LMFDB - Embedded newform 93.3.l.b.8.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [93,3,Mod(2,93)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("93.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(93, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	93.l (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.53406645855$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.1
Character	$\chi$	$=$	93.8
Dual form			93.3.l.b.35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.46751 - 1.12666i) q^{2} +(2.05322 + 2.18730i) q^{3} +(7.51820 + 5.46229i) q^{4} +5.25837i q^{5} +(-4.65521 - 9.89779i) q^{6} +(-8.69344 - 6.31616i) q^{7} +(-11.3431 - 15.6125i) q^{8} +(-0.568590 + 8.98202i) q^{9} +(5.92441 - 18.2335i) q^{10} +(-5.73550 + 7.89424i) q^{11} +(3.48882 + 27.6599i) q^{12} +(2.39173 + 7.36097i) q^{13} +(23.0284 + 31.6959i) q^{14} +(-11.5017 + 10.7966i) q^{15} +(10.2557 + 31.5637i) q^{16} +(-11.7236 - 16.1361i) q^{17} +(12.0913 - 30.5047i) q^{18} +(-8.21254 + 25.2756i) q^{19} +(-28.7228 + 39.5335i) q^{20} +(-4.03419 - 31.9836i) q^{21} +(28.7821 - 20.9114i) q^{22} +(11.4195 + 15.7176i) q^{23} +(10.8593 - 56.8667i) q^{24} -2.65047 q^{25} -28.2189i q^{26} +(-20.8138 + 17.1984i) q^{27} +(-30.8584 - 94.9723i) q^{28} +(18.2102 + 5.91685i) q^{29} +(52.0462 - 24.4788i) q^{30} +(-30.9204 - 2.21980i) q^{31} -43.8097i q^{32} +(-29.0433 + 3.66332i) q^{33} +(22.4717 + 69.1606i) q^{34} +(33.2127 - 45.7134i) q^{35} +(-53.3372 + 64.4229i) q^{36} +36.1145 q^{37} +(56.9542 - 78.3907i) q^{38} +(-11.1899 + 20.3451i) q^{39} +(82.0963 - 59.6464i) q^{40} +(-10.7369 - 3.48863i) q^{41} +(-22.0462 + 115.449i) q^{42} +(3.28404 - 10.1072i) q^{43} +(-86.2414 + 28.0215i) q^{44} +(-47.2308 - 2.98986i) q^{45} +(-21.8889 - 67.3670i) q^{46} +(46.0524 - 14.9633i) q^{47} +(-47.9822 + 87.2393i) q^{48} +(20.5403 + 63.2165i) q^{49} +(9.19055 + 2.98619i) q^{50} +(11.2235 - 58.7739i) q^{51} +(-22.2263 + 68.4056i) q^{52} +(8.46907 + 11.6567i) q^{53} +(91.5490 - 36.1854i) q^{54} +(-41.5109 - 30.1594i) q^{55} +207.371i q^{56} +(-72.1475 + 33.9330i) q^{57} +(-56.4777 - 41.0335i) q^{58} +(0.297119 - 0.0965397i) q^{59} +(-145.446 + 18.3455i) q^{60} +91.8176 q^{61} +(104.716 + 42.5341i) q^{62} +(61.6749 - 74.4934i) q^{63} +(-8.33613 + 25.6560i) q^{64} +(-38.7067 + 12.5766i) q^{65} +(104.835 + 20.0195i) q^{66} +38.4531 q^{67} -185.352i q^{68} +(-10.9324 + 57.2497i) q^{69} +(-166.669 + 121.092i) q^{70} +(13.0939 + 18.0222i) q^{71} +(146.681 - 93.0072i) q^{72} +(37.0554 + 26.9223i) q^{73} +(-125.227 - 40.6888i) q^{74} +(-5.44200 - 5.79739i) q^{75} +(-199.806 + 145.168i) q^{76} +(99.7226 - 32.4018i) q^{77} +(61.7234 - 57.9396i) q^{78} +(-24.6102 + 17.8803i) q^{79} +(-165.974 + 53.9281i) q^{80} +(-80.3534 - 10.2142i) q^{81} +(33.2998 + 24.1937i) q^{82} +(-113.176 - 36.7730i) q^{83} +(144.374 - 262.495i) q^{84} +(84.8496 - 61.6469i) q^{85} +(-22.7749 + 31.3469i) q^{86} +(24.4475 + 51.9798i) q^{87} +188.307 q^{88} +(67.0402 - 92.2729i) q^{89} +(160.405 + 63.5806i) q^{90} +(25.7007 - 79.0987i) q^{91} +180.545i q^{92} +(-58.6310 - 72.1901i) q^{93} -176.546 q^{94} +(-132.908 - 43.1846i) q^{95} +(95.8251 - 89.9509i) q^{96} +(-108.734 - 79.0002i) q^{97} -242.346i q^{98} +(-67.6451 - 56.0050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 5 q^{3} + 36 q^{4} - 10 q^{6} - 54 q^{7} + 5 q^{9} + 114 q^{10} + 14 q^{12} + 26 q^{13} + 35 q^{15} - 184 q^{16} + 15 q^{18} - 90 q^{19} + 71 q^{21} - 114 q^{22} - 101 q^{24} - 188 q^{25} + 116 q^{27}+ \cdots - 616 q^{99}+O(q^{100}) $ 72 * q + 5 * q^3 + 36 * q^4 - 10 * q^6 - 54 * q^7 + 5 * q^9 + 114 * q^10 + 14 * q^12 + 26 * q^13 + 35 * q^15 - 184 * q^16 + 15 * q^18 - 90 * q^19 + 71 * q^21 - 114 * q^22 - 101 * q^24 - 188 * q^25 + 116 * q^27 - 84 * q^28 - 18 * q^30 + 28 * q^31 - 242 * q^33 - 82 * q^34 + 74 * q^36 + 364 * q^37 + 13 * q^39 + 252 * q^40 - 46 * q^42 - 146 * q^43 + 52 * q^45 - 88 * q^46 - 170 * q^48 - 60 * q^49 - 301 * q^51 - 222 * q^52 - 118 * q^54 + 308 * q^55 - 20 * q^57 - 280 * q^58 - 407 * q^60 + 84 * q^61 + 556 * q^63 + 1450 * q^64 + 550 * q^66 - 324 * q^67 + 355 * q^69 + 728 * q^70 - 631 * q^72 - 140 * q^73 - 17 * q^75 - 622 * q^76 + 679 * q^78 - 200 * q^79 + 5 * q^81 + 598 * q^82 + 1197 * q^84 - 200 * q^85 + 202 * q^87 + 388 * q^88 + 1068 * q^90 + 834 * q^91 + 74 * q^93 - 384 * q^94 - 1016 * q^96 - 1074 * q^97 - 616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−3.46751	−	1.12666i	−1.73376	−	0.563332i	−0.739772	−	0.672857i	$-0.765067\pi$
$2$	−3.46751	−	1.12666i	−1.73376	−	0.563332i	−0.993984	+	0.109526i	$0.965067\pi$
$3$	2.05322	+	2.18730i	0.684406	+	0.729101i
$3$	2.05322	+	2.18730i	0.684406	+	0.729101i
$4$	7.51820	+	5.46229i	1.87955	+	1.36557i
$5$			5.25837i			1.05167i	0.850585	+	0.525837i	$0.176248\pi$
$5$			5.25837i			1.05167i	−0.850585	+	0.525837i	$0.823752\pi$
$6$	−4.65521	−	9.89779i	−0.775868	−	1.64963i
$7$	−8.69344	−	6.31616i	−1.24192	−	0.902308i	−0.244196	−	0.969726i	$-0.578524\pi$
$7$	−8.69344	−	6.31616i	−1.24192	−	0.902308i	−0.997725	+	0.0674178i	$0.978524\pi$
$8$	−11.3431	−	15.6125i	−1.41789	−	1.95156i
$9$	−0.568590	+	8.98202i	−0.0631767	+	0.998002i
$10$	5.92441	−	18.2335i	0.592441	−	1.82335i
$11$	−5.73550	+	7.89424i	−0.521409	+	0.717659i	−0.985791	−	0.167977i	$-0.946277\pi$
$11$	−5.73550	+	7.89424i	−0.521409	+	0.717659i	0.464381	+	0.885635i	$0.346277\pi$
$12$	3.48882	+	27.6599i	0.290735	+	2.30499i
$13$	2.39173	+	7.36097i	0.183979	+	0.566229i	0.999929	−	0.0118931i	$-0.00378580\pi$
$13$	2.39173	+	7.36097i	0.183979	+	0.566229i	−0.815950	+	0.578122i	$0.803786\pi$
$14$	23.0284	+	31.6959i	1.64489	+	2.26400i
$15$	−11.5017	+	10.7966i	−0.766777	+	0.719772i
$16$	10.2557	+	31.5637i	0.640979	+	1.97273i
$17$	−11.7236	−	16.1361i	−0.689622	−	0.949183i	0.310377	−	0.950613i	$-0.399545\pi$
$17$	−11.7236	−	16.1361i	−0.689622	−	0.949183i	−0.999999	+	0.00143078i	$0.999545\pi$
$18$	12.0913	−	30.5047i	0.671739	−	1.69470i
$19$	−8.21254	+	25.2756i	−0.432239	+	1.33029i	0.463651	+	0.886018i	$0.346539\pi$
$19$	−8.21254	+	25.2756i	−0.432239	+	1.33029i	−0.895890	+	0.444277i	$0.853461\pi$
$20$	−28.7228	+	39.5335i	−1.43614	+	1.97668i
$21$	−4.03419	−	31.9836i	−0.192104	−	1.52303i
$22$	28.7821	−	20.9114i	1.30828	−	0.950519i
$23$	11.4195	+	15.7176i	0.496501	+	0.683375i	0.981570	−	0.191101i	$-0.0612057\pi$
$23$	11.4195	+	15.7176i	0.496501	+	0.683375i	−0.485069	+	0.874476i	$0.661206\pi$
$24$	10.8593	−	56.8667i	0.452471	−	2.36945i
$25$	−2.65047			−0.106019
$26$		−	28.2189i		−	1.08534i
$27$	−20.8138	+	17.1984i	−0.770883	+	0.636977i
$28$	−30.8584	−	94.9723i	−1.10208	−	3.39187i
$29$	18.2102	+	5.91685i	0.627937	+	0.204029i	0.605661	−	0.795723i	$-0.292909\pi$
$29$	18.2102	+	5.91685i	0.627937	+	0.204029i	0.0222762	+	0.999752i	$0.492909\pi$
$30$	52.0462	−	24.4788i	1.73487	−	0.815960i
$31$	−30.9204	−	2.21980i	−0.997433	−	0.0716063i
$31$	−30.9204	−	2.21980i	−0.997433	−	0.0716063i
$32$		−	43.8097i		−	1.36905i
$33$	−29.0433	+	3.66332i	−0.880101	+	0.111010i
$34$	22.4717	+	69.1606i	0.660931	+	2.03414i
$35$	33.2127	−	45.7134i	0.948934	−	1.30610i
$36$	−53.3372	+	64.4229i	−1.48159	+	1.78952i
$37$	36.1145			0.976066			0.488033	−	0.872825i	$-0.337714\pi$
$37$	36.1145			0.976066			0.488033	+	0.872825i	$0.337714\pi$
$38$	56.9542	−	78.3907i	1.49879	−	2.06291i
$39$	−11.1899	+	20.3451i	−0.286922	+	0.521670i
$40$	82.0963	−	59.6464i	2.05241	−	1.49116i
$41$	−10.7369	−	3.48863i	−0.261875	−	0.0850885i	0.175137	−	0.984544i	$-0.443963\pi$
$41$	−10.7369	−	3.48863i	−0.261875	−	0.0850885i	−0.437012	+	0.899456i	$0.643963\pi$
$42$	−22.0462	+	115.449i	−0.524909	+	2.74878i
$43$	3.28404	−	10.1072i	0.0763730	−	0.235052i	−0.905581	−	0.424174i	$-0.860564\pi$
$43$	3.28404	−	10.1072i	0.0763730	−	0.235052i	0.981953	+	0.189123i	$0.0605644\pi$
$44$	−86.2414	+	28.0215i	−1.96003	+	0.636853i
$45$	−47.2308	−	2.98986i	−1.04957	−	0.0664413i
$46$	−21.8889	−	67.3670i	−0.475845	−	1.46450i
$47$	46.0524	−	14.9633i	0.979838	−	0.318369i	0.225057	−	0.974346i	$-0.427743\pi$
$47$	46.0524	−	14.9633i	0.979838	−	0.318369i	0.754781	+	0.655977i	$0.227743\pi$
$48$	−47.9822	+	87.2393i	−0.999629	+	1.81749i
$49$	20.5403	+	63.2165i	0.419190	+	1.29013i
$50$	9.19055	+	2.98619i	0.183811	+	0.0597238i
$51$	11.2235	−	58.7739i	0.220069	−	1.15243i
$52$	−22.2263	+	68.4056i	−0.427429	+	1.31549i
$53$	8.46907	+	11.6567i	0.159794	+	0.219937i	0.881405	−	0.472361i	$-0.156598\pi$
$53$	8.46907	+	11.6567i	0.159794	+	0.219937i	−0.721611	+	0.692298i	$0.756598\pi$
$54$	91.5490	−	36.1854i	1.69535	−	0.670099i
$55$	−41.5109	−	30.1594i	−0.754743	−	0.548353i
$56$			207.371i			3.70306i
$57$	−72.1475	+	33.9330i	−1.26575	+	0.595316i
$58$	−56.4777	−	41.0335i	−0.973754	−	0.707474i
$59$	0.297119	−	0.0965397i	0.00503591	−	0.00163627i	−0.306498	−	0.951871i	$-0.599157\pi$
$59$	0.297119	−	0.0965397i	0.00503591	−	0.00163627i	0.311534	+	0.950235i	$0.399157\pi$
$60$	−145.446	+	18.3455i	−2.42410	+	0.305758i
$61$	91.8176			1.50521			0.752603	−	0.658475i	$-0.228798\pi$
$61$	91.8176			1.50521			0.752603	+	0.658475i	$0.228798\pi$
$62$	104.716	+	42.5341i	1.68897	+	0.686033i
$63$	61.6749	−	74.4934i	0.978966	−	1.18243i
$64$	−8.33613	+	25.6560i	−0.130252	+	0.400875i
$65$	−38.7067	+	12.5766i	−0.595488	+	0.193486i
$66$	104.835	+	20.0195i	1.58842	+	0.303325i
$67$	38.4531			0.573926			0.286963	−	0.957942i	$-0.407354\pi$
$67$	38.4531			0.573926			0.286963	+	0.957942i	$0.407354\pi$
$68$		−	185.352i		−	2.72577i
$69$	−10.9324	+	57.2497i	−0.158441	+	0.829705i
$70$	−166.669	+	121.092i	−2.38099	+	1.72989i
$71$	13.0939	+	18.0222i	0.184421	+	0.253834i	0.891210	−	0.453590i	$-0.149857\pi$
$71$	13.0939	+	18.0222i	0.184421	+	0.253834i	−0.706789	+	0.707424i	$0.749857\pi$
$72$	146.681	−	93.0072i	2.03724	−	1.29177i
$73$	37.0554	+	26.9223i	0.507608	+	0.368799i	0.811915	−	0.583775i	$-0.198425\pi$
$73$	37.0554	+	26.9223i	0.507608	+	0.368799i	−0.304307	+	0.952574i	$0.598425\pi$
$74$	−125.227	−	40.6888i	−1.69226	−	0.549849i
$75$	−5.44200	−	5.79739i	−0.0725600	−	0.0772985i
$76$	−199.806	+	145.168i	−2.62903	+	1.91010i
$77$	99.7226	−	32.4018i	1.29510	−	0.420803i
$78$	61.7234	−	57.9396i	0.791325	−	0.742816i
$79$	−24.6102	+	17.8803i	−0.311521	+	0.226333i	−0.732549	−	0.680714i	$-0.761670\pi$
$79$	−24.6102	+	17.8803i	−0.311521	+	0.226333i	0.421028	+	0.907048i	$0.361670\pi$
$80$	−165.974	+	53.9281i	−2.07467	+	0.674101i
$81$	−80.3534	−	10.2142i	−0.992017	−	0.126101i
$82$	33.2998	+	24.1937i	0.406095	+	0.295045i
$83$	−113.176	−	36.7730i	−1.36356	−	0.443048i	−0.466332	−	0.884610i	$-0.654425\pi$
$83$	−113.176	−	36.7730i	−1.36356	−	0.443048i	−0.897231	+	0.441562i	$0.854425\pi$
$84$	144.374	−	262.495i	1.71874	−	3.12495i
$85$	84.8496	−	61.6469i	0.998231	−	0.725257i
$86$	−22.7749	+	31.3469i	−0.264824	+	0.364499i
$87$	24.4475	+	51.9798i	0.281006	+	0.597469i
$88$	188.307			2.13986
$89$	67.0402	−	92.2729i	0.753261	−	1.03677i	−0.244484	−	0.969653i	$-0.578619\pi$
$89$	67.0402	−	92.2729i	0.753261	−	1.03677i	0.997745	−	0.0671211i	$-0.0213814\pi$
$90$	160.405	+	63.5806i	1.78228	+	0.706451i
$91$	25.7007	−	79.0987i	0.282426	−	0.869217i
$92$			180.545i			1.96245i
$93$	−58.6310	−	72.1901i	−0.630441	−	0.776237i
$94$	−176.546			−1.87815
$95$	−132.908	−	43.1846i	−1.39904	−	0.454575i
$96$	95.8251	−	89.9509i	0.998178	−	0.936988i
$97$	−108.734	−	79.0002i	−1.12097	−	0.814435i	−0.136617	−	0.990624i	$-0.543623\pi$
$97$	−108.734	−	79.0002i	−1.12097	−	0.814435i	−0.984356	+	0.176189i	$0.943623\pi$
$98$		−	242.346i		−	2.47292i
$99$	−67.6451	−	56.0050i	−0.683284	−	0.565707i
$100$	−19.9268	−	14.4777i	−0.199268	−	0.144777i
$101$	108.169	+	148.881i	1.07098	+	1.47407i	0.869084	+	0.494664i	$0.164709\pi$
$101$	108.169	+	148.881i	1.07098	+	1.47407i	0.201891	+	0.979408i	$0.435291\pi$
$102$	−105.136	+	191.154i	−1.03075	+	1.87406i
$103$	−12.6080	+	38.8033i	−0.122407	+	0.376731i	−0.993420	−	0.114530i	$-0.963464\pi$
$103$	−12.6080	+	38.8033i	−0.122407	+	0.376731i	0.871012	+	0.491261i	$0.163464\pi$
$104$	87.7934	−	120.837i	0.844168	−	1.16190i
$105$	168.182	−	21.2133i	1.60173	−	0.202031i
$106$	−16.2335	−	49.9614i	−0.153146	−	0.471334i
$107$	41.0718	+	56.5305i	0.383849	+	0.528322i	0.956599	−	0.291408i	$-0.0941236\pi$
$107$	41.0718	+	56.5305i	0.383849	+	0.528322i	−0.572750	+	0.819730i	$0.694124\pi$
$108$	−250.425	+	15.6095i	−2.31875	+	0.144532i
$109$	45.2145	+	139.156i	0.414812	+	1.27666i	0.912419	+	0.409257i	$0.134212\pi$
$109$	45.2145	+	139.156i	0.414812	+	1.27666i	−0.497608	+	0.867402i	$0.665788\pi$
$110$	109.960	+	151.347i	0.999636	+	1.37588i
$111$	74.1509	+	78.9933i	0.668026	+	0.711651i
$112$	110.204	−	339.173i	0.983965	−	3.02833i
$113$	−43.3920	+	59.7239i	−0.384000	+	0.528530i	−0.956639	−	0.291277i	$-0.905920\pi$
$113$	−43.3920	+	59.7239i	−0.384000	+	0.528530i	0.572639	+	0.819808i	$0.305920\pi$
$114$	288.404	−	36.3771i	2.52986	−	0.319098i
$115$	−82.6491	+	60.0481i	−0.718688	+	0.522157i
$116$	104.588	+	143.953i	0.901623	+	1.24098i
$117$	−67.4763	+	17.2972i	−0.576721	+	0.147839i
$118$	−1.13903			−0.00965280
$119$			214.326i			1.80106i
$120$	299.026	+	57.1023i	2.49189	+	0.475852i
$121$	7.96797	+	24.5229i	0.0658510	+	0.202669i
$122$	−318.379	−	103.447i	−2.60966	−	0.847930i
$123$	−14.4145	−	30.6477i	−0.117191	−	0.249169i
$124$	−220.341	−	185.585i	−1.77694	−	1.49666i
$125$			117.522i			0.940177i
$126$	−297.787	+	188.820i	−2.36339	+	1.49857i
$127$	−16.3095	−	50.1956i	−0.128421	−	0.395241i	0.866087	−	0.499893i	$-0.166627\pi$
$127$	−16.3095	−	50.1956i	−0.128421	−	0.395241i	−0.994509	+	0.104652i	$0.966627\pi$
$128$	−45.1915	+	62.2007i	−0.353058	+	0.485943i
$129$	28.8504	−	13.5692i	0.223647	−	0.105187i
$130$	148.386			1.14143
$131$	53.2428	−	73.2824i	0.406433	−	0.559407i	−0.555911	−	0.831242i	$-0.687630\pi$
$131$	53.2428	−	73.2824i	0.406433	−	0.559407i	0.962344	+	0.271835i	$0.0876303\pi$
$132$	−238.364	−	131.102i	−1.80579	−	0.993195i
$133$	231.040	−	167.860i	1.73714	−	1.26211i
$134$	−133.336	−	43.3236i	−0.995048	−	0.323311i
$135$	−90.4354	−	109.447i	−0.669892	−	0.810718i
$136$	−118.943	+	366.068i	−0.874579	+	2.69168i
$137$	−119.940	+	38.9708i	−0.875474	+	0.284459i	−0.712077	−	0.702102i	$-0.752245\pi$
$137$	−119.940	+	38.9708i	−0.875474	+	0.284459i	−0.163397	+	0.986560i	$0.552245\pi$
$138$	102.409	−	186.197i	0.742097	−	1.34925i
$139$	20.8631	+	64.2100i	0.150094	+	0.461943i	0.997631	−	0.0687943i	$-0.0219152\pi$
$139$	20.8631	+	64.2100i	0.150094	+	0.461943i	−0.847537	+	0.530737i	$0.821915\pi$
$140$	499.400	−	162.265i	3.56714	−	1.15903i
$141$	127.285	+	70.0075i	0.902730	+	0.496507i
$142$	−25.0983	−	77.2446i	−0.176749	−	0.543976i
$143$	−71.8271	−	23.3380i	−0.502287	−	0.163203i
$144$	−289.337	+	74.1697i	−2.00928	+	0.515068i
$145$	−31.1130	+	95.7559i	−0.214572	+	0.660386i
$146$	−98.1576	−	135.102i	−0.672312	−	0.925359i
$147$	−96.1000	+	174.725i	−0.653742	+	1.18861i
$148$	271.516	+	197.268i	1.83457	+	1.33289i
$149$		−	62.1327i		−	0.416998i	−0.978023	−	0.208499i	$-0.933142\pi$
$149$		−	62.1327i		−	0.416998i	0.978023	−	0.208499i	$-0.0668578\pi$
$150$	12.3385	+	26.2338i	0.0822567	+	0.174892i
$151$	−59.2931	−	43.0789i	−0.392669	−	0.285291i	0.373879	−	0.927477i	$-0.378027\pi$
$151$	−59.2931	−	43.0789i	−0.392669	−	0.285291i	−0.766548	+	0.642187i	$0.778027\pi$
$152$	487.771	−	158.486i	3.20902	−	1.04267i
$153$	151.601	−	96.1265i	0.990855	−	0.628278i
$154$	−382.295			−2.48244
$155$	11.6725	−	162.591i	0.0753065	−	1.04897i
$156$	−195.259	+	91.8359i	−1.25166	+	0.588692i
$157$	79.0115	−	243.172i	0.503258	−	1.54887i	−0.300422	−	0.953806i	$-0.597127\pi$
$157$	79.0115	−	243.172i	0.503258	−	1.54887i	0.803680	−	0.595062i	$-0.202873\pi$
$158$	105.481	−	34.2729i	0.667603	−	0.216917i
$159$	−8.10783	+	42.4581i	−0.0509926	+	0.267032i
$160$	230.368			1.43980
$161$		−	208.768i		−	1.29669i
$162$	267.118	+	125.949i	1.64888	+	0.777463i
$163$	−128.681	+	93.4923i	−0.789455	+	0.573572i	−0.907802	−	0.419400i	$-0.862241\pi$
$163$	−128.681	+	93.4923i	−0.789455	+	0.573572i	0.118347	+	0.992972i	$0.462241\pi$
$164$	−61.6662	−	84.8763i	−0.376013	−	0.517538i
$165$	−19.2631	−	152.721i	−0.116746	−	0.925580i
$166$	351.007	+	255.022i	2.11450	+	1.53628i
$167$	−166.487	−	54.0949i	−0.996928	−	0.323921i	−0.235291	−	0.971925i	$-0.575604\pi$
$167$	−166.487	−	54.0949i	−0.996928	−	0.323921i	−0.761637	+	0.648004i	$0.775604\pi$
$168$	−453.584	+	425.779i	−2.69990	+	2.53440i
$169$	88.2603	−	64.1248i	0.522250	−	0.379437i
$170$	−363.672	+	118.164i	−2.13925	+	0.695084i
$171$	−222.356	−	88.1367i	−1.30033	−	0.515419i
$172$	79.8987	−	58.0498i	0.464527	−	0.337499i
$173$	131.212	−	42.6333i	0.758451	−	0.246436i	0.0958371	−	0.995397i	$-0.469447\pi$
$173$	131.212	−	42.6333i	0.758451	−	0.246436i	0.662614	+	0.748962i	$0.269447\pi$
$174$	−26.2085	−	207.785i	−0.150623	−	1.19416i
$175$	23.0418	+	16.7408i	0.131667	+	0.0956618i
$176$	−307.993	−	100.073i	−1.74996	−	0.568596i
$177$	0.821211	+	0.451672i	0.00463961	+	0.00255182i
$178$	−336.423	+	244.426i	−1.89002	+	1.37318i
$179$	54.4343	−	74.9224i	0.304102	−	0.418561i	−0.629428	−	0.777059i	$-0.716711\pi$
$179$	54.4343	−	74.9224i	0.304102	−	0.418561i	0.933531	+	0.358498i	$0.116711\pi$
$180$	−338.759	−	280.467i	−1.88200	−	1.55815i
$181$	−211.666			−1.16942			−0.584712	−	0.811241i	$-0.698792\pi$
$181$	−211.666			−1.16942			−0.584712	+	0.811241i	$0.698792\pi$
$182$	−178.235	+	245.320i	−0.979314	+	1.34791i
$183$	188.522	+	200.833i	1.03017	+	1.09745i
$184$	115.858	−	356.574i	0.629663	−	1.93790i
$185$			189.903i			1.02650i
$186$	121.970	+	316.377i	0.655752	+	1.70095i
$187$	194.623			1.04076
$188$	427.965	+	139.054i	2.27641	+	0.739651i
$189$	289.572	−	18.0496i	1.53212	−	0.0955004i
$190$	412.207	+	299.486i	2.16951	+	1.57624i
$191$			215.396i			1.12773i	0.825868	+	0.563863i	$0.190685\pi$
$191$			215.396i			1.12773i	−0.825868	+	0.563863i	$0.809315\pi$
$192$	−73.2333	+	34.4437i	−0.381423	+	0.179394i
$193$	75.3781	+	54.7654i	0.390560	+	0.283759i	0.765685	−	0.643216i	$-0.222400\pi$
$193$	75.3781	+	54.7654i	0.390560	+	0.283759i	−0.375125	+	0.926974i	$0.622400\pi$
$194$	288.031	+	396.441i	1.48470	+	2.04351i
$195$	−106.982	−	58.8409i	−0.548627	−	0.301748i
$196$	−190.881	+	587.472i	−0.973884	+	2.99731i
$197$	−16.6863	+	22.9667i	−0.0847018	+	0.116582i	−0.849265	−	0.527966i	$-0.822955\pi$
$197$	−16.6863	+	22.9667i	−0.0847018	+	0.116582i	0.764563	+	0.644549i	$0.222955\pi$
$198$	171.461	+	270.411i	0.865967	+	1.36571i
$199$	−22.8563	−	70.3445i	−0.114856	−	0.353490i	0.877061	−	0.480379i	$-0.159501\pi$
$199$	−22.8563	−	70.3445i	−0.114856	−	0.353490i	−0.991917	+	0.126889i	$0.959501\pi$
$200$	30.0647	+	41.3805i	0.150323	+	0.206902i
$201$	78.9525	+	84.1085i	0.392799	+	0.418450i
$202$	−207.337	−	638.117i	−1.02642	−	3.15900i
$203$	−120.937	−	166.456i	−0.595751	−	0.819981i
$204$	405.421	−	380.568i	1.98736	−	1.86553i
$205$	18.3445	−	56.4586i	0.0894854	−	0.275408i
$206$	87.4366	−	120.346i	0.424449	−	0.584204i
$207$	−147.669	+	93.6335i	−0.713377	+	0.452336i
$208$	−207.811	+	150.983i	−0.999090	+	0.725881i
$209$	−152.429	−	209.800i	−0.729324	−	1.00383i
$210$	−607.073	−	115.927i	−2.89082	−	0.552034i
$211$	−269.469			−1.27710			−0.638552	−	0.769578i	$-0.720466\pi$
$211$	−269.469			−1.27710			−0.638552	+	0.769578i	$0.720466\pi$
$212$			133.898i			0.631593i
$213$	−12.5354	+	65.6438i	−0.0588516	+	0.308187i
$214$	−78.7262	−	242.294i	−0.367879	−	1.13222i
$215$	53.1476	+	17.2687i	0.247198	+	0.0803195i
$216$	504.604	+	129.872i	2.33613	+	0.601261i
$217$	254.784	+	214.596i	1.17412	+	0.988921i
$218$		−	533.466i		−	2.44709i
$219$	17.1955	+	136.329i	0.0785184	+	0.622506i
$220$	−147.348	−	453.489i	−0.669762	−	2.06131i
$221$	90.7379	−	124.890i	0.410579	−	0.565113i
$222$	−168.120	−	357.453i	−0.757298	−	1.61015i
$223$	199.030			0.892509			0.446255	−	0.894906i	$-0.352758\pi$
$223$	199.030			0.892509			0.446255	+	0.894906i	$0.352758\pi$
$224$	−276.709	+	380.857i	−1.23531	+	1.70026i
$225$	1.50703	−	23.8066i	0.00669793	−	0.105807i
$226$	217.751	−	158.205i	0.963500	−	0.700023i
$227$	44.9099	+	14.5921i	0.197841	+	0.0642824i	0.406261	−	0.913757i	$-0.366832\pi$
$227$	44.9099	+	14.5921i	0.197841	+	0.0642824i	−0.208420	+	0.978039i	$0.566832\pi$
$228$	−727.772	−	138.976i	−3.19198	−	0.609543i
$229$	−57.0832	+	175.684i	−0.249272	+	0.767179i	0.745633	+	0.666357i	$0.232147\pi$
$229$	−57.0832	+	175.684i	−0.249272	+	0.767179i	−0.994904	+	0.100822i	$0.967853\pi$
$230$	354.241	−	115.100i	1.54018	−	0.500434i
$231$	275.625	+	151.595i	1.19318	+	0.656257i
$232$	−114.184	−	351.422i	−0.492172	−	1.51475i
$233$	−257.266	+	83.5908i	−1.10415	+	0.358759i	−0.803697	−	0.595039i	$-0.797137\pi$
$233$	−257.266	+	83.5908i	−1.10415	+	0.358759i	−0.300449	+	0.953798i	$0.597137\pi$
$234$	253.463	+	16.0450i	1.08318	+	0.0685684i
$235$	78.6827	+	242.161i	0.334820	+	1.03047i
$236$	2.76113	+	0.897145i	0.0116997	+	0.00380146i
$237$	−89.6398	−	17.1177i	−0.378227	−	0.0722265i
$238$	241.473	−	743.179i	1.01459	−	3.12260i
$239$	−23.0892	−	31.7796i	−0.0966077	−	0.132969i	0.757977	−	0.652282i	$-0.226188\pi$
$239$	−23.0892	−	31.7796i	−0.0966077	−	0.132969i	−0.854584	+	0.519313i	$0.826188\pi$
$240$	−458.737	−	252.308i	−1.91140	−	1.05128i
$241$	91.3269	+	66.3529i	0.378950	+	0.275323i	0.760912	−	0.648855i	$-0.224752\pi$
$241$	91.3269	+	66.3529i	0.378950	+	0.275323i	−0.381962	+	0.924178i	$0.624752\pi$
$242$		−	94.0107i		−	0.388474i
$243$	−142.642	−	196.729i	−0.587002	−	0.809585i
$244$	690.303	+	501.535i	2.82911	+	2.05547i
$245$	−332.416	+	108.009i	−1.35680	+	0.440851i
$246$	15.4527	+	122.512i	0.0628160	+	0.498015i
$247$	−205.695			−0.832774
$248$	316.078	+	507.924i	1.27451	+	2.04808i
$249$	−151.941	−	323.053i	−0.610203	−	1.29740i
$250$	132.408	−	407.509i	0.529631	−	1.63004i
$251$	250.326	−	81.3360i	0.997316	−	0.324048i	0.235524	−	0.971869i	$-0.424319\pi$
$251$	250.326	−	81.3360i	0.997316	−	0.324048i	0.761793	+	0.647821i	$0.224319\pi$
$252$	870.589	−	223.170i	3.45472	−	0.885596i
$253$	−189.575			−0.749310
$254$			192.429i			0.757595i
$255$	309.055	+	59.0174i	1.21198	+	0.231441i
$256$	314.078	−	228.191i	1.22687	−	0.891372i
$257$	4.59218	+	6.32060i	0.0178684	+	0.0245938i	0.817858	−	0.575420i	$-0.195162\pi$
$257$	4.59218	+	6.32060i	0.0178684	+	0.0245938i	−0.799989	+	0.600014i	$0.795162\pi$
$258$	−115.327	+	14.5465i	−0.447004	+	0.0563819i
$259$	−313.959	−	228.105i	−1.21220	−	0.880713i
$260$	−359.702	−	116.874i	−1.38347	−	0.449517i
$261$	−63.4994	+	160.200i	−0.243293	+	0.613793i
$262$	−267.184	+	194.121i	−1.01979	+	0.740919i
$263$	−312.777	+	101.627i	−1.18927	+	0.386416i	−0.835801	−	0.549032i	$-0.814997\pi$
$263$	−312.777	+	101.627i	−1.18927	+	0.386416i	−0.353465	+	0.935448i	$0.614997\pi$
$264$	386.636	+	411.885i	1.46453	+	1.56017i
$265$	−61.2951	+	44.5335i	−0.231302	+	0.168051i
$266$	−990.256	+	321.754i	−3.72277	+	1.20960i
$267$	339.477	−	42.8192i	1.27145	−	0.160372i
$268$	289.098	+	210.042i	1.07872	+	0.783738i
$269$	187.172	+	60.8159i	0.695807	+	0.226081i	0.635503	−	0.772099i	$-0.280793\pi$
$269$	187.172	+	60.8159i	0.695807	+	0.226081i	0.0603042	+	0.998180i	$0.480793\pi$
$270$	190.276	+	481.399i	0.704726	+	1.78296i
$271$	172.367	−	125.232i	0.636042	−	0.462111i	−0.222446	−	0.974945i	$-0.571404\pi$
$271$	172.367	−	125.232i	0.636042	−	0.462111i	0.858488	+	0.512834i	$0.171404\pi$
$272$	389.082	−	535.525i	1.43045	−	1.96884i
$273$	225.782	−	106.192i	0.827041	−	0.388980i
$274$	459.800			1.67810
$275$	15.2018	−	20.9235i	0.0552793	−	0.0760854i
$276$	−394.907	+	370.698i	−1.43082	+	1.34311i
$277$	−104.370	+	321.217i	−0.376786	+	1.15963i	0.565480	+	0.824762i	$0.308691\pi$
$277$	−104.370	+	321.217i	−0.376786	+	1.15963i	−0.942266	+	0.334866i	$0.891309\pi$
$278$		−	246.155i		−	0.885449i
$279$	37.5193	−	276.466i	0.134478	−	0.990917i
$280$	−1090.44			−3.89441
$281$	−60.0994	−	19.5275i	−0.213877	−	0.0694928i	0.200119	−	0.979772i	$-0.435867\pi$
$281$	−60.0994	−	19.5275i	−0.213877	−	0.0694928i	−0.413996	+	0.910279i	$0.635867\pi$
$282$	−362.487	−	386.159i	−1.28541	−	1.36936i
$283$	−129.050	−	93.7606i	−0.456009	−	0.331310i	0.335955	−	0.941878i	$-0.390941\pi$
$283$	−129.050	−	93.7606i	−0.456009	−	0.331310i	−0.791963	+	0.610568i	$0.790941\pi$
$284$			207.017i			0.728934i
$285$	−178.432	−	379.379i	−0.626078	−	1.33115i
$286$	222.767	+	161.850i	0.778906	+	0.565908i
$287$	71.3058	+	98.1441i	0.248452	+	0.341965i
$288$	393.500	+	24.9098i	1.36632	+	0.0864922i
$289$	−33.6260	+	103.490i	−0.116353	+	0.358097i
$290$	215.769	−	296.981i	0.744032	−	1.02407i
$291$	−50.4581	−	400.040i	−0.173396	−	1.37471i
$292$	131.532	+	404.815i	0.450453	+	1.38635i
$293$	151.121	+	208.001i	0.515773	+	0.709900i	0.984879	−	0.173241i	$-0.0554240\pi$
$293$	151.121	+	208.001i	0.515773	+	0.709900i	−0.469107	+	0.883141i	$0.655424\pi$
$294$	530.084	−	497.589i	1.80301	−	1.69248i
$295$	0.507642	+	1.56236i	0.00172082	+	0.00529614i
$296$	−409.651	−	563.837i	−1.38396	−	1.90485i
$297$	−16.3902	−	262.951i	−0.0551860	−	0.885357i
$298$	−70.0026	+	215.446i	−0.234908	+	0.722972i
$299$	−88.3847	+	121.651i	−0.295601	+	0.406860i
$300$	−9.24702	−	73.3118i	−0.0308234	−	0.244373i
$301$	−92.3884	+	67.1241i	−0.306938	+	0.223004i
$302$	157.064	+	216.180i	0.520079	+	0.715828i
$303$	−103.555	+	542.283i	−0.341765	+	1.78971i
$304$	−882.016			−2.90137
$305$			482.811i			1.58299i
$306$	−633.980	+	162.517i	−2.07183	+	0.531101i
$307$	−132.855	−	408.885i	−0.432752	−	1.33187i	−0.895373	−	0.445318i	$-0.853091\pi$
$307$	−132.855	−	408.885i	−0.432752	−	1.33187i	0.462620	−	0.886556i	$-0.346909\pi$
$308$	926.723	+	301.111i	3.00884	+	0.977632i
$309$	−110.762	+	52.0943i	−0.358452	+	0.168590i
$310$	−223.660	+	550.636i	−0.721484	+	1.77624i
$311$		−	555.849i		−	1.78730i	−0.448768	−	0.893649i	$-0.648137\pi$
$311$		−	555.849i		−	1.78730i	0.448768	−	0.893649i	$-0.351863\pi$
$312$	444.567	−	56.0745i	1.42489	−	0.179726i
$313$	−28.6387	−	88.1409i	−0.0914975	−	0.281600i	0.894828	−	0.446412i	$-0.147298\pi$
$313$	−28.6387	−	88.1409i	−0.0914975	−	0.281600i	−0.986325	+	0.164812i	$0.947298\pi$
$314$	−547.947	+	754.184i	−1.74505	+	2.40186i
$315$	391.714	+	324.309i	1.24354	+	1.02955i
$316$	−282.692			−0.894595
$317$	127.509	−	175.501i	0.402236	−	0.553631i	−0.559067	−	0.829122i	$-0.688841\pi$
$317$	127.509	−	175.501i	0.402236	−	0.553631i	0.961303	+	0.275492i	$0.0888406\pi$
$318$	75.9500	−	138.089i	0.238836	−	0.434243i
$319$	−151.154	+	109.820i	−0.473836	+	0.344262i
$320$	−134.909	−	43.8345i	−0.421590	−	0.136983i
$321$	−39.3199	+	205.906i	−0.122492	+	0.641451i
$322$	−235.211	+	723.905i	−0.730469	+	2.24815i
$323$	504.130	−	163.802i	1.56077	−	0.507126i
$324$	−548.320	−	515.706i	−1.69235	−	1.59169i
$325$	−6.33921	−	19.5101i	−0.0195053	−	0.0600310i
$326$	551.538	−	179.205i	1.69183	−	0.549710i
$327$	−211.541	+	384.615i	−0.646914	+	1.17619i
$328$	67.3239	+	207.202i	0.205256	+	0.631712i
$329$	−494.864	−	160.791i	−1.50415	−	0.488727i
$330$	−105.270	+	551.264i	−0.318999	+	1.67050i
$331$	−86.2306	+	265.390i	−0.260515	+	0.801784i	0.732177	+	0.681114i	$0.238504\pi$
$331$	−86.2306	+	265.390i	−0.260515	+	0.801784i	−0.992693	+	0.120670i	$0.961496\pi$
$332$	−650.013	−	894.666i	−1.95787	−	2.69478i
$333$	−20.5343	+	324.381i	−0.0616647	+	0.974117i
$334$	516.349	+	375.149i	1.54595	+	1.12320i
$335$			202.200i			0.603583i
$336$	968.148	−	455.347i	2.88139	−	1.35520i
$337$	−192.442	−	139.818i	−0.571046	−	0.414889i	0.264439	−	0.964402i	$-0.414813\pi$
$337$	−192.442	−	139.818i	−0.571046	−	0.414889i	−0.835485	+	0.549513i	$0.814813\pi$
$338$	−378.291	+	122.914i	−1.11920	+	0.363651i
$339$	−219.727	+	27.7148i	−0.648164	+	0.0817547i
$340$	974.650			2.86662
$341$	194.868	−	231.362i	0.571460	−	0.678480i
$342$	671.723	+	556.136i	1.96410	+	1.62613i
$343$	58.0102	−	178.537i	0.169126	−	0.520517i
$344$	−195.050	+	63.3757i	−0.567006	+	0.184232i
$345$	−301.040	−	57.4868i	−0.872580	−	0.166628i
$346$	−503.012			−1.45379
$347$			652.114i			1.87929i	0.342150	+	0.939645i	$0.388845\pi$
$347$			652.114i			1.87929i	−0.342150	+	0.939645i	$0.611155\pi$
$348$	−100.127	+	524.334i	−0.287722	+	1.50671i
$349$	19.4049	−	14.0985i	0.0556014	−	0.0403968i	−0.559637	−	0.828738i	$-0.689060\pi$
$349$	19.4049	−	14.0985i	0.0556014	−	0.0403968i	0.615239	+	0.788341i	$0.289060\pi$
$350$	−61.0363	−	84.0093i	−0.174389	−	0.240026i
$351$	−176.378	−	112.076i	−0.502501	−	0.319306i
$352$	345.844	+	251.271i	0.982513	+	0.713837i
$353$	325.272	+	105.687i	0.921451	+	0.299398i	0.731062	−	0.682311i	$-0.239025\pi$
$353$	325.272	+	105.687i	0.921451	+	0.299398i	0.190389	+	0.981709i	$0.439025\pi$
$354$	−2.33868	−	2.49141i	−0.00660644	−	0.00703787i
$355$	−94.7674	+	68.8526i	−0.266950	+	0.193951i
$356$	1008.04	−	327.533i	2.83158	−	0.920037i
$357$	−468.796	+	440.058i	−1.31316	+	1.23266i
$358$	−273.164	+	198.465i	−0.763028	+	0.554372i
$359$	527.574	−	171.419i	1.46957	−	0.477491i	0.538590	−	0.842568i	$-0.318957\pi$
$359$	527.574	−	171.419i	1.46957	−	0.477491i	0.930977	+	0.365077i	$0.118957\pi$
$360$	489.066	+	771.305i	1.35852	+	2.14251i
$361$	−279.355	−	202.963i	−0.773836	−	0.562225i
$362$	733.953	+	238.476i	2.02749	+	0.658773i
$363$	−37.2790	+	67.7792i	−0.102697	+	0.186720i
$364$	625.284	−	454.295i	1.71781	−	1.24806i
$365$	−141.568	+	194.851i	−0.387856	+	0.533838i
$366$	−427.430	−	908.791i	−1.16784	−	2.48303i
$367$	452.194			1.23214			0.616069	−	0.787693i	$-0.288724\pi$
$367$	452.194			1.23214			0.616069	+	0.787693i	$0.288724\pi$
$368$	−378.991	+	521.637i	−1.02987	+	1.41749i
$369$	37.4398	−	94.4554i	0.101463	−	0.255977i
$370$	213.957	−	658.492i	0.578262	−	1.77971i
$371$		−	154.829i		−	0.417328i
$372$	−46.4764	−	862.999i	−0.124937	−	2.31989i
$373$	−57.4975			−0.154149			−0.0770744	−	0.997025i	$-0.524558\pi$
$373$	−57.4975			−0.154149			−0.0770744	+	0.997025i	$0.524558\pi$
$374$	−674.857	−	219.274i	−1.80443	−	0.586295i
$375$	−257.056	+	241.299i	−0.685484	+	0.643463i
$376$	−755.993	−	549.261i	−2.01062	−	1.46080i
$377$			148.196i			0.393093i
$378$	−1024.43	−	263.662i	−2.71013	−	0.697520i
$379$	−214.102	−	155.555i	−0.564914	−	0.410434i	0.268340	−	0.963324i	$-0.413525\pi$
$379$	−214.102	−	155.555i	−0.564914	−	0.410434i	−0.833254	+	0.552890i	$0.813525\pi$
$380$	−763.346	−	1050.66i	−2.00881	−	2.76488i
$381$	76.3059	−	138.736i	0.200278	−	0.364137i
$382$	242.678	−	746.887i	0.635284	−	1.95520i
$383$	334.725	−	460.710i	0.873956	−	1.20290i	−0.104102	−	0.994567i	$-0.533197\pi$
$383$	334.725	−	460.710i	0.873956	−	1.20290i	0.978058	−	0.208331i	$-0.0668032\pi$
$384$	−228.840	+	28.8642i	−0.595937	+	0.0751672i
$385$	170.381	+	524.378i	0.442548	+	1.36202i
$386$	−199.672	−	274.826i	−0.517286	−	0.711983i
$387$	88.9160	+	35.2442i	0.229757	+	0.0910702i
$388$	−385.965	−	1187.88i	−0.994756	−	3.06154i
$389$	−287.037	−	395.073i	−0.737884	−	1.01561i	−0.998738	−	0.0502322i	$-0.984004\pi$
$389$	−287.037	−	395.073i	−0.737884	−	1.01561i	0.260853	−	0.965378i	$-0.415996\pi$
$390$	304.668	+	324.564i	0.781200	+	0.832216i
$391$	119.744	−	368.533i	0.306250	−	0.942540i
$392$	753.976	−	1037.76i	1.92341	−	2.64734i
$393$	269.610	−	34.0066i	0.686030	−	0.0865309i
$394$	83.7355	−	60.8374i	0.212527	−	0.154410i
$395$	−94.0215	−	129.409i	−0.238029	−	0.327619i
$396$	−202.654	−	790.555i	−0.511752	−	1.99635i
$397$	65.7682			0.165663			0.0828315	−	0.996564i	$-0.473604\pi$
$397$	65.7682			0.165663			0.0828315	+	0.996564i	$0.473604\pi$
$398$			269.672i			0.677568i
$399$	841.537	+	160.700i	2.10911	+	0.402758i
$400$	−27.1824	−	83.6587i	−0.0679559	−	0.209147i
$401$	426.313	+	138.517i	1.06312	+	0.345430i	0.787806	−	0.615923i	$-0.211217\pi$
$401$	426.313	+	138.517i	1.06312	+	0.345430i	0.275318	+	0.961353i	$0.411217\pi$
$402$	−179.007	−	380.600i	−0.445291	−	0.946766i
$403$	−57.6133	−	232.914i	−0.142961	−	0.577949i
$404$			1710.17i			4.23309i
$405$	53.7100	−	422.528i	0.132617	−	1.04328i
$406$	231.812	+	713.445i	0.570966	+	1.75725i
$407$	−207.135	+	285.096i	−0.508930	+	0.700482i
$408$	−1044.92	+	491.454i	−2.56107	+	1.20454i
$409$	537.376			1.31388			0.656939	−	0.753944i	$-0.271851\pi$
$409$	537.376			1.31388			0.656939	+	0.753944i	$0.271851\pi$
$410$	−127.220	+	175.103i	−0.310292	+	0.427080i
$411$	−331.504	−	182.329i	−0.806579	−	0.443624i
$412$	−306.744	+	222.863i	−0.744525	+	0.540929i
$413$	−3.19275	−	1.03739i	−0.00773062	−	0.00251183i
$414$	617.538	−	158.302i	1.49164	−	0.382372i
$415$	193.366	−	595.120i	0.465943	−	1.43402i
$416$	322.482	−	104.781i	0.775197	−	0.251877i
$417$	−97.6103	+	177.471i	−0.234077	+	0.425590i
$418$	292.174	+	899.220i	0.698982	+	2.15124i
$419$	−358.145	+	116.368i	−0.854760	+	0.277728i	−0.703439	−	0.710756i	$-0.748353\pi$
$419$	−358.145	+	116.368i	−0.854760	+	0.277728i	−0.151322	+	0.988485i	$0.548353\pi$
$420$	1380.30	+	759.174i	3.28643	+	1.80756i
$421$	4.86659	+	14.9778i	0.0115596	+	0.0355768i	0.956670	−	0.291175i	$-0.0940460\pi$
$421$	4.86659	+	14.9778i	0.0115596	+	0.0355768i	−0.945110	+	0.326751i	$0.894046\pi$
$422$	934.387	+	303.601i	2.21419	+	0.719433i
$423$	108.216	+	422.151i	0.255830	+	0.997994i
$424$	85.9238	−	264.446i	0.202651	−	0.623694i
$425$	31.0730	+	42.7683i	0.0731130	+	0.100631i
$426$	117.425	−	213.498i	0.275646	−	0.501168i
$427$	−798.211	−	579.934i	−1.86935	−	1.35816i
$428$			649.354i			1.51718i
$429$	−96.4293	−	205.026i	−0.224777	−	0.477915i
$430$	−164.834	−	119.759i	−0.383334	−	0.278509i
$431$	399.122	−	129.683i	0.926036	−	0.300887i	0.193096	−	0.981180i	$-0.438147\pi$
$431$	399.122	−	129.683i	0.926036	−	0.300887i	0.732941	+	0.680292i	$0.238147\pi$
$432$	−756.303	−	480.581i	−1.75070	−	1.11246i
$433$	312.047			0.720663			0.360332	−	0.932824i	$-0.382664\pi$
$433$	312.047			0.720663			0.360332	+	0.932824i	$0.382664\pi$
$434$	−641.691	−	1031.17i	−1.47855	−	2.37597i
$435$	−273.329	+	128.554i	−0.628343	+	0.295527i
$436$	−420.179	+	1293.18i	−0.963712	+	2.96600i
$437$	−491.056	+	159.554i	−1.12370	+	0.365111i
$438$	93.9708	−	492.095i	0.214545	−	1.12350i
$439$	649.045			1.47846			0.739232	−	0.673451i	$-0.235189\pi$
$439$	649.045			1.47846			0.739232	+	0.673451i	$0.235189\pi$
$440$			990.190i			2.25043i
$441$	−579.491	+	148.549i	−1.31404	+	0.336846i
$442$	−455.344	+	330.827i	−1.03019	+	0.748476i
$443$	261.238	+	359.563i	0.589701	+	0.811654i	0.994717	−	0.102656i	$-0.0327340\pi$
$443$	261.238	+	359.563i	0.589701	+	0.811654i	−0.405016	+	0.914310i	$0.632734\pi$
$444$	125.997	+	998.921i	0.283777	+	2.24982i
$445$	485.205	+	352.522i	1.09035	+	0.792185i
$446$	−690.137	−	224.239i	−1.54739	−	0.502779i
$447$	135.903	−	127.572i	0.304033	−	0.285396i
$448$	234.517	−	170.386i	0.523475	−	0.380327i
$449$	416.366	−	135.285i	0.927318	−	0.301304i	0.193853	−	0.981031i	$-0.437902\pi$
$449$	416.366	−	135.285i	0.927318	−	0.301304i	0.733465	+	0.679727i	$0.237902\pi$
$450$	−32.0477	+	80.8518i	−0.0712171	+	0.179671i
$451$	89.1215	−	64.7506i	0.197609	−	0.143571i
$452$	−652.459	+	211.997i	−1.44349	+	0.469020i
$453$	−27.5149	−	218.142i	−0.0607393	−	0.481550i
$454$	−139.285	−	101.197i	−0.306796	−	0.222900i
$455$	415.931	+	135.144i	0.914133	+	0.297020i
$456$	1348.16	+	741.496i	2.95649	+	1.62609i
$457$	−451.849	+	328.287i	−0.988728	+	0.718353i	−0.959642	−	0.281224i	$-0.909260\pi$
$457$	−451.849	+	328.287i	−0.988728	+	0.718353i	−0.0290861	+	0.999577i	$0.509260\pi$
$458$	395.873	−	544.873i	0.864352	−	1.18968i
$459$	521.527	+	134.228i	1.13622	+	0.292436i
$460$	−949.373			−2.06385
$461$	145.342	−	200.045i	0.315274	−	0.433938i	−0.621743	−	0.783222i	$-0.713575\pi$
$461$	145.342	−	200.045i	0.315274	−	0.433938i	0.937017	+	0.349284i	$0.113575\pi$
$462$	−784.935	−	836.195i	−1.69899	−	1.80995i
$463$	−256.897	+	790.649i	−0.554854	+	1.70767i	0.141474	+	0.989942i	$0.454816\pi$
$463$	−256.897	+	790.649i	−0.554854	+	1.70767i	−0.696328	+	0.717723i	$0.745184\pi$
$464$			635.461i			1.36953i
$465$	379.602	−	308.304i	0.816349	−	0.663019i
$466$	986.251			2.11642
$467$	−781.449	−	253.908i	−1.67334	−	0.543700i	−0.689737	−	0.724060i	$-0.742274\pi$
$467$	−781.449	−	253.908i	−1.67334	−	0.543700i	−0.983601	+	0.180360i	$0.942274\pi$
$468$	−601.783	−	238.532i	−1.28586	−	0.509684i
$469$	−334.289	−	242.876i	−0.712771	−	0.517858i
$470$		−	928.343i		−	1.97520i
$471$	694.120	−	326.464i	1.47371	−	0.693129i
$472$	−4.87748	−	3.54370i	−0.0103337	−	0.00750784i
$473$	60.9533	+	83.8950i	0.128865	+	0.177368i
$474$	291.541	+	160.350i	0.615066	+	0.338290i
$475$	21.7671	−	66.9923i	0.0458255	−	0.141036i
$476$	−1170.71	+	1611.35i	−2.45948	+	3.38518i
$477$	−109.516	+	69.4415i	−0.229593	+	0.145580i
$478$	44.2573	+	136.210i	0.0925885	+	0.284958i
$479$	125.314	+	172.480i	0.261616	+	0.360084i	0.919537	−	0.393003i	$-0.128564\pi$
$479$	125.314	+	172.480i	0.261616	+	0.360084i	−0.657921	+	0.753087i	$0.728564\pi$
$480$	472.995	+	503.884i	0.985406	+	1.04976i
$481$	86.3759	+	265.838i	0.179576	+	0.552677i
$482$	−241.920	−	332.974i	−0.501909	−	0.690818i
$483$	456.638	−	428.646i	0.945421	−	0.887465i
$484$	−74.0465	+	227.892i	−0.152989	+	0.470850i
$485$	415.412	−	571.766i	0.856520	−	1.17890i
$486$	272.964	+	842.870i	0.561654	+	1.73430i
$487$	382.398	−	277.829i	0.785212	−	0.570490i	−0.121327	−	0.992613i	$-0.538715\pi$
$487$	382.398	−	277.829i	0.785212	−	0.570490i	0.906539	+	0.422123i	$0.138715\pi$
$488$	−1041.50	−	1433.50i	−2.13422	−	2.93750i
$489$	−468.706	−	89.5045i	−0.958500	−	0.183036i
$490$	1274.35			2.60071
$491$			359.976i			0.733149i	0.930389	+	0.366574i	$0.119469\pi$
$491$			359.976i			0.733149i	−0.930389	+	0.366574i	$0.880531\pi$
$492$	59.0359	−	309.152i	0.119992	−	0.628358i
$493$	−118.013	−	363.208i	−0.239378	−	0.736730i
$494$	713.250	+	231.749i	1.44383	+	0.469128i
$495$	294.495	−	355.703i	0.594940	−	0.718592i
$496$	−247.044	−	998.727i	−0.498073	−	2.01356i
$497$		−	239.378i		−	0.481646i
$498$	162.885	+	1291.37i	0.327078	+	2.59312i
$499$	15.3502	+	47.2430i	0.0307619	+	0.0946753i	0.965259	−	0.261296i	$-0.0841500\pi$
$499$	15.3502	+	47.2430i	0.0307619	+	0.0946753i	−0.934497	+	0.355972i	$0.884150\pi$
$500$	−641.940	+	883.555i	−1.28388	+	1.76711i
$501$	−223.512	−	475.226i	−0.446132	−	0.948555i
$502$	−959.648			−1.91165
$503$	186.158	−	256.224i	0.370095	−	0.509392i	−0.582832	−	0.812593i	$-0.698055\pi$
$503$	186.158	−	256.224i	0.370095	−	0.509392i	0.952927	+	0.303201i	$0.0980554\pi$
$504$	−1862.61	−	117.909i	−3.69566	−	0.233947i
$505$	−782.873	+	568.791i	−1.55024	+	1.12632i
$506$	657.355	+	213.588i	1.29912	+	0.422110i
$507$	321.478	+	61.3897i	0.634079	+	0.121084i
$508$	151.565	−	466.468i	0.298356	−	0.918244i
$509$	−188.617	+	61.2853i	−0.370564	+	0.120403i	−0.488378	−	0.872632i	$-0.662411\pi$
$509$	−188.617	+	61.2853i	−0.370564	+	0.120403i	0.117814	+	0.993036i	$0.462411\pi$
$510$	−1005.16	−	552.845i	−1.97090	−	1.08401i
$511$	−152.093	−	468.095i	−0.297639	−	0.916038i
$512$	−1053.68	+	342.361i	−2.05797	+	0.668675i
$513$	−263.765	−	667.325i	−0.514161	−	1.30083i
$514$	−8.80227	−	27.0906i	−0.0171250	−	0.0527054i
$515$	−204.042	−	66.2974i	−0.396199	−	0.128733i
$516$	291.022	+	55.5738i	0.563996	+	0.107701i
$517$	−146.009	+	449.371i	−0.282417	+	0.869189i
$518$	831.660	+	1144.68i	1.60552	+	2.20981i
$519$	362.659	+	199.465i	0.698765	+	0.384325i
$520$	635.408	+	461.651i	1.22194	+	0.887790i
$521$		−	920.376i		−	1.76656i	−0.468848	−	0.883279i	$-0.655331\pi$
$521$		−	920.376i		−	1.76656i	0.468848	−	0.883279i	$-0.344669\pi$
$522$	400.676	−	483.953i	0.767579	−	0.927113i
$523$	210.096	+	152.644i	0.401714	+	0.291862i	0.770239	−	0.637756i	$-0.220137\pi$
$523$	210.096	+	152.644i	0.401714	+	0.291862i	−0.368525	+	0.929618i	$0.620137\pi$
$524$	800.580	−	260.124i	1.52782	−	0.496420i
$525$	10.6925	+	84.7718i	0.0203667	+	0.161470i
$526$	1199.06			2.27958
$527$	326.679	+	524.959i	0.619884	+	0.996127i
$528$	−413.486	−	879.145i	−0.783118	−	1.66505i
$529$	46.8318	−	144.133i	0.0885289	−	0.272464i
$530$	262.716	−	85.3615i	0.495690	−	0.161059i
$531$	0.698183	+	2.72362i	0.00131485	+	0.00512922i
$532$	2653.91			4.98855
$533$		−	87.3778i		−	0.163936i
$534$	−1225.38	−	234.000i	−2.29473	−	0.438202i
$535$	−297.258	+	215.971i	−0.555623	+	0.403684i
$536$	−436.178	−	600.348i	−0.813765	−	1.12005i
$537$	275.644	−	34.7677i	0.513303	−	0.0647443i
$538$	−580.502	−	421.760i	−1.07900	−	0.783940i
$539$	−616.856	−	200.429i	−1.14444	−	0.371853i
$540$	−82.0806	−	1316.83i	−0.152001	−	2.43857i
$541$	393.302	−	285.751i	0.726991	−	0.528190i	−0.161619	−	0.986853i	$-0.551672\pi$
$541$	393.302	−	285.751i	0.726991	−	0.528190i	0.888610	+	0.458663i	$0.151672\pi$
$542$	−738.780	+	240.044i	−1.36306	+	0.442886i
$543$	−434.596	−	462.977i	−0.800360	−	0.852628i
$544$	−706.918	+	513.606i	−1.29948	+	0.944128i
$545$	−731.733	+	237.755i	−1.34263	+	0.436247i
$546$	−902.544	+	113.840i	−1.65301	+	0.208499i
$547$	579.589	+	421.096i	1.05958	+	0.769828i	0.974010	−	0.226504i	$-0.0727297\pi$
$547$	579.589	+	421.096i	1.05958	+	0.769828i	0.0855675	+	0.996332i	$0.472730\pi$
$548$	−1114.60	−	362.156i	−2.03395	−	0.660869i
$549$	−52.2066	+	824.707i	−0.0950939	+	1.50220i
$550$	−76.2862	+	55.4252i	−0.138702	+	0.100773i
$551$	−299.104	+	411.681i	−0.542838	+	0.747152i
$552$	1017.82	−	478.708i	1.84387	−	0.867225i
$553$	326.882			0.591107
$554$	723.807	−	996.235i	1.30651	−	1.79826i
$555$	−415.376	+	389.913i	−0.748425	+	0.702546i
$556$	−193.881	+	596.704i	−0.348707	+	1.07321i
$557$		−	281.363i		−	0.505139i	−0.967579	−	0.252570i	$-0.918724\pi$
$557$		−	281.363i		−	0.505139i	0.967579	−	0.252570i	$-0.0812757\pi$
$558$	−441.582	+	916.377i	−0.791366	+	1.64225i
$559$	82.2535			0.147144
$560$	1783.50	+	579.494i	3.18482	+	1.03481i
$561$	399.603	+	425.699i	0.712305	+	0.758822i
$562$	186.395	+	135.424i	0.331663	+	0.240967i
$563$			528.345i			0.938446i	0.883080	+	0.469223i	$0.155466\pi$
$563$			528.345i			0.938446i	−0.883080	+	0.469223i	$0.844534\pi$
$564$	574.552	+	1221.60i	1.01871	+	2.16595i
$565$	−314.051	−	228.171i	−0.555842	−	0.403843i
$566$	341.847	+	470.512i	0.603970	+	0.831294i
$567$	634.034	+	596.321i	1.11822	+	1.05171i
$568$	132.846	−	408.856i	0.233883	−	0.719818i
$569$	403.247	−	555.021i	0.708694	−	0.975433i	−0.291131	−	0.956683i	$-0.594031\pi$
$569$	403.247	−	555.021i	0.708694	−	0.975433i	0.999824	−	0.0187498i	$-0.00596860\pi$
$570$	191.285	+	1516.53i	0.335587	+	2.66058i
$571$	−237.411	−	730.677i	−0.415782	−	1.27964i	−0.911550	−	0.411189i	$-0.865113\pi$
$571$	−237.411	−	730.677i	−0.415782	−	1.27964i	0.495768	−	0.868455i	$-0.334887\pi$
$572$	−412.531	−	567.801i	−0.721209	−	0.992659i
$573$	−471.136	+	442.254i	−0.822226	+	0.771823i
$574$	−136.679	−	420.653i	−0.238116	−	0.732846i
$575$	−30.2672	−	41.6592i	−0.0526385	−	0.0724507i
$576$	−225.703	−	89.4631i	−0.391845	−	0.155318i
$577$	−69.0509	+	212.517i	−0.119672	+	0.368314i	−0.992893	−	0.119012i	$-0.962027\pi$
$577$	−69.0509	+	212.517i	−0.119672	+	0.368314i	0.873221	+	0.487325i	$0.162027\pi$
$578$	233.197	−	320.968i	0.403455	−	0.555308i
$579$	34.9792	+	277.320i	0.0604131	+	0.478964i
$580$	−756.961	+	549.964i	−1.30510	+	0.948214i
$581$	751.622	+	1034.52i	1.29367	+	1.78058i
$582$	−275.746	+	1443.99i	−0.473790	+	2.48109i
$583$	−140.595			−0.241158
$584$		−	883.910i		−	1.51354i
$585$	−90.9548	−	354.816i	−0.155478	−	0.606523i
$586$	−289.669	−	891.508i	−0.494315	−	1.52134i
$587$	690.965	+	224.508i	1.17711	+	0.382467i	0.831293	−	0.555834i	$-0.187601\pi$
$587$	690.965	+	224.508i	1.17711	+	0.382467i	0.345820	+	0.938301i	$0.387601\pi$
$588$	−1676.90	+	788.693i	−2.85187	+	1.34131i
$589$	310.042	−	763.302i	0.526387	−	1.29593i
$590$		−	5.98945i		−	0.0101516i
$591$	−84.4956	+	10.6577i	−0.142971	+	0.0180333i
$592$	370.378	+	1139.90i	0.625638	+	1.92551i
$593$	407.240	−	560.518i	0.686746	−	0.945225i	−0.313244	−	0.949673i	$-0.601416\pi$
$593$	407.240	−	560.518i	0.686746	−	0.945225i	0.999990	+	0.00444798i	$0.00141584\pi$
$594$	−239.424	+	930.252i	−0.403070	+	1.56608i
$595$	−1127.01			−1.89413
$596$	339.387	−	467.126i	0.569441	−	0.783768i
$597$	106.936	−	194.426i	0.179122	−	0.325672i
$598$	443.535	−	322.247i	0.741697	−	0.538874i
$599$	−499.264	−	162.221i	−0.833496	−	0.270819i	−0.138979	−	0.990295i	$-0.544382\pi$
$599$	−499.264	−	162.221i	−0.833496	−	0.270819i	−0.694517	+	0.719476i	$0.744382\pi$
$600$	−28.7823	+	150.724i	−0.0479705	+	0.251206i
$601$	−60.7571	+	186.991i	−0.101093	+	0.311133i	−0.988794	−	0.149288i	$-0.952302\pi$
$601$	−60.7571	+	186.991i	−0.101093	+	0.311133i	0.887700	+	0.460422i	$0.152302\pi$
$602$	395.984	−	128.663i	0.657781	−	0.213726i
$603$	−21.8640	+	345.386i	−0.0362588	+	0.572780i
$604$	−210.467	−	647.752i	−0.348456	−	1.07244i
$605$	−128.951	+	41.8986i	−0.213141	+	0.0692538i
$606$	970.048	−	1763.70i	1.60074	−	2.91040i
$607$	−151.946	−	467.640i	−0.250322	−	0.770412i	−0.994715	−	0.102671i	$-0.967261\pi$
$607$	−151.946	−	467.640i	−0.250322	−	0.770412i	0.744393	−	0.667741i	$-0.232739\pi$
$608$	1107.32	+	359.789i	1.82124	+	0.591758i
$609$	115.779	−	606.298i	0.190113	−	0.995563i
$610$	543.965	−	1674.15i	0.891746	−	2.74451i
$611$	220.289	+	303.202i	0.360539	+	0.496239i
$612$	1664.84	+	105.389i	2.72032	+	0.172205i
$613$	292.838	+	212.759i	0.477712	+	0.347078i	0.800439	−	0.599414i	$-0.204600\pi$
$613$	292.838	+	212.759i	0.477712	+	0.347078i	−0.322727	+	0.946492i	$0.604600\pi$
$614$			1567.50i			2.55293i
$615$	161.157	−	75.7968i	0.262044	−	0.123247i
$616$	−1637.04	−	1189.38i	−2.65753	−	1.93081i
$617$	−970.646	+	315.382i	−1.57317	+	0.511154i	−0.960286	−	0.279018i	$-0.909991\pi$
$617$	−970.646	+	315.382i	−1.57317	+	0.511154i	−0.612885	+	0.790172i	$0.709991\pi$
$618$	442.760	−	55.8465i	0.716440	−	0.0903666i
$619$	34.9517			0.0564649			0.0282324	−	0.999601i	$-0.491012\pi$
$619$	34.9517			0.0564649			0.0282324	+	0.999601i	$0.491012\pi$
$620$	975.877	−	1158.63i	1.57399	−	1.86876i
$621$	−508.002	−	130.747i	−0.818038	−	0.210543i
$622$	−626.255	+	1927.41i	−1.00684	+	3.09874i
$623$	−1165.62	+	378.733i	−1.87098	+	0.607918i
$624$	−756.927	−	144.543i	−1.21302	−	0.231640i
$625$	−684.237			−1.09478
$626$			337.896i			0.539770i
$627$	145.927	−	764.173i	0.232739	−	1.21878i
$628$	1922.30	−	1396.64i	3.06099	−	2.22394i
$629$	−423.390	−	582.747i	−0.673116	−	0.926465i
$630$	−992.886	−	1565.88i	−1.57601	−	2.48552i
$631$	718.788	+	522.230i	1.13913	+	0.827623i	0.986997	−	0.160738i	$-0.0513873\pi$
$631$	718.788	+	522.230i	1.13913	+	0.827623i	0.152128	+	0.988361i	$0.451387\pi$
$632$	558.313	+	181.407i	0.883407	+	0.287036i
$633$	−553.279	−	589.411i	−0.874058	−	0.931138i
$634$	−639.869	+	464.892i	−1.00926	+	0.733268i
$635$	263.947	−	85.7616i	0.415664	−	0.135058i
$636$	−292.875	+	274.921i	−0.460495	+	0.432266i
$637$	−416.209	+	302.393i	−0.653389	+	0.474715i
$638$	647.857	−	210.501i	1.01545	−	0.329940i
$639$	−169.321	+	107.362i	−0.264978	+	0.168016i
$640$	−327.075	−	237.634i	−0.511054	−	0.371303i
$641$	−895.735	−	291.042i	−1.39740	−	0.454043i	−0.489052	−	0.872255i	$-0.662657\pi$
$641$	−895.735	−	291.042i	−1.39740	−	0.454043i	−0.908350	+	0.418211i	$0.862657\pi$
$642$	368.329	−	669.681i	0.573721	−	1.04312i
$643$	44.0098	−	31.9750i	0.0684445	−	0.0497278i	−0.553037	−	0.833157i	$-0.686531\pi$
$643$	44.0098	−	31.9750i	0.0684445	−	0.0497278i	0.621481	+	0.783429i	$0.286531\pi$
$644$	1140.35	−	1569.56i	1.77073	−	2.43720i
$645$	71.3517	+	151.706i	0.110623	+	0.235203i
$646$	−1932.63			−2.99168
$647$	−637.012	+	876.772i	−0.984563	+	1.35513i	−0.0502276	+	0.998738i	$0.515995\pi$
$647$	−637.012	+	876.772i	−0.984563	+	1.35513i	−0.934335	+	0.356396i	$0.884005\pi$
$648$	751.991	+	1370.38i	1.16048	+	2.11478i
$649$	−0.942018	+	2.89923i	−0.00145149	+	0.00446723i
$650$			74.7936i			0.115067i
$651$	53.7416	+	997.903i	0.0825524	+	1.53288i
$652$	−1478.13			−2.26708
$653$	651.675	+	211.742i	0.997971	+	0.324261i	0.762055	−	0.647513i	$-0.224191\pi$
$653$	651.675	+	211.742i	0.997971	+	0.324261i	0.235917	+	0.971773i	$0.424191\pi$
$654$	1166.85	−	1095.32i	1.78418	−	1.67480i
$655$	385.346	+	279.970i	0.588315	+	0.427436i
$656$		−	374.674i		−	0.571149i
$657$	−262.886	+	317.524i	−0.400131	+	0.483294i
$658$	1534.79	+	1115.09i	2.33251	+	1.69467i
$659$	−373.416	−	513.962i	−0.566640	−	0.779913i	0.425512	−	0.904953i	$-0.360094\pi$
$659$	−373.416	−	513.962i	−0.566640	−	0.779913i	−0.992152	+	0.125040i	$0.960094\pi$
$660$	689.382	−	1253.41i	1.04452	−	1.89910i
$661$	−211.765	+	651.745i	−0.320370	+	0.985998i	0.653117	+	0.757257i	$0.273461\pi$
$661$	−211.765	+	651.745i	−0.320370	+	0.985998i	−0.973487	+	0.228741i	$0.926539\pi$
$662$	598.011	−	823.092i	0.903340	−	1.24334i
$663$	459.477	−	57.9551i	0.693027	−	0.0874135i
$664$	709.649	+	2184.08i	1.06875	+	3.28927i
$665$	882.672	+	1214.89i	1.32733	+	1.82691i
$666$	436.671	−	1101.66i	0.655662	−	1.65414i
$667$	114.953	+	353.788i	0.172343	+	0.530417i
$668$	−956.201	−	1316.10i	−1.43144	−	1.97021i
$669$	408.651	+	435.338i	0.610839	+	0.650729i
$670$	227.812	−	701.133i	0.340018	−	1.04647i
$671$	−526.620	+	724.830i	−0.784829	+	1.08022i
$672$	−1401.19	+	176.737i	−2.08511	+	0.263001i
$673$	827.295	−	601.065i	1.22926	−	0.893113i	0.232430	−	0.972613i	$-0.425332\pi$
$673$	827.295	−	601.065i	1.22926	−	0.893113i	0.996835	+	0.0795001i	$0.0253324\pi$
$674$	509.769	+	701.637i	0.756334	+	1.04100i
$675$	55.1666	−	45.5838i	0.0817282	−	0.0675316i
$676$	1013.83			1.49974
$677$			1003.50i			1.48227i	0.671356	+	0.741135i	$0.265712\pi$
$677$			1003.50i			1.48227i	−0.671356	+	0.741135i	$0.734288\pi$
$678$	793.133	+	151.457i	1.16981	+	0.223388i
$679$	446.299	+	1373.57i	0.657289	+	2.02293i
$680$	−1924.92	−	625.445i	−2.83077	−	0.919772i
$681$	60.2924	+	128.192i	0.0885351	+	0.188241i
$682$	−936.373	+	582.699i	−1.37298	+	0.854398i
$683$		−	791.515i		−	1.15888i	−0.815015	−	0.579440i	$-0.803271\pi$
$683$		−	791.515i		−	1.15888i	0.815015	−	0.579440i	$-0.196729\pi$
$684$	−1190.29	−	1877.21i	−1.74019	−	2.74445i
$685$	−204.923	−	630.689i	−0.299158	−	0.920713i
$686$	−402.302	+	553.722i	−0.586447	+	0.807175i
$687$	−501.478	+	235.859i	−0.729954	+	0.343318i
$688$	352.701			0.512647
$689$	−65.5488	+	90.2201i	−0.0951361	+	0.130944i
$690$	979.092	+	538.507i	1.41897	+	0.780445i
$691$	−251.497	+	182.723i	−0.363961	+	0.264433i	−0.754702	−	0.656068i	$-0.772219\pi$
$691$	−251.497	+	182.723i	−0.363961	+	0.264433i	0.390741	+	0.920500i	$0.372219\pi$
$692$	1219.35	+	396.192i	1.76207	+	0.572532i
$693$	234.333	+	914.134i	0.338142	+	1.31910i
$694$	734.713	−	2261.21i	1.05866	−	3.25823i
$695$	−337.640	+	109.706i	−0.485813	+	0.157850i
$696$	534.222	−	971.301i	0.767560	−	1.39555i
$697$	69.5818	+	214.151i	0.0998304	+	0.307246i
$698$	−83.1709	+	27.0239i	−0.119156	+	0.0387161i
$699$	−711.061	−	391.088i	−1.01726	−	0.559497i
$700$	81.7893	+	251.722i	0.116842	+	0.359602i
$701$	−547.175	−	177.788i	−0.780563	−	0.253620i	−0.108482	−	0.994098i	$-0.534599\pi$
$701$	−547.175	−	177.788i	−0.780563	−	0.253620i	−0.672080	+	0.740478i	$0.734599\pi$
$702$	485.320	+	587.345i	0.691339	+	0.836673i
$703$	−296.591	+	912.815i	−0.421894	+	1.29846i
$704$	−154.723	−	212.957i	−0.219776	−	0.302496i
$705$	−368.126	+	669.311i	−0.522164	+	0.949378i
$706$	−1008.81	−	732.944i	−1.42891	−	1.03816i
$707$		−	1977.50i		−	2.79703i
$708$	3.70687	+	7.88146i	0.00523569	+	0.0111320i
$709$	504.378	+	366.452i	0.711394	+	0.516858i	0.883623	−	0.468199i	$-0.155097\pi$
$709$	504.378	+	366.452i	0.711394	+	0.516858i	−0.172229	+	0.985057i	$0.555097\pi$
$710$	406.181	−	131.976i	0.572086	−	0.185882i
$711$	−146.609	−	231.216i	−0.206200	−	0.325198i
$712$	−2201.06			−3.09137
$713$	−318.207	−	511.345i	−0.446292	−	0.717173i
$714$	2121.35	−	997.733i	2.97109	−	1.39738i
$715$	122.720	−	377.693i	0.171636	−	0.528243i
$716$	818.497	−	265.946i	1.14315	−	0.371433i
$717$	22.1044	−	115.754i	0.0308290	−	0.161442i
$718$	−2022.50			−2.81686
$719$			223.636i			0.311037i	0.987833	+	0.155519i	$0.0497048\pi$
$719$			223.636i			0.311037i	−0.987833	+	0.155519i	$0.950295\pi$
$720$	−390.012	−	1521.44i	−0.541683	−	2.11311i
$721$	354.695	−	257.701i	0.491948	−	0.357421i
$722$	739.995	+	1018.52i	1.02492	+	1.41069i
$723$	42.3802	+	335.997i	0.0586172	+	0.464726i
$724$	−1591.35	−	1156.18i	−2.19799	−	1.59693i
$725$	−48.2656	−	15.6825i	−0.0665733	−	0.0216310i
$726$	205.630	−	193.024i	0.283237	−	0.265874i
$727$	652.168	−	473.828i	0.897067	−	0.651758i	−0.0406437	−	0.999174i	$-0.512941\pi$
$727$	652.168	−	473.828i	0.897067	−	0.651758i	0.937711	+	0.347416i	$0.112941\pi$
$728$	−1526.45	+	495.975i	−2.09678	+	0.681285i
$729$	137.432	−	715.928i	0.188521	−	0.982069i
$730$	710.418	−	516.149i	0.973176	−	0.707054i
$731$	−201.592	+	65.5012i	−0.275775	+	0.0896049i
$732$	320.335	+	2539.66i	0.437616	+	3.46948i
$733$	−865.788	−	629.032i	−1.18116	−	0.858161i	−0.188856	−	0.982005i	$-0.560478\pi$
$733$	−865.788	−	629.032i	−1.18116	−	0.858161i	−0.992302	+	0.123844i	$0.960478\pi$
$734$	−1567.99	−	509.471i	−2.13623	−	0.694102i
$735$	−918.770	−	505.330i	−1.25003	−	0.687523i
$736$	688.584	−	500.286i	0.935576	−	0.679736i
$737$	−220.548	+	303.558i	−0.299251	+	0.411883i
$738$	−236.242	+	285.343i	−0.320112	+	0.386644i
$739$	−813.197			−1.10040			−0.550201	−	0.835032i	$-0.685449\pi$
$739$	−813.197			−1.10040			−0.550201	+	0.835032i	$0.685449\pi$
$740$	−1037.31	+	1427.73i	−1.40177	+	1.92937i
$741$	−422.337	−	449.918i	−0.569956	−	0.607176i
$742$	−174.440	+	536.870i	−0.235094	+	0.723544i
$743$		−	652.059i		−	0.877603i	−0.898584	−	0.438802i	$-0.855403\pi$
$743$		−	652.059i		−	0.877603i	0.898584	−	0.438802i	$-0.144597\pi$
$744$	−462.007	+	1734.24i	−0.620977	+	2.33096i
$745$	326.717			0.438546
$746$	199.373	+	64.7803i	0.267256	+	0.0868368i
$747$	394.647	−	995.638i	0.528309	−	1.33285i
$748$	1463.21	+	1063.09i	1.95617	+	1.42124i
$749$		−	750.861i		−	1.00248i
$750$	1163.21	−	547.090i	1.55094	−	0.729453i
$751$	1002.24	+	728.171i	1.33454	+	0.969603i	0.999626	+	0.0273551i	$0.00870848\pi$
$751$	1002.24	+	728.171i	1.33454	+	0.969603i	0.334918	+	0.942247i	$0.391292\pi$
$752$	944.595	+	1300.12i	1.25611	+	1.72889i
$753$	691.881	+	380.539i	0.918833	+	0.505364i
$754$	166.967	−	513.872i	0.221442	−	0.681528i
$755$	226.525	−	311.785i	0.300033	−	0.412960i
$756$	2275.65	+	1446.02i	3.01012	+	1.91273i
$757$	302.425	+	930.769i	0.399505	+	1.22955i	0.925397	+	0.378998i	$0.123731\pi$
$757$	302.425	+	930.769i	0.399505	+	1.22955i	−0.525893	+	0.850551i	$0.676269\pi$
$758$	567.145	+	780.608i	0.748213	+	1.02983i
$759$	−389.240	−	414.659i	−0.512832	−	0.546323i
$760$	833.380	+	2564.88i	1.09655	+	3.37484i
$761$	721.309	+	992.797i	0.947844	+	1.30460i	0.952478	+	0.304606i	$0.0985249\pi$
$761$	721.309	+	992.797i	0.947844	+	1.30460i	−0.00463416	+	0.999989i	$0.501475\pi$
$762$	−420.901	+	395.099i	−0.552363	+	0.518502i
$763$	485.861	−	1495.33i	0.636777	−	1.95980i
$764$	−1176.55	+	1619.39i	−1.53999	+	2.11962i
$765$	505.469	+	797.173i	0.660744	+	1.04206i
$766$	−1679.73	+	1220.39i	−2.19286	+	1.59320i
$767$	1.42125	+	1.95619i	0.00185300	+	0.00255044i
$768$	1144.00	+	218.458i	1.48958	+	0.284451i
$769$	−460.298			−0.598567			−0.299283	−	0.954164i	$-0.596748\pi$
$769$	−460.298			−0.598567			−0.299283	+	0.954164i	$0.596748\pi$
$770$		−	2010.25i		−	2.61071i
$771$	−4.39631	+	23.0221i	−0.00570209	+	0.0298600i
$772$	267.563	+	823.475i	0.346585	+	1.06668i
$773$	210.213	+	68.3023i	0.271944	+	0.0883601i	0.441815	−	0.897106i	$-0.354335\pi$
$773$	210.213	+	68.3023i	0.271944	+	0.0883601i	−0.169870	+	0.985466i	$0.554335\pi$
$774$	−268.609	−	222.388i	−0.347040	−	0.287323i
$775$	81.9538	+	5.88351i	0.105747	+	0.00759163i
$776$			2593.72i			3.34243i
$777$	−145.693	−	1155.07i	−0.187506	−	1.48658i
$778$	550.191	+	1693.31i	0.707186	+	2.17649i
$779$	176.354	−	242.731i	0.226385	−	0.311593i
$780$	−482.907	−	1026.75i	−0.619112	−	1.31634i
$781$	−217.372			−0.278325
$782$	−830.425	+	1142.98i	−1.06193	+	1.46161i
$783$	−480.784	+	190.033i	−0.614028	+	0.242699i
$784$	−1784.69	+	1296.65i	−2.27639	+	1.65390i
$785$	1278.69	+	415.472i	1.62891	+	0.529263i
$786$	−973.189	−	185.841i	−1.23815	−	0.236439i
$787$	141.136	−	434.372i	0.179334	−	0.551934i	−0.820471	−	0.571688i	$-0.806289\pi$
$787$	141.136	−	434.372i	0.179334	−	0.551934i	0.999805	+	0.0197550i	$0.00628861\pi$
$788$	−250.901	+	81.5228i	−0.318403	+	0.103455i
$789$	−864.489	−	475.475i	−1.09568	−	0.602630i
$790$	180.220	+	554.660i	0.228126	+	0.702101i
$791$	754.451	−	245.136i	0.953794	−	0.309907i
$792$	−107.070	+	1691.38i	−0.135189	+	2.13558i
$793$	219.602	+	675.867i	0.276926	+	0.852291i
$794$	−228.052	−	74.0986i	−0.287219	−	0.0933232i
$795$	−223.260	−	42.6340i	−0.280831	−	0.0536277i
$796$	212.404	−	653.712i	0.266839	−	0.821247i
$797$	−819.499	−	1127.94i	−1.02823	−	1.41524i	−0.906268	−	0.422703i	$-0.861081\pi$
$797$	−819.499	−	1127.94i	−1.02823	−	1.41524i	−0.121962	−	0.992535i	$-0.538919\pi$
$798$	−2736.98	−	1505.36i	−3.42980	−	1.88641i
$799$	−781.348	−	567.682i	−0.977907	−	0.710491i
$800$			116.116i			0.145146i
$801$	790.679	+	654.622i	0.987115	+	0.817256i
$802$	−1322.18	−	960.622i	−1.64861	−	1.19778i
$803$	−425.063	+	138.111i	−0.529343	+	0.171994i
$804$	134.156	+	1063.61i	0.166860	+	1.32289i
$805$	1097.78			1.36370
$806$	−62.6403	+	872.541i	−0.0777175	+	1.08256i
$807$	251.282	+	534.270i	0.311378	+	0.662045i
$808$	1097.44	−	3377.56i	1.35821	−	4.18015i
$809$	−249.968	+	81.2195i	−0.308984	+	0.100395i	−0.459405	−	0.888227i	$-0.651937\pi$
$809$	−249.968	+	81.2195i	−0.308984	+	0.100395i	0.150421	+	0.988622i	$0.451937\pi$
$810$	−662.287	+	1404.61i	−0.817638	+	1.73408i
$811$	843.842			1.04050			0.520248	−	0.854015i	$-0.325839\pi$
$811$	843.842			1.04050			0.520248	+	0.854015i	$0.325839\pi$
$812$		−	1912.05i		−	2.35474i
$813$	627.828	+	119.891i	0.772237	+	0.147467i
$814$	1039.45	−	755.204i	1.27696	−	0.927769i
$815$	−491.617	−	676.653i	−0.603211	−	0.830249i
$816$	1970.23	−	248.510i	2.41449	−	0.304547i
$817$	228.496	+	166.012i	0.279677	+	0.203197i
$818$	−1863.36	−	605.441i	−2.27794	−	0.740148i
$819$	695.853	+	275.819i	0.849638	+	0.336776i
$820$	446.311	−	324.264i	0.544282	−	0.395444i
$821$	−762.329	+	247.696i	−0.928537	+	0.301700i	−0.733964	−	0.679188i	$-0.762332\pi$
$821$	−762.329	+	247.696i	−0.928537	+	0.301700i	−0.194573	+	0.980888i	$0.562332\pi$
$822$	944.070	+	1005.72i	1.14850	+	1.22351i
$823$	−211.638	+	153.764i	−0.257154	+	0.186833i	−0.708892	−	0.705318i	$-0.750804\pi$
$823$	−211.638	+	153.764i	−0.257154	+	0.186833i	0.451737	+	0.892151i	$0.350804\pi$
$824$	748.830	−	243.310i	0.908775	−	0.295279i
$825$	76.9786	−	9.70953i	0.0933074	−	0.0117691i
$826$	9.90210	+	7.19430i	0.0119880	+	0.00870980i
$827$	757.328	+	246.071i	0.915753	+	0.297546i	0.728724	−	0.684808i	$-0.240114\pi$
$827$	757.328	+	246.071i	0.915753	+	0.297546i	0.187030	+	0.982354i	$0.440114\pi$
$828$	−1621.66	−	102.656i	−1.95853	−	0.123981i
$829$	−482.413	+	350.494i	−0.581922	+	0.422791i	−0.839416	−	0.543489i	$-0.817103\pi$
$829$	−482.413	+	350.494i	−0.581922	+	0.422791i	0.257494	+	0.966280i	$0.417103\pi$
$830$	−1341.00	+	1845.73i	−1.61566	+	2.22377i
$831$	−916.893	+	431.240i	−1.10336	+	0.518942i
$832$	−208.791			−0.250950
$833$	779.263	−	1072.56i	0.935490	−	1.28759i
$834$	538.415	−	505.409i	0.645582	−	0.606006i
$835$	284.451	−	875.450i	0.340660	−	1.04844i
$836$		−	2409.93i		−	2.88269i
$837$	681.750	−	485.578i	0.814516	−	0.580141i
$838$	1372.98			1.63840
$839$	215.934	+	70.1611i	0.257370	+	0.0836247i	0.434860	−	0.900498i	$-0.356798\pi$
$839$	215.934	+	70.1611i	0.257370	+	0.0836247i	−0.177490	+	0.984123i	$0.556798\pi$
$840$	−2238.90	−	2385.11i	−2.66536	−	2.83942i
$841$	−383.782	−	278.834i	−0.456340	−	0.331550i
$842$		−	57.4188i		−	0.0681934i
$843$	−80.6847	−	171.550i	−0.0957114	−	0.203499i
$844$	−2025.92	−	1471.92i	−2.40038	−	1.74398i
$845$	337.192	+	464.105i	0.399044	+	0.549237i
$846$	100.382	−	1585.74i	0.118655	−	1.87439i
$847$	85.6213	−	263.515i	0.101088	−	0.311116i
$848$	−281.071	+	386.862i	−0.331452	+	0.456205i
$849$	−59.8858	−	474.783i	−0.0705368	−	0.559227i
$850$	−59.5606	−	183.309i	−0.0700712	−	0.215657i
$851$	412.410	+	567.633i	0.484618	+	0.667019i
$852$	−452.809	+	425.052i	−0.531467	+	0.498887i
$853$	−220.549	−	678.779i	−0.258556	−	0.795755i	−0.993108	−	0.117202i	$-0.962607\pi$
$853$	−220.549	−	678.779i	−0.258556	−	0.795755i	0.734552	−	0.678553i	$-0.237393\pi$
$854$	2114.42	+	2910.24i	2.47590	+	3.40778i
$855$	463.455	−	1169.23i	0.542053	−	1.36752i
$856$	416.698	−	1282.47i	0.486797	−	1.49821i
$857$	90.9187	−	125.139i	0.106090	−	0.146020i	−0.752671	−	0.658397i	$-0.771235\pi$
$857$	90.9187	−	125.139i	0.106090	−	0.146020i	0.858761	+	0.512377i	$0.171235\pi$
$858$	103.375	+	819.572i	0.120484	+	0.955213i
$859$	−720.975	+	523.819i	−0.839319	+	0.609801i	−0.922180	−	0.386760i	$-0.873594\pi$
$859$	−720.975	+	523.819i	−0.839319	+	0.609801i	0.0828612	+	0.996561i	$0.473594\pi$
$860$	305.247	+	420.137i	0.354939	+	0.488532i
$861$	−68.2644	+	357.479i	−0.0792850	+	0.415190i
$862$	−1530.07			−1.77502
$863$		−	657.353i		−	0.761707i	−0.924635	−	0.380854i	$-0.875630\pi$
$863$		−	657.353i		−	0.761707i	0.924635	−	0.380854i	$-0.124370\pi$
$864$	753.455	+	911.848i	0.872055	+	1.05538i
$865$	224.182	+	689.961i	0.259170	+	0.797643i
$866$	−1082.03	−	351.572i	−1.24945	−	0.405972i
$867$	−295.406	+	138.937i	−0.340722	+	0.160251i
$868$	743.335	+	3005.08i	0.856376	+	3.46208i
$869$		−	296.832i		−	0.341578i
$870$	1092.61	−	137.814i	1.25587	−	0.158407i
$871$	91.9691	+	283.052i	0.105590	+	0.324974i
$872$	1659.69	−	2284.37i	1.90332	−	2.61969i
$873$	771.407	−	931.736i	0.883627	−	1.06728i
$874$	1882.50			2.15390
$875$	742.288	−	1021.67i	0.848329	−	1.16763i
$876$	−615.388	+	1118.87i	−0.702498	+	1.27725i
$877$	83.1868	−	60.4387i	0.0948538	−	0.0689153i	−0.539347	−	0.842083i	$-0.681329\pi$
$877$	83.1868	−	60.4387i	0.0948538	−	0.0689153i	0.634201	+	0.773168i	$0.281329\pi$
$878$	−2250.57	−	731.256i	−2.56330	−	0.832865i
$879$	−144.676	+	757.619i	−0.164591	+	0.861910i
$880$	526.220	−	1619.54i	0.597978	−	1.84039i
$881$	−536.520	+	174.326i	−0.608990	+	0.197873i	−0.597246	−	0.802058i	$-0.703738\pi$
$881$	−536.520	+	174.326i	−0.608990	+	0.197873i	−0.0117443	+	0.999931i	$0.503738\pi$
$882$	2176.76	+	137.796i	2.46798	+	0.156231i
$883$	116.526	+	358.629i	0.131966	+	0.406148i	0.995106	−	0.0988163i	$-0.0315056\pi$
$883$	116.526	+	358.629i	0.131966	+	0.406148i	−0.863140	+	0.504964i	$0.831506\pi$
$884$	1364.37	−	443.311i	1.54341	−	0.501483i
$885$	−2.37506	+	4.31823i	−0.00268368	+	0.00487936i
$886$	−500.739	−	1541.12i	−0.565168	−	1.73941i
$887$	199.812	+	64.9229i	0.225268	+	0.0731939i	0.419476	−	0.907766i	$-0.362214\pi$
$887$	199.812	+	64.9229i	0.225268	+	0.0731939i	−0.194208	+	0.980960i	$0.562214\pi$
$888$	392.178	−	2053.71i	0.441642	−	2.31274i
$889$	−175.257	+	539.386i	−0.197140	+	0.606733i
$890$	−1285.28	−	1769.04i	−1.44414	−	1.98768i
$891$	541.501	−	575.746i	0.607745	−	0.646180i
$892$	1496.34	+	1087.16i	1.67752	+	1.21879i
$893$			1286.89i			1.44108i
$894$	−614.976	+	289.240i	−0.687892	+	0.323535i
$895$	393.970	+	286.236i	0.440190	+	0.319817i
$896$	785.739	−	255.302i	0.876941	−	0.284935i
$897$	−447.561	+	56.4521i	−0.498953	+	0.0629343i
$898$	−1596.17			−1.77748
$899$	−549.932	−	223.374i	−0.611716	−	0.248470i
$900$	141.369	−	170.751i	0.157077	−	0.189723i
$901$	88.8056	−	273.315i	0.0985634	−	0.303347i
$902$	−381.982	+	124.114i	−0.423484	+	0.137598i
$903$	−336.514	−	64.2610i	−0.372663	−	0.0711639i
$904$	1424.64			1.57593
$905$		−	1113.02i		−	1.22985i
$906$	−150.365	+	787.411i	−0.165965	+	0.869107i
$907$	749.703	−	544.691i	0.826575	−	0.600542i	−0.0920134	−	0.995758i	$-0.529330\pi$
$907$	749.703	−	544.691i	0.826575	−	0.600542i	0.918588	+	0.395216i	$0.129330\pi$
$908$	257.935	+	355.017i	0.284070	+	0.390988i
$909$	−1398.76	+	886.920i	−1.53879	+	0.975709i
$910$	−1289.98	−	937.227i	−1.41756	−	1.02992i
$911$	1070.10	+	347.697i	1.17464	+	0.381665i	0.830374	−	0.557206i	$-0.188127\pi$
$911$	1070.10	+	347.697i	1.17464	+	0.381665i	0.344269	+	0.938871i	$0.388127\pi$
$912$	−1810.97	−	1929.24i	−1.98571	−	2.11539i
$913$	939.415	−	682.525i	1.02893	−	0.747563i
$914$	1936.66	−	629.259i	2.11888	−	0.688467i
$915$	−1056.05	+	991.316i	−1.15416	+	1.08341i
$916$	−1388.80	+	1009.02i	−1.51616	+	1.10155i
$917$	−925.726	+	300.787i	−1.00952	+	0.328012i
$918$	−1657.17	−	1053.02i	−1.80520	−	1.14708i
$919$	322.118	+	234.032i	0.350509	+	0.254660i	0.749082	−	0.662477i	$-0.230495\pi$
$919$	322.118	+	234.032i	0.350509	+	0.254660i	−0.398574	+	0.917136i	$0.630495\pi$
$920$	1875.00	+	609.224i	2.03804	+	0.662201i
$921$	621.576	−	1130.12i	0.674893	−	1.22706i
$922$	−729.357	+	529.909i	−0.791060	+	0.574739i
$923$	−101.344	+	139.488i	−0.109798	+	0.151125i
$924$	1244.14	+	2645.27i	1.34648	+	2.86285i
$925$	−95.7204			−0.103482
$926$	1781.59	−	2452.15i	1.92396	−	2.64811i
$927$	−341.364	−	135.308i	−0.368245	−	0.145964i
$928$	259.215	−	797.783i	0.279327	−	0.859680i
$929$			995.146i			1.07120i	0.844471	+	0.535601i	$0.179915\pi$
$929$			995.146i			1.07120i	−0.844471	+	0.535601i	$0.820085\pi$
$930$	−1663.63	+	641.363i	−1.78885	+	0.689637i
$931$	−1766.52			−1.89745
$932$	−2390.78	−	776.810i	−2.56521	−	0.833487i
$933$	1215.81	−	1141.28i	1.30312	−	1.22324i
$934$	2423.61	+	1760.86i	2.59488	+	1.88529i
$935$			1023.40i			1.09455i
$936$	1035.44	+	857.270i	1.10624	+	0.915886i
$937$	−959.334	−	696.997i	−1.02384	−	0.743860i	−0.0567700	−	0.998387i	$-0.518080\pi$
$937$	−959.334	−	696.997i	−1.02384	−	0.743860i	−0.967066	+	0.254527i	$0.918080\pi$
$938$	885.514	+	1218.81i	0.944045	+	1.29937i
$939$	133.989	−	243.614i	0.142694	−	0.259440i
$940$	−731.199	+	2250.40i	−0.777872	+	2.39404i
$941$	287.017	−	395.045i	0.305012	−	0.419814i	−0.628805	−	0.777563i	$-0.716456\pi$
$941$	287.017	−	395.045i	0.305012	−	0.419814i	0.933818	+	0.357749i	$0.116456\pi$
$942$	−2774.68	+	349.979i	−2.94552	+	0.371527i
$943$	−67.7772	−	208.597i	−0.0718740	−	0.221206i
$944$	6.09430	+	8.38808i	0.00645582	+	0.00888568i
$945$	94.9113	+	1522.68i	0.100435	+	1.61130i
$946$	−116.835	−	359.581i	−0.123504	−	0.380107i
$947$	656.885	+	904.124i	0.693648	+	0.954725i	0.999996	+	0.00280505i	$0.000892877\pi$
$947$	656.885	+	904.124i	0.693648	+	0.954725i	−0.306348	+	0.951920i	$0.599107\pi$
$948$	−580.429	−	618.333i	−0.612266	−	0.652250i
$949$	−109.548	+	337.154i	−0.115435	+	0.355273i
$950$	−150.956	+	207.772i	−0.158901	+	0.218708i
$951$	645.677	−	81.4411i	0.678946	−	0.0856374i
$952$	3346.17	−	2431.13i	3.51488	−	2.55371i
$953$	−327.233	−	450.397i	−0.343371	−	0.472610i	0.602051	−	0.798458i	$-0.294350\pi$
$953$	−327.233	−	450.397i	−0.343371	−	0.472610i	−0.945422	+	0.325848i	$0.894350\pi$
$954$	457.985	−	117.402i	0.480068	−	0.123063i
$955$	−1132.63			−1.18600
$956$		−	365.046i		−	0.381847i
$957$	−550.560	−	105.135i	−0.575298	−	0.109859i
$958$	−240.202	−	739.264i	−0.250732	−	0.771675i
$959$	1288.84	+	418.768i	1.34394	+	0.436672i
$960$	−181.118	−	385.088i	−0.188664	−	0.401133i
$961$	951.145	+	137.274i	0.989745	+	0.142845i
$962$		−	1019.11i		−	1.05937i
$963$	−531.111	+	336.765i	−0.551517	+	0.349704i
$964$	324.175	+	997.709i	0.336282	+	1.03497i
$965$	−287.977	+	396.366i	−0.298422	+	0.410742i
$966$	−2066.34	+	971.857i	−2.13907	+	1.00606i
$967$	1097.09			1.13453			0.567267	−	0.823534i	$-0.308001\pi$
$967$	1097.09			1.13453			0.567267	+	0.823534i	$0.308001\pi$
$968$	292.482	−	402.566i	0.302150	−	0.415874i
$969$	1393.37	+	766.364i	1.43795	+	0.790882i
$970$	−2084.64	+	1514.58i	−2.14911	+	1.56142i
$971$	503.466	+	163.586i	0.518502	+	0.168472i	0.556566	−	0.830804i	$-0.312119\pi$
$971$	503.466	+	163.586i	0.518502	+	0.168472i	−0.0380632	+	0.999275i	$0.512119\pi$
$972$	2.18450	−	2258.20i	0.00224743	−	2.32325i
$973$	224.188	−	689.981i	0.230409	−	0.709127i
$974$	−1638.99	+	532.540i	−1.68274	+	0.546756i
$975$	29.6587	−	53.9242i	0.0304191	−	0.0553069i
$976$	941.650	+	2898.10i	0.964805	+	2.96936i
$977$	−343.155	+	111.498i	−0.351233	+	0.114123i	−0.479319	−	0.877640i	$-0.659116\pi$
$977$	−343.155	+	111.498i	−0.351233	+	0.114123i	0.128087	+	0.991763i	$0.459116\pi$
$978$	1524.40	+	838.432i	1.55870	+	0.857293i
$979$	343.916	+	1058.46i	0.351293	+	1.08117i
$980$	−3089.15	−	1003.72i	−3.15219	−	1.02421i
$981$	−1275.61	+	326.995i	−1.30032	+	0.333328i
$982$	405.572	−	1248.22i	0.413006	−	1.27110i
$983$	510.708	+	702.929i	0.519540	+	0.715085i	0.985491	−	0.169725i	$-0.0542879\pi$
$983$	510.708	+	702.929i	0.519540	+	0.715085i	−0.465952	+	0.884810i	$0.654288\pi$
$984$	−314.982	+	572.688i	−0.320104	+	0.582000i
$985$	−120.767	−	87.7426i	−0.122606	−	0.0890788i
$986$			1392.39i			1.41216i
$987$	−664.366	−	1412.56i	−0.673116	−	1.43116i
$988$	−1546.46	−	1123.57i	−1.56524	−	1.13721i
$989$	196.364	−	63.8024i	0.198548	−	0.0645121i
$990$	−1421.92	+	901.608i	−1.43629	+	0.910715i
$991$	−1963.82			−1.98166			−0.990828	−	0.135128i	$-0.956855\pi$
$991$	−1963.82			−1.98166			−0.990828	+	0.135128i	$0.956855\pi$
$992$	−97.2486	+	1354.61i	−0.0980328	+	1.36554i
$993$	−757.540	+	356.292i	−0.762880	+	0.358804i
$994$	−269.698	+	830.046i	−0.271326	+	0.835057i
$995$	369.898	−	120.187i	0.371756	−	0.120791i
$996$	622.287	−	3258.72i	0.624787	−	3.27181i
$997$	189.265			0.189835			0.0949175	−	0.995485i	$-0.469741\pi$
$997$	189.265			0.189835			0.0949175	+	0.995485i	$0.469741\pi$
$998$		−	181.110i		−	0.181473i
$999$	−751.681	+	621.110i	−0.752433	+	0.621732i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.3.l.b.8.1	✓	72
3.2	odd	2	inner	93.3.l.b.8.18	yes	72
31.4	even	5	inner	93.3.l.b.35.18	yes	72
93.35	odd	10	inner	93.3.l.b.35.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.3.l.b.8.1	✓	72	1.1	even	1	trivial
93.3.l.b.8.18	yes	72	3.2	odd	2	inner
93.3.l.b.35.1	yes	72	93.35	odd	10	inner
93.3.l.b.35.18	yes	72	31.4	even	5	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	93.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.46751 - 1.12666i) q^{2} +(2.05322 + 2.18730i) q^{3} +(7.51820 + 5.46229i) q^{4} +5.25837i q^{5} +(-4.65521 - 9.89779i) q^{6} +(-8.69344 - 6.31616i) q^{7} +(-11.3431 - 15.6125i) q^{8} +(-0.568590 + 8.98202i) q^{9} +(5.92441 - 18.2335i) q^{10} +(-5.73550 + 7.89424i) q^{11} +(3.48882 + 27.6599i) q^{12} +(2.39173 + 7.36097i) q^{13} +(23.0284 + 31.6959i) q^{14} +(-11.5017 + 10.7966i) q^{15} +(10.2557 + 31.5637i) q^{16} +(-11.7236 - 16.1361i) q^{17} +(12.0913 - 30.5047i) q^{18} +(-8.21254 + 25.2756i) q^{19} +(-28.7228 + 39.5335i) q^{20} +(-4.03419 - 31.9836i) q^{21} +(28.7821 - 20.9114i) q^{22} +(11.4195 + 15.7176i) q^{23} +(10.8593 - 56.8667i) q^{24} -2.65047 q^{25} -28.2189i q^{26} +(-20.8138 + 17.1984i) q^{27} +(-30.8584 - 94.9723i) q^{28} +(18.2102 + 5.91685i) q^{29} +(52.0462 - 24.4788i) q^{30} +(-30.9204 - 2.21980i) q^{31} -43.8097i q^{32} +(-29.0433 + 3.66332i) q^{33} +(22.4717 + 69.1606i) q^{34} +(33.2127 - 45.7134i) q^{35} +(-53.3372 + 64.4229i) q^{36} +36.1145 q^{37} +(56.9542 - 78.3907i) q^{38} +(-11.1899 + 20.3451i) q^{39} +(82.0963 - 59.6464i) q^{40} +(-10.7369 - 3.48863i) q^{41} +(-22.0462 + 115.449i) q^{42} +(3.28404 - 10.1072i) q^{43} +(-86.2414 + 28.0215i) q^{44} +(-47.2308 - 2.98986i) q^{45} +(-21.8889 - 67.3670i) q^{46} +(46.0524 - 14.9633i) q^{47} +(-47.9822 + 87.2393i) q^{48} +(20.5403 + 63.2165i) q^{49} +(9.19055 + 2.98619i) q^{50} +(11.2235 - 58.7739i) q^{51} +(-22.2263 + 68.4056i) q^{52} +(8.46907 + 11.6567i) q^{53} +(91.5490 - 36.1854i) q^{54} +(-41.5109 - 30.1594i) q^{55} +207.371i q^{56} +(-72.1475 + 33.9330i) q^{57} +(-56.4777 - 41.0335i) q^{58} +(0.297119 - 0.0965397i) q^{59} +(-145.446 + 18.3455i) q^{60} +91.8176 q^{61} +(104.716 + 42.5341i) q^{62} +(61.6749 - 74.4934i) q^{63} +(-8.33613 + 25.6560i) q^{64} +(-38.7067 + 12.5766i) q^{65} +(104.835 + 20.0195i) q^{66} +38.4531 q^{67} -185.352i q^{68} +(-10.9324 + 57.2497i) q^{69} +(-166.669 + 121.092i) q^{70} +(13.0939 + 18.0222i) q^{71} +(146.681 - 93.0072i) q^{72} +(37.0554 + 26.9223i) q^{73} +(-125.227 - 40.6888i) q^{74} +(-5.44200 - 5.79739i) q^{75} +(-199.806 + 145.168i) q^{76} +(99.7226 - 32.4018i) q^{77} +(61.7234 - 57.9396i) q^{78} +(-24.6102 + 17.8803i) q^{79} +(-165.974 + 53.9281i) q^{80} +(-80.3534 - 10.2142i) q^{81} +(33.2998 + 24.1937i) q^{82} +(-113.176 - 36.7730i) q^{83} +(144.374 - 262.495i) q^{84} +(84.8496 - 61.6469i) q^{85} +(-22.7749 + 31.3469i) q^{86} +(24.4475 + 51.9798i) q^{87} +188.307 q^{88} +(67.0402 - 92.2729i) q^{89} +(160.405 + 63.5806i) q^{90} +(25.7007 - 79.0987i) q^{91} +180.545i q^{92} +(-58.6310 - 72.1901i) q^{93} -176.546 q^{94} +(-132.908 - 43.1846i) q^{95} +(95.8251 - 89.9509i) q^{96} +(-108.734 - 79.0002i) q^{97} -242.346i q^{98} +(-67.6451 - 56.0050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 5 q^{3} + 36 q^{4} - 10 q^{6} - 54 q^{7} + 5 q^{9} + 114 q^{10} + 14 q^{12} + 26 q^{13} + 35 q^{15} - 184 q^{16} + 15 q^{18} - 90 q^{19} + 71 q^{21} - 114 q^{22} - 101 q^{24} - 188 q^{25} + 116 q^{27}+ \cdots - 616 q^{99}+O(q^{100}) \) 72 * q + 5 * q^3 + 36 * q^4 - 10 * q^6 - 54 * q^7 + 5 * q^9 + 114 * q^10 + 14 * q^12 + 26 * q^13 + 35 * q^15 - 184 * q^16 + 15 * q^18 - 90 * q^19 + 71 * q^21 - 114 * q^22 - 101 * q^24 - 188 * q^25 + 116 * q^27 - 84 * q^28 - 18 * q^30 + 28 * q^31 - 242 * q^33 - 82 * q^34 + 74 * q^36 + 364 * q^37 + 13 * q^39 + 252 * q^40 - 46 * q^42 - 146 * q^43 + 52 * q^45 - 88 * q^46 - 170 * q^48 - 60 * q^49 - 301 * q^51 - 222 * q^52 - 118 * q^54 + 308 * q^55 - 20 * q^57 - 280 * q^58 - 407 * q^60 + 84 * q^61 + 556 * q^63 + 1450 * q^64 + 550 * q^66 - 324 * q^67 + 355 * q^69 + 728 * q^70 - 631 * q^72 - 140 * q^73 - 17 * q^75 - 622 * q^76 + 679 * q^78 - 200 * q^79 + 5 * q^81 + 598 * q^82 + 1197 * q^84 - 200 * q^85 + 202 * q^87 + 388 * q^88 + 1068 * q^90 + 834 * q^91 + 74 * q^93 - 384 * q^94 - 1016 * q^96 - 1074 * q^97 - 616 * q^99

Introduction

L-functions

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