757	+	0.324874i	$0.105322\pi$
$744$	58.8881	+	572.371i	0.0791507	+	0.769316i
$745$	61.9929	−	107.375i	0.0832120	−	0.144127i
$746$		−	261.096i		−	0.349994i
$747$	70.1153	+	337.141i	0.0938626	+	0.451326i
$748$	−1118.86			−1.49580
$749$	420.889	+	243.001i	0.561935	+	0.324433i
$750$	55.1753	+	76.2941i	0.0735671	+	0.101725i
$751$	334.413	+	579.220i	0.445290	+	0.771265i	0.998072	−	0.0620605i	$-0.0197672\pi$
$751$	334.413	+	579.220i	0.445290	+	0.771265i	−0.552782	+	0.833326i	$0.686434\pi$
$752$	218.348	−	126.063i	0.290356	−	0.167637i
$753$	844.807	+	378.358i	1.12192	+	0.502467i
$754$	−148.704	+	257.564i	−0.197221	+	0.341596i
$755$			108.085i			0.143159i
$756$	−247.163	+	78.5119i	−0.326936	+	0.103852i
$757$	933.487			1.23314			0.616570	−	0.787300i	$-0.288522\pi$
$757$	933.487			1.23314			0.616570	+	0.787300i	$0.288522\pi$
$758$	−236.537	−	136.564i	−0.312054	−	0.180164i
$759$	133.795	−	298.742i	0.176278	−	0.393599i
$760$	49.9573	+	86.5286i	0.0657333	+	0.113853i
$761$	−823.237	+	475.296i	−1.08178	+	0.624568i	−0.931377	−	0.364057i	$-0.881391\pi$
$761$	−823.237	+	475.296i	−1.08178	+	0.624568i	−0.150406	+	0.988624i	$0.548058\pi$
$762$	−11.0940	+	8.02308i	−0.0145590	+	0.0105290i
$763$	28.3949	−	49.1813i	0.0372148	−	0.0644579i
$764$			199.899i			0.261647i
$765$	−41.9723	+	127.273i	−0.0548658	+	0.166370i
$766$	−252.675			−0.329863
$767$	−1100.90	−	635.608i	−1.43534	−	0.828693i
$768$	−151.636	+	15.6010i	−0.197442	+	0.0203138i
$769$	−142.532	−	246.872i	−0.185347	−	0.321030i	0.758347	−	0.651851i	$-0.226007\pi$
$769$	−142.532	−	246.872i	−0.185347	−	0.321030i	−0.943693	+	0.330822i	$0.892674\pi$
$770$	−32.1499	+	18.5618i	−0.0417531	+	0.0241062i
$771$	42.2374	+	410.533i	0.0547827	+	0.532468i
$772$	−415.950	+	720.447i	−0.538795	+	0.933221i
$773$		−	161.128i		−	0.208445i	−0.994554	−	0.104223i	$-0.966765\pi$
$773$		−	161.128i		−	0.208445i	0.994554	−	0.104223i	$-0.0332354\pi$
$774$	−8.84862	−	2.91812i	−0.0114323	−	0.00377018i
$775$	987.454			1.27413
$776$	343.641	+	198.401i	0.442837	+	0.255672i
$777$	92.9237	+	128.491i	0.119593	+	0.165368i
$778$	64.3816	+	111.512i	0.0827528	+	0.143332i
$779$	−271.550	+	156.780i	−0.348588	+	0.201258i
$780$	−170.629	−	76.4185i	−0.218756	−	0.0979725i
$781$	−29.0095	+	50.2460i	−0.0371441	+	0.0643354i
$782$		−	42.8053i		−	0.0547383i
$783$	−793.507	−	174.137i	−1.01342	−	0.222397i
$784$	81.9042			0.104470
$785$	76.3226	+	44.0649i	0.0972263	+	0.0561336i
$786$	10.4983	−	23.4409i	0.0133566	−	0.0298230i
$787$	−775.200	−	1342.69i	−0.985006	−	1.70608i	−0.641910	−	0.766780i	$-0.721858\pi$
$787$	−775.200	−	1342.69i	−0.985006	−	1.70608i	−0.343096	−	0.939300i	$-0.611476\pi$
$788$	−869.670	+	502.104i	−1.10364	+	0.637188i
$789$	−710.113	+	513.548i	−0.900016	+	0.650885i
$790$	−12.4932	+	21.6388i	−0.0158141	+	0.0273909i
$791$			431.241i			0.545184i
$792$	−893.417	+	185.804i	−1.12805	+	0.234601i
$793$	748.257			0.943577
$794$	317.405	+	183.254i	0.399754	+	0.230798i
$795$	114.519	−	11.7822i	0.144049	−	0.0148204i
$796$	−250.184	−	433.331i	−0.314301	−	0.544385i
$797$	−601.600	+	347.334i	−0.754831	+	0.435802i	−0.827437	−	0.561559i	$-0.810202\pi$
$797$	−601.600	+	347.334i	−0.754831	+	0.435802i	0.0726061	+	0.997361i	$0.476868\pi$
$798$	−10.0736	−	97.9113i	−0.0126235	−	0.122696i
$799$	−151.934	+	263.157i	−0.190155	+	0.329358i
$800$		−	613.156i		−	0.766445i
$801$	391.388	−	349.307i	0.488624	−	0.436089i
$802$	−303.234			−0.378097
$803$	−1562.22	−	901.947i	−1.94548	−	1.12322i
$804$	267.452	+	369.822i	0.332652	+	0.459977i
$805$	6.97383	+	12.0790i	0.00866315	+	0.0150050i
$806$	353.896	−	204.322i	0.439077	−	0.253501i
$807$	−1112.85	−	498.402i	−1.37899	−	0.617598i
$808$	251.071	−	434.867i	0.310731	−	0.538202i
$809$		−	67.6861i		−	0.0836664i	−0.999125	−	0.0418332i	$-0.986680\pi$
$809$		−	67.6861i		−	0.0836664i	0.999125	−	0.0418332i	$-0.0133198\pi$
$810$	−5.88989	+	51.6686i	−0.00727147	+	0.0637884i
$811$	951.824			1.17364			0.586821	−	0.809716i	$-0.300379\pi$
$811$	951.824			1.17364			0.586821	+	0.809716i	$0.300379\pi$
$812$	250.280	+	144.499i	0.308226	+	0.177955i
$813$	−202.120	+	451.299i	−0.248610	+	0.555104i
$814$	132.735	+	229.904i	0.163065	+	0.282438i
$815$	−70.7232	+	40.8321i	−0.0867769	+	0.0501007i
$816$	401.100	−	290.073i	0.491544	−	0.355481i
$817$	−17.3642	+	30.0756i	−0.0212536	+	0.0368123i
$818$			322.947i			0.394801i
$819$	257.763	+	288.815i	0.314729	+	0.352644i
$820$	−58.9334			−0.0718700
$821$	209.051	+	120.695i	0.254629	+	0.147010i	0.621882	−	0.783111i	$-0.286368\pi$
$821$	209.051	+	120.695i	0.254629	+	0.147010i	−0.367253	+	0.930121i	$0.619702\pi$
$822$	−284.460	+	29.2665i	−0.346059	+	0.0356041i
$823$	682.725	+	1182.51i	0.829556	+	1.43683i	0.898387	+	0.439206i	$0.144740\pi$
$823$	682.725	+	1182.51i	0.829556	+	1.43683i	−0.0688301	+	0.997628i	$0.521927\pi$
$824$	−432.135	+	249.493i	−0.524436	+	0.302783i
$825$	160.275	+	1557.81i	0.194272	+	1.88826i
$826$	62.8928	−	108.933i	0.0761414	−	0.131881i
$827$		−	278.115i		−	0.336293i	−0.985762	−	0.168147i	$-0.946222\pi$
$827$		−	278.115i		−	0.336293i	0.985762	−	0.168147i	$-0.0537782\pi$
$828$	33.2132	+	159.702i	0.0401126	+	0.192876i
$829$	−384.271			−0.463536			−0.231768	−	0.972771i	$-0.574451\pi$
$829$	−384.271			−0.463536			−0.231768	+	0.972771i	$0.574451\pi$
$830$	−21.2735	−	12.2823i	−0.0256307	−	0.0147979i
$831$	605.386	+	837.102i	0.728503	+	1.00734i
$832$	253.565	+	439.187i	0.304765	+	0.527869i
$833$	−85.4876	+	49.3563i	−0.102626	+	0.0592512i
$834$	−183.894	−	82.3594i	−0.220497	−	0.0987523i
$835$	168.624	−	292.065i	0.201945	−	0.349779i
$836$			1618.24i			1.93569i
$837$	824.585	+	752.355i	0.985168	+	0.898871i
$838$	−179.942			−0.214728
$839$	1380.43	+	796.989i	1.64532	+	0.949928i	0.978896	+	0.204358i	$0.0655106\pi$
$839$	1380.43	+	796.989i	1.64532	+	0.949928i	0.666427	+	0.745570i	$0.267823\pi$
$840$	15.8931	−	35.4865i	0.0189203	−	0.0422458i
$841$	32.1586	+	55.7004i	0.0382386	+	0.0662311i
$842$	−172.829	+	99.7831i	−0.205261	+	0.118507i
$843$	1038.55	−	751.073i	1.23197	−	0.890952i
$844$	410.182	−	710.457i	0.485998	−	0.841773i
$845$			100.627i			0.119085i
$846$	−36.9292	+	111.981i	−0.0436515	+	0.132365i
$847$	−943.607			−1.11406
$848$	−368.252	−	212.610i	−0.434259	−	0.250720i
$849$	−165.764	+	17.0545i	−0.195246	+	0.0200878i
$850$	102.395	+	177.353i	0.120464	+	0.208650i
$851$	86.3773	−	49.8699i	0.101501	−	0.0586016i
$852$	−2.95901	−	28.7605i	−0.00347301	−	0.0337564i
$853$	22.9378	−	39.7294i	0.0268907	−	0.0465761i	−0.852267	−	0.523107i	$-0.824773\pi$
$853$	22.9378	−	39.7294i	0.0268907	−	0.0465761i	0.879158	+	0.476531i	$0.158106\pi$
$854$			74.0393i			0.0866971i
$855$	184.078	+	60.7057i	0.215296	+	0.0710009i
$856$	−852.196			−0.995556
$857$	−594.744	−	343.375i	−0.693983	−	0.400671i	0.111119	−	0.993807i	$-0.464556\pi$
$857$	−594.744	−	343.375i	−0.693983	−	0.400671i	−0.805102	+	0.593136i	$0.797890\pi$
$858$	379.780	+	525.144i	0.442635	+	0.612056i
$859$	−633.367	−	1097.02i	−0.737331	−	1.27709i	−0.953693	−	0.300781i	$-0.902753\pi$
$859$	−633.367	−	1097.02i	−0.737331	−	1.27709i	0.216362	−	0.976313i	$-0.430581\pi$
$860$	−5.65271	+	3.26359i	−0.00657292	+	0.00379487i
$861$	111.366	+	49.8767i	0.129345	+	0.0579288i
$862$	104.797	−	181.513i	0.121574	−	0.210572i
$863$		−	521.316i		−	0.604074i	−0.953296	−	0.302037i	$-0.902333\pi$
$863$		−	521.316i		−	0.604074i	0.953296	−	0.302037i	$-0.0976667\pi$
$864$	467.172	−	512.023i	0.540709	−	0.592620i
$865$	−70.9498			−0.0820229
$866$	−352.025	−	203.242i	−0.406496	−	0.234690i
$867$	110.531	−	246.797i	0.127487	−	0.284657i
$868$	−198.544	−	343.888i	−0.228737	−	0.396184i
$869$	−736.618	+	425.287i	−0.847662	+	0.489398i
$870$	46.9587	−	33.9602i	0.0539755	−	0.0390347i
$871$	340.637	−	590.000i	0.391087	−	0.677383i
$872$			99.5800i			0.114197i
$873$	753.653	−	156.738i	0.863291	−	0.179539i
$874$	−61.9105			−0.0708359
$875$	−118.275	−	68.2860i	−0.135171	−	0.0780411i
$876$	894.204	−	91.9997i	1.02078	−	0.105023i
$877$	492.536	+	853.098i	0.561615	+	0.972745i	0.997356	+	0.0726734i	$0.0231531\pi$
$877$	492.536	+	853.098i	0.561615	+	0.972745i	−0.435741	+	0.900072i	$0.643514\pi$
$878$	−281.161	+	162.328i	−0.320229	+	0.184884i
$879$	−21.7309	−	211.216i	−0.0247222	−	0.240291i
$880$	−135.011	+	233.846i	−0.153422	+	0.265735i
$881$		−	1229.69i		−	1.39579i	−0.716198	−	0.697897i	$-0.754119\pi$
$881$		−	1229.69i		−	1.39579i	0.716198	−	0.697897i	$-0.245881\pi$
$882$	−28.5780	+	25.5054i	−0.0324014	+	0.0289177i
$883$	105.285			0.119236			0.0596180	−	0.998221i	$-0.481012\pi$
$883$	105.285			0.119236			0.0596180	+	0.998221i	$0.481012\pi$
$884$	−720.769	−	416.136i	−0.815350	−	0.470742i
$885$	145.156	+	200.716i	0.164018	+	0.226797i
$886$	51.5022	+	89.2044i	0.0581289	+	0.100682i
$887$	563.427	−	325.295i	0.635205	−	0.366736i	−0.147560	−	0.989053i	$-0.547142\pi$
$887$	563.427	−	325.295i	0.635205	−	0.366736i	0.782765	+	0.622317i	$0.213809\pi$
$888$	−253.764	−	113.651i	−0.285770	−	0.127986i
$889$	9.92951	−	17.1984i	0.0111693	−	0.0193458i
$890$			37.4220i			0.0420472i
$891$	−1053.08	+	1422.98i	−1.18191	+	1.59706i
$892$	−622.093			−0.697414
$893$	380.611	+	219.746i	0.426216	+	0.246076i
$894$	87.5414	−	195.465i	0.0979210	−	0.218641i
$895$	145.650	+	252.273i	0.162737	+	0.281870i
$896$	−278.737	+	160.929i	−0.311091	+	0.179608i
$897$	197.302	−	142.687i	0.219958	−	0.159072i
$898$	77.1715	−	133.665i	0.0859371	−	0.148847i
$899$		−	1243.92i		−	1.38367i
$900$	−519.633	−	582.233i	−0.577370	−	0.646926i
$901$	512.484			0.568795
$902$	176.918	+	102.144i	0.196140	+	0.113241i
$903$	13.4439	−	1.38317i	0.0148881	−	0.00153175i
$904$	−378.087	−	654.866i	−0.418238	−	0.724410i
$905$	250.986	−	144.907i	0.277332	−	0.160118i
$906$	19.1082	+	185.725i	0.0210908	+	0.204995i
$907$	513.312	−	889.083i	0.565945	−	0.980246i	−0.431016	−	0.902344i	$-0.641845\pi$
$907$	513.312	−	889.083i	0.565945	−	0.980246i	0.996961	−	0.0779017i	$-0.0248220\pi$
$908$			1073.64i			1.18242i
$909$	−198.346	−	953.724i	−0.218203	−	1.04920i
$910$	−27.6147			−0.0303458
$911$	374.455	+	216.192i	0.411038	+	0.237313i	0.691235	−	0.722630i	$-0.257067\pi$
$911$	374.455	+	216.192i	0.411038	+	0.237313i	−0.280198	+	0.959942i	$0.590400\pi$
$912$	−419.540	−	580.122i	−0.460022	−	0.636098i
$913$	−418.108	−	724.184i	−0.457949	−	0.793192i
$914$	124.949	−	72.1395i	0.136706	−	0.0789272i
$915$	−133.066	−	59.5954i	−0.145428	−	0.0651315i
$916$	14.0740	−	24.3770i	0.0153647	−	0.0266124i
$917$			37.2554i			0.0406275i
$918$	−49.6217	+	226.117i	−0.0540542	+	0.246314i
$919$	1340.78			1.45896			0.729478	−	0.684004i	$-0.239763\pi$
$919$	1340.78			1.45896			0.729478	+	0.684004i	$0.239763\pi$
$920$	−21.1804	−	12.2285i	−0.0230222	−	0.0132919i
$921$	−69.3163	+	154.771i	−0.0752620	+	0.168047i
$922$	−220.837	−	382.501i	−0.239520	−	0.414860i
$923$	−37.3759	+	21.5790i	−0.0404939	+	0.0233792i
$924$	510.294	−	369.041i	0.552266	−	0.399395i
$925$	−238.588	+	413.246i	−0.257933	+	0.446753i
$926$		−	398.385i		−	0.430222i
$927$	−303.172	+	919.310i	−0.327047	+	0.991704i
$928$	−772.407			−0.832335
$929$	959.943	+	554.223i	1.03331	+	0.596580i	0.917930	−	0.396741i	$-0.129859\pi$
$929$	959.943	+	554.223i	1.03331	+	0.596580i	0.115377	+	0.993322i	$0.463192\pi$
$930$	−79.2084	+	8.14932i	−0.0851704	+	0.00876271i
$931$	71.3853	+	123.643i	0.0766760	+	0.132807i
$932$	5.53826	−	3.19751i	0.00594234	−	0.00343081i
$933$	−173.558	−	1686.92i	−0.186021	−	1.80806i
$934$	−52.0570	+	90.1654i	−0.0557355	+	0.0965368i
$935$		−	325.436i		−	0.348060i
$936$	−644.646	−	212.593i	−0.688724	−	0.227129i
$937$	862.090			0.920053			0.460027	−	0.887905i	$-0.347840\pi$
$937$	862.090			0.920053			0.460027	+	0.887905i	$0.347840\pi$
$938$	58.3800	+	33.7057i	0.0622388	+	0.0359336i
$939$	25.6570	+	35.4774i	0.0273237	+	0.0377821i
$940$	41.3012	+	71.5358i	0.0439375	+	0.0761020i
$941$	−1516.31	+	875.439i	−1.61138	+	0.930329i	−0.622325	+	0.782759i	$0.713812\pi$
$941$	−1516.31	+	875.439i	−1.61138	+	0.930329i	−0.989052	+	0.147570i	$0.952855\pi$
$942$	138.937	+	62.2249i	0.147492	+	0.0660561i
$943$	38.3764	−	66.4699i	0.0406961	−	0.0704877i
$944$		−	914.917i		−	0.969192i
$945$	−22.8363	−	71.8911i	−0.0241654	−	0.0760753i
$946$	22.6259			0.0239174
$947$	−446.988	−	258.069i	−0.472005	−	0.272512i	0.245074	−	0.969504i	$-0.421188\pi$
$947$	−446.988	−	258.069i	−0.472005	−	0.272512i	−0.717079	+	0.696992i	$0.754521\pi$
$948$	173.250	−	386.837i	0.182753	−	0.408056i
$949$	−670.921	−	1162.07i	−0.706977	−	1.22452i
$950$	256.510	−	148.096i	0.270011	−	0.155891i
$951$	591.874	−	428.039i	0.622370	−	0.450094i
$952$	86.5455	−	149.901i	0.0909092	−	0.157459i
$953$		−	447.867i		−	0.469955i	−0.972001	−	0.234977i	$-0.924498\pi$
$953$		−	447.867i		−	0.469955i	0.972001	−	0.234977i	$-0.0755016\pi$
$954$	194.698	−	40.4915i	0.204086	−	0.0424439i
$955$	−58.1435			−0.0608832
$956$	298.321	+	172.235i	0.312051	+	0.180163i
$957$	1962.41	−	201.902i	2.05059	−	0.210974i
$958$	257.519	+	446.036i	0.268809	+	0.465590i
$959$	359.218	−	207.395i	0.374576	−	0.216261i
$960$	−10.1133	−	98.2981i	−0.0105347	−	0.102394i
$961$	−374.081	+	647.927i	−0.389262	+	0.674222i
$962$			197.473i			0.205273i
$963$	−1233.43	+	1100.81i	−1.28082	+	1.14311i
$964$	−307.163			−0.318634
$965$	−209.553	−	120.985i	−0.217153	−	0.125373i
$966$	14.1188	+	19.5228i	0.0146157	+	0.0202100i
$967$	594.482	+	1029.67i	0.614769	+	1.06481i	0.990425	+	0.138053i	$0.0440843\pi$
$967$	594.482	+	1029.67i	0.614769	+	1.06481i	−0.375655	+	0.926759i	$0.622582\pi$
$968$	1432.93	−	827.301i	1.48030	−	0.854650i
$969$	787.482	+	352.684i	0.812675	+	0.363967i
$970$	−27.4561	+	47.5553i	−0.0283052	+	0.0490261i
$971$			142.452i			0.146706i	0.997306	+	0.0733531i	$0.0233700\pi$
$971$			142.452i			0.146706i	−0.997306	+	0.0733531i	$0.976630\pi$
$972$	9.68592	−	882.117i	0.00996494	−	0.907527i
$973$	292.270			0.300380
$974$	36.7375	+	21.2104i	0.0377182	+	0.0217766i
$975$	−476.147	+	1063.15i	−0.488356	+	1.09041i
$976$	269.267	+	466.384i	0.275888	+	0.477853i
$977$	−427.287	+	246.694i	−0.437346	+	0.252502i	−0.702471	−	0.711712i	$-0.747920\pi$
$977$	−427.287	+	246.694i	−0.437346	+	0.252502i	0.265125	+	0.964214i	$0.414587\pi$
$978$	−114.307	+	82.6659i	−0.116878	+	0.0845255i
$979$	−636.952	+	1103.23i	−0.650615	+	1.12690i
$980$			26.8337i			0.0273814i
$981$	128.631	+	144.127i	0.131123	+	0.146919i
$982$	148.744			0.151471
$983$	1335.95	+	771.312i	1.35905	+	0.784651i	0.989496	−	0.144557i	$-0.0461757\pi$
$983$	1335.95	+	771.312i	1.35905	+	0.784651i	0.369558	+	0.929208i	$0.379509\pi$
$984$	−212.846	+	21.8985i	−0.216307	+	0.0222546i
$985$	−146.044	−	252.956i	−0.148268	−	0.256808i
$986$	223.416	−	128.989i	0.226588	−	0.130821i
$987$	−17.5043	−	170.135i	−0.0177348	−	0.172376i
$988$	−601.869	+	1042.47i	−0.609180	+	1.05513i
$989$		−	8.50077i		−	0.00859532i
$990$	−25.7128	−	123.637i	−0.0259725	−	0.124886i
$991$	228.500			0.230576			0.115288	−	0.993332i	$-0.463221\pi$
$991$	228.500			0.230576			0.115288	+	0.993332i	$0.463221\pi$
$992$	919.111	+	530.649i	0.926524	+	0.534929i
$993$	−541.942	−	749.374i	−0.545762	−	0.754656i
$994$	−2.13522	−	3.69831i	−0.00214811	−	0.00372063i
$995$	126.041	−	72.7696i	0.126674	−	0.0731353i
$996$	380.307	+	170.325i	0.381835	+	0.171010i
$997$	−486.398	+	842.467i	−0.487862	+	0.845002i	−0.999903	−	0.0139596i	$-0.995556\pi$
$997$	−486.398	+	842.467i	−0.487862	+	0.845002i	0.512041	+	0.858961i	$0.328890\pi$
$998$		−	253.534i		−	0.254043i
$999$	−514.094	+	163.303i	−0.514609	+	0.163466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.r.a.29.7	✓	24
3.2	odd	2		189.3.r.a.8.6		24
7.2	even	3		441.3.j.h.263.6		24
7.3	odd	6		441.3.n.h.128.6		24
7.4	even	3		441.3.n.g.128.6		24
7.5	odd	6		441.3.j.g.263.6		24
7.6	odd	2		441.3.r.h.344.7		24
9.2	odd	6		567.3.b.a.323.14		24
9.4	even	3		189.3.r.a.71.6		24
9.5	odd	6	inner	63.3.r.a.50.7	yes	24
9.7	even	3		567.3.b.a.323.11		24
63.5	even	6		441.3.n.h.410.6		24
63.23	odd	6		441.3.n.g.410.6		24
63.32	odd	6		441.3.j.h.275.7		24
63.41	even	6		441.3.r.h.50.7		24
63.59	even	6		441.3.j.g.275.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.r.a.29.7	✓	24	1.1	even	1	trivial
63.3.r.a.50.7	yes	24	9.5	odd	6	inner
189.3.r.a.8.6		24	3.2	odd	2
189.3.r.a.71.6		24	9.4	even	3
441.3.j.g.263.6		24	7.5	odd	6
441.3.j.g.275.7		24	63.59	even	6
441.3.j.h.263.6		24	7.2	even	3
441.3.j.h.275.7		24	63.32	odd	6
441.3.n.g.128.6		24	7.4	even	3
441.3.n.g.410.6		24	63.23	odd	6
441.3.n.h.128.6		24	7.3	odd	6
441.3.n.h.410.6		24	63.5	even	6
441.3.r.h.50.7		24	63.41	even	6
441.3.r.h.344.7		24	7.6	odd	2
567.3.b.a.323.11		24	9.7	even	3
567.3.b.a.323.14		24	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.526549 + 0.304003i) q^{2} +(1.22623 - 2.73795i) q^{3} +(-1.81516 - 3.14396i) q^{4} +(0.914466 - 0.527967i) q^{5} +(1.47801 - 1.06889i) q^{6} +(-1.32288 + 2.29129i) q^{7} -4.63929i q^{8} +(-5.99274 - 6.71469i) q^{9} +O(q^{10})\)	\(q+(0.526549 + 0.304003i) q^{2} +(1.22623 - 2.73795i) q^{3} +(-1.81516 - 3.14396i) q^{4} +(0.914466 - 0.527967i) q^{5} +(1.47801 - 1.06889i) q^{6} +(-1.32288 + 2.29129i) q^{7} -4.63929i q^{8} +(-5.99274 - 6.71469i) q^{9} +0.642015 q^{10} +(18.9272 + 10.9276i) q^{11} +(-10.8338 + 1.11463i) q^{12} +(8.12859 + 14.0791i) q^{13} +(-1.39312 + 0.804317i) q^{14} +(-0.324207 - 3.15117i) q^{15} +(-5.85030 + 10.1330i) q^{16} -14.1018i q^{17} +(-1.11419 - 5.35742i) q^{18} -20.3958 q^{19} +(-3.31981 - 1.91669i) q^{20} +(4.65129 + 6.43160i) q^{21} +(6.64405 + 11.5078i) q^{22} +(4.32361 - 2.49624i) q^{23} +(-12.7021 - 5.68881i) q^{24} +(-11.9425 + 20.6850i) q^{25} +9.88447i q^{26} +(-25.7329 + 8.17411i) q^{27} +9.60495 q^{28} +(26.0574 + 15.0442i) q^{29} +(0.787255 - 1.75780i) q^{30} +(-20.6710 - 35.8032i) q^{31} +(-22.2319 + 12.8356i) q^{32} +(53.1282 - 38.4219i) q^{33} +(4.28699 - 7.42528i) q^{34} +2.79374i q^{35} +(-10.2329 + 31.0292i) q^{36} +19.9781 q^{37} +(-10.7394 - 6.20039i) q^{38} +(48.5155 - 4.99149i) q^{39} +(-2.44939 - 4.24247i) q^{40} +(13.3140 - 7.68686i) q^{41} +(0.493903 + 4.80056i) q^{42} +(0.851359 - 1.47460i) q^{43} -79.3416i q^{44} +(-9.02530 - 2.97638i) q^{45} +3.03545 q^{46} +(-18.6613 - 10.7741i) q^{47} +(20.5699 + 28.4432i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-12.5766 + 7.26112i) q^{50} +(-38.6100 - 17.2920i) q^{51} +(29.5095 - 51.1119i) q^{52} +36.3418i q^{53} +(-16.0346 - 3.51882i) q^{54} +23.0777 q^{55} +(10.6299 + 6.13720i) q^{56} +(-25.0099 + 55.8427i) q^{57} +(9.14700 + 15.8431i) q^{58} +(-67.7180 + 39.0970i) q^{59} +(-9.31865 + 6.73918i) q^{60} +(23.0131 - 39.8599i) q^{61} -25.1362i q^{62} +(23.3129 - 4.84840i) q^{63} +31.1941 q^{64} +(14.8667 + 8.58326i) q^{65} +(39.6550 - 4.07988i) q^{66} +(-20.9530 - 36.2917i) q^{67} +(-44.3354 + 25.5971i) q^{68} +(-1.53285 - 14.8988i) q^{69} +(-0.849306 + 1.47104i) q^{70} +2.65470i q^{71} +(-31.1514 + 27.8021i) q^{72} -82.5384 q^{73} +(10.5194 + 6.07339i) q^{74} +(41.9904 + 58.0625i) q^{75} +(37.0217 + 64.1235i) q^{76} +(-50.0766 + 28.9117i) q^{77} +(27.0632 + 12.1206i) q^{78} +(-19.4593 + 33.7045i) q^{79} +12.3551i q^{80} +(-9.17407 + 80.4788i) q^{81} +9.34731 q^{82} +(-33.1355 - 19.1308i) q^{83} +(11.7778 - 26.2979i) q^{84} +(-7.44529 - 12.8956i) q^{85} +(0.896565 - 0.517632i) q^{86} +(73.1426 - 52.8962i) q^{87} +(50.6963 - 87.8086i) q^{88} +58.2883i q^{89} +(-3.84743 - 4.31093i) q^{90} -43.0125 q^{91} +(-15.6961 - 9.06216i) q^{92} +(-123.375 + 12.6934i) q^{93} +(-6.55071 - 11.3462i) q^{94} +(-18.6513 + 10.7683i) q^{95} +(7.88190 + 76.6092i) q^{96} +(-42.7655 + 74.0720i) q^{97} -4.25604i q^{98} +(-40.0502 - 192.576i) 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

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