LMFDB - Embedded newform 48.3.i.b.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(5,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("48.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.i (of order $4$, 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:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 $ x^20 - 2x^18 + 6x^16 - 24x^14 - 24x^12 + 1216x^10 - 384x^8 - 6144x^6 + 24576x^4 - 131072*x^2 + 1048576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.1
Root			$-1.96139 - 0.391068i$ of defining polynomial
Character	$\chi$	$=$	48.5
Dual form			48.3.i.b.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96139 + 0.391068i) q^{2} +(-2.99548 + 0.164573i) q^{3} +(3.69413 - 1.53408i) q^{4} +(3.61305 - 3.61305i) q^{5} +(5.81096 - 1.49423i) q^{6} -12.2792i q^{7} +(-6.64572 + 4.45358i) q^{8} +(8.94583 - 0.985948i) q^{9} +O(q^{10})$	\(q+(-1.96139 + 0.391068i) q^{2} +(-2.99548 + 0.164573i) q^{3} +(3.69413 - 1.53408i) q^{4} +(3.61305 - 3.61305i) q^{5} +(5.81096 - 1.49423i) q^{6} -12.2792i q^{7} +(-6.64572 + 4.45358i) q^{8} +(8.94583 - 0.985948i) q^{9} +(-5.67366 + 8.49955i) q^{10} +(-1.76932 + 1.76932i) q^{11} +(-10.8132 + 5.20325i) q^{12} +(-2.38826 + 2.38826i) q^{13} +(4.80199 + 24.0843i) q^{14} +(-10.2282 + 11.4174i) q^{15} +(11.2932 - 11.3342i) q^{16} -20.0754i q^{17} +(-17.1607 + 5.43226i) q^{18} +(-8.77090 + 8.77090i) q^{19} +(7.80438 - 18.8898i) q^{20} +(2.02081 + 36.7820i) q^{21} +(2.77840 - 4.16225i) q^{22} +13.1821 q^{23} +(19.1742 - 14.4343i) q^{24} -1.10820i q^{25} +(3.75035 - 5.61830i) q^{26} +(-26.6348 + 4.42563i) q^{27} +(-18.8372 - 45.3609i) q^{28} +(6.51544 + 6.51544i) q^{29} +(15.5966 - 26.3940i) q^{30} +37.5922 q^{31} +(-17.7180 + 26.6472i) q^{32} +(5.00877 - 5.59113i) q^{33} +(7.85085 + 39.3758i) q^{34} +(-44.3652 - 44.3652i) q^{35} +(31.5346 - 17.3658i) q^{36} +(10.0057 + 10.0057i) q^{37} +(13.7732 - 20.6332i) q^{38} +(6.76096 - 7.54704i) q^{39} +(-7.92028 + 40.1023i) q^{40} +4.57407 q^{41} +(-18.3479 - 71.3538i) q^{42} +(21.2835 + 21.2835i) q^{43} +(-3.82182 + 9.25035i) q^{44} +(28.7594 - 35.8840i) q^{45} +(-25.8553 + 5.15509i) q^{46} +54.8366i q^{47} +(-31.9633 + 35.8098i) q^{48} -101.778 q^{49} +(0.433383 + 2.17362i) q^{50} +(3.30386 + 60.1356i) q^{51} +(-5.15878 + 12.4863i) q^{52} +(-21.5215 + 21.5215i) q^{53} +(50.5107 - 19.0964i) q^{54} +12.7852i q^{55} +(54.6863 + 81.6039i) q^{56} +(24.8296 - 27.7165i) q^{57} +(-15.3273 - 10.2314i) q^{58} +(53.6617 - 53.6617i) q^{59} +(-20.2691 + 57.8683i) q^{60} +(-19.2186 + 19.2186i) q^{61} +(-73.7331 + 14.7011i) q^{62} +(-12.1066 - 109.847i) q^{63} +(24.3312 - 59.1945i) q^{64} +17.2578i q^{65} +(-7.63766 + 12.9252i) q^{66} +(31.5603 - 31.5603i) q^{67} +(-30.7972 - 74.1612i) q^{68} +(-39.4867 + 2.16941i) q^{69} +(104.367 + 69.6678i) q^{70} +65.1220 q^{71} +(-55.0605 + 46.3934i) q^{72} -50.2451i q^{73} +(-23.5379 - 15.7121i) q^{74} +(0.182380 + 3.31960i) q^{75} +(-18.9456 + 45.8561i) q^{76} +(21.7257 + 21.7257i) q^{77} +(-10.3095 + 17.4467i) q^{78} +20.9299 q^{79} +(-0.147933 - 81.7538i) q^{80} +(79.0558 - 17.6403i) q^{81} +(-8.97156 + 1.78877i) q^{82} +(6.35791 + 6.35791i) q^{83} +(63.8916 + 132.778i) q^{84} +(-72.5334 - 72.5334i) q^{85} +(-50.0687 - 33.4221i) q^{86} +(-20.5891 - 18.4446i) q^{87} +(3.87858 - 19.6382i) q^{88} -166.399 q^{89} +(-42.3755 + 81.6295i) q^{90} +(29.3259 + 29.3259i) q^{91} +(48.6964 - 20.2223i) q^{92} +(-112.607 + 6.18664i) q^{93} +(-21.4449 - 107.556i) q^{94} +63.3793i q^{95} +(48.6886 - 82.7370i) q^{96} +139.213 q^{97} +(199.627 - 39.8021i) q^{98} +(-14.0835 + 17.5725i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	$ 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.96139	+	0.391068i	−0.980697	+	0.195534i
$2$	−1.96139	+	0.391068i	−0.980697	+	0.195534i
$3$	−2.99548	+	0.164573i	−0.998494	+	0.0548575i
$3$	−2.99548	+	0.164573i	−0.998494	+	0.0548575i
$4$	3.69413	−	1.53408i	0.923533	−	0.383519i
$5$	3.61305	−	3.61305i	0.722609	−	0.722609i	−0.246527	−	0.969136i	$-0.579289\pi$
$5$	3.61305	−	3.61305i	0.722609	−	0.722609i	0.969136	+	0.246527i	$0.0792893\pi$
$6$	5.81096	−	1.49423i	0.968494	−	0.249038i
$7$		−	12.2792i		−	1.75417i	−0.480338	−	0.877083i	$-0.659486\pi$
$7$		−	12.2792i		−	1.75417i	0.480338	−	0.877083i	$-0.340514\pi$
$8$	−6.64572	+	4.45358i	−0.830715	+	0.556698i
$9$	8.94583	−	0.985948i	0.993981	−	0.109550i
$10$	−5.67366	+	8.49955i	−0.567366	+	0.849955i
$11$	−1.76932	+	1.76932i	−0.160847	+	0.160847i	−0.782942	−	0.622095i	$-0.786282\pi$
$11$	−1.76932	+	1.76932i	−0.160847	+	0.160847i	0.622095	+	0.782942i	$0.286282\pi$
$12$	−10.8132	+	5.20325i	−0.901103	+	0.433604i
$13$	−2.38826	+	2.38826i	−0.183713	+	0.183713i	−0.792971	−	0.609259i	$-0.791467\pi$
$13$	−2.38826	+	2.38826i	−0.183713	+	0.183713i	0.609259	+	0.792971i	$0.291467\pi$
$14$	4.80199	+	24.0843i	0.342999	+	1.72031i
$15$	−10.2282	+	11.4174i	−0.681881	+	0.761162i
$16$	11.2932	−	11.3342i	0.705826	−	0.708385i
$17$		−	20.0754i		−	1.18091i	−0.807072	−	0.590453i	$-0.798949\pi$
$17$		−	20.0754i		−	1.18091i	0.807072	−	0.590453i	$-0.201051\pi$
$18$	−17.1607	+	5.43226i	−0.953374	+	0.301792i
$19$	−8.77090	+	8.77090i	−0.461626	+	0.461626i	−0.899188	−	0.437562i	$-0.855842\pi$
$19$	−8.77090	+	8.77090i	−0.461626	+	0.461626i	0.437562	+	0.899188i	$0.355842\pi$
$20$	7.80438	−	18.8898i	0.390219	−	0.944488i
$21$	2.02081	+	36.7820i	0.0962292	+	1.75153i
$22$	2.77840	−	4.16225i	0.126291	−	0.189193i
$23$	13.1821			0.573134			0.286567	−	0.958060i	$-0.407486\pi$
$23$	13.1821			0.573134			0.286567	+	0.958060i	$0.407486\pi$
$24$	19.1742	−	14.4343i	0.798925	−	0.601431i
$25$		−	1.10820i		−	0.0443281i
$26$	3.75035	−	5.61830i	0.144244	−	0.216088i
$27$	−26.6348	+	4.42563i	−0.986475	+	0.163912i
$28$	−18.8372	−	45.3609i	−0.672756	−	1.62003i
$29$	6.51544	+	6.51544i	0.224670	+	0.224670i	0.810462	−	0.585792i	$-0.199216\pi$
$29$	6.51544	+	6.51544i	0.224670	+	0.224670i	−0.585792	+	0.810462i	$0.699216\pi$
$30$	15.5966	−	26.3940i	0.519885	−	0.879800i
$31$	37.5922			1.21265			0.606326	−	0.795216i	$-0.292643\pi$
$31$	37.5922			1.21265			0.606326	+	0.795216i	$0.292643\pi$
$32$	−17.7180	+	26.6472i	−0.553688	+	0.832724i
$33$	5.00877	−	5.59113i	0.151781	−	0.169428i
$34$	7.85085	+	39.3758i	0.230907	+	1.15811i
$35$	−44.3652	−	44.3652i	−1.26758	−	1.26758i
$36$	31.5346	−	17.3658i	0.875960	−	0.482384i
$37$	10.0057	+	10.0057i	0.270423	+	0.270423i	0.829271	−	0.558847i	$-0.188756\pi$
$37$	10.0057	+	10.0057i	0.270423	+	0.270423i	−0.558847	+	0.829271i	$0.688756\pi$
$38$	13.7732	−	20.6332i	0.362452	−	0.542979i
$39$	6.76096	−	7.54704i	0.173358	−	0.193514i
$40$	−7.92028	+	40.1023i	−0.198007	+	1.00256i
$41$	4.57407			0.111563			0.0557814	−	0.998443i	$-0.482235\pi$
$41$	4.57407			0.111563			0.0557814	+	0.998443i	$0.482235\pi$
$42$	−18.3479	−	71.3538i	−0.436854	−	1.69890i
$43$	21.2835	+	21.2835i	0.494966	+	0.494966i	0.909867	−	0.414901i	$-0.136184\pi$
$43$	21.2835	+	21.2835i	0.494966	+	0.494966i	−0.414901	+	0.909867i	$0.636184\pi$
$44$	−3.82182	+	9.25035i	−0.0868595	+	0.210235i
$45$	28.7594	−	35.8840i	0.639098	−	0.797422i
$46$	−25.8553	+	5.15509i	−0.562071	+	0.112067i
$47$			54.8366i			1.16674i	0.812208	+	0.583368i	$0.198266\pi$
$47$			54.8366i			1.16674i	−0.812208	+	0.583368i	$0.801734\pi$
$48$	−31.9633	+	35.8098i	−0.665903	+	0.746038i
$49$	−101.778			−2.07710
$50$	0.433383	+	2.17362i	0.00866765	+	0.0434724i
$51$	3.30386	+	60.1356i	0.0647816	+	1.17913i
$52$	−5.15878	+	12.4863i	−0.0992073	+	0.240122i
$53$	−21.5215	+	21.5215i	−0.406065	+	0.406065i	−0.880364	−	0.474299i	$-0.842702\pi$
$53$	−21.5215	+	21.5215i	−0.406065	+	0.406065i	0.474299	+	0.880364i	$0.342702\pi$
$54$	50.5107	−	19.0964i	0.935383	−	0.353638i
$55$			12.7852i			0.232459i
$56$	54.6863	+	81.6039i	0.976541	+	1.45721i
$57$	24.8296	−	27.7165i	0.435607	−	0.486255i
$58$	−15.3273	−	10.2314i	−0.264264	−	0.176403i
$59$	53.6617	−	53.6617i	0.909520	−	0.909520i	−0.0867132	−	0.996233i	$-0.527636\pi$
$59$	53.6617	−	53.6617i	0.909520	−	0.909520i	0.996233	+	0.0867132i	$0.0276364\pi$
$60$	−20.2691	+	57.8683i	−0.337819	+	0.964472i
$61$	−19.2186	+	19.2186i	−0.315059	+	0.315059i	−0.846866	−	0.531807i	$-0.821513\pi$
$61$	−19.2186	+	19.2186i	−0.315059	+	0.315059i	0.531807	+	0.846866i	$0.321513\pi$
$62$	−73.7331	+	14.7011i	−1.18924	+	0.237115i
$63$	−12.1066	−	109.847i	−0.192169	−	1.74361i
$64$	24.3312	−	59.1945i	0.380174	−	0.924915i
$65$			17.2578i			0.265505i
$66$	−7.63766	+	12.9252i	−0.115722	+	0.195836i
$67$	31.5603	−	31.5603i	0.471049	−	0.471049i	−0.431205	−	0.902254i	$-0.641911\pi$
$67$	31.5603	−	31.5603i	0.471049	−	0.471049i	0.902254	+	0.431205i	$0.141911\pi$
$68$	−30.7972	−	74.1612i	−0.452900	−	1.09061i
$69$	−39.4867	+	2.16941i	−0.572271	+	0.0314407i
$70$	104.367	+	69.6678i	1.49096	+	0.995254i
$71$	65.1220			0.917211			0.458606	−	0.888640i	$-0.348349\pi$
$71$	65.1220			0.917211			0.458606	+	0.888640i	$0.348349\pi$
$72$	−55.0605	+	46.3934i	−0.764729	+	0.644352i
$73$		−	50.2451i		−	0.688290i	−0.938917	−	0.344145i	$-0.888169\pi$
$73$		−	50.2451i		−	0.688290i	0.938917	−	0.344145i	$-0.111831\pi$
$74$	−23.5379	−	15.7121i	−0.318080	−	0.212326i
$75$	0.182380	+	3.31960i	0.00243173	+	0.0442614i
$76$	−18.9456	+	45.8561i	−0.249284	+	0.603369i
$77$	21.7257	+	21.7257i	0.282152	+	0.282152i
$78$	−10.3095	+	17.4467i	−0.132173	+	0.223676i
$79$	20.9299			0.264935			0.132468	−	0.991187i	$-0.457710\pi$
$79$	20.9299			0.264935			0.132468	+	0.991187i	$0.457710\pi$
$80$	−0.147933	−	81.7538i	−0.00184916	−	1.02192i
$81$	79.0558	−	17.6403i	0.975998	−	0.217781i
$82$	−8.97156	+	1.78877i	−0.109409	+	0.0218143i
$83$	6.35791	+	6.35791i	0.0766013	+	0.0766013i	0.744369	−	0.667768i	$-0.232750\pi$
$83$	6.35791	+	6.35791i	0.0766013	+	0.0766013i	−0.667768	+	0.744369i	$0.732750\pi$
$84$	63.8916	+	132.778i	0.760614	+	1.58069i
$85$	−72.5334	−	72.5334i	−0.853334	−	0.853334i
$86$	−50.0687	−	33.4221i	−0.582194	−	0.388629i
$87$	−20.5891	−	18.4446i	−0.236657	−	0.212007i
$88$	3.87858	−	19.6382i	0.0440747	−	0.223161i
$89$	−166.399			−1.86966			−0.934828	−	0.355102i	$-0.884446\pi$
$89$	−166.399			−1.86966			−0.934828	+	0.355102i	$0.884446\pi$
$90$	−42.3755	+	81.6295i	−0.470839	+	0.906994i
$91$	29.3259	+	29.3259i	0.322262	+	0.322262i
$92$	48.6964	−	20.2223i	0.529308	−	0.219808i
$93$	−112.607	+	6.18664i	−1.21083	+	0.0665231i
$94$	−21.4449	−	107.556i	−0.228137	−	1.14422i
$95$			63.3793i			0.667151i
$96$	48.6886	−	82.7370i	0.507173	−	0.861844i
$97$	139.213			1.43519			0.717593	−	0.696463i	$-0.245244\pi$
$97$	139.213			1.43519			0.717593	+	0.696463i	$0.245244\pi$
$98$	199.627	−	39.8021i	2.03701	−	0.406144i
$99$	−14.0835	+	17.5725i	−0.142258	+	0.177500i
$100$	−1.70007	−	4.09385i	−0.0170007	−	0.0409385i
$101$	125.879	−	125.879i	1.24632	−	1.24632i	0.288994	−	0.957331i	$-0.406679\pi$
$101$	125.879	−	125.879i	1.24632	−	1.24632i	0.957331	−	0.288994i	$-0.0933207\pi$
$102$	−29.9973	−	116.657i	−0.294091	−	1.14370i
$103$			26.3937i			0.256250i	0.991758	+	0.128125i	$0.0408958\pi$
$103$			26.3937i			0.256250i	−0.991758	+	0.128125i	$0.959104\pi$
$104$	5.23539	−	26.5081i	0.0503403	−	0.254885i
$105$	140.196	+	125.594i	1.33520	+	1.19613i
$106$	33.7957	−	50.6284i	0.318828	−	0.477627i
$107$	−83.9534	+	83.9534i	−0.784611	+	0.784611i	−0.980605	−	0.195994i	$-0.937207\pi$
$107$	−83.9534	+	83.9534i	−0.784611	+	0.784611i	0.195994	+	0.980605i	$0.437207\pi$
$108$	−91.6033	+	57.2087i	−0.848179	+	0.529710i
$109$	2.29518	−	2.29518i	0.0210567	−	0.0210567i	−0.696500	−	0.717557i	$-0.745260\pi$
$109$	2.29518	−	2.29518i	0.0210567	−	0.0210567i	0.717557	+	0.696500i	$0.245260\pi$
$110$	−4.99990	−	25.0769i	−0.0454536	−	0.227972i
$111$	−31.6184	−	28.3251i	−0.284851	−	0.255181i
$112$	−139.174	−	138.671i	−1.24263	−	1.23814i
$113$			177.630i			1.57195i	0.618260	+	0.785974i	$0.287838\pi$
$113$			177.630i			1.57195i	−0.618260	+	0.785974i	$0.712162\pi$
$114$	−37.8616	+	64.0731i	−0.332120	+	0.562045i
$115$	47.6275	−	47.6275i	0.414152	−	0.414152i
$116$	34.0641	+	14.0737i	0.293656	+	0.121325i
$117$	−19.0103	+	23.7197i	−0.162481	+	0.202733i
$118$	−84.2663	+	126.237i	−0.714122	+	1.06981i
$119$	−246.509			−2.07151
$120$	17.1253	−	121.429i	0.142711	−	1.01191i
$121$			114.739i			0.948257i
$122$	30.1794	−	45.2110i	0.247372	−	0.370582i
$123$	−13.7016	+	0.752766i	−0.111395	+	0.00612005i
$124$	138.871	−	57.6693i	1.11992	−	0.465075i
$125$	86.3222	+	86.3222i	0.690577	+	0.690577i
$126$	66.7036	+	210.719i	0.529394	+	1.67238i
$127$	−152.167			−1.19816			−0.599082	−	0.800687i	$-0.704468\pi$
$127$	−152.167			−1.19816			−0.599082	+	0.800687i	$0.704468\pi$
$128$	−24.5739	+	125.619i	−0.191984	+	0.981398i
$129$	−67.2571	−	60.2517i	−0.521373	−	0.467068i
$130$	−6.74898	−	33.8494i	−0.0519152	−	0.260380i
$131$	65.6955	+	65.6955i	0.501492	+	0.501492i	0.911901	−	0.410409i	$-0.134614\pi$
$131$	65.6955	+	65.6955i	0.501492	+	0.501492i	−0.410409	+	0.911901i	$0.634614\pi$
$132$	9.92584	−	28.3382i	0.0751957	−	0.214684i
$133$	107.699	+	107.699i	0.809769	+	0.809769i
$134$	−49.5599	+	74.2443i	−0.369850	+	0.554062i
$135$	−80.2428	+	112.223i	−0.594391	+	0.831280i
$136$	89.4076	+	133.416i	0.657409	+	0.980997i
$137$	−53.1509			−0.387963			−0.193982	−	0.981005i	$-0.562140\pi$
$137$	−53.1509			−0.387963			−0.193982	+	0.981005i	$0.562140\pi$
$138$	76.6006	−	19.6971i	0.555077	−	0.142732i
$139$	−161.324	−	161.324i	−1.16060	−	1.16060i	−0.984343	−	0.176261i	$-0.943600\pi$
$139$	−161.324	−	161.324i	−1.16060	−	1.16060i	−0.176261	−	0.984343i	$-0.556400\pi$
$140$	−231.950	−	95.8313i	−1.65679	−	0.684509i
$141$	−9.02460	−	164.262i	−0.0640043	−	1.16498i
$142$	−127.730	+	25.4671i	−0.899506	+	0.179346i
$143$		−	8.45118i		−	0.0590992i
$144$	89.8523	−	112.528i	0.623975	−	0.781445i
$145$	47.0811			0.324698
$146$	19.6493	+	98.5505i	0.134584	+	0.675004i
$147$	304.874	−	16.7498i	2.07397	−	0.113945i
$148$	52.3117	+	21.6128i	0.353457	+	0.146032i
$149$	116.911	−	116.911i	0.784638	−	0.784638i	−0.195971	−	0.980610i	$-0.562786\pi$
$149$	116.911	−	116.911i	0.784638	−	0.784638i	0.980610	+	0.195971i	$0.0627859\pi$
$150$	−1.65591	−	6.43972i	−0.0110394	−	0.0429315i
$151$			10.9723i			0.0726643i	0.999340	+	0.0363321i	$0.0115674\pi$
$151$			10.9723i			0.0726643i	−0.999340	+	0.0363321i	$0.988433\pi$
$152$	19.2270	−	97.3509i	0.126493	−	0.640466i
$153$	−19.7933	−	179.591i	−0.129368	−	1.17380i
$154$	−51.1089	−	34.1165i	−0.331876	−	0.221535i
$155$	135.822	−	135.822i	0.876273	−	0.876273i
$156$	13.3981	−	38.2516i	0.0858854	−	0.245203i
$157$	49.8246	−	49.8246i	0.317354	−	0.317354i	−0.530396	−	0.847750i	$-0.677957\pi$
$157$	49.8246	−	49.8246i	0.317354	−	0.317354i	0.847750	+	0.530396i	$0.177957\pi$
$158$	−41.0517	+	8.18501i	−0.259821	+	0.0518038i
$159$	60.9253	−	68.0090i	0.383178	−	0.427730i
$160$	32.2614	+	160.293i	0.201634	+	1.00183i
$161$		−	161.865i		−	1.00537i
$162$	−148.161	+	65.5157i	−0.914574	+	0.404418i
$163$	−66.4240	+	66.4240i	−0.407509	+	0.407509i	−0.880869	−	0.473360i	$-0.843041\pi$
$163$	−66.4240	+	66.4240i	−0.407509	+	0.407509i	0.473360	+	0.880869i	$0.343041\pi$
$164$	16.8972	−	7.01698i	0.103032	−	0.0427864i
$165$	−2.10410	−	38.2980i	−0.0127521	−	0.232109i
$166$	−14.9567	−	9.98399i	−0.0901008	−	0.0601445i
$167$	182.851			1.09492			0.547459	−	0.836832i	$-0.315595\pi$
$167$	182.851			1.09492			0.547459	+	0.836832i	$0.315595\pi$
$168$	−177.242	−	235.443i	−1.05501	−	1.40145i
$169$			157.592i			0.932499i
$170$	170.632	+	113.901i	1.00372	+	0.670006i
$171$	−69.8153	+	87.1106i	−0.408277	+	0.509419i
$172$	111.275	+	45.9736i	0.646946	+	0.267288i
$173$	−123.809	−	123.809i	−0.715661	−	0.715661i	0.252052	−	0.967714i	$-0.418894\pi$
$173$	−123.809	−	123.809i	−0.715661	−	0.715661i	−0.967714	+	0.252052i	$0.918894\pi$
$174$	47.5965	+	28.1254i	0.273543	+	0.161640i
$175$	−13.6078			−0.0777589
$176$	0.0724429	+	40.0350i	0.000411608	+	0.227471i
$177$	−151.911	+	169.574i	−0.858257	+	0.958045i
$178$	326.375	−	65.0734i	1.83357	−	0.365581i
$179$	−168.642	−	168.642i	−0.942134	−	0.942134i	0.0562807	−	0.998415i	$-0.482076\pi$
$179$	−168.642	−	168.642i	−0.942134	−	0.942134i	−0.998415	+	0.0562807i	$0.982076\pi$
$180$	51.1923	−	176.679i	0.284402	−	0.981552i
$181$	−162.162	−	162.162i	−0.895920	−	0.895920i	0.0991520	−	0.995072i	$-0.468387\pi$
$181$	−162.162	−	162.162i	−0.895920	−	0.895920i	−0.995072	+	0.0991520i	$0.968387\pi$
$182$	−68.9880	−	46.0512i	−0.379055	−	0.253029i
$183$	54.4061	−	60.7318i	0.297301	−	0.331868i
$184$	−87.6045	+	58.7076i	−0.476111	+	0.319063i
$185$	72.3018			0.390821
$186$	218.447	−	56.1714i	1.17445	−	0.301997i
$187$	35.5198	+	35.5198i	0.189945	+	0.189945i
$188$	84.1236	+	202.574i	0.447466	+	1.07752i
$189$	54.3430	+	327.053i	0.287529	+	1.73044i
$190$	−24.7856	−	124.312i	−0.130451	−	0.654273i
$191$			60.8777i			0.318731i	0.987220	+	0.159366i	$0.0509449\pi$
$191$			60.8777i			0.318731i	−0.987220	+	0.159366i	$0.949055\pi$
$192$	−63.1418	+	181.320i	−0.328863	+	0.944377i
$193$	177.871			0.921611			0.460806	−	0.887501i	$-0.347561\pi$
$193$	177.871			0.921611			0.460806	+	0.887501i	$0.347561\pi$
$194$	−273.052	+	54.4418i	−1.40748	+	0.280628i
$195$	−2.84016	−	51.6955i	−0.0145649	−	0.265105i
$196$	−375.981	+	156.135i	−1.91827	+	0.796608i
$197$	−66.9411	+	66.9411i	−0.339803	+	0.339803i	−0.856293	−	0.516490i	$-0.827238\pi$
$197$	−66.9411	+	66.9411i	−0.339803	+	0.339803i	0.516490	+	0.856293i	$0.327238\pi$
$198$	20.7514	−	39.9741i	0.104805	−	0.201890i
$199$			0.826328i			0.00415240i	0.999998	+	0.00207620i	$0.000660875\pi$
$199$			0.826328i			0.00415240i	−0.999998	+	0.00207620i	$0.999339\pi$
$200$	4.93548	+	7.36480i	0.0246774	+	0.0368240i
$201$	−89.3443	+	99.7322i	−0.444499	+	0.496180i
$202$	−197.671	+	296.125i	−0.978568	+	1.46597i
$203$	80.0041	−	80.0041i	0.394109	−	0.394109i
$204$	104.457	+	217.080i	0.512046	+	1.06412i
$205$	16.5263	−	16.5263i	0.0806162	−	0.0806162i
$206$	−10.3217	−	51.7685i	−0.0501055	−	0.251303i
$207$	117.925	−	12.9969i	0.569685	−	0.0627868i
$208$	0.0977852	+	54.0401i	0.000470121	+	0.259808i
$209$		−	31.0370i		−	0.148502i
$210$	−324.096	−	191.513i	−1.54332	−	0.911965i
$211$	−181.344	+	181.344i	−0.859448	+	0.859448i	−0.991273	−	0.131825i	$-0.957916\pi$
$211$	−181.344	+	181.344i	−0.859448	+	0.859448i	0.131825	+	0.991273i	$0.457916\pi$
$212$	−46.4876	+	112.519i	−0.219281	+	0.530749i
$213$	−195.072	+	10.7173i	−0.915830	+	0.0503159i
$214$	131.834	−	197.497i	0.616048	−	0.922884i
$215$	153.797			0.715333
$216$	157.298	−	148.032i	0.728230	−	0.685333i
$217$		−	461.601i		−	2.12719i
$218$	−3.60419	+	5.39933i	−0.0165330	+	0.0247676i
$219$	8.26897	+	150.508i	0.0377579	+	0.687253i
$220$	19.6135	+	47.2303i	0.0891524	+	0.214683i
$221$	47.9454	+	47.9454i	0.216947	+	0.216947i
$222$	73.0932	+	43.1918i	0.329249	+	0.194557i
$223$	−17.7339			−0.0795241			−0.0397621	−	0.999209i	$-0.512660\pi$
$223$	−17.7339			−0.0795241			−0.0397621	+	0.999209i	$0.512660\pi$
$224$	327.205	+	217.563i	1.46074	+	0.971261i
$225$	−1.09263	−	9.91380i	−0.00485614	−	0.0440613i
$226$	−69.4654	−	348.402i	−0.307369	−	1.54160i
$227$	−7.53766	−	7.53766i	−0.0332055	−	0.0332055i	0.690309	−	0.723515i	$-0.257475\pi$
$227$	−7.53766	−	7.53766i	−0.0332055	−	0.0332055i	−0.723515	+	0.690309i	$0.757475\pi$
$228$	49.2046	−	140.479i	0.215810	−	0.616136i
$229$	223.748	+	223.748i	0.977063	+	0.977063i	0.999743	−	0.0226794i	$-0.00721971\pi$
$229$	223.748	+	223.748i	0.977063	+	0.977063i	−0.0226794	+	0.999743i	$0.507220\pi$
$230$	−74.7907	+	112.042i	−0.325177	+	0.487139i
$231$	−68.6545	−	61.5036i	−0.297205	−	0.266249i
$232$	−72.3168	−	14.2827i	−0.311710	−	0.0615634i
$233$	123.585			0.530406			0.265203	−	0.964193i	$-0.414561\pi$
$233$	123.585			0.530406			0.265203	+	0.964193i	$0.414561\pi$
$234$	28.0107	−	53.9580i	0.119704	−	0.230590i
$235$	198.127	+	198.127i	0.843095	+	0.843095i
$236$	115.912	−	280.554i	0.491153	−	1.18879i
$237$	−62.6951	+	3.44448i	−0.264536	+	0.0145337i
$238$	483.502	−	96.4019i	2.03152	−	0.405050i
$239$		−	118.501i		−	0.495820i	−0.968783	−	0.247910i	$-0.920256\pi$
$239$		−	118.501i		−	0.495820i	0.968783	−	0.247910i	$-0.0797437\pi$
$240$	13.8976	+	244.868i	0.0579065	+	1.02028i
$241$	−264.162			−1.09611			−0.548053	−	0.836443i	$-0.684631\pi$
$241$	−264.162			−1.09611			−0.548053	+	0.836443i	$0.684631\pi$
$242$	−44.8708	−	225.048i	−0.185416	−	0.929952i
$243$	−233.907	+	65.8515i	−0.962581	+	0.270994i
$244$	−41.5132	+	100.479i	−0.170136	+	0.411798i
$245$	−367.728	+	367.728i	−1.50093	+	1.50093i
$246$	26.5798	−	6.83471i	0.108048	−	0.0277834i
$247$		−	41.8944i		−	0.169613i
$248$	−249.827	+	167.420i	−1.00737	+	0.675081i
$249$	−20.0913	−	17.9987i	−0.0806881	−	0.0722838i
$250$	−203.070	−	135.554i	−0.812278	−	0.542216i
$251$	−152.477	+	152.477i	−0.607478	+	0.607478i	−0.942286	−	0.334808i	$-0.891328\pi$
$251$	−152.477	+	152.477i	−0.607478	+	0.607478i	0.334808	+	0.942286i	$0.391328\pi$
$252$	−213.238	−	387.218i	−0.846181	−	1.53658i
$253$	−23.3233	+	23.3233i	−0.0921869	+	0.0921869i
$254$	298.459	−	59.5076i	1.17504	−	0.234282i
$255$	229.210	+	205.336i	0.898861	+	0.805238i
$256$	−0.926457	−	255.998i	−0.00361897	−	0.999993i
$257$		−	113.118i		−	0.440147i	−0.975483	−	0.220074i	$-0.929370\pi$
$257$		−	113.118i		−	0.440147i	0.975483	−	0.220074i	$-0.0706298\pi$
$258$	155.480	+	91.8753i	0.602636	+	0.356106i
$259$	122.861	−	122.861i	0.474367	−	0.474367i
$260$	26.4748	+	63.7526i	0.101826	+	0.245202i
$261$	64.7099	+	51.8621i	0.247931	+	0.198705i
$262$	−154.546	−	103.163i	−0.589871	−	0.393753i
$263$	−129.324			−0.491727			−0.245864	−	0.969304i	$-0.579072\pi$
$263$	−129.324			−0.491727			−0.245864	+	0.969304i	$0.579072\pi$
$264$	−8.38631	+	59.4641i	−0.0317663	+	0.225243i
$265$			155.516i			0.586853i
$266$	−253.359	−	169.123i	−0.952476	−	0.635801i
$267$	498.446	−	27.3848i	1.86684	−	0.102565i
$268$	68.1719	−	165.004i	0.254373	−	0.615685i
$269$	−129.457	−	129.457i	−0.481253	−	0.481253i	0.424278	−	0.905532i	$-0.360528\pi$
$269$	−129.457	−	129.457i	−0.481253	−	0.481253i	−0.905532	+	0.424278i	$0.860528\pi$
$270$	113.501	−	251.494i	0.420374	−	0.931458i
$271$	170.727			0.629990			0.314995	−	0.949093i	$-0.397997\pi$
$271$	170.727			0.629990			0.314995	+	0.949093i	$0.397997\pi$
$272$	−227.538	−	226.716i	−0.836537	−	0.833515i
$273$	−92.6714	−	83.0189i	−0.339456	−	0.304099i
$274$	104.250	−	20.7856i	0.380474	−	0.0758600i
$275$	1.96076	+	1.96076i	0.00713004	+	0.00713004i
$276$	−142.541	+	68.5897i	−0.516453	+	0.248514i
$277$	114.051	+	114.051i	0.411737	+	0.411737i	0.882343	−	0.470606i	$-0.155965\pi$
$277$	114.051	+	114.051i	0.411737	+	0.411737i	−0.470606	+	0.882343i	$0.655965\pi$
$278$	379.509	+	253.331i	1.36514	+	0.911264i
$279$	336.294	−	37.0640i	1.20535	−	0.132846i
$280$	492.423	+	97.2544i	1.75865	+	0.347337i
$281$	−136.468			−0.485650			−0.242825	−	0.970070i	$-0.578074\pi$
$281$	−136.468			−0.485650			−0.242825	+	0.970070i	$0.578074\pi$
$282$	81.9385	+	318.654i	0.290562	+	1.12998i
$283$	−132.657	−	132.657i	−0.468752	−	0.468752i	0.432758	−	0.901510i	$-0.357540\pi$
$283$	−132.657	−	132.657i	−0.468752	−	0.468752i	−0.901510	+	0.432758i	$0.857540\pi$
$284$	240.569	−	99.9021i	0.847075	−	0.351768i
$285$	−10.4305	−	189.852i	−0.0365982	−	0.666146i
$286$	3.30499	+	16.5761i	0.0115559	+	0.0579584i
$287$		−	56.1658i		−	0.195700i
$288$	−132.230	+	255.850i	−0.459131	+	0.888369i
$289$	−114.022			−0.394541
$290$	−92.3447	+	18.4119i	−0.318430	+	0.0634894i
$291$	−417.010	+	22.9106i	−1.43303	+	0.0787307i
$292$	−77.0799	−	185.612i	−0.263972	−	0.635658i
$293$	143.968	−	143.968i	0.491360	−	0.491360i	−0.417375	−	0.908735i	$-0.637050\pi$
$293$	143.968	−	143.968i	0.491360	−	0.491360i	0.908735	+	0.417375i	$0.137050\pi$
$294$	−591.428	+	152.079i	−2.01166	+	0.517277i
$295$		−	387.764i		−	1.31446i
$296$	−111.056	−	21.9337i	−0.375189	−	0.0741005i
$297$	39.2951	−	54.9557i	0.132307	−	0.185036i
$298$	−183.589	+	275.029i	−0.616069	+	0.922916i
$299$	−31.4823	+	31.4823i	−0.105292	+	0.105292i
$300$	5.76626	+	11.9833i	0.0192209	+	0.0399442i
$301$	261.344	−	261.344i	0.868252	−	0.868252i
$302$	−4.29092	−	21.5210i	−0.0142083	−	0.0712617i
$303$	−356.352	+	397.784i	−1.17608	+	1.31282i
$304$	0.359116	+	198.462i	0.00118130	+	0.652837i
$305$			138.875i			0.455328i
$306$	109.055	+	344.509i	0.356389	+	1.12585i
$307$	−89.3258	+	89.3258i	−0.290964	+	0.290964i	−0.837461	−	0.546497i	$-0.815961\pi$
$307$	−89.3258	+	89.3258i	−0.290964	+	0.290964i	0.546497	+	0.837461i	$0.315961\pi$
$308$	113.587	+	46.9288i	0.368788	+	0.152366i
$309$	−4.34368	−	79.0619i	−0.0140572	−	0.255864i
$310$	−213.285	+	319.517i	−0.688017	+	1.03070i
$311$	314.507			1.01128			0.505638	−	0.862746i	$-0.331257\pi$
$311$	314.507			1.01128			0.505638	+	0.862746i	$0.331257\pi$
$312$	−11.3200	+	80.2660i	−0.0362822	+	0.257263i
$313$		−	103.874i		−	0.331867i	−0.986137	−	0.165934i	$-0.946936\pi$
$313$		−	103.874i		−	0.331867i	0.986137	−	0.165934i	$-0.0530638\pi$
$314$	−78.2408	+	117.210i	−0.249175	+	0.373281i
$315$	−440.625	−	353.142i	−1.39881	−	1.12108i
$316$	77.3178	−	32.1080i	0.244676	−	0.101608i
$317$	321.109	+	321.109i	1.01296	+	1.01296i	0.999915	+	0.0130482i	$0.00415349\pi$
$317$	321.109	+	321.109i	1.01296	+	1.01296i	0.0130482	+	0.999915i	$0.495847\pi$
$318$	−92.9024	+	157.218i	−0.292146	+	0.494398i
$319$	−23.0557			−0.0722750
$320$	−125.963	−	301.782i	−0.393634	−	0.943069i
$321$	237.665	−	265.297i	0.740388	−	0.826472i
$322$	63.3002	+	317.481i	0.196585	+	0.985966i
$323$	176.079	+	176.079i	0.545138	+	0.545138i
$324$	264.981	−	186.443i	0.817843	−	0.575442i
$325$	2.64668	+	2.64668i	0.00814363	+	0.00814363i
$326$	104.307	−	156.260i	0.319961	−	0.479325i
$327$	−6.49746	+	7.25291i	−0.0198699	+	0.0221801i
$328$	−30.3980	+	20.3710i	−0.0926768	+	0.0621068i
$329$	673.348			2.04665
$330$	19.1041	+	74.2945i	0.0578911	+	0.225135i
$331$	−313.858	−	313.858i	−0.948213	−	0.948213i	0.0505107	−	0.998724i	$-0.483915\pi$
$331$	−313.858	−	313.858i	−0.948213	−	0.948213i	−0.998724	+	0.0505107i	$0.983915\pi$
$332$	33.2405	+	13.7334i	0.100122	+	0.0413658i
$333$	99.3740	+	79.6439i	0.298420	+	0.239171i
$334$	−358.643	+	71.5073i	−1.07378	+	0.214094i
$335$		−	228.057i		−	0.680768i
$336$	439.715	+	392.483i	1.30868	+	1.16810i
$337$	−236.028			−0.700380			−0.350190	−	0.936679i	$-0.613883\pi$
$337$	−236.028			−0.700380			−0.350190	+	0.936679i	$0.613883\pi$
$338$	−61.6293	−	309.101i	−0.182335	−	0.914499i
$339$	−29.2330	−	532.088i	−0.0862331	−	1.56958i
$340$	−379.220	−	156.676i	−1.11535	−	0.460812i
$341$	−66.5125	+	66.5125i	−0.195051	+	0.195051i
$342$	102.869	−	198.161i	0.300787	−	0.579417i
$343$			648.069i			1.88941i
$344$	−236.232	−	46.6563i	−0.686722	−	0.135629i
$345$	−134.829	+	150.506i	−0.390809	+	0.436248i
$346$	291.257	+	194.421i	0.841783	+	0.561911i
$347$	−441.946	+	441.946i	−1.27362	+	1.27362i	−0.329445	+	0.944175i	$0.606862\pi$
$347$	−441.946	+	441.946i	−1.27362	+	1.27362i	−0.944175	+	0.329445i	$0.893138\pi$
$348$	−104.354	−	36.5515i	−0.299869	−	0.105033i
$349$	−476.643	+	476.643i	−1.36574	+	1.36574i	−0.499321	+	0.866417i	$0.666417\pi$
$349$	−476.643	+	476.643i	−1.36574	+	1.36574i	−0.866417	+	0.499321i	$0.833583\pi$
$350$	26.6903	−	5.32158i	0.0762579	−	0.0152045i
$351$	53.0414	−	74.1805i	0.151115	−	0.211341i
$352$	−15.7985	−	78.4960i	−0.0448821	−	0.223000i
$353$		−	452.246i		−	1.28115i	−0.767895	−	0.640575i	$-0.778696\pi$
$353$		−	452.246i		−	1.28115i	0.767895	−	0.640575i	$-0.221304\pi$
$354$	231.643	−	392.009i	0.654359	−	1.10737i
$355$	235.289	−	235.289i	0.662785	−	0.662785i
$356$	−614.701	+	255.269i	−1.72669	+	0.717049i
$357$	738.415	−	40.5687i	2.06839	−	0.113638i
$358$	396.724	+	264.823i	1.10817	+	0.739729i
$359$	−617.295			−1.71948			−0.859742	−	0.510728i	$-0.829376\pi$
$359$	−617.295			−1.71948			−0.859742	+	0.510728i	$0.829376\pi$
$360$	−31.3147	+	366.557i	−0.0869853	+	1.01821i
$361$			207.143i			0.573803i
$362$	381.479	+	254.647i	1.05381	+	0.703443i
$363$	−18.8829	−	343.699i	−0.0520190	−	0.946829i
$364$	153.322	+	63.3455i	0.421214	+	0.174026i
$365$	−181.538	−	181.538i	−0.497364	−	0.497364i
$366$	−82.9615	+	140.395i	−0.226671	+	0.383594i
$367$	−11.3588			−0.0309505			−0.0154753	−	0.999880i	$-0.504926\pi$
$367$	−11.3588			−0.0309505			−0.0154753	+	0.999880i	$0.504926\pi$
$368$	148.868	−	149.408i	0.404533	−	0.406000i
$369$	40.9189	−	4.50980i	0.110891	−	0.0122217i
$370$	−141.812	+	28.2749i	−0.383277	+	0.0764187i
$371$	264.266	+	264.266i	0.712306	+	0.712306i
$372$	−406.494	+	195.602i	−1.09272	+	0.525811i
$373$	−59.4092	−	59.4092i	−0.159274	−	0.159274i	0.622971	−	0.782245i	$-0.285925\pi$
$373$	−59.4092	−	59.4092i	−0.159274	−	0.159274i	−0.782245	+	0.622971i	$0.785925\pi$
$374$	−83.5589	−	55.7776i	−0.223419	−	0.149138i
$375$	−272.783	−	244.370i	−0.727421	−	0.651654i
$376$	−244.220	−	364.429i	−0.649520	−	0.969226i
$377$	−31.1212			−0.0825495
$378$	−234.488	−	620.229i	−0.620339	−	1.64082i
$379$	435.432	+	435.432i	1.14890	+	1.14890i	0.986770	+	0.162129i	$0.0518359\pi$
$379$	435.432	+	435.432i	1.14890	+	1.14890i	0.162129	+	0.986770i	$0.448164\pi$
$380$	97.2287	+	234.132i	0.255865	+	0.616136i
$381$	455.813	−	25.0425i	1.19636	−	0.0657283i
$382$	−23.8073	−	119.405i	−0.0623228	−	0.312579i
$383$			272.117i			0.710488i	0.934774	+	0.355244i	$0.115602\pi$
$383$			272.117i			0.710488i	−0.934774	+	0.355244i	$0.884398\pi$
$384$	52.9373	−	380.334i	0.137857	−	0.990452i
$385$	156.992			0.407772
$386$	−348.875	+	69.5596i	−0.903821	+	0.180206i
$387$	211.383	+	169.414i	0.546210	+	0.437763i
$388$	514.271	−	213.563i	1.32544	−	0.550421i
$389$	−260.985	+	260.985i	−0.670913	+	0.670913i	−0.957927	−	0.287013i	$-0.907338\pi$
$389$	−260.985	+	260.985i	−0.670913	+	0.670913i	0.287013	+	0.957927i	$0.407338\pi$
$390$	25.7871	+	100.284i	0.0661208	+	0.257140i
$391$		−	264.636i		−	0.676818i
$392$	676.387	−	453.277i	1.72548	−	1.15632i
$393$	−207.601	−	185.978i	−0.528248	−	0.473226i
$394$	105.119	−	157.476i	0.266800	−	0.399686i
$395$	75.6206	−	75.6206i	0.191445	−	0.191445i
$396$	−25.0690	+	86.5202i	−0.0633055	+	0.218485i
$397$	258.248	−	258.248i	0.650500	−	0.650500i	−0.302614	−	0.953113i	$-0.597859\pi$
$397$	258.248	−	258.248i	0.650500	−	0.650500i	0.953113	+	0.302614i	$0.0978592\pi$
$398$	−0.323150	−	1.62075i	−0.000811935	−	0.00407225i
$399$	−340.336	−	304.887i	−0.852972	−	0.764128i
$400$	−12.5605	−	12.5152i	−0.0314014	−	0.0312879i
$401$			430.073i			1.07250i	0.844059	+	0.536250i	$0.180160\pi$
$401$			430.073i			1.07250i	−0.844059	+	0.536250i	$0.819840\pi$
$402$	136.237	−	230.554i	0.338899	−	0.573517i
$403$	−89.7801	+	89.7801i	−0.222779	+	0.222779i
$404$	271.905	−	658.121i	0.673033	−	1.62901i
$405$	221.897	−	349.367i	0.547894	−	0.862635i
$406$	−125.633	+	188.207i	−0.309440	+	0.463563i
$407$	−35.4063			−0.0869935
$408$	−289.775	−	384.930i	−0.710234	−	0.943456i
$409$			207.501i			0.507337i	0.967291	+	0.253668i	$0.0816372\pi$
$409$			207.501i			0.507337i	−0.967291	+	0.253668i	$0.918363\pi$
$410$	−25.9517	+	38.8776i	−0.0632969	+	0.0948233i
$411$	159.213	−	8.74718i	0.387379	−	0.0212827i
$412$	40.4900	+	97.5019i	0.0982767	+	0.236655i
$413$	−658.921	−	658.921i	−1.59545	−	1.59545i
$414$	−226.214	+	71.6086i	−0.546411	+	0.172968i
$415$	45.9428			0.110706
$416$	−21.3252	−	105.956i	−0.0512624	−	0.254701i
$417$	509.793	+	456.694i	1.22253	+	1.09519i
$418$	12.1376	+	60.8757i	0.0290372	+	0.145636i
$419$	108.717	+	108.717i	0.259467	+	0.259467i	0.824837	−	0.565370i	$-0.191267\pi$
$419$	108.717	+	108.717i	0.259467	+	0.259467i	−0.565370	+	0.824837i	$0.691267\pi$
$420$	710.575	+	248.888i	1.69184	+	0.592591i
$421$	−484.985	−	484.985i	−1.15198	−	1.15198i	−0.986155	−	0.165829i	$-0.946970\pi$
$421$	−484.985	−	484.985i	−1.15198	−	1.15198i	−0.165829	−	0.986155i	$-0.553030\pi$
$422$	284.768	−	426.604i	0.674807	−	1.01091i
$423$	54.0661	+	490.559i	0.127816	+	1.15971i
$424$	47.1779	−	238.873i	0.111269	−	0.563380i
$425$	−22.2476			−0.0523474
$426$	378.421	−	97.3072i	0.888313	−	0.228421i
$427$	235.988	+	235.988i	0.552665	+	0.552665i
$428$	−181.344	+	438.926i	−0.423701	+	1.02553i
$429$	1.39083	+	25.3154i	0.00324203	+	0.0590102i
$430$	−301.656	+	60.1450i	−0.701525	+	0.139872i
$431$		−	213.570i		−	0.495522i	−0.968821	−	0.247761i	$-0.920305\pi$
$431$		−	213.570i		−	0.495522i	0.968821	−	0.247761i	$-0.0796947\pi$
$432$	−250.632	+	351.863i	−0.580167	+	0.814498i
$433$	440.669			1.01771			0.508856	−	0.860852i	$-0.330069\pi$
$433$	440.669			1.01771			0.508856	+	0.860852i	$0.330069\pi$
$434$	180.517	+	905.381i	0.415939	+	2.08613i
$435$	−141.031	+	7.74826i	−0.324209	+	0.0178121i
$436$	4.95772	−	11.9997i	0.0113709	−	0.0275222i
$437$	−115.619	+	115.619i	−0.264574	+	0.264574i
$438$	−75.0777	−	291.973i	−0.171410	−	0.666604i
$439$		−	400.367i		−	0.911998i	−0.889980	−	0.455999i	$-0.849282\pi$
$439$		−	400.367i		−	0.911998i	0.889980	−	0.455999i	$-0.150718\pi$
$440$	−56.9401	−	84.9671i	−0.129409	−	0.193107i
$441$	−910.488	+	100.348i	−2.06460	+	0.227546i
$442$	−112.790	−	75.2899i	−0.255180	−	0.170339i
$443$	324.076	−	324.076i	0.731549	−	0.731549i	−0.239378	−	0.970926i	$-0.576943\pi$
$443$	324.076	−	324.076i	0.731549	−	0.731549i	0.970926	+	0.239378i	$0.0769435\pi$
$444$	−160.256	−	56.1316i	−0.360936	−	0.126423i
$445$	−601.208	+	601.208i	−1.35103	+	1.35103i
$446$	34.7831	−	6.93515i	0.0779891	−	0.0155497i
$447$	−330.965	+	369.446i	−0.740414	+	0.826500i
$448$	−726.860	−	298.766i	−1.62245	−	0.666889i
$449$			691.918i			1.54102i	0.637427	+	0.770510i	$0.279999\pi$
$449$			691.918i			1.54102i	−0.637427	+	0.770510i	$0.720001\pi$
$450$	6.02005	+	19.0176i	0.0133779	+	0.0422613i
$451$	−8.09298	+	8.09298i	−0.0179445	+	0.0179445i
$452$	272.498	+	656.189i	0.602872	+	1.45174i
$453$	−1.80574	−	32.8674i	−0.00398618	−	0.0725549i
$454$	17.7321	+	11.8366i	0.0390574	+	0.0260718i
$455$	211.912			0.465740
$456$	−41.5728	+	294.777i	−0.0911685	+	0.646441i
$457$			385.436i			0.843404i	0.906734	+	0.421702i	$0.138567\pi$
$457$			385.436i			0.843404i	−0.906734	+	0.421702i	$0.861433\pi$
$458$	−526.357	−	351.357i	−1.14925	−	0.767154i
$459$	88.8463	+	534.705i	0.193565	+	1.16494i
$460$	102.878	−	249.006i	0.223648	−	0.541318i
$461$	312.070	+	312.070i	0.676942	+	0.676942i	0.959307	−	0.282365i	$-0.0911190\pi$
$461$	312.070	+	312.070i	0.676942	+	0.676942i	−0.282365	+	0.959307i	$0.591119\pi$
$462$	158.711	+	93.7841i	0.343529	+	0.202996i
$463$	718.961			1.55283			0.776416	−	0.630220i	$-0.217035\pi$
$463$	718.961			1.55283			0.776416	+	0.630220i	$0.217035\pi$
$464$	147.427	−	0.266768i	0.317731	−	0.000574932i
$465$	−384.501	+	429.206i	−0.826884	+	0.923024i
$466$	−242.398	+	48.3300i	−0.520168	+	0.103712i
$467$	82.7894	+	82.7894i	0.177279	+	0.177279i	0.790169	−	0.612889i	$-0.209993\pi$
$467$	82.7894	+	82.7894i	0.177279	+	0.177279i	−0.612889	+	0.790169i	$0.709993\pi$
$468$	−33.8387	+	116.787i	−0.0723049	+	0.249545i
$469$	−387.534	−	387.534i	−0.826298	−	0.826298i
$470$	−466.087	−	311.124i	−0.991674	−	0.661967i
$471$	−141.049	+	157.448i	−0.299467	+	0.334285i
$472$	−117.634	+	595.607i	−0.249224	+	1.26188i
$473$	−75.3145			−0.159227
$474$	121.623	−	31.2740i	0.256588	−	0.0659790i
$475$	9.71993	+	9.71993i	0.0204630	+	0.0204630i
$476$	−910.638	+	378.164i	−1.91311	+	0.794463i
$477$	−171.308	+	213.746i	−0.359137	+	0.448106i
$478$	46.3419	+	232.427i	0.0969497	+	0.486249i
$479$		−	749.099i		−	1.56388i	−0.623353	−	0.781941i	$-0.714230\pi$
$479$		−	749.099i		−	1.56388i	0.623353	−	0.781941i	$-0.285770\pi$
$480$	−123.018	−	474.847i	−0.256288	−	0.989265i
$481$	−47.7923			−0.0993603
$482$	518.125	−	103.305i	1.07495	−	0.214326i
$483$	26.6385	+	484.864i	0.0551523	+	1.00386i
$484$	176.018	+	423.861i	0.363675	+	0.875746i
$485$	502.983	−	502.983i	1.03708	−	1.03708i
$486$	433.032	−	220.634i	0.891012	−	0.453980i
$487$			533.210i			1.09489i	0.836843	+	0.547443i	$0.184399\pi$
$487$			533.210i			1.09489i	−0.836843	+	0.547443i	$0.815601\pi$
$488$	42.1297	−	213.313i	0.0863313	−	0.437116i
$489$	188.040	−	209.904i	0.384541	−	0.429251i
$490$	577.453	−	865.067i	1.17848	−	1.76544i
$491$	6.75013	−	6.75013i	0.0137477	−	0.0137477i	−0.700200	−	0.713947i	$-0.746906\pi$
$491$	6.75013	−	6.75013i	0.0137477	−	0.0137477i	0.713947	+	0.700200i	$0.246906\pi$
$492$	−49.4605	+	23.8000i	−0.100530	+	0.0483741i
$493$	130.800	−	130.800i	0.265315	−	0.265315i
$494$	16.3836	+	82.1715i	0.0331651	+	0.166339i
$495$	12.6056	+	114.375i	0.0254658	+	0.231060i
$496$	424.537	−	426.076i	0.855921	−	0.859025i
$497$		−	799.644i		−	1.60894i
$498$	46.4457	+	27.4454i	0.0932645	+	0.0551112i
$499$	556.347	−	556.347i	1.11492	−	1.11492i	0.122448	−	0.992475i	$-0.460925\pi$
$499$	556.347	−	556.347i	1.11492	−	1.11492i	0.992475	−	0.122448i	$-0.0390746\pi$
$500$	451.310	+	186.461i	0.902620	+	0.372921i
$501$	−547.728	+	30.0923i	−1.09327	+	0.0600645i
$502$	239.439	−	358.696i	0.476969	−	0.714534i
$503$	−304.892			−0.606147			−0.303074	−	0.952967i	$-0.598013\pi$
$503$	−304.892			−0.606147			−0.303074	+	0.952967i	$0.598013\pi$
$504$	569.672	+	676.097i	1.13030	+	1.34146i
$505$		−	909.612i		−	1.80121i
$506$	36.6251	−	54.8671i	0.0723817	−	0.108433i
$507$	−25.9354	−	472.065i	−0.0511546	−	0.931095i
$508$	−562.125	+	233.436i	−1.10654	+	0.459519i
$509$	118.591	+	118.591i	0.232988	+	0.232988i	0.813939	−	0.580951i	$-0.197319\pi$
$509$	118.591	+	118.591i	0.232988	+	0.232988i	−0.580951	+	0.813939i	$0.697319\pi$
$510$	−529.870	−	313.107i	−1.03896	−	0.613936i
$511$	−616.968			−1.20737
$512$	101.930	+	501.751i	0.199082	+	0.979983i
$513$	194.795	−	272.428i	0.379716	−	0.531049i
$514$	44.2368	+	221.869i	0.0860638	+	0.431651i
$515$	95.3617	+	95.3617i	0.185168	+	0.185168i
$516$	−340.887	−	119.400i	−0.660634	−	0.231396i
$517$	−97.0233	−	97.0233i	−0.187666	−	0.187666i
$518$	−192.932	+	289.026i	−0.372456	+	0.557966i
$519$	391.244	+	350.493i	0.753843	+	0.675324i
$520$	−76.8591	−	114.691i	−0.147806	−	0.220559i
$521$	105.077			0.201683			0.100842	−	0.994902i	$-0.467846\pi$
$521$	105.077			0.201683			0.100842	+	0.994902i	$0.467846\pi$
$522$	−147.203	−	76.4161i	−0.281998	−	0.146391i
$523$	−479.455	−	479.455i	−0.916740	−	0.916740i	0.0800507	−	0.996791i	$-0.474492\pi$
$523$	−479.455	−	479.455i	−0.916740	−	0.916740i	−0.996791	+	0.0800507i	$0.974492\pi$
$524$	343.470	+	141.906i	0.655476	+	0.270813i
$525$	40.7619	−	2.23947i	0.0776418	−	0.00426566i
$526$	253.656	−	50.5746i	0.482235	−	0.0961494i
$527$		−	754.679i		−	1.43203i
$528$	−6.80566	−	119.912i	−0.0128895	−	0.227106i
$529$	−355.232			−0.671517
$530$	−60.8174	−	305.028i	−0.114750	−	0.575525i
$531$	427.141	−	532.956i	0.804408	−	1.00368i
$532$	563.074	+	232.636i	1.05841	+	0.437287i
$533$	−10.9241	+	10.9241i	−0.0204955	+	0.0204955i
$534$	−966.940	+	248.639i	−1.81075	+	0.465615i
$535$			606.655i			1.13393i
$536$	−69.1843	+	350.297i	−0.129075	+	0.653539i
$537$	532.918	+	477.410i	0.992399	+	0.889032i
$538$	304.543	+	203.290i	0.566065	+	0.377862i
$539$	180.077	−	180.077i	0.334095	−	0.334095i
$540$	−124.269	+	537.665i	−0.230128	+	0.995675i
$541$	726.230	−	726.230i	1.34238	−	1.34238i	0.448704	−	0.893680i	$-0.351886\pi$
$541$	726.230	−	726.230i	1.34238	−	1.34238i	0.893680	−	0.448704i	$-0.148114\pi$
$542$	−334.864	+	66.7660i	−0.617829	+	0.123184i
$543$	512.439	+	459.065i	0.943719	+	0.845423i
$544$	534.953	+	355.697i	0.983370	+	0.653854i
$545$		−	16.5852i		−	0.0304316i
$546$	214.231	+	126.592i	0.392365	+	0.231854i
$547$	314.507	−	314.507i	0.574966	−	0.574966i	−0.358546	−	0.933512i	$-0.616727\pi$
$547$	314.507	−	314.507i	0.574966	−	0.574966i	0.933512	+	0.358546i	$0.116727\pi$
$548$	−196.347	+	81.5376i	−0.358297	+	0.148791i
$549$	−152.978	+	190.875i	−0.278648	+	0.347677i
$550$	−4.61261	−	3.07903i	−0.00838657	−	0.00559824i
$551$	−114.292			−0.207427
$552$	252.756	−	190.275i	0.457891	−	0.344701i
$553$		−	257.002i		−	0.464741i
$554$	−268.301	−	179.097i	−0.484298	−	0.323281i
$555$	−216.579	+	11.8989i	−0.390232	+	0.0214394i
$556$	−843.436	−	348.469i	−1.51697	−	0.626743i
$557$	−134.274	−	134.274i	−0.241066	−	0.241066i	0.576225	−	0.817291i	$-0.304525\pi$
$557$	−134.274	−	134.274i	−0.241066	−	0.241066i	−0.817291	+	0.576225i	$0.804525\pi$
$558$	−645.110	+	204.211i	−1.15611	+	0.365969i
$559$	−101.661			−0.181863
$560$	−1003.87	+	1.81649i	−1.79262	+	0.00324373i
$561$	−112.244	−	100.553i	−0.200079	−	0.179239i
$562$	267.667	−	53.3681i	0.476275	−	0.0949610i
$563$	−102.810	−	102.810i	−0.182612	−	0.182612i	0.609881	−	0.792493i	$-0.291217\pi$
$563$	−102.810	−	102.810i	−0.182612	−	0.182612i	−0.792493	+	0.609881i	$0.791217\pi$
$564$	−285.329	−	592.962i	−0.505902	−	1.05135i
$565$	641.785	+	641.785i	1.13590	+	1.13590i
$566$	312.070	+	208.315i	0.551361	+	0.368047i
$567$	−216.608	−	970.739i	−0.382024	−	1.71206i
$568$	−432.783	+	290.026i	−0.761941	+	0.510610i
$569$	−78.4572			−0.137886			−0.0689430	−	0.997621i	$-0.521963\pi$
$569$	−78.4572			−0.137886			−0.0689430	+	0.997621i	$0.521963\pi$
$570$	94.7032	+	368.295i	0.166146	+	0.646131i
$571$	363.164	+	363.164i	0.636013	+	0.636013i	0.949570	−	0.313556i	$-0.101520\pi$
$571$	363.164	+	363.164i	0.636013	+	0.636013i	−0.313556	+	0.949570i	$0.601520\pi$
$572$	−12.9648	−	31.2198i	−0.0226657	−	0.0545800i
$573$	−10.0188	−	182.358i	−0.0174848	−	0.318251i
$574$	21.9646	+	110.163i	0.0382659	+	0.191922i
$575$		−	14.6084i		−	0.0254060i
$576$	159.300	−	553.534i	0.276562	−	0.960996i
$577$	−566.880			−0.982460			−0.491230	−	0.871030i	$-0.663453\pi$
$577$	−566.880			−0.982460			−0.491230	+	0.871030i	$0.663453\pi$
$578$	223.643	−	44.5905i	0.386925	−	0.0771462i
$579$	−532.809	+	29.2727i	−0.920223	+	0.0505573i
$580$	173.924	−	72.2261i	0.299869	−	0.124528i
$581$	78.0698	−	78.0698i	0.134371	−	0.134371i
$582$	808.962	−	208.016i	1.38997	−	0.357416i
$583$		−	76.1565i		−	0.130629i
$584$	223.771	+	333.915i	0.383170	+	0.571772i
$585$	17.0153	+	154.385i	0.0290860	+	0.263907i
$586$	−226.077	+	338.680i	−0.385798	+	0.577953i
$587$	−73.3693	+	73.3693i	−0.124990	+	0.124990i	−0.766835	−	0.641845i	$-0.778169\pi$
$587$	−73.3693	+	73.3693i	−0.124990	+	0.124990i	0.641845	+	0.766835i	$0.278169\pi$
$588$	1100.55	−	529.576i	1.87168	−	0.900640i
$589$	−329.717	+	329.717i	−0.559792	+	0.559792i
$590$	151.642	+	760.559i	0.257021	+	1.28908i
$591$	189.504	−	211.538i	0.320650	−	0.357932i
$592$	226.402	−	0.409672i	0.382436	−	0.000692014i
$593$			458.708i			0.773538i	0.922177	+	0.386769i	$0.126409\pi$
$593$			458.708i			0.773538i	−0.922177	+	0.386769i	$0.873591\pi$
$594$	−55.5817	+	123.157i	−0.0935719	+	0.207335i
$595$	−890.650	+	890.650i	−1.49689	+	1.49689i
$596$	252.534	−	611.236i	0.423716	−	1.02556i
$597$	−0.135991	−	2.47525i	−0.000227790	−	0.00414615i
$598$	49.4375	−	74.0609i	0.0826714	−	0.123848i
$599$	423.611			0.707197			0.353599	−	0.935397i	$-0.384958\pi$
$599$	423.611			0.707197			0.353599	+	0.935397i	$0.384958\pi$
$600$	−15.9962	−	21.2489i	−0.0266603	−	0.0354148i
$601$			795.376i			1.32342i	0.749759	+	0.661711i	$0.230169\pi$
$601$			795.376i			1.32342i	−0.749759	+	0.661711i	$0.769831\pi$
$602$	−410.395	+	614.802i	−0.681719	+	1.02126i
$603$	251.216	−	313.450i	0.416610	−	0.519817i
$604$	16.8324	+	40.5332i	0.0278682	+	0.0671079i
$605$	414.557	+	414.557i	0.685219	+	0.685219i
$606$	543.385	−	919.569i	0.896675	−	1.51744i
$607$	−631.699			−1.04069			−0.520345	−	0.853956i	$-0.674197\pi$
$607$	−631.699			−1.04069			−0.520345	+	0.853956i	$0.674197\pi$
$608$	−78.3167	−	389.123i	−0.128810	−	0.640004i
$609$	−226.484	+	252.817i	−0.371896	+	0.415135i
$610$	−54.3096	−	272.389i	−0.0890322	−	0.446539i
$611$	−130.964	−	130.964i	−0.214344	−	0.214344i
$612$	−348.626	−	633.070i	−0.569650	−	1.03443i
$613$	385.264	+	385.264i	0.628490	+	0.628490i	0.947688	−	0.319198i	$-0.103414\pi$
$613$	385.264	+	385.264i	0.628490	+	0.628490i	−0.319198	+	0.947688i	$0.603414\pi$
$614$	140.271	−	210.136i	0.228454	−	0.342240i
$615$	−46.7846	+	52.2241i	−0.0760724	+	0.0849173i
$616$	−241.140	−	47.6257i	−0.391462	−	0.0773144i
$617$	−953.333			−1.54511			−0.772555	−	0.634947i	$-0.781022\pi$
$617$	−953.333			−1.54511			−0.772555	+	0.634947i	$0.781022\pi$
$618$	39.4382	+	153.373i	0.0638159	+	0.248176i
$619$	−574.046	−	574.046i	−0.927377	−	0.927377i	0.0701591	−	0.997536i	$-0.477649\pi$
$619$	−574.046	−	574.046i	−0.927377	−	0.927377i	−0.997536	+	0.0701591i	$0.977649\pi$
$620$	293.384	−	710.108i	0.473200	−	1.14533i
$621$	−351.103	+	58.3390i	−0.565383	+	0.0939437i
$622$	−616.872	+	122.994i	−0.991755	+	0.197739i
$623$			2043.24i			3.27969i
$624$	−9.18644	−	161.860i	−0.0147219	−	0.259391i
$625$	651.477			1.04236
$626$	40.6220	+	203.739i	0.0648914	+	0.325461i
$627$	5.10783	+	92.9707i	0.00814646	+	0.148279i
$628$	107.624	−	260.493i	0.171375	−	0.414798i
$629$	200.868	−	200.868i	0.319345	−	0.319345i
$630$	1002.34	+	520.336i	1.59102	+	0.825930i
$631$		−	138.048i		−	0.218777i	−0.993999	−	0.109389i	$-0.965111\pi$
$631$		−	138.048i		−	0.218777i	0.993999	−	0.109389i	$-0.0348893\pi$
$632$	−139.094	+	93.2130i	−0.220086	+	0.147489i
$633$	513.367	−	573.056i	0.811007	−	0.905301i
$634$	−755.397	−	504.246i	−1.19148	−	0.795341i
$635$	−549.786	+	549.786i	−0.865805	+	0.865805i
$636$	120.735	−	344.698i	0.189835	−	0.541979i
$637$	243.072	−	243.072i	0.381589	−	0.381589i
$638$	45.2214	−	9.01636i	0.0708799	−	0.0141322i
$639$	582.570	−	64.2069i	0.911691	−	0.100480i
$640$	365.080	+	542.654i	0.570438	+	0.847896i
$641$		−	784.889i		−	1.22448i	−0.790673	−	0.612238i	$-0.790269\pi$
$641$		−	784.889i		−	1.22448i	0.790673	−	0.612238i	$-0.209731\pi$
$642$	−362.404	+	613.296i	−0.564493	+	0.955289i
$643$	−238.456	+	238.456i	−0.370850	+	0.370850i	−0.867787	−	0.496937i	$-0.834458\pi$
$643$	−238.456	+	238.456i	−0.370850	+	0.370850i	0.496937	+	0.867787i	$0.334458\pi$
$644$	−248.313	−	597.951i	−0.385580	−	0.928495i
$645$	−460.695	+	25.3107i	−0.714256	+	0.0392414i
$646$	−414.220	−	276.502i	−0.641208	−	0.428022i
$647$	681.751			1.05371			0.526855	−	0.849955i	$-0.323371\pi$
$647$	681.751			1.05371			0.526855	+	0.849955i	$0.323371\pi$
$648$	−446.820	+	469.314i	−0.689538	+	0.724250i
$649$			189.889i			0.292587i
$650$	−6.22621	−	4.15615i	−0.00957879	−	0.00639408i
$651$	75.9668	+	1382.72i	0.116693	+	2.12399i
$652$	−143.480	+	347.279i	−0.220061	+	0.532636i
$653$	−636.071	−	636.071i	−0.974075	−	0.974075i	0.0255977	−	0.999672i	$-0.491851\pi$
$653$	−636.071	−	636.071i	−0.974075	−	0.974075i	−0.999672	+	0.0255977i	$0.991851\pi$
$654$	9.90770	−	16.7668i	0.0151494	−	0.0256372i
$655$	474.721			0.724766
$656$	51.6560	−	51.8433i	0.0787439	−	0.0790294i
$657$	−49.5391	−	449.485i	−0.0754020	−	0.684147i
$658$	−1320.70	+	263.325i	−2.00714	+	0.400190i
$659$	91.6052	+	91.6052i	0.139006	+	0.139006i	0.773186	−	0.634179i	$-0.218662\pi$
$659$	91.6052	+	91.6052i	0.139006	+	0.139006i	−0.634179	+	0.773186i	$0.718662\pi$
$660$	−66.5248	−	138.250i	−0.100795	−	0.209469i
$661$	721.715	+	721.715i	1.09185	+	1.09185i	0.995331	+	0.0965216i	$0.0307717\pi$
$661$	721.715	+	721.715i	1.09185	+	1.09185i	0.0965216	+	0.995331i	$0.469228\pi$
$662$	738.340	+	492.860i	1.11532	+	0.744502i
$663$	−151.510	−	135.729i	−0.228522	−	0.204720i
$664$	−70.5684	−	13.9374i	−0.106278	−	0.0209900i
$665$	778.245			1.17029
$666$	−226.058	−	117.351i	−0.339426	−	0.176203i
$667$	85.8871	+	85.8871i	0.128766	+	0.128766i
$668$	675.477	−	280.508i	1.01119	−	0.419922i
$669$	53.1215	−	2.91851i	0.0794044	−	0.00436250i
$670$	89.1859	+	447.310i	0.133113	+	0.667627i
$671$		−	68.0074i		−	0.101352i
$672$	−1015.94	−	597.856i	−1.51182	−	0.889666i
$673$	417.305			0.620067			0.310033	−	0.950726i	$-0.399660\pi$
$673$	417.305			0.620067			0.310033	+	0.950726i	$0.399660\pi$
$674$	462.944	−	92.3031i	0.686861	−	0.136948i
$675$	4.90449	+	29.5168i	0.00726592	+	0.0437286i
$676$	241.759	+	582.167i	0.357631	+	0.861194i
$677$	−585.326	+	585.326i	−0.864587	+	0.864587i	−0.991867	−	0.127280i	$-0.959375\pi$
$677$	−585.326	+	585.326i	−0.864587	+	0.864587i	0.127280	+	0.991867i	$0.459375\pi$
$678$	265.420	+	1032.20i	0.391475	+	1.52242i
$679$		−	1709.42i		−	2.51756i
$680$	805.070	+	159.003i	1.18393	+	0.233828i
$681$	23.8194	+	21.3384i	0.0349771	+	0.0313340i
$682$	104.446	−	156.468i	0.153147	−	0.229425i
$683$	104.261	−	104.261i	0.152651	−	0.152651i	−0.626650	−	0.779301i	$-0.715574\pi$
$683$	104.261	−	104.261i	0.152651	−	0.152651i	0.779301	+	0.626650i	$0.215574\pi$
$684$	−124.273	+	428.900i	−0.181685	+	0.627047i
$685$	−192.037	+	192.037i	−0.280346	+	0.280346i
$686$	−253.439	−	1271.12i	−0.369445	−	1.85294i
$687$	−707.054	−	633.409i	−1.02919	−	0.921993i
$688$	481.590	−	0.871434i	0.699986	−	0.00126662i
$689$		−	102.798i		−	0.149199i
$690$	205.595	−	347.928i	0.297964	−	0.504243i
$691$	−335.701	+	335.701i	−0.485818	+	0.485818i	−0.906984	−	0.421165i	$-0.861621\pi$
$691$	−335.701	+	335.701i	−0.485818	+	0.485818i	0.421165	+	0.906984i	$0.361621\pi$
$692$	−647.301	−	267.435i	−0.935406	−	0.386467i
$693$	215.775	+	172.934i	0.311364	+	0.249544i
$694$	693.999	−	1039.66i	0.999999	−	1.49807i
$695$	−1165.74			−1.67733
$696$	218.974	+	30.8822i	0.314618	+	0.0443710i
$697$		−	91.8264i		−	0.131745i
$698$	748.484	−	1121.28i	1.07233	−	1.60642i
$699$	−370.196	+	20.3386i	−0.529608	+	0.0290968i
$700$	−50.2690	+	20.8754i	−0.0718129	+	0.0298220i
$701$	490.458	+	490.458i	0.699655	+	0.699655i	0.964336	−	0.264681i	$-0.0852666\pi$
$701$	490.458	+	490.458i	0.699655	+	0.699655i	−0.264681	+	0.964336i	$0.585267\pi$
$702$	−75.0255	+	166.240i	−0.106874	+	0.236809i
$703$	−175.517			−0.249669
$704$	61.6843	+	147.783i	0.0876198	+	0.209920i
$705$	−626.093	−	560.881i	−0.888075	−	0.795575i
$706$	176.859	+	887.033i	0.250508	+	1.25642i
$707$	−1545.69	−	1545.69i	−2.18626	−	2.18626i
$708$	−301.041	+	859.472i	−0.425200	+	1.21394i
$709$	435.817	+	435.817i	0.614692	+	0.614692i	0.944165	−	0.329473i	$-0.106871\pi$
$709$	435.817	+	435.817i	0.614692	+	0.614692i	−0.329473	+	0.944165i	$0.606871\pi$
$710$	−369.480	+	553.508i	−0.520394	+	0.779589i
$711$	187.235	−	20.6358i	0.263341	−	0.0290236i
$712$	1105.84	−	741.074i	1.55315	−	1.04083i
$713$	495.544			0.695012
$714$	−1432.46	+	368.341i	−2.00624	+	0.515884i
$715$	−30.5345	−	30.5345i	−0.0427056	−	0.0427056i
$716$	−881.696	−	364.276i	−1.23142	−	0.508765i
$717$	19.5020	+	354.968i	0.0271994	+	0.495073i
$718$	1210.76	−	241.404i	1.68629	−	0.336218i
$719$			1083.05i			1.50633i	0.657831	+	0.753166i	$0.271474\pi$
$719$			1083.05i			1.50633i	−0.657831	+	0.753166i	$0.728526\pi$
$720$	−81.9284	−	731.210i	−0.113789	−	1.01557i
$721$	324.093			0.449505
$722$	−81.0069	−	406.288i	−0.112198	−	0.562726i
$723$	791.292	−	43.4738i	1.09446	−	0.0601297i
$724$	−847.814	−	350.278i	−1.17101	−	0.483809i
$725$	7.22042	−	7.22042i	0.00995921	−	0.00995921i
$726$	171.446	+	666.744i	0.236152	+	0.918380i
$727$			513.215i			0.705935i	0.935636	+	0.352968i	$0.114827\pi$
$727$			513.215i			0.705935i	−0.935636	+	0.352968i	$0.885173\pi$
$728$	−325.497	−	64.2863i	−0.447111	−	0.0883053i
$729$	689.828	−	235.752i	0.946266	−	0.323390i
$730$	427.061	+	285.074i	0.585015	+	0.390512i
$731$	427.276	−	427.276i	0.584508	−	0.584508i
$732$	107.816	−	307.814i	0.147290	−	0.420511i
$733$	73.6001	−	73.6001i	0.100409	−	0.100409i	−0.655118	−	0.755527i	$-0.727381\pi$
$733$	73.6001	−	73.6001i	0.100409	−	0.100409i	0.755527	+	0.655118i	$0.227381\pi$
$734$	22.2791	−	4.44208i	0.0303531	−	0.00605188i
$735$	1041.01	−	1162.04i	1.41633	−	1.58101i
$736$	−233.561	+	351.265i	−0.317338	+	0.477263i
$737$			111.680i			0.151533i
$738$	−78.4944	+	24.8475i	−0.106361	+	0.0336688i
$739$	152.386	−	152.386i	0.206206	−	0.206206i	−0.596447	−	0.802653i	$-0.703421\pi$
$739$	152.386	−	152.386i	0.206206	−	0.206206i	0.802653	+	0.596447i	$0.203421\pi$
$740$	267.092	−	110.917i	0.360936	−	0.149887i
$741$	6.89467	+	125.494i	0.00930455	+	0.169358i
$742$	−621.675	−	414.983i	−0.837837	−	0.559277i
$743$	574.044			0.772603			0.386302	−	0.922373i	$-0.373752\pi$
$743$	574.044			0.772603			0.386302	+	0.922373i	$0.373752\pi$
$744$	720.800	−	542.619i	0.968818	−	0.729326i
$745$		−	844.811i		−	1.13397i
$746$	139.758	+	93.2919i	0.187343	+	0.125056i
$747$	63.1454	+	50.6082i	0.0845319	+	0.0677486i
$748$	185.705	+	76.7246i	0.248268	+	0.102573i
$749$	1030.88	+	1030.88i	1.37634	+	1.37634i
$750$	630.600	+	372.630i	0.840800	+	0.496840i
$751$	−1014.28			−1.35058			−0.675289	−	0.737553i	$-0.735981\pi$
$751$	−1014.28			−1.35058			−0.675289	+	0.737553i	$0.735981\pi$
$752$	621.527	+	619.282i	0.826499	+	0.823513i
$753$	431.649	−	481.836i	0.573239	−	0.639888i
$754$	61.0408	−	12.1705i	0.0809560	−	0.0161412i
$755$	39.6435	+	39.6435i	0.0525079	+	0.0525079i
$756$	702.475	+	1124.81i	0.929200	+	1.48785i
$757$	−1003.73	−	1003.73i	−1.32594	−	1.32594i	−0.908880	−	0.417057i	$-0.863062\pi$
$757$	−1003.73	−	1003.73i	−1.32594	−	1.32594i	−0.417057	−	0.908880i	$-0.636938\pi$
$758$	−1024.34	−	683.771i	−1.35137	−	0.902072i
$759$	66.0261	−	73.7028i	0.0869909	−	0.0971052i
$760$	−282.265	−	421.201i	−0.371402	−	0.554212i
$761$	−54.1069			−0.0710997			−0.0355499	−	0.999368i	$-0.511318\pi$
$761$	−54.1069			−0.0710997			−0.0355499	+	0.999368i	$0.511318\pi$
$762$	−884.236	+	227.372i	−1.16042	+	0.298389i
$763$	−28.1829	−	28.1829i	−0.0369370	−	0.0369370i
$764$	93.3911	+	224.890i	0.122240	+	0.294359i
$765$	−720.386	−	577.358i	−0.941681	−	0.754716i
$766$	−106.416	−	533.728i	−0.138925	−	0.696773i
$767$			256.316i			0.334181i
$768$	44.9055	+	766.686i	0.0584707	+	0.998289i
$769$	143.904			0.187132			0.0935659	−	0.995613i	$-0.470173\pi$
$769$	143.904			0.187132			0.0935659	+	0.995613i	$0.470173\pi$
$770$	−307.923	+	61.3946i	−0.399900	+	0.0797332i
$771$	18.6161	+	338.843i	0.0241454	+	0.439485i
$772$	657.079	−	272.868i	0.851138	−	0.353456i
$773$	−339.143	+	339.143i	−0.438736	+	0.438736i	−0.891586	−	0.452850i	$-0.850407\pi$
$773$	−339.143	+	339.143i	−0.438736	+	0.438736i	0.452850	+	0.891586i	$0.350407\pi$
$774$	−480.858	−	249.623i	−0.621264	−	0.322510i
$775$		−	41.6598i		−	0.0537546i
$776$	−925.171	+	619.997i	−1.19223	+	0.798965i
$777$	−347.809	+	388.248i	−0.447630	+	0.499676i
$778$	409.832	−	613.958i	0.526776	−	0.789149i
$779$	−40.1187	+	40.1187i	−0.0515003	+	0.0515003i
$780$	−89.7967	−	186.613i	−0.115124	−	0.239247i
$781$	−115.221	+	115.221i	−0.147531	+	0.147531i
$782$	103.491	+	519.055i	0.132341	+	0.663754i
$783$	−202.372	−	144.703i	−0.258458	−	0.184805i
$784$	−1149.40	+	1153.57i	−1.46607	+	1.47139i
$785$		−	360.037i		−	0.458646i
$786$	479.918	+	283.590i	0.610583	+	0.360801i
$787$	−924.878	+	924.878i	−1.17519	+	1.17519i	−0.194241	+	0.980954i	$0.562224\pi$
$787$	−924.878	+	924.878i	−1.17519	+	1.17519i	−0.980954	+	0.194241i	$0.937776\pi$
$788$	−144.596	+	349.982i	−0.183498	+	0.444140i
$789$	387.389	−	21.2832i	0.490987	−	0.0269749i
$790$	−118.749	+	177.895i	−0.150315	+	0.225183i
$791$	2181.15			2.75746
$792$	15.3349	−	179.504i	0.0193622	−	0.226646i
$793$		−	91.7980i		−	0.115760i
$794$	−405.534	+	607.519i	−0.510748	+	0.765138i
$795$	−25.5937	−	465.846i	−0.0321933	−	0.585970i
$796$	1.26765	+	3.05256i	0.00159252	+	0.00383488i
$797$	−707.837	−	707.837i	−0.888127	−	0.888127i	0.106216	−	0.994343i	$-0.466127\pi$
$797$	−707.837	−	707.837i	−0.888127	−	0.888127i	−0.994343	+	0.106216i	$0.966127\pi$
$798$	786.764	+	464.909i	0.985920	+	0.582593i
$799$	1100.87			1.37781
$800$	29.5305	+	19.6352i	0.0369131	+	0.0245439i
$801$	−1488.58	+	164.061i	−1.85840	+	0.204820i
$802$	−168.188	−	843.542i	−0.209710	−	1.05180i
$803$	88.8995	+	88.8995i	0.110709	+	0.110709i
$804$	−177.053	+	505.485i	−0.220215	+	0.628712i
$805$	−584.826	−	584.826i	−0.726492	−	0.726492i
$806$	140.984	−	211.204i	0.174918	−	0.262040i
$807$	409.092	+	366.482i	0.506929	+	0.454128i
$808$	−275.943	+	1397.17i	−0.341514	+	1.72917i
$809$	−1107.83			−1.36938			−0.684689	−	0.728836i	$-0.740062\pi$
$809$	−1107.83			−1.36938			−0.684689	+	0.728836i	$0.740062\pi$
$810$	−298.602	+	772.024i	−0.368644	+	0.953116i
$811$	217.697	+	217.697i	0.268431	+	0.268431i	0.828468	−	0.560037i	$-0.189213\pi$
$811$	217.697	+	217.697i	0.268431	+	0.268431i	−0.560037	+	0.828468i	$0.689213\pi$
$812$	172.813	−	418.278i	0.212824	−	0.515121i
$813$	−511.411	+	28.0970i	−0.629042	+	0.0345597i
$814$	69.4458	−	13.8463i	0.0853142	−	0.0170102i
$815$			479.986i			0.588940i
$816$	718.897	+	641.678i	0.881002	+	0.786370i
$817$	−373.351			−0.456978
$818$	−81.1469	−	406.991i	−0.0992016	−	0.497544i
$819$	291.258	+	233.431i	0.355627	+	0.285019i
$820$	35.6978	−	86.4031i	0.0435339	−	0.105370i
$821$	761.374	−	761.374i	0.927374	−	0.927374i	−0.0701619	−	0.997536i	$-0.522352\pi$
$821$	761.374	−	761.374i	0.927374	−	0.927374i	0.997536	+	0.0701619i	$0.0223516\pi$
$822$	−308.858	+	79.4197i	−0.375740	+	0.0966176i
$823$		−	46.9015i		−	0.0569884i	−0.999594	−	0.0284942i	$-0.990929\pi$
$823$		−	46.9015i		−	0.0569884i	0.999594	−	0.0284942i	$-0.00907122\pi$
$824$	−117.547	−	175.405i	−0.142654	−	0.212870i
$825$	−6.19611	−	5.55074i	−0.00751044	−	0.00672817i
$826$	1550.09	+	1034.72i	1.87662	+	1.25269i
$827$	116.383	−	116.383i	0.140729	−	0.140729i	−0.633232	−	0.773962i	$-0.718272\pi$
$827$	116.383	−	116.383i	0.140729	−	0.140729i	0.773962	+	0.633232i	$0.218272\pi$
$828$	415.691	−	228.918i	0.502043	−	0.276471i
$829$	821.995	−	821.995i	0.991550	−	0.991550i	−0.00841482	−	0.999965i	$-0.502679\pi$
$829$	821.995	−	821.995i	0.991550	−	0.991550i	0.999965	+	0.00841482i	$0.00267855\pi$
$830$	−90.1120	+	17.9668i	−0.108569	+	0.0216467i
$831$	−360.408	−	322.868i	−0.433704	−	0.388530i
$832$	83.2630	+	199.481i	0.100076	+	0.239761i
$833$			2043.23i			2.45286i
$834$	−1178.50	−	696.393i	−1.41307	−	0.835004i
$835$	660.650	−	660.650i	0.791198	−	0.791198i
$836$	−47.6131	−	114.655i	−0.0569535	−	0.137147i
$837$	−1001.26	+	166.369i	−1.19625	+	0.198768i
$838$	−255.752	−	170.721i	−0.305194	−	0.203724i
$839$	−1328.92			−1.58393			−0.791966	−	0.610565i	$-0.790942\pi$
$839$	−1328.92			−1.58393			−0.791966	+	0.610565i	$0.790942\pi$
$840$	−1491.05	−	210.285i	−1.77506	−	0.250339i
$841$		−	756.098i		−	0.899047i
$842$	1140.91	+	761.585i	1.35500	+	0.904495i
$843$	408.786	−	22.4588i	0.484919	−	0.0266415i
$844$	−391.712	+	948.102i	−0.464114	+	1.12334i
$845$	569.389	+	569.389i	0.673833	+	0.673833i
$846$	−297.887	−	941.036i	−0.352112	−	1.11234i
$847$	1408.90			1.66340
$848$	0.881176	+	486.974i	0.00103912	+	0.574262i
$849$	419.203	+	375.540i	0.493761	+	0.442332i
$850$	43.6364	−	8.70034i	0.0513369	−	0.0102357i
$851$	131.896	+	131.896i	0.154989	+	0.154989i
$852$	−704.180	+	338.846i	−0.826502	+	0.397707i
$853$	−74.3835	−	74.3835i	−0.0872022	−	0.0872022i	0.662160	−	0.749362i	$-0.269640\pi$
$853$	−74.3835	−	74.3835i	−0.0872022	−	0.0872022i	−0.749362	+	0.662160i	$0.769640\pi$
$854$	−555.153	−	370.578i	−0.650062	−	0.433932i
$855$	62.4887	+	566.981i	0.0730862	+	0.663135i
$856$	184.037	−	931.824i	0.214997	−	1.08858i
$857$	−1113.91			−1.29977			−0.649887	−	0.760030i	$-0.725184\pi$
$857$	−1113.91			−1.29977			−0.649887	+	0.760030i	$0.725184\pi$
$858$	−12.6280	−	49.1095i	−0.0147179	−	0.0572372i
$859$	−78.5892	−	78.5892i	−0.0914891	−	0.0914891i	0.659881	−	0.751370i	$-0.270607\pi$
$859$	−78.5892	−	78.5892i	−0.0914891	−	0.0914891i	−0.751370	+	0.659881i	$0.770607\pi$
$860$	568.145	−	235.936i	0.660634	−	0.274344i
$861$	9.24334	+	168.244i	0.0107356	+	0.195405i
$862$	83.5203	+	418.895i	0.0968913	+	0.485957i
$863$		−	814.226i		−	0.943483i	−0.881737	−	0.471741i	$-0.843626\pi$
$863$		−	814.226i		−	0.943483i	0.881737	−	0.471741i	$-0.156374\pi$
$864$	353.986	−	788.156i	0.409706	−	0.912218i
$865$	−894.658			−1.03429
$866$	−864.326	+	172.332i	−0.998067	+	0.198997i
$867$	341.552	−	18.7650i	0.393947	−	0.0216436i
$868$	−708.131	−	1705.21i	−0.815819	−	1.96453i
$869$	−37.0316	+	37.0316i	−0.0426140	+	0.0426140i
$870$	273.587	−	70.3500i	0.314468	−	0.0808621i
$871$			150.748i			0.173075i
$872$	−5.03135	+	25.4749i	−0.00576990	+	0.0292144i
$873$	1245.38	−	137.257i	1.42655	−	0.157224i
$874$	181.559	−	271.989i	0.207734	−	0.311200i
$875$	1059.96	−	1059.96i	1.21139	−	1.21139i
$876$	261.438	+	543.313i	0.298445	+	0.620220i
$877$	−36.8840	+	36.8840i	−0.0420571	+	0.0420571i	−0.727823	−	0.685765i	$-0.759468\pi$
$877$	−36.8840	+	36.8840i	−0.0420571	+	0.0420571i	0.685765	+	0.727823i	$0.259468\pi$
$878$	156.571	+	785.277i	0.178327	+	0.894393i
$879$	−407.562	+	454.948i	−0.463665	+	0.517575i
$880$	144.910	+	144.386i	0.164670	+	0.164076i
$881$		−	69.7752i		−	0.0792000i	−0.999216	−	0.0396000i	$-0.987392\pi$
$881$		−	69.7752i		−	0.0792000i	0.999216	−	0.0396000i	$-0.0126084\pi$
$882$	1746.58	−	552.884i	1.98025	−	0.626853i
$883$	410.405	−	410.405i	0.464785	−	0.464785i	−0.435435	−	0.900220i	$-0.643406\pi$
$883$	410.405	−	410.405i	0.464785	−	0.464785i	0.900220	+	0.435435i	$0.143406\pi$
$884$	250.668	+	103.565i	0.283562	+	0.117155i
$885$	63.8153	+	1161.54i	0.0721077	+	1.31248i
$886$	−508.905	+	762.376i	−0.574385	+	0.860470i
$887$	−1290.54			−1.45495			−0.727475	−	0.686135i	$-0.759306\pi$
$887$	−1290.54			−1.45495			−0.727475	+	0.686135i	$0.759306\pi$
$888$	336.276	+	47.4254i	0.378689	+	0.0534070i
$889$			1868.48i			2.10178i
$890$	944.093	−	1414.32i	1.06078	−	1.58912i
$891$	−108.664	+	171.086i	−0.121957	+	0.192016i
$892$	−65.5113	+	27.2051i	−0.0734432	+	0.0304990i
$893$	−480.966	−	480.966i	−0.538596	−	0.538596i
$894$	504.674	−	854.058i	0.564512	−	0.955322i
$895$	−1218.62			−1.36159
$896$	1542.50	+	301.747i	1.72154	+	0.336771i
$897$	89.1236	−	99.4858i	0.0993574	−	0.110909i
$898$	−270.587	−	1357.12i	−0.301322	−	1.51127i
$899$	244.930	+	244.930i	0.272447	+	0.272447i
$900$	−19.2448	−	34.9467i	−0.0213832	−	0.0388297i
$901$	432.052	+	432.052i	0.479525	+	0.479525i
$902$	12.7086	−	19.0384i	0.0140894	−	0.0211069i
$903$	−739.841	+	825.861i	−0.819315	+	0.914575i
$904$	−791.090	−	1180.48i	−0.875100	−	1.30584i
$905$	−1171.79			−1.29480
$906$	16.3951	+	63.7597i	0.0180962	+	0.0703749i
$907$	395.420	+	395.420i	0.435964	+	0.435964i	0.890651	−	0.454687i	$-0.150249\pi$
$907$	395.420	+	395.420i	0.435964	+	0.435964i	−0.454687	+	0.890651i	$0.650249\pi$
$908$	−39.4084	−	16.2818i	−0.0434014	−	0.0179314i
$909$	1001.98	−	1250.20i	1.10229	−	1.37536i
$910$	−415.642	+	82.8718i	−0.456749	+	0.0910679i
$911$		−	1451.84i		−	1.59367i	−0.604195	−	0.796837i	$-0.706505\pi$
$911$		−	1451.84i		−	1.59367i	0.604195	−	0.796837i	$-0.293495\pi$
$912$	−33.7372	−	594.432i	−0.0369925	−	0.651789i
$913$	−22.4983			−0.0246422
$914$	−150.732	−	755.991i	−0.164914	−	0.827124i
$915$	−22.8550	−	415.998i	−0.0249782	−	0.454643i
$916$	1169.80	+	483.307i	1.27707	+	0.527628i
$917$	806.686	−	806.686i	0.879701	−	0.879701i
$918$	−383.369	−	1014.02i	−0.417613	−	1.10460i
$919$			1626.08i			1.76940i	0.466161	+	0.884700i	$0.345637\pi$
$919$			1626.08i			1.76940i	−0.466161	+	0.884700i	$0.654363\pi$
$920$	−104.406	+	528.632i	−0.113485	+	0.574600i
$921$	252.873	−	282.275i	0.274564	−	0.306487i
$922$	−734.133	−	490.052i	−0.796240	−	0.531510i
$923$	−155.528	+	155.528i	−0.168503	+	0.168503i
$924$	−347.970	−	121.881i	−0.376591	−	0.131906i
$925$	11.0883	−	11.0883i	0.0119874	−	0.0119874i
$926$	−1410.17	+	281.163i	−1.52286	+	0.303632i
$927$	26.0228	+	236.114i	0.0280721	+	0.254707i
$928$	−289.059	+	58.1773i	−0.311486	+	0.0626911i
$929$		−	864.883i		−	0.930983i	−0.885052	−	0.465491i	$-0.845878\pi$
$929$		−	864.883i		−	0.930983i	0.885052	−	0.465491i	$-0.154122\pi$
$930$	586.309	−	992.208i	0.630440	−	1.06689i
$931$	892.684	−	892.684i	0.958844	−	0.958844i
$932$	456.538	−	189.588i	0.489848	−	0.203421i
$933$	−942.100	+	51.7592i	−1.00975	+	0.0554761i
$934$	−194.759	−	130.006i	−0.208521	−	0.139193i
$935$	256.669			0.274512
$936$	20.6994	−	242.298i	0.0221147	−	0.258866i
$937$			177.635i			0.189579i	0.995497	+	0.0947893i	$0.0302177\pi$
$937$			177.635i			0.189579i	−0.995497	+	0.0947893i	$0.969782\pi$
$938$	911.658	+	608.554i	0.971917	+	0.648779i
$939$	17.0949	+	311.154i	0.0182054	+	0.331368i
$940$	1035.85	+	427.966i	1.10197	+	0.455283i
$941$	−49.5787	−	49.5787i	−0.0526872	−	0.0526872i	0.680272	−	0.732959i	$-0.261862\pi$
$941$	−49.5787	−	49.5787i	−0.0526872	−	0.0526872i	−0.732959	+	0.680272i	$0.761862\pi$
$942$	215.079	−	363.978i	0.228322	−	0.386388i
$943$	60.2958			0.0639404
$944$	−2.19713	−	1214.22i	−0.00232747	−	1.28625i
$945$	1378.00	+	985.315i	1.45820	+	1.04266i
$946$	147.721	−	29.4531i	0.156154	−	0.0311344i
$947$	801.785	+	801.785i	0.846658	+	0.846658i	0.989714	−	0.143057i	$-0.0456931\pi$
$947$	801.785	+	801.785i	0.846658	+	0.846658i	−0.143057	+	0.989714i	$0.545693\pi$
$948$	−226.320	+	108.903i	−0.238734	+	0.114877i
$949$	119.999	+	119.999i	0.126447	+	0.126447i
$950$	−22.8658	−	15.2635i	−0.0240692	−	0.0160668i
$951$	−1014.72	−	909.032i	−1.06701	−	0.955869i
$952$	1638.23	−	1097.85i	1.72083	−	1.15320i
$953$	633.331			0.664565			0.332283	−	0.943180i	$-0.392181\pi$
$953$	633.331			0.664565			0.332283	+	0.943180i	$0.392181\pi$
$954$	252.414	−	486.234i	0.264585	−	0.509679i
$955$	219.954	+	219.954i	0.230318	+	0.230318i
$956$	−181.790	−	437.758i	−0.190156	−	0.457906i
$957$	69.0630	−	3.79434i	0.0721662	−	0.00396483i
$958$	292.949	+	1469.28i	0.305792	+	1.53369i
$959$			652.649i			0.680552i
$960$	426.985	+	883.253i	0.444776	+	0.920056i
$961$	452.174			0.470525
$962$	93.7395	−	18.6900i	0.0974423	−	0.0194283i
$963$	−668.259	+	833.807i	−0.693935	+	0.865843i
$964$	−975.848	+	405.244i	−1.01229	+	0.420378i
$965$	642.656	−	642.656i	0.665965	−	0.665965i
$966$	−241.863	−	940.592i	−0.250376	−	0.973698i
$967$			734.798i			0.759873i	0.925013	+	0.379937i	$0.124054\pi$
$967$			734.798i			0.759873i	−0.925013	+	0.379937i	$0.875946\pi$
$968$	−511.000	−	762.523i	−0.527893	−	0.787731i
$969$	−556.421	−	498.465i	−0.574222	−	0.514412i
$970$	−789.847	+	1183.25i	−0.814276	+	1.21984i
$971$	−1255.23	+	1255.23i	−1.29272	+	1.29272i	−0.359625	+	0.933097i	$0.617095\pi$
$971$	−1255.23	+	1255.23i	−1.29272	+	1.29272i	−0.933097	+	0.359625i	$0.882905\pi$
$972$	−763.063	+	602.096i	−0.785044	+	0.619440i
$973$	−1980.93	+	1980.93i	−2.03589	+	2.03589i
$974$	−208.521	−	1045.83i	−0.214087	−	1.07375i
$975$	−8.36365	−	7.49251i	−0.00857811	−	0.00768463i
$976$	0.786886	+	434.866i	0.000806236	+	0.445559i
$977$		−	75.9504i		−	0.0777384i	−0.999244	−	0.0388692i	$-0.987624\pi$
$977$		−	75.9504i		−	0.0777384i	0.999244	−	0.0388692i	$-0.0123756\pi$
$978$	−286.735	+	485.240i	−0.293185	+	0.496156i
$979$	294.413	−	294.413i	0.300728	−	0.300728i
$980$	−794.313	+	1922.56i	−0.810524	+	1.96180i
$981$	18.2694	−	22.7953i	0.0186232	−	0.0232368i
$982$	−10.5999	+	15.8794i	−0.0107942	+	0.0161705i
$983$	−211.646			−0.215306			−0.107653	−	0.994189i	$-0.534334\pi$
$983$	−211.646			−0.215306			−0.107653	+	0.994189i	$0.534334\pi$
$984$	87.7042	−	66.0237i	0.0891302	−	0.0670973i
$985$			483.723i			0.491089i
$986$	−205.399	+	307.702i	−0.208315	+	0.312071i
$987$	−2017.00	+	110.815i	−2.04357	+	0.112274i
$988$	−64.2693	−	154.764i	−0.0650499	−	0.156643i
$989$	280.561	+	280.561i	0.283682	+	0.283682i
$990$	−69.4527	−	219.404i	−0.0701543	−	0.221620i
$991$	−728.452			−0.735067			−0.367534	−	0.930010i	$-0.619798\pi$
$991$	−728.452			−0.735067			−0.367534	+	0.930010i	$0.619798\pi$
$992$	−666.060	+	1001.73i	−0.671431	+	1.00980i
$993$	991.810	+	888.505i	0.998802	+	0.894768i
$994$	312.715	+	1568.42i	0.314603	+	1.57788i
$995$	2.98556	+	2.98556i	0.00300056	+	0.00300056i
$996$	−101.831	−	35.6678i	−0.102240	−	0.0358110i
$997$	−955.300	−	955.300i	−0.958175	−	0.958175i	0.0409850	−	0.999160i	$-0.486950\pi$
$997$	−955.300	−	955.300i	−0.958175	−	0.958175i	−0.999160	+	0.0409850i	$0.986950\pi$
$998$	−873.646	+	1308.78i	−0.875396	+	1.31141i
$999$	−310.780	−	222.218i	−0.311091	−	0.222440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.i.b.5.1	✓	20
3.2	odd	2	inner	48.3.i.b.5.10	yes	20
4.3	odd	2		192.3.i.b.113.10		20
8.3	odd	2		384.3.i.c.353.1		20
8.5	even	2		384.3.i.d.353.10		20
12.11	even	2		192.3.i.b.113.5		20
16.3	odd	4		192.3.i.b.17.5		20
16.5	even	4		384.3.i.d.161.5		20
16.11	odd	4		384.3.i.c.161.6		20
16.13	even	4	inner	48.3.i.b.29.10	yes	20
24.5	odd	2		384.3.i.d.353.5		20
24.11	even	2		384.3.i.c.353.6		20
48.5	odd	4		384.3.i.d.161.10		20
48.11	even	4		384.3.i.c.161.1		20
48.29	odd	4	inner	48.3.i.b.29.1	yes	20
48.35	even	4		192.3.i.b.17.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.i.b.5.1	✓	20	1.1	even	1	trivial
48.3.i.b.5.10	yes	20	3.2	odd	2	inner
48.3.i.b.29.1	yes	20	48.29	odd	4	inner
48.3.i.b.29.10	yes	20	16.13	even	4	inner
192.3.i.b.17.5		20	16.3	odd	4
192.3.i.b.17.10		20	48.35	even	4
192.3.i.b.113.5		20	12.11	even	2
192.3.i.b.113.10		20	4.3	odd	2
384.3.i.c.161.1		20	48.11	even	4
384.3.i.c.161.6		20	16.11	odd	4
384.3.i.c.353.1		20	8.3	odd	2
384.3.i.c.353.6		20	24.11	even	2
384.3.i.d.161.5		20	16.5	even	4
384.3.i.d.161.10		20	48.5	odd	4
384.3.i.d.353.5		20	24.5	odd	2
384.3.i.d.353.10		20	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96139 + 0.391068i) q^{2} +(-2.99548 + 0.164573i) q^{3} +(3.69413 - 1.53408i) q^{4} +(3.61305 - 3.61305i) q^{5} +(5.81096 - 1.49423i) q^{6} -12.2792i q^{7} +(-6.64572 + 4.45358i) q^{8} +(8.94583 - 0.985948i) q^{9} +O(q^{10})\)	\(q+(-1.96139 + 0.391068i) q^{2} +(-2.99548 + 0.164573i) q^{3} +(3.69413 - 1.53408i) q^{4} +(3.61305 - 3.61305i) q^{5} +(5.81096 - 1.49423i) q^{6} -12.2792i q^{7} +(-6.64572 + 4.45358i) q^{8} +(8.94583 - 0.985948i) q^{9} +(-5.67366 + 8.49955i) q^{10} +(-1.76932 + 1.76932i) q^{11} +(-10.8132 + 5.20325i) q^{12} +(-2.38826 + 2.38826i) q^{13} +(4.80199 + 24.0843i) q^{14} +(-10.2282 + 11.4174i) q^{15} +(11.2932 - 11.3342i) q^{16} -20.0754i q^{17} +(-17.1607 + 5.43226i) q^{18} +(-8.77090 + 8.77090i) q^{19} +(7.80438 - 18.8898i) q^{20} +(2.02081 + 36.7820i) q^{21} +(2.77840 - 4.16225i) q^{22} +13.1821 q^{23} +(19.1742 - 14.4343i) q^{24} -1.10820i q^{25} +(3.75035 - 5.61830i) q^{26} +(-26.6348 + 4.42563i) q^{27} +(-18.8372 - 45.3609i) q^{28} +(6.51544 + 6.51544i) q^{29} +(15.5966 - 26.3940i) q^{30} +37.5922 q^{31} +(-17.7180 + 26.6472i) q^{32} +(5.00877 - 5.59113i) q^{33} +(7.85085 + 39.3758i) q^{34} +(-44.3652 - 44.3652i) q^{35} +(31.5346 - 17.3658i) q^{36} +(10.0057 + 10.0057i) q^{37} +(13.7732 - 20.6332i) q^{38} +(6.76096 - 7.54704i) q^{39} +(-7.92028 + 40.1023i) q^{40} +4.57407 q^{41} +(-18.3479 - 71.3538i) q^{42} +(21.2835 + 21.2835i) q^{43} +(-3.82182 + 9.25035i) q^{44} +(28.7594 - 35.8840i) q^{45} +(-25.8553 + 5.15509i) q^{46} +54.8366i q^{47} +(-31.9633 + 35.8098i) q^{48} -101.778 q^{49} +(0.433383 + 2.17362i) q^{50} +(3.30386 + 60.1356i) q^{51} +(-5.15878 + 12.4863i) q^{52} +(-21.5215 + 21.5215i) q^{53} +(50.5107 - 19.0964i) q^{54} +12.7852i q^{55} +(54.6863 + 81.6039i) q^{56} +(24.8296 - 27.7165i) q^{57} +(-15.3273 - 10.2314i) q^{58} +(53.6617 - 53.6617i) q^{59} +(-20.2691 + 57.8683i) q^{60} +(-19.2186 + 19.2186i) q^{61} +(-73.7331 + 14.7011i) q^{62} +(-12.1066 - 109.847i) q^{63} +(24.3312 - 59.1945i) q^{64} +17.2578i q^{65} +(-7.63766 + 12.9252i) q^{66} +(31.5603 - 31.5603i) q^{67} +(-30.7972 - 74.1612i) q^{68} +(-39.4867 + 2.16941i) q^{69} +(104.367 + 69.6678i) q^{70} +65.1220 q^{71} +(-55.0605 + 46.3934i) q^{72} -50.2451i q^{73} +(-23.5379 - 15.7121i) q^{74} +(0.182380 + 3.31960i) q^{75} +(-18.9456 + 45.8561i) q^{76} +(21.7257 + 21.7257i) q^{77} +(-10.3095 + 17.4467i) q^{78} +20.9299 q^{79} +(-0.147933 - 81.7538i) q^{80} +(79.0558 - 17.6403i) q^{81} +(-8.97156 + 1.78877i) q^{82} +(6.35791 + 6.35791i) q^{83} +(63.8916 + 132.778i) q^{84} +(-72.5334 - 72.5334i) q^{85} +(-50.0687 - 33.4221i) q^{86} +(-20.5891 - 18.4446i) q^{87} +(3.87858 - 19.6382i) q^{88} -166.399 q^{89} +(-42.3755 + 81.6295i) q^{90} +(29.3259 + 29.3259i) q^{91} +(48.6964 - 20.2223i) q^{92} +(-112.607 + 6.18664i) q^{93} +(-21.4449 - 107.556i) q^{94} +63.3793i q^{95} +(48.6886 - 82.7370i) q^{96} +139.213 q^{97} +(199.627 - 39.8021i) q^{98} +(-14.0835 + 17.5725i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6}+O(q^{10}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6	\( 20 q - 6 q^{3} + 4 q^{4} - 12 q^{6} + 32 q^{10} - 88 q^{12} + 92 q^{13} - 116 q^{15} - 16 q^{16} + 4 q^{18} - 52 q^{19} + 48 q^{21} + 24 q^{22} - 8 q^{24} + 18 q^{27} + 56 q^{28} + 28 q^{30} - 80 q^{31} + 60 q^{33} + 104 q^{34} + 92 q^{36} - 116 q^{37} + 88 q^{40} + 304 q^{42} + 172 q^{43} + 60 q^{45} - 424 q^{46} + 176 q^{48} - 364 q^{49} + 128 q^{51} - 208 q^{52} + 40 q^{54} - 512 q^{58} - 240 q^{60} - 244 q^{61} + 296 q^{63} + 88 q^{64} - 492 q^{66} + 356 q^{67} - 20 q^{69} + 200 q^{70} - 472 q^{72} - 146 q^{75} + 328 q^{76} + 84 q^{78} + 384 q^{79} - 188 q^{81} + 560 q^{82} + 816 q^{84} + 48 q^{85} + 416 q^{88} + 616 q^{90} + 136 q^{91} - 132 q^{93} + 32 q^{94} - 24 q^{96} + 472 q^{97} - 452 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 4 * q^4 - 12 * q^6 + 32 * q^10 - 88 * q^12 + 92 * q^13 - 116 * q^15 - 16 * q^16 + 4 * q^18 - 52 * q^19 + 48 * q^21 + 24 * q^22 - 8 * q^24 + 18 * q^27 + 56 * q^28 + 28 * q^30 - 80 * q^31 + 60 * q^33 + 104 * q^34 + 92 * q^36 - 116 * q^37 + 88 * q^40 + 304 * q^42 + 172 * q^43 + 60 * q^45 - 424 * q^46 + 176 * q^48 - 364 * q^49 + 128 * q^51 - 208 * q^52 + 40 * q^54 - 512 * q^58 - 240 * q^60 - 244 * q^61 + 296 * q^63 + 88 * q^64 - 492 * q^66 + 356 * q^67 - 20 * q^69 + 200 * q^70 - 472 * q^72 - 146 * q^75 + 328 * q^76 + 84 * q^78 + 384 * q^79 - 188 * q^81 + 560 * q^82 + 816 * q^84 + 48 * q^85 + 416 * q^88 + 616 * q^90 + 136 * q^91 - 132 * q^93 + 32 * q^94 - 24 * q^96 + 472 * q^97 - 452 * q^99

Introduction

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