LMFDB - Embedded newform 48.3.l.a.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(19,48)]

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([2, 3, 0]))

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

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$0.125358 + 1.99607i$ of defining polynomial
Character	$\chi$	$=$	48.43
Dual form			48.3.l.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.125358 + 1.99607i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.96857 - 0.500444i) q^{4} +(3.32679 + 3.32679i) q^{5} +(-2.59820 + 2.29114i) q^{6} -4.04088 q^{7} +(1.49641 - 7.85880i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-0.125358 + 1.99607i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.96857 - 0.500444i) q^{4} +(3.32679 + 3.32679i) q^{5} +(-2.59820 + 2.29114i) q^{6} -4.04088 q^{7} +(1.49641 - 7.85880i) q^{8} +3.00000i q^{9} +(-7.05755 + 6.22347i) q^{10} +(6.82458 - 6.82458i) q^{11} +(-4.24757 - 5.47340i) q^{12} +(4.29091 - 4.29091i) q^{13} +(0.506555 - 8.06588i) q^{14} +8.14895i q^{15} +(15.4991 + 3.97210i) q^{16} +30.1192 q^{17} +(-5.98820 - 0.376073i) q^{18} +(-19.7548 - 19.7548i) q^{19} +(-11.5377 - 14.8675i) q^{20} +(-4.94905 - 4.94905i) q^{21} +(12.7668 + 14.4778i) q^{22} -28.2345 q^{23} +(11.4577 - 7.79230i) q^{24} -2.86488i q^{25} +(8.02705 + 9.10285i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(16.0365 + 2.02224i) q^{28} +(-21.3607 + 21.3607i) q^{29} +(-16.2659 - 1.02153i) q^{30} +38.0396i q^{31} +(-9.87151 + 30.4393i) q^{32} +16.7167 q^{33} +(-3.77567 + 60.1200i) q^{34} +(-13.4432 - 13.4432i) q^{35} +(1.50133 - 11.9057i) q^{36} +(-42.8916 - 42.8916i) q^{37} +(41.9084 - 36.9556i) q^{38} +10.5105 q^{39} +(31.1229 - 21.1664i) q^{40} +48.2343i q^{41} +(10.4990 - 9.25824i) q^{42} +(32.6765 - 32.6765i) q^{43} +(-30.4991 + 23.6685i) q^{44} +(-9.98038 + 9.98038i) q^{45} +(3.53941 - 56.3580i) q^{46} -15.8305i q^{47} +(14.1177 + 23.8473i) q^{48} -32.6713 q^{49} +(5.71849 + 0.359134i) q^{50} +(36.8883 + 36.8883i) q^{51} +(-19.1761 + 14.8814i) q^{52} +(-0.476870 - 0.476870i) q^{53} +(-6.87343 - 7.79461i) q^{54} +45.4079 q^{55} +(-6.04682 + 31.7565i) q^{56} -48.3893i q^{57} +(-39.9596 - 45.3151i) q^{58} +(9.97719 - 9.97719i) q^{59} +(4.07809 - 32.3397i) q^{60} +(37.9455 - 37.9455i) q^{61} +(-75.9296 - 4.76855i) q^{62} -12.1226i q^{63} +(-59.5215 - 23.5200i) q^{64} +28.5500 q^{65} +(-2.09557 + 33.3677i) q^{66} +(20.0705 + 20.0705i) q^{67} +(-119.530 - 15.0730i) q^{68} +(-34.5801 - 34.5801i) q^{69} +(28.5187 - 25.1483i) q^{70} +40.0818 q^{71} +(23.5764 + 4.48923i) q^{72} +30.8095i q^{73} +(90.9912 - 80.2377i) q^{74} +(3.50874 - 3.50874i) q^{75} +(68.5123 + 88.2846i) q^{76} +(-27.5773 + 27.5773i) q^{77} +(-1.31758 + 20.9798i) q^{78} +130.125i q^{79} +(38.3480 + 64.7767i) q^{80} -9.00000 q^{81} +(-96.2789 - 6.04653i) q^{82} +(-2.26155 - 2.26155i) q^{83} +(17.1639 + 22.1174i) q^{84} +(100.200 + 100.200i) q^{85} +(61.1282 + 69.3207i) q^{86} -52.3228 q^{87} +(-43.4206 - 63.8454i) q^{88} -72.2232i q^{89} +(-18.6704 - 21.1726i) q^{90} +(-17.3391 + 17.3391i) q^{91} +(112.051 + 14.1298i) q^{92} +(-46.5888 + 46.5888i) q^{93} +(31.5986 + 1.98447i) q^{94} -131.441i q^{95} +(-49.3705 + 25.1903i) q^{96} -112.343 q^{97} +(4.09559 - 65.2140i) q^{98} +(20.4737 + 20.4737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 - 12 * q^8	$ 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * 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 $

$2$	−0.125358	+	1.99607i	−0.0626788	+	0.998034i
$2$	−0.125358	+	1.99607i	−0.0626788	+	0.998034i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$	−3.96857	−	0.500444i	−0.992143	−	0.125111i
$5$	3.32679	+	3.32679i	0.665359	+	0.665359i	0.956638	−	0.291279i	$-0.0940809\pi$
$5$	3.32679	+	3.32679i	0.665359	+	0.665359i	−0.291279	+	0.956638i	$0.594081\pi$
$6$	−2.59820	+	2.29114i	−0.433034	+	0.381857i
$7$	−4.04088			−0.577269			−0.288635	−	0.957439i	$-0.593201\pi$
$7$	−4.04088			−0.577269			−0.288635	+	0.957439i	$0.593201\pi$
$8$	1.49641	−	7.85880i	0.187051	−	0.982350i
$9$			3.00000i			0.333333i
$10$	−7.05755	+	6.22347i	−0.705755	+	0.622347i
$11$	6.82458	−	6.82458i	0.620416	−	0.620416i	−0.325222	−	0.945638i	$-0.605439\pi$
$11$	6.82458	−	6.82458i	0.620416	−	0.620416i	0.945638	+	0.325222i	$0.105439\pi$
$12$	−4.24757	−	5.47340i	−0.353964	−	0.456117i
$13$	4.29091	−	4.29091i	0.330070	−	0.330070i	−0.522543	−	0.852613i	$-0.675017\pi$
$13$	4.29091	−	4.29091i	0.330070	−	0.330070i	0.852613	+	0.522543i	$0.175017\pi$
$14$	0.506555	−	8.06588i	0.0361825	−	0.576134i
$15$			8.14895i			0.543263i
$16$	15.4991	+	3.97210i	0.968694	+	0.248256i
$17$	30.1192			1.77172			0.885859	−	0.463954i	$-0.153570\pi$
$17$	30.1192			1.77172			0.885859	+	0.463954i	$0.153570\pi$
$18$	−5.98820	−	0.376073i	−0.332678	−	0.0208929i
$19$	−19.7548	−	19.7548i	−1.03973	−	1.03973i	−0.999177	−	0.0405505i	$-0.987089\pi$
$19$	−19.7548	−	19.7548i	−1.03973	−	1.03973i	−0.0405505	−	0.999177i	$-0.512911\pi$
$20$	−11.5377	−	14.8675i	−0.576887	−	0.743375i
$21$	−4.94905	−	4.94905i	−0.235669	−	0.235669i
$22$	12.7668	+	14.4778i	0.580309	+	0.658083i
$23$	−28.2345			−1.22759			−0.613794	−	0.789466i	$-0.710358\pi$
$23$	−28.2345			−1.22759			−0.613794	+	0.789466i	$0.710358\pi$
$24$	11.4577	−	7.79230i	0.477406	−	0.324679i
$25$		−	2.86488i		−	0.114595i
$26$	8.02705	+	9.10285i	0.308733	+	0.350109i
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	16.0365	+	2.02224i	0.572733	+	0.0722227i
$29$	−21.3607	+	21.3607i	−0.736575	+	0.736575i	−0.971914	−	0.235338i	$-0.924380\pi$
$29$	−21.3607	+	21.3607i	−0.736575	+	0.736575i	0.235338	+	0.971914i	$0.424380\pi$
$30$	−16.2659	−	1.02153i	−0.542195	−	0.0340511i
$31$			38.0396i			1.22708i	0.789662	+	0.613541i	$0.210256\pi$
$31$			38.0396i			1.22708i	−0.789662	+	0.613541i	$0.789744\pi$
$32$	−9.87151	+	30.4393i	−0.308485	+	0.951229i
$33$	16.7167			0.506568
$34$	−3.77567	+	60.1200i	−0.111049	+	1.76823i
$35$	−13.4432	−	13.4432i	−0.384091	−	0.384091i
$36$	1.50133	−	11.9057i	0.0417037	−	0.330714i
$37$	−42.8916	−	42.8916i	−1.15923	−	1.15923i	−0.984641	−	0.174590i	$-0.944140\pi$
$37$	−42.8916	−	42.8916i	−1.15923	−	1.15923i	−0.174590	−	0.984641i	$-0.555860\pi$
$38$	41.9084	−	36.9556i	1.10285	−	0.972515i
$39$	10.5105			0.269501
$40$	31.1229	−	21.1664i	0.778072	−	0.529159i
$41$			48.2343i			1.17645i	0.808699	+	0.588223i	$0.200172\pi$
$41$			48.2343i			1.17645i	−0.808699	+	0.588223i	$0.799828\pi$
$42$	10.4990	−	9.25824i	0.249977	−	0.220434i
$43$	32.6765	−	32.6765i	0.759918	−	0.759918i	−0.216389	−	0.976307i	$-0.569428\pi$
$43$	32.6765	−	32.6765i	0.759918	−	0.759918i	0.976307	+	0.216389i	$0.0694281\pi$
$44$	−30.4991	+	23.6685i	−0.693162	+	0.537921i
$45$	−9.98038	+	9.98038i	−0.221786	+	0.221786i
$46$	3.53941	−	56.3580i	0.0769437	−	1.22517i
$47$		−	15.8305i		−	0.336818i	−0.985717	−	0.168409i	$-0.946137\pi$
$47$		−	15.8305i		−	0.336818i	0.985717	−	0.168409i	$-0.0538630\pi$
$48$	14.1177	+	23.8473i	0.294118	+	0.496818i
$49$	−32.6713			−0.666760
$50$	5.71849	+	0.359134i	0.114370	+	0.00718268i
$51$	36.8883	+	36.8883i	0.723301	+	0.723301i
$52$	−19.1761	+	14.8814i	−0.368772	+	0.286181i
$53$	−0.476870	−	0.476870i	−0.00899755	−	0.00899755i	0.702594	−	0.711591i	$-0.252025\pi$
$53$	−0.476870	−	0.476870i	−0.00899755	−	0.00899755i	−0.711591	+	0.702594i	$0.752025\pi$
$54$	−6.87343	−	7.79461i	−0.127286	−	0.144345i
$55$	45.4079			0.825599
$56$	−6.04682	+	31.7565i	−0.107979	+	0.567080i
$57$		−	48.3893i		−	0.848934i
$58$	−39.9596	−	45.3151i	−0.688959	−	0.781295i
$59$	9.97719	−	9.97719i	0.169105	−	0.169105i	−0.617481	−	0.786586i	$-0.711847\pi$
$59$	9.97719	−	9.97719i	0.169105	−	0.169105i	0.786586	+	0.617481i	$0.211847\pi$
$60$	4.07809	−	32.3397i	0.0679682	−	0.538995i
$61$	37.9455	−	37.9455i	0.622057	−	0.622057i	−0.324000	−	0.946057i	$-0.605028\pi$
$61$	37.9455	−	37.9455i	0.622057	−	0.622057i	0.946057	+	0.324000i	$0.105028\pi$
$62$	−75.9296	−	4.76855i	−1.22467	−	0.0769121i
$63$		−	12.1226i		−	0.192423i
$64$	−59.5215	−	23.5200i	−0.930024	−	0.367500i
$65$	28.5500			0.439230
$66$	−2.09557	+	33.3677i	−0.0317510	+	0.505572i
$67$	20.0705	+	20.0705i	0.299559	+	0.299559i	0.840841	−	0.541282i	$-0.182061\pi$
$67$	20.0705	+	20.0705i	0.299559	+	0.299559i	−0.541282	+	0.840841i	$0.682061\pi$
$68$	−119.530	−	15.0730i	−1.75780	−	0.221662i
$69$	−34.5801	−	34.5801i	−0.501161	−	0.501161i
$70$	28.5187	−	25.1483i	0.407410	−	0.359261i
$71$	40.0818			0.564532			0.282266	−	0.959336i	$-0.408914\pi$
$71$	40.0818			0.564532			0.282266	+	0.959336i	$0.408914\pi$
$72$	23.5764	+	4.48923i	0.327450	+	0.0623505i
$73$			30.8095i			0.422049i	0.977481	+	0.211024i	$0.0676799\pi$
$73$			30.8095i			0.422049i	−0.977481	+	0.211024i	$0.932320\pi$
$74$	90.9912	−	80.2377i	1.22961	−	1.08429i
$75$	3.50874	−	3.50874i	0.0467833	−	0.0467833i
$76$	68.5123	+	88.2846i	0.901477	+	1.16164i
$77$	−27.5773	+	27.5773i	−0.358147	+	0.358147i
$78$	−1.31758	+	20.9798i	−0.0168920	+	0.268971i
$79$			130.125i			1.64716i	0.567203	+	0.823578i	$0.308025\pi$
$79$			130.125i			1.64716i	−0.567203	+	0.823578i	$0.691975\pi$
$80$	38.3480	+	64.7767i	0.479350	+	0.809709i
$81$	−9.00000			−0.111111
$82$	−96.2789	−	6.04653i	−1.17413	−	0.0737382i
$83$	−2.26155	−	2.26155i	−0.0272476	−	0.0272476i	0.693352	−	0.720599i	$-0.256133\pi$
$83$	−2.26155	−	2.26155i	−0.0272476	−	0.0272476i	−0.720599	+	0.693352i	$0.756133\pi$
$84$	17.1639	+	22.1174i	0.204333	+	0.263302i
$85$	100.200	+	100.200i	1.17883	+	1.17883i
$86$	61.1282	+	69.3207i	0.710793	+	0.806054i
$87$	−52.3228			−0.601411
$88$	−43.4206	−	63.8454i	−0.493416	−	0.725516i
$89$		−	72.2232i		−	0.811496i	−0.913985	−	0.405748i	$-0.867011\pi$
$89$		−	72.2232i		−	0.811496i	0.913985	−	0.405748i	$-0.132989\pi$
$90$	−18.6704	−	21.1726i	−0.207449	−	0.235252i
$91$	−17.3391	+	17.3391i	−0.190539	+	0.190539i
$92$	112.051	+	14.1298i	1.21794	+	0.153585i
$93$	−46.5888	+	46.5888i	−0.500955	+	0.500955i
$94$	31.5986	+	1.98447i	0.336156	+	0.0211113i
$95$		−	131.441i		−	1.38358i
$96$	−49.3705	+	25.1903i	−0.514276	+	0.262399i
$97$	−112.343			−1.15817			−0.579085	−	0.815267i	$-0.696590\pi$
$97$	−112.343			−1.15817			−0.579085	+	0.815267i	$0.696590\pi$
$98$	4.09559	−	65.2140i	0.0417917	−	0.665449i
$99$	20.4737	+	20.4737i	0.206805	+	0.206805i
$100$	−1.43371	+	11.3695i	−0.0143371	+	0.113695i
$101$	−1.61933	−	1.61933i	−0.0160330	−	0.0160330i	0.699045	−	0.715078i	$-0.253609\pi$
$101$	−1.61933	−	1.61933i	−0.0160330	−	0.0160330i	−0.715078	+	0.699045i	$0.753609\pi$
$102$	−78.2559	+	69.0074i	−0.767214	+	0.676543i
$103$	27.9974			0.271819			0.135910	−	0.990721i	$-0.456604\pi$
$103$	27.9974			0.271819			0.135910	+	0.990721i	$0.456604\pi$
$104$	−27.3005	−	40.1424i	−0.262504	−	0.385984i
$105$		−	32.9289i		−	0.313609i
$106$	1.01164	−	0.892086i	0.00954381	−	0.00841590i
$107$	−40.3835	+	40.3835i	−0.377416	+	0.377416i	−0.870169	−	0.492753i	$-0.835990\pi$
$107$	−40.3835	+	40.3835i	−0.377416	+	0.377416i	0.492753	+	0.870169i	$0.335990\pi$
$108$	16.4202	−	12.7427i	0.152039	−	0.117988i
$109$	36.8336	−	36.8336i	0.337923	−	0.337923i	−0.517662	−	0.855585i	$-0.673198\pi$
$109$	36.8336	−	36.8336i	0.337923	−	0.337923i	0.855585	+	0.517662i	$0.173198\pi$
$110$	−5.69223	+	90.6373i	−0.0517475	+	0.823976i
$111$		−	105.062i		−	0.946508i
$112$	−62.6301	−	16.0508i	−0.559197	−	0.143311i
$113$	−55.5952			−0.491993			−0.245997	−	0.969271i	$-0.579115\pi$
$113$	−55.5952			−0.491993			−0.245997	+	0.969271i	$0.579115\pi$
$114$	96.5882	+	6.06596i	0.847265	+	0.0532102i
$115$	−93.9305	−	93.9305i	−0.816787	−	0.816787i
$116$	95.4612	−	74.0815i	0.822941	−	0.638634i
$117$	12.8727	+	12.8727i	0.110023	+	0.110023i
$118$	18.6644	+	21.1659i	0.158173	+	0.179372i
$119$	−121.708			−1.02276
$120$	64.0410	+	12.1942i	0.533675	+	0.101618i
$121$			27.8503i			0.230167i
$122$	70.9850	+	80.4985i	0.581844	+	0.659824i
$123$	−59.0747	+	59.0747i	−0.480282	+	0.480282i
$124$	19.0367	−	150.963i	0.153522	−	1.21744i
$125$	92.7007	−	92.7007i	0.741606	−	0.741606i
$126$	24.1976	+	1.51967i	0.192045	+	0.0120608i
$127$		−	109.927i		−	0.865569i	−0.901497	−	0.432785i	$-0.857531\pi$
$127$		−	109.927i		−	0.865569i	0.901497	−	0.432785i	$-0.142469\pi$
$128$	54.4090	−	115.861i	0.425070	−	0.905160i
$129$	80.0407			0.620470
$130$	−3.57895	+	56.9876i	−0.0275304	+	0.438367i
$131$	75.6795	+	75.6795i	0.577706	+	0.577706i	0.934271	−	0.356565i	$-0.116052\pi$
$131$	75.6795	+	75.6795i	0.577706	+	0.577706i	−0.356565	+	0.934271i	$0.616052\pi$
$132$	−66.3415	−	8.36579i	−0.502587	−	0.0633772i
$133$	79.8270	+	79.8270i	0.600203	+	0.600203i
$134$	−42.5780	+	37.5460i	−0.317746	+	0.280194i
$135$	−24.4468			−0.181088
$136$	45.0707	−	236.701i	0.331402	−	1.74045i
$137$		−	2.14751i		−	0.0156752i	−0.999969	−	0.00783762i	$-0.997505\pi$
$137$		−	2.14751i		−	0.0156752i	0.999969	−	0.00783762i	$-0.00249482\pi$
$138$	73.3591	−	64.6893i	0.531588	−	0.468763i
$139$	−109.246	+	109.246i	−0.785941	+	0.785941i	−0.980826	−	0.194885i	$-0.937567\pi$
$139$	−109.246	+	109.246i	−0.785941	+	0.785941i	0.194885	+	0.980826i	$0.437567\pi$
$140$	46.6227	+	60.0778i	0.333019	+	0.429127i
$141$	19.3883	−	19.3883i	0.137505	−	0.137505i
$142$	−5.02455	+	80.0059i	−0.0353842	+	0.563422i
$143$		−	58.5673i		−	0.409562i
$144$	−11.9163	+	46.4973i	−0.0827520	+	0.322898i
$145$	−142.125			−0.980174
$146$	−61.4979	−	3.86221i	−0.421219	−	0.0264535i
$147$	−40.0140	−	40.0140i	−0.272204	−	0.272204i
$148$	148.753	+	191.683i	1.00509	+	1.29516i
$149$	79.6950	+	79.6950i	0.534866	+	0.534866i	0.922016	−	0.387151i	$-0.126541\pi$
$149$	79.6950	+	79.6950i	0.534866	+	0.534866i	−0.387151	+	0.922016i	$0.626541\pi$
$150$	6.56384	+	7.44354i	0.0437589	+	0.0496236i
$151$	105.546			0.698982			0.349491	−	0.936940i	$-0.386355\pi$
$151$	105.546			0.698982			0.349491	+	0.936940i	$0.386355\pi$
$152$	−184.811	+	125.688i	−1.21586	+	0.826894i
$153$			90.3576i			0.590573i
$154$	−51.5892	−	58.5032i	−0.334995	−	0.379891i
$155$	−126.550	+	126.550i	−0.816451	+	0.816451i
$156$	−41.7118	−	5.25994i	−0.267384	−	0.0337176i
$157$	190.060	−	190.060i	1.21057	−	1.21057i	0.239733	−	0.970839i	$-0.422940\pi$
$157$	190.060	−	190.060i	1.21057	−	1.21057i	0.970839	−	0.239733i	$-0.0770598\pi$
$158$	−259.739	−	16.3122i	−1.64392	−	0.103242i
$159$		−	1.16809i		−	0.00734647i
$160$	−134.106	+	68.4250i	−0.838162	+	0.427656i
$161$	114.092			0.708649
$162$	1.12822	−	17.9646i	0.00696431	−	0.110893i
$163$	−59.4130	−	59.4130i	−0.364497	−	0.364497i	0.500969	−	0.865465i	$-0.332977\pi$
$163$	−59.4130	−	59.4130i	−0.364497	−	0.364497i	−0.865465	+	0.500969i	$0.832977\pi$
$164$	24.1386	−	191.421i	0.147186	−	1.16720i
$165$	55.6131	+	55.6131i	0.337049	+	0.337049i
$166$	4.79772	−	4.23071i	0.0289019	−	0.0254862i
$167$	65.3894			0.391553			0.195777	−	0.980649i	$-0.437277\pi$
$167$	65.3894			0.391553			0.195777	+	0.980649i	$0.437277\pi$
$168$	−46.2994	+	31.4878i	−0.275592	+	0.187427i
$169$			132.176i			0.782107i
$170$	−212.568	+	187.446i	−1.25040	+	1.10262i
$171$	59.2645	−	59.2645i	0.346576	−	0.346576i
$172$	−146.032	+	113.326i	−0.849021	+	0.658873i
$173$	−212.939	+	212.939i	−1.23086	+	1.23086i	−0.267228	+	0.963633i	$0.586108\pi$
$173$	−212.939	+	212.939i	−1.23086	+	1.23086i	−0.963633	+	0.267228i	$0.913892\pi$
$174$	6.55905	−	104.440i	0.0376957	−	0.600229i
$175$			11.5766i			0.0661522i
$176$	132.883	−	78.6670i	0.755016	−	0.446972i
$177$	24.4390			0.138074
$178$	144.162	+	9.05372i	0.809901	+	0.0508636i
$179$	196.852	+	196.852i	1.09973	+	1.09973i	0.994442	+	0.105289i	$0.0335768\pi$
$179$	196.852	+	196.852i	1.09973	+	1.09973i	0.105289	+	0.994442i	$0.466423\pi$
$180$	44.6025	−	34.6132i	0.247792	−	0.192296i
$181$	−27.4330	−	27.4330i	−0.151564	−	0.151564i	0.627252	−	0.778816i	$-0.284179\pi$
$181$	−27.4330	−	27.4330i	−0.151564	−	0.151564i	−0.778816	+	0.627252i	$0.784179\pi$
$182$	−32.4364	−	36.7835i	−0.178222	−	0.202107i
$183$	92.9471			0.507907
$184$	−42.2505	+	221.890i	−0.229622	+	1.20592i
$185$		−	285.383i		−	1.54261i
$186$	−87.1541	−	98.8346i	−0.468570	−	0.531369i
$187$	205.551	−	205.551i	1.09920	−	1.09920i
$188$	−7.92226	+	62.8243i	−0.0421397	+	0.334172i
$189$	14.8472	−	14.8472i	0.0785564	−	0.0785564i
$190$	262.364	+	16.4771i	1.38086	+	0.0867214i
$191$			244.409i			1.27963i	0.768530	+	0.639814i	$0.220989\pi$
$191$			244.409i			1.27963i	−0.768530	+	0.639814i	$0.779011\pi$
$192$	−44.0927	−	101.705i	−0.229649	−	0.529712i
$193$	255.040			1.32145			0.660726	−	0.750627i	$-0.270249\pi$
$193$	255.040			1.32145			0.660726	+	0.750627i	$0.270249\pi$
$194$	14.0830	−	224.243i	0.0725927	−	1.15589i
$195$	34.9664	+	34.9664i	0.179315	+	0.179315i
$196$	129.658	+	16.3501i	0.661522	+	0.0834191i
$197$	−194.229	−	194.229i	−0.985936	−	0.985936i	0.0139666	−	0.999902i	$-0.495554\pi$
$197$	−194.229	−	194.229i	−0.985936	−	0.985936i	−0.999902	+	0.0139666i	$0.995554\pi$
$198$	−43.4335	+	38.3004i	−0.219361	+	0.193436i
$199$	−169.797			−0.853252			−0.426626	−	0.904428i	$-0.640298\pi$
$199$	−169.797			−0.853252			−0.426626	+	0.904428i	$0.640298\pi$
$200$	−22.5145	−	4.28703i	−0.112573	−	0.0214352i
$201$			49.1624i			0.244589i
$202$	3.43529	−	3.02930i	0.0170064	−	0.0149965i
$203$	86.3160	−	86.3160i	0.425202	−	0.425202i
$204$	−127.933	−	164.855i	−0.627125	−	0.808111i
$205$	−160.466	+	160.466i	−0.782759	+	0.782759i
$206$	−3.50969	+	55.8847i	−0.0170373	+	0.271285i
$207$		−	84.7036i		−	0.409196i
$208$	83.5492	−	49.4614i	0.401679	−	0.237795i
$209$	−269.637			−1.29013
$210$	65.7284	+	4.12789i	0.312992	+	0.0196566i
$211$	−132.691	−	132.691i	−0.628868	−	0.628868i	0.318915	−	0.947783i	$-0.396681\pi$
$211$	−132.691	−	132.691i	−0.628868	−	0.628868i	−0.947783	+	0.318915i	$0.896681\pi$
$212$	1.65385	+	2.13114i	0.00780116	+	0.0100525i
$213$	49.0899	+	49.0899i	0.230469	+	0.230469i
$214$	−75.5458	−	85.6705i	−0.353018	−	0.400330i
$215$	217.416			1.01124
$216$	23.3769	+	34.3732i	0.108226	+	0.159135i
$217$		−	153.713i		−	0.708357i
$218$	68.9050	+	78.1398i	0.316078	+	0.358439i
$219$	−37.7338	+	37.7338i	−0.172301	+	0.172301i
$220$	−180.205	−	22.7241i	−0.819112	−	0.103292i
$221$	129.239	−	129.239i	0.584791	−	0.584791i
$222$	209.712	+	13.1704i	0.944647	+	0.0593260i
$223$		−	26.3436i		−	0.118133i	−0.998254	−	0.0590664i	$-0.981188\pi$
$223$		−	26.3436i		−	0.118133i	0.998254	−	0.0590664i	$-0.0188124\pi$
$224$	39.8896	−	123.002i	0.178079	−	0.549115i
$225$	8.59463			0.0381984
$226$	6.96928	−	110.972i	0.0308375	−	0.491026i
$227$	−70.3362	−	70.3362i	−0.309851	−	0.309851i	0.535001	−	0.844852i	$-0.320311\pi$
$227$	−70.3362	−	70.3362i	−0.309851	−	0.309851i	−0.844852	+	0.535001i	$0.820311\pi$
$228$	−24.2161	+	192.036i	−0.106211	+	0.842264i
$229$	−215.607	−	215.607i	−0.941516	−	0.941516i	0.0568658	−	0.998382i	$-0.481889\pi$
$229$	−215.607	−	215.607i	−0.941516	−	0.941516i	−0.998382	+	0.0568658i	$0.981889\pi$
$230$	199.266	−	175.717i	0.866376	−	0.763986i
$231$	−67.5504			−0.292426
$232$	135.905	+	199.834i	0.585797	+	0.861352i
$233$			183.853i			0.789069i	0.918881	+	0.394534i	$0.129094\pi$
$233$			183.853i			0.789069i	−0.918881	+	0.394534i	$0.870906\pi$
$234$	−27.3085	+	24.0812i	−0.116703	+	0.102911i
$235$	52.6647	−	52.6647i	0.224105	−	0.224105i
$236$	−44.5882	+	34.6021i	−0.188933	+	0.146619i
$237$	−159.370	+	159.370i	−0.672449	+	0.672449i
$238$	15.2570	−	242.938i	0.0641052	−	1.02075i
$239$			315.183i			1.31876i	0.751811	+	0.659379i	$0.229181\pi$
$239$			315.183i			1.31876i	−0.751811	+	0.659379i	$0.770819\pi$
$240$	−32.3684	+	126.301i	−0.134868	+	0.526256i
$241$	−327.804			−1.36018			−0.680090	−	0.733128i	$-0.738059\pi$
$241$	−327.804			−1.36018			−0.680090	+	0.733128i	$0.738059\pi$
$242$	−55.5910	−	3.49124i	−0.229715	−	0.0144266i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	−169.579	+	131.600i	−0.694996	+	0.539343i
$245$	−108.691	−	108.691i	−0.443635	−	0.443635i
$246$	−110.512	−	125.323i	−0.449234	−	0.509441i
$247$	−169.532			−0.686366
$248$	298.945	+	56.9228i	1.20543	+	0.229528i
$249$		−	5.53965i		−	0.0222476i
$250$	173.416	+	196.658i	0.693665	+	0.786631i
$251$	219.813	−	219.813i	0.875747	−	0.875747i	−0.117344	−	0.993091i	$-0.537438\pi$
$251$	219.813	−	219.813i	0.875747	−	0.875747i	0.993091	+	0.117344i	$0.0374381\pi$
$252$	−6.06671	+	48.1096i	−0.0240742	+	0.190911i
$253$	−192.689	+	192.689i	−0.761616	+	0.761616i
$254$	219.422	+	13.7802i	0.863867	+	0.0542528i
$255$			245.440i			0.962509i
$256$	224.445	+	123.128i	0.876738	+	0.480969i
$257$	150.042			0.583823			0.291911	−	0.956445i	$-0.405709\pi$
$257$	150.042			0.583823			0.291911	+	0.956445i	$0.405709\pi$
$258$	−10.0337	+	159.767i	−0.0388903	+	0.619250i
$259$	173.320	+	173.320i	0.669188	+	0.669188i
$260$	−113.303	−	14.2877i	−0.435779	−	0.0549526i
$261$	−64.0820	−	64.0820i	−0.245525	−	0.245525i
$262$	−160.548	+	141.574i	−0.612780	+	0.540360i
$263$	14.8922			0.0566242			0.0283121	−	0.999599i	$-0.490987\pi$
$263$	14.8922			0.0566242			0.0283121	+	0.999599i	$0.490987\pi$
$264$	25.0151	−	131.373i	0.0947542	−	0.497627i
$265$		−	3.17290i		−	0.0119732i
$266$	−169.347	+	149.333i	−0.636643	+	0.561403i
$267$	88.4550	−	88.4550i	0.331292	−	0.331292i
$268$	−69.6069	−	89.6952i	−0.259727	−	0.334684i
$269$	95.4169	−	95.4169i	0.354710	−	0.354710i	−0.507149	−	0.861858i	$-0.669301\pi$
$269$	95.4169	−	95.4169i	0.354710	−	0.354710i	0.861858	+	0.507149i	$0.169301\pi$
$270$	3.06460	−	48.7976i	0.0113504	−	0.180732i
$271$		−	46.4991i		−	0.171583i	−0.996313	−	0.0857917i	$-0.972658\pi$
$271$		−	46.4991i		−	0.171583i	0.996313	−	0.0857917i	$-0.0273420\pi$
$272$	466.821	+	119.636i	1.71625	+	0.439840i
$273$	−42.4719			−0.155575
$274$	4.28657	+	0.269206i	0.0156444	+	0.000982505i
$275$	−19.5516	−	19.5516i	−0.0710967	−	0.0710967i
$276$	119.928	+	154.539i	0.434522	+	0.559924i
$277$	30.5071	+	30.5071i	0.110134	+	0.110134i	0.760026	−	0.649892i	$-0.225186\pi$
$277$	30.5071	+	30.5071i	0.110134	+	0.110134i	−0.649892	+	0.760026i	$0.725186\pi$
$278$	−204.367	−	231.757i	−0.735134	−	0.833657i
$279$	−114.119			−0.409028
$280$	−125.764	+	85.5308i	−0.449157	+	0.305467i
$281$			217.239i			0.773093i	0.922270	+	0.386547i	$0.126332\pi$
$281$			217.239i			0.773093i	−0.922270	+	0.386547i	$0.873668\pi$
$282$	36.2698	+	41.1307i	0.128616	+	0.145854i
$283$	−136.055	+	136.055i	−0.480760	+	0.480760i	−0.905374	−	0.424614i	$-0.860410\pi$
$283$	−136.055	+	136.055i	−0.480760	+	0.480760i	0.424614	+	0.905374i	$0.360410\pi$
$284$	−159.067	−	20.0587i	−0.560096	−	0.0706292i
$285$	160.981	−	160.981i	0.564846	−	0.564846i
$286$	116.904	+	7.34186i	0.408756	+	0.0256708i
$287$		−	194.909i		−	0.679126i
$288$	−91.3180	−	29.6145i	−0.317076	−	0.102828i
$289$	618.167			2.13898
$290$	17.8165	−	283.691i	0.0614361	−	0.978246i
$291$	−137.591	−	137.591i	−0.472821	−	0.472821i
$292$	15.4185	−	122.270i	0.0528030	−	0.418732i
$293$	−56.8362	−	56.8362i	−0.193980	−	0.193980i	0.603433	−	0.797414i	$-0.293799\pi$
$293$	−56.8362	−	56.8362i	−0.193980	−	0.193980i	−0.797414	+	0.603433i	$0.793799\pi$
$294$	84.8866	−	74.8545i	0.288730	−	0.254607i
$295$	66.3841			0.225031
$296$	−401.260	+	272.893i	−1.35561	+	0.921935i
$297$			50.1502i			0.168856i
$298$	−169.067	+	149.086i	−0.567339	+	0.500289i
$299$	−121.152	+	121.152i	−0.405190	+	0.405190i
$300$	−15.6806	+	12.1688i	−0.0522688	+	0.0405626i
$301$	−132.042	+	132.042i	−0.438677	+	0.438677i
$302$	−13.2310	+	210.677i	−0.0438113	+	0.697608i
$303$		−	3.96654i		−	0.0130909i
$304$	−227.714	−	384.650i	−0.749060	−	1.26530i
$305$	252.474			0.827782
$306$	−180.360	−	11.3270i	−0.589411	−	0.0370164i
$307$	245.927	+	245.927i	0.801067	+	0.801067i	0.983262	−	0.182196i	$-0.0583205\pi$
$307$	245.927	+	245.927i	0.801067	+	0.801067i	−0.182196	+	0.983262i	$0.558320\pi$
$308$	123.243	−	95.6416i	0.400141	−	0.310525i
$309$	34.2897	+	34.2897i	0.110970	+	0.110970i
$310$	−236.738	−	268.466i	−0.763671	−	0.866019i
$311$	−359.964			−1.15744			−0.578721	−	0.815526i	$-0.696448\pi$
$311$	−359.964			−1.15744			−0.578721	+	0.815526i	$0.696448\pi$
$312$	15.7281	−	82.6003i	0.0504106	−	0.264744i
$313$		−	131.023i		−	0.418605i	−0.977851	−	0.209303i	$-0.932881\pi$
$313$		−	131.023i		−	0.418605i	0.977851	−	0.209303i	$-0.0671194\pi$
$314$	355.547	+	403.198i	1.13231	+	1.28407i
$315$	40.3296	−	40.3296i	0.128030	−	0.128030i
$316$	65.1205	−	516.412i	0.206077	−	1.63421i
$317$	89.0470	−	89.0470i	0.280905	−	0.280905i	−0.552565	−	0.833470i	$-0.686351\pi$
$317$	89.0470	−	89.0470i	0.280905	−	0.280905i	0.833470	+	0.552565i	$0.186351\pi$
$318$	2.33158	+	0.146429i	0.00733202	+	0.000460468i
$319$			291.555i			0.913966i
$320$	−119.770	−	276.262i	−0.374280	−	0.863319i
$321$	−98.9189			−0.308159
$322$	−14.3024	+	227.736i	−0.0444172	+	0.707255i
$323$	−595.000	−	595.000i	−1.84210	−	1.84210i
$324$	35.7171	+	4.50400i	0.110238	+	0.0139012i
$325$	−12.2929	−	12.2929i	−0.0378244	−	0.0378244i
$326$	126.040	−	111.144i	0.386626	−	0.340934i
$327$	90.2236			0.275913
$328$	379.064	+	72.1783i	1.15568	+	0.220056i
$329$			63.9690i			0.194435i
$330$	−117.979	+	104.036i	−0.357512	+	0.315261i
$331$	95.5992	−	95.5992i	0.288819	−	0.288819i	−0.547794	−	0.836613i	$-0.684532\pi$
$331$	95.5992	−	95.5992i	0.288819	−	0.288819i	0.836613	+	0.547794i	$0.184532\pi$
$332$	7.84336	+	10.1069i	0.0236246	+	0.0304425i
$333$	128.675	−	128.675i	0.386410	−	0.386410i
$334$	−8.19706	+	130.522i	−0.0245421	+	0.390783i
$335$			133.541i			0.398629i
$336$	−57.0478	−	96.3640i	−0.169785	−	0.286798i
$337$	583.717			1.73210			0.866050	−	0.499958i	$-0.166651\pi$
$337$	583.717			1.73210			0.866050	+	0.499958i	$0.166651\pi$
$338$	−263.833	−	16.5693i	−0.780570	−	0.0490215i
$339$	−68.0900	−	68.0900i	−0.200855	−	0.200855i
$340$	−347.508	−	447.797i	−1.02208	−	1.31705i
$341$	259.604	+	259.604i	0.761302	+	0.761302i
$342$	110.867	+	125.725i	0.324172	+	0.367617i
$343$	330.024			0.962169
$344$	−207.900	−	305.695i	−0.604362	−	0.888649i
$345$		−	230.082i		−	0.666904i
$346$	−398.347	−	451.734i	−1.15129	−	1.30559i
$347$	191.655	−	191.655i	0.552320	−	0.552320i	−0.374790	−	0.927110i	$-0.622285\pi$
$347$	191.655	−	191.655i	0.552320	−	0.552320i	0.927110	+	0.374790i	$0.122285\pi$
$348$	207.647	+	26.1846i	0.596686	+	0.0752432i
$349$	−19.4781	+	19.4781i	−0.0558112	+	0.0558112i	−0.734462	−	0.678650i	$-0.762565\pi$
$349$	−19.4781	+	19.4781i	−0.0558112	+	0.0558112i	0.678650	+	0.734462i	$0.262565\pi$
$350$	−23.1077	−	1.45122i	−0.0660221	−	0.00414634i
$351$			31.5316i			0.0898337i
$352$	140.367	+	275.105i	0.398769	+	0.781547i
$353$	−82.9610			−0.235017			−0.117509	−	0.993072i	$-0.537491\pi$
$353$	−82.9610			−0.235017			−0.117509	+	0.993072i	$0.537491\pi$
$354$	−3.06362	+	48.7819i	−0.00865428	+	0.137802i
$355$	133.344	+	133.344i	0.375616	+	0.375616i
$356$	−36.1437	+	286.623i	−0.101527	+	0.805120i
$357$	−149.061	−	149.061i	−0.417539	−	0.417539i
$358$	−417.606	+	368.253i	−1.16650	+	1.02864i
$359$	357.792			0.996634			0.498317	−	0.866995i	$-0.333952\pi$
$359$	357.792			0.996634			0.498317	+	0.866995i	$0.333952\pi$
$360$	63.4991	+	93.3686i	0.176386	+	0.259357i
$361$			419.507i			1.16207i
$362$	58.1971	−	51.3193i	0.160766	−	0.141766i
$363$	−34.1095	+	34.1095i	−0.0939655	+	0.0939655i
$364$	77.4886	−	60.1341i	0.212881	−	0.165204i
$365$	−102.497	+	102.497i	−0.280814	+	0.280814i
$366$	−11.6516	+	185.529i	−0.0318350	+	0.506909i
$367$		−	651.729i		−	1.77583i	−0.460010	−	0.887914i	$-0.652154\pi$
$367$		−	651.729i		−	1.77583i	0.460010	−	0.887914i	$-0.347846\pi$
$368$	−437.610	−	112.150i	−1.18916	−	0.304756i
$369$	−144.703			−0.392149
$370$	569.643	+	35.7749i	1.53958	+	0.0966889i
$371$	1.92698	+	1.92698i	0.00519401	+	0.00519401i
$372$	208.206	−	161.576i	0.559693	−	0.434343i
$373$	199.720	+	199.720i	0.535442	+	0.535442i	0.922187	−	0.386745i	$-0.126401\pi$
$373$	199.720	+	199.720i	0.535442	+	0.535442i	−0.386745	+	0.922187i	$0.626401\pi$
$374$	384.526	+	436.061i	1.02814	+	1.16594i
$375$	227.069			0.605519
$376$	−124.408	−	23.6889i	−0.330873	−	0.0630023i
$377$			183.314i			0.486243i
$378$	27.7747	+	31.4971i	0.0734781	+	0.0833257i
$379$	−330.204	+	330.204i	−0.871251	+	0.871251i	−0.992609	−	0.121358i	$-0.961275\pi$
$379$	−330.204	+	330.204i	−0.871251	+	0.871251i	0.121358	+	0.992609i	$0.461275\pi$
$380$	−65.7787	+	521.631i	−0.173102	+	1.37271i
$381$	134.633	−	134.633i	0.353367	−	0.353367i
$382$	−487.857	−	30.6385i	−1.27711	−	0.0802055i
$383$		−	174.284i		−	0.455049i	−0.973772	−	0.227524i	$-0.926937\pi$
$383$		−	174.284i		−	0.455049i	0.973772	−	0.227524i	$-0.0730631\pi$
$384$	208.537	−	75.2625i	0.543064	−	0.195996i
$385$	−183.488			−0.476593
$386$	−31.9712	+	509.077i	−0.0828270	+	1.31885i
$387$	98.0294	+	98.0294i	0.253306	+	0.253306i
$388$	445.839	+	56.2212i	1.14907	+	0.144900i
$389$	207.835	+	207.835i	0.534279	+	0.534279i	0.921843	−	0.387564i	$-0.126683\pi$
$389$	207.835	+	207.835i	0.534279	+	0.534279i	−0.387564	+	0.921843i	$0.626683\pi$
$390$	−74.1786	+	65.4120i	−0.190202	+	0.167723i
$391$	−850.402			−2.17494
$392$	−48.8896	+	256.757i	−0.124718	+	0.654992i
$393$			185.376i			0.471695i
$394$	412.043	−	363.347i	1.04579	−	0.922200i
$395$	−432.900	+	432.900i	−1.09595	+	1.09595i
$396$	−71.0055	−	91.4974i	−0.179307	−	0.231054i
$397$	−37.2994	+	37.2994i	−0.0939533	+	0.0939533i	−0.752521	−	0.658568i	$-0.771162\pi$
$397$	−37.2994	+	37.2994i	−0.0939533	+	0.0939533i	0.658568	+	0.752521i	$0.271162\pi$
$398$	21.2854	−	338.927i	0.0534808	−	0.851574i
$399$			195.535i			0.490063i
$400$	11.3796	−	44.4031i	0.0284489	−	0.111008i
$401$	−524.704			−1.30849			−0.654244	−	0.756284i	$-0.727013\pi$
$401$	−524.704			−1.30849			−0.654244	+	0.756284i	$0.727013\pi$
$402$	−98.1315	−	6.16288i	−0.244108	−	0.0153305i
$403$	163.224	+	163.224i	0.405023	+	0.405023i
$404$	5.61605	+	7.23682i	0.0139011	+	0.0179129i
$405$	−29.9411	−	29.9411i	−0.0739288	−	0.0739288i
$406$	161.472	+	183.113i	0.397715	+	0.451017i
$407$	−585.434			−1.43841
$408$	345.098	−	234.698i	0.845829	−	0.575240i
$409$		−	787.357i		−	1.92508i	−0.271141	−	0.962540i	$-0.587401\pi$
$409$		−	787.357i		−	1.92508i	0.271141	−	0.962540i	$-0.412599\pi$
$410$	−300.184	−	340.416i	−0.732157	−	0.830282i
$411$	2.63015	−	2.63015i	0.00639939	−	0.00639939i
$412$	−111.110	−	14.0111i	−0.269684	−	0.0340076i
$413$	−40.3166	+	40.3166i	−0.0976190	+	0.0976190i
$414$	169.074	+	10.6182i	0.408392	+	0.0256479i
$415$		−	15.0475i		−	0.0362589i
$416$	88.2548	+	172.970i	0.212151	+	0.415794i
$417$	−267.596			−0.641718
$418$	33.8010	−	538.213i	0.0808637	−	1.28759i
$419$	30.1767	+	30.1767i	0.0720209	+	0.0720209i	0.742200	−	0.670179i	$-0.233783\pi$
$419$	30.1767	+	30.1767i	0.0720209	+	0.0720209i	−0.670179	+	0.742200i	$0.733783\pi$
$420$	−16.4791	+	130.681i	−0.0392360	+	0.311145i
$421$	−261.021	−	261.021i	−0.620003	−	0.620003i	0.325529	−	0.945532i	$-0.394458\pi$
$421$	−261.021	−	261.021i	−0.620003	−	0.620003i	−0.945532	+	0.325529i	$0.894458\pi$
$422$	281.494	−	248.227i	0.667048	−	0.588215i
$423$	47.4914			0.112273
$424$	−4.46122	+	3.03403i	−0.0105217	+	0.00715574i
$425$		−	86.2878i		−	0.203030i
$426$	−104.141	+	91.8330i	−0.244462	+	0.215571i
$427$	−153.333	+	153.333i	−0.359094	+	0.359094i
$428$	180.474	−	140.055i	0.421669	−	0.327231i
$429$	71.7300	−	71.7300i	0.167203	−	0.167203i
$430$	−27.2547	+	433.977i	−0.0633830	+	1.00925i
$431$		−	459.989i		−	1.06726i	−0.845718	−	0.533630i	$-0.820828\pi$
$431$		−	459.989i		−	1.06726i	0.845718	−	0.533630i	$-0.179172\pi$
$432$	−71.5418	+	42.3530i	−0.165606	+	0.0980392i
$433$	−445.246			−1.02828			−0.514140	−	0.857706i	$-0.671889\pi$
$433$	−445.246			−1.02828			−0.514140	+	0.857706i	$0.671889\pi$
$434$	306.822	+	19.2691i	0.706964	+	0.0443989i
$435$	−174.067	−	174.067i	−0.400154	−	0.400154i
$436$	−164.610	+	127.744i	−0.377546	+	0.292990i
$437$	557.768	+	557.768i	1.27636	+	1.27636i
$438$	−70.5891	−	80.0495i	−0.161162	−	0.182761i
$439$	356.467			0.811998			0.405999	−	0.913874i	$-0.366924\pi$
$439$	356.467			0.811998			0.405999	+	0.913874i	$0.366924\pi$
$440$	67.9489	−	356.852i	0.154429	−	0.811027i
$441$		−	98.0138i		−	0.222253i
$442$	241.768	+	274.171i	0.546987	+	0.620295i
$443$	358.752	−	358.752i	0.809824	−	0.809824i	−0.174783	−	0.984607i	$-0.555922\pi$
$443$	358.752	−	358.752i	0.809824	−	0.809824i	0.984607	+	0.174783i	$0.0559224\pi$
$444$	−52.5779	+	416.948i	−0.118419	+	0.939071i
$445$	240.272	−	240.272i	0.539936	−	0.539936i
$446$	52.5837	+	3.30237i	0.117901	+	0.00740442i
$447$			195.212i			0.436716i
$448$	240.519	+	95.0415i	0.536874	+	0.212146i
$449$	−44.6564			−0.0994576			−0.0497288	−	0.998763i	$-0.515836\pi$
$449$	−44.6564			−0.0994576			−0.0497288	+	0.998763i	$0.515836\pi$
$450$	−1.07740	+	17.1555i	−0.00239423	+	0.0381233i
$451$	329.179	+	329.179i	0.729886	+	0.729886i
$452$	220.634	+	27.8223i	0.488128	+	0.0615538i
$453$	129.267	+	129.267i	0.285358	+	0.285358i
$454$	149.213	−	131.579i	0.328663	−	0.289821i
$455$	−115.367			−0.253554
$456$	−380.282	−	72.4102i	−0.833951	−	0.158794i
$457$		−	84.2332i		−	0.184318i	−0.995744	−	0.0921589i	$-0.970623\pi$
$457$		−	84.2332i		−	0.184318i	0.995744	−	0.0921589i	$-0.0293768\pi$
$458$	457.394	−	403.338i	0.998678	−	0.880652i
$459$	−110.665	+	110.665i	−0.241100	+	0.241100i
$460$	325.763	+	419.777i	0.708180	+	0.912558i
$461$	205.347	−	205.347i	0.445438	−	0.445438i	−0.448397	−	0.893835i	$-0.648005\pi$
$461$	205.347	−	205.347i	0.445438	−	0.445438i	0.893835	+	0.448397i	$0.148005\pi$
$462$	8.46795	−	134.835i	0.0183289	−	0.291851i
$463$		−	270.647i		−	0.584550i	−0.956334	−	0.292275i	$-0.905588\pi$
$463$		−	270.647i		−	0.584550i	0.956334	−	0.292275i	$-0.0944123\pi$
$464$	−415.918	+	246.225i	−0.896376	+	0.530657i
$465$	−309.983			−0.666629
$466$	−366.983	−	23.0474i	−0.787517	−	0.0494579i
$467$	230.389	+	230.389i	0.493338	+	0.493338i	0.909356	−	0.416018i	$-0.136575\pi$
$467$	230.389	+	230.389i	0.493338	+	0.493338i	−0.416018	+	0.909356i	$0.636575\pi$
$468$	−44.6443	−	57.5284i	−0.0953937	−	0.122924i
$469$	−81.1024	−	81.1024i	−0.172926	−	0.172926i
$470$	98.5203	+	111.724i	0.209618	+	0.237711i
$471$	465.549			0.988428
$472$	−63.4788	−	93.3387i	−0.134489	−	0.197751i
$473$		−	446.006i		−	0.942931i
$474$	−298.136	−	338.092i	−0.628978	−	0.713275i
$475$	−56.5952	+	56.5952i	−0.119148	+	0.119148i
$476$	483.008	+	60.9082i	1.01472	+	0.127958i
$477$	1.43061	−	1.43061i	0.00299918	−	0.00299918i
$478$	−629.127	−	39.5106i	−1.31616	−	0.0826581i
$479$		−	575.911i		−	1.20232i	−0.799129	−	0.601159i	$-0.794706\pi$
$479$		−	575.911i		−	1.20232i	0.799129	−	0.601159i	$-0.205294\pi$
$480$	−248.049	−	80.4424i	−0.516768	−	0.167588i
$481$	−368.088			−0.765255
$482$	41.0926	−	654.318i	0.0852545	−	1.35751i
$483$	139.734	+	139.734i	0.289305	+	0.289305i
$484$	13.9375	−	110.526i	0.0287965	−	0.228359i
$485$	−373.740	−	373.740i	−0.770599	−	0.770599i
$486$	23.3838	−	20.6203i	0.0481149	−	0.0424286i
$487$	600.355			1.23276			0.616381	−	0.787448i	$-0.288598\pi$
$487$	600.355			1.23276			0.616381	+	0.787448i	$0.288598\pi$
$488$	−241.424	−	354.988i	−0.494721	−	0.727434i
$489$		−	145.531i		−	0.297610i
$490$	230.579	−	203.329i	0.470569	−	0.414956i
$491$	79.7182	−	79.7182i	0.162359	−	0.162359i	−0.621252	−	0.783611i	$-0.713376\pi$
$491$	79.7182	−	79.7182i	0.162359	−	0.162359i	0.783611	+	0.621252i	$0.213376\pi$
$492$	264.006	−	204.879i	0.536597	−	0.416420i
$493$	−643.367	+	643.367i	−1.30500	+	1.30500i
$494$	21.2522	−	338.398i	0.0430206	−	0.685017i
$495$			136.224i			0.275200i
$496$	−151.097	+	589.580i	−0.304631	+	1.18867i
$497$	−161.966			−0.325887
$498$	11.0575	+	0.694437i	0.0222039	+	0.00139445i
$499$	−13.4912	−	13.4912i	−0.0270365	−	0.0270365i	0.693459	−	0.720496i	$-0.256086\pi$
$499$	−13.4912	−	13.4912i	−0.0270365	−	0.0270365i	−0.720496	+	0.693459i	$0.756086\pi$
$500$	−414.281	+	321.498i	−0.828562	+	0.642996i
$501$	80.0853	+	80.0853i	0.159851	+	0.159851i
$502$	411.205	+	466.316i	0.819134	+	0.928916i
$503$	892.196			1.77375			0.886875	−	0.462009i	$-0.152871\pi$
$503$	892.196			1.77375			0.886875	+	0.462009i	$0.152871\pi$
$504$	−95.2695	−	18.1405i	−0.189027	−	0.0359930i
$505$		−	10.7744i		−	0.0213354i
$506$	−360.465	−	408.775i	−0.712381	−	0.807855i
$507$	−161.882	+	161.882i	−0.319294	+	0.319294i
$508$	−55.0125	+	436.254i	−0.108292	+	0.858768i
$509$	−44.9128	+	44.9128i	−0.0882374	+	0.0882374i	−0.749848	−	0.661610i	$-0.769873\pi$
$509$	−44.9128	+	44.9128i	−0.0882374	+	0.0882374i	0.661610	+	0.749848i	$0.269873\pi$
$510$	−489.915	−	30.7677i	−0.960617	−	0.0603289i
$511$		−	124.498i		−	0.243636i
$512$	−273.908	+	432.572i	−0.534976	+	0.844867i
$513$	145.168			0.282978
$514$	−18.8090	+	299.495i	−0.0365933	+	0.582675i
$515$	93.1416	+	93.1416i	0.180857	+	0.180857i
$516$	−317.647	−	40.0559i	−0.615595	−	0.0776277i
$517$	−108.036	−	108.036i	−0.208967	−	0.208967i
$518$	−367.685	+	324.231i	−0.709816	+	0.625929i
$519$	−521.592			−1.00499
$520$	42.7225	−	224.368i	0.0821586	−	0.431478i
$521$			866.038i			1.66226i	0.556078	+	0.831130i	$0.312306\pi$
$521$			866.038i			1.66226i	−0.556078	+	0.831130i	$0.687694\pi$
$522$	135.945	−	119.879i	0.260432	−	0.229653i
$523$	359.579	−	359.579i	0.687531	−	0.687531i	−0.274155	−	0.961686i	$-0.588398\pi$
$523$	359.579	−	359.579i	0.687531	−	0.687531i	0.961686	+	0.274155i	$0.0883981\pi$
$524$	−262.466	−	338.213i	−0.500889	−	0.645444i
$525$	−14.1784	+	14.1784i	−0.0270065	+	0.0270065i
$526$	−1.86684	+	29.7257i	−0.00354913	+	0.0565128i
$527$			1145.72i			2.17405i
$528$	259.095	+	66.4005i	0.490709	+	0.125759i
$529$	268.189			0.506973
$530$	6.33332	+	0.397747i	0.0119497	+	0.000750466i
$531$	29.9316	+	29.9316i	0.0563683	+	0.0563683i
$532$	−276.850	−	356.748i	−0.520395	−	0.670579i
$533$	206.969	+	206.969i	0.388310	+	0.388310i
$534$	165.474	+	187.651i	0.309876	+	0.351406i
$535$	−268.695			−0.502234
$536$	187.764	−	127.696i	0.350305	−	0.238239i
$537$			482.187i			0.897926i
$538$	178.497	+	202.420i	0.331779	+	0.376245i
$539$	−222.968	+	222.968i	−0.413669	+	0.413669i
$540$	97.0190	+	12.2343i	0.179665	+	0.0226561i
$541$	−9.41176	+	9.41176i	−0.0173970	+	0.0173970i	−0.715752	−	0.698355i	$-0.753916\pi$
$541$	−9.41176	+	9.41176i	−0.0173970	+	0.0173970i	0.698355	+	0.715752i	$0.253916\pi$
$542$	92.8154	+	5.82902i	0.171246	+	0.0107546i
$543$		−	67.1970i		−	0.123751i
$544$	−297.322	+	916.809i	−0.546548	+	1.68531i
$545$	245.076			0.449680
$546$	5.32417	−	84.7767i	0.00975123	−	0.155269i
$547$	−37.6377	−	37.6377i	−0.0688075	−	0.0688075i	0.671866	−	0.740673i	$-0.265493\pi$
$547$	−37.6377	−	37.6377i	−0.0688075	−	0.0688075i	−0.740673	+	0.671866i	$0.765493\pi$
$548$	−1.07471	+	8.52253i	−0.00196115	+	0.0155521i
$549$	113.836	+	113.836i	0.207352	+	0.207352i
$550$	41.4772	−	36.5753i	0.0754131	−	0.0665006i
$551$	843.953			1.53168
$552$	−323.504	+	220.012i	−0.586058	+	0.398573i
$553$		−	525.821i		−	0.950852i
$554$	−64.7186	+	57.0700i	−0.116821	+	0.103014i
$555$	349.521	−	349.521i	0.629768	−	0.629768i
$556$	488.221	−	378.878i	0.878096	−	0.681436i
$557$	369.172	−	369.172i	0.662786	−	0.662786i	−0.293250	−	0.956036i	$-0.594737\pi$
$557$	369.172	−	369.172i	0.662786	−	0.662786i	0.956036	+	0.293250i	$0.0947369\pi$
$558$	14.3056	−	227.789i	0.0256374	−	0.408223i
$559$		−	280.424i		−	0.501652i
$560$	−154.960	−	261.755i	−0.276714	−	0.467420i
$561$	503.495			0.897495
$562$	−433.624	−	27.2326i	−0.771573	−	0.0484565i
$563$	−141.210	−	141.210i	−0.250817	−	0.250817i	0.570489	−	0.821306i	$-0.306754\pi$
$563$	−141.210	−	141.210i	−0.250817	−	0.250817i	−0.821306	+	0.570489i	$0.806754\pi$
$564$	−86.6464	+	67.2410i	−0.153628	+	0.119222i
$565$	−184.954	−	184.954i	−0.327352	−	0.327352i
$566$	−254.520	−	288.631i	−0.449682	−	0.509949i
$567$	36.3679			0.0641410
$568$	59.9788	−	314.995i	0.105596	−	0.554568i
$569$		−	134.928i		−	0.237131i	−0.992946	−	0.118566i	$-0.962170\pi$
$569$		−	134.928i		−	0.237131i	0.992946	−	0.118566i	$-0.0378296\pi$
$570$	301.149	+	341.509i	0.528332	+	0.599139i
$571$	−486.485	+	486.485i	−0.851988	+	0.851988i	−0.990378	−	0.138390i	$-0.955807\pi$
$571$	−486.485	+	486.485i	−0.851988	+	0.851988i	0.138390	+	0.990378i	$0.455807\pi$
$572$	−29.3097	+	232.429i	−0.0512407	+	0.406344i
$573$	−299.339	+	299.339i	−0.522406	+	0.522406i
$574$	389.052	+	24.4333i	0.677790	+	0.0425668i
$575$			80.8885i			0.140676i
$576$	70.5600	−	178.565i	0.122500	−	0.310008i
$577$	−310.050			−0.537349			−0.268674	−	0.963231i	$-0.586586\pi$
$577$	−310.050			−0.537349			−0.268674	+	0.963231i	$0.586586\pi$
$578$	−77.4919	+	1233.90i	−0.134069	+	2.13478i
$579$	312.359	+	312.359i	0.539480	+	0.539480i
$580$	564.034	+	71.1257i	0.972472	+	0.122631i
$581$	9.13868	+	9.13868i	0.0157292	+	0.0157292i
$582$	291.889	−	257.393i	0.501527	−	0.442255i
$583$	−6.50888			−0.0111645
$584$	242.126	+	46.1037i	0.414599	+	0.0789448i
$585$			85.6499i			0.146410i
$586$	120.574	−	106.324i	0.205757	−	0.181440i
$587$	−301.021	+	301.021i	−0.512812	+	0.512812i	−0.915387	−	0.402575i	$-0.868115\pi$
$587$	−301.021	+	301.021i	−0.512812	+	0.512812i	0.402575	+	0.915387i	$0.368115\pi$
$588$	138.773	+	178.823i	0.236009	+	0.304121i
$589$	751.465	−	751.465i	1.27583	−	1.27583i
$590$	−8.32175	+	132.507i	−0.0141047	+	0.224588i
$591$		−	475.763i		−	0.805013i
$592$	−494.412	−	835.150i	−0.835155	−	1.41073i
$593$	6.08782			0.0102661			0.00513307	−	0.999987i	$-0.498366\pi$
$593$	6.08782			0.0102661			0.00513307	+	0.999987i	$0.498366\pi$
$594$	−100.103	−	6.28671i	−0.168524	−	0.0105837i
$595$	−404.898	−	404.898i	−0.680501	−	0.680501i
$596$	−276.392	−	356.158i	−0.463746	−	0.597581i
$597$	−207.958	−	207.958i	−0.348339	−	0.348339i
$598$	−226.640	−	257.015i	−0.378997	−	0.429790i
$599$	−756.472			−1.26289			−0.631446	−	0.775420i	$-0.717538\pi$
$599$	−756.472			−1.26289			−0.631446	+	0.775420i	$0.717538\pi$
$600$	−22.3240	−	32.8250i	−0.0372067	−	0.0547084i
$601$			753.072i			1.25303i	0.779409	+	0.626516i	$0.215520\pi$
$601$			753.072i			1.25303i	−0.779409	+	0.626516i	$0.784480\pi$
$602$	−247.012	−	280.117i	−0.410319	−	0.465310i
$603$	−60.2114	+	60.2114i	−0.0998531	+	0.0998531i
$604$	−418.868	−	52.8200i	−0.693490	−	0.0874504i
$605$	−92.6521	+	92.6521i	−0.153144	+	0.153144i
$606$	7.91748	+	0.497235i	0.0130651	+	0.000820521i
$607$		−	47.1200i		−	0.0776277i	−0.999246	−	0.0388139i	$-0.987642\pi$
$607$		−	47.1200i		−	0.0776277i	0.999246	−	0.0388139i	$-0.0123579\pi$
$608$	796.334	−	406.314i	1.30976	−	0.668280i
$609$	211.430			0.347176
$610$	−31.6495	+	503.954i	−0.0518844	+	0.826155i
$611$	−67.9271	−	67.9271i	−0.111174	−	0.111174i
$612$	45.2190	−	358.591i	0.0738872	−	0.585932i
$613$	637.192	+	637.192i	1.03947	+	1.03947i	0.999189	+	0.0402769i	$0.0128240\pi$
$613$	637.192	+	637.192i	1.03947	+	1.03947i	0.0402769	+	0.999189i	$0.487176\pi$
$614$	−521.717	+	460.059i	−0.849701	+	0.749282i
$615$	−393.059			−0.639120
$616$	175.458	+	257.992i	0.284834	+	0.418818i
$617$		−	514.635i		−	0.834092i	−0.908885	−	0.417046i	$-0.863065\pi$
$617$		−	514.635i		−	0.834092i	0.908885	−	0.417046i	$-0.136935\pi$
$618$	−72.7430	+	64.1460i	−0.117707	+	0.103796i
$619$	313.704	−	313.704i	0.506791	−	0.506791i	−0.406749	−	0.913540i	$-0.633338\pi$
$619$	313.704	−	313.704i	0.506791	−	0.506791i	0.913540	+	0.406749i	$0.133338\pi$
$620$	565.553	−	438.891i	0.912182	−	0.707888i
$621$	103.740	−	103.740i	0.167054	−	0.167054i
$622$	45.1243	−	718.513i	0.0725471	−	1.15517i
$623$			291.845i			0.468452i
$624$	162.904	+	41.7489i	0.261064	+	0.0669053i
$625$	545.171			0.872273
$626$	261.532	+	16.4248i	0.417782	+	0.0262377i
$627$	−330.236	−	330.236i	−0.526693	−	0.526693i
$628$	−849.380	+	659.151i	−1.35252	+	1.04960i
$629$	−1291.86	−	1291.86i	−2.05383	−	2.05383i
$630$	75.4449	+	85.5561i	0.119754	+	0.135803i
$631$	−1226.20			−1.94326			−0.971631	−	0.236502i	$-0.923999\pi$
$631$	−1226.20			−1.94326			−0.971631	+	0.236502i	$0.923999\pi$
$632$	1022.63	+	194.721i	1.61808	+	0.308103i
$633$		−	325.025i		−	0.513468i
$634$	166.581	+	188.906i	0.262746	+	0.297960i
$635$	365.706	−	365.706i	0.575914	−	0.575914i
$636$	−0.584563	+	4.63564i	−0.000919125	+	0.00728875i
$637$	−140.189	+	140.189i	−0.220078	+	0.220078i
$638$	−581.964	−	36.5487i	−0.912169	−	0.0572863i
$639$			120.245i			0.188177i
$640$	566.452	−	204.437i	0.885081	−	0.319432i
$641$	241.218			0.376314			0.188157	−	0.982139i	$-0.439749\pi$
$641$	241.218			0.376314			0.188157	+	0.982139i	$0.439749\pi$
$642$	12.4002	−	197.449i	0.0193150	−	0.307553i
$643$	−736.141	−	736.141i	−1.14485	−	1.14485i	−0.987550	−	0.157304i	$-0.949720\pi$
$643$	−736.141	−	736.141i	−1.14485	−	1.14485i	−0.157304	−	0.987550i	$-0.550280\pi$
$644$	−452.784	−	57.0969i	−0.703081	−	0.0886598i
$645$	266.279	+	266.279i	0.412835	+	0.412835i
$646$	1262.25	−	1113.07i	1.95394	−	1.72302i
$647$	−680.082			−1.05113			−0.525565	−	0.850753i	$-0.676146\pi$
$647$	−680.082			−1.05113			−0.525565	+	0.850753i	$0.676146\pi$
$648$	−13.4677	+	70.7292i	−0.0207835	+	0.109150i
$649$		−	136.180i		−	0.209831i
$650$	26.0785	−	22.9965i	0.0401208	−	0.0353793i
$651$	188.260	−	188.260i	0.289186	−	0.289186i
$652$	206.052	+	265.518i	0.316030	+	0.407235i
$653$	−716.929	+	716.929i	−1.09790	+	1.09790i	−0.103244	+	0.994656i	$0.532922\pi$
$653$	−716.929	+	716.929i	−1.09790	+	1.09790i	−0.994656	+	0.103244i	$0.967078\pi$
$654$	−11.3102	+	180.092i	−0.0172939	+	0.275371i
$655$			503.540i			0.768763i
$656$	−191.591	+	747.589i	−0.292060	+	1.13962i
$657$	−92.4286			−0.140683
$658$	−127.686	−	8.01900i	−0.194052	−	0.0121869i
$659$	276.868	+	276.868i	0.420133	+	0.420133i	0.885250	−	0.465116i	$-0.153988\pi$
$659$	276.868	+	276.868i	0.420133	+	0.420133i	−0.465116	+	0.885250i	$0.653988\pi$
$660$	−192.873	−	248.536i	−0.292232	−	0.376570i
$661$	251.780	+	251.780i	0.380907	+	0.380907i	0.871429	−	0.490522i	$-0.163194\pi$
$661$	251.780	+	251.780i	0.380907	+	0.380907i	−0.490522	+	0.871429i	$0.663194\pi$
$662$	178.838	+	202.807i	0.270149	+	0.306354i
$663$	316.569			0.477480
$664$	−21.1573	+	14.3889i	−0.0318634	+	0.0216700i
$665$			531.136i			0.798700i
$666$	240.713	+	272.974i	0.361431	+	0.409870i
$667$	603.109	−	603.109i	0.904211	−	0.904211i
$668$	−259.502	−	32.7238i	−0.388477	−	0.0489877i
$669$	32.2642	−	32.2642i	0.0482275	−	0.0482275i
$670$	−266.556	−	16.7403i	−0.397845	−	0.0249856i
$671$		−	517.924i		−	0.771869i
$672$	199.500	−	101.791i	0.296876	−	0.151475i
$673$	674.332			1.00198			0.500990	−	0.865453i	$-0.332969\pi$
$673$	674.332			1.00198			0.500990	+	0.865453i	$0.332969\pi$
$674$	−73.1734	+	1165.14i	−0.108566	+	1.72869i
$675$	10.5262	+	10.5262i	0.0155944	+	0.0155944i
$676$	66.1468	−	524.550i	0.0978503	−	0.775962i
$677$	109.048	+	109.048i	0.161075	+	0.161075i	0.783043	−	0.621968i	$-0.213666\pi$
$677$	109.048	+	109.048i	0.161075	+	0.161075i	−0.621968	+	0.783043i	$0.713666\pi$
$678$	144.448	−	127.377i	0.213050	−	0.187871i
$679$	453.963			0.668576
$680$	937.396	−	637.514i	1.37852	−	0.937521i
$681$		−	172.288i		−	0.252992i
$682$	−550.731	+	485.644i	−0.807523	+	0.712088i
$683$	−784.278	+	784.278i	−1.14828	+	1.14828i	−0.161394	+	0.986890i	$0.551599\pi$
$683$	−784.278	+	784.278i	−1.14828	+	1.14828i	−0.986890	+	0.161394i	$0.948401\pi$
$684$	−264.854	+	205.537i	−0.387213	+	0.300492i
$685$	7.14432	−	7.14432i	0.0104297	−	0.0104297i
$686$	−41.3710	+	658.750i	−0.0603076	+	0.960277i
$687$		−	528.128i		−	0.768745i
$688$	636.250	−	376.662i	0.924782	−	0.547474i
$689$	−4.09241			−0.00593964
$690$	459.259	+	28.8425i	0.665592	+	0.0418007i
$691$	−99.4915	−	99.4915i	−0.143982	−	0.143982i	0.631442	−	0.775423i	$-0.282464\pi$
$691$	−99.4915	−	99.4915i	−0.143982	−	0.143982i	−0.775423	+	0.631442i	$0.782464\pi$
$692$	951.628	−	738.500i	1.37518	−	1.06720i
$693$	−82.7320	−	82.7320i	−0.119382	−	0.119382i
$694$	358.531	+	406.582i	0.516615	+	0.585853i
$695$	−726.877			−1.04587
$696$	−78.2964	+	411.194i	−0.112495	+	0.590796i
$697$			1452.78i			2.08433i
$698$	−36.4379	−	41.3213i	−0.0522032	−	0.0591996i
$699$	−225.173	+	225.173i	−0.322136	+	0.322136i
$700$	5.79346	−	45.9427i	0.00827637	−	0.0656324i
$701$	177.909	−	177.909i	0.253794	−	0.253794i	−0.568730	−	0.822524i	$-0.692565\pi$
$701$	177.909	−	177.909i	0.253794	−	0.253794i	0.822524	+	0.568730i	$0.192565\pi$
$702$	−62.9393	−	3.95273i	−0.0896571	−	0.00563067i
$703$			1694.63i			2.41057i
$704$	−566.723	+	245.695i	−0.805005	+	0.348999i
$705$	129.002			0.182981
$706$	10.3998	−	165.596i	0.0147306	−	0.234555i
$707$	6.54353	+	6.54353i	0.00925535	+	0.00925535i
$708$	−96.9880	−	12.2304i	−0.136989	−	0.0172745i
$709$	−208.080	−	208.080i	−0.293484	−	0.293484i	0.544971	−	0.838455i	$-0.316541\pi$
$709$	−208.080	−	208.080i	−0.293484	−	0.293484i	−0.838455	+	0.544971i	$0.816541\pi$
$710$	−282.879	+	249.448i	−0.398421	+	0.351335i
$711$	−390.376			−0.549052
$712$	−567.587	−	108.076i	−0.797173	−	0.151791i
$713$		−	1074.03i		−	1.50635i
$714$	316.223	−	278.851i	0.442889	−	0.390547i
$715$	194.841	−	194.841i	0.272506	−	0.272506i
$716$	−682.707	−	879.734i	−0.953501	−	1.22868i
$717$	−386.019	+	386.019i	−0.538381	+	0.538381i
$718$	−44.8519	+	714.176i	−0.0624678	+	0.994674i
$719$			1013.84i			1.41007i	0.709171	+	0.705036i	$0.249069\pi$
$719$			1013.84i			1.41007i	−0.709171	+	0.705036i	$0.750931\pi$
$720$	−194.330	+	115.044i	−0.269903	+	0.159783i
$721$	−113.134			−0.156913
$722$	−837.364	−	52.5883i	−1.15978	−	0.0728370i
$723$	−401.476	−	401.476i	−0.555291	−	0.555291i
$724$	95.1413	+	122.599i	0.131411	+	0.169335i
$725$	61.1957	+	61.1957i	0.0844079	+	0.0844079i
$726$	−63.8089	−	72.3607i	−0.0878911	−	0.0996703i
$727$	697.156			0.958949			0.479474	−	0.877556i	$-0.340827\pi$
$727$	697.156			0.958949			0.479474	+	0.877556i	$0.340827\pi$
$728$	110.318	+	162.211i	0.151536	+	0.222817i
$729$		−	27.0000i		−	0.0370370i
$730$	−191.742	−	217.440i	−0.262661	−	0.297863i
$731$	984.189	−	984.189i	1.34636	−	1.34636i
$732$	−368.867	−	46.5148i	−0.503917	−	0.0635448i
$733$	−39.9608	+	39.9608i	−0.0545168	+	0.0545168i	−0.733840	−	0.679323i	$-0.762274\pi$
$733$	−39.9608	+	39.9608i	−0.0545168	+	0.0545168i	0.679323	+	0.733840i	$0.262274\pi$
$734$	1300.89	+	81.6991i	1.77234	+	0.111307i
$735$		−	266.236i		−	0.362226i
$736$	278.717	−	859.441i	0.378692	−	1.16772i
$737$	273.945			0.371703
$738$	18.1396	−	288.837i	0.0245794	−	0.391378i
$739$	−236.377	−	236.377i	−0.319860	−	0.319860i	0.528853	−	0.848713i	$-0.322622\pi$
$739$	−236.377	−	236.377i	−0.319860	−	0.319860i	−0.848713	+	0.528853i	$0.822622\pi$
$740$	−142.818	+	1132.56i	−0.192998	+	1.53049i
$741$	−207.634	−	207.634i	−0.280208	−	0.280208i
$742$	−4.08794	+	3.60481i	−0.00550935	+	0.00485824i
$743$	804.248			1.08243			0.541217	−	0.840883i	$-0.317964\pi$
$743$	804.248			1.08243			0.541217	+	0.840883i	$0.317964\pi$
$744$	296.416	+	435.848i	0.398409	+	0.585817i
$745$			530.258i			0.711755i
$746$	−423.691	+	373.618i	−0.567950	+	0.500828i
$747$	6.78466	−	6.78466i	0.00908255	−	0.00908255i
$748$	−918.610	+	712.877i	−1.22809	+	0.953043i
$749$	163.185	−	163.185i	0.217870	−	0.217870i
$750$	−28.4649	+	453.246i	−0.0379532	+	0.604328i
$751$			607.492i			0.808911i	0.914558	+	0.404456i	$0.132539\pi$
$751$			607.492i			0.808911i	−0.914558	+	0.404456i	$0.867461\pi$
$752$	62.8801	−	245.358i	0.0836171	−	0.326274i
$753$	538.429			0.715045
$754$	−365.906	−	22.9797i	−0.485287	−	0.0304771i
$755$	351.131	+	351.131i	0.465074	+	0.465074i
$756$	−66.3522	+	51.4918i	−0.0877674	+	0.0681109i
$757$	−11.6797	−	11.6797i	−0.0154289	−	0.0154289i	0.699350	−	0.714779i	$-0.253473\pi$
$757$	−11.6797	−	11.6797i	−0.0154289	−	0.0154289i	−0.714779	+	0.699350i	$0.753473\pi$
$758$	−617.716	−	700.503i	−0.814929	−	0.924147i
$759$	−471.989			−0.621857
$760$	−1032.96	−	196.689i	−1.35916	−	0.258801i
$761$		−	659.125i		−	0.866130i	−0.901363	−	0.433065i	$-0.857432\pi$
$761$		−	659.125i		−	0.866130i	0.901363	−	0.433065i	$-0.142568\pi$
$762$	251.859	+	285.614i	0.330524	+	0.374821i
$763$	−148.840	+	148.840i	−0.195073	+	0.195073i
$764$	122.313	−	969.954i	0.160096	−	1.26957i
$765$	−300.601	+	300.601i	−0.392943	+	0.392943i
$766$	347.882	+	21.8478i	0.454154	+	0.0285219i
$767$		−	85.6224i		−	0.111633i
$768$	124.087	+	425.688i	0.161572	+	0.554281i
$769$	−178.802			−0.232512			−0.116256	−	0.993219i	$-0.537089\pi$
$769$	−178.802			−0.232512			−0.116256	+	0.993219i	$0.537089\pi$
$770$	23.0016	−	366.255i	0.0298722	−	0.475656i
$771$	183.764	+	183.764i	0.238345	+	0.238345i
$772$	−1012.15	−	127.633i	−1.31107	−	0.165328i
$773$	−91.8171	−	91.8171i	−0.118780	−	0.118780i	0.645218	−	0.763998i	$-0.276766\pi$
$773$	−91.8171	−	91.8171i	−0.118780	−	0.118780i	−0.763998	+	0.645218i	$0.776766\pi$
$774$	−207.962	+	183.385i	−0.268685	+	0.236931i
$775$	108.979			0.140618
$776$	−168.111	+	882.877i	−0.216637	+	1.13773i
$777$			424.545i			0.546390i
$778$	−440.906	+	388.798i	−0.566717	+	0.499741i
$779$	952.860	−	952.860i	1.22318	−	1.22318i
$780$	−121.268	−	156.265i	−0.155472	−	0.200340i
$781$	273.541	−	273.541i	0.350245	−	0.350245i
$782$	106.604	−	1697.46i	0.136323	−	2.17066i
$783$		−	156.968i		−	0.200470i
$784$	−506.376	−	129.773i	−0.645887	−	0.165527i
$785$	1264.58			1.61093
$786$	−370.023	−	23.2383i	−0.470767	−	0.0295653i
$787$	214.856	+	214.856i	0.273006	+	0.273006i	0.830309	−	0.557303i	$-0.188164\pi$
$787$	214.856	+	214.856i	0.273006	+	0.273006i	−0.557303	+	0.830309i	$0.688164\pi$
$788$	673.612	+	868.014i	0.854838	+	1.10154i
$789$	18.2391	+	18.2391i	0.0231167	+	0.0231167i
$790$	−809.831	−	918.365i	−1.02510	−	1.16249i
$791$	224.654			0.284012
$792$	191.536	−	130.262i	0.241839	−	0.164472i
$793$		−	325.641i		−	0.410645i
$794$	−69.7764	−	79.1280i	−0.0878796	−	0.0996574i
$795$	3.88599	−	3.88599i	0.00488804	−	0.00488804i
$796$	673.852	+	84.9740i	0.846548	+	0.106751i
$797$	−332.028	+	332.028i	−0.416598	+	0.416598i	−0.884029	−	0.467432i	$-0.845179\pi$
$797$	−332.028	+	332.028i	−0.416598	+	0.416598i	0.467432	+	0.884029i	$0.345179\pi$
$798$	−390.302	−	24.5118i	−0.489100	−	0.0307166i
$799$		−	476.801i		−	0.596747i
$800$	87.2050	+	28.2807i	0.109006	+	0.0353508i
$801$	216.669			0.270499
$802$	65.7756	−	1047.34i	0.0820144	−	1.30592i
$803$	210.262	+	210.262i	0.261846	+	0.261846i
$804$	24.6031	−	195.105i	0.0306008	−	0.242667i
$805$	379.562	+	379.562i	0.471506	+	0.471506i
$806$	−346.268	+	305.346i	−0.429613	+	0.378841i
$807$	233.723			0.289619
$808$	−15.1492	+	10.3028i	−0.0187490	+	0.0127510i
$809$		−	421.989i		−	0.521618i	−0.965390	−	0.260809i	$-0.916011\pi$
$809$		−	421.989i		−	0.521618i	0.965390	−	0.260809i	$-0.0839893\pi$
$810$	63.5179	−	56.0112i	0.0784172	−	0.0691496i
$811$	532.822	−	532.822i	0.656994	−	0.656994i	−0.297674	−	0.954668i	$-0.596211\pi$
$811$	532.822	−	532.822i	0.656994	−	0.656994i	0.954668	+	0.297674i	$0.0962107\pi$
$812$	−385.748	+	299.355i	−0.475059	+	0.368664i
$813$	56.9496	−	56.9496i	0.0700487	−	0.0700487i
$814$	73.3885	−	1168.56i	0.0901579	−	1.43558i
$815$		−	395.310i		−	0.485042i
$816$	425.212	+	718.261i	0.521094	+	0.880221i
$817$	−1291.04			−1.58022
$818$	1571.62	+	98.7012i	1.92129	+	0.120662i
$819$	−52.0172	−	52.0172i	−0.0635131	−	0.0635131i
$820$	717.123	−	556.515i	0.874540	−	0.678677i
$821$	−797.754	−	797.754i	−0.971686	−	0.971686i	0.0279241	−	0.999610i	$-0.491110\pi$
$821$	−797.754	−	797.754i	−0.971686	−	0.971686i	−0.999610	+	0.0279241i	$0.991110\pi$
$822$	4.92024	+	5.57966i	0.00598570	+	0.00678791i
$823$	863.777			1.04955			0.524773	−	0.851242i	$-0.324150\pi$
$823$	863.777			1.04955			0.524773	+	0.851242i	$0.324150\pi$
$824$	41.8956	−	220.026i	0.0508442	−	0.267022i
$825$		−	47.8914i		−	0.0580502i
$826$	−75.4207	−	85.5287i	−0.0913084	−	0.103546i
$827$	−1154.08	+	1154.08i	−1.39550	+	1.39550i	−0.583098	+	0.812402i	$0.698160\pi$
$827$	−1154.08	+	1154.08i	−1.39550	+	1.39550i	−0.812402	+	0.583098i	$0.801840\pi$
$828$	−42.3894	+	336.152i	−0.0511950	+	0.405981i
$829$	473.183	−	473.183i	0.570788	−	0.570788i	−0.361561	−	0.932349i	$-0.617756\pi$
$829$	473.183	−	473.183i	0.570788	−	0.570788i	0.932349	+	0.361561i	$0.117756\pi$
$830$	30.0357	+	1.88631i	0.0361876	+	0.00227266i
$831$			74.7269i			0.0899241i
$832$	−356.324	+	154.479i	−0.428274	+	0.185672i
$833$	−984.033			−1.18131
$834$	33.5452	−	534.141i	0.0402221	−	0.640456i
$835$	217.537	+	217.537i	0.260523	+	0.260523i
$836$	1070.07	+	134.938i	1.27999	+	0.161409i
$837$	−139.766	−	139.766i	−0.166985	−	0.166985i
$838$	−64.0177	+	56.4519i	−0.0763934	+	0.0673651i
$839$	561.776			0.669578			0.334789	−	0.942293i	$-0.391335\pi$
$839$	561.776			0.669578			0.334789	+	0.942293i	$0.391335\pi$
$840$	−258.782	−	49.2752i	−0.308074	−	0.0586610i
$841$		−	71.5574i		−	0.0850861i
$842$	553.737	−	488.295i	0.657645	−	0.579923i
$843$	−266.063	+	266.063i	−0.315614	+	0.315614i
$844$	460.189	+	592.998i	0.545248	+	0.702605i
$845$	−439.723	+	439.723i	−0.520382	+	0.520382i
$846$	−5.95340	+	94.7959i	−0.00703712	+	0.112052i
$847$		−	112.540i		−	0.132869i
$848$	−5.49689	−	9.28524i	−0.00648218	−	0.0109496i
$849$	−333.266			−0.392539
$850$	172.236	+	10.8168i	0.202631	+	0.0127257i
$851$	1211.02	+	1211.02i	1.42306	+	1.42306i
$852$	−170.250	−	219.384i	−0.199824	−	0.257493i
$853$	−431.517	−	431.517i	−0.505881	−	0.505881i	0.407378	−	0.913259i	$-0.366443\pi$
$853$	−431.517	−	431.517i	−0.505881	−	0.505881i	−0.913259	+	0.407378i	$0.866443\pi$
$854$	−286.842	−	325.285i	−0.335881	−	0.380896i
$855$	394.322			0.461195
$856$	256.935	+	377.796i	0.300158	+	0.441350i
$857$			448.237i			0.523030i	0.965199	+	0.261515i	$0.0842221\pi$
$857$			448.237i			0.523030i	−0.965199	+	0.261515i	$0.915778\pi$
$858$	134.186	+	152.170i	0.156394	+	0.177354i
$859$	−617.299	+	617.299i	−0.718625	+	0.718625i	−0.968324	−	0.249699i	$-0.919668\pi$
$859$	−617.299	+	617.299i	−0.718625	+	0.718625i	0.249699	+	0.968324i	$0.419668\pi$
$860$	−862.830	−	108.804i	−1.00329	−	0.126517i
$861$	238.714	−	238.714i	0.277252	−	0.277252i
$862$	918.169	+	57.6631i	1.06516	+	0.0668946i
$863$		−	1588.33i		−	1.84047i	−0.391363	−	0.920236i	$-0.627996\pi$
$863$		−	1588.33i		−	1.84047i	0.391363	−	0.920236i	$-0.372004\pi$
$864$	−75.5710	−	148.112i	−0.0874665	−	0.171425i
$865$	−1416.81			−1.63793
$866$	55.8149	−	888.740i	0.0644514	−	1.02626i
$867$	757.096	+	757.096i	0.873237	+	0.873237i
$868$	−76.9250	+	610.023i	−0.0886233	+	0.702791i
$869$	888.050	+	888.050i	1.02192	+	1.02192i
$870$	369.270	−	325.629i	0.424449	−	0.374286i
$871$	172.241			0.197751
$872$	−234.350	−	344.586i	−0.268750	−	0.395168i
$873$		−	337.028i		−	0.386057i
$874$	−1183.26	+	1043.42i	−1.35385	+	1.19385i
$875$	−374.593	+	374.593i	−0.428106	+	0.428106i
$876$	168.633	−	130.866i	0.192504	−	0.149390i
$877$	535.285	−	535.285i	0.610359	−	0.610359i	−0.332680	−	0.943040i	$-0.607953\pi$
$877$	535.285	−	535.285i	0.610359	−	0.610359i	0.943040	+	0.332680i	$0.107953\pi$
$878$	−44.6858	+	711.532i	−0.0508950	+	0.810401i
$879$		−	139.220i		−	0.158384i
$880$	703.783	+	180.365i	0.799753	+	0.204960i
$881$	517.437			0.587330			0.293665	−	0.955908i	$-0.405125\pi$
$881$	517.437			0.587330			0.293665	+	0.955908i	$0.405125\pi$
$882$	195.642	+	12.2868i	0.221816	+	0.0139306i
$883$	−1192.91	−	1192.91i	−1.35097	−	1.35097i	−0.884574	−	0.466399i	$-0.845551\pi$
$883$	−1192.91	−	1192.91i	−1.35097	−	1.35097i	−0.466399	−	0.884574i	$-0.654449\pi$
$884$	−577.570	+	448.217i	−0.653360	+	0.507032i
$885$	81.3036	+	81.3036i	0.0918685	+	0.0918685i
$886$	671.121	+	761.066i	0.757473	+	0.858991i
$887$	−1750.36			−1.97335			−0.986675	−	0.162704i	$-0.947978\pi$
$887$	−1750.36			−1.97335			−0.986675	+	0.162704i	$0.947978\pi$
$888$	−825.665	−	157.217i	−0.929803	−	0.177046i
$889$			444.203i			0.499666i
$890$	449.479	+	509.718i	0.505032	+	0.572717i
$891$	−61.4212	+	61.4212i	−0.0689351	+	0.0689351i
$892$	−13.1835	+	104.547i	−0.0147797	+	0.117205i
$893$	−312.728	+	312.728i	−0.350199	+	0.350199i
$894$	−389.656	−	24.4713i	−0.435857	−	0.0273728i
$895$			1309.77i			1.46343i
$896$	−219.860	+	468.179i	−0.245380	+	0.522521i
$897$	−296.760			−0.330836
$898$	5.59802	−	89.1373i	0.00623388	−	0.0992620i
$899$	−812.551	−	812.551i	−0.903839	−	0.903839i
$900$	−34.1084	−	4.30113i	−0.0378982	−	0.00477904i
$901$	−14.3630	−	14.3630i	−0.0159411	−	0.0159411i
$902$	−698.328	+	615.798i	−0.774199	+	0.682703i
$903$	−323.435			−0.358178
$904$	−83.1933	+	436.912i	−0.0920280	+	0.483310i
$905$		−	182.528i		−	0.201689i
$906$	−274.231	+	241.822i	−0.302683	+	0.266911i
$907$	86.0833	−	86.0833i	0.0949099	−	0.0949099i	−0.658058	−	0.752968i	$-0.728622\pi$
$907$	86.0833	−	86.0833i	0.0949099	−	0.0949099i	0.752968	+	0.658058i	$0.228622\pi$
$908$	243.935	+	314.333i	0.268651	+	0.346182i
$909$	4.85800	−	4.85800i	0.00534433	−	0.00534433i
$910$	14.4621	−	230.280i	0.0158925	−	0.253055i
$911$		−	44.7701i		−	0.0491439i	−0.999698	−	0.0245719i	$-0.992178\pi$
$911$		−	44.7701i		−	0.0491439i	0.999698	−	0.0245719i	$-0.00782228\pi$
$912$	192.207	−	749.990i	0.210753	−	0.822358i
$913$	−30.8683			−0.0338098
$914$	168.135	+	10.5593i	0.183955	+	0.0115528i
$915$	309.216	+	309.216i	0.337941	+	0.337941i
$916$	747.753	+	963.552i	0.816324	+	1.05191i
$917$	−305.812	−	305.812i	−0.333492	−	0.333492i
$918$	−207.022	−	234.768i	−0.225514	−	0.255738i
$919$	498.982			0.542962			0.271481	−	0.962444i	$-0.412487\pi$
$919$	498.982			0.542962			0.271481	+	0.962444i	$0.412487\pi$
$920$	−878.740	+	597.622i	−0.955152	+	0.649590i
$921$			602.397i			0.654068i
$922$	384.144	+	435.628i	0.416642	+	0.472481i
$923$	171.987	−	171.987i	0.186335	−	0.186335i
$924$	268.078	+	33.8052i	0.290128	+	0.0365857i
$925$	−122.879	+	122.879i	−0.132842	+	0.132842i
$926$	540.229	+	33.9276i	0.583401	+	0.0366389i
$927$			83.9922i			0.0906065i
$928$	−439.343	−	861.067i	−0.473430	−	0.927874i
$929$	−1460.97			−1.57262			−0.786311	−	0.617831i	$-0.788012\pi$
$929$	−1460.97			−1.57262			−0.786311	+	0.617831i	$0.788012\pi$
$930$	38.8587	−	618.746i	0.0417835	−	0.665318i
$931$	645.415	+	645.415i	0.693250	+	0.693250i
$932$	92.0082	−	729.634i	0.0987213	−	0.782869i
$933$	−440.865	−	440.865i	−0.472524	−	0.472524i
$934$	−488.753	+	430.991i	−0.523290	+	0.461446i
$935$	1367.65			1.46273
$936$	120.427	−	81.9014i	0.128661	−	0.0875014i
$937$		−	594.005i		−	0.633943i	−0.948435	−	0.316972i	$-0.897334\pi$
$937$		−	594.005i		−	0.633943i	0.948435	−	0.316972i	$-0.102666\pi$
$938$	172.053	−	151.719i	0.183425	−	0.161747i
$939$	160.470	−	160.470i	0.170895	−	0.170895i
$940$	−235.359	+	182.648i	−0.250382	+	0.194306i
$941$	767.764	−	767.764i	0.815902	−	0.815902i	−0.169610	−	0.985511i	$-0.554251\pi$
$941$	767.764	−	767.764i	0.815902	−	0.815902i	0.985511	+	0.169610i	$0.0542507\pi$
$942$	−58.3601	+	929.268i	−0.0619534	+	0.986484i
$943$		−	1361.87i		−	1.44419i
$944$	194.268	−	115.007i	0.205792	−	0.121830i
$945$	98.7868			0.104536
$946$	890.259	+	55.9102i	0.941077	+	0.0591017i
$947$	−205.644	−	205.644i	−0.217153	−	0.217153i	0.590145	−	0.807297i	$-0.299071\pi$
$947$	−205.644	−	205.644i	−0.217153	−	0.217153i	−0.807297	+	0.590145i	$0.799071\pi$
$948$	712.228	−	552.716i	0.751296	−	0.583034i
$949$	132.201	+	132.201i	0.139306	+	0.139306i
$950$	−105.873	−	120.062i	−0.111445	−	0.126381i
$951$	218.120			0.229358
$952$	−182.125	+	956.480i	−0.191308	+	1.00471i
$953$			1714.17i			1.79871i	0.437215	+	0.899357i	$0.355965\pi$
$953$			1714.17i			1.79871i	−0.437215	+	0.899357i	$0.644035\pi$
$954$	2.67626	+	3.03493i	0.00280530	+	0.00318127i
$955$	−813.098	+	813.098i	−0.851412	+	0.851412i
$956$	157.732	−	1250.83i	0.164991	−	1.30840i
$957$	−357.081	+	357.081i	−0.373125	+	0.373125i
$958$	1149.56	+	72.1948i	1.19995	+	0.0753599i
$959$			8.67783i			0.00904883i
$960$	191.663	−	485.038i	0.199649	−	0.505248i
$961$	−486.009			−0.505733
$962$	46.1426	−	734.728i	0.0479653	−	0.763750i
$963$	−121.150	−	121.150i	−0.125805	−	0.125805i
$964$	1300.91	+	164.047i	1.34949	+	0.170174i
$965$	848.466	+	848.466i	0.879240	+	0.879240i
$966$	−296.436	+	261.402i	−0.306869	+	0.270603i
$967$	−1375.76			−1.42271			−0.711356	−	0.702832i	$-0.751919\pi$
$967$	−1375.76			−1.42271			−0.711356	+	0.702832i	$0.751919\pi$
$968$	218.870	+	41.6754i	0.226105	+	0.0430531i
$969$		−	1457.45i		−	1.50407i
$970$	792.862	−	699.160i	0.817384	−	0.720783i
$971$	−1081.41	+	1081.41i	−1.11371	+	1.11371i	−0.121062	+	0.992645i	$0.538630\pi$
$971$	−1081.41	+	1081.41i	−1.11371	+	1.11371i	−0.992645	+	0.121062i	$0.961370\pi$
$972$	38.2281	+	49.2606i	0.0393294	+	0.0506797i
$973$	441.449	−	441.449i	0.453699	−	0.453699i
$974$	−75.2590	+	1198.35i	−0.0772680	+	1.23034i
$975$		−	30.1114i		−	0.0308835i
$976$	738.844	−	437.398i	0.757013	−	0.448154i
$977$	−18.0081			−0.0184320			−0.00921601	−	0.999958i	$-0.502934\pi$
$977$	−18.0081			−0.0184320			−0.00921601	+	0.999958i	$0.502934\pi$
$978$	290.491	+	18.2435i	0.297025	+	0.0186539i
$979$	−492.893	−	492.893i	−0.503465	−	0.503465i
$980$	376.953	+	485.740i	0.384646	+	0.495653i
$981$	110.501	+	110.501i	0.112641	+	0.112641i
$982$	149.130	+	169.116i	0.151863	+	0.172216i
$983$	579.164			0.589180			0.294590	−	0.955624i	$-0.404817\pi$
$983$	579.164			0.589180			0.294590	+	0.955624i	$0.404817\pi$
$984$	375.856	+	552.656i	0.381968	+	0.561643i
$985$		−	1292.32i		−	1.31200i
$986$	−1203.55	−	1364.85i	−1.22064	−	1.38423i
$987$	−78.3457	+	78.3457i	−0.0793776	+	0.0793776i
$988$	672.802	+	84.8416i	0.680973	+	0.0858720i
$989$	−922.605	+	922.605i	−0.932866	+	0.932866i
$990$	−271.912	−	17.0767i	−0.274659	−	0.0172492i
$991$		−	1389.22i		−	1.40184i	−0.713242	−	0.700918i	$-0.752774\pi$
$991$		−	1389.22i		−	1.40184i	0.713242	−	0.700918i	$-0.247226\pi$
$992$	−1157.90	−	375.508i	−1.16724	−	0.378536i
$993$	234.169			0.235820
$994$	20.3036	−	323.295i	0.0204262	−	0.325246i
$995$	−564.880	−	564.880i	−0.567719	−	0.567719i
$996$	−2.77229	+	21.9845i	−0.00278342	+	0.0220728i
$997$	867.073	+	867.073i	0.869682	+	0.869682i	0.992437	−	0.122755i	$-0.0391730\pi$
$997$	867.073	+	867.073i	0.869682	+	0.869682i	−0.122755	+	0.992437i	$0.539173\pi$
$998$	28.6206	−	25.2381i	0.0286779	−	0.0252887i
$999$	315.187			0.315503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.l.a.43.4	yes	16
3.2	odd	2		144.3.m.c.91.5		16
4.3	odd	2		192.3.l.a.79.4		16
8.3	odd	2		384.3.l.b.31.5		16
8.5	even	2		384.3.l.a.31.1		16
12.11	even	2		576.3.m.c.271.2		16
16.3	odd	4	inner	48.3.l.a.19.4	✓	16
16.5	even	4		384.3.l.b.223.5		16
16.11	odd	4		384.3.l.a.223.1		16
16.13	even	4		192.3.l.a.175.4		16
24.5	odd	2		1152.3.m.f.415.7		16
24.11	even	2		1152.3.m.c.415.7		16
48.5	odd	4		1152.3.m.c.991.7		16
48.11	even	4		1152.3.m.f.991.7		16
48.29	odd	4		576.3.m.c.559.2		16
48.35	even	4		144.3.m.c.19.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.4	✓	16	16.3	odd	4	inner
48.3.l.a.43.4	yes	16	1.1	even	1	trivial
144.3.m.c.19.5		16	48.35	even	4
144.3.m.c.91.5		16	3.2	odd	2
192.3.l.a.79.4		16	4.3	odd	2
192.3.l.a.175.4		16	16.13	even	4
384.3.l.a.31.1		16	8.5	even	2
384.3.l.a.223.1		16	16.11	odd	4
384.3.l.b.31.5		16	8.3	odd	2
384.3.l.b.223.5		16	16.5	even	4
576.3.m.c.271.2		16	12.11	even	2
576.3.m.c.559.2		16	48.29	odd	4
1152.3.m.c.415.7		16	24.11	even	2
1152.3.m.c.991.7		16	48.5	odd	4
1152.3.m.f.415.7		16	24.5	odd	2
1152.3.m.f.991.7		16	48.11	even	4

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.125358 + 1.99607i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.96857 - 0.500444i) q^{4} +(3.32679 + 3.32679i) q^{5} +(-2.59820 + 2.29114i) q^{6} -4.04088 q^{7} +(1.49641 - 7.85880i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-0.125358 + 1.99607i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.96857 - 0.500444i) q^{4} +(3.32679 + 3.32679i) q^{5} +(-2.59820 + 2.29114i) q^{6} -4.04088 q^{7} +(1.49641 - 7.85880i) q^{8} +3.00000i q^{9} +(-7.05755 + 6.22347i) q^{10} +(6.82458 - 6.82458i) q^{11} +(-4.24757 - 5.47340i) q^{12} +(4.29091 - 4.29091i) q^{13} +(0.506555 - 8.06588i) q^{14} +8.14895i q^{15} +(15.4991 + 3.97210i) q^{16} +30.1192 q^{17} +(-5.98820 - 0.376073i) q^{18} +(-19.7548 - 19.7548i) q^{19} +(-11.5377 - 14.8675i) q^{20} +(-4.94905 - 4.94905i) q^{21} +(12.7668 + 14.4778i) q^{22} -28.2345 q^{23} +(11.4577 - 7.79230i) q^{24} -2.86488i q^{25} +(8.02705 + 9.10285i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(16.0365 + 2.02224i) q^{28} +(-21.3607 + 21.3607i) q^{29} +(-16.2659 - 1.02153i) q^{30} +38.0396i q^{31} +(-9.87151 + 30.4393i) q^{32} +16.7167 q^{33} +(-3.77567 + 60.1200i) q^{34} +(-13.4432 - 13.4432i) q^{35} +(1.50133 - 11.9057i) q^{36} +(-42.8916 - 42.8916i) q^{37} +(41.9084 - 36.9556i) q^{38} +10.5105 q^{39} +(31.1229 - 21.1664i) q^{40} +48.2343i q^{41} +(10.4990 - 9.25824i) q^{42} +(32.6765 - 32.6765i) q^{43} +(-30.4991 + 23.6685i) q^{44} +(-9.98038 + 9.98038i) q^{45} +(3.53941 - 56.3580i) q^{46} -15.8305i q^{47} +(14.1177 + 23.8473i) q^{48} -32.6713 q^{49} +(5.71849 + 0.359134i) q^{50} +(36.8883 + 36.8883i) q^{51} +(-19.1761 + 14.8814i) q^{52} +(-0.476870 - 0.476870i) q^{53} +(-6.87343 - 7.79461i) q^{54} +45.4079 q^{55} +(-6.04682 + 31.7565i) q^{56} -48.3893i q^{57} +(-39.9596 - 45.3151i) q^{58} +(9.97719 - 9.97719i) q^{59} +(4.07809 - 32.3397i) q^{60} +(37.9455 - 37.9455i) q^{61} +(-75.9296 - 4.76855i) q^{62} -12.1226i q^{63} +(-59.5215 - 23.5200i) q^{64} +28.5500 q^{65} +(-2.09557 + 33.3677i) q^{66} +(20.0705 + 20.0705i) q^{67} +(-119.530 - 15.0730i) q^{68} +(-34.5801 - 34.5801i) q^{69} +(28.5187 - 25.1483i) q^{70} +40.0818 q^{71} +(23.5764 + 4.48923i) q^{72} +30.8095i q^{73} +(90.9912 - 80.2377i) q^{74} +(3.50874 - 3.50874i) q^{75} +(68.5123 + 88.2846i) q^{76} +(-27.5773 + 27.5773i) q^{77} +(-1.31758 + 20.9798i) q^{78} +130.125i q^{79} +(38.3480 + 64.7767i) q^{80} -9.00000 q^{81} +(-96.2789 - 6.04653i) q^{82} +(-2.26155 - 2.26155i) q^{83} +(17.1639 + 22.1174i) q^{84} +(100.200 + 100.200i) q^{85} +(61.1282 + 69.3207i) q^{86} -52.3228 q^{87} +(-43.4206 - 63.8454i) q^{88} -72.2232i q^{89} +(-18.6704 - 21.1726i) q^{90} +(-17.3391 + 17.3391i) q^{91} +(112.051 + 14.1298i) q^{92} +(-46.5888 + 46.5888i) q^{93} +(31.5986 + 1.98447i) q^{94} -131.441i q^{95} +(-49.3705 + 25.1903i) q^{96} -112.343 q^{97} +(4.09559 - 65.2140i) q^{98} +(20.4737 + 20.4737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 - 12 * q^8	\( 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Introduction

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