LMFDB - Embedded newform 120.4.m.b.59.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,4,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	120.m (of order $2$, degree $1$, 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:	$7.08022920069$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.14
Character	$\chi$	$=$	120.59
Dual form			120.4.m.b.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.12434 - 1.86740i) q^{2} +(0.659128 + 5.15418i) q^{3} +(1.02565 + 7.93398i) q^{4} +(-10.6502 - 3.40199i) q^{5} +(8.22469 - 12.1801i) q^{6} +28.2468 q^{7} +(12.6371 - 18.7698i) q^{8} +(-26.1311 + 6.79452i) q^{9} +(16.2718 + 27.1151i) q^{10} +38.5985i q^{11} +(-40.2171 + 10.5159i) q^{12} -36.1882 q^{13} +(-60.0059 - 52.7480i) q^{14} +(10.5146 - 57.1353i) q^{15} +(-61.8961 + 16.2750i) q^{16} -74.9762 q^{17} +(68.1995 + 34.3633i) q^{18} -136.377 q^{19} +(16.0679 - 87.9876i) q^{20} +(18.6183 + 145.589i) q^{21} +(72.0787 - 81.9963i) q^{22} +114.614i q^{23} +(105.072 + 52.7620i) q^{24} +(101.853 + 72.4636i) q^{25} +(76.8760 + 67.5777i) q^{26} +(-52.2439 - 130.206i) q^{27} +(28.9714 + 224.110i) q^{28} -109.327 q^{29} +(-129.031 + 101.740i) q^{30} -57.1138i q^{31} +(161.880 + 81.0110i) q^{32} +(-198.943 + 25.4413i) q^{33} +(159.275 + 140.010i) q^{34} +(-300.834 - 96.0952i) q^{35} +(-80.7090 - 200.355i) q^{36} +100.427 q^{37} +(289.712 + 254.671i) q^{38} +(-23.8526 - 186.520i) q^{39} +(-198.442 + 156.911i) q^{40} +173.978i q^{41} +(232.321 - 344.049i) q^{42} +86.0147i q^{43} +(-306.239 + 39.5886i) q^{44} +(301.416 + 16.5347i) q^{45} +(214.030 - 243.480i) q^{46} -239.821i q^{47} +(-124.682 - 308.296i) q^{48} +454.882 q^{49} +(-81.0522 - 344.137i) q^{50} +(-49.4189 - 386.440i) q^{51} +(-37.1165 - 287.116i) q^{52} -476.921i q^{53} +(-132.162 + 374.162i) q^{54} +(131.311 - 411.081i) q^{55} +(356.957 - 530.186i) q^{56} +(-89.8901 - 702.913i) q^{57} +(232.247 + 204.156i) q^{58} +762.283i q^{59} +(464.095 + 24.8218i) q^{60} +614.842i q^{61} +(-106.654 + 121.329i) q^{62} +(-738.120 + 191.924i) q^{63} +(-192.609 - 474.390i) q^{64} +(385.411 + 123.112i) q^{65} +(470.132 + 317.460i) q^{66} +382.405i q^{67} +(-76.8994 - 594.859i) q^{68} +(-590.742 + 75.5455i) q^{69} +(459.626 + 765.915i) q^{70} -124.611 q^{71} +(-202.689 + 576.338i) q^{72} -267.766i q^{73} +(-213.342 - 187.538i) q^{74} +(-306.356 + 572.731i) q^{75} +(-139.876 - 1082.01i) q^{76} +1090.28i q^{77} +(-297.636 + 440.775i) q^{78} -586.207i q^{79} +(714.572 + 37.2378i) q^{80} +(636.669 - 355.097i) q^{81} +(324.885 - 369.588i) q^{82} +282.399 q^{83} +(-1136.00 + 297.040i) q^{84} +(798.510 + 255.068i) q^{85} +(160.624 - 182.724i) q^{86} +(-72.0602 - 563.489i) q^{87} +(724.484 + 487.771i) q^{88} +604.782i q^{89} +(-609.434 - 597.989i) q^{90} -1022.20 q^{91} +(-909.347 + 117.554i) q^{92} +(294.375 - 37.6453i) q^{93} +(-447.841 + 509.461i) q^{94} +(1452.44 + 463.954i) q^{95} +(-310.845 + 887.756i) q^{96} +1041.15i q^{97} +(-966.325 - 849.446i) q^{98} +(-262.258 - 1008.62i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54}+ \cdots + 256 q^{99}+O(q^{100}) $ 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.12434	−	1.86740i	−0.751068	−	0.660225i
$2$	−2.12434	−	1.86740i	−0.751068	−	0.660225i
$3$	0.659128	+	5.15418i	0.126849	+	0.991922i
$3$	0.659128	+	5.15418i	0.126849	+	0.991922i
$4$	1.02565	+	7.93398i	0.128206	+	0.991748i
$5$	−10.6502	−	3.40199i	−0.952582	−	0.304283i
$5$	−10.6502	−	3.40199i	−0.952582	−	0.304283i
$6$	8.22469	−	12.1801i	0.559619	−	0.828750i
$7$	28.2468			1.52518			0.762592	−	0.646880i	$-0.223926\pi$
$7$	28.2468			1.52518			0.762592	+	0.646880i	$0.223926\pi$
$8$	12.6371	−	18.7698i	0.558485	−	0.829515i
$9$	−26.1311	+	6.79452i	−0.967819	+	0.251649i
$10$	16.2718	+	27.1151i	0.514559	+	0.857455i
$11$			38.5985i			1.05799i	0.848625	+	0.528994i	$0.177431\pi$
$11$			38.5985i			1.05799i	−0.848625	+	0.528994i	$0.822569\pi$
$12$	−40.2171	+	10.5159i	−0.967473	+	0.252973i
$13$	−36.1882			−0.772061			−0.386031	−	0.922486i	$-0.626154\pi$
$13$	−36.1882			−0.772061			−0.386031	+	0.922486i	$0.626154\pi$
$14$	−60.0059	−	52.7480i	−1.14552	−	1.00696i
$15$	10.5146	−	57.1353i	0.180991	−	0.983485i
$16$	−61.8961	+	16.2750i	−0.967126	+	0.254297i
$17$	−74.9762			−1.06967			−0.534835	−	0.844957i	$-0.679626\pi$
$17$	−74.9762			−1.06967			−0.534835	+	0.844957i	$0.679626\pi$
$18$	68.1995	+	34.3633i	0.893043	+	0.449972i
$19$	−136.377			−1.64669			−0.823345	−	0.567541i	$-0.807895\pi$
$19$	−136.377			−1.64669			−0.823345	+	0.567541i	$0.807895\pi$
$20$	16.0679	−	87.9876i	0.179645	−	0.983732i
$21$	18.6183	+	145.589i	0.193468	+	1.51286i
$22$	72.0787	−	81.9963i	0.698510	−	0.794621i
$23$			114.614i			1.03908i	0.854448	+	0.519538i	$0.173896\pi$
$23$			114.614i			1.03908i	−0.854448	+	0.519538i	$0.826104\pi$
$24$	105.072	+	52.7620i	0.893657	+	0.448750i
$25$	101.853	+	72.4636i	0.814824	+	0.579709i
$26$	76.8760	+	67.5777i	0.579870	+	0.509734i
$27$	−52.2439	−	130.206i	−0.372383	−	0.928079i
$28$	28.9714	+	224.110i	0.195538	+	1.51260i
$29$	−109.327			−0.700050			−0.350025	−	0.936740i	$-0.613827\pi$
$29$	−109.327			−0.700050			−0.350025	+	0.936740i	$0.613827\pi$
$30$	−129.031	+	101.740i	−0.785257	+	0.619170i
$31$		−	57.1138i		−	0.330901i	−0.986218	−	0.165451i	$-0.947092\pi$
$31$		−	57.1138i		−	0.330901i	0.986218	−	0.165451i	$-0.0529079\pi$
$32$	161.880	+	81.0110i	0.894271	+	0.447527i
$33$	−198.943	+	25.4413i	−1.04944	+	0.134205i
$34$	159.275	+	140.010i	0.803395	+	0.706223i
$35$	−300.834	−	96.0952i	−1.45286	−	0.464087i
$36$	−80.7090	−	200.355i	−0.373653	−	0.927569i
$37$	100.427			0.446221			0.223110	−	0.974793i	$-0.428379\pi$
$37$	100.427			0.446221			0.223110	+	0.974793i	$0.428379\pi$
$38$	289.712	+	254.671i	1.23678	+	1.08719i
$39$	−23.8526	−	186.520i	−0.0979353	−	0.765824i
$40$	−198.442	+	156.911i	−0.784409	+	0.620243i
$41$			173.978i			0.662701i	0.943508	+	0.331350i	$0.107504\pi$
$41$			173.978i			0.662701i	−0.943508	+	0.331350i	$0.892496\pi$
$42$	232.321	−	344.049i	0.853522	−	1.26400i
$43$			86.0147i			0.305049i	0.988300	+	0.152525i	$0.0487403\pi$
$43$			86.0147i			0.305049i	−0.988300	+	0.152525i	$0.951260\pi$
$44$	−306.239	+	39.5886i	−1.04926	+	0.135641i
$45$	301.416	+	16.5347i	0.998499	+	0.0547743i
$46$	214.030	−	243.480i	0.686023	−	0.780416i
$47$		−	239.821i		−	0.744286i	−0.928175	−	0.372143i	$-0.878623\pi$
$47$		−	239.821i		−	0.744286i	0.928175	−	0.372143i	$-0.121377\pi$
$48$	−124.682	−	308.296i	−0.374922	−	0.927056i
$49$	454.882			1.32619
$50$	−81.0522	−	344.137i	−0.229250	−	0.973368i
$51$	−49.4189	−	386.440i	−0.135687	−	1.06103i
$52$	−37.1165	−	287.116i	−0.0989832	−	0.765690i
$53$		−	476.921i		−	1.23604i	−0.786162	−	0.618021i	$-0.787935\pi$
$53$		−	476.921i		−	1.23604i	0.786162	−	0.618021i	$-0.212065\pi$
$54$	−132.162	+	374.162i	−0.333056	+	0.942907i
$55$	131.311	−	411.081i	0.321928	−	1.00782i
$56$	356.957	−	530.186i	0.851792	−	1.26516i
$57$	−89.8901	−	702.913i	−0.208881	−	1.63339i
$58$	232.247	+	204.156i	0.525785	+	0.462190i
$59$			762.283i			1.68205i	0.540997	+	0.841024i	$0.318047\pi$
$59$			762.283i			1.68205i	−0.540997	+	0.841024i	$0.681953\pi$
$60$	464.095	+	24.8218i	0.998573	+	0.0534079i
$61$			614.842i			1.29053i	0.763958	+	0.645266i	$0.223253\pi$
$61$			614.842i			1.29053i	−0.763958	+	0.645266i	$0.776747\pi$
$62$	−106.654	+	121.329i	−0.218469	+	0.248529i
$63$	−738.120	+	191.924i	−1.47610	+	0.383811i
$64$	−192.609	−	474.390i	−0.376190	−	0.926543i
$65$	385.411	+	123.112i	0.735451	+	0.234925i
$66$	470.132	+	317.460i	0.876808	+	0.592070i
$67$			382.405i			0.697287i	0.937256	+	0.348643i	$0.113358\pi$
$67$			382.405i			0.697287i	−0.937256	+	0.348643i	$0.886642\pi$
$68$	−76.8994	−	594.859i	−0.137139	−	1.06084i
$69$	−590.742	+	75.5455i	−1.03068	+	0.131806i
$70$	459.626	+	765.915i	0.784797	+	1.30778i
$71$	−124.611			−0.208291			−0.104145	−	0.994562i	$-0.533211\pi$
$71$	−124.611			−0.208291			−0.104145	+	0.994562i	$0.533211\pi$
$72$	−202.689	+	576.338i	−0.331765	+	0.943362i
$73$		−	267.766i		−	0.429310i	−0.976690	−	0.214655i	$-0.931137\pi$
$73$		−	267.766i		−	0.429310i	0.976690	−	0.214655i	$-0.0688627\pi$
$74$	−213.342	−	187.538i	−0.335142	−	0.294606i
$75$	−306.356	+	572.731i	−0.471666	+	0.881777i
$76$	−139.876	−	1082.01i	−0.211116	−	1.63310i
$77$			1090.28i			1.61363i
$78$	−297.636	+	440.775i	−0.432060	+	0.639846i
$79$		−	586.207i		−	0.834854i	−0.908710	−	0.417427i	$-0.862932\pi$
$79$		−	586.207i		−	0.834854i	0.908710	−	0.417427i	$-0.137068\pi$
$80$	714.572	+	37.2378i	0.998645	+	0.0520414i
$81$	636.669	−	355.097i	0.873346	−	0.487101i
$82$	324.885	−	369.588i	0.437532	−	0.497733i
$83$	282.399			0.373462			0.186731	−	0.982411i	$-0.440211\pi$
$83$	282.399			0.373462			0.186731	+	0.982411i	$0.440211\pi$
$84$	−1136.00	+	297.040i	−1.47558	+	0.385831i
$85$	798.510	+	255.068i	1.01895	+	0.325482i
$86$	160.624	−	182.724i	0.201401	−	0.229113i
$87$	−72.0602	−	563.489i	−0.0888007	−	0.694395i
$88$	724.484	+	487.771i	0.877617	+	0.590870i
$89$			604.782i			0.720301i	0.932894	+	0.360151i	$0.117275\pi$
$89$			604.782i			0.720301i	−0.932894	+	0.360151i	$0.882725\pi$
$90$	−609.434	−	597.989i	−0.713777	−	0.700373i
$91$	−1022.20			−1.17754
$92$	−909.347	+	117.554i	−1.03050	+	0.133216i
$93$	294.375	−	37.6453i	0.328228	−	0.0419746i
$94$	−447.841	+	509.461i	−0.491396	+	0.559010i
$95$	1452.44	+	463.954i	1.56861	+	0.501059i
$96$	−310.845	+	887.756i	−0.330474	+	0.943815i
$97$			1041.15i			1.08982i	0.838494	+	0.544911i	$0.183437\pi$
$97$			1041.15i			1.08982i	−0.838494	+	0.544911i	$0.816563\pi$
$98$	−966.325	−	849.446i	−0.996057	−	0.875581i
$99$	−262.258	−	1008.62i	−0.266242	−	1.02394i
$100$	−470.459	+	882.422i	−0.470459	+	0.882422i
$101$	512.592			0.504998			0.252499	−	0.967597i	$-0.418748\pi$
$101$	512.592			0.504998			0.252499	+	0.967597i	$0.418748\pi$
$102$	−616.655	+	913.216i	−0.598608	+	0.886489i
$103$	−588.625			−0.563097			−0.281548	−	0.959547i	$-0.590848\pi$
$103$	−588.625			−0.563097			−0.281548	+	0.959547i	$0.590848\pi$
$104$	−457.312	+	679.244i	−0.431184	+	0.640436i
$105$	297.004	−	1613.89i	0.276044	−	1.50000i
$106$	−890.602	+	1013.14i	−0.816065	+	0.928351i
$107$	1877.68			1.69647			0.848233	−	0.529624i	$-0.177667\pi$
$107$	1877.68			1.69647			0.848233	+	0.529624i	$0.177667\pi$
$108$	979.467	−	548.048i	0.872678	−	0.488296i
$109$			833.606i			0.732523i	0.930512	+	0.366261i	$0.119362\pi$
$109$			833.606i			0.732523i	−0.930512	+	0.366261i	$0.880638\pi$
$110$	−1046.60	+	628.065i	−0.907178	+	0.544397i
$111$	66.1945	+	517.621i	0.0566028	+	0.442616i
$112$	−1748.37	+	459.717i	−1.47505	+	0.387849i
$113$	990.495			0.824583			0.412292	−	0.911052i	$-0.364729\pi$
$113$	990.495			0.824583			0.412292	+	0.911052i	$0.364729\pi$
$114$	−1121.66	+	1661.09i	−0.921519	+	1.36469i
$115$	389.916	−	1220.66i	0.316173	−	0.989804i
$116$	−112.131	−	867.395i	−0.0897508	−	0.694272i
$117$	945.637	−	245.881i	0.747215	−	0.194288i
$118$	1423.49	−	1619.35i	1.11053	−	1.26333i
$119$	−2117.84			−1.63144
$120$	−939.543	−	919.379i	−0.714735	−	0.699396i
$121$	−158.840			−0.119339
$122$	1148.15	−	1306.13i	0.852041	−	0.969277i
$123$	−896.712	+	114.673i	−0.657348	+	0.0840631i
$124$	453.140	−	58.5788i	0.328171	−	0.0424237i
$125$	−838.233	−	1118.25i	−0.599791	−	0.800157i
$126$	1926.42	+	970.653i	1.36205	+	0.686291i
$127$	1517.02			1.05995			0.529976	−	0.848013i	$-0.322201\pi$
$127$	1517.02			1.05995			0.529976	+	0.848013i	$0.322201\pi$
$128$	−476.707	+	1367.44i	−0.329182	+	0.944266i
$129$	−443.335	+	56.6946i	−0.302585	+	0.0386952i
$130$	−588.846	−	981.247i	−0.397271	−	0.662008i
$131$		−	968.122i		−	0.645689i	−0.946452	−	0.322844i	$-0.895361\pi$
$131$		−	968.122i		−	0.645689i	0.946452	−	0.322844i	$-0.104639\pi$
$132$	−405.897	−	1552.32i	−0.267643	−	1.02358i
$133$	−3852.22			−2.51151
$134$	714.102	−	812.359i	0.460366	−	0.523710i
$135$	113.449	+	1564.45i	0.0723269	+	0.997381i
$136$	−947.478	+	1407.29i	−0.597394	+	0.887307i
$137$	−508.245			−0.316951			−0.158476	−	0.987363i	$-0.550658\pi$
$137$	−508.245			−0.316951			−0.158476	+	0.987363i	$0.550658\pi$
$138$	1396.01	+	942.667i	0.861133	+	0.581486i
$139$	−136.471			−0.0832756			−0.0416378	−	0.999133i	$-0.513258\pi$
$139$	−136.471			−0.0832756			−0.0416378	+	0.999133i	$0.513258\pi$
$140$	453.867	−	2485.37i	0.273991	−	1.50037i
$141$	1236.08	−	158.073i	0.738274	−	0.0944121i
$142$	264.717	+	232.699i	0.156441	+	0.137519i
$143$		−	1396.81i		−	0.816832i
$144$	1506.83	−	845.838i	0.872009	−	0.489489i
$145$	1164.35	+	371.927i	0.666854	+	0.213013i
$146$	−500.026	+	568.826i	−0.283441	+	0.322441i
$147$	299.825	+	2344.54i	0.168226	+	1.31547i
$148$	103.004	+	796.790i	0.0572084	+	0.442539i
$149$	−17.4717			−0.00960627			−0.00480314	−	0.999988i	$-0.501529\pi$
$149$	−17.4717			−0.00960627			−0.00480314	+	0.999988i	$0.501529\pi$
$150$	1720.32	−	644.588i	0.936424	−	0.350869i
$151$		−	2010.13i		−	1.08332i	−0.840596	−	0.541662i	$-0.817795\pi$
$151$		−	2010.13i		−	1.08332i	0.840596	−	0.541662i	$-0.182205\pi$
$152$	−1723.41	+	2559.77i	−0.919651	+	1.36595i
$153$	1959.21	−	509.427i	1.03525	−	0.269181i
$154$	2035.99	−	2316.13i	1.06536	−	1.21194i
$155$	−194.300	+	608.273i	−0.100688	+	0.315211i
$156$	1455.38	−	380.551i	0.746949	−	0.195311i
$157$	−1184.99			−0.602372			−0.301186	−	0.953565i	$-0.597382\pi$
$157$	−1184.99			−0.602372			−0.301186	+	0.953565i	$0.597382\pi$
$158$	−1094.68	+	1245.30i	−0.551191	+	0.627032i
$159$	2458.14	−	314.352i	1.22606	−	0.156791i
$160$	−1448.46	−	1413.50i	−0.715691	−	0.698417i
$161$			3237.49i			1.58478i
$162$	−2015.61	−	434.567i	−0.977538	−	0.210758i
$163$		−	2466.08i		−	1.18502i	−0.805564	−	0.592509i	$-0.798137\pi$
$163$		−	2466.08i		−	1.18502i	0.805564	−	0.592509i	$-0.201863\pi$
$164$	−1380.33	+	178.440i	−0.657232	+	0.0849625i
$165$	2205.33	+	405.847i	1.04052	+	0.191486i
$166$	−599.913	−	527.352i	−0.280495	−	0.246569i
$167$			1316.99i			0.610249i	0.952312	+	0.305125i	$0.0986981\pi$
$167$			1316.99i			0.610249i	−0.952312	+	0.305125i	$0.901302\pi$
$168$	2967.95	+	1490.36i	1.36299	+	0.684426i
$169$	−887.416			−0.403922
$170$	−1219.99	−	2032.99i	−0.550408	−	0.917194i
$171$	3563.69	−	926.619i	1.59370	−	0.414388i
$172$	−682.439	+	88.2210i	−0.302532	+	0.0391093i
$173$			1714.78i			0.753598i	0.926295	+	0.376799i	$0.122975\pi$
$173$			1714.78i			0.753598i	−0.926295	+	0.376799i	$0.877025\pi$
$174$	−899.177	+	1331.61i	−0.391761	+	0.580166i
$175$	2877.02	+	2046.86i	1.24276	+	0.884162i
$176$	−628.190	−	2389.09i	−0.269043	−	1.02321i
$177$	−3928.94	+	502.442i	−1.66846	+	0.213366i
$178$	1129.37	−	1284.76i	0.475561	−	0.540995i
$179$			3149.55i			1.31513i	0.753397	+	0.657566i	$0.228414\pi$
$179$			3149.55i			1.31513i	−0.753397	+	0.657566i	$0.771586\pi$
$180$	177.962	+	2408.39i	0.0736916	+	0.997281i
$181$		−	3071.89i		−	1.26150i	−0.775985	−	0.630752i	$-0.782747\pi$
$181$		−	3071.89i		−	1.26150i	0.775985	−	0.630752i	$-0.217253\pi$
$182$	2171.50	+	1908.85i	0.884409	+	0.777438i
$183$	−3169.00	+	405.259i	−1.28011	+	0.163703i
$184$	2151.28	+	1448.39i	0.861928	+	0.580307i
$185$	−1069.57	−	341.653i	−0.425062	−	0.135777i
$186$	−695.651	−	469.743i	−0.274234	−	0.185179i
$187$		−	2893.96i		−	1.13170i
$188$	1902.73	−	245.973i	0.738144	−	0.0954223i
$189$	−1475.72	−	3677.90i	−0.567953	−	1.41549i
$190$	−2219.10	−	3697.89i	−0.847318	−	1.41196i
$191$	−1462.25			−0.553953			−0.276977	−	0.960877i	$-0.589332\pi$
$191$	−1462.25			−0.553953			−0.276977	+	0.960877i	$0.589332\pi$
$192$	2318.14	−	1305.43i	0.871339	−	0.490682i
$193$			1745.22i			0.650901i	0.945559	+	0.325450i	$0.105516\pi$
$193$			1745.22i			0.650901i	−0.945559	+	0.325450i	$0.894484\pi$
$194$	1944.24	−	2211.76i	0.719528	−	0.818531i
$195$	−380.504	+	2067.62i	−0.139736	+	0.759310i
$196$	466.550	+	3609.03i	0.170026	+	1.31524i
$197$		−	3.00587i		−	0.00108710i	−1.00000		0.000543552i	$-0.999827\pi$
$197$		−	3.00587i		−	0.00108710i	1.00000		0.000543552i	$-0.000173018\pi$
$198$	−1326.37	+	2632.39i	−0.476065	+	0.944828i
$199$			5110.77i			1.82057i	0.413986	+	0.910283i	$0.364136\pi$
$199$			5110.77i			1.82057i	−0.413986	+	0.910283i	$0.635864\pi$
$200$	2647.25	−	996.032i	0.935943	−	0.352150i
$201$	−1970.98	+	252.054i	−0.691654	+	0.0884502i
$202$	−1088.92	−	957.213i	−0.379288	−	0.333412i
$203$	−3088.13			−1.06770
$204$	3015.32	−	788.441i	1.03488	−	0.270598i
$205$	591.869	−	1852.89i	0.201649	−	0.631277i
$206$	1250.44	+	1099.20i	0.422924	+	0.371771i
$207$	−778.749	−	2995.00i	−0.261482	−	1.00564i
$208$	2239.91	−	588.962i	0.746681	−	0.196333i
$209$		−	5263.95i		−	1.74218i
$210$	−3644.71	+	2873.83i	−1.19766	+	0.944348i
$211$	1204.36			0.392946			0.196473	−	0.980509i	$-0.437051\pi$
$211$	1204.36			0.392946			0.196473	+	0.980509i	$0.437051\pi$
$212$	3783.89	−	489.155i	1.22584	−	0.158468i
$213$	−82.1349	−	642.270i	−0.0264215	−	0.206608i
$214$	−3988.82	−	3506.37i	−1.27416	−	1.12005i
$215$	292.621	−	916.072i	0.0928212	−	0.290584i
$216$	−3104.15	−	664.813i	−0.977826	−	0.209420i
$217$		−	1613.28i		−	0.504685i
$218$	1556.67	−	1770.86i	0.483630	−	0.550175i
$219$	1380.11	−	176.492i	0.425842	−	0.0544576i
$220$	3396.19	+	620.196i	1.04078	+	0.190062i
$221$	2713.25			0.825851
$222$	825.985	−	1223.22i	0.249714	−	0.369806i
$223$	−2027.95			−0.608974			−0.304487	−	0.952516i	$-0.598485\pi$
$223$	−2027.95			−0.608974			−0.304487	+	0.952516i	$0.598485\pi$
$224$	4572.60	+	2288.30i	1.36393	+	0.682560i
$225$	−3153.89	−	1201.51i	−0.934485	−	0.356003i
$226$	−2104.15	−	1849.65i	−0.619318	−	0.544410i
$227$	−1702.71			−0.497853			−0.248926	−	0.968522i	$-0.580078\pi$
$227$	−1702.71			−0.497853			−0.248926	+	0.968522i	$0.580078\pi$
$228$	5484.70	−	1434.13i	1.59313	−	0.416568i
$229$			1511.84i			0.436268i	0.975919	+	0.218134i	$0.0699970\pi$
$229$			1511.84i			0.436268i	−0.975919	+	0.218134i	$0.930003\pi$
$230$	−3107.78	+	1864.98i	−0.890960	+	0.534665i
$231$	−5619.51	+	718.636i	−1.60059	+	0.204687i
$232$	−1381.57	+	2052.04i	−0.390967	+	0.580702i
$233$	−5111.87			−1.43730			−0.718648	−	0.695374i	$-0.755239\pi$
$233$	−5111.87			−1.43730			−0.718648	+	0.695374i	$0.755239\pi$
$234$	−2468.01	−	1243.54i	−0.689483	−	0.347406i
$235$	−815.867	+	2554.14i	−0.226474	+	0.708994i
$236$	−6047.94	+	781.837i	−1.66817	+	0.215649i
$237$	3021.42	−	386.385i	0.828110	−	0.105901i
$238$	4499.01	+	3954.84i	1.22533	+	1.07712i
$239$	4889.33			1.32328			0.661641	−	0.749820i	$-0.269860\pi$
$239$	4889.33			1.32328			0.661641	+	0.749820i	$0.269860\pi$
$240$	279.064	+	3707.58i	0.0750562	+	0.997179i
$241$	−3939.29			−1.05291			−0.526456	−	0.850202i	$-0.676480\pi$
$241$	−3939.29			−1.05291			−0.526456	+	0.850202i	$0.676480\pi$
$242$	337.431	+	296.618i	0.0896318	+	0.0787907i
$243$	2249.88	+	3047.45i	0.593950	+	0.804502i
$244$	−4878.14	+	630.613i	−1.27988	+	0.165454i
$245$	−4844.58	−	1547.50i	−1.26330	−	0.403536i
$246$	2119.06	+	1430.91i	0.549213	+	0.370860i
$247$	4935.25			1.27135
$248$	−1072.01	−	721.751i	−0.274488	−	0.184803i
$249$	186.137	+	1455.54i	0.0473734	+	0.370445i
$250$	−307.529	+	3940.87i	−0.0777994	+	0.996969i
$251$		−	5503.76i		−	1.38404i	−0.721878	−	0.692020i	$-0.756721\pi$
$251$		−	5503.76i		−	1.38404i	0.721878	−	0.692020i	$-0.243279\pi$
$252$	−2279.77	−	5659.38i	−0.569889	−	1.41471i
$253$	−4423.93			−1.09933
$254$	−3222.67	−	2832.88i	−0.796096	−	0.699807i
$255$	−788.345	+	4283.79i	−0.193600	+	1.05200i
$256$	3566.25	−	2014.72i	0.870666	−	0.491874i
$257$	4939.16			1.19882			0.599410	−	0.800442i	$-0.295402\pi$
$257$	4939.16			1.19882			0.599410	+	0.800442i	$0.295402\pi$
$258$	1047.67	+	707.444i	0.252809	+	0.170711i
$259$	2836.76			0.680569
$260$	−581.468	+	3184.11i	−0.138697	+	0.759501i
$261$	2856.82	−	742.822i	0.677521	−	0.176167i
$262$	−1807.87	+	2056.62i	−0.426300	+	0.484956i
$263$		−	318.680i		−	0.0747174i	−0.999302	−	0.0373587i	$-0.988106\pi$
$263$		−	318.680i		−	0.0747174i	0.999302	−	0.0373587i	$-0.0118944\pi$
$264$	−2036.53	+	4055.63i	−0.474772	+	0.945479i
$265$	−1622.48	+	5079.30i	−0.376106	+	1.17743i
$266$	8183.44	+	7193.63i	1.88631	+	1.65816i
$267$	−3117.16	+	398.629i	−0.714482	+	0.0913696i
$268$	−3033.99	+	392.214i	−0.691532	+	0.0893966i
$269$	4006.24			0.908048			0.454024	−	0.890990i	$-0.349988\pi$
$269$	4006.24			0.908048			0.454024	+	0.890990i	$0.349988\pi$
$270$	2680.45	−	3535.28i	0.604173	−	0.796853i
$271$			2562.23i			0.574333i	0.957881	+	0.287166i	$0.0927132\pi$
$271$			2562.23i			0.574333i	−0.957881	+	0.287166i	$0.907287\pi$
$272$	4640.73	−	1220.24i	1.03451	−	0.272014i
$273$	−673.761	−	5268.60i	−0.149369	−	1.16802i
$274$	1079.69	+	949.096i	0.238052	+	0.209259i
$275$	−2796.98	+	3931.37i	−0.613325	+	0.862074i
$276$	−1205.27	−	4609.46i	−0.262858	−	1.00528i
$277$	825.382			0.179034			0.0895170	−	0.995985i	$-0.471468\pi$
$277$	825.382			0.179034			0.0895170	+	0.995985i	$0.471468\pi$
$278$	289.911	+	254.845i	0.0625456	+	0.0549806i
$279$	388.061	+	1492.45i	0.0832710	+	0.320252i
$280$	−5605.34	+	4432.22i	−1.19637	+	0.945986i
$281$			5330.02i			1.13154i	0.824564	+	0.565769i	$0.191421\pi$
$281$			5330.02i			1.13154i	−0.824564	+	0.565769i	$0.808579\pi$
$282$	−2921.04	−	1972.45i	−0.616827	−	0.416517i
$283$		−	1059.77i		−	0.222603i	−0.993787	−	0.111301i	$-0.964498\pi$
$283$		−	1059.77i		−	0.222603i	0.993787	−	0.111301i	$-0.0355019\pi$
$284$	−127.808	−	988.665i	−0.0267042	−	0.206572i
$285$	−1433.95	+	7791.96i	−0.298035	+	1.61949i
$286$	−2608.40	+	2967.30i	−0.539292	+	0.613496i
$287$			4914.31i			1.01074i
$288$	−4780.54	−	1017.01i	−0.978111	−	0.208082i
$289$	708.423			0.144194
$290$	−1778.94	−	2964.40i	−0.360217	−	0.600261i
$291$	−5366.27	+	686.251i	−1.08102	+	0.138243i
$292$	2124.45	−	274.635i	0.425767	−	0.0550403i
$293$		−	8474.01i		−	1.68961i	−0.535072	−	0.844807i	$-0.679715\pi$
$293$		−	8474.01i		−	1.68961i	0.535072	−	0.844807i	$-0.320285\pi$
$294$	3741.26	−	5540.50i	0.742160	−	1.09908i
$295$	2593.28	−	8118.46i	0.511818	−	1.60229i
$296$	1269.11	−	1885.00i	0.249208	−	0.370147i
$297$	5025.75	−	2016.53i	0.981897	−	0.393977i
$298$	37.1158	+	32.6266i	0.00721497	+	0.00634230i
$299$		−	4147.68i		−	0.802230i
$300$	−4858.25	−	1843.20i	−0.934971	−	0.354724i
$301$			2429.64i			0.465256i
$302$	−3753.71	+	4270.20i	−0.715238	+	0.813651i
$303$	337.863	+	2641.99i	0.0640586	+	0.500919i
$304$	8441.22	−	2219.54i	1.59256	−	0.418748i
$305$	2091.68	−	6548.18i	0.392686	−	1.22934i
$306$	−5113.33	−	2576.43i	−0.955261	−	0.481322i
$307$		−	4523.38i		−	0.840921i	−0.907311	−	0.420461i	$-0.861869\pi$
$307$		−	4523.38i		−	0.840921i	0.907311	−	0.420461i	$-0.138131\pi$
$308$	−8650.28	+	1118.25i	−1.60031	+	0.206877i
$309$	−387.979	−	3033.88i	−0.0714284	−	0.558548i
$310$	1548.65	−	929.343i	0.283733	−	0.170268i
$311$	−6896.96			−1.25753			−0.628763	−	0.777597i	$-0.716438\pi$
$311$	−6896.96			−1.25753			−0.628763	+	0.777597i	$0.716438\pi$
$312$	−3802.37	−	1909.36i	−0.689958	−	0.346462i
$313$			5946.35i			1.07383i	0.843637	+	0.536913i	$0.180410\pi$
$313$			5946.35i			1.07383i	−0.843637	+	0.536913i	$0.819590\pi$
$314$	2517.32	+	2212.84i	0.452422	+	0.397701i
$315$	8514.04	+	467.052i	1.52289	+	0.0835409i
$316$	4650.96	−	601.244i	0.827964	−	0.107034i
$317$			5914.79i			1.04797i	0.851726	+	0.523987i	$0.175556\pi$
$317$			5914.79i			1.04797i	−0.851726	+	0.523987i	$0.824444\pi$
$318$	−5808.95	−	3922.53i	−1.02437	−	0.691713i
$319$		−	4219.84i		−	0.740644i
$320$	437.458	+	5707.59i	0.0764207	+	0.997076i
$321$	1237.63	+	9677.88i	0.215195	+	1.68276i
$322$	6045.68	−	6877.53i	1.04631	−	1.19028i
$323$	10225.0			1.76141
$324$	3470.33	+	4687.11i	0.595050	+	0.803689i
$325$	−3685.87	−	2622.32i	−0.629094	−	0.447570i
$326$	−4605.14	+	5238.79i	−0.782378	+	0.890029i
$327$	−4296.55	+	549.453i	−0.726606	+	0.0929199i
$328$	3265.52	+	2198.57i	0.549720	+	0.370108i
$329$		−	6774.17i		−	1.13517i
$330$	−3927.00	−	4980.39i	−0.655074	−	0.830793i
$331$	3816.59			0.633772			0.316886	−	0.948464i	$-0.397363\pi$
$331$	3816.59			0.633772			0.316886	+	0.948464i	$0.397363\pi$
$332$	289.643	+	2240.55i	0.0478802	+	0.370380i
$333$	−2624.28	+	682.357i	−0.431861	+	0.112291i
$334$	2459.34	−	2797.73i	0.402902	−	0.458339i
$335$	1300.94	−	4072.68i	0.212172	−	0.664222i
$336$	−3521.86	−	8708.38i	−0.571825	−	1.41393i
$337$			6334.65i			1.02395i	0.859001	+	0.511974i	$0.171086\pi$
$337$			6334.65i			1.02395i	−0.859001	+	0.511974i	$0.828914\pi$
$338$	1885.17	+	1657.16i	0.303373	+	0.266679i
$339$	652.862	+	5105.19i	0.104598	+	0.817922i
$340$	−1204.71	+	6596.97i	−0.192160	+	1.05227i
$341$	2204.50			0.350090
$342$	−9300.86	−	4686.37i	−1.47056	−	0.740965i
$343$	3160.31			0.497495
$344$	1614.48	+	1086.97i	0.253043	+	0.170365i
$345$	6548.52	+	1205.12i	1.02191	+	0.188063i
$346$	3202.18	−	3642.78i	0.497544	−	0.566003i
$347$	1191.58			0.184344			0.0921722	−	0.995743i	$-0.470619\pi$
$347$	1191.58			0.184344			0.0921722	+	0.995743i	$0.470619\pi$
$348$	4396.80	−	1149.67i	0.677279	−	0.177094i
$349$			4817.79i			0.738941i	0.929242	+	0.369471i	$0.120461\pi$
$349$			4817.79i			0.738941i	−0.929242	+	0.369471i	$0.879539\pi$
$350$	−2289.47	−	9720.78i	−0.349649	−	1.48456i
$351$	1890.61	+	4711.91i	0.287503	+	0.716534i
$352$	−3126.90	+	6248.33i	−0.473478	+	0.946128i
$353$	−1191.94			−0.179718			−0.0898592	−	0.995954i	$-0.528642\pi$
$353$	−1191.94			−0.179718			−0.0898592	+	0.995954i	$0.528642\pi$
$354$	9284.68	+	6269.54i	1.39400	+	0.941307i
$355$	1327.14	+	423.926i	0.198414	+	0.0633794i
$356$	−4798.33	+	620.296i	−0.714357	+	0.0923472i
$357$	−1395.92	−	10915.7i	−0.206947	−	1.61826i
$358$	5881.47	−	6690.72i	0.868282	−	0.987753i
$359$	7172.59			1.05447			0.527235	−	0.849719i	$-0.323229\pi$
$359$	7172.59			1.05447			0.527235	+	0.849719i	$0.323229\pi$
$360$	4119.37	−	5448.56i	0.603082	−	0.797679i
$361$	11739.8			1.71159
$362$	−5736.45	+	6525.75i	−0.832876	+	0.947475i
$363$	−104.696	−	818.692i	−0.0151381	−	0.118375i
$364$	−1048.42	−	8110.12i	−0.150968	−	1.16782i
$365$	−910.936	+	2851.76i	−0.130632	+	0.408953i
$366$	7488.82	+	5056.88i	1.06953	+	0.722206i
$367$	−1909.09			−0.271536			−0.135768	−	0.990741i	$-0.543350\pi$
$367$	−1909.09			−0.271536			−0.135768	+	0.990741i	$0.543350\pi$
$368$	−1865.35	−	7094.17i	−0.264233	−	1.00492i
$369$	−1182.09	−	4546.23i	−0.166768	−	0.641374i
$370$	1634.13	+	2723.10i	0.229607	+	0.382614i
$371$		−	13471.5i		−	1.88519i
$372$	600.603	+	2296.95i	0.0837091	+	0.320138i
$373$	9250.82			1.28415			0.642077	−	0.766640i	$-0.278073\pi$
$373$	9250.82			1.28415			0.642077	+	0.766640i	$0.278073\pi$
$374$	−5404.18	+	6147.77i	−0.747175	+	0.849982i
$375$	5211.17	−	5057.48i	0.717610	−	0.696445i
$376$	−4501.38	−	3030.63i	−0.617397	−	0.415672i
$377$	3956.33			0.540481
$378$	−3733.16	+	10568.9i	−0.507971	+	1.43811i
$379$	−13617.5			−1.84561			−0.922803	−	0.385272i	$-0.874108\pi$
$379$	−13617.5			−1.84561			−0.922803	+	0.385272i	$0.874108\pi$
$380$	−2191.30	+	11999.5i	−0.295819	+	1.61990i
$381$	999.911	+	7819.00i	0.134454	+	1.05139i
$382$	3106.33	+	2730.61i	0.416057	+	0.365734i
$383$		−	4191.08i		−	0.559149i	−0.960124	−	0.279575i	$-0.909807\pi$
$383$		−	4191.08i		−	0.559149i	0.960124	−	0.279575i	$-0.0901934\pi$
$384$	−7362.26	−	1555.71i	−0.978395	−	0.206744i
$385$	3709.13	−	11611.7i	0.490999	−	1.53711i
$386$	3259.03	−	3707.45i	0.429741	−	0.488871i
$387$	−584.429	−	2247.66i	−0.0767653	−	0.295232i
$388$	−8260.46	+	1067.86i	−1.08083	+	0.139722i
$389$	−9075.46			−1.18289			−0.591445	−	0.806346i	$-0.701442\pi$
$389$	−9075.46			−1.18289			−0.591445	+	0.806346i	$0.701442\pi$
$390$	4669.39	−	3681.78i	0.606267	−	0.478037i
$391$		−	8593.34i		−	1.11147i
$392$	5748.37	−	8538.04i	0.740655	−	1.10009i
$393$	4989.87	−	638.116i	0.640473	−	0.0819051i
$394$	−5.61316	+	6.38549i	−0.000717733	+	0.000816489i
$395$	−1994.27	+	6243.22i	−0.254032	+	0.795267i
$396$	7733.39	−	3115.24i	0.981357	−	0.395320i
$397$	−4124.77			−0.521451			−0.260726	−	0.965413i	$-0.583962\pi$
$397$	−4124.77			−0.521451			−0.260726	+	0.965413i	$0.583962\pi$
$398$	9543.84	−	10857.0i	1.20198	−	1.36737i
$399$	−2539.11	−	19855.0i	−0.318582	−	2.49122i
$400$	−7483.64	−	2827.55i	−0.935456	−	0.353444i
$401$		−	3706.51i		−	0.461582i	−0.973003	−	0.230791i	$-0.925869\pi$
$401$		−	3706.51i		−	0.461582i	0.973003	−	0.230791i	$-0.0741314\pi$
$402$	4657.72	+	3145.16i	0.577876	+	0.390215i
$403$			2066.84i			0.255476i
$404$	525.740	+	4066.89i	0.0647440	+	0.500830i
$405$	−7988.68	+	1615.91i	−0.980150	+	0.198260i
$406$	6560.24	+	5766.76i	0.801919	+	0.704925i
$407$			3876.34i			0.472097i
$408$	−7877.91	−	3955.89i	−0.955918	−	0.480014i
$409$	2721.73			0.329048			0.164524	−	0.986373i	$-0.447391\pi$
$409$	2721.73			0.329048			0.164524	+	0.986373i	$0.447391\pi$
$410$	−4717.42	+	2830.92i	−0.568236	+	0.340998i
$411$	−334.999	−	2619.59i	−0.0402050	−	0.314391i
$412$	−603.724	−	4670.14i	−0.0721926	−	0.558450i
$413$			21532.1i			2.56543i
$414$	−3938.52	+	7816.63i	−0.467555	+	0.927938i
$415$	−3007.61	−	960.718i	−0.355753	−	0.113638i
$416$	−5858.15	−	2931.64i	−0.690432	−	0.345518i
$417$	−89.9517	−	703.395i	−0.0105634	−	0.0826029i
$418$	−9829.89	+	11182.4i	−1.15023	+	1.30849i
$419$		−	5358.54i		−	0.624777i	−0.949954	−	0.312389i	$-0.898871\pi$
$419$		−	5358.54i		−	0.624777i	0.949954	−	0.312389i	$-0.101129\pi$
$420$	13109.2	+	701.136i	1.52301	+	0.0814569i
$421$			9513.73i			1.10136i	0.834718	+	0.550678i	$0.185631\pi$
$421$			9513.73i			1.10136i	−0.834718	+	0.550678i	$0.814369\pi$
$422$	−2558.48	−	2249.02i	−0.295130	−	0.259433i
$423$	1629.47	+	6266.78i	0.187299	+	0.720334i
$424$	−8951.71	−	6026.89i	−1.02531	−	0.690310i
$425$	−7636.55	−	5433.04i	−0.871593	−	0.620097i
$426$	−1024.89	+	1517.78i	−0.116564	+	0.172621i
$427$			17367.3i			1.96830i
$428$	1925.84	+	14897.4i	0.217498	+	1.68247i
$429$	7199.40	−	920.675i	0.810233	−	0.103614i
$430$	−2332.30	+	1399.61i	−0.261566	+	0.156966i
$431$	−13279.4			−1.48410			−0.742049	−	0.670345i	$-0.766146\pi$
$431$	−13279.4			−1.48410			−0.742049	+	0.670345i	$0.766146\pi$
$432$	5352.79	+	7208.96i	0.596149	+	0.802874i
$433$		−	9112.89i		−	1.01140i	−0.862709	−	0.505701i	$-0.831234\pi$
$433$		−	9112.89i		−	1.01140i	0.862709	−	0.505701i	$-0.168766\pi$
$434$	−3012.64	+	3427.16i	−0.333206	+	0.379053i
$435$	−1149.53	+	6246.41i	−0.126702	+	0.688488i
$436$	−6613.81	+	854.989i	−0.726478	+	0.0939141i
$437$		−	15630.8i		−	1.71103i
$438$	−3261.41	−	2202.29i	−0.355791	−	0.240250i
$439$			17049.8i			1.85363i	0.375519	+	0.926815i	$0.377464\pi$
$439$			17049.8i			1.85363i	−0.375519	+	0.926815i	$0.622536\pi$
$440$	−6056.50	−	7659.54i	−0.656210	−	0.829896i
$441$	−11886.6	+	3090.71i	−1.28351	+	0.333734i
$442$	−5763.87	−	5066.72i	−0.620270	−	0.545247i
$443$	−1354.27			−0.145245			−0.0726224	−	0.997360i	$-0.523137\pi$
$443$	−1354.27			−0.145245			−0.0726224	+	0.997360i	$0.523137\pi$
$444$	−4038.90	+	1056.08i	−0.431707	+	0.112882i
$445$	2057.46	−	6441.04i	0.219175	−	0.686146i
$446$	4308.05	+	3786.98i	0.457381	+	0.402060i
$447$	−11.5161	−	90.0521i	−0.00121855	−	0.00952867i
$448$	−5440.60	−	13400.0i	−0.573759	−	1.41315i
$449$			18871.3i			1.98350i	0.128173	+	0.991752i	$0.459089\pi$
$449$			18871.3i			1.98350i	−0.128173	+	0.991752i	$0.540911\pi$
$450$	4456.23	+	8441.98i	0.466820	+	0.884353i
$451$	−6715.27			−0.701130
$452$	1015.90	+	7858.56i	0.105717	+	0.817778i
$453$	10360.6	−	1324.93i	1.07457	−	0.137419i
$454$	3617.13	+	3179.63i	0.373921	+	0.328695i
$455$	10886.6	+	3477.51i	1.12170	+	0.358304i
$456$	−14329.5	−	7195.54i	−1.47158	−	0.738952i
$457$		−	667.236i		−	0.0682976i	−0.999417	−	0.0341488i	$-0.989128\pi$
$457$		−	667.236i		−	0.0682976i	0.999417	−	0.0341488i	$-0.0108720\pi$
$458$	2823.21	−	3211.67i	0.288035	−	0.327667i
$459$	3917.05	+	9762.34i	0.398327	+	0.992738i
$460$	10084.6	+	1841.61i	1.02217	+	0.186664i
$461$	18594.5			1.87860			0.939300	−	0.343097i	$-0.111476\pi$
$461$	18594.5			1.87860			0.939300	+	0.343097i	$0.111476\pi$
$462$	13279.7	+	8967.24i	1.33729	+	0.903017i
$463$	3391.85			0.340460			0.170230	−	0.985404i	$-0.445549\pi$
$463$	3391.85			0.340460			0.170230	+	0.985404i	$0.445549\pi$
$464$	6766.89	−	1779.29i	0.677036	−	0.178020i
$465$	−3263.21	−	600.529i	−0.325436	−	0.0598900i
$466$	10859.4	+	9545.90i	1.07951	+	0.948938i
$467$	−11937.5			−1.18287			−0.591437	−	0.806351i	$-0.701439\pi$
$467$	−11937.5			−1.18287			−0.591437	+	0.806351i	$0.701439\pi$
$468$	2920.71	+	7250.48i	0.288483	+	0.716140i
$469$			10801.7i			1.06349i
$470$	6502.77	−	3902.31i	0.638192	−	0.382979i
$471$	−781.059	−	6107.64i	−0.0764104	−	0.597506i
$472$	14307.9	+	9633.02i	1.39528	+	0.939398i
$473$	−3320.03			−0.322738
$474$	−7140.06	−	4821.37i	−0.691885	−	0.467200i
$475$	−13890.4	−	9882.39i	−1.34176	−	0.954600i
$476$	−2172.16	−	16802.9i	−0.209162	−	1.61798i
$477$	3240.45	+	12462.5i	0.311049	+	1.19626i
$478$	−10386.6	−	9130.33i	−0.993875	−	0.873664i
$479$	−6583.62			−0.628003			−0.314001	−	0.949423i	$-0.601670\pi$
$479$	−6583.62			−0.628003			−0.314001	+	0.949423i	$0.601670\pi$
$480$	6330.69	−	8397.28i	0.601990	−	0.798504i
$481$	−3634.29			−0.344510
$482$	8368.39	+	7356.22i	0.790809	+	0.695159i
$483$	−16686.6	+	2133.92i	−1.57198	+	0.201028i
$484$	−162.915	−	1260.24i	−0.0153000	−	0.118354i
$485$	3541.98	−	11088.4i	0.331614	−	1.03814i
$486$	911.294	−	10675.2i	0.0850559	−	0.996376i
$487$	−19593.7			−1.82315			−0.911576	−	0.411133i	$-0.865133\pi$
$487$	−19593.7			−1.82315			−0.911576	+	0.411133i	$0.865133\pi$
$488$	11540.4	+	7769.79i	1.07051	+	0.720742i
$489$	12710.6	−	1625.46i	1.17545	−	0.150319i
$490$	7401.74	+	12334.2i	0.682401	+	1.13715i
$491$			5466.42i			0.502436i	0.967931	+	0.251218i	$0.0808311\pi$
$491$			5466.42i			0.502436i	−0.967931	+	0.251218i	$0.919169\pi$
$492$	−1829.53	−	6996.88i	−0.167646	−	0.641145i
$493$	8196.89			0.748822
$494$	−10484.1	−	9216.07i	−0.954867	−	0.839374i
$495$	−638.213	+	11634.2i	−0.0579506	+	1.05640i
$496$	929.527	+	3535.12i	0.0841471	+	0.320023i
$497$	−3519.88			−0.317682
$498$	2322.65	−	3439.65i	0.208997	−	0.309507i
$499$	4021.21			0.360750			0.180375	−	0.983598i	$-0.442269\pi$
$499$	4021.21			0.360750			0.180375	+	0.983598i	$0.442269\pi$
$500$	8012.46	−	7797.47i	0.716656	−	0.697426i
$501$	−6787.99	+	868.063i	−0.605319	+	0.0774096i
$502$	−10277.7	+	11691.9i	−0.913777	+	1.03951i
$503$		−	17774.3i		−	1.57558i	−0.615946	−	0.787788i	$-0.711226\pi$
$503$		−	17774.3i		−	1.57558i	0.615946	−	0.787788i	$-0.288774\pi$
$504$	−5725.31	+	16279.7i	−0.506003	+	1.43880i
$505$	−5459.20	−	1743.83i	−0.481052	−	0.153662i
$506$	9397.94	+	8261.24i	0.825671	+	0.725805i
$507$	−584.920	−	4573.90i	−0.0512371	−	0.400659i
$508$	1555.94	+	12036.0i	0.135893	+	1.05120i
$509$	−20544.9			−1.78907			−0.894537	−	0.446995i	$-0.852494\pi$
$509$	−20544.9			−1.78907			−0.894537	+	0.446995i	$0.852494\pi$
$510$	9674.24	−	7628.07i	0.839966	−	0.662307i
$511$		−	7563.53i		−	0.654777i
$512$	−11338.2	−	2379.66i	−0.978677	−	0.205405i
$513$	7124.89	+	17757.1i	0.613200	+	1.52826i
$514$	−10492.5	−	9223.38i	−0.900395	−	0.791490i
$515$	6268.97	+	2002.49i	0.536396	+	0.171341i
$516$	−904.521	−	3459.26i	−0.0771692	−	0.295127i
$517$	9256.71			0.787446
$518$	−6026.24	−	5297.35i	−0.511154	−	0.449329i
$519$	−8838.29	+	1130.26i	−0.747510	+	0.0955932i
$520$	7181.24	−	5678.31i	0.605612	−	0.478866i
$521$			18770.8i			1.57843i	0.614114	+	0.789217i	$0.289514\pi$
$521$			18770.8i			1.57843i	−0.614114	+	0.789217i	$0.710486\pi$
$522$	−7456.01	−	3756.82i	−0.625174	−	0.315003i
$523$			2828.70i			0.236502i	0.992984	+	0.118251i	$0.0377287\pi$
$523$			2828.70i			0.236502i	−0.992984	+	0.118251i	$0.962271\pi$
$524$	7681.06	−	992.956i	0.640360	−	0.0827814i
$525$	−8653.58	+	16177.8i	−0.719377	+	1.34487i
$526$	−595.103	+	676.986i	−0.0493303	+	0.0561178i
$527$			4282.17i			0.353955i
$528$	11899.8	−	4812.52i	0.980815	−	0.396663i
$529$	−969.434			−0.0796773
$530$	12931.8	−	7760.36i	1.05985	−	0.636016i
$531$	−5179.35	−	19919.3i	−0.423286	−	1.62792i
$532$	−3951.04	−	30563.5i	−0.321991	−	2.49078i
$533$		−	6295.93i		−	0.511646i
$534$	7366.30	+	4974.15i	0.596949	+	0.403094i
$535$	−19997.6	−	6387.83i	−1.61602	−	0.516205i
$536$	7177.66	+	4832.48i	0.578410	+	0.389424i
$537$	−16233.3	+	2075.96i	−1.30451	+	0.166823i
$538$	−8510.62	−	7481.25i	−0.682006	−	0.599516i
$539$			17557.7i			1.40309i
$540$	−12296.0	+	2504.68i	−0.979877	+	0.199601i
$541$		−	16230.2i		−	1.28982i	−0.764260	−	0.644908i	$-0.776896\pi$
$541$		−	16230.2i		−	1.28982i	0.764260	−	0.644908i	$-0.223104\pi$
$542$	4784.69	−	5443.04i	0.379189	−	0.431363i
$543$	15833.1	−	2024.77i	1.25131	−	0.160021i
$544$	−12137.2	−	6073.89i	−0.956574	−	0.478706i
$545$	2835.92	−	8878.06i	0.222894	−	0.697788i
$546$	−8407.28	+	12450.5i	−0.658971	+	0.975882i
$547$		−	9520.53i		−	0.744184i	−0.928196	−	0.372092i	$-0.878641\pi$
$547$		−	9520.53i		−	0.744184i	0.928196	−	0.372092i	$-0.121359\pi$
$548$	−521.282	−	4032.41i	−0.0406352	−	0.314336i
$549$	−4177.56	−	16066.5i	−0.324761	−	1.24900i
$550$	13283.2	−	3128.49i	1.02981	−	0.242544i
$551$	14909.7			1.15276
$552$	−6047.28	+	12042.8i	−0.466285	+	0.928577i
$553$		−	16558.5i		−	1.27331i
$554$	−1753.39	−	1541.32i	−0.134467	−	0.118203i
$555$	1055.96	−	5737.95i	0.0807618	−	0.438852i
$556$	−139.971	−	1082.76i	−0.0106765	−	0.0825883i
$557$			7627.12i			0.580200i	0.956996	+	0.290100i	$0.0936885\pi$
$557$			7627.12i			0.580200i	−0.956996	+	0.290100i	$0.906311\pi$
$558$	1962.62	−	3895.13i	0.148896	−	0.295509i
$559$		−	3112.71i		−	0.235517i
$560$	20184.4	+	1051.85i	1.52312	+	0.0793728i
$561$	14916.0	−	1907.49i	1.12256	−	0.143555i
$562$	9953.27	−	11322.8i	0.747070	−	0.849862i
$563$	−4278.28			−0.320263			−0.160131	−	0.987096i	$-0.551192\pi$
$563$	−4278.28			−0.320263			−0.160131	+	0.987096i	$0.551192\pi$
$564$	2521.93	+	9644.90i	0.188284	+	0.720077i
$565$	−10549.0	−	3369.65i	−0.785483	−	0.250906i
$566$	−1979.01	+	2251.31i	−0.146968	+	0.167190i
$567$	17983.9	−	10030.3i	1.33201	−	0.742919i
$568$	−1574.72	+	2338.93i	−0.116327	+	0.172780i
$569$		−	10517.7i		−	0.774910i	−0.921889	−	0.387455i	$-0.873354\pi$
$569$		−	10517.7i		−	0.774910i	0.921889	−	0.387455i	$-0.126646\pi$
$570$	17596.9	−	13875.0i	1.29308	−	1.01958i
$571$	21394.5			1.56801			0.784003	−	0.620756i	$-0.213174\pi$
$571$	21394.5			1.56801			0.784003	+	0.620756i	$0.213174\pi$
$572$	11082.2	−	1432.64i	0.810091	−	0.104723i
$573$	−963.813	−	7536.72i	−0.0702685	−	0.549478i
$574$	9176.98	−	10439.7i	0.667316	−	0.759135i
$575$	−8305.36	+	11673.8i	−0.602361	+	0.846663i
$576$	8256.34	+	11087.6i	0.597247	+	0.802057i
$577$		−	11001.0i		−	0.793725i	−0.917878	−	0.396862i	$-0.870099\pi$
$577$		−	11001.0i		−	0.793725i	0.917878	−	0.396862i	$-0.129901\pi$
$578$	−1504.93	−	1322.91i	−0.108299	−	0.0952002i
$579$	−8995.19	+	1150.32i	−0.645643	+	0.0825663i
$580$	−1756.65	+	9619.39i	−0.125760	+	0.688661i
$581$	7976.88			0.569599
$582$	12681.3	+	8563.13i	0.903190	+	0.609885i
$583$	18408.4			1.30772
$584$	−5025.91	−	3383.78i	−0.356119	−	0.239763i
$585$	−10907.7	−	598.360i	−0.770902	−	0.0422891i
$586$	−15824.3	+	18001.7i	−1.11552	+	1.26901i
$587$	4095.31			0.287958			0.143979	−	0.989581i	$-0.454010\pi$
$587$	4095.31			0.287958			0.143979	+	0.989581i	$0.454010\pi$
$588$	−18294.0	+	4783.49i	−1.28305	+	0.335490i
$589$			7789.03i			0.544892i
$590$	−20669.4	+	12403.7i	−1.44228	+	0.865513i
$591$	15.4928	−	1.98125i	0.00107832	−	0.000137898i
$592$	−6216.07	+	1634.46i	−0.431552	+	0.113473i
$593$	−11978.2			−0.829490			−0.414745	−	0.909938i	$-0.636129\pi$
$593$	−11978.2			−0.829490			−0.414745	+	0.909938i	$0.636129\pi$
$594$	−14442.1	−	5101.26i	−0.997585	−	0.352369i
$595$	22555.4	+	7204.85i	1.55408	+	0.496420i
$596$	−17.9198	−	138.620i	−0.00123159	−	0.00952700i
$597$	−26341.8	+	3368.65i	−1.80586	+	0.230937i
$598$	−7745.37	+	8811.09i	−0.529652	+	0.602529i
$599$	13370.9			0.912056			0.456028	−	0.889965i	$-0.349272\pi$
$599$	13370.9			0.912056			0.456028	+	0.889965i	$0.349272\pi$
$600$	6878.60	+	12987.9i	0.468029	+	0.883713i
$601$	−3829.24			−0.259897			−0.129948	−	0.991521i	$-0.541481\pi$
$601$	−3829.24			−0.259897			−0.129948	+	0.991521i	$0.541481\pi$
$602$	4537.10	−	5161.38i	0.307174	−	0.349439i
$603$	−2598.26	−	9992.66i	−0.175471	−	0.674847i
$604$	15948.3	−	2061.69i	1.07438	−	0.138889i
$605$	1691.68	+	540.373i	0.113680	+	0.0363129i
$606$	4215.91	−	6243.41i	0.282606	−	0.418517i
$607$	274.138			0.0183310			0.00916549	−	0.999958i	$-0.497082\pi$
$607$	274.138			0.0183310			0.00916549	+	0.999958i	$0.497082\pi$
$608$	−22076.8	−	11048.1i	−1.47259	−	0.736937i
$609$	−2035.47	−	15916.8i	−0.135437	−	1.05908i
$610$	−16671.5	+	10004.6i	−1.10657	+	0.664054i
$611$			8678.68i			0.574635i
$612$	6051.25	+	15021.8i	0.399685	+	0.992192i
$613$	9402.87			0.619541			0.309770	−	0.950811i	$-0.399748\pi$
$613$	9402.87			0.619541			0.309770	+	0.950811i	$0.399748\pi$
$614$	−8446.94	+	9609.20i	−0.555197	+	0.631589i
$615$	9940.26	+	1829.31i	0.651756	+	0.119943i
$616$	20464.4	+	13778.0i	1.33853	+	0.901186i
$617$	11725.6			0.765082			0.382541	−	0.923938i	$-0.375049\pi$
$617$	11725.6			0.765082			0.382541	+	0.923938i	$0.375049\pi$
$618$	−4841.26	+	7169.51i	−0.315120	+	0.466666i
$619$	7217.50			0.468653			0.234326	−	0.972158i	$-0.424712\pi$
$619$	7217.50			0.468653			0.234326	+	0.972158i	$0.424712\pi$
$620$	−5025.31	−	917.699i	−0.325518	−	0.0594446i
$621$	14923.5	−	5987.90i	0.964344	−	0.386934i
$622$	14651.5	+	12879.4i	0.944487	+	0.830250i
$623$			17083.2i			1.09859i
$624$	4512.00	+	11156.7i	0.289463	+	0.715744i
$625$	5123.06	+	14761.3i	0.327876	+	0.944721i
$626$	11104.2	−	12632.1i	0.708967	−	0.806517i
$627$	27131.4	−	3469.62i	1.72811	−	0.220994i
$628$	−1215.38	−	9401.68i	−0.0772279	−	0.597401i
$629$	−7529.67			−0.477309
$630$	−17214.6	−	16891.3i	−1.08864	−	1.06820i
$631$			7589.28i			0.478803i	0.970921	+	0.239401i	$0.0769511\pi$
$631$			7589.28i			0.478803i	−0.970921	+	0.239401i	$0.923049\pi$
$632$	−11003.0	−	7407.94i	−0.692524	−	0.466253i
$633$	793.828	+	6207.50i	0.0498449	+	0.389772i
$634$	11045.3	−	12565.0i	0.691898	−	0.787100i
$635$	−16156.6	−	5160.89i	−1.00969	−	0.322525i
$636$	5015.26	+	19180.4i	0.312685	+	1.19584i
$637$	−16461.4			−1.02390
$638$	−7880.11	+	8964.37i	−0.488992	+	0.556274i
$639$	3256.23	−	846.675i	0.201588	−	0.0524162i
$640$	9729.04	−	12941.8i	0.600897	−	0.799327i
$641$		−	812.707i		−	0.0500780i	−0.999686	−	0.0250390i	$-0.992029\pi$
$641$		−	812.707i		−	0.0500780i	0.999686	−	0.0250390i	$-0.00797099\pi$
$642$	15443.3	−	22870.3i	0.949374	−	1.40595i
$643$			9472.41i			0.580957i	0.956882	+	0.290478i	$0.0938145\pi$
$643$			9472.41i			0.580957i	−0.956882	+	0.290478i	$0.906186\pi$
$644$	−25686.2	+	3320.53i	−1.57170	+	0.203179i
$645$	4914.47	+	904.410i	0.300011	+	0.0552110i
$646$	−21721.5	−	19094.2i	−1.32294	−	1.16293i
$647$		−	10796.3i		−	0.656024i	−0.944674	−	0.328012i	$-0.893621\pi$
$647$		−	10796.3i		−	0.656024i	0.944674	−	0.328012i	$-0.106379\pi$
$648$	1380.54	−	16437.5i	0.0836923	−	0.996492i
$649$	−29423.0			−1.77959
$650$	2933.13	+	12453.7i	0.176995	+	0.751499i
$651$	8315.14	−	1063.36i	0.500609	−	0.0640189i
$652$	19565.8	−	2529.33i	1.17524	−	0.151927i
$653$			19320.8i			1.15786i	0.815378	+	0.578929i	$0.196529\pi$
$653$			19320.8i			1.15786i	−0.815378	+	0.578929i	$0.803471\pi$
$654$	10153.4	+	6856.15i	0.607078	+	0.409934i
$655$	−3293.54	+	10310.7i	−0.196472	+	0.615071i
$656$	−2831.48	−	10768.5i	−0.168523	−	0.640915i
$657$	1819.34	+	6997.02i	0.108035	+	0.415494i
$658$	−12650.1	+	14390.7i	−0.749470	+	0.852593i
$659$			8746.91i			0.517043i	0.966006	+	0.258521i	$0.0832353\pi$
$659$			8746.91i			0.517043i	−0.966006	+	0.258521i	$0.916765\pi$
$660$	−958.082	+	17913.3i	−0.0565050	+	1.05648i
$661$		−	24966.4i		−	1.46911i	−0.678552	−	0.734553i	$-0.737392\pi$
$661$		−	24966.4i		−	1.46911i	0.678552	−	0.734553i	$-0.262608\pi$
$662$	−8107.73	−	7127.08i	−0.476006	−	0.418432i
$663$	1788.38	+	13984.6i	0.104758	+	0.819179i
$664$	3568.70	−	5300.57i	0.208573	−	0.309792i
$665$	41026.9	+	13105.2i	2.39241	+	0.764208i
$666$	6849.10	+	3451.02i	0.398494	+	0.200787i
$667$		−	12530.4i		−	0.727404i
$668$	−10449.0	+	1350.77i	−0.605213	+	0.0782378i
$669$	−1336.68	−	10452.4i	−0.0772479	−	0.604055i
$670$	−10369.0	+	6222.41i	−0.597892	+	0.358795i
$671$	−23731.9			−1.36537
$672$	−8780.38	+	25076.3i	−0.504034	+	1.43949i
$673$			28415.4i			1.62754i	0.581188	+	0.813769i	$0.302588\pi$
$673$			28415.4i			1.62754i	−0.581188	+	0.813769i	$0.697412\pi$
$674$	11829.3	−	13457.0i	0.676036	−	0.769055i
$675$	4113.98	−	17047.6i	0.234589	−	0.972095i
$676$	−910.179	−	7040.74i	−0.0517853	−	0.400588i
$677$		−	13799.2i		−	0.783377i	−0.920098	−	0.391689i	$-0.871891\pi$
$677$		−	13799.2i		−	0.783377i	0.920098	−	0.391689i	$-0.128109\pi$
$678$	8146.51	−	12064.3i	0.461452	−	0.683373i
$679$			29409.2i			1.66218i
$680$	14878.4	−	11764.6i	0.839059	−	0.663456i
$681$	−1122.30	−	8776.05i	−0.0631522	−	0.493831i
$682$	−4683.12	−	4116.69i	−0.262941	−	0.231138i
$683$	34785.2			1.94878			0.974392	−	0.224858i	$-0.0721917\pi$
$683$	34785.2			1.94878			0.974392	+	0.224858i	$0.0721917\pi$
$684$	11006.9	+	27323.9i	0.615290	+	1.52742i
$685$	5412.91	+	1729.04i	0.301922	+	0.0964428i
$686$	−6713.58	−	5901.56i	−0.373653	−	0.328459i
$687$	−7792.30	+	996.497i	−0.432744	+	0.0553402i
$688$	−1399.89	−	5323.97i	−0.0775730	−	0.295021i
$689$			17258.9i			0.954300i
$690$	−11660.8	−	14788.8i	−0.643364	−	0.815941i
$691$	−19390.7			−1.06752			−0.533760	−	0.845636i	$-0.679221\pi$
$691$	−19390.7			−1.06752			−0.533760	+	0.845636i	$0.679221\pi$
$692$	−13605.0	+	1758.77i	−0.747379	+	0.0966160i
$693$	−7407.95	−	28490.3i	−0.406068	−	1.56170i
$694$	−2531.33	−	2225.16i	−0.138455	−	0.121709i
$695$	1453.44	+	464.272i	0.0793268	+	0.0253393i
$696$	−11487.2	−	5768.29i	−0.625604	−	0.314147i
$697$		−	13044.2i		−	0.708871i
$698$	8996.74	−	10234.6i	0.487867	−	0.554995i
$699$	−3369.38	−	26347.5i	−0.182320	−	1.42568i
$700$	−13289.0	+	24925.6i	−0.717536	+	1.34586i
$701$	−21164.3			−1.14032			−0.570160	−	0.821534i	$-0.693119\pi$
$701$	−21164.3			−1.14032			−0.570160	+	0.821534i	$0.693119\pi$
$702$	4782.71	−	13540.2i	0.257139	−	0.727982i
$703$	−13696.0			−0.734787
$704$	18310.7	−	7434.42i	0.980271	−	0.398005i
$705$	−13702.2	−	2521.62i	−0.731994	−	0.134709i
$706$	2532.09	+	2225.83i	0.134981	+	0.118654i
$707$	14479.1			0.770215
$708$	−8016.09	−	30656.8i	−0.425513	−	1.62734i
$709$		−	4868.59i		−	0.257890i	−0.991652	−	0.128945i	$-0.958841\pi$
$709$		−	4868.59i		−	0.257890i	0.991652	−	0.128945i	$-0.0411590\pi$
$710$	−2027.65	−	3378.85i	−0.107178	−	0.178600i
$711$	3983.00	+	15318.2i	0.210090	+	0.807987i
$712$	11351.6	+	7642.67i	0.597500	+	0.402277i
$713$	6546.06			0.343831
$714$	−17418.5	+	25795.4i	−0.912987	+	1.35206i
$715$	−4751.92	+	14876.3i	−0.248548	+	0.778099i
$716$	−24988.5	+	3230.34i	−1.30428	+	0.168608i
$717$	3222.69	+	25200.5i	0.167857	+	1.31259i
$718$	−15237.0	−	13394.1i	−0.791979	−	0.696188i
$719$	−20252.9			−1.05049			−0.525246	−	0.850950i	$-0.676027\pi$
$719$	−20252.9			−1.05049			−0.525246	+	0.850950i	$0.676027\pi$
$720$	−18925.6	+	3882.11i	−0.979603	+	0.200941i
$721$	−16626.8			−0.858826
$722$	−24939.3	−	21922.8i	−1.28552	−	1.13003i
$723$	−2596.49	−	20303.8i	−0.133561	−	1.04441i
$724$	24372.4	−	3150.69i	1.25109	−	0.161733i
$725$	−11135.2	−	7922.19i	−0.570417	−	0.405825i
$726$	−1306.41	+	1934.69i	−0.0667845	+	0.0989023i
$727$	8380.16			0.427515			0.213757	−	0.976887i	$-0.431430\pi$
$727$	8380.16			0.427515			0.213757	+	0.976887i	$0.431430\pi$
$728$	−12917.6	+	19186.5i	−0.657635	+	0.976783i
$729$	−14224.1	+	13604.9i	−0.722662	+	0.691202i
$730$	7260.50	−	4357.03i	0.368114	−	0.220905i
$731$		−	6449.05i		−	0.326302i
$732$	−6465.61	−	24727.2i	−0.326470	−	1.24855i
$733$	26525.6			1.33662			0.668311	−	0.743882i	$-0.267018\pi$
$733$	26525.6			1.33662			0.668311	+	0.743882i	$0.267018\pi$
$734$	4055.57	+	3565.04i	0.203942	+	0.179275i
$735$	4782.91	−	25989.8i	0.240027	−	1.30428i
$736$	−9285.01	+	18553.8i	−0.465014	+	0.929214i
$737$	−14760.2			−0.737721
$738$	−5978.44	+	11865.2i	−0.298197	+	0.591820i
$739$	16456.9			0.819184			0.409592	−	0.912269i	$-0.365671\pi$
$739$	16456.9			0.819184			0.409592	+	0.912269i	$0.365671\pi$
$740$	1613.66	−	8836.38i	0.0801612	−	0.438962i
$741$	3252.96	+	25437.1i	0.161269	+	1.26108i
$742$	−25156.7	+	28618.1i	−1.24465	+	1.41591i
$743$			11323.5i			0.559112i	0.960129	+	0.279556i	$0.0901873\pi$
$743$			11323.5i			0.559112i	−0.960129	+	0.279556i	$0.909813\pi$
$744$	3013.44	−	6001.07i	0.148492	−	0.295712i
$745$	186.077	+	59.4384i	0.00915076	+	0.00292302i
$746$	−19651.9	−	17275.0i	−0.964487	−	0.847830i
$747$	−7379.41	+	1918.77i	−0.361444	+	0.0939814i
$748$	22960.6	−	2968.20i	1.12236	−	0.145091i
$749$	53038.3			2.58742
$750$	−20514.6	+	1012.47i	−0.998784	+	0.0492938i
$751$			17017.6i			0.826872i	0.910533	+	0.413436i	$0.135672\pi$
$751$			17017.6i			0.826872i	−0.910533	+	0.413436i	$0.864328\pi$
$752$	3903.08	+	14844.0i	0.189270	+	0.719819i
$753$	28367.3	−	3627.68i	1.37286	−	0.175564i
$754$	−8404.59	−	7388.04i	−0.405938	−	0.356839i
$755$	−6838.43	+	21408.3i	−0.329637	+	1.03196i
$756$	27666.8	−	15480.6i	1.33100	−	0.744741i
$757$	32951.4			1.58209			0.791044	−	0.611759i	$-0.209538\pi$
$757$	32951.4			1.58209			0.791044	+	0.611759i	$0.209538\pi$
$758$	28928.2	+	25429.3i	1.38618	+	1.21852i
$759$	−2915.94	−	22801.7i	−0.139449	−	1.09045i
$760$	27062.9	−	21399.0i	1.29168	−	1.02135i
$761$		−	26158.8i		−	1.24607i	−0.782196	−	0.623033i	$-0.785900\pi$
$761$		−	26158.8i		−	1.24607i	0.782196	−	0.623033i	$-0.214100\pi$
$762$	12477.0	−	18477.5i	0.593170	−	0.878435i
$763$			23546.7i			1.11723i
$764$	−1499.76	−	11601.5i	−0.0710203	−	0.549382i
$765$	−22599.0	−	1239.71i	−1.06806	−	0.0585904i
$766$	−7826.41	+	8903.28i	−0.369164	+	0.419959i
$767$		−	27585.7i		−	1.29864i
$768$	12734.8	+	17053.1i	0.598344	+	0.801239i
$769$	14374.4			0.674065			0.337032	−	0.941493i	$-0.390577\pi$
$769$	14374.4			0.674065			0.337032	+	0.941493i	$0.390577\pi$
$770$	−29563.1	+	17740.8i	−1.38361	+	0.830306i
$771$	3255.54	+	25457.3i	0.152069	+	1.18914i
$772$	−13846.6	+	1789.99i	−0.645529	+	0.0834497i
$773$		−	10943.3i		−	0.509189i	−0.967048	−	0.254595i	$-0.918058\pi$
$773$		−	10943.3i		−	0.509189i	0.967048	−	0.254595i	$-0.0819420\pi$
$774$	−2955.75	+	5866.15i	−0.137264	+	0.272422i
$775$	4138.67	−	5817.21i	0.191826	−	0.269626i
$776$	19542.2	+	13157.1i	0.904024	+	0.608649i
$777$	1869.78	+	14621.1i	0.0863296	+	0.675072i
$778$	19279.4	+	16947.5i	0.888430	+	0.780973i
$779$		−	23726.6i		−	1.09126i
$780$	−16794.7	−	898.254i	−0.770959	−	0.0412342i
$781$		−	4809.81i		−	0.220369i
$782$	−16047.2	+	18255.2i	−0.733818	+	0.834788i
$783$	5711.65	+	14235.0i	0.260687	+	0.649701i
$784$	−28155.4	+	7403.20i	−1.28259	+	0.337245i
$785$	12620.3	+	4031.31i	0.573808	+	0.183291i
$786$	−11791.8	−	7962.50i	−0.535115	−	0.361340i
$787$			39944.3i			1.80922i	0.426235	+	0.904612i	$0.359840\pi$
$787$			39944.3i			1.80922i	−0.426235	+	0.904612i	$0.640160\pi$
$788$	23.8485	−	3.08297i	0.00107813	−	0.000139374i
$789$	1642.54	−	210.051i	0.0741138	−	0.00947784i
$790$	15895.1	−	9538.63i	0.715850	−	0.429581i
$791$	27978.3			1.25764
$792$	−22245.7	−	7823.47i	−0.998066	−	0.351004i
$793$		−	22250.0i		−	0.996369i
$794$	8762.42	+	7702.59i	0.391646	+	0.344275i
$795$	−27249.1	−	5014.64i	−1.21563	−	0.223712i
$796$	−40548.7	+	5241.87i	−1.80554	+	0.233408i
$797$			18167.9i			0.807452i	0.914880	+	0.403726i	$0.132285\pi$
$797$			18167.9i			0.807452i	−0.914880	+	0.403726i	$0.867715\pi$
$798$	−31683.3	+	46920.4i	−1.40549	+	2.08141i
$799$			17980.8i			0.796141i
$800$	10617.6	+	19981.6i	0.469238	+	0.883072i
$801$	−4109.21	−	15803.6i	−0.181263	−	0.697121i
$802$	−6921.54	+	7873.90i	−0.304748	+	0.346680i
$803$	10335.4			0.454205
$804$	−4021.33	−	15379.2i	−0.176395	−	0.674606i
$805$	11013.9	−	34479.8i	0.482222	−	1.50963i
$806$	3859.62	−	4390.68i	0.168672	−	0.191880i
$807$	2640.62	+	20648.9i	0.115185	+	0.900712i
$808$	6477.65	−	9621.23i	0.282034	−	0.418903i
$809$		−	9630.14i		−	0.418514i	−0.977861	−	0.209257i	$-0.932895\pi$
$809$		−	9630.14i		−	0.418514i	0.977861	−	0.209257i	$-0.0671045\pi$
$810$	19988.2	+	11485.3i	0.867055	+	0.498213i
$811$	23594.1			1.02158			0.510791	−	0.859705i	$-0.329353\pi$
$811$	23594.1			1.02158			0.510791	+	0.859705i	$0.329353\pi$
$812$	−3167.34	−	24501.1i	−0.136887	−	1.05889i
$813$	−13206.2	+	1688.83i	−0.569693	+	0.0728536i
$814$	7238.68	−	8234.68i	0.311690	−	0.354577i
$815$	−8389.55	+	26264.2i	−0.360581	+	1.12883i
$816$	9348.15	+	23114.9i	0.401042	+	0.991644i
$817$		−	11730.4i		−	0.502321i
$818$	−5781.87	−	5082.54i	−0.247137	−	0.217246i
$819$	26711.2	−	6945.36i	1.13964	−	0.296326i
$820$	15307.9	+	2795.46i	0.651920	+	0.119051i
$821$	−41624.9			−1.76945			−0.884726	−	0.466111i	$-0.845655\pi$
$821$	−41624.9			−1.76945			−0.884726	+	0.466111i	$0.845655\pi$
$822$	−4180.16	+	6190.47i	−0.177372	+	0.262673i
$823$	−15420.0			−0.653106			−0.326553	−	0.945179i	$-0.605887\pi$
$823$	−15420.0			−0.653106			−0.326553	+	0.945179i	$0.605887\pi$
$824$	−7438.50	+	11048.4i	−0.314481	+	0.467097i
$825$	−22106.5	−	11824.9i	−0.932910	−	0.499017i
$826$	40208.9	−	45741.5i	1.69376	−	1.92682i
$827$	−4715.44			−0.198273			−0.0991367	−	0.995074i	$-0.531608\pi$
$827$	−4715.44			−0.198273			−0.0991367	+	0.995074i	$0.531608\pi$
$828$	22963.5	−	9250.41i	0.963814	−	0.388253i
$829$		−	1973.01i		−	0.0826603i	−0.999146	−	0.0413302i	$-0.986840\pi$
$829$		−	1973.01i		−	0.0826603i	0.999146	−	0.0413302i	$-0.0131595\pi$
$830$	4595.14	+	7657.29i	0.192168	+	0.320227i
$831$	544.032	+	4254.17i	0.0227103	+	0.177588i
$832$	6970.18	+	17167.3i	0.290442	+	0.715347i
$833$	−34105.3			−1.41858
$834$	−1122.43	+	1662.23i	−0.0466026	+	0.0690146i
$835$	4480.37	−	14026.2i	0.185688	−	0.581312i
$836$	41764.1	−	5398.98i	1.72780	−	0.223358i
$837$	−7436.55	+	2983.85i	−0.307103	+	0.123222i
$838$	−10006.5	+	11383.4i	−0.412493	+	0.469250i
$839$	3038.49			0.125030			0.0625150	−	0.998044i	$-0.480088\pi$
$839$	3038.49			0.125030			0.0625150	+	0.998044i	$0.480088\pi$
$840$	−26539.1	−	25969.5i	−1.09010	−	1.06671i
$841$	−12436.7			−0.509931
$842$	17765.9	−	20210.4i	0.727143	−	0.827193i
$843$	−27471.9	+	3513.16i	−1.12240	+	0.143535i
$844$	1235.26	+	9555.39i	0.0503783	+	0.389704i
$845$	9451.14	+	3018.98i	0.384768	+	0.122906i
$846$	8241.03	−	16355.6i	0.334908	−	0.664679i
$847$	−4486.73			−0.182014
$848$	7761.89	+	29519.6i	0.314321	+	1.19541i
$849$	5462.22	−	698.521i	0.220805	−	0.0282370i
$850$	6076.98	+	25802.1i	0.245222	+	1.04118i
$851$			11510.4i			0.463657i
$852$	5011.51	−	1310.40i	0.201516	−	0.0526920i
$853$	−36888.5			−1.48070			−0.740350	−	0.672221i	$-0.765340\pi$
$853$	−36888.5			−1.48070			−0.740350	+	0.672221i	$0.765340\pi$
$854$	32431.7	−	36894.1i	1.29952	−	1.47833i
$855$	−41106.3	−	2254.96i	−1.64422	−	0.0901963i
$856$	23728.3	−	35243.6i	0.947450	−	1.40724i
$857$	−31671.9			−1.26242			−0.631209	−	0.775613i	$-0.717441\pi$
$857$	−31671.9			−1.26242			−0.631209	+	0.775613i	$0.717441\pi$
$858$	−17013.2	−	11488.3i	−0.676949	−	0.457115i
$859$	−5370.36			−0.213311			−0.106656	−	0.994296i	$-0.534014\pi$
$859$	−5370.36			−0.213311			−0.106656	+	0.994296i	$0.534014\pi$
$860$	7568.23	+	1382.08i	0.300086	+	0.0548004i
$861$	−25329.2	+	3239.16i	−1.00258	+	0.128212i
$862$	28210.0	+	24797.9i	1.11466	+	0.979839i
$863$		−	30609.9i		−	1.20738i	−0.797218	−	0.603692i	$-0.793696\pi$
$863$		−	30609.9i		−	1.20738i	0.797218	−	0.603692i	$-0.206304\pi$
$864$	2090.84	−	25310.1i	0.0823287	−	0.996605i
$865$	5833.66	−	18262.7i	0.229307	−	0.717863i
$866$	−17017.4	+	19358.9i	−0.667753	+	0.759632i
$867$	466.941	+	3651.34i	0.0182908	+	0.143029i
$868$	12799.7	−	1654.66i	0.500520	−	0.0647039i
$869$	22626.7			0.883266
$870$	14106.5	−	11122.9i	0.549719	−	0.433449i
$871$		−	13838.5i		−	0.538348i
$872$	15646.6	+	10534.3i	0.607639	+	0.409103i
$873$	−7074.12	−	27206.4i	−0.274253	−	1.05475i
$874$	−29188.9	+	33205.1i	−1.12967	+	1.28510i
$875$	−23677.4	−	31587.1i	−0.914792	−	1.22039i
$876$	2815.80	+	10768.8i	0.108604	+	0.415346i
$877$	−22759.7			−0.876331			−0.438165	−	0.898894i	$-0.644372\pi$
$877$	−22759.7			−0.876331			−0.438165	+	0.898894i	$0.644372\pi$
$878$	31838.8	−	36219.6i	1.22381	−	1.39220i
$879$	43676.5	−	5585.45i	1.67596	−	0.214326i
$880$	−1437.32	+	27581.4i	−0.0550592	+	1.05655i
$881$			28404.1i			1.08622i	0.839662	+	0.543109i	$0.182753\pi$
$881$			28404.1i			1.08622i	−0.839662	+	0.543109i	$0.817247\pi$
$882$	31022.7	+	15631.2i	1.18434	+	0.596747i
$883$		−	17364.5i		−	0.661790i	−0.943668	−	0.330895i	$-0.892649\pi$
$883$		−	17364.5i		−	0.661790i	0.943668	−	0.330895i	$-0.107351\pi$
$884$	2782.85	+	21526.9i	0.105879	+	0.819035i
$885$	43553.3	+	8015.11i	1.65427	+	0.304435i
$886$	2876.94	+	2528.96i	0.109089	+	0.0958942i
$887$		−	19856.5i		−	0.751654i	−0.926690	−	0.375827i	$-0.877359\pi$
$887$		−	19856.5i		−	0.751654i	0.926690	−	0.375827i	$-0.122641\pi$
$888$	10552.1	+	5298.75i	0.398769	+	0.200242i
$889$	42851.0			1.61662
$890$	−16398.7	+	9840.88i	−0.617626	+	0.370637i
$891$	13706.2	+	24574.4i	0.515347	+	0.923989i
$892$	−2079.96	−	16089.7i	−0.0780744	−	0.603949i
$893$			32706.1i			1.22561i
$894$	−143.699	+	212.806i	−0.00537586	+	0.00796120i
$895$	10714.7	−	33543.3i	0.400172	−	1.25277i
$896$	−13465.4	+	38625.9i	−0.502063	+	1.44018i
$897$	21377.9	−	2733.85i	0.795749	−	0.101762i
$898$	35240.3	−	40089.1i	1.30956	−	1.48975i
$899$			6244.06i			0.231647i
$900$	6297.97	−	26255.2i	0.233258	−	0.972415i
$901$			35757.7i			1.32216i
$902$	14265.5	+	12540.1i	0.526596	+	0.462903i
$903$	−12522.8	+	1601.44i	−0.461498	+	0.0590174i
$904$	12516.9	−	18591.4i	0.460517	−	0.684004i
$905$	−10450.5	+	32716.3i	−0.383854	+	1.20169i
$906$	−24483.6	−	16532.7i	−0.897805	−	0.606249i
$907$		−	24108.8i		−	0.882601i	−0.897359	−	0.441300i	$-0.854517\pi$
$907$		−	24108.8i		−	0.882601i	0.897359	−	0.441300i	$-0.145483\pi$
$908$	−1746.38	−	13509.2i	−0.0638279	−	0.493744i
$909$	−13394.6	+	3482.82i	−0.488746	+	0.127082i
$910$	−16633.0	−	27717.1i	−0.605911	−	1.00968i
$911$	32678.2			1.18845			0.594224	−	0.804300i	$-0.297459\pi$
$911$	32678.2			1.18845			0.594224	+	0.804300i	$0.297459\pi$
$912$	17003.7	+	42044.6i	0.617380	+	1.52657i
$913$			10900.2i			0.395119i
$914$	−1246.00	+	1417.44i	−0.0450918	+	0.0512961i
$915$	35129.2	+	6464.82i	1.26922	+	0.233574i
$916$	−11994.9	+	1550.62i	−0.432668	+	0.0559323i
$917$		−	27346.4i		−	0.984794i
$918$	9909.02	−	28053.2i	0.356260	−	1.00860i
$919$		−	35471.6i		−	1.27323i	−0.771182	−	0.636615i	$-0.780334\pi$
$919$		−	35471.6i		−	1.27323i	0.771182	−	0.636615i	$-0.219666\pi$
$920$	−17984.2	−	22744.2i	−0.644480	−	0.815060i
$921$	23314.3	−	2981.48i	0.834128	−	0.106670i
$922$	−39501.2	−	34723.4i	−1.41096	−	1.24030i
$923$	4509.46			0.160813
$924$	−11465.3	−	43848.0i	−0.408204	−	1.56114i
$925$	10228.8	+	7277.33i	0.363592	+	0.258678i
$926$	−7205.45	−	6333.94i	−0.255708	−	0.224780i
$927$	15381.4	−	3999.43i	0.544976	−	0.141703i
$928$	−17697.8	−	8856.65i	−0.626034	−	0.313291i
$929$		−	40281.5i		−	1.42260i	−0.702889	−	0.711299i	$-0.748107\pi$
$929$		−	40281.5i		−	1.42260i	0.702889	−	0.711299i	$-0.251893\pi$
$930$	5810.75	+	7369.45i	0.204884	+	0.259843i
$931$	−62035.6			−2.18382
$932$	−5243.00	−	40557.5i	−0.184270	−	1.42543i
$933$	−4545.98	−	35548.1i	−0.159516	−	1.24737i
$934$	25359.3	+	22292.1i	0.888418	+	0.780962i
$935$	−9845.22	+	30821.3i	−0.344356	+	1.07803i
$936$	7334.93	−	20856.6i	0.256143	−	0.728333i
$937$			49586.1i			1.72882i	0.502784	+	0.864412i	$0.332309\pi$
$937$			49586.1i			1.72882i	−0.502784	+	0.864412i	$0.667691\pi$
$938$	20171.1	−	22946.5i	0.702143	−	0.798754i
$939$	−30648.6	+	3919.41i	−1.06515	+	0.136214i
$940$	−21101.3	−	3853.42i	−0.732178	−	0.133707i
$941$	13962.8			0.483714			0.241857	−	0.970312i	$-0.422244\pi$
$941$	13962.8			0.483714			0.241857	+	0.970312i	$0.422244\pi$
$942$	−9746.16	+	14433.3i	−0.337099	+	0.499216i
$943$	−19940.3			−0.688596
$944$	−12406.2	−	47182.4i	−0.427739	−	1.62675i
$945$	3204.57	+	44190.7i	0.110312	+	1.52119i
$946$	7052.88	+	6199.82i	0.242398	+	0.213080i
$947$	−49832.8			−1.70998			−0.854989	−	0.518646i	$-0.826436\pi$
$947$	−49832.8			−1.70998			−0.854989	+	0.518646i	$0.826436\pi$
$948$	6164.49	+	23575.6i	0.211196	+	0.807699i
$949$			9689.96i			0.331454i
$950$	11053.7	+	46932.5i	0.377504	+	1.60283i
$951$	−30485.9	+	3898.60i	−1.03951	+	0.132935i
$952$	−26763.2	+	39751.3i	−0.911136	+	1.35331i
$953$	6247.53			0.212358			0.106179	−	0.994347i	$-0.466138\pi$
$953$	6247.53			0.212358			0.106179	+	0.994347i	$0.466138\pi$
$954$	16388.6	−	32525.8i	0.556184	−	1.10384i
$955$	15573.3	+	4974.57i	0.527686	+	0.168558i
$956$	5014.75	+	38791.9i	0.169653	+	1.31236i
$957$	21749.8	−	2781.41i	0.734661	−	0.0939501i
$958$	13985.9	+	12294.2i	0.471673	+	0.414623i
$959$	−14356.3			−0.483409
$960$	−29129.6	+	6016.77i	−0.979327	+	0.202282i
$961$	26529.0			0.890504
$962$	7720.47	+	6786.66i	0.258750	+	0.227454i
$963$	−49065.7	+	12757.9i	−1.64187	+	0.426914i
$964$	−4040.34	−	31254.2i	−0.134990	−	1.04422i
$965$	5937.22	−	18586.9i	0.198058	−	0.620036i
$966$	39432.9	+	26627.3i	1.31339	+	0.886874i
$967$	−2279.95			−0.0758204			−0.0379102	−	0.999281i	$-0.512070\pi$
$967$	−2279.95			−0.0758204			−0.0379102	+	0.999281i	$0.512070\pi$
$968$	−2007.28	+	2981.40i	−0.0666491	+	0.0989936i
$969$	6739.61	+	52701.7i	0.223434	+	1.74719i
$970$	−28230.9	+	16941.4i	−0.934474	+	0.560777i
$971$			41890.0i			1.38446i	0.721675	+	0.692232i	$0.243373\pi$
$971$			41890.0i			1.38446i	−0.721675	+	0.692232i	$0.756627\pi$
$972$	−21870.8	+	20976.1i	−0.721715	+	0.692190i
$973$	−3854.87			−0.127011
$974$	41623.7	+	36589.2i	1.36931	+	1.20369i
$975$	11086.5	−	20726.1i	0.364155	−	0.680786i
$976$	−10006.5	−	38056.3i	−0.328178	−	1.24811i
$977$	9928.15			0.325107			0.162554	−	0.986700i	$-0.448027\pi$
$977$	9928.15			0.325107			0.162554	+	0.986700i	$0.448027\pi$
$978$	−30037.0	−	20282.7i	−0.982084	−	0.663159i
$979$	−23343.7			−0.762070
$980$	7309.00	−	40024.0i	0.238242	−	1.30461i
$981$	−5663.96	−	21783.0i	−0.184339	−	0.708949i
$982$	10208.0	−	11612.5i	0.331721	−	0.377364i
$983$		−	48280.0i		−	1.56652i	−0.621692	−	0.783262i	$-0.713554\pi$
$983$		−	48280.0i		−	1.56652i	0.621692	−	0.783262i	$-0.286446\pi$
$984$	−9179.41	+	18280.2i	−0.297387	+	0.592228i
$985$	−10.2259	+	32.0131i	−0.000330787	+	0.00103555i
$986$	−17413.0	−	15306.8i	−0.562416	−	0.494391i
$987$	34915.3	−	4465.04i	1.12600	−	0.143996i
$988$	5061.84	+	39156.1i	0.162995	+	1.26085i
$989$	−9858.51			−0.316969
$990$	23081.4	−	23523.2i	0.740986	−	0.755168i
$991$		−	29940.0i		−	0.959714i	−0.877347	−	0.479857i	$-0.840689\pi$
$991$		−	29940.0i		−	0.959714i	0.877347	−	0.479857i	$-0.159311\pi$
$992$	4626.84	−	9245.60i	0.148087	−	0.295915i
$993$	2515.62	+	19671.4i	0.0803934	+	0.628652i
$994$	7477.42	+	6573.01i	0.238601	+	0.209742i
$995$	17386.8	−	54430.6i	0.553967	−	1.73424i
$996$	−11357.3	+	2969.68i	−0.361315	+	0.0944759i
$997$	18921.6			0.601056			0.300528	−	0.953773i	$-0.402837\pi$
$997$	18921.6			0.601056			0.300528	+	0.953773i	$0.402837\pi$
$998$	−8542.42	−	7509.20i	−0.270948	−	0.238176i
$999$	−5246.72	−	13076.2i	−0.166165	−	0.414128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.4.m.b.59.14	yes	64
3.2	odd	2	inner	120.4.m.b.59.52	yes	64
4.3	odd	2		480.4.m.b.239.29		64
5.4	even	2	inner	120.4.m.b.59.51	yes	64
8.3	odd	2	inner	120.4.m.b.59.16	yes	64
8.5	even	2		480.4.m.b.239.30		64
12.11	even	2		480.4.m.b.239.34		64
15.14	odd	2	inner	120.4.m.b.59.13	✓	64
20.19	odd	2		480.4.m.b.239.35		64
24.5	odd	2		480.4.m.b.239.33		64
24.11	even	2	inner	120.4.m.b.59.50	yes	64
40.19	odd	2	inner	120.4.m.b.59.49	yes	64
40.29	even	2		480.4.m.b.239.36		64
60.59	even	2		480.4.m.b.239.32		64
120.29	odd	2		480.4.m.b.239.31		64
120.59	even	2	inner	120.4.m.b.59.15	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.4.m.b.59.13	✓	64	15.14	odd	2	inner
120.4.m.b.59.14	yes	64	1.1	even	1	trivial
120.4.m.b.59.15	yes	64	120.59	even	2	inner
120.4.m.b.59.16	yes	64	8.3	odd	2	inner
120.4.m.b.59.49	yes	64	40.19	odd	2	inner
120.4.m.b.59.50	yes	64	24.11	even	2	inner
120.4.m.b.59.51	yes	64	5.4	even	2	inner
120.4.m.b.59.52	yes	64	3.2	odd	2	inner
480.4.m.b.239.29		64	4.3	odd	2
480.4.m.b.239.30		64	8.5	even	2
480.4.m.b.239.31		64	120.29	odd	2
480.4.m.b.239.32		64	60.59	even	2
480.4.m.b.239.33		64	24.5	odd	2
480.4.m.b.239.34		64	12.11	even	2
480.4.m.b.239.35		64	20.19	odd	2
480.4.m.b.239.36		64	40.29	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12434 - 1.86740i) q^{2} +(0.659128 + 5.15418i) q^{3} +(1.02565 + 7.93398i) q^{4} +(-10.6502 - 3.40199i) q^{5} +(8.22469 - 12.1801i) q^{6} +28.2468 q^{7} +(12.6371 - 18.7698i) q^{8} +(-26.1311 + 6.79452i) q^{9} +(16.2718 + 27.1151i) q^{10} +38.5985i q^{11} +(-40.2171 + 10.5159i) q^{12} -36.1882 q^{13} +(-60.0059 - 52.7480i) q^{14} +(10.5146 - 57.1353i) q^{15} +(-61.8961 + 16.2750i) q^{16} -74.9762 q^{17} +(68.1995 + 34.3633i) q^{18} -136.377 q^{19} +(16.0679 - 87.9876i) q^{20} +(18.6183 + 145.589i) q^{21} +(72.0787 - 81.9963i) q^{22} +114.614i q^{23} +(105.072 + 52.7620i) q^{24} +(101.853 + 72.4636i) q^{25} +(76.8760 + 67.5777i) q^{26} +(-52.2439 - 130.206i) q^{27} +(28.9714 + 224.110i) q^{28} -109.327 q^{29} +(-129.031 + 101.740i) q^{30} -57.1138i q^{31} +(161.880 + 81.0110i) q^{32} +(-198.943 + 25.4413i) q^{33} +(159.275 + 140.010i) q^{34} +(-300.834 - 96.0952i) q^{35} +(-80.7090 - 200.355i) q^{36} +100.427 q^{37} +(289.712 + 254.671i) q^{38} +(-23.8526 - 186.520i) q^{39} +(-198.442 + 156.911i) q^{40} +173.978i q^{41} +(232.321 - 344.049i) q^{42} +86.0147i q^{43} +(-306.239 + 39.5886i) q^{44} +(301.416 + 16.5347i) q^{45} +(214.030 - 243.480i) q^{46} -239.821i q^{47} +(-124.682 - 308.296i) q^{48} +454.882 q^{49} +(-81.0522 - 344.137i) q^{50} +(-49.4189 - 386.440i) q^{51} +(-37.1165 - 287.116i) q^{52} -476.921i q^{53} +(-132.162 + 374.162i) q^{54} +(131.311 - 411.081i) q^{55} +(356.957 - 530.186i) q^{56} +(-89.8901 - 702.913i) q^{57} +(232.247 + 204.156i) q^{58} +762.283i q^{59} +(464.095 + 24.8218i) q^{60} +614.842i q^{61} +(-106.654 + 121.329i) q^{62} +(-738.120 + 191.924i) q^{63} +(-192.609 - 474.390i) q^{64} +(385.411 + 123.112i) q^{65} +(470.132 + 317.460i) q^{66} +382.405i q^{67} +(-76.8994 - 594.859i) q^{68} +(-590.742 + 75.5455i) q^{69} +(459.626 + 765.915i) q^{70} -124.611 q^{71} +(-202.689 + 576.338i) q^{72} -267.766i q^{73} +(-213.342 - 187.538i) q^{74} +(-306.356 + 572.731i) q^{75} +(-139.876 - 1082.01i) q^{76} +1090.28i q^{77} +(-297.636 + 440.775i) q^{78} -586.207i q^{79} +(714.572 + 37.2378i) q^{80} +(636.669 - 355.097i) q^{81} +(324.885 - 369.588i) q^{82} +282.399 q^{83} +(-1136.00 + 297.040i) q^{84} +(798.510 + 255.068i) q^{85} +(160.624 - 182.724i) q^{86} +(-72.0602 - 563.489i) q^{87} +(724.484 + 487.771i) q^{88} +604.782i q^{89} +(-609.434 - 597.989i) q^{90} -1022.20 q^{91} +(-909.347 + 117.554i) q^{92} +(294.375 - 37.6453i) q^{93} +(-447.841 + 509.461i) q^{94} +(1452.44 + 463.954i) q^{95} +(-310.845 + 887.756i) q^{96} +1041.15i q^{97} +(-966.325 - 849.446i) q^{98} +(-262.258 - 1008.62i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 32 q^{4} - 72 q^{6} - 112 q^{9} - 72 q^{10} - 128 q^{16} + 672 q^{19} - 416 q^{24} + 496 q^{25} - 248 q^{30} + 240 q^{34} - 608 q^{36} - 1344 q^{40} + 336 q^{46} + 3520 q^{49} - 544 q^{51} - 952 q^{54}+ \cdots + 256 q^{99}+O(q^{100}) \) 64 * q - 32 * q^4 - 72 * q^6 - 112 * q^9 - 72 * q^10 - 128 * q^16 + 672 * q^19 - 416 * q^24 + 496 * q^25 - 248 * q^30 + 240 * q^34 - 608 * q^36 - 1344 * q^40 + 336 * q^46 + 3520 * q^49 - 544 * q^51 - 952 * q^54 - 2064 * q^60 + 2176 * q^64 - 176 * q^66 + 672 * q^70 - 1600 * q^75 + 2304 * q^76 - 2304 * q^81 - 736 * q^84 - 1432 * q^90 - 2752 * q^91 + 4496 * q^94 + 640 * q^96 + 256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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